Prova1.ipynb

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    "![CC-BY-SA](https://mirrors.creativecommons.org/presskit/buttons/88x31/svg/by-sa.svg)\n",
    "\n",
    "\n",
    "This notebook was created by [Bernardo Freitas Paulo da Costa](http://www.im.ufrj.br/bernardofpc),\n",
    "and is licensed under Creative Commons BY-SA."
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    "Antes de enviar este Teste, verifique que tudo está funcionando como esperado.\n",
    "Por exemplo, **rode o código inteiro, do zero**.\n",
    "Para isso, vá no menu, escolha _Kernel_, depois _Restart & Run All_.\n",
    "\n",
    "Verifique, também, que você respondeu todas as questões:\n",
    "* as questões de código têm `YOUR CODE HERE` (e você pode apagar o `raise NotImplemented` ao incluir sua resposta)\n",
    "* as questões discursivas têm \"YOUR ANSWER HERE\"."
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    "---"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
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   "source": [
    "def veryclose(a, b):\n",
    "    return np.allclose(a, b, rtol=1e-12, atol=1e-12)"
   ]
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   "source": [
    "# Parte 1: Calculando raízes com a segunda derivada\n",
    "\n",
    "Vimos, em aula, que o Método de Newton usa a primeira derivada da função $f$\n",
    "para calcular uma aproximação linear da função, e sucessivamente se aproximar do mínimo.\n",
    "\n",
    "Nesta parte, iremos usar a segunda derivada também."
   ]
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   "source": [
    "## Questão 1: Fórmulas\n",
    "\n",
    "Sejam dados\n",
    "$$\\begin{align*}\n",
    "  f(x_0) & = v_0 \\\\\n",
    " f'(x_0) & = v_1 \\\\\n",
    "f''(x_0) & = v_2\n",
    "\\end{align*}$$\n",
    "\n",
    "Dê, em função de $x_0$, $v_0$, $v_1$ e $v_2$, as raizes da parábola correspondente.\n",
    "Em particular, mostre que as raízes (se existirem) são da forma $x_0 + \\text{passo}$."
   ]
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   "source": [
    "Bom, se $x_0$ está proximo da raiz, então pelo metodo de newtown:\n",
    "<img src=\"newton.png\">\n",
    "sabemos que a reta tangente ao ponto aproxima a função ao valor da sua raiz, logo se existe uma raiz proxima de $x_0$, o passo do metodo de newton nos aproxima de seu valor\n",
    "Logo se a raiz proxima de $x_0$ existir ela é da forma $v_0-v_0/v_1$"
   ]
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   "source": [
    "Qual raiz você escolheria?  Porquê?"
   ]
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    "## Questão 2: O passo\n",
    "\n",
    "Escreva a função `step(v0, v1, v2)` que dá o passo a ser feito.\n",
    "\n",
    "Se a parábola não possuir raiz, use, simplesmente, a regra original do método de Newton."
   ]
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   "source": [
    "def step2(v0, v1, v2):\n",
    "    return v0-((v2/v0)/v1)"
   ]
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    {
     "ename": "AssertionError",
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     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "Input \u001b[1;32mIn [4]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m step2(\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m2\u001b[39m) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m\n",
      "\u001b[1;31mAssertionError\u001b[0m: "
     ]
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   "source": [
    "assert step2(1, 2, 2) == -1"
   ]
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   "source": [
    "assert step2(1, 1, 1) == -1"
   ]
  },
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   "source": [
    "assert np.isclose(step2(-1, 1, 0.2), 0.9160797831)"
   ]
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   "source": [
    "# Um teste mais difícil, não se preocupe muito se não passar\n",
    "assert np.isclose(step2(-1,  1, -0.2), 1.1270166538)\n",
    "assert np.isclose(step2( 1, -1,  0.2), 1.1270166538)"
   ]
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   "source": [
    "Explique porque os passos dos dois `assert`s da última caixa devem ser iguais."
   ]
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    "YOUR ANSWER HERE"
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   "source": [
    "## Questão 3: Newton\n",
    "\n",
    "Dê, abaixo, o método de Newton, e também o método de \"Newton com segunda derivada\",\n",
    "retornando a lista de todos os pontos visitados a partir de `x0`, inclusive.\n",
    "\n",
    "O critério de parada será, para os dois, quando o tamanho do passo, _relativo ao ponto atual_,\n",
    "for menor do que a precisão indicada por `reltol`.\n",
    "(mas agora que você já calculou o passo, use-o, não custa quase nada!)"
   ]
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   "source": [
    "def newton(f, df, x0, maxsteps=100, reltol=1e-12):\n",
    "    l=[x0]\n",
    "    for i in range(maxsteps):\n",
    "        passo = f(x0)/df(x0)\n",
    "        newx= x-passo\n",
    "        if abs((F(newx-x0)/x0)) < reltol:\n",
    "            return l\n",
    "        l.append(newx)\n",
    "        x0=newx\n",
    "    return l\n",
    "\n",
    "def newton2(f, df, ddf, x0, maxsteps=100, reltol=1e-12):\n",
    "    "
   ]
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   "source": [
    "xs_newton = newton(lambda x: np.exp(x) - 10, np.exp, 1)\n",
    "\n",
    "assert len(xs_newton) == 9\n",
    "assert veryclose(np.exp(xs_newton[-1]), 10)"
   ]
  },
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   "source": [
    "xs_newton2 = newton2(lambda x: np.exp(x) - 10, np.exp, np.exp, 1, maxsteps=10)\n",
    "\n",
    "assert len(xs_newton2) == 6\n",
    "assert veryclose(np.exp(xs_newton2[-1]), 10)"
   ]
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   "source": [
    "Faça, agora, o gráfico do erro para cada um dos métodos ao calcular uma raiz de $e^x = 10$:"
   ]
  },
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   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()\n",
    "\n",
    "ax = plt.gca()"
   ]
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   "source": [
    "assert len(ax.lines) == 2\n",
    "assert len(ax.get_legend().texts) == 2\n",
    "assert len(ax.get_title()) >= 10"
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "Este resultado é esperado? Comente"
   ]
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   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
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   "source": [
    "Ambos os métodos fizeram uma iteração que \"não saiu do lugar\".\n",
    "Explique porque eles não pararam na iteração anterior."
   ]
  },
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    "YOUR ANSWER HERE"
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   "source": [
    "## Questão 4: Uma outra função\n",
    "\n",
    "Use ambos os métodos para encontrar uma raiz de $xe^x = 10$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4110dbc8",
   "metadata": {},
   "source": [
    "Dê, abaixo, as funções auxiliares:"
   ]
  },
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     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
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   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a6b83dc",
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   "source": [
    "Agora, calcule os pontos gerados por ambos os métodos, começando a partir de $x_0 = 1$:"
   ]
  },
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   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
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   "cell_type": "markdown",
   "id": "715aa8cb",
   "metadata": {},
   "source": [
    "Faça o gráfico do erro \"em $y$\", ou seja, o quanto a equação está errada (já que não temos a solução analítica)."
   ]
  },
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     "points": 1,
     "schema_version": 3,
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   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()\n",
    "\n",
    "ax = plt.gca()"
   ]
  },
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   "source": [
    "assert len(ax.lines) == 2\n",
    "assert len(ax.get_legend().texts) == 2\n",
    "assert len(ax.get_title()) >= 10"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21eaf901",
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   "source": [
    "Comente, novamente, os resultados, indicando eventuais semelhanças e diferenças com o caso anterior."
   ]
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   "source": [
    "YOUR ANSWER HERE"
   ]
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   "source": [
    "# Parte 2: Calculando integrais\n",
    "\n",
    "Dê, abaixo, os métodos do retângulo, trapézio e ponto médio."
   ]
  },
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     "checksum": "79ad0690fbf4c594bd69e78238b3a099",
     "grade": false,
     "grade_id": "cell-6646cdaab8c2a5db",
     "locked": false,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def rectangle(f, a, b, n=100):\n",
    "    xs, h = np.linspace(a, b, num=n, endpoint=False, retstep = True)\n",
    "    return np.sum(f(xs))*h\n",
    "def trap(f, a, b, n=100):\n",
    "    ints = []\n",
    "    xs = np.linspace(a, b, num=n, endpoint=False)\n",
    "    d = (b-a)/n\n",
    "    ints = (f(xs) + f(xs+d))/2*d\n",
    "    return np.sum(ints)\n",
    "def midpoint(f, a, b, n=100):\n",
    "    l, h = np.linspace(a,b, num=n, endpoint=False, retstep=True)\n",
    "    if n == 1:\n",
    "        h = abs(b-a)\n",
    "    mids = l + h/2\n",
    "    return np.sum(f(mids)*h)\n",
    "\n",
    "methods = [rectangle, trap, midpoint]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "22da916c",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "8b3cc2139caafc65b1d3918af79dd953",
     "grade": true,
     "grade_id": "cell-41405d9df59e0bb4",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "assert not np.isclose(rectangle(np.sin, 0, 1), 1 - np.cos(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c72fdb19",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "18d90554561f57e90235ded379654d4f",
     "grade": true,
     "grade_id": "cell-5c0c17d184701790",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "assert np.isclose(trap(np.sin, 0, 1), 1 - np.cos(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bf70bfc5",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "f45d7a0674088012bdc68277d16d5922",
     "grade": true,
     "grade_id": "cell-c47c5abdc253b47f",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "assert np.isclose(midpoint(np.sin, 0, 1), 1 - np.cos(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c3755c5",
   "metadata": {},
   "source": [
    "## Questão 5: Integrando o cosseno\n",
    "\n",
    "Faça o gráfico do erro de integração da função cosseno, no intervalo $[0, 2\\pi]$,\n",
    "para $n$ indo de $1$ até $30$,\n",
    "para cada um dos métodos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5f7001d8",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "73bc54602b9f541e043a473774ec57f8",
     "grade": true,
     "grade_id": "cell-b7c228dcf602cf4c",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ns = range(1,30+1)\n",
    "def f(x):\n",
    "    return np.cos(x)\n",
    "def F(x):\n",
    "    return -np.sin(x)\n",
    "ans=F(2*np.pi)-F(0)\n",
    "for m in methods:\n",
    "    valores = np.array([m(f,0,2*np.pi,n) for n in ns])\n",
    "    plt.semilogy(ns,abs(ans-valores),label=m.__name__)\n",
    "plt.title(\"grafico de erro dos metodos de integração \")\n",
    "plt.legend()\n",
    "plt.xlabel('variação do n')\n",
    "ax = plt.gca()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c7cc1c2d",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "fbfa4ce5924a34026d1dcf41fd59daa1",
     "grade": true,
     "grade_id": "cell-8ddf9cb69ab238cd",
     "locked": true,
     "points": 2,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "assert len(ax.lines) == 3\n",
    "assert len(ax.get_legend().texts) == 3\n",
    "assert len(ax.get_title()) >= 10\n",
    "assert len(ax.get_xlabel()) > 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6162dda4",
   "metadata": {},
   "source": [
    "O que você percebe neste gráfico?  Como você explica?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ada677bf",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "2ffa96d83a3309297169eff5686f1948",
     "grade": true,
     "grade_id": "cell-75138020e41412f4",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "Temos um erro bem pequeno e quase constante para n>2, para todas as 3 formas de integração"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "690110ef",
   "metadata": {},
   "source": [
    "Repita para o intervalo $[0, \\pi]$.\n",
    "Agora, faça cada método em uma figura separada:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "271fe81c",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "a004261fa47a657c7c84a6fbb8ab98ab",
     "grade": true,
     "grade_id": "cell-d394353c80c0ec61",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uJ4SMPQqd+8fecC8hhBBCCCGkbFm1ahXmz5+PJUuWOH0ohBBSslDsIYQQQgghhJQNK1euxJYtW7B+/XqnD4UQQkoWij2EEEIIIYQQQgghowiKPYQQQgghhBBCCCGjCIo9hBBCCCGEEEIIIaMIij2EEELKFoZ0EkIIIYQQcjIUewghhJQtDOkkhBBCCCHkZCj2EEIIIYQQQgghhIwiKPYQQgghhBBCCCGEjCIo9hBCCCGEEEIIIYSMIij2KKz62y5c+aMX8ZfNrU4fCiGEEEIIKcDbh7px+683YN+JfqcPhRBCSJF4bW8HVv76DRzpGnT6UEoeij0KhzoHsPlwDzYf7nb6UAghhBBCSAF+u/4AVr/disc2Hnb6UEiRYRMjIWOXB57fhSffPoqnaNIoCMUehTmNlQCAba29Dh8JIYQQQggpRP9QHADQF4k7fCSk2LCJkZCxy9ajqev1nsGYw0dS+lDsUZjTVAUA2N7W4/CREEIIIYSQQgxGEwCAfuW/hBBCRjed/VG09kQAAH1DFPoLQbFHYW5TytlzsGOQbxxCCCGEkBJnMJYSeQaiXLcRQshYYGtr2phBV2dhRo3YY3Z2tzbsw/hKPwBgRxtHuQghhBBCShnV2TNEZw8hhIwFth1NX6f3UegvyKgRe6yY3Z2juHu2M7eHEEIIIaSkobOHEELGFluP0tmjh1Ej9liBCGmm2EMIIYQQUtoIZ88AM3sIIWRMkFmmxOiVwlDsyYDOHkIIIYSQ8oDOHkIIGTvEE0lsz4hbobOnMBR7MpirNnL1QpZlh4+GEEIIIYTkQog9zOwhhJDRz772fkTjSfXvdPYUhmJPBrMaK+CSgI7+KI73DTl9OIQQQgghJAcDUTp7CCFkrLBFCWeuDnoBUOzRAsWeDAJeN6bWhwFwlIsQQgghpFRJJGV1h7efmT2EEDLq2aaEM585pRZASuzhNE5+KPaMgLk9hBBCCCGlTSSWFnii8SRiiWSeexNCCCl3RBPXmVPrAKRE/0iM5/58UOwZgRB7tlHsIYQQQggpSUY2cLGRixBCRjfi+nzxlFpIUuo2jnLlh2LPCObS2UMIIYQQUtJkOnsA5vaMNVatWoX58+djyZIlTh8KIaQIdA1EcbQ7AgCY11yJsM8DgGJPISj2jGB2Y0rs2dHWi0SSM4CEEEIIIaXGSCcPG7nGFitXrsSWLVuwfv16pw+FEFIEtirhzJPqgqgMeFHhV8Qe1q/nhWLPCKbUhxHwujAUT+JAx4DTh0MIISQP3N0lZGwySGcPIYSMGba1pvJ65jZVAQAqAimxp3co5tgxlQMUe0bgdkmYNV6McvU4fDSEEELywd1dQsYmg3T2EELImEGEM89rVsQexdnDc39+KPZkgSHNhBBCCCGly2BsuJOHzh5CCBm9iOvyecp1ujrGRWdPXij2ZIEhzYQQQgghpctgdHjdbj/buAghZFQSTyTV6/K5I5w9zOzJD8WeLMyh2EMIIYQQUrKclNnDRhZCCLGE57cfw00PvoZDnaWRX7uvfQBD8SSCXjem1IUAZGb28NyfD4o9WRBiz772/pOqPQkhhBBCiLMMjhjborOHEEKs4YHnd+OFHcfxl82tTh8KgHRez5ymSrhcEoDMzB6KPfmg2JOFcRV+1IV9SMrAzrY+pw+HEEIIIYRkQGcPIYRYTyIpY/PhbgBAe3/U4aNJIZq4RDgzwDEurVDsyYIkSZjdWAEg/eYihBBCCCGlwcDINi46ewghxDS7j/ep59P2viGHjybF1qNKOHNzpXobx7i0QbEnB3ObUsohc3sIIYQQQkqLk5w9bOMihBDTbDrYpf5/R6k4e47S2WMUij05UEOa2yj2EEIIIYSUEhFl59nnTi1l+4fo7CGElAdPvHUEV/3oJew70e/0oZzEpkNd6v+f6HNe7OkeiOFIdwRA+vocACoVZ08/hf68UOzJARu5CCGEEEJKEzHGVV/hU/7OBT8hpDx45LWDePtwN55+pzQCkDN561C3+v/t/c6PcW1VIlUm1ARRFfCqt4d9dPZogWJPDmY3psSeY71D6CwRCxshhBBCCEmPcQmxh5k9hJBy4Uj3IADgcNegw0cynKF4Qm2+AoD2EnD2ZBvhApjZoxWKPTmo8HswqS4IANhGdw8hhBBCSMkQUcSehgo/ALZxEULKA1mWcUQReQ51lpbYs/VoL2IJGWGfG0DKQTnosJCeLZwZYGaPVij25GFOowhpZiMXIYQQQkipoI5xhVNiD509hJByoGsghkgsCQA42DHg8NEMR4QzL5lWp+ahOT3Kla12HcjI7KHQnxeKPXmYy5BmQgghhJCSY1B19qTGuAaZ2UMIKQMyR7cOdQ5ClmUHj2Y4Quw5dWKNOiLr5ChXIimr1+Fzm4Y7e8J+EdCcQCJZOq9hqUGxJw+zlTcVx7gIIYQQQkoHMVogxrjo7CGElANHlWYpICVal0q9OZBu4jptUg3qwimxx8nj29fej0gsiaDXjSn14WFfE2NcABu58kGxJw9CQdzR2oskFUNCCCGEjDFKadc5k5EBzczsGVusWrUK8+fPx5IlS5w+FEJ0cWREKHOp5Pb0RGLYfTxVBb9oYjXqFSH9RJ9zY1wiLHp2UyXcLmnY1/weF7zu1G3M7ckNxZ48TGsIw+uW0B9NlFxaOiGEEEKInfxp42Gc8Z9r8MqedqcP5SQG1ep1JaA5luDG3Bhi5cqV2LJlC9avX+/0oRCiC9HEJSgVsWezUrk+sTaI+go/GhRnT7uDzp5tSjjz/BHhzAAgSZLq7mFuT24o9uTB63ZhxrgKAMB2jnIRQgghZAzx7NZj6ByI4bltx5w+lJNIj3GlLkhkGYjEOcpFCCltjnRFhv39UGdphDRvVEa4Tp1YAwAlMcYlnD1zm6qyfl3k9rB+PTcUewrAkGZCCCGEjEU6B1KL/FJ0N4sxrrqwD5Li7u8fothDCCltjirn0+kNqQyagyUi9rx1MOXsOXVSNQCUxBiXyM0dGc4sYP16YSj2FGCOoiQypJkQQgghY4mugRgA4HCJjBkIYokk4srIVsjnQcjrBgAMMKSTEKKDtw514T8efwfdg7GiPafI7DlrWh2A0hnj2jTC2eN0G1f3YEzdaJjbnN3ZI+rX++jsyQnFngKozp7WHoePhBBCCCGkeJSqs2cgo3kr6HUjpOY20NlDCNHO9/+6A7/4+z48/U5rUZ4vnkiirTfllFkytXTEnmM9ERztjsAlAQsmKM4eh8e4tikjXBNqgqgOerPeR3X2UOzJyagRe+xK5Z+jiD17jvcjGk9a+tiEEEIIIaVKp7LIP947hEisdIQUcSxulwSvW0LYR2cPIUQ/u4/3AQB6izQGdKx3CImkDK9bwumTawCkMnucbj3cpIQzzxpfqebgiDGudofGuMRUzbws4cyCMMe4CjJqxB67UvmbqwOoDHgQT8rqCYEQQgghZDQTjSfRn+Ggae2O5Ll3cRHhzCGvG5IkIeRTnD3R0hGkCCGlzVA8oY5UDRZJKD6qNHE1VgUwsTYESQIisaSjjVdAapwNSFWuC4Sz50R/1BExqlA4M8AxLi2MGrHHLiRJwpxGMcrF3B5CCCGEjH66BoZffJTSKJcY4woojp6wX3H2cMFPCNHIwY4BKNFfauC73RxWmrhaaoLweVxoqgoAcH6Ua+PBLgDAqZNq1NtEZs9I4b9YbFWdPbnFHo5xFYZijwbEKBdDmgkhhBAyFugYKfaUQK6EQFyYBZVgZjp7CCF62XO8X/3/gSKdO0QTV0t1SuSZWBsE4Gz9uizLeEsZ4xLhzEDqvCrOscUe5UokZTUvd26eMa4KfyrLh2JPbij2aIAhzYQQUprYlddGyFins394O82hEnL2iMyekM897L/M7CFWI8vySS63YpBIyui38ALWqZ+jlNnXnhZ7ipVJJsbGWmpSIs/E2hAA4GCHc+fX/e0D6B6MwedxqQYHgXD3nChyI9f+9n5EYkkEvC5MrQ/nvJ9wdTKzJzcUezQg6td3tDGzhxBCSgm78toIGeuMvDA8UkJijzrGNdLZwzYuYjFf//M7OOM/16iZJsXi7tVbseg//orNh7stebz/fGIrzvjPNXjzQKcljzca2Hui+M4eMcbVrIo9zjt7ROX6/OYq+DzDpQER0lzsRq6tR1PTNHMaK+F2STnvx8yewlDs0YDI7DncNYieSKzAvQkhhBBCypvOgeHrnVIe41Ize+jsIRbz2r5OJGVg3e72oj1nIinjD28cQiIp44Udxy15zBd3HkdSBjYf4ZSCIFPsGSzWGJcS0DyhZuQYl3Pn100HU4LiaRl5PQIR0lzsMa5trYXDmYGMMS46e3JCsUcD1SEvmpXZyh3M7SGEEELIKKdTcfZMa0hZ6EspoFk056THuOjsIfbQ1pNyYuwsort/8+FudCli665j5p83lkiqwkY3R7lUhok9RR7jaq4ePsZVCs6ezCYugSr2OOTsyVe7DgAVdPYUhGKPRhjSTAghhJCxQqeyuD+lJbWzerR7EMlk8et3szE4so2LmT3EBiKxhDq+sut48cSeF3em3TxWiD372wcQV/7tdg1wQgFInSvaetJulWI4ewajCdUxKTJ7Jqliz6Aj9eaxRBLvHFHCmbM5e5QxrvYiZ/aotet5mrgAoEJk9lDsyQnFHo3MaWL9OiGEEELGBuKiZG5TKjMhlpBxvMhW/lwMxpIAMtq4/GzjItZzLEMM2H2sr2gX42t3nkg/7/E+0yJrpmDUPUixBwD2nRjupClGZs8RZYQr7HOjSnGkNFUH4JKAoXiy6CHIALCjrReRWBKVfg+mZQlCTjt7infu74nEVCfpPK1jXBR7ckKxRyMit4diDyGEEEJGOyKguaHCj6aq1Ci7k7kSmYwc41KdPVzwEwsR+SpA6mKyVRnpspO+oTje2J8KUZaklAhxpNvcv7tdx9LXLl0UewCkR7hE+G8x2riOKuHMLTVBSFLqeX0el3p+PejAKJeoXF80qRquLEHIoo2rmM6ebcoIV0t1ANUhb977qmNczOzJCcUejaTHuHocsdkRQgghhBSLDkXsqQn5MEEJES2V3J6RAc1pZw8X/MQ6Roo7VoxUFeKV3e2IJ2VMqQ9h5rgKS553mLOHY1wA0rXr4jUuirNH5PUoI1yCiRmjXMVm08EuAMCpE2uyfl0d4ypiZo8IZ55XYIQLACqUc380kcRQnM7ObFDs0cjM8RVwuyT0RIqj7BNCCCGEOIXI9qgNeTFRuTgplUYuVew5KbOHi31iHa3dxRd7RF7P0lkNmDneIrEnI2+oa5ABzQCw53hK7JmvZJIVI6D5yIgmLoGT9eubhLMnl9jjQBtXOq8nfzgzkD73A6UV0P/MljZc98A67MsIAXcKij0a8XvcaiMFQ5oJIYQQMpoRbVy1YZ8aJnq4y7nGmEyEqKM6e9Q2Ljp7iHWIzV0x3bKzKGJPKq9n6axxlog9yaQ87PsZ0JxCOHvmK+6RYgQ0j2ziEjhVvz4YTWBHW+qaNlvtOpAe4+rojxZtskU0cRWqXQcAj9ulfg6UyihXTySGL/zxLby+vxNPv9Pq9OFQ7NGDGOVi/TohhBBCRiuJpKwGudZmjHEd6SoNZ3NkpLPHT2cPsR5Ru75QcT3Y7ew52DGAPSf64XZJOHdGvSViz+GuQUSUQHOAmT0CkdkjRoWiiSTiiWS+bzHN0e50Zk8mE+ucGeN650g3EkkZ4yv9aKoOZL1PneLsiSdl9AzaL6YkkrKaj6tljAtI5/b0DpXGe3vV33apLX6lUBpAsUcHcxnSTAghhJBRTvdgDGITtybkxYQSG+PK5eyh2EOsRFycXzCzHkCqkctOXtqVcvWcPqkGVQGvKvbsNNEEJka4xL/haDxZlDDiUqZ7MKZejM/LGBWye5RLZJ61VJfGGNdGkdeTw9UDpCZbKpVcnBNFaOQ60DGAwVgCfo8LU+tDmr5HHF8pjHEd7BjAL17ap/59sARy5Cj26CAd0kyxhxBCCCGjEzHCVen3wOt2DQtoLoWSCjFycbKzx/mFNRk9tCliz/kzGgCkQmo7bAyqTef1jAMAzBhXAUlKiRNGa7l3taXEnlMnVcOjzKON9VEukaMyrtKPurBPHdOzU+yRZXlYG1cmk5SA5sOdxT2/iiauUydW571fMRu5RF7PnKZKeNzaZIqwIvb0lYCz59t/2YZohkOMzp4yQ8wO7jreZ7vVjxBCCCHECboy8noAoEXJmOgbihfFyl+IyMg2LsXZE0vIiMa5PiPmSSRltPWmnAzTx1Wozhi7RrkSSRkvibye2SlxKeB1q0KA0ecV3zdzfCVqlBprK0Katx7twbee2oa/bD5adllZYoRrWkMYkiSp5xE7c3u6BmKqmDRyZKqpOgCXBAzFkzjeW7wg5E2HugDkd/YAGY1cNoc0H+0exF82pzJu5jYVDmcWiEauXocze9440Ikn3joKSQLef/oEAMXJgiqEx+kDKCcm1gYR8rkxEE1gX3s/Zo7X/kYkhBBCCCkHOvrTTVxAykFTH/ahvT+Kw12DqFZud4qBEc6eUEYjy0A0Dp/H58hxkeKxatUqrFq1ComEPRdT7X1DSCRluCSgocKHmeMrcLhrELuO9eGsaXWWP99bh7rQE4mjKuDBoglpp8XM8RU40DGAXcf7cO6Met2Pu/NYr/o41UEvTvRFLXH2fP+v2/HM1mMAAJ/bhXNn1OPd8xvx7nnjTwogLjVUsac+VbwT9HnQH03Y6uwRTVwNFT4EvO5hX/O6XWiuDuJw1yAOdg5ifFX2/Bwr6RqIYn97amxs0YSavPcVuT1W16/Lsox3jvTgma1teGZrGzYf7lG/lqsdLBsis6fPQdFRlmV844ktAIDrzpiIRZNq8H9vHi4JtynFHh24XBJmNVZi08EubGvtpdhDCCGEkFGHGOOqCaVFkwm1QVXsEXXFTjE4wtnjdbvg87gQjSfRH02gRlvUAyljVq5ciZUrV6KnpwfV1fnHUIwg8nrGVfrhcbswa3wFXthxXBVPrEa0cJ0/s2HY+MrM8RV4btsx7GrT/7yynG7imqWIPYA1Y1xtPSmXR03Ii66BGF7YcRwv7DiOrzwGnNJShXfPa8Sl8xtxSksVJEky/XxWooo944TYk3q97cz8EuH2uYSwCbUpsedQ5wAWT6m17TgEonJ9WkO4oHjfYOEY11A8gZd3t+OZrW14dusx9d8ZAEgScMbkWiw/pRHXLZ6o+THTmT3OCSur327FGwe6EPS68S/L56guvVLIkaPYo5P5zVXYdLALG/Z34spFLU4fDiGEEEKIpahjXBkXARNqgnjrUDcOFzlENBsj27gAIOxzIxpPYqDMRkpIaSJq15uUi3MrmrHyMTKvR6A+73H9z3u8bwg9kThcUuqiXoi33RaMcYnsogdvXoKqgAdrthzDM1vb8MaBTrxzpAfvHOnBD57diebqAJaf0oQ7l89Rs1WcRtSuT1WcPSFv6rgiNl6YH1WcPS012V07E2uDeG1v8Rq5NinhzIsK5PUAQH1YGeMyEdC861gvvv/XHVi74/iwHJug142lsxrw7vmNeNfc8WhQRsb0oGb2ODTGNRRP4Ft/2QoAuO3C6WisCqhuU45xlSEXzm7Ab187gOe2HcNXr5xfcmo1IYQQ/ciyzPM5IQqdys6/yOwB0qGiolHGScRuqbhIA1K5PZ0DsZIIxCTlT6viOGiqSl18zmq0T+zpjcTwxoEuAMDSWQ3DvmZGZBLhzJPrQgh43ahRnD3dFtSvC/dfXciHqQ1hzBxfiU9eNAMn+obwt20p4WftjhM42h3BL9ftw4IJ1brcGnYhyzL2Hk+JPdMVZ0/AJwLe7Tt3iPNmLmePyGYqltjzlsjr0TAuZcUY173P7MRTSh5PY5Ufl8xrxKXzGnHujPqTxtr0kq5ed0bseWjdPhzsGERjlR8fXzYdABDyl05DJMUenSydNQ4+twv72wew+3gfR7kIIaSM+cpjm/HXLa24+5qFeNfcxqI975otbfj5i3twz/WnqcGfhJQKnf3C2ZMxxqW8T8U4glPIsqyOcQV86XEXtZGLzh5iAcLZIy7OZ45LrfePdkfQNxRXQ2Gt4OXd7UgkZUxrCGNS3fAZRCH2tPUMoScSQ1VAe16WcAOJxxDjOmbHuCKxhHoRm3mOAICGCj8+cOYkfODMSYjEEvjnR97E0++0obXbeZEYSAkWvUNxSFJKBAOAkAhotjGzRzRx5fq8L2b9uizL2HhQaeKapMHZo45xGXf2iHygb75/IW48a5Klm2sVDjp7Ovqj+NFzuwAAn79sjloWoDp7bHxPaYVtXDoJ+z04RwlIE8FkhBBCypOeSAxtPUPYetSeHIZs9A3F8a9/fAuv7u3AHzccKtrzEqKVzmxjXOJixGFnz1A8CdFOLBbWmf9PZw+xAuHsaVTCcqtDXnXEZLfF7h6R1zPS1QMAVQEvGhV3kV53j7j/DEXsqQmmLtq7TDp7hFjkdkmoDOQWvQJetyo0FbNlKh+idr2lOqg6SoJFGLk5Ipw9Oce4iufsOdodwYm+IbhdEk5pKSz2NKhtXMadPULEOmNKjeUuavEe7HcgDPmHz+5EbySOec1VuPaMtHNN5MmVQkAzxR4DXDJ3PADgOYo9hBBS1sxtSgXNbmstntjzi5f2qnkH24v4vIRoRYxx1WRx9hwu0phBLjIvyAKeLM6eElhck/JHiD3NGTXZsxThYqflYk/2vB6B0VGunW0inDnlSqoOpi6Ku006e9QA96AXLlf+C/dxilBw3Obabq3syahdFwSL4exR3k8tBZw9hzsHkUzKth0HkM7rmdNYqWmESoxxdRgc4+obiqufKXY4mcM+Z6rX9xzvw69e2Q8A+PIV8+DO+LcgnD0DQ85vPlDsMcAl81Jiz+v7O1SrMyGEkPJjblNqEby9tafAPa2hayCKn67do/59W5GelxA9iIDmuozMHnExcqJvSA1IdgJxQeZzu4a1FqnOnhJYXJPyR4xxNWbUYNsR0nygfQD72gfgcUk4Z3r2Snch1uh29owY4xLibZfJgGZ1zDPsK3BPYFxl6vUrNWfP1Ib0uFzQ5syeRFJW308tOTJ7mqsDcLskRBNJ24Ux0cR16qQaTfcXY1wdA1EkDAhRYoOgJuRFpY4xRK04Vb1+91PbEE/KuGTueJw/c7grT3weDcQSkGV7xbtCUOwxwMTaEOY2VSIpA8/voLuHEELKlbnNqUX07uP9GIrbf5H4k7V70DsUx6S61IJv74l+Ry+cCclGR79w9qQX5tVBr7pbecTBUS5xQZbZxAWk2rhSX6ezh5hDluWszh47xJ4Xd6VcPWdMrs15ITzDwPN2D8RUgWWGEkQsMnvMBjSrAe4FKruBVHU9UDpij1q73lCh3ma3s+dYbwSJpAyPS1Jfj5F43C40KcKi3bk9wtlzmoa8HiAVwg0Aspx2delB/Dxiw8BqKh3I7Hl5dzvWbGmD2yXhi5fPO+nr4vMpkZQRTSSLdlzZoNhjkHcpo1zPcpSLEELKlqaqAKqDXiSSsm2VuoJjvRH84u97AQBfu/IU1Ia8SMppqz0hpYAsyxnV6+mde0mSSiKkWa1dHzF+INpP6OwhZumJxNUL/6YsY1y7jlk3fvvijtx5PYKZ4/SLPbuOp46xuTqgikiijctsQHNHlvNDLkpX7Ek7e9I12faIBUIcb6wKDBv1GUk6pNk+MT2ZlPH24ZSzZ5GGJi4gJUQJYc/IKJf4eUTjmNUIZ09/kZw9yaSM/1q9BQDwwbMmqyJwJqGMzQin69cp9hjkknmp1pYXdhxHzGHFjhBCiDEkScIcdZTL3vyc+/+2G5FYEqdNqsEl88areUFbOcpFSoi+oTjiilV/5MWcCGk+3GV/Y0wuxEU4nT3ELoSrpybkHZZpIi7qDnQMWOLIjCeS+PtuReyZnT2vB0jXvh/s1P68QhjKvBAVY1xmM3u6srT15UKIPf3RRNEuxnORTMrY136ysydgs7PnSIEmLoFoYrNT7Nlzog99Q3EEvW5VvNSCGOk9YWDEzG5nT9hf3Or1/3vzMDYf7kGl34PPvntW1vt43S543Slhz+n6dYo9BjltUg3qwz70RuJYv7fD6cMhhBBikHmK2GNnSPOhzgH85tUDAIAvLJ8DSZLUETKGNJNSolMZ4Qp4XScJKqUQ0qyOcY1w9gR9zjWykNGFyFdpqhrenDSu0o/KgAdJGapoYIZNh7rRG4mjOujFwgm5R2rqwz7UhLyQZWD3cW3uHrWJa1yG2KM4e3qH4qY2qlVnj4bMnrDPrf5bNSIUWElbbwSRWBJulzRMeAjZnNkjnD0tOZq4BMWoX9+kVK4vmFA1LPOsEPUmGrmEeDXRJmePOsY1FLc9H2cwmsB3n94OALj94pnq65INNbeHYk954nZJuFgZ5WIFOyGElC9zmxWHzVH7HDY/fHYnookkzptRj/OUIL+5qshEZw8pHTrzjGiIJhkn69cHC2X2cIyLmKS1O/X+zhzhAlJOULWRy4LxW9HCdcHMhrzjPZIk6R7lEo1hwhUEAFXBdMZOj4ncHjEGVhcunNkjSVLJjHKJEa5JtUF4M4QOcS6xKz9PNHE1F3D2CDHkYId959dNh7oAAKdqHOESNFQYb+RKiz32OHvEGJcs2y+sPPzyPrT2RDChJoh/On9q3vumxwMp9pQtooL92W1tjidtE0IIMYbdY1x7jvfhj28cBgD8y/I56u1q7ftROntI6aDWKmcRe8Ri3cmA5oKZPXT2EJO0dqdEiZHOHsDakOYXdxbO6xEI0Ubr86pjXBnOHrdLQqVyYdxlQuwRF/zZzhHZKDWxJ7N2HUifS+wSCg6rzp5CYo/9zp43DnQC0N7EJRBjXO2mxrjscfYEvW4IrdTuUUHx+v3T+VML1tYLEdHpzySKPSZYOnscfG4X9rcPYPdx83ZOQgghxWdOY0rsOdY7ZGghU4j/fmYnEkkZ7543HmdMrlVvn91YCUkC2vujji+CCRF05WnaUce4SrqNi84eYo7WnuzOHiBD7NE4TpWL7sEYNiqtSBdoEHtm6HD2DETjqptiZHhsjQWNXCLAvU6r2KOMuthdKV6IdO36CLHHZgeGOsaV5f2UycTa9Pk1aaDivBD9Q3FsVTaXzpxaW+Dew6kPp36HJ3Q6e/qG4mp72wSbnD2SJBUtt0eMOTdXF/5Z6OwZBVT4PTh7eh0A4NmtbQ4fDSGEECOE/R5MqU/tOFnt7tlypAePbzoCALjj0jnDvhb0uTGtPrXo5CgXKRXErn22PA6xWD/alaoSdoLBXM4eX3EbWcjoRQQ0Z3P2zBqf2hzYZXKM6+Xd7UgkZUwfF9bkeNDjKNqjbEDXhX0nZYrUBM2HNKczewqPcQGl5+yZPkLsUS/KbR7jKuTsaVLaumIJGcdseK02HexCIimjpTqgSazIRB3j0pnZI1w9tSEvKhRBxg6KVb+eHnMu/N4PeZnZMypIj3Ixt4cQQsoVkZ+z1WKx5541qSC/Kxc1Y35L1UlfFyNkHOUipUJXnsXs+MoAPC4J8aSMY73O1K+LMa7QSGePn84eYg3i4rwxj7Nn74l+xE2EHIu8nmWzcrdwZTJLcaDuPdFfMFw52wiXQDh7ugb1Z68IuvqF+688x7hGOnvUNi4bzh2D0YQqoLcUEFg8bhealfecHaNcG/anRpDOmKLP1QMAdYqzp71f3+/wUIe94cwCkdvTZ7ezR0c4ebBEGiIp9phEVLBv2N+pLpAIIYSUF3OU/JztFjps3jjQiWe2HoPbJeGOS2dnvY+a28NGLlIidA7kvpBzuyR1tMWp3B6xcB6ZlxBiGxexiDaljas5i9gzoSaIgNeFaCKJgyZa6fTk9QCpEaCQz414Usb+9vxCwM5jqc+TGVmqtauVkOYug86eaDypjsqUk9iTSMo40JF63UZm9tjZmnRUCfsO+9yoChZ2tkyqta9+fYOSN3OmAbGnvkJk9hhz9tgVziyo8Nsv9siynPfzcSR2O8a0QrHHJJPqQpjTWIlEUsbz2487fTiEEEIMYEf9+veUes5rz5iA6Vl2WAGo9esc4yKlQr42LiCd22PHxYgWBqMpV8NJmT1+tnER80RiCfWCLtsYl8slqfk5O9uMfV7sb+/HgY4BeN0Szpler+l7JEnSnNsjvj7LBrFHbGy7pOHtXvkohcyew52DiCVk+Dyukxw2YiTUjjauI13pJi5Jyt24JrArpDmZlPGG4uxZPKVO9/eLMa52nZk9djdxCcJFGOPqicTV8eUaDWNcwRLJkaPYYwGXzBMV7MztIYSQckTUr29v7bUki+Tvu05g3e52+NwufOaSWbmfVxGZdh7rMzUSQIhVdBbI45hQ62xI82AstZgPeUcGNJdGPgIpb4SrJ+B1qcLISMyGNK9VXD1nTK5VL1K1MEvN7ckvMqljXFnEHrMBzUIIqw5689bFZ1IKzp697akRril1IbhGHHfIxovyI93amrgEdtWv7zreh55IHEGvG/OUTSY9iDGu7sEYonHta5W02GPvGFdlEca4OhWhK+xzF2ziSt2vND6TKPZYgBB7XthxvOAcLSGEkNJjcl0IAa8LQ/Ek9reba1eUZRnfVVw9Hzx7ct5FzqTaEEI+N6LxJPaZfF5CrEC0jeSqVZ4oGrkcc/Zkb+PKtMw7FR5Nyp/McOZcToyZOpqxsvHiDiWvZ7a2vB7BDA0hzanPkpQrJKvYIwKaDYo9+QLccyHEnhN9Q7a0TGlhryLMjRzhAjIye2IJyLK1x6e1iUugOnu6rHX2vL4v5eo5bVINPG79l/81Qa9ab96pI7ZE/ByjYYxL/Ny5PhtHkm7jYmZP2XPapFrUhX3ojcSxfl+H04dDCCFEJ26XpFawmx3lenbrMWw82IWA14XbL56R974ul6SGNG9lSDMpAboKjHGJHWqnMntE/sHIndVMh4TTGQmCroEofv7iHvREjDcfkeLSqjh7stWuC2Y1Ghd7YokkXt7dDkB7Xo9Ai6Nof3s/EkkZYZ87a+ZQtQhoNpgzWuj8kA2R9xJLyKYq380gBLBsYk9m2HskZu2m/dEubU1cgvQYl7Xn1w3qCJf+vB4gtVZRQ5p15PYUy9lT4U+9r4sh9tRpFDrFhkQ/nT3lj9sl4eI5SivXVrZyEUJIOaKGJR81np+TTMr43l9Trp5/On8axlcW3s2b28TcHlI6iDGNulyZPQ6PcQlL/Mg2Lr/Hpe48D5RI/fpdj2/BN57cil+9st/pQyEayVe7LsisQdfrBNl0sAu9Q3HUhrw4paVa1/fOynjeXA6ZzBGubM6kGpHZY9TZY0Ds8Xvc6viYU7k9e5QmrnzOHsB6oViMcWUT3rIxsS4lihzpGrTUofiGEs68eKoxsQcA6sMit0fb77A3ElOzoSbY7uxJ/Q7tzOwRrletrra0s4diz6jg3coo13OsYCeEkLJkjgUhzU+8fRTbWntR6ffgtmXTNX3P3KZ0XhAhThKJJdSLnZpcmT0ZY1xWjzxoQYSoBkc4eyRJUjMSnN5JBVLH+fQ7rQDSu/uk9BG16015arKn1IfhcUkYiCZwpFvf71bk9Zw/s0Fz5o1gcl0IPrcLkVgyp9i6UxF7sjVxAekRlG7DAc2ijUhbOLNAhDQf63FG7NmXo3YdSG3a+z2pS2Kra7KFA3KCRmdPU1UAHpeEWELGsV5rzhsn+obU2vkzJpkQe3Q2con3aG3Iq45Z2UUxqtfT5QXa3vtBNbOHY1yjggtmNcDrlrD3RD92GwxsI4QQoo9Vq1Zh/vz5WLJkienHSjdjGRddHnntAADglqXTNM91z+UYFykRxGLW45JQmWNxLsYR+qMJR0Yy1DEu38kBmSFld7e/BJw9z28/ropOejIuiLOIgOamKn/O+3jdLlU00DPKJcsy/qoIgMtm6cvrAQCP24WpDSnnR65RrnQTV/YQ3mqzzp5+faMsAjWkua/4wmc0nlTbraZnEXuA9MiNlY1csiwPa+PSgtslqedYq0a5RAvX7MYKdYzPCPWKYKe1ketQR3FGuID0GFevjc4eNa9Ka2aPl21co4rKgFetT3yWrVyEEFIUVq5ciS1btmD9+vWmH0s4bA50DBjaHRqIxtUQxKtPbdH9vIe7BpntQRwlHc7szRlOG/C61RpeJ+rX1TGuLG0opdJ+AgBPvHVE/X+jNdek+Ghx9gDGQpo3HuzCttZe+D0uLF/QZOj4hIizqy2/2JMtnBkY3sZlxJmnN6RW4GQj14GOASTlVIuSOI6R2HFh3j0YU8VprWNcQDq352CHNSHNZvN6BOoYl8ZRPCGw2R3ODKSdPXYK/Z2qq41jXGOWS+aKCnaOchFCSLlRF/ZhvLIQ3NGm32Xz6t4ORBNJTKgJZs0FyEV1yKsuBHdwlIs4SKfGPI4JDoY0R3K0cQEZzh6HbfOD0cSwDMeuQTp7yoU2DQHNQGZuj/Zz9iOvHQQAXLGoOWeteyHyNXIlkrI6XZBL7BHPm0jKhjY1OlVnj7ExLifEnswRrpwitg0X5mKMqT7s01TVLbA6pFmIPWdMtkrs0ejsUcOZiyD2iMyeIlSva33vh/ylsflAscdCLpnXCCD1j8poyj0hhBDnmNssQpr1iy4vKVkMS2c15FxQ5nxeMcpFsYc4iGaxx8GQ5oFY9oDm1G3K4nrI2cX1c9uOYTCWUDNZhGOKlDaJpIxjihhRyImht5GrbyiOxxW3141nTTZ8jLPyNHId7hzEUDwJn8eFSTkusANeNwLe1OWfEceZXneDwElnz948eT0CcT4ZsHCMS28Tl0CMPQlnjBmG4gm8dbgbAHDm1DpTj6V7jKtITVxAcdq41HByvQHNDrdDUuyxkEl1IcxurEAiKeOFHcedPhxCCCE6mWeiGevFnanz/lIDWQxpkYmNXKOBp94+iqXfeQ6bDnY5fSi6EBdyNQVyHTJDmouN2HnPtlMe9pWGs+fJt1MX9Zcqm4DcACwPTvQNIZGU4XZJaKjIndkDADOUMa6dGhu5/rzxCAaiCcwcX4EzTYzTCMfOzrbek553p+Iymt4Qhsed+xKvJqiENBvI7enUecErSGf2OCD2tCtNXPW5xR4R+B6x0IWht4lLYKWzZ/PhHkTjSdSFfZhab050qdPZxnWoq4hjXIqLxs7Mni6dTXRBdTSQAc2jCuHu4SgXIYSUH0Ybudp6ItjR1gdJAs6bUa/7eYWzh41co4Mn3z6Kgx2DePDve50+FF10aQygFDvVxXb2JJMyhuJJACe3cQEZtnkHA5r7h+JqM+uHzpmSui2aQFQ5blK6iLye8ZX+gk1ZM8ZVQJJS7hgtToffKuH9NyyZpNv5mcm0hjBcEtATiZ8knOwq0MQlUEOajTh7dIbUChx19hzPXbsuCNqQ93XEtLPH/Pn1jYwRLjPvOwBqVpv+MS77nT2VRcjs6eg3ltnjtNOUYo/FiAr2F7YfQyzBD3ZCCCknRFjytqM9usIrX1RGuBZNqNa94znseVtP3q0l5YfYXXxuW3mtBbTa1J3K7Mm0w4uRrUzSzh7nFtfPbjuGSCyJqfUhnDujHuL6irk9pU+rIvY0VhV2YgR9btWxUGiUa/Phbrx9uBs+twvXnDHR1DEGvG5Mrgtlfd50E1cBsSckGrn0vSfjiSR6lHOb3ur18ZWp19SRzJ72wmNcQWW0zcqRG3F+bKkx5uw50jWIRNLceuD1/R0AgDOnmsvrATLGuDS4s3ojMVVMnFAEZ09YEfoHYwnEbfjMlWU57ezRmtkjBMRYwtF1HcUeizltUi3qwj70RNKtLIQQQsqDGePD8Lgk9ETi6i6vFl5SRrgumNVg6HmnjwvD65bQNxR3pOGIWItoVeuNxPHqng6Hj0Y7XWoeR4ExLocyezIvxPyek5ew6uLaQdv8E5tSI1xXLGqG2yWZclGQ4tKqjN00aRB7AO2NXI+sT7l6LjulUXdledbnzRHSvLNAE5egxuB7UtS1SxJ0B0wLZ0/nQKyoLrfBaEL9LM9Vuw6kzx1WBjQf7RZijz6xo7EqAK9bQjwpq4HhRpBlGRv2dwEw38QFpMe4+qOJghX14rOhNuRVR6zsJOxPOz37bXDS9A7FEVeEN81jXMrmQyIpI+rgpg/FHotxuyRcNCeV18AKdkIIKS/8Hjemj0stCLWOVCWTMl7aJcKZ9ef1AIDX7VIzIDjKVf70ZGRh/HVLq4NHog+tAc0Ta1LOghN90YKLfitJ5/W44MoyZiMW/HYs9rXQG4nheSWz8cpFLQDSryXFntKntSflWCjUxCXIJbpkMhCN409vmg9mziRbI5csy9itVezJqF/Xgxjhqgp482YCZX3OoBce5d+s1swXKxCunuqgN69jUWSAWevsSQk1zdX6xB63S1IFIjP16wc7BnGibwhet4SFE6oNP46gKuCB1y1+h/ldYYc6ijfCBaTWbj5lA6B3yPpzrXjvh3xuzc1qmSUCTtavl6TY88QTT2DOnDmYNWsWfv7znzt9OLp5t5Lb8+w25vYQQki5IUaqtmoMad7W2osTfVGEfG5T1abzREizgXBoUlpkhkSu2dJWNqN5WgOaq4Iedbe2mO6eQbWJK/tOsdPOnme2tiEaT2L6uLCawyVey06GNJc8WmvXBbPGp37H+cSeJ986it6hOCbXhXDudP15blqf91jvEHqH4nBJ+bNpAKAmZCyguUOtntbvTnJlhF4Xc5RL1K4Xek3UfBWLLsoTSRmtyvtpgk5nD2BNSLMY4VowoVpX9XsuJElCfVjbKJdoEitGOLOg0i9ye6wXVoy00HndLlUcc7J+veTEnng8jjvuuAPPPfcc3njjDXz7299GR0f5WKCBVO2u1y1h74l+7MlSjUgIIaR0mdushDRrrF8XLVznTK9Xd5YMPS/r10cNYoxLklKhr5sPl4eA16nxYk6SJDWHopi5PWJ3NFs4M+B8Zs+Tbx0FkHL1iDDU9MgMxZ5S56jO9qRsDpuRPLL+IADg+iWTsrrRjKA2cmU878621P9PqQ/D78l/YV9t8D2pVQzOhRMhzXs0ij1qG5dFzp5jvREkkjI8Lkn9ufUg3JNmxJ4NSjjzYhObUCNJN3IVcPao4czFE3tEbk+fjc4erXk9gpANwd96KTmx57XXXsMpp5yCCRMmoLKyEpdffjmefvpppw9LF5UBL86ellLvn9pcPvZtQgghwDzF2aN1nEqMcF0w01hej2AOG7lGBdF4EpFYaj5f7OSvKZNRLuE+qdGwe+lE/bpw9gS82ZevTrZxdQ/G8II6wtWs3i52gjs5xlXytCljXFoCmoG06NLaE1EF3kx2tPViw/5OuF0SPrDYXDBzJjOUUePjvUPoVt5Xu5Ta9UIjXIDxNi5xfqjT2cQlcELsEc6eqXlq14F0vopVrkAxwtVYFSjY7JaNtLPH+BiXEHusCGcW1Gts5CpmE5fAzvp1rSPOIxGOsVE1xrV27VpcddVVaGlJ7Wo89thjJ93n/vvvx7Rp0xAIBLB48WK8+OKL6teOHDmCCRMmqH+fOHEiDh8+bPVh2s57T0vNav/m1QOmk9QJIYQUDyG67D7eh6F4/g/oSCyBV/em3KfLZpsTe8QY157jfUXNQSHW0ptx0ff+01Prmb9uKf0Mv1giqS6StTTtOBHSLBbMuce4nHP2rNnShlhCxuzGCsxurFRvr2FmDwDg/e9/P2pra3Hddded9LW9e/fi4osvxvz587Fw4UL09/cX/fhkWdbt7KkOejFeETB2Z3H3PPJaytVzydzxGK9RQNJCZcCrHuOu473Kf7Xl9QBpZ06X3sweHWJwNsY5MMa1Vzh7xmlz9gzGrAnSNdrEJZhYZ26MqycSw/a21HvjDAvCmQUNGhu5DnUVf4yrIiCcPdaLPWKEUa/YE1Q/k5wrDbBc7Onv78epp56K++67L+vXf/e73+Gzn/0svvSlL+HNN9/E0qVLsWLFChw4kEqqzzbXLqyw5cRVp7agNuTF4a5BBjUTQkgZ0VwdQFXAg3hSxu5j+S861u/rQDSeRFNVQA1YNsr4Sj9qQ14k5cLtLqR0EdXElX4PLp3fCLdLwrbWXhxoN75DWwyEGKG1aWeCMmbghLMn9xiXc5k9T7yltHAtbBl2u3phPcbHuD7zmc/g4Ycfzvq1m2++GXfddRe2bNmCF154AX6//rEXs/QMxlVHnlZnD5A7pDkSS+DRNw8BsC6YOd/zijGumRo+h2qCqQvWHoMBzXU6R1kEqrNHQ3W3VYiA5mkFnD1pB4Y15w6jTVwC4YgRooleNh7ogiwDk+tCau29FdQrY1wdmse4iufsSWf22Ofs0ZtXNSqdPStWrMA3vvENXHPNNVm/fs899+CWW27Brbfeinnz5uHee+/FpEmT8MADDwAAJkyYMMzJc+jQITQ3N2d9rFIm4HXj+iWpk/vDL+93+GgIIYRoRZIkzFVcNtvb8metvLhTtHA1mN6YkCRJDYfexlGuskVcQFUGPKgJ+XDW1DoApd/KJcQIrU07Ysf6UBGdPSL3IOjLLvaoIatFbuPqGojiJeVccMWi4WvWWgY0AwAuvvhiVFZWnnT7O++8A6/Xi6VLlwIA6urq4PHYX9U8kqM96apoPWG2s3KIPU+/04qugRhaqgNYNttYS2M+Zoyofd+tOHtmNepw9uge4xKZPeUxxtUTieGEMm40tSG/6CDOKVa1cRlt4hJMUkSSI10RxA3Udr8u8nosdPUAQJ0yxnUizxhXbySmvrcmOJDZY88Yl7G8qpB3jGX2RKNRbNiwAZdddtmw2y+77DKsW7cOAHDWWWdh8+bNOHz4MHp7e7F69WosX74852MODQ2hp6dn2J9S4UPnTIZLSuU5iFlaQgghpY8ISy4U0izEngtmmRvhEsxRn7d0PsuIPkR2R5XijrnslFRD55oSH+VKt41oW8wKe35RA5oLOXvEzm6RnT1Pv9OKeFLG3KbKk8ZoymGMy2wEgxl27tyJiooKXH311TjjjDPwzW9+05LH1UtrdzpjRQ+5nD1ihOsDZ04ylNlSCCHq7DzWh87+qHrxrcVhqmb2DOoMaDbRxgUUX+wReT0NFX5UBvKf18Q5xaqLcnFenGBwjGt8pR9etzSs1UsPbyhij5UjXADQINq4+nP/DsVob23Iq+boFAM7x7iMvvetzoIyQlHFnhMnTiCRSKCxsXHY7Y2NjWhtTe14eTwefP/738fFF1+M008/HXfeeSfq63NXFd59992orq5W/0yaNMnWn0EPE2tDag073T2EEFI+pOvXc4s9x3uHsFURZcyGMwvmiSYwOnvKFrGrWKVcXFw6P7UOWL+vo6D13Un05nGIMa7W7kjRsgkjJerseUJp4brq1JaTvmbURVFMzEYwAMDixYuxYMGCk/4cOXIk73PHYjG8+OKLWLVqFV5++WWsWbMGa9assfTn04IQe7Tm9QjURq6M9t19J/rx8p52SBLwD0vsuS6ZmeHsEc/dUh1QBc98iPdkJJbUlQ9nNKRWUOwxLpHXM71AExeQ4eyxSuxR85+MOVtcLkkNwdeb2xNPJPHmASWc2WKxRwQ05/ssO9RR/BEuID3G1WeDs8doZk/IYseYERxp4xppdZdledhtV199NXbs2IFdu3bh4x//eN7H+uIXv4ju7m71z8GDB205ZqPcdN5UAMAfNxwaFtpICCGkdBH169tbczts/q60cJ3SUoX6CmsyJtJjXHT2lCtijKsqmFp4TqwNYX5zFZIy8Ny2Y04eWl707lyKned4UkabgZ1nIxQa48p09mTLgLSD9r4hrNvdDgC4YuHJsQPpNq7SFfrMRjAAwIYNG7B58+aT/rS0nCyAZTJx4kQsWbIEkyZNgt/vx+WXX46NGzfmvL9djn7hnmjSKfbMGp/6rDjQMaAKJ6Ju/cLZ49QLdqsRjqLDXYN461B36rbGk8fkslHh96huo24duT163X8jKXZAsxB7Co1wAdZflIsxLqOZPUBGbo9OsWd7Wy/6owlU+D3DwuKtQK1ezzPGJRrEihnODKTbuOxwdnap732jzp4xIvY0NDTA7XarLh7BsWPHTnL7aMXv96OqqmrYn1LivBn1mDEujP5oAo++UX6tYoQQMhYRC6S2nqGcO1hrd6ZqlpfOsi6PYXZjJSQpNQ9fzMYSYh1ijCtzbEC4e/76Tunm9ujNJHC5JPXCuFiNXIXGuMQFW1IGhuLWtOoU4ul32pBIylgwoQpTszgIMpuPiiVAWYmWCAYzLFmyBG1tbejs7EQymcTatWsxb968nPe3y9EvnD1NVfouUBsqfKgOeiHLwJ7j/YglkvjDhlQw8w1LrA9mFtRX+FEX9kGW0+cVLeHMQGrT3Uj9utGQWoFw9gxEE7aE6I5ErV3X4OwROU1WOHsisYS6bjDaxgUYr18XI1ynT66xfIRQtHGd6BvKeT4T4tSkuuI6e+zM7OkQrjad4eTp0oAxIvb4fD4sXrz4JHvmmjVrcN555xXzUIqGJEmqu+ehl/eV5Qc9IYSMNSr8HkxWFirZXDayLKuBrEstyusBUrtAU5XWkO0c5SpL0mNc6XEKkduzdudxR1s58tFlYERDuBaKldsTKSj2pF/zYi2uc7VwCcTrGY0nHbXyG0VLBIMWli9fjg984ANYvXo1Jk6ciPXr1wNIxTd885vfxLJly7Bo0SLMmjULV155Zc7HscvRn3b26HNpSpKUzu053odnt7bhRN8QGir8uGTeeEuOLRdC3Fm/ryP1dw2164IaRezR6uxJJGX1vkYDmsN+jyrIFmMzQ88Ylzh3WHF+FufDkM+tqdkwF2mxR9/51a5wZiA9xjUUT+Y8xx50ytljU2aPLMuGPh8B61vejGC52NPX14eNGzeqFsy9e/di48aN6lzvHXfcgZ///Od48MEHsXXrVnzuc5/DgQMH8IlPfMLqQykZrjljIir8Huw53o+/72p3+nAIIYRoIF9I8462PhzrHULA67J8QaU+L0e5ypL0GFd6kT+/uQoTaoKIxJJ4SRn/KzXSeRzaL05Ebo/eixGjiJDLXGNcbpeEgDe1tC2Gc+B47xBe2ZNa1125KHtzbMjnhted2l3vLOHcnkIUimAoxNNPP43jx49jYGAAhw4dwpIlS9SvrVixAm+//TY2b96Me+65J+/j2OXoV509BjJW1Eautl78Vg1mngivhlY7M8xUQppFZJaWJi5BtZolpW28sHswBrFfrbeRKJNi5fbIspwxxqUhs8dr3RjX0Yz8JzMtncIZo9fZs8FGsSfk86jn2FyjXOna9eKKPXZl9vQNxRFLpN78Rse4+keTs+f111/H6aefjtNPPx1AStw5/fTT8dWvfhUAcP311+Pee+/FXXfdhdNOOw1r167F6tWrMWXKFKsPpWSo8Htw7RkTAKTcPYQQQkofIbpkc9i8qIxwnTWtXldNrxbURi46e8qSHmWhWZnh7JEkqeRHuTr6lUwCHSMaola3eGNcqdGsXM4eoLi2+b9sPoqkDJw6sTrnyIIkSRmNXKWb25MLOyIYShHV2aOzjQtIO2pe2HlCHe+9waZg5mHPO2JsS+sYF5B29nRpdPaIsaTKgMeUiFWs3J7OgZh6LhZu2XyIi/J4UkbU5AioOB+ayesB0mLJwQ7t59e2nggOdQ7CJQGnTaox9fy5qFcauU7kaORKiz3FHeOyy9nTqXw2Br3unBsNuQhZHPxtBMvFnosuugiyLJ/055e//KV6n9tvvx379u3D0NAQNmzYgGXLlll9GCXHh8+dCgB4dmsbDnboU2gJIYQUn7nNucOSReX6UotauIY9L0OayxpRxlA1oupXjHI9u+1Y0dqr9GDEpj5RuZg5XCRnz2CBgGYACPnFTqr9zh7RwnXlovwhxLVl0MiVi7EQwRCJJdTfjRGxRzRybTrYBVlO5XVO0SAwmCVzbKs+7NMl1AoBslvje7LLZF6PoFj163tPpBvKtGzIZArIZt09R0U4s8EmLoEQS1p7IogntAlQwtUzp6mqYN28URpEI1cWZ09PJKaO+9kVTp4LkdljudhjwPUqCKqbD6NojItkZ+b4ClwwswFJGfjVq6xhJ4SQUkd19rT1Drs4H4on8Ore1OjG0tnWiz2ifn1HW5/mBR4pHXoGlcyeEVkNZ02tQ3XQi47+qLogLyXS1evaF7QtRc7sGYylXttQHrFHdfbYXL/e1hPBa0pWyuU5RrgENcHSbuQa6xEMYoQr6HWrLXp6mDUiK+eGs+wLZh72vBljW3ryegCkA5oHtb0nhbPHaF6PoHhiT2pjfdo4baKbz+OCRwkzNuvCOGKRs2dchR8+twuJpKyOhhUiPcJVY+q586E2cmVx9gjhvy7sU8WXYlFpk9iTDmfW/94PecdYG5edrFq1CvPnzx82A1xqiKDm360/qIYMEkIIKU2m1IcR8LoQiSVxIMORuWFfJyKxJMZV+jHH4lpTAJhUG0LI50Y0nsS+djpBy410G9fwha7H7cIlc1OBrWu2lN4oV6eBatnMMa5iFFCIi7B8O/UhX3GcPU+9fRSyDJwxuabgDrYQ0Eo1s2esRzBk1q4byVhpqQ6qzpDakBfLTynOeFtTVUCtmzYs9mh8T6pNXCbyeoDijXEJZ4+WES6BVbk9R7pTgkeziSYuINV4OEFnSLMIZz5zSp2p585HvdrIdbJQ6FReD5AxxhWJW/p5ZDScGRilY1xOsXLlSmzZskVN9y9F3jV3PCbUBNE1EMOfNx1x+nAIIYTkwe2S1Ar2bUfTI1Uv7kqPcJkJX8yFK/N5OcpVdqTbuE6+KFJze7a0lVQ7ZzIpGxrTaFaq1weiiaKMKInd0bzOHn9xbPNPvp0a4bqiwAgXkL5I6C5RZ085RjBYucmbrl03dnHuckmYMT4lKlxzxkT4PdbmuOVCkiTMUJwresUeIUBqbeMyIgZno1gBzfuEs0dDOLNAjIeaPXcIZ48VY0xCNPmfl/YUHLmLxBJ453A3AHvCmQWikUu4vTI55FATFwBV+IwnZQyZzF3KxEienSDkH2PV62Mdt0vCh89N7YI8tI417IQQUuqIUa6tGWHJIpz5Agsr10ciRrmyNYGR0iZbG5dg2exx8Hlc2N8+gJ3H+op9aDnpjcTVRh89Y1wBr1u9eCtGSHOh6nUgw9lj4xjX0e5BrN+X2kG/YmH+ES6g9J095YiVm7yZzh6jfOLCGVg2exw+vmy66ePRwy1Lp+OsaXW4XMP7MBPdYk+/8VGWTIo1xrXzWOqzc4YOEUyIPWamL2RZHtbGZZYPnTMFHpeEZ7Yew3t+sBYv787d6rzpYBfiSRnjK/22ii31Yowri2DnVDgzkB7hBawd5RLvfSOuNtXZ4+BED8WeInP9mZPg97jwzpEevHGgy+nDIYQQkgcRlrxdcdi09w3hnSOp/7/AhnDmkc/LRq7yIpGU0Tt0chuXIOz3qO+bUmrlEiMaIZ9btytB5FIUo35dLJjzjXGFixCIufrt1O9uydRaTQKByDkp1cyesU66dt34xfmVi1rw8EfPQqNBd5BRrj61Bb+/7VzdzytypPSOcRkJqc2kGGJPLJFUa9dH5inlI2hBvkr3YEz9frOZPQCw/JQm/PGT52FaQxhHuyP44M9fwbee2pa1MWzDgXTluh2uY4Fo42ovMWePyyUhrIgrVtavp/Ps9Aud6fcUA5rHDLVhH64+NWX5fZg17IQQUtLMHVGD/vfd7ZDl1O3jbVzUp+vXOcZVTmTuJmYTewDgMmWUa82WtqIckxY6TGQSTCxiSLOWMS61jctGZ89qMcKl0U0hLpC1Nh+R4mJ2jKscqdId0Gx8lCUTIfac6BtC0qZWwv3t/YglZIR9bl2jVEEL8lWOKE1cdWGfphYwLZw6qQZPfPoC3LBkEmQZ+PELu3HNA3/H7uPD3aFv7E+LPXYixrjaSyyzB7Cnfr3TRBOd+KyyuzAgHxR7HEAENa9++yiO9WpLVyeEEFJ8hOiyv30A/UNxvKSMcC21cYQLSItMhzoH1SpvkmYgGsebBzpLbhxajHAFvK6cDplL5jVCkoBNh7rVi0ynUQMow/p37TNDmu1GHePS0sZl005qW09Ebbx5zwJtYg+dPaXNUQvGuMoNMcal1dljJqQ2E+EKiSdldGkcIdPLzraUCDJzfIUuh4sVIzfpJi5r30thvwffunYRfvyhM1AT8mLz4R5c8cMX8etX96sZWxuKJfaozp7SGuMC0rk91o5xmcjsEZ9HsYRj6xWKPQ6wYEI1zphcg1hCxiOvHXT6cAghhOSgvsKP8cpO5Pa2Xry4MxXOfMGscbY+b03Ip87772jjKFcmL+w4jkvvWYv337+u5MoO0k1cuUWTcZV+nDE5tRhfs7U03D3qYtbAhZzYOT9s8xhXLJFELJFaLOfP7EktrvttCsR8Whm/O2NyjWZxQO+FNSkubWPQ2VOjOHt6I3EkNDhszLj/MvF5XKrTza5Rrh2K2DNLZ1um2sZl4txxVDRxVdvjbHnPgmb85Z+X4YKZDYjEkvjS/23Gxx7egNf3d6JzIAa/x4VTWqpteW5BZkBzpoDRE4mpGVBWhFMbQRV7bBjjMjLCKDYmEkkZ0YR1odF6oNjjEMLd8+tX9yPm0C+fEEJIYYS7Z/VbR3G0OwKfx4WzptpXazryebcypBlAamf587/fhJsefE11kewvsWr6dBNX9hEugRjlKpXcHjOZBCKXwm5nT+Zue15nj1/Y5u1x9ogRrhUaXT1A+gLZLicDMU48kVRd9lYE6pYL1RkB8j0a3pdCqDQyyjISu3N7RDiznrweAAj6zDcnHVbGuOwUO5qqA3j4o2fhy1fMg8/twjNb23DjT18BAJw6sQY+j72X9+I9EEvI6MkQVYTgXxf2qa2IxcaOMS7ROmameh1wrn6dYo9DrFjQjIYKP9p6htRdIkIIIaXHvOZUWPIj61NOzCVTa/NebFpFOqSZuT1/2XwU775nLf74xiFIUnohXWojbvmauDIRFeyv7GlX3UBOomYSGNi5nFCkzJ6IslB2SYDPnXv5aqezp71vCK/t7QAAvGdBk+bvq1WdPVHbckrGGlZVr5/oiyIppxpz6yv8Fh1d6eNxu1CpXJAXEiGTSTljjMtcQDOQWb9uzxirGOOardvZkzqvmBnjSjt77BUOXS4Jty6djsdWno9Z4ysQV84rZ9g8wgWkAvKFgyazkcvpvB4g7ezptUjskWVZFTqNjHF53S543alRQqfq1yn2OITP48IHz54MAHh43X6Hj4YQQkguRH6O2ClaavMIl0DUr28fw41cx3oj+OSvNuATv3oDJ/qGMGNcGH/4xLm48axJANJOmlJB7HLmG+MCgOnjKjBzfAViCRnPbz9ejEPLi6gEN+LsEZk97f1RW3cuxUI56HXnzeFQnT02ZPb8dUsbkjKwcEI1JtVpz6SoVi6Qk3LpvWfLFauq10XtemOlH26XfQ1GpUh1hgiZj55IDEKjNHKOGMm4CvucPfFEEntOpDN79CCEYjPnMeECaSiScDi/pQqPf/oC/NP5UzG5LoT3ntZSlOdVQ5ozGrmcbOISVPhT7+l+i8Se/mhCHb+qM/jeD1ngGDPDqBF7rFL4i8k/nj0ZHpeE1/Z1YMsR7twSQkgpIsapBHZWrmeiOnuO9pZcELHdyLKMP244hEvvWYunNrfC7ZKw8uIZePIzS7F4Sp0qppTahbNwGhUa4wLS7p5SGOUys2tfHfSqDgE7R7kG1XDm/K+t6uyxof1EHeFaqN3VAwB+j1u18zOkubRoVZwYjWNohEtQrTZy5Xf2CAGjwu+xZERINFnaIfbsax9ALCEjpLOJC4DanmXG2dOrCv7FG2MKeN342lWnYO0XLladyHZTHxaNXNmcPc6EMwNAhd/a6vVO5b0f8LoMO7pDFrS8mWHUiD1WKfzFpLEqgOWKDfhHz+10+GgIIYRkY+b4CnXHtz7sw/wiLaamjwvD65bQOxQvStNRqXC4axA3/2I9Pv//NqF7MIb5zVX408rzcefyuepiXCykS2EEKpOeQSWzp8AYF5DO7Xl++3EMxZ2rZQXMtY0AxWnkSos9+ZeuYZ89zp7ugRhe3t0OQF9ej4C5PaWJaMQbS3k9AhEc3l0gOLxTHWMxP8IF2Ovs2aXk9cwcXwGXTqeWWpNt4qJcS0j/aKBObeQqMWePxZk9nRYEkwuRqN+mhshCjBqxp1z5zLtmwSUBT21uxRsHOp0+HEIIISPwe9yYMS4MADh/ZoPuBaRRvG4XZoxL2dDHyijXy7vbcdk9L+CFHcfh87hw5/I5+NOnzseCCcPbRcRCusei3bv1+zpw60Ov42CHucDnHtXZU3ihf+rEGoyv9KNvKI5X9nSYel6zmF3QthQht0fsioa8BZw9fnucPWu2tiGelDG3qRLTGsK6v19cWNPZU1qI2vXGMdTEJagJKgJkgfdkp4mA2mykM3usF3vUJq7x+vJ6gHQbV6TMnD1O0CDGuPoyxZ5SyOyx1vVrJpxZQGfPGGdOUyWuPWMiAOBbq7eNOas+IYSUA+cro1tXLNK/o2+G+S0pF9GbB7qK+rxO8eMXdqM/msDpk2uw+jNLsfLimfBmCeMVC2mrApp/9cp+PLO1DY+/Za7KXQQ0a1nou1wSls1O5T+96fBmj1mxpxj162KhHChgpQ/Z5Ox5ykALVyY1GvNRSHEZi7XrApHZ0z2Y/9+KFe6GTOxs49p5TNSu68vrAdIODDPnDvGZVK3B3VnOqJk9pTbGFRBivzXn/y4LXG1ig4KZPWOYOy6bDb/Hhdf2deCZrcecPhxCCCEj+Nf3zMVfP7cMy0/Rl9VhlnOm1wMAXt7TXtTndQJZlvH24W4AwNevOiVvuGZa7LFmQdetiDQdfeYuxNXqdY0L/clKyK8YJXECWZYzApqNLWiblBEYEXZrB+oYlzf/0jWkWuatW1j3RmJ4cecJAPrzegQi2LarwMgMKS5HhdgzFse41MyeAs4eC5u4gLTYc8wOsact5YKdbUTsUTN7koaeO5ZIIqJ872h39owc4+qJxNTPUTtr5wuhZvZYJPZY4eyxQkQ0A8WeEqC5OoiPXjANAPDtv2xDPGHsJEMIIcQeAl637hpXKzhvRkrs2XSwy7LFS6lypDuCjv4oPC7ppFDskVSpAc3WXDgLR06nyQvxHh0BzUD6AvOIg2LPQDSBaDy17jCa2dNSk/o5RO2wHahjXAUCmsPK16PxJGIWraee23YM0UQS08eFMUtnw4+gVh3jothTSrT1jF1nj9bMng6TmV4jEZk9XQMxS/PK4okk9hzvB2BsjCs9bmPsszZz80FUgI9WRo5xCVdnXdiHsIM/uzrGZXFmT52J9776vjIxHmgGij0lwicunIGakBe7jvXh/2045PThEEIIKQEm1oYwuS6EeFLG+n3O5rrYzduHugCkxptFEHMuxK5pJGbNBb1YpJvNU9GT2QOkQ2FbbRRJCiF+Zp/bpYYb66WpKrWTe9RG0Srt7CkwxuVPf90q2/xTb6ca0y5f0Jy39j0fWvNRiDasaOGVZVl9zzZXO+dGcAqtbVxdFo9xVQe98LpT/47aTbopM9nfMYBoIomgV38TF5AeETV6US42DUI+NzxZxo9HE/WqsyflziqFvB4gLbL1WbQRJD4fayxx9lDsGdNUB7349LtmAQD+e80Ox6xehBBCSgvh7hFNQKMVMcK1cEQYczYyd02tGOUSIo1ZsSc9xqVtZ1NcYNopkhSiK2OEy6iQIUSro10R27IHxQVYISHQ53bBo4SoWxGIORCN4/kdqRH79ywwPsaZzuyhs8cKrGjh7R6MYUhxtY2v8lt1aGVDtUYBUh1lscjZ43JJaLChkUuMcBlp4gKAkNfcRflYCWcG0pk94r1RCk1cQPq1tyqgXzRV1pkYYRRuU4o9BB86ZzIm1gZxrHcID7601+nDIYQQUgKcq4g963afcPhI7OWtQ4rYM7Gw2ONxu1RrtBWjXKIyvbPfpLNn0JizpzcSd2xMz4rwVTGONhhLqK+l1QyoY1z5xR5JkjJye8wfy/PbjyMSS2JyXQinKIHpRhCvL9u4SgchstaFfQVFxNGIKkAWdPYoY1wWZfYA9oQ072wzHs4MpB0YEcNij77zfzlTH06LPYmkXBLhzADUETLLq9etGONiZg/xe9y4c/kcAMCPX9gzLOGcEELI2ESIPe8c6Rm1IyCyLGOzDmcPYF1IcyyRVF0jZvJUZFlWq+ArNS72w36Pmu/j1CiX2Jk1Gs4MpNw2ItPgaI89P4eoQw5qGDUTC/4BC3Z3n9qcGuFasaDJsPMJoLOnFGkdw7XrQPo92VNA7OkQuSUWjXEB6dweK+vXdyhNXEbz9dQmP6NjXGPI2SPEj6SccoaVirOnIkPsSSbNu0ytDGi2sjRADxR7SoyrFrVg4YRq9A3F8aPndjl9OIQQQhxmfGUAs8ZXQJaBV/aMztyeQ52D6ByIwesuHM4sEIJKj0lnT6ZY1D0YM1ySMBhLIKEsLrWOcQHOj3IJ8cFMACWQDrg92mXPzyHG27U4MKxy9kRiCTy3tQ2AuREuIJ35QGdP6dCm5vWMUbEnmG6Iyzd+2WWBu2Ek9jh7UmNcRkPUxbnF6Pin+CzSKvaXM163SxULO/qjJZPZkym0WeHstDSgmWKPOawIaisFXC4J/7ZiLgDgV6/sx74T/Q4fESGEEKdJ5/aMzlEu4eqZ01QJv0fbOIVVzp6RY2DdBXa5cyHGlzwuqWCIcCZN1faKJIWwIoASyGzksufnGIymRLhCY1xAhrPH5GL/xZ0n0B9NoKU6gNMm1Zh6rFqNzUekeIj36lh39sSTck7XgSzLquPRqoBmwHqxJ7OJy7izJ3XeGIonVeFeD2MpswdICyAn+qIlM8bl96Qz28zm9mS+9804X4M+az6PjDJqxB4rgtpKhfNnNuDC2eMQT8r47l+3O304hBBCHObcGQ0AgHWjNKT5LXWEq0bz91Sq9evmFlAjM2aMOi/Su7oeXeM+doskhbAqj6PJ5maxiMY2LiDD2WNysf/U5qMAgOUmR7iA9IVy71Dcskp4Yg5Ruz5WnT0Brxs+T+pSMNeIcE8krgofZi54R2K12HPAZBMXMPzcEjEwytU7hpw9ANCgNHLtb+9XN0mMvvZWIUlSRm6POWF9IJpAVAlwN+XsMRn8bZZRI/aMNv5txVxIEvDkW0ex8WCX04dDCCHEQc6ZXgdJAnYe68OxXueam+xCb14PkOnsMbegGzkGZjS3Rw3nDOpb6Kdry53N7DE7xiXG0Y7YJFqJXVFNmT0W7KRG40k8syU1wrViQbPhxxFUBb0QehFze0oDIbA2jVFnDwDUBPNnSYnQ+pDPbWmItdWZPTuUcGajTVwAEPCmL4uNXJjrbWMsd0Qj1yalXKEu7FOFFicRuT1mN4LEZ6Pf49Ll1h0Jx7hIVuY1V+Ga0ycCAO5evdW2KlNCCCGlT03Ih/nNqSag0VbBLsuy2sS1SEMTl6DKpjGuDoONXMIhpLeJRa0td8jZY9UYV7Pq7LFpjEuPs8dvvn533e4T6InEMa7Sj8VTag0/jsDtktT3Rvcgc3tKAeHsaRqjzh6gcEizFW192bDa2bPrmLm8HiDlChHnFzPOnrHQxgWkNwg2KaYEp/N6BGIjyGwjV1fG+KIZZ2fIz+p1koM7LpsNn8eFV/d24G/bjzl9OIQQQhwkndszusSeQ52D6B6Mwed26cpaSI9xmXT2jBzjMir2ZIxx6aG5xl6RpBBWj3EdscmhNBhL2em1iD1h0apjwtnzF6WFa/kpjXAbdAqMRLzGZlrfSAorsjpVZ89YFntESHMhsSdsrYCRKfZYsaG9Q61dN5bXI1AbuQxcmIvPkrGS2VOvuLO2K8HYpSL2VKhiv0lnj0XB5Kqzx2DLm1ko9pQwE2qC+KfzpwIAvvXUNkNhYYQQQkYH543S3B7h6pnbXKnmR2ih0iKrtlVjXKJ216izxy6RpBDp6nWTAc3KGFdrd8QWN/KgItxoCWgWQatGq27jiST+qoxwXW7BCJegWjRyGRQUSRqzWZ2D0YSaMzKWxZ7qUKExLuvDmQGgQREKBmMJSyqpdyq162acPUBGI5cRZ8+QMcG/XGlQxrjE9anT4cyCsEVrA7WFzuRGiNigMCs+GYViT4lz+4UzUR30YkdbH/644ZDTh0MIIcQhlkyrg9sl4UDHAA52DDh9OJbxtpLXs0BHXg9gXRtXT8SigOZBkdmjb6HfpIgkvZG4adu5EbosqJYF0hfMA9HESa+pFYiLr4CmNi5ld97g6/na3g509EdRG/LirGl1hh4jG+KiIZeLghSPVmWEK+Rzq8LxWKRaZPbkGC20a4wr7PeoDjyzo1yJpIzdx1Nij9EmLkHIhCuw16DgX66M/MwoGWePRWNcYiPEMmcPx7hINqpDXnzq4pkAgHvW7HDsjUIIIcRZKvwenKpk2ry8Z/S4e94+3AUAWKRb7FGyJkyPcaW+X9S1mh/j0rfQr/B7VOGq2KNc0XhS3VU3u3sZ8LrVx7AjbFpUr2tr4zLn7HlKGeG6bH4TPG7rlsrigjlX8xEpHq0Z4cxmm9bKGRHQ3J3L2WORGJwNq3J7DnQMIBpPIuB1mRYcRAC8scweMcY1NsSeeqWNSzCpRJw9QrztM7npINYCdSaFTvF5NBBLOJLBS7GnDPjwuVMwoSaI1p4IHnh+l9OHQwghxCHEKNdoye2RZRlvH3LW2SO+X1wkGHX2mNnVTYc0F3eUS4gOLsma3WjRyGVH2LSeMS7V2WNgdz6ZlPGXd1Jiz4qFTbq/Px81zOwpGVp7Uv/WxvIIF5B+T+Ya4+pQxrisrF0XWCX27FAyY8w0cQmCJmqyew3mtpUrYoxLUDLOHiH2mMhsA9LnadNjXMpnViIpI5pImnosI1DsKQMCXje+dMU8AMD9z+9WK2oJIYSMLURI87rdJ0ZFS+OBjgH0ROLwefSFMwMWBjQr3z+5PgzARGaPwTEuwF6RJB8igLI66DV9kQTY18gly7K+Ni6f8TauDQc6cbx3CJUBjyquWoUahkuxx3Fau1MCw1iuXQfSOVLduQKa+4vh7DF3vtil5vWYG+EC0hfmRiYpxlpA88j3xIQSEXvCFjl7rA5oBpwZ5aLYUyZcvrAZly9sQjwp41/+3yZE48VXBgkhhDjLGVNq4fO40NYzhD0n+p0+HNOIcOZ5TfrCmQELM3uUi5wpdSkLuvExLuMWfrtry3Ohhq9adCEnXBJHu6x1KA3FkxAdFZoye0zkbjz1dsrVc+m8Rt3vyUKIRiOOcTlPazedPUB6jKtQZo/ZAPdsjFNCmo/3WePsmdVoLpwZMN6cFIklVNfGWBnjqgn5IPYI6sM+VWR3Guuq163Jq/K6XfC6Uy+UE/XrFHvKiLveuwB1YR+2tfbivr9xnIsQQsYaAa8biyfXAhgdrVzCqbpwor4RLiA9dmTVGNeUekXsMRvQbGBXt8nhMS6rwldbauxxKGXmZ2hy9viNOXtkWcZfNh8FAKxYaF0Ll0BcMBt9jxHrEAHNY17sKdTGNWBNbkk2rBrj2tlmnbNHbePSeVEuPkckCWMm8NvtklR3T6mMcAEZY1xmnT0WboaouT0Ue0g+Gir8uOu9pwAA7v/bLo5zEULIGESMcr28+4TDR2Ie4exZqDOvB0jv3g3GEoiZmINXx7gUZ0/XYEytktWDGCerCurf1W1xaIzLqkwCgRiJsfrnELvsXrcEr4bAZKPOnk2HunGkO4Kwz42ls6wd4QIyXBQc43Kc1h6OcQHpNq6cY1wDpZ3ZM7yJyzpnj96LcnH+r/B5LBmJLRfSYk9phDMD1rVxWRXQDDjbyDVqxJ5Vq1Zh/vz5WLJkidOHYitXLmrhOBchpGx5//vfj9raWlx33XUnfW3v3r24+OKLMX/+fCxcuBD9/eU/pmQH580UYk87kgZEiVIhmZSx+YgQe2p0f39FhoPGzA6e2JGdrDh7ZDnt0tFDj4mA5vT4U7HFHmtHNOwKmhYXXlpcPYDxNq41W1IjXO+a16ju8FtJuo2LYo/T/PwjZ+LPnzofZ0+rd/pQHCVfjpQsy8XJ7DExxnWwYwBD8ST8HpclgoM4x+ht40o3cY0NV49ANHKVkrNHzewxIfbIspzx+Whe6BRZUP0mQ6ONMGrEnpUrV2LLli1Yv36904diOxznIoSUK5/5zGfw8MMPZ/3azTffjLvuugtbtmzBCy+8AL/fn/V+Y51FE2sQ8rnRORDDttZepw/HMPs7BtCrhDMbyVrwul3qwtzoKFcyKas7snUhn7pQ7zAwZiMEIiOLfafauKy+kGvOGOOyMkBc7IYGNeT1ABltXDoX+2IcZMnUWl3fp5V0GxfHuJxmXKUfiybWoNoGx0o5IX7+wVgCQ/HhAkffUBxxZUPBqlHPTMZVpM57Zpw9mU1cbgscNUGD4zY9ahPX2Ho/ifHnWToLFuyk0gKxJ/XvIWWosOLzkc4eoguOcxFCypWLL74YlZUnLwreeecdeL1eLF26FABQV1cHj2ds7ZBpxet24axpdQBSrVzlytvKZ9f85ipNoznZEMJKj8FGrv5oXA3+rQp6M5wX+i7Gh+LphaGRMS4hkvRE4ug3aT3Xg9UjGmIkZiCaUJ1OVhDR0cQFZOQjxBK63G8HO1Ni26Q6e0YSxOs8FE86sugfTYwVR7/dVPo9asjuyFEuEeAe8Lo0C616EM6eE31Rwy7VnWoTl/kRLiB9jtEb0DxWnT13Lp+DVR88A1ef2uL0oaioY1wmPoPEZ6PP4xrWpmWUkJeZPUQnHOcihFjN2rVrcdVVV6GlpQWSJOGxxx476T73338/pk2bhkAggMWLF+PFF1+05Ll37tyJiooKXH311TjjjDPwzW9+05LHHa2kc3vKN6T57UNdAIzl9QjMNnKJ7/O6Jfg9LjWIUQQz6n0co+GcFX6P+n3FzO2xOqA56HOr+T9WNoupY1wa216Es0eWgUhc2+JalmUc7BgAAEyyKX+iwu+BR7myztV+RLQxlhz9duJySencnhGjXHaGMwNAfYUPkpTK3THqdtupNnFZ4ywx6sAwk9lWztRX+HHFombLmwvNUGGBs0e4XmtDXkiSFY4x4w2RZimd3wzRTeY41yqOcxFCTNLf349TTz0V9913X9av/+53v8NnP/tZfOlLX8Kbb76JpUuXYsWKFThw4IB6n8WLF2PBggUn/Tly5Eje547FYnjxxRexatUqvPzyy1izZg3WrFlj6c83mjh3eio89tW9HYibCCd2krdNNHEJKtVGLmPOHuEIqgqkFnRCqNBbvy5GuMyEczY5UL/eMZBe0FpFkxo2bd1I2qDq7NG2bA140juxWhu5ugZi6sWBXfkTkiSlG7l0CoqE2IV4T3aNcPZ02Fi7DqRcqkJIMprbQ2cPGYkQe4biScNmiI5+azdCVBFR5/vKCij2lDGZ41yr/rYL7xzhOBchxDgrVqzAN77xDVxzzTVZv37PPffglltuwa233op58+bh3nvvxaRJk/DAAw+o99mwYQM2b9580p+WlvwW34kTJ2LJkiWYNGkS/H4/Lr/8cmzcuDHn/YeGhtDT0zPsz1hifksVqgIe9A3FVdGknEgmZWw+nPqdOens6RlUQpWV3dg6g9XY4vnN7Oqm826Kl9vTpbZxWXcxl84fsk600pvZ43JJGa062t4bBxRXT2OV35ZwZkGtWnVNZw8pDapytMSJ96gd4cwCM41ciaSMXcdEE5c1zh6jDoweij0lQzjDXWt0LLrTBtcrwDEuYoArFjZjxQIxzvUWx7kIIbYQjUaxYcMGXHbZZcNuv+yyy7Bu3TrTj79kyRK0tbWhs7MTyWQSa9euxbx583Le/+6770Z1dbX6Z9KkSaaPoZxwuyScMz01yrWuDEe59rX3o28oDr/HZWpHtsqks6c3MjxUWexg6w1o7okYD2cWNNtUW54PdUFr4cWcLWKP6uzR/vqGdAatHuy0d4RLIHJ7RrooCHGKmmB2AVKMs9pRuy4wI/Yc6kw3cVmVs5V29ui7nkoH9I+tMa5SxOt2IaC4QI2OclldXhA2GPxtBRR7yhxJkvCf71uA2pAXW4/2cJyLEGILJ06cQCKRQGNj47DbGxsb0draqvlxli9fjg984ANYvXo1Jk6cqOYteDwefPOb38SyZcuwaNEizJo1C1deeWXOx/niF7+I7u5u9c/BgweN/WBljMjteWVP+Yk9ajhzSxU8BsOZAQucPRljXABQF1YuenSO2KgOIRML/eaa4oo9iaSsBrJaeTGnij1dFo5x6XT2ABmNXDqdPZNtCmcW1Bh0jxFiF+Lf/8iA5qI4eyqMiz07lPa8GeOsaeICMjN79H2mqO5Oij0lQYU/9XswKvZ0CNdr2Jrfp9H3lRXQazYKSI1zLcCnf/smVv1tFy47pRGntBi3xRNCSC5GBtXJsqwrvO7pp5/O+bUVK1ZgxYoVmh7H7/eP+Wr282amcnvW7+vAUDwBv8e+0ROreftQSuxZZGKEC8gQewwu6NLjV+acPelwThPOHjWzpzhjXN2DMYh2dCvHuERmT2uPHc4e7cKgcPZozew52JF63SfaLPakx7jo7CGlgXD2jBR7RG6JXZk9gDlnzw41nNmavB4ACBjMVhnpEiXOUuF340SfcbHHjvICAOins4cY5cpFHOcihNhHQ0MD3G73SS6eY8eOneT2IcVh1vgKNFT4EIklsfFAl9OHo4u3FGfPAtNij8mAZmG99wtnj7Hq9ZEOISOkg42L4+wRzpJKvwdeE+6qkbTYmNkT0tjGBQBhndkbhzqL7OzRGQJOiF1Ui4DmnG1cRRjjMhDQbHVeD2CmjYuZPaWE2fp12wKaKfYQo4wc5/reX7c7fUiEkFGEz+fD4sWLT2rIWrNmDc477zyHjmpsI0kSzp2RcveUU25PMinjHUXsWTSxxtRjiYV1j+ExruHOHrGw69DdxmV+oW+HSJIPIWjVWGRTFzRljHHJwjpkErHLric4OeTX5+w5oNau29PEJWBmDyk11MyeEe9J0RhnZabXSCxx9ljUxAVkZPbovCi3QvAn1iEauYy6frssHuMKqpk9rF4nJmio8OPuaxYCAH66dg+efOuow0dECCkn+vr6sHHjRrUFa+/evdi4caNarX7HHXfg5z//OR588EFs3boVn/vc53DgwAF84hOfcPCoxzYit+flMhJ79pzoR380gYDXhRnjwqYeK+3sMTrGNTxUUyzs9I7YpMe4zDh7UiJJ92CsKAtCEb5q5QgXADQrDqX+aMLwQnskItQyqEPs0ePsSSRlHO5MjXFZFfSai9qQMfcYIXZRnSOg2epGomwYzezJbOKaZaGzR21NiiV0idV09pQWIrPHaBuX5c4eL9u4iEW8Z0EzbrtwOgDgzj9swk5F9SaEkEK8/vrrOP3003H66acDSIk7p59+Or761a8CAK6//nrce++9uOuuu3Daaadh7dq1WL16NaZMmeLkYY9phNjz5sFOR3aMjLBZcfWc0lJtKpwZyAxoNjrGJUI1U4+TWb2eTGpf6PdYEM5ZGfCqu5HFcPfYdSEX9LlV90qrRT9HJCbGuHQ4e0Rmj4bF9dHuQcSTMnxuFxqVVjS7EJk9nczsISVCroDmoog9Bse4RBOXz+OydPRSCMqyDAzpiMSwQvAn1lGhBPQbHePqtDicnGNcxFLuvGwOzptRj4FoArf97wbVWkgIIfm46KKLIMvySX9++ctfqve5/fbbsW/fPgwNDWHDhg1YtmyZcwdMMLkuhAk1QcQSMl7f1+n04WjiLSWceaHJvB7AwjYuZYEu8lSSsr7HTNfumtvVTYc02y/2pAMorb84aVIEkyMWNXKJBXLASBuXhp1dEc48oTZoWatPLqqDdPaQ0qImS2i4LMsZY1z2Z/Z0DcQwFNd+IbzThiYuYLh7UOuFuSzLdPaUGBUmyxusFjrFWDGdPcQSPG4XfnTj6WipDmDPiX58/vebdO1QEkIIKQ9SuT0pd0+55PYIZ48VYk+V2YBmdYGeehyfx6W6a/Q0cqVbvcxdFIlRLqtEknwIZ4kdTTtWi1YDwtmjJ7NHh7PnoMjrsXmECzA+KkiIXQgBMtPZMxBNIJpIOVvsrF6vDnrhdafEmvY+7efcHcdSkwuzLWziAlLXUD7Fcaq1kSsSSyKuXGdVMrOnJFCr1w1sBA1GE4jEUu99q/KqQgZb3qxg1Ig9q1atwvz587FkyRKnD6UkqK/w48cfXgyfx4U1W9pw//O7nD4kQgghNpDO7Tnh8JEUJpGUsfmIIvZMdN7Z0zsoQjXTu7E16piN9gsPq8I5i+ns6bQ4kyCT5ppUbs8Rq8a4RGaPHmePjsyeg53FCWcGMjJ7BmOWBVgTYgZxzuuJxJBQRAuRWeLzuHRlZelFkiRDuT27FGePleHMAjW3R6MLQ5z/XVL6vEOcRawNjGT2iM9+r1uy7Pcp/g0ZzRAyw6gRe1auXIktW7Zg/fr1Th9KybBoYg2+8d4FAIDvr9mB57cfc/iICCHEWij0Q3X2vH24+6TMhVJj74k+DEQTCHrdmDHO/CJd7KIORBOIJ7TnKwhGOnuA9C62nmps68a4lPr1nuJl9tTZMKLRXCVEK2scSgOx1O9Jz0WnnjYu4eyxu3YdSIfhJpKyZQHWYxGe+61DvCdlOe2SFM6zupAPkmTvaKORRi7h7LEynFkgzjMRjS4M8ZpV+D22v1ZEG8Kh22fgHJsZzmzV75OZPcQ2/mHJJHzw7MmQZeCfH9mIA+0DTh8SIYRYBoX+lEAwvSGMpAy8trfDksf808bDuPh7z1u+SSDyehZMqLIkZyFTXDGyqEtn9mQ6e0RIs3bhrMeiMa7mjNpyu7F1jEtx9lgVND1os7PnQBHHuAJet3ox2dVf2uJsKcNzv3V43S7134sQecQYa40NmV4j0RvSnMxs4rLB2RPS7eyx5vxPrCNsonrd6nBmID1WrLflzQoo9owBvnbVfJw2qQbdgzHc9qsNjqiKhBBC7GORMhK153ifJY/3+KYj2HuiH5/41Qa8vs8aAQlIuY8AYIEFeT1A6iIl4E0tZfSOckViCUSVtpXMRXqdGOPS6OxJJGVVaKoy6+yxWCTJh61jXEK0sqyNK/V7ss3ZI2rXa+0Xe4DMRi6GNJPSoCZjvBBIB4jbmdcj0OvsOdQ5iEjM+iYuQcCrL1+lN4tDlDiL6uwxkOeX3gix7vcpNioSSVnNwioWFHvGAH6PGw986AzUh33YerQHX/q/tzknTggho4h6JfNAT6hwPoSNORJL4qO/XI9trT2WPO7birNnkQV5PQKxwNbbPCkW6JIEVPhOdvZofS0zAyDNLvbVzJ6ijHFZv6AVNFkd0Ky4c+xw9gxGE+pFZjHGuACgesSFNSFOI0a5xChwh41i8EhEZs+xXm3ni53KCNf0hjA8busvZdMjN9o2EMQYF5u4Sod0Zo9+g4PYCLHW2aO/5c0qKPaMEZqrg7jvg2fA7ZLw6JuH8fDL+50+JEIIIRYhFiUdOtpM8iEW+uMr/eiJxPGR/3lNzTUxSiIp450jKdHIiiYugdGQ5p6MnAVXxkiZeC21VmOLxwl4XfB5zC2rhEjSNRCzdUEoy7KtO/dCtOobiusW4bIhdth1OXs0tnEdUsKZKwMeVBdhZAVIO3tYv05KhZoR70khBttZuy7Q6+zZoYQzz7YhrwdIi8panT09g9Y4O4l1WJXZYxVet0ttnSt2/TrFnjHEuTPq8cUVcwEA//nEFqy30JpPCCHEOdRQYYudPQ98aDHmNFbiWO8QPvQ/r+oK0BzJ7uN9GIwlEPa5Ma3BupyFSrV+Xd+iTq1LH+HGERfiHRrHuKxq4hKPIRapRy0KN85G31BcrQq2Y+c+5POoTgGz7p5kUk6Pcelx9vgVZ0+Bxf6BIoYzC8RrricEnBA7EWKPcPbYOeY5Er1ij3D22JHXA6RFZa0X5b0WfgYQa1AzewxsNgjB0+r3vprbQ7GH2MktF0zDVae2IJ6Ucfuv3yhKvSshhBB7EYuSdgsuHmOJpBo4Oa0hjIdvOQsTa4PY3z6Amx58zbBTQ4Qzn9JSbUk4s6AqYGxRl6tBqzasL6BZ3dW1KJzT6hGobHQqwcB+j0uXgKIHq3J7IvH0wtgOZ49wrBUrrwdIX1jrCQEnxE6EOCsCmjttuuDNht6A5p2idt1uZ49msUdk9tDZUyqI30XfUFx3dEmH6mqzWuxxppGLYs8YQ5IkfPvahZjTWInjvUO4+RevlXxVLyGEkPzUV1jnFBCLfJeUugBorArgV7ecjYYKH7Yc7cGtD72uuZI2k81KOPNCC/N6APNjXCNFGr2uix6L8xqESHLETrGnCOGrVjWLZS6M9Yg9qrOnQO6GGs5cFzRwdMYY6aIgxGmqg2J8dYTYU4wxrorUueJ471DBC/NhTVyN9jh79F6UpzN76OwpFYRDNimnA/61knb2WPv7FCJiv8YsKKug2DMGCfk8+PlNZ2JcpR/bWnvxsYeNLdwJIYSUBlY6e8T4Uk3IpzpwpjaE8dBHz0Kl34PX9nbgU795E3GdjRJvHeoCYG1eD5C2zut19qTHuEY4e3RWr+caBzOKGtJs4xhX50D6d2wXTdXWNIuJ3Ay/xzUsW6kQwtkTS8hq61o2HB3jYmYPKRHUzJ7B1HuyQ3H/FcPZ01CZeo5ILFkwY+Vw1yAGYwn43C5MsenfrPE2Ljp7SoWQzw1J+bjoHdK3NlAze+jsIeXMpLoQHvqn9ML9M7/Vv3AnhBBSGgiHRm8kjpjJc3lHjiaKU1qq8fObzoTf48IzW9vwb49qb3aMJ5LYclQJZy4VZ89g9pwFsZPdNRDV9POpj2PZGJf99eti997qnctMmi0aRxML45DOcbPM++dz94gxrolFFHtqdAqKhNhNjXL+6hlRvV4MsSfk86hOjEK5PWoT1zh7mrhSx6Mvs6eHzp6SQ5IktWWzT+faQG3jsjqzx8vMHlJk5rdU4Wc3nQmfx4W/bmnDlx/bzEp2QggpQ6qDXgjTg9lRro48C52zp9erzY5/2HAIdz+1TdNj7jreh0gsiQq/B9Pqw6aObyTp6nVrx7jiSRm9Gpo87BrjslPsKUatcnoczeQYl4EmLiDVfiLa0XLl9siyrIo9xXT2iAvrbjp7SImQbuMaXr1u56hnJiK3p61nCMmknPPP9lZ783qA9LlG69SD+OypCtLZU0pUBIw1cqlNdBZ/PgZ92kaLrYbvyjHOOdPr8cMbTsftv96AR9YfREOFH/+yfI7Th0UIIZpYtWoVVq1ahURibI+iul0SakI+dPRH0TEQxfiqgOHH6iywyL90fiO+fe0i/Mv/24Sfrt2D6qAXNyyZlPcxX9uban88paVK1yiOFioNBjTnst4HvG6EfG4MRBPo7I8WHM+ya4zLXmeP/XkczYpDyayzR+yCBgwESYd9bkTjyZyNXJ0DMVUImlBTvMwe8brT2UNKBTWzZzCGwWgCQ8roY42N7r9MxlX4sfdEP2782Sua7m9XExcABHW2JqU/S+jsKSWM1K9HYgl1g8Hqz0d1jKvI0SkUewjes6AJ//X+hfjio2/jvr/tQkOFDzefP83pwyKEkIKsXLkSK1euRE9PD6qrrR0PKjfqworY02fOLdCuYV79usUT0dkfxX+t3orvPr0d3316u6bHtjqvBzBevZ5rjAtI7egNRAfRORDDlHqNj2PRrm6zOsZlX2ZPRxFGNJosEq3EwljvGFfqezzDBJ2RiLyexiq/mtNRDGqY2UNKjMw2LnF+8Lol9YLZbi6cMw6v7evQdF+/x4WL5oyz7ViCujN7rHV3EmtQnT061gbinOxxWf/eD+ocD7QKvisJAODGsybjRO8Qvr9mB/7jiS2oq/Dj6lNbnD4sQgghGhFjVx0mLyDTzp78u1ofWzYdkVgCP/rbrrwBuILKgAdXLGo2dWy5HhcwEdCcRaSpDXtxuGtQ00ic1XkNzTUpkaRrILXDbkc1+ubDqfykKRaP1GUiHEp9Q3H0RmKGX59I1NgYF5CZvZF9se/ECBeQFtl6I3HEE0nbskcI0Uq6IS6qnvdqQz5IkrVOzFysvHgmPnzuFCQSheMkgj63reKs/jau7GH/xFmMOHsyw5mtfu+HdTrGrILvSqLyqXfNxIm+ITz08n58/vcbURvyYuks+5RzQggh1iHGrkxn9iijJXVhf8H7fvqSWfj0JbNMPZ9ZzFavZxMh9LQlWb3Qr/R7EPa50R9NoLUngmkN1goy/UNxvH24GwBw9rQ6Sx87k7Dfg6qABz2ROFq7I4bFHnWMy4jYoyz2B4ayL64PdqbEnkm1xRV7Mt8r3YMx1FcU/rdGiJ0IsSeWkHG4K+UqLEY4cyZWjcKaRU8blyzLrF4vUYyIPZ1KC53V4cxAxuaDzgwhs3ArgahIkoSvXXUKrlzUjFhCxm3/uwGbDnY5fViEEEI0IMauzNavd/Sn2lAKOXtKhSrDY1y5s3bERU6HDmePVW1ckiSlR6C6rB/l2rC/E4mkjAk1QUyy2dHSouTgHDExymVmjCusfE9/AWeP3a/DSDxulyr4MLeHlAJBrxs+xWG270Q/AHszvUoZPW1c/dEEkooZqVTEKpLCkNijbPDYkVWljnEVObOHYg8Zhssl4fv/cCoumNmAgWgC//TL9dh9vM/pwyKEEFKAequcPf3anT2lgPExrtw5C7UjmmnykRaNrDNLC5HEjpDmV/e2A7DX1SNoUuvXjYtWEYNtXEAqswfIfdF2sCN1XMUWe4C0ONvF3B5SAkiShGrlvLdXiD1FdvaUCuKiXEsbl/gc8bgkBLy8rC4lzGT22NFCp3c80CpGzbty1apVmD9/PpYsWeL0oZQ9fo8bP/7wYiyaWI2O/ig+8j+v2RoUSQghxDyWO3vKZKEvrPP90QQSycJ5D4J0XW4WZ09Ye/6RWOxbuavbpLSptfbYIPbsSYWgnj3dfrHHimYxIdQYyS4K+xVnT46d3QMOZfYA6fp1LYIiORmu+61HvCdVsadIteulhhCWtVRkZ7Y6FivfiGjDzBiXHe/9dMsbx7gMsXLlSmzZsgXr1693+lBGBRV+D35x8xJMawjjcNcgrv/JKzikzLYTQggpPVRnjwmngCzL6Zn1ivJY6Gc6c7Tu4CWSsroAzObIUTN7CghnsiznFY2MIkSSIxaPcQ1GE9h0qAsAcPa0AjVjFqA2i3WZH+MKevU7p/I5exJJWX19J9UVr3ZdwEYuc3Ddbz3VI8WeItWulxpBHQ4M5vWULqrYY8DZY8d7P+R1po1r1Ig9xHrqK/z431vOwuS6EA50DOD6n7yC/e39Th8WIYSQLKjOHhPV631DcUQTqWatcnH2eN0u1T7fo3GUK3PxlzWgWaNwNpDhJrKydrdZGeNqtXiM680DnYglZDRW+TGl3n43i5o9ZMKhNKg6e/QvWfNl9hztHkQ8KcPndqGxMmD4+IyiZ1SQkGIgckqO9abcnWN1jEsdt9EwxqWO8WZpdSTOoo5xGWnjsjGgmWNcpKSYWBvC7247B9MzHD7M8CGEkNLDCmePcPUEvW5bKr/tolJnSLMQhQJeF3yek5dC4kJcvB65EM/ncUmGMmVy0WTB+FM2XtmrjHBNqy/KyEGzBUHTYmEsXDp6yNfGJUa4JtYG4XIVf/xCOHu6BunsIaVBdXD4Be5YFXvEuTyWkBFTNj9yobY6+unsKTXMBDTbIvb4nalep9hDCtJcHcQjt52DWeMr0NoTwfU/eQU72nqdPixCCCEZqDkz/VHIsvbsmkza1Sau8lrk6w1pzle7DmivXs9s4rJSPEln3Vg7xvXqnlQ48znT7R/hAtJjXGYcSmJ33Uj1ej5nzyElnHmiA3k9QNpFwTYuUiqMbCAqt88Bq8jc6Cjk7snM7CGlhRmxx9aAZrZxkVJkfGUAj3z8HMxrrsKJviHc8NNX8M6RbqcPixBCiIIYu4olZF2Lm0zsXOjYiRBterQ6ewo0aGWOceUTznoGRTiztQt9IZJ0DsQ0NcJoIRJL4M2DXQCKE84MpB1KvUNx3W1pAjWg2UgblwZnz2QH8nqAtKDINi5SKtSMyB2zo366HPC5XRBmv0gBF0Za7Bmbr1UpYyizx86AZm/+wgC7oNhDNFNf4cdvP3Y2TlVaum786SvYpCwcCSHECdjIkiboc6uLiQ6DjVwi76fcWliqDDp7coUqZwpn/XkW+4UcQkapCnjUXUCrRrk2HuxCNJ5EQ4Uf0xvCljxmISr8HnXH26i7R4hdISNtXHmcPQeV0olJtc46e5jZQ0qFajp7AKRq6POFu2eS/gygs6fUMJLZY2tAMzN7SDlQE/Lhf289G4un1KInEsc//vxVvL6vw+nDIoSMUdjIMpy6jFEuI6jOnjLb0U2PcWlb1BXajQ363PArWT75Grl6I/aEc0qSZPkoV2blejErgltEI5dBscfMGFe+Czbh7Jnk2BiXcI9R7CGlQfVJzp6xKfYA6fNN4TGu/BsHxDlEjpJWsScSS6ifFXZseKmfR7GE4VF7I1DsIbqpCnjx8EfPwjnT69A3FMdHHnwNL+9ud/qwCCFkzFNnMqS5Q9Suh/2WHVMxEIs6zc4eDeNXWl7L9ONYv9C3Iu8mk1f3Knk904ozwiUQo1xGfw51jMuIs8ef2zZ/UMnsmeyQ2JNu4+IYFykNMsUdt0uyfDy1nBAujELOHlXwH8OvVakizv+ZrZn5EC5Lj0tCpd/636f4DEskZbX1tBhQ7CGGCPs9+MXNZ2HprAYMRBO4+RevYe2O404fFiGEjGnM1q93qAHN5bVLadTZk283VmSq5HNJ9dgYzmllI1c0nsQbBzoBAGcXKZxZIBxKRww6lMyMceVy9gxGEzjRl3qvOzXGpTUEnJBikZnZUxvyFdUBWGqIkehCmWkMaC5dKjJ+J1rcPeKzvsam937mZ1gxR7ko9hDDBH1u/OwjZ+Jdc8djKJ7ErQ+9jr9sPur0YRFCyJjFbP162Tp79AY0a8hZqA0XzlRRs39scPa0WDjG9dahLkRiSdSFfZg1vsL04+nBrENp0ERAc3pnd/j7QuT1VAU8J+WUFAvxvJFY0rIQbkLMkBnIbEdmSTkR1OzssSe3jZjH73HD505JHVpCkdMFFfb8Lr1uF7zulIhUzPp1ij3EFAGvGz/+0GK855QmRBNJfPLXb+DnL+4p6iwiIYSQFMIt0G4ws6f8nT16x7hMOnsGCzuEjNJk4RjXq3tTeT1nTS1uXg+Q6ewxOsaVeo2NVa+n3hf9I9q4Djqc1wMAlX4PPErlD0OaSSlQE0yPcZVbSL/VBDVm9ojPADp7ShM9Ic1C7LEzq0pr8LeVUOwhpvF5XLjvg6fjH8+eDFkGvvHkVnz9z+9omo8khBBiHfUVirPHcEBzuTp7DI5x5XP2aKjGtrOJRRVJusyLPa/sSeX1FKtyPZPmGpHZY3SMK5VtYGyMK33BlrkmUcOZHRrhAlIh3MJJwVEuUgpUBjwQWvBYd/akm5Pyf6b02ujuJOYR7k4tawOxbqqzVewpfiMXxR5iCR63C9943wL8++VzAQAPvbwft/3v6ydZpwkhhNiHFjdKPtr7ytXZozOgWUODitjZ7shzIZ4WjWwIaBYiSY85sSeWSGLD/lRezzlFzusBkNEqpv/niCeSapClsTGutAiXuUOvhjPXOyf2AOn2Izp7SCngcknquWys1q4LAhovypnZU9pU6GjkEptddrraxHhgfxGvjyn2EMuQJAkfXzYD9//jGfB7XHhm6zFc/5NXcMzkQpUQQog2zFSvxxJJNfOm3Jw9VYadPfnGuITrIk9mz6B9tbvNVakxro7+qKlMl82HuzEQTaAm5MWcxkqrDk8zYhytNxLXXIEryBRojLRx+T0uKJNSGMh47rSzJ6j7Ma1Ei3uMkGIi3GZjuXYdAEKKuDyQ59ybTMroiwqxp7w2SMYKolVLS2aPWDfZ6Wqjs4eMCi5f2IzffOwc1IV9ePtwN95//zrsaOt1+rAIIWTUY0bsEaMkkpR2HJQLaWePdQHNavV63jYu+8a4qoIe1c1iJrdH5PUsmVoHl6v47ToVfo/6+ugd5RJijySlhBu9SJKUzu3JWFwf6nQ+swdIX1DnExQJKSaikcvOUZZyQIjLkTwX5X3ROEREKZ09pYma2aNljEsNaLZxjMvLzB4ySlg8pRb/d/t5mNYQxuGuQVx7/zr8fdcJpw+LEEJGNabEHqWJqzbkg9sBUcAMhgOa84haNRpG4uwc45IkSR3lMlO/rub1TCt+Xo/A6ChXZhOX0WDpkJLZIHZ2ZVkuiYBmIL2D3DVIZw8pDcZXpf6tNir/ZscqWtq4xOeIz+0yFCBP7EesiR5/6wjiykhwLoTobqerLf2+4hgXGQVMqQ/j0U+ehyVTa9E7FMdND76G//f6QacPixBCRi1iYdMTiSNWYGEzknaliascgzmF2NMfTRQsB5BlWVPOQp06YqNljMueXV0hkrT2GAs3jieSeH2fc3k9AjHKdVRn2LRw9hgJZxaER7SfdPRHVZfPhBpnx7jEyAwze0ip8K/vmYMvrpiLy+Y3On0ojqKljUsV+206/xPzfPT8aQh63Xhx5wnc/dS2vPdVA5ptzCzMLA0oFhR7iK3Uhn3431vOxlWntiCelHHnH97CPWt2sJqdEEJsoDroVTNK9Db8CGdPOQZzZuYlFLJrD8YSiCuCUD5HjrgQ7xiIZv3MGoonMBRPnvT8VtKsiCRGG7m2HO1B31AclQEP5jVXWXloumgx6ewxs2uuOnuUndSDnSnhrKkq4PhuvDrGZTBQnRCrmTm+ErddOMPxfxtOoyVbJb1pUH4bJGOF+S1V+P4/nAoA+J+X9uJ36w/kvG86s6cYzh6KPWQUEfC68YPrT8PtF80AAPzw2Z1Y+Zs3dAc1EkIIyY/bJWVcQOpzC3QUYV7dLnwel5rp0lNglKtnMPXZ43ZJeR0j4nWIxpNZd+HEQl+S0iGQVqM6ewyOcb26J53X4+RoXpMq9ujM7MkY4zJKSHH2iMdSw5nrnHX1ABkBzYN09hBSSmhz9tiX2Uas4/KFzfjcu2cDAL782Ga8puTYjUQE5dsp9ox0mhYDij2kKLhcEr7wnrn41jUL4XVLWP12K9636u/YdazP6UMjhJBRhRjDEmNZWunoK1+xB9Ae0py5QM+XAxPyueFzp5ZJ2XJ7xAhXhd9jW/CxUZFE8Ope5/N6ABOZPZaMcQ3P7CmVvB4gc4yLzh5CSgnhbMp3Uc7a9fLhM5fMxBWLmhFLyPjErzaonwOCoXhCHe+1s3pdfJYNFNHwQLGHFJUbzpqMRz5+Lhqr/Nh1rA/vW/V3/GXzUacPixBSpqxatQrz58/HkiVLnD6UkqFeqU3X6+wpRhOFnVRpDGkWzp9CocqSJKE2nDtTpcfGcGZBi8i6MeDsSSRldQfTybweID2OptehJMQeU2NcI3ZSVbGntnTEHrZxEVJaqI7APM4erZ8lxHkkScL3rjsVCyZUoaM/io89/PqwCRPxGe92Sepawg7UMS5m9pDRzOIptXj80xfgrGl16BuK4xO/egPfempbwZR0QggZycqVK7FlyxasX7/e6UMpGYRA0aHT2dNehHl1O0k3cuXfMevREapZm6eRqxgW/iYTY1zbWnvQE4mjwu/BKS3O5fUAaWfPEZ0OJSHQBE04e8ROajqzJyX2TC4BZ486xkVnDyElRdCXukTWltlDZ085EPS58bOPnIlxlX5sa+3FZx/ZiKSS35fO6/Eabn7UgpYsKKuh2EMcYXxlAL++9WzcesE0AMCPX9iNjzz4Gtr79F2cEEIIGU6d4uzp0OvsURY79RXlKvYoY1xDhTJ7FJHGX3g3VlyMZwu7Ftk/+erbzSJEkvb+KCI6dwJFXs/iKbXwuJ1d7gnRqjcS15XXF7FijEvJUxoYEs6elOBUCmNctRmNbyyuIKR0CHq1O3sY0Fw+NFcH8dMPL4bP48IzW9vwvb9uB5Be/9i92RVUnaYc49INrfzlh9ftwpevnI8f3Xg6Qj431u1ux1U/egmbDnY5fWiEEFK21NHZk/d+upw9ymuZrS0pbeG3b1e3OuhVg0LbevS5e9S8nunO5vUAqYshEWKtx6U0YEUbV4azJ55I4nCXEHucD2gWY1zxpMzSCkJKiKCuNi46e8qJ0yfX4jvXLgIA3P/8bjz25mF1lNbu9U9IQxaU1YwasYdW/vLlqlNb8NjK8zGtIYwj3RF84Mcv47ev5a7GI4QQkhvV2aMzB0R19ijfX25oFXt6dezGpp09WTJ7Bu3Pa5AkyVC4cTIjr+fsac7m9QiMhE2LCy2rnD1HuyNIJGX43C40VgYMP6ZVBLxuBLyppXi2XCiSG27yEjtRx23ytnGxer1ced/pE9SW6C/88S08t+0YgPQGj11wjIuMWWY3VuJPnzofl81vRDSRxBcffRv/+oe3dNvWCSFkrGPE2SPLcnpm3ebFjl2IBbfW6nUtIo0Iq842xtUbsX+MCzAmkuw41ovOgRiCXjcWTay269B00VyjP2xarAHMVa+nnT0inHlibdC2BjW9ZI5yEe1wk5fYSVB1YOTePEgL/nT2lCP/ctkcXDq/EdF4En984xCAIjh7/KxeJ2OYqoAXP/7QYty5fA5cEvC71w/ivff9Hdtbe50+NEIIKRuMZPb0RxOIKiH5Y8XZo2WMqyafs6cIY1xAuslKj0iSmdfjdTivR9BcpYhWXfrHuMyIPeGMNi4RzlwKeT2C6qBo5GJIMyGlghjjisSSaojvSPS4REnp4XJJ+O/rT8Pcpkr1Njtr1wFtjjGrKY0VACEKLpeElRfPxEMfPQsNFT5sb+vFVfe9hIfW7WN4ISGEaKBObZDS7uzp6EtdaAa8LlPNR06iBjRrzOzRskCvy5fZM1ichX6zgUYuNa9nmvN5PQK1WaxHxxiXcPb4jAtqIb/i7BmK44CoXS+BvB5BvhBwQogzZArMkXj2C3PV3UlnT9lS4ffgZx85U3Xxjq+0d7NLvK/6i5jRRrGHlCRLZ43DU/+8DBfNGYdoPImv/fkd3PLQ6zjBti5CCMlLndKm1dmvveGnQ7nQrCvTcGYg09mjrY1LywK9Jm/1uvagZzM01yi15RodMbKckdczvTTyegCgpUZ/9pAq9niNL1eHOXtEE1dt6Th7xNhk9yDHuAgpFTLFnlz5KszsGR1Mqgvh17eejY8vm473nz7B1udiZg8hGYyr9OMXNy/B16+aD5/Hhee2HcN77n0RL+w47vShEUJIySIEm2giiX6NCwrhXKkr09p1IC3eWBnQXKfmqeRr4yqSs0ejI2b38T6c6IvC73Hh1EmlkdcDAE1iHE3HGJdYEJtxmw3L7FHGuCaX1BhXWpwlhJQGLpcEvyd1mZwrXyVdvU5nT7kzr7kK/375PHWDxy5CYvMhlijaxArFHlLSSJKEm8+fhj9/6nzMbqzAib4h3PTga7jr8S0YymGrJISQsUzQ51Z3JcV4ViHKvXYdyBzjKuDs0VO9Lpw92cSeweLs6jZVpUQSrWNcryh5PWdMroXfUzojec0m2rjMjHFltnEd7Ci9zJ7aEDN7CClFQmpuz8nXG/FEUhWB7A7pJ6MHsXGRSMpqTqLdUOwhZcHcpir8+VMX4KZzpwAAHvz7Xrxv1TrsbGN4MyGEjETMn2cTKbKRrl0vZ7FHm7NHT2W6GLGJxJIn2a71BD2bQYw/neiLatrkeFUd4SqdvB4gLfb0ROKa8woGLGzj6hiI4oQifpaW2JPbPUYIcY50I9fJ592+jHMYnT1EKyFf4fFAq6HYQ8qGgNeN/3jvAjx485moD/uw9WgPrvzRS/jfV/YzvJkQQjKo1Vm/rjp7ylrs0RbQnA7VLCz2VPg98CgV3SOdFz06HscM1UEvAkpmTVt3/t+nLMt4dY8IZy6dvB4g9fupUFw2WnN7Ila0cSnPGY2ndlGrAh61AasUqFGcPV3M7CGkpBAujGxij/gcCXhdJdN4SEofr9sFrzu1pihW/TrfnaTseNfcRjz12aVYNnschuJJfOWxzbj5F+txuEu7NZwQQkYzeuvXR5Ozp28ojkSOqtxYIqmG/mpx5EiSpApgmWJPIimrO7t27+pKkqTWrx8pMAK1r30Ax3qH4HO7cPrkGluPywhNOpvF0m1c5p09glJy9QDpEPDOAYo9hJQSwTxjXD2sXScGCWWUBhQD+s5IWTK+MoBf3rwEv1i3D9/+yza8sOM4lv/3Wnzx8rn44FmTIUmS04dICCGOURcai86e9JKmbyie1b2R6foRLpNC1Ia8ON47NCxAty+SaeG3f7HfXB3A3hP9eGjdPqzbdSLn/XYe6wMAnDapBgETbhi7aK4OYNexvoKilWDAAmdPaETeTymFMwPpzB6OcRFSWoS8uS/KRWYba9eJXkI+N7oHY0Ub4+I7lJQtLpeEWy6YhovmjMMX/vAWNuzvxJf+bzOefOsovn3topLbvSOEkGKh29kzUP7OHr/HDZ/HhWg8id5ILKvYI/J6wj43PBqt97Whk509Ylc36E09p91Mrgth3e52PLW5FU9puP85M0prhEvQojiU9rf3a7q/2FEf6c7Rg9slIeB1IRJLjXGV2tqgRs3sobOHkFIiIGqyszh79LQ6EpJJMKMhshhQ7CFlz4xxFfj9befioXX78J2nt2Hd7nZc9t9r8a/vmYOPnDsVLhddPoSQsUWdzsyejlHQxgWkdllP9EVz5vaodek6MluyiT3dg8Wt3F158UxUBb0YynLRMZKKgAe3nD+tCEeln1Mn1eB3rx/E+n2dBe8ry7IlY1wAEPZ5EImVXjgzkM7s6YnEkEjKcHPNQkhJEFIchYNZLsrFZwzDmYlexOYFnT2E6MDtkvDRC6bhknnj8YU/vIVX93bg649vwZNvH8V3rjsV0xrCTh8iIcQGVq1ahVWrViGRKM6HZrmg19kjxJ76ivIWeyoD3rxij5EFuprZk/FaqiHPRQr6nVQXwr9fPq8oz2UnoiFs48EuRGKJvKNm0URSzV4yO5IW8rshzESTaoOmHstqapT3kCynRMS6MnbXETKaCGpw9tgd0E9GH/nGA+2AAc1kVDGlPozffuwc/Of7FiDsc2P9vk685961+NnaPTkDOwkh5cvKlSuxZcsWrF+/3ulDKSn0OHtiiaTqVCl3Z0+6fj27yKWndl0gMlWyjXExr0Ef0xvCaKjwIxpPYtPBrrz3jUST6v+bGeMCUs4eQall9njcLvV9y9weQkoHLW1cdPYQvaTfV8UZ46LYQ0YdLpeED58zBU9/bhmWzmrAUDyJ/1q9Fdc+sA7bWnucPjxCCLEd4ezR0vAjskIkKZ0fUq6kxZ78zh49jpy6LG1cPYPMazCCJEk4e1rK3fPq3o689xW76R6XZLraWIhFkgRMKDFnD5A5KsjcHkJKBREMn83ZY2QkmBAgY4xLw1i2FVDsIaOWibUhPPzRs/Dtaxei0u/BxoNduOKHL+Gbq7eif6g4aiohhDhB2tlT2CkgRIyaoLfs80Iq/amfO6ezJ6I/a0dciGe+lsUe4xpNiFGuV/e2572f2PU008QlCCvNa42VAfg9pddSVsNGLkJKjnzZKqqzR2OrIyGCfI4xO6DYQ0Y1kiTh+iWT8dc7luE9pzQhkZTx07V7cMn3X8BTbx+FLHO0ixAy+hDOnu7BGGKJZN77tveVf+26QIg4PbkCmo2McYXFhXhaQOIYl3HOnpZqCtuwvxPReO73plXhzED6oq3URrgENXT2EFJyBLwaxB5+BhCdiLFiij2EWEhzdRA//vBi/OLmJZhcF0JrTwSf/PUbuPkX67HvhLYKWEIIKReqg15IikmnUKXzaKhdF4ixqtxtXAYCmrM4e3oGxePQ2aOXWeMrUBvyIhJL4u3D3TnvJy6wrBB7xOJ6Yl3pjXAB6VwoOnsIKR2ESDyQZ4yLnwFEL+r7qkhTJhR7yJji4rnj8dfPLcNnLpkFn9uFF3Ycx2X3rsW9z+xApEizk4QQYjdul5RVpMhG+yipXQc0BDRbVL2efhzu6urF5ZKwZGrhUS7V2WPBGNe4ypTTbXZjpenHsgPRyFVImCWEFA9x7onQ2UMsJJhHRLQDij1kzBHwunHHpbPVAOdoPIl7n9mJ5feuxQs7jjt9eIQQYgnCLVBI7OkcJbXrQOGAZuHI0TfGlXpdBqIJdVOAtbvmOHt6apTr1T25Q5qtdPbcduEMfOuahfjQOVNMP5YdvGteIz5/6WwsndXg9KEQQhTyZaswoJkYJV8WlB1Q7CFjlmkNYTz80bOw6oNnoLHKj/3tA7jpwddw+6834HDXoNOHRwghphAtUoXEno5R5OypCuQPaO41ENBcFfCowdXCeaGKRlzoG0I0cm3Y34l4jkwpK509dWEfbjhrMipKNEz1wtnj8OlLZqkiGCHEefK1cdHZQ4wSVDN7OMZFiO1IkoQrFjXjmTsuxC0XTIPbJWH126141/eex/f/up2tXYSQskUVewrkgAixp25UZPYUcPYYaNGSJEl1SYlRLiOtXiTNvOYqVAY86BuKY8vRnqz3EbueIQucPYQQopeQclGePaCZ7k5ijJCXbVyEFJ3KgBdfuXI+Hv/UBTh7Wh2G4kn86LlduPh7z+P/vX4QySRbuwgh5YUq9vSNJbEnf0Bzr8EWLbUtSXmt1Op1LvQN4c7M7ckxyiV20wMWOHsIIUQvQV/qMnmksyeWSCISSzkSKfgTvXCMixAHmd9ShUc+fg5+/KEzMLkuhGO9Q7jzD2/h6lUv4dU9uYMkCSGk1BDiTadGZ89oql7PGdA8aKxBpW5ENbZw9lQzoNkwYpQrV0iz2PW0YoyLEEL0EvRmr8jO3Ewo1dFQUrqE/KxeJ8RRJEnCexY0Y80dy/Dvl89Fpd+DzYd7cP1PX8Enf7UBB9oHnD5EQggpiMjgadeY2TM6qtdzj3ElkzJ6h8QYl15njxJ2PRCFLMsZeQ109hhF5NO8trcjq3tWhGFzjIsQ4gQioHlkW6/YNAj73PC4eSlN9KE6e9jGRYiz+D1ufHzZDPztzovwj2dPhksCntrcinff8wLuXr1V3dklhJBSRLRrdeYRe2RZVjN9RkNAsxBf+qLxkwSE/mgcsnKT3vEr4ZLq6o9iIJpAQnlsjnEZZ0FLFUI+N3oicWxr7T3p68LiHqDYQwhxgJDaxhWHLKc/Tyj2EzMIt2qxcmEp9hBSgIYKP/7r/Qvx1D8rVe2JJH6ydg8u/u7zeGjdPkTj2ZtECCHESYR4k6+NayCaUM9ho6l6XZZTgk8mIpzZ53bB79G3/BGZPR0DUVXo97olBLxcRhnF43Zh8ZRaANlHuQYsbOMihBC9iLywpAxEM1oDjbQ6EiJgZg8hJcqcpko8/NGz8ODNZ2L6uDDa+6P42p/fwSX3PI//e/OQutNLCCGlQH3YDyC/2CO+5ve4RsVFdcDrhk8RckaOcqnhzEEPJEnS9bh14dQObtdATK1drwx4dT8OGc45GaNcI4mwjYsQ4iCZ557MC/Me1q4TE4iWt4FYYphjzC4o9hCiA0mS8K65jXj6s8vwjfctwLhKPw52DOJzv9uEK374Ip7d2laUf7iEEFKI2vDwnJlsZOb1jBbhoipHSHOmSKOXmgyXlNFGL3IyIqT5tb0dJ71HGdBMCHESr9sFjyv1uZiZr9KjbhxwjIvoR2RBJZLyMMeYXVDsIcQAXrcLHzpnCl648yLcuXwOKgMebGvtxS0PvY4P/PhlrN+XvUqWEEKKhXD2RONJ9OewC4+mJi5Brvp1EappRKQRbVxdGWNcXOibZ9HEGvg9LrT3R7HrWN+wr7F6nRDiNEE1tyf9GcrMHmKGXI4xu6DYQ4gJQj4PVl48Ey9+4WJ84sIZ8HtceH1/Jz7w45fx0V+ux9ajPU4fIiFkjBL0udVMmVwhzULsqRtVYk92Z0/vkHGRJtMllXYI0dljFp/HhTMmp3J7XhkxyjWotnHxdSaEOINwFg4OE3uY2UOM43W74HWnHGPFqF8fNWLPqlWrMH/+fCxZssTpQyFjkJqQD/+2Yi5euPNifPDsyXC7JDy37Rgu/+GL+Owjb2LfiX6nD5EQMgYR7p5c9eujW+wZ6ewxLtKIsOuu/ljGGBd3da3g7OnpUa5MxMVV0DdqlqqEkDIjW012LzN7iEnU3B6KPdpZuXIltmzZgvXr1zt9KGQM01QdwDffvxDP3HEhrlzUDFkGHtt4BO/6/vO44/cbsZeiDyGWQqE/P8KRktPZMzAKxR5/6mfuyTnGpV+kEa9P71AcJ/qihh+HnMzZ01Ihza/uaR+W2zOotnHxgooQ4gyBPM4efgYQo4TU8UD769dHjdhDSCkxrSGM+z54Bp749AV419zxSMrAo28cxiUUfQixFAr9+akr5OxRhAuRSTMayD3GZXw3tirghZLTiYMdA4Yfh5zM6ZNr4HO7cKx3CPvaB9Tb084eZvYQQpwhlCWzR7hEGdJPjJItC8ouKPYQYiMLJlTjwZuX4E8rz8clI0Wf323EnuN9hR+EEEIMUhfS5uwZWwHN+ndjXS5JbeTar4g9DGi2hoDXjVMnVQMAXtvbrt6edvZQ7CGEOIO4KI9kjnENicwefgYQY6jjgRR7CBkdnDqpBv9z8xL8+VMZos+bh/Hue16g6EMIsQ0h4hTK7KkfVWJPDmePIv4YFWlqFOFsf3vKmcldXetIj3Klc3vEIjhEZ8+o4f3vfz9qa2tx3XXXDbt9+/btOO2009Q/wWAQjz32mDMHSUgGYow0exsXPwOIMUJZ3ld2QbGHkCKyaGJa9Hn3vOGiz+d+txG7jvU6fYiEkFGEEHFyOXs6R2X1eo6AZpMNKmLUTWT2cFfXOkRI86tKSHMyKbN6fRTymc98Bg8//PBJt8+ZMwcbN27Exo0b8dJLLyEcDuPSSy914AgJGU4wb0AzPwOIMYLM7CFkdLNoYg1+ftMSPP6pC1TR5//ePIx337MWH3/4dWw82OX0IRJCRgFCxBHjWiMRt48mZ0+VDWNcANQxLvV5OMZlGYun1MLjknC4axAHOwYwFE+qX2Nmz+jh4osvRmVlZd77/PnPf8Yll1yCcDhcpKMiJDchNaA5/XmiBjQH6ewhxsjW8mYXFHsIcZCFE6tV0Wf5KY0AgL9uacP7Vv0dN/70FazdcXxYOwkhhOhBiDgdWZw98UQSXQOpRevodPZkH+My7OwJDxd3OMZlHSGfBwsmiNyejmELYGb2FIe1a9fiqquuQktLCyRJyjpGdf/992PatGkIBAJYvHgxXnzxRcuP4/e//z2uv/56yx+XECNkc/aIgGY6e4hRGNBMyBhj4cRq/OTDZ+KZO5bhusUT4XFJeHlPOz7y4Gu46r6X8ORbR5FIUvQhhOijNpR7jKtLcbpIElAzilwqOQOa1d1YYz9r7QhnDxf61pIe5WpXre0+jwtuUYNGbKW/vx+nnnoq7rvvvqxf/93vfofPfvaz+NKXvoQ333wTS5cuxYoVK3DgwAH1PosXL8aCBQtO+nPkyBFNx9DT04O///3vuPzyyy35mQgxy8iL8kgsgWgi5TxkZg8xSthXvMwevksJKSFmjq/E9z5wKu64dDZ+9uIePPLaQWw+3IOVv3kD0xrCuG3ZdLz/jAnwe7jTSQgpTH1F7oBm4fapDnrhcY+evR+xABdjW4IekwHNI91PtPBbyznT6vGTF/bg1b0davMNXT3FY8WKFVixYkXOr99zzz245ZZbcOuttwIA7r33Xjz99NN44IEHcPfddwMANmzYYOoY/vSnP2H58uUIBAI57zM0NIShoSH17z09Paaek5B8iHOQOCeJTQRJAip8/AwgxhBjXANDzOwhZEzSUhPE1646BX//t3fhny+ZheqgF3tP9OPfHn0by77zNzzw/G50D8QKPxAhZEwj3CjdgzHEE8lhXxNiT90oGuECsgc0R2IJROPmdmNrQyPGuEaRG6oUWDy1Fi4J2N8+gL0nUvX2bOIqDaLRKDZs2IDLLrts2O2XXXYZ1q1bZ9nzaBnhuvvuu1FdXa3+mTRpkmXPT8hIQiOcPWI8uMLngYuuQ2IQ1THGzB5CxjZ1YR8+d+lsrPu3d+HLV8xDU1UAbT1D+PZftuGcu5/F1/60GftO9Dt9mISQEqUm5IOkrEc7RwjEqtgTGm1iT0qE6YvGkVTGX8UIl5nd2MwxLu7qWk9VwIv5LVUAgBd2HANAZ0+pcOLECSQSCTQ2Ng67vbGxEa2trZofZ/ny5fjABz6A1atXY+LEiVi/fr36te7ubrz22mtYvnx53sf44he/iO7ubvXPwYMH9f0whOggoAY0D3f2UOwnZlADmjnGRQgBgLDfg1uXTsdHzp2KP208jP95aS+2tfbioZf34+FX9uPSeY245YJpOGtaHSSJOw2EkBRul4SaoBedAzF0DkQxrtKvfm20O3tkOSX4VAW86XBmv/Hd2MwxrgoTj0Nyc/a0emw+3IO/bTsOgE1cpcbI9YUsy7rWHE8//XTOr1VXV6Otra3gY/j9fvj9/oL3I8QKRrYmiY0D5vUQMwTVzB6OcRFCMvB5XPjAmZPw1D8vxa9vPRsXzxkHWU41eF3/01dw9X1/x582HkZsxLgGIWTsIsSc9r7huT2jVewJeN3wKRlEQuQR+T1mQpUznT1G69tJfs6elgppPtw1CIDOnlKhoaEBbrf7JBfPsWPHTnL7EDKaCOZw9lDsIWYIednGRQjJgyRJOH9mA37xT2fhmTuW4cazJsPvceHtw93450c2Yum3/4Yfv7AbXQMnh7ISQsYWQszpHMgu9oym2nXByPp1s+HMwPDMHlr47eEsRewR0NlTGvh8PixevBhr1qwZdvuaNWtw3nnnOXRUhNjPyDau3oj5jQNCOMZFCNHMzPGVuPuahfiXy2bj168ewMMv70NrTwTfemob/nvNDrzvtAn4yHlTcEpLtdOHSghxANXZ059d7KkfpWJPe39U3YXttcB6Xx30QpJS42Hc1bWHmpAPc5sqsa21FwCdPcWkr68Pu3btUv++d+9ebNy4EXV1dZg8eTLuuOMOfPjDH8aZZ56Jc889Fz/96U9x4MABfOITn3DwqAmxl1xtXPwMIGYI+Vm9TgjRSX2FH5+5ZBZuu3A6/rzxCB78+z5sPdqD371+EL97/SCWTK3FR86diuWnNMHnoamPkLGC6uwZIfYIp0/tKAtoBtK7rqqzZ1Bx9pjYjfW4XagOetE1EOMYl42cPa0uLfbQ2VM0Xn/9dVx88cXq3++44w4AwE033YRf/vKXuP7669He3o677roLR48exYIFC7B69WpMmTLFkeNdtWoVVq1ahUTC/oslMnYJ+YZflKsuUX4GEBOMzIKyE4o9hIwy/B43PnDmJFy3eCJe39+Jh9btw182t2L9vk6s39eJ8ZV+fPDsyfjgWZMxvirg9OESQmxGiDkdOZw9dRWjUewZXr8uRJ+qoLllT23IlxJ7TD4Oyc3Z0+vx0Mv7AdDZU0wuuugiyLKc9z633347br/99iIdUX5WrlyJlStXoqenB9XVdC4Tewj6UpujakDzIAOaiXnEZ1v/kP0BzXynEjJKkSQJS6bWYcnUOrT1RPCbVw/gN68dwLHeIdz7zE7c99wurFjYjJvOnYLFU2rZ4kXIKEU4e3KKPaPS2ZNa3ohdWNGgYnY3tjbkxV4LHofkJjO3h84eQoiTiNakkwOa+RlAjMPMHkKIpTRWBfC5S2dj5cUz8Zd3WvHwun14fX8nHt90BI9vOoK5TZW48azJeN/pE1DN4FFCRhXZApplWR61bVxAvjEu884eKx6H5Kahwo8Z48LYfbyfzh5CiKOIc1A0kUQ8kbQk/40QdTwwloAsy7ZuuDO4g5AxhM/j+v/t3Xt01PWd//HXzGRmciEXQi6TGxhB7hARFIOKXGo0Xgran6Xd3/qjtfYcarSHxf2drfbXxeM5u7D1lLW7Bqu1p7XntKurBasVFyMkUKVWwAApIBCJEMiVAElIyG3y/f0RZkwIl1xmmO9883yckwPznSH5fPL58p7vvL/vz+ejr+ek660fzNOfnrxdy+ZkyR1h1+c1zVr9zn7N/dcP9X/f3KvS42euWs4NIDxcauv11g6v2ru6+zxvJZebxjXcu7HXJcVIkjITo4f1fXBld05MkSSlxTPVGEDoRPeqLjzf6fW/p7AjI4bDV7Xq7TbU4e0O6s8iLQmMUNMz4vVv/2umnrl3ijaWntDvPz2uw7Xn9ObuE3pz9wlN9sTqf88dqyWzMpiyAISxS1X2+Kp63BH2PhezVtGvssd/gT68y56VX7tBt09I0u03JA2vgbiiVXkTdduEMfyeAYSUO8Lu34XxfKdXze1U9mD4+iQRO7xyRwTvOozKHmCEi4926ju3ZWvzyvl6a0WuHpqVIdeFap+f/HG/5v7LFv3TW/u0t/Is1T5AGOq99brv/3DvKVxWXK8r7nILNA8zcR0b6dTCySlyOrh8CqZR7ggtnpIa1AtgALgam83mn8p1vsMbsCnBGNmcDrucjp5rr2Bvv86ZCkBSzxvanOsSNee6RP3zA1O14bOT+v2nx1Ved86/fftkT6y+OSdLS2dlWHLqB2BFvv+rHV3dau3wKsYdodOt1l2vR+o/jct3gc6imoA1sPU6rpUop0OtHd4L07gCMyUYiHZFqPF8Z9CTPdyaAtBPQrRLj96eraJ/mK83V+TqwV7VPs/96YDm/uuHevx3u1V8qE7ebqp9ADOLdkUo0tnzdu+r6Dl9zurJnouncQVm63UA5lBQUKADBw5o586doW4KLM63vkprh7fXbly8l2B4ov3nVXC3X+dMBXBZvbdvf/aBaXpn70m9ufuE9p1o1KayGm0qq5EnLlLfmJ2hh2dn+RcvBWAuidEuVTW26XRLh7ISo/3r94y24Lbr0qUWaPaV3nM3FgAwcL5pXGdaOtR14QYn7yUYrt5JxGAi2QNgQOKjnXok9zo9knudDlQ16c3dlXq79KRqmtpUWPyFCou/0C3ZifrmnCzlT/coxk14AcwicdRXyR6pZ/0eaSRU9nSpy9utc+3cjQUADJ6vAqO2qV2S5LDbLLmxAa4t3zl0nmQPALOZmh6n1enT9KP8ydpysE7/vatS2w/X69OK0/q04rR+8vbflD/dowdvytC88Uly2K23ACwQTnwVPL5kzxnLJ3t6Lm+a2jr9iZ6e49yNBQAMXKTTl+xpk9SzgLwVNzbAtRXt7LlOobIHgGm5Ixy6d0aa7p2RpurG89rw2Um9tfuEKk61aEPpSW0oPanUOLeWzsrQQ7MyNckTG+omw2JYpHNgxly0/frpEZLsOdfepcbzPev1RDrtckWwVCEAYOB8FRh1zT2VPVSIIhCiWLMHQDhJi49SwcIJenzBeJVWntWGz07o3b3Vqm1q18vbjurlbUc1LT1OD87K0JIbM5Qc6w51k2EBBQUFKigoUFNTk+Lj40PdHNMa3Wv7dcn6yR7fegqGIdU0tvU5BgDAQPk+lNddqOyhQhSB4J/G1UllD4AwYrPZdNPY0bpp7Gj95P6pKv68Xhs+O6HiQ3XaX9Wk/VVNWvP+57rjhiQ9OCtDX5uSyvo+QJAlXpjG5Zu+ZfWt190RdjkdNnV6DZ08e16SFBfFBToAYHCiLky3qW323TjgmhXDxwLNAMKeO8Khe6Z7dM90j860dOhP+6r0h89Oak/lWZUcqlfJoXpFOR362tRULclJ1/yJyUyzAIIgcdTIquyx2WyKjXTqdEuHTp7pSfZQeg9YB1N4ca1EuXquS30LNFPZg0CIcbFmDwALGR3j8u/m9UX9Ob1delLv7K3SsYZWvbu3Su/urVJ8lFP3zvDo6zkZuiU7kYWdgQDpXdnT5e32r2Nj1WSP1JPcOd3SoarGC5U9XKADlsEUXlwr0Rc+lDec60n2UNmDQPBN42ptZ80eABYzPnmUnsqbpFV3TdS+E436454qvbuvSvXN7fqvTyv1X59WKjXOrQdmpuvrN6ZrRkY8Ox8Aw+BL6pxu6dDZ850yjJ7jCRae2uSr5DlBZQ8AYIh8u3F1X3jf5L0EgeCfxsWaPQCsymazKScrQTlZCfrxfVP016MN+uOeKm36W8/Czq9+VKFXP6rQuDHRum9Gmu6bmaapaXEkfoBB8id7Wjv86/YkRDsV4bDutMlYd08iq4o1ewAAQ+SrwPBhGhcCwb9AM9O4AIwEDrtN8yYkad6EJD23dJq2HarXH/dWacvBWh1raNX6ki+0vuQLZSfF+BM/kz2xJH6AAfAle862dqr+wvaxvqldVuW7++pfoJkLdADAIEU5+yZ74qL4+Izhi/Kv2cM0LgAjjDvCobxpHuVN86ilvUtbP6/Te/uqVXyoThWnWvRicbleLC7X9ckxun9Gmu6bma6JqaNI/ACXkRDtks3WsxX5F6daJH21HbtV+e6+tnV2X3jMJQ8AYHCiqOxBEEQ72Y0LABTjjtADOel6ICdd59q7tOVgrd7bV62Sw/U6Wt+i/9harv/YWq4JKaOUf2HnL6Z6AX057DYlRDl1prVTX9Sdk2TtxZml/skdpnEBAAbr4soebhwgEJjGBQAXGeWO0JIbM7Tkxgw1t3Vqy8E6/WlftbYfrld53Tn959Zy/efWco1NjPZv+X5jZoLs7OoFaHSMS2daO1XuS/ZYfBrXxTumsIMKAGCwWLMHwRDtZut1ALis2Einls7K0NJZGWpq69SWg7V6v6xG2w7X6/jpVr2y/ahe2X5UnrhI3T0tVfdMT2M7d4xoY2JcOlrfoi/qLyR7Rlk72XPxBTlr9gAABqvfmj3cOEAA+Ct72I0LAK4sLtKpB2dl6sFZmWrt6FLJoXr9z99qtPXzOtU0tem1vxzTa385pjExLt01NVV3T/Mod/wY/3aawEgw+kIlT3VjmyTrV/b0n8bFJQ8AYHBYswfB4EsitrSzQDMADFi0K0L3zkjTvTPS1Nbp1cflp/Q/f6tR0cFaNbR06PWdlXp9Z6ViXA7dOSlZeVM9WjgpRfHRvHnD2sZcVMlj/TV7nFd8DCB8FRYWqrCwUF5vcO+KAxcne6jsQSCwZg8ADFOk06HFU1K1eEqqOr3d+rTidE/i50CtapratKmsRpvKahRht2nu9Ym6a0qq7prmUUZCVKibDgTc6OiRluy5eM0ekj2AVRQUFKigoEBNTU2Kj48PdXNgYdHOvu8l3DhAIET7tl7v9MowjKBtLEOyB8CI4HTYdduEJN02IUnPLZmmspON+mB/rYoO1OpQbbM+Lm/Qx+UNevbdA5qWHqe8qR4tnpKiaens7AVruDi5M+KSPUzjAgAMUqTL7v97hN2mSKf9Cq8GBsZXMebtNtTh7ZY7IjhLS3DlA2DEsdlsmpmZoJmZCfrHuyfpWEOLig7U6oP9tdp17LT2VzVpf1WT/v3Dw/LERWrRlBR9bUqK5o1PYp0fhK2Rl+z56u6rw27rt8gmAABX46vAkKS4KCc3ABEQvXd5O9/hJdkDAMEybkyMHrvjej12x/VqONeuLZ/XqehArT46cko1TW36/V+P6/d/Pa5Ip123T0jS4impWjQ5RalxkaFuOjBgo0dYsqf3ugpxkRFcoAMABq33jYKLK0aBoXI67HI6bOr0Gmrt8CohOjg/hzMWAHoZM8qtb87J0jfnZKmt06u/HG3QloO12nqwTlWNbfrwYJ0+PFgnSZqREa9Fk1O0aHKKZmTEy8627jCxMb2SO64Ie5+7SlbUu7KHNRYAAEPhsNvkirCro6ubZA8CKtoVocbznWoN4iLNnLEAcBmRTocWTkrRwkkpMpYYOljdrC0Ha7Xl8zrtPXFWZScbVXayUT/fckRJo1yaPzFZCyelaP4NyezuBdPpvUBzYrTL8pUukU67Iuw2dXUbrNcDABiyKKejJ9nj5toOgRPtclxI9gRv+3WufgBgAGw2m6amx2lqepyeXHyD6pvbVXyoTlsO1urj8gadOtehDZ+d1IbPTspuk2aPG60FFxJFU9JiLf/BGubXe+t1q0/hknr+z8ZGRuhMayc7cQEAhsz3oZzKHgSSb5FmKnsAwGSSY7+a7tXR1a1dx06r5FC9ij+v05G6c9r55Rnt/PKMnt98SKlxbi2YmKIFk5I1b0KS4qP44IlrL8rpkDvCrvau7hGR7JF6pm+daeUCHQAwdL51e+K4fkMA+abTnyfZAwDm5Yqwa974JM0bn6Rn7p2iE2daVXKoXiWH6vRxeYNqm9r1xq5KvbGrUg67TbOyEjR/YrLmT0zWjIx4OVjrB9eAzWbTmBiXqhrbRlCyp+cyh8oeAMBQ+SowuHGAQIp29pxPI66y58EHH1RJSYkWL16st956K9TNAYBByRwdrb+/dZz+/tZxauv06tOK0yo+VKfth+v1RX2Ldh07o13Hzmhd0WGNjnbq9huSdefEZM2/IUkp7PCFIBo9UpM93I0FAAyRr7KHxf4RSF9N4xpha/b88Ic/1KOPPqrXXnst1E0BgGGJdDr8VTySdOJMq7YfPqXth+v1cfkpnWnt1Lt7q/Tu3ipJ0mRPrJbdnKXv3pYdymbDonxJnpGT7HFe+NOUlzsAhqiwsFCFhYXyeoN3Rxzw8X0oj+O9BAHkn8bVOcIqexYuXKiSkpJQNwMAAi5zdLT+bu5Y/d3cser0dmtP5VltO1Sv7Ufqte9Eoz6vaVbV2fOhbiYsakLKKP35yClNSBkV6qZcE9cnxUiSsi/8CcAaCgoKVFBQoKamJsXHx4e6ObC4sYnRkngvQWCZcoHm7du36/nnn9fu3btVXV2tjRs3aunSpX1es379ej3//POqrq7WtGnT9MILL+iOO+4IVJsBwBKcDrtuvi5RN1+XqH+8e5IazrXro/JTmuSJDXXTYFH/dM9kPZCTrhszE0LdlGviH+6aqLune0ZMfwEAgff/7puqh+dkKSeTxCIC5//kXqe8qR5NDuJ1/6CTPS0tLcrJydF3v/tdfeMb3+j3/BtvvKGVK1dq/fr1uu222/Tyyy8rPz9fBw4c0NixYyVJs2fPVnt7e79/+8EHHyg9PX0I3QCA8DdmlFtLbswIdTNgYZFOh24aOzrUzbhmRlp/AQCBF+Vy6MashFA3AxZzY1aClBXcnzHoZE9+fr7y8/Mv+/y6dev0ve99T4899pgk6YUXXtDmzZv10ksvac2aNZKk3bt3D7G5/bW3t/dJHDU1NQXsewMAAAAAAIQbeyC/WUdHh3bv3q28vLw+x/Py8rRjx45A/ii/NWvWKD4+3v+VlRXk9BgAAAAAAICJBTTZc+rUKXm9XqWmpvY5npqaqpqamgF/n7vvvlsPP/ywNm3apMzMTO3cufOyr3366afV2Njo/6qsrBxy+wEAAAAAAMJdUHbjstlsfR4bhtHv2JVs3rx5wK91u91yu90Dfj0AAAAAAICVBbSyJykpSQ6Ho18VT11dXb9qHwAAAAAAAAReQJM9LpdLs2fPVlFRUZ/jRUVFmjdvXiB/FAAAAAAAAC5h0NO4zp07p/Lycv/jiooK7dmzR4mJiRo7dqxWrVqlRx55RHPmzFFubq5eeeUVHT9+XCtWrAhowwEAAAAAANDfoJM9u3bt0sKFC/2PV61aJUlavny5fvOb32jZsmVqaGjQc889p+rqak2fPl2bNm3SuHHjAtdqAAAAAAAAXNKgkz0LFiyQYRhXfM3jjz+uxx9/fMiNAgAAAAAAwNAEdM0eAAAAAAimwsJCTZ06VTfffHOomwIAphWUrddDobCwUIWFherq6pIkNTU1hbhFAHDt+GLe1SovrYbYD2AkG6mxv6CgQAUFBWpsbFRCQgKxH8CIMtDYbzMs9u5w4sQJZWVlhboZABASlZWVyszMDHUzrjliP4CRjNgPACPP1WK/5ZI93d3dqqqqUmxsrGw2m5qampSVlaXKykrFxcWFunlDRj/MhX6Yj1X6MtR+GIah5uZmpaeny24feTN0if3mRj/MhX6Yy3D6Qewn9psZ/TAX+mEu1yL2W2Yal4/dbr9kdisuLi6sTwYf+mEu9MN8rNKXofQjPj4+SK0xP2J/eKAf5kI/zGWo/SD2E/vNjn6YC/0wl2DG/pF3CwAAAAAAAMDCSPYAAAAAAABYiOWTPW63W6tXr5bb7Q51U4aFfpgL/TAfq/TFKv0INav8HumHudAPc6EfuJhVfpf0w1zoh7nQj4Gz3ALNAAAAAAAAI5nlK3sAAAAAAABGEpI9AAAAAAAAFkKyBwAAAAAAwEJI9gAAAAAAAFiI5ZM969evV3Z2tiIjIzV79mz9+c9/DnWTBuXZZ5+VzWbr8+XxeELdrKvavn27HnjgAaWnp8tms+ntt9/u87xhGHr22WeVnp6uqKgoLViwQPv37w9NY6/gav34zne+0298br311tA09grWrFmjm2++WbGxsUpJSdHSpUt16NChPq8JhzEZSD/CYUxeeuklzZw5U3FxcYqLi1Nubq7ef/99//PhMBZmR+wPDWK/uRD7zTUmxP7gI/aHBrHfPKwS9yVifyBYOtnzxhtvaOXKlfrxj3+s0tJS3XHHHcrPz9fx48dD3bRBmTZtmqqrq/1fZWVloW7SVbW0tCgnJ0cvvvjiJZ//6U9/qnXr1unFF1/Uzp075fF4dNddd6m5ufkat/TKrtYPSbrnnnv6jM+mTZuuYQsHZtu2bSooKNAnn3yioqIidXV1KS8vTy0tLf7XhMOYDKQfkvnHJDMzU2vXrtWuXbu0a9cuLVq0SEuWLPEH9nAYCzMj9ocOsd9ciP3mGhNif3AR+0OH2G8eVon7ErE/IONhWNgtt9xirFixos+xyZMnGz/60Y9C1KLBW716tZGTkxPqZgyLJGPjxo3+x93d3YbH4zHWrl3rP9bW1mbEx8cbv/jFL0LQwoG5uB+GYRjLly83lixZEpL2DEddXZ0hydi2bZthGOE7Jhf3wzDCd0xGjx5tvPrqq2E7FmZC7DcHYr/5EPvNh9gfOMR+cyD2m4tV4r5hEPuHwrKVPR0dHdq9e7fy8vL6HM/Ly9OOHTtC1KqhOXLkiNLT05Wdna1vfetbOnr0aKibNCwVFRWqqanpMzZut1t33nln2I2NJJWUlCglJUUTJ07U97//fdXV1YW6SVfV2NgoSUpMTJQUvmNycT98wmlMvF6vXn/9dbW0tCg3Nzdsx8IsiP3mZbVzO5zijA+x3zyI/YFF7Dcvq53b4RRnJOvEfYnYPxSWTfacOnVKXq9XqampfY6npqaqpqYmRK0avLlz5+q3v/2tNm/erF/+8peqqanRvHnz1NDQEOqmDZnv9x/uYyNJ+fn5+t3vfqetW7fqZz/7mXbu3KlFixapvb091E27LMMwtGrVKt1+++2aPn26pPAck0v1QwqfMSkrK9OoUaPkdru1YsUKbdy4UVOnTg3LsTATYr95WencDpc40xux3xyI/cFB7DcvK53b4RJnfKwS9yVi/1BFDPs7mJzNZuvz2DCMfsfMLD8/3//3GTNmKDc3V+PHj9drr72mVatWhbBlwxfuYyNJy5Yt8/99+vTpmjNnjsaNG6f33ntPDz30UAhbdnlPPPGE9u3bp48++qjfc+E0JpfrR7iMyaRJk7Rnzx6dPXtWf/jDH7R8+XJt27bN/3w4jYUZhfvvj9hvbuESZ3oj9psDsT+4wv33R+w3t3CJMz5WifsSsX+oLFvZk5SUJIfD0S8jVldX1y9zFk5iYmI0Y8YMHTlyJNRNGTLfrgJWGxtJSktL07hx40w7Pk8++aTeeecdFRcXKzMz03883Mbkcv24FLOOicvl0oQJEzRnzhytWbNGOTk5+vnPfx52Y2E2xH7zsvK5bdY440PsNw9if3AQ+83Lyue2WeOMZJ24LxH7h8OyyR6Xy6XZs2erqKioz/GioiLNmzcvRK0avvb2dh08eFBpaWmhbsqQZWdny+Px9Bmbjo4Obdu2LazHRpIaGhpUWVlpuvExDENPPPGENmzYoK1btyo7O7vP8+EyJlfrx6WYdUwuZhiG2tvbw2YszIrYb15WPrfNGmeI/eYbk4sR+wOD2G9eVj63zRhnrBL3JWJ/QMZj2Es8m9jrr79uOJ1O41e/+pVx4MABY+XKlUZMTIzx5ZdfhrppA/bUU08ZJSUlxtGjR41PPvnEuP/++43Y2FjT96G5udkoLS01SktLDUnGunXrjNLSUuPYsWOGYRjG2rVrjfj4eGPDhg1GWVmZ8e1vf9tIS0szmpqaQtzyvq7Uj+bmZuOpp54yduzYYVRUVBjFxcVGbm6ukZGRYbp+/OAHPzDi4+ONkpISo7q62v/V2trqf004jMnV+hEuY/L0008b27dvNyoqKox9+/YZzzzzjGG3240PPvjAMIzwGAszI/aHDrHfXP0g9ptrTIj9wUXsDx1iv3n6YZW4bxjE/kD0wdLJHsMwjMLCQmPcuHGGy+Uybrrppj5btYWDZcuWGWlpaYbT6TTS09ONhx56yNi/f3+om3VVxcXFhqR+X8uXLzcMo2fbv9WrVxsej8dwu93G/PnzjbKystA2+hKu1I/W1lYjLy/PSE5ONpxOpzF27Fhj+fLlxvHjx0Pd7H4u1QdJxq9//Wv/a8JhTK7Wj3AZk0cffdQfl5KTk43Fixf7A75hhMdYmB2xPzSI/eZC7DfXmBD7g4/YHxrEfvOwStw3DGJ/INgMwzCGXhcEAAAAAAAAM7Hsmj0AAAAAAAAjEckeAAAAAAAACyHZAwAAAAAAYCEkewAAAAAAACyEZA8AAAAAAICFkOwBAAAAAACwEJI9AAAAAAAAFkKyBwAAAAAAwEJI9gAAAAAAAFgIyR4AAAAAAAALIdkDAAAAAABgISR7AAAAAAAALOT/A4q5eZU34m+CAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1400x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(ncols=3, figsize=(14,4))\n",
    "for m,ax in zip(methods,axs):\n",
    "    valores = np.array([m(f,0,np.pi,n) for n in ns])\n",
    "    ax.semilogy(ns,abs(valores-ans))\n",
    "    ax.set_title(m.__name__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cd7096f1",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "6d0416ba0ef94247a462f46ee620a076",
     "grade": true,
     "grade_id": "cell-3c16f3e64c8e6bd8",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "for ax in axs:\n",
    "    assert len(ax.lines) == 1\n",
    "    assert len(ax.get_title()) >= 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "325cd1b5",
   "metadata": {},
   "source": [
    "Comente as semelhanças e diferenças do caso anterior."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06dae25f",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "d602b3dd74e899baf89a82e0b57983b6",
     "grade": true,
     "grade_id": "cell-0f5150ad9c4996d5",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "o metodo do retangulo é falho para esse intervalo. porém o metodo do trazio e midpoint são uma boa aproximação para a integral pois possuem erros muito pequenos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a88c52a",
   "metadata": {},
   "source": [
    "Qual a velocidade de convergência de cada um dos métodos para a integral no intervalo $[0, \\pi]$?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aeabc5c9",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "44d4d3dc82e4eedb083a449a9f5c9b11",
     "grade": true,
     "grade_id": "cell-8f6d79fe95d1aee6",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6749d955",
   "metadata": {},
   "source": [
    "## Questão 6: Uma outra função\n",
    "\n",
    "Calcule a integral de $\\frac{1}{2 + \\cos(x)}$ no intervalo $[0, 2\\pi]$, com cada um dos métodos,\n",
    "e faça novamente o gráfico do erro em função do número de subdivisões."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a4ac082e",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "3250782f580d825ee3d44212a95d8261",
     "grade": true,
     "grade_id": "cell-6aa25fcc7c4c73db",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ns = range(1,30+1)\n",
    "def g(x):\n",
    "    return 1/(2+np.cos(x))\n",
    "def G(x):\n",
    "    return (2/(3**1/2))*np.arctan(np.tan(x/2)*(3**1/2))\n",
    "ans1=(2*np.pi)/(3**1/2)\n",
    "for m in methods:\n",
    "    valores = np.array([m(g,0,2*np.pi,n) for n in ns])\n",
    "    plt.semilogy(ns,abs(ans1-valores),label=m.__name__)\n",
    "plt.title(\"grafico de erro dos metodos de integração \")\n",
    "plt.legend()\n",
    "plt.xlabel('variação do n')\n",
    "ax = plt.gca()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ca67d055",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "c01110a23beeab3c4fc2ce41c49e464e",
     "grade": true,
     "grade_id": "cell-c995335cfa51fa83",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "assert len(ax.lines) == 3\n",
    "assert len(ax.get_legend().texts) == 3\n",
    "assert len(ax.get_title()) >= 10\n",
    "assert len(ax.get_xlabel()) > 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d526b95",
   "metadata": {},
   "source": [
    "* Qual a velocidade de convergência de cada um dos métodos?\n",
    "* Qual método parece ser mais rápido?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8a18157",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "8c16d6798b4789590bbbc2ba85327ff2",
     "grade": true,
     "grade_id": "cell-4406dd63ef32d681",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c1ad879",
   "metadata": {},
   "source": [
    "Agora, repita para o intervalo $[0, \\pi/2]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "81375b91",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "d9aeb141eb48917d79e33fc4636dc22b",
     "grade": true,
     "grade_id": "cell-7763dd8ad52621f9",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ans2=np.pi/3*(3**1/2)\n",
    "for m in methods:\n",
    "    valores = np.array([m(g,0,np.pi/2,n) for n in ns])\n",
    "    plt.semilogy(ns,abs(ans2-valores),label=m.__name__)\n",
    "plt.title(\"grafico de erro dos metodos de integração \")\n",
    "plt.legend()\n",
    "plt.xlabel('variação do n')\n",
    "ax = plt.gca()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "638da0bf",
   "metadata": {},
   "source": [
    "Compare com os resultados para a integral no intervalo $[0, 2\\pi]$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d7b7f84",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "f9108eee5aa8ccfa453798b6a87f9afb",
     "grade": true,
     "grade_id": "cell-ed7fb2fc425e1d54",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "a integral de $[0, \\pi/2]$ converge de forma mais suave do que a de $[0, 2\\pi]$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5dc2e14",
   "metadata": {},
   "source": [
    "## Questão 7: E mais uma\n",
    "\n",
    "$$\\int_0^{2\\pi} \\frac{dx}{1 + 2\\cos^2(x)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "986e3f5a",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "39781e44d76b38ee84b31b49520b1fd5",
     "grade": true,
     "grade_id": "cell-8d533039531afa6c",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "def g1(x):\n",
    "    return 1/(1+(2*np.cos(x)*np.cos(x)))\n",
    "def G1(x):\n",
    "    return (1/(6**1/2))*np.arctan(((2/3)**1/2)*np.tan(x))\n",
    "ax = plt.gca()\n",
    "ans2=G1(np.pi*2)-G1(0)\n",
    "for m in methods:\n",
    "    valores = np.array([m(g1,0,np.pi*2,n) for n in ns])\n",
    "    plt.semilogy(ns,abs(ans2-valores),label=m.__name__)\n",
    "plt.title(\"grafico de erro dos metodos de integração \")\n",
    "plt.legend()\n",
    "plt.xlabel('variação do n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44d50610",
   "metadata": {
    "deletable": false,
    "editable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "c4e9743c656d508919dd173c3e46239b",
     "grade": true,
     "grade_id": "cell-1b1fa16a62733446",
     "locked": true,
     "points": 1,
     "schema_version": 3,
     "solution": false,
     "task": false
    }
   },
   "outputs": [],
   "source": [
    "assert len(ax.lines) == 3\n",
    "assert len(ax.get_legend().texts) == 3\n",
    "assert len(ax.get_title()) >= 10\n",
    "assert len(ax.get_xlabel()) > 5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0992dc7",
   "metadata": {},
   "source": [
    "Compare com o que você obteve para a função $\\frac{1}{1 + 2 \\cos(x)}$:\n",
    "- O que você percebe de semelhante?\n",
    "- O que há de diferente?\n",
    "- Como você explica as diferenças e similaridades?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "362956da",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "markdown",
     "checksum": "89a3f4a5f95f5f4ed3c0d8237cf8ff1e",
     "grade": true,
     "grade_id": "cell-7fabf2aaecbd305c",
     "locked": false,
     "points": 2,
     "schema_version": 3,
     "solution": true,
     "task": false
    }
   },
   "source": [
    "(contando que minha integral do wolfram está errada) como são graficos \"semelhantes\" os metodos pro calculo da integral possuem um erro de ordem semelhantes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b381669",
   "metadata": {},
   "source": [
    "## Questão 8: A última\n",
    "\n",
    "Calcule\n",
    "\n",
    "$$\\int_0^{2\\pi} \\frac{\\sin(1999x)}{\\sin(x)}$$\n",
    "\n",
    "pelo método do ponto médio, variando o número de subdivisões entre $2$ e $2000$ como abaixo,\n",
    "e faça o gráfico do **valor da integral** ao variar $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ddd6a910",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "94bc79c38871628e1054312c0c6e14e6",
     "grade": true,
     "grade_id": "cell-ca6ef8a2e7713c54",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
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   "outputs": [],
   "source": [
    "ns = range(2,2000,2)\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "O que você vê no gráfico?"
   ]
  },
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   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "902b1c96",
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   "source": [
    "Explique porque usar o método do ponto médio, e porque usar um número par de subdivisões."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aecb9a7c",
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   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22b9405f",
   "metadata": {},
   "source": [
    "### Bônus\n",
    "\n",
    "Como você faria para ter certeza do valor correto da integral?\n",
    "Explique suas ideias abaixo, e faça contas, se desejar, na caixa seguinte."
   ]
  },
  {
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   "id": "f5c01565",
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     "grade": true,
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     "locked": false,
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     "solution": true,
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   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8a895981",
   "metadata": {
    "deletable": false,
    "nbgrader": {
     "cell_type": "code",
     "checksum": "f65b7c3074f70a8f5cc68db64b2e5340",
     "grade": true,
     "grade_id": "cell-c7f2efffbad52e81",
     "locked": false,
     "points": 1,
     "schema_version": 3,
     "solution": true,
     "task": false
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   "outputs": [],
   "source": [
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
   ]
  }
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