Aproximacion_de_taylor.ipynb

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        "<a href=\"https://colab.research.google.com/github/Mgobeaalcoba/proyectos_platzi/blob/main/Aproximacion_de_taylor.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "54lPwMpNy3Ky"
      },
      "source": [
        "# Aproximación de Taylor"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VXaBTQpEy3K8"
      },
      "source": [
        "La mayoría de los fenómenos de la realidad solo pueden ser aproximados a través de funciones no-lineales y algunas veces es más sencillo aproximarnos con funciones afines o lineales.   "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0PEc4Jt5y3K-"
      },
      "source": [
        "En este caso nos referiremos a la aproximación como *modelo* para recordar que la aproximación es solamente eso, una aproximación."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xQ7l1N3Py3K-"
      },
      "source": [
        "Ahora, el cálculo diferencial nos otorga una forma organizada de encontrar ese modelo. Supongamos entonces que $f:\\mathbf{R}^{n} \\to \\mathbf{R}$ es una función diferenciable, sea también $\\mathbf{z}$ un $n$-vector. La aproximación de Taylor de primer orden de $f$ cerca del punto $\\mathbf{z}$ es la función\n",
        "\n",
        "$$\n",
        "\\hat{f}(\\mathbf{x}) = f(\\mathbf{z}) + \\displaystyle\\frac{\\partial}{\\partial x_{0}} f(\\mathbf{z})(x_{0}-z_{0}) + \\displaystyle\\frac{\\partial}{\\partial x_{1}} f(\\mathbf{z})(x_{1}-z_{1}) + \\cdots + \\displaystyle\\frac{\\partial}{\\partial x_{n-1}} f(\\mathbf{z})(x_{n-1}-z_{n-1})\n",
        "$$\n",
        "\n",
        "Donde $\\displaystyle\\frac{\\partial}{\\partial x_{i}}f(\\mathbf{z})$ denota la derivada parcial de $f$ evaluada en el vector $\\mathbf{z}$ respecto al i-ésimo argumento. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "auk0epHVy3K_"
      },
      "source": [
        "Algunas veces $\\hat{f}(\\mathbf{z})$ también se escribe como $\\hat{f}(\\mathbf{x};\\mathbf{z})$ o también $\\hat{f}_{\\mathbf{z}}(\\mathbf{x})$ para mostrar en qué punto se evalúa o respecto al que se está desarrollando. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oo1a9w7uy3K_"
      },
      "source": [
        "Notemos que \n",
        "\n",
        "$$\n",
        "\\hat{f}(\\mathbf{x}) = f(\\mathbf{z}) + \\nabla f(\\mathbf{z})^{T} (\\mathbf{x}-\\mathbf{z})\n",
        "$$\n",
        "\n",
        "El por de la formula de la aproximación de taylor es en verdad un producto interno o producto punto cuando se trate de vectores. Si se trata de escalares es una multiplicación. \n",
        "\n",
        "Donde $\\nabla f(\\mathbf{z})$  representa el vector gradiente\n",
        "\n",
        "$$\n",
        "\\nabla f(\\mathbf{z}) = \\begin{bmatrix}\\displaystyle\\frac{\\partial f}{\\partial x_{0}}(\\mathbf{z}) \\\\ \\displaystyle\\frac{\\partial f}{\\partial x_{1}}(\\mathbf{z})\\\\ \\vdots \\\\ \\displaystyle\\frac{\\partial f}{\\partial x_{n-1}}(\\mathbf{z}) \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "Notemos que le primer término de la aproximación es la constante $f(\\mathbf{z})$ (esto es la función $f(\\mathbf{x})$ evaluada en $\\mathbf{z}$). El segundo término es el prodcuto itnerno del vector gradiente de $f$ en $\\mathbf{z}$ y la *desviación* o *perturbación* de $\\mathbf{x}$ por parte de $\\mathbf{z}$, el $n$-vector $(\\mathbf{x}-\\mathbf{z})$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D8iJf8Bgy3K_"
      },
      "source": [
        "La aproximación de primer orden de Taylor nos da una forma de consturir una función afín que aproximará la función $f: \\mathbf{R}^{n} \\to \\mathbf{R}$ alrededor del punto $\\mathbf{z}$, siempre y cuando exista una forma explícita  de la función $f$ y sea diferenciable. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MFVwyu4Ky3K_"
      },
      "source": [
        "## 6.1 Breves ejemplos"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MOa4shvyy3LA"
      },
      "source": [
        "**Ejemplo 1.** Considera la función $f:\\mathbf{R}^{2}\\to \\mathbf{R}$ dada por $f(\\mathbf{x}) = x_{0}+\\exp{(x_{1}-x_{0})}$ la cual no es lineal ni afín. Para encontrar una aproximación de Taylor $\\hat{f}$ cerca del punto $\\mathbf{z}^{T} = [1 \\; 2]$. Tenemos que el vector gradiente en este caso será:\n",
        "\n",
        "$$\n",
        "\\nabla f(\\mathbf{z}) = \\begin{bmatrix}\\displaystyle\\frac{\\partial f}{\\partial x_{0}}(\\mathbf{z}) , \\\\ \\displaystyle\\frac{\\partial f}{\\partial x_{1}}(\\mathbf{z})\\end{bmatrix} = \\begin{bmatrix} 1 - \\exp{(z_{1}-z_{0})} , \\\\ \\exp{(z_{1}-z_{0})} \\end{bmatrix}\n",
        "$$\n",
        "\n",
        "Ahora vamos a evaluar $\\nabla f(\\mathbf{z})$ en el vector $\\mathbf{z}^{T} = [1 \\; 2]$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BdGfgzsNy3LA"
      },
      "source": [
        "import numpy as np"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XQbzXQHUy3LB"
      },
      "source": [
        "def gradF(z): # La función gradiente se construye con las derivadas de la función de X evaluada en X0 primero y en X1 dsp. Esto nos dará cada componente del vector gradiente.\n",
        "    return np.array([1-np.exp(z[1]-z[0]),np.exp(z[1]-z[0])])"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dveCh4cCy3LB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "537aa351-9987-41cb-cec3-d9f49845de62"
      },
      "source": [
        "z = np.array([1,2]) # Defino el punto del cual quiero encontar una aproximación de Taylor\n",
        "print('grad(f)[1,2] = ', gradF(z)) # Al vector gradiente le paso el punto Z"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "grad(f)[1,2] =  [-1.71828183  2.71828183]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yWzXrDtzy3LC"
      },
      "source": [
        "Ahora vamos a programar la función $f$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9uXthCIFy3LC"
      },
      "source": [
        "def F(x): # Defino la función f(x)\n",
        "    return x[0] + np.exp(x[1]-x[0])"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_oDLbu07y3LC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5cc7feda-4e3d-4497-bc1f-7ece4b32ab62"
      },
      "source": [
        "print('f([1,2]) =',F(z)) # Ahora a F(x) le paso el punto Z"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f([1,2]) = 3.718281828459045\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mSvQvCmoy3LC"
      },
      "source": [
        "Así pues, nuestro aproximación de Taylor a primer orden será:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cRdagvtIy3LD"
      },
      "source": [
        "def taylor_F(x,z): # Ahora que ya tengo mi función F(X) y mi vector gradiente gradF(Z) puedo construir mi función de aproximación de taylor_F(X,Z)\n",
        "    fz = F(z)\n",
        "    gz = gradF(z)\n",
        "    return fz + gz@(x-z)"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xOMMoKLgy3LD"
      },
      "source": [
        "Para corroborar que nuestra aproximación es correcta si la evaluamos en $x=z$ deberíamos de obtener que $\\hat{f}(\\mathbf{z})=f(\\mathbf{z})$\n",
        "\n",
        "Es decir, la función F(X) me tiene que dar igual que la función de aproximación de Taylor siempre que en la misma X y Z sean iguales"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YxQkf8pXy3LD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "49266dc6-1e5c-4ddd-9202-8e7786141f57"
      },
      "source": [
        "print('taylor_F([1,2],[1,2]) = ',taylor_F(z,z))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "taylor_F([1,2],[1,2]) =  3.718281828459045\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nLv96_Wry3LD"
      },
      "source": [
        "Esto significa que lo hicimos bien, nuestra aproximación viene dada por\n",
        "\n",
        "$$\n",
        "\\hat{f}(\\mathbf{x}) = 3.7183 + [-1.72\\; 2.72]\\begin{bmatrix}x_{0}-1\\\\ x_{1}-2\\end{bmatrix}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wOU6K9lxgFaI"
      },
      "source": [
        "Tarea: Calcular el error muestral para distintos valores vectoriales de X en el primer ejemplo"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WQpgJhu3gBca",
        "outputId": "cd648350-ea58-43ad-bb99-2e73aed13fe7"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format([1,2],F([1,2]),taylor_F([1,2],z),np.abs(F([1,2])-taylor_F([1,2],z))))"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = [1, 2], f(x) = 3.718281828459045, Taylor f(x) = 3.718281828459045, |f(x) - Taylor f(x)| = 0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aHG-MCFbgBfG",
        "outputId": "2cab6a00-9d1d-4cf0-89d4-f4239da77fc2"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format([0.5,1.5],F([0.5,1.5]),taylor_F([0.5,1.5],z),np.abs(F([0.5,1.5])-taylor_F([0.5,1.5],z))))"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = [0.5, 1.5], f(x) = 3.218281828459045, Taylor f(x) = 3.218281828459045, |f(x) - Taylor f(x)| = 0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3hQeHYSLgBiG",
        "outputId": "c7466577-5b4b-45eb-dd1f-a4173f06a19d"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format([4,8],F([4,8]),taylor_F([4,8],z),np.abs(F([4,8])-taylor_F([4,8],z))))"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = [4, 8], f(x) = 58.598150033144236, Taylor f(x) = 14.873127313836179, |f(x) - Taylor f(x)| = 43.72502271930806\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BS5VwYvEgBkh",
        "outputId": "88cab186-0ad1-4936-f34f-9d2506b0e30a"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format([3,5],F([3,5]),taylor_F([3,5],z),np.abs(F([3,5])-taylor_F([3,5],z))))"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = [3, 5], f(x) = 10.38905609893065, Taylor f(x) = 8.43656365691809, |f(x) - Taylor f(x)| = 1.9524924420125611\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wTBH45pRgBm1",
        "outputId": "9bcf247b-a1f8-4931-80fc-b5d3fc2f555b"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format([3,4],F([3,4]),taylor_F([3,4],z),np.abs(F([3,4])-taylor_F([3,4],z))))"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = [3, 4], f(x) = 5.718281828459045, Taylor f(x) = 5.718281828459045, |f(x) - Taylor f(x)| = 0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HT8xWYa_y3LD"
      },
      "source": [
        "**Ejercicio 2.** Para tener un mejor idea de lo que significa hacer una aproximación lineal vamos a realizar la aproximación de una función unidimensional\n",
        "\n",
        "$$\n",
        "f(x) = x^{2} - x^{3}\n",
        "$$\n",
        "\n",
        "Con lo que obtenemos\n",
        "\n",
        "$$\n",
        "\\nabla f(z) = 2z - 3z^{2}\n",
        "$$\n",
        "\n",
        "Ahora, si lo aproximamos en $z=0.4$. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zNPBHIlNy3LE"
      },
      "source": [
        "def df(z):\n",
        "    return 2*z - 3*z**2"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nP1s8PvTy3LE"
      },
      "source": [
        "def tf(x,z):\n",
        "    return f(z) + df(z)*(x-z)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2l2IDUHly3LE"
      },
      "source": [
        "def f(x):\n",
        "    return x**2 - x**3"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LuJwlxeey3LF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "86aea349-f3e7-4f0e-fc16-f5cd9e550dda"
      },
      "source": [
        "print('f(0.4) =',f(0.4))"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "f(0.4) = 0.09600000000000002\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8zvc6v3wy3LF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "23a5b01f-d058-4e63-8134-53ec50a0e88b"
      },
      "source": [
        "print('Df(0.4) =',df(0.4))"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Df(0.4) = 0.31999999999999995\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3qZkI5uPy3LF"
      },
      "source": [
        "Usando los resultados anteriores tenemos que la aproximación de Taylor es\n",
        "\n",
        "$$\n",
        "\\hat{f}(x) = 0.09600000000000002 + 0.31999999999999995 * (x - 0.4)\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_hl_leOky3LG"
      },
      "source": [
        "import matplotlib.pyplot as plt #Biblioteca con funciones para visualizar"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mR9UMvHCy3LG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 704
        },
        "outputId": "7c1d7445-2026-4aba-ff5e-6b135d344da4"
      },
      "source": [
        "fig, ax = plt.subplots(1,1,figsize=(7,7),dpi=120)\n",
        "\n",
        "x = np.linspace(0,1,1000)\n",
        "taf = lambda x:tf(x,0.4)\n",
        "\n",
        "ax.plot(x,f(x),label='original')\n",
        "ax.plot(x,taf(x),label='aproximación')\n",
        "ax.scatter(0.4,f(0.4),color='red')\n",
        "ax.legend()\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LD7Jptm/fzoABAxg5ciT33XcfDRs25MiRI9x0003ExMTw8MMPU6FCBaZNm0ZkZCQLFy6kV69eNG7cmJdffpnRo0fTp08fIiMjOXfuHMOHD6dRo0b8/e9/z/FzGjt2LEFBQTz99NPs3LmTCRMm4Ofnh4+PD6dOnWLMmDF8++23TJ06lbp16/LCCy+kHztx4kSaNm1KZGQkvr6+LF++nFGjRpGSksJf//rX9P2mTp3K3XffTdOmTXnmmWcoV64cP/74IytXrmTgwIHZ9mWtJTIyki+++IJ77rmHFi1asGrVKkaPHs2ff/7J+PHjM+2/du1aFi9ezKhRoyhbtixvvfUWvXv35o8//qBChQq5+u8rIiLiiuhjMP0OOLrFqZvcAb0ng+fiv7UtSUzWWbKSzhjTFNi8efNmmjZtesH23bt3A1CvXr0LD/7kaTj8awF3mEtVroIu/5enQ2JjYy9YfvHtt99y4403Mn36dIYMGQI44XHEiBFcd911rF+/Pn0Jw7///W+efPJJli5dSmRkJODMTO/bt4+VK1fSuXPn9PP+7W9/44033uDrr7+mdevWAERHR9O8eXOstezatQsfHx9SUlJo27YtO3bsYMuWLbz44otMmjSJ9evXc/3116efL21Wes2aNekf27dvT7Nmzdi0aVN6jwMHDmTu3LncfvvtrFixIv34m266iYMHD2aahc/u63H77bezY8cOdu3aBUBUVBQ1a9akSZMmrFmzhsDA8z9hW2vTf6gYPnw4a9asST//0qVL6dmzJ6+88grPPfdc+jF9+/Zl0aJF7Nixg/r16wPOzLS/vz9bt25NH/vll1+4+uqrmTBhAg8++OBF/5te8vtVRESkoJ097MxIH9/u1Ff1hZ7vgqf4ztdu2bKFZs2aATSz1m7Jaf/i+5m64fCv59+ZWgxlDI6JiYmcOXOGBg0aUK5cOTZt2pQeptPcf//9mdYCP/DAAzz77LOsWLEiPUwD1K1bN1OQBlixYgUtW7ZMD9IAISEh3H///TzzzDNs3bqVZs2a4ePjw9SpU7n66qvp0qUL33//Pc8//3ymIH0pQ4cOzdRjq1atmDNnDnfffXem/Vq1asVbb71FUlISvr6+F3w9oqKiSExMpG3btqxatYqoqCjCwsL49NNPOXv2LE8//XSmIA1kmp3PasWKFXg8Hh5++OFM448//jgLFy7kk08+yRSSO3bsmB6kAZo3b05oaGh6WBYRESlyov6EaT3gpDMBRYtBEDkBfErXLWAVpvOiylVud3CeF73ExsYyduxYpkyZwp9//plp7W5UVNQF+19xxRWZ6pCQEKpWrXrBGuu6detecOy+ffto1arVBeONGzdO3576Ux/169dnzJgxjB49mmbNmvG///u/uf6catWqlakOCwsDoGbNmheMp6SkEBUVlb5s4ptvvuHFF19k/fr1xMTEZNo/LUynzVCn9Zpb+/bto1q1apQtWzbTeMbP/1KfB0B4ePgFa9RFRESKhNN/OEH61F6nvm44dBsPPqXv7XgK03mRx2UVRc1DDz3ElClTePTRR7nxxhsJCwvDGEP//v0velu33MiPO3ek3fru4MGDnDhxgipVquTquIs9AOVi42k/QOzatYsOHTrQqFEjXn/9dWrWrIm/vz8rVqxg/Pjxl/X18EZO/YqIiBQZJ/c4QTpqv1O3vB+6jINL/Ma2JCt9Pz6UYgsXLmTYsGG89tpr9OnTh9tuu43WrVtz+vTpbPffsWNHpjo6OppDhw5d8kl/aWrXrs327dsvGN+2bVv69jTvvvsun376Kf/4xz9ISEhg5MiRefisvLN8+XLi4+NZtmwZI0eOpGvXrnTs2PGCHwzSll5s3rw5T+evXbs2Bw8e5OzZs5nGs/v8RUREio3jO2FK1/NB+sYHS3WQBoXpUsXj8Vww0zlhwgSSk5Oz3f+9994jMTExvZ44cSJJSUl06dIlx2t17dqVjRs3sn79+vSxc+fO8d5771GnTh2aNGkCwJ49exg9ejS9e/fm2Wef5dVXX2XZsmVMnz7dm08x19JmgrMudZkyZUqm/Tp16kTZsmUZO3YscXFxmbZdata4a9euJCcn8/bbb2caHz9+PMaYXH0NRUREipSj22BqVzh70KlbPwadXinVQRq0zKNU6d69OzNmzCAsLIwmTZqwfv16Pvvss4veei0hIYEOHTrQr18/tm/fzjvvvEPr1q0zvfnwYp5++mnmzJlDly5dePjhhylfvjzTpk1jz549LFq0CB8fH6y13H333QQFBaXf33nkyJEsWrSIRx55hI4dO1KtWrV8/Rqk6dSpE/7+/vTo0YORI0cSHR3N+++/T0REBIcOHUrfLzQ0lPHjx3Pvvfdyww03MHDgQMLDw/n555+JiYlh2rRp2Z6/R48etG/fnueee469e/dy9dVXs3r1apYuXcqjjz6a6c2GIiIiRd7hzc7t72KOO3W7Z6DtU6U+SIPCdKny5ptv4vF4mDVrFnFxcdx888189tlnF9yJI83bb7/NrFmzeOGFF0hMTGTAgAG89dZbl7yLRZrKlSuzbt06nnrqKSZMmEBcXBzNmzdn+fLldOvWDXBmxdesWcOiRYuoVKlS+rGTJ0+mWbNm3HfffZke8pKfGjZsyMKFC3n++ed54oknqFKlCg888ACVKlW64E4g99xzDxEREfzf//0fL7/8Mn5+fjRq1Ii//e1vFz2/j48Py5Yt44UXXmDevHlMmTKFOnXq8O9//5vHH3+8QD4nERGRAnHwJ5jR03nCIUCHF6CN/i1Lo/tMZ6H79p6/z/R3332X61vUiTv0/SoiIgXqwA8wsxfEpd71q9MrcNND7vZUwHSfaRERERG5fH9sgJm9ISH1zfRdxkGrgr9JQHGjMC0iIiIime1dC7P6QeI5p+7+Blw/wt2eiiiFaRERERE5b9cXMGcAJMUCBu54G64Z7HZXRZZujScXGD58ONZarZcWEREpbXZ8CrPvcoK08YE731OQzoFmprNR2t6UKcWXtTZXd1cRERHJ0bYVsGAYJCeA8UDvD6DZnW53VeRpZjoLY0yhP0paxFspKSkK0yIicvm2LoX5Q5wg7eMH/aYrSOeSwnQWfn5+JCUlkZSU5HYrIpeU9n3q5+fndisiIlKc/boQFoyAlCTwBED/WdC4u9tdFRsK01mEhoYCcPToUS33kCLLWsvRo0eB89+zIiIiefbTbFh8H9hk8A2EAXPgyuwf5ibZ05rpLMqWLUtwcDBRUVFER0fj8Xj0a3QpUqy1JCcnk5ycTHBwMGXLlnW7JRERKY5+mAbLHwEs+AXDwHlQ9xa3uyp2FKazMMZQvXp1Tp06RXR0tGanpcgxxuDn50d4eDjh4eH6YU9ERPJu4/uw4gnntX8IDFoAtW9yt6diSmE6G76+vlSqVIlKlSq53YqIiIhI/lr/Dqx6xnkdEAaDF0HNG9ztqRhTmBYREREpLdaOh8/GOK8Dy8HQJVDtGldbKu4UpkVERERKgy/HwRf/cF4HV4ChS6HKVe72VAIoTIuIiIiUZNY6Ifqrfzt1mQgnSFdu4m5fJYTCtIiIiEhJZS18+gKse8upQ6rAsOVQ6Up3+ypBFKZFRERESiJrYeUzsGGiU4fWgGHLoEJ9d/sqYRSmRUREREqalBRY8Th8/x+nLlcLhn0E4bXd7asEUpgWERERKUlSkmH5w/DjTKcOrwvDP4KwGu72VUIpTIuIiIiUFMlJsPSv8Mtcp65whbNGOrSqu32VYArTIiIiIiVBciIsvh+2LHbqSo2dNdIhEe72VcIpTIuIiIgUd0kJsHAEbPvIqStf5TyQpUxFd/sqBRSmRURERIqzxDhYMAx+X+nUVVvAkA8huLy7fZUSCtMiIiIixVViLMwdBLs+d+oaN8CghRBUzt2+ShGFaREREZHiKOEczOkPe75y6lo3wqAFEFDW3b5KGYVpERERkeIm/izM6gd/rHPqOm1g4DzwL+NuX6WQwrSIiIhIcRIXBTP7wIGNTl3/VrhrFvgHu9tXKaUwLSIiIlJcxJ6CGb3g4I9OfUVn6Dcd/ALd7asUU5gWERERKQ7OnYAZd8DhX526UXfoMwV8/d3tq5RTmBYREREp6qKPwvQ74OhWp27aC+58Hzx+7vYlCtMiIiIiRdqZQzA9Eo7/7tTN74I73gGPYlxRoP8KIiIiIkVV1AGY1gNO7nbqFoMh8i3w8bjbl6RTmBYREREpik7tc4L06X1Ofd0I6PY6+Pi425dkov8aIiIiIkXNyd0wtdv5IN1yJHQfryBdBGlmWkRERKQoOb7DmZE+e8ipb3oIbnsZjHG3L8mW1z/eGGMCjDH/MsYcNMbEGmM2GGNuy8Vxdxpj5hljdhtjYowx240xrxljLniIvDFmrzHGZvPnXW/7FhERESmyjv4GU7qeD9JtnlCQLuIuZ2Z6KtAHeAPYAQwHVhhj2ltr117iuPeAg8BM4A/gKuBBoKsx5lprbWyW/X8CXssy9vtl9C0iIiJS9Bz+1bn9XcwJp273LLR7yt2eJEdehWljTEugPzDaWvtq6th0YDMwDrjpEof3sdauyXK+H4BpwCDggyz7/2mtnelNnyIiIiLFwsGfYEZP5wmHAB1ehDaPuduT5Iq3yzz6AMk4s8wAWGvjgMnAjcaYmhc7MGuQTvVh6sfG2R1jjPE3xpTxslcRERGRouvA9zAt8nyQ7vxPBelixNtlHtcAv1trz2QZ35j6sQWwPw/nq5L68Xg2224FYgCPMWYfMN5a+2ZuTmqMiQAqZRmun4e+RERERArOvvUwqy8knHXqrq9Cy/vc7UnyxNswXRU4lM142li1PJ7vKZyZ7oVZxn8B1gLbgQo467LfMMZUs9bmZhHRKODFPPYiIiIiUvD2fA2z74LEc4CBHm/AdcPd7kryyNswHQTEZzMel2F7rhhjBgL3AOOstTsybrPWRmbZdwrwCfCYMWaCtfZADqd/B1iQZaw+sDS3/YmIiIjku13/hTkDISkWMNDzHWgx0O2uxAvehulYICCb8cAM23NkjGmDs856FfBcTvtba60xZjzQGWiHc0eQS+1/FDia5Zq5aU1ERESkYPy+GuYNhuR4MB7oNQma93W7K/GSt2H6EFA9m/GqqR8P5nQCY8zVwDKcO4D0sdYm5fLaaWuxy+dyfxEREZGiYdvHMH8YpCSCjy/0ngxNe7rdlVwGb+/m8RNwpTEmNMt4qwzbL8oYUx9YiTNr3NVaG52Ha9dL/XgsD8eIiIiIuGvLhzB/aGqQ9oN+0xWkSwBvw/RCwAPcnzZgjAkARgAbrLX7U8dqGWMaZTzQGFMFWA2kAJ2ttdmGYmNMeWOMJ8uYH/A0kAB84WXvIiIiIoXrlwWw8G5ISQJPAPSfDY26ud2V5AOvlnlYazcYYxYAY1NvP7cTGAbUwXkzYZrpQFsg40LllTizy+OA1saY1hm2HbHWfpr6OhJ43hizENiDs6xjINAMeNZae9ib3kVEREQK1U+zYckowIJvEAyYDfVvdbsrySeX8zjxocDLwBAgHOc2dt2ttV/lcNzVqR+fzGbbl0BamP4V2AoMxrlXdALO8pF+1tqsd+gQERERKXp+mArLHwUs+JWBgfOgbhu3u5J85HWYTn3i4ejUPxfbp102Y7m6nYa19gec2WkRERGR4mfj+7DiCee1f1kYvBBq/cXdniTfXc7MtIiIiIhkZ93bsDr1rr8BYTBkMdS43t2epEAoTIuIiIjkp69fh89fcl4HhcOQJVCthbs9SYFRmBYRERHJD9bCl+NgzT+dOrgCDF0KVa5yty8pUArTIiIiIpfLWvjvy/D1a05dJgKGLYOIxu72JQVOYVpERETkclgLq5+H9W87ddmqMGw5VLzC3b6kUChMi4iIiHjLWvjkKdg4yanDajoz0uXrXfo4KTEUpkVERES8kZICHz8GP0xx6nK1nRnp8Nru9iWFSmFaREREJK9SkmHZw/DTTKcuX9+ZkQ6r4W5fUugUpkVERETyIjkJljwAv8536opXOjPSZau425e4QmFaREREJLeSE2HRvbB1iVNHNHFufxcS4W5f4hqFaREREZHcSEqAhSNg20dOXeUqGLIUylRwty9xlcK0iIiISE4S42D+UNixyqmrXQODF0NweZknPcIAACAASURBVHf7EtcpTIuIiIhcSkIMzBsEu/7r1DVawuCFEBjmbl9SJChMi4iIiFxMwjmYfRfs/dqpa98MA+dBQFl3+5IiQ2FaREREJDtxZ2B2P/hjvVPXvQUGzAX/Mu72JUWKwrSIiIhIVrGnYVYfOPCdU9fvAP1ngV+Qu31JkaMwLSIiIpJRzEmY0QsO/eTUV94OfaeBX6C7fUmRpDAtIiIikubccZjeE4786tSNe0Dv/4Cvv7t9SZGlMC0iIiICcPYITL8Djv3m1M16Q69J4PFzty8p0hSmRURERM4cgmk94MQOp27eH+74f+BRVJJL03eIiIiIlG5RB5wgfXK3U18zGHq8BT4ed/uSYkFhWkREREqvU3udIH36D6e+/h7o+ir4+LjalhQfCtMiIiJSOp3YBdMi4cwBp271ANw+Foxxty8pVhSmRUREpPQ59rszIx192KlvfgQ6vqQgLXmmMC0iIiKly5GtMD0Szh1z6ltGQ/vnFKTFKwrTIiIiUnoc/tW5/V3MCadu/xy0fdLdnqRYU5gWERGR0uHPTc6TDeNOO3XHl6D1o+72JMWewrSIiIiUfPu/g5l3QvwZp+48Fm4c5W5PUiIoTIuIiEjJtm89zOoDCdFO3e01uOFed3uSEkNhWkREREquPV/B7LsgMQYwEPkWXDvU7a6kBFGYFhERkZJp5+cwdyAkxYHxgTvegRYD3O5KShiFaRERESl5fl8F8wZDcgIYD9z5HlzVx+2upARSmBYREZGS5bflsGAEpCSCjy/0+Q80ucPtrqSEUpgWERGRkmPzYlh0L9hk8PhDv+nQsIvbXUkJpjAtIiIiJcMv8+HDkWBTwBMA/WfDFR3d7kpKOIVpERERKf5+nAlLHwQs+AbBwLlQr53LTUlpoDAtIiIixdv3/4GP/ua89isDg+ZDndbu9iSlhsK0iIiIFF8bJsEnTzqvA0Jh0EKo1crdnqRUUZgWERGR4mndBFj9vPM6MAwGfwg1rnO3Jyl1FKZFRESk+PnqVfjvy87roHAYsgSqtXC3JymVFKZFRESk+LAW1vwffPl/Th1cEYYtg8pN3e1LSi2FaRERESkerIXPX4K14506pDIMXQYRjdztS0o1hWkREREp+qx11kevf9upy1aDYcuhYgN3+5JST2FaREREiraUFFj5FGx8z6nDajpLO8rXc7cvERSmRUREpChLSYGPHoVN05w6vI4zI12ulqttiaRRmBYREZGiKSXZearhz7OdukIDZ410WHV3+xLJQGFaREREip7kJFjyP/DrAqeu1AiGLoWyVdztSyQLhWkREREpWpITYdE9sHWpU0c0dYJ0SCV3+xLJhsK0iIiIFB1J8bBgBGz/2KmrNHeCdHB5d/sSuQiFaRERESkaEuNg/hDYsdqpq18Hgxc5TzgUKaIUpkVERMR9CTEwdwDsXuPUNVvBoIUQGOpqWyI5UZgWERERd8VHw5z+sPdrp659MwycDwEh7vYlkgsK0yIiIuKeuDMwqy/s/9ap67aFAXPAv4y7fYnkksK0iIiIuCP2NMzsDX9+79QNOsJdM8EvyN2+RPJAYVpEREQKX8xJmNETDv3s1A27Qt+p4BvgalsieaUwLSIiIoUr+pgTpI9sdurGkdB7Mvj6u9uXiBcUpkVERKTwnD0C0yPh2DanbtYHek0CjyKJFE/6zhUREZHCceYgTOsBJ3Y69dUD4I7/Bz4ed/sSuQwK0yIiIlLwTu93gvSpPU597VDo/ib4+Ljbl8hl0newiIiIFKyTe2BK1/NB+oZ7FaSlxNDMtIiIiBScE7ucGekzfzr1X/4Knf8Bxrjbl0g+UZgWERGRgnFsO0yLhOjDTn3zo9BxjIK0lCgK0yIiIpL/jmx17tpx7phTt30K2j2jIC0ljsK0iIiI5K9DP8P0nhB70qlvfR5uGe1uTyIFRGFaRERE8s+fP8CMXhAX5dS3vQw3P+xuTyIFSGFaRERE8sf+jTCzN8Sfcerb/wV/+R93exIpYArTIiIicvn2fgOz+0FCtFN3ex1uuMfdnkQKgcK0iIiIXJ7da2DOAEiMAQxEToBrh7jdlUihUJgWERER7+38DOYOgqQ4MD7Q8124+i63uxIpNArTIiIi4p3tK2H+EEhOAOOB3u9Ds95udyVSqBSmRUREJO9+Ww4LRkBKIvj4Qd8p0LiH212JFDqFaREREcmbzYtg0X1gk8HjD/1mQMPb3e5KxBUK0yIiIpJ7P8+FJQ+ATQHfQOg/Cxp0dLsrEdcoTIuIiEjubJoByx4CLPgFw4C5UK+t212JuEphWkRERHL23WT4+DHntX8IDFoAtW9ytyeRIkBhWkRERC7t23dh5VPO64BQGLwIarZ0tyeRIsLH2wONMQHGmH8ZYw4aY2KNMRuMMbfl4rg7jTHzjDG7jTExxpjtxpjXjDHlLrJ/pDFmkzEmzhjzhzHmJWOMfggQEREpDN+8eT5IB4bB0CUK0iIZeB2mganAY8As4BEgGVhhjGmdw3HvAY2BmcDDwErgQWC9MSYo447GmC7AEuA08FDq6+eBCZfRt4iIiOTGl/+GT19wXgeVh2EfQfXr3O1JpIjxaobXGNMS6A+Mtta+mjo2HdgMjAMutYiqj7V2TZbz/QBMAwYBH2TY9CrwC9DJWpuUuu8Z4FljzJvW2m3e9C8iIiKXYC188U/4apxTl6kEQ5dB5Sbu9iVSBHk7M90HZyb6vbQBa20cMBm40RhT82IHZg3SqT5M/dg4bcAY0wRoAryXFqRTvQOY1B5EREQkP1kLn405H6RDqsDwFQrSIhfhbZi+BvjdWnsmy/jG1I8t8ni+Kqkfj2e5BsD3GXe01h4EDmTYLiIiIvnBWlj1LHzzhlOHVocRK6DSle72JVKEeftGvqrAoWzG08aq5fF8T+HMdC/Mco2M58x6nRyvYYyJACplGa6fx95ERERKvpQU+GQ0fJe62jKsFgxfDuF1XG1LpKjzNkwHAfHZjMdl2J4rxpiBwD3AOGvtjizX4BLXCc3F6UcBL+a2FxERkVIpJQU+egQ2TXfq8LowbDmUu+iqTRFJ5W2YjgUCshkPzLA9R8aYNjjrrFcBz2VzDS5xndxc4x1gQZax+sDS3PQnIiJS4qUkw9K/ws9znLrCFTBsGYTm9ZfMIqWTt2H6EFA9m/G0pRkHczqBMeZqYBnOHUD6ZHmTYdo10s65P5vrbCQH1tqjwNEs183pMBERkdIhOQk+HAmbU1dZVmrk3LWjbGV3+xIpRrx9A+JPwJXGmKxLLVpl2H5Rxpj6OPeXPgp0tdZGX+QaANdnObYaUCOna4iIiMglJCXAwhHng3TlZjD8YwVpkTzyNkwvBDzA/WkDxpgAYASwwVq7P3WsljGmUcYDjTFVgNVACtDZWnssuwtYa7cA24D7jTGeDJseACyZ36woIiIiuZUUD/OHwm/LnLrq1c4a6TIV3e1LpBjyapmHtXaDMWYBMDb1jhk7gWFAHZw3E6aZDrTFuS90mpVAPZyHu7TO8sTEI9baTzPUo3GWgqw2xswFmuE8LfEDa+1v3vQuIiJSqiXGwrzBsPMzp65+PQxeBEHl3O1LpJjyds00wFDgZWAIEI7zpMLu1tqvcjju6tSPT2az7UsgPUxbaz8yxtyJc0eOCcAx4J/A3y+jbxERkdIpIQbm9Ic9Xzp1zb/AoAUQmJsbZIlIdrwO06lPPByd+udi+7TLZixP7wC01i4BluS1PxEREckgPhpm3wX71jp1nTYwYC4EhLjbl0gxdzkz0yIiIlIcxEXBrL6wf4NT12sP/WeDf7C7fYmUAArTIiIiJVnsKZhxJxzc5NRXdIJ+M8Av8NLHiUiuKEyLiIiUVDEnYfodcPgXp27YDfpOAd/snocmIt5QmBYRESmJoo85QfroFqdu0hN6fwAeP3f7EilhFKZFRERKmrOHYVokHN/u1Ff1hZ7vgkf/7IvkN/2tEhERKUmi/oRpPeDkLqduMQgiJ4CP59LHiYhXFKZFRERKitN/OEH61F6nvm44dBsPPt4+8FhEcqIwLSIiUhKc3OME6aj9Tt3yfugyDkyeHu8gInmkMC0iIlLcHd/pBOmzB536xgeh0ysK0iKFQGFaRESkODu6DaZHQvQRp279GHR4QUFapJAoTIuIiBRXhzc7t7+LOe7U7Z6Btk8pSIsUIoVpERGR4ujgTzCjp/OEQ3Bmo9s87m5PIqWQwrSIiEhxc+AHmNkL4qKcutMrcNND7vYkUkopTIuIiBQnf2yAmb0h4axTdxkHrUa625NIKaYwLSIiUlzsXQuz+kHiOafu/gZcP8LdnkRKOYVpERGR4mDXFzBnACTFAgbueBuuGex2VyKlnsK0iIhIUbfjM5g7EJLjwfhAr0nQvJ/bXYkICtMiIiJF2/ZPYP5QSE4A44E+k6FpL7e7EpFUCtMiIiJF1dalsPBuSEkCHz/oOxUad3e7KxHJQGFaRESkKPp1ISy+H2wyeALgrhlwZWe3uxKRLBSmRUREipqf5sDSUWBTwDcQ+s+GBh3c7kpEsqEwLSIiUpRsmg7LHgYs+AXDwHlQ9xa3uxKRi1CYFhERKSo2vg8rnnBe+4fAoAVQ+yZ3exKRS1KYFhERKQrWvwOrnnFeB4TB4EVQ8wZ3exKRHClMi4iIuG3tePhsjPM6sBwMXQLVrnG1JRHJHYVpERERN305Dr74h/M6uAIMXQpVrnK3JxHJNYVpERERN1jrhOiv/u3UZSJg2DKIaOxuXyKSJwrTIiIihc1a+PQFWPeWU4dUgWHLodKV7vYlInmmMC0iIlKYrIWVz8CGiU4dWsOZka5Q392+RMQrCtMiIiKFJSXFufXd95OdulwtGPYRhNd2ty8R8ZrCtIiISGFISYblj8CPM5w6vC4M/wjCarjbl4hcFoVpERGRgpacBEv/Cr/MdeoKVzhrpEOrutuXiFw2hWkREZGClJwIi++HLYudulJjZ410SIS7fYlIvlCYFhERKShJCbBwBGz7yKkrX+U8kKVMRXf7EpF8ozAtIiJSEJLiYf5Q+H2lU1e7BgYvhuDy7vYlIvlKYVpERCS/JcbC3EGw63OnrnEDDF4EgWHu9iUi+U5hWkREJD8lnIM5/WHPV05d60YYtAACyrrbl4gUCIVpERGR/BJ/Fmb1gz/WOXWdNjBwHviXcbcvESkwCtMiIiL5IS4KZvaBAxuduv6tcNcs8A92ty8RKVAK0yIiIpcr9hTM6AUHf3TqKzpDv+ngF+huXyJS4BSmRURELse5EzDjDjj8q1M36g59poCvv7t9iUihUJgWERHxVvRRmH4HHN3q1E17wZ3vg8fP3b5EpNAoTIuIiHjjzCGYHgnHf3fq5nfBHe+AR/+0ipQm+hsvIiKSV1EHYFoPOLnbqVsMhsi3wMfjbl8iUugUpkVERPLi1D4nSJ/e59TXjYBur4OPj7t9iYgr9DdfREQkt07uhqndzgfpliOh+3gFaZFSTDPTIiIiuXF8hzMjffaQU9/0ENz2Mhjjbl8i4iqFaRERkZwc/Q2mRcK5o07d5gm49XkFaRFRmBYREbmkw786t7+LOeHU7Z+Dtk+625OIFBkK0yIiIhdz8CeY0dN5wiFAhxehzWPu9iQiRYrCtIiISHYOfA8z7oT4KKfu/E+48a/u9iQiRY7CtIiISFb71sOsvpBw1qm7vgot73O3JxEpkhSmRUREMtrzNcy+CxLPAQZ6vAHXDXe7KxEpohSmRURE0uz6AuYMgKRYwEDPd6DFQLe7EpEiTGFaREQE4PfVMG8wJMeD8UCvSdC8r9tdiUgRpzAtIiKy7WOYPwxSEsHHF3pPhqY93e5KRIoBhWkRESndtnwIi+6FlCTw8YN+06BRN7e7EpFiQmFaRERKr18WwIf3g00BTwD0nwVX3OZ2VyJSjChMi4hI6fTTbFgyCrDgGwQD5kD99m53JSLFjMK0iIiUPj9MheWPAhb8ysDAeVC3jdtdiUgxpDAtIiKly8b3YcUTzmv/sjB4IdT6i7s9iUixpTAtIiKlx/r/B6uedV4HhMGQxVDjend7EpFiTWFaRERKh69fh89fcl4HhcOQJVCthbs9iUixpzAtIiIlm7Xw5ThY80+nDq4AQ5dClavc7UtESgSFaRERKbmshf++DF+/5tRlImDYMoho7G5fIlJiKEyLiEjJZC2sfh7Wv+3UZavCsOVQ8Qp3+xKREkVhWkRESh5r4ZOnYOMkpw6r6cxIl6/nbl8iUuIoTIuISMmSkgIfPwY/THHqcrWdGenw2u72JSIlksK0iIiUHCnJsOxh+GmmU5ev78xIh9Vwty8RKbEUpkVEpGRIToIlD8Cv85264pXOjHTZKu72JSIlmsK0iIgUf8mJsPg+2PKhU0c0cW5/FxLhbl8iUuIpTIuISPGWlAALR8C2j5y6ylUwZCmUqeBuXyJSKihMi4hI8ZUYB/OHwo5VTl3tWucR4UHh7vYlIqWGwrSIiBRPCTEwbxDs+q9T12gJgxdCYJi7fYlIqaIwLSIixU/COZh9F+z92qlr3wwD50FAWXf7EpFSR2FaRESKl/izMKsv/LHeqeveAgPmgn8Zd/sSkVLJx9sDjTEBxph/GWMOGmNijTEbjDG35eK4hsaY8caYdcaYOGOMNcbUuci+e1O3Z/3zrrd9i4hIMRZ7Gmb0Oh+k63eAgfMVpEXENZczMz0V6AO8AewAhgMrjDHtrbVrL3HcjcDDwFbgN6BFDtf5CXgty9jvXvQrIiLFWcxJJ0gf+smpr7wd+k4Dv0B3+xKRUs2rMG2MaQn0B0Zba19NHZsObAbGATdd4vBlQDlr7VljzBPkHKb/tNbO9KZPEREpIc4dh+k94civTt24B/T+D/j6u9uXiJR63i7z6AMkA++lDVhr44DJwI3GmJoXO9Bae9JaezYvFzPG+Btj9Ds8EZHSKPooTO1+Pkg36w19pihIi0iR4G2Yvgb43Vp7Jsv4xtSPOc0258WtQAwQnbqG+pF8PLeIiBRlZw7B1G5w7Denbt4f7nwfPH7u9iUiksrbNdNVgUPZjKeNVfPyvFn9AqwFtgMVcNZlv2GMqWatfSqng40xEUClLMP186k3EREpSFEHYFoPOLnbqa8ZAj3eBB+Pu32JiGTgbZgOAuKzGY/LsP2yWWsjM9bGmCnAJ8BjxpgJ1toDOZxiFPBifvQiIiKF6NReJ0if/sOpr78Hur4KPl7fhEpEpEB4G6ZjgYBsxgMzbM931lprjBkPdAbaATm9MfEdYEGWsfrA0vzvTkRE8sWJXTAtEs6kzpe0egBuHwvGuNvXZbLWci4hmajYRGITkohJSCYmIZnYhGSSUyw+PmAwGAM+xhDs7yEk0JeygX6EBPgSEuCLx6d4fw1ESiJvw/QhoHo241VTPx708ry5sT/1Y/mcdrTWHgWOZhwzxfx/xiIiJdqx350Z6ejDTn3zI9DxpWIRpOMSk9l/MoY/Tsaw74Tz8cCpWI5Fx3MiOp7j0fHEJaZ4fX4fAxVDAqgSFkjl0ECqhAZSPTyI+pVCqF+pDLXKB+Pr0cy9SGHzNkz/BLQ3xoRmeRNiqwzbC0q91I/HCvAaIiJS2I5shel3wLnUOZBbRkP754pckLbWcjAqji1/RrHt8Fm2HT7DtkNn2XPiHNYW3HVTLBw9G8/Rs/FA1AXb/TyGOhXK0LhqKFfXLEeLmmE0rRZGoJ/WmIsUJG/D9ELgCeB+IO0+0wHACGCDtXZ/6lgtINhauy2vFzDGlAeirLXJGcb8gKeBBOALL3sXEZGi5vCvTpCOOeHU7Z+Dtk+621OqhKQUfv0zih//OMUP+06x6Y9THDmT3duGMgvy81CrfDARoQFUKONPxZAAKpYNIDzYj2B/X4L8PAT7ewj09+DrY7AWUqzFAikpzpKQ6LgkouMTORuXxOmYRI6ciePwmTiOnInjUFQcZ+OS0q+XmGzZcTSaHUejWfaz8wtij4+hUZWytKxbntYNKtKqXgVCAi7neW0ikpVXf6OstRuMMQuAsal3zNgJDAPqAPdk2HU60BZIn1YwxoQBD6WWN6d+fNAYcxo4ba19O3UsEnjeGLMQ2IOzrGMg0Ax41lp72JveRUSkiPlzk/Nkw7jTTt3xJWj9qGvtWGvZfuQsa3ccZ+3O42zYfZLYxOSL7l+9XBCNq5alYZWy1K8UQu0KwdQsH0ylkIACX1p46lwCu49Hs/NoNLuOnWPHkbP8+ucZjkc7YT85xbLl4Bm2HDzDlG/24utjaFGzHDc3qMhtTSrTtFqolj+KXCZjvfydlDEmEHgZGAyE49zG7n+ttasy7LMGaGutzRim6+CE4+zss9bWSd3vOpw7cVyLc3u7BJzlI29Za7O+qTAvfTcFNm/evJmmTZt6exoREckP+7+DmXdCfOqKwc5j4cZRhd5GTEISX/1+jNVbj/D1juMcO5v9zHPl0ACurRXOdbXDaV6jHA2rlCUsqGjd8zptGcrP+0/z8/7T/LDvFD/tP01SyoX/3tcsH8TtTatwe7MqXFMzHB+9wVGELVu20KxZM4Bm1totOe3vdZgurhSmRUSKiH3rYVYfSIh26m6vwQ33FtrlT55L4LPfjrB6yxG+3nGM+KQL3xxYvVwQrRtU5KYGFbi+TnmqhQUWy5nc6PgkNu45wdodJ1i78xi/H4m+YJ/KoQH0uqYGfa6rToOIsi50KVI0KEznQGFaRKQI2PMVzL4LEmMAA5FvwbVDC/yyMQlJrN5yhMU//sk3O4+TnGW2NsjPQ+srKtLmioq0blCRuhXLFMvwnJMDp2JYteUIqzYf5rt9Jy944+TVNcvR57oa9GxRjbKBRWvmXaSgKUznQGFaRMRlOz+HuQMhKQ6MD9zxDrQYUGCXS0pO4ZtdJ1jy45+s2nKYmITM65/Dg/3o2LgynZpWoc0VFUvd3S+OnY1n1ZbDLPnxT77fdyrTtpAAX3pfW52hN9WhfqUQlzoUKVwK0zlQmBYRcdHvq2DeYEhOAOOBO9+Dq/oUyKUOno5l7nf7mf/dfg6ficu0LTzYj27Nq9LtqmrcUCdc92dOtef4ORZvOsCiHw5wMCrz16zNFRW5/5Z6tG5QsUTO1oukUZjOgcK0iIhLfvsIFgyHlETw8YU+/4Emd+TrJZJTLGu2H2X2hj/4YvtRMq7i8Pf14bbGlel1TXVuubIS/r4K0BeT9nWcum4vX+84nmlb8xphjGrXgE5NKusNi1Ii5TVM62aTIiJS8LZ8CIvuhZQk8PhDv+nQsEu+nf5MXCLzNu5n6rq9/Hk6NtO25jXCGNCyFt2aVyVU639zxeNj6NC4Mh0aV2bXsWhmrN/H/O/3E5OQzC8HovifmT/QICKEh25tQI/m1RSqpVTTzLSIiBSsX+bDhyPBpoAnAPrPhis65supD5yKYco3e5n33X6i488/wKSMv4fIFtUZ1KoWzaqH5cu1SrtT5xKYum4vU9ftJSo2MX28cdVQRne+kvYNI7T8Q0oELfPIgcK0iEgh+nEmLH0QsOAbBAPnQr12l33an/ef5r2vd7Ny8+FMd+SoX6kMI26uS89rqutJfwUkOj6J2Rv28d5XuzkenZA+fkOdcJ7u0ojrapd3sTuRy6cwnQOFaRGRQvL9f+Cjvzmv/crAoPlQp/XlnXLvSd78fMcF63hvql+Be9vUpd2VEVpyUEjOxSfxn7V7eO+r3ZzN8FuBni2q8XSXxlQJC3SxOxHvac20iIi4b8Mk+ORJ53VAKAxaCLVaeX26b3ef4K3Pd7Bu14n0MV8fQ+TV1bi7dV0t5XBBmQBfHupwBYP/Upt3v9zFlHV7SUhKYclPB/8/e/cZHkW1gHH8P5seQhJCCIRA6L13EFAULBRpAiIgTZqA5WJHxN7LxQKiWJAuSJGioGJBQanSe++9JKTtZnfuhwmIXGpIMsnm/T1PHjKzM9n3gyZvTs6cww8bjzDo1tL0aVyCAN/ctdSg5D4amRYRkYy15EP4YZj1eWAYdJsJRWql70ttP86IhdtYtuvk+XP+vg661I2l/y0liQ4LyojEkgH2nUzk1XmbmL/h8PlzxfIH81KbytxStoCNyUSuj0amRUTEPovegZ9ftj4Pygf3z4LC1a/7y6zbf4Y352/mj+3/TOcI9HPQtV4x+t9ckqhQTSHIbopGBDP6/los3n6cF+dsYOuRs+w5kUiPL5bRvmYMz7WsSL48/nbHFMlwKtMiInLjTBN+fQN+e8M6Do6EHrOh4PX9BXDX8QTe+WEL89YeOn8uyM+H7g2K0adxSQrkDcjI1JIJGpaO5LuHGzP+rz28s2ALCU43M1YdYNHWYzx/dyVaVY3Wqh/iVVSmRUTkxpgmLHwJ/njPOg4pCN1nQ1T5a/4SR+OSGbFwG18v33d+dQ4/H4Ou9Yox6NbSKtE5jK+Pg14NS3BnpUIMm7Wenzcf5fhZJw9N/ptvVx/ktfaVicqrvy6Id1CZFhGR9DNNa370nx9Zx3kLQ485EFn6mm5Pdrn5/I9djPxlO4lONwCGAW2qFWbI7eWIzR+cWcklCxQOD+LzHrWZveYgL87ZyMkEJz9tOsLfI07xVoeqNK1Q0O6IIjdMZVpERNLH44H5T8GyT63jsKJWkY4ocdVbTdNk/vrDvPrdJvaf+mfHwiblCvDkneWpWDg0s1JLFjMMgzbVY2hcpgDPz97AnDUHOZHg5IGvVtCtfizPtqhIkL9W/JCcS2VaRESun8cDcx+FVV9Zx/mKW0U6PPaqt246FMeLczbw185/VugoXygvw1tV5KbSkZkUWOwWkcefD++rQdPyUTw3az3xKalM+Gsvf+44wfuda2h5Q8mxVKZFROT6eNzWroZrJlnH+Utbc6TDYq5426kEJ+/8sIXJy/ZybtPCfMF+PHZHOTrXKYqvjyOTg0t20LZGDLWK5WPI1NUs332KHccSaD9qCc+3rkiXurF6OFFyHJVpERG5du5UmDUA1k2zjguUh+7fQt5Cl73FNE2+WbmffX+BsAAAIABJREFU177bxKlEFwA+DoP76xfj0WZlCA/Wcmm5TdGIYKb0a8DHv27nvz9tw+n28OzM9azcc4pX21bRtA/JUVSmRUTk2rhdML0PbJxlHUdVsop0yOU35Nh+9CzPzlzH0gs2XWlcJpLhrSpSpmDezE4s2ZiPw2DwbWWoWyI/gyet4mh8CjNWHWDjwTg+7laLEpF57I4ock30NzUREbm61BSY2uOfIl2oKvSce9kinexy8+4PW2j+/qLzRToqbwAju9RkXO+6KtJyXt0SEcx9uBH1S0YAsPlwPK0//IMfLthJUSQ7U5kWEZErcyXD191gyzzrOKaWtSFLcMQlL/992zHuHLGID3/ejsttYhjQ86biLHzsFlpqww65hKi8gUx4oB4DbikFQHxKKv0nrOTjX3dgmqbN6USuTNM8RETk8pyJMKUL7PzFOi5aD7p+A4H/v3TdmSQXr87byNQV+8+fqxwTymvtqlC1SHhWJZYcytfHwdPNy1MjNpwhX68mwenmzfmb2XY0ntfbVyHAV/OoJXvSyLSIiFxaylmY1OmfIl2sEXSbccki/fPmI9z530Xni3Qefx+Gt6rIrIENVaTlutxZqRDfPHgTMeFBAMxYdYCuY5Zy4myKzclELk1lWkRE/l9yHEy4B3b/bh2XbAJdp0FAyL8uO5PoYsjU1fQeu4LDccmA9YDhgv/cTO9GJbTcnaRLhehQZg1qSM1Y6xexFXtO0WbkYrYdibc5mcj/03c5ERH5t6TTML4d7PvLOi7dDO6bAv7/3tr7x41HaPbf35ix6gAAeQN8efOeKozrXZci+bQNuNyYAnkDmNS3Pm2rFwZg/6kkOoz+k5V7Tl7lTpGspTItIiL/SDwJ41rDgRXWcbkW0HkS+AWdvyQu2RqN7jtuBcfirT+9NylXgB+G3My9dbTphmScQD8f/ntvdR67vSxgzcvv+tlSFm46YnMykX+oTIuIiCXhOHx1NxxaYx1XaA0dvwLfgPOXLNt1kuYjfj8/Gh0a6Ms7HavxZc86RIcFXeqritwQwzB4qGkZ3rqnKg4Dkl0e+o1fydQV++yOJgJoNQ8REQGIP2KNSB/bbB1X7gDtPgEf68eEM9XDf3/ayujfdnBupbLGZSJ5u0M1CoUF2hRacpNOdYqSL48/gyetIiXVw5PfrOVYfAoDm5TSX0PEVhqZFhHJ7eIOwtgW/xTpavdB+0/PF+ntR+NpN2px2pq/EODr4IW7K/JVr7oq0pKlbq9YkIl96hEW5AfA2wu28NaCLVqLWmylMi0ikpud3gdftoAT263jmt2hzShw+GCaJl8t2U3LD/5gw8E4ACpGhzL3oUb0bFgCh0OjgZL1ahePYNqABhQKtX6R+/jXHbwyb5MKtdhGZVpEJLc6tdsq0qd2Wcd1+kCr98Hh4GSCk95jl/P87A2kpHowDBhwSylmDWqorcDFdmUL5mVq/wbn16L+/I9dDP92Ax6PCrVkPZVpEZHc6MQOq0if2Wsd1x8ELd4Bh4O/dp6g+fuL+GXLMQBiwoOY0rc+Tzcvj7+vfmxI9hCbP5ipAxpQLL+1DOP4v/YwdOY6FWrJcvquKCKS2xzbYhXpOGtFDho+Cne+ituEDxZuo8uYvzgSZy1517JqNN8/2ph6JfPbGFjk0mLCg/i6XwNKFsgDwJTl+3j8mzW4VaglC6lMi4jkJkc2wtiWcPawdXzLU9DsBY7Gp3D/50t578eteEzw93XwarvKfHRfDUID/WyNLHIlhcIC+bpfA8oWtHbnnLHqAM/OXKc51JJlVKZFRHKLQ2usIp1gTd/gtmFw61AWbTtO8/d/Z8mOEwCUKpCHbwc1pGu9YlpyTHKEAnkDmNy3PuXS5vNPWb6PF+dsVKGWLKEyLSKSGxxYaW3IkpS2FfPtL+Nu9DhvL9hM9y+WcSLBCcA9NYswe3AjKkSH2hhW5PrlDwlgfJ+6lIy0pnyMXbJby+ZJllCZFhHxdvuWwbi2kHzGOr7rTU5U60/3L5Yy8pcdAAT7+/Bux2q826kaeQK0n5fkTFF5A5nQpx5F8lmrfHz86w4++nm7zanE26lMi4h4s92LYXw7SLHWiable6yO6UyrD/9g8XZrWkfZgiHMHtyIe2oVsTGoSMYoHB7EpD71z69D/e6PW/ns9502pxJvpjItIuKtdv4KEzuA8yxgYLb+kAnuZnQcvYRDZ5IBaF2tMDMHNqR0VIitUUUyUmz+YCb0qUdkiD8Ar8zbxKy/D9icSryVyrSIiDfa/hNMuhdciWA4cLb+mMe2V2XYrPW43Ca+DoPn767I+52ra1qHeKXSUSGMf6AeedP++3582hoWbT1mcyrxRirTIiLeZst8mHwfpCaD4cOxO0bSelEMM1ZZI3NReQOY0q8+vRqW0God4tUqRIfyaffa+Ps4SPWYDJiwkrX7T9sdS7yMyrSIiDfZNAe+7gZuJzj8WNfwA25bkJ/Nh+MBqFcigrkPN6J28Qibg4pkjQal8jOic3UMAxKdbnp9uZzdxxPsjiVeRGVaRMRbrJ8OU3uAx4Xp4893Fd+m9cJ8xCenAtDv5pJM7FOPqLyBNgcVyVotqkTzYutKAJxIcNL9i2Uci0+xOZV4C5VpERFvsGYKTO8DphvTN5DR0a8wcEUUpglBfj6M7FKToS0q4Oujb/uSO3VvUJzBt5YGYO/JRPqOW0Gyy21zKvEG+q4qIpLTrRoPMweA6cHjG8RzwcN5c7u1zF1MeBDfPNiAllWjbQ4pYr/H7ihLh7QlIFfvO83j09bg8WhTF7kxKtMiIjnZ8s9h9mDAxO2bh37mUCYcLQ5A3RIRzB7ckEqFw2yNKJJdGIbBa+2qUK+E9czA3LWHGLFwm82pJKdTmRYRyan+Gg3zhgDg9A3hvuSn+CmhFABd68Uy4YF65A8JsDOhSLbj7+tgdLdaFM8fDMAHC7dpDWq5ISrTIiI50eL3Yf5TACT55KVDwlMsSy2Nr8PglbaVebVdFfx99S1e5FLy5fHn8551CA201qB+8pu1rNh90uZUklPpO62ISE7z29vw43AA4h2h3JP4DGvNUkTk8WdCn3p0q1/M5oAi2V+pAiGM7lYLX4eB0+2h3/iV7D+VaHcsyYFUpkVEcgrThJ9fhV9eAeCUEcY9Sc+y0SxO+UJ5+XZQQ+qXzG9zSJGc46bSkbzStjIAJxOc9B+/Uit8yHVTmRYRyQlME356ARa9BcAx8tEheRhbzaI0q1CQ6Q/eRNGIYHsziuRAnevG0qthcQA2HIzjmRnrME2t8CHXTmVaRCS7M01YMBQWjwDgkBlBx5Rh7DBj6NOoBJ/cX4s8Ab42hxTJuYa2qHB+hY+Zfx/gy8W77Q0kOYrKtIhIdubxwHePw1+jANhvRtLROZx9RmFebVeZYa0q4uMwbA4pkrP5+TgY2bUm0WHW7qCvfreJP3ecsDmV5BQq0yIi2ZXHA3MfgeWfAbDbU5BOKcM541+YL3vWoWs9PWgoklEiQwIY3a0W/r4O3B6TwZNWceB0kt2xJAdQmRYRyY48bvh2EKwaB8AOTzT3Op/DCC/K9IE3cXPZAjYHFPE+1YqG82raA4knEpw8OGElKal6IFGuTGVaRCS7cafCjH6wZhIAWz0xdHY+R3TRkswa1JCyBfPaHFDEe3WsXZTuDay/+qzdf4bX5m2yOZFkdyrTIiLZSaoTvukF678BYJMnls7O56hbtQJT+tWnQF7taCiS2Ya1rEi1ouEAfPXnHuatPWRzIsnOVKZFRLKL1BSY2h02zQZgnac49zmfpdMtNfiwcw0C/XxsDiiSO/j7OhjZpQZhQX4APDV9LbuPJ9icSrIrlWkRkezAlQRTusDW7wH421Oarq5nGdKmPk83L49DK3aIZKki+YJ5t2M1AM6mpDJo0ipt6CKXpDItImI3ZyLm5M6w/ScAlnnK8YBnKG93u5nuDYrbm00kF2tWsSB9G5cArA1dXpm30eZEkh2pTIuI2CnlLJ6JHTB2/grAn+6KPOLzLGP63sqdlQrZm01EePKu8tSMteZPT/hrL3PWHLQ5kWQ3KtMiInZJPoN7XDscexYDsMhdhedChjNhYFNqFYuwOZyIgLWhy4ddahIebM2fHjpjHftOJtqcSrITlWkRETskncI1ti0+B5YB8LO7OiMKvMSkgbdSqkCIzeFE5EIx4UG808GaPx2fksqQqatJdXtsTiXZhcq0iEhWSzxJyhet8Du8CoAf3LWYWPxVxve/mai8gTaHE5FLaVaxIN3qxwKwfPcpPv51h82JJLtQmRYRyUpnj5H8WXMCjq0HYK67HgurvM3onjeRJ8DX5nAiciXPtqhI6SjrL0cjFm5j1d5TNieS7EBlWkQkq8QfJmnMXQSe3AzALPdNbG74Hm90rImfj74di2R3Qf4+vN+5On4+Bm6PyaNTVnM2JdXuWGIzffcWEckKZw6Q8MmdBJ3ZDsC01Js5eceHPH5XZQxDa0iL5BSVCofx5J3lAdh7MpHnv91gcyKxm8q0iEhmO72Xs5/cQZ6zuwGY7G6KT7uR9G5c2t5cIpIuDzQqQaPSkQBMX7Vf243ncirTIiKZ6eQu4j++nZDE/QCM99xJ1H2jaF8r1uZgIpJeDofBu52qkS9tubxhs9ZxLD7F5lRiF5VpEZFMYh7fRtzHt5M35TAAX9GK8r0+pmlFbcYiktMVDA3k5baVATiV6GLozHWYpmlzKrGDyrSISCZIPbyR+NF3EOo6BsCXjvbU7TeKOiXy25xMRDJKq6qFaVk1GoAfNx5h5t8HbE4kdlCZFhHJYCkH1pH4aXNCU08C8IVfZ5oO/IgKhcNsTiYiGe3lNpWJDPEH4PnZGzh0JsnmRJLVVKZFRDJQ4p5VpHzeglDPaQC+DOxOq4ffJzYyj83JRCQzROTx5/X2VQGIT07lqema7pHbqEyLiGSQ+B1/4Rl7N6GeOADG5e3LPY++p10NRbzc7RUL0r5mDACLth5jyvJ9NieSrKQyLSKSAU5t/h3H+LaEmGcBmBgxiE4Pv0looJ/NyUQkKzx/dyUKhVq/OL8ydyP7TyXanEiyisq0iMgNOr5+IYFTOpAHa67k5KghdBr0CoF+PjYnE5GsEhbkxxv3VAEgwelm2Kz1mu6RS6hMi4jcgMN/zyfkm84EkYzHNJga8zSdBgzX9uAiuVCTclF0qFUEgF+3HOPb1QdtTiRZId3f7Q3DCDAM403DMA4ahpFkGMZSwzBuv4b7yhmG8V/DMJYYhpFsGIZpGEbxK1zf2jCMVWnX7jUM40XDMHzTm1tEJKPsXz6b8G/vJxAnbtNgZonhdHjgaXwc2h5cJLca1rLC+dU9XpyzgRNntZmLt7uRoZOxwBBgIvAI4Aa+Mwyj0VXuawA8DOQFNl3pQsMwmgOzgNPAQ2mfDwM+vIHcIiI3bPfib4ia14tAnKSaDuaVe5X2Pf6DQ0VaJFcLD/bnhdaVAGszl5fnbrQ5kWS2dJVpwzDqAp2BZ0zTfMI0zU+B24A9wFtXuX02EG6aZhWsIn4l7wBrgTtM0xxjmubDwOtAf8Mwyqcnu4jIjdr+60RifuiHP6k4TR9+rPw2rbsMwjBUpEUEWlaJplmFggDMWn2QX7YctTmRZKb0jkx3wBqJ/vTcCdM0k4HPgQaGYRS93I2maZ40TTP+am9gGEZFoCLwqWmaqRe8NAow0jKIiGSpzT9+QfFfBuNnuEkx/fij1giad+xjdywRyUYMw+DltpUICbBmpQ6buZ6zKalXuUtyqvSW6RrAVtM04y46vyzt3+rpj/Sv9wBYceFJ0zQPAvsveP2yDMOIMgyj0oUfQKkMyCYiudC6eaMp88cQfA0PyaYfy+qP5LbW3e2OJSLZUHRYEE83t/6IfuB0Eu8s2GJzIsks6S3T0cChS5w/d65wOr/uxe9x4de8+H2u5T0GAusv+vg2A7KJSC7z96wPqLTsaXwMk0QzgNU3j6Fx83vtjiUi2ViXurHULR4BwFd/7mbt/tP2BpJMkd4yHQRc6vHU5Atev1Hnvsbl3uda3mMUUPmijzYZkE1EvJXLBb/+CjNmWP+6XKyc9jY1Vj+HwzBJMAPZfPtY6jdtZ3NQEcnuHA6D19pXwc/HwDTh2ZnrcXu09rS3Se8Sc0lAwCXOB17w+o069zUu9z5XfQ/TNI8C/5r1rweEROSSXC544w0YORKOHDl/ekWXutQusxmAODOYPc3HU7N+M7tSikgOUzoqhP43l+KjX7az7sAZJi3dw/0NitsdSzJQekemD/HPNIwLnTuXEauUn5vecbn30UroIpIxXC5o2xaGD4ej//z+vbxTtfNF+oyZhwOtJlFFRVpErtOgW0tTJJ/1B/W3FmzhaHzyVe6QnCS9ZXo1UNYwjNCLzte74PUbde5r1L7wpGEYhYEiGfQeIiLWiPR331mfp23/u+K+6tSpsAuAk54QjnzjT4UFi+1KKCI5WJC/Dy+mrT0dn5zKa/OuuM2G5DDpLdPfAD5Av3MnDMMIAHoBS03T3Jd2Lja960GbprkB2Az0MwzD54KXHgTMtAwiIjfG5bKmdlwwBWx5t+rULrsTgOOeUE5M9aXspr3WdS6XXUlFJAdrWqEgd1T8Z+3pJTuO25xIMkq6yrRpmkuBacDrhmG8ZRhGP+BnoDjw5AWXjuOiXQ4NwwgzDGOYYRjDgKZppwennRt80Vs9AVQFfjAMo69hGO8DQ4HPTNPUr3UicuMWL7bmSJsmJrCiR3XqlLKK9DFPGHGTocyWvdaI9eHD1vUiIunwfOtKBPlZ44PPzVqPM9VjcyLJCDeynXh3YARwP/AB4Ae0Mk1z0VXuywe8nPZxV9q5x9KOH7/wQtM05wLtgQisLcTbA68Bg24gt4jIP06eBKw/d63qXZ3axa0ifdidj4SJbkpu33/J60VErldMeBCPNCsDwI5jCYz5fafNiSQjpLtMm6aZnLaVeLRpmoGmadY1TXPBRdc0MU3TuOjcbtM0jct8FL/E+8wyTbNG2nsUNU3zOdM09XdWEckYERGYwN99qlOrqPWD7aA7Aue4FIrvvMRzzhERWZtPRLzKA41KULZgCAAf/bydQ2cyYgE0sdONjEyLiOR4Zv16/D2oFjVjrCK9LzUSz9hEYvce/veFhgGFCkHDhjakFBFv4efj4IW0hxGTXG7e+H6zzYnkRqlMi0iu5Ul1sfqTHtSM3AbAntQoHF/EU2T/0f+/2DRh0CDw88vilCLibW4qFUnzyoUA+Hb1QVbs1vSxnExlWkRyJY/LyboPO1HjlDU7bac7moDPThFz+KIn7M+t8tGyJTz1VBanFBFvNbRFBQJ8rRr2wpwN2hkxB1OZFpFcx+1KYf0H91DtzM8AbHeUIE//+RQa/CgULPjviwsWhJdfhpkzNSotIhmmaEQw/W8uCcD6A3FMW7HP5kSSXirTIpKrpKYksXFEW6rGWwsPbXGUJmzA9xQsUhyGDYO9e+GXX2D6dOvfvXut8yrSIpLBBjQpRXRYIABvL9jCmSStr5ATqUyLSK6RmpzA1vfvpkrCEgA2+ZSjwKD5FIiK/uciPz9o0gTat7f+VYkWkUwS7O/LMy0qAHAiwckHC7fZnEjSQ2VaRHKF1KR4dnzQioqJywFY71uRQoPnE5G/gM3JRCQ3u7tqNHWLW0tufrVkN9uPxtucSK6XyrSIeD13Uhx7PmhBucRVAKzxrUqRwd+RL5/WjBYRexmGwfC7K2IYkOoxeWmuNnjOaVSmRcSruRNPs/eDuyiVtBaAlb41iB08h/DwfDYnExGxVI4Jo3OdWAAWbT3Gb1uP2ZxIrofKtIh4LXfCKQ58cCclkjYAsNS3NiUemk2+8HCbk4mI/Ntjd5QlJMAXgNfmbdJSeTmIyrSIeCXP2eMc/vB2YpOt3cUW+zWgzMPfEhEWanMyEZH/FxkSwINNSgGw5Ug801futzmRXCuVaRHxOp64Ixz5sBkxydaT8b/5NaL84G+ICA2xOZmIyOX1blji/FJ57/ywhURnqs2J5FqoTIuIV/GcOcTxkbcTnbILgJ/8mlDpoankD1ORFpHsLcjfh8fuKAfA0fgUPvt9l82J5FqoTIuI1/Cc3s/Jkc2IStkDwHy/plQbPJnI0Dw2JxMRuTbtasRQMdqajjb6tx0cjU+2OZFcjcq0iHgF89RuTo9qRqTTmmc4x+9Oaj40gQJhwTYnExG5dj4Og6FpG7kkOt2M+EkbuWR3KtMikuOZJ3ZyZtQdRDgPATDDryX1Bn9FVKiKtIjkPI3KRNKknLWh1NfL97HtiDZyyc5UpkUkRzOPbSV+9O2Eu44AMMWvLQ0Hf05UWJDNyURE0u+Z5hVwGOD2mLzx/Wa748gVqEyLSI5lHt1Ewid3Euo6DsB4v440GTSagirSIpLDlSuUl061iwKwcPNR/txxwuZEcjkq0yKSI5mH15H46V2EpJ4E4HO/+2g2+EMKhatIi4h3GHJ7WYL8fAB4a8FmTFMbuWRHKtMikuOYB/8maUwL8qSeBuATv/tpPui/RGtEWkS8SFRoIL0aFgfg772n+WnTUXsDySWpTItIjmLuW07K560IdscB8KFfL1oNepvCGpEWES/U/+ZShAZa24y/s2ALHm0znu2oTItIjmHu+RPnl60JdJ8F4D2/vrQb+BoxKtIi4qXCgv3of8s/24zPXnPQ5kRyMZVpEckRzF2LcH3VjgBPIh7T4A3fB+n44EsUyafl70TEu/VqWJzIkAAA3vtxK85Uj82J5EIq0yKS7Zk7fiF1fAf8PUm4TYPX/AfTdeBwikaoSIuI9wv29+XhpqUB2Hsykakr9tmcSC6kMi0i2Zq5dQHuCZ3w86SQajp4ye8Rug8YqiItIrlK5zqxFMlnTWn7YOE2kpxumxPJOSrTIpJ9bZ6HZ3IXfE0nLtOH4X5D6P3gk8TmV5EWkdzF39fBf5qVBeBofArj/txtax75h8q0iGRPG2bh/vp+fMxUnKYPQ/2eoN+AIRTLn8fuZCIitmhbI4YyUSEAfPzbDuKSXTYnElCZFpHsaO00PNN642O6STH9eML3aQYOeJjikSrSIpJ7+TgMHrujHACnE12MWbTT5kQCKtMikt2snoQ5oy8O3CSZ/gzxfYaHBwykhIq0iAh3VipItaLhAHy5eDenEpw2JxKVaRHJPlaOxZw1EAOTBDOAR32f5T/9+1OqQIjdyUREsgXDMBhyuzV3+mxKKp//scvmRKIyLSLZw7IxMOcRDEzizSAe9h3OE/0foHSUirSIyIVuLhNJjdhzo9O7NDptM5VpEbHfnyPhu8cBiDODGez7HE/360HpqLw2BxMRyX4Mw+DRtJU9EpxuPvtDc6ftpDItIvb6/T1YMBSAU2YID/q8wLP9ulOmoIq0iMjlXDg6PXbxbk5qdNo2KtMiYg/ThF/fhIUvAnDCzMsAnxcY3q8LZVWkRUSuyDCM8+tOJzjdfPa7RqftojItIlnPNOHnl+HX1wA4ZobRz/EiL/a7l3KFVKRFRK5F4zKR1Ewbnf5qiUan7aIyLSJZyzThx+fg93cBOGzmo6/jRV7u25HyhUJtDiciknNcPHd6jEanbaEyLSJZxzRh/tOw5EMA9puR9HG8xKt921OxsIq0iMj1alwmklrF8gEanbaLyrSIZA2PB+b+B5aOBmCvpwB9jRd5o08bKhUOszmciEjOZI1OlwEgUaPTtlCZFpHM53HD7Idg5ZcA7PQU4gHHi7zd924qx6hIi4jciEal/z06rXWns5bKtIhkLncqzBwAqycAsN1TmD6OF3mvTysVaRGRDGAYBo80/Wd0+sslu+0NlMuoTItI5nG7YEYfWDcVgM2eovRxvMB/H7iLKkVUpEVEMkrjMpFUTfu+OnbxLuKTXTYnyj1UpkUkc6Q6YVpP2DATgA2eYvQ1nue/ve+gWtFwe7OJiHgZwzAYdGtpAOKSU5m4dK/NiXIPlWkRyXiuZPi6G2yeC8BqT0n6Gs/z/gPNqBGbz+ZwIiLe6fYKBSlbMASAz37fRbLLbXOi3EFlWkQyljMRptwH2xYAsNJThv48x4e9b6OmirSISKZxOAwGNrFGp4+fTWHqin02J8odVKZFJOM4E2BSJ9jxMwBLPeUZwLOM7N3k/JPmIiKSeVpVjSY2IhiAT37bicvtsTmR91OZFpGMkRIPEzrA7t8BWOyuxECeYVTvW6hdPMLmcCIiuYOvj4MBt5QC4MDpJGb9fcDmRN5PZVpEblzSaRjfDvYuAeBXdzUGG0/zca+bqaMiLSKSpe6pFUPB0AAAPv5tB26PaXMi76YyLSI3JvEkjGsD+5cD8KO7Jg/zBB/3bEjdEirSIiJZLcDXh76NSwKw81gCCzYctjmRd1OZFpH0SzgOX7WGQ6sB+N5dhyEM4ZOeN1G/ZH6bw4mI5F5d6sWSL9gPgJG/bMc0NTqdWVSmRSR9zh6Fsa3gyDoAZrsb8ASP8EmPBjQopSItImKnYH9fejcsAcCGg3H8uvWYzYm8l8q0iFy/uEMwtiUc2wTAdHcjnjIf4pMeDbipdKTN4UREBKD7TcUJCfAF4NPfdtqcxnupTIvI9TmzH8a2gONbAZiS2oRh5kA+61mPhirSIiLZRliQH/fVLQrAnztPsHb/aZsTeSeVaRG5dqd2w5fN4aQ1wjE+tRkv0I8xPVSkRUSyo14NS+DrMAD4ZJFGpzODyrSIXJsTO+DLlnB6LwBfpN7FKzzAmB51aVRGRVpEJDsqHB5E62qFAfh+3SH2nki0OZH3UZkWkas7ttWaIx23H4DRqXfzBj0Y070OjcsUsDmciIhcSd+brWXyPCZ8/odGpzOayrSIXNmRjVaRjj8EwPup7XiPLnzWvQ43l1WRFhHJ7ipEh57/fj11xX5OJThtTuRdVKZF5PIOr4OvWkHCUQDedXVgJPcyRkVaRCRH6Z82Op3kcjP+rz02p/EuKtMicmkHVlnrSCeeAOB11318YnTg0/trcYuKtIhIjnJTqfxUKhym4eCcAAAgAElEQVQKwFdLdpPsctucyHuoTIvI/9u33NoiPNlaRukl1/18SRs+ub8WTcpF2RxORESul2EY9EsbnT6R4GT6qv02J/IeKtMi8m97/oTxbSElDoBhrl5MoCWf3F+LW1WkRURyrJZVookJDwJgzKKduD3aYjwjqEyLyD92LYIJ7cF5Fo9p8KSrL1O5k9H31+TW8irSIiI5ma+PgwcaWVuM7z6RyI8bD9ucyDuoTIuIZftCmNgRXIm4TYPHXf2ZyW183K0mt5UvaHc6ERHJAPfWKUpYkB8An2oTlwyhMi0isHUBTO4Mqcmkmg4edQ1ijnELo7vVomkFFWkREW+RJ8CXLvViAVi19zSr92mL8RulMi2S222aC1O6gtuJy/RhsOth5hsN+birirSIiDfq3qDY+S3Gv1y8y+Y0OZ/KtEhutmEmTOsBHhdO05cBrkdZaNRjVNdaNKuoIi0i4o2iw4JoUSUagHlrD3H4TLLNiXI2lWmR3GrtVPimN3hSSTH96Ot6jEVGbUZ2qcntKtIiIl6td9qDiKkekwnaxOWGqEyL5EZ/T4AZ/cD0kGT608v1BEuM6nzUpSZ3VCpkdzoREclk1YuGUzM2HICJS/doE5cboDItktus+BK+HQSYJJgB9HQ+xQqjKqO71eJOFWkRkVzj3Oj0qUQXs/4+YHOanEtlWiQ3WfopzH0UgHgziPudz/C3TyU+6a6HDUVEcpu7KhWicFggAF8s3oVpahOX9FCZFsktlnwI3z8BwBkzD12dQ9ngU57PutfWzoYiIrmQr4+D7jcVB2DrkbMs3n7C3kA5lMq0SG6w6B34YRgAp8wQujifZatvGb7oWYebyxawOZyIiNilc52iBPn5ANbotFw/lWkRb2aa8Mvr8PPLABw3Q+nsHMYuv1J82bMuDUtH2hxQRETsFB7szz21YgD4efNRdh47a3OinEdlWsRbmSYsfAl+ewOAo2Y4nZ3D2O9XgrG96tKgVH6bA4qISHbQ86YS5z8fu2S3fUFyKJVpEW9kmta0jj/eA+CQGcG9zuc47F+ccQ/UpW6JCJsDiohIdlE6KoQm5awpf9NW7OdMksvmRDmLyrSIt/F44Psn4c+PANhvRtLJ+RzHA4oy/oG61CqmIi0iIv/Wq6E1Op3kcjN95X6b0+QsKtMi3sTjsZa+W/YpAHs8Udyb8hxnAmKY2KceNWLz2RxQRESyo8alIymePxiACX/twePRMnnXKt1l2jCMAMMw3jQM46BhGEmGYSw1DOP2a7w3xjCMqYZhnDYMI84wjG8Nwyh5ievMy3w8nd7cIl7L44bZg2HVVwDs8ERzr/M5EoILM6lvfaoWCbc5oIiIZFcOh0G3+sUA2Hk8gT+2H7c5Uc5xIyPTY4EhwETgEcANfGcYRqMr3WQYRgjwC3AL8BrwPFAD+M0wjEs9EfUjcP9FH3NuILeI93Gnwsz+sHoiAFs9MXR2DiMluBCT+tSnckyYzQFFRCS761jrn2Xyxv25x+Y0OYdvem4yDKMu0Bl4wjTNd9LOjQPWA28BN13h9oFAGaCuaZrL0+79Pu3ex4ChF12/1TTNCenJKZIruF0wvQ9snAXAJk9RujmHQp4CTO5bj/KFQm0OKCIiOUFYsB9taxRm8rJ9LNx8hH0nEykaEWx3rGwvvSPTHbBGoj89d8I0zWTgc6CBYRhFr3Lv8nNFOu3ezcBCoNOlbjAMI8gwjMB0ZhXxXqkpMLXH+SK93lOc+5zD8MkbxZR+9VWkRUTkutxfvzhgLQo1celee8PkEOkt0zWwRozjLjq/LO3f6pe6yTAMB1AVWHGJl5cBpQzDyHvR+Z5AApBkGMZGwzC6XGtIwzCiDMOodOEHUOpa7xfJ1lzJ8HU32DIPgNWeUnRxDiVPeBRT+zegTMGL/1cSERG5soqFQ6lT3HpY/evle0l2uW1OlP2lt0xHA4cucf7cucKXuS8CCLiOe5cAzwJtgQexRsMnGobx4DXmHIg1feTCj2+v8V6R7MuZCJM7w7YfAFjhKUs35zNE5I9i6oAGFI/MY3NAERHJqe5vUByAU4ku5q69VGWTC6VrzjQQBKRc4nzyBa9f7j6u9V7TNBteeIFhGF8AK4HXDMMYa5pm0lVyjgKmXXSuFCrUkpOlnLWK9O7fAfjLU4HezieIiYpkYp96RIVqRpSIiKTfXZUKERkSwPGzKYz/czcdahWxO1K2lt6R6SSsEeaLBV7w+uXuI533YpqmE/gICAdqXS2kaZpHTdPccOEHsONq94lkW8lxMOGe80X6d3dlejqfpHi0NUdaRVpERG6Uv6+DLvViAViz/wyr9522OVH2lt4yfQhrqsfFzp07eJn7TmKNSqfn3nP2pf2rbdwkd0k6DePbwb6/APjVXY0+rscpX7Qgk/vWJ3/IpX5HFRERuX5d6sbi4zAAGPfnbluzZHfpLdOrgbKGYVy8VEC9C17/P6ZpeoB1QO1LvFwP2GmaZvxV3vvc5i7HrjGrSM6XeBLGtYYD1rO7P7pr0c81hOolCjGhTz3Cgv1sDigiIt6kUFggd1YqCMDctYc4cfZSM3QF0l+mvwF8gH7nThiGEQD0Apaaprkv7VysYRjlL3FvHcMwal9wbzngNi6Y32wYRoGL3zRtpY9HgeNYc6dFvF/Ccfjqbji0BoDv3HUZ6HqEemWiGdurLiEB6X30QURE5PK6pz2I6Ez1MG3lfnvDZGPp+ilsmuZSwzCmAa8bhhEFbAd6AMWBBy64dBzWTofGBedGAX2BeYZhvAO4sHZSPAK8e8F1gwzDaIu12+FerGkgvYFY4P60+dMi3i3+iDUifWwzAN+6b2KI60Fuq1iYj7rUIMDXx+aAIiLireqViKBMVAjbjp5l8rK99GtcEofDuPqNucyNbCfeHRiBtb33B4Af0Mo0zUVXuiltGkcTYBEwDHgZWAPcYprmhVM3FgNHgT7ASOA/wBagmWmaE28gt0jOEHcQxrY4X6SnuxvzH9dAWlQryqiuNVWkRUQkUxmGwX11rQcR95xIZMmOEzYnyp7S/ffhtB0Pn0j7uNw1TS5zfj/Q8Spf/0fgx/TmE8nRTu+zpnac2gXA5NRbGZr6AB1qxfLGPVXPPxQiIiKSme6pWYQ3528mJdXDpGV7aFQm0u5I2c6NjEyLSGY4tRu+bHG+SI9LvZ2hqQ/Qq2Ep3lSRFhGRLBQW7EfLqtaCaz9sOMLR+OSr3JH7qEyLZCcndlhF+sxeAD5Lbc7w1J4Mub08z7WqoLlqIiKS5bqmrTmd6jGZtkIPIl5MZVokuzi2xSrScQcAGJXamldSu/FSm8o81LQMhqEiLSIiWa9mbD7KFcwLwJTle/F4TJsTZS8q0yLZwZGNMLYlnD0MwPup7XnX05kR99Y4vzSRiIiIHQzDOL8j4r6TSfy+/bjNibIXlWkRux1aaxXpBGsxm7ddnRhFJz69vzZta8TYHE5ERATa1ogh0M+qjZOW7rE5TfaiMi1ipwOrML+6G5JOAvCqqwvjfDswrnddmlYoaHM4ERERS1iQH3dXLQzAT5uOciRODyKeozItYpd9yzDHtcFIPg3AC67uzAhsz+R+9alXMr/N4URERP7t3FQPt8dk6vJ9NqfJPlSmReywezHm+HYYKXEAPOvqzQ8hbZk2oAGVY8JsDiciIvL/qhcNp3yhcw8i7sOtBxEBlWmRrLfzV8yJHTCcZ/GYBk+4+vFXRBu+efAmShYIsTudiIjIJRmGcX6ZvAOnk1i09dhV7sgdVKZFstL2nzAn3YvhSsRtGgxxPcjW6DZM7d+AwuFBdqcTERG5ojY1Ygjy8wFg0rK9NqfJHlSmRbLKlvmYk+7DSE0m1XTwiGswp0q3Y1Lf+uQPCbA7nYiIyFWFBvpxdzVrR8SfNx/VjoioTItkjU1z8HzdDcPjxGn6MMj1CP7VO/BZj9rkCfC1O52IiMg1u7dOUcB6EHHGqgM2p7GfyrRIZls/HXNqDxweFymmLwNc/6HkzZ15t2M1/Hz0v6CIiOQsNWPzUapAHgCmLt+HaebuBxH1k1wkM635GvObPhimm2TTj36ux2jcshtP3VVe24OLiEiOZBjG+dHpnccTWLHnlM2J7KUyLZJZVo3HnNkfAw+JZgD93E/R4d6e9GpYwu5kIiIiN6R9zSL4OqxBoa9z+ZrTKtMimcCz7HOYPRgDk7NmIAMYyoCevbi7WmG7o4mIiNywyJAAmlaIAmDe2kPEJ7tsTmQflWmRDOZaMgrHd0MAiDODeNh3OE/178VNpSNtTiYiIpJxzk31SHK5mbf2kM1p7KMyLZKBEn5+F78fngHgjBnM03le5sVBvahUWLsaioiId7m5TAEKhlpLu369IvdO9VCZFskgJ79/lTyLXrI+N0N4tcDbvD64J0Ujgm1OJiIikvF8fRx0qFUEgL/3nmbbkXibE9lDZVrkRpkmB2Y+R8TStwA4ZoYypuSHvDzgPsKC/WwOJyIiknk61S56/vPc+iCiyrTIjTBNtk16nJg1HwBwxAxnbs3PebJ7OwJ8fWwOJyIikrmK5c9D/ZIRAMz4+wDOVI/NibKeyrRIOpkeD6s/G0iZbZ8BcMiMYNWtE+nV5g6tIS0iIrnGuQcRTyY4WbjpiM1psp7KtEg6uFJT+euj3lQ/MAmAA2YBDrSbQfMmjWxOJiIikrWaV44mb6AvkDsfRFSZFrlOp84ms+i9rjQ4OROA/UYhkrvNpXb1GjYnExERyXqBfj60qW7to7Bo6zEOn0m2OVHWUpkWuQ7bD5/mrxGdaZo4H4D9jiIE9plPqTLlbU4mIiJin461rKkeHhNmrT5gc5qspTItco1+23SQrR93oXnqLwAc8i9G/sE/Ehmj7cFFRCR3q1okjNJRIQBMX7kf0zRtTpR1VKZFrsI0TcYu2kripB60MBYDcCy4DIUeXkhQhLYHFxERMQyDe2paa05vO3qWdQfO2Jwo66hMi1yBy+3huemriPlxAM19lgFwJrwiBQb/gBFSwOZ0IiIi2Ue7GjE40hazmr5yv71hspDKtMhlnEpw0vuzRTRd8x9u91kJQGKBGoT1/x6CI2xOJyIikr0UCgukYelIAGavOZhr1pxWmRa5hK1H4rl35M/02/8st/qsAcAZU4/gB2ZDULjN6URERLKnc1M9TiW6+GXLUZvTZA2VaZGLfL/uEF1GLuSlsy/Q2Gc9AO5ijfDvPgMCQ21OJyIikn3dWakQIQHWmtO5ZaqHyrRIGrfH5K35m3ly4h+M5lXqOzYBYJa8FZ+u0yAgxOaEIiIi2VuQvw8tqhQC4JctRzmZ4LQ5UeZTmRYBTic66TV2ORN+XcN4/9ep7dhqvVDmDoz7poB/sL0BRUREcohzUz1cbpPZuWDNaZVpyfU2HYqj9UeLWbt1J5P8X6O6Y4f1QrmWcO8E8Au0N6CIiEgOUqd4BEUjggCYvkplWsSrzVlzkPajlpBw8hCT/V+hsmO39ULFttDpK/ANsDWfiIhITuNwGLSvYY1Orztwhq1H4m1OlLlUpiVXSnV7eO27TTw0+W9CXMeZ4v8KFRz7rBerdIR7PgcfP3tDioiI5FDnpnoATF/l3Q8iqkxLrnP4TDJdxizl00U7KcQJvgl8hTKOtD9DVe8K7T4BH197Q4qIiORgsfmDqVvc2pNh1t8HcHu8d3txlWnJVf7YdpyWH/zOst0nieEYM4NfpRiHrBdr9YTWH4HDx9aMIiIi3qB9zRgAjsSl8Mf24zanyTwq05IruD0mI37ayv1fLOVEgpOixhHm5n2NaM9h64K6/aDVCHDofwkREZGM0KJqNAG+1s9Vb15zWs1BvN7xsyn0/HIZI37ahmlCBb8jLAh7g3yuI9YFDQZD87fAMOwNKiIi4kVCA/24s5K15vSCDYeJT3bZnChzqEyLV1u26yQtP/id37dZf166LeIEc/K+TnByWpFuNATueEVFWkREJBO0S5vqkZLqYcGGIzanyRwq0+KV3B6TDxdu474xf3EkLgWAAeWT+ZwX8U08al3U5BloOlxFWkREJJM0Lh1J/jz+AHzrpRu4qEyL1zl4Oon7xvzFuz9uxe0x8fdxMOo2H5468jhGYtoDEE2HQ5OnVaRFREQyka+Pg1ZVowFYvP04R+OTbU6U8VSmxavMX3+I5u//zrJdJwEoVSAP8zsG02JVP4wk6xx3vAqNH7MxpYiISO7RpoY11cNjwtw1h2xOk/FUpsUrJDndPDNjLQMmrOJMkvWAw311Y5nXzp+S33WF5DPWhc3fhpsG25hUREQkd6lRNJxi+YMB75zqoTItOd7Gg3G0+vB3Ji+zdjAMDfTl4641eb1mHIGTO4AzbRvTViOgXj8bk4qIiOQ+hmHQplphANbsP8Ou4wk2J8pYKtOSY7k9Jp/8toO2Ixez45j1P2bdEhHMf/RmmufZAhPuAVcCYECbkVC7l72BRUREcqnW1WPOfz7rb+8anVaZlhxp9/EE7v3kT17/fjNOtwcfh8GQ28syuW99Ch9bDJPuhdQkMBzQ/lOo0c3uyCIiIrlW6agQKseEAtZUD9P0nu3Ffe0OIHI9TNNkwtK9vDZvE0kuNwAlIvPwTsdq1CqWD7Z8D1O7g9sJhg90+BwqtbM5tYiIiLStHsP6A3HsPpHImv1nqF403O5IGUIj05JjHDqTRPcvlvHcrPXni3SPBsWY93Ajq0hv/Ba+7mYVaYcfdBqnIi0iIpJN3F2t8PkVab1pqofKtGR7pmnyzcr93PHfRed3MiwcFsjEPvV4sU1lgv19Yd03MK0XeFLBJwA6T4QKrWxOLiIiIucUDA3kplL5AZi79iCpbo/NiTKGpnlItrbvZCJDZ647X6IBOtQqwvC7KxIa6GedWD0Zvh0Ipgd8A6HzJCjd1KbEIiIicjltqsewePsJjp91smTHCW4uW8DuSDdMI9OSLbk9Jp//setfo9GRIQGM6V6bdzpW+6dIrxoHsx60irRfMHSdpiItIiKSTd1VuRD+vlb9nOUla05rZFqync2H43hq+jrW7Dt9/ty9tYsytEUFwoL9/rlw2Rj47nHrc/8Q6PoNFGuQxWlFRETkWoUG+tGsQhTfrTvMgvWHSWrrJsjfx+5YN0RlWrKNZJebUb9sZ9SvO0j1WEvmxEYE80b7KtxUOvLfF/85ChY8Y30eEAbdpkPROlmcWERERK5Xm+oxfLfuMAlONz9tOsLdaRu65FQq05It/LL5KC/M2cCeE4kAOAzo27gkjzYr+/+/sf4xAn563vo8MBy6z4LCNbI4sYiIiKRHk3IFCA30JS45lW9XH1CZFrkR+04m8tLcjfy48cj5cxWjQ3nznqpUKRL2/zf89hb88qr1eXB+6P4tFKqSRWlFRETkRgX4+tCyajSTl+3jt63HOJPo+vc0zhxGZVpskZLqZsyinXz0y3aSXdbSOHkDfBlyR1nur18MX5+Lno01TatEL3rbOs4TBT1mQ1SFLE4uIiIiN+ruqoWZvGwfLrfJgg2H6VSnqN2R0k1lWrKUaZr8uvUYL87ewO60KR0A7WvG8HTz8kTlDbzUTfDjcFjygXWcNxp6zIHIMlmUWkRERDJSvZL5iQwJ4PjZFOasPagyLXItNh2K47XvNv1rzejyhfLyUpvK1C0RcembTBPmPwNLP7aOQ4tYI9L5S2VBYhEREckMPg6DFlUKMe7PPSzZcYITZ1PIHxJgd6x0UZmWTHc0Lpl3f9jKtJX7SFukg7wBvvzn9rJ0b3CJKR3neDzW0ncrPreOw2Ohx1zIVyxrgouIiEimaVW1MOP+3IPbY/L9+sN0q58zf76rTEumSXK6GfP7Tkb/toNEpxuwfhPtWi+WR5qWufJvoB43zHkE/h5vHUeUtKZ2hBXJguQiIiKS2WoXy0eh0EAOxyUzd+1BlWmRc1JS3UxZto+PftnOsfiU8+eblo/imRblKR2V98pfwJ0K3w6CtVOs4/xlrCIdGp2JqUVERCQrORwGLapE88XiXSzddZKjcclEhV7i2alsTmVaMkyq28P0Vfv5YOF2DpxOOn++QnQow1pWoOHFG69citsFM/vD+unWcYEK1hzpkKhMSi0iIiJ2ubuaVaZNE75bd4ieDUvYHem6qUzLDfN4TOasPciIn7ax63jC+fOxEcE82qwMbarH4OMwrv6FUp0wvTdsmmMdF6xibciS5xpKuIiIiOQ41YuGUyRfEPtPJTFnrcq05DIut4dZfx9g9G872HHsnxIdHRbIQ7eVoWPtIvhd7uHCi6WmwNQesPV767hwDeg2A4Ivs8qHiIiI5HiGYdCyajSf/LaTlXtOcfB0EoXDg+yOdV1UpuW6JTndfL18L2N+3/Wv6RyRIf4MbFKaLvViCfTzucJXuIgrCaZ0hR0LreMidaDbdAi8xA6IIiIi4lXurlqYT37bCcC8tYfoe3NJmxNdH5VpuWZnEl1MWLqHL/7YxYkE5/nzUXkD6Nu4JF3rxxLsf53/STkTYHJn2LXIOo5tAF2nQcBVHlIUERERr1CpcCjF8wez+0Qic9ceVJkW77PtSDxfLtnNzFUHSHK5z58vlj+YAbeUon3NGAJ8r2Mk+pyUeJjYCfYusY6LN4YuX4N/ngxKLiIiItmdYRi0qlr4f+3deZhdVZnv8e9blZkUSchABkgTMhCUMAmkQZRRUeYhAs1so+0FuxW8ij6Ct6Xpi7aCtIB0C7c1hKGZFBkVaGaaWQmJSAyEIaRTIfNEpkpq3T/2CVaKqqSyz6naNXw/z7OfqrXPXue8JytV51f7rLM21z7+Jq/OWcbsRasYObBP0WW1mGFaTaqvTzw2Yz6Tn32HZ95cuMlt44fWcN7BozlqwrDmL7iyJWuWwc2TYM6LWXv0oXDKLdCj4/zwSJKkyjhmjyxMA9w3bS5fPWRMwRW1nGFam6hdtpq7Xp7D7S+/x5wlqze57dDxQzjngJ341NhBRLRgdY7mrF4CN50Ic/+QtcceASdPge4db21JSZJUvl2G1jB2SF/emL+S+6fVGqbVsdRtqOfR1+dz+0uzeXLmgg8v+Q3Qt2c3Jn1iB84+YCdGDarA9IsPFsFNx8G86Vl7/NEw6ZfQrUf59y1Jkjqso3cfzlX/NZPXa5cza8FKRg/uW3RJLWKY7qLq6xN/mL2Ee1+dy4PTa1m4ct0mt+86bFtO3XdHTtx7BDW9ulfmQVcugCnHwvw/Ze2PnwAn3gDVFbp/SZLUYR29xzCu+q+ZANz/ai1fP3xswRW1jGG6C0kp8drc5dz76lzuf3Uuc5et2eT2mp7dOHbP4Zy670h2G7FteVM5GlsxD248Fhb+OWvvfgocdx1U+19QkiTB6MF92XXYtrxeu5z7p801TKt9WFO3geffWsSjr8/nsRnzN1kXGqC6Kjhg9ECO33MER04YRu8eOVbl2JJl/wM3HgOLZ2XtPc+AY6+GqlZ4LEmS1GEdvfswXq9dzhvzV/LG+ysYu337XyrXMN3JpJR4Z9Eqnpu1iCdnzufpNxayat2Gjxy3307bccwew/j8hGEM6tuz9Qpa8m4WpJe+m7X3+Vs48kqoyrkKiCRJ6rSOnDCMHz+UvYv9wPRaLujMYToiegL/BJwJDACmAZeklB5pQd8RwFXAZ4Eq4HHgwpTSW00cey7wTWAU8B5wdUrpmrx1dzYpJd5dtIoX3l7E828t5rlZi5i3fM1HjuteHUwcNZBDxw/hc7sNbZtLdS5+K5vasey9rD3xf8HnfgiVnD4iSZI6jVGDtvlwqseD02u54PBxRZe0ReWcmZ4MTAL+FXgDOAd4MCIOSSk901yniOhLFp77AZcDdcCFwJMRsWdKaVGDY78C/DvwK+AnwKeAqyOiT0rpX8qovUNKKVG7bA2vzV3OtDlLeXXOMqbNWcrSVXVNHj+gT3cO2WUIh+26PZ8eN6hyHyRsiYVvZGekV9Rm7QP+AT5zmUFakiRt1lEThvJ67XJmvr+SN+evYMyQ9n12OleYjoj9gFOBb6WUrijtmwL8EfgRcMBmup8PjAX2Sym9VOr721Lf/w18t7SvN/B/gQdSSpNKfW+IiCrgexFxfUppSZ7627OUEgtXrmPu0tXMXbqa2YtXZfOG5q9k1vyVrFy7vtm+Nb26MXHUQPYfPZD9dx7I+KE1VFUVEF7nz8iC9Afzs/anvgmHXmKQliRJW3TkhGFc8XC2qseD0+fxtcM6YZgmOyO9Abh+446U0pqI+A/g8ojYMaX03mb6vrQxSJf6zoiIR4GTKYVp4BBgIHBdo/4/A04HjgJuzll/m1mxpo4Hp9eybkOibn09dRuybd36elasXc/SVXUsXbWOpavrWPLBOuYuW8O69fVbvN8I2HnQNuyxY3/22KE/e48cwMeGb0t1EeG5oXl/hCnHwarSVRMPuRgOuqjYmiRJUoex8+C+jB9aw4x5K3hwei1fO6x9r+qRN0zvBcxMKS1vtL90bWj2JJvfvInSWeXdgV80cZ8vAp+NiJqU0orSYwC83Oi43wP1pds3G6YjYggwuNHu0ZvrU2lLV9Xx7V9NL+s+Bm7TgzFD+jJ2+76MGdyXcUNrmDCiX9tO22iJuVPhpuOzKxwCHP59OPDCIiuSJEkd0JEThjFj3gpmzFvR7i/gkjdMDwNqm9i/cd/wZvptB/RsQd8/lx5jQ0ppfsODUkrrImLRZh6jofOBf2zBca2me3Xzq1bU9OxGvz7d6d+nOwP69KBf7+4M69eL4f17M7x/b0aUtgHbdICrA855ObtE+NplWfuIy2H/rxZbkyRJ6pCOnDCMnzwykz49qnnj/RWdMkz3BtY2sX9Ng9ub60cL+/YG1jVx3MZjW7IcxXXAnY32jQbuaUHfihhc05P//s6hdK8OelZX071b0L26im5VUdmLohRp9vNw8yRYtyJrH3kF7PflYmuSJEkd1pghfbnxb/dj4qjt6NW9fV+XIm+YXk12hrmxXg1ub64fLey7GmjulGyvzTzGh0pntTc5s93WAba6KhjRFgdE4SkAABBXSURBVMvQFeXtp+HWU6DuAyDgmH+FT5xTdFWSJKmDO2hc45m67VPeK2fUkk3DaGzjvrnN9FtMdla6JX1rgerSvOcPRUQPsg8mNvcYaiuzHodbvpAF6aiC468zSEuSpC4lb5ieCoyLiG0b7Z/Y4PaPSCnVA9OBfZq4eSLwVunDhw3vo/Gx+5DV3eRjqI3MfDg7I71+NUQ1nHA97Hla0VVJkiS1qbxh+i6gGvi7jTtKV0T8IvDCxmXxImJkRIxvou++EbFPg767AIey6fzmx8jOZJ/XqP95wCrggZy1q1wzHoDbToMNa6GqG0z6Bez+haKrkiRJanO55kynlF6IiDuBH5SmYbwJnA3sBJzb4NApwEFAw4nK1wFfBh6IiCvIroD4DeB94MoGj7E6Ir4H/Kz0WA+RXQHxDODilNLiPLWrTK/9Bn51LtSvh6rucPKNMP6ooquSJEkqRDmXEz8LuAw4ExgATAOOTik9tblOKaUVEXEwcBVwCdnZ8SeAC1NKCxode11E1JFdGfFYsrWrLwR+WkbdymvanXD3VyBtgOqecOotMPYzRVclSZJUmNxhOqW0BvhWaWvumIOb2T8HaNG8gJTSDcANOUpUJU29FX5zPpCgW2/4m/+E0YcUXZUkSVKhyjkzra7i95PhvguABN23gdPvgJ0OLLoqSZKkwhmmtXkv3gAPfjP7vkcNnHEXjPzrYmuSJElqJwzTat5zP4OHvpt937MfnPlr2KGpVQ0lSZK6JsO0mvb0T+DRS7Pvew+AM38Dw/cstiZJkqR2xjCtTaUET/4Inrg8a/cZCGfdC0N3K7YuSZKkdsgwrb9ICR77Z3j6iqy9zRA4+14YsmuxdUmSJLVThmllUoJHvgfPXpO1a4bB2ffBoLHF1iVJktSOGaaVBenffQde+Pes3W/H7Iz0djsXW5ckSVI7Z5ju6urr4YFvwO9/mbX7/xWccz/0H1lsXZIkSR2AYborq98A934Npt6ctbcbnU3t6Dei2LokSZI6CMN0V7VhPfzmPJh+R9YeNC4L0jVDi61LkiSpAzFMd0Ub6uDXX4bX7s7aQz4GZ90DfYcUW5ckSVIHY5juatavg7u+CDPuz9pDJ8CZ98A2A4utS5IkqQMyTHcldWvgjrPgjYey9vC9s0uE9x5QbF2SJEkdlGG6q6hbDbedBrMey9o77Adn3AW9+hVblyRJUgdmmO4K1n0At54C7zydtf/qk3Da7dCzpti6JEmSOjjDdGe3dgXccjLMfjZrj/o0/M1t0GObYuuSJEnqBAzTndnqpXDLJJjzUtYecziccjN0711sXZIkSZ2EYbqzWrUYbjoBaqdm7XGfh5NvhG49i61LkiSpEzFMd0YfLIIpx8H707P2rsfASb+Abj2KrUuSJKmTMUx3Nivnw43HwoLXs/ZuJ8EJP4fq7sXWJUmS1AkZpjuT5bUw5VhYODNr734qHH8dVFUXW5ckSVInZZjuLJbNgRuPgcVvZe29zoRjfmqQliRJakWG6c5gybtw49GwdHbW3udcOPIKqKoqti5JkqROzjDd0S2alc2RXj4na088Dz73A4goti5JkqQuwDDdkS2Ymc2RXlGbtT/5dTj8UoO0JElSGzFMd1Tv/ylb/u6D+Vn70xfBId81SEuSJLUhw3RHNG96FqRXLcrah1wMB11UbE2SJEldkGG6o5n7Ckw5HtYszdqHXwoHXlBsTZIkSV2UYbojee8luPkkWLssax/xA9j//GJrkiRJ6sIM0x3Fu8/BLZNg3cqsfdSVsO+Xiq1JkiSpizNMdwRvPwW3ngJ1q4CAY6+Gvc8quipJkqQuzzDd3r35KNx2GqxfA1EFx/8b7HFq0VVJkiQJw3T7NvMhuP0M2LAOohpOvB4mTCq6KkmSJJUYptur1++HO8+B+jqo6gaTfgEfO67oqiRJktSAYbo9eu1u+NWXoH49VPeAk6fALp8vuipJkiQ1Yphub6bdAXd/BVI9VPeEU2+FsYcXXZUkSZKaYJhuT165Be75KpCgW2847TbY+eCCi5IkSVJzDNPtxcu/hPtLVzLsvg2cfgfsdGCxNUmSJGmzDNPtwQvXw2+/lX3fc1s4/S4YObHYmiRJkrRFhumiPXsNPHxJ9n2vfnDm3TDiE8XWJEmSpBYxTBfpqSvgscuy73sPgLPugWF7FFuTJEmSWswwXYSU4IkfwpM/zNp9BsHZ98L2Hy+2LkmSJG0Vw3RbSwke/Sd45idZu+/2cNa9MGR8sXVJkiRpqxmm21JK2fzo567N2jXD4ez7YNCYYuuSJElSLobptlJfD7/7Nrx4fdbuNzKb2rHdqGLrkiRJUm6G6bZQXw8PXAi/n5y1B+yUnZHuP7LIqiRJklQmw3Rrq98A9/4DTL0law8ck82R7jei2LokSZJUNsN0a3vl5r8E6cHjs+XvaoYWW5MkSZIqwjDd2vY6A955Bt5/LQvSfQcXXZEkSZIqxDDd2qqq4fh/g3UroXf/oquRJElSBVUVXUCXUN3NIC1JktQJGaYlSZKknAzTkiRJUk6GaUmSJCknw7QkSZKUk2FakiRJyskwLUmSJOVkmJYkSZJyMkxLkiRJORmmJUmSpJwM05IkSVJOhmlJkiQpJ8O0JEmSlJNhWpIkScrJMC1JkiTlZJiWJEmScjJMS5IkSTkZpiVJkqScDNOSJElSToZpSZIkKSfDtCRJkpSTYVqSJEnKyTAtSZIk5WSYliRJknIyTEuSJEk5dSu6gAL0AHjzzTeLrkOSJEntTIOM2KMlx0dKqfWqaYci4ljgnqLrkCRJUrt2XErp3i0d1BXDdD/gIOA9YF0bPexosgB/HDCrjR5Trc9x7bwc287Jce28HNvOqahx7QHsCDyZUlq2pYO73DSP0j/KFv/KqKSI2PjtrJTSa2352Go9jmvn5dh2To5r5+XYdk4Fj+srLT3QDyBKkiRJORmmJUmSpJwM05IkSVJOhum2sQC4tPRVnYfj2nk5tp2T49p5ObadU4cY1y63mockSZJUKZ6ZliRJknIyTEuSJEk5GaYlSZKknAzTkiRJUk6GaUmSJCknw7QkSZKUk2G6DBHRMyL+JSLmRsTqiHghIj7Twr4jIuKOiFgaEcsj4p6I2Lm1a9aW5R3XiDgxIm6PiLciYlVE/DkiroyI/m1Rt7asnJ/ZRvfzSESkiLi2NerU1il3XCPilIh4LiI+KP1OfjYiDm3NmtUyZb7OHh4Rj0fEwtK4vhgRZ7Z2zdqyiOgbEZdGxO8iYnHp9+k5W9G/f0RcHxELSj+3j0fE3q1Y8mYZpsszGfgGcAvwdWAD8GBEHLi5ThHRF3gcOAi4HPhHYC/gyYgY2JoFq0Umk2NcgeuBXYGbga8BvwP+HnguInq3WrXaGpPJN7YfiogTgf1bpTrlNZmc4xoR3wf+E3ivdB+XANOAEa1Uq7bOZPK9zh4LPAz0AL4PXAysBqZExIWtWK9aZhDwf8heM1/dmo4RUQU8AJwGXAtcBAwBnoiIsRWus2VSSm45NmA/IAHfbLCvF/Am8OwW+l5U6rtvg33jgfXA5UU/t668lTmuBzex76zS/X2p6OfW1bdyxrbR8W8D3yvd17VFP6+uvpX5M/vXQD1wYdHPw63iY/sw8D9Azwb7upX6vlr0c+vqG9ATGFr6fp/SOJ/Twr4nl46f1GDfYGAJcGsRz8cz0/lNIvsL+fqNO1JKa4D/APaPiB230PellNJLDfrOAB4l+0+i4uQe15TSE03svrv0ddcK1qh8yvmZ3egisnf0rmiVCpVHOeN6ATAP+Glk+rZqpdpa5YzttsCSlNLaBn3XAwvJzlCrQCmltSmleTm7TwLeB37d4P4WAHcAx0VEzwqUuFUM0/ntBcxMKS1vtP/F0tc9m+pUentid+DlJm5+ERgdETUVq1JbK9e4bsbQ0teFZVWlSihrbCNiJPAd4NspJV+M249yxvUw4CWyaVkLgBURURsRf1/5MpVDOWP7BPDxiLgsIsZExOiI+B7ZWdAfVb5UtaG9gD+klOob7X8R6AOMa+uCurX1A3Yiw4DaJvZv3De8mX7bkb29saW+fy6rOuWVd1yb822yMyt3lVOUKqLcsb0SeCWldFtFq1K5co1rRAwgm7f5SeBQ4FJgNvBF4JqIqEsp/bzy5WorlPMzexkwimyu9CWlfauAk1JK91SsQhVhGPBUE/sb/r+Y3nblGKbL0RtY28T+NQ1ub64fOfuq9eUd14+IiNOAc4EfpZTeqEBtKk/usY2IQ4CTgImtUJfKk3dcN07pGAicmlK6HSAi7iJ7Ib4EMEwXq5zfx2uBmWQnMn4NVAN/B9wcEZ9JKT1fyULVpir2Ol0phun8VpOdYW6sV4Pbm+tHzr5qfXnHdRMR8SmyeX0PkZ0ZUfFyjW1EdAOuBm5q+DkHtRvl/i6uo8E7Ryml+oi4Hbg0IkamlGZXrFJtrXJ+H19L9gHTvTdOB4iIO4DXgJ/iH8YdWUVepyvJOdP51ZK91dDYxn1zm+m3mOwvqjx91fryjuuHImIP4F7gj2SfNl5fufJUhrxjexawC/DziNhp41a6rabU7lPRSrU1yvldvAZYlFLa0Oi2+aWvA8ovT2XINbYR0YPsXcEHGs6rTSnVAb8F9ikdo46p7NfpSjNM5zcVGBcR2zbaP7HB7R9R+sGeTvYhiMYmAm+llFZUrEptrVzjulFEjCZbX3o+cGRKaWXlS1ROecd2JNAd+G+yZfE2bpAF7beBz1a2VG2Fcn4XTwUGNxGsNs7FXVCxKpVH3p/ZgWTvvFc3cVt3suzT1G3qGKYCe5cWdGhoItm8+JltXZBhOr+7+MscLCC7UhPZh1deSCm9V9o3MiLGN9F334jYp0HfXcg+BHNnaxeuzco9rhExlGxt03rgiNJSPWo/8o7tbcAJTWwAD5a+f6HVq1dzyvldfHup79kN+vYCTgf+lFLyXcJi5R3b+cBS4ISGfyiVlj48BpjhijwdQ0QMi4jxEdG9we67gO2BExscNwj4AnBfw+UQ20qUFrtWDqX5VycAV5EtBH822SLzh6WUniod8wRwUEopGvSrAV4BasjWq60ju8JTNbCnIaxYZYzrVGAPsmWXGn+S+P2U0iOtX702J+/YNnNfCfhZSsll1ApWxs9sb7Kl8caRzaOdDZwJ7A0ck1L6bRs+DTWhjLG9GPhnstfaKWSvr+eSrfl/RkrpljZ8GmpCaQnK/mTvBJ1H9kHRV0o3X5NSWhYRk8nGfFRK6Z1Sv2rgGWA34MdkS8+eT/Yu4r4ppbZfDa2IK8V0lo1ssvuPyebvrCFb4/CIRsc8kf0zf6TvDmRnoZcBK4D7gDFFPye3/ONKdkWm5rYnin5ebuX9zDZxX14BsZ1sZf4uHkJ2yepFpb7PN+7r1mHH9jSyd42WkL39/zzZ0niFPy+3BPDOZl4zdyodM7lhu0HfAcD/IwvSH5T+D+xT1HPxzLQkSZKUk3OmJUmSpJwM05IkSVJOhmlJkiQpJ8O0JEmSlJNhWpIkScrJMC1JkiTlZJiWJEmScjJMS5IkSTkZpiVJkqScDNOSJElSToZpSZIkKSfDtCRJkpSTYVqSJEnKyTAtSZIk5fT/AYfaIxosvlhhAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 840x840 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GMurqcZhy3LH"
      },
      "source": [
        "Ahora vamos a calcular algunas diferencias y errores de la aproximación"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dDXMhkkUy3LH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "125890f8-90f0-447b-dbde-fff61f2bbc24"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format(0.3,f(0.3),taf(0.3),np.abs(f(0.3)-taf(0.3))))"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.3, f(x) = 0.063, Taylor f(x) = 0.064, |f(x) - Taylor f(x)| = 0.0010000000000000009\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mB_lsavQy3LH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9399eee2-94b0-4583-eb46-7f7f1c223258"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format(0.35,f(0.35),taf(0.35),np.abs(f(0.35)-taf(0.35))))"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.35, f(x) = 0.079625, Taylor f(x) = 0.08, |f(x) - Taylor f(x)| = 0.00037500000000000033\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ip7Yr8MAy3LH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "736b3a05-d949-49fe-b834-dd515f0a7b91"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format(0.4,f(0.4),taf(0.4),np.abs(f(0.4)-taf(0.4))))"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.4, f(x) = 0.09600000000000002, Taylor f(x) = 0.09600000000000002, |f(x) - Taylor f(x)| = 0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LFwesB0sy3LI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fdd45a85-985e-49b6-b189-c8f759b36483"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format(0.45,f(0.45),taf(0.45),np.abs(f(0.45)-taf(0.45))))"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.45, f(x) = 0.111375, Taylor f(x) = 0.11200000000000002, |f(x) - Taylor f(x)| = 0.0006250000000000144\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "snWq_5cHy3LI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca7faa80-8e8d-419e-a503-61d0f8fde943"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format(0.5,f(0.5),taf(0.5),np.abs(f(0.5)-taf(0.5))))"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.5, f(x) = 0.125, Taylor f(x) = 0.128, |f(x) - Taylor f(x)| = 0.0030000000000000027\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hJhFnnBNy3LI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fc317e3f-6ee0-4fd1-fda2-33b3c622fab1"
      },
      "source": [
        "print('x = {}, f(x) = {}, Taylor f(x) = {}, |f(x) - Taylor f(x)| = {}'.format(0.8,f(0.8),taf(0.8),np.abs(f(0.8)-taf(0.8))))"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x = 0.8, f(x) = 0.128, Taylor f(x) = 0.22399999999999998, |f(x) - Taylor f(x)| = 0.09599999999999997\n"
          ]
        }
      ]
    }
  ]
}