{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# More examples of orthogonal projection\n", "Let $f$ be the function $f(x)=\\sin(x)$. We'd like to approximate $f$ by a polynomial of degree at most $5$. To put this problem in the context of orthogonal projection, let $V$ be the space of continuous real valued functions and let $W=P_5(\\mathbb{R})$, the space of polynomials of degree less than or equal to $5$. We'd like to find the polynomial $p\\in W$ that is ``closest'' to $f\\in V$. While there is no single natural notion of distance in the vector space $V$, if we have an inner product\n", "$$\\langle \\, ,\\,\\rangle:V \\times V \\to V$$\n", "then we define distance between two functions $f$ and $g$ to be $$\\|f-g\\| \\text{ where } \\|v\\|:=\\sqrt{\\langle v,v\\rangle}.$$\n", "Then, one has an orthogonal projection operator $$P:V \\to W$$ that maps a vector $v\\in V$ to the vector $Pv\\in W$ that is closest to $v$. There's a nice formula for $Pv$:\n", "$$Pv = \\langle v,e_1 \\rangle e_1+\\langle v,e_2 \\rangle e_2+ \\cdots +\\langle v,e_n \\rangle e_n$$\n", "where $e_1, \\ldots, e_n$ is any orthonormal basis for $W$.\n", "\n", "So, this suggests the following approach to approximating a function $f$:\n", "\n", "### Step 1: Choose an inner product\n", "### Step 2: Choose a basis for $W$\n", "### Step 3: Apply Gram-Schmidt to obtain an orthonormal basis $e_1, \\ldots, e_n$ for W\n", "### Step 4: Then orthogonally project $v$ to $Pv$\n", "\n", "There's one important point to make here. It's not essential that $$\\langle \\, ,\\,\\rangle:V \\times V \\to V$$ actually be positive definite on all of $V$. As long as $\\langle \\, ,\\,\\rangle:V \\times V \\to V$ satisfies:\n", "\n", "### $\\langle v , v' \\rangle = \\langle v', v \\rangle$ for all $v,v' \\in V$\n", "### $\\langle u+v , v' \\rangle = \\langle u, v' \\rangle+\\langle v, v' \\rangle$ for all $u,v,v' \\in V$\n", "### $\\langle v , v \\rangle \\geq 0 $ for all $v,v' \\in V$\n", "### $\\langle w , w \\rangle = 0 \\Leftrightarrow w = 0$ for all $w \\in W$\n", "\n", "Then $\\|v\\|:=\\sqrt{\\langle v,v\\rangle}$ defines a semi-norm on $V$, the formula for $Pv$ above defines an operator $P:V \\to W$ and for any $v\\in V$, the vector $Pv\\in W$ solves the minimization problem in the sense that \n", "$$\\|v-Pv\\| \\leq \\|v-w\\| \\text{ for all }w\\in W.$$\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the examples below, we vary the formula for $\\langle f,g\\rangle$ and illustrate how this gives different approximations." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sympy as sym" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x**3 + sin(2*x*y)\n" ] }, { "data": { "text/latex": [ "$\\displaystyle 2 x \\cos{\\left(2 x y \\right)}$" ], "text/plain": [ "2*x*cos(2*x*y)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sym.Symbol(\"x\")\n", "y = sym.Symbol(\"y\")\n", "myf = x**3+sym.sin(2*x*y)\n", "print(myf)\n", "sym.diff(myf,y) # how to use sympy to differentiate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You might want to use \"display\" instead of \"print\" here:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x**3 + sin(2*x*y)\n" ] }, { "data": { "text/latex": [ "$\\displaystyle x^{3} + \\sin{\\left(2 x y \\right)}$" ], "text/plain": [ " 3 \n", "x + sin(2⋅x⋅y)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(myf)\n", "display(myf)\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 2 \\cdot \\left(3 x - 2 \\sin{\\left(2 x \\right)}\\right)$" ], "text/plain": [ "2*(3*x - 2*sin(2*x))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myf.diff(x,2) # higher derivatives " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def gramschmidt(listofvectors, ip): # input a list of vectors and an innerproduct\n", " obasis = [] # we'll start with an empty list and add the vectors in our orthonormal basis as we create them\n", " for v in listofvectors:\n", " for e in obasis: ## think inductively. \n", " ## If we have e_1, e_2, ..., e_k and v=v_{k+1} we define e_{k+1} by\n", " ## e_{k+1}:= v - *e1 - *e2 - ... - *ek\n", " v -= ip(v, e) * e # take the old q and subtract e for each e in the obasis\n", " norm = ip(v,v) \n", " e = 1/sym.sqrt(norm) * v ## now normalize\n", " obasis.append(e)\n", " return(obasis)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def project(func,onbasis,ip):\n", " p = 0\n", " for e in onbasis:\n", " p += ip(func,e) * e \n", " return(p)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def myip1(f, g):\n", " return sym.integrate(f*g, (x, 0, 10))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "basis = [x**0, x, x**2, x**3, x**4, x**5]\n", "ortho_basis1 = gramschmidt(basis,myip1)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[ \\frac{\\sqrt{10}}{10}, \\ \\frac{\\sqrt{30} \\left(x - 5\\right)}{50}, \\ \\frac{3 \\sqrt{2} \\left(x^{2} - 10 x + \\frac{50}{3}\\right)}{100}, \\ \\frac{\\sqrt{70} \\left(x^{3} - 15 x^{2} + 60 x - 50\\right)}{500}, \\ \\frac{21 \\sqrt{10} \\left(x^{4} - 20 x^{3} + \\frac{900 x^{2}}{7} - \\frac{2000 x}{7} + \\frac{1000}{7}\\right)}{10000}, \\ \\frac{63 \\sqrt{110} \\left(x^{5} - 25 x^{4} + \\frac{2000 x^{3}}{9} - \\frac{2500 x^{2}}{3} + \\frac{25000 x}{21} - \\frac{25000}{63}\\right)}{250000}\\right]$" ], "text/plain": [ "⎡ \n", "⎢ ⎛ 2 50⎞ \n", "⎢ 3⋅√2⋅⎜x - 10⋅x + ──⎟ ⎛ 3 2 ⎞ 21⋅√10\n", "⎢√10 √30⋅(x - 5) ⎝ 3 ⎠ √70⋅⎝x - 15⋅x + 60⋅x - 50⎠ \n", "⎢───, ───────────, ─────────────────────, ────────────────────────────, ──────\n", "⎣ 10 50 100 500 \n", "\n", " ⎛ 2 ⎞ ⎛ 3 \n", " ⎜ 4 3 900⋅x 2000⋅x 1000⎟ ⎜ 5 4 2000⋅x 2500⋅x\n", "⋅⎜x - 20⋅x + ────── - ────── + ────⎟ 63⋅√110⋅⎜x - 25⋅x + ─────── - ──────\n", " ⎝ 7 7 7 ⎠ ⎝ 9 3 \n", "──────────────────────────────────────, ──────────────────────────────────────\n", " 10000 250000 \n", "\n", "2 ⎞⎤\n", " 25000⋅x 25000⎟⎥\n", "─ + ─────── - ─────⎟⎥\n", " 21 63 ⎠⎥\n", "────────────────────⎥\n", " ⎦" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(ortho_basis1)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "╒═══╤═══╤═══╤═══╤═══╕\n", "│ 1 │ 0 │ 0 │ 0 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 1 │ 0 │ 0 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 0 │ 1 │ 0 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 0 │ 0 │ 1 │ 0 │\n", "├───┼───┼───┼───┼───┤\n", "│ 0 │ 0 │ 0 │ 0 │ 1 │\n", "╘═══╧═══╧═══╧═══╧═══╛\n" ] } ], "source": [ "from tabulate import tabulate\n", "table = [[myip1(ortho_basis1[i],ortho_basis1[j]) for i in range(5)] for j in range(5)]\n", "print(tabulate(table, tablefmt='fancy_grid'))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "p1 = project(sym.sin(x),ortho_basis1,myip1)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.plotting import plot\n", "plot(p1,sym.sin(x),(x,0,10))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def myip2(f, g):\n", " return sum([f.subs({x:i})*g.subs({x:i}) for i in [0,2,4,6,8,10]])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "ortho_basis2 = gramschmidt(basis,myip2)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[ \\frac{\\sqrt{6}}{6}, \\ \\frac{\\sqrt{70} \\left(x - 5\\right)}{70}, \\ \\frac{\\sqrt{21} \\left(x^{2} - 10 x + \\frac{40}{3}\\right)}{112}, \\ \\frac{\\sqrt{5} \\left(x^{3} - 15 x^{2} + \\frac{274 x}{5} - 24\\right)}{144}, \\ \\frac{\\sqrt{7} \\left(x^{4} - 20 x^{3} + \\frac{860 x^{2}}{7} - \\frac{1600 x}{7} + \\frac{192}{7}\\right)}{384}, \\ \\frac{\\sqrt{7} \\left(x^{5} - 25 x^{4} + \\frac{1960 x^{3}}{9} - \\frac{2300 x^{2}}{3} + \\frac{56192 x}{63} - \\frac{320}{21}\\right)}{640}\\right]$" ], "text/plain": [ "⎡ ⎛ \n", "⎢ ⎛ 2 40⎞ ⎛ 3 2 274⋅x ⎞ ⎜ 4 \n", "⎢ √21⋅⎜x - 10⋅x + ──⎟ √5⋅⎜x - 15⋅x + ───── - 24⎟ √7⋅⎜x -\n", "⎢√6 √70⋅(x - 5) ⎝ 3 ⎠ ⎝ 5 ⎠ ⎝ \n", "⎢──, ───────────, ────────────────────, ────────────────────────────, ────────\n", "⎣6 70 112 144 \n", "\n", " 2 ⎞ ⎛ 3 2 \n", " 3 860⋅x 1600⋅x 192⎟ ⎜ 5 4 1960⋅x 2300⋅x 56192⋅x \n", " 20⋅x + ────── - ────── + ───⎟ √7⋅⎜x - 25⋅x + ─────── - ─────── + ─────── \n", " 7 7 7 ⎠ ⎝ 9 3 63 \n", "───────────────────────────────, ─────────────────────────────────────────────\n", " 384 640 \n", "\n", " ⎞⎤\n", " 320⎟⎥\n", "- ───⎟⎥\n", " 21⎠⎥\n", "──────⎥\n", " ⎦" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ortho_basis2" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "p2 = project(sym.sin(x),ortho_basis2,myip2)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "plot(sym.sin(x),p2,(x,0,10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\langle f,g \\rangle := f(1)g(1)+f'(1)g'(1)+f(5)g(5)+f'(5)g'(5)+f(9)g(9)+f'(9)g'(9)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When is $dist(f,g)$ small using this inner product? $\\|f-g\\|$ is small $\\Rightarrow$ $\\langle f-g, f-g\\rangle$ is small \n", "$$(f(1)-g(1))^2+(f'(1)-g'(1))^2+(f(5)-g(5))^2+(f'(5)-g'(5))^2+(f(9)-g(9))^2+(f'(9)-g'(9))^2 \\text{ is small}$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "def myip3(f, g):\n", " df = sym.diff(f)\n", " dg = sym.diff(g)\n", " result = 0\n", " for i in [1,5,9]:\n", " result += f.subs({x:i})*g.subs({x:i}) + df.subs({x:i})*dg.subs({x:i})\n", " return result" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[ \\frac{\\sqrt{3}}{3}, \\ \\frac{\\sqrt{35} \\left(x - 5\\right)}{35}, \\ \\frac{\\sqrt{42} \\left(x^{2} - 10 x + \\frac{43}{3}\\right)}{112}, \\ \\frac{\\sqrt{1190} \\left(x^{3} - 15 x^{2} + \\frac{2017 x}{35} - \\frac{267}{7}\\right)}{1632}, \\ \\frac{\\sqrt{14} \\left(x^{4} - 20 x^{3} + \\frac{890 x^{2}}{7} - \\frac{1900 x}{7} + \\frac{887}{7}\\right)}{512}, \\ \\frac{3 \\sqrt{34} \\left(x^{5} - 25 x^{4} + \\frac{33658 x^{3}}{153} - \\frac{40790 x^{2}}{51} + \\frac{166493 x}{153} - \\frac{22655}{51}\\right)}{4096}\\right]$" ], "text/plain": [ "⎡ \n", "⎢ ⎛ 2 43⎞ ⎛ 3 2 2017⋅x 267⎞ \n", "⎢ √42⋅⎜x - 10⋅x + ──⎟ √1190⋅⎜x - 15⋅x + ────── - ───⎟ √14\n", "⎢√3 √35⋅(x - 5) ⎝ 3 ⎠ ⎝ 35 7 ⎠ \n", "⎢──, ───────────, ────────────────────, ─────────────────────────────────, ───\n", "⎣3 35 112 1632 \n", "\n", " ⎛ 2 ⎞ ⎛ 3 2\n", " ⎜ 4 3 890⋅x 1900⋅x 887⎟ ⎜ 5 4 33658⋅x 40790⋅x \n", "⋅⎜x - 20⋅x + ────── - ────── + ───⎟ 3⋅√34⋅⎜x - 25⋅x + ──────── - ────────\n", " ⎝ 7 7 7 ⎠ ⎝ 153 51 \n", "─────────────────────────────────────, ───────────────────────────────────────\n", " 512 4096 \n", "\n", " ⎞⎤\n", " 166493⋅x 22655⎟⎥\n", " + ──────── - ─────⎟⎥\n", " 153 51 ⎠⎥\n", "────────────────────⎥\n", " ⎦" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ortho_basis3 = gramschmidt(basis,myip3)\n", "ortho_basis3" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "p3 = project(sym.sin(x),ortho_basis3,myip3)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.plotting import plot\n", "plot(sym.sin(x),p3,(x,0,10))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[ x^{3} + \\sin{\\left(x \\right)}, \\ 3 x^{2} + \\cos{\\left(x \\right)}, \\ 6 x - \\sin{\\left(x \\right)}, \\ 6 - \\cos{\\left(x \\right)}, \\ \\sin{\\left(x \\right)}, \\ \\cos{\\left(x \\right)}\\right]$" ], "text/plain": [ "⎡ 3 2 ⎤\n", "⎣x + sin(x), 3⋅x + cos(x), 6⋅x - sin(x), 6 - cos(x), sin(x), cos(x)⎦" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Make a list of higher derivatives\n", "[(x**3+sym.sin(x)).diff(x,n) for n in range(6)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\langle f,g \\rangle := f(5)g(5)+f'(5)g'(5)+f''(5)g''(5)+f'''(5)g'''(5)+f''''(5)g''''(5)+f'''''(5)g'''''(5)$$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def myip4(f, g):\n", " result = 0\n", " for i in range(6):\n", " dif=f.diff(x,i)\n", " dig=g.diff(x,i)\n", " result += dif.subs({x:5})*dig.subs({x:5})\n", " return result" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, x - 5, x**2/2 - 5*x + 25/2, x**3/6 - 5*x**2/2 + 25*x/2 - 125/6, x**4/24 - 5*x**3/6 + 25*x**2/4 - 125*x/6 + 625/24, x**5/120 - 5*x**4/24 + 25*x**3/12 - 125*x**2/12 + 625*x/24 - 625/24]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ortho_basis4 = gramschmidt(basis,myip4)\n", "print(ortho_basis4)\n", "p4 = project(sym.sin(x),ortho_basis4,myip4)\n", "plot(sym.sin(x),p4,(x,0,10),ylim=[-1.2,1.2])" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.00236385154552689*x**5 - 0.0990514667491362*x**4 + 1.34278941769047*x**3 - 7.75947354756359*x**2 + 19.3078886291108*x - 16.8400753039969\n" ] }, { "data": { "text/latex": [ "$\\displaystyle 0.958924274663151$" ], "text/plain": [ "0.958924274663151" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(p4.evalf())\n", "p4.evalf().diff(x,2).subs({x:5})" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0.958924274663138$" ], "text/plain": [ "0.958924274663138" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sym.sin(x).diff(x,2).subs({x:5}).evalf()" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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Rk5gUOYkoz6iWMVLQINplxKW0tJSYmBjmzZtXr/Xx8fFMnz6dcePGERsby1NPPcWDDz7I+vXrm9lSx6SVpJFcnIxaUjM4cHDjN4r9FnLPgas/XP1c0xnYGNQauGkRuPhB1gnY+o7dZSpJZYu6fHvyW9EaLRAImpQyUxkrz67kwfUPMmn5JN7Z/w5Hco5Qbi5HJakIcQ1hWNAwJkRMoL9/f8LcwnBSOwFwMu8kHx76kBmrZjD7l9n8cOoHTFZTK78jwcVIcjv/1pAkqc6Iy1//+lfWrFnDsWMXtEZuvfVWCgoKWLdund1jDAYDBoPB9u+ioiLCw8MpLCzEw8Pjsu1eeXYlL+18iRj/GJZc00gZfLMRPhoEhUkw9U0l4tICmCxWEnJKOZtVQnxOKQBOWjXOWjX+7nquKt+K+68PgkqjKO0G96uxR4mxhAk/TqDMXMZnkz5jeMjwFrFdIBC0H2RZJiW/nFMZxcRll2CyWJEkCbVKIsrXld4hHoR5O9ukJExWEyvOrGD+4fnkVeTZ9hkQMIBrO13LkKAhhLmFoVVr7b5WXkUeW1K2sCFxA3vS9mCWlS7JSI9Inhr4FBMiJly+bIXgsmmXqaKGsmvXLiZOnFjtsSlTpvDUU085POaNN97glVdq75C5LJvSdwGXWd9y+DvFaXELhEH3No1hDig1mFl/PIOfDqayJz4Xk6U2f9eFr9yGM8a8i/Llj+D82Ba45EThpnNjZpeZfH/qe749+a1wXAQCAQBmi5Vdcbn8HJvGhuMZFFU4llgA8HTWMqqLHz27JLI29UuSihMBCHMLY3bX2VzT6RpC3ULrfF1JkvB19mV219nM7jqbQkMhq+NW89mRz0gsSuTpzU/T378/r4x8pWnEQgWN5opwXDIyMggMrN4eHBgYSFFREeXl5Tg7O9c45oUXXmDu3Lm2f1dFXJoCWZZthbmNrm8xG2Hbu8r9kU+BtuZ7aApySwz874+zrDiYQpnRYnvcVaemS6A7Xfzd0Kgkyk0WyowWkvJKOZNZwjMld/O7/ijeucf59t2n8Z72D6b1Cap2tXJbj9v4/tT3bE3ZSlpJGiFuIc3yHgQCQdvHZLHy4/4UPtx4loyiCtvjWrVEZ383ugW646JTI8tgtFg5k1nMmcxiCg3FbMz9hq3mWACcVZ481v9R7uh9M1pVzchKffHUe3JHzzuY2Xkmi48v5usTXxObHcttq2/j3yP/zeSoyZf7lgWN5IpwXBqDXq9Hr69ZWNoUnC84T15FHk5qJ2L8Yxq3yfGfoCAJXANg8H1NayDKSeSbXYn8748ztiueKF8XZg8M49p+wUT7uToMmRaUGdmXkM/PW/+PezNe56bS77j2uz4sjorh5Rm96B2iTMCO9oxmWNAw9mTs4aezP/HEgCea/H0IBIK2jSzLrDmazrsbzthSz14uWqb3Dea6mBAGRnqjVdsvx9ydto8Xtv2dnIoMZFmFMXcMxbljmZfkgb+cwzV9gy47teOmc+OJAU9wU7ebeGH7C+zL2MczW57hnux7+Mugv1yWcyRoHFeE4xIUFERmZma1xzIzM/Hw8LAbbWluDmYdBCDGPwadWtfwDWQZdlUWJg97uMmjLTvP5fDyL8c5m1UCQK9gD/55bU+Gd/Kt10nAy0XHpF6B0PN5DN8cQB+3nnd1nzIr/hWu/Wg79wyP4oVreqDXqLmx243sydjDynMreSTmETSqK+JPUiAQAPmlRp5bfpg/TirjQnxddTwxvgu3D4tAr1E7PM5sNTP/8Hy+OPoFVtlKmFsY/7rqNeJS/fh8axxxOaU8/t1BJvQI4NVZfQj1uvxzZKBrIJ9N+owPD37IouOL+OrEVxzNOcp7Y9/D19n3svcX1J922VXUUIYPH87GjRurPfb7778zfHjr1FXEZsUC0D+gf+M2SNqlSPtrnGBQ00VbrFaZD/44y+1f7OFsVgneLlpev74vvz45ihGd/Rp+5SJJ6Gd9AE6e9JXieCPiALIMi3cmcOP8XSTnlTE+Yjzeem+yyrLYnrq9yd6LQCBo2+xPyOOaD7fxx8ksdGoVT03sypbnx3HfyOhanZYyUxlPbXqKz458hlW2MrPzTJZft5xhoQO5bWgEv/1lNP83oStatcTGU1lMem8Lqw6lNonNGpWGuYPn8v7Y93HVunIw6yD3rb+PrLLa57QJmpZ26biUlJQQGxtLbGwsoLQ7x8bGkpSUBCj1KXfffbdt/SOPPEJcXBzPP/88p06d4pNPPmHZsmU8/fTTrWE+h7IOAUqle6PYPV+57XcLuDaNp19iMPPIkgO8/4ciHHfb0HA2PzuO24dFoFZdRqjVIxjGvwjAzSVL+ObOHni7aDmaWsj0D7ex5XS+bX7R8jPLL/t9CASCto3VKjNv0zlu+Ww36YUVRPu5svLxETw1sRtu+tojrjnlOdy3/j62pGxBr9bz9tVv859R/8FV62pb46RVM3dSN377v9GMjtDT03SCvcvfZevCvyP/+RpseBF2fACn1ihCmWZjg9/DxMiJfD/9e4Jcg4gvjOe+dfeRUZrR4H0EjaNdtkNv3ryZcePG1Xj8nnvuYfHixdx7770kJCSwefPmasc8/fTTnDhxgrCwMF588cUGCdAVFRXh6el52e3QOeU5jFs2DgmJHbftwF3n3rAN8hPhw/4gW+HRXRDYq9G2VJGcV8b9i/dxNqsEnVrFf2b14eYhTVOIDCgieZ9cpejNjH6WtEHP8vh3BzmUVADA09O8+CLhEVSSivU3rCfINajpXlsgELQZLFaZF346wrL9KQDM6h/Cf67vW6fDAhBXEMejfzxKWmka3npvPhz/of2ode55ZezIiZ8hPbZuo1Ra6Dwe+syG7teAU/3P76klqTyw/gFSS1IJdw/n62lfX/74FkGdtEvHpTVoKsfl98Tfmbt5Lt28u7HiuhUN3+CPf8H29yF6DNzzS6PtqCI5r4xbP9tNakE5Ae56Ftw1iIER3pe9bw1OroaldyjprScPYnQN5tXVx1myW4mSde+/hDTDMR6LeYxH+7eMHo1AIGg5TBYrTy+NZfWRdFQS/HtWH24fGlGvFPT5gvPcv/5+8iryiPSI5JMJnxDhEXFhgSzDmfVKp2XK3uoHu4eQ7tyFnRkSpVYd3h5uTIuU0BScV5wcY8mFtRonGPKg0qnp5l+v95VRmsG96+4ltSSV3r69WThlIS5al3odK2gc7TJV1J65rDSRxQyx3yn3hzxw2bakFZRz+xeK09LJz5VfnhjVPE4LQI/pEDEczBWw6TV0GhX/ntmHJ8d3AeB8XB8Afjr7ExarpbadBAJBO6PCZOHRJQdYfSQdrVri49sHcsewyHo5LfGF8Tyw/gHyKvLo6dOTb6Z9c8FpkWU4+St8ejV8f4vitEhq6DQOrv0fPHMGnjlJ8GO/Enn/Yt7RzOHJvJu4o+Ahyu/bBC+kwGN7YMzfwLercn7a9TF8EAMbXwVjaZ32BbkGsWDiArz0XhzPPc4zW54RSrvNjHBcWphDmYrj0qjC3LMboCRTkdTvNu2y7MgorOC2z3eTnFdOlK8L3825ikAXNaa0NEyZmVjLa5/n0WAkCSb/R7kf+x1kHEWSJJ6Z3J2/TeuBubg3stmFjLIMdqTtaNrXFggErYbZYuWxbw/yx8ks9BoVn901mGv6Btfr2KSiJB5c/yC5Fbl09+7O55M/x9up8uIqLw6+uR6W3qk0K2hdYeRfYO5JuHuVIhPhfkG/a3CUD988MAx3vYY98Xk8+PU+KsxWCOgB416AJ/bBnSsgZACYSpXozYLRkLyvTjujPKP4eMLHOKmd2J66nY8OfdSYX5WgngjHpQUpN5dzKu8U0MiIy6FvlNuYW0HTiDbqSrKKK7j9890k5pYxypLFl4VbKL15Fqdi+nNu/ATOjRnL6YGDOD/tGtJfeYWyffuaZp5Q2GDoPRuQlQK5Sh4Z05mXpsdgKhwIwId7v7n81xIIBK2OLMu89Mtx/jyVhZNWxeL7hjKuR0C9jk0uTub+9feTVZ5FF68ufD75czz1nmC1wvb/wSfDIW4TqPUw+hl4+hhMerWas3IpMeFeLL5/KK46NTvO5fLwNwcwWazKk5IEXSYqY0puWQLuIZB3HhZOhs1vKq9bCzH+Mbw26jUAFh1bxNaUrfV6n4KGIxyXFuRYzjHMspkAlwBCXBuoElucoeRwAQbeXfvaWqgwWZjz9QGs58/x3u7P+Mevb2NcvhRjYqLywdRqQa0GWcYYH0/B9z+QeNfdJNx4E8V/brp8B2bCS0oxXNwmOPeH7eH7R0Uzu+sNAJwq2svPR09c3usIBIJWZ8GWOL7bk4QkwYe3DmB45/p1QeZV5PHQhofILMukk2cnvpj8hRJpMZTAj3fDHy8raZ3oMfDYLuW84uJTr70HRXqz6L6hOGvVbDmTzWtrTlZfIEnQcwY8tlPp3JStsPkNWPkQmA32N61kctRkbu+hDJD9+/a/i06jZkI4Li3IxfUtDdZEOfojyBYIGwr+3Rv1+rIs89LKI/T8Yzkfb36fnhlnQKvFY8YMwuZ9TNdtW+lxOJYex47Sdfs2wj75BM/Zs5GcnKg4fpyUxx4j5ZFHMWVehmaBT7QimgdK1OWiepbXpk/AS+qOJFn5++8LOZZa2PjXEQgErcovh9N4a50SYX7p2l5M7l2/bkGDxcBTm54ipSSFMLcwvpj8hSLwlp8IC6coNS1qHcz4AO7+GXw7N9i2odE+fHBrf0DRlfp+b1LNRc7eMPszmDlPGRh79Ef4ZjaU59e69zODn6GXby8KDYU8t+U5Ue/SDAjHpQW5rMLco5UaJ/1ubvTrf7v5FN3mv849J9ehlq24T5pIl3VrCf3v27hPmIDG3x9JpUKSJDR+friPH0fI66/R5c+N+D74AGi1lGzZQvyNN1B28GCj7WD0M+DkCVknLhQbAyqVxDPDK6NJ7nt4eMk+CsoarrEgEAhal0NJ+Ty77DAA94+M5r6R0fU6TpZlXtrxEoeyDuGudWfexHn4u/hDwnb4fBxkHlPGnNyzWhksexly/pN7B/Hs5G4AvPTzMfbG59lfOOBOuGM56D0gcTssnAol2Q731al1vDPmHdy0bsRmx/LxoY8bbaPAPsJxaSGsspXD2coHucGFuTnnFD0CSQ29r2/U6+8+nozTP59hZPoxrBoNwf/5N2EffYQ2tO6pqRofHwKefZZOq1ai79oVS3YOiXffQ/733zcudeTiA1c/r9zf9Fq1yv2p0ZNx13mg0hWQYTzK3GWHsVpFx75A0F4oKDPyxHeHMFqsTO4VyD+m96z3sZ8c/oTf4n9DI2l4f9z7yhTm/Qvh65lQlgvB/eGhTRDRyOG0l/D4uC5c2y8Yk0Xm0SUHSMkvs7+w8zi4f51S95J9CpZcD+UFDvcNdw/n1ZGvArDw2EJ2pIqGg6ZEOC4tRGJRIsXGYpzUTnT3bmCq51hltKXzeHBtuLhRSmYBaY8+Ru/ceAx6F6K//hqvG29s8D76zp2J+uF73KdNBbOZjFdeJevNtxrnvAydA16RUJx+Ye4S4KRx4rrOM5T7Pnv581QWn2w+1/D9BQJBiyPLMs/+eJjUgnIifV149+aYeitv/3r+VxYcXgDAi8NfZFjgEPjteVj9NFjN0OcGuG8teIY1mb2SJPHfG2PoHeJBbqmRR5ccxGh2UIQb2Bvu+RVc/SHjKHx3c63t0pMiJ3Fr91sBeHXXq5SZHDhFggYjHJcW4njucQB6+PRo2CBBWVZyqwB9G+5smMwWtj70ND2zzlGucyJq0Ze4DGzkqAFA5epK6HvvEfDsMwDkffUV2R980PCNNHqloA6UDoHiC0Mwb6gs0tW4nUTSFPHe72fYcS6n0TYLBIKW4fNtccrsIY2KebcPxN2pfpOTT+ae5F87/wXA/X3uZ3aX6+H3F2Hvp4CknCtu+BJ0TS/s5qxT89ndg/GqHEXy0Z9nHS/26wJ3rVJS3cl7YMWDtXYbPT3oaUJcQ0grTeOT2E+a3PYrFeG4tBDHcxTHpbdf74YdmH5YkcrXOCkibg1k7YvvMuD0biySCu933sdrYP8G73EpkiTh++CDBL6ktDTnLviUnM8+b/hGfW6A0EGKZsLmN2wPd/XuSox/DFYsDO4Vj1WG5348THGFKHITCNoqB5PyeWvdaUApxu0T6lmv40qMJTy75VmMViNjwsbwl4F/UTRUdlXWhsz6RKmLu4x6lroI9XLm9ev7AjBv0zkOJNZSgBvUB+5YobRhn/4Ntr7tcKmL1oV/XPUPAJacXMLJ3JMO1wrqj3BcWoiqiEtv3wY6LidWKbfdpoC+YXONjm3cRfSqrwDIuvtRoiePbdhr14HP7bcT8NyzAGS/9x55S75t2AYXi9Id/BqyTtmeur6LUstjcN5DhK8zaYUVvLn2lL1dBAJBK1NutPDMssNYrDLX9gvmjmERdR+Eklp6eefLJBUnEewazGujXkO1fyH8+W9lwZQ3oP/tzWj5Ba7pG8zsAaFYZZi7LJZSg9nx4vAhcO37yv3Nb8Cp3xwuvTrsaqZGTcUiW3hl1ytCGbwJEI5LC2C2mm3Ccw2OuJxcrdz2vK5Bh5UVFpP797+hka2c6TWMsX99rGGvW098H3gAv8eUvTP/8x+K//yzYRtEjoDu05VW74uuXCZHTcZJ7UR8URyPTtID8O2eJHaeFykjgaCt8d/1p4nPKSXQQ89rs/rWW+7hh9M/sCFxAxqVhnfGvIPnmd9hjXIxxNXPw/DmOW854l8zexPq5Uxibhn/uVTf5VIG3AFDH1Lu//SQMmnaAX8d+lfcde4czz3O96e+b0KLr0yE49ICxBfGU24ux0XjQpRHVP0PzD4NuWcVwbaukxv0mr8//x8CCrPIdfFi5Lx3UKma77/a78kn8L5duSpKe/6vGBMSGrbBuBeU2+MrlaFngLvOnQmREwA4X7HJdgX3txVHKTPWciUkEAhalD1xuSzaGQ/Amzf0w9OlfnUtx3OP8999/wVg7qC59MvPgJUPAzIMmQPj/t5cJjvEw0nLOzfFIEnw/d4kNp7MrP2AKa9D5EgwFsPy+8FsX77Bz9mPpwc9DcCHhz4kq+wytLAEwnFpCarSRL18e6GSGvArP/mrcttpTINGrR/8cw+dtyqRGmnu3/ALbt4x65IkEfjC33AeOBBrSQkp//cXrGUNqKAP6qs4ZrIVdlwo9J3ZeSYAa+PX8vTkaEI8nUjKK+PdDY6vbAQCQctRZjTz3PIjyDLcMjiccd3rJ+dfZCzimc3KMMIJERO406UzLLtb6R7qexNMe7tZa1pqY3hnXx4cpejO/HXFEXJLalHLVWvhxkXg7AOZR2HLWw6X3tD1Bvr596PcXM78w/Ob2uwrCuG4tAC2wtyG1recqkwT9bi23ocYzRbSX/k3atlKfO+rGHnnzIa9ZiORtFpC//c+an8/DGfOkP7Syw1rkx41V7k9/D0UpQMwNGgoQa5BFBmLOJC9g9dnK8VzC3fE1148JxAIWoQPN54jKa+MEE8n/nFt/fVaXtn5CqklqYS6hfJql1uRvr8VzOXQdQrMmg/NGCGuD89M7k73QHdySoy8XVlw7BD3wAv1Ltvfg5T9dpepJBXPDlbSYD+d/Ym4grimNPmKQjguLcCJXGXuToPqWwpTIO0QIDWom+iXj76jU+Z5KtQ6hr7zagMtvTy0AQGEvf8+qNUUrV5NwY8/1v/gyOEQMRwsRls3gVqlZkYnRdNl1blVjO0ewA0Dw5BleH75YSpMoshNIGgt4rJL+HK78uX7ysw+eNSz9XlDwgalrkXS8O7gv+Hxw11gKFQ+/zctVqIYrYyTVm27UFp2IJmjKXWMH+k9C/rcqESNVz4MRvsR5wEBAxgXPg6rbOV/B//XtEZfQQjHpZkxWU0XCnMbEnE5s065DR8KbvULvyZlFeL9rdKWXDTjJvyiwxtka1PgMngwAXOVXG7Wm29hTEmt/8GjFW0Y9i+CMkV+e2YXJWK0M20nWWVZvHhtT/zd9ZzPLuXDjbXoLQgEgmZDlmVeXX0Ck0VmTDd/Jvas3zkqvyKf1/YoE5Qf7HM/vTe+BaVZENAbbvuhWXRaGsugSG+uHxCKLMO/fj1edwT5mv+CW5AiX/Hnfxwue2rgU6gkFZuSN3Ew8zJGp1zBCMelmTlfcB6j1Yi71p1w9wY4Emd/V267TanXclmWWfWf+YSUZFPi4sHIfz7VcGObCJ9778V50CCsZWWk//OfyHWMg7fRZaJS72Iqhb2fARDpEcmAgAFYZSur41bj5aLjP7P6APDp1jiOp4lBjAJBS7PxZBabT2ejVUu8PKNXvbuI3tr3FnkVeXTx6sJDebmQtBN07nDLN+Ds1bxGN4K/TeuBi07NgcR8fo5Nq32xiw9c95Fyf88CyDxud1knr042uYd3D7zbOOXxKxzhuDQzVfUtvfzq/+HGVAHxW5X7XSbV65ANh1OI2fYzAB5zHkLj5tZgW5sKSa0m5PXXkJydKdu9m/zv69n+J0kwSonWsGeBMsKeC0W6P5/7GVmWmdI7iOl9g7FYZf6z+qT44AsELUiFycKrq5X09/2jounkX79zzebkzayJW4NKUvHv8Blot1fWhVz3QaMmPLcEgR5OPD6uCwBvrD1Zu7YLQLfJ0HOGIu/w2/OK8rkdHuv/GE5qJ45kH2Fj0samNrvDIxyXZqZRwnNJO8FUpoQdg/rWudxssbLt468IKC+gwsObrvff2VhzmwxdZCQBzyipn6x33sWYmFi/A3vNAp9Oyuj4g4p4XpWmS1xhHMdyjgHwwjU90GlU7IrL5c9TorVQIGgpvtweT1JeGQHuep4c37VexxQZi/j3LkVU7p7Os+nzR2UqZfADioJ2E2POzaVs3z4KflpJ9ocfkvn2f8n+5BPyvvqKghUrKI+NxWqs3+T5B0ZFE+HjQmaRoX5z06a8riidJ26H4z/ZXRLgEsBdve4C4IODHwhRugYiHJdmplGOy9k/lNsuE+vVEvjj3kTGH1RqYgLnPIBKr2+wnc2B9+234TJsGHJ5Oen/fLF+kRGVGkY+pdzf+RGYDdU0XX4+r0SVwrxdeKCyZfH1305istQzHSUQCBpNWkE5H/+pfHn//ZqeuOnrN3ft3f3vklWeRaR7BI+d3qlMeg7qp3zJNxHG5GRyv/yShFtu5ezIUSTedTfpf/87OZ/MJ2/hQnI+/IjMN94k/R//JOHW2zgzeAiJd99DwfLlWEocD0t00qptE64/3xZPUm4dUg9eERe6JNf/0xY5vpT7+9yPh86DhKIEEXVpIMJxaUaMFiNn8hXNkQZ1FJ2rrG/pOrHOpeVGCzsWLSe4LBeTmwdBd9zWGFObBUmlIvi1/yA5OVG2bx9Fq9fU78CYW8E9WJkcffgH4EK66Lf43zBYFF2FR8d2xsdVx/nsUn7Yl9ws70EgEFzg9d9OUm6yMCTKm5n9Q+p1zM60nfx09ickJF7Vd8IpabdS13LTYtA6XZY9stVK0bp1xM++gfOTJpP133coP3wYAG14OK4jRuB1yy343H8/Xrfcgsf06biOHIna2xvZaKRs717S//kiZ0ePJv3FFzGl2a9jmdwrkFFd/DCarfxnzYm6DRv5f+AVCcVpytwlO7jp3Lith3K+/vLYlyLl3QCE49KMnM0/i9lqxkvvRYhr/T7k5CdAzhmQ1NBpXJ3Lv9qVwNhjisy+/523o3JpO1X5ALqwMPweeQSAzLffwlJi/+qjGho9jHhSub/jf2C12DRdio3FbEreBCgql09NVELV//v9jBjCKBA0I7vO57L6SDoqCf51Xe961eyVmkp5ZecrANwWNIqB+75Wnrjuw8uqa5FlmZJt24i/8UZSn3qaihMnQK3GZfhVBL70Il22bKHL7xuIWPglwa/8i8DnnyP4lX8R+u47RHz5BV137qDT2t8IePYZdNHRyOXlFPy4nPNTp5H59n+xFBVVez1JUoqQ1SqJDScy2X62jtEjWmeYWjk4dvcnUGTfIbq95+04qZ04kXuC3em7G/37uNIQjkszcrFibr0Lc6u6icKH1VllX1hmYt2KP+mdl4BVrcHv9rYTbbkYn/vvQxcZiSU7h5yPPq7fQQPvAWdvyIuDE6uqabr8fO5n27LbhkbQyd+V3FIj8zefbw7zBYIrHotV5pVflfPZ7cMi6B1Sv8nP/zvwP9JK0wh1CeQvRyolHoY8CH1mN9qWilOnSLzrLpLnPIThxElUrq74PfEEXbdvI3LRInxuvx1tYO3t2ZIkoY+OxvfBB+n02xoil3yDy9ChyEYjeQsXEjfjOkp27Kh2TNdAd+66KhKAV349Xnd6uvs1ijaNuQK2/tfuEh8nH2Z3VX4XXx77sp6/AYFwXJqRqjRRd5/u9T/oXGWusx5povlbzjPh5BYAPKdNRRtQPy2Flkal0xH4z38CkLdkCRWn6yHZr3eDYUqkhm3vgyzX0HQB0KpVvDBNyT9/uT2e1ILypn8DAsEVzqpDqZzKKMbTWcszk+p3PtufsZ8fTiup3n8Vm3Epraxrmfxao2yQZZm8r78h4aabKd9/AEmnw+e+++j8x+/4P/E4Gm/vRu0rSRIugwcT8dViwj9dgC4yEnNmJskPPEjmG28imy90Ej09sRveLlrOZpXw7e46Gg4kCca/qNw/+DXkxdtddk/ve1BLavak77F1oQpqRzguzcjZfEUgratX/SrvsZghsdLL7zy+1qUZhRX8uOkYV6cq+Vzfu+9qtJ0tgdvoUbhPngwWC5n/+U/98rlDHwKtqzID5NwfNTRdqpjYM4CrOvlgMFt5Z30d8twCgaBBmCxW/rdRudh4dGxnvF11dR5Tbi7n5Z0vA3CDazRXJR26rLoWc34+KY8+RubrryObTLiNG0fnDesJ/OvzjXZYLkWSJNzGjCF65U+2obF5X31F8sOP2FJHni5anp2iOG7v/X6G/NI6OpOiRkLnCcoMps1v2l0S4hbCtOhpgIi61BfhuDQTsizbHJdu3t3qd1D6YTAUgZOncmVSCx9sPMvI+P3orGb0PXvg1LfutunWJvBvf0XS6Sjbt4/SrVvrPsDFBwbfp9zf9h5QU9MFlBPOP67pBcDKQ6l1y3MLBIJ6s2x/Msl55fi56bl7eGS9jpl3aB5JxUkE6L155sR25cFG1rWU7t5D/HUzKdm8Gakyehv2yTy0QUEN3qs+qFxcCHrpRUI//ADJ2ZnSHTtIuOVWW+HurUMi6BHkTlGFmS+324+iVGNCZdTlyFLIOml3yX19lPPcH4l/kFCY0BRvo0MjHJdmIrMsk2JTMRpJQ7RndP0OilfSPkSOUtqCHXA+u4Rl+5KYmrgHAK8bb6x/DU0rog0JwftORWMm673366eoO/wJUOsUbZvEXUyOmoxerSeuMI4TeReq+/uGeXL9gFAAXvvthKjQFwiagAqThY82Ku3Pj4/rjIuu7vbnU3mn+ObkNwC8XFiBu9WizPFpRF1L/rJlJN1/P+bsbHSdOhG1bCk+d97RIuc7j8mTifp2CZrgYIzx8STedTfGlBTUKsnWFPDVzgQKy+toCggZoIjSIcMm+2mybt7dGBM2BhmZxccXN+0b6YAIx6WZqKpvifKMQqeuO7QKQMI25Tb66lqXvbvhNJ3zkoguykDS6/G8tv7To1sbv4fmoHJ3x3D6NEVr6tEe7REM/ZWwLdvfw13nztjwsQCsPr+62tLnpnRHp1GxOy6PPfF5TWy5QHDl8e2eJDKKKgjxdOL2YRF1rpdlmbf2voVVtjLFJZKr00+Dsw9Me6tBryvLMtmffELGSy+D1YrnzJlEL/8Rpx49GvtWGoVTr15Eff8dushITKmpJN55F8aUVCb3CqJ7oDvFBjOLdyTUvdG4fwISnPwVsk7ZXfJA3wcA+OX8L7YaPoF9hOPSTFQ5LvWubzEbIXGXcr8Wx+VwcgG/Hc1gSuJeANynTEbtWb8K/7aA2ssL3weUD2j2Bx8i10e9cuRfQFLB2Q2QfdrWXfRb/G+YrRcK50K8nLllsDIPqkokSyAQNI5Sg5n5lUqxT07oil7jOAoMYCw3s2rdn+h2h3PNqYe4asc4NhQ8zR7fj0hL12C11i8KKlssZP77P+R8qMz98X30EYLffKPVpB60QUFEfPM1us6dMWdkkPzIw8ilJTw+XhkFsHBHfN1SDAE9oMd05f7Oj+wuGRAwgIEBAzFZTSw5saQp30KHQzguzYStMNe7no5L6n4wl4OLHwT0dLjs7fWn0FrMTMg4CoDX7Ma3FbYWPnffhdrfD1NKCvlLl9XjgE5KayHAnk8ZEToCHycf8iry2JW2q9rSh8d0QqOS2H4uh4NJ+c1gvUBwZfDVrgRySoxE+Lhw46Awh+sKMsvY+PVJvnxuG2k/S/TLGEtEfm8yKwZwtuJq9u93YeU7B/n+lT2c3JmOtZY2YtliIe2558n/7juQJAL/8Q8C/vKXVk+FawMCiPjyCzQBARjPnSf1L09xTQ8/Ovm7Ulhu4pu6Oozgwhy2I0uhMNXukqpal+Vnl1Nhrmgq8zscwnFpJs4WNNBxqRqqGH21Q5n/bWez2XEul6uyT6OvKEUTGIjLkCFNYW6LonJxwf/xxwHImT+/VrltG8MeVm4Pf4/WUMrUqKkA/Br3a7VlYd4uzB6o1LrME1EXgaBRFJab+HRLHABPTeyKVl3zq8JisrLnlzi+f2UPp3amYzXL5DtlcjZkO8M9FjDe5zNGTPejy+AAdM4aCjLL+PPrk6z470EKsmrK5suyTOZrr1H022+g1RL67jv43NX6c9eq0AYFETb/E6Vgd+dOsl9/nSfGKsXGX2yLp8xYxwDGsMFK/aLVpIjS2WF06GhC3UIpNhazLmFdU7+FDoNwXJoBk9VEfKFSbV7vjqKLHRc7WK0yb61TcqN3lSm3Htdcg6SuPXzbVvG64Qa0kRFY8vLI+2px3QdEjYaA3srwyUPfcG0npa5nU9ImSk3VHZ9Hx3ZBJcHGU1kcSxUdRgJBQ/lyezyF5Sa6BLgxs39ojecLsspY9sY+9v+WgNUqE9zTnbX957N0wOuMc1/EQJf19Jw1gQEz+jHlwT7c88YIhs/ujN5FQ1ZCEcte20fcoexqe+Z+9jn5330PkkTof/+LxzXXtNTbrTfOvXsT+s5/QZIoWLqU0Yf/INLXhbxSI9/tSap7g5F/UW4PLIbyghpPq1Vqbux2IwA/nv6x6QzvYAjHpRlIKEzAbDXjpnUj2DW47gOMZZCs1Kw4clw2nMjkWGoRfpKJ8NMHAfC4dnpTmdziSFotAX9RPsR5Xy7EnFdHMa0kXYi67P2MPj49ifKIosJSwe+Jv1dbGu3nyrX9lBEL9ZrmKhAIbBRVmFhU2eY7d1I31KrqEeDU0/ksf3M/eWmlOLtrmfpQH44MWUOi8yl6o2dGYZ6iGDv4AdsxOicNAydHcss/hxLS1QuTwcK6z45yYofSYlywchXZ778PQODf/47H1Ckt9G4bjvuECQQ8/zwAOf/9L8/7Kxovn26No8JUx5TnrpOUCzBjCey3r9kyq8ssNCoNR3KOcDLXfvv0lY5wXJqBqsLcLl5d6pebTT2ghA/dg5V6jkuQZZkFWxQ5+7nO6WAwoOvUCadevZrU7pbGfepUnHr1wlpWRs6CBXUf0PcmZQxAQRLS2fW2qMvFYnRVPD5OKZxbeyyDc1nFTWq3QNCRWbI7kWKDma4BbkztXV0r5fzBLH75IBZDmZmAKA9u+edQTFF5/HT2JwD+mpaISq2H6z4CVc2vF3cfJ2Y+PYBeo0OQZdi05BRHvtlC+ouK1onvgw+0qfSQI3zuvQfPG28AWabrov/RxVkmu9jA0rqGvUrShajL7gVgNtRY4ufsx8QIRTl92Zl61ABegQjHpRlocGFuUuVwrYjhdutb9iXkE5tcgE6jYmhyLAAe06a1esHa5SKpVPg/o4x/L/j+B4wp9gvWbOhcYNC9yv3d87m2s+K47E3fS0ZpRrWl3YPcmdI7EFmGTzaJGUYCQX2oMFlYuD0BgEfGdEZ1UbQl7lA2G744jtUq02VQANfPHYCLh4639r6FjMzUchMDDEYY+1fwc3zuU6kkxt7enT5jQkGGHdsqKHQOw2PGDPznzm3ut9gkSJJE0N//jjYiAktmBi8nKvUo8zefx2CuI+rSZzZ4hEJpFhxfZXfJzd1vBmBN3BpKjPUYTHuFIRyXZqDBhblJlZ0xEcPtPv1pZbTllt6+mPcoTo775MmXZ2QbwXXECFyuugrZZCJnwfy6Dxj8gDI5O2EboaUFDAwYiIzMb/G/1Vj6xDjl9//z4TQSc+tRACwQXOGsOJhCTomBEE8nrut/YaJ98qk81n9xDKtVptuwQCY90BuNTs2fSX+yP3M/eiSezsmCoL4w4v/qfB1JkrhqlAv+RSexqrQcG/g4ns+/hGQnStNWUbm4EPLmm6BS4bdzI9fknySjqILlB1JqP1CtvaAIvu8Lu0sGBw6mk2cnys3ldiPKVzrt56+kHdGgGUVWy4X6loirajx9OqOYjaeykCS4R52ObDSijYxA362eTlEbR5Ik/P/vSQAKf/4FU0ZG7Qd4hUPPSsG9PZ/aoi6/nv+1hlpu3zBPxnb3x2K9kGoTCAT2sVhlPtuqdBI9OLqTrZMoP6OU9Z8dw2pRIi0T7u6JSiVhtBh5Z/87ANyTX0CIRVZSRGptna9lzs8nZc5D9Dz8OW6mHAySC5u+P9fuFK9dBg7A98EHAXjkwI94VRQzf/P5uidHD7gbVFpI2auMerkESZJsUZdlZ5a1u99LcyMclyamyFhEemk6UM+IS+ZxMBYrA8gCe9d4uupEMrV3EM67lc4j94kT232a6GJcBg7EZfBgMJnIW7S47gOGParcHlnK5IChaFVazhWc43R+zQGLT1aKRC0/kEKamBwtEDhk7bF0EnPL8HLRcutQRcixosTEmnlHMJSZCerkyYR7e6KqdGiWnFxCSkkK/laJBwqLYMgcRd6+DqwVFaQ88ijGhAScAn2Y9vRVqLUqkk7kcXRzHeniNoj/E4+j79EDbUkRzx1dQUpeGSsP1fE+3AOh13XKfQdRlxmdZ+CkduJs/llis2Ob1uh2jnBcmphz+UoXS6BLIJ76eijaVtW3hA+tMZ8ovbCcn2OVD8BDV4VRskWZZeQxaVLTGdxG8H1Y6RjKX7YMc34dwnERVylDKM0VeB77yeEIAIBBkT4M7+SLyXLhalIgEFRHlmXmb1aikvcMj8JFp0G2yvy+8DiF2eW4+zgx7ZG+aLTKOSqnPIfPjnwGwFO5Obg4ecO4F+r1Wllv/5fyw4dReXoS8fnnBPSJYMRs5QJj16rzFOe1L+E1Sacj5K03kbRaBqYeY1LSPj7ZdA5zXVGXIUqkhiM/2m2N9tB52KZGLz29tImtbt8Ix6WJaXBhbnJVYW7NNNHC7fGYrTLDon3omnoKa2kpGn9/nPrVPjm6PeI6aiT6Xj2Ry8vJ/6YOuWtJgmGPKPf3fsG1UcqH+7f437BYaxbGPVEZdfl+bxLZxTWr+AWCK53t53I4nlaEs1bNPSOiADj0RxJJJ/JQa1Vc81g/XDwuzFz7+NDHlJpK6W00c21JKYz/p9LxVwfFmzYpqrhA6DvvoO+sCLj1HRNKcBdPzAYLO3482/RvsJlx6t4dv8qU95wTa8hJz2H1kfTaD4oYrrRGm8vh8Pd2l1Sli/5I/EMU6V6EcFyamAYV5sryhflElzguhWUmm6DRI2M7U7JFSRO5TRjfrgrY6oskSfg9pERd8pYsqVtNt88NyniEohRGFxfipfciuzybPel7aiwd0dmXARFeGMxWvtguoi4CwaVURVtuHRqOj6uOjPhC9qxSPiujb+6KX5ibbe2pvFMX2p9zclAF9r3Q7VcLpqws0v/+DwB87rkHt9GjbM9JKokxt3VHUkmcP5RN0vHcpnprLYbvvfei69wZd0Mpt5/+nY83nat9PpMkwZBKrZt9XyjfB5fQ27c30Z7RGCyGGnpVVzId7xuwlWlQYW5hMhSngUoDoYOqPbVkTyKlRgvdA90Z282fku3bAXC7uvbJ0e0Z90kT0UVHYy0qomDpD7Uv1jrZKvO1+75kSpQiWHXpCABQnKKqWpcluxIpqmsgmkBwBXE4uYCd53PRqCQeHN0Jk9HCHwtP2Nqee4260F1UNf1ZRmZaSanS/nzN2zXS3JciW62kv/B3LPn56Hv0sMkgXIxvqBv9xikzkXauPI9cz6GMbQVJqyXwb38DYEbcDirOx7H+eB3NBv1uVuobc89B/Jaae0qSbais6C66gHBcmhBZlm2OS72k/qvqW4JjQOdqe7jCZGFR5aj0h8d0wpSUhCkpCTQaXIYOa2qz2wySWm2r0M9dvBiroY60zuD7FacvaSfXeirj7jcmbaTMVHMOyrjuAXQLdKPUaOHH/XW0KwoEVxBVHXfX9Q8h1MuZvb/EUZhdjquXnrF3dK/WCGBrf5bhqfwCJfIZOaLO18j76mtKd+xAcnIi9N13UOl0dtcNnhaFzklNbkoJZ/dnNsn7a0ncRo/CbexYNLKVh479YjuPO0TvrjgvAIfsp8irhDb3ZuwlvaSO9NMVgnBcmpCM0gyKTcVoJA2dPGsq4NYgZZ9yG17dGVl5KNWmpTAjJsQWbXEZOBC1m+ulu3QoPGdciyY4GEt2DoUrV9a+2CMEes0EIObURiLcIyg3l7MxaWONpZIkce+IaAC+3pVQewhXILhCiMsuYV1lVOCRMZ3JiCvk8EZF/XXsHd3Ru1xobTZZTbx34D0A7ikoJAQdTHq1zteoOHmS7PeU4wL/9ldbXYs9nNy0DJgcCcCeX+KwmOsocG2DBPz1edBoGJJ5Cnn3Do6n1TEvbcAdyu3JX+0W6Qa7BTMkSBmmuyZ+TRNb2z4RjksTUlXfEuUZhbYeWgakKjOHLk4TXayl8ECllkLp9h0AuI4aVWOLjoak0+F7//0A5H7xJbK5jomrla3R0rHlTA8bCzj+cM8aEIKHk4bE3DI2n8lqMpsFgvbK17sSkWUY3yOAzj6u/Pn1SWQZug8LIqqvX7W1P5/7maTiJHysMvcXFsHoueAZVuv+1vJyUp95Ftlkwm3CBLxuuaVOm2ImhOPsoaMop4Kz+9pf1EUfHY3P3XcDMOfYL3yztY55aSEDwb8nmCvguP2Ltap0kT29qisR4bg0IVUziupV32I2QsYR5f5F2ge/n8ggPqcUT2cttw4JRzYaKd2jFJy6jRrZ5Da3RbxuvAG1jw+mlBSK1q6tfXHYYOWDbzEyvVgZdrY7bTc55Tk1lrroNNw6NAKg7hCuQNDBKa4w8eN+Jbpy38goYjcmkZ9RhrO7llE3VT+HVZgrmH9YUbaek1+Aq2c4jHiyztfIfPMtjHFxaPz9Cf7Pv+ulP6XVq4kZrzhEBzcktbtaFwC/Rx9B9vImvCSb0l9WkVdqdLxYki5EXWK/tbtkUuQk9Go9cYVxnMg70QwWty+E49KExBcqE1U7ezkOhdrIOg4WIzh5VRus+GlltOWuqyJx1WsoO3gIuawMtZ8f+h49msPsNofK2dl2xZL72efI1lrCxRe1RkfG/khf3z5YZAvrE9bbXX7XVZFIEmw7m8O5LNFeKLhyWXEghVKjhc7+rgzwd+fA2kQARt7QBSe36hHjpaeXklWWRZDZws1FxTD5NdA617p/8R9/ULB0KUgSIW+/hca77nbpKvpcHYrWSU1+eikJx9pfh5Ha3Z3Ax5Tz0o0n/2DprjqUu/verIwySdkH2WdqPO2mc2Nc+DjAvl7VlYZwXJqQKscl2jO67sW2NNFA22DF2OQCDiUVoFOrbFoKpTsqu4lGjuiQbdCO8L79NlRubhjOnqVk8+baF/e+HtwCoTid6c7KldqaOPvponAfFyb2DASUWheB4ErEapX5epfiqNw7Ioo9v8RjMlgIiPKg29DqE6FLjCV8cVRRd30svwBd9BjoOaPW/U2ZmaT/458A+Nx/H67D7c9hc4TeRUuf0aEAHNqQ2KBj2wreN9+MycuHgPICkpYsq12Qzj0QulbOn3MQdZnRWfmd/xb/Gybrld0ZeeV8EzYzsiw3znEJGWh7qOqL9NqYYPzd9QCUbFMcF9dRo5vO2HaA2sMD79tuBah7DIBGp3QYAVPi96OW1BzNOUpikf0T3n2VTuHyAymiNVpwRbL1bDZxOaW46zVc7e/JqV1Kt8rom7siqaqnc74+8TUFhgKijCZmlFbAtLfsTrGvQrZaSfvr37AUFuLUqxcBf/lLo2yMmRCOSiORfq6QjPg6ClzbIConJwIfeQiAqYfX8ceROroZq9JFh39QZthdwvCQ4fg4+ZBXkceutF1NbW67ot06LvPmzSMqKgonJyeGDRvG3r17Ha5dvHgxkiRV+3FycmpSe3IrcikxlaCSVER4RNR9QFr1wtzcEgOrDysnj3uGRwGKYJPh1CmQJFxH1t1y2NHwvuMO0Ggo27ePihN15HUH3QcqLX4pB7nKpxfgOOoyvLMv3QLdKBOt0YIrlK92JgBw46BQDqyMAxm6DQ0kqFP1MSX5Ffl8dfwrAJ7IL0Az8G4I6Fnr3nmLFlG2ezeSszMh77yD5KD1uS5cvfR0HaRER49vaX8zjAD8b72FCg9vAsoLOPKF/UiKja5TwNkHSjIgYXuNp7UqLddEXwMoRbpXMu3ScVm6dClz587l5Zdf5uDBg8TExDBlyhSyshx3inh4eJCenm77SUxs2vBjVbQlxDUEvVpf+2JDCWSfUu6HKhGXH/YlY7RYiQn3IibcC4DSHTsBcOrdG42PT5Pa2x7QBgXhMUURlsv7+pvaF7sHQp/ZAEwvVfRf1sStsVuBL0mSLRUnWqMFVxoJOaVsPpONJMEkdw/Szxei0akYfn3N2rwvjn5BmbmMngYjk0wSjP1brXsbExPJ/uBDAAL//gL6TvWIPtdCnzFKuujsgSwqSttfdFTl5IR3pTbVsJ2/cDKplnodje7C4MVjK+wuubazoumyKXkTpaY61MU7MO3ScXnvvfeYM2cO9913H7169WLBggW4uLiwcOFCh8dIkkRQUJDtJzAwsEltalCaKP0wyFZwDwH3IMwWK9/uVhype4ZH2paVbq9KE10Z3UT28LlHKdItWrMGc3Z27YuHzAFgwrkdOKudSCpO4mjOUbtLrx8QKlqjBVckVS3Q47r4cfZ3pato4JRI3LyrR6EzSjP44ZSiYP1/+QWohj8O7kE19qtClmUy/v0fZKMR1xEj8Lrxxsu2NTDaA98wNywmqy2d1d6IuPt2St28CCgvYNe8xbUv7nODcnvyF6Xz9BJ6+fQiyiMKg8XAluSaSrtXCu3OcTEajRw4cICJEyfaHlOpVEycOJFduxzn/UpKSoiMjCQ8PJyZM2dy/PjxWl/HYDBQVFRU7ac2GuS4pF1UmAv8cTKLtMIKfF11XNM3GFBOAqU7lYiL2xWg3+II5379cO7fH9lkIv+HOiakhg2GoL64mMoZ51J7ka6LTsMtQ8IB0RotuHIoNZhtLdDTdG6U5Blw89bTf1LN9PaCwwswWo0MKq9gpOQKI/6v1r2L12+gdPt2Rfr+xX/Wq/W5LiRJos/VStTl+La0dqlhonJyQn3nvQB02bCc/MJaIiWRI5VGg/J8iNtc42lJkpgUOQngip5d1O4cl5ycHCwWS42ISWBgIBkZ9udCdO/enYULF/Lzzz+zZMkSrFYrI0aMICXFcX3DG2+8gaenp+0nPDy8VrviixTHJcozqu43kVrdcakqyr11aDhOlWPjjefPY8nPR3JywrkDToNuCFVRl/zvv699DIAkwWBlaNn0DKWtfF3COocV+HcPjxKt0YIrip8OplBsMNPVx4Wi2DwArprZCa2u+qyhhMIEVp1bBcBf8guQrn4enDwc7mspKSXzjTcA8J0zB3305aWILqbb0EA0ejUFmWVkxtd+AdlW6ffw3RS5eOBfXsCmz2qZw6ZSQ69Zyn0H6aIqx2Vb6ja7402uBNqd49IYhg8fzt13303//v0ZM2YMP/30E/7+/nz66acOj3nhhRcoLCy0/SQnJ9f6GgmFCQBEe9Sno+iAchsykLOZxew8n4tKgjuGXUgTle3fD4Bz//6NLm7rKLhPmqSMAcjLo2h1HZLXfW8CnTvDsxLw0bqRV5HH7rTddpeK1mjBlYQsyyyuLMq92dubilITHv7OdB1SM20+//B8LLKFq8vKGeAcbOvac0TORx9hzsxEGx6O70NzmtRunZOGzv39ATi9u46hhW0UtbMz5dNmAeC0qo7W6Kp00ak1YKqo8XQPnx6EuYVhsBjYlrqtGaxt+7Q7x8XPzw+1Wk1mZnUp6MzMTIKCHOdfL0ar1TJgwADOnXMsxazX6/Hw8Kj244gKcwVpJWlAPVJFpblQUFkYHDLApqUwuVcQIV4XBJ3K9imOi8vgwfV5Sx0aSaPB547bAcj7+uvaw8V6N+h/G1pgikUpkq5tvse9ojVacIWw/VwO57NL8dCqUZ0pBmDQ1EhU6upfA3EFcayNVxSrH88vgAkvKYWjDqg4dYq8JcqAwKCXXkTVxB2bAN2vUs7tZ/dnYjG1v/lFAEP+70GMKg3RuUlsW1VznpqNsCHgGQ7GYjhXMx0kSRKTopSoy4aEDc1lbpum3TkuOp2OQYMGsXHjhf94q9XKxo0bGV5PkSOLxcLRo0cJDg5uEpsSixKRkXHXuePjVEf3T9oh5da3C0WSKysOKumqu0dciLbIsmyLuAjHRcHrppuQnJ0xnD5N2R7Hre+A7epweupJQJlo6yikOqKzL10DlNbo5aI1WtCBqWqBvt3fl4piE24+eroPq3mxt+DIAmRkxpWW0cu3N/Se7XBP2Wol41+vgMWC+5QpuI1uHr2p0O7euHrqMJSZSWyHSroAroH+pA8dCyjTsh2iUkHvWcp9B+miKZFKt+W21G2Um8ub0Mr2QbtzXADmzp3L559/zldffcXJkyd59NFHKS0t5b777gPg7rvv5oUXXrCtf/XVV9mwYQNxcXEcPHiQO++8k8TERB6sbFO7XBKKEgAl2lJnQVpVmih0ECsOpFBmtNA1wI3hnXxtS0wpKZgzM0GrxTnmyq5vqULt6YnX9bMAJepSKwE9IXIk/SoqCNe4UW4u58/kP+0ulSSJe0dGAfCVaI0WdFCScsvYeCoLtQz+KUqd2KApkag1NaMt6+LXAfBoQSFMekX5InVA4U8/UR4bi8rFhcAXam+VvhxUKolulU7Wqd3ts7sIoNeTiiBd9zMHOB172vHCqnTR6XWKfMal+/j2IsQ1hHJzOTtSdzSHqW2adum43HLLLbzzzju89NJL9O/fn9jYWNatW2cr2E1KSiI9/cIfd35+PnPmzKFnz55cc801FBUVsXPnTnr16tUk9tg6iupT31LZUWQNHsA3lWmiu0dEVXN4qtJEzn36oHKufR7IlYT3nXcBULJpE8a6dHgG348ETC9UFDcddReBaI0WdHy+2Z2ALMMsby8qioy4euroMaJmxHnBYSXaMr60jJ7ho6HTWId7mvPzyfrvOwD4Pfkk2nqm6htLVXQo8Vhuu9R0AYgY1Jek6D6okTk67wvHC4P7KzPszOVwZl2Npy/uLtqQeOWli9ql4wLwxBNPkJiYiMFgYM+ePQwbNsz23ObNm1m8eLHt3++//75tbUZGBmvWrGHAgAF2dm0cVY5LnR1FsmzrKDps7WST3J49ILTaMpEmso++UzSuY64GWSZvSR0qlD2vA1d/pucptVC70naRW24/xHxxa/Tine1zLopA4IgKk4UfD6SgkqF7nlIfMmByJBpt9U6i8wXnWZdQFW0pgomv1Lpv1jvvYCksRN+9Oz533dk8xl+Eb6gbPiGuWC0yCUdrTn9vL/jeew8AUbv+ID+7wP4iSboQdXHUXVRZ57IleQsV5ppFvB2Zduu4tCUuThXVSkkmlGaBpGLhOXcAbhgUhqteU22ZzXEZIhyXS6maGl24YgWWklpamDU6GHg3UWYzfdBhkS22k7I9qlqjt57JJj7nylWkFHQ81h/PoKDMxHCNE6YiE87uWnqNDqmx7tPKaMuE0jJ69Lgegh2nqcsOHqRwxU8ABL38EpJG43BtU9J5gNJddP5gHWKUbZiBN04jyzMQV3MFO2sTpOt9vXJ7bqPddFE/v34EuQZRZi5jZ9rO5jG2jSIcl8ukQcMVM48BYPbuzNrTBQDcNrS68JMpMxNTUhKoVDg3YVSoo+A6YgS6Tp2wlpVR+MsvtS8edC8gMT1XibrUli4K93FhbDflpPjDvqQmslYgaH1+2JuMJMNwgxaA/hMjaui2nMs/x7qE9QA8UlQG4/7hcD/ZZFIKcgHPG2/AZeBAh2ubms4DAwBIPpGHsdzcYq/blKjUagwzbwLA9beVWK0OuqQCeoF3NFgMcL5mF5IkSUyMUIRYrzQxOuG4XCaZZZmUm8tRS2rC3WoXqSNDcVwS1FGYrTIDI7zoHuRebUlVfYtTjx6o3d1rbHGlI0kS3rfdBkDB99/X3hrtFQHdpjC1pBQ1Uq0TowFurXQiVxxIwWhuny2XAsHFxOeUsisulx5mNVKJGb2Lxjb/52KqRVv63wfekXZ2U8j7ZgmGM2dQe3oS8MwzzWl+DXxCXPEKdMFitpJwrP2mi4Y/ehflGj2BRVkc+HWT/UWSBD2mK/dP/WZ3yfiI8QBsT92Oxc5E6Y6KcFwuk6o0Ubh7OFq1tvbFmcqYgU0FylXDrUNrymyX7d8HiDRRbXjOmqm0Rp89R3llWs0hQx7Ez2rlqgpl7kdtUZfxPQLwd9eTU2Jk48lMh+sEgvbCD/uSQIbxVkVbJWZCODqn6mmdc/nnWF9Z4PloiQlGO3ZGTFlZZH/8MQABzz2Lxtu7mSy3jyRJdB7Y/tNF7t4epPRXZtClfVfLKJMqx+XMOrDULEjuH9Afd607BYYCh3PZOiLCcblM6l2YCzbHZVdpMO56Ddf2q1nVX35Q0XlxHjioyWzsaKjd3fGcMQNQxgDUSucJ4BXJ9KIL3UWOojRatYqbBikzjr7bK9JFgvaN0Wxl+f4UuppUuJRb0Tmp6TcurMa6BYfnIyMzsbSM7oMfBldfO7sp5Hz0MXJZGU4x/fCc7VjfpTnpPEC58Es6lovZ2H6jDJF3K6Kakcd2k5/pQJsmfBi4+EJFASTVnMWnVWkZEToCgK0pW5vL1DaHcFwuk3q3QpsNkKP07Z+0RnJd/xBcdNWvfKylpRgq1Xyd+8c0vbEdCO/bbgWgaMPvtU+NVqlg8H1MKCvHWabWidGArbto+7kckvOuzDkggo7BHyczyS0xMtqkqN72HReG3qV6VPhs/llbO+0jZVYY/rjD/SrOnKFghdLhEvjXvyLVou/SnPiFu+HmrcdsspJ6pqBVbGgK+k4cTrp3CHqLid1fOLgAU6mh2zTl/in70eKrw64GhOMiaAC2GUV1FebmnAGrmULZlXR8ahTlAlScOAFWK5rAQLSBNeeHCC7g1LOnUrxsNlOwfHntiwfchYtKy7hSpVtoddxqh0sjfV0Z2cUXWYZl+2ufTyUQtGW+35tEtFmFr0lCo1cTM6FmDd6nh+cjA5NKy+g+7Alw9nK4X9Y774DVivukSS1akHspkiQR2dcPoF23RatUKgxTrgVAvfZXx/V6tjqXNYqkxiWMCh2FhMTp/NNklLbPWU4NRTgul0m9p0JXFuaeksPpG+pFn1DPGkvKjxwBwLlf3ya1saPifbtSpJu/dBmyuZYOA1c/6DWLa0sUx2V9wnqHE6PhQqfXsv3JtQ9DEwjaKMl5ZWw7m8NVFUpUt8/VoTi7VZ83pERblG6UhyskGPqww/1Kd+6kdOs20GgIeGZu8xleT6L6KumshKM5tRfot3GGzbkdk0pNeE4Sxzbvs7+o01jQOENhMmTUjBb7OPnQ10/5zrhShi4Kx+UyMFqMZJYqRZwR7jUjKBcjV7ZCn7BGcutQ+91H5UeUP0qnfkLmvz64T5mC2tsbc0YGxZscVOZXMeQBhpdX4GOxkleRx660mvniKib1CsTHVUdmkYHNp9tvAaDgymXpvmQCzBJhFjUqlUR/O9GWzw8vuBBtGf60MqDUDrLFQubb/wXA+7bb0EVFNaPl9SO0uzdqrYqSPAN5ae1Xd8knNJDEnkMAOP/Vd/YX6VygywTlvoN00egwZUbUlZIuEo7LZZBWkoaMjLPGuc7hikUJStFtnCqS62Jqij/BRRGXvsJxqQ8qnQ6vG28ElNboWgkfhiagN1NL6k4X6TVqbhiotIwKTRdBe8NssbJsfzIDjEq0pfNAf1y99NXWxBfGs66ytuVho9Y2mNQehb/8iuHUKVRubvg99mjzGd4AtDo1YT2Ujqb2nC4CCLz1ZgDCDmyhtMiBE9b9GuX2dO11LnvS92CwGJrcxraGcFwug5QSZZpwmHtYncMVVVknAAjoMhh3p5pt06asLMzp6SBJOPXp0/TGdlC8brkFJInSnbswxMU7XihJMOR+W7poU9ImSk2Or9RuGaJE0P48lUVG4ZUlpy1o3/x5KouiQgO9jIrIXN9xNaMtXxz+FBkYW1pG95HPgtb+TDRreTnZH3wAgN8jD7d4+3NtRFXVuRxpn9Oiqxh0/WRy3HxwNVWwa9GP9hd1mwqSSkkVFdS8mOrp0xN/Z3/KzeXsz6hDIqIDIByXyyCluNJxcavZYngxRVkpuFvyscoSo0fZH/tecVRJE+m7dEbt5tq0hnZgdGGhuI0ZA0DB0h9qX9zvFvqgI8JkosJSwZ9J9idGA3QJcGNolA9WGX4URbqCdsQP+5LpZ9SgQcIv3I2gTh7Vnk8pTmFNvCJoNsfsAgPudrhX3ldfY87IQBMSjPdddzWr3Q0lso9S55IZX4ihrH0OXQRQa9QUjZ0KgGG1AzVwV18IG6rcP2dfRfdK6i4SjstlYHNc3Gt3XPbsVv6Q0tQhxETX1G4BUd9yOVQV6Rb8tBJrWS0tzHp3pH632KIutYnRAbZapB/2JWO1tt8CQMGVQ1pBOVtOZdHfoERb+o2rGQ1eePhTLMgMLy+n3+i/KnO97GDOzSX3888BCHj6aVR6vd11rYW7jxNegS7K7Np23BYN0P8BRdMlKvkU504m2F/UWVHJJc5+Pd/FdS7tuWC5PgjH5TKwpYpqibjIskzCib0AmP17O0wplR85DIj6lsbgOmoU2rAwrMXFFP1mXxrbxuD7mV6iODe70naRU+44P35N32A8nDSkFpSz7Vz7zqMLrgyW7U8m2qTCU1ahd9XQdXB1WYWM0gxWnVeu6h+2uEG/Wx3ulTNvHtbSUpx69cJj+vRmtbuxhFfWuSSfzGtlSy6P0J6dSQvpjAqZA185kHewOS6bwY68//Dg4WhVWlJKUmzdrh0V4bhcBvWJuMQmF+BbehaAoK721XBlq5WKo0rXkXOMcFwaiqRS2QTp8r77rvarjaA+RAQPol+FAStW1savdbjUSavm+gGVRbpCSVfQxrFYZZbtS2aAQSnK7TUyBM0lwxQXH/4UE1YGlVcw6Op/gtr+VGdDXBz5S5cBEPD8860mNlcXYT2Vpoj27rgAOE9R0kXO2zfan5UWMgCcPKGiENIO1XjaRevC4EBlVMy2lI7dFt02/xrbAbIsVyvOdcQPe5PpKSlfek7h9tVwjfHxWEtKkJyc0Hft2vTGXgF4zp6NpNNhOHGSisruLIcMvp/ptnSR4+4iuDBP6vcTmWQXd/xqfUH7ZeuZbCryDESZ1UiSot1yMTnlOSw/txKAh/CC3o4l+7PefQ8sFtzGjcP1qmHNafZlEdrdG0klUZhVTlFueWubc1kMuOcmrEh0zUlgy9bDNReoNRCt1PNx3n59XlWdi3BcBHYpMBTYulJC3WpOWwUoNZhZdySJzlKq8kBgb7vrbPUtvXsjaexfAQlqR+Ptjcc0RRo7/7s6WqN7zWKKVYdaljmee4K4wjiHS3sGexAT7oXZKrPiYEpTmiwQNCnf702yRVui+vnh4Ve9U+jrw59hkC30qzAwfNTflXEYdig7cICSjRtBrSbg2Zad/txQ9M4aAqPcAUg5ld/K1lwezkGB5HZVviPOLV1lf1FVuqgOx+VA5gFKjCVNbWKbQTgujaQqTRTgEoBebb9o7bej6QSbktFJFmS9B3jaF56rOFqlmCvSRJeDbX7RunVYCgsdL9Q64dvvdkaUK23OdRbpVs4vWn4gpcMXvQnaJzklBrafzKKPrQW6ehS4oKKApWeUVtuH8ELqNdPuPrIsk/3+/wDwmj0bfefOzWd0ExHWo+Oki4KvV/5fImK3k1ZgJ4LUeZxym7wXKopqPB3hEUGURxRm2cyudMcim+0d4bg0kvoU5i4/kEJPKREAKbCPoiVih/LDQuq/KXCKiUHfvTuywUDhL7/WvnjwBU2XNed+rtUhmd4vGCetinNZJRxOqcUhEghaiVWHUuleoUKHhHeQC2Hdq+utLDn6BWWyme4GI1fXEm0p3bmTsv37kbTaNiM2VxfhlXUuKafykdt591/09dOxqNR0Kkxj7Ro7jod3FPh0BtkCCfbTQVeCiq5wXBpJXYW5Sbll7InPo6eqsqjTQZrIajBQcVqZGi0iLpeHJEl43XwTAAXLliHLMsYKM+nnCog7lE3isVzy0ksVJ8W3M2MDBuNstZJalsnhbDs55Uo8nLRM7R0EwPIDQtNF0LaQZZkf9yUzsDJN1Hds9RboYmMx351U5OQfwhOp53UO98n+nyI253XbrWiD7Us3tDUCoz3Q6FRUlJjIy2i/8v+gpLzLY5QC25xfVtuXYahnumhbyjascsectSYcl0ZSV2Fu1RfccNd05QEHjovhzBkwm1F7e6MJsT8KQFB/PGfMQHJyIj1HxS9vbOeLp7fy0zsHWfvpUVZ/fJjvX9nDoue3s/Onc1h6zGFiqRKOXX3u51r3vXGQki76JTaNClPNVkSBoLU4llpERWoZPlYVWr2a7lcFVXt+6bHFFMsmOhlNTBzpONpSsmkTFUePIjk74/fQQy1hepOg1qgIjFaG1qafa/8R0eibrwdg4Pn97DhnZ1ZaHY7LoIBBuGpdya3I5WTuyeYys1URjksjqU0112qVWXFQKcjtSmXEJch+Gqji1CkAnHr2qHNsgKBuDDhxavTzxMb8HylJJmQZXL30BHXywC/cDbVWRXmxiUMbkljytTuDMq5HZVWzLm4NJotj9c0RnX0J8XSiqMLM7ycyW/AdCQS1s/zAhWhLjxHB6JwuFPiXm8v55vhXADwou6NyFG2xWsn+4EMAfO68E42fXzNb3bQEd6l0XM4XtK4hTYD3pImYNVrCSrLZ+KuddFDUKFBpIC8O8mrqtWjVWoYHDwc6brpIOC6NpMpxCXevWXC7Ky6X1IJyopxKcDLkABIE9LS7j+Gk4rjoe9h/XlB/spOLWfb6PlJNgUiyhbD0bdz6bG/ufXMkNzw/mFv+MZQ571/NtEf6EtLVC6tFJiNnOrcefg5K3Nia6vhDrlJJ3DBIcVKXHxDdRYK2gcFs4c8DaXQ2K6fyvmOqdziuPPEteVYDoSYzU0f+w2G0pWjtWgynT6Nyc8P3AccDF9sqIZ29gI4RcVG7uaIeqaR7tJv/IK/UWH2Bk8cF+X8HKrodXf5fOC6NwGQxkVGWAdhPFVV9sd3VqbIq3DsKdPbnD1XVtzj16N70hl5BZCcV8/P7hygtMOAV5MLw7KV0O/0D0u4/qq1Ta1R06u/PrLkDmPxgb5zd1HhUBDP76Fw2bnE8uwjghoHK//W2s9li8KKgTfDHiSw6FcpISIT19MY76MJ5xmQxseiIItl/n+yG1lG0xWwm56OPAfC5/z7UXl7NbndTE9jJA0mC4twKSvLb/2cz7Abl/2pUSiw/7bcjfllHuqiqQPdY7jHyKtp/t9WlCMelEaSXpmOVrTipnfB18q32XFGFibXHlLqWyUHFyoN+3ezuI1utGE5VRVx6NJ/BHZyinHJWf3wYQ5mZ4M6e3Pj8ICJnK22DVUW6lyJJEl0HB3LLi1fh6Z6O3uJC4M6rOXnYcfFtlJ+rbfDiT4dE1EXQ+vy0N4m+RiU1FHPJFOg1p5eRYSnDz2xh1gjHtS2FP/+CMSEBtZcXPnc7HrjYltE5afALV/Rc0s+3/6iL25gxmJ1dCCgvYN9aO+kim/z/VrCYazzt5+xHF68uAB1yWrRwXBrBxR1Fl9alrDmSToXJSpcAN8IslcJzfvbVcE2pqVhLS5G0WvTR0c1qc0fFbLTw2/wjlBUZ8Q1149onYtC7aPG8bgaSXo/hzBnKY2MdHu/qqee2+wPI9oxFI2v587MzJJ3Idbj+xovSRULTRdCaZBZVkHUiH2dZwtlbT0SfCxdRFquFLw/NA+Ae2RV9r1l297AajeTMU9b5zpmD2s2t2e1uLoI7V9a5nC1oXUOaAJVej9vVSron+Ph+jqdd4oyF9AcnLzAUQtpBu3sMDVLSSXsz9jajpa2DcFwaQW0aLlVpopsGhSHlnlMe9LUv4lRxUqn41nftiqTVNoOlHZ+dP50nN7UUZw8d1z7RD52zcvWp9vCwKekWLPux1j3U3ccTFfE18d5HwCKx9tNj5KTYV528pl8wzlo1cdmlHEouaNL3IhA0hJ8OptKncgp0zJhQVKoLF1Ebz/1MgrkYD4uFm4a/4FBDqmD5ckxpaWj8/fG+4/YWsbu5CO7iBUBaB4i4APhMngjA8IxjNevqVGroNFa57yBdNDRYcVz2ZexrLhNbDeG4NAJHGi7ns0s4kJiPWiUpw/lyleGK+NqPuBhOKfUtIk3UOJKO53J0s/J/MeGenrh5O1V73uvmmwGl8NBSVFNl0oZKzfReN7Kx6yJSPM5gNlhY88lhyoqMNZa66TVM66u0m/64X6SLBK2DLMus35VEmEUNEvS4Krjac1/sfx+AO6wuuPa63u4e1vJycucvAMD30UdQOTnZXddeqIq45KaWYCivmT5pb7iNHo2sVhNRnMWerbGYLJdostjqXOwX6A4OHIyERFxhHNlldtqq2zHCcWkEjjRcVlR6xWO6+RPgIkFBZVGVg1SRrRVaOC4NxmKysuWHM4Aibx7Z27fGGucB/dF37YpcUUHhr7Ur6foPeZhhxjJ+77YI3MsoyTOwdsFRLHamtFali1YfFpougtbhUHIBXhmKYx3W2wdXrwtjR3bEreWkqQBnq5Xbh/3VYbQl/7vvMWdnow0JwfvGG1vE7ubE1UuPh58TyJAR1/6jLmoPD1yGDAGge/xhNp++xPmokv9P2adMjL4ET70nPXyU75aOFnURjksjsKfhYrHK/FSp3XLjoDClv162gs4N3ALt7nOhMFd0FDWU2I1JFGWX4+Kp46qZneyuUZR0lahLwVL7Rbo23PyZ4dULg7aMP7vMQ++sISOukP2/JdRYelW0L6FezhQbzKw/ntEUb0cgaBA/7k2md2VRbr+rq19Afb73bQButjjj1ce+Q2IpKSX3c6XjyO/xx5F0uma0tuWoShelnytoVTuaCo8JEwAYnn7cdmFswysCfLso8v/x9uX/O2qdi3BcGogsyyQXK50nF0dctp3NJqOoAi8XLRN6BlyUJupi94rHUliIKS0NAKfuwnFpCCX5BptDMWJ2l2qCW5dycZFuxWHHsv4A44f8BRerlTNOKUROU5ycA2sTaly9CU0XQWtSYbJwYl8GLrKExlVDZG8f23MHEjdx0JiLVpa5e+izjqMtS5ZgKShAFxWF50z7bdLtEVuBbgfQcwFwH69EVXrlxrP3cBz5l2q61NEWXVXnIhyXK5wiYxElJqVwM8TtgkR/1RfYzJgQ9Bo1VBXmOkoTVeq3aENCUHt6NqPFHY8DaxMwG60EdfKk21D70awq1J6eeEydCkB+HUW6zp3GMcmiFEnvLF9At2GByDL8vugExorqOfMbKzVdtp/LsT/FVSBoJtYfz6BrqeKQ9BsVikp94TT++a7XAZhl0RPQ9xa7x1tKSslbtAgAv8cfQ9I4dvzbGyFdvQDITCiym+Ztb2hDQ9H36IEamQFpJ/j1SFr1BXXJ/wcOQi2pSS5OJr0kvZmtbTmE49JA0kqUPxx/Z3+cNc4AFJaZ2FApA3/T4EothZyqjqIudvcR+i2NozivghM7lP+Dq2Z1qteYBK9bKot0f/sNS3Gx44WSxIxOMwBYn3+MYTdE4uatpyi7nJ0rzlVbGuHrwrBoH2QZVh5KbeS7EQgazi87k4iqVMrtNepCUe6J1N3sMGSgkmXuG/iXWmpbvsNSWIguKgqPa65pEZtbCq9AF5xctVhMVrKTavmstyOqoi5XZdhJF1XJ/+fHKyMALsFV60pvX2VOXkeKugjHpYHYK8z95UgaRrOVHkHu9A7xUB7Mrd1xqThVpZgrHJeGcHBdIlaLTGh3L0K7edfrGOcBA9B37aIU6f7yS61rhwyfS5DZQrEEu08vZMK9vQA4vi2NhKM51dYKTRdBS5NeWE7FmSIkJPw6eeDp72J77osdrwAwzaIjvP9ddo+3lpaSt3AhAH6PPoKkVje/0S2IJEkX5hZ1kHSR2zglqjIo8zQnEnM4m3mRQ6Z3h/Bhyn0H3UUdMV0kHJcGUhVxubgwt8oLvnHQRYJ0VTUuDjuKKjVcRGFuvSkvMXJylxLuHHJN/QX7JEnC66bKIt1lP9bqZKicvZnuphT7/np6GWHdvYmZqETRNi85VS1ldE3fYFx0auJzSjmQmN/g9yMQNJSVBy5otwwYd+EcFJ95mD/KlNq7B2IedRhtyfvuOywFBWgjI/CYPr35DW4FgqvmFnWAgYsATn16owkIwNliJCbnHMsPXhJ1qeoucpAuGhKkdCbtzdjbYS6whOPSQGyOS2XE5Xx2CbHJBahVEjP7Vw44K8uDskr1VZ+a4nOyyYTxrBKRceophivWl+NbU7GYrPhHuBPSzatBx3peNwNJp8Nw+jQVR4/WunbGoMcB2G4uIC/nFFfN7ISHvzOlhUb2r0mwrXPVa7imrxKqF0W6guZGlmV27EjBQ1Yh6ZSZW1Us3PYisiQx1qyh68AH7B6vRFsqa1sefbRD1bZcTFXEJSOusEN8UUuShFtVuij9BKsOpWKxXvS+qupc4u3L/w8IGIBGpSGjNMPWEdveEY5LA0ktUeoZqhyXlZUt0GO6+ePvXqmlkHteuXUPAX1NCW1DfDyyyYTK1RVtaGiN5wU1sZisHNms/K77TwyvV23Lxai9vHCfMgWAgh+X17q2c5dp9JK1mCWJtTvfQqNVM/pmJXJ2eGMyeWmltrU2TZcj6ZQbhaaLoPk4mlqIb5YJgO5XBaHRKpGX9JzTrC5R6hse7HOfw5lE+T/8gCU/H21kBJ7XXtsyRrcCfmFuSCqJ8mITJfmG1janSXCvaovOPEFWYTnbz12Utg7uD3oPMBRB1vEaxzprnOnn1w+APRl7WsLcZkc4Lg3k4lSR1SrbCjNnD7zIAbGlieouzJUcnGQE1Yk7nE15kRFXTx2dBwU0ag+vmxRNi6I1a7CWlta69rpw5USxOmsvWExE9fUjqp8fVqvM1qVnbFdyQ6N8CPdxpsRgZsMJoekiaD5W7kqmi0k5X8RcpN3y1dZ/YJYkhppVxAx5wu6x1rIycr+srG15+JEOG20B0OjU+AQrtT8dpUDXZdgwVC4u+JQX0qUgtXqRrkoN4UodC0m77R7f0epcxLdmA8ksU7qHwtzD2B2fS2pBOe5OGib2vKgtN+ciDRc72ApzhX5LvTmxXXEYe44MQa1u3J+ty5Ah6KKisJaVUfjbb7WunTpsLmpZ5phWRVzsVwCMvrkraq2K1NP5nDuQBSiaLrMHKF8iKw6K7iJB82A0Wzm/LxM1Ek5BzviFKZHcvIIEVhQpF0IP9LyjlmjLUix5eWjDw/G8bkaL2d1a+Ecok6I7iuOi0ulwHTUKULqL1h/PoKjCdGFBxFXKbdIuu8dXCdHty9jXIdJnwnFpIBbZgl6tx8/Zz6aUe22/YJy0F1Xn2zqKHM0oqizM7Sk6iupDYXY5KafyQYKeI4LrPsABSpGuEnWpK13k6xbMKGdFp+fXY4sB8PBzZuCUSAB2rzpv04moirZtP5tNZlFFo+0TCByx6VQmXSrnfg4dH257/NvNf6dCkuhtkRg+bK7dY63l5eR++SUAfo883KGjLVX4RyjdnR3FcQFwn6DUsozJPonBbOW3IxfpskSMUG4Td4EdxyTGPwa9Wk9OeQ7xhfEtYW6zIhyXRhDqFkqFycrao8ofzg0DL5kSLVqhm5STO5VoS3hPHzz8nC9rL89Zs0CrpeLIEZsIoCNm9LkXgF/MuViyTgAwYFIELh46inIqOLZVcVwjfV0ZHOmNVYafY0XURdD0rN+ShK9VhayW6D5UGfJZUpzO9/lHAHiwy01IavsOSf4PS7Hk5qINC8Pzuo6jklsbAZFKxCUrqbhDRBgAXK++GtRqQvNSCSjLY8XF3UWhA0GlhZIMyE+ocaxOraN/QH+gY6SLhOPSCMLcw9hwPJNSo4UIHxcGRV6kJ2K1XijOtVPjYs7Lw5KXB4C+c82OI0F1ZFnmzB4lPXc50ZYqNL6+uI9XrlwK6lDSHdfjRjxRk6XRsGvnfwHQ6tUMuVZpxd7/WwLGyim0syud1xUHUjvMiVLQNigoM2I4o0w3D+nraxtxsWzT3yhWSURbJMaP/JvdYy+Otvg+/BCSVtsyRrcyvmFuSBKUFxkpLag55b09ovH2xjkmBoBBWWfYl5BPQk5lrZ7WGUIGKPcd1bl0oLlFwnFpBGFuYTZvd/bA0OodLoXJYDEo3q9XZI1jjecVp0YbGorKxaXG84LqZMQVUZxXgVavJrqfX5Ps6XXTTQAU/vor1grHqR2dWsf0YCUEuypjJxiUWH2vkcF4BbpQUWLi4IZEAKb3DUanUXE6s5gT6UVNYqdAAPDL/hS6GpRT9YjJyjmlojSHr3P2A/BA9AxUavsOScGyZVhyctCGhuI1c2bLGNwG0OrUeAe7ApCd1HE+j64jlfPRpHLlvPPTxVGXyOHKbT3qXKxy+x6HIByXRuCpCWRHZTtaVWGmjaqOIp9OSrX3JRjOK22Lui4i2lIfzu5Toi2d+vuj0TWNyqfriOFoQ0KwFhVRvH59rWtnDVQ0Xf500lJ46GsAVGoVw2cp/3+H/0imtNCAp4uWSZUF2itFka6gCdm7OQUtEpKnlsBopXbj580vkKtWEWyFa0a/aPc4a0UFOV98AVRGWzrIBOj6UlWgm9WB6lzcRo4EoFvKSVSylRUHU7FWabpE1O649PbrjbPGmQJDAWfzz7aEuc2GcFwaQVKWM1YZhkR5E+F7SdTEliZyUJhbGXHRdxKOS11YLVbOHVAcl65Dah+m2BAklQrPG28AIP/H2tNFPf16013vi0mSWHN0ka3wLbq/H0GdPDGbrOyrFKW7foBSpLsqNg2zpX1f0QjaBuezS/DKVFId/UYr0V1zeT6LMnYCcE/4FLQaJ7vHFixfgSU7B01IMF6zZrWUyW2GjtZZBODUty8qDw/UpSX0L0kjtaCcfQlK6YFN+j/nDJTm1DhWq9IyMHAg0P7TRZfluJhMJpKTkzl9+jR5lXUbVwJ7Kp3V2ZcW5UKdrdDG80rhrl5EXOok5XQ+5cUmnNy0hPWs31yi+uI1ezaoVJTvP4AhruZwsouZ1fN2AFbJRZCsCDhJksTw65XRACd3plGSb2BMd398XHXklBjYdq7miUMgaCirNicQbFFhlWDQGOV8s3bTP0nVqPCxwuzRL9s9zmo0klsZbfGbM+eKi7YABHRAx0VSq3EdrkRWbpSVyG5VdysuPuBf2fCRbF9obliQ4txccY5LcXEx8+fPZ8yYMXh4eBAVFUXPnj3x9/cnMjKSOXPmsG/fvuawtVUpNFwY2BWf7oROo7LJvVejjo4iw7nKiIsozK2T+Fjly79Tf/9Ga7c4QhsUhNvVVwN1t0ZP734TGiRO6nWc3v2B7fGQrt6EdPXCapY59HsiWrWK62KUFuqfRLpIcJlYrTLx+xS9INcoN5zddVgriliYpgzTuzN0LM56d7vHFq5ahTkjA01AAJ6zZ7eYzW0Jv3B3JAnKCo2UFnYMBV24UOfSN0PR71lzNJ0KU6Vqdx3poqo6lwMZB7BY26/Sd4O+Dd577z2ioqJYtGgREydOZNWqVcTGxnLmzBl27drFyy+/jNlsZvLkyUydOpWzZ9t3Hu1i0kuV1me95AGyjsm9AvF0tlMQV+W42EkVWYqLMWcpJyKdcFxqRbbKxB/OBqg2k6Up8bq5skh31Spko+POA28nb8YFDAZgVeZuKMmyPTd4WhSgTI8uKzLaWuM3XCoQJRA0kF3ncogoVlKTIycpRbmbt7zEOa0aVxluGf2q3eNks5nczz4HwPeB+1Hp9S1jcBtDq1fjFVRZoJvYcaIuriOUOhfN6RN0daVStVtJqdscl0T7jksPnx64a90pNhVzKu9US5jbLDTIcdm3bx9bt25l7969vPjii0yZMoW+ffvSpUsXhg4dyv3338+iRYvIyMhg1qxZbNu2rbnsbnGqpP6NFV6AHe0WAGOZ0lUEdsXnqjqKNAEBqN3tXykJFLKSiiktNKLVqwnr3rRpoircrr4aTUAAlvx8iv+0P1m1ill97wVgjaszpgOLbI+H9fQmMNoDi8lK7B9J9An1oGuAGwbzBZ0fgaAxrNuYgKssYdFJdInxR64o5sukDQDcGjgcD2f7n4uiNWswpaSg9vGxddBdqQR0wAJdXVgouqgosFi4x1mJSq+s6i6qUtBNj1W+jy5BrVIzKGgQ0L7TRQ1yXL7//nt69+4NKCkjR+j1eh555BHuv//+y7OuDWFzXAye+LnpGN3VTmtuXmWthJOXkm+8BFthrqhvqZP4WCXaEtHbF7W2eWrIJY0Gz9nXA0rbaG2MCBmBv8aNfLWaLUe/tk1hlSTJFnU5uiUVQ6n5gqaLSBcJGkmZ0UzpKSU9HRrjh1qtYt+2f3NEp0Yvw52j/233ONliIWfBpwD43HvvFS+50BELdAFcK7uLhmQrWY2tZ3PIKq4ArwjwCAWrGVIP2D22qs6lPQ9cbPQ3wujRo8nIuHKGylVNhbYavZnZPxSNvZoL23DFrmBnenFVfYuus/36F8EF4o8oVxLRMU2j3eIIrxtvBEmidOcujMnJDtdpVBqu7arUCqxSG+D0hVlHkX198Qt3w2ywcPjPZGYNCEGSYG98Hsl5Na96BIK6+G1/KlEG5Rxy9eQoMJbyefxqAGb5DcTPzX6XXfGGDRjj41F5euJ9+20tZW6bxea4JHYcLRe44LioD+5lQIQXFqvML7FpyveObW6RfSG6wUFK2vtw1uF2W+fSaMdlwIABDBs2jFOnqufJYmNjueaaay7bsLqYN28eUVFRODk5MWzYMPburT3s9eOPP9KjRw+cnJzo27cvv9UxZO9SkgqVUJxs8q4+CfpicuqYURQnCnPrQ1FOOXlppUgqicg+vs36WrqwMFxHKMVudRXpzuqutFBvd3Yie+8ntscvjroc2ZSCj07LyM6Kw1U1PVwgaAi7NyejRkL20uIf7s7RbW+wW69GLcN9jqItVis58xcA4HPXXajd3FrS5DaJX7gbSFDa0Qp0hw0FrRZTcjK3hSlf47aGAFuB7k67x3b16oqLxoUSUwnnC8+3hLlNTqMdl0WLFnHvvfcyatQotm/fzpkzZ7j55psZNGgQanXTCIU5YunSpcydO5eXX36ZgwcPEhMTw5QpU8jKyrK7fufOndx222088MADHDp0iFmzZjFr1iyOHTtW79c8n684LqFuofQK9rC/yNZRZN8xMdo6ijrV+3WvRJJPKq31QZ08cHJtfolyr5tvBqBg5U/IJscFtZ08OxHj0xOLJPFr/jHIuPD306m/P97BrhjLzRzdlGJzbn86mCJGAAgaREZhBS6piqJz31GhYCzls3MrAJju04dQzwi7x5Vs2oThzBlUrq743HVni9nbltE5afAOVNJlHSldpHJ1xaV/fwBG5p9Hq5Y4kV7EyfSiCxGX5L22lPbFqFVq+vr3BeBw9uGWMrlJuazigVdeeYW5c+cyadIk+vTpQ3FxMbt27eLXX39tKvvs8t577zFnzhzuu+8+evXqxYIFC3BxcWHhwoV213/wwQdMnTqV5557jp49e/Lvf/+bgQMH8vHHH9fr9SxWCwUmpWp7Wo9e1SX+L+biVNElWMvKMKUqHrGui0gV1UbSCcVxCe9Zs06oOXAfPw61nx+W7ByKN2+ude2s7oqTs8rNDXn3fNvjkkpi8DSl8+PwxmTGd/HHRacmIbeMg0kFzWW6oAOyalM8gZXaLcPGhnNmxztsdtIgyfDgKAedRLJsi7Z433EHak/PljS5TdPR61ys+3YzvkcAUBnhDegFek8wlkDWcbvHxvgrM49is2JbxNamptHzzTMzM3n99df5/PPP6dWrF6dOneLee+9l6NChTWlfDYxGIwcOHOCFF16wPaZSqZg4cSI7d+6kqKhmLnPHjh088cQT1Z4bO3Ysq1evtrsewGAwYDAoocXYjCQsla2t0zqH2z9GliH1DBhk0AXDJWvKT56kxGJB7e1NmVpd43mBgtVi5ezhFIxGM97hWof/P02NetpUChd/RfK33xI+bJjDdSN8RqA1qDlntbDzyE/0HfYcuCoOVkBXJ3QeVvJzCji68RzjOrnx6+F0vt9+iq7evVvkfQjaN7Isc3TreaKNMtpwV4wVOcw7/C0WJw3jPbriqwm0+5ko2bmLnMOHkZycCJx9fYt9btoDzr5Qbiwl8XQ63Uc3b+q5JbHExFBisVC2YydTbnuctQfLWLHrDI+OCEHtNwDiNsHJTeAaXePYrk5dsZRbOJB4gKJ+betvxd3d3XFwoAq5kTg7O8v9+/eXV69eLcuyLK9du1b28PCQ33777cZuWS9SU1NlQN65c2e1x5977jl50KBBMiB+xI/4ET/iR/yIn3b4U1hYWKcf0OiIy8KFC7n11ltt/546dSqbNm3i2muvJSEhgXnz5jV260ajUqkoLCys8bivry8LFizgpos0DT7//HPefPNNzp+3X5x0ccQFID09naFDh3LixAlCQ+0U5ybtgW9vAM8weKxmNXf2x/PIW7QIzxtvIOiiaJGgOjt/PsOxTelE9PZi6pyYFn3tpEcepXzfPnznPIjfI484XLc/Yz9P/PkELlYrawpknB/dCZXTeS0WK8v+s4/i/ApG3NCFv+w9S2aRgfdvjmFS76CWeit1UlRURHh4OMnJyXh4OKjZElw2Df09v7s4FvfYQixaiYdfGcCb34/lF2ctI9yieO+6H+weU7p/PykPP4Kk0xH9889oA5pHsLGt4+h3bawws/iFHSDDna8Ox8Wj44w/SHvhBYo3/I7vnAf5NPxqvt+bzPS+Qbw1tEL5PnINgCcP2O1yvWX1LSQWJfLO1e8wKmxUvV+zuc8d7vXQOGu043Kx01LFwIED2blzJ9OmTWvstnXi5+eHWq0mMzOz2uOZmZkEBwfb/UUGBwdTXFxc7bmioiJCQkIa/It3d3e3f4wxHfQShHYHO88Xpqbiplbj16u3+KKohaIUC846Vzr3a/j/zeUScecdpB48iGXNb7jPnYuksf/xGOs+logj4aSWprG3NIcZqVugzwVZ9auu6cH2H8+SsK+QG4Z1ZcHWONadLeKG4d1a6q3UGw8PD/H32ALU5/dstlgpjzMRoHPFZ6AvFacWst5bj1qSeGLiqw6PL1iyBDe1Gq+bb8JXaETV/F17QHCYPwWZZRgKJILCOs7fu2XMGOSNf6I+cpRbb53D0sO5bIovQXXLaNxc9GDOBkse+NRMFw2JHELKuRTOVpzlGo+GdwK35rmjyZW9oqKi2LnTfhtWU6DT6Rg0aBAbN260PWa1Wtm4cSPDK4dPXcrw4cOrrQf4/fffHa5vFLbhivZboY1CfK5ODGUmcpJKAQjp1vIfCLeJE1F7e2POzKRkq2PVZ5WkYmaXWQD87O4Gez6t9nzPEcFondTkZ5RxtYfSkrrpVBZ5pY7HCggEmw5nEKY0EzF+YiCLTizBLEkMcY2gf6X2xqWUHz5M6c5doNHg9+CDLWht+8I/XPkc5qaWtLIlTYvL4CEAlB85Qr9AFzr5uVJhsrL2ZD6EDFAWOdBzqSrQbY+dRQ1yXJKSkuq1zttbkaJOTW0eDYu5c+fy+eef89VXX3Hy5EkeffRRSktLue+++wC4++67qxXv/uUvf2HdunW8++67nDp1in/961/s37+fJ554oumMqmVGkdVoxFj5uxMzihyTfr4QWYasghRcvVt+vopKp8Nz1iwACn78sda1M7vMREJij7MTKen7IO2Q7Tmds4ZeI5RhizkHc+kb6onZKvPr4bRms13Q/tn6RwJqJEyeGjSJn7PCWYn4zbnKcWq5SiXXc8YMtPZS2AIAfEIUxyUvrbSVLWladNFRqH19kY1GDMeOXSTDkHqREJ39QEL/gP4AHMs5htlas226LdMgx2XIkCE8/PDDtU5/Liws5PPPP6dPnz6sWLHisg20xy233MI777zDSy+9RP/+/YmNjWXdunUEBipqkklJSaSnX5gTM2LECL777js+++wzYmJiWL58OatWraJPnz71fk195aAyvaOBZbVouBjjE8BqReXhgcb/ysw/14f0c0p9knuwxvHvuZmpmu1SsmULplqUoUPcQhgWrHQf/WQn6tJvfBiSBMkn8pjVSfk//6lqnkgbQK/X8/LLL7fa7/lKob6/54IyI+pERWW591AfvjnxDQaVir4uIVwVOtLuMRWnT1OyaRNIEr4PzWly29sbtf2ufUKUYYu5aR0r4iJJEi6DlWhc2b79zBqgOC6743PJ9VVmEjmKuER7RuOuc6fcXM6Z/DP1fs22cO5okOMyffp03NzcmDRpEkFBQUyfPp05c+bw5JNPcueddzJw4EACAgJYuHAhb7/9Nv/3f//XXHbzxBNPkJiYiMFgYM+ePQy7qIV18+bNLF68uNr6m266idOnT2MwGDh27FiD1X1rdVwsZsiLV+7bG65YpZjbqVPdbV5XMOnnCwCYftPYVvtQ6DtF4zJkCFitFNTheN/UTXFyVrq5YTq2otrUaA8/Z6Irp1qHZJnRqCQOpxRyLqttaEno9Xr+9a9/Ccelmanv73n1lkT8LSosEsS4/MwPLkqx95yhzzs8Z+R+qjjLHtOmoo+uWcNwpVHb77rKcclPL8NqlVvatGbFZZDioJTt30+YtwtXdfJBlmFlTuUg4JwzUJpT4ziVpKKffz+gYemitnDuaJDjsmTJEp5//nnS0tIoLi4mODiYnJwczp5V6jvuuOMODhw4wK5du1pE9r/NUJAIVhNonJUBV5dgTKxME0VGtrRl7QazyUJmgqInENzZq1Vt8bpZcUgKVqxAtjie5TEuYhy+Tr7kaNRs1qth/6Jqz8eMDwcg8WA2Ezop+hHLD4gRAIKaHN+ppBG1oTp+Or+YUpWKrk4BjIkYZ3e9IS6eorXrAPB9+OEWs7O94uHnjEarwmK2UpRd3trmNCkuQ5SIS/mhQ8hmM7MHKA7L90eLkf17KItS7GdJ2qsQXYMcl5CQEGJjY3FxcaG8vJzXX3+dlStXsm7dOpYsWcIzzzzToPRLh+HiNJGq5q/UmKIM79NGhLekVe2K7MRirGYZZ3ctngHOrWqL++TJqDw9MaelU7pjh8N1WpWW67sq06WXebjB/i/BfKEAN7iLJ/4R7lhMVsaoFdnxlYdSsHSwKz7B5ZGYVYJPjlJjMDx0P0uqoi2D56KS7J+icz//HGQZt3HjcOrevcVsba+oVBLewUrUpaPVuei7dUPl7o61tJSKU6eZ1jcIvUbF+exS8rwUaf+La/Aupr9/f6D9Feg2yHF55plnmDFjBqNHj0aSJL799lv27dtHeXnH8mAbjK2jyL6UvylJcVx0EfZnjAiUwlyA4C5erZ5OU+n1eM68Dqi7SPeGrjcgIbHb2Zmkilw4scr2nCRJxExQnFXDyUK8nbRkFhnYca5m2FZw5fLz2vO4yBImrUxs0TwK1Woi9D5Mjp5qd70pNZXCyrEqfo+IaEt98e2odS5qNc4DlQ6isv37cHfSMqVSM2pneeV3jgPHpa9fXyQkUktSySlvP+elBjkuTz75JPv372fq1KnIssy8efMYPnw4Hh4e9OzZk1tvvZU333yTtWvXNpe9bZNaOooAjMmVjku4iLg4wua4dPZsZUsUvCuLdIv/3ITJwfBOgDD3MEaEKtOll7u7wa6P4aKhil0GBeDiqaOsyMiNAcpogBVtqEhX0LrIskzm4VwAogPP87Wb0kn0wIAnUavsD6vN/fJLMJtxHTEc55iWFWlsz3iHdMyIC2Ar0C0/cACAGwYp6aKlqZUjDtIOVTsvVeGmc6Ort/K9dTir/URdGqzj0q9fP/7xj3/QuXNndu/eTXFxMdu3b+epp57C29ubn3/+mZsrp+12FObNm2dLgY0fP569e/dWX2BLFdWMuFiNRsyV3SlaEXGxi2yViTumdIHd9sBMAgICmDVrFqdPn241m/Rdu+I8cCBYLBT+9FOta6uKdH92d8OYfhgSttueU2tU9B2jnERCs0wgw/rjGRRXOJ5C3ZK8+eabSJLEU0891dqmdDhSU1O588478fX1xdnZmb59+7J///5qa3afzCaoTPlCKdEtIlujIUjnyYwuM+3uacrKomC5UjTu+7BjdecrBYvFwosvvkh0dDTOzs507tyZf//733YnsvtWtkTndmDHpWzffmRZZlQXPwI99OwrD8EqaaA0GwrtXzDZ6lyyY6s9vnXrVmbMmEFISAiSJLFq1apqz8uyzEsvvURwcDDOzs5MnDjRVu/a3DRagO7s2bP4+fnh7OzMsGHDePjhh5k/fz67du3qUAO+li5dyty5c/nb3/4GQJ8+fZgyZQpZF1+F2xyXmhEXU0oKyDIqFxfUlfo2gurkZ5ShsmpBZWXZr9/w+++/YzKZmDx5MqWlrXeS8b71FsW+ZctqLdIdEzaGAOcA8tQqNrq6wM6Pqj3f++oQ1FoVpRnlDHNXBKJ+O5ruYLeWY9++fXz66af069evtU3pcOTn5zNy5Ei0Wi1r167lxIkTvPvuuzaNqyo2rY9HhYSTczaLfQsAuL//42grR0hcSt6ixchGI84DB+IydEhzv402z1tvvcX8+fP5+OOPOXnyJG+99RZvv/02H330UY21VZ1FhZllWMzWlja1WXHu3RvJyQlLQQHG8+dRqySuHxCGAR3J2ihlkaM6l0o9l0vrXEpLS4mJiXE4vuftt9/mww8/ZMGCBezZswdXV1emTJlCRUVFU70thzS5ci7Q6jUKTcl7773HnDlzuPPOOwH43//+h4uLCwsXLlQWGIqhuPJLyJ6GS6XwnDYiokP9XpqSqjbo0K6+9O3Xh5iYGBYvXkxSUhIHKkOfrYH7lCmoK4t0S7Y5VtLVqDTM7qZI/v/o7gZn10PWKdvzzm46ug9Tcs5X4wTAilbuLiopKeGOO+7g888/r/FlKrh83nrrLcLDw1m0aBFDhw4lOvr/2zvv+KbK/Y+/T3bSvRd7tmwURRCVK1zc4sIfggP1ur1uvep1K+579er1OnCACuIEUREHIoJskCkbCi2lu01HdnJ+f5wkbWla2kKbNHner1de0pznJE9qk3zOd3y+PZkwYQK96xlQ2pwu3HuVegtNzHcUajSk6uL8f0tH4qqooOLTTwGltkV8nsCKFSuYOHEi5513Hj169OCyyy5jwoQJjaPiQHSCHp1BjccjU1lkCcJu2w9Jp/OnDS3eqN5lJyodrius3m7WJoSLL+KyrXQbTnddJPicc87hmWee4eKLL250jizLvPrqqzzyyCNMnDiRIUOG8OGHH1JQUNAoMtMetItwCRccDgfr169n/Pjx/vtUKhXjx49n5cqVyh0+/xZTMhjjGz2GvzBX1Lc0ic94LqNPXX2Lb1hmYmJiUPYE3iJd75u2cu6nza69tO+lqCQVa40G9mk1Sq1LPXyt0RyyEO+RWJNbzsGy4H143nbbbZx33nkN/rYFx48FCxYwYsQIJk2aRGpqKsOHD2fGjBkN1nz/20ESXRLg4rPMrQBcN/Rm9OrA/hjlH36IbLFgGDCAqNNOa++X0CkYPXo0ixcvZtcuxUBt06ZNLF++POC8PEmS/FGXcK5zsaxTLvb6pMYwtEscmzxej5+CDQHP6xbTjQR9Ag6Pg+3l21v0XPv376ewsLDB50dcXBwjR46s+25sR4RwaYbS0lLcbrffkddHWloahT5X1UrvGIT4wPUrvsJc0QrdNL6IS6bXv8Xj8XDXXXdx6qmnBr29Pt5br1Xz2284C5q27E+PSue0LOXL5IuYaNj8KVTXDQJNzIyi64BEkOF8o5JrD1aR7ty5c9mwYQPPPfdcUJ4/Eti3bx9vvvkmffv25YcffuCWW27hjjvuYNasWf41G39Tom766LUcNDpJ1sVyab/LAj6eu7qaio9nA4pvi4i2KDz44INMnjyZ7OxstFotw4cP56677mLq1KkB1yf661zCq7MI6vxcLGvX+mt8Lj2xC1s8vZQFTRToSpLUaj8X3/dfs9+N7YgQLseKWREmTQkXp29GUVdRmBuImgo7VaU2JAnSeimDFW+77Ta2bt3K3Llzg7w7r5PuyJGKk+4XXzS79vL+ishZEBuH3eOANe80OO5rjc4s96CT4as/8jvcxTMvL48777yT2bNnYzAYOvS5IwmPx8MJJ5zAs88+y/Dhw7nxxhu54YYbeOuttwA4XGEhpljx/FmaoYT2rx1yEwZN4P8nFbPn4KmuRte7NzF/FVEyH5999hmzZ89mzpw5bNiwgVmzZvHyyy83EIj1CeeIi3HoUNBocBUV4fTOCbxgSCb7Vd2wy1qwmaFif8Bzh6Z2roGLQrg0Q3JyMmq1mqKiogb3FxUVkZ6u1CxQ6RMugSMq/lZoEXEJiC/aktw1Bp1Bw+233863337LkiVL6NKlS3A358VXpFv5+RfIzqa7gU7NPJWMqAzMksyPJhOsfRccdR+Q3XISSUg3ITs9jHDryCu3sja3vN33X5/169dTXFzMCSecgEajQaPRsHTpUl577TU0Gg3uZoqQBS0nIyODAQMGNLgvJyfHP6h2wXd7McoSKnU5m5L2kqiLZVL/SQEfy2OxUO4dYZJ8801IAUwuI5X777/fH3UZPHgwV111FXfffXeT0cSkMBYuKqMR48CBQF2dS0KUjjNyMvlTblmdy5GdRU3h+/5r9ruxHRHvgGbQ6XSceOKJLF682H+fx+Nh8eLFjBo1Srmj8oDy37jGERXZ41G6ihCt0E3hs/lP6xnL7bffzrx58/jll1/oGUKzV2LGjUOdlISrpITqJUuaXKdWqbmkr1JY+UViMtgqYeMc/3FJJTHEW+tyslsLcseni8aNG8eWLVvYuHGj/zZixAimTp3Kxo0bUasDe4cIWsepp57aqJ1/165ddO/eHVmWyf9DMfvalbIGWZK5dvANGDWBHaMrPv0Md2Ul2m7diA1QuxHJWCwWVEcIObVajccTuGvIlyoyl1pxOsJPpPvTRfXa7i89oQubvXUu7vzAdS4DkwailtQUW4oprD16qqdnz56kp6c3+G6sqqpi9erVdd+N7YgQLkfhnnvuYcaMGcyZo3wB3X333dTW1nLttdcqC5pJFbmKi5EdDtBo0HaACu2MlB5Uhg7+8Nt8Pv74Y+bMmUNMTAyFhYUUFhaGhCuzpNMRf+mlAFR++lmzay/pewlqSc0GDezRapUiXU/dB2T/kenojBq0Vg89XCq+23wYi6PjRsrHxMQwaNCgBreoqCiSkpKCXk8UTtx9992sWrWKZ599lj179vin0992221s2FlGaq3yxbo2fT0J2hh/mvFIPDYbZe+/B0DyjTcgaTQd9ho6AxdccAHTp0/nu+++Izc3l3nz5vHvf/87YCcMgDFGiyFauWioOBx+URejz4hubZ1wOaN/Cvu1/QCo2tu42wrApDXRP1EZHeGrc6mpqfFf3IBSkLtx40YOHjzo93565plnWLBgAVu2bOHqq68mMzOTiy66qH1eXD2EcDkK//d//8fLL7/M9OnTAdiyZQuLFi2qK0ryF+c2TgX5W6GzMsUHTgBkj0yJV7jM+uwdzGYzY8eOJSMjw3/79NPmu3k6ivjLJ4EkUfv77/7/r4FINaUytutYAD5PSIKKXNjxrf+4Vq8me5QiYkfLemodbn7Y1v7FbIKO5aSTTmLevHl88sknDBo0iKeffppXX32VqVOn8vOifaiQqIjah9lYzDWDr8ekNQV8nMovv8RdUoomM4O4Cy/s4FcR+rz++utcdtll3HrrreTk5HDfffdx00038fTTTwdcL0lSWKeLTCecAJKE48ABXCUlAGjVKtIHKFEQY+kWaCIa5UsX+epc1q1bx/Dhwxk+XBkncM899zB8+HAee+wxAB544AH+/ve/c+ONN3LSSSdRU1PDokWLOqR2TgiXFnD77bezbds2AH755RdGjhypHLBXg7VC+XdcY+Hi9Fv9izRRIKrKrDhsbtQaFQeLdyPLcqPbtGnTgr1NAHRduhA1ZgwAlZ81H3XxOel+Ex2FVZLg99caVPP7nHQzLRDnloLu6fLrr7/y6quvBnUP4cj555/Pli1bsNlsbN++nRtuuAG7043KO6tqc9oa4rQxTM6eHPB82eGg7F0l2pL0t78h6XQdtvfOQkxMDK+++ioHDhzAarWyd+9ennnmGXTN/K586aJwFC7q2Fj03qGblnoeWKePGoNF1mOQrZjz/wx4rm/goi/iMnbs2ICfyTO99VaSJPHUU09RWFiIzWbj559/pl+/fu322uojhMux4CvMNcSDIbbRYcdBUZjbHCUHlZbEpKwo1OrQ/1P0F+l++RUeh6PJdaMyR5EVnUW17OSHmFg4tA7yVvuPx6eZ6DogEQkY6lDz+95SCiqDnxITtD+Llh3E5DLglhzsTfqDqwdNI0obFXCtecECXIcPo0lJ8acqBcdOon/YYvgJF2ho/+9jQJcE9mkV88MtawPX6fk6i3aU78Dman/322Mh9L8tQpmjtULneVNFXYRwCUTJQaUwN6VbTJB30jKizzgDTVoa7ooKqn/6qcl1KknFZV4/jrmpXZABfv9PgzWDz1BcLU9waVF7YN4fwY26CDqG3F+Uro59SZvRGzVMyZ4ScJ3sclH6ttJOn3j9daj0gU3pBK2nriU6/LxcoL4RXcO5WHKGkvKp2B24ziUzKpMUYwou2cW2sm3tu8ljRAiXY+Fo5nMi4tIsvvqWziJcJI2G+MsUQVL5SfMeM5f0vQSdSsc2dzUb9XrYuRAKt/qPdx+cTEyiAa0b+jvUfLkhP+BgOEH4UFxei6FMmUG0M2UNVw28mmhddMC1VQsX4szLQ52QQEKYDa0NNokZinCpqbBjt3ZcYXxHYRpxIgD2Xbtwex3IAXoMPhWADMsO9hRXNzqvvhFdqPu5COFyLLTUNVfUuDRClmV/qqizCBeA+EmXgVqNZd06bF6b8UAkGhI5v/f5AHzUNVu5c9nL/uMqlcTA0zMBONGpYV9JLRvzKttt34Lgs/KTr3DJUVTrKqhKPsTUnMDurrLHQ+lbbwOQOG0aKlPgwl1B2zBEaYmKU2pgKgrDL12kSU5G16MHyDKWDXXtzzG9lNrMgVIuX647EPBc38DFljroBgshXI4FX6ooQGGu22zG41W7uq6hYaQWStRU2LHVOlGpJP+4+c6ANj2dmHHjAKiYM6fZtb4vpsXuSgo0atg2H0rqxM6AUzNRaSTSXCrSXVLQRgAIOgCXHecupZB/V8oapgy8klhd47o4gOoff8Sxbx+q2FgSpgZOJQmOjbhURQyai8OztiyQnwuJvXBqojFKDjZvWIU7gGu3L+KypXRLh+yzrQjhciw02wqtiBp1SrK4YgqAL02UmBWFWtu5/gwTvHNQzF8vwF1V1eS6fgn9OCXjFDzIzOk+FJBh2b/8x40xOvqeqLTVD7dr+GbTYeyu8DPFEsD+b9+myK446eZnbuOqAVcFXCfLMqVvKmMBEq+6CnV05xH1nYn4VMXsr7I4vKZE+whY56JSoc5S6lwyrTtZ7u1uq0//xP6oJBWl1lKKLcUdste20Lm+MUKNyqaLc32FuaIVOjD++paunSdN5MN08kno+/ZBtloxH2WEu+8L6iuVhVpJgi2fQ/k+//FBY5Ui3RynGketk8XbQ/fDQtBGrJUUrtgGqDgcs49JJ01sMtpSs+RX7Dt3ojKZSLzqyo7dZwQR7hEX44mKcLFt+xOPpU6cqbzCZai0ly/XN47wGjVGesUpQxm3l7VsUnQwEMKlrTitUOv9kgmQKvIX5nYVhbmB6GyFufWRJImEKUoIv2LOJ8hNGDoBjMkaQ4/YHlS7LMzveQLIblj+iv94Wo9YUrrFoEZisEMT8MNE0Llx/fYKm6ynA5Cbvrnp2hZZpvTNNwFImDoFdXx8R20x4ojzRlzMYRpx0WZlosnIAJcL66Z6hbZZJwAwWLWfH7YVUmVrPHttQJISGfyzLLDfSygghEtbMXu/YHQxYExodNiR7y3MFR1FAenMwgUg7sILUUVH48jNpXbFyibXqSSV/4tqtgE8ABs/8UfrJElisDfqMsyuZunOEkqq7e29fUFHYc4nb9kS3M4MnCo7Z/5lRJMuubW/r8C2ZQuSwUBiiBgvhivxvohLiTUsu/kkSQro50KmEnEZoDqI7LLz3ebDjc7NScwBhHAJT3zDFeO7giQ1Ouz0t0KLVNGR1JrtWKocSBIkZXXOHL4qKoo47zyUitmzm117Ye8LidHFkGct4bceJ4LHCSte8x/vOyINfZSGOFlFd4fE1xuFp0vYsOQ5frYrxdz7k7cxZUjTrc2lb3mjLf93OZqkpA7ZXqQSm6JEXOwWF/ba8GuJhnp1LvUcdInvDsYEtLjoJ+UFjPCKiEs400x9C9S1QotUUWN80Zb49Ci0+s47jTjhiisAqPn1Vxz5Tad4TFqT35Duo3hvdG79LKhWZhRpdGoGjFZao4fbNcxdmxeWV4ERR9E2Kv+Yj6VWaUPtdXIWBk3gOS61q9dgXbceSasl8brrOnKXEYlWpyYqXjH1C98CXcXPxbpxozLsF5SLbG/UZZhqH+sOVLCvpKERX3ZiNhISxdZiSq2NC3hDASFc2oqvoyhAfYvH4cBVqHwpaUXEpRF1aaLOGW3xoe/Vk6hTTwVZpuKTT5pde0X/K1BLataYd7Gzy3Bw22HF6/7jA0/PAgl6utSUHq5lw8GK9t5+p+GTTz7BaDRy+HBdWPvaa69lyJAhmOsZbIUcPz/BF/KZaDw6KozF3HJ207b9pW+8ASg+QVrfAFdBuxIf5nUuul69UCckINvt2P6sFz3JVOpcJiQo76dP1+U1OM+kNdEjrgcQulEXIVzaSjN2/878fJBlVCYT6oTG9S+Rjk+4pHYL3FnRmfC3Rn/xJR5b0/M9MqIzGN99PAAfZSpV+6x7H2rLAIhLMdJ9oJIeGO7QMHdNXsDHiUQmT55Mv379ePbZZwF4/PHH+fnnn/n++++Ji4sL8u6aYP9v1O75iYLaM5Wfe6vRaQIP/rOsXYtlzRrQakm64YYO3GRk4+ssqgzTziJJkjAOGQKAdUuda7c/4qLeD8CX6/Nxuhs2GIR6ukgIl7biTxUF6ijyzijq1g0pQP1LpFOSpwiX5K6dO+ICEH3G6WgzM3GbzVR9t7DZtb7W6IVlGynNGAxOC6x6w398kHd+0SCHmkWbDlMdoOI/EpEkienTpzNjxgymT5/O66+/zqJFi8jKygr21gLj8cBPj/GRfgBJtd1xS26uv/ysJpeXvPE/AOIvvQRtRkZH7TLi8XcWlYSncAEwDBkMgHXL5ro7vcIlpmo3WVFQWuNoZMMwIFERLqHaEi2ES1vxp4oCRFxEK3STOGwuasqVrpnOWphbH0mtJmGKUutSPvvjZmtThqYMZUjyEJweJ5/3VgrnWP0OWJW0UPeBScQmGzDIEj1q4ZtNjSv+I5Xzzz+fAQMG8NRTTzFv3jwGDhwY7C01zbavMBduZJtVibBVJFnISA0cXbSsW4dl1SrQakm+8caO3GXEE5/i83IJz1QR4I+42DbXc8KNzYSoVCTZzU39lZEHnx2RLvJHXMpFxCV8cDmg2vulEiBV5J9RJFqhG1F+WHmjmGJ1GKK0Qd7N8SHu0kuR9Hrsf27HunFjs2uvHKCYis0t+wN7ag44qhXxAkgqiUGnK+Mhhjs0fLom8DyRSGTRokXs2LEDt9tNWijXgDgs8PMTzIpJokfpSQCM+suQJpeX+GpbLr4YbWZmh2xRoBDnd88Nz5ZoAMOgQQA4cnPrXL4lye/ncm6SUov5685iDpvrIk/Zicp8tcLaQspt5R2445YhhEtbqMoHZNAYISq50WHnQeGa2xTlBYpw8Y2WDwc0CQnEnnceoBjSNcf47uNJM6VRbivn+wHKFTmr/gc25UMlZ3QGao2KNLeKkgM1/FnQ9EiBSGHDhg1cfvnlvPfee4wbN45HH3002FtqmhWvUV59iOXuUzG4o6jVOhg3tnvApZYNG7CsXAUaDUki2tLhxHlboh1WF7ba8EzLahIS0Hoj/7atjetcks3bOLlnIh4ZvlhX1xkZrYumR2wPIDTrXIRwaQv161sC1LD4W6FFxKURvoiLb7R8uOAbhle1aBGu0qZbCLUqLVdkK6mlj6u2Iyf1BlslrFSuvA3RWvqelArAcLu6UQg30sjNzeW8887j4Ycf5oorruCpp57iyy+/ZEO9qbchQ2UeLH+Vd+Nj6V0yCoCofsmo1YE/Zkv/64u2XISuS4jW64QxGp2a6ASlJTpcrf8BjIO9dS7100Ve4ULBH0w+Sfme+nRdHp56gxdzkhQjulCscxHCpS000wotezxKVxGiFToQFWEYcQEwDhyIcdgwcDqp+OyzZtde1u8yjBojOyt2sXaE1/595X+hRimQGzxWSRf1c6pZuDYfmzMyBy+Wl5dz9tlnM3HiRB588EEARo4cyTnnnMPDDz8c5N0F4OfHycfBt7oedDH3R0bm3Av7BFxq+eMPalesUKItN93UwRsV+IgL82GLUL9AN4BwKd3FOX2jidFryK+wsmJvmX/JwCSljkxEXMKFZlqhXcXFitmPRoM2Pb2DNxb6hGvEBepaoys++QSPz/ApAHH6OC7sfSEAH1n2Kx8ijhr47SUAUrvHktojBg0SPavhh22F7b/5ECQxMZEdO3bw1ltvNbj/u+++Y9GiRUHaVRMcWAFbv+S1hHj6lJwCQE2chp7d4wMuL/V2EsVdNBFdly4dtUvBEYT7sEWoK9C1bt5UV8sTnQqxXQAZY9k2Jg5X6qvqe7qEsvW/EC5twRdxaa4VOisTSaPpyF2FPHari5oKpaMo3CIuALFnTUCTloa7pJSqhc23Rk/NmYqExK/5S9k1ylvfsO4DKFe8FQafoXyZDbWrmbv6YLvuW3CMeNzw/T/YqtOxKCqa/iWKU27/0YFbm62bNlG7fDmo1SSLaEtQiYTOIkNODqjVuEtKcRUV1R3IHKb8t2ADk09SLsJ/2FpIRa1y0eVLFRXUFlBpq+zAHR8dIVzagr/GpXHRndNv9S/SREdS4Y22RMXp0JvCo6OoPpJO54+6lM+c1WynQs+4nkzoMQGAd8o3QK+/KDOMlkwHoM+IVHQmZX5Rya5Kcktr2/8FCNrGxtnIhZv5V3IyXStziHbEY1fJnHtWr4DLS7y1LXETJwrLhCBTv7MoXFEZjej79QPAurmxnwsFfzAoK46BmbE43B7m/aHMSovRxdAtRvkeC7W2aCFc2oK56RoXx0FRmNsU4dhRdCQJl09CMhqx79iBZfXqZtfeOESJtPyY+yN7T/E6pm75HA5vRqNVM3BM3fyiSC/SDVlsZlj8FEuNRtbpNWQXK0W5qp7R6A2NI66WDRuoXbZMibbcLKItwSaunu1/uLZEQ12Bri1QnUvBRoC6It16s9JC1UFXCJfW4naB2Tu9N0CqyJnnTRV1EcLlSOrqWzq/8VxTqOPjifdOjS7/YGaza/sl9GNct3HIyLxT+BsMvEQ5sPhJAAadrnSa9HCp+WFVY1tuQQiw9EVctSW8kpKKwRlN93LFN2PcuU1EW/6jTAWPv+QSMTk+BIhLMYIEDpsba3V4tkQDGAYrf5cNrP/Tvf5C5fvAUcuFw7LQa1TsLKpmY14lUJcuEsKls1NdCLIbVFqIblx8KyIuTeMXLmEccQFIvPoqkCRqli7Fvm9fs2tvGqJcdS/KXcT+k68FlQb2/Az7lxGbbKTrwEQAulV4WLKjuLmHEnQ0pbth9VvMi4lin1pmYOkY1KioNqkYPDCl0fLaVauwrF6NpNWSfMvNQdiw4Eg02not0WFs/e930N2yBdnjvQCKToGoVECG4h3EGbWcO1ipy/JFeH0Rl1BriRbCpbWYvSY9cV1A1fjX53fNFTUujfClihLCsKOoProePYg+UxmuVz7rw2bX5iTlMLbLWDyyh3fzfoATrlEO/Pw4yDJD/6II4EF2NZ+vEkW6IYMsw/f/wCK7eSM5FWSJfgVnAND1xMaiRZblumjL5ZcLl9wQIi4CCnT1vXsjGY14amtx7N9fdyDNOzqjSInE/J83XbRgYwG1dpe/syi/Jh+zPXQmsQvh0lqqvMIlQCu022zGY1b+5+q6ihbH+tgtTmorvR1FGaYg76b9SZqmCBDz/Pm4KiqaXXvTUCXq8t2+7zh44pWgNcGh9bD9G7oNSMSUqMeARPG2cgrNTU+gFnQg276CvYuZmZBAGW4GWE4hzmHCIclcEMC7pXb5cqx//IGk15N0k3DJDSXiI8DLRdJoMAxUoicNjOj8wmUbACN7JtIjyUStw813mw8Tp48jK1pJWW8vD52oixAurcUXcQnYCq1EW9QpyahM4f/l3BrKDysfClHx+rDsKDoS44gRGAYORLbbqZw7t9m1g5IHMSZrDG7Zzbv75sMptyoHFj+FJLsZ5o26DLdp+GKdiLoEHZsZFj1EiVrFzPh4ALLzlJEP7m4mYmP0DZbXj7YkTJmCNjW1Q7craB6/l0sYp4oAjIN96aJ6nUVpSu2LT7hIksT/eVuj565VPmtCsUBXCJfW4hcugVqhxYyipigvqAHCv77FhyRJJE6bBkD57DnNGtJBXa3LN3u/IX/oZWBMhLLdsHE2OaMzkDQSKR4VS5bnN7DlFgSBxU9DTRH/S++GVXYxxHAyyRVKwfn4CxpHW2p++QXb1q1IJhNJN/yto3crOArx/s6iMBcuQwJY/9dPFXk7iS49MQu1SmLDwUp2FVWHZJ2LEC6txeea21wrtPBmaEQ4O+Y2RezZZymGdKWlVH37XbNrh6UOY1TGKFyyi/d2fwan36cc+PV5DDoX/U9Riua6lrhZua+smUcStCv562Htu+zVavhKp3zQ5+RdigoJc7SKYYMa1rfIHo8/2pJ41VVoEhM7fMuC5vHVuFSGeUu0wRdx2bmz7kIqpT9IamVeWlUBAKkxBsZlK1HBj1cdEBGXsKDK1wrdOKriyPcW5oqOokZEgofLkUhaLYlXXQlA+cyZR/1QvHmo0mkyf898Duecp4jj6gJY8V+Gj1P+pvq4VHy+dH9zDyNoL9wu+PZOZGRe6j4ADzJjM89Ev09JDfUb09gpt/qHH7Dv2oUqOpqka6d18IYFLSE2xQASOMO8JVqblYk6IQGcTuw7dih3avSQrJjT+dJFAFeNUjIKX204RPdo5fjB6oNUO6o7dM9NIYRLa2nOw8XfCi1SRUdSEYERF4D4SZOQTCbsu3ZhWbmy2bUnpJ3Ayekn4/K4eG/HxzD+CeXAspdJNJSQ0CsWCQnzlgpRpBsM1rwDhVtYEpfM7+5KtCotg0svx+SRsKhlLji3d4PlsttNyev/BSDx2mmovfUwgtBCo1UTk2AAwruzSJKkuoGLTaWLvJzaO5leyVHU2F38sq2GzCilCy5U0kVCuLQWj1MJrcU0bmd05IlUUSAcNhe1ZiU0mZAeWUXL6rg44i9RjOXKZs486npf1OWr3V9R1GsM9DgNXDb4/kFGn9MDgEE2NbN/F1GXDsV8CJZMxyZJvJim+DddM/AaStYpf9eGfnHodQ2dcqu+/RbHvn2o4+JIvOaaDt+yoOVEgvU/NFWg27CzCEClkrjyFCXq8uHKA34julDpLBLCpS3EZoG64YeUx+HAVahM8dWKiEsDfEVvxhhtRHQUHYnPkK72t2XYdu5sdu2ItBGckHoCTo+TD7bNhHNfVkzpdn1Pd+1aNHE6DEj88dsh7C53x7wAAXz/ADhqeK9bDoecVaRHpXOCfBHxtTIeZC68pG+D5bLT6Z9JlPi361FHh69bdDhQNyU6fCMu0FSBbsPOIh+XntgFk07N7uIaYqSeAGwra7gmWAjh0hYCpYny80GWUZlMSh5R4MfnjxCXYgzyToKDrls3Ys4+C4Cyt99pdq0kSX5fly92fUFpTDKMuk05tugfnDxOqaPoVwXfbipox10L/GybDzu+JU+n532N4kV0/4j7WfG9kjauSdbRvWtcg1Mqv5qHMy8PdVISid7Bm4LQxd9ZFOYt0QbvzCLH/v24q6qUO30Rl9Jd4LL718YZtVw0XPFw2Z0XC4hUUZspLy9n6tSpxMbGEh8fz/XXX09NTU2z54wdOxZJkhrcbr75GCy3AxXmHvTOKOrWDUmS2v7YYYgv4uK7qolEkm9SxEjVokU4cnObXTsqYxRDUoZgd9v5YOsHcPoDSpSv8gAD5c9AI5HkUfHtj/vDugsiJKgthe/uBeDF3sNxeJyMzBjJ8Lgx6PKVv+sR4xp+HnisVkr/q9S2JN90o/B06gT4PpvC2YQOQJOQgNZbymDb6q1pic0EQ7wyyqakYUT4am+R7tpdSm1iblUuNY7mv287gk4nXKZOncq2bdv46aef+Pbbb/ntt9+48cajO1HecMMNHD582H978cUX276JAK3QTtEK3STmEuXDwHdVE4kYsrOJPuMM8HgonTGj2bWSJHHzEEVYf7rzUw47q+Hs5wDQrfk3/Ycrv8fEQ3b+8A5DE7QT390LllJ+y+jPr7YCNJKGh09+mHnzdqNDoloH485o+J4v//AjXCUlaLOyiJ88OUgbF7QGXzTYXGwN+4sB36Rof7pIkppMF2Wnx3Jyj0Tcziii1MkA7Cjf0WF7bYpOJVy2b9/OokWLePfddxk5ciRjxozh9ddfZ+7cuRQUNB82N5lMpKen+2+xsbFt30igiEueaIVuChFxUUi6WYm6mL9egPMof69jssZwYtqJ2N12XvvjNci5EHqfCW4HI9xvIwO9XGrm/Ly3A3YeoWz9Cv6cj12l5vmEGACuGnAVPWJ7ULZR8dJJGZaEqt7MMldFBWVeYZpy152odLqO37eg1cQlG5EkcNrdWKqaN4vs7Pg7i7Y031nkw9caba1RitJDwc+lUwmXlStXEh8fz4gRI/z3jR8/HpVKxerVq5s9d/bs2SQnJzNo0CAeeughLJbmQ4J2u52qqqoGNz8BW6GFa25TRHqNiw/T8OGYRo4El4uy9z9odq0kSdw/4n4Avt33LdvK/lQKddU64gu+Ii1LyUWbN5dTXC1ao487NSWwUDEBnDn4bPKsxaQaU7lp6E389OtBYh3glGQuurhfg9PK3nobT00N+pwcYs87Lxg7F7QBtVZFdKK3JTrM61x8ERdbQOHSuPj2rIHppMTosdYo9XV/lgvh0ioKCwtJPWLOh0ajITExkUJvR08gpkyZwscff8ySJUt46KGH+Oijj7jyyiubfa7nnnuOuLg4/61r/RRQgIiL7wpa20UMV6yPw+rymzrFR3jEBSDZG3Wp/PxzXKWlza4dmDyQ83udD8BL615CTuwFp94JwCkoRb4DbGrmLM9tvw1HIrIM390DljIK0gfwbu0uAO4dcS9R2ijWLVaiq84uRpIS6sS4I/8QFXPmAJB6771IAabHC0KXunRReNe5GHJyQK3GVVyMs6hIubOJVBGATqPiipO74bZ6hy2GQIFuSLyzHnzwwUbFs0feduxoe17txhtv5KyzzmLw4MFMnTqVDz/8kHnz5rF3b9Nh9oceegiz2ey/5e/a5D0iQWxjceL7A9BmpLd5n+GI7+rFGKNFZ9QcZXX4YzrlFAxDhiDb7ZTP+vCo6+8Yfgd6tZ71RetZkrcExtwD8d3o4vqFKFM1OiT+WJqPw+XpgN1HCNu+gu0LQKXhpe452Nx2RqSN4Jye57Avz0xMmZJK+Mt5DQ3nSl9/DdnpxDTqFKJOHR2MnQuOgXh/gW54R1xUJhP6vkr7vnWz188lNRuQoLYYaoobnTPl5G7gUL739pv3Y3EGV9yFhHC599572b59e7O3Xr16kZ6eTnFxw1+qy+WivLyc9PSWC4aRI0cCsGfPnibX6PV6YmNj/bcYd4VyIDoVNA3z1h6LBY83laRJS2vxPiIBX5pIRFsUJEnyR10q5szBbTY3uz4jOoOrBlwFwCvrX8Gp0cI5LyJJMEKrXN33q4KFm0Vr9HGh6jB8p6SIVoyYws/Fa1FLah4e+TCSJPHNV7tRI2GOUjFiWN173bZjB+YF3wCQes+9orOwExKXGhkRF6iXLvIV6OqiILGX8u8AUZf0OANnZffB44xFRg56gW5ICJeUlBSys7Obvel0OkaNGkVlZSXr16/3n/vLL7/g8Xj8YqQlbNy4EYCMjMazRZrEZ/UfqKPIG21RRUUJo6kjMIv6lkZEjx2Lvl8/PLW1lM+efdT11w+6nkRDIrlVuXy28zPofw70O4f+hl/QqqzEe1Qs/GFfB+w8zPG4Yd6NYC3Hkj6Ip627Abgi+wr6JvTFZndh36UIzd6jG14oFf/r3yDLxJ57DsbBgzp864Jjx3dxFe41LlCvQHdry+pcAK46pQcem5Iu2lC0JeCajiIkhEtLycnJ4eyzz+aGG25gzZo1/P7779x+++1MnjyZzEzFgv/QoUNkZ2ezZs0aAPbu3cvTTz/N+vXryc3NZcGCBVx99dWcfvrpDBkypOVPbs5X/hub1eiQyytcNK2I+kQKoqOoMZJKRdJNSgt/xawP8dTWNrs+WhfNbcMUE7q3Nr1FlaMKznkBrV7HYONCAFLyHWzKq2jfjYc7v/8H9v8GWhP/yRlDfs0h0qPS/b/7rxfuIcotYVXJXHhuH/9ptatWUbtsGWg0pNx5Z7B2LzhG6tv+h3tLtCFHmfhs376j7rU2U+cCcEqvROLVioPuT3vWB1zTUXQq4QJKd1B2djbjxo3j3HPPZcyYMbzzTp0bqdPpZOfOnf6uIZ1Ox88//8yECRPIzs7m3nvv5dJLL+Wbb75p3RNXeYVLXID6Fp/Vf1pqo2ORTqVfuIiIS31izz4bbfduuM1mKj77/KjrL+l7Cb3ielFpr+Tdze9CQnc450WGmL5FjYNMt4pPFzad+hQchby18MszAKw97Xbm5CqC8MlRTxKti8bj8bBn2WEAtH1jMXrrtWRZpvjlfwGQcPnl6Lp3D8LmBceDWG9LtCsCWqL1ffuAWo27stJ/4d1cSzQoae4JfU4EYGfFjqCKu04nXBITE5kzZw7V1dWYzWbef/99ouulZ3r06IEsy4wdOxaArl27snTpUsrKyrDZbOzevZsXX3yx9T4ulU0LF1eRUnejSRMRlyOpM58TEZf6SGo1yTfcAED5++/jsdubXa9Rabh3hOLg+vH2j8mvzodhU4gadDo5xsUAuLdWUFrT/OMIAmAzw5fXg+zGMmAij5UsB+DSvpcyOkspsl2yPJ94i4wLmYsv7+8/tWrhQmxbtyKZTCTfektQti84Pqg1KmKSfFOiwztdpNLr0fdSalps271dQj7hUrID3K6A5007aQySK4UsU2+sjuDNSut0wiVomJsTLkrERZMuCnPrY6/XCi0iLo2Ju/BCNBkZuEpKMM+bd9T1p2WdxsiMkTg9Tl7b8JrieHnBfxiWugIJN92cGj75QURdWoUsw7f3QOUBiO/Gf7J6kV+TT3pUOveNuM+/bPVCZRq3rYuRblnKRY/HaqX4pZcBSLr+OjTJyR2/f8FxJVKs/wH0OdkA2H2DX+O7gy4a3A4oC/w50jM+kz+uXcx3V7yJSR+8LlEhXFqCLNcTLgGKcwu9rdCio6gBvsJcY6wOnUG0Qh+JpNORdN11AJS9MwPZ0Xx4WpIk7htxHxIS3+d+z9rCtWBKJG7SU/Qx/A5A7fI/cbpFa3SL+eMj2PoFSGrWnvkAc/Z8CdSliAA2bCoirtKNB5lzJ9UZzpW99z6uwkI0mRkkXX99ULYvOL7Ut/4PdwzZOQDYtns7hFQqSFVqX5pKFwGoVcHvmBPCpSXYKsHpHSwVm9nosL84VwiXBvje/JE8o+hoxE+6DE1KCs6CghbVumQnZnNZv8sAeGrlU9jddugzjqEjlbdyrDWBH5Zsbtc9hw0HV/sHKFrOuI/Hdivt5fVTRAA/faV0F1UlaxncX4mqOAsKKHv3XQDS7r8flcHQkTsXtBP+zqIIiLgYspWUp21HPUO5o3QWhQpCuLSEyry6f+sa12r4zedEV1ED/Fb/or6lSVQGA8m3KV0rpW++edQOI4C7TryLZGMyuVW5zNiszMVJu+x+Mox/IqPCsugXJUooaBpzPnx6pRIWz7mA14xSwBTRnn2VmIqUuqHTJ9YZzhW//C9kmw3jiBOJOfvsDt++oH3wdxZFQEu0PltJFTkPHMRd4/3cEcIljEjpD9f/FPCQ7HDg9lq3i4hLQ0TEpWXEX3qJ0mFUVkb5h0d3043VxfLQyQ8B8N7W99hTsQe0RgZcdBIAZTUD2b7gneYeIrJxWGDuFMUlNG0Q60bfxOwdSrTliVFP+FNEAN98tgMVEmUxKk47SbFCsKxfT9XChSBJpD/8sDCbCyP8qaKS8G+J1iQm+r+z7Lu8dS5HaYkOFYRwaQkaPaTmBDzkKikBQNJqUSckdOSuQh5fR1Fcioi4NIek1ZJyxx2At26i4uh+LH/t/lfGdhmLy+PiyZVP4pE9ZJ8xEn1UBR60lP62HUpFoW4jZBm+vg0ObwJTEpbL3ufRNc8CSoro1KxT/UuLimtR5SpXosMmKPPJZI+HounK+vjLLsMwYEAHvwBBexJJLdEABm/UxeYbqZPm/Xuuygdr6PpCCeFyjDjrmc+JK6+GCA+XlhN7zjnoc3Lw1NRQ9s6Mo66XJIl/nvJPTBoTG0s28sWuLwAYesnJAGy3jKdy1jSwVTXzKBHIspeVWUQqDVz+Ea/tnxcwRQTw5Sfb0SBRZoDzzuwBgHnePGx//okqOpqUu4TZXLih1qiIitcDUFMe/tYC/s4iX4GuIQ7ivEOEi4I/BbophHA5Rlxe8zmNMJ9rgN3ixFbjbYUWdv9HRVKpSL3nbgAqZs/GefjwUc9Jj0rnjhOUSM0r61+h2FLMiNFdcJlknLKJPYf7wRfXNenJEHHs+M5vMse5L7NCKzF7uzJy4cgUUU21A/sOxd6/52kZqNUq3DU1FP/7FQCSb70VTVJSx+5f0CFEJyiF1tXltiDvpP1pFHGBTlHnIoTLMVLXCi0Kc+vji7aY4kQrdEuJGjMG00knITsclLzxRovOmdx/MoOSBlHjrOH5Nc8jSRInnKsUkW6qvQDn7qXw06Ptue3OQdE2+EoZs8BJN1CQfRYPLHsAgMv7Xd4gRQTwxWfb0ckSFVqZSRcok3RL33wTd1kZuu7dSbxyaoduX9BxxCR6Iy4VkSNc7Lt2Ibu8FzhHcdANBYRwOUbq5hSJwtz61NW3iGhLS5EkiRRv1MX81Tzs+44+OFGtUvPE6CdQS2p+OvATvxz8hVP/0g2HQYVNjmOHZRys+h+s+6C9tx+61JbBJ1eAowZ6nIb9r09wz6/3YLabGZA0gAdOfqDBcofNRdmGMgAST0zGoNPgyM2l/MOPAEh96EEkna7R0wjCg+jEyIm4aLt1QzKZkO12HLm5yp2+OhcRcQlf/K3QoqOoAXUdRaIwtzWYhg8netw48HgoefU/LTqnf2J/rh54NQBPrHiCUnspg89UjBKX1k7BLath4X3KAMFIw16jdBBVHlCcQS//kOfX/4ttZduI08fxythX0Kv1DU5Z8PVuDG6oUslMmaRckRa9+BI4nUSddhrRZ5wRjFci6CBivMIlEmpcJJUKQ3+fn8sRnUXFf4InNM0shXA5RupqXESqqD51Hi4i4tJaUu+6EySJ6h9/xLqlZePjbxt2G9mJ2VTYK3hw2YOcNqErTq2E5InmJ+lG8Ljg06ugbG877z6EsFfD7MsgbxXoY+GKucwv+I0vdn2BhMSLp71IZnRDQ0mP20Pu796hqQPjiI/SU7NsOTW//AIaDWkP/kMU4Yc5kRRxATD4CnR9RnSJvUGlBacFzHnNnBk8hHA5RpzFPvM5EXGpj4i4tB19377ETZwIQPG//92yc9R6Xjr9JYwaI2sL1/L+jvfoNyYDgDXF47CmnqA4QM/5v5Buczxu2Kvh48vg4ErQx8FV89mhVfHMKqU499ZhtzZwx/Xx84/7MTpkLJLM5Mtz8FitFD71FACJU6eg79270TmC8CKSalwA9P29Bbq+ziK1BpL6KP8u3RWkXTWPEC7HgOx24ypWfFyE+VxDqkoV4RIralzaRPLttyNptVhWrqJ2xYoWndMjrgePnqIU4r61+S0STq7CrYYkj5pX3Y9CbBco261EXpxh7Axqq4KPL/VGWuLg6nmYU/pw15K7sLvtnN7ldG4ccmOj02RZZtNPyhWmvaeJLilRlP7vTZx5eWjS0kj++987+pUIgoCvq8ha7cQVxAnIHYUv4mLbvr3OdC/FO5OrZGeQdtU8QrgcA66yMnC5QKUSk2Hr4bS7/VOhY5PEDJe2oOuSRfwVkwEo/te/W+zieUHvC5jYeyIe2cMjax8i7YQ4AGw7PBw+933QRkHuMpg7FZxheEXpFy2rFU+Kq+fjyRzOw8sf5lDNIbKis3h2zLOopMYffT8tPoDJ4sGBzKTJOdh27qLsA6WoOf3RR1BHRzc6RxB+6E0atHo1ADUV4V/nou/bF1Qq3OXlfkNVkpW6F0qFcAk7XEXFAGhSUpA0ouXXR3WZ8oWoN2nQm7RB3k3nJfmmm1CZTNi2baNqwYIWn/fwyIfpGdeTYmsxy9M/wqWGVLeKdxerYOrnoDXB3sXw2VXgCqMPZpsZPr4E8teAIR6u/hqyTmDG5hn8lv8berWeV8a+Qpw+rtGpsiyz5vv9ANh7mOjXJZbCxx4Dl4vo8eOIGT++g1+MIFhIkhRRdS4qoxFdz54A2Hd6hUqKV7iUiFRR2OEq8hXmijRRfXxvdt+bX9A2NElJJN18M6B0tbirWuaCa9KaePmMl9Gr9fxauhjHIOUqSr2tivyYYTDlM9AYYfeP8NnV4SFebGb46BLIX1snWjKHs+LQCt7YqHji/HPkP8lJCjy6Y8HP+0molXEjM3nqQCrmzsW6aROqqCjSH3mkA1+IIBTw1blEgnCBekZ0vjqXZF+qaEdIDmwVwuUYqDOfE8KlPtVl3voWkSY6ZpKmXYOuZ0/cZWWU/Oe1Fp/XL6EfD5yk+JN8Zvg3Nq2bOI/E7Nl/Qs/TYMqnoDHArkWKx4m9ur1eQvvjEy2H1oExAa5ZAJnDOFB1gH8s+wcyMpf2vZSL+14c8HSX28O6RbkAeLpHkaWzUeJ1yE256y4x9T0Cifa3REeGcNFnKxEWf2dRcl9AUgr6a0uCtq+mEMLlGHDVm1MkqKPKmyqKERGXY0bS6Uh/TCm4rfjkE2x/tnx+yKR+kzirx1nYVBa29vwRAPX2Kg6V1ECvM+CKuXVpow/OgaqjjxkIOYq2wYwz60TL1QsgYyiFtYXc8OMNVNorGZg0kIdGPtTkQ3z6/R7Sa8GDzKVTB1A0fTqemhoMQ4aQMOWKDnwxglAhxmf7HwE1LgCGbCUS6Y+4aI2Q0F35dwgW6Arhcgw4vakirZhT1ABfeDVGRFyOC1GjRhF77jng8VD45FPILTSFkiSJx0c9TpfoLqxP/JFKQzlGWWLuR17x0/svMO1biEqBwi3w7ngo3t6Or+Q488fHMGMclO2BmEy45hvIGEKZtYwbfryBw7WH6RHbgzfGvdHIZM6H1eFil7eTSNM7hvg966n+8UdQq8l46kkktbojX5EgRPC3REdIxMXXWeTIzcVjUTy4QrlAVwiXY8DlTRUJ87mG+IpzY5NEK/TxIvUf/0BlMmHdtAnzV1+1+LwYXQxvjn+TeEMcq7rNA0C9q5oDh7z1MlknwvU/QVJfZZT9e2fBjoXt8RKOH45amHcLfH0buKzQexzcvAzSB1PlqOLmn28mtyqXjKgMZkyYQZKx6WGIs77YTqpdwiXJXDapJ4VPPw1A4rRr/Hl/QeQRScW5AJrkZNQpySDL2HfvVu70t0SHXoGuEC7HgC9VJMznGuITLiLicvzQ1vMRKX75X7gqWm4i1yOuB2/+9U2KU/dQGL0fLRJzP6jnyJvYE67/EbqNArsZ5l4BCx8IzXbpkp1KamjTHJBUcOajMPULiErG4rRw28+3saN8B0mGJGZMmEF6VNMXFRW1DkpWKJ2BMUMScb7zKq7Dh9F26ULKbbd11CsShCD1bf9bakXQ2WmULhIRl/BDlmX/nCLRVVSHy+HGUuUAhHA53iReORV93764KyspeeXVVp07MGkgr417jbU9lGiKKd/Khq3FdQtMiUp9yKjblZ/XvA3vjYfS3cdp98eBTZ/CO2OVTofoNGW/p98HKhUOt4O7ltzFxpKNxOhiePuvb9M9tnuzD/fBx1tJdEk4VHB+lxIlkiVJZD7/HCqTcHyOZKLi9SCB2+Xxe1KFO4Zs38wib7o4hFuihXBpIx6zGdmmXJEK4VKHL7Sq1avRm4S3zfFE0mpJf/wxACo//xzr5s2tOn9kxkjuOf8mchO2okLFF7MXN1yg0cFZ02HK52BKUupe3j4dlr8CLsfxehmtp2QXfHolzLtRmZ/S83S4ebnSHQW4PC7uX3o/Kw+vxKgx8ub4N+mf2L/Zhywoq8WxSYlaZQ2LoXL64wAk/e16TCNGtO/rEYQ8ao2KqFhlAnjEWP97U6P2I1uiqwuUzr0QQgiXNuL0ms+pExJQ6QMX/kUi9QtzxTC6449pxAhljpEsU/jEk8ju1lmST+gxgZ5npuLBQ1ZFGtO/nNV4Ub8JcPPvikBwWuDnJ+DNUbBnceO17Yn5EHx9O/xvJGz/RkkNnfEPuGo+RCsF8U63k4eXPcwveb+gU+l4/czXGZoy9KgPPXPWVmI8EjYtnLT2PdyVlehzckgRtv4CL76IsS/1He4Ycrypol27lM8VYzxEe1OtoRR5RQiXNiPM5wJTV5gr0kTtRer996GKicH2559UfPppq8+/9a+TKclQvBksq+zM3x3AlTc2A676Gi56C6JSlc6djy+BWRfCrh/ad9y9pRx+fAReGw5/fASyB/qfp4ipvzwMKq8du6OGWxffyve536ORNLx8xsuMzBh51Iffvr8C/e4aAAallmBbthRJpyPrxReQdLr2e12CTkWkFejqundHMhiQrVYcBw8qd4bozCIhXNqIs9DXCi2ES32Eh0v7o0lOJuXOOwEoefU/OIuLj3JGY268/jxckpvM6j7M+G42MzbPaFyEqFLBsCvg7+vglFtBUsP+pTDncnjjJFgzQ+nwOR7IMhRshB/+Cf8ZCiteB7cduo2G636EK+ZA2gD/8mJLMdMWTWPV4VUYNUZeH/c6f+n2lxY91Zczt2GQJex6N92+fAGA1HvvUWa2CARefF4uNeWR4eUiqdXo+ytCxb4jtAt0hXBpI/45RcJ8rgF1HUWiFbo9SbhiMoYBA/BUVXH4oYdb7O3io0uXWPQ5CQCMzr2I/65/g38s+wc2V4CrS0McnP0c3PGHUryrj1UiMAvvg3/nwJd/UzxVzIda9yKcNji0Hn59Af57ErxzBqz8L9irIG2w0i107ULo1jCKsrdyL1cuvJKdFTtJMiTxwdkfMCZrTIuecvmqQyQUKfU6owvmgc2KadQpJFx1Vev2Lgh7/BGXCKlxATD0P8L6P0QLdEX1ZBtx+lNFwnyuPqIVumOQ1GoyX3yB/ZdeRu3vv1Px0UckXnNNqx7jymuH8NaDy4m3pXHCoQl8r/qevKo8/nPmf0g1Bfi7TuiuFO+OfRA2zoFVb0LFftjyuXIDxQ8mbQDEdVVu0angcYHLpsxEclqgdBcUbIKS7coxHxoD9DsbhlwO/c5RIj5H8M3eb3h61dNYXVZ6xPbgzfFv0iWmS4ter8vlYfmnu4gBtBQQt2UJqthYMp97DinAcwkim0gzoYM6Izp/Z5GvQDfEIi5CuLQRl39OkYi41Mc3p0gIl/ZH36cPaQ/+g8Inn6L45X9hOuUUDP2b76apT3SMjj5ndeHQwnyG5U+gIH0nW8u2csW3V/Dama8xMHlgE08cAyNvgpP+BgdXwt4lsO9XKNgAZbuVW0sxJUGXk2DgxdD/XDDEBlxmdVl5fs3zfLVbMd87Of1kXj7jZRIMCS1+qtmf/EmMVcaJmzGr/gtA+uOPiVlEgoBEWo0LBOgsSvGaMFbkKhFSbWh8rgvh0kbq5hSJGhcfbqeHWq+HiyjO7RjiJ0+m5rdl1CxZQsF999Hj889RGVr+u594QV9eWFlITIWLU7ffxvox/2Nf1V6uWXQNT5/6NOf0PKfpk1Vq6DFGuY17FKwVcHCV8iFXmQfmPKgtVdqsNYa6W3xXyBgGmcMgNguO0n22t3Iv9y29jz2Ve5CQuGXoLdw45EbUqpbb8RcU1VC6oggDEn0P/4TOZib2/POJO++8Fj+GILLw1elZq524HG40uvAf/2Do1w8kCVdJCa6yMjSJqUqq2GZW0sPpg4K9RUAIlzbjM58Txbl1VFfYQAaNVoUhWhvs7UQEkiSRMf0Z9l04EfvuPRS/9DLpjz7SqvMvv2kIC55fT1KthnOqHmVz1nssO7SMB357gB9yf+C+Efe1LB1jTID+zQidVmJxWnh3y7vM3DYTp8dJsjGZ5097vkWdQ0cy6+1NxMoSGnspPXZ9hzYz0z+8UiAIhN6kQaNX47K7qamwE58W/qaEqqgodN2748jNxbZjB9GnnqoU6OavUdJFISJcRGK3DXhqa/FUKbNeRHFuHfXrW4SHS8ehSUwk87nnAKiYPZuapUtbdX6vHvFEn6jM86lZVcl9Oc/yt8F/Qy2pWXxwMRd9fRFvbHwDq8t63PceCFmW+enAT0z8eiIztszA6XFyWtZpfH7B520SLYsW7ye2QOkMGfLnh6gNerr87w3UsYHTUgIBKKI+JkGpc4mkAl1/usjXWRSCM4uEcGkDPvM5VVQU6ujoIO8mdKgznxMdRR1N9GljSLzmagAKHv4nrtLSVp1/9bTBVBskjLLEnLe3cOcJd/LFBV8wMn0kdredtza9xYXzL+SH3B/abXaLR/awLH8Zf/vxb9zz6z0U1haSGZXJq395lTfGvUGyMbnVj1lptrFl3n4AuuT/Srx5L5nPPSsGKApaRN3MosgRLr73RijPLBLCpQ24isWMokCIjqLgknLPPej798ddVkbBww+3SmDotGrGTumPjExCsZO583fSJ6EPMybM4N9j/01GVAaFtYXct/Q+LllwCTM2zyC/Ov+47NvitDB3x1wmzp/IrYtvZU3hGnQqHTcPvZn5F81nXLdxbY7gvfPaBkwuMFhL6b3va5JuvonYs88+LvsWhD91BbqR4eUCATqLQrAlWtS4tAG/+ZwozG2AcM0NLiq9nqyXX2L/ZZOo/W0ZFbPnkHjl1Baff8rJmaxelo9mdw2Hfshn97A0+vaI56/d/8qYrDHM3DqT97e+z57KPbz2x2u89sdrDE0Zyjk9z+GsHme1KiJSYilh1eFVrChYwdL8pVQ7qgGI1kZzcd+LmZozlazorFb/Durz9fd7iDpkA9nDgB0fEnfGqaTccccxPaYgsojElmi9d0q0Y38uHpsNlU+4lO0BtwvUwZcNwd9BJ8TXCq0RrdANqBKt0EFH37cvqfffT9Ezz1D84ouYRpzYqrTIzbefwL8eXEacFT5/fSP3P38aWq0ao8bILcNuYeqAqSw+sJiF+xeypnANm0o2salkEy+ufZH+Cf3pE9+HXvG9SDQkYtKYMGqM2Nw2imqLKLIot33mfeyuaNgy3S2mG1NypnBRn4uI0kYd8++hoLiWXd8cwIRE1/xfSU2SyXzpReHXImgVkdgSrUlNQR0Xh9tsxrF/v2KxoDGCywqVByCpd7C3KIRLW6hLFQnzufpUC7v/kCBh6hRqly2jZulS8m6+hR5zP2mxV4ler+GiW4bwwysbiav18M5bf3Db3+umJcfqYrm478Vc3PdiSq2l/JD7Awv3LWRz6Wa2l29ne/n2Fu8zJzGH0ZmjOTXrVE5MOxGVdHxEhcfj4f1X15PgkTBaiuhTsoQun34s6tEErcZv+18ROakiSZLQ9e2Ddd167Hv2KMMXk/so0+JLdgrh0llx+sznREeRH7fbQ22l8uYWEZfgIkkSmS88T+6UqTj27SPvppvpPrvlX9wD+iWx/ox0qn4twrPNzG+/53H6qV0brUs2JjM1ZypTc6ZSUFPA9rLt7Kncw/6q/VQ7qrG6rFicFnRqHWmmNOUWlUZmVCbD04aTaEg83i8dgFmztpJQ7kLyuMnZ+THd/vU8+p492+W5BOFN/YiLLMsR0y2p7+0VLrv3KHck91eES+lO4Nyg7g2EcGkTrkIxGfpIaivsyDKoNSpMMWLCbrBRx8fT9Z13yJ08GfvOnRy64w66vv02krZl/jpX/t8Apm8vJ6HIyeo5u+nXN5H01KZTOJnRmWRGZzKu+7jj9RLaxNIV+dSsKkElSfTZ+xX9briY6NNOC+qeBJ2X6Hg9SIq5pq3GiTFCPtv0ffoAYN/jFS4hVqArEr5twDeNV5jP1VFV38NFFRlXJaGOrksWXd96C8lkonbFSg4/+liLO40kSeKmu0ZQpQWTG9751zocTnc77/jYOFBQxYYPt6GSJFKL1zNgeAyJ118f7G0JOjFqrQpTrCJWIqnORd/3COESYjOLhHBpJbLDgdvrkSHM5+rwVd1Hew2bBKGBcdBAurzyb1CrMc+fT+nr/23xuSkJRsZfNwA3MklmN6+8srYdd3psWGxOPnv2N3RoMVkKGZ5xmKznpkdMaF/QftR5uUROnYsv4uLMy8Njs9XNLCrZBe3k49QahHBpJc4SRbRIWi3qhJYPeAt3as3Km1oIl9Aj+owzSH/8MQBK//c/Kr/4osXnnjQ8nczxSlty9D4L783a3C57PBY8bg8z/vkjJpcJldvOUN1Ger/yfIvTYgJBc8REYGeROikJdXw8yDKOffsgsRdIanBUQ/XhYG9PCJfW4ipR0kSatDRxNVeP2kpluKIpTgiXUCTh8stJuvkmAA4//gQ1y5a1+NzLLsuGgXEAWFaW8O2ive2yx7YgyzLvPfkjmlojkuwmx/E7w/73DJIuMmoRBO2Pv0A3gmz/JUlqWOei0SniBaBkRxB3piCESytxeetbxFTohli8EZcoIVxClpQ77yRu4oXgdnPozruw/PFHi8+95bbhmNN1qJDYMz+Xn5YfbMedtpyZz/6Io1gRKd2ql3H6O4+iEqJFcBzxm9CVRY5wAdD1Udqe/Z1FIVSgK4RLK3EV+QpzRX1LfXypoqh48aURqkiSRMbTT2MadQoei4WD115H9eLFLTpXpVJx90MjMceq0SKxZfZufl56oJ133DyzXvgeS56SDso0r+Dc9x9GpRfCWXB8iU6IvFQRgL5PXyA0C3SFcGkl/oiL6ChqgC9VJCIuoY2k09H1jTeIPuMMZJuN/Nv/Tvns2S0616jXcvsjp1AVo0IvS2z7ZA8//bS/nXfcGI/Hwyf/mE3NPkW0pFat58J370ZlEP5BguOPv8YlgkzooF5L9F5valhEXDov/lZokSryI8tyvYiLEC6hjspkossb/yV+0iSQZYqefoail15C9niOem5srJ6/PzGa8jg1GiR2fLmPuZ+13C33WHFUW/jkhncpN2eApCLevouL37kFddSxjwkQCALhEy7WKgeuELcEOJ74WqKdeXl4rNY64SIiLp2PuoiLSBX5sNU68biVFjmf54EgtJE0GtKfepKUu+4EoPy99ym47348DsdRz42O0nHPE6MpTdagQqLsl8O8+t91uN1HFz7HQumO/cy9eTaVWuUDNdqQx+R3b0AjrPwF7Yg+SoNGp3xVRpL1vyYpSemclWXs+/bVpYpqS8BSHtS9CeHSSnxdRVoxp8iPL01kjNGi1og/qc6CJEkk33wzmS88DxoNVQsXknf933CbzUc9N8qo5Z9PjMHeS4l0aLdW8eLDyzh8uKZd9rph7mK+mf471TG9kdxOUvrbuObVa1Cr1e3yfAKBD0mS6nm5RFqdi3KR4NizB3RREOcd/VES3KiL+JZpJa4SYT53JL40kSlWpIk6I3ETJ9LtnbdRRUVhWbuW/ZdcSu2q1Uc9T6NRcff9JxN3agouZGLNbuY8vZpPvtzRYofeo1Fb6+DDO2ezcokHS1QmKmctAy9K5/K7gz8vRRA51M0sipyIC9TrLAqxAt1OJ1ymT5/O6NGjMZlMxMfHt+gcWZZ57LHHyMjIwGg0Mn78eHbv3t22DbhcoFKhSU5u2/lhiG+4ougo6rxEjR5N9zmz0WZm4jx0iIPTplH4zHQ8Fkuz50mSxJVXDebkmwZQoQeDR6L8pwKe/cdv/P57fpsFjMvtYf6HK/nwju+ptmeApEZnz2PCQyM547yhbXpMgaCtxHiNNWsiyMsF6hXohlhLdKcTLg6Hg0mTJnHLLbe0+JwXX3yR1157jbfeeovVq1cTFRXFWWedhc3Wtj9CTXIykkbMp/RhMYuOonDA0L8/PRcsIP7yywGo+Phj9l18MbWr1xz13FHDM7jnhdOQc2LxIBNf5WbjR7t4/p5f+eTLHVgdrhbtobLKznvvruPNm+ZzaIUVjzYGva2crukFXP/eVfTuI1K0go4nOgLdc6FeS7SvsyhEIi6d7tv3ySefBGDmzJktWi/LMq+++iqPPPIIEydOBODDDz8kLS2N+fPnM3ny5FbvQaSJGiI6isIHdXQUGU89ScyECRx+5BGcBw5y8JpriBozhpQ778A4eHCT55oMWm6/cwR/7i7jyznbiT1sJ9YK5T8V8L+fD2FJ0BCdFU3XLjGkZ0TjQcbhcFNZZuXA/ioseTXE17hRSSpUmnhUbgeJ1u2MufuvZJ04qAN/CwJBQyK2xsXXWZSfj8dqRVV/ZlEQ6XTCpbXs37+fwsJCxo8f778vLi6OkSNHsnLlyiaFi91ux26vy2dWVVX5/y2mQjfEnyqKE6micCF6zKn0WvA1xa+8QuXnX1C7fDm1y5cTPW4cSdddi/GEE5oceTGgbxIDHh9DXkE18z/fiWOnGYNHwlDuhnIzRVvMFB1xjsF7Q1JhtJaQWrWZ4deNJfP8u8RoDUHQidQaF01iIurERNzl5dj37sPYOxtG3wGpOcqwxSC9N8NeuBQWFgKQdoTYSEtL8x8LxHPPPeeP7hyJMJ9rSK1ZzCkKR9SxsWQ8/jhJ111H6Rv/w7xgATWLF1OzeDHabt2Im3ghceedh7Z794DiomtmDH+/cwQOh4sV6w6ze3MpFQW1OKudGOweNB4XWreD6NoSTNZiYqsOkOTKo9uUiSRd+7iw7heEDH7b/3IbsixHlJjW9+6Npbwc+57dGAcNhAlPB3tLoSFcHnzwQV544YVm12zfvp3s7OwO2hE89NBD3HPPPf6fq6qq6NpVaQUT5nMNsYhUUVij69qVzOefI+nGGyh79z2qFi3CefAgpa//l9LX/4smLQ3TiBEYhw5B26UL2owM1IlJIHvA4wGXi5NUBQyNP4CjMhfrvi1Y/9gI7jozL8OgQST8fSqx55wjbPsFIUd0vBJxcTk92GqdGKMjR1Tr+/bBsnat0hIdIoSEcLn33nuZNm1as2t69erVpsdO99ajFBUVkZGR4b+/qKiIYcOGNXmeXq9H38QHqDCfq0P2yP6Ii0gVhTf6Xr3IfHY66Y/8k+qffqJy/nws69bjKiqi6rvvqPruu1Y9nq5XL6JPG0PsuediHCo6hQShi1qrwhSrw1LloKbcHlHCRXdkZ1EIEBLCJSUlhZSUlHZ57J49e5Kens7ixYv9QqWqqorVq1e3qjOpPhphPufHWuNE9sgggVG45kYEKpOJuIkTiZs4EY/VinXTZixr12LftQvn4cM4CwpwV1aCWq2E1NVqtKmp6Hr0QNejO7revYkaPRpdly7BfikCQYuJTjRgqXJQXW4jpVtMsLfTYTSaWRQChIRwaQ0HDx6kvLycgwcP4na72bhxIwB9+vQh2mv9nZ2dzXPPPcfFF1+MJEncddddPPPMM/Tt25eePXvy6KOPkpmZyUUXXdTi563vR6EVXUV+fB1FxhgdanWn664XHCMqo5GoU0YSdcrIYG9FIGhXYhL1FOdGYEt0X6Ul2pmfj8diQWUyBXlHnVC4PPbYY8yaNcv/8/DhwwFYsmQJY8eOBWDnzp2Y69mWP/DAA9TW1nLjjTdSWVnJmDFjWLRoEYZWTJP11Hs8UZxbh+goEggEkUCktkRrEhJQJyXhLitTOosGB9+aoNMJl5kzZx7Vw+VIt05Jknjqqad46qmn2vy8zpISANRxcaJ4sB5+8zlRmCsQCMKYSG2JBm9nUVkZ9j17QkK4iNh+C/FNhVaLaEsD/OZzohVaIBCEMf6IS4TZ/kO9Opc9bRyVc5wRwqWFOIsUyyxtqijMrY9IFQkEgkjAJ1yqyyJQuPT1CZfQ6CwSwqWFuL0RF40QLg0Q5nMCgSAS8KXDLdUOPG5PkHfTsfgiLo49odFZJIRLC/HVuGhS26dtu7NSNxlaCBeBQBC+GKO1SCoJZLBUOYO9nQ7F5+XiPHQIT21tkHcjhEuLcRX5Ii6ixqU+dTUuIlUkEAjCF0klYYrRAmCpiqwCXU1CAurkZADs+/YFeTdCuLQYV7FS4yJSRXV4PDLWKtFVJBAIIgNfStyXIo8k9L17A6HhoCuESwtxlZQCoBWpIj/Waod/QKgxRkRcBAJBeOOvczFHVsQF6ncWCeHSKfDU1uKpqgKE+Vx9fPUtplgdKlXkTEsVCASRicmbEo/IiEvf0GmJFsKlBTi99S0Aau9YAUHdm1ekiQQCQSQQ5Z3HFskRl1DoLBLCpQWoY6JJvrVtAxnDGX/ERbRCCwSCCCCSa1x03hoXZ0FB0DuLhHBpAZqUFJKuvz7Y2wg5REeRQCCIJHyfdZEYcWnQWRTkSdFCuAjajEV4uAgEgggikiMuUK9AN8idRUK4CNqMv8ZFpIoEAkEE4Iu4WKscyB75KKvDj1DpLBLCRdBmfKkik0gVCQSCCMAYqwPJ62FVE1nuuVBPuOwVwkXQSRFdRQKBIJJQq1UYoyPTPRdCZ9iiJqjPLui0uN0erNUiVSQQCCILU6wea7WTWrOD5C7B3k3Hou/bl8Trr0Pfty+yLCNJwfHvEsJF0CasVQ6QQaWS/FcgAoFAEO5ExesoOxSZnUXq2FjS7r8/2NsQqSJB26itVKItpjidMjFVIBAIIoBI7ywKBYRwEbSJusJckSYSCASRQ517rhAuwUIIF0Gb8LnmCvM5gUAQSdRFXCIvVRQqCOEiaBOWKtFRJBAIIo9Ids8NFYRwEbSJuoiLEC4CgSByEDUuwUcIF0Gb8M8pihepIoFAEDnURVwcyHLkueeGAkK4CNpEXVeRiLgIBILIwecU7nZ5sFtcQd5NZCKEi6BN1E2GFsJFIBBEDhqtGr1JsUATnUXBQQgXQatxOz3YvHM6RKpIIBBEGv46lwi0/Q8FhHARtBrfm1WlljBECddcgUAQWdSvcxF0PEK4CFqN780aFacP2qwKgUAgCBa+Ohfh5RIchHARtBrRUSQQCCKZqFglVWSpFBGXYCCEi6DV+DqKRGGuQCCIRPwRF1HjEhSEcBG0GjGnSCAQRDK+izZR4xIchHARtBpLpUgVCQSCyEXUuAQXIVwErUZ4uAgEgkhGRFyCixAuglZTaxY1LgKBIHLxRVycdjcOm3DP7WiEcBG0Gt+ARZNIFQkEgghEZ9Cg0asBEXUJBkK4CFqFy+n2z+cQEReBQBCp+E3oRGdRhyOEi6BV+K4u1FqVf16HQCAQRBq+C7daEXHpcIRwEbQKX5ooKk4nXHMFAkHE4u8sqhQRl45GCBdBqxCFuQKBQFDPPVdEXDocIVwErcJfmCuEi0AgiGCEe27wEMJF0CrEnCKBQCAQE6KDiRAuglYhzOcEAoGgLuosinM7HiFcBK3CP2AxXggXgUAQuZj8EReRKupohHARtAqLua6rSCAQCCIVX9TZbnHhcrqDvJvIQggXQavwhUVFca5AIIhk9CYNao3yFSrqXDoWIVwELcZpd+Owel1zRapIIBBEMJIk1aWLqoRw6UiEcBG0GF9hrkanQmdQB3k3AoFAEFyihAldUBDCRdBiLPU6ioRrrkAgiHREZ1FwEMJF0GJER5FAIBDUERUrOouCgRAughZTKzqKBAKBwI8/4iJqXDoUIVwELcZv9y8iLgKBQCC8XIJEpxMu06dPZ/To0ZhMJuLj41t0zrRp05AkqcHt7LPPbt+NhiGWam8rdIyIuAgEAkGUqHEJCppgb6C1OBwOJk2axKhRo3jvvfdafN7ZZ5/NBx984P9ZrxdRg9Ziq3YCYIzRBnknAoFAEHxExCU4dDrh8uSTTwIwc+bMVp2n1+tJT09vhx1FDtYar3CJFhEXgUAg8EVcrDVOPG4PKnWnS2J0SiLmt/zrr7+SmppK//79ueWWWygrK2t2vd1up6qqqsEt0rF5hYtBRFwEAoEAY7QWSSWBDJYqZ7C3EzFIsizLwd5EW5g5cyZ33XUXlZWVR107d+5cTCYTPXv2ZO/evTz88MNER0ezcuVK1OrARmpPPPGEP7pTH7PZTGxs7LFuXyAQCAQCQRsICeHy4IMP8sILLzS7Zvv27WRnZ/t/bo1wOZJ9+/bRu3dvfv75Z8aNGxdwjd1ux26vy1vKsozD4SA5OVmYrwkEAoFAECRCosbl3nvvZdq0ac2u6dWr13F7vl69epGcnMyePXuaFC56vV4U8AoEAoFAEGKEhHBJSUkhJSWlw54vPz+fsrIyMjIyOuw5BQKBQCAQHDudrjj34MGDbNy4kYMHD+J2u9m4cSMbN26kpqbGvyY7O5t58+YBUFNTw/3338+qVavIzc1l8eLFTJw4kT59+nDWWWcF62UIBAKBQCBoAyERcWkNjz32GLNmzfL/PHz4cACWLFnC2LFjAdi5cydmsxkAtVrN5s2bmTVrFpWVlWRmZjJhwgSefvppkQoSCAQCgaCTERLFuQKBQCAQCAQtodOligQCgUAgEEQuQrgIBAKBQCDoNAjhIhAIBAKBoNMghItAIBAIBIJOgxAuAoFAIBAIOg1CuAgEAoFAIOg0COEiEAgEAoGg0yCEi0AgEAgEgk6DEC4CgUAgEAg6DUK4CAQCgUAg6DQI4SIQCAQCgaDT8P/bDMvwZFtrJgAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "myplot = plot(sym.sin(x),p1, p2, p3, p4,(x,0,10),ylim=[-1.5,1.5])\n", "myplot.save(\"myplot.pdf\") # save a hires copy" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0.00083988 x^{5} - 0.032295 x^{4} + 0.40347 x^{3} - 1.9769 x^{2} + 3.2765 x - 0.58015$" ], "text/plain": [ " 5 4 3 2 \n", "0.00083988⋅x - 0.032295⋅x + 0.40347⋅x - 1.9769⋅x + 3.2765⋅x - 0.58015" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle 0.00099728 x^{5} - 0.035755 x^{4} + 0.42765 x^{3} - 2.0063 x^{2} + 3.0268 x + 1.1176 \\cdot 10^{-6}$" ], "text/plain": [ " 5 4 3 2 \n", "0.00099728⋅x - 0.035755⋅x + 0.42765⋅x - 2.0063⋅x + 3.0268⋅x + 1.1176e-6" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle 0.0010604 x^{5} - 0.038374 x^{4} + 0.46432 x^{3} - 2.2454 x^{2} + 3.7863 x - 1.1265$" ], "text/plain": [ " 5 4 3 2 \n", "0.0010604⋅x - 0.038374⋅x + 0.46432⋅x - 2.2454⋅x + 3.7863⋅x - 1.1265" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle 0.0023639 x^{5} - 0.099051 x^{4} + 1.3428 x^{3} - 7.7595 x^{2} + 19.308 x - 16.84$" ], "text/plain": [ " 5 4 3 2 \n", "0.0023639⋅x - 0.099051⋅x + 1.3428⋅x - 7.7595⋅x + 19.308⋅x - 16.84" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# the formulas for the five polynomials approximated to 5 significant digits\n", "for p in [p1,p2,p3,p4]: display(p.evalf(5)) \n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 2 }