リソースヒストグラム(関数解析).ipynb

-ipynb.ipynb

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  "metadata": {
    "colab": {
      "name": "リソースヒストグラム(関数解析).ipynb ",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMM9tam7VvpOqIuEopCtvzg",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/hirokidaichi/49d1f6d5d44c0b4b1ca41ccc2eb96cc4/-ipynb.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9DedxHqX9rYf",
        "outputId": "511a2f80-151c-4dfe-d9d1-32934cb5b5e5"
      },
      "source": [
        "! pip install japanize-matplotlib"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting japanize-matplotlib\n",
            "  Downloading japanize-matplotlib-1.1.3.tar.gz (4.1 MB)\n",
            "\u001b[K     |████████████████████████████████| 4.1 MB 8.2 MB/s \n",
            "\u001b[?25hRequirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from japanize-matplotlib) (3.2.2)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->japanize-matplotlib) (2.8.2)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->japanize-matplotlib) (2.4.7)\n",
            "Requirement already satisfied: numpy>=1.11 in /usr/local/lib/python3.7/dist-packages (from matplotlib->japanize-matplotlib) (1.19.5)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->japanize-matplotlib) (0.10.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->japanize-matplotlib) (1.3.2)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from cycler>=0.10->matplotlib->japanize-matplotlib) (1.15.0)\n",
            "Building wheels for collected packages: japanize-matplotlib\n",
            "  Building wheel for japanize-matplotlib (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for japanize-matplotlib: filename=japanize_matplotlib-1.1.3-py3-none-any.whl size=4120274 sha256=1bd554c5f3ab11ece01cd3e48efedb7d62442460e29f4a10cc793f893f6c7b04\n",
            "  Stored in directory: /root/.cache/pip/wheels/83/97/6b/e9e0cde099cc40f972b8dd23367308f7705ae06cd6d4714658\n",
            "Successfully built japanize-matplotlib\n",
            "Installing collected packages: japanize-matplotlib\n",
            "Successfully installed japanize-matplotlib-1.1.3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w5HymyFZK-zb"
      },
      "source": [
        "import numpy as np\n",
        "import pandas  as pd\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.style.use('grayscale')\n",
        "import japanize_matplotlib\n",
        "plt.rcParams[\"font.size\"] = 15\n",
        "plt.rcParams['axes.facecolor'] = 'white'\n",
        "plt.rcParams['figure.facecolor'] = 'white'\n"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6etvw3Weh3SU"
      },
      "source": [
        "import sympy as sp"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B9q8eLoHiPt6"
      },
      "source": [
        "# シンボルの定義\n",
        "L = sp.Symbol(\"L\") # プロジェクトの長さ\n",
        "a = sp.Symbol(\"a\") # a プロジェクトスタイル\n",
        "c = sp.Symbol(\"c\") # c コミュニケーションコスト\n",
        "t = sp.Symbol('t') # 時間を表す変数\n",
        "to_func = sp.lambdify\n",
        "Eq = sp.Eq\n",
        "\n",
        "def print_expr(expr):\n",
        "  display(expr)\n",
        "  print(\"\\n\")\n",
        "  print(sp.latex(expr))\n",
        "\n"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "id": "SeZrjeiQlvK4",
        "outputId": "905b8946-35d7-4c30-e241-26686fa77066"
      },
      "source": [
        "# プロジェクトのリソースヒストグラムを単純化すると\n",
        "# 放物線になる。\n",
        "Rt = a * ( -t**2 + L * t)\n",
        "Rt_func = to_func((t,L,a),Rt,\"numpy\")\n",
        "Rt\n",
        "R = sp.Function(\"R\")\n",
        "R_eq = sp.Eq(R(t),Rt)\n",
        "print_expr(R_eq)\n"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle R{\\left(t \\right)} = a \\left(L t - t^{2}\\right)$",
            "text/plain": [
              "Eq(R(t), a*(L*t - t**2))"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "R{\\left(t \\right)} = a \\left(L t - t^{2}\\right)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 346
        },
        "id": "orNiWgV7mSbv",
        "outputId": "8433dc9d-5686-45ae-befb-0e59997148e7"
      },
      "source": [
        "# それを積分するとL^3に比例する工数になる。\n",
        "E= sp.integrate(Rt,(t,0,L))\n",
        "E_func = to_func((L,a),E)\n",
        "print_expr(E)\n",
        "print_expr(sp.Eq(sp.Symbol(\"E\"),sp.Eq(sp.Integral(R(t),(t,0,L)),E)))\n",
        "\n",
        "print_expr((sp.solve(sp.Eq(sp.Symbol(\"E\"),E),L)[0]**3)**(sp.Rational(1)/3))\n",
        "sp.solve(sp.Eq(sp.Symbol(\"E\"),E),a)[0]"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle \\frac{L^{3} a}{6}$",
            "text/plain": [
              "L**3*a/6"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\\frac{L^{3} a}{6}\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle E = \\int\\limits_{0}^{L} R{\\left(t \\right)}\\, dt = \\frac{L^{3} a}{6}$",
            "text/plain": [
              "Eq(E, Eq(Integral(R(t), (t, 0, L)), L**3*a/6))"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "E = \\int\\limits_{0}^{L} R{\\left(t \\right)}\\, dt = \\frac{L^{3} a}{6}\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle \\sqrt[3]{6} \\sqrt[3]{\\frac{E}{a}}$",
            "text/plain": [
              "6**(1/3)*(E/a)**(1/3)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\\sqrt[3]{6} \\sqrt[3]{\\frac{E}{a}}\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{6 E}{L^{3}}$",
            "text/plain": [
              "6*E/L**3"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_JaWS_mH6kdk"
      },
      "source": [
        "\n",
        "$$ L=\\sqrt[3]{\\frac{6E}{a}} $$ "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 105
        },
        "id": "g_H2u7Q6V5tD",
        "outputId": "de6d6291-61cf-45a9-ec92-9df46f876621"
      },
      "source": [
        "# Rtの累積関数\n",
        "cul_Rt = sp.integrate(Rt,t)\n",
        "cul_Rt_func = to_func((t,L,a),cul_Rt)\n",
        "print_expr(cul_Rt)\n"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle \\frac{L a t^{2}}{2} - \\frac{a t^{3}}{3}$",
            "text/plain": [
              "L*a*t**2/2 - a*t**3/3"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\\frac{L a t^{2}}{2} - \\frac{a t^{3}}{3}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 193
        },
        "id": "Y4yQzd0XmgVM",
        "outputId": "da85cad7-821c-4451-8b91-34de81abeb7d"
      },
      "source": [
        "# Rtの微分が0になるところがピークリソース\n",
        "# ピークリソースは、プロジェクトの長さの二乗に比例する。\n",
        "dt_Rt=sp.diff(Rt,t)\n",
        "\n",
        "peak_time = sp.solve(dt_Rt,t)[0]\n",
        "peak_resource = Rt.subs(t,peak_time)\n",
        "peak_resource_func = to_func((L,a),peak_resource)\n",
        "print_expr(peak_resource)\n",
        "print_expr(sp.Eq(sp.Symbol(\"R_peak\"),peak_resource))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle \\frac{L^{2} a}{4}$",
            "text/plain": [
              "L**2*a/4"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\\frac{L^{2} a}{4}\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle R_{peak} = \\frac{L^{2} a}{4}$",
            "text/plain": [
              "Eq(R_peak, L**2*a/4)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "R_{peak} = \\frac{L^{2} a}{4}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OqN-_C0k8jyn"
      },
      "source": [
        "$$ L = 2.7 \\sqrt[3]{E}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 41
        },
        "id": "eY9TGeg5m972",
        "outputId": "39704867-19b5-4328-e733-38ebef5e65ce"
      },
      "source": [
        "# ここでコミュニケーションコストがプロジェクトに入っているリソース人数の二乗に比例すると仮定する。\n",
        "# すると実効的なリソースヒストグラムであるStがみつかる。\n",
        "St = Rt - c * Rt**2 \n",
        "St\n",
        "St_func = to_func((t,L,a,c),St,\"numpy\")\n",
        "St\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle - a^{2} c \\left(L t - t^{2}\\right)^{2} + a \\left(L t - t^{2}\\right)$",
            "text/plain": [
              "-a**2*c*(L*t - t**2)**2 + a*(L*t - t**2)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 89
        },
        "id": "LmSmRFCn19Iw",
        "outputId": "bcb9e5a5-10ee-46b0-b2e6-dcff49eda484"
      },
      "source": [
        "Sf = sp.Function(\"S\")\n",
        "print_expr(sp.Eq(Sf(t),R(t) - c* R(t)**2))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle S{\\left(t \\right)} = - c R^{2}{\\left(t \\right)} + R{\\left(t \\right)}$",
            "text/plain": [
              "Eq(S(t), -c*R(t)**2 + R(t))"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "S{\\left(t \\right)} = - c R^{2}{\\left(t \\right)} + R{\\left(t \\right)}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dPIZff4n8brH"
      },
      "source": [
        "$$ S{\\left(t \\right)} =  R{\\left(t \\right)} - c R^{2}{\\left(t \\right)} $$\n",
        "$$ c = コミュニケーションコスト $$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 131
        },
        "id": "Zcpj4UqHZCLF",
        "outputId": "12abf026-9253-4917-959e-cb19892e2589"
      },
      "source": [
        "# Stに関して積分する。\n",
        "# 実効的なL^3 - aL^5の関数に生産力は律速される。\n",
        "S = sp.integrate(St,(t,0,L))\n",
        "S =S.factor(L)\n",
        "S_func = to_func((L,a,c),S)\n",
        "print_expr(sp.Eq(sp.Integral(sp.Function(\"S\")(t),(t,0,L)),S))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle \\int\\limits_{0}^{L} S{\\left(t \\right)}\\, dt = - \\frac{L^{3} a \\left(L^{2} a c - 5\\right)}{30}$",
            "text/plain": [
              "Eq(Integral(S(t), (t, 0, L)), -L**3*a*(L**2*a*c - 5)/30)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\\int\\limits_{0}^{L} S{\\left(t \\right)}\\, dt = - \\frac{L^{3} a \\left(L^{2} a c - 5\\right)}{30}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "id": "r0hYq60tikEa",
        "outputId": "03a7334e-e755-44ea-99c3-d6dd28d4bff9"
      },
      "source": [
        "# そこでSをaに関して微分し、もっとも実効工数が大きくなるaを探す。\n",
        "# すると、プロジェクトの長さの二乗、コミュニケーションコストに反比例するとわかる。\n",
        "diff_S = sp.diff(S,a)\n",
        "a_opt = sp.solve(diff_S,a)[0]\n",
        "a_opt_func = to_func((L,c),a_opt)\n",
        "a_opt"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5}{2 L^{2} c}$",
            "text/plain": [
              "5/(2*L**2*c)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "-kuDM8zujVlG",
        "outputId": "2e645aa7-ca4a-462f-dc00-6c8eedb4c283"
      },
      "source": [
        "# これを代入し、最適なプロジェクト工数を\n",
        "E_opt = E.subs(a,a_opt)\n",
        "E_opt"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5 L}{12 c}$",
            "text/plain": [
              "5*L/(12*c)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "id": "A9b9CpFHkcb6",
        "outputId": "1c704c4d-dac0-416e-ec5e-f7f50f7f580f"
      },
      "source": [
        "# このときのピークリソースは、コミュニケーションコストに反比例する。\n",
        "# つまり、コミュニケーションコストがかからないように分割しなければ、ピークを構築できない。\n",
        "peak_resource_opt = peak_resource.subs(a,a_opt)\n",
        "peak_resource_opt\n",
        "sp.Eq(sp.Symbol(\"R_max\"),peak_resource_opt)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle R_{max} = \\frac{5}{8 c}$",
            "text/plain": [
              "Eq(R_max, 5/(8*c))"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "id": "4HzqI9G5kf4p",
        "outputId": "85a0adaa-efe5-42c8-88a4-645217336c9f"
      },
      "source": [
        "# またその場合の有効稼働率は工数の半分\n",
        "S_opt = S.subs(a,a_opt)\n",
        "S_opt\n",
        "S_opt/E_opt"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{1}{2}$",
            "text/plain": [
              "1/2"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 379
        },
        "id": "XP_rQWoK_4lb",
        "outputId": "cc4a459a-86ec-47f8-d432-3f2231a7123f"
      },
      "source": [
        "\n",
        "def TIME(L):\n",
        "  return np.linspace(0,L,num=L)\n",
        "\n",
        "len = 15\n",
        "x = TIME(len)\n",
        "plt.figure(figsize=(8,5))\n",
        "plt.title(\"リソースヒストグラム\")\n",
        "plt.bar(x,Rt_func(x,len,0.3),label=\"a=0.3 の放物線\")\n",
        "plt.bar(x,Rt_func(x,len,0.2),label=\"a=0.2 の放物線\")\n",
        "plt.bar(x,Rt_func(x,len,0.1),label=\"a=0.1 の放物線\")\n",
        "plt.ylabel(\"人員数\")\n",
        "plt.xlabel(\"時間(月)\")\n",
        "plt.legend()\n",
        "\n",
        "\n",
        "#x = TIME(15)\n",
        "#plt.plot(x,R_t_func(x,0.3,15))"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb1268d9110>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "NOAtG61jTsbv",
        "outputId": "0ede065e-9ff1-4687-9050-9f983fc5b9e6"
      },
      "source": [
        "S_opt"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5 L}{24 c}$",
            "text/plain": [
              "5*L/(24*c)"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "slUAkTNdeOlT",
        "outputId": "018e6d30-6cd0-4410-998b-db30aff99405"
      },
      "source": [
        "eq = Eq(sp.diff(S,L),0)\n",
        "sp.solve(eq,L)[1]\n",
        "L_max = sp.solve(eq,L)[2]\n",
        "L_max"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\sqrt{3} \\sqrt{\\frac{1}{a c}}$",
            "text/plain": [
              "sqrt(3)*sqrt(1/(a*c))"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z3rfr3Fjhv0S",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 61
        },
        "outputId": "4d8c407b-29ce-4bea-c3e2-af47ef5abd18"
      },
      "source": [
        "S_max = S.subs(L,L_max)\n",
        "S_max"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{\\sqrt{3} a \\left(\\frac{1}{a c}\\right)^{\\frac{3}{2}}}{5}$",
            "text/plain": [
              "sqrt(3)*a*(1/(a*c))**(3/2)/5"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 309
        },
        "id": "S-HEblQeWC3H",
        "outputId": "564492f0-a3f8-4ea7-f0a9-c2661d47d0aa"
      },
      "source": [
        "S1 = S.subs(a,0.3).subs(c,0.05)\n",
        "r= sp.Eq(L,L_max).subs(a,0.3).subs(c,0.05)\n",
        "p = sp.plot(S1,(L,0,17), legend = True, show = False)\n",
        "#sympy.plot(S1,(L,0,17), legend = True, show = False)\n",
        "p.show()\n",
        "r"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle L = 8.16496580927726 \\sqrt{3}$",
            "text/plain": [
              "Eq(L, 8.16496580927726*sqrt(3))"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 56
        },
        "id": "xjxjW_BFWUle",
        "outputId": "d47f21d8-849d-4ba5-c886-cdc167cac2ff"
      },
      "source": [
        "S"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle - \\frac{L^{3} a \\left(L^{2} a c - 5\\right)}{30}$",
            "text/plain": [
              "-L**3*a*(L**2*a*c - 5)/30"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 380
        },
        "id": "CjesTzBMj6P6",
        "outputId": "369f87a8-207a-431c-86a9-75e41fce41e7"
      },
      "source": [
        "def plot_S(a,c):\n",
        "  l = np.linspace(0,30)\n",
        "  s = S_func(l,a,c)\n",
        "  plt.plot(l,s,label=f\"a = {a}\")\n",
        "  plt.ylim(0,100)\n",
        "\n",
        "\n",
        "plt.figure(figsize=(8,5))\n",
        "plt.title(\"プロジェクトの有効工数には上限がある\")\n",
        "for i in range(1,7,2):\n",
        "  plot_S(i/10,0.05) \n",
        "plt.ylabel(\"プロジェクト規模(有効工数)\")\n",
        "plt.xlabel(\"プロジェクトの長さ(L)\")\n",
        "plt.legend()"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb115d5cbd0>"
            ]
          },
          "metadata": {},
          "execution_count": 49
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 56
        },
        "id": "mA-GxkuekdAn",
        "outputId": "bee0b649-bf45-4cc9-ed23-c885d541c119"
      },
      "source": [
        "a1 = sp.Symbol(\"a1\")\n",
        "a2 = sp.Symbol(\"a2\")\n",
        "l1 = sp.Symbol(\"l1\")\n",
        "l2 = sp.Symbol(\"l2\")\n",
        "beta = sp.Symbol(\"beta\")\n",
        "alpha = sp.Symbol(\"alpha\")\n",
        "S1 = S.subs(a,a1).subs(L,l1)\n",
        "S2 = S.subs(a,a2).subs(L,l2)\n",
        "DS = (S1 - S2)*30\n",
        "DS2 = DS.subs(l2,l1*alpha).subs(a2,a1*beta)\n",
        "DS2\n",
        "DS2_func = to_func((beta,alpha,a1,l1,c),DS2)\n",
        "DS2\n",
        "sp.Eq(S1,S2)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle - \\frac{a_{1} l_{1}^{3} \\left(a_{1} c l_{1}^{2} - 5\\right)}{30} = - \\frac{a_{2} l_{2}^{3} \\left(a_{2} c l_{2}^{2} - 5\\right)}{30}$",
            "text/plain": [
              "Eq(-a1*l1**3*(a1*c*l1**2 - 5)/30, -a2*l2**3*(a2*c*l2**2 - 5)/30)"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "eW7IQgmxoTeH",
        "outputId": "b18772a3-e3a9-40a1-b015-571d8e54325b"
      },
      "source": [
        "x = np.linspace(1,50)/10\n",
        "y = DS2_func(x,0.9,0.2,18,0.05)\n",
        "plt.plot(x,y)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fb115e0ff90>]"
            ]
          },
          "metadata": {},
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "id": "BZLSw_FUrWu8",
        "outputId": "92d8559b-0c44-402b-c085-a621bd984355"
      },
      "source": [
        "# DS2が0にタッチするかを知りたいので、最小値を見る。betaに関して微分して、0になる点をさがす\n",
        "min_beta = sp.solve(sp.diff(DS2,beta),beta)[0]\n",
        "min_DS = DS2.subs(beta,min_beta)\n",
        "sp.solve(min_DS.subs(a1,0.3).subs(l1,12).subs(c,0.03),alpha)[0]\n",
        "# 0.3のプロジェクトを最も短くできて、76%\n",
        "# それ以降は短くできない。\n"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle 0.76806144$",
            "text/plain": [
              "0.768061440000000"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 56
        },
        "id": "AF_xxpQNtrdi",
        "outputId": "cf5d2906-3243-4626-82db-46adf5d7ddef"
      },
      "source": [
        "# 短くしたプロジェクトの差が最も小さくなる時のbeta\n",
        "min_beta_func = to_func((alpha,a1,l1,c),min_beta)\n",
        "min_beta"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5}{2 a_{1} \\alpha^{2} c l_{1}^{2}}$",
            "text/plain": [
              "5/(2*a1*alpha**2*c*l1**2)"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        },
        "id": "M7f-mGGnwA4g",
        "outputId": "55686947-8511-4e7d-d16e-c309ffcd1576"
      },
      "source": [
        "shortest_period = sp.solve(min_DS,alpha)[0]\n",
        "shortest_period_func = to_func((a1,l1,c),shortest_period)\n",
        "shortest_period\n",
        "P_shortest = sp.factor(shortest_period.subs(l1,L).subs(a1,a))\n",
        "# -(peak_resource * (peak_resource-5)) / 25\n",
        "print_expr(1-P_shortest)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle \\frac{4 L^{2} a c \\left(L^{2} a c - 5\\right)}{25} + 1$",
            "text/plain": [
              "4*L**2*a*c*(L**2*a*c - 5)/25 + 1"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\\frac{4 L^{2} a c \\left(L^{2} a c - 5\\right)}{25} + 1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NgwIz9ApbsUg"
      },
      "source": [
        "$$短縮可能割合 = \\frac{4 L^{2} a c \\left(L^{2} a c - 5\\right)}{25} + 1$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zTqvCldOw8aU",
        "outputId": "b466aaad-7d4c-4190-a824-096488bd1d5a"
      },
      "source": [
        "1-shortest_period_func(0.3,12,0.03)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.23193856000000002"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 380
        },
        "id": "BS0Q_11jE-Ca",
        "outputId": "dfa59579-26dd-44f6-bf97-d1ab51209355"
      },
      "source": [
        "def plot():\n",
        "  l1 = np.linspace(5,20)\n",
        "  a1 = 0.3\n",
        "  c = 0.03\n",
        "  plt.figure(figsize=(8,5))\n",
        "  plt.ylim(0,1)\n",
        "  plt.xlabel(\"プロジェクト期間(L)\")\n",
        "  plt.ylabel(\"短縮率\")\n",
        "  plt.title(\"納期短縮率と同規模のリソースヒストグラム\")\n",
        "\n",
        "  y = shortest_period_func(a1,l1,c)\n",
        "  plt.plot(l1,y)\n",
        "  plt.legend()\n",
        "  plt.show()\n",
        "\n",
        "plot()"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "No handles with labels found to put in legend.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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XgwYNEi3r7+8PoVCIsWPH4tSpU6VuU15e/rPzxMTEICcnB8DHgVoyMjLw7NkzaGpqQlNTE/n5+SUGePl34zIlJSVs374dDRo0wDfffCPaY9+wYQPmzJkjGmzj7NmzYi3di49mli9fLnYkl5OTgzVr1mDbtm3Yvn07Xr9+DR8fH1hZWcHY2Biurq6YOnUqDhw4AG9vb+zbtw9//vknrKysJL5HoVCItWvXwtnZGcbGxggMDCwxfkFlDB48uEQ3uh9++KHU5du2bYuCggIAH7unmZmZITc3FwKBADIyMpg8eTJkZWVLfFFL+rmmpKTA09MT3333Hd6+fYtevXqJCtzBgwclNnicO3duiZ/Zs2fPkJmZWaIxk6enJxQVFcV+D4sVF6b379+X+l5L8/79eygqKlao4MvKypbosVBs5cqVEAgEpTbWCwsLq9TR4qfatm1boYKfnp6OqVOnYsyYMbCwsKjUa+zYsQP/+9//PitfdeQp1rhxY9y/fx+7d+/GqlWrcOrUKcybNw9OTk6igvlvQUFBsLCwgJaWFi5cuCCxId6GDRvQqFGjEmeMPiUvL1+h77CsrCwcO3YMI0eORPPmzctc9vjx40hPTxfbaezQoQMePXqECRMmwMfHp1p7d0gTF/xaRFFREWlpaZCXl8eLFy/Qrl07uLm5IT4+Hn369MHVq1cBfDwq9PX1xaNHjzB58mTMnj271CNi+mT0qk+PFoqKinDo0CHRKXmSMMrVjh07RP/v0qULpkyZgh9//BHAxy5yISEhEludDx8+XPR/GRkZ3LhxA3l5eThx4gSOHj2KoUOHokePHhg6dKjYH7Oenh7u378vej5jxgyx7d67dw8WFhbIz8+Hj48PwsPD0bx5cygoKCAsLAwBAQH4/vvvISsri6CgINy5cwcrVqyAjY0NFBUVMXLkyBJZp02bhuPHj8PNzQ329vYSP8PKkJeXL3GEUF7r4eKzMMnJyZCXl0dSUpLoyByo+Cn9HTt24LvvvoOuri6aN2+O5ORkeHt7A0CpOzwASrzv4m6Q/z6Ts3//fpibm0s86xETEwNAci+E8iQlJZX7JV2eS5cu4ciRI1iyZAnatm0rcZkpU6ZIPMtRVfLz82FpaYmEhAQYGhoiOzu7Ukfon3NJqDrzfEpWVhazZ8+Gra0tZs+ejS1btsDDwwP79u2TOHYAEaFnz544cuQINDQ0SswPCwvD/v37xc7ufYn169cjPT1d1FOlLLt370bPnj3Fujrr6enBzc0N48ePx8qVK+Hs7PzFmWol6TYhYP929+5d6tSpk6ghj7+/P6mrq1N+fr6o0Z61tTVZWVkREVFcXBypqKjQwIEDydzcnAoLCyk+Pp58fHwIAMXHx4seSkpKdP78eUpOTqbhw4fTqFGj6MiRI3TkyBFyd3cv0WjvU40aNaLOnTuLtaS9efMmPXv2TPT81atX5OLiUqJVu7u7O/Xt25d27dpF/fv3J1NTU1q0aBGNGTOGtLW1KTAwkM6cOUMdO3YUW8/e3p6WL18uep6dnU0ODg6iBj75+fmiBm7m5uaixmdnz56lGzduiNa7d++exPfk6elJAMjT07PMn0lZihvtEREtXLhQYoPFLl260K5du4iIymy05+joSCoqKtS8eXMKCwsjoo8N4lJTU6lp06Z08OBB2rlzJ+nr61Nqaiq9fftWtG5CQgIpKyvT/v37yc7OjhYuXEi5ubklGnn5+fmRhoZGme+p+HfP29tbNO3GjRsEgC5duiRxnYkTJ5KiomKZPRpKo6OjQyNHjqz0esWio6NJXV2d9PT06P3795+9nS+Rm5tLI0eOJBUVFfr999+pSZMm1KlTJ3ry5Em565bXSr+m83yqtEZ7Hh4epKmpWerfVlmysrKoQ4cOpK+vT3l5eZVe/9/8/PxIVlaW5s6dW+6yxQ1j9+zZI3H+nDlzSCAQVKhnT11UP89b1GHPnz8XneIFPjYmIyLR0f25c+dw9epV/P777wCANm3a4Ny5c6LT0PHx8WjdurVor7t169aiR05ODiwsLGBiYoLU1FQYGRlh/PjxGD9+fJlHgE+fPkVmZiY6dOiAvn37IikpCQCwatUqsWvLXl5eEq8rx8XFifUfNjY2Rnx8PP755x+x5aKioiAQCESPTwfRKSoqQnx8PObNm4e3b98iMjISz58/x4sXLxAZGYn3798jMzMTkZGR6NixI5o0aYLIyEhERkaiQYMGiIyMFPtciz/Lrl27VmkDrwsXLoi9B4FAIHFwIUnOnj2LFStWYPz48TA1NcXt27ehoqKCJk2a4M2bN9DV1YWKigpkZWWhqakpdkR4584d6OjoiI0jcO/ePcjJyYllGThwIN68eVMi46cNwtq2bQt9fX0cPHgQwMfLHosXL4aBgYHE4XjPnTuHw4cPw8HBoVJtHoCPjQCfP38udlaoMp4+fQozMzMUFRXh/PnzEq/dV7ekpCSYmZnh8uXLOHPmDObNm4ewsDDk5+fD0NAQXl5eZa5f/Nn/e1hraeWpCFtbW8TFxaFbt26VWu/Dhw8YM2YMEhIScOzYMYmn+isjJCQEo0ePRo8ePfDbb7+Vu7yrqysaN24sGmjnw4cPiI2NRUBAANzd3aGiogKBQIAZM2aUuNRVL0h7j4OJW79+PQ0YMEC015+bm0tDhgyhRYsWkb29PU2aNImuXLlSYr1/d8sjIvLy8qLg4GAiIjp06BDt3r2biIiEQiGpqKiIHVHk5uaWeoS/Zs0a6tSpExUUFJCJiQkZGhpSbm4ueXl5UYMGDSgjI4OIiMaMGSM68/CpCRMmkKOjo+gI//Tp09SuXTsiohJH+AUFBaLH5MmTRUf4qamp5fZzL+8RGxsrlmv69OmkpaX1WUelxf59hD948GBKTU0t8Sg+E1HaEf6lS5dITk6OXrx4QUQfu7+1bNmS8vPzKSAggOTl5endu3e0b98+sb7UhoaGlJSUREQkOnorPsIXCoWUm5sreuTk5JCxsTHp6+tTjx496PXr12LzP3X8+HECQBs3biR7e3uSl5cv0eUpMzOTVq5cSXJycmRoaEg5OTmV+uwKCwupX79+pK6uTllZWZVal4jo3LlzpKmpSU2aNBF1N61px44do6ZNm5K6ujoFBQWJzUtJSaHu3buTnJwc7d+/v9Rt5OTkkIyMDI0dO5bi4+NFR70FBQWiMzzR0dEUHBxMZ8+eFY0zUV15PlVV/fCJiNLT08nMzIzk5eW/6Kwa0cfPZtu2baSgoEDdu3cvtZsmEVFSUhItWrSIZsyYQWpqatSoUSPq1KkTaWhoiH0/aGhoUJ8+fWjixIkkIyNDs2fP/qKMtREX/FrG1NSUfv75Z7GCv3TpUpo4caJYP/x/+3fBj42NJTU1Nfrtt9+IiMjf358aNGhAHh4eFBwcTADo8ePHouVLK/gpKSmkrq5OLi4uRPTxj0dfX59iYmKooKCAmjRpQv/88w9lZmZSw4YNxU4DF9PS0qLTp0+LCn50dDTNmjWLhEJhpU7pl+XTU/oVFRwcTAoKCqSvr09bt24lf39/evz4MUVFRdGdO3fo+vXrdPToUdq0aVOpp/g+Lfi3bt2SuDP2KUkFPyMjg/T09GjmzJmiaZmZmXTo0CEi+lj8R4wYIVq/uOC/e/eOAIh2EooVF/xPFRQU0KxZs0hXV5fevXtHQ4YMIR0dHbp8+XKpWVeuXEkyMjKkqqoq6teel5dH27dvp3HjxpGKigrJyMjQzJkzK30qPS8vj2xtbT+rL3RERASNGzeOAFCnTp3o4cOHlVq/Kvj5+dGAAQMIAPXu3bvUQYfevn1LPXv2JIFAQJs3by51ewsXLqzwjmtgYGC15ylWVQXf39+fOnToQGpqahK/IyoqOTmZduzYQbq6ugSApk6dWu7vXmFhIWlpaZGqqirp6+uTqakpTZkyhVasWEF79uyhwMDAEjsMs2bNIlVV1VLHB6iruODXMjY2NnT27Fmxgl/8Cy2p4Ht7e1N4eDhNmDCBhg0bRkQfr+vr6elRv379xAZNWbt2LfXt25cmTpxInTp1IqKPA/gEBQXR1atXCYDYF8WHDx/IxMSEunbtKnatLSoqip48eUJPnjwhV1dXCg8Pp02bNpGWlhY9fvxYNK+goICEQiG5urrS69evRQX/U58WfElfbtVZ8Ik+jsZnaWlJampqpX7BNmzYsNTR3T4t+JIUFBTQsWPHKCgoiCIiImjOnDmkqKgomp+Tk0MGBgakp6dX4ig3Ly+P5s2bR0pKSqKiduDAAWrWrBndv3+ftm7dSnJycvThwwex9T49wn/06BFt27aN2rVrR926daOEhARRrkWLFpGcnBx169aNVq9eLXG0wzdv3pTYvr29PRkYGNDy5ctLbfNRlitXrlCXLl0IAP3666+VWregoICMjIyoQYMGtHDhwkqfVagK+fn5NHDgQFJXV6dt27aVOxhOWloaffvtt+Tu7l7mcklJSeTn50cnTpyggwcPkru7Ox09epTOnDlDvr6+dPv2bYqLiysxQFF15SH68oJ///59sra2JoFAQAYGBpVuQ/CpyMhIkpeXJwA0cOBA0SBZFVHZtgKpqakUExNT2Yi1Xo0X/JSUFNqzZw8ZGhqWOKKTJCcnhxwdHUlbW5uUlJTIxMSEHj16VANJpevTgl9MUsHv3bs3ycvLk5KSErm6uhIRkZOTE/Xo0UOsURfRxy+G4sZdxaNezZo1ixo2bEiysrLUu3dvsS/9UaNGkYaGhtiZACIiIyOjCh2JFA/HWqy8gq+npyd2itne3p6cnJwq9Hl9bsH/VHJyMj18+JBu375NDx48oGfPnlF6enqZ65RX8ImIvvvuO1JRUSE5OTlq2LAhTZs2TWz+1q1bS3xWN27coNatW1ObNm3ETs3eu3ePNDU1CQDJy8vTTz/9VOL1igt+8dmZ7777jnbt2iWxEDx9+pTmz59f4c/5S2VkZJCOjg41b96czpw581nbSElJKXFWo6ZlZmaW+7vxKUk7U1WpuvKcPHmy0jtlnzp69Cg1bdqU/vjjjwqNpFie8+fPf9FOw9dOQCShP1Y1CQkJwcCBA2FoaIjCwkKkp6cjMjKyzHXGjh2L6OhoHDlyBM2bN4eTkxOOHz+OiIiIL+7KU18REd69e1fqgDNPnjyp0IhZAQEB0NTURJcuXao6IitHYWEhjhw5grFjx0psiFZ8V8XyZGZmVmqgpJqQkJCAxo0bV0l3LFb7FRQUfNF4IKzq1GjBz8/PR15eHtTU1LB69WocPXq0zIIfHByMvn37Ijw8XDT6mFAoROfOnWFlZVVi9DHGGGOMSVaj3fIUFBQqNMxpsfPnz6NTp06iYg98HMjFzs4OR48erY6IjDHGWL1Uq0fai4qKEt0T/FO6urp48eIFiKjEDSVcXV3h6uoKAIiMjKzwfcoZY6y+KCoqwocPHyQ+8vPzq+x1ZGVl0aBBAygoKKBBgwZi//+ccfvZl3vx4gXS0tIkzqvVBT8nJ0dswJZiGhoaKCwsREZGRonhKGfOnImZM2cC+DhojaQ7tzHGWH3x5s0bhIWFITQ0FKGhobh9+zZSU1PFltHU1ETnzp2ho6MDHR0dNG3aFGpqalBVVRX7t/j/cnJyyM3NLfWRmZmJuLg4xMbGIjY2Fi9evMCLFy/w4cMH0WuqqKjAyMgIffr0QZ8+ffD999+L7gDJqo+BgUGp82p1wdfU1ER6enqJ6VlZWZCTk+NfHsbYV6WgoAB3794VFffQ0FDRbZUFAgG6dOmCESNGQF9fX1Tc27dvX6lLqcX+fbvs8giFQiQnJyM2NhbPnj1DWFgYQkJC4OzsLBpFsHPnzqIdABMTE7F7RrDqV6sLfvv27XHu3LkS0yMjI6Gtrf1F94dmjLG6ICkpCZcuXYK3tzd8fX2RlZUF4OONioyMjDBt2jQYGRnBwMCg1LvX1QQZGRloaWlBS0sLxsbGopsyvXv3Drdu3cKNGzdw48YNnDx5Env27AHw8bbK48aNw7hx49CuXTupZf9a1OqCb21tDWdnZ0RERIjuGU5EOHXqFGxsbKScjjHGql5RURHCwsLg7e0Nb29v3LlzBwCgpaUFa2trDB48GN9//z1atWpVJw56VFVVMWjQINFtlYVCIZ48eQJPT0+cPMYAyjEAACAASURBVHkSS5YswZIlS/Cf//xHVPw7dOgg5dT1U626ec6ZM2egr6+PsLAwAMB3332HUaNGwd7eHk+ePMHbt2/x888/4+XLl2L3MmaMsbqssLAQvr6+sLe3R9OmTdGnTx9s2LABysrKWL9+Pe7du4eEhAS4ubnBysoKrVu3rhPFXhIZGRl06dIFy5YtE9086bfffoOsrCwcHR2hq6uLHj16YOPGjaU2PmOfp1YV/MzMTERFRSEnJ0c07fDhw+jbty/69++P1q1bIyIiAv7+/mjZsqUUkzLG2JchIoSHh2PBggVo1aoVzM3Nce7cOYwYMQLHjh1Damoqrl+/DkdHR3Tr1q3OFvjytG/fHosXL0ZoaChevHiBbdu2oWHDhnB0dETr1q0xY8YMPHz4UNox64UaHXinpnErfcZYbRMTE4PDhw/j0KFDiIqKgoKCAkaMGAE7OzsMGzaMu7P9n0ePHmHHjh1wd3dHXl4eTE1NMX/+fAwdOrRCo0x+rcqqe1zwGWOsmuXn5+PkyZP466+/EBwcDADo378/7OzsMG7cuBLdi9n/l5aWBjc3N/z555949eoVdHV1MW/ePNjb29er4ZmzsrKQkpKCgoKCUpeRl5cXdaksDRd8xhiTgsTEROzevRuurq54/fo1dHV18d///he2trbcJa2SCgoKcPLkSWzfvh23bt1C48aNsXTpUsybN6/SXQhrm6ysLLx+/RotW7ZEw4YNJV6+ISLk5uYiMTERzZo1K7Xol1X3+LwIY4xVISJCYGAgrK2toa2tjXXr1sHQ0BCXLl1CZGQkli1bxsX+M8jLy2PChAkIDQ3FjRs3YGxsDEdHR3Ts2BHu7u6ivv51UUpKClq2bAklJaVS22oIBAIoKSmhZcuWSElJ+azX4YLPGGNVIDc3F25ubujevTv69euHK1euYMGCBXj27Bk8PT1hbm7O156rgEAgQO/eveHl5QU/Pz80bdoU9vb2+M9//oMrV65IO95nKSgoqPBZioYNG5Z52r8s/NvHGGNfIDs7G1u2bEG7du0wc+ZMCAQCuLm5ISEhAZs3b0b79u2lHbHeGjBgAMLCwuDh4YH09HSYmZlh2LBhdbJVf0V7YXxJbw0u+Iwx9hkyMjKwdu1aaGtrY/Hixfj2229x7do13L17F9OnT4eSkpK0I34VZGRkYGtri8jISGzevBkhISHo1q0bpk+fjuTkZGnHq1W44DPGWCWkpqbil19+QZs2beDk5ARjY2PcvHkTly9fxsCBA+ttf/naTlFREYsWLcKzZ88wb948uLu7o0uXLjh8+DDqcdv0SuGCzxhjFZCUlIQFCxZAW1sbGzduxNChQ3Hv3j2cP38eRkZG0o7H/o+Ghga2bduGiIgI6Onpwc7ODmPHjsXr16+lHU3quOAzxlgZMjMzsXz5cujo6GDnzp2wsrLC48ePcezYMXTr1k3a8VgpOnbsiKCgIPz222/w9vZGly5dcPTo0a/6aJ8LPmOMSfDhwwds374d7du3x/r162FpaYmoqCgcOHAA+vr60o7HKkBWVhaLFy/G3bt3oaOjgwkTJsDKyuqzu7VVp4ruiHzJDgsXfMYY+0RRUREOHjyIjh074ueff4aBgQFu374NDw8P6OjoSDse+wydOnVCcHAwNmzYAE9PT3Tp0gXHjx+XdiwReXl55ObmVmjZ3NxcyMvLf9brcMFnjDF8PHK6ePEievbsicmTJ0NDQwOXL1+Gj48PevbsKe147AvJyclh2bJluHPnDtq2bQsbGxtMmDAB2dnZ0o6Gpk2bIjExETk5OaUewRMRcnJykJiYiKZNm37W68h9SUjGGKsPHj58iHnz5uHatWto3749jhw5Amtrax4opx7q0qULQkJCsGHDBqxevRoRERE4e/YsOnToILVMxcPkvnr1qtyx9MsaVrc8XPAZY1+tjIwMrFq1Ci4uLmjUqBF27NiBWbNmQUFBQdrRWDWSk5PDypUr8f3332P8+PEwMDCAh4cHhg8fLrVMampqn13IK4p3XxljXx2hUIh//vkHenp62LlzJ2bMmIGnT5/if//7Hxf7r4iZmRnCw8PRrl07jBw5EmvXrq3TY/KXhws+Y+yrEhYWht69e2PatGnQ1dXF7du3sWvXLmhoaEg7GpOCdu3aITg4GHZ2dnBycoKlpSUyMzOlHatacMFnjH0VUlJSMH36dBgZGeHly5dwd3dHUFAQevToIe1oTMqUlJTg7u6OP/74AxcuXICRkRGePHki7VhVjgs+Y6xeEwqFcHV1RceOHXHgwAEsWrQIUVFRmDRpEg+Dy0QEAgF++uknXL16Fenp6ejVqxfOnDkj7VhVigs+Y6zeioqKwsCBAzFr1ix0794dDx48wObNm6u9cRSru/r374/bt2+jc+fOGDNmDP744w9pR6oyXPAZY/VOfn4+nJ2d0a1bNzx48AB79uzBtWvX0KlTJ2lHY3VAq1atEBAQAEtLS8yfPx9OTk71Ykhe7pbHGKtXQkNDMWPGDERERMDKygo7duxA8+bNpR2L1TGKioo4fvw4HBwcsHbtWrx58wY7d+6s02MzcMFnjNUL2dnZWLFiBXbs2AEtLS2cO3cOFhYW0o7F6jA5OTm4ublBXV0dmzdvxtu3b3HgwIE623WTCz5jrM7z9fXFjBkz8PLlS8yePRsbNmzg6/SsSggEAvz222/Q1NTE0qVLkZGRgZMnT0JZWVna0Sqt7p6bYIx99bKzszF79myYm5tDSUkJQUFBcHFx4WLPqtySJUvg5uYGX19fDB48GOnp6dKOVGlc8BljdVJQUBC6d++Ov//+Gz///DPu3LkDY2Njacdi9dj06dNx/PhxhIeHo1+/fkhKSpJ2pErhgs8Yq1Py8vKwZMkS9OvXD0KhEH5+fti6dSsaNmwo7WjsKzB27Fh4e3vjxYsXMDY2RmxsrLQjVRgXfMZYnXH37l0YGBhg8+bNmDFjBu7fv4/+/ftLOxb7ypiYmODatWvIyMiAqakpXr16Je1IFcIFnzFW6xUWFmLt2rXo1asX3r59C29vb+zevRuqqqrSjsa+UoaGhrh06RJSUlJgZmaGtLQ0aUcqFxd8xlit9vz5cxgbG8PJyQnW1tZ4+PAhhg4dKu1YjKFXr17w9PRETEwMhgwZUutvusMFnzFWax06dAg9evTA06dPcfz4cXh4eEBdXV3asRgTGTBgAE6ePIn79+9j5MiRyMnJkXakUnHBZ4zVOllZWZg0aRImTZqE7t274/79+7CyspJ2LMYkGj58ODw8PBAcHIwxY8bgw4cP0o4kERd8xlitEhoaih49euDw4cP49ddf4efnhzZt2kg7FmNlsra2hqurK3x8fGBnZ4fCwkJpRyqBCz5jrFYQCoXYuHEj+vbti8LCQly/fh1OTk6QlZWVdjTGKmTatGnYvn07Tp06hRkzZkAoFEo7khgeWpcxJnWJiYmYPHkyrl27Bmtra+zevRuNGzeWdizGKm3+/PnIzMzE6tWroaqqij/++AMCgUDasQBwwWeMSdmlS5cwceJE5ObmYu/evZg6dWqt+YJk7HM4OTkhKysL27Ztg7q6OlavXi3tSAD4lD5jTEoKCwuxYsUKDB06FFpaWrhz5w7++9//crFndZ5AIMCWLVswZcoU/Prrrzhy5Ii0IwHgI3zGmBQkJSXB1tYW/v7+mDZtGnbu3MlD47J6RSAQYPfu3Xj+/DmmTp0KHR0d9OrVS6qZ+AifMVaj/Pz80KNHD4SGhmL//v3Ys2cPF3tWLykoKODUqVNo0aIFRo0ahYSEBKnm4YLPGKsRQqEQzs7OMDU1RZMmTRAWFgZ7e3tpx2KsWn3zzTfw9PREdnY2LCws8P79e6ll4YLPGKt2aWlpGD58OFasWAEbGxvcunULXbt2lXYsxmpE165dcfToUdy7dw/29vZS667HBZ8xVq2KB9K5du0adu3aBQ8PD6ioqEg7FmM1avjw4di8eTNOnToltVb7XPAZY9XG1dUVP/zwA+Tl5RESEgIHBwduhc++Wj///DOmTp2KtWvXSqXlfo0X/Js3b6J///5QVVVFmzZtsH79+jJPb9y4cQPm5uZQV1eHuro6TExMEBgYWIOJGWOVlZeXhxkzZmDWrFkYNGgQwsPD0bNnT2nHYkyqBAIBdu3ahb59+2Lq1KkICwur0dev0YJ/69YtDBgwABYWFkhMTISHhwd27tyJVatWSVz+7t27GDBgAL777js8efIEkZGR+M9//gMTExOEhobWZHTGWAXFx8ejX79+2LNnD5YvX44LFy7wHe4Y+z8NGjTA6dOnpdJyX0BEVFMvZmZmBkVFRXh6eoqmeXh4YObMmUhKSoKamprY8osXL8a5c+fw9OlTseldu3bF4MGDsW3btjJfz8DAAOHh4VX3BhhjZfL394e1tTXy8vJw4MABWFpaSjsSY7XSw4cP0bt3b+jq6iIwMBDKyspVst2y6l6NHeFnZ2fDz88PkyZNEps+duxYABDbCSimrq6OwsJC/HufpKioCM2aNau+sIyxSiEibNu2DaamptDQ0EBYWBgXe8bKUNxy38jICAoKCjXymjVW8J89e4aioiLo6emJTVdUVETr1q0RExNTYh0HBweoqalhxowZSE9PR0ZGBn766Se0bt0ac+bMqanojLEyvH//Hra2tli4cCFGjRqFsLAw6OvrSzsWY7Xe8OHDsWvXLsjLy9fI69XY0Lo5OTkAAA0NjRLzNDQ0kJaWVmJ6kyZN4OPjg6FDh2LYsGGQk5ODgoIC9u7dW2q3HldXV7i6ugIAUlNTq/AdMMb+LS4uDqNGjcKDBw+wYcMGLF26lFvhM1ZL1dgRvqamJgAgPT29xLysrCzR/E89ePAA33//PX799VeEhIQgMDAQixcvhrGxMS5fvizxdWbOnInw8HCEh4fjm2++qdo3wRgTuX79OgwMDPDixQt4e3tj2bJlXOwZq8VqrOC3atUK8vLyiI6OFpuen5+PmJgYtGvXrsQ6ixcvxrBhwzBy5EjRtCFDhuDHH3/EggULqj0zY0wyV1dXmJiYiK7XDxkyRNqRGGPlqLGCr6SkhBEjRuDw4cNi0y9evAgiEivqxRISEiT20c/Pz0dKSkq1ZWWMSVZQUIC5c+di1qxZMDU1xc2bN0u0y2GM1U412g/f0dERXl5e2LFjB969e4eQkBDMnTsX8+bNQ6NGjfDnn39CX18fiYmJAABbW1v8888/+Pvvv/HmzRukpKTgn3/+wbZt2zB16tSajM7YVy8tLQ3m5uZwcXHBokWL4OXlhcaNG0s7FmOsgmqs0R4AGBoawtvbG46OjliyZAmaNm0KBwcHODo6Avj4hRIVFYWCggIAwC+//IJmzZrBzc0NS5YsARFBT08PmzdvxqxZs2oyOmNftYcPH8LCwgKvXr2Cu7t7ie61jLHar0YH3qlpPPAOY1/u3LlzmDhxIlRVVXHmzBkYGRlJOxJjrBS1YuAdxljdQkTYvHkzLC0t0alTJ9y6dYuLPWN1GBd8xlgJ+fn5mD59OpYsWQIrKysEBASgZcuW0o7FGPsCXPAZY2Levn0Lc3Nz/PPPP1i5ciWOHDmChg0bSjsWY+wL1WijPcZY7fb06VOMGDECcXFxOHToEOzs7KQdiTFWRbjgM8YAAH5+fhg7dizk5OTg5+eHPn36SDsSY6wK8Sl9xhj27NmDwYMHo0WLFggNDeViz1g9xAWfsa9YUVERFi9ejBkzZsDU1BQ3btyQOMw1Y6zu41P6jH2lcnJyMHHiRJw5cwZz587F9u3bISfHXwmM1Vf8183YV+j169ewsLDArVu38Pvvv2PevHnSjsQYq2Zc8Bn7yjx58gTDhg3D69evcebMGYwaNUrakRhjNYALPmNfEX9/f1haWkJBQQEBAQEwNDSUdiTGWA3hRnuMfSUOHTok1hKfiz1jXxcu+IzVc0SENWvWYNKkSejbty+Cg4PRtm1bacdijNUwPqXPWD2Wn5+PWbNmYf/+/Zg8eTLc3NygoKAg7ViMMSngI3zG6qmsrCwMHz4c+/fvx+rVq7F//34u9ox9xfgIn7F6KDExEcOGDcPjx4+xb98+TJkyRdqRGGNSxgWfsXrm0aNHGDp0KNLT03HhwgUMHjxY2pEYY7UAn9JnrB4JCAhA3759UVBQgOvXr3OxZ4yJcMFnrJ44fvw4Bg8ejObNm+PmzZvo0aOHtCMxxmoRLviM1QPbtm2DjY0NevXqheDgYGhra0s7EmOsluGCz1gdVlRUhPnz52PhwoUYN24cLl++DHV1dWnHYozVQlzwGauj8vLyMH78ePzxxx+YP38+jh07BkVFRWnHYozVUtxKn7E6KCMjA6NHj0ZAQAC2bNmChQsXSjsSY6yW44LPWB3z6tUrDBkyBJGRkfDw8ICtra20IzHG6gAu+IzVIZGRkTA3N8fbt2/h7e0NU1NTaUdijNURXPAZqyNCQkIwYsQIyMnJISAgAD179pR2JMZYHcKN9hirA7y8vGBiYgJ1dXXcuHGDiz1jrNK44DNWy+3duxejR49Gly5dEBwcDB0dHWlHYozVQVzwGauliAjOzs6YPn06TE1N4efnh6ZNm0o7FmOsjuJr+IzVQkKhED/99BNcXFwwceJE7N27l29tyxj7InyEz1gt8+HDB9ja2sLFxQULFy7EgQMHuNgzxr4YH+EzVou8e/cOY8aMwZUrV/Dbb79h8eLF0o7EGKsnuOAzVkukpqZi2LBhuHv3Lvbt24cpU6ZIOxJjrB7hgs9YLfDixQsMHjwYCQkJOHv2LEaMGCHtSIyxeoYLPmNSFhERAXNzc+Tm5uLKlSvo06ePtCMxxuohbrTHmBQFBQWhX79+EAgECAwM5GLPGKs2XPAZkxIvLy+YmZmhWbNmuHHjBrp27SrtSIyxeowLPmNS4O7ujtGjR6Nr164IDAyEtra2tCMxxuo5LviM1bBt27bB3t4eAwYMwLVr1/DNN99IOxJj7CvABZ+xGkJE+OWXX7Bw4UKMGzcOFy5cgKqqqrRjMca+EtxKn7EaUFRUhB9//BFubm6YNWsWXFxcICsrK+1YjLGvCB/hM1bN8vLyYG1tDTc3Nyxfvhy7du3iYs8Yq3E1XvBv3ryJ/v37Q1VVFW3atMH69eshFArLXMfHxweGhoZQVFRE8+bN8eOPPyIzM7OGEjP2+d69e4fhw4fj9OnT2L59O9atWweBQCDtWIyxr1CNFvxbt25hwIABsLCwQGJiIjw8PLBz506sWrWq1HUuXbqEiRMnYvny5UhLS8OVK1dw69YtODs712ByxiovNTUVgwYNQkBAANzd3TF//nxpR2KMfcUEREQ19WJmZmZQVFSEp6enaJqHhwdmzpyJpKQkqKmpiS1PRNDV1cWyZcswffp00fT3799DWVm53NczMDBAeHh41b0Bxiro5cuXMDMzw8uXL3HixAkeKpcxViPKqns1doSfnZ0NPz8/TJo0SWz62LFjAUBsJ6BYaGgoYmJiYGVlJTa9IsWeMWmJjIyEsbExkpOT4evry8WeMVYr1FjBf/bsGYqKiqCnpyc2XVFREa1bt0ZMTEyJde7evYvmzZvjzZs3GDduHNq1awcjIyMcPHiwpmIzVinh4eHo27cvCgoKEBAQgB9++EHakRhjDEANFvycnBwAgIaGRol5GhoaSEtLKzH97du3KCgowMSJE2Fvbw9fX19MmDAB06dPx6FDhyS+jqurKwwMDGBgYIDU1NSqfROMleHatWsYOHAgVFVVERQUhO7du0s7EmOMidRYwdfU1AQApKenl5iXlZUlmv8pBQUFpKWlYefOnRg5ciR0dXUxf/58zJo1Cxs2bJD4OjNnzkR4eDjCw8N5BDNWY86cOYOhQ4dCW1sbwcHB6NChg7QjMcaYmBor+K1atYK8vDyio6PFpufn5yMmJgbt2rUrsU779u0hLy+Pnj17ik3v0aMH4uLiqjUvYxX1zz//YNy4cejZsyeuX78OLS0taUdijLESaqzgKykpYcSIETh8+LDY9IsXL4KIMHLkyBLrDBo0CDIyMrh586bY9AcPHqBjx47Vmpexiti6dSumTZsGExMTXL58Gerq6tKOxBhjEtVoP3xHR0d4eXlhx44dePfuHUJCQjB37lzMmzcPjRo1wp9//gl9fX0kJiYCAJo0aYIVK1bAxsYG165dw5s3b7Bv3z789ddfWLFiRU1GZ0xM8bj4ixYtgpWVFTw9PaGioiLtWIwxVqoaHUvf0NAQ3t7ecHR0xJIlS9C0aVM4ODjA0dERAJCWloaoqCgUFBSI1lmxYgWUlZUxY8YMxMfHo127dti9ezcsLS1rMjpjIkVFRZgzZw52796NmTNn4q+//uKhchljtV6NDrxT03jgHVbV8vPzMWnSJBw/fhyOjo5wdnbmoXIZY7VGWXWP75bHWAW9f/8eY8eOhY+PDzZv3oxFixZJOxJjjFXYF1/DDw4OroocjNVq6enpMDMzw+XLl7Fnzx4u9oyxOqfcgm9tbS1xupOTE7KzszF06NAqD8VYbZKUlIT+/fvj9u3bOHHiBKZNmybtSIwxVmnlFvwrV64gPj4eEyZMQH5+PgBgx44dOH78OIgI9bgJAGOIiYlB3759ERMTgwsXLmDMmDHSjsQYY5+lQqf01dXVkZaWhqlTp+LVq1dYs2YNTpw4AVVVVW6wxOqtiIgI9O3bFxkZGbh69SpMTU2lHYkxxj5bhQq+srIyzp8/j7i4ONy/fx/r16/HvXv38Pr16+rOx5hUhISEoH///hAIBLh+/TqMjIykHYkxxr5IhVvp37t3D1evXsWLFy+wYsUKZGdnw9jYuDqzMSYVvr6+sLS0hJaWFnx9fSUO+8wYY3VNhVvp//XXX+jTpw+ioqKwdOlSaGlpoX379nwNn9UrJ06cwIgRI6Crq4ugoCAu9oyxeqPMgi8jI4PMzEy4uLhgx44d+Omnn+Dg4AAlJSVcv34dsrKyyMnJgaysLGRkZHi0MVanubm5wcbGBr169YK/vz+aNWsm7UiMMVZlyiz4L1++hKqqKmJjY9GzZ09ERUVBXl4eq1evhpqaGl6+fImGDRvi5cuXiI+Px8uXL2sqN2NVatOmTZg5cyaGDBkCX19fNG7cWNqRGGOsSpV5Db9Vq1aQkZHBli1b0KhRIxw8eBDBwcFo0qQJtLS00LJlSwgEArRs2bKm8jJWpYgIS5cuxebNmzFhwgTs378fCgoK0o7FGGNVrsKN9qytrTFkyBA8e/YM3t7ecHFx4ev3rE4rKirCrFmzsHfvXsyePRs7d+6EjEyN3kCSMcZqTIW/3aKjozFs2DBoa2vDy8sLBQUF3Aef1VkfPnyAjY0N9u7dixUrVuDPP//kYs8Yq9cqdIT/5s0bTJkyBceOHUO7du2wb98+DBkyBGZmZlz0WZ2TnZ0NS0tLXLlyBdu3b8f8+fOlHYkxxqpduQXfxMQEGhoaCA0NhY6ODgDAyMgITk5OEAgEfFqf1Slv3rzBsGHDcPv2bezfvx/29vbSjsQYYzWi3IJ/4sQJABAV+2ILFiwAAFy8eLEaYjFW9RISEjB48GDExMTg9OnTsLCwkHYkxhirMeVetIyJicHTp0/x/v17nD9/vsT8vn37VkswxqrS06dPYWxsjISEBPj4+HCxZ4x9dco9wjc2NkaTJk2wdetWzJ8/HxYWFhg1ahTi4+NLbkxODmFhYdUSlLHPdefOHQwZMgQA4O/vj549e0o5EWOM1bwKNdp7/PhxiecXLlyAUCjEiBEjcOHCBZibm8PX17daQjL2uQICAjBy5Eg0adIEly9fhp6enrQjMcaYVJRb8D9thZ+eno7x48cjIyND9MWpoKCAjh07Ql5enr9MWa1y/vx5WFtbo3379vD19UWrVq2kHYkxxqSmzGv4jo6OyM7OFj1XVVWFjY2NxK543D2P1Sbu7u4YM2YMvvvuO1y/fp2LPWPsq1dmwW/QoIHYc1lZWVhaWkJNTQ1aWlpo0aIFoqOj0aJFC8TGxkJLS6tawzJWEdu2bYO9vT0GDBiAq1evQlNTU9qRGGNM6so8pb969Wq4uroCAE6ePAlTU1MAQEREBIRCYfWnY6wSiAi//PILNm7ciHHjxuHQoUMldloZY+xrVaFGe5mZmdi/fz+uX7+Ohw8fQlVVtdRlueEek4aioiI4ODhgz549mDVrFlxcXPh2zYwx9olyCz4RQV1dHaNGjUJKSgquXr2KnTt3wt/fH5MnT4a9vT3k5Cp8Dx7GqlxeXh7s7Oxw+vRprFixAmvWrOE2JYwx9i/lVuqVK1eiT58+6N69OxISEnD+/HnExMTgzJkz2L9/P/766y8kJyfj6tWrNZGXMTFZWVkYPXo0/Pz88Pvvv2PevHnSjsQYY7VSmQU/PDwcDRo0wJAhQzBixAgYGhrim2++ga2tLfT19dG0aVP07dsXXbp0qam8jImkpKRg6NChuH//Pg4ePIiJEydKOxJjjNVaAirj7je9evVC//794ejoiLFjx+Lp06dwdHTEggULIC8vX+LGOQKBADk5OdUeuqIMDAwQHh4u7RisGsTFxcHMzAzx8fE4efIkhg8fLu1IjDEmdWXVvTK75QUHByM9PR0mJiZ49uwZNm/ejFOnTqFPnz7IyMjA+fPncf/+fWRnZyM3N7dWFXtWfz18+BB9+vRBamoqLl++zMWeMcYqoMyCLy8vj65du0JFRQX37t2Dra0tzpw5g9evXyMrKwtubm6wtbXFN998gz///LOmMrOvWHBwMH744QcIhUIEBATwzZsYY6yCyjylDwD5+fkgIlF/5qKiIjx79gwdO3YULfP+/XsUFRUhJCQE5ubm1Zu4EviUfv3i5eUFKysrtG7dGj4+PmjXrp20IzHGWK3y2af0i1du0KABEhIS8PLlSyQmJqJhw4ZITEwULaOsrAw1NTVYWlpWXWrGPrF//36MHj0aXbp0QVBQEBd7xhirpHK75UVGRgIAv2ju2wAAIABJREFUvv32WzRp0kTUUO/9+/dwcXFBcnIyrK2t0axZsxKN+BirCps3b8aSJUtgamqK06dPlznwE2OMMcnKPcL/VExMDGJjYxEbGwsigpycHC5evAg9Pb1Sb6rD2OcSCoVYtGgRlixZAhsbG3h5eXGxZ4yxz1Spgv8pgUAAS0tLeHt7Iz4+XjTOPmNVoaCgAFOmTMHWrVsxd+5cHD58mMfFZ4yxL/DFY+Lm5OTg/Pnz6NSpU1XkYQzv37+HtbU1vL29sXbtWixfvpzPHjHG2Beq1BF+fHw8Xr58ibi4OADA4cOH0apVK7i7uyM7O7taArKvS1paGkxMTHDp0iXs3r0bK1as4GLPGGNVoEI3zwGA1q1bo1+/fqIv39atW6NXr164c+cO2rZtW60h2dfhxYsXGDJkCOLi4nDq1CmMHj1a2pEYY6zeKLfgL126FHFxcXjw4AEA4MaNG4iOjoa9vT0AIDo6Gv369YObmxu30mef7f79+xg6dChyc3Nx+fJlHlCHMcaqWLmn9NetW4dNmzaJnt+9exfnzp0DANy5cwe9e/dGv3790LFjR+Tm5lZfUlZv+fn5oV+/fpCVlUVQUBAXe8YYqwYVarQXGhqKJUuWAPhY8BMSErBu3Tr88ccfcHR0xMKFC6s1JKu/Tpw4gYkTJ6JDhw64dOkSWrduLe1IjDFWL5V5hH/8+HE8ePAADRo0gKamJjQ0NKCsrAwZGRmkp6djwIAB2Lp1K7p164bz58/XVGZWT+zcuRM2Njbo1asXAgMDudgzxlg1KvMI//jx4/D394e8vDyEQiHmzJkDFRUVyMjIYOvWrQA+jq2/d+9eODg44MqVK9ixY0eNBGd1FxFh+fLl2LBhA0aNGoUjR46gYcOG0o7FGGP1WplH+CdPnkRaWhqOHz+OgIAALFiwAADEGufJyspi5syZCAoKwoULF3D9+vUyX/DmzZvo378/VFVV0aZNG6xfvx5CobBCYQMDAyEvL4/Vq1dXaHlW+xQUFGDq1KnYsGEDZs6ciZMnT3KxZ4yxGlCha/g//PADLl68CADIysrCuHHjSizTvn17PH78uMzR0G7duoUBAwbA2dkZnp6euH//PqytrZGbm4u1a9eWmSElJQV2dnY8wE8d9u7dO4wbNw6+vr5YvXo1nJycuI89Y4zVkHJvj1uVzMzMoKioCE9PT9E0Dw8PzJw5E0lJSVBTU5O4nlAoxODBg/H/2rv3uJrvPw7gr24kXaxiUZnlUni4x2r4heRe6OrWEpOmlhhGMzXDtMuDJUwuY6qHQnO35ZZrpUYuGymJlZqOolrIOZ3fHx7OY0el+/lW5/V8PM7jsT7f7/d835+R1/f6+QwYMAD//PMPOnXqVK2zfE6P23jk5ORg/PjxuH79OsLCwjBr1iyhSyIianbqND1ufSkuLsaZM2fg7u4u1+7k5AQAcgcBbwoKCoJIJMLKlSsbtEZqGLdv34a1tTXu3LmDw4cPM+yJiARQ57H0qys9PR0SiQTdunWTa9fU1ISpqSkyMjIq3O73339HSEgIkpKSqjV5SlhYGMLCwgAAeXl5dS+c6uTixYtwcHCAuro64uLiYGlpKXRJRERKSWFn+CUlJQAAAwODcssMDAwgEonKtWdlZWHGjBkICwtD165dq7UfLy8vJCcnIzk5GW3btq1b0VQnMTExsLW1hYGBAeLj4xn2REQCUljgGxoaAgAKCgrKLSssLJQtf00sFsPNzQ0uLi5wdXVVSI1UfzZs2ABnZ2f0798fly5dgpmZmdAlEREpNYUFvomJCTQ0NJCWlibXXlpaioyMDLz//vty7VlZWbh06RK2b98OTU1N2Wf37t1YtWpVuYf/qHEoKyvDkiVL4OfnBwcHB5w8ebLcwRwRESmewu7ha2lpYcKECYiMjJQ9qAcAx48fh1Qqhb29vdz6xsbGuHXrVrnvWbZsGYyNjeHr6wsTE5MGr5uq7/nz5/Dw8EB0dDQ++eQTbNiwAWpqakKXRUREUOAZPvAqrI8cOYKQkBAUFRUhPj4evr6+mD9/PvT09BAaGgoLCwtkZ2dDQ0MDFhYW5T56enowNDSEhYUFtLW1FVk+vcXjx48xcuRIREdH49tvv8XGjRsZ9kREjYhCA3/gwIE4duwYwsPD0bZtW7i5ucHb2xurV68GAIhEIqSmpuLly5eKLIvq6O7du/jwww+RnJyMqKgoLF68mAPqEBE1MgodeEfROPBOw0tISICDgwMkEgkOHjzIqW2JiATUKAbeoebn119/xfDhw6Gjo4P4+HiGPRFRI8bAp1pZv349nJyc0LdvXyQkJJQbUImIiBoXBj7ViEQiwfz587FgwQJMnjwZp0+f5gBHRERNAAOfqq24uBiTJ09GSEgI/P39ER0dzaltiYiaCIW9h09NW1ZWFuzt7XH9+nWEhobCx8dH6JKIiKgGGPhUpStXrsDe3h6FhYU4cuQIxo4dK3RJRERUQ7ykT2918OBBDB06FGpqarh48SLDnoioiWLgU4WkUinWrVuHyZMno2fPnrh8+TJ69+4tdFlERFRLDHwqRywWY968eVi4cCEcHR0RFxcHIyMjocsiIqI6YOCTnKdPn2L8+PH46aef8PnnnyM6OhpaWlpCl0VERHXEh/ZI5u7du7C3t0daWhq2bt2Kjz/+WOiSiIionjDwCQBw9uxZODo6QiqVIjY2FsOHDxe6JCIiqke8pE/Ytm0bRo4ciXbt2uHy5csMeyKiZoiBr8TEYjEWLFiAOXPmwNbWFvHx8ejSpYvQZRERUQPgJX0l9fTpU0yZMgW//fYb/Pz88MMPP0BdnX8diIiaK/4Lr4T++3Deli1b4OXlJXRJRETUwBj4SiYuLg5OTk4AwIfziIiUCO/hKwmpVIpNmzbBzs4O7dq1Q2JiIsOeiEiJMPCVwIsXL+Dl5QUfHx+MHj0aCQkJfDiPiEjJMPCbudzcXIwYMQLbtm1DQEAADh48CD09PaHLIiIiBeM9/GYsOTkZkyZNQkFBAaKiouDq6ip0SUREJBCe4TdT4eHhGDp0KNTV1XHx4kWGPRGRkmPgNzMSiQSLFy+Gu7s7PvjgAyQlJaFv375Cl0VERALjJf1mJD8/H1OnTkVsbCx8fHywbt06aGhoCF0WERE1Agz8ZuLq1atwdHTEw4cPOdMdERGVw0v6zcCuXbvw4YcfQiwW4/z58wx7IiIqh4HfhJWWlsLHxwczZ86EtbU1/vjjDwwaNEjosoiIqBFi4DdRDx8+xLBhw7Bp0yYsWrQIsbGxaNeundBlERFRI8V7+E3QuXPn4OrqiuLiYr5fT0RE1cIz/CZEKpUiJCQEtra20NXVRWJiIsOeiIiqhYHfRBQVFWHKlCmYP38+xo8fj6SkJPTs2VPosoiIqIlg4DcBN27cgKWlJfbt24dvvvkGMTExHA+fiIhqhPfwG7mdO3di3rx50NPTw+nTp2FjYyN0SURE1ATxDL+RevbsGWbPng1PT09YWVnh6tWrDHsiIqo1Bn4jlJaWBisrK+zYsQNffPEFTpw4ASMjI6HLIiKiJoyX9BuZffv2YdasWdDQ0MCxY8cwduxYoUsiIqJmgGf4jcTz58/x6aefwsXFBT169MDVq1cZ9kREVG8Y+I1AamoqrK2tERoaCn9/f5w7dw4dO3YUuiwiImpGeElfYL/88gvmzZsHTU1NHD58GBMmTBC6JCIiaoZ4hi+QoqIiuLu7w8PDA5aWlrh27RrDnoiIGgwDXwBXrlxB//79ERkZiaCgIJw6dQrGxsZCl0VERM0YA1+BpFIpfvzxR1hbW+PZs2c4c+YMAgMDoaamJnRpRETUzCk88BMSEmBjYwMdHR107NgRa9asQVlZWaXr5+XlYe7cuTAxMYGOjg6sra1x6tQpBVZcPx49egQHBwf4+/tj9OjRuHbtGv73v/8JXRYRESkJhQZ+UlIShg0bBgcHB2RnZyMiIgIbNmxAYGBgheuLxWKMGTMG9+/fx8mTJ3H//n24uLhg9OjRSExMVGTpdXLs2DH06tULJ06cwI8//oiDBw/CwMBA6LKIiEiJqEilUqmidmZnZyd7Gv21iIgIeHl5IScnB7q6unLrHzx4EJ6ennjw4AG0tbVl7SNHjoSZmRnCwsLeuj9LS0skJyfXbydqoKSkBIsXL8amTZvQq1cvREREoFevXoLVQ0REzdvbck9hZ/jFxcU4c+YM3N3d5dqdnJwAQO4g4LWJEyciJSVFLuwBQEVFBYWFhQ1XbD24cuUKBgwYgE2bNmHhwoW4fPkyw56IiASjsMBPT0+HRCJBt27d5No1NTVhamqKjIyMCrd7cwCa/fv349SpU7IDhcZGIpFg7dq1+OCDD1BUVISTJ0/ihx9+gKamptClERGRElNY4JeUlABAhfeuDQwMIBKJ3rp9WVkZVq1aBTc3NwQEBMDFxaXC9cLCwmBpaQlLS0vk5eXVvfAauH//PkaMGIFly5Zh0qRJuH79OmxtbRVaAxERUUUUNtKeoaEhAKCgoACmpqZyywoLC2XLK5KXl4cpU6YgNTUVhw4dwrhx4ypd18vLC15eXgBe3ctQBKlUil27dmH+/PkoKyvDzp078dFHH0FFRUUh+yciIqqKws7wTUxMoKGhgbS0NLn20tJSZGRk4P33369wu5ycHAwZMgTvvPMObt68+dawF0JOTg4cHBzg6emJPn364Nq1a/Dw8GDYExFRo6KwwNfS0sKECRMQGRkp1378+HFIpVLY29uX20YsFsPJyQmDBw/G3r170aZNG0WVWyWpVIrIyEj07NkTJ0+exLp16xAXFwczMzOhSyMiIipHoe/hL1u2DEeOHEFISAiKiooQHx8PX19fzJ8/H3p6eggNDYWFhQWys7MBANu3b0dubi5CQ0MhkUggFotlH4lEosjS5Tx69AhOTk6YPn06zM3NkZKSAn9/f6iqcuBCIiJqnBSaUAMHDsSxY8cQHh6Otm3bws3NDd7e3li9ejUAQCQSITU1FS9fvgQAxMfH4969e2jdujU0NDTkPp07d1Zk6TJ79+5Fz549cfToUQQHB+PChQswNzcXpBYiIqLqUujAO4pWnwPvPH78GD4+PoiKioKlpSV27dqFHj161Mt3ExER1YdGMfBOUxcVFYWYmBisWrUK8fHxDHsiImpSFPZaXlPn7e0NW1tbXr4nIqImiWf41aSqqsqwJyKiJouBT0REpAQY+EREREqAgU9ERKQEGPhERERKgIFPRESkBBj4RERESoCBT0REpAQY+EREREqAgU9ERKQEGPhERERKgIFPRESkBBj4RERESoCBT0REpAQY+EREREqAgU9ERKQEGPhERERKgIFPRESkBBj4RERESoCBT0REpAQY+EREREqAgU9ERKQEGPhERERKgIFPRESkBBj4RERESoCBT0REpAQY+EREREqAgU9ERKQEGPhERERKgIFPRESkBBj4RERESoCBT0REpAQY+EREREqAgU9ERKQEGPhERERKgIFPRESkBBj4RERESoCBT0REpAQY+EREREqAgU9ERKQEFB74CQkJsLGxgY6ODjp27Ig1a9agrKys0vULCgrg7e0NY2Nj6OrqYvLkycjOzlZgxURERE2fQgM/KSkJw4YNg4ODA7KzsxEREYENGzYgMDCwwvXFYjHGjh2LtLQ0XLx4Ebdv34aqqipGjBiBkpISRZZORETUpKlIpVKponZmZ2cHTU1NHD58WNYWEREBLy8v5OTkQFdXV279iIgIzJw5E3///TeMjIwAACUlJejQoQN++OEHzJ49+637s7S0RHJycv13hIiIqBF6W+4p7Ay/uLgYZ86cgbu7u1y7k5MTAMgdBLx26NAh2NnZycIeALS0tODk5IQ9e/Y0bMFERETNiMICPz09HRKJBN26dZNr19TUhKmpKTIyMsptk5qaWm59AOjatWuF6xMREVHF1BW1o9f33A0MDMotMzAwgEgkqnCbmqwPAGFhYQgLCwMA3L59G5aWlnUpWzB5eXlo27at0GU0iObaN/araWG/mhb2q3oyMzMrXaawwDc0NATw6ql7U1NTuWWFhYWy5W9uU1BQUK69svUBwMvLC15eXvVQsbCa8/MHzbVv7FfTwn41LexX3Snskr6JiQk0NDSQlpYm115aWoqMjAy8//775bYxMzMrtz7w6sy9ovWJiIioYgoLfC0tLUyYMAGRkZFy7cePH4dUKoW9vX25bVxdXREbGyt3+f758+c4evQo3NzcGrxmIiKi5kItKCgoSFE7MzMzw9KlS6Gnp4cePXrgypUr8PT0hJeXF8aPH4/Q0FB89NFHmDx5MnR1ddG5c2ccOXIEx48fh42NDUpKSjBv3jyIRCJs3LgRLVq0UFTpghgwYIDQJTSY5to39qtpYb+aFvarbhT6Hj4AnDp1CsuWLcP169fRrl07zJ07F8uWLYOqqiqCgoLw1Vdf4d69e+jUqRMAQCQSYcGCBThy5AgkEglsbW0REhJS7jkAIiIiqpzCA5+IiIgUj5PnEBERKQEGfiNTWlqK5cuXw9TUFJqamujVqxd27twpdFl1VlZWhvXr16Nnz57Q0tLCe++9Bx8fH+Tl5QldWo3k5eVh+/btGDRoECwsLMotf/bsGQICAtCpUye0bt0aI0eOxF9//SVApTVTVb9KSkqwZMkSWb/69u3bJEa7rKpf/3Xnzh3o6upi5syZiimuDqrTr6SkJAwfPhxaWlowMDDAtGnT8PDhQwVXWjNV9evPP/+Ek5MT2rVrB11dXVhbW+PgwYMCVFozcXFxGDZsGPT09NChQwe4u7vjn3/+kVtHERPFMfAbGU9PT1y6dAknTpyASCRCQEAA/Pz8cPXqVaFLq5PPP/8cK1euxHfffYfc3FwcPHgQiYmJGD16NCQSidDlVUt8fDxMTU2xc+dOqKmpVbjOjBkzcOTIERw9ehQPHjyAubk5bGxskJubq+Bqq686/ZoyZQpOnz6NmJgYZGdn47PPPoOHhwf27dun4Gqrrzr9eu3Zs2dwdnZG586dFVRd7VWnX9euXcPo0aPh7u6O3NxcJCUloaCgAP7+/gqutvqq6ld2djYGDx4MLS0tJCcn4/79+3B1dYWjoyNiYmIEqLh64uPjMXbsWEycOBEZGRk4e/YscnJyMHr0aIjFYgAKnChOSo3G2bNnpdra2tLHjx/LtRcXFwtUUf0xNDSUrlq1Sq4tKSlJCkB67do1gaqqmRcvXkifPn0qlUql0sDAQKm5ubnc8gsXLkgBSJOTk2VtEolEam5uLl2+fLlCa62JqvqVkpIiVVNTk96/f1+uffbs2VI7OzuF1VlTVfXrv2bOnCl1dXWVBgYGSj08PBRUYe1Up1/Dhw+XfvHFF3JtJSUlUolEopAaa6OqfoWGhkq1tLSkpaWlcu3jx4+XTp48WWF11tSkSZOkc+bMkWv7+++/pQCkFy9elEqlUml4eLhUXV1dmpOTI1vn33//lerp6Um3bdtWb7XwDL8RiYyMhJ2dHfT19eXaW7duLVBF9UdfX192NPuaWCyGmppapaMmNjYtWrQoN6Pjfx06dAjdu3eXe8VGVVUV06dPb9SXv6vqV58+fZCRkYGOHTvKtauoqKCwsLChy6u1qvr12o4dO3DixAls3LhRAVXVXVX9ysnJwZkzZ+Dq6irX3qpVK6iqNt5/8qvql76+PsrKyspdERSLxXj33Xcburxai4iIwJo1a+TaVFRUAED2+6OoieIa75++Erp69SosLCywZ88efPDBB+jUqROcnJyQmpoqdGl1tm7dOoSGhiIqKgpSqRRXr16Fr68v1q1bhw4dOghdXr1422RPmZmZkDbhF2LeDPtLly4hPDxcNttlU3X9+nX4+/sjKiqqyRx4ViUlJQUA8M4778DT0xNmZmbo27cv1q1b16T/Djo7O2Pw4MFwdXVFdnY2SkpK8M0330AkEmHFihVCl1cpLS0tub9bYrEYfn5+aNu2LYYMGQJAcRPFMfAbkfz8fBw9ehQHDhzAli1bEBMTA7FYjKFDhyI/P1/o8upk3Lhx2L59O+bOnQs3NzdMmDABjo6OzWLeg9feNtmTWCzGkydPBKiq/m3btg22traYMmUKFi5cKHQ5tVZYWAhnZ2csX74cgwcPFrqcepOfnw9VVVXMmDEDI0eORGxsLBYsWICgoCCsXr1a6PJqTUNDAwcOHMCLFy9gZ2cHZ2dnREdH4+eff0b79u2FLq9aHj58CFtbW5w/fx6HDh2CtrY2gNpNFFcbDPxG5PXIgZGRkejbty/69++PqKgoqKioYPv27QJXVzfBwcFYs2YN/vzzT0RHRyM9PR2PHj3C4MGDUVxcLHR59eJtkz2pq6ujTZs2AlRVf/79919MnToVS5YswebNm/Hzzz9X+TBcY/bxxx+jW7duWLx4sdCl1KsWLVqgrKwMfn5+mD59Orp06QIPDw8EBgYiODi4yZ7lZ2VlwdLSEs7Ozvjrr79w7NgxbNmyBRMnTsQvv/widHlVio2NRe/evaGjo4OUlBRYWVnJltVmorjaYOA3ImZmZhg0aJDcfTZNTU1YWFjg/v37AlZWN1lZWQgICMCGDRtgbGwM4NX9xPXr1+PJkyf46aefBK6wfrxtsqf33ntPdt+uKSoqKsKoUaPw8OFD3Lhxo0m8ulaVvXv3IjY2Fq1atYKmpiY0NTWxatUq7N69G5qamggNDRW6xFoxMzMDALlAAYB+/fqhuLgYjx8/FqKsOvv666/RuXNnzJkzR9Y2aNAgrFy5Ep9++inKysoErO7toqOj4ejoiODgYBw5cqTcbUxFTRTHwG9Exo0bh4sXL8r9xS0tLUVqairMzc0FrKxucnJyUFZWVu4X8vUDOI8ePRKosvrl6uqKmzdv4saNG7I2qVSK/fv3N/nJnmbNmgUdHR3ExsbKDtqaulu3buH69etISUmRfby9veHg4ICUlBRMnz5d6BJrpW/fvmjfvj3OnTsn1379+nXo6+s32WcVsrKyKgz10tJSFBUV4dmzZwJUVbUrV65g9uzZOHDgAGbPnl3hOoqaKI6B34jMmjULqqqqmDZtGjIyMpCZmQkPDw+oq6s36TOqfv36oXv37pgzZw7i4+NRXFyMO3fuwMPDAzk5OZg2bZrQJdaL3r17Y+LEifDw8MCtW7eQn5+PhQsX4sGDB5g3b57Q5dXa77//jtjYWOzatQtqamoQi8Vyn6bKwsKi3MfQ0BB6enqwsLDAO++8I3SJtaKmpobg4GD4+Pjg119/RX5+Pg4dOoTAwEAsX75c6PJqbdq0afj999+xatUq5OTkID8/H/v370dAQABcXFwa7dtMPj4+8PPzw7Bhw8r97rw+gBk3bhx69+6N6dOn48GDB8jJyYGnpydat25dr/8+MvAbkZYtW+LkyZNQV1fHgAED0KNHDxQUFODUqVPQ0dERurxaU1dXx9mzZzF8+HBMmzYNhoaGGDJkCIqLi3H+/Hn07dtX6BLrTWRkJIYMGQIbGxuYmprixo0biIuLa9JnxfHx8SgsLISRkRE0NDTKfajxcXd3R0hICL788ksYGRnh008/RUBAQKMeeKcq06dPx759+3Dy5En06NEDJiYmWLFiBfz8/LB7926hy6tUQkIC1qxZU+HvzsqVKwG8+jfy+PHjaNeuHfr06QNzc3M8f/4cp0+frtcDGU6eQ0REpAR4hk9ERKQEGPhERERKgIFPRESkBBj4RERESoCBT0REpAQY+EREREqAgU+kYLm5uRg9ejSsra3LjYbWUB48eIC7d+8qZF9E1Dgx8IkU7Oeff0ZQUBBOnz5dr+O1VzaWeGJiIm7duoVRo0bh3r179ba/Nx04cAAODg413m7mzJnw9vau0frh4eEAXg232qVLFwDAnj17oKmpCUNDQxgaGkJLSwtr166Vbbdo0SIYGhrKRtXr3LkzLCwsAACdOnVC165dZcuMjIwqHN3y+PHjuHDhQpU1RkdH49q1a9XuE5EiMPCJFKCsrAwvX77Es2fP0KdPH+zatQs7duxA9+7d6+X7MzMzYWZmho0bN5abDS00NBS//PILVq5cKReA9e27777De++912DfDwBdunTB3r174efnBxMTEwwcOBCZmZkwMTFBSUkJnJ2dIRKJIBKJsGTJknLb+/r64vbt27h9+zZOnTolt+z8+fOyZRUNQXvv3j34+/ujZ8+eAF4deIwZM6bCOnv37o2pU6fi6dOn9dBrovrBwCeqR05OTtDR0YGWlhZatmwJdXV1qKioQE1NDS1atICWlha+/PJLeHt7o2vXrggKCgIAhIeHQ0VFpcpPXFxchfs1NTXFokWLEBAQAFtbWzx58kS2bOfOncjMzET79u2xefPmBun3vn37cOnSJYSGhsrVa2BggD///LPe9pOeng4XFxeEhIQgKysLSUlJ6NSpE7KysqClpVXl9mFhYbC0tISlpWW5qxFjxoyRLfvuu+/Kbbt06VLMnTu3WmPsW1hYwMbGBt9++231O0fUwNSFLoCoOQkODsaKFSugrq4OdXV1aGhoyP331q1bERERUeH8AcbGxpUGOgDZ5ec3PXv2DK1atYKvry9GjRqF0NBQ6OnpyZarqanhxIkTaNmypdzUy/Xl8ePHmD9/PgIDA+Hr6ytrv3fvHgYNGqTQSWgKCwtx+/ZtAIBIJIKJiYncci8vL9lBVmZmptwZ+m+//QYjIyMAr66KJCcny5alpaXh8OHDNTpg+uSTTzBkyBAsXbq0Sc+FQc0HA5+oHr2+n1yZpKQkWFtbV7hMXV29yu3fVFxcDAsLC4wdOxZr165Ft27dEBISUm49kUgEJycnnDt3Dq1atZJbFhQUhK+++qrSfaxbt67SSVfEYjGcnZ3Rq1cvrFixQu6AYteuXRg4cGC5ub8r8ttvv2HPnj1wdXWt1kHJokWLEBQUBIlEAjU1NVl7YmKi7HmAzMzMcs8GbNq0Cfv27ZP93K1bNwCAubk5Ro7bNa2kAAAGE0lEQVQcKWvPz8/HqFGjZD8fPnwYlpaW0NfXr7K213r37g1dXV2cOnUKkyZNqvZ2RA2Fl/SJFOTJkyc4fvw4Jk+eXG/fqa2tjYiICFy6dAm9e/eu8EExiUQCT09PmJmZlQt7AAgICEBRURGKiopk27/+uaioCD4+PhXu+8WLF3Bzc0NOTg7Cw8PlgloikWDz5s2YM2dOtfrRpk0bfPbZZ+jVq5dcIFfm+++/R3p6Os6fPy/Xbmdnh7i4OMTFxVX40N28efNw8+ZN2efQoUMAXk0B/N/2gIAAue3OnTsHKyuravXlv6ysrBT2JgZRVRj4RAqyfv16GBkZyZ051gcbGxskJSVhxowZMDMzK7d84cKFSEtLw5YtWyrcvkWLFtDW1oa2trbsPvjrn7W1tSudAnfr1q24desW4uLiYGhoKLdsy5YteP78OWbMmFGtPlhZWeHOnTtwdHTEjBkzMGLECPz111+Vrr9kyRJYWFhg2LBh1fr+N+3cuRN6enro0qWL7KOvr49Vq1ZVuH52djbat29f4/20b98e2dnZtaqRqL4x8IkUIDU1Fd9//z2WL1/eIHPIa2lpITg4WO5ecVlZGT777DPs3LkTUVFRaNOmTb3u09fXFwkJCbL73q+lp6dj6dKlWLt2bYVXFCrTunVrfP3110hKSoJIJIKVlRUKCgoqXPfbb7/F7du35Z55EIvFOH/+PJydneHs7Izo6Oi37s/FxQXp6emyj5+fX6XrPnnypFb34XV1dSvtA5Gi8R4+UQP7559/MGnSJAwePBizZ89W2D5nz56Ny5cv48yZM+jfv3+D7EdXV1fuZ5FIBHt7e0yYMKHaZ/dv6tWrF5KSkpCQkCD3wN/FixcxceJEFBcXY//+/fD390dZWRmePn0KQ0NDTJo0CWPGjJFdyXj9cF5lYmJikJCQIPv50aNHlYZ+mzZtUFRUVOO+FBYW1vuBFlFtMfCJGtAff/wBNzc36OvrY+/evVBRUal03ZcvX8qeMK+tkpISbN68GatXr0bnzp1x4cIF2YNpDS09PR0ODg7o0KEDduzYUafvatmyJWxsbOTaBg8eDJFIhOLiYhw+fBhTp07F1q1b0adPHwwaNAjLli2r0VsIjo6O2LZtm+zntx0gtG/fHrm5uTXuR25uLoyNjWu8HVFD4CV9ogaQmpoKLy8vWFlZYciQIYiLiyt3Nvymhw8fonv37pV+JBJJhdv9+++/OHbsGLy9vWFsbIy1a9ciODgYiYmJVYZ9UFCQ3HvzXbt2BYBy7/9///33lX7Hy5cvERISgv79+2PgwIE4duwYNDU1q/g/VHsrV66UBXWLFi3g4uKCoqIi/PHHH+jRo0e1v2fv3r1y9/ArervhtaFDh+Ly5cvl2qVSKcRisdznv39OiYmJGDp0aA16R9RweIZPVM/S09PRr18/9OvXD7GxsRg+fHiV23Tr1g0BAQFYvXp1pev4+PhU+Irbo0ePMG3aNHz44YfYsGEDJk2aBG1t7WrVunTp0kpfufuvyu7Fl5WV4X//+x/u37+PsLAwTJkypVr7ra2YmBiEhoYiKSkJAODh4YGIiAhs27YN586dQ0REBDIyMqCnp4enT5++9RkCFxcXuTN84NX79jdv3kR6errc1QJ7e3sEBQXh6dOncmMcxMbGlnsmo0+fPkhJScGtW7fw+PFjudf9iISkIn1zHE4iqrO8vDy0bdtWYft78eIFWrZsqbD9/de9e/fQrl07tG7dulbb5+TkQFVVFe+++26V644dOxZTpkyBh4eHrK24uBghISG4desWdu/ejenTp2Pv3r1o2bIlDh06JDvgWrRoEbS1tREUFIQXL17g5cuX5Q6MfvrpJ3zzzTcoKyvD6tWr8dFHH8mWOTo6YsSIEXKDC73N/Pnz0aJFiwpH7SMSAgOfiJqMyg5sXr58KXt4r6HcuXMHDg4OuHz5cpW3Z+7evYtx48bh0qVLMDAwaLCaiGqCgU9EVE2//vor9PX1yz1Q+KbIyEh06dIFgwYNUlBlRFVj4BMRESkBPqVPRESkBBj4RERESoCBT0REpAQY+EREREqAgU9ERKQE/g9H+zQoOGRtEAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 61
        },
        "id": "f5IMnzeexrog",
        "outputId": "965b712b-70b3-4858-f6b7-1b0ea6ca4905"
      },
      "source": [
        "ans = sp.solve(sp.Eq(DS2,0),beta)\n",
        "beta_zero1 = ans[0]\n",
        "beta_zero2 = ans[1]\n",
        "beta_zero1"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5 \\alpha^{3} - \\sqrt{\\alpha^{5} \\left(4 a_{1}^{2} c^{2} l_{1}^{4} - 20 a_{1} c l_{1}^{2} + 25 \\alpha\\right)}}{2 a_{1} \\alpha^{5} c l_{1}^{2}}$",
            "text/plain": [
              "(5*alpha**3 - sqrt(alpha**5*(4*a1**2*c**2*l1**4 - 20*a1*c*l1**2 + 25*alpha)))/(2*a1*alpha**5*c*l1**2)"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 160
        },
        "id": "zI1HWv7md4iR",
        "outputId": "0f8c8c26-4650-40a2-ac2f-e035ef6b1e07"
      },
      "source": [
        "n = sp.Symbol(\"n\")\n",
        "print_expr(n*(n-1)/2)\n",
        "print(\"\\n\")\n",
        "sp.Eq(L,2.7*sp.Symbol(\"E\")**(sp.Rational(1)/3))"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle \\frac{n \\left(n - 1\\right)}{2}$",
            "text/plain": [
              "n*(n - 1)/2"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "\\frac{n \\left(n - 1\\right)}{2}\n",
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle L = 2.7 \\sqrt[3]{E}$",
            "text/plain": [
              "Eq(L, 2.7*E**(1/3))"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 61
        },
        "id": "gO_KpQynzVdJ",
        "outputId": "f469d2d6-92f4-4024-94d5-9dfe81877388"
      },
      "source": [
        "beta_zero2_func = to_func((alpha,a1,l1,c),beta_zero2)\n",
        "beta_zero1_func = to_func((alpha,a1,l1,c),beta_zero1)\n",
        "\n",
        "beta_zero2"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5 \\alpha^{3} + \\sqrt{\\alpha^{5} \\left(4 a_{1}^{2} c^{2} l_{1}^{4} - 20 a_{1} c l_{1}^{2} + 25 \\alpha\\right)}}{2 a_{1} \\alpha^{5} c l_{1}^{2}}$",
            "text/plain": [
              "(5*alpha**3 + sqrt(alpha**5*(4*a1**2*c**2*l1**4 - 20*a1*c*l1**2 + 25*alpha)))/(2*a1*alpha**5*c*l1**2)"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cmHvYYl3zsIO",
        "outputId": "3be8c608-b451-4b75-bf0f-3cdfc253242c"
      },
      "source": [
        "print(beta_zero1_func(0.9,0.3,15,0.01))\n",
        "print(beta_zero2_func(0.9,0.3,15,0.01))"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.4012728149246088\n",
            "7.743674601627746\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "fYLz-wUq0kdg",
        "outputId": "3e85ae7a-2e5e-4642-9409-3402f81aab25"
      },
      "source": [
        "def plot():\n",
        "  a1 = 0.1\n",
        "  l1 = 15\n",
        "  c = 0.05\n",
        "  p = shortest_period_func(a1,l1,c)\n",
        "\n",
        "  alpha = np.linspace(int(p*100)+1,100)/100\n",
        "  #plt.plot(alpha,beta_zero1_func(alpha,a1,l1,c))\n",
        "  #plt.show()\n",
        "  l2 = l1 * alpha \n",
        "  a2 = a1 * beta_zero1_func(alpha,a1,l1,c)\n",
        "  ratio = E_func(l2,a2) / E_func(l1,a1)\n",
        "  ratio2 = peak_resource_func(l2,a2) / peak_resource_func(l1,a1)\n",
        "\n",
        "  print(ratio2[0],ratio2[49])\n",
        "  plt.plot(alpha,ratio2)\n",
        "plot()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.0894190434072857 0.9999999999999997\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lnR1XE8X1Yup"
      },
      "source": [
        ""
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 379
        },
        "id": "dsnQIIRK2iwE",
        "outputId": "bdf9f7d2-1d99-4b15-b58b-290928ccf04f"
      },
      "source": [
        "\n",
        "\n",
        "def plot_Rt(L,a,c,label):\n",
        "  Li = int(L)+1\n",
        "  x = np.linspace(0,Li,num=Li*10)\n",
        "  y = St_func(x,L,a,c)\n",
        "  #plt.plot(x,y,label=label)\n",
        "  plt.fill_between(x,y,alpha=0.2)\n",
        "  y = Rt_func(x,L,a)\n",
        "\n",
        "  plt.plot(x,y,label=label)\n",
        "\n",
        "def plot_Rt_alpha(alpha,l1,a1,c):\n",
        "  l2 = alpha * l1\n",
        "  beta = beta_zero1_func(alpha,a1,l1,c)\n",
        "  a2 = beta * a1\n",
        "  return plot_Rt(l2,a2,c,f\"短縮率={alpha}\")\n",
        "\n",
        "def plot():\n",
        "  l1 = 10\n",
        "  a1 = 0.3\n",
        "  c = 0.03\n",
        "  print(l1,a1,c)\n",
        "  plt.figure(figsize=(8,5))\n",
        "  plt.ylim(0,25)\n",
        "  plt.xlabel(\"時間(t)\")\n",
        "  plt.ylabel(\"人員数\")\n",
        "  plt.title(\"納期短縮率と同規模のリソースヒストグラム\")\n",
        "  plot_Rt_alpha(1,l1,a1,c)\n",
        "  ims = []\n",
        "  min = shortest_period_func(a1,l1,c)\n",
        "  for i in reversed(range(int(min*10)+1,10,2)):\n",
        "    alp = (i/10)\n",
        "    #print(alp)\n",
        "    plot_Rt_alpha(alp,l1,a1,c)\n",
        "  plt.legend()\n",
        "  plt.show()\n",
        "\n",
        "\n",
        "\n",
        "plot()"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10 0.3 0.03\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "V5ZSelpF4d99",
        "outputId": "d8ae1207-91c1-4994-f433-9f95bcdc9fcd"
      },
      "source": [
        "E1 = E.subs(L,l1).subs(a,a1)\n",
        "E2 = E.subs(L,l2).subs(a,a2)\n",
        "\n",
        "cost_ratio = (E2/E1).subs(a2,a1*beta).subs(l2,l1*alpha)\n",
        "cost_ratio"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\alpha^{3} \\beta$",
            "text/plain": [
              "alpha**3*beta"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 61
        },
        "id": "pIy-Nb608Gm4",
        "outputId": "566672de-cb92-4dc0-bbde-2f6a4c95af36"
      },
      "source": [
        "cost = cost_ratio.subs(beta,beta_zero1)\n",
        "cost_func = to_func((alpha,a1,l1,c),cost)\n",
        "cost"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5 \\alpha^{3} - \\sqrt{\\alpha^{5} \\left(4 a_{1}^{2} c^{2} l_{1}^{4} - 20 a_{1} c l_{1}^{2} + 25 \\alpha\\right)}}{2 a_{1} \\alpha^{2} c l_{1}^{2}}$",
            "text/plain": [
              "(5*alpha**3 - sqrt(alpha**5*(4*a1**2*c**2*l1**4 - 20*a1*c*l1**2 + 25*alpha)))/(2*a1*alpha**2*c*l1**2)"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "id": "QEbsJLNEBhcQ",
        "outputId": "9bc41661-6758-45a8-a39a-06f8d2d35c00"
      },
      "source": [
        "def plot_cost_graph(a,L,c):\n",
        "  alpha = shortest_period_func(a,L,c)\n",
        "  alpha_vec = np.linspace(int(alpha*100)+1,100)/100\n",
        "  print(alpha)\n",
        "  y = cost_func(alpha_vec,a,L,c)\n",
        "  plt.plot(alpha_vec,y,label=f\"a={a},L={L},ピーク人員={peak_resource_func(L,a):.1f}\")\n",
        "plt.figure(figsize=(8,5))\n",
        "plt.title(\"納期の短縮率とトータル工数の関係\")\n",
        "plot_cost_graph(0.3,8,0.03)\n",
        "plot_cost_graph(0.3,10,0.03)\n",
        "plot_cost_graph(0.3,15,0.03)\n",
        "plt.legend()"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.40771584\n",
            "0.5903999999999999\n",
            "0.9638999999999999\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb11df6a590>"
            ]
          },
          "metadata": {},
          "execution_count": 39
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 61
        },
        "id": "BYwO-wkqv7wq",
        "outputId": "70b524e9-d89d-4b6d-ca15-4172e011b3e2"
      },
      "source": [
        "sp.expand(cost)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{5 \\alpha}{2 a_{1} c l_{1}^{2}} - \\frac{\\sqrt{4 a_{1}^{2} \\alpha^{5} c^{2} l_{1}^{4} - 20 a_{1} \\alpha^{5} c l_{1}^{2} + 25 \\alpha^{6}}}{2 a_{1} \\alpha^{2} c l_{1}^{2}}$",
            "text/plain": [
              "5*alpha/(2*a1*c*l1**2) - sqrt(4*a1**2*alpha**5*c**2*l1**4 - 20*a1*alpha**5*c*l1**2 + 25*alpha**6)/(2*a1*alpha**2*c*l1**2)"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "mXJRHiS028S4",
        "outputId": "21672b07-667f-42a8-cc80-340dcd6d665d"
      },
      "source": [
        "pr1 = peak_resource.subs(L,l1).subs(a,a1)\n",
        "pr2 = peak_resource.subs(L,l2).subs(a,a2)\n",
        "\n",
        "pr_ratio = (pr2/pr1).subs(a2,a1*beta).subs(l2,l1*alpha)\n",
        "pr_ratio"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\alpha^{2} \\beta$",
            "text/plain": [
              "alpha**2*beta"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "id": "ev-FTp8SJpyD",
        "outputId": "7bb46aae-3e5f-4b3b-d824-9845fbe0eaf0"
      },
      "source": [
        "pr_ratio_func = to_func((alpha,a1,l1,c),pr_ratio.subs(beta,beta_zero1))\n",
        "\n",
        "def plot_pr_ratio_graph(a,L,c):\n",
        "  alpha = shortest_period_func(a,L,c)\n",
        "  alpha_vec = np.linspace(int(alpha*100)+1,100)/100\n",
        "  print(alpha)\n",
        "  y = pr_ratio_func(alpha_vec,a,L,c)\n",
        "  plt.plot(alpha_vec,y,label=f\"a={a},L={L}　ピーク人員={peak_resource_func(L,a):.1f}\")\n",
        "\n",
        "plt.figure(figsize=(8,5))\n",
        "plt.title(\"納期の短縮率とヘッドカウントの関係\")\n",
        "plot_pr_ratio_graph(0.3,8,0.03)\n",
        "plot_pr_ratio_graph(0.3,10,0.03)\n",
        "plot_pr_ratio_graph(0.3,15,0.03)\n",
        "plt.legend()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.40771584\n",
            "0.5903999999999999\n",
            "0.9638999999999999\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb115c52390>"
            ]
          },
          "metadata": {},
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7wtoAxE-KSRA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "outputId": "31e4ac8d-3b55-4597-8ba9-a6af0c9726c7"
      },
      "source": [
        "cost_perfomance = S/E\n",
        "cost_perfomance_func = to_func((L,a,c),cost_perfomance)\n",
        "print_expr(cost_perfomance)\n",
        "\n",
        "def plot(c):\n",
        "  L = 15\n",
        "  a = np.linspace(0,10)/10\n",
        "  rp = peak_resource_func(L,a)\n",
        "  plt.plot(rp,cost_perfomance_func(L,a,c),label=f\"c={c}\")\n",
        "\n",
        "plt.figure(figsize=(8,5))\n",
        "plt.title(\"プロジェクト人員規模とコストパフォーマンス\")\n",
        "plt.ylabel(\"コストパフォーマンス\")\n",
        "plt.xlabel(\"最大人員数\")\n",
        "plt.ylim(0,1)\n",
        "plt.xlim(0,50)\n",
        "plot(0.05)\n",
        "plot(0.03)\n",
        "plot(0.01)\n",
        "plt.legend()"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/latex": "$\\displaystyle - \\frac{L^{2} a c}{5} + 1$",
            "text/plain": [
              "-L**2*a*c/5 + 1"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "- \\frac{L^{2} a c}{5} + 1\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7fb115be4f50>"
            ]
          },
          "metadata": {},
          "execution_count": 43
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RnZ0d5ebmtrh/U1nl0maDf/XVV6SiolIvsWvWrFmkrq7e4OyJurSXx8DW1pa+//57WrhwIWlpaXEPO5FIRIqKivTvv//Szp07qW/fvvX6HjlyhBwcHLjww6JFi7gZHtJuL+Pn59dk/FxaGkqIa2jT0tKSShhkZGTQ8OHDSUVFhU6cOEFENcLb0tKSNDQ0WiRkWnP//PHHH8Tj8eitt96S+jxr1qxpNreoLoWFhTR+/Hji8XgtjsEfOXKEDAwMyNPTk6qqqrjZNrIUBkREFy5cIA0NDbK3t29xmK8u9+7d47w6/fv3b7GnoD3vn64IEwYyprKykjZu3EgqKipkbm5ON27ckKpfrXtLmk0aYVBZWUkHDx6kwYMHEwCytrZu9mVXl4amJjo6OtJ7771Xb39TWdN1EYvFtGXLFurWrRs5OTlRRkaG1PbUpa3Tzb777jsCQL/88ku9YxUVFTRs2DBSU1NrMgejrTkGRDVfVHw+nx49ekRERFOmTKHu3btTZWUl/fPPP6SkpEQlJSX1hMGgQYMoMzOTiIgTnbXCQCwWSyQslpWVkaurK/Xp04cGDBhA2dnZEsdfxs/Pj0xMTNqUZFhSUtIicdKcMNi7dy8JhULS1dWlM2fOSBzLycmh/v37E5/Plzr00Zr7Z+3atWRiYkJZWVlS9ykuLiZfX1/Kzs5utu3Ro0fJ3NyclJWVm8xfeJkHDx6Ql5cXKSgo0IoVKzjvm7wIA6IaL5SCggJ5eHhIPfOIqOY+OnToEE2ePJkUFRVJVVWVVqxY0aIxiNr//umKMGEgI3JycmjTpk3Uq1cvAkCTJ0+mvLw8qfu7ubmRra0thYaGNrn17du3SWFw6NAh+vDDD0lfX58AkJGREf30008t/mNqyYNdIBA0O95ff/1FQ4cOJQDk4+PTpnnerRUGBQUF5OXlRQBo5cqVjbYrLCykESNGcLH4hh7sIpGIHjx4QB9//DG5urrSvXv3uITC33//nXr27EkzZ86k/fv3N/iSLSwsJGtra5o7dy63r6ioiItJT5kyhd555x0iIglhUPvSrRUTtdQKg7pUVVXRvHnzyMrKikpKSmjs2LFkaWnJfTE1xNmzZ0lZWZn69OlD69evp4SEBEpMTKSUlBS6evUqnTp1iqKiomjt2rUUFxfX4BgikYj2798v1aamptaoMDh58iS5u7sTABo6dCg9ePCgwXb5+fnk5OREPB5PKo9Ya++foqKiFvdpitLSUgoPD+f+Lmxtbenff/9t0RgLFiwgJycnTvRnZmZSfn4+JScnEwBKSEhoV5tby/r16wkA+fv7S9W+dhpirbBetGgRPX36tEXn7Kj7pyvChIGM2L9/P/F4PBo+fHiTD97GCAsLk8p9GB4eTmFhYY0e37RpE6mrq9PEiRNp3759LSra01FkZWWRiYkJ2djY0NGjR9s8Xmse7L/99hvp6emRsrJyo/UU6lJeXk6+vr6ckKklPz+ffv31V5o8eTLx+XyytbWtN+VJLBbT33//TT4+PqSqqko6Ojr06aefcp6VsrIycnZ2Jmtr63ru1YqKCvrPf/5DampqdPv2bSKq+T+vnW2wfv164vP59YReXY/BnTt3aMOGDdSrVy9ydHTkHqhVVVW0ePFi4vP55OjoSKtXr27w/rh48SJ5enqSlpZWo2JQVVWVvvjiCyl+802zY8eOBmPplZWV9Oabb5Kuri5t2LCh2SS8vLw86tevX7NZ/ETtWyCrLSQnJ5NAIKDevXvTli1bqKqqqlXj1M3R2bZtm4SnShpvRWexbNkyqfJ/iGrc/AsWLKCjR4+2KEejlo68f7oiTBjIkJe/4mRBdXV1q/6QOpr09PRWP/he5sCBA/T111+3qM/NmzdpzJgxUod2aomNjZXIXA4KCiIlJSWaOHEiHTx4UKoHTnBwMLm7u3Puf6KaL6iXa0icO3eOzMzMqEePHhIuz+vXr3MeICUlJVqwYEG989QKg5ycHNLV1SUHBwf6v//7vwbtu3v3Li1cuLBJr0ktWVlZdPv2bbpy5QrdvHmT7t+/TwUFBc32aw+KiopadC5pRXBr7p+O4unTpw3O928tYrGY8vLy6MGDBy2exveq0VH3T1eER9TIShwdRG5uLo4cOYJt27ahuLgYycnJTbYvLy9HUFAQIiMjkZubi6FDh2Lz5s2ws7PrJIsZjLZRUFDQISveiUQi7NmzB1OmTIGamlq942KxWKLOe2MUFRVBIBC0u30MBqNr0vxTox05f/48zMzMsGvXLigqKkrVZ+bMmfjjjz9w9OhRPHnyBDY2NnBzc0NWVlYHW8tgtA8dtQwun8/HrFmzGhQFAKQSBQCYKGAwGBJ0qjAYOHAgcnJycPr0aYwZM6bZ9mfPnsWhQ4ewc+dO9O3bF3p6eggJCYGenh62bt3aCRYzGAwGg/F60anCQFlZGVpaWlK3P3LkCGxtbTFw4EBun4KCAry9vREVFdURJjIYDAaD8VrTqcKgpaSkpMDa2rrefisrKzx69AidnB7BYDAYDMYrD1/WBjRFWVkZzMzM6u3X09ODSCRCYWFhvfjtL7/8gl9++QUAkJycDD09PQA1ngYlJSVu4/Pl+tIZDAaDwWgxjx49Ql5eXpvGkOu3o76+PgoKCurtLy4uBp/Ph7a2dr1jc+fOxdy5cwHUCIhRo0bB0NAQDg4O4PF4KCoqAlCTuGVkZAQjIyMYGxtDKBRKnRDJYDAYDIY84uzs3OYx5FoYWFhYICYmpt7+5ORkmJubg8fjNdnf3Nwct27dQnZ2Np49ewYHBwdMnz4dxcXFyMzMRGZmJi5fvgwAUFRUhFAohLGxMScUlJSUOuS6GAwGg8GQV+RaGEyfPh3BwcG4desW+vXrBwAgIhw8eBDvvfdes/0VFBRw4MABDBo0CM+fP4eioiJ+/PFHzJkzB8OHDwcAVFRUICsrixMK165dw9WrV8Hj8SAUCjmPgpGREZSVlTv0ehkMBoPBkDVyJQwOHz6MpUuXYvfu3XBxcYGDgwPeffddfPDBB4iIiIChoSGCgoLw5MkTfPzxx1KN2aNHDxw6dAhvvvkm1NXVMWDAAGzcuBHjx4/H22+/DRUVFfTs2RM9e/YEAFRWVnJCISsrCzdv3sSNGzfA4/Ggp6cHIyMjmJiYwMjICCoqKh3422AwGAwGo/ORK2FQVFSElJQUlJWVcfsiIyOxZMkSuLm54fnz5xg6dCgSEhLQvXt3qcd1dXXFf//7X/j6+sLS0hJDhgzB0aNHkZKSAl9fX+jq6nJtlZWV0aNHD/To0QMAUFVVhZycHM6jkJSUhNu3bwOoKVxTG3owNjZutNAMg8FgMBhdhU4vidyZODs7czkEAPDZZ59h06ZNCAsLg729PSIiIqCoqIjZs2djwIABUo1ZXV2N3NxcTihkZWVBJBIBqKkgVxt6MDY2hqamZodcF4PBYDAYDfHye681vFbCQCQSYfz48UhISMDJkydhZWWFsLAwPH78GG5ubpg6dWqL8wjEYjHy8vIkhEJlZSUAQENDgxMJRkZGEAgEzSZMMhgMBoPRWpgwaIaGfkEFBQUYPHgwioqKcOnSJZiYmCA6OhonTpxA9+7d4e/vD2Nj41afk4iQn5/PCYXMzExUVFQAAFRVVSVCDzo6OkwoMBgMuaO4uBg5OTmoqqqStSmMOigpKUEoFDZZQZgJg2Zo7BeUnJyMwYMHw8LCAmfOnIG6ujpu376NXbt2oaKiAl5eXnB1dW2XlzYRoaioSEIoPH/+HADQrVs3idCDnp6e1AvfMBgMRkdQXFyM7OxsdO/eHaqqquzjRU4gIpSXlyM9PR2GhoaNigMmDJqhqV/QsWPH8Pbbb2Pq1KnYu3cvV/xo586dSEpKwsCBAzFr1iyoqqq2q01EhJKSEgmhUFJSAqBGDdadHmlgYMCKLjEYjE7l/v37MDExYcnUckpZWRkyMjLQu3fvBo+3hzCQq1kJncm4ceOwbt06fPHFF+jXrx8CAwMhEAiwYMECxMXFISYmBo8ePYKfnx8sLCza7bw8Hg9aWlrQ0tKCjY0NAKC0tFSilkJaWhqAmqJLhoaGEkWXWClnBoPRkVRVVbX7BxGj/VBVVe3wEM9r/ZZZtGgRbt68iZUrV8Le3h6enp5QUFDA2LFjYW1tjbCwMPzwww9499138dZbb3WYm19DQwO9e/fmFGB5ebmEULhy5QqAmoJNBgYGnFAwNDRkRZcYDEa7w8IH8ktn/N+8tqGEWioqKuDu7o7bt2/j3LlzcHBw4I6VlZXht99+w5UrV2Bra4sPP/wQAoGgo82ux4sXLySKLuXm5oKIwOPxoK+vLzHzoVu3bp1uH4PBeHVISkqCra2trM1gNEFT/0ftEUp47TPdVFRUcPjwYQgEAkycOBG5ubncMTU1Nfj7+2PmzJm4f/8+goKCuOJGnUm3bt1gbm6OIUOGYNKkSfDx8cH48ePRv39/KCoq4vbt2zh+/DjCw8Nx4MABnD17Fg8fPpQoFMVgMBiMllNQUICAgAB0794dWlpa8PT0RHp6erP9wsPDYW9vDzU1NTg4OCA6OrpeGzs7O/B4vHpbcnJyR1yK1LzWoYRajI2NER0djREjRmDq1Kk4ceIE56Ln8Xh44403YGlpidDQUISEhGD06NGYNGmSzOL9SkpKMDU1hampKYCa+gx1iy6lpKTgzp07AABtbW2JMs4aGhoysZnBYDC6GiKRCOPGjYO6ujrOnj0LZWVlzJ8/HyNHjsS1a9caTdAMCQlBYGAgoqKi4Orqin379mHatGmIjY3F6NGjuXZpaWlISEiAq6urRH9Z55K99qGEukRGRsLb2xtz587Ff//733qxnMrKShw4cAD//PMPzM3N4efnB6FQ2N5mt5nq6up6RZdqk1U0NTUlailoamqyeCKDweBgoYT/ERERAR8fH6SlpcHIyAhATYjZxMQE69evh6+vb70+z58/h6mpKVasWIFFixZx+/39/ZGcnIzTp08DAAoLC6Gjo4MnT57AzMysRXZ1dCiBeQzqMGPGDNy6dQvff/89HB0d6y3UpKysjBkzZqBPnz749ddf8c0338Db2xuDBw+WkcUNUzubwdDQEP3794dYLJYouvT48WPcvXsXAKCuri5RS0FbW5sJBQaD0eUhImzYsAFbt25FRkYGrKyssHz5cnh5eUk9xpEjRzB69GhOFAA1IeYpU6YgKiqqQWFw6tQpFBYWYtasWRL7Z8+ejREjRuDp06cwNTVFWloalJSUWrTuT2fBhMFLfPPNN7h9+zYWLFiAPn36YOTIkfXaODk5oWfPnggLC8OOHTuQlJQELy8vuV1tUUFBAfr6+tDX10e/fv1ARCgoKEBWVhYyMjKQkZGBBw8eAKjJuaibzKinp8eEAoPxmrNw4UJcv35dJufu378/Nm3a1OJ+a9aswYYNGxAeHo6RI0ciPj4eM2fOhK6uLn766SdutldDBAUFwd/fHykpKXB3d6933MrKCgkJCQ32TUlJgUAgqOdNtrKyAgCkpqZywsDExATh4eEICwtDXl4enJycEBwc3K5T5FsDEwYvoaioiIiICAwdOhTTpk3DxYsXYWlpWa+drq4uFi1ahKNHjyI2NhYPHz6En58ftyqjPMPj8aCrqwtdXV3Y2dmBiFBcXCxRdCk1NRVAjZekrkdBX1+fVWdkMBhyTVlZGdatW4egoCBMmjQJADBp0iTEx8fD0dERzs7O3Jo2DVFbVbCsrAx6enr1juvp6SEvL6/RczfWBwDXLy0tDU+ePMGjR4+wc+dOlJeX48cff8TAgQNx+/ZtmXoSmDBoAC0tLRw5cgSDBg3CxIkTcf78+QbLTyoqKmLixImwsbHBjh07sHbtWkyePBkjR47sUl/ZPB4PAoEAAoEAffr0AQCUlJRI1FJ48uQJgJqkGCMjI04sCIVCVp2RwXjFac0Xuyy5c+cOysrKJBL9AMDFxQUApJ7Wra+vj4KCgnr7i4uLoa+v3+I+tccB4L333sOwYcPQr18/rk14eDj69u2LzZs3Y+3atVLZ2BEwYdAIlpaW2L9/P8aMGYOZM2ciOjq60S9lGxsbBAYGIjw8HPv27UNSUhJ8fHy69AwATU1NaGpqcu6vsrIyiWTG2uQWRUVFCIVCieqMSkpKsiVhFT8AACAASURBVDSdwWAwAKDRj5axY8c2maAXHByMefPmwcLCAvfu3at3PDk5Gb169Wqwr4WFBQoKCpCXlychHmqnINb209bWhra2tkRfBQUF2Nvbc6FdWcGEQRN4eHhg06ZNmD9/PgIDAxEcHNxoWw0NDXz88cc4efIkDh48iKCgIMyZM4cre9zVUVNTg6WlJRdWqaiokPAoXLt2DVevXgWPx4NQKJRY84FVZ2QwGJ1J3759oaamhri4ONjZ2XH7ExMTYWxsjMjISKlCCdOnT8e0adMkXvIVFRU4evQovv766wb7uru7QygUYs+ePZg/fz63/8CBAxg2bBg3zby0tBSPHj2Cvb0916a6uho3b97E5MmTW3/x7QG9wgwcOLDNY4jFYvL39ycAFBkZKVWfx48fU2BgIM2bN4+io6NJJBK12Q5558WLF/T48WO6cOECRUdHU2hoKG3bto1++eUXOnjwIJ09e5ZSU1OpvLxc1qYyGIwmSExMlLUJ7UJQUBBpaWlRVFQUFRYW0tmzZ8nMzIxCQ0OlHqOqqoqcnZ3prbfeosePH1NGRgZ5eXlR7969qbS0lIiInj59SjY2NhQSEsL127hxI+no6FBcXBwVFxfT7t27SVlZmWJjYyXaaGtr06+//kqFhYWUmppKH3zwAWlpaVF6enqTdjX1f9Qe7z3mMWgGHo+HLVu2IDk5GXPmzIGVlRWcnZ2b7NOjRw8sW7YMUVFRiI2NRUpKCvz8/KCrq9tJVnc+ysrK6NGjB5d8KRKJkJ2dzYUekpKSuKqROjo6ErUU2CpuDAajvVmxYgW0tLSwbNkyzJ49G7169UJgYCD8/PykHoPP5+PYsWP47LPP4OjoiOrqanh4eCA+Ph7q6uoAahadSklJkUhGXLhwIfh8PgICApCeng5ra2tERUVh3LhxEm309PSwefNmzJs3DwoKCnB1dcWpU6dgYmLSfr+IVsAKHElJTk4OXFxcIBKJcOnSJRgbG0vV7+LFi4iIiICCggJmzZoFJyendrGnq1FdXS1RnTE7O5sruiQQCCRmPmhqasrYWgbj9YUVOJJ/WIEjOUEoFCImJgbDhg2Dp6cnEhISpKpb4OLigl69eiE0NBTbtm3DiBEjMG3atNcu7q6oqMjNZhgwYADEYjHy8vK4PIVHjx4hJSUFQE2+Rt0yzgKBoEvN8mAwGIyuDBMGLcDR0RG7d+/G1KlTMW/ePOzatUuqF5aBgQG+/PJLREdH48SJE7h//z78/f1l7i6SJQoKChAKhRAKhXBwcAARSVRnTE9Px/379wHUrD9eN/Sgo6PDhAKDwWB0EEwYtJApU6Zg9erVWL16NRwcHCRqYTcFn8/H1KlT0adPH+zatQvffvstpk+fjjfeeIO95FCTy6Gnpwc9PT3Y29uDiFBUVCRRdOnhw4cAauYg1w096OnpsaJLDAaD0U4wYdAKAgMDcfv2bXz55Zews7OTSChpDnt7ewQGBmLnzp2IiIhAcnIyZs6cyRLwXoLH43HzfG1tbUFE9YouPX78GEDNapN1p0caGBiwoksMBoPRSpgwaAUKCgrYtWsX7t27By8vL1y4cIGrGCgNAoEACxYsQFxcHGJiYvDo0SP4+vo2WHqZUQOPx4OWlha0tLRgbW0NoGYVs7pFly5evAjgf4tI1S26JOtlTBkMBqOrwGYltIHHjx9j0KBB0NbWxoULF6Cjo9PiMR4+fIiwsDAUFBRg4sSJGDNmDHOLt5Ly8nIJj8KzZ88A1Ag5AwMDTigYGhq+dsmfDIa0sFkJ8k9Hz0pgwqCNnDlzBiNHjoS7uztiY2Nb9WVaXl6OX3/9FVeuXEGfPn0wZ84cCASCDrD29eLFixfIzs5GRkYGsrKykJubCyICj8eDvr6+xCqS0tZOZzBedZgwkH+YMGgDnSEMAGD79u3w8/PDZ599hg0bNrRqDCLC2bNnERUVBRUVFfj4+EiUymS0naqqKomiSzk5OaiurgZQs1pmXaHAcj4YrytMGMg/rI5BF8DX1xc3b97Exo0b0a9fP3z44YctHoPH42H48OGwtLREWFgYQkJCMGrUKHh6erL4eDuhpKQEU1NTrla5SCSSKLqUkpKCO3fuAKjJA6k7RbIrL4jFYDAYLYEFs9uJ9evXY9SoUQgICMC5c+daPY6xsTGWLFkCd3d3/PXXX1i7di1ycnLa0VJGLXw+H8bGxnBycsLbb78NHx8fTJo0CS4uLtDS0sKDBw9w8uRJREZGYs+ePUhISEBKSgqKi4vxCjvaGAxGHQoKChAQEIDu3btDS0sLnp6eSE9Pb7ZfeHg47O3toaamBgcHB0RHR9drExYWBkdHR6ipqaF79+748MMPkZGR0RGX0SJYKKEdyc/Ph4uLC0pKSnDp0iVu3YDWcv36dYSHh6O6uhozZszAkCFD2slShjSIxWKJoktZWVmoqKgAAKirq0vUUtDW1mb1KBivBCyU8D9EIhGGDx8OdXV1bN++HcrKypg/fz5u376Na9euNRpyDAkJQWBgIKKiouDq6op9+/YhICAAsbGxGD16NADg+++/R0hICMLCwvDGG28gOzsbixcvxsOHD3H9+vUmnycsx6ANdLYwAGr+wwYPHozevXvjzJkzbY5V5+fnY/v27bh//z6GDh0KLy8vqUoxM9ofIkJhYaFE0aWysjIAgIqKioRQ0NXVZbNLGF0SJgz+R0REBHx8fJCWlgYjIyMAQFlZGUxMTLB+/Xr4+vrW6/P8+XOYmppixYoVEgXw/P39kZycjNOnTwOoebYXFBRITFO/cuUKnJ2dkZKSwk3LbgiWY9DFsLW1xZ49ezBhwgR8+OGHiIqKatOXpK6uLj7//HPExsbi6NGjePjwIfz8/NrsjWC0HB6PBx0dHejo6MDOzg5EhOLiYs6bULvmA1Cz2mRdoaCvr8+EAoPRiRARNmzYgK1btyIjIwNWVlZYvnw5vLy8pB7jyJEjGD16NCcKAEBNTQ1TpkxBVFRUg8Lg1KlTKCwsxKxZsyT2z549GyNGjMDTp09hamoKXV1diRV3nz59iuDgYPD5fAiFwlZccfvBhEEH8Pbbb+P777/HV199hX79+mHFihVtGk9RURETJkyAjY0Ntm/fjrVr12Ly5MkYOXIkc1/LEB6PB4FAAIFAwBW4Ki0tlfAoPHnyBEBNPkPdoksGBgYsqZTB6EDWrFmDDRs2IDw8HCNHjkR8fDxmzpwJXV1d/PTTT7hy5UqjfYOCguDv74+UlBS4u7vXO25lZYWEhIQG+6akpEAgENR7uVtZWQEAUlNTuQRoAPjPf/6DXbt2obi4GEpKSggJCYG2tnbLL7gdYU+mDuKLL77AzZs3ERgYiL59+8LT07PNY1pbWyMwMBDh4eHYt28fkpKS8MEHH7BliuUIDQ0NWFlZcQ+BsrIyZGVlcbUUal18ioqKEAqF3PRIQ0NDKCkpydJ0BqNR9u7di6dPn8rk3Kampnjvvfda1KesrAzr1q1DUFAQJk2aBACYNGkS4uPj4ejoCGdnZ1RWVjbaX0tLixtHT0+v3nE9PT3k5eU1eu7G+gCo12/NmjX4+OOPce7cOWRnZ2PGjBnSXWQHwoRBB8Hj8RAaGoq7d+9i1qxZOH/+PPr169fmcTU0NPDxxx/j5MmTOHjwIIKCguDr6wsbG5t2sJrR3qipqcHCwgIWFhYAgIqKCmRlZXGhh2vXrnFFl+pWZzQyMmLVGRmMVnLnzh2UlZVxiX61uLi4AIDUBc309fVRUFBQb39xcTH09fVb3Kf2eF1qvY42Njb4448/4OLigmvXrkFVVVUqGzsCJgw6EFVVVURHR8PZ2RkTJ07EpUuXGr2ZWgKPx8PIkSNhZWWF0NBQbNy4EePGjcM777zDFg+Sc1RUVNCzZ0/07NkTAFBZWckVXcrMzMStW7dw48YN8Hg8iaJLxsbGLOmUITNa+sUuLzT2PBw7dmyTCXrBwcGYN28eLCwscO/evXrHk5OT0atXrwb7WlhYoKCgAHl5eRLP++TkZABotB8AjB49Gnfv3kV8fDzefvvtRtt1NEwYdDAmJiaIjo7GiBEjMHXqVMTFxbXbl6CZmRmWLVuGvXv3IjY2FikpKfD19W3QjcWQT5SVlWFmZgYzMzMANdOjcnJyOKGQlJSE27dvAwB0dHQ4b4KxsTHU1dVlaTqDIbf07dsXampqiIuLg52dHbc/MTERxsbGiIyMlCqUMH36dEybNk3iJV9RUYGjR4/i66+/brCvu7s7hEIh9uzZg/nz53P7Dxw4gGHDhsHU1BRVVVXw9fXFf/7zHwwcOJBrk5qaCiKSfViRXmEGDhwoaxM4fv31VwJAAQEBHTL+hQsXaMGCBbRw4UK6cuVKh5yD0fmIRCLKzMykq1evUmxsLO3YsYO2bdtG27Ztoz179lBCQgKlpKRQcXExicViWZvLeAVITEyUtQntQlBQEGlpaVFUVBQVFhbS2bNnyczMjEJDQ6Ueo6qqipydnemtt96ix48fU0ZGBnl5eVHv3r2ptLSUiIiePn1KNjY2FBISwvXbuHEj6ejoUFxcHBUXF9Pu3btJWVmZYmNjuTa+vr5kZmZGf/75JxUVFdH169fJxcWFLCwsuLEbo6n/o/Z47zGPQScxc+ZM3Lp1C+vWrYODgwM++uijdh3fxcUFvXr1QlhYGLZt24YRI0Zg2rRpLE7dxVFUVISRkRE3XUosFuPZs2ecR+HRo0dISUkBUFN0qW7oQSAQsFkrjNeWFStWQEtLC8uWLcPs2bPRq1cvBAYGws/PT+ox+Hw+jh07hs8++wyOjo6orq6Gh4cH4uPjOY9dVVUVUlJSJJIKFy5cCD6fj4CAAKSnp8Pa2hpRUVEYN24c1+aXX37B5s2b8fnnn+Phw4fQ09ODm5sb9u3bJ3NvICtw1IlUV1fj3XffxfHjxxEXF4c333yz3c8hEokQExODuLg4mJiYwN/fHyYmJu1+HoZ8QEQoKCiQmCJZXl4OoCbHpW7oQVdXlwkFRrOwAkfyD6t82AbkTRgANZmpQ4YMQXZ2Ni5dusRlq7c3d+7cwc6dO1FRUYHp06fjjTfeYC+F1wAiQlFRkYRQeP78OYCaTOy6RZf09PRY0SVGPZgwkH+YMGgD8igMAOD+/ftwcXGBiYkJzp8/32F1CIqKirBz504kJSXByckJs2bNYssJv4aUlJRICIXaaVNKSkpcmKK26BKb1cJgwkD+6Whh0OmfC//++y/c3NygqamJHj164Ntvv4VYLG60/blz5zBmzBiufKSHhwdXa7qr0rt3b+zbtw/JycmYOXNmk9ffFgQCARYsWIDJkyfj+vXr+Oabb/DgwYMOORdDftHU1IS1tTXc3Nzg5eUFb29veHh4wMrKCqWlpbh06RKOHDmCXbt24Y8//sCVK1eQkZEBkUgka9MZDIYM6FRhcOnSJbi7u2PixIlIT09HREQEQkJCsGrVqgbbX7t2De7u7nBwcEBSUhKSk5MxcOBAeHh44MKFC51perszatQobNy4EUeOHMHKlSs77DwKCgoYM2YMvvzySwDAjz/+iNjY2A4TIwz5R11dHZaWlhg+fDimTZuG2bNnY/To0bC1tUVlZSWuXr2KP/74A7t27UJMTAwuXryItLS0Jqd3MRiMV4dODSWMHj0aKioq+P3337l9ERERmDt3LjIzM7m5o7V88cUXiImJwd27dyX229vb46233sKGDRuaPJ+8hhJqISLMnTsXYWFhiIqK6vAiIuXl5fjtt99w+fJl2NjYYM6cOTKvyc2QPyorK7nKjJmZmcjNzeWqM+rr63OhByMjI1Z06RWEhRLkn1dmdcXS0lKcPHkSkZGREvunTJmCuXPn4vfff4e3t7fEMV1dXYhEIu6hVEt1dTUMDQ07xe6OhMfjYevWrUhOToaPjw969+4tUeyivVFVVYWfnx9sbW0RFRWFoKAg+Pj4tEupZsarg7KyMnr06MGt4FlVVYXs7GxOLCQmJuLWrVsAIFGd0cjIiOWwMBivAJ0mDO7fv4/q6up6a0yrqKjAzMwMDx8+rNcnICAAe/fuhb+/P3744QfweDysXLkSZmZm+OSTTzrL9A5FWVkZBw8exKBBg/Duu+/i8uXLEkt8tjc8Hg/Dhw+HpaUlwsLCsGXLFnh4eMDT01P21bYYcomSkhJMTU25FeFEIhFyc3M5j0JKSgru3LkDoCavpW4tBQ0NDVmazmAwWkGnCYOysjIAaNFKVTo6Ojh+/DjGjRuH8ePHg8/nQ1lZGdu3b2/0gfPLL7/gl19+AQDk5ua24xV0HEKhEDExMXB1dYWnpycSEhKkXuSjtRgbG2PJkiU4cOAA/v77b9y7dw9+fn6vhCeG0bHw+XzuxQ/UFF3Ky8vjhMLDhw+5uvCampoSUyS1tLTYtFkGQ87pNGFQW2e6oKCAqwtfS2MrVd28eRPvvvsuNm/ejAkTJgAA/vzzT7i6umLXrl31Vs4CgLlz52Lu3LkAamItXYX+/ftj9+7dmDp1KgICArBjx44Of4AqKSnh/fffh62tLcLDwxEcHIwZM2ZgyJAhHXpexquFgoIChEIhhEIhHB0dIRaLkZ+fzy03nZaWxi1Eo6amJhF60NHRYUKBwZAzOk0YmJqaQklJCffu3YODgwO3v7KyEg8fPmxwxakvvvgC48eP50QBULMq1kcffYTPPvuMW1zmVWHKlClYtWoVvv76azg4OOCzzz7rlPP2798fPXr0wPbt27m6B++//z5LLGO0CgUFBejr60NfXx/29vYgIhQWFkrUUqidNquioiLhUdDV1WVFlxgMGdNpf4Fqamp455136iUfHjt2DEQk8fKv5enTpw1Oq6usrEROTk6H2SpLVq5ciSlTpmDx4sU4fvx4p51XV1cXn3/+Od555x1cuHABwcHBePLkSaedn/HqwuPxoKOjAzs7O3h4eMDb2xteXl5wc3NDjx498OzZM5w/fx6HDh3C7t278eeff+L69evIzs5m02oZMqegoAABAQHo3r07tLS04OnpifT09Gb7hYeHw97eHmpqanBwcEB0dHS9NkVFRYiKioKHhwdUVVU7wvzW0eZlmFrAxYsXSVlZmX766ScqLi6mc+fOkampKS1ZsoSIiEJCQsjGxoaePn1KRETffPMNKSsr0//93/9RXl4eZWdn0/bt20ldXZ2+/PLLZs8nT6srtoTS0lJydHQkgUBAycnJnX7+lJQU+vLLL+mjjz6iEydOsFX7GB1OSUkJ3bt3j/755x/au3cvt4Lk9u3b6Y8//qArV65QRkYGVVVVydrUV55XZXXF9qCqqooGDx5MI0eOpNTUVEpPT6fJkyeTtbU1PX/+vNF+mzdvJoFAQMeOHaPi4mIKCwsjPp9PcXFxXJu0tDTq1q0bOTs706hRo6hbt25S29XRqyt2+rLLf/31Fw0aNIi6detGZmZm9M0331B1dTUREa1atYoAUGpqKhERicViCg0NJRcXF9LU1CQNDQ1ycnKin3/+mevTFF1VGBARPXr0iAwMDMja2poKCgo6/fwlJSW0detWmjt3LoWEhFBxcXGn28B4fXn+/Dk9ePCAzpw5Q/v37+eEQmhoKMXExNDFixcpLS2NKisrZW3qKwcTBv/jt99+Iz6fT5mZmdy+58+fk0AgoLCwsAb7lJaWkra2Nv34448S+/38/Gj48OES+/Ly8oiIaOfOnXIlDNhaCXLM6dOnMXLkSHh4eODo0aOdXseeiJCQkIADBw5AXV0dvr6+sLGx6VQbGAwAqKioQHZ2NpejkJeXx9U3MTAwgJGREUxMTGBoaNjhM3pedV6VAkdEhA0bNmDr1q3IyMiAlZUVli9fDi8vL6nHeO+991BSUoLY2FiJ/b6+vnjy5AlOnDhRr8+xY8cwfvx4ZGdnQygUcvtPnz6NESNGIC0tjZv6W8uuXbsQEBCAiooKqex6ZQocMVrOG2+8gZ9//hlz587Fl19+ifXr13fq+Xk8Ht5880307t0boaGh2LhxI8aOHYsJEyawxXYYnYqKigrMzc1hbm4OoCbPqFYoZGVl4fbt27h58yaAmunPdWc+yFXstoty7tw5PHv2TCbn1tPTw7Bhw1rcb82aNdiwYQPCw8MxcuRIxMfHY+bMmdDV1cVPP/2EK1euNNo3KCgI/v7+SElJgbu7e73jVlZWSEhIaLBvSkoKBAKBhCio7QMAqamp9YSBvMGEgZzj7++PW7duYcOGDXBwcMAHH3zQ6TaYmZlh+fLl2Lt3L44dO4a7d+/C19e3wZoUDEZnoKysDDMzM27qs0gkQk5ODudRSEpK4mYt6ejoSMx8UFdXl6XpjE6grKwM69atQ1BQECZNmgQAmDRpEuLj4+Ho6AhnZ+cm1/6oLc9fVlbWoto7zfUB0Gg/eYIJgy7Ahg0bkJiYiLlz58La2hpDhw7tdBu6deuG2bNno0+fPoiIiMA333yDWbNmwcnJqdNtYTBehs/nw8TEBCYmJgBqyqbn5uZyZZzv37+PpKQkADUP/drQg5GRETQ1NVkthWZozRe7LLlz5w7Kysrq1bpxcXEBAKnDTfr6+igoKKi3v7HaO831qT0u7zBh0AXg8/nYu3cvBg8eDE9PT1y+fFlmrigXFxf06tULYWFh2LZtG0aMGIFp06ZBWVlZJvYwGA2hqKgIIyMjGBkZoX///hCLxXj27BnnUXj8+DG3OJu6urpEGWeBQMCEwitCYyHPsWPHNhmHDw4Oxrx582BhYcEV56pLcnJyg7V3AMDCwgIFBQXIy8uTEAG11UAb6ydPMGHQRdDT00NMTAyGDh2KSZMm4dSpUzJbsMbAwIBb+TIuLg7379+Hv78/97XGYMgbCgoKMDAwgIGBARwcHEBEKCgo4IRCeno67t+/D6BmsbGXiy4xodC16Nu3L9TU1BAXFwc7Oztuf2JiIoyNjREZGSlVKGH69OmYNm2axEu+oqICR48exddff91gX3d3dwiFQuzZswfz58/n9h84cADDhg2T+/wCoJ2FQVFREQQCQXsOyahD3759ERkZiYkTJ8LX1xeRkZEye2Dx+XxMmTIFtra22LFjB7799ltMnz4db7zxBnuIMuQeHo8HXV1d6Orqom/fviAiFBcXS1RnTE1NBVDjdjY0NORCD/r6+qw6o5yjpqaGpUuXYtWqVTA2NsbYsWNx584deHl5YeXKlfDz85NqnPHjx8PBwQHe3t4IDQ2FkpISPv/8c6irq2PGjBkAgPT0dHh4eODTTz/Fp59+Cj6fz527T58+GDJkCKKjo/Hzzz83WORIHmk3YbBlyxasW7cON27cgI6OTnsNy3iJd955B9999x2WLFmCfv36YdmyZTK1x87ODitXrsTOnTsRERGBpKQkzJw5kyV4MboUPB4PAoEAAoEAffr0AQCUlJRwIiErK4urBKqkpARDQ0POo2BgYMBm6cghK1asgJaWFpYtW4bZs2ejV69eCAwMlFoUADUfQMeOHcNnn30GR0dHVFdXw8PDA/Hx8dwzrqqqCikpKRJJhQsXLgSfz0dAQADS09NhbW2NqKgojBs3rt2vsyNolzoGUVFR8Pb2xsqVK7Fq1ar2sKtd6Op1DBqDiDBz5kxERkYiOjoa7777rqxNglgsxokTJxAdHQ1tbW34+fnB0tJS1mYxGO1GWVmZhEehNsFMUVERQqGQEwqGhobg87tulPZVqWPwKtPRdQykEgalpaVwc3ODra0tFi1ahAEDBnDHLly4ADc3NwQGBmL58uVtMqa9eVWFAQCUl5djxIgRSE5Oxvnz52Fvby9rkwDUzNENCwtDfn4+JkyYgLFjxzK3K+OVpKKigpv1kJmZiWfPnoGIuHyG2joKRkZGXSo5lwkD+UcuhEFSUhIGDBiASZMm4cCBA5gyZQpCQkKgoKAAJycnTJs2rdOL70jDqywMgJrYlrOzM1RVVXHp0iW5qStQXl6OiIgIXLp0CTY2NpgzZw60tbVlbRaD0aFUVlZyQiErKws5OTlcdcaXiy7J88qlTBjIP3IhDFJSUjBgwACUlZUhMTERa9asQVxcHMzNzdGzZ08cPny4TUZ0FK+6MAD+57EZOnQo4uLioKSkJGuTANSEO86dO4eoqCgoKyvDx8cH/fr1k7VZDEanUVVVJVF0KScnB9XV1QBqii7VnSIpqxlGDcGEgfwjFyWRFRUVIRKJANQkm0VFRSEiIgLz5s3DyJEj22QAo20MHjwYoaGhmD17NhYuXIitW7fK2iQANclcrq6usLS0RGhoKLZs2QIPDw94enrKjXhhMDoSJSUldO/eHd27dwfwv6JLGRkZyMrKwt27d5GYmAgAEAgEnDfBxMQEGhoasjSd8ZojlTBQUFDglG4t3t7ecHR0xLhx41BZWYmQkJAOMZDRPLNmzcKtW7fwww8/oF+/fggICJC1SRxGRkZYsmQJDhw4gL///hv37t2Dn58fDA0NZW0ag9Gp1C26BNQk7Obl5XEehYcPH3JFcDQ0NCQ8ClpaWmwaMKPTkFoYAODiZbXY29sjJiYGI0aMgLm5ORYvXtwxVjKa5bvvvsPt27cxf/582Nraws3NTdYmcSgpKeH999+Hra0tdu/ejeDgYMyYMQNDhgyRtWkMhsxQUFCAUCiEUCiEo6MjxGKxRNGltLQ0ruqempqaRNElHR2dDhUKLz/rGfJDZyyILFWOwZMnT9CrVy9UVFQ06AY+fPgwvLy8cObMGQwaNKhDDG0Nr0OOQV2KioowZMgQ5Obm4tKlS3JZejM/Px87duzAvXv3MHjwYMyYMUOuE7EYDFlBRCgqKkJGRgaX0Pj8+XMANUWX6noUdHV12232z/3792FiYiJXeQ+M/1FWVoaMjAz07t27weOdlnz49OlT9OjRA2VlZY0+xKdMmYKHDx/i2rVrbTKoPXndhAEA3L17F4MHD4apqSnOnTsHTU1NWZtUD7FYjKNHj+Lo0aMwMDCAn58ft5wug8FoGCKSKLqUmZmJkpISADVePqCLPwAAIABJREFUuboeBQMDg1YLheLiYmRnZ6N79+5QVVVlngM5gYhQXl6O9PR0GBoacmWbX6bThIFYLEZmZiaXRNMQKSkpcHBwkCuvwesoDAAgLi4O48aNw8SJE3Hw4EG5rSNw9+5d7NixA8XFxfD09ISHh4fc2spgyCOlpaUStRQKCwsB1FTsMzQ05MSCUChsUdGl4uJi5OTkoKqqqqNMZ7QCJSUlCIXCRkUB0InCQFpu3bolV1PSXldhAAA//fQTFi5ciMDAQKxZs0bW5jRKaWkpdu/ejRs3bsDe3h4+Pj5y6eVgMLoC5eXlXNihtugS8L98hrrVGdnsoFcTuRMG8sbrLAyICH5+ftixYwf27t2L6dOny9qkRiEiJCQk4MCBA1BXV8ecOXO4evUMBqP1vHjxQsKjkJeXxyUW6uvrSxRd6tatm6zNZbQDTBg0w+ssDICah8LIkSNx7do1nDlzBk5OTrI2qUnS0tIQFhaG7OxsjB07FhMmTGCL0zAY7UhVVRWys7O5Wgo5OTkQi8UAwFVnrA0/qKqqythaRmvodGFQVVXVpdxPr7swAIDs7GwMGjQIRITLly/Lff2AFy9eYO/evTh79iwsLCzg6+vLrYPOYDDaF5FIxFVnzMrKQlZWFlezRltbW2LmA1sxtWvQ6cLA29sbN27cwLp16zB+/Pg2nbgzYMKghmvXrsHV1RUDBgxAfHx8l3AZXrp0Cb/99ht4PB5mzZqFgQMHytokBuOVp7q6WqLoUlZWFpeAqKmpKSEUNDU12YwFOaTThUF+fj6Cg4OxefNmzJw5E//973/l+iXDhMH/2L9/P6ZPn44PP/wQ27dv7xJ/0Lm5uQgLC8OjR4/wxhtvYPr06V1qlToGo6sjFouRn58vMUXyxYsXAAB1dXWJ0IO2tnaXeK686sgsx+DChQuYPn06TExM8Oeff0IgELTJiI6CCQNJVq5ciaCgIGzcuBELFy6UtTlSUV1djZiYGBw/fhwmJibw8/Nrctosg8HoOIhIojpjZmYmysvLAQAqKir1ii4xodD5yDT5MDMzEx4eHjAwMMDff//dojmynQUTBpKIxWJMnToVMTExOHbsGN566y1ZmyQ1iYmJ2LlzJ8rLyzFt2jSMGDGCPXQYDBlDRCguLpYQCqWlpQAAZWVliaJL+vr6rE5JJyDzWQlpaWlwcXHBrFmzsG7dujYZ0hEwYVCf0tJSDBs2DGlpabhw4QKsra1lbZLUFBcXY+fOnUhMTISTkxNmzpzJEqIYDDmjpKREYopkUVERgJriPLVFl0xMTGBgYMBmHXUAMhcGAPD7779j8uTJuH79Ovr27dsmY9obJgwa5tGjRxg0aBD09PRw4cIFuQ0FNYRYLMaJEycQHR0NbW1t+Pr6NloznMFgyJ6ysjKJZMb8/HwANatN1i26JBQKu9SsN3ml04XBn3/+iaFDh9Z7kYwZMwYaGho4ePBgm4xpb5gwaJx//vkHo0aNwqhRo/DHH390OeWempqKsLAw5OfnY8KECRg7dixzUzIYXYCKigoJj8KzZ8+4oktCoZALPxgZGbFk41bQqcKgdsrbkiVLsHLlSolj8fHxGDt2LFJTU+UqMYwJg6bZtm0bAgICsHjxYvzwww+yNqfFlJeXIyIiApcuXYKNjQ3mzJkDbW1tWZvFYDBaQGVlJVdDITMzE7m5uRCLxeDxeNDT0+NCD0ZGRmwlVinoNGFQXV2Nfv36wdDQEH///Xe9LzMiQo8ePfDFF19gwYIFbTKoPWHCoHk+/fRTbN26FeHh4Zg9e7aszWkxRIRz584hKioKysrK8PHxkav1OhgMRssQiUTIzs7mPAo5OTlc0SUdHR2JmQ9saej6tMd7T6qpBLt370ZaWhqOHz/eoLuWx+PBw8MDt2/fbpMxjM5n48aNSExMhL+/P6ytrTFkyBBZm9QieDweXF1dYWlpidDQUGzZsgUeHh7w9PRk8UoGowvC5/PRvXt3zvtcXV2N3NxcTijcu3cPiYmJAACBQCAx84EtwNY+SOUxqKysxMWLFzF8+PBG2zx8+BDm5uZyFatmHgPpePbsGQYNGoTy8nJcvnxZrsJBLaGqqgoHDx7EyZMnYWZmBn9/f7kvAc1gMFqG+P/bu/OwGvP/f+DPc+pUSrtshcpSjWVsEWMbZGxTkYQkQkKjDCNtH8ZJyDZiMJEsRZZosa9jSZF9iZS9FEVJJXVO9+8P3zm/OVM41enc59TrcV1dF+9z391P93V0Xt33/X69y8uRm5sruvWQnZ0tarrUsGFDsYWhtLW16920ZrmYlSDPqDCQ3P3792FlZQVzc3NcuHBBoRdQuX37Nnbs2AGBQIDx48ejV69ebEcihNQShmHEujNmZ2eLmi41aNBA7NaDrq5unS8UqDD4BioMqiY+Ph62trYYN24cIiMjFfo/UF5eHrZt24ZHjx6hZ8+emDBhAj24REg9wDAM3r9/L9Z0qaioCACgqqoqdutBX1+/zs1mosLgG6gwqLply5bB19cXy5Ytw8KFC9mOUyPl5eU4evQoDh8+DAMDA0ybNg2tWrViOxYhRIYYhhE1XfpnuemCggIAn5su/bc7ozzdDq8OmRYG6enpCtdIhgqDqmMYBhMmTMDevXsRGxuLn3/+me1INZaWloawsDAUFBRg1KhRGDRoUJ37LYEQIrmioiKxWw95eXkAPjddatKkiVjTJXls9/81MisMSktLoauri3HjxiE0NFRhKioqDKqnuLgY/fr1Q2pqKpKSkuSuo2V1FBUVYefOnbh16xY6dOgAFxcXaGlpsR2LECIHPn78WKHpEgBwuVyxpktNmjSR+6ZLMisMSkpKoK6ujlatWsHMzAwHDhxAw4YNa3RgWaDCoPoyMjJgaWkJdXV1XL16Ffr6+mxHqjGGYXD+/Hns378f6urqcHV1hYWFBduxCCFy5tOnT3j9+rXo1kNOTo6oO2OjRo3EZj6oqqqyHVeMTK8YNGjQACkpKXBzc0NxcTHOnTsn98UBFQY1k5SUhP79+6NPnz44fvx4nekLkJGRga1btyI7Oxs//fQTbGxsFOYqGCFE9srKyio0XSovLwcA6OnpiRUKbDddkllhUFZWBlVVVWRlZUFXVxdjx47Fhw8fcOzYMaioqCAtLQ2LFy9GeHi4XF1mocKg5nbu3AkXFxd4eHhg/fr1bMeRmk+fPmHfvn24dOkSTExMMG3aNDRq1IjtWIQQBSAQCMSaLr1+/RoCgQAAoKOjI/ZAo6x/gZZpS2Qej4eMjAw0b94cpaWlGDp0KHR1dfHrr7/Czs4OFhYWiIuLk6te9VQYSMf8+fOxevVq/PXXX3Bzc2M7jlQlJycjIiICHA4Hzs7O6NatG9uRCCEKpry8XFQo/POsQllZGQBAU1NTrJeCpqZmrU4Fl1lhwDAMlJSU8OLFCxgZGQEACgsL0bt3b9y/fx8TJ07Eli1b5OpqAUCFgbQIhUKMHDkSp0+fxpkzZ9CvXz+2I0lVbm4utm7diqdPn6JPnz5wdHSUu/cyIURxlJeXizVdysrKEnVn1NDQELuioKOjI9VCQabTFblcLp4+fSqaB37jxg0MGDAAXl5eWLJkicQHTEpKgre3N27cuAFdXV24u7tj4cKFX50+duLECfj7++Pu3bvQ0dHBqFGjsHz58grLP/8XFQbSk5+fDysrK7x9+xbJyckwNjZmO5JUCYVCxMbG4sSJE2jWrBmmT5+usK2hCSHyhWEY5OXlic18KC4uBgCoqamJrSCpp6dXo+nUMi0MlJSUkJ6eDhMTEzx//hw9evTAuHHjsG7dOokPlpycjL59+2Lp0qWYPn06bt++jbFjx2LatGng8/mV7nP8+HE4Oztjy5YtGDx4MJ49e4bJkydj4MCBCA4O/urxqDCQrkePHqFHjx5o1aoVEhIS5P7h0+pISUlBeHg4Pn78CAcHB/Tr10+hO0ASQuQPwzAoKCgQu/Xw4cMHAICKikqFpktVKRRkWhjweDw8fPgQrVu3xokTJxAREYFdu3ZV6WDW1tZQU1NDfHy8aCwyMhJubm7IysqqMK+cYRi0bdsWCxcuxLRp00TjRUVF0NDQ+ObxqDCQvhMnTmD48OGwtbXFgQMH6mSjoIKCAoSHhyMlJQVdunSBs7OzRO83QgiprsLCQrFbD+/fvwfwebXJfzddMjAw+GrTJZkWBioqKrh37x7atWtXrQMVFhZCR0cHu3fvxtixY0XjJSUl0NfXR2hoKJycnMT2SUpKQu/evZGXl/fN2waVocKgdqxduxa//vorFi1ahMWLF7Mdp1aUl5fj9OnTOHToELS1tTFt2jSF6/xJCFFcxcXFYrce3r17B+Dz1fvGjRuLpkc2adJEbCq5ND73JO71yOVyRfM2qyM9PR1CobBCYaGmpoYWLVrgyZMnFfa5efMmmjZtirdv32Lq1Km4fv06GjduDA8PDzg7O1c7C6kZLy8v3LlzB7///jvat28PBwcHtiNJHZfLxZAhQ9CuXTts2bIFq1atws8//4xhw4bVyaskhBD5oq6uDlNTU5iamgL4/Et0dna2qFi4efOmqOmSgYGB6IqCNEhcGJw6dapGC9D886BFZR309PX1kZubW2H83bt3KCsrw8SJE+Hj44Nly5bhyJEjmDZtGjgcDiZOnFjtPKT6OBwONm/ejNTUVLi4uKBNmzbo0qUL27FqhbGxMfz9/bF7927ExcXh4cOHcHV1ha6uLtvRCCH1iJqaGoyNjUUPfpeWloo1Xbp79y5u374tlWPJbHXFR48ewczMDLdv30anTp3EXuvYsSPGjh2LgIAAsfGVK1diwYIFuHbtmtj88jlz5uDMmTO4f/9+heOEhoYiNDQUAJCTk4Pnz5/Xwr+GAEB2djYsLS3B4XCQnJyMJk2asB2p1jAMg8TEROzZswc8Hg+TJ0+u8D4mhBC2CAQCvHnzBjY2NjW+lSCza6JGRkbg8XhIS0sTGy8tLcWTJ09gYmJSYR9TU1PweDx07dpVbLxLly5f/MB3c3PDtWvXcO3aNRgYGEjvH0AqaNq0KWJjY5Gbmwt7e3uUlpayHanWcDgc9O7dG35+ftDT08Off/6JvXv3ipqYEEIIm5SVldG8eXOpfK9qFQavX7+ucgc8dXV1jBw5Ert37xYbP3bsGBiGqXR534EDB4LL5SIpKUls/M6dOzAzM6t6cCJ1Xbt2RXh4OBISEjBr1izI6AIUa5o2bQpvb28MHDgQZ8+exYoVK5Cdnc12LEIIkZpqFQb5+fkICwur8n4+Pj44fPgwQkJC8OHDByQmJsLDwwOenp7Q1tbGhg0bYG5ujszMTACArq4u/P394ejoiLNnz+Lt27cIDw/Hxo0b4e/vX53opBY4OjrCz88PYWFhdWo9hS/h8XhwdHTErFmz8O7dOwQFBSExMbHOF0WEkHqCqYaHDx8yXC63Orsyp0+fZiwtLRlVVVWmRYsWTGBgICMUChmGYZhFixYxAJinT5+K7bNmzRrG1NSU4fF4TLt27Zjw8HCJjtWtW7dqZSRVJxQKGVtbW4bL5TInT55kO47MvHv3jlm1ahXj5ubGbN26lSkuLmY7EiGkHpPG5161Hj5MTU3Fd999B6FQWAulivRQHwPZ+vDhA3r37o3MzExcuXIFbdu2ZTuSTJSXl+PYsWOIj49Ho0aNMG3atDrXMpoQohik8blHE7KJ1GhqaiIuLg5cLhe2traizl11HZfLxYgRIzB//nwIBAIEBwfj1KlTNer7QQghbKHCgEiViYkJDhw4gLS0NDg5Ocn9VSVpatOmDQICAtCxY0ccOHAAGzZsQEFBAduxCCGkSqgwIFI3YMAAhISE4MiRI/D19WU7jkxpaGjA3d0dEyZMQGpqKvh8Ph48eMB2LEIIkRgVBqRWzJw5EzNnzkRwcDAiIiLYjiNTHA4H/fv3h6+vLzQ0NLBu3TocOnSoXl09IYQoLioMSK1Zt24dBgwYgGnTpuHq1atsx5E5Q0ND+Pr64ocffsDx48excuXKSlt/E0KIPKHCgNQaHo+H/fv3o1mzZrCzs8OrV6/YjiRzKioqcHZ2xvTp05GVlYXAwEBcv36d7ViEEPJFVBiQWtWoUSPExcXhw4cPsLOzw8ePH9mOxIru3bsjICAATZs2RWhoKHbt2lWnW0gTQhRXtQuDarQ/IPVUx44dERERgeTkZEyfPr3evncaNWqE3377DUOHDkVCQgKCgoJEXT4JIUReVKsw0NbWhouLi7SzkDrM1tYWgYGBiIyMxMqVK9mOwxolJSWMGjUKnp6eKCoqQlBQEM6fP19viyVCiPyR2bLLbKDOh/KFYRiMHz8e+/btQ3x8PEaMGMF2JFYVFBRg+/btuH//Pjp37oxJkyZBQ0OD7ViEEAVGnQ+JQuFwONi2bRu6dOmC8ePH1/v5/VpaWvDw8MCYMWNw9+5d8Pl8pKensx2LEFLPUWFAZEpdXR0xMTFQV1eHjY0N3r17x3YkVnG5XFhbW2PBggVQVlbGqlWrcOTIEWqnTAhhTbUKA/qhRWqiRYsWOHToEF68eAFHR0cIBAK2I7HO2NgYfn5+sLS0RFxcHNauXYu8vDy2YxFC6qFqFQY8Hk/aOUg906tXL2zevBmnT5/GvHnz2I4jFxo0aABXV1dMnjwZz58/B5/Px+3bt9mORQipZ6pVGNTh5xWJDE2ZMgVz585FSEgItm7dynYcucDhcNCrVy/4+vpCT08PGzduxN69e1FWVsZ2NEJIPaEs6YZ37tzBw4cPAXz+4RUeHi5WIHA4HHTq1AndunWTfkpSZwUHByMlJQWzZs2Cubk5+vTpw3YkudC0aVN4e3vj4MGDOHv2LNLS0jBt2jQ0bdqU7WiEkDpO4umKmzdvxt69ewEACQkJUFZWxqBBg0SvFxYW4tq1a3j//j24XPl4ppGmKyqG/Px89OzZE3l5eUhOTkarVq3YjiRX7ty5g+3bt0MgEGDcuHHo1asXOBwO27EIIXJIGp971epjYGBggO7du0NZWRmRkZHQ0tLCp0+f0KBBA5SWlkJZWeILEbWKCgPFkZqaip49e8LY2BgJCQk0n/8/8vLysG3bNjx69Ag9evTAhAkT0KBBA7ZjEULkDGt9DDgcDiIjI9GhQwcMHjwYHz58QH5+PlxdXeWmKCCKxczMDFFRUbh79y5cXFxo5st/6OrqYu7cubCxsUFycjKWLl2KZ8+esR2LEFIH1ejhw2XLlqFr164YP348mjRpQg+QkRoZOnQoVq5ciejoaAQGBrIdR+5wuVyMGDEC8+fPh0AgwIoVK3Dy5EkqogghUlXjhwFCQkLw8uVL/Pnnn9LIQ+q5uXPnwsXFBYsWLUJ0dDTbceRSmzZtEBAQgE6dOiE6Ohrr169HQUEB27EIIXVEtQoDU1NTKCkpAfi83vyff/6JZcuW0TRGUmMcDgebN2+GlZUVJk2aRPP4v0BDQwPu7u6YMGECHj16BD6fj5SUFLZjEULqAKktopSamgozMzNpfCupoYcPFVdWVhYsLS2hpKSE5ORkNG7cmO1IciszMxNbtmxBdnY2hgwZAltbW1HhTgipX+RqESV5KwqIYmvWrBliY2Px5s0bjBkzBqWlpWxHkluGhobw9fXFDz/8gBMnTmDlypXIzc1lOxYhREHJR8MBQirRrVs3hIeH4+LFi/Dw8KBbVV+hoqICZ2dnuLm5ITs7G3w+H8nJyWzHIoQoICoMiFwbN24cfH19sWXLFnrAVQLdunWDv78/mjVrhq1bt2Lnzp349OkT27EIIQqECgMi9/h8PmxsbODl5YUzZ86wHUfuNWrUCL/99huGDh2Ky5cvIygoCBkZGWzHIoQoCIkLgwcPHuDx48e1mYWQSnG5XERERMDc3BwODg70PpSAkpISRo0aBU9PTxQXF2PZsmU4d+4c3Y4hhHyTRIXBx48fYWlpiXbt2qFZs2aYNWsW7t27V9vZCBHR1NREXFwcOBwObGxsaN6+hCwsLBAQEABzc3NERUVh8+bNKCoqYjsWIUSOSVQYlJeXo7i4GLdv38aKFSvw9OlTdOnSBU5OTnj37l1tZyQEwOf+GQcOHEBqaiqcnJwgFArZjqQQtLS0MHv2bIwZMwZ3794Fn89HWloa27EIIXJKosJASUkJHA4HhoaGmDRpEo4dO4bExESkpqbi+++/Fy3HTEht+/HHHxESEoLDhw8jICCA7TgKg8vlwtraGgsWLACPx8Pq1atx+PBhaqdMCKlAosJAWVkZDMOgrKxMNNa9e3ckJiaiT58+6N+/Pz3cRGRm1qxZcHd3x7Jly7B792624ygUY2Nj+Pn5oUePHoiPj8fatWuRl5fHdixCiByRqPMhwzBQUlJCRkYGmjdvLvaaUCjE0KFDUVRUhMuXL9da0Oqgzod1V2lpKYYMGYIrV67gwoULsLS0ZDuSwklMTMSePXugrKwMFxcXfP/992xHIoTUkMw6H3I4HAAQu2LwDyUlJezYsQP37t3Dtm3bahSGEEmpqKhg//79aNq0Kezs7JCVlcV2JIXTq1cv+Pn5QU9PDxs3bkRUVFSl/8cJIfWLxNMVlZSUvvhDo3nz5vD09MSKFSukFoyQbzEwMEBsbCzev3+PUaNGoaSkhO1ICqdJkybw9vbGoEGDcO7cOSxfvhzZ2dlsxyKEsEgqhQEAuLu7o6SkBG/fvpVKMEIk0alTJ0RERODKlStwc3OjefrVwOPxMHbsWHh4eCA/Px9Lly5FQkICnUtC6qkqFQYCgeCLrxsaGiIlJQX6+vpSCUaIpOzs7MDn87Fr1y6sXr2a7TgKq2PHjggICICJiQl27tyJsLAwfPz4ke1YhBAZk7gwmDt3Lho1avTVbTQ0NGociJDq8PPzg4ODAxYsWICjR4+yHUdh6ejowMvLC7a2trh+/ToCAwPx7NkztmMRQmRIolkJiopmJdQvRUVF6Nu3Lx4/fowrV67A3Nyc7UgKLT09HWFhYcjPz8eoUaMwePBgcLm0vAoh8kxmsxIIUQQaGhqIiYmBmpoabGxsaH5+DbVp0wb+/v7o3LkzoqOjsX79empFTUg9QIUBqVNatmyJgwcP4tmzZ3B0dPzqczHk2zQ0NODm5oYJEyYgLS0NfD4fKSkpbMcihNSibxYGoaGhsLGxwZYtWyp9/dChQ3BwcKC+9URu/PDDD9i8eTNOnTqF3377je04Co/D4aB///7w8fGBhoYG1q1bh+joaPo/T0gd9c3CYMeOHYiLi8OOHTvExm/fvo1+/frB3t4e2dnZePXqVa2FJKSqXF1d4eXlhT/++IMab0mJoaEhfH190bdvX5w8eRLBwcHIyclhOxYhRMq+WRhoampi//79ohkHRUVFmDNnDrp164aioiIcOXIEFy9eRIsWLSQ6YFJSEvr37w9NTU20bNkSQUFBEi/kcvHiRfB4PCxevFii7Un9tnLlSlhbW8Pd3R0JCQlsx6kTVFRUMHHiRLi5ueH169cIDAxEcnIy27EIIVL0zcIgMjISAoEAUVFROHv2LCwsLLB3717s2LED169fx7BhwyQ+WHJyMgYMGAAbGxtkZmYiMjIS69evx6JFi76575s3b+Dk5AQLCwuJj0fqN2VlZezduxetWrXC6NGj8eLFC7Yj1RndunWDv78/mjdvjq1bt2Lnzp349OkT27EIIVIg8XTF+/fv4/vvv8ekSZOwatUq6OnpVflg1tbWUFNTQ3x8vGgsMjISbm5uyMrKgpaWVqX7lZeXY8iQIejWrRtev34NY2Njia4a0HRFAgAPHjyAlZUVTE1NcenSJeq3IUVCoRBxcXE4ceIEmjRpgunTp8PIyIjtWITUWzKdrti+fXtcv34d27Ztq1ZRUFhYiHPnzsHZ2Vls3N7eHgDEioX/Wrx4MXJzc7FkyZIqH5cQCwsL7NmzB7dv38aUKVOo1a8UKSkpYdSoUfD09ERxcTGWLVuGc+fO0TkmRIFVabpiTZZlTU9Ph1AoRLt27cTG1dTU0KJFCzx58qTS/U6cOIGQkBDs378fqqqq1T4+qd+GDx+O4OBg7N+/H0uXLmU7Tp1jYWGBgIAAmJubIyoqCps2bUJRURHbsQgh1SCzPgbFxcUAUOlaCvr6+sjNza0wnpGRgYkTJyI0NBRt27aV6DihoaHo3r07unfvTk9MEzHz5s2Ds7MzAgICcOjQIbbj1DlaWlqYPXs2xowZg3v37oHP5+PRo0dsxyKEVFGVCoPZs2dj+/btyM/Pr/KB/llnobJudAUFBRXWYRAIBHB0dISDgwPGjh0r8XHc3Nxw7do1XLt2DQYGBlXOSeouDoeD0NBQ9OjRA87Ozrhz5w7bkeocLpcLa2trLFiwAMrKylizZg3i4+MlnnlECGGfxIVBSUkJ3r17B09PTxgaGmLmzJl4/PixxAcyMjICj8dDWlqa2HhpaSmePHkCExMTsfGMjAxcvnwZYWFhUFNTE33t2rULgYGBFR5iJEQSampqiImJgba2NmxsbOiqUi0xNjaGv78/LC0tcfjwYaxZs4ZaVBOiIKq8iNKnT5+we/du/PHHH3j48CE8PDywePFiaGpqfnPf0aNHg8PhIDo6WjQWGxuL8ePHIysrC9ra2qLxsrKySgsPHx8fGBoawsPDA0ZGRmjYsOEXj0ezEsiXJCcno1+/fujRowdOnToFFRUVtiPVWYmJidizZw+UlZXh4uJSo2eVCCFfx8oiSqqqqpgyZQpu376NTZs2ISIiAl27dsWNGze+ua+Pjw8OHz6MkJAQfPjwAYmJifDw8ICnpye0tbWxYcMGmJubIzMzEzweD+bm5hW+tLW10ahRI5ibm3+1KCDkaywtLREWFoYLFy5gzpw59BR9LerVqxf8/Pygp6eHjRs3Ys+ePSgrK2M7FiHkC2r08KGrqytu374NIyMjvHv37pvbW1pa4ujRo4iIiICBgQEcHR3h7u4ueko8NzcXqamp9EODyMSECROwcOFC/PXXX9i0aRPbcergS5iBAAAgAElEQVS0Jk2awNvbG4MGDcLff/+N5cuXIzs7m+1YhJBKVPlWgiKhWwnkW4RCIezs7HDs2DGcPHkSAwcOZDtSnXfnzh1s374dZWVlGDduHHr37g0Oh8N2LELqBFZuJRBSlygpKSEyMhJmZmZwcHD4Yj8NIj2dOnVCQEAAjI2NsXPnToSFheHjx49sxyKE/B8qDEi9p6Wlhbi4ODAMAxsbGxQUFLAdqc7T1dXF3LlzYWtri+vXryMwMBBPnz5lOxYhBDUsDN6/fy+tHISwqnXr1ti/fz8ePnyIiRMn0rx7GeByuRg+fDjmzZuH8vJyBAcH48SJE3TuCWFZtQuDBw8eoFWrVrh48aI08xDCmkGDBuGPP/5AfHw8AgIC2I5Tb7Rp0wb+/v7o3LkzDh48iPXr19NVG0JYVO3CwMPDA61atYKVlZU08xDCqtmzZ8PNzQ1BQUHYs2cP23HqDQ0NDbi5uWHChAlIS0sDn89HSkoK27EIqZeqVRhER0fj8uXL2L17N3g8nrQzEcIaDoeD9evXo2/fvnB1daVZLTLE4XDQv39/+Pj4QENDA+vWrUN0dDSEQiHb0QipV6pcGDAMg0WLFuG3335D+/btayMTIaxSUVFBdHQ0mjRpAjs7O2RlZbEdqV4xNDSEr68v+vbti5MnTyI4OJhaVxMiQ1UuDPbt24f379/Dx8enNvIQIhcMDAwQGxuL/Px8jBo1CiUlJWxHqldUVFQwceJEuLm54fXr1wgMDERycjLbsQipF77Z4GjWrFlifz9+/Dh0dHS++GzB77//LjerGlKDI1JTBw8ehL29PVxcXBAeHk6NeFiQm5uLsLAwPHnyBD/88AMcHR2hqqrKdixC5JI0PveUv7XBfxuP9O/fv9Lxf9BUI1KXjB49Gr///jsWLVqEjh07Yt68eWxHqncaNWqE+fPnIz4+HsePH8fjx48xffp0GBkZsR2NkDqJWiIT8g3l5eVwdHTEwYMHcfjwYQwbNoztSPXWw4cPsW3bNhQVFWHMmDEYMGAAXcUh5F+oJTIhMsDlcrF9+3Z06tQJ48aNw8OHD9mOVG+Zm5sjICAA5ubmiIqKwubNm1FUVMR2LELqFCoMCJGAhoYGYmNjoaqqCltbW+Tl5bEdqd7S1NTE7Nmz4eDggLt374LP5yMtLY3tWITUGVQYECKhli1b4uDBg3j69CnGjRsHgUDAdqR6i8vlYvDgwfD29gaPx8Pq1asRHx9PzzgRIgVUGBBSBX369MGmTZtw8uRJLFiwgO049V6rVq3g5+eHnj174vDhw1izZg1dzSGkhqgwIKSKpk6dijlz5mDt2rUIDw9nO069p6amhilTpmDy5Ml48eIF+Hw+bt++zXYsQhSWVAsDWm2R1BerV6/G4MGD4e7ujsuXL7MdhwDo1asX/Pz8oKenh40bN2LPnj0oKytjOxYhCkdqhcGGDRvQsWNHuoxH6gVlZWXs3bsXLVu2xOjRo/Hy5Uu2IxEATZo0gbe3NwYNGoS///4by5cvR3Z2NtuxCFEoUikMoqKi4OnpialTp0JXV1ca35IQuaenp4e4uDgUFxfDzs4OxcXFbEciAHg8HsaOHQsPDw/k5+dj6dKlSEhIQB1u2UKIVElUGBQWFqJbt26YOHEibt68KfbalStXMHnyZCxZsgSLFi2qlZCEyCsLCwtERUXh5s2bmDJlCn34yJGOHTsiICAAJiYm2LlzJ8LCwr7YsZUQ8v9JVBi8fPkS9+/fh0AggKWlJRwdHfHmzRvk5ubCwcEBs2fPhp+fX21nJUQuDR8+HCtWrMC+ffsQFBTEdhzyLzo6OvDy8oKtrS2uX7+OwMBAPH36lO1YhMg1iQoDLpcLLpeLqKgo3LlzBxwOB+bm5rC2tka3bt2wevXq2s5JiFybP38+Jk6cCH9/f8TGxrIdh/wLl8vF8OHDMX/+fJSXlyM4OBgnTpygngeEfIFEhYGSkpKomct3332HqKgorF+/HmlpaTA1Na3VgIQoAg6Hgy1btqBHjx6YOHEi7t69y3Yk8h+tW7eGv78/OnfujIMHD2L9+vUoKChgOxYhckfiKwZCoVBszMnJCUlJSdi3bx9++eWXWglHiCJRU1PDoUOHoKWlBRsbG+Tm5rIdifyHhoYG3Nzc4OTkhLS0NCxZsgQpKSlsxyJErkhcGACo8GBVhw4dEBsbi/DwcKxatUr66QhRMM2bN0dMTAyysrIwZswYmkcvhzgcDvr16wcfHx9oampi3bp1iI6OphbXhPyfKhUGlf3H6dq1K3bt2gU/Pz8kJydLNx0hCsjS0hJhYWE4f/48PD092Y5DvsDQ0BA+Pj7o168fTp48iZUrVyInJ4ftWISwTuLCgGGYCrcT/jFq1CiMHDkSbm5uUg1HiKJycnKCt7c3Nm3ahE2bNrEdh3yBiooKnJyc4Obmhjdv3iAwMJB+wSH1HoeRYOJ1eXk5srKyYGho+MVtUlNT0alTJ1y6dAmWlpZSDVld3bt3x7Vr19iOQeopoVAIW1tbnDhxAqdOncKAAQPYjkS+4u3btwgLC8Pjx4/xww8/wNHREaqqqmzHIqRKpPG5J1FhIKm7d++iY8eO0vp2NUaFAWFbQUEBrKys8ObNGyQnJ8PExITtSOQrhEIh4uPjcfz4cTRp0gTTpk1DixYt2I5FiMSk8bkn1UWU5KkoIEQeaGlpIS4uDuXl5bCxscGHDx/YjkS+QklJCXZ2dvDy8sLHjx+xfPlynDt3jjpaknqFll0mpJa1adMG+/fvx4MHD+Ds7EyNdRSAubk5AgICYG5ujqioKGzatAmFhYVsxyJEJiS+lfDixYtvbqOjowMtLa0ah5IWupVA5Mn69esxZ84c+Pv7g8/nsx2HSIBhGJw5cwYHDx6ElpYWXF1d0a5dO7ZjEfJFMn3GgMvlgsPhVLikxuFwRH/28/PDkiVLahRImqgwIPKEYRi4ublh69atiIqKgqOjI9uRiIRevHiBLVu2ICcnByNGjMCIESNE07gJkScyLwyuXr1a6cNTaWlp+OGHH1BUVAQ1NbUaBZImKgyIvCktLcWgQYNw/fp1XLp0CV27dmU7EpFQSUkJ9uzZg6SkJLRt2xaurq7Q09NjOxYhYmT+8KGenh709fUrfOnq6gKAXBUFhMgjFRUVREdHw8DAALa2tsjOzmY7EpGQmpoapkyZgilTpuDFixcIDAzErVu32I5FiNTRtTBCZKxx48aIjY3Fu3fvMHr0aHz69IntSKQKrKys4OfnB319fWzatAl79uyh1tekTqHCgBAWdO7cGTt37kRiYiLc3d1pOpyCadKkCRYsWIDBgwfj77//xvLly5GVlcV2LEKkggoDQlhib2+PRYsWYfv27fjjjz/YjkOqiMfjwcHBAR4eHsjPz0dQUBASEhKoyCMKjwoDQlj0v//9D/b29pg/fz5OnDjBdhxSDR07dkRAQABMTEywc+dOhIWF4ePHj2zHIqTaJC4M/j0tkRAiHVwuFzt27EDHjh3h6OiIR48esR2JVIOOjg68vLxgZ2eH69evIzAwEE+fPmU7FiHVInFh8K3LY3T5jJDq0dDQQGxsLFRUVGBjY4P8/Hy2I5Fq4HK5GDZsGObPnw+GYRAcHIwTJ05Qp0uicCQuDPbv349mzZpV+pqBgQF1ciOkBlq1aoXo6Gg8fvwY48eP/+IS50T+tW7dGv7+/ujcuTMOHjyIkJAQvH//nu1YhEhM4sLA3t4eDRo0qPQ1PT09+Pn5SfR9kpKS0L9/f2hqaqJly5YICgr6akWdk5ODGTNmwMjICJqamujVqxfOnDkjaWxCFEbfvn2xceNGHD9+HN7e3mzHITWgrq4ONzc3ODk5IT09HXw+H/fv32c7FiESkenDh8nJyRgwYABsbGyQmZmJyMhIrF+/HosWLap0e4FAgKFDh+L58+c4ffo0nj9/DgcHB/z000+4cuWKLKMTIhPTp0+Hh4cHVq9ejR07drAdh9QAh8NBv3794OvrC01NTYSEhCA6OhoCgYDtaIR8lcQtkaXB2toaampqiI+PF41FRkbCzc0NWVlZFRZgio2NFXUZa9iwoWh88ODBMDU1RWho6FePRy2RiSIqKyvD0KFDcenSJZw/fx5WVlZsRyI1VFpaiv379+PChQswNjbGtGnTYGBgwHYsUgfJvCVyTRQWFuLcuXNwdnYWG7e3twcAsWLhH7a2trh165ZYUQB8rsQLCgpqLywhLOLxeNi3bx9atGgBOzs7ZGRksB2J1JCKigqcnJwwY8YMvHnzBoGBgbh69SrbsQiplMwKg/T0dAiFwgpLlqqpqaFFixZ48uRJpfu1bNlS7O/R0dE4c+aMqKAgpC7S19dHbGwsiouLYWdnh+LiYrYjESno2rUr/P39YWhoiLCwMOzYsYNaYhO5I7PC4J8fbPr6+hVe09fXR25u7lf3Ly8vR2BgIBwdHeHr6wsHB4dKtwsNDUX37t3RvXt35OTk1Dw4ISxp3749IiMjcePGDUydOpWmBNcR+vr6mDdvHoYPH47ExEQsXboUL1++ZDsWISIyKwwaNWoEAMjLy6vwWkFBgej1yuTk5MDa2hqbN29GXFwcAgMDv7itm5sbrl27hmvXrtE9PKLwfv75ZwQFBSEqKgrLly9nOw6REiUlJdja2sLLywslJSVYvnw5zp49S8UfkQsyKwyMjIzA4/GQlpYmNl5aWoonT57AxMSk0v2ysrLQp08f6Orq4t69exg+fLgs4hIiN7y9vTF+/Hj4+fkhLi6O7ThEiszNzREQEAALCwvs3bsXmzZtQmFhIduxSD0ns8JAXV0dI0eOxO7du8XGjx07BoZh8PPPP1fYRyAQwN7eHj/88AP2798PHR0dWcUlRG5wOByEhYWhW7ducHJywr1799iORKRIU1MTs2fPxtixY3H//n3w+XxqjU1YJdM+Bj4+Pjh8+DBCQkLw4cMHJCYmwsPDA56entDW1saGDRtgbm6OzMxMAEBYWBiys7OxYcMGCIVCCAQC0Rd1hiP1SYMGDRATE4OGDRvCxsYGb9++ZTsSkSIOh4NBgwbB29sbKioqWLNmDeLi4ujnHGGFTAsDS0tLHD16FBERETAwMICjoyPc3d2xdOlSAEBubi5SU1NRVlYGAEhMTMTTp0+hoaEBHo8n9tW6dWtZRieEdYaGhoiJicGrV6/g4OAg+n9C6o6WLVvCz88PPXv2xJEjR7BmzRq8e/eO7ViknpFpgyNZowZHpC7auXMnXFxcMGvWLPz5559sxyG1JCkpCbt374aSkhJcXFzQuXNntiMRBaBQDY4IIdIxadIkzJ8/Hxs3bsTmzZvZjkNqiZWVFfz8/NCoUSNs2rQJu3fvpqtERCaoMCBEAS1fvhzDhg3DL7/8gvPnz7Mdh9SSJk2awNvbG4MHD8b58+exbNkyZGVlsR2L1HFUGBCigJSUlLBnzx60bt0a9vb2ePr0KduRSC1RVlaGg4MDfvnlFxQUFGDp0qW4dOkS9TwgtYYKA0IUlLa2tujJdVtbW3z48IHtSKQWdejQAQEBAWjdujV27dqFrVu34uPHj2zHInUQFQaEKLB27dph7969uH//PiZNmoTy8nK2I5FapK2tDU9PT9jZ2eHGjRsIDAykq0VE6qgwIETBDRkyBKtXr0ZMTAwWL17MdhxSy7hcLoYNG4b58+eDYRgEBwfj+PHjVBQSqaHCgJA6wNPTE66uruDz+di3bx/bcYgMtG7dGv7+/ujSpQsOHTqEkJAQvH//nu1YpA6gwoCQOoDD4WDjxo3o3bs3Jk+ejBs3brAdiciAuro6pk+fjokTJyI9PR18Ph/3799nOxZRcFQYEFJHqKqq4uDBg9DX14etrS1ev37NdiQiAxwOB3379oWvry80NTUREhKCAwcOQCAQsB2NKCgqDAipQ5o0aYK4uDi8ffsWo0ePxqdPn9iORGSkefPm8PHxQf/+/XHq1CmsXLkSOTk5bMciCogKA0LqmC5dumDHjh24fPkyZs6cSfPd6xEVFRVMmDABM2bMwJs3bxAYGIirV6+yHYsoGCoMCKmDHBwcEBAQgPDwcKxbt47tOETGunbtioCAABgaGiIsLAzbt29HSUkJ27GIgqDCgJA6avHixbCzs8O8efNw8uRJtuMQGdPT08O8efMwYsQIJCUlISgoCC9fvmQ7FlEAVBgQUkdxuVzs2rUL7du3h6OjIx49esR2JCJjSkpKsLGxwdy5c/Hp0ycsX74cZ8+epdtL5KuoMCCkDmvYsCHi4uKgrKwMGxsbmudeT5mZmSEgIAAWFhbYu3cvNm7ciMLCQrZjETlFhQEhdZyxsTEOHDiAx48fY/z48RAKhWxHIixo2LAhZs+eDUdHR6SkpIDP5yM1NZXtWEQOUWFASD3Qv39/bNiwAceOHYOPjw/bcQhLOBwOBg4cCG9vb6iqqmLt2rWihbgI+QcVBoTUEzNmzMCsWbOwcuVK7Ny5k+04hEUtW7aEr68vrKyscOTIEaxZswbv3r1jOxaRE1QYEFKP/PHHH/jxxx8xffp0JCUlsR2HsEhNTQ2TJ0+Gq6srXr58CT6fj5s3b7Idi8gBKgwIqUd4PB72798PQ0NDjBo1CpmZmWxHIizr2bMn/P39YWBggM2bN2P37t0oLS1lOxZhERUGhNQz+vr6iIuLQ2FhIezs7PDx40e2IxGWNW7cGAsWLIC1tTXOnz+P5cuX49WrV2zHIiyhwoCQeqhDhw6IjIzE9evXMW3aNJrXTqCsrIwxY8bgl19+QUFBAYKCgnDp0iV6b9RDVBgQUk/Z2Nhg6dKl2L17N4KDg9mOQ+REhw4dEBAQgNatW2PXrl3YsmULiouL2Y5FZIgKA0LqsYULF2LcuHHw8fFBfHw823GInNDW1oanpydGjRqFmzdvIjAwEE+ePGE7FpERKgwIqcc4HA7CwsLQtWtXTJgwAffv32c7EpETXC4XQ4cOxW+//QYAWLlyJY4fP47y8nKWk5HaRoUBIfWcuro6YmJi0LBhQ9jY2ODt27dsRyJyxNTUFP7+/ujSpQsOHTqEkJAQaq1dx1FhQAiBkZERDh06hIyMDIwdOxZlZWVsRyJyRF1dHdOnT4ezszPS09PB5/Nx7949tmORWkKFASEEAGBlZYXQ0FCcPXsWv/76K9txiJzhcDjo06cPfH19oampifXr1+PAgQMQCARsRyNSRoUBIUTExcUF8+bNw4YNGxAaGsp2HCKHmjdvDh8fH/Tv3x+nTp1CcHAw3rx5w3YsIkVUGBBCxKxYsQJDhw7F7NmzceHCBbbjEDmkoqKCCRMmwN3dHTk5OQgMDMSVK1fYjkWkhAoDQogYJSUl7NmzB6amprC3t8fz58/ZjkTkVJcuXRAQEIAWLVpg27Zt2L59O0pKStiORWqICgNCSAU6OjqIi4tDWVkZbGxsUFhYyHYkIqf09PTw66+/YsSIEUhKSkJQUBBevHjBdixSA1QYEEIqZWZmhr179+LevXtwcXGh+evki5SUlGBjY4O5c+fi06dPWLFiBc6cOUPtlBUUFQaEkC/66aefsGrVKhw8eBBLlixhOw6Rc2ZmZggICMB3332Hffv24c8//6SrTQqICgNCyFd5eXlh8uTJ+P3333HgwAG24xA517BhQ8yaNQuOjo548OAB+Hw+UlNT2Y5FqoAKA0LIV3E4HGzevBm9evWCi4sLbt26xXYkIuc4HA4GDhwIb29vqKqqYu3atYiLi4NQKGQ7GpEAFQaEkG9SVVXFwYMHoaenB1tbW5q3TiTSsmVL+Pr6wsrKCkeOHMGaNWvw7t07tmORb6DCgBAikaZNmyImJgY5OTkYPXo0Pn36xHYkogDU1NQwefJkTJ06FRkZGeDz+bh58ybbschXUGFACJFYt27dEB4ejoSEBMyePZueOicS69GjB/z9/WFgYIDNmzdj9+7dKC0tZTsWqQQVBoSQKnF0dISfnx/CwsKwYcMGtuMQBWJgYIAFCxbA2toa58+fx/Lly/Hq1Su2Y5H/oMKAEFJlS5Ysga2tLebOnYvTp0+zHYcoEGVlZYwZMwa//PILCgoKEBQUhIsXL9LVJzlChQEhpMq4XC527doFCwsLjB07FmlpaWxHIgqmQ4cOCAgIQJs2bRAREYEtW7aguLiY7VgELBQGSUlJ6N+/PzQ1NdGyZUsEBQV9taNaXl4e3N3dYWhoCC0tLYwaNQqZmZkyTEwIqYympibi4uLA5XJha2uL9+/fsx2JKBhtbW3MmTMHo0aNws2bNxEYGIjHjx+zHavek2lhkJycjAEDBsDGxgaZmZmIjIzE+vXrsWjRokq3FwgEGDZsGNLS0pCQkICHDx+Cy+Vi4MCBVFkSIgdMTExw4MABpKWlwcnJieapkyrjcrkYOnQoFixYAABYtWoVjh07Ri24WcRhZHhjx9raGmpqaoiPjxeNRUZGws3NDVlZWdDS0hLbPjIyEpMnT8bLly/RtGlTAEBxcTGaN2+O1atXY+rUqV89Xvfu3XHt2jXp/0MIIWI2bdqEWbNmYcGCBVixYgXbcYiC+vjxIyIiInDt2jWYm5vD1dUV2trabMdSKNL43JPZFYPCwkKcO3cOzs7OYuP29vYAIFYs/CMuLg7W1taiogAA1NXVYW9vj6ioqNoNTAiR2MyZMzFz5kwEBwcjIiKC7ThEQTVo0ADTpk2Ds7MzHj9+DD6fj3v37rEdq96RWWGQnp4OoVCIdu3aiY2rqamhRYsWePLkSYV9UlNTK2wPAG3btq10e0IIe9atW4cBAwZg2rRpuHr1KttxiILicDjo06cP/Pz8oK2tjfXr12P//v0QCARsR6s3ZFYY/PNMgL6+foXX9PX1kZubW+k+VdmeEMIeHo+H/fv3o3nz5rCzs6OHhEmNNGvWDAsXLsSAAQNw+vRprFixAq9fv2Y7Vr2gLKsDNWrUCMDnWQYtWrQQe62goED0+n/3ycvLqzD+pe0BIDQ0FKGhoQCAe/fuoXv37jWNTr4iJycHBgYGbMeo8xTpPOvp6QEAbG1tWU5SNYp0jhVVTc7x9evXcejQISknqnsePnxY4+8hs8LAyMgIPB4PaWlp6NSpk2i8tLQUT548gYmJSYV9TE1NK50f/fDhw0q3BwA3Nze4ubkBoIcPZYHOsWzQea59dI5rH53j2ieNX4ZlditBXV0dI0eOxO7du8XGjx07BoZh8PPPP1fYZ+zYsTh58qTYbYOSkhIcOXIEjo6OtZ6ZEEIIqW9k2sfAx8cHhw8fRkhICD58+IDExER4eHjA09MT2tra2LBhA8zNzUX3JocPH45OnTrByckJL168QFZWFqZMmQINDQ1MmDBBltEJIYSQekGmhYGlpSWOHj2KiIgIGBgYwNHREe7u7li6dCkAIDc3F6mpqSgrKwPwuaf2sWPH0LhxY3z//fcwMzNDSUkJzp49Cw0NjW8e759bCqT20DmWDTrPtY/Oce2jc1z7pHGOZdrgiBBCCCHyjRZRIoQQQohInSwMqrpQE/m2nJwchIWFoUePHjA3N6/w+sePH+Hr6wtjY2NoaGhg8ODBSElJYSGpYvr7778xYMAAaGtro3nz5nB2dq4wZ5sWFKsZoVCIFStWwMzMDGpqajA2NoaXl5fY4k/0PpauGTNmgMPh4NmzZ6IxOsc1p66uDg6HU+GrpKQEQM3PcZ0rDKq6UBP5tsTERLRo0QLbt2+HkpJSpdtMnDgRhw8fxpEjR/DixQuYmZmhf//+yM7OlnFaxZOYmIhhw4bB1tYWT548wfnz55GVlYWffvpJ1O2NFhSrudmzZ2PHjh3Ytm0b3r59i8OHD+PatWtibdrpfSw9ERERlXbApHNcM2/fvsXHjx/x9OlTlJWViX2pqakBkMI5ZuqYwYMHMyNHjhQbi4iIYNTV1Zn379+zlEqxffr0SXTuFi1axJiZmYm9funSJQYAc+3aNdGYUChkzMzMGH9/f5lmVUR2dnbM9OnTxcZevnzJAGASEhIYhvn8HlZWVmaysrJE2xQVFTHa2trM1q1bZZpXUWVkZDCZmZliYwcOHGC4XC5TXFxM72Mpun//PqOjo8Pcvn2bAcA8ffqUYRj6WSENN2/eZHg8HiMUCit9XRrnuE5dMajOQk3k21RUVCqsfPlvcXFxsLCwQLdu3URjXC4XTk5OtNiVBCIjIxEUFCQ2xuFwAHzu8gnQgmLSYGhoiObNm4v+npqairVr10JPTw8NGjSg97GUFBUVYcyYMfD29hZrZgfQzwppePnyJVq0aAEut/KPb2mc4zpVGFRnoSZSc19b7OrZs2dgaOLLV6mrq4u1+BYIBJgzZw4MDAzQp08fALSgmDSNHj0aDRs2hLm5OW7duoWwsDAA9D6WFjc3NxgbG8Pb27vCa3SOa+7ly5do2rQpVq9ejR49euC7777D9OnT8ebNGwDSOcd1qjCozkJNpOa+ttiVQCBAfn4+C6kU06tXrzBo0CBcvHgRcXFxaNiwIQBaUEyatm7diqSkJGzatAmBgYEYOnQoAHofS8PmzZtx4cIF7Nq1S3TV69/oHNfcy5cvcf36dSgrKyMqKgrbt2/Hy5cvYWVlhcLCQqmc4zpVGPx7oab/+trCS6RmvrbYlbKyMnR0dFhIpXhOnjyJTp06QVNTE7du3YKVlZXoteosKEYqp6enhw4dOsDd3R3KysoYMmQIGIah93EN3bhxA7/99hv27t1b6QcTQD8rpGHu3Lm4ffs2PD09YWpqih49eiA6Ohr5+fnYtWuXVM5xnSoM/r1Q0799baEmUnNfW+yqVatWlf7mQMTt27cPo0ePxooVK3D48GGxe+FA9RYUI9/2008/4fz580hJSaH3cQ3FxcWhqKgIAwcOhJqamugLAMzMzNC0aVM6x1LQuHFjmJmZiY1paGigdevWePz4sVTOcZ0qDKqzUBOpubFjx+LevXu4e/euaIxhGERHR9NiVxK4ceMGpk6dipiYGEydOrXSbWhBseU4hW0AAAnBSURBVJrJz8+Hvb09MjIyxMYfP34MAODxePQ+riEPDw+kpKTg1q1bYl8AcPToUVy8eJHOsRTk5uYiPT1dbOzDhw9IS0tD27ZtpXOOazBrQi5dvXqVUVFRYdatW8cUFBQwly9fZoyMjJiFCxeyHa1OqGy6IsMwjK2tLdOlSxcmJSWFefv2LePl5cXo6+szGRkZLKRULFZWVoyvry9TVlZW4eufKUllZWVM9+7dmSFDhjDPnz9nXr16xYwbN45p06YNU1hYyPK/QP4JhULG2tqa6dixI3Pp0iWmoKCASUhIYNq2bcv06tWLKS8vZxiG3se1Af+arsgwdI5rytPTkzEyMmIOHz7MFBQUMA8ePGCGDRvGtGzZkikqKmIYpubnuM4VBgzDMKdPn2YsLS0ZVVVVpkWLFkxgYOAX53ySqvlSYVBUVMT88ssvjIGBAaOurs4MGjSIuXv3LgsJFQ+AL34tWrRItF1OTg4zceJERkdHh9HU1GTs7OyYFy9esBdcwZSUlDABAQGMqakpo6qqyhgbGzMzZ85kcnJyRNvQ+1j6/lsY0DmuGaFQyPzxxx9Mhw4dGDU1NUZHR4ext7eX6jmmRZQIIYQQIlKnnjEghBBCSM1QYUAIIYQQESoMCCGEECJChQEhhBBCRKgwIIQQQoiIMtsBCCHSIxAIwOPxYGFhUenqawKBANnZ2d/sl56eno62bdviw4cPovUaJPXs2TOYmJggJydHonbNdnZ2uHLlCrS1tSu89v79e/Ts2RMxMTFi49nZ2bh79y6sra2hrKwMgUCALVu2YOTIkWjWrBn69++Pv/76C+bm5lXKTgihwoCQOuny5cuV9kTPyMhAhw4davXYAoEAwOdW5JJatmwZJk+eXGF8+/btFYoC4HOnt7Fjx4pWlkxLS8PChQvh6OiIkpISJCQkVGgrTQiRDBUGhNRBffv2hZKSUoXxsrKyWj/2P6ucvn//XuIPZ39/f6xatarCeH5+Prp3715hvG3btvDy8hItNfvmzRts2LABWlpauHLlCtTU1LBt2zaxfVxdXaGlpVXVfw4h9Q4VBoTUQW5ubmjQoEGF8by8PCxdulRsrLi4GOXl5RXGAKCoqKjC9+ByuVBXV//isV+/fg3g8+0ICwuLr+ZkGAYHDhz46jb/bPfP4i95eXmwtLQEAKxfvx5CoRAuLi4AgNjYWHTv3h1t27ZFRkYG3r9/j6ioKMyYMQNCofCbxyGEUGFASJ2ipKSEPXv2fPH1hg0bVvhN+rvvvsPz588r3b5p06YVxlq1aoVnz5598RiPHz8Gh8NBcnLyNxcuW7duHRYsWPDVQqO4uBjBwcHw8vICAOjq6iI9PR2PHz+Gs7MzEhMTMWTIEHh7e6NVq1b48ccfMX36dMyaNQtJSUlISUmp9GoEIaRyVBgQUgdkZGSgT58+Em//66+/AgBu3rxZ6Yf8oUOHMHr0aAQFBcHHx6dKWS5fvoxJkyYhJiYGS5Ys+eb2EyZMwPbt27/4emXPHsTExCAgIAB79+5Fp06d0KNHD/Ts2RPr1q3DhQsX0LVrVwCfr1rU9jMVhNQ1VBgQUgcYGRnh2bNnGDlyJObPn48BAwbg4cOHGDNmDM6ePVvhQUA1NbWvzhi4fPkyfvzxR2zevBkLFiyo9HmFypSWluL48eO4evUq+vbti7Nnz2LgwIFf3Sc2NvarH96ZmZno3Lmz6O+vX79GeHg4jhw5gqKiImhqamLy5Mn48ccfsWXLFjg6OuL06dMAgFu3bqFnz54SZSeEfEaFASF1zIwZM6CpqYmSkhIAwPz587Fv3z6YmZmBx+NBIBAgJSUFmZmZMDAwqLC/UCjEoUOHEB4ejoULFyIsLAxubm4SHXvXrl1o164djI2NMW/ePMybNw9Xr14Fj8f74j62trZVumJQVlaG27dvo1+/fnj9+jU0NTVhbGwMAFBXV8f9+/cxZMgQXLlyBVevXsXixYslyk4I+YwKA0LqmL/++kvsisHOnTvRuHFjNG/eHL/++itCQ0MRHx9faVEAAHv37oVQKETv3r3B5/MxatQoWFtbw8TE5KvHffPmDXx9fXHo0CEAgIeHB3bt2gVPT09s3Ljxi/tV9YrBP1dH/ve//6GkpATBwcFYtWoVsrKysHr1agAAn8+Hu7s7unfvXuU+DITUe1JeKpoQwqIRI0Yw7dq1Y7p168a0b9+ead++PcMwDJObm8u0adOGiYmJYQwNDZl79+5Vun9GRgZjYGDAxMTEiMY8PDwYCwsLJjMz84vHLSgoYCwtLRlXV1ex8fT0dKZRo0aMh4cHIxAIKuy3du1axsXF5av/JhcXF2bt2rViY3l5eYyOjg7j5ubG3L9/n2nXrh1z8+ZN0evZ2dlMy5YtmcaNGzMPHz786vcnhIijlsiE1DEbN25EfHw8+Hy+aExfXx/r1q2DnZ0d7Ozs0L59+wr7vXz5EoMHD8bPP/8MW1tb0fiqVatgamqKvn374u7duxX2e/DgAXr27AkDAwP89ddfYq+1bt0aR48exZ49ezBw4EA8evRI7HU9PT0kJSXB3Nwcbdq0gbm5uejLyMgI5ubmSEpKgp6enth+Ojo6ePLkCYyMjNChQwfk5+fj48ePAIBXr17hp59+woYNG+Dl5YVBgwYhMTGx6ieSkPqK7cqEEFJz5eXlTJcuXRgNDQ3GxMSEGTp0KDNp0iSmffv2THl5ORMfH8+Ympoy8+fPZ1q3bs04ODgwFy9eZBiGYUpLS5nQ0FBGV1eXcXV1ZYRCYYXvX1JSwjg4ODDKysrMwoULReOLFi1ieDweM3XqVKa4uPiL+VJTU5lOnTox7dq1Y8rKykTjAoGAiY2NZXr37s0MHDiQKSkpYRjm85WLjh07Mu3bt2f8/PyYR48eiX2/mzdvMkFBQYyRkRGzcOFC5q+//mLatWvHrF69mjEwMGC2bNki2vZ///sfo6yszFy/fr16J5eQeoYKA0LqiFevXol96D548IBp3749Y29vz/Tq1YtJTExkGIZhCgsLmaVLlzK2traMQCBgFi9ezBgYGDA7duz45jHCwsKY33//XfT3S5cuMfHx8RLl+/TpE/PkyROGYT4XMnPmzGEaNWrEtGvXjtm4caNY9n9cvnyZGT9+PMPj8Zjg4GDROJ/PZ3x8fMRuE5SXlzNxcXGiguffTp8+LVFGQgjDcBiGYdi+akEIqT2FhYVffQBPIBDgw4cP0NXVlWEqICEhAcrKyhJNJ8zMzETjxo2/OruBECIdVBgQQgghRIQePiSEEEKICBUGhBBCCBGhwoAQQgghIlQYEEIIIUSECgNCCCGEiFBhQAghhBARKgwIIYQQIvL/AE/5HTiDb4U2AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "4JILKSXSi1Up",
        "outputId": "b2ce3349-7867-443d-ca24-056d8a62134e"
      },
      "source": [
        "L_s =sp.solve(sp.Eq(sp.Symbol(\"E\"),E),L)[0]\n",
        "L_s"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\sqrt[3]{6} \\sqrt[3]{\\frac{E}{a}}$",
            "text/plain": [
              "6**(1/3)*(E/a)**(1/3)"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-P5GmXCekiGM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 56
        },
        "outputId": "82b0d6f0-4b77-4931-a794-ee8c4f8f433e"
      },
      "source": [
        "S"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle - \\frac{L^{3} a \\left(L^{2} a c - 5\\right)}{30}$",
            "text/plain": [
              "-L**3*a*(L**2*a*c - 5)/30"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "id": "PTguBP8nJWDq",
        "outputId": "25e5bdf8-9f4a-4a97-8e02-8087448e5d48"
      },
      "source": [
        "S/E"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle - \\frac{L^{2} a c}{5} + 1$",
            "text/plain": [
              "-L**2*a*c/5 + 1"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "id": "xAbAbweqJ6FQ",
        "outputId": "1afd9f70-4687-48e1-da94-f3754830c73c"
      },
      "source": [
        "E"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{L^{3} a}{6}$",
            "text/plain": [
              "L**3*a/6"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x4uMCNl4KFco",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "1a0e7fdd-556d-430b-9d71-119118147dc7"
      },
      "source": [
        "peak_resource"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\frac{L^{2} a}{4}$",
            "text/plain": [
              "L**2*a/4"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OQMUI9pTZ8gz"
      },
      "source": [
        ""
      ],
      "execution_count": 48,
      "outputs": []
    }
  ]
}