Higgs_discovery_4l_invMass.ipynb

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      "source": [
        "The data we use here is actual, meaningful data from the CMS experiment that confirmed the existence of Higgs boson."
      ],
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        "id": "c18e-Pkrya6u"
      }
    },
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      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
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        "id": "g1unC0gHyqTh"
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      "outputs": []
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      "source": [
        "# Data for later use.\n",
        "\n",
        "csvs = [pd.read_csv('http://opendata.cern.ch/record/5200/files/4mu_2011.csv'), pd.read_csv('http://opendata.cern.ch/record/5200/files/4e_2011.csv'), pd.read_csv('http://opendata.cern.ch/record/5200/files/2e2mu_2011.csv')]\n",
        "csvs += [pd.read_csv('http://opendata.cern.ch/record/5200/files/4mu_2012.csv'), pd.read_csv('http://opendata.cern.ch/record/5200/files/4e_2012.csv'), pd.read_csv('http://opendata.cern.ch/record/5200/files/2e2mu_2012.csv')]\n",
        "\n",
        "fourlep = pd.concat(csvs)\n"
      ],
      "metadata": {
        "id": "yqT6Jchu1FKO"
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      "execution_count": 2,
      "outputs": []
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      "source": [
        "According to the Standard Model of particle physics, one of the ways the Higgs boson can decay is H-->ZZ-->4 leptons.\n",
        "But there are other standard model processes which can also produce such a final state."
      ],
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        "fourlep.head()"
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        "outputId": "90ecf873-7259-4d8e-a110-b40bf9a85d64"
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      "execution_count": 3,
      "outputs": [
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      "source": [
        "# Let us set some values here in regards to the region we are looking at.\n",
        "\n",
        "rmin = 70\n",
        "rmax = 181\n",
        "nbins = 37\n",
        "\n",
        "M_hist = np.histogram(fourlep['M'], bins = nbins, range = (rmin,rmax))\n",
        "\n",
        "hist, bins = M_hist\n",
        "width = 1.0*(bins[1] - bins[0])\n",
        "center = (bins[:-1] + bins[1:]) / 2\n",
        "print (width)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k1pawgUt2FPF",
        "outputId": "6b1364e8-c2f6-4112-850d-fb298c13b114"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "3.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let us look at some simulations from higgs and other processes which can give same final state of 4 leptons. Here are some simulated values for such events (weighted). Basically, we create a set of values that have some randomness in them, just like a real measurement would have, but which follows the distribution that has been observed in those processes."
      ],
      "metadata": {
        "id": "vjRhfaYZ2rKf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dy = np.array([0,0,0,0,0,0.354797,0.177398,2.60481,0,0,0,0,0,0,0,0,0,0.177398,0.177398,0,0.177398,0,0,0,0,0,0,0,0,0,0,0,0.177398,0,0,0,0])\n",
        "ttbar = np.array([0.00465086,0,0.00465086,0,0,0,0,0,0,0,0.00465086,0,0,0,0,0,0.00465086,0,0,0,0,0.00465086,0.00465086,0,0,0.0139526,0,0,0.00465086,0,0,0,0.00465086,0.00465086,0.0139526,0,0])\n",
        "zz = np.array([0.181215,0.257161,0.44846,0.830071,1.80272,4.57354,13.9677,14.0178,4.10974,1.58934,0.989974,0.839775,0.887188,0.967021,1.07882,1.27942,1.36681,1.4333,1.45141,1.41572,1.51464,1.45026,1.47328,1.42899,1.38757,1.33561,1.3075,1.29831,1.31402,1.30672,1.36442,1.39256,1.43472,1.58321,1.85313,2.19304,2.95083])\n",
        "hzz = np.array([0.00340992,0.00450225,0.00808944,0.0080008,0.00801578,0.0108945,0.00794274,0.00950757,0.0130648,0.0163568,0.0233832,0.0334813,0.0427229,0.0738129,0.13282,0.256384,0.648352,2.38742,4.87193,0.944299,0.155005,0.0374193,0.0138906,0.00630364,0.00419265,0.00358719,0.00122527,0.000885718,0.000590479,0.000885718,0.000797085,8.86337e-05,0.000501845,8.86337e-05,0.000546162,4.43168e-05,8.86337e-05])"
      ],
      "metadata": {
        "id": "qW7a9mnH3G34"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "len(dy)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iiamdXDc3WAa",
        "outputId": "ebbc53c1-725e-4378-d4d3-5da4d9c03309"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "37"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "len(ttbar)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O41kSSct3eMm",
        "outputId": "c141c626-bd9a-4ac2-b5be-1ab68826df2d"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "37"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "len(zz)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZdlJrKvZ3g_S",
        "outputId": "29272d0f-e938-42e3-b1ee-dad0493ad233"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "37"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "len(hzz)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZerFwGD93kn5",
        "outputId": "215535d4-1e73-4532-95e3-3d8215a2e049"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "37"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ZZ\n",
        "\n",
        "plt.figure(figsize = (15,3))\n",
        "plt.bar(center, zz, align = 'center', width = width, color = 'b', linewidth = 0, edgecolor = 'black', alpha = 0.5)\n",
        "\n",
        "plt.xlabel('4l invariant mass (GeV)', fontsize = 15)\n",
        "plt.ylabel('Events / 3 GeV\\n', fontsize = 15)\n",
        "plt.xlim(rmin,rmax)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "O7J6eiCN3uGz",
        "outputId": "93e19dd8-efc9-4f99-c2b7-d8a0c136d585"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x300 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# DY\n",
        "\n",
        "plt.figure(figsize = (15,3))\n",
        "plt.bar(center, dy, align = 'center', width = width, color = 'g', linewidth = 0, edgecolor = 'black', alpha = 0.5)\n",
        "\n",
        "plt.xlabel('4l invariant mass (GeV)', fontsize = 15)\n",
        "plt.ylabel('Events / 3 GeV\\n', fontsize = 15)\n",
        "plt.xlim(rmin,rmax)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "gyq0-ljf4Jnl",
        "outputId": "a06fa9a1-6b8a-451e-85ff-5cfe7caf67bc"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ttbar\n",
        "\n",
        "plt.figure(figsize = (15,3))\n",
        "plt.bar(center, ttbar, align = 'center', width = width, color = 'gray', linewidth = 0, edgecolor = 'b', alpha = 0.5)\n",
        "\n",
        "plt.xlabel('4l invariant mass (GeV)', fontsize = 15)\n",
        "plt.ylabel('Events / 3 GeV \\n', fontsize = 15)\n",
        "plt.xlim(rmin,rmax)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "TthruTin4XOl",
        "outputId": "f5f2fb44-f030-4d80-c981-36764f24fa52"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let us stack them together and see what kind of shape we might expect from the real data of the experiment."
      ],
      "metadata": {
        "id": "ftvwKKbU5eTA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize = (15,5))\n",
        "\n",
        "# ttbar\n",
        "ttbar_bar = plt.bar(center, ttbar, align = 'center', width = width, color = 'gray', linewidth = 0, edgecolor = 'b',\n",
        "                    alpha = 0.5, label = r'$t\\bar{t}$')\n",
        "\n",
        "# DY\n",
        "dy_bar = plt.bar(center, dy, align = 'center', width = width, color = 'g', linewidth = 0, edgecolor = 'black',\n",
        "                 alpha = 0.5, bottom = ttbar, label = 'Z/$\\gamma^{*}$ + X')\n",
        "\n",
        "# ZZ\n",
        "zz_bar = plt.bar(center, zz, align = 'center', width = width, color = 'b', linewidth = 0, edgecolor = 'black',\n",
        "                 alpha = 0.5, bottom = ttbar+dy, label = r'ZZ $\\rightarrow$ 4l')\n",
        "\n",
        "plt.title('$ \\sqrt{s} = 7$ TeV, L = 2.3 $fb^{-1}$; $\\sqrt{s} = 8$ TeV, L = 11.6 $fb^{-1}$ \\n', fontsize = 12)\n",
        "plt.xlabel('$m_{4l}$ (GeV)', fontsize = 15)\n",
        "plt.ylabel('Events / 3 GeV\\n', fontsize = 15)\n",
        "plt.ylim(0,25)\n",
        "plt.xlim(rmin,rmax)\n",
        "plt.legend(fontsize = 15)\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 522
        },
        "id": "f-x33pG14dvj",
        "outputId": "b4afc398-ec9e-42f0-f5ac-ca19018086cf"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let us add our measured data on top of that. How well do they line up?"
      ],
      "metadata": {
        "id": "knqUJAjy5nLw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize = (15,5))\n",
        "\n",
        "xerrs = [width*0.5 for i in range(0, nbins)]\n",
        "yerrs = np.sqrt(hist)\n",
        "\n",
        "# ttbar\n",
        "ttbar_bar = plt.bar(center, ttbar, align = 'center', width = width, color = 'gray', linewidth = 0, edgecolor = 'b',\n",
        "                    alpha = 0.5, label = r'$t\\bar{t}$')\n",
        "\n",
        "# DY\n",
        "dy_bar = plt.bar(center, dy, align = 'center', width = width, color = 'g', linewidth = 0, edgecolor = 'black',\n",
        "                 alpha = 0.5, bottom = ttbar, label = 'Z/$\\gamma^{*}$ + X')\n",
        "\n",
        "# ZZ\n",
        "zz_bar = plt.bar(center, zz, align = 'center', width = width, color = 'b', linewidth = 0, edgecolor = 'black',\n",
        "                 alpha = 0.5, bottom = ttbar+dy, label = r'ZZ $\\rightarrow$ 4l')\n",
        "\n",
        "# Measured data\n",
        "data_bar = plt.errorbar(center, hist, xerr = xerrs, yerr = yerrs, linestyle = 'None', color = 'black',\n",
        "                        marker = 'o', label = 'Data')\n",
        "\n",
        "plt.title('$ \\sqrt{s} = 7$ TeV, L = 2.3 $fb^{-1}$; $\\sqrt{s} = 8$ TeV, L = 11.6 $fb^{-1}$ \\n', fontsize = 12)\n",
        "plt.xlabel('$m_{4l}$ (GeV)', fontsize = 15)\n",
        "plt.ylabel('Events / 3 GeV\\n', fontsize = 15)\n",
        "plt.ylim(0,25)\n",
        "plt.xlim(rmin,rmax)\n",
        "plt.legend(fontsize = 15)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 522
        },
        "id": "bFJ4XJRp4nUH",
        "outputId": "0d103de4-32f8-4846-f3dd-be2e3cb4c53c"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "There are clearly some points in there that do not seem to arise in our simulated processes. For comparison purposes, physicists made simulations for Higgs at varying masses, one of which is shown here. This graph shows us what the Higgs boson should look like, if it had a mass of 125 GeV."
      ],
      "metadata": {
        "id": "TeWscOKl5s16"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# HZZ, our theoretical assumption of a Higgs via two Z bosons.\n",
        "\n",
        "plt.figure(figsize = (15,3))\n",
        "plt.bar(center, hzz, align = 'center', width = width, color = 'w', linewidth = 1, edgecolor = 'r')\n",
        "\n",
        "plt.xlabel('4l invariant mass (GeV)', fontsize = 15)\n",
        "plt.ylabel('Events / 3 GeV\\n', fontsize = 15)\n",
        "plt.xlim(rmin,rmax)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "id": "KSzZAh_I4wv-",
        "outputId": "123b53c8-144c-4541-cc87-16011bf1ab89"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x300 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Bonus question: how can something, that seems to have a mass of roughly 125 GeV decay via two Z bosons, with mass over 90 GeV?\n",
        "\n",
        "Add that in the previous graph and see how it lines up."
      ],
      "metadata": {
        "id": "lWM-7F_H6C7w"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize = (15,5))\n",
        "\n",
        "# ttbar\n",
        "ttbar_bar = plt.bar(center, ttbar, align = 'center', width = width, color = 'gray', linewidth = 0, edgecolor = 'b',\n",
        "                    alpha = 0.5, label = r'$t\\bar{t}$')\n",
        "\n",
        "# DY\n",
        "dy_bar = plt.bar(center, dy, align = 'center', width = width, color = 'g', linewidth = 0, edgecolor = 'black',\n",
        "                 alpha = 0.5, bottom = ttbar, label = 'Z/$\\gamma^{*}$ + X')\n",
        "\n",
        "# ZZ\n",
        "zz_bar = plt.bar(center, zz, align = 'center', width = width, color = 'b', linewidth = 0, edgecolor = 'black',\n",
        "                 alpha = 0.5, bottom = ttbar+dy, label = r'ZZ $\\rightarrow$ 4l')\n",
        "\n",
        "# HZZ\n",
        "hzz_bar = plt.bar(center, hzz, align = 'center', width = width, color = 'w', linewidth = 1, edgecolor = 'r',\n",
        "                  bottom = ttbar+dy+zz, label = '$m_{H}$ = 125 GeV')\n",
        "\n",
        "# Measured data\n",
        "data_bar = plt.errorbar(center, hist, xerr = xerrs, yerr = yerrs, linestyle = 'None', color = 'black',\n",
        "                        marker = 'o', label = 'Data')\n",
        "\n",
        "plt.title('$ \\sqrt{s} = 7$ TeV, L = 2.3 $fb^{-1}$; $\\sqrt{s} = 8$ TeV, L = 11.6 $fb^{-1}$ \\n', fontsize = 12)\n",
        "plt.xlabel('$m_{4l}$ (GeV)', fontsize = 15)\n",
        "plt.ylabel('Events / 3 GeV\\n', fontsize = 15)\n",
        "plt.ylim(0,25)\n",
        "plt.xlim(rmin,rmax)\n",
        "plt.legend(fontsize = 15)\n",
        "\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 522
        },
        "id": "qg-aEsH743CA",
        "outputId": "006df5ac-7214-43ac-bc53-c387b7241abd"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x500 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "As we can see, there is certainly some interesting activity going on in the 125 GeV region. Our plot but is not too far off from actual analysis results. The most telling differences mainly arise from our somewhat rough methods compared to the more sophisticated ones used at CMS."
      ],
      "metadata": {
        "id": "C2pfYQjY6N-N"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![Screenshot from 2024-10-02 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UkhERERE4OxjIiIiImJSSERERERMComIiIgITAqJiIiICEBUax/v22/BR1c+QkVFBWclJcGjGzZg65atmQ6DiIiIstQ/nn0Df5qdTes5o5p9bDKbYbfZAAAqlQo7KivxQkMDqquqUh7gcrRSrcZ9AO5XqRS3r1lTiOk//iGm+3xg9eq4jovWSrUan92+nZL7Lnrk6wDA2BWkOvbr1+fw6c2bKbn/lWo1dtfX4/Xu7qTfd6pjf2D1atR++9spiX2fxYIzv/oVY1eQyvexfRYLBqzWlL2elnLsS/19DFiasavVatzFfF61kM/nA4CUnTucqFoKA/l8PthtNthtNmg0GmwrL2eCGIf77rsfa9YUKm7TrtOmORoiIiJKq/vuA+7eVcwFPJ70thBKokoKhwYHcaKjA6Ojo/jd+fNyBuv1eoMSxGeeeRYWy/6UFFhebjT5mpR9syEiIqLsdt99/xPu3r2rmAtIrYhpjynaHQ8fPIjR4WF8evMmWo8fR7XRCI1GI2/3er0YGLCirKwMDxcVYd9+CyZcrpQETURERETJFdfs48MHD2JocBB/unYNQ0NDIQmiKIpBCWJzSws8opi0oImIiIgouRIuSVNdVbVogtjV1YWioiI8XlbGBJGIiIgoCyW1TuFiCeKkyxWUIBIRERFRdoiqJE2i7A4HftbbizGnE16vV7493VOts8VKtRoFBQW4+vHHmQ4laqmclk/h8XnPjFSWdaHwUl1ai5SluqwLKftPD+Tjz3/+D8X3eGmiSbrf/9OyosnvP/gAs7OzQQkhEREREWWPmOsURkuphI1EpVJh85YtqTo1EREREcUoqUmh3eHA33Z2KiaCAKA3GPBUeTna29qSeVoiIiIiSlDCSWG48YISQRBQW1uLpqYmaAUh0dMRERERUQrElRROuFx4ua0tbCIoLX/3UksLVzchIiIiWgKiTgonXC50d7+Gc+dGICrUGVSpVNhRWcl1kKP02eefY5/Forjtq1/5Cn78ox+lOSIiIiJKm7vzxV+UcoFMLHEHRJkU7ttvwcCANeR2acJIRUUFDh88mPTglrPP7tzBgDX0OQXmn1cmhQTMXwuUfmvWFOKrX/lKpsPIOWvWFEK7TpvpMHIOn/PM+PPdPwNA2FwgE6KqU2gym2G32eT/SxNGOE4wPkuxTiERERGlR6bqFEbdfSwIAnbsqITFsp/jBImIiIiWmbSsaELB2FJIRJQ+j27YEHbbqlWroP+Gng0elFUy1VKY80nhhMuFwcFBuGdmAADFOh3MZnPENwdp9vVidtXUYG99fcjtTAqJiNJnpVq96D4qlQq1td/G668lZ2nDPqsVhYWFnHhJccn67uPFSInS1NQUZtxu+fbu7m7sra+HyWxGsU6XVeMQF46VlHR1dWFbeTn6e3sVY52cnFQ8TolSUkhElIsmXC5MTk4CyMx74+7d9SgreyLotsuXL+NtpxOTLpc8oTIZiaHFYoGuuJhJIS0pSUkKm1ta0NPTo7iKiWRqagp2mw09PT146ejRjM9Wrti5E2NOJ4D58ZKbHnsMAOSkdszpRMXTT+P9S5dCjh0f/y2A+W+W6x58MOw5inW6FERORLS0eEQRf2kyYdLlkm9rbm7GDw8dSutnQVnZE2GT0eaWFnR1dWFgwMquZMpZCSeF0gtJIiVYCwtba7VazLjd8Pl8OHb0KArXrMlYK5rd4ZATwhdffDFk2T3pMc243TjR0RHypnXjkxsAgM1btmB0eDg9QVPMTGYzpqamcOvWLaxatQolJSUYGhzMdFhEOafi6aeDepAAwOv14uXjx/GN9euzojWtva1NbjFsbmlRfG8PbOkEgMrKyrh7vpJ5X0RJ40/A1WvX/Jr8fP+KvDy/Jj/f39vfL29br9f7V+TlBd3W298v718oCImcOiHP1db6V+Tl+R/S6cLu85BO51+Rl+d/rrY2ZJv02JS2RWNFXp5fu25dXMdS9M4OD/t7+/vl6/Ds8HCmQyLKOe9dvOhfkZcX9ife99FYSOcK/DxS0n7ypPx5Fujs8LD8vr9Y/Er7rdfr47ovyl15966JdLsvkYTy2LFWucv49OnTi7b87a2vR2dnJ4D5b4knOjoSOX3cpqamAEDuMlaSt2pV0L5KHn/88eQGRklVXVUlX5N76+uzojWCKNcEtoYpifQem25Sr5DP58PEva5ujyiirq4OM273/BhBo1H+UalUsNtsMJnN8n0Yq6tRbTQCmF/ytdpohLG6Oq77Ikq3hLqPJ38//2LXGwxRf+Dura9Ha2srRFHEhQsXEjl93IzV1XDPzGBXTc2i+5aUlITcJnWDFK5ZA+CLbgC9Xs9xKEREMVh17wt4tlCpVPD5fJicnMQmgwGdnZ3w+XzQFReHjDHvs1phsViCEltpONJKtRprCguDhqzEel9E6ZZQS+GtW7cAAOvWrYvpOKmFbnZ2NpHTx629rQ1Dg4NhWzb7rFY58VuYOHoC1n2+fPkyvrx2LcrKymCxWFBWVoYvr13Lb3pERPfsra+PuFyj/hv6NEazuIWTB0tLS1FtNOLQD38Ysm+s4+KTeV9EqZC0kjSxCJyAkg0C6w4GltSpNhpDXqgjIyPy79IEG0EQcOfOHXi9Xni9XthtNlTs3MlJKEREABobG4MmJEoEQUhaXcBkuT43F/T/vfX1igmbRxTx/aammO47mfdFlAoJJYXSjOKJd9+N6TipLEGsLYypolR3UG8w4NV74x8DXb58OWif7lOn5C5jjyhiT0MDxpxOjDmdMJnNYWe73rhxI6qCqko0Gg3+dO1aXMcSEaVbe1sbSktL8YvTp+HxeAAAW7dszbqEEPii0aKwsFC+zSOK6OzsxITLBY/Hg9krVyKWYIskmfdF2e0/PZCPP//5PzIdRkwSSgorKiow5nRCFEU0t7SElHZRYjKb5RfdCw0NiZw+afR6vTww2Ov14nfnz2PS5cLGjRvR29sbNF5Sav4vyC8IeUPTCgJGh4fxeFkZJl0unAtoVVRy//3/c1zxClptXMcREWVKuFaybGJ3OOTfpfd9u8OBhoYG+XNLV1yMzVu2QKPR4IWGBphMppjuP1n3RdkvL28l7tyJ79iMJZOJTl8OnFq/o6rK/97Fi0G3SyUA3rt40b+jqkpxin62uXrtmlySJp44zw4PRyyBwJI06ZWJaf1ElD2iLUkjlSvbvHWrfJv0Wbajqsp/9do1xftW+pxQuj3e+6LcsyRL0gDA6JtvQrhXcHPM6ZQnW8xeuQIAaG1txcNFRSgrKwtaQWT0zTcTPXXKaAUBlgMHAMzPNJ4IqMIfjcCWRWn1EyIiyl52h0MeRmTZv1++XRpjPjo8HFJcOnDiYTSSeV9EqZBwUqgVBIyPj2Nbebl8m9frlcdIiKIIMeBi31ZejvHx8YxVbp9wuWAym2EymyMmezu+9S3598XqbBER0dLkEUXs229BXV0dgPmx4uEmgyy0J84hUMm8L6JkSsrsY2ks3YTLhe7u1zD5+0m5XA0wX4dK/w19VqwnuclgkL8N7qqpCRuPGOZbm1Ru5qWWlrDHBr7gFy6+TkREmWGxWGCxWMJu1xsM+PXQUMhtky4XKp5+Wi4lM3f9Ovr7++UesdkrVzDhcoV8Jsy43eizWlFYWIjqqqqE7osoLdLeYZ0FCgVh0SWFDh85Io9DCSSNNdxRVbXosZr8/LDjRjimMH04ppAot0VaZk+Tn+/fvHWr//CRI4rHvnfxovyZEfhTKAj+s8PD8mfCwjGLgbdL4wTjvS/KPZkaU5iROoWZtq28HHabDedGRmB3OEJWY7E7HOjp6ZH3DbTpscdgt9kw5nQqzrgOPHYHFzgnIsq4z27fjvvYTQYD/nTtGppbWuCemQEwv8SptCTe0NCQXOe2srJSPm58fBzHjrXixic3UKzTJXRfROnyJb/f7890EOnmEUVs3LhRLguwrbwcGo0GwPx4SGlCjEqlwuXLl4MSO48ooqysTO5e1hsMcr3F2dlZuQajcG+spVJSuFKtRkFBAa5+/HHqHiTJVqrVCX0oEBERpZNarcZdJPaFJh5xJ4UTLhcGBweDWsrsDgcONTdHfR+vtLdHvWZysk24XPjOnj3ybLCFdMXF+Hl/v+K4jsAi1UqkcSnhWgmZFKYXk0IiIlpKMpUUxtx9vDAhCkwK5+bmwiZZSuYWLCeUTpsMBrx/6RLsDgd+1tsbtO2FhoaIyerCiTU3PrkBACjIL8iKyTREREREsYopKbQ7HKirq4tqSZ5qoxFTU1O4c+tW0ExevcEAk8mE3c8/nxXj7aqrquJurdxkMGTlMk1EREREsYq6TqFHFIMSQo1Gg927wy9ZNDQ4iPcvXcKH09MYGhqCrrgYADD1wQf4xvr1WZEQEhEREdG8qFsK9zQ0yAnhtvJyjA4PR30SqTWuYudOjDmdqKurC5nAkWs++/xz7AtTL+urX/kKfvyjH6U5IiIiIkqXv/nJT/BvYeYW3E1zLJKoJppMuFwoKysDMD8B4/1LlxT367Na5cKg4QZHPlxUBFEUY04sl5OVanXE7SqVCp/evJmmaJY/TjQhIqJs88Dq1YsOx0v3Z1dU3ceDg4Py71IV9nhJawqPOZ05vdZjQUEBPrt9W/GHCSEREdHy9unNm2HzgITXII5TVOeV1gjWaDSKa0LG4vDBg1CpVACAzs7OhO6LiIiIiJIjqqTQ4/EAANYUFiblpOsefBAA5IruRERERJRZSW2h3FtfLzd9RmNqaiqZpyciIiKiOGWk2/rOrVsAgFWrVmXi9ERERES0QFRJYUlJCQBg9sqVhE/oEUW5mLW0ZjARERERZVZUSWGxTgcA8Pl86LNaEzph4OSSxx9/PKH7IiIiIqLkiKpOoUcUUVRUBAAQBAEfTk/HdTKPKGLjxo3wer1QqVQ5W8B6pVqNgoICXA1TtJKSi3UKiYhoKVGr1biLLK1TqBUEVBuNAABRFFGxc2dcJ9vT0ACv1wsA2FFZmZMJIREREVE2inqiyaudndBoNADmC08/umGDXL9wMX1WKx4uKsKY0wlgvrXxVdYoJCIiIsoaUXUfS+wOB+rq6oKWZdlWXo5NBgOefPJJVFdVybf3Wa0YH/8t3jn/Dmbcbvl2lUqF06dPB+2ba9h9nF7sPiYioqUkU93HMSWFwPy4wIqnnw5K9KKlKy7G6Jtv5ny3MZPC9GJSSERES8mSSQolzS0tOHPmjFxeJhJBEFBbW4v2trZ4TrXsrFSrcR+A++8t97fQmjWFmP7jH9Ib1DLGpJAocSazOesWHHj/0qVMh0AUt6JHvo7r1+cUt0k9sksmKZRMuFwYHByEe2Ym6A2jpKQExTodzGYzNhkMCQe6nKxUq3H/ffejMEyLqXadFr956600R7V8MSkkSkxzSwt6enqChg5lA11xMRNDWrK+uX07PLMexW0ezyyAJZgUUuzYfZxeTAqJEmMym2G32aBd/5/xYNUDmQ4HAHC+4wMA6f/QJEqHTHUf35/WsxER0ZK1ouBLECryMh3GvI5MB0C0/GRk7WMiIiIiyi5MComIiIiISSERERERMSkkIiIiIjApJCIiIiIwKSQiIiIiMCkkIiIiIjApJCIiIiKweDURES1jsa7Z/Ep7O6qrquI61+NlZbh16xZKSkowNDgYdr8Jlwvf2bMHALBnzx4cPngwrvMRJVvcSaFHFDEyMgIA2FtfH7K9z2pF92uv4datW/JtW7dsRWvrMWjDrPmbSz77/HPss1gUt331K1/Bj3/0ozRHRES0/ExNTWHG7Y56/7m5ubjPZTKZcOzoUcy43eizWhU/GwHgO3v2YMbthq64mAlhDvubn/wE/xZmudu7aY5FEvPax31WK145eTLoRaZSqbCjslL+ZiStk6lEpVKhsbER7W1tCYS9tK1UqyNuV6lU+PTmzTRFs/xx7WOixEjv6bpt66B/KTu+1P/DzncBLL42rN3hWDTRkz7TVCoV3nrrLWwyGOKOS3quNBoNLl68GNIIsm+/BQMD1qSci5a2B1avhs/ni7hPVq99fKKjA8eOHg253efzwW6zwWQ2Y1dNTVBCKAgC8latwuyVK/D5fPD5fOjq6kJpaWnYb1G5oKCgAFfDfEMgIqLkWKwr+ERHh9zI0djYmHCS9mpnJ8acTni9Xny/qSmoG9kjijhz5lcAgNrabzMhzHGRGn/UanVGWgujXgLAjAAAIABJREFUnmjiEUW8fPy4/P9t5eWoNhpRbTRCf+/CtttsaG1tBTCfDI6Pj+PD6Wm8f+kSPr15Ey+++CJUKhUAoLm5OZmPg4iIKCZ2h0P+XKs2GpPSg6UVBLS3t8/fv82GPqtV3vaXJhN8Ph/0BgNef6074XMRJVvUSeGxY61yM+eLL76I0eFhDA0OYmhwEBfGx1FtNAIARFGESqXC+Ph4yLeg9rY2vHSvpdHr9eJER0eyHgcREVHUPKKIAwcOwOfzQRCEiBNDYrW3vl7+TGxuboZHFHGiowOTLhdUKhV+PTSUtHMRJVPUSeHk7ycBALriYsVvU692dsq/b96yJexkksMHD0Kj0QAALly4EFOwREREybCnoSGoESMaj27YgOaWlqj2fbWzExqNRu5GllokXzp6lJMtKWtFnRRKs4hLSkoUt2sFAcK9C11K+sJZU1gIAJidnY329EREREmxb78FY04nAKCzszPqJG3G7YZ7ZiaqfbWCgN7eXgDz3cg+nw/byss525iyWlKLV+etWhXVfqvu7RdYroaIiCjV7A4HBgbmx/nt3l2f0gmP1VVV0BUXy//P5aobtDTEnBRGat0zVlej2mjErpqaiPexWKsjERFRsnlEEXV1dQCQlskegTObAcgFq4myVdQlabZu2YoZtxuTLhfsDofiNP9ovgVNuFzyi6RYp4shVCIiovhVPP00fD4fNBrNopM9wtU39Hq9QTOKAaCysjKkCzqwYke10YhzIyOYcbuxb7+FM48pa0VdvHrC5UJZWRmALwpQNzU1xTRg1u5w4MCBAxBFEQAwPT2dkwNuV6rVrFOYRixeTZSYpVy8WiI9BpVKhdOnTy9av/DRDRuiXgmlu7s7pBv68bIyTLpc0BUX4/1Ll+Q6vyxaTdGQ6hRmbfHqTQYDdu+ux8CAVS5A3dXVBWDxoKW1JwNfYNVGY04mhERElF4nOjrkRRUaGxujWtvYWF0dMqnEbrNBV1wcMvRJr9cH/X/ffotcfubn/f0A5itvDA0NYdLlgslkwofT04k8JKKUiGlFk9df60ZBQT56enoWXZol0MIl76qNxqTWhCIiIlISWKB6W3l51JM9lPZbqVajpKQk4ufXhMsVdtWSXw8NobS0FKIowmQ283OQsk7ME03a29rw6c2baD1+XF7RJBoajQbbysvR3d3NFwIREaXcwgLVo8PDKT/nd/bsgc/ng664OGTsoFYQ0NjYCGC+scTucKQ8HqJYxNRSGCiWWksczxXqkxs38MDq1Yrb1qwpxPQf/5DmiIiIlpeRkRF5DLsoilipVi96TCI9WSazGTNud1C38ULtbW2w2e2Ycbtx4MABjI+PcyhVjip65Ou4fj10MhOAjKx7DCSQFFJi7rvvfqxZU6i4TbtOm+ZoiIgoEXaHQx4qtbDbeKGf9/dj+/btEEUR329qYu9Zjor0We/xZGZxDyaFGaLJ17A1kIgohfbWJ7c4dXd3d8ikEkl1VVXUvWKbDAZ8evNm0uKipek3b70Vdps0+zjdmBQSERFFIZWrnxBlg6Quc0dERERES1POtxROuFwYHByU61EV63Qwm81RFxbts1rxxtmz8rGxFvQmIiIiygY5nRRKFe4X6urqwrbycvT39oZN8BauziLp6elBbe23uYwRERERLSk5mxRW7NyJMacTACAIAjY99hgAyCuvjDmdqHj6abx/6VLIsRMuF+rq6uDz+aBSqbB5yxZoNBqMOZ3wer0YGJhfF5OJIREtJx7Xv+OT/bcyHQYRpUhUSeGEywVBEJZNt6jd4ZATwhdffDGkcn1zSwu6urow43bjREdHSE3G5pYWOSFcuIamlGyeOfMrtLYeWzbPGRHlrl01NXj77bdx59YtfH7r/8t0OLJoF08gouh8ye/3+xfbSepm1RsMeKq8PKYxd9lIejyCIIRdf/LhoiKIohhSyHTC5UJZWRkA5YTSI4ooLS2Fz+fD7t31iq2FK9VqFBQU4OrHHyfxUVE4K9VqFlAnSpDd4cDcnHKh3UzhbGBarqSSNOn+7IqqpfCllhYAwJjTiS6XC11dXRAEATt2VMJi2b/kEsSpqSkAkLuMleStWhW0r2QwIEFsamoKOU4rCNi8ZQvGnE68c/6dZIRLRJRxgT0iRLQ8RVWSZpPBgKHBQfzp2jUMDQ3JTfYDA1aUlZXh4aKi+da3JbKOo7G6GtVGI3bV1Cy6b0lJSdD/J1wuAICuuDhs17CUJM+43QlGSkRERJQeMU80qa6qkr8xTrhc6O5+DefOjcwv7m2zQaPRYFt5OXbV1GRt0/7CLt+F+qxWOaFbmDh6PB4AgFYbfnma0tJS+fcJl2vJtaQSERFR7klo9vEmg0EeMyfV+3vb6ZQTxKamJmzesgUVFRUhkzWyyYTLhZfvJYrS7GNgfhBzuMRWo9GEvb/AZZAmJycVk8LPPv8c+yyWuOLd/uSTeP7b347rWCIiIkq9v/nJT/Bvcc4dyMQSd0CUE01i5RFFdHZ24m2nE1MffCDP1C1Zvx5PlZdnXYHnPqsVlgUJmt5gwK+HhkLifHTDBsy43SETUBZaqVYDmF8rc2FiKW2Ll1a7jusmx4ATTYiIKN0eWL0aPp8vofvIyokmsdIKQlAX7YmODoyOjuJ3589j8t5EFb3BAMv+/VnRxazX6+Vxkl6vV45z48aN6O3tTckAa84+JiIiWr4+vXkz7mOl2cfplpa1jw8fPIjR4WF8evMmuru7UW004qOZGXl5uEyTJtIMDQ5idHgYly9fhiAI8Hq9ONTcHPP9SZNRiIiIiJaKtCSFgfbW18szmV/t7Ez36aOiFQRYDhwAMD+DWCnJ83q9YY+fnJyUfy8sLEx+gERERERJlvakMFAmxhVOuFwwmc0wmc0RW/R2fOtb8u+BSZ4061iahaxk7vp1+XfW9iIiIqKlIKNJYSZsMhjk2dGByd5CoiiGPR6IXIPwwoULAObXVCYiIiJaCnIuKQS+KCcTaUzjv/zLv8i/B06GMZvN8u8nOjoUj5XWVY60YgoRERFRNsnJpHBbeTkA4NzIiOIqLHaHAz09PUH7SjYZDNDfay3sPnUKngUtivv2W+TxhtLygERERETZLiV1CrOdRxSxceNGOXnbVl4utx56vV65pU+lUuHy5cshYx8nXC5s374dPp8PGo0GzzzzLAoK8jHhcsnHRqpjuFKtZkmaNGKdQqLEzMzcxV9924uLFxOruZZsbw4XoHJHSiqrEWWUVJIm3Z9dOZkUAvOJ3Xf27Ak7NlBXXIyf9/eHXaLO7nCgoaFBcRZyNIWtmRSmD5NCosQcar6D/6vjVqbDUOT/D1Z4oOUnU0lhzn7F2mQw4P1Ll2B3OPCz3t6gbS80NCw6a7i6qgp/unYNzS0tcM/MAAAK8gtgseznWsdZwCOK2NPQILfcrlSrsa28HP29vVm1mg7RUmL83ir89Ut5mQ4DAFD31blMh0C07ORsUiiprqpKqGxM4MotlD3KyspCZpCPOZ0oKyvDh9PTGYqKiJYzk9mMXTU1WbFSF1E8cnKiCS1vJzo6wpYUEkUx7KxxIqJ42B0OPF5WhtnZWbxx9iweLioKmYRItBSkpaXwREcHLly4wO7VAN5PvCh65OuK27TrtPjNW2+lOaLlQ6oTGe92IqJYVFdVYW5uDhaLBR/NzKCXw1QoCt/cvh2eWeWFMDKx7jGQpKSwz2rFL06fhsfjwfuXLsm3e0QxpBtvYMC66EQMIiKipeSNs2dRbTRiamoKv//gA65mRUtSwklhc0sLurq6FLftaWhQ7Maz22wwmc05nRhq8jWY/uMfMh3GsrSrpgZ2my3idiKiZHq1sxNaQWC3MUUtUo+gNPs43RIaUzjhcgUlhLriYvl3jyjKMz8FQcD4+DjGx8flfew2G188lBJ76+vlAuML6Q0GDgInoqSTuou1gsCuY1qyEkoKX74381alUmFoaCio67izs1P+/dSpU9hkMGCTwYDRN9+ESqUK2YcomX49NIRqo1EuSq7RaFBtNOLXQ0MZjoyIiCg7JdR9PDU1BQDYvGVLyPiJCZcLwL0P44BtWkHAugcfxIzbLdf3I0rELw+M4J9GQgvr5sMM4yozfun9DoyrTgETwNFvvhOy319UrsLzpyrTESoREVHWSspEE6k1JtDkvaRQqRuvpKQEM263nFQSJeLQL78Gz63wBXVXqID//tG2sNsdv7yD50+lIjIiyjST2RzTZ80r7e0ZnSQSb7xL7XFSdkpJSZoJl0te/k2p/Iy0bdWqVak4PeUoQXs/Ch4KHREx8y6wfqsq5PYbH92F6PlzOkIjogyZmpoKu5ypkrm5zK6UEm+8S+1xUnZKKCnUarWKLX7d3a/Jv5vN5pDjpFbEdevWJXJ6oiCPGVcoLsHV8Ahw9HR+yO2/ePkObD/NzvVciSg5XmlvXzQBeuXkScy43VCpVNDr9WmKLEwscca71B4nZaeEksJNBgPGnE7MuN3Yt9+C11/rht3hwJkzvwIwP+t4YUvhvv0WuaWwWKdL5PREREQRLdZFeqKjQ25ha2xszPjiCvHGu9QeJ2WnhGYft7e1Qbg39X5gwIqVajVMJhN8Ph8AoLa2Vt73REcHHi4qwsCAFcD8jGWuG0xERJlidzjw8vHjAIBqozHrP5PijXepPU7KnITXPj516pTiRJNt5eVBF96FCxfkQtYqlQovHT2a6KmJiIji4hFFHDhwAD6fD4IghCymYDKb8eiGDTApDIGyOxwwmc2K21JlsXiTfRzlpoQnmlRXVeHixYvo7OyUS8wU63SK30Q0Gg30BgPa29rYdE1ERBkjrbilUqkwPj4etM1kNsurIs243WhuaQn6TPvbzk6MOZ3YVl6eFfGm4jjKTUmZfawVhEWbo/nthIiIssG+/RZ5xa3Oe8vTBZqamsLu3fUoK3sCra2tOHPmTNBn3O/OnwcA/KCpKSviTfZxlLsSSgr7rFa8cfZs2JbBxY7bVVOTs0uO3bhxAyvVasVtKpUKn968meaIiIiWP7vDIY9t3727XvEzSKvV4vXXuuX/WywWTLhc2GQw4ERHB3w+H3TFxWmp8xdNvMk8jtLngdWr5TkY2SKhMYVvnD0Lu80Gm90e13FvnD2byOmXtIKCAnx2+7biDxNCIqLk84gi6urqAMwvrBCY+AUKHN60t74egiDg3D//MwBgdHQUAHDohz9McbTRx5us4yi9Pr15M2wekPCEjzhl5LxSSRquaEJEROlS8fTT8Pl80Gg0EddBX9jztemxx3DhwgUA813HuuLitLS8RRtvso4jiqn7OHDwbaAZtztsV2gkJSUlMR9DREQUK5PZLBdu7u3tjWl83a6aGrxy8qTcdWysrk5hpPPijTeRx0mUqRZKAMALDQ2ZPD0REeWAEx0dcoNGY2NjzGMB99bXY/bKFYyOjkKj0aS8zl+88Sb6OIliaincVVMT9H9prUWNRhPz1PyXWlpYloaIiFIqsHDzwvq5sSgoKMDvzp9HY2NjMsMLEW+8yXqclNtiSgr31gfPYJKaqdcUFrLkDBERZZWFhZtHh4fjvq+8Vatw586dmJMtqcB1NNU24o03mY+TcltCJWmklkOuYUxERNlmZGREXklLFMWoxr5XG42KjRxarTaucfCB4/AXSwrjjXdXTU3SHifltoSSwoUth0RERMvR786fx+YtWzIdBlFKJWVFE2B+PMPc3FxMxzChJCKiVElWw0VzSwt8Ph88Hk/Mx352+zYe3bAhqn0TiZefp5QMCSeFdocDDQ0Ncu3BWPAiJiKibPf2vaXiErFwoiZRNkooKZSqpmfbMi1ERETJ8tHMTNzHmsxm3Ll1i40gtCQklBQeO9YqJ4R6gwGW/fuTEhQREVG2+PzzzwEAq1ativnYXTU1eLWzM9khEaVEQknhO+ffAQDoiotxYXw8KQHlCu8nXhQ98nXFbdp1WvzmrbfSHBERESnZUVmJcyMjOHb0aMzHsoWQwvnm9u3wzCqPU72b5lgkSZlosnXL1mTcDRERUdZh6RbKFUlJCh/5+iPJuJucosnXYPqPf8h0GEREUbP99BZsP72V6TCIloVIPYJqtTojrYUJrX0sFfK8cOFCUoIhIqLs80p7Hr71lCrTYYTw/0dhpkMgWlYSail8qaUF50ZGcG5kBB5RhFYQkhUXERFlkX8azc90CESUYgm1FG4yGNDY2Aifz4eysjLYHY5kxUVEREREaZRQS+GEy4XS0lLs3l2PgQErTCYTBEHApscei+p4Dt4lIiIiyg4JJYUvt7UFLfYNzC/GvfA2IiIiIspuCXUfExEREdHykFBLIbt/iYiIiJYHthQSEREREZNCIiIiImJSSERERERIYlI44XLBZDbj0Q0bsFKtln/6rFYAgMlsRnNLCzyimKxTEhEREVGSJGXt4+aWFvT09MDn84XdZ2pqCnabDT09PXjp6FEcPngwGadesm7cuIGVarXiNpVKhU9v3kxzRERERJQuD6xeHTFvyoSEk8LmlhZ0dXXJ/5eKV485nfB6vfLtWq0WM243fD4fjh09isI1a7C3vj7R0y9ZBQUFuPrxx5kOg4iIiDIgUuOPWq3G3TTGIkkoKfSIInp6egDMt251dnbKid6jGzYEJYWjw8Pos1rR1NQEn8+H5ubmnE4KiYiWlIGfAh9NZzqKYD9uz3QERMtKQknhsWOtctPn6dOnUV1VFXF/KQm0WCzwer040dGR893IRERZb+CnwP95BMi2YS2XJoC/H810FETLRkJJ4eTvJwEAeoNh0YRQsre+Hq2trRBFERcuXEjk9ElzoqMjKJZdNTURWzEnXC683Na26P0udj9EREvCR9PzCeGmzcA3n8p0NPM6TwBvn8t0FETLSkJJ4a1btwAA69ati+m4TY89BrvNhtnZ2UROn7BwE2TsNhuam5vR29urmOxOTk5Gvb4zk0IiWja++VT2dNl2nsh0BETLTlJmH8cqcKxhpgROkFGpVNhRWQlgPjZpkkxdXZ1it/j4+G/l49Y9+GDYcxTrdCmKnoiIiCi5EkoKpRnFE+++G9Nxky4XgNhbGJMlcIKMIAgYHx+HVhDk7XaHA3V1dfD5fDhw4AA+nA4eXH3jkxsAgM1btmB0eDh9gRMRERGlSELFqysqKgAAoiiiuaUlqmNMZrPcUvhCQ0Mip49bZ2en3GW8MCEEgOqqKrx09CiA+cdmdziCtk9NTQEANBpNGqIlIiIiSr2EksLDBw9CV1wMAOjq6kLFzp2YuNcKuNCEy4WKnTvlsXi64uKoJ6ckm3tmRo5hYUIoCZwVPTc3p7jP448/nvzgiIiIiDIg4WXuRt98E8K9xGrM6URZWRm+vHYtZq9cAQC0trbi4aIilJWVYczpBDDfZTv65puJnjpuUkvfqlWr4jp+xu0GABSuWQNgPuHts1rDJsRERERE2S7hiSbae2Py9jQ0yElf4EQSccFax9vKy9Hf2xu2hS4d3r90adF9ArvD9Xq9/Hvg2s2XL1/Gl9euDXq8Go0G28rLMTQ4mKRoiYiIiFIvKbOPtYKA0eFhTLhc6O5+DZO/n5TL1QDzLXL6b+hhsezHJoMhGadMKbvDIU9E0RUXB8U8MjIi/y7NXhYEAXfu3IHX64XX64XdZkPFzp2chEJERERLRkJJ4YTLFZQwbTIY8Ppr3QkHlUmBtQtVKlVIN/fly5fl3/UGA7pPnZKfA48oyi2mY04nTGZz2BZD7ydeFD3y9bhi/NaOb+H17qX9PBMRES1n39y+HZ5ZT1zHZmLdYyDBMYUvt7XhgdWrYTKbl/x4uj6rFQ8XFaGrqws+nw+CIOD06dMh3dylpaWoNhqxe3c9LoyPByXFUoup/t5t5wJaFYmIiFJJGt8eLbvDgT6rNaTCRiQeUUSf1RrTecLps1pRsXMnvrx2LVaq1VipVuPLa9fi8bIynOjoSPj+JRMuFx7dsAGPbtgQNAQsnH37LXh0wwaYzOakxbBk+BPwXG2tf0VenvzzkE7nP3zkiP/qtWuJ3G1aXb12zb9561b5MWjy8/3P1dYmdJ9nh4fl++vt7w/ZviIvz69dty6hc9AXtPkf+nH/n/zG/3rbf/qqP+RnRV6e4u3G/3rbj/v/5Nfmf5jph0CU3Y4f9vvXYP7fbLEG8z8k21FV5V+Rl7fofs/V1vo1+flBn9+Lffa9d/Gif71eH3LMd7/XGHOcCz93w/2s1+uTlk8UCoJ/RV6e//CRI0ndN1Xy7j0H6ZZQS+Gumhp55jEwP6mkq6sLpaWlqNi5MynfJFKpz2pFaWmpXEy72mjE5cuXE54kElhqR1r9hIiIKFU8oojfnT+/6H5SaTifz4dt5eWoNhqhNxjg8/nk8fAL2R0ObN++HTNuNwRBQLXRiG3l5fD5fBgYsGLffktMcZaVlWHS5YJKpcKLL76I6elpfHb7Nj67fRvT09N48cUXoVKpMON2o6ysLKbnIZxt5eUAAJvdHnE/u8MhTx5tampKyrmXkoSSwr319fhwehrj4+OoNhrlYs4+nw9jTicsFgu+vHYt9u23ZF338omODlgsFvh8PuiKizE+Po6hwcGMzoomIiKKhd3hwL79FmzcuFFelCGc5pYWjDmdUKlUGBoawujwMIYGB3FhfBxDQ0NQqVQYczpDGnQONTfD5/Oh2mjEh9PTGBocxOjwMLrvjW0/c+ZXUXXLAsD3m5ogiiJUKhXeeusttLe1BX3uagUB7W1tOH36NFQqVUyLY0Ty0r37mHG7I+YjP+vtBTA/ZyAX84GE6xQC8xNMhgYH8adr1zA0NBSUIHq9XgwMWFFWVpb0cQLx8ogiXj5+HMD8t4f3L12Kela0yWxedAxl4IujrOyJxIIlIqKkkcbdKdWWjbQtGz26YQNMJhMGBqxBpdHCefte2bgdlZUhi0dUV1VhR2UlAOAXp0/Lt/dZrZhxu6HRaEJ60fbW18utjAO//OWi559wueQFLDo7OyN+7lZXVaGxsREAcObMmbD7BY5xjNQ7uclgkHs2u7tfC7ufVFrvqXsti7kmKSVpAlVXVckXm93hwN92duJ358/D5/Nh0uXCpMuFl48fx47KyozV8jt2rBU+nw8ajSbmsjET774LURTh9XrDHtvZ2QkAUKlUqLz3IiMiovQzmc2w22yoNhoBQE5KJNVGI17t7AyqtRu4LZtrzhqrq+UVuoDQx7aQVCpuV02N4vZdNTWw22zweL6YMfvG2bMAgGeeeVbxmAvj41HHKyVjuuJi7K2vX3T/pqYmlJaWht0u/W0XHlNb+23FSig7dlRiYMCKc+eUJ4FKXccqlSonu46BFCSFgQITxBMdHRgdHcWY0ymPXcgU6YLQGwxRjXusrKyUm5E3PfYY7DYbxpxONLe0oL2tLWjfwBqHOwKOIyKizJGqQVQbjdhVU4NfnD6NMacTdpsNU1NTmL1yBbt316Os7ImgbXaHI2NLsi5m4efPSrU64v5SEhm4IEMgKQHUarXybdIKYMno9Xrn/DtyHNHQCkLY5LFi5065K1xq4fR6vRhzOjEwYMWNT26EJPStrccwMGCFKIohJfWAL7qON2/ZkrOf3SlNCiVSQhjNINh0kFZZkeoJLqa7u1u+MF/t7JRbC7u6uvC204l169YBAGZnZ+VJK4Ig4NV7LYZERJRZPp9vfnjTvQRvb329nFjMuN0h2x7dsAEzbjd+1tubtUlhrBYmkYE8oignzn9dVyffLi3rqtfrYTKbcW5kRB67KAgCLAcO4PDBg1GdX1r+NlLrXzT6rFaMOZ3QaDS4ePFiUAJndzhgMplgt9lCEj+tIEBvMGDy3kIbC1sTpXygoqIiofiWsqSMKVRyoqMDFTt34oHVq3Hs6FG5hRCYXwpu9+7Fm46zkbSsnzSTafLeGAm7zSYnhHqDAePj4zn7TYOIKNvoDYaQ5E4a+76tvDxkW0lJSdpiy7Q+q1WeqLKtvFyxdU5KtAoKCqArLoYgCBBFEceOHo26nt9iE2FMZrNcT3DhT2Atxe7X5ruh9+7dG/I5W11VJQ8VeFkhCZbGCv7jP/5D0O0TLpfcdRxtkrscJbWlMLBFcOEfX1oT+IWGhox/6/rs9u2Ejl+4rN+NT24AAAryC5bMUn5ERLlE6tFRIiWHqSS1PEYjsHcqlSZcLlgOHJAbNLaVl4cdKy+KIlqPHw9KmJpbWtDV1aXYKhePqampsM/R3NzcF/t98AGA8C2f0thIqes7UFNTE3p6euaXpA0YGiCNd9y8ZUtCj2GpSygp9IgiOjs7MeFyKSaCKpUKm7dswQ+amjKeCKbCcljWj4iIUm/hpJBIwo35S6bASRoajQbt7e0RE9FqozGkBa29rQ0TLhfGnE683Na26KQcjUYDr9eLuevXFbe/f+lSxDglUq6x2BhKJVpBwOYtWzDmdAYNDZDmGuRy1zGQYFL4/aamkD+WlAhWVFTkdBMsERGRJNJ4vnSSikdLtQIbGxujii3cjOWKigqMOZ2KrXILPaTTYdLlwoULF6KON9L96oqLIx4bbgiAFLM0hnDC5YIoitBoNDmftySt+1hvMOCp8nI0NTVxLB0RES0rj27YAEC5NSvSNond4QjqAo2kMkWVKwITQr3BgF8PDS16Hl1xccRu78I1a6I+/1Pl5Zh0uXBuZAQeUVz03B5RlCenKIn0fEdy+OBBnHzlFbkL+de//r8BfLHqSS5LKCl8/PHHUazTMRGMw40bN8I2fatUKnx682aaIyIiolQ51Nyc8TGF0moieoMh6vqCJSUlmHG7cfnyZcXtSmVswmlva0NfXx+8Xi++39S0aHfz95uaFCenSJNcwpULam5pgc1uh7G6Omwr6LbycthtNvystxcT774LAHihoWHRx5BMD6xevejkm3RLKCnM9WbWRBQUFODqxx9nOgwiIkqDbBhTKHWXHjt6NOpjXmhogN1mQ19fX0gDULgyNpH88NAhHDt6FHabDSazOWxiuG+/JWw9Y6kI9YFsZ9Y8AAAgAElEQVQDB/Dh9HTQNo8ooqenBz6fD08++eSij2vM6YTX64VGo0n73IdIjT9qtRp30xiLJC11ComIiHJZNowplJbCM5lMEffTFRfLXbNSiRe7zYaNGzfimWeeRVnZExgf/y3OnPlVxDI2Sg4fPIj/99//XZ61/OW1a7GtvBwF+QUoKMiHe2ZGTtR0xcUoKSkJSQ5ff60b586NQBRFPFxUhNraWpSWluLy5cvo6+uTY4qU5FVXVckTXwB2HUuiSgr7rFa5iTjRJX8CZxIlWhqGiIgoXe7cuqW4CtadW7eQt2pVBiKKXjSrd4XzamenvDjDwIAVAwNf3Je0TGAs2tvaUFpaiubm5vlxfQoTVqUlBvusVsUWw/HxcVQ8/TRm3G50dXUFbYtUWifQM888Kz+WdHcdZ6sv+f1+/2I7RZPI9VmtsFgsACKPh2BSOD+Nnt3HyfOfV38Ez608GL+3Cn/9Up58+7++7YD3xhz+rtmC77Z3Q1NQiP/tqS++Of7i5Tuw/fQWtKvu4OrNhzIQOdES8TfNQOcJoOkw8OP2TEcz73/90vy//77oR1hSLFZnMLB1bbmyOxzyUnDJqssbeJ/A/FyF3c8/H/U8hVTElA2k7uN050nsPqZly/n3vfD8P1NYtUoDe/dJaL9WEpQUEhHFIlziJ80+Xu6qq6qSPu4u0ftMRUy5jEkhLVsHTiU21IGIiCiXpGztYyIiIiJaOpgUEhERERG7j4kWMpnNmJqawtzcHB7Iz8f/olIt+wHkRFH5zdvzk06IaFliUki0wAsNDZibm4PFYsGzzz6LsieeyHRIRJlVXgH8w98DE7+b/8kWTYfTdqpIXwz5pZGWCyaFRAtIM9ksFgvKnngiJctNES0p5TuA/+MI8NH04vumU7aUxyFaJpgUEhHR4nZ/L9MREFGKMSnMEO8nXhQ98nXFbdp1WvzmrbfSHBERERGlyze3b4dn1qO4LRPrHgOcfUxEREREiKOl0GQ2K94uLSoNAL84fVpeK3mhqampWE+5LGnyNZj+4x8yHQYRERFlQKQeQWmZu3SLOSlUWph6oTGnM65giIiIiCgz2H1MRERERNG1FL7U0oJdNTWpjoWIiIiIMiSqpHCTwYBNBkOqYyEiIiKiDGH3MRERERExKSQiIiIiJoVEREREBCaFRERERAQmhUREREQEJoVEREREBCaFRERERIQ4lrmj5Lhx4wZWqtWK21QqFT69eTPNEREREVG6PLB6NXw+X6bDCMKkMEMKCgpw9eOPMx0GERERZUCkxh+1Wo27aYxFwu5jIiIiImJSSERERETsPibCnc+BF/73txW3nT75R/zmVeVtXy35T/hvP/8vqQuMiIgojZgUUs775M95+O+u9SG3r1AB52fXwusN3XYfgPtdd/Hffp6GAImIiNKASSHlrMKv3of1W1Vht8+8Cwi6+7EuL3ifO5/cxUcf/DnV4REREaUVk0LKWRW7V6Bi94qw2xseASr3rEDZc/lBt/+r88/4yXducEQuEREtK/xYIyIiIiImhURERETEpJCIiIiIwKSQiIiIiMCkkIiIiIjA2ccZ4/3Ei6JHvq64TbtOi9+89VaaIyIiIqJ0+eb27fDMehS3ZWLdY4AthUREREQEthRmjCZfg+k//iHTYRAREVEGROoRVKvVGWktZEshERERETEpJCIiIiJ2HwMATnR04MKFC/L/d9XUYG99fVTH9lmteOPsWQBAsU6HpqYmaAUhJXESERERpUpOJ4XNLS3o6emBz+cLut1us6G5uRm9vb2orqpSPNbucODAgQMQRTHo9p6eHtTWfhuvv9adsriJiIiIki1nk8LmlhZ0dXUBAFQqFXZUVgIAvF4vxpxOeL1e1NXV4fTp0yGJ4YTLhbq6Ovh8PqhUKmzesgUajUY+bmDACgBMDImIiGjJyMmk0COK6OnpAQAIgoDx8fGgLl+7wyEnfQcOHMCH09NBxze3tMgJ4cKksWLnTow5nThz5ldobT3GrmQiIiJaEnJyoklnZ6fcZbwwIQSA6qoqvHT0KABAFEXYHQ5524TLhTGnEwDQ2NgY0orY39sLlUoFn8+HY8daU/kwiIiIiJImJ5NC98wMAEBXXBy2Je/wwYPy73Nzc/Lvg4OD8u9NTU0hx2kFAZu3bAEAvHP+naTES0RERJRqOZkUTk1NAQBWrVoV87ETLheAyAnlJoMBADDjdscZIREREVF65eSYwvcvXVp0n+aWFvl3vV4v/+7xzK9TqNVqwx5bWloq/z7hcslJIhEREVG2ysmWwsXYHQ55IoquuFgxqdNoNGGPD0wiJycnkx8gERERUZLlZEthJIG1C1UqFUbffDPm+4imZfDGjRtYqVbHEyK02nVcN5mIiCiLPbB6dUgd5GzHpPCePqsVra2tcjFqQRBw6tSplJWUWZmXB9Nf/VVcx25/8skkR0NERETJdOjQIfzbxx/HdeyA1ZrkaKKT80mhRxTxlyYTJu9NIJEKWQ8FzDKOlTQZJZKVK1bg9W4WtyYiIlqOfvyjH8V97C+tVtxNYizRyukxhX1WK0pLS+WEsNpoxOXLl6NKCL1eb9htgeMICwsLEw+UiIiIKMVyNik80dEBi8UCn88HXXExxsfHMTQ4uGh3sTTrWJqFrGTu+nX593BrJxMRERFlk5xMCj2iiJePHwcAbCsvx/uXLkVdNiaaGoQXLlwAMD8ukYiIiGgpyMmk8NixVvh8Pmg0GowOD8d0rNlsln8/0dGhuI+0DN6mxx6LP0giIiKiNMrJiSbnzo0AAPQGA/qimOFTWVkpdytvMhigNxgw6XKh+9Qp7H7++aAu5337LfJ4w5cCCmATERERZbOcTAqlsjNjTqfcqhdJd3c39tbXf/H/U6ewfft2iKKIjRs34plnnkVBQT4mXC75/qqNRq5kQkREREtGTiaFidpkMOD06dNoaGiA1+vFwEBwa2O10ZhQSRsiIiKidMvJpPCz27cTvo/qqir86do1NLe0wD0zAwAoyC+AxbKfLYRERES05ORkUphM7W1tmQ6BiIiIKGE5OfuYiIiIiIKxpTBDvJ94UfTI1xW3addp8Zu33kpzRERERJQu39y+HZ5Z5YUwMrHEHcCkMGPu3v0zrl+fy3QYRERElAGeWU/W5QFMCjMkv6AAVz/+ONNhEFEGTbhcQWulA8F1UYlo+Zr+4x/CblOr1RlpLWRSSESUIS+3tcFuswXdtrAuKhFRujApJCLKEKmeqene8pmsb0pEmcTZx0RERETEpJCIiIiImBQSEREREZgUEhERERGYFBIRERERmBQSKRr/H1YAwO//ZRTeOTHD0RAREaUek0KiAP/6tgPf/y9r8XfNFgDAefv/wKHtpfj79pYMR0ZERJRaTAqJ7vHOifjpDxtwy+sNut3n88H+d1248ntXhiIjIiJKPSaFRPf869hISEIY6I3utjRGQ0RElF5c0SRDbty4gZVqteI2lUqFT2/eTHNE5PqnsxG33/DMpikSIiJa7h5YvRo+ny/TYQRhUpghK/PyYPqrv1Lc9tWvfCXN0RAAGP6iBu+O2MJuL9CuS2M0RES0nB06dAj/9vHHitsGrNY0RzOPSWGGrFyxAq93d2c6DArwla/poVKpwn5zM/xFTZojIiKi5erHP/pR2G2/tFpxN42xSDimkOieB79hwLM/OKq47bFKI8qeq09zREREROnDpJAowM7vHkTrr8fxWKURAFCs34TvtnfjwKnBDEdGRESUWkwKiRZ48BsGOQl86q/3sYWQiIhyApNCIiIiImJSSERERERMComIiIgI/z979x/fVH33D/9FiaG0XSy5+81ih4C1OKpYul5cipShbFBLqV6TOiubq/SrCP3263pNbuwqY9y9GHJ13rircPcODDcgdkL1AjctpUO3sUpRr7ESKkLF2mGpMdYudrlCKCGm3z9CQtKck9/NSZrX8/Hoo+n5nJN8+jkn57zP53x+MCgkIiIiIjAoJCIiIiIwKCQiIiIiMCgkIiIiInCaO8mYhky4eebXBdMyp2birT/9Kco5IiIiomj55qJF0PfrBdOkmOIOYFAoGbvdhsHBAamzQURERBLQ9+tjLg5gUCiRdKUSn1y4IHU2iIiISAIfffiBaFpqaqoktYVsU0hEREREDAqJiIiIiEEhEREREYFBIRERERGBQSERERERgUEhEREREYFBIRERERGBQSERERERgUEhEREREYFBIRERERGBQSERERERgXMfS8ZoNGJyaqpgmlwuxz+++CLKOSIiIqJouX7KFFitVqmz4YFBoUQmp6Sg9MEHBdOm33hjlHNDRERE0bRu3Tp8fOGCYFqTVhvl3DgwKJTI5ORk7NJopM4GERERSeAnzzwjmvaSVgt7FPPixDaFRERERMSgkIiIiIj4+NjDHq0Wrx86hAPNzT7X69TpsHnLFr/vd9+yZVhZXh6p7BERERGNGQaFburq6mAwGPyu19XVhdaWloDek0EhERERxQMGhVft0WoDCggBoKPjbQCOoWOmTpsmul52VlZE8kZE40D7m+JpQ0P+11m4OLL5ISIaJeGDwk6dDhrNTrz88v6AtzEOGQEAd8ybhzcOHx6rrBHReFK6RDwtWe1/nc9HIpsfIqJREjYobG1rQ2lpaUjbdnd3AwAUCkUks0RE4930m4DvfNd7+aE/On4vE2hu0vDzsc0TEdFVCRsUAkBWdrbrtcVsDvjxsdOdd94Z6SwR0Xh2083AT+q9l79X5vgtlMagkIiiJGGHpCkuKsL7p065fjZu3Bjwtr09PQAAVUYGAMcj6D1aLTp1ujHJKxEREdFYS+iawlDo3WoTz549i6/ecANMJpNrmUKhwIKFC/0Oa0NEREQUSxgUBunIkSOu19u2bQMAqNVqWCwWmEwmmEwmtLa0YMnSpT47oZiGTLh55tdDysO3Fn+LU+QRERHFsG8uWgR9vz6kbaWY4g5gUBi0s2fPul7n5uVB09iI/Lw8AI5axEcrKnCsvR3H2ttRWlYmWmNot9swODgQUh6cHV2IiIgoNun79SFf56XCoDBIOTk5KC4pgTJdiV07PWvrMtVqvHH4MO4sKECXToc33WoVR0tXKvHJhQtjnV0iIiKSwEcffhDytqmpqZLUFiZsR5NQrSwvx4HmZq+A0N3GDRsAAFarFXu02mhljYiIiChkDArHQHFRkeu1c/YTIiIioljGoJCIiIiIGBQGq7SsDKVlZT7HJHQftqag4K5oZIuIiIgoLOxoEqTOEydgMBhgMplEh5xpaGgAAMjlchQWFkYze0REREQhYU1hkPLnzgUAHGtvR01trVd6a1sbduzYAQBYXFiITLU6qvkjIiIiCgVrCoO0vaHBVVu4bds2HG1vx9SpUwEA/f396Lr6WFmtVmP71RpDIiIioljHoDBImWo1Ojo6XINUd+l0rkDQKTcvD68eOMBaQiLyq7WtDT09PZg4cSI6dTrXYPhERNHGoPCqleXlWFleHtC6zkGqO3U6aDQ7YRwyAgCU6UpUVq7mSZ2IAuIc6N6poKAAxSUlnDudiCTBoDAM+Xl5PgexJiISU1pW5vWUAQBaW1qwanUlzy1EFHXsaEJEJAFf02Aef+d4FHNCROTAmkKJGI1GTE5NFUyTy+X4xxdfRDlHRBQteoMBVqtVNL23pyeKuSEiKVw/ZYrP84AUGBRKZHJKCkoffFAwbfqNN0Y5N0QUTf46oSkUiijlhIiksm7dOnx84YJgWpNWG+XcODAolMjk5GTs0rDNUCx672gbTMYBAEDPCcfc1QXLA+uERBSo3Lw8wTaFzjQiGt9+8swzomkvabWwRzEvTmxTSDTK/s01eKGmEgBw9BWt6zVRJGkaGyGXy72Wq9Vq7N29W4IcEVGiY00h0Sib3zgldRYoAeTn5eHs2bPYuLEOLa0tAICS4hL2OiYiyTAoJCKSSKZajV07NSgtc4x1yoCQiKTEx8dERERExKCQiIiIiBgUEhEREREYFBIRERERGBQSERERERgUEhEREREYFBJFTGlZGSanpnr8EBERxQuOUygR05AJN8/8umBa5tRMvPWnP0U5RxSu9bW1uG/ZMmysq0NhYSEK7rpL6iwREVGM+uaiRdD36wXTpJjiDmBQKBm73YbBwQGps0ERlJ+Xh/y8PDy3dSsK7roLK8s5XzIREQnT9+tjLg5gUCiRdKUSn1y4IHU2iIiISAIfffiBaFpqaqoktYVsU0hEREREDAqJiIiIiEEhEREREYFBIRERERGBQSERERERgUEhEREREYFBIRERERGBQSERERERgUEhEREREYFBIRERERGBQSERERERgXMfS2bIaMT1U6YIpmVkqHzOiZho9mi1Hn+rVCoUFxVJlBsiIqLw3Tzz6xgcHBBMk2LeY4BBoWQmpaSg9MEHBdOm33hjlHMT2yorKz3+zsrOZlBIRERxraLiUXx84YJgWtOoypBoYVAokcnJydil0Uidjbhw6eJF7NFqUVlZiUsXL0qdHSIiorD95JlnRNNe0molqS1km0IiIiIiYlBIRERERAwKiYiIiAgMComIiIgIDAqJiIiICAwKiYiIiAgMComIiIgIDAqJiIiICAwKiYiIiAgMComIiIgInOZOMpeGh7Fq1Jy+TtNvvNHn9DdEREQU33727LOicx9LMcUdwKBQMpctFry8f79gWkaGikEhERHROLZ7914MDg5InQ0PDAolkq5U4hOROwQiIiIa3z768APRtNTUVElqCxkUEhHRuNHa1oaBAc/al5Xl5RLlhii+MCgkIqJx41e7d6O7uxv9fX3IyMhAckoKg0KiALH3sZs9Wi1Ky8pC2qa0rAw1tbXQGwxjlDsiIvLnQHMz3j91ClarFRs2bMD7p05JnSWiuMGaQjd1dXUwBBjUtba1oaqqymv9HTt24KGHHsaunZqxyCIRERHRmGBQeNUerTbggLBTp8OKFStgtVohl8txx7x5UCgUONbeDpPJhKYmLQAwMCQiIqK4kfCPjzt1OqxaXYnq6uqAt6mprXUFhPv27cMbhw/jQHMzPvv0UyxYuBAA8PLL+/komYiIiOJGwgaFrW1tmJyaioKCAjQ1aWG1WgParlOnw7H2dgDAmjVrUFxU5JG+d/duyOVyWK1WbNxYF/F8ExEREY2FhA0KASArO9v1o1arA9qmubnZ9VqodjFTrcYd8+YBAI6/czwyGSWicam0rAyTU1PR2tKC1pYWTE5NxR6tVupsEVGCStg2hcVFRR61fHu0WlSKTDvnrlOnA+AIKDNFAsn8vDwca29Hb09PZDJLROPS+tpa3LdsmceywsJCiXJDRIkuYYPCUOn1egBAZmam6Do5OTmu1506HfLz8sY8X0QUf/Lz8nh+IKKYkdCPj8OhUChE03Jzc12vu7q6opEdIiIiorCwpnAMBHLnP2Q04vopU0J6/9y8PLz1pz+FtC0RERGNvZtnfh2DgwP+VxQgxbzHAINCyUxKSUHpgw+GtO2iu++OcG6IiIgokioqHsXHFy6EtG2TRB3OGBSOAWdnFF8mJydjl4aDWxMREY1HP3nmmZC3fUmrlaS2kG0KQ2QymUTT3NsRqlSqaGSHiIiIKCwMCoPk7HXs7IUsZGBw0PV69ODWRERERLGIj4+DFMgYhO+++y4ABDwgNiW2Tp3Oq5d6YWGh6DiYNHaE9sXK8vKQtuM+JKJ4w6AwSGVlZdi2bRsA4OfPP4+nn3rKax3nNHj5c+dGNW8UnzZv2YLWlhaPZRqNJqBghCJLaF8Esh+4D4loPODj4yDl5+Uh9+qQM5rGRugNBo/0VasrXe0N19fWRj1/FH8ONDfj0sWLyMrORnFJCS5dvMhgQiLu+0Kj0eDSxYshb8d9SETxhjWFIdA0NmLRokUwGAz4xje+gfvv/w6UynR06nSuWsLikhLOVEBERERxg0FhCPLz8rBv3z5UVFTAZDKhqclzPKHikhIcaG6WKHdEREREwWNQeNXK8vKgHvcUFxXhs08/RU1tLXp6ewEAynQlKitXs4YwVF2dwJBROO3DDxy/298USMwesywFY49WC83Onejv68PGujq8fugQbw6IiChuMCgMU/2WLVJnYdyY9M+ZsNqnCqYpFOcAABO+nSuYLrWa2lpXByQAGDAY0NrSgptuvhl/++gjCXNGREQUGHY0IYqAHTt2CC43GAxYtboyyrkhIiIKHmsKJXJpeBirKoWDhek33hjW9Djx7pkXlbh9oeeh2XEwDS/UAPs+jr0ZYvZotbBaraLpXae7RNOIiCgx/ezZZ0XnRpZiijuAQaFkLlsseHn/fsG0jAxVQgeF443ZbJY6C0REFGN2796LwcEBqbPhgUGhRNKVSnwicodA8SU313c7x1mzZkUpJ0REFC8+cnagFJCamipJbSHbFBKFyX1AcyGPVVREMTdEREShYVBIFAGvHjjgFRgqFArUbdqE4qIiiXJFREQUOD4+JoqATLUa73Z0oFOnwwOlpSgsLMQujUbqbBEREQWMNYVEEZSfl4e0tDQU3HWX1FkhIiIKCoNCIiIiImJQSEREREQMComI4s4erRaTU1M9fvZotVJni4LAfZi4hPZ9aVmZ1NkCwKCQ4kTPibcBAO8dbZM4J0TSKywshEajQV5+PvLy86HRaFBYWCh1tigI3IeJy33fq9RqaDQarK+tlTpbABgUUozrOKjFk/90A46+4riDfn5VKdYvmYO+0zqJc0YknUy1GivLy5GZmYnMzEzHa7Va6mxRELgPE5f7vk9LS8PK8nLk+xjrNpoYFFLM6jutg3ZDNcwmk8dy/fkeNKwulShXRERE4xODQopZr2u2wGq1CqYZBwzoOMj2N0RERJHCwaslMmQ04vopUwTTMjJUPudETBRGfb/P9J4Tb6NgeXmUckMEoP1NoHSJaLJdpgLW/whY+2gUM0VE8ejo0aMYtlgEYwEp5j0GGBRKZlJKCkoffFAwbfqNN0Y5N7FJmTkVvT7aDqqyZkYxN0RERJEzffp0fPrppygpKfFKa5KoJzqDQolMTk7mNGh+qKZl+Uy/bd63opQTolHuWQy88obX4qQ5c4C1a4Fy1mATkW833XQTLl++LBgLvKTVSlJbyDaFFLO+W7MFs+ctFEy757vlmDY7NnprERERjQcMCimmrX3xMIof/yG+Nm0aAGD2vIV4vF6DR59lLSsREVEk8fExxbzv1mxB5swcvFBTibUvHpY6O0REROMSawqJiIiIiEEhERERETEoJCIiIiIwKCQiIiIiMCgkIqJxZI9WiyVLlwIAttTXo6a2VuIcEcUP9j4mIqKYU1Nbi57eXtff2VlZqN+yxe8227Ztc/3dd/48tm3bhpbWVrx/6pTPbfdotXj90CGPZQeam0PI+fhTWlbm8Xcg+4LiE2sKiYgoZrW1tga0nt5gwI4dOwTTent6Aq4xPNbeDr1eH3D+EoVer0drS4vU2aAxxppCiVwaHsaqykrBtOk33oifPPNMlHNERBQ7nDVRk1NTA6qxO3LkCKxWq2i6e62jkJXl5VhZXo7b5szB6lWrsJJTFbocaG7GHq0WlZWVrD2NoL/97W8wGo2CsYAUU9wBDAolc9liwcv79wumZWSoGBQSEQXh7NmzPtO7u7ujlBOiwHz88ccY9hELSIFBoUTSlUp8cuGC1NkgIhoX7r77bo/2hKPNmjUrirkh8u+ee+5Bd3e3YHvX1NRUSWoLGRQShchmT8JjMw96LTddtGDfplN4a5N3GgBMnyHDT9+4f6yzR5RQiouKoFarYTAYvNLkcjnWsxcykV8MColCZAfw6/MLvJYr0+V4x3gzTCbvNACQ99nx0zHOG1EiOnDgAH7w6KPo7elxLVMoFFi7bh3y8/IkzBlRfGBQSBSk1HTg1vly0fS/905AhlqGqSme61iG7Dh/xjbW2SNKWPl5eXj/1Cm0trWhtLQUj5SXY5dGI3W2iOIGg0KiIGXlyrBhX7po+volE1H4aDIKlnuu8167Dc/+wDjW2SNKeMVFRQCAgrvukjgnRPGF4xQSEREREYNCIiIiImJQSERERERgm0KimKA3GGA2mzm9Vgzo1OlgNpvRdfp0UNs592HH22+PzWwY7W96LxsaEk9zWrg48nkhonGJQSGRxErLylxzig4YDLh+yhSsWbOGE85Hmd5gwAOlpejS6QAAmsZG/ObFF7F23To8/dRTPrd7tKICx9rbAQBNWi1e3r8f6zds8Lld0EqXeC9LVounOX0+Erk8ENG4xqCQSELuAaGT1WrFtm3bkJOTw/lXo2jJvfd6jG8HACaTCZs3bcLsW2919WgdzT0gdLJardi4YQNUGRnh78N7fNT0dfc7fs+a7Z126q/AF1+E99lElFAYFBJFSMdBLXR/OATT4ACO/mYXdH84hKpG35PHjw4I3T23dSuDwijp1Om8AkInq9WKX+3eLRoUjg4I3Wl27gx/H77yhnhaWZnjd7PAcfbdJcBRH4+ViYhGYVAokSGjEddPmSKYlpGhwkcffhDlHFGkTJ11K5LTFH7Xa21r85k+ODAQqSyRH11dXT7Tu7u7BZfv0Wp9bne+tzfkPBHR+Hb06FEMWyyCsYAU8x4DDAolMyklBaUPPiiYNv3GG6OcG4qEguXlKFgeeK1Qnp9pt1JSUnymt7a1YV1NDS5brQCASXI5nquvF63RktJtc+bAZrNheHgYaWlpmDVrFg4I1W6NUlpWhu7ubpjN5qC2i7TMzEzB5bm5uT63y1CpxiI7IXM/ZkZsNiSnpKCkuDig9qvOfWizWoPajmJHtPdhrHx//amprUVLayuGLRZMkMmidi6dPn06Pv30U5SUlHilNfm54RwrDAolMjk5mdMvJbhMtRoKhQImk0kwPfuWW3xur1arMWvWLOg6HR0jZuXOglqtjng+I2HWrFnQ6/XQdXZibkkJsrOyAtrOuV5rS0tQ2wWrsLAQcrkc1qsB9mgzps0QXJ6fl+dzu0DTaTEAACAASURBVFmzZkUqixHhfsyYzWbk5ecjJycnoG2d+7C3pyeo7Sh2RHsfRuv7G66cnBz09PbiWHs70tIUUTuX3nTTTbh8+bJgLPCSVitJbSGDQiIJ1dfXo7Ky0mu5QqHA3t27fW6bn5eHA83NKL3ariwW78CdDjQ3Y49Wi8rKyqDy6azFmJyaOqb/X6ZajTVr1mDbtm1eaWq1Grt2it/ANTQ0CO5DtVqN7Q0NEc1nuNyPme7u7qDK1LkPn9u6NaaPNRIX7X0Yre9vuFaWl2NleTlumzMnZmszo4WDVxNJaGV5OTo6OrBg4ULI5XKkKRQoLinByZMnkRmjtX7jVf2WLdBoNMi9WvunUqvxyCPl+NtHH/ncbmV5OQ4cOODahyq1GsUlJejo6OA+JKK4wprCEHTqdNgcQDuM+5YtY+9R8is/Lw9vHD7Mu9QY4F5jsG7t2oC/v8VFRSguKgp6OyKiWMKgMARdXV0+hxJxx4sDERERxQMGhSHo6HgbACCXyzF12jTR9WK1US0RERHRaAwKQ2AcMgIA7pg3D28cPixxboiIiIjCx44mIXAOZKtQ+B+gmIiIiCgeMCgMw5133il1FhJCY1UZjv5ml+v1K/W1EueISFp6gwGrVleivb0d7e3tKC0rg95gkDpbFITR+3DV6kruwwThvu/7+/pi6vvLoDAEzjlSVRkZABy9kfdotejU6aTM1rilP9cNi8kEpUoN/bluDPRx6jBKXHqDATk5OWhq0sJsMsFsMqG1pQU5OTl+p06k2NCp03ntw6YmLXJycngdGef0BgMKCgpc+95qtcbU95dtCoPkHs2fPXsWX73hBo8ZKRQKBRYsXMhhRSJo8xunpM4CUcx4oLRUcAYVq9WKuk2bYnKaQ/JUWVUlug8rq6rwbkeHBLmiaHi0ogIGgVpBq9WKdTU1kn9/GRQG6ciRI67XztkP1Go1LBYLTCYTTFfv2pcsXeqzE8ql4WGsEpgFIRCL7r4b33v44ZC2JaL4dr5XvKa8i7VMcaH7zBnRNO7D8eNnzz6Ljy9c8FjW2dkpun5vT48rLpBiijuAQWHQzp4963qdm5cHTWMj8vPyADhqER+tqMCx9nYcu9rOR6zG8LLFgpf37w8pD93d3QwKiRKU2FzZFD/E5sqm8WX37r0YHBzwWOZv34caF0QKg8Ig5eTkoLikBMp0pdd8qJlqNd44fBh3FhSgS6fDm261iqOlK5X4ZNQdBBGRP1nZ2a52zaPJ5fIo54ZCoVarBR8hAhzVYjz56MMPvJbdNmeOz+/vP774AgCQmpoqSW0hO5oEaWV5OQ40N3sFhO42btgAwHFHsEerjVbWiCgBzJ83XzRtcWFhFHNCoVq8WHw/LVi4MIo5oWgrKS4WTYuF7y+DwjHg3lDUOfsJEVEk7NqpQXFJiddydnCLH2L7sLikhPtwnKvfsiWmv798fBwj9mi1eP3QIY9lsXCARFJpWZnH3/ctW8a5oSXQqdNh85YtHsu4L+LLgeZmdOp0qHrySQBA4/btrrbNFF1C5+71tbV+9wf3YYJof9Nr0YGqVehcugRV2zXQ//3vePX/+Qnys2Z4rJuWnAzz8HAUM+rAoDBIzsDG15fefdiagoK7Anrfs2fPoru7G/19fUhXKpGWlhZ+ZmNMd3c3zGYzhoxGTJ02jXNDS8RgMKC7uxsDAwOwDg9zX8Sp/Lw8ZGZmul6TNNzP3fLkZKhUKtH2gqNxH45/E76dK5KSC2XGIcA2jH9adb9XqjJjISZPjH5PdAaFQeo8cQIGgwEmk0l0yJmGhgYAjkajhQG2EajfsgX1W7bgtjlzsG7t2nFZa/P+qVPYo9Xiua1b8f4pjj0oleKiIhQXFaG0rAzd3d3cF0RhcD93z5o1a9w94SHpTJZFP0RjUBik/Llz0drSgmPt7aiprUX9qMdwrW1t2LFjBwBHo9FMtVqKbBIRJaSa2lr0XB3LceeuXXj90CEGaiS5fR+rvJY1VsmhPydD4ynhtO7j5mhkzQODwiBtb2hw1RZu27YNR9vbMXXqVABAf3+/a+BRtVqN7VdrDImIKDp6envR3d0NlVoNo9HIcR2JgsCgMEiZajU6Ojpcg1R36XReI9Dn5uXh1QMHWEtIFKv6egHtTvF0swn4/etA3/uey78YGtt8kQfnPMCdOl3Abe7CqRXUGwwwm83oOn065PcYr/r7+wE4yojXtvGLQWEInINUd+p00Gh2wjhkBAAo05WorFzNBsNEse58L9Dwc9Fku0wFtP8ROPKfUcwUObW2tWFdTY1rkN+CggJkZWfjufr6MZkb1n02KgDQNDbiNy++iLXr1uHpp56K+OfFk9a2NlRUVLhqXG+++WZWfIxjDArDkJ+X53MQayKKcfcsBubkey1O2v0yMG8ukCPSK3vGzWOcscSlNxhQVVXl1YO3t6cHFRUVOHnyZMSDEfeA0MlkMmHjhg2YfeutYxKIxgO9wYAVK1Z4Tc3WpdNhyb33spPaOMSgkIgS15x84Cf13stfaQPuvQ8Yh6MAxLqml14SHdLFZDKhoaHBq4NfOPQGg1dA6O4XDQ0JGxQ+WV0tOldvb08P9mi143KkjETGoFAiQ0Yjrp8yxWu5zWbD+vXr+UUjooT07rvv+kx39iyOlCM+5qgHAL1eH9HPiyfOdoRiOjre5rUqDOdP62AaHMD6JXO80kyDA7BLMPsxg0KJTEpJQemDD3otb2lpwfwFCyTIERGR9JTpyqh+nkrlPRwIOUydOtWrI6W7mV+fGcXcSOuxfz4a4pa3iqZkZE6F3WZDceVar7Sjv9kFfe+5ED8zdAwKJTI5ORm7NN7tEW87fhzLli6VIEdERNJ74IF/QVOTVjT9sYqKiH5ecVER5HK56GPS+fPmR/Tz4om/mY4Wf+tbUcqJ9H6tEw/uQpWmzIBpcBAFy71rW3V/OARDb0/EP9MfBoVEROPZz2q8l/X1OobdEUpzKl8NTIv+9IfFRUUoLilBa0uLV1puXt6YtO9bv2EDNm7Y4LVcrVajrm5jxD8vXtRv2YKW1lZXL3B3xSUlCTnSxq3z5VJnYUwxKCQiGs+Eht5JVsNus/sclgcLl0gSFAKOsQZramtdAUlWdjZKiosj2sHE3dNPPQVVRgY0O3ei+8wZpCuVmDt3LrY3NCT8sCvvnzqF0rIynDhxAgMGA7Kys8ftVKyB2LAvXeosjCkGhUQS26PV4vVDhzA4MACdZRilZWVYX1ubkHfhUnPfF8FMkSa0neT78F++KzjcDgDg0B+RNDAIVDztnfbbV4CP/za2eQuAc07hyampURn6ZGV5OVaWl4/r+edDdaC5GXu0WlRWVnIYmnGOQSFRjFiwcKHUWaCrQt0XMbUPH3lCPO29MsBiFR6O51RnTASFRBR9DAqJJOasoSDphbovuA+JaDxgUEhEFMMmJQ+KpqVNsfpd55EfJHstO/OhHRYL8Ngqs/cGukpg+D5U1/wKuVNH1SQOmoEhI/DdJeIZ3lAP5Io8tiaimMagMM516nTo6uryWFZYWOi3cbTeYPAatDXU7XJzc9n+LUHs0XoOFRKr+761rQ0DAwMey6SuyRMMwAJg/VJ4ANukANYBgF/vsXhtl55hA2w2rzQHxzip7bp5WHj6HY+U/pRTME0cxGNt94l+XvUyK3Jzr/09+phRqVQJO0NIJPAcLE7oejiW33vTgAHvHfPcF7cvKIRCFb+dkxgUxrnm5ma0tLZiYGAAcpkM6UolVCoVMv2cdHU6HZ7buhVDRiMAhLSd1WaDSqVCSXExT0gS0BsM2LixDu3t7ZDJZFi1uhJ1dRvHtLfkc1u3YthigclsDmrf19TWou3qhay0rAyPVVQEFBjs0Wrxm337XNvdt2yZ50m+6ZfA717x2u5X3f3oNpnRbzIjM1mOJLkcK19/8doKJpPfz4404QAscM+86D2oc9tOx/AYa1Z7px1/fRgD/Tav5ZeHtuILw3HYbDZMy6pEmvJHgHy2K/3j0zZcNNnRY5uBHtsM13Kl8t8A/BXWi5/jt2l/gsX8JIaHZ3u9P/b04VdZb7r+fG7LFgwPD2NwaAhT1WrMmjYNxSkCl54ZWZL1do4n4ZyDnd/D/r6+qHRo8/v9jTD366EiLQ3JKSkBfZ7eYMCT1dXo7+uD0WjEqtWV2LXTexzh0T4+o0OrZissJsd1NEWhhEKpwu2q+L3pmTAyMjIidSYSzeTUVCiVSnxy4YJXWqg9326bMwezZs0KqKeku9KyMgAIabvu7m7Bnmh33tSF/sEUwe0mJB/ElYl7ILv4mleaflgBwHHxu33h+Ltfea/dhmd/YIQ8yY7LG34R2ptc7RjQqdNh0aJFXgPuyuVynD17NqDA0Nc+9GWPVovntm4NeLslS5cKzi37wx/+0OcQI6VlZYJj1T3ySPm1E/bPanwOqzLZkgKNMhkrh40ey7vseWiwVgCzcoG8uQH9HwBw8pQN73d5B1qBsH5pR6oiCdNnh3ZsCw2F0Vjl+P5WNfr//poGDKh7oADGAc95heVyOf534z7cfo/jQvabzRb0nvY8rj7vuR8XTSdht1+rkUxKSsINWf+KSemO2Rg+Pm3DFZMNKbJhpNg9a0UnKFrxd0sdlDbxKeyKcgfxq7/c47V8cmoqLl286Pf/i5TxcA4Wy5/QeIMajSag/9XZ+zjQfSH2/S0uKQn6fw2W2D586efnsG5TkseyJMVRDJn/b9hsVzyWp6aqMOnKPsCWAeDa9Wnfx94z4ATzPRy9nf5cNza/4b0PG6vK0H28HZ9/9mlQ7xmu8XflJcnp9CpY7UmCaQp5GmSYgIGrX7BEZLUnYUKd97RGgRj5ieN3ZVWV4AwMVqsVD5SW4t2OjnCyGDE1tbWCASEA7NixA9XV1YIBbGtbm+AFBQCamrSorFztWcNR/oRjCJbRlv4LsHINsGSRx+KG56bh123pgA6ALrAaPPcjOtQZSafPlkk2ztmLddVeASHgOGZ+ubYC2//quPh8f30KgGs3da/U1+J8519hH/VP2+12fN73S+w8vAkAsGnFEM4ct8NqS8EQPG8KFfY0AIDeLj6lXFtPWij/FgVg1epKwYAQAKqrqyNee+fr+9va0oLWtjZJmhD84a1rwZ2T4rqfegWEAHDx4gBGFPUwDu6MVvZiAoNCiVwaHsaqykqv5UajEYcOH5a8/VMk3PNQCtLSPYNDY58cH+kmoOQJ8QvAV2cIB5R0ja/5SLvPnIliTnzr6e0VTbNarThy5Ijgsf6r3bt9vm9zc7NnUDglHVi4WHjlmV/3TnvRDMACdaYMyhCON9VUGebf592Bw59UCce91Z/rFk0zm0zoO63DtNnejxL7Tuu8AkInq9WMjoNaFCwvx7xlyciaLTzbg7FPjs4/QvB733vaijPHrbAMi88vK7T89PkU9JuEn0j4M2jPEE1LS7eh+kdmrH7MO4AGgIxkMz757+yQPlcqXae7RNOsVmvEg7RXX/2d33Qp25WqM2WYW5IMm9WAoy/9Q3S962Qf+rxWhctsHMSwxfEdGm3IoIc95NvP0DEolMhliwUv79/vtdxms+H4sWMS5Cjy5t+X7PUYuOOgHIbeiVdrIxLL7Qtlgo8eArFi+oD/la4Sm8NVCt3d4oEIAJw9e9bxov1NoP2Nawl94sEkAPQcfRP4md0xpl4Y5pYkJ8yxaDL6PoYunOsSDAqNBn1A77/kEfEgueOgIygUKuvfbAbOHLdiyJYiOL9ssnxs5p31xwrhm4VBa/zVaJrNvjs5je6UFS7jkDGs9LGmnJGE769PQcfBYzj6kvh6l8yfjOn5YVDfD/OQEa2arV5ppsHI7pNAMSiUSLqfNoVEvigUCphEOkuoY2harlmzZok+tgKAu+++2/Gi/Q2PtoHKZN//w53680DDz/HYcAParL8AtqbBvsv7QpOUBGyotaJ2g2faf5ujfwcuNdW0LJhPi9cwFywXfjqRecss6M+L70OFMrQbHVe+pif5nE+294Tv+WazZsuR+83IzUfbtEGGucXJmHWXZ+ed3lNW7P9/Q+tBPuk64VpHJAFpSqvvdQBcvhLedzozM9Pn9zDXvbt4BGRn+e4wdOedd4b1/l1H+tGwXvz/MX1uwb6tH+Kt7Uc9lv/hQ89yLFhejhdqvJ/YOWVkTgsrn/7MmJ3nt01htDEoJIpDCxYuFG2zs3hxYZRzI+6xigrRfKrVau9HSPcsBubko+7iMF7eoRWs9VQkJ+OR730PSE1G29b7oR9OAcwAzN4dQJLlgGnYimGz1aOda7w3UOg4qPW4mFXMTMXj9RrRwA4A5i4rRa9IUJglUEPotPC7FThxRHgfZs7IdnVQCdWSR5J91jJWzIzufLMyOZA5Uyba2c1mT8JjMw96LTddtODUFybBNOvVYX7cKRT/CevwOliu3tslyW+GPPk5mEwPeq0r9Pj81GcmXLnOIvrIHQCqN2cjt3Aqvr9ihWjb3qzs7LB7ID92zwm0/dVtH8n+BTKZRrCtnkx2HRo2zUfDxmtBXdE/DeFXRwPv8NWw3eKz9liZLsc7/TfAZLq2TtKo306z5y3E6XeEy2ZB2aMB5ykYQt/fuYUlQXdUGQsMConi0IHmZsFevcUlJQENpRAtxUVFqNu0CZs3bfII8LKys/Hi3r2uv+/81fehG/oR8BqA1x2npeTUr0M+6WewXr7W5kc+6XpY7M/jpl842gg6x+e7db5csD3bm3uA2fPlUE4T7tgUyRqmaCpYXu4zABSy9PGnMND7IY7/br/nvpidh+qdB0S3u/2eIhQ//kO8qd3hsV3mjGys/sVe0e3GKzuAX5/3DvJU/9d1sFxJRtNn82GzJwm2BvMcVuiJqz/inv2Bo4Z7dAAkn5iEtCnJwCU5ft0nHhztWQbIYACSCpGWXgHrcJNHoJaSMgM955q8ainXr7Hgp9sDHx6o7VSG4+bMRYG0tB2QT3rK6/trH3keenPWqO1DC0XEevP/vXcCMtQyTE0R/n67nytWbd2NhtWeN0xyuRy59xRi6eNPhZQvf0L5/kYLg0KiOPXG4cPo1Onw+BOOC8sLv/xlTI4X+fRTT+GR730PG+vq0KTVCg6B0T+kcLThsgPOvr1W04OQy76J5JS3YB1eN6oWxfOSmzVbLtj25809QP69chQsT4x2g/48+qwGi763Gi9ufBKD+gv4n1t2BFTT992aLbi3ohqv/kcddH9owYM1m2P2ojZWvjojyWeng7+8lgTV/5Bh/nLxkRWCHWrL12NzsyEJly0TBNdxjjVpB1zfK6Pxp5DLViNNsRO2KwdhH3kexqFvuWrO3L9Rm3ekYPMOz0AxWeF4dC70mNt6tbe5583Z/QDuh7HvJXT+sRr532qActr3PLZzdjIatCTja18Rfxw8msXm+Ayx3vzrl0xE4aPJKFjuv4ZZoVJjw6sdeO9oG35duwYZmTfiB3XbBdvXJgIGhURxLD8vDzfffDPsdntMBoROmWo1Cu66C01arc+e9SVPpI0K7lQAbkfFzHXY+d7/GvN8JoJps/OQrs6ExWQK6tGvQqVG9ty7cO4vxxMuIAQA1bQkn50OzhydiIzpvtcJlq/H5o1VMujPTRRcp7fLhotDQlsp0f12Pk60voVHNnk/pn5piwnnz9gEO9k4H/CLdcABxG7OHkfFzGo8ufNxr/WdnYys9iSvoWKi7fZ7ipCSdj3S1ZkJGxACDAqJ4p5dbLwQKfysRrxH8ODVRvpC8+ZafgGAtXlEkZCVK35pNw3KIJML11quSleIBJNA99vJaH1BeGYdp2CHE3M03wi9N7dqery3Do49DAqJKGL+rflmfHz+a4Jp/SmnAHQJzptrSUoLfURoIooIf8EkEPwjcF9uXyjeoYekwb1BRBGz+dz9PmazkQHYj18PPxzdTBERUUAYFMYYs9mM/v5+qbMxZoyf9GPYEtpYXwTHIM+jDQ2JpzkJzPYxODgoPqht0y+B8x8Jp53tBcwmx6NiLz8CAMy4VYaUUbPZ2Cwy9J3x3Xiej4MoXg1bzDAbB6XOBlFYGBTGAL3BgCerq13juW3evBnbt2/H2nXr8PRTY9MlPto6Dmqxf3MNzFcHXK6YmYrZ8xZi1dbdUKhiZ7DlWDfp27O9lqVlpIimOV12Gy7s588/7zFEzPVTpmBxYaHHJPV3/igP/ab5gu81QdGKKxPfx9c2/cArzVlL+L1ahcBsNsl4oSa6Y84RjbXGqjLXOI7GAQNW3zYF3/nRhjEbzoRoLDEojAHuAaGTyWTCxg0bMPvWWyWdIzIS3jvaBu2Gaq+BiE+/045dayuw9sXDEuUs/vjq+ecrzVmLuOeNP2Hj8//huZ3VitaWFpTeey8OrF8HANCZZos/BranQYYJGLCHN5MFUbxzDwidrFYrXq7fAIUyIyF7aVN8Y1AYA8RmfACAXzQ0xH1Q2P7KbtH5eE+/0w7TgIG1hX746vHXttPxOHbNau91nIPffm2Jo3xtU14VfZ8j77zrWs8ZEN7zUArSRj0GNvbJ8ZFugs8x24LthUg02volc1zT61XMTEXmjGzB6cAixT3Ae6GmEi/UVGL3hxd9btN19IhoWqtm67gJCitmpnq8Hut9QdJhUCiRIaMR10+Z4nc9vT6wyehjmf5ct8/0944dGTcnz7Hiq4dee7P/dfRXa/XSLokfTzbbFRjlAxgevvYYev59yQKPgeUw9E4c04niiR5eXw+TccD1d7hzLPtzX2Ut8r69LOD1+07rRG92AWBQ3xeJbMWEx+s9Z0ka632RKBqrykSvj6bBAdglGJKBQaFEkpJkyMhQwXblMgY+/1zq7NA4Nbo2753/nAyz2Xs+Uqd7Hp4BmfzaNqzxI6mEO6dysKbNzgtq0OJ0P0835Mni8znHG960jw3VNPGpBK3WYVhMIoNGjiEGhRJRpCvw0YcfAHA09Be745w/T7ixfzy55Z/nux4DjSaXy3nCGUOja/N6T2TB7DbHp7s0hQKP1gU+3ylRIlOo1EhTKFyd50bzdcEnAhzTR4pprCpD9/F20fSxwmqAGLBmzRrB5QqFAnV1G6Ocm8h74F83QilyV724XPh/p7Hx6KZGyOXCQ8I8vL4+yrkhim9i3xm5XI7qnQeinBui8DEojAH1W7ZAo9EgNy8PsiQZVGo1iktKcPLkSWSq478DhkKlxsZXOzC3sARKlRqyJBkyZ2Tj8XqNzzslirxps/OwvvlPmD1vIZKTUyCTXYes2Xl4atcB1tgSBalgeTme2nUAWbMd5+7k5BTMnrcQz/3pLDvPUVzi4+MYsbK8HCvLy3HbnDlYt3YtVpaPrwu0QqVGVWMzOg5q0arZyp5rEpo2Ow9rXzzsauS84dUOqbNEFLduv6cIt99ThPVL5iDzllmoamz2vxFRjGJNIRERERExKCQiIiIiPj4mH7425bxo2nCyFbKRK4LrWO0cvy4aTAMGvHfsCIYMjrEHOw5qcfuCwphsy9RxUIueE2+7XiuUqoCGHHnvaJtrrLpgtiNh7sfMsMWMjoNa3HhLbkBDsTj3YbDbUeyI9j6Ml+9v32kdLpzrwrDFjCGDPqbPpWONQSGJ0pvFgztlsv91aGy9d+wIXqipdP3d01WJx+s1MdlhxD2fL9RUInNGdkAXh/2ba1zDGQWzHQkbfcy8UFOJuYUlAbWDC3U7ih3R3ofx8v19XbPFY/7qWD6XjjUGhXFObzBg48Y6fKrXw2w2Y9XqSuzaqQl4u+PHjwMAVq2uRF3dRsHezqMHQO4/vREXzuowfMWEWbdXYcY/1UMm996OAx+PrYLl5VE/ab1SX4szb72BQX0fGqvKcF9lbUA1Df6mCxMTaoek9462of2V3QCAo7/ZBYAD8ALhHTOh7sOOg1rXPmisKsPC71bEZGAQT16pr0Wv7gQsJhMaq8rwg40NAdVqhboPQxXtDoV9p3V4XbMFg/o+vPnrbdB/eDagES5CDYxNAwa8+h91OPcXR2e9vc9U4oF/3RjXNYwMCuNYa1sbVqxY4Rr4+pLFgqYmLd588wg6OjpEh7PRGwz4xje+AZPboKtNTVq89tpvBYfBcQ6AbBowoO6BAhgHDK608x+0Qv+3N/G/G/fxRD/OrS242WPfnzjSgq6jR1C+qSGmAq5X6mvR+sI21989XZ3o6aqE7g+HWLMVZe7zCQOOY+bEkRYUP/5DDkcVAqFzsPN7mOjn4I6DWmg3VLuuh+c/OIvzH5xF9zvtYzLCQt9pHTaXLfKYeOLoK1qc+P1vsfnwybgNDFmVE8fW1dQIzoRiMBjwZHW16HaPVlR4BIROJpMJD5SWCm6z95lKvFhX7XEycrJardizviqInFOgOg5qpc4CAMf+F9v3+zfXSJAjYX2ndR4BobsTR1oCLs/3jrbBJPD/UuA6Dmo9AkJ3rS9sQ5/AzDrvHW0TXE4OY3UO7juti/tydw8I3fWe1uGV+tqIf97eDVWCn2c2mbBrbUVA7/Hua/vx+vZnI521sLCmUCKXhoexqrLSa7nRaMShw4cDGqewt0d46jgA6DxxQjTtv955RzSt+8wZweVHX9Eic0a26HbGAQNMA4a4vTuKVS/UVMZELdy5vxwXTTObTOg7rYuJTgfvv/NHn+m6PxwKqDz3b65BceXamCj7eKX7wyGf6e+/80evY2b/5hqO9eeD/ly3aFo45+DXNY5a23gt9/eOtolOFQsA3e9Efrq4Xh9B9PkzgQXY+7f8GOahISi/NtUrbcighx32kPMXKgaFErlksaBJK1xrcaStze/2rX7WMRjEazl8fXl8pQ3q+3x+5nvHjvAimqAunOuKiaCw9+S7PtOHReappcjzV9b+9hV583cO/viMDrerEu8RsrOHs5hhszlKOXEQmw97NIvpH7DZrnh0AHI3OSX6HTn5+FgiSqUSly5e9PrJys5GQ0OD3+2Li3x/8bOyxWv11D6mzlMoFKJpGZnTfH4mA8LxS6nO9Jl++4LCKOXEt7xvL/OZnnHjRAl1jQAAIABJREFUjOhkhJDs41wC+N9X5M3fOThR2xTeeEuuz/TMW2ZF/DPTfBzfygBraxUZKsjlcuz+8KLXz9zCEkxMin69HYPCOFZcUiKaNn/e/Gt/tL/p8ZPvI2BckJt7bd3RaWWPim6XFQO1RDR2br17iWha5ozsmGk2cPuCQtGTtVwux6LvrY5yjhLXfZW1kMvlgmlpCkXM3EjEE1/n4NnzFkYxJ7Fl2uw8n82bxuIGZJaP8s7Kmxvxz4sWPj6OEZ06Hbq6umA2m9HxtmOQX3/tCrc3NKC/vx9dOs/2C8UlJR7D0kz49ui7qBehzFgNi+mIx9KvpP8TDv7xRUwQaZa19PGn0HvyXa/G45kzslG984DPvAIc/DZWhDKA8dLHn8JA74c4/rv9Hk0MMmdko+Y3v49GtgU11i3F+a5Oj2WyDDtkw0mwWa+1x0lKSkLqDZOwfeO9AADbFSusl3w0o9AnoWlrFV7SCD/WiSdJstDu/ZWZmVBNywp6u3u/uw7Zt34L02bn4Ts/2oDf/mKTxzGTplDgia27Y+ZGIlzRHPjY1zl41dbdEf+8eLL6F3ux80ePusZFBBw3govL14zJU6yqxmZs/cFSnB7VXjHex++cMDIyMiJ1JhLN5NRUKJVKfHLhgmtZTW0tWlpbMWQ0YnJaGibJ5Xj/VGBjPLW2tWHVqlX46g034IVf/hL5eZ4X9wnXCbe3SEv7I+TyfwcAWK0/htn8LcH19n2sQsXMVNcYV32nddj948cx9Pln+J/1uwJ+ZLF+yRxYrcOwDVuQolAib3Exh6Xww73cI+W9o23Yv7kGwxYz7DZrUPui77QOh3dtRfc7R4Pa9/6sK/0qLKbItvuxW5IwPGCHPD0JMoU9qOciVn0SZOlAUkpkG3rLJ8uR8tXggrSh88MRzUPU2QGbKQnWITuSVUmiZZokS4LVkASZbCJSpl0X8NunpKeHFLwqVVOxonJX0NuN9kp9LXRvtsJiMiJJJkdyShoeXl8/po9yQz0Hi2msKgMQvx1N3HUc1OLlf38G+Yvvw6LvrR7zigfn+VQ+6TpU/PsLQX3euru/DtPgAHa+/4VXWmNVGbqPt+Pzzz6NZHb9Yk1hmPZotXj9kKOXXXZWFqqrq0XHB/SlfssW1G8JLUAqLipCulKJm266ySsgdLfvY9WoJQ+jsepVAEBV48MBf9602XnImH4zrJevBHUyivZApiTs9nuK/O63fZpVMA70C6YNDQ3CNnIF7X9uQPufPdu/dh9vhz36HeaQPiMZaVO9G2WfazJCmTMZipsnCW6XcVs6VHlKr+Xtq3twy4OZUC+J3xl7hs6ZYLXYgt7O8JdBDBvFa1HFWD6zC9e+JgFJV58i+wqy7TY77FbANgGwmC4H/rkmMwb7hI9Vf44dfCnobZKSgOQ0zwH9oQBkCgCwwgoztNsfBbZ7b/vcgc9CyudooZ6DE0HB8nK0arYie+5dUXkSdfs9Ra6B8sfDky8GhSFqbWtDVVWVVy/fHTt24KGHHg5oVpFg/NuTvdj8S/ELVHKKAQbDBEyaJNTrOLabjjrHkBqrWsP1S+aMWUA61nkPV2PdUtE0fedHsF20Y9o3Z3ql+Qru7JYk2C4CZ475HubBapBBprAHVds2dYESt37ff63Pud0DGNbbkbve9w1Yz0tDmHHX9JgK7ownhtH/+yG/eQ9V12YDpt6bDuVc3x09xAgFyU6h5t3whgXvPH8GhRrvtlYDOiMG3x8CAPS3XMSk6+X4Hwv81xTaLLagglerUQZz7xWk3y6D6dPQa9/tdgjWatv+LgMm2iFLFz/eq5akhvihgHVAhuSp197b+lkS7FeAJ5d+RXSz5AB7r1r6rgBw1NgDgCrra0hJ+2rQ2Zz1jUX49v1Pey2P53PwWOY9FjEoDEGnTueaSUQul+OOefOgUChwrL0dJpMJTU2OoWYiGRh+fN4Gq108uJPbL2PCyD98rhOrBvp6x/T93duYRNpY5z1cYoFbUhJgN06C1XIF5mPijycUN6QiadKXHsusRhnMlitInzFBdLtbHpiGo9XnMPd/3TomAdmw3o6hvgAeN0tRbemH9YsA8x6ioT4zVF+EFhD6MxZ5V+UpXYHoYHsP0m9Mw63fj3zA7AxM5/309pC2txiGcf4PetF0R0A7WTCg7T9mDOkznezDSbAN22D3qPhNAux22G3ix3igTTJsX8quru+ooT2v+wDAB0Hn88yxdhzcXuedj/O+A+IkWVLAAazXe18NaP/rv37tWmYaHMaB//9p/PY36wS3SUlPR92vAvv/xvL6EYsYFIagprbWFRDu27fPY3iYJUuX4lh7O15+eb/oXMKpqSpMGK7E174S+MFmsTmev8y4VYbv1Xqf8P+/yomYlJqEZ7aJ3+VT/Aq5huGq9BnJXsvMJhnscvgJ7r6G9Fs8jzfDGxac+0897qgR7+1HNN6kqJN91mL7CmgDqf0WMqBzBJNDJ20483If8lZfe5+/7f8HLn5yGbNXj24WBPz3BQsumwKvRf38LUdg9ZVZI7ANB9/kYHjIhuGh4LdzstvsIbcpHh3QAoDdmoRLly4iaYJwwGwxmYM6p7qvK9Rxy/qZY1mwtbZDxmHYbXZXDa1HHvuuYMQ+MeA8RgqDwiB16nQ41u6ofVmzZo3XeIF7d+9GTk4OrFYrNm6sE6wtlE1KxX9b0mAaDv5uPiU9CbcvFNptdiTJZCJpFAv2aVbh+Gv7g97O14kmUHfUzPZa1rXZgKE+M4M7ohjlrEG1f27x+BsADIesuJzypeDjfl9NAIR0nXc0O8qtHpsmDb9desJv04FQOQNa9xra/paLUNws82pLbLPYYOgMbwB74ZrZJB9pDoJBrz0JgHBAbPtShiQJHvwxgghSc/O13lnVAvMLZ6rVuGPePBxrb8fxd8SnBps9Xw7ltDTRdDGq6fH3eHi8+cNrP0fb3q0AvNvi+GK7YvV50hDjvo3QiTVRya3etZ9EFD/cmw6EyhnQutfQDr31CWbcNUWw6YrvYa69OQNaZ62tkL/t/wcA4KaHr/dK8xX09v32Imz2LzF1gXcF0edvXcEVCSZgYlAYpM6rYwJmZWeL9jLOz8vDsfZ20bmJJ8kvI/9eOQqWh9/WqrGqzDVm1aC+HxUzU/F4vcbvuEwdB7UeU+uEs128jsskNMZdINzHuBN6dOGP4oZUZN0fWCPu47W9Ho+MpPbbpSc8XmctmDpmHSb8scrFh2o5Xv4xBj//HADwX8+fAZ4H7j8ceECdPCw86DIFb/Qxo5yWjoU7WTsdKmfbSKfXlp7ADAm/h7Gka7MBvcccPdEHnv8UeB74ThDfe1+EgtfR++LTU3/HvKc821H7CnoNbd2wWb8UbF7Qdd4AY3fg15VIYVAYJL3e0dA4M1N82q+cnBzX606dzmuYGKt1GEd/tx269/aFnyEVMPeRheg+dBIpijRM++ZM6N7bF9B7z33Ec0R2f9s5e7KO3g4w+ezl6k/fBx8CAJ55cBqujAT/JbBdscJ2xXd7FsFHsHZ7WP0QktNlGBmZDAAB9ZZ0mqSQB3F33Bv2nXQkBXOClbJOe752OoDpIW8/nBz8kCwkLFIXZXJQL0nBd5awTIXkrlcjF9ELjsPdF7IUGRBj07Fz8Oog3TZnDnp7elBcUoIDzcK1Y506HQoKCgAAGo3Ga2aS1K98BXa7PYz2AkkYPSWi4xGj9/JIsVntkMnH+DLvLJAI9xj1l3eZ/LqQyk0muw7WYcfj4xTl5FCz55OxbwjKaelj8t4W4yXYrF9CoQ6+GUMgjH1DUGSkQZYig+zSdbBNvoLkYTmGk61h/z1stMFmtSJNneK1jpDR24/+PTrdbLAgWSF3nLQBr/XE8udvOQDAnASz2Yw0dYpX/kL9293ovEeSzWKDxTQ8ZseMyWCGTD5xTL5PNosNpkHzmH2fpM67+zEh9lrobwC4NGjFSNKXcXseA2LzHGwbGIbFbkOSwC2y3T4Cu+0K7ABkcu/vqt1mR3JKCv7+WWTGtgwUg8IgBRIUAo5ZSwDhoHDKV5WwWYVP6AFJSkJS4BVTCSNpZCLsdvGetKLb2ZNgj9ZQPhNG9SYb+VJ4vXEmKcnuUcbh/i303oLrTJgIjHzpc3ux90hKssM+cp3HPhL7rECWAxB+7wkTkTThyrXtgv3b7f90/abE4Lbf3Y8Jr+PYx7HE4yWCRn0P7bZh2BF6JUdKShpnNEkEX3wW3phVRERERJHGrqxjwNkZhYiIiCheMCgMkckk3jq0q6vL9Vql8h5YlIiIiCjWMCgMkrPXsbMXspCBwUHX69GDWxMRERHFIgaFQXIOLyM2BiEAvPvuuwAAtcg4hkRERESxhkFhkMrKylyvf/7884LrOKfBy5/LsaSIiIgoPnBImhDcWVCALp0OarUaHR0dHjObrFpdiaYmLQCgo6PDa+DqWKM3GND00kuu2k1luhKVlasDzvcerRavHzoEAMjOykJ1dbXoTC+JzFlOvoYxElofCL5cuU+uCbbcf/78867vAgDct2yZ15BS/j4LSOxyD7bMR9MbDHiyuhrZWVmo37IloM8CErvMgdDKvVOnQ3NzM3p6ewEEfryz3K8Jttxj/po7QkH768mTI4r09JHklJQRlVo98vgTa0ae/vGPRxYXFY0kp6SMJKekjCx/6CGps+nX0z/+sev/GP1zx/z5I598+qnotocOHx6ZkZXltZ0iPX3k8SfWRPG/iA/OsvInnHLlPvEWaLn7+i6o1OqRQ4cPi27LcvcUaJmLWf7QQyPJKSkjt+bmiq7DMvcWbLk7y3n0z4ysLNHjneXuLZhyj4drLoPCEB06fHhEpVYL7tx4CQjdL3rLH3poZPlDD43cMX++x8lBiHtQrEhPH1lcVDSy/KGHPMojUU8QQnbv3esqF1/CKVfuE2+Blrv7d0GRnu76Lrjf5CnS0wUvlCx3T4GWuZj6rVtd24sFhSxzb8GWu/uxfcf8+V7Hu0qt9gpQWO7egin3eLnmMigM09M//rFr5z7+xJqRv548KXWW/Prk009dB9gd8+d7pbsfvE//+Mde6c6Th9CF0j3N111PIvjryZMjjz+xxuPO0JdwypX75Jpgyt39uzAjK8urfA4dPuyRPhrL3SHYY12I+77wFRSyzK8Jpdwff2KNa93de/d6pLkf76MrN1ju1wRb7vF0zWVQmIDc727Egthbc3MFD+C/njzp8+B1P/gT7a7R6dDhw4I1yL5OHOGUK/eJQyjl7n4yFjuhutdeuZ+QWe6hlbkY5znHWWZCQSHL3CGccnfWLok90XI+Vlap1a5lLHeHUMs9nq657H2c4MQat86aNQsAYDabPZY3uzWmra6u9touU63GHfPmAQCOv3M8UtmMO1nZ2a6fQIYmCqdcuU+uCbbcnQ3ss7KzRRtrP/3UU67XAwMDrtcsd4dgy1xIaVkZent6kJWdjcWFhaLrscyvCaXc92i1rokXtjc0CK6zvaEBGo0G9fX1rmUs92vCPd5j/ZrLoDDBiU3J13niBIBrg3WPXt/XRTSQsRzHs+KiIrx/6pTrZ+PGjX63CadcuU8cQin37u5uAEBaWlrQn8dyD63MR2tta0NrSwvkcjle3LvX57osc4dQy93Za1WtVouWX6ZajZXl5R69kFnuDpE43mP9msugMAGtLC933eGUlpZCbzB4pK9aXQnD1WXfX7HCI805k8voA9ddTk6O6zXngQ5MOOXKfRK690+dwqWLF/FuR4foOjW1ta7Xubm5rtcs9/DpDQZUVFQAANZv2OB3WA6WeXicN0HZt9wCwFE+q1ZXorSsDKVlZaJj77LcwxNP11wGhQmqo6MDarUaBoMBOTk5uG3OHNw2Zw6+esMNaGrSQi6X44c//KHomFUKhUL0vd0vnO7zQJN/4ZQr90nktba1YceOHQAcd+pCQQvLPXQPlJbCZDJhwcKFHo/p/WGZh0ehUKC0rAwFBQVoatKitaUFrS0t2LhhA756ww1obWsT3U4My923eLnmMihMUJlqNR566CEAgNVqRW9PD3p7elztTaZOmybYfiEQsT5gd7wKp1y5T4JXU1uLFStWwGq1Qi6X443f/z7o92C5i6uprUWXTgeFQoG9u3dH7H1Z5v69eeSI65H9goULUVxSggULFwIATCYTVqxYIRoYimG5+xYv11xZxN6J4sqSpUtd0/EtWLgQS5YsgSojAx0db+O1136L3p4e5OTkYN++fSguKpI4t0TRs0erRV1dnetxjlqtRmNjY8LO2DAWOnU6Vw3s7t27WbZRZrVaBWfkam1rc90Iraup4bk/guLlmsugMAGtWl3pOjgPHDjgcQCuLC9HXd1GFBQUwGAwoKqqCn/76KOg3p/tScZGOOXKfeKf3mDAA6Wl6LpaVnK5HIsLC0Oerg1guYspLS2F1WpFcUlJxC+ALPPAjA4IAUdHijVr1mDbtm3o7elBa1tbwPuH5S4unq65fHycgF577bcAHHcrQl/4zKs1IwBgMBgEHyM4q7yFuLdpUKlU4WY3oYRTrtwnoduj1SInJ8cVEBaXlODs2bMBBYQs9+Ds0WphMBggl8sBwNXJwfnj7AwxODDgWrZHq/V4D5Z5eHz1ZHWfb/rPf/6zRxrLPTTxdM1lTWECch5cS5YsEV3H/cB99dXfuf7OzMxEb0+Pq0eUkIHBQcH3IXHhlCv3SXh+/vzz2LhhAwDHxfLFvXsDaqPDcg+P1WpFa0uLaLrJZPJIX1lezjIPk3PoJV89Wd05x/FkuYcnnq65DAoT2N8//zyg9ZTKdNfr/Lw8HGtv9zke0rvvvgsAIQ9km4jCKVfuk9DpDQZs3rQJgOMu/o3DhwPeluUemtzcXBSXlIimd3d3o7enBwqFwtX54b5lywCwzMM1depUdOl0PgMM9+FS7rzzTgAs90iJh2suHx8nIOeB46sdgvvjmrvvvtv1uqyszPVabEwrZ9uJ/Llzw8pnIgmnXLlPQrdxYx2sVisUCkVQASHAcg9Vfl4eDjQ3i/44Z3bIUKlcy5zDdLDMw/PY1TEhe3t6RM//DW4znSz+1rcAsNzDFVfX3LAnyqO442/y7b+ePOmaH1No/tE75s8fSU5JGZmRleU1X6z7ZOticzwmGvd5L30Jp1y5T7wFUu4zsrJGklNSRhYXFY3s3rvX78/osmW5ewr0WPfFOfeu0LlnZIRlLiSYcnfOsStUfocOH3bNo7u4qMgjjeXuLdByj6drLh8fJ6D6LVvQ0tqK3p4ebNu2DS2tra67c5PJhP965x3X2GzPuc1/6aRpbMSiRYtgMBjwjW98A/ff/x0oleno1OlcdyzFJSUctypI4ZQr90lonMPOHGtvd5WTLxqNxmNwWZZ79LHMw/NcfT1WrFjhGkTZOde0yWRylZ9cLvcaO5LlHrq4uuaGHVZSXPrk009dd+RCPzOyskYOHT4suv2hw4dddzajf5Y/9FAU/5PYF8xdfDjlyn3iKZByFzv+xX52793r9R4s92uiUVM4MsIyHy3YcvdVfrfm5orWOLHcPQVT7vFyzZ0wMjIyEn5oSfGqU6eDRrMTxiGja9ljFRUB92Cqqa119VBTpitRWbmad4oREE65cp9Ig+UefSzz8Pz8+eddnRSAwM/9LPfQxfo1l0EhEREREbH3MRERERExKCQiIiIiMCgkIiIiIjAoJCIiIiIwKCQiIiIiMCgkIiIiIjAoJCIiIiIwKCQiIiIiMCgkIiIiIjAoJCIiIiIwKCQiIiIiMCgkIiIiIjAoJCIiIiIwKCQiIiIiADKpM0D0f9q7v9C2rjsO4N++iNQpWhqGe2NMaWSVxetwFBPirDLuKLYrK263VmDRLnNj0jYRYTXLQxxRQjAmmKTEQ+qDKaPY1rJ4CfSpsqzGpl1F1MUjtVWzJaYobhmpchdCuomEBr1oD/I9vUrula7+WXbz/YDgkvvT1bnOy4/fOed3iIjo4ZSQZfy+vx8v7tmDfb29eWN9Ph/iy8tYWloS/15XV4dmmw1utxvNNltFx+tyuwEAmzdtxp/eHy35u28e8ABAwc+qlEfS6XS62oMgIiKih0+L3Y6lK1dw9epV1EmSZoySOIaCwbzPa21rw8TYmO6zSrW1oQGyLAMAotGo4SQ0FA7D5XKJMc5MTwMABrxe+P1+DA4N4cjhwxUZcyE4fUxERESr7tTICBZjMbR3duomcaFwGDt27MhKCE0mEyxWq/iYzWZx72IkgsbGRoTC4YqMub29U1yPjr5v+HsfjI2J646ODnF9cngYZrMZJ4aGkFhJNquJlUIiIiJadU9s2YJ79+7pVgkTsozGxkakUikAgCRJ8Bw6pFlRGw8E8O7p01iOxwFkEsdPP/207NPJ87EY7Ha7GM/X164Z+t4TW7YgmUzCZDLhf999l3VPqRY6u7vx4blzZR1voVgpJCIiolU14PUimUxi1+7dulXCjhdeEAlha1sbvr52TXeKdV9vL/715ZdobWsDAKRSKQx4vWUfd7PNhqaVRFOWZUMVyVA4jGQyCQDYtXv3A/eVamEoGMR8LFbeAReISSERERGtqvHxcQDAH/r7Ne8PeL2i6mexWsUavHxmpqfFdPLFSKQiSdavVhJPIHtaWI865revvqoZoySzJ4aHSxxdaZgUEhERrRMDXi9cbjfGAwEAmelMl9uNZ7ZvxzPbt6PFbsepkZGs7xiJWU2nRkaQTCZhNpvhdDg0Y86fPy+u/zwxUdDzX3rpN+I637q/8UAAHV1dWX+bNw94cq7v6+/vh8lkApBJPPNRYsxms+4O6/19fQCA2QsX8j6votJERES0LjxlsaQ31NSk33jrYPqVnp70hpoazc8bbx1Mf3vjRs6Yk6dPV+Ud2h2O9IaamvQrPT2a979YWBBj3PXssxUZw7c3bqR/3tSk+7cxb9qUPnL0aN532FBTk56antaNm5qeFnF676uolaSq/r+k0+k0K4VERETrQEKWRTuU2dkLCAWDaG1rw+DQEAaHhsRaNwA4f/6vsNvtCAWDsFitePvttx+IOf3uu6v+DgDwj0uXAAAv7tmjef+carOFeqq2XBKyDLvdLqanJUmCs7sbzu5u8fdJpVLw+/266xLVO4hzTSGr7ynVQD3Kb8/MzBh7kUqoWjpKREREho1NTGRVs7QqWfdXv7RilGrjhpqa1Rh2FvU76FFXN8cmJso+BnWVT+vvMzU9nTZv2iQqhl8sLGg+R4mplSTd31Kqf7liFEeOHjUcWyk80YSIiGgd+GhqSlzv3duLkxqbErZt2yYqYHoxzTt3GmoEXQnR6N8BIKu34P3Up5XkO+VEWVupp7a2Nmvd4nwsJtb4tba1af59nA4HfD4fPB4PUqkUTgwPa7aKae/sRCgYRDKZxKmRkQd2Rqt3HbcaqHg2NjYCAJLJJOZjsYqfzqKFSSEREdE6cP36dQCZhErvWLRCYixWawVGmds3//4GAPDT2tqyPM/j8eS8b7Fas5JC9cYTrYRQsa+3F4ODg5BlGfOXL2vG7O/rE8n1zMzMA0mheur4HQPtcfb19or3WVxcrEpSyDWFRERE68A3y8sAcledjMQsXbkCIFNVXG2JRAJA5rxiQ/FlPuVj8Z+LADJJc76kq3nnTgAQ6zjv53Q4RMVTWSepplQkJUkqOMFTKqqrjUkhERHRGjcfi4mpSKvFUlKM0hC6paWlAiM1Jtf0sTpZvZCnRcv3d+9qfpzd3Zrxd+7cAQDcu3dPtKHR+xhpN6O0v0mlUlltftRTx+qj8Yy6/d/bBX+nHJgUEhERrXGzn3wirp977rm8MW63O29M+/PPl2l05aVOaIutmCkJmZ5UKoXleDznJ98zAMDjOSCu1buG1VPH6ph8JJ3TXVYL1xQSERGtcXNzcwAyZ/rqNXxWx+hNVxqJqTa32w2/3w8A+PzS50U9I/7VVznvS5KE48ePF/VstWabDZIkQZblrCnkYqeO9aaqVwuTQiIiojVO2ZFb/+STFY8BgDcPeHDmTACjo6OaO4ATsiymdvPtENaSqwqnTrSW43GMBwIF/cZ8LKabXD322GPiuphxa+np6YHf7xfnLbvd7pKmjgFg86bNZRlboTh9TEREtMYpbWZybQ4pV0woHMaZM/qtXga8XrzscsHj8eDmrVs5x30/5XeVDSd6enp6xPXg4GBBv/G711/Xvdf0iyYAmYpcvnORlePvXDpT8Yp+1fnNf4tEsnY4Dw4WV420239Z1PdKxaSQiIhoDQuFw+Jab3OIOkbvpBAjMQlZxqFDh3KO5+TwMOrr6wEAe197LWfs/ZQK2K2bN/P+htIyR5ZldHR1GdqJ3NHVJRJfLer1fZ4c7zkeCOBiJILleDxv1a5OksRpJIuxGGZnMxXUJpsNdQWsEVT3XOzsLK7CWComhURERGvYZ599Jq71kjB1jF5CYSTm9b4+3L59O2+z5aWlJVis1oKSHgB4+eVfA8hMH+dL8mY+/hgmkwlAZo3ejh07MOD1an7v1MiI2DFsMpmyjvNTa7bZxLstxmKaVcBQOCyqfyaTyVC1z+VyiWtl6rrQI/rUjb0L/buWC5NCIiKiNSy+0nswV7KgTIWWEnNqZAQXIxEcPHgwZ8sYIDMNXUyfQ3VvvzNnz+aMrZMkTE5Oih25yWQSfr8fDQ0N2NrQIFrH/OTxx3H82DEsx+MwmUyYnJyE54D+jt+JsTHxzFAwiCe2bEFHVxdcbje2NjTA5XKJtj3vHDtmKEE7cviwSGAV6mllI5TG3kZOP6kUJoVERERrmHKixlM6vQeBH3bbFhszH4vhxNAQmmy2nCd9AD9Mc+pNQeejVPGUndC5OB0ORKNROLu7s5IuZRPKcjwuErjWtjZcvXoVTocj5/RrnSQhGo2K6elkMomLkQhCwaCo8pnNZoyOjj5wSkkuu3bvznrHQqt9iytJezX7Rz6STqfTVft1IiIiqrpntm/HrZs3sbCwgDpJgsvtRigY1Nx9rNz7/u7don6uu5GWAAAB6klEQVQrFA7D5XLBbDbjPzduGP5eQpZx5uxZzM3N4fr167hz5w62bdsGq8WC/v7+oqZcQ+EwPhgbE0f/1dfXo6WlpaBksByK/ZuUG1vSEBERPcRcbjeW43GMjo4aSqzmL1/WXbNnhNPhEC1nCmk3UydJZU/WnA6Hbt/H1fRHnw9AdaeOAU4fExERPbTGAwGEgkE4u7sNJWcJWYYsy6K1S7GUljN/mZws6Tk/BomVxtcmkwnvrSSH1cKkkIiI6CH10dQUgMyGi0c3bhSfUDAIAPB4PHh040axjlDZHKLsIi7WyeFhSJKEi5FI3n6BP3Y+nw+pVArtnZ1V23WsYFJIRET0kLJaLLBYrQ98lB3CkiTBYrWitrYWQGZzSK6j9gqhHDM34PWW/Kz1bHx8HGazGR+eO1ftoXCjCREREWXT22iytaEBtZKEuWgU87FYyecnK78TjUbX7FnMlZRrQ081cKMJERER5aWsJ2xv7xTTyaUmcu/5fEW3tvkx2N/Xh/19fWtiswvApJCIiIgMiK2s/ZudvYCnf/Z0WXYC10nSmqiQVctaSQYVnD4mIiIiQ0LhMGxFNGam9YFJIRERERFx9zERERERMSkkIiIiIjApJCIiIiIwKSQiIiIiMCkkIiIiIjApJCIiIiIA/we11bpi7y9GqwAAAABJRU5ErkJggg==)"
      ],
      "metadata": {
        "id": "fYdlGkes5IbW"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "eMrzEwhn5KFN"
      },
      "execution_count": 16,
      "outputs": []
    }
  ]
}