{
    "cells":
      [
        {
          "cell_type": "code",
          "execution_count": 1,
          "id": "7478fb00",
          "metadata": {},
          "outputs": [],
          "source": [
            "import matplotlib.pyplot as plt\n",
            "import numpy as np\n",
            "import scipy.stats as sc"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "7a6aed8c",
          "metadata": {},
          "source": [
            "### Barplot"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 2,
          "id": "467b09c4",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  "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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "u = [1, 2, 3, 4, 5, 6]\n",
            "v = [0.2, 0.3, 0.1, 0.2, 0.1, 0.1]\n",
            "ax.bar(u, v, width=0.05)\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "ax.spines[\"bottom\"].set_visible(True)\n",
            "ax.spines[\"left\"].set_visible(True)\n",
            "fig.savefig(\"pmf.png\")"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "b74ab662",
          "metadata": {},
          "source": [
            "### CDF (discrete)"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 3,
          "id": "44c9a299",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  "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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "ax.plot(\n",
            "    np.sort(np.hstack((0, u, u)))[:-1],\n",
            "    np.sort(np.hstack((0, 0, np.cumsum(v), np.cumsum(v))))[:-2],\n",
            ")\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "ax.spines[\"bottom\"].set_visible(True)\n",
            "ax.spines[\"left\"].set_visible(True)\n",
            "fig.savefig(\"discretecdf.png\")"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 4,
          "id": "fe1b5cce",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "u = [1, 2, 3, 4, 5, 6]\n",
            "v = [1.0 / 6.0 for i in range(6)]\n",
            "ax.bar(u, v, width=0.05)\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "ax.spines[\"bottom\"].set_visible(True)\n",
            "ax.spines[\"left\"].set_visible(True)\n",
            "fig.savefig(\"uniformdiscretpmf.png\")"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 5,
          "id": "2367f333",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "from math import comb\n",
            "\n",
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "n = 10\n",
            "p = 0.6\n",
            "\n",
            "u = np.arange(n + 1)\n",
            "Cnp = np.array([comb(n + 1, i) for i in range(n + 1)])\n",
            "\n",
            "v = Cnp * p**u * (1 - p) ** (n - u)\n",
            "\n",
            "ax.bar(u, v, width=0.09)\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "ax.spines[\"bottom\"].set_visible(True)\n",
            "ax.spines[\"left\"].set_visible(True)\n",
            "ax.set_title(\"Binomial (10,0.6)\")\n",
            "fig.savefig(\"binomialpmf.png\")"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "86143aa8",
          "metadata": {},
          "source": [
            "### Density and proba"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 6,
          "id": "62cf53a7",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "\n",
            "v = np.linspace(-5, 5, 100)\n",
            "lim = 1\n",
            "w = np.linspace(-5, lim, 100)\n",
            "\n",
            "plt.plot(v, sc.norm.pdf(v))\n",
            "plt.fill_between(w, sc.norm.pdf(w), alpha=0.5)\n",
            "plt.text(-1.5, 0.1, r\"$F(z)=P(Z\\leq z)$\")\n",
            "plt.text(lim, -0.015, \"z\")\n",
            "plt.text(lim, sc.norm.pdf(lim), \"f(z)\")\n",
            "plt.plot([lim, lim], [0, sc.norm.pdf(lim)])\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "plt.savefig(\"density.png\")"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "2bcfacee",
          "metadata": {},
          "source": [
            "### Density infinitesimal"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 7,
          "id": "4b385e13",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 500x500 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(5, 5))\n",
            "\n",
            "v = np.linspace(-5, 5, 100)\n",
            "limmin = 0.8\n",
            "limmax = 1\n",
            "w = np.linspace(limmin, limmax, 100)\n",
            "\n",
            "plt.plot(v, sc.norm.pdf(v))\n",
            "plt.fill_between(w, sc.norm.pdf(limmin), 0, alpha=0.5)\n",
            "plt.text(1.4, 0.2, r\"$P(z \\leq Z\\leq z+dz)\\simeq f(z)dz$\")\n",
            "plt.text(limmin - 0.15, -0.015, \"z\")\n",
            "plt.text(limmax, -0.015, \"z+dz\")\n",
            "plt.text(limmin, sc.norm.pdf(limmin), \"f(z)\")\n",
            "plt.plot([limmin, limmin], [0, sc.norm.pdf(limmin)])\n",
            "plt.plot([limmax, limmax], [0, sc.norm.pdf(limmax)])\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "plt.savefig(\"density.png\")"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 8,
          "id": "85000410",
          "metadata": {},
          "outputs": [],
          "source": [
            "colors = plt.rcParams[\"axes.prop_cycle\"].by_key()[\"color\"]\n",
            "cc = colors[0]"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 9,
          "id": "2622dae1",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "a = 4\n",
            "b = 8\n",
            "\n",
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "\n",
            "plt.plot([a - 3, a], [0, 0], c=cc)\n",
            "plt.plot([b, b + 3], [0, 0], c=cc)\n",
            "plt.plot([a, a], [0, 1 / (b - a)], c=cc)\n",
            "plt.plot([b, b], [0, 1 / (b - a)], c=cc)\n",
            "plt.plot([a, b], [1 / (b - a), 1 / (b - a)], c=cc)\n",
            "plt.title(r\"Uniform on $[4,8]$\")\n",
            "plt.text(1.5, 0.25, r\"$f(x)=\\frac{1}{b-a}$\", c=cc)\n",
            "\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "plt.savefig(\"uniformpdf.png\")"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 10,
          "id": "f9600a5d",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "\n",
            "plt.plot([a - 3, a], [0, 0], c=cc)\n",
            "plt.plot([b, b + 3], [1, 1], c=cc)\n",
            "plt.plot([a, b], [0, 1], c=cc)\n",
            "plt.title(r\"c.d.f of the uniform on $[4,8]$\")\n",
            "plt.text(3, 0.5, r\"$F(x)=\\frac{x-a}{b-a}$\", c=cc)\n",
            "\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "plt.savefig(\"uniformcdf.png\")"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "0827a30c",
          "metadata": {},
          "source": [
            "### CDF continuous"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 11,
          "id": "23c3f550",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "ax.plot(v, sc.norm.cdf(v))\n",
            "ax.spines[\"top\"].set_visible(False)\n",
            "ax.spines[\"right\"].set_visible(False)\n",
            "fig.savefig(\"cdf.png\")"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "7e200afe",
          "metadata": {},
          "source": [
            "### Law of large numbers "
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 12,
          "id": "93dad7b3",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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Kam3/9ttvw8vLC0ZGRnB1dcWUKVOQl5dXj1VX0uEcCBFpIZUCJDc3F9999x3mzp2LnJwcAMCxY8dw/fp1tRb3oJCQEJw5cwbR0dGIjIzEwYMHMX78+Brb37hxAzdu3MCyZctw+vRp/Pjjj4iKisLYsWM1VmNNmB9EpI0kQgihzAYnT55Enz59YGFhgStXriAlJQXu7u6YP38+0tLSsHHjRrUXmZycjNatWyMhIQGdOnUCAERFRSE4OBjXrl2Dk5NTnT5ny5YtGDFiBO7duwc9Pb06bZOfnw8LCwvk5eXB3Ny8TtsUl1XAe0GU/P2hd3rDxdq4TtsSEWmaKt9r1VF6BDJjxgyEhobiwoULMDQ0lC8PDg7GwYMHVS6kNnFxcbC0tJSHBwD06dMHOjo6iI+Pr/Pn3P9h1RYeJSUlyM/PV3gREVFVSgdIQkICJkyYUGW5s7MzMjMz1VLUwzIzM2FnZ6ewTE9PD9bW1nXeZ3Z2NhYvXlzrYS8ACA8Ph4WFhfzl4uKict338RAWEWkjpQNEKpVW+1f5+fPnYWur3PUOc+bMgUQiqfV17tw5ZUusIj8/H/3790fr1q2xaNGiWtvOnTsXeXl58ld6evpj75+T6ESkjeo2EfCAgQMH4sMPP8Rvv/0GoPIq67S0NLz77rsYMmSIUp81c+ZMhIaG1trG3d0dDg4OyMrKUlheXl6OnJwcODg41Lr93bt3ERQUBDMzM/z555/Q19evtb1UKoVUKq1T/XXF/CAibaR0gCxfvhyvvPIK7OzsUFRUhJ49eyIzMxP+/v5YsmSJUp9la2tbp1GLv78/cnNzkZiYiI4dOwIA9u7dC5lMBj8/vxq3y8/PR2BgIKRSKbZv364wZ1OfOAIhIm2kdIBYWFggOjoaMTExOHnyJAoKCtChQwf06dNHE/UBAFq1aoWgoCCMGzcOa9euRVlZGcLCwjB8+HD5GVjXr19HQEAANm7ciM6dOyM/Px99+/ZFYWEhfv75Z4UJcVtbW+jq6mqs3ocxPohIGykdIPd1794d3bt3V2cttYqIiEBYWBgCAgKgo6ODIUOG4IsvvpCvLysrQ0pKCgoLCwFUXpdy/wwtDw8Phc9KTU2Fm5tbvdXOBCEibaR0gDz4pf0giUQCQ0NDeHh4oEePHmr/C9/a2hqbNm2qcb2bmxsevKSlV69eUPISF43hISwi0kZKB8jKlStx69YtFBYWwsrKCgBw584dGBsbw9TUFFlZWXB3d8e+ffvUcgqsNmB8EJE2Uvo03o8//hjPPvssLly4gNu3b+P27ds4f/48/Pz8sGrVKqSlpcHBwQHTp0/XRL1NEp8HQkTaSOkRyPz58/HHH3/g6aefli/z8PDAsmXLMGTIEFy+fBlLly5V+pRebcb4ICJtpPQIJCMjA+Xl5VWWl5eXy68Kd3Jywt27dx+/Oi3BAQgRaSOlA6R3796YMGECjh8/Ll92/PhxTJw4Ec8//zwA4NSpU2jRooX6qmziJByDEJEWUjpAvv/+e1hbW6Njx47yq7Y7deoEa2trfP/99wAAU1NTLF++XO3FNlWSJvPUFSKiulN6DsTBwQHR0dE4d+4czp8/DwDw8vKCl5eXvE3v3r3VV6EW4PiDiLSRyhcSent7w9vbW521aC2ehUVE2kilALl27Rq2b9+OtLQ0lJaWKqxbsWKFWgrTJowPItJGSgfInj17MHDgQLi7u+PcuXPw8fHBlStXIIRAhw4dNFFjk8cBCBFpI6Wnd+fOnYtZs2bh1KlTMDQ0xB9//IH09HT07NkTQ4cO1USNTR7PwiIibaR0gCQnJ2PUqFEAKp8KWFRUBFNTU3z44Yf49NNP1V6gNuAIhIi0kdIBYmJiIp/3cHR0xKVLl+TrsrOz1VdZE8bAIKIngdJzIF26dEFMTAxatWqF4OBgzJw5E6dOncLWrVvRpUsXTdTY5DFQiEgbKR0gK1asQEFBAQDggw8+QEFBAX799Vd4enryDKwacA6EiLSRUgFSUVGBa9euoW3btgAqD2etXbtWI4VpE45AiEgbKTUHoquri759++LOnTuaqkcrMT+ISBspPYnu4+ODy5cva6IWrcUr0YlIGykdIB999BFmzZqFyMhIZGRkID8/X+FFVTE+iEgbKT2JHhwcDAAYOHCgwl/WQghIJBJUVFSorzotwQEIEWkjpQNk3759mqhDq/EQFhFpI6UDpGfPnpqog4iImhiVHnV06NAhjBgxAl27dsX169cBAD/99BNiYmLUWhwRETVeSgfIH3/8gcDAQBgZGeHYsWMoKSkBAOTl5eHjjz9We4FERNQ4qXQW1tq1a/Htt99CX19fvrxbt244duyYWosjIqLGS+kASUlJQY8ePaost7CwQG5urjpqIiKiJkDpAHFwcMDFixerLI+JiYG7u7taiiIiosZP6QAZN24cpk6divj4eEgkEty4cQMRERGYNWsWJk6cqIkaiYioEVL6NN45c+ZAJpMhICAAhYWF6NGjB6RSKWbNmoW3335bEzUSEVEjpHSASCQSvPfee5g9ezYuXryIgoICtG7dGqamppqoj4iIGimlD2H9/PPPKCwshIGBAVq3bo3OnTszPIiInkBKB8j06dNhZ2eH119/HTt37uS9r4iInlBKB0hGRgY2b94MiUSCYcOGwdHREZMnT8bhw4c1UV+TxCcQEtGTQOkA0dPTw4svvoiIiAhkZWVh5cqVuHLlCnr37o2nn35aEzUSEVEjpPQk+oOMjY0RGBiIO3fu4OrVq0hOTlZXXURE1MipdDPFwsJCREREIDg4GM7Ozvj888/x0ksv4cyZM+quj4iIGimlRyDDhw9HZGQkjI2NMWzYMCxYsAD+/v6aqI2IiBoxpQNEV1cXv/32GwIDA6Grq6uJmoiIqAlQOkAiIiI0UQcRETUxKk2i37t3DwcOHEBaWhpKS0sV1k2ZMkUthRERUeOmdIAcP34cwcHBKCwsxL1792BtbY3s7GwYGxvDzs6OAUJE9IRQ6Ur0AQMG4M6dOzAyMsJ///2Hq1evomPHjli2bJkmaiQiokZI6QA5ceIEZs6cCR0dHejq6qKkpAQuLi5YunQp5s2bp4kaiYioEVI6QPT19aGjU7mZnZ0d0tLSAFQ+kTA9PV291RERUaOl9ByIr68vEhIS4OnpiZ49e+L9999HdnY2fvrpJ/j4+GiiRiIiaoSUHoF8/PHHcHR0BAAsWbIEVlZWmDhxIm7duoVvvvlG7QUSEVHjpPQIpFOnTvJ/29nZISoqSq0FERFR06DSvbCIiIiaTIDk5OQgJCQE5ubmsLS0xNixY1FQUFCnbYUQ6NevHyQSCbZt26bZQh/S3cOmXvdHRFRfmkyAhISE4MyZM4iOjkZkZCQOHjyI8ePH12nbzz//HBJJwzzkaXwP9wbZLxGRpj3W80DqS3JyMqKiopCQkCCfg1m9ejWCg4OxbNkyODk51bjtiRMnsHz5chw9elQ++U9ERI+vSYxA4uLiYGlpqTCB36dPH+jo6CA+Pr7G7QoLC/H6669jzZo1cHBwqNO+SkpKkJ+fr/B6HOKxtiYiarzqNAL54osv6vyBmrgXVmZmJuzs7BSW6enpwdraGpmZmTVuN336dHTt2hWDBg2q877Cw8PxwQcfqFwrADTQ0TIionpVpwBZuXJlnT5MIpEoFSBz5szBp59+WmsbVR+Tu337duzduxfHjx9Xaru5c+dixowZ8vf5+flwcXFRqQYiIm1WpwBJTU3VyM5nzpyJ0NDQWtu4u7vDwcEBWVlZCsvLy8uRk5NT46GpvXv34tKlS7C0tFRYPmTIEDz33HPYv39/tdtJpVJIpdK6duGRzmfeRc+Wtmr7PCKixqJBJ9FtbW1ha/voL1d/f3/k5uYiMTERHTt2BFAZEDKZDH5+ftVuM2fOHLz55psKy9q0aYOVK1diwIABj198HV3PLaq3fRER1SeVAuTatWvYvn17tQ+UWrFihVoKe1CrVq0QFBSEcePGYe3atSgrK0NYWBiGDx8uPwPr+vXrCAgIwMaNG9G5c2c4ODhUOzpxdXVFixYt1F4jEdGTRukA2bNnDwYOHAh3d3ecO3cOPj4+uHLlCoQQ6NChgyZqBFD5KN2wsDAEBARAR0cHQ4YMUZjcLysrQ0pKCgoLCzVWAxER/Y/SATJ37lzMmjULH3zwAczMzPDHH3/Azs4OISEhCAoK0kSNAABra2ts2rSpxvVubm4QovaTZh+1noiI6k7p60CSk5MxatQoAJWn0hYVFcHU1BQffvjhI8+oehLxlF4i0lZKB4iJiYl83sPR0RGXLl2Sr8vOzlZfZURE1KgpfQirS5cuiImJQatWrRAcHIyZM2fi1KlT2Lp1K7p06aKJGomIqBFSOkBWrFghvwvuBx98gIKCAvz666/w9PTUyBlYTR2nXYhIWykdIO7u/7u7rImJCdauXavWgoiIqGlQeg4kISGh2hsYxsfH4+jRo2opSptwEp2ItJXSATJ58mSkp6dXWX79+nVMnjxZLUVpEwmYIESknZQOkLNnz1Z7waCvry/Onj2rlqKIiKjxUzpApFIpbt68WWV5RkYG9PSaxPOpiIhIDZQOkL59+2Lu3LnIy8uTL8vNzcW8efPwwgsvqLU4IiJqvJQeMixbtgw9evRA8+bN4evrC6DysbH29vb46aef1F4gERE1TkoHiLOzM06ePImIiAgkJSXByMgIY8aMwWuvvQZ9fX1N1EhERI2QSpMWJiYmGD9+vLpr0UqCT0UnIi1VpwDZvn07+vXrB319fWzfvr3WtgMHDlRLYU0ZT9wloidBnQJk8ODByMzMhJ2dHQYPHlxjO4lEgoqKCnXVphV4HQgRaas6BYhMJqv230RE9ORS6jTesrIyBAQE4MKFC5qqh4iImgilAkRfXx8nT57UVC1ERNSEKH0h4YgRI/D9999rohatxJspEpG2Uvo03vLycvzwww/YvXs3OnbsCBMTE4X1fCaIIj4PhIi0ldIBcvr0afnNFM+fP6+wTsI/t4mInhhKB8i+ffs0UQcRETUxSs+BEBERAXUcgbz88sv48ccfYW5ujpdffrnWtlu3blVLYdqCR/WISFvVKUAsLCzk8xsWFhYaLUjbMD+ISFvVKUDWr19f7b+JiOjJpfIjBLOyspCSkgIA8PLygp2dndqKIiKixk/pSfT8/HyMHDkSzs7O6NmzJ3r27AlnZ2eMGDFC4SmFVImXgRCRtlI6QMaNG4f4+HhERkYiNzcXubm5iIyMxNGjRzFhwgRN1EhERI2Q0oewIiMjsWvXLnTv3l2+LDAwEN9++y2CgoLUWpw24CQ6EWkrpUcgzZo1q/ZMLAsLC1hZWamlKCIiavyUDpD58+djxowZyMzMlC/LzMzE7NmzsWDBArUWR0REjZfSh7C+/vprXLx4Ea6urnB1dQUApKWlQSqV4tatW1i3bp287bFjx9RXKRERNSpKB0htj7SlSrypJBE9CZQOkIULF2qiDiIiamJUvpAQAAoKCqo8I93c3PyxCiIioqZB6Un01NRU9O/fHyYmJvIzr6ysrGBpacmzsIiIniBKj0BGjBgBIQR++OEH2Nvb83g/EdETSukASUpKQmJiIry8vDRRDxERNRFKH8J69tlnkZ6erolaiIioCVF6BPLdd9/hrbfewvXr1+Hj4wN9fX2F9W3btlVbcURE1HgpHSC3bt3CpUuXMGbMGPkyiUQCIQQkEgkqKirUWmBTxykiItJWSgfIG2+8AV9fX/zyyy+cRK8D/nyISFspHSBXr17F9u3b4eHhoYl6iIioiVB6Ev35559HUlKSJmrRSkLwkVJEpJ2UHoEMGDAA06dPx6lTp9CmTZsqk+gDBw5UW3FERNR4KR0gb731FgDgww8/rLKOk+hERE8OpQPk4XtfUe04iU5E2krpOZCGkpOTg5CQEJibm8PS0hJjx45FQUHBI7eLi4vD888/DxMTE5ibm6NHjx4oKiqqh4qJiLRbnQMkODgYeXl58veffPIJcnNz5e9v376N1q1bq7W4B4WEhODMmTOIjo5GZGQkDh48iPHjx9e6TVxcHIKCgtC3b18cOXIECQkJCAsLg45Ok8lNIqJGSyLqeJqQrq4uMjIyYGdnB6Dytu0nTpyAu7s7AODmzZtwcnLSyBxIcnIyWrdujYSEBHTq1AkAEBUVheDgYFy7dg1OTk7VbtelSxe88MILWLx4scr7zs/Ph4WFBfLy8up8q/oKmcDT83YCAMb3cMe84FYq75+ISN1U+V6rTp3/FH84Z+rz9NS4uDhYWlrKwwMA+vTpAx0dHcTHx1e7TVZWFuLj42FnZ4euXbvC3t4ePXv2RExMTK37KikpQX5+vsLrcXAGhIi0VZM4lpOZmSkf+dynp6cHa2trZGZmVrvN5cuXAQCLFi3CuHHjEBUVhQ4dOiAgIAAXLlyocV/h4eGwsLCQv1xcXB6r9h4tbR9reyKixqrOASKRSKqcUfS4ZxjNmTNH/rk1vc6dO6fSZ98/W2zChAkYM2YMfH19sXLlSnh5eeGHH36ocbu5c+ciLy9P/lLlzsMP/lQsjPRrbEdE1JTV+TReIQRCQ0MhlUoBAMXFxXjrrbdgYmICoPLQj7JmzpyJ0NDQWtu4u7vDwcEBWVlZCsvLy8uRk5MDBweHardzdHQEgCoT+61atUJaWlqN+5NKpfI+EhFRzeocIKNHj1Z4P2LEiCptRo0apdTObW1tYWv76EM8/v7+yM3NRWJiIjp27AgA2Lt3L2QyGfz8/Krdxs3NDU5OTkhJSVFYfv78efTr10+pOomIqKo6B8j69es1WUetWrVqhaCgIIwbNw5r165FWVkZwsLCMHz4cPkZWNevX0dAQAA2btyIzp07QyKRYPbs2Vi4cCHatWuH9u3bY8OGDTh37hx+//33BusLEZG2UPpK9IYSERGBsLAwBAQEQEdHB0OGDMEXX3whX19WVoaUlBQUFhbKl02bNg3FxcWYPn06cnJy0K5dO0RHR+Ppp59uiC4QEWmVOl8H8qRS5XxpmUzA/f+vA4l8uzt8nC00WSIRkVLq/ToQIiKiBzFAiIhIJQwQIiJSCQOEiIhUwgAhIiKVMECIiEglDBAiIlIJA4SIiFTCACEiIpUwQIiISCUMEA17zEemEBE1WgwQIiJSCQOEiIhUwgDRMN7rmIi0FQNEAzjvQURPAgYIERGphAFCREQqYYAQEZFKGCBERKQSBoiGcUKdiLQVA4SIiFTCACEiIpUwQIiISCUMECIiUgkDhIiIVMIAISIilTBAiIhIJQwQIiJSCQNEwyTglYREpJ0YIEREpBIGCBERqYQBQkREKmGAEBGRShggGibAh6ITkXbSa+gCtJGE93DXKjKZDKWlpQ1dBlGd6evrQ1dXV+P7YYAQ1aK0tBSpqamQyWQNXQqRUiwtLeHg4KDRP2gZIEQ1EEIgIyMDurq6cHFxgY4Oj/hS4yeEQGFhIbKysgAAjo6OGtsXA4SoBuXl5SgsLISTkxOMjY0buhyiOjMyMgIAZGVlwc7OTmOHs/gnlYbxSvSmq6KiAgBgYGDQwJUQKe/+Hz1lZWUa2wcDhOgReFIENUX18XvLACEiIpUwQIhIbUJDQzF48OBHtpNIJNi2bZva9uvm5obPP/9cbZ9HdcMAIdIyoaGhkEgkVV5BQUEa3/eqVavw448/PrJdRkYG+vXrp/F6SLN4FhaRFgoKCsL69esVlkmlUo3v18LCotb1paWlMDAwgIODg8ZraWhCCFRUVEBPT3u/ZjkCIaojIQQKS8sb5CWEcrfEkUqlcHBwUHhZWVnJ10skEqxbtw4vvvgijI2N0apVK8TFxeHixYvo1asXTExM0LVrV1y6dEm+zaJFi9C+fXusW7cOLi4uMDY2xrBhw5CXlydv8/AhrF69eiEsLAzTpk2DjY0NAgMD5ft/8BDWtWvX8Nprr8Ha2homJibo1KkT4uPjAQCXLl3CoEGDYG9vD1NTUzz77LPYvXu3Uj+PhIQEvPDCC7CxsYGFhQV69uyJY8eOyde//vrrePXVVxW2KSsrg42NDTZu3Aig8o4E4eHhaNGiBYyMjNCuXTv8/vvv8vb79++HRCLBP//8g44dO0IqlSImJqZO9WdkZKB///4wMjJCixYtsGnTpiqH5XJzc/Hmm2/C1tYW5ubmeP7555GUlKTUz0HdtDcaidSsqKwCrd/f1SD7PvthIIwN1Pu/6+LFi7FixQqsWLEC7777Ll5//XW4u7tj7ty5cHV1xRtvvIGwsDD8888/8m0uXryI3377DX///Tfy8/MxduxYTJo0CRERETXuZ8OGDZg4cSJiY2OrXV9QUICePXvC2dkZ27dvh4ODA44dOya/+r+goADBwcFYsmQJpFIpNm7ciAEDBiAlJQWurq516uvdu3cxevRorF69GkIILF++HMHBwbhw4QLMzMwQEhKCoUOHoqCgAKampgCAXbt2obCwEC+99BIAIDw8HD///DPWrl0LT09PHDx4ECNGjICtrS169uwp39ecOXOwbNkyuLu7w8rKCunp6Y+sf9SoUcjOzsb+/fuhr6+PGTNmyC8EvG/o0KEwMjLCP//8AwsLC6xbtw4BAQE4f/48rK2t6/RzUDcGCJEWioyMlH8R3jdv3jzMmzdP/n7MmDEYNmwYAODdd9+Fv78/FixYIB8lTJ06FWPGjFH4jOLiYmzcuBHOzs4AgNWrV6N///5Yvnx5jYelPD09sXTp0hpr3bRpE27duoWEhAT5F6GHh4d8fbt27dCuXTv5+8WLF+PPP//E9u3bERYW9sifBQA8//zzCu+/+eYbWFpa4sCBA3jxxRcRGBgIExMT/Pnnnxg5cqS8roEDB8LMzAwlJSX4+OOPsXv3bvj7+wMA3N3dERMTg3Xr1ikEyIcffogXXnhB/t7a2rrW+s+dO4fdu3cjISEBnTp1AgB899138PT0lG8TExODI0eOICsrS34octmyZdi2bRt+//13jB8/vk4/B3VjgGgYLyHQHkb6ujj7YWCD7VsZvXv3xtdff62w7OG/Utu2bSv/t729PQCgTZs2CsuKi4uRn58Pc3NzAICrq6s8PADA398fMpkMKSkpNQZIx44da631xIkT8PX1rfGv6IKCAixatAg7duxARkYGysvLUVRUhLS0tFo/90E3b97E/PnzsX//fmRlZaGiogKFhYXyz9DT08OwYcMQERGBkSNH4t69e/jrr7+wefNmAJUjr8LCQoVgACrndHx9fRWW3Q+ButafkpICPT09dOjQQb6Nh4eHwiHHpKQkFBQUoFmzZgqfXVRUpHCYsb41mQDJycnB22+/jb///hs6OjoYMmQIVq1aVeWvrAdlZmZi9uzZiI6Oxt27d+Hl5YX33nsPQ4YMqcfKSVtIJBK1H0bSFBMTE4W/4qujr68v//f9i86qW/a4N5I0MTGpdf39227UZNasWYiOjsayZcvg4eEBIyMjvPLKK0rdIXn06NG4ffs2Vq1ahebNm0MqlcLf31/hM0JCQtCzZ09kZWUhOjoaRkZG8jPXCgoKAAA7duxQCFCg6skJD/dXHfUXFBTA0dER+/fvr7LO0tKyzp+jbk3j/wZU/sfNyMhAdHQ0ysrKMGbMGIwfPx6bNm2qcZtRo0YhNzcX27dvh42NDTZt2oRhw4bh6NGjVf5qIKJHS0tLw40bN+Dk5AQA+O+//6CjowMvLy+VP7Nt27b47rvvkJOTU+0oJDY2FqGhofK5iIKCAly5ckWpfcTGxuKrr75CcHAwACA9PR3Z2dkKbbp27QoXFxf8+uuv+OeffzB06FB5oLZu3RpSqRRpaWkKh6vquu/a6vfy8kJ5eTmOHz8uH61dvHgRd+7ckbfp0KEDMjMzoaenBzc3N6X2r0lN4iys5ORkREVF4bvvvoOfnx+6d++O1atXY/Pmzbhx40aN2x0+fBhvv/02OnfuDHd3d8yfPx+WlpZITEysx+qJ6l9JSQkyMzMVXg9/YarC0NAQo0ePRlJSEg4dOoQpU6Zg2LBhj3Va7muvvQYHBwcMHjwYsbGxuHz5Mv744w/ExcUBqJxD2bp1K06cOIGkpCS8/vrrSo+KPD098dNPPyE5ORnx8fEICQmpduTz+uuvY+3atYiOjkZISIh8uZmZGWbNmoXp06djw4YNuHTpEo4dO4bVq1djw4YNj9x3bfV7e3ujT58+GD9+PI4cOYLjx49j/PjxMDIyko8C+/TpA39/fwwePBj//vsvrly5gsOHD+O9997D0aNHlfpZqFOTCJC4uDhYWloqHFvs06cPdHR05Kf6Vadr16749ddfkZOTA5lMhs2bN6O4uBi9evWqcZuSkhLk5+crvIiamqioKDg6Oiq8unfv/tif6+HhgZdffhnBwcHo27cv2rZti6+++uqxPtPAwAD//vsv7OzsEBwcjDZt2uCTTz6R30F2xYoVsLKyQteuXTFgwAAEBgYqzBfUxffff487d+6gQ4cOGDlyJKZMmQI7O7sq7UJCQnD27Fk4OzujW7duCusWL16MBQsWIDw8HK1atUJQUBB27NiBFi1a1LrvutS/ceNG2Nvbo0ePHnjppZcwbtw4mJmZwdDQEEDl4cSdO3eiR48eGDNmDFq2bInhw4fj6tWr8vmrBiGagCVLloiWLVtWWW5rayu++uqrGre7c+eO6Nu3rwAg9PT0hLm5udi1a1et+1q4cKEAUOWVl5enVM3N340Uzd+NFGdvKLcdNR5FRUXi7NmzoqioqKFLaRQWLlwo2rVr19BlPBHS09MFALF7926VP6O239+8vDyVvtce1qAjkDlz5lR7y4UHX+fOnVP58xcsWIDc3Fzs3r0bR48exYwZMzBs2DCcOnWqxm3mzp2LvLw8+Ss9PV3l/QOAktd/EdETaO/evdi+fTtSU1Nx+PBhDB8+HG5ubujRo0dDl1arBp1EnzlzJkJDQ2tt4+7uDgcHhyoX1ZSXlyMnJ6fGY6+XLl3Cl19+idOnT+OZZ54BUHk++aFDh7BmzRqsXbu22u2kUmm93PKBiOi+srIyzJs3D5cvX4aZmRm6du2KiIgIhbPiGqMGDRBbW1vY2to+sp2/vz9yc3ORmJgoP0th7969kMlk8PPzq3abwsJCAKjyGFJdXV0+35pIBYsWLcKiRYsaugytFBgYKL+AsylpEpPo9yesxo0bhyNHjiA2NhZhYWEYPny4/HTC69evw9vbG0eOHAFQeWaDh4cHJkyYgCNHjuDSpUtYvnw5oqOj63S7aXXhhYREpK2aRIAAQEREBLy9vREQEIDg4GB0794d33zzjXx9WVkZUlJS5CMPfX197Ny5E7a2thgwYADatm2LjRs3YsOGDfJzwYmISHVN5kJCa2vrWi8adHNzq3LHUk9PT/zxxx+aLo2I6InUZEYgRETUuDBAiIhIJQwQIiJSCQOEiJq8K1euQCKR4MSJEw1dyhOFAUKkhUJDQ6u9s8P925M3Br169cK0adOU3u7hx+YCgIuLCzIyMuDj46Oe4qhOmsxZWESknKCgIKxfv15hmbbeZUFXV/ex7ghMquEIRMN4IaEWEQIovdcwLxVuqiaVSuHg4KDwsrKywv79+2FgYIBDhw7J2y5duhR2dna4efMmgMrRQVhYGMLCwmBhYQEbGxssWLBA4VT5kpISzJo1C87OzjAxMYGfn1+VBx7FxsaiV69eMDY2hpWVFQIDA3Hnzh2EhobiwIEDWLVqlXx0dOXKFVRUVGDs2LFo0aIFjIyM4OXlhVWrVsk/b9GiRdiwYQP++usv+Xb79++v9hDWgQMH0LlzZ0ilUjg6OmLOnDkoLy+Xr+/VqxemTJmCd955B9bW1nBwcOCV9kriCISorsoKgY+dGmbf824ABrU/2a+u7h86GjlyJJKSknD58mUsWLAAW7ZsUbg1+IYNGzB27FgcOXIER48exfjx4+Hq6opx48YBAMLCwnD27Fls3rwZTk5O+PPPPxEUFIRTp07B09MTJ06cQEBAAN544w2sWrUKenp62LdvHyoqKrBq1SqcP38ePj4++PDDDwFU3tpIJpPhqaeewpYtW9CsWTMcPnwY48ePh6OjI4YNG4ZZs2YhOTkZ+fn58tGVtbV1lecCXb9+HcHBwQgNDcXGjRtx7tw5jBs3DoaGhgohsWHDBsyYMQPx8fGIi4tDaGgounXrVuXRtVQ9BgiRloqMjKzyyOd58+Zh3rx5+OijjxAdHY3x48fj9OnTGD16NAYOHKjQ1sXFBStXroREIoGXlxdOnTqFlStXYty4cUhLS8P69euRlpYmv53QrFmzEBUVhfXr1+Pjjz/G0qVL0alTJ4Xnhdy/sSlQ+RwQY2NjhUNPurq6+OCDD+TvW7Rogbi4OPz2228YNmwYTE1NYWRkhJKSkloPWX311VdwcXHBl19+CYlEAm9vb9y4cQPvvvsu3n//ffk98tq2bYuFCxcCqLzw+Msvv8SePXsYIHXEACGqK33jypFAQ+1bSb1798bXX3+tsOz+I2MNDAwQERGBtm3bonnz5li5cmWV7bt06SJ/Ih5QeVPT5cuXo6KiAqdOnUJFRQVatmypsE1JSQmaNWsGADhx4gSGDh2qdN1r1qzBDz/8gLS0NBQVFaG0tBTt27dX6jOSk5Ph7++vUH+3bt1QUFCAa9euwdXVFUBlgDzI0dGxyp2/qWYMEKK6kkjUdhipPpiYmMDDw6PG9YcPHwYA5OTkICcnByYmde9bQUEBdHV1kZiYKH9y4H33Rz3VPTL2UTZv3oxZs2Zh+fLl8Pf3h5mZGT777LNanzz6OB6+XbpEIuHdupXASXSiJ9ClS5cwffp0fPvtt/Dz88Po0aOrfHE+/KX933//wdPTE7q6uvD19UVFRQWysrLg4eGh8Lp/aKlt27bYs2dPjTUYGBigoqJCYVlsbCy6du2KSZMmwdfXFx4eHrh06dIjt3tYq1atEBcXpzDpHxsbCzMzMzz11FO1bkt1xwAh0lIlJSXIzMxUeGVnZ6OiogIjRoxAYGAgxowZg/Xr1+PkyZNYvny5wvZpaWmYMWMGUlJS8Msvv2D16tWYOnUqAKBly5YICQnBqFGjsHXrVqSmpuLIkSMIDw/Hjh07AFQ+3TMhIQGTJk3CyZMnce7cOXz99dfIzs4GUHkD1Pj4eFy5cgXZ2dmQyWTw9PTE0aNHsWvXLpw/fx4LFixAQkKCQl1ubm44efIkUlJSkJ2djbKysip9nzRpEtLT0/H222/j3Llz+Ouvv7Bw4ULMmDGjyjOCSHX8SRJpqaioKDg6Oiq8unfvjiVLluDq1atYt24dgMrj/t988w3mz5+PpKQk+fajRo1CUVEROnfujMmTJ2Pq1KkYP368fP369esxatQozJw5E15eXhg8eDASEhLk8wstW7bEv//+i6SkJHTu3Bn+/v7466+/oKdXeeR81qxZ0NXVRevWrWFra4u0tDRMmDABL7/8Ml599VX4+fnh9u3bmDRpkkK/xo0bBy8vL3Tq1Am2traIjY2t0ndnZ2fs3LkTR44cQbt27fDWW29h7NixmD9/vtp/zk8yiXj4HuikID8/HxYWFsjLy4O5uXmdt3ObU/lX2P5ZveBm03SOm9P/FBcXIzU1FS1atIChoWFDl1OvevXqhfbt2+Pzzz9v6FJIRbX9/qr6vfYwTqJryNx+3rhTWMbwICKtxQDRkAk9n27oEoiINIoBQkRVPHxLEqLqcBKdiIhUwgAhegSeZ0JNUX383jJAiGpw/wrr0tLSBq6ESHmFhYUAql5tr06cAyGqgZ6eHoyNjXHr1i3o6+vzAjRqEoQQKCwsRFZWFiwtLavcakadGCBENZBIJHB0dERqaiquXr3a0OUQKcXS0lLjD9ligBDVwsDAAJ6enjyMRU2Kvr6+Rkce9zFAiB5BR0fnibsSnagueFCXiIhUwgAhIiKVMECIiEglnAN5hPsX4+Tn5zdwJURE6nH/++xxLzZkgDzC3bt3AQAuLi4NXAkRkXrdvXsXFhYWKm/P54E8gkwmw40bN2BmZgaJRFLn7fLz8+Hi4oL09PTHut9+Y6Xt/QO0v4/sX9Onah+FELh79y6cnJwe6wJZjkAeQUdH57GeoWxubq61v7yA9vcP0P4+sn9Nnyp9fJyRx32cRCciIpUwQIiISCUMEA2RSqVYuHAhpFJpQ5eiEdreP0D7+8j+NX0N3UdOohMRkUo4AiEiIpUwQIiISCUMECIiUgkDhIiIVMIA0YA1a9bAzc0NhoaG8PPzw5EjRxq6pGqFh4fj2WefhZmZGezs7DB48GCkpKQotCkuLsbkyZPRrFkzmJqaYsiQIbh586ZCm7S0NPTv3x/Gxsaws7PD7NmzUV5ertBm//796NChA6RSKTw8PPDjjz9quntVfPLJJ5BIJJg2bZp8WVPv3/Xr1zFixAg0a9YMRkZGaNOmDY4ePSpfL4TA+++/D0dHRxgZGaFPnz64cOGCwmfk5OQgJCQE5ubmsLS0xNixY1FQUKDQ5uTJk3juuedgaGgIFxcXLF26tF76V1FRgQULFqBFixYwMjLC008/jcWLFyvcw6kp9fHgwYMYMGAAnJycIJFIsG3bNoX19dmXLVu2wNvbG4aGhmjTpg127typfIcEqdXmzZuFgYGB+OGHH8SZM2fEuHHjhKWlpbh582ZDl1ZFYGCgWL9+vTh9+rQ4ceKECA4OFq6urqKgoEDe5q233hIuLi5iz5494ujRo6JLly6ia9eu8vXl5eXCx8dH9OnTRxw/flzs3LlT2NjYiLlz58rbXL58WRgbG4sZM2aIs2fPitWrVwtdXV0RFRVVb309cuSIcHNzE23bthVTp07Viv7l5OSI5s2bi9DQUBEfHy8uX74sdu3aJS5evChv88knnwgLCwuxbds2kZSUJAYOHChatGghioqK5G2CgoJEu3btxH///ScOHTokPDw8xGuvvSZfn5eXJ+zt7UVISIg4ffq0+OWXX4SRkZFYt26dRvsnhBBLliwRzZo1E5GRkSI1NVVs2bJFmJqailWrVjXJPu7cuVO89957YuvWrQKA+PPPPxXW11dfYmNjha6urli6dKk4e/asmD9/vtDX1xenTp1Sqj8MEDXr3LmzmDx5svx9RUWFcHJyEuHh4Q1YVd1kZWUJAOLAgQNCCCFyc3OFvr6+2LJli7xNcnKyACDi4uKEEJX/Q+jo6IjMzEx5m6+//lqYm5uLkpISIYQQ77zzjnjmmWcU9vXqq6+KwMBATXdJCCHE3bt3haenp4iOjhY9e/aUB0hT79+7774runfvXuN6mUwmHBwcxGeffSZflpubK6RSqfjll1+EEEKcPXtWABAJCQnyNv/884+QSCTi+vXrQgghvvrqK2FlZSXv7/19e3l5qbtLVfTv31+88cYbCstefvllERISIoRo2n18OEDqsy/Dhg0T/fv3V6jHz89PTJgwQak+8BCWGpWWliIxMRF9+vSRL9PR0UGfPn0QFxfXgJXVTV5eHgDA2toaAJCYmIiysjKF/nh7e8PV1VXen7i4OLRp0wb29vbyNoGBgcjPz8eZM2fkbR78jPtt6utnMnnyZPTv379KDU29f9u3b0enTp0wdOhQ2NnZwdfXF99++618fWpqKjIzMxVqs7CwgJ+fn0L/LC0t0alTJ3mbPn36QEdHB/Hx8fI2PXr0gIGBgUL/UlJScOfOHY32sWvXrtizZw/Onz8PAEhKSkJMTAz69eunNX28rz77oq7fWQaIGmVnZ6OiokLhywYA7O3tkZmZ2UBV1Y1MJsO0adPQrVs3+Pj4AAAyMzNhYGAAS0tLhbYP9iczM7Pa/t5fV1ub/Px8FBUVaaI7cps3b8axY8cQHh5eZV1T79/ly5fx9ddfw9PTE7t27cLEiRMxZcoUbNiwQaG+2n4fMzMzYWdnp7BeT08P1tbWSv0MNGXOnDkYPnw4vL29oa+vD19fX0ybNg0hISEK+2/KfbyvPvtSUxtl+8q78RKAyr/ST58+jZiYmIYuRW3S09MxdepUREdHw9DQsKHLUTuZTIZOnTrh448/BgD4+vri9OnTWLt2LUaPHt3A1anHb7/9hoiICGzatAnPPPMMTpw4gWnTpsHJyUlr+tiUcQSiRjY2NtDV1a1yFs/Nmzfh4ODQQFU9WlhYGCIjI7Fv3z6FW9c7ODigtLQUubm5Cu0f7I+Dg0O1/b2/rrY25ubmMDIyUnd35BITE5GVlYUOHTpAT08Penp6OHDgAL744gvo6enB3t6+SffP0dERrVu3VljWqlUrpKWlKdRX2++jg4MDsrKyFNaXl5cjJydHqZ+BpsyePVs+CmnTpg1GjhyJ6dOny0eU2tDH++qzLzW1UbavDBA1MjAwQMeOHbFnzx75MplMhj179sDf378BK6ueEAJhYWH4888/sXfvXrRo0UJhfceOHaGvr6/Qn5SUFKSlpcn74+/vj1OnTin8UkdHR8Pc3Fz+5ebv76/wGffbaPpnEhAQgFOnTuHEiRPyV6dOnRASEiL/d1PuX7du3aqcdn3+/Hk0b94cANCiRQs4ODgo1Jafn4/4+HiF/uXm5iIxMVHeZu/evZDJZPDz85O3OXjwIMrKyuRtoqOj4eXlBSsrK431DwAKCwurPPBIV1cXMpkMgHb08b767IvafmeVmnKnR9q8ebOQSqXixx9/FGfPnhXjx48XlpaWCmfxNBYTJ04UFhYWYv/+/SIjI0P+KiwslLd56623hKurq9i7d684evSo8Pf3F/7+/vL1909z7du3rzhx4oSIiooStra21Z7mOnv2bJGcnCzWrFlT76fx3vfgWVhCNO3+HTlyROjp6YklS5aICxcuiIiICGFsbCx+/vlneZtPPvlEWFpair/++kucPHlSDBo0qNrTQn19fUV8fLyIiYkRnp6eCqeF5ubmCnt7ezFy5Ehx+vRpsXnzZmFsbFwvp/GOHj1aODs7y0/j3bp1q7CxsRHvvPNOk+zj3bt3xfHjx8Xx48cFALFixQpx/PhxcfXq1XrtS2xsrNDT0xPLli0TycnJYuHChTyNt7FYvXq1cHV1FQYGBqJz587iv//+a+iSqgWg2tf69evlbYqKisSkSZOElZWVMDY2Fi+99JLIyMhQ+JwrV66Ifv36CSMjI2FjYyNmzpwpysrKFNrs27dPtG/fXhgYGAh3d3eFfdSnhwOkqffv77//Fj4+PkIqlQpvb2/xzTffKKyXyWRiwYIFwt7eXkilUhEQECBSUlIU2ty+fVu89tprwtTUVJibm4sxY8aIu3fvKrRJSkoS3bt3F1KpVDg7O4tPPvlE430TQoj8/HwxdepU4erqKgwNDYW7u7t47733FE5RbUp93LdvX7X/z40ePbre+/Lbb7+Jli1bCgMDA/HMM8+IHTt2KN0f3s6diIhUwjkQIiJSCQOEiIhUwgAhIiKVMECIiEglDBAiIlIJA4SIiFTCACEiIpUwQIgaieqeUKcuV65cgUQiwYkTJzTy+fRkYoDQE+PWrVuYOHEiXF1dIZVK4eDggMDAQMTGxjZ0aRrn4uKCjIwM+a36idSBt3OnJ8aQIUNQWlqKDRs2wN3dHTdv3sSePXtw+/bthi5N43R1dRv1HaGpaeIIhJ4Iubm5OHToED799FP07t0bzZs3R+fOnTF37lwMHDhQ3m7FihVo06YNTExM4OLigkmTJqGgoEC+/scff4SlpSUiIyPh5eUFY2NjvPLKKygsLMSGDRvg5uYGKysrTJkyBRUVFfLt3NzcsHjxYrz22mswMTGBs7Mz1qxZU2vN6enpGDZsGCwtLWFtbY1BgwbhypUrNba/c+cOQkJCYGtrCyMjI3h6emL9+vUAqh7CCg0NhUQiqfLav38/AKCkpASzZs2Cs7MzTExM4OfnJ19HdB8DhJ4IpqamMDU1xbZt21BSUlJjOx0dHXzxxRc4c+YMNmzYgL179+Kdd95RaFNYWIgvvvgCmzdvRlRUFPbv34+XXnoJO3fuxM6dO/HTTz9h3bp1+P333xW2++yzz9CuXTscP34cc+bMkT/sqjplZWUIDAyEmZkZDh06hNjYWJiamiIoKAilpaXVbrNgwQKcPXsW//zzD5KTk/H111/Dxsam2rarVq1CRkaG/DV16lTY2dnB29sbQOUzYuLi4rB582acPHkSQ4cORVBQEC5cuFDjz46eQErffpGoifr999+FlZWVMDQ0FF27dhVz584VSUlJtW6zZcsW0axZM/n79evXCwDi4sWL8mUTJkwQxsbGCndEDQwMFBMmTJC/b968uQgKClL47FdffVX069dP/h6A+PPPP4UQQvz000/Cy8tLyGQy+fqSkhJhZGQkdu3aVW2tAwYMEGPGjKl2XWpqqgAgjh8/XmXdH3/8IQwNDUVMTIwQQoirV68KXV1dcf36dYV2AQEBCrexJ+IIhJ4YQ4YMwY0bN7B9+3YEBQVh//796NChA3788Ud5m927dyMgIADOzs4wMzPDyJEjcfv2bRQWFsrbGBsb4+mnn5a/t7e3h5ubG0xNTRWWPfzkuIcf1uPv74/k5ORqa01KSsLFixdhZmYmHz1ZW1ujuLgYly5dqnabiRMnYvPmzWjfvj3eeecdHD58+JE/k+PHj2PkyJH48ssv0a1bNwDAqVOnUFFRgZYtW8r3bWpqigMHDtS4b3oycRKdniiGhoZ44YUX8MILL2DBggV48803sXDhQoSGhuLKlSt48cUXMXHiRCxZsgTW1taIiYnB2LFjUVpaCmNjYwCAvr6+wmdKJJJql91/ap4qCgoK0LFjR0RERFRZZ2trW+02/fr1w9WrV7Fz505ER0cjICAAkydPxrJly6ptn5mZiYEDB+LNN9/E2LFjFfatq6uLxMRE6OrqKmzzYEgSMUDoida6dWv5tReJiYmQyWRYvny5/DGqv/32m9r29d9//1V536pVq2rbdujQAb/++ivs7Oxgbm5e533Y2tpi9OjRGD16NJ577jnMnj272gApLi7GoEGD4O3tjRUrViis8/X1RUVFBbKysvDcc8/Ved/05OEhLHoi3L59G88//zx+/vlnnDx5EqmpqdiyZQuWLl2KQYMGAQA8PDxQVlaG1atX4/Lly/jpp5+wdu1atdUQGxuLpUuX4vz581izZg22bNmCqVOnVts2JCQENjY2GDRoEA4dOoTU1FTs378fU6ZMwbVr16rd5v3338dff/2Fixcv4syZM4iMjKwxoCZMmID09HR88cUXuHXrFjIzM5GZmYnS0lK0bNkSISEhGDVqFLZu3YrU1FQcOXIE4eHh2LFjh9p+HtT0MUDoiWBqago/Pz+sXLkSPXr0gI+PDxYsWIBx48bhyy+/BAC0a9cOK1aswKeffgofHx9EREQgPDxcbTXMnDkTR48eha+vLz766COsWLECgYGB1bY1NjbGwYMH4erqipdffhmtWrXC2LFjUVxcXOOIxMDAAHPnzkXbtm3Ro0cP6OrqYvPmzdW2PXDgADIyMtC6dWs4OjrKX/fnTdavX49Ro0Zh5syZ8PLywuDBg5GQkABXV1f1/DBIK/CRtkT1wM3NDdOmTcO0adMauhQiteEIhIiIVMIAISIilfAQFhERqYQjECIiUgkDhIiIVMIAISIilTBAiIhIJQwQIiJSCQOEiIhUwgAhIiKVMECIiEglDBAiIlLJ/wGyBOmAWlwpuAAAAABJRU5ErkJggg==",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            },
            {
              "data": {
                "image/png":
                  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IRWhztjNWqQGC74x8j+eDxboTNE3fYoShSZCL0Hb8MFFKG6c0C1XaUL2r8XFAG45TU+D749Bs07scYWAS5CK02XYCsE9LRguyX3cHkRzREl0P3HUK0R3B9ZstRKC5OxL3qMk6F9Ix6fAUgSBBLkKb+0x3T5BcCHSu3We3kwvRTRLkIrS5z3T3BtmIFQ85IxeBIEEuQtf3J7yX5u/TgrRpxfMB07gP2lv1LUYYVreCfOXKlaSkpBAVFUVmZiZbt27tdNu//OUvTJ06lYEDB9K3b18yMjJ4/fXXfbbRNI38/HwSExOJjo4mKyuLAwcOdKc0Ic6o3w1AjRaHnb46F9OxOi6DqFhQ26Fxv97lCIPyO8jXrVtHbm4uBQUFlJeXM3nyZLKzs6mvr+9w+8GDB/PII49QVlbG9u3bycnJIScnh08++cS7zbPPPsvzzz9PUVERW7ZsoW/fvmRnZ3P6tEwmJC6Bt6MzOJtVXBSIn+j6VppXRDf5HeTLly9n0aJF5OTkMGHCBIqKioiJiWH16tUdbj9z5kxuvfVWxo8fz6hRo3jggQdIT09n06ZNgOtsfMWKFTz66KPMmTOH9PR0XnvtNerq6vjggw8u6eBEmLO6rpgMtguBzhN/heurXOEpusmvIG9tbWXbtm1kZWWd2YHJRFZWFmVlZRd9vaZplJSUsG/fPq677joAjhw5gtVq9dlnbGwsmZmZne7T4XBgt9t9FiHOlrJkPV9/9QUQvB2dXt4glzNy0T1+BXljYyNOp5P4+Hif9fHx8Vit1k5f19TURL9+/YiMjOTmm2/mhRde4MYbbwTwvs6ffRYWFhIbG+tdkpODsyNL6EdBZax3sqwg//2QphVxiXpl1Er//v2pqKjgyy+/5I9//CO5ubmUlpZ2e395eXk0NTV5l+rq6sAVK0LCMKWRvooDhxZBpZagdzkXNmSc62uzzXUTDCH85Nc9O+Pi4jCbzdhsvvNC2Gw2EhI6/89iMpkYPXo0ABkZGezZs4fCwkJmzpzpfZ3NZiMxMdFnnxkZGR3uz2KxYLFY/CldhJlx7rPxQ9ownJh1ruYiLP1h4Ag4UQX1eyDlh3pXJAzGrzPyyMhIpkyZQklJiXedqqqUlJQwffr0Lu9HVVUcDgcAqampJCQk+OzTbrezZcsWv/YpxNnGKrUA7NeG6VxJFw0Z7/rasEffOoQh+XVGDpCbm8vChQuZOnUq06ZNY8WKFbS0tJCTkwPAggULGDZsGIWFhYCrPXvq1KmMGjUKh8PBhg0beP3111m1ahUAiqLw4IMP8vTTTzNmzBhSU1N57LHHSEpKYu7cuYE7UhFWxppcZ+T7g3SOlfMMHQ8HPnGdkQvhJ7+DfN68eTQ0NJCfn4/VaiUjI4Pi4mJvZ2VVVRUm05kT/ZaWFu677z5qamqIjo4mLS2NN954g3nz5nm3eeihh2hpaeGee+7hxIkTzJgxg+LiYqKiogJwiCIcjXPPQb5PG65zJV00dAIAW7ZsIvNmnWsRhqNomvFntLfb7cTGxtLU1MSAAQP0LkfozdmO48kELEob1zqeo1qLv/hrdFS59GY4+g28eB3HtX4MfrwGFEXvsoTO/Mk1mWtFhJ7vjmBx30yiRhuidzVdEzcWp6YwWGmG5o6vkhaiMxLkIvS451g5oA0LuptJdKpPNN96/nJw1y9EVxnkt1wIP9TvBWC/apD2cbf9nguXGvbqW4gwHAlyEXrcZ7TBOnVtZ7wds3JGLvzk96gVIYKeewjfAYOMWElZsh6An5g8QS5DEIV/5IxchJZ2Bxw/BMA+gzWteP+CqN8Lxh9MJnqRBLkILccOgtqOXYvBymC9q/FLpZZAq2aG1pPQVKN3OcJAJMhFaHE3S+zXhgPGGovdRgRHNPd8Q9K8IvwgQS5CiyfIDdas4rHf064vc64IP0iQi9DiDnKjjVjx2OeZG8YmI1dE10mQi9DS4BmxYpBZD8/hHWkjY8mFHyTIReho+x6+qwTggEGbVrwfQI37QVX1LUYYhgS5CB3HDoKmQvQgGojVu5pu+VaLB3MktJ2CJrnzlegaCXIROtyX5jMkDaONWPFwYobLxrgeSPOK6CIJchE6PMHnuQemUXnqlyAXXSRBLkKHN8jH61vHpRrque3bPn3rEIYhQS5CR6idkctFQaKLJMhFaGh3wPHDru+HpOlby6Xy1N+wT+ZcEV0iQS5Cg2fESlQs9E/Qu5pLM3gkmPpAW4vMuSK6RIJchAZPM8SQNOPf79LcBy4b7fpeOjxFF0iQi9Dg7hh8+0iMd35vQ5ORK8IPEuQiNDQY62YSF+UZuVIvQS4uToJchAb3GblR51g5j5yRCz9IkAvja2+FY667Ah1QQyXIZeSK6Dq5Z6cwvmMHQXOCZQDW08a6K1BHUpaspw/t7LaY6dN6Euy1EBsiTUaiR3TrjHzlypWkpKQQFRVFZmYmW7du7XTbl156iWuvvZZBgwYxaNAgsrKyztv+rrvuQlEUn2X27NndKU2EI58LgQw+YsWtjQgqNfcwSmleERfhd5CvW7eO3NxcCgoKKC8vZ/LkyWRnZ1NfX9/h9qWlpcyfP59PP/2UsrIykpOTmTVrFrW1tT7bzZ49m6NHj3qXt99+u3tHJMKP51J2o1/ReQ5ve79cqi8uwu8gX758OYsWLSInJ4cJEyZQVFRETEwMq1ev7nD7N998k/vuu4+MjAzS0tJ4+eWXUVWVkpISn+0sFgsJCQneZdCgQd07IhF+Gs6e9TB0eEfgyKX64iL8CvLW1la2bdtGVlbWmR2YTGRlZVFWVtalfZw6dYq2tjYGD/ZtyywtLWXo0KGMGzeOe++9l2PHjnW6D4fDgd1u91lEGPOekRt8sqxzeDtuG/d716UsWR8a4+RFQPkV5I2NjTidTuLj433Wx8fHY7Vau7SPP/zhDyQlJfl8GMyePZvXXnuNkpISnnnmGT777DNuuukmnE5nh/soLCwkNjbWuyQnG/P+jCIAnG2uzk4I4aaVvTJyRVxQr45aWbp0KWvXrqW0tJSoqCjv+jvuuMP7/aRJk0hPT2fUqFGUlpZyww03nLefvLw8cnNzvY/tdruEebg6fgTUNojs5x7ZsV3vigLmiJYIiglON0GzzfhzyIge49cZeVxcHGazGZvN5rPeZrORkHDhX7Jly5axdOlS/vrXv5Kenn7BbUeOHElcXBwHDx7s8HmLxcKAAQN8FhGmPO3jcWONP8fKOVrpwyGn+69fGbkiLsCvII+MjGTKlCk+HZWejsvp06d3+rpnn32Wp556iuLiYqZOnXrR96mpqeHYsWMkJib6U54IR9728dDq6PQ4KCNXRBf4PWolNzeXl156iTVr1rBnzx7uvfdeWlpayMnJAWDBggXk5eV5t3/mmWd47LHHWL16NSkpKVitVqxWK83NzQA0Nzfz+9//ns2bN1NZWUlJSQlz5sxh9OjRZGdnB+gwRcgKlZtJdMKnnVyITvjdRj5v3jwaGhrIz8/HarWSkZFBcXGxtwO0qqoKk+nM58OqVatobW3l9ttv99lPQUEBjz/+OGazme3bt7NmzRpOnDhBUlISs2bN4qmnnsJisVzi4YmQ5z5T/acNJ/m/j0NvNId35IqckYsL6FZn5+LFi1m8eHGHz5WWlvo8rqysvOC+oqOj+eSTT7pThgh3qtM7NC9kJss6x0HPWHI5IxcXIJNmCeP6rhKcDoiIplYbonc1PeKQloiqKXDqGLQ06l2OCFIS5MK4PM0NcWNQQ/RX+TQWqj0fUnJWLjoRmr/9Ijy4g+392v46F9KzpMNTXIwEuTAuz80kQmUO8k6caSeXDk/RMQlyYVzuM9SDIdrR6XFm5IqckYuOSZALY1LVs0ashPZNF2Q6W3ExEuTCmJqqoe0UDi2CKm2o3tX0qENakuubZhuxNOtbjAhKEuTCmNxnp4e1RJyYdS6mZ7UQDbGuSeFGK7UX2VqEIwlyYUzu9uJDId4+7uWegmCsqUbnQkQwkiAXxuQO8v1qaLePe7knBRsjZ+SiAxLkwpjcQR6ql+afx31GLk0roiMS5MJ4NM3bRr4/xEeseLlvYydNK6IjEuTCeJpqoLUZTH34Vou/+PYhYNLKSgASlO8YQIu+xYigI0EujMdzYcxlo2nv3bsV6uYkMRzVXDcsl+YVcS4JcmE8IX4zic54rvAcY5IgF74kyIXx1LuDfOh4fevoZZ4rWMco0k4ufEmQC+MJ0zNyT8fuWAlycQ4JcmEsmsbJml0AZL1Rr3MxvcvTtDJamlbEOSTIhbHYa+mvfE+bZuZbLUHvanqVZ5bHJOU4nG7SuRoRTCTIhbG428ePaAm0hcmIFQ87fbFqg1wPGvbrW4wIKhLkwljC7YrOc8jc5KIjEuTCWBr2AGfdNSfMeOdelyAXZ5EgF8biuTQ/XCbLOofcv1N0RIJcGMdZc6yEa9OK9wOsXoJcnNGtIF+5ciUpKSlERUWRmZnJ1q1bO932pZde4tprr2XQoEEMGjSIrKys87bXNI38/HwSExOJjo4mKyuLAwcOdKc0EcrsdeCw066ZOKIl6l2NLrz3J7XXwGm7vsWIoOF3kK9bt47c3FwKCgooLy9n8uTJZGdnU1/f8Zje0tJS5s+fz6effkpZWRnJycnMmjWL2tozY2GfffZZnn/+eYqKitiyZQt9+/YlOzub06dPd//IhOGlLFlPypL1Z1a428crw3DEikcT/ajXBroeNMrIFeHid5AvX76cRYsWkZOTw4QJEygqKiImJobVq1d3uP2bb77JfffdR0ZGBmlpabz88suoqkpJSQngOhtfsWIFjz76KHPmzCE9PZ3XXnuNuro6Pvjgg0s6OBFannrlLwDsC9OOTo993uaVPfoWIoKGX0He2trKtm3byMrKOrMDk4msrCzKysq6tI9Tp07R1tbG4MGumdyOHDmC1Wr12WdsbCyZmZmd7tPhcGC3230WEfrGuS9NPxDmQe45/pf/cs5fLCJs+RXkjY2NOJ1O4uN954COj4/HarV2aR9/+MMfSEpK8ga353X+7LOwsJDY2Fjvkpyc7M9hCIMaa6oGYJ8a3v/e+zTX8cucK8KjV0etLF26lLVr1/L+++8TFRXV7f3k5eXR1NTkXaqrqwNYpQhKquq9X2XY3BWoE56RK3K3IOHhV49RXFwcZrMZm83ms95ms5GQcOF5L5YtW8bSpUv53//9X9LT073rPa+z2WwkJp4ZiWCz2cjIyOhwXxaLBYvF4k/pwuiaquirOHBoEVSG2Rwr5/IMvUxQviOWZp2rEcHArzPyyMhIpkyZ4u2oBLwdl9OnT+/0dc8++yxPPfUUxcXFTJ061ee51NRUEhISfPZpt9vZsmXLBfcpwoy7Y++wloQTs87F6KuZGGq0OECaV4SL32O4cnNzWbhwIVOnTmXatGmsWLGClpYWcnJyAFiwYAHDhg2jsLAQgGeeeYb8/HzeeustUlJSvO3e/fr1o1+/fiiKwoMPPsjTTz/NmDFjSE1N5bHHHiMpKYm5c+cG7kiFsdXvBmTEisd+dTjDzY2MM0mzouhGkM+bN4+Ghgby8/OxWq1kZGRQXFzs7aysqqrCZDpzor9q1SpaW1u5/fbbffZTUFDA448/DsBDDz1ES0sL99xzDydOnGDGjBkUFxdfUju6CDHuKxn3h3lHp8d+LZkfUyFn5ALoRpADLF68mMWLF3f4XGlpqc/jysrKi+5PURSefPJJnnzyye6UI8KBu2lFzshd9kmHpziLzLUigp+zHRpdc6x4ht6Fu/3eIYjVrjloRFiTIBdB78ePvgLOVk5pFmrdnXzh7qCWhFNTGKw0Q3N43fJOnE+CXAQ9Tzvwfm0YmvzKAuAgkm8190V07o5gEb7kf4UIeuMU18gM6ej05WlekTlXhAS5CHreS/Olo9OH9+fRIEEe7iTIRdAb6740P9wnyzrXAZkFUbhJkIugFkkbqcpRQCbLOte+s5tWZORKWJMgF0FtlFJHhKLSpMVgY5De5QSVI1oCrZoZWpvhRJXe5QgdSZCLoObp6NyrjQAUfYsJMu1EcMhz6zcZuRLWJMhFUEszuc4090qzSof2aCNc39h26luI0JUEuQhq4xV3kHsCS/jwfsDZdulbiNCVBLkIamfOyCXIO+L5gDu4Y4vOlQg9SZCLoDUYO/HKCUDmWOmM5wMuVTkKbd/rXI3QiwS5CFqeubYr1XhOIVMad6SegRzX+mFWNGjYq3c5QicS5CJopUn7eBcoZ5qdbDJyJVxJkIugleYdeijNKhfi/aCTDs+wJUEugpano3OPdHRekAxBFBLkIjipznMuBhKdOdO0slMu1Q9TEuQiOB0/TJTSxinNQpU2VO9qgtoBbRhOTYFTx+QmE2FKglwEJ3czwX5tuNxM4iJOY6FSS3A9kOaVsCT/Q0RwcnfcSft413jayf/4yns6VyL0IEEugpM7yKV9vGs87eSeDmIRXiTIRXByNxHIpfld4/nAG+/uIBbhRYJcBJ/TTd75tWUMedd4gny0UgPtrTpXI3qbBLkIPtYdANRocTTRT+dijKFGi6NJiyFSccql+mGoW0G+cuVKUlJSiIqKIjMzk61bt3a67a5du7jttttISUlBURRWrFhx3jaPP/44iqL4LGlpad0pTYSCo9sB2K1ernMhRqKwW01xfWvdrmslovf5HeTr1q0jNzeXgoICysvLmTx5MtnZ2dTXdzx+9dSpU4wcOZKlS5eSkJDQ6X6vuOIKjh496l02bdrkb2kiVLiDaJcnmESX7NLcH3xHJcjDjd9Bvnz5chYtWkROTg4TJkygqKiImJgYVq9e3eH2V199NX/605+44447sFgsne43IiKChIQE7xIXF+dvaSJUuJtWdmkp+tZhMN4PPvfPT4QPv4K8tbWVbdu2kZWVdWYHJhNZWVmUlZVdUiEHDhwgKSmJkSNHcuedd1JV1fkwKofDgd1u91lEiGh3eNt45YzcP94PPusOUFVdaxG9y68gb2xsxOl0Eh8f77M+Pj4eq9Xa7SIyMzN59dVXKS4uZtWqVRw5coRrr72WkydPdrh9YWEhsbGx3iU5WUY2hIz63aC2Q/RgjjJY72oM5ZCWxGmtD7SehO+O6F2O6EVBMWrlpptu4uc//znp6elkZ2ezYcMGTpw4wTvvvNPh9nl5eTQ1NXmX6moZOxsyPO27iemAomspRuPEfGa4pnR4hhW/gjwuLg6z2YzNZvNZb7PZLtiR6a+BAwcyduxYDh482OHzFouFAQMG+CwiRHgCKGGSvnUYlHekj3R4hhW/gjwyMpIpU6ZQUlLiXaeqKiUlJUyfPj1gRTU3N3Po0CESExMDtk9hEJ4ASpisbx0GtdvbTi5BHk4i/H1Bbm4uCxcuZOrUqUybNo0VK1bQ0tJCTk4OAAsWLGDYsGEUFhYCrg7S3bt3e7+vra2loqKCfv36MXr0aAB+97vf8dOf/pTLL7+curo6CgoKMJvNzJ8/P1DHKYxAdZ6ZvS8xHej4LzLROW8HsZyRhxW/g3zevHk0NDSQn5+P1WolIyOD4uJibwdoVVUVJtOZE/26ujquvPJK7+Nly5axbNkyrr/+ekpLSwGoqalh/vz5HDt2jCFDhjBjxgw2b97MkCFDLvHwhFGkLFnPKKWWEssp6BMDl41Ggtx/e7QRoJigpR5OWqF/4Jo8RfDyO8gBFi9ezOLFizt8zhPOHikpKWgXuWvJ2rVru1OGCDFXKN+6vom/AkxmfYsxqNNY4LIx0LjPdVYuQR4WgmLUihAAE0zuIE9I17cQo0t0//yknTxsSJCLoDFBqXR9kyhBfkkSJMjDjQS5CBIaE03ui1jkjPzSJLpH/NRV6FqG6D0S5CIoJCv1DFaacWgRED9R73KMzRPkJ76FlmP61iJ6hQS5CAqTlcOAe9RFRKTO1Rhc9ED3qB+g7mtdSxG9Q4JcBIV0kyvIt6ujdK4kRCRd5fpaV65vHaJXSJCLoDDZdAiA7dpInSsJEcPcQV4rQR4OJMiF/lQnExVXR+d2VYI8IJLcF+HVlcNFruMQxtetC4KECKjG/fRVHLRoFg5qw/SuxvBSlqwnCgd7o83QbAN7HcTKzzWUyRm50J/7z/+dWiqq/EoGxGksMHS864G0k4c8+V8j9OcOGmlWCTBP84q0k4c8CXKhv1oJ8h4xTEauhAsJcqGv9lbv1LXfaDL0MKC8QxC/lg7PECdBLvRVvwucrXyn9aNKG6p3NaEl/gowW+B0Exw/rHc1ogdJkAt9uZtVdqipyD06Ayvlkb/ydZv7Hp5yhWdIkyAX+nK330qzSs/4xtPvULtN30JEj5IgF/qq/hKAb+TS/B5RobrnXKn5St9CRI+SIBf6OXXcdScbYJs6RudiQtM2zf1zPVoBbad1rUX0HAlyoR/PWeJlo/mOAfrWEqKqtaHQdyg4W11hLkKSBLnQT/UWAN61JelcSChTKLZfDsC/vPiqvqWIHiNBLvTjDvJt2lidCwltnmarKaYDOlcieooEudCHs907kmKbKkHekzw/36tM++XCoBAlQS70YdsJbaewazEc1KRppSft0lJwaBEMUezw3RG9yxE9QIJc6KN6KwDl6hg0+TXsUQ4i2amluh64f+4itHTrf9DKlStJSUkhKiqKzMxMtm7t/Jdj165d3HbbbaSkpKAoCitWrLjkfYoQUL0ZgK+kWaVXeH/O7n4JEVr8DvJ169aRm5tLQUEB5eXlTJ48mezsbOrr6zvc/tSpU4wcOZKlS5eSkJAQkH2KEOA+M+yoozNlyXpSlqzv7YpCWrk3yOUEKRT5HeTLly9n0aJF5OTkMGHCBIqKioiJiWH16tUdbn/11Vfzpz/9iTvuuAOLxRKQfQqDa6qFpmpQTHJFZy8p91xwZdsFp+36FiMCzq8gb21tZdu2bWRlZZ3ZgclEVlYWZWVl3SqgO/t0OBzY7XafRRhIjfusMH4ip4jSt5Yw0cBAvlWHAhrUyuX6ocavIG9sbMTpdBIfH++zPj4+HqvV2q0CurPPwsJCYmNjvUtycnK33lvopMrVPk7yNH3rCDPeZqxvu3fSJYKXIYcL5OXl0dTU5F2qq6v1Lkn4o3KT6+vlP9S3jjCzVU1zffPtF/oWIgIuwp+N4+LiMJvN2Gw2n/U2m63Tjsye2KfFYum0vV0EuZZj3jsCkXItIJ1vvaVMneD6puZLaPse+kTrW5AIGL/OyCMjI5kyZQolJSXedaqqUlJSwvTp07tVQE/sUwSxb91n40PGQ78h+tYSZr7V4mHAMNcEWjIMMaT43bSSm5vLSy+9xJo1a9izZw/33nsvLS0t5OTkALBgwQLy8vK827e2tlJRUUFFRQWtra3U1tZSUVHBwYMHu7xPETrWvPU6AK8eTZYhhr1OgZQZrm+PfK5vKSKg/GpaAZg3bx4NDQ3k5+djtVrJyMiguLjY21lZVVWFyXTm86Guro4rr7zS+3jZsmUsW7aM66+/ntLS0i7tU4SOa0x7ANjs+TNf9K6Ua2H7ujP9FCIkKJpm/Fl07HY7sbGxNDU1MWCAzGsdtJobYJnrjjVXni6SOch1MFypZ5PlQTD1gSXfQmRfvUsSnfAn1ww5akUYVKXrz/k96ggJcZ3UaEOo0eJAbTszDFQYngS56D3uP+fLpFlFR8qZZi1pXgkZEuSi97jPyDer43UuJLyVOT1BLh2eoUKCXPSOk1Zo3I+qKRLkOvP+/GvLwXFS32JEQEiQi97h/jN+t3Y5dvrpXEx4q2UIDLwcNKdcrh8iJMhF7zj4vwBsUifqXIgAYORM19dDJRfcTBiDBLnocalLPqKhwnXxz2fqZJ2rEQCMudH19cBf9a1DBIQEuehxVyiVDFHsNGtRfKWO07scAUxcc5o2zQzHD8OxQ3qXIy6RBLnocTNN3wDwhTqRNv8vJhY9oJmYMx+q7mYvYVwS5KLHzTS7grxUmlWCiuff49OP39S5EnGpJMhFj0lZsp7JS9ZxpXIAgFJnhr4FCR+eIJ9u2u2a1lYYlgS56FHXmnZgVjT2qcM5ymV6lyPOsk9Lpk4bTJTSBpVyswkjkyAXPUqaVYKZQqnT/e9ycKO+pYhLIkEueoyCyvUmT5Bn6FuM6NBnnn+XAxLkRiZBLnrMRKWSIUqTDDsMYl+oV7iHIR6SYYgGJkEuesxss+t+nH9T02XYYZBqJubMbJR7/lvfYkS3SZCLnqFp3GRyBfn/OKfpXIy4kGLV/e+zW4LcqCTIRc+o381IkxWH1of/U6+8+PZCN391TgXFBHXlcKJK73JEN0iQi57hPrv7m5pOC9E6FyMupJFYGPED14M9H+lbjOgWCXLRM3Z/CMAGaVYxhglzXF/d/27CWCTIReA17IeGPbRqZkrUq/SuRnTF+J+4vlZvAXudvrUIv0mQi8Db4zqr+0KdiB25S7sRpPzL13yljnU92POxvsUIv0mQi8Bz/3n+P6o0qxjJ/zivBmDz+tWkLFmvczXCHxLkIrAaD4B1ByhmNjqn6F2N8EOxuz9jmrKXeI7rXI3whwS5CJiUJetZteIJ14MxN/IdA/QtSPilliFsUdMwKRq3mT/Xuxzhh24F+cqVK0lJSSEqKorMzEy2bt16we3fffdd0tLSiIqKYtKkSWzYsMHn+bvuugtFUXyW2bNnd6c0oSMTKreaXTdZJuNOfYsR3fKe8zoAbjP/DTRN52pEV/kd5OvWrSM3N5eCggLKy8uZPHky2dnZ1NfXd7j93//+d+bPn8/dd9/N119/zdy5c5k7dy47d+702W727NkcPXrUu7z99tvdOyKhm+tM20lQvoPowTBWPoiNaIMzk1OahVGmo1B94RM0ETz8DvLly5ezaNEicnJymDBhAkVFRcTExLB69eoOt/+3f/s3Zs+eze9//3vGjx/PU089xVVXXcWf//xnn+0sFgsJCQneZdCgQd07IqGb282fAfDKyatJeVRm0zOiFqLZoGa6HlS8oW8xosv8CvLW1la2bdtGVlbWmR2YTGRlZVFWVtbha8rKyny2B8jOzj5v+9LSUoYOHcq4ceO49957OXbsWKd1OBwO7Ha7zyJ0duo4N5q2AfCu83qdixGX4t1297/fzvehtUXfYkSX+BXkjY2NOJ1O4uPjfdbHx8djtVo7fI3Var3o9rNnz+a1116jpKSEZ555hs8++4ybbroJp9PZ4T4LCwuJjY31LsnJyf4chugJO97DorSzS72c3VqK3tWIS7BVG0eVOgRaT8ol+wYRFKNW7rjjDm655RYmTZrE3Llz+fjjj/nyyy8pLS3tcPu8vDyampq8S3V1de8WLHxpGnz9OiBn46FAw8R7nn/Hr6V5xQj8CvK4uDjMZjM2m81nvc1mIyEhocPXJCQk+LU9wMiRI4mLi+PgwYMdPm+xWBgwYIDPInRUtRms23FoffjQ+QO9qxEB8J7zOteMiJWfg3XnxV8gdOVXkEdGRjJlyhRKSkq861RVpaSkhOnTp3f4munTp/tsD7Bx48ZOtweoqanh2LFjJCYm+lOe0MvmlQD8l3OGjB0PEXXEwfhbXA82r9K3GHFRfjet5Obm8tJLL7FmzRr27NnDvffeS0tLCzk5OQAsWLCAvLw87/YPPPAAxcXF/Ou//it79+7l8ccf56uvvmLx4sUANDc38/vf/57NmzdTWVlJSUkJc+bMYfTo0WRnZwfoMEWPOX7YOzfHaudNOhcjAmq66/+o4+u1XL3kTZ2LERfi9/235s2bR0NDA/n5+VitVjIyMiguLvZ2aFZVVWEynfl8+MEPfsBbb73Fo48+ysMPP8yYMWP44IMPmDhxIgBms5nt27ezZs0aTpw4QVJSErNmzeKpp57CYrEE6DBFj9nyIqDB6CwO7hyudzUikJKvhuHTsNRs5f+J2AjIRV7BStE041++ZbfbiY2NpampSdrLe9P3J+C5K6C1GX75Pikvfa93RSKAKpfeDLs+gHcXckzrz2WPHoA+cpOQ3uJPrgXFqBVhPClL1vPHp/OgtZm9ajIpL53SuyTRE9J+Qo0Wx2XKSfhmrd7ViE5IkItuieY0iyJcc+asds4GFH0LEj3DHMEr7e7pFr5YAe2tupYjOiZBLrrlLvNfGaqcoEodwvvOa/UuR/Sgt5w/pkGLhe8qebTgIZmrPAhJkAv/ff8dv4pw3Vz5ufbbafO/z1wYyPdE8UL7XAB+HfE+UTj0LUicR4Jc+O+L54lVTrFPHc6H6g/1rkb0gredN1CtDiFeOcFd5k/0LkecQ4Jc+Oek1XuByLL2X6DKr1DISlmy3tuM0kYEz7XfBsCvIj5yjVgSQUP+Fwr/fPpHaP+ecnU0G1W5lVs4+UCdwT51OAOVFvjbn/QuR5xFglx0XeUXUP4aAIVt/4iMVAkvKiYK2+e7HmxeBUe/0bcg4SVBLrqm7TR89IDr+6sW8qWWpm89Qhel6pV87LwGNCfbVy0EZ7veJQkkyEVXbVoOxw5A36Fw4xN6VyN09ETbApq0GNJNR2BLkd7lCCTIRVfU74HPl7u+/4dnIVpuwxfOGhjIv7S751359I9w/Ii+BQkJcnERjmZ4ZyGoba4bKk+Yq3dFIgi847yeLWoatJ2Cd+9yNb0J3UiQi85pGnz0G2jcB/0T4ZYXQJEOTuG6i1Bu672uv86OVkDxEr1LCmsS5KJzW/8Ddv4XmCLg569Cv6F6VySCSC1D4GcvAwpsewUq3tK7pLAlQS46drgUPnnY9f2NT8GIawDfi0SEYEwWzHSfjX/8z1C9Vd96wpQEuThf1WZ4ez6o7XDFz+CaeyXAReeuewjGzIL20/DG7TK+XAcS5MJXXQW8+XNXJ9aoG+DWImkXFxdmMrma3kZMB0cTvH4rNOzTu6qwIkEuvG7P+1e+e/FmcNjh8h/CvDcgQm63J7ogsi/84zq+UUfCqWOw5qdQ97XeVYUNudWbIGXJen5m+huFfV7GorTDsKnwy/chaoA0pwi/DOQkb0f+kfGmKoiIhp+9CBPmdLjt2b9blUtv7q0SDUNu9Sa6rr2VJRFvsTyyCIvSznrnNFj4EUTJB6Lw3wn68/PWfBh9I7R/D+8sgNKlcil/D5MgD2d1FfAfM/lVxMcAvNA+l8Vtv4HIGH3rEobWTAzMXwuZv3KtKC2E/7wR6vfqW1gIk1u7hKNTx2HTc1C2EjQnx7T+PNJ2N8XqNL0rEyEi5ZFPgOu41aTwRJ81DKgrhxevhR8+CD/4tfzFF2DSRh4mUpaspx+n2PkPlfDFC67RBQAT5jClfDbHiNW1PhG64jlOYZ+X+bG5wrUiejDM+GfGfzSM74kCpI28I/7kmgR5qNM0OFrBW//+BHPMf6ev4r7fYvxE+PFjMG62dGiKXqBxk2krv4t4h1GmowDYtWjed87gLecN7NNGABLoZ5MgD3ftrVD7FezbAHvXw/HDZ54bkgbX/R6u+BkpD/+PfjWKsGTGyaF5J+HzZT6/lwfUYWxUp3Df//drSLoSzH10rDI49PiolZUrV5KSkkJUVBSZmZls3Xrhy3Lfffdd0tLSiIqKYtKkSWzYsMHneU3TyM/PJzExkejoaLKysjhw4EB3Sgs/7a1k563iNw8/DBsL4JV/gKXJ8MpN8PcX4PhhHFoEHzp/wC8cj8F9m2HS7a6LOIToZU7McOWdsHgbd7bmscE5jTbNzBhTLfdF/LerU3TpCHj1J1DypGuun/q94GzTu/Sg5vcZ+bp161iwYAFFRUVkZmayYsUK3n33Xfbt28fQoedPqvT3v/+d6667jsLCQn7yk5/w1ltv8cwzz1BeXs7EiRMBeOaZZygsLGTNmjWkpqby2GOPsWPHDnbv3k1UVNRFawqZM3LVCW3fQ/tpZjz9Ef04TT9OEau08J+/GO260KLZxvufl5OkHCNzYDOcrANNPW9Xx7T+/E1N56/OqfxNTaeFaB0OSIiLG0ALM03fMMv8FTNMO1z3BD2HU1MwD0yGQZfDgGGuCdz6J7ja26MHQfRAsPR3XZgU2R/6REFEFJjMvX9AAdKjTSuZmZlcffXV/PnPfwZAVVWSk5P59a9/zZIl509lOW/ePFpaWvj444+966655hoyMjIoKipC0zSSkpL47W9/y+9+9zsAmpqaiI+P59VXX+WOO+44b58OhwOHw+F93NTUxIgRI6iurvYvyLe/AxVvd/JkBz8W749KO+v7sx9r7KxrQkHDhIYCKKiMG9oPVBU0p2tRna55TFQnOFtdZxvOVtC6N9bWrkVxUBvOVVdlQsJkGJHJxOcPIPfUFEajoJKqHGWK6QDjlUrGmmoZrdTST3Fc/MUd7jACzJEQEQmmPq5gN0eAYj6zmEyAAorJ9V9G8TxWfL9693n2+o6PokPT/l9I63ofgN1uJzk5mRMnThAbe5HBCJofHA6HZjabtffff99n/YIFC7Rbbrmlw9ckJydrzz33nM+6/Px8LT09XdM0TTt06JAGaF9//bXPNtddd532m9/8psN9FhQUuFJTFllkkSXEl+rq6otms1/jyBsbG3E6ncTHx/usj4+PZ+/ejgf7W63WDre3Wq3e5z3rOtvmXHl5eeTm5nofq6rK8ePHueyyy1CCfIInz6es3389GIQcn/GF+jEa5fg0TePkyZMkJSVddFtDXhBksViwWHwncxo4cKA+xXTTgAEDgvqX6FLJ8RlfqB+jEY7vok0qbn4NXYiLi8NsNmOz2XzW22w2EhISOnxNQkLCBbf3fPVnn0IIIc7wK8gjIyOZMmUKJSUl3nWqqlJSUsL06dM7fM306dN9tgfYuHGjd/vU1FQSEhJ8trHb7WzZsqXTfQohhDjLRVvRz7F27VrNYrFor776qrZ7927tnnvu0QYOHKhZrVZN0zTtl7/8pbZkyRLv9l988YUWERGhLVu2TNuzZ49WUFCg9enTR9uxY4d3m6VLl2oDBw7UPvzwQ2379u3anDlztNTUVO3777/3t7ygd/r0aa2goEA7ffq03qX0CDk+4wv1YwzF4/M7yDVN01544QVtxIgRWmRkpDZt2jRt8+bN3ueuv/56beHChT7bv/POO9rYsWO1yMhI7YorrtDWr1/v87yqqtpjjz2mxcfHaxaLRbvhhhu0ffv2dac0IYQIOyFxib4QQoQzuU5bCCEMToJcCCEMToJcCCEMToJcCCEMToI8CDgcDjIyMlAUhYqKCr3LCYjKykruvvtuUlNTiY6OZtSoURQUFNDa2qp3aZfE3ymcjaKwsJCrr76a/v37M3ToUObOncu+ffv0LqtHLV26FEVRePDBB/Uu5ZJJkAeBhx56qEvzKRjJ3r17UVWVF198kV27dvHcc89RVFTEww8/rHdp3bZu3Tpyc3MpKCigvLycyZMnk52dTX19vd6lXbLPPvuM+++/n82bN7Nx40ba2tqYNWsWLS3nTykbCr788ktefPFF0tPT9S4lMPQe/xjuNmzYoKWlpWm7du3S4PxZIEPJs88+q6WmpupdRrdNmzZNu//++72PnU6nlpSUpBUWFupYVc+or6/XAO2zzz7Tu5SAO3nypDZmzBht48aN2vXXX6898MADepd0yeSMXEc2m41Fixbx+uuvExMTo3c5Pa6pqYnBgwfrXUa3tLa2sm3bNrKysrzrTCYTWVlZlJWV6VhZz2hqct2c26j/Xhdy//33c/PNN/v8WxqdIWc/DAWapnHXXXfxq1/9iqlTp1JZWal3ST3q4MGDvPDCCyxbtkzvUrqlO1M4G5Wqqjz44IP88Ic/9N7FK1SsXbuW8vJyvvzyS71LCSg5Iw+wJUuWoCjKBZe9e/fywgsvcPLkSfLy8vQu2S9dPb6z1dbWMnv2bH7+85+zaNEinSoXXXX//fezc+dO1q5dq3cpAVVdXc0DDzzAm2++2aVbSBqJXKIfYA0NDRw7duyC24wcOZJf/OIXfPTRRz43wnA6nZjNZu68807WrFnT06V2S1ePLzIyEoC6ujpmzpzJNddcw6uvvorJoDd9bm1tJSYmhvfee4+5c+d61y9cuJATJ07w4Ycf6ldcAC1evJgPP/yQv/3tb6SmpupdTkB98MEH3HrrrZjNZ+7j6XQ6URQFk8mEw+Hwec5IJMh1UlVVhd1u9z6uq6sjOzub9957j8zMTIYPH65jdYFRW1vLj370I6ZMmcIbb7xh2P8kHpmZmUybNo0XXngBcDVBjBgxgsWLF3d4v1oj0TSNX//617z//vuUlpYyZswYvUsKuJMnT/Ltt9/6rMvJySEtLY0//OEPhm5GkjZynYwYMcLncb9+/QAYNWpUyIT4zJkzufzyy1m2bBkNDQ3e54x6w5Dc3FwWLlzI1KlTmTZtGitWrKClpYWcnBy9S7tk999/P2+99RYffvgh/fv3995mMTY2lujoaJ2rC4z+/fufF9Z9+/blsssuM3SIgwS56CEbN27k4MGDHDx48LwPJqP+EThv3jwaGhrIz8/HarWSkZFBcXHxeR2gRrRq1SoAZs6c6bP+lVde4a677ur9goRfpGlFCCEMzpg9T0IIIbwkyIUQwuAkyIUQwuAkyIUQwuAkyIUQwuAkyIUQwuAkyIUQwuAkyIUQwuAkyIUQwuAkyIUQwuAkyIUQwuD+fyMfP89GcSXsAAAAAElFTkSuQmCC",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "\n",
            "np.random.seed(1345)\n",
            "n = 10000\n",
            "x = np.random.normal(size=n)\n",
            "\n",
            "plt.plot(\n",
            "    np.arange(1, n + 1), np.cumsum(x) / np.arange(1, n + 1), label=\"Empirical average\"\n",
            ")\n",
            "plt.plot([1, n + 1], [0, 0], label=\"Expectation\")\n",
            "plt.xlabel(\"Sample size\")\n",
            "plt.ylabel(\"Empirical average\")\n",
            "plt.legend()\n",
            "plt.savefig(\"lln.png\")\n",
            "plt.show()\n",
            "\n",
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "\n",
            "a = plt.hist(x, density=True, bins=100)\n",
            "v = np.linspace(-5, 5, 100)\n",
            "plt.plot(v, sc.norm.pdf(v))\n",
            "plt.savefig(\"llnhisto.png\")"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "29e5b5e3",
          "metadata": {},
          "source": [
            "### Scatter plot and Histo 2D"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 13,
          "id": "0e636c19",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            },
            {
              "data": {
                "image/png":
                  "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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "n = 10000\n",
            "rho = 0.8\n",
            "np.random.seed(2354920)\n",
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "u = np.random.normal(size=n)\n",
            "v = np.random.normal(size=n)\n",
            "w = rho * u + np.sqrt(1 - rho**2) * v\n",
            "plt.scatter(u, w, s=1)\n",
            "\n",
            "plt.savefig(\"scattergauss.png\")\n",
            "fig, ax = plt.subplots(figsize=(4, 4))\n",
            "\n",
            "a = plt.hist2d(u, w, bins=50)\n",
            "plt.savefig(\"hist2dgauss.png\")"
          ]
        },
        {
          "cell_type": "markdown",
          "id": "abe0f12c",
          "metadata": {},
          "source": [
            "### Bivariate density"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 14,
          "id": "d7ec1c9d",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  "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",
                "text/plain": [
                  "<Figure size 400x400 with 1 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "um = -3.5\n",
            "uM = 3.5\n",
            "wm = -3.5\n",
            "wM = 3.5\n",
            "\n",
            "x, y = np.mgrid[um:uM:0.01, wm:wM:0.01]\n",
            "pos = np.dstack((x, y))\n",
            "rv = sc.multivariate_normal([0.0, 0.0], [[1.0, rho], [rho, 1]])\n",
            "fig2 = plt.figure(figsize=(4, 4))\n",
            "ax2 = fig2.add_subplot(111)\n",
            "ax2.contourf(x, y, rv.pdf(pos))\n",
            "plt.savefig(\"densitygauss.png\")"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 15,
          "id": "03c6db12",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 800x400 with 2 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "x, y = np.mgrid[um:uM:0.01, wm:wM:0.01]\n",
            "pos = np.dstack((x, y))\n",
            "rv = sc.multivariate_normal([0.0, 0.0], [[1.0, rho], [rho, 1]])\n",
            "fig2 = plt.figure(figsize=(8, 4))\n",
            "ax2 = fig2.add_subplot(122)\n",
            "ax2.contourf(x, y, rv.pdf(pos), vmin=0, vmax=0.28, levels=10)\n",
            "ax2 = fig2.add_subplot(121)\n",
            "ax2.hist2d(u, w, bins=50, density=True, vmin=0, vmax=0.28)\n",
            "plt.xlim([um, uM])\n",
            "plt.ylim([um, uM])\n",
            "\n",
            "plt.savefig(\"density2dhisto.png\")"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 18,
          "id": "8db96ccc",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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6Ozsxb948/PSnP8U999xjj12StVkwdWDtQCCE6Id9LWlUjvsYc/BaCeTu1J4euGlGGG6acTkoHCtvQV5FC46Wt+BMjRbVrd2obq3BxwU1AIAQX+XAqZRxgUiLC0ByuB9kUgYFZ2aXYHDbbbfhtttus8euyBZsGArGCgRXB4Gxvm/tkDBhHC0gF6b29EDWzDBkzRwICh36fhRcajUtrlRY1YbGdj2+OFWHL04NvBd8VXKkxgYgPS4Q6XGBmBulhspDJubLIDM5ZI+BXq+HXn/5Q1+n04lYjZuzwtSBOYFgvDAwGiFEb5NwMO40ApEb8VHKsXRaCJYOnhrZ02dAYVUbjle0IK+iFQWXWtHe04/9xY3YX9wIAFDIpJgXrUZaXCDS4wKQGhMItRdXZnRkDhkMsrOz8dRTT4ldBpkZCiYzSmBpILj6Oew6csDRAnJzKg+Z6TRHAOg3GFGkaUdeeQuOX2pBXnkrmjr0OFbRimMVrXh58HHTw3yRFjcwqpAWF8C1FByMQwaDzZs3Y9OmTaavdTodoqOjRazIDdkgFNgqEFgD+wuIJk8uk2J2pBqzI9X46fXxEAQBFc1dOFbRguMVLThe0Yqypk4U17ejuL4dfz860NA4Ra26PKIQyz4FsTlkMFAqlVAqRZozpkmHgomMEowXCMJCRp8+qm/0G/Ox45noqodjTiNwtIBoXBKJBPHB3ogP9saP0gb+uGvq0ON4RSuOV7Tg2KVWnK3Rok7bg3+drMW/Tg4suuSjlOO62ACkxQYgLS4AKdH+8FI45OHKJfEnTcNZORSYM0owVhi4ervJhgMiEkewjxK3zg7HrbPDAQBdvf0orGzD8UutOH5poE+hQ9+P7y404rsLA30KcqkEsyLVSI8NQNrg9EOwD/94tBW7BIOOjg6UlJSYvi4vL0dhYSECAwMRExNjjxJoImwcCkYKBBMNAyM9zlrhYKRpBI4WENmHl0KORUnBWJQUDAAwGAUUaXQ4XtE6OAXRCo2uByer2nCyqg2vHioHACSEeCM9NtDUqxDL9RSsxi7B4Pjx41i+fLnp66H+gTVr1uDNN9+0Rwk0HjNCwXj9BBMZJbA0EBCRa5NJJZgVocasCDXWLIqDIAiobu1G/qVW5A32Klyo70BZYyfKGjvx/vGBpZxDfJVIjwvAgrhApMcHsk9hEuwSDJYtWwZB4NXsHNYoocDRRglGep7xRg2uXvXw6v4CjhYQOTaJRILoQC9EB3ph5fxIAEBbVy/yLw2c6XC8ogWnqrVobNfjy9MafHlaA+DyegpDiy/NiVJDKed6ChPBHgN3Z8dQMFYgmB00+gH3TPPYCyzZDUMBkUPw91IMW6Gxp8+AU9Va5JU3I6+iFfkVLdesp6CUS3FdTAAyEgKRER+E+TH+XHhpFAwG7sxGoWCigWCsMHD1dtYIB5MeLSAih6TykA2MDMQHAhhYT+F8XTvyKlpMSzq3dPYit6wZuWXNAC5CIZMiJdrfFBRSYwPgqWBQABgM3JeVQoElowQTDQSTZdUrK3K0gMhpyGVS0+Wm1w+up1DS0IEj5S04WjZwJcnGdj3yKgZCw4sogYdMgvkxAchMCMKixCCkxPi77dQDg4E7skMosHYgGGnU4Or+grFWPeRoAZH7kkgkmBrmi6lhvnhoYSwEQUB5UyeOXhEU6rQ9pmtA/E/ORag8pEiPC0RmYhAWJQZjTqTabZoZGQzcjQihwF4jBFcyd7SADYdE7kMikSAhxAcJIT74yYIYCIKAS81dOFzajMOlTcgtbUZzZy8OXmzCwYtNAIqh9vTA4qQgLJkaguuTghEd6LrLODMYuBMbhILxpg7GCgUL/UqHfX1ElzjqtpMxkdGCUTEUELk8iUSCuGBvxAV744GMgaBwob4DuaVNOFw60Jeg7e4bdtZDfLA3lkwNxpKpIViUGARvpescTl3nldDYLAwFE20ynGgguDoMjPQ9SwLCldMIVh0tICK3I5FIMD3cF9PDfbF2cTz6DUacrNbi0MUmHLzYiBNVbShv6kR5Uyf+lnsJCpkUGQmBuDE5FDcmhyI2yFvslzApDAbuwAFCwViBwBITXfWQowVENFlymRSpsQMXePqPrKnQ9fThSGkzDl5swv4LDahq6TZNOzz1r3NICPHGTcmhuGlGGNLjAp2uN4HBwNWJHAqsFQjGOl3RJqMFDAVENAo/lQdumRWOW2aFQxAElDZ2Yl9RPfYVNQxcQbKxE2WN5dh5sBxB3grcMisMt86egkWJQfCQScUuf1wMBq7MjqHAHqME5hpvtIBTCEQ0WRKJBEmhPkgK9cHPlyZC19OHgxeakFNUj5zzDWju7MV7eVV4L68Kfio5smaG4Qdzp2DJ1BCHDQkMBq5KxFBg60Bw5TTCREcLOIVARPbgp/LAHXOn4I65U9BnMOJIWTO+OqPB12c1aOroxccFNfi4oAZB3grcOS8C91wXiTmRaoe6ABSDgStysVBgyaqHV48WXPN9TiEQkY15yKRYMjUES6aG4Om7ZyP/Uiu+PF2Hz0/VoqmjF28ersCbhyuQFOqDe6+Lwo/SohDkAJeTZjBwNWNcJfFq9goFSzyvvf9gt2WnJk5ktIBTCETkaGRSiWnZ5ifumIFDF5vwj4Jq7D1Xj5KGDjy7uwh//uYC7poXgbWL4jA7Ui1arQwGrmSSl042bWtmKDAnEJhrstdI4BQCETkaD5kUy5NDsTw5FLqePnx1ug5/P1qJU9VafJRfjY/yq5EaG4BfLE3AzTPD7D7N4JidD2S+SYSCiSxeZK9QMNYaBpaMFlyNUwhE5Ej8VB5YlR6Dzx5ZjI9/uQh3p0TAQyZB/qVW/PztfKz838M4eLERgjD2Z5s1ccTAFThQKLDGKMGQK0cLOIVARK5MIpHgupgAXBcTgCdun2HqPzhZ1YaHXsvDwoRA/PHu2ZgW5mvzWjhi4MKcLRRYc0lkTiEQkbMK9VPhv25NxoHfLMe6xXFQyKQ4UtaCH7x4CH/9rhQGo21HDxgMnN0Ez0Bw9FBwtcmMFph15USGAiJyUCG+Smy5cxa+/c0y3Jgcit5+I/70ZRF+/NdcNHfox38CCzEYODMzTksc9n0HDAVXjhZMdgrhagwFROTMIv098dqaNDx77xx4K2Q4VtGK//PqUbR09tpkf3YLBjt27EBcXBxUKhUyMjKQl5dnr127JiusVTDZULDEs9SiUHD1qYoTmUJgXwERuTOJRIJV6TH456+uR4ivEkWadjz46lF09xqsvi+7BIP3338fmzZtwpYtW1BQUIB58+ZhxYoVaGhosMfuXY8V1iqw1tkH5hpv/YLRRgsmgn0FROTqEkN88N6GhQj2UeBcnQ5/P3rJ6vuwSzB44YUXsGHDBqxbtw4zZ87EK6+8Ai8vL7z++uv22L1rsdJaBUPE7imw1hQC+wqIyF0khfrgNyumAwBeOVAGfb91Rw1sHgx6e3uRn5+PrKysyzuVSpGVlYXc3NwRH6PX66HT6YbdaGyWNhsOGe+CSFeyNBSMNYXAvgIioom757ooeClkaOrQo6ql26rPbfNg0NTUBIPBgLCwsGH3h4WFQaPRjPiY7OxsqNVq0y06OtrWZToHG56BMJqR+gos4RB9BQwFROQiPGRSyKW2WRHRIc9K2Lx5M7RarelWVVUldknic4AzEKwVCq42Xl+BOVdNZLMhEbmD3NJm6Hr6oZBJEWLlCy/ZfOXD4OBgyGQy1NfXD7u/vr4e4eHhIz5GqVRCqRT/ClMOw4mbDUdi7hTClcbrKxgVRwuIyEV09fZj61fnAQCr0qOh9vKw6vPbfMRAoVAgNTUVOTk5pvuMRiNycnKQmZlp6907Pys3G17JmfsK2GxIRO6ou9eA9W8ex8lqLXyVcvxyufVWjB1il2slbNq0CWvWrEFaWhoWLFiA7du3o7OzE+vWrbPH7l2SPfsKLMVmQyIi6ylt7MCmD07iZFUbvBUyvPnTBZii9rT6fuwSDFatWoXGxkY8+eST0Gg0SElJwe7du69pSKSrOEBfAWD+aMFIPQXWDAVsNiQid2I0CngrtwLP7i5CT58Rvio53libjtTYAJvsz25XV9y4cSM2btxor905Pyv0FYzGnCkEczEUEBFZhyAI2F/ciG1fF+Ns7cDn9vVJwXjuvrmI8Lf+SMEQXnbZEVmpr8DeUwgOEwqIiJyYIAg4Wt6CbXuKcfxSKwDAWyHDb29LxoMZsZDa6DTFIQwGTsSWV0ycLIcKBRwtICIn1NNnwOen6vDW4QqcrtECAJRyKdYsisO/3ZCIQG+FXepgMHA0VugrsKfR1iiYTCi4GkMBEbmymrZuvHe0Eu/lVaJ58IqJCrkUq9KisfHGJIT5qexaD4OBI7Gwr+BqlowWmDuNMJFAAFgWCrhWARG5uvaePnx1RoOPC6pxpKzFdH+EWoUHM2Px4/QYu40QXI3BwAnY8tTEiRhv5cIh9ggFbDYkImel7zfg+5ImfHKiFl+f1UDfbzR9LzMhCKszY3HzzDDIZeIuSsxg4ChsPIVgyzMRAIYCIqKRdPcacOBCA746o8G+8w1o11/+bEsM8cY910Xh7pQIRAV4iVjlcAwGjsDGUwi2NNLFkBgKiMidtXX1Yn9xI/ac1WB/cSO6+y5fFjnUV4nb50zBD+dHYm6UGhKJOP1hY2EwcGC2GC2wprFGCQCGAiJyD4IgoEjTjn1FDfi2qAEFla0wXnFiVaS/J26bHY7b5oRjfnSAzU83nCwGA7GZMYXgKKMF440SAAwFROTa2nv6kFvajAMXGvFtUQNqtT3Dvp8c7osbk0Nx2+wpmB3p55AjA6NhMBDTJKYQLB0tmEx/wUiBAGAoICLX128w4lSNFocuNuHgxUYUVLbBcMWwgFIuxeKkYCxPDsWNyaGItOHKhLbGYOCAxptCuGb70LEvMDQRQwf9q09bHC0MAGMHAoChgIiclyAIKGvqxOHSZhwuacL3JU3Q9Qz/rIoP9saSqcFYPj0UmYlBUHnIRKrWuhgMxGKj0YLJTiOMFQSuZGkoGG9FQ4ChgIjEUdXShdzSZuSWNeNwaRPqdcM/T/1Uclw/NRhLpobg+qRgRAc6zpkE1sRgIAYzroUwHmuMFpjj6kAAjD51ADAUEJHjqm7twtGyFhwtHwgDVS3dw76vkEuRGhOAzMQgLJkajLlR/pA5eOOgNTAYODhrjxacaZ5iUZ/BeIEAYCggIsclCAKqWrpxpLzZFAaqW4cHAZlUgnlRaixKDMaixCBcFxvgMtMD5mAwsDc7jhZY4zTFkQIBYHk/AcBQQES2JwgCSho6kFfRgmPlLTha3oK6q84ckEklmB2pxsL4QCxMCEJ6fCB8lDws8ifgICZyeqK1LpQ03qjBaGEAMG+UAGAoICL76DcYcbZWh2MVLcgrb8HxS61oGbwg0RAPmQRzo/yRER+IjIQgpMYGMAiMgD8RezKj4dAa6hv9Rh01GOvgP9bzXYmhgIjE0tXbj8LKNhyraMXxSy0ouNSKzl7DsG2UcimuiwlAenwgFsQFIjU2AJ4K95saMBeDgb2YOYUw1mJG9nZ1IADM6ycAGAqIaHKaOvQ4XtEyEAQqWnCmVjdsHQFg4KyB9LhApMcHIj0uEHMi1VDIxb0gkTNynKMPjenqaQR7nI1gbiAAJjlKADAUEBEEQUB5UyeOV7TiWEUL8i+1oqyp85rtpqhVA0EgLgBpcYGYHubr8MsNOwObB4NnnnkGX3zxBQoLC6FQKNDW1mbrXToeKzYcmmus6YTRth/J1YEAYCggIuvo7TfibK0W+ZcGgsDxilY0X9UfAADTw3yRFhdgGhVw5tUFHZnNg0Fvby/uv/9+ZGZm4rXXXrP17lyCtacRhg72owWE0cLAkPFGCQCGAiKauPaePhRUtg1ODbSgsKoNPX3GYdso5FLMi1IjLS4QabEBSI0NgL+XQqSK3YvNg8FTTz0FAHjzzTdtvSvHZIWGQ2udjTBeALiaJaMEAEMBEQ2n0fYMjgQM9AgUaXS4qj0A/l4eSIsNHBwRCMDsSDWUcjYKisEhewz0ej30+suL9eh0trlssNgctelwIoEAYCggomsJgoDSxk4cG1w/IK+i5ZqFhAAgJtDLNC2QFhuAxBAf9gc4CPGPQiPIzs42jTQ4NTufnihpVE7qWgkjBQLA8qkDgKGAyNX1GYw4N876AVIJMDPCD2mxA2cLpMUFIMxPJVLFNB6LgsHjjz+OZ599dsxtzp8/j+TkZIuK2rx5MzZt2mT6WqfTITo62qLnclS2ajo0NxyMFgYAG44SAAwFRE6qp8+Ak1VtyBscDci/1IquEdYPmB/jP3jGQCCu40JCTsWi/6lHH30Ua9euHXObhIQES54aAKBUKqFUjn7Acgp2Hi240pUH+ytDwlgh4EojBQKAoYDIHXXq+1FQ2Yq8wWWFC6va0Ns/vFFQ7elhOmWQ6wc4P4uCQUhICEJCQqxdi9szp7/As0EyobUMJhoGhp5zxPsnGAgATh0QObtOfT/yL7XiSFkzjpQ141S1Fv1XdQoG+yiRkRCIjPhALIgPxLRQrh/gSmw+tlNZWYmWlhZUVlbCYDCgsLAQAJCUlAQfH9uew++obL12gblGCwQAQwGRq+vq7cfxirGDQKS/pykEZCQEIS7ICxIJg4CrsnkwePLJJ/HWW2+Zvp4/fz4A4Ntvv8WyZctsvXtx2GkaYaKjBmM9ftTvWSsQAAwFRA6kt9+Iwqo2fF/ShNzSZpyoakWf4dogsDAhCAsTBq46GB3oJVK1JAabB4M333zTfdcwsANzw8FYYQAYORAADAVEzspoFHC2VofvS5vwfUkTjle0ortveLMggwBdiW2i1iZC0+F4B/sJPYeZgQBgKCByVLVt3Th0sQkHSwbCwNWnDwZ5K5CZGITFScFYlBiEmEBODdBlDAZ2Zkl/gWejYLXVD0d67tFYPEoAMBQQ2VF3rwFHyprx3cVGHLzYhJKG4e9Rb4UMmYlBWJQYjEVJQZge5ssgQKNiMHBTlgQCgKMERI6ioqkT3xY3YH9xI46UNUN/xSmEUgkwL9ofS5KCsWRaCFKi/eEh4+mDNDEMBtZkw2kEa4wajBUGhjAUEDmm3n4jjpY3I+d8A/YXN6CiuWvY9yP9PbF0WgiWTg3GosRgqL08RKqUnB2DgRMZOrCbExAmEgaASQYCgKGAyAbaunqxv7gRe8/X40BxIzr0l9+nHjIJ0uMCsWx6CJZPD0VSqA+nB8gqGAwciHdd/4QWOZrowX6i+xxzXxwlILKrmrZu7D6jwd5zGhyraIXhijUFQnyVuCk5FMumh2JxUhB8VRwVIOtjMLAWEZdAtsSkAwHAUEBkJZeaO/HVGQ2+OqPByaq2Yd9LDvdF1owwZM0Mw9xINVcYJJtjMHAzVgkEAEMB0SRVtXThnydr8cWpOpyru3xpeYkEWBAXiBWzwnHzzDCuKUB2x2DgYCY6nWDuc04ERwmIbKupQ48vTtXhs8IaFFS2me6XSSXITAjCrbPDccusMIT68pLEJB4GAwdkrXBg1UAAMBQQWaCnz4Cvz9XjH/nVOFTSZOoZkEiARYlBuGteBG6eGY5Ab4XIlRINYDBwUEMHdXMCwkSDwJAJBwKAoYDIDIIg4EyNDh8cr8JnhTXQ9Vx+b86LUuOulEjcOXcKQv04MkCOh8HAwZl7sJ8IBgIi22jv6cMnJ2rw7tFKFGnaTfdHqFW4LzUKK+dHIiHEsa6uSnQ1BgNrMOOMBM+aDlEvu8xQQGR9F+rb8XbuJXxcUI3O3oELFCnkUqyYFY4fpUVhUWIwZDybgJwEg4EbMCsMAAwERBNgNArYf6EBO78rR25Zs+n+hBBvPLQwFvfMj+Lqg+SUGAxEYK9RA7MDAcBQQDSO3n4jPiuswV+/K8PFwYsVSSXAzTPDsDozDosSg7gCITk1BgOR2DIcMBAQWV9PnwG78irxyoEyaHQ9AAAfpRw/WRCNtYvjEenvKXKFRNbBYCAia4YDi8IAwEBANA59vwEfHK/Gjn0lpkAQ6qvEusXxeCAjBmpPTheQa2EwENnQAd3cgGBxELgSQwHRqARBwL9O1eHZr4pQ09YNAAj3U+GRG5Pwo7QoKOUykSsksg0GA2uorJv0tRKscqCfKAYCojEVVLbi6c/P4cTg6oShvko8sjwJq9KjofJgICDXZtNgUFFRgaeffhr79u2DRqNBREQEHnzwQTzxxBNQKLjKl90xEBCNqbWzF898eR4f5VcDALwUMjx8QyJ+tiQBngoGAnIPNg0GRUVFMBqN+Mtf/oKkpCScOXMGGzZsQGdnJ7Zt22bLXdOVGAiIxiQIAj4trMHTn59HS2cvJBLgvuui8NiK6Qjj6oTkZmwaDG699Vbceuutpq8TEhJQXFyMl19+mcHAHhgIiMbV1KHHbz86hZyiBgDA9DBf/OmeOUiNDRC5MiJx2L3HQKvVIjAwcMxt9Ho99Hq96WudTjfG1g7CCn0GVsNAQDQh+4sb8NiHp9DUoYdCJsV/ZE3FhiUJUMilYpdGJBq7BoOSkhK8+OKL444WZGdn46mnnrJTVS6EgYBoQoxGAX/+5gJe3FcCAJgW5oP/+fF8zJjiJ3JlROKzKBY//vjjkEgkY96KioqGPaampga33nor7r//fmzYsGHM59+8eTO0Wq3pVlVVZUmZ9ifWgbmyjqGAaILae/rw87ePm0LBmsxY/HPj9QwFRIMsGjF49NFHsXbt2jG3SUhIMP27trYWy5cvx6JFi/DXv/513OdXKpVQKpWWlCY+e00pMAgQma1B14PVr+ehSNMOhVyKrffMwT3XRYldFpFDsSgYhISEICQkZELb1tTUYPny5UhNTcUbb7wBqdQN5u5sGQ4YCIgscqm5Ew+9lofKli4E+yjx2po0zIv2F7ssIodj0x6DmpoaLFu2DLGxsdi2bRsaGxtN3wsPD7flrsU3dACfbEBgECCatKqWLvz4r0dQp+1BTKAX3l6/ALFB3mKXReSQbBoM9u7di5KSEpSUlCAqavhwnSAItty147jywD5eSGAIILK6Bl0PHnztKOq0PUgK9cG7P8tAKNcmIBqVTYPB2rVrx+1FcCs88BPZVXevAT996xguNXchOtAT76xnKCAajxtM+BOROxIEAf/1j1M4U6NDoLcCf1+/EOFqhgKi8TAYEJFLeudoJf51shZyqQQv/5/rEBPkJXZJRE6BwYCIXE5JQwee+eIcAODx25KRkRAkckVEzoPBgIhciiAIePwfp9DTZ8SSqcH46eJ4sUsicioMBkTkUv5RUIPjl1rhpZDh2XvnQiqViF0SkVNhMCAil9HTZ8DzewaWY//3m6Yiwt9T5IqInA+DARG5jL8frUS9To8ItQrrFseJXQ6RU2IwICKX0GcwYud3ZQCAX900FUq5TOSKiJwTgwERuYSvzmig0fUg2EeJe66LFLscIqfFYEBELmFXXiUA4P9kxHC0gGgSGAyIyOnVtnUjt6wZAHBfKi+jTDQZDAZE5PS+OqOBIAAL4gIRHcgVDokmg8GAiJze3nMaAMAts8JEroTI+TEYEJFT6+rtR/6lVgBA1gwGA6LJYjAgIqd2vKIVfQYBkf6eiOWFkogmjcGAiJza0GjBgvhASCRc/phoshgMiMipnaxuAwDMj/EXtQ4iV8FgQERO7VytDgAwK0ItciVEroHBgIicVmtnLxra9QCA6eG+IldD5BpsHgzuuusuxMTEQKVSYcqUKXjooYdQW1tr690SkRsoa+oEAESoVfBRykWuhsg12DwYLF++HB988AGKi4vxj3/8A6WlpbjvvvtsvVsicgOXmgeCQVywt8iVELkOm0fs//zP/zT9OzY2Fo8//jhWrlyJvr4+eHh42Hr3ROTCqlu7AQBRAZ4iV0LkOuw69tbS0oK///3vWLRo0ZihQK/XQ6/Xm77W6XT2KI+InExt20AwiPBnMCCyFrs0H/72t7+Ft7c3goKCUFlZic8++2zM7bOzs6FWq0236Ohoe5RJRE5mqPEw3E8lciVErsOiYPD4449DIpGMeSsqKjJt/5vf/AYnTpzA119/DZlMhtWrV0MQhFGff/PmzdBqtaZbVVWVJWUSkYtrHAwGIb5KkSshch0WTSU8+uijWLt27ZjbJCQkmP4dHByM4OBgTJs2DTNmzEB0dDSOHDmCzMzMER+rVCqhVPKNTkRja+nsBQAEeitEroTIdVgUDEJCQhASEmLRDo1GIwAM6yEgIrJEa9dAMAjwYjAgshabNh8ePXoUx44dw/XXX4+AgACUlpbi97//PRITE0cdLSAimog+gxFdvQYAgNqTZzgRWYtNmw+9vLzw8ccf46abbsL06dOxfv16zJ07FwcOHOBUARFNSkdPv+nfvioubkRkLTZ9N82ZMwf79u2z5S6IyE1JJMCqtGjo+w2Qy7i6O5G1MGYTkVPy91Lg2fvmil0GkcthzCYiIiITBgMiIiIyYTAgIiIiEwYDIiIiMmEwICIiIhMGAyIiIjJxitMVhy641C/0ilwJkXMbeg+NdREzRzBUHy+5TjR5Q++jib7vnSIYtLe3AwAOaHeJXAmRa2hvb4darRa7jFENved5yXUi65no+14iOPqfDhi48FJtbS18fX0hkUjELmdCdDodoqOjUVVVBT8/P7HLsQt3e83O+HoFQUB7ezsiIiIglTruTOJE3/PO+H9wJdYvLmevH5jYazD3fe8UIwZSqRRRUVFil2ERPz8/p/2Fs5S7vWZne72OPFIwxNz3vLP9H1yN9YvL2esHxn8N5rzvHfdPBiIiIrI7BgMiIiIyYTCwEaVSiS1btrjV5aXd7TW72+t1RM7+f8D6xeXs9QO2eQ1O0XxIRERE9sERAyIiIjJhMCAiIiITBgMiIiIyYTAgIiIiEwYDIiIiMmEwsLGKigqsX78e8fHx8PT0RGJiIrZs2YLeXte6INSOHTsQFxcHlUqFjIwM5OXliV2SzWRnZyM9PR2+vr4IDQ3FypUrUVxcLHZZLsnc36sPP/wQycnJUKlUmDNnDr788ks7VTo6c17D2bNnce+99yIuLg4SiQTbt2+3X6GjMKf+nTt3YsmSJQgICEBAQACysrJE/ywwp/6PP/4YaWlp8Pf3h7e3N1JSUvD222/bsdqRWfr5umvXLkgkEqxcudK8HQpkU1999ZWwdu1aYc+ePUJpaanw2WefCaGhocKjjz4qdmlWs2vXLkGhUAivv/66cPbsWWHDhg2Cv7+/UF9fL3ZpNrFixQrhjTfeEM6cOSMUFhYKt99+uxATEyN0dHSIXZpLMff36vvvvxdkMpnw3HPPCefOnRN+97vfCR4eHsLp06ftXPll5r6GvLw84bHHHhPee+89ITw8XPjzn/9s34KvYm79DzzwgLBjxw7hxIkTwvnz54W1a9cKarVaqK6utnPlA8yt/9tvvxU+/vhj4dy5c0JJSYmwfft2QSaTCbt377Zz5ZdZ+vlaXl4uREZGCkuWLBHuvvtus/bJYCCC5557ToiPjxe7DKtZsGCB8Mgjj5i+NhgMQkREhJCdnS1iVfbT0NAgABAOHDggdikuxdzfqx/96EfCHXfcMey+jIwM4Re/+IVN6xzLZN4bsbGxogeDyb63+/v7BV9fX+Gtt96yVYljssZn0/z584Xf/e53tihvQix5Df39/cKiRYuEV199VVizZo3ZwYBTCSLQarUIDAwUuwyr6O3tRX5+PrKyskz3SaVSZGVlITc3V8TK7Eer1QKAy/yfOgJLfq9yc3OHbQ8AK1asEO330NnfG9aov6urC319faK8NyZbvyAIyMnJQXFxMZYuXWrLUkdl6Wv44x//iNDQUKxfv96i/TrF1RVdSUlJCV588UVs27ZN7FKsoqmpCQaDAWFhYcPuDwsLQ1FRkUhV2Y/RaMSvf/1rLF68GLNnzxa7HJdhye+VRqMZcXuNRmOzOsfi7O8Na9T/29/+FhEREdcENnuwtH6tVovIyEjo9XrIZDL87//+L26++WZblzsiS17DoUOH8Nprr6GwsNDi/XLEwEKPP/44JBLJmLer/+Nqampw66234v7778eGDRtEqpys6ZFHHsGZM2ewa9cusUshcihbt27Frl278Mknn0ClUoldzoT5+vqisLAQx44dwzPPPINNmzZh//79Ypc1Ie3t7XjooYewc+dOBAcHW/w8HDGw0KOPPoq1a9eOuU1CQoLp37W1tVi+fDkWLVqEv/71rzauzn6Cg4Mhk8lQX18/7P76+nqEh4eLVJV9bNy4EZ9//jm+++47REVFiV2OS7Hk9yo8PNyhfg+d/b0xmfq3bduGrVu34ptvvsHcuXNtWeaoLK1fKpUiKSkJAJCSkoLz588jOzsby5Yts2W5IzL3NZSWlqKiogJ33nmn6T6j0QgAkMvlKC4uRmJi4rj75YiBhUJCQpCcnDzmTaFQABgYKVi2bBlSU1PxxhtvQCp1nR+7QqFAamoqcnJyTPcZjUbk5OQgMzNTxMpsRxAEbNy4EZ988gn27duH+Ph4sUtyOZb8XmVmZg7bHgD27t0r2u+hs783LK3/ueeew9NPP43du3cjLS3NHqWOyFo/f6PRCL1eb4sSx2Xua0hOTsbp06dRWFhout11111Yvnw5CgsLER0dPbEdW9YnSRNVXV0tJCUlCTfddJNQXV0t1NXVmW6uYteuXYJSqRTefPNN4dy5c8LPf/5zwd/fX9BoNGKXZhMPP/ywoFarhf379w/7/+zq6hK7NJcy3u/VQw89JDz++OOm7b///ntBLpcL27ZtE86fPy9s2bLFIU5XNOc16PV64cSJE8KJEyeEKVOmCI899phw4sQJ4eLFi05R/9atWwWFQiF89NFHw94b7e3tTlH/n/70J+Hrr78WSktLhXPnzgnbtm0T5HK5sHPnTlHqFwTzX8PVLDkrgcHAxt544w0BwIg3V/Liiy8KMTExgkKhEBYsWCAcOXJE7JJsZrT/zzfeeEPs0lzOWL9XN9xwg7BmzZph23/wwQfCtGnTBIVCIcyaNUv44osv7Fzxtcx5DeXl5SP+bt1www32L3yQOfXHxsaOWP+WLVvsX/ggc+p/4oknhKSkJEGlUgkBAQFCZmamsGvXLhGqHs7c98GVLAkGEkEQBPMHOIiIiMgVuc5kNxEREU0agwERERGZMBgQERGRCYMBERERmTAYEBERkQmDAREREZkwGBAREZEJgwERERGZMBgQERGRCYMBERERmTAYEBERkQmDAREREZkwGBAREZEJgwERERGZMBgQERGRCYMBERERmTAYEBERkQmDAREREZnIxS5gIoxGI2pra+Hr6wuJRCJ2OUROSxAEtLe3IyIiAlIp/y4goms5RTCora1FdHS02GUQuYyqqipERUWJXQYROSCnCAa+vr4ABj7M/Pz8RK6GyHnpdDpER0eb3lNERFdzimAwNH3g5+fHYEBkBZySI6LRcJKRiIiITBgMiIiIyITBgIiIiEwYDIiIiMiEwYCIiIhMLAoGO3bsQFxcHFQqFTIyMpCXlzfm9h9++CGSk5OhUqkwZ84cfPnllxYVS0RERLZldjB4//33sWnTJmzZsgUFBQWYN28eVqxYgYaGhhG3P3z4MH7yk59g/fr1OHHiBFauXImVK1fizJkzky6eiIiIrEsiCIJgzgMyMjKQnp6Ol156CcDAcsXR0dH41a9+hccff/ya7VetWoXOzk58/vnnpvsWLlyIlJQUvPLKKxPap06ng1qthlar5ToGRJPA9xIRjcesBY56e3uRn5+PzZs3m+6TSqXIyspCbm7uiI/Jzc3Fpk2bht23YsUKfPrpp6PuR6/XQ6/Xm77W6XTj1rb9mws4U6ODn0oOP08P+Ht5INBbgWAfJUJ9lZji74kwXyXkMrZVkHPS9xtQ19aDOm0PGjv0aGrXo7WrF21dfWjv6YOupx93zYvAyvmRYpdKRE7MrGDQ1NQEg8GAsLCwYfeHhYWhqKhoxMdoNJoRt9doNKPuJzs7G0899ZQ5pSH/UisOXmwacxu5VIKoAE/EB3tjapgvZkzxxZxIfyQEe0Mq5Upw5Bj6DEYUa9pxqlqLYo0OFxs6UNHUiTpdD8Yb35sWxqWOiWhyHHJJ5M2bNw8bZRha330sP1+agFtnh6O9px/a7j60dfWhpVOPpo5e1Ot6UK/rQZ9BQEVzFyqau/BtcaPpsf5eHkiPC8SSqcG4MTkUUQFeNnttRFcTBAFFmnbsK2rA4dIm5F9qRU+fccRtVR5STFF7IsRXiRAfJQK8PeDvqYDa0wO+KjlmRajtXD0RuRqzgkFwcDBkMhnq6+uH3V9fX4/w8PARHxMeHm7W9gCgVCqhVCrNKQ1LpoaM+X2jUUB9ew8qmrpQ2tiBi/XtOFurw5laLdq6+rD3XD32nqvHk5+dxexIP9w9LxIr50cixNe8OogmqqyxAx8X1OCzkzWoauke9j21pwfmRqkxY4ofpob6ICHEB7FBXgjyVvA6B0RkU2YFA4VCgdTUVOTk5GDlypUABpoPc3JysHHjxhEfk5mZiZycHPz617823bd3715kZmZaXLQlpFIJpqg9MUXticzEINP9/QYjztTqcLi0CfuLGnH8UgvO1OhwpkaH5/YU4Y45U/CzJQmYHcm/xGjyBEHAgQuNeO1Q+bCpL6VciuuTgnHD9BBkJgQhKdSHAYCIRGH2WQnvv/8+1qxZg7/85S9YsGABtm/fjg8++ABFRUUICwvD6tWrERkZiezsbAADpyvecMMN2Lp1K+644w7s2rULf/rTn1BQUIDZs2dPaJ/27KRu6ezFF6dq8VFBDU5WtZnuv3lmGB67ZTqmh3MOlyxz6GITnv+62PR7JZEAy6aF4IfXReHmGWHwVMhsXgPPSiCi8ZjdY7Bq1So0NjbiySefhEajQUpKCnbv3m1qMKysrIRUernzf9GiRXj33Xfxu9/9Dv/93/+NqVOn4tNPP51wKLC3QG8FHsqMw0OZcThdrcWrh8rwr5O12HuuHvuKGvBgRgw23TIdak8PsUslJ1HV0oWnPz+Hr88NTKmpPKR4MCMWaxbFITqQ/SxE5FjMHjEQg9h/5ZQ0dGDbnmLsPjtwJsUUtQrP3Td33L4Gcm+CIOC9vCr83y/OoavXAJlUgocWxmLjjUkI9hGnd0Xs9xIROT4GAzN8X9KEJz45jYrmLgDAL5Ym4DcrpnNtBLpGe08fHv3gpGmUYEFcIJ754WxMFfl0Qkd5LxGR42IwMFNXbz+2flWEv+VeAgBcnxSMlx6YD38vhah1keMobezAhr8dR1ljJxQyKf7r1un46eJ4h1grw5HeS0TkmPinrpm8FHL88e7ZeOmB+fD0kOFQSRPufyUXGm2P2KWRAyisasN9Lx9GWWMnpqhV+ODfMvGzJQkOEQqIiCaCwcBCP5gbgU8eWYRwPxUuNnTg3pcP41Jzp9hlkYgOlzbhgZ1H0NrVh3lRavxz4/VIifYXuywiIrMwGExCcrgfPno4EwnB3qhp68YDO4+itq17/AeSyzle0YL1bx5HV68BS6YG490NC7k4FhE5JQaDSYoK8ML7v7gcDh589SiaOvTjP5BcxpkaLda9cQzdfQYsnRaCV9ekwVvpkKuNExGNi8HACkJ8lXjnZxmI9PdEWVMn/u3tfOj7DWKXRXbQoOvBz946jnZ9PxbEB+IvD6ZCKbf9QkVERLbCYGAlEf6e+Nv6BfBVyXH8Uiue+OQMnOCED5qEnj4DNvztODS6HiSF+uDVNWl2Wb2QiMiWGAysKDHEBzseuA4yqQQf5VfjnSOXxC6JbOgP/zyLk9Va+Ht54LU1afBTcTVMInJ+DAZWtnRaCDbflgwAePqL8zhfpxO5IrKFf56sxa5jVZBIgB0PXIfYIG+xSyIisgoGAxtYf308bkoORW+/ERvfLUBXb7/YJZEVVTZ34b8/Pg0A+NXyJCxOCha5IiIi62EwsAGJRILn75+HMD8lShs78f++viB2SWQlRqOA//rHSXTo+5EeF4B/v2mq2CUREVkVg4GNBHorsPXeuQCA178vR0Flq8gVkTW8d6wSR8pa4Okhw/+7P4XXySAil8NPNRtaPj0U98yPhCAA//XRKZ7C6OTqtN3I/rIIAPDYiumICeIlk4nI9TAY2NiTd85EsI8SJQ0deOP7CrHLoUl45ovz6ND3Y36MP9YuihO7HCIim2AwsDF/LwUeHzxL4cWci2jQ8WJLzuhoWTM+P1UHqQT4vytnQ8aLIhGRi2IwsIN75kdiXrQ/OnsNeG5PsdjlkJkMRgFP/escAODHC2IwK0ItckVERLbDYGAHUqkEf7hzJgDgo/xqnKnRilwRmePjgmqcq9PBVyXHozdPE7scIiKbYjCwk/kxAbhrXgQA4IW9PH3RWej7Ddj+zUUAwK9uTEKQD6+YSESujcHAjjbdPA0yqQT7ihpwvKJF7HJoAnblVaGmrRthfkqszowTuxwiIptjMLCjuGBv/CgtGgDw/J5iXmTJwXX19uPFfSUAgH+/aSpUHrxAEhG5PgYDO/v3m5KgkEtxtLwFeeUcNXBk7+VVoalDj5hAL1OgIyJydQwGdjZF7Yn7U6MAAP+7v1Tkamg0vf1G7PyuDADw8LJEeHCFQyJyE/y0E8EvliZCKgEOXGjkGQoO6pMT1dDoehDmp8Q910WKXQ4Rkd0wGIggJsgLdw6eofAyRw0cjsEo4JUDA6MFP7s+AUo5ewuIyH0wGIjk4WWJAIAvz9ShqqVL5GroSjnn61He1Am1pwd+khEjdjlERHbFYCCS5HA/LJkaDEEA3j5ySexy6ApvHq4AAPxkQQx8lHJxiyEisjMGAxENXYhnV14lunr7xS2GAADFmnYcLm2GTCrBQ5mxYpdDRGR3DAYiWj49FLFBXtD19OOTEzVil0O4PFqwYlYYIv09xS2GiEgEDAYikkolWDO4mt6b31dwwSORabv68MmJagDA2kXxIldDRCQOBgOR3ZcWBU8PGS42dCD/UqvY5bi1T05Uo6fPiORwX6THBYhdDhGRKBgMROan8sAP5k4BMLDSHolDEATsOjbw8//JghhIJBKRKyIiEgeDgQP48YKBU+K+OF0LbXefyNW4p8KqNhRp2qGUS7EyhQsaEZH7YjBwANfF+GNamA96+oz4ZyGbEMWwa3C05o45U6D28hC5GiIi8TAYOACJRIJV6QOjBkPD2WQ/nfp+/OtULQBgVTovlkRE7o3BwEHcMz8SHjIJztbqUKxpF7sct7L7jAZdvQbEBXlhQXyg2OUQEYnKomCwY8cOxMXFQaVSISMjA3l5eaNue/bsWdx7772Ii4uDRCLB9u3bLa3VpQV4K7BseigAcE0DO/t0cPrmh/Oj2HRIRG7P7GDw/vvvY9OmTdiyZQsKCgowb948rFixAg0NDSNu39XVhYSEBGzduhXh4eGTLtiV3TN/oOnts8IaGI1c08Ae6nU9+L6kCQDww/lsOiQiMjsYvPDCC9iwYQPWrVuHmTNn4pVXXoGXlxdef/31EbdPT0/H888/jx//+MdQKpWTLtiVLU8Oha9KjjptD46UNYtdjlv4rLAGRgFIjQ1ATJCX2OUQEYnOrGDQ29uL/Px8ZGVlXX4CqRRZWVnIzc21WlF6vR46nW7YzR2oPGSmNQ0+5nSCXXxcMDSNwNECIiLAzGDQ1NQEg8GAsLCwYfeHhYVBo9FYrajs7Gyo1WrTLTrafTrFfzg/CgCw54wG+n6DyNW4tov17SjStMNDJjEFMiIid+eQZyVs3rwZWq3WdKuqcp9T+NJiAxDmp0S7vh8HLzSJXY5L+/xUHQBgydQQ+HspRK6GiMgxmBUMgoODIZPJUF9fP+z++vp6qzYWKpVK+Pn5Dbu5C6lUgtvnDPz1+sXpOpGrcV2CIJh+vnfM4WgBEdEQs4KBQqFAamoqcnJyTPcZjUbk5OQgMzPT6sW5q6Fh7b3n6tHTx+kEW7hQ34GShg4oZFLcPCts/AcQEbkJs6cSNm3ahJ07d+Ktt97C+fPn8fDDD6OzsxPr1q0DAKxevRqbN282bd/b24vCwkIUFhait7cXNTU1KCwsRElJifVehYuZHx2ACLUKHfp+fHehUexyXNIXgysdLp0WAj8Vl0AmIhoiN/cBq1atQmNjI5588kloNBqkpKRg9+7dpobEyspKSKWX80ZtbS3mz59v+nrbtm3Ytm0bbrjhBuzfv3/yr8AFDU0nvHqoHJ+fqsMts7j+gzUJgoDPB6cR2HRIRDScRBAEh19JR6fTQa1WQ6vVuk2/Qf6lVtz78mH4KOXI/30WlHKZ2CW5jIv17bj5z99BIZMi//dZ8HWjEQN3fC8RkXkc8qwEAuZH+yPUV4kOfT9yS7nYkTXtOTtwau2ipCC3CgVERBPBYOCgpFIJbp45MD3z9bn6cbYmcwz9PFdwioaI6BoMBg5s6MC191w9r51gJbVt3ThVrYVEAmTN4NkIRERXYzBwYAsTguCrkqOxXY8TVa1il+MS9g6OFqTGBCDEl9fuICK6GoOBA1PIpbgxeeBSzHvOcjrBGr4+N9BfwGkEIqKRMRg4uFtmDhzAvjnPYDBZup4+HC1rAQBT/wYREQ3HYODglkwLhlwqQVljJyqaOsUux6kdvNCEfqOAxBBvxAV7i10OEZFDYjBwcH4qDyyIDwQA7CtqELka55ZTNDDqchObDomIRsVg4ASG+gwYDCxnMArYXzywvPTy6aEiV0NE5LgYDJzAUDA4Wt6MDn2/yNU4p8KqNrR09sJXJUdaXIDY5RAROSwGAyeQEOKD+GBv9BkEHLrIiypZ4tvB0ZYbpoXAQ8ZfeyKi0fAT0kkMDX/nnOd0giVyBoPB0OgLERGNjMHASSxPDgEAfHexEU5w3SuH0qDrwfk6HSSSgREDIiIaHYOBk0iPC4TKQ4p6nR7F9e1il+NUvrvYBACYE6lGkA9XOyQiGguDgZNQeciQmRAEADhQzD4Dcxy4MPDz4mgBEdH4GAycyNLBA9vQgY7GZzAKODjYsLmUwYCIaFwMBk5k6C/eYxUt6ORpixNyqroNbV198FXJMT/aX+xyiIgcHoOBE4kP9kZ0oCf6DAJyS5vFLscpDI2uXJ8UDDlPUyQiGhc/KZ2IRCIxjRp8x/UMJuS7C5xGICIyB4OBk1kydeAAd2iw055Gp+vpw8lqLQAGAyKiiWIwcDILE4IglQBlTZ2oaesWuxyHdqS0GQajgPhgb0T6e4pdDhGRU2AwcDJqTw/MG2yi+56jBmM6VDLw87k+KVjkSoiInAeDgRMaOtANHfhoZKZgMJXBgIhoohgMnNBQMPi+pAlGI5dHHkltWzfKGjshlQxMvxAR0cQwGDih+TEB8FLI0NzZiyINl0ceydBowbxof6g9PUSuhojIeTAYOCGFXIqM+EAAwKESnrY4ku8Hg8ES9hcQEZmFwcBJLR484B3mQkfXEAQB35cM/FwWMRgQEZmFwcBJLUocOODllbegz2AUuRrHUtLQgaYOPVQeUsyP8Re7HCIip8Jg4KSSw30R4OWBrl4DTlW3iV2OQxkaRUmPC4RSLhO5GiIi58Jg4KSkUgkyEwe67Q+XcDrhSodLB/oLeDYCEZH5GAycWGYi+wyuZjAKOFLWAgBYlMhgQERkLgYDJzZ04MuvbEVPn0HkahzD+TodtN198FHKMSdSLXY5REROh8HAiSUEeyPMT4nefiMKLrWKXY5DGJpGyIgP5GWWiYgswE9OJyaRSExnJ3A6YUDu4M8hk9MIREQWYTBwcgsTBhY6OlrOYNBvMOJYxcDICRsPiYgsw2Dg5IYOgIVVbejude8+g7O1OnTo++GnkmPGFD+xyyEickoMBk4uJtALU9Qq9BkEFFS6d5/BkbKBUZMF8UGQSSUiV0NE5JwsCgY7duxAXFwcVCoVMjIykJeXN+q2O3fuxJIlSxAQEICAgABkZWWNuT2ZRyKRmEYNhg6M7mro9Q9NrxARkfnMDgbvv/8+Nm3ahC1btqCgoADz5s3DihUr0NDQMOL2+/fvx09+8hN8++23yM3NRXR0NG655RbU1NRMungaMHQgdOdgwP4CIiLrMDsYvPDCC9iwYQPWrVuHmTNn4pVXXoGXlxdef/31Ebf/+9//jl/+8pdISUlBcnIyXn31VRiNRuTk5Iy6D71eD51ON+xGo2OfAfsLiIisxaxg0Nvbi/z8fGRlZV1+AqkUWVlZyM3NndBzdHV1oa+vD4GBow/3ZmdnQ61Wm27R0dHmlOl22GfA/gIiImsxKxg0NTXBYDAgLCxs2P1hYWHQaDQTeo7f/va3iIiIGBYurrZ582ZotVrTraqqypwy3Y5EIkFGvHtPJxwtH1gGmf0FRESTI7fnzrZu3Ypdu3Zh//79UKlUo26nVCqhVCrtWJnzy0gIwqeFtaYDpDsxGAUcG3zdGfHsLyAimgyzRgyCg4Mhk8lQX18/7P76+nqEh4eP+dht27Zh69at+PrrrzF37lzzK6UxDY0YFFa1ud11E87X6dCu74ePUo6ZEewvICKaDLOCgUKhQGpq6rDGwaFGwszMzFEf99xzz+Hpp5/G7t27kZaWZnm1NKr4YG8E+wxcN+FkVZvY5djV0ChJWlwA+wuIiCbJ7LMSNm3ahJ07d+Ktt97C+fPn8fDDD6OzsxPr1q0DAKxevRqbN282bf/ss8/i97//PV5//XXExcVBo9FAo9Ggo6PDeq+CBvoMTMsju9d0wtHBvgpOIxARTZ7ZPQarVq1CY2MjnnzySWg0GqSkpGD37t2mhsTKykpIpZfzxssvv4ze3l7cd999w55ny5Yt+MMf/jC56mmYhfGB+OJUHfLcKBgYjQKOVQz2F7DxkIho0ixqPty4cSM2btw44vf2798/7OuKigpLdkEWWDD4F3P+pVb0GYzwcIPLDl9s6EBrVx88PWSYE6kWuxwiIqfn+kcONzI11AcBXh7o7jPgVLVW7HLsIm/wqpKpsQFuEYSIiGyNn6QuRCqVYMHg2QlDw+uubqifYuh1ExHR5DAYuJih6QR36DMQBMH0OjMYDIiIrILBwMUsiLs8YmAwCiJXY1uXmrvQ0K6HQibFvGh/scshInIJDAYuZsYUX/go5Wjv6UeRxrUvPjU0WjAvWg2Vh0zkaoiIXAODgYuRy6RIjQ0AANMywa4qr4L9BURE1sZg4IKGDpR5Lt6AmGdqPOTCRkRE1sJg4IKGGvHyylsgCK7ZZ1Cn7UZlSxekEphGSIiIaPIYDFzQnCg1lHIpmjp6UdbUKXY5NjE0WjA7Ug0fpV0vEkpE5NIYDFyQUi5DymCXvquetji0TkN6HPsLiIisicHARQ1NJ7hqA2IeFzYiIrIJBgMXlR7vuldabO3sxYX6gatzcsSAiMi6GAxc1HUxAZBJJahp60ZNW7fY5VjV0DTC1FAfBHorRK6GiMi1MBi4KG+lHLMj/AC43nQCpxGIiGyHwcCFDQ2zu9p0Ahc2IiKyHQYDF+aKV1rs0PfjbO3AUs/sLyAisj4GAxc2dOAsaehAc4de5Gqso+BSKwxGAVEBnojw9xS7HCIil8Ng4MICvBWYFuYDwHVGDYZexwKOFhAR2QSDgYszXTehvFXkSqxjqF8iI4HBgIjIFhgMXNzQBYbyKppFrmTyevoMKKxqA8ALJxER2QqDgYsbGnI/V6uDrqdP5Gom51S1Fr39RoT4KhEX5CV2OURELonBwMWFq1WIDfKCUQDyLzn3dEJe+cCox4L4QEgkEpGrISJyTQwGbuDKyzA7M1N/AdcvICKyGQYDN2DqM3DiYNBvMJpGPLiwERGR7TAYuIGhv7BPVbehu9cgcjWWOVurQ1evAWpPD0wL9RW7HCIil8Vg4AaiAjwxRa1Cn0HAiUrn7DM4OthfkB4XAKmU/QVERLbCYOAGJBKJafj9iJNOJxwtG+ov4GmKRES2xGDgJoYOqEfLnG89A4NRMF04iQsbERHZFoOBmxg6oJ6oakNPn3P1GZyv06G9px8+SjlmTvETuxwiIpfGYOAmEoK9EeKrRG+/EScHVw90FkOnKabHBUAu468sEZEt8VPWTUgkEtPZCUedrM9gaPojI4H9BUREtsZg4EaGDqxDHf7OwHhlfwHXLyAisjkGAzeycPDAmn+pFb39RpGrmZgLDe1o6+qDl0KG2ZFqscshInJ5DAZuJCnUB0HeCvT0GXGquk3sciYkt3RgdCM1NgAe7C8gIrI5ftK6EYlEgoWD0wlDB1xHN1RnZiL7C4iI7IHBwM0sHDzA5jrBegZGo2BqlMxk4yERkV1YFAx27NiBuLg4qFQqZGRkIC8vb9RtP/74Y6SlpcHf3x/e3t5ISUnB22+/bXHBNDlDB9j8S63Q9zv2egbn6nTQdvfBWyHDHPYXEBHZhdnB4P3338emTZuwZcsWFBQUYN68eVixYgUaGhpG3D4wMBBPPPEEcnNzcerUKaxbtw7r1q3Dnj17Jl08mS8xZGA9A32/EScq28QuZ0xHBkc10uMDuX4BEZGdmP1p+8ILL2DDhg1Yt24dZs6ciVdeeQVeXl54/fXXR9x+2bJl+OEPf4gZM2YgMTER//Ef/4G5c+fi0KFDky6ezOdMfQam/gJOIxAR2Y1ZwaC3txf5+fnIysq6/ARSKbKyspCbmzvu4wVBQE5ODoqLi7F06dJRt9Pr9dDpdMNuZD1DB1pH7jPoNxiRN9RfwMZDIiK7MSsYNDU1wWAwICwsbNj9YWFh0Gg0oz5Oq9XCx8cHCoUCd9xxB1588UXcfPPNo26fnZ0NtVptukVHR5tTJo1j6EBbWNmG7l7H7DM4W6tDu74fvio5ZkWwv4CIyF7sMnHr6+uLwsJCHDt2DM888ww2bdqE/fv3j7r95s2bodVqTbeqqip7lOk24oK8EKFWoddgxPFLjrk88velTQAGrgopk0pEroaIyH3Izdk4ODgYMpkM9fX1w+6vr69HeHj4qI+TSqVISkoCAKSkpOD8+fPIzs7GsmXLRtxeqVRCqVSaUxqZQSKRYHFSMD7Mr8ahkiYsmRoidknX+L5kIBgsmRosciVERO7FrBEDhUKB1NRU5OTkmO4zGo3IyclBZmbmhJ/HaDRCr9ebs2uyssVJAwfcoQOwI+npM+BYRSsAYHES+wuIiOzJrBEDANi0aRPWrFmDtLQ0LFiwANu3b0dnZyfWrVsHAFi9ejUiIyORnZ0NYKBfIC0tDYmJidDr9fjyyy/x9ttv4+WXX7buKyGzLBo84J6t1aG1sxcB3gqRK7rseMXAtRzC/JRIDPERuxwiIrdidjBYtWoVGhsb8eSTT0Kj0SAlJQW7d+82NSRWVlZCKr08ENHZ2Ylf/vKXqK6uhqenJ5KTk/HOO+9g1apV1nsVZLZQXxWmh/miuL4duWXNuH3OFLFLMhnqL1icFAyJhP0FRET2JBEEQRC7iPHodDqo1WpotVr4+fmJXY7L+OO/zuH178vxQEYM/vTDOWKXY3LXS4dwqlqLF340D/dcFyV2OS6F7yUiGg+Xk3Nj108dmE44dNFx+gzaunpxukYL4HIfBBER2Q+DgRtbEB8EuVSCypYuXGruFLscAMD3Jc0QBGBqqA/C/FRil0NE5HYYDNyYj1KOtLgAAMB3FxpFrmbAgQsD19y4YZrjnUJJROQOGAzc3NLBA/ABBwgGgiCY6ljKYEBEJAoGAzc39Jf54dJm0S/DXFzfjnqdHioPKRbEB4paCxGRu2IwcHMzp/ghxFeJrl4D8gcXFRLL0HTGwoQgqDxkotZCROSuGAzcnEQiwdKpjjGdMLR/9hcQEYmHwYBww/SBA/H+YvGCQVdvP46VD4xYMBgQEYmHwYCwJCkYUsnAHH91a5coNRy82IRegxHRgZ6ID/YWpQYiImIwIAAB3gqkxQ40++0rahClhpzzA1fszJoRxmWQiYhExGBAAICbZoQCAPaeqx9nS+szGgVTIMmaEWb3/RMR0WUMBgQAyJo5cEA+UtaM9p4+u+67sLoNTR298FXJeZoiEZHIGAwIAJAY4oP4YG/0GQQctPO1E74ZHKW4YVoIPGT8lSQiEhM/hckka3A64Zvz9p1OyDk/MI1w80xOIxARiY3BgEyG5vf3FTWgz2C0yz4vNXeiuL4dMqkEy6aF2mWfREQ0OgYDMkmLC0SwjwJtXX3ILW22yz6/OF0HAFiUGAS1l4dd9klERKNjMCATmVSCFbPCAQBfnKqzyz6H9nP7nCl22R8REY2NwYCGuWPwAL3nnMbm0wmXmjtxtlY3LJAQEZG4GAxomAXxgQjyts90wpXTCIHeCpvui4iIJobBgIaRy6S4dbZ9phM4jUBE5HgYDOgad8wdOFB/daYOPX0Gm+yjpKGd0whERA6IwYCukREfhAi1CrqefpstkfxhfjUAYPn0UE4jEBE5EAYDuoZMKsG9qVEAgI8GD+DW1G8w4pOCGgDA/WlRVn9+IiKyHIMBjeje6wYO2AcvNkKj7bHqcx+82ISGdj0CvRVYPp2LGhERORIGAxpRXLA3FsQFwigAH5+w7qjB0CjE3SkRUMj5K0hE5Ej4qUyjum9wOmFXXhUMRsEqz9nQ3oOvz2mGPT8RETkOBgMa1Z3zIqD29EBlSxdyrHRhpXdyL6HPICA1NgCzItRWeU4iIrIeBgMaladChgcyYgAAr39fPunn6+kz4J2jlQCAny6On/TzERGR9TEY0JhWZ8ZCLpXgSFkLztZqJ/VcnxXWoKWzF5H+nlgxi5dYJiJyRAwGNKYpak/TyoQ7vyuz+HkMRgGvHhwYdVizKBZyGX/1iIgcET+daVw/X5oAAPjsZC3O1+kseo5PT9TgYkMH/FRyrEqPsWZ5RERkRQwGNK7ZkWrcMXcKBAF4fk+x2Y/X9xvwwt4LAICHlyVB7elh7RKJiMhKGAxoQh67ZTrkUgn2FTXgSJl5V11850glatq6Ee6nwrrFcbYpkIiIrILBgCYkPtgbq9KjAQC/+/TMhC+uVNXShe2DowW/zpoKlYfMZjUSEdHkMRjQhD16y3SE+CpR0tCBrV8Vjbu9wSjg0Q9Ool3fj+ti/LmgERGRE2AwoAkL9Fbg+fvmAgDePFyBr89qxtz+xX0XkVfRAm+FDH9elcIzEYiInIBFn9Q7duxAXFwcVCoVMjIykJeXN6HH7dq1CxKJBCtXrrRkt+QAlk0PxZrMWADAI+8WYM8o4eClfRex/ZuLAIAtd81CbJC33WokIiLLmR0M3n//fWzatAlbtmxBQUEB5s2bhxUrVqChoWHMx1VUVOCxxx7DkiVLLC6WHMMTd8zE7XPC0WcQ8Mu/F+DZ3UVo7tADAMoaO/Cf7xdi29cDfQX/mTUN93MKgYjIaUgEQTDr6jgZGRlIT0/HSy+9BAAwGo2Ijo7Gr371Kzz++OMjPsZgMGDp0qX46U9/ioMHD6KtrQ2ffvrphPep0+mgVquh1Wrh5+dnTrlkI/0GI/7ro1P4+EQNAEAmlUAhk6L7iqbE/749GT9fmihWiTQCvpeIaDxmjRj09vYiPz8fWVlZl59AKkVWVhZyc3NHfdwf//hHhIaGYv369RPaj16vh06nG3YjxyKXSfH/fjQPf30oFXOj1DAYBVMoyJoRik8fWcxQQETkhOTmbNzU1ASDwYCwsOHr3IeFhaGoaOQu9UOHDuG1115DYWHhhPeTnZ2Np556ypzSSAQSiQS3zArHzTPDUK/To89ghJdChiAfpdilERGRhWzaJt7e3o6HHnoIO3fuRHBw8IQft3nzZmi1WtOtqqrKhlXSZEkkEoSrVYgO9GIoICJycmaNGAQHB0Mmk6G+vn7Y/fX19QgPD79m+9LSUlRUVODOO+803Wc0Ggd2LJejuLgYiYnXDjcrlUoolTzAEBER2ZtZIwYKhQKpqanIyckx3Wc0GpGTk4PMzMxrtk9OTsbp06dRWFhout11111Yvnw5CgsLER0dPflXQERERFZj1ogBAGzatAlr1qxBWloaFixYgO3bt6OzsxPr1q0DAKxevRqRkZHIzs6GSqXC7Nmzhz3e398fAK65n4iIiMRndjBYtWoVGhsb8eSTT0Kj0SAlJQW7d+82NSRWVlZCKuUKd0RERM7I7HUMxMBzr4msg+8lIhoP/7QnIiIiE7OnEsQwNKjBhY6IJmfoPeQEA4VEJBKnCAbt7e0AwLMYiKykvb0darVa7DKIyAE5RY+B0WhEbW0tfH19IZFIxC6HyGkJgoD29nZERESwSZiIRuQUwYCIiIjsg38yEBERkQmDAREREZkwGBAREZEJgwERERGZMBgQERGRCYMBERERmTAYEBERkQmDAREREZkwGBAREZEJgwERERGZMBgQERGRCYMBERERmfz/KwTQxhOZ/dsAAAAASUVORK5CYII=",
                "text/plain": [
                  "<Figure size 600x600 with 3 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "vu = np.linspace(um, uM, 100)\n",
            "vw = np.linspace(wm, wM, 100)\n",
            "\n",
            "\n",
            "def f(v):\n",
            "    return 1.0 / np.sqrt(2 * np.pi) * np.exp(-(v**2) / 2)\n",
            "\n",
            "\n",
            "x, y = np.mgrid[um:uM:0.01, wm:wM:0.01]\n",
            "pos = np.dstack((x, y))\n",
            "rv = sc.multivariate_normal([0.0, 0.0], [[1.0, rho], [rho, 1]])\n",
            "fig2 = plt.figure(figsize=(6, 6))\n",
            "ax2 = fig2.add_subplot(221)\n",
            "ax2.contourf(x, y, rv.pdf(pos), vmin=0, vmax=0.28, levels=10)\n",
            "\n",
            "ax2 = fig2.add_subplot(222)\n",
            "ax2.plot(f(vw), vw)\n",
            "ax2.set_yticks([])\n",
            "ax2 = fig2.add_subplot(223)\n",
            "ax2.plot(vu, f(vu))\n",
            "ax2.set_ylim(0.42, -0.025)\n",
            "ax2.set_xticks([])\n",
            "plt.savefig(\"marginal.png\")"
          ]
        },
        {
          "cell_type": "code",
          "execution_count": 20,
          "id": "4c10e01d",
          "metadata": {},
          "outputs": [
            {
              "data": {
                "image/png":
                  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",
                "text/plain": [
                  "<Figure size 800x400 with 2 Axes>"
                ]
              },
              "metadata": {},
              "output_type": "display_data"
            }
          ],
          "source": [
            "def f(v, x, rho):\n",
            "    return (\n",
            "        1.0\n",
            "        / np.sqrt((1 - rho**2) * 2 * np.pi)\n",
            "        * np.exp(-((v - rho * x) ** 2) / (2 * (1 - rho**2)))\n",
            "    )\n",
            "\n",
            "\n",
            "x0 = 0.8\n",
            "\n",
            "x, y = np.mgrid[um:uM:0.01, wm:wM:0.01]\n",
            "pos = np.dstack((x, y))\n",
            "rv = sc.multivariate_normal([0.0, 0.0], [[1.0, rho], [rho, 1]])\n",
            "\n",
            "fig2 = plt.figure(figsize=(8, 4))\n",
            "ax2 = fig2.add_subplot(121)\n",
            "ax2.contourf(x, y, rv.pdf(pos), vmin=0, vmax=0.28, levels=10)\n",
            "\n",
            "ax2.plot([x0, x0], [wm, wM - 0.1])\n",
            "ax2.plot([um, uM - 0.1], [x0 * rho, x0 * rho])\n",
            "\n",
            "ax2 = fig2.add_subplot(122)\n",
            "ax2.plot(f(vw, x0, rho), vw)\n",
            "ax2.plot([0, 0.65], [x0 * rho, x0 * rho])\n",
            "plt.ylim([wm, wM])\n",
            "# ax2.set_yticks([])\n",
            "\n",
            "plt.savefig(\"conditional.png\")"
          ]
        }
      ],
    "metadata": {
      "hide_input": false,
      "kernelspec": {
        "display_name": "Python 3 (ipykernel)",
        "language": "python",
        "name": "python3"
      },
      "language_info": {
        "codemirror_mode": {
          "name": "ipython",
          "version": 3
        },
        "file_extension": ".py",
        "mimetype": "text/x-python",
        "name": "python",
        "nbconvert_exporter": "python",
        "pygments_lexer": "ipython3",
        "version": "3.10.5"
      }
    },
    "nbformat": 4,
    "nbformat_minor": 5
  }