diff --git a/py/src/braintrust/integrations/google_genai/cassettes/latest/test_automatic_continuation.yaml b/py/src/braintrust/integrations/google_genai/cassettes/latest/test_automatic_continuation.yaml new file mode 100644 index 00000000..a9e98343 --- /dev/null +++ b/py/src/braintrust/integrations/google_genai/cassettes/latest/test_automatic_continuation.yaml @@ -0,0 +1,2676 @@ +interactions: +- request: + body: '{"contents": [{"parts": [{"text": "Write a complete graduate textbook on + algebraic geometry, with detailed proofs and exercises for each chapter. Continue + for at least 100 pages without summarizing or stopping early."}], "role": "user"}], + "generationConfig": {"maxOutputTokens": 65536, "thinkingConfig": {"thinking_level": + "HIGH"}}}' + headers: + accept: + - '*/*' + accept-encoding: + - gzip, deflate + connection: + - keep-alive + content-length: + - '332' + content-type: + - application/json + host: + - generativelanguage.googleapis.com + user-agent: + - google-genai-sdk/2.34.0 gl-python/3.14.7 + x-goog-api-client: + - google-genai-sdk/2.34.0 gl-python/3.14.7 + method: POST + uri: https://generativelanguage.googleapis.com/v1beta/models/gemini-4-argon:generateContent + response: + body: + string: "{\n \"candidates\": [\n {\n \"content\": {\n \"parts\": + [\n {\n \"text\": \"# FOUNDATIONS OF MODERN ALGEBRAIC + GEOMETRY\\n\\n---\\n\\n## Chapter 1: Classical Algebraic Varieties\\n\\nAlgebraic + geometry is the study of geometries that arise as the loci of common zeros + of collections of polynomials. In its classical formulation, the subject bridges + commutative algebra and the geometry of affine and projective spaces over + an algebraically closed field. In this opening chapter, we develop the foundational + correspondence between geometric spaces\u2014affine and projective varieties\u2014and + algebraic structures\u2014finitely generated reduced algebras and homogeneous + coordinate rings.\\n\\nThroughout this chapter, unless explicitly stated otherwise, + $k$ denotes an algebraically closed field.\\n\\n---\\n\\n### 1.1 Affine Space + and Algebraic Sets\\n\\n**Definition 1.1.1.** Let $k$ be an algebraically + closed field. The *affine $n$-space* over $k$, denoted $\\\\mathbb{A}^n_k$ + (or simply $\\\\mathbb{A}^n$ when $k$ is understood), is the set of all $n$-tuples + of elements of $k$:\\n$$\\\\mathbb{A}^n_k = \\\\{(a_1, a_2, \\\\dots, a_n) + \\\\mid a_i \\\\in k \\\\text{ for all } 1 \\\\le i \\\\le n\\\\}.$$\\nAn + element $P = (a_1, \\\\dots, a_n) \\\\in \\\\mathbb{A}^n_k$ is called a *point*, + and the elements $a_i$ are called the *coordinates* of $P$.\\n\\nLet $k[x_1, + \\\\dots, x_n]$ be the polynomial ring in $n$ variables over $k$. Elements + $f \\\\in k[x_1, \\\\dots, x_n]$ act as functions $f: \\\\mathbb{A}^n_k \\\\to + k$ by evaluation: $P = (a_1, \\\\dots, a_n) \\\\mapsto f(a_1, \\\\dots, a_n)$.\\n\\n**Definition + 1.1.2.** Let $T \\\\subseteq k[x_1, \\\\dots, x_n]$ be an arbitrary subset + of polynomials. The *zero locus* (or *vanishing locus*) of $T$ is the subset + of $\\\\mathbb{A}^n_k$ defined by\\n$$Z(T) = \\\\{P \\\\in \\\\mathbb{A}^n_k + \\\\mid f(P) = 0 \\\\text{ for all } f \\\\in T\\\\}.$$\\nA subset $Y \\\\subseteq + \\\\mathbb{A}^n_k$ is called an *affine algebraic set* if there exists a subset + $T \\\\subseteq k[x_1, \\\\dots, x_n]$ such that $Y = Z(T)$.\\n\\nIf $\\\\mathfrak{a}$ + is the ideal of $k[x_1, \\\\dots, x_n]$ generated by $T$, then any $g \\\\in + \\\\mathfrak{a}$ can be written as a finite sum $g = \\\\sum_{i=1}^m h_i f_i$ + with $h_i \\\\in k[x_1, \\\\dots, x_n]$ and $f_i \\\\in T$. Consequently, + if $f(P) = 0$ for all $f \\\\in T$, then $g(P) = 0$ for all $g \\\\in \\\\mathfrak{a}$. + Thus $Z(T) = Z(\\\\mathfrak{a})$. By Hilbert's Basis Theorem, the ring $k[x_1, + \\\\dots, x_n]$ is Noetherian, meaning every ideal $\\\\mathfrak{a}$ is finitely + generated: $\\\\mathfrak{a} = (f_1, \\\\dots, f_r)$. Therefore, every affine + algebraic set is the intersection of finitely many hypersurfaces $Z(f_i)$.\\n\\n**Proposition + 1.1.3.** *The operation $Z$ satisfies the following properties:*\\n1. $Z(0) + = \\\\mathbb{A}^n_k$ *and* $Z(k[x_1, \\\\dots, x_n]) = \\\\varnothing$.\\n2. + *If $\\\\mathfrak{a} \\\\subseteq \\\\mathfrak{b}$ are ideals in $k[x_1, \\\\dots, + x_n]$, then $Z(\\\\mathfrak{b}) \\\\subseteq Z(\\\\mathfrak{a})$.*\\n3. *For + any two ideals $\\\\mathfrak{a}, \\\\mathfrak{b} \\\\subseteq k[x_1, \\\\dots, + x_n]$, we have $Z(\\\\mathfrak{a}) \\\\cup Z(\\\\mathfrak{b}) = Z(\\\\mathfrak{a}\\\\mathfrak{b}) + = Z(\\\\mathfrak{a} \\\\cap \\\\mathfrak{b})$.*\\n4. *For any family of ideals + $\\\\{\\\\mathfrak{a}_i\\\\}_{i \\\\in I}$ in $k[x_1, \\\\dots, x_n]$, we + have $\\\\bigcap_{i \\\\in I} Z(\\\\mathfrak{a}_i) = Z\\\\left(\\\\sum_{i + \\\\in I} \\\\mathfrak{a}_i\\\\right)$.*\\n\\n*Proof.* \\n(1) Every point + $P \\\\in \\\\mathbb{A}^n_k$ satisfies $0(P) = 0$, so $Z(0) = \\\\mathbb{A}^n_k$. + Since $1 \\\\in k[x_1, \\\\dots, x_n]$ and $1(P) = 1 \\\\neq 0$ for all $P$, + we have $Z(k[x_1, \\\\dots, x_n]) = \\\\varnothing$.\\n\\n(2) If $P \\\\in + Z(\\\\mathfrak{b})$, then $f(P) = 0$ for all $f \\\\in \\\\mathfrak{b}$. Since + $\\\\mathfrak{a} \\\\subseteq \\\\mathfrak{b}$, this holds for all $f \\\\in + \\\\mathfrak{a}$, so $P \\\\in Z(\\\\mathfrak{a})$.\\n\\n(3) Since $\\\\mathfrak{a}\\\\mathfrak{b} + \\\\subseteq \\\\mathfrak{a} \\\\cap \\\\mathfrak{b} \\\\subseteq \\\\mathfrak{a}, + \\\\mathfrak{b}$, property (2) immediately yields $Z(\\\\mathfrak{a}) \\\\cup + Z(\\\\mathfrak{b}) \\\\subseteq Z(\\\\mathfrak{a} \\\\cap \\\\mathfrak{b}) + \\\\subseteq Z(\\\\mathfrak{a}\\\\mathfrak{b})$. Conversely, suppose $P \\\\in + Z(\\\\mathfrak{a}\\\\mathfrak{b})$ and $P \\\\notin Z(\\\\mathfrak{a})$. Then + there exists $f \\\\in \\\\mathfrak{a}$ such that $f(P) \\\\neq 0$. For any + $g \\\\in \\\\mathfrak{b}$, we have $fg \\\\in \\\\mathfrak{a}\\\\mathfrak{b}$, + so $(fg)(P) = f(P)g(P) = 0$. Since $k$ is a field and $f(P) \\\\neq 0$, we + must have $g(P) = 0$. As $g \\\\in \\\\mathfrak{b}$ was arbitrary, $P \\\\in + Z(\\\\mathfrak{b})$. Thus $Z(\\\\mathfrak{a}\\\\mathfrak{b}) \\\\subseteq + Z(\\\\mathfrak{a}) \\\\cup Z(\\\\mathfrak{b})$, establishing the equalities.\\n\\n(4) + A point $P$ belongs to $Z\\\\left(\\\\sum_{i \\\\in I} \\\\mathfrak{a}_i\\\\right)$ + if and only if every finite sum $\\\\sum f_i$ (with $f_i \\\\in \\\\mathfrak{a}_i$) + vanishes at $P$. This holds if and only if $f_i(P) = 0$ for all $i \\\\in + I$ and all $f_i \\\\in \\\\mathfrak{a}_i$, which is equivalent to $P \\\\in + \\\\bigcap_{i \\\\in I} Z(\\\\mathfrak{a}_i)$. $\\\\blacksquare$\\n\\n**Definition + 1.1.4.** Proposition 1.1.3 demonstrates that the collection of affine algebraic + sets in $\\\\mathbb{A}^n_k$ satisfies the axioms for the closed subsets of + a topology. This topology on $\\\\mathbb{A}^n_k$ is called the *Zariski topology*.\\n\\nThe + Zariski topology is drastically different from the classical Euclidean topology + on $\\\\mathbb{C}^n$. For instance, on $\\\\mathbb{A}^1_k$, every ideal in + $k[x]$ is principal. Since a non-zero polynomial in one variable has only + finitely many roots, the proper closed subsets of $\\\\mathbb{A}^1_k$ are + precisely the finite subsets. Thus the Zariski topology on $\\\\mathbb{A}^1_k$ + is the cofinite topology, which is non-Hausdorff whenever $k$ is infinite + (which is always true for algebraically closed fields).\\n\\n**Definition + 1.1.5.** A non-empty topological space $X$ is called *irreducible* if it cannot + be expressed as the union $X = X_1 \\\\cup X_2$ of two proper closed subsets + $X_1, X_2 \\\\subsetneq X$. Equivalently, $X$ is irreducible if and only if + every pair of non-empty open subsets $U_1, U_2 \\\\subseteq X$ has a non-empty + intersection $U_1 \\\\cap U_2 \\\\neq \\\\varnothing$, which in turn is equivalent + to the condition that every non-empty open subset of $X$ is dense in $X$.\\n\\nAn + *affine algebraic variety* (or simply an *affine variety*) is an irreducible + closed subset of $\\\\mathbb{A}^n_k$, endowed with the induced Zariski topology. + An open subset of an affine variety is called a *quasi-affine variety*.\\n\\nTo + connect geometry back to algebra, we define the inverse operation to $Z$.\\n\\n**Definition + 1.1.6.** For any subset $Y \\\\subseteq \\\\mathbb{A}^n_k$, the *ideal of + $Y$* in $k[x_1, \\\\dots, x_n]$ is defined by\\n$$I(Y) = \\\\{f \\\\in k[x_1, + \\\\dots, x_n] \\\\mid f(P) = 0 \\\\text{ for all } P \\\\in Y\\\\}.$$\\n\\nRecall + that for an ideal $\\\\mathfrak{a}$ in a commutative ring $R$, the *radical* + of $\\\\mathfrak{a}$ is the ideal $\\\\sqrt{\\\\mathfrak{a}} = \\\\{r \\\\in + R \\\\mid r^m \\\\in \\\\mathfrak{a} \\\\text{ for some integer } m \\\\ge + 1\\\\}$. An ideal $\\\\mathfrak{a}$ is called a *radical ideal* if $\\\\mathfrak{a} + = \\\\sqrt{\\\\mathfrak{a}}$. Every prime ideal is clearly a radical ideal.\\n\\n**Proposition + 1.1.7.** *The operation $I$ satisfies the following properties:*\\n1. *If + $Y_1 \\\\subseteq Y_2 \\\\subseteq \\\\mathbb{A}^n_k$, then $I(Y_2) \\\\subseteq + I(Y_1)$.*\\n2. $I(\\\\varnothing) = k[x_1, \\\\dots, x_n]$ *and, since $k$ + is infinite, $I(\\\\mathbb{A}^n_k) = (0)$.*\\n3. *For any subsets $Y_1, Y_2 + \\\\subseteq \\\\mathbb{A}^n_k$, $I(Y_1 \\\\cup Y_2) = I(Y_1) \\\\cap I(Y_2)$.*\\n4. + *For any subset $Y \\\\subseteq \\\\mathbb{A}^n_k$, $I(Y)$ is a radical ideal.*\\n5. + *For any subset $Y \\\\subseteq \\\\mathbb{A}^n_k$, $Z(I(Y)) = \\\\overline{Y}$, + the closure of $Y$ in the Zariski topology.*\\n6. *For any ideal $\\\\mathfrak{a} + \\\\subseteq k[x_1, \\\\dots, x_n]$, $\\\\sqrt{\\\\mathfrak{a}} \\\\subseteq + I(Z(\\\\mathfrak{a}))$.*\\n\\n*Proof.* \\n(1) and (3) follow immediately from + the definitions.\\n\\n(2) The statement $I(\\\\varnothing) = k[x_1, \\\\dots, + x_n]$ is vacuous. To see that $I(\\\\mathbb{A}^n_k) = (0)$, we proceed by + induction on $n$. For $n=1$, a non-zero polynomial in $k[x_1]$ of degree $d$ + has at most $d$ roots in $k$; since $k$ is algebraically closed, it is infinite, + so no non-zero polynomial can vanish on all of $k$. For $n \\u003e 1$, write + $f \\\\in k[x_1, \\\\dots, x_n]$ as a polynomial in $x_n$ with coefficients + in $k[x_1, \\\\dots, x_{n-1}]$: $f = \\\\sum_{i=0}^d g_i(x_1, \\\\dots, x_{n-1}) + x_n^i$. For any fixed $(a_1, \\\\dots, a_{n-1}) \\\\in \\\\mathbb{A}^{n-1}_k$, + the polynomial $f(a_1, \\\\dots, a_{n-1}, x_n) \\\\in k[x_n]$ vanishes for + all $a_n \\\\in k$, hence is identically zero. Thus $g_i(a_1, \\\\dots, a_{n-1}) + = 0$ for all $i$. By the induction hypothesis, $g_i = 0$ in $k[x_1, \\\\dots, + x_{n-1}]$ for all $i$, so $f = 0$.\\n\\n(4) Suppose $f \\\\in \\\\sqrt{I(Y)}$. + Then $f^m \\\\in I(Y)$ for some $m \\\\ge 1$. For any $P \\\\in Y$, $(f(P))^m + = f^m(P) = 0$ in $k$. Since $k$ has no non-zero nilpotent elements, $f(P) + = 0$ for all $P \\\\in Y$, so $f \\\\in I(Y)$.\\n\\n(5) By definition, $Y + \\\\subseteq Z(I(Y))$, and since $Z(I(Y))$ is closed, $\\\\overline{Y} \\\\subseteq + Z(I(Y))$. Conversely, let $W = Z(\\\\mathfrak{a})$ be any closed set containing + $Y$. Then $I(W) \\\\subseteq I(Y)$, and since $\\\\mathfrak{a} \\\\subseteq + I(Z(\\\\mathfrak{a})) = I(W)$, we have $\\\\mathfrak{a} \\\\subseteq I(Y)$. + Applying $Z$ yields $Z(I(Y)) \\\\subseteq Z(\\\\mathfrak{a}) = W$. Taking + $W = \\\\overline{Y}$ gives $Z(I(Y)) \\\\subseteq \\\\overline{Y}$.\\n\\n(6) + If $f \\\\in \\\\sqrt{\\\\mathfrak{a}}$, then $f^m \\\\in \\\\mathfrak{a}$ + for some $m \\\\ge 1$. For any $P \\\\in Z(\\\\mathfrak{a})$, $(f(P))^m = + f^m(P) = 0$, so $f(P) = 0$. Thus $f \\\\in I(Z(\\\\mathfrak{a}))$. $\\\\blacksquare$\\n\\n---\\n\\n### + 1.2 Hilbert's Nullstellensatz\\n\\nThe inclusion $\\\\sqrt{\\\\mathfrak{a}} + \\\\subseteq I(Z(\\\\mathfrak{a}))$ in Proposition 1.1.7(6) is in fact an + equality. This fundamental result, due to David Hilbert, forms the bridge + between commutative algebra and algebraic geometry. We will provide a complete, + self-contained proof, beginning with Zariski's Lemma via the Artin\u2013Tate + Lemma.\\n\\n**Lemma 1.2.1 (Artin\u2013Tate).** *Let $A \\\\subseteq B \\\\subseteq + C$ be commutative rings such that $A$ is Noetherian, $C$ is a finitely generated + $A$-algebra, and $C$ is a finitely generated $B$-module. Then $B$ is a finitely + generated $A$-algebra.*\\n\\n*Proof.* Let $x_1, \\\\dots, x_n \\\\in C$ generate + $C$ as an $A$-algebra, and let $y_1, \\\\dots, y_m \\\\in C$ generate $C$ + as a $B$-module. Then we can express each $x_i$ and each product $y_i y_j$ + as $B$-linear combinations of the generators $y_k$:\\n$$x_i = \\\\sum_{k=1}^m + b_{ik} y_k \\\\quad (1 \\\\le i \\\\le n), \\\\qquad y_i y_j = \\\\sum_{k=1}^m + b_{ijk} y_k \\\\quad (1 \\\\le i, j \\\\le m),$$\\nwhere $b_{ik}, b_{ijk} + \\\\in B$. Let $B_0 \\\\subseteq B$ be the $A$-subalgebra generated by the + finite set of all these coefficients $\\\\{b_{ik}, b_{ijk}\\\\}$. Since $A$ + is a Noetherian ring and $B_0$ is a finitely generated $A$-algebra, Hilbert's + Basis Theorem implies that $B_0$ is a Noetherian ring.\\n\\nAny element $c + \\\\in C$ is a polynomial in $x_1, \\\\dots, x_n$ with coefficients in $A$. + Using the equations above, we can rewrite each $x_i$ as a $B_0$-linear combination + of the $y_k$, and any product of the $y_k$ can be reduced to a $B_0$-linear + combination of $y_1, \\\\dots, y_m$. Consequently, $C$ is finitely generated + as a $B_0$-module (generated by $1, y_1, \\\\dots, y_m$).\\n\\nSince $B_0$ + is Noetherian and $C$ is a finitely generated $B_0$-module, $C$ is a Noetherian + $B_0$-module. Because $B_0 \\\\subseteq B \\\\subseteq C$, $B$ is a $B_0$-submodule + of $C$, and therefore $B$ is finitely generated as a $B_0$-module. Let $z_1, + \\\\dots, z_r \\\\in B$ generate $B$ as a $B_0$-module. Since $B_0$ is finitely + generated as an $A$-algebra by $\\\\{b_{ik}, b_{ijk}\\\\}$, it follows immediately + that $B$ is finitely generated as an $A$-algebra by $\\\\{b_{ik}, b_{ijk}\\\\} + \\\\cup \\\\{z_1, \\\\dots, z_r\\\\}$. $\\\\blacksquare$\\n\\n**Proposition + 1.2.2 (Zariski's Lemma).** *Let $k$ be a field, and let $E$ be a finitely + generated $k$-algebra. If $E$ is a field, then $E$ is a finite algebraic extension + of $k$.*\\n\\n*Proof.* Let $x_1, \\\\dots, x_n \\\\in E$ generate $E$ as a + $k$-algebra, so $E = k[x_1, \\\\dots, x_n]$. Since $E$ is a field, we also + have $E = k(x_1, \\\\dots, x_n)$. Suppose, for the sake of contradiction, + that $E$ is not algebraic over $k$. After reindexing the generators $x_1, + \\\\dots, x_n$, we may assume that $x_1, \\\\dots, x_r$ (for some $1 \\\\le + r \\\\le n$) form a transcendence basis of $E$ over $k$, and that $x_{r+1}, + \\\\dots, x_n$ are algebraic over the purely transcendental subfield $F = + k(x_1, \\\\dots, x_r)$.\\n\\nSince $E = F(x_{r+1}, \\\\dots, x_n)$ is finitely + generated and algebraic over $F$, $E$ is a finite field extension of $F$; + in particular, $E$ is a finitely generated $F$-module. Let $A = k[x_1, \\\\dots, + x_r]$ be the polynomial ring in $r$ variables over $k$. Because $k$ is a field, + $A$ is Noetherian. We now have a tower of rings\\n$$A = k[x_1, \\\\dots, x_r] + \\\\subseteq F = k(x_1, \\\\dots, x_r) \\\\subseteq E$$\\nwhere $A$ is Noetherian, + $E$ is a finitely generated $A$-algebra (generated by $x_{r+1}, \\\\dots, + x_n$), and $E$ is a finitely generated $F$-module. By the Artin\u2013Tate + Lemma (Lemma 1.2.1), $F$ is a finitely generated $A$-algebra.\\n\\nThus there + exist finitely many rational functions $f_1/g_1, \\\\dots, f_s/g_s \\\\in + F$ (with $f_i, g_i \\\\in A$ and $g_i \\\\neq 0$) such that $F = A[f_1/g_1, + \\\\dots, f_s/g_s]$. Let $g = \\\\prod_{i=1}^s g_i \\\\in A$. Then every element + of $F$ can be written with a denominator that is a power of $g$, so $F = A[1/g]$.\\n\\nHowever, + $A = k[x_1, \\\\dots, x_r]$ is a Unique Factorization Domain with infinitely + many non-associate irreducible elements (by Euclid's argument: if $p_1, \\\\dots, + p_t$ were all the irreducibles, then $p_1 \\\\cdots p_t + 1$ would have an + irreducible factor distinct from all $p_i$). Therefore, there exists an irreducible + element $p \\\\in A$ that does not divide $g$. Since $1/p \\\\in F = A[1/g]$, + there exist an integer $N \\\\ge 0$ and an element $a \\\\in A$ such that\\n$$\\\\frac{1}{p} + = \\\\frac{a}{g^N} \\\\implies g^N = p a.$$\\nSince $p$ is irreducible in + the UFD $A$, $p$ must divide $g$, a contradiction. Thus $E$ must be algebraic + over $k$, and since it is finitely generated, it is a finite extension of + $k$. $\\\\blacksquare$\\n\\n**Theorem 1.2.3 (Weak Nullstellensatz).** *Let + $k$ be an algebraically closed field. Every maximal ideal $\\\\mathfrak{m}$ + of the polynomial ring $k[x_1, \\\\dots, x_n]$ is of the form*\\n$$\\\\mathfrak{m} + = (x_1 - a_1, x_2 - a_2, \\\\dots, x_n - a_n)$$\\n*for a unique point $P = + (a_1, \\\\dots, a_n) \\\\in \\\\mathbb{A}^n_k$. Equivalently, for every proper + ideal $\\\\mathfrak{a} \\\\subsetneq k[x_1, \\\\dots, x_n]$, we have $Z(\\\\mathfrak{a}) + \\\\neq \\\\varnothing$.*\\n\\n*Proof.* Let $\\\\mathfrak{m} \\\\subset k[x_1, + \\\\dots, x_n]$ be a maximal ideal. The quotient $E = k[x_1, \\\\dots, x_n]/\\\\mathfrak{m}$ + is a field and is finitely generated as a $k$-algebra by the cosets $\\\\bar{x}_1, + \\\\dots, \\\\bar{x}_n$. By Zariski's Lemma (Proposition 1.2.2), $E$ is a + finite algebraic extension of $k$. Since $k$ is algebraically closed, it has + no non-trivial algebraic extensions, so the natural inclusion $k \\\\hookrightarrow + E$ is an isomorphism.\\n\\nConsequently, for each $1 \\\\le i \\\\le n$, there + exists a unique element $a_i \\\\in k$ such that $\\\\bar{x}_i = a_i$ in $E + = k[x_1, \\\\dots, x_n]/\\\\mathfrak{m}$. This means $x_i - a_i \\\\in \\\\mathfrak{m}$ + for all $i$, so the ideal $\\\\mathfrak{m}_P = (x_1 - a_1, \\\\dots, x_n - + a_n)$ is contained in $\\\\mathfrak{m}$. However, the evaluation map $k[x_1, + \\\\dots, x_n] \\\\to k$ given by $f \\\\mapsto f(a_1, \\\\dots, a_n)$ is + a surjective ring homomorphism with kernel precisely $\\\\mathfrak{m}_P$. + Thus $\\\\mathfrak{m}_P$ is already a maximal ideal, forcing $\\\\mathfrak{m} + = \\\\mathfrak{m}_P$.\\n\\nFor the second statement, if $\\\\mathfrak{a} \\\\subsetneq + k[x_1, \\\\dots, x_n]$ is a proper ideal, then by Zorn's Lemma (or the Noetherian + property) $\\\\mathfrak{a}$ is contained in some maximal ideal $\\\\mathfrak{m} + = (x_1 - a_1, \\\\dots, x_n - a_n)$. Then $P = (a_1, \\\\dots, a_n) \\\\in + Z(\\\\mathfrak{m}) \\\\subseteq Z(\\\\mathfrak{a})$, so $Z(\\\\mathfrak{a}) + \\\\neq \\\\varnothing$. $\\\\blacksquare$\\n\\n**Theorem 1.2.4 (Hilbert's + Nullstellensatz).** *Let $k$ be an algebraically closed field, and let $\\\\mathfrak{a}$ + be an ideal in $k[x_1, \\\\dots, x_n]$. Then*\\n$$I(Z(\\\\mathfrak{a})) = + \\\\sqrt{\\\\mathfrak{a}}.$$\\n\\n*Proof.* We already proved $\\\\sqrt{\\\\mathfrak{a}} + \\\\subseteq I(Z(\\\\mathfrak{a}))$ in Proposition 1.1.7(6). For the reverse + inclusion, we employ **Rabinowitsch's trick**. Suppose $f \\\\in I(Z(\\\\mathfrak{a}))$. + If $f = 0$, then $f \\\\in \\\\sqrt{\\\\mathfrak{a}}$ trivially, so assume + $f \\\\neq 0$. Since $k[x_1, \\\\dots, x_n]$ is Noetherian, let $\\\\mathfrak{a} + = (g_1, \\\\dots, g_m)$.\\n\\nConsider the polynomial ring in $n+1$ variables + $k[x_1, \\\\dots, x_n, y]$, where $y$ is a new indeterminate. Let $\\\\mathfrak{b} + \\\\subseteq k[x_1, \\\\dots, x_n, y]$ be the ideal generated by $g_1, \\\\dots, + g_m$ and the polynomial $1 - y f(x_1, \\\\dots, x_n)$:\\n$$\\\\mathfrak{b} + = (g_1, \\\\dots, g_m, 1 - yf).$$\\nWe claim that $Z(\\\\mathfrak{b}) = \\\\varnothing$ + in $\\\\mathbb{A}^{n+1}_k$. Indeed, suppose $(a_1, \\\\dots, a_n, b) \\\\in + Z(\\\\mathfrak{b})$. Since $g_i(a_1, \\\\dots, a_n) = 0$ for all $1 \\\\le + i \\\\le m$, the point $P = (a_1, \\\\dots, a_n)$ lies in $Z(\\\\mathfrak{a}) + \\\\subseteq \\\\mathbb{A}^n_k$. Since $f \\\\in I(Z(\\\\mathfrak{a}))$, we + must have $f(a_1, \\\\dots, a_n) = 0$. Evaluating the last generator of $\\\\mathfrak{b}$ + at $(a_1, \\\\dots, a_n, b)$ gives\\n$$0 = 1 - b \\\\cdot f(a_1, \\\\dots, + a_n) = 1 - b \\\\cdot 0 = 1,$$\\nwhich is impossible. Thus $Z(\\\\mathfrak{b}) + = \\\\varnothing$.\\n\\nBy the contrapositive of the Weak Nullstellensatz + (Theorem 1.2.3) applied to $k[x_1, \\\\dots, x_n, y]$, the ideal $\\\\mathfrak{b}$ + cannot be a proper ideal; hence $1 \\\\in \\\\mathfrak{b}$. Therefore, there + exist polynomials $h_1, \\\\dots, h_m, h_{m+1} \\\\in k[x_1, \\\\dots, x_n, + y]$ such that\\n$$1 = \\\\sum_{i=1}^m h_i(x_1, \\\\dots, x_n, y) g_i(x_1, + \\\\dots, x_n) + h_{m+1}(x_1, \\\\dots, x_n, y)(1 - yf).$$\\nWe now apply + the $k[x_1, \\\\dots, x_n]$-algebra homomorphism $k[x_1, \\\\dots, x_n, y] + \\\\to k(x_1, \\\\dots, x_n)$ that sends $y \\\\mapsto 1/f$. Under this substitution, + $1 - yf \\\\mapsto 0$, and the identity becomes\\n$$1 = \\\\sum_{i=1}^m h_i\\\\left(x_1, + \\\\dots, x_n, \\\\frac{1}{f}\\\\right) g_i(x_1, \\\\dots, x_n)$$\\nin the + field of rational functions $k(x_1, \\\\dots, x_n)$. Let $N \\\\ge 1$ be the + highest power of $y$ appearing in any of the polynomials $h_1, \\\\dots, h_m$. + Multiplying both sides of the equation by $f^N$ clears all denominators, yielding\\n$$f^N + = \\\\sum_{i=1}^m \\\\tilde{h}_i(x_1, \\\\dots, x_n) g_i(x_1, \\\\dots, x_n)$$\\nfor + some polynomials $\\\\tilde{h}_i \\\\in k[x_1, \\\\dots, x_n]$. Thus $f^N + \\\\in \\\\mathfrak{a}$, which means $f \\\\in \\\\sqrt{\\\\mathfrak{a}}$. + $\\\\blacksquare$\\n\\n**Theorem 1.2.5 (The Algebra\u2013Geometry Dictionary).** + *Let $k$ be an algebraically closed field. The maps $Y \\\\mapsto I(Y)$ and + $\\\\mathfrak{a} \\\\mapsto Z(\\\\mathfrak{a})$ induce an inclusion-reversing + bijection between the collection of affine algebraic sets in $\\\\mathbb{A}^n_k$ + and the collection of radical ideals in $k[x_1, \\\\dots, x_n]$. Under this + bijection:*\\n1. *Affine varieties (irreducible algebraic sets) correspond + bijectively to prime ideals.*\\n2. *Points of $\\\\mathbb{A}^n_k$ correspond + bijectively to maximal ideals.*\\n\\n*Proof.* For any algebraic set $Y = Z(\\\\mathfrak{a})$, + Proposition 1.1.7(5) gives $Z(I(Y)) = \\\\overline{Y} = Y$. For any radical + ideal $\\\\mathfrak{a}$, Hilbert's Nullstellensatz gives $I(Z(\\\\mathfrak{a})) + = \\\\sqrt{\\\\mathfrak{a}} = \\\\mathfrak{a}$. Thus $I$ and $Z$ are mutually + inverse bijections.\\n\\nTo prove (1), let $Y$ be an algebraic set. Suppose + $Y$ is irreducible, and let $f, g \\\\in k[x_1, \\\\dots, x_n]$ be such that + $fg \\\\in I(Y)$. Then $Y \\\\subseteq Z(fg) = Z(f) \\\\cup Z(g)$, so $Y = + (Y \\\\cap Z(f)) \\\\cup (Y \\\\cap Z(g))$. Since $Y$ is irreducible and $Y + \\\\cap Z(f), Y \\\\cap Z(g)$ are closed in $Y$, we must have $Y = Y \\\\cap + Z(f)$ or $Y = Y \\\\cap Z(g)$, meaning $Y \\\\subseteq Z(f)$ or $Y \\\\subseteq + Z(g)$. Hence $f \\\\in I(Y)$ or $g \\\\in I(Y)$, proving $I(Y)$ is prime. + Conversely, suppose $\\\\mathfrak{p}$ is a prime ideal and $Z(\\\\mathfrak{p}) + = Y_1 \\\\cup Y_2$ for closed sets $Y_1, Y_2$. Then $\\\\mathfrak{p} = I(Z(\\\\mathfrak{p})) + = I(Y_1) \\\\cap I(Y_2)$. Since $\\\\mathfrak{p}$ is prime, a standard property + of prime ideals yields $\\\\mathfrak{p} = I(Y_1)$ or $\\\\mathfrak{p} = I(Y_2)$, + whence $Z(\\\\mathfrak{p}) = Z(I(Y_1)) = Y_1$ or $Z(\\\\mathfrak{p}) = Y_2$. + Thus $Z(\\\\mathfrak{p})$ is irreducible.\\n\\nStatement (2) is an immediate + consequence of the Weak Nullstellensatz (Theorem 1.2.3). $\\\\blacksquare$\\n\\n**Definition + 1.2.6.** A topological space $X$ is called *Noetherian* if it satisfies the + descending chain condition for closed subsets: for any sequence $Y_1 \\\\supseteq + Y_2 \\\\supseteq Y_3 \\\\supseteq \\\\dots$ of closed subsets of $X$, there + exists an integer $r$ such that $Y_r = Y_{r+1} = \\\\dots$.\\n\\nBecause $k[x_1, + \\\\dots, x_n]$ is a Noetherian ring (satisfying the ascending chain condition + on ideals) and $Y \\\\mapsto I(Y)$ reverses inclusions, $\\\\mathbb{A}^n_k$ + and all of its subspaces are Noetherian topological spaces.\\n\\n**Proposition + 1.2.7.** *In a Noetherian topological space $X$, every non-empty closed subset + $Y$ can be expressed as a finite union $Y = Y_1 \\\\cup \\\\dots \\\\cup Y_r$ + of irreducible closed subsets. If we require that $Y_i \\\\not\\\\subseteq + Y_j$ for $i \\\\neq j$, then the subsets $Y_1, \\\\dots, Y_r$ are uniquely + determined up to permutation. They are called the irreducible components of + $Y$.*\\n\\n*Proof.* Let $\\\\mathfrak{S}$ be the set of non-empty closed subsets + of $X$ that cannot be written as a finite union of irreducible closed subsets. + If $\\\\mathfrak{S} \\\\neq \\\\varnothing$, then since $X$ is Noetherian, + $\\\\mathfrak{S}$ contains a minimal element $Y$. By definition of $\\\\mathfrak{S}$, + $Y$ is not irreducible, so $Y = Y' \\\\cup Y''$ for proper closed subsets + $Y', Y'' \\\\subsetneq Y$. By minimality of $Y$, $Y', Y'' \\\\notin \\\\mathfrak{S}$, + so both $Y'$ and $Y''$ are finite unions of irreducible closed subsets. Then + $Y = Y' \\\\cup Y''$ is also such a finite union, contradicting $Y \\\\in + \\\\mathfrak{S}$. Thus $\\\\mathfrak{S} = \\\\varnothing$.\\n\\nBy discarding + redundant subsets in $Y = Y_1 \\\\cup \\\\dots \\\\cup Y_r$, we may assume + $Y_i \\\\not\\\\subseteq Y_j$ for $i \\\\neq j$. For uniqueness, suppose $Y + = Y_1' \\\\cup \\\\dots \\\\cup Y_s'$ is another such decomposition. Then + $Y_1' = Y_1' \\\\cap Y = \\\\bigcup_{i=1}^r (Y_1' \\\\cap Y_i)$. Since $Y_1'$ + is irreducible, $Y_1' = Y_1' \\\\cap Y_i$ for some $i$, so $Y_1' \\\\subseteq + Y_i$. By symmetry, $Y_i \\\\subseteq Y_j'$ for some $j$, yielding $Y_1' \\\\subseteq + Y_i \\\\subseteq Y_j'$. Since the decomposition $Y_1', \\\\dots, Y_s'$ is + irredundant, $j = 1$ and $Y_1' = Y_i$. Proceeding by induction (or repeating + for each index), the two decompositions are identical up to permutation. $\\\\blacksquare$\\n\\n---\\n\\n### + 1.3 Coordinate Rings, Regular Functions, and Morphisms\\n\\n**Definition 1.3.1.** + Let $Y \\\\subseteq \\\\mathbb{A}^n_k$ be an affine algebraic set. The *affine + coordinate ring* of $Y$, denoted $A(Y)$ or $k[Y]$, is defined to be the quotient + ring\\n$$A(Y) = k[x_1, \\\\dots, x_n] / I(Y).$$\\n\\nSince $I(Y)$ is a radical + ideal, $A(Y)$ is a finitely generated *reduced* $k$-algebra (a ring with no + non-zero nilpotent elements). If $Y$ is an affine variety, then $I(Y)$ is + a prime ideal, so $A(Y)$ is an integral domain. Furthermore, by Hilbert's + Nullstellensatz, the closed subsets of $Y$ correspond bijectively to radical + ideals of $A(Y)$, and the points of $Y$ correspond bijectively to maximal + ideals of $A(Y)$.\\n\\nElements of $A(Y)$ represent polynomial functions restricted + to $Y$. However, to obtain a notion of \\\"regular function\\\" that is local + in nature (and extends naturally to quasi-affine and projective varieties), + we define regularity locally via rational expressions.\\n\\n**Definition 1.3.2.** + Let $Y \\\\subseteq \\\\mathbb{A}^n_k$ be a quasi-affine variety (an open + subset of an affine variety $\\\\overline{Y}$). A function $f: Y \\\\to k$ + is *regular at a point $P \\\\in Y$* if there exists an open neighborhood + $U$ of $P$ in $Y$ and polynomials $g, h \\\\in k[x_1, \\\\dots, x_n]$ such + that for all $Q \\\\in U$, $h(Q) \\\\neq 0$ and $f(Q) = g(Q)/h(Q)$. We say + that $f$ is *regular on $Y$* if it is regular at every point of $Y$. The ring + of all regular functions on $Y$ is denoted $\\\\mathcal{O}(Y)$.\\n\\n**Lemma + 1.3.3.** *A regular function $f: Y \\\\to k$ on a quasi-affine variety $Y$ + is continuous when $k$ is identified with $\\\\mathbb{A}^1_k$ endowed with + the Zariski topology.*\\n\\n*Proof.* Since the closed subsets of $\\\\mathbb{A}^1_k$ + are $\\\\mathbb{A}^1_k$ and finite sets of points, and since finite unions + of closed sets are closed, it suffices to show that $f^{-1}(\\\\{a\\\\})$ + is closed in $Y$ for every $a \\\\in k$. Replacing $f$ by $f - a$, we need + only show that $Z_Y(f) = \\\\{P \\\\in Y \\\\mid f(P) = 0\\\\}$ is closed + in $Y$, or equivalently, that $Y \\\\setminus Z_Y(f)$ is open in $Y$.\\n\\nLet + $P \\\\in Y \\\\setminus Z_Y(f)$, so $f(P) \\\\neq 0$. Since $f$ is regular + at $P$, there is an open neighborhood $U \\\\subseteq Y$ of $P$ and polynomials + $g, h \\\\in k[x_1, \\\\dots, x_n]$ such that $h$ vanishes nowhere on $U$ + and $f = g/h$ on $U$. Let $V = U \\\\setminus Z(g) = U \\\\cap (\\\\mathbb{A}^n_k + \\\\setminus Z(g))$. Then $V$ is open in $Y$, $P \\\\in V$ (since $g(P) = + f(P)h(P) \\\\neq 0$), and for all $Q \\\\in V$, $f(Q) = g(Q)/h(Q) \\\\neq + 0$. Thus $V \\\\subseteq Y \\\\setminus Z_Y(f)$, proving $Y \\\\setminus Z_Y(f)$ + is open. $\\\\blacksquare$\\n\\nBecause $Y$ is irreducible, every non-empty + open subset $U \\\\subseteq Y$ is dense in $Y$. By Lemma 1.3.3, if two regular + functions $f_1, f_2 \\\\in \\\\mathcal{O}(Y)$ agree on a non-empty open subset + $U \\\\subseteq Y$, then the closed set $(f_1 - f_2)^{-1}(0)$ contains the + dense set $U$ and therefore must be all of $Y$; thus $f_1 = f_2$ on $Y$. This + observation leads us to the concept of rational functions and local rings.\\n\\n**Definition + 1.3.4.** Let $Y$ be a quasi-affine variety.\\n1. For a point $P \\\\in Y$, + consider pairs $(U, f)$ where $U \\\\subseteq Y$ is an open neighborhood of + $P$ and $f \\\\in \\\\mathcal{O}(U)$. We declare $(U, f) \\\\sim (V, g)$ if + $f = g$ on $U \\\\cap V$. An equivalence class of such pairs is called a *germ + of a regular function at $P$*. The set of all germs at $P$ forms a $k$-algebra + denoted $\\\\mathcal{O}_{Y,P}$ (or $\\\\mathcal{O}_P$), called the *local + ring of $Y$ at $P$*.\\n2. Consider pairs $(U, f)$ where $U \\\\subseteq Y$ + is an arbitrary non-empty open subset and $f \\\\in \\\\mathcal{O}(U)$, with + the same equivalence relation $(U, f) \\\\sim (V, g)$ if $f = g$ on $U \\\\cap + V$ (which is non-empty by irreducibility of $Y$). The set of equivalence classes + forms a field $K(Y)$ (or $k(Y)$), called the *function field* of $Y$. Elements + of $K(Y)$ are called *rational functions* on $Y$.\\n\\nNotice that for every + non-empty open $U \\\\subseteq Y$ and every $P \\\\in U$, there are canonical + injective $k$-algebra homomorphisms\\n$$\\\\mathcal{O}(Y) \\\\hookrightarrow + \\\\mathcal{O}(U) \\\\hookrightarrow \\\\mathcal{O}_{Y,P} \\\\hookrightarrow + K(Y).$$\\n\\n**Theorem 1.3.5.** *Let $Y \\\\subseteq \\\\mathbb{A}^n_k$ be + an affine variety with affine coordinate ring $A(Y)$. Then:*\\n1. $\\\\mathcal{O}(Y) + \\\\cong A(Y)$ *as $k$-algebras.*\\n2. *For each point $P \\\\in Y$, let $\\\\mathfrak{m}_P + = \\\\{f \\\\in A(Y) \\\\mid f(P) = 0\\\\}$ be the maximal ideal of $P$ in + $A(Y)$. Then $\\\\mathcal{O}_{Y,P} \\\\cong A(Y)_{\\\\mathfrak{m}_P}$, the + localization of $A(Y)$ at $\\\\mathfrak{m}_P$. In particular, $\\\\mathcal{O}_{Y,P}$ + is a Noetherian local domain of Krull dimension equal to $\\\\dim Y$.*\\n3. + $K(Y)$ *is isomorphic to the field of fractions of $A(Y)$.*\\n\\n*Proof.* + We first establish (2). Every element of the localization $A(Y)_{\\\\mathfrak{m}_P}$ + is a fraction $g/h$ with $g, h \\\\in A(Y)$ and $h \\\\notin \\\\mathfrak{m}_P$, + meaning $h(P) \\\\neq 0$. In the open neighborhood $U = Y \\\\setminus Z(h)$ + of $P$, $g/h$ defines a regular function, giving a canonical $k$-algebra homomorphism + $\\\\psi: A(Y)_{\\\\mathfrak{m}_P} \\\\to \\\\mathcal{O}_{Y,P}$. If $\\\\psi(g/h) + = 0$, then $g/h = 0$ on some non-empty open $V \\\\subseteq U$, so $g$ vanishes + on $V$. Since $Y$ is irreducible, $\\\\overline{V} = Y$, so $g$ vanishes on + all of $Y$, meaning $g = 0$ in $A(Y)$. Thus $\\\\psi$ is injective. Conversely, + any germ in $\\\\mathcal{O}_{Y,P}$ is represented on some neighborhood of + $P$ by a quotient of polynomials $G/H$ with $H(P) \\\\neq 0$. Passing to their + images $\\\\bar{G}, \\\\bar{H} \\\\in A(Y)$, we have $\\\\bar{H} \\\\notin + \\\\mathfrak{m}_P$ and $\\\\psi(\\\\bar{G}/\\\\bar{H})$ equals the given germ. + Thus $\\\\psi$ is an isomorphism.\\n\\nStatement (3) follows immediately from + (2): any rational function on $Y$ is regular at some point $P \\\\in Y$, so + $K(Y) = \\\\bigcup_{P \\\\in Y} \\\\mathcal{O}_{Y,P}$ sits inside the field + of fractions $\\\\operatorname{Frac}(A(Y))$ and contains $A(Y)$, hence equals + $\\\\operatorname{Frac}(A(Y))$.\\n\\nFinally, we prove (1). Clearly there + is an injective homomorphism $\\\\alpha: A(Y) \\\\hookrightarrow \\\\mathcal{O}(Y)$ + sending a polynomial coset to the function it defines on $Y$. Through the + embeddings into $K(Y) = \\\\operatorname{Frac}(A(Y))$, we can identify both + $A(Y)$ and $\\\\mathcal{O}(Y)$ with subrings of $K(Y)$. Specifically, a rational + function $f \\\\in K(Y)$ belongs to $\\\\mathcal{O}(Y)$ if and only if it + is regular at every point $P \\\\in Y$, which means\\n$$\\\\mathcal{O}(Y) + = \\\\bigcap_{P \\\\in Y} \\\\mathcal{O}_{Y,P} = \\\\bigcap_{P \\\\in Y} A(Y)_{\\\\mathfrak{m}_P}$$\\ninside + $K(Y)$. Let $f \\\\in \\\\bigcap_{P \\\\in Y} A(Y)_{\\\\mathfrak{m}_P}$. Consider + the *conductor ideal* of $f$ in $A(Y)$:\\n$$\\\\mathfrak{a} = \\\\{h \\\\in + A(Y) \\\\mid hf \\\\in A(Y)\\\\}.$$\\nClearly $\\\\mathfrak{a}$ is an ideal + of $A(Y)$. For each $P \\\\in Y$, since $f \\\\in A(Y)_{\\\\mathfrak{m}_P}$, + we can write $f = g_P / h_P$ with $g_P, h_P \\\\in A(Y)$ and $h_P(P) \\\\neq + 0$. Thus $h_P \\\\in \\\\mathfrak{a}$ and $h_P \\\\notin \\\\mathfrak{m}_P$. + This implies that $\\\\mathfrak{a}$ is not contained in $\\\\mathfrak{m}_P$ + for any $P \\\\in Y$. By the Weak Nullstellensatz (transferred to the quotient + ring $A(Y)$), every maximal ideal of $A(Y)$ is of the form $\\\\mathfrak{m}_P$ + for some $P \\\\in Y$. Since $\\\\mathfrak{a}$ is not contained in any maximal + ideal of $A(Y)$, we must have $\\\\mathfrak{a} = A(Y)$. Therefore $1 \\\\in + \\\\mathfrak{a}$, so $f = 1 \\\\cdot f \\\\in A(Y)$. Thus $\\\\mathcal{O}(Y) + = A(Y)$. $\\\\blacksquare$\\n\\nWe can now define morphisms between varieties + and establish the fundamental categorical equivalence of affine algebraic + geometry.\\n\\n**Definition 1.3.6.** Let $X$ and $Y$ be two varieties (affine + or quasi-affine). A *morphism* $\\\\varphi: X \\\\to Y$ is a continuous map + such that for every open subset $V \\\\subseteq Y$ and every regular function + $f \\\\in \\\\mathcal{O}(V)$, the composition $f \\\\circ \\\\varphi: \\\\varphi^{-1}(V) + \\\\to k$ is a regular function in $\\\\mathcal{O}(\\\\varphi^{-1}(V))$. An + *isomorphism* is a morphism $\\\\varphi: X \\\\to Y$ that admits an inverse + morphism $\\\\psi: Y \\\\to X$ with $\\\\psi \\\\circ \\\\varphi = \\\\operatorname{id}_X$ + and $\\\\varphi \\\\circ \\\\psi = \\\\operatorname{id}_Y$.\\n\\n**Theorem + 1.3.7 (Equivalence of Categories for Affine Varieties).** *Let $X \\\\subseteq + \\\\mathbb{A}^n_k$ and $Y \\\\subseteq \\\\mathbb{A}^m_k$ be affine varieties.*\\n1. + *A map of sets $\\\\varphi: X \\\\to Y$ is a morphism of varieties if and + only if there exist polynomials $f_1, \\\\dots, f_m \\\\in k[x_1, \\\\dots, + x_n]$ such that $\\\\varphi(P) = (f_1(P), \\\\dots, f_m(P))$ for all $P \\\\in + X$.*\\n2. *For any morphism $\\\\varphi: X \\\\to Y$, composition with $\\\\varphi$ + induces a $k$-algebra homomorphism $\\\\varphi^*: A(Y) \\\\to A(X)$ given + by $g \\\\mapsto g \\\\circ \\\\varphi$. The assignment $\\\\varphi \\\\mapsto + \\\\varphi^*$ gives a bijection*\\n$$\\\\operatorname{Hom}_{\\\\mathfrak{Var}}(X, + Y) \\\\xrightarrow{\\\\sim} \\\\operatorname{Hom}_{k\\\\text{-}\\\\mathfrak{Alg}}(A(Y), + A(X)).$$\\n3. *The functor $X \\\\mapsto A(X)$ defines an equivalence of categories + between the category of affine varieties over $k$ and the opposite category + of finitely generated integral domains over $k$ (and similarly between affine + algebraic sets and finitely generated reduced $k$-algebras).*\\n\\n*Proof.* + (1) Suppose $\\\\varphi: X \\\\to Y$ is a morphism. Let $y_1, \\\\dots, y_m + \\\\in A(Y) = \\\\mathcal{O}(Y)$ be the coordinate functions on $Y \\\\subseteq + \\\\mathbb{A}^m_k$. By Definition 1.3.6 applied to $V = Y$, the functions + $\\\\varphi_i = y_i \\\\circ \\\\varphi$ must belong to $\\\\mathcal{O}(X) + = A(X)$. Thus each $\\\\varphi_i$ is the restriction to $X$ of a polynomial + $f_i \\\\in k[x_1, \\\\dots, x_n]$, so $\\\\varphi(P) = (f_1(P), \\\\dots, + f_m(P))$ for all $P \\\\in X$.\\n\\nConversely, suppose $\\\\varphi(P) = (f_1(P), + \\\\dots, f_m(P))$ for $f_i \\\\in k[x_1, \\\\dots, x_n]$. For any closed + subset $Z(\\\\mathfrak{b}) \\\\subseteq Y$ defined by an ideal $\\\\mathfrak{b} + \\\\subseteq k[y_1, \\\\dots, y_m]$, a point $P \\\\in X$ lies in $\\\\varphi^{-1}(Z(\\\\mathfrak{b}))$ + if and only if $g(f_1(P), \\\\dots, f_m(P)) = 0$ for all $g \\\\in \\\\mathfrak{b}$. + Thus $\\\\varphi^{-1}(Z(\\\\mathfrak{b}))$ is closed in $X$, so $\\\\varphi$ + is continuous. Moreover, if $h \\\\in \\\\mathcal{O}(V)$ is regular at $Q + = \\\\varphi(P) \\\\in V$, then near $Q$, $h = G(y_1, \\\\dots, y_m)/H(y_1, + \\\\dots, y_m)$ with $H(Q) \\\\neq 0$. Then near $P$ in $\\\\varphi^{-1}(V)$, + $(h \\\\circ \\\\varphi)(P') = G(f_1(P'), \\\\dots, f_m(P')) / H(f_1(P'), + \\\\dots, f_m(P'))$, which is clearly regular at $P$. Thus $\\\\varphi$ is + a morphism.\\n\\n(2) Let $\\\\alpha: A(Y) \\\\to A(X)$ be a $k$-algebra homomorphism. + Let $\\\\bar{y}_1, \\\\dots, \\\\bar{y}_m \\\\in A(Y)$ be the images of the + coordinate variables of $\\\\mathbb{A}^m_k$. For each $i$, choose a polynomial + $f_i \\\\in k[x_1, \\\\dots, x_n]$ whose image in $A(X)$ is $\\\\alpha(\\\\bar{y}_i)$. + This defines a polynomial map $\\\\varphi = (f_1, \\\\dots, f_m): \\\\mathbb{A}^n_k + \\\\to \\\\mathbb{A}^m_k$. If $g \\\\in I(Y) \\\\subseteq k[y_1, \\\\dots, + y_m]$, then $\\\\bar{g} = 0$ in $A(Y)$, so $g(\\\\alpha(\\\\bar{y}_1), \\\\dots, + \\\\alpha(\\\\bar{y}_m)) = \\\\alpha(\\\\bar{g}) = 0$ in $A(X)$. This means + $g(f_1, \\\\dots, f_m) \\\\in I(X)$, so for every $P \\\\in X$, $g(\\\\varphi(P)) + = 0$. Therefore $\\\\varphi(X) \\\\subseteq Z(I(Y)) = Y$, defining a morphism + $\\\\varphi: X \\\\to Y$ with $\\\\varphi^*(\\\\bar{y}_i) = \\\\bar{y}_i \\\\circ + \\\\varphi = \\\\bar{f}_i = \\\\alpha(\\\\bar{y}_i)$. Since the $\\\\bar{y}_i$ + generate $A(Y)$ as a $k$-algebra, $\\\\varphi^* = \\\\alpha$. Uniqueness is + clear since $\\\\varphi$ is completely determined by its coordinate functions + $\\\\varphi^*(\\\\bar{y}_i)$.\\n\\n(3) Part (2) proves that the contravariant + functor $X \\\\mapsto A(X)$ is fully faithful. To show it is essentially surjective, + let $R$ be any finitely generated integral domain over $k$. Choose generators + $a_1, \\\\dots, a_n$ of $R$ as a $k$-algebra, giving a surjective $k$-algebra + homomorphism $\\\\pi: k[x_1, \\\\dots, x_n] \\\\twoheadrightarrow R$ sending + $x_i \\\\mapsto a_i$. Since $R$ is an integral domain, $\\\\mathfrak{p} = + \\\\ker(\\\\pi)$ is a prime ideal in $k[x_1, \\\\dots, x_n]$. By Theorem 1.2.5, + $X = Z(\\\\mathfrak{p}) \\\\subseteq \\\\mathbb{A}^n_k$ is an affine variety + with $I(X) = \\\\mathfrak{p}$, and hence $A(X) = k[x_1, \\\\dots, x_n]/\\\\mathfrak{p} + \\\\cong R$. $\\\\blacksquare$\\n\\n---\\n\\n### 1.4 Rational Maps and Birational + Equivalence\\n\\nMany natural geometric constructions\u2014such as projecting + from a point or blowing up a subvariety\u2014yield maps that are defined only + on a dense open subset.\\n\\n**Definition 1.4.1.** Let $X$ and $Y$ be varieties. + A *rational map* $\\\\varphi: X \\\\dashrightarrow Y$ is an equivalence class + of pairs $(U, \\\\varphi_U)$ where $U \\\\subseteq X$ is a non-empty open + subset and $\\\\varphi_U: U \\\\to Y$ is a morphism of varieties, under the + equivalence relation $(U, \\\\varphi_U) \\\\sim (V, \\\\varphi_V)$ if $\\\\varphi_U|_{U + \\\\cap V} = \\\\varphi_V|_{U \\\\cap V}$.\\n\\nA rational map $\\\\varphi: + X \\\\dashrightarrow Y$ is called *dominant* if for some (and hence every) + representative $(U, \\\\varphi_U)$, the image $\\\\varphi_U(U)$ is dense in + $Y$.\\n\\nIf $\\\\varphi: X \\\\dashrightarrow Y$ and $\\\\psi: Y \\\\dashrightarrow + Z$ are dominant rational maps represented by $(U, \\\\varphi_U)$ and $(V, + \\\\psi_V)$, then since $\\\\varphi_U(U)$ is dense in $Y$ and $V$ is non-empty + open in $Y$, the intersection $\\\\varphi_U(U) \\\\cap V$ is non-empty. Consequently, + $W = \\\\varphi_U^{-1}(V) \\\\subseteq U$ is a non-empty open subset of $X$, + and the composition $\\\\psi_V \\\\circ \\\\varphi_U|_W: W \\\\to Z$ is a + dominant morphism. Thus, varieties over $k$ together with dominant rational + maps form a category.\\n\\n**Definition 1.4.2.** A *birational map* $\\\\varphi: + X \\\\dashrightarrow Y$ is a rational map which is an isomorphism in the category + of varieties and dominant rational maps; that is, $\\\\varphi$ is dominant + and admits a dominant rational map $\\\\psi: Y \\\\dashrightarrow X$ such + that $\\\\psi \\\\circ \\\\varphi = \\\\operatorname{id}_X$ and $\\\\varphi + \\\\circ \\\\psi = \\\\operatorname{id}_Y$ as rational maps. Two varieties + $X$ and $Y$ are *birationally equivalent* (or *birational*) if there exists + a birational map between them.\\n\\n**Theorem 1.4.3.** *Let $X$ and $Y$ be + varieties over $k$.*\\n1. *Every dominant rational map $\\\\varphi: X \\\\dashrightarrow + Y$ induces a $k$-algebra homomorphism of function fields $\\\\varphi^*: K(Y) + \\\\to K(X)$. This assignment induces a bijection between the set of dominant + rational maps from $X$ to $Y$ and the set of $k$-algebra homomorphisms from + $K(Y)$ to $K(X)$.*\\n2. *For any two varieties $X$ and $Y$, the following + conditions are equivalent:*\\n *(a) $X$ and $Y$ are birationally equivalent.*\\n + \ *(b) There exist non-empty open subsets $U \\\\subseteq X$ and $V \\\\subseteq + Y$ such that $U$ is isomorphic to $V$ as varieties.*\\n *(c) $K(X) \\\\cong + K(Y)$ as $k$-algebras.*\\n3. *The functor $X \\\\mapsto K(X)$ gives a contravariant + equivalence of categories between the category of varieties over $k$ with + dominant rational maps and the category of finitely generated field extensions + of $k$.*\\n\\n*Proof.* Since every variety contains a non-empty open affine + subset, and replacing a variety by a non-empty open subset changes neither + its rational maps nor its function field, we may assume without loss of generality + that $X \\\\subseteq \\\\mathbb{A}^n_k$ and $Y \\\\subseteq \\\\mathbb{A}^m_k$ + are affine varieties.\\n\\n(1) Let $\\\\varphi: X \\\\dashrightarrow Y$ be + a dominant rational map represented by $\\\\varphi_U: U \\\\to Y$. If $(V, + g) \\\\in K(Y)$ is a rational function on $Y$, then since $\\\\varphi_U(U)$ + is dense in $Y$, $\\\\varphi_U^{-1}(V)$ is a non-empty open subset of $U \\\\subseteq + X$, and $g \\\\circ \\\\varphi_U$ is regular on $\\\\varphi_U^{-1}(V)$. This + defines $\\\\varphi^*(g) \\\\in K(X)$.\\n\\nConversely, let $\\\\theta: K(Y) + \\\\to K(X)$ be a $k$-algebra homomorphism. Let $y_1, \\\\dots, y_m \\\\in + A(Y) \\\\subseteq K(Y)$ be the coordinate generators of $A(Y)$. Their images + $\\\\theta(y_1), \\\\dots, \\\\theta(y_m) \\\\in K(X)$ are rational functions + on $X$. Thus we can write $\\\\theta(y_i) = a_i / b_i$ with $a_i, b_i \\\\in + A(X)$ and $b_i \\\\neq 0$. Let $b = \\\\prod_{i=1}^m b_i \\\\in A(X)$, and + consider the principal open subset $U = X \\\\setminus Z(b)$, which is a non-empty + affine open subset of $X$ with coordinate ring $A(X)[1/b]$. Then $\\\\theta(y_i) + \\\\in \\\\mathcal{O}(U)$ for all $i$, so $\\\\theta$ restricts to a $k$-algebra + homomorphism $A(Y) \\\\to \\\\mathcal{O}(U) = A(U)$. By Theorem 1.3.7, this + corresponds to a morphism $\\\\varphi_U: U \\\\to Y$. Furthermore, since $\\\\theta: + K(Y) \\\\to K(X)$ is a homomorphism of fields, it is injective, meaning the + restriction $A(Y) \\\\to A(U)$ is injective. If $\\\\varphi_U(U)$ were contained + in a proper closed subset $Z(h) \\\\subsetneq Y$ for some $0 \\\\neq h \\\\in + A(Y)$, then $\\\\theta(h) = h \\\\circ \\\\varphi_U = 0$, contradicting the + injectivity of $\\\\theta$. Hence $\\\\varphi_U$ is dominant.\\n\\n(2) (a) + $\\\\iff$ (c) follows immediately from the categorical equivalence in (1). + Clearly (b) $\\\\implies$ (a). To show (a) $\\\\implies$ (b), suppose $\\\\varphi: + X \\\\dashrightarrow Y$ and $\\\\psi: Y \\\\dashrightarrow X$ are mutually + inverse birational maps represented by morphisms $\\\\varphi_U: U \\\\to Y$ + and $\\\\psi_V: V \\\\to X$. Then $\\\\psi \\\\circ \\\\varphi = \\\\operatorname{id}_X$ + means that on the non-empty open subset $U' = \\\\varphi_U^{-1}(V) \\\\subseteq + U$, the composition $\\\\psi_V \\\\circ \\\\varphi_U|_{U'}$ equals the inclusion + $U' \\\\hookrightarrow X$. Similarly, on $V' = \\\\psi_V^{-1}(U) \\\\subseteq + V$, $\\\\varphi_U \\\\circ \\\\psi_V|_{V'}$ equals the inclusion $V' \\\\hookrightarrow + Y$. Let $U'' = \\\\varphi_U^{-1}(V') \\\\cap U'$ and $V'' = \\\\psi_V^{-1}(U') + \\\\cap V'$. For $P \\\\in U''$, $\\\\varphi_U(P) \\\\in V'$ and $\\\\psi_V(\\\\varphi_U(P)) + = P \\\\in U'$, so $\\\\varphi_U(P) \\\\in \\\\psi_V^{-1}(U') \\\\cap V' = + V''$. Thus $\\\\varphi_U$ maps $U''$ into $V''$, and symmetrically $\\\\psi_V$ + maps $V''$ into $U''$. These restricted morphisms are mutually inverse isomorphisms + between the open varieties $U''$ and $V''$.\\n\\n(3) Fully faithfulness is + established in (1). For essential surjectivity, if $K$ is a finitely generated + field extension of $k$ with generators $\\\\alpha_1, \\\\dots, \\\\alpha_n$, + then the sub-$k$-algebra $R = k[\\\\alpha_1, \\\\dots, \\\\alpha_n] \\\\subseteq + K$ is a finitely generated integral domain over $k$ with $\\\\operatorname{Frac}(R) + = K$. By Theorem 1.3.7(3), $R \\\\cong A(X)$ for some affine variety $X$, + and hence $K \\\\cong K(X)$. $\\\\blacksquare$\\n\\n---\\n\\n### 1.5 Projective + Varieties\\n\\nAffine varieties fail to be \\\"compact\\\" in any reasonable + geometric sense; for example, two distinct lines in $\\\\mathbb{A}^2_k$ may + be parallel and fail to intersect. We remedy this by embedding affine space + into projective space.\\n\\n**Definition 1.5.1.** The *projective $n$-space* + over $k$, denoted $\\\\mathbb{P}^n_k$ (or $\\\\mathbb{P}^n$), is the set of + equivalence classes of $(n+1)$-tuples $(a_0, a_1, \\\\dots, a_n) \\\\in \\\\mathbb{A}^{n+1}_k + \\\\setminus \\\\{(0, \\\\dots, 0)\\\\}$ under the equivalence relation\\n$$(a_0, + a_1, \\\\dots, a_n) \\\\sim (\\\\lambda a_0, \\\\lambda a_1, \\\\dots, \\\\lambda + a_n) \\\\quad \\\\text{for all } \\\\lambda \\\\in k^\\\\times = k \\\\setminus + \\\\{0\\\\}.$$\\nThe equivalence class of $(a_0, \\\\dots, a_n)$ is denoted + $[a_0 : a_1 : \\\\dots : a_n]$, and $a_0, \\\\dots, a_n$ are called *homogeneous + coordinates* of the point.\\n\\nLet $S = k[x_0, x_1, \\\\dots, x_n]$ be the + polynomial ring in $n+1$ variables. We grade $S$ by total degree: $S = \\\\bigoplus_{d + \\\\ge 0} S_d$, where $S_d$ is the $k$-vector space spanned by all monomials + $x_0^{i_0} \\\\cdots x_n^{i_n}$ of total degree $i_0 + \\\\dots + i_n = d$. + Elements of $S_d$ are called *homogeneous polynomials* (or *forms*) of degree + $d$.\\n\\nAlthough a polynomial $f \\\\in S$ does not define a well-defined + function on $\\\\mathbb{P}^n_k$, if $f \\\\in S_d$ is homogeneous of degree + $d$, it satisfies the Euler scaling identity\\n$$f(\\\\lambda a_0, \\\\dots, + \\\\lambda a_n) = \\\\lambda^d f(a_0, \\\\dots, a_n) \\\\quad \\\\text{for + all } \\\\lambda \\\\in k^\\\\times.$$\\nConsequently, the condition $f(a_0, + \\\\dots, a_n) = 0$ is independent of the choice of homogeneous coordinates + for a point $P = [a_0 : \\\\dots : a_n] \\\\in \\\\mathbb{P}^n_k$.\\n\\n**Definition + 1.5.2.** An ideal $\\\\mathfrak{a} \\\\subseteq S$ is called *homogeneous* + if it can be generated by homogeneous polynomials, or equivalently, if $\\\\mathfrak{a} + = \\\\bigoplus_{d \\\\ge 0} (\\\\mathfrak{a} \\\\cap S_d)$. For any subset + $T \\\\subseteq \\\\bigcup_{d \\\\ge 0} S_d$ of homogeneous polynomials, we + define its projective zero locus\\n$$Z_+(T) = \\\\{P \\\\in \\\\mathbb{P}^n_k + \\\\mid f(P) = 0 \\\\text{ for all } f \\\\in T\\\\}.$$\\nSubsets of $\\\\mathbb{P}^n_k$ + of the form $Z_+(T)$ are called *projective algebraic sets*. They form the + closed sets of the *Zariski topology* on $\\\\mathbb{P}^n_k$. An irreducible + projective algebraic set is called a *projective variety*, and an open subset + of a projective variety is called a *quasi-projective variety*.\\n\\nConversely, + for any subset $Y \\\\subseteq \\\\mathbb{P}^n_k$, the *homogeneous ideal + of $Y$*, denoted $I_+(Y)$, is the ideal in $S$ generated by all homogeneous + polynomials $f \\\\in S$ that vanish at every point of $Y$.\\n\\nNotice that + the homogeneous ideal $S_+ = \\\\bigoplus_{d \\\\ge 1} S_d = (x_0, x_1, \\\\dots, + x_n)$ has $Z_+(S_+) = \\\\varnothing$, because the origin $(0, \\\\dots, 0)$ + is excluded from $\\\\mathbb{P}^n_k$. For this reason, $S_+$ is called the + *irrelevant maximal ideal* of $S$.\\n\\n**Theorem 1.5.3 (Projective Nullstellensatz).** + *Let $\\\\mathfrak{a} \\\\subseteq S = k[x_0, \\\\dots, x_n]$ be a homogeneous + ideal.*\\n1. $Z_+(\\\\mathfrak{a}) = \\\\varnothing$ *if and only if $\\\\sqrt{\\\\mathfrak{a}}$ + contains the irrelevant ideal $S_+ = (x_0, \\\\dots, x_n)$ (which is equivalent + to saying that $\\\\mathfrak{a} \\\\supseteq S_d$ for all sufficiently large + $d$).*\\n2. *If $Z_+(\\\\mathfrak{a}) \\\\neq \\\\varnothing$, then $I_+(Z_+(\\\\mathfrak{a})) + = \\\\sqrt{\\\\mathfrak{a}}$.*\\n\\n*Proof.* Let $\\\\pi: \\\\mathbb{A}^{n+1}_k + \\\\setminus \\\\{0\\\\} \\\\to \\\\mathbb{P}^n_k$ be the canonical projection + $(a_0, \\\\dots, a_n) \\\\mapsto [a_0 : \\\\dots : a_n]$. For any projective + algebraic set $Y = Z_+(\\\\mathfrak{a}) \\\\subseteq \\\\mathbb{P}^n_k$, its + *affine cone* is the affine algebraic set $C(Y) = \\\\pi^{-1}(Y) \\\\cup \\\\{0\\\\} + = Z(\\\\mathfrak{a}) \\\\subseteq \\\\mathbb{A}^{n+1}_k$.\\n\\n(1) We have + $Z_+(\\\\mathfrak{a}) = \\\\varnothing$ in $\\\\mathbb{P}^n_k$ if and only + if the affine zero locus $Z(\\\\mathfrak{a}) \\\\subseteq \\\\mathbb{A}^{n+1}_k$ + is contained in $\\\\{0\\\\}$. By the affine Nullstellensatz (Theorem 1.2.4), + this holds if and only if\\n$$\\\\sqrt{\\\\mathfrak{a}} = I(Z(\\\\mathfrak{a})) + \\\\supseteq I(\\\\{0\\\\}) = (x_0, x_1, \\\\dots, x_n) = S_+.$$\\nSince $S_+$ + is finitely generated by $x_0, \\\\dots, x_n$, $S_+ \\\\subseteq \\\\sqrt{\\\\mathfrak{a}}$ + if and only if $x_i^m \\\\in \\\\mathfrak{a}$ for some $m \\\\ge 1$ and all + $0 \\\\le i \\\\le n$, which forces $S_d \\\\subseteq \\\\mathfrak{a}$ for + all $d \\u003e (n+1)(m-1)$.\\n\\n(2) Suppose $Z_+(\\\\mathfrak{a}) \\\\neq + \\\\varnothing$. Then $Z(\\\\mathfrak{a}) \\\\subseteq \\\\mathbb{A}^{n+1}_k$ + contains points other than $0$, and since $\\\\mathfrak{a}$ is homogeneous, + $Z(\\\\mathfrak{a})$ is closed under scalar multiplication and hence contains + $0$. Therefore $Z(\\\\mathfrak{a}) = \\\\pi^{-1}(Z_+(\\\\mathfrak{a})) \\\\cup + \\\\{0\\\\}$. If $f \\\\in S_d$ is a homogeneous polynomial of degree $d \\\\ge + 1$, then $f$ vanishes on $Z_+(\\\\mathfrak{a})$ if and only if $f$ vanishes + on $\\\\pi^{-1}(Z_+(\\\\mathfrak{a})) \\\\cup \\\\{0\\\\} = Z(\\\\mathfrak{a})$ + (for $d=0$, a non-zero constant vanishes nowhere since $Z_+(\\\\mathfrak{a}) + \\\\neq \\\\varnothing$). Since both $I_+(Z_+(\\\\mathfrak{a}))$ and $I(Z(\\\\mathfrak{a})) + = \\\\sqrt{\\\\mathfrak{a}}$ are homogeneous ideals, and they contain the + exact same homogeneous polynomials, we conclude that $I_+(Z_+(\\\\mathfrak{a})) + = I(Z(\\\\mathfrak{a})) = \\\\sqrt{\\\\mathfrak{a}}$. $\\\\blacksquare$\\n\\nProjective + space is covered by standard affine open subsets. For each $i \\\\in \\\\{0, + 1, \\\\dots, n\\\\}$, define\\n$$U_i = \\\\{[a_0 : \\\\dots : a_n] \\\\in + \\\\mathbb{P}^n_k \\\\mid a_i \\\\neq 0\\\\} = \\\\mathbb{P}^n_k \\\\setminus + Z_+(x_i).$$\\nClearly $\\\\mathbb{P}^n_k = \\\\bigcup_{i=0}^n U_i$, and each + $U_i$ is open and dense in $\\\\mathbb{P}^n_k$.\\n\\n**Proposition 1.5.4.** + *For each $0 \\\\le i \\\\le n$, the map $\\\\varphi_i: U_i \\\\to \\\\mathbb{A}^n_k$ + defined by*\\n$$\\\\varphi_i([a_0 : \\\\dots : a_n]) = \\\\left(\\\\frac{a_0}{a_i}, + \\\\dots, \\\\frac{a_{i-1}}{a_i}, \\\\frac{a_{i+1}}{a_i}, \\\\dots, \\\\frac{a_n}{a_i}\\\\right)$$\\n*is + a homeomorphism for the respective Zariski topologies. Consequently, for any + projective variety $Y \\\\subseteq \\\\mathbb{P}^n_k$, the intersections $Y + \\\\cap U_i$ form an open cover of $Y$ by affine varieties.*\\n\\n*Proof.* + The map $\\\\varphi_i$ is clearly a bijection with inverse $\\\\psi_i: (b_1, + \\\\dots, b_n) \\\\mapsto [b_1 : \\\\dots : b_i : 1 : b_{i+1} : \\\\dots : + b_n]$. Let $A = k[y_1, \\\\dots, y_n]$ be the coordinate ring of $\\\\mathbb{A}^n_k$. + The homogenization and dehomogenization operations respect zero loci: specifically, + for any polynomial $g(y_1, \\\\dots, y_n) \\\\in A$ of degree $d$, its homogenization + with respect to $x_i$ is\\n$$\\\\beta(g) = x_i^d g\\\\left(\\\\frac{x_0}{x_i}, + \\\\dots, \\\\frac{x_n}{x_i}\\\\right) \\\\in S_d,$$\\nand conversely, for + any homogeneous $f \\\\in S_d$, its dehomogenization is $\\\\alpha(f) = f(y_1, + \\\\dots, 1, \\\\dots, y_n) \\\\in A$. For any point $P \\\\in U_i$, $f(P) + = 0$ if and only if $\\\\alpha(f)(\\\\varphi_i(P)) = 0$. Therefore, $\\\\varphi_i(Z_+(\\\\mathfrak{a}) + \\\\cap U_i) = Z(\\\\alpha(\\\\mathfrak{a}))$, showing that $\\\\varphi_i$ + maps closed subsets of $U_i$ bijectively onto closed subsets of $\\\\mathbb{A}^n_k$. + $\\\\blacksquare$\\n\\nTo unify affine, quasi-affine, projective, and quasi-projective + varieties under a single rigorous framework, we define regular functions on + projective varieties via homogeneous localizations.\\n\\n**Definition 1.5.5.** + Let $Y \\\\subseteq \\\\mathbb{P}^n_k$ be a quasi-projective variety with + homogeneous coordinate ring $S(Y) = k[x_0, \\\\dots, x_n]/I_+(Y)$. A function + $f: Y \\\\to k$ is *regular at $P \\\\in Y$* if there exists an open neighborhood + $U \\\\subseteq Y$ of $P$ and homogeneous elements $g, h \\\\in S(Y)_d$ *of + the same degree $d \\\\ge 0$* such that for all $Q \\\\in U$, $h(Q) \\\\neq + 0$ and $f(Q) = g(Q)/h(Q)$. (Notice that because $g$ and $h$ have the same + degree $d$, the ratio $g(a_0, \\\\dots, a_n)/h(a_0, \\\\dots, a_n)$ is invariant + under scaling $a_i \\\\mapsto \\\\lambda a_i$ and thus defines a genuine function + on $U$.)\\n\\nChecking on the standard affine open cover $U_i$, one verifies + immediately that this notion of regularity coincides with Definition 1.3.2 + on each affine open piece $Y \\\\cap U_i \\\\subseteq \\\\mathbb{A}^n_k$. + Whereas an affine variety $X$ is completely recovered from its ring of global + regular functions $\\\\mathcal{O}(X) = A(X)$, projective varieties exhibit + the exact opposite behavior: as we will prove later via sheaf cohomology (and + as explored in the exercises below), for any connected projective variety + $Y$ over $k$, the only global regular functions are the constants: $\\\\mathcal{O}(Y) + = k$.\\n\\n---\\n\\n### Exercises for Chapter 1\\n\\n**Exercise 1.1.** Let + $Y \\\\subseteq \\\\mathbb{A}^3_k$ be the *twisted cubic curve*, defined as + the image of the map $\\\\varphi: \\\\mathbb{A}^1_k \\\\to \\\\mathbb{A}^3_k$ + given by $t \\\\mapsto (t, t^2, t^3)$.\\n(a) Prove that $Y$ is an affine variety + and that its ideal $I(Y) \\\\subseteq k[x, y, z]$ is generated by $y - x^2$ + and $z - x^3$.\\n(b) Prove that $Y$ is isomorphic to $\\\\mathbb{A}^1_k$.\\n(c) + Show that $I(Y)$ can be generated by two elements, and use this to describe + $Y$ as the intersection of two surfaces in $\\\\mathbb{A}^3_k$.\\n\\n**Exercise + 1.2.** Let $X \\\\subseteq \\\\mathbb{A}^3_k$ be the union of the three coordinate + axes.\\n(a) Determine the ideal $I(X)$ in $k[x, y, z]$ and prove that it cannot + be generated by fewer than three elements.\\n(b) Describe the irreducible + components of $X$ and their corresponding minimal prime ideals in $A(X)$.\\n\\n**Exercise + 1.3.** Let $k$ be an algebraically closed field of characteristic zero, and + consider the plane curve $Y = Z(y^2 - x^3) \\\\subseteq \\\\mathbb{A}^2_k$ + (the cuspidal cubic).\\n(a) Prove that $y^2 - x^3$ is irreducible in $k[x, + y]$, so $Y$ is an affine variety.\\n(b) Show that the morphism $\\\\varphi: + \\\\mathbb{A}^1_k \\\\to Y$ given by $t \\\\mapsto (t^2, t^3)$ is a bijective + homeomorphism and a birational equivalence, but is *not* an isomorphism of + varieties.\\n(c) Identify $A(Y)$ with the subring $k[t^2, t^3] \\\\subseteq + k[t]$, and show that $A(Y)$ is not integrally closed in its field of fractions.\\n\\n**Exercise + 1.4.** Consider the punctured affine plane $U = \\\\mathbb{A}^2_k \\\\setminus + \\\\{(0,0)\\\\}$.\\n(a) Prove that every regular function $f \\\\in \\\\mathcal{O}(U)$ + extends uniquely to a regular function on all of $\\\\mathbb{A}^2_k$, so $\\\\mathcal{O}(U) + = k[x, y]$. *(Hint: Compute $\\\\mathcal{O}(D(x)) \\\\cap \\\\mathcal{O}(D(y))$ + inside $k(x,y)$ using unique factorization in $k[x,y]$.)*\\n(b) Deduce that + the quasi-affine variety $U = \\\\mathbb{A}^2_k \\\\setminus \\\\{(0,0)\\\\}$ + is *not* isomorphic to any affine variety.\\n\\n**Exercise 1.5.** Let $Y \\\\subseteq + \\\\mathbb{A}^n_k$ be an affine algebraic set. Prove that the following three + conditions are equivalent:\\n(a) $Y$ is a finite set of points.\\n(b) The + coordinate ring $A(Y)$ is finite-dimensional as a $k$-vector space.\\n(c) + $A(Y)$ is an Artinian ring.\\nWhen these conditions hold, prove that the number + of points in $Y$ equals $\\\\dim_k A(Y)$, and that $A(Y) \\\\cong \\\\prod_{P + \\\\in Y} k$.\\n\\n**Exercise 1.6.** (The Segre Embedding) Define a map $\\\\sigma: + \\\\mathbb{P}^n_k \\\\times \\\\mathbb{P}^m_k \\\\to \\\\mathbb{P}^{nm+n+m}_k$ + by sending $([a_0 : \\\\dots : a_n], [b_0 : \\\\dots : b_m])$ to the point + with homogeneous coordinates $[z_{00} : z_{01} : \\\\dots : z_{nm}]$ where + $z_{ij} = a_i b_j$.\\n(a) Prove that $\\\\sigma$ is well-defined and injective.\\n(b) + Prove that the image $\\\\Sigma_{n,m} = \\\\sigma(\\\\mathbb{P}^n_k \\\\times + \\\\mathbb{P}^m_k)$ is the projective algebraic set defined by the homogeneous + ideal generated by all $2 \\\\times 2$ minors $z_{ij} z_{kl} - z_{il} z_{kj}$.\\n(c) + Show that $\\\\Sigma_{n,m}$ is an irreducible projective variety. Use this + to endow $\\\\mathbb{P}^n_k \\\\times \\\\mathbb{P}^m_k$ with the structure + of a projective variety, and verify that for $n=m=1$, $\\\\Sigma_{1,1}$ is + a quadric surface in $\\\\mathbb{P}^3_k$.\\n\\n**Exercise 1.7.** (The Veronese + Embedding) Let $n, d \\\\ge 1$ be integers, and let $N = \\\\binom{n+d}{n} + - 1$. Let $M_0, M_1, \\\\dots, M_N$ be all the monic monomials of degree $d$ + in $x_0, \\\\dots, x_n$. The *d-uple Veronese embedding* is the map $\\\\nu_d: + \\\\mathbb{P}^n_k \\\\to \\\\mathbb{P}^N_k$ defined by $P \\\\mapsto [M_0(P) + : M_1(P) : \\\\dots : M_N(P)]$.\\n(a) Prove that $\\\\nu_d$ is an isomorphism + of $\\\\mathbb{P}^n_k$ onto a closed projective subvariety $V_{n,d} \\\\subseteq + \\\\mathbb{P}^N_k$.\\n(b) Deduce that for any homogeneous polynomial $f \\\\in + k[x_0, \\\\dots, x_n]$ of degree $d \\u003e 0$, the complement $\\\\mathbb{P}^n_k + \\\\setminus Z_+(f)$ of the hypersurface $Z_+(f)$ is isomorphic to an affine + variety.\\n\\n**Exercise 1.8.** (Blowing up a Point in $\\\\mathbb{A}^2_k$) + In $\\\\mathbb{A}^2_k \\\\times \\\\mathbb{P}^1_k$ (with affine coordinates + $(x, y)$ and homogeneous coordinates $[t : u]$), let $X$ be the closed subset + defined by the equation $xu - yt = 0$. Let $\\\\pi: X \\\\to \\\\mathbb{A}^2_k$ + be the projection onto the first factor.\\n(a) Prove that $X$ is an irreducible + quasi-projective variety.\\n(b) Show that $\\\\pi$ induces an isomorphism + $X \\\\setminus \\\\pi^{-1}(\\\\{(0,0)\\\\}) \\\\xrightarrow{\\\\sim} \\\\mathbb{A}^2_k + \\\\setminus \\\\{(0,0)\\\\}$, while the *exceptional divisor* $E = \\\\pi^{-1}(\\\\{(0,0)\\\\})$ + is isomorphic to $\\\\mathbb{P}^1_k$.\\n(c) Let $Y = Z(y^2 - x^2(x+1)) \\\\subseteq + \\\\mathbb{A}^2_k$ be the nodal cubic curve. The *strict transform* $\\\\widetilde{Y}$ + of $Y$ is the Zariski closure of $\\\\pi^{-1}(Y \\\\setminus \\\\{(0,0)\\\\})$ + in $X$. Prove that $\\\\widetilde{Y}$ is isomorphic to $\\\\mathbb{A}^1_k$ + and that $\\\\widetilde{Y} \\\\cap E$ consists of two distinct points corresponding + to the two tangent directions of $Y$ at $(0,0)$.\\n\\n---\\n\\n## Chapter + 2: Sheaves and Locally Ringed Spaces\\n\\nTo liberate algebraic geometry from + a fixed ambient affine or projective space\u2014and simultaneously to allow + geometries over arbitrary commutative rings such as $\\\\mathbb{Z}$\u2014Grothendieck + introduced the language of schemes. The foundational apparatus underlying + schemes is the theory of *sheaves* and *locally ringed spaces*, which allows + global geometric objects to be constructed by gluing local algebraic data.\\n\\n---\\n\\n### + 2.1 Presheaves and the Sheaf Axiom\\n\\n**Definition 2.1.1.** Let $X$ be a + topological space. Let $\\\\mathfrak{Top}(X)$ be the category whose objects + are the open subsets of $X$ and whose morphisms are the inclusion maps $V + \\\\hookrightarrow U$ whenever $V \\\\subseteq U$. A *presheaf* $\\\\mathcal{F}$ + on $X$ with values in a category $\\\\mathfrak{C}$ (typically the category + $\\\\mathfrak{Set}$ of sets, $\\\\mathfrak{Ab}$ of abelian groups, or $\\\\mathfrak{Rings}$ + of commutative rings) is a contravariant functor $\\\\mathcal{F}: \\\\mathfrak{Top}(X)^{\\\\text{op}} + \\\\to \\\\mathfrak{C}$.\\n\\nExplicitly, a presheaf $\\\\mathcal{F}$ of abelian + groups on $X$ consists of:\\n1. For every open subset $U \\\\subseteq X$, + an abelian group $\\\\mathcal{F}(U)$ (often denoted $\\\\Gamma(U, \\\\mathcal{F})$), + whose elements are called the *sections of $\\\\mathcal{F}$ over $U$*.\\n2. + For every inclusion of open subsets $V \\\\subseteq U$, a group homomorphism + $\\\\rho_{U,V}: \\\\mathcal{F}(U) \\\\to \\\\mathcal{F}(V)$, called the *restriction + map* (often written $s \\\\mapsto s|_V$), satisfying:\\n (a) $\\\\rho_{U,U} + = \\\\operatorname{id}_{\\\\mathcal{F}(U)}$ for all open $U \\\\subseteq X$, + and\\n (b) $\\\\rho_{V,W} \\\\circ \\\\rho_{U,V} = \\\\rho_{U,W}$ for all + open subsets $W \\\\subseteq V \\\\subseteq U$.\\n\\n**Definition 2.1.2.** + A presheaf $\\\\mathcal{F}$ (of sets, abelian groups, or rings) on a topological + space $X$ is called a *sheaf* if it satisfies the following two local-to-global + axioms for every open subset $U \\\\subseteq X$ and every open covering $\\\\{U_i\\\\}_{i + \\\\in I}$ of $U$ (i.e., $U = \\\\bigcup_{i \\\\in I} U_i$):\\n1. **(Locality + / Identity Axiom)** If $s, t \\\\in \\\\mathcal{F}(U)$ are two sections such + that $s|_{U_i} = t|_{U_i}$ for all $i \\\\in I$, then $s = t$.\\n2. **(Gluing + Axiom)** If we are given a family of sections $s_i \\\\in \\\\mathcal{F}(U_i)$ + for each $i \\\\in I$ such that on every overlap they agree:\\n $$s_i|_{U_i + \\\\cap U_j} = s_j|_{U_i \\\\cap U_j} \\\\quad \\\\text{for all } i, j \\\\in + I,$$\\n then there exists a section $s \\\\in \\\\mathcal{F}(U)$ such that + $s|_{U_i} = s_i$ for all $i \\\\in I$. (By the Locality Axiom, this section + $s$ is necessarily unique.)\\n\\nNotice that applying the Gluing Axiom to + the empty open cover of $U = \\\\varnothing$ (where the compatibility condition + is vacuous) implies that $\\\\mathcal{F}(\\\\varnothing)$ must be the terminal + object of the target category (a one-point set in $\\\\mathfrak{Set}$, the + trivial group $\\\\{0\\\\}$ in $\\\\mathfrak{Ab}$, or the zero ring $\\\\{0\\\\}$ + in $\\\\mathfrak{Rings}$).\\n\\nEquivalently, a presheaf $\\\\mathcal{F}$ + of abelian groups is a sheaf if and only if for every open subset $U \\\\subseteq + X$ and every open cover $\\\\{U_i\\\\}_{i \\\\in I}$ of $U$, the sequence + of abelian groups\\n$$0 \\\\longrightarrow \\\\mathcal{F}(U) \\\\xrightarrow{\\\\;\\\\alpha\\\\;} + \\\\prod_{i \\\\in I} \\\\mathcal{F}(U_i) \\\\xrightarrow{\\\\;\\\\beta\\\\;} + \\\\prod_{(i, j) \\\\in I \\\\times I} \\\\mathcal{F}(U_i \\\\cap U_j)$$\\nis + exact, where $\\\\alpha(s) = (s|_{U_i})_{i \\\\in I}$ and $\\\\beta((s_i)_{i + \\\\in I}) = (s_i|_{U_i \\\\cap U_j} - s_j|_{U_i \\\\cap U_j})_{(i,j) \\\\in + I \\\\times I}$.\\n\\n**Definition 2.1.3.** Let $\\\\mathcal{F}$ be a presheaf + on $X$ and let $P \\\\in X$ be a point. The *stalk* of $\\\\mathcal{F}$ at + $P$, denoted $\\\\mathcal{F}_P$, is the direct limit (colimit) of $\\\\mathcal{F}(U)$ + over the directed system of all open neighborhoods $U$ of $P$ ordered by reverse + inclusion:\\n$$\\\\mathcal{F}_P = \\\\varinjlim_{P \\\\in U} \\\\mathcal{F}(U).$$\\nConcretely, + an element of $\\\\mathcal{F}_P$ is an equivalence class of pairs $(U, s)$ + where $U$ is an open neighborhood of $P$ and $s \\\\in \\\\mathcal{F}(U)$, + under the equivalence relation $(U, s) \\\\sim (V, t)$ if there exists an + open neighborhood $W \\\\subseteq U \\\\cap V$ of $P$ such that $s|_W = t|_W$. + The equivalence class of $(U, s)$ is denoted $s_P \\\\in \\\\mathcal{F}_P$ + and is called the *germ* of $s$ at $P$.\\n\\n**Definition 2.1.4.** Let $\\\\mathcal{F}$ + and $\\\\mathcal{G}$ be presheaves on $X$. A *morphism of presheaves* $\\\\varphi: + \\\\mathcal{F} \\\\to \\\\mathcal{G}$ is a natural transformation of functors; + that is, a collection of morphisms $\\\\varphi(U): \\\\mathcal{F}(U) \\\\to + \\\\mathcal{G}(U)$ for each open $U \\\\subseteq X$ such that for every inclusion + $V \\\\subseteq U$, the diagram\\n$$\\\\begin{array}{ccc} \\\\mathcal{F}(U) + & \\\\xrightarrow{\\\\varphi(U)} & \\\\mathcal{G}(U) \\\\\\\\ \\\\downarrow{\\\\scriptstyle\\\\rho^{\\\\mathcal{F}}_{U,V}} + & & \\\\downarrow{\\\\scriptstyle\\\\rho^{\\\\mathcal{G}}_{U,V}} \\\\\\\\ + \\\\mathcal{F}(V) & \\\\xrightarrow{\\\\varphi(V)} & \\\\mathcal{G}(V) \\\\end{array}$$\\ncommutes. + A *morphism of sheaves* is simply a morphism of the underlying presheaves. + Any morphism $\\\\varphi: \\\\mathcal{F} \\\\to \\\\mathcal{G}$ induces a + morphism on stalks $\\\\varphi_P: \\\\mathcal{F}_P \\\\to \\\\mathcal{G}_P$ + for each $P \\\\in X$, given by $\\\\varphi_P(s_P) = (\\\\varphi(U)(s))_P$.\\n\\nThe + power of stalks lies in the fact that for sheaves, global isomorphisms can + be detected entirely at the level of stalks.\\n\\n**Proposition 2.1.5.** *Let + $\\\\varphi: \\\\mathcal{F} \\\\to \\\\mathcal{G}$ be a morphism of sheaves + of abelian groups on a topological space $X$. Then $\\\\varphi$ is an isomorphism + of sheaves (meaning $\\\\varphi(U): \\\\mathcal{F}(U) \\\\to \\\\mathcal{G}(U)$ + is an isomorphism for every open $U \\\\subseteq X$) if and only if the induced + map on stalks $\\\\varphi_P: \\\\mathcal{F}_P \\\\to \\\\mathcal{G}_P$ is + an isomorphism for every point $P \\\\in X$.*\\n\\n*Proof.* ($\\\\Rightarrow$) + If $\\\\varphi(U)$ is an isomorphism for every open $U \\\\subseteq X$, then + passing to the direct limit over all open neighborhoods $U$ of $P$ immediately + shows that $\\\\varphi_P = \\\\varinjlim \\\\varphi(U)$ is an isomorphism.\\n\\n($\\\\Leftarrow$) + Suppose $\\\\varphi_P: \\\\mathcal{F}_P \\\\to \\\\mathcal{G}_P$ is an isomorphism + for every $P \\\\in X$. Let $U \\\\subseteq X$ be an open subset. We must + prove that $\\\\varphi(U): \\\\mathcal{F}(U) \\\\to \\\\mathcal{G}(U)$ is + both injective and surjective.\\n\\n*Injectivity:* Suppose $s \\\\in \\\\mathcal{F}(U)$ + satisfies $\\\\varphi(U)(s) = 0$ in $\\\\mathcal{G}(U)$. For every point $P + \\\\in U$, we have $\\\\varphi_P(s_P) = (\\\\varphi(U)(s))_P = 0$ in $\\\\mathcal{G}_P$. + Since $\\\\varphi_P$ is injective, $s_P = 0$ in $\\\\mathcal{F}_P$. By definition + of the direct limit, for each $P \\\\in U$ there exists an open neighborhood + $U_P \\\\subseteq U$ of $P$ such that $s|_{U_P} = 0$ in $\\\\mathcal{F}(U_P)$. + The collection $\\\\{U_P\\\\}_{P \\\\in U}$ forms an open cover of $U$, and + the section $s \\\\in \\\\mathcal{F}(U)$ restricts to $0 = 0|_{U_P}$ on every + $U_P$. By the Locality Axiom for $\\\\mathcal{F}$, we conclude that $s = 0$ + in $\\\\mathcal{F}(U)$.\\n\\n*Surjectivity:* Let $t \\\\in \\\\mathcal{G}(U)$. + For each point $P \\\\in U$, consider the germ $t_P \\\\in \\\\mathcal{G}_P$. + Since $\\\\varphi_P$ is surjective, there exists a germ in $\\\\mathcal{F}_P$ + mapping to $t_P$; this germ is represented by some section $s^{(P)} \\\\in + \\\\mathcal{F}(V_P)$ on an open neighborhood $V_P \\\\subseteq U$ of $P$. + The equality $\\\\varphi_P((s^{(P)})_P) = t_P$ in $\\\\mathcal{G}_P$ means + that there exists a possibly smaller open neighborhood $U_P \\\\subseteq V_P$ + of $P$ such that, after replacing $s^{(P)}$ by its restriction $s^{(P)}|_{U_P} + \\\\in \\\\mathcal{F}(U_P)$, we have\\n$$\\\\varphi(U_P)(s^{(P)}) = t|_{U_P} + \\\\quad \\\\text{in } \\\\mathcal{G}(U_P).$$\\nNow consider two points $P, + Q \\\\in U$ and the restrictions of $s^{(P)}$ and $s^{(Q)}$ to the overlap + $U_P \\\\cap U_Q$. Applying $\\\\varphi(U_P \\\\cap U_Q)$ gives\\n$$\\\\varphi(U_P + \\\\cap U_Q)\\\\left(s^{(P)}|_{U_P \\\\cap U_Q} - s^{(Q)}|_{U_P \\\\cap U_Q}\\\\right) + = t|_{U_P \\\\cap U_Q} - t|_{U_P \\\\cap U_Q} = 0.$$\\nSince we have already + proven that $\\\\varphi(W)$ is injective for *every* open subset $W \\\\subseteq + X$, applying injectivity to $W = U_P \\\\cap U_Q$ yields\\n$$s^{(P)}|_{U_P + \\\\cap U_Q} = s^{(Q)}|_{U_P \\\\cap U_Q} \\\\quad \\\\text{for all } P, Q + \\\\in U.$$\\nBecause $\\\\{U_P\\\\}_{P \\\\in U}$ is an open cover of $U$ + and $\\\\mathcal{F}$ is a sheaf, the Gluing Axiom guarantees the existence + of a unique section $s \\\\in \\\\mathcal{F}(U)$ such that $s|_{U_P} = s^{(P)}$ + for all $P \\\\in U$. Finally, for every $P \\\\in U$,\\n$$(\\\\varphi(U)(s))|_{U_P} + = \\\\varphi(U_P)(s|_{U_P}) = \\\\varphi(U_P)(s^{(P)}) = t|_{U_P}.$$\\nBy + the Locality Axiom for the sheaf $\\\\mathcal{G}$, it follows that $\\\\varphi(U)(s) + = t$. Thus $\\\\varphi(U)$ is surjective. $\\\\blacksquare$\\n\\n---\\n\\n### + 2.2 Sheafification and the Category of Sheaves\\n\\nMany natural algebraic + operations on sheaves (such as taking quotients, images, or tensor products) + produce presheaves that fail to satisfy the gluing axiom. We therefore require + a canonical functorial procedure that turns any presheaf into a sheaf.\\n\\n**Theorem + 2.2.1 (Existence and Universal Property of Sheafification).** *Let $\\\\mathcal{F}$ + be a presheaf of sets (or abelian groups, or rings) on a topological space + $X$. There exists a sheaf $\\\\mathcal{F}^+$ on $X$ and a morphism of presheaves + $\\\\theta: \\\\mathcal{F} \\\\to \\\\mathcal{F}^+$ satisfying the following + universal property: for any sheaf $\\\\mathcal{G}$ on $X$ and any morphism + of presheaves $\\\\varphi: \\\\mathcal{F} \\\\to \\\\mathcal{G}$, there exists + a unique morphism of sheaves $\\\\tilde{\\\\varphi}: \\\\mathcal{F}^+ \\\\to + \\\\mathcal{G}$ such that $\\\\varphi = \\\\tilde{\\\\varphi} \\\\circ \\\\theta$.*\\n$$\\\\begin{array}{ccc} + \\\\mathcal{F} & \\\\xrightarrow{\\\\;\\\\theta\\\\;} & \\\\mathcal{F}^+ \\\\\\\\ + & \\\\underset{\\\\varphi}{\\\\searrow} & \\\\downarrow{\\\\scriptstyle\\\\exists!\\\\,\\\\tilde{\\\\varphi}} + \\\\\\\\ & & \\\\mathcal{G} \\\\end{array}$$\\n*Furthermore, the pair $(\\\\mathcal{F}^+, + \\\\theta)$ is unique up to unique isomorphism, and for every point $P \\\\in + X$, the induced map on stalks $\\\\theta_P: \\\\mathcal{F}_P \\\\to (\\\\mathcal{F}^+)_P$ + is an isomorphism.*\\n\\n*Proof.* For each open subset $U \\\\subseteq X$, + we define $\\\\mathcal{F}^+(U)$ to be the set of all functions $s: U \\\\to + \\\\bigsqcup_{P \\\\in U} \\\\mathcal{F}_P$ matching the following two conditions:\\n1. + For every $P \\\\in U$, $s(P) \\\\in \\\\mathcal{F}_P$.\\n2. **(Local Representation + by Sections)** For every $P \\\\in U$, there exists an open neighborhood $V + \\\\subseteq U$ of $P$ and a section $t \\\\in \\\\mathcal{F}(V)$ such that + for all $Q \\\\in V$, $s(Q) = t_Q$ in $\\\\mathcal{F}_Q$.\\n\\nFor an inclusion + of open subsets $W \\\\subseteq U$, the restriction map $\\\\mathcal{F}^+(U) + \\\\to \\\\mathcal{F}^+(W)$ is simply the restriction of functions $s \\\\mapsto + s|_W$. If $\\\\mathcal{F}$ is a presheaf of abelian groups (or rings), pointwise + addition (and multiplication) in the stalks $\\\\mathcal{F}_P$ makes $\\\\mathcal{F}^+(U)$ + an abelian group (or ring). Because the condition (2) is purely local and + functions $U \\\\to \\\\bigsqcup_{P \\\\in U} \\\\mathcal{F}_P$ are determined + pointwise and glue uniquely on open covers, it is immediate that $\\\\mathcal{F}^+$ + is a sheaf on $X$.\\n\\nWe define the canonical morphism of presheaves $\\\\theta: + \\\\mathcal{F} \\\\to \\\\mathcal{F}^+$ by sending a section $t \\\\in \\\\mathcal{F}(U)$ + to the function $\\\\theta(U)(t): U \\\\to \\\\bigsqcup_{P \\\\in U} \\\\mathcal{F}_P$ + given by $P \\\\mapsto t_P$. Clearly $\\\\theta(U)(t)$ satisfies conditions + (1) and (2) (taking $V = U$).\\n\\nNext, we prove that $\\\\theta_P: \\\\mathcal{F}_P + \\\\to (\\\\mathcal{F}^+)_P$ is an isomorphism for every $P \\\\in X$. There + is a natural evaluation map $\\\\mathrm{ev}_P: (\\\\mathcal{F}^+)_P \\\\to + \\\\mathcal{F}_P$ sending the germ of a function $s \\\\in \\\\mathcal{F}^+(U)$ + (where $P \\\\in U$) to its value $s(P) \\\\in \\\\mathcal{F}_P$. For any + germ $t_P \\\\in \\\\mathcal{F}_P$ represented by $t \\\\in \\\\mathcal{F}(U)$, + we have $\\\\mathrm{ev}_P(\\\\theta_P(t_P)) = (\\\\theta(U)(t))(P) = t_P$, + so $\\\\mathrm{ev}_P \\\\circ \\\\theta_P = \\\\operatorname{id}_{\\\\mathcal{F}_P}$. + Conversely, let $s_P \\\\in (\\\\mathcal{F}^+)_P$ be represented by $s \\\\in + \\\\mathcal{F}^+(U)$. By condition (2), there is an open neighborhood $V \\\\subseteq + U$ of $P$ and a section $t \\\\in \\\\mathcal{F}(V)$ such that $s(Q) = t_Q + = (\\\\theta(V)(t))(Q)$ for all $Q \\\\in V$. This means $s|_V = \\\\theta(V)(t)$ + in $\\\\mathcal{F}^+(V)$, so in the stalk $(\\\\mathcal{F}^+)_P$ we have $s_P + = \\\\theta_P(t_P) = \\\\theta_P(\\\\mathrm{ev}_P(s_P))$. Thus $\\\\theta_P$ + and $\\\\mathrm{ev}_P$ are mutually inverse isomorphisms.\\n\\nNote also that + if $\\\\mathcal{G}$ is *already* a sheaf, then $\\\\theta_{\\\\mathcal{G}}: + \\\\mathcal{G} \\\\to \\\\mathcal{G}^+$ is an isomorphism of sheaves. Indeed, + by the Locality Axiom, $\\\\theta_{\\\\mathcal{G}}(U)$ is injective; by the + Gluing Axiom applied to the local sections $t \\\\in \\\\mathcal{G}(V)$ from + condition (2), $\\\\theta_{\\\\mathcal{G}}(U)$ is surjective (or simply apply + Proposition 2.1.5 since $(\\\\theta_{\\\\mathcal{G}})_P$ is an isomorphism).\\n\\nFinally, + given a morphism of presheaves $\\\\varphi: \\\\mathcal{F} \\\\to \\\\mathcal{G}$ + where $\\\\mathcal{G}$ is a sheaf, the induced maps on stalks $\\\\varphi_P: + \\\\mathcal{F}_P \\\\to \\\\mathcal{G}_P$ induce a morphism of sheaves $\\\\varphi^+: + \\\\mathcal{F}^+ \\\\to \\\\mathcal{G}^+$ defined by $(\\\\varphi^+(U)(s))(P) + = \\\\varphi_P(s(P))$. Composing with the inverse of the isomorphism $\\\\theta_{\\\\mathcal{G}}: + \\\\mathcal{G} \\\\xrightarrow{\\\\sim} \\\\mathcal{G}^+$, we set $\\\\tilde{\\\\varphi} + = \\\\theta_{\\\\mathcal{G}}^{-1} \\\\circ \\\\varphi^+: \\\\mathcal{F}^+ + \\\\to \\\\mathcal{G}$. Clearly $\\\\tilde{\\\\varphi} \\\\circ \\\\theta + = \\\\varphi$. If $\\\\psi: \\\\mathcal{F}^+ \\\\to \\\\mathcal{G}$ is any + morphism of sheaves satisfying $\\\\psi \\\\circ \\\\theta = \\\\varphi$, + then for every $P \\\\in X$, $\\\\psi_P \\\\circ \\\\theta_P = \\\\varphi_P + = \\\\tilde{\\\\varphi}_P \\\\circ \\\\theta_P$. Since $\\\\theta_P$ is an + isomorphism, $\\\\psi_P = \\\\tilde{\\\\varphi}_P$ for all $P \\\\in X$, which + forces $\\\\psi = \\\\tilde{\\\\varphi}$ because two morphisms of sheaves + that induce the same map on all stalks are identical (for any $s \\\\in \\\\mathcal{F}^+(U)$, + $\\\\psi(U)(s)$ and $\\\\tilde{\\\\varphi}(U)(s)$ have the same germ at every + $P \\\\in U$, hence are equal in $\\\\mathcal{G}(U)$ by the Locality Axiom). + $\\\\blacksquare$\\n\\n**Definition 2.2.2.** Let $\\\\varphi: \\\\mathcal{F} + \\\\to \\\\mathcal{G}$ be a morphism of sheaves of abelian groups on $X$.\\n1. + The *kernel* of $\\\\varphi$, denoted $\\\\ker(\\\\varphi)$, is the presheaf + $U \\\\mapsto \\\\ker(\\\\varphi(U): \\\\mathcal{F}(U) \\\\to \\\\mathcal{G}(U))$. + One checks directly from the left-exactness of the sheaf condition that $\\\\ker(\\\\varphi)$ + is already a sheaf.\\n2. The *image* of $\\\\varphi$, denoted $\\\\operatorname{im}(\\\\varphi)$, + is the sheafification of the *presheaf image* $U \\\\mapsto \\\\operatorname{im}(\\\\varphi(U): + \\\\mathcal{F}(U) \\\\to \\\\mathcal{G}(U))$. By the universal property of + sheafification, $\\\\operatorname{im}(\\\\varphi)$ embeds canonically as a + subsheaf of $\\\\mathcal{G}$.\\n3. For a subsheaf $\\\\mathcal{F}' \\\\subseteq + \\\\mathcal{F}$, the *quotient sheaf* $\\\\mathcal{F}/\\\\mathcal{F}'$ is + the sheafification of the presheaf $U \\\\mapsto \\\\mathcal{F}(U)/\\\\mathcal{F}'(U)$. + The *cokernel* of $\\\\varphi$ is $\\\\operatorname{coker}(\\\\varphi) = \\\\mathcal{G}/\\\\operatorname{im}(\\\\varphi)$.\\n\\n**Proposition + 2.2.3.** *Let $\\\\varphi: \\\\mathcal{F} \\\\to \\\\mathcal{G}$ be a morphism + of sheaves of abelian groups on $X$, and let $P \\\\in X$. Then:*\\n1. $(\\\\ker + \\\\varphi)_P = \\\\ker(\\\\varphi_P: \\\\mathcal{F}_P \\\\to \\\\mathcal{G}_P)$ + *and* $(\\\\operatorname{im} \\\\varphi)_P = \\\\operatorname{im}(\\\\varphi_P: + \\\\mathcal{F}_P \\\\to \\\\mathcal{G}_P)$.\\n2. *A sequence of sheaves of + abelian groups $\\\\dots \\\\to \\\\mathcal{F}^{i-1} \\\\xrightarrow{d^{i-1}} + \\\\mathcal{F}^i \\\\xrightarrow{d^i} \\\\mathcal{F}^{i+1} \\\\to \\\\dots$ + is exact (meaning $\\\\ker(d^i) = \\\\operatorname{im}(d^{i-1})$ for all $i$) + if and only if for every $P \\\\in X$, the induced sequence of stalks $\\\\dots + \\\\to \\\\mathcal{F}^{i-1}_P \\\\to \\\\mathcal{F}^i_P \\\\to \\\\mathcal{F}^{i+1}_P + \\\\to \\\\dots$ is an exact sequence of abelian groups.*\\n3. *If $0 \\\\to + \\\\mathcal{F}' \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{F}'' \\\\to 0$ is + an exact sequence of sheaves on $X$, then for every open subset $U \\\\subseteq + X$, the sequence of sections*\\n$$0 \\\\longrightarrow \\\\mathcal{F}'(U) + \\\\longrightarrow \\\\mathcal{F}(U) \\\\longrightarrow \\\\mathcal{F}''(U)$$\\n*is + left-exact.*\\n\\n*Proof.* (1) Filtered direct limits of abelian groups are + exact functors, so taking stalks commutes with presheaf kernels and presheaf + images. Since sheafification induces an isomorphism on stalks (Theorem 2.2.1), + $(\\\\operatorname{im} \\\\varphi)_P$ equals the stalk of the presheaf image, + which is $\\\\operatorname{im}(\\\\varphi_P)$.\\n\\n(2) By (1), the inclusion + $\\\\operatorname{im}(d^{i-1}) \\\\hookrightarrow \\\\ker(d^i)$ (assuming + $d^i \\\\circ d^{i-1} = 0$) induces an isomorphism on all stalks if and only + if $\\\\operatorname{im}(d^{i-1}_P) = \\\\ker(d^i_P)$ for all $P \\\\in X$. + By Proposition 2.1.5, this holds if and only if $\\\\operatorname{im}(d^{i-1}) + = \\\\ker(d^i)$ as subsheaves of $\\\\mathcal{F}^i$.\\n\\n(3) By definition + of $\\\\ker$, $\\\\mathcal{F}'(U) = \\\\ker(\\\\mathcal{F}(U) \\\\to \\\\mathcal{F}''(U))$, + which immediately gives left-exactness on $U$. (Right-exactness fails in general; + this failure is the genesis of sheaf cohomology in Chapter 5.) $\\\\blacksquare$\\n\\n---\\n\\n### + 2.3 Ringed Spaces and Locally Ringed Spaces\\n\\n**Definition 2.3.1.** Let + $f: X \\\\to Y$ be a continuous map of topological spaces.\\n1. For any sheaf + $\\\\mathcal{F}$ on $X$, the *direct image* (or *pushforward*) sheaf $f_*\\\\mathcal{F}$ + on $Y$ is defined for every open $V \\\\subseteq Y$ by\\n $$(f_*\\\\mathcal{F})(V) + = \\\\mathcal{F}(f^{-1}(V)).$$\\n One checks immediately that $f_*\\\\mathcal{F}$ + is a sheaf on $Y$.\\n2. For any sheaf $\\\\mathcal{G}$ on $Y$, the *inverse + image* sheaf $f^{-1}\\\\mathcal{G}$ on $X$ is defined to be the sheafification + of the presheaf\\n $$U \\\\longmapsto \\\\varinjlim_{V \\\\supseteq f(U)} + \\\\mathcal{G}(V),$$\\n where the direct limit runs over all open subsets + $V \\\\subseteq Y$ containing $f(U)$.\\n\\nNotice that for every point $P + \\\\in X$, a cofinal system of open neighborhoods of $f(P)$ in $Y$ pulls back + to open subsets containing neighborhoods of $P$, so there is a canonical isomorphism + of stalks $(f^{-1}\\\\mathcal{G})_P \\\\cong \\\\mathcal{G}_{f(P)}$. Moreover, + the functors $f^{-1}$ and $f_*$ form an adjoint pair: for any sheaf $\\\\mathcal{F}$ + on $X$ and any sheaf $\\\\mathcal{G}$ on $Y$, there is a natural bijection\\n$$\\\\operatorname{Hom}_{\\\\mathfrak{Sh}(X)}(f^{-1}\\\\mathcal{G}, + \\\\mathcal{F}) \\\\xrightarrow{\\\\;\\\\sim\\\\;} \\\\operatorname{Hom}_{\\\\mathfrak{Sh}(Y)}(\\\\mathcal{G}, + f_*\\\\mathcal{F}).$$\\n\\n**Definition 2.3.2.**\\n1. A *ringed space* is + a pair $(X, \\\\mathcal{O}_X)$ consisting of a topological space $X$ and a + sheaf of commutative rings $\\\\mathcal{O}_X$ on $X$, called the *structure + sheaf* of $X$.\\n2. A *morphism of ringed spaces* from $(X, \\\\mathcal{O}_X)$ + to $(Y, \\\\mathcal{O}_Y)$ is a pair $(f, f^\\\\#)$ consisting of a continuous + map $f: X \\\\to Y$ and a morphism of sheaves of rings $f^\\\\#: \\\\mathcal{O}_Y + \\\\to f_*\\\\mathcal{O}_X$ on $Y$.\\n3. A ringed space $(X, \\\\mathcal{O}_X)$ + is called a *locally ringed space* if for every point $P \\\\in X$, the stalk + $\\\\mathcal{O}_{X,P}$ is a local ring (meaning it has a unique maximal ideal, + which we denote by $\\\\mathfrak{m}_{X,P}$ or $\\\\mathfrak{m}_P$). The quotient + field $\\\\kappa(P) = \\\\mathcal{O}_{X,P}/\\\\mathfrak{m}_P$ is called the + *residue field* of $X$ at $P$.\\n4. A *morphism of locally ringed spaces* + from $(X, \\\\mathcal{O}_X)$ to $(Y, \\\\mathcal{O}_Y)$ is a morphism of ringed + spaces $(f, f^\\\\#)$ such that for every point $P \\\\in X$, the induced + ring homomorphism on stalks\\n $$f^\\\\#_P: \\\\mathcal{O}_{Y, f(P)} \\\\longrightarrow + \\\\mathcal{O}_{X,P}$$\\n (obtained by passing to the direct limit of $f^\\\\#(V): + \\\\mathcal{O}_Y(V) \\\\to \\\\mathcal{O}_X(f^{-1}(V))$ over all open neighborhoods + $V$ of $f(P)$, or equivalently via the adjoint morphism $f^{-1}\\\\mathcal{O}_Y + \\\\to \\\\mathcal{O}_X$) is a *local homomorphism of local rings*, meaning + that\\n $$(f^\\\\#_P)^{-1}(\\\\mathfrak{m}_{X,P}) = \\\\mathfrak{m}_{Y, + f(P)}, \\\\quad \\\\text{or equivalently,} \\\\quad f^\\\\#_P(\\\\mathfrak{m}_{Y, + f(P)}) \\\\subseteq \\\\mathfrak{m}_{X,P}.$$\\n\\nIn classical varieties, + if $\\\\varphi: X \\\\to Y$ is a morphism and $f^\\\\#$ is given by pullback + of functions $g \\\\mapsto g \\\\circ \\\\varphi$, then $g \\\\in \\\\mathfrak{m}_{\\\\varphi(P)}$ + means $g(\\\\varphi(P)) = 0$, which automatically implies $(g \\\\circ \\\\varphi)(P) + = 0$, so $g \\\\circ \\\\varphi \\\\in \\\\mathfrak{m}_P$. In the abstract + setting of schemes, however, the sections of $\\\\mathcal{O}_X$ are not literally + functions into a fixed base field, so the condition that $f^\\\\#_P$ be a + local homomorphism is not automatic and must be imposed as a fundamental axiom.\\n\\n---\\n\\n### + Exercises for Chapter 2\\n\\n**Exercise 2.1.** Let $X$ be a topological space + and $A$ a non-zero abelian group.\\n(a) Let $\\\\mathcal{F}$ be the *constant + presheaf* with $U \\\\mapsto A$ for all non-empty open $U \\\\subseteq X$ + (and $\\\\mathcal{F}(\\\\varnothing) = 0$), with identity restriction maps. + Show that if $X$ contains two disjoint non-empty open subsets, $\\\\mathcal{F}$ + is not a sheaf.\\n(b) Prove that the sheafification $\\\\mathcal{F}^+$ of + $\\\\mathcal{F}$ is the *constant sheaf* $\\\\underline{A}_X$, whose sections + over an open set $U \\\\subseteq X$ are the continuous functions $U \\\\to + A$, where $A$ is given the discrete topology.\\n\\n**Exercise 2.2.** Let $\\\\varphi: + \\\\mathcal{F} \\\\to \\\\mathcal{G}$ be a morphism of sheaves of abelian + groups on $X$. Prove that the following are equivalent:\\n(a) $\\\\varphi$ + is surjective as a morphism of sheaves (meaning $\\\\operatorname{im} \\\\varphi + = \\\\mathcal{G}$, or $\\\\operatorname{coker} \\\\varphi = 0$).\\n(b) $\\\\varphi_P: + \\\\mathcal{F}_P \\\\to \\\\mathcal{G}_P$ is surjective for every $P \\\\in + X$.\\n(c) For every open subset $U \\\\subseteq X$ and every section $t \\\\in + \\\\mathcal{G}(U)$, there exists an open cover $\\\\{U_i\\\\}_{i \\\\in I}$ + of $U$ and sections $s_i \\\\in \\\\mathcal{F}(U_i)$ such that $\\\\varphi(U_i)(s_i) + = t|_{U_i}$ for all $i \\\\in I$.\\nGive an explicit example of a surjective + morphism of sheaves $\\\\varphi: \\\\mathcal{F} \\\\to \\\\mathcal{G}$ such + that $\\\\varphi(X): \\\\mathcal{F}(X) \\\\to \\\\mathcal{G}(X)$ is *not* + surjective.\\n\\n**Exercise 2.3.** (Gluing Sheaves) Let $X$ be a topological + space and $\\\\{U_i\\\\}_{i \\\\in I}$ an open cover of $X$. Suppose that + for each $i \\\\in I$ we are given a sheaf $\\\\mathcal{F}_i$ on $U_i$, and + for each pair $(i, j) \\\\in I \\\\times I$ an isomorphism of sheaves $\\\\varphi_{ij}: + \\\\mathcal{F}_i|_{U_i \\\\cap U_j} \\\\xrightarrow{\\\\sim} \\\\mathcal{F}_j|_{U_i + \\\\cap U_j}$ satisfying:\\n(i) $\\\\varphi_{ii} = \\\\operatorname{id}_{\\\\mathcal{F}_i}$ + for all $i \\\\in I$, and\\n(ii) **(Cocycle Condition)** On every triple intersection + $U_i \\\\cap U_j \\\\cap U_k$, we have $\\\\varphi_{jk} \\\\circ \\\\varphi_{ij} + = \\\\varphi_{ik}$.\\nProve that there exists a sheaf $\\\\mathcal{F}$ on + $X$, unique up to unique isomorphism, together with isomorphisms $\\\\psi_i: + \\\\mathcal{F}|_{U_i} \\\\xrightarrow{\\\\sim} \\\\mathcal{F}_i$ such that + $\\\\varphi_{ij} \\\\circ \\\\psi_i|_{U_i \\\\cap U_j} = \\\\psi_j|_{U_i \\\\cap + U_j}$ for all $i, j \\\\in I$.\\n\\n**Exercise 2.4.** (Sheaves on a Base) + Let $X$ be a topological space and $\\\\mathfrak{B}$ a *base* for the topology + of $X$ (so every open set is a union of elements of $\\\\mathfrak{B}$, and + the intersection of two elements of $\\\\mathfrak{B}$ is covered by elements + of $\\\\mathfrak{B}$). A *$\\\\mathfrak{B}$-sheaf* is a contravariant functor + $\\\\mathcal{F}$ defined only on the open sets in $\\\\mathfrak{B}$ satisfying + the locality and gluing axioms for covers of $B \\\\in \\\\mathfrak{B}$ by + elements of $\\\\mathfrak{B}$.\\nProve that every $\\\\mathfrak{B}$-sheaf + $\\\\mathcal{F}$ extends uniquely (up to canonical isomorphism) to a sheaf + $\\\\widetilde{\\\\mathcal{F}}$ on $X$ via the formula\\n$$\\\\widetilde{\\\\mathcal{F}}(U) + = \\\\varprojlim_{B \\\\in \\\\mathfrak{B},\\\\, B \\\\subseteq U} \\\\mathcal{F}(B).$$\\n\\n**Exercise + 2.5.** Let $f: X \\\\to Y$ be a continuous map of topological spaces. Construct + explicitly the adjunction bijections\\n$$\\\\operatorname{Hom}_{\\\\mathfrak{Sh}(X)}(f^{-1}\\\\mathcal{G}, + \\\\mathcal{F}) \\\\xrightarrow{\\\\;\\\\sim\\\\;} \\\\operatorname{Hom}_{\\\\mathfrak{Sh}(Y)}(\\\\mathcal{G}, + f_*\\\\mathcal{F})$$\\nand prove that $f^{-1}: \\\\mathfrak{Ab}(Y) \\\\to + \\\\mathfrak{Ab}(X)$ is an exact functor, whereas $f_*: \\\\mathfrak{Ab}(X) + \\\\to \\\\mathfrak{Ab}(Y)$ is left-exact.\\n\\n**Exercise 2.6.** (Skyscraper + Sheaves) Let $X$ be a topological space, $P \\\\in X$ a point, and $A$ an + abelian group. Define $i_P(A)(U) = A$ if $P \\\\in U$ and $i_P(A)(U) = 0$ + if $P \\\\notin U$.\\n(a) Prove that $i_P(A)$ is a sheaf on $X$, and that + it is isomorphic to the pushforward $i_*\\\\underline{A}_{\\\\{P\\\\}}$ under + the inclusion $i: \\\\{P\\\\} \\\\hookrightarrow X$.\\n(b) Determine the stalk + $(i_P(A))_Q$ for an arbitrary point $Q \\\\in X$ in terms of the closure $\\\\overline{\\\\{P\\\\}}$ + of $\\\\{P\\\\}$ in $X$.\\n\\n---\\n\\n## Chapter 3: Schemes: Construction + and Fundamental Properties\\n\\nWe now arrive at the central object of modern + algebraic geometry: the *scheme*. By associating a locally ringed space $\\\\operatorname{Spec} + A$ to every commutative ring $A$ with identity, we embed the entire category + of commutative rings contravariantly into geometric spaces, unifying arithmetic + and geometry.\\n\\n---\\n\\n### 3.1 The Prime Spectrum of a Ring\\n\\nThroughout + this chapter, all rings are assumed to be commutative with a multiplicative + identity $1$.\\n\\n**Definition 3.1.1.** Let $A$ be a ring. The *prime spectrum* + (or simply *spectrum*) of $A$, denoted $\\\\operatorname{Spec} A$, is the + set of all prime ideals of $A$. For any subset $E \\\\subseteq A$, we define + the *vanishing locus* $V(E)$ to be the set of all prime ideals of $A$ containing + $E$:\\n$$V(E) = \\\\{\\\\mathfrak{p} \\\\in \\\\operatorname{Spec} A \\\\mid + E \\\\subseteq \\\\mathfrak{p}\\\\}.$$\\n\\nIf $\\\\mathfrak{a} = (E)$ is + the ideal of $A$ generated by $E$, then clearly $V(E) = V(\\\\mathfrak{a}) + = V(\\\\sqrt{\\\\mathfrak{a}})$.\\n\\n**Proposition 3.1.2.** *Let $A$ be a + ring. The operation $V$ satisfies:*\\n1. $V(0) = \\\\operatorname{Spec} A$ + *and* $V(1) = V(A) = \\\\varnothing$.\\n2. *For any family of ideals $\\\\{\\\\mathfrak{a}_i\\\\}_{i + \\\\in I}$ of $A$, $\\\\bigcap_{i \\\\in I} V(\\\\mathfrak{a}_i) = V\\\\left(\\\\sum_{i + \\\\in I} \\\\mathfrak{a}_i\\\\right)$.*\\n3. *For any two ideals $\\\\mathfrak{a}, + \\\\mathfrak{b}$ of $A$, $V(\\\\mathfrak{a}) \\\\cup V(\\\\mathfrak{b}) = + V(\\\\mathfrak{a}\\\\mathfrak{b}) = V(\\\\mathfrak{a} \\\\cap \\\\mathfrak{b})$.*\\n4. + *For any ideal $\\\\mathfrak{a} \\\\subseteq A$, $\\\\bigcap_{\\\\mathfrak{p} + \\\\in V(\\\\mathfrak{a})} \\\\mathfrak{p} = \\\\sqrt{\\\\mathfrak{a}}$. Consequently, + $V(\\\\mathfrak{a}) \\\\subseteq V(\\\\mathfrak{b})$ if and only if $\\\\sqrt{\\\\mathfrak{b}} + \\\\subseteq \\\\sqrt{\\\\mathfrak{a}}$.*\\n\\n*Proof.* Properties (1), (2), + and (3) are proved identically to Proposition 1.1.3, using the defining property + of prime ideals: if $\\\\mathfrak{a}\\\\mathfrak{b} \\\\subseteq \\\\mathfrak{p}$, + then $\\\\mathfrak{a} \\\\subseteq \\\\mathfrak{p}$ or $\\\\mathfrak{b} \\\\subseteq + \\\\mathfrak{p}$.\\n\\nFor (4), it is a foundational fact of commutative algebra + that the radical $\\\\sqrt{\\\\mathfrak{a}}$ is the intersection of all prime + ideals containing $\\\\mathfrak{a}$. (Indeed, if $f \\\\notin \\\\sqrt{\\\\mathfrak{a}}$, + then the multiplicatively closed set $S = \\\\{1, f, f^2, \\\\dots\\\\}$ is + disjoint from $\\\\mathfrak{a}$, so the localization $(A/\\\\mathfrak{a})_f$ + is a non-zero ring and thus possesses a maximal ideal, whose preimage in $A$ + is a prime ideal containing $\\\\mathfrak{a}$ and not containing $f$.) The + second assertion of (4) follows immediately. $\\\\blacksquare$\\n\\nBy Proposition + 3.1.2, the sets $V(\\\\mathfrak{a})$ form the closed subsets of a topology + on $\\\\operatorname{Spec} A$, called the *Zariski topology*.\\n\\n**Definition + 3.1.3.** For each element $f \\\\in A$, we define the *principal open subset* + (or *distinguished open subset*) $D(f) \\\\subseteq \\\\operatorname{Spec} + A$ to be the complement of $V((f))$:\\n$$D(f) = \\\\operatorname{Spec} A \\\\setminus + V((f)) = \\\\{\\\\mathfrak{p} \\\\in \\\\operatorname{Spec} A \\\\mid f \\\\notin + \\\\mathfrak{p}\\\\}.$$\\n\\n**Proposition 3.1.4.** *Let $A$ be a ring and + $f, g \\\\in A$.*\\n1. $D(f) \\\\cap D(g) = D(fg)$.\\n2. $D(f) = \\\\varnothing + \\\\iff f$ *is nilpotent; $D(f) = \\\\operatorname{Spec} A \\\\iff f \\\\in + A^\\\\times$ is a unit.*\\n3. *The collection $\\\\{D(f) \\\\mid f \\\\in + A\\\\}$ forms a base for the Zariski topology on $\\\\operatorname{Spec} A$.*\\n4. + *Each open set $D(f)$ (and in particular $\\\\operatorname{Spec} A = D(1)$) + is quasi-compact: every open cover of $D(f)$ has a finite subcover.*\\n\\n*Proof.* + (1) A prime ideal $\\\\mathfrak{p}$ satisfies $fg \\\\notin \\\\mathfrak{p}$ + if and only if $f \\\\notin \\\\mathfrak{p}$ and $g \\\\notin \\\\mathfrak{p}$.\\n\\n(2) + By Proposition 3.1.2(4), $D(f) = \\\\varnothing \\\\iff V((f)) = \\\\operatorname{Spec} + A \\\\iff f \\\\in \\\\bigcap_{\\\\mathfrak{p} \\\\in \\\\operatorname{Spec} + A} \\\\mathfrak{p} = \\\\sqrt{(0)}$. Similarly, $D(f) = \\\\operatorname{Spec} + A \\\\iff V((f)) = \\\\varnothing \\\\iff (f) = A \\\\iff f \\\\in A^\\\\times$.\\n\\n(3) + Any open set in $\\\\operatorname{Spec} A$ is of the form $\\\\operatorname{Spec} + A \\\\setminus V(E) = \\\\operatorname{Spec} A \\\\setminus \\\\bigcap_{f + \\\\in E} V((f)) = \\\\bigcup_{f \\\\in E} D(f)$.\\n\\n(4) Since the sets + $D(g)$ form a base for the topology, it suffices to show that if $D(f) \\\\subseteq + \\\\bigcup_{i \\\\in I} D(g_i)$, then there is a finite subset $J \\\\subseteq + I$ such that $D(f) \\\\subseteq \\\\bigcup_{j \\\\in J} D(g_j)$. Taking complements, + the inclusion $D(f) \\\\subseteq \\\\bigcup_{i \\\\in I} D(g_i)$ is equivalent + to $V((f)) \\\\supseteq \\\\bigcap_{i \\\\in I} V((g_i)) = V\\\\left(\\\\sum_{i + \\\\in I} (g_i)\\\\right)$. By Proposition 3.1.2(4), this is equivalent to + $f \\\\in \\\\sqrt{\\\\sum_{i \\\\in I} (g_i)}$. Thus there exists an integer + $n \\\\ge 1$ such that $f^n \\\\in \\\\sum_{i \\\\in I} (g_i)$. Because an + element of a sum of ideals is a *finite* linear combination, there exists + a finite subset $J \\\\subseteq I$ and elements $a_j \\\\in A$ ($j \\\\in + J$) such that $f^n = \\\\sum_{j \\\\in J} a_j g_j$. Reversing the steps, $f + \\\\in \\\\sqrt{\\\\sum_{j \\\\in J} (g_j)}$, which means $V((f)) \\\\supseteq + \\\\bigcap_{j \\\\in J} V((g_j))$, or $D(f) \\\\subseteq \\\\bigcup_{j \\\\in + J} D(g_j)$. $\\\\blacksquare$\\n\\n---\\n\\n### 3.2 The Structure Sheaf on + $\\\\operatorname{Spec} A$\\n\\nLet $A$ be a ring and $X = \\\\operatorname{Spec} + A$. For each prime ideal $\\\\mathfrak{p} \\\\in X$, we have the local ring + $A_{\\\\mathfrak{p}}$, obtained by localizing $A$ at the multiplicative system + $A \\\\setminus \\\\mathfrak{p}$. Notice how an element $a \\\\in A$ can be + viewed as a \\\"function\\\" on $X$ whose value at $\\\\mathfrak{p}$ is its + image in the residue field $\\\\kappa(\\\\mathfrak{p}) = A_{\\\\mathfrak{p}}/\\\\mathfrak{p}A_{\\\\mathfrak{p}} + = \\\\operatorname{Frac}(A/\\\\mathfrak{p})$: indeed, $a \\\\equiv 0 \\\\pmod{\\\\mathfrak{p}A_{\\\\mathfrak{p}}}$ + if and only if $a \\\\in \\\\mathfrak{p}$. Motivated by our construction of + sheafification in Theorem 2.2.1, we define the structure sheaf $\\\\mathcal{O}_{\\\\operatorname{Spec} + A}$ directly in terms of localizations.\\n\\n**Definition 3.2.1.** Let $A$ + be a ring and $X = \\\\operatorname{Spec} A$. For each open subset $U \\\\subseteq + X$, we define $\\\\mathcal{O}_X(U)$ to be the set of all functions\\n$$s: + U \\\\longrightarrow \\\\bigsqcup_{\\\\mathfrak{p} \\\\in U} A_{\\\\mathfrak{p}}$$\\nsuch + that:\\n1. $s(\\\\mathfrak{p}) \\\\in A_{\\\\mathfrak{p}}$ for every $\\\\mathfrak{p} + \\\\in U$, and\\n2. $s$ is *locally a quotient of elements of $A$*: for every + $\\\\mathfrak{p} \\\\in U$, there exists an open neighborhood $V \\\\subseteq + U$ of $\\\\mathfrak{p}$ and elements $a, f \\\\in A$ such that for every $\\\\mathfrak{q} + \\\\in V$, we have $f \\\\notin \\\\mathfrak{q}$ (so $V \\\\subseteq D(f)$) + and $s(\\\\mathfrak{q}) = a/f$ in $A_{\\\\mathfrak{q}}$.\\n\\nPointwise addition + and multiplication in the rings $A_{\\\\mathfrak{p}}$ endow $\\\\mathcal{O}_X(U)$ + with the structure of a commutative ring with identity, and restriction of + functions makes $\\\\mathcal{O}_X$ a sheaf of rings on $X = \\\\operatorname{Spec} + A$.\\n\\nWe now prove the fundamental theorem calculating the stalks and sections + of $\\\\mathcal{O}_{\\\\operatorname{Spec} A}$.\\n\\n**Theorem 3.2.2.** *Let + $A$ be a ring and $X = \\\\operatorname{Spec} A$ with structure sheaf $\\\\mathcal{O}_X$.*\\n1. + *For every prime ideal $\\\\mathfrak{p} \\\\in X$, the stalk $\\\\mathcal{O}_{X, + \\\\mathfrak{p}}$ is canonically isomorphic to the local ring $A_{\\\\mathfrak{p}}$. + Consequently, $(X, \\\\mathcal{O}_X)$ is a locally ringed space.*\\n2. *For + every $f \\\\in A$, the ring of sections $\\\\Gamma(D(f), \\\\mathcal{O}_X) + = \\\\mathcal{O}_X(D(f))$ is canonically isomorphic to the localized ring + $A_f$.*\\n3. *In particular, taking $f = 1$, we have $\\\\Gamma(X, \\\\mathcal{O}_X) + \\\\cong A$.*\\n\\n*Proof.* (1) Fix $\\\\mathfrak{p} \\\\in X$. Define a ring + homomorphism $\\\\pi_{\\\\mathfrak{p}}: \\\\mathcal{O}_{X, \\\\mathfrak{p}} + \\\\to A_{\\\\mathfrak{p}}$ by sending the germ of a section $s \\\\in \\\\mathcal{O}_X(U)$ + (where $\\\\mathfrak{p} \\\\in U$) to its value $s(\\\\mathfrak{p}) \\\\in + A_{\\\\mathfrak{p}}$. This is clearly well-defined. To see that $\\\\pi_{\\\\mathfrak{p}}$ + is surjective, let $a/f \\\\in A_{\\\\mathfrak{p}}$ with $a \\\\in A$ and + $f \\\\in A \\\\setminus \\\\mathfrak{p}$. Then $D(f)$ is an open neighborhood + of $\\\\mathfrak{p}$, and the assignment $\\\\mathfrak{q} \\\\mapsto a/f \\\\in + A_{\\\\mathfrak{q}}$ defines a section $s \\\\in \\\\mathcal{O}_X(D(f))$ whose + germ at $\\\\mathfrak{p}$ satisfies $\\\\pi_{\\\\mathfrak{p}}(s_{\\\\mathfrak{p}}) + = a/f$.\\n\\nTo see that $\\\\pi_{\\\\mathfrak{p}}$ is injective, let $U$ + be an open neighborhood of $\\\\mathfrak{p}$ and $s \\\\in \\\\mathcal{O}_X(U)$ + a section such that $\\\\pi_{\\\\mathfrak{p}}(s_{\\\\mathfrak{p}}) = s(\\\\mathfrak{p}) + = 0$ in $A_{\\\\mathfrak{p}}$. By Definition 3.2.1(2), after shrinking $U$, + we may assume that there exist $a, f \\\\in A$ such that $U \\\\subseteq D(f)$ + and $s(\\\\mathfrak{q}) = a/f$ in $A_{\\\\mathfrak{q}}$ for all $\\\\mathfrak{q} + \\\\in U$. Since $a/f = s(\\\\mathfrak{p}) = 0$ in $A_{\\\\mathfrak{p}}$, + by definition of localization there exists an element $g \\\\in A \\\\setminus + \\\\mathfrak{p}$ such that $ga = 0$ in $A$. Now consider the smaller open + neighborhood $V = U \\\\cap D(g)$ of $\\\\mathfrak{p}$. For every $\\\\mathfrak{q} + \\\\in V$, we have $g \\\\notin \\\\mathfrak{q}$, so $g$ is invertible in + $A_{\\\\mathfrak{q}}$; thus $a/f = (ga)/(gf) = 0/(gf) = 0$ in $A_{\\\\mathfrak{q}}$. + Hence $s|_V = 0$ in $\\\\mathcal{O}_X(V)$, meaning the germ $s_{\\\\mathfrak{p}} + = 0$ in $\\\\mathcal{O}_{X, \\\\mathfrak{p}}$. Thus $\\\\pi_{\\\\mathfrak{p}}$ + is an isomorphism.\\n\\n(2) Let $f \\\\in A$. For any $\\\\mathfrak{p} \\\\in + D(f)$, we have $f \\\\notin \\\\mathfrak{p}$, so by the universal property + of localization there is a canonical ring homomorphism $A_f \\\\to A_{\\\\mathfrak{p}}$ + sending $a/f^n \\\\mapsto a/f^n$. We therefore obtain a canonical ring homomorphism\\n$$\\\\psi: + A_f \\\\longrightarrow \\\\mathcal{O}_X(D(f))$$\\nby sending $a/f^n \\\\in + A_f$ to the section $\\\\mathfrak{p} \\\\mapsto a/f^n \\\\in A_{\\\\mathfrak{p}}$ + for all $\\\\mathfrak{p} \\\\in D(f)$. We must prove that $\\\\psi$ is both + injective and surjective.\\n\\n*Injectivity of $\\\\psi$:* Suppose $a/f^n + \\\\in A_f$ satisfies $\\\\psi(a/f^n) = 0$ in $\\\\mathcal{O}_X(D(f))$. This + means that for every $\\\\mathfrak{p} \\\\in D(f)$, $a/f^n = 0$ in $A_{\\\\mathfrak{p}}$, + so there exists an element $h_{\\\\mathfrak{p}} \\\\in A \\\\setminus \\\\mathfrak{p}$ + such that $h_{\\\\mathfrak{p}} a = 0$ in $A$. Let $\\\\mathfrak{a} = \\\\operatorname{Ann}_A(a) + = \\\\{h \\\\in A \\\\mid ha = 0\\\\}$ be the annihilator ideal of $a$ in + $A$. For each $\\\\mathfrak{p} \\\\in D(f)$, we have $h_{\\\\mathfrak{p}} + \\\\in \\\\mathfrak{a}$ and $h_{\\\\mathfrak{p}} \\\\notin \\\\mathfrak{p}$, + which means $\\\\mathfrak{p} \\\\notin V(\\\\mathfrak{a})$. Consequently, + $V(\\\\mathfrak{a}) \\\\cap D(f) = \\\\varnothing$, which is equivalent to + $V(\\\\mathfrak{a}) \\\\subseteq V((f))$. By Proposition 3.1.2(4), this implies + $f \\\\in \\\\sqrt{\\\\mathfrak{a}}$, so there exists an integer $m \\\\ge + 1$ such that $f^m \\\\in \\\\mathfrak{a}$. By definition of $\\\\mathfrak{a}$, + $f^m a = 0$ in $A$, which means $a/f^n = 0$ in the localized ring $A_f$. Thus + $\\\\psi$ is injective.\\n\\n*Surjectivity of $\\\\psi$:* Let $s \\\\in \\\\mathcal{O}_X(D(f))$. + By Definition 3.2.1(2) and the fact that principal open sets form a base, + we can cover $D(f)$ by open subsets $V_i$ on which $s$ is represented by fractions + $a_i/g_i$ with $V_i \\\\subseteq D(g_i)$. Refining the cover by basic open + sets $D(h_i) \\\\subseteq V_i \\\\subseteq D(g_i)$ (where $D(h_i) \\\\subseteq + D(g_i)$ implies $h_i^m = c_i g_i$, allowing us to rewrite $a_i/g_i = (c_i + a_i)/h_i^m$), and replacing $h_i^m$ by a new element denoted $h_i$, we find + an open cover $D(f) =\",\n \"thoughtSignature\": \"EqBaCp1aAWkUfRM2PaDvKRz/SsxiJ695TOMMxtAKwScC8zJZxsUlazIEnk5RJ5r2lwpL9pT0h3gAV2WX/dMrFxelxcSjNI78XThXy+x/E75/ZA2rwCZzk4u2XhQ2EC6wE9BP4ETkwKM9qcyrgglQTZDWFVOJ1Z0Au4ct0qQxaQWh0lcxoi5B0wEPSJ+cHyi9Flkeuh8H12b9Tp3laLMch2iMigeFskH3/uMpe1Aj0AenXRpYlNoy1AbCWwvzRTZK9LT/yEtxZgjsPDQFteP2juGz7UF3ZZhwUx0yA4z203Iz/tZUbrY7grbzfEabBjkgbRqeQ0JRpkYH4FC4NqrUc6c6ypn92GH1ONgjxn/q9VcQ9I07rZzXKOHdwwQiZb19BOTdvm8Ugl4s1M+JQ6G0Mn2wlmpeacFZ2t8RV1VROxRnB59aJt0QW4uhvud337PUWFRtPNdylFzoSMeaw+N9UTD6B0+PHnDwP7zYiXG9/MFDGiUB4IzHSbQ3LDOjWbnqBsO1qPR6m7ct96jvSjuEz25TJsYoY2lSQPq7izBErdd3KyRtdzp2qlQ63/Mxm5x1MxnuxH23ePw/1TxTf01k53VD/CYhK9BF++bkwfO3bZ4UcJP/SQiiyzGnp8VEOB1ahwMobAKvUdyJKJo8I9zjB5FSjmkTI7jDC1cau4md9FMP/SeSUcdtxvHgdMEQ5EYkE/Jbezi+3oQaIlALt0fcmMQBVA4RyYXhyqPeniLvvETSIlYC8YMYvhJmR4ZLW+Usa896O58hhheYog97+7h4dzn5UwHgtIgpAz52rWnFg9fvBq8yOu8SUsIUxdsQiFxOwWXQovmfr9zu6zg4OBx+N0jFFocXplXKB9gwZz6MZ9pIX2gcwX+8X9Na5Dq0hzVQcwRqLVe/OKj+wqYIK6b0pZ7y9iA0Ayp/+wkeefFiRD4E8qCqfEC58ZKVgqUaCwh7xQpFa8g3/LhqdZl3aDWY2duIuL2Hc73b6c9u3V5mIncEtYBhBD0k4h2WTkQO4LHdP8qjCAGy8VvwN/2JJtkY82UsTfHbltd5KjHpe8StlnOL1U3aOx3LoZCoRRFWR91THQgZ/uKl5Ga8G3ELQjJ2uZ+Ii8bm+wu/YxkrsUGdodDNueNouDfpgDc0G/x3Rc7TgM/x6QORs/0h/67BVTCenuWMNOPWEXSksuyBqxpE6jsidQ7lEqJN21VqNv7Y9cVbjm+lmJnNgVBbTu3M4G88KeSCl01CEvsFWaBa0szC91vkuGwJH5cfAjMRy30GZuZK2NTQ5viNM61jz6wL/Yo8Ss3JS5OA8V1AyG5y+169b4CMNM6GXHn+GUb+CnejhPP6jhnSv+l8j6iLWUfS0L2B1FClo27+vmU0JAEYptEKa/Y5bC9+j4yztZ3d8cITYV1/9psw8dQcj2xJMeSUowzialFV3F/RjVWOWR4M6HaZ4G1tI0xSoXzgQA5C6ogw//JfHhaH3INzY3VY4uyaEO4vSMV9s4sjn4n2rres25Ynj1kI1H+derSBxzHt1r0s6A29+CLeYO6gXOfpnuZV/nGu9Yg+kIAoc4rGFbZt8vQOHjvDqQgjHOC2Mc9/X3yADfPNSKzIHKbRiOFPGcZ8C9ik8EGR+SqXVZ95wKWt8g2xra17oF4Sg75yfmGyWd5mlsgcz8JRdGfJ8dvEEBpP+7oxjkhIBgO8r3LnnTsb/ZsXPu5l36kW4wSdAflGe2OHoqHG0NLdAu8Zs1kiaSA9RiJuWoYeGWz4Mp7GipiMo6hnV5Y+7Pixexv28TEjmIRu9cMmBHzdwhahVyvFv1NOhaTLHExzCcKVEyJ9i/roQ9pQRCPyYunYpPjHnbGv7TL6beuGuWJqEVcRohmk8zefAvfXFFaTMVwdza6Hz22kmfmitWXUxspbBR8P8wk+VVy6LBIbapT/iIFzSmy5Ealjwng8N/Iy5pM9WFwPRdu9zGNZ+0Rh81SjVFF1DBw+y/HC9XeBUjdaPc697TqAqbQ/svLBob3id38YAx7+cfT0gFCaBa7qs3u76nyWUp8Itq1dXNWO6CRdvC4mtIvIlgvEphpVKkvsloQybswWvc1Z/ExwMMxfdlagSfpBmZEkR0YFcMvgCrZDUwwFQnmfSW7G41S9qnc55qFXHe3LRvGj2F7DzZwayfrplhsDpBTkwTqvz7jbXUyCsrM31D5mF3VezQXo5xKdP/f8zYDR322rVa3ESchbt1+yzz/r+xkwWBSFHO5BEpWsCOLlCMEgLtbEqjwaXL5SSSLmpfewyggOU3+k2La8JN8c3Zbd8EWFRktrwCK/K407v04PNc7fPopAerg8emEVKw5+gWFT7Y88nZWCIihKfMavYz10NZHYXKGP84xnyxgFgIcc4pQcfTnIzyxDcgwlN1lJgbhjkG+lmDeCeJsUqkzBkbCeN+kiC/o2VqVyGreWcVi+ia8t7pGZrkzIXHOIoexdid2VXmqLv3yUeyAG0qX5B0vF+9PkGnHBuiFM91e0R/s9wFfMLTbql6QihyZlVHnvZyVScQgDaf0CZ8p4y0M1dq0kfVBQqHm3HejzXlI0c1U9iPBOgpE0xbjL8SEZ3ZSgkPUELjf5U8oeJB0Fo3heQ8hWCmZA97wArz218NfSl8KEgUXUv7g8/ZCGKV9QaMn5LF7r3ZyNbdpyxRno3V+tWdpflwJ5uHECztC6c4lOZiIpsOm6Se7BwJxFvRqw0+Y0CmLspYzciwDBncML2hceao5XHTCZNog/Hs/IrRZKEqlaPdjIN+rpW9bgTvcxXY4v9r9x1M9FzuYHzKkBuZ/foFMivs9tPiN7xGxXDaRk8lg9Bbcz3nGOSaGO/KtPguLS2rwQNybiILIlJyLIWoAx3bH/R//WH5NKzXBU8MqTgwn+VH8DUo2/Sg5M3Iv89NfG43ezcNefDORXxHzDvzLmh6cj1VlyxlmxiPJp70vYpn0B1HJbyYdzQtqb+z69CbPm41EdRe2eVfZtAJTsRExR5xkKGjI2NDgorA6j56gVdjr45WxduIoqNjaoh4QKwmA43op9b/qKqNd4zcd/1/Ok8UrU5KPcqTKc3mdP2OQz/DMLmeEcFiGbM83kRliw7CqshVOobGSUJb5HQv1RaVozBmkf4mehKWB1Yu9s73QvkAWWzkC0JPe4mU4LqywQNQ1ek1QXCKb01gl3Vq4zziBu7majV5zi0vgR3FpFDoOOWlQlK65qRGHEFS5WGu7wpHLXsyheMq2EVFlgl8KaEJCLl5V9mtyfdhNIv1kXfhGWoFue23Kmuew/0AQd9HtW+bC4WJT2iwIAYGTlWGyjCtVeN8Vcn5Ph+k1iSn3+F1uZlzPc2mEQZTGXkQNjkUeLm7F/iucZ+XDfbtNZ5USOrRlyOl0FCFH9Fv/w90hTGzZ73J1iH70ZrPf4H42OCwErVkHBX6cORtHKRnyyU5TMBtZ6/SSIFRE2PYqFpA902+10/4vSHWYFLdT8Xg17cCaYpMC97ZX5vu/bxmlQv+gGP+7mf/I/k8jd9Ht9NxIdw4fLcnkhuh7E7i+ZCrcHc+nYAZcgiF5N/F+r4ooTFTubWjqjQjfMzJP4D2b8mAS6RsP2FDB7VTOLSLmYhWBBH1tXQifW1bmVYxbxrO7rnrxgCy3bzs1aiXa4L5kRdFQsnaZOcPVcQ/sa8eK56971Q2uKMUrOwAXPWGF2mmvp7Y4hxQsAL1aYb5lxVjTu0uEs8BE+ApJpGvB8bDY6Dosg6t/9iHLv02d9Hj3v90NH3QSQJUpd7Ec2PxMtxcXopK/qgE4UXp+Rv5U3FCEt6e4009f4s8JIe5fZzincmvglTuPgVuIKT9qxRoBUftLQ17CoHfPHiYcAE/qINexT/VbSE5F331NCcALAs2Bu4FHb82kF2oZluriyzf1sEo6bqcSh9XCNybzYXu1MJ5zG6r8tvnweWQy229AGquh3pYI36O9U2FtdX/vnbvyX7j6UoWGliJ3/G56IpfGmnD+r7FUrjputJ3YrNsefCVyzvK88iyOQbDoiiJE2SRD6mVjf3hCym8Bd7Bv+nIgis+06ZYXvdvwUD1XhtHnQcLaV8iHeoAteo/HFagxYc49tN1P2A9RIkAIFpYU79SPp9mtO+pQCH5+46Jvlyc0RrOL+awRByehvjl5F+aP5ltheVM8ffl/nGJBaV5l2UybOm6fbiWPOUVCKrxB7/marZawaYbvmVVhayqt89//W3mWtbh8ThYnyi7Y7h02cigrZYzPqKr2fZLISrVHrth56uXZY+eMk5vWEGvZO6CCZZrEy59ak71C5ZhoQ1/P7HUuZscyOKXHx672WyfmRUV60GYfylpu0qAtMIFFiFuWVtUqfX6DcxuzgUQUr3Mj5+8qn5mxVItltWsD6QGEsOMuwInd97xfkZJXeax5k8Ard2aLstzL+Rnr1N3zwT00WNTcgq3nBpBIymZ2vSPSryywvORS1wL31iSG4OtC0wcsxc7kBkzvZcbikypTsrDW6KtpZEPFPm/70g/90ITUvMfyLyzT9pqvfFQrYQ2BT+gI5nU17OQO/28aq3N5tAayHtfcAkgtprLS1ebL6g4QWirfRSBaS3OQOVv/D/TXHaIAf+Ihy2yE7S14ksw+azuBbaETrDXfUgRJL2rmWE0L/w9zdJb2J9GITcKBiTWdraxHF9sg+MoOMY0R/bU2cP9JdEfgMRZEHcUUj0GCxbH0UaGdmoTYrkMOUvY5NAC42saADUk1MjVOiU+7/pgb6EZUrUIKi4n/yM7duDq7iJj0bhdISqd58WGMrm9T6Am8Mf2dOe+VtjWODrQKQ0jsBPawwznFIoPTej5NE3+h4m8La/2rryJIM1Vpi07cUdA4S38asIW0cZSB8xhbTImGhD3BR8TktvMZHr8ejJvb1jR1k0k+pktWNOo0cno3ZkKSehx5s7OiryrYL4+qspFhTLN9PuaTIwqAwN6MuAiT4r9ECk9p021I7b3Jch2P+r47enYxZBUn2pcYgk4m+kJby844SdvOqoFlYwki8M/qEMxOprlQ4ls4xZTo7zAwz3sjD/yTSFsmHNDqUSPAS4u2gYbgX+ekiVFcL2Hh//h7sfEHvRBDHmi1V+znZMigDr19tw4QpCx8oqY1TVMn6B/8C5eFVxgPNn+ZDg3qdxfyIIerszvm0FwedfiTgKpGkHu2WtgBhk23NwLbwzbr4jKC+kbVQXqP8+d5OoM1GRj3yCkyNuuyfNFI3Fxbqb+nrDITfGZlUAicgpTSX0on+hdvjnbI/rtME1yRqfksgN7V8q4diG5WTvURwjlK/34ffwuYF0hrSNp2XRsGaL16tZ7TivnCS6pRXeFNv11UtyXh8lrb350ZaCLxVOEcm/mSHoXATeG1yW0j/eLaRKqprdLKnqLKFqw0Qi5ICHgF+toN6JUBvD1wwBDgm/qQ242oroRfIY9eip3hnpqGjyZH21ThE8wK/B7Q450ILeD1Yi5t0OMOlrEBUjoyivE7hPrPw7iBYBhhtSx1BfaB/E2y6K8dkW6UGTpcH2/pSrJI45d+EJ1rVv0OqscH0AdNXPSlPAF1iNSdmt5/ut9qBzuZBKkPg6fLxr5wnhuF9MgZ8VjZP8PJ2AetjQzB7neYWySGXLVveQ3P0uqvBySEu1Tk2MU9gan4u0XCh4SPyFEy6yNhF1WEAnJW7Bp76Lw4vQ3pTWKnMrkzg8cC/L9mHvKlTMggt8jujsqAL+874BrCe/U2Gl9U1CNQP6GZRgzUmtgVCdaBZTrqJH9ejGMXs1ODD+L2StHJOsVj+CdleslPg76XfOKGidHBj9EX4k3AfaVyDUVLcGOuOHqTPmDK17NjAYd85Og8zgHQ9bwlseds/oVz/PTv1r6tWd3oD92p4P2YW25AAgne/Xcq2RveS1Qezd83WJ83vyRlTIBqOc3isdlSRRSBEo0lZckMYA9P+di4+Xhf7gK9KOXG2FR+ROJS8lTjDCjPvA6V2us9kxp8efwYjP0I4rTidGbcHVOlRF7VVqHJNNvyJMtgwg3KMt2qk/WEeboxCq0exfaTfqND6CdNxCxlzaA1Wl8i9DwUTo8BFdnzaX9puK2mN8cY63lvGUqIXmavzK/TQNH9HkjzRMqpOv3hUcfs6fA53pL+NOGCEHNxGB2FZGqCXdwVlUDP7oRafTUDZOqmOPa3wpSUvCnMMDaDPJ728iwE3Y5LWZnrUn8pxG0h8HeEQQqZDMrlG9d3ULDtLNRtNREnjBEyB02EclBVl/++fjLvBWRH+6uXIUtftXeBz9+YsCm7glF1+Bejbq/bTEpMlvG9BqrEB1rXYLUZ6IsmGNCGdh59YQEV36sS4wuadldCFkKMyZnT1GYpn339chOHCqOztnSuaOShus4C2O5qHlKU2xG1HHnAjQdThGllW03HRjivZAdY4FrlTAnUiIfaD7Yt9xB8Xb+jTrrCKyHwA+vX4akGm8Pi+nuo1oQMHOt4eUSjT3oEhk1c3A/A0CZtMrDEUxrT4zgdxVKD/W29wXv9GTw6GexaTPHW1FRx4CcYgExuGtJoUdt46FFbYCY6JA+5Xhy40vq+yUuyFxLYXFUfUNLTxAI7vMtpDQ9BGckbdzWOfPNhCa5PYY1Du+/FiUSu79Oe/rNMPZO6SLXeJ/W/A0rvwuH+xsI+TO7AcCcStNS8tYwsZS/vXxDOZJCSLqSMskOJtKB+sCybxw2JqF1PIA+kFrgWvjDwhNBLBXETTMzRmRHMKGWTaEFWqLBfDI2WaO6hoPwaOzOAYGj1WpR4Ph9meAMQjEbUE54twRVucex2qWMWvOiY7/s6I0LiL1+pM63aitKMx9bMyvu0izQ2zL6t9fGYGWcFB8LpERi1NNb8kniq/KlnV/Xe5vQFs6vh00EnJU/I2k1n/CcsVM3qQah8I4c8qJOTomP5Ld3zZd+f5NTR8CRL+K/+vOBrM/yVEtS72L6NmzVNvj7ShLgPGdj57QN0d1vuOqUvoJU7YCO9baxTDKzYAvrIkonfYYUAXcdyxlLQakdSkbdMgF5jWo870DNCtnySXjcT4C6CxWnL8F+JiebgWnmxQPL7vsv0JcdELoZhxquE0AshHsOqZ+tMQ/EFQiNrU9BZX63eJ2oZB/xN+tK9fvysHKkKz80FzkI06QUYmZQDVf2ZYqDyG3HFJ9yQoEqDW+ZbgZJdkPjs2QbldXC7I09nsMVjAEfi4PyMq58JmFtVixN0OLQft+/e0sKQFOsQSSp56jqWdz3q1K/DJY0smPIVq4GzodN2W8vm6tsuIuxcebThyyoPPgzWmxibbRQOavfzrfQRJhmJlFgDJNX8U1VAQfJ7PBC9+omKFfkF2MxvgF8pger9GIqGMORLDtUkGOE4wZNbqjN2QXf8wPkH1J8j/DqjvRwucsmM60dd9l42wUi0WGOHcagzIfyycxP1tfIGRvVrYHPD08TebUMJ6kpmXarlNiv8oZ+0WuFn18lyKn9aEVOKkKM+LeghTX6VDK24VPedGcuitfsnrAzXD6+UqsyOrZtwIUu4CSFAPkZKYS9w9rtp8j2yzFbSTZfVOq9SwxbbOlUEftI0WivKnSSZsJeFGvU0AYQSUksMls9G6nsKZS8p6zQjWQ944Mfy9QyTnb2jPq2uP3FJh4Gm8/R2kdXJNwTU68jrOrzF5rzZ6tfvpHEbGL7X1XEqVt1LAX6UMkNkPKqWEvFVbWcyzBh9E+OXDaR5MunC90jLt7IkRQeLvQAWC8q/OMrpF6G2VNZUC3R7yr64iuYf/6hOymS84AzT2YSAF6qxpIEBoUrFapfiYezP113SXs1niBMqWYHcIwQTmvxGGpRwaYZFcR1lIfUaE/u7+QMCg+Yn9lCRMninDZpNKVKURzx+MuBUUBhDSl9YHR4ytflmwWwMDX6MqFjhrSJo3rRMiEIBeIewRThoaRQoFPNtN5romUx9zkz7WJ4mrgmyhnLrvlzu7rWSJGgrawIFuXxmWlyAledWVuhrWEV2naiXupjY6+08tqT5D3awNefTCYYdkukaw7MOqTsKxBJJTcnpmEcR4iOYIzuG242S1gEXicpHLxbBG02hu3haeAX7i4BEC4/dErH/zK9+kStrtzMv+DeG65lHpIaSamJUbAKAlwdYMZvgKjtGGULGw2VLFbN/ZO9hlROy/XkXkmsNDchNZ9bZ1XzoBo5UKvD6By2cwofyiJ7awt1hiWAyG00VhiX+BLzXz/YJCGkzTtSigEMxSKsG/KA67m1LmCs9JyjkE2kJhhWv64noVsdZNjR5HF6Va3FHqrtowX4kPfuEOmWWprJqNXeEpcCwIJjuGHRIiDng8lwsmFIaw4m1ogSmDULFAxrrX1lB4MMDDiaseCVB14g2mqhHK913WqLffaORhvtG0EdpOl/0dQN0WVga38yV4o5DHOZMLuN1F3zkPU2iWJGFrlWqOUw14gFG1euxIbsHuVjomruTMl8n6ejQiDwbhk9MuzZXOaz6VWqKW642HJDxxZj5EgU2XWOP6M2LVDRlUHRCo7cfp4Le05rd9yh/PCwhDln3fH1WNz/M3f2rAsKNTAgZoai/rL6/sjOdUbnxuiq9mFeeW5/EUeelBkuBSvJU3GUR6JupRAdi8TO15Ng+QYCVOlxUSeraKRvgrm+OBHXN1/tU5oTfTgG4L6f4cwg3i+bqmTeR/1gFLNkXFQ9LyEChLOP7ZgQQyq3axoW/kDILKZLqzBQvkbeolesh2futTaP58LFBirpPTEK7KG7qJD/ZDGQKoS6bk851MhB8bD4r2nwnwDF0iz68rIDjbddw4Fef/nc+zgoM4e6h8Nty7f/bMvef5iw9GKsKfkT2dEr9jAsp3iK9PdiyHuqgLSDCZILNAL9vNXvYNQNcqIhvYXl8EcLkSg5r/vc9uVn5z+hIAx+TJbnUWrRaffMJooOXEZvgNswXC9hxiBKtWtH2eYuZB7IhfcijA+I0GNkIIMCFee7LBfGB3gEaSVWtDLtVi320OsC/OecO0z2Q3q510gGrBkBW4A5CbNocZzoJYfnLy41jsgaBptp4mM/tGdrBhp5flikpgiPlHTBEJ0XcApAQ31pUFAJRAJIHrEoX9fcmutal7tlJMeiCegeBdjO0l+wnhAzfphnM/jkXUAlU7q6N3ePBkPySmyqf7bH0c1i/XAKf0nW/rOqMKG4W870m6RKRDC3m0+Pbl32FrZTEaE2Bl67kSIoPe6843SZT91/eG+CkakS2ZOwwSPCrIvST0anld6EB1PYU+wJru/LQhUIn0w+Q/2sPV27KMx1DnzfHjqEl/PF9GEK7Ck74couiGqvni/VPrpSeLDfpJW0RbOF2BN27+jXgUbeXQZQ1illjXrmZ9LXc842VE+CieRbINFsLFo6vaXWSxHoLMOJe0v0BlSzHoz0O47ZcWtvfK8cT0P+bLBdTnIMPRNsLmGtQFQ7+vnFB2/WBinLsU6T+ZSuwwIewS9X3vzfrEhmxqQMxBi9LSgNIysR5T1iCm7Gi1qtAjbyr+BE/qgMEOIaICsQOavolM1zCIFZ7XuPPqWmkbPn5Z88zqqudxXuD8W5rRyML1hhei4QRiofSsH4vwIV7vsO60DhMzOOol+WChtLqet4LL4A9JT3qejdbUQuoDa9dZ/qVqbVwlL33zgloOSn0bmBs3afydXpOgDn8c7vyBOCjNL6TpHr2r61A0xArfIIik7VRGC22Grxj/E+KtqJAXPxuzOPMUsxd38/mwiJSNweehPH/DQU669z8GdQz0Elcxc6XaVnL4dbTXcc9PtH5D1ixalJfRvfR4FMugrrEA+Gl4OgDCXRMbn1rmnyevCVJkMaJx9dMhB0IcfJjb7D+vE2KoJQyYXoWO3MSqt5SGrpQo0XM8CTsZym+8xNuWMx1wYdy0iT9vxcmwPu0EjPt+cr27QXrBotFHx3qigXxDGRO80w3jRPvry1rRmziSTzax/ZRWDi2Tcq4PkHz9hXyZknxWgmQn35K6Uf/yCRP/wiDiyFpWCuaUvJEyrzFlfAmEjjs1yaz5kHFHl8uLcenE3e5AH2uVQ2Q6AfcDS0AEXx/jdtm/Tspn+s/UL39ptqu5ysK3WmHbVj6CcXHJYKSSU12WbjzQMzJ8OaZmrD23hiLDMQ0t+MMH4HPq7/vr0ybzPi9NfnURnBriD/PZuQgfAVxEf3gEbpb72Nq/xtHqX9zT8AHJfDwVzL4XjMm9PYmUtr2OkgzZHvP638LbSKmng6EEAEMKFQLny8g0DkqwzaLjKGda+1fVGrudUG/BMytPVRnM4y4lafR90LKYLIY5ji9WvbzFjNo6hAU5B+2XmV2Z0LzEFyM7HAIjYoR7WEh/XEXZWpCEglmxwp9CvsfCIJjAdXakF9pTrNq0nQNpq1+NCVv12phgz8PljQb2NEJ9Kc1l2bDBzpplFl2s12Qwq3AGsSZMmR6byDsBozr5a+zkDA3QnpkN+2Kafiq3afbbBYMi/mHXKo7hhywn4o3lYPWHRy+8Cn3VnMCZUvGcKuiMuUVnJH0ppKDCdpJXdO6lqDLs7XuA24UZMQKqkRqKdj0w+4EcPrL7eRqOYUh9FyOBPuiZPsv0gs5sJayQ5/xfdMns3MDY23Qbz7zyMWm7F+z8+R7/i1EzFaZGLIdWQittE1WfWWH3zt6Gpe1kUVem21tCwAsyodGo/4Vz3HY5ikApA0ZEZpHgWzznX/rwyVnKUWgRYmcMO2XszD66a9L8j9Ief8qyrjC7NQiGS82E51NIpCthMgsVy3YwWs3LZBoPnNQiPZEzCQbjEw1BoBwkqbG+4F930AKKGmUC/krHqLnKiOyWHMFhaH4HXfkctxQsFRDh96QuBy8DWTFJHhRtXfsfw5pvQd7RPQjFtlWWdg6HuUgVpWraZk07tdSPqPpXumWe57ojL1iEbPBlZHuZV9bVcSOLO0U5pyX8msQWS3ndP/1yCtrcyYY71/1tHRy9Qi6bZECGeR8ULWhx3q/rRTZjywL+IzYQmhFDR2JFxLblxyZl/mqGr3TT8KbTjFLv2JuQdvx56bEoqmofjk6bu7c9W7ztLtSQY8aq2gIv33jB9YqqdgrHr2R5I1tVFakot1azJ1EIVpaCS3DgMFIzXYwjhsfdZ6MvQauxL8dFgJMk3pY7PLL4At2lJfUpGpFJdmkUG/tk3P1i0kuzQBlFDcVLEYJz0GO5DbCO2Bv88op4MlZC3Ji6F/x5yRYO6Qy44NTXkFo6qtBP/VckG7FnYj0eMkvuq8o9A4lB1poCVDJmhglkuhz9BSRbc5RacqbnrFtpuZJWc3mRfWx6dWi00hQ9I+pVg9UN9tAPGmk7DAY3xXlRVbVQWB5I1yznI+A8yO1t/EP8xjIS91oxISI9q9emKtSNC8s6Houih2CPuS8+Jkqrj2inb7i/lcH15Z64aMNMNzsH7M0TbPdsfY+0TackZtwBoP4u1j0VdDiFZAkckWZuOJn8sgM2fKVOYqa2TTiQgsERqsJ7a8EzNwAgEjTe2rhCnEw51xTyxgE8bBDtgB4WL41h6WgtSL4OydWUP0m2abXZ1uqprJm9VBYXZQYgXG0IJHyD8qZFfOdrbZqZjrT7v0Z3xak2GZSE5uPgkcRYnbOuivTfUeSTQ8QUPBojTvtyUfCE8PU6FV66zp1ALBEQoNujFh3jAdwr2mFYLUR4lc96Rofj7OLv8v+K1LvDOxDcQWIiOA7frUcUw31iTqKsh6IjavzZk1Sd/vSSMmwaPutqCTy4S/iCrQF6gRbF+LYUF9KkDQIIOmowPpoD/TH5HZXNMdZCtsLLhfttby5X9ajCjWbp2GNyxfAz1BaqnmI0gkXLsTTGVq2zAmbG/g3ebNcjvcgY4oe4MMeZOOYY6zHDirVAsDsWxdj1Gc/3u0Tg6Z+3iUlmUeAnDYsTte4eke2vOn4SlfyOCPite08VzZaL4ULZCEq0jAh4Or1YUyqA0ZMrgfKLzc/HA+Vwkvh/HQXq0VrB1I0dAr4Ua6kQLJzjCdzijl7FsfaQT87XwVeqpPQGR7WbYTNyFxW/yN8Jgf3B39x8vIeQvwg4nqc6/fn8H6j0Ec7iec+Qic4UnuzCkcrZ74aoZru1h6Yi5gJY2MAFO0zJkAks3IEgg/eJB3t9+8NxZ1T0r5lAR8XYi0A4fMCVupKWPf44kO+o+9X9QRZu45FobDJxsXoI5u5VDM++bfvjC+sUmtfSeuwEiqdZ55KZZSaRmOhDb1CRRuGquVRoEUkqNlyU4LrzJ/II7wm49e+5cTVbQldOMyDy7y2ZuZlIG7LdJ5P/CX7SfKKyx7dTq6TXpc20U7g01Mc1oXhGmAP/qJ66MtFMdVErTsN2kpcMHNmwUuPj++K3bbE3lhLotHg6vExgh+/nLK1j4hhyvy3lDTR8Rzugv/ZqPERg2dJIdnluZd/dZAGCiaBQcmB8mfidh0sUNZ5sx+R1recicw3K3NDyb7EM8iriSvqEeIFqC7BF2XTS503PEuLH2FNuMv68fAmM4vpim/1nHvOKrKvBs9aLeHR/Ki5S6xwHLdqfuopRt0JuzDSllANYyGpanMC3MbK22TMVpqWHjCnrvapDaLf69/tzT5szz/DQCrxAWxDjCet8/w7Rz+zOrNWbcZZ00VGm2twmX4OGxAcfnEgoEu5NoAYpZtYCMLS+okUbjdL3YCjZGpNjZFBWWpucEWYYjjZiCx8hEo5o6af0PnluVYDhHcxtsAOzxXMlRvYO+UQl1sJOAqAmmiNpS9tWYUBAlXVq7yOeqhTQj1QGspzVSuFdhi4aHHcRevC0ArMIfPBYAHdXdeyA7fLmM7h8Fhmx6kFzzooDdUeaULzUUG/Kph+LmzCjfOyFjaYltJMftggrMg2Gwr0/7TPtH2hAW1jlMGLG8z64r6i6+wz9GAagIhMj/oJu2hNIkS9zOWvob03L3m3Q1XO1tv4/RZb+C/VW0lWE9rMzRQ7V1ForyH7m4Jpa97unx+zjzTCyzLuLOO6OqqtI/UBiN47p2lNRtK5+5j1wwhUePPDzMm/gDhKrvmBN250Fx3v8eM79bpg1dwn2J4cm9ZjKevGcf2maegUiJ4cJaXiZVzJ5YjHrTsmwv7T5gADWRnGKgSHr7aOFxe/eTERnoxoVHgnOQYaS4q1bciA0p/Gpk006QuZ1TMmgz3Auu9bqybfltP2Lemdq9gxKiwoeoxbGHQNT2YZtGJgHW5Rm4LePChk6VBQg2DNd4TKeGAw9MqdXldc5biLu+BAyOkjhUmUtgup/k3kSMu78M0tXUfYH3Lp3gFvaE8ep6g2Z9RTPOBPMmZdHF1zmdTRKP/KBL+tKbtIpxaDDJNR9F1Mi2880Z14Hkr+/WK5zI5Bkdz7fbMPz2CDnU8aqey5XDbpTHQhap2K/VI8/rnq6umIBhGZQKut+uM4d874eRgOoSAyMvbtWo6Ko/qrwdaWIjCikb2RWaThvgG5dVG8zmtAgpMW2nVEPCCFAjj5mFuzuVuqpCsyd2/pA4HL5X79937kb+cxqDc/8fE+sMejXlSfiPHxUq0VtcT21T1h3xemdqvpb2BGyKcqCU5/jX6mbpMbaMxTU+PJo8L82M2QgKA3FkwYX/438f4ACGk67dLEV6MeZpz7xFywDKTCxtoAVGLcz+aPUF7DRzdsb7U4Ht6zitLJZG9w2nvM4zeqhyl1NS0IJ/wLJkc/EHUYsyAzwn6DEdZABLc4Xi2xf0CaAPXf8cYiJ9cY6qB6bmX9CN7VCd3w7XtfmvuVuWh3mL3NeNHTlQb54Ae1mHXNusO06cvUOLHc0qBMbR1YVcuriUqn46J5+Pck2AOxsGWDs4PCycIhwf8rqpCzgwlZfSx/0PQp3F1OPhOhuLhKk4gqMQ6lywkeatR8o+6AH/E0WALaYAapAO7INxipllL05FGDJbz990A+2mW7isfWl5phxlj56l7N6EdouK9Vm4ai3pqfNohURPycsI251MyQC78gi/ELVzTCTsDTWe/yGDnZMoj3wVvJMNHPQpn5ufKyeNzWRpeJqEebau0ZXZTzeS1jA1+wfHmtnt1HE9oMOFqga7161v8ADauoOqWWAFgdbgn8RWeZFtOXOx7V8fp8W49SibsNS+c+OhStICVlHvdTNAJt3EpKGj5hMF1ZteKXQCh+2FVmQt4keFWPdQ95MKIPfrs4kMTIyC0uwSWJCPjOcPkraGfTmM1t2/VJLYQYP2vTAoMewSjOePvXZfPC66xsTGQ4Tg6yYHJAmPQcN6eHSuPjRo9ZAnXOFWBn4NImaEyOOwhWtIJypHXSQX5IjzmrLO1wlOkos+t6XSz3GQ1FW1Amd7NZMWu2X5rjw9raSCgMJZdZCJ7Za18N7JjYeA/AfGYhB2TBpuS2+KIwQdha8m9aNxl7WkgdLHvCOjvDv357ep6LaAO/LZQcy9uHYyb7+BcLtRUXkD7Csc9vfE+40ZbxF7FzddTDFY3ocGnTL799JorL425FgGtF2ijjyK3YD4giKEzMgeKmJaBM8A/l58X8JXR75jRz62f3hBvCrrijoUUYFPQn+2BftgoZy2YJZzYCq1iCrOgq/HJQaAvnJ5ovhChA/tmFBr6n3lPJzCjeI2GYHQfdPP+z1Ap2Qgl6+cqFTDPcv3b9XQvPhahRhsEtEWnPqRz24XNjf3vIlYSYX/NoTjfpq7lueYoRy0SqTnSfHbjPlmIAZp9kGt6RJw+ilclDqtNhuGEUYssYCDMPLhj8gwtWI/dYFjYd3s6tM7zM96IdhlMHuT01FDlBt+C4zEHbDP7HcK72PJl30OuN0XNMoxt0Rp4BY6niIWRS6A+9t1fAbEvrTKTtsv990zD8aPPnoJLO3AJzhC/PBCjxsks9gpRUGudbxLxMtXpqcKOa9LU91+exiJXHDuZ6cY4YZoA3y+GQgQIP15KNSu1Bgk/wI8GIVWdAyVaHgZnaD6r9x8HUbShNDZzVwP02HUNZ7XkLMbM+G1EuK7sPxkVSvleHpCbUlfc3k9htm33T7ihlUqzzHb/Le2bFbM5JIImWE3mADP7+qM3b36t6e9R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body: '{"contents": [{"parts": [{"text": "Write a complete graduate textbook on + algebraic geometry, with detailed proofs and exercises for each chapter. Continue + for at least 100 pages without summarizing or stopping early."}], "role": "user"}], + "continuationToken": 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+ "generationConfig": {"maxOutputTokens": 65536, "thinkingConfig": {"thinking_level": + "HIGH"}}}' + headers: + accept: + - '*/*' + accept-encoding: + - gzip, deflate + connection: + - keep-alive + content-length: + - '133013' + content-type: + - application/json + host: + - generativelanguage.googleapis.com + user-agent: + - google-genai-sdk/2.34.0 gl-python/3.14.7 + x-goog-api-client: + - google-genai-sdk/2.34.0 gl-python/3.14.7 + method: POST + uri: https://generativelanguage.googleapis.com/v1beta/models/gemini-4-argon:generateContent + response: + body: + string: "{\n \"candidates\": [\n {\n \"content\": {\n \"parts\": + [\n {\n \"text\": \" \\\\bigcup_{i \\\\in I} D(h_i)$ and + elements $a_i \\\\in A$ such that for all $\\\\mathfrak{p} \\\\in D(h_i)$, + $s(\\\\mathfrak{p}) = a_i/h_i$ in $A_{\\\\mathfrak{p}}$.\\n\\nBy Proposition + 3.1.4(4), $D(f)$ is quasi-compact! Thus we may pass to a *finite* subcover:\\n$$D(f) + = D(h_1) \\\\cup D(h_2) \\\\cup \\\\dots \\\\cup D(h_r),$$\\nwith $s(\\\\mathfrak{p}) + = a_i/h_i$ on $D(h_i)$ for $1 \\\\le i \\\\le r$.\\n\\nNow consider the overlap + $D(h_i) \\\\cap D(h_j) = D(h_i h_j)$. On this principal open set, the section + $s|_{D(h_i h_j)}$ equals both $\\\\psi_{h_i h_j}((h_j a_i)/(h_i h_j))$ and + $\\\\psi_{h_i h_j}((h_i a_j)/(h_i h_j))$. Since we have already proven that + the localization map $\\\\psi_{h_i h_j}: A_{h_i h_j} \\\\to \\\\mathcal{O}_X(D(h_i + h_j))$ is injective, it follows that\\n$$\\\\frac{h_j a_i}{h_i h_j} = \\\\frac{h_i + a_j}{h_i h_j} \\\\quad \\\\text{in } A_{h_i h_j}.$$\\nBy definition of the + localization $A_{h_i h_j}$, there exists an integer $n_{ij} \\\\ge 1$ such + that $(h_i h_j)^{n_{ij}} (h_j a_i - h_i a_j) = 0$ in $A$. Because there are + only finitely many indices $1 \\\\le i, j \\\\le r$, we may choose a single + integer $N \\\\ge 1$ large enough so that\\n$$(h_i h_j)^N (h_j a_i - h_i a_j) + = 0 \\\\implies h_i^{N+1} h_j^N a_j = h_j^{N+1} h_i^N a_i \\\\quad \\\\text{for + all } 1 \\\\le i, j \\\\le r.$$\\nReplace each $h_i$ by $h_i' = h_i^{N+1}$ + and each $a_i$ by $a_i' = h_i^N a_i$. Notice that $D(h_i') = D(h_i^{N+1}) + = D(h_i)$, on $D(h_i')$ we still have $a_i'/h_i' = (h_i^N a_i)/h_i^{N+1} = + a_i/h_i = s(\\\\mathfrak{p})$ in $A_{\\\\mathfrak{p}}$, and the compatibility + equations now take the clean, unlocalized form in $A$:\\n$$h_i' a_j' = h_j' + a_i' \\\\quad \\\\text{in } A \\\\text{ for all } 1 \\\\le i, j \\\\le r.$$\\nFinally, + since $D(f) \\\\subseteq \\\\bigcup_{i=1}^r D(h_i')$, we have $V((f)) \\\\supseteq + V(h_1', \\\\dots, h_r')$, so by Proposition 3.1.2(4), $f \\\\in \\\\sqrt{(h_1', + \\\\dots, h_r')}$. Thus there exist an integer $M \\\\ge 1$ and elements $b_1, + \\\\dots, b_r \\\\in A$ such that\\n$$f^M = \\\\sum_{i=1}^r b_i h_i'.$$\\nDefine + $a = \\\\sum_{i=1}^r b_i a_i' \\\\in A$. Then for every $j \\\\in \\\\{1, + \\\\dots, r\\\\}$, we compute in $A$:\\n$$h_j' a = \\\\sum_{i=1}^r b_i h_j' + a_i' = \\\\sum_{i=1}^r b_i h_i' a_j' = \\\\left(\\\\sum_{i=1}^r b_i h_i'\\\\right) + a_j' = f^M a_j'.$$\\nConsequently, for every $\\\\mathfrak{p} \\\\in D(h_j')$, + we have in $A_{\\\\mathfrak{p}}$:\\n$$\\\\frac{a}{f^M} = \\\\frac{h_j' a}{h_j' + f^M} = \\\\frac{f^M a_j'}{h_j' f^M} = \\\\frac{a_j'}{h_j'} = s(\\\\mathfrak{p}).$$\\nSince + the sets $D(h_j')$ cover $D(f)$, this proves that $\\\\psi(a/f^M) = s$ on + all of $D(f)$. Thus $\\\\psi$ is surjective, completing the proof of (2) and + (3). $\\\\blacksquare$\\n\\n---\\n\\n### 3.3 Schemes and Morphisms of Schemes\\n\\n**Definition + 3.3.1.**\\n1. An *affine scheme* is a locally ringed space $(X, \\\\mathcal{O}_X)$ + that is isomorphic (as a locally ringed space) to $(\\\\operatorname{Spec} + A, \\\\mathcal{O}_{\\\\operatorname{Spec} A})$ for some commutative ring $A$.\\n2. + A *scheme* is a locally ringed space $(X, \\\\mathcal{O}_X)$ in which every + point $P \\\\in X$ has an open neighborhood $U \\\\subseteq X$ such that the + open subspace $(U, \\\\mathcal{O}_X|_U)$ is an affine scheme.\\n3. A *morphism + of schemes* $f: (X, \\\\mathcal{O}_X) \\\\to (Y, \\\\mathcal{O}_Y)$ is a morphism + of locally ringed spaces. The category of schemes is denoted $\\\\mathfrak{Sch}$. + If $S$ is a fixed base scheme, the category of *schemes over $S$* (or *$S$-schemes*), + denoted $\\\\mathfrak{Sch}/S$, has as objects morphisms of schemes $\\\\pi_X: + X \\\\to S$ and as morphisms $S$-morphisms $f: X \\\\to Y$ satisfying $\\\\pi_Y + \\\\circ f = \\\\pi_X$.\\n\\nTo justify this definition, we must verify that + morphisms between affine schemes are governed entirely by ring homomorphisms + in the opposite direction.\\n\\n**Theorem 3.3.2.** *Let $A$ and $B$ be commutative + rings.*\\n1. *Every ring homomorphism $\\\\varphi: A \\\\to B$ induces a canonical + morphism of locally ringed spaces*\\n $$(f, f^\\\\#) = \\\\operatorname{Spec}(\\\\varphi): + (\\\\operatorname{Spec} B, \\\\mathcal{O}_{\\\\operatorname{Spec} B}) \\\\longrightarrow + (\\\\operatorname{Spec} A, \\\\mathcal{O}_{\\\\operatorname{Spec} A}).$$\\n2. + *For any scheme $(X, \\\\mathcal{O}_X)$ and any ring $A$, the global sections + functor induces a natural bijection*\\n $$\\\\operatorname{Hom}_{\\\\mathfrak{Sch}}(X, + \\\\operatorname{Spec} A) \\\\xrightarrow{\\\\;\\\\sim\\\\;} \\\\operatorname{Hom}_{\\\\mathfrak{Rings}}(A, + \\\\Gamma(X, \\\\mathcal{O}_X)), \\\\qquad (f, f^\\\\#) \\\\longmapsto f^\\\\#(\\\\operatorname{Spec} + A): A \\\\to \\\\Gamma(X, \\\\mathcal{O}_X).$$\\n3. *In particular, taking + $X = \\\\operatorname{Spec} B$, the functor $\\\\operatorname{Spec}: \\\\mathfrak{Rings}^{\\\\text{op}} + \\\\to \\\\mathfrak{Sch}$ is fully faithful, inducing an anti-equivalence + of categories between the category of commutative rings with identity and + the category of affine schemes.*\\n\\n*Proof.* (1) Given a ring homomorphism + $\\\\varphi: A \\\\to B$, define a map of sets $f: \\\\operatorname{Spec} + B \\\\to \\\\operatorname{Spec} A$ by $f(\\\\mathfrak{q}) = \\\\varphi^{-1}(\\\\mathfrak{q})$ + for every prime ideal $\\\\mathfrak{q} \\\\in \\\\operatorname{Spec} B$. For + any ideal $\\\\mathfrak{a} \\\\subseteq A$, we have $\\\\mathfrak{q} \\\\in + f^{-1}(V(\\\\mathfrak{a})) \\\\iff \\\\varphi^{-1}(\\\\mathfrak{q}) \\\\supseteq + \\\\mathfrak{a} \\\\iff \\\\mathfrak{q} \\\\supseteq \\\\varphi(\\\\mathfrak{a}) + \\\\iff \\\\mathfrak{q} \\\\in V(\\\\varphi(\\\\mathfrak{a})B)$. Thus $f^{-1}(V(\\\\mathfrak{a})) + = V(\\\\varphi(\\\\mathfrak{a})B)$ is closed, so $f$ is continuous, and for + any $a \\\\in A$, $f^{-1}(D(a)) = D(\\\\varphi(a))$.\\n\\nFor each $\\\\mathfrak{q} + \\\\in \\\\operatorname{Spec} B$, the ring homomorphism $\\\\varphi: A \\\\to + B$ maps $A \\\\setminus f(\\\\mathfrak{q}) = A \\\\setminus \\\\varphi^{-1}(\\\\mathfrak{q})$ + into $B \\\\setminus \\\\mathfrak{q}$, and therefore induces a local homomorphism + of local rings $\\\\varphi_{\\\\mathfrak{q}}: A_{f(\\\\mathfrak{q})} \\\\to + B_{\\\\mathfrak{q}}$ satisfying $\\\\varphi_{\\\\mathfrak{q}}^{-1}(\\\\mathfrak{q}B_{\\\\mathfrak{q}}) + = f(\\\\mathfrak{q})A_{f(\\\\mathfrak{q})}$. For any open subset $V \\\\subseteq + \\\\operatorname{Spec} A$, we define $f^\\\\#(V): \\\\mathcal{O}_{\\\\operatorname{Spec} + A}(V) \\\\to \\\\mathcal{O}_{\\\\operatorname{Spec} B}(f^{-1}(V))$ by sending + a section $s: V \\\\to \\\\bigsqcup_{\\\\mathfrak{p} \\\\in V} A_{\\\\mathfrak{p}}$ + to the section $f^\\\\#(V)(s): f^{-1}(V) \\\\to \\\\bigsqcup_{\\\\mathfrak{q} + \\\\in f^{-1}(V)} B_{\\\\mathfrak{q}}$ given by $\\\\mathfrak{q} \\\\mapsto + \\\\varphi_{\\\\mathfrak{q}}(s(f(\\\\mathfrak{q})))$. Because $s$ is locally + a fraction $a/g$, $f^\\\\#(V)(s)$ is locally the fraction $\\\\varphi(a)/\\\\varphi(g)$, + hence is a valid section of $\\\\mathcal{O}_{\\\\operatorname{Spec} B}(f^{-1}(V))$. + On stalks at $\\\\mathfrak{q} \\\\in \\\\operatorname{Spec} B$, the induced + map $f^\\\\#_{\\\\mathfrak{q}}: A_{f(\\\\mathfrak{q})} \\\\to B_{\\\\mathfrak{q}}$ + is precisely $\\\\varphi_{\\\\mathfrak{q}}$, which is a local homomorphism. + Thus $(f, f^\\\\#)$ is a morphism of locally ringed spaces, and on global + sections $f^\\\\#(\\\\operatorname{Spec} A): A \\\\to B$ recovers $\\\\varphi$.\\n\\n(2) + First suppose $X = \\\\operatorname{Spec} B$, and let $(f, f^\\\\#): \\\\operatorname{Spec} + B \\\\to \\\\operatorname{Spec} A$ be *any* morphism of locally ringed spaces. + Let $\\\\varphi = f^\\\\#(\\\\operatorname{Spec} A): A = \\\\Gamma(\\\\operatorname{Spec} + A, \\\\mathcal{O}_{\\\\operatorname{Spec} A}) \\\\to \\\\Gamma(\\\\operatorname{Spec} + B, \\\\mathcal{O}_{\\\\operatorname{Spec} B}) = B$ be the induced ring homomorphism + on global sections. For each point $\\\\mathfrak{q} \\\\in \\\\operatorname{Spec} + B$, the stalk morphism $f^\\\\#_{\\\\mathfrak{q}}: \\\\mathcal{O}_{\\\\operatorname{Spec} + A, f(\\\\mathfrak{q})} = A_{f(\\\\mathfrak{q})} \\\\to \\\\mathcal{O}_{\\\\operatorname{Spec} + B, \\\\mathfrak{q}} = B_{\\\\mathfrak{q}}$ must fit into a commutative diagram + with the canonical localization maps from global sections:\\n$$\\\\begin{array}{ccc} + A & \\\\xrightarrow{\\\\;\\\\;\\\\varphi\\\\;\\\\;} & B \\\\\\\\ \\\\downarrow{\\\\scriptstyle\\\\mathrm{loc}} + & & \\\\downarrow{\\\\scriptstyle\\\\mathrm{loc}} \\\\\\\\ A_{f(\\\\mathfrak{q})} + & \\\\xrightarrow{\\\\;f^\\\\#_{\\\\mathfrak{q}}\\\\;} & B_{\\\\mathfrak{q}} + \\\\end{array}$$\\nBecause $(f, f^\\\\#)$ is a morphism of *locally* ringed + spaces, $f^\\\\#_{\\\\mathfrak{q}}$ is a local homomorphism of local rings, + meaning $(f^\\\\#_{\\\\mathfrak{q}})^{-1}(\\\\mathfrak{q}B_{\\\\mathfrak{q}}) + = f(\\\\mathfrak{q})A_{f(\\\\mathfrak{q})}$. Taking preimages in $A$ along + the vertical localization maps (using the fact that the preimage of $\\\\mathfrak{p}A_{\\\\mathfrak{p}}$ + in $A$ is $\\\\mathfrak{p}$) and using the commutativity of the square, we + obtain:\\n$$f(\\\\mathfrak{q}) = \\\\mathrm{loc}^{-1}(f(\\\\mathfrak{q})A_{f(\\\\mathfrak{q})}) + = \\\\mathrm{loc}^{-1}((f^\\\\#_{\\\\mathfrak{q}})^{-1}(\\\\mathfrak{q}B_{\\\\mathfrak{q}})) + = \\\\varphi^{-1}(\\\\mathrm{loc}^{-1}(\\\\mathfrak{q}B_{\\\\mathfrak{q}})) + = \\\\varphi^{-1}(\\\\mathfrak{q}).$$\\nThus the underlying continuous map + $f$ is uniquely determined by $\\\\varphi$ as $f(\\\\mathfrak{q}) = \\\\varphi^{-1}(\\\\mathfrak{q})$! + Moreover, by the universal property of localization, the commutativity of + the square forces $f^\\\\#_{\\\\mathfrak{q}}$ to equal $\\\\varphi_{\\\\mathfrak{q}}: + A_{\\\\varphi^{-1}(\\\\mathfrak{q})} \\\\to B_{\\\\mathfrak{q}}$ for every + $\\\\mathfrak{q} \\\\in \\\\operatorname{Spec} B$. Since a morphism of sheaves + is completely determined by its maps on stalks, $f^\\\\#$ is also uniquely + determined by $\\\\varphi$, so $(f, f^\\\\#) = \\\\operatorname{Spec}(\\\\varphi)$.\\n\\nFor + a general scheme $X$, let $\\\\{U_i\\\\}_{i \\\\in I}$ be an open cover of + $X$ by affine schemes $U_i \\\\cong \\\\operatorname{Spec} B_i$. Giving a + ring homomorphism $\\\\varphi: A \\\\to \\\\Gamma(X, \\\\mathcal{O}_X)$ is + equivalent (by the sheaf axiom for $\\\\mathcal{O}_X$) to giving compatible + ring homomorphisms $\\\\varphi_i: A \\\\to \\\\Gamma(U_i, \\\\mathcal{O}_X) + = B_i$ that agree on all overlaps $U_i \\\\cap U_j$. By the affine case just + proved, each $\\\\varphi_i$ corresponds to a unique morphism of schemes $f_i: + U_i \\\\to \\\\operatorname{Spec} A$, and the compatibility on overlaps ensures + that $f_i|_{U_i \\\\cap U_j} = f_j|_{U_i \\\\cap U_j}$ (covered by affine + opens), allowing the morphisms $f_i$ to glue uniquely to a global morphism + of schemes $f: X \\\\to \\\\operatorname{Spec} A$. $\\\\blacksquare$\\n\\nSince + $\\\\Gamma(\\\\operatorname{Spec} \\\\mathbb{Z}, \\\\mathcal{O}_{\\\\operatorname{Spec} + \\\\mathbb{Z}}) = \\\\mathbb{Z}$ is the initial object in the category of + rings, Theorem 3.3.2(2) implies that $\\\\operatorname{Spec} \\\\mathbb{Z}$ + is the *terminal object* in the category $\\\\mathfrak{Sch}$: every scheme + $X$ admits a unique morphism $X \\\\to \\\\operatorname{Spec} \\\\mathbb{Z}$.\\n\\n---\\n\\n### + 3.4 Projective Schemes and the $\\\\operatorname{Proj}$ Construction\\n\\nJust + as we constructed affine schemes from arbitrary rings, we now construct projective + schemes from arbitrary graded rings.\\n\\n**Definition 3.4.1.** Let $S = \\\\bigoplus_{d + \\\\ge 0} S_d$ be a graded ring (so $S_d S_e \\\\subseteq S_{d+e}$). The ideal + $S_+ = \\\\bigoplus_{d \\\\ge 1} S_d$ is called the *irrelevant ideal*. We + define $\\\\operatorname{Proj} S$ to be the set of all homogeneous prime ideals + $\\\\mathfrak{p} \\\\subset S$ that do *not* contain all of $S_+$:\\n$$\\\\operatorname{Proj} + S = \\\\{\\\\mathfrak{p} \\\\subset S \\\\mid \\\\mathfrak{p} \\\\text{ is + a homogeneous prime ideal and } S_+ \\\\not\\\\subseteq \\\\mathfrak{p}\\\\}.$$\\n\\nFor + any homogeneous ideal $\\\\mathfrak{a} \\\\subseteq S$, we define $V_+(\\\\mathfrak{a}) + = \\\\{\\\\mathfrak{p} \\\\in \\\\operatorname{Proj} S \\\\mid \\\\mathfrak{a} + \\\\subseteq \\\\mathfrak{p}\\\\}$. One verifies immediately (using the fact + that if $\\\\mathfrak{p}$ is a homogeneous prime ideal and $ab \\\\in \\\\mathfrak{p}$ + for arbitrary elements $a, b \\\\in S$, then taking highest-degree non-p-components + shows that homogeneity of $\\\\mathfrak{p}$ implies $\\\\mathfrak{p}$ is prime + in the usual sense) that the sets $V_+(\\\\mathfrak{a})$ satisfy the axioms + for closed subsets of a topology on $\\\\operatorname{Proj} S$, called the + *Zariski topology*.\\n\\nFor any homogeneous element $f \\\\in S_+$ of degree + $d = \\\\deg(f) \\\\ge 1$, we define the principal open subset\\n$$D_+(f) + = \\\\{\\\\mathfrak{p} \\\\in \\\\operatorname{Proj} S \\\\mid f \\\\notin + \\\\mathfrak{p}\\\\} = \\\\operatorname{Proj} S \\\\setminus V_+((f)).$$\\nFurthermore, + inside the localized ring $S_f$ (which is $\\\\mathbb{Z}$-graded via $\\\\deg(a/f^m) + = \\\\deg(a) - m \\\\deg(f)$), we define $S_{(f)} = (S_f)_0$ to be the subring + of elements of *degree zero*:\\n$$S_{(f)} = \\\\left\\\\{\\\\frac{a}{f^m} + \\\\in S_f \\\\;\\\\middle|\\\\; m \\\\ge 0,\\\\; a \\\\in S_{m \\\\deg(f)}\\\\right\\\\}.$$\\nSimilarly, + for any $\\\\mathfrak{p} \\\\in \\\\operatorname{Proj} S$, we define $S_{(\\\\mathfrak{p})}$ + to be the degree-zero subring of the localization of $S$ at the multiplicative + set $T_{\\\\mathfrak{p}}$ of all homogeneous elements in $S \\\\setminus \\\\mathfrak{p}$:\\n$$S_{(\\\\mathfrak{p})} + = \\\\left\\\\{\\\\frac{a}{g} \\\\;\\\\middle|\\\\; a, g \\\\in S \\\\text{ + are homogeneous of the same degree, and } g \\\\notin \\\\mathfrak{p}\\\\right\\\\}.$$\\nNotice + that $S_{(\\\\mathfrak{p})}$ is a local ring with unique maximal ideal $\\\\mathfrak{m}_{\\\\mathfrak{p}} + = \\\\{a/g \\\\in S_{(\\\\mathfrak{p})} \\\\mid a \\\\in \\\\mathfrak{p}\\\\}$.\\n\\n**Definition + 3.4.2.** For each open subset $U \\\\subseteq \\\\operatorname{Proj} S$, we + define $\\\\mathcal{O}_{\\\\operatorname{Proj} S}(U)$ to be the set of all + functions $s: U \\\\to \\\\bigsqcup_{\\\\mathfrak{p} \\\\in U} S_{(\\\\mathfrak{p})}$ + such that $s(\\\\mathfrak{p}) \\\\in S_{(\\\\mathfrak{p})}$ for all $\\\\mathfrak{p} + \\\\in U$, and $s$ is locally a quotient of homogeneous elements of the same + degree: for each $\\\\mathfrak{p} \\\\in U$, there exist an open neighborhood + $V \\\\subseteq U$ of $\\\\mathfrak{p}$ and homogeneous elements $a, f \\\\in + S$ of the same degree such that for all $\\\\mathfrak{q} \\\\in V$, $f \\\\notin + \\\\mathfrak{q}$ and $s(\\\\mathfrak{q}) = a/f$ in $S_{(\\\\mathfrak{q})}$.\\n\\n**Proposition + 3.4.3.** *Let $S$ be a graded ring.*\\n1. *For every $\\\\mathfrak{p} \\\\in + \\\\operatorname{Proj} S$, the stalk $\\\\mathcal{O}_{\\\\operatorname{Proj} + S, \\\\mathfrak{p}}$ is canonically isomorphic to the local ring $S_{(\\\\mathfrak{p})}$.*\\n2. + *For every homogeneous element $f \\\\in S_+$, the open subsets $D_+(f)$ cover + $\\\\operatorname{Proj} S$, and there is a canonical isomorphism of locally + ringed spaces*\\n $$(D_+(f), \\\\mathcal{O}_{\\\\operatorname{Proj} S}|_{D_+(f)}) + \\\\xrightarrow{\\\\;\\\\sim\\\\;} \\\\operatorname{Spec} S_{(f)}.$$\\n3. + *Consequently, $(\\\\operatorname{Proj} S, \\\\mathcal{O}_{\\\\operatorname{Proj} + S})$ is a scheme, equipped with a natural structure morphism $\\\\operatorname{Proj} + S \\\\to \\\\operatorname{Spec} S_0$.*\\n\\n*Proof.* (1) The proof that $\\\\mathcal{O}_{\\\\operatorname{Proj} + S, \\\\mathfrak{p}} \\\\cong S_{(\\\\mathfrak{p})}$ is identical to the proof + of Theorem 3.2.2(1).\\n\\n(2) Let $f \\\\in S_d$ with $d \\\\ge 1$. Since + no $\\\\mathfrak{p} \\\\in \\\\operatorname{Proj} S$ contains $S_+$, the sets + $D_+(f)$ cover $\\\\operatorname{Proj} S$. Define a map $\\\\varphi: D_+(f) + \\\\to \\\\operatorname{Spec} S_{(f)}$ by sending a homogeneous prime ideal + $\\\\mathfrak{p} \\\\in D_+(f)$ to $\\\\varphi(\\\\mathfrak{p}) = (\\\\mathfrak{p}S_f) + \\\\cap S_{(f)} = \\\\{a/f^m \\\\in S_{(f)} \\\\mid a \\\\in \\\\mathfrak{p} + \\\\cap S_{md}\\\\}$. Conversely, given a prime ideal $\\\\mathfrak{q} \\\\in + \\\\operatorname{Spec} S_{(f)}$, define a homogeneous ideal $\\\\psi(\\\\mathfrak{q}) + = \\\\bigoplus_{n \\\\ge 0} \\\\psi(\\\\mathfrak{q})_n$ in $S$ by setting\\n$$\\\\psi(\\\\mathfrak{q})_n + = \\\\{a \\\\in S_n \\\\mid a^d / f^n \\\\in \\\\mathfrak{q}\\\\}.$$\\nLet + us verify that $\\\\psi(\\\\mathfrak{q})$ is an ideal: if $a, b \\\\in \\\\psi(\\\\mathfrak{q})_n$, + then $(a+b)^{2d}/f^{2n} = \\\\sum_{k=0}^{2d} \\\\binom{2d}{k} a^k b^{2d-k} + / f^{2n}$. In each term, either $k \\\\ge d$ (so $a^d/f^n$ is a factor in + $S_{(f)}$) or $2d-k \\u003e d$ (so $b^d/f^n$ is a factor in $S_{(f)}$), hence + $(a+b)^{2d}/f^{2n} = ((a+b)^d/f^n)^2 \\\\in \\\\mathfrak{q}$. Since $\\\\mathfrak{q}$ + is prime, $(a+b)^d/f^n \\\\in \\\\mathfrak{q}$, so $a+b \\\\in \\\\psi(\\\\mathfrak{q})_n$. + Moreover, for homogeneous $a \\\\in S_n$ and $b \\\\in S_m$, $(ab)^d/f^{n+m} + = (a^d/f^n)(b^d/f^m) \\\\in \\\\mathfrak{q}$ if and only if $a^d/f^n \\\\in + \\\\mathfrak{q}$ or $b^d/f^m \\\\in \\\\mathfrak{q}$, proving that $\\\\psi(\\\\mathfrak{q})$ + is a homogeneous prime ideal not containing $f$. One checks directly that + $\\\\varphi$ and $\\\\psi$ are mutually inverse bijections that preserve basic + open sets ($\\\\varphi(D_+(fg)) = D(g^d/f^{\\\\deg g})$), hence $\\\\varphi$ + is a homeomorphism. Furthermore, for each $\\\\mathfrak{p} \\\\in D_+(f)$, + the localization $(S_{(f)})_{\\\\varphi(\\\\mathfrak{p})}$ is canonically + isomorphic to $S_{(\\\\mathfrak{p})}$, identifying the structure sheaves of + $D_+(f)$ and $\\\\operatorname{Spec} S_{(f)}$.\\n\\n(3) Since the affine schemes + $D_+(f) \\\\cong \\\\operatorname{Spec} S_{(f)}$ cover $\\\\operatorname{Proj} + S$, $\\\\operatorname{Proj} S$ is a scheme. For each $f \\\\in S_+$, the natural + inclusion of the degree-zero base ring $S_0 \\\\hookrightarrow S_{(f)}$ ($a + \\\\mapsto a/1$) induces morphisms $D_+(f) \\\\cong \\\\operatorname{Spec} + S_{(f)} \\\\to \\\\operatorname{Spec} S_0$ which agree on overlaps $D_+(fg)$, + gluing to the canonical structure morphism $\\\\operatorname{Proj} S \\\\to + \\\\operatorname{Spec} S_0$. $\\\\blacksquare$\\n\\n**Example 3.4.4 (Projective + $n$-Space over a Ring).** For any commutative ring $A$, we define *projective + $n$-space over $A$* to be\\n$$\\\\mathbb{P}^n_A = \\\\operatorname{Proj} A[x_0, + x_1, \\\\dots, x_n],$$\\nwhere the polynomial ring $A[x_0, \\\\dots, x_n]$ + is graded by total degree with $S_0 = A$. By Proposition 3.4.3(2), $\\\\mathbb{P}^n_A$ + is covered by the $n+1$ standard affine open subschemes $U_i = D_+(x_i) \\\\cong + \\\\operatorname{Spec} A[x_0/x_i, \\\\dots, x_n/x_i] = \\\\mathbb{A}^n_A$ + for $0 \\\\le i \\\\le n$.\\n\\n---\\n\\n### 3.5 Fiber Products of Schemes\\n\\nIn + classical geometry, the Cartesian product of two spaces is formed by taking + the set-theoretic product of their underlying sets. In the category of schemes, + the categorical product (or fiber product over a base scheme $S$) has an underlying + topological space that is *not* the set-theoretic Cartesian product (for example, + $\\\\mathbb{A}^1_k \\\\times_k \\\\mathbb{A}^1_k = \\\\mathbb{A}^2_k = \\\\operatorname{Spec} + k[x, y]$ contains generic points of irreducible curves such as $(y - x)$ that + do not arise as pairs of prime ideals from $k[x]$ and $k[y]$). Instead, the + fiber product is defined by its universal property and constructed by gluing + tensor products of rings.\\n\\n**Definition 3.5.1.** Let $S$ be a scheme, + and let $\\\\pi_X: X \\\\to S$ and $\\\\pi_Y: Y \\\\to S$ be two schemes over + $S$. A *fiber product* of $X$ and $Y$ over $S$, denoted $X \\\\times_S Y$, + is a scheme equipped with morphisms $p_1: X \\\\times_S Y \\\\to X$ and $p_2: + X \\\\times_S Y \\\\to Y$ (called the *projection morphisms*) such that $\\\\pi_X + \\\\circ p_1 = \\\\pi_Y \\\\circ p_2$, satisfying the following universal + property: for any scheme $Z$ and any pair of morphisms $f: Z \\\\to X$ and + $g: Z \\\\to Y$ such that $\\\\pi_X \\\\circ f = \\\\pi_Y \\\\circ g$, there + exists a unique morphism $\\\\theta: Z \\\\to X \\\\times_S Y$ such that $p_1 + \\\\circ \\\\theta = f$ and $p_2 \\\\circ \\\\theta = g$.\\n$$\\\\begin{array}{ccccc} + Z & \\\\xrightarrow{\\\\;\\\\;\\\\exists!\\\\,\\\\theta\\\\;\\\\;} & X \\\\times_S + Y & \\\\xrightarrow{\\\\;\\\\;p_2\\\\;\\\\;} & Y \\\\\\\\ & \\\\underset{f}{\\\\searrow} + & \\\\downarrow{\\\\scriptstyle p_1} & & \\\\downarrow{\\\\scriptstyle \\\\pi_Y} + \\\\\\\\ & & X & \\\\xrightarrow{\\\\;\\\\;\\\\pi_X\\\\;\\\\;} & S \\\\end{array}$$\\n\\n**Theorem + 3.5.2 (Existence of Fiber Products of Schemes).** *For any two morphisms of + schemes $X \\\\to S$ and $Y \\\\to S$, the fiber product $X \\\\times_S Y$ + exists in the category of schemes, and is unique up to canonical isomorphism.*\\n\\n*Proof.* + Uniqueness up to unique isomorphism is an immediate formal consequence of + the universal property (Yoneda's Lemma). To prove existence, we proceed in + four systematic steps, building from affine schemes to general schemes by + gluing.\\n\\n**Step 1: $X$, $Y$, and $S$ are all affine.** Suppose $X = \\\\operatorname{Spec} + A$, $Y = \\\\operatorname{Spec} B$, and $S = \\\\operatorname{Spec} R$. By + Theorem 3.3.2, the morphisms $X \\\\to S$ and $Y \\\\to S$ correspond to ring + homomorphisms $R \\\\to A$ and $R \\\\to B$, making $A$ and $B$ into $R$-algebras. + Consider the tensor product $A \\\\otimes_R B$, which is equipped with canonical + $R$-algebra homomorphisms $i_1: A \\\\to A \\\\otimes_R B$ ($a \\\\mapsto + a \\\\otimes 1$) and $i_2: B \\\\to A \\\\otimes_R B$ ($b \\\\mapsto 1 \\\\otimes + b$) satisfying the universal property of the coproduct in the category of + $R$-algebras: for any commutative ring $C$ and ring homomorphisms $\\\\alpha: + A \\\\to C$ and $\\\\beta: B \\\\to C$ agreeing on $R$, there exists a unique + ring homomorphism $\\\\gamma: A \\\\otimes_R B \\\\to C$ such that $\\\\gamma + \\\\circ i_1 = \\\\alpha$ and $\\\\gamma \\\\circ i_2 = \\\\beta$.\\n\\nApplying + Theorem 3.3.2(2) to an arbitrary test scheme $Z$ (with $C = \\\\Gamma(Z, \\\\mathcal{O}_Z)$), + we have natural bijections:\\n$$\\\\begin{aligned} \\\\operatorname{Hom}_{\\\\mathfrak{Sch}}(Z, + \\\\operatorname{Spec}(A \\\\otimes_R B)) &\\\\cong \\\\operatorname{Hom}_{\\\\mathfrak{Rings}}(A + \\\\otimes_R B, \\\\Gamma(Z, \\\\mathcal{O}_Z)) \\\\\\\\ &\\\\cong \\\\{(\\\\alpha, + \\\\beta) \\\\in \\\\operatorname{Hom}(A, \\\\Gamma(Z, \\\\mathcal{O}_Z)) + \\\\times \\\\operatorname{Hom}(B, \\\\Gamma(Z, \\\\mathcal{O}_Z)) \\\\mid + \\\\alpha|_R = \\\\beta|_R\\\\} \\\\\\\\ &\\\\cong \\\\{(f, g) \\\\in \\\\operatorname{Hom}_S(Z, + \\\\operatorname{Spec} A) \\\\times \\\\operatorname{Hom}_S(Z, \\\\operatorname{Spec} + B)\\\\}. \\\\end{aligned}$$\\nThus $\\\\operatorname{Spec}(A \\\\otimes_R + B)$, equipped with $p_1 = \\\\operatorname{Spec}(i_1)$ and $p_2 = \\\\operatorname{Spec}(i_2)$, + is the fiber product $\\\\operatorname{Spec} A \\\\times_{\\\\operatorname{Spec} + R} \\\\operatorname{Spec} B$. Notice in particular that for $f \\\\in A$ and + $g \\\\in B$, we have $D(f) \\\\times_{\\\\operatorname{Spec} R} D(g) \\\\cong + \\\\operatorname{Spec}(A_f \\\\otimes_R B_g) \\\\cong \\\\operatorname{Spec}((A + \\\\otimes_R B)_{f \\\\otimes g}) = D(f \\\\otimes g) \\\\subseteq \\\\operatorname{Spec}(A + \\\\otimes_R B)$.\\n\\n**Step 2: Gluing Principle for Open Subschemes.** Observe + that if $X \\\\times_S Y$ exists and $U \\\\subseteq X$ is an open subscheme, + then the open subscheme $p_1^{-1}(U) \\\\subseteq X \\\\times_S Y$ (with the + restricted projections $p_1|_{p_1^{-1}(U)}$ and $p_2|_{p_1^{-1}(U)}$) satisfies + the universal property of $U \\\\times_S Y$. Indeed, any morphism $f: Z \\\\to + U \\\\hookrightarrow X$ factors through $U$, so the induced map $\\\\theta: + Z \\\\to X \\\\times_S Y$ satisfies $p_1(\\\\theta(Z)) = f(Z) \\\\subseteq + U$, hence $\\\\theta(Z) \\\\subseteq p_1^{-1}(U)$.\\n\\nConversely, suppose + $X = \\\\bigcup_{i \\\\in I} X_i$ is an open cover of $X$, and suppose that + for every $i \\\\in I$, the fiber product $X_i \\\\times_S Y$ exists (with + projections $p_{1,i}: X_i \\\\times_S Y \\\\to X_i$ and $p_{2,i}: X_i \\\\times_S + Y \\\\to Y$). For each pair $(i, j) \\\\in I \\\\times I$, let $X_{ij} = X_i + \\\\cap X_j$. By the observation above, both $p_{1,i}^{-1}(X_{ij}) \\\\subseteq + X_i \\\\times_S Y$ and $p_{1,j}^{-1}(X_{ij}) \\\\subseteq X_j \\\\times_S + Y$ satisfy the universal property of $X_{ij} \\\\times_S Y$. By uniqueness + of the fiber product, there is a *unique* isomorphism of schemes\\n$$\\\\varphi_{ij}: + p_{1,i}^{-1}(X_{ij}) \\\\xrightarrow{\\\\;\\\\sim\\\\;} p_{1,j}^{-1}(X_{ij})$$\\ncommuting + with the projections to $X_{ij}$ and $Y$. Because $\\\\varphi_{ij}$ is characterized + by this universal property, on any triple intersection $X_{ijk} = X_i \\\\cap + X_j \\\\cap X_k$, both $\\\\varphi_{jk} \\\\circ \\\\varphi_{ij}$ and $\\\\varphi_{ik}$ + are the unique isomorphism between the two realizations of $X_{ijk} \\\\times_S + Y$, so the cocycle condition $\\\\varphi_{jk} \\\\circ \\\\varphi_{ij} = \\\\varphi_{ik}$ + holds automatically!\\n\\nBy the Gluing Lemma for schemes (the locally ringed + space version of Exercise 2.3), we can glue the schemes $\\\\{X_i \\\\times_S + Y\\\\}_{i \\\\in I}$ along the open subschemes $p_{1,i}^{-1}(X_{ij})$ via + $\\\\varphi_{ij}$ to obtain a scheme $W$ together with morphisms $p_1: W \\\\to + X$ and $p_2: W \\\\to Y$ such that $p_1^{-1}(X_i) \\\\cong X_i \\\\times_S + Y$. For any test scheme $Z$ with morphisms $f: Z \\\\to X$ and $g: Z \\\\to + Y$ over $S$, let $Z_i = f^{-1}(X_i)$. The universal property of $X_i \\\\times_S + Y$ gives unique morphisms $\\\\theta_i: Z_i \\\\to X_i \\\\times_S Y \\\\subseteq + W$, and by uniqueness on $Z_i \\\\cap Z_j = f^{-1}(X_{ij})$, we have $\\\\theta_i|_{Z_i + \\\\cap Z_j} = \\\\theta_j|_{Z_i \\\\cap Z_j}$. Thus the $\\\\theta_i$ glue + to a unique morphism $\\\\theta: Z \\\\to W$, proving $W = X \\\\times_S Y$.\\n\\n**Step + 3: $Y$ and $S$ are affine, $X$ is arbitrary.** Let $X = \\\\bigcup_{i \\\\in + I} X_i$ be an open cover of $X$ by affine open subschemes. By Step 1, $X_i + \\\\times_S Y$ exists for every $i \\\\in I$. By Step 2, $X \\\\times_S Y$ + exists. By symmetry, $X \\\\times_S Y$ exists whenever $S$ is affine and $X, + Y$ are arbitrary (cover $Y = \\\\bigcup_{j \\\\in J} Y_j$ by affines and apply + Step 2 to $Y$).\\n\\n**Step 4: $X$, $Y$, and $S$ are all arbitrary.** Let + $S = \\\\bigcup_{\\\\alpha \\\\in A} S_\\\\alpha$ be an affine open cover + of $S$. Let $X_\\\\alpha = \\\\pi_X^{-1}(S_\\\\alpha)$ and $Y_\\\\alpha = + \\\\pi_Y^{-1}(S_\\\\alpha)$. By Step 3, $X_\\\\alpha \\\\times_{S_\\\\alpha} + Y_\\\\alpha$ exists for every $\\\\alpha \\\\in A$. Moreover, we claim that + $X_\\\\alpha \\\\times_{S_\\\\alpha} Y_\\\\alpha$ is also the fiber product + $X_\\\\alpha \\\\times_S Y$: indeed, any pair of morphisms $f: Z \\\\to X_\\\\alpha$ + and $g: Z \\\\to Y$ satisfying $\\\\pi_X \\\\circ f = \\\\pi_Y \\\\circ g$ + automatically satisfies $\\\\pi_Y(g(Z)) = \\\\pi_X(f(Z)) \\\\subseteq S_\\\\alpha$, + so $g$ factors uniquely through $Y_\\\\alpha = \\\\pi_Y^{-1}(S_\\\\alpha)$. + Thus $X_\\\\alpha \\\\times_S Y = X_\\\\alpha \\\\times_{S_\\\\alpha} Y_\\\\alpha$ + exists for every $\\\\alpha \\\\in A$. Since $\\\\{X_\\\\alpha\\\\}_{\\\\alpha + \\\\in A}$ is an open cover of $X$, applying Step 2 one final time glues the + schemes $X_\\\\alpha \\\\times_S Y$ into the global fiber product $X \\\\times_S + Y$. $\\\\blacksquare$\\n\\n**Definition 3.5.3 (Fibers and Base Change).** + Let $f: X \\\\to Y$ be a morphism of schemes.\\n1. If $Y' \\\\to Y$ is any + morphism of schemes, the projection $f': X' = X \\\\times_Y Y' \\\\to Y'$ + is called the *base change* (or *pullback*) of $f$ along $Y' \\\\to Y$.\\n2. + Let $y \\\\in Y$ be a point with local ring $\\\\mathcal{O}_{Y,y}$ and residue + field $\\\\kappa(y) = \\\\mathcal{O}_{Y,y}/\\\\mathfrak{m}_y$. There is a + canonical morphism $\\\\operatorname{Spec} \\\\kappa(y) \\\\to Y$ whose image + is $\\\\{y\\\\}$ (induced on any affine open $\\\\operatorname{Spec} A \\\\ni + y$ by $A \\\\to A_{\\\\mathfrak{p}_y} \\\\to \\\\kappa(y)$). The *schematic + fiber* of $f$ over $y$ is defined to be the scheme\\n $$X_y = X \\\\times_Y + \\\\operatorname{Spec} \\\\kappa(y).$$\\n One verifies that the projection + $X_y \\\\to X$ induces a homeomorphism of the underlying topological space + of $X_y$ onto the set-theoretic fiber $f^{-1}(y) \\\\subseteq X$, endowing + $f^{-1}(y)$ with the natural structure of a scheme over the field $\\\\kappa(y)$.\\n\\n---\\n\\n### + 3.6 Separated and Proper Morphisms\\n\\nAs observed in Chapter 1, the Zariski + topology is almost never Hausdorff. In scheme theory, the role of the Hausdorff + condition is played by *separatedness*, and the role of compactness (or properness + of maps between locally compact Hausdorff spaces) is played by *properness*.\\n\\n**Definition + 3.6.1.** Let $f: X \\\\to Y$ be a morphism of schemes. Applying the universal + property of the fiber product $X \\\\times_Y X$ to the identity morphisms + $\\\\operatorname{id}_X: X \\\\to X$ and $\\\\operatorname{id}_X: X \\\\to + X$ produces a canonical morphism\\n$$\\\\Delta = \\\\Delta_{X/Y}: X \\\\longrightarrow + X \\\\times_Y X,$$\\nsatisfying $p_1 \\\\circ \\\\Delta = \\\\operatorname{id}_X$ + and $p_2 \\\\circ \\\\Delta = \\\\operatorname{id}_X$, called the *diagonal + morphism*.\\n\\nBefore stating the definition of separatedness, we formalize + the notion of closed immersions.\\n\\n**Definition 3.6.2.** A morphism of + schemes $i: Z \\\\to X$ is a *closed immersion* if $i$ induces a homeomorphism + of the underlying topological space of $Z$ onto a closed subset of $X$, and + the morphism of sheaves $i^\\\\#: \\\\mathcal{O}_X \\\\to i_*\\\\mathcal{O}_Z$ + is surjective (as a morphism of sheaves on $X$). A morphism $j: U \\\\to X$ + is an *open immersion* if it induces an isomorphism of $U$ onto an open subscheme + $(V, \\\\mathcal{O}_X|_V)$ of $X$. An *immersion* (or *locally closed immersion*) + is a morphism that factors as $Z \\\\xrightarrow{i} U \\\\xrightarrow{j} X$ + where $i$ is a closed immersion and $j$ is an open immersion.\\n\\n**Proposition + 3.6.3.** *For any morphism of schemes $f: X \\\\to Y$, the diagonal morphism + $\\\\Delta_{X/Y}: X \\\\to X \\\\times_Y X$ is a locally closed immersion.*\\n\\n*Proof.* + If $X = \\\\operatorname{Spec} A$ and $Y = \\\\operatorname{Spec} B$ are affine, + then $X \\\\times_Y X = \\\\operatorname{Spec}(A \\\\otimes_B A)$, and $\\\\Delta_{X/Y}$ + corresponds to the multiplication homomorphism $\\\\mu: A \\\\otimes_B A \\\\to + A$ given by $a_1 \\\\otimes a_2 \\\\mapsto a_1 a_2$. Since $\\\\mu(\\\\sum + a_i \\\\otimes 1) = \\\\sum a_i$, $\\\\mu$ is a *surjective* ring homomorphism! + For any surjective ring homomorphism $\\\\mu: R \\\\twoheadrightarrow R/I$, + the induced map $\\\\operatorname{Spec}(R/I) \\\\to \\\\operatorname{Spec} + R$ is a homeomorphism onto the closed subset $V(I)$ with surjective sheaf + map $\\\\mathcal{O}_{\\\\operatorname{Spec} R} \\\\twoheadrightarrow i_*\\\\mathcal{O}_{\\\\operatorname{Spec}(R/I)}$, + hence is a closed immersion.\\n\\nFor general schemes $X$ and $Y$, choose + an affine open cover $Y = \\\\bigcup_\\\\alpha V_\\\\alpha$ and for each $\\\\alpha$ + an affine open cover $f^{-1}(V_\\\\alpha) = \\\\bigcup_i U_{\\\\alpha, i}$. + Then the open subschemes $W_{\\\\alpha, i} = U_{\\\\alpha, i} \\\\times_{V_\\\\alpha} + U_{\\\\alpha, i}$ are open in $X \\\\times_Y X$. Let $W = \\\\bigcup_{\\\\alpha, + i} W_{\\\\alpha, i} \\\\subseteq X \\\\times_Y X$. Since $\\\\Delta_{X/Y}(U_{\\\\alpha, + i}) \\\\subseteq W_{\\\\alpha, i}$, the image of $\\\\Delta_{X/Y}$ is contained + in the open subscheme $W$. Moreover, $\\\\Delta_{X/Y}^{-1}(W_{\\\\alpha, i}) + = U_{\\\\alpha, i}$ (since $p_1(x, x') \\\\in U_{\\\\alpha, i}$ and $p_2(x, + x') \\\\in U_{\\\\alpha, i}$ implies $x \\\\in U_{\\\\alpha, i}$), and on + each $W_{\\\\alpha, i}$, the restriction of $\\\\Delta_{X/Y}$ is the affine + diagonal $U_{\\\\alpha, i} \\\\to U_{\\\\alpha, i} \\\\times_{V_\\\\alpha} + U_{\\\\alpha, i}$, which is a closed immersion by the first paragraph. Because + being a closed immersion is local on the target, $\\\\Delta_{X/Y}: X \\\\to + W$ is a closed immersion into the open subscheme $W \\\\subseteq X \\\\times_Y + X$. $\\\\blacksquare$\\n\\n**Definition 3.6.4.** A morphism of schemes $f: + X \\\\to Y$ is called *separated* if the diagonal morphism $\\\\Delta_{X/Y}: + X \\\\to X \\\\times_Y X$ is a *closed immersion*. By Proposition 3.6.3, $\\\\Delta_{X/Y}$ + is already a locally closed immersion, so $f: X \\\\to Y$ is separated if + and only if the image $\\\\Delta_{X/Y}(X)$ is a *closed* subset of the topological + space $X \\\\times_Y X$. A scheme $X$ is called *separated* if its canonical + morphism $X \\\\to \\\\operatorname{Spec} \\\\mathbb{Z}$ is separated.\\n\\nBy + the proof of Proposition 3.6.3, every morphism between affine schemes is separated.\\n\\n**Definition + 3.6.5.** Let $f: X \\\\to Y$ be a morphism of schemes.\\n1. $f$ is *locally + of finite type* if there exists an affine open cover $Y = \\\\bigcup_i \\\\operatorname{Spec} + B_i$ such that for each $i$, $f^{-1}(\\\\operatorname{Spec} B_i)$ can be covered + by affine open subschemes $\\\\operatorname{Spec} A_{ij}$ where each $A_{ij}$ + is a finitely generated $B_i$-algebra.\\n2. $f$ is *quasi-compact* if the + preimage $f^{-1}(V)$ of every quasi-compact open subset $V \\\\subseteq Y$ + is quasi-compact.\\n3. $f$ is *of finite type* if it is locally of finite + type and quasi-compact (meaning each $f^{-1}(\\\\operatorname{Spec} B_i)$ + can be covered by *finitely many* $\\\\operatorname{Spec} A_{ij}$ with $A_{ij}$ + finitely generated over $B_i$).\\n4. $f$ is *universally closed* if $f$ is + a closed map (maps closed subsets to closed subsets) and for every morphism + $Y' \\\\to Y$, the base change $f': X \\\\times_Y Y' \\\\to Y'$ is also a + closed map.\\n5. $f$ is *proper* if $f$ is separated, of finite type, and + universally closed.\\n\\nTesting universal closedness directly from the definition + requires checking all possible base changes $Y' \\\\to Y$. Remarkably, Grothendieck + proved that separatedness and properness can be tested using only *valuation + rings*, providing a scheme-theoretic analogue of the sequential compactness + criterion in metric spaces (where $\\\\operatorname{Spec} R$ plays the role + of a convergent sequence with generic point $\\\\operatorname{Spec} K$ and + limit point $\\\\operatorname{Spec}(R/\\\\mathfrak{m})$).\\n\\nRecall that + an integral domain $R$ with field of fractions $K$ is a *valuation ring* if + for every non-zero element $x \\\\in K^\\\\times$, either $x \\\\in R$ or + $x^{-1} \\\\in R$. Every valuation ring is a local ring.\\n\\n**Theorem 3.6.6 + (Valuative Criteria of Separatedness and Properness).** *Let $f: X \\\\to + Y$ be a morphism of schemes of finite type, with $X$ Noetherian (or more generally, + let $f$ be quasi-separated and of finite type). For any valuation ring $R$ + with field of fractions $K$, consider a commutative diagram of solid arrows:*\\n$$\\\\begin{array}{ccc} + \\\\operatorname{Spec} K & \\\\xrightarrow{\\\\;\\\\;u\\\\;\\\\;} & X \\\\\\\\ + \\\\downarrow{\\\\scriptstyle i} & \\\\nearrow{\\\\scriptstyle\\\\exists!\\\\,v} + & \\\\downarrow{\\\\scriptstyle f} \\\\\\\\ \\\\operatorname{Spec} R & \\\\xrightarrow{\\\\;\\\\;g\\\\;\\\\;} + & Y \\\\end{array}$$\\n*where $i: \\\\operatorname{Spec} K \\\\to \\\\operatorname{Spec} + R$ is induced by the inclusion $R \\\\hookrightarrow K$. Then:*\\n1. **(Valuative + Criterion of Separatedness)** *$f$ is separated if and only if for every valuation + ring $R$ and every diagram as above, there exists at most one morphism $v: + \\\\operatorname{Spec} R \\\\to X$ making both triangles commute.*\\n2. **(Valuative + Criterion of Properness)** *$f$ is proper if and only if for every valuation + ring $R$ and every diagram as above, there exists a unique morphism $v: \\\\operatorname{Spec} + R \\\\to X$ making both triangles commute.*\\n\\n*Proof (of the Direct Implications + and Geometric Mechanism).* We give the complete proof that separatedness implies + uniqueness of $v$, and that projective space $\\\\mathbb{P}^n_Y \\\\to Y$ + satisfies the valuative criterion of properness.\\n\\nSuppose $f: X \\\\to + Y$ is separated, and let $v_1, v_2: \\\\operatorname{Spec} R \\\\to X$ be + two morphisms satisfying $f \\\\circ v_1 = f \\\\circ v_2 = g$ and $v_1 \\\\circ + i = v_2 \\\\circ i = u$. By the universal property of $X \\\\times_Y X$, the + pair $(v_1, v_2)$ defines a morphism $w: \\\\operatorname{Spec} R \\\\to X + \\\\times_Y X$. Since $v_1 \\\\circ i = v_2 \\\\circ i$, the composition $w + \\\\circ i: \\\\operatorname{Spec} K \\\\to X \\\\times_Y X$ factors through + the diagonal $\\\\Delta_{X/Y}(X)$. Let $\\\\xi \\\\in \\\\operatorname{Spec} + R$ be the generic point $(0)$ (the image of $\\\\operatorname{Spec} K$), so + $w(\\\\xi) \\\\in \\\\Delta_{X/Y}(X)$. Because $R$ is an integral domain, + the closure of $\\\\{\\\\xi\\\\}$ in $\\\\operatorname{Spec} R$ is all of + $\\\\operatorname{Spec} R$. Since $f$ is separated, $\\\\Delta_{X/Y}(X)$ is + closed in $X \\\\times_Y X$, so $w^{-1}(\\\\Delta_{X/Y}(X))$ is a closed subset + of $\\\\operatorname{Spec} R$ containing the dense point $\\\\xi$, hence equals + all of $\\\\operatorname{Spec} R$. Moreover, $\\\\operatorname{Spec} R$ is + reduced (since $R$ is a domain), and any morphism from a reduced scheme whose + topological image lies in a closed subscheme factors uniquely through that + closed subscheme. Thus $w$ factors through $\\\\Delta_{X/Y}: X \\\\to X \\\\times_Y + X$, which means $v_1 = p_1 \\\\circ w = p_2 \\\\circ w = v_2$.\\n\\nConversely, + if $\\\\Delta_{X/Y}(X)$ were not closed in $X \\\\times_Y X$, there would + exist a point $z_1 \\\\in \\\\Delta_{X/Y}(X)$ and a point $z_0 \\\\in \\\\overline{\\\\{z_1\\\\}} + \\\\setminus \\\\Delta_{X/Y}(X)$ (a specialization of $z_1$). By Chevalley's + theorem on the existence of valuation rings dominating local rings of integral + closures, one constructs a valuation ring $R \\\\subseteq \\\\kappa(z_1)$ + whose local homomorphism $\\\\mathcal{O}_{X \\\\times_Y X, z_0} \\\\to R$ + gives a morphism $w = (v_1, v_2): \\\\operatorname{Spec} R \\\\to X \\\\times_Y + X$ sending the generic point $\\\\xi$ to $z_1 \\\\in \\\\Delta_{X/Y}(X)$ (so + $v_1 \\\\circ i = v_2 \\\\circ i$) and the closed point $\\\\mathfrak{m}$ + to $z_0 \\\\notin \\\\Delta_{X/Y}(X)$ (so $v_1 \\\\neq v_2$).\\n\\nSimilarly, + a morphism $f: X \\\\to Y$ is closed if and only if it is *stable under specialization* + (for any $x_1 \\\\in X$ and any $y_0 \\\\in \\\\overline{\\\\{f(x_1)\\\\}} + \\\\subseteq Y$, there exists $x_0 \\\\in \\\\overline{\\\\{x_1\\\\}}$ with + $f(x_0) = y_0$). The existence of the lift $v: \\\\operatorname{Spec} R \\\\to + X$ in (2) is the exact translation of stability under specialization for all + base changes $Y' \\\\to Y$, because sending the closed point of $\\\\operatorname{Spec} + R$ to $x_0 = v(\\\\mathfrak{m}) \\\\in X$ produces the required specialization + of $x_1 = u(\\\\xi)$ lying over $y_0 = g(\\\\mathfrak{m})$. $\\\\blacksquare$\\n\\n**Corollary + 3.6.7.** *For any scheme $Y$ and any integer $n \\\\ge 0$, the projective + space $\\\\mathbb{P}^n_Y = \\\\mathbb{P}^n_{\\\\mathbb{Z}} \\\\times_{\\\\operatorname{Spec} + \\\\mathbb{Z}} Y \\\\to Y$ is proper over $Y$. Consequently, any closed subscheme + $X \\\\subseteq \\\\mathbb{P}^n_Y$ is proper over $Y$.*\\n\\n*Proof.* Since + properness is stable under base change (as the valuative diagram over $Y$ + immediately projects to a valuative diagram over $\\\\operatorname{Spec} \\\\mathbb{Z}$), + it suffices to verify the Valuative Criterion of Properness for $\\\\mathbb{P}^n_{\\\\mathbb{Z}} + \\\\to \\\\operatorname{Spec} \\\\mathbb{Z}$. Let $R$ be a valuation ring + with fraction field $K$, and suppose we are given a morphism $u: \\\\operatorname{Spec} + K \\\\to \\\\mathbb{P}^n_{\\\\mathbb{Z}}$. Since $\\\\operatorname{Spec} K$ + consists of a single point, its image lies in at least one of the standard + affine open charts $U_i = D_+(x_i) \\\\cong \\\\operatorname{Spec} \\\\mathbb{Z}[x_0/x_i, + \\\\dots, x_n/x_i]$. On the intersection $\\\\bigcap_{j \\\\in J} U_j$ of + all charts containing $u(\\\\operatorname{Spec} K)$, the morphism $u$ is given + by assigning non-zero elements $a_j \\\\in K^\\\\times$ representing the homogeneous + coordinates (Specifically, $x_j/x_i \\\\mapsto a_j/a_i \\\\in K^\\\\times$ + for $j \\\\in J$, and $x_j/x_i \\\\mapsto 0 = a_j/a_i$ for $j \\\\notin J$).\\n\\nIn + the valuation ring $R$, the finitely many non-zero ratios $a_j / a_k \\\\in + K^\\\\times$ ($j, k \\\\in J$) are totally ordered by divisibility in $R$ + (since for each pair, either $a_j/a_k \\\\in R$ or $a_k/a_j \\\\in R$). Therefore, + there exists an index $m \\\\in J$ such that $a_j / a_m \\\\in R$ for *all* + $j \\\\in \\\\{0, 1, \\\\dots, n\\\\}$! This defines a ring homomorphism $\\\\mathbb{Z}[x_0/x_m, + \\\\dots, x_n/x_m] \\\\to R$ sending $x_j/x_m \\\\mapsto a_j/a_m \\\\in R$, + which corresponds to a morphism $v: \\\\operatorname{Spec} R \\\\to U_m \\\\subseteq + \\\\mathbb{P}^n_{\\\\mathbb{Z}}$ extending $u$. Uniqueness holds because on + overlaps $U_i \\\\cap U_m = \\\\operatorname{Spec} \\\\mathbb{Z}[x_0/x_m, + \\\\dots, (x_i/x_m)^{\\\\pm 1}, \\\\dots]$, any two lifts agree after localizing + to $K$, and $R \\\\hookrightarrow K$ is injective. Finally, a closed immersion + is clearly proper, and the composition of proper morphisms is proper, so any + closed subscheme $X \\\\subseteq \\\\mathbb{P}^n_Y$ is proper over $Y$. $\\\\blacksquare$\\n\\n---\\n\\n### + Exercises for Chapter 3\\n\\n**Exercise 3.1.** Describe completely the topological + space and stalks of $\\\\operatorname{Spec} A$ for the following rings:\\n(a) + $A = \\\\mathbb{Z}$.\\n(b) $A = k[x]/(x^2)$ (the ring of dual numbers over + a field $k$).\\n(c) $A = \\\\mathbb{Z}[x]$ (describe the prime ideals of height + $0$, $1$, and $2$, and sketch the fibers of the natural morphism $\\\\operatorname{Spec} + \\\\mathbb{Z}[x] \\\\to \\\\operatorname{Spec} \\\\mathbb{Z}$).\\n(d) $A = + k[x]_{(x)}$, a discrete valuation ring.\\n\\n**Exercise 3.2.** Let $X$ be + a scheme.\\n(a) $X$ is called *reduced* if $\\\\mathcal{O}_X(U)$ has no non-zero + nilpotent elements for every open $U \\\\subseteq X$. Prove that $X$ is reduced + if and only if the stalk $\\\\mathcal{O}_{X,P}$ has no non-zero nilpotent + elements for every $P \\\\in X$.\\n(b) $X$ is called *integral* if $\\\\mathcal{O}_X(U)$ + is an integral domain for every non-empty open $U \\\\subseteq X$. Prove that + $X$ is integral if and only if $X$ is both reduced and irreducible.\\n(c) + For any scheme $X$, let $\\\\mathcal{N}_X$ be the sheaf of nilpotent elements + of $\\\\mathcal{O}_X$ ($\\\\mathcal{N}_X(U)$ is the nilradical of $\\\\mathcal{O}_X(U)$), + and define $\\\\mathcal{O}_{X_{\\\\text{red}}}$ to be the sheafification of + $U \\\\mapsto \\\\mathcal{O}_X(U)/\\\\mathcal{N}_X(U)$. Prove that $X_{\\\\text{red}} + = (X, \\\\mathcal{O}_{X_{\\\\text{red}}})$ is a reduced closed subscheme of + $X$ (with the same underlying topological space) satisfying the universal + property that every morphism from a reduced scheme $Z \\\\to X$ factors uniquely + through $X_{\\\\text{red}} \\\\hookrightarrow X$.\\n\\n**Exercise 3.3.** (The + Affine Line with a Doubled Origin) Let $X_1 = \\\\operatorname{Spec} k[x]$ + and $X_2 = \\\\operatorname{Spec} k[y]$ be two copies of $\\\\mathbb{A}^1_k$. + Let $U_1 = D(x) = \\\\operatorname{Spec} k[x, x^{-1}] \\\\subseteq X_1$ and + $U_2 = D(y) = \\\\operatorname{Spec} k[y, y^{-1}] \\\\subseteq X_2$.\\n(a) + Let $X$ be the scheme obtained by gluing $X_1$ and $X_2$ along $U_1$ and $U_2$ + via the isomorphism $U_1 \\\\xrightarrow{\\\\sim} U_2$ induced by $y \\\\mapsto + x$. Prove that $X$ is *not* separated over $k$ by showing that the image of + $\\\\Delta: X \\\\to X \\\\times_k X$ is not closed, and also by exhibiting + a failure of the Valuative Criterion of Separatedness using $R = k[t]_{(t)}$.\\n(b) + Let $Y$ be the scheme obtained by gluing $X_1$ and $X_2$ along $U_1$ and $U_2$ + via the isomorphism induced by $y \\\\mapsto x^{-1}$. Prove that $Y$ is isomorphic + to $\\\\mathbb{P}^1_k$, and is therefore separated and proper over $k$.\\n\\n**Exercise + 3.4.** Let $f: X \\\\to Y$ be a morphism of schemes, where $Y$ is separated.\\n(a) + Prove that the *graph morphism* $\\\\Gamma_f = (\\\\operatorname{id}_X, f): + X \\\\to X \\\\times_{\\\\operatorname{Spec} \\\\mathbb{Z}} Y$ is a closed + immersion. *(Hint: Show that $\\\\Gamma_f$ is the base change of the diagonal + $\\\\Delta_Y: Y \\\\to Y \\\\times Y$ along $f \\\\times \\\\operatorname{id}_Y: + X \\\\times Y \\\\to Y \\\\times Y$.)*\\n(b) Prove that if $X$ is an affine + scheme and $Y$ is separated, then for any two affine open subschemes $U, V + \\\\subseteq X$ (or more generally, for any two affine open subschemes $U, + V$ of a separated scheme $Y$), the intersection $U \\\\cap V$ is again an + affine scheme! Give a counterexample when $Y$ is not separated using Exercise + 3.3(a).\\n\\n**Exercise 3.5.** Let $X$ be a proper scheme over a field $k$, + and assume $X$ is connected and reduced. Prove that $\\\\Gamma(X, \\\\mathcal{O}_X)$ + is a finite field extension of $k$ (and hence $\\\\Gamma(X, \\\\mathcal{O}_X) + = k$ if $k$ is algebraically closed). *(Hint: Any $s \\\\in \\\\Gamma(X, \\\\mathcal{O}_X) + = \\\\operatorname{Hom}_k(X, \\\\mathbb{A}^1_k)$ can be composed with the + open immersion $\\\\mathbb{A}^1_k \\\\hookrightarrow \\\\mathbb{P}^1_k$. Use + the fact that $X \\\\to \\\\operatorname{Spec} k$ is proper to show that the + image of $X$ in $\\\\mathbb{P}^1_k$ is closed, connected, and misses $\\\\infty + \\\\in \\\\mathbb{P}^1_k$, hence must be a single closed point of $\\\\mathbb{A}^1_k$.)*\\n\\n**Exercise + 3.6.** Let $S$ be a graded ring generated as an $S_0$-algebra by $S_1$. For + any integer $d \\\\ge 1$, define the *Veronese subring* $S^{(d)} = \\\\bigoplus_{n + \\\\ge 0} S_{nd}$ (with grading $(S^{(d)})_n = S_{nd}$). Prove that there + is a canonical isomorphism of schemes $\\\\operatorname{Proj} S \\\\xrightarrow{\\\\sim} + \\\\operatorname{Proj} S^{(d)}$.\\n\\n**Exercise 3.7.** (Flatness and Going-Down) + A morphism of schemes $f: X \\\\to Y$ is called *flat* if for every $x \\\\in + X$, the local ring homomorphism $f^\\\\#_x: \\\\mathcal{O}_{Y, f(x)} \\\\to + \\\\mathcal{O}_{X,x}$ makes $\\\\mathcal{O}_{X,x}$ a flat $\\\\mathcal{O}_{Y, + f(x)}$-module.\\n(a) Prove that open immersions are flat, and that flatness + is stable under base change ($X \\\\times_Y Y' \\\\to Y'$ is flat if $X \\\\to + Y$ is flat).\\n(b) Using the Going-Down Theorem for flat homomorphisms of + rings, prove that if $f: X \\\\to Y$ is flat, then for every $x \\\\in X$, + the map $\\\\operatorname{Spec} \\\\mathcal{O}_{X,x} \\\\to \\\\operatorname{Spec} + \\\\mathcal{O}_{Y, f(x)}$ is surjective (i.e., generalizations lift along + flat morphisms).\\n\\n---\\n\\n## Chapter 4: Quasi-Coherent and Coherent Sheaves\\n\\nJust + as modules over a ring $A$ are the linear objects through which one studies + $A$, sheaves of $\\\\mathcal{O}_X$-modules\u2014specifically *quasi-coherent* + and *coherent* sheaves\u2014are the linear objects (generalizing vector bundles + and ideal sheaves) through which one studies a scheme $X$.\\n\\n---\\n\\n### + 4.1 Quasi-Coherent and Coherent Modules\\n\\n**Definition 4.1.1.** Let $(X, + \\\\mathcal{O}_X)$ be a ringed space. A *sheaf of $\\\\mathcal{O}_X$-modules* + (or simply an *$\\\\mathcal{O}_X$-module*) is a sheaf $\\\\mathcal{F}$ of + abelian groups on $X$ such that for every open subset $U \\\\subseteq X$, + $\\\\mathcal{F}(U)$ is equipped with the structure of an $\\\\mathcal{O}_X(U)$-module, + and for every inclusion of open subsets $V \\\\subseteq U$, the restriction + map $\\\\mathcal{F}(U) \\\\to \\\\mathcal{F}(V)$ is compatible with the ring + restriction $\\\\mathcal{O}_X(U) \\\\to \\\\mathcal{O}_X(V)$:\\n$$(a \\\\cdot + s)|_V = a|_V \\\\cdot s|_V \\\\quad \\\\text{for all } a \\\\in \\\\mathcal{O}_X(U),\\\\; + s \\\\in \\\\mathcal{F}(U).$$\\nA morphism of $\\\\mathcal{O}_X$-modules $\\\\varphi: + \\\\mathcal{F} \\\\to \\\\mathcal{G}$ is a morphism of sheaves such that $\\\\varphi(U): + \\\\mathcal{F}(U) \\\\to \\\\mathcal{G}(U)$ is an $\\\\mathcal{O}_X(U)$-module + homomorphism for every open $U \\\\subseteq X$. The category of $\\\\mathcal{O}_X$-modules + is denoted $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$.\\n\\nNow let $A$ be a commutative + ring, $X = \\\\operatorname{Spec} A$, and $M$ an $A$-module. Exactly as we + constructed the structure sheaf $\\\\mathcal{O}_{\\\\operatorname{Spec} A}$ + from $A$ in Definition 3.2.1, we associate to $M$ a canonical $\\\\mathcal{O}_X$-module + $\\\\widetilde{M}$.\\n\\n**Definition 4.1.2.** Let $A$ be a ring, $X = \\\\operatorname{Spec} + A$, and $M$ an $A$-module. For each open subset $U \\\\subseteq X$, we define + $\\\\widetilde{M}(U)$ to be the set of all functions\\n$$s: U \\\\longrightarrow + \\\\bigsqcup_{\\\\mathfrak{p} \\\\in U} M_{\\\\mathfrak{p}}$$\\nsuch that + $s(\\\\mathfrak{p}) \\\\in M_{\\\\mathfrak{p}}$ for every $\\\\mathfrak{p} + \\\\in U$, and for every $\\\\mathfrak{p} \\\\in U$ there exist an open neighborhood + $V \\\\subseteq U$ of $\\\\mathfrak{p}$ and elements $m \\\\in M$, $f \\\\in + A$ such that for all $\\\\mathfrak{q} \\\\in V$, $f \\\\notin \\\\mathfrak{q}$ + and $s(\\\\mathfrak{q}) = m/f$ in $M_{\\\\mathfrak{q}}$. Under pointwise operations + and restriction of functions, $\\\\widetilde{M}$ is clearly a sheaf of $\\\\mathcal{O}_X$-modules + on $X = \\\\operatorname{Spec} A$.\\n\\n**Theorem 4.1.3.** *Let $A$ be a ring, + $X = \\\\operatorname{Spec} A$, and $M$ an $A$-module.*\\n1. *For every $\\\\mathfrak{p} + \\\\in X$, the stalk $(\\\\widetilde{M})_{\\\\mathfrak{p}}$ is canonically + isomorphic to the localized $A_{\\\\mathfrak{p}}$-module $M_{\\\\mathfrak{p}}$.*\\n2. + *For every $f \\\\in A$, the module of sections $\\\\Gamma(D(f), \\\\widetilde{M})$ + is canonically isomorphic to the localized $A_f$-module $M_f$. In particular, + $\\\\Gamma(X, \\\\widetilde{M}) \\\\cong M$.*\\n3. *The functor $M \\\\mapsto + \\\\widetilde{M}$ from the category $\\\\mathfrak{Mod}(A)$ of $A$-modules + to $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$ is an exact, fully faithful functor + that commutes with arbitrary direct sums, tensor products ($\\\\widetilde{M + \\\\otimes_A N} \\\\cong \\\\widetilde{M} \\\\otimes_{\\\\mathcal{O}_X} \\\\widetilde{N}$), + and localizations ($\\\\widetilde{M}|_{D(f)} \\\\cong \\\\widetilde{M_f}$).*\\n\\n*Proof.* + The proofs of (1) and (2) are word-for-word identical to the proof of Theorem + 3.2.2, replacing elements $a \\\\in A$ in numerators by elements $m \\\\in + M$.\\n\\nFor (3), let $M' \\\\to M \\\\to M''$ be an exact sequence of $A$-modules. + For every $\\\\mathfrak{p} \\\\in X$, localization at $\\\\mathfrak{p}$ is + an exact functor, so $M'_{\\\\mathfrak{p}} \\\\to M_{\\\\mathfrak{p}} \\\\to + M''_{\\\\mathfrak{p}}$ is exact. By (1) and Proposition 2.2.3(2), the sequence + of sheaves $\\\\widetilde{M'} \\\\to \\\\widetilde{M} \\\\to \\\\widetilde{M''}$ + is exact. Full faithfulness follows from the adjunction between global sections + $\\\\Gamma(X, -)$ and $\\\\widetilde{(-)}$: any morphism of $\\\\mathcal{O}_X$-modules + $\\\\varphi: \\\\widetilde{M} \\\\to \\\\widetilde{N}$ induces an $A$-module + homomorphism $\\\\varphi(X): M \\\\to N$, which in turn determines the stalk + maps $\\\\varphi_{\\\\mathfrak{p}} = \\\\varphi(X)_{\\\\mathfrak{p}}: M_{\\\\mathfrak{p}} + \\\\to N_{\\\\mathfrak{p}}$ and hence uniquely determines $\\\\varphi$. Commutation + with direct sums and tensor products holds because both operations commute + with localization on stalks. $\\\\blacksquare$\\n\\n**Definition 4.1.4.** + Let $(X, \\\\mathcal{O}_X)$ be a scheme.\\n1. An $\\\\mathcal{O}_X$-module + $\\\\mathcal{F}$ is called *quasi-coherent* if there exists an affine open + cover $X = \\\\bigcup_{i \\\\in I} U_i$ (with $U_i = \\\\operatorname{Spec} + A_i$) and for each $i \\\\in I$ an $A_i$-module $M_i$ such that $\\\\mathcal{F}|_{U_i} + \\\\cong \\\\widetilde{M_i}$ as $\\\\mathcal{O}_{U_i}$-modules.\\n2. Suppose + $X$ is a locally Noetherian scheme (meaning it can be covered by affine open + subschemes $\\\\operatorname{Spec} A_i$ where each $A_i$ is a Noetherian ring). + An $\\\\mathcal{O}_X$-module $\\\\mathcal{F}$ is called *coherent* if it is + quasi-coherent and for each $i \\\\in I$, the $A_i$-module $M_i$ can be chosen + to be a finitely generated $A_i$-module.\\n\\nWe denote the category of quasi-coherent + $\\\\mathcal{O}_X$-modules by $\\\\mathfrak{QCoh}(X)$ and, when $X$ is locally + Noetherian, the category of coherent $\\\\mathcal{O}_X$-modules by $\\\\mathfrak{Coh}(X)$.\\n\\nA + crucial property of quasi-coherence is that if $\\\\mathcal{F}$ is locally + of the form $\\\\widetilde{M_i}$ on *some* affine open cover, then it is of + the form $\\\\widetilde{M}$ on *every* affine open subscheme of $X$.\\n\\n**Theorem + 4.1.5.** *Let $X$ be a scheme and $\\\\mathcal{F}$ an $\\\\mathcal{O}_X$-module. + Then $\\\\mathcal{F}$ is quasi-coherent if and only if for every affine open + subscheme $U = \\\\operatorname{Spec} A \\\\subseteq X$, there exists an $A$-module + $M$ such that $\\\\mathcal{F}|_U \\\\cong \\\\widetilde{M}$ (namely, $M = + \\\\Gamma(U, \\\\mathcal{F})$).*\\n\\n*Consequently, on an affine scheme $X + = \\\\operatorname{Spec} A$, the functors $M \\\\mapsto \\\\widetilde{M}$ + and $\\\\mathcal{F} \\\\mapsto \\\\Gamma(X, \\\\mathcal{F})$ form an equivalence + of categories between $\\\\mathfrak{Mod}(A)$ and $\\\\mathfrak{QCoh}(\\\\operatorname{Spec} + A)$. Since $\\\\mathfrak{Mod}(A)$ is an abelian category, $\\\\mathfrak{QCoh}(X)$ + (and $\\\\mathfrak{Coh}(X)$ for locally Noetherian $X$) is an abelian subcategory + of $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$: the kernel, cokernel, and image + of any morphism of quasi-coherent (resp. coherent) sheaves are again quasi-coherent + (resp. coherent).*\\n\\n*Proof.* ($\\\\Leftarrow$) This is immediate by choosing + any affine open cover of $X$.\\n\\n($\\\\Rightarrow$) Suppose $\\\\mathcal{F}$ + is quasi-coherent, and let $U = \\\\operatorname{Spec} A \\\\subseteq X$ be + an arbitrary affine open subscheme. Since $\\\\mathcal{F}$ is quasi-coherent, + every point $P \\\\in U$ has an affine open neighborhood $V_P$ in $X$ on which + $\\\\mathcal{F}|_{V_P} \\\\cong \\\\widetilde{N_P}$. Shrinking $V_P$ to a + basic open subset $D(g_P)$ inside $U \\\\cap V_P$, and using the fact that + the restriction of $\\\\widetilde{N_P}$ to a basic open subset is again tilde + of a localized module, we can cover $U = \\\\operatorname{Spec} A$ by finitely + many principal open subsets $D(g_1), \\\\dots, D(g_r)$ (by quasi-compactness + of $\\\\operatorname{Spec} A$) such that for each $i = 1, \\\\dots, r$,\\n$$\\\\mathcal{F}|_{D(g_i)} + \\\\cong \\\\widetilde{M_i}$$\\nfor some $A_{g_i}$-module $M_i = \\\\mathcal{F}(D(g_i))$. + Moreover, on each overlap $D(g_i) \\\\cap D(g_j) = D(g_i g_j)$, we have $\\\\mathcal{F}(D(g_i + g_j)) \\\\cong (M_i)_{g_j} \\\\cong (M_j)_{g_i}$.\\n\\nLet $M = \\\\Gamma(U, + \\\\mathcal{F})$. Multiplication by sections gives a canonical morphism of + $\\\\mathcal{O}_U$-modules $\\\\alpha: \\\\widetilde{M} \\\\to \\\\mathcal{F}|_U$. + To prove that $\\\\alpha$ is an isomorphism, it suffices to prove that for + every $f \\\\in A$, the localization map $\\\\psi: M_f \\\\to \\\\mathcal{F}(D(f))$ + is an isomorphism (then taking $f = g_i$ shows $M_{g_i} \\\\xrightarrow{\\\\sim} + \\\\mathcal{F}(D(g_i)) = M_i$, so $\\\\alpha|_{D(g_i)}$ is an isomorphism + for each $i$, whence $\\\\alpha$ is an isomorphism). Replacing $U$ by $D(f)$, + it suffices to prove the following two fundamental lemmas for any $\\\\mathcal{F}$ + covered by $D(g_1), \\\\dots, D(g_r)$ with $\\\\mathcal{F}|_{D(g_i)} \\\\cong + \\\\widetilde{M_i}$:\\n1. **(Uniqueness / Injectivity)** If $s \\\\in \\\\mathcal{F}(U)$ + and $f \\\\in A$ satisfies $s|_{D(f)} = 0$ in $\\\\mathcal{F}(D(f))$, then + there exists an integer $N \\\\ge 1$ such that $f^N s = 0$ in $\\\\mathcal{F}(U) + = M$.\\n2. **(Extension / Surjectivity)** For any section $t \\\\in \\\\mathcal{F}(D(f))$, + there exist an integer $N \\\\ge 1$ and a global section $s \\\\in \\\\mathcal{F}(U) + = M$ such that $s|_{D(f)} = f^N t$ in $\\\\mathcal{F}(D(f))$.\\n\\n*Proof + of (1):* Let $s_i = s|_{D(g_i)} \\\\in M_i$. By hypothesis, $s_i|_{D(f g_i)} + = (s|_{D(f)})|_{D(f g_i)} = 0$ in $\\\\mathcal{F}(D(f g_i)) = (M_i)_f$. By + definition of the localization $(M_i)_f$, there exists an integer $n_i \\\\ge + 1$ such that $f^{n_i} s_i = 0$ in $M_i = \\\\mathcal{F}(D(g_i))$. Letting + $N = \\\\max(n_1, \\\\dots, n_r)$, we have $(f^N s)|_{D(g_i)} = f^N s_i = + 0$ for all $i = 1, \\\\dots, r$. By the Locality Axiom for the sheaf $\\\\mathcal{F}$ + on the cover $\\\\{D(g_i)\\\\}$, $f^N s = 0$ in $\\\\mathcal{F}(U)$.\\n\\n*Proof + of (2):* Let $t \\\\in \\\\mathcal{F}(D(f))$. Restricting $t$ to $D(f) \\\\cap + D(g_i) = D(f g_i)$ gives an element $t_i = t|_{D(f g_i)} \\\\in \\\\mathcal{F}(D(f + g_i)) = (M_i)_f$. Thus for each $i = 1, \\\\dots, r$, we can write $t_i = + m_i / f^{n_i}$ for some $m_i \\\\in M_i = \\\\mathcal{F}(D(g_i))$. Choosing + $n = \\\\max(n_1, \\\\dots, n_r)$ and replacing $m_i$ by $f^{n - n_i} m_i$, + we have sections $m_i \\\\in \\\\mathcal{F}(D(g_i))$ such that\\n$$m_i|_{D(f + g_i)} = f^n t|_{D(f g_i)} \\\\quad \\\\text{in } \\\\mathcal{F}(D(f g_i)).$$\\nNow + consider the overlaps $D(g_i) \\\\cap D(g_j) = D(g_i g_j)$ and the difference + $m_i|_{D(g_i g_j)} - m_j|_{D(g_i g_j)} \\\\in \\\\mathcal{F}(D(g_i g_j))$. + When restricted to $D(f g_i g_j)$, this difference equals $f^n t|_{D(f g_i + g_j)} - f^n t|_{D(f g_i g_j)} = 0$. Since $D(g_i g_j)$ is affine with $\\\\mathcal{F}|_{D(g_i + g_j)} \\\\cong \\\\widetilde{(M_i)_{g_j}}$, property (1) applied to $D(g_i + g_j)$ shows that there is an integer $m_{ij} \\\\ge 1$ such that $f^{m_{ij}} + (m_i|_{D(g_i g_j)} - m_j|_{D(g_i g_j)}) = 0$ in $\\\\mathcal{F}(D(g_i g_j))$. + Taking $m = \\\\max_{i,j} m_{ij}$, the sections $f^m m_i \\\\in \\\\mathcal{F}(D(g_i))$ + agree on all overlaps $D(g_i g_j)$! By the Gluing Axiom for $\\\\mathcal{F}$, + there exists a global section $s \\\\in \\\\mathcal{F}(U) = M$ such that $s|_{D(g_i)} + = f^m m_i$ for all $i$. Then on each $D(f g_i)$, $(s|_{D(f)})|_{D(f g_i)} + = (f^m m_i)|_{D(f g_i)} = f^{n+m} t|_{D(f g_i)}$, so by the Locality Axiom + on the cover $\\\\{D(f g_i)\\\\}$ of $D(f)$, $s|_{D(f)} = f^{n+m} t$ in $\\\\mathcal{F}(D(f))$. + This establishes that $\\\\psi: M_f \\\\to \\\\mathcal{F}(D(f))$ is an isomorphism. + $\\\\blacksquare$\\n\\n---\\n\\n### 4.2 Operations on Quasi-Coherent Sheaves + and Ideal Sheaves\\n\\nLet $(X, \\\\mathcal{O}_X)$ and $(Y, \\\\mathcal{O}_Y)$ + be schemes and $f: X \\\\to Y$ a morphism of schemes.\\n\\n**Definition 4.2.1.**\\n1. + For any $\\\\mathcal{O}_X$-modules $\\\\mathcal{F}$ and $\\\\mathcal{G}$, + the *tensor product* $\\\\mathcal{F} \\\\otimes_{\\\\mathcal{O}_X} \\\\mathcal{G}$ + is defined to be the sheafification of the presheaf $U \\\\mapsto \\\\mathcal{F}(U) + \\\\otimes_{\\\\mathcal{O}_X(U)} \\\\mathcal{G}(U)$. The *sheaf Hom* $\\\\mathcal{H}om_{\\\\mathcal{O}_X}(\\\\mathcal{F}, + \\\\mathcal{G})$ is the sheaf $U \\\\mapsto \\\\operatorname{Hom}_{\\\\mathcal{O}_X|_U}(\\\\mathcal{F}|_U, + \\\\mathcal{G}|_U)$.\\n2. For any $\\\\mathcal{O}_X$-module $\\\\mathcal{F}$, + the direct image $f_*\\\\mathcal{F}$ is naturally an $\\\\mathcal{O}_Y$-module + via $f^\\\\#: \\\\mathcal{O}_Y \\\\to f_*\\\\mathcal{O}_X$.\\n3. For any $\\\\mathcal{O}_Y$-module + $\\\\mathcal{G}$, the inverse image sheaf $f^{-1}\\\\mathcal{G}$ is a module + over the sheaf of rings $f^{-1}\\\\mathcal{O}_Y$. Using the canonical ring + homomorphism $f^{-1}\\\\mathcal{O}_Y \\\\to \\\\mathcal{O}_X$, we define the + *pullback of $\\\\mathcal{O}$-modules* $f^*\\\\mathcal{G}$ by\\n $$f^*\\\\mathcal{G} + = f^{-1}\\\\mathcal{G} \\\\otimes_{f^{-1}\\\\mathcal{O}_Y} \\\\mathcal{O}_X.$$\\n\\nOn + affine schemes $X = \\\\operatorname{Spec} B$ and $Y = \\\\operatorname{Spec} + A$ with $f$ induced by $\\\\varphi: A \\\\to B$, if $\\\\mathcal{G} = \\\\widetilde{N}$ + for an $A$-module $N$, then $f^*\\\\widetilde{N} \\\\cong \\\\widetilde{N + \\\\otimes_A B}$ (since both have the same universal property as left adjoint + to $f_*$), showing that $f^*$ always preserves quasi-coherent sheaves (and + coherent sheaves when $X, Y$ are locally Noetherian). Similarly, if $f$ is + quasi-compact and quasi-separated (which holds whenever $X$ is Noetherian + or $f$ is affine/separated of finite type), covering $Y$ by affines and $f^{-1}(V)$ + by finitely many affines shows via the exact sequence of the cover that $f_*\\\\mathcal{F}$ + is quasi-coherent whenever $\\\\mathcal{F}$ is quasi-coherent.\\n\\nAn especially + important class of quasi-coherent sheaves is the class of *quasi-coherent + sheaves of ideals*, which classify closed subschemes.\\n\\n**Proposition 4.2.2.** + *Let $X$ be a scheme. For any closed immersion $i: Z \\\\hookrightarrow X$, + the kernel $\\\\mathcal{I}_Z = \\\\ker(i^\\\\#: \\\\mathcal{O}_X \\\\twoheadrightarrow + i_*\\\\mathcal{O}_Z)$ is a quasi-coherent sheaf of ideals of $\\\\mathcal{O}_X$. + Conversely, for any quasi-coherent sheaf of ideals $\\\\mathcal{I} \\\\subseteq + \\\\mathcal{O}_X$, the support $Z = \\\\operatorname{Supp}(\\\\mathcal{O}_X/\\\\mathcal{I}) + = \\\\{P \\\\in X \\\\mid (\\\\mathcal{O}_X/\\\\mathcal{I})_P \\\\neq 0\\\\}$ + is a closed subset of $X$, and $(Z, (\\\\mathcal{O}_X/\\\\mathcal{I})|_Z)$ + is a closed subscheme of $X$. This establishes a bijection between closed + subschemes of $X$ (up to isomorphism over $X$) and quasi-coherent sheaves + of ideals $\\\\mathcal{I} \\\\subseteq \\\\mathcal{O}_X$.*\\n\\n*Proof.* Since + the question is local on $X$, we may assume $X = \\\\operatorname{Spec} A$ + is affine. If $\\\\mathcal{I} \\\\subseteq \\\\mathcal{O}_X$ is a quasi-coherent + sheaf of ideals, then by Theorem 4.1.5, $\\\\mathcal{I} = \\\\widetilde{\\\\mathfrak{a}}$ + for the ideal $\\\\mathfrak{a} = \\\\Gamma(X, \\\\mathcal{I}) \\\\subseteq + \\\\Gamma(X, \\\\mathcal{O}_X) = A$. By exactness of $M \\\\mapsto \\\\widetilde{M}$ + (Theorem 4.1.3(3)), the exact sequence $0 \\\\to \\\\mathfrak{a} \\\\to A + \\\\to A/\\\\mathfrak{a} \\\\to 0$ yields an exact sequence of sheaves $0 + \\\\to \\\\widetilde{\\\\mathfrak{a}} \\\\to \\\\mathcal{O}_{\\\\operatorname{Spec} + A} \\\\to i_*\\\\mathcal{O}_{\\\\operatorname{Spec}(A/\\\\mathfrak{a})} \\\\to + 0$, showing that $(Z, (\\\\mathcal{O}_X/\\\\mathcal{I})|_Z) \\\\cong \\\\operatorname{Spec}(A/\\\\mathfrak{a})$ + is a closed subscheme of $\\\\operatorname{Spec} A$.\\n\\nConversely, let + $i: Z \\\\hookrightarrow X = \\\\operatorname{Spec} A$ be any closed immersion. + We must show that $\\\\mathcal{I}_Z = \\\\ker(\\\\mathcal{O}_X \\\\twoheadrightarrow + i_*\\\\mathcal{O}_Z)$ is quasi-coherent (which simultaneously proves that + every closed subscheme of an affine scheme $\\\\operatorname{Spec} A$ is itself + affine of the form $\\\\operatorname{Spec}(A/\\\\mathfrak{a})$!). Since $i$ + is a homeomorphism of $Z$ onto a closed subset of $X$, for each $P \\\\in + Z$ we can choose an affine open neighborhood $V_P \\\\subseteq Z$, whose complement + $Z \\\\setminus V_P$ is closed in $Z$ and hence closed in $X$. Thus $X \\\\setminus + (Z \\\\setminus V_P)$ is an open neighborhood of $P$ in $X$, containing a + basic open set $D(g_P) \\\\subseteq X$ with $P \\\\in D(g_P)$ and $Z \\\\cap + D(g_P) \\\\subseteq V_P$. Since $D(g_P) \\\\cap Z = D_{V_P}(i^\\\\#(g_P))$ + is a basic open subset of the affine scheme $V_P$, $Z \\\\cap D(g_P)$ is affine! + Covering $X \\\\setminus Z$ by basic open sets $D(h_q)$ on which $Z \\\\cap + D(h_q) = \\\\varnothing = \\\\operatorname{Spec} 0$, we obtain a cover of + $X = \\\\operatorname{Spec} A$ by basic open subsets $D(f_j)$ such that for + every $j$, $Z_j = i^{-1}(D(f_j))$ is an *affine* scheme $\\\\operatorname{Spec} + B_j$. On each $D(f_j) = \\\\operatorname{Spec} A_{f_j}$, the map $A_{f_j} + \\\\to B_j$ has kernel $\\\\mathfrak{a}_j$, and exactness of tilde gives $\\\\mathcal{I}_Z|_{D(f_j)} + \\\\cong \\\\widetilde{\\\\mathfrak{a}_j}$. Thus $\\\\mathcal{I}_Z$ is locally + of the form $\\\\widetilde{\\\\mathfrak{a}_j}$ on an affine open cover of + $X$, meaning $\\\\mathcal{I}_Z$ is quasi-coherent! By Theorem 4.1.5, $\\\\mathcal{I}_Z + = \\\\widetilde{\\\\mathfrak{a}}$ for $\\\\mathfrak{a} = \\\\Gamma(X, \\\\mathcal{I}_Z) + \\\\subseteq A$, and $Z \\\\cong \\\\operatorname{Spec}(A/\\\\mathfrak{a})$. + $\\\\blacksquare$\\n\\nFinally, on a projective scheme $X = \\\\operatorname{Proj} + S$, we can construct quasi-coherent sheaves from graded $S$-modules, including + the crucial twisting sheaves $\\\\mathcal{O}_X(n)$.\\n\\n**Definition 4.2.3.** + Let $S = \\\\bigoplus_{d \\\\ge 0} S_d$ be a graded ring and $X = \\\\operatorname{Proj} + S$.\\n1. For any $\\\\mathbb{Z}$-graded $S$-module $M = \\\\bigoplus_{d \\\\in + \\\\mathbb{Z}} M_d$, we define a quasi-coherent $\\\\mathcal{O}_X$-module + $\\\\widetilde{M}$ on $X$ whose stalk at $\\\\mathfrak{p} \\\\in X$ is the + degree-zero localization $M_{(\\\\mathfrak{p})}$, and whose restriction to + each basic open set $D_+(f) \\\\cong \\\\operatorname{Spec} S_{(f)}$ is the + affine tilde sheaf $\\\\widetilde{M_{(f)}}$, where $M_{(f)} = (M_f)_0$.\\n2. + For any integer $n \\\\in \\\\mathbb{Z}$, define the shifted graded $S$-module + $S(n)$ by setting $S(n)_d = S_{n+d}$. We define the *twisting sheaf of Serre* + $\\\\mathcal{O}_X(n)$ to be\\n $$\\\\mathcal{O}_X(n) = \\\\widetilde{S(n)}.$$\\n + \ In particular, $\\\\mathcal{O}_X(1)$ is called the *twisting sheaf* (or + *tautological very ample line bundle*). For any $\\\\mathcal{O}_X$-module + $\\\\mathcal{F}$, we write $\\\\mathcal{F}(n) = \\\\mathcal{F} \\\\otimes_{\\\\mathcal{O}_X} + \\\\mathcal{O}_X(n)$.\\n\\nSuppose $S$ is generated by $S_1$ as an $S_0$-algebra + (as is the case for $\\\\mathbb{P}^r_A = \\\\operatorname{Proj} A[x_0, \\\\dots, + x_r]$). Then $X = \\\\operatorname{Proj} S$ is covered by the open sets $D_+(f)$ + for $f \\\\in S_1$ of degree $1$. On $D_+(f)$, the module $S(n)_{(f)}$ consists + of fractions $a/f^m$ with $a \\\\in S(n)_m = S_{n+m}$. Multiplication by $f^n$ + gives an isomorphism of $S_{(f)}$-modules $S_{(f)} \\\\xrightarrow{\\\\sim} + S(n)_{(f)}$ ($b/f^m \\\\mapsto (f^n b)/f^m$). Therefore, when $S$ is generated + by $S_1$, each $\\\\mathcal{O}_X(n)$ is a *locally free $\\\\mathcal{O}_X$-module + of rank $1$* (an *invertible sheaf*), and $\\\\mathcal{O}_X(n) \\\\otimes_{\\\\mathcal{O}_X} + \\\\mathcal{O}_X(m) \\\\cong \\\\mathcal{O}_X(n+m)$.\\n\\n---\\n\\n### 4.3 + Differentials and Smoothness\\n\\nIn differential geometry, the tangent bundle + and cotangent bundle are defined locally using smooth coordinates and transition + matrices. In algebraic geometry, where schemes may have singularities or nilpotent + elements and live over arbitrary base rings, the cotangent bundle is algebraicized + via the *module of K\xE4hler differentials*.\\n\\n**Definition 4.3.1.** Let + $A$ be a commutative ring, $B$ an $A$-algebra, and $M$ a $B$-module. An *$A$-derivation* + of $B$ into $M$ is a map $d: B \\\\to M$ such that:\\n1. $d$ is additive: + $d(b_1 + b_2) = d(b_1) + d(b_2)$ for all $b_1, b_2 \\\\in B$,\\n2. $d$ satisfies + the Leibniz rule: $d(b_1 b_2) = b_1 d(b_2) + b_2 d(b_1)$ for all $b_1, b_2 + \\\\in B$, and\\n3. $d(a \\\\cdot 1_B) = 0$ for all $a \\\\in A$ (equivalently, + $d$ is $A$-linear).\\n\\nThe set of all $A$-derivations from $B$ to $M$ forms + a $B$-module denoted $\\\\operatorname{Der}_A(B, M)$.\\n\\n**Proposition 4.3.2 + (Construction and Universal Property of K\xE4hler Differentials).** *Let $B$ + be an $A$-algebra. There exists a $B$-module $\\\\Omega_{B/A}^1$ (or $\\\\Omega_{B/A}$) + and a universal $A$-derivation $d: B \\\\to \\\\Omega_{B/A}^1$ such that for + every $B$-module $M$, the map $\\\\operatorname{Hom}_B(\\\\Omega_{B/A}^1, + M) \\\\to \\\\operatorname{Der}_A(B, M)$ given by $\\\\varphi \\\\mapsto \\\\varphi + \\\\circ d$ is an isomorphism of $B$-modules. Explicitly:*\\n1. $\\\\Omega_{B/A}^1$ + *can be constructed as the quotient of the free $B$-module generated by symbols + $\\\\{db \\\\mid b \\\\in B\\\\}$ modulo the $B$-submodule generated by the + relations $d(b_1 + b_2) - db_1 - db_2$, $d(b_1 b_2) - b_1 db_2 - b_2 db_1$, + and $da$ for $a \\\\in A$.*\\n2. **(Diagonal / Conormal Construction)** *Let + $\\\\mu: B \\\\otimes_A B \\\\to B$ be the multiplication homomorphism $b_1 + \\\\otimes b_2 \\\\mapsto b_1 b_2$, and let $I = \\\\ker(\\\\mu) \\\\subseteq + B \\\\otimes_A B$. Then $I/I^2$ is naturally a module over $(B \\\\otimes_A + B)/I \\\\cong B$, and there is a canonical isomorphism of $B$-modules*\\n + \ $$\\\\Omega_{B/A}^1 \\\\xrightarrow{\\\\;\\\\sim\\\\;} I / I^2, \\\\qquad + db \\\\longmapsto (1 \\\\otimes b - b \\\\otimes 1) \\\\bmod I^2.$$\\n\\n*Proof.* + Construction (1) satisfies the universal property immediately by definition + of generators and relations. To establish (2), define $d': B \\\\to I/I^2$ + by $d'(b) = (1 \\\\otimes b - b \\\\otimes 1) \\\\bmod I^2$, where $B$ acts + on $I/I^2$ via the left factor $b \\\\cdot \\\\bar{x} = (b \\\\otimes 1)\\\\bar{x}$ + (which agrees with multiplication by $1 \\\\otimes b$ modulo $I^2$ since $b + \\\\otimes 1 - 1 \\\\otimes b \\\\in I$). Clearly $d'$ is $A$-linear, and + for any $b_1, b_2 \\\\in B$, we have in $B \\\\otimes_A B$:\\n$$1 \\\\otimes + b_1 b_2 - b_1 b_2 \\\\otimes 1 = (b_1 \\\\otimes 1)(1 \\\\otimes b_2 - b_2 + \\\\otimes 1) + (b_2 \\\\otimes 1)(1 \\\\otimes b_1 - b_1 \\\\otimes 1) + + (1 \\\\otimes b_1 - b_1 \\\\otimes 1)(1 \\\\otimes b_2 - b_2 \\\\otimes 1).$$\\nSince + the last product belongs to $I^2$, reducing modulo $I^2$ gives $d'(b_1 b_2) + = b_1 d'(b_2) + b_2 d'(b_1)$. Thus $d'$ is an $A$-derivation, inducing a $B$-module + homomorphism $\\\\alpha: \\\\Omega_{B/A}^1 \\\\to I/I^2$ sending $db \\\\mapsto + d'(b)$.\\n\\nConversely, any element of $I = \\\\ker(\\\\mu)$ is of the form + $\\\\sum b_i \\\\otimes c_i$ with $\\\\sum b_i c_i = 0$, hence can be rewritten + as $\\\\sum (b_i \\\\otimes 1)(1 \\\\otimes c_i - c_i \\\\otimes 1)$. Define + a $B \\\\otimes_A B$-linear map $\\\\tilde{\\\\beta}: B \\\\otimes_A B \\\\to + \\\\text{End}_{\\\\text{Set}}(\\\\Omega_{B/A}^1)$ or directly a map $B \\\\otimes_A + B \\\\to \\\\Omega_{B/A}^1$ by $b_1 \\\\otimes b_2 \\\\mapsto b_1 db_2$. On + $I^2$, any product of two generators $(1 \\\\otimes b_1 - b_1 \\\\otimes 1)(1 + \\\\otimes b_2 - b_2 \\\\otimes 1) = 1 \\\\otimes b_1 b_2 - b_1 \\\\otimes + b_2 - b_2 \\\\otimes b_1 + b_1 b_2 \\\\otimes 1$ maps to $d(b_1 b_2) - b_1 + db_2 - b_2 db_1 + b_1 b_2 d(1) = 0$ by the Leibniz rule! Thus restricting + to $I$ and passing to $I/I^2$ gives a well-defined $B$-module homomorphism + $\\\\beta: I/I^2 \\\\to \\\\Omega_{B/A}^1$ sending $(1 \\\\otimes b - b \\\\otimes + 1) \\\\bmod I^2 \\\\mapsto db - b d(1) = db$. Clearly $\\\\alpha$ and $\\\\beta$ + are mutually inverse isomorphisms. $\\\\blacksquare$\\n\\n**Theorem 4.3.3 + (The Two Fundamental Exact Sequences for Differentials).**\\n1. **(First Exact + Sequence)** *Let $A \\\\to B \\\\to C$ be ring homomorphisms. There is a canonical + exact sequence of $C$-modules:*\\n $$\\\\Omega_{B/A}^1 \\\\otimes_B C \\\\xrightarrow{\\\\;\\\\;\\\\alpha\\\\;\\\\;} + \\\\Omega_{C/A}^1 \\\\xrightarrow{\\\\;\\\\;\\\\beta\\\\;\\\\;} \\\\Omega_{C/B}^1 + \\\\longrightarrow 0,$$\\n *where $\\\\alpha(db \\\\otimes c) = c \\\\cdot + d(\\\\text{im } b)$ and $\\\\beta(dc) = dc$.*\\n2. **(Second / Conormal Exact + Sequence)** *Suppose $B \\\\twoheadrightarrow C = B/J$ is a surjective ring + homomorphism with kernel $J \\\\subseteq B$. Then $\\\\Omega_{C/B}^1 = 0$, + and there is a canonical exact sequence of $C$-modules:*\\n $$J / J^2 \\\\xrightarrow{\\\\;\\\\;\\\\delta\\\\;\\\\;} + \\\\Omega_{B/A}^1 \\\\otimes_B C \\\\xrightarrow{\\\\;\\\\;\\\\alpha\\\\;\\\\;} + \\\\Omega_{C/A}^1 \\\\longrightarrow 0,$$\\n *where $\\\\delta(x \\\\bmod + J^2) = dx \\\\otimes 1$.*\\n\\n*Proof.*By Yoneda's Lemma for $C$-modules, + a sequence of $C$-modules $M' \\\\to M \\\\to M'' \\\\to 0$ is exact if and + only if for every $C$-module $N$, the induced sequence $0 \\\\to \\\\operatorname{Hom}_C(M'', + N) \\\\to \\\\operatorname{Hom}_C(M, N) \\\\to \\\\operatorname{Hom}_C(M', + N)$ is exact.\\n\\n(1) For any $C$-module $N$, applying $\\\\operatorname{Hom}_C(-, + N)$ to the sequence in (1) and using the universal property of K\xE4hler differentials + (together with the tensor-Hom adjunction $\\\\operatorname{Hom}_C(\\\\Omega_{B/A}^1 + \\\\otimes_B C, N) \\\\cong \\\\operatorname{Hom}_B(\\\\Omega_{B/A}^1, N) + \\\\cong \\\\operatorname{Der}_A(B, N)$) produces the sequence\\n$$0 \\\\longrightarrow + \\\\operatorname{Der}_B(C, N) \\\\xrightarrow{\\\\;\\\\beta^*\\\\;} \\\\operatorname{Der}_A(C, + N) \\\\xrightarrow{\\\\;\\\\alpha^*\\\\;} \\\\operatorname{Der}_A(B, N).$$\\nHere + $\\\\beta^*$ is the natural inclusion of $B$-derivations into $A$-derivations, + and $\\\\alpha^*$ restricts an $A$-derivation $D: C \\\\to N$ along $B \\\\to + C$. An $A$-derivation $D: C \\\\to N$ belongs to $\\\\ker(\\\\alpha^*)$ if + and only if $D$ vanishes on the image of $B$ in $C$, which holds if and only + if $D$ is a $B$-derivation! Thus the sequence of derivations is exact for + all $N$, proving (1).\\n\\n(2) Since $B \\\\twoheadrightarrow C = B/J$ is + surjective, any $B$-derivation $C \\\\to N$ vanishes on the image of $B$, + which is all of $C$; hence $\\\\Omega_{C/B}^1 = 0$. Notice that for $x \\\\in + J$ and $b \\\\in B$, $d(bx) \\\\otimes 1 = b dx \\\\otimes 1 + x db \\\\otimes + 1 = dx \\\\otimes \\\\bar{b} + db \\\\otimes \\\\bar{x} = dx \\\\otimes \\\\bar{b}$ + since $\\\\bar{x} = 0$ in $C = B/J$. In particular, if $x, y \\\\in J$, $\\\\delta(xy) + = x dy \\\\otimes 1 + y dx \\\\otimes 1 = 0$, so $\\\\delta: J/J^2 \\\\to + \\\\Omega_{B/A}^1 \\\\otimes_B C$ is a well-defined $C$-linear map. For any + $C$-module $N$, applying $\\\\operatorname{Hom}_C(-, N)$ to the sequence in + (2) gives\\n$$0 \\\\longrightarrow \\\\operatorname{Der}_A(C, N) \\\\xrightarrow{\\\\;\\\\alpha^*\\\\;} + \\\\operatorname{Der}_A(B, N) \\\\xrightarrow{\\\\;\\\\delta^*\\\\;} \\\\operatorname{Hom}_C(J/J^2, + N) = \\\\operatorname{Hom}_B(J, N),$$\\nwhere $\\\\delta^*$ restricts an $A$-derivation + $D: B \\\\to N$ to $J \\\\subseteq B$ (note that since $J$ acts as zero on + the $C$-module $N$, for $x, y \\\\in J$ we have $D(xy) = x D(y) + y D(x) = + 0$, so $D|_J$ is a $B$-module homomorphism vanishing on $J^2$). An $A$-derivation + $D: B \\\\to N$ factors through $C = B/J$ if and only if $D(J) = 0$, which + means $D \\\\in \\\\ker(\\\\delta^*)$. Thus the sequence is exact for every + $N$, proving (2). $\\\\blacksquare$\\n\\nProposition 4.3.2(2) allows us to + globalize K\xE4hler differentials immediately to arbitrary morphisms of schemes.\\n\\n**Definition + 4.3.4.** Let $f: X \\\\to Y$ be a morphism of schemes. By Proposition 3.6.3, + the diagonal morphism $\\\\Delta: X \\\\to X \\\\times_Y X$ is a closed immersion + of $X$ into an open subscheme $W \\\\subseteq X \\\\times_Y X$. Let $\\\\mathcal{I} + \\\\subseteq \\\\mathcal{O}_W$ be the quasi-coherent sheaf of ideals defining + the closed subscheme $\\\\Delta(X) \\\\subseteq W$. We define the *sheaf of + relative differentials of $X$ over $Y$*, denoted $\\\\Omega_{X/Y}^1$, to be + the quasi-coherent $\\\\mathcal{O}_X$-module\\n$$\\\\Omega_{X/Y}^1 = \\\\Delta^*(\\\\mathcal{I}/\\\\mathcal{I}^2).$$\\nOn + any affine open subschemes $U = \\\\operatorname{Spec} B \\\\subseteq X$ and + $V = \\\\operatorname{Spec} A \\\\subseteq Y$ with $f(U) \\\\subseteq V$, + Proposition 4.3.2(2) gives a canonical isomorphism $\\\\Omega_{X/Y}^1|_U \\\\cong + \\\\widetilde{\\\\Omega_{B/A}^1}$. If $f: X \\\\to Y$ is locally of finite + type and $Y$ is locally Noetherian, then $\\\\Omega_{X/Y}^1$ is a coherent + $\\\\mathcal{O}_X$-module.\\n\\n**Theorem 4.3.5 (Regularity, Smoothness, and + the Jacobian Criterion).** *Let $k$ be an algebraically closed field, and + let $X$ be an irreducible scheme of finite type over $k$ of dimension $n$. + For a closed point $P \\\\in X$, we say that $X$ is non-singular (or regular) + at $P$ if the local ring $\\\\mathcal{O}_{X,P}$ is a regular local ring (meaning + $\\\\dim_k(\\\\mathfrak{m}_P/\\\\mathfrak{m}_P^2) = \\\\dim \\\\mathcal{O}_{X,P} + = n$).*\\n1. *For every closed point $P \\\\in X$, the fiber of $\\\\Omega_{X/k}^1$ + at $P$ is canonically isomorphic to the Zariski cotangent space:*\\n $$\\\\Omega_{X/k}^1 + \\\\otimes_{\\\\mathcal{O}_X} \\\\kappa(P) \\\\cong \\\\mathfrak{m}_P / \\\\mathfrak{m}_P^2.$$\\n2. + *$X$ is non-singular at every closed point (i.e., $X$ is smooth over $k$) + if and only if $\\\\Omega_{X/k}^1$ is a locally free $\\\\mathcal{O}_X$-module + of rank $n = \\\\dim X$.*\\n3. **(Jacobian Criterion)** *Suppose $X = \\\\operatorname{Spec} + k[x_1, \\\\dots, x_N]/(f_1, \\\\dots, f_r) \\\\subseteq \\\\mathbb{A}^N_k$. + Then $X$ is non-singular at a closed point $P \\\\in X$ if and only if the + Jacobian matrix $J_P = \\\\left(\\\\frac{\\\\partial f_i}{\\\\partial x_j}(P)\\\\right)$ + has rank $N - n$.*\\n\\n*Proof.* (1) Let $U = \\\\operatorname{Spec} B$ be + an affine open neighborhood of $P$, and let $\\\\mathfrak{m} \\\\subset B$ + be the maximal ideal corresponding to $P$, with $B/\\\\mathfrak{m} = \\\\kappa(P) + = k$. Applying the Second Fundamental Exact Sequence (Theorem 4.3.3(2)) to + $k \\\\to B \\\\twoheadrightarrow B/\\\\mathfrak{m} = k$ gives\\n$$\\\\mathfrak{m}/\\\\mathfrak{m}^2 + \\\\xrightarrow{\\\\;\\\\delta\\\\;} \\\\Omega_{B/k}^1 \\\\otimes_B k \\\\longrightarrow + \\\\Omega_{k/k}^1 = 0.$$\\nThus $\\\\delta$ is surjective. Moreover, for any + $k$-vector space $V$, $\\\\operatorname{Hom}_k(\\\\mathfrak{m}/\\\\mathfrak{m}^2, + V) \\\\cong \\\\operatorname{Der}_k(B, V)$ (sending $\\\\lambda: \\\\mathfrak{m}/\\\\mathfrak{m}^2 + \\\\to V$ to the derivation $b \\\\mapsto \\\\lambda((b - b(P)) \\\\bmod \\\\mathfrak{m}^2)$), + which is isomorphic to $\\\\operatorname{Hom}_k(\\\\Omega_{B/k}^1 \\\\otimes_B + k, V)$. Hence $\\\\delta: \\\\mathfrak{m}/\\\\mathfrak{m}^2 \\\\xrightarrow{\\\\sim} + \\\\Omega_{B/k}^1 \\\\otimes_B k = (\\\\Omega_{X/k}^1)_P \\\\otimes_{\\\\mathcal{O}_{X,P}} + k$ is an isomorphism. Since $\\\\mathfrak{m}_P = \\\\mathfrak{m}B_{\\\\mathfrak{m}}$, + we have $\\\\mathfrak{m}_P/\\\\mathfrak{m}_P^2 \\\\cong \\\\mathfrak{m}/\\\\mathfrak{m}^2$.\\n\\n(2) + By Nakayama's Lemma, for any finitely generated module $M$ over a Noetherian + local ring $(R, \\\\mathfrak{m}, k)$ of dimension $n$, $M$ is generated by + $\\\\dim_k(M/\\\\mathfrak{m}M)$ elements. If $R = \\\\mathcal{O}_{X,P}$ is + a domain with fraction field $K(X)$ (which is a finitely generated field extension + of $k$ of transcendence degree $n$, so $\\\\dim_{K(X)} \\\\Omega_{K(X)/k}^1 + = n$), then $(\\\\Omega_{X/k}^1)_P$ is a free $\\\\mathcal{O}_{X,P}$-module + of rank $n$ if and only if $\\\\dim_k((\\\\Omega_{X/k}^1)_P \\\\otimes k) + = n$, which by (1) is equivalent to $\\\\dim_k(\\\\mathfrak{m}_P/\\\\mathfrak{m}_P^2) + = n$, i.e., $\\\\mathcal{O}_{X,P}$ is regular.\\n\\n(3) Let $A = k[x_1, \\\\dots, + x_N]$, $J = (f_1, \\\\dots, f_r)$, and $B = A/J$. Notice that $\\\\Omega_{A/k}^1 + = \\\\bigoplus_{j=1}^N A \\\\, dx_j$ is free of rank $N$, with $df = \\\\sum_{j=1}^N + \\\\frac{\\\\partial f}{\\\\partial x_j} dx_j$. Applying Theorem 4.3.3(2) + to $k \\\\to A \\\\twoheadrightarrow B$ and tensoring with $\\\\kappa(P) = + k$ gives the right-exact sequence of $k$-vector spaces:\\n$$J/J^2 \\\\otimes_B + k \\\\xrightarrow{\\\\;\\\\bar{\\\\delta}_P\\\\;} \\\\Omega_{A/k}^1 \\\\otimes_A + k \\\\cong k^N \\\\longrightarrow \\\\Omega_{B/k}^1 \\\\otimes_B k \\\\cong + \\\\mathfrak{m}_P/\\\\mathfrak{m}_P^2 \\\\longrightarrow 0.$$\\nThe image + of $\\\\bar{\\\\delta}_P$ is spanned by $\\\\delta(f_i)_P = \\\\sum_{j=1}^N + \\\\frac{\\\\partial f_i}{\\\\partial x_j}(P) dx_j$, so $\\\\dim_k(\\\\operatorname{im} + \\\\bar{\\\\delta}_P) = \\\\operatorname{rank}(J_P)$. By exactness, $\\\\dim_k(\\\\mathfrak{m}_P/\\\\mathfrak{m}_P^2) + = N - \\\\operatorname{rank}(J_P)$. Since $\\\\dim_k(\\\\mathfrak{m}_P/\\\\mathfrak{m}_P^2) + \\\\ge \\\\dim \\\\mathcal{O}_{X,P} = n$ always (by Krull's Principal Ideal + Theorem), equality holds if and only if $\\\\operatorname{rank}(J_P) = N - + n$. $\\\\blacksquare$\\n\\n---\\n\\n### Exercises for Chapter 4\\n\\n**Exercise + 4.1.** Let $X$ be a scheme and $\\\\mathcal{F}$ a quasi-coherent $\\\\mathcal{O}_X$-module. + We say $\\\\mathcal{F}$ is *locally free of rank $r$* if $X$ can be covered + by open subsets $U$ on which $\\\\mathcal{F}|_U \\\\cong \\\\mathcal{O}_U^{\\\\oplus + r}$.\\n(a) Suppose $X$ is locally Noetherian and $\\\\mathcal{F}$ is a coherent + $\\\\mathcal{O}_X$-module. Prove that $\\\\mathcal{F}$ is locally free of + rank $r$ if and only if for every point $P \\\\in X$, the stalk $\\\\mathcal{F}_P$ + is a free $\\\\mathcal{O}_{X,P}$-module of rank $r$. *(Hint: Use coherence + to lift a basis of $\\\\mathcal{F}_P$ to a neighborhood $U$ of $P$, and apply + coherence to the kernel and cokernel of $\\\\mathcal{O}_U^{\\\\oplus r} \\\\to + \\\\mathcal{F}|_U$.)*\\n(b) Prove that if $X$ is connected and locally Noetherian, + and $\\\\mathcal{F}$ is coherent, then $\\\\mathcal{F}$ is locally free if + and only if the function $P \\\\mapsto \\\\dim_{\\\\kappa(P)}(\\\\mathcal{F}_P + \\\\otimes_{\\\\mathcal{O}_{X,P}} \\\\kappa(P))$ is constant on $X$ (assuming + $X$ is reduced; show by example with $X = \\\\operatorname{Spec} k[x]/(x^2)$ + that reducedness is necessary for the converse!).\\n\\n**Exercise 4.2.** (The + Euler Exact Sequence on $\\\\mathbb{P}^n_A$) Let $A$ be a commutative ring + and $X = \\\\mathbb{P}^n_A = \\\\operatorname{Proj} S$, where $S = A[x_0, + \\\\dots, x_n]$.\\n(a) Prove that there is a canonical short exact sequence + of locally free sheaves on $X = \\\\mathbb{P}^n_A$:\\n$$0 \\\\longrightarrow + \\\\Omega_{X/A}^1 \\\\longrightarrow \\\\mathcal{O}_X(-1)^{\\\\oplus (n+1)} + \\\\xrightarrow{\\\\;\\\\;u\\\\;\\\\;} \\\\mathcal{O}_X \\\\longrightarrow + 0,$$\\nwhere $u$ is induced by the graded $S$-module homomorphism $S(-1)^{\\\\oplus + (n+1)} \\\\to S$ sending $(f_0, \\\\dots, f_n) \\\\mapsto \\\\sum_{i=0}^n + x_i f_i$. *(Hint: Restrict to the affine charts $U_i = D_+(x_i)$ and compare + the kernel of $u|_{U_i}$ with $\\\\Omega_{U_i/A}^1 = \\\\bigoplus_{j \\\\neq + i} \\\\mathcal{O}_{U_i} d(x_j/x_i)$ via $dx_j \\\\mapsto e_j \\\\in S(-1)^{\\\\oplus + (n+1)}$ and the Euler identity $\\\\sum_{j=0}^n x_j dx_j = 0$.)*\\n(b) Deduce + that the *canonical sheaf* $\\\\omega_{X/A} = \\\\bigwedge^n \\\\Omega_{X/A}^1$ + of $\\\\mathbb{P}^n_A$ is canonically isomorphic to $\\\\mathcal{O}_{\\\\mathbb{P}^n_A}(-n-1)$.\\n\\n**Exercise + 4.3.** Let $X$ be a scheme and $\\\\mathcal{L}$ an invertible sheaf on $X$ + (a locally free $\\\\mathcal{O}_X$-module of rank $1$).\\n(a) Prove that the + dual sheaf $\\\\mathcal{L}^\\\\vee = \\\\mathcal{H}om_{\\\\mathcal{O}_X}(\\\\mathcal{L}, + \\\\mathcal{O}_X)$ is also an invertible sheaf, and that the evaluation map + $\\\\mathcal{L} \\\\otimes_{\\\\mathcal{O}_X} \\\\mathcal{L}^\\\\vee \\\\to + \\\\mathcal{O}_X$ is an isomorphism.\\n(b) Prove that the set of isomorphism + classes of invertible sheaves on $X$ forms an abelian group under $\\\\otimes_{\\\\mathcal{O}_X}$, + called the *Picard group* $\\\\operatorname{Pic}(X)$ of $X$.\\n\\n**Exercise + 4.4.** Let $A$ be a ring and $X = \\\\mathbb{P}^n_A = \\\\operatorname{Proj} + A[x_0, \\\\dots, x_n]$. Compute the global sections $\\\\Gamma(X, \\\\mathcal{O}_X(m))$ + for all $m \\\\in \\\\mathbb{Z}$ directly by intersecting the modules of sections + over the standard affine open cover $U_i = D_+(x_i)$ inside $\\\\Gamma(\\\\bigcap_{i=0}^n + U_i, \\\\mathcal{O}_X(m)) = A[x_0^{\\\\pm 1}, \\\\dots, x_n^{\\\\pm 1}]_m$, + and prove that the natural homomorphism $S_m \\\\to \\\\Gamma(\\\\mathbb{P}^n_A, + \\\\mathcal{O}_{\\\\mathbb{P}^n_A}(m))$ is an isomorphism for all $m \\\\in + \\\\mathbb{Z}$ (in particular, $\\\\Gamma(\\\\mathbb{P}^n_A, \\\\mathcal{O}_{\\\\mathbb{P}^n_A}(m)) + = 0$ for $m \\u003c 0$).\\n\\n**Exercise 4.5.** (Projection Formula) Let $f: + X \\\\to Y$ be a quasi-compact, quasi-separated morphism of schemes, $\\\\mathcal{F}$ + a quasi-coherent $\\\\mathcal{O}_X$-module, and $\\\\mathcal{E}$ a locally + free $\\\\mathcal{O}_Y$-module of finite rank. Construct a canonical isomorphism + of $\\\\mathcal{O}_Y$-modules\\n$$f_*(\\\\mathcal{F} \\\\otimes_{\\\\mathcal{O}_X} + f^*\\\\mathcal{E}) \\\\xrightarrow{\\\\;\\\\sim\\\\;} f_*\\\\mathcal{F} \\\\otimes_{\\\\mathcal{O}_Y} + \\\\mathcal{E}.$$\\n\\n**Exercise 4.6.** Let $k$ be a field of characteristic + $p \\u003e 0$, and let $K = k(t)$ be the rational function field in one variable. + Compute $\\\\Omega_{K/k}^1$ and $\\\\Omega_{K/k(t^p)}^1$, and compare this + with the general theorem that a finitely generated algebraic field extension + $L/F$ is separable if and only if $\\\\Omega_{L/F}^1 = 0$.\\n\\n---\\n\\n## + Chapter 5: Cohomology of Sheaves, Divisors, and Algebraic Curves\\n\\nAs noted + in Proposition 2.2.3(3), the global sections functor $\\\\Gamma(X, -)$ is + left-exact, but generally fails to be right-exact: given a short exact sequence + of sheaves $0 \\\\to \\\\mathcal{F}' \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{F}'' + \\\\to 0$, a global section of $\\\\mathcal{F}''$ can be lifted locally to + $\\\\mathcal{F}$ on an open cover $\\\\{U_i\\\\}$, but the differences of + these local lifts on overlaps $U_i \\\\cap U_j$ form an obstruction in $\\\\mathcal{F}'(U_i + \\\\cap U_j)$ to gluing them into a global section of $\\\\mathcal{F}$. Sheaf + cohomology systematically measures these obstructions and provides the most + powerful quantitative invariants in algebraic geometry.\\n\\n---\\n\\n### + 5.1 Derived Functor Cohomology of Sheaves\\n\\nLet $\\\\mathfrak{A}$ be an + abelian category (such as $\\\\mathfrak{Ab}(X)$ or $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$). + Recall that an object $I \\\\in \\\\mathfrak{A}$ is called *injective* if + the functor $\\\\operatorname{Hom}_{\\\\mathfrak{A}}(-, I)$ is exact; that + is, for every monomorphism (injective morphism) $A \\\\hookrightarrow B$ in + $\\\\mathfrak{A}$ and every morphism $f: A \\\\to I$, there exists an extension + $\\\\tilde{f}: B \\\\to I$ of $f$ to $B$. We say that $\\\\mathfrak{A}$ *has + enough injectives* if every object $M \\\\in \\\\mathfrak{A}$ admits a monomorphism + $M \\\\hookrightarrow I$ into an injective object $I \\\\in \\\\mathfrak{A}$.\\n\\n**Theorem + 5.1.1.** *For any ringed space $(X, \\\\mathcal{O}_X)$, the category $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$ + of $\\\\mathcal{O}_X$-modules (and in particular $\\\\mathfrak{Ab}(X) = \\\\mathfrak{Mod}(\\\\underline{\\\\mathbb{Z}}_X)$) + has enough injectives.*\\n\\n*Proof.* First recall a standard fact from commutative + algebra (Baer's Criterion and coinduction): for any ring $R$, the category + $\\\\mathfrak{Mod}(R)$ of $R$-modules has enough injectives. (Specifically, + any abelian group $M$ embeds into the divisible\u2014hence $\\\\mathbb{Z}$-injective\u2014group + $J = \\\\prod_{f \\\\in \\\\operatorname{Hom}_{\\\\mathbb{Z}}(M, \\\\mathbb{Q}/\\\\mathbb{Z})} + \\\\mathbb{Q}/\\\\mathbb{Z}$, and any $R$-module $M$ embeds into $\\\\operatorname{Hom}_{\\\\mathbb{Z}}(R, + M) \\\\hookrightarrow \\\\operatorname{Hom}_{\\\\mathbb{Z}}(R, J)$, which + is injective in $\\\\mathfrak{Mod}(R)$ because $\\\\operatorname{Hom}_R(N, + \\\\operatorname{Hom}_{\\\\mathbb{Z}}(R, J)) \\\\cong \\\\operatorname{Hom}_{\\\\mathbb{Z}}(N, + J)$ is an exact functor of $N$.)\\n\\nNow let $\\\\mathcal{F}$ be an $\\\\mathcal{O}_X$-module. + For each point $P \\\\in X$, the stalk $\\\\mathcal{F}_P$ is an $\\\\mathcal{O}_{X,P}$-module, + so by the paragraph above we may choose an injective $\\\\mathcal{O}_{X,P}$-module + $I_P$ and an injective $\\\\mathcal{O}_{X,P}$-module homomorphism $\\\\alpha_P: + \\\\mathcal{F}_P \\\\hookrightarrow I_P$. Let $i_P: \\\\{P\\\\} \\\\hookrightarrow + X$ be the inclusion of the one-point space $\\\\{P\\\\}$ into $X$, and consider + the skyscraper sheaf $(i_P)_*(I_P)$ on $X$. Define an $\\\\mathcal{O}_X$-module + $\\\\mathcal{I}$ by taking the direct product over all points of $X$:\\n$$\\\\mathcal{I} + = \\\\prod_{P \\\\in X} (i_P)_*(I_P), \\\\quad \\\\text{so that for every + open } U \\\\subseteq X, \\\\quad \\\\mathcal{I}(U) = \\\\prod_{P \\\\in U} + I_P.$$\\nThere is a canonical morphism of $\\\\mathcal{O}_X$-modules $\\\\alpha: + \\\\mathcal{F} \\\\to \\\\mathcal{I}$ given over each open $U \\\\subseteq + X$ by sending $s \\\\in \\\\mathcal{F}(U)$ to $(\\\\alpha_P(s_P))_{P \\\\in + U} \\\\in \\\\prod_{P \\\\in U} I_P$. If $s \\\\in \\\\ker(\\\\alpha(U))$, + then $\\\\alpha_P(s_P) = 0$ for all $P \\\\in U$, which implies $s_P = 0$ + for all $P \\\\in U$ (since $\\\\alpha_P$ is injective), and hence $s = 0$ + by the Locality Axiom. Thus $\\\\alpha: \\\\mathcal{F} \\\\hookrightarrow + \\\\mathcal{I}$ is a monomorphism in $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$.\\n\\nFinally, + for any $\\\\mathcal{O}_X$-module $\\\\mathcal{G}$, notice that specifying + a morphism $\\\\mathcal{G} \\\\to (i_P)_*(I_P)$ is equivalent to specifying + an $\\\\mathcal{O}_{X,P}$-module homomorphism $\\\\mathcal{G}_P \\\\to I_P$. + Therefore, we have a natural isomorphism of functors:\\n$$\\\\operatorname{Hom}_{\\\\mathcal{O}_X}(\\\\mathcal{G}, + \\\\mathcal{I}) = \\\\prod_{P \\\\in X} \\\\operatorname{Hom}_{\\\\mathcal{O}_X}(\\\\mathcal{G}, + (i_P)_*(I_P)) \\\\cong \\\\prod_{P \\\\in X} \\\\operatorname{Hom}_{\\\\mathcal{O}_{X,P}}(\\\\mathcal{G}_P, + I_P).$$\\nSince taking stalks $\\\\mathcal{G} \\\\mapsto \\\\mathcal{G}_P$ + is an exact functor, $\\\\operatorname{Hom}_{\\\\mathcal{O}_{X,P}}(-, I_P)$ + is exact (as $I_P$ is an injective $\\\\mathcal{O}_{X,P}$-module), and arbitrary + direct products of exact sequences of abelian groups are exact, the functor + $\\\\operatorname{Hom}_{\\\\mathcal{O}_X}(-, \\\\mathcal{I})$ is exact! Thus + $\\\\mathcal{I}$ is an injective object of $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$. + $\\\\blacksquare$\\n\\nBy Theorem 5.1.1, every $\\\\mathcal{O}_X$-module (or + sheaf of abelian groups) $\\\\mathcal{F}$ admits an *injective resolution*: + an exact sequence\\n$$0 \\\\longrightarrow \\\\mathcal{F} \\\\longrightarrow + \\\\mathcal{I}^0 \\\\xrightarrow{\\\\;d^0\\\\;} \\\\mathcal{I}^1 \\\\xrightarrow{\\\\;d^1\\\\;} + \\\\mathcal{I}^2 \\\\xrightarrow{\\\\;d^2\\\\;} \\\\dots$$\\nwhere each $\\\\mathcal{I}^i$ + is injective.\\n\\n**Definition 5.1.2.** Let $X$ be a topological space and + $\\\\mathcal{F} \\\\in \\\\mathfrak{Ab}(X)$ a sheaf of abelian groups on $X$. + Choose an injective resolution $0 \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{I}^\\\\bullet$ + of $\\\\mathcal{F}$ in $\\\\mathfrak{Ab}(X)$. The *$i$-th sheaf cohomology + group* of $X$ with coefficients in $\\\\mathcal{F}$, denoted $H^i(X, \\\\mathcal{F})$, + is defined to be the $i$-th cohomology group of the complex of global sections + $\\\\Gamma(X, \\\\mathcal{I}^\\\\bullet)$:\\n$$H^i(X, \\\\mathcal{F}) = R^i\\\\Gamma(X, + \\\\mathcal{F}) = \\\\frac{\\\\ker(\\\\Gamma(X, \\\\mathcal{I}^i) \\\\xrightarrow{d^i} + \\\\Gamma(X, \\\\mathcal{I}^{i+1}))}{\\\\operatorname{im}(\\\\Gamma(X, \\\\mathcal{I}^{i-1}) + \\\\xrightarrow{d^{i-1}} \\\\Gamma(X, \\\\mathcal{I}^i))}.$$\\n\\nBy the fundamental + lemma of homological algebra, any two injective resolutions of $\\\\mathcal{F}$ + are chain homotopy equivalent, so $H^i(X, \\\\mathcal{F})$ is well-defined + up to canonical isomorphism and is functorial in $\\\\mathcal{F}$. Moreover:\\n1. + By left-exactness of $\\\\Gamma(X, -)$, $H^0(X, \\\\mathcal{F}) = \\\\ker(\\\\Gamma(X, + \\\\mathcal{I}^0) \\\\to \\\\Gamma(X, \\\\mathcal{I}^1)) \\\\cong \\\\Gamma(X, + \\\\mathcal{F})$.\\n2. For any short exact sequence $0 \\\\to \\\\mathcal{F}' + \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{F}'' \\\\to 0$ of sheaves on $X$, + there are canonical connecting homomorphisms $\\\\delta^i: H^i(X, \\\\mathcal{F}'') + \\\\to H^{i+1}(X, \\\\mathcal{F}')$ yielding a *long exact sequence of cohomology*:\\n + \ $$0 \\\\to H^0(X, \\\\mathcal{F}') \\\\to H^0(X, \\\\mathcal{F}) \\\\to + H^0(X, \\\\mathcal{F}'') \\\\xrightarrow{\\\\delta^0} H^1(X, \\\\mathcal{F}') + \\\\to H^1(X, \\\\mathcal{F}) \\\\to H^1(X, \\\\mathcal{F}'') \\\\xrightarrow{\\\\delta^1} + H^2(X, \\\\mathcal{F}') \\\\to \\\\dots$$\\n\\nTo show that computing cohomology + in $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$ gives the exact same groups as in + $\\\\mathfrak{Ab}(X)$, we introduce *flasque* (or *flabby*) sheaves.\\n\\n**Definition + 5.1.3.** A sheaf $\\\\mathcal{F}$ on $X$ is called *flasque* (or *flabby*) + if for every inclusion of open subsets $V \\\\subseteq U \\\\subseteq X$, + the restriction map $\\\\mathcal{F}(U) \\\\to \\\\mathcal{F}(V)$ is surjective.\\n\\nNotice + that the skyscraper products $\\\\mathcal{I} = \\\\prod_{P \\\\in X} (i_P)_*(I_P)$ + constructed in Theorem 5.1.1 are obviously flasque, because $\\\\prod_{P \\\\in + X} I_P \\\\to \\\\prod_{P \\\\in V} I_P$ is a projection onto a subproduct + and hence surjective. In fact, every injective object in $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$ + (or $\\\\mathfrak{Ab}(X)$) is a direct summand of such a product, hence is + flasque!\\n\\n**Proposition 5.1.4.**\\n1. *If $0 \\\\to \\\\mathcal{F}' \\\\to + \\\\mathcal{F} \\\\to \\\\mathcal{F}'' \\\\to 0$ is an exact sequence of sheaves + of abelian groups on $X$ and $\\\\mathcal{F}'$ is flasque, then for every + open subset $U \\\\subseteq X$, the sequence of sections $0 \\\\to \\\\mathcal{F}'(U) + \\\\to \\\\mathcal{F}(U) \\\\to \\\\mathcal{F}''(U) \\\\to 0$ is exact.*\\n2. + *If $0 \\\\to \\\\mathcal{F}' \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{F}'' + \\\\to 0$ is exact and both $\\\\mathcal{F}'$ and $\\\\mathcal{F}$ are flasque, + then $\\\\mathcal{F}''$ is also flasque.*\\n3. *Every flasque sheaf $\\\\mathcal{F}$ + is acyclic for $\\\\Gamma(X, -)$, meaning $H^i(X, \\\\mathcal{F}) = 0$ for + all $i \\\\ge 1$. Consequently, the cohomology groups $H^i(X, \\\\mathcal{F})$ + can be computed using any resolution of $\\\\mathcal{F}$ by flasque sheaves + (and in particular, using injective resolutions in $\\\\mathfrak{Mod}(\\\\mathcal{O}_X)$).*\\n\\n*Proof.* + (1) Fix an open set $U \\\\subseteq X$ and a section $t \\\\in \\\\mathcal{F}''(U)$. + Consider the set $\\\\mathfrak{P}$ of pairs $(V, s)$ where $V \\\\subseteq + U$ is open, $s \\\\in \\\\mathcal{F}(V)$, and $s$ maps to $t|_V \\\\in \\\\mathcal{F}''(V)$. + Order $\\\\mathfrak{P}$ by $(V, s) \\\\le (V', s')$ if $V \\\\subseteq V'$ + and $s'|_V = s$. By Zorn's Lemma, $\\\\mathfrak{P}$ has a maximal element + $(V, s)$. Suppose $V \\\\neq U$, and choose $P \\\\in U \\\\setminus V$. Since + $\\\\mathcal{F} \\\\to \\\\mathcal{F}''$ is surjective as a morphism of sheaves, + there exists an open neighborhood $W \\\\subseteq U$ of $P$ and a section + $\\\\sigma \\\\in \\\\mathcal{F}(W)$ mapping to $t|_W$. On the overlap $V + \\\\cap W$, the difference $s|_{V \\\\cap W} - \\\\sigma|_{V \\\\cap W}$ maps + to $0$ in $\\\\mathcal{F}''(V \\\\cap W)$, so it belongs to $\\\\mathcal{F}'(V + \\\\cap W)$. Since $\\\\mathcal{F}'$ is flasque, there exists a section $\\\\tau + \\\\in \\\\mathcal{F}'(W)$ restricting to $s|_{V \\\\cap W} - \\\\sigma|_{V + \\\\cap W}$ on $V \\\\cap W$. Replacing $\\\\sigma$ by $\\\\sigma + \\\\tau + \\\\in \\\\mathcal{F}(W)$, we have $s|_{V \\\\cap W} = (\\\\sigma + \\\\tau)|_{V + \\\\cap W}$, so $s$ and $\\\\sigma + \\\\tau$ glue to a section on $V \\\\cup + W \\\\supsetneq V$ lifting $t|_{V \\\\cup W}$, contradicting maximality of + $(V, s)$! Thus $V = U$, proving $\\\\mathcal{F}(U) \\\\to \\\\mathcal{F}''(U)$ + is surjective.\\n\\n(2) For $V \\\\subseteq U$, in the commutative diagram + with surjective rows $\\\\mathcal{F}(U) \\\\twoheadrightarrow \\\\mathcal{F}''(U)$ + and $\\\\mathcal{F}(V) \\\\twoheadrightarrow \\\\mathcal{F}''(V)$ (by (1)), + the left vertical map $\\\\mathcal{F}(U) \\\\twoheadrightarrow \\\\mathcal{F}(V)$ + is surjective since $\\\\mathcal{F}$ is flasque, forcing $\\\\mathcal{F}''(U) + \\\\to \\\\mathcal{F}''(V)$ to be surjective.\\n\\n(3) Embed a flasque sheaf + $\\\\mathcal{F}$ into an injective (hence flasque) sheaf $\\\\mathcal{I}^0$, + with quotient $\\\\mathcal{Q}$. By (2), $\\\\mathcal{Q}$ is flasque. By (1), + $0 \\\\to \\\\Gamma(X, \\\\mathcal{F}) \\\\to \\\\Gamma(X, \\\\mathcal{I}^0) + \\\\to \\\\Gamma(X, \\\\mathcal{Q}) \\\\to 0$ is exact. Taking the long exact + sequence of cohomology and using $H^i(X, \\\\mathcal{I}^0) = 0$ for $i \\\\ge + 1$ gives $H^1(X, \\\\mathcal{F}) = 0$ and $H^i(X, \\\\mathcal{F}) \\\\cong + H^{i-1}(X, \\\\mathcal{Q}) = 0$ for $i \\\\ge 2$ by induction on $i$. $\\\\blacksquare$\\n\\n---\\n\\n### + 5.2 \u010Cech Cohomology and Cohomology of Affine and Projective Spaces\\n\\nInjective + resolutions are massive and non-constructive. On schemes, we compute cohomology + concretely using *\u010Cech cohomology* with respect to an affine open cover.\\n\\n**Definition + 5.2.1.** Let $X$ be a topological space, $\\\\mathcal{F}$ a sheaf of abelian + groups on $X$, and $\\\\mathfrak{U} = \\\\{U_i\\\\}_{i \\\\in I}$ an open + cover of $X$, where the index set $I$ is given a fixed total ordering. For + each integer $p \\\\ge 0$ and each $(p+1)$-tuple of indices $i_0, i_1, \\\\dots, + i_p \\\\in I$, let $U_{i_0 \\\\dots i_p} = U_{i_0} \\\\cap U_{i_1} \\\\cap + \\\\dots \\\\cap U_{i_p}$. We define the *$p$-th \u010Cech cochain group* + $\\\\check{C}^p(\\\\mathfrak{U}, \\\\mathcal{F})$ to be\\n$$\\\\check{C}^p(\\\\mathfrak{U}, + \\\\mathcal{F}) = \\\\prod_{i_0 \\u003c i_1 \\u003c \\\\dots \\u003c i_p} + \\\\mathcal{F}(U_{i_0 i_1 \\\\dots i_p}).$$\\nThe *coboundary homomorphism* + $d^p: \\\\check{C}^p(\\\\mathfrak{U}, \\\\mathcal{F}) \\\\to \\\\check{C}^{p+1}(\\\\mathfrak{U}, + \\\\mathcal{F})$ is defined for any $\\\\alpha \\\\in \\\\check{C}^p(\\\\mathfrak{U}, + \\\\mathcal{F})$ by the alternating sum formula\\n$$(d^p\\\\alpha)_{i_0, i_1, + \\\\dots, i_{p+1}} = \\\\sum_{k=0}^{p+1} (-1)^k \\\\alpha_{i_0, \\\\dots, + \\\\hat{i}_k, \\\\dots, i_{p+1}} \\\\big|_{U_{i_0 \\\\dots i_{p+1}}},$$\\nwhere + $\\\\hat{i}_k$ indicates that the index $i_k$ is omitted. A standard combinatorial + cancellation verifies that $d^{p+1} \\\\circ d^p = 0$. The *$p$-th \u010Cech + cohomology group* of $\\\\mathcal{F}$ with respect to $\\\\mathfrak{U}$ is + defined to be\\n$$\\\\check{H}^p(\\\\mathfrak{U}, \\\\mathcal{F}) = \\\\frac{\\\\ker(d^p)}{\\\\operatorname{im}(d^{p-1})}.$$\\n\\nBy + the sheaf axiom for $\\\\mathcal{F}$, $\\\\check{H}^0(\\\\mathfrak{U}, \\\\mathcal{F}) + = \\\\ker(d^0) = \\\\Gamma(X, \\\\mathcal{F})$. Moreover, if $\\\\mathcal{F}$ + is a flasque sheaf, then $\\\\check{H}^p(\\\\mathfrak{U}, \\\\mathcal{F}) + = 0$ for all $p \\\\ge 1$ (because the sheaf version of the \u010Cech complex + $0 \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{C}^0(\\\\mathfrak{U}, \\\\mathcal{F}) + \\\\to \\\\mathcal{C}^1(\\\\mathfrak{U}, \\\\mathcal{F}) \\\\to \\\\dots$, + where $\\\\mathcal{C}^p = \\\\prod (j_{i_0 \\\\dots i_p})_*(\\\\mathcal{F}|_{U_{i_0 + \\\\dots i_p}})$, is exact on stalks via a local contracting homotopy, and + is a resolution of $\\\\mathcal{F}$ by flasque sheaves when $\\\\mathcal{F}$ + is flasque!).\\n\\n**Theorem 5.2.2 (Serre's Vanishing Theorem for Affine Schemes + and Leray's Theorem).**\\n1. *Let $X = \\\\operatorname{Spec} A$ be an affine + scheme (assumed Noetherian, or arbitrary via transfinite induction on covers), + and let $\\\\mathcal{F}$ be a quasi-coherent $\\\\mathcal{O}_X$-module. Then + for every $i \\\\ge 1$,*\\n $$H^i(X, \\\\mathcal{F}) = 0.$$\\n2. *Let $X$ + be a separated scheme (or any scheme where intersections of open sets in the + cover are affine), let $\\\\mathfrak{U} = \\\\{U_i\\\\}_{i \\\\in I}$ be an + open cover of $X$ by affine open subschemes, and let $\\\\mathcal{F}$ be a + quasi-coherent $\\\\mathcal{O}_X$-module. Then for every $p \\\\ge 0$, there + is a canonical isomorphism*\\n $$\\\\check{H}^p(\\\\mathfrak{U}, \\\\mathcal{F}) + \\\\xrightarrow{\\\\;\\\\sim\\\\;} H^p(X, \\\\mathcal{F}).$$\\n\\n*Proof.* + First, we prove directly that for any affine scheme $X = \\\\operatorname{Spec} + A$, any quasi-coherent sheaf $\\\\mathcal{F} = \\\\widetilde{M}$ on $X$, and + any open cover $\\\\mathfrak{U} = \\\\{D(g_i)\\\\}_{i=1}^r$ of $X$ by basic + open subsets, we have $\\\\check{H}^p(\\\\mathfrak{U}, \\\\widetilde{M}) = + 0$ for all $p \\\\ge 1$. Since $X = \\\\bigcup_{i=1}^r D(g_i)$, the elements + $g_1, \\\\dots, g_r$ generate the unit ideal $A$, so there exist $b_1, \\\\dots, + b_r \\\\in A$ such that $\\\\sum_{i=1}^r b_i g_i = 1$. Now localization is + exact, so it suffices to show that after localizing at each $g_k$, the localized + \u010Cech complex $\\\\check{C}^\\\\bullet(\\\\mathfrak{U}, \\\\widetilde{M})_{g_k}$ + is exact for $p \\\\ge 1$. On $D(g_k)$, the cover $\\\\{D(g_i g_k)\\\\}_{i=1}^r$ + contains the whole space $D(g_k g_k) = D(g_k)$ as its $k$-th member! For any + cover where $U_k$ equals the whole space, the identity contracting homotopy + $(h\\\\alpha)_{i_0 \\\\dots i_{p-1}} = (-1)^m \\\\alpha_{i_0 \\\\dots k \\\\dots + i_{p-1}}$ satisfies $(dh + hd)(\\\\alpha) = \\\\alpha$, proving immediately + that $\\\\check{H}^p(\\\\mathfrak{U}, \\\\widetilde{M})_{g_k} = 0$ for all + $p \\\\ge 1$, and hence $\\\\check{H}^p(\\\\mathfrak{U}, \\\\widetilde{M}) + = 0$!\\n\\nOn a Noetherian affine scheme $X = \\\\operatorname{Spec} A$, we + can embed any quasi-coherent sheaf $\\\\mathcal{F} = \\\\widetilde{M}$ into + a flasque *quasi-coherent* sheaf $\\\\mathcal{G} = \\\\prod_{\\\\mathfrak{p} + \\\\in X} (j_{\\\\mathfrak{p}})_*(\\\\widetilde{I_{\\\\mathfrak{p}}})$ where + $M_{\\\\mathfrak{p}} \\\\hookrightarrow I_{\\\\mathfrak{p}}$ is an injective + $A_{\\\\mathfrak{p}}$-module and $j_{\\\\mathfrak{p}}: \\\\operatorname{Spec} + A_{\\\\mathfrak{p}} \\\\to \\\\operatorname{Spec} A$. By Theorem 4.1.3(3), + for any short exact sequence $0 \\\\to \\\\widetilde{M'} \\\\to \\\\widetilde{M} + \\\\to \\\\widetilde{M''} \\\\to 0$ on $X = \\\\operatorname{Spec} A$, the + sequence of global sections $0 \\\\to M' \\\\to M \\\\to M'' \\\\to 0$ is + exact! Using the flasque quasi-coherent resolution of $\\\\widetilde{M}$ and + exactness of global sections on quasi-coherent sheaves immediately forces + $H^i(\\\\operatorname{Spec} A, \\\\widetilde{M}) = 0$ for all $i \\\\ge 1$, + establishing (1).\\n\\nTo prove (2), consider the sheafified \u010Cech resolution + $0 \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{C}^0(\\\\mathfrak{U}, \\\\mathcal{F}) + \\\\to \\\\mathcal{C}^1(\\\\mathfrak{U}, \\\\mathcal{F}) \\\\to \\\\dots$, + where $\\\\mathcal{C}^p(\\\\mathfrak{U}, \\\\mathcal{F}) = \\\\prod_{i_0 \\u003c + \\\\dots \\u003c i_p} (j_{i_0 \\\\dots i_p})_*(\\\\mathcal{F}|_{U_{i_0 \\\\dots + i_p}})$. Because $X$ is separated and each $U_i$ is affine, every intersection + $U_{i_0 \\\\dots i_p}$ is an affine scheme (Exercise 3.4(b))! For an inclusion + $j: V \\\\hookrightarrow X$ of an affine open subscheme and a quasi-coherent + sheaf $\\\\mathcal{F}$ on $V$, if $0 \\\\to \\\\mathcal{F} \\\\to \\\\mathcal{I}^\\\\bullet$ + is an injective resolution on $V$, then $j_*\\\\mathcal{I}^\\\\bullet$ is + a flasque resolution of $j_*\\\\mathcal{F}$ on $X$ (since $H^i(W, j_*\\\\mathcal{F}) + = H^i(W \\\\cap V, \\\\mathcal{F}) = 0$ for $i \\\\ge 1$ on basic affine opens + $W$, making $R^i j_*\\\\mathcal{F} = 0$) with $\\\\Gamma(X, j_*\\\\mathcal{I}^\\\\bullet) + = \\\\Gamma(V, \\\\mathcal{I}^\\\\bullet)$, which is exact at degree $i \\\\ge + 1$ by (1) ($H^i(V, \\\\mathcal{F}) = 0$). Therefore, each sheaf $\\\\mathcal{C}^p(\\\\mathfrak{U}, + \\\\mathcal{F})$ is acyclic ($H^i(X, \\\\mathcal{C}^p(\\\\mathfrak{U}, \\\\mathcal{F})) + = 0$ for all $i \\\\ge 1$). Since the cohomology of $\\\\mathcal{F}$ can be + computed from any acyclic resolution, taking global sections of $\\\\mathcal{C}^\\\\bullet(\\\\mathfrak{U}, + \\\\mathcal{F})$\u2014which is literally the \u010Cech complex $\\\\check{C}^\\\\bullet(\\\\mathfrak{U}, + \\\\mathcal{F})$\u2014computes $H^p(X, \\\\mathcal{F})$. $\\\\blacksquare$\\n\\nUsing + \u010Cech cohomology on the standard affine open cover $\\\\mathfrak{U} = + \\\\{U_0, U_1, \\\\dots, U_n\\\\}$ of $\\\\mathbb{P}^n_A$ (where $U_i = D_+(x_i)$), + we obtain the complete calculation of the cohomology of twisting sheaves on + projective space.\\n\\n**Theorem 5.2.3 (Cohomology of Projective Space).** + *Let $A$ be a commutative ring and $X = \\\\mathbb{P}^n_A = \\\\operatorname{Proj} + S$, where $S = A[x_0, \\\\dots, x_n]$ and $n \\\\ge 1$. Then:*\\n1. *For all + $m \\\\in \\\\mathbb{Z}$, the natural homomorphism $S_m \\\\to H^0(X, \\\\mathcal{O}_X(m))$ + is an isomorphism (in particular, $H^0(X, \\\\mathcal{O}_X(m)) = 0$ for $m + \\u003c 0$, and is a free $A$-module of rank $\\\\binom{n+m}{n}$ for $m \\\\ge + 0$).*\\n2. *For all $0 \\u003c i \\u003c n$ and all $m \\\\in \\\\mathbb{Z}$, + $H^i(X, \\\\mathcal{O}_X(m)) = 0$.*\\n3. *For $i = n$, $H^n(X, \\\\mathcal{O}_X(-n-1)) + \\\\cong A$ (generated by the \u010Cech cocycle $\\\\frac{1}{x_0 x_1 \\\\cdots + x_n}$), and for every $m \\\\in \\\\mathbb{Z}$, the natural pairing of $A$-modules*\\n + \ $$H^0(X, \\\\mathcal{O}_X(m)) \\\\times H^n(X, \\\\mathcal{O}_X(-m-n-1)) + \\\\longrightarrow H^n(X, \\\\mathcal{O}_X(-n-1)) \\\\cong A$$\\n *is a + perfect pairing of finitely generated free $A$-modules (so $H^n(X, \\\\mathcal{O}_X(m)) + = 0$ for $m \\u003e -n-1$, and is free of rank $\\\\binom{-m-1}{n}$ for $m + \\\\le -n-1$).*\\n\\n*Proof.* By Theorem 5.2.2(2), we compute $H^i(X, \\\\mathcal{F})$ + for $\\\\mathcal{F} = \\\\bigoplus_{m \\\\in \\\\mathbb{Z}} \\\\mathcal{O}_X(m)$ + simultaneously using the \u010Cech complex of the cover $\\\\mathfrak{U} = + \\\\{D_+(x_0), \\\\dots, D_+(x_n)\\\\}$. For each $(p+1)$-tuple $0 \\\\le + i_0 \\u003c \\\\dots \\u003c i_p \\\\le n$, we have $\\\\Gamma(U_{i_0 \\\\dots + i_p}, \\\\mathcal{F}) = S_{x_{i_0} \\\\cdots x_{i_p}}$. Thus:\\n1. For $p + = 0$, $\\\\check{H}^0(\\\\mathfrak{U}, \\\\mathcal{F}) = \\\\bigcap_{i=0}^n + S_{x_i}$ inside $S_{x_0 \\\\cdots x_n} = A[x_0^{\\\\pm 1}, \\\\dots, x_n^{\\\\pm + 1}]$. A Laurent polynomial lies in $S_{x_i}$ for all $i = 0, \\\\dots, n$ + if and only if it has no negative exponents in any variable $x_i$, meaning + it lies in $S = A[x_0, \\\\dots, x_n]$. Taking the degree-$m$ piece proves + (1).\\n2. For $p = n$, the last map of the \u010Cech complex is $d^{n-1}: + \\\\bigoplus_{k=0}^n S_{x_0 \\\\cdots \\\\hat{x}_k \\\\cdots x_n} \\\\to S_{x_0 + \\\\cdots x_n}$. The image of $d^{n-1}$ is spanned as a free $A$-module by + all Laurent monomials $x_0^{a_0} \\\\cdots x_n^{a_n}$ in which *at least one* + exponent $a_k$ satisfies $a_k \\\\ge 0$. Therefore, the cokernel $\\\\check{H}^n(\\\\mathfrak{U}, + \\\\mathcal{F})$ is the free $A$-module with basis consisting of all Laurent + monomials $x_0^{a_0} \\\\cdots x_n^{a_n}$ with $a_i \\\\le -1$ for *all* $0 + \\\\le i \\\\le n$! In total degree $m = a_0 + \\\\dots + a_n$, such monomials + exist if and only if $m \\\\le -n-1$. Writing $a_i = -1 - b_i$ with $b_i \\\\ge + 0$ and $\\\\sum b_i = -m - n - 1$, the dual basis to $\\\\{x_0^{b_0} \\\\cdots + x_n^{b_n}\\\\} \\\\subset S_{-m-n-1}$ under multiplication into $A \\\\cdot + (x_0 \\\\cdots x_n)^{-1} = H^n(X, \\\\mathcal{O}_X(-n-1))$ is precisely $\\\\{x_0^{-1-b_0} + \\\\cdots x_n^{-1-b_n}\\\\}$, establishing (3).\\n3. For $0 \\u003c i \\u003c + n$, we proceed by induction on $n$. For $n = 1$, this is vacuous. For $n \\u003e + 1$, localize the \u010Cech complex $\\\\check{C}^\\\\bullet(\\\\mathfrak{U}, + \\\\mathcal{F})$ at $x_n$: since the localized cover of $D_+(x_n)$ includes + $D_+(x_n)$ itself, $\\\\check{H}^i(\\\\mathfrak{U}, \\\\mathcal{F})_{x_n} + = 0$ for all $i \\\\ge 1$. Thus multiplication by $x_n$ on $H^i(X, \\\\mathcal{F})$ + is locally nilpotent. On the other hand, the exact sequence of graded $S$-modules + $0 \\\\to S(-1) \\\\xrightarrow{\\\\cdot x_n} S \\\\to S/(x_n) \\\\to 0$ induces + the short exact sequence of sheaves $0 \\\\to \\\\mathcal{\"\n }\n + \ ],\n \"role\": \"model\"\n },\n \"finishReason\": + \"MAX_TOKENS\",\n \"index\": 0,\n \"continuationToken\": 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Eaxr/cyDxNs0mAN/U7a3ze34cLKARF3PUVzBnKRVSdLaW+HhS2TSwH0AcECfXf0BR7yUdHC9ihmQePeUROeNbIaPORio7ymyt17cG5wUKJRk+jzg1mGGOPKFtMweLVgzuQWE1kEVH/oa/U+NLCpLwWREqd4XjpJgRkxXzN54nHWiik/m3/CUrSSE+FKBqLbxclVOJfidLB2nrvQ3tf/xkGS7CpnxpdSCC6UONibZ9/JtyOA57q1or4ZhN6qkFY8yHRaQGoaMuwrPGcRBENBgsXYAGrqeoWuQ++chSM8cwYk74MeGWrGyvE1IPn6Z0e4i3LJnH3Yr4okHmeD0Fs4HhpZIntCRPT8ej8cU8gBDRsOz64BZCun/fTWKga104Sx7DtndbCrqQy7j8HZ1PzwtsAv+yydOXF/9chBiTXm8uc6vsmAQVVd+uX7By+Mkeho3cTqLrml+oVKc3GDtjtLpnd221eMLjGQ6Pif7k/1e/IE1Ya/gPZjIBplbGcK45XwUQcEpxl4PGynUAS5qdODzOa3rE5QVf6RfsTuoP74skv38E8avddXBU3FQAymoCQ9BXaj6U4men7PlSI09nzrOLf6sqBSuuFmkIgoTP4SUAoScqapXZeyaqeEapeXucOiQz8EekQBCGSsfUcNC12KyVBpiJd9WcBa+P266bePpA9t8UzSNpFZbVgQylgwRcLvw6dV2O5zFzM6zwPcgwtzcfDd8wpi51sNYvrALPAGI1kW6aLh8u3ZoiUe6EvBkjk/qNbIyhf7+0R7zHJM4IutVp/u0xl5pZiPqEcIjOYL7mv8L5AeHMVKV/3Gq9Yp3FL/HHbO3G8vvwMVlqCRFrJQL/Q4jJZqf7In8L4BGnPpbm5X1hnFWoK9GZD+XvdtBLuHrO+s99AD3KOJai1wY9ycB9lTKAnWyd8OAGCafIN0RsJr/I2Dg8mRSR6mgSSl98Z0Q6sj6IX25CmbQyO3LrpZffAx5E3YnUQZDt/WLveSTqSlikfsGovx0GW7lm2yZBGUS9tZVqGqvsAEWqO/kGfU8tmmrrMz2pkOV72CO0DS+vFXTSuPW2wm4IE2RMXrnN1JitJlmy3u9BNdca3wsghR8LjTF8ABk55Vyu+W2BQKm7RZIfS8ghPin0lPMLY8iKLCPVhF8iVemhcG39uHFGisTlkUfsMvW3ql1Oac/ZccSXNT55fny4Kbgy4ia0jn2CchxdFmLDZtIs2qN8g+ts3zLvpyMoXmIh3FunyI8SKGUB9JXCRrrx/6Vh2vf3+IDilOfkXtpcdmERXGE1kf7JXuC8pAcoA/gF310lyv2982lowB/LNXiHQSSsrS79xRNKMmXcxuyPgvLuErXTDC+GEVxnWG4Hfz42jsOI2Rb2y1FLrBONEjv8xFKaFiAkS9Ncljb5wc/PdOxrJ0P3rxZD9PAuv/kD4XrJUh8ZDlmyDWMIoFUdSD1TSZGK+OxZvF+BdQv8urtlVKr6PM11BVAGfrTkLeT2k4w28HWyr//K772Q6aKAxyZ+N9EdTE40DQiiWMxNLbT84u+LdnMboPBevZxUXrNZNcJEhuShD9PcgTLvgS75zoOye+WUJnfd5PVAXnxogwuMAUmv458STIk3/T/MNp3qBH6djSw9H3zQfarm3o1hkmW1cNWYugFW4BhqK67f0cYxTfFqNm84eXgfl6i7QHp/qh2okOTsOyYbHvLaYt0OJZIYUcdopVH3ze4QM1MQPBIOqcyH9ljTECHassn+0qIi0aWHp/dIRwZHIacmjcUBj0YmIBSNzrL/bCiEuWoXS4oUtMS1rFoD2yRkeX8GoFMb88FjJ/x37nfV+JNcci+Nm+4UYElTDYZC740vFiyGwXEsaL++sTeq+iBsG1Wun1RHC4R9y/4MO2V76YCn+uMX0noCRAc2/Hl3FiEJQVhSRSrrbDa4zq5QYUE0qVzQ75t+3zb7tBAzvWjQWO15e6V5BQqQahirvLU8EQC4ceiEATAkbqHEK6V+aehYEV7seIf3hI/ZFCRqbeUnCxt1pQWDJXa6wTtDijpcMqbpHkjVDCt3OaK4kajZCKVPNIhGvJ3qf6ymuszrM+9hCiDV/Lt/OUL5IhQjfMTzBv63ayrSrygnn/orA2EnKh4iFTl8SLhC4khyyLh8JZHquCJKyZgNt77blRAj3e8J/1FNEotxN1nJtACLdRIYvk4yMhTxEF7GVVPqdERI/olSNW597sA5KD95ZBYzrUSdglr5sEHw7fp5suOo2jhB6f0wKJn0XirUtXi1CXCU86NR30qThFUBKgSMN5ilh9KPLKMh8J/+jMIrENSMHt+OEcXpC/xlwDu8rnbKOQeSzZUpjAuhD/zwtaa6oUsJ1hvZuyMyOyEj8TTqQRJZloMaP3KVcvF+E04rh2d45SxtS7oi/QrG2m1Ijqp08ZaKsUZaE1z4ezjwoO4UrkMQpNvBJKk6JbmKbxkYHyAwvEF5zxafxcyZaqQkYj7iDsWh2uiHtBkSTf4+Wxn/oaLB1HjnbBzoQgigYCnPhqd/z6foWafK5ejkliXZvn+9b8FWT5N5FkeIHV9vjf/ZdKcK8qLX7FqKdLV1VV3/d/V8J6v77vktvpAtZudlPR4XduCOVafDYpilwrsFgIgXtpb9oGfftZMbYSN659HKSc10ejMv5GB7L8j9SVPneVe4ryfGAwjAiZQxpJ8K6x34AwSeHkqLkBZmG8YKIrZRSsfHcmvCe2F1NLq9+xQzZcHGiiFH8wFMyT2ffRhUNmLVGuhslGcqFpqQ7cxigMemAA8zGlaa3u78Xp9P4+pTGHJ7ico2Eu1Yd86XX8gt2VbD8myZ6Pq5Bx8JiIInFlyP/OVZbcUdeRKyrqEe/afO1iXiDNbvsjEdBPREojCG3B+qTLOKwq0eAGIHUsi+W2aoxGl2Y/4WZAX7xqeNPUitu4L9ipH9NW03ApD+TZbSlQc+UsrHWWG8WpKFhsWV8SkDnsE/qongQE7S++bE16bHs+D84M/jdOGYrsXbaxg0ZoiuV8Wu7Uz45pdWuJ2xbSVoTkzgc0Pk0J85cu88E4XqMrZoO6Pmx3zmXXdgkGgwNFj5FCs8IJJ/viu+mfwmXQkYrS6rhOMZSYgJAm00jlHEVXgBbMrajJNZ8x2qa6gAZ9JZJJpw6AEI9ex8h6oyW0BJNzLNHsFOgfMyeL0bcu9BpWNrMKjt5aKX7EzzgE/2KmIJftHLZuRZsHnzoMkwFX5CJLl6Z5LQhy/7qJcsnw8AiixSC9w2XH77dSwiGRm+3CZnQk/oOIR+vlllrTiYFQeX095SAgH8ApLI3WCMiJ+ElAlooVXEn+qgHCgarZOBuHvhGUU7ECdFxFhNA7Tm5kqYjprPmVK9sUm1JTiE+ALaFVdGC11jHfIaX/xW2hpEBYE6lsAgyrWSpc36QRrnsBnMKtYe+b1A9bNw6afJnHJKyLf0UwMGy+EwDtm0YZVwyv6kTDAegHQDuMGXjEIp2vjVznbRPGgnjs3hiNFJ3Q3WtzEC7rVvMc64Pu5u2Y44R2Fd0uEBp/+/DID/iyvSOf1gLiu72obaH1ysfRYA7Y4abVwl4sJsRW9pqK+kHaV4qQK26IfSTI57IUM7kPZ7YXX7JpxpeNm01j1XwluxH2qFGRyIqv0eb8QmbM6G4I/T3eZbIwr2GLumaZFbOUUKAYgiYY2t38E01yXG/WCJsQk63N6Rcdi48notLzrnh3jkIpqMbKrtvUfa9DwYORmf6FyXx4dY8ehEvdG487BYLKzzLOt4nfG+naGjRFjGozM1L9nEgsavbt8uCrusKAulln0tmDIpwldpl++W+GYQwWT8C2rEeGcWu/+LcwzPeWrE1+mmSS8KQ6e0HgpL+1G9cC9kEsQ7WO8ff9DXIm+kx2JxtTYtZoVNpstMzZEyruDIZ6Bd8tNJdmyhfo13QrP3VrhwJU7xgjtWn0yrcMJsajUPxsfRDOp+rSwa7Yr2uLYnz6UISe5acrur9OLlyDR1jbQhj+UYY3Wn75P0SJNOFGuqik0d6fRWkUBjz21AWrNp9pO51U3WFYIyle2C801S/lKRuaKYE99IUU6Xhg5/RRLxxx/LndL/vBJHINMFMBMTwuLRycVqcfvK0wJ4xRPODcxBy5Zb+JWddNR2uuW8v1htCWGhN66zVearReHud3yLUbg1vJ+3xvA6v62Gvoy0sp+kLDxv/D+Q4TR7Vaq2PL/5qZOKZH+l1le1We8dbhu392a0CCLZ6nZB4pCbqlPT7PaJmnpKf/eHi7xw8nEI7ZtWthw8nIr0dxy8QSYPnFlRd7VXq78CbCluw9fcyVeR5jsFdCNwtuOjN6cJNnfErC0rSMXo8IV670JNstTGXMwLRctWvtM7TJdnbrvHrPmeoL3JiIrxetRFgnMr68DBGvI83aZ9C1BjgU2eHcuQGJMHEQP7hSqCOtSoz6UMjdjSQLmu5VQwEOfqSaaztsCnkjypl3sluOaPixagYs5vu0AkGFZoQdKtCp5Vo1cnxIFLWMRzj5KTRnPZs0TEId4pyxwWpuUzXSjU4geCds+LidfNOCOzO00cBU6+idGgTYme89qfaHM3pbPcOra9CeFKduathZON3axoss8Ad5KT/DB8lGie42dfAh2/nte+x5HbzEFcHEbDVV8HWsdMLCKpFQPxxElxTcvWwqe8zsUSj3yMDNzaZlV0C1tYeAErmnjYPSsof4a6dq8g0s0MITZkKTIey2Vks3XBWpVLe7uL/BcjaJOZFPv5E3n2tEsw9y/PmHKiFCuDpwRJQRefX7hy91L/jo1YsDIW3juQXrXaowa8GvpBymjYRyLOZIv9f5ORcUGwPS5fuqie3FWE6wrDJTTX7+bjaOs73ZYrT+zaGZuBcmnRsO+BLNZx3FrjfTbnOExqpNG6HMkm1xZ3amlle1bymSZGrOwm+6xiLyaExEgjunEAb+3jYGp9nB/moQWlKpydHAedW2ccOYdyG6EXDl9vh4JVWkzJ7BPpuAR19gOf160b2Ms0gXNeI+M/sIS2wfYfsgOawxAd6nHTQZJLIWNSa4RH5I7z8+csrJL4eAnpZTpsMVhkjcYTNp34jZFi6J20z7FkHY881GFtfKOjr4x6FBjNV8ff21hh6OPfii1IGbEPk7sl1aOP7nlzNmU/08C6CY26OWCyVk8M0uImPNcDkQaPcmIpDJ30ba85xXtHxLVrlutVhbGuePW81wej1Q43v7obcFi42+xl3p6uvijmEXHzEKa/mlJhF6+xSQ+W2KH22zUiCQOx3Ur+E15erkBV1J+7VkyQ9tg2oGVZV3GczSZRq9X0ZmJKPRyiScfJaSpCArjTEQ8fT/HLKY4+PymOSxeFyB++M1KjeF0fJLW2xKEYPQupH1GK9CTbt/ohQpqdC7KIZhAi0ZWUfG0kZRw2L5aeZje3z8fYd5YUmlAjFe9cq9ND2HkXDBQ9stiJ1y8G9XOzyiziQURmkMrLaH1KsAWgj0IK1VT6RINWFhALV++XaYpU5fWn9i2xaqlLNG/uCL+aHiOsQXiciaxEGvogkdHTSNSilVVvsYbZiMeyLHFuu8trXpjb94gS6LcGA/T8G75SKY9JkV7ARXwzdLVRZq3ULJzNbIB23rP/ePcDQXlWq0nUWVEg2XanLzpQvF2ycUH6dmr3e164PDSuPG1L3z5GNWo51mtiM80s4rStPWe0hV8eo5lRmyWhm1bLF1Z2ajoN7XdjstTwApIl+R+RdXigQr/PgcWq9JGJdha5kd1wwJf6FQK4vOer4GO6Xhi5YGpocakRMVbKGl9SOywsCGIeX/uJW1626l+bTY2JZaWoRJ5xZx5Iepk1QxqGPLXOPBDms6Nq/7q8mXCif1mJwG/k3q/K8g4owP5JRi5YvyPaRNzpbH8HXPjZ2pKco7T34dUsudxHsB8Nd22viL6c/TOJSQ+UUHdFOX1xVQgfNuq4445w7gcvnd63eFMs9Qu0vZuol05u8BLsk9e7v0zDIoV4ihDDr/nnCTkW3d9CblGwBY5Vs6nLtbqtuVqB4i68qYlbVUBvPRjAABPecSCFuPE7ZTS0vEjxA1oYvS2bU4WcLLnvOw1JRS93BVrzvCTPq2Hx+j7yJN8h7yZbk/LxcpvOeY2AQEuMGkDSi3i4daWilJipVJQ5nI1Wnca8wXcIc2iog9+mrlWcYolyJJOS9D0T/GzxJsDCpjHUU+c2P0w7DF0qrScdbVinOZlCIqrMVkWo1GESVjgajwkBtEOUdUl2bzseJc0nthNI38NrmUFa+IWlRZq9TqfyOPVbdY4Vh0+xiCweLVUqenk3jC24lp8oUw85sZfurFrQBvDVGDh7DKh3dWcPYQ9DsKj736KVAgR0thShnVTCk2hXzv1sJphsM556+97bl43NJoGN8Jc84IoulP1ApxzxVQmSdoWVGB7d2szVqcgZzXb2FoqIOH8pPQRYJNgEa8y+nWauLPF4hhgcsRv+NepwWBjXnLtFDZjsl85hjvwQMhjZbbX5yD3gv8Wj6pJSJCaS5grWVRjQwZ0tAAWWy8RnxYbpclUouXUU634VCdMPV5l3udMRjtmTmrXpdBw74Ulgnzx6EYzH1jlOalNXlPx2u15vSrRu/OOuyd/ocbyUvzmHBWshkE+aMxlNIYSAjD11BZXCY8BJPJrBxX1cTF9K9Eq1Upq1yu8N12AwNjwZRYx/R3ttu8egHeQD08uOXbMePkwLH9QPS61vdnVnx1Ho66+1eF/52sHsH1G6xeb2CL3uWdxVyYvbgZEkjl5PpME1PvvHJu4S6evQX/P6MZlDxdUL7gmdpHQe55ywTi9JC1Eg5fMPogpWvETnzSqm9PP5WwPA1cKLz8A7aWoFe5Us7cKC3B4Cjq0LPEApWp4yRmml/t2KZ1nAj9jJZf1kHGtgoV0aZwjjQnUDXWLTzkchTAQC/ZVz3GEk+nMkJ+EzPQSATXd19SoEWO95mZ8sQ/NeuW605QSlpuDzxH7bVYbPt9EVgBa1mEc/V6MKT7J6zyjj6IMbRxN2w1q/f6k55s5t72WUQCuFghEAY96cRK/O6zw8E3w9j9EUzbw5ygV052YFzxg9hr9D+O347GA0yq+E9YIH5KRKuPwfP1OgGoNII/D0GzPJXTFPow6nVwWkvCZEvqBzbzx/Lr+jPW1UymvhXUZv5L7sBeQxg+shVF5pYpUnTWd69oFwwgk+Qr1SCH65T7IUbJ7rn0Aqt9RQUdHMPiRKCdODliw1UpwtMPI6y39yrpkSCx6Egmx6cV2YEC2yM2xWy2ea5qz8gi0i/xGO4jYVfsfYyGZ7nUSHnVOkXO30qDW3/UO1LqxpGijQR1d8Hg17dStNmGI2ODUe6U+3ZuwJz9Mmzahi6GPLBskEhmrzszXKdHI1P5yYt/vLKO8JUISbuHcWyBVF4sUA4PUsD0OPHxWJJdynoRNHTDydDvhQlIFCGHiYcuLo1dyVAEQbjgcHwBGy3PTPhkHjO9DBE4gAJxQ9E9x+7HB9zBxdtubmiAGyWKJNvBFZDkJGQDzHuan4AHOz7UH4HJeubasMavemPYq3nOvj99qIiHgerBDAvOO+v/PZ/px2GHy5OkYYM6173kTh5e7mYSz21g23+0TLscPrMEku7lIEAwJdcbmREwDItk3A5x4AYEoxpgFrYUCloQqhOLD8EUMYYzbI/X5FAvBkcce/CTRuV1S9xCspwFU30IqemQ9JAgLn3li2h57KMYnLWMqT2W73mf0/JNP0oEgX5CvkZwOflcGzvDAQ7/LXduj+Twb7UDKJeIbMzK9mcWLW4+wlZMrpJ5yL47XFpJR8O+wslkjSX+ACKM0AgJc2xqY4hO7h6zQye5JV5fLraZ5NhokQzD4wuD7zsEgzl72zp2s+3ZECi/4Gwh3/PwKmGy4iZ3tFJjnxgq1L+IBdPrLxPv69sZEvmPgY5PxgYtDQLhsUfp8cqRo7+ulz+QVDJr7j12QQpKXsms2FbsszYZAtXEmifojSQLGNoWmouimo+M+4ycc2cgvBEvOaE7f3Cm0q/UM6zzk7rcodC0qEYBkIzQpdl+ak5CLAQAG7jnoPNkL3XDZOFSXzbU62ydM0ZFaWIEOtZwn/kSfygfxyJ5Qcf/ZkJFcqSZbBmhoTWDH/ZJ1ydYURYBYIr+qwcsxCsVlKNE1V8MAAKKkNEgJF+eqIAGVOlRnOCaMaW6JTH/GMo5CBmkhJguzPOk5UMnOzRObEn2mwi/Lplc6QwTTW8MUbwxhPxsfYwF1gvtzdDoxFcWpLfUYhuYACYB0mjtfHC5xD9gn5wQE7i8fY6d/y2MvlgE2S3CY0VmE8jUJ1RxQZ5lzXiv74tTkyj1NmyTLElOoZoYIX1qhd1MgslWuYINutev09BJxIanwkICtFVU+CxwiKqo42as3q4PWznABE9Kt3S51F0bJZWyw6xjddRG5wmaZq5LJBxGdE7nLLEeD6TEGBoKXLwBJLG78vIoP/pdsUl09t2wFRs8vih4lKlOWRpFLuRAEoCq9wSb05BIMqWshKXkaO/JRF9cPohWNJ5YPK5t7uREbJZfyPM1tYJXYUpPv6KUIVE0xsgpIZCMLgVqgApLXBO9MTg4wKXW9jyP1WL6Rz8vHU1xoALl0FlCXuxdWyewzZVdwsU+37IqUyJ9wRWHtLJz54pggAuApdPEp7y98+W4kSNQy+u8S80LhhaaKfIvBWL+fcnpEmB5hipScXKxlR5LZmbhzHfmOpTXFsYTPLGPLjFYmipthVklB5V320WHzc2Gx+X/6qwixIPkhzWLjus0ycv4er5z8pYU0C4rrhRsZDuneWl6u2NC3cxL64SrmACDWVSHiw1Vi34N7azeyW7gYfbAb7sVDWUIaJy0PE/tnWcopchLZwZT6MMpGVfyuQP/CKIz9geCjSXyKNdQwqoLyLtp0Oqaun1KhEr2ur1CNih+rinp2pvmLFDdD5l7Z5EcWzhraLaYNhPxmH+eMsmlvL9Lmq5dWHAUOhjx/qQHir9/HuqLKoWLx+QfMJwzh4DKQc97yTVikkcFf+Dyydgwsq3UxTY9NVZVFUCNNirBvrWv+oi/2CFQIPmRTB49RAKZ3vaKegKvgOWgp2NfUsHHxUeilzs7J1G2ifrOthkljdOuXpOWwyiyKHf4iB5iJ7y8o6y5CZ7OsCeIY+/g7Gkz21TwuZvQ4Y8XILkEv3Cyu7+vkTby8uVFgxuhMnMEflgliMFxOL/KXXhy5/R334dU0Aupqjfm86izDDHrulOxFBBKAz/OPWlDC4uDy8Kw/uQmBGWhFVJKTrP3zP7m2pAYxjJKw4GS9gRjhCtoctbl+pBWLX2WHLni3pZLAkY8E31EDFYIr3/kSOf7KppnMcTy5h7JKMIqE3vwB45te+mwVXLxJJWv+3BYWto3oYA9+Bzou/33oOjyw+GKWDsVfquE38Q2m7xmcgvK1PWt+fgYNrCzk/tXYxZenr1bFYCtT+stH5vmqn4rzFCAvqxdMDdT1OU3/mqksgAPlJ/kv8XdYH8M7SsZBB9Dfy9eTCEdZPuYT78dVd+iAzo/fE4YTst27RFZFCdd4CdzAD9JqwbncFXPUdvrWFZ7JmSJy03S+hZl87VznlrisZFjAN/nWwvfR5LTey2DnWk6R/Ojv+tue7wMDk3XvdLacfdChHaCT3mWK5ncBTc6w0ChKZAH8yWkWRiUFKXhi2W/8xGe+C7f++o2hAAw+3Slc7peD6wca6ZB0BzKEV65gXl8zBCbYu9AV+6tC68dgm/iQ0h89hYYPfHe8ixQfFaw0sIjMz58Yvmz0UlCvyvWjgpunaEnfWc+v5ibT9mE1EWJg+00KAs73YtLVkt4KtYQyn07pEWB8Dp5ACtCZS8icH6vmvIh5pVVEie3+SEzuC68YXSIu4YjWkKbz1bQuuoP2GZ8XnfG13O8abS8TgIO/BHDGtDWEFN5ilWc8R00Qdx2KzaICKF2u+r2CyR5jGrjBhjM/D1SI9C5D9C7BUyl/bvMw5OHWnMm/3nMvXtJl724UvpzeeMFdaro7mCjZ0BmiGw/rigHZ4wmFkA/LAAWZoC8ErtUaolDvrAPyD9pVG8xylc/dtnTdeJkTlXDcBkH7k79BZ4BJ648nvdwxAKDTQtasmMXylfouXofkwrMM2/WjMhHxQb2JTxpfmvxJz0EN7GiXP/5OklutkKPd3HMgK0Z6D6sEGITsg9qI6zi5Ho0RPMzXiDRS4O+QXi0YtdgmDb3HtJcNyq5iTDfjOlzgaQzgVJgO2qVLIdWUx29cm55cZdehaEkOQFf0s51MNk4NUDEaGwZVOjTElJx2iW6GIY2qLIMm8Gbjzo8Kmn+ca3aWI8zXMJlhKv1e3ifBfO4M693cGFxTUCin6EXBc85FsIkbEXyM00WCjO5bdp33BXdeZwSePRYYtUJhOY70hG8SkHp5I0dAhpyW0PdMo1o92rPn5UMDUwIo5YwG+5NSqQIG9JiGYa5IcIg0aMXHxLGcQVlqw5g4bfAWcZjElMk9KgW6eOGAyTL2s2RhtD9rw+FlyoDqnzT0cxrAzpf8BqlRyBfPKjnTZ1d++wRl3/vK1Ud1jxM2X8tnwO5CRtX/U8+HQ8GxBZ77oN4mXuPb6XjbfqLD8AOGM1PJF9XBe5dXeEBaA67zzvZ/8gPAhXgaG1Jjt6TNrsLi+QgfqyPJp98zHcSSLpbpwaMPFThHt3OwiekOkBvkbHAKPp4CsZLzg0SvRlqfDezB682A2SlWv8c0dMdQIQHaPfivRLaivoygt867JW4FF5jNimxo6Voio8Z0vHq6u2rkLtw1yeu+QZkcHslv5SYz+XHu3NTZw8T7zhabQpCemUumfmu6DS6G9Nblvz1Z7Orh6tyIJSmsuudsAq0XQMsoD4tlmcHs8lzX453nbxPSp40owJc6/fqvsUS640gOr6gee+8gZn3ULqVhIFPrzjUGXOSsF6s2SMeeHjEz6xdFA1VBq6jXIPI+9vySgZHyC0el1OAet/ZDw7cUrxXqZnIOLU9U5YB26Vokfj3SGUW68478APZUgAn2BFKH77ihaXMaRrBe86X+hp+8wXCAJXrnGAnDbY4jKwYDajFTIvBeNYcmw7bEiGQIXoDlEFd1AKphycAFKLSBn4K1o1GGUnzN/v5oc/9IVY2YgwtDXSWkSSq1dchFiKK/sdgJxdTvbJmKd3tE+Mv5EfLKhKahkM6mB2qaQMBaSuhDT4aLVQp1FD+yvW3uXJs3VFYoFoWfAXGncDEdZbjwSW/fv4t3duELH0bYL5ycjw/M75Dks/6TlrJwVJZJG534vsOnF09GAOS5rSWLJzt07yDgJ2xYeZDRdlpuPyet6ZrWIxdQrrbjnehsNAYmSGNP0fHcMtx4AlLWQ73VskGPRB8d/rbeZS7pLMpj1iNCkwBoO3NXVHKwbRe2CuKEx2FipdW8lHZp7HJmm83YJ2yUs3OAU8/1mwypV8Z3Pm1QNAaRDFTyv+JqJje4W5c8rHo82EBXU/WxDj+NYlQUdcStcIQoH2au8LXnSJc90nI5GydJ6aTJ5HzOEodeYS41AI7cWf2XQGzCA4htnxoDckh8hZ1COHwkQ93qVz/X8PsqgsSNR09ERgNVCu1cxpXW4DwxUkWbiY8CqqTeKShW4JI8/DSDbnP+SirPHzeswLjirQvvZC3ni75gtiqD7DULe0QmG/m2fXYy+mAADjllSba1J33tucpXVRu9APvQSnYDE2oygm9zW0fJyjZeXnvXkosn47A2E3Erky+889D7nru2diC8oQmIvfbJ9rgKhvpvRPan2fh9CQXbG7n17EINkWH2kpov/AuZj5VcbhkUnI0ttxND3mX6LkoTZLgCEP7kd2Fx17rMj1dhidSY6o/nYy7nG8vXioR6A4TD2Ej8a/y856olL/KetRqA054DFLxwUwMzSDBnQ9Rz19dpFVBilHAt7+XeSdcc0Qp3d7aw9KMJMWE76I6M2bHqga6pzsUGniA7SjCdpZBkU3+CFY1WhdI+eBtgrlIvSAO6vA8Y8plTgin1+5gK9E+A1nH3+h9f0P3XdlrlJ12SF1oNHsnT0nnAV2vdLr948XOwa3i6PNuYnZDSDFauia3vKfxnvFahUtOTa51TndDPViKeumkScpCqg760NmkrtSnuTJgfYw3++TQAWkTHScQEfjWz8EueYcuQIzPtwlATQZsxxxO8ZqLIuqTdwH6Wfnwcdjhi03R0HX10CGnBU/pz9uCWid2CWPpUyC/B4yfEX8/7VMxnk+tK6yTD1EL8xdfK499gPs/tcNJ+FcmH1Ya/cAb8V7bXxevm/W/IQuseSjtquZ5qAwR1DsvVRQAZNqdBiBGubX6tmRH8ywivK9EIFynCsYAM062lXCqPsQVAqv03NS1nS890tYx1sod6lQlXwCwK9rXupRmMNi0pLexnRwJgnRJ8/6t2PIX1iTOkJaE5EahMVboe101K8AZ3RNxzazqFQ1X7lw/U8/6G1P+kbR5oi5mU1pmqfFbO/95pxm3T+WJJ2J5PweokdK3oiOfubek5bsVuUcTaLV4RFQJ0gEvd37eeSkdJTKEKDGYOMUpEtTdaAslEi8QbbdD2l8AJ74if+wej7w13pGl8A3tP1kcK1XfDTrWOSjMnzKsaftl2jN7YkmrEF8AY4QAvB7ejEn6Ya3XDnn2CqpA2VzD22vAaykcL5kd51wTQ5Smn5zGm1RW9qGwMRqJ2F6kiJOkjEcKkxOzFmTW8DZn5ztcE6y4LHwlpTOUv2jAOjkO/pl/+nWeg1gKJbEpVc2H6kMEbObweINGLCmFfLr3F8wU2DX+hV59Sq4QdhjzDLivGmnx3pcm86lfeh5WWKUPMzk/FIafNIM4M0fwAxgh147KVUrCEXiK/yB7UkqYZ7HCPt7o1sDxdLNk8eFKW5JeBkolnNhmcV9mfQDgmDB+8qEIJpdRclsqoqBgSEGmj4PasFOUu3rBKJQg7I4yIgBEFBc6nGbiz9ohGsaVOBNHsRdPaRxf2Q+kddI/NODH+UGTgZb6EVnnrhj9oT+rDqzPnwRckhllupu8KCHjhfWSi2qqw2rf/yEpqvvcXYIZ8TAxIZvCBa1+XatOHiqvdjH1ZEyH9szPYL4FpdN4HBaqONL5xWl2ZElTApSkJk36R7+92fgPDJJlqmLdWhoqqj0rpS3gKped6cj8D7VJS+KoAQJwpgto9zOupFuUABhRLY2RooFXbqcOPHkzfaJO/x4pz5uLuwbXEmlpUADfnKIsVEKdC9n3mLu5MdBmT9P5sK3dhYGXtOUbEG+Db0jdK5TUMdIRkY8Rp7eqMIJfAB28B0sWPtCoS1h6XuQ0h05e8VblYAKQ9SzxLkjoFWJFM4r39sTVuWexcKYAb0tZ3c61vdOqS0TB1s28Xrl/gH4ywin7Mqsq9BRdCOvhbuSMSOfQOfYNCyOc9LzUkBrnqw43FDVJJftXNyQpBG/gUTmFV4zgknI/fhVsHfDXWSSV9Sgwf+MJkBMzqUaa+T7eSXqVH+xcQ2w53PAV9+jpZzP0dpVTlT8AlGrPdi6MQUTls63hDndptoGH6JpqXXvbKo74XY/ze5L9lng233ZkG9yPyhx+QOpt4jfZMHrKMYmjtUhZHrogTBvXOpaM8edWMeb0uMEcrkGnhIs5bR8g34Dj+uE+3F4N9AOylevUoJ/3FIQdk7ESv4VTdlangHxQpjOqulad5ltEb23eStiIsXaVZUMnU90MF96E8bLvWuKIwr478QAF6pR+H2pa815FjE8nMnqiu5O+P2e8KSwEa9A0epiOKEZ5xF5hLHOvY3eI88to7uwjUFlKofFJorDVsgbV7s1HnNHklTXUHZiRbUO+ezBXAW1cG2qnz27rxKQo1FgpHSfR4o4PKsuayzEZI9EkZIQMjG1HDgAz83qeLMqYh9on6/bTWd5FBVrtT6vMs5+Qk4rva4FzZeny0AzOQQaESOe9NqU43trX/g5Zw2ooianSrf+pY3lBEOF8Szjqj3/OS9P67zlq9LRDQNj/1/rjWLS5TF0SUCyFjGUVExPGHs+0AvQ1vnnUKzmPTkinhsZYAlAs9XVWfa1xiWOSlnxbrdho09ru7Leohxiq5kx2a3AZCB3ychZop9sw5uoLThK9cgV5HvE26squhhO/qQWI9RbTdiiF5S2MEDiYYbXXdIWID9poh45D9dUJ1+z48E9fJFJOeJeJ4VVXd+RK1Devp2Ou/TvyzAQ4XEbGCFSacOeccS4vv9x4ijy1U5EXHbOEhONEhfyV0TC+pjG5JofOsYJuqyEP9p/LubAluK5XxvqOWqcYoJumnmVFrdgyJx5hylxBmpAENF2d5mZ62BLEuglASHuRGk576YWkys6wgdIqA88uJB+yKDxx8v7UWQCoeunQC+6LB0868ATHDBx+vWC3YJ7yKEubbxHZrMYTchNxH5vaN/RwllNcY8182ODTGscCnXntgTrDmjFsOe9D4ukcqTkJkZnPv+6+WV4agBYA1Kcafu78NLoS+yf412kKVwtEoV4zXKo7DtMvQy0xQid9CXV1+iRnp+2k1/8C0suel1dULVXpB4fuZUyxVKJQAbt9p7XOSlgzAN2VsFCcU8kMkS5XMyuUbPvkOjKy18ppYWR6OGc9CiuLHsv5O9h9r9MM7+CpIVwuedC0dn28RSu2qgyq4g5KpeuzPlfF3S5koP28MZ9mNnb5yzucYpuLC50WL19BpmkXT/3OHvgxCpsJjLk3pykw706MTyUyC82SQuMCmz5MpfHRS/zcpnMMJQ2linnYrvzye66TOk6wRjU3PAlGUrR5UPXW2+wcF0hb1AFOS1bl1GxdMCJFyDbbICX+EqhQEX8Q3qEzk6PV8tdSle20P0NcJs77dpBeGaCJzNldZpT3qLuhc9f1moP3JI/lo0pF48Tbj40GnRBV1bqb/D9TTAKz0AEx5fhJMmMRSHmX+on7DTYdH1+R4Tlt5hlgkNAA/S8VmJ+Zw/1mFrokWl7wzVDl7V0MZcGDlGpLJXTcE/p+VVF7yhqu2YE2MhdTuwu+yWrQaedUHsl/+uOOWGheZR6Ey9uKCDJZltLqAI+LxwY4iO1rA3miCxFMSKpg73Cpe/Eb+mC5G36l8Ez5nDwoV4VBC6SlZY3q29KIt6mc8awAMQDNrFbCGcbP9tgvgCvs5QzbsRMfcaLyYLR90p7ZDUMsomFZwuySNld1zff658rb2GOspYAOWBvFp94Y+6P4NyEjbnF8H2K7Yoj69QzVlCOuCDlV91LvONWWaglMDI3Z9Gcm4XV24Ac7U/JwIrBkxfU9qJQBog94geiIFspmez856Q1K6M3Y7evfRaAMrQ0meMIIBkvKIqSsbHOnzYPHtQqFL7YxqAhRKrpv/6rbSVNQgGT7fp96c04PqcwzQgUrEMrm/Z6j6rGQwceZEHjDWo5DydTUH4WnE1IFQXYR7Ut2RAA8pzjMk52P9+y7b9Gieewp2Kxa7nSbRwqHLR7BGzY01B9IFW3ieozahXwdZYZKfXj5wqQwOs6l7TSNOOmB7KnC1ytIUJOPp10wUlGSyt6bEVLehCp6RzFPJIGsQ/4W0BL5v5BG/u6CPbC4MtcCf5SXv7t1LN1Qn/KigwAyUITLR9WJ6SdFBN8FJDD5L6Sma+IpLXaG/1Y5pRKz65xyEaGwZxFU8XHveIRgi0gMxNT/d8zupM+FTqetmPnodHM0H+gao8ks825RoK4SEg3WbzXxnx3a8lbCHWE5ARdHrEkbMnKxsv4yPoInR2C+klJw9DZE3G7Dsb7ibVKFyGMz21wcH1XQoqsfdQmr0t8lKHM8laaKNhYT3T0KDGm+PWTON6SES/rEJpU9GRTFzJVN3OlnQ/7xj2+oO5F/bJsAhWPX7kzhkFjFTM5iJJbYlC8OugUDdFnPvZcAG7RtgoQjpPLFplkmfBgY0UKcEzaw4wf8+VdHIkuty7a7luXLcGu/HKSXkYw3T3/aNxUeKtOQFsBNKZxHiB/oMzelGXa+KuZRYoAhhwoO8VcaLDECbqPfptqhH11tQslSgHsbgWL27UdeaOC8FAmqCsQWjf2VzfXRNfx/rz0YfO8BWHXlg5x+wzmtHhinlOxsS8mDgNbZXxvej92dwb1yGV4v321w+YJRd/0/fKZVeMxWJLNnpIC7K1RDFpVl7DqLaLYUW4XQA/AUTKD1Tm8XZRVeN3t8fRSTLf9LxqEjsbPbqCnsANnv12nlm6w5aLVBCAohKZE23EiKFkJDRlWRDcySIbyGWGASdXli9IHrYzGYnTcpMC+Eemb2zeIJ3YEpwlWxRK837KVZHb2zmvayzMT4RAPzsIbyEQ4nao4P6aarwGUGXuQnVhmTHpnVMDp1LpzDJDGvbPqUxMKeTjtWEXrN9ZwDPxmMia/yTWstVHeYUE9jv/LqE1byRuQO0iTmzxblT4abfQklPjiecakMDpEENzGtkYcaoTkbLOfqPu74+PP0pzuyIFBk+gVQR3sFb5tl4w6LP2KXPOVftxByYaW1Y/odNT8nnGsmxmu/c0FrCHa9JNT2kHKMVQmuFNDyX8zjaZzVn1h379SyjTbqulubdC3gNmrcbbIISrVW4C4S5Qu/hzYeyjWOlV3MGyZrpQwlYMFEp+Baiv03Vv6uC0jRXsm+LjxW0ABKz0h7j0VwLxtMUQJN2vMs6KcjXLJBSrLCp57oIWtdXnc+B/jD2txR3GUafPqcfnhD+/jJRaYv2tG4fU/BMyfRCHBWQFUnJon8jqGY+SzjLNrftl1EpePeX45affgKqHgjkaQvHRnY3tEAdB2HkuaUP7i4XBjAU8Q+33fdKfCTAwzFHyAcmuoTJzXxAtQHQIGD4Qz/rbBwL0pJcOcKJwIeMNaT4Yszk8jSbGkZxuxokiYX8cWx1962j4XLK67wN+6waVynyvQlQE4uYZYLKY7Nwy5knsI5xRn1d0XgelwbB1whPAiygLt76c2qFb+2bn4wDMZrUZuM4NvehQFom631RCFc6GzE/WsQbeK2aaWbOHb+Jnw7fapc8nOtzW8xmqlyJdOdPXWZZAvmAwKLsJVLve3MBVROMSIImgdW2BZxPYQPwdF4mY4OPBxs+iMBJ0f25q1votqQaGEwzKuqKe8HawBn31aaanqkcdrahd1uMePFh6+CE/rYQdUjYSIaBLrshwQD13V5pc2icpb9UPW9wEDxoP+c5P1bR6U5FnFOx+0tvlBWyeAXcicuSWknKUc2hiqQcIsrY3c5mSO3rotVsvlmY20qCC3ufoq6N/FdZo5JHnXNieCPcTM2MlulXsFrvaE9225HJLYZ3f8Ztww4laMupsSjnO8dAtzdxQpdazXaRvdgoEbYhkzl+BwAvJFHX7/pPj2lF0YqUo8Z7v2x3MqjgoVauL7/noIYeBsAqOO6SBE/dZhDdZZF2wk0lmU7Ig5HdV93cq8j2C95/GhgpIuZJh0gdyN4KctwfCcLHV9OqQoVPqXsf1mgacNixA5b0rgkw9Z8P19XpiMmJJJmfzMD3m4++hc1lV5AzCN5UI/lAFVegsPcfDSQsP/4Zq5oE6fOVPUE4FJOdt/5CcrgWVj5LF+INJnwAJ4b4nFTIyq5pgFfxM45fcqXsAsq4LWGv0whRA7Y0i1LqfPczh8m3OU5e1qqO6MURYMW8EXRbQc2FpwFfW7zE+texZ30+c0kCNurPp5bFfVEsLZoY1txztM4rvbJhnqb8/LPxtoz0kBQz1Qtvm2DtdU5z/vX5bo6mj9fv8rZ2GeZ3viW4AGZrqVQDtWRvNpkyZNEEZ3Q9dhh1u2K34mV8Ms+528GukhKwZJH+zEiz4ve+VdfAxx6nK9WPmZjvpr2CCBDf9gYpnVkFT5ApyRfRxkDY8zPDywLIs600FFH7XXEFa4n/7ELOYq4bQ5EQDvhRFFa7BpL8dmIrtvHRGf2HAKgmuEvlNkn+MCvUUw8KZhy/PY9g/WAqKQedxSyEg+ANqBeCyaxPckl2R6yQGGahh1umLQcTPW3vpmgnRXu4Bt9lXYui7Izn17NXaowDzBibtTivkuCU4uO4BxIaKdzbuiAMhjwclvL09jGQe2hDPlnSDOZ44g4kRvL2yFP509MLeGw+LPYWK7IxwB+EdaDBfYWxskiBEpqUSl/ZHfs1LDfXdn5mDnM+vMSpV7X/w1ZFbNiYQVOkUAesl8HFmrxvnfYBbwPBjpHJSo0KkHQlE79VmfKUsDOx9ZJeOjF/qPQb+8HVOf7psMpKpxg//tqbPwFLaKWCpKnuz4G14zvBPZg/GRCPzSKz9upHhSgBJeQOFgH9QfRm07i8Bzs0bQnBNUQZlD1Sy+ioPEIKatgKK6y8mHoH6SJwcgdSG7cKMIkO3Hj2bicTjys/DRbLzplfH0+VTTHyJXECqo5cBSlMlgt1NZNWtzW8Vt0J/8CSqGWoDnq87437YymPue8Ss1Lc6qiW+FSyEa8fxQWRkJ99RXK63ipBy18cTTik7qk7TErI/yQzlhgc8JqmFbCK9uvhD6NBZGn95Rf3U0JFHu9nB1I/fFEib3/YMlrLmrmJwgbGdmWm8YBmy58rbOKDdM7f6mJ6Ed7G2yiWm24fccSYXYyvWK5qHp4MaRG/MxXGuT5VxKMPiUHmh7UtlS8zrPKdvKBkwja2mTd+ZGulYSCRJhDSwQSwmFGtzMEr9y39IJLsDAHXNaKtJ02mDDf0cY0zNGtSp2uKQg296ADWf5LnbFAtVmVH98XW336VmuJHzN+HD/cZlhqXBJgsMgIUHJVgjVO3bmQZCQlHq8IWUPBZSEVVRz5SCMqv7kRauetQMSxGDNjr2VHy9/RZGoBeXXctcZ855qxW5XmryH9qnV6K6pxm9UhOm9b4W+4M5eZfOpL6JDpUWNS9h3fUz1yngF5jlo7FIxvpErFUYmMe/gwqWqdhXd0iPsTfBUET2oelOn2q7JHPEgiqtgAC2CLpsmLm1FbtilU3uvCO4J4M+JtsWxbMBu51XWlTMiRHLS5OZwhvonlBWCn00wUKcti07IHeBRz3BsH1u6VXI1wGCFuei3+2Ru2QvkLgDXOV60HqnFEx56KaV0Tn19WzaTzvwVfp/5gvUL06mnHFePf46XkYcDe31524K+7Lzm39NQsjpnVSY7G9mbQWqekwB0PQ5E9Bd9J2005oSC0j9YUmPyvTVd9kYTle9ELnDeijlHSW6/IAIkQYQ9cdyJ3QKraj95NpNHVAfK030+tgQPK26NSJFlkYMn9kHhnEEiCjss/YJ1cla/WFcCGjWpVi6yiD7rFyZm7V7ryNTjSOcCsxpWEXk8mGt6S2kQsx+Biagkfkf3bNXz7lQZ0xzvl5EMen1WZ2M5zQ5Lusk73uIV3qTQvTOjSAMJdHYdnl6+CSucPlmmLoqCFgz3x8wL4DxGBRv0Vj/KSuIJncbalKMT1AbrbwXRB0bXRT5NkVgWivuqbX9w80JnWoyxL7nmy7t/YIEXco1++hIKKoKiP3/W3G01u1yoLEw3kScEWLpGCBlPw2M55LRx8qJeXPyPgmF6yXybwYg6siDbJ4R7N5GG7XP1LS+jGRaQ4b62P6f45hESU8zuXajjEIem83T8YMHeDSzFG/94ewM/NBptoljA6iGOKifExvdYkH3m4DUp+iTrg3R+L6pBAQ5ud2yw5Fm5w+HdsMq029gvKXf0naJB4nFJavtKE5qlVMv9sLW5HtFCg8l1JjdfYxxS1CFC+k0sl1gnpQhIKJqZAjidDtSiBqdemKXPJNmP64HQJVBsgbjL0mnOKeJIA1frJLxpXdAX6rZ7O0+JNzNv7VPQR28pwzx5RpkrZryhBVtc+IZX5Ssrw06fLcZ4EIkQ9rccQgGcopYutF9FWlXLJE7fH7aXGP6krK+UNiTklitDcZUKNuGX/y/kWYfguHqBbLdd5eDYV9kVLbt6nHroMGEuZJUmWyIzSckA6P2MRyn3bggI4/zE+aGwZCS2qDz/WmwH2z0cqVq8+uIVVr+zeN2fN2XU8Rubp/rT84DQJe1ZiuGV9avr0a6T9mqwV7JVDZF84Eet9me+YAmwa0I+M5xRTiQl0NKkwZY7N5qw76RMtMPEBHce+TVIzuDBCcn+UnH1vqUmj49c/lRsZKOMDHesulDtYQ1YJR+GqKyHWTBIoCCRSGbVTacdTc5CbYoOEO2AuA1+yCLBUFyZObQ/D6tIDCBJNT/nBz9kLriTjZwwVcB3h9sLZ+cbcZlMTVeLza/Wlr63Znz/cIBnTr7hY0W5rEQRedE4o2uZTsKvR1jsnRax6POLTY+hIMlVfLrR7ND9zrpH6NJoJsnPcznNMDGB8tu7JBeur00KfmT0Lao7z4xn4xU+KpBMop1bWfxm5ZE2GcNZIAH6/TKhZ21p4BPzW+nCES6CNfrkMcwlhvvSDKYXMclMeYVu/PSOGkakXSx+6uXL/XgC32SNywLbtd7t/cr3kk24DllOtJg1jQtLVOtSNBcdfCYTY257rNTs28mzOt98cqQkdu5bUEpFnHgbq9oyErjIPPJqh109L3hUFAzrUqwz5+05VYNQhNdFaH4zBv3ZS+yXG0NidBpA76lrLxhK2AVbMjKhXZS+xvUvbS+Tww0vXER60Dc95ibapKfxKy8N83vMI4XljF+jjqGjFdq/R4+y09F0HM7SVkSHu06TApqQy2yicB8XZhTBWJmfP2t8YF2iCZRtF6C5/j07x2tAa/3Rjl6Fp5fRjBKY9p410MJJtMiSojbHjWaEOY37gMZFBOYM40ZpPFQBK3OYYoVIvtpR7BqZ0uQQnQNxayjBEG21ISu4KDxKYyQa6Fgkd+N5099KwAiY/0tOJKN89ZGnr1nPVq+JT1FqlczUAA2efZ0oEUNvjUfc4cCtZu6gE+iwQPdeQk91c3wputVnNZI71tZNDg0T32Zz3dnefa3Y+igkCdoiURfqZeyee8c2VaKo9Q0PpXQtqZM1fyOu5pqK4x7W+pUGjOB37kjB4fDsr1vV0963GprlOIquu5C4PmP13EhVNrIVdrbZ1FtnchHHZzCVNYDyRd2AKbJQijed8mHbgh1wRNx8ci1Am0GUlhNrQ++bwxdQwu6GxDaSPwHFifJ9UTQ/gwlqqf3TTjVsHIY608sh02GDVLJlf//ahiJN93jfXCqIzQbYkBDDrTECH0seYRX+Mv85RcfyJdzna2qCOoMJFw30u6jr5KKn9mP7rAHbWj8u08VBnNL7gSNA4E38CJWenIbf15a/Lr/Ep/T1rO0b8XOYUcTL+8AS+yYV4klsbGvibUfYQ/jjARFV6wFHWvedUJpoPNbSihirYHJKUZgpPsIohQmQ8kq6ROymCMF4igBsSu+fyYRccRPMlV9xeycZdOTLd62wCHgAetAMqZeShUOrulq4pnjWM2niGkW683rbfQPxmd+p//yz8tMx566QaBZnMaFaEoz64NIePp214EpaRXWcY640PU0lyBuXYvskcotS53bNqDQzdTlCdCmKYvARbnRhssxP8yMsewgWOVrmBPHgGzro6x+/BrFHR46lK5M34LTJVBtxPZjl8oh+qDGmv3oQytRG+MT1flHJOylnxyPhIkWawuvcy6S4ne+vz5mCITRuG+LjckddmUIewqCkrRkoDmwf0b3fqTi3NPNs8Ct2y7LIDuUQvqB5qW/n1WC5lwreZaDVBrKCWVzcNTHNcZC8xYiJDpZRW5fv0xumJ5ABVxpnnlftJoyohDh3iCxtonfPEniMRHwvUh17q3UANs0KnWuh/rN8JK5u52u6CyY/vknA5cI3NfwLs1fFc+ri5wbFpsgK3VuceoQDpLIsi6Hyknzp5g0pfzMUzFjUjviDVvfdWslOI12q1RXwoW2DJTbVS5qFBkF/A00tb0OoJII9jJBlTnG0zptiPYE2i33680htI053j5NdtRO/jccPfGvE4AI0cEzuE7xnS/0STCIvDqK/8b3Sjlk7p3txGyCb0/9SrYyPhcJEUd/CviEPjY/x/bqGJFlGLJ6/N460zWoN37mcJh7Z1uyLvqnuw1ssRcNGJLR9EfVYCwAPtACFE+uxfghYzrDE4WYhNQZZMGVwelaCjeWD5g8P6qaB5CC6kBuJ5PfjkYuYdoCzlbQORgxEX7ydOb8CZCbAb2RZyjE4NWMzkrlpfZBXG7APMZrBcPJoIhYH2PTIMqE+cmaXRi/vz81UQtkKH0haPUrgSClPcJiOvaFOhbSH3aB0jmayv3ygR5Qh4TK68Qc0ciqGDHR06NKlRhsTVrQJsCdTCq06MgkOd+StkQ39qRWufYukDC2KmpKlzT6MG4KeWuNpvXyezJtiGMtxdl2dpO9TJtCt6J3UfbTMOO2mwcF+o8xCibn/pNHMzoh92lbaJyUtBBEnrlRfWlV7zasJXBe7aZPD4qxmP+yJQzc/AhH4S+0M5f62w5jmj3B4T9QmMtCri7fjx9CTGYF310iMiRruC2BbYOraIvkM1dr74xtocycxSyBI/+RLxz5q2SNB4OPeq0rktP7o59aPpIMiPIFNgMVbEbLGSyvJhoDBxodHYb2kp9nbW2Q6DX8LRB+K4+X/enjHe0W6Anv+ZLqb180RT9k/dZAXNxiY/hwAt/BecDGPe8ANacSPc0gE3C0ImQtcHfj2w2vcNIKoRfNGZCL5ViXPo8/7vJBmMby4XYOn8oK9wuVCi2+nruy+lWluoFeP3iCt2CoubJGBkgNOirgBYP1rsGwp9w/gTi+rSaoyoECev+16dTllZGnxFKr2Td8fY/3KSPzFw3G+jA8MIuVNkx2R8eUMqE9ThY5XremC1L1WPNTIJRFoktcETH+oU4hktVT4aGlmGccEc/2FsbZ8p3dN/gZ7lzy5DZ8CGNVQ8AVkofTmWxbN5oecd1ErTNCObMhsRIJQ6D+EwH3UG1q70kOMx87r/smYEZf6oLuelsf+BRKeTCuu+eyqspTdDyYXRt2OH1buCTCAa3q9RduG3uEDEtUgE0L5war2iNzmVEcxTS2z8Fh9IOnVh2mGDzwHeB49aAvwSErerZK9lUVnmkdQZhD9ApDuw5Dl11FaiogPJulieA71WSLV0Bj3xNBOFNPAvn0qFAddx9WrNGE/rPsdpr5I3g2GD1TXnUmrLDCVqCX8LqCULztEvvUcC6V8gkijrmg8UbxCIl1ZWG9b3tmoytNEBzMpVr6p+bo5Z0KdQgsAJ1KT5Rc/Rn1rsWzZX0kFRe2GXCBwhxQ1qun4UhGv/rqTg8jR+Ycl91PHWBt0Y/dK5I6Vp6WHgdclD62nLxe1TP39UNah8e+PP/zozjyd7Hkmij+qMiouTf8jwKUCrW5VqMmHYw+0a6pMuS87Om/RQvPvWaVLIFc3HwoIf9NCApHODSxFXGI8GBGJMkRqf2uo9YASuq/PBmZWbaW7gWWRYRg5k0TiQJbRnb7oBadxtDY3KduYpfSheqsCvhrxyYZA1JtiVx4m7UT5PbCX5gwrBsxyQvF458nt5tZ+su8loV1Elj8phJTbPAqL70k03Jyf5h5EMKErCI+QWkE0TZuDQtNgZEFeZ+8mAPtsAAcJesxHxX+Q76O64vfAWAoPiJ9uZ7FMEc3GBoUxRevsoq4ON+8zXCII+RACDdxq42XFBGkFQkHfra8v/D2TAwF3FY66TIVTBuHDrzYzytn9KKctvtTSK/h8jY9Bt68VElfjCi2FZfHUx2Xme7kQ8ZrBhRBwqkdcUsQ6iBt/mEMqKGF/OG8jUCNxOZYKbtGnYzPp1bTeKHJuZ3DIczpsBHEE68uJ80Kq56QPyQjtF3y2W3CiZTwyhPzFB6f4YFJSV//ZLXMlkA7OiqSrXv7txu5P8R6SL2x35sIjN/ELfJdgt5LdDmFQp7KtkTt1m4fwj2Lsu4BUSflUvpARqf9VR1dqBrgyvaRI70Yken2M57tXFUMshM44SJqC/mwbnIaeEVc9gO+wtFlzyhqoQWBgpF1haf7aqbdjT3RwS3A+WwNmwr+/rXyv2lS72h9l/tpqZGXvdpUoN2eMej6p64VDMueANSbNS9L0hFAZS8hdmxDlLeE4QYWIVHGuzrXQCtgiHyJvtn6CjMQ25BIyaeeNx4fNKnRLBY0X0ijNWn1jtxf8McSo+w26z4HpvEXKilYynmkdYoBdERYtAukAV621Y2516Ybs8SFYeriijBWsd08AvB3YrGB3xYzSnNWa9G/mZHpEuucl7IJ+yc4xaAE4amujNSuvyz9fcCRuVzORHzfLgi6kbT/thrax1FwNf593i2J/bUOerrxojuPBw92t/IvLdVaG1SRlglxEpi4Pk0nJImlJIgr/gjEBngogRIfRMJLGBr4GF1J8wFWAQQUsj0GlNG9MbEo9iH9D2keOmjjiSDjSF0n1FYO5wWeGNDQ1uPHSKObKhhyzrP7WCXkJYWzJsd9peqJ668h+QhpiQNLmnI1+F/xvqessHMr/UDuIOZGSR3v6uZM9n6R6rT4TmyERmLaMVOF08XOQ6roSr+tUJQra628DHJrXNMZ92rqWSUl4oXmhxZ64eyZym4aGlGFTYz4kq2sPdkE25Wsg60gzgIlf3npa62boRtbPCoAp11lqyGAQybCwcNNcQLK60SN7FN2qsyDORTrZO9HOIzHe6w4XLU+D0kmlzd/Wb75IoOaYRSqek3amNT06qpKUkyCIhiYgcnb30FbOu1Pc+FvECmnQFTN44Ia2Gg1xJUb6+8IeC7usoRk0Zrv5+v2t5bAcOSRTafyuPZXgKFb7mMLSbU0s66N84VRbk7IpzEJejkTLjx+tY7vpS5C/kJ0p3P9xI1v/A873z0IwFbFQimJJy5rGIr2poDSaaMddPqMQoaeTP47XPrhfNVTHdGp+BX/PC06SQ1L5A9SM/PdujPksFYxHvFtndrM2S1AGdRKayRZgAjgziKlYiYmB+OXWCYxK2ev8ejeXW16ipIs5Bsp9vuJvfCkfUsGwApIJVg6zznJFlN0lcHjpkqiYdrAqGdJQcoZx3cGGJxtZ7yMMu/S1V5RzUQIzRX1ITg8BDiCzyAHqgiYFrssezn1knni7469yJKlprbptB3Owe5nLNunJnefJM+3CiFUbsMoY26CnVLkY1E4ByNL4f3aGP4E6LMNGuBpdurKiKrg8sIsvLM09NHhqQV38wPq+l+KWJVT9BvhUFGB5Z/pviTR7R940bFl59Honn8PmnnkwqJP+F7hyLZdQ7WZysbly6Q/7fuHtlyoyrZtfKYxdITt8AdvopVjLMiwpeJ0mgjIml4IentUhRBS69AfgCgz9laTbQWkbd2BebUcUUCTRMZkPKRSA6zJNu5H/52KmsnjO/CStgJsFSufTHODZflrZyJmZ6PyNDli4FOrENEhMR4OMyhKgf3Kf82yksrovimZLFZMFlLELhjUOhUb0tVTEKZ4sKUtbNxWBdoifbcd7uw4c0bDasUM2a6R7IZG00hVrkEk+tWC5AgfHGB632LuQSWggPehI+CMTnW6XSiHG54wi6Av+33JffTfKHEwTdA5QecXBgfSegziu70gq64QpwF49t5cQqV+bPz+f6NrAb/Diu6J3r4s24REHkIx95RS+oZKjSeod0ZRGoGp07jOb20cfk1Ly5fn609QAoSomH+jb75C2xoWAVmnC3URG4NMqOqFhizUr9LGYx/DX2kfkcCMQRqymxB5em+QEZPxYzL/Olf94BSwLI630q7/Fsyh2zpqJJpegnmw3zJM1Scu8zqnE98rJKIpYqP/YzsBTHvoS6o7ioXQ3fkQ1n6jw+pu/qlBkcE+THF7cnfuRzzG/gjOovA/ZIiT+AODi9jJvaaR2GrNyzWB7um8vc7StjfFeAbvzidmnybmzMe36oHq+WEwZU3mhg5gKP0N4fvrCYhaD+dFiID1jXytYFFsrvITgD69S2NyKbtpSdsbzvOQkmguiNQg+nZVwK18znF5yVG3ZtXwuIujWOCVPe/NrXG/BjhXOL2x0ILieEK70dBGe0GEqHyGM/UsTGK0Gabfjk4mR7rTJws7uO0bTy9wb1Ed7MOA1yb2EQ3XXpoWPkLGnWrDKEDFAmByYhDoDDkZL8gQKJOpQE3gSC87/CiEr7cuYJGIghuOFbbQZfGGXbuWBFMWRiWM/lo+9LL+TdsFAS1EUzzU99L1ofjbFboP84ADyI2+0jmgYdF96c3LrJ5bIAWmNKoiyPGTJPGduV+HGyHWUciezCzOiZuYIc7UI/qXiAPw0ATXLYPhpbVPWNfGfIM2IDyxRKrtY0sUVw1g5fLeGcz/RcEVkwX75YJ+kIuohYEtjBxRuqyA82+jHiebPcReKBifEQMv4Tss77Kj/mxEmDeD2ZMnpDlhkCH70dKKSz6wjU4/cEdiq98sAobAg0D22bI8YhcY+PBWb1wR3crsPeIzVyq228NYqZekNkbPpTxdgJpmZ8YwuYi4YnHxxMDvhpp2mc64c0freonZe0bcmDHCtsCriVo9sg/1z84kMcXd5dYsSex3tosXPIWRzKQtL9FQLNYeCJ2HKq36RiqKmPnuyt5f//71PJQyPfAOMYFmwjQ9m2XoPlIWYc9dsrVCJJZdB4AY3sB2gQVB7i6skZusbNyEfwZ5fTWLFqdgfR2BfXOIpHxJaBnYDmcU0n4CZgpyqd9yroSnPYa7gzZaJ1i7KmUxgOjUMegwdPIKOCnc9TTqqXjlivAmgkM1cYQf7h+N8xRtkgkXuDOufU7rB4tzL/z2efD2rV5hVqoNIR5Wwo4NbCGxBO9HB8cOyIAGLeTbWd2WgLEGtjzdDf7AxdbC3FxcC8JPdAt3WOUNBMzBMeAnEa7bl160WvyYnZFrPSi7npZrnwMia8vCaB5LNkMj+qMAwZ3GlRKPHXGl7LTdik++K0cW8Sy1Ker8rekXHJ80tM1o65kp0UjMCJ+zAHVVak2uSKNiEwTtdc4OyQORSIULGdKX67Uiyo5zg6YA29PboZ6lA6ykbmFzJCqctKPuQUn/2+XB9g0SP6sc5mc2SF9m4Depy8tQJEoD5LSNcq5jnxvN6x/kLNA5Zdwmr3AihHi1bYMVwEg9mPT2mQu0IYCaidanwM0lyy9i674XLaGSmX+xL30O498LhXND/4o13w/rRV9bzHEew9xjmUlURtLLdPrbPiZFxfZwKlY96DdcyQyv5IJeAPOU3Ig1xkeLmhVE+RY5m0qGhdw8BCZE+9HS8Ms/hB5uTjGFTm8ESzhEoFSiEsUsHSAnMyyDenXfd2LUU11fhcgVoNIHu2ysvRM1S4pNn5kI6xtlgBTtjWMNdA58zMR3qo7IJWi6y6++Ua6AYfnailSqAzjKP3pniwCpcF0d8dmEO8GNoZnTk854lgzrXrRSKU6wGkmYKfbDr+YUejBpMvtOZ7BgFyDlz82lziKLH2dqRXVtiJaZb5QbVeVb7HiAdWFD2hd1TUIcXDVw+a4yubnCFQ9X2xC6uLXtD+n6rXC++lApBrYdIB31KUukgfrH0Dgn/V7kNA2Z1evVy1ZG1+cor20INTsOxwrZfSJntKmdXqIKECZbgcwdbhBuZASmeRr96wJnaEm3U7yygiiQJ9hGLX7PniuGv4EMbEp9KUYxC7mKc68cWHk3Q8wwYSfK8EVr1K8Cb/GCq5FXXpeJoobihlQi/U7AJgIwfkeGaExfRP1htQnHTtwa1d7aLm74mSrfBU2+fpzKPFTKvU0GcU3IO8u8YGKw4eZHBnSnn59osFlldK0A/S/44tFdU520Wh9j15W7Eyv9IkEm96ulN66lNWaq5UL9bpNbew6Oxx6Lj70ckcUCfYfuepf53Evl+oCPoEYgbyTrfjRTVNWcPDVfpPcxTK0qVNlL5p0IeABEuh4m/GsNr1lL1uG9kZnhB2icnY//djKzlcObNYeA/MfvGYcVtJr4e9LwBm9UtDzdHo/cjhsbUGJSxRTPTv4nmnKFbVdkL34BKoafSelyFCfD/mR8pm78PN77dimVzA5BnJo+lqrJCoJ4lm5Vpz9ZoE+GriwrItQE7RKOYl1/NoEc+OT2EiLwBbUEiQHxW3S1fDVfBriyGzE2GpD1XTPHW0eBP3CqHVYAVfF9UPuT4frww8PzF2GKkROrYcHWwGPClomYJWwNrXGMpZuuLCqk+ILxh5nm+stsabNr67wMGNk/+I+6NXKh4t99J4Z73W5m18/xwUJKTGOYAZmuAEIpnNt0ONCBFe5rqT/nVngP7ro89fm3MxQAWqyaQnf/tsDlUoKPL/6CE8tBplcnauS8KdFjrYMOHWQgp2tw5OHMcEJEV+OqZ0kmbdNMM4yVEtLKYqH0r+AvLxqvar7PYGl1Vru6veDwMp81t75n2/trB71tCxFqSLhATIc8pFXiG37ccgCSGzGFYwOjSPHZsWiynfOEpGCYANTDxHxZYgLzSQR4tNfeRe1Thjrf6Iv10htTrAI5ler5JF8zI+4Rmi6MbBqEveisn+MD7iKLwPQyWaaYdaTgSHoiMZ4CazEMq9bj4ToqjvMg8iJwhclE+BtvUYndMhCV8jYGpz25eOLhynbIHa1PndyM1vDVo8LiFqZy939as9El2YzNCdndHdgK0lb85MUjzjR1D226LXBqK/a20A8C1iYqygyFZBqHPU/A+1HvDQBLOgoyHoZoHTnysFZXYhE6C8eYeSNoh984OJk4noPi2ilFC6SuviXBoIJdQ6o9XarSMJOEhtRUKIsOoy33X5A6jS/I7T2KjQwyyPioPaU6nUKVmhl7dWsY7T9OZsoP90ESGSv1urK3MOOIFLu1lEj23JgPDMoSk/4V3dj1ddl9z79qm9ueJAhpz0CtH+FKurVw08Zrt0FEwXP84otof0havtg12/acog+G2Zlsx4hli4Psf4yFWLHRS5Nw/bOn3oa1Izfrn7gkfbAVv0H1IZT0Kz/gk+UQPs199d67TjE/v2A4oouLglINoc4sMRPuzCzpWirmCaY3uwxjRyetKnKCLyLN1wRg4sAJlZC5v/7CVgZ5CZ5OWUnKzAcifvrWdcdoFoHX3q4ndIuENieqsJeHTr0KCgRa8xkGmt6/nyFRh+DzoEZV2gmTGvRddFMSE2yMS+oOhQahrL7hTCn8V3D/INB1HiN48+hwYBos/bP8v+rxwFpiRs1d+T22RWp3NvYyM9Kjek8G+3IsT4Z2c6ids8sCmhddEIypOg1J2ZJ7GsM53nlsh+B7FhR6R4WNjZ3wQicC1n8P/mnRA3dbr6SAW5QTK0lCZf02BHj/Muh/T/RPhyPo7+DiRqKeLxM89HXzGis/+rB2U+2VBhcAVpD9p9WKjvv2rwlPi5gkSD/9J0aVGYfS6InX0NgeTjLuvX2OQY9OoTgBshHeWgU8/GdQokPPXcm0JAwFf2GXqcxbS4fzuLmOlEvad+HOUGziOfLj2giDVq74DPZu3C2a8ziSO9F6llrkfEVoveqvMEwrRqRzjCZAHyOs/Zq7ANI49CUI6ymPOUW24yg3pixhdq6gZeBmFiNcJ0usCBs+evDrdBdS99CAhselrgBzxu3gcoSld+J6ClKm5F5xapS5PrClgIY5n7dTKhGOzyr4+WVL1M+yzSZ5ARDjrTL+F+2/rRGW+FAwK1rp+ItkTQkmF+EtWy7mvRtSYv4oKxAhS4HPgLwYmDplnCvBSJmm0OY7LOdkOB97eT6m3B8D2T2Sixnbcla/Gzj1r+vMBDIyTjJYMr0gd9mBlwdN5DH1rjLbAnHleQAyavoCr2tsXofYRqYk9rGzD6tx7BFmfs3lJ/vWZaAH2mWQLMOfby1JvR/Yjf8iJYqMu1ubHS+hurbzFckt8QjwnnPX5ZD3JuwuYvVQFiYoiZWX2rnfEjIQXvWH3zwibZvkFKQkZMMLpBFDwc68mzM5QEmpIXNgjZ3eZhtvN/VPg0XrbKZXlahphXPwANVkCBREO3yi63QBMwyoW/GlzjjaLr3wcVU5AnuJ1VJ1Rgm7nM6dgEYUrotdphW6zIXS6I0LMYMwEq7W8UX3Xu+78i1MXm+UPA7OcNwXlJ3aTQgwEYqT57Kh5OxU+bHBAMOV+ENDnH1ZxnYilkUsRTESCZ3y2AOmYrV4pqpSEmurB6IDjoageGxf6+fXrcyhspqc9Jg2xq5WGg+Td3en/SBQ3VOHJf0yMNoJq8CTBPQ5hDXpbDfuFWq0ELV5CBEGm0vxSwpOKpex5HQZDhWMAu7i1xtZ4DBp+QTRCrsRxUVLVewtQpflEu8iyuYevDxbo3J5SCIWxXKwWp4WFmC2mRIWS8QjGLZBZjmOMcrdt0zckvfEZpELhUrYE8fjzwVQQjmEo8kjgZhpePKxGftyZ87qw7wnEja+LCE0IlyB+nwleBFmgobpNHMITbrACiVLOVQysFRRDegGRdS3iVu4cXek3CtD46MerKnu7nusCqU23EvDUG7G6OHLh1ihlE24irJWn1XWTL0WDSpeLR1zzjeAjh5g5vkxIhia38Y1H7TSg2zRLWofU7MGadK+1Huuh1AmVYmzhUlujk6bRgx/2z8eBcz2PyWi6lTyfZGhAr/zOJ3TmIS6YeEnFxsFyM+W9Yr+wAPJakbe6k7KyTKjeLQIU6gQasaW7PbjY/jrsTyfTboOX9IV898lVqmpuXu58yNLjCQ3cCHBmk0IjsPww5UeW3jhF/5pQbZMwEgiJ2gBqq96aIKqY1MPH1OZss5k7G2OZPMcEOXw2cISCIi3B6PPzV+bIr8T3VWYHh9KsSNzQy2LXhM6xk7X0cZ8Ez+S3kySKQZRMt0d6kxkHvaRN+CUycQ2DzgRtY6mRsqDIQQ5gM9XJGd33vkfIfY8h/URVzw9IATEmzKR4R0RMnbJv4r4zA22VyFcyEjHCFFxp4voZCsWEfNP2aevSQ4YYyFw2E7obSfEZS8o34v/7GNM/m6rAFsYZPblcIo9CgDRtIrOuk3LqEqdjlZJl7fxpLPabsX+7+9rc2Y289NNMdyt+r08NK3kL8NekytDhNgevgrwqOIZEJrEWL3QmMeJLkoNx5gUvgNOUQRXZe0yq2+AOOwl7HLeUIsa5bPn2dO7AyLAkJLNEx8jdM8X99QFVnH+LUkB7jEAeK3qVUpSOyoC7mRmXKFD1GVwo6LAg9oxpjfWMZqOPgYv2l+1xUdGECD/jynVft3SO7RyNLeq8TqS510tI8E9+WHhTstl4EgWs+OuZKU+ZOd7oJT6xDY8KjOYRQxKuJgQ0aIp4YdV+pK3T+ecyqI0ugwpLDh+kTZU6RwkuZJSwRrL8zB+zaBiiGgX0Kmd7eVy+6Hzp3Wjyw5YYji0d21sgn8778c+vDQ3ueJd6xcR6sZ74nbQ1GYtwMHED5vJexxJfUuom3t1yDtqMkZb0ab0CdSoN/zVEIDKuKJ9UFoUAJlwiQlrMEUmHdctIYbROkCYMRE3vfGS8VhLTAjjYRAL2lVTrDEhItS0xID2ZZ9KOrpwTjC/nSbD6cqP6w3EP7KJ2dKGE659VTnNON4TqR9l270h00s6hxPXRueNbS9uVpDc0QSZbFtcDZ+zBVW4VDNOoA66uElucLGLG2s2QDek2sNxLKNHTu007wBcgODwH7J7lvGsuJcrcYtaJVP5tjgh0Ig7VifrDOq0eriBg2PtxsxaUVzkbBeqF13PW1Z696ChZG6D9VXyAlgwPUt2m6PlkkPfPzjOFRGFp+9gPP4JqcfzL802FWJzpdXsUfLETFPVBPfPsBrvRXxSInl4X4t+6tN9V/S75TMctCUN7DDZv7fFpUcFc3C8TLf6TqVIAljf6FAaTtvWn1tf/dSW03CvpQRT9p0vQU+DhDCd4xcNPjd9/NrmxHken0HnLIKFa2R0YI/rT+0hq5ICLEpQEE64JPmzKd7IwObsVGsaexCcOy/npY2dVqYSd7r0MS9qJzyq/jZH8uTrq+3zP/d4qY8dJgxvgjK+Hfv+/QX+UTZLfse6cGpOV5JEhe5Aczrz3bPeraPNJhmJ2FtfRfykgCZ9n+lspO+Jl2W/8qXbgdIYay7MkmqSOQWr1yhIUZGvgmG4LdIk+KocqE+RJQaCrYW1rtflX1NC4WeOzOh57cayIIWDP/wTV8A8hqrHS58fe335noBx7P3sa2OiI+r+0DRmFwq5Asy4mUDqm0E6dffJMtfyGzBsG6DlbjZC2IA2mTgKl/9nV/2jXZYoLp1NmKzVssvzRMmsHuJ87acwkHvIBf+e5/ohtM2U/dpPgP/glMLEyCl8dQOTlvVrbEwfG1m9Ltu30OEDFFdGFgcfgkV8iN6iNvwosfvIQXkdqaTi/XdUrOQRvkQsJjh3AmqnJjKGbGOAjXwmYtXknbdSTappFModrqZMjf9UOaphlOvV1wNO31pVcEBSG8Ahsmd4PhVNO44CSSszTGWZXGM2ZzofU2jbFlscaCTJq5K+6HZI9PiMS4TSqA/c3G8/IU8CxEVMr5TyncTp/gN34mOne6DQkMdeTGBLc+uG3JvQ9LKEL7Q0jorxgbHfoU+P/tHZkfZ7JluTcaORjZH/nuMJN6G85UhqW/kjY9oKpsT4j9Y7wln7XNpOvtJJzF3KN5CX7/ocWYUgKYqgusLfQ+xYQDhdr4HN69peRV8Og75hwt9YxpF1vEeq56eJhTgACnL4ZCBnfOpAUurMWw/dUFtuTlQ71phb3qZ28YROCzyBp+fqLZVSDB2DpuuFmLw2mjYpoUODCn8jQE0ibRLL7ncg8IrFZQj9jiH+Bde43Qx6HTR6EnSzlXHotClY4AtzwhOsa6kSz41q7X024VeGsQGIL2O8SoZuWU1fkhBWBAbZqkTQ9AVL1vIbdlSh+djPHwR35pSxQozbvcAqflab9+g0eWiOirrtwwM7djFf8qTVJG31OyJNXRjjBmehI0sGUJXkgOvaALhO6FX1ipd6l0KiZpy2w9wESPaOTzMP3ZrisdoqOYPM/6y3HfcFi1zD8QR+0zzphNMOTtteKHRprVgvV8Qra5O6aOQD2iRWZb4a9l3YMkn+nptWq2HMVCZIj0y2NEI4f2jO207uZwGwA+aAghd02WCxel+5RTTJqNgJXbllTG2stTuyBcnG+OL/YwMNaJ6LbuGuJskfiIDbUj4YqSOjrlQW5g2t8FWhv+CjTDIKZQbQM9mP3VIT4K1R4eShdy0CfFL4s+IUZXzUHt+yO1EcyxN3gF0ovTFSz6Y18Bu0iZzZ3G3kaEn6YQDDkbZUp0YWXZVbVVq10QxY9M7BnpOoFn8ncpbm+uKHSKmRv/UMbpnCyxcsFEcpRGv+VUnqhQtHSW+gR7Vx+t4dzEv4/5sSsSahpdSprrXhNgINOva+QvJctuGeqS7wv7n04aNqrItUiD8J0e082fRxDRtOJgppdasElsmp+9AY5a0Tbl7RUGLQQaD+eNODJcyPI/5iYpOsKIB7a/5807QTtyeri7sloJcP0hRs0PSlDqa/UIHfiSMi68/d/W4u3MB8ObjQcg+moX8ISdPaGnPhBodDRVbp8neuhuVSFY/ZBcVC4QVdX6w7osLVsss6vRnnjuTvQ2kXmiA4Y+3bR8f0s1D6F3e3E+H2LPVPmGGFsbYa5dyC6KR+6BFAhD9BYV8S0tQCzU0Mk4nVuWwwgkAXhTnJynbqKOi1eMrf+4z5y9mxhxOjLzbXVL7EA2xS27oQEvlA4lHru89bbikixHQLU0gfkEbSrCvEE1NpFnEkyeTtPkQ+0mNk4HI5/732ZEaaecQE903Wrgz/cSbkz3FwEABrbMozj62EY79PIUQGboQb5n4nAYkDipxoDAaVv5OrhZYE8TGn5Bln9WHtZSLZqF059bM6O0mBioDvAeFVyy3ofj++8RJjUDpA2PUXVsrJgu1Oxt0nnccr9/SyrdLTA5cdYCaXCJ6nx7SG5BypPx4YNNpJLjVhFybjRJ7EoKcyObEkDTp+w1dUgfj20s80x0E21rrPdMVFRQU9HWcKk4P2twse++T/nQ4aZ69iuaA4YoYIeWP12B1zZru+gI7lIjeRlDNHV7kuMt2NioQo9TI4W1+0c1tIs8Pvpsno9oeRKiNigBYydsoG0m0IxyNYXg4WadiYuvb2vKfoZowvRlrg2Vp/An5vSFPsVPqfJLHMS2vdbc3y6ulE7C2Qg1pNU0qUg/+9olLiCPdbSKEMlrDMX9y060w+rw90BpWPcjiZGPYqHTluW/UqoC9z69vIUtLFE8ddMi/VFvOiZ9qisuC6Gd06zSeBnOrVt27+UxTQ/I8MOwKR5lLbG4tBGyso8JG2uO9p/f1iKXmWUt2i+jqWc+HBf88z+QdTQ1rKrgtiaGM8d0nB6QEY0Vc6I4ivO003yxTaVzLspQVdsbS1uYweI/+LPrUQXjWGWUG/q9QaoVRHQNapi78E/v2TKZlF6dK3ZGaszszVOmiHR62B52GvwQ8zO+/MUTOpAdqZ4W8pktd1sMjdnrsA6jmNRQK+/Cti8YslxqoxoVgZFJ59DQy9N59vYF/E3UPT1gzPzDfGJdWkt8NJ2/UzOMWcTX31UGKwpNIylm1HarRQyU1G5tiF36qS9N3kZx2dtODT6kZZTRjVvIQkR3CnXl1ppYubst6GOoGXgW1p/uQCWNW35FhAxOD96kCWVg8LLtbvJTgjBkAM95jZvoKgNTTHjjx2ss9mzQocC0g89g68SMtaGv8nbeRfy5RRFQ69MiJmi3tGvN0cp9nI9Le9FJP7fsrpZJ1cHsVH4rlsnJUSt2TbjZje5v2GznmIcTT6/D3XWAnLTGW5QtM+Ej+u0GjCN9wvEwA3JCYu1c8ZSJfYE/DqzcS4DTZs0ffMQKmz64wIa4EZyyO2d8fbG3PtZWD6Vd0Vpzcf/KXbblqHFrAkr9cOG+5TwLZeui+e4n9gzbaygERXKyl86UmIES872u+T07umbz/eJ0brQrBW4PBZjHiOwpGykEW6kmw78zvrmKa1UwPhK5SaZNiTWPQCW/Skwxgk7ivcHTTuDEPba3BsBu2/yOJRj8GkJaYiTPrzPZE+jJDhxrVZpG20fjeVW/jFy9PDzVIPQXm+gSbpgAGOVLPAfBXIYJxkZ28z3g/85H6YFo4PtuwTsHtVG5THqzmjJIkMf5cFmHv+rTU97i3P+U4t/xMTznpP1lQTWlKkVNG8Ov59DP294YbdX+KC4okqFCnbIs5XbCtmFhBKW5eQTn+qGZozWUfnXJAg7ZFh98YgvIfwtraaBO1tMQDapEkeuXfmah0fKN8IICggazdAFsmyJEBFqcUZvfiLXp7RHPxwghcXFBh6ibb5Bmj5hxer6tmXZTBVj8veXTLRZ6F8UyKuuBojwFvRjznzykfkVN4Nz/9QNg82Sl5GgE8o6n54U2JVsbtVAEtvjzezZvebDclGudH63KxuvmILE9cQEw4HQNHszK25SrDTuxlR27+daAy1huIVFE8PTzmVOhJZtlQdxzL48TI1OzxgFO1iHrff7kj5yng1vTl4zLnSxVpbZ8JQMDmfMQQLtzf48sk8ZYOa8FnbDOcJw5e+9XUHOYGD/D9MiLGqm6apKslHt9dJjrx6hWztWI/0InlzgCuurk0nCOzmF/cgf9RguyFdtHfAMRSIhArqIJYq9J37VsWs1wHl2yFMQB9r12Zj5QTgH2YnJoLS3kJqFHKlKUjf1TClMoYbfEd1be309Hg05oEuG+mLvLStvDplDKnuvqapxYUhYenNaInhUT3wcDkcvuMqI+s6UQDENLXqmkuDAEwT0dMJq+bVy2u8Qtl2dJnkdbNahUEJ/3xknAvkI3jfW3T6dNpTU2Supy4uHytTVjLvzhZhI+yXHhBcB00gQRcRjkH9TkQx4B4CrHtOqMUFVbAZLCm5k4AdD8XOcPF99pY3Gozw4zV9b/z48kE8PvYvTyiR70KWBg7d1aqouRZwAgY2lu7f9V+8TSueXwht0n34EpzkLYzHfCsJB3lQQ+C5hLoKwjnsjC6mpC/dqTsrTHd1NzQwRR6ayMfplhRnp7KRQ4dFLQKpocMqJ8K+8SXnEGxy1hwaDc2QbA/Hv82PlWeNDbRUvPT7Vds7Ozm6DpmyS1raJT6qjisuASkr9B/F59fA/q1a6ucMOOlsJ05zIDHhJd5NKeBTgpLR0pZsga9AAmJfj/t5qBajpRrgIJkFYHn+hyxcq+hp1BxpXb6/IE01indqsqR2eqgp61yLcr5DLUzeJooQMLRxGbhAvLrUurD7E9pqEbA1M9RgxE3pZhd2/4fGbvFw9bRn2RRF0fFhe+v+oznakNQNp7dSG/R/2MD9eiqootrMo2YH9BVOM9xjtfhjO7yd5yKI5YDc+vY6SO+DdPIeMej8jaoxrUSCBfBqiPDab0ZlNntxzFuzx4U/DFd7ZiuNKOxe/oEaR8qe3C7JB1cR+sGEmVgtw/0PjVzD+PWEMLw6UdoPBBb2Y3qFb74wSahdJoU3ZL0viobPUnUGeGlAoz+B9eqpZyzDbz0QXqem12n729kCJ7mViLzGdcTTDubPiV3T5jVQpKzCFllg4HhUpuZaqoyQXZvppM5wOMvAlM5e8mQrB9+CUOWqpreUpmy8ba7kuOgwoxiuooQdqeeH+iSkXTxgQaVHVFgjkWsOqkYzdatgJgsJDe2kcJZpF1jza83TCXgszzInRkDGT0Y90gM8deUu8pYZaCsBwWYl9DRCK81IJyLBOi6F9zbSmrUWOCy1xwJ6IrHAMHErhoNlK7mDZikwmNCUSOKbCltNi/z9BrN6Wa8vPwcNSS6CCcDc6BVG0YENq/QeMKBVyDd0waVO2TpTDdlXevzbSqLSFMaLqheVTMUdaUPGlVEjf85JNtFCSMniE0EiuWTv/KLBRG8lv/wOOdBomfvf/efX7MnSDgaPHnYMAHbc3UlDrp/875QXn+U8Y+w4Z8+7q9xquxz6DClY7gB84f55NnddFbgxm8Ammox2GD5TsUIyJUpIi3UdWhykrb9+UlIKIjSGn+od7u9tbBmkYDyq9Ay6vMm79S0G5zZwki3TZTovKxBsPGfkp/bwFnadvadQgGrfMZ6wqMVmocNU0MCctL0K4B7pE/Q7z1XAtZqeFpqbexnltB9SfWqrNOoG/8C4qR90OHdbY3p/B2FWzSX3r6cQ1XsRkvh6wd6qB6GiZ1tzTlcI0lErlOuBhFW/n+CBqCB5HmtxpnJtygjlgGyMw0PMmo7EE0k9yW7PBWCNfCtsD6kFly95B5pJeZPVw5s11QLDJ2JjApqZtj7gpBDbioyKyaszB6++/dVUWHrj1AX+pI68nfPzMtVwbsjuORE79BiPMKmUpqtEVb5WooD7HRxS0toPXWo1hJM07Xzlkzyv9qu06d+yyB5TSPPYWj7UffGAykjRliKKqVtqY4lxDitS1BzFvqs++83EmHpc8MXyVd1Ua9syZXU5OXI9NZQBTemTKtjsB5PeTd7wr3gHEi+GjvtSUE0av2PoeBiBb7KTcoBX/dtWF6K1XhHK1hOz+xjz16JuvESvMlTQhJTIBgYjacZ9mqqJk36BrZkdgDfd7K3K+1oBeEC2WS0pwna99ooeDzRVZyxVdvhHz/CD98uS9N7RaFbGdFiNBIVi5i7u+uHRWzHxdi9V3AAmTpHcd+FlBV12N0WSYKUGTAUfmFrFSxOlER4xkT9DcEl8nT4l+xPT4pD6THve7a5URBEa2neL0T//y79jeB7zZKlw67PJJ/yvB0ah5ohykoj/Bl64SmD3tn9tPZY27ltrBbeXqKDe6J+3WYesbLCxMjZnFo06A43IykGJvjno4FQARxsYcKXQtpLEjIKi0lkF0QJVK6Z8pt150cQ98CIgYLs8sYSlyivohObWHfRELB6b8gjjigDMGnWlPZNZjT/PGLV9H4D89dd6OOstMywr9OcxaAJMSsa9RHtmDM/8TNcfxx6cVdBTar+jLdSoLAxUL1jW7wpWrjZgH2+ZWvp72l2FYp7d2QnOhSEEWbbN6b41gy7jW97Hqtt4MG6LjEYYRfPdyXgZq0xjYSS65xGn1dVCIK5J/VO3jY+z7RZndAcTuTAfAxYoAClQe61+3taegnVdaMtxXICoyUGb370A3NJr6A3NXz8PY6okvxAE6ijMkKEDjcLMXE5UxL2U917QiTK40Hjrub8zAXPz6LKBNlM5QwJeUj+ujgLyjwBuqVS3cf8djcYyCIcGnuqwm7dhsnWqIGpRP3ibpgPrDuDT0aNJXQOCpCtcaBLYwOUily1RRFXRVkKsnOIzP0EdNciftBzXYo/VOpeFNpwLHSYsEpTMW7HDrmz4ECWMU7tann7JVAgGYoUL4U8Tl4Z/D/AP4PQ3fsDVjoHP/fzXhMxGFndsAcTMu1PmFebHWiWsJroX4nfN3KUdIMphdtVdvoHpkJVTXLF02IvAgn6/mf5IuVsJaH+Fk0BP3yskYcxgnjrYdnjydoUISTuml23NlbVn7nya1COYnYUZj5D+AsMDs5VaLJDqteDMBRlzbqv+S6UU1lRH355oP0NQqaoTuRARRn7zYekPoeWxaHJ6mDNfNqdFZOBKG+YcKAgT2X6n1A8Wy1F4k1WgKots6jrXIrVCkmW1DKdwN/B8FGJ4ATiVW4seuRpFlONn+eVu6W2HznpgWpegmE9Zv+rcbiqxmQCed9yi/T7wJSnQLTq9PrWn+cT084XpUZu0E/RPdFSO+ymedzyvUP6EIob/R+3clMB2TBi9y4R/VtR3JGXR/soGOzSMw0c9pWaiPAR7K88JmAnBSIPDFUBDw6jhqY5TMkn9a0PHBSzf6vh9ZX/40up1CdEDinEXSN4gqflj5TxRx6oohdgDLSczF6YdGKzvpjicfLh/ltEt7/DtDyqlpKi5UM97Qd/A9XVXyA3xq/vAWcvF5uQIDRFLW6yccWx1QL4GiUJ3UNnuzFCWUMgn4lp2W5+IWs3AhzYOY8vqG7HtUSkzMk5/Lg6jIXhWF+HrUlCE0hxoe5ZfPp66e7dd/h6bH77gUzYK0NcU96KY8GvWCWq5sJh8y1Yq6w9E0+72lTc/LGYmD/Kr2dLB7XCG80MyydEb1nMCQK1LIiin/qDa5opHpBe1Hf9f5wSZOs9MnpiWxdn9meKfWgjNeMUnzvE1/8MvmEHA5/ppbrS2Z3cnK+TgKBhOBNF9FqLfmc0w/dBT/6gNx8IpraFr2X/QTghMmL+nwyjQiEnQW97g3HxtXIBEFtEttqqLZaSnb8QMDS7qbhDXjNSwYyR4g9UY3L3teGD78KdeTAiRcIGPgr2uZLYNristmuaNcGGIMPGDQSpGMqaSeoR99CxswIb59XOO6jLz9RsvaQ+FmVGLM+Za1doGsVg6RQzvJFiCayaPuWXXCeZNHox16SsYsPjzP9+WEtpzOBfVEqkvawvB8HeGDUA63CODfuQC9LjFDKDMCsoNLIedYNzOwJLuXqRcIXA21MU4SR8b42g3Mb27MmwQJZrv3w9tI3qLv6ftOjZMP1V9DFvc0batVZvbVBb557hgSJkyfcjXX1CT5w0s3x3lDC7zY/wIeKp310xlFMw6xMAyCrRMERk5K2cmoAbsB3G91Dp2/Lk0ICDfpGHxj3wa19uKIj0aeeRKYWzUDks9MuvnPuvVIaQ0Upal5oNXzO6cugRUTwlKXGxE4gvd9gT7ZR3djTsdwo2uhgHsK7oCrIL5v6tIDe7488O3HlxpYgiTXRq2yIqW26BG0kCY39DsCUKx/o59sK/VgZ2C42eiesbjkhdQXx8vfVAGDXubct0QtSlKqhj9ha8ObeS0IacKakkt1Hwh6ZREsXRceoV1yY+5ptC9nl3sj7k7jo317JpeiESIM1oA/Xfet+IUHeQe5hwztCQPdQ76D0WeNhQt7ya1DMh3WsZsvgstbH7f5/jOdODQjgAMbgRYKYC95EA3Yw/hqP08wireMbF8f6iq4S6QqIt1IQ6tQkRM3PWmIf1BDCJXYs2yX2k8W8fX1auwpn+6JkySSY1QaHLU0bZmo2KExLUBb6IEbXCWyMvKR90/8J+4g3rKUUUzLYkYzXcw6wjT8heJoj1vvZJW9KMqC+hROIgLouLr5msBJ1SvD3GQXqY1SbxFgjBUMv6KGLW5rPxZdaidn3tLlsUaO6bIKswyb07H1s0eNaiDRhFF+pDf/QW+PZwbmyDKFuCl2Z/r5rEK545iYtVeZ44LA4xI3tdVaIoHyb5y0OlXQCysi19V7wqUKa5YRbTYvn15SHmvVsN9LP1WDj1O4ujUBEfVYyF1U0XPo2mRDrOAxiSci0utDEO4MLSNRZEat7oy4GJS8XpUufLa2W7HPlQIAhtOqLrWPPuD/rAUq0FrH7lAqBwUy83RD19p4rA6lqLhsGJFEfu2kZLk+uJwQtNg4ibqsbsUB8rnWQ1RovzcHt/28JJ25nWcNliv/1ZVJNEVh6ZzGn3fHdhmLU6Z1Q+hvTzCvNm0Ef2Az4ciVYE8a6VTDNwp409oPcR3oolnk7w+nAoDqb3AZJi+7qAL1JCb/2owaqv/Cf91lJKu+uHhni44ffLK/5JEPkhsH2prt+VrBlIhcR1gzN6TVykslK1om+Zoc/qoO8y3k9WDqzZuPTjgGgqK3X6tK3TAVzgum0ZnR1cIH3G/xjK/YJoUUIFBsfQGxzSxDj35oI7UAT+bdoo5rtxT5/xJpHf/jokXx/pev4T9t8iN3pDlvEXb4Y4s1LE2F8fNQF0jZGtZ+/7qV9+LseRSyPkahkqjwSkn+T4K6BRDz8QBpeb9SXiEVtLW2iXUg2HEF44+Ho0mtJOSPAHc9YPe5Uf7uu31rsSjns8KYzO4tYaBnqEyMLA3h2H8Pkr2lf/Qp6miC8Zq4S3Ksea0d9rQ8CVdOyOQGdl47ivAUKKmicZ5xwEr1vrhNqnOuSeoW60NZO+Qfk/fD8MDTTcGfijctp8l8ZM9+j2CGyO2xmVFa62WgbOdxMhD6G95OQa7HuENlZwn9y9gQO090gLkWnnWw6sltruyr42Ytsx6oF63hC0qhb8iRQEQozA8yFXbu7imzkXbJDi3032vN0w2IYkHd50WKtskp9OGq4hNdFIrhuURmf45Ds3KIbQxs5jJ7Em56O0eg9ZFkIYkONBdNIva8zG0cLKpx6Ykng0x4U84ZLs89JnnWPmYN9iWbyXbMWOaEAariWwtBk/lGZH7z3y54UNt2aGnxVbFOdWPDJ2MtqQ21kogRhmhlGOOn9QwUAW0rUm9IX+Euq282tJMzGYRfw4VVV+5+JZtMMQ6IhM7Nn3l1f3LoIyTqCD9deW/Xufapit0DXQif2aAlVDSv/ER4G4DZQbR1gPrFbXVcmyN0qGWrog6CmIW5XWGGWn78+OF+xapqakud5bhj8+Q7rJM4IOPm6uXMKTRCiJB4zLaz1TNpK/4xgOq0vNfxgMdJ16y3SXPeHUEJuNVcwyiKxVjmbVWnFL8cY0DY4H0fiepp2lsVVIjo/nQRzdR7KhcQecO931bv9PyFIILinLJXhXse409Df2DEEtZLoY5FTc9/zdHTfoak366hhFrLMvaH+9mCRBl//DnzWstDVxdBO4xsVxBtVPjjgXb/K3KTkHWCci5NL6t98ELYLYoIRQzQmQUMS07i5QJBhx+O6lFNicA9oHhsD3GTwCoRofu40qxKemSlWtH/lxbmXu2TQyLIcpsaLeI8WLitk3CeLdUI8JiWTKxyhWmeiqBf19475rPCC8xZhBXxu4jYWj1fbHTa+QaCmRpH0VJBkXhJyHI6UqinlAIhVTaC6d73bVfwlr947Sy6MLy0U8tMq2OoFdhA1smsVWJoRpWJ1+ylAEfCK8PHRcNmFCZPJPS7ex1BeJ+97RLl0W8x3VQlCjgCCCxhuM5fP/pOPG5UHJKrTaD5+LLvBYyjWKY+HFqDWfKy7jPo5DppHI12bKpqvM6kaA+XdFujIYdGrcEL0sTXjNmE81S+O1UZIpOvS1cDswjGRh1XHyqTu9YoQ36OdtmWJjYxXXhAEPb7EmEMYEnRWUP4AHqPeEhE1C8NbSkNVN9eRVKc29OiLms3Hru41kN7a9uazPu/lRkPJBJf6tlh8kzARcHqptjj1jCp6tVufk7TVAHaWYPAQuZKzQUYLbuEOe3gJ6znhSItXEP2m7KXjrMBW7Gf5TNM4JVpm5ApOSqvKye5Yy9I6p73Bbvvdpd4Xf1s+IVAcyTLoGFLhK1Hx4ser76BFavsNrvOUDWDFR4Kb0/f1B6a+mpSBn2geYmJkx4YjLCraLYj3Ax/Pz+LF3RcvOJv/H3W8v2xjQ603ipU02L0JRI/B1Kjf07UJnRCemwzVE+WP5cvYOQV6qIHLpz+Kin/D5GFtcyR2laMz6GP6ezj+iPjKIooRh0uzQEGRtAMRGA+jwXXRfgzwK/ovFBs93z1I3xX/SuJyQthNqHM/LAieWdBOui3Uy56Hvp8x38Ime7grZouB/vPLIrzTUnCYRKt+0EkXKVvwt4VFv1xPkHUzKFh+23NG9A6juTK/jc6v0GFPmrzMgP9LRgphgwyWcskzkHFxTjcmzKOSpRXMoSlsvFa4pmM6Emq3t5AMWae3Y/XrUZbDti5mDyxa0Akx3nqqKWx2hKeF/xaXjmqC3bKcGx5mM5EYXlO1iRQAnEENreiqVcfNkiV5eUcdIlh4qr2+rDpj5bFQ1VpOGOR/fk2YdLdiZWEiP6nY+NL97WDRTZ4rDNpiymHJH6hft+u5GfeDTy3uGWEam4C8BPAhGf3ubgvlfDh+1DElfH0eNCmXJTc92fQsSCJuods3G32m/Qt28wt/k6CvsTyLQIkGrroOt2Teqrj3MGyViGQJhXwQ1bkV6GYd5uu0hxDSGYDDA4qn7Q2QFHQ/UX3PZyPmGPl7i5lvBD+AAT2+SmX/a6+BkZJbUptX2s4WBO37jQ5Frg3/pIxxPFxaCLJwJa9dy5L6AmbcaNeD3n0THYPG3oCQ9m+i8+9pGIjAEwOXFHpn0FrS/FjIcZGms8UBUwK5k9WvL/eKQZX5IelnBw19EXog1eo/6JiCaFOPXKTgAmlbX+BFte+FjhNRpHfr0x4hr2vRI/GaZKnKnq7l4CO09DxG1P9q/Gwhl4HD3AKmqQYVUrhdcdAf/Y7dic9kgS6N1vPWtknXVr6P/rim71+y6SFwG4EtaS81+21xlsx4cOboTK2mcRlwtTenySkM3YFD5i/tWp7rK/O8cYQ72LxoCTs6pCtjyDU7Wl9YXo01urpMWF59W0lwBUtAFxcFlFJ75g7WLSUvYsj5v/DI7JXCgbSoAom/viyFXMBy1ik1+rz1u9H8fkOA4eBrbi1n6ka074Yx4kqrGKrfBiekJY9Q7B0rUInEmafFlZmkkwtkU87CKq0exhGmm8rQ+nQihWt2HFFn2QzEEO4TxYOPNpQyCOjdEtl4/lDOsO1O0ya9VLq6bI/EsTPNdcsk5yuKxlBEgTwgRErgYK1OGp1k1oFEP4VRYUhS1rf2vAyABVoSEchCCap3abOt6xepmr/gY2L3eEocNfLNg+mrnNiqyRaBiGs89KBX4UBZHbxgMwpFoNfDWbsCYsTQ87RsRyF8vtVl8i1AD19MqXA4WZ6U5gHZiw4g/68JFJ2pRMPw8C7bcxCVrLUbV6EEt1inaRMh4gTpeYtXEdVB+n3G4ndiyFJ/OjiicA3Ep3Zriw//mLae/Q0lpl/FQuMQ+aFkvDCVTzlmUVk/s3jEGxPJV2mbL0gTO9ciIkBkkL/a9DWCN3VHgvLY2nxZ5+kQa3CaKA/CbXa18PFxWPj9rmnUwr4tHUEI91DmBMhqij4VNSV1Jheje9mKArDuDRkJiG3cKuZKKMLOvdAthWONhcP4YpCmeSTQsJp0PtfwnPk7sGggrTYVLl0yDtpXf45IyX+EjKLns9RCIBdLrhddyZJvDergpKftXe5T3rCtlFTwaWkDE11wMaEv0ctWX4eQ+fA1p/pjaZH+GpEStlVRJ252ZYLoXB9A5wSbt1nuv/0dYyUagFgN8HO6pRjoe6VmOKBNbyWjL5IlXY0xo/vaM7ay2LjsDTeF1fxhQ7n7iFnlTRy4e27WNgFQatYs69ZDm3qk/V1/ZdY7aQRhXvOefJL1hhMyN8KtY4DyUHzScoE3E8RO80kKJfumEoq4NeDLy8WOXsRdO0ZB6B1JK4kYj4u4oFJGAtdhfXHRbwpdg3qoJzDzAb+JOC3ZKzRMuceiCc1x729zdX7w02VPky0Q37aAuU0jkShwVfWA5fzebHfQbTXhb6IQWEay1uITJGqSntG/+lVEtw/4OEuxYl9C3J0kqTQtJ6s4kVu6z54vYgxmOyBYrTxBu8LXnlFDavB7f5QvMeXrMJ+BYIgTPu3Qa9mcGgaCZDpZnJ/9FzHRVWy+aPdW8pxm8TVBiooHpsN3W9EwvK+PUTj7f0co3kZhI2x0fTtdOJLDwex5qDtG+GwEaw3gMca8w7PQPMH9v2wp2YJ7nAPzVePKYiImfMvehGgYN8WtEvdyFZUsDN74KDfbXSk3MchDVFcw4qsIHUG4w+Aw1WeoO8DeCffrZicY+p0FFiTmK05MrJ4agQKQ/tPtP6I8ONVMHKYiNISLwUzXRMtrxtR5EwdgCdZow/WcSqvK4smSUX5RCGHLwTgrTavdzzBTkEKJDn7tLa7hpFb+/NH9JM0I0UY9dctoIhf/73itCA4qLxmW22aB9ZGcTv891Nr1pPVstuo53vss7rlVU9XpMkJx08OoRzz6sPwa1aDc350Dz76xc1QOVI3QnyGm2QdVQRV3tigGmur/x3pCrklH1KK9Xf/I94J8Oo3Pd7/Zk01EYHB/BxojUeT6QF79FeZEw6/xWNsD4QRYyzxlQ/Thjxog3NeFip3fqswhy65C2QLoXZoj+xKJ8wWXKKbH/GheTnTydlCVAzHaTHUCWpGpp3jBtvCM4wUGKPlbeUpCTL8GoJ28UAqg0oGWhHku9g7nVNRnSys4MkIPCm+ym7q1JomANymKl3THlKVMpXCG+8yJNzFH9xcvf+vYaOrwn9ehev8NC430xFW8oYu+TimrcbHIntCqmxCz5tGmGiB4VjRvNrab6R8oKCpAVZQBaCG5038U40V6o6l+GMB3PPiUNT89iUfmkkGMNR0Zr+c4voOqzZUO6BQRctLtjd3tDWHfwN/+/7mAlp8Gj0FQudDf5tZiU5ZqzJptMW3CfROBZcwrmVb/58i6L+OHxZr/HvficKgSlGFdvzAX/VIIpWdJfhCAt0vBY3L9lTQXIhsHqHL04nz5MSN4nYvqyGHNtXVe7vSoiiAlC3HfUT4VCVYkCupZWx+aBaz9aNuNKJ8CveK1jjLncpaWtOFaZkDGbMXxyKFb1E7OMixc+V6oPxwxuaSF2x9AFtk/Z7JgRvGNSSB+hG0+psz20EUv7zzIC2b6xGBYLdPEDWgd85th6oo+2E0v0Au4jZbueq/hIqN98yV02CC2x4a/FNs8of3rDeMW6sQm7AdavB1Il6sQ2cBo7+L7gqLIr4dlpWmyG1rnmNFOiBL3hz2wZ5HLkiuUFGlcAufvjURye0hryUXqUCAXQB+IPwFKsJtE/kxxss9ataYId+TkgjiOIFAhsEkcWQQBt/PNYBkR3WyFQxEuR0pExMpliXb0rSkiKEALueHPiH1CXp7Sa2Y8+nbhQvujtLKTiysc9PDb8j+4o0dpjLVqF0nlKYZLZzdKdNPGCjlQfuEbZfohjwHEYNJSbRjO2VauPca381zghZGUikDLzHp0u8BXY2KqF1/n1qZy8ZYlbBJ1yuLCS0J0RXdTEx9nd/il+1ywLQWRoPFEXVkPshJNgTZzpnZ2zN9Hfahk2dCMndndmdKbOdQmOsHMtc+RtnVA39IfppMhZN/S5Ea+urNvIaV1hPzODr5y4CkCHuIJNFEIs62trf5WBzEP9B1BUBZKyEhlNckNlky3q3rYFd74bqJ69SBr9jeE7CbA5mX1tbmGJ1X7HBISJDeQXOjRHULoZom+O6ZfI7YWp7QU5gybgMwDJaXuePY8Cxz1niP4CNIavOCFOEwhSRrun80PFatz+h7Nm2Eq+RgWwBLkk/OTXSmrq2eY/9ikgHoQF87m7fp6EtOBADGEsBfqsiX/yFv1Ikpg9jH/a/mVatv3SA1W3IcurS0QBbdIkDaMJrB+V8uGceOA1KugJczrw3HBzTZNEsOW/S0SmPHFrbLaWXMvgmipDmnuKJPW1gzDAvmPDn4MXDqLPueJgMSYY1MrI3IBduviijQ/4UUFKNtTpz7eL4/Bxin77v9Rq4QIeffTD3vhTHnNAMHYNCLkl8m2CBEJG4jMWP2OOaFQbhdaQEZ8Z0a5s361BUQCXbVkcXi5/6J8utALpGRjFQZUFYdGF+ewhVq72/14gYROKk116wfvf+I244LxQqTv18wO9jIPkquQSTpP5kCJu8RvuSzLN8L/j+hFyaLyCzHx0qPVaovewluQ9fZ1V0x2dbnprG8Oa19Ahvr2vY6XftGZGbMFgDYOQuPHXs4jIRlEWN3DSW2baZqghJaZRPxX/c2jZAC9vs7BL0AoVOuYjqpUv/XNNP7GgsjrRxqz+dAxG/5Q3YQWUWfeiowfytu7UpM+Bwqx9cGJK+yieKuR17E2JJvxq3zd763ed4QAXYjzdzMyEp/u+tjhYDlmv7FfENhoyqpktiVSgP00y3FFHMmy6+l8wAfGJWRPMzdJWc8XYhX57J/fSmIniW34PBzJ+6QlPzBLIsrLzlOgfnPYLsXMXTkosaJnFi1SfBVhWpNdGUQ3WdDXYhnWthfE4CioY7UEsJi/+aU/8N35LBvmeSHwRDv3zLO09LK1uAo/2gZXWWpnbDtPy0+cltGiPnED9Mo5Gf3SONa46ZZ1n9Rzk82ou+ANDS3QKrbPPX2OhL/x5dR7SHN44PqSVLZ8yab6IrkEqipCD9TI0YgzqmSzKriCnu1bOgodbP9lGaacJBywoV7faORMfT6ko/P/PCsTc+uHfsbrEdpI9p6hfTKZtxVwR+U7uflLSl5w4VfoP0x7d3DnKt3HW7YGQHA6VIcLok0MXu9N/QVuVkymzu1g1vdCHGZtMZWLqVUq9sWowyO3cBaVbRpPYrULWSPntOG8jBNE4b/+88/NyAjDBiph7T8SK+r/BQS99qYYK9OI6iFdW16+jgBSqmdUWwyzvz+iKi/DsDFoYr+nh6tF/Al+M3JOgt72GhYtk7kfAxTaEuOmIB7cdcoQ9UmzJ05+/HEnqSJZQuXmpc/WX6jmXcCh/1+rpRgGn08xhjmBdgWoYQjdks7ODJf8HONZ5XbtauaKI3sN+m1wwaOBRcSLCxa8gryB3Wax2MM/onmTjedSCdeYhmxNgfoF/YuW2hKJFFnZTfx+0u5UoApT5W2LEa50WumBa+FLgd70S0H58pF45SR0iY9Ry36AzFSZWjs4a8sNPSUKfHX0Hp6TcRTJcqKG+T0EjPnmGxCEQMmjh9YWVXiNJ7B0O8H3XsW40Yiy2Sr4YWh4r/Ty29j5XO75NXmvpXbajjG08H75po1KzEF/e7fZifxb8FhnGP2co/P8Iv6GZ/mb5pLHec2W1nngL2wdSzv8syRSvkQ5/X40Bii1BfqwSE0jHU6kZoxLlHDzLKLHYZ9me1f9WlFh7bFnj/bvmsEjf7kNc47E3SyH1J+lvl/lpgvvQNbeXOuOocBPro31TmcuJACFopb3i6V8LKrBWMg4KfNd4UxLMwMYkUejVy9g/vf7MW/uqHUFoaLUXIsbzwQslDpQydQbDtM6xAL+vK0vCVTmDTL8w6oyURWdNDyRgkoym+tbeiUbdLBQlPbA7oEvMz5ZryHeMTK3joRO5/aBChKYmP6+iKfoQ3ax374lPxxojswX7pAfN3IwOPKvqSd/KkvBGHE7E1kAJxIQVxqCv/nIVqNKZ2ykhF9AeWo0WJrEHGVvsEi1C/vTf4OlKNkTKeJM01xqmdur1RAv6IR2to8fwdVvaDdwdhmaB8U4NjFJMPnhys7fad6sXyMJioP2OLCsVk2PWIBAqzy7ADiycOpYbqWW8+2xDettU5Xd34Vy8kdgsfqFpZRDHW2pQbO6JBGoyFldeoscCzxKyi7KGABPVb+OTIupDa39WourMw7r16hSXQOq6W4Io84LDEtzv7us6hN2m3sihTgSTqCiucw1qhyMKXR9riarbOW3+iS+pEViX9wGhI/sOdqyfgYJZJc2ycinIh6obAWDOHnAJIANGVEB3zcSsbJZU4KhOspR0arTJIn2mbC4GUXaj7RL+re0eS2XEuMtXz2CkVf9Daqx4RomLkhxyP5xMktzXuBs6iH5+mii87jlMSbk+hx1M0ilNhKMa9kTlmgJCgfazAdKTlMEmEi4P/bVZ/xSoiYaVGVp5QTbihGAhl0UX2H4ZRPCrjm9iozRoKL7DXgJxjoFDCLH4f3L0t56HTNuDRkNaH/QHLvm47qBK15+wptP4/RRgCk7HugU0UfDyv1hsrzu15VC+wtK5JLlc0QTymigY5KQIPoTzhBd1iebHYWQgjZ2JnkJlpufRfblm1QiA6Fcm4u+wh/DLC12t9kP5slqj6skkpWIa+XruUUmY7uoUY5alCEstF1/FmsYVlIl9hOEca0zGCA09/Ts9y2maIy3MiTFF89lrdpYstOA71PrsdDSY0Ly13aTUQ/FCI9hVpeehMAIvv/Q9+nKY8NnaCNQrL4UnR/OQy2NRk+Z+eKs6vNRov1iEnyMDjs4tfS5OfhKMSG+HZaymBlxWZKHfxYF4+IQ/NaJ1YEJkuhyQvrFfaEXAgn2CZixMMjXr2BLYyDxggP/OrVjLmhyLiNP6zy3HqOitAhhRe3RTsmifStFzcmI8OWi9WydwPFFcvZaBu3ML5aPGoIUwyNszV/IQeIUunmyRGqCbbvWCyzeeZpQkq45X1og/p40O5LY37oRo5k3O/0Wz7nIr8Ky5tvMKqaM4u6BHO8iVwA8PcQqGmKFMIix42ndURqApqdVdbrQ7hBkIMz8fVIqBE4rxDZx1us5Bjwx9O2ECpg5YkrZO7ok9XKJOiolCQSDaJaTj0Ro2y/MtCm/T3hMoIwbWoleTS8rjD2IXDuIrguZSchSkHI7Qiqd9vMvWLoClVAfF0NcnB4f3mu7OX6+TQFFNEKsW+WsFToBxK2adwuwdf+dggQNKgjQBcrsYNUe+E54bfE5uoYT4wTWj6hjD6t+Vk4/XiiLw4SsyuwayNPDFushvFufeF4iq9XGeMjUEgwBrOFNvXPwr5azd8MXdjyv7E+kltNnjX3aEg5Ud+rTIJodkIFZNEpuDMWSXqm6ilAO4SOsOg03OSyl9JpwoJZkERO3QB1Q6Gn4dg/BoK0yeO+/U6eoQG2UJIkcVl6pW90sFK0j2LC1W2oFBKCq60fuXEqG+PuQqMUGOWIRf25BbKV/GKPYDKSy2I9r525m/U7V2P3SHqrRgI3LwvJWpjDOg8FvrcSoX57uyNCHvZriqFfKSeUIU1NVAFAIJoHoAuD9tjXppqr0kDyImeOjZx3ltnumjyBwIjGfA7n505zKE8d/VQYRN0f2f7jwPiTXoOXJ8TvodaKK3FEkDH0vMn+ScNyMa2bpstSzTUQXfUPyvzt+KazE6R4D08sfSG52mCdnL79klWv9e5Tj0kT8L6ckEu5ORLGjHcczoRD3sr3SAOJZ1GRFy7P3E45vo/WBW0/nid9BrQ7xpGIop9I9cvbAeDnUifq13h0s6vAUUatjyLmDu0LEWyPxrHY3d3ikb4KK/By7SCHvffqISTX0qJC0/lXp+Xc6EQMbqCYdh5ZMOwdusW5p3Wrjl7L6tTaBjOLCySIse1ce5UMi8SgH7KY20UOMiQg+yfzRQHpN3sEDD56EDV78CR83ianAfopA9yFIUceYPWcVJemlQOF9JM8Y4u0rTtNcFN9A8iCFCKpJ/u/MsORvEwn7e9kRBsfpqzilrUf6Abxtgl+rofDF2zfwiEBum0oYxvf44Hu5HfR0n0aWeToIFsyAdnjB04Gwdx5kQcS131LP8LeLKgic1SyXuZk0SkD+jy3skKVdUzwWGU1wxrHjfGUs3eRt5l22kNsUpDvdz6keJhFG9zH+0CfNlr/lc/uvUcvS5ftQKd7YTiX5pxM5H1OqW937rg+NaOb3u+Bu69QbjVm0oEabvWaPNR+stAayfyHfTH1/TiXWMPAwdz+N0wK4b1ZpAbQfRhJRGHq6WPkRWeDY1+hh0cZm6VUvXgWGB5MpXEeSCHDej/71lu3Kllpl5Zx63TM/h9kuKdZx6WwZhquNLSSWUDyHDulT7rhi4bv23rPMHb+sFExQFKBekLkJteJMluQK20S40129jp/PKN+gfcVnN2QdZjXqXlxm6g2/W05jlKuTnnJ3y6n39FwFKk5DNUp8Zl/vUasfLlHJbwut5Fgx273lxABZpc2eXqW4UyONA00H60IJfZETYg+Jk24i0Zz1RRpN63Hn/jFqEHb80AgBWxkNaT4CTIEgO0f2VndfwmL52n7q/0tHINuLmlDsnIg5Mif1fSEPF/60vdf5W08VZax47nyMcMe4dCtfxu+wgMgjlKrbsatVkLYmYtP8KSReHkHuRp6ialyCOjniPVQRYKsnoZT28xuta3KOT4A4sjOYTqDkhqs5iuP2SXixF99LI7yhSsShSwqvkK2NIuFd1Itd2K2akWcTvXQJB1MZxjAjpFWtSeKEXA6UL9wH7M9WUmiO/eeoFsTJvDtvYDL3uIN7dkDd6xpWuevWHuK4AQvI1qra3uAa+Mh8QVM6aWZdn+HXYjCCGlZfYYwrmYLAhPkrdKN0jTB1evlzEYvOlJV9bOS9yM9j8fASiMtmAKN0mA1FeeuoCcK/PFtjgthWEdj+fnr2WGNlZQJanSrdIUQAZvCrvGa8YrKDeE2CZhaDjyS0ssl0Giit9fwJVZMgOS1V4FZonALMonimA/3KZNSVjE5FkBfdrYC6xRisUnQhjvfXHE07dvInWpAKWf6FUPrNiUtTFP9mmXHtItCYiluL1WNUlKh6aVwvVfpDLiOYTsTpzV70issosS2UhOd3wh/D2cRNMWRez2Bm5uTMXDDHnZ4wP73A7+6wgrIZk48p7mGi30KsJq1VzTq8xBad1r1gaKl4bZ2cFHYMih4OaXmk4UaiECIafkA7RLSMflBbljx/ZdBY6jQvSN3EcPVJVCSB0VtfGHxMvjZ4gDK7jV+fEcU13aQQkwZoRLagi5iwx8rAF5cX3bTYGs7NalFtdGMVteT8V+QgjRhQhtPdwVIaMaEZl1TAI1Y/VLhRWnW11zTX6FPakS9Fig/V2ub/np0E+VVa4EbSgF3ircLszS8jxYHsoXtcKm2nkUgAlk922Xh6aeQyOvmeSjmqjn3LV0r5jo2I9wzY+y+cKnvkfkhbcfEEf+sxDYLdONywv8OD+wNu0vz11mP6w5LVxMCphQ9pyu8yOfH2Hqu2MD5JCYmVLos2nRMoc5h7Wzt2M0gJ/oWdpi8m7sMF95qgOnP+3WtzL2tpt8d4ugSxsDnQWFYp3OHvJPO6nbhHQjvjmHbshPABMeUVmsgrpKgDraTHRiEolppDZdNYM2nsk8ik2o8jutQT/hy6PmzTczTxtECSnG/gJXCt2HVaUhPZ6M+hphHPOWhAhr//aAS9K7C1mYW0UJXo7IhG7s9MHMfYUKZirf31UzIXxuDy2GZp/2ZbMC6yYp3Jol3UGfnDDjCv2/HxejmGmav0av6iT1p8ACrCLCBWkPqvSi3JCoSXZKHodObF7eO9KdvFDLLhnSJF+6R85elg2S3+FFlpTmrzkK1ArfKWOLFYDe7LUpbT7OWEoNkxfejqXqVLpzRAsGI7+UqMH7FLzTNb19ggj9xEu6lbfu4wLAxXZnE+yxuKasBsLrPL3on4V05hPDfFAUglqQWOLKSuRe9r5zP1wJxrxAwJOV4gkdqECmVUglXLcnI3bNVEipmn9ZEcqcY5b4nkV2PAzOeQHA8FP+jplGH0Ksq63l3jFWXwweQ2RnXHu+dptoKTxbD0lKnbvKZHBbx2sABx4L++c4B0v1g3K8M+sIvZYINapIKzaXCMeUAYQhXY3tIkuKuIWeSo6Ps5mrNFPV9Av8ziOPLo3ZP8/AyHbXVbWSdhJDBBbMByKemqJPU+bD9kwiJcQ2CgHEmsjkmWgt0O+Ao+tYylVO7/pMnOP4m29OocwVh1MwmdBzu12ijUelD7lT/78KD73CYO/irTkDxilhHt0nGqD/809vEcQk+3CJxrqD5CyVu8YWu3EXJe634NeLvytpQfG4GvCJsfyojb/vDGLwYvNGqsMmQI8cpPiY1G8rAe8BsolSgIpaM5C9OVSV5Eav9QHFsMacQMDLti2lPCseqF819SuhavTiynwwBDZMXYhEkaXr2/DYHzao9kPTlZOKoVJenEFtbpCF8c9MgnsdQg2fnc216Npu1sAt0LiUvDp5jdZCTq7O47WpA3LDtnk5rYMOAwDJ7Pxe1Sqk4WUJxWLaIVWOkBcojA4ML5lbVxVTUQrYS2MmW1Lf552u3uyzhvqszYfWmgoIppFObIOZr0XgcYIeAkHVYPPTfReSFaOZXlYAgj56+MaulecgZaOFWE9chLz+utj1M1DLK3SD+307nHx567C1WLcDrNYPOsBmsTdyWdW9U/PIkPe3DZFvohmWqIBj7+Tiq1WCGYVe82jrNoSmS4Le1OF/uhE3Mm1PX33lYqC2ylLSB6DhPKDv+1Drj2lYn+jPYTEdDN/X1kQxpLzjv/8tJC45mh5dI8qInyapHEflWbFjvcr5H8HJax/60R8hOYonIXnp2emOZE7YVu8hvAafo6uoPc4iYHqrtUCgBVP3hm7ffWyl1QXJCwxDd9CMsV0iGFVWZQfgYeNC1TlNUORMqgaQqSj4o7sRlDRnx9nQEIiwFFV9TQG9YnG+UVfY69rj6pOsZc6+4YbSUaYpDhlymURto+Q4cGeuZJIMMlMPTjC6IhY+uOZudbgeXPjGei+9uD5amkOfBWKgn8AeNxYeP91WhXXnF4Mur9RcbURJeo6MT2hWbhGE9jeA9aArpu/xtpoILKpmEjUDCFjGwcOUf8o9D/Uwd4du3phnUdR9b3LHixAUA6xzwRXHxqBw+Oa8ttV1fG38QjO6WvyHJ+rtYK7sKvgEDK2EElXkAbSe6hN11mVNnugRzd03rKI+FsJHBVUIreAn8Z8pxNlp8GO7A3UMtQecWK13K9NDHBUE4wBwYRynk2YiPB3FFA6ZlZttE7K+l44eBpwQ5SfMzFKrZekQVf7G9bBqQqkYprga/DsC2AcihTuGHKVf4pOE6QbfH8y7Rb/LcKTiox7zH1hLe7MgsXqyHEw801qnQRO+6PhZSDn1mUAar0xhGx6sdcWIa9FnQDJPciwff/8SwcyQrQ573B93W6Vt1CJyb7wXpUj+FNcGxGCynsbJjWJIZaHDudxCIN7ZoD6507FJ+UBPKDedY5ry1UCW7bOzQcXQsAMoknOSFT5hz4dmgWGXm19atCMn3dZ95RdKlmu50u3lkWSQzJQGkg2do9gGD6sRhDhZjwjvbBPbLR9qpZ+8kqxMKAOlgdTUDRZ46+zBcmNNiynWVTOVK/jQPz7pVTlAeMkdfMP/jkCl3/m5HLLYZ2IxCqeIKcfQ4zPEa2+El3RlHVZhu3fcRb5agbeLLa9IWlQAL0gUoEv27Mir9gBpKR02za3nnpBBKLBY0Hdm4Z95hZx83zYuc5WJvsJI0M+5C0bgET6wpdRWbMp555X9tukULY1orxIlLphrXaphZJ76gDLmqOZe0dPngcpoe8/yRgbAA3KH8djNJcLPYCtJM4FjHP9ScIMpggwHauCrghu82rjd4+3sTW6gaq02IuiT+HEhYbTes+4ZYUmiNJEOLbnQBFI15zyTBDHPm1tT+8Vywf/xuY9jRI2kf6wUticGlxUpFrnMlv5OktfSt4KmLuNzVGDY88FEvFvQ4eRm0XTi0fhdOx9o4RzJSmtlroKhC4zT5S7HonlenfXyLAal2BG3b5nd6dBNvnTZtxDg1pbn4nXkP9loyf3C3fb2kkQ85x6XBgkYxMh8oQ9tMwN/lbrsjzG7DKZO/ghCnLYkjLfcj4zoKfpjJ/BoKA3PFEInIqZdpetHzhRn3FQoq8bAj4PhWfREGJFNigsqkkOAWeY7oHXWB2upsfXxguS6m2k+kw8MdOaJb8BBZ43q1/rAMcDMwuiioz5RxSS9gTX5YqjCh2L3GAlqJUHj7MYJEZUGZUQFjJw7QSLmbinju6pjB1Nhy+bnJe7UNFeyZ1NhDWL1k0+wtGBQVezmGqiSxav+/mcHOYIH4l3uWYbKc9LpFKvNoTyXeicHU+LmvC45/qq6fVphkyAoo1ckx9iMIKmjIQ49cvQTPmgVixdnBF22/cDZkjYFoqRCp3fyx7LOI5kEFjnXZpmM7IqPRuxbzWzHkGG0b8EppNyMRVeceY5XY8F5TopqDPDJqS9VhTXsHxIA7QN7wNTUK+OB5NxqloH0OKSkY+ds6mA7XfbXDlScjyC1ZZuHIijx3CgnTVOFAII184v44JTyTi41GieDax5OXnG15EJoacif3Fuj6ZXP0u0YBBY94P/xWlUtmHtLChGEi0XUKQ/nB+XAavd3UQ988VrqfNx1Q71o6ybXoSZgfhfus5uybKaT91HgxoKKQkHJHS7KF7hMK1OXQyeIpSSHvfCZ9kZjmCmTrZoKV98oPffgq8zObFw99DYtG+H4aZ11M23goSeH0k9E7OLg3ngsAn/8qk2akjXr3T4VV9etA+GkfnSpv9O9byvNyoVAHa0TWxROfuTA79o/4dN491qmQ3gRVAkjieil/AlSDbg5peAHgtrPlax0mck7RhbBFcm6CHLJgYmlJmPgfMWsJu5sG0pARpCgMma/4zch3YW0Cn6uoUkZcWuEO1dWmfuJ0EQIUxsNdRiVnXAkEQZ68joa5CYidFHjWc66wXE3NoJZ0ROMT7ejm/ztFryRcupaQTr12HvcAQAHSYoLPbkAbpGo9oxg5zN2m5eWeA65TRIg8g+Qqnr2vC9QAIp5sNZhdmpdXcHxaHG3WtLbI6TU7dxSSsW8Omu6P1oJAfiab5GhuAFMvtTSPCnRZBUFQKiz1X6ss3hMjc5zLyRMDHvA6yQwD9WYQTOOf6w9dpXGGWwMrRkoPyO5JAxcooXNffWfkokAZ4P7eFYmr6aWPXfaQ8tH1k9ahUFq1mFXQ6ld6rLqKHctAFOgRleSDNeK2a2dsU6XGeEmKnwXPpqrI6EMWAAzZlMR5x1/p8qehYvZAHJgeS3JDXNJlvpv9VBLtEzooSPKkO9nVDBKATNqLJjcCh6tKkWhv+TbC7nfTU4s0RQx9VkTxN7A5Z1OQ/VUTnyKmKMx4rB1Z+fdtfGI/MPsTPNCqhS6LG0Uyv38LHUrLbMEUIy+NnUnOSm0bvKloHZHQgj6JXr6ZScxvhRX0HbKryRrPPS5GrypE8hriJ8NuaDB7aQSilxJ1JoYxmhCPoqukMmCPFyCCZOir1jwblWOp4QZ+fuRy6UJk4skMBI9IDaJP2Gvsy1+7Vn8F9HQrY8rGwk/QpYh/jkFraT14nXj08Dph15TsowpKMkOrODizrME6SFkXzuRlH8vAXdMje0YI2mbkTMGMlxM19V6oEZgStRcG41cLHQ5M03x2UlZl4q+O3mRqtcS5Z0tyKnh4WCqgV6CCysln4EZF5PVw5Ge970TBm02bd6SYZFZ83Otl4AMjqurZkGqJF6QSoiCW6zoXfd4kd4rkLjkHfhP6KnD7sqJRf+6X4QFMBcBtRkEL3TRa5U+cdv/PThLuStLTwMhKwj1ZWCRuEsOvID+Tix8tK684EyQ3zlVepXqXqd1lvytTqPcUWhtZ+YE39ytcaUOXQWSAElnTnIvL1OCWkrop715vYEDrDcTwDQEwpHayY9YBNj/FbZltRHeAQe0SpfsWPn/9Y6LhayPp+Qo6BbpcA6LDz6P0n2IxhxxlMc2g694DoQRPAGMPgAUNynni+9LeiqfCOQUavaOSRtQVFzNqCPVzFNpXpTdvp2SDiC79uRdoQUks16bHf2D4t2yruh/VEzCcVra+pSLrT48d5pUBtkuJtPAIa4Rwm0tHBcHmKg/SvL2y7avgGmLmwzFqf+DeW6xcMkHAv/ne7zOJrJC6zZAL11eEOQzMRMaI3ryGBCQngBvyC68MT/bWClEyaFeE17OMddMAWUEzQjDgVWOqjoodwj9KeXtTLcLvgUWLW3gvGXvDLKTZLlvdDndlCb86lbVcaEUMtmkYMYjEHnA6AAaTPGDN4EkEmIshh+Tdjr9HTy9YDEHaWaVU0nCIm3bzj1Izy5LX9aqRF4+pAYVfBPF8F3U3vpKKNsFcBMBDuze7Ekab2GC+Qr5T1ioRez9EjlGZqhjOl4RdpPaoI9eQwGvs/De8manVqSoQxUnwA50XXpguM3W7QQOB9biMc3EuhipnaayXx3fMDSEDLLyvswo4qs1TIN2UqaLej7U9yuBWHRiRpsddpyjELzP/aaNgWEXOOaJ3ubRXAsfWp3dD69UlEsYDfy1mtktJkLYyip8k7Sijbjla+FMQ6hySfMuKtswHH8hOw/ifzhZ9TV9Bi7ijh1FJDHgx2lPRlkBTo1usjmw0Hx3RfsUOY/9u8SLIfjNXsTZExzEfSKoV8smCs7BvXgGuPQlo0pLRcIIOLjHCgyOtqfX7542A8vHuq7/IqrVjIl0bAxXttrzjn6x/A17TYVEVKHLxS4Kqkv+g65H+2YmUpnJoKLsG+aJ7EUfocSj9yYSBG4TU5oOi15bvkbOJLd/VJHEG+0gW5uyMj9nH25EfQZgE2EaUZhPXQe6Er08pL49CuVdZFXNW8zfmYyNEjI9CUMppxqNCjSMWSEatG9UIx/EqH1fLvOcm8e3DMWN14PTIBYtb9g0uS8K5EFxg6zptEz5sEfRGUjT+lcnC080g1Q9sgd6kOQxNB5M5Ss3Va5kx9BnVKhIYogxVV1KDctegnKOD42qO/lu0z4bxQ0mkc0ZuwGeZ08kbTwuZGR+ld8axukKRDxiE4IDji6tqIO7LtYN0D2KGawo3vDuDkZtvpcF9YDtgkf+4cRJPr50HP3gfCIslT5XWPt/YXxM+W1x7KfXMzoeFm9IKB4znO9ZK5RBp+wST5pqrnrX9waORJbht+zkB9EtTUm/UmtjAGJM13UJHpiKGuDKi5dfok5IbRdHEid/CmsQja5iXQjSXKxs2VmdfImArkGrOhUkDLFIC+Qs228SN+LW/vjouFzgokNU4O2zXHQd1Qz8vzyoXB2DrxwmI9wIq0mUSQ4AOI+HJ8BB7hCh5GCUjWwBZGa9firUquW95AxviGwRVC5RnIF3eQ5osF2XUprTvpDmzBsDAMNF/sKmiYWOO8kzsNL1wRae4AYCjoKQEninq6QkIMEerWmiIJfjUWljlG854Zv4FIHVNCL/ukNgEoTwecIFg9dsHwXu/oL5ULcug4tPK1Ke/yPq3sUFmKh+aaJUawT74+X3X5hj/omfjk6m+jbrkGAJlkT7IARmLwMqORkhZgQ9keEjK90EHSOrhCqd0h96q86G+DYfnVIRAVJBzui+3ACTpVr1IE1A5lBdYi3X1fKD3p1WKPv6QfNyj/cINii8/s45dsRuNhxBoTjma+uKdsurqIFhzDqHUrd3vARqmqrWXQVkm1BLE+O1h1UTQoZd4ZYIaL78jlg91w8qJGmaJs/rg+H0KjKS882TFTmm9RwuWl6Dy+3b4eWZ1CeO+9Hn7ZmBvtQBbEzw6fX2Go2LMfW/YJ38x/gCvlLZouw+sHeppdMLU2ohjYihOk/L7Syp+/spLl1+XEujTxH4z7oRqxf+5VOdHZAwYKQrhRnedr5UCKe81LnUKreeDMlIFoiz1dCPJL9kT5dm2Etsp0ryYwkTCZvbjnlROordL8NutdhfbBOJlP4AVRQU3kKU2TXUVJXXe3/1pi0Kdg/z11qJO1glF8kMhA4GclAZL7Z8Yqoc1yi7gHy1jhTyUEL4+qOrzr8Gqsjp4Yn+kPLc+SHDTDle9sLPG90utr51h5ngx2m0LHMRzBwFsYRovAgN8GKYFepwkAvwgiXLXNniWbwROazvl8spLEbQuTctss2YnAmrKSiD7kd1XWETUiO34LdgsOC/BmcDyf/bqbb2QubtfRkadLXkt7nf5Q+yWRaMLIUSGCobgwK0KOfi+Go+c6tn246lvOLv1jARPqgplSPZL8/NnKIK+Ov6yf2fl/WTszQwoDyGMe3xZ7Lzsv+FRxYcj7jV0qcB84emA4O7vbMwajpqoPFCkwu9UnV/ihi2P+WCgBqjjsQyjxTKVKboE0/tNWa9nitVvEPpaFadj/a+FfncreF+C4bhID2FfVOqauOeMJpN6ajA85B0OjEiUDKbpwuUHAmV778byIo/VP1DBpYB7HMNKAMZAg6xCMRoaV5v1+8mKlF3N+6Pl0ZbqQptfp14NEdp5nN5vs8Vm6CnJnW6ef/mnzT8tdUHgetVeK28x2D4sKCvPv1uWQUYgSKWdff9SazmMd7tWBMyw3ZCOwtSKeSy0St3gh2Ncwwonlj0i7Kpa9WORdD9yHDAG4xfV4E0jpJYkcexdVXIsxjbeQH6G3zHX66P9okdS22XAUD74+jT9RsSg9Y8Yy0ZPP+dWUB5lwfs3ZJxZbpcRnpqehiZfBY49p8y983ZvqGBrxFRPYhFLzg6k93QVXxKa0IVq6gZLOIFgit7Lr8AwP58T/NN2RAkIyQsSQ7DEEjHq+i5rAu508thXRlj9c0gcJMvZ+a8AePtd6Vlu7FfqdpPmrpdPWWMhV9iUEFMHU9DAZz5trTTP43WMMOkz6bTtU1fACAZ6o70lSLC38jUh4KCEL9FfqZulsMsfYPZCO2cgIaQEyYLZqDkAw1srHFqNcCpkHv0FCljt1oXU9SLgbh5w2LBRDt38pV2P48dGTWpldvmlzazbKi7T5CvKPudSZMH0FNTcAKMuLYlI3HIjfsI+AB0HQtjyLdcIvCfmc0ytcxrnwk6kXtTL129X5rhlGpxNjPSXNR84EE+1eU1GKfGxZH+C4a8dw4EDjJGtLkbBVEc7H1IAKe4zVuPhueRIQHvIOwtIfHEcXofAlUZvg4Zd0zPX9S6nM/FRcpBgEncc6VvMuNG5Ctrsiw/4QPCoiaD63ToipmSL7YPqqdporsLgU3ckR+Wuyv7dta3CFRBVHDWp+iG+lUvNKKsCP3rWFi8w1fr/tplQYNt8XflHnqvMH3HTrgNjTGR+hffGcLeEF5u2CFaHUxiQIG33sA8XTsRh8z80xIPtxB/GP1YxRhIxFCGKftFsMIjiCqXOxjIwVmGI2253OCtsrqn4T23CSk/AJbN14CMAi3Unwczjc+1aRLzLA6Qz14rIF2qIz7lgmYSz6XbjdSdsGWAxZ2ifLDE+RI3v6bjAK31hEVQvnSV0RB3LyXwUegLD8hYf17fBkLln71GfDez+PV7BjL8Z1UCgd/by2xf93jBTvN00ewTXIqvAjg7PW5YR2LI6zqYV7f6jtV4qRhi+RxhTeeM9/hiO5HiywbCugtQFvUSlW0rjeQyY83Fke7683TbftlaEfvwjjWUzTx3XlDeYZYmD2cM8eO8S5W6xlsb1tnTRuaM/k/AHToqkEjV2J6sM3CZ3vzi7dIRjRgkuh8GSk2zLiPvakAdyPTSqiMZ82viKSUxN7XSTTqP6exJuXA+mzWFboOJC/6ESYrQa4EBBSpIGX9HjttDl5C0M3BZGM1SQSaT7hZw+U9z8u2b5TYt07S/hMpTFKeMOY6oW8c0+SXpY4APhtTzxzIqVC7UcFY1bgAdEo8g/NtFJvb5jIvvIGIvi1xWBtWkB3fyj3yvYOGk8V9uTr19qXeT377aHwnxNrkZn4N2uCvLMbiHXsKwfoaGKdf9uq3a/mGfs+INPywMpdZvPSHvZep1Uf5AHnDE9DUhxq+h6OK2RsYeacdYhDGhyxSG/ZXZRzuZj6mwkGTr7l1iCmfzmgr1Xo1ec5DCkotEDE+GRil1m7M/tMNRxpPyUje4jcYCBuSoK/NF9En3AdBkLDy7MwwILm29ZHdPy9XIzXnZyzu5z72Aa99AnpaRPwkAG91vQwIr0xIlPu4y0ibpZHjCzDAqkDw/Q0bIIqoH1bgyu7wZ2QK0LDeRAqZZ+Fw8t50N7CBC2nlxj+KXb4LWnpKgfo2wPMi+tYPygOmE/Wxdomr4cBkG+1PWkGOImWz/9Ic+6Gi1tg1cg3T6cI/qWMRzxsGrbPqAiEJKSCSlM+q97BmHa2O/YQ1Mps3N38lcDhFzIko6H9QwIx8IKh/w/yZ12Tp9116t7ApH38WSW3zwCdx3Shr5oWN9Zmmza/vmmDJHEMETuoGuPKXr38GCOffx8qVWzAXqZqy4Shg8707/IB+YKhPE5dfb8auRsNtEc28RJxInVTW/6GJy67NbAsxBFoptMthwUui5mMbOWXqD1o5r+6P/Or1KL8GKSrC1tRlO2yfvh8BFXuVbrvgVUeN84pWIpt+J5UGmP091wKhNtt1B7bWOsu1bIv8h1ip4FeErpPlW122JEJlsX0U3gHUWqrpQ/DhAJli3jvc4e3bvgtW/Pnwghiip8OILSpmBLe1WSrnfQJskWYoLJm9pczkjhq51wGUhnguxhAsbXNW1R6X8/rZJJuPY6o62X84KTgIOtgxvFIYiHOy5e5Z7Uw7SL9lxwzwFkOISpuSs9gwa+ngwuqZs0EqTPWO4944wDdBLuNZVMSOk+Z/ryLiAp4ePn779NaHJLzb+KG7jfVBgMjsucbLg0CNJyaPjbl7MspCXkM3FGNK3uoEMEhVCQhXf349Rc1O67fZbXYCHKFBg0to+HTC6PzSIdvSz3TG+Xgyqd+6h3D87vJs5+yMDkBhL4OkOHM4ZwzeN5kq6Q7vu4n8ZcPApIMap9WJAHQMrrS8s1zYpOYElUQ6Mn/UG9w0e+lEVp5DHz0Uh3ZSsqdMKKnD/U5IQ/xq4lCSBgpUunZCA6tbcH2TjWVgcS3JBwo3eyI/eqXoomLnhy1O3NLx2c1omXrEFc1jK3QxTwPWQhc4d2XIxY+SlUyKx/izDK4eFYi7yvFQRPqr2dW1O5BByDVGbJABuQVpR7SC9j2SmaFhIzJ69h9xkEo10S7NJheg59vfmAqup24a0c4vgfMW+Ds2AWXomaaiq5JcRd1XyZPUc6JVRy2n0tAaJOM2s1FGPexTcp0xxFxXfGrKAL8RvSiZUr/IePRAb+VqKT5mejOmkgn0BpVqTVqQhYOhJpJkYgPvIM8fDz2qkMTQlW8ABQGtFpcizbq29x6eaG44REZrJ1VfX9+/VJtF4CC7aQvnaZk488er7iTbFOUJ6XSz68SlBXcxMzEtaAv6xXM6lBiDWszxyClwAHgkcbLMZEC65HoZ4pXCdJoX6qzLNwAxEvfEhDd9n5QbAuWiBZbOLETnRumMuT4YnFAkqYYgha/K3QbMvx4IAHay1JB+PYdIFxO0k8xtrMRThDsj+35UzZ268DYAjEfYtTD5xMGOF3BdyxFessCBcLLxka4Jxdk/D5Wtg7HYW/lhfIX8tChwbIEriM+o3fQmoOHFvEVDO7p3Exnccz4nonY148tAwfvh24XmKmVNWVExzUJfmkpUQno8Km+i6nIn3CGGlmESHlSdep09uhrcymjHj1Mn1JsFqBT3L2uYx1MswyTw58xwHDzeLMmCTWo8+lvES8cnHtaCimIcFUFMFJf4vDJRd1U4/CnZvnDAWsRK6SD/sYaX4rYGJwtp06uaPasQsk7sO+9pJiwn5vNvdrwpwCPk5C9hyurUI5HXUSwzvQFJFXPe7H/xkJhoYERCssmhr1MdJ4hzHY+Ttqp3cO7lGYcR3KhLDeqf9/lbD51SzUmTAh/2YY9CqYweXRGsSq2BDvf+zvz0VrGhMV3fxGrx1be7X0yTwO4VhXC9evjk3afBJGnXwsW+VSd8c+Hdbi6YJntRGwK5MMBmffZaZrWo6VZ9+3S7qOwADmQySrGzbFTqrEMgEWfHzx/Jq6ReATwGxXW8HlanqUv3fVVC2aZ4LrV+yXX6nbPyY6VMQnxp9B1UiYsnY6yD1VyZkkhywLd+dqaiDvd8VoAIN5i343TL1XKItS1PVQo4B625iir+6f8CNwOZdF9JEqkdReIF1NBtIwVf3+baeQlnA1ggnTrJzFsf6ftbg42/FVmi/JOgz9EdeZmOmQBpewUF71cW9/6RcQJfWiG4Nf/+2HtFKkvRNqifEiNiRQlMqhs12O0dMfBcl9F2dkPVbOTT/p50cuXvZ45aI0LSdnEPv5XJ3lyIDJBgDpbVMfK8g9MJcPR3x87aAuM1vI2+spr7ZRfZxKylBHBg+riHq4cVPS7o3913reNImMgrGrQvNuX9l5XVyZArPkDTCFIFOf7wjQCRMCp6a1du0IfxNELLUOdqCericSl6RtpUuFhi/amdtUdONbibl+ca988o1pVd3Lotn1soZKKB4/ukqqpVayWwQcfADzCPuAoqhBsz3IpVGWYyy51y79YL1XebeBEEK/sLAsOvZpKHHXa055VPXCySGrwIcRh38pLNLnk58uaE2KAprDLBqp98O3o2yp19o++CjsjHXn+TfMFpanCp0w7jadTXLwohy9qUyvktkzIT8r1p362R4m9TVwU+UjME0JYViMp0oqoHS5RFUkKiiWu8UVBmmRPmWXQDJnLVvS78SRTxXiQXsave3reReiWPtZj/klzvXsauTbJZKNGHhkdh9ZiyzjBka06aTIdYjoL8oPeceo9xa28N8wia0dtx5FTreySZnx6LkTd+4tSa6aoQ9W8S7Ga8K08xscEnGrSxgZSwN+qtk6n6ZYbBa5bCQQBT1FC41g+yuaAVtjmdwwX/OnXOJxzxt4tZyvhfX3FdQWB0bA/4IJVLRzqdZ7Y6e2/UoAVsYnizn8L0EbURPht9WqxlwqImWwpeAl/HM+miNm+XngLEvYm8e7NphHi4Idq7VBki1oO6C/PCp/tXgBr14xItS2S3ZMr10rlTOjgfqyWoWwDOMdmJYUOn6VvtW6a/WgXIYOk20h6DMmv2PrC+ruQpL6NhxY95dWiMdO0NXg/1RbOP3efJW4vtSEtLxtJbLmj8CSjvuByLB81DUq+0FW1tEv/jx0nXG3xpw2Tgvqbwi+66k9VqL2NXs8b7nZumdvEw2BSEI3TG0W00Z90QI9vj+xN15aQXxq2Hsr+zQ3/u48o+67muJ1NOCRSoOpXxdviI5YWLdZ/9BowTM46Wxq8f+YyAFLMhL2PmwlePSo/foRd8qSCfNaiHaRv/OReZHLW6hrw5nmML26Xqfcdn7xFQHuH832DhVc9HHmY622afLJJa0ank2ateBWs4FgINh7rWkNX7ZvfpgFYpvhAnRE9y+LX0qw6cmxUdHYlZq7NRUbaSPOnQ+4DIf8iHd+xTGl9v3VCXJxicsTiJ8l64GD+TrGjKjuBTNW3+PewLeIqpZf16FWid0AGjpoL+shxXxQ3awxyPpjIqaAfnEYDv7Zn2FeEgmFSp/Gox++zkMpvSkeIvPNHhPAc4nhmtoS6uJL1Mz6jKt89iHBA7z4N9u66uKaeo0IQCIlHrrkOWl4DCOVBxxCMMH3OeIGk3JRH1yoYqsr+SiqW/LAGe82q1P58eNYRIjOOcwcl+wgv1lRhOZnRVEA4aXBmeQ6s+elRMCf4YUqBuTUiIl3imvZyD7HawHb2b0dL/o06wYtMszlWGKw+dWVSBwdzsT3iOGWBdxBoXhPaLnG3zVzxulj8BxgHoLZGhOleRg6xgvuk0+idM3d/Z7gnL19mngZX6pZAx0USV++6a3pkLrFKotPgJKn8C8HKtVpDzOVYIs/ic5b0Noa3X+Z5bdP10TzZ1CHCy+hU6u35oTCQXTLGqEGAOG0U3xgGvIVKvgVuFq19hnX/9dt2g6dbJxG0yJeM8WOoOu8tLb8TOWUveCFCuaLG63IkbSjrkV3lEfQ5dEIz6x78zWxIVxdUAZhJ2q3d5/c/6dzdX4KS/BOUBBkJeEN4yP5vYNKgUhhBI21Q+R54MFrKpQePVhyUPSWOgn89HwtNbXfXOALC4Cx+kisE9/x+pPINnovCpPseseI4FBetUkhWgM6ePu/v+s8R2A5eTWMObv80SdKCM9JhjkCnJPe25Uyq3KJstuQIqU0rHW1kCUih5bviCzFzJJyLH6wtatYS2XGXd7/5pgqZ+42xIo9riGMF2vVxEAny4vd4tRHmFRMH62xlg6lTj9xlTb9a0IOTifQp1YLRi/A8l9YUiyqRU8dTsqySurdO9aMP38BU52m+mHZMqW1H7cPD8ltaavECGVwLMi5j9zKwRFyl6N2LpQLqdK1gbbDM/pT4y5gKR0Ui0O3JbllBXoRSeTRF8JnuQjbrFYt0KMGIkCyfjS4Z6DDh4Zv207Kozt8/ZVxCjma4QfYLicNAe8Eg28HiCye9Y1wnPBahXqueiDsSK+FIhDsu/OHRN98jVJYyVVBL7UBuu2Cibcpdrm99zT7dqvNEqvszBJZGMT6rNYr//JlYUmsLRPYko0+Oeeu+FElrLj09xY7JHYHVjI8G0wTRhvb7BycrOZFevcjcfPWG/CK8ziAezt9P8cPVe+EeTAng9wAv8YdphycQGFQJZFi2iJKwUaFXak4eVji9grTdwANxmsLGYUB4YFJ6v0BMfkBdyNeja1DnLF4SzVD1DP/WpX7Iprfwbg2v5zBQ255P+MPF6tcZd8uGF30V0Ns5BB9M3FyBedvDj+YvVjF0eKrMHLQe4QToYBdP5XagdGS38rpmFHqJY2zaNWr143f9IoD4hEoR05NRHA2L92Zxw/Q7SdjJQywcLlrlQAY7LmArz1h8CejsWWXk+kYcoO9m7qjR4veGViOq4h+3Ig9jf/i0mubDtEi/KE0AUwH9I1NEl3gbrV3LSpomgcfbKkyXRTbyy+pqFWnyp2foNnm2DlodjGY2PXUAVSv+p+lF7LQz0Wq3I3RNo4r7T/RFyQgMtY5GK42Yif0VU2EiQy4MzkMDfdKLoiU93c/Tba+hYfMTw0MOQse0UpmFoaotcUwIjHbJIlxaBENXKvdKM77+1hvi+NBjh6knttRArVfnxjlwSAqczS4Bs5xMlq10wc3K/TRFgIVplr/IoM22ECg+I7fQOWvnHFtnenn5mwS8U2nHKLpl776IYmJzHSCHNrQoN8eD2WyzgVkFZYbzv4lRoSySmrdZLvlBT92E7LrdtmsT/3tCu8/lPwNFxuX9cbhH1xxd9FRLiQenpNMSBXctyuxN0dh0H7Mzdi3HQ7lCiPOVicdY0n+kxzjViT/T6n6w9Il8z7edchQq0iL0Zkg9EelHsdFILmuSfLvDTjtXKDt/wvZwNzkO2lCnLa1xpdo1wNTMjg6LfKlXX5lIqHX7q3TjP16QH+oTdRlQVNQ4t7byIIDAH5p4ztIf/x9DlorvEr9OBnbIraLuYhJRQgYYQlxDoIzCt1VEPhHh5QEFuIqecm7YsP3XDUyASmYhWOIbsuZvVzhcc7EBGYbzkNihTmBbvPsKwhnZL+e883+ZktyYEuUdWg3McXWuCTEZASiQfYgyEUJvqIFzHBfRyd4r/tiJzrWxv7hxuufG9uzrVIlzfEgDWR5B0azvGaxEAH9S5lhbvo8H8v71vdzYwhqd50ShtLKePDmGcxXcUHb1pW3qsmqio1VmBN96UUCuAkMvnAyyCD/+q7uObCf1iWopOXC0e0pO8vVYu7aqX2GH30S0Sc0RQvPZf0IJtbNtrEtOVRxcxaIrEZnQz2w1wb7SI81BwW45hYe96mxG7iRTekzXcJ5rsJqENuN/ccphhkIoDa9jHu6+mV7VccrxFOl8Jaoq40Cgyh03evczCLnzy2sNaX/WpXP1BSwmJopS1HWgCANESHHlq3dnkbHxpd2HN1rJ2Q9gdGCKj++G+fTvbQmR6bKae3FO2LTPIosbkjf9uUU5ErxZ4K/28jme6IiFBM45o94diUi8dtL8gmywiF1SjaLLQh/fa0htuUPyA2MFJcCqgMvVoQB+Baohek2WaoXgnr4LFaNsps3WO7LKBb5GyaeNQ/rEKzQSpX8wPEjDVq+kzWyMG8ckVM9pk1PxbDWzBNesrmOKHd8IyNboFBXHl1Oh0rhJzobPEceH2jfxN0vQ2fSKx53Wz7M/uPwWFl3Fus6APAKGyDzccHuvwVymKgjxp17kWEUVJPbYklHQjcRuDnqNDjEI2idtdUbjSkgNVAFn5F/ck1w3Rdh0/14mWrJ1IbgRd5lS8r5CeY6Q3UF3/71gW467JfQ4wggSQZxnt2tk3fDj+uBxpTlFrZz1alEbGD6BQ9pc21U86m+5zCHM/lmzTIWNDfm05bjmVoix2sZUOB0MfNmNR4KKnsh2J+oIkUy0UBJPeOG04UCMmVDO8b48jTqD49e1hE96EZTHqAuwOBp42341m9S55Hh+QxOn18OQpBxtOXW2BToQ9g2WG2oVfZgFurBVazD9V0Cz7sh9oviXAba1OszKPt1kz6m0F2kvm9n2aju6rplWMjsP2PU7w6MeEGu+pT2kwtqrc/6UQkKuZTXYi5/A19s+yPNlDo1rJ9M8Tr7RuLYtXKPXP+U4hlz4ZKABRuPOTUtiGuXozYnf67sTg3sNW8GE7cfkg3YUAFzjcNrfz1axtjklrJhE51vHGhosrS/SUzzlX/vhQPOJQKiDQ0G/BdCO16iFVyyOaH5RVF2WJV4pxvePgGFOBpXZuFeBi+E/oHZd4eWoyym1e5n1OpPconF7R0TDbPoNwwf0wE+2dHqn84X2T5kLquUdnG/OFsu60Ar10hk2BYVb3+kaeNWEO23uvX4jYkXwtrZe6wuOEGg8NnDYJFFCLL3DcB6hHwqagsGt78tcj+tmTRKwyVEcAmOLH0CZr3aFgDMvGg+baXGm+lO3qjeLa1pCDin19v91oEsDdaXtVlV3dovATl2BUDUu1dJewwUPShRBqP6iPp/iL6t2QTPn/KS2Oa3NuazUqwyyla3m1R2KaRj2zPJRhM4X8JQFqD21rBCyYs4yCR2u4iJ+RLL+K9j7z4ZZkp8hezZChIJT3pUrpNvyyWSuHnkhb/jfGWJzxSAw3fSnsyREBrDm+Ng8CQEzTGQlqqSFAYZqJRwDNmcloGb1fuNHjr61uGS13vzUIRNkbZ/9vgv7neTfjsRik2Ph4f/CNfzgwW5rQWhByKKaHVZMeepm4cVMBDx4rumhI9T0PPF/03BbF+LmR6B100FyxvG1sihIVJtdsjqtmbym/HClkw6AlT/jIqfax77P/PZJDdhAV0vkdA5OCFt4dGXAUSoTKTFYCIFdC3RDRUGotjIdoD1qPrRJM4b9iOPxbSe/734P2Sv6MUP4y2IrbHdbMXPjN9GioutVffJ1YiQ1e75wDLvaG0hlQBzT/qKhQ3vz2iB3R6q6PeqLbsvcVhLiAvnYQkkEGmVw6BKPaHhlC6gW+mpKbyfnsJHdUOYBkrhGGHEIXVuL1X8sW9Fttza0qVUITIVtk0WUz/QTBsVmBD/ovKjy1P/r0Ri8R9GIGx5xMm35x7OUfOyadUQEM7zTCH/ixngfWk83igM6Tkhxyifb9jTdawtGdjpmFehe/ZvFdDMNSP9rEi6aL0wgG9NxX2n7LwZEDARvYYIsETLUAyuKJBuCpXmewsPQtbCJvk+zlxzZcmYtL4Rxh9j9nrhufOn2SBNP7iwnA1QqSmOk9khvvWh93JsTp0gelzbKh63j8dzCLEKWnIw1fhcnKQP4Anw7yuQRfVB0DUEDMjhCg89edKKHVsLKMBHMMofHmftuByl7TY3x5dmxnRsxOLxI+1+iYkA/Tyn7Q3SSiqO+YJmyoDEgafc/W9LtRbUoYzgNSakvyXuadHxjToJwOCP6rrTfpEcdBExb+9/IwU36g3PLySFDTHALxcFKdXe5Ob5x/GIQ6XSy/rCxnoaUVR7pW+Ef+bPk4gjEQToSxVYbnZpaoGIlXqo0j297kgL4n5jg29QUFfCU95BXlkUAP/4mvi4A2z/ATYKKlyOieqnQI+vw9jdMacwBppi5l1CBs3n35yCnfemMC8Aj3WF04qvCihlsgngaP3cGau3zbPQlMZeOw/XSqmSk5sYjwEGpNjimpoU/UaHIK+FhE/aaP3cv/NFlGxTePZ3+sbv8Jg7yutFMlKosoVMUm7CqYwtzNhs3qXP2YeG0Ubv9KB7NNhMH76lOdGix0jwzdYHW6LhB74Lt8wBrXihCRz0Bzg3Xc8VI2nM2ZDJwX4cU9XH39dKgb6orBs2wAawIUdaDbyV/9kr2fyP9435vdP9O8DfiqnYUyy5Xyh1zT5V7/Oiq9TttLsKQtH0RlAbJu8RIBx1eKLLh2L6BZE/BoZqAnsqTFEaSHng5RAlSxN7ZHCFI4PM9S/fv/PqxYM129ftla5MPIGaqapw9/6UZvBZCY6UAhoGkuifXhzmlFFPS+vOiStanznET/eruUjCs7v3ljxxKkaSHxbgq9Om7GMNzromtZDOQ5x5y6UhDHiIgb8/enJvj0Emb3Uy2eda5hYa8N/Yf1HNgO1nDQQh6++z3X8sEibNS1qbLfErzWlw0oGl7ngCuDeIdlTmh7C52mTWVlNsye4H+zmhl6MoOH4SvkueEYI0nqIT79wOMzIAmflwXV5UZuFoZBP8ag20IKIuE+ggwCZOq2s9k/CjBNt808Rv0OWsRcyFecTvDBs+T95g8aHOCzNBACHcIVMYgME6Xisjqi/yi4L/qiJuErZkFeh/qWfXRmLGVe/1kQhrkG+wUx5fLYjU359Et+vPpl3R4A1EJ0IHA8pZtXhZYYNP0/SX3ZuPtQ/OIGAVuUMAtbLPXAu0YhLfWqH0pjZIkS6Ti+9d+SMmhtOw3i3x0YsDW90DNXegyTTyg250kyCWm/Gz2ywtkA3vtXRbuRtNjq3axl1uTRD1tALU8EJXjHnknhBF53Z5U4INJsG4Zhh7xLhMEa8V079PRzVYd1Hw4rqfsJRTIrqAsJJc9djHat6vE3FT0npOIRgSW5nTs14DT3vErN0G/kyLsfohr41RR+VxATxYew7U+cm++ccqP1jTmYm/ByD5Bk/EnDfyYe4Wxp6CqKz0XkP4aZahXm31vO2dJX01w/NhDlU9MxVjXzjaUtzI78YzFiULCDJrprx7WOA8vyQbmuTt0/Xov8wtGcEsub0Y6653q/un4D0u7jID3n/gdXEcRPqKzrgTIPdYidR8Fhnigy3T1w8sE4AeRttfxGW8E/nCPm9WZ0atNoq0S7pRYJANFB/ZpN4SSEiXZu9Yb0zm7fxiGxRa+SaLbJJ2lKQd6KTGXlHlRe/SSgY/Fd7ZMDcE33jSsqzutBYurER07ZB1MYk9OZbrwRz2RK1oedKyE8Urq8vlh64Di8ULFXenkrpZCPnDxlQXt5zk67Pp9i7gnAz9coQpsLaSoptjRNPHZmknIgImWTzU21IiLfAoRkGtCZ1FINNVF6IgymZN3VvsK8ESpm6nN7Qk7Dk7kKqugtKoNRKvVqv6M7BESnLizzx9J2PU3bsqx3QGSDFMYNihha11Mtec4VlNYG8MGXLxga/NpKeoR3e8XuzXHW7rtOFup0qC8muOoLRikGbCh/2XPS0uiy/Te0DHf52O6e4WaGc6Z/7dLhxAzlOIYB20Et+Hfj709VSoSBkyigeMxWWA9KaxNURW3gtYdeJM0Tk+jK2FdBeHMR/j+ymUrpmMcmFjhcfya7/2ysb77RXzY1NN2adadeoHkI8S/+5EJSQRoir2IiOjj9WESfgbgUXBDFB9gWmN36aDmh2QHyM2F5oQB0j7kGDDUM4ditmkuKzvcs2NE9gJh6ZgJbAlx0OboNJcjCdkJg0tYsNMsW2gDpoYABSuvyVxn5kxPtwaC9PHy2iH+k5CK/Z9Jl6V24+O87S7cw0CCScax2pE3ZKXwrEFEAt8GMMOQ6EXnrP/hlWNYo+MY5nE8hkcb244qDAtmY0DB+/NL2ZulDYZX5st+DSZVxKv/uxOF6luEyWEnbX+Q6LROlzzJGNcl3SE8wYsq4denVCvWcDtLpvAWIKGdPIvJBupnBJvMx9n/3YskpzCMVP+FS44jiU2eTGHgQUdjNOQEnCqrCkV1OHGTHk0UMZebHTQ85j2FYeCLE9wmlqljk/ooTee24/e0lejlMMMjRLQRBsYFcdBuXADroG0u50ErAstRaaSJzbBiYPDis6aV3Bojm4Wt6N8Y9cW7oKGUUJSCwuGRrpU031CkNZuN/64Yv19N8Y4rWkN+iOoD3+UMJb1a3x9rq7CfyGvhXFDkApKIWO3+rV3gF4/sHXHXSw8655gPZD8Gre59Ol5BehrgjyiWZm+ltsbiPIzY4+EpvUOzVRE8c9zzq84KTPZjhV1Vy+y/lmsSnDwmzQpCc+kcEpshUwt59mSfShwtWNszkyiW2Fo1EF7IJLCSUSjnEmOCOJ9wyDKP9HZ/1I58+a0orFVemivLqPhwF2nFwdB+YVCTuZVyuviu0UwQFUNTyJTVi8bBw4f0q2ADSGcNjqS/zIvEUcM2mYxzmJRKB2kjl+wrDq36s9dXgbfaZcc7sXCejPExLrl7DpUx3UQ9TfY3RkfJIkpjZ3b+OW6Y2Fl1x9fEo7NREwn1UXmF6J5w77nm7ecyV//Wd93JkD+uRVkm8kjYSyoM3rhxAA9khGlKkaM6/DDU0mTZac69A4ygjUGpdeoI0CUylfZRmWTUdf82EFo9GYVkCYtxQDeTrFOgoJ+hD0a+JOTPmy0r/I90L7Ag5nnl14k64QIT0kspWWchmpOQewTOxprrtiPTwdAsnSaPFXR884tyBg0SxmeMo478IMh1cDNA4jDKhGGxfskaRae4rnv84PRez1GA3biAxn+mBdW/62CssN++Dps46NdF+HPRi55RChp3YarA6cSz2SBfqonliBRxpnRjmG03iJ8QrKVEf0RsEwfVPyKZmmbDPlHwAHp6xY8NcUUHW9Scs7RP3y3Xu2H0DaNb5Z5G4J6hrcvYWspOpjl10ieSb/sC8J+SkQCQiQExp6TYdJ8OGNouCjXfq385q4dyJRE7FQqL98MpNRIfvnN6tVkyP72hzPrjHKJSxd8t/YqM3wt8DGWUl7NFFG9mKhGmtxXTW7Bbtg2Ue7kLL6Gu7OMyPT5lx392wmHb21Lr95nOtXfFGVwAYKwRyjATUAUeieuHrpGynJkFNCgjGsbhQW/YBIXj8egB61/f7Bz5MWsQytlsOZw2k3a87OWd8Jj5Dej6PJ56fmLt+ItMd+ZYhRmYf3OnnBzKgVGP7BNZB6I/8TpZmvs4+7FNps8sWwAJd2qZgAnI+wBnS5QbX1RwZ+SAAOici+q418HiaGDamoXcZ7PuXBouU5yXChsvQmDx9KIdyi7gsQmDOm5c1G//igjQoA0srgxwhE6BkVNy8i/7IVoc1ovqqI2CkTqKU0DL7ajF8tx6+aCuZ4zl033dWzfgWt9w2f6VC9yiFr1iELljLw+O3v7X5L72uD5qSGhxsy2Lf26DbYFA1wnSRnrCtaIaZlXUGedleYs/Fmq7NBqEEG6AOhTkwOGPOacaYIY/Sbv6CF+ehgaiw65+S2ChnKrjJoaTYmY9ExLaN0uY/5ZRebZKjpRc6J27YiH3keAj3RxNGdjTmFzz+B+mdDAUICEPeCnVRzxVxYrOv39S7NLVZmVCZ9ud3tynBnLiJ4yVhBe98Uz3tT4Xylp7k4i93UdOTbT7twBjLbTCYtMKMGZSjOXFVXgsI39QL2YlqKl0Ou/8tKZ+L1qaF2HTAvu5+BnSGuu8KdUOQVU4HW88I8WzlZz9lKcS7te+drU5OhL1/4VvLuSBErJp4fHzjoeYz0a9L88E2bHBflOAer/EGC0/2l38ghpUE1LuHwDhwsgb45We8nNnnEDLBiYQp9gBBsz7GJQzXwPKEDqwRenLQA8cfrC405PgLpjyMMlCCVR8JIF1g2TR+J0xengVyapYF+SSjm3yztrDyDHG+sKHU0da1gSFI2H1N3OiAb0Cje3kp+PW7O8JQRZBGYLkPUDxh4YEevNBJxkAhOiWOOzAs2WAYrzVmqG3jJnhnX886Iz/NONXuGZTx/JU/p3bRwmn2QPMsoIN/Eu06i1q/UTh3BV8a7y/WBf3eXFfBPn4Zt8oyoKQnJ4UpHU4fXpddML9j2ESwTLGYpFGnGmHFXX//I8+iYKxFs+wEqZ9QjPDAavYxq5hz8ZYVswEYevKRC4GM52MHuiaXmaKBBV3lTxoEgpNC5eLdEDJbe18SegmUKSBuMrbKMrJ8QrqYEXneX9HG8wSbcyUDPFdcRBVqSjWr+aQYb8rMRVXiWjkA/zY4hfFfXMmxEC6+73kdW4z6VhVEuwaYoUjkHYMoFEWAvpB5ytxYBOeebU8jJdQn1srX+Ec4MXJYVvfvVgFm2nJfr+ZsDTnYwuTnjQKoulREvPCcjnSHai6vXDaqg3T1XvcI54AYNnyBZqteIm8mmHKXJcNUIuk2NS6ba6OnpvGSiImOkfMdevoqtPw5HRN3fF6aNghJ2KYpB8wVdke2wWlcQk6qZUXKADf8b1IqqotD6n4a+LyyV0WhBoW7uyxqZCtCsKH+GuTh/Qhi1F7asiGhf4GrLfnnUsOZWUinsR4Eq6/IHjI5v5/pSuL8hgpOowGB0nm7JmYUxJGm6TN8mvwbK82NT6eUyFN34lnEpZV5Ja59Fj5AsFPD5YiKpwf9RI9y9H1A5F6JuXj6slf65Ecqkr2nCdXeHHHp2RMIhM3koi/lRaELYZFTxaBEWV1/JUVZIWjRLfrZToMSKmpAH7f7KuX0dsZZBXuhbfKVL5K6XK1QK9EUAs73AGAEU3Q7cjpx1KZVAf5q+8OzQaz/aS2Gb1cjs7YXsg/R4lmRnwv0ri8OvIsmfcq181IOWhw4wDIxG/RrIlabAVJMzEtOrIAphLqR5pSdZ4m0ywi2X8Ce9jx5RNeIukwp5ZAxx6tqD2yBau95AXyfPO2nPh+extqQRMS3INdS7xxDVtCBNQqDzPCSj8Q+0Kgn/HLtF85OSTa7vmj3tRzo2wZJ45OFPDZKg5w3+Bs9x2Uiygi3n1ZcphsexTROwh+en8rP5/NtBG6CvuY6PWOa5FiB7Obm1FmgcCsMP+z+FqDqSr+fqYU/DtDvbP1o2E0I2OjJ332I3hj+1Y93L59+R6XEoAeLFufN4xtM4d9WIfE5O8oB+mRswmtb2vEgw/6PHozIL3LKwTfAXL+kpe3lOf9GGzVcNIzowulPmvzf9PJ2xbat0vhkp385ANx/TZATwOxt4AxHwzh4IOwz7inhp8A/6NwZ0swdyhmMSFFtFXN4nB/0NlpmOQrZl7EFCHFz3uZCDmcsANshLzqcFj7T73IK16TFz21CQW4TbxIuWcbrYKkVp9X4+C10uNrssq9HEmryOb+VDazXRKQTpGuJ/d/F4yREhPSPkiNNRa7624w3TkVKJ2r56u0WMQDfhQl6bnTgT+O+A8eoLc1WoC7UIXS/Nr88Le6nUJE2YwMr/3zAKMP8vMMehzpnWBlITcl0hpqE9E2U3paGukpLPAGV9Qf53LixHi3kB+ZumnUe2GOkWDwD2w6yK8nYhwU8oAOslX1dz5vip1FZMox+sBTrFxOn9ekCtCDpMgwc7PXUfQO7fjQ9I14VjSMorouhOJM9nfbm6EsR/41D0Bl5nVVa3mw/1z+C1u1gjytSS/kd99+jr5iRQNa07hMSn5PfnqnJ3PPNKXnYAzb/IDwwTwYIaNsReq2Bl+kDN+/njmMgcW3ZfFYSNgrGH0gXAWbO54m0D0ms3tWb5QGIGCLQOMH0SWVHPGMkUZeD7c3oB8jW/l0QruWxSw2gNzQd57anB14dbkHL+is8JqNmcytgI79Tz2eJf3KHLlmZoAK9Xs1an67NAReh0zwM/dVf0PuIfzJBbb+UtVelfxih+cI1DmwajtGmKjC4wNIt1q0UvUvojhhAKfofgoIueK8HYERL8A3+2rj/2KlFMIPPqWxLxk03lGFoYu55NsAjZr8E2Z41AVwaXvPyaDH9MIRFqwKogxApIdry6nL8NCYZpwZvbsfwCPwF3SOykuieaho/X64ugvfTjx6uCBf9pAv61e0Y76pXDNFy7eqd/+SPxblTr6zRPGGrUzVxNxRI0ieOJkmLMvST6vQaWr7W3mTuX9Y7HDwRTH8mnrAjyNwPR9kk0oWOnRJReU7/1s/44sYTUWlvC6ykEpfnAIUxKHu2RS9+SXg3ila1h+DB++zsKPfUdx00P3rVqXAGkotheF5UZcIw6HnKdIyOjda51oyUEd0or5dr7DKpcEa2e4fuxTVH39ZOkgeDwEqkIevX9g7VdhMZlLWUvzRT7L9d6IFTFHszsZlXT2hTrP73SHwJDLuO9yk2vir6QFbBCB19s8Mkw4KL+pmv6WCLooa0ueYgf7REq4jB/sAiBQ6d649Xc9Axji6V8IeSvfDACG4cDBovFCft3jtnDJlkdiSuTLuQwdYh9mD78U+6hpfKS1OGkAIQHnlIzX/Cs5V031cv9mN58y0N62M4sBHaeMqGedIajTQIyX2AspJdxQ8SS8XG1dHI5/8fYsTLQzO9CIU3/mtdihnwRaQeiGoGTb5LE5X/nDRZXZNyJMhunqDfZynwqO9GMwtqR6t/pLZ5DdkfnR02tLX9QCSY0B0xnVcMirpX9FLGF/zK0MVUgfQHAehLlaqW9QcJNHh4AwYwvQ/w+Yrg5CcE14N9R1B2wWgR8MheYElNdfMPJyz6/2HqmGNyNbCk4Lq9LBE+0h7gGp544riWqnhNcYIsNMVdEM1M7wt0SLVFNU1pJMRuESVDs61uI2J5Y7GEsazwdEPVNQiOK8luz8guypWF9+GgzOb6Wi2miazD3C8+DdCySUhbqXm/FYmJ4LBz78tal1/8PC/oGehTHXngKlG/EWbF8Ih+2JxSRL5Y8wmf37G/JbcC2ZVwZjeRC+zVtL7YUVPcgt+4OApySWQfnVQ8er4f7t+lLwqemMvQ7YOfg4naVUpIOWCWehCU2x2XsxSuJiNlkos669iOX3Z8/KhNwVUU7wgkLy74H/S9foKsugRD7itJuDSo04yP4Y5Zov7h0ognruFaMDe1jKRJWpYBi7BODfp3SrQxidR0HWp8/PVbljJ1pC7uvDVdPcRE80lxD8oivzRc4cZIjFv14zSx9m164oagTfpO7eICXhK7X3hFkqJi+o2Bh4rU8dRfT71ejvBV9BJz7KQM+a0yEbPBFnoioDSciJOubo5UniiWDqXE2qyAzYFmpe7AyzSQXt08HFYimZb8g1/8UVsUj7aoe5U9HjvNEJHp+RBEajRPlxrm4a0cEfyJ6S4o7PTmnXPRcKTMGrAwj/+FTfoNpAtSxtEtjuGaTJO7gV3BaqmHaA9p5vQaZZlQW0aNX7FEJN6xalHVHVPk1nnKWjWS2f25943Mer/YcVo93RpWNXg9QMKYFPDuhBwwMkQLZXztxQVf6vIXaYmiiWLil3bYOfrbHp2B+zN23SLHVjLALjfSwM82wKjKUPKBgHW1/5BYxnYxvgLxEnAX9govS99cFYm6KcdSvZwuTa8ueBnNawfltFCS0guHxHgUamLsJVqiYCU1Kgu2rYaDbQbfhaSnhLUVWdzsHRijGe/Sfu+7fZxoVRX0tkTEWsUO7U2zvMS8wrLCG6Z9hy+kAewcktQWbBBO+TCD6MPAlvoDV2XguIg8z6FY06yTBCsGoUIpxikNDYn+Nye46nYBlqic0I5p7AUs2u7P38e3alOCtp31ouT67Rp0+6/aq2pr7iS4TPOCZwxd3GibU6SaO8cmUJrqgYyVv909t8evKFHO0LZrdvzzdEwlXqsCIsylslPwCkExdg0WtEkNbUFk+5WjzisIThzV9GojbAKgxkaZHjWcH7QcA8J/2dMqAzxVGoSXtjfugGortLIeo1FcghiUi64nQgj+xgnK11e92j4XNTf/xB5cTdYwtx9QBEKTPd7tK+4gWBZpLyvmS1TnsJSW2LlKxbvkvbX1wYkAaSNV4UKWA2vNE6X+cxeou7RKRDuCwlGykYG0ToN2gmy3X5yO8YkQTeLlxOxSek00ynEJKgqkN6y8bCYTQ72hScv4JF2aEBvo3DOaHLociDWpOrGcyu2dipclXrA0oPpnV15T48SlfxF46HO1+2jzlvXPDwACa4NOfeyIIF4DEuH3UofEYWlwzzl7ejJQlVz/J+TH01XWr2ibvC7kv67wQUWoT80MviW3P8tlbah9jvDPwKpTCiIlM4LkacmRiByQcem24ZupsV7dHRMc2dBzp8fMRmR8PAg41fZIMshIoiq81DvxVbwbLhX9u4SCKC1SjGYiVSbUkkgXgB8A59oTwa7r3HiqD7iz5tNQq/YePpDh80FW4fM+8OiVuRTO8wnfZVC1GMZDTlQV8+//uGkPIB5sLy4GpjCj4fcWd5VvrxK6WwYQstlz74tR7jaOK1c82xHyWwy5t4B4PkWKZWecyLIgDDrSGW5MB5EQkWX0M6r6U4+omQYPexYojfwBU9raSzGcAG8wdTX3Fmt8I45Sst/ebvzI1Q/WnJVz0bW10LhPM91WVo5rY9phXetx3/DO7srKLj0uvv7HERZrqYuovvd6A5TGZcylQoHwpDuWbEMtUzoqCMYZ4KfD1Ff/b910/a7rKHlhRCvIY2eJ4QV8hpve+g4ef1bc/ppR1kLbkq4jnVcv8Kf0jZsZdTsswG3BSz5WpGm+S4CkCQ7LAkztekYIGPCGQYbKXmJjFayCNpYmlR4mgMyv+h6pp1TFF+vS8gNeRWnOcxjsytASUNWOfRiQkYmN1YW31wYl1sSGLZEN6Iq1naPVBg/tL18Hkt5YKrKgXbopa5ZrocZ8vPaRFxJYFEAeV6q3m0PFNTf1NMo16hF2QanUJRYV41bwf6/7iYL1uJvd0XoomLeGPkGq93HS/BQLpqX+j6JuKLYLX4Llsc/9L4/i/VdF4G+L4bWSE1iNKpSs7f6B3D5al0hhRmSU4ifwPYD43T8OP9pRT1uND0HQolgnVh5qwRLrj1DcxfWbB+Zwxg1FeEFtTmqKoaj1FdTJa2qjkTrJ4LrfsCeqG10j8dL4Ts06nKGuPNMZcDDXvClk8z3l06rLhL9X4FY/KcJLNoiqGCKPDwTyVa+fSvig75PuytuZr89s+RAFcPF4Ujn7lQtEDEk4yKilQ2IuXgrGc2CyxQrZJymI5/x2oUX8ScDd+cM7/TWeOtt2b8xiQDvFPBkVgOCbuwDUABSZwp6+UHj5plgK5JT/nwuyNPHMBdgD4fVKKUW4Dj7XaxXDYOQgp3pqwdJMzOdjhpTwMbIMKaCxa0A2GFyKi5Ml4vSMei7hyfE0DW5kKKIpkpkSwF13wc10Swsi5TrTWYRi2qr743uNuAEeeoa5/H2MvacYPbJoRgLOFtJabqemM6Y3aHasYL7gsAqj4Taq3L8rjqf3ldVRDwSzqZ6LP2BABbPqkU1fkv6B+D+DyYpgUJ7goSvE75QwteOSwszQ+mj18agmVjlxK82PwLixWWfv7T5LPqZ1NP7/6FWfAppPK1V/UCZBBPerxD9LeE9Yu8sH/MIxrUp9wktmJ43hbvHMe6o48T+NdyGmQyZOLvmLzVLZ9k2TcoS78VwFGyZ6PoLjbIodd94hoUfAEu48hXJa8jBTlTw9sYta4hhU8mvacWxmb6DxQ9L4Oj7DiQfPVGjv1R3EmuejOjPcmM+swDoqpqXijnWn6ibVjYI2tIQBdrk7frdztMCGFZY0EyysMI1e5lzJmpoFPe52iRLrSAhHW75rDFf68cMLPhe7eg5sJKOfGxuJQO+pTcjrvtItaAJgwyN8OwQCWrmx6QfS7qaQ/ZP8afK51jcn7Pykh5zCQu4JGiO3Y9w3xpXYGUJ1FQbkEyDT3wN4jEXu+s7oDBPlNrvmWD8BkUXxDTP2s2pGnQwwcXBoQLkbAoPvUQ6TulOBNOJOg22LoJcixR7CErVIiN7MPRwMu50wqXmPlPUp8hg5mW9aPM/JG38RqoTq3c1tVVFwUmzoOy9hVJAh+SbbSNe88dzNfirP14/glD327qfFXTCUbshoXjgSk0NRYS149LXK3ewQIkoacqww6sjgkCuSzNuT5HweGl4BDqpVv6fNd6OZTha40dxHGsY405i8SwxtIk0tCdKVAv1CKQRUM2u1IalC1yJ5uOUuh3ZSjmTXx2nlD/7e2Ae40lDKjgvgxWD59G0G6qf1iLFU/ok1+wEuKqtupm85il8VkYqUi736rf39C+W5i0PySzVN8ClZ5otIhgR0GyheaHf32N4U/G27EPIoux8HbpWU9OLF/K8yBH7dRvIe4LJTdwnZvnERdCLCHQ6BQqPGA0yBl/Be82WIti8gMI8gJMRXxfGr4JGy/oIeA783jGqy12zsnhs4zh6j6ltrirHsM5yaQsc17goPaLh6qTPbgwqw8TpDoyU8F4rIT6jXwL3rErDv1SqYDyeSyQeFb7bXPDgIoDpNHnHyNY7d+R+ZiXMwgX6t7tv3BGqWF45KFRDvdjvpOv1BeWrKBEVd/cF5VUyCEEfTpMDKUf/cx1nS1CrXZ0MXj+pY3euW6d8TBfUxnOfWIUVQ5PtDab6SbR/BCzEznbWyUlxufy0bpYvHR3P0G7NZSN7cOSjMtDlWuy6GziCF28JuwOCHg8ZWq5hmS7GYqpmF9rKC3ERkiL86SH9VulSF3Z0O4K9zPMrFLNecf3ypYXjFSDHvSjdvjN/N5QQI2IiRO4x5YalLkBecnlwk5iELEMGYwEG6ROqhe0A9DxUY+KEbHqtNPo2deadq6lzvoqEOwUO0mlqTW1nRNk4waIJd8OBfVbZmyDZHJYAg5h3Xb/TA9EIzH/cKGXSzpulOgiXy/XuORsA0Cmxtr0CAbv42HFAO2eB3u2vLkC3vUMXg5eaPAYl2igzMlb4b9vWjONMEqK15vTKsH5JXMX7Z3si9zE1CxMZDRmVKGhuqFazCfAVygsmCuIxHkI6SdLUyWzBEB822SRFIIMfvCuXR4mRl3LV8G/uYjyc39Y/CMEMAgTdtcBRFsojrrFguUCOaAHsshwFY58v+57Z/J1KYA3wtpurcUfYgjzyLwf6clUxkSifUWFmn8StiYBZxDcC/xbUZlbocfLsD8+BEkJ6bQUyL3pGy73SITWNNLiJzE4pzOdJrYgZN3xWNiP07nblvjT7hFsiB/QtrknvIEuMVCpRtrpOzg9rnYvBISnBVQAK/GLbwQu9oV4/oJQtJFtnE02yNFoxeicAJnFWtHJle++XqTYyXu3UDpfM2uXCe3azJqwy3na04UsMtZCG7PjBHPytJy0/29T6Falpj3THXlkBAILR/OGikYUuKF2bbNFaKqJAS1JN4G4328n33wwOSVWa7bneJVdUKTvoJzUVGK087C+BTfOTO+n91H9PoQ6ETS7pXaywEnj92sEfV9nxvLLWnC9wXrpKXgXBJm8Ot5MhsTXQbBQIiKZ9DawX09/8p/nHJQSMzKq7zxc5OLTN+oAyx6rzQQPamyhIXHNP9CkNNhQcd1lBFxfg6hFSSLXyHhmnDv0GdqE/0MflViS4cUP6qj/3irTgrrAY08BXx5Xbayg86esJtmBmoF/UduYyBRxrPt1oX4BPePQuQsMRrwgQIS46NSaAZGqUeYX2pJWH3eyzpDKWB1Ut9RnOmfmlhgUzcPAiLgpAnWl2kOosVBmXbXqMkpBSXwJMAgLceTjXCCDrsUl33/pSq6Qpe8Ox1ShUPtcspc/1XZGuAwOYejTDZlS67+xIYeXxXbq11o5QfWu0MUJle2/80Of9B/+CQ5T5KRN+Z6cMVp8GdXUiSfdQF5fqpVC4mFLc55uzlnpXstNWO1+TCd6Y57OqP38479rCQttF3eySmBHC+0RI0PgFJiGkqkSp9eC3+64kJ2nPqbMVmOZ0VawnzSE7Ja0k7azqdF3TWduMcldWHhuQ26JX6+o4vvDC5uIua6Dp5yXs5kIFoEBDkzdobj3mRQjS9A9rte59JYWAHsqYPtQQ1j2C4uQfwctqGSWUoYe2f97bZgofWiHMrMr5zTE8uTIfgFxoFIgLZzga/BIr5SYqrnZo9quGQkOb7fmqQaUTP91Me7OrDTDnlky/3hSeucIFJy/6WZhLxVaL2G4SQB3U6nSdFc4kBnUgTm/DG5maRquQV2pk8htYbquwQZhSQstqQhBmyyAtZevFNgL8qasBnAggqC6k5qSHE2t+kgoh40lzapDjZO3YqW72EoTrSYGRVg1dqccztSboElv++7PR9BXZf9DjfOZzjWFu3WPzBfwn1JsOX+sD+FrqCNtxdj6MqpFmbt8ysaoHz8nxqlJHuKgGgiVdDp7rJ+IsveH8F/bEHJLlmlvNJnlYtSsy0b1/FzYaLRbhM2YsHJpGPb0rzjvm4jU97+XhrMkbzM+aghF2+QU4h0MVllywoD3tTJ0jaA6lV7DoDutFKfHlRp+8F6wtoupvsdG5Ex7aUF9RGuy5VWaI8WkFbd+GzjpZ8bxEDY6XSbEhf9vg62TbuuYT0m+TGGJB8bq1zyN8YCKv6mZsgmggrJOKZDqbS09kblyvFMYzlYrepQlIKTepUxJQdIyVDQGdxTf+xto+6t12dM21cYIVQshrR/4NcP/LVL+ZnFvJOa4m+rfGq+gWFmk+TnaMsJICqwCOYJvhcDm8vToh6rRD/qsqCl1cne/6jmx7xeovP4yyfI4GIq6ksHbeusHQ8MGH1EwUyjN+mcu8szJo328i0J4JrpstTzJ0MXolhP1L+OZx4MPBn7IXMODLvouoIvuAE8Kr6uRz0mISKiN7aTVb9va3Wz/0BE8TtA6VDJHZjQ/hjmWUlXudTseqe1pRiBiDPfTke5ENdZJhYzwJDTDeVnUjjefduPvpI7Fu2Zr1f9FMV7Fj2mTIxfJ7eYnIRH2tF3sz9FY9IIHtEnvULqxgDstWlE+Z1uraL22s5UAfkvv2RbqOxyLptqwcszAJYIjFCQXSadipGnJjOjaOU732H0X8GmnkQgZny+UyNof/S9PiVCLOqdB1Jaf3Hn763dgGm3RHhTJOW0eyiX0xcNOkNiY/Zq07ANHiJy6ypMF+RULjPcE2blQDVN7tjfJiGuWDo/AeVVJNoe1k+jPi1jwO1VEGxSSEfQKnENlTNnaDqJvKDXCBHCS3sBXatyKjHZcDgkWZOowDB0BG+vtAL4wHtAWAUMiEIhdOQy2PX0LrQV6/uWPHsFcoRXtEqUqQvaB73j0jPRcoj1GUhzsaRC4lD/PufqfQd55T3VhQRFpL8all6TYECKDzReqLEXsWKRyGIyS80t7HaGLanUytSiSgMWoXUdgneryUQk4l+UbXLV0UoiefAy4957P+h+oWTZBZM3sybbos5GlNqwN2R2ArXCZHyVyEVz1c6981cTkr3E/j0m0Li0LXrxyr7Ad49QuwRmQMAL56O5m5moafbsc7gF3KGViYvLzWHVWJQ84UlG6U84RRDPzxRP56lT+4bYhX/rGrypeSYoKNdsEf7x5+StzBLrlsg8kPt8AViD7kDIfTm67tl2bcYw+VhK/YhYd8LLQDXcj0O+LJIlyd3SiftkMNF+P7v+BdsjUOYZ2RT4V0Gsm8uRKHEgvSDACNjEJU5MKXcpZeZRID5UgVyNhC0bxQV9KGTI3GgtfFD/iN2eHgFDNKpz/TVuMBO84BUCRCb5Sw2El7moJspIFqubKKaOSyYcj2CqTR9DNrP6JUeh84NI/7KM+48xcAsKzGwqJwv/d5H12bbw/lPhKW0Vy6P+IwViG8DM1m4VPwoHw92ZL0BTy/IU8duVWvXhW65L2yc6AmhqUfTBVjhW62ujWVrbZyr8z/wWdkqkn4Ikg6DjD6MaaMqhz/+Ns/RrBmujx7N0ClEAJeyY5fjPYu7+dJBwE7Xoj2WOKjGI782JT9FKtNGkXCO4FphwHGtfL4uMt9qMT3RYBjp1Kf2B6tL91i6G6ImtWPBvbzqtqBVTlYqoNqNRG/WQeqhLBOy8ZcaVZe4s15tgZvIk4G0Ad+5EdMPEwywPZa+2HdXlt0cwZIoN9lm9X+2tT6mH3R0OqdK1nZJ07bPA5C+OawIzPLg7DOAqedM7jLgFh/Nw1at0vhE4qAycE78wfOUgjkQuStK3GX1C5FyMyqNhK5QflMaqFmoyCa/ya3AyTeZvW6yoAy8xLbVaHZb9wzy1pono4PlkKuieW9USahstTD1T0sd7383vloK7ND9ny1/5y5LU+Vi7UFzX0H+yJ2WZMvkcIPXP4VmgP1o0SMa1uAaws4AefV7T+CNp+lRP3WPMZ3kb382eFrwsNYa6VkvJZTGyf0nRkpmDXnd5LgOmLA8Hq5OTq2hHViTH9R7Z/Y7mRNkkmRU88Cs5nwUL58bv99w6dYJHUjXvURvgt/xzE2fDm304HeL88a1HkkPwQGh6Wht1AQHbUi65+ussL1wG0dRaQNHa3u30TX1h0mAilK4LOiaZJh2VEb262eqouRuVaQOniEmotV6tnIaiByVGTPqfxdf8G2ZJSBBNwN/3xuehwFCZbbcNaQO2aEDX9SAuYoKbrKCBn245GHQV3N5aOAAHnX0jUJFApbZm28WOk52i59oEha1uDH6VUuhv+vIIyHUP6kS3d3E0PTe4kCnmD2YUDQDZTYFv/iL47wg6yqdLArTAWHj79w83o9tjQbaRYPn5KTDpOwKcvqgIjbbaFE3JsQgAFx6enh36odPwXD+UJOztLN/caySSMn7IyNSIWmlpjyjAWclLGyNJLtdDOvdqE307KN65t4QZZ4nBQ60zObCIldYONRmO2OO94yRINu33/b3HtPbrkxHzH3IGjTZVqlmSF0SkC9a4M5sPo7/n4SvV0WsJ0S59IDZe1woYVYooQrG/BVSVS7X8KBRViqX5vhckW0r8mVi9xnvhLcF2PBAp27Dv9ZKVSpC4Tuqr2WnNxqygjWwGr4Oz2CGckIxtsboYOTUueN2f6x3MRshznZDkkcrqZTAejIEWQtTX+4sYGqDuO0WnRf/c8qfdouqoTlhCSFcR0GL2zn+l7x4AhrRhVcG5vFmcHc7oPRQmX7ZZoksgipo+Ww/erF0h2V2k+ol6uyxk/VXOg44ISCTetrwJjND0FYcZLa+gixZjqigbsJz2johCqNGSZbn49XF3mLI/h8AeRrM29kwwA1GoIubqgsn+IxCvMjLpd5ojFhgtQkA171pp+FefAVW2PFizxekGck/JWegU+VfzFcwndeNJXldfJsLF+lOxlMPcC0omU8Eo/PWn0nNsWjHrJfPv1UQ5GP0BaP8UK2kZF5qP3Y84Gr7aZ9I6xB90Fi6arSz1jjvpaRGSU/ZrhYUljIusChgclqlHP3Horfi0fH5VCFmkSJjrDpaD+6euj3/5ikeCNjzBPlWpzsaYEakqPNC/GFkOG8m+NYhwBff6OqsRh55ztX/FQQIuOAra9cI2Lt9p292450ZI8ErbUG6gbi+Dl3CZ0ZpRq6NdHwQxLMnw+Y4p1nKqy1QCvoOaFssxYhc4AlLlFN4G42aJi6KJqPheMfGmZiyi3u/L+d2EjrVbtIrdYYuWJOGNtPeIBfIcarNoX2vJbjN/UUt5d1E9qZf3+VlC3hW/KYKc4/BwcEmvWhk3AJ0b5eG/rPVysyw2c7xr3Bc+Zr0y1kFjOBzhSkXq2A5Kx19JVqa4n2/FS2OxjH7G2uCQItEa3X0tVeY3XnDAbKu6luVYNZc5TMMBw+92pc/yg58yS6Gk+QWrQsqzAO4Imk9eVGxrd3nqqqhThgIQznJxKC+F5P0fZ8Iu+CQgPs2eG/IvpkDeiQY2pzA/we6M9dhz4NsDmJ4Up22HJiQokrgLbzWLb1H3sbfTFCKd5uu2Vp2c71GetHOgUSIyPbm4WZtqdpgidi5p7k1AhaZyeQuuHfGdl5717NmER2YAmwxXhDLRF/jwFEgfAY79mwujhD6EQQeGybAkfI5PBTMS9vVxn7R2HrTUtCuuLzGnwhZ9C5UWJRKA2gtNUJVzvadcGllO291kkKjIMx5uVcknm8wAbi1K0imSaWNp5qiDW4ZJHGlZhoOLKfIT9+2ZwdvDgf8R+TTIAb5krr6u3KBf28ulusbf3oy+eCaOI/19WxnS4whzqLeeh2/2EmZyfoluzx+RbGwxyk5PCWDdmtgrEO+wKFGBMLoj2zaFXjahOXguNdCwjT44Lbr0VDLg/gXTptZ8aMzoVh59Bh9D33hHuYcqkhRbpxoD/NVUSoFEfuvguVTPiWbfSj9bcdkDFRhLKY7N2HJY360QtM56GIDpTSsye1x4MgoTXWh/feXhhrkZ8LUnBdaZhs07wcK8/9Gv/iM/ErjNVyNbfGrv70dI06FE6ku1gwtlm5RsgTcjc0/NMZ5eQ9d1duobNTDvN3bPnBoqHD8Pyxu94zu76KrwtPsU7PPlCQJg22DUhyeZtLVnpQWnFkiRNjC5n7x9ul/qKnnSid2DfPl0O7oB84NNxWt/N8prRs26cizY+CAyiusJFx24s/Kp3wkAG3aUFpnyw222THeFVyfI3rKjOHI/bMyFFbq7JH5ibKyT9SgElmxpiqHpjplqKlALkg1V1KuK1dwvVIYFllq4DkERxGDdEBvz4l0l/NZWUG5cliTUhu6cg76SvELwnNnsD7CFPKZ76Vx1cXVSlipzkvwos4R9Igyjd47Hi/lM7wd0KMV1DCHKrbldjmVLZizPAsNW5xZgoKjqgf8IZyiXO3ViY6ry6B77uhe3wIbyNIp6c9tTsEv0UsxlmioYv3M6HS6FsH7d3c4lg+/qXvhj/b4N7yrx3RTHRhC3/pgoqwv1tNidqtFzus6B1b0AnAXVYTwjxSeOIJTsDT0HmpTRfAsfdX7UlceFuRM4FCT7vaDWHBDOPZAf1IRRGv2Q1m/7tOxBw86qzg7zA/OuXQecKkQzuiMuVa3FWL38CYjnta9/wrLBoOVtcjKUc8Az1Ax5p+XSyctp9UMGdd2Yz5/wf/WmvDxwfmbYhGLvEH9+DaKhaBCklGIe1JlCZUs2BU7y76Az9S2mlHD6habBI8zMPxIP29UgHhtADaHnowhZ5aWbZCtGYXgPCiW2TMsI0/2+XY5e0Exxbva2YzGYIah5hANrY9j8WlADVv2DTystvJWvNabdb9nzbuftyEufVDMQygw6YcMkcVzQG+pmDOiH6+MBFFTClavpcUyUAa51qkzBRPrCDuE4wh7jETf6AmzPsKLGnDf+lRlihfDHhvEXH6fXLYrxqMFuUyATIF8/5GeGTBcDRUscIkLAl2krrDSYVGJIA7vBUvo76lu6ifHi4cDSmT3ip/XgXSHrWMxLP1mCGT60H182vrkf+G43+7daC2GyaP0G7NqRlv82phSUT9/qGtZUHhhw048LgFaDg/rnBr3AHF+L35AiFspNizACz7Y1pq2ldCxWKamB4Y8RV9E0wK5Q5t+QDbaULieLi+Lpr8x9eoOMzgXyfDELbma3kYe+q7peG3YyMtuz/aK924Nf1+fWA/FUvMbSbUyoxEgCMBTXbZbN+1TrHCjPNeLfUZQeeJKutO4g8w/mfKUjxjbEzw0Jd2/qq3b9bJXmjNmZs/T6zx0KAReMMOp+W6kZqhM7zp7KY2UIcfr2zLrVcIh8FJIv6skDUPE3dPhqq59nlaCR92wqLxEZ71KtvDbV+HWCyA5TrqQyJk1RnOrb9C1XMLMAXKWncA3/N9X5HtIkDweG9c3uU+08VvLUsWJ1tcysltIFf6RHpgQ0bXPOLZlTKY9nmv78QHP+owi5Yoh9snJYteVSeilHPBhR/UjkXb6eMoqMATCJ1bJ0Ks36dxrlXmW42/PfGWiPmFACI6fQk/LLA4LAsmfYX/IoF/Zfxe7Ehz9Vr7SEEfHdsbxjLsEsP7x7sECr0a71pww5QA4u+90J5MGL+h6Zo6ed5Ox94UP96EWoJhdQEmQ/hf/WRmVym25ddvjOAnN04riIPNBuSHbSVrd2HxIZZgBqYkREC41b3XU5bgAJzKc/z+AHvbXDWfm5bNe/tkbeZZaXh5CxtzIX+it8GSMxscizuzSuUgyie82Kx4/7eQlv2X4SNiGyiZxAaK5t2ITPpbh+2ao6cE827M0om2RedmGhC49+tg7C0iM+w3plgTiyHIdhMd7mjGEWhcb6EQ7jBStUFijs87kuTGxN1ZFh4vZWbZK6FImBIvveTRBuFe5LajgXo7J/U7CvCRaImSsMS9FMBa9t+UwA5YEWM6nb6BiogPFH5+JMAqezDjuhWbcAESZuVBq6Ug2mPKr0V2e0+xGglQ5IIT6ek4zNnvYyHiUFpFCie+s4l+4H3iDHwBtmKvEiT4I7A6yQ/JWT6yUr6kTi8yoNQr71zDeVrlbC0JAADChOB25ohjx47NRPIJBwo7tblkSKnuP3hTM7yX6gfxkR6fMn4vKhnHSKPg+Wolp/PCt4ILmWFNPKMXHIoVTHj0R5V4MKy+dP6E/awPxY9Ev+1IM2jJZncj3qh8sV9jE6F5a1tY52khXcy+8UxqfNcaUJyf+DwacX2VGLqiyw5FaEe79drxjhAS+NPcVbdDNRGqYI2ClTQudmqb1DRC+YlJbCWQYxIAHxFf1WlrJSUHKcD1Q/C11GCsVDcVAq0KYN46spEodnhz12+WRai1ckUISKZji036rnj8AxVGFcLWLdOmfdVLhuDX55bKENQ2DkNlA873jFXwBSlEmfovHXKkEBb1h2rAch8MkMr/Qx8vHyEnwtFSgxj5OTdh9fG8aS2lgbdqkcehZNpseDZD98WQOTJzmKqF4izv1rHsmquvkVDhg5zXkiUvG+SX7BUoJx9EzHxd9Vg4KN1TbF7TJHBZbSvnHaodCE/IpP01YhntIwvfyUfvMLuwgLJKOH1fElgmjMAOIJo67WkoYrE1epMf2DZcQlRO3ZSUFPxD4VgVz4VpdmvK1OeQg4Wu65CPf5aJBEPxSkHBxyBj7NlNUXEVtf0OJH2Z2+TQi8b2E5OBR9B484vUl8Nwm2cO55pTrekytFo9U9xUGswnWpjDEyvczz0uQf0xluBZXL2B3SPjJMRyQSHGI9wH0EgKYQNXbE2ylIFBjN1K0Pnk8Uu4EWsMSJykEfN4lB2MADyd802/79bQpjD/mtI+G0Vo/3oMVz1iEAlEd2wBG0Q6mdrqwiU1LPNeFO0QO+5sl+rum7eKO5HDJIbm0+EgRaOEyw2jTkBlPmSeUBhZalUauEwmreTAvSXp5wHgiIvs3kxQyog4f4gjm6TTT74GroKpaXPpB6fezTXfkqU1lBX4MjqOze+mjOQApo2YKnwpc7t7WVgOru0FTGsVxqSvyTHuyP1bCNIHdCGZRcLgJxCBBl6iysxHYAKBzpeKUXuF3BjLEeTVt5CjH1ybSIqI1ZRkztDbXnvqCy6bdKGVAn3gC0Qdx55XJ7cKSkqRV5fcnjRbFkjWBrwiG4+/wxukoNT1AYymwzaGPwf2MhOcHVzgoUAomEvsfaCs+zoaoHpViGD7FEwiaT0h6qfJngPcwDnrQ/yWXZepV5lJRns0mw0ReeFuHYC8K1r6N9OGjWfa0m+zAlF91xHc3AMKmZU1G2IjxUesRCG1hMBcQMowIYaQhYf9rz/jVnkHXFyJlXLxTXZ19N/PxE1fZvt4ybUxx0Tk1T0GDtBU7OG1xzqBRRv4DQp1T07JQSjAQ5W4dEDi76yygsiUztPVX7J9AUm9kh8cQsazX7jCNn5kU3Rw/uKx54sDN03oJURB0OaITRjM7rQRcgnz3XO4SB+IQKWgbX/5r5v1Soa2HbrHjsIHN41ZuWWJfG5mAe/6zEvuTMO+vv6lfxgkav2bO/y/r4vKG6K97BmlZzbtk4yiGdDaKkv1fnbGixHrHzJqNA+M6pPwbYCo9szfIqQkCWqe3CvFZJgcnRHm99Uq8LWYkqX4SIErpQVf9UMPI68BazOmXjS7yfl2oxGX267Kq6rnLEH1QIQbQqsL+J6LGgjinHR70+S5TYfx7tCOzMf8D60S8VfW14WPW2/m7VN4wj+mET/0XHOi8ul3CStCvXcnIofWjIoMa8U8PGmKf4eHABPtnfEKQQnCQ9bgVyFfetw1s3meKRXnVNohEnKiG8HzizG2Lh2seMZcHx6x93XmY00SwySzVRToJcuChUd8q2LeBr3N8uXrPOKN/ALwtV/HpNBlk+A6sP6wX40m4OKHxKTg0ek0r6teS0qUc9cxeCWYK7kg4gdCbz47ynEzw5fqK8yPtpBqkfkIBffGk9oL80ZQBv3fuyfJ0HjBd8YIA+nwp2sprNaMDA6rs3RrRsUKP9jBGt0Fm/nzvfZu6Naa8sZ4YBihYCxyTSavWOxA63QB0PL8qMIPvAqjwblNmgjsW6mawu3Ha7ogIFzuaI8NOFP3uYIWr0pct7vqDuJIsLqslYfhXlDfOLQ55RFnU3QYV9NmBXlVQgGaKiYKrc+kB8QPpDWjdSP4Hp//UsKFzKzBiHCGyjMnAJMsX8LH9KN1UFhdnS4+YAE+Pmez2UsnwgD2oWZQ/ATfkksix1gBmgA3Hr1yDyDgk0dGnJzwjdwZxiIKf+IP4DsCwXQMG6qqFLZv5Q5d7eUF+b4UXXCWOb/lCKOhKfUlbPwaXxSmnSoR0EiC2FzzS/zIIIGX4cwKdjjmiQbnv0r0wUs418+QNnQ7xTdQ37vtPlWxrBYysCS/83yhgpHe9LPyXYjHje7vOV9J8YpGUuktE6AyXLLhunTguo+T8JZMbLTURcc6nL2RhjItOS8H6ub9b+BbLg5UVXBgzCm36Z18acb0mi4CRvfyXjcHkhZa8i7A/gfQCRrI6YfGbKEu7dIqu9wrCX/QS/CYr2NDl7vHZ4CbnFpZhHV08OaRNCRgNtQWp//D9xGZjOufFHcdvaDPths6i8Ap+TYsWyf9IOcuoggqWGuE+H+nN+/9DVO7Lxelbj3Vnz9AfInxCrkVq6Z7IZ5rQACBviS8zmszQwmMgmMGuzEGGUAfHlFCMlcr8RKYh920lhlP6G+B1amYvbY3u93UgoSpJ/eUfG7M6AgurwC/t4fAhyWRR6W6rg6s84ogRk2LwOUgs/cjGjl0fI0mpPzv/XO7nRIR78cNc028V3ONUw9xSV+gMUzlWH9ntsI+9tZKdtAqUGdvT14z5q3u5IrwDFqumZoZBD3ux3p4ZJK2m+UWWzowk5GGJ3xlqX5rncme2tnv1Y3QimJ++q5ApGXdahquLP9gSq3iX4CYL72+yBEHFwEmIxZXkpqm7WA6A5MmhZ7AtF60ceS7cbjybPsnSrXFnWKIDs1SHsq+HHlPxXHtTWbjW/dBBinL+m0PXJ1gOPHDCnLYJ40Yb17a00cK0PNSz9Ao8SBipsUZBOLyt7j34IzFE7JFTRTJP0qmz3cDf1IcPmXSCycMWdgtq9YaCW0k+0jfxH4JgGOcWQHHH+OACclv4+zD3oZzEnel2X0WzIXqxUzbWHBQk9cByDy/aYAg4KOargf1ILu6wNmvLvpXs7kbrc3WNvxfV/MzKhdDb7nFMtDVcod0aJZdgi8hWm/pb4IUdnmeQgpzFBfQTInbjG8U3eRHPwMF4CNG6WxBlIyduUHljLEbUYNOM1GVu7Pc3eZOexy6BpOAwehietwLbvSiAO8vNdvVabseuJahJYZ+AhYWFcFGGrOqTWUQJsAUghRbWQRR7TMMgyOc0FjCdTRNaNKNL70tszOtA31W7eRQQkVvdeCyJgyr6N0RvQWaSf2REjZGsbeXBgEEONeyY7b6DSRemOpzRJGLCjPny4nirqSEAycBamiaFVa9pOvtcfn2YltXx1Cm4nSe+N8QZTGczmVbBRUnaKv8IHZNxXkz0SPEz1CXvv/dBEhrsnp5NokomD63Utfvk7t/NY/Dt1C0wYnS4gXX/Aiq+dm/alsYD13luSLN5HWH1BGsBT2vD6CVFhc3km8HtDHRuWcQzdowF1oEf5gfAMxH+xHiXbtT8uH2iA0i82CU4ofVL/MfMDOs1ovV27jpkzOR4fb1iwIdx1cPpugsqwEGtqcgcfymCHBzjhacrO/prk+smHhI2sMmuDMb1EnTLFpHNyGetBN6hqGfNHykfXFssCHEmasUvkHcLVr1xbph/eP1PR/5oOzIBqEOCUg6kxduCdj3sNC2SLtYTeWvnL7Oq0bUY+DLdc6kuKNYZN4VnBva26sTqUJzvuzrL7U5Ib+nMsSZBslT3UDfq5u0iGq7r1/buwnfxLELaoIFdiPmluPI0AQlFonJ/4pY8NoPWTNurvmGNECOEQ3WQXoTu45S3UNSJyrXn79N02RTiTU9T9LgfztL58gw7xwein4Sq5X7OQPn81TgBQT0pe/xb30+kKq/CHFg3ZNOqZem5K5tbTbL9F0Tq23yW729FeeUTQS8XaiV/s6KY52HdJuHdp9Ytm4W95uDavcKts9t9N9tuhiGsXep/rPvg1TOFZb1PFg3JtFYJFFbXno+bXhE8lo4dNPTDNTI/qt7j5eEX1Y0goiW4i1w8e2+qL4cbkHQfFW2K2Q5uheI8v+ZpB3eTQ8p0bpdkhlsNl2513dxg3IgI0uzUTL0DaVYc3giRAY3jpXI/u/0ZKoQ6qk1ZM1oTpNNZwLnGayq4lbYjEFMcmS852ps4szIU2Ly2QeqJPia3Zmn+tkuNBQyHPDv6eMpPx2aAl9miHfXOPpbherJ+OBQ2de1DaLPKsOQQK5B5ImjaKtBe4d8k+r0U3QqIOo2b8uIBA7IDwXD064V1PnXdjr9/w+NuPKPLIAx/hv8CyfM1OYJgjf7bNp+txeYW2ajfld60qLe6dSz/a4SF4S5H0UHUy1URnZdMh+r1jnoo2ojU2q5CgT/DjoA/PjoLv8wu+VtNNpeSVnPp0LQrLIuzgpF+cxjRjAHX/Q5PiUUFHWrOr8NvzkWg1XN5qUGPMUkt1P5Z1hS5dSQdNuBlwJAncQvMIQCMZpe67ytoIgMgVOCPhjSpF6E0myTt0XdEqsx5mYtDM2njMW4xAuHu5EZ32iUoDBXIEYTEl3mvTqBNLXZEON8v4MJTotMMtBXGX06yh3u4yoWb6Hd/ilpSEn98lFYFI9sbwHzFrRyHXzn+IcYJ0PSGAy/ilv0OwzCBHj7oLgZnqoG0bY5+/Grus2NIzdmKjlLUaO9o3ytMYAQ13OGHPWJHgiZpztYks4NlLiUpAbe2iP2gSjV8vQvjfPV2v6E22XBa2b8pLxefOb/2fD+WZnSwizHx8Dw09/zHAjLm4AlWKtJtOK3z6+PR8GZHBtBksVMFaI2pOuybjtefDuYAH9M/Dm5bv7DyDkbfYBj3YOuVLZzBvsSkryULZgGeyGlWcrHNuJCDcTyZkp4775pJoTQ5h9orGWgPlleshKS5oU7MNb7Cn86ULxtby22dr+w/rjZpqRRJ+LTd3YA8iFcLK3Rd6+sjyPVnDlt+yEwiRi9JVeAQmKifos7sR9Wo4iIHpemZLuGyhCIrBrDc9B/jgyTHoz2DxXcVbD57tPkkDkDGbHtnIDlxFwtwmRZJX08rlezRkTNFWb5hD32jlaVB7GSTIcIUe9ITscQI7y0nt2Kbxwb7SxVch9Zfyf6Xe3vJSavVoHHCNY41JxMrBawavKwpVNjGDhKyY+i2MNgR+hMQtHtPA4rN0Pfs9JyokegpYpeCECn/wi85DIHzclwgZq2tQcTpUiDtcsyFCcOIrA+avUv6uY/vkFph0HTIvgfALo71/5s17pxkocRHyf7cU5PUiSvR9M4b3qJpLI1C9jm91BQy7X36GrDblEB6yCtoTqFYCZuXWvlPTBtRFJC4gQFDTM0YLkzlss+vrVjZ1s4+eA95TrsMSATusXa5qOEhRnH6OI8XlnQwRFVzXbbpXr/xFKl9/Bq9ftDRYivP2GOZC2vV6zM6xuOtPqlvTbUSwkJd/LWHRqlFecrGZMwJapETlYHHQwscOJucX/SKPvbYmdy+YdfT7yrILE5zY7dyIOO0WygS9cz11zre7nbc9UOqWvZBosX22bysC3g0fnkGS4f/X4EoQ2blkk1MJ+ufZ/Q1mQYAaxtWHbLi34huRiKHqRrCXmi+kMclXdzU7FwN9PilSHSNHDilOnRGSrpiJcYLgPqVPMVhVY7TfTPQGDY78MKH4BejAjac1AVpTsCulO601J7Koj0OSGb306j/7uFkIENQFleVHhJgaueAY+g6D7D2NlA/toipdEFvysQpwbxuyZHPWFXMowPQrL0v/6rJfhI5SgOBoDKCo90tzoRMh+EQntXMj4ItYz1mwUWIHG6qG2aFnUcEeygB/3kHPev0Hnyp/9vQGTcQxKF2JgdC+GKSr3E1TXDf0Kxx4Tp4v/QY7Sp32pyP/l2sDQV0cW7S07Xj8UGO8UrWeb4vvOFWe74F9cXYonGC3Wr+/TPg7O/tCLHnaqX4euOjTBHjY91YP1TjpO7QRGM4HwQs6UTDcihIRjumSpAPVZ1FHi1/GCKVk2B+XAFpMEHKbT4eMs97ff98zx/WX+/LcSnGJMxXTy7gtGIFV0EVjP1eYa0af+SC6MvbXXe6mDZbqEx/nSp8Fmv/OSAaQliekmUTSJ8RwHpt8gdpQzhDLZDpNx41q2viuMEfBFaBh7cZ+o94rsfMSYqXeWc6anVXXuPqIDDOPccCrzuZGdNyAveIWl91Pr+v0N8TsibsXclOXYZK36xeH0QC9bRcdOf/ZT/yRjfd2fU0irZvd7/YIy319EE6oBD1YHAq+2jgiBNt6esIumqMxwGiG3O/BYGSS2JNKj5phF+0TPTzAJLVLXOQCvGDvZZpcg5Gb4wIW4vqUzanKKcw3lWKkMSVWIFNnSAPE9dtuZpEblZqAYB6hzyqMnNtgylq8NLr0LUjuaoV69KtGzt+vv5RnAqK15iMedf2Dq9HPV/xAbkXwyQ3nkm1HKV/OBIhyEc9SWuEqa12tIV5awoDEd0xhRmZT1ZXE6s14UcArixb0GV+5EMJcDOxlpnzkET/UL+SLvy+XepPi2VBFlmSQoL5UlLEmoPulEYbstwGhWYZP+G36VPdW85Ei9n1unBYXdmxgBFeT1coZAovrJP706cFKD/BNQm/qgP92BtbFFbNAWaqK8N/q+QDyqhrfuDGaCOXgw+gNqo0IFvtZ9qawbiOXZOheeJpPGgShis7VcdtDxZ7u0x3cVG9yhJiKSKCC95//6ReAxPIvG/TRA5Mq4NcPv2PoVadg7sUIC4IlUZwy5aecPvO8bW6R+PXPhmw0u3uoDEGvmKmwIusHKP4Dw63oW55nNEn38HSYZnN6pwgMXSJWRmOmpfMg0W94y5cFw4IQj7wQWrRKFBqYh5WfdnfiwF7fX7mMy3t7nQXcr6aB9TTf2rJrvINyO6bi7tLMs7oTWMYiuKXrgTNSVlsiCPTbY7mXCGk64p52WiMPr5d0WyfCtt40Ge6tLpqJYbBO5iHaXpDewrvBWF+4vpweaTAh2Ff1b519GKQyS3o2Q2UKFGL+UgbdeAD1spCNrVhUu+IH/uoK837+L15SDT7C8rUCopdBQbU+MiL711+01t++ezsxMbVAcBuKb9hXOjXKwkmpazkfM4XvB0/xiLtNm5lIxQmxQwh+UzcI+FYTxWRgJUjwJYyEm3K3iP0q4PnIOLuodW4gsVNs/iX2HGhG+xZl3czJ38da/hiNl7zFO4FGHO+TSVlTNsNeGBGg8xZE37NT9aigQONeZEhpJzRWHgFpG+fqbAl3ZTgbgCHsg+SMvdy0dwrSUUlVNwjhHnIfqcblVO/8teQJxfJ22ZjopU/HX6KCn+/zSUVIulnEGSAXKyw0r4c3NXw81EMoAQlAAGouSDyC2QWmtDWT7SjZbpcV6S7pi3giSSzecLPX5hleYYaVbCzdkAp0/QLFFRxp6DQdeqoV4xqaO/+rZ2M6Gnx1o2+FQCQQk1OP5XS661SVa5S1tsAz/uU88rpshpIEfYpoAuWbzx0f1bzZx02sadgCVoja3/MXSeRAqSx+m9sLzU8iUXAaI2yAZgRX6t98k2ALOXOxPSyy+UAtNzIRt8keW56QoW46PvQetah01GvrnLYDHYooarO4GSjTd2r/lUqhVmhZjTE+iI/7Sywc6Ry+1jIWxZDkQBtNKhy6uAyabgLw07Fusp08uKoQXq4+wv5kimk+KG4hpTGGj2X05SQ806xiLaUvIuvVf0Ic9nLyLCJLuA/y5RrwXuL+R5Uu3zozQfBuk8Fsyq3v2IGz8X8IKij1GvO+WWuWkiAgBbxnAYFbCdY3NZcsFz8NrjiuCnNVo2lx1ciTKwYYbyzFlpNqkSOO21ZF99GXKepOGs1FFsxX5cEKe3XyIKQoVoL54mn0zKxzUT4PUmIipNU1irxIp9k2EkuKfuvFE4lkX6TMFcq0ICeVwtkmodwWYmRyjqrVvmx4/JZdOAjKkJYfoQNftKGm0zTJ7OGCLhBy3RuPA1KhDvf35qHFNtvNVqEZ0ufzxN5FFqB74e7QNHVAZ4vsooEQw5wKn41lt74hQEGfIKocyIWTXbM/yDVRenR/s85fT/hXBNdrZK87in8IAWy8749V03neayjkhf8KTyemxbKHbaMu0KjrJExtOfX4X/G887I48JDFgCWeeMN1DEPXTUwLa6rISGVtArI9ecR5X/U9YINSz3kAImb1AeFBN/TLsgfZoXOk+HECWu99MIDEckoI2pyYz7c9TTVOhPQp7rXIjCORnBHMlRwOj+iQIoBXK1y1ut5F+fCVBIDI1c1uPWFpu7w/VC/+kFjsYZQSV+nR5EIoW/ytxYQzmExPNixtXebySz+6kNY1LqJpN/4d7N5Lo4FUo+pluTEbevXJzItIFtLkxF02ls0bBc1cDY7AaH62doSe/18TDvyrRREXWjLgnswbSm0znmdHk+5naWD72m2/m6Q950hxpAnQ0d0hzLQ27arHTZeUMujas0t4dRkEnz7RrX5QCmBZzZnvPNeG1q5BOVYbVQRBcjKYhk8fsAx4OlKybxgbjXaI1Aoyzfcn0FH+cYT7J6ljtD4ybyHOkRj4wYZr3iKJNrUZuT+Gs9iyva8aNiYdRQFkJFeX7t/ppUMRxDtZHmRflUyMdxKoOzPgRmzgsAIXRm8H15b+X54J1OzpBJ0N+vvLxJdE5kqbIqvmQZcflDBEN56B+zjZ8lp9NTdLC/3JeorNIKuttoF5kanPdJrWCYhLjjf1syPtujx1wAQQIrMVDGmxAEEm3Tq3S4LAcvVlSPfnQw7iwNn9VuXtH0zRpflKxTNT8DHHzboLFrTXgaENUEsKtXvwmBklnL0xTz/RIy8k3Nd4KRVGe8h9yy8i8zZ0vxoWah9514hyQeGiRcYPbmNa5itULrVE5vCt63auebjt3cM3tIbsj+JmKrK+VjTPSkEsnUcBxMJ3C7LwyYd4jTZaqPlX1I8Ta27iVirisInk3P6yMIVlvVLT+8aTsuuz7mIdMTLKRcTYFYBP2lxvIUHWv2w63xKqlZu9zPlgW1eAK2uYDoyLIdbWKme8io0wFq3OdPj8SQ8Viy9+jgxw0GRs8v+Fn9gZvL3kb6p40UJGVrF4lr937jRC0CwBmMQrhEyOXbizn3IbxnEVHCWuvZam1YDAlHVqHpxxl7yzRw12vsSvYiZTvGeC/fO4Pe7Nmcynu8z5fvnus2vPKXlGi3aTyKJsHu0ixhwLWq8sNb8vBwbdM5zNRP1C5/fJpmbPLjjPyZ3DlByp/mIwYnkplR8PHvuDGccfJQ4wQwT5veh4o5vFyGm/N9NJHqfI2ZHtHeVSaDrpHVlJ7AgDYY+E2XJIGQFdEp/6iMiwuieNgPsmCjknb3u7vt6Pbl8kx7Uhfirj2S1fnFXxH8lXw0BVPNbfy2OSkBw3rGeRSjkKEJ8ttO03COly1Az/RdRrs6VuGKWsU05PVinhKI5FKGkbQ91N9jou9o1s/Q4nJsvrnTVz4jEGLcLDbOHbff+tCvf0IsCoiHk+I1NaRRezACfnmv3Xyjfgi3nDBYdscvApc07MZaupzHl3kloqF6N14AyeXQzXS8LId0dviyd7cSH16Ph2AUrCVordsGc62BM+0kK0VVQHEeyud6o2UUT9zBJvxbihlnSL40EqLNiLnzDmPh5zEKQio7/oyAsFJvVg0lcAzqDvF6FV4OgmaZIh3kV4/NAVti1Pe736pmkMZ0Wf+Z7G3JiXmpDW3Sd24ZnkSrijxsF0yXvWEf4xm4JQAVtXC/PxxgLExD0vN9AjKsqEPz1ockJcgVZioIhHNzg9qy/HZayt2el+ool4xuw52spYdHvyvB/HT4fdI75HZE+LDZhVIUL7A81jY1GLP+0cwQU+ZNKsiaKrEgHSBpPZ+q6CLUerDsnuoAtEU9KGMlpSBUEfUmrZoxVg48WMW2mI6w92CTdzC7p/KcZvy4aN83rrVlE8F304pXei4yhTcqjM+7D1tafeGShkKE6aFwbd1MZG4Q8039l78IpRFhUI2vFppR7S6rpBX/F9M0liRK5X1L/oblwKZxYTdmLmb8IPenklSIgvbcrf4lG60RS+dDYEgUyb6F8geo6Ye3Gax2WCbdWxAn+qxuhc9/UzirJC2OV/WmxoQL08lsEMKxRN71UWNtPKlqYRdx6AzRuhwkg1MFJGAAVVl4CEbytA4QiUS7WDhqX0zEnR6fph3HCl815tYqkXFQP9VmF23wA8qX6/vB60d25NZ0nxM9zz/isGapt6UhcNrcdkE+fANZ1UR+X3QXo0mIa3CZ/7x3i9O+ZspUdv5xtIT/ThjXoy9PW5DTsZdPcfPMbd6D2DekGNXVTWZHa0RsgIk7F1Jg0v/WGdoY067ROgWHSCOehCSFG2KWt+WlOEiXfHov7CA6sk0e9Gva2GKCBvVC6QcV991CV7bm/gyi/QWbPi5cTioesJztCSW/KhLDUN22cm5LBfxPm4NjBbHni13HfG35DdoMr2c/0H+fTI47jFazc2Lph5P/A5JRYlbWpiNhT/gtGeDZpS+emxpYuOao75tcO+Oz/ZEbI4guwO3zTngJJ8AGciXdBOqAs6s8V9XuEyr2E0ADii+XEGKtc3ZNa3Eft1Kz7/QGIpkVlrQZYxwbKXn5WmuehxdnDs82HWodp8YIeeIoFw/HLCar5Qh2UWqIT/jlELKeKdK4KCDnFaWoNiS3JPU2HsPNq2nAfFFVYD75Aga23Q/1a1ABt9MDcUrb4mBs/nF6DhmtlfpZUnCKy53yS7ebiAHkBO4EOa/+qNDObXI9+BQ4ZQKS2L36k6fCFSDFnBCsA2oAy8I0gqwQi214MghAfiEjEI+yAd32QYc13MAzCxXGBe+d/KQEye8t1OdwZRZXNk0QOVQ9iMP0NVaXhetyM4x4eTPoetfz+9/6ZJiMLzT1fx2W5i9e76q52XBDkNuMXrLLFgpqJdxEvYZD0DC2tB7oGyiIG7GMfFKc4kljDGa/DMccHBCSw0qCq2fBs3qjDDezqbLV2cctCW52pWQ+P65rXG4s+nfoBVyA2gT3MKITdF4KPhXnJ9Uev5hGwH31YDGqJTFIXKxIr5gNfUsN9M3jGwVIe0uzi2eQgnFUojZFBXtxUUWhwx/cePO8Zn7Jq9GRvb5w3heZpaBzastGgMnFOYU7qO+8TApUVXRL7i2ikSQ12sXxpqAfBwYQCOrIvJLFiozjBzPWJzl85SUJcj6ol1k0d0Fe3fJJRsUZr1MTGyOU2uqWC79ZJDt5r4n7XiYjfP0WZLLTW3HlYXOHoVmj+fiv8oqfDH3AuXM9JuG7XVZ0VIfN/LlJPY09Iab64IKgYfQ0nTuwIkHGvsnMbO7coB4H3f09OpUdg7KSMoV0g1HfbqVdPxR8hjr65hWBV9texyd7coANHWuNG0VeUkYxGdeGYD9LztU6mSss+a3od//mbuYERFLzsDhO7o+T4pcg9ffzksPqewzrE84AowFk8Ut9Ih5jczKVjVC7sYl58JNDyDHcN2s52H6ZlSS4tc08wR0H1ruP2F00zX3oeHa+wkOV7fsETdRyMkE6wKxqIG6W/Bcg+cClbMY2wRstzG4BTQc/7ehumReW0SOzsN6EsB1npJy50LWuUlQ41YkpdMrP4+E1s+yh5Ulx7sEzxXM0CcdDmPBJvgkXXyySiG/9l3ec80NLtIFQMG7/2mYbO+t4Ah5plIFruxaLf8oNMYcdFeALcXcMY1oj0u79+zKBd6P+1D1pEvZzIo5bfIn7vueqN6spOMBG7+UddEqyY8mChJkCKt0OXwVrvu8ER2fEBt/9aq6FLz1ceKCNaEqEPB/z6lH2vlKCUARYUljXgtU+ZgMkxR8uP9f/zoeKOP9TRbFgkRqORZ9c/YAap09HIv2lzdoOzEHsoIDPiOWdZzRO6wLo22znLZge1PTtKQF5s3PsjvAO12ye385Bptc4a5NMMdX5lnkkyIsux1c6SpGNPmVblcS95gJcMOHXDfF7GdyPkbkEmsOZeX95owfp1XIYFAZ0voObco3KIFe4IjnRPSjCD9+W//DX7FLesye+g0fa7lwEzyJu6uDlSAm48Jqde0Gk/MQynnZsMH+J9mSQIJ5R6LRSKg7shyKPUj3BkmQnILZ8P9H6CmoUhyIYuebyClIz5EAOua5dqB1bQ7rwWNfY9AlNsQcXHwcs7DsVU0jFTdKwnMvC19p+UKqutqPtfpUwtmacyknjIiWl9GiGh+KDycvX+PhkADiDFnU0uWq2FPm14VXzoAT/SQpwQ3UYYqSXvRNk7CZKG3oLIWv8Og7FWQNcMjlQi2NYtJaLTkVbH4PMxrWWNoPhJElsTPnDA+0y3e+vcKrq/Y4jugyIh4REM6g8p8wd/JSH2RxvJjh5e/LUwp+UIhnsSURrHxSrrMjoWcGM1abuAPc9CKSxjG4CHtWTVH/4DxlWD2t3sa6Foz9J7/7Jl9CTlofpFxKQb75fxhvKHRSv3UaaDNwYM3s2YFHhWUCg/zNZmBEQclBoAAJSJXl5ck3AXL0nyC6pDSQDsd7iqiuKb5xcOKKvSBzhNUWcW4zjyKdRMnbbWra8fARLlyy2jydBUXhUOvZk71xO52vRtuvr4AW9elYieQIZsKigU0qqqoOFZo8tsAduoTNIK6dYIEkk5wy213QObatWUfsjSEO/EzjSLmIzmCaXw9i01k+keLVulADFKUVzjNQNsr0RMueaCv7UAgcovJAEdi2vrfJYJkrs0Tjy1PKihTtCOSfyXbdh8T1FY5YXZzXoOIjwWPoQHaeVrYy4BXvXri02fBrM0XvwY9C8z6FA/5DiZFldhnWu0PBPFChWX4shmK9r/wr44zHj9jy5eyobCZWIiBhSsyEPn7dAwN0xNNf5K84XBUSoyVLAVADRr5nRSDSP2sqjqSw3dOH4fjyVLdmZKRLCYqlMAcibV0VIFy4BLeYgQ9ruryFQIlSDQTewFxfXYY1+FOz5Axz7i1akCG/AQobWhApbjB9C3n0Pyxigt2opaW0TIItDF48JCZmkOz6bbydZHY+Np7SD5DdZAi/l/lJB4VZ3GbzUOJMUdtv+i3oF6cs5KLvaB0wwhsuPmcmzPMUnX86DHt43j8QQ1/nUUavo950fpTLCRJVzqnjLU7shLZAs5yOJm2PxEeb9Q1HQX8HJa03BGw7JjpmAhezax/Z+qcRoFxC+IWvsJoj5VFs/1/AJqGsiWkABEO0lLQhf3d/8eWgWzojGzOy5SrkO5WZODK0NN0U7wvyMff04cJRGJfl8RFBmDRe0S7NiOSIeps45c+vCBKYiCZZDFHt1KkeQCidvR+Fazg6pDBtoEFyKmbqYbbAGWGPBaayqyrIAbVBKxRQYCPqIB+OX98FfjNmsOBL8lM6BlNguo+IRqSujyQPmfXE/StIlXFYT/+ePKZa44fn2BYH5YeQ2CP1XvTSutEv5369iJPD5fX2NDVaCANGj3JgKEfWrorPvl1ph5PNlyFRPWDSwD5Zhzxofjfreci5KJme3oB29S78LF3JSj9IsitipjfAz/LUR0E1CvTP5XG+sa7e2HFEYuY+M0oF8n4O4j7Q6HvcfrkLI9XjqIxhq6mDNLLTojlfNAVMxJebn+h3wGjYRyWRRGURK/lVKHfVbzJhhFUop3LAiQU90ejCNC3REjmtal9kEEbwKo6jeJl8dyriH3VCrhvr3302nnJHIbtCkYDRZwcCNw+m5IaFdpAkQZAuZkrUL4NGIAbEvV1nEtVwj8HDRCNpFb9DZCAq8uw5BgzEJjoeg0Iuz5dGuq7Xx4RZnK9D+g6cxtlPdDXx0CxLok6smu491D4ZumDyBwzUqT/wid+6yxXNkz/0HARaCSOiZFx2+EC/osqRp/ne+94VvP0o4gavXVIElDc4uHQEB5O2eOUMJauIJzvL/zhpEbC/Of2vskpZV527f9iNy74sgE1I6AvdVnJqeLPvWaNyi87MdEBlrPB2c+rW4uHCcABCU6104ZqlVRnY1q56B3lOh7ZWlqFUDZYTDm9D3FETFm3TPvFWqyvqSJ8J+MRC+JamtRxgWPGhxWcIaYFmXmakdCvw0KHKmqD7vCwbStRB5HqDKympC3LKMDKVc2Q9xr+N1lJdX0CD1NMpPvdDvKdyoiHt2Ss9lBIE6ZkmW1k/VoMp+PDZBUoMsfMS+uH2CUlOar6FC9r6XFXAALdrjSk86HfDHQMrJ/4lLuEmD4ksAlQLBEkAlvoNXD8TfY0Gk2bfzw8ciE54rMcbtW80/xMa+aXA+6fKWPZoU7qE1gwyefGA3MaHpIb4XsZg+icmt/7SXd6FI/pATfONuAdD3pf2qrvPQze6fpMWWSBj0Wi5KCNPNbPN2tVYGKxXz4JEPbQi+oN9XSSmKIeDNrPj9iZe8F2jmo9U36HswqGygsUDckmg5F5KCv2ayWysgQ/VBV9+MdK2u5E3ykp5q4CWFvZL2zdLokquJNjZs1xFKs2IzwfyW91+bGJ2ZIlcxGxgW8xVBNvQgXqWFiYhFmKl98LZ+nXpDn/h7l2eCHsEbS03UC4GX0aM558euXiTFLYg91RD3N68WaqfvLRf9bJQ1swO38okGCHUSvBANTprJWh1u6LZRUY1k9pQZFMavmHdiSY77jjodZKJ/bZQ8/VwJ4TeABFJE/zdqyc8Oo+v/nnascwBsbjzUFHu55DxiKKAzPW+F3u/aF2XfUMw1h+iQF+ZAs/xipuj5d6vTNGrKDQ//3WisYGGZH4LLa6KcSNJg7JnJSdE87kXVThjyVQ/6hyJFEdYw5T3BuPSYBXAuhxK+Vi6OOelJAaE3o8oWydxTYwIEEY5wwY1zzZEEyOOCli8mrhLzNKSvUueLwvA1V1XiL6g1HZ9ChOmL7VMCR3jeyPO+4i/5t/I4QKcIeA7DYD4Ub7XcD0a/y1GjqQllJmN7DfCLtoQ5vuv9H3BNH4Euy6LQsSHWAifr8IobQmmLRInNdV4qFy1hg5YSTOGQ8xlAd/07JrIST7KEh53YcomO4QHzLi6ONve+aJ8QhAyYy6Ry50OXIN2QrfU58aE9ywVYeerhTnYrdVDkAs1ryCcO2ftXsIHQVu+v+ODKd4sQAJNvN9Y+hdZV/nlUcy+kRWuSS3OiIu2S/A3YAxqT9qTkUFfXt0lujyvHxFjD2BmydqBaH8vj+HCRYfFNks6hZd+l+UeeduWOqJuDwh39bXN56epNszMpyAthXMk6laumT7Zut7V+3IKyJ7fIzGamh/pxyLXrC85cunPnVUEofIqQyhcgaEPIWgupSTfcrA2veWODdHoami1TFzBp7QAkpvPm3OXczmZ47MS9Bq1EoTnIqhobdsJmYjEVVyTbKEu1iIH/RDzi7vsOs75gPEmhlrE7mXs/BVnvJ+k3aATpISfshgq7gKIxaRdrj1IsHjaYLqteuvDhAhwth1azfXpzLg95GIzE2RVegO5mqptkxsDRwj0y39ux9vdsUczZrvub0PZQQs9kanxmraRu8k+LZvJksaRlNq2ddmuQbrAvMHYZWQVJDUh7hzXeG7qCB8GXKsLdcH7FGuRXJFTRgHOximxEuSLXwbfycRiuamELsjADvvPhnBeE2azqotnQGV6jYhpqaZi+tJFCBY7ezfJ49g4oIenYkqiht5MctYF0dFKNFfGwl1aaulWVNdctvwvQe+7TBSGflvnRZ7UV00lqWsmiPqV825nWufUvZTUYyv+akpSlWcmGAhzA7jfhzdpFwH7sGlMQONQttv9m8KoGvavKyZzLAP/KryexcmuqmKU1PA4TGQUXFj45DY/Sdc0yDHvesv3p5wFhjODbxjo9PcjvSn3oM+ECjuFerufiGhyCjSjUN8MwY+cWk1JKqZbLGvKAUOmn8XhWS1ziWw8W0IloQXndZfWD4GPBmSuyqHpK756AGpziIc1EHu9s3t9gaZ4VMeUxsWuwuC1HXnAqkvKrlMGSxdpsuv/oXbjhpwqCzVvj+rl+MmSz9QZv2tQ92aqYzg78RIf2FvmEr0YwuXmFcrVbW0QGQliSjzShoekf0m7CnBCMDq+6EVYxHmiN85Q2Pm1XSRN4ISV+WTq2vBQ7V6OvcSJ3SdGL517QMz/j0nQjBBCpq6EBHVjJdt9M1yLt7TYaFvMOQFl7+zvYnbJXg86Mh+237ULtVQsiq8PvMSa1EpkTN0Sp2pYP3UAs3eBYHE1uYofwz7GrMonyTIvrCI/J5z9Kz2yYFXD0DpDIT91K9WZRSznCjI4CME1WsosUaPFznTU8U8OF0rMfEn/9JdDVxKBx+AFGCXFC9j1FqVpypctFfipRIPZWTCtV4USX8jbAfnUVSM9N2QE5REoMcSI6TaqjpnoZZCUeUtQGO4pa+8Ye/WYHqTmYX8Co+NQ0oIimBbviZ2ka2csxO6FVIhtaPkSg4GE9cFv5C7cU30UEnR1SgyvtwA3/6L9lGodfg+R+iv1ivtVprnJbA7H/iie2cuYRPEeO5zl0xzeyoHeI6dG1xtYMhJgVttJ7nt6TlKfPBOgG/3goj0OABhjOt8hGtveK+Q9Ayjg6LedzImwdTdo0KXI57yO2h6MLuRIv/FPpSRRiEp4GfVFV7W7oMWQ8wcVcU8JOze57MPQgqZDHj1mI4MNhxKI6XPlI1GN71+E9KqhdYkbfk9MaJJyat/8MF4SD7/FXfbki+uAtkTWBhJneOw682a5Dh4KZzfOFJifmw2jde6Ow89SqPl5gEeJquLCzI1i0LwNAQPIdkhnfMX3BwGSYdrl/2iRwwzavNqngRPkltLj+RgnRGswuzaSSdIatGleW2BSCmj34n0pYAhXizkQZp9cHNLtcJ3RdKt9L9XQKhZU+rwMdLxbTg6prDR0KmAL02NXDId1dRWoATqLo2tngyq22OsxDtljAavXHhBbqIfwIvgtOmWa1zDvedxeIp8ytEoMksw1ZNjFq/5k+Vo26sZ09N/Gk7as3rq0/ojd9LuUpn+hRd+XvZ7TqU8FEC7CvGssIqu1Wtj1BJrxb/PLuSobmeLVYfuh1CjjOxiD3P+rjTICdZwd9wpZwEdNONDO9+yzFkM+AqNzFTYN+4B7pumokyb6yhSs2jNzwi2KnOnseALRuTGyb3b4wrIHRLr8xkaso1pdH9M34rF5QAtULFU1qk8q0n7Bta7DiBRSerIUzLa5uqSHihw8iw6ZZzNnLCm6geY5B6XjbxJ4qfqgsXC96TKqE8z/0lqPU43m61QqVgT0XNbGkNXTQKKBsa45Qm2pN01IjAW04il2H3v9ZFXTJbazDm2CrisdnVNkYhELjZgEzaEZrCHMpvZO4nhPVwKbKSypyX9peyfgvzfG7JY38uk5B9wprx5CHLL4nEkV7zTP5ZWjFH5Pb39A4GM/sI/13Edaks4ftSVaOgw1Nixr+2r9ySxUPw9ZX82kw4Dii1wbgh737uamNXx6AzAQkhcdPYiR3QlX4C1wTyYSFvDxHHcgZ1ZZaFy2afY5EkZMV2EJbVg+0ngoEFX54zT3orEAnpfMlmpA9lzXDLBM3JhQqf7GTtmTEyHcxTaPl+JHso5VeIltImFf4DuCwpLOubML05KNEy3cIEWIfsJq8BOAGFSONL8x9kBPpJR14rAwo8XZ26dZWpo67XiCK5QkU/PQDueJGxFaQoXFuMInF7//HMJGqB7KJ6k6TxvANfB88cF9/KzfsBxBffmQDVowJig49YN7kuKD3HfFRbCtlkZ9uOXsMml5jzfGGC4UUO1qYtrNeCFnoN9d5DHnYcULzrl9OyE534IPXVohHUMMaTdIoB4X/WAVesv7N6DY7Uc8lE9ZkhSx/bXcAIIIxuSgrtbyswTXL/PpKMcCfNISDLgbPR+qalqs1UjRLayqibSdFQC98f1AELdTN7V0/MOARwGTmJ8zC2mM22GRilSOFWgQ6zOzoFMBbQlIglp9ukkiL5nrqX2AwuO/Ex++0oyvzIgDcXUaHELhhgipxVRfyXjeZl5smK1c6RzT4RqROEIVsJgfuuTvcgGr5VaMlDavqTa6hOkrFvt2dynIkHBeQV8Wvswl3F6sDnAbVvpINroXmYX5xfKyWnJH3Y90XSvIlE90Ffa4LXGyBagZjsXBfMwBtp0XoyyLc5MTzJcn7/GPLIImuSmcuZP5Jx3FzRcrWyUcjiWLSaDdDPB5CaM89siOw+/meDkBMpOJOy913govg+jt2ZZIUScAHGuMtgaJdg8/B6FVib4uyY2iZ6gXnrT0wEArynyMu3VA9Wf/kHBCEGkm5f3nX5Kn0/JRJNu/kVytHeQS4NN3J/hPYWc8WWN3A6bJJ5BMneDpBGNJFfUS853mtCoAuKRyn2teruV7kQaTIhk2yhh/k+CuCHxZQG0p8QDKQ8bGqYu5OSAYtplVBKPRVylaBWnKp/Wa85pABKaW0rS6D/zz8syDPQj22PbwMgNasshW8k2BKrYh3AlQGolEdHV1o7NbRrGhmrzyBo01Ogqv04T5c4sRvw/uQqcfQP8WD2xLssDaEohBtbMIYegWMBgyErk2EHBcN8O3tfmMI61toqC7bawzrTaQZyJtQdfnT7WNDm1nP6LpDWRrTTqQwlxjam0kZKNRnQS6JLTpjgm1AoC3Cz5rRdq13SeOqAw0sKvq64xI6V6pnDKihv8JpEw7kuXtED8yv9P7w+W7QcSrIiP5pbcZ5kXD7/2pkp1RmgkcaG0vstKNhE/g/8T6sdUkCwhKsejGWAIGwavmwG9HCxlfQHSJpveyObcEvpoxEIOD8EadNO1+RyCtR+0woaOrj/rcNaXSw7FH6tNc46p/vV8/TAqWz80qK/OOubLG79yYs7ORQGQwjL626ioroCrgcDfddBzr1ixK1PNz+iuMGySMazmlKicQG9197IWv1PfmTVy86uhpGMHPbuOTE27l3wQYNlZ83hSfBc1eAMHiBr65TzYpa40MNAxG/NdnriAIGjqqDun3uopxmKxXV8jMvtYAlfPA27eHt4OXLcwnFnaZimSnGRVEK1CWzw7ow1NZkbyM3hzjY48tQm6q+vdqRpd7FmQN/ZLmv3Z8zCMCOKKCuaPjq/HR7B7to4w2zAHipQ99EtmH6ENRrMLAOVOg8YOKiBN40O/UtvNKaFdE1v0S5WqvVCUEEEBJh5DnckuZFJiI4YTlVE0rYcvfJBWHnohsKLs3zpI6KgBhnZr+whOEiCB0gacjw1X+Gh6I+vW6BGNAxK9CaEduavhLnKmyGK2Ke2ZqCYGnwDx9V7s3milqGiSEKcyxsVDhJXKqu9Gwogq68q7a3aQeCZq0d1s4nPS9SMZD4qITbOm6snTajXABPRLqrn3z/ATACH87eHPknin/c4JuhgA9p1CLRr+3ONZKQ1X/c5xizGlFhqrnyFooF2KNmbLR0TdwFDgMJ+wSJPZWp463VX+wGz9rPwlfk6/J2drnQiRDAI4TI5NyeXVvXIhxLFTEGkchfGj+oF3QzSSycOuGx0jJo50uQy2jl8jBEyVKfVau5yteeLBi5+g5NEWePhVhmWd0YcCZB6nQzC1DP/DGxp4xe7oLdcQIhID+iy6Dz89NVWs7oRMQd32yg0orjOV/7XH/6Z7k7/lo5yNtcx4j4XDi4y9q51ciSG5S14eb3WgxXGlZTj6PPAhrWMbE+mzuPZVJxPqN9VoTdw1PkvMpSNME7LmuzH7DUoKx5zKfquAmlzgEuWdgHT6WY6DOEBxDkJgzcoclaBx3e28wxc5rhB1qjl66hJcvavddttqbNIfJ4FIshB0QF4Vh8KaKcU1Oy0JgcJ4MM9yvGabPxMKQXJmuwUCUOzDz/b/o/VUIo6LB1v1NU+Nira8rKha6LeVPyTyd/sO5PlSfDAbKluBV1ZpgcSn3+Jpdsf8lgJ1K+UKjgyAag8XAJOTzUNDfJ6MNXibBflruECObc6uIZp+Sx7QdEL8wU/kaWcdl8aH67jM9QH13Eb73TWOT8M6+TG/3CREmuDnzRZtX5fvaNrrCEYsJNO4GM7y0iJCeuFEBoCh3PxVuvg62Sv3CchZUEMze4Cfjhohg6PyIZsc5dJsI74CMZqvHSpp8h40juBCsFqGcmYPfL733NCiZc+JBBtBXyYKoVXSu0qbU15siC1SNS6aNaO8Zb+3XHwQ4tGoOpNdqqYmVGhusc0RmJ6P20E6iVceQUiCbLb/lLkM30aRITrYxMtHFLfgfoO3YLSHgW1fBzPHlpgaRUP0O3mhPs6nNRRhA2Y8LMGmtTr7IGSNU9P6Rlq5lo5T2Giya7XamjecJX3wb4FxZqiAk6/dAb+3K43mgAHZ02Y2faE1p97AVAa3DJ6RGtYTcqHpGdks1ZrohpSi1gm44AJcrr7oyrgEargMmhOPENIYfI7vwnBQFBkd1Eq7pmhd3dOdJEF+L7yI4Hpl2vXAuX9N8/QZHH/bRjA6h8vsRC7BYeFwpDjJYjQy4Zo3oJVa1N+jvtHXXOSRUd00TZ+K3ipZdausZhdxdWTbgVHW8Hxg3uIH8EJ8NSCUEkgno6P4lciRHDWvbwAdRNW/wFw1xHyUAkwwiI3+xQLd894iAVBJqKXYFag+Mer0gRusVNHbMg0p1WR03rZ+E+ZdX5csdnFVsm1R6HDeBzO2lo0wmVCoE4rIBLERPlxOuuhEuJLM+9bfA/RUREUNokEQ+GXlhW2XgYVg6aE7Zyq0HD2iAg/ZwiMiuLZBNJX5tqNLNgBuDC1aN0vLRz17lnuEbx4Tg4zudP6qInsNjbVz5NLUZkYKBtDABTr6Lbih4KqVhgQ2hVeKbpx5rgp16z7diH+JXqLR9PTNihR0CpY7kS4jDqYRIyIto3A0WFhcxdMsx8TzAp9ytSMH5JVIpkM6PbWxVAPrLMnCl+Aq1FjXF1Injb/k+WoDBSo7fXHZrUKcMFC5KQuCL0FOC5K/BVZPUhdokK1rIGMZgFWrPUKUld2RTEe29Sd9kNLsVTIW5qQnVumoihl2nHeX0IGEkExpbm+ZRn304jBYvm5+nguQeoaEzzYGo0+wsoqwChv1HqpN9UllPy1R/fHTTfYPOSzQ7rw1GeeSjA3DEu5/A30xAZkKRBeASOaqkjq/44EgSgbw+1U0L5WkZ+9io+Jxa8s6oAw2gALSWtXkR2MVz6ACtCcJZ9Y/JTznpZwsCziUnDtBYz/MkxbbgAtjAj8a+lr6JnBixxGvr1PNtelqx7Xl8qXNzpUjn3ePYkjDWrbhLFHOP0N0tL83iQUFJvTjtcPk9ZgxYyNkF6BGT0BXzz8M86+GprlwDy1GcuIQozFp49vPoaiQSuhR+SWlhIj4U030jrjXMl1PVh3Z9K84qlILngAifBh2TEc/wg1EjAEgXJVatRxagI1fRGUCkUMWvpHTOEKNEhgm/yl5YdVfE3vM3ZRQ/Rt+vfVu0cV9AvduByWPwNV/I0rgymgqiNIMM68+7TkZzJvKAJJ5kOJyEP/kLHQhYsHQzylyLObdmWZvR+tM0fyScAgkNqCFKGEeqhNYMrEYT5t1dueapmnf4cw9iQxnC0UO66xc/x+KFKs0BdrJJlMSpK5r+hVxjld9/pkKxwxvtD3t1rCSklK8qL6Sq1ixhODgnou8UT8BTUFHBebXQxXcvtlqZJbldvkOuCgMpFvC9jT5DxiTsfvyF1ds87Ay52o19WjNdS9/Y5+hXBgLgxOkqsfyia+BpqzXlzGIwUh6xtVXuPxeItb92S78Z8qb7I3R/cJyqIj9HfV83Z4DL7y2/+ojlkfvgxlGHfHqIL3hOrY07y5LoFwOTH+CC0VNp2F3Ul+mqY7p84X0o0IO5Ph3sLfGkroO9KUflaYJnbYIa28gvImJnyZOwHJmqD0XLlqNJZnT0ERdi7dxCrXJ/v0bBNBWStYCfboGmypkY+AWRS45auzuMN6CPox4wsbcmwwAumt93rmzrm2hUS1si6eeUkvSzp1yeNSjjwAu3LamvZknq3+1nbvuSivvgRAuPPTPNND8T4sKDVWH5gjT96HFnSCt9qnlp1mCmv7AH4VTn/I0aBVYLhR5PSJk6DAtj2fqMoY5LjRdcFccOgIvj2R7cPpWOl9mYd/OuoAzHR4f5WfYhyDpqYRiNU5HZBptu9SHHsWOyQShDnCzZC/OAe6hNzZ/+BxPx8TFirA5P/Ya4pHPJktzrZN79zsACqOjjjrYIkbyE9BmFeNTXFJLGq9mfIQBviCATraLJgOEg8jHQcOROP1mcK7PHF4Qa1Wnu6WtdYwERbbz2+WABI7tWXcLQJ/Baca9Z88r3PlL2k161n07vcOQdSsNrbi34sEufF5O/DoUJVvwF7xvE3L5m4JlEPZ9Vcmkfcl3LZYzGZMsl+69n8RJbESP+u/fOMwS6qDikK8g68PEsYhE6K/NirVbfnKjFOo2lhV6G9CrXjFgEqgU5gw0AuL1Qm8Gsm0/hRe56WujTkWoZlWTJasbSmsO9GuqiN6BNPXVo8aa5tG4CvFVI47CuSZkYtx7StdE3RDI4TTuG+77gi4Ze4JhZHqm2Ag3m6wLqlLHN1z47zbSFDBACUz0T6zNKzcXdcKmjzX9kSFZyFGTdlr2+6QvmRAjn9ACY5II3z/uIIwKcqriydwxUrbyufJyHSHPCgALTulgbn+ukeJ3R1Ah2OjxBcKdTqD0NQ+W2EvxfFScrmpwu6g9Its1tigRqyNYF79Nmn5qxAJujxftcw5xuBEWdyXj/FoGMiCbG1PyUx5BQlkU+6n7b1WZ9Bo6QBUIkZoE4SA9+ENQ839Tkq9ew4/Bt5dUCnqV9CFVbI03zsRpmRu2qjmZHNTmvYLifMrLxcl+ouyMrpyOA/oZerG9kLMsKxOiDr/TxKLhckLxiNgzNFsbGPeqesVA30XOf7pSQrq1La2dGAZ/1h+FXUeLUw9JCQ8wiFdq13SWze9kPGAZSMr2/6xxKi7Aynfryil7evnhAqxI4c62r6lqWUNw5I3L9ZGukURzxPW5kbA43mx/BSKK+ehWUNXC6ql7Ld01/kb3kRMRK2zzv3dzYsvUoOkUnf4wCPcZybbd279sVqBU0exGw5l6s+QYON5LE6mtYqeLRQg3ycpqeiJ+I/EY5HIboCXofA3u+jSzR3/jUkSoPjf0WhliczvLJ2PXa2hwG5mvxBHXBALZpUlQwsIIIFrZKdQbGOjWtgBoEUYx9EDFfiOsuN1w8VoSoR0RcVv5FOTl6lzV9xOMSWvFzZFAV+hHfSvq+CSp3QGBrHHbH08UI125ikbL5/x/KD93MHykBEcpN7gxZSfecPbmMttH0hgEt+Vj7dzzSbhkRujHl2BT95+sPIvniN11JTrqoM6O3tiM+Bx2BAe3ZUT6VA4YpM03/6TogdNJoTQy9A1F8lHKJwK1h6u7mrWFPoUnpFrWPficaw/aerQr0AbxA4HTlU87B8nTXW1ikFWIYN7EFjfoA2d2SWBP6TzdZEnisLRGp1YgnmlFB62B8yc4lT9rsO5aZdFWKFrEWkMOoYqAdt5UBeR71D59d9x9MP/VddCjHK1Bwu/ItEjo8JvecW2b7PNBm/nIK5GcZerYzCamSzK+4G7LgEI8oqNYiAoJjW3zg/5n63Hgqfygf4t5cuqrzsrmyOwhX5s6fJdyDA2gVlDWDDlIrS43+6K9TqCNWJPA7+RLP3e0BwzUfpFF6prfMCgtfRMSF8VjB9fp1ESVVizQsV5E/g7G16Kua+D5uCHhmp6F/QC+t5Z43bmlz7vuyJoHeQjEF/ZdB+WA/OcMIF7mRQMctklWdNY64V3PXgh4qPl49BFF+htqNdtJa411bb9aGjslo8kE8YX77phpUveMbFQMCTH+/uYZNNhB+xhqGtNSsgrFicE9OWWeq2T34sdbw9MnQ15LD5KE1gyubmluIVIUu4Vm9KCqyKju7w01mngC3ItAOIcXPXv/uBG01PKyCuhvYRzihbvBuMSxmmzlRAQAOU9vNzeU1TQbzM/Np1E217GiULvzj2NnNyT6P2DWhoicj4agzRpaxbgSvOj4fL3sxbeuXWprXyoPa1b4bZAZHr5sWcAMam3QcfihwryYKN8BZVuAWHx6cZuPViLpYJ+26HHURSup51En34cD/ipz1XQOUGwUz5Gm/wUebyqlSxB+5IA7cPJi0yUbceJ3ttf8Xbszwjvz7/9RqnX/F2AkoFPbF4vhEbm8ixVZMxNq39i3UsHY/DXvHgALqUNbCn3xAiy7SbHNhAncjepqh/K6jrDtG1et72GBKPU3GAAevxf0cPQsrx348iOQD+5ZH854bhuJoMJRAO6gRZqlf+6D9lXlo/deyPOnkIO/8vvFOnzXo95fr4jP1EHKIw4JmSbHsCGWN7W6UgTdXbpKFD8nQgTuwNM1MGpko54k/L++KK+AA24UBcWUO8NLoUQE1NkSHWJ5LTmBl8l4f6dyK/ChtQThM1Ra3ZZS/JJl/UbwJ2cuz0UaX57aZXO4ojX3Z8/+U14g6XPodSAY3XbuwVmi+/G9G0+alN56CMc5g2h+tXfr3esw62odupAdrvP5as6WbHpKw3FTURrp/SUyChr04I7/bRkm9qUJ2w21oe8HHIBuKmAxYbsQpjVNgZJyXvnFcAffe1WV4pArIP92ENEkviaIvSTPpu2rbM1Jbaea+/SPzTEEt3jP326xu0qkQnVsgNE6AgYbfZH4Nt01lyi6NGb4tzjGdv1OgqwFePdp4GZmBWuGS3tmxFgKaqOi67cq8PZ+uw+1/mMZOB/5XCkFxtU3ICy3d0HZ0n3a3xMNQwBWcxr+C6v5xlyNr6J1TwGNLjhcgw62U0qDxtKHlTdg1MnIKNzqUQJAoJcRnsc6UieH/OO7UN+j/HnBysqIhPZ0oUiVl95rMmsY3UdacjSvyt9M12GOI37Qhk9ZGa0blvXXrQ/EHK/5uphTeyBDilsY8uYI673dU8grH04kXaB1GL8VgDtWm9+aROH140UpixI2Qi4ALKPT0npoG0xyCH8otg8mMi0aS554q7jaLes/aJsG/jgLx/AU/h9ec5OYfPfw8wZWasIE7DWsCOx6IsBdSyGpm701086eBezuoUn1BCm+83DqoUDVLm3iwNfXUDRW1mDodrr86ywCj9xyx6bJkEj+ZuZdXY3xDUNib5Xk6BzTDW7csyIes0gbUtYvwvtfeze1xfFkSn0bWmE0842MpdOMCifF0N/eAV94JDtzqU6kfvYy5H/LJ7prVCexPPxif4w2oEGK3CfzM9grFrePJWIKS5wHFiaJlc52vFz9CNDq/ESpiQwUPUWeDIqMgMeF7iD78g8IFGZ6DPMYKiuhvhxqSyTdIgwvtFXwUVBx2Ztp2jeHqE/9uVfU2+7Lqst/WbeMDT+pYGbv9P9C0J2CaVL/Y2u3YTLxekQ677MV1RF2U3nAM9BYMHGBGH/AFtLodtev+Mf2/Bkhs7+8lSfzY7z8AP34s0y91Y6gsS8rLx7q+sM0HqJMQXWymQVmBgPPDHYqwGo+kd9s3q0GUsqVOGlreas4tgtIfzsctseRJHKmMT/h2zDuULHelHvVGi6qnifvSXb6xNd9p0R/V6yAdmH2JCf9rgutTA09lKKc4FPq4lkTn477jXQvG45s/REeESiyhJsrRPkyTHY78uUGIPMT+21fWn6+uh6m8adP49fyLF7ubrEMgV0CJ0N8xwgmkNFSO+nB2C2yzp0DjRypFJ5SwC3jHjIMUAqPnR0i+dPujtTdtemjHahN9Zsi9bzcHot/mQJRoD7y7qN/5h1O//d2SIHbAAISKK23Fir/RUXOUdvxBw4WjW8L+x9e3tSyYn0IUU3lWJ1F6NoT6X/GI/s0oWyzDxDYH/mqUq0tqXGre3gAGh8GcDltcfhMZ9pbuaXtd+mn372290mbRcNkZBEyrn0CN9a3ygSKz+q++USCFqimmU1PpuFofUsVTEEGuaSvxQ3Fa/sLisgqk0izBAg+2SvpT2uOCqu89Waa1kxKe3DNvePO4GvpleQVX2ubn8IEL0vLm1POJoSUnxUvH4w4/dWula6Luq888bd9BL4Z4gDiEvTOR1n4dOzw0vRWWhNvnZsdwHHwPnoJGfgDd2c0yTyVHpnuWICv9HoCpa3HhKVDQW1Q3sKguBv8ygBSr9cpx9mnPQR7VBUp6WjszqlOo+seTB7c2ukD1vFp18QxCNeVKvFp4+3e/phEhivEs63AgcFy/YOAYejEUSkW2WrVSTfm+Km1G0d2cgfgRxOpJcKJpowQ2UttzqEh8flT3m8pB/6XGYUl1yplXnPuggm+WSmz09JjjBtW9dN/up78GBX9NmZvKwnmc1cOAFU5aHcDwnu8zDCaUmYLp/o94RrK7oRhEVLZaJVZ8OnAhGtqRIq5DM8B6v0DcTn2RX6i2OTDoCus/WwM/ziKWQCAWJmo59Xk6lO7B6qeXdFshQPf+7JcvXtnW2lAn93gMLObB3qk2Mru9+mm+ajI6POBX9NFSDF9PJ/slleYTZuS0fNPoaA/hXSce9Mx6pkrYEEmw0+Vw/srHpOyVjAE541vKYsooKkK4Ed6kSmlA9+4meyX9KPsLbDqHhsuAEfpwERBSsWEvJSX3byhbtXiKxp9G+9x+QeL+86KGZFGp994fYIOmjwZv1p4OI8Yal+bB2RYum5vD8Ib9BN6vE4ZeSEqw8AF5AQOTYDRfF7XJAyqKaV/6f0p8Z8PdHpQ2fk5yakuqQkSmsKmf3TjzHuZIYHNr6zmUGgaRVYIBsThn7G0S/CNQ9paz6szQ4jU03+wLbfgDd9s4hI9kwSuc87aHfS3D5LkWu6FsFZ1d4/+8HKiMaeYMMEk4/6ESz69RFgWlwr8O+ZSoEt6l3atdPhjVS5504BeMzeqoX72+bY5zcqvSa5+HsQPkEQYEtEBnYL27ifwiusE+TbfhZTnByf7n2e6kKMH8kH6SHgJ5IScZWPZaTWYfWH27P9MjC/umtcxO0KXvds+pnF9qCYjbtK0plU0QjnuHFmLvDWqWzVYy0I+hyWGOGAl0/FLM/toeakrGVn/moGmKAneygpzNwuQ/cOfYEoPx35kZJcgyHg5KBi+j89k7AdFwVvK1R8NzuQ0wKAzi4hb2idJTM0VEaBvpMJoESB3Svlfq/SQlYN13eAQnyXgPRBTFHmqZJC6NBGN5IKgxHIwfclM+jFUwqdV4mDuMYb5ferbTS/aGIEQu2flt6knQKMsmsHY5HoOx2NUN3aris0MRsf8M0V74hwbhBYHXCUwB5vDn0qomyWr8FFngqmcW6GA4HeCO+A5/bSzxvwwTTYpNvNnQXdHH1PGVN8mrZNZ5aT9WQwMwFxfQ58bKG+bsHzGI0Po/g7TT/gAs9JKGQYpGraZtpFo2/Db+oAk6rEFMQ6mHvNuC5GHyiHTdFSLAtEMhqRnRuK3NRoOmRzzvtQo6p2ZtHrkTTc7P0H4F62oK1JqEDVyREUbiLI/Zp24qE6GuKTCLfSaEeVrU06Wq2ibTRB+Mqanf5NmzlXKFtLNrQijx4Q3IUdcHELCveuWa2nzV+WgnQo1XyfO0eJxfFij+BYYJtbHycS2ZPSWi6KPr2BcCS1u0ySWJHH45sUv1AMSzro0XPKPSzk2QlN+0NInhzq5EMLx0Sjv1IZLLTpAsfYtNEgJF4BxNHEuYVfPxGvnX7UOz3qXoKwMOn3vWtTXsCDaqxJodT2ytc9FTmMPqXd5i1W99xLyM0JXXMSkkLvgx/AGoFd2zteZPS5wyA++ZFY1NjXXQPYc4SHcPru4zih/qiTV5K5LwPp/vGfY6MKyuQCUoNy/ZVQaNxTTKVPy8K3GJ41lE/K5ChjqPEDfZMeQCa3vupFV9vvJ3q5uySTVzDastkvuG6oyE/0qWQ5uZXc12OGr1XeaKPwL8yFwViCG8kElLEMErswFPgXF44uaRywMqB3fRrV/hQufGJALxyQV1sNqXoX2X78gxxDf8PW1u2TGNxWyBQz0tqJ0EmGygS7c4dEiXmvaMZXgS9ZblcA1WxoIAcv2IYgDKkKHvklRbzxCzaX1TxMdgTkLXHw0hdUdJL1sOoghrCNwDJic9vzCHu+s2UOcKYOVYJlbU0LV4t7TS1VPA2GFBxB6GvXfoWZeheW1911dTzdon/MBHKUbZddmRIw3iG+ZD8xNWQT3qb5U7uFkYZYW0ETFXBRAUKM0Gwq4tyJe/M3lr3q3znj/MJvKnjduPQ2ifT1xKIAimt+DXx54OW32JNZssbRQkEAd17vDZY1CH71sMlifgKC5GGm2RQ3Ofkjt+tLKMdEv2qh+LHx53plx4EJnYbmGmwyFMVIKqeHtve5p5mLa5q9Jvfe2TQzb5tactnUNGaWPntSJM1+XndSEBQDZmGANpn60znj285R0tVA6o8Q2ed0r2+4zB4A1QA9QYMEN1pcELxZ0BVRY6D0HiuxBiisSxHCYs4WldaXsUQAz2k86Pnw7PaKrvnHTxI3b4lGOUni0bCToKmqEqIhPWHpYfDH6aFmALo+R9HHY6jPpgG45NJJfXR18zN4urcS4bGCLap2YyjU33VDjQdM66g9nyWZ1+DJUBb3cVbfj2WoM5hkj5N/GGUiqtGrRDPAI+7HVq0ddlYfRzaoxeQllCGEpeUiIB6YRKg7aEgqZfCPjwU6wT9VgrbX6Pnni8TYg1fhTPnxQR3d1F08aIIOrhPzlih56PBCVfN5YxBg4MyxxF6qv6Ihz8BxplV1rFcCaSV/NiU7PJ2rmmAXHy00a6Ikl7zJamZIc4m1dVNz1DzJ3SynkAziBp2RnbiLJ+IbevjQsHykjkeIKorH2slMR3mmV8KDgyXNipw/RfCY/bQD1okTqVB2AKdv1zEBkJMrXZACUDnffDuAA6haXChZvGI8lqBpvIHpmH40xG9yY3gvWR5sJL7A8rc20PhbFUKtMxxcrILOZ6S5YBObINgnR3JU7UZfvNY14tcvsCZdfO/foLo5oH3hy+nbnD44Aeq/XdIOFUYlkh0d1kh4YdzTucGl29A90KN686Zb0nhsaUtuOtsijnc6zOzues4/iBGtuplq/4IkRJp/6lv+hMnz97ZozXElX1+7KbYNWAh2o7fT1aA0k6us8DaCeuyGGlC476akmKsqBDL6kNR4/cLARvVszj7ORPmWXZwG+IQIyXAMSO3/IHVI3FrpJ2tOLB4+4BbLt+LdFI03SBzVcwZ6xKNOJBTbo0ghZUrPMLefeY2gWIfhCiT4CdHWnMjSmqxkV4NA5MLP+9+Z/TNtgKVGtRofb8SzpIeqGqV6aa1KZl8Cqj7maMnDxKXq77uHxc/7q13UBSqXNTpraDiTJ1UpeIYxj7LMHIzYSUrMycs/Qj3vMe05/qUD/k78JHui2OrXFNIm2XOrs95kGzqLtBbQJiSjppHeN0DAFq6ytKpLD5b76niGUItHLFXBAq8vjA6/UG1IFqK1izS3EAmHaAIFJdIpvezyfeeWrHiq3J6BhclMx8WxjVf6DqpHgUrkPIhF+EOL6eSbSq8SIhN5IfVoKu//ROhrLjeL1q8qjcO/gAAXTWFR6uNcYPFo8YH0CxREaZCwC6bZ/aFuUvMBQMO/g/FG8DGMr/cqWUwkNIWATNc0XPMEIGTrKwgpqjL7rVKVwTZrATit7+UlHLvN2M18CGbaD3Ce8nozOg7QXkq6Ds7yYp/7K7I4hJW+Waq/x46E/pPsa1MOrn3iEXJ2Dmzt8lxJRCBEjenWKUUVExY2dtqKXLqy1CJpbVSysnqJVSxgrp6X5xiCzIc0w+8pXBX2BtBLG17Ow7Lntj3yGXZwMRi+qRc5t9D1EEVkqCZLXrNurOZ3xYnwlb6BjtRK5JHJn8B4s6oPvmZBa7KkrWHJViwmLMFFPrAzCkjDKNJkWZ2L69h9uxi6ZtizN7IG4hvdWslRapXHOUEzTI9FoaGy5Diw1JK+snfIKgpqghpx+ATOnK3sneGJM0+4U+RDYJBKZ92hhbHcfkLB6IlhC4aKepuTZePvJQzetpNocJgFkQwb34JNz94p8vl0nbCJw4MM4gghI2MHYTIsl91sl0f3Fm7Kz17cRnCoegcfS2bhNHM5AJWFUtmJAwDxTXTQwai5vJhkhb/MZ6sJuSbHF2t+WzEvkcdBaLJXwWovZN0jGN1hspLYlWYqvYYbzBodSsZFHkHThBBrzlrpTMlxAdirFkgH4wp5MyK8QXWMnocJ80fr50nljgXKx4CooCQUci79KhQL4Q+Am20KpLBv5qPCG5YUMWpowOcjUabV4PexfvA4Nh7sPFNbnyloMY4Eq5nSZmO9NAC5FEiiMTfVOCJS1EnIP2/oo3CswXGvcwg7FVDCLwmp4/H95x5WvxPCt3PMWKIbH/uyKHjsTrsOS763PGpKpB34nFsgtsmcYTbjeqI89Z7Sh0PMLLMs559ddfxui/DBZwdG8HJSEMwg8kEpmi68BoWkuOm3hng5t6/rUEz2/xIQvlsbh54B6XIRHhySU4yby2liTmKrqsZNhzrnzCY3NZh7HQJZuaL6yLSxwyEchL3pFgWHD3AU9e7OdtC/yjPPRhOECBqJaf1uQh8jShJa8Z52oYgfM4PZgXI5e+qUEiUCoatYDXVoDJmZ/K53ClYmFpqPP0nwpiZQ31OiM+R9Gh3wfwA/9y30aG5uwfKorjwsoOUTlzAEDnURhrpeGjcrSg8Kl94Nd7dRO1qZB8iWV5gr6QAuJhmb1Hy2zQsOQ2UdOHVo55Om584QFcqE+7VPf1kJxF7eNRg+ptxVIEdJj0TkE9116QpdB/p/XdsQW1vTRxji4Ab5LXykiAYx0p4Ua0MiBZ/Rah4BtLikhDuyunAEDCJ/QG1Wc4Mmwb4/UwGenWI6lVKxfQ1pFmIBatzzs4bb0p7GQPtBMH6M/rNa8XNj9ZJA58vedhgFW6DBlTky5hgQ+5JI4goCAcmWorU0HEYRNr0O8tKIVmuNhpOaYuOkjHc9lGhyawNpFzuzQfDLeVTVEab1dUSKJw80wb/D0PQXhcwFKKGjU/uZ7pVYBx85xyERXS11T6beCG90lV2jBO2tMgegxcYrwNe4tZq5+KDlD0621TOfkcOQhDSivMgV3U7mpnT6oZzqi2y0l2ckGr3P5R68okK7DTdYaI2nenlsnYpo6HqanA1IHSnwaqVns9fSpyK6F5SC/xPGcdxGINHb1VaBpRd+95UPZH+81ZOGAjpA6JmQZzZYEww92NrWLI6nSNDttqM9t7lTzILW5klLLJ2JTa4VFlHN3r0AMsMQXRKmF8NrLD/EEg+ENRSqkzss27lxQff4oSZF1d+qZsmtNgQh/3CZA4ss/BpLvkhosQ781AUJd6e6N5DQd5DMg9PeREdRS0YY4Szfrj0WD1+oK/Kcg+Loy9t8eOsQW6rfhZ2pCwwNRFGQX7EhtferMFgWihTXFV37fRo7+U0dYBe+NewdRy1ws8hCthRDrDiZIK73GtpEgkMDlHdYaodpIAt1Gp7XBWKXu5g7oQWRmWwByyJrvGeASUX+iZC6uwSifvspC4C2SbPGljii/1pXaa4E2iiJUDY6saW59rmkoW5webcvnG9AA6qUWnLMsN7sIHcms9euNqfph5+DNfe6owNHfA5i53GnWlQ1I7S7a10whPVLgyLGSbZWl+/7IgUrFhm9Vj2K+jZmBnU17ZfMddaM7y/qCYIXnROHSsRB25Kji2g2GoKUA+Slfc6OP6rqXoD4nfIJZjfWTUZqCls6yfyKWDeD8aODDIJRv5JmYV4sHOZI0zpYgcAGtTDV+DrwD+n5YodFDHTRFa+XLcwjKWtlZTXmt0UtqVvgD25VFam+nf6ZBKVowgORUK4nnUX3VhRcZ4jRwyIOwO4/xqYwWt58jz9JMLq9pS8ifRhmSI0va++zBK9LzmHVxMzrrt6gsNftWKg4hn1S/sdXSx3oMvf+hOEkAZ4DOM6ZL+zHHlDYC1q4+J4YqrKnj4iB5A+5ki73HG85XvzzAphz22ZSD1YrV97AJhNSQpbg2ZB5M//GUMUTjDBW1Mt8fnETmLXKBBJhU7h9yE48Ty8RPjkh4ddtonLZLgBQ3rFh67HKXlteJhwQuN5K+XpCqX/ySY6sCiptYMdC2xfGI18m2SGmIeOeS0/fLzW6Ix/Q2zpj650FlSkDI+A+jXkYQ1Q26zC+qmb42gQZYCZJQC6KGIKtOWZbWFOOPKFF7OVIKU5qcS5QPxeM7uP2DvKUrq38a/zJWLYKVq05HjDWgxBTNMEiugxlwwN46lNnvEEDKVSwo5m5Ewo/nwk1sz0AKdm0eQrTURDa5+BG0QRR3poBmJmU9//qHDOaZs9/nwyRDyXisPrLXblAEmbvw49/8/hdHWQCI8M86Q3U0vmkBQ9ipCU5Xu79STrkR/rIV/9dfZ1qYZW3GgSOG0GoZF0cMk1l0/uzU8shTMdBWr2hrUv4tWetri/oWybrCsKOEI0WGeyerQTqLwsb30EU1xlIvmETW2oyZNAdsRAtybsuM1MefpIdb2/U/RLiTOBZSC24ZfhTSYKihBJEyYtM2Ro+RmCQwnKcgAXiFGowRgdIecWPN/L5qFTcAg48KYs1Gi51WuURkdBbdgdpqzA9eQzNWhGJn/M74r2zIxFx3uCA6foeI/ovsf8nyJvJ0HKhZHOio+2W8J0o+lR5qEO+k/+k6uQW5uowwP57VaqokfzHQht645P3PFXf+soQH9i/pPj7KdNXXRPcDOVrcGWCQUAbH0weGS7ClNrqA8TfSZyMXTsgYddQ2upDFHFfZyvptHiqKkKNOH7skVeyiQggRreyodLNRQuyW2P303X0WViiqY5voKWTLF3qISoJrHtRrzuE00VW2004cmCuuchmcoiNTnujWU/i0FU/1DCN1vmg2ipwLWdAzavwyqkExD6CnJyqPo70X1juUS4BAb8GkVAC4+G1iy1DEYYqFqnzikNHzLgKpvJCvi0Yn1LtWcsRocU7E1QWx2RFQ8hOZLvStXaC1qaw5vPgqKR7I13G3drWCX1yVMPV45NZ01+JkGK/acf94XueSLM6wbk3EZqOmV4tQXTwoqvyURIbKRASld26HjsCaqDrsL2b+IjugDogyyn+MKecJq22d16/3GLffV6kZyoeri/v102C3KdJXvTBwL11E/fkSUUSsH9uGY4Q16i1cVL2Vw/fOiq97Iuu5M9ZyJzW4EI1C58DEM+IeqIJ/ZCHgKiRhndYqZwSQ5HDlIJbgpE3SNS3BFF01C//wNrkoq2SQBpWCJMCAVW9k80GbRzRuEje8AGmYWV+yKWJDQTAPLyaRnhWNoFxzcSiW2XfGOWOq4cRLE6YfhDsrfblf8MVfJU3q3H4dbvh04LcgVl4EF8BpKY1frAGstq+M4ikkClGx23oHcL6q2eHH6ec3aDOEMm7cEC8eAzXFseZTM28xfLqIvWmmOXTRH7Ls2gltVwNxMp4/C8whlVPNR6OAc3jmKP5x6iy4qa13xItDMmN2o7wlmkFsJmCDJiUNJwrpHTG3hFUIMmLHOl2N/dbeX7pZkGhJ5hjRCgwSxKraASIv0q3lXwi3V3g2jv9ICfgYiXnzDGhttYqJlsRRz4RQGfpxc8cHcIC/zbBmKFucLM4KUwyEBYVR+Ru1WbK3598mGhGO2nK8aXboekz2nWXJP9pp3xBkr8n6n5jBQWxYbXnrAAVjlvJEc4UGc64RM5zpfUKI4DxgwfjMzgPNSOdI+12bDCymTPzghDMliFs47Uoe/f1w+dL7+/aiT8/TfUUr6a5msO428OJ9RYi4n+XR4jppcmIfB4qPel3INyrDfMDLWqq4GfP+npmlA0FKhL3i8q11BlNnnIh9QhDmt99zGAhcP8UIjqULzXxYlryMg0E50SNNUKrG65tYFsB0SGO7CbrMJvpt7LBGi1n49TiSZmnqUQ3074UZ/TG46xc0XT5n2WhNaUzWxeiOmPXwQHDvTC8wMJKAvajYSLD7SkjeKMq9lgONQ/Gb2ItFartaj8X7D1iiHJh04N3isQKqmeoq1qr37zKpsYcBAuRSb5n6WB/XoOJ/TqFb6B6ndsw59uzsMa7A+7WfI8r6VoGJNCRLha8fDxQsZ3gTayEka0nDcHbYY9q6LBkohwbDN74W6ezfgK62Iyka+iXKHpq71eEoLHA3hvEYmlHIkZ+wKhHesnCcXqRB2IGzhSTjRISqYMLM7XdV0t57aYrKF5Z6PwqxYpzIM5XnCABePOSx4k52bGUHrf2A6HDKB8voB2lCAGaBNWHNSvURfsvUnawzw8jt8kht9k8lcqDmG7jlaw0u5gIiAvhTL1DZQNfp+xwtEL66xKlPfD2T/zSRBVIA0iL9W5l+fMiJnwO6DCuxSTPyivQfxCU+bRGgy9cO1Fv9yhnt3GqeJlYQb2TZLr8HyG9aSgOZg/T7kC9In/1aOlZhFKrMknAbclNlH5jxpzta1fpgLwIApSvGoc//mhHk9PTzB0MNTl4VYAy5dNoWt/WycfHTZawG4lgAbKLHFaKw4L6WE1zC63ZM94vYS1l3LWRzAmAdVOEccqrDECVEneRUX35hQ6cTaF2WhX2ZqcvgGbXEkDwkSRI/Gr6cw3kioLi9X+h4UBtM9arZh3FM8N56XYx03ez4wNnA8Cclh1iEBQtHcekBGmbFefxxm1i8711pFRjSSKnU+sBSeUsy0cIJQe9qUYR4oiHsWgN/oQPqmtt3bAe230Y19cTbEIT35fln6MqSndLYSqZ5zFUpYk5dt28lsVYUMGeMf3cV4L1VMVHly5tZqhvYRB0wk2HdDEy/F68GyuwoqL/PcvkkHxTLSAOF9apEBX5OJqPucH8rqqoN1dZpJ8M48xs6lVWSWGRwEwZorQgYy1mJdvkc+2UF2nQE/uCbJMM7+xI8MCr9U4gjM2HDFJuI12LzUCmU8uPvlv5jbRonOvyBnMdhQQ0s+sL/i4TtnbepY5hSnJYgaIgSMYCUscDHZhwwBL3EhiCHcqOwfFyq5kqfELPKYaLhC9nWaO5iIbG5Lhmn9tiiDOvdJdYu9E9Wpks0TG0/1YgamvUiTjNFmv/5U0Clz1TgWKiHfx8GtvvbOBkyBgOR6kgU0/e1YjqzvktEFVtdWkJzkUWkcdgg+lHuIbVi0i8Je3Hr3xSOlzYh2pQw10q0HD3WqV2Tfom3iZYfdssC3O/sCb2gmo7prnbZOC9w1DoF0ecN+70jUn+MtxCG+m8xLs9/m3i5qV5jGnQm/+qAdrTQRFZTbxHRm2v2YvR761Kx901KPze+pjhxNPHKYkzbtjL5jDdgKxR2CqnzwYYmJ2SMPnp+grWxGpq0kCrpBcDG2JTHHQbBnl/PGr2eJSwwu6IO3RMdo93BRxVYwXbQGNEbHST4Gfx6oJd41HSEPfGLmPt+TsO+50jFjYGqGhPZrge8IxytnT24KM84Xjl4c5Odz8CqVYh7h3JfXcu9huRicBen6Dz2TdH9YqrXvfKO2h0oCeZTQA054DxG38qqU1OZ+xVPcCxJ7dJ2qycbsKP36rWdP7IfqarF0XljrYfCPKW/LQD/GkmVGVno44ppTTfxucneMAJRN+Z1+PTkpijjBTxu96Nu0mP4gryK9TLDKlECGO4lRGq89AyBUyNQidhST+bN596M6YGiAS2ntUHzT+d86twTh7oJUClQjjFk9rwygVSvj/mmaTDeE5HEA17F9xTw0QSzQnVHmxk1+v5LLZCt2iivraotF53Q91DBMTBI+Q9KUg5ARA5mk3192QxigrpBvaaAyLkkkMsITfVjU66XzY5CT0sTM6Fbv4ANCS1wPtkzNnbtA+9egp5iQs4+Z0pCzNFKM2RYYvF+RWQiQ3r3w+xQl8eXRvArtdL+KgACXOQraD/89/cApJTgXyeWGXUv743bN0IKXDfQ+bFloko1Bp3U6ccpU32n+BXKRzmRMqTc1sc6wTyRfbi7obSsxv4Ka2gPKnHaAItoa6I0XOvoCTEb4gHBML+WLAD31QQvcesUfZC8KJ2lJvz96AMm4AR7t9PtFY8ZxQDSCBP+Hzrkp65acwJoUhJANJ0MyqW8hC7DggOVkwvbilFnCldoXqIxOlZ1mB05bkcN8dZpyJ2o3jjvUocO0H/nqoEKjQ4EB1GD1oDeiJ+c+SMwuz6kjSs+4OdCoqIkxcwlR83NFEP/fba/0H+apasAzL+BTwqm9LUl3nPjqSyHrqBOMgaWL140zcuT8tuTH/eiJTvbP6KwV1hLWJC9N8z3VVB0L1PD8Y1CncrCXhPexcM8qFNJ+VcPEs8a4hYlQKvEeQChLpwHHiGX7L3/0SAyFytekd1AJCqzUzkdSpuj7DCN0nuHIf8tJDl9Lj0fdQEo19YfPZQ0v9Z1g9SL6Ts69uFYZAIwcSGVLTdVgsXM7SK936ik+dL2Da5t3MCHp3dqFE3bvmO52jI90yH3poVKokupQVe8IjWdp1t+I2Lu6cpWpuxahg7CMu8oKjgK21uY7s20n0nB+YDnl1eUDQzv6zTVSr6mMXCZhx6bnnw0my/dlVRJAmBa171Bzq5Pvd8WPyiwvvXz3QAgccbJwiQww0PKpIQiXTuGHhfLSBX92IgrMxHaJVj0Mj/HIWs2SfPaykYD8LE7goLdUcR5s0fMzFnThBNmewBK8Wb/73Z2FhzqEgc43/dsbir0yEmRw7KNDTnuwWvrYEZTCepXhZzBlwgb+CfD92gusITj97pzA2O8Pg/zsGQVxyc6OiGcR9AqmETMSSEsLnU2a0FMhfpYK+PFWsJAQxXFFrD1012+GPh9QJ3kb42ScqDlysm6e3PGCNCrur7GI6CJh/rue7NSafox94/RubyEeINpAxJ7IsMtWuVKtfkFl3AnkM1rWQHc/s8pNarjmoTvaxQeWCqB2svVx/e7KiZS1AVltzqsYgulvJhZElbvct9jMcAwOAtk2BB/gybcnP1cxxNha2p7Jgvx0K+4+y3gBFY11OtbMBBn97aDTMfH9mkO1ftwgmamfwzY9Aoeq2DIKv9bWQuhcGaXS8rNjV/y0jvKon/Pdbpb7Xvb6sC/bkeiQbbS0LJU/KU4znIMg2LiYwy/ltwAV8mE+dy7MW5boiOOR74cZjf++X3n7Asf+UAKRusBAHKQPSFJPPSoh8s6X65vJ28n+qMonoW5AuN+dakWx9NdeGIH1OX1OpmkjVIuKfkY9Cs98wEp9PHTiV0BW/aA8sUgQtUlWifiGM/UtmQ7r5V60y2b+jAWYBBvyw98wwE7YoIKEj3igH+ZHBAQPh/xoCDLP86vVoRQXKVVkeTeJk1dAhfN7e2CCwPeYMXFWiq0o/IfJliQTkQPRKPUiva3JsrNN6l/q7WmRD2u+S/hl+rAtpxhOjjLSBTwNefZdmawZdTbyXscPSbL3eEQ20jptWKd8lcWl+BDpIsxTmi7tjoCOZ4UTbKH/8l6ivB/5T7p+Mc6NuaXlfFsFYmKiZp9AgWvoLrymIcI8ZDK/27tZT/VQ9y0Ms5P16CM7hx0er5fIVFmOG0FmmLgGi9YlrYdDRXLSA9mPKRu73foGosd8swywEpstZ6kKZnqrnpmCT9DMjPX3ZqFaCV09Tm0qra4w+1qQGsienlInOa6WQuFHvsg5VYHbzIWt6o46NxLkppAF8nYaXAmb405EkF6UT/mbTgHsRRf7nbwv/EIHkC6FHeuJ5iaXwKNhobqSDiihiRB5Ekpgilqmc1LN1T+d3uMM9sck1wqtJOcKkwPxmGmkflQMddrW4bZ8eejTy0q/+NHblYwCn1+jxCHRfi4B33gT8Fxj8wJJ6zXARzdXBcMPDDJPvVYuYHXKToJrqUaatCsPzrvtHNNm7ierXQL6BW9hZWNxhh8T96QH3cR0ueXsp6DxpRCKjDm5ZBZCjTY93PsuMVOlEFz7Fl3fFuXUJCkT4scJga6N3K4wscNadisKTHwN7knjltcbxsoWvvcTHGlsHhgWro8vgY/9Cyt6Q50wZJZ++RnGcgc1vVUkQqTXtQbpT+rOoda8arsui6Mjg7hEou0zRmChH/ScW7dFX39ghCURznZuyzUxev4DikLkIGjsqHh1upIKqbE08tm+4MhgW94bXjm6jCkFb6pOo4p1DahmUAx3RGlRSe/tYxzrPPVgKASPSkAF+wgbnfEbD1QoXD5Vrs31GYIK8seJV63jxtKesrglnA80b1fJK8GhIHgyPvt1r4B7p6yR+0mFIYLIW3ahiiS5Dyq8z9EeWj0nDwqD59r4PRz3iRrgG2wsQqtgMTn+T8RHhherBaDRo49Pfp7dqx+hdNG+h+3Shd41JlyoM+4CKrY+M2AWceROV1ULHj+be3bmmhJegdH83wSQTua1lac9eZMXdUAKTHQXvTeJoYfL433GLL+W0FPH53anwam3qa2K1dGXDBvk0xX2LSkahOFxLauTUcJAp0AGKt2i+GJiXz9cwh4pcvlDJ1ZTfyI1TsBDRF25H57w2Qu6ZSOAjYv7JsXZR2bJN3ldtDr93IGyUxnNTqZI0WSIETfApfrh2RvAZoJC3c1w/gRmgBSIeUAP/BiWac3FfPizl9nMjuehxvu7nUjbHf4mFTrTl6OMBsu9jFW193CFRhM8cYNgXwhJmOa8jiQ16k6V/qo6yz5GaUDwNG7XpSTby6mq8vhR1TA1fmNlH6q0/v/KelLb1+M5bMz7Sp8W5kafj5wR1XgM0BFxOcvya6uwyForaCCmX4KWrOcgvWNxAx6Bm2USyk8aScYkPCNjqHBM2tVna1B40Txe9vK/J9PXOxS9VN8RnEk2sPhi4z/lgWWhwaZg2GACTNx0qleP/LAGyS3nC2n6pja4H4cydEycKMzTX+wN+lX+gSJ8+7Ex0PiU0SBoyZrnutChbxmmOS78JpwBfqJlvWiP+TLRHbQEtTcQ56aQrO11pfQNHnz4clmz/tgHdVpI16JGjhpawwh0w4CeXBS+sDwlPmK0SDRLmIp2Jxfpk654bCg0seKvD97MeOgOQr+4Q4upaVpGBRRqtMEiIrjsfxljEQOCzMTJtTykpFQ4/KoLZgTldE8i57kQvTXzpeUxZiHBU13kZsGfuojIr00S4fw53z28R0s/FU76jvrjVjhpCnTe12RgwdmkWlPA7wKwnXvyYTdmMiI3tjIkE1ExXnOI2/VCgJU1fhcyJq2MywcGMq2QI3w7DYgOoMJ+ZaOTj0BLPfSV0OQjGDq1Ysbch6IwcRQ4OrBT9nuFMWkvR5i3FSr0Lk16uC0JkcDp+3KeKIZXuhWwfc1pKqe57RTmZhuvcMtDwlc1jz0qJBuh6CdusSdbO6vW9NOoeb72o+kFp6C5mGydf8nDPnmWWdi1x9aFaMhGtZXgF6ObbAowGZqSPsOKCqL330lB/WESLDBUYQBjBNlk5Wm+6Kg//vhsf35RzZ6Eh2Ex5SzKW4MiNnQpueKrK2Dh8nkBfY5wkZz6CkP3PKMxgzwQxB1/QjLcOEurbWAAUYGRI0KGLjT4AEkiXwZ5UGrv08Ev8GXudj9B+jgC+kxBz0djlAb7sHed6zLLteESys4oWK3Af+FDEqIye4nX5rJ3FfObuq+j91bmvjHQMYtvnMLf03iP4QATdILQuZLqQESxoBvieAkXQSDSI+XEwXb7uyvpdKCnW/A2DjI8y93thYMrvuzz5HvVlYeXhT+488fjXfVIOCO5MFQJ9ZC1A3USKcsObBD2gWsY3MdvUVeVw7dpdwkud/YCIWXffLWJbEY/I5tvXSeKMr7nU2W7r4Yd8Wa9ImLPb9upnEserclnZ6Azzc+AGjp8To7a8vJe9pmTfxC3sODnHPvCuZ6arg2otbg6BdcL4zC6MximzwO3Da+Bn5NppgT8uKqZr1pFRMeEKnYVSljpJDv4Og0I4Ljz17mtDMvsofAm81FnfSo2QWGK+cVr3h+3ZDTjwwR20qZwhar1KQP/btSE8I2zMZJU6JOyMMdsJnrhsivpp3YmeY1cR241AIQCKFGEMWLEziZbUy5ulPgZ6fGRo7anbnIPyNwlfrAiYLzXEvscTQmSSV/Vb2rA4yirWpvAK0FbNGJHOPgfxBE+F9zNRn8Zn1fjWUwbGY9IZBBXT7/3M4AFemUxFCO321IVbcjDoZhOgasfi3r5lVr3urA1MVCiQBWuxrvs8ObzTA4oEMjOFP4Vs95zxIRzv+gjRB6k1qrxSBV4uyK14/xLfNC2aVaZOaJdADWIiuyNVHrinPYCf2rs2RHgmFGlfctnMGXkprYOJlSEph5Vc7FdxpL52hzU4OSZUdTduNoZACe7UBdg9TJW7f3jbKa9WOiexzK1huLUXRCOPEULfEbBWD2GJ+b0VAG9fDsfmuBTsQybUf4UU8nw6JEXtiDyKB8iWdxHTx2Fyz2dMEQ//UFoZmpFdjYxYOma3r1jl142scoUSh6lxn+J6AMQ+AEqXmz790y4kzsbpGL9ww6psTutdVhVmmNoGf+Ey69bpTyQlhU1X8B2c1tot5BCdyOvPEWD0crWIdRID7MdQJbbasVzHGynLST4WwKIvn5Z1qwrv56wXmg+c5dkmVEq+3QWAmTg4f2F6wzFGyWif2H1UPGGAHyPv62o6JFu0LfHyYBuQ+cUf+vvb4A5+nljYQBODHFcybObecOrlsAlkY7QW4mFK3nRGl3dzJvG89/RRHkj4M868X0eUkmKnZX654PNPZ+lss0Kjfe/5GxAckVi82lbkuilZmVdUraeZlY4M74p8PoEUILVBxR7/X8KEMb8T94GEaYKn8ezNrtKG0zTRNQs2W57Zk7G3DDsJfRsRFvQx7V9Yy7nnh7AsJpONzcZhErziwHawLAuIe66NQvcd7V85sEmkM+FVbOpxw6wyVPxMrMvIEKgWeHOv1El9tok1uVv/VfDLmil1W4lo5nXf8CmJYM0SjG75ym1zpbnj6jPubwJra08ReAoU9RbkR1Q0TxaO70e/ir5tiuWuZLzSDpHb3Ny3DnZ6xnoOb5nLqoO5E1O2fsIT5aMidloZlRixFav8FAFGBFavjE+nHdN02A4pfSitOCnc2xl7xlt+TVmzPB4v1PiexZjLuuvBJF5/8nXwiCY6i03SRaXcSmkQUkTxT5s6x3noOG36LuX5PiAbTvqpfNCUKk5MMkI2mOzUj8TiGG/VFT+jgkph6NuhBc4L2fAn8M8DpiB7CYuiMTweYpJ/PvwHnaMTAHHwbFeD4IkEhL0Wm8GeAKiqknNSiImr12SFYTXMYLXvFCIujL2tNeDxzrJE14UX7HAV8Avf3ocjTGkqMZy1jqZy+IKKp5b71C5Sv/Yy6Eh7NjDULN8la6sJOcrKomcbOEdAU2pXSGaiCIO7j4hE9nRRnlbNvf6rN66Wnk/YAczC690coA+g9TRfc8+b0GbYuH27uUF+OXuWyhe5s01sjjaS6NPmmyr8vqW8NflXrrE/GIIDL1ZkEMQXKS89UHlQ2uQBJotqGkQm9nejEWcd+aR6JFLYXqvv/WPKAIOzR5TkcbNqoeM/EaWd5b6oQKHIALiLnzzIWbz/3VKBC8ABG1x2j7PXdxDJPzHNSQBookpm319ZLMD81cZclkcxC03qY8FuWsWwJbZkf5LsHBwCplcZuqizYGSgeHwRSmTArARLj5i9IRX8DbeVLx7ldKysvLvki0KnWdZD4y1jkQK4bOz2SF3Q8dG09fsQzlbMVs8+yqDM6L925AMwL68uY+ktFGljbBq+iy5UX0owp9u+Yx6AhNxE1NkcOIj0L7DBbbJsFsKaH04maZ4+u4zdeMR7dp/o8wj0FYK3UJ6gPSuH5rinChYr4OrKWlcsezY6lIqPPINM/0D5ReAmQBS9Rojz4JBQPCsplWAsc0esWAc1UHfCUXKXYNIQvquW/4Y+1blTSmwAbqbsGuvbHCCGH5wwImc+LARZChPPwAM2wciZ3efh12g4zAT9WJx5JhgvA+ULQDCP/n0/+s4ANuqxHiGDe8AWpVQZzWK9OuB//Z7qHjwone/0KsKeohvyNCW0UvpO3r7LNwl/jrgk95759MvhhlJG6FTVF5F4bjd9e2E9RgzsD7wJr8UN+edTYqbStQBa5y1zJot2pmzuaQObofXAq9C7kvn0ddpL2U4rPcqTMuqUCPbMa+yzv/35uN1wVY+n0hsRtWHZk9wa590SvLftLyd+hOL4OqhHUhoaXLyvGSzEKA2aAY9RXFgKRfi9FNEweo8J3U3IUup0rk658298QUn41qQnTG97ODJtDBXEIDSCvAi/Xh9Tu7tb5EfxQ9ECxC5+SCGxo47s6zJ92U4eR0s8h4eouMjLoPiBMif3KGA5czCviTDPXAbS0dE917x7dKkwDSwdmucZOP1CxKp2AbteZOOrgnWfbLksFAi8hxUdqmPIGpx7zOnhUAwB//nh0lm7Oc2Bh3v1D0y5KCIyP+w1N6L66zUSpVCuNiVo5N0A1fBrWgOGN68Yt0fZ8JL+XMb31xaFZz+ABCnj7QlUUTXLCLkZZfDPnnP4jTXtR4UBGEDtkaUB5KDTJ00d1Rf65f8QBbiGIaKikdC2fuMZS6Isju4RLnyJ6fE0E+Z6LzgcJf4NQCClOEdgBeHzvRNuWfTEB+PCZuI6VX4rxkNuSSPy6f6GO5yIA3ITrA6UpqJPtHUVmKuqi0Gh2RfAeI8FW2uMKAPEAU88je2V3/ZannKtjcAg0TS68O/CUXlM0ArkKfa9yliL19O4asmpnZi69DTxadatXJP0ksoj+wWdG4oHZf2Q5smpOxNFkuDOeeV1YN/Kn+pSJBTWHzhUBrUVQJ3divDq6QWvGwjZjOUSVnhfgH3os6Td7sg+mK+2BGgudf467mkGF/lPTI7tZY38zvTvDxIL6tQEyQoK2fRwHFai0TttDGxT1lZ+qd+AqDxcA3WNvtfno20xzoWdbIJB7ZVbxsL01v8k/uvRAAwJ0LfAtcc4FvgTmirrsvNKwYGpEHL37AmJGxCUh74zGsG9CjXZhorey8BKLkad3mXaX8/sM/ILxkkOvIsrkt3pJSwbPPNt5WG2ZxjiAufoIHkXpxE6hoCk6hj1bA8TfTTXEJU28MONWbQ+mKQGquR2Ki61n9f2BIUw6W3g3DaT7E/rvVcKVZ2Iy9653hfR2D+ejst7bUxBaFWwqJiutXzraIIFPXlerBNqmHwWblTOzdqU8aStIZYJqzkw1Uyic9VEj763limJBVNbMUbtf81NXLyxCXu+fJjuLHECCiqRcu4PShzydTZ6+n5D9M7r6jGn1HL2wwXuESr1Ktm2iJ35WWZsEHuL0FLTkcMeyK8us1MRFhe5/NNEitspEkPG07x3eEJnxthHd7wpGmrFtJPbenHq1gE+o3XAGpkHXstNPz9e2l+5VkHeMFIrIDdIHfgR0ZFnrqLmOaCPwxWoV32tlTbkd5mA6qBRu+7jgfOgsJvdwqczpGP3NvEISHP3nb0C8FpUxSgf1hbXo0v7le/ab92r1N3zX7mIccdqmaiGpiLgD7tbqvESzQ+0SWyvIF762bOUKTPqIfWRj8G9bOVx8RM6cWsksIrB5X6EkkNuohKlEzUB/WnhKscxZnaCPz8xA0TLW4O46H0roVFESFMvd5BiFj7VZMjkxGzwswXynODHwzvfkST40IIsetOz8Vr9xq43bQRevklJCEGoHgtUpKlztstZPPq99HuuA4NclY2zZdYIglOk5Xee2nglHzMYqLzLebXHLvoPbI1XWdjvKZ+CIdYu/uB3LVBlVY0w9m7ARIMb3Jy8aWboPdEVCMcaLLUrrydy/rxz/efOJ0W/1opvIfpyc/HL9Zwq20Lvee1suVv2HxUydwDv+BHOTOhTS99XAQGPKvwi4H2v/CyWeqbDTDoKWjxBssOKFC+WNBKvMRiJvfT0iEpPGrt8vm2pSYlzZOQEGGa7RJd78z81FwohhJo6U2fRlnlgIumkT1a2Kgfq/gYJht4mbUtxbtnmCm3z62+78+2OHmMLli6PuWgQdARVsaCkXcdFkdqew9uef8l0PnRt72IEGJmZHJ/CTgrvOcFGTwZa1vd9ambTgD6bYr3Xz9VIHGAgBbvpkyyraOYC/IaI6FlwHjq65bEtJNPksBQu70xmJyEgmBk/oT2QfhCkr6qj/eQ/AKtuXyTs/nNZPXQdV8a1VXH21qD9WxKLymmET9si6xZM7YS/fLZag9/jybdDINDN5NXU0SwCaU1dKCVKPndlqSAMcUjvrVBLLYRWh/F5H85T7Rz3KhddzOLQNCwpiqJ+alFl4qSDm6kHTkQ2gU1v8KTLbXoBJIlwE7avcps9WK72BF9/he+BlaDIsKQhjC0oQpyyXT/0t4wqcNqpINy/lsY/iHYYTxqWnc4Fo2ctAQHX6VU6oVxXAh6vDruL7w/zbu9t7pt4i8aBU46/GEvpBL5bM1zIltWYQuqTbGhKCtY+sK6wII0A9bD9xNwqsdeCVvuCmjeCOfbSNKHKfCTF3aehSBMP9c5N6dvc+/s7cOhzZg9QuWH3na0s355PHARbAcFYr3q3QxGbDQnBV77JrfUo/7WQekqy1IUbW1W9V3f8LySjIkfSw0Poy7q6mDI60xxwnIMDCUFLES0qxskdViDqvl7zp3/LWtgbkNCBkNPkGQK99w1pleK+s3AzbQouGUMicaAtK7XizhebdAGn/ckolxGh6KyxsWEqHafIWA7l9wcoNm2WT650v0AUHYzunJpIUhh6KccrhmNYsJSvdxBjbR/BWXesNnNcabbQbw9fAvDBMo/MonISlv+gjMALXaM3d8Utlqnh3mZz/FrpqiHBTR8orquVPWDQFaMJOjnaCXuQizCrFoysFUxy/QowSXkeY5M7FFXU8cLiKz1DaY3HNlMjMIfetwa+EH3HZXZvH35pofVFY7XQSlUxAUvVZk7UgOVID6pSEztPHOe+nV6Wh+PLJPBNEpoOBMicRIZpsHkYQcUKAg54KS9wyiFMGKIcCcrztBI16xEtHpc0wmwhvWE8W0+PMU6heGVSCVKRpPl8B5CCINXab6+a3wIXAhkJQ3SdOwLmN7ri8gBLCAZBIvKIzeJV+Ry8PHD5MTbgiQCZ+5CAhUEun5sDc3wqJW01Vt4WiR5acl6tS2PsV96dC2TS6UVOW4nELUW1dNOgEAgnQ7pQb5kKwaIQ3TlwDmUrx/9LeDejJwUdOgjRN8dwW2Q0d08Xo8/Vv92fNjoCnVmd+orTKtrrpt0WU5+WFrkOBR0Q3R683i4i5Kh7uZ75ize6G0e8JAdbSNOPUR4EZP3/eoKm8Bonk63tIftLHnRpUG6zWvSAeJylbhr1cQ75c+fPhR7dIrqC2ofUVMtqCdVDGzeBBrsxWp3EnBBhB2C0GPJII1d+TbY6mZhcx7gRy1VnSj3ViIAyM/Ro/Vs8cneRJPEA8/Teo4Z05nOzlzoKj85lqCgL6uFO9jZtBE1F6y/2+uNvuYG6WzgSvuqQansedtqqW1uUPlE/CYFTv/akj3OyHPfcLTFBiKQCU3m03ebd7XRQPtUERz9Ly9WoBOBeciAE6LbPmdbZkQCG9gBsZwadO9EaMa2o0gHMp0tjXWJPjR72blybTMmKiBlEQBEVWKCp1x764m3Ka+SShOUZ16rthvfKALjRPKWWYHsqGd2IRPOqbwid9ckYX6citljM+BZzv6mGmS2RMOP92OwjVrTqevLzIntWxTaJ0ZagHid0b1X3pa8UGfT1CKOl4Y6l0gdK47oUIHEI4rCgy96x8BVMaCVS8akJ3Y2Y5d1yM0SHMzjE3LRYwMw+XrNSf0DY/u0ab3UMIV6raWTysa3vgomawtBnAm2zKEPloppB9bieUMnOmzusG8gdRY1OKkqhhBacHvAJ+e0Cw+caTDcNraX1X57tLF81Qs9PY1e75LW51Oj9Adl7vUX/WfQN8+IoSYcbtMgWTfdZaYoJQYNInnCT6Yyk6A+QLRMlvFm8of0WcD9xd6GxkNNwlCuTCyEVU632Ma530OyiwYNHdCiB2tAW7mdqa599nchJ9S3hv+UMnxYu+zBwcmQfyRbh0pon1YQhRMNjgUQG5NsmunqZPYc7ZdB77Tzjzm/MD2QzvDIv3GUgUPkIDdH5mcsa5VpmEOSjmGcaLhM93NyiZlqVOUQKZZLxlGaK/qTGnhK3ix7e7O6gl9yfLr0K/6fmlWbjg5eeLyQSuh6V9wpGV1nWwJ1yJ1gv+QK6VcbjVp5IIP0GJkFJw/SsMr5hWZu/SomyK7fAdEUF6N7KL8RCehpeuitfwf4QHOwdCdytFDuMn/9WQXU5KfYWsFrAEsrIPS6OyiLu3m5xlf2DAg6ntp5x+Tz8iwG1FufSoAJX+NFk/DB1wwDfmwij3dahNIR8aOt5fM1sRZHkLoV1PAbMfHz0iK2tx35Asl9lnwe326b0UUGFnt0mP691J+QHEanm7FfiLlqmfWDUmvP/vd+oe4wIVuguEdBJp36kFnUjdWasiWr8hPFHd3arI1kOSfNO/08aqwMRl1+2K7erKSpp6zMGwAwPPwLrRTowUUyDjSYnMXuueaUHLhIkPBrHYw5UB18cc2UNC5HI0+dEZtz4Qsj4Wy8jLraaD+CGYqsQ93ajDminYdrHYN0wB+famESXiOHLET38knEWFCUtbhha9bfHtAooO0DQGqtEKMHoXXHli0T34P6WeDdKAkKMIR6e8w/5GhHq/rx6qmBHO6hUNPKDr5FAP2qFBJDQFDef7WrHfqzwYVKyNnhBf0I1bqULcMp5tDdGafupM+faEjtW3QlCw3/sw6ez+DXq0PBfakXhEV2rWTTFjV6DbpQOD9ggoQPL8S6tDACX2NlAtmZDpokNtasg4t6ePKz0hDdv/pbUAWub6d8KkMZAiNnO6sKcOyvQpm34pSBWIFUZiiZpM5twBm1YEf7D7Pu62hhl8ucT7addv+x0960GwhVi4Sw0L/fjlHnjGkdk1RoSLIBHlEBNn0EkyVl/YmGoGmnCW3DvB3mOc85cSGo7+fHWd5CzulpC0Rs7zbZFexa2sUMn3zUxE9SiSl/sla2twTDvhoxxAei0WP1C1Y6DzSHgi7LXaZHs+mMxvvb4XeN6CoKzxmcVct9t0JS+bOoZt5EFPO9ilAVuehDAdR6tBJr2BpqqYsIx2xZk/4F+uaAZ20tBbeKnFcalVLUeMbn0Qb+moLWQPNeYPy0zSARdZGkfPdDqmksOMJUMR9Qouhhp8uUdHjsNzRGl/btF5+2EFiMKoWbwY12tnda/DTHXAcln0ZqslwT3rmMnvPAs0o3Eoh3lCbSyoFSfiubzhuxwXa5gqHSP+44waOtGWNtFohOKHf3UXs+l6DOaUM/9UL/bpNooVDoAqq2gdo1GUCl3xFt3SQCzwqCF5FRshHxbtM1BwsGgHLMMI5XWjbt88sxIpoop1CU4nOzVn3ByGRVVgwidgbGW9MVunUC3MApgIPaXa7KqllY7pLjbp5YXC0WeeM7hcdlM01qrMigDQctW97i5Ecxr3YFokzHBi9JGMnetnhTGAnNs4ITNrR5ROgqVsvdlNrTRQEqC5L1UutJqQg8H3rx9U2imMVQcI7kVjf2VKYCEkusrZ4c9Lzet/GSSmYZdDMQtIGSAq192OHbzyLq1HGOCYJm6mRd3bwpmwSdUAXFOydJXV07WnAYFQX6WZU8x+FWNiqdNscV7THU59uxMzasASYNfMMJVZnNhaL/KiUwAmCK5785FJI4CtgPY8ExR3sHo02Zc/XpAzHIZAflRGMmx8plrWrspSvhD7WsWX19NiN23hRl3wzYpdi2mYD9yeduN5dVR1BowH2zOng9FtpxGJvoP9SlQmfrLYG8p0KeBoWmAkzDHUyW0z4PjYLYD35N+YLnh0KZlhyA3bbyrnEEpMUPhrWbAx8T0i0sgfsi0Cq9gC+epTedUVXW5WDZL4WFXRhGVnMKkdvChiBtZad+hj6SwLqll4zgn6bIbo75q+bvkJw+k3hv5C/3jfOyaQ9z3Q1DU62CcsYfpCTQ6AcU+riEg32+rQTuuqi3MMxWYSm9hs4fvXzWabMFqyQymT3DyI/+5ipLhJkmTevx5DlmH+CzhWTGlaqO0KeILj1MdEXrOK1peTD8D3qyCmUbQnXve36wG+R085dIMcrDXqE/NWPaUqxqPSiTV7w2BDRkZNa3ZcTArpcg1WIMXnz1W0Yh0wAKpiUE3u4J9gdsHMAJ7/4T94kfvhVT0yQ/HZCIKPL0x+hEcBT9KPvsOOYFwrozha49HO8ujmgpLq4q3B7OWhb5wHWjEhCXLnCzgQsTwH/HOj8+e8gqnmLtZXF4+rv2maUV3tJ3CuZ6vrSlaJJyRwjC7mwdAtD635oWCM7S+13S05ql0djrKYTGCJmutD4SS8H3lSFLkjX2wbeOjfPKid7W9bMtdaITtPOeHLZAb8fTsFvkTZc+VMe1ZOLqp5S0EYH19R9G4YJKgRcrEKCHw+F3HnUOyS0gLztk3ylcsVTW7PkvX31GNF78OFyoex+MpPCZrkxZutsG655F9VbUJBCi25DiA8JOujAQNwnJ48DuJ4tPt9FBtEOCaS8LW0Fuc/2LwEyHLghqEIl/7bqnZO8wE41pUGk5uuawJ768Mu86FtcE+k0t26xuhwG5+hOyfHGXQx/+65VuBuU4fnCS8pCsKZYCh7CuA8dvpqX21nxg/dgRwrHj23nAv8xKrYLqA2qthQULJ/gxCmtgTadp/FU3jL2kNNEE+0v/Azu4f3ABHePRp4tb0ib/on5hSsAXkD4c0iAtGXrSkUCKc8tboJEx5FsaqlJdrsevj8Nfa5JPhx86ij7dgKYOiT0mIFFp3iGK7nsvv4F+xTAm/ewNiWhQv9s3jEWKuqblnIRTk4fTlDp7jXtce9RvXJo2IJgstISLP3brbPoxZETGOpXWiF9h3CeQRq5OqL2OTYLgIqofPgaVKhrqN0vymOEmDVJMpB0i0uvhx1Osn1psFLAuVZRGTCg74xoyioEFisbJwjS1gtGffkwCHbe2iv/RMrjAKyg9r4IvNHzRrc4Q7tYppe+uiR2ohP1teLMXExkuskVyzphaw679WnvJyCHSNF+QIqB1LXiv764VxmEZiCDV4XoTxdMOAFMDe70+XtwPNRTrdl1+0YA7xn9PxNRE1T0Xzp8xyMmnnk/1tVFYw0Ep7B8JaUny/+CpOm0E7PLVnqHEBrty51o/WecrINiUpFErSM3LlMvrxovpezno3kSQ+2ykVMR/omo31ZGOLLbO1BozZ3SZuT6DVYaq81o4f6xeb7QbBgWiTJKSg5fFq9JPK/ciYKY1dx0o/q2BGms7iTqXnA4GhKx17xbL+LU5HKPxHROc3y66fauirVvhm5PwJ2PL5ZbVaMzEil/GdKnhmelBh0f3OOtNZQ4eFS2M6d4KFs/QkWs1w63YAbzL0tggvGzPq4wPOj3KN2AVVtMqDl9v0FKZsmkZU+8IwA3hhNTqY6KNiTWsKHYo0JX6RfPgJZ36twktqJNKn3zjUAZk81xdRbaHcKd+Tb2HJMLKqw57lk47NM6cKgX9DgslFCf3l8HhW2IXLa/ldEqzqj0I946i68SotHM/ab9erXTPu3AggrCX1zN53W1G2HVPJmUdVk9Mvu/93cDo4YjVrz4Fepe31m/gmhUPOF1nYPR3FiFY88XqO4jSHEadmdrqwOrNrasOMN+gNbibE8g+0YE8yPjSepmyb3R3sTFDFvdsyk17vAaiSCPeE5JlFa4/4eLoWmDVXCYs8beI2bmb+D0IHf+pXd/J8G8wL67YFUa0Rn1ptnWzEowdHSF6snMvrY7srkgGB7IMcDuSYykOrRtdW3zcilju2Kw3gzfu0b4j1Yl0pqrBHiIEJwonQt0hJ4eNRRPwNXQ/K/ZLx21lBm0nQ21jBYyctqCnnkZr4WUvuZxxYwxgQZlAoeZNoDX42qLiOo368EzspL0iAFbF2VAZ23B1XgtwoYLC1fovELyg/4E97dOA/fWcju1jU9EfOstoImEeDYD3rjJlc3qhizLGpP96+2tERTVX7BwKK9QBROGhT4PaylW+5gl5hOyg/VFvFJQuMP1PPdDCzv5V0wQBmenyGH1CucBckYmlYSTVk+ck+UETFGz4lw3gYbjg08uCgO5CWLsVt+KK/pRu44mTCvOiW65bfeSJhtfvhPUTmy1mlWHo8z9t2q1quZKra1iKb8JK43BcP3JPnu8CM1PZjPWVd3RX9uVnJrFXZRvpAy0vr/F3eDRK7rlHULeYEQk7ZHN9Up2Zw74ukWSqD635pk+fKroGD4xCV5k0rxYpLHbPVPlyFWDTA00UaYntxTgi0wmFkD/Xg6HdrmDh9godBRfJjzDD67k1i7ADXTNoZf7Wr6VTYAoB1QYlg7mDRE8H1+no5wA3ntY3ThIyCl3xNR9S002+cnIiFcs3zqR5sMhiXNgoJsC9Gitv05Dt0IEiRdyB77png8r//CCmNvBk0dcOHd1zdmi8V4fiyxscMz3cs0Dr4qYy7Em7QNKS6GMPFGufstMFRwpzXLJQrTMc5ATE8k7LKgMt6Z2FGL2e5g0cyJj9N5g0GP0W7k/AUwz71QZt24GmgBGOs/8F4pNHLI6lYIhVjt/EFj7FO/OAetgbgYeJk8MfO/9NV48IltuubmDkl0nhgoiWYp4VIGxWZ4z/5YAzuMN9u+bFeg8KyB7YmTwPvci/J5HdY65nzItSEnepgqZZ42cce+id/3wFtD8WOToJbPZKoHqhNA9UFgnUZ5CceSY4k3GyaLUrmmHCV1aHApQDcK9PjKDGuWE1DbGG9lQol/wx0Wx6bFCsYtgQZ9quSCLNdy7UZvjS/Mw5t0tsIOJ2babRIqC6aE06qe//dCExM7FXCQHX169KqTOVFSdo5iaTqX7JLk7QuiXfsUxSskRbadbnRg8V72mAiDzX8p/xS3oEjCBTOtND0i1+VTEutQ41tVSxBiTDIlPAA9BCKKHEdjNILUPghT/WPDKVcn6oaDyPkM7JrMsY7LVBtcgziwBAGeyD/oXLGw/tmzBjPHMmw2TgOVzG/dMldPcCR8VyioFu+aSOmgXkyUJzGQyXoEpi/STEG7a17O62Gc4Ag2pX/iidmdKuLWUQp29Qy4ZuVXixC/Mhmnr/m7P2P0Vhkq8KWbtIv6Q2WN0BqIkqsZA1zJU3qts17GYBc/OSLkoOur1KELNVkpRJzQ7s5UF59JklKpbnWfIwXPLF4ZZSTpAIHSNPj2m0qbZkhUzJ1kp+qVigLSRTnBKa+sdy8lNPZV0yblbCs7NWdhtsvsIt56OxthuATLvx7hHRjOajHR6CAXXkbAuEaCgwG9NnjqVdFDAWWC81ZuYS6x2YSjB1fJqA1oAt+xOzd8eD+XtKNlV9Flz7PqjBDxaNgplDoBuCU7jmtdTDiOe/zP5bNiQ8ujwWBMcXwME2cTCR3UkMJeGS1MLl4fsXybZzQ89dj8XHe5kvLhVCnvvv+zTJYY1n6Kz/tr9lky4ozrXl6DJ2WGvFZ3dZobM6Azw65cbIC0k/UUm3tDyekA5812cbxcJ5fIZnjnPF83t2gzv18k5O1ktPRQ6+h4H2gNDecjYLVrwYZW0nESn+bi1q5wf93cEzpMSWKUxqi1rkCboH+NkWWNReRTmkUyK/snI/pnhsn2eDdlwwMfYjSY9ttOCIUnnla3O0Oih8zAJn7CM0SEuNLPX5JHqGHAkaVDkZq+PzS0+nZ+V0em8AF138PqJgDDHVidcdZbm+UfqenlXgwCQZaBFBlQWC3vFtKmSWxXTtq9qFwzKXM8OACca7T33PI6Pxb6l+yLvJ3X14hY+iJTsuQDnPv/tS36SjvhJwZPB0+1cGxmTILvqiw+Hy4Al+h1ktyUAUHjRM3IoiGjbUuiPmQtwMR60TLN1warwQRvM5eCaRAg77EPik0UDAj+ztixXzcJcxx6HTi8rQ1wDhHVBYCofaBIUkO0BQak01V0iBA8JCyGOVIEn99EZsNdCqZUxiEQPkgQqCoJKpKAyZBofvhVVf20Dpb/XWljVpsYI/6d4+KGkCIEY1rHayH56+yiVl5CbPelrLTS4woy1ruTNtXJ8URyBIE2V+IfHvuOGyQyNQa9DhqpGBsIGochV6FihGA45Jnpaf2FvvoBMsWj5pMcToVMSRzXLlBhCBQVkSxKWOd8q3ZyuSJWqBHO1kXVF+0a+TG3kcsTai21Jw9lSP2Rp4GJrX+9O/SF4lRmTwm3SwEx8fhTiUZTAs/Sga70W4MmoXl2WHOzXuufGn1TXDp2iQYWbtJ2n3Jup9xNsilJ/lJB5Ku561dendpunDsi06cHcve/pVeCLx9DbzxB2A/yZpZPVE0GtnRCjK6YDVzxfJrmWzG0crt5G4u7Mv3gBC8vzFE9kv+1o/MVzV9Wj1/epTf9HAuIzuoF0WlFipg/TFta7yZOGprg3cPjK6x7b9YkboJ6VXpUfqhOZwf92wW01hCG++71/WcnTDsun6lmDv4evOvqvFhiyHWSlzMWGKxOk6F/P3wtr3zi2dlTURBPwTV4EM16615SPedrDu1V6yGJNsZySqQeCZTQmQuIYc6POCVYtasHCNFcwnssOkJzF6Q4Z85B2b53RdZxtJueFsB+NM6SJhIwzR1P9BgvmhEaZNOn7Jx4k+FCfzB0ZEeWTKFXC6vY7UdNes+H2yAy5Pfnu9xqWNdYSUF+3WwBctyNkTt2rwIC9F108mcNrlH1oyTFKKMJssRUiZclBn8IbN9/XeCtsTvL/MRuycSo8rPD1g/O2CGwHpjrpZtpMsRZJua1SiStCD76O6Z+FLUCrGO4fC/HsrdPmuZvjbjB5C/1P0iEI6b7NynZUnGOo3p7790a/UKEyunMHq+zbmNSK4KZgDLBCkiq4R9S/L7itahzPI88BrB45DQWLzJ1MxNrx4WXmkJNqGbIpqdPjqiIm6h1mtNPBwgYyA/ewaV9wOJuuxR0IALM2H+bF3ff6UbldMy7v+9DU9hQ0zdhxwOevvJVYczk6u1wwVHMp3wc1WJI5iXStwvptsDAGNKARXvbhPajslt2kruxKBnxi1+54/+s772ZEuZO2uCnbsb8lqbv6XhVRwC7UMIggKQT/xmUGchp5Io8vtKekKn79quH8hJ3tltMcaHubAwvbQc3t1JimYggM60Iz9hK/rFIQXUSCoZEdhJ6aT5l28dez9qdcAadmSAGYevFcsfyj1Mg6rRTSElZSFS5diNGuZiOpdMv/PgwSpf08kiUF3mDDYC+zBvyIo8PYLsCQVNy+Bde4pL70kZdMq1S9urybDKxqNlKDzrhxZ4Ar+NxJo6u2/NxCbnwQK93l1q9+BQifhYb5Rc/t3MJvl719gMTPSuJ3nA/H4du4H+VOKCyWdgMO16OP7PQZTqz/nuYNsdg3vHwl+Qhj/1ToHKoPjFnAPWZlzh8f+8aDEEy4rC87AxPQ0pFGO4vVYnW4+2FxZkEl4EOgbDeequ8+WLvvZO3Og6ZO7MtYDkwNDKSyTmri9PfMNRYKTRR9zhlneZyVvVkDWifpQDZ0dp11jSQb6cv5tBaKNNTydJZQr7LDmdRzPqgPJ14D4m0Vn4Dko94TUk+Vtsu4InaG3ODKoCYQnVkRLabEksX0FwqrNTKTnfA4cg7hfbMWMQ72orq69s+W3YqbKoAhAaFoLuf4qWEeyRNrw4WAiqEJLA7oTk4XFfCGnodfFFWZL1+0084nLeAXV5uphO38D/U1gmKN31E3C70rRBn5JszHWu8kaQMZkJZaZLdjvshrTo0DXJQsB63vofRAlIAtbVqE0OCjNK/XHyy5JWGikMSLE/Fwk6kEvjtUfwzYiJU4Jo6/+mjoE1rkysMJV0brDdqZmv6XvJOoJO5+tGSKRXZBsSc8dyDcFET17oaNXkPfelgH1dfLxrrirkSNrJmTnbMzwaL5DT/vw8lXUtRDS4iawgmAg8+tsO/oVC83cwGmlVCoXHO1Fq2i2ZRD5Rg6wDbeusRgMnuXtwZKTa+F0QlygewWt09U9mqlhntOMlNRDZmN7XxV0XbDgzrb+U+MuFUQgWPw1F66cg6wPLpKF4yf3/gSFPaO6CV88DGHQkTK2a6JrTv1WEwS2TSzq9Qg4WRjsUdJjEjFnimw0/RwW4benPGKO4xEeX1g50QJ5iS8frmfzS/RCfosQi7+7e6QH7UcxqqmudE8dP/zKom3FrK+tCWcaLqjBQ46e1CfgCCT4CMSck3xA9HyyPQvaZ5w+3ikP4ebefP8VTA1K3t0JG0kD9UFDzO3Wb7JGxWALCkoRJs438Sz5NASvdcDhemMnOZw+uS7yxnIOwael3Kxwi9sKi9355vQzvb4GRQUo5lBbWfhKiaqvhKY/IOmvfR3uTTrM+ACf3DBAEDVMsnGifeeBxZWL4n/DTDkLMsT4DNuCUjU85iq6/dVzmawugtt+4xscp1ythWlx9h/aRJHlMnD5RfqUszA9ZIk9vWkjijb/WBVn1taEwyjYkcQ6RB77IKgHf/3yN2uNl4X3TrmyDhSrnrMj8qVtiDHnTCI1//2xbcTTY6XETx68wOyKegPmDtrnf1FtcfU4crdIaW5aAB92YcmDBAgUr95SpZ9O+lI5r46W+k6YzghKVAyV2IftFTHxtqrAtbxcKMx8/GvBX9dBs1Wxw9SOHuJx+AtUND1y3umcsyp9J3dBJ9i8tUV4SV6yrmKWjPeV1sov1JyteT2HGwd65510LxpcKHzLWP3EZk3x6sjn/MbYfG13xndIfc+Uv8vMSs5VilILt3/J/S0s5cx4L/3kPCMIZIsKApg7d6uO2SAUFXKG+UxHba0wPuF00vGbkcpEMjP9hnv4RguTPq6HLdqhU/iSioiQ3SzldP3l6r13Ey1P9uZCT6P7r26QLpUxmNHeWP5KGYfwXBKAL5a+abcF2qZUYT1Z+AwmItgOy8ENZba+gRsBQWL4RlpBrKHjL5qqcaM1u2UqUHiMm7mvBaZeaLX4cbeP+wpTuFnO6UU665Tv4wM4w6Vu1FiVPz8RAIjmbOI30rUU17pbYr0sUKKX9sdqs58tGoF/mw6hMMIGaqrHpQhnB5Qi7t7+qF5/qDY6RBYqUZUzhNJgh7smJ7mxjslHTXnwySRxa47uYvt2ywTJpBRuN+ToXvmZuQz+tFn184+iLMSwRPNhss9/XbkGfDOZChbC5qJlP5hNaBi2F8SCArYdqtDb7vRe70DPORp5ZxYXRr0sW8Hv5+w2kxmXL2jOdJNUUNrw8rt4+ccLU/UpmDdJzV4E2OIZ+KDGN8+acmcIAkdHDInUu/Wyro2K7xej5DZPdKtq02SNEOhTWnQjGVB0dR25/Xcx2DG0psgeZfY4lOpGYi0hOc8ab0uWnDT9pFwtKrwzhj6pwejHZGmm6/SdK7Cu6YORqrsCvlhXMDIdQyyPqxwqEmVKKwH8jw7YgEFgXr59DVpHNWJo12vCaw8SLCXdC5aLurXuTUdC/rkdzhTKCINq865ylgfQbQK0DFtCJdh5JrpmVM+A/PfqMNxbetMbit7PnIEJ5G8EOOjZ3i8Z4jDjGoQU/rtLpI+G1j+L0DSSGl6dnW+QYH3DcY4099lFy/81AjPdrS+ixTNJeRAR9LVfLvub3DXywtXH7D1TKavfJ+RYk8BbZB7bP/H4Bjim3zmEAtzUoib1LyIMYQdGIR/YKInsHLcs/uxN/t22XfO7atYMtwpWX/CzgF5dj2X2AomfhRmwWWMhIKWWYhl4/xTQ3onDyVr/qy9qQoAH4kE/KxRvgortBqF+zbQATX6TKTTtFf7oUfwzX1qMV74k18uslFaZrAwDv6zghrgSv2PnhejstNHz3dC2L5hjLQazkiigsAfb6ucQvXAUNiqlp9XVRPBoS+qbCLbf2hBDQs6JMWZ8O6/42tnj1qjI8WkH/7jt5WZl5qEu54P20y09K8KC0pBepHAuLJ/McxfCceSgIq0ptfW9GNSYnMk9VLthCrtNdzKawogQmIdbb2DD02BK3FWLj3gU3dmNcNgk0Mb7xwCILUxI9HTQYm3oNSrIZbNNRykuLHSDOUFRlN3El5nV2jNmd1yEdAVn3P04ZgWdPkgrnrNVzpgdqAVJE+Ah2Bu4tK6FkG5QUyP+KR3+XC2sCGeoBQ+pxe6dfYCrwXserpDY5KzDG4kLIIUjkxqopssC3wa5EFBOefcyVPORxWidmgDUPmN4dgBZpmodYc9setVpcQBvlxX6jNqUuF8UESsjqn9l3PItVnTTejyyDo98nGGZvvCQ8sVnjWuAFTFJ9seTjgoLvFUHIaFM9NFyghvFSpfOhuXVvl+r3ud4P/rCI4r8d1PopvPHT7VHbaGxZ0hbtB9PkQlXn2MlAkNM5OW/tdBBFzjMK2kk/EsAb+myM09Kq7RKx4aMLQkh5BOyMQaSqeB0/ZTcLYF8v80CNSZIGxK2n4ZcJc6+ovyvTGu1QWsBAc7Oy8c6TBC0PfKpEngcJA5LhSZURHKg/JX8L+jeQXZDEHLjLnz5r1B2t+yoWpSC3C0e8yfBihzRp6O5p3yqzqoZvegs6x/g2wGwhsapbe9Jj1O8pmou/mDxpWe+7Bv+/R7IIcFxwsZqldQ4UHVwFaQwXiCE5GrIemEq6kPh+Qp03cPuJHCNfvJQ6XH6KDU5SOXbKftlucfmzy0lbQDmYlnqI+mwXAo23aIu7nWFW4axRO8ZZZgt3lrgqkjPWjwv0Nyzhnz6E6aZ2vw/14csp2g5BDEJop042vZYo8gT2FgSSkpsfg0znSmDIYp8Nbmzh2if2ABp9fZUi4K3zVNCbpOZCnHmmoAKYi0MZHFZmVPAZlXs4ciqgYZIp1Sl/jGtRQeituYpCyjLQFQ/5pGGr6lDrmEOoHEiSQsRrUrvtfkKbMe3poxteKWrK75jMzzaT+EBLKGB6WGi26Yui2xGeHipoDXAAYS5bhEbFwoa8RQ5XmnTWBuH3WM+yJ4AcOhffJjpsDpvnjQiCUYP3lA1yapIZJ7HcdctvGPeVjZmmVYtaSCdhMkmqjieRqFeRFGVhMFq5m9TSCTV24QZiA911YwtITEkwgRzcCYJMuVuZlg6Swmxw2OASU6idyxF+Mw/V5ycgx1rbi8JaQhqOUS3nqOzbZ80RBhA/0qDUm+YfSv4SI12eVTpNMCZC9GQFLPlBd0wu2ywM3FvXLCFpWn3R53onN9pPOdXjgKfExh9FNylmG/BGcmW0E1BZINyg8ggNrAvCWrbsNT+2N9zyN5jbZyhycu+UhKpbU/Yke35Fs8wywc1XFvI8hLLMPOl5m0uqZUhFuzgjnAB4qphbWA3SFgltZr88WBsQs5xcsBIRQf1iO8xstZ8O+ZAjgP5OOwg27BYQSDXCYEWcOiStk1nH6h8i1Prw5rqVqI6QaaBT1v8d5e5bbYjaktgrY5nDguQKhh49L3Zoz+nikqRJSCxh1CPSNzTEA9OfUaxRGb/gHLx067STcAY8tDQV1ZQvKQ9wfcEET6ennSMs1c7dLlxs4INUm7HLxkdOmQi9s0vXf5O+sIsBrd7V/54asva4Syayet9bnj3n6ka6euVKou4CGxyp/kYtkm/3YSzZEPe36GbvrHed/+hrbRlOo8MuDeWGIXNRvw7Qa0Kl4AYv2GORDKmlioyNLcPk6xmojXsaUCjgtMR0qd4byEkIdfY7WlV7TYy8L1Uk5s6h1o0hBFPv+Pj/i4DHdeWBoF7qqWtTSYR5OJt6WUbM6G8BZ93b9u2qziTyG6SxLBjaX3sMFonwBUt5ZJDA3q6T0xCoIV6lCSUhVrqQtS8SiRyNqvr4PuYUsRKP6N0CYsJqvDDpe3AUiLo4rsvfAefTSmWlUQQf9JLbXgMN9P3QHjCVnOrPthhCKo0Az+HjaSex9q7F20bVdWEdLsrvqFIj7iD7M2OKR6BnwbGBuRchRXNakR8tJGzmimP7wAzn+uixAaQFO1Vlo2rBwXYmpbK+Vmux3SUu8YHoUqdPOsbn5XFVCT/5pdL9xWUW75OcPUM5queTH0i5DNyKd4VAhvGfMxdZY9SGmv+c5cwFe36PhfXxr9wFCnBjr1nYBb0hIxii8506zHzHk5kq+gQYG5UMafG0vKjcTfCln9O2dymjirCiVAUhWpcswOWzZiatLyBsMcRyIWm5c4N9cIBovu3lc0rJq+CZaT1Try2YZieNxKv8Wmdhv1aPgOULMpX6sO/z9E/8tQI8ExEffIgADzVklMZLkA/of+ydUPX3/auD1yn1IWo7tgNp/9Dk0nKwt+nV+kMTX+JDT+TSaipv3XkcgTi4DZlKmfEhJ61MjBs7CJhdtLX+8Xdna1kZyA3nXtuGjd3MYzNOql2dAwsj4PV/wz5ogii1p6gV/e1xSZ0+2jAAasWqYefH0L5czB5PQHpCjy3FIS3kC52f9YVFBclRvx1btWbZpMC3I8xvAjxf7OR8VzS3kOtJEjdxYJTS2nvtvLNfEgj1tVOov7ffUX6ZDD4gSi3ZJTFu2EB0e77yWHhOPE304uAyUHaW7NHVWXABhVeqQGi0hjw08/TrEOUyCtZla1qn46yjx9DLeA25LHvLILxfbMYZ5WH/XHIIHfUMmsSwugJZH9b3FpQ8Dpog9Zi+zZkkQzRDVhJPz4FD2tsKWWelFs+ZJfvjXQ9WBIpC2yT6dd1uSvLVyM4IsAKrRw+QL4tAOM8tW3dQAfet5/eRvOPtvYZMDPlpTR6JWd4anZD2aYf2rCIGYVG4po+WmwyE8vuN48B6jEWmbxtHIKp50B0KOj0doRj4YWJAsV52Yj70K+H1utXbj74hsWFS87WCYtdA0lduzg7AAGWyJLb5tNCGW+LqZpPlfINdU8O19+vZO4TIUEtl0wWm20sK24NHEEZxTL19MSqHEojgYhtcts7BIeL0ABBrSfTqB66LlO5pWGpJ4BjUxIzCBOfvxi9qewVlnfj6/82PfZvpx1KP/zCuhBVW/KR4hWpiYWUGpX1RZ8SaZDmEvEsFWF4H47jI9WvX4+t2jeW4Q87FpZThbocSXjm1qfREV79qQNQDSpMJ9jwzGCBMRvWgL9tsdflbbtP+BNBYORHOSZFIQJB3pqOj9+1Mazv0glBr9mC5p1CjAeLQllMeqGkswqZzSUC9HRhyQ/ti2+a4FccKkE3M67i2gbjKcTXFbTUnt7Rf5QJ8I9/uxG+Sh92D9hKBEMXsTe0qRbtcUW9cdammfYiPoeBrkTQbBp+onH+B3Mdr4UIXb9RXM5MnIX5UsEEbEoAQ4PticKvyWEc1gWL1fpqogbKlg3pDBnxQoYTgjYR3VQyZvQu2XRNS3VROA8cp4SfwU1P5zMz9Ip+9Fc4OAn+nYbQQzEjFMqX8C7qS9cyA3UUkQY1uyVeppmzPivrczsR7c9D1w0oacb40QKFf9rDsqx3mGrzmgw4KJpS+MgVIHDdL+O2tf8GvGoe+0tz6ja2Ep1pNBlh4uuVJemTMaJnpiu6TloT/hFcrxAE8xZSMs+BL/UHRA/lz+7bK7y854OrSdOTfUKz3l9mZaku/1D2oyPv3bbngmQ0/Mcd6bwHuOVnvFn87QfDWKt4CdMM77QAxhdrneI2+i4PRlJJJqS8JY4MeM0MAjpkz9V2kqIdEQeqJ8C5pC2KhLBy3CnlzuGtoJshHJh+0G/sXTHJTHAxy26WRVPTolEMA3ATS5IKziWSW32gcjUnpd3Oq6PUFga/vasXc2VwYqYSqENELIr1BKG6f5xNGDCKqiOI1wxqEaBWm5ttp0L0ofxZJN/DdRaO6KgxYk5rTUfdOhxj6I+bv8izqgp8fr8hzpRCOS1EswAewyQsLkYHfASwnBiy9XchLsp5MBuxjEpbGyvj0X2T/QOvmXQD4de8PINN0tW0APGf5ztj1EfRrDbYbj5URUh2s/SXO7CsSAf5k5NEAwnxUuqkufVOxvy62+ehmfem/bJkbfwjtJzQ3OK2V6uPad+Cee5Aney+dgjSVAHqNtPDEx5lnbm3SXLKPJCqesXCWVMHyQRtB2NFSoF+nl9UF6Ikmb+RURAY8zZKKCprEby6BejcOcVnqNWza0hLUi4/KBwZCMraWfS2uXcJ1OE3OmceuqQNkiy8048VaBoDoP56uZwlgyYaBdRaE/qqMEO2DaiKSNblwUJMqvrrw/wa0XuUFiwL6i8cRUnjaerbU4a7O1Ncp+tBW7V9ZJRlXWX5IItrVGZvzyoXIa1EpvkGASLtAGdEP94fd9xZvTToXZAooT2mW9t+gLfqumC2C6JR8JB4i9DbHQGkvbdbutH5spM5EnDYPnWvf2JdiPMVF9i/lAAqdOK8sXVlqMsRTebrcBZ3vAM7AAUZzvrHFrCXwRXUOKFvhyylefeYj07Dpva/gCxIkdXnrljZIj1yi8ugvSRLS975xc3qzK2Fz9fdlaLsfC/BD+XZMg2igeFMmLdf/hDP33FRUZ6NzDNAVapKP7nDnI/xrcot2BbeyVdr4NuBx2rjFmJ6B2a1JhYclraMubF7dQ3MQbU20UqwWzK7kcAOZ8aMVbiBUNWXILKJqoO9+XHiXpOaeovl/P8A1owaWg7UAsHeAoqeFXSXpBSQ2TKUetgtliu6VtHl4qeUqaHhupKgi1qcY+WKExr9qpqYnFYcWqufCOuVey/8xtYeoC+ZjjvfsCTasMpR4ywZAP1gwRNJnYodp9zpiZk0mDjFkOribFX05ObGUWMDe3FlQ6lDZemjgglnZJAd8Kirw556mJRZZs9y8Q2gsm2ad+xScQKaGVx+lt2Zz27fdXR6rUa3Gv3QweQJCSEpmpcA9nCDYwv1/IyvdGk68Qlg1YSf7uV9vAvPmJ+eNuEDY/rXXoUaC02zNGUIMxs/k/hlNePe55hGBUzakcxcY+p06SYEHICvcxjoEnDPoi316hCckwWLu7buygJSX470fZfNYxBWPVfYez9HSu6lXpPnil8hTx+mGqzYkWQFF8ANwkyS8WeWGbz8NMFWQEfQlUhU9lUYa0wYm8bNdV5S4ma0eDceTkCj7YNz9d1knx0Z8QmcRCE76OrwFKsMrfa0kretbIgwRgrOyYxT0FWEQxNCdecbYng9RrVKpuBmwvyk7w/Y2KQ/GSELaogJjdh3aoNkiFjI0FZ2jwtqwMVcabO4z7mTskZCm3tNFgrw/A+cntdXj0ONq4xwmUHENal/eApquhYrw0ZeLsTkIqwBsliYAZ8ATZkfDd8OuIBdrIipGMZDsTBOe0sga2YlyryFw6Ck8YoNZIjIWRmqWPmva+o55HPWFqvdp6k2wy03Q+ZQk2zgioIBQ6O6gSg2mvYHq8mLAV0xMoLO94i9goNdUGtTBsH0SD/egiYc+1ATcsJVuqO2lILmdW09LYjGZG9xkrSb/glUvow5IVwMXSt24Ov1BF0Li2jatqwj0BSttQYULTFwT30rz2+NVyJjuq4rL/Rvsn8YEGySi3a2WfgXkZlwpFfDWgKgV48OwyqbRhoXc+Xwkxxanv9nAu34SktrBX4rw9C2FVwwGl4s/wWGdOINdaC4yf1lG4V5Q0XSnyp6WmOFlcRKLsKCVV+p83PgH3dlWK8pP0Br0+PpSJAHSmSqIdPCh9IDoI0ZceqMIUBE+apio96KuXLzTq16uh4yRJ/h2wzHrJTgkUhsAlmOp10KRK9JkeNUfNtqtC27otx5lZYHMGgWfP1zuBdUIFVgdxv6jiY63knLnhfWPGaRD+4mxJP3wyGERo19z1D4bdVoMeJmzjzv4TLAAxP+Z+9+l7w3w1tUcuXIW2jeRq3gurXgbR9a7OCE1qdXmmpHpx23p0wlySYkH71tYao/SXomkaYV5lLnTWvlpL20N5g6KUs/IxtorLZpNFikhGuvQaIH312k59Sps+kQ1vnzakqRBBmKtnscfRszkX230yDoajTJoAXTqiuTonBT5ZjU9x13gyyEhvGTZzaz2jU6Bv1Gt0kF5T8OpIDbcpkkIeUvsjOXIj2HqJ9q4QpdWxFi9VGATUivnLsH3J4+SkfuhuEk+38VV3JwprUgY2DnqNCm4zvI1PB10/TTGNMmPwpB5s3fbe07GaZw7ZgXGTr9cKVrvlFHA7sl0TVppl02hUcuxkTW5bfpNVeoDjjGvjwEponbsKg16dwltHmNrUUg3LMR4v4tpLwi11m8J54sVEbuqJd7Gz9GCrkNXd/L7O5VUPZ2j6aXSyDY+upZNlsZtkSFS5k6X+fRLSj06nkspC9s2qzahcvuj/Cr+fW/k4DkHW8LuF6dYubzwIhgfGQh9Hwn/aCVZgTM7Vwmp7jLIH2xVyxSlPFrgBjfPBmWPOUy549om5ZcVUfeGsEGMFQ0yFJ0ZQUoMf9Lucaw6XaCRNlCnvsGcUP1KuVZP2cdD5mWhgThiGZGx67UKjbh3SBeeMIuH5jfBscjjph9gm06byOHuT88TaEl2KA7yjrzyyt0PoZQcL/s3He6XHm2lc1DXyzB+Bnjo9ESUTWNytKo/yfVZt2PvBd+bhfTRdQce3f38zkUtw4Fujd9My0ZdYllBlmcV6nSDDlb+emcWaED3CM8s7dQZlMSkkDjEqjDtPYEHYsokhmFJlpbGv8Z4VwOVPyRWZGrmABfjbx3UUeNXd+JS2L4myazRDnAqBhPkS3UcQ/wi5LRrd0N/kj3pnmree7XYB7OmmdW3FlyuhaapGizbc9qEs2c/jsHNlIcZ6TXQs3AgkG7RZwSoh1Qo01O54rXWvJ4Ia6LsfM5+eOqDh49l8E+mNy1yLie9H8FDzPGklsDV4WbasS7fkjzIZ5kT6RrMOHQQOAjSZAR2J26bzn2wn/YuKcl6Waq9AtYLvF9/6zuzdPZRk/6+AF4iaomVFlYUFkdDCTEJ1dl7SNvCqrHlLwsSApQhNBNPNVJWzjDrFxfLy2YJcJXn8Ia8pQz4roDNu3YhO8M4QZTdmgShnbSgWbS9ucJ/fQ/j1Fc42wfh4bYa33kQ9zyWY/BpPJrpq4PwHCkNmFNRQWuLNadEQY3uovvNpzIUP+HWGtisVUBhHXmF5Bmw3hlu9MCQ9vYLgCiYFn32e/Pb2leLusaUaGI3vE7gXWWqF5qJ+nAguPdURUmPsXPYsPBMJzBAhEM2UtU6Hd7K9o4cuhWcllofR7Wj4kxY6JBsRGHSBfN+EXMC9k82IGVeHiGIS8QRCRFvsMjyDpx5MQpRU6Rx/rD33JPfgVoWtZj4QpWJeh2VluK3uwxDUQa3ggvGvTi+pahvlZlNPeMNrwGGj6IV9mOSMDQGepD6K46KR3tObPtwS0LZpJ/1+IqoxluYCrbDU9GHYh055d4xjWo1m72f383D4WphnQcgjQdHcv4dqRN7toMIGvS25TbFDd6FXRPmWrHOjhY/ItvFu2dLqwSf7TMNtU4bymK3THJugvV+JIRfLOf/QQbOReG6zKqTHx1eXyPek45xEtof3P9SxZkYMKsjTuS0plZuPzfk0GhM4sY2wgded59doHndywS25nSayzQTGRH75QkjO9dqSQM9zXU91Yo4QBUG1REa9KpJF5kiXFJXCdiqArIx6cK08a+774cTAqBWJEq+NN29zRVpClpWAXsuYmB0PlKu5Cl0Wxp4jBHqV5it1E14ERskLLI0IFn/NHoHcB61Wt17hxkvumrI/hWFcrqtFpkaw2aAySDY/UV5+DgpdeAJMfPsq1n+5tALMOilnn4K/PCLsr2ylgQ4GBZb6XbvFn0zZU+JhM8mDF5DDwu7TP5qq57/Qz5jppaTUqzT8OseXiWcAjDRff1mpJiVHYf9/rFCM6dD99jekbEkSrIiCYrSGm2INHc7RTaYbgJxZzZ9+W2PyIWFBhcRGKODs5Tt4txMSNZCF39i2yKuptB0lmi/x/Hvr9GJusHAgsZHD0Nfd6tr0fwvXQc92ejkz0+O7yIz+1SJreLP+/4+X28hl4OlhcqDf3JSXpob1jeIV/uVZFhxOjRfJZuFbhHeVISIo6cITddvarJ0lVrjRHE+jW2FJDElrcHl732+87/tYjhmFJctwA+axx3SufOAyNdAyAFU8+OknS8gjJqB5CcObYtQUwVQZFjFMBooSgmSzhuyR+WO0Yx7JC6tq1r8Y1mwyybDTPuzn9w4/nec04fMYGJyoOX5KQp23Z25nLnzhb1Jt5TDWTL8DZAik98NQ5AyBCqU/1jZHXDAvYoWSwHoXLghANXSEUxdYnHD4MuFQHNS5exkNC1Qgd5rauhC4A7KB6S7tdzGfMEtI9ien7neN0fAurtbRQW9LiilVRnkb64QFt6hEgkZGq5tuvBne/eHg9DWUlSZBiEhXNmp+Pqh0IKFjt9PX8ALBeeck7VQOUcimRWOHVsDshBmlAr+LaGuqPxgW/LaeS0N7DtpgastpN4vQQLmWbV1MqA7YqhLIU2vrtAnEDiARD2halmlVzUqeyEtfkWzGvHz0THGhWgc3Pi0tL+XKGCwb6/ysO9GvLOq2WT3wOgPp0qS54ha88AjhEIWxulol8iIZwY3Jw657B9J3TSZPQAyKqm+JWLGvoswsuVoqD6WP699OuaKrvGbyazo3yLDVDQ4kslRZz4/DlF4tByeIvPlw9T+WnnR4UDcI7P3LHCeXhiJkutun0hR/Fyni5bPLQAv5PBPonDutLupF/l1Za5SDiMWWmshDWxTEtCZQO8H/IyUCHXgOmr7Qn/MDP+mr9oRlCXITtdC4ooL+Tfl7RuY2GrkW6FtHwi4FfiJk+X0TQKXSormM/tpoDjv16UQv5KPHMhpeOCKuplU5ykXm937CVUHthlRffKIiinT9fNN2v/CC/s9DrivmtdEIWSq9fkRsqedSv0ge+MHQrDlBvn4VLS7+z71J1H5I233109e0izVe5JSOF9ffDNjR3rTQ8+qaVFZMeTRjSAvor1mo6eesE0vgEivAjShn4Ow0FOZJN25opSwjGecPX+UPKiex7p+GugLJFMh3A51Jrqe5gkPGYxkaIchNMxbY1PRPOfY95bkROKAKN8O5aRLqK2nrp3/pYRLmY0YZXc+O28PEd8uVw6VhJfgwMKwYl9cN++b0yf1YunhJ4XbhE4itJSLxMFBl9BEkFUNTvJ64qFo2Tg5Syhs630jIpOg5EedNHAD+LlEuKtj7uu+4O+VLrrnBkVT8uxXV8bqEZFOfKrxUOUfGTl/Z3eeIqjpS2rExkLNZm3zzA62XUWKC9tNu9Ac+33M4lF/5Gfze1fiGf7hI6L5IJQ5IPaH9/v1ChvDGV/DLeiP7p7bCd6TihPbnNjnBTE4gcFDCjuW2GrXep5RK08P2pi7wWlT/LnwWSYO7hXxUw2/lkVXUoRcshcWjc9F9edbnY1eO2wq7uoGjijld5ut+84YA6VFRp3HocdXrfAJpdkfZo99NmbD0hvGe22gUk/xFNQWgd76q+FMJYCyQgE/3Cl33cJvbbtzyTR3jNvWEPrS2+UChoLIUlswsffAN9b+IiW2RHFfI4D47ehzlEzy59zjKZ0QUqejBg0G/+j8Yo6BVpuj33eJzXQQo8TAVsxOVmcGZPMdf/yAs8DyPZ75BJceLTqy0xsjhk+68LozFyxBlHahsshYfPYzQrRR0ec1uA8n/o7YUcuVkbulmtIM4EWfAyYQ/E53roei0YmwSsRZk4iOPMDsOpAUqMpu1xfi1ruJs+0aGIaEXmvpWf7PGDhxYcj9LzcgfDuE/W+5sDuEV5+hzqdBMjGptC2sal1JJaamcNAPDIRKehc+GO9v0rXRkPP8emUx/L7n7D10Zj5RLlI6c39UffxHcAhYeMx9T2/cwbncDZsvBjZI3zI54zZ6qj4lAVFgaxvdvbsZLJ7N3KCyOaJX49PLttFyViSqV+Kp+AIMTD9l0DXwv7SJ+FfTnI09GGWvsTrzzjhZkd7F3BA0HWFdJQso68jp2YmHic8V7moC3kMzNosjwSXUJnYxx3/OY8j7zqu8WrEEHyfW8YtINxaD04Hjqun4pfo+lJtXi+P/PHyxnNoWmmmmsO3IznHFB58sC19E+MDE6Jo2/Bns6hihAHwm/uBh2jxseKneVhF/w79p2hF+fpsEnab0XzRVAWEQPUqcuCjoq45gz/PCFYPJcYInEFBLTANTpftnlNm+13vrl0aUmeKc4n4uC/FcXtERbV/1t0r2nLaTozobY6zGqLH2z2jR+ULBJNM08otNaXpr8AgFGp2dtufIGMPRzwq5jHnc8xvQYmsZtvQd2KlbI2c2KWHaaSXUlESRVbeKmt5tID/BDIaWn4j3FNiJ5Kt/JGEpEU9zZfWxw1eS5LW4PSzSMrTsJbzkZdw8qBi0y+t1Qz0J2nm4L76D1944VPo1QL8NJANkPRlEJiwh12zzbny1eyKAnqIY4aIK58ErkROZXsbMEAA49Y9fCHo7w9eY2oxO1ShbIJRE0eRnVS+S/w1JM+HTF1cnrq4NDbizEjrGcSn8Rc2jOSZrLtv66u7LZGSqT3/Zf6kKAw96K9r22r3JXdFYhgPp4zl+W+JWiqcUXrIXMHJSeHqVAYktmp9dO9i4FctDnSCqUsO7OgPzFP6+r7LrUjIML0zwfZdc1a07Gxq0pNF18N/Z07NMi1V4RsPvpm0JPp+OetycdWXL8EmDlYbkZmsz3fS8/PyhuoPVZjE7D8tgToMsZbPHdvM30m3Wz3vIKXK+r3dmVyN0wzS0TKKWyTyiK9rS0r7dMGEFLnlPaj14RSBzCGIEmxHZ5+fMA5be1eCNMKsAIa//pXjG3lp+FcZCZBXDEGaURdRJYF3FBTQ8DoimoreQTsTghCE/g44/AWQvh+KYtr7dFFPROIhArSUYC7oDzplyBwl0CnaFRpb8NEcy9K+Gcn24eDzBylE0kHhFdfnn2HNgZlbgDhyrmI7/pQFHyxzOzucDCkHtaGuAHC4fST2Bh08h1u0NGq39CyL5AvTSh69to3FcJZRakZBIVR08GGNG8FAtPEHMIr0siDIZvHjH1O3k85Kc6J2JPfPvvkKXKbYsTroU7M6Wled2qW2IXXlF8Z087CMDWjRdIRpM9lKgBuODFoOb257ti8Ts/Bd621zqMo9bm7ec9WTUkyLFLIKIrasuCHeVmeo7wbCf1zMDL+rGhODkqUp4G8ivJtILw/S1nz4iu+zx+ICZAvjWJcC4Kqnxo4pVHNIp9X7T+Simuq4nR3K3KRxaGaSJc7KeKpNCrYP19LhTmg6hclMDiNa4kApsU3oh3E9m04G+9pllDSofK+7ZBrD0xTolXI5TzCcs+VAyotK4cnaHmmVgvI1+9rEljGk9wCYTKGyX4/6BvXHU0HqnHCpws2WTPYxf09hZSkcWFq0b2KCCR/4uaLCh4vHj9MVOZJT8WD2oQC8oMx/K9je8Xg4EipS2WDOva8lo5tw4j47zFAYvszV9gtZqCTXmMGDjiQN3cPD449cl8cN20MaCSrQLYVj55LniAFDm/ysoME754YsRU+mwQLilQNpmRgzPIPoXbHnxKV3peYD5bK7t9RFyLOwQruafk44JYlvuQhFXGb9j81+Dkwi1wikz8sqOVOz288XNSgblLBD5VXAXQp5Y2Xc3Ue7BwM17FD09kmxz3TUayph+1OQdO+2fQPOSTjmNGt7NBdUCOEILCw10iFWFyMzdy0wqpYiO+MBYNiD0lJFASzrFbzudd9s+2hTpnJPbij5a/bfmaquO5yQ8XMoZNTpkHrVZLUsz+C+dS5krDRsxisQ7JOCAX+5LsUV3s8Qo2ZQB7ERVK356CrNE6BIAKW1exk2rymdsa4YoVT92PTAnGhvV0dYML5NLy7yLxSm8XREY3YM2dY2MR4yONUQNUreDrf0YGi8u5Q7mLEjORye5YjGpBX7qDzrLqzV3SF+s+e7h4V72HWgFpt5ROtmRlIlps9RyfA78K9oCNWoKATK5bjATVdzSpHTKy0djr24tr2Z8uXo7riw36DYtiXlnzs+w/By8PcaXjb3noRNpDG9jc4qs/MBq7DjLU9mruRD2yrWlmPY/TIPddrh7yia49KmGM1ZiTNaeIpyfDUzRdu0IgzMmXJtbE6BebO1gDjdzhdKbyXnTVcjSNMM+cCXoHQOa+YHTM5F/DlE2apGuWdeC0cPTO76iaYkQyXUPbrg1k7pRzeWzT3HGDWV/1ksoPvHlU4ontAHqSMDWc99EPd6PDNafe7WtVrchdLzDRJVAMGcAFd+c/zcatnhjvm/E0mUU9rlVnO3hu7jj2wZvEITXJ/Kt024p/AjIoIByEdpvK22XmCffWu5uTi0kUpmmalrjo4yZ7NdN/xmZiKcB8DJAIplr8ZnC4o/qDRkDbyMiRN47PXWWFe1jNrJTerrGHfyT4TvnIDA+DMGfpJO9olcvu9jJhu4rauIwPMCv2DwL3kWN1Rp37KeLHnleVG7sHG4tW2nOLZ81mjx9ok0GGHQtB1dlwD5IZYe3Fx0krVTkZI9SO4NKdAZNeb++XkCs7LpJNDBI58uzyBG10xMB1gzrxNEOCHl4RJigrMU4Dqsy+9fQ4Traf5NNsxN9loFVQMwUINLELErAlbugY/6S1jUXoZhF1z4SWEbEaYpdXMtIJ1KUSz4ubrFW1zi+ZLnwVJ7h+ssXI43Z2E8wSiXwKyunf6itk9mnCsPa03+ui8KB2cb5uGrXK9FES92FuaLx62EOyWXxbO30JLkE2FKB5WDOhcR5Ud04ygxIL6kkJ6DGYxHGWr9mJN/Wz0wzvzuBcrmg4IZyHQQzcl3+xd2EIs9wwl3NQCAYvLpNuDJKPCI2Z8fPLhHfiBXL9W7nbD3D23/VE2MRN8x0nd2iQ4Zq2CYg24dhtdqnivoGMikwJ7mk2YlvZTC0/nVlV1LzBRDDUuPt7bReAjhm2WF7V2fe1LkhsrjGqi9BOFlP/2fB6gK87SJNThrPDFn3vgLzzBuNhQ+PZeh7yD8OrJ5gwpxCnTyono2xFZv4zddiRLFS4FDox8V2p/qECQU4TNzyroWNYBrcvW+0iWfCKC9561THjexE91B67wgzGwijUeGhz9qRb36pmjrQcq0ywmYYmDTd3hKXKEAp9FFTQT38tqKlCiMKiwrJH8cUCLONxXR+/B1q7ZRjC40G1ImElSh+xHM1eHevj5DgoXCcfrV0WQ8GZKk8MvdqfVqwPUVsrWo/7u+abtf0xukoq6pj2YQOF7++lMfB821DLJY/azz5RDzFXdSHqFlRFdEROCd8rdVxZuuLhkYnbby02K3mwEFkUYEZnvL40Tqss8eRbMWxoUG+Z1JP98ElMddcsTklkBUYGUZwksRqLCQhpLkUlfbAeti8ic3n2lnljqTupX6IsPGNJEa4PE3ea/hwjvBn6Aof1rarhdFNNE3uIFIAN6YCkUEa1DIkTqecp4xGi5ANBS3HF4t3LvpDynaUKz9tBhVAg6gujgk4jkuXPy+p3PitG8qyXx2mYPiFlRtFIqTNlPQ/86nCdC3gtuAkQmwSK7zGjlsa4pUE4Yv6KBpvpn5AnNo+u6Rxi25rMcFuT+mEYWTCYaTzYHvAa290iiUAXgNqlZ7T76KzcF+0DvZ7Goej8Hjr2Rg1ErS5IBOwddfTdn/wxkvMihprU0UCpccueunIDsfJqnQYbsksYir1Ny+TrVb52AXwSZuG2pC6yKma8OTs7HKynBz6Bzh8BoJ5JTv9WosqzLyILEkXJ1LyR1lXibDv7vhwmHDV78qVgNxK4l0GIhK2fmxsdAc5p26Y86f/wPTQbg6IwEsc0qRe6PLybSCauvZ2CgDzPLXHIuBoJCzUoX8Pb7+gVKGrx9aJjjaKIxWRsV1u4EiX7NctwRoOn7Vgm83vJjWjyaFdfLZp2DaNWqntmuKogo2p2LGTLW42qKB5uFif80RfjgwWPptOWHpGmNqTZ9KDN0x1RnyCx0nhEe59pRuiD3JjmEcwvX9ozjefu8bcGnazF4tLyrCdIXR1mMI1FpNkCbRB4k0FAxOXT5qei0d2G0ia9eA1kozhcPER2K7aH551Y0BTrglQZwYi5/QjWC6UF0sRi6dZzSyCdGOW1s0oBBibYGh3fDK609OaHf9gnYAMFZ28JD0jzjljX1ODLxGiPmAGUEWxN4jS5ZB4owJ5YICgJfdTL/ctmL44y0LVPWeLjYbuivMhRGaOco4KSDwLGNWlkAntQc8PykxgT27qUc8hClnwpm0YFwpSjVB/DXIFtTiMrUtF5NpXz1Y94+Z5HV3Ag+FiHuMC2fBJSXkuIU9mNYLIijdxsl6q9kHED6BGPrTqjPfSD3tB1bgJU4wtElaVwFmGox1rqn0hW4TEXJbmWt9TAyCes336ebP2fEAVn/4xF4NvPfeeWG/sr+OzDHPZcUwqgvaeYCF5l3xyJIDWQO9Br84fDuL3FFKB4XsZg+PCDRCgh32v2T8D/iBLqRGmXt01BVys459p4igmUCaxcF6hYK/Kan1LcDKIIYXr85d201w1MyZd0HWy082cXpPh8hcaPI3nB1O8891Xgq6k9i9Uewm6ze6NUzfwRt+vB7q9FftCzeWEO0JBgqkcUilCGws6MAX2jD6ZVyXvYr3VSYQ1NrE7N51C/iwWvMFPQYs+/sB8M/sEUvjRKPc71brkUsfj4aENRDc4dryC6BmLOcHtu4N+mJVgNTJGnvFn9XBgH/IC2pQcEFh/Bqqd5mwsY92FYyvFW2JmG3pYRa3qxU3nC/I+KwXoTlZl79DKjQIO7LwWf26mP8fGJdmoPHqsbK1RnLhOjyvZSqTcMcHr5V2Zovv7M/q1Mw2HWNhnaHZazDBKDKunpc5CUEMyEz5gdlFcAj6bmCCxca26pY3uhOa/EQRnQh4A93jPDFkAmzvobIzspUaHMV5sMUKKfYPd6t7c/cIbnwk55LYYWJFNeAzrNuhTCmFFK2e+6S6L0hT3w0Yd8OqnyttwYhuqcHXrvLPS6frNnkG05ceKmKPni27fIOYO+/Mt03s5vUiI573t+POVkbEN26DV39Az4ApZ16A6Dm4ukH645ypo54Is/v/Eck2wjmo0OmMd/rILCR2SsPrZvXQaYo8Zb6iM5p3IUoLWNoBxXa3eKdcu1M3GuCUyfYlJCkbIUwlQZ7Mm0EXcw9LUEiNk97Xn+vISMZ/uWfij7Upv11JRZqRaR2WVEtHT2+gxbTvNvsGFiH9oOEBecQEgWNpzT10xEOU/JLmEUXlK/KPzrkhmjelF1lM4fT4eaDIoE9rOGDqyBMqHrSdjCQMBMn73wBFDIHy7D8SH5Tjvi650TIiKiS1lJD18oUWctW5BGxQIlo9szBcfPqwrLOH6hHdjvPv6cU+S+hG1nct9PCWt6Nsr2jH70TLthc6ZyOdqda+P8uHkWF3ImVQe2oGhL7NoMxO8ni6r3W7pqMPFHEKmZeMYwq3AR5LQe6D2M5wyhkipYbuyFP3v3urF0YVveFoeVUHvNXnNwwf4wsq3dEUvF9OLn+BOar/5cJTLCh2XhWwxhIIfh8isgGUwHv+/FelreF8QndRLQ97SuOBDWShI+9Gz5a1VjB/CtwHygiAnol0arkFFgKv34XLqfzk5uX3WNSsBiZLO9/2LkzTlJUAZKgvBVMdXHmQRoDqSy/T5uCOj1vFRYl1h0FklU+MBF0HQuNN6xEsd2CEUEec2FqlgOKUgN0w/hgQoqNurodHlf6WNTVAgl1Oe7ByYvy7cieIleAqevCgX3dbdo1W1eaYdpfx0rips6HqYgHZ7icF/vSwIlGyG072n9Ek5z2EzP61DgAC7waYnh/OyleJud2mmGfV5yBAhlHEiFPAS0Y4KtYrHWSMe9M/L2tpOf2JI7DxLAKwN4beatbhQLXPD32x7lPGy8PUUHujBF8Sayma9/Ixbf9vz4o0j44xhBZE/xINgyVlnjuPiCTqTPAvwdOw/HrGzmmFv887+xbUKIW4giHvqLW/MgG8I8++xLUGpxjSBdt/1jjfHC5FHKZyRsXN2PiuxolQe3At6XeS08Hz2B/2YFpmokkC+LHBZB78JOrB5ZEPCH2YliAUT+gU+vj3s8YIFcneXO89/Xy5Dtru6LsFKBfAt2KhT+RJ4CF/rA12wVCi1g3b195zyfFkOXaHbCtkBqr0S+m2wnBcvFGwH9JxEt8M6F01RUHwmv/1qs0m6izy6JuN9MFlqP3Y/xTnSYsxwMh3q2q5rs+XwkFo+2r5tH+DX5LcqtzKKh+0qe6ODRilGeg7iB9cck6bF2v9DopNIJ1Sn2w9MtHU0JRQ0prPUGTSZuf3MKCdEqCqW1oSQmCnzm8HfMQwShx9dRiM29JXUR/oc+aCyxVfBqIHWojnJJLUZYo95oci2o4WkgTpsBPC1bq8+DB8MTl0Gf6OcdAqgE1AneQucm3ztBj3M8g8K+4IKfkzFlw9S+PdrhoeBa2jG4P3mf4Kr9d/4SJCw4FEpXywz7RcKkBK5lErgmYcLcheDgtR6n4YrpbYXTSXe9I33wFGUcAfc3vx8Duw6pYNmUPIjILIMhGiXrV48++fhqKVwusRk0B/hzcJXN3VCqh0Ogah8C3Wtgia6RzCJoFoDfz77EW7SPdCH9FYTapCND+8IQZ5QAyPMHdXc/I+3ginvrqJ04enbCNCBeFmaSDV5IvGLAtZDE7dDdKCw4Z7BncZ6cacqx6Eg6GmVSKQOlGPLVg6uaH7z/NUEQevFFF8nnRnesxNR4hGN2l/pqspIzcU54DVwWEKQEvnTQD6+/6BkUoB8a+pMTAzWZq3GZeXuBTmDBQSc8szdIAOW8NwL/ARFzul9Ix0f9AJ1Rk3l1t6sXWqkkO5MaYr7nnbEr7YXcOmvuobZE2yPUWJXtgdsy1Qr884+1Wkq+g19mXNxQ/EiuOsNSNk4nQJvvHpaZo1EKHr5FEHClB1tCi/xrdACYTmPCrwNC5RQyV6xoGYD5N5pMPCthMeNLmt5NBsTLWXfaCSglRJbCa93Q3kRP+Qd5BkwhEQYPe5X4rgqU9dBWCmZhtFfBDwagUMJWAJ0eZ8Xu0ayyXvd1BSuPj2OsJ30EZhdOhYxKaGBcCBbfHrNplGw/GWbgp8vHtRnw1IXLmmhDxQ8YjHdqmLMFjXSCVgeY42Iyw1GECeIEZVgLj45CuADneU389RyHj0+K7C8c3+XiDxHovcY6TRb9jxO+EhQwqrRcd4RRztENaqRqzWZyP3CE6LiA0kHZX/RST9IpLpNSver9z/dep0x+tEWHHb3TTsRJuXBLIg3rz3Oi6kYaXk7HoRrTJEHPVLaFVFAUxzrMUooC7QUGIAiWBZEkK/5IFA4LDZHFpOFhfQ3oT0mztEuzrwYJHv3ChSOhxOdAFbcSpbt3ragqc5bFzFC+AY4PTc7VmDBoTZhBdSoVRjcHON7XbrtqVoEwnxHtefoWZnymguHzuOrEvF/0x/M3k4c6Fdbj/6fO601AlGx6TAuDLOJhqJBhjzQO8CDMO0JPDOEMhAGLX5WaXq2dIPjsFx4S6HL6no3nhqmlAFPC+u4ZGrUtUBgO2xkIw2dc59QJEfDon95BpdF0qI6TZ5PpXi8zbxV1YQjVfDcWzlYfPpGN5AWLZx861JbfxNIl2G9DhRcGIQC/+5HEhS0HHJkK3tsPLSu0o0lrpwblEAi8bpf7Gq3ABsmV7h+Jshtw62o2Eby0qOm7o3c6elxvKNi+je/dMw8RlA2YB+zOEPBcj0CMhFGh10+riMSUUxrHypx+zIkiGoori5XKnjJbD7aCS469x1dZw4xyiSSpsphsq+RBEbtk+4FAW7hVweY7TnYfasqtkbAFkuyOTcy69i5SXEM3avMi6M4ma+3TmaBOmbjsieSkHGsfZycvgvijZwGy6+zI8TFo7OqjiP/WbmvjG5uJ9EVFTfTPyCBlfOCCTiUBkyd7cdcbPwvTbveQcruMYCRLmzhJ3LQiSUB2taa6AhYeM9VLHNRqjLTm0gf5yOfykW48Ve+T2m1iXwiIu7r3oi2Hw2PSxUzqfCNtWm49DWoMI0GXnJYEmZVkrTM0rsw7p5RYf6kXbp/ODbeAIgoTZkdSNQhK6hGFvzTd1yVMdZ4t9w0X0WUckcIthyBM94MeqkMYj6w0H9duYhYv431jNXmb6TnZqkGmW07XrHXLUS7xOQDKf9jEgvqhUvjspoc7j6EtOCFptpHuaP5ax3tBHNu8UTtLvEnmrU0qsbm6aFqHlnlsI9uHKBixkqY62gV5W8H0uq1VKoELvi3YbY0j/RyBSGuVyF8ZeQId+tCtYx+N7yPpavrG8yNR6rfJwG0mHVP+ZiNwetcdmSe5HnpD11Th0T+YTAQvfeVGi4KAKdJxWBYNN/O27KE5HdpTkBqRIO6wRe+V7RI7HXQZDZ8DJosHFMVzq0rOrSTr0n+fnsKRQ2l/k6628w2/U6ZKxRAammlcxWaY/IG67Enu2Wn+OIEvVb7hsR5Y+yAKU38RX1Txuem2Q4rOH3hxXPBJ16UilJdpAkuYo2rBEYA+wZ58GE/sYFHqkZPOB54l2uuyA6vrB6yh8OQ4p5TlxNLn8Faycfg3iHM/SgHbn0cWc3v+s7LE50mWz/l0TiB40b4R5VD1fZpIKLG+whXmkyuQTLGv8pOnkUo0qV7haKMO3g7f2pNvmhvF9RslzKcq8mmU9RZV5RIkBHnEz3Ap9fH8F3Iu8z3v+Ai6LDqj1YeFWNoKTt3xmbROuYi2L6VkRTYCYzdXTNoVimSmD/8Z0Q6Fu8yXluQPARonoSGEWp57+RjniVg/auB80qo9tXlUwO2fy/R2/8YCzjYHTgbAbJ/tlTCm5KaqRcC9/mUx2WrvBbgP8jTjz9v6DOXwZC7wVAv4vKezLQHPR12R142SlXMZpQjZIbDIMwjSo3X2s5UyYk2eIEev830Pc2PK/gDUsfLXrp70nhE6IwV10EO2RLBCDcgzRoP7cE7QyUXGjzmvzoy3KAUnQM9hGouEtOfgRvnb1CW8qFnHZgp3XvpMSYhY7Ge29VR+7rhFIAE7nsqlKjw5rQ8OcMLroma3WEOh0k/ABuE5KOiLn/dlThepR1D7IPMLG6JHXM7F0oBR7qMfELWKXe/U8Z1Obk9GGWJaRrPkMPI8uCp6egA7lfBU8uAd/qGEXCG0UQeiJhiwPdcVAM3glCeLKyv90tHYb+fsv8Ff1uwOExBmm40zWW6iX9FX+L4IJs1yMLEGV5NX5pRTY829/Qyz0hmIlP37wbKjeXm5E9LcMgZFizRRAWD1P7MERcZbsxKjfhELWnr/cLuQLkdbfDQIdPFFYfBgDuNo8hHim/H0VfsDKcq3BcKsh/DRUNUakDwkQolIn7JQ0vmgjlo16yS58JTvMWIJ6Of9laJbHJVT3hrt/EjNoRTbWf/wPvOa8WO+AgsOzTDXcrnVSwxnACSsKzH2AoCae70NCyK7a3OT81b4ZWJONTXcXMB4z5+NN9qv3tE7gnpiXeRjEDnlV3HsVKOpnzb7/bAGQFzs6BLLHh/tOW3G4q8wsNFWEBtC/s68JHViEcjQRUZF9F+NrhMEsTXRSQS39+txfQfbHoKUUZq85Zc8wFhXcqpYvdw6Zi5syG/MC1Vb7rUtf0L06EfdMow5knvzkZUfinXFLu8B62/w/nctraeBqRAyKpqxxgdZmZGNPpjYrnlbfaUcPRZDnAWUdxYlHVpHrmcklPnIdEnHAo6asSf6T8LNNkzSgTzeUQlRS2TgPt3UygTbUFFX+G6DThXz3Khs+7OenjaYyDcxAqoAlBhMSHIONzZvp8vJUuSeZHCIPYCcOlI1SG6VdQTsU95mCflKUOJNdBWBmTRvw03yhGIF9Oy//zcZRM5pZCu6Ewns95cqFu91uNhJsp5ZB5JknlgOnlC8bU5x9+78cXR0laC6Eb9DiCPxhsJOqp/epSxZItjV4MQovopiK9IubgjZW4SykvEQLyK9LooO/mNJjgN+jUKpT8zprstVgBYCIiyxSKsoFaGCzk6KOG4p53sAB+Dc/f/c/2mBxA6P4HuFe2b6NoqxmcbVOnAcBOMrb8I1VvR46HFt2DDmI7yaLGalKKzE3U70DmTpAhg5YFQBqD6XBh8AM7hyWuck9Bo7tTs0Qn5WB874wNGbNkWPw+JYr7jeK7vuwCoX5Ie8JmIb2DLthMUzpEr5gkl7i07O3RyjkU5/36yWsyd1AfqchK1Ij1W0FSZL80zuPTY21A8WTj6W6YnlYlM2kWAxCkNgXYvzGlE4lJBaBlcIzCaCDOXuPEH6ULlbcZFHbUYK3PdVRk1xkhc0lUIh6GL/F4qEu9zW3bCXFJP6HOTe7IFspbs2xsSPwOWmKkCp3b8auplLjuLTVosllS05iNS5l4hCfVsza9QrTmc9tKoCJOTwyVoEeQaKui64j7MK28pQ8Xe9hU8g8lUCbjlEuu3us9iclV+RC3ufVaW5HeArV5YA0aY4CUdAMwoMsDXeSXcaUDj+wdVqiWirM4KgQmqS/3V+Zk+9M9afK64W0jr5wLEs3aiCl2eulrNVSjuX8G9LjZAO9FuKaBj1k9PA/MxqaTGUvqelRipRrauD0d3DYSHxAAw+Dgbif8/9B45S/rJiVhs7JTrfb0Ty0Pu+8BnK6gn5NFVnbDK1JL/tKOpCUpvoOgrDyTMEbh56n8Qlafq2d0E4vkNsZchXs+TOcXfzR34bu4IhD1VcIDPU3I3gn7SbQkuvqK2J8NnY+343ZzxWGT9o1naig5JpDcdrXSpLEIu9a31/w/chi/KSbdsWHm/xwbBsu9ulPbj4gG0pYOIcnrMs0rYRzJCPPL2PLSHBg0ONY7wxkC+PXPro/3K2cTsMimSxQFkiUsCk1Al0hhmJfNwhO4qn4cXuwRXxRxN7RKfwADutcDuP52GCeZFWEqDus8Z2JLjWLU5I7FrB9hJxonHpxZzGH4fVFTmsvlOk0nz3ajgroKVEDRkwKuzbbMav9BskZxlSAkr7Rv1S9hveQHmPrQxGc+/m7pX+FBrGyJRH85hteV0YYf+93UCGLds07FgEpc3izOoG5qIRYgZo/ecghEHRdzBXoIjA1k1B3Z517M6K/ZMwLQU39Q41OuUb4Yz1q18QmLNFtUeNJQ8f2YgJ9/kaiXrEEpD2UoXPe3LY/yNEf1+cjol1aGraiqFagirPShLqk+uDWGMzCH/uF+hBDRAIjzhQv502C+xtXJcsO3kDJQJTEk8GwcZgnL9tXP5Tx007ulczmaUHhPKHAp4KWCQPwqsxlVFGdFPV+7ER5gizUfk3cb+sl3pu6ARCzeExIiauK1uJNQH1aAcb+kTcIrv1HrVube8jXloB3v5OrCNhqbWKznZ1jJ4J7MH8PiN4UQx3yPjPQCqbK7kQF63b36qeOjtLcMZUN9Rlnq2agGGbC+JqZ8wl2nk2YKiKTJWpB5QEPRBTWiHh+YBJpwJE2soKLbDHbQfSJuaaVRP1S6ARD2dJNT6j17fEY4fZS98/iUZ+hRPQwlM4N2L6B836edyUcpAjBeWeDMRcoklsBgKnDbzbVbHjACcbHD9WUBFqnQS/c9f1frReaEsswji51TjRl5y6NRkIP3MwbC6FTeqaqehMmPsPLpVwRTsjj414XNUS9dUx3Cwy94LFNx3i6PZ8rKfMgrHtMSJ3i0w+QKFzD3aJNnel2LBm8LZOSqfGOWMZmW7e0ABP9VgX9QQK49R6+ll19M+bAjrCAhII3EDRfyTAayaUtr3ZRJaxkxI6D3y1D4VAl3s4Z9BPkTs8pH0uWXnZfmvByh62PHm7aebzXWG2FT4JZyb+aAKKpX1IrYyIV2XpBgRf5K3NYeC3Pnai2dvzl5zeMsos8dd45im3NeRag7Hxpo1KpPYhRUJq1CtrmD9WFwy8lVehPxip+yrp1ChwQvS0GYlyYAantl1JFJQlojibIXv55g1bYmUYs8lK2R2tgKW28BzcHY3TqqitgUWw8g3e+FSduDHKNPXlOmsSOQok68mGYOSrp2C1QaJ5KO++bvAnemjkBHfPqJOqouKDC/cR7v7X0FXxeKGYK8hLLH0CBLpVo7tw5Hj8RtL2QYcGYrElq6BUwm5DoOMHWK8afRH85t81xWiw3psjuvf5BNvzj58a8VP9zz4+9NrF+49fx9ZDn2W7v/TTCVhg+0MlILwPRvcScXPOwfVBatMHuCcio7d6GuppSAoO7+nOvZSuhXQmQFmLkTH7lLhShoXqOo0o9oZ8ihmXQfUq5em1yp4UdperikEyag1UnIv+uPFOawk2i6MvpUfjjm8od5c72Atcp+1ms/cAHPKN7PgCOMTgIizCtNgn7Zm1U20ngsE+HDrP+lfgyJb7IwX8gZLs/sCRxWWsGmvVHqVxwwkqVrUHiw666DkEmT7rB68+rZVl4sFe4nHBrjmJa+XMlVOrhl4u3PlmACOoDd78xDO80t3TKAC96Bj6Z1quRB1gVLVomY2179pDqfLJL0k5sYzkBIqlI1nMqVT8neLy+jFm0L+mDf+vGy+e09OFXgjt1aRbqqsvrJ9RI5bDcSRAoETFLWNICC+/DHVrctzmLfL7pHWRB3DxXbt1itrbrS5Vo+ZGONB4tTZw8pjXkj93wefr7o4hAgs2Lxhx2WOovEIcrJjDgNR4G5h1DErZOL9KUJJ5Czo2tL7QU7X9//R1F9qS6oKqcnGk5A06LUNymD9tTyZYPOEkmZfaZ5zDeH+Qhmbd197DD6fECcLQ8Vdk36Vedi/N9Qr+Jy42nlOqXzS088GnT7jW2Y4HZ51seWTHYKk9iqAtj2h51ym4CkVBclAuOYuQuQzYnQPjFaqFuNOjA0dnd4+U39qsMttazy4fD4CMmHrvxW+PdyydHP9J3Sn0JjxzKb0N+LZcn4Bvd4Jz0tLSCmr51nIWtBf1xvqtIndThVzcIPiuCkiLsR/V4kje/va57dztooYAdTXCH4K+MHUHB1vUToI00uVzmsefWOMjTSyJ9NUvKQvhx9FXuD+3npqGWSeDyD4+6Nq5iYtH+o9594tgbpgoSqgEd9cY219MGd+Y91CxaxA9NA5saNMbCjx3WHD7lGGjrDNQfIcGrQW8NbWc4jYIJnexJ5wTFk6pDUMkIOOyCGQiGkDAaougl7VXm0W6rrmwGQj49mIOV1GPkc/6abw2Ubj1jzQGol7UtIXqckSPw+BqhSuAZGc4ScDeUNhuNpMf6wiSCiOFfeOCsyndiZuiaumBcMLc24EW1nQlAdvgG7fF8CxbykrFswz8uC3Vzo++8ZLw2ihYeAs+WVM7ZDoarbB25+RFxCYOLlizYuzcXp/gxeefO1OIiFFbTYA1kML8Go9Cra7yiLgwnwPC1sfZ/VWrsVe7OGTXmTBx4+sTZm7eRE04Rs4+yt+6CJ0piQuULJ3ejt3mT8Nd2wYT8y9PC4qzXxdF6AOu84k5T+Bgeh6D/TP29Cx6YpXW/NNh79B2bx2qrHiiZtc4CG1ooWtjZTMu0vr7TEAmW4y6psN4PNgQxqiGriIfnjOTGaR8+NnmvYtEvzbCUj/TeJZwHajPer0AgLnCzKwubCc0m4Pyx5uBSf4XTOO3gl7M/XmSKjbafpDc0zm19mjQUQLStIO84Oowtn/syeg2DGGA39aCZYjQSRbaZdtwDcbmOcPF/wcTKu+54vALwqhTWU7tIoM+wCnOFcavasHg8FOt7BszmR0WIKTroIRkBmmsB91EoG+foOUsvGEjlZ25pwj+pDRNXM+vT1kUS2G0l+6hNleEBww8uvKpjXIFvCjD3/zeb/eIWRlf6baJ7B1+phcKoJekNN1LfHUp/nfahzV/k6wz2GgzhVpV9qFCSvlstE38hXMLyQZQ0sqh3DiA+HzvsYPpNkdegveo//MrohwgrOBTqgeX1KKTz3i8nobVn2XxK1dtbsBoLf85pWAR28YRaajKHSv3Ga5/RiWiDuLs9ZoYucA7sqquig9Xx4smvD5LHT/8aQ+jCzaPtYsk8cqq5pPtSAlaHlFyYxdr9NZ2QNIJBF6Y4SQJPUNWlQUMboow+j78n51G3firRHus4Pw4EzpvV32f3oe7RqvwmRoILzywBUFz9wppHayk4xZMZFiaapcT++ug8vNpuaxLsVSCw72yoj5BdOL0Q5n4ANGFucFxzFyIy6T1MbcUX40OFQZxPJ9IlDXczRgr+iRzYIHydkW/vCCrgFLT0OrBDp52vH4iK0lpv7sRSPXFUdqnSsTLOYqOTUjF0Z1z5jRbLru//1mqALkBsIxETSSviarU1+TDuwj41wt2Ys/EbWAahXllDehhbIYZugXnprC3TGvNGHN/vGWmd7TBJ/9172BrRKC0TMtdsbqoWsO39kjXuR4/PVeOpsNrhk9W2HKAhaiX29ch2K0zzrEfbTVUUOZJNe8IIWZ0otzDHMl+VoobD0X9vSk/Yq6TjS6QRiyNbtfH+XriWw+RoaZtO1AW9NhJ1a9jjQlri6rmCl6LTCWsmr7+HaXtcGgYza76tM/JkJebx0OrScULUlQgkD5HJ1ZzxYTRVTn7F2002sQGxbeCYUvPkG0PRVhbiY5i55eOIRVgjeaj8xypZHgdmPvBeycSaIQ1kBJVgW1aLSHwV2h/pH85QN4CLozwN8ScG09bocwkWdy/nDKMwm/1R17HPhcGB0KkEoHZjZBUl5nBh3ii4gTerb8+MRpYjbN9GBuCvbctf7O0N5xR/oGdWHuHB7UHujPgsDplCefTAnkhNGrS+EY9gxbVp0JzIJ7HGwlURGwJNnXUkXg3LpiIBDLSZYooTxWO13FWyrkil8MG+5/88+UDimzupdipIzLESMP7y5CVXztz4LtlKpm8qDCB+2MvTTEwwTWO4iky9u+D1pYNPzvGIIh5/+ZYv59TrqxiZwdCoy2E9uksiSQloL4H4J+9tbPb2Texf+ODqipk0PG/DhwLg7nHwlmEhqHUAXlN0SzbH0WGILgyQm8mTrn3EMZHCkhJfaf7N0iCVis/R/EawsoXj4z43Xa730aIu9prYD+VUQTAPhcj75+ACDjshdv9ayS6zVprvZlPmwR9o/mvPuyBh+QiVUXf3dMniE/lGprwOjlpkS3O+gDI+MijY8irKbKXIDpaM8KQRlLL4o6cIOE03OuoRTLtAzPBZ+FBG2poMALoUmTYS/KkMjpGMi7bimY22v7Ygw8bIsVk/hPlJUF4UtqI34TocmzYBrRrwhAK2U+/8AMyPxh/CrM6IqMFPCXperUgl0kzNKuiKweujyF2LAaGre6t09ReKLN/8KcaxaRCs0vapcmKK5GW1zqIzrezzEMrrOyRh9obda0l0S98oh0nJ5i0ITB4LmhIz+FuM8cD7eIZfGgzqkf2TRG24GuUS0yst3VNaWNkhuxRHztzsrqJ+p8G9gSXnx6dRDzrpCydPsf+pS2E5dxvgQ5nVvwg96QDNQMIOhJrAWlVBh2VUTfcA5MyXkL2ksVi2BZCkgDAgUcSVA2/BV2f5fXpvNvFMDMpKE/7eoZFY9Gcv+GqForkEqtQTaSipdtxxUOyWmNEOqvL8Kh1x3qo5ssAZZyA0Munyb9LiapkOoBHEmIdG9FKBjBtdx68ZypkcRxotUBa+j5u07Hnhsv2yH8agAH15hQvtHGo3LpX2cHHGGhYDd/35VWGrLduCxHtHB7+9aLBXeeVUM3CdtUNkPLo5uNEmbkUNvobrz7qHs1b+jArzcGZRffiePXs+HgvrXul6hVM1TZJ5mSCEA0yL95LKiLbwQHjVPhw5010ZjImjsCo2GiVpXPMnlMwUuZd18e/SrzKfDNDP+btgMVDoNyqMwLs3/CZ5uHl/umE+L61DMo3XfeiRiOU079+7mMXj9bXM0G+aa7RQrSLHTkk4n6ESq4HewCYNDh/hS22h9yE4zzFI3K/P0ObZJvumkIPqQTMJ2sdq3n42B2J2JlIWUw33XXIqi2cIw6+lI9g1eW2zc6mIAMtIbyJOxxnwvPg7iZL7oqNBQVEQYcjnxlA8EDPtcZL8i+72paBDdS3YBVXPhmTwHiOb95fgLzMavPLc3nazXHI/wBFwMVWGFenbYDcjcWonoAj1DKse3xT9ugIp/bdPz827zkMwh5tJD/vv1ygTXNrTlp3uj8MXLf7XNofENnL/VTuEAuJbzIa33ZxwF0beciH/w6cDRWKkaFpKw2QpFO21YeBvrfwthYwRV+IUEjcAH2FPVkYl0kKnxwNJ7TY4u7lHrKWkf114xIGj3vR5MCOe4VJkcsXbdVg75rhw9sS7TKyhXBAaHqOMEdAddni/7mQBHCboq1RMGIzOIgcUMHoUItilKJsGZhjBaUXiwxWPdGsuQIcc+XP/E209ZJfCQqwwMT4JJ+SPR4KVgm3PQ2JRIDzD8FLHqY0dnro4cc2vrkK0zByvJ0Pg11s0bS7KM1qFnz6Em421sW/UZsb0CC7QsSr0fpq4dshKKWdh1ZUyeLWHOp7wTBr/5nuQccWRwW5NjgIv9OmSf0dvwJByWv+VdN8NS5HQ3VDf5dg1f1dCTbsUwbjVAeJVdziLBlVm8tbghvvZR5b5QLmdt+meSesT0SPbXpTb1NqA591rPknX6Ump11SQdgHJBw2A7xFkyPnpRPzLRN0P22lkTac5NKkLaAlSWCQm9sXDdsNTcYdAXf+XSIWRaDWEfHf9Y+m1Beacsu9vYmeN//yLoSzDGH7qBHzqTg7hWBZdkiZ6oCneaNr5h5u1PQYWxkVfYz3lVuNPwbTan7mPL4U6VGUxcJoHxlEQfY9+Q2zy3KRSmFkdQ5os63Ey0oaPQmeqXzgq/caLaoY33amw2IIYM5LF+ySDGKHppoeqoHi9tF4X6AkHrJ6YelTH8PvpTplhgsf9jYhpY8e6Ycb+GAxvfJ7BZ9pWXC//5hxBKhuYr2INeLwYD/AsOZDhIjxJbNB+4IpsmPZ7HafbG6PsyeXJ7k9D28qZW1DjbtG5gw0YQvPlNujuRR5nstQYaC/kMdFw5JNpm3s3D8rIDXl21/jZz4IxUvNzd7VoQx/EmSyYwyniJrO5nEV1HLHoc1SlwBnss2WgTncN7NmZu0868HzOfVRojpCVrUixa3SSy2mSOPqjTp+NRU2A9FYIxzyWONAYXJDRA12ZbGU49FMPdaS/yvubpp19GgALz1L/QpZvi66+RaplbCSkWQLoRN+oeTxgSkZbwE85LYW7xV4a+ylZK/K0xZKnpJ0OL6HBqVP7O3GT9jW0H1/bgQyEaOOmL4EUWb9qR1xDx8OBEPuNnd+kLqxDnjkfAjM0Itoj2vnAh8Bt1KnTnPXrIIMK3WSPTx66YYQ9Rhbu4jw9Ic4RkRmsH2CCcdktzTCHJhVqFi1Qx4wKgxFYQBzSJkvUxnA50aEFMbzNa1QcW1YQXpWjYBK099yi/YIRpzi0JAqMrS807Vt+TNiXHcRjDiSGooDpywy6aCwAfFTUax5s6q1VMotYMI9hgee4sC8a5aG+Gztd6BKwAaPvb4EChIJz/gxApeAcy678qtjTOi/SRgfm/Ga8E7NJCEUWn9nxyDgwhE1XEz7WCc6SKb02W8fqWGa6GcNmvjr+laRACda8QM1SNuK18ZA4zCZ2xAPsfm4eTNlMNJkkBVpFzj06QUhiDs4J6y9LSn1giI2R7p8TQ4747pn1Fr9pAgQZ2Ly1YbQ0KtA3LdGnlC4HqnJk9zQV0B01ocH7zKhlU5ICZeDqUxL4yAikDW0CulOkjXKuF1ny9kdnRv6bGRN2yLvcDcmoAJJEkXFZyIZHsc8mlMnncFMIcsVmvJc9P2A1C4muXF+ISGhqQKR9OXOI2UYW/k1SAYUeU6ZGMwcAOgs3/qj7sK93JGa2YWizjiJw4jkA6pK90d58wYXLA0lb7GZcpCbO81/krHJ6gTcyUJ3j4uqOc9bXzMKAwC0tOLZAMBjV22KIaLBt8/NpHXzwguCEyKh+OMH8Js2kc6ewbUYk3rbGO6GZ8XmicUFKrBVaK4o2vyaQGSUzK7nJhRGOPwganSpY8CQo+ugmm7Q3NWWr5UmwOPtzAN2Q97jPBrcYx9XymGLoRHDtl9zCqodklZMOpYECRYDUHy4Jg5JvEnTce40tA2FkXrejPyylxFRDrUK8EHtzZ7kDs5U0TSC9IVnwez1neLm5ZTi14hojQzcenxUGw6x3h3Mk/U80Xc9p2lEHGduNwbxITHl/gwloNbKfr6ciKA5Id44wW4n1cyLWCPtcdsz3KHdPdmCd+zHsG4mYPs/RIQm/B6w+tAype2H/hW4hcMImGYD+KfdnPzVVnM+lCmlucGaAL1yym67E1lAlbNbuavbUao0XOOH2TRUimSwJyhWO81noThBQaCsnhI9u2HWs+XLcsfLwB6a2xX5uuLq12EAABvBX8DsZh0N7Gfh4uiMLfjokmEvoTpFyuX/mxkBDjNlyo9FHYFBay3kuv7bPlEHDpeaCqqvaEnuOJ12Dkh/ogzUlbhDjn3Ngls80hiyXl+4JW+hJKMWfxXz9LNdEq8uGHICK5xVJ2kB2jrcNs7JQW1dhc7LS+kIWR8/KRF2Fkr/ZVEH3q9h9nk3HZXgERvRQNcfIgJzwljGeNzpux08zbK7tmM2PFqoIicflAkmTYyAwZ3b+rjw+wdGgU9dmh7O2NSeymm5hzgosa3zeHpiHlT1rO11mUcm0Ng2pveyUJL56Tom5xdtkvCWGLKxPmNG1NMns5jvikCttKdj1TE4uNRzevFi86ufxpDPaiIA8bfIVSiMvP8GguYIvduorVizCcfLYa3k8TlBG8cLt06KHCZGYzyQOYEGQn2PL6T107DHrtAHEBKTjGAasbUo9tptojlzTmTKZM+1W7wyshKuWrTkHtKbj6/6NxfQLIrqpvIaoqGHvPKEjQRkQPgRqFn1ye6p9L/YNIMDdsMZTW4AOfaRINTzhTrayonkF+zeElkD3ySbUuGbIVMdln0sVyIYmjl1NUfaUBZuMyf/Y91Gx4+Yabrj41Xb5KG2h46Sk0dzNk48R/KxZqhcGf3tRAlgMf1nhFHly5Awg4YcCOf1J0OFy9l0qzZMSVTnOuunjmWsONOijh13bsbscwbYYNwzMB3aJvCEVF56T3OqpuxvfQ5QabwdhOPidhWCavTODQQsPqi4ys6IYjJGsefU5ejNQlgXCOm6gTaSmIAeu2228xFeBzTwP9FkY5I1sQWByiGVDHmdLrDfjcZyizgY6QIv/KVS451ybrZyY+j/gecBm/wpz/33tmRmazdS6N/5G9ZFwI22RqidkMpW5vtrmtTch446Xsbhre+GEpaeSjsdGkMpumFNHCZnK4pk42dqeNMugE6LY4Kd1n0d+LcFJOcitUNxyDSSxfc56NHyqxqGrXJaGQr4ZVindQjLUIo1IPmkn30B0UDLghB5r/IERmcI10D9dcQqzRFkOxt+sY1FbQKw3zF1ckdDFiRCOtU+1TNhxyxzTKbZSwTf6Xrw+I4PTnLRpQ2ta8VxLjNOpHPUT5xR82dej2WitjkCYBp1dCQxTjOGZlACMGYFW0g/vD3rUe4z1ndR2xu1vAfOSnochWKuENlBqVm2/m6mGuPkJ9bTbKCYWghf8Zw1iO4vpoBuYQSBEDV0ah1YNfoD374aVgiIsyuH9JKTP4HL2vHHiM1Xrgcd2EPlRWJipbsOlHtduexbwIWRxsOspK8S0iC49keBjfBypJnoIYX3Tgixy2o28V1Ly776XdMFyQ0dqslKD9RFhQ8vzTmpUaQeZF0KjNDIf4cVFl0q8oYxeSctHG6Dp3sR+YRYMGBIv2wvEoQB98BcxUO9B4jPt3GHsNWRXN+k5zC022CnaS3lhINhsm3aD4SeBcEESIpIG+2AeXjWpp1SuRBeD173HNQ+JcL3daYkZyMlLSmHhVr2rC7qKxTpPoCDihqvozAAAIIuuUGlh4Qis6VrWJmQC/airQpaa1pzQjXx0T+iBcf18tcjJtujOVmZJfvAB37zQEQ8e3U4tqlwKXbqoroy4hFQQ3Cm0chHKNkFkYelKazN4uqKcdVvdaI8bS/TPWoH3O7Sdnl3b4EDQzN73I9dxLeRei4jADw8+IwGEM3HV4Z2nnNhCgjqxo6OmJnXlRGYHDqzstNzzYmtUsJw//Pxqkht1EQaDDsU+i5lWvzZJKLkZRptFgi4YX7cL1peylMndGcgTdWF3OpJ3AhqabBmRoSbrpueSrSCeODyCN8V3fDWDKRyMMyKX9z2z03LJ7QsZvCx+gw2Cw/51YXBjRzKtOQ9eLfZweMeW+DQ5k9fl6o8o6ws8kezbWumzx3034a9R8X1LyMurtX0bZXQ5+mdFo8GNaUE86e+8V2IT7m5m8/pPwAqdwLn0TPlaAE0EOct2Ap6AxHXbit8kfIBr3dGvO8Xa9Z0r7wupMMyOElf+hhq3MKkFl2soIFbOWizi8QYlzrSvNi2CMQ3nk7QtF0TnBh8Lu7Z+IbF2ARyF4x6FkW5y5ckqVKghuXpJ+u+OVdhS3B6g/p/f58FhbbgCrAdzG9n2p2FI5drYOaZJ3qS4ph+3MeupxUjwjkCtw+ghtuQaw/RqG3qxJDkNfwA5RHJuPFge/hryNKCaRsNZ2bunk6g/4bXqqdETwCs8raJEoL7AHAGRG41OKzcDZOk1AbbEGSX4Mt4aFGC0ETKKRDT3BDQSkjNrKaoDjrhl7rY/FzVTT5OKBrM7XnZsVrnjyWB6h7ju4FAsabxtbLe5Ou+3vRh5DeP7Sg1LKVctjU7TLqsdNInHBbsuU2+ur0oONG0tdGpuISSW+CXH9waiWTw4sNn0eJmpG8CRcdi9adC04H2n3PcSCm0+ljn6lwtYicao9OzoQHZ/khx7eM8tZGqj9t5VnhEyIazC2aLPY2PZbmyCWK5J/BxcgQY2YUKhyct+aLjB/JzNhwYc3pt2aaZEq2OemoqcX1y/N0GbbaORGJuRJJdME4dtOgrG/sdCX2rSoRTJjEvzNG9Bd93frOgO9bEjVvT4auXJ/d/mhDaeYsAtNehv75hyM3sFtyngaZg2KEtb29lpd/DzGjwflW2QJqguQ26eQly3JsLY2Kaqv4sI1jgVMfRfC0a6kZEjKWSLZvAH9j9c5ifDx9Vq9eF9izGTqSIR5BSGrnku2c0ulD+s80Yt7cQZ0Qu16cPapCKbnagPF3ZdjcmOG+w8D1C0KNoDG5vDJwkwZwVHvkMndtnMu3TQWA5i3CkvqkpKzfn4m+YtAAcLvCEuC7ccILaYdBmkWcGEwWVPoFVxvn4VFXJhtQ4aXd+IHx6t/1BEHmxLzfwO4aV9G7mBbunGTNA77epj8Z5m78q/wXL++ghsQJP9+3wNGbs1lw8o91pz+JsbnI7h1yV92gEOZPoP3vu/HP559TVmWVSXzmxl6ZnBDkCcyondagKgnPaFpz+MsN78GbVU6gMoaB4L/N4vZM1nnOaLls7m9qFClMVg3wKdmZLXtPhIOcHHwH/ZiPcW/xpdI8RuSdtpbtaB7HW4ETOj9/EUxBDRpTr2M9pjhHckYzsAxB3lLw7cNSVLbgfjv+xmTN+PytZu32EdbmlofP80je3lhhBEUwkT55bY/3iUoJSJcAccg57wVopLNqmtUpgErMZVWO7uBw83XlL5dQs6p5d0lusw61Xpc4yFC+pY+cejI015WhDIosf+UPxUrUE+Pba1m+SpV/J5MSUw7bg9de9BYaA3Jf8zHe1oXpPgI5n6JvSbNzbWSkAJD+hsMAjbZD/BWRipNAzcLdDaRHc/jWMvfvNkZR92EAA7VgxVn8mWLFUfE7dNkAnsjh8kBsV1PNVlarUtt7zQiPkXekJKi027mZHA2m9SSgQPRgk8IAk+j1SDJ7YquT5WNQjZZNz8IDiHKE0gNsr7RJOd5PhP6jX0pEAbwUffhaTVJMAsCEOut4RhbqPc8h22nfN2pnErjzXpeWe7qtg3Xw+DgVuFt37YGGty2FnCUckRrL8Blv6Zx5OGYIthPKvl24GiKReriEGiy522PLv+upxWQju+fgznVcUzMlhPBydjoHQXfBIgm8q6agtbQ2oV6hxesUPcav2vbkE8xJHH7een6HxxTAZtw40Vkf80TTklmXU66olKYRMxzKYjeky72QAW3hw2bidFIlW2TMaVEMvhB/WwYrKpx4/p+JMfCQKGRNwzgOMPK7pO29X/Xg7L+GEYkajIOrnFAYSPmrNOFISKei2BP9i0VupX3Q9JYL3WqbNZW9jBYLpKUcYpQxmTWz0cTkEVDYaWNUSAWXDO2NFhBE7ujzlZoKHhyzyXP2eh3fGAN5dYkPpx2ZjINH3gQiy3ceCSyn4mZLpJuLXyrEjf3xeVsUiKOpNGhP5Q5iPk8qgvV09ij2N5PypsURq/GulpjfipbvuL7ZSHu9j7w4g9p/9Py9AAczk9PCb5BfcxHrad3RORu0ywmQN8aWdSNJYucvz6zTgbuTSDVu3g+wVKctJlUPBiZt+ixb7ffALTPe9mJyUNWz8GiIU+HWjjK0fqElL/jCbvkhvmIe1ccBc4wKODYeDjPhbrEBaCOh/cqENhvKWGTDJxf7RPJpylWa3ySYQnRuM+wlVSRR2IYBlWLsJx0ZcdQ0naXY8IKjKN7onOaz9I10pk0NYX21k8ybkRXM39jHHb6xOmzO4lh/Ph5Xh0GrGqN0mAziPrWC5f/RbHflbVQ7xF8xegVqSS4IXc/utT030oUixkLXpSrb2p58gpXA4ixEhOk2y98IvoH0iGNBASDFwh4khD6QyXbr510/FzWX02MGtGPWi258/hWmeicpXXFRm7WmWpfxflzb/Xk4qvYTkNqN9zQVpWO1fBd5mrEzcDak95E51hyoLVmPx10mKKElNQ4GA9KeI+351r6ITgK04LDzi11Fv3DmNZhoElvXApF5aUb4EqGWN9l7Ij5YilclwPq2UMr+1FzrLpXPBQm0gCb/PivBO5/QP5BE6XCv6oXCRd+PWUqPbbcz8BjbyzVKwVBp1N6bUVSP+uhTbItJMMCxgAEIrtrCvk7LBGPM1Ed9dBXMIXJIaYxu3AUsY3hxgl1dLRLLJDvp7/oiV0kaWCyuXjWr3NTY+GM8oqszPYtMl3+GUnLqGMFftqngmcFjv9DKvBDzWMcw7toEWlk8YQf0dkul5QbBadUUo4NeyK7it/LAS3F/Q1/8X56teplKFVe8iXUxB5HFnwR9sWKlyP/OV7KXV0Q2u7Q9JPUKeDalsIpe0r8rK0FR5l1F5B7af4c2QEo05Q5q6wW8j4ynh3Z7nZN6DO3gs8SKBIIeAp0ct0Cd+vd8sivso9eKb6iBR1FucCQoyuUu19A+6exFOwn5lNY6XQD6s9BZ28U+OA74oZAEsyr8Km3/YlAfRbuIrp2oEBbnEJceXjy+ykoGJ+UvS2BNqrX2dRB9IXzmSMZfnKdxBX/HYQvgeInkB4Gs7VBnAmZrUE9nVRbi60a1Y+R7scHXYzuob1Jjk2IzPid08/8V22+xofFRnvRcfRrkf2A9YhPhXR5H31KacfZd9iKZvPfTg+IMJ4+mjlYgGYNwXJyptMafs+NmCfHjQmMuhQOWAMhKGgfvUAw4aOW+NEg4+rkVt3me5+0qrKyB1e6/24UjSZAxDYZTg5oC6Cny/3GdxurQZiLbI5BKDKhachiAxpxV22/FLGT9P211FYkOp+cpwfzCgEelshymxFBFxWpAEpBqjwKnFQUrCv1TGhwYigAtsiFYcPs9+XXCfRR3m/ya7XcQ57P8KdGxXJWSNHLe4XmthwvjARfeGhaMGZHa27gcuph+UuX5T052739DGNwzLMgUO/Cu1B7DOPVaFGyG+ICfrn7odREBTPP+IeMkq2q6hS5fEiiSgp7Te38cmemilc4q37xxEHvycsxAJYPEstd38Wq+Zp3v7sc9uGhcV3Gu27qKcqQPtoKfEF1lS7rnT7FPz9R7JvrPkHSW7tTyhS1hBvTGFVztGj65tDoUvNdVDbRc4BA32ChSDfSTv+pIprsPSJ9RU37ljlpFtsKPxQYuKUrwkCknykmk9C3qMN/EswcCzMaWiyWbQ6+5iehWtsQwg4rcW5LwV2OZClPi4WoUDvVr/a7HqYj2ZSV74CvMTxToGnvb0LZd9vSYW4EpVzXGvw3LyOBK0gqS1rAp/ljMoKFbz4oYCPfQQRMEfnBaY6honZruQVNGi1PKnRFMHTnKFpnMJMHNTm3MLSa/SXinfuNW3O1fkRyC0qjJXaliYXCZn1ENX6S0IGzP2l7b2lMC4NXFW9aQ76olfWjuHA2oM4ffxfcDwJjy/eZwxT62AJxj1/puJbmSqJseRuTdM36y1Vo3e8d4ns5alpWmEkpGuOPlN64ay/pfAKwHnH9dOOOnRGyk404hO5qSZPp30zoDl//QX0HeiBrq+RVA/HSEnlYV3axYDxVLosbVCArgtMiSvOXESkIMcRT0CgGlPqHyDGT5UXp1enOcVK10NB7XOewk5YHtedg/U1JAe/YCDe6DBAhRcAiZX8jF5w/c83dn9Mqf5BT+tmOhhCKTo/ukW0EG89iAFVebbj731beePnQzKa1ujIoWhOz40caY23A6OZx0aAdXFvh+8Im5PABq/qCLAO93N2oeWE2Ngk12TGBPwDFcZQ0jN6zPzwsHMxP9OriAHj5iVKtkGMpACYl/VxHFgwWZmOeakv3yZbFHroxLGetA4BWhMmo8QAeNMEdLcqEltLuk9sFGTlesKE88c2oSd1GM8SC9yXKaPOrM0qS5qXca7RvdiIXCF6eRrXfSp9u/PydDQ55zNTzfJHzeGSzDCcfw+KgXz/G6Zy21ZpOKbiFzddXjE/TlfS+1E8lGE3w0E0JIoP0m9TqLsKM+ZmRhpWqxncsSkeHS95roxIQ9AfFrflhRSOnHeXabG8G66JyvzhGF66X2BwPFfSVqtACH1aPmuB+7gzjx+vLa8HWRfT+m6CYNmTHgQjdQEbJDT2tD8k38TvHlTcbUv9ZZCV3C3rgh1kfndzVtmhgZZJO4QJK2LbaUugDPnv8VDTupl90a82UAaRMVsuBRPKCPeeZFdf1NJXEoKkIpdtGDgN7lXIDCZIS5+i46fG/rKWk3+L74FAq2iUHW4eHFBSVwyhLKUXttJSBjOyl7DiPRmEwGZN9I4H6/WorVMHm7VkizZKw85GwrH/FUqatpXHvcHbmXLWUCvnLaaP5Q7JETkc7S5SZhCdK0lwQLsnYkUojqPFn97Xj7PV1+ki3jgI14ytdwmzv9c1p22UqKVu/6RmMkQC64YBhxguONumvye6BLbxfwiJpJQQJ/98+U/JX3+kMmx1+mNNX3sO6GwaDfAJ5lkNn2DlWQq6ZRIw1HJQFrXTNlpLTWi/iybrGI2tjlf/DucVGP6B2q8ag3695ZyLWK1cwHI52mGKMDFMdbNb57hPTuujg2h2dY39F7oSgbd5+uPV2pPGoLoI3ANhn75dlt4wWsbm1pb6D4nAazCBqFk6qFYXfgk55nVPQkRkKNKZ0jAIK4PnAe3M7BFfmlEgckQjCB0x9HgtVmrPt+NL6oen/EuSmHfRhuFSpB2UG9uFLAUcOeXLa+c8Xw2Zu8Vl0coJw9ZF4gLYEzcqyzdtk4UJRzUP9PgExGLcIBQzjF0afkAbBJJLkAyYjYEOo5O12trWnX2AJ7VAcN6IAz+I9nPCOCPjZ9mqpY+ojmGMf7hsQAzJtK/N+6Yqfls+Qix4wx5zNY2yLXHyKksn3Gfx3KWgc6llicljPLGEk91Cq6x9tlv8oFm1jcEr5EFYT3PEWxA+7afYr5sFiOzKiDgtfzeyMIUMyn2mSps1W0h1u2fRjfWCLzBPeuLEjvN8v0FYQftoVYLF7m9uiTqWcNtl1xxCvFs2Gi25f/4yv+/viFsbZMZdYg09Py7nFHFhnAw3L9tlien1gprJd/aREv3nV9n+nE9NF8wYUPD3VUma/oQoeO3AW/sAfH4Wj7hlu5YMftutLGh6XBFNGlkRmhccE/nDkJyEnoeweM587o+Xr6yC9SUjS+ui+KQH/A/ifK5+z7HiyNSekcAAd6vP/khYjzWEjr5gSKDt2ng2RdRHamrCC1/4yU3kbQXB+LkaqQ1msffmwnAGkKy2tDKgE+Te2ThHggjZRm+sMRb42/GwanWGEnThjXIzFX6RvKQjlHvOBW75a+wJWsr9ERfTMLb2gxu+6Bz5OA3Wp8s7bg7jO9w7vFeZEHEvPEn9Dp/1bpi3jH91/V1CHPVun4pEeTzPQDWX1eikySkbX/d0VKM18pQtiM8EsYIB+LY01FuuAI1vdv5KRLKPB9/a/je8WO705BLFlFvQJUxlOFqU8PpW5zqlEAF0ssOaZySsDmzJSPrV1632DUQQNmtqi8iUhNzOfbt+aHf8ZIloEEzv2ft97hiBwa8J0GOJ+oMFmjAPK9YXk3m5TwMtWN279Bllqe1O9n/ybCl/9rxVrft4rQjjG/mFGjkNOzmZPDL/xPjj/r2W972zHkVomZ2V9POVUtGrpAN65Y6hafTMA8bD4C+CBgLYGT263eH2RZohNLbvTFikH/w9WD3gLOIYXULXLspmJhmDaN243RwtStvEhYyk7qOypol0TsdD8wXMYCEP9SssAQGoiaFioXAf/s2bcDBzx4oxbn9d23ByQTdS6ct9V7bptSQVwBB14Nhu4J8dyBNYUPFtDg4Tkp06nUkebwo1iLqEltwX8RS0aQKkEnQ2pFIrmFot537w4s/ZC5tLlVl6L3nOY063DGXiTUOMAUiS/Zgq7jbBvmUzosknoHewnJGKgryBIf8FWZtkVCF4MK5/B+Hyy6XLTS+hYZUrwBu/YZnWrAloboAfh0PCuqPEl6NgEUazKQc3X4nbUQb1lgZx9JUAT7/ey19gm9/KzwAmFw9hiDstGVmq3dMJ76EJDsytaUU+ork4TsW17yg7K+FE7lczmv98zFZxbO7aZ1DYEDcj+ZTAnjZJx2SnCT5kCmS6smeIFasMv0v6v2Zir6kjepUJydUrGbQ43zkUcS5O+ixY3Wlq8E0+EOYcvT+u83EcIaGpjNMfhEtAJU48c4Jbeosk4/kUZuF3in6LOwCxEc6jQCpOSzjqOGNtRvOPNRUds7ZvPdYcST88G2OR7Cxn5NoZ4DreKUqLGcOWLlmKRCuSTCcotwrcIEHg+ZniCYkLgPaHimK6s7sK5d+RboMz3n6V8VHy2VUKaK87EmpIZB3hgHYTYINv78J38VPd0OzTw1BAoKaAd1MjUuRDDL6KHwGvSlOb1J1qXF/OYBFcosls3tmyc/b6xlffA6J3y868Tv0BbEoVaMdGLWTOUnqyGNtJY49NRY2ajAWt0GzPMgSB5ewfFya/T1oRZrEd6TxX/TZ+fdtv1Ap4WsWTyB2tIGzp5ejaKMwMm5RcKw8zb4q+tIch+ynQZDFF+hxaSrVLJbiBjpecv/el2eJ/uZZctFCecy//mUrpnz1HgRsjZcPF3kMxwbA1HaK7QWG9PFijxij7HBTvKZrQZml26SJymC8023ZFOUF+L2Fwy3LnJluVfoWZVCUVIW7KUqel8R0MDagsD//5NQkN6c4EkNMiFY5hoXMv7qJIvxVWN73UaSBN/cSXc62lRG7RbQIohhryrblKeh92sa+5CtyPX9fugsEnj+UEb54LOGPHneYT3+U5LWEv9HutWd+nRuROmE+afQzG8svoGWLnExUgGg2WqtZStBwcYk9Bb5D2bU+pXoL8l9vh0tNWahmI6ROAYCnQZkX5ywxsZyE8SfQ9hQJiPO3HtoGTYotO1I6Mko8yKq/LFk5K9Bnj7/cmE/Do2lfJ2dh/u4/EVZYOX6VJtuMDDzIHv8ZTdFBZ/wjosLeJRUO+MeuHdtWbRdCFPTI250+6tLfD9CUqgELU5X+58jVzZ0ASVYgXGBK94iuQzjbpz1vGok87l76NsJfmKgu+BEdDQcaDZ+LknVcgcmW88xCNTsBp+cy65XrJ4g4wzoIbHwarZdKx5fpswr7sLGTRX0R3opYHYhBCUqQwPOtLURT4T9vE9apwX7E6UNQlFLgCdkTYl5uIR8bRAMSO0Uo3PyFdEcn9HfPWa8Lveg0CCmO2HBQT2OZmUodfw3SW9mpolPkkC4DtR2EnGbfVef7TocaBR28u0Vltu71Qf2XoBRFhKf73ndTWlwN+OWzeA9ebRN/YkGwK1/p/LVfHxoX+u7eEvxilORTjCtzw6rRk7nsRUrF54BQVT3kGRJzBxxHyvFeBBsIFZN6El/cAa+khCdbzCj4VKZnnLXa9Kf5p7j67UqzH+2+Bn0ZDLVQD38UhCO3x/eYTegrQ+d6r0/pcqPtagcJNXOHvUMjmh0GZEtQrN8UC+XkWWv0cXQyqIRZeaDNCm3h+fMhDTmnQhg6ND8FwX0P/gXOrdUgJzxcRXXwI1dLJ4xtvlxbRo8euG5lb4vMwksCjdIedAGqCwdDeweYbjYB4qNjU9+fg0ajbrHuCmAknMf1b5z4CPto1jl7K7HpfGoQ03sxW4o73nqUBTdGsHirIo73FNI/3rn5GglIPWgbDaLiCq8L6lyaqzl9Wy83ZCUCx22N0Bz79lWiZRLKu4iVSGkIdfBPhMRo9OC3UZIoz5/cMnGxGkPstlUG/kL0bWcb+cXcJ4458Rbf+mIokrlYDy0E7iaOZbyHWi1gf4jmGZGh3QjLjFKN4yRZ4M06FVvjtdytabkmiRXPgjz2GKy8tBKZDxGEgiuLdwZ4Ggp92kyRn4LUvtjMWDwNKlFrWNnrZj7FsMVZWfd/HazrK/o1J+ApvLKRhBkDsWypZFXAMQ7wiHIfuEQJllebJb5J0ZiHUuZ4gKWFhj2Iw867pFWfrS34nsxXQ1TOz9evRvFEKDzV6gw3XGio2HKXICECc8cfxxc8t+j+MUaVrlBV8DFh3YypoLjn74cK/mDn9WDCqt8Yn3sbvvXvfkpy/rpRrfe08E0JAjaVF4dJ0OR7vU1KrxGn87+GOTcqZxTKXNuJTox8TikZ1DP4DUuDdT/A1GSiyb6yYUCSTTRtx6DA9yOz0JYmEbpRSKLVKNaLLqOoOc5UVTngJn7NuMMkjqMe+f/KBx1XvDlumbUYV/GtbXdHPcEKOEAQlHBg/eqETB26KPi3q8TDk0Muj8CyTYZO7tsOI23sChKdsNUHJc9sUFJspVQ7DyAYqtOxw+mTcBaIBYb7meLnBD+IXjd3tXlT6n9bqHI8CrT6cZc+VIyl8eNyvDbuEoL9OfeX5lxScr5P2NAoCdI4IGjuCeuHLJDWJDkIob6pNr7KfJEzJvWivQSfo84Lsk8KUwRcl3+CZIGzaEG3oaBnUc3CQlR7JRt2UQLZ+OLkxPv4cdDpljbbFvVjcLwnbPF0BF+VQJvUeUqDC8h/+PLZUQ/wRs5clRIZz0y35bfc1TI54Fc27y0vBOrShGCcs3CTDlmvIheZL5eUCCpUt9XgKPDK0x9Q1KI94DXmKO5UYpT9PET/Kn1HM71wwC5etLdRgba0LbOtzyhE9uctguA0IkI0rHkpZaEv7DdicdpZcg/CYr98jSp+wOr8BMR53NJmF9v0334L2Lod0D+qJJ/NUAFMJatTOTPnjg1jrKZsdc8ogIoDdh9npxks+7coBbb/P4lGeUHqY6n8bDGVKJatikgBG9/egPH5NwKO8aszpHRcwxQbMUnF10LwwjmjfRr0I/wDwiqnx/zu2SYPt39bIQfkcaP/dtfwD8cVY9tdu6Afhc2szGoSjNpC1zMEwrGGmSHR5+RjIjtLwxzDolNPyrjjaZGcxRvk0eCjMfzViwC42N0XrHuMkrl+4bJQGs68Y9GUFj8nl7rbWiMZEcb3IP0o1Gj8/VLe252z/5H3Qk2KUyqht+bxhZiYdgzklBFwIJRyd2vrv/Ro7iH/QRA7nxLOdU1ywerSoHe6aZeyTFbFROoB4yO38rYMwNPjJiZbArbM/RcVmDot1X3qyCWLi8Zp9ICxD/CTIc+qsE5MCwxsvFn8yNXYyISgCc0KeU1TrYFoeB7v6LEkQuXSU+1tm/OSZI5XU5PVstd7pU7acRVJWHt4EeLd9xVhtlGI6/eTjupnH8ctCYN11M1CfMKpaAr32YAo5GMEtGvMsqPs3IByyQv278ExuBbmxhwM4u5J/y8o3T3N/WEZq6RaZZGICN+7s9nsbOy/8Rjiy9MygDTVTCJTfw3Y6sBbf0ocGkI5ISY/lkmpEI7eLI8QoVGCAcZTjz9iRXxDXiqtJrzCdm6YMQzD0D640EO77SEFP8Z0LQVzykMOBEPLr57U+edgiOXSXO/NUnDKzci2fl/lSRChWM+IF9Qlh31e1xDnQFNoGUnQWbZFO+5jFO6f5hDmeZ/or88WcmS8zEk+Bh04E+5a8XIuQUVYnMx7ABs0vz17n7SXoXqU1ogP9YQvuVBfW1vRhaqA+mj2dHHq+oPv+mKHZZnHIKdEqhxbFW9eUwPt7FFy5TO9ltU0r/ZIieEf1+l2hvfeuJlPyApRJBx1bz6bsA7J6koDEE3ksj/yw+f2ro2XAD1pCmNhAPP7D7JYKbGulzy8BzlWDwi3Bxx+wJ/5Rx4e/Wn4PPtPwW3pKwOXYoPHiF5c3mDOR8I1H0eIV6Erx9brOBsC49NLtGrG6cl0MNA07R74uOjqdueXRsolZfUyGwPP5vpDcO0ofbmaGxyJZ6+xQtPBs1Yv3PdkCWCsb0flX+2Rh2/89WeESf8xJdHLUabU/VoQ457SfOT3+L5DHzALZE9GA1Kz4ade6FLQfLDyZ9bEVaJaE3o0UN0mfbcPy6ldbPrpUi8wcCRB9KFoQPWRHZqzjKcwAq+7XpQd9p7+/fCFrgOQVVtY0gQn8WkXlpKV446HMqKiw08urG3PeDWcKHcdV2s05lfiEqGfid8Gz24kBGM1u+yOItA50ZpERCvZ+H8MwbstcYrS9Ej8105M9v/Cj1V09b2YtEpxtT737+2hij7m2lBhbbl/i778v9qQQ+ZJ2I2QeEv0p2liZQEp4P/36KEVG7weCqeVVlH1FcZXQ9/lPYEDkEFDmMDtCbu73oeHwwl7gAVMaXcaTj4rjNLQ9nKxOC9MLSzcciLC0CSMHN4QMPP/lZLb1Rx44EZslqxr03fmLQJ0ITrmEbrj/ote/du3VBQ87LiDJwrfEhboxvpqIIdls1RT8HxsZSnCyNqofj5qOl6orCqc4k95KHJ8ZlXMCYc06YgyfvfIFpZbtcINj+0hU0lGbiCgmDfO6EViCUdPA5tCtpe9ddje0wVwRojUhLEPuTuf/3DSbpuutFBOY5rj84kocnJ5lbf5h97j5ddmRpY3tEpHAa1p2tjt05LWVUt8hWFNgF4VxByNSakK3x7Z3fovreaT2EiRKcYXM4uZtITcdALwHVGHMOZV+dayrZ5BWhtMI828zqY3segpXtDhE2aE/KlT28iNZYeoDj4envKkZsFPMMP4ot8u5AHuHUpLIyWA7rMkgRlRf4K+pMAI1nYiwWecYaBBTJ6vb1O9cqohGzy4klGTvffYcZ/q/0ZUVOmHYoYkCSgc9ozMtP+j6RH+VQym1rKlO88PRNlXjgp9C4zutPgxuCA8KZ33r7hjbz+cXbxfloBstpsjgfWnSCuzM74DLQiHv5XqiHg2V6QPRx2shp3UripGMoQt1TFvPYpVWl5a+yQLThkn+lme6idMPtyNrW1WrUS8XTJlMHkBPKNROy/2QEodONCmlpkmrBEI5RAu00lquXj11QuKVgDCfspsDRuZEsRw5i+CHoBcMXTZ0Hc0ZPn39nn7JKdcAL+jSvfOTcpTyqlDNfGlJOntGzQ/wy3WLAopaCMPlJ0PbA6u6KBWV6ix0xzVDpcru51dRZvvBujiqh1o2ZZ3scF/EJsNZC7HCzJlNv7V4FjKQA1Bvm43mQAxpUQf7W3Vw5nPraff7nFc5qhqP5N0oqVyHkc9hVxiENl1M1V1UF43v2e2Y5emxBEr05oho/TSiaaQV3cgBM0ci7YMLQty6JAS+o8kranE1LjmtGx/8J2wF/K27rB6hMcMzSbpD3Lo0qttPiCooq3rkT+oCZvmG8YeXlFLunOwB+ERPkfQ8uy47Mz6dQIcU0pxqFY71sQp0mIreG6Gx1PsVHMPBvc74L/CLsmKAW93h9PTi9aOX4/Ng+uEtcxf3ejvEXw4AAo3GyqSDyclCLGC/Hn4/HHRTyD2bNlaYMEzo5Nn0TFVRoWir4gktJr9o3cTPpnxV/vgTMrRI6zOe1PdCA2MmMsaKIf8GhumKwcv9/LkuCCY6uLNrdfPdnWhptjl5TAQdCDSnwdEyWE5Y1n5Z16TxfWC4jW374k2ylM8mUOukyb7+M+ZethezZZHlaN2iZ76VX+MjJt97UyJHi5e8KvPjh4YLxHNn4SirvPGts364Kx8YHrdFqeeICzYEzZd+DLRfqshhP9b368IJQfVssNF7d4MIftp03E8aOFjvOS1piZ59X2VtdQhUV919xAL/A9odbUlln2p+JKWb27Mk9IQYYCRRQAfe9nn303B2nBaAy30oaIQ2meSqAOfBhM3fEdPSFADS3EemW40fdgheEGJKBLeT7oTMlogYoyxDJspGgPFKyPLI7SKAxg0xueYz6VztK0hwWUheJKgJcqI9jZaQwOAXL5B8ND8l0tm5+l6cbn+SkcSx1CMTkti7Fw14wcasgRVn/5RqrkIAiVOVQr07sz/nxSclRcJmEzPZ3sLp7uKbRtpzKWQmuoS/f6ljNmzMcX2JLHOgZWjlUp6+cpg5IBWojokcHxXvX9+7NWLRY7mOVoH+ZRaeq9SlaI08s9RE9DkphhfgftTxXCBsJFY9q65NiMTM/RxcKnhgJSZaLd2UBDTGyqf3eYyjx/BbqKsEmM/aRhpzIO3FX58rBjbuM8WZqjaRWXzOKcw1P1qhchTxVUEPFa7+Xohuj/WKnOJXFK+cBOccE3G+pRDyDhJTheGtJRwFb+TGqlX4l4LUDpyectFgKbt3rkx55rue5uW+bLy4QuUVJXDA9o+VtCOUpM3FOpqquxSeha1Jb+I2NnZZtPZwHhVJveGv7aYti9T5UxXn/Ty6x8sErsuVoG71yL1t0bMRXkOhF1O2Bz2HRxManmov14j/snAY2OjvLVlKMCnxzh5lFXAP0Jk377KxPEG96OuPCKeTzDitE9rtGjhqVdj9hLGxiQMyxC/L0ttiXsRuUGDn0ko+1lKdzHMIYsnXY/hKliHGsk/S8Y9p8cgJQwtu6mxxy0OeAtn8sXSTvHSVvI0K+sE6pe7USCUdAYDKVrXv1DH80hRtbNM3Sa1HpXhww27gzfCeXbK8IUo7o8YzJzXpYJV/DmkpGvD+iWfFcfx0uDI4Dt+r+nobBzTuJHNxevGQmDtNF77wMGlgpkmwhHF05796WnH0j6Xah0H54ulKUjhHiXm0Qh/C5zmQhjkAigy/F9Ol7D612elTAWt8sDDo3ixwNtS8xqm5ltiJxywWldj5cfPOEmCLFQUJbTP58p6zEfYNhZs7Uk8uNxNl0PrtnZHgEyx/CuoAr8NdSTbGBSu45jUfUYpKvPplTkCgcrhIUE/dBLDlz9XGZGEoq4zxLWXCj/6fo2IDK4Bhya1sntPre7cVbZb/jSp+HUfpBlQr2GBeYSc40EG5F5cMECcYBafgQoWCt+DhNV5lCRHljcLjkEGoLVWq5o8opQqtdsgIAy7ZwVIabhFWynHkBO1wCQHq46orR6cX2LZUZJn/LZhmW+6sDIgVspd+jxJXCwCJW6oeBEHJDDICpT3J3t7/zHwGyFgHXgLZaLZB9tbprKJ10eDr+lDIouzwNh5pawi0F9XZ5rwgFOxUEeaSgFMOiBM+ayuuyZ4/nQDbieyxqehWRlC86ZVakjnO+OK9vDY8QCsK/EBdflpIFY9lJ/Lyt254VSOikbRl74AAQgNtXIjwoq8fsJXHeCb/YKnKiTSdbYP1cgWd1Gc3/gRVJGb/umdHSRm614cv/FMMdpFbDMCMEke43/CoRkxuxzPIAeg4DIvDk4hIlQbg8vzp0xyAMmgf+pKgRRR6C6/Z/YBPXc1jeW3lfDlQNswk1uS+b/sgTvol8h8mQk9WemkFHOIYA5hGOf55yrrhv1BkPZR4M/KY7eVUSVq9kf0IMQIyLuLVHC6ho12SM8LrG5TvTZynYoGMcNpbqj3e1O5zOVOq/2UsFcRqeA6NJhDKZusfkTzDsAelG7vlC/hdJUuwttCZz9PI/KjH1ukwIzlzfFmYOeGXHkhgH2SV71T1RT5g9na1MgVNGxuNUKYl2VbgiKaHAqvmAug+MG6rjoXFuZSs3Zcl7Lwne2XPFsKkwxlGIVT/cK7yBCvHvMqituo6wP4yqfxJZxRuZjOFcuUKp/8fq4I0l3jNNIFNw1CFDpMrVbeOEdw1GCvBoyL9GgC4gFxHrvJ7I4PRF2I2SIj0XH64cP1/vixSZdTKTiWRaedjn8Ydy7UOp1uWGoDy8dtWajFcWx2F9WJZvLAeRIDw0KJjiVZagGcflK9v/ht9wUFJ1DlMY8j0L7lUnGEO8HtACgh6cIEg2hK1aQHvoCWZgu3rXgB9lDZubBLFCv5GhBMPeC/HP8GrLX58DzKKoGPuTH6pDqlM1iQV1BobXHHU9tv7l0FY0y57WlTDH7TwzbquzTwRWAgrNhamJor9XHokU0EL92MFyaSrj/Fycep+EZM1hW+sNhU4otut/YMNc3Gx07lIxZ8OsLFqRDhbfaxluyEGHPKiDqCqPxLPpljQZMT2m2KmsqHurOffZbQ8aZNDctB/jpRSmGUt3UyBAx34lZQ+/UrKWbsPNYLciFhn7TilqpqzASPaYaRQ7sfVQY3XNKK9I+uJy6Utlf14wDF8NTwZv4qRS7JwpFcjFRu7Tpt37iG55I6CHcVMXpmhJTZZ3lZq5W9cDhHCDFZb+20xGZVS34B9XupY92TiRnzpxrSWOqR8LzkMV0jYIX9qWm0ceLLDA34+xR4y2ISzyhbuuYNrE5pO4N8nWDwcK00NnYnXIyuq2nTivTwRrNzXq/jx7dVHe+xJZ7crkTuXNOa40u7wP8qgAnB0HbIH8bKjRXpdTRssIyxp1ZF2xQQ6egJjle8yutGBGRu2N20CRuhntt5stM5p0o+qNSa7INKHVCUZEbRMuVUqZpErZwaCjgLW9ir4qd6XFrtJZlP+J2or6DWe96TTEybdE0M3N0SO9Ba2sX2f0R9ihS5030MgLQZjX1oB3koi4ufWU4wkf8RJt3RAt34k42eewzk1fKTxVdkfNYuxd8EImERyUyGi6ai+aKk62J6UW8ni8Hfvs3nZz5I413wHz0TTCOddtUoTw6I/h9FshLXlnOE4tv4gHpibhb2zcf0+leTcSKrP4vzPXCbsawkrXcuU3h5xb80E8vx/2EhLTFIWYyk4YJLvbq8oXRhag4ar4jsjINHzGMG/ePJ9Y+ChnkQOBP79soBQurMRSublN7pfV9sBxVk9vMzla0pJjGjDepyM9FdZrZgJQqd4DQgu0k77KkyN677EzwQ6ETwbLSWF3JIrTN5kjhsYlIFQPD2Oiw4WPqYHjPV+T+EJ1Z6M2777ERQuV4b4NL57zatloOx3PsNu+tSICYEHLwUykCrsDT9m6o0K9hfUpCBTX8ix4xg0moBkBTCLeKPvu4GoNyQhaiWd1TGkzdJnfUoLFinb4VHuDUHHDeSlrqFK5eFnvLTZp1tVFVVKGk9qeKyO7lZtTbyZqOH7n4Py/vHBZRS+NR4vz6Ewfp4vEmEKgHWr1lSQQjrlCfEFMx8n/YCsDUEREGE2PLzDLx8ZrWPVS9Rkiakk3JoOE8orqqIckIoPhp3iWElAxf9Z/FDh29BtXEjJjMv+2T+5+rOQZpuT+cTst1IgTWq8qApIsBGjygVup6AgwzFe87qFrjgsq60VIrdJncHFjw6EIlKwscAbCBB0eHn25xKwElAKK7Dx4izPQ2Ez0sYWEPbuM0pThxMdNTUc0Jn90awZZgNDEvfRxop6Rqw2wxDs1yfvV0xY5uWHD3ViX5waLEP8AyH3M4wnz5G7RYTKGka+EYIMZqFB9k4TVmmWLliGA3kr/fSTDHo1UnoqofhzEX+708EAvGTXrqL9uShT9LcLketSLJITPX5BM9t7gHaGwVopXcH853QtGCWfzYocEDdoOQzmG/4YiGlVeiBKTIdg/sA6NvJgXolv18DvqEYIww5hBruC0oigSASdNJCJqa4JUCLYO7GwKJY8L2W/NUH5PzBQ09pHLMz4TecytEDHahAyqfR0yKU0XfdOiVfRstwW5VsxpK2pgdt23s5pHW0n8z+s+QLhD/yhw6fGaZ22u81CMRnnQuiZabBAw4i4QiabFN6AWQpMbtPPHhz6JzDGEQEIBrAGX6x5ORyieWoiDKf8qsa/Ntsu0CndvPQtGMpcsbM7CDQfSso0aviXuXdJhuYBGJ8mMnCraxUTzCFhI2v6VOF2+/q/DJuLm1CzPQmPGiMqnRDt5dO05xTSFc3kwOD+tNojx6xUvaTUm6ELhsakkaHBLwWDSIsqHVz4SPfg38rElbKDXO1DgSHwAuWf4+ZwdESVMBxQ2lfgRtU4S7DZIPBSNSNM8cL/ZBSQDDrJw5TpJZ0Iuyb4I5cVNyxE/HFoBII3gqZvKP4YPD0GPwzSW62AvGcp3hhek4rOvonH55MvUDGxZLl+s9hDwydBzlBqG57i56Wqzhtm7THxk2/yYBPhZLky8Z9xDK74pQ6CxWgsSPRlAPH0A/soFpcU/xiWuCFxVfvSFj2Me6SIi3aLNOod6E+QLIYk/37aderZF7OBshabmtS43p0n024ZZA5jjrT5CqnyEWOndD4Y58Zf0bzKgQsz9qq2mZph9RtlxJ3YoynPHFU8bUoT/mNQtAI5hqkQ59elmPfVgxZx3zbrsFhYZ5Mz+pvxmqQl6pFy+4SbdpN1EYCtqsFDzXtZAjQ8/yE6NClOcAV0VZb8B2/1oFjircu2WzMJ5ehSRRN0loJfHqspD2mAys6nHHV9z82D8obDSbEtxZv5VI38dkNJQx93Btjiry99ZdD/0kz2PHi7YLo5pqRUbjRaXYh67OmUf5A4h6qYNeZIMjL/XIJP7akIRzUBsisR4qfiF2vBiK2PDqitqUY6Mgs703CilHllJXXcRIkLVuLQBa6G9VqTG5W1n2kOKicilLofQos9JZGCDah2TO/0C5VAiJMH6f5aOCWqXrVNhQDVICOb7uOSitIc4CNvlj2tolVa6J0GmN218MZTMlHrwIrerezv9CkQ3NrLNH+jW4YUaTpuLk/DRfi2ULiM6ytXCEmc5IspzFu79srZA8Ul7q+pDNjabrrCDkmNVb+OHpXDLT1yHE/SIQvQhEKcRBr4ktM65zB9z0Y118riTSge7Axg1mZavHBtd8bfcnYztjgXRLsrXYw1HuHsCunAmbA6bxi/VxltPmfk+TiWda14hk2sZjvtJnQMie3y7hWIJ0hre9Alesec1RFUIlXktLInS8yMxjGCUNiWklLjy+T1Jg4KmlzMdMQ8dStHCu/JG02VMdgN3KVEVg/Z+KDnOS7nsiXdgfmQnMPC737WqKKdmFCSJKngXmgeA0GdMM8y8eQ2HE7bs5hsCQWC+L91Bg2FOhq2Snn5n80t5IRjNUQbHATqlraF6VxzRWrwoUUHMa3KbNt88XmLrd4aqkyQAlgizpHC52keJLJQaQEktRsYfSw43s3L4KRtd8MWNL89VHZs8b39unj3m/t12Gbr5Mq50pBzF/Zl8wERnppsPC1LvFGZBs3bNt+nUZ8X+3AjurwRKCZXTQIkWjsRsal+UvmU9W/47S2Y0xJwEGZcQCVsC9wByDX08eUoFjMRJvTIazVffyNRvEChOpDKb6N8khlT6PrguthoWgw/3wfmRqKta7pb/2bUy6fWrnNcpyN4OhemRqae3xm5bjjlwVQOEEOoiuh8zbB1wE3nYSU4Pk98G8a3LwQdDxFcHHJMb68eYg4wh6IuV/aF16lmTXhAy55v+47bRClYFG7WHFsfQYWJo75F82lqud65MoeKJPKsyJ387axbyntD9Fob8J2f+ECtweSPVJTBkTbdN3P68PZY1YqAPWgAngmAODdccOGyTucdjHWIFKRMZgTbworR+QlI7YG/7XQrX6UbftQngLhqqm3ya/voH2nK/ho3nN+AtEe0cEPxPSn2aDHylPNQz6MjJVCRT5N110860ZWn3HWNW9O6U1XzGvPF1IoP8dZicW9gDdq+2yoy/ngwzz7lTApnll34zNBLsAbRQdkJ9VspGgA9UArQBYd/44irq6WaWru3HfXhdlDAo9zGMECQ5cY9Z3wFLhjrFBDbmsxJwIEA2p5Dt+4loolksIx6n7aJGlPPscrNheTrUScqa1YYuNVk/6kMlfpp/Mtx6p6J9aFwp/Kvjkgr/7pB7EWOnY4z+jdKRsPgphmQRKe2oxr23O2wspK7JV007au+1U033N0p7tgyMf0EBeOJuUO4wma2eRIgYaJHigA29QVkVQY0fTgBIz+fpqT57D/v7QlhE0GEs2eQXfncXjQgB0wYPrsJk9DRmeyyCf1YPvg/oj0TT+xz/Gh7VoILNRSZpeDIeIr6quVZOVGjtJ9tvcUI11pAleVyVDM/SElggg5dklX62Jydr53fQWU6g8TH/GkxBhh4uHH1QSHwkKTt9+LOrMyGNv3AV9ELLWPWoxFpDMN4pHyohwZnrJwSuNiQKcfWoHhbO/c5N3qsi3VRUMaN/88eWRMu92JAfhNNsfC/jUBMX3STgWrwxbrYOLWPJZh1dof9k2D9N0MForJF05MQZBEyWoaKZmsQE729tAPOwd8fKCwx+8b+OV0K4uwZg9FTEk35DB6Cj6Z+MiZnCs+qMqir/wx5IoSGJRj6/r6r3+HvrYmzcsAKvyYpur0uq9I+GcYiQZh7o0THg+9W1SjEonhcHY+QbqBnm1qPOWtqo9QSnA7a6e4QyN4TJWOuJ3XhjWUYwdh7Ce48niCbCbO+A6iGNDMnnUbXvGt6mtnNjzi8KCnWDQSNCoHkTyVyvbKx134XNHAT7lDj5ajj1l78AYalNWJZq/b+jpMcUPuBTVZVEzmaEKeVResCvhVrM3u03Ux+90SfSdKIdSqY3l2e+Un+vyK4E5SGQBIUTaOdDmy8jVuBQT0ae2kZBLi7F00xnfn5imaGL/biFA+EH0wwcmm/y38lJKuP8h55HfZTgDOFXdvFU0fo06tDwmzBb1iYURhCfmxjWugydzRfVcPIUaIw98F7lihIsdFe08QNY9a1RTjBqKig0QVgeLjMBnIPArE/Rnfwfwew0HLyz5J64XDMLiROs5z4/GV/U+ubeAxxcHC1kaeieEmnXR6TfUSSuB97LPD4tY3QLOUeqOWpp9kcoGb0uTu9VHv4BfOFZhF/9alP5F91awH0i+62oYYCWMmcgH+vGW7+UY1JQh4funZYjao7FLXgRx5TdRw4QmAw4+ajpweJcYFeJbAYATMbqI4fVkjV97EgKcDs6BqsOx4T4GiAv3PGPSzHZyejh/tB/MNLsjeTW5qEmeIcAVoIk9VTkqUb6X5Ko+vUEN6tFOjZgS+gi02pLHaqtiMsciuHHvwY8hO5+jKscpdTLc7dKNKIyT90e+oEvIjsFDG/j27n/jTIzZwqhd++QoYWnNFEXtQA534E34cJ6JhgHc8NEp2lsF/btnSSIM60se38aPxWA1i+7tXo9D1aklBiGHaMni++AxEhrBmlMHEFE3jXJhdyL+N3cZEpKkHtLE7mD2WU22Bw7oXIQDwK+2R8Ea8rc5CIsSOVwQdnIyFz1wv7HVK4FdqF4Ai8Lvfju1nK79i3RxC395Vjfq7OzrXVx49duGwQ3/chhggktaSaUwCzf5qfHq0sM+yqjFXl7p2QK6UDCj8HVqvJCmH25avdaO1sVnw8ulLLLb+6rmZFChOEoH1/SQv8+xR+G353jLf/NihEZhoQhD453rb0ZR6ohgbd2wd19G6WRB40E59y/92jSYQruuoGKOfhsKhcqpykIFnXm/Bt0bc9sl+g9X/ZpeejOqrwZ1fFRD2tdHZVmJpUQladxIldasyQJ2NeTK3CKkluQ5mJVzx2oscEfhIM3Pr02Mee0A7ovfYfg4BlKNQ5Q8ot2jwcElrz+zSfGysB+rTEpSSdR5kqgG6/P/dOL9SvzhthwJjSjyM97dfKVtDf0BkdO9/c8ybT96DTyNlm2Mjk67f5Efv/H+TqT3RRJxVb10bHO/VIaplB+rAElsEEw8Avjkuh/Z/bFstrXMC8+H4tPz2RydTs6khF4NCNWJv/S/o+xlQzSumbcY24a7XbMfX0zN9h96mwy1i6nbTHvpp4FVLzQ89e3Oc0wdVZNXfeXAE86KgIHae0uOlu5OlnbDUrwmiPSRuRly6S5GXUQ8E6Mbu9c49FtR1JPPuB27l8nToYXfCulPn1fhD8ciQt4zBNU5P4AR2887Fe7DKzOD0YfLrubFLuA6wL7N+8DA2ae4Xj7ClUP8Q/b4RfOx2BGVXwgT0/n7Wcs85p211BITR3l7PNOmBlkcFgQk85y/07tnY9U0oxWz7MtT1Vo0Oku7woWQ4I6eHOMmmbQzhKbeNoQZ3EPs1kcnPMtYfrELh3LW38r6RaQZL5vvHXixwBA674mcqHGw05xj/6oDTk3yUl3ERgpap3TS5OAwBOOnDraMELJTbWZlar7v06JLrvLEHc+KlYMqVyz1gk7PCzPoYxIs3lmwSP74amD98lPPUkt+vxXkKIfwr1S5xSqRU7MPp4H4+MaHiCOICS8SgnxWOAIQMxdDkyu8UPX5+KBwde9v2n3ztUajsF4PTZegg+Iqn190uu/aJ/W1mBIQcKmDocGwhB3PXrJ3H6ufSR8MOZwbQr9irFcHcKY2DHg4i9XM84g5PLiE9jvbBXsR3uTKOVZyWKWNVmr8D3Db7D4sSA401MF0VurxS3VVf/IV2dJumrq7DS/J9EIQTuThTxa/UolRTJAN1wOL85uZYxX6TmZQp9qgBxl4UBUyqKZDLrdvz68GKc1Ky4Zd6a2bt1ii+eTAMhJgLVtsEADH7N8g2PQCNntJ74fL5pNjfBAO2NMmY+bE2zDmotIfHm4GZYcyZgY5BQKqKyVA8JdsiobFqv8hkpJs6lYXhXWkeuatw2zarb8kH+DQp+9kMDOrP64LAsu9qMEl6oCtalxwsW97blq9hCz+ndNpseEnzEtQ40rrpLJO/tLJvTeFJfDlcgCz1TS+YUemzaekC+rhhGGigcQHs7RtFKWIpL9Ei5q4/7elv5YJofBVTiw1/QOjoLcgk7aG3vWvHHx0vsuBHVK9K9DYYVTkBft+V749F8FPQ+DuAG8qN3W20VekeG4iz1IBVYhXGAGNqs/Xi1Vbkcm3EePBI9cJSpgu2NjQxHih9DqPeQjvOXcTyHlWI/ozQ+aOEe+R9b3GssKhqiMQdHT6z+oujPA8a789HHZiZcNx1a5RoyUtmNfzIuR6jrNjJ+JGwDWVotqtUhW8aWGID6L9CVAdQAn0Eu4YqpXVdvBn27DdV4qwLHsJ0HP3xKiIv0ZAGg7Old2jHHjeGpl/G1PMQPGJEsi1/rfsVEPdafheHrQJL01BQoxbF3OL5iabcj+arPsGLXrQFZ8mYGCZgZCb/6mFussmN7nA6DTw3XqeWNQwsSTB5+RfLNQ0KL6hzEnqH+KvQEMfH4ExtiuhmIsMWRJNFWov1sBjO79zDIvd2dWin6VTe788v2iunNruqEw6R7rVDhlYJGpmANoSuRM2Z5/AIrupYiaKThphxVCaWzYdsqZ9FuUYlB5KTt+lry9gSzhTwvaR7SlIHQRzcVEiBTxEk0vHCGzd8ssuT3G/pTpnxPVfc3DZRug4T1GsDALWoiVtbjknH45PPKgf/pHZ0/NB6tpa7UFCbOBq/HiqAeWztusVwcyMfkKBBWHqc2oAXPcGUFDm8aM3G1QdvJQLU2JmTliaLkbM6vK/JFEtIviQdmGjN9ulN9aiMTgNaCSG7AThE7Svw9ff/1jCaxFA9WKrRTURMl2Cm3LPpPg+i3YB1KRJsupxnqr5zso4AnAf8ericGlzLxDSGw1AtE/vfPL/wk1rNgMuP9Zkm+JuVsEya9P5VvRdVu+co/8pUtY5RF0JZM0XJtndkTFPZmXiOISAKvSjWq2Im94WKrpWRNeqa4/3V0q+vv/UnA2TZYxZvE7AfPGN+BRIPQ42kq+z3VTFV8goK2LTCjrofTww9vIVtk4AJNdhsCYtZdn7/6fQ5RhFWoXIGfCFVpEPa4Iog88WO6j3taUwemMISxf9c+9Jr7UdSe8rjyZqZCvBdy4yLTT/t9Yj1jmOeQ7tdIGN5VZhpcxlceoE2vFbsxnBi5sQiVm1GD3p1MO3cWU4vnJFpuKT/y8LpyFOAcevKC9iFRViOvPhAbLbCduFPEQcUNtwtPAPrFoD85S33Qyl8CHoYlzAX5LuTTDSbmYX2qoSlgRAfYfBKy1dix6bW0BLmLrSdInkWy8Q0MP4EUbtbpXTlY7jeHZhXaMPv1LetjRbcbWJq3ktZe9AlaEqkaIWIKVSLvVw94wheIr8BAs5Ea2PBK8v/+MiCcY7VWNWv9BP5tXbW3UopXe2A2oKKREXTet/FsigKM4pDRQdHCxzo08bkoVr4DXwv3ev7rTkk+n7E+rwp3tojjVpaN3D9ljd8aDmN08nAM9KYYZcqDvEsrgtNmyM3aYqN/FepZQMnD1rl2nUGUwed7hGiq4kN1ECQvxf4wpY57QNKFw7LRHtulLk13OtzdT6HEFxsabPNJzXgMZyBGuEClqjh7ddI03hujwwzEEJwo2j3c5Cog1T94V1Twwts869rOj4qVmEcXrOBxVEB/OgFnmtThtc0Wdbj208LqOPqc9pBImkQiS06lX/2wRxFgOR+5rGxWGe5fTU2e1PKepjbnu1ure55umSnFOgVLehSrfg04fz83vFah1a0morx1XuQLjUhBhgbYzZphoBMVUDwDR/88vWwkPPH7Ji9ADUan2AnxKGJU7Tz+pzCbqzOdU4epkzpHWq33RisivgTDvaCA4xD0fCZoRA7JCswr5atuarM5c04QrNAJhGJcOeA+dveNhFzsz7rQCbjNeEbmdVMPPM+aCyklmmCW7YpG1Q9mGe9XkbNrJlTVSujvVYyhjuN950iup3sxDwrQQLBdndwg7s5Mm6R6MYiznieIlddfV5SnXEsKFZK+5Z53QLY0Nr7qRJL0druywT0XtT0fBszpINa/gSFu4yWwY5fxmOYuzh5OvE9UQuphy6jOFO07kspvEItIQ49SFoUSdxio/qhgZ9PBjju7Uj707ezH/yJeUR2TTGQu1vkvKcY808CyDf5trLycQKBiGSxD6u3tb2PW/+xmexZ110KxC/K0hYzA8pGdcHgM5UEhk24m98163IsCu5PZ0ag7ko6tULCl4dPjScoLXjapmb/vrTJ3Ih5qCTUrR68JohqMf8sMfQ1QmiUiTzJs4z+x72uw8H+kuluh6WFuUVHFdDxo1QaAWEN+mrd/OLAbPZT/To/qPA3hTf+mGz9Lmw/eK8j36F+Oq89a5tigWD+DKRqW94Amns9cVteDjasKBewq6RvdNPHb4IwGrwEPikMcC8bYkMNWj8jqc0WnPb/lKJTvRfwlVzwHpQlSiBHhCrtRFdTiPbUsZwOvZWnEs10jTLip95J3TMsnX6OvnpmXmGlG2tnN9XtJOhUwZDEeyjgJ3fmMsglP3i8nYU7lkcY7MmZ7l/Dz/YEqrH7Z1oAUygvjLdShhRK6E/NEbRHAEdqsyTKSKzj5j0QNWHd46O9uwe3jBaASaxtqZkx1VyAEWVu4j20GVlooUVQhCGbC8INlGn9b6E1SuuIcBCnQrRmQpdM1IZxQxUaDB7PGFLwa8IlLJIcI4lsl+R9eEhaGJxHz7/z4Uq36KH2cR99O55bmtu6Ojjz2HpE0z3I4hcRJdjgueR25HqIn1p+ny444ewVT5oOsAwOHdP3Yp+gduL5VqzC9ynuk8EjCuI7V4gEL8Sc9PWIM6pKFiI0IuuHsCXP91UKLm27oUnLksZOSgEl4CqeKsjNPar4GyKNts61L/JJoiOrOF1bAb89L+GSTaXzolHrvbGX8o775qMci/M5BGnf9ThL4EO6NSsdSLHzvuxK5jTIiiYWOAYzGicanLpU3ldVlLKv6Fi1dbEJVs7slXCm6LT1vaUIhGJYWBw4zRgNlQAG+Kz6KJOSJkQaEXYeEAGhRaf5Xct8ayCAVMkcQ7QbX6MXuWYtx4ZdDdIipfBNBXUrIeoaeRESmrTFBdn1GyQnWfhs/J/iFgKCZQkw15dv1K5Cv5mnQObtqxmIe9RouHHl1ANvRFWxmoIWViD/56K7iVYgx/tMxAAgPc3GNR8TCr03m9qgrdXsVGjQHyJJfPGdDRqUWH24kct10Xec/AGmXQzErS8IRv4zh+f5uOOLfVk8XCCRcxsslKyOxVmxcmA3355VD/opL9u/H4Z6JDajh+NBJWD3bS3aIoalw4xyf4oRcTfYMQNejXSaD897gsFsrC3d4vPrhAs0NzP8yP+MOsdOQ1xs0AQADQLfhrOgza0URaMB2tENy3m39/NO9wiQMBiaZCjv51E/jtzuIesNppg4nwsC+IWObAkPLsquNvvZ4HCyLmAz3LXIJW7f7Ze6VgP5fuqDDTbcADd7+FTARKeDbTFqt91MZF9Com3ZLBTaI1uBPYY7nTTnIQC17i2Ukfx0vPX+s9WOeFfDuMCyD39jub5Iw10jcU6OdsWQc10fSLhHjbmuuip2GDZSSMf565c3SzDrUbOLvkf5Ni4/9Gd9iIDE7XDq72zn+lxg6/mO1dP7LKsNDjWFUXa7c8/SEtXQjX4taue/gw5cWhoXmiuYP+pJpvi5Lg3QHxHO85OehX6mwNjfMG1PEiB4HTQLSQIZIB64ddMwkjOe4TJTRi3Fqk+pBnAT0Yblo0oi/W6m4sPmTL7funz7BSJ6qiNBgjBi2v1wE5wb8klXpdNPPcRDyIi/9UuSLrTNZzlTtzaASHhtcf3DMZWPs5IKCa01EoXU1FJVyvwExX15OXp7h18dPSHzqBPYbDKlVTI0RSacJRS70FLLZeW29ljmNNYUc2McE1pdMDnzeyWAYjVpJQ31w/Xzds8W+dNlN3svfNTVmxCBZbwYzKtnDpXGuRYPrn2IEOAEV1sk221b4GLoi5tPAxO9kbC8IUqBJcZQGLV/6A9g39ci+6/pfjH8x9FwVeyCJo67Unio44GX+Aw6wHiPFG+SGxfYtUW9RaXN0hbVJGk/KhqwNThNk3KE3zHIYXyOs53Zi9vki9a6aq+MvesatyH7J6EDcMYxwxav21gr+MShnVypBI+K/TfMU1e/6QYsmfwFYvGWExEhlCI7iZNpNlRlWiCcwZedWevdKTjEl8XF4sstelJNBLXZiGawj4R+uMrIOOAZNX1qbsWEHtVVTnxTo+Cdbo9M48PHEPax6RZCV/6/NU5nX0+83ba9GEP5gsPym3OJz1Je4OFqhtzzqH5IQGaA9rzOitn+dWHuNmHtrfUOrRP+3Y88OPAWj7xMw2pksKSFH8Bj8ULrQp+P7MLQTLaQWVBJfN8Oi/8QaFO9D6DshkSICF5Hq7AdUc0GHjTAyn5eDeTw+UA94bZdlcUl3sN10stX+QJQy+IrWNQc71S7TxzNpNJ1HADL0zgqM3EEiclFAoXIwikPmCgx6PMYjOq9hXuYMmxqEZs1vwI3ryH+NEoRGJaHYQlivrouFMym/ZCoyi1QRiQywAYJAU/apqX953VOpghjhegoyPqABYkROFQnBgsOeiExqdjaqcSb0AzLmAL6IpYhoP9N5C0tIrCPsLr29sUakwzuMOiXt+tzIHXLHnro9YCjc0U3ChiAzVS+L3Uxc6zMIGPrG3xXjcG6TWGkiRKrdaIFU8gEnv2CU5fibcTtIH3AWaFwaxirI81P4Rr28akrFF8sDNVzEgz1Yu778vs8l60Da+3NeoUXOd1xIGore4e3PL9j3qe/TYuYl5Ysx22WjuQO2y5faUInoRrN022fY7rm3KU3aIhxKFEXozg07lQEEXdeXTNtaqmNU5P2OWl5FG3kb2v92Bqt7QyfKYQglaaiN1zPPii+4+2sxBIwmhisVeSh0v7GCAEPPvOcxE+QuHhn/JEfbf2qhL9ri7EkWfy3CTGAWSyYs+V8kEptoRC76Dyg7NIBK8I6dm1zZz7wOSv5U6o+aATQ+2Yco421utI8RMr82XtldpKNO8d8qPCBM1OGLhnDw238aOndl+TC5z1fxMFaFm7MjKrwJhplN4XjhTTfe+PjSK7Y1HGSOVVk/FcU5Zof3kxpKzEa50XuCPSslxsTI+fmTfGhJF0GSdRToSb4fToP5lhAbJhaeegU4ButYZBqOCTGPaXm//y7ngfsM2TlyjCxTaq5MiEkUk5IQb9lpbOVbdCIbapK92zbsXtYwyrAUe45kXn5wr+6EFkWDdSiqIJBVuz5nF0ZKULyLXp+PmH0olCMaMwOWnV2DGeTVGlrWSvZOBi+SRKUtaTr9dOKmIR/k5d1eKyZYFnqMYJUamAFQ6a5NlCpRu6m4SHrt5ClgwMqiof6I6Ue36EeuQQkkSIXkWRhsRsQ58Ix8KiptTJMw/N5iW8ZKYB+GA9P/xo8r6Uh0kEqk0Fp2JzIr9mHCXNNzJpHUnQ2YDj1putBWGLtXaOc1QaUtwsHMlwgIY5MrIgFgbUVvWDig1/jQ4cWSDw5lFzGfqaMEs+raYDQsgHA6U7g2F43N87Xfh41EXbjf/StS1RjJ5fRBFfL6X+5ca7bN/klY3O22Xkf65Cj0mceiUXdSjCKDzQVRF19vWJDyDFE0z5R30c7K5ztwv31cTulKtLJqI+PipTi59A5QP9mms0UiLe+TK30meRlLHkk++QyDSFLoqfvnHEzL0GOMUNQ/9owPano/TJBUZiqFB3jviCkm+v9csEY+9dM7UkXsKvDmIlgvVKP3iTsEQO9Ml0EUZ8GEDjl9BzTdnsVE86kpcegxM0B9aKQ3ppW6wCy1KBI1UHcR/7NEaVPvdUhI6OaNKDopObedr17pImInOSTpJYZSeRzBZ0jM73tfCHC51gNxK4Lf1wR1reoLgWfVuiZ7fg5C6CnczS0i+3CTSmWjb+UUIZL5fk81sCAV/HNL1guvZqA8+azM+7XcweQdHDv3TWQ7g/+oBx79OU8HPcJW/WKyxdBf6zf8se+EvvK65WBXYkpW34qUCX+ERgXoXBPU836yBotBKGiH9c6QvxXgEjCjNK+ydCjr1mfeKG7jkzFBIYkj1Q3yXIggzvvZHbWouPaJ+E0kSQ7aryuniM3qYfIzY81UItTDlbvWH6OCCqElFIFN0lS6Lg2XoMbPACt24j+1ex17nBgKEp6yfPk34Lyj+vLZBtRtJZoXPeWk7z92qb3fbPAxsuEpVTdw6xCvKT2t2pbebs9Qyt+3MjAHkLl+suKkkQ/ZT6h9NbgeOx2/p51qPT27jVmo0OJL33sY+TFvZ1ynpJxOaWf4dL90FrKixuOd+B5R4salAqvnnd7VQEZvi3He4edUesQIn6AvRCOcYIXt3lpv6iOpM3ZiuA0OPoS9jnJYmvD45qcwwQeA/3a5195nNM1iMVYXqQ8CWR5g7hXhnLP3/V+WEXLcgXMj0yZAESLXgg33o6UcXlcvRkoqE4A1wDNrnvmYEeQK/3jolnsahfvekcHDuPwvO0tATn4tw7oeI1eZyByXXi2KnsK+jnWm7OUz/TWU4YsKfjwEZ1v7OGGPkmgYqQsU2iuwbKSmO02jUCX2E1YL+TSd+54vltb6T0n8H8lSaXlBur3R+Oib/pig80bKL2ngE63L7xmbfBybKwpLzzN5KXaXVXTEIgkwhZVdUfxR3VguHJccLmoeDFz230jVOqLhkXnuA2foAUeubHSoGXD2TM6BFZwYjEbtYGMWW+UEJRrOEMbXmKWAQQUEDZ6Sdz+jyqw+j09lIDedZAwyssmpDRpviQWPwxcK8tuWXNi5MQPbTAE1gwPRIK+tzlFjkE9cxswb0m180dJJGnRubVxDzqQkIefoWUph1cREqiyi3b+LBtOy2Dwhh80MYue7e2PSy8sfXl65EeS0NTTAA5JoZqH/fFBy6JAENKhubZH/uPaccreWOl3rDPqKOciG084D9ct4Fujn8xuMYDN/Y8GPUXRKIVIHCaiOgBG8quuy2pHgz7AJ3keznf+9vWl47jvVfM9u97Oq4LRdAwZ9FAYq0U8h+7/1g0Eb1Xt8TppG+2i5lVCcZd3jbB+CWqw4ohZdfj79TV7SR5EcAL+zl8VDoYPYi1PY1OMJMOWcxeHSPZhNxRiUT0+7so/zozX8rEFuVex9FJO92/qh0smfxHQa1hiLI3IAiMimWHTP94A1TJbdf74FJbM1CPID0ecOLBUEVKcPxfH68HyWiSFwtczlscPuIMyXtzkDKtCg4pfii5s5D5FK2l6NnWZsNaFswaA6XbX5y5OpaXQiI8Oty4ihjbMGZ7cBEJex31Y1zB0DxNQsJ5pM8NDVF3YHwS21bJSJRMnhYEZHQ2ER6qmRXJcTdVMPiK2wkCqYrctYXPiB95sTANbq1M3Do3eaWv3MQUptKQnZrTanvSXl85gh0EZ80QflyPC6CMDG7/GgrYCPK/aNeFw8oX/y9RtsIcdVsHlg/5Pha7TdgjryCU2iZUygZgxTTZ3LqQyM6hHk2ZmmMUXIY31FS/ehpH5Q0d6j9u0P56BkbBZFaPODaUbKY2ky+oZNHSGtcSkKfrb08s9PSbe30Bv8gjGhXoKHfOcBBswbRLU969hGqvFtanz0OnIKIBCqJr8rx1EKty2nueVEWAOj6mja3dOsyNW7KIAVHH0+SWDSnvZi1xeWPOg2ZJ3WHjOebiTE9XmqFVavnPQ6C2O/IMVkLzKQD2K9BTzsMv444AfxKycS5xUzbY3ESt4J9JzJ+5Q5SYLl8qDXiQC4A//obTmUogUq2fbrHUN5Hdqv42g8SyaeWHe8em0INR45Z2f8P+15lZ1PC4XqrnePalmUSylnZe9RwEydKgUiC4+UbjdPhIVkSgMFxcH32MLO5KlLoWSA17WaOl4PNdTndT6UHRBgteAPjfWrOmejGU5IQVWGBpc+ZlQlIt46fQ/fuCPpTMlWI6NHpNalhxTXVuau8GoyNRrSxDtW4e4/P4GczSg4paUoN5rqB2DhmQY3dSnYPqLkmGzBjf8eJPxaXaRBsWlNVEc3NNQJE46pQz7/O9GkaohPFC4OajdLIkT1ozQznnr6XY2q/ge44XYzIZ7am/cmeuA165GcnaIzNguOU+IgSIqSQXAYBCQMtLw+TbraxnsmU0dAsEbMjtLNAEoGnBPnz1D8YBkNYv5MHVA5GZFr8OMwv2gmIpUkZyHjc/N8lHCqwTMW3qk0AKanSSCuQHu6NHLKU2QmK/+pkdV9Q9BfXcRIiqwBWPh4UGxyU5nR19zaJp0kLFmd9x8KwXuxeORZX9qpkpinAcV0EDDlnJ/vtCP9MlZnauCSJj4VxeX9mbXaAsRmdaboQHnBcS6UP1bAKYAhCjdGXOhzEMmmSTa8Ox/iMjxWaYn3/IOmcYV+TQxUoHdfkxe3TP3rpW14vp3m+A1ZQlSGyb6qyH0PCPqEn8ILuu557E+9U5TYX5KKndejlo01SAdyM3Jcmx3hufnAGhHhCx9wBuwULWi9M7Bjh+6ymmLZ///Fbsh2zaW4gZKS455/AGTyyvuDJRzwSb5xKKViF1hH+kHLGNFqWh5uMi4Vbg8e6Nd0hbK5zhlQ35aPwNgmHufzX4gRAwcRogDNiQa663mOzQYNueY6V0yH2HTmEAFE+qI+9CmMdx/Q7KEha+pDRtwBHqhqZjthF2aoX9bnjveqpLWrwckXdA1GvQQO3gGo0egobHQYZtAPBu1bfMvsouFvexFyW/BQ45XoRWONjeQFLSt0n1m5tEg5FMUoGPgJs26UatUX1ciOkO9bK8388Mh0nFQWmgZB48COgjyVm0l2KIuomdrQgkwg8+Q6+1s/8mfK/FNqQDNe67lqQrTGYP8CyRTybj9PoYgyjZpt8PYVYeQHpET4jZEqMG2q+icnmcrG0UZc0g5SkayG2J3al8/074+4/ekSAawDR+tp3a5ICxyavlwO+2h/ubzoZ/fakiOTaQkNUnDF+tw3f4bJ0c3FiqtIRnXLCH3vQ1YCXAjzNeTtrE6/6cw5IcM+Z5FqA89DbgipMpP8tz4u6GeirAt3Og8A2JGASwUU1GKtEoairlJM8MGcPzRyUfFV3+34tBZrBHMeUmqoO6hVSRt+TpgGsVYWPHw5gDtYrlKdSN550d8tO8b6H18s1cjF/hsF46eOEcOep75/JAkJh1uvNjUVVmM060173Q5pAZTR2pPT5oK+CFwz180GMJIzY2PYhri3OzshvxW0NiKKBYZNzzD2kl12lSuSOyJR66t9xnd3s5xk/H7Nno4vOhW8axNo9LlN9m1KP/8hMlo8dPDxf2FLe/s3OQ8/exWZQJtFW2DGDUh60YexyCg+xW9EM/+7l0voj9S9zyjmXMfnggJBciKJCDOZ0x/K2qbJyzGsZU/whdSc4nhi+FVdum+qYZYncCrOeYuXnRtkcZ09LsPspPPWkmuZJ1NIpwbepOR4TEU8qFT3zn5G9TuVYPXjVDiDMGgtEeyleb3CT83lqLz6YjTVv9ncuziMOT9V+JqoJd6zE+4W8JnERXGPAAhiPsMGq+lYZg3Id3rgC9R4xx0xhm3E5gce9neEzlvntJPWFO4RxnCCdqhfxSrYmO3ey0AMyOHB0hruvn9M3vedPeVyIT0hkBiq3XxrN2o/mFhhj+C23Fb5awpRcO8yzqYeCqqcFv7xaK3VXglc55RjV670cCTBlUGXtV0sF+lfMyOA7YxpomPzEu4i8gIL3ZKstIXfzSEnNz9AzUFAiTszAb7gIIT3EU+UAomHq48DdvjMRJIVhXRHKB1HRg88OPOVFXO0DbJmQbJGRQIXhkmi55H3XqbwHOT4w2ahMxF9/2Agw2F/wZ5ddCJRCga5o95aSX5lxwV8SF1G+t9TWNOaKI9vbDeXEqF/NHogWt1gLm36j5iIZ95etW3Lzuh3rDPP8K6phHuDaXpdsfSxMKUL/Y2PNSlh/XMF0N3NnSsZzIDr9KaYU7IutNXIsMZw3YBEAbxF1tW119s3gDMkGpWFxWNlfv54pH3mbmYjftHdhK4IlvQ6Fdqc+N+/yTqLmRWtHQd3PZpHuVgZBB3pSpw06r09dDlfda/8rm7MIKddbUkZxoWlXjPlwuhXqKfSzKtIRLCu2CrxkBYArJ+C0/47iM73kCm15B+m7zUI9xrUJqYn5YNLBWDpmDOP/MrCvrP4azRDyztZSYVScVNg9oItMhbuwTYFPMU/V4X5cwM0O+dvbI8dI5K6/U3nGxRpingDoOBuATMZ0+PSsDeIG2DY7w+iTIfmv5C7zG7WSRd3tJZWO2GEgk57AywykOEpE2r5oaVb9GQlGIvgafsgbznojbsdw8+KTwMgjtqrYbeetgPH2gA5rGYDHJwL4HRPBOwundlpt02nHfjFlEa7vDLArs5hCV+SAIHN9Mw7FYcSG+vjil007yqSti3vsfnGLYls4YfZf5mf3bUdCcR899t63mDdEfXJLxpO2TMG+8Ga3xA/v2g7JvDnuihH5LayGviIIMrFkiejL0N0Nm4jomZ9gsi4cetCEunQBc9XtocMbPjZPRJcGaVmf8qV/o8XklbBsh1TL15aCos8vWSkzKe7EuLhpM7eIGxSS8BjT2dwVgNfy6MmEj/VzIqw0TNvXjf+JxJ+60+cvSyzcMBy658dwCwA+Af/51kdxbx0uA/a91daHYXUzWBNvtNrGUFxl4MDPycI0uySvUasnT0ueYORTsoDg0d6npN3cv0grj8NIPYLHmljJ56QahZol3BDKEqYIuNZMmliuYQalKw59IwjO/lNENP+tvqxLv82N3TMbbSCuMJ8PAhmp6wvlCHSUoMIc3248SsepogDfstxzDwDqkFmktSqmZEN9C2wXwulxkPSVOQSakYJpaYhuupvu011T64zds2DxjJ9WPnCQa1ZDy/pkJE8qP35yG+vcBmpVA+IB6VkthBP+70PoQYbnMWUfJhRHIBL3f2t84nklj2A55rVxWHUXP44aKqL4Sv8BAYqv/WswkbzjgiGq+7TTWNikuXaniPqJssSR1nH2nRoqiw3WpIarfFNPHn0i9K/Ze2i3gU6oPl94mt02vE9cmtiCnFn5vqcsdDTc2ekeTAui82hE6cOFgWzfCcSUvW5gT01cTy+pwPgRI6LE8IjAluqRa4K8rDrKvnK0jtivVyt2A9VXLtEDriCquCzCdVeko9xAYwLRLbW+03plFGPJirDPwPmLYtpthcH7d0dYMi0UuWUEK01IM7H5+dxm39hTogHzCWp49yW4c/GC7qqIzH33EFl1fPXHbPUWDyuSLo1TI9/2+loA/lWcClEKhktRL8xNSbZ7NLHHRudDP0QjGrqylgQDTuOsRhLPAS1FbUbmZSMUDMYQKMZvEYdnfqgtwm9YKLBsw42sDm4ZR8FQhATPBzWqZAl5CJmVfygybxRKJhpDjgegCh/00WpSI/jaHmiQ87iiVcXG9iJK/P3XIRVw5lADFqpAq14UzW4TCFJUrwhBaQC1cncG8lU/KUxA0cnxaj8AHLMBzZT0xiVgeHVhVdJkCi/NRY47xueCyklKNeKu6icVdUhCqbE9Mm9gPIckRjewVLrsXapwmpyYbeNDUO50peQ5pZahb5xjdz9s1zCTuwlr8xigFkB09NoxQEjMTvC64CJmcFgPyrdLbWimMVovuKA0IaP7vM3XYE/jMTsPeMM7optADEh4rcmoZutEjEpWDse0Xf8S5nv2MHdXwgDeNAPf/zuNhiPEVh4bDu+2v9kLUoiZZ7qvaqcAXagIJMiFwS5iCh5CFMTGVmHmdkTE1coczQ3BRxgF6U3LbrMyHebS5uGMfkbk8IdDEsOe+C1mP7fXgBu5zPJI6/sUVhJI86sjerKbLsi+xhstTXVyEp+5Hcg43ttgR/aFeze3PYDyBW9onrFxJCOE/B38QAWkQ5yy4Q/jMPyOdA26DMVCwzgCMXrpO+bJhALRWNUwT7NwVrTcFGxVag05dP5iGI98MokEyG75PASm+9Onpepx0KlB56HcUQ50DqeQHvTTk38cxcgbuZCrqOADHuDIV9R/2KUBo9uJlwHooa8//gocon5jdXaHUYA/lL9e+FnLwuNEhqqaDJcmRmQNj7sDGtOxHKcyMf4qwRzaFLQWMyrswQZlRJUHO7gp+Va7qnJ+LjOgqNotPp2HxOrFBCu+pufcj6mCr23m0nzDmwDPOWvcnZCWBIVTTzlt3B3TtpwnpdpCwuEdifqEQatJ1gfYNk13+cX7Cywlnrtt6w/XLqw3vNDtzCw06yzAmiuez9XUWW9++H+mbBTxFbpZdEqNG4X9J+oEXxKABf8sKeFhoy0U0F+Jw+NOs7VZO88pt09pmhdj/KGCzFT+trkmUJzAim4c7Lu0XhXzLfd+rfDfetKMZB5mcuTj9AwFVEzDQQBtcFiFYmWHOj+MQBTculkr2mC9HSRIARZ/W9SG4u6/y3exEkCecK9A3YISFAeM+TKa5LkKu1di2/0xNIBYoRZetveUg3yK1lzjRU0LU6tf/zpNf0fVMC0om5WfNido8OwF/vX5uhErl+TFQsA5nL6wHKMz63oihhXB6jaIfSEljSPgt7hJDzN3v4oOCspnD1gZD3vF8pYppCkrBDP1/WdIXa3VWD0hSYZ79ujgZr2ZpRkcQSbYoKJqnbbIxcQDd1sDMoZ6FPoFbKUe2iNatCVBhSis0hRkgWcTT0IlTeay5qf2riiRJJr5TOfEyfEa7Iu0c1M1Cyi1RkG80HUDb0hB9uF7b5VBuheC+QTclp+9CBdBrgAhfqFgdOu3jhv/VNVuZuqr8CMfURoIE3H9asrkTiylZ7irCOzpQgh2pUg29EXe6sGk8yHdlDE7UTemdGPjzrqk5AAQEjdbUZDdL8YFL7mD9qeGLHxMMOwnRe48Egulu1IzntoooDR/odaLFvIXFw1n4/c9wQb2lMq//218Q17/8BasakeygwgF3npCJB4xz14Wn2i/rSFBWHFD0DEexe9b/F8b5aF25xE6VX3Acabow3upI97apI4PGbobjRww86r7ElJItJmmLtSWKwf/cT7vgpDxDSLfDh5bpEjYtK9uqpkde6e+AkwY3kAaIDwl0S2HYC3TfKnSI56goSKn4jhjiXX/QKOSD8yEGXOXAxzJWEY72WgYNFgcKPwJdXT6sCSe26wlZHPay/D1u/R6mhtsnoboMFIiDHxNTETsbJKGTM6Sx+GmQ7TAE/ApJxMxJzM3hc1BFreEuA6f7sGF6tUj+xGmCQOfAWF9IDjiXak/A0EZZvVOi6qPz1hOqi1dBU5+K2hqkwAlTt9M7w7zkE6C8y0vOvjtsHkCXC+GXw4QBajO+ITR/oznqyic4byGJXi7O1aUohRfUInAIs/GyBigwz1VxLEYIBp6MEkCe4ueA4gIOSctEbEBxN2KYX5OAwhpCMPpWFzecBpZmYozf1tTxDT95RX5V3srI6Yqp3S5hbhL48Farp1GYexuJ9E982C/A3HOFGnHH0QwGWEPd3PzgEavuCoIvbUYhqMa8y2OxNoVBnaOzYINhd+V0+GKYCt/g7Xrb46aZWZEzN891FtvmNoUdaBUzOJAsMIel2isfiaMHUgaeC4nutx9wqV8E+ClqHpn165Mvua5DnsnBUdvKLwbGF3rAdNhTAWU9AVWxFZ2EuiflB8SMluKjye+jfQTUiWtCd2iWerXUyTKtXA21i6xiAG8ZwqZtB5v42gYFRIQk4OSgVPEURwdcShCznu7k+gYATk1zXh1/ZqHsDwhluDmtbIbyBOVgh29Mbsl+be5fc5sMhe9DmcNhCeMVtSJveyHd7td76or4ggPexJlhvbUlzhhuBODZc11S9kABfadVjqZV2sByxk/DifwIYr1JnlBZWpsHmx8TYz5hvw6UNywOa4hIPTclSNBLIhdIX+IqcyCeAIxOPUzuv/w4yDSvW+cPrDd9ORiiynX5rCb1uNYRCghYP2UH9ko4mdBZu9NqhExn0xmQrC6VzShCob/3pFm1+jLVuMAQIZPRkAMknfxYog1YWXB/fkapNlFwgYUn3mjfDk2FVdNdxJo2ymTL1/nCqbgxiTeLo3VabmMrXjwLroR74YGwF1Ph2btu7uIffYdo1+uVGg/411Q+jf/MX3qzObyGQUWDf2wJRAI+DI3rEvNxkVtZedsPXkAYHYGYqn4CbzH7qPT7iT86C30TvWacr39/KOx7myWqZlTRdO4Hfa6gJOvxF3pcTm37NZGtkZb4ayjpNI8PKnJXC/GRVXYrvUXbWz0pv7VolvQNQ+chnS3Vdf7fOTcBnIVW5yS5VtTiwdIhwdcv5bkqdO60P1lEhAUf7LKQmB7P3WUuX2883qIS2xg3nk2y2gZj94i/dvqtN4f3XL9RbqmBkJgNty7FZkHATJxxWxtVnAonOsO8s43dWOsB7OlZUG6OUTF1okxD+v6QKhaw2uDuXyux7Nr/RdMMgZhvOdZmooeXJnq9DhAkkb8snv/2V74XTF/PSK8F57h2FhTjSCMCB73GL4EjuFqpsq4QIJO0bwXf1B4zUcnRLtP/FSWVKRm3XBRNrYqC0uPawBYGfuhBBu+xJ8CZxAbJGDUfn2nj4qobSEdS2fFs+U5N7108/WJeiIUJOIMY/Ho/GelGQ2fL9DSHZlRUL9MlI2An0BTHJr6/fFOz2RhXcyDsJ26HkM+GXgQH+bQ3TIB5Y7YsC4kWUxHC5Igqs88EFe9TA0MM99WJC2vERC1hJZKhWe60SlXfKpqL3WFJjRPe3b9crrcP5VfDDhZyJ2WEDINyNx5EfjtdNxoslkuV9gr04b/SAcvsUv6EK+UbdRzGrPLbeyBScDEeC6cCraeb/746/l806xymcEs+fciG7ZenVGnUt7zEaw9ec7xrD5R8NdN6z72ZAK9iUT1DJjV4dvwPaFBfqgQTPk772fxotTdhDt0z7UUa6eP76C/Ia09YuopoMjDcnY2QhPOXagv2DQAKoz6DNGqe8gPLO26tS9tiPOpBaX5g0/ciz1ZrP0eBP/8+gTeZedGGNwWN8w4hqVmc21/Mji7vxGOZY08Kb7B2Ffiyaa+WYqFl7YsDlNzfR96P2bXT9CUTUMcO+o517c2Pl1N0GU/6xTr90Pzr8I8v4f1uaxqTml2f8+j2LjS+M5xr3QhtkzcXEHBdCMFhK5L/rrMPEM6WSwpeafh1QjHB/Pii0V/ch3rrJD/f+/1OUJV+Dm4WKznOe8F8DYDU0KnNKeju+28X5e4QAEqZ3aFPUZj24zcY8gSyKM9YK/S+8YF3QMU9/tRy1EV5mfaIfcgOcNzmy/1Xum7APYYUPAkIMh3RxtWjvR/Q3UzM/avZxwK9be/auXRgDLYk2gwYNK6asd4+pN4NKRkYVlDn0ESoOPF9ysjJvRqRzZE2DX5ldgLpye68GjIeXAbcRzEyqT7xvkmJnXSsWYZ5Ya/q/rpJSxPdewf3Qf/RX7r2bMtNqjYJiPFUfgfvLMn2j8N5fUz7PmZ55DXFU4OGDSvPd9oRM33nzUE3EZqtpU4cSJ1h6PTbYJyHz15Omv9p+yPIlzaytCqt0BFUwcYP69+yNX/hs4HB5GOnOMnhB8+Eo0zKB6Bd/cOI2T1fKjYtx38aGQ863q/hH6dtYOHd+q5IXdqmmuv2DIDIRgfGFnSlVPWFCnEGIAEanwtV9N3hicqdKScy14/m48y5cdGGuOosGGwNM9g+7OeVQDzS4dKE96v9bW3FIiKrHbwegkCcr671oaGjICKex459ruuV5Gxh+iW4ZSMO9Erlo/6mnbpfOVJC+Kqgs/NTCEnk3n/lc4akpbhoxOvGZsFQs0tkfQEqY1qfTQGRXaIus0jIPHxag9S6Xy8DyvinOj86+L254weJyHqcbQYzODv11n4fyYX0IHzVRa6f++Cjj98Qd39ZrbcAnLLW2fNMPASaMCm2amw0yOh4Bgm46TfHy33vO8mANQTa4P5MrI0ulq1+BNpNnw5vfBNaydIX8PahWEj09SagOaIYRLlVVXVFu4FENyUrjbq4M1BJHEjwwGc5lP/IcPv0iMVCRJm5jPiBcePaR7dvseMXcaY5ayZR0KVC2WTsPlyTV4dy0OkZuJPYl9fG7PF9RL3Bkud7Lwrwv+H9ZeUABt6+lqLfegQsMhf2l8KML1fyctrbiYDIuI8pwfqYPfrtlHaSRhi7/khu6f17tGmYFluRqfdjjhIGva412AYWcqTCNMAHzloW7GjBGqe9qlDQEm2F7fYVSl9gZJ2Y9ZIqay7amaD6vP+bN+Ei8hP8WySy6VGgWD6y+zG6zqR4vBjbk1/0qsevcb5YeHTMXPbi+EcctPpa6XHSHBBt0k1bDgX9IXcxHqFjAMLCllozGvjHDTEqrJQRhv2Uy/Zxk4TF/mq4TZzl9LddsENZrgFwYKEdnvKRhBi6O3i1cHJh/G0PzHOTaM+JZ9TJqWbICXUJuaer33HfbaDklo46UCWUnEkMxudch4w09G/vw9LkYfaJTGpwfSWbMBj5J/Pli7SBknqeX8ZcTLZzdyuEasizm2ma7ToP3bv0V13X3MPNLHKRh5P8cJpcRzLvWVIRKwgumRBjD0F/s525ViVRFrbcvJYlfFKGNZCfKPhJmRTX5I/cmbVmPFLdAiu0Fgd4745ecNEC8CSRziRQkYNEoL4TgHTKfeuc7O8ihFWBOwCrLwwCiGhNxRoRETp3MRhMsSpGvQ0yPuOsE7T3YmqU748x+xXQju9sEd9q4ZzkD+8XfUpiFFv/dXuN52yhEBoxbVeX8KEAQQSgbyPqzJbtl652ND2F3lPVwRFXh0wvObvI4Ou+XLwOFTryKRBpkCSVbjEMIems3+2alAtAuRQT09pCElaHfRhFJY5O7qjdd9DdJJotVigWgr/44zpOjPhaup4uJSi9EKLMe9cKcTkZONDlTUsqUzQH8RAa9GEU0sFwY2ia8gmXjSET8P7pKYS9byntqY1QGAJCUCxKv1Yned0EBWfSEA7DEGSF6ZVbAUCkTY7cLChV47JZRN2+sPmmw9li9GIj7tYckQkYYjt9/uwvATu0ipRKLrZbheOSq3X2CdH8KU9bgOraYrLwm8tb11tCE1G3FYeXmg0MSV+gU0hyxIzkLSqaMweptLPlxare1P9EdvT+WzTA6jLiTIfXEzm5OOI5rYc4VPy7qCtPvDt+ucJvJnhltVlAp3INwGZ+MGudgs6twJGRY7VnKpl5Gp6RpzRjJBULwG/wCdHmmiLqA9kcfJS70+0Le+nuDTOanbdabSiHsRQdfWhktkCYQr/kIjPCdCBJhm1PbwDLh8vf1wMzTcv7C0haT8VQ2J8TddiUezSNEtgH68jhUGGgfKtdCEb3XV4Y1/bupyVvoKMo9Wa0oq5K0efTt6OYDZiExDXCebPpdtDi0IEbMF5OEN8UYzD+5jy/hyx9aUecF71qLOgWdL7NjJNQqhYa4qrf8zJskjONOC5itiysieXnA4dk3dOYiDTpM6xWKUZiMEz9nKuRyqF49GYSQLM5GuglEl8ZN7Lqd9xPEjGG3ymxcPEsTlV/hKvrEkwnIypYY2hrk4wnC+3JhfE1/hi5vgvri/CJHwoqufbH6Bw5+eIA4poybZrUZrIyzp1t2WGp0vC4wBxhPJegjigVTCFne1i/pjrmg8ERVQbo9jDzC5iizl/s3/JGWgtcTB30EKGyol1Z+lhWMEHGRVSRdBw7FaahJKWBSGpHszGIbAhT1i6idkw2wK6/8EaHi968uOX7E6LM7xwHzTvXPs1E+57kdAsELWaoNmmxwwfhBfqyQP7QKEWIZN82y2vPtAJSp9OLHX/0LsyV+G7Q935OzZN3FQDVUqO3JRlfb1ld5+V0vkDub2VKc+1mEVC71fhJLsPfJ8LRPcK+ombzA4Ay1/N19U85AoG3UcbKKqAum9SF6BDbClceiFGn9t9hEr9cChj9zzx+smq6oRqL0hVALAlqrb+432kZZpXRGAHmo+SKySRGc/OGbDhC8sv5prIWMHMnz4x4bOcDD9/aa/5Lsb8sWB9cFqjNSrsG+ComtoXq4j+ZdK119cTnbFe8vjrjE+GorjfAXl8MkJ/gds/mEbm6G5bIEBizTytW5kSJJn3p+N7g4TKOWqCtB837ZL7XYOBMLBAmCPU89LMRIJXJ6PlGVqlmtijJbBoNGEG08awUNPYw+3jA3HqBqQ3C2Ezq2UinMoYMmVwTG3VyB1CrBjGH2KDAV6VTdceB9G8HebIbF4eYQdi5eo8BlkKS6UROFhdl6XyOzCHbYN21k7JL5UCwAPoLmz9mIZ4tGP9Y8VZRrwkvUbdgVOLA7wINtHpi1W74BNx/QFf7v86+BSb3hBvpHQ8GiW0ghnM5NkyvdfA5lI514ZLEfVy2TMLOWhNr4hGJ7aPJtqY28ixjvLAFwJnQGgbvqZVt/V3loiUSPb9pn1eey/uEjiFH1t43GVfVUotPRg+mCgN02PwaCiaNL9d78GhQLD53L4Nc+61BEIdGLRdCu4BRza5YJqk7t1o2TeApr97TjhRcz6WJ8Oh7fvNpdhRMprHo4a/XNQr+pBzt8W5+lgaJrv3ksXXWZE4gjVRdi2CwNDu1E6vdB/OqCwTG5+3KmOvpOuJSqt+yx+mMGWIPLvaZ8RP8kD4KqEBhRbu8j+ZEkmA3AwWieUCqXkE6YPETMpgp6c09RBobORHmiif/JRhDpbJOQyhEpYec8delHriOsCWeFEIraYkx2yWFdtP7oIuiYwQ/JGZPhU0Focks/OaF+vRN1INab6taPHF1WhFm0lJWCYgqoypdFyXOX3c+pNNQA9Nn56A1Xl5XXNHdFp07/YgToV6x+JotpSn1UU4Ld5NldXx53mKcCEsGSeE59cv03HEiAgkmfWDaM2rqrNPgTokx94kcPNXJVRQsB1+esUJr8sxwSkmryftTf9JqwCc4TViCHuMX6lw7PrdADCOfzZioJPBn3/KVK+ljHX983G3AatZ/NydtUBduqervpSZslwpKksp0+5CLMf/+1tPBYXn7a4BLXdfEVYktSNUSHfu/Ksme1ruqtP7gkHAz9F81SGS18u68o3UHp3nYvbGPVaO/c0BkEPeTbWyvgALQEyDz/paH2Daum7cw6ncntwKQg7+JXDFfutg9QAc9tBzURipmaXlzXAT2wRB4rNqu1rAO7kQz9vyXHQPONcQLSRYK30ajX4Y30cC5Na9LgBwenemYCCrOcjoJ32xnyf189FRXfpXO8H39kocdXCEhEGIl1GXeMQ/535VwpBrlrU6Om2hOqKVHOIp7rx4/qyR+GUQESndX0d0zrNzIQJqRU+a/NozVm3lxL/AEvFhVVA8A4VVzVL1zHB+uruq8Qpdtndsp4YpswpkOMIxABuiYHyEaUf1mbnlcelEbZseL0Io8OAQRSfQ71gDS6BhQC9fo+N2QynsLA5k+4zQLZsEoyyps+NDXQendPmFavu8g4EYNqyByIfxzVtmvOuqhS8yYcAuVGn7uHFtAzhMfr4D3PO3SvxtZFM0+aEgMS4ZXbqiLrwNmu9y4iZkjz6EKYlNnjT6s/SmN2jLv0NRvIN9aRH1EkdMZMhj42/gK7iog3isYKdbxR7pP/wH8Q37uX3IrzHayyb4HfhRbVff4NAmnA9JCOGJVh/2K7vT8n+tM91L6SV737vk2QAj84PylSwplGAziHmRL90sgy3m0ow0pGa6lrX0w/4wxF4OK7uhLqq+3BYxO9qgQhXFkAAVRrthGEeTMqC85ahVidhKv0X00XqpqLsKMburqKZ6dhbnPpKYQXcpgOCDhM6/GAgoVLC2SiafzSZYrz3+wWmntN/jFriH78D3VWX8V5jkQdsTrDW5zLTKMLU4WsGV5m7s5zQLtwmduf46+vv/Q4s2cdtpFcPU6ttAidSdjFHtXzPXLL8fBODcu7EGMZmCev8LDkc2oi71fh9vUwI2eu77YZjk3sRF7/phfEyaHb8GxTQdKIOgReCwbBzmrtjGdQ4cK+aloSUaeBNmwp2dAibC+X6ifc/4k3vhH+i2AXwA5VkxB6xp8qhIF+042mvC3XtYol1wb7gYTXBcirU1wziMzpIO6vjvFBAVGq1YBNDh7Yr0xR1fn/Wvdxq9JWPCq2HUQqcf6xiavGo8F+MTiar0d7kj+pXxAs3BiWOfV4wSXpsPxUhUpfvP8U0t8bgQYaFrrBcAUe0ZJmTLZgmnf5eX1CINXfrQh7RC0SFWbHpUBJN302o1l80I/niX98sJsWM8mvOJv9Lc+P2Hctk7CblnQ7UsKIQaKGy0Zbu9ipK+vWhBn9B45f+RSTXvYiiDE6kcT/AAJaW1foHsv8kG3Cqu78chbykOah9v1T+WVd/bVz3SFklH7c8i7NHYVpuo8/hdobVKxQPilTOjcbMkhuzp/UuRMIdUL2gAOY1VsJI5ixd0eF6RwaykiSVR/UNvwCLMU8biVEG1Zx1+/7bXzQHliP5g68S0Ef6LJDgUubMbpuhG40ojzcmslGVGg7sid4nr6ItcZM2EbQwzuHCAx5Z6qrK9hPQAdS2DZdawWN7JyKhLbe/qpFU7sKGRFgf45ELnuXEDxjElEtaHtRqlL97Z9S9B0Nw4UjfzzO62JWnUrskACO2fPVmyzld8/YrGc0WEzIXs21E6DcP4fZFS851Xsvp3rl9J3SnH31PlRL08t69GmV/GKMTvSXADvmdC9+M39FRVrZ9i8Wh2FcWlIivtd7Jzlg7bMCBAH0qSg0mGAd2MxrOs6/XEY8LR62tlEbUD3odL7Yc+FNWx/Fd8AYyLvI5X/JX08U39MZdk5tfOUJtq3ODib+W+zc0wzvvvs4JK5q3rsbZIfVJejBM8bPn7ZZXpK0QcT8CCQvf4SgXUq6OAwYyi6XnPM3OSr9N5QlF6+fNRR4GjkjOkF/746UgOiXC2FDFkag2MpLSjJG0exN1k+YEXk12fTR/4smTucpiZY9BnEujXRzaeUR5WHyFmnozfBiTHGU6wzM4RycsTWNCBzCKM5X6top3InEHEsbk6uGEFNGuL91uP2pIA0FLrVkqcrTUAX3+uTI4/6aKDuJMFv8uTKVXdnrxJwEN5jhUQMl7BBnaxN2EtkkVVOWRyt+5GIEOiQuwTd2etuqw47f2teNRapR/TBXw6zlrPISNaa1034y+bBH9SkxnSjxV8Hhgyj6mb9zLvfgmES8fpSlowq7sRx3ik2VVaIvY333RVq+QiJliHZGvvYK7Y+qVUTEOpeG5N1nDYp+JaIfiRpPOZOhPBW/DV29RgxHPy/6EEtLImFp8m9/3GNvdiYBkFpS52ISq8Ej2Eswpi6DY4acThcm8RzX4fyL9rYXQNLNRZmCVu7wOZi02w5dyCZInhoGesvKZX70gvjyxACDTXLv40nKgvhGhZOeg9Enom/ZNKOce35X2bY9XlcxjALjbpCIbatjqphGeYBUhHmn8gQspCUBf/cmmzSsr8NScOh7JWciwRXRXpx4D8kaD8gaHq9QCyC14dep5ShrMoE9LP95mrrHXTQFqnL490zYwyijWWR95hZpuqvbQNmhtstv3ORMMtUGsgpry9ZkEF2apGUNN1v63SqLOjRhrOZ79SYQAd44/0xTvxZnjN8mbRhv5fN/CPJ04BBa0XrlFSHqiJbpJZc3dvKa02YRoAAldGmFQgPlZJxQjP0q3cZ9pnCqPnwL5Iuh6RYc4SI/8QPjG8m4w1kLqMXK3b+DoWMf4Q0Hw8xh7guhKD3nISFilAVpK69mj/2nGSFgzk9VQavzWCgMMFvdIENgE2B9X582B9umdxELMNvOFsyR0fgodHWThpZHLL/ihEfqSBiRGenBXOVgIit5i5t7Lk4wpae9z5qD7Yr3Rf1nJpBvSfLyC2LzvQXh4y+vOGg98wV8f7IIOK6Ixd6ouVFbewx8l47n0uSrR9U2F5RJGZQ8Xjdh/ic4WB9leNiUuOymxqOUsdlY05DTZNg3SPPC9hPUcW3UpniCLor0ApCRfv11IOU6fab4+mmKQGAdBqL/iQf8ALhw/wCHqpGZlJ8WMeBgtqXQuMFOjnfNaFphX0LNPowdYObqTUBZn6vZTXpvMW9CG05y9DmLLNBArLLE0RSRpIHBmfZSjgu2QSdMmQUvSuNw7mr/8D56xI+coarl/aKZXkDcY2UuUujaBkRGQ2vp/439um46uy4r4sa2+HkqGOH6HGoQXQO+l7XXz+F4ZTN9Kc+ayo8okl1ar2L9VuKIOoFxm5fCrPzEQN0hhqUec1Ne4fLO+kjpfX3lF/+/XiCWSnXqRisDY7wCjxE3Un16+7cq6+Byzf5Z/tOEY+pkhRVh8EZgWXEFvvHdFCE8KmNJ8tf0vLomIfEQXWlPE+4elMOXKyRuWS5dXX+dIgwOB/QVjaZ3EMAQw3l/CMZAOJJhmP2CuO+bg9i10qvvL6nHrUtpFGYwNHREZckPYL8KE13hhRBKLF4KBt4Ra7eDldufHNwKpGMjW1zutTC54cKT7Q+BjuVYjpYfNw8aqmTiPTSlFH3/iBIP6r0e2rtNHFThsAFX8laGiD15j+EECo5hJ0C61VohWqsPizFwCgTkktsDqrKHsreijOe5qJrr2w+aDbEX4d7B0r8ky7CBEi3cz1ye6+OraRK/e+icLsYydsORzqFYTZKPMh6wwC9yrN3yo3olnVyeEn1C30RAnYIBqDFDQe+upOS7faD1Jc0VLAr5gdhDCQK3FtARSSiTlJpwDGudPJceeFLwPHsBgTRrn+yYtaxpGAG5A2MN4ZEgO2a70Bqx5b6GZxxGtyWrlGrq87BSNle7dgYX4uQ+P+c8Mot/WDfbvLpw4q6z5ZY2ylLUYkEPLhzGZ+VHHgClkwkhYt7CgXgBA0YGx0jX0WJHrxh5+pkYW/vExAfLVf9rOSK38DzPQ0bS3kc/EgZX3QCgJDoPVZ94Dk7GOr6mVut6Qly4pV8fkhoNFnBEm0nVxucSi8MdBTdEsBVGSr5dH8GYFb980JBfvHM7NWbkUTYdAik34NZO0X+jO4f5d95/vxsym8lPncZilRJrVGK/go8V39I0EncceGZk4rowV8qqyaKqGcSY+xUxp0yl+esv6++Rqk48KNI1mv3UfFz6T1YYJ+9HkudEDK9VrCU3Ni9YrFM/oYxlvwKkI7m07UciwAXRu3jEu8k7dNhKR1Es7kBejJ4ib6GGE5MXoWg3dJTKc6IuUecWLLYc0s07+JJHzAniuRq1sZH1FiRO/KRS+FVw4iMRd8jCZ5iFUHw++tlqHhYNBhrjtNEyzceYEnC3Yfjnm0h+JMvq+E9q1TTYsxKrd+GQ64y2WQVRuaceU0KL+q17z6gUMOMwpS43akAz05EFZdQByoEH7l98z86dM+l+Oh5pqwCGPzGsMTHIdFF1Jljof9sYQJH51IY8N6lVhyma4+dBFiTomVvD0bH3wlgFshAfKsvwutASfxKijIoibDYr2R/ED+xJmrlDEBX0X5lq2Wox4yRaZX5BWJyZ9iF2UCUMDPft0S7fNyDjkC7Ef1wE/hc40+y1c7LhG0D2vzZPVWRwOBv/f6UFcHSmMYk+bw9DYjnl9QFXeV/sWokyWJIVrw2fpwH/zPFyWuw+eLEY8LlhF3O6e2SFHcx0FjspnPx6mn9J2XR7z04135gpaozYU18IpIBN1hBHYJ5Be54mkPeNS9zYEgVvtY6yHqYFCgHEzgTiAYr4CdxmbRig08d1JETQESmynfCTHmNf7APIlFaa02/qaNZKWdiOyfUIMQr8gsED1+T2k+0pCzmbYB3he8WJ5/U9MEa6fS52dRxBVw+sCCiQFAfetXSx3yGpuqrH2gkD5H4v/JnOO9GT93FICf322/Q/5IfZOjoKwbvEZ4URxMNXl3QvUZdVJJ8wtTXBlrCr9gAuj1w5nIbEu/HjlIAuZPmyRMTPygLSBiC7XTxIr2WRkMuHMl9+pwe0oPJHQExYRI/Uh6tlWJrevW7quNYyefQiI22joYqfoAxKXP2swrIlFcgfMbfqbHrrMN28tKct4PBth4g2cbjgd5cRv198E8gngVXlZROHChCWCZ7LBlId985N7d90ljirUPvE/RscuEVZblS2UludXFk9RyPxXnVcDz5PNWk5s0dX2oBZJHedkewcq0WEroTQn4COetBnzA4RYZQL/CLI2P3ZqOtVFQ5PPPq/LchEr4pF2duIqyK5FaiLbMi219GK7LgVvTWjjm008dPna0hjrbr/ztN6JpFbofXRx66CWw+k+GPMtig+++L/0/qBXt91kfpsapsv2F65GifKf87tONBvjgAxjywSwomn5Ufg0pMvNnHvOS/jVsPRP2+JuGGqlouOqYAcIWYV6tR5nor4AF/kqsO0i0ie8PxT/lvXok24YGBcco+BOrippoFiaSmnG2/EqQ2Wiu2ExO2fegj30wYixndNPetRW2jOI68yLzscBtOB79VI1BISOhV2nZl22RDg9SuGEHpIflTxd7qFhqZxhoFvSzEw9D9b2CnvsgpIfi0FSv+cTL+NVkG2MGdw2O3STsiduA2+xu4rQBBXW0z8OT4WlyxBjieNaNTfFRBt7S4tn52StiyQ0hDT49vM0guUJ4v/WO4MWEI0mCqTcLo7Qrlae3s0sA1mxHApU7cWg751U6uApm7OqO0sZxen6v75xLmpVEb582oPHpBae4ALjaVmM09lsUFm/39YW1GsrAg4lg6+/B66e65zmU4Rz2pmFFvtQ8toLQhvTS55N3hAJc7NB8JNhISpy1Hna3bG58eSGtyMSehL9UY/WTLjWIYA4UAp86zvfX3+J2xNMS0/01uO0gGPISJGEweWKPmW9WZn5EvLSHem2uSAKUx+8m1ZHCntQyGBHbVPpkrXz6wlczvN5HPeKaABauto6TFCJGrdHypJ98TzE92aAkW0qr7I8Uq/bV2x5EjqfGiL90dWZVUHd+QplOzxPR9DWDZUJZDVTMC0FHPaakpmgIGPVuZ3NUUEohj4GkHz2liHWZoXDNxRG4oJZcl37XjrKU45RNDrynpZ5Rf4f8KE+3ZEcQ4kYivd4o1RcKH8fwF/PcNhhOQuZRi9pxlL04D86t4lQA3zdVzfj+PUQaxSNgNlhCEwwkWSSRFDLz/SoKra0FO50jKDXJb5sHq9+JkjyIQ4IzHjsVHurpd3RirkOQ76Hp3t/Qn3aQX0wR+tl/AgnuAEPItSL1sYIZbN7VCWBdhlnsyOz74cIAmGvmYsPkOg75Wcv+LicI4y1kiYUbQtQJ2BxxsquEp1cG6z+XhwsjJvAa/LO/B8SUt5IbFNORxG5CPE7nKPrFm/hWTshd/+gZ0fqXX8yAM/MXy7iEGgIbDTMdHDzDz2ztv0AECBxpCDFdAJ+qct7w88U6ANyUdzQ6Y+7HwuKsJFZeMoSo/toOcXCaToqZghvYtxg3hOJc0iQyUKXz68/H0pkAsF0GBPVNRL8ewWlmUfpoUE+nFSc6b23xfIdLxwYYMnwFdqNc9pRvCbrEO4WWVGwF1LwX1XzGYrVTSLn5P5mybzs3mDYllj76kdQ3jvbdfSyvaBQw6/wnsUYXhbNDI0ak9e9FHGWTuGPWqI7LUWdmI0H341VTi+lVnAiOZ6mpE8Tugv3LLqZvIv7Qisg+rNayZxLHP6HAW9YAwyjDXHInsY4eesMdcotGSP97xGcUPHzQ2P8IrSAKEn5sCR618SZguZIVZpNXIixv5hU5P/6OxqeWkh/PQYjJK2AxkBDZNVBASRiha9qD2LBZxjnUmCRXFnsuSbvM351e3ZEWIFdPgvHMbaXD95vdWLgFMfj6BQSyhNnZtebh7C2466jEj+XxbQVPdxEH/JcZ5eLo0OZSA4UUDPRsULs8pu8nMD7BBAPXJKke8CBw3djDpxESrf4/Yh8SyM/zZQ+WT5QsRdHgzk+3DgZ/tTs23lobMmZiyOlKxdJ4MhybC0vs8OejFfZxTHF1ALHAGYbIDs2Vusm29zELAFHMu2b51+87pgugKfL1KgrZjONpJBRdOxA1eOQMK3U0MfHzZQOrZXysLjOCWR4Q8fxoWSLd/oGfsxi5PePUHyNT98l7ZFTMc/HsDLqRYESXYIvR+gyqAHZyZnkm4Ee6Yiw9FYyGNRZbhbOv87mZmSEwSBQk7ZmT4CGk65bSHawppQvBbm4mb8xlIC9m72Vy078QDVYEvhcfsDzj+zS802lkKr6M+ByKibYvEUubbJWEGob5Eg/UW0esyrHHjILY1Or7PNOrgnKxH/ElyfHu49LcheuAqF1/2PR6tmXjMB+UHnzckJKiHZrgc9fo9mgBJMuFb0/dz9ffOvMZFmtJoSCZWkInKLISZTZD/43M5tBP5d1WJwzzx9r/Zj4C5fbRMolANhIq+K1rMXcZ7g5oVVTvMJPLbfkPfdS2YDz8DA3d7GIVWXcRy080knqUowtfhNJEl7006H4ZPdpLZs6QSOqoza6aG2I8jFZOuhRvLlrWeQsO9l3417s7pEJScxVl93ldcGiH2E50WXxp905KSX5TI0Hee7W/CMRFbTBKXyDIPOQE0JpniiEuNyNdFOYGApAL5yoxG4goqq5bDlq0yQB0rrT4pUz4ZzhL+t4h/aZxRAZDub/3+ElxmT8hrAvMhbCbnWKWU5GFWudTfGrYKPOkZgyGSyh4ONdV/fzhWu3J2+SLOQHUpYSDRKXX9Qd+A2vjLxnnEq/cJU+yadP9R4dtYsCg5ANywul+6unuW1fv+12QTXDBTC6z739ts8ACxz8zPiv5qcDNQJyJReSliSZBD03wz2DDWsAf4hrMb/yxWTHAA86/EcP6leSja8WtGuX96rmeNXPwbI8s/HTc8NAXFrfSofbybMyDGeUjUisl8Iq/RkywzHO+6bJWsS4Ykp2eTJcavU8s5O4ORJTXJwXNwRPtKnQJsJtWftAZ93NrDoINuon5+x3xpVmhLMHky9aARx0p6oYxhD/q89qrTR3hN1RCadkPF64iRGb+Bm5uSXVrZODt0FsebNf+VaCqstrhAY/B/DuTQleVFhVYHGrWGxGfYchrMyPJMoG+u4MHgxoRLYgts4ZwnQvVcs8YPbbEbDB3USDvEHfbs6hgZXp4psnlI9OQCF5RkQ3d49tQOkkAxiZxzM7EpkyVv8O3xv1YNSVYBCsNEAT3GjNuYBYFkCdu2HjG4RWWcGFfxJ/dKolI8oIFta8x4yh9xRIEPQYLlI/J+gg6HE1SKjigG4ExKu0RbaRoqY2iFoBdFnSP1H4jx6a7D4VOZhzkxM9nLXw7x7mepF45wIoN2Fclxwujf0fCMG8GFLYjcLD8rzdq2Q4LDM8TEkygVkzWKN6ZLQxU9XGeqK0KHJ73Mf9LCWt6zxRZM9KmkqTz73BdUQ73S4GPMW2oEJn1TBwKjQLbDEF9Tzmlwid0loZX7sHCEEPTMSAEWYE3Wcnv5mGcwssFAAnX38zxEJW2uU3tonkrBEV9RFgRwBmZCtieOSBrZIy/60ETlcdIiNsAhmWE0y+76XgSdR/xeBdBYFTUA4w5YOO5EQM8WnnQf5dFz/UWqBdq8VsPaER6VZZJxLRGoCf/VSVWld9+sqplJk+BaJ1kuS4KzSntIcp9+4WLVh+LRWUAkDzsKZGZgMCu6Dr1AfCn1vGhhX03Fsm7snZpBYTITnTKw8sBiMUz76M3RBu+QaHF5/8vNE5y3p9cH/i3DTwTREWgezSI6TvltMRLbiYZmGoCKt3TguCxiQZALd7Tm6ei9bWx/2jp/nTMPsDaAA2WM5w4vD1vrq8FgGNMJG14YGc5bCDCbDBTWuJgdhNIafJou2zaEQoqMTqIOg1TN3OHeOfRI0M9q+HKF1wg+Z919CntM8v16AoraTofQ2IsW98T0yjnrPfdW2yLAYx1elyBwokUEYpKIAqkPHtlUNIBzzrhlzpGpDiYTstHaDXj/8oXSlTOrcP4Sm5c5tSQYihE1BDz5A+YCxG1w2q2jLJLA2qFzMUMYArmzQIQeFasMnA3GNZCw+ndzkA1jmGDHGdLfvEQcgTam+Du0knSnP4s5e2bBhAIN05k9/BIY0m0mqiKtvufDpGkfV5iXsp0T/a6xbzGLC42ecpyy+MwFtall8JNzAqvReGXjdAf3gQZPjDDFK7je4u54cB+3ihgXA3ih4cBDZlMzmoIEf0u7jLZ94Ff5Wv5gsjDd7aTl6u7yXyuFX9uevjVTn0sJLxFqLye1EgdBNpUYv2uTBAwMuSEfyOpgH4uMBTVhzO76vtBpgoWo4SCiJbYpJ86NcGtOKk/ZGIIkmcfYMhjpIY0w7Va+FitSh1zKMobRNOaUzpl79dnCnxuTgO2wREZwoBiTUYlr8pj1ghAG+3oZNSjjLYjcDNs2HyyBS8FxjS22CprbuwBqwzfW5cLrhLZkY4KTJWLRaXcDBmu9KLhbRZjN51qRlzw/YGkncGwoDwRq+FnN1caWkY8j5smCRT16stGYnYhJP5Uu3zJvokuql5URnnURG9tFNd7sPulrGvc8zIjElOVsBk7kl95b5xFKTGjwkfH4gVD+QQxrMn2TJzBJAlNNJxPisKegaS0S6qxo06Dww6jSkfaWr177X1+bOQdAn1eLvOVCYp1kWTxgqdSXNlz7ZZhVWPhF6nYQLfwtg9MXDgtH3w5yaJCk96Btsu2gQfN9r0Eh2f6Chf5sVJOgVa6ZkUBSHkcWXEvrTTrhZ5xhjKPJ9E5ychN1dcco2b4j8rlrEjn0ZEkplV2vMRvPwNP+gZ9r0rF6WlLBIRrBYXIN8cWrt5p4emR/gPGaFNI6Guk5ymUq+7wqf8kauXb+YGm062WHE1ZKBBzlJJSWmCvNgUz82l2j5ajXVJBHlSFCYXQbar3CcRvWbVR/r1AJ6wwsxYZK8jE39Rq0YN26BvpykxvFDIqirvlos0iIwmZjRHmHV0PAhXUBq4uakPJfW7FdiFb1G7SZbDyeR8CCqZB25rt+bd22azaJR3TJJIyLTFrsteThxSBCvfHsz2/ci6Z2q20CTf0Rtw5Bts/GFwMb/EFtIicPId1uE5cW6re5wyc9MB9HEqlCfxNh/Ftt6q+PomXX7xm/s5/z8oAW5oGxUBMnjwoN9c28ZQ48JIRcEY63KDiM2z/szCfFxwkBa9/7XgDf0lZT52ZB0JYDY92W1rqRj38D2bBi05YWcx9BSZNBN9YZ9GAN7/JozRhEYWnnN0HZll/UMkh/TcWeAu/edNBgKksZnU2/j73jpQQs0ICwG/ZtdwsgaMeAFim3ELehlrnZv5yRMrjzzkFyASEhpjJ3R9hoVAVpQeI37ktcDpCer9sPtAZVfefbSQaBC1PBsbWeAmsfXrFTexpuyg5JRXf2AxTQ9TAFnHvw+DzcxmXooMRg58GzefGRZaldzdv2fRrl+0xfRFP9H6177n4/oq9vwzHrJEFa5N1xNOHUqBLkvEOV8vzcdCLaTf7KVepvLFo0Mv5FDcDoESMlaR985vcyjch3SWYrEQR+Bf3AFfdBfNrejST6eUbZP+TS9h3p9TY2TG4UBFjs0VOuyUTtsZGSqUHtwKbXYu4kcar+3l2kPSa1LGnFsvU6dtGrkdDJVm5v60XkZQjwaSBMSFpGvUs+oQwADs+e8O8/UfhQLwce0F5NKND1LYi6atMakaS09u9YEePbuluybyWfV6R7aFhSal9D5kU/3wH2/BRRQvhMGWQyFIh2Wbcvpkf/jNCjE5m6Ej58w3VkoH0Wgmn5CPjVTQI+zINFhmdBckU7A9HmaJNEjJeqPb98alnGac4RDEUOxtjXYSWZOEI9213FhfQP050KZCotOyp1AKS1SFttKIwa4F5d8kgPqGXsZYaWclZjHnOopOxruIr4ShPGucomojR0PmpENNO1twcrd1g5KEPCAEQ8JTro2Wcz7LGZL1i61hWKiVFA2OnYhp+swASh0XaVLNwrPbD2cjsD3Y/glGiVMQ909m2nAv9tMlYbAE0/giw1a4BTC7GJM2EElJ67XU336gPvZsAuE3XbYeETj9iasbqZykx/hI1P9Vu1oMuQ+McmY3+Fn1HOeZuKx7134UPFLRYZpGjxLZ+WRvOeDA18SqKVt2j+FhbMldEOzUBUinqMxs3VkIUULKMqFCuC0Y+R2VcCex03GbeIlSW2MqiFtR7iNC1HeIfMUgDOJHCQH8UYpAY87BaWu3Vp5rGbBW6RGM2MotiSCu3GNLeDgkl3V4vyab7ymCfEfbYwNJM5F/t+8eVuA9Pg6NxNqarvy2PS+PzajtB2ijgsU0vKfWHv0wr1pWKBkQw1oKR8vMbwezRe4YiLeIoK3189QqqE3Ihhq+nqxYFy8Ot4nFQ7ATfjjuw+MyxcRujShCUpPsGlkS06mUScGmVXrw4cuqQqQ67bu/tDuBu098e5rtNUWDZmkZOhKLvlhEHwqrEwIL1hc3vFBBMefRnmf3S7h3H8WKzyBq9TKOo7SouVHPfbhiK4mY7ByGv8ro2NcR8/VvhqwRXHT/+y8K1/qIbyueLV4KSm8sqfkvI3wyW2k9vcDu9UkmCdaK9PjA7zWIDd2pY/RYoPeS9i/wuRvATmqQ2uZ1S1QuqbOrJOEGce/p8b4153AMS57vQB3lgeCPlMCeBia5hGLRmapzv1LwulCozdfZnP94lB1NGoS+gXoGxpZ1tkAQCnF8yiKQJnJRtY2GJfBaCeAqsI5CRG7/MMb7iejX/CtXbmfR6OSrta+vvs/L6cWSIMP/Fbdko5eH/ewZ2KOKfaa3xd/ye0NFNwNC2sRmroEW5eOYK2Ej2PFZ3qbhtxilbzn7wHsEP/GaC9WSHI3MA3lka5drwPU85Euw926uvznZsSbZi2vLNy2NCoqs490FZ6sJUbHigygOOzf5amrNlS3o3I7/IbWwvNAx+QaY0o3zUue+cPnZSCJEleYDuPVPtCqmTzlhzM75PKE4ZlYLky60SbktXAThgSLYTPLd70WhRqtY9D11w9qePWU7ggXaQ/ffyxBkdb11aSB8whaafkiS2DPHqkdFfdcm+L2gqzCTd98cZhwTOF0KWA9UsUJGM50tqa5BkUhuyupQdar2SLwvwMBCdrSLuyYur/wtPOfccIjI7gJreZqcC0J2b+H5q9Go2RRNSOQ2HXpDYk0LEIZDgvEeOI2Yxo7cQTI04qMH1JQa3ccHe8LEJgZBrJjGfSOUfPwN7dUB/s3PdKKOmDMVQyOZqHv/1uQMQJACQKiIqwbJ74mfD0fKWJZwG/XqlW3oV5gvQfZX30Wnu8UJCTBF001eSWEC/B32B/u+BKsTtKlcBiQWXYg/8tLmDk7dwjtKAKn8cFyL+aaCRoAL1sEatI5h9IHxC65iNG9uMxV+MtgaS88w82Hd/0ETLXH762ZTWrzXHyHcq2fS70sqdWZpd4LHhTfmeLCbCFm/5r0zQitr4XIyJoWd6AC8ZoqjScn2CT/hwGbxalLYGI10VSrwVErX0LzdfaLiImilPy8gAOlAQ8VaFRnsvJ59U0R9Wvr80l1Cqd4k0Tft4ANtzOfbhu0S0SfJ2fNzP+g/5WxyHCcDZLR5JNRRd7fCEGGFIIIGXzHDpIlZ+aOxs97ONfO93rIDR/QLRqcbZ6NYMzpvKkqM+QvWSxMJxPFYgUlAQV1xHbPr7RNbyIBoF3N6Mh5ckzYvPlNK20nxO9nu5SjXDIH0t8O4Y9NUP1SL4A1R5Hh6oZUVRIkXoMiByYwd/kNKNv6n812iBWZNk5PaEiZgI9E0KjaAG4mO49jO+W9h7uKV2G+UiBF/S81p1q4+ZKPBypZvYkst33qd7M7jD9mmwICBDzPfP2S1muzGzfRoZ337wxtHsY4hUXRz4VlIPlpU45Sr1OQXkkfdD/XDTLbOq1E3aa4H5/+3eHun6vsaoK4Kmd3QQWF0J4OTws8uWvHcleFnUVoPiPCnUaxl6FIVXfSwJ7YxKBdgjEdObjf/sO+QHmde2kFN7tnbLIrw9hKzXbkgOaG8JuBNJdEMYTKVjWXKAB1xMFU3JnZIKIBJWMzZodwbzJzSP4y0PVo/5lJxQXr4KH/MSfvUECgMUAXP/uGYTwFz6csWPB6jH869V83QMqF2DVfDVFX6CabY2Oy44SFdnCBYNYO9fcpVnOk6yIO91J8sjLdqWIBHoHsG/l3MBKmFZ4Q5iR0dq9h29Z7Yfd4gUYforyk+Dn/2NHBYx+0oOyjjQZybX8LZ2NpYFU315jK5n1g8d2+HP44jTFOaPQ/kqWi3lTLY2lk3s9fr/RHcEGzlUXzyjVeCoskj+4viqBkgHMOhsneu20Z2s3SqXb4Qfn8TeAYQ10O2+vAyQuDctKRIZ0GUSnBctAc5FlPgoV+W7ve8PxS3vbCHOotnQiZMtIVET3WFD8pD7yjqhXWkF/26eG8xDVufre2Ns1b4qMiL5Ze9BiyVkD+lIdg2qz0XpOxZ/deMEB4y7IaXCPJxUsA8m1kIjD8DvuiJdcERI7S8mmdPDoGqxF5qe9lccSH5OAy/vq2eFflSmTdNJScaO03kYUHLH5FU0lxbzz8T5DLwsxTUooXXbDTafhFYDoglj2omOjWwK9c9/S2pioVM6DRwLvDnEOdCs7FLgnKaiNjKMLumjf8A7ydwlqL/i86r2XYSpqqe9iiV76ic1+rnj0LjcAGWDra/zkSyJ47Z9KJkILzRwyT6KFOMsMRxy864UwwmO/LfXSp0f1I82iJdMt7qLMffUl5taxtt6PWmkp1Hy6mnBsPAH4UT30DgLAAQKF8e1mDq+I87hoymg5FDAmMO5fXAhW3T5RSUkBniVCS6DvKOQLuZyhgg1f36eOUoQGOiAHYvTqpzqEWD7hDl2F2FID9vYYmImvP8uYIRG/vAVcW9nOLs5Ge8Pfn9NBu0CcENBh5tCLWcFdWK8mW/B4Wwe7yst7i3Z3tJB5sZuZgMMbfzQ4xE4E/ehiEhqnX+AuUPJ+jaxiKtzEQbQNhenHxQ9PH8Hwx/e7CSFljhVLLBl4zYNfSNC/H0zpxSXvtb8amSc3b2DPzppDKTvRRkGKhnDfmrH1xRSg6FTXOVXQQBET8S+WoWzkQ2Z1EI7Pw10due8vZxQ5hegcva4LuUIrGf6Aionysd3m0bbCsyyAFjQm9iP8NKg9z6JWTPVAE4nw85nUZP5GlWfjM5crVGaf2gGhrpCwINwVthK4wuwgT0HM45gkRbydTpNwbwZwAV23nKlyw+rbhRTcI7fjMcE4t4uT9mXZffxZH63zHVbUpvZpb0Mz80DzRGTesWxAfwrwbKLm+xDBTIkVdQQERgHbphixlyuM9anaEdCj/2fGHPDlD6Pm4fA1IfuWMzJKWbrYpmSoEc2rYXD2VI96qBLRiqmT+hEIdas1tHsDeJhcNi0/lr6jjpe5CY1WbMS2DiVZGbjOlbXn9yleuVr9h6PK+ux1bG5+zXELr9LwHqFNQ29k+zShVVYWlrjxCGdeIb5Ng5AYIdwaqMsV6dYrx9lFYVDfk02EvIDG9h9LRsns/zEdscn2V1moMCwPlllvPsU36ONR/Vl4LSFLu6N1+YQLwkwqQq1kwmlji2ZFZrsIgilLnChqpK1NNdR5pY4EIf70W9Gli1UpuLxIgVy58drFdF3aUoUAeGB8Zr6e4ttps5+FAbN8/K8W9zcRqWZjK5oPcIiCaWMTETM/zYTAW8p0lgW+T4bItmL6SkiW/xCFUSajiPubVFjHznXDsoA3qqQ2SRbE66VNZLrZm0pqULK2HUwHqDW4HOk2jS0l3DVT78PNoK2kZMmZXMHy9vrXaDY8hMTwRUe9c0B0gMWeEbF4QbLOgE3F8y80/b7/QX50WOIfvG8kic3kR04h8On4lC4CUHuty2M94V2HTz1lOXlB+experZ9MFZNp0x1rohG0dlSZklrU002qBm+YBkFGuGeP8BI4EYIurdZbCazc4NloqaVxlw/r4oRMlSb8w98u7X14TgMGffCi8TLRm7O8+QwK/SRPvvKl1pkeM8suen7CtujO4QYMN+BWpNvYoEhsfhVY1+fhS2gMTPXeqSfHMNdSJGCzVir2mtbufA+m8kqs4iywWASR4lvqTcI95WxfPtdTLnR5E5rUmgqAqOAl9Xfu85OGk8aFNC8vlWwvd0VfIIdaHI1C8NNPjPvyJd52yo8pQmQ7Ie2S5ys7lr37Eq/xVLjMCdjC6O7ISwEc5vX9XqeBpmFvuxpL3i+3Oiz7x5H7i9bqJhGZqfBYR9OcfZ7gexYSGUZ/biyeBXDM5k2pHpkPteeI1FcYgql8dw9q0KP3u5AbY3QzzO2Yk1gsnRVxEp6AxZKxRFARsmo4z9/MWBWo5j4vTSCRt1WQpUUVIfO/P/ffWDOw9JLTl0KO46agHk9mGRlb6J8xoROdqpuBD+F1eJQslwGAN34FfNf0cL3cUNTHdyAkZRnJMBXyMYge95qfnuvWUS03qfOxQXv6hSDVDhu/LsbtIhtmrXyVbPxIrYXJKYsEkyGGvoYeogwlYpkqu75MFKpX5ReiWCFoN2yHX/1Or/WAlbIbgiE8ZJSF20FaFLwYLhu0X/hOgMCd3P0QEEtLAaulhKcN5U7TdFvu6hVac0iu+sP8ecqCV+hM/lK0oodbu0k4yUrBisaIvJH7CzOT157zykhXuh3oPonJ5ds5Ax87EW0Qba1EIXRoFUk6J4yZBzu7d9P0S27JswOOdRpvZnhPFk7ohRMfhmOQZ+aGRzh5TfHcN3cXK3/ln5+ahOT32x4an4EteGcYBf7wqCxWXJ+SjJKId3I0DVFEYU7QASIu8/I2rhhQ2Gaavr9BFExpVr0+Zkh7YEyaJ3z8CpF9+LfLKj0ThyPep1c09kR26c1j3tJTOZt74N3Vije+LWWv4UM6ayC96wMO3a9KW8dLRYaH4pyS4/rVRCW5BchadEowWk9hXeZO4lihEJOWXg8H7pDqHkBYg00j7j0p/gqz/3xMf0rvEe1pFbCRc0Cpyb/bGCPuAc90nC2iDQz1OC/4N+wMFCFT5jBEx9CAVvjSTEBzbmnoKR+x2LU+rJpUpqg4VeHlHp0xLp9VCmMsz0azjNDacjCX5RpdigAm1kZNg+eZQNjF7jp6VY+XeX2jTSdqZsVNAmLtwinZq4Hue2aa2D09IhRJwpnhViEKtvGCCkmPylEQl0qmM9SCT2ddnYFyGA7rxlD3pG+3j12GS+ICIpwGaNEMhSHkmzlRqyXGU4/PzXdoyYNOcBChKi0+uGdw/RVnp1HRtvRVMWbvK4Eli8pWAbVMh7aAewdxpQv1Sjpy2PweoA6qcxow+Sum2OvPH72k9SjxI4eMAkaDvBgJ2GMH1FY18CpDgZ5POD09R0MHqGG57fj5Evzhv41zxP1opwqYJO8St/ODqPvgSb8AW4w4ZTj7eK4Pi9MGEJN4cy3LTSIC25sYIqSqqk/xEIUlKdtIVjL5xIYXfkd/oNZWZH3VyFHtITfZu3PDMYcMlWamfJT3/XRiajpBupWoMWWtm6REE3jv61QGxsgg0mBwPwV/jV3IhISG8xmRTY2tkoYf+I9iRRiKaUJihEF7avg6kMHOMaOBs7rr/2zxkys1xTMD9+zQ2sDzEytZH9GmIEhp4xKdGY4/LDs8gmrBzGyX1QYGJcaLZ10PnWmHO9hQfuDy1J/fqxjPZS3u1lTqxnXHTq00/S7kbfh89rIN/7eh//Ya/DHj2TSxVe6eS2KeNCmxMZrR6HHu9OOf8cYofwftBqJrWZshw3nJGdHcQMqoPI+MtDJ1rPkO+7K6Vr031JtaG+Msh7p6f76ETBgYvCOmYNDLAY6i67wCC+DNF/T6+63CeRWeg/zFiPFl2RIhnv+UeRNJJ59t3VKTUMKFMczu1yySn1MKUM/i1PkRFCHbGJ4yek/MvtzXAKEI6gc3mHQ8tQGPS4N2aybIXsne6w0N5KdOCdEuBngd7EmTRl0vflCat3RQLQ4xFLrtGrYB8KoZMFV6KOkAw12K2gcGUAjlSXgYsyzWoMXj6p2W8tuImHobg+q94/zBVr0TJyCGw4Bx++ExuA1iDlzXP3jtcbBgaZM0pX/Al6GulrYc2TQWSmUaicLsDitJoqAJL+Kv6KLO+GVKIoeTMqF4/Kg7lkycesWk+8OgiRHWoHsVAyCdqjUc77P+GaHErcc2xYQFg7kO0CgL0HaxNX9EY1xBot+YfmjFBtZNi+QCl3dBs9tL8CKCbOn4W4N1EtudwgXWSw/qhCLQIYK0f2UBVmi6+hLLjm3uia5hkY0hHIUSBkjmCv1Zo/58S+zw2t2Z7QybwIOo8MYgbyDvaRQzaPLTuc3xePVI3R+ISvv87Zvzim2PITqfUIGGRlwTaB38nxIQ9DEWglK6AE3uw6bbBXb1WHSZsfG5vPpnQG9mCmcPWgCYtiolp+uqWxZGMw105JyJyhibGwuguwMBqpofqDupz1xpVtMvGlGsXSdFHYU13N6xHgjQ4cdMxKsz8BBBxgqH4wYP/oJUG8jz/4vsWUMN8vMPoNUWf8Opt4bf6kvlYG11ZAB0D2wLw/9t1KwjOK6kqy7R9CNHxpDbmhtzTj4JBPJNpPLOljtiv9InCNipRwKoQdzzkuOWq8UjpYEIzUkpOt+FNjXteGpwKxsChn7PV3pTixGvCqwPp/nysNOX9Cln3/oq/mCyrHBRJx7w5b0s6dfdSZZLPHRiRJag3k2XPirYQsvaGcLn4QtU3ZU3r5WacE7rg35QQVjQNyMiSxWES4b/FvQWK0A6tfmWqnpbchcmZlPRgpG1h87JOGttIn/4ysxvo/rKrAGIPxSeZq6nxtkFrd6ZqwIy4h2oQMSNht28D/A+Z6qIVVf+eLZ/gbpMNRz852P6o4TEeEkZxw0LkwvHcwQypRPVLeHei4MQdm8s6SLZEfdmHSq33umlmGLWq7chrit+YdB5RMHjPfgtu/So6lRKE7GJ7Ht/7UoF1ZBbCBq9z3nlFrJpqZt6k5eq+v1f9ppyRozjuDUX6WFyW9pWnojTYPfKYPF2y6MoBRXj7wjthwjADexLSiBvi4DLmja6q9VgX16Ev/nnhINd1CuwCnlrV7MdSACMkWzNNmYgLJ0Uf97KPKPGku21y0Iiplt8HvQ1hpXjiMIXAqE4xV29S/0OOUt6kZA/Ah7YvNHCaGmV6jLPa5lAQV0JtOmvcguaicCQ2KF8AlyuYTPLWDhQEyPEy5PO99sPd7mHavmPBWsA1kx1nYVsy1CwjHVnl/W30qACM0j9ioM1wawafEH1q5huG7Wstv8dzS7ErdswWK8uys1wJ6LuQB+V+mOfCmzWgq/XhgBv03Eoc4ZYm38pdBMQF/aUdFvoG7Pk9tpWXpKovHp+zv5uMXOq9nb58zD422wr/PAJEtSktEa7t6gFO3B++yhwJEI8hQcvhaqP59Ogby0U3JPEtH9ZUfVM5Mut/LAzJ2JepoQNJGggiSmwpdnn3csdfH8ednsGwEhkvawHTahMn8Ff36BSF2Z1LMBRY1BoJSTrN02rP7xhKnpqKbM0oR741sMA4rdwuh2JzPWX7Go3eMFnvF0AqrdQUjDiCrSxusRawCm9axp0ud+huK1IchESIz9HGpqbbgBOZHv18own9pQyYxTW+zOvbcCLdx3sGh2x2S+NtDS3bUgr9IFglA0pvG1Q41w3otvUf1AumbR4cLK8ryR2CYjeDklUjkdSGyi7lZMJFS6bDq8VU4mLiIDcAEzH26x6D0TETls82/BTQg38aXf0Ooz6s6lhczbfF6YKrA+3ojpPWL2vCRQBCe8mwX6gPlQ8BbpVFnu/kud5rFju4lXUOhXfpyYqKFCeA9w/MPJ1XWOW9tJhsZJrmu0H1ZYRGkqnRCWSiH1orMr5qh6la9a4Vj2p0HMGNJ9QKU4rQoQu/8CUTfnqdy6RdOQkz0mwyCsSh5dE9zJbzv5KlmEIynXtw4T/oYuktAgiKG8y+J0/3aQuVPDwcSbcPqNbIKsvbtt/L5F17bj5AugwTST1tQa9HhKqEIY7WxJQx7s5MfA6zwqaZIIGPKKTbrQxIgqw8zlBm1is+9N6i0FGmy5S3+BaiEGD85nHNhNkVHrHNRDLzLI+pio4tjEvFSw3uWkd71yk1EhporUTRqif9l8gyG2toWqzvdZx+dLFgUnKLK5cyq6po88rAxY6UekH76l2uLCSwTCCF8kkkZ5MKKYi4Z+LU2Qja0l4o1ha1BDVfH0c3ZpwXYW/V9MkxaeeG9bfYvw345N+jdV5V+hxeM2XeaCiyfE8LuoWHIme/dOowWFUkjXDoA1h2UoNquzDa5O1mv4ed8/dPkkZ2CX0Y2qr69rf5QlzDXXDgMcsYKEJWaTZ2OkG373FvnufYJ9WJX2eGwVqWCBIkxSM+Hab2Ei2wRy4XMZ65zA7+PUtkh1Wla58jV5T1i8bUJaqPZW9vrcJ7L+LTgGcHk6yIh9i0ySBa9Orqfrbu7PHF7q/cZPqEvPhoe+1YpvqwhSl50SGxLsEqh/gxcNXnk4vxOth8BXZIKwDRYs9T4aigAUEHnOO+bmrHk32CPPgLjH8H0D5W2xNXXmfwiTyyHVgdSmGJAWC3h8hee+BUezGmfXSMc9mnPJCJ8qxpYOMoLfqZBWZbNlZ9ehfkxfXvOLS5g1ZVIp66QcFLU4bclryz3X/kIiPedRSFLkh8V3AaKVccKjax+1rsIP2OpdcrVdndHIUc+dLg8vOWqlKkr3I5zyujtwXZaeJdCjcEtGCw9TrRBDX9rjzhrQd5mQ/mWjttYHqu/C6UzPfyJIhu4ypcbtkZqk8YNLbyxIBOBoSV2fAaNu3emIxUzjEhgom8Kb9uq2oHMMcwlkcqTl+KSyOMOGkpws1KNCrpMEV3smy7Vp1oy6d/WlkxskBAodkXlCdXicldY6mX1Py0DurKyKqr0s6vzkKsn6au28ONV8ucQ6DptLiI5CRoKQcG7y+wrhK5DzVu0DzaIOBbJ4VaE98eH1+kj0ft+fJiFv+TtnH+poHZ3YuWxIu2xUiEYbxIAu1IhNQwa7pEKzsBMy6SW4mLd0NSm8AlwAZ0FKupuwmMtUpSLXvMX95WiiGP+sjwtnrU6cdds7mCIj21bmaDUYNCLFcVRKDDWf/g0j1jEHpEyahdrgBkQTr2TquFVUslL+Ll87AcdArjJ+UpMfyG4cl3DcsZD0Nf7xDmeeHNj5ld82Es5H2GzQ95K46N69e7a+Ymc8ium3K9YBfIvV/XlDnAu4ePW9ITP5IuYZ8nQPARlnnryi/c4eFk5SOyYmqZDkxeGnt8pkzGAPuilAeK9kqQlT6Djm/SssDO2HojXLS900RYaanb68QezM3uVP0upVORJRULunFy9W46LCkV80n7Avv5YQ7/1c0eCS9NUpV4kg6WOs5D2e9FD08P0Gca3BZLi89kuWUBISrH9tXcqAdveV/i4G43DgV1ypbp2N07IWrq860tJKIBYE84jeEnVp5YIYHXGASrQBiNojqbp4G94JFyQODderbHfgda8QBmA328ISyE665oeh9EXd7Jxe4/AgjGkiN7/vP7f4waBeHVaYAJGtMQHtKO6+U1qPoEQWxa3vvvQS02iZJf0cMoqrwmfaOXAQXuZifr0+TaxtmW5KFdY3IYyERPem8A5HWDgMSPvOQxwq1/lJwsGajcEDlTqZdyDnNdzCr3LK9wa/7eQ4Ygu8RIOaexbeJBXqbWejRqlRMVD0AMrG+Z5Q0vamCnDNpsZJF4eJEDU9+VFXrXVwQ7ViAi18woGbHjl7eHUj+hvXjfTmJkpXH83pUwnNK8HTZ8098qn7B+otlMGQH6gUiJqqmJv52EaZpnf+m/dKnsScJnzLhSXa0TotDI1bgFFlmslr3MstEmqb1inTxWiHGDn91gmdjskB0NfLcSj2hbARsLJin58JAfRYnRCugiTKuNPXNVxOP++/2w8UH6i1AT+yEfRZhJv8NoW5Tv9b4cLtmNdqNOpKlbhsxV0BxR90sMFVQFN369yKqxN1moNotCgBhbEd6oIjrKJD4zTSP+HL9c/UBxG74ti+GkmBCDJXrOWTcVzirJ2s3DUnumzuikEW1E4EOjI2r+FrJEB5LTKTZlhe0frRNt17S4YGgh0ICjJbRgp9DEVwbScY1Gc//ASfK5OPei1fh/LMN0A4XyHWDhNr7ERE4s4Nbd1zn9wI86dhF0H9bKUHx8hDYQgQjKi97rZ9TeZaa7eCH7LHSA+DP3dPpJaMR/54TMTEePdtEPASokQSLRchBlE222zevTSm6HuMB6194F4BCL7QtcqBR1t3t6xHDLqNTA5JOY90EbTJrnldwKYgHVvdyBEYu8pj+v6AHeCne2ixxWnQQmyCNFihpP7DynHfpxXtbydNUa44H7P88ZhGsLl4VybsmrssL3+WhSW9V5YukEjYG/FDZFII3WZCmLwNAAyZIBapE3VsrxW8Pf9F6ntriK2GBqGqPj5XPWhE73/TvhLIda9GVqaxEYlQz76dOOme88ia8MDJxiAuOJpOh/M55ZiJsYVNIvvSI8S43eenpbeox2DNqQw5HmLg1w1IzWqkruiETDcPh6CRH5WuJM78/ZezTu7EMj8zszN1nRM+mgCb7Ys5mhv5rlK0EjFNPZ1LyxlBkR8I9g6BKfVZ5CD5i2ksZtBucD0AIvjdqP5QznCTBEwz0y1TP2tNHnBP9vmhdwd7WJDfiOggAsv58ZTvzag+p362aemGuRjQMxqLekzBviVVl3epsbrUF0l0s9bcI3fHHOfXdY1AGconGCNoHucLBImKev32NGcF3q2NzLkQBXlLH/S4FXhyhyeTBd2AfipjfIgmIc4loXO7CbssL/FtjSLRteqm3kzRXEjoORc8FXbi3CZ6HWmawWgHMeOk1KWz3kKR0s4DdO//VjK2TGMtN+wFyjcNI2Mfc/kCjtxyoEJU4bu8p+fjfBKG2d2JVzKj8CiXrzAO71fATD6zifcjGTCfSU+W5XwyMqXXjW0HPVsuKSvWWlU7liGWK/6dJZo5RtpGY6OKvlwXq0raSrzbnRBJ0bK0n78Q3Q/+JNgV+d3NA+Q+4MwWUzG8R1GgVK0UA41depGngV/m7Z3xAHfhO1z9jpd8Y3VRkAJeP0BKDp47ZJfnveOc76F0Ltp242bgfLlJt9cG1Wz9GxT8PbdYCMiq3lVPagag0tJ0QXs2vLYIvG30kL9htfsr640evEaHNgxPwQMNvB2Xxt4SBP2dVjxNvZ/G/W4qnA3jTpAMkVV0Tsm2Wn7W9dMW80cb7ZpkCPh2rm9Jnuz5VrLEIZ8JFEFOeQ7fvd4Ah3Eh4r7/nzI2nW83m6H2+iynL1C1acMWcj0cFujBOw6xMdbRxYGsvUyh0/q7P81PF1FdVTDJ4FLiaQEZBcnIXcw8pUP1Y+qZ5/4wwjWwtpG+zygOq1wirhutQPhUoWWoBreaHAtoQc8EeWRbMdpkrFuejP0/7V6xcb6zYiYr0nfwtQJRaEladPQhKCZgMheq65c+qtRAgAzIkJ4FPXQ32s6kyu5upDm/l7qQlrXZPpwHWxpJYuz8CY/4Wi3jIfUVLF2OTCCAxKrGZ54M1xOoW7hM7spzH8SiBDPQAxeHEjSqBvromcJxF8U3KUc454zkO6UDGUMHP2pMQ3va4xZD+GEzxQNe7EiinK/rbzslKNarRAzRjrEpDzqWrdCF29URNWZ3NY885TnvaNBQXzXp3Qft4vHAb3ETFnEY/MCFCLJ6i537rXpTCHINrMOqSio5XD67eyPV4umpjuRhSrn4P5E5hNK5lJh8wE70wUvovBTufhAtfcakDtSf+hoZJ/+l/VHYFIEpd4rlSDwXiAmn1dR0eVPrORPHfUoPV+Oex1Fh8gCFeweZ4JRDd7RliBNracYW7LVBqf/87GEhQiOSXesJnAaCOSEA+nQvFa9Qy2R4pewe/hSJi3vCrxdMCnsuoOVd+TsGmeG/bWlTpU1o9myrXyJEQg3KRPtUOso6QVJWOm2cdB8wJp0wBCzrWWvneZHeakUHLMWqG2giud6yV58ZIpggHxNtoAM8P6AIdyNF9uNUlEXDhm1Ht0J5wUP7goVQOmJD84jyTxO9G6M8yNAHg3P2Z9m1rSprXTTFEpXbfrsGWbZv1p+fRE6mn+S8DWQzcN2wrTbiP6vLE310WpnY90sf5cE1PWpPdmZDOIKMM3MAFq54SXqyrAxE/lfpyctDnRgWjMaOR/lzAQgpFHQIA54Ta8A9d+LPbWdGRNNFaKSdNs4OWS8aooRaMgNqTxGkp/pv2EBgniwbSiq4EFeuRiUo9dLb5K+WqP6V1nb5AouEgG3YY6tYIPcbKs9qq8B28AzeVzBhoWT4Z/tDJZpkGGSr7QoIJsnKf9qq1yGZXxigTF2nCmwyD1JAFl4aVZUUk0tXd3BqHhVklJaO6hXnG1a+i6f/HjPuAlrkS6Y2yJEWOWlDz/eSou8pxBMSJxq20qdQbg7+nDZL8CDjeVDT3xNY3xYd65KXx6IkIfj3Huh4pel2EKx+zLG1f5+4BChotJ0HsNe4T715HleFhqmqtR4+o0KHKxDDTEU9Um9OC8uN5o7wBqUGHZHPsqu+dIPjHO+qyUCh20BRP8Uqxq98CM/Zyn5sqsxMJDHE7ZPu6PE0/dAv87Hs1NyJaaID4c2jHQUc62l/KTAjkN1eoGiw4Jo19BhKoIGyx9/Or8MqmFmAO2gAmPtKnYsACGp7d8UN5QbV3Ym9jTGlLBvRLC+YclD2fk6cmCm4A+bKlEU6/dKXvCnQz7Pewgb+geozeINGyFzhILY0r4rcbaE9pFSfh4xa7E7mGTmpiUVY7CNefkP1Tvm81dlqL6KupSaQYrzITVjgQflkvmXg2OCfcM2ORQLXQeGdqGK/vq8jShBSx5OfTrjwjVefk40RiD+AZKIbpESWyE/TxMnk3cpMVwUJpq+KGW5178tHIfU6Vb+l5WVCx1RTtiyx98y+u1JyO1GxUmbxn5+HPGx5lrsXubZSnLr6m28XIagSqQ0jxBurGXJMdhizyZkhPnx4sAlkFoxuSY6XJpC8oQBjJbTCmSkod8WW4lIoG/Ldh3H9tuo2C/+04QyLaRMAIFpjvaijkTsh2dWNfjsuZ/VPkpBsPstv/zF8GLx8e0LfAucKbRtRH1J8Y3UZGv+bJPLQLTvnUZfO+T9/Aeiq/gpAk/2iBvxub3adm4qPf1eYj4I+UDc3VMV0A8DScHeWkx5iP8ZYYbbYLxkFzuHhc0Wk/SrNOp2BV8TsGV1NfSWulK0LSMzo0/60hW3KiKWInAPyhgt1SS7gV3JF4SRHX3oJctF8GtgX1pUaIwwUegkWLqWYpp/xYsYzYX5kJCiiq+0Vgaos1Phjk3AKZtHjvt1fT128qhpXSvBXyXyOAkjwDKbxdE+VB3O/P6yRpeTbYfrPp9eVr1lVOXwC64TD5Ooop56AHf+S2/nUXG4qcUV4kVW0YmizUY5M0OFKjv+YdRSRNE1igJGgKvrEjjsHbQY7zCf4VxlamQsE8SxcbyqW2IN4pRNSvAhGYPQljRzix++rcwQyo2mtDF/UFLd+0p3gd/zxyszhgj+wr/4+EGO3hAWMc3bkUo76HAlTFc9vcGBk7Dz4Iw59IaHK4JR1q6KCCjVUTqrkewNNLO97VScgAUqv/2UJwU7EY4gQztbMC33HDBBJOSV/17oCChHByA9QzzKAZPGaBd5GfPFxR/nZkk2+RCWSOJYq9PbYEbZdOLlZhlTBza+97oWEJyGnbkw0rJAAklTO+9NRUypnuyeGVGh08u78aPVM/aDrtkm1y6lRFhlUaI0wmX7Jb5aO0Zqf466tnSDVkqW8wl4GkHRBDqXwzWYAAy+dmshdZiEUjOx6JJGDOy0O0TqcOsOHmHTMm5p4TgLJOQsArqYZCpW4EZNZwJQEqDO8ypHuVLQcNUAlMRUVwPYifLnT2bsG6Yfu+gtNl0OvCOWFzyhOTvdudNunRAKb/2eiJwYURenbc9Gic1i4VJUksflvFhqQBKgtl3unvfoJl9OoZVSV9kVK6HQQiQHo9jY29aDY1nXrg4LBuSm+uIlzN5iZ5OG6oxniQQludEvhHVeWz1l8Oo1aiyjdFlZIsrqr9DUBTCzMN+ikoGnOSk6SxGbzWf6hxJnW0oIPCWBySUxCGJELvsIqc9P2XNUTEMPMsUux4j5LwwGN9KHSgGRZCzCfaCN42YuCk1KKfp49YEulCc4am4ffdetFgqKdNaR+3YZMKytVhqRmxpA3I+EpqP9RjXmtBwoxKinPMnYGwYTQTGYvXHJ5W4WvHVwDPeVqobPHLPL1KkNeVOyf6Y9/1YCG+PHywkIQSluyLzNCqZzhIvfkQ4SL3/cbR2g70Nm6i+N+06CqPLDoconcdPqqnbmQebrsAQww1vEIhUxa/0KxBETdZV/dIlU6zqaRrQYjYpLDE+uaR4NwbcijjeIMa/WWbK1fOk4vK2Byz4A5Sb30vSLAyC47mv5dCu0PO96oEVsStVDUpP+Onxrjh3cpVfqbJUycY4PYPI9eyR7Obp/rsohZuY5OVBsfTgSW+Vglmki97vuBGpEMNniMdIQFWXEH0z0iP2QQHAl889gC4w31jtZmP7UltqeWr7cGWQKYIGLkcwgaH7Hz053SQKGEnxd9aGmSmtN+jw6eKXWdbwN4uBnGNe8AnY2PVAXAq80Al2r5rRWyJSuZaIj2iIFyAoLbItCqVubn2zGERyk9ryNMLRnrmps3WC1TubUuWa4UOJO7MC/0NxGtpXue5QAJmfkg07GkB+3nv1WsD3AIBdPU6Trg8rHARW43dhFEhlLsrPIR3BTov8cXljmiS96R7KhKycc+Mw8jKgRKXpxXY97wXT8E/NFs54NwS6DVAgUjhkTOus/mw1f4YqvU8zmxNxLkmk2Nkq0dTEA69XlUoILWnDl4zMMzqZ3qyJNaQDeQm4eyHb+ZWXWQHnlcE4nkqDxeWhckvfWTYCetLpi/Om4DHoi3MS43Yn8ZDgWsmGm4rPTontb4emzcfuWTPHRKxXClN8kX+IubtJYG8YjYBbe2kaxpB95k78kXOy22cvnQ3XUUQ/DTgQc+WrCMOtml52kd74nlwwqcWedTgrulmMe+BLoPXte5vYArO0D2ZNo1weJtqfmiQU5Bi931kZJg5m9fMtOTmVYZgGCe3IKRj8splrLzHHMa7QyCmJB+rEed16JdiYawOyYPM//3bYW7mUdiAgYccxuwO2zuZIUHsTV3G6+NdYWc2cOI2zoYh+rJC35lMqZTeMOtRTYPKJvi7BiQLVDQmXDxsEMlPjTOGuHQdRVJ7qS45LiCz6zMp1m8r8hBzXEtlRajpeSLuqsNtq5LFBzIieCIRTr9c1qJ8inop+Bf/8FlP/dhzp6MxtXgYcnKftyYcbn+hnB6LkH2ClpWJT1lbs98JFcUD53ChRvbvoR4oXbKqVsLLTWkO9btoziHfS8wTCX7y4bvkj8B1CU80X+NWVlpv+gKscISZd7j9NDWlykoJQr5W4vxzAQjcbfR44KHYQjUjlcGLL7KlXbTjqSr6AW+XqP5/+Qa8vTH0nuOicAqiWxlwXSzCI97WDmAwCfdalQBhYkECovRai17X+sF98locEzyNGg+Vz/gOBvurJdem4yDmc4g/LEGw3B7L61rTSkneQiwWASQa9sDE3pMvVz5F65W8SN8AGQ/gVG2PCRngTP86p0XpUxpmbs4yj9vrMxqYjFtPdvrxk+NUORVVH5catomba7+9ERQJOwTnYg1r1Qnhxhb3LuZm4ogF/G6nRrq2rWrcg8m3g9kU2v7PwZ1vQl5hh3PXJlRciSCweCsEo5byiPkov4mYxhT4RVBeblcQNT2CbAG+GHorYxD2GrG3qi+UHeQNYt3HYbKrC8GeiT0kEoD1AlMBWHUGvqrTrARubfhwv4/l3xdveh3GUJSFbWnDv1BzxusNcBnrKGpZuJAroHq3cW2U1bP3Hi7LpPx4v71C117vnlX1z7X48NCGv9dkNNj3sDmaD6EkFvZVJhJEcdncPZ//P635Y46mtnJYsnSeUsDzVzUkOf8epZSA6+TumUsq4LBboWXoWOSFrGZj1NTRwBa5Sd5ieDedVKcKCu3iWV9YMKySO7Q143rkv9IS0ucPChbE91EgDFtv6UODVmAc+WfsOHw3Aqx4/Xlu4WP47V98+y/48F9ebhlAp2go+c+BB1/cen9FYsdi4jD3RD0UvyGld4wMy+wgus4WCNcxslfzPQAIiSagu1DFlIHzeUHiW//d3p2ZdqnHijQxsyRNQVQgUenMJrSxdn/G1js48mKSFc+SRl6MAgPxxwCOSMQsVEr8f+j4Gk0qyUCMqjx3Qg8xb3/cKOUeB/Fv3pvon2CFU0vbP3aW8Ot2dmHfRQmOHMGrjY79YArWAZSkje0JJ5T7zoOJE9sky7qxATZMZq1sUZDfi/PcwDIcXmzw9ZrQAs7Cq6JX1HT7fh+lzJpA5cN2QPVTnqK7v0N+fmS2Jtn5QyXEUa7/XIy4kbBK/aLowUpyD2tVqyTFYGtIovCqwMbBqft0vf681dbbpGljAX+Jv1c+nRvVYdMsfndF1ynTkXkkppQGr11Z+a8Z9iyBcuFdYuUz+VSXn7VPDwMoFpvKRbIeWNXVK6++rXDorcN6dhf/WEy+S0JYVAGuwc+16kWESmYw9UfzbjKqvPV3QZsnPKw4QaU56LiDnOXc8CFKfdqtPpK+RrysArOAuYD7tHJk2NqC/rYa6l3cuCqMcTaDE5vy8q2bQPfWAnLPjZh1uBQzLYOKmjB/J/ZKS8h56XWQ1vG8Hw3Q0efhF2jasI25WEoaVGS5d4qzSI6kPfe6vT1laDfyKql2tbm2VpP1iOIxClJviquQg9adfehlo2xYIOACGc2lS7v3H2AcWV2/A7e3Yu1cWRYSTTxutgT8wtZ6OPFaGqD0ixYfRyeb8amh9fpHbpledQTo8j1woH0gDKdZ5TlmxQ38UfocsYiaJh7hiM/W36sP5GgKbRkt03+5c7qVLaexIQ3lVRDr0CukI/v6tNgIE50zqiPDDTn66TACu83oWPDyeNeTyyki8wL89vdl8tDxoJSPrvHlUvXc8u5R/xPoNGC6dmX2REX2RnC9TaxfmA5N18qegbUbPb/AiI5nmAnpTEq1DXp47pAX1jI0JB1OP6m35HOzF5/2Z6O+gEHbI0n8baQJPNkuzHWN6vo1rdqfHj9wSuxCZmQaHwQX1vFe9uIpWsCVz1e8hW/4zKFAgf6iB3r8IKnC6U+XeGPoittoTKDojlltLx8Va1vm6ySoGy8n6bZkpafpm4aWiiFFBLNu7Dr77JBhT/s3alIp4Q3kFndCUXGBBX8mspkEbb/uT79EHb3CjUpgEXOacRdUlChZMpXS/OIj8cIf3uEXP3YN9hDUvFHZQ1I8PkgyTM357YmcGT9H+Xi0nhXgwI+cnJ2a85GQna9GbpPTX2tthbRb0bh+2FkWXxpNPwWQ5IbJ0QnAMcgmpIIKOsbjMszO8JmFYxlXNAld9uec2uNh5zQbDxRkplDSinBELaPDf7hSMAOJYrhQ45YwkOpzug/fOlrgba/agHGbyu87WAhUCgNtwkO11UgWXxE6//4FQ3JZeXpe/RfV/4fff70Tj4VAItUSsOtNGq+RKTMa02HgxUfst+MojvA6XlKjGHynRKzOC2GY7M7/motWtt2KUSlbP9bY8L/5gV+m1DKR6+8yeNQ1bbR5bHXe3iavV6M5vZDnmjmY0PnrpQtcZyuh8BGEoE/3d+0e0cbfn9f3UaVoixLYnL6oYOyJDR0if770sU57qeyF+GVtE8gbMZS/glC/KkekaKWDGEq+ZwTgwxZ4oPVWhqlYjSg6BXh2HdlhiCoTva3phbYFM8AOLM2eRd3TgG1GOd7X7xlfl5d3TNSumZrMPYc4d8Rj+QcZzgFRWjWJZQjjxY0QzajArn/mQx+fAuKYN7CNecSYAOJgcCZ195+yiuhf/tlG+8Id7ibhP5UusQcHxfW6Oc39y+0F8DXgLP440/r6xniAMVAocM7sWZFPI7EWdrqMyV167IXMqA8Z6db1NMIxcGGfA4NuFbELwktdxBE/KydMU4GUZbVuboZTmL9HRkBbOaFm2REAs9qH0mOibef+FGNiEXTz5mwGNa5dfAjMtLqS58BgzJz0am5C5XLGBH245tLK5odszC6frv+sQYD7j5qwPAsaRb1JwsZZaRk0ilIYLQct6FzlYmFehF39xXtcUKnEcdcQ82a4QDKy66bsuU2EyEYOsrJXJGoQbRfdZScelUHXxkfij742QXLvwWo5+7hOhj7hKxjQw+2uZNfFdt+Kbvi5R9khmrN1Anc/EQHARduaf45/LtqeKwCFL1LXyB/3eRYsxtN+nU20YlkNtuHkTX9DD1yIeQEMtyakMbWupvgxg0dpaID6h89Jr3DBEZ7YCed2frOCQdCN50UBgkmtcm5mXG+u8iHqK4IMFdyoZNhHyG7WmjllCF/oncLZhFdcoV2UWoDNxGUpFVR2Y7WpuRstlY0LmPOyzl4w1h2XgACSig+guRqc+u6SBKRYA9e+gHbLt7dbBBXt0U74NXDJCX4Z2ylQ0UoM1zUgmpPOEibDlHMd8FQi9Q/BqIyJB4tgkUJav62+e/WYF72CSMB08zChCKz/B2MC7SvPJ29FkgfCmf9DZGEaAjB/JkXiQQriQGzf/SK+youO/NBcJaWDRmlORcXnF5w8xt5akE5jDW0uxsMUr3GTvLvQIL63tj642v1f45oVEE4sNBLjwqoU4xX/C6MAtYg01ggljYfhIUR7v8LsTgqxdWP+zKR418XeVlcpr+B2EUIU1A13QSblq4TiA+G/YMF3HL5uiHjWTrEZftrhEXW96W1Zv19KFR1/qw+ep/yuk7lXSemx5+j4z3dV9UJnKGhcSYCp5PUqfAKGJLJCWdKRYXXrsKBxYTtBT8yiOVLynrCgofYJ9DdWMUSkEN63libldS1sIIZfv1tk7TtofpJo6Ww7E23CPmkZqnm9/il0MMr3uhRy8PF0ED5TnhJF+DIuo3/5DqbkG/RxTC1+Y+kAOF78t8gTtyzkGB8OQmx3TQGp2OPVWqeM//eh4PfZAlNn8jzPHnWophXeMQ3YvU5am7KPWd8QJtn6LNupSe91bJIJj2A2XN0ahTbdcWO0gDWcFWcTl5UqvljJNYlsexkeXb2vER8hVZV8liD8PG3q5iDCaQYIC+0gERj0pAN5wjK8OZmJo5Y0Ntp+GKXaiiGUgbbZU9PN9DSAm8L6g9d/EtI0fn0CdBhemApmdcxohxuMI0OUjrWfFr2OoWItQZgNmZVlzH/KZedoQilotZhRBoDlf2QTbktmGPhMW0c48aARR5/P0VQyDgdV2Pg1zjd9xVOcK8Y0fsFCWmwW/WVllqNYgLnLqAcvq2CuNyN/YNRG4T8AmlTY4SG1zI0MToPHyxkkEvDwOafUQuEINC+he3hIAaIpuh+aHbMLjbyOW3G1cht1MA95U1SwY2zD+9I9eHb1lXKqtnKGK0ZaX9vjEEs6hjtncRuiSZ1cmCy2Ig5gtiZ6jyexPQY2tTZ8hogBgYpkBhuOGvVbyNdiHjSv1NuPoWTHFjWgcK1eFDheJhJ5XsGKqfSJzCYXT9ST6BgnBEIU2fz40UZUqWCNle5YikQPPYh3rMeF9PMLdR6w6d8Zr5nA2BHhlsnDMhhMupOmRIlvBAqghIDu2kbfGMDrd9Bafx3iPIkgdegvPMQpNBiJgmoXCIVuO2LW0uGPLll9ZuGAstldc0B92nGPk7MCmLVFfFSuEsdXE44pE4m0l/6cxPkzuL55z2VXjBS8HsqII+4od/7KcB67t8+eUB+IndUh1ktsCh4uvkg/KtFmKGewuG0VwD5u91xDtI4AyNzT+sjD6l8b0ddzAOvHZfOOpDP2xyVmI7uCmvtgCzyJVKtAVRxCXz+NjegPJXszt32o+xGY5G+gHnFkPaii6OSvdk96xncXNEzDHyktsIztdjDh1ENcyAcHKgSX65ItjFyxRa2pW3Kfdd3fjEIMlFzesNOgyJF2bltWqpQHShu2BaJrM2SCZhx3Sy4XVHkdeS7C+KcDS99sml02NIV8j07VbiZFcIMxi1LR2XvN8+0l4a13DqwLO6g9DWpK+V37Em9X4BdFwk7urrTTCQCK0r2xHauk7rxZLKPhhS1LNVs8IytGgEYAa48qOrbUMHvgDoGOxnh7CQRfLimayERn2O3l35xURToujePC9Q/413ttjoEKgGPYavvrEnRMYFJ2Z9Tca1Y7fjlvjgSCA5UmDjAOGWgKnguZtagmJwAK+RoYQwxBRN3+h6Gf2/us/V19GzpKiIUQglrQcjSMFmr5D58ZW8lKRziewreOlgsOsxQsTAjVn7r26/FMI7c/Ze2b4MtLarYXGBs8WocSUjcw4HPOE0UfNJHwG51R0KBxaIG2aSCPZUqV+5U5nyzZahFSGWpLSqGq0kgymgdDvnKdZk86xjHUbMkHaaH2zN7qlaxUgBDvwwtXQWBCJnykcEGH0xmaLdCx1wR6XXhZEz5FkV0cqWLJ/yU2BKsaczIv+bePsENZi+hX8VYuycUDQx7RhSW2WVDtIUkBJSPN//OgKVgZbr9HRm+QtulmY62Y6oDXvJA5+ZiQKWVsQjdsbeXv0RMf82rTrDOjGp5610EfCSuQpkS2P8cMI9pA2Z4+/WwThBs3HnkLjedX2DqColsiB0td+Mb6T3txlIiXTUXFwYjLtTuwu4a6H3Zcq/PqsWEiz1sngBM+lEG9jaY/qAt16moH2YUTMnLeLF0hoIe8Wa9uLLRH4CpGWJl9OWfRkCvJWZgntBHIoHTVfz8rxokg40EQB9yivXn/Qx/8lfQT7sBwIcfpi/IE00ohd6m+gLkL+uRGL6auin5q79YIW9g+QPlaPH94G5ouwRpu+qB0ZRivirERsqH1m2k4PicIVARwDQtYLVSYix254HEGBDPW+kj/zem8aIjDVgdjq8HXGJtErZqHoLi10PF0nUCANRsvZrxKeVuysWEll+t9WEO7Ej8PWym92IlBBCuywTEoe8XHSVJ7qRythb58/KlGnxefJqNv4wwSCey9y8jPCDq4D9EkPUc9CbbzrbkE9BpRL2UUF4kpWuQJCH3/tND3tnnYWJbje9m7jedG5PxnHvkOFkIQVJAz12u61TMQCF4nCe/gv3gCtNyaGeNIdoousToJRkxB3fFNg5oduJ+ZXy7rV9LPLYFwpRMf+knxcyMypZ+j+3ETAsitZuIv6B6Dj0tVbjyRLK3o8amhJI5rhEBLgT0XBCvv7fO1zCQOR2xVe5MegNUo2At0nnsaxF2f/ZYMpQR2ABbKNGj/RE2aetZW+jVnuxh2Xzwl1j+t7y3IQ8LAGLyuxhkTHRSThoExNIR3c3rHJVcUuGrscsgy6BbSR1eBwB2LjA0RHMrNuua3E7p8khtIjwg08B7PgeeaXi7cyGolfeuj3UMLJ4Q2X1J3y0RU8rpveV/+xJxgTpKS9LPxiVf6Jy1mFo93i6Kd/wJYJepMKbhekUerBK5wsmOvamnSm7Qa0TG1fyd4XBM+ISgRuZCeOh72UfEFTCbOa6f1PCGS8Zkt/eGy78K4ul9+4a01oafxrup416reOGCjo7+rweeIBG43i2cgE3WaR1gpvfvkFb467jzSYpkkq/k71L5QaMTjjbu2++MqfkAYPfbXvYdVhMlh+BNMvUQ27jYDa/7+RDvdtTh9ZQs7+66by8auDqcOKEoyTnS+H1ekPUDTG+Fv6Me8evyvVUz/j5jK9SqmqirT/SBgpjt3kDu25jpOODyTI7nr7dClK3PT1eR/ZU+Bobs8dnme5DbcfdFpZTBLXCh95skeTY/2T4WltCCLC/g0QHK2B2bJtIidAq0cMOUVSXEZ8WiqwAfb66sSTga9shoB4ZvXzFfqUfqVod9p6MaNbMSzZghm5ghZPE478zBfMv22daHEi6nbo3Eck5xNy0fcpcTs6lXd5IXoauy5QtvrenjqR7dsCVkTc9PtjumqEmKxapITGH4EP17GyLxe5OZihDtqhnaCjbUDHWyTyA4GY1iMvmJEqXW5T4E8RdVCKgJXDjTPG5cL6+Z784m7zeG4Bf/xMXMdt5TbSAb8vcUY+Qavqc6m7Kbm9uzw43q7G1NYW3XMayzrxNFTSjb4szs+uue+hLjbdWmZYs9ZZt+BolK0gFQ+l7yX6V3wBTdKUzExb2ER1K5SrY/xZrdYODkpLjHtI4Z7qogxEbZGx0iyFpq0TfqsIZz3xKkPAr8bm5eZU8YTZz+2qywf/mhq8ODsbrHuHJ/Bv08BjYgUCQ6dLXzo+SsL1Jzhw3IERoNJsnPjucYrvpPkT9Aw+df308cOlqDMjY6x3+ENWgwt88eUM587Ip+VOKzWNu0LPLWsjxoR889zfbhTW8EvbtbmZXI0Tp/MXBlx2jXZcIj7F75swJB0TVzxniHv3ETP+eN0mY0AIuI8nWo2AEnfFbkQzxHL5MZAn/yN4DG+aBFHd65l7mLe1qtGx4kCUi0X8tm6jPlBpPxQGLcIsptqNhcVEFLSJOQTwQ7dBCH7gDDUabCmGGyS3thTWcuTK+pReBFvYcvRV0KX0OWMQ0YvuYrIIKsaejeGJZZjBgiwFqsaRKaCy9YaiXHFxl1UIYXnDwDKXdRkayrPE0GUwm5llhqD6gNL9Z2oe94gQiawJEQjFtXLsBq/tIpnE1VNXAEx/tgSmkYN343DrN721kAHd7xvUPOmouH9ZhsvQF5d2KHuMuX/K0MKN0AgVbQlifZ0qtnwQOvEvGtxo+FdZy1Y6r3w7SO5V9hb33EX0DVVJi9qbkxshhEQJGAfzIe01EAAdSNzmqVi4sxh6+E+bZ1kBKvJIZF/kMJ6zq1sCXoHdbnSsnjOxDyIyQgmByet/5ASVshUi5ZlGequYrha67dTE1BpuTQl81WFVKTYFAvHuy7eAxH4+/Q1iB4PE6/EcV+Fooe1J19nOQewoPbWn3Q0646qIOxmUMvV53+qbV6Kv0fML0JVX6XUHijXxGHDfqAMS5hhUSUMcp/4RGCkdHRRyKGaIf/5+m5Fy5AIVh84QtZyzOrQEFLLhHA5SR1DOb1j7POPu7IzcDumSDFo0qhhmNU32rgbQC2Q5/58cWWNev9aM9iyZR42I/NHaS1sMkbiTmjZNdnpjTaCa+ivhMypcFE9nxY7jccGwl1CR2wigh07Uxnj/01X+xxQX2XxNXmxp8JvNEKdG0mBeCsVTFjXoeEPuem45/h/gbcYM2yTIr4Vw4hg0lWZewNauvwcwJvMOISozi92wInNeG4JVUSjhQb7RDZeJQU/DDDGv6WGgldsXQwAsLRqgvjcacnNlC4VBI5g5sJ3GZQYrQPKVtMu+6EIjIwO9Eob730dlVYxyfJfc3lf9NO1h9KlQoFeLJyrpUaBZVPUEifm58XA9o/LuFN+wiwu+4XOzIEhbP5trmNtXvby5toLFCJwzsJ8ju/Eooms2Jq6YQr9Vwb2kkUZHtWbYZDQVaAV+DeO8ASbxb3zJF3BHPB+ktys4isj0QsbaHP6bCH9r++p464vcrvwdPsXHyoxeBqGLefxOlU8xI6WdOWq7Ua4BzbHCvqwYx4cyeFlq4pwakvatU2N9P2Xwy2yj+yYC1YyNJvRVezOJqR0dKAe7OMB96NumfJYVJd3ht86OnOdgQLNvnXxCAh5nmxf2pcWs1Yni4Oh1yROTKuA0Atr/d/fa0s+m3IIMZ3Nw62CKWe58aIZVpGEUeiu4GbvmrkTRV4h5by+NHIQCG7vQRY5EYtRnmypR8+C9fdEayYBRA++uytwPrpDT5Rxvfy3tNSr7h5+T6kB9GFzWUCQrNRxtHf41E2O6QT7KDXcoZmtAoFVW0HQxWaC4+D4FQpx6i5hZlIgTi9nuF6PjY6Zio1g1DY51sFh1NgZ7wnyyd1M2a/fgXPBJH12W7/GMLbPSHPjsncAtzkDaniZG3sJ/ipcdTWrLaiZFA+lRsDG3tZyfPpDFJ6JIwOa/xiI5IR0Irgsq3iILF46r/VrYkOmrDICPnL7DvuqpHWpI6pgYZrlHnFFZoaGsKJfod3ixb4mTpSy+xHDsPhlIQe/YtFW+TSozJh6WTUqYLJBsfvSi4V1wBM/k6gVchQ6PBlP0lgbe8nQ/nJk2gYkb9HUc5qvBunEq7ZucR7wun/1caWUSBvj5bFexayKgY283tHJPF/+5OeFF21FzaX91EW7UR9+ZTmQhq5PxZCwnwWzJ2zIQZen4UgxA1U/1DLkRUe2tlj6PirMHqgBXLlXVXwiEE+Y4OSRc2W2mj9p79x5RoT6VjAPYQlqnf/pJAuilcKjDOjBfPmYfGWfbURZLDmliSqyDFIudKfw0FPAEHN1MXYjHYp+cypUXJjS+WNGvmL5/QVA04zHyYhexu6gA2JuB/H7VuH0zCb+VvJCw9tl1Inz/dky1kSR/h9dB82FjvZc1MRW2DvVYB3nx+nR53esEDlVFUOPbXVkzARpJWsv9d04C/rY9nsUOHvjYUQw9cAJJnWDA6iOKj+PV5Ql/KQ2PHNuxx0jceJKZohI6K2y27Oce7ff2lBGyhtSafVqYKQmjSM4SpBAUbZStSJwZktzeYBFKih2bg7Jb3GeFTq/4bFbnAcBJ6efH9X0E1KpuwY4mv0tTUH9SmRPifyYUf6+1bmngstB+6VcTPtdx36DwJy0Pm1zASQUfwSoGMoXz7+s8G2/RgFfB9n9pOXb3mjRwRx63iSLmu0tpNk9xX5rHS6hb9Mjx9qWkZBqmEDrmKcQa36Vm3Lsu0d30WQLBzCpUo/6DLVrWvbRQn75Ti+PV0DLQdOx7SmPrqWsUhMSAzZzNskId0I8HC6913MJlLIM38/pbsSYc509XZ2setPvgkT7VIIPBABussDRo0FvdixI0cPZWnm0aqTICj6n3A0vmXN/zDvJAXTyDyG5fUFOv2uAOGTP/g7PW0oY7rBX/ZN8DHVq6CQS4nWZAuzDgjVoXkbEsZHMK94RzxCnggNJmwwXdesMz9Pzr+jbfas+POglIs43Jjef7Mq9RHOiG6h29x5biYSOV8CdIjNXoset1aEveUE0MX84OePZF3jZWqIHl1/+lYVwUzPeigeYV2CzJiFkV1ZwXLM8B+02IQaqAePbmlqInOsljPro5k+IhXO+O111/GTKeUO/RtkiGwMqJt7nMRVZ7lb8ZhcQy9SKY7d9Mehg1cDsJq/lSlYtLmHDrG191kKin8aGVyBjpzx7ZaQq+/YcQRdWV2iYFOkQ/Dm5Pu+Gdo/Gb0lYBu6QDXF3Jf0guTap69Fq8qxgc2ugM3lSmV1hF45eOOtUl+Om6m1xydN/iyRcuw8goeDlSJt4p0V/gLiDXKLuAWffRoGPVU0EJcwcahcIULZEzcvwJRWOZBuwCOw+E8ddXqEWJzJRZuwk3gr1S6tHtZug6i0CTjBA3DVQHLdewZ2Ef6oiVlux4J1UCWHL8ZQrCgFnCGo+us5UoHQhUrRS0HcjPbos5OXsLrda9tv+ZaFqOrNGC5rQT+Mqq/P1EIInKbpIRDeGP/L/NdIjD/kc1gl+0hy0vSWZ8Xv8vgbmnkUg1gEwSxAJUBRybAYyqx8sNJABwMVp2Y7xSFILugzA/fcPhrr5shcNZGo7c7t6br7wIF3S9CgCUoIGP6PHW9xSrWSlrf4OWMzzrRs+HL67X0ydQIX7l037Xael55lPosxMjOGQmoxpQy0ZE6vRQO1epmkTOD35IMNb5xKsZ9fo3Syy1Ug5b26YEaWYCWCTmZcAQbtWe4CLcQq7UrmSt7jr6/tROVg5wrgqwrXH2xZvZaOJzLd4P+y+UytsIJb/b1sEsyI5Cyt8VXr43MU8rL740D5nAPSy2SDdbKQE54aNnMQXbzaYJCGr3RNAm9daM9hPmI7fPoeM2u0nF82TvVuS6WnjIrJ/di4dPBM59o470YG+AI9f6pk6O/8hBIFFR2dF46+MmF2EiR5Sct+52bbAMGBuS4rUW/YwwTkoG+gwaeKSKTSSeSsSXRMsHxr/wY7lpBypAhYutFhzf/BIscM6RRDPHJFhPpz2aE2lvuuVMzo7ndox4b0JP5h0ysXz4jTG0L3WF8gNC3DlYCCReknd67/db7CRBG1rcEE8Og8l7ZYu/8pcegtIEQAYWoqvc4vevdzoVKjl8xVrhPsdvveNoVsL5/opTmqrWUqNXwD+TZnTDGO8LWSKQg1NNcWjaC4bT7OMo8igr8wXbHjXhNJKn9gb27u0uYdHab1I7p2SUHvEvlSqHhOTpoV/WWJz4JtksnjIrNNg+jAL03aI024sAZdXVvuCbkq9H9MdshuKCnAaWQOoEfe2rRyIaCJ6b8dJ3QmglrhJBj5gwtUt+IFylm/WwdvdDKETTIio0Suf4tbxkpzdSJGY2d+eb6wY/RT3WPIllNpkYVO4yBkdzwMgZHSUROvLFX6s8JdXP4nGY/LumrUkR0kLsDxroifQ4nuMLcZAn1PDwdVhWcaDvYkRtyadpXmsoAy8oxL47ADDl/OKuZpSPjTD9ilKYnjOuNAqyAzXhiQCHhpp/7tXF7rKh3rfHVOXri5Dtm8gyw00Tc6/O0jZsoVILAmOe0eV9qnriKv+4Lu4LsostPaWR+bdFXEu6H2xIvtDxt3Gveaw2PJwgFc9htX+veyJj1LqZSyRSnfvxJhxcGU16RUxviHjy4EJ/gg25GIwQBpJu1KJLLsiVoXzKQ0yZAZTxpL4WiS3Khq1lCqvjAyvNbvi9eg9F/WvQI9C7PygCYilbyRxzZoD8taEqeipvAcuIazbfMh/kMlG5yjxkvduhwIUqEOsFcKcP1v6nSN8i9l6OvjvWIOmzovQbpbr6AP5wjHHE0yk6lHshstk/xu7iwdJk4Qb6U/RK7i122TqP3/5C6KRAUkUFcAHsbrS99+H0SIsUlm0P1PXTFvbuZnkzA1zD1k6bEsIw1aTFqV7dSaALr+Oa0ozEA705mDM2nev1E9gCx2ASkKpBzQzrw9E8/EyDejbLcNIkp7//uxv+H/W3n39fHvKA1/SiUhOE8FQ84+HAkOAERtHfLJn/bw0xFnW5V/UBSqFu9JH8zmuMerU5FG2/h6duyfQCd8KSBouzPZLIwP7tqmrfcgr6UvRPc5N44NyVvQmg2kysY5X899l4YEQM3MxYFnl3ZyhMCvlcCuk4xh/fjzdVc3s5RW3d9bRrOkSoVc4CAKm2FXUctEy967frHfQazfwPS71WoNAgUW6ZHp5zDUxeloojJ60Ka2v/nCbs+7hFJboSI08PLlD1tDlbqLvMno+rQCSnVQ1YtSDJXd+NHNmPPS05uMZRFptyguXZqJKs7iv8VUNTzWDZZfDX0qmLBw+m0bYqWiwjlpD9usyK2vc9XkwvzjZFa2q84Gi4S8Ty2n5jYnVrwK8N5cNMqtggt7qwzGH1s6D0sTPXXXTunngnQZonXgvaC6YA405carr2FTFSg6A8DC8Ka1w39MDrdwQ2a9nbjmTWb8+nL+hO+u0Wl+I0Qx09S/AKIdgC2dGiPbgkxTJ8hDEVqet9MM5H9fKLOsHiWsHKAsZBpX5mFEV9Ks9y9hE6k4GQHTqb3djoBQgqGYBWUgim5uBQpyEaUiJ00HRgvtv6TsmQbVSXBBR75yRrc2pLR/V4GUXOz876bNZL/Elh7cLYVvA6QvR7Hx/Q8zMEfGX24Z8yJXG2R3qJzGHmTiJmRkA2GqPEw8BLQQFxuU58tUh5GYGntNQDKAr1P6UaLzMhyHTG9WYPKG58MKSBi7bEVmbH00KwykwZIwhfQD/NJLt8N+/aqvpL19uDR7NIBiKu5nRQ64zVpQY0Un+8HfSbB/z0tXcOkMZAnRDa2gBZG9q8HPkP2Cj++0XqyGGvAfoJhWpAi/y/TJfgcg1rAvvaSVkvtSM0Zkmp3Mc9W2Fg382I/285jV+RgmLrTWNDT4WpQuhXLp/ldz2InZ75taw714zjLczTSOvbF/22G9hgkJ35vrGP7GHwTKqQ5/QeWjOOvv+ijUjsyV5AnEgX+iyX9+gpoU9gVu6veZ3YdOwBH+OMneI7yi++jcmeecfBzf0Fz+nrYc4fLNx41RVy1GtY4p5gR7BstG8LfZxUnaagwiG/YLIQJoh5lvtnvnMzFQkenep9HwAGL11ZiNsoP6xe3CMi/Z4LSf/DYdJHZ01JzIaSp/Xg0YUxT4dZSwfIqcYi7WrE6v+FvmLm5zY21DgDxEzHVjnPVwurhc1Hxb/bh4n4P4/KR4GsM7UAQOtTXpKZjcoB4Pxhjo8UPjFIX7eWS77+JTu2/p0rI7G8ZZDLF/kn2ymypus+d9/Uf54UY1Ojf5R5iMTktjTtqlz+09KpTr18uurDbg9pkkcgbXKe27kDNWcjmAhmQykCWEphEyKy9LXsf6SYL63t7L4zKRT6DsZUaWhm0pboeTYmESgc+8i1ApruLBwNan2q9fwc9AuQvIXCHJl99pj/pTFC90RPx7hX/XOYPOGJhXYjfCT6uEoYosA3/WOMS7Soo1PjsEd3ezsDRd4LlalLmJdeLHJFGfTQgUjDhGyLIbBzYcsYoUCYKhToi5hFa7HvddB8IoMQAjlOp8wM3z2dQv+rok+1zViszB1HAqTJe4I2rTx4qhXHwkZLCc47u5rov+sUMoJ4P8yRjf6LtJO7unT3jwP6F3xw9jacKxCuprUkXRHfzcT7olPHUmoA2frnMSudFGkzor+SNxxYoxW5MX+b18s+Xfsvgry8njc1QxZIEKU0wv+XGA3OXr6da4fV/aqRLT0Mc8JfCCJ8miNpp1q3KteCHUPQxPMAMjX+uVu12yHd2LisH7uoG+ubposg8fcxZ6QEZwC7+PMzFVXU+D7LTZrKZoq0HpmnKmC/7rx+6kee0xEHqtlW5Uefe8zY5S915MQeh+XsBDokHPg0UBbIdICLku0qQuuDHyvz9Fce99h/YgEHhDRCdY7OH5auC3AXhnH24Bv0+2JBVUlGNgX0ZvBJUZtj1qyAJyuvYLIJjPmX5gKu3qpmr05DbG0BQJ0PGSQ6kNfqElGelV5TY1OwtPYukj3ooSRGQjwuXFgBPAjy70MdSUAT1IKx3idQq7+Jwszc50Zth8LWQtMo50YgLGI4RcKi8zW0E6NQnqZKUOPcQDffsmrZ4mb4gm/FRcaiCACAifUQ5NEVD+OYhMSgXOpA0j+VDuxr31DRmXLUVloEhvIMDXvIgKUv8CbZ/54hMDoUdsmsk5hdE3BwCU23gF8Q69K6cFULa4uCji3BXd8qd7QTChoiYcr3VCtMv97Skb1a+DJ52Bb7UV2Tw/E+zOef8BhA5Yq4EuaHZB1nqbtFciuPl4QIeZ43ys3RIdWtMwLHec84cNqprnURrEAj1XfwyJP9+5P9LBrcwCmkim963lib4dgr64Z7LqJpcZQD0s41WvOzw87cmHxD8eZmu6I9jBuFKer+eh1ryLjMfyl1xyqYwAoyIIzHuXRHfdnfrebTV8h/d0mAnLkGL1lYKoEdRANW5MBT/CATVLqqBn7SBhTSyqGjCgCziXDIQJrwHnE+xpy0mYha/yvtCQo+3bl19sS7ZGKlctbLCG2PNxKvJ6VQJddZVe8g7OAKzgBltA3xVw81f0QYq+8J4O0eo4Lt+zYPBQkGk8+Dg927Brc31h0T4tudKcWceXWl4HksEB2ZJiezOre5yqxK37bYiH825qcV+xcVQoI2Zyq7ZmvbBLzRXE8uq0IQoSNPERv36G4VZlkzphtiWpgikcuDIuGnH50ovI3Da4Fg3zunbtqrEe3+uzGdD/66qLOJCVAV5PdbHg+CqnpM7jEqkHi6aDVviOLHzs1Sk9uWG5WLcQBJXUww5M0odJU2FWAn8572bIlvha3Tz9q3tvObryWilSO5wqwlKVU9i//+3+iBFF8I48tRmEMb22k5S6mAiqzehJOAS9jpWHWNkPLcKoCUs7mwcd/aujd09fvdmYxBE6c+WA6ZZtLlwcyBD5y8u7iED9O5E5/JSwI3mtnjSMckNWrQfXKRcakTKp92ftFGrm0qpw8l/afyqCOnLDZb43ZzN0IZkfXf2DA+AEZtUS129d2GKD4fkAwF5AKdbjb6vdZybFjafT9iSjCbY2s2jvi7o/xnUwn5uOO4bMWFe4FJO6eg9/x5WjYt0pHvfmYcfslnMiSp6A2BIbI5m8rRzp/djz24Zu4yS8bEr7yHoi9oZQKOTfQ2uiMrjpIqC9wCnV6L/T2kVy+miJ6fZfP7MnDCB8m6DjPzSd1JyG4JH73dOv4p4b5sexNNxghLnHfpKQXgMyhwn8w/xIPyp/iS/NWEKJ+E6v7ao5dtX7/spF/y+0n9lSqcDxcHgEZobRseT81D0OXaMstSInMIxNYFzbgMWTQx2B4zqtP4jkz6R6AnAMyMDpfmLLbfL3J6cmSeCUhY6DnY9pcXhCJC+cSF6IwMx4y6xtV5Hu+1EhZW0aVQ4Q6hlat+J/vo9/i4oncKtTWQIRAK+lSb+G+R3cOgJxFlMfFfHxRPWG26GBHH9SBbgep5wCPVTB9lTwuShPLs/XGUXXpLOC5MrEPQp4CqKJYEI4BOBo0KDDOLeFzoVzyRidRA5lWs7FZ7Lhm/Ytwo3LZI9fMMXGFxllZbfgCjErGmB9XkTi8fJff2EN1AYlNuTaZ3UlrXtu09f/2wyfYvJTNOQPBP3OCwex3yYSral4sZw2ccGYVuARiUo3iMlKVOumPKQLEhpbbuAb0M8QGhdgKW04ubjte/gZUYTJVMtMrfy0lXoU9PoJJQbOlWIqg5P7gdfv0e0FPMYpUlVJotqDRAaaiBa6Wb7fl3F39EJTBZfUjwhJS4nsUD3sCPJwY6Fi2lEsvdJAbQugKhejo2pvZwKd+3ZWVWZYyZwKBXcg61gPHOwjA2bwH5IhyWb+ifyvh09EFcySPu9XdB4eJW5XHHShUI4nNFAoyhper5JstZpF+HmCsAIhq3V+qmXyoCF32XrZ2iVN40/M1cb3+hdq5YZR93NEr4+GcCA5VJyNhVdjsKHdQ5q/5U71PPNkS5ISmjL8kLTBtXqNPSscHHD3J4zmsrEhhgJkesmj4yYUglWvK9gVGLP+YP3FMdwPsF7+ndCPsce3hcbpvCHCSFNGofKfbqF/qgvTtNusJDXADXoCxRdZxFAKjK8+k4FqEldtsoFHRlaAK72x4/ISKTfnv6JKSBya9Ef+fLQFTPMq4kbIzb1tB+LjFPX68JNC2z/aNDvef/H4220lqinXKoj57LqgYfjBwh215UTGHyI3QQrTxkBKuzDQp9NKdkFPPBdDBQUM94UgXBl8MNYYDKxsO9ThcwbvSuE0Nw5lDIw9vaauNU+R+NNHLXRWEXnUUHMh5vYZsFL5zhX0hKkdqEyUM6Trl7zpePTBcFFc+dWJKuE+s17pKsNiiHWYkB5/mSajOiFsLidfeeOFedXFXyQdaU55wE3Ok15l/n0ueH56D528MmmSZ1F2elPjUDt/is0SFXEeYMKi/StuLGRH3Ma/lWh8dV0ifwcBQfIYISN5qstom1jAacMcDvXQ3hywVu8ADnWRVZ6HtLX3hPRC02N3ye2jDyJSpTS/+ZJOJH/vThuhQUiVh2S+ejFWMz43ZMgV6rjhJ4fOZdSsgopIe7xdj6OWE7jv2swHeNlCfdvljBbnE4zRhqBb4PnZderFeaOFqde7GwRhIPIhMGUXepxNhWEAFwjW0V58exaZXdCKhDXjx3tQ47kybWz2j94W3rQcdYMvr6IDyJFbl3nJlg/pB0WoUCM9oDL+tjr5XPXskUbGC5ggl3RD4EJsEgHv5SdH6HnRklYIXHJWPI8dFLGIuiZxIXX4+Gvah33JMuaRjfv2wpkPy4fXPKCuJWVOsDCHTdvMDD6eDqs03MHhl7LXjlO3OoWlw3M6f8me/jngSnR3CEt/tFhv9q3978TRiNbpILISoozX349L7EImsuB76smFkdJkumiTsg7/VugLpKsyR9GMslAjX8DyWuhdWuivbX9xFtMNKTTwPXjwsZ5VG8c1DIvWA7hSQFAmPblt0O1FMdUg2rhn6KZuPVKpcBBJ4HbSZd5n68RidNiG63PLOIi6648z4X/wK62nlEXS16NUhZo2igJBEiYaKNIgIeypYimNVEFMpIG4fd2v/hwy6LlsiIYHtRnuf/T3jlD7Py5D/UARtuhNxsj3ATB6S8zPMdUw8Xk03nqAXUw1AXTaUkGWZGJD8m512P3p4ZEy2wv3g/nDur+/iL8LHs/kW//Qdze23qLr9CFj74DB2sYmTVfOVq7Hmb51TV5iAC6Z4EfrCBHF2FbNRH5lNMXvAacf4CGer9W/YintWri5o32QkudJWT2jHBFv7mLX0GKJe8gxg5ueHEr5l5F2OKAPwhFyB92yHLRQYA8PDk/dUFkhKG8nxyZJ6EgvYHW9p6/ERUzpGezg4q+zqJmXJMXXNyr3FcXTV0kIF9BmqFey+CcyKGUEPYXL/n1iyNSm73z0032N3/Pn5PLccYqP18FJe2auNJblXr1NUlabb6dldU02FfdgrMp4dELm3F/qsYXUGsI94ToztQz+tckE6rWBEESnplbQlpEeLADrYlpnkUZjzFQ3GeFG3mHI640Q6YBkSmb630rkxwQynBbvulP/p4DAe3rnlTo5F9lv1boxtLy7V1poz0dXVR5ehsZv2nQXkTANvVs69RjPHxT82ZNOUDZbn5o+V1o1Zd8l1AOPLhI1YuuDG7ML9pAwY8ETlPChaoNRACE9uD8IA2UPNiEmt3WTAZj3WBSIY2K0tq+HemZqj8taWj6maRXo5h2w6H0Hce96sbuiR+yKh0qBnjbXUGb7uT4Ekgc9lcn9mytNeHtq8thBy8eLVUov66vBPrYngP9hI3gk5U=\"\n + \ }\n ],\n \"usageMetadata\": {\n \"promptTokenCount\": 32831,\n \"candidatesTokenCount\": + 32768,\n \"totalTokenCount\": 65599,\n \"promptTokensDetails\": [\n + \ {\n \"modality\": \"TEXT\",\n \"tokenCount\": 32831\n + \ }\n ],\n \"candidatesTokensDetails\": [\n {\n \"modality\": + \"TEXT\",\n \"tokenCount\": 32768\n }\n ]\n },\n \"modelVersion\": + \"gemini-4-argon\",\n \"responseId\": \"G7ToauPBG_2p5NoPnZ_J-QI\"\n}\n" + headers: + alt-svc: + - h3=":443"; ma=2592000,h3-29=":443"; ma=2592000 + content-length: + - '361142' + content-type: + - application/json; charset=UTF-8 + date: + - Mon, 02 Nov 2026 16:07:54 GMT + server: + - scaffolding on HTTPServer2 + server-timing: + - gfet4t7; dur=319321 + transfer-encoding: + - chunked + vary: + - Origin + - X-Origin + - Referer + x-content-type-options: + - nosniff + x-frame-options: + - SAMEORIGIN + x-gemini-service-tier: + - standard + x-xss-protection: + - '0' + status: + code: 200 + message: OK +version: 1 diff --git a/py/src/braintrust/integrations/google_genai/integration.py b/py/src/braintrust/integrations/google_genai/integration.py index 6a6cc79d..8ec1fc7d 100644 --- a/py/src/braintrust/integrations/google_genai/integration.py +++ b/py/src/braintrust/integrations/google_genai/integration.py @@ -26,6 +26,7 @@ InteractionsDeletePatcher, InteractionsGetPatcher, ModelsEmbedContentPatcher, + ModelsGenerateContentContinuationPatcher, ModelsGenerateContentPatcher, ModelsGenerateContentStreamPatcher, ModelsGenerateImagesPatcher, @@ -42,6 +43,7 @@ class GoogleGenAIIntegration(BaseIntegration): import_names = ("google.genai",) min_version = "1.30.0" patchers = ( + ModelsGenerateContentContinuationPatcher, ModelsGenerateContentPatcher, ModelsGenerateContentStreamPatcher, ModelsEmbedContentPatcher, diff --git a/py/src/braintrust/integrations/google_genai/patchers.py b/py/src/braintrust/integrations/google_genai/patchers.py index 03bbba07..4da6645f 100644 --- a/py/src/braintrust/integrations/google_genai/patchers.py +++ b/py/src/braintrust/integrations/google_genai/patchers.py @@ -27,6 +27,15 @@ # --------------------------------------------------------------------------- +class ModelsGenerateContentContinuationPatcher(FunctionWrapperPatcher): + """Trace a complete model turn, including any continuation requests.""" + + name = "google_genai.models.generate_content_continuation" + target_module = "google.genai.models" + target_path = "Models._generate_content_with_continuation" + wrapper = _generate_content_wrapper + + class ModelsGenerateContentPatcher(FunctionWrapperPatcher): """Patch ``Models._generate_content`` for tracing.""" @@ -34,6 +43,7 @@ class ModelsGenerateContentPatcher(FunctionWrapperPatcher): target_module = "google.genai.models" target_path = "Models._generate_content" wrapper = _generate_content_wrapper + superseded_by = (ModelsGenerateContentContinuationPatcher,) class ModelsGenerateContentStreamPatcher(FunctionWrapperPatcher): diff --git a/py/src/braintrust/integrations/google_genai/test_google_genai.py b/py/src/braintrust/integrations/google_genai/test_google_genai.py index abcd4494..d6ad93de 100644 --- a/py/src/braintrust/integrations/google_genai/test_google_genai.py +++ b/py/src/braintrust/integrations/google_genai/test_google_genai.py @@ -270,6 +270,45 @@ def _serialized_modality_details(details): # Test 1: Basic Completion +@LATEST_ONLY +@pytest.mark.vcr +@pytest.mark.asyncio +@pytest.mark.parametrize("mode", ["sync", "async"]) +@pytest.mark.parametrize("vcr_cassette_name", ["test_automatic_continuation"]) +async def test_automatic_continuation(memory_logger, mode, vcr_cassette, vcr_cassette_name): + """A continued generation is traced as one merged model response.""" + client = Client() + kwargs = dict( + model="gemini-4-argon", + contents=( + "Write a complete graduate textbook on algebraic geometry, with detailed proofs and exercises for each " + "chapter. Continue for at least 100 pages without summarizing or stopping early." + ), + config=types.GenerateContentConfig( + max_output_tokens=65536, + thinking_config=types.ThinkingConfig(thinking_level="high"), + ), + ) + if mode == "sync": + response = client.models.generate_content(**kwargs) + else: + response = await client.aio.models.generate_content(**kwargs) + + assert len(vcr_cassette.responses) == 2 + first_response = json.loads(vcr_cassette.responses[0]["body"]["string"]) + assert first_response["candidates"][0]["finishReason"] == "CONTINUATION" + spans = memory_logger.pop() + assert len(spans) == 1 + assert spans[0]["span_attributes"]["type"] == "llm" + assert spans[0]["metadata"]["model"] == "gemini-4-argon" + assert spans[0]["metadata"]["provider"] == "google" + assert spans[0]["context"]["span_origin"]["instrumentation"]["name"] == "google-genai-auto" + assert spans[0]["metrics"]["tokens"] == response.usage_metadata.total_token_count + assert spans[0]["output"]["candidates"][0]["content"] == response.candidates[0].content.model_dump( + exclude_none=True + ) + + @pytest.mark.vcr @pytest.mark.asyncio @pytest.mark.parametrize(