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    {
      "cell_type": "markdown",
      "source": [
        "# **Linear regions**\n",
        "\n",
        "The purpose of this notebook is to compute the maximum possible number of linear regions for shallow networks with different numbers of hidden units and parameters.\n",
        "\n",
        "You can save a local copy of this notebook in your Google account and work through it in Colab (recommended) or you can download the notebook and run it locally using Jupyter notebook or similar.\n",
        "\n",
        "Contact me at iclimbtreesmail@gmail.com if you find any mistakes or have any suggestions."
      ],
      "metadata": {
        "id": "DCTC8fQ6cp-n"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Imports math library\n",
        "import numpy as np\n",
        "# Imports plotting library\n",
        "import matplotlib.pyplot as plt\n",
        "# Imports math library\n",
        "import math"
      ],
      "metadata": {
        "id": "W3C1ZA1gcpq_"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "The number of regions $N$ created by a shallow neural network with $D_i$ inputs and $D$ hidden units is given by Zaslavsky's formula:\n",
        "\n",
        "\\begin{equation}N = \\sum_{j=0}^{D_{i}}\\binom{D}{j}=\\sum_{j=0}^{D_{i}} \\frac{D!}{(D-j)!j!} \\end{equation} <br>\n",
        "\n"
      ],
      "metadata": {
        "id": "TbfanfXBe84L"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "4UQ2n0RWcgOb"
      },
      "outputs": [],
      "source": [
        "def number_regions(Di, D):\n",
        "\n",
        "  N= 0\n",
        "  for j in range (Di+1):\n",
        "    N = N+  math.comb(D, j)\n",
        "\n",
        "  return N"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the number of regions for 2D input (Di=2) and 3 hidden units (D=3) as in figure 3.8j\n",
        "N = number_regions(2, 3)\n",
        "print(f\"Di=2, D=3, Number of regions = {int(N)}, True value = 7\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AqSUfuJDigN9",
        "outputId": "1a4b51c9-7f76-48e8-a8a5-7060da16e358"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Di=2, D=3, Number of regions = 7, True value = 7\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the number of regions for 10D input (Di=2) and 50 hidden units (D=50)\n",
        "N = number_regions(10, 50)\n",
        "print(f\"Di=10, D=50, Number of regions = {int(N)}, True value = 13432735556\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "krNKPV9gjCu-",
        "outputId": "156e1ec4-9146-4235-90f3-29c35dbddf3a"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Di=10, D=50, Number of regions = 13432735556, True value = 13432735556\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the number of regions for 5D input (Di=5) and 50 hidden units (D=50)\n",
        "N = number_regions(5, 50)\n",
        "print(f\"Di=5, D=40, Number of regions = {int(N)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7g4j7OXaSniQ",
        "outputId": "ba9dbaf9-2af9-42e1-f253-7f473a11ed29"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Di=5, D=40, Number of regions = 2369936\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the number of regions for 10D input (Di=10) and 50 hidden units (D=50)\n",
        "N = number_regions(10, 50)\n",
        "print(f\"Di=10, D=50, Number of regions = {int(N)}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OfgVQzHBfgI7",
        "outputId": "be3ac953-cad6-45b0-cc7c-749415a6e586"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Di=10, D=50, Number of regions = 13432735556\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "This works but there may be a complication. If the number of hidden units $D$ is fewer than the number of input dimensions $D_i$ , the formula may fail, depending on how you implemented it (it will work with Math.comb(). In this degenerate case, there are just $2^D$ regions."
      ],
      "metadata": {
        "id": "rk1a2LqGkO9u"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Test calculation when $D_i < D$\n",
        "# If it fails, then rewrite your function number_regions() to cope with this degenerate case\n",
        "try:\n",
        "  D_i = 10\n",
        "  D = 8\n",
        "  N = number_regions(D_i, D)\n",
        "  print(f\"Di={int(D_i)}, D={int(D)}, Number of regions = {int(N)}, True value = 256\")\n",
        "except Exception as error:\n",
        "    print(\"An exception occurred:\", error)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uq5IeAZTkIMg",
        "outputId": "01fd40a5-50d7-442e-ca00-23e27652dc76"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Di=10, D=8, Number of regions = 256, True value = 256\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Now let's plot the graph relating the number of hidden units to the number of regions\n",
        "# for different numbers of input dimensions\n",
        "dims = np.array([1,5,10,50,100])\n",
        "regions = np.zeros((dims.shape[0], 1000))\n",
        "for c_dim in range(dims.shape[0]):\n",
        "    D_i = dims[c_dim]\n",
        "    print (f\"Counting regions for {D_i} input dimensions\")\n",
        "    for D in range(1000):\n",
        "        regions[c_dim, D] = number_regions(np.min([D_i,D]), D)\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.semilogy(regions[0,:],'k-')\n",
        "ax.semilogy(regions[1,:],'b-')\n",
        "ax.semilogy(regions[2,:],'m-')\n",
        "ax.semilogy(regions[3,:],'c-')\n",
        "ax.semilogy(regions[4,:],'y-')\n",
        "ax.legend(['$D_i$=1', '$D_i$=5', '$D_i$=10', '$D_i$=50', '$D_i$=100'])\n",
        "ax.set_xlabel(\"Number of hidden units, D\")\n",
        "ax.set_ylabel(\"Number of regions, N\")\n",
        "plt.xlim([0,1000])\n",
        "plt.ylim([1e1,1e150])\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
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        },
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      },
      "execution_count": 21,
      "outputs": [
        {
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          "name": "stdout",
          "text": [
            "Counting regions for 1 input dimensions\n",
            "Counting regions for 5 input dimensions\n",
            "Counting regions for 10 input dimensions\n",
            "Counting regions for 50 input dimensions\n",
            "Counting regions for 100 input dimensions\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Finally, let's compute and plot the number of regions as a function of the number of parameters\n",
        "# First let's write a function that computes the number of parameters as a function of the input dimension and number of hidden units (assuming just one output)\n",
        "\n",
        "def number_parameters(D_i, D):\n",
        "  N = D_i * D + D +  D + 1\n",
        "\n",
        "  return N ;"
      ],
      "metadata": {
        "id": "Pav1OsCnpm6P"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Now let's test the code\n",
        "N = number_parameters(10, 8)\n",
        "print(f\"Di=10, D=8, Number of parameters = {int(N)}, True value = 97\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VbhDmZ1gwkQj",
        "outputId": "d03fe328-1c27-43bf-95f4-5dc01e5e5656"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Di=10, D=8, Number of parameters = 97, True value = 97\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Now let's plot the graph from figure 3.9a (takes ~1min)\n",
        "dims = np.array([1,5,10,50,100])\n",
        "regions = np.zeros((dims.shape[0], 200))\n",
        "params = np.zeros((dims.shape[0], 200))\n",
        "\n",
        "# We'll compute the five lines separately this time to make it faster\n",
        "for c_dim in range(dims.shape[0]):\n",
        "    D_i = dims[c_dim]\n",
        "    print (f\"Counting regions for {D_i} input dimensions\")\n",
        "    for c_hidden in range(1, 200):\n",
        "        # Iterate over different ranges of number hidden variables for different input sizes\n",
        "        D = int(c_hidden * 500 / D_i)\n",
        "        params[c_dim, c_hidden] =  D_i * D +D + D +1\n",
        "        regions[c_dim, c_hidden] = number_regions(np.min([D_i,D]), D)\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "ax.semilogy(params[0,:], regions[0,:],'k-')\n",
        "ax.semilogy(params[1,:], regions[1,:],'b-')\n",
        "ax.semilogy(params[2,:], regions[2,:],'m-')\n",
        "ax.semilogy(params[3,:], regions[3,:],'c-')\n",
        "ax.semilogy(params[4,:], regions[4,:],'y-')\n",
        "ax.legend(['$D_i$=1', '$D_i$=5', '$D_i$=10', '$D_i$=50', '$D_i$=100'])\n",
        "ax.set_xlabel(\"Number of parameters, D\")\n",
        "ax.set_ylabel(\"Number of regions, N\")\n",
        "plt.xlim([0,100000])\n",
        "plt.ylim([1e1,1e150])\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 541
        },
        "id": "AH4nA50Au8-a",
        "outputId": "55555d33-f75e-45ef-e197-d48a3c9066d9"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Counting regions for 1 input dimensions\n",
            "Counting regions for 5 input dimensions\n",
            "Counting regions for 10 input dimensions\n",
            "Counting regions for 50 input dimensions\n",
            "Counting regions for 100 input dimensions\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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ENYSGTkGjaeP8QqJLkxAmhBBCuFFNzRHKyv5NWdlnlJdvwumscW1TqXQYjROJiJhBePg1GAwp0trVg0kIE0IIITrA6bRhMn3vau06e7JUP79eRERcQ3j4NYSFXYFWK7dpE/UkhAkhhBBtZLOVUFb2GSUlH1Fe/iUOR+UZWzUYjZcSHn4NERHXyNgucU4SwoQQQogLaJxCorT0Y0pLP8Jk2go4Xdt1uhhXF2NY2JXodKFeq1V0HRLChBBCiBY4nXbM5h8oKfmI0tKPqanJbrI9KGgEEREziYiYSXDwKFQqtZcqFV2VhDAhhBCigd1uoqzsc0pKPqas7DPs9nLXNpXKj9DQKURGziIi4ifo9YlerFR0BxLChBBC9Gg1NXmUln5MSclHmEz/QVHsrm1abQQRET8hMnImYWFXyaB64VYSwoQQQvQoiqJQWZlOScmHlJZ+hMWyr8l2gyGFiIhZREbOIiTkElQqjZcqFd2dhDAhhBDdntNpx2T6npKSDygp2YjVevyMrRpCQye4xncZDAO9VqfoWSSECSGE6JYcjlrKy79uCF4fYbeXurap1YFERFxDZOR1hIfPQKcL92KloqeSSzmEy6RJk1CpVKhUKrRaLXFxccyePZvt27e75fhbtmxh5syZxMfHo1Kp2LhxY4v7rVmzhqSkJPR6PePGjWPHjh1uOb8Qovuz280UFr7F/v03snVrFPv2zaSg4HXs9lK02nBiY+cxbNhHXHZZMUOHvktMzC0SwITXSAgTQP0YiV27dvHss8+Sn59PTk4Ob775Jmq1mgkTJvDVV191+BwWi4XU1FTWrFlzzn3eeecd0tLSePzxx8nIyCA1NZXp06dTVFTU4fMLIbonm62IU6de5ccfr+GHH6I4ePAXFBe/h8NRhb9/b3r1uo/U1G+49NJCUlLWERk5E40mwNtlC4FKURTF20V0JWazGaPRiMlkIiQkpMm22tpa8vLy6Nu3L3q9HkVRcFY7z3Ekz1Ib1G2aofnQoUMkJyezdetWxo8f71qvKAqTJk2itrbWrS1SKpWKDz/8kOuvv77J+nHjxjFmzBheeeUVAJxOJwkJCdx3330sXry43ec7+7MRQnRtVutJiov/SXHx+5hM3wOnv8oCApKJippNZOQNBAePltnqBXD+729vkTFhHuSsdvJd0HdeOfeEqgloAlt/RU96ejoajYbU1NQm61UqFVdeeSVPPfVUs9csW7aMZcuWnfe4Bw4cIDGxdXPp2Gw20tPTWbJkiWudWq1m2rRpbNu2rVXHEEJ0X/XB632Kit7DbP6hybbg4NFERt5AZOQNBAYO9lKFQrSNhDABQEZGBsnJyRgMhmbb/Pz80Ol0AHzzzTfs2rWLhx56iIULF3LjjTee97jx8fGtrqGkpASHw0FMTEyT9TExMWRmZrb6OEKI7qO29gQlJf9sMXiFhFxKVNTPiYqaLROnii5JQpgHqQ1qJlRN8Nq52yIjI4NRo0a1uC0rK4uUlBQApk6dytSpUwEIDw8nPFwGtAoh3Ku29gTFxe9TXPweZvPWJttCQi4jOvrnREb+FL2+t5cqFMI9JIR5kEqlalOXoDdlZGQwc+bMZustFgsfffQRaWlpAMyaNYtnnnmG4cOHu707MjIyEo1GQ2FhYZP1hYWFxMbGtvKdCCG6otra42cEr6bDD+qD141ERf0Uf/9eXqpQCPfrFiHshhtuYPPmzVxxxRW8//77ABw/fpzbbruNoqIitFotjz32GD//+c9dr/nkk0946KGHcDqd/Pa3v+WXv/ylt8r3utzcXCoqKhg5cmST9Q6Hg4ULFxIQEMA999wDQGZmpqtVzN3dkX5+fowaNYpNmza5Buw7nU42bdrEvffe24Z3JIToCqzWfIqL36Wo6J2zgpcKo/Gyhq5GCV6i++oWIWzRokXMnz+fDRs2uNZptVpWrVrFiBEjKCgoYNSoUVxzzTUEBgZit9tJS0vj22+/xWg0MmrUKG644QYiIiK8+C68Jz09HYC4uDgKCgowm82kp6fz0ksvcfz4cT755BOMRiOVlZXo9XrX+LC2dkdWVVWRk5Pjep6Xl8fu3bsJDw93tZalpaUxd+5cRo8ezdixY1m1ahUWi4V58+a58R0LIbylrq6ckpIPKCx8i4qKb4HGK8hVGI2XnxG8Wv8POCG6qm4RwiZPnszmzZubrIuLiyMuLg6A2NhYIiMjKSsrIzAwkB07djB06FB69ar/19WMGTP48ssvufnmmzu7dJ+QkZEBwKBBg9BoNISGhpKcnMysWbNYuHChK2jt37+foUOHtvs8O3fuZMqUKa7njV2cc+fOZf369QDMmTOH4uJili5dSkFBASNGjODzzz9vNlhfCNF1OBzVlJZ+TGHhW5SV/RtFsbm2hYRcQnT0zURF/UyCl+hxvB7CtmzZwooVK0hPTyc/P7/FuaPWrFnDihUrKCgoIDU1lZdffpmxY8e2+hzp6ek4HA4SEhIAOHXqlCuAAfTq1YuTJ0+65f10RcuXL2f58uUX3G/v3r0MHz683eeZPHkyrZmW7t5775XuRyG6OKfTRnn5VxQWvklJyb9wOi2ubYGBw4iOvpno6JsICOjnxSqF8C6vh7DGWdTnz5/P7Nmzm21vnEF97dq1jBs3jlWrVjF9+nSysrKIjo6+4PHLysq4/fbbefXVVz1Rfo+yd+9epk2b5u0yhBA+SlGcVFRsoajoLYqL38duL3Nt0+uTiI7+BdHRNxMUNMyLVQrhO7wewmbMmMGMGTPOuX3lypUsWLDANSZo7dq1fPrpp6xbt+6CM6hbrVauv/56Fi9ezKWXXupaHx8f36Tl6+TJk+dsWbNarVitVtdzs9ncqvfVHa1evdrbJQghfIyiKFRV7aKw8B8UFb2DzXb6b6tOF0N09Byio28mJGSczFwvxFm8HsLOpyMzqCuKwh133MHUqVO57bbbmmwbO3Ys+/bt4+TJkxiNRv7973/z2GOPtXic5cuX8+STT3b8zQghRDdSW3uCoqJ/UFDwd6qr97vWazRGoqJ+SnT0zYSGTkat9umvGSG8yqf/72jtDOrTpk1jz549WCwWevfuzXvvvYfD4eCdd97hoosuYuPGjQD8/e9/Z/jw4Wi1Wl544QWmTJmC0+nkkUceOeeVkUuWLHENIIf6lrDGsWVCCNGT2O1VlJR8QEHBG1RUfEPj/RpVKn8iI2cRHf0LIiJmoFb7e7dQIboInw5hrfX111+3uN7pPPfNs2fNmsWsWbMueGx/f3/8/eUPihCiZ1IUB+Xl31BY+AbFxR/gdFa7thmNE4iJuY2oqJ+j04V6r0ghuiifDmEyg7oQQnhHVdVeCgv/TmHhP7DZTrnWBwQMICbmdmJibiUgoK8XKxSi6/PpECYzqAshROepqyulsPAfFBS8TlXVbtd6rTac6OibiIm5TQbYC+FGXg9hF5pFXWZQF0IIz1EUB2VlX1JQsI6Sko9cE6mqVDoiIn5CTMztRERcg1rt5+VKheh+vB7CLjSLusygLoQQ7lddnU1BwesUFLzRZFqJoKCRxMbOIybmZnS6nnkrNyE6i9dDWGtmUZcZ1IUQouPs9iqKi9+joOB1TKbvXOu12ghiYm4lLm4eQUGpXqxQiJ7F6yFMCCGE5yiKgtm8lfz8dRQVvXPG7YPUhIdfTWzsPCIjZ8q0EkJ4gYQwIYTohmy2EgoLN3Dq1KvU1GS51gcEDCA2dj6xsbfj79/rPEcQQnia2tsFCN8xadIkVCoVKpUKrVZLXFwcs2fPZvv27W45/hNPPOE6fuOSkpLSbL81a9aQlJSEXq9n3Lhx7Nixwy3nF6K7UxSF8vJvOXDgZrZt68Xhww9TU5OFWh1IbOw8Roz4jrFjD9GnzxIJYEL4AAlhAqj/471r1y6effZZ8vPzycnJ4c0330StVjNhwgS++uort5xn6NCh5Ofnu5bvv/++yfbGG7Y//vjjZGRkkJqayvTp0ykqKnLL+YXojmy2Yo4de54dO5LZs2cqRUVvoyg2goJGMWjQX7n00nxSUtYRGnq5TC8hhA+R7kgBQHZ2NpWVlUycONE1EW5SUhKTJ09m0qRJPProo1x55ZUdPo9Wqz3vRLsduWG7ED2JoihUVGwmP/+vFBd/4JpaQqMJIjr6FuLjFxAcPMrLVQohzkdCmAcpikL1eW6d5EkGtbpN/+JNT09Ho9GQmtr0yiiVSsWVV17JU0891ew1y5YtY9myZec97oEDB0hMTHQ9z87OJj4+Hr1ez/jx41m+fLlre0du2C5ET2GzFVNQsIH8/L9SU5PtWh8cPJq4uLuIjr4ZrTbIixUKIVpLQpgHVTudBH333YV39ICqCRMI1GhavX9GRgbJyckYDIZm2/z8/NDpdAB888037Nq1i4ceeoiFCxdy4403nve48fHxrsfjxo1j/fr1JCcnk5+fz5NPPsmECRPYt28fwcHBrb5huxA9TeMVjidPrqG4+H0UpQ4AjSaYmJhbiItbQHDwSC9XKYRoKwlhAqgPYaNGtdx1kZWV5RpAP3XqVKZOnQpAeHg44eHhrT7HjBkzXI8vuugixo0bR58+fXj33Xe58847O1C9EN2Tw1FNYeGbnDq1pslthOpbvX5FdPRN0uolRBcmIcyDDGo1VRMmeO3cbZGRkcHMmTObrbdYLHz00UeuOxnMmjWLZ555huHDh7erO/JMoaGhDBo0yHXbKrlhuxD1qqtzOHXqzxQUrMNurwBArdYTHf0LevX6tYz1EqKbkBDmQSqVqk1dgt6Sm5tLRUUFI0c27c5wOBwsXLiQgIAA7rnnHgAyMzNdrWJt7Y48W1VVFYcPH+a2224D5Ibtomerv4fj55w8+QplZZ+71uv1/YiPv5u4uHlyGyEhuhkJYYL09HQA4uLiKCgowGw2k56ezksvvcTx48f55JNPMBqNVFZWotfrXePD2tod+fDDDzNz5kz69OnDqVOnePzxx9FoNNx8882ufeSG7aKnqasrJT9/HadO/Zna2jzX+vDwGfTqdS/h4VejUslsQkJ0RxLCBBkZGQAMGjQIjUZDaGgoycnJzJo1i4ULF7qC1v79+xk6dGi7z3PixAluvvlmSktLiYqK4vLLL2f79u1ERUW59pEbtoueoqpqDydOrKao6E2czloAtNpQYmPnEx9/NwbDAC9XKITwNJVyobtniybMZjNGoxGTyURISEiTbbW1teTl5dG3b1/0er2XKvScV199leLiYn73u995u5Q26+6fjegaFMVJaemnnDixioqKb1zrg4JG0KvXvURH34xG0/wKZSFEx53v+9tbpCVMtNrevXuZNm2at8sQostxOCwUFKznxImXzpjbS0NU1E/p3ft+QkIulZnsheiBJISJVlu9erW3SxCiS6mtPc7Jk6+Qn/9X11WOGo2R+Pi76NXrXvT6lq8cFkL0DBLChBDCzczmHZw48SJFRe8BDgACAgbQq9ciYmPvkLm9hBCAhDAhhHALp9NOSclGTpx4EbN5q2t9aOhkevd+kIiIa1GpfH/KGiFE55EQJoQQHeBwWMjPf50TJ16gtvYIACqVjujom+nd+wGCgy/2boFCCJ8lIUwIIdrBZivh5MlXOHnyFez2UgC02gh69bqb+Phf4+8f5+UKhRC+TkKYEEK0QU3NEU6ceIH8/L/hdNYA9bPaJyQ8TGzsXJliQgjRahLChBCiFSord3P8+HMUFb1L42D7oKCRJCb+lsjI2ajV8udUCNE28ldDCCHOQVEUKiq+5dixP1Je/qVrfVjYlSQm/pbQ0Kkyv5cQot0khAkhxFkURaGs7DOOHn0as3l7w1o10dE3kpDwiAy2F0K4hYQwIYRooChOSko+5OjRp6mq2g2ASuVPXNydJCQ8REBAP+8WKIToViSECSF6PKfTTlHR2xw7tozq6oMAqNWB9Or1a3r3TsPfP9bLFQohuiO1twsQvmPSpEmoVCpUKhVarZa4uDhmz57N9u3bL/ziVtiyZQszZ84kPj4elUrFxo0bW9xvzZo1JCUlodfrGTduHDt27GjXPkJciNNp49Sp19ixI5nMzNuorj6IRmOkT5/HGD/+KP37PycBTAjhMRLCBFA/BmbXrl08++yz5Ofnk5OTw5tvvolarWbChAl89dVXHT6HxWIhNTWVNWvWnHOfd955h7S0NB5//HEyMjJITU1l+vTpFBUVtWkfIc7H4ajlxIlX+O9/+3Po0AJqa3PR6SLp2/cZxo8/St++f0Cni/B2mUKIbk6lKIri7SK6ErPZjNFoxGQyERIS0mRbbW0teXl59O3bF71e76UK2+fQoUMkJyezdetWxo8f71qvKAqTJk2itrbWra1NKpWKDz/8kOuvv77J+nHjxjFmzBheeeUVAJxOJwkJCdx3330sXry41fucrSt/NsJ9nE4r+fl/4+jRZdhsJwHw84sjIeE3xMffhUYT6OUKhRCecr7vb2/pFi1hN9xwA2FhYfzsZz9rsv6TTz4hOTmZgQMH8tprr7nWV1RUMHr0aEaMGMGwYcN49dVXPVKXoig4HBavLG3N1unp6Wg0GlJTU5usV6lUXHnllezevbvZa5YtW0ZQUNB5l2PHjrW6BpvNRnp6OtOmTXOtU6vVTJs2jW3btrV6HyHOVt/t+Bf++9+BZGffg812En//3gwcuIZx43JJSHhQApgQotN1i4H5ixYtYv78+WzYsMG1zm63k5aWxrfffovRaGTUqFHccMMNREREEBwczJYtWzAYDFgsFoYNG8bs2bOJiHBv94PTWc133wW59ZitNWFCVZu+VDIyMkhOTsZgaD7bt5+fHzqdDoBvvvmGXbt28dBDD7Fw4UJuvPHG8x43Pj6+1TWUlJTgcDiIiYlpsj4mJobMzMxW7yNEI6ezjsLCNzhy5Cms1qMA+PnF06fP74iL+yVqtb+XKxRC9GTdIoRNnjyZzZs3N1m3Y8cOhg4dSq9evQCYMWMGX375JTfffDMajcYVNqxWK4qitLnlqLvJyMhg1KhRLW7LysoiJSUFgKlTpzJ16lQAwsPDCQ8P77QahWit+qsd/8GRI3+gtjYXAD+/WBITlxAXdxcajXRJCyG8r9UhrG/fvhecGVqlUnH48OE2FbBlyxZWrFhBeno6+fn5LY4TWrNmDStWrKCgoIDU1FRefvllxo4de97jnjp1yhXAAHr16sXJkyddzysqKpg0aRLZ2dmsWLGCyMjINtXdGmq1gQkTqtx+3Naeuy0yMjKYOXNms/UWi4WPPvqItLQ0AGbNmsUzzzzD8OHDWbZsGcuWLTvvcQ8cOEBiYmKraoiMjESj0VBYWNhkfWFhIbGxsa3eR/RciuKgqOhtjhx5kpqabAB0umgSE39LfPxCua+jEMKntDqEPfDAA+fcduTIEf7yl79gtVrbXEDjFXPz589n9uzZzbY3Xgm3du1axo0bx6pVq5g+fTpZWVlER0e3+XyNQkND2bNnD4WFhcyePZuf/exnzbq4OkqlUnWJcSa5ublUVFQwcuTIJusdDgcLFy4kICCAe+65B4DMzExXq5i7uyP9/PwYNWoUmzZtcgVxp9PJpk2buPfee1u9j+h5FEWhtPQT8vJ+h8WyDwCtNoLExN/Sq9evu8T/h0KInqfVIWzRokXN1pWVlfHUU0/x5z//mXHjxvHHP/6xzQXMmDGDGTNmnHP7ypUrWbBgAfPmzQNg7dq1fPrpp6xbt+6cV8JB/Zf/mS1fJ0+ebLH1LCYmhtTUVL777rtmA/uhvrvyzHBpNptb9b66kvT0dADi4uIoKCjAbDaTnp7OSy+9xPHjx/nkk08wGo1UVlai1+td48Pa2h1ZVVVFTk6O63leXh67d+8mPDzc1VqWlpbG3LlzGT16NGPHjmXVqlVYLBbX59/afUTPUVHxHbm5izGbtwKg1YaSkPAbevW6D6022MvVCSHEubVrTFhNTQ0rV67k+eefp0+fPnzwwQdcc8017q7NdSXckiVLXOtaeyXc2LFj2bdvHydPnsRoNPLvf/+bxx57DKjvujIYDAQHB2MymdiyZQt33313i8dZvnw5Tz75pPvelA/KyMgAYNCgQWg0GkJDQ0lOTmbWrFksXLjQFbT279/P0KFD232enTt3MmXKFNfzxi7OuXPnsn79egDmzJlDcXExS5cupaCggBEjRvD55583aaVszT6i+6uq+pHc3CWUlX0GgFodQO/ei0hIeASdLszL1QkhxIW1KYQ5HA5effVVnnzySfR6PatXr+bWW2+94Fix9mrtlXDTpk1jz549WCwWevfuzXvvvcf48eN54YUXmDJlCk6nk0ceecR19ePRo0e56667XAPy77vvPoYPH95iDUuWLHGFBahvCUtISPDAu/We5cuXs3z58gvut3fv3nP+nlpj8uTJrboA4t57771g12Jr9hHdU01NLnl5SykqehNQAA3x8Qvo0+cx/P1b3/0thBDe1uoQ9u677/L73/+eiooKHn30Ue6++278/Pw8WVurff311y2unzVrFrNmzWq2fuzYsS3Oe9USf39//P3lMnaoD2Fnzs8lRGey2Qo5cuQp8vP/iqLUARAVNYe+fZ/CYBjo5eqEEKLtWh3CbrrpJgICArj55ps5evToOcdjrVy50m3FyZVwvmX16tXeLkH0QA6HhePHn+fYsRU4nRYAwsKm06/fMoKDR17g1UII4btaHcImTpx4wSko3N0tKVfCCdFzKYqDgoI3yMv7PTbbKQCCg8fSr9+zhIVNucCrhRDC97U6hJ09Gaq7XOiKObkSToiep7z8Gw4ffoiqqt0A6PV96dfvWaKifu6xMahCCNHZvD5j/oWumJMr4YToOSyWTHJzH6G09GMANBojffr8nt6975NbDAkhuh2vh7DWXDEnV8IJ0b3ZbCUcOfIEp06tBRyAhl697qZPn8fx83P/3SyEEN2f1enklNXKcauVE1YrOSUl3i6pGa+HsO6op9+H0hfJZ+KbnE4rJ06s5ujRZ3A4TABERMyif//nMBiSvVydEMJX2c4IWI0hy/WztpYTViuFdXVNX2SxeKfY85AQ5kaNM8lXV1cTEBDg5WrEmaqrq4HTn5HwvtLST8nJeYCamvoxoUFBI+jff6UMuheih6tzOjl5drA662ehzUZr/mmtV6vp7e9Pgr8/0YGBvOPx6ttGQpgbNc42X1RUBIDBYJBBxF6mKArV1dUUFRURGhqKRqPxdkk9XnV1DocPP0hp6ScA+PnF0bfvMmJjb0Olks9HiO7OZLdzrLaWo7W1HLNa6x83/DxmtXLKasXZiuP4q1Qk6PWukNXSzwidzvU9bDabu3cIO3bsGL169erRX3SN85c1BjHhG0JDQ2VuOS9zOCwcPbqM48efR1FsqFQ6evd+gD59HpN7PArRTTgUhXyrtUmoOlpb2+Sx2eG44HH8Var6MHWekHVmwOqq3BrCkpKSGDhwIMuXL2f27NnuPHSXoVKpiIuLIzo6mrqz+6OFV+h0uh79DwNvUxSF4uL3OXw4Dav1BABhYVcxYMBLBAameLk6IURbVNntrtYrV8BqbM2qreWkzYa9FWNwI7Ra+uj1JOr19PH3J1GvJ9Hf37UuSqdD3cUDVmu4NYR9++235Obm8s477/TYENZIo9HIF7/o8SyW/WRn30dFxbcA6PVJ9O//IpGR13X5f8EK0R1V2u3k1dZypGE58/Gx2lrK7PYLHkPb0IrVUrjq09C6FSjfjwCoFLlsrE3MZjNGoxGTyURISIi3yxHCJ9ntJo4ceYITJ14GHKjVehITF5OQ8AgajVy0IoS3WBwOV6g6UltLXk1Nk8DVmpBl1GhaDFeN6+L8/dH44D+yfPH7u80tYTU1NSiKgsFgAODo0aN8+OGHDBkyhKuuusrtBQohuo76rsd3ycl5AJutAIDIyBvo338lAQFJ3i1OiB6gxuHg6DlasvJqayluxTCZcK2Wvno9SQ1L34AA+pwRuIxauabPXdr8m7zuuuuYPXs2CxcupKKignHjxqHT6SgpKWHlypXcfffdnqhTCOHjampyyc6+h7KyzwEICBjEwIEvEx4u/zgTwl3qnE6OnhGuzg5ZBTbbBY9h1GjoGxBwOmSdEbiS9HpCJGR1mjb/pjMyMnjxxRcBeP/994mJiWHXrl3885//ZOnSpRLChOhhnE4bx48/z9GjT+F01qJS+dGnz+9ITFwstxoSoh1MdjuHa2o4XFNDbm1t/c+aGg43jMu60PQNQRpN05ass36GynyJPqPNIay6uprg4PrLyb/88ktmz56NWq3mkksu4ejRo24vUAjhuyoqvufQoV9RXX0AgNDQqQwa9GcMhkFerkwI3+VUFE5arU1C1pmPLzQuK0CtbjlkNbRuhWu1cuFLF9HmEDZgwAA2btzIDTfcwBdffMGDDz4I1M+L5SsD3YQQnlVXV05u7iPk578GgE4XRf/+K4mJuUX++AtB/dis3Nra+hashlasxsd5tbXYLnBNXLROR/+AAPrp9fQPCGjyONbPT/4/6ybaHMKWLl3KL37xCx588EGuuOIKxo8fD9S3il188cVuL1AI4VuKiz8kO/vXroH3cXEL6NfvWXS6cC9XJkTnqrTbyampIbtxqa7mcENrVv4FxmZpVSqS9Hr66/X0Oytk9dPrCZJxWT1Cu6aoKCgoID8/n9TUVNRqNQA7duwgJCSElJTuPfmiL17iKkRnsFoLyMm5j+Li9wEwGFIYNOhVQkMv93JlQnhOVUPQahK2GgJXsxtEn8Wo0dSHqoAA+jcGrIbHvf390TZ8f4rO4Yvf3+2K2rGxsc1uATN27Fi3FCSE8C2KolBY+Hdych7Abi8HNCQm/pY+fR5Do9F7uzwhOqza4TgdsqqrmwSuC7VoRel0DAwIYEBAgOtnY/dhmIzNEhfQ5hBmsVh49tln2bRpE0VFRTidTa/TyM3NdVtxQgjvqq09xqFDv3JNOxEUdDHJyesIDh7h3cKEaCOb08nhmhqyqqs51BCwchpC18kLBK0IrZaBBkOTsNX4WK40FB3R5hD2y1/+kv/85z/cdtttxMXFScoXohtSFCenTv2F3NxHcDiqUKn8SUp6goSEh1Cr5UtH+CZFUSiuqyOzupqshiWzupqsmhryamo4322jw7TaJuGqMXQNDAggTIKW8JA2h7B///vffPrpp1x22WWeqEcI4WW1tcfJyppPefnXABiNl5Oc/BoGQ7KXKxOintXpJKehVcsVtBrCVsV5pncI0mhIDghg0NmtWgYDERK0hBe0OYSFhYURHi5XQQnR3dSP/XqD7Oz7cTjMqNUB9Ov3LL163YtKJQOIRedSFIVCm42shrB1ZutW3nkmLFUBffR6kgMCSDEYSD5jiZepHYSPaXMIe+qpp1i6dCkbNmxw3T9SCNG12WyFZGX9itLSfwEQEnIJKSkbZNJV4XFOReFIbS0HLBYOVFdzsLqaAxYLmdXVmB3n7kAM1mhOh6yAAJINBlIMBgYEBBCg0XTiOxCi/docwl544QUOHz5MTEwMSUlJ6M5qws3IyHBbcUIIzysqep9DhxZit5eiUulISnqShITfoFbLPEXCfexOJ7lnhK3Gn5nV1dQ4W27XUgF99frTrVlntG7JhKWiO2jzX9nrr7/eA2UIITpbXV052dn3UlT0JgCBgRcxePDfCQq6yMuVia7M5nSSXVPTLGwdqq4+5yzxfioVKQYDQwIDGWIwMPiMVi29tGqJbqxdk7X2ZL442ZsQbVVR8R8OHrwNq/U4oCYxcQlJSUtRq/28XZroImxOJ4eqq9l7VtjKrq4+51WIBrWawQ1ha/AZoauvXi8TlwqP88Xv73b3N6Snp3Pw4EEAhg4dKrcsEqILcDrrOHLkCY4dWw4oBAQMICXl7xiNl3i7NOGjFEXhaG0tey0W9los7Gv4mVVdTd05/g0frNEw5IyQ1fgzUa9HLV2IQri0OYQVFRVx0003sXnzZkJDQwGoqKhgypQpvP3220RFRbm7RiGEG9TUHObAgV9QWbkDgNjYeQwYsBqtNsjLlQlfUWKzNQlaey0W9lssVJ5jgHyIRsOwwECGNiyNXYm9/P1lvJYQrdDmEHbfffdRWVnJ/v37GTx4MAAHDhxg7ty53H///bz11ltuL1II0X6np564F4ejCo3GSHLyX4mOvtHbpQkvqXY4OHBG0GoMXQXnmDlep1Ix2GBgWGAgwwMDGR4UxLDAQBIlbAnRIW0eE2Y0Gvn6668ZM2ZMk/U7duzgqquuoqKiwp31+Rxf7FMW4lzq6irIzr6boqK3ATAaJzB48P+h1yd6uTLRGRRF4YTVyu6qKvZUVdX/tFg4XFPDuf7w99Xr64NWYGB96AoKYlBAADoZsyW6OF/8/m5zS5jT6Ww2LQWATqdrdh9JIYT3mM072L//RqzWo4CGvn2fJDFxMSqVXG3WHdmcTg5WV7vCVmPwKjvHDPJROt3poNUQtoYaDARpZWoSITpLm/9vmzp1KosWLeKtt94iPj4egJMnT/Lggw9yxRVXuL1AIUTbKIrCiRMvkZv7CIpSh17fj8GD/yGD77uR8rq6Ji1bu6uq2G+xtDhQXgMMCQwkNSiIEUFBpDYErhg/uRJWCG9rcwh75ZVXmDVrFklJSSQkJABw/Phxhg0bxv/93/+5vcCOePHFF3nttddQFIVp06bx0ksvoVKpyMvLY/78+RQWFqLRaNi+fTuBgYHeLleIDqurqyAraz4lJR8CEBX1M5KTX0OrNXq5MtEejd2J6ZWV7DqjheuY1dri/iEaDSMawtaIoCBSg4IYYjDIXFtC+Kg2h7CEhAQyMjL4+uuvyczMBGDw4MFMmzbN7cV1RHFxMa+88gr79+9Hp9MxceJEtm/fzvjx47njjjt4+umnmTBhAmVlZfj7+3u7XCE6zGzeyYEDN1Jbm4dKpaN//xca7vsoA6e7AkVRONYQuNIrK8moqiK9spLiuroW90/S610tW42hq49eL5+3EF1Iuzr/VSoVV155JVdeeaW763Eru91ObW0tAHV1dURHR7tC2YQJEwDkZuSiy1MUhVOn/kROThqKYkOvT2LIkHcJCRlz4RcLr2iceyu9IWg1hq6SFgKXBhgaGMjI4GAubmjdSg0MJLSFsblCiK6lVSFs9erV3HXXXej1elavXn3efe+//363FLZlyxZWrFhBeno6+fn5fPjhh81umbRmzRpWrFhBQUEBqampvPzyy4wdOxaAqKgoHn74YRITE9FqtSxcuJD+/fuzceNGgoKCmDlzJidPnuRnP/sZv/vd79xSsxCdzW43k5X1S4qL3wMgIuI6UlJeR6cL83JlopGiKOTV1rrCVnpVFRmVlS0OmNeqVAwLDGRUUBCjgoMZGRzMRYGBckNqIbqpVoWwF198kVtuuQW9Xs+LL754zv1UKpXbQpjFYiE1NZX58+cze/bsZtvfeecd0tLSWLt2LePGjWPVqlVMnz6drKwsoqOjKS8v55NPPuHIkSMEBAQwY8YMtmzZgt1u57vvvmP37t1ER0dz9dVXM2bMmHO26lmtVqxnjL8wm81ueX9CdJTFcpB9+26gpiYLlUpLv37P0bv3A9Id5WUFVis7KivZYTazo7KSnZWVlLcQuHQqFcMDAxkVHFwfuIKCGB4YKOO3hOhBWhXC8vLyWnzsSTNmzGDGjBnn3L5y5UoWLFjAvHnzAFi7di2ffvop69atY/HixXz99dcMGDDA1d147bXXsn37diZMmMDo0aNdFxVcc8017N69+5whbPny5Tz55JNufndCdExx8UYyM2/D4ajC3783Q4a8J1c/ekGV3U56VZUrcO0wm1scNO+nUnFRUBCjgoIY2RC6hgUG4i9zbwnRo3XJCWFsNhvp6eksWbLEtU6tVjNt2jS2bdsG1F9AsHXrVmpra9HpdGzevJm77rqLMWPGUFRURHl5OUajkS1btvCrX/3qnOdasmQJaWlprudms9kV4ITobIri5MiRxzl69GkAjMZJDB36Ln5+0V6urPuzO53ss1iatHLtt1g4e3ZEFfVjuMYGBzMuJIQxwcEMDQzETwKXEOIsbQ5hZwaSM6lUKvR6PQMGDOC6667z6ID3kpISHA4HMTExTdbHxMS4rti85JJLuOaaa7j44otRq9VcccUVzJo1C5VKxbJly5g4cSKKonDVVVfxk5/85Jzn8vf3l6snhU+oq6vg4MFbKCv7DIBevRbRv/8K1GoZoO0Jp6xWtpnNbDWZ2NEwnqumhQmpE/z9GRsczNiQEMaFhDAyKIhgmfBUCNEKbf5LsWvXLjIyMnA4HCQnJwNw6NAhNBoNKSkp/OlPf+Khhx7i+++/Z8iQIW4vuC2eeeYZnnnmmWbrL9TVKYSvqarax/79N1BTk4NarWfQoFeJjb3V22V1G3VOJz9aLGwzmdjaELyOttCtGKLRMDYkxBW6xgYHEyf/SBNCtFObQ1hjK9frr7/uuveSyWTil7/8JZdffjkLFizgF7/4BQ8++CBffPGF2wsGiIyMRKPRUFhY2GR9YWEhsbGxHjmnEN5SVPQ+mZl34HRa8Pfvw7BhHxAcPNLbZXVppXV1rsC1zWxmh9lM9VmtXGpgeGAg441GxjcErkEGA2q58EEI4SZtDmErVqzgq6++anLzS6PRyBNPPMFVV13FokWLWLp0KVdddZVbCz2Tn58fo0aNYtOmTa5pK5xOJ5s2beLee+/12HmF6EyKonDkyJMcPVp/YUho6BUMGfI2fn6RXq6sa3EqCgerq9naGLpMJrJqaprtF6rVMj4khPEhIVxqNDI2OFi6FYUQHtXmvzAmk4mioqJmXY3FxcWu6RtCQ0Ox2WwdKqyqqoqcnBzX87y8PHbv3k14eDiJiYmkpaUxd+5cRo8ezdixY1m1ahUWi8V1taQQXZnDUUNW1nyKit4GoHfvNPr1+yNqtYSCC6lzOtlVVcWWigq2mEx8bzK1OEVEisHApQ2Ba3xICCnSyiWE6GTt6o6cP38+L7zwAmPG1M/I/b///Y+HH37Y1Sq1Y8cOBg0a1KHCdu7cyZQpU1zPGy8ImDt3LuvXr2fOnDkUFxezdOlSCgoKGDFiBJ9//nmzwfpCdDVWawH79l1PZeV/Uam0DBq0lri4O71dls+qcTj4r9nMdyYTW0wmtppMzboWA9VqxoaEuELXJSEhhMuM80IIL1MpiqK05QVVVVU8+OCDvPHGG9gb/nWp1WqZO3cuL774IoGBgezevRuAESNGuLterzObzRiNRkwmU5MuWSHcoarqR/bunYnVegytNpyhQ/9JWNhkb5flU0x2O1sbAtd3FRXsqKyk7qw/Y+FaLROMRiaEhjLRaOTioCC0MkWEED2aL35/tzmENaqqqiI3NxeAfv36ERQU5NbCfJUvfoiieygt/ZQDB27C4agiIGAQw4d/gsEw0NtleV1ZXR2bKyrYUlHBdyYTu6uqms3NFefnx0SjkYkNoWtIYKB0LQohmvDF7+92DzApKCggPz+fiRMnEhAQgKIocrsUIdpBURROnFjF4cMPA05CQ6cwdOj76HQ98+bylXY735lMfFNezjcVFeyuquLsfyn21+tdrVwTQ0Ppp9fL3x8hRJfT5hBWWlrKjTfeyLfffotKpSI7O5t+/fpx5513EhYWxgsvvOCJOoXolpxOOzk593Hq1FoA4uIWMHDgmh41AWuNw8FWs5lvysv5tqKCHWYzjrP2GWwwMLkhdE0IDaWXzM0lhOgG2hzCHnzwQXQ6HceOHWPw4MGu9XPmzCEtLU1CmBCt5HDUcODAzZSW/gtQ0b//8/Tu/WC3b9GxOZ38r7LS1dK11WTCdtaoiH56PVPDwpgaGsrk0FCZEFUI0S21OYR9+eWXfPHFF/Tu3bvJ+oEDB3L06FG3FSZEd1ZXV8bevTMxm7eiUvkzZMibREXN9nZZHqEoCtk1NXxZVsaXDa1dVY6mbV3xfn6u0DUlNJSkgAAvVSuEEJ2nzSHMYrFgMBiarS8rK5N7LArRCrW1x/jxx6uprj6IVhvKsGEfERo6wdtluVV5XR3fVFTwZVkZX5SVNbsFUIRWy5SG0DU1LIxBAQHdvgVQCCHO1uYQNmHCBN544w2eeuopoP7G3U6nk+eee67JvF5CiOaqqvby449XY7Odwt+/Nxdd9DmBgUO9XVaH2Z1OdlRW8kVDa9cOs7nJFYw6lYrLjUamh4dzVVgYqUFBcvWiEKLHa3MIe+6557jiiivYuXMnNpuNRx55hP3791NWVsYPP/zgiRqF6BYqKv7D3r3X4XCYMBiGcNFFn6PXJ3i7rHY7UVvLpw0tXZvKyzGf1cU42GDgqrAwrgoPZ1JoKIEajZcqFUII39TmEDZs2DAOHTrEK6+8QnBwMFVVVcyePZt77rmHuLg4T9QoRJdXVPQeBw/eiqLYMBovZ9iwj9DpwrxdVps4FIX/ms18UlrKp6Wl/GixNNkertUyrSF0XRUWRoJe76VKhRCia2hTCKurq+Pqq69m7dq1PProo56qSYhu5eTJtWRn/xpQiIy8gcGD/4FG0zUGnpfV1fFFWRmflpbyeVkZpWfcg1EFXBISwjXh4UwPD2dkcDAa6WIUQohWa1MI0+l0/Pjjj56qRYhu59ixFeTmPgJAfPxCBg58BZXKd7vlFEVhv8XCpw3B6weTqcnYrlCtlqvDw7k2PJyrw8OJ9PPzWq1CCNHVtbk78tZbb+Vvf/sbzz77rCfqEaJbUBSFI0eWcvTo0wAkJv6Ovn2f9skrAOucTv5TUcHGkhI+Li3l2FlXMg41GLg2IoJrIyK4NCRE7sEohBBu0uYQZrfbWbduHV9//TWjRo0iMDCwyfaVK1e6rTghuiJFcZKT8yAnT64GoF+/Z0lM/K2Xq2qqym7ni/JyNpaU8ElpKRVndDP6q1RMDQurD17h4TJnlxBCeEibQ9i+ffsYOXIkAIcOHWqyzRf/lS9EZ1IUB1lZd1FQsA6AgQPX0KvXr71cVb1im42PS0vZWFLCV+Xl1DpPdzRG6XTMiojgushIpoaFyZWMQgjRCdocwr799ltP1CFEl+d02snMvJ2iorcADSkprxMbe5tXazpeW8s/i4v5sKSE788a39VPr+eGyEiuj4xkvNEog+qFEKKTtTmECSGaczrtHDx4K8XF76BS6Rgy5G2v3YboeG0t7xcX825xMdvN5ibbRgYFcX1D8BoWGCit10II4UUSwoToIKezjoMHf0Fx8fuoVDqGDn2fyMhZnVrDuYKXCphgNPLTqCiuj4wkUebuEkIInyEhTIgOcDptHDhwMyUlH6BS+TF06D+JjPxJp5z7QsHr51FR/DQqiji5p6sQQvgkCWFCtJPTaWP//hspLf0XKpU/w4Z9QETENR49Z2ldHe8VFfGPoiK+N5lc6yV4CSFE19OqEDZy5Eg2bdpEWFgYf/jDH3j44YcxGAyerk0In+V01nHgwJwzAthGIiKu9si5qh0OPi4t5R+FhXxeVkadogASvIQQoqtTKUrDX/TzCAgIIDs7m969e6PRaMjPzyc6Oroz6vM5ZrMZo9GIyWQiJCTE2+UIL1AUBwcP3kpR0duoVP4MH/4vwsOnu/UcDkXhm/Jy/lFYyD9LSqg64+bYI4KCuDUmhpuio+klwUsIIVrFF7+/W9USNmLECObNm8fll1+Ooig8//zzBAUFtbjv0qVL3VqgEL5EUZxkZt7ZEMC0DB36vlsD2K7KSv5eWMhbRUUU2Gyu9X38/bklJoZbYmIYctYEyUIIIbqmVrWEZWVl8fjjj3P48GEyMjIYMmQIWm3z/KZSqcjIyPBIob7CF5O06ByKopCd/WtOnVoLaBg69B2ion7a4eOW1tXxZmEh6woK2F1V5VofrtVyY3Q0t0RHc6nRiFqmkxBCiHbzxe/vVoWwM6nVagoKCqQ70oc+ROF5iqJw+HAaJ06sAlQMHvx/xMT8ot3HcygKX5eXsy4/n40lJdga/jf0U6m4LjKSW2NiuDo8HD+5T6MQQriFL35/t/nqSKfTeeGdhOhmjhxZ2hDAIDn5tXYHsMM1NawvKGB9QQEnzrhR9sVBQcyPjeUXMTGE63TuKFkIIYSPa9cUFYcPH2bVqlUcPHgQgCFDhrBo0SL69+/v1uKE8AUnTrzE0aNPAzBw4CvExc1v0+trHA7eLy5mXUEBmysqXOvDtFpujYlhXmwsFwcHu7NkIYQQXUCbQ9gXX3zBrFmzGDFiBJdddhkAP/zwA0OHDuXjjz/myiuvdHuRQnhLQcH/kZPzAAB9+z5Nr173tPq1h6qr+cupU6wvKKDMbgfqp5W4KiyM+XFxzIqIQC83yhZCiB6rzWPCLr74YqZPn86zzz7bZP3ixYv58ssvZWC+6DZKSz9l797rAAe9ei1iwIAXL3ivxTqnk3+VlLD21Ck2ndHq1cffnzvj4rgjNpYEuXWQEEJ0Ol/8/m5zCNPr9ezdu5eBAwc2WX/o0CEuuugiamtr3VpgR+Tl5TF//nwKCwvRaDRs376dwMBAnn/+eV5//XVUKhWLFy/m1ltvbfUxffFDFO5XUfE9P/54JU5nLTExt5KSsgGV6tyD5I/X1vLX/Hxey893TS2hAq6NiGBhfDxXh4ejkasbhRDCa3zx+7vN3ZFRUVHs3r27WQjbvXu3z10xeccdd/D0008zYcIEysrK8Pf3Z+/evbz55pukp6ejKApTpkzhJz/5CaGhod4uV/iIqqof2bv3JzidtYSHX0ty8roWA5iiKGw1m3npxAk+KC6mcTrVaJ2OX8bFcVd8PH2k1UsIIcQ5tDmELViwgLvuuovc3FwuvfRSoH5M2B//+EfS0tLcXmB77d+/H51Ox4QJEwAIDw8H4ODBg4wfPx59w5djamoqn3/+OTfddJPXahW+o7b2BD/+eA0Ohwmj8XKGDn0Xtbrp1YpWp5N3i4p46cQJ0s+Y12uS0cive/Xi+shImVpCCCHEBbX5m+Kxxx5j6dKlvPzyy0yaNIlJkybxyiuv8MQTT/D73//ebYVt2bKFmTNnEh8fj0qlYuPGjc32WbNmDUlJSej1esaNG8eOHTtc27KzswkKCmLmzJmMHDmSZcuWATBs2DA2b95MRUUF5eXlbN68mZMnT7qtbtF12e0m9u69BpvtJAbDEIYN+wiN5vQ9UgttNp48coQ+27Zxe2Ym6VVV+KtUzI+NZc/o0Wy++GJujI6WACaEEKJV2twSplKpePDBB3nwwQeprKwEINgDl9dbLBZSU1OZP38+s2fPbrb9nXfeIS0tjbVr1zJu3DhWrVrF9OnTycrKIjo6GrvdznfffefqJr366qsZM2YMV155Jffffz9Tp07FaDRyySWXoDnPFWpWqxXrGfM5mc1mt79X4X1Op439+3+GxbIXP784Lrro3+h0YQActFh4/vhx/q+w0DWparyfH7/u1Yu74uKI8vPzZulCCCG6qA79kz04ONgjAQxgxowZPP3009xwww0tbl+5ciULFixg3rx5DBkyhLVr12IwGFi3bh0AvXr1YvTo0SQkJODv788111zD7t27AfjVr35FRkYG3377LTqdrtn4tjMtX74co9HoWhISEtz+XoV3KYpCVtZdlJd/jVodyPDhn6LXJ7LVZOK6vXsZ8r//sa6gAJuiMC44mLcGD+bIJZfwaJ8+EsCEEEK0W5fsN7HZbKSnpzNt2jTXOrVazbRp09i2bRsAY8aMoaioiPLycpxOJ1u2bGHw4MEAFBUVAfX3xNyxYwfTp5/7BsxLlizBZDK5luPHj3vwnQlvOHLkSQoLNwAahgx5l83WBC7PyOCyXbv4qLQUFXB9ZCRbL76Y7aNGcVNMDDrpchRCCNFB7Zox39tKSkpwOBzExMQ0WR8TE0NmZiYAWq2WZcuWMXHiRBRF4aqrruInP/kJANdddx0mk4nAwEBef/31Fm9G3sjf3x9/f3/PvRnhVfn56zl69EkASmKWMyk3kgPV+4D6+zjeFhPDwwkJpAQGerNMIYQQ3VCXDGGtNWPGDGbMmNFsfWNrmejZKiq2cOjQXQB8ormdFwrHANWEaDQsjI9nUe/exEsAF0II4SFt6lOpq6vjiiuuIDs721P1tEpkZCQajYbCwsIm6wsLC4mNjfVSVaIrMVsOs3PvDShKHZuZxErHXGJ0Ov7Yrx/Hxo/nj/37SwATQgjhUW0KYTqdjh9//NFTtbSan58fo0aNYtOmTa51TqeTTZs2MX78eC9WJnyd1enkL8ez+NfOq9A6yshiEK/rlrKy/0ByL7mERxITMZ6ne1oIIYRwlzaPLr711lv529/+5olamqiqqmL37t2uKxrz8vLYvXs3x44dAyAtLY1XX32VDRs2cPDgQe6++24sFgvz5s3zeG2i67E5nfzp5EkGbt9K6eF5JCi5lBOBI+n/yLxkEg8kJGCQm2kLIYToRG3+J7/dbmfdunV8/fXXjBo1isCzBiyvXLnSLYXt3LmTKVOmuJ43zsY/d+5c1q9fz5w5cyguLmbp0qUUFBQwYsQIPv/882aD9UXP5lQU3ioq4rG8PPJqa7mLv3Ap23Cq/JmQ+jGRoWO8XaIQQogeqs038D4zGDU7mErFN9980+GifJkv3gBUNKcoCv8uK2NJbi4/WiwA/FyziV87ngZg8OA3iYm52ZslCiGE6ES++P3d5pawb7/91hN1COE220wmFufmssVkAsCo0fCHGBOp+StQgD59fi8BTAghhNe1ewRyTk4Ohw8fZuLEiQQEBKAoCiqVyp21CdEmBy0WluTm8q/SUgD8VSru692bh+MM5O65BKtiJSJiJklJT3q5UiGEEKIdIay0tJQbb7yRb7/9FpVKRXZ2Nv369ePOO+8kLCyMF154wRN1CnFO5XV1PHHkCGtOnsRB/dUm82JjeTwpiV5+Wn788Wqs1mMEBAxk8OC/o1LJbPdCCCG8r83fRg8++CA6nY5jx45hMBhc6+fMmcPnn3/u1uKEOB+708mfT55k4H//y+qGAHZdRAT7xozhtZQUEvR68vJ+T0XFJtTqQIYO/QCt1ujtsoUQQgigHS1hX375JV988QW9e/dusn7gwIEcPXrUbYUJcT7flpezKCeHvQ2D7ocaDKwaMIBp4eGufYqL/8nx438EICVlHUFBw7xSqxBCCNGSNocwi8XSpAWsUVlZmdxjUXhcXk0NDx8+zAclJQCEa7U81bcvd8XFoT3jptoWywEyM+8AICHhYaKjb/RGuUIIIcQ5tbk7csKECbzxxhuu5yqVCqfTyXPPPXfe6SuE6Ihah4PH8/IYvGMHH5SUoAHu7dWL7HHj+HWvXk0CmN1exb59s3E4qggNnUrfvsu9V7gQQghxDm1uCXvuuee44oor2LlzJzabjUceeYT9+/dTVlbGDz/84IkaRQ/3dVkZd2dnk1NTA8AVoaGsGjCAYUFBzfZVFIVDhxZSU5OFn18vhgx5G7VabkMkhBDC97T522nYsGEcOnSIV155heDgYKqqqpg9ezb33HMPcXFxnqhR9FCFNhsP5eTwj6IiAOL9/HhpwAB+GhV1zulQ8vP/RlHRPwANQ4e+g59fVCdWLIQQQrReu5oIjEYjjz76qLtrEQKob836W34+v8nNpcJuR0191+NTffsScp6ba1dV/UhOzn0A9Ou3DKPxsk6qWAghhGi7doWw8vJy/va3v3Hw4EEAhgwZwrx58wg/48o0IdrjSE0NCw4d4uvycgBGBgXxl0GDGH2BW0zY7ZXs3/9znM5awsOvISHh4c4oVwghhGi3Ng/M37JlC0lJSaxevZry8nLKy8tZvXo1ffv2ZcuWLZ6oUfQATkXhzydPMnznTr4uLydAreaF/v3578iRFwxg9ePAfkVNzSH8/XuTkrJBJmQVQgjh89rcEnbPPfcwZ84c/vznP6PRaABwOBz8+te/5p577mHv3r1uL1J0b7k1NdyZlcXmigoAJhiN/C05mYEtTIXSkvz81ygqegvQMGTI2/j5RXquWCGEEMJNVIqiKG15QUBAALt37yY5ObnJ+qysLEaMGEFNwxVs3ZUv3oW9q1IUhXUFBSzKzsbidGJQq/ljv378ulcv1K28D6nFcoD09FE4nbX06/cciYm/8XDVQgghuiJf/P5uc0vYyJEjOXjwYLMQdvDgQVJTU91WmOjeSmw27jp0iA8bJl2dZDSyLiWFfgEBrT6G02nlwIFf4HTWEhY2nYSEhzxVrhBCCOF2rQphP/74o+vx/fffz6JFi8jJyeGSSy4BYPv27axZs4Znn33WM1WKbuWLsjLuyMykwGZDp1LxTN++PJSQ0OrWr0a5ub/DYtmDThdJSsp6GQcmhBCiS2lVd6RarUalUnGhXVUqFQ6Hw23F+SJfbM7sKqxOJ789fJiXTp4EYLDBwD8GD+bi4OA2H6us7Et+/HE6AMOGfUxk5E/cWqsQQojuxRe/v1vVEpaXl+fpOkQ3l1dTw8/37ye9qgqon/frj/36YWi4uKMtbLYSMjPnAhAf/2sJYEIIIbqkVoWwPn36eLoO0Y39q6SEuQcPYnI4CNdqeWPwYK6NiGjXsRRFISvrTmy2AgyGwfTvv8LN1QohhBCdo12TtZ46dYrvv/+eoqIinE5nk23333+/WwoTXV+d08ni3FxWnjgBwPiQEN4eMoREvb7dx8zP/yulpR+hUvkxePCbaDStm8ZCCCGE8DVtDmHr16/nV7/6FX5+fkRERDS5h59KpZIQJgA4abXy8/372WY2A/BQ794s79cPnbr9g+ctloPk5DwIQL9+ywkOHuGOUoUQQgivaHMIe+yxx1i6dClLlixB3YEvVNF9bTeZmL1/P/k2G0aNhvUpKVwf1bEbaTudVg4e/AVOZw1hYVfSu/cD7ilWCCGE8JI2h7Dq6mpuuukmCWCiRRsKCrgrKwubojDUYOBfw4fTvw1zf51LXt7vqarajVYbIdNRCCGE6Bba/E1255138t5773miFtGF2Z1OHszJ4Y7MTGyKwvWRkWwbOdItAay8fBPHjz8PQErK3/D3j+/wMYUQQghva/NtixwOBz/5yU+oqalh+PDh6HS6JttXrlzp1gJ9jS/OM+Jt5XV1zDlwgK/KywFY2qcPjycltXny1ZbY7Sb+97/hWK3HiYu7i+Tkv3T4mEIIIXoeX/z+bnN35PLly/niiy9cty06e2C+6FmO1dZy9Y8/crC6GoNazRuDB/PTDo7/OlNOThpW63H0+n707/+C244rhBBCeFubQ9gLL7zAunXruOOOOzxQjuhK9lRVMePHH8m32ejl58enF11EalCQ245fUvIJBQXrABUpKevRat13bCGEEMLb2hzC/P39ueyyyzxRi+hCvi4rY/b+/VQ6HAw1GPj3RReR0IH5v85WV1fKoUMLAOjd+0FCQye47dhCCCGEL2jzwPxFixbx8ssve6IWt0tKSuKiiy5ixIgRTJkyBYDjx48zefJkhgwZwkUXXSQXGbTD3wsKmLF3L5UOB5NDQ/n+4ovdGsAAsrPva5gVP4W+fZ9267GFEEIIX9DmlrAdO3bwzTff8MknnzB06NBmA/M/+OADtxXnDlu3biXojC4yrVbLqlWrGDFiBAUFBYwaNYprrrmGwMBAL1bZdTx/7Bi/yc0F4KboaNanpODv5ulKiorep6joLUBDSsoGNJqOX2EphBBC+Jo2h7DQ0FBmz57tiVo6RVxcHHFxcQDExsYSGRlJWVmZhLALUBSFp48eZemRIwD8JiGBZ/v1c8sVkGey2QrJzr4bgMTExYSEjHXr8YUQQghf0eYQ9vrrr3uijma2bNnCihUrSE9PJz8/nw8//JDrr7++yT5r1qxhxYoVFBQUkJqayssvv8zYsae/tFUqFZMmTUKtVvPAAw9wyy23NHl9eno6DoeDhISEznhLXZaiKDyal8fyY8cAWNa3L0s8cFN3RVE4dGghdXUlBAZeRFLSUrefQwghhPAVPjvtuMViITU1lTVr1rS4/Z133iEtLY3HH3+cjIwMUlNTmT59OkVFRa59vv/+e9LT0/noo49YtmwZP/74o2tbWVkZt99+O3/961/PW4fVasVsNjdZehJFUUg7fNgVwFb27++RAAZQWPh/lJRsRKXSMXjwG6jVfh45jxBCCOEL2jxZa9++fc87H1huw3ghd1KpVM1awsaNG8eYMWN45ZVXAHA6nSQkJHDfffexePHiZsf4zW9+w9ChQ7njjjuwWq1ceeWVLFiwgNtuu+28537iiSd48sknm633pcnePMWpKNyTnc3aU6cA+NPAgdzdq5dHzlVbe4L//W8YDoeJvn2fpk+fRz1yHiGEED1Tt5is9YEHHmjyvK6ujl27dvH555/zm9/8xl11nZfNZiM9PZ0lS5a41qnVaqZNm8a2bduA+pY0p9NJcHAwVVVVfPPNN9x4440oisIdd9zB1KlTLxjAAJYsWUJaWprrudls7hHdl05F4VeHDvFafj4q4LXkZOY3jKVzN0VRyMr6JQ6HieDgMSQk/NYj5xFCCCF8SZtD2KJFi1pcv2bNGnbu3NnhglqjpKQEh8NBTExMk/UxMTFkZmYCUFhYyA033ADU32ppwYIFjBkzhu+//5533nmHiy66iI0bNwLw97//neHDh7d4Ln9/f/z9/T33ZnyQoig8dPgwr+Xnowb+Pngwvzjrd+1O+fmvUl7+BSqVPykpG1Cr2/yfpRBCCNHluO3bbsaMGSxZsqTTBu5fSL9+/dizZ0+z9ZdffjlOp9MLFXUdfzh6lFUnTgCwLiXFowGspiaPw4cfAqBfv2UEBg722LmEEEIIX+K2gfnvv/8+4eHh7jrceUVGRqLRaCgsLGyyvrCwkNjY2E6pobtadfw4TzRMQ/HSgAHM9eDvU1GcZGbOw+GowmicQO/eLbeyCiGEEN1Rm1vCLr744iYD8xVFoaCggOLiYv70pz+5tbhz8fPzY9SoUWzatMk1WN/pdLJp0ybuvffeTqmhO3o9P58HDx8G4A9JSdzfu7dHz3fy5CuYTP9BrTaQkvI6KpXGo+cTQgghfEmbQ9jZc3Wp1WqioqKYPHkyKSkp7qqLqqoqcnJyXM/z8vLYvXs34eHhJCYmkpaWxty5cxk9ejRjx45l1apVWCwW5s2b57YaepJ/Fhfzy6wsANJ69+b3HpqGolF1dRa5ufUD8Pv3f56AgP4ePZ8QQgjha9o8RUVn2bx5s+t+j2eaO3cu69evB+CVV15xTdY6YsQIVq9ezbhx4zxaly9e4tpRW00mpuzejU1RuDM2lleTk887DUlHKYqDXbsux2zeTljYNC666EuPnk8IIYTwxe9vnw1hvsoXP8SOOFJTw9iMDIrr6rguIoJ/DhuGxsOB6NixP5KbuxiNJoQxY/ai1yd69HxCCCGEL35/t7o7Uq1WX7C1QqVSYbfbO1yU6Bxmu52f7N1LcV0dI4KC+L/Bgz0ewKqq9pGXV387ogEDXpIAJoQQosdqdQj78MMPz7lt27ZtrF69WqZ+6ELsTic3HTjA/upq4vz8+HjYMIK0np2fy+msIzPzdhTFRkTET4iNnevR8wkhhBC+rNXfutddd12zdVlZWSxevJiPP/6YW265hT/84Q9uLU54zsOHD/PvsjIC1Go+GjaM3nq9x8959OgzVFXtQqsNZ9Cgv8o4MCGEED1au+YJO3XqFAsWLGD48OHY7XZ2797Nhg0b6OPhK+qEe/z55EleOnkSgDdSUhjdCX3jlZXpHD36NACDBv0Jf3/P3AJJCCGE6CraFMJMJhO//e1vGTBgAPv372fTpk18/PHHDBs2zFP1CTf7rqKC+7KzAXi6b19+Fh3t8XM6HLUcPDgXcBAV9XOio+d4/JxCCCGEr2t1d+Rzzz3HH//4R2JjY3nrrbda7J4Uvq3AamXOgQM4gJuio/ldYucMij9y5HGqq/ej00UzcGDnTOgrhBBC+LpWT1GhVqsJCAhg2rRpaDTnntn8gw8+cFtxvsgXL3FtDbvTybQ9e/iPycRQg4H/jhpF4Hk+R3cxmbaya9flgMKwYRuJjJTwLoQQovP54vd3q1vCbr/9dhlI3YUtPXKE/5hMBGk0/HPYsE4JYA6HhczMuYBCTMztEsCEEEKIM7Q6hDXOUi+6nk3l5Tx77BgA65KTSTYYOuW8ublLqKnJwc+vFwMGvNQp5xRCCCG6inZdHSm6jmKbjdsOHkQBfhUXx887YSA+QHn5t5w8+TIAKSl/Q6cL7ZTzCiGEEF2FhLBuTFEU5mVmkm+zMcRgYOWAAZ1yXrvdTGZm/Y3U4+J+RXj49E45rxBCCNGVSAjrxv6an8+nZWX4q1S8NWQIhk4YBwZw+PBDWK1H0ev70r//ik45pxBCCNHVSAjrpnJrangoJweA5f36cVFQUKect7T03+TnvwZASsrraLXBnXJeIYQQoquRENYNORWF+ZmZWJxOJhqNLOrdu1POW1dXRlbWnQD07v0AoaGTOuW8QgghRFckIawbevnkSf5jMhGoVvN6SgrqTppaJDv7fmy2fAICBtG377JOOacQQgjRVUkI62aO1NTwu9xcAFb070+/gIBOOW9x8QcUFf0DUJOSsgGNpnPOK4QQQnRVEsK6EUVR+HV2NtVOJ5OMRhbGx3fKeW22Yg4dWghAYuJvMRov6ZTzCiGEEF2ZhLBu5N3iYv5dVoafSsVfkpM75Q4HiqJw6NBC6uqKCQwcTlLS4x4/pxBCCNEdSAjrJirq6liUnQ3A7/r06bRZ8YuK3qKk5ANUKi0pKRtQq/075bxCCCFEVychrJtYeuQIhXV1pBgMLE5M7JRzWq2nyM6+B4A+fZYSHHxxp5xXCCGE6A4khHUD+6qq+NPJkwC8MnAg/mrPf6yKopCVtQC7vYKgoFEkJi72+DmFEEKI7kRCWBenKAqLcnJwALMjI7kiLKxTzltQsI6yss9QqfwZPHgDarWuU84rhBBCdBcSwrq4D0tK+KaiAn+Viuf79++Uc9bWHiUn50EA+vZ9isDAoZ1yXiGEEKI7kRDWhVmdTh4+fBiA3yQm0rcT5gRTFCeZmfNxOCoJCbmUhIQ0j59TCCGE6I4khHVha0+dIq+2ljg/v04bjH/y5J+oqPgGtdpASsoGVKrOuSm4EEII0d1ICOuizHY7Tx89CsATSUkEajwfhqqrs8nN/S0A/fr9EYNhgMfPKYQQQnRXEsK6qBeOH6ekro5BAQHMj431+PkUxUFm5h04ndWEhk6lV69fe/ycQgghRHcmIawLKrTZeOH4cQCe6dsXbSdMSXH8+ErM5q1oNMGkpKxDpZL/dIQQQoiO0Hq7AE+pqKhg2rRp2O127HY7ixYtYsGCBQAkJSUREhKCWq0mLCyMb7/91svVts2yo0exOJ2MCQ7mp1FRHj+fxbKfvLzfAzBgwIvo9X08fk4hhBCiu+u2ISw4OJgtW7ZgMBiwWCwMGzaM2bNnExERAcDWrVsJCgrycpVtV2C18tf8fKC+FczT94d0Ous4eHAuimIjPPwaYmPne/R8QgghRE/RbfuUNBoNhob7J1qtVhRFQVEUL1fVcc8fP06t08klISFM64SJWY8de5aqqnS02jCSk1/tlJuCCyGEED2Bz4awLVu2MHPmTOLj41GpVGzcuLHZPmvWrCEpKQm9Xs+4cePYsWNHk+0VFRWkpqbSu3dvfvOb3xAZGQmASqVi0qRJjBkzhn/84x+d8Xbcothm48+nTgHwWJ8+Hg9ElZW7OHr0DwAMHPgK/v7xHj2fEEII0ZP4bAizWCykpqayZs2aFre/8847pKWl8fjjj5ORkUFqairTp0+nqKjItU9oaCh79uwhLy+PN998k8LCQgC+//570tPT+eijj1i2bBk//vjjOeuwWq2YzeYmi7e8eOIE1U4no4KCmBEe7tFzOZ1WMjNvR1HsREb+lOjomz16PiGEEKKn8dkQNmPGDJ5++mluuOGGFrevXLmSBQsWMG/ePIYMGcLatWsxGAysW7eu2b4xMTGkpqby3XffAdCrVy8A4uLiuOaaa8jIyDhnHcuXL8doNLqWhIQEN7y7tiuvq+OVhpt0P5aU5PFWsCNHnsRi2YdOF8WgQX+WbkghhBDCzXw2hJ2PzWYjPT2dadOmudap1WqmTZvGtm3bACgsLKSyshIAk8nEli1bSE5OxmKxuNZXVVXxzTffMHToue99uGTJEkwmk2s53jA1RGf7a34+lQ4HwwMDmdVwcYGnmEzbOXbsjwAMGrQWPz/PX4EphBBC9DRd8urIkpISHA4HMTExTdbHxMSQmZkJwNGjR7nrrrtcA/Lvu+8+hg8fTm5urqt1zeFwsGDBAsaMGXPOc/n7++Pv7++5N9MKNqeT1SdOAPBQQoJHW6UcjmoyM+cCTmJibiUqarbHziWEEEL0ZF0yhLXG2LFj2b17d7P1/fr1Y8+ePZ1fUAe8V1zMKZuNWD8/boqO9ui58vIepabmEH5+8QwYsNqj5xJCCCF6si7ZHRkZGYlGo3ENtG9UWFhIbCfcwqczKYrCyoYu0Ht79cLfg7PjV1T8hxMnVgGQnPwaOp3np8AQQggheqou2RLm5+fHqFGj2LRpE9dffz0ATqeTTZs2ce+993q3ODfbYjKRUVVFgFrNr+LiPHYeu72SzMx5AMTF/ZKIiBkeO5cQQoieQVEUlDoFp82JYjv9s9m69uxTpzTZ/0L7VNZUevvX0YzPhrCqqipycnJcz/Py8ti9ezfh4eEkJiaSlpbG3LlzGT16NGPHjmXVqlVYLBbmzZvnxard78WGVrC5sbFE+vl57DyHD/+G2to8/P370L//Cx47jxBCCPdQFAXFruC0OlGs9UGj3Y+tzvrQcubjswNOS8HIpuCsO/c+it13Jkm3YPF2Cc34bAjbuXMnU6ZMcT1PS0sDYO7cuaxfv545c+ZQXFzM0qVLKSgoYMSIEXz++efNBut3ZSdqa/m4tBSA+xum1fCEsrIvyM//CwApKa+j1YZ47FxCCNHVuFpzrOcJLdaGINLOx+19Pb6TcVpHBSo/FWo/9emfuubPPbGPpc4CN3r7F9CUSukO9/LpRGazGaPRiMlkIiTEs2Hlibw8njx6lElGI5svvtgj56irq+B//xuGzXaSXr3uY+BAGYwvhPAditLQnVTrrF+szpYfn/VcsSrn3Ha+YzR53RnbukTYUYPaX43avyGItPex/xlhxl/dcujRqVsMQRcMRhrvzTnZmd/freWzLWE9nd3p5LWGG3UvjPfc7YJychZhs50kIGAg/fo967HzCCG6rsYg5Khx4KxxuhZHjaM+pJy9rqV9zhNwzheMFKvvpR+VVuUKKq7Q0hhW2vu4o8HJT4Va2yWvtevRJIT5qE/LyjhpsxGp03FDlGcmSy0p+ReFhW8AalJS1qPRGDxyHiGEeznrzh16nLXnCELtDU8Nz32lJUitbwguenX94q9u+fFZz5u8pr2vaww8armDiHAPCWE+6i8NN+qeHxvrkWkpbLYSsrLuAiAh4WGMxkvdfg4heiKnzYmj2oGzuuGnpelzh6WV26qdLT53VDvA4cU3qAJ1gBp1gBpNgMb1uMlz/VnrGp+fFXbOGabOEZJUfiq5hZroViSE+aAjNTV8XlYGwAIPTUuRnf1r6uqKMBiGkpT0pEfOIYQvUpxKfeCpar44Lc7TzxsCT1uDUmdfDXZm4GkpGKn15wlLLQWlC+wjQUgI95EQ5oPWFxSgAFeEhjLA4P4uwqKidygufg/QMHjwBjQavdvPIURHKUr9VWDNwtGZi6XlMHW+bc5qZ+e8ATVoAjVoAjWoDWo0hoafLTx3PTZoUAdeYFtA/fPGliUJREJ0XRLCfIxTUXij4U4A8zzQCma15nPo0K8B6NPn9wQHj3L7OUTPpSj1A68dZgf2SjsOswNHpQO72d5knd1sx1HpaPK4ybpKO44qD3e7qUATpDm9BJ5+rA5U1z9ub1AyaOqvFJOAJIQ4DwlhPuZ7k4m82lqCNRpuiIx067EVReHQobuw28sICrqYPn0edevxRdfVGJ7sFXbsJnv9zwo7DlMbAlRD4PJEd5w6QN0sKJ25uELT2cs59tcE1ne1SUgSQniThDAfs6GgAIAbo6IwaDRuPXZBwQZKSz9BpfIjJeUN1GqdW48vvEdRFBwWhys8uQLUGc/PDlhnr1Ns7g1PmmANmmAN2hAtmpCmj7XBDT/PtS24aWDy5txCQgjhKRLCfEi1w8F7xcVA/W2K3Km29hg5OYsA6Nv3DwQFDXPr8YV7OOuc2Mvt1JXVYS9r4WdpC+sbgpRbuu5UoDVq0YbWLxrjGeEoRNu6UNUQoOQyfiGEOD8JYT7kw5ISKh0O+un1XG40uu24iqKQlXUnDoeZkJBLSEh42G3HFi1TFAWH2YGt2EZdSR11xXX1P1sKUWf8dFR2LEmptCpXgGoSpM5cZ9Se87mEJyGE6DwSwnxIY1fk7bGxbh2rcurUWsrLv0atDiAlZQMqlXu7OXsCp92JvdTeNFQ1BqviuhbXK3Xt7N5TUR+KwrXownXn/xmmQxt2OkTJOCchhOg6JIT5iAKrlU3l5QDc5sabkNfUHObw4fqWr379nsVgGOS2Y3d1ilOhrqQOW4Gtfim0nX585lJow15qb9c5NEEadJE6dFG6+p+RFwhV4Tq0Rq2MgRJCiB5AQpiPeK+4GCdwSUgI/QIC3HJMRXGQmTkPp7Oa0NDJ9Op1r1uO6+ucVifWk1asJ6zY8lsOVbYCG7YiW9vGUalAF6E7HaqiTj/2i/Jrvj5ShyZAWh2FEEK0TEKYj3irqAiAm6Kj3XbMEydewmT6Do0miOTkdahUXf/mrvYqO9YTDQHrpM312HrC6gpedcV1rT+gCnSROvxi/ZouMU2f66J16MJ10kIlhBDCbSSE+YAjNTVsM5tRUT81hTtYLAfJzf0dAP37ryQgoK9bjutJilPBVmCj9kht0+VorStgOUyta7pS69X49/bHL86vfjlHyNJF6VDrun44FUII0fVICPMB7zRMSzE5NJQ4f/8OH8/ptJOZORdFsRIefjVxcb/s8DHdQVEU6orqqDlc0zxoNYSt1sxVpTFq8O/lj3/vhqWFx9pwrQxQF0II4dMkhPmAtxpuU3Szm7oijx//I5WV/0OrDSU5+bVODyN1ZXXUZNdQfaiamuya+sfZ9Y8d5gu0ZGlAn6BHn3R68e/TNGRpg+U/WyGEEF2ffJt52UGLhT0WC1qVip+6oSuyqmoPR448CcCAAS/j79+rw8dsidPupCanBss+C9UHq5uELnvZea4kVIF/gj/6vk2Dlj5JT0DfAPx6+aHWSvegEEKI7k9CmJe93TAgf3pYGOG6jt1GyOm0cfDg7ShKHZGR1xMTc0uH61McCjV5DWFrfzWW/Zb6x1nV5+069Iv3wzDIQMDAANdiGGhA31+PRi9XDAohhBASwrxIURTXVZE3u2FusCNH/oDF8iM6XSSDBq1tczek0+bEst9CVUYVlRmVVKZXYvnRgrPG2eL+aoOawKGBGIYYMCQbXEErYEAAmkAJWkIIIcT5SAjzooyqKrJraghQq7kuIqJDxzKbd3Ds2LMADBz4Z/z8zh/qnHVOqvZUUZV+RuDaa2mxdUvlryJwSGB94BpqIHBY/WN9H73c4kYIIYRoJwlhXtTYFfmTiAiCtO3/KByOGjIz5wIOoqNvJjr6Z832sZXYMG8zY95qxrTVROX/Klts4dKGagkaGUTwyGCCRgURfHEwAQMCZH4sIYQQws0khHmJU1FcIayjV0Xm5f2e6upM/PxiGTjwFaA+dFV8W0HFNxWUf1tOTVZNs9dpw7UEjw4meFSwK3jp++plagchhBCiE0gI85KtJhMnrFZCNBpmhIe3+zgVFd9x4sSLAMRVruTo4jLKNx3GssfSbF/DYAMhl4ZgvMyI8VIjAYMCJHAJIYQQXiIhzEsaB+TfEBmJXtO+Qew1+WXs33cb6BT44hqOPhsHnHBtDxwWSOgVoYRNDcN4uRFdeMeuvhRCCCGE+0gI8wK708l7DbPkt/WqyNqjtRS+VUjpv0oxj/sDXH8UCmJg9a/x7+1P+NXh9cFrShh+MX6eKF8IIYQQbiAhzAu+qaiguK6OSJ2OqaGhF9zfbrZT/H4xBW8UYPqPqX7lqJ1w/b8AiCl6gd4/TCQoNUi6F4UQQoguQkKYFzR2Rf48KgqduuXZ4RWnQtmXZRRuKKRkYwnO2oYrGVVgvFqD5cGV2IH4+HsYNLnjk7IKIYQQonN16/vD3HDDDYSFhfGznzWdsuHFF19k6NChDBkyhPvvvx9FufBNo92l1uHgg8auyBauirSb7BxfdZz/Dvove2fspejtIpy1TgyDDfRd3pdLjl5CwMrXsevy0ev707//HzutdiGEEEK4T7duCVu0aBHz589nw4YNrnXFxcW88sor7N+/H51Ox8SJE9m+fTvjx4/vlJo+LyvD7HDQ29+fy4xG13pbkY0TL57g5JqTOCrrb3KtDdUSc1sMsXNjCRpZ39VYUvIxBYdfB1SkpKxHownslLqFEEII4V7dOoRNnjyZzZs3N1tvt9upra0FoK6ujugOztPVFo1dkXOiolCrVNSV1nF02VFO/fmUa/JUwxADve/vTcytMU1u/1NXV0pW1gIAEhIeIjT08k6rWwghhPAGRQGnExyO08uFnre0zmz29jtpzmdD2JYtW1ixYgXp6enk5+fz4Ycfcv311zfZZ82aNaxYsYKCggJSU1N5+eWXGTt27HmPGxUVxcMPP0xiYiJarZaFCxfSv39/D76T06rsdj4uLQXgxvAojq88ztGnjmKvsAMQPCaYPo/1IeInES0OsM/Ovpe6ukIMhsEkJT3VKTULIYToGEWpDwF2++lA0NbHHX29Jx5faL/WBKPW7NOJI4Y6nc+GMIvFQmpqKvPnz2f27NnNtr/zzjukpaWxdu1axo0bx6pVq5g+fTpZWVnnbdkqLy/nk08+4ciRIwQEBDBjxgy2bNnCxIkTPfl2APiotJQap5N++OEcd5DDOfWtcYEXBdLvj/0Inx5+zqsbi4reo6jobUBDSsoGNBq9x+sVQoj2cjrrv4jbutTVte917jquJ0JLdw4RvkKtrl80mqbLmetUKsjP93alTflsCJsxYwYzZsw45/aVK1eyYMEC5s2bB8DatWv59NNPWbduHYsXLz7n677++msGDBhAeMMs9ddeey3bt28/ZwizWq1YrVbXc3MH2jPfPFUIwGVv2KjNAV2Mjn7P9CP2jtjz3pvRZivk0KG7AejT53eEhIxpdw1CCN/gdNYHg8alMSi0dmnL/hfa1xPBRoJH62m1p4OCtx576rhnB6MLBaX2vE6trg9YF2I2wxlDsX2Cz4aw87HZbKSnp7NkyRLXOrVazbRp09i2bdt5X5uQkMDWrVupra1Fp9OxefNm7rrrrnPuv3z5cp588skO13xsTwVflJaBFqZ+A3EL4uj/fH+0Ief/CBRFISvrLuz2UoKCRtCnz+87XIsQ3UVjN4/N1jmLO4OP0+nt3553aLXeW3S6c287Mzx0ZuA5xyxFoofokiGspKQEh8NBzFmzzcfExJCZmel6Pm3aNPbs2YPFYqF379689957jB8/nmuuuYaLL74YtVrNFVdcwaxZs855riVLlpCWluZ6bjabSUhIaFO9xRuLeeWNA9jvhwHHVMz663DCr2rd/SILC/9OaelHqFQ6UlI2oFbLLPii8zmdYLVCbW39z7Mfn2/b2Y/dHYy6U4uLRlMfFBqXxuDQ1qU9r+uMENTYJSSEqNclQ1hrff311y2uf+aZZ3jmmWdadQx/f3/8/f3bdX5FUTj6zFGOPHaEr1+oX3fH2ETCU1oXwGprT5CdfT8ASUlPEBR0UbvqEF2f3Q41Nc2X2tqW1zdua29QOvs1dru3fwOtp9OBn597l/YEobYGIq1WWkWE6Gm6ZAiLjIxEo9FQWFjYZH1hYSGxsbFeqqq5I0uPcPTpo5SGw+6L69f9ok/r6qvvhrwTh8NEcPBYEhIe8WCloj2cTqiuBovl3Mu5AlJbF18KQSoV+PvXL3p92x6fuXQ0FJ1rvbS0CCG6ii4Zwvz8/Bg1ahSbNm1yTVvhdDrZtGkT9957r3eLa3Ds+WMcffooAPtXR6KoSrgkJIS+AQGten1+/l8pL/8StVrf0A3ZJT8qn+BwQGXl6cVsPv34fAHqfEt1dX048gZ/fwgIuPDSGH5aG45aG6i0Wgk6QgjhDj77zV5VVUVOTo7reV5eHrt37yY8PJzExETS0tKYO3cuo0ePZuzYsaxatQqLxeK6WtKbTv31FLm/yQWg7/K+LBlcCma4qZWTwtbU5JKT81D96/suIzAwxWO1+ipFqQ85FRX1S3l50/B0dpg637bqas/XGxhYvxgMpx83Pm9NWGpNqGrcV7qshBCie/DZELZz506mTJniet44OH7u3LmsX7+eOXPmUFxczNKlSykoKGDEiBF8/vnnzQbrd7aK7ys4tPAQAImLE3Euimb7f/NQAzdGRV3w9YriJDNzPk6nBaNxIr17L/JwxZ7jcNSHp9LS02GqMVC15nldnXvr8fOD4GAICan/GRzcNDCdazk7WJ29BARIy5AQQoi2UymdeffqbsBsNmM0GjGZTISEhDTZ5qh2sHPETmqya4i5NYaUN1L447FjLMnLY2poKJtGjLjg8U+ceImcnAdQqwMZM+ZHAgL6eeidtI2igMkEJSWtX8rKOn7lmkYDoaH1S0hI0wB1dqC60GM/ubBUCCF6rPN9f3uLz7aEdUV5j+VRk12DX7wfA14egEql4u2Ge0W2piuyujqL3Nz6iWb793++UwKYzVY/g3BBQdOlpXVnzFnbJiEhEBZWvzQGqtDQ1j0PDJRWJiGEEN2ThDA3MW01ceLFEwAk/zUZXaiOgxYLeywWdCoVP71AV6TTaefgwbk4nbWEhV1JfPyvOlyT0wmFhXD8OBw71vLPgoK2HTMoCCIjW7+Eh9dfsSaEEEKIpiSEuYHT5iRzfiYoEDM3hohrIwB4q6EVbHp4OOEXSCLHjz9PZeV/0WhCSE7+2znvIXk2qxXy8iA7G3Jy6pfsbDh8uD5ktWZclZ8fxMVBbGzLS+O26Oj68U9CCCGE6DgJYW5Q8lEJNVk16KJ1DHhxAFA/z1druyKrqvZy5MhSAAYOXI1e33xGfqsVsrJg717Yt+/0cvTo+cddqdUQHw+JiZCQ0PLPiAjp8hNCCCE6m4QwNyh4vb5PL+7OOHRh9S1eGVVVZNfUEKBWc11ExDlf63TayMyci6LUERExi5iY27HZYNcu2LYN/vtf2LMHDh2qv9qwJUFBMHAgDBhQvwwcCP37Q1JSfQDTyqcshBBC+Bz5eu4g6ykrZZ+XARB7x+nZ8N9qmM3/JxERBJ0nBR09+gxVVbtwOsN5++2/sHmzivT0lgfBh4bCsGEwfHj9z6FDISWlvptQWrKEEEKIrkVCWAcVvFEATgi5LATDIAMATkXhneJiAG5uoSvSbocffoAfftjJuHHPoNHAU0/9mc2bT4e4iAgYP75+GTmyPnjFx0vYEkIIIboLCWEdoCjK6a7I+XGu9T+YTJywWgnRaJgRXn+zbqezPni99Ra89x6YTLX89a9z0WgcfPPNHMrKbmThwtPBa8AACVxCCCFEdyYhrAPM28zUHKpBbVAT9fPTU1A0XhV5Q2Qk1ioNa16Dl1+uH0Tf6IEHlpKUdACHI4a7717DH/7Q2dULIYQQwpskhHVAYytY1M+j0AbX/yrtTifvNXRFmj6MofdyqKqq3z8kBGbPhl/84gd0uucBSE39K5GR5x64L4QQQojuSW4F3E6OWgdF79S3eMXNO90V+VVZBSV1dahMOjY+FkpVFQwZAq+9Vj8x6muvWQgJuQNQiImZS2TkLO+8ASGEEEJ4lbSEtZMt34aj0oFar8Y4wQjA/v0w9/MiGAXK5ijGjFLzhz/A9Omnx3dlZy+mpiYHf//eDBiwyntvQAghhBBeJS1hHaTSqlCpVWzeDKPGOyhOru+KXDQ8mm3b4OqrTwew8vJvOHnyFQCSk/+GThfqnaKFEEII4XXSEuYG6ekwaxZYU8sgyEGcxp+V84yoz7i60W43k5k5D4D4+IWEh1/lpWqFEEII4QukJay9Gm4V5HTWt3ZVVkLUnPoxYr+Ii0J91vwSOTlpWK3H0Ov70q/fis6uVgghhBA+RkJYB1XXQEkJjBhvp2p4KQA3x8Q02ae09DMKCv4GqEhJWY9WG+SFSoUQQgjhSySEdZBTgeRkuGtDKTWKkwEBAYwMOh2y6urKyMr6JQC9ez9AaOhEb5UqhBBCCB8iIaydFEVxPV6wAD6rre+KvDk6GtUZXZHZ2fdhs+UTEJBM377PdHqdQgghhPBNEsI6SAFqtHV8UVZ/E++bzrhXZHHxPykqehNQM3jwBjSaAO8UKYQQQgifIyHMDX4MLaZOUbgoMJAhgYEA2GxFHDq0EIDExMWEhIzzZolCCCGE8DESwtxgd/jprkio76o8dOhu6upKCAy8iKSkpd4sTwghhBA+SEJYB5WFK+QEVQAwpyGEFRW9SUnJB6hUWlJSNqBW+3uxQiGEEEL4IglhHfT9ZAVFBZeEhNA3IACr9STZ2fcC0KfP4wQHj/BugUIIIYTwSTJjfgdtmVp/leTN0dEoikJW1gLs9gqCg8eQmLjYy9UJIYQQXZeiKK7ZCDr6uLKysrPLvyAJYe2lQH4sZA0FlQI/j4oiP/9vlJX9G5XKv6EbUn69onto/GPmdDpxOp2ux+f62d5tZ/709aWr1OlL7/nM/5a642Nvn787Pe4pJCV0wLdT6n8OqAol1JnPzsMPAtCv3zMEBg72YmW+ofGPtt1ux26343A4XI8v9NzhcOBwOHA6nef82d5t3np9R4NJZ4Sfc20TQgjhfhLCOmDTFfU/R1ZEkpV1Ow5HFSEhl9G79wNuP5eiKNhsNqqrq6mpqWn2s7a2FpvNRl1dHTabrcly9rq27tPWAHXmOiHUajUqlarJz5bWqVSqZo99eekqdfraewa69WNvn18en/txZWUlMWfdVtDbJIS1U5atltz+oK2DqzTvU1HxLWq1gZSU9ahUGtd+ilLfD33q1ClOnTpFWVkZJpOpxaWysvKcIau6urpbtUhoNBq0Wq1rOfu5Wq1Go9Gg0Whcjxu/vM9ed75tbd3fU8c6cznzy+x8gcRXtrX3WGf+8RNCCG+rq6vzdgnN9MgQdsMNN7B582auuOIK3n///XYd4wtrOQDT9p0kKfV3AISGLubxx//C8ePHOXXqFPn5+Zw6dYrq6mq31Q71LQsGg4GAgADXT39/f/z9/fHz83MtOp2uyfP2rNfpdE3CUUuBqa3PG7+ghRBCiJ6sR4awRYsWMX/+fDZs2NDuY5idTtQqB7clLEetriE09ApWrcrl9dfXt7i/0WgkLi6OyMhIjEZji0twcDAGg6FZwGr82fhYp9NJiBFCCCG6uB4ZwiZPnszmzZs7eBSFG3mX+Mj9OBzBpKSsw2xOA+DGG29k9uzZxMfHEx8fT1xcHAaDocN1CyGEEKL76HKTtW7ZsoWZM2cSHx+PSqVi48aNzfZZs2YNSUlJ6PV6xo0bx44dO9xeR5BymHm8DsCpU6vQ6xNdY7YmT57MnDlzmDBhAv3795cAJoQQQohmulwIs1gspKamsmbNmha3v/POO6SlpfH444+TkZFBamoq06dPp6ioyK119LJ/gh91HMkfQ0XFPKBnzW0ihBBCiI7pct2RM2bMYMaMGefcvnLlShYsWMC8efXBaO3atXz66aesW7eOxYvbPoO91WrFarW6nptMJgBsVVVY/OHIyf4YnJWYzaevvKitrcVsNrf5XEIIIYTwjMbvZZ9qMFG6MED58MMPXc+tVqui0WiarFMURbn99tuVWbNmNVn37bffKj/96U8veI7HH39cAWSRRRZZZJFFlm6wHD582B0RxC26XEvY+ZSUlOBwOJpNxhYTE0NmZqbr+bRp09izZw8Wi4XevXvz3nvvMX78+BaPuWTJEtLS0lzPKyoq6NOnD8eOHcNoNHrmjYhWMZvNJCQkcPz4cUJCQrxdTo8mn4Vvkc/Dd8hn4TtMJhOJiYmEh4d7uxSXbhXCWuvrr79u9b6N82+dzWg0yv9QPiIkJEQ+Cx8hn4Vvkc/Dd8hn4TvUat8ZDu87lbhBZGQkGo2GwsLCJusLCwuJjY31UlVCCCGEEM11qxDm5+fHqFGj2LRpk2ud0+lk06ZN5+xuFEIIIYTwhi7XHVlVVUVOTo7reV5eHrt37yY8PJzExETS0tKYO3cuo0ePZuzYsaxatQqLxeK6WrKj/P39efzxx1vsohSdSz4L3yGfhW+Rz8N3yGfhO3zxs1Apii9dq3lhmzdvZsqUKc3Wz507l/Xr1wPwyiuvsGLFCgoKChgxYgSrV69m3LhxnVypEEIIIcS5dbkQJoQQQgjRHXSrMWFCCCGEEF2FhDAhhBBCCC+QECaEEEII4QUSwtpgzZo1JCUlodfrGTduHDt27PB2SV3K8uXLGTNmDMHBwURHR3P99deTlZXVZJ/a2lruueceIiIiCAoK4qc//Wmzed+OHTvGtddei8FgIDo6mt/85jfY7fYm+2zevJmRI0fi7+/PgAEDXBdtnEk+z9OeffZZVCoVDzzwgGudfBad6+TJk9x6661EREQQEBDA8OHD2blzp2u7oigsXbqUuLg4AgICmDZtGtnZ2U2OUVZWxi233EJISAihoaHceeedVFVVNdnnxx9/ZMKECej1ehISEnjuueea1fLee++RkpKCXq9n+PDhfPbZZ5550z7I4XDw2GOP0bdvXwICAujfvz9PPfVUk/sNymfhGVu2bGHmzJnEx8ejUqnYuHFjk+2+9HtvTS2t4rUbJnUxb7/9tuLn56esW7dO2b9/v7JgwQIlNDRUKSws9HZpXcb06dOV119/Xdm3b5+ye/du5ZprrlESExOVqqoq1z4LFy5UEhISlE2bNik7d+5ULrnkEuXSSy91bbfb7cqwYcOUadOmKbt27VI+++wzJTIyUlmyZIlrn9zcXMVgMChpaWnKgQMHlJdfflnRaDTK559/7tpHPs/TduzYoSQlJSkXXXSRsmjRItd6+Sw6T1lZmdKnTx/ljjvuUP773/8qubm5yhdffKHk5OS49nn22WcVo9GobNy4UdmzZ48ya9YspW/fvkpNTY1rn6uvvlpJTU1Vtm/frnz33XfKgAEDlJtvvtm13WQyKTExMcott9yi7Nu3T3nrrbeUgIAA5S9/+Ytrnx9++EHRaDTKc889pxw4cED5/e9/r+h0OmXv3r2d88vwsmeeeUaJiIhQPvnkEyUvL0957733lKCgIOWll15y7SOfhWd89tlnyqOPPqp88MEHCtDsPtC+9HtvTS2tISGslcaOHavcc889rucOh0OJj49Xli9f7sWquraioiIFUP7zn/8oiqIoFRUVik6nU9577z3XPgcPHlQAZdu2bYqi1P9PqlarlYKCAtc+f/7zn5WQkBDFarUqiqIojzzyiDJ06NAm55ozZ44yffp013P5POtVVlYqAwcOVL766itl0qRJrhAmn0Xn+u1vf6tcfvnl59zudDqV2NhYZcWKFa51FRUVir+/v/LWW28piqIoBw4cUADlf//7n2uff//734pKpVJOnjypKIqi/OlPf1LCwsJcn0/juZOTk13Pb7zxRuXaa69tcv5x48Ypv/rVrzr2JruIa6+9Vpk/f36TdbNnz1ZuueUWRVHks+gsZ4cwX/q9t6aW1pLuyFaw2Wykp6czbdo01zq1Ws20adPYtm2bFyvr2kwmE4DrZqrp6enU1dU1+T2npKSQmJjo+j1v27aN4cOHN7lJ+/Tp0zGbzezfv9+1z5nHaNyn8RjyeZ52zz33cO211zb7fcln0bk++ugjRo8ezc9//nOio6O5+OKLefXVV13b8/LyKCgoaPJ7MhqNjBs3rsnnERoayujRo137TJs2DbVazX//+1/XPhMnTsTPz8+1z/Tp08nKyqK8vNy1z/k+s+7u0ksvZdOmTRw6dAiAPXv28P333zNjxgxAPgtv8aXfe2tqaS0JYa1QUlKCw+Fo8mUDEBMTQ0FBgZeq6tqcTicPPPAAl112GcOGDQOgoKAAPz8/QkNDm+x75u+5oKCgxc+hcdv59jGbzdTU1Mjn2eDtt98mIyOD5cuXN9smn0Xnys3N5c9//jMDBw7kiy++4O677+b+++9nw4YNwOnf5/l+TwUFBURHRzfZrtVqCQ8Pd8tn1lM+j8WLF3PTTTeRkpKCTqfj4osv5oEHHuCWW24B5LPwFl/6vbemltbqcrctEt3DPffcw759+/j++++9XUqPdPz4cRYtWsRXX32FXq/3djk9ntPpZPTo0SxbtgyAiy++mH379rF27Vrmzp3r5ep6lnfffZd//OMfvPnmmwwdOpTdu3fzwAMPEB8fL5+FcDtpCWuFyMhINBpNsyvDCgsLiY2N9VJVXde9997L/7d39zFNXf8fwN+FWkALgkJaFCmoDBF5RmdFBZVY3cbQzGh8AFETdMJARabLwjAw/RbDUCEsy7JFzWZ82nxgc7KJoA42QVkLGkslTGSbdTqUKWoi2M/vj/248wpocc4K+7ySJr3nnnPu555D6Sf3qV9//TXKysrg4eEhlCuVSty/fx8tLS2i+g+Ps1Kp7HIeOtY9ro6TkxMcHBx4PvHX6cZr164hNDQUUqkUUqkUJ0+eRH5+PqRSKRQKBc/Fc+Tu7o7Ro0eLyvz8/NDU1ATg7/F83DgplUpcu3ZNtL69vR03btx4JnP2X5mP9PR04WhYQEAA4uLisHr1auGIMc+FdbxI425JLJbiJMwCMpkMYWFhOH78uFBmNptx/PhxqNVqK0bWuxARkpOTcfDgQZSWlsLb21u0PiwsDP369RONs9FoRFNTkzDOarUa586dE33Qjh07BicnJ+FLTK1Wi/roqNPRB88nMG3aNJw7dw56vV54hYeHY+HChcJ7novnJyIiotPjWi5evAiVSgUA8Pb2hlKpFI3TrVu3UFlZKZqPlpYWVFdXC3VKS0thNpuF385Vq9U4deoU2trahDrHjh2Dr68vXFxchDqPm7O+7u7du7CxEX812trawmw2A+C5sJYXadwticViPbqM/z9sz549ZGdnRzt27KALFy5QYmIiOTs7i+4MY4/35ptv0sCBA+nEiRNkMpmE1927d4U6K1asIE9PTyotLaWzZ8+SWq0mtVotrO94LML06dNJr9dTcXExubm5dflYhPT0dDIYDFRYWNjlYxF4PsUevjuSiOfieaqqqiKpVEobN26k+vp62rVrF/Xv358+//xzoY5WqyVnZ2c6fPgw1dbWUmxsbJe354eEhFBlZSWVl5eTj4+P6Pb8lpYWUigUFBcXR+fPn6c9e/ZQ//79O92eL5VKKTc3lwwGA2VmZvbpxyI8avHixTR06FDhERUHDhwgV1dXevvtt4U6PBf/jtu3b5NOpyOdTkcAKC8vj3Q6HV2+fJmIXqxxtyQWS3AS1gMFBQXk6elJMpmMxo0bR6dPn7Z2SL0KgC5f27dvF+rcu3ePVq5cSS4uLtS/f3+aPXs2mUwmUT+NjY00c+ZMcnBwIFdXV0pLS6O2tjZRnbKyMgoODiaZTEbDhw8XbaMDz6fYo0kYz8Xz9dVXX9GYMWPIzs6ORo0aRR9//LFovdlspoyMDFIoFGRnZ0fTpk0jo9EoqtPc3Ezz588nuVxOTk5OtGTJErp9+7aoTk1NDU2cOJHs7Oxo6NChpNVqO8Wyb98+eumll0gmk5G/vz8dOXLk2e/wC+rWrVuUmppKnp6eZG9vT8OHD6d3331X9EgDnot/R1lZWZffEYsXLyaiF2vcLYnFEhKihx4DzBhjjDHGngu+JowxxhhjzAo4CWOMMcYYswJOwhhjjDHGrICTMMYYY4wxK+AkjDHGGGPMCjgJY4wxxhizAk7CGGOMMcasgJMwxhhjjDEr4CSMMdYjjY2NkEgk0Ov11g5FUFdXh/Hjx8Pe3h7BwcHWDocxxizCSRhjvUxCQgIkEgm0Wq2o/NChQ5BIJFaKyroyMzMxYMAAGI3GTj+829d5eXlh69at1g4DwN8JesfL0dER/v7+SEpKQn19vbXDY+yFw0kYY72Qvb09cnJycPPmTWuH8szcv3//qds2NDRg4sSJUKlUGDx48DOM6vGICO3t7c9te/+mfzL+jyopKYHJZEJNTQ02bdoEg8GAoKCg/1yCzNiTcBLGWC8UHR0NpVKJ//3vf93W2bBhQ6dTc1u3boWXl5ewnJCQgFmzZmHTpk1QKBRwdnZGVlYW2tvbkZ6ejkGDBsHDwwPbt2/v1H9dXR0mTJgAe3t7jBkzBidPnhStP3/+PGbOnAm5XA6FQoG4uDj88ccfwvqoqCgkJydj1apVcHV1hUaj6XI/zGYzsrKy4OHhATs7OwQHB6O4uFhYL5FIUF1djaysLEgkEmzYsKHLfjq2l5ycjIEDB8LV1RUZGRl4+OdzP/vsM4SHh8PR0RFKpRILFizAtWvXhPUnTpyARCLB0aNHERYWBjs7O5SXl6OhoQGxsbFQKBSQy+UYO3YsSkpKRNv38vLC+++/j/j4eMjlcqhUKhQVFeH69euIjY2FXC5HYGAgzp49K2pXXl6OSZMmwcHBAcOGDUNKSgru3Lkj7NPly5exevVq4eiTJe064snOzkZ8fDycnJyQmJiI+/fvIzk5Ge7u7rC3t4dKpXrs31h3Bg8eDKVSieHDhyM2NhYlJSV4+eWXsWzZMjx48KDH/THWV3ESxlgvZGtri02bNqGgoAC//vrrP+qrtLQUV65cwalTp5CXl4fMzEy89tprcHFxQWVlJVasWIHly5d32k56ejrS0tKg0+mgVqsRExOD5uZmAEBLSwumTp2KkJAQnD17FsXFxfj9998xd+5cUR87d+6ETCZDRUUFPvrooy7j27ZtGz744APk5uaitrYWGo0Gr7/+unB6y2Qywd/fH2lpaTCZTFi7dm23+7pz505IpVJUVVVh27ZtyMvLwyeffCKsb2trQ3Z2NmpqanDo0CE0NjYiISGhUz/r16+HVquFwWBAYGAgWltb8corr+D48ePQ6XSYMWMGYmJi0NTUJGq3ZcsWREREQKfT4dVXX0VcXBzi4+OxaNEi/PTTTxgxYgTi4+OFxLChoQEzZszAG2+8gdraWuzduxfl5eVITk4GABw4cAAeHh7IysqCyWSCyWSyqF2H3NxcBAUFQafTISMjA/n5+SgqKsK+fftgNBqxa9cuUdL+tGxsbJCamorLly+jurr6H/fHWJ9BjLFeZfHixRQbG0tEROPHj6elS5cSEdHBgwfp4Y90ZmYmBQUFidpu2bKFVCqVqC+VSkUPHjwQynx9fWnSpEnCcnt7Ow0YMIB2795NRESXLl0iAKTVaoU6bW1t5OHhQTk5OURElJ2dTdOnTxdt+5dffiEAZDQaiYgoMjKSQkJCnri/Q4YMoY0bN4rKxo4dSytXrhSWg4KCKDMz87H9REZGkp+fH5nNZqFs3bp15Ofn122bM2fOEAC6ffs2ERGVlZURADp06NAT4/b396eCggJhWaVS0aJFi4Rlk8lEACgjI0Mo+/HHHwkAmUwmIiJatmwZJSYmivr9/vvvycbGhu7duyf0u2XLFlEdS9vNmjVLVOett96iqVOnisaoJzr+NnQ6Xad1BoOBANDevXufqm/G+iI+EsZYL5aTk4OdO3fCYDA8dR/+/v6wsfn7X4FCoUBAQICwbGtri8GDB4tOywGAWq0W3kulUoSHhwtx1NTUoKysDHK5XHiNGjUKwF9HaTqEhYU9NrZbt27hypUriIiIEJVHREQ81T6PHz9edMpOrVajvr5eOEVWXV2NmJgYeHp6wtHREZGRkQDQ6YhWeHi4aLm1tRVr166Fn58fnJ2dIZfLYTAYOrULDAwU3isUCgAQjXVHWcdY19TUYMeOHaJx1Gg0MJvNuHTpUrf7aWm7R/cjISEBer0evr6+SElJwXfffdftNnqK/v/o3n/15hHGuiK1dgCMsac3efJkaDQavPPOO51Om9nY2IiudwL+Ot32qH79+omWJRJJl2Vms9niuFpbWxETE4OcnJxO69zd3YX3AwYMsLjPf9udO3eg0Wig0Wiwa9cuuLm5oampCRqNptNF64/GvXbtWhw7dgy5ubkYOXIkHBwcMGfOnE7tHh7XjmSkq7KOsW5tbcXy5cuRkpLSKV5PT89u98XSdo/uR2hoKC5duoSjR4+ipKQEc+fORXR0NL744otut2WpjqTZ29v7H/fFWF/BSRhjvZxWq0VwcDB8fX1F5W5ubrh69SqISPhyf5bP9jp9+jQmT54MAGhvb0d1dbVwzVFoaCi+/PJLeHl5QSp9+n8zTk5OGDJkCCoqKoSjUgBQUVGBcePG9bi/ysrKTvvg4+MDW1tb1NXVobm5GVqtFsOGDQOAThfJd6eiogIJCQmYPXs2gL+SoMbGxh7H96jQ0FBcuHABI0eO7LaOTCbrdLG7Je264+TkhHnz5mHevHmYM2cOZsyYgRs3bmDQoEE97quD2WxGfn4+vL29ERIS8tT9MNbX8OlIxnq5gIAALFy4EPn5+aLyqKgoXL9+HZs3b0ZDQwMKCwtx9OjRZ7bdwsJCHDx4EHV1dUhKSsLNmzexdOlSAEBSUhJu3LiB+fPn48yZM2hoaMC3336LJUuW9PjuuPT0dOTk5GDv3r0wGo1Yv3499Ho9UlNTexxzU1MT1qxZA6PRiN27d6OgoEDox9PTEzKZDAUFBfj5559RVFSE7Oxsi/r18fHBgQMHoNfrUVNTgwULFvToyGF31q1bhx9++AHJycnQ6/Wor6/H4cOHRRfYe3l54dSpU/jtt9+Eu08tadeVvLw87N69G3V1dbh48SL2798PpVIJZ2fnHsXd3NyMq1evCuMYHR2NqqoqfPrpp7C1te3xODDWV3ESxlgfkJWV1elL38/PDx9++CEKCwsRFBSEqqqqx9452FNarRZarRZBQUEoLy9HUVERXF1dAUA4evXgwQNMnz4dAQEBWLVqFZydnUXXn1kiJSUFa9asQVpaGgICAlBcXIyioiL4+Pj0OOb4+Hjcu3cP48aNQ1JSElJTU5GYmAjgryOHO3bswP79+zF69GhotVrk5uZa1G9eXh5cXFwwYcIExMTEQKPRIDQ0tMfxPSowMBAnT57ExYsXMWnSJISEhOC9997DkCFDhDpZWVlobGzEiBEj4ObmZnG7rjg6OmLz5s0IDw/H2LFj0djYiG+++UaYs4SEBERFRT0x7ujoaLi7uyMgIADr16+Hn58famtrMWXKlKcfDMb6IAk9etEIY4z1QVFRUQgODn5hni7fG0VGRmLKlCndPouNMdYzfE0YY4yxJ/rzzz/R0NCAI0eOWDsUxvoMTsIYY4w90cCBA//xg4EZY2J8OpIxxhhjzAr4wnzGGGOMMSvgJIwxxhhjzAo4CWOMMcYYswJOwhhjjDHGrICTMMYYY4wxK+AkjDHGGGPMCjgJY4wxxhizAk7CGGOMMcas4P8AjeB/Ssr3N4kAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "daA1dAPsLD0h"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}