{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eKdBA03tDnbx"
      },
      "source": [
        "# Teaching Physics to an AI\n",
        "\n",
        "In this Notebook, I will run simple physics simulations, and then show how neural networks can be used to \"learn\" or predict future states in the simulation."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "nxOvYXjzZ4uz"
      },
      "outputs": [],
      "source": [
        "import time\n",
        "import numpy as np\n",
        "from scipy.integrate import solve_ivp\n",
        "from scipy.integrate import odeint\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "sns.set()\n",
        "\n",
        "import pylab as py\n",
        "\n",
        "from matplotlib.animation import FuncAnimation\n",
        "from matplotlib import animation, rc\n",
        "from IPython.display import HTML, Image\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "%config InlineBackend.figure_format = 'retina'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o_VMgnFHDnb2"
      },
      "source": [
        "## Double Pendulum Equations of Motion\n",
        "\n",
        "<img src=\"img/double-pendulum.png\" width=\"100px\" />\n",
        "\n",
        "$$\n",
        "F = ma = -kx\n",
        "$$\n",
        "\n",
        "with the initial conditions of $x(0) = 1$ and $v(0) = x^\\prime(0) = 0$.\n",
        "\n",
        "\n",
        "### Computational Solution\n",
        "\n",
        "Writing this as an ODE:\n",
        "$$\n",
        "x^{\\prime\\prime} = -\\frac{k}{m}x\n",
        "$$\n",
        "\n",
        "Scipy's ODE solver can solve any system of first order ODEs, so we will rewrite this 2nd-order ODE as a system of first-order ODEs:\n",
        "$$\n",
        "\\begin{align}\n",
        "x_1^\\prime &= x_2 \\\\\n",
        "x_2^\\prime &= -\\frac{k}{m}x_1\n",
        "\\end{align}\n",
        "$$\n",
        "\n",
        "Now let's code this up in Python."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Image(\"double-pendulum.png\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "v72hSiz6OVsH",
        "outputId": "5bdfbcf6-34bc-47f2-b59f-ef7f91c27f16"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "dn5_xN16Dnb3"
      },
      "outputs": [],
      "source": [
        "m1 = 2                 # mass of pendulum 1 (in kg)\n",
        "m2 = 1                 # mass of pendulum 2 (in kg)\n",
        "L1 = 1.4               # length of pendulum 1 (in meter)\n",
        "L2 = 1                 # length of pendulum 2 (in meter)\n",
        "g = 9.8                # gravitatioanl acceleration constant (m/s^2)\n",
        "\n",
        "u0 = [-np.pi/2.2, 0, np.pi/1.8, 0]    # initial conditions. \n",
        "# u[0] = angle of the first pendulum\n",
        "# u[1] = angular velocity of the first pendulum\n",
        "# u[2] = angle of the second pendulum\n",
        "# u[3] = angular velocity of the second pendulum\n",
        "\n",
        "tfinal = 25.0       # Final time. Simulation time = 0 to tfinal.\n",
        "Nt = 751\n",
        "t = np.linspace(0, tfinal, Nt)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Differential equations describing the system\n",
        "def double_pendulum(u,t,m1,m2,L1,L2,g):\n",
        "    # du = derivatives\n",
        "    # u = variables\n",
        "    # p = parameters\n",
        "    # t = time variable\n",
        "    \n",
        "    du = np.zeros(4)\n",
        "  \n",
        "    \n",
        "    c = np.cos(u[0]-u[2])  # intermediate variables\n",
        "    s = np.sin(u[0]-u[2])  # intermediate variables\n",
        "\n",
        "    \n",
        "    du[0] = u[1]   # d(theta 1)\n",
        "    du[1] = ( m2*g*np.sin(u[2])*c - m2*s*(L1*c*u[1]**2 + L2*u[3]**2) - (m1+m2)*g*np.sin(u[0]) ) /( L1 *(m1+m2*s**2) )\n",
        "    du[2] = u[3]   # d(theta 2)   \n",
        "    du[3] = ((m1+m2)*(L1*u[1]**2*s - g*np.sin(u[2]) + g*np.sin(u[0])*c) + m2*L2*u[3]**2*s*c) / (L2 * (m1 + m2*s**2))\n",
        "    \n",
        "    return du"
      ],
      "metadata": {
        "id": "TSfqsK--F_b_"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "sol = odeint(double_pendulum, u0, t, args=(m1,m2,L1,L2,g))\n",
        "\n",
        "\n",
        "#sol[:,0] = u1 = Θ_1\n",
        "#sol[:,1] = u2 = ω_1\n",
        "#sol[:,2] = u3 = Θ_2\n",
        "#sol[:,3] = u4 = ω_2\n",
        "u0 = sol[:,0]     # theta_1 \n",
        "u1 = sol[:,1]     # omega 1\n",
        "u2 = sol[:,2]     # theta_2 \n",
        "u3 = sol[:,3]     # omega_2 \n",
        "\n",
        "\n",
        "# Mapping from polar to Cartesian\n",
        "x1 = L1*np.sin(u0);          # First Pendulum\n",
        "y1 = -L1*np.cos(u0);\n",
        "\n",
        "x2 = x1 + L2*np.sin(u2);     # Second Pendulum\n",
        "y2 = y1 - L2*np.cos(u2);\n",
        "\n",
        "\n",
        "py.close('all')\n",
        "\n",
        "py.figure(1)\n",
        "#py.plot(t,x1)\n",
        "#py.plot(t,y1)\n",
        "py.plot(x1,y1,'.',color = '#0077BE',label = 'mass 1')\n",
        "py.plot(x2,y2,'.',color = '#f66338',label = 'mass 2' )\n",
        "py.legend()\n",
        "py.xlabel('x (m)')\n",
        "py.ylabel('y (m)')\n",
        "\n",
        "#py.figure(2)\n",
        "#py.plot(t,x2)\n",
        "#py.plot(t,y2)\n",
        "\n",
        "\n",
        "fig = plt.figure()\n",
        "ax = plt.axes(xlim=(-L1-L2-0.5, L1+L2+0.5), ylim=(-2.5, 1.5))\n",
        "#line, = ax.plot([], [], lw=2,,markersize = 9, markerfacecolor = \"#FDB813\",markeredgecolor =\"#FD7813\")\n",
        "line1, = ax.plot([], [], 'o-',color = '#d2eeff',markersize = 12, markerfacecolor = '#0077BE',lw=2, markevery=10000, markeredgecolor = 'k')   # line for Earth\n",
        "line2, = ax.plot([], [], 'o-',color = '#ffebd8',markersize = 12, markerfacecolor = '#f66338',lw=2, markevery=10000, markeredgecolor = 'k')   # line for Jupiter\n",
        "line3, = ax.plot([], [], color='k', linestyle='-', linewidth=2)\n",
        "line4, = ax.plot([], [], color='k', linestyle='-', linewidth=2)\n",
        "line5, = ax.plot([], [], 'o', color='k', markersize = 10)\n",
        "time_template = 'Time = %.1f s'\n",
        "time_string = ax.text(0.05, 0.9, '', transform=ax.transAxes)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        },
        "id": "6w1BTIhYGYWW",
        "outputId": "1f5ba78a-2683-4083-df30-c85a167ea532"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Jd0QQBEEQymT9Duqp7DUhIeBmhfcoC1BSTlE2Oo09yxxIEYlj1apVWLZsGcrKyrBkyRKUl5cDAI4ePYrZs2dj9erVePHFFzFnzhym61VXV+ORRx6B3+9HVVUVRowYAQBoa2vDf/3Xf+Hjjz/GH/7wB9xxxx1m3RJBEARBqJLtu3lTaBqRhIpyKp71GjiPj+1a5FWRhZLV43jqqacAAAsWLIgpIQDQp08f3HPPPQC6PByCIDBd7+mnn4YoivjP//zPmBICAHl5efj9738PnuexbNkytLS0GHYPBEEQBKGZLE/oVQ1Na9hvbgdCAbi2vwf32qVw7VhLxQFsgJpy2rn9fabr8PW1yF00B77lD8G7ugq+lx9E7sOzwdfXGtldx0IekW4OHz6MmpoauN1uTJ48Oen4mDFj0K9fPxw5cgQ7duzAueeeq3i9UCiEDRs2AACmTZuWdHzIkCEYOXIk/vWvf+H999/H1KlTjbkRgiAIgtBBNif0qoWeuTe9js4zzjclHIfKJtsTNeVUbDiofpFUQv6yBPKIdLNr1y4AwGmnnQafT9rVdvbZZwMAPv/8c9Xr1dXVoaOjA8XFxfjOd76jeL3obxMSqFmJyIpEEARhHN35DuGLZ3WFImWJkKRWipcPtnWF44QCxv4wlU22LWrKKVc2UPUaLCF/2Q55RLrZv7/L7TpwoPzAGjBgQEJblutFz5Ei+lsHDhxg7qdWPB4XysoKTLu+mQh1uxB84hagpbHnj4Wl8M5fBL5imOpxI3DqsyOMhcYBEYXGQqZSAOHGxQg+egPQ0SbZIhqO4zp/kmHjIPLRhwgrCKol9Z/Adf4kQ36L0IY4YRIC//xroowRpbAUOaMmAFCeE8LBRkQUfiM/2Ah3ls8p5BHppr29HQAUK1jl5eUB6Eo2N+J6ubm5zNfLdMRgAJEtqxD+x3OIfLQKQmtzspIBAC2NCD5xi+rxqNWq93UNt2YRBJEAfXOEU+ErhiFn4gzFNkzhOBpQu57Rv0eww3l88M5fBBSWJh7oNniyJKqreU1YvCqZDnlEMpxQKILm5o50d0MRqfhY0ZcHLiCjoLU04sTfn4RHykrRffz4+6sgnDQo6bpBxrjbqIWjoeGEtpshMoqsHwdSlV5EUbb6C19fC1/VneDbjscuEcwrRmDO/Y6Pdc/6seAEDKhM5MrtCyXxMio4GjUOXN5Sxd9r9ZYiQmMufeQPARZUJeVNtbq9KOtuojgWhpyHXIVqdE1DzgMy5P0WFfnh8WhXK0gR6SbqnejokBfao56LqGck1etFvSYs18tYZOJjZZWQbviGesXjXMN++N5+ihLECIIFCQGOP7w32UDgL4AIgO/oWThjSbX9y+F77o6EYwDAtx2H77k70P7bZfTN2Y0MKilqVMK3WhnjaDiOUWR72WRHoHcjxO5zA7Pvk9+LxKHfm5GQItLNoEGDAAAHD8q7QQ8fPpzQluV6hw7JV12IHmO5XqailMilhFA2BPhqh+xxrr2ZasITBAOSAlxeMSB0JikVXMcJcL3P71buQxOvTWofa9NxAq5P1yMymmLd7UJGVWoysjKRiuCYx7pvBCskqGY82VyNjgVSRLoZNqwruXnPnj0IBAKSlbOqq6sBAGeeeabq9SorK+Hz+XD8+HHs27dPsnLWZ599xny9jKGXBY5T8WxIIeSXIHTpHLh2fiBrRRJzCxWvkVCWT8oqiOxOHiOyBDkBLi60igW+tQnuDf9PsY1r+3ukiNiFDCspavRmhFYLjiSoZgGpeFUyHFJEuhkwYACGDx+OmpoarFy5EpdddlnC8a1bt+Lw4cMoKyvDqFGjVK/n8Xgwfvx4vPvuu3jrrbdw/fXXJxyvr6/Hjh074Ha7cdFFFxl5K7ZFLhdECcGbBz7YE6YVsxLlFipakfhjypXIomX55KyCwo2LDau8RRC2Ik7x5k406vJISpGjUnM/Z19NVylSEq7STqbtIq66GaHKcUmsFhxJUCWyFFJE4rjuuutw4403YvHixRg1ahROPvlkAMCxY8dw7733AgDmzZsHnu8pNrZkyRIsWbIE55xzDh5++OGE682bNw+rV6/G3/72N4wfPx7nnHMOgK5ckzvuuAOCIODaa69FYaGy9T4jUMgFETkOnCgmnSLkl6D9pqfh2r1N0kqkZEUS+perx90qWAWDT9wC34OvGvgACCL9SCneVsFFwo4TcDMVUwT3NKK234PacYIwhQzKwTITUkTimDx5MmbOnImXXnoJU6dOxYUXXgiXy4XNmzejtbUVEydOxDXXXJNwTlNTE+rq6lBWVpZ0vXPOOQc333wzFi9ejKuuugpjx45FQUEBPv74Yxw7dgwjRozATTfdZNXtpRUlCxwnioqeD0XBRc6KxBB369qxVl4ga2lE5/b3gcoLme6PIGyPjOJtJU4TcDOVTBPcNSV8k3BIWEBG5WCZDCkivbjnnntw3nnnYenSpdi6dSsEQUBlZSUuv/xyzJw5M8EbwsK8efMwdOhQPPfcc6iurkYwGMSQIUNw7bXXYu7cufB4PCbdib1QE0DC434CsWywofGxanG3an0SGw4ClSl1gSBsg9bCEKK/ACKfk5AvIlU1SwtOE3AzlYyr1MSY8E3CIWEJGZaDZTakiEgwdepUTJ06lant/PnzMX/+fMU248ePx/jx443ommNRtcCVDTYnZEMh7latT7TREJFJaPFGxJfkTVLkgdjfuBON8GxZwXRNkeMQOX20rr4TBpOBlZpUE75JOCQsItNysMyGFBHCXKJu8KMHksKvoqTLAqdkFURhaVe9+OZwz9/IpU84GDXFOzR2KsSC0qSxLbVgxv4WDspWr+sNJ4pw7d5GC7BNyMhKTQqGJxIOCavItBwssyFFhDANySpZvRLT02qBk7MKevPg+8X/gPP4AHQpIuTSJxxHb8X59NGK4TihKddp/w5lviE59JTrJkzELpWaLDDykHBIWIWmHCwycJIiQpiEXJUsUYToy0Powssglg0x76Nj/LiFIUMRmLUQ/qq7Yru588E2hP7yO3jnLwLyh5BLn3AccopzaNJceFY9Y2g4Trxl3bXpdbj218q25dpbdP0GkblYZeTJiAR9ElodAWsOFhk4uyBFhDAFxSpZgbYuJcQkS5ymjzschG/pAzElJEZLI4JP3AIsqFJ16XuXP4zO4eNoUSDsgYLi7Fn1jGJJbN10W9a5hv2Kigg6w/LHiOzDQiOP0xP0SWh1ECw5WGTgjKGtBBRBMJI2N7jKx41wMOHvipWEWhpj8dNKuHduhO/lB5H78Gzw9QpCGEFYgGosfHeeRvjiWV3GAAMXO7FssHLfPtuY9A0S2QtL3oZhdAuHQn5Jwp8dkaCvcV0j0k/UUxyYcTuCl85BYMbtaL/1hZjSaOnYtznkESFMwTQ3uIprWmtCIovCxNrXbLRkEPYjnbHwkeHjIPrykj2M3fDBNkoKJmLwddWKx40eq05N0KdEe4eikINFOUs9kCJCmIIZbnAW17TWj5tFYVKsrtW7j2qLAsX4EiaT1lh4txfhcy6CZ+vbsk0oYT1N2G3uCQfh/my9YhNTxqpdEvQ1QEJr5pEROUsGQYoIYQ5G16lnjKfU+nGrlfCNLtaaKgPJLAoU40tYQbpj4YWKswEFRcTz4RvoPGMsjXkLMWzuMVCZcdVskvWcAV3VC5nHqt2ULIMhoTXzSPc8bSdIESGMJ25RCE3+OSACXMvRlBYIVte05o9bTskoLIV3/iK0dvc13qWfU7MJ7p0bZfvKtTTCvXZp4v1SYhphFhJCWDo3q1PzIHKBNhrzVmLQ3GO0IUXNih8ZcVHq/ep3ckYoKCS0ZiAZuKmoXkgRIQzFLKs/s2tax8ctFTdcPGFS1z4iDSd6Gna79CPDxyFn707JRUHkOHg+6tlpOvq7/LEDFONLGI7S95a2WPjoN/jM7ZIbmAI05q3EkPwCEwwpalZ8oeJs9Yso9eu5OwA+B3zb8Z5rOtUDbYLQ2h7uxDtfHse+5iBOLvJiyqkl8LupfpGVODVnyWhIESGMw0SrvxbXtK6Pu1fccNdmhvJtpRaF3ps1Aj33Hh7zQ8X+U4wvoRmG7y1dgr4wZCjC434C79olsm1ozFuDEfkFZiRLG2HlV+xXx4nkvznYA22k0Lr9cBtmvb4HR9sjsb/1ya3H0p+chlH984zsNqGGA3OWjIYUEcIwUl6sFOJ89YRcmflx914UuBON8GxZIdmWb20C196seD2K8SW0YvdKOmJpP+XjRX0s6kl2Y0R+gSnJ0gZY+fX8rh2+Dd0YsK51hAVc9epuNAU6E/5+tD2Cq17djR3XjSDPSDrI8DwnJUgRIQwjlcVKNaTLjvGUcYuCe+1SxaZibqF+618WT1CEPLavpCOmeJwwBCM8D2KhstLIH/oarh1rNc9NqVr59Rpw0v5tpJE3ahuTlJAoTYFOvFHbiJlnkZHASrK9kA0pIoRh6La8MYZ02TmeUvXey4boUqSyfYIi5LF7JR2u5WhKxwmDSNGIw9fXwrPyGeWf2LkR7p0b9c1NKVj5tZRWjyfd30Y6WfWV8rNa9VUTKSJWQoVsSBEhjEOv5U1TiIlN4ymZ7t3t1aZI0QRFKGD3Sjp2V5SyCd1GnOgcFJfwrYTk3GSmR1dOycorBid0gpPIE7HDt5FODrWGUzpOGIvdQ2ytgBQRwjh0Wt5sH2LCAuu9a1CknDpBHWsP46EPD+KrpgBOLfHh9nGDUOKnqcZw7BiuGIeiopRXnNXCYFrQYcRRmoPkiJ+brPDoyilZ/OG9tv020knfXHdKxwljyQj5J0VIOiAMRY/lLVMsp0aHjjlxgvp7zVHcuHJvLPx/474TeP7TBvxxcjmuGk7ufqOxc7hiTFF67o6kCkac0An+8F4KL7Qajd4JvXMM13jIWo+uhJJl628jjfTNU1FEVI4TxpIp8k8qkCJCGI9Gy5vdQ0w0YWDomNMmqKaOSIISEkUEcOPKvZhUWUyeETlSCV+xabgiAAj9ywE+J+nvXMcJ+KruRPttL2a9YGgVerwTeucYsXSAMR7dVMO6bPxtpAtBVK4SQYqItWSU/KMTkgoIY1FbOGSO2znExBQYFlinTVD3btgnWwhJ7D7+2KRKK7vkCJgFRAdWT3PVbJLNL+DbjsO94RWEL5llca+yiOiYObofng/fABdI3GBSzTuhNAdJ7ZsE9MxN7o2vKHZNzdti+0IdDvweO8IC3tqtHGp3aqnCHlqE8WSj/NMLUkQIw1BbONSOZ4sbnXmBTXWCsnihXFvXktLxrIQxfMX2QpkMasKme8PLCI+fnpHfebqRGjOS7ZS8EwpzUGjSXHhWPSM7N6Xk0bV5oQ6hbhdy/7jAcd/jO1824URIkD1e4OEx5dQSC3tEABRGSIoIYQxqC8dNTzMtLBnvRte4wOqdoNIhuHZE5Bc4ADgRkq5dn80wha8MH2droUwJNWGU71aWM/67txqZeUYOJYVRaQ6KjJggOzel4tG1c6EOMRRA8Ilb7Ps9KhigvmwMKJ467fRS2swwXcTLP6EAXDs/cJS3LRVIESEMQW3h8Kyusu3CYiW6FlitClqarIn57hw0B+WVkbawiI6wQAtdHCwFCewslKkRGT4OoscHLiQvANmx6ILT0VrtSjUXRG4OUpqbUvDo2rlQR+f294GWRslj6f4e1QxQjR0RxfM9OZzZXSRUcKr3OxVIIiAMQTXet6E+pfMzBSsWWBbB1Qx4htlk+S7axC4elvAVw8ZMKADX9vfgXrsUrh1rgXCQtZv6cXsRGj9DsYndii5kAlrmEdGXh8jpo03pR9SbEphxO4KXzkFgxu1ov/UFVYHKzoU6xIaDisfTtpapGKAQDqJUpViI2nHCZBjeYSZCighhCGoLg1A2JKXzMwUrFth0WRN9LvXpZNlOUkTiiYavSBENXzFizPD1tchdNAe+5Q/Bu7oKvpcfRO7Ds8HX1+rqtxbC46dDyCuWPGbHogsZgXJhpAS4QBty/zDPvLHQ7TUJXzyry1PA4I1V+i5EjoNQXGZ0L5nhygYqHk/XWsZigFJLRKdE9fSSLiNiuiFFhDAENYEqdOkcVYErG2ARPFMlXdbEsYMKVNsca6ddexPoDl/pPSbiw1dSHjPpsLLFe19qNiEw63S+jdUAACAASURBVM7ke/TmIjLswq7FNUMtfWkhHIR785uyh6V0FNtZXN1eBK5eCJFLDhXiRBG+pQ+kra85oyYAhaWSx9K5lrEYoAYVeCAXfFWW66JE9TRj55BEMyE/HGEMavHAuYVZX6IOgCWl+tJV9nfh9wbjxWplj0dDGykivVEtSMA6ZmSSVK3OMZGNcb7yVrhqPgS/vxY5334DPtgOz9a3ga1vZ3wMtKn0eu+IhGVLJgOQFUTTnd/QG765QbI8MJDevnIeH7zzF6FDpmpWutYyNQNTsKg/5q74SlIR5QA8M/UUyt9LM3YOSTQTUkQIw1ATqLK9RF0U059DmuqSl/hd4AEo1c5SqByZeWgpn6xSkEBtzCglOFpqZVPwvvifvQOcTMyQbSoOOQyp9y669G9IxzXsT/5jmvbLsLN1mK8YZru1TM0A9ZZnGBraD0ieKwI4cCJkcg8JNZy2d5hRkCJCGItahadsKNHLgsnPIV1Kn4tXVjY6RWRF5SxTKp/IjRmV0KvQ5J8rXpbJysYojCp5X+SUkPj+umo2xcK1sqV0pW5k3jsX0e91dG96HZ1nnB8bo6aMY8axZHvrsN3WMhUD1NcHlL+/b5ptEpaXzWTp5oakiBDm4cCdZzMKvQtlCu/tpFwXDrUql4hcvuso5ozoq71fTsHi8slqoVcQkZKVTVIY9eYiMuL7ECrOThgfqVqp+bpq5L79VFaVrtSL1hK9AGJFA2R3uw+29YxRwPBxrEWxyVbrcCooGaBObj2meO7JRbQ224FsjBwhRYQwjjgBFiLg3vxmwoJHAoUOLFbmUrWAFnhycAjKisiS6sxWRKzOyVANYWk5qt/KJqdUxed3eHwIj5+B8NgfgZPZX4EV92frwQXaEn+LwrYk0ar0CXnFCMy5HwDgf/b2pOccJb46j6HjWKuCnqXW4ZSRMUBdXF4EDtLFCrju44RNkDMiZqhxlxQRwhCkBNikNiRQaMLyjY0MsOSfP6gAuxuVXfzfZnjCekqx7ToWGpYQFr1WNharOx8KwLumCp41L6iGXyn20+1VFY5tFQqTZrSGJoV+MDc2b4QuvAzetUtl27IoOVoVIT0KejZah81i7d5m2a9T7D5++ZknWdklQgOZvNEhKSJE6sgIsFKQQMFIGnZHN8KSz1I5q09uju4+poRF1iS9se16FxrmEBYdoXpahM1UlBAA6Ox7MlwHdhvSl2xA6b1LwTX3fJeiAfs68Ye+hmvHWubvSLeCbrdcDIeilgNCOSI2Jg3ygJVkdsYoYQlaY5VJoFAnHRsbGVGlpsTvwvmD8hTbNLYrh26ZgZUb+una9yOVvT4Y9iLRi5UJwWpWPa6l0dpd4e1C/J4s8fcu897liH+XLGNUqQ0AuHdu1PQd2T75PMNRywGhHBH7kukbHZJHhEgZrYoFLTjqpKN0pVGCwr8NKcRHB6RDbADgQGsEnze048yyXE39043V1iQdse2peqPMCmHRanXXS3TTU9fODyR/S+Q4eD5akdA+E0IS1JD0krl96Bw6GkLfkyGWDUH7TU/DvXkFPOtfAheRLsGapAAzjlGpNkl9ZPyOFD13ecWUfG4y3z+5CAUeHickyhrSZob2xs6lrI2AFBEiZbQoFlTthI10WA+NqlJzaqlPtc1Vr+3Bp/81QnMf9WB18jigXTEwZKExI4RFRmBNBSHHDb6zJ09IbdNTEVzSxnZ8axN8VXei/bYXHR2SoIicAh0OgN/5AYAPAHQJ8ZzQKa+E5BVLKsAsYzS+TU7NJrh3bpT8DabvKDqWnrsDfMeJhEOc0An+8N6MVyzTxfbDbbjm9T2ySsiSn5yW8SXVnUymexNJESFShtVqStVO2ElL6UqDqtR0WdbqFNs0dlgXnpU2a5IGxcDOC028MMrXVcP96TpwwXbd1+scOgahM8eCazmquukpf+hreeG37TjcG15B+JJZuvtiZ1hDXpV2UQeA0OTuJHWZHCnVMdrdhms8BMi8CwDgGurh2v6eYg6W0L8c4JNzxLiOExkR625HOsICrnl9DxokQmILPDw++I+zUOInUdDOZHopaxp9ROrICbB5xQhf8GOAA1U70UqaSlcaEeLjd/M4yZeDY4FO2TYlPusS1u0s5EcxbaHRmqAv1z4qsI68GKEf/QLuDa/As+FlcKFA7FSRS/ZcSOHetQk5+3bJh1ZFfyscRN4DVyhey7NuGcLjp2fkvMLXVRtyHa7lqL5CCL3GgljYR/F33JveAB/sCcmUur6rZpP8HiZmFTJxUslTE/r6zpdNkkoIAJwICVQtywlkeClrUkQIQ6Ayi8aTtmdqQIjPL8/riwc2yXsappxiXc16R1iTTFhoNAmfoQDcG1+BZ8PyBOVCsr3bi/AlsxAePz1xbJ4+Gq7d28A17Id70+sJQmlS3xjyClw1mxL6IgXXGYZ73d8R/vc5iu1sTygA16frkbP7YwBA52mj4P50nSGXFov6aM6Rkhw7ecUQ/AVJYVVAlxLa+31LXd9q76STSp6a1VeqlpUZZLKMRYoIYRxUZtF4nPRM46x5ZzT64BMHIsC5JZsu29WIuy862Zq4ZIdYkwxdaDQk6PP1tfBV3SlpqVZUGCTGZvT/nWecz5Tk7KrZhMiwCyWtwKxCqWfDcoS/f5Vt3qNW+K+r4Xv+DvBxlcDkwtG0IuSXAKLGjQnlxk7bcYj+Agh5xQljRfTlMe//Yql30kklT03sK1XLyiCcJA9ogBQRgiBSprc176cAxnH5mF44G5+4Bye1D0REvFHbiJlnKYd7GIVjrEkGLTTMCfpRAUghz0BPyEz0eXuXP6woVPN11ch9+ylJBZFVKOU6w47dm4jfWw3/0zeDS/E6gr8A4HMS3mP0Oebs2aZ4bm+FT2nscB0nEJx+M5Djjn1HXEM98+aIVnon01GkQi9m9nVQgUd2R3WqlkXYAVJECONxUkwukToy1rx+YiteaXkBZ5beIukZeWdPtyJi1XjJUGuSFKwhMKwJ0cwhM73eZedpoxQVEdeOdeBDiYnvMSvwTU8zlw6W7J/d56FwEP6qu1JXQqLhO/3Lu8K7arcC6CoKIPQvB3/sgOL5vRU+1bHTfBThi3sKBLh2rGW/voXeSSeVPDWrrx1hAXNXfCWphHAAnpl6ClXLItIOKSKEoTgpJpcwBiVhtp/YimnBGiz3jUw6tuNIG40Xk2ANgWEVcJh22pZ6l17lvWJ6KyGxv7c2wbV7W5fQ+sxt4FWqdPXe5dsJ48pVs0k2pEkJEUB49CSIhX0glg1JuGfPqmdj9+zeuRHCqmcRuHqhJi+E1vAprV4Oq7yTTihSEcWsviolqosADpyQLvlMEFZCqjBhHKnsDk2kjtwOzCajJsxWCI2Sf29uDcBXRePFDCLDx0H0F0geE/0FMeGQRcBhCpmR+/ZTKPPLNR6KCa2iipCasMt3XbV95iGFb1KvlZsDIJwyCuFL53R5+Nxe5bl32QMIzFqYtEu6nBeCZdf1BGR2eE+4fu/ngK58ovDFs3ruwWA030caMauvUonofjGEGYEduK19LQpq1tM8a3fStK5bCXlECMNwUkxuppFOC7CaMFvHl0r+fVqwBnwbjRezEAHJsJ/4MA21PYDkNsPrDWuIlxZi4yq3EB3zFsP37G/BB1oVz+Fbm+B79g7wEenF2spxpfZNpmKR15LXwbc2gT/ewO6FkAmfEl1uhL87RfI3lLwcaZubHFKkAoBpfe2diH5eeD9eaXkB/cTu7+iTNRBql9vKU0j04ATPrhGQIkIYBtewP6XjhE7SXB1GSZg9wuXjLe9wyfPkPCVR7BTD7TRcNZsky6wCAN9xokcYlxOAPD6Ex8/o2aNDJd9Cz7sS8oq7+iORKN/bCiwMGYr2O16K5UBwx7+Fa3+t9P3JKCG6+9p97+FQE7jiMrhaOsCdOKYszCt9k907wke9VpzMe1JCc15H4yFNOVLCkKEIXL0Q/ud+By7cVUKZi4ThXbcU7i1vIfCz/00WhKSun+a5yTFFKmBOX6ecWoKy3Ho0tEfgE8OJSkg3tqwiRqT927ESUkQIw+Dam1M6Tugj7Z4o2Q0tS3CVZ6ZsCV85T0kUO8VwG4ZFCdRakl/VBCAWq5xqjHuvEq8xSy/AbgV2exEZPQmR0ZPgXl0lq4ioIRYpVGrr9X6EojL4lj0AvrUJ0Uh7X1zzhOcQdy53olH+m4zuCD9+uqzXSnB5wLk94DqSPUDxoXWxvxmdYxAOwrf0/pgSEg/fcSKmTKXiKbPMO+WkIhUG91WEiJ+P7IsnPj6MH52oSVJCopAH2n7Y4tuxCFJECMMQcwtTOk7oww7VYeSE2VPXHsRHO49JnvOWdziOtOVLLo52i+E2Arlk7siI70OoONtQpUSzYConADFa5dQSlttverprs0MJRUerFZivr4XnwzcU708Jzzt/A3e8AeA41RAitd3io88hMGshfEsfYA5Pc294GWJRH3mvVSQEkZdO4ZTqjdFlcZV2QAe6lCkWQcgOc1O2sv1wG655fU8sWZ080M4im74dUkQIwxDLhqR0nNCHbarDSAiz//adQiyVUUQCnBvTC2djRfuLKA73CGS2jOFOFYVkbs/Wt4Gtbxsa+2uUYMpslVOLcc8tlBdatViBu5+jnmpTsX63N8O75oXEPl69MOb5iEdJCYldr7Wpqwyvhj7xoUCszK4ccrvKJ4TWRTE4x4BFyGFpY5u5KcvoCAsJSgiQpR5oB5NN3w4pIoRhWLlZFdGDnZ/7lFNL4MnZi1CntED3iXswLjt1IVae02T7GO5UYEnmNjT21yDBVHOI12/+Cs/qF8AfrYdQNgShS+cARnlCQwF43nna8KT4rryNu8AH9Ss3qShGun5P4r0YmWPAIuSwtLFsbrL7njEWI1W2N9s80E7Hzuu60ZAiQhiHk6qUZBI2fu5+N4/rR/fHox/JC7RbGzrRMHQ8SvyZOx2xutGNjP1NEkwLu3IjcvZsA3/sAJOwpsUqlxTa9NUOuHZ+YIiXRypsykhSUUL00nnGGOTs3SktaHjzFPsk+160eJcUhPfI8HEQ8oplw7OEvGI2QUhubvLmIXD1QkPmpmypLKSFD/Ylh/xFPdC9E9btsE4QEmhZ1x2uiHOiyOB7JhxLKBRBc3OHtT8aDjqiSokSZWVdezA0NGivaJM2bPrcO8ICTnniX4hIzDR+MYRpwV24rCyISWPOtE2foxg1Dlw71sL38oNMbYOXzknYudoIdAtr4WDX3hxyuR9R7w1rO1biF9bCPvCsfEYxZyGK6PaCs7jOvprSIIXoy0PbHX8Hf3iv9HuRCRWLHk/Va8YyHvi6avif/11SiJjgL5CumqX0e3urk8LXDFEWjB53DNh9begICxj65HYEZLzQPjGMh/vtw7WDIrZaJ5yIJWNBZV23kyJeVOSHx6PdoJi5JkgifTipSkkmYdPn7nfzGFTgwTctibv4JtS0bwVQ92Z6JlALrElq+3XEY3jsbyplIBmtckZWeNHr/RDyS9B+/Z+Q+4frdHk4RG8uOI0bMAr5JQhccRv8y+4Hp+E3w+dcBLi9iuFUoUlz4X3tkYQ8FZHjEJo0V79SVzoAkdNHq44H/vBe+JY9kKCEiDluhMZfifD3r9L2++EgfEsfSApfMyIUMZsqC7HyzpdNskoI0OUZWVl4Lq66+DQLe0XoRmldz5ASv6SIEAQhj0FCemmuK0ERsUtNe8usSTICfW+SYn+lnr8oanonqQprLLkHaqFnOTWb2MaOzMKqRkwxKipDYO6Dmq8h+AsAUZQspdub0HenQCwu6yrvW1zWJWRrVHyEirN7/iOz/4Zn1TNJyfKcKMKz6hlERkxg+j4kK4H1KqWc0L61Ca5P18Oz6tnkxP3OMNwfv9OliGjATGUhmyoLsfL5UfUIiByeZaQTdidTFHFSRAhzcHjMImGskD7rrDJsP/xN7P/Tgjaoac9iTUKBYT8XL9DzddVwf7Zeem8Npf07/AXggIRN8NTeiSHCmoq3Tc2L4965ETl7d6qOHT07tIfGTkVoynWx5yaZG8MBXPNRQATcm99MCPMS8orBCRFwKru2AwAKSxGa+kv1cDRvLpDjBi+xdxJLoqkhAobM+FZLrM+p3WqocGOmspBNlYVY+eSg+jieWFFkQU8Is8kURZwUkV58/fXX+POf/4wtW7bg+PHjKCsrw/jx4/HrX/8affv21XSt/fv345JLLlFs8+ijj+KHP/xhKl22HXaKWSR0YrDL94phJ+F36/Yh2B0yYIea9izCHgb+2NgfjQr0Iy9G6Ee/kPcyyD1/iX0n1N6JFcIaS+gZ39oE/99uQXDqrxEZcZFkX7W+dyG/JEEJiaGgOIXHT0947lxDPbxrl6r/WGEpvPMXoZUlHC3YjkjlSODAnoQwMSG/BIGZC+Ha+YGikUazgCFh+NGj1LGg9R2ZOf6yqbIQK/t6hcD2hgNw2dCTrOkMYSqZooiTIhLH1q1bMW/ePAQCAQwfPhzf/e538cUXX+Dvf/873n33XSxbtgwVFRWar5ubm4tJkyZJHhs8eHCq3bYXGRKzmO0Y7fL1u3kUeTl8296liNihpn3arUkKwrJWIVLpnVgirDGGnnGhAHyvPgJh1bOShgkt7113tZ/45x4OIveBKxSbR04ZicjoySieMAmcxwd0J6aqjQ/X1zsAdIVChc+5CELF2bFQLjUjTUrVyrqvGTnjfMVrSCHkl6DzjDFw79zI9NssmDr+bFwxMB10hAUcPKGsiJx+kg9+t/RmmYSzyBRFnBSRbtrb2/Hf//3fCAQCuPPOO3HNNdfEjj300EN49tlncfPNN+PVV18Fx2mLrywpKcGDD7JVzHE6mRKzmO2YIaQ3B3vi3e1Q097O1iQ9z1f2HIuEtWhIlHf5w4qCLCBvmFBcWPOKEfrBXHDNRw0L93TVbAIvs3FgrE+jJyMy8uIuJSQO1vHBBdrg2vUh2if9DLl/mMdkpGEWMBQMP+5tKxX71bvaV0wh6l8OYWVyjkjSb7Ni8vgzcv+UBBwYXvxG7TEo5KkDAOaN6mdNZwjzyRBFnBSRbl577TU0NDTg/PPPT1BCAGDBggVYs2YNampqsGHDBkyYMCFNvbQ/agIUX1cNkCKSXhgWWDOEdJ+LR7CzE4B8TfsOXxFEiyZQO1uT9DxfpXMMFdaUxo/bi87h41QVEUDGMKGysBod2qk2X4ken+w40FIJjW9tgmd1lbqRZtiFsWcbHjstOZ9FQ7UyJXOZkF+C9puehmv3tsTxIIpw7fwAkWEXquYwacE0ZSGKwRUDlcKLUTbasN8xmjV1yTlJ8bj4rjBZInMw/duyAFJEulmzZg0AYOrUqUnHcnJyMGXKFPzlL3/BmjVrSBFRQE2Acn26HqEf/cJRH0kmwZq/Y4aQPumUIizf1ZMb8ol7MM4svQXTgjWoEBpRx5cicOYF+JtVeUQ2tiZpEXIBxndigLDGMn609N3sHcLVUJuvQuNnaC5tLAffUK98vK4auW8/lfhs84oRnDgH4KCrWpkUoi+va3znFiaMB8l3681DZERXWBnTO1BRUh3hDVcJLxbPei3JO2YXQhFB8fgFg/MpLCsTccq3JQMpIt18/vnnAICzzz5b8nj077t27dJ87fb2djz11FM4cOAAPB4PKioqcMkll6B///76O2xTIsPHKZeHDLZReFa60JK/Y4KQfv9F30lQRIAuz8hy38ieP9R1oKkjYtku67a1Jsk9f4WqWabvtMs6fjQI6Lp3CA8F4PpsPXJqPwYAdA4dI5sAr4RaKFh4/HTF8+PHT07NJkVPkFA2BPhqh+xx9/b3wIUTw8T4tuNwb3lLdyECKUIXXpbsWZJ7t8HusDIG45GhRUrSGBalFl7cuf19uM6XzvlMJ3+vOYpVX7fE/h/dLLa828jzlnc4pp/ZJ409JAhpSBEB0NraiuPHu9zfgwYNkmwzcOBAAF2VsLTS1NSERx99NOFvv//97zF37lz85je/0ZxzYmvcXoTPuQierW/LNnFKSblMQ2v+jtFCeonfhcmVRVj5tXL4wM2r9+LZaafq+g1d2NSaJPv8Af077fY7WbeAp2X8xPr+2Xp43npSMg9Dr2eNr6+F/7k7EpQx986NEN75q+Ydvw1RuLvHT2T4OOTs3SnrRQxddBXcW/4BDtJB/L2VkCiSIWxRQf3ofogeX9Lu50qIZUOS/pZybp9RRUpCAbg3vgL3huUJY8bKqouq4XoNB03vg1aaOiK4ceXe2P8TNovt5tv2fLjz/wcAKSOEvSBFBEBbW4/13u/3S7bJzc1NaquGx+PBjBkzMHnyZJxyyikoKirCvn378NZbb+H555/HX/7yFwDATTfdlELv1frgQlmZcXshsBAZ8V2EFRSR/PIKuCzuk16sfnZmEg42IqJwPD/YCHfS/RYYWsL22jGDVBWRlV81Iz+Xh7v6A4hHD4IrG4icURPSGg6RvnEg8/xl3okYCiDw+7sBCYEwt+p3AJ8DnIg71l2Slq8YptoT7eOnABg4HcLQYQg+cQvQEucNKyyFf/4i5A3UJhSJoQAC/3sXIFXGuOMEcl+8C76HNIbOlI2GeNZr6Nz+PsSGnvGWJ3MN+bFQAOHGxbL36v12D8IySoga8c9WqNuV/BusFJb2VP+KQ9/c0EPkow8RVlBkSuo/UfUiCHW7EHx8QeL4jLtG7pK74XvwVdPngUh5BcIKx7myLqOkndaGha99ERtZcpvF9hVagZfuteQZZht2GgtOJCMUkYcffhhr167VfF5VVRX69TOvgkTfvn1x3333Jfzt9NNPx4IFC3Duuefil7/8JZ555hlcffXVpvbDanJGTUC4sFR6oSwsRc4oyrFJB9EFVO9xI/jJ8D7wu3l0hOVjmUcE69Fx+0NAR0+SbjhOYBaDgS6h0SZKip3o3P6+vIDa1pL8t5ZGBJ+4hUk40Tt++Iph8D34apKgr+eddW5/X1JQjXFCX+gM5/EZEm6jdK+dNR/pvm702YqhQEpKiHf+IsnnnurcoOYlUD0evS+ld9vSaElYlBPXr017e4w7SpvFWvUMCUILGaGIfPvtt6irq9N8XjjcZffIy8uL/a2jowMFBcnabXt7e1LbVLj44osxbNgw7Nq1C5s3b8Zll11myHV7EwpF0NzcYcq1leCvuVc63OGae9HaHAYUbU7pJ2rhaGhItrw6liHnIVchAb1pyHmxPRLM5IVpp+KKV3dLHota8/y9F9KWRnT8cQECsxYm7cMQNDFsw2njwL23DpoD51oacfz9VerhaamOn8oLgcruf+ucA1jur3VvHcKVKu9LRw6C4liQul7lhV3Huu/V5S2FHnU5/tm6dqyFT4MSEj7rexAGVMb61Or2Sr+jFN+t2r21eksRUTqf8b6Y3q0BKK1f/m5Fzk5zQmug51tS2yzWqmeYDThtfTCboiI/PB7takVGKCKLFy/G4sWLdZ+fn5+PoqIiNDc348CBAzjjjDOS2hw61BU3KpdDoofKykrs2rULR44cMeyadsG2ScDZjE2qRE0oL8TgAjf2n0gWRJWseXxrE/xVdyUVQqDNMnvQu/cJU96WDcaPWKgeyqX2DAxNqtZwvcjwcRDyihPK8arR+9lq3tU8r5itYYrvNtUqe6z3ZdXePk5av5o6IvimpWcutcNmsQShhYxQRIxg2LBh2Lx5M6qrqyUVkc8++yzWziiiCfLR/JOMw6ZJwNmMXRbYk3JdkoqImjVPthqb3TfLtKgKkNayv1FYhZN0jh++vhaelc8o9y+vWFnoNSqpWs/13F4E5twP33N3gJfIcUm69FnfQ/DKWxP6o0WIFDkOno9WxP6vpmyl9G5TVGRY7svyvX0csn59/4WahP/bYbNYwmAcuLmmFkgR6eaSSy7B5s2bsWLFClxxxRUJxzo7O/HOO+8AAC699FJDfq+hoQHbtm0DIF8ymCBMwQYL7KACDz49khwyqGbNU8Ku1diMtsArIooIj52aXHUorxgQOiUFYM3CCev4MXLxjAr8Ct4EwV+AwJz7FX9Dd3WoUACRLR9CPHoQLm9p7F50VaL77TK4Pl0P10f/gGt/rWxfO4eOgWvnBwnPj1XRFDkOnJiYGM+kbKUwNyQpMt3eq5w928AfO6D4/tXuS8grTvvePnbk84Z2HGxNNOjIbRZrh/2RCO1Yun6kCVJEuvnpT3+Kp556Ch999BGWLl2KWbNmxY4tXrwY+/btw7BhwzB+/PiE844cOYI5c+YASE5+X758OSZMmJCUiP7ll1/i9ttvRyAQwKhRozBy5EhkPBmu0RPamHRKMd75Mrl6lqI1z5sHPihftc6WIQdGW+AVkFqwRI8PofEzEB4/HfzhveaFVfX6voWiMviWPWDY4qkk8ANAaMwUhH70S9X7UFNWpY5Hn2u0KpQPPfei53pwexEZPQmRERch9+HZkvcl+gvgWfmM5K7qkp6HvGKEL/gxwAHciUZ4tqxIuiZggeewW5FhEp56jRmp/K/48UvrRTJXviqtyMZvFjsUTbjph+epr7m0RtsPC9ePdEKKSDd5eXl49NFHMW/ePNx333149dVXUV5eji+++AJfffUVSkpK8MgjjyTt+REOh2OJ8tHk9yhLly7FXXfdhdNPPx3l5eXIycnBvn378MUXXyASiaCyshKPPfaYZfeYLrJBoye0cdnQk/Df736Dzl7VTBWteVcvTBJu44/bMeQg5f0ZWJFZsLhQAO4tbyE8frppYVWSCpBei7wMqns7FJUxXVNNWU06riIIhCb9XP/vyYUzRb1Xvbw/8c9P6T261y5V7JNhnkM5wZVBeJJViq9eCL65wfZ5GXbh27ZO2WPRzWLHDsrD/JFnKl6H1mh7Ytn6kWZIEYljzJgxeP311/Hkk09iy5Yt2L17N/r06YMZM2bg+uuvR9++fTVd75prrsHGjRtRW1uLzZs3o729Hfn5+Rg1ahQuvfRSzJgxAz5fhpcdzRKNPq040JLld/P4Aw0v1wAAIABJREFU9Xf74/Gth5OOxVvzzs5pxq8nj4rdU7qTpbWiy2KuA+YFy+iwPDkFSJTeL0Pv4qlZgZBBa1K12nMFh5SStKWUQ0TC8L36iOxvRp+f3DM06lkpoSS48scOKI/Fz9bDs/JZ6TVh2QPKa4ID5zqz6AgLTLvSPPXDU5Qb0BptW6xaP9INKSK9qKysxCOPSC8CUgwePBi1tdLu0SuuuCIp3yTbyBaNPl042ZJ189iB+NPWw5DaUSRqzVsO4MqhI1Hi7pqq7JJsz4oVQiGQvgVLLWTKqL6kWpUphkZlVvW5Nh81bGf22H9T9GgY9qzkUBFcw2OmKJ6e88VWXWuCk+c6M3ho037VNif5eAwo8Ci2oTXavli1fqQbUkQIU8kWjT4tONyS5Xfz+PWY/nhCwisSz2/e3YuqH5/a8wcbJNuzYrpQ2G0h5g99rdgsYcEy0Kqs5/vVtXga6A3TosyyCAIpK8e93odaiWLV52ey51BNcOXaJTbO1IDkmLJqrnOIx6UjLOAvn3yr2u72fxus2obWaPti+vphE0gRIUxFddFk8S0TkmSCJWvB2IGqisjKL4+jIyzA7+Yt6pWBmCgUSlmIpYhfsIy2KmtVKlJZPA31hrEos6EAEAlDcHvBh4PJ/Ym/F53KseT7yCuG4C9IqcKZmZ5D1Xyd3CJF4alz6Bi4d26UP19iTFkx1znJ4/LLd76S9CT35sphqe+7kylWd0eidf1wiCLdG1JECFNR28TLvflNqoiiE9MtWRZMan43j6EneVF7LFnQiyIC+O3ab/DYpApDf9sqTBEKZSzESb8dv2CZYFVWstj1Tlg3xCJvkTdMTckT/AWp34vc+2g7DtFfkDRvan5+Jj0rVcG1bLCi8CT0L4ewKjlHJNpGStEyfa5zkHf50ImQZMXB3ozo62cy3mSL1d2psK4fTlKke0OKCGEubi/CF/wY3jVVkof5tuOOsNzbETMtWYqTWr+TDVVQ/nNUX9yypl6xzbKdx3D3+CEo8Tt0yjJYKFTLzQif9T10du87EX03qlblT9cjMnqSto4oWexmLQR/3IEVkFiUPD4HQv/ylH5G6X1wHScQnH4zkOO23fNjElzdXkXhSauX0LS5rtvYkrPrQ8d4l69+TX7vmXheuOw0tgs6sAhI1qG2fjhIkZbCoas64Sg4lcMUg6oL0yxZSpPac3cAfI6kpVav1eXKYWW4fU095AtRdnHDyjq8+BPGxTUeO7irW5vhWVMF/tt9AJ+DzsFDIfYv190XtW9GGFCZtHCpneNd8SSEfuWa36OSxY4lfEQTFrxLlgR8IwwoLInw4YtnKbZJC3KCqzcPgasXJuwkL/d8tHoJzZjrWEMbAfusUR1hATVH5b3HUW78bj/VJPV4nFYEhEjE6WHapIgQpkMxqCZhkiVLcVKTiFtP1erid/O48fwBePQj5cV+1dfNmnNF7OCudm17F97XHkkIU3J9tT2lvuj5ptTO4UIB/e/RgpApq94lq9CZqnDq5HlRGDIUgVkL4a+6C1yga5NRPtgG37IH2N+HljFj9FzHGNoYxS7v4pHNB1Tb5HDA78YP0X5xBxUBIRJxesEBB2Z/Ek4jas2SgmJQUyNqyQrMuB3BS+cgMON2tN/6QkqCmZ5JK2p10cuN57Mt9Mt2NrBfVMVdDYkEZMNpb0lSQozoi55vSumc+P6k8h5Nw8J3ySp06hJOQwG4tr/XVaK3M9y1eaEEtp8Xw0H4lj4QU0KimPltGTnXaSk7bZd30REW8KePj6i2G5DntqA3hJ1wslEDIEWEsIJua1ZvIYhiUA2i25IVvnhWbNO6VNA7aaVidfG7eZxSrB5K8PhHyhW24mFxV5uNZ3WVrBKSUl/0fFPRczzKm6ja0Xpm5btkUdgEby64hv1w7VjLJnSHAnC/twR5/3MlfMsfgnd1FXyvPAJO6ITgL0i6dmTYhV33ZIWyrIO0fVsGzXWsY9xOa9QbtceYQh1/9d1+pveFsBdON/ZSaBZhCRSD6hyU4rGVSNXq8ovR/XHLmn2KbQ61hZnDs+zgruYblJPwo+jpi55vShgyFKFpv4bvFflNW+1oPWN6l0blj8iEAUUROQ58sB3etUsAqIeH8fW18FXdKVk5kOs4ATGvGIHLbwZf/wXcn60HH2iDZ+vbwNa3jQ09s3D/GNXxbHXeVu+9WoqUy9pKFXtIN0s+O6rahgMw6+y+5neGsBcOLzhAighhHRSD6gzkJrW8YnBCJ7gU9jdQ4sphfXDbmn2qVr8/fnQIt//bINXr2cFdLZQNAb7aodpOd190fFORcy6CsFJb+dR0w7IfUe6iOYbljyQoeQ314Npb4C8tQee6V8F1SIcjSebWREPKZMqXA4gdc+36UDbUSTZvh1Ggt3r/GKXjVudtye3VIvoLZOey4JW32kp46wgL+PhQm2q7+d/t58z9loiUcbKxl0YskX7i4qaZQx0IU5GMx77tRXT87H9NC7Hzu3m8cNkpqu3+uPUQOsLqQQp2cFeHLp0DkVMuG2e58O/AUEnFd5lXDPfmN43PH4mGAV06B6Efzwc/qBLokBYG5cKRWHMRcmq3ag514utrkbtoTk+o18sPIvfh2eDre5V3NSG/Rve3ZXXeltJeLUBSjo5dv4Fb1+xlanfzBeoGGiKDMThM2yrII0KkFTtUNSJkkLC2m211+fdTSnBKiRdfNckLJJ0i8Nv3vsFjk1U2OLSDuzq3EMGf3iybsK7YFxZrt84QF8dZzxTeZXjsNPl9igwsXSk2HFQ8LhWOZFT4X9J1NOwbYEppT53flqF9YRj7ahUAA5ffDLgM2KvFxFCzpo4IXt7VqNruHMYNDAnCbpAiQqQPh2/Ck7WYHGJ3w5gBuHHVXsU2y2qO4e4J6hsc2kHgjoz+d0SGjYVndRX4I98AOTnoHKS8jwiLgp6yEq/nPaZxTxa5d+ne+IrieYYpA2UDlY+faOyy6Mc9D5aQOyG/BJ1njIF750bZNr2vo0WgNytXSs+3ZVRfWMe+6u+1pL5Xi9nGtN++9w1TuxdZNzAkCJtBigiRNpy+CQ9hDpcNLcWC1d8gLChXm/rNu3Wo+jHD4muH3KTcQoR+PJ+tLYuCDliuxNvCeynxLq3KBcoZNQHhwlKgRdo67dmyAq6dHyQ8D7XCD0JecVf7/uWa8na0CPSmPh+N35YhfdFgwDJ9bFhgTHt7t3po39llPk0bGBKEnSA/HpE27FDViLAffjePG8b0V2337lfNTLkiToNFQbe8fKod9mSRwapcIM7jg3f+IsXSvknPQy4fx+NDcOIctN/2YpfSojFvR4uAbYdcKSP7omXsm33vZn+HD2ysR1DZHgMAeOWKM1L6HYJIJ6SIEGnDDlWNCHtyw5gBqpNTpwj8eRv7viJOgUVBt1qJt8OeLLKkmnyvoVgGXzEM7be+gNDYqfJt4p9HKAD+6H6Ex/wQobFTEbx4Vlfhh4X/D+FLZiX0TcuGfZoEbDsVJzCgL5rGvsn3buZ3eOhECI9vVd/AsF+eSzVElSDsDI1eIm0ohS3YtYwoYQ1+N48xA/Ow5aByycrFHx7Er0b3z6gkTSMUdKOVeLt7L/XmAukKN3N7IRaUKl7XtW0luGOHuqp5xZXuVRWAWUOdNCaL2yFXyqi+qH4fhYl7hJh572Ya0677x1dM7d6aQd4QwtmQIkKkD7cXoUlzkyoKiRyH0KS5lKie5cw8u0xVEekEcMuavfjTDyqt6RQrKSR1MynooQAEby74YLt8GwNxhPdSay5QCvH9avfr+moHXBL7xxiZO6BZwLZDrlQULX0JBeD6bD1yaj8GAHSeNgpCXrHs3iyelc9A6FeeqEiadO9mGdO2H27DRypzHwBcODgPFSU+Xb+hShoLUxDZBSkiRPoIB+FZ9UxSWVNOFOFZ9QwiIyZk5sRHEzwTlw0txd3r9+F4UDkPZPmuRtx/0XeMC0+Iez+R8grkjJqg6XS+rhr+qrvABXsECa3VrJSs3fzhvV3HZJQQM8JtMtF7mUqxDLUkdCUMLcRhJ+XCBPj6WvifuyNh40H3zo0QvbkQfPngA63J57Qdt67qogklwjvCAq56dTdT25d+ak6RCFsUpiCyBlJEiLSRjVWzLJ3gHa7w+N08Xp4+FD9Y9jlUCmjh3g378dik8pR/s/f7CQMIF5aCv+ZepvfD11XD//SCJOVaqyVc1toNdG1aJ/HdiL48tN/0NJBbyHCnGrHDniwGk1K4mczzMOq3CXR5rKrulNz9nAu2Ax6/7KlWrh9Gh369UduIpkCnaruJ5YXmhKRSWX3CYkgRIdKG3ePODcfCCT5TFJ5R/fNw1fA+WLbzqGK7l2uOYs6IMozqn6f/x2TeD1oa2d5POAhf1V2SGxcCOoQjCWu3a8daWcGXC7TBtXubacKXnfIMjCDVcLP45+HatlIyFEvvtYluQ5VM+BUAcKEOxfMtXT8M9Ew99EE9U7snp2gMR2Wcp7PRQGhrHG5QZIEUESJtOCLu3EAsm+AzTOG5e/xgVUWkUwRmvb4Hn/znObqthJrfT68FApEw+KByXHeqwlHalfcMCgUyJNzM7UVk2IXg99YAjIqIU0PZrCbVsezE9eMfuxtxsK0TfjGEacFdKBcaUceX4i3vcAQ4d6zd45PLNYWiapmnNc0xWSAkp5NsCZEjRYRIG5kYd66EVUJkpik8JX4XrjzzJCz//Jhiu6PtEfx522HcfIHyDthyaHk/UguE6FFPGlUUjhgW9axR3q0QcAwIN5MaB0o4OZTNaph2pffmSSr/tls/GMZzR1jAvH98jfPC+/FKywvoJ/bkvxxpy8f0wtn4xD0YlcUeXDW8T+9fkEfjPM06x2SLkJw2sihEjhQRIn1kYNy5ElYJkRmn8ABYdOnJ+MeeY2iPKLd74uPDusv5Mr8fmQWCCwWUz/flyQpHrIt6NijvVgo4KYWbyYXyxV8/rxjhC34McCCLsUYiw8cpVscS8ooRmHUnfMsesM/6IaFwxIpLqIznd75sglsIJykhANBPbMUrLS/gzNJbMG6IBiUE2udppjnGLCGZPCwxsilEjhQRIq1kWty5ElYJkZmm8ABdieuvzzgTP335c7QpKCPtYQHvfNmEy888SfNvsL4fpQVCDpHj0DFHRjjSsqhnuvJuthVQRtBRXdBDAUS2fAjx6EG4vKWIDB+nOg5CY6ciNOU657+TdOH2IjDn/qSqWQAg+AsQmHO/fdaPUADuja/AvWE5+DiDhJBXDE7oTOq/1HhevvMYpgVrkpSQKP3EVkwL1mDh976rqWua52mGOUYpV02vkEwelkTSHoZrIaSIEOlHTRDIFCuJRUJkpik8UUb1z8O/rhuJs//yKUIKZbQ+PtjKroj0GluBWQvhW5poYUVhKQLX3Bt7P2oLgODxJQoj3jwE5twHofxsyfZaLV+2Eb5MwEwroF5BJ3peuPs8X/d5kWEXKv6eWFCaEe8knQhDhqLtt8u69hH5YisAoHPoGERGXJSgnKfTMszX18JXdaek50Yp2T5+PN+2Zi/W7WvBbUKj4m/9bHBEc5lyPfN0bI75dD1yanueu9C/HIAJQnIWhSGxwvzeMkA+IkWEsDWZZiWxRIjMMIUnnhK/CwMK3PimOSTb5tkdDRjZXW1LCdmxdfVC8M0N4BoPIb97H5HW5nCsjdoCEZr2ayDHzfx+dS3qGZQ0Ho9pVkC9go7Cee5/vav4kxmTr5Nu3F5EzpuEyHmT9F/DLGEtOj4UFA4luMZD+L9th/Hcp13FOOr4UsX25484HSrRqUnonaf5w3vhWfVs7Dz3zo0QVj2LwOz7DDdCZVMYEiss7y1T5CNSRAj7kqlWEguEyExSeHojUx03gRtW7sWkymJ566HS2Fr2QGxsucoKoifE2qguEOdcpOnesyYBnQGznoVeQUfpPC4Slvw7oEERzwBrpt2RFdZmLgTf/G1Kz15PmGY8rfl9cff7+2P/f8s7HEfa8iXDs3Qbd/TM02pr701PG2qEMsUA4fRvS+29ARkjH5EiQtgWspKkSKYoPL0oL/ZiX4u8RyTK7Dd2Y8XMYZLHUhpbBitg2ZCAzopZz0JV0Gmoh2v7e0lCix4BiHUcZIo109YoCNT+vyVuPKrn2acSpy/kl+D6A4MAtMf+FuDcmF44OylhvcVTCFcKxh2t87Tq/Lh7m6FzoNEGiEz5tpTemxl5OumCFBHCtmRTspajsThM6InJFRjx189U2310sB3v723BhPLkncZTHVuGKmB2SkBPtxXRpGehJsh4PnwDXKCnDGz097QIQOGzvofO4ePYnlkmenvTPXYkUPRo9XKt6nn2TCWG/QUAn5MQviXkl6B51j1489Xk0sOfuAfjzNJbMC1Yg4rufUQemD8TxYUpbNYKaJqnWeZHYeTFhs2BhhogMu3bknlvmSQfkSJC2BYKWSGkGFDgwc0XDMAjm9Un2mvf3IPaX41KKudryNgyUAGzQwK6XayIZjwLJUFH5LgEJQRgC0FJ6veASubxoMkjZ0MBvzeWjR2Nz0KrMKbVksxUYnjO/RD6lyeN51lv7pW9boBzY7lvJADgvgmDU1dCNMI8Pxo1BxpogMiWSIpMko9IESFsC4WsEHLcduEg+HN4PPDBAcV2gYiI29bsxeM/qEz4uy3HVjoT0O1mRTT6WcgJOjIb4gHKIShSaFn4Wa2ZqgK+HZQUi8aOHmVHjzCmRXnhD+8FhM7k33V5ELpoJsLjp8fuPX48/+XjQ1j/zYmk83ozfnA+fjG6P3N/jCId86NRBohM8hQoYcs1TCfad/0iCKvoFh6E/JKEP2fMnglESsw7tx/k9i30iyHMCOzAbe1rIfxrLZ7/uD6xAY2tBFisiE4nKugEZtyO4KVzEJhxO8LjfqJ4Dtd4KHae+2e/A7x+6WtrXPiZrJkqAj5fV43cRXPgW/4QvKur4Hv5QeQ+PBt8fS1zP4zAkrGj8iwQDkqeFhXWtMCdaJS9nmSfOpIVCtGbm6CExNPUEcFdG5QNKACQA+DFn57O0mXjSdf82G2ACF88q0tx0/E7meQpUCSD1jDyiBD2JRQAf3Q/wmOmgGtvgZhbBLFssC1DEwjr8bt5LPvJabji1T0Jfz8vvD8p2fPI6++greQB5J3ak7yesgUuFOiqs7/7YwBA5xljNFfMsgvZYkXs7Wlx7Vir2Dw+BMU17kfgB1ai448LUg4fYbFmqgn4vqq7krw56fBgWTF2dIfbyHjCRI5LyhGJ4tmyAq6dH6iGlSn2qe24bJ8e2Lhf4oxkfjN2QFJIqZXYIVxUD5nkKVDDqe+oN6SIELZEyQ3vtI+MMI8J5UV48PuDcfu6rsXdJ4aTlBCga1fixqo7gbuWJY4fnSFA/NfV8D1/B/g4y6l750aIb/8VHT/7X0dVZgGyyIrYC61CC18xzJiFnyEmXk2AVwwpszAO3oqN11JRdqSENaG4LHnj0jhYFDq9fVq3t1nxPADgANwwxgbfnBP3KzK64IUdwh+VcOI76gUpIoT9sFu8OmFrfn5uf6z95gTe/boZ04I1kjX4AaA0cgLb16/GaZf+KKXf4/dWw//0zeAkjnEdJ+CruhPtt73oqDGaTVbEBDQILWIwgM7t78P9TR3E0gEIf69X6I1GgUXNmpmK8melB8vwjdcknmPKirKEsNZ+6wvwvPNXeLaskDxFTaHT06cXP/0W+0/I7z8T5ZfnlaXVG+J0jPIU2KWAR6ZjqCIiiiJ27dqFTz/9FA0NDWhqakIwGERxcTFKSkpQWVmJc889F6WlyruHEtlNtlS9IIzjickVGPrnHagQGhXbvf3RLvzXRVP0L/LhIPxVd0kqIVGUwjJsi51KCFsMi9DC19cisORuoKUR0b/GCyS6BRYFa6ZipS9fXlKlr4TjVnqwDNx4TfY5Xr3QeEXZ7YVYoCyLKCl0WpX3rxo7cPOafardcnHAbeOGqLYjVEjVU8BiEEWB9LmEJlJWRARBwLp16/Daa69hy5YtaG9vTzguiiI4LnHZrqiowJQpU/DTn/4UAwcOTLULRIaRNfHqhGGU+F2YMawUdf9SFiy+5Erx2/e+wWOTK3T9jqtmk6IAGMWJYzRT4o11oSS0dAskUNhl2hQPrpKAP2uhbGhROjxYhmy8piT4LXtA8p7N3l9G8bgG5f3vNUdxw8q9TH167cqh5A2xAUxFGAb+2OJeZSa6FZFAIICqqiq8+OKLOHbsGMTuxC+3242KigqUlJSgqKgIHo8HLS0taGlpwf79+3H06FF8/fXXePLJJ/HnP/8Z48aNw/z583HOOecYdlOEs8nWeHUiNR6eWI7hu4bjSFu+ZHjWES4fb3mHI1BzDBMrC/Gj00/S/BusCoZjx2gGxBsbjZpA4lldZZoHV0nAt50HK8WN19SeM3+8wdL9ZVgUOhblvakjwqyE/PfYARg7mKzsdoAMotahSxFZunQp/u///g9Hjx4FAIwcORI/+MEPcO6552Lo0KHweDyy5x45cgTV1dVYt24d1qxZg40bN+KDDz7AxIkTccstt+A73/mOvjshMoasjVe3e1KczfG7eTx3+TBM//vs5KpZXD6mF85GgHMDAH6+og6PTOzEtSP6avoNpp2U84ozd4xmOhLfoGrSeEO94vGUBRYZAT8tHiwdcxSrYYlJ8GNRlLX00QiFTqVPN/zza/VroGsvhRvtkKBOACCDqJXoUkTuv/9+FBQU4Je//CWmT5+OQYMGMZ/br18/9OvXDxMnTsS9996LDRs24Nlnn8Xq1asxdOhQXH/99Xq6RGQSehcHBwvyWZMUZ/I7mlBehC///QKcubYfpgVrUCE0oo4v7fKEcG74xRCmBXehXGjER/8oxdSKmZp2LVZSkgFA9OcjMOd+Y8edg8e1k5D7BsNjpymeJ5QNAb7aIXvcVIHFQg+W3jmK1bBkhOCnp49mKnQdYQGr6v4/e2ceX0V1/v/P3P3mZiGBsKOJIghBFFFRqEJViqIiaoRWFKzW6te9X0Fpq99Sy8+qYFu1UsVqi4pWJC6gVBSjKAgqsu+7bAKBQEJyc9eZ3x83N9xl9jvLmbnn/XrxepE725mZM+c8z3OepVHWvvde0Jm6ZBFE3hpETYDhOIFk2iK89NJLGDduHAoLCzVryPfff48TJ05g2LBhmp2TAkQiMTQ0tJjdDHVEw7InB60F+fLyxPJ4XZ109duciYYThcgEBjy7ZAkzUtm6+b1t+GRneppMvvoidc5CBO78s+D1+foB331wLjcil4xBdNjPNX1XtlNQSVWqxL7BQDsAiSQEWdsKSxH8zcso+Osd9v5+cxyjZPXjXMdBg8ZRJXPDLe9tw8Kd0ul6nQB23n+uPEWE1G/Ihkj1W0PlBAtQUuKHx6N8fUOVIkKxDpZWROSiwwQkOcBoOBm4VtfC9/aTgttDYydb32/fYGXrWEsMZ85YjeTg5uOi2FQ/jTd2pMVXgvjv3uC9vmA/UKAkq8ZmCipRSlXG94tYFL6aZwR3j/a7GO4f1gMn+NtO1L3pgCZjlIxvJpfnmFMbxcbzjG3tho4A4/FJCp8bDjfjp69vavs7dTU2dZUWAGaP7onhp7cTPR9A2DeUL4j0W1E5IQ8VRrWKCK0jQrE8Rqf71XoyyIegOKPfUanfhemXn9KWLlOsvog/1IDGtUvgGHiZ/AsY4BJjqzTWBNUG4l3R8vhEj3Gv/wooKoXr2jvQHIxkCRZ2zzimyRgl45vJ5TmqbaNo8Vxkpx4O/XcmvPdNAwqFU+y+tvYwJn56MlUv32rsoeZE3NrAQefKUkJI+obyChVjPVUYlUEVEYrlMVSQ12EyyIegODOUrVvO7ohXVh/GxiMhyfoi367biguVKCJSaGANk3omzg1LLSPsEqNUCXy/TCQkfeyJY4h9XoPoxFn8z9wqGcd0DDjXBJXPUVUbxcbzWY8l/p/pktdYj/DzkwCBfrB4d2OaEuLjollKCAB04powP/g6XD+5UrTdSSSzt300E1xxme2UYMtBFUbF6KKIHDx4EFu3bkVjYyNisZjovqNHj9ajCZQ8wshJUg+BKh+C4qTeAXOiHoiGNR+g37q+F86euRa7HOL1Rd7Y7wb2ndAkdaZW1jCpZ+Ze/xWcu9dbwspGyqqf2Pcri8Z6Zd84Ye4Zegecm4maNoqO5zwxQW0I9IOWKItx721N+01sNbZd9ARCMvuT1Dfi+eZkhXhqfTcPYowuFkJTRWTVqlX485//jHXr1sk+hioilFwxcpLURaAisSaAxkhlm/Isnw/X+iWaT55dijwYdkoh5v0gXV/kg3e2YOu9MgNGhdDQGib1zBSf10ShmJRVP6nvk/X44JBYHZH7jRPnnpFL37TCGKWijbkowHzH3j5/OyJs+m9Sq7F61Cai1nfzIMXoYiU0U0RWrFiB2267DdFoFABwyimnoEOHDnA4aDo6is4YOEnqJVDZ3cdc6B2lotfkOWt0L5z23EpUF0vUF2GBSZ/uxt9Hnqb6Wppaw2Q8M7nnNVsoJsWiLvV9RkbdA8e+rfAsny+4j6xvnED3jFz7phXGKKVtzEUBzjz2uW8OYBFPql6p1Vi5bZBjmEiFWt/NIScZgbAVVKPQTBH529/+hkgkggEDBuCZZ55B165dtTo1hSKJUZOkrgKVVXzMVZJ8R54FMwUFPT0mT7/bgQXj+uDa/wB9XJN464skmbOpHr+/uDu6FAkXZRVDa2tY8pl55zydCJhWc14ShGJCLOqS32//YUD/YXCtX8Iv8BWXyfrGSXTPMCrg3HQUtFG0P4ikbc7sB5/sOI6pSw7wXmOeV3g1VtGcIdMwkQq1vhuPWhnBbGORmWi2XLFhwwYwDIO//OUvVAmhmEPrBBS9dFxiItJDuGmdDNjC0rSfiXJRIBm3F1yRuIVQj8lzQOcA1tx5DsKMG3N85+Cpgksxx3dOmhKSZNCr67DqYLPwySIhuFZ9BnftbLhW1yZiW1rRZcXM7UVcQlgRO6/eWYR1AAAgAElEQVQcodgIkkpVaOxkhIdPQGjsZAQffs3YSVbO9yuwD4rLEtmSdMzgpCekuMcRhVh/mPAnhCb8SbIfLN93Aje/v13wEiHGjXFFv0AD0vuNmjkj8xuKXHiN6P55+U7NRo2MIGEsQnOD4JxjBzRbEfF6vXC5XOjShXZ8ir2xgosCyZglEJX6Xbji9BL8d4d4gbFQjMO4d7fh+zv6Z22TslpJWsPOGAjXqs8UL73nshJHlFBMgEVdzvfLt0+yfgRkFC/TtI9r5K5BinscaUj1B7F+0BJlceOcLaLnHxjdh9kn3kIJUgwWvgBC4x5Vp4SnfkPRsODqXT6/U7NRKiNIGYsC028FEzppHLPbSolmikhVVRWWL1+OpqYmTSuuUyiCmOlPSYBAZVVUCUQaveu/jajEf2esltzvSEsMv639AbNvTlFGZLo4CbkgRUbcjoK//Vrd0nsOrk3UEs6D1PfL098YoVojPPtqJfRLumso+S4IcY8jErH+kLEttR9c9eZGhEVKQgul7mVCzfDNnpq7WyRJ7zRP4xsEUSAjSBqLQukr9HZLRqBZZfVly5bhtttuw5133okHH3xQi1NSNMCuldX19qeUrKxOyQkl70/rd/3KysP47ed7pHcEcM+FXTHtqp5oOh5UVrk5sxpvr/NQ8Nc7cq+Srqaiu80qtOuNUH/zPzAdjsq+aWOC0mJ4ivqtxHsLjXsUvtlTlZ9fTR+itJGcG176cifuWvCD6L5jQqvx76Y5gttlVaSXg8nvNF/jG7SSE6TmFiE06z8aobayunPKlClTtGhAjx49UFpaiueeew4HDhxAz549UVJSosWpKTkQj7MIh8VruViOaBj+GffzFiVzblqO6EWjAGdui32BQOuyfDCS03ko/HAlHRC9aBTYjqci3vV0xM6/EuHrHgBX2il9Rx3e9bldAijzO/AZT4abTL7bdwJ//WoPhlaUoPueFXDtXCO4b7zr6WArW1dQnC6wnSvBVvYH27kSrg1L4V61iPc4JhIC2/FUsJ0rpRufcV5Z9+50IV7ZH85Ny9MK9yUFhaxnbjciIbjWLoZz0zI4Go6Abd9V+LmJ9Lf4miVw/fQGBMOs5L7OTcsRGfFLRIdcJ93HBXCt+1K0z7g2LIUj2Jj1u+R3oaYPmYmS92cAgYAXLdE4Lpq5VnLfqyMbMSy6U3B72piRC2a+UwPmY1LJWU5o7dvMkf1wHNgBJh5VdLhm/UcjfD43nE7loeea9o5x48ahoaEBzz33HGpqauD1etG+fXvB/RmGwaJF/AMthSIEiRlpKCqQsXSt17u+fUBnjOxZhgEvrwUrsSYcjHGofmcLtg3uDDEbo5iLk9lxGvka16TUUita8LCxHvFVi4HTBkvum9o30/pna6IDOe4rSt01Uq/tWTATkZG/tvz7JdHSfqQpghveWC9rX61S95IMnY/Vwde3OYYBk+KkxHoDcISFE6fYof8AGioikUgEDz74ID7//HMAAMdxCIVC2L9/v+AxDMNodfmcCQaDWLRoEdatW4d169Zh8+bNaGlpwbBhw/DSSy/ldO6dO3dixowZWL58OY4fP47y8nJccskluOeee9CxY0eN7iB/MFuooxiHnu+6S5EHI3u2w4fbRCoot3IiwmLige54UaXfPxFxGvkW16QibbFUf+LqDgCnyds3c7tioToHp2nP8vlwr/wUkUvGInpJtTUVEhLSTmfw2prDmLRoj+xXc97PRoD95FNbB5PT+VgFAn2b4ThwvgAig0eDK+8h6dJrh/4DaKiIvPjii6itrYXL5cK1116LwYMHo6ysDE6nU6tL6MoPP/yASZMmaX7eb7/9FnfccQdCoRCqqqpw/vnnY/PmzfjPf/6DTz75BG+++SYqK2W4ZFDa0Eyoo8F1xKO3AP/M8Ap8uE06eB0A3th6AtXDHsLlXzyjODCUZiwyHjWWWqn+xJSfTE2vqG8qFaqjYbiXfSB8bpcXTEw8hScTCcG7aBbcyz5IpKG1mK8+aZb2T3Ycx8RF8mLLAGD+mF4Y1KMYoc6EBJPrBBFGFosh1reZUHNCCWnt28QkI9ARzRSRefPmgWEYTJkyBdXV1Vqd1jACgQBuuOEG9OvXD/369cPGjRvxhz/8IadzBoNB/O///i9CoRAee+wx3HzzzW3bnnrqKbz66qt46KGHUFNTQ9TqEOloIdSRuORPyUZvAb7U78L04adg4qfyBIzRyx342xXPYLxzqzIXJ5Ky2+QJaiy1otWri8vgHDAUaEj4ccfOGAjWWwBHOJi1a2bfVCpUuzYs5S+k1wrHAHJnDEfzcekVBAKNMiRZ2qVqhWTSvdCNQT2KAdjALVKib1Aji3KU9G3L9x8ZaKaI1NXVweVyYfTo0Vqd0lBOOeUUPPHEE21/b98uf9AR4t1330VdXR0GDRqUpoQAwMSJE7Fo0SJs2LABX375JYYOHZrz9fKGXIU6OdZJFOnQcIpiDBDgx/fviEK3E3ct2CVr/we/OIif/von6HKOsurr+TChkIRiS22rwBXrOxjutV9k5e333zetNXVr9KQhQ0AJyeybSoVqqf0dCguaia0gkGqUIcXS3hJlMfYd8VohqTAAPhtflf6jRd0iZfUNamRRjOK+bdH+IxfNFJGOHTvi6NGjcLnsmR1BDclA/Guuya5+6nQ6MXLkSLz44otYtGgRVUQUkotQJ6vSdNdrtW4yRSVGCPDX92mPtYebMWPFYVn7D3x5LT66qQ8GdA4ou5DNJxSSUGKp5RW4vAHEzh4GtvIsxKqGINC1Q2KDgCEDSBSqC/7mZaCgOP13KcGjuENaEDtX0kHJrcqCV7khMA4jCSmW9l9/uB0trLx9GQDPXlGBUr8N5CAFfYMaWZRBSt8mBc2+luHDh+Nf//oXVq1ahQEDBmh1WkuzadMmAMBZZ53Fuz35+8aNGw1rk61QKdSRtORPkYkBAvyUoacgFOXw6po6yX1jHHD9nM3Y+D8D4HcrT1doeQh05clCrqW2uQG+Vx7JWt1whJvh2vg1glfflXZvUv7drq0rsvpqrGoI2EA7Xncrzl8Ez8evpG1jA+3A+YvAtGTXJ+B8AcGMWWLwKUOaxGHo1ReMtLQL3MNb6w5j4U7pNN8AMLh7AP8adYY9lBCo6BvUyCIfuoqUhmZfzN13343a2lr8/ve/x0svvYQePXpodWpL0tTUhOPHExNLt27dePfp2jUR+Lhv3z7d2uHxuNqK7lASxCoqIZatu7DiZPIAJc+OC4cQX7UY3JEDYMq7wjlgqHA1Zotg5j2Zce2/V/fBnE1H0RSRNoE2Rzn87st9eOPnVZL72gl210aEn58ENNaf/LG4DN77psFR2de8hvFRfh64fu8m+lHdyX4UaO1H7K6NCP/lfoDHxQpICFyle7+Ha9CItt8Kw/UQq8xUsP0beIaOSOur7K69CIOnTxUUgWEYMBkKiqP5OBAoBopKgRMpwmBxGbx3/T9EXvx9+vOXorgM7TLaBABRiXspDNfDLTIG6t4XJN6fFgjdwwtn34dJm+QLhIvuHAi/2xrJefjIHG/Z4GHERfaX6hv5hCoZy4C+bRU0U0QWLVqEn//853jhhRdw5ZVX4oorrkCvXr0k09NaNaZEiubmkxYrv9/Pu09BQUHWvhT9cQ4YimhxGf9EngxIVQjfZBYlVTiTiZn3ZNa1/W4nau8YgOH/XIWGsLQyMnv1Yfzi7I64qk+5bm0iCS4SyhbaAKCxHuHnJ8H3ZA1xyjfj8aUpEkna7qVFfPzl6g6kny8lcxYf7PefI7RtTVtfbbtOM49lnY0DIX4lCM2NcP3y92Bc7jRBhfH44L1vWvZ7KCqFc8BQxL9ZCIRbTv7e+t3wvRepexHbblRfEHp/WiB2D9VLnsFjZZMQYtyS56kZV2VpJYRXGfOLu51K9R2KNHr2bSuhmSIyefJkMAwDrrUYy0cffYSPPvpI8jgtFJGnn34atbW1io+bNWsWOnWyd1XhSCSGhoYW6R3zDMfNf+RfFr35j2hqiKK8PDGB1tVlu0ZkEQ2j4NmJ2cvYjfVoeXaiqX7WqjHznkx+nhU+BmvvPAeXv7EB2+qlg4KvnrUeD13YBfdf0MX2blqu1bXwCVniG+txfPFCy7hniN5LCk3eMsTqTrRZPY/1GIgCocxaSVL6qmvDUuHrCCkhrTTv24fopePaapckMnZFgcIewMRZ/D75l9+e9XuT2wvwjWUi98IWluJYj4H8x8EefUHsHjpxTRgV3oA5vnNEzzG2Txku7uyXN1eQiNB429KcVWAviVTfyBeSY4Im794K7q4SlJT44fEoVys0U0TOP/98rU6lmMOHD2PXLnkZb1KJRsUcdHIjEDhpTWhpaUFRUfbSXTAYzNqXYgxaBteRlu9eC8y8JxKep9/twIc/74PeM+TVGHlm+Y/4+3cH8cboMzC0olj6AC0xcAKzU3yVnLbyBo4K+HdnkuyruTwT0SB3IZ98Jb76Ofiqa9IXTBa+pNpYyYorqslaIVZGNOaJ47Kqe+drHIOekJq5zig0U0Ref/11rU6lmOnTp2P69OmmXZ+PwsJClJSUoKGhAfv378eZZ56Ztc+PPyYGQaEYEorOaBRcZyfhLImZ90TK8yz1u/D8qJ64b568VN7hOIcba7Zi+vBTML6/uEuqVhg9gZGSUlULpNrKegOCAlfSkOGd8zTc678SPEfSyCHaDoHgc6Oy56g1yuTaF0gQvqTauMtRJrjt/gs6y1dCCLZ2S42n0SHXgSvvTrNh6QXBmeuMwt5+BCbTt2/Cl33dunW829euXZu2H8Wa2Ek4S2LmPZH0PO8d3ANPXXGa9I4pTPx0D348EdGpRSlITGBQWGtCDsm0k3yYmnYyEoJr1Wdw186Ga3WtrHsXuxfOF0Dw4VniAjHHgQu0E71GUnATe2YtEx7P2m641bnVKBO9dFzCOCPjujn1BRP6Lh9i93CIKcQ8L38iin/f0AuPXtxd1jUce7egYNoE+OY8Be+ns+B7+0kUPD0ejr3ya5PoieR4W95dcd+gyEdWOQGbQxURHbnssssAAPPnz8/aFo/HsWDBAgCJ1McU60KscJYDZt5TrNd54Bj+utEcwyDW6zzdrs3Hw8NOxZ8Hd8DY0Go8EqzFmNBq+Dhxt87z/7kWqw7qm4TClAms1ZXHdME5BdWCnsi9tNz2ZFYtEL5rer7JHttTz5O0Hos9M7biLAQffg2hsZMRHj4BobGTEXz4NfJdMnLoC7L6rgrlUjFuL54/624cYgrTfj7EFKK6eDxvoPqDQ7phwvkyvRgIUbjEsOP8ZSVI8QAwE1WuWU1NTSgsLJTekZDz6snatWvx8MMPAwA+/vjjtG3XX389XnrpJXzzzTeYPXs2xo0b17Zt+vTp2LNnD/r27YtLLrnE0DZTRGhdQo9GjiWygvQYKC1c2TEnuIn35Nq6gjdAEkj4LPPVadATdtdG3Ff7SNpzONScEFS+d/NbRSMsMGbuVqy98+zcAthFXDrMmsCIKl6Wo1uDqnsRKWjYdt6M70TyOhatwaC2L0hWjt+1DgUfvSTttpWjy9Ofv9qLv24L4I9lkzAqvAGVbD12Ocowz1vFq4T87wWd8cw1vWSfn4R4N0nsOH9ZCJI8AMxClSLy05/+FLfccgsmTJiAkpKSnBuxZMkSvPjii7jwwgtx77335nw+tdxzzz2oq0sUM6uvTwSprVy5EmPGjGnb5+6778awYcPa/m5paREMlA8EAvjLX/6CO+64A48//jhqampQUVGBzZs3Y8eOHSgtLcUzzzwDRsD6S9EImZNVqs9yMrd+gUyfZaKEM40w656IsBAlFdKWOsQWvQ1HRorXTlwT5ja+hj4i6T0bwnE8s/yAbBeOTKR86E2dwMwQnHm+Y00EPYX3InZNAIj1HID4KVVwHN0PtnOF5ZUNSVTcl1TfdK35Ii1AGshWLnONMZm8aDdeXXMEABBi3JLZsW7v3wGTFX7LhoxlGsSf2HH+sgq0yrpKRaS4uBgzZszAv//9b4wYMQJXXnklhgwZAqdTfh7tvXv3YsGCBfjwww+xfft2MAyDG264QU1zNGPTpk3Yv39/2m+NjY1Ys2ZN299JBUUuF1xwAd577z288MILWL58ObZu3YoOHTpg7NixuPfeeyXrrFByQ/ZkpUXAmB0FDRPuyWwLEZ9Cyoec9J7PfXsQTeE4/jC0h7KVERn9MZ8mMKHvONZ3sOhxzg1LNReopIRH1/ZVcG1f1dbGfMl8owSxvsv5AnAIVI5vUy6rhuQ0Xj/7zf42JUQOo3uV4s/DK2TvDwCIhMBIpIfOdSzTNOA/dayPhOBav4TI4HrbQVekwHCcgA+ECNFoFG+99RZefPFF1NfXg2EYFBcX46yzzkJVVRV69+6N0tJSlJSUwO12o7GxEY2Njdi3bx/Wr1+PdevWta0icByHYcOG4aGHHsIZZ5yh+Q3mO3ldRyQaTviKCwhqqZOVa3UtfG8/KXiq0NjJiUGa4OwntkHBezPy2nz8seByPFUgT1F7Y3RP/Ox08eDmJHL7IwmZh3RHrD9kpBblQ6vn0VZH5NMPRN8N3/XzIfONUsSUS8+3wjXIwsMngCvrIm+85mHx7kbcWLNVdjtLvA6svfOcNkOCnNoRfPeWSc79QqdxMi/GFI3QtI5INGz5FSlD64i43W6MHz8e1dXVeP/99zF37lxs3LgRS5YswdKl4gGSSb0nEAhg5MiRGDt2LPr166emGRSKKErcNuQsodMB2iDMjE+RcLvJZI9TOL1nJje/vx13n9cRU4aeIrmvXJcO27hUiCj4ot9xuFkw/W3bPhqnwRSz5gtdn4hYAMIQ6ruuDUsBEUWEK+ui2uVpe30LxvAoIX4uglHhjajIiBEp87vw1vVnaLKamXYPHh+iF46Sf04edIk/oalkzcOOHhUyyamOSEFBAW666SbcdNNN2LJlC5YuXYqVK1di7dq1OHr0KOLxeNq+lZWVOPfcczFw4EAMHToUfr8/5xugUIRQMllJugOVdKADtIGQGp+SCltYinE3jcZbNbtlHzNjxWEM7l4suTKiyD3N4hOYlIIvWeeg/zC4Nn4tq7igJs9JZkHDVPIh840qePquHJdDqYxwXFmXNOW2MdAR1Zs74Lsj8ax9B0b3YW7ja+jENbX9dqi5EE+d+T/47S8uU5xsQo4xg4mE4F00C+7l81QbsvSIP7FEcL0diITgWvMFnFu/AwDEz7wAsf7D8laG0KygYe/evdG7d2/cdtttbb81NDQgEomgpKQEHo9Hq0tRKLJQIsxJTX7gQAdooyEwPiVJUlC+oEcHvHODR5Grxy/nbcf2e88VFXBiZwwE5w2A4XE7slX8hwwLrGThwcqzELz6LlnFBbUiU1FmTtTDs1w4la/hmW+s7EIqY0VUarxmS8pRMG1C2/ZyAHOY7Ex3Pi6apYQAifiv6Xv/iSAuAaDsuSnpZ7kYsvSIpSMiUYidiYTg/mouPF/8B0zsZK0p9/qvwH00Ey2/fCIvvSs0U0T40CKjFoWiFkXBvBKTn3PbCtFr0QHaHkgF0UYGjwZX3iNNsBtaUYx3bjgDN9ZsyzqG1+WDdWPB9mO4oU973jYkVwiElBA7BTDKssDK+Y7dXsSrhogqIporA6mKcjQM1/olRCQOsIMLqZx0x4Lj9bhH4Zs9Netd8GW6GxXekKWEJFFrYFLaz9ReR49kFWYnCrEzjr1b4Jv1GBzNx3m3My0n4Jv1GIKPvG6b8V0uuioiFIqpKIw1SJ38CsP1YMq74lhrHRHH0f2ZZ0+DDtA2QaLPCAlyQytK8NLICty5YHfbb0IuH9XF4/Hm+kSQ48iepekrIyL+5aw3gOBvXgZcHrhWfWZNa3cGsiywMr9jU7OIKY1r0mvFwk4+/hIromIxJkLKbWamu0pWPKuVGgNT7IyBYL0FcISDso9RZcjSIZYunzLxGUryuxRQQpI4mo/npXcFVUQotkZxrEHr5OduzYaB1mwYdIDOH8QUUjGu69MBn+xqQM2mY6IuH3MbX0OfHybhqz0n4GB24eyOBfj3tT3RpcgjGZjtXjYf7uXzLG3tTkWuBVbWd2xyGky5Y42eKxZ55+PPF2NSd0D0kFTlY5dDPNmE4tWN5LtVoIQAAFfcQdH+STSPpaOpZHVBSRKUfPSuoIoIxf5oEWtgpQHayv7hpCCgkErxj5GnY3jlEdS++76gy0eqVZblgFWHgjh75lpccVoJXi8UF6I8X74NJhJK+82S1u5WlLpPSn3HpmcRk2qjzisWin38bTZWLNvXiLkrI3hJZJ9U5WOetwqHmgt5v1XFBiaR1UzOWwDO6YYj2MB7qOfjV8B2qlCniGocS2f6N2RDlCgX+ehdQRURCkUmVhigifIPt5mQI5fr+3TAkCon8I3wPnwuIR/vbMCDkRBeFjl3phKSRJG1m6T3ooeCLyWYmXj/eq9YKPHxJ2qs0IBPdhzDze/vgM/ZB48z/MrFIaYQ87xVbX+HGDfe+8lv8OtVf8+5/4m9WyYcROTyCXAv+4DXPcfRfJxfETWrr1o8E5+p8Lwz2UlQAu3y0ruCKiIUihJIHqAJ8g+3m5CjlG4Vp4oqIkIuITXuKkwVEKJYjw8OAUUEkGd10/y9aCAoGangm90vNc9KlPn8e50nb4WJoLEiV44Go5jw/jZ8+2PCHSrEuFFdPD47Pqs1axYDDmNDq9HP2YBxw85C4cChCA7Pvf9JvjsGiFx5O3xzn+HdnKmImt1XKcoRfGfjHpWsPcT5ixCa8CfLfHdaQhURCsUmEOMfTqKQY7BlUczlKNMqm4qQEMUWliJ64Sh4F80SvKak1U3j96KpoGSEgi/n/jlO136iZVYioecfGXE7PAtfEbXwEzNW5Mhraw5j4qI9Wb9/7+6OPmWTMCq8AZUpGeuqYoewsX76yW/rg4VgP3sFofGP53y/ct6tbEWUxDGUIo7YO5s9FaGbHoXvzfRsbqzTDfbUKsTOvYzWEaFQKNaHlBzwpAk5plgWBVyOklbZZPpQPpJC1OjIBtzUNYoLzuoFR/+fJE6bEaieRI4/u6bvxYKCktT9u7+cq3siANH00AwDtqRc3olEnr9n4SsI/uZluLauELTwkzJW5ML8LUd5lZAkIcbdlh0LEK4ZolWf1awQI3QaQ0lyybQhUu/M0VBHvGu3WVBFhEKxCaTkgCdKyDFRYM50OdrlKMPV60pxICI97IYYNz7w9AW3fyO+3b8S1zSEUXnxZTnFU2j5XkhTNuUgdX+SiQBQlHsj3F6Exj0K/8yJYDguvX0cB9+bU2X1Scnnv3WF6PMnZaxQyysrD+K3n+9TdIweNUPS0KAQY9KYoPUYqosxxs6KjYp7k5uKnLRxkQQ0U0S+/vprDB48WKvTUSgUhZCSYpgkIcd0gTll4ukOYNkQFr/+cAcW7uTPnpMkqwbJp58itORfYH85VbVVTcv3YsXsTFL3J5UIAF2vBRcO5VzDxXG8LksJybyWVJ/MVVAlZaxQSjAax1NL9uEfK+sUH/uYRAIJLQwkORViTDEmaDqG6mCMsXP8itp7I2nesxqaKSK33XYbunXrhuuuuw7XXXcdunXrptWpKRTzIUCQkoSQFMOmCjkZ74mpE7eaGu2C4nc78Pp1Z+D1NQfx0CL+tgm5kPhaGnDin79H6JHX4VehPGn5XqyYnUn0/mUkAmB3bUT4+UnwNZ7MeKbmPrSwducs9BAyVihh3uajuOOjXeBX4cR554Yz0O14o6giopmgqLIQY+oz1/Jb1dwYI6XYPDgz4RaoZK7Ucn7N5Vw5KG1WVe5JQDNFxO/3Y//+/XjhhRcwY8YMDBo0CNXV1Rg+fDg8Ho9Wl6FQDEcTQcogRYaIFMMmCTm878kbED3GLCvVLWd3xrcHWvD2xqNZ28RcSIoijXjgb7Nx9dhq/Oz0dsouquF7kT3pkhRLInL/kokASjog/PwkoDE97bKa+1CkRAiMG1oIPUSMFTIIRuO4/u2tWHmoWfGxHgcw98beuLB7EWJRggRFKRcdDb9Vrd28pBSbgmm3whE++a6k5kotDRW5nisnpc2Cyj0pMBwnsEaskGAwiI8++gjvvvsuVq1alTg5w6CoqAhXX301rr/+evTr10+LS1EUEInE0NDQYnYzLEd5ayG7ugNHUPD0eMHJS44AQopF2HCiYeOEnGhY8D1xDMPrCiPn/bX1A5kFDZWyqS6In762EWzKb48Ea/GH4CLBY/5YcDmeKrgUl1cW45VresLvdii7qEbvRU6/dq2uhe/tJwXPERo72Xifab77B0S/88iI2+Cr4U+7Cii8D5G+mtonpZ5vPowry/adwA1vb0FMxbF3n9cRjwzunvZ9aPHM9B4T0tDgW9X6G3TXzob3U2GlnQ/BsVbmtyALDc4ldW/h4RMQvXRc29+8fcHIeY8wSkr88HiUr284p0yZMkWLBrjdblRVVaG6uhpXX301/H4/9u7di/r6eqxfvx7vvPMOPvnkE8RiMZx66qnw+XxaXJYiQTzOIhxWM4znIZEQXGsXw7lpGVzNR8F07I7Id5/DvYpfKGQiIbAdTwXbuVL4nNEw/DPuzxocmUgIzk3LEb1oFOC0ac4Ipwts50qwlf0Tz0jH+3St+1L4PQHgfAEwsWjbb0nhgyvtJHreQCAxgQSDEc3amkp5wI3LTivBh9uOIRRLKEvd4g0YHdkgeMy/vedhg6szdh4P49VVh3DxqcXoUqhg1Vmj98KVdED0olFgO56KeNfTETv/SoSveyDtmTo3fg3XzjWC54h3PR1sZX9V11cN3/07XYhX9odz0/K0WJFkP3H8uF27+5C4FlfaSda4wZV2knz+Vmb+lqP4xXvb05R0ubxzwxm49ZxOcDuZtN/l9Fkp9B4T0tDgW2Xbd4Xru495Y6DYwlKEr3tA0XkdDUfg2rBEURuYSAhoaUL89HPSriU6bsuZX1PQ4lxS9xY7/8q0c/D2BQPnPVtci10AACAASURBVNLw+dxwOhUaxqBT1qyKigo89NBD+M1vfoOvvvoKNTU1+Pzzz7F161Y88cQTmDZtGi699FJcf/31uPjii8EwjPRJKRQdybSURQFEi8vgOPMi0eOklrVND5bOE6TeQ2TwaHDlPYi0Ug3oHMCaX5+N5779Ec9++yPmeatwqFleZejGCIsrZm9CdZ8yTP3pKSj1u4yNZ5JwMbFSAKeYq5Lj6H7RY5Xeh5RblOxxw2ZZePY1hPHAJ7ux5mAzGiPKVRAPA8wdk3DFEsRmz0wSjV2GxNwCxfAsnw/X+iVpq09auo1pcS4a52EOuqpqDocDQ4cOxdChQ3Hs2DHMnz8f77zzDrZt24aFCxdi4cKF6NSpE6qrqzF27FiUl8vMoU6haImAHzsa6+Fa84XooZKZeEhKZWtjJAXe8h5ECx9+twOPDOmG+y/ogunLDqD6a+HK0Jk1SDgA72yqxzub6nFLuyOY8eOrcDYfb9ue5XpioKJiuYldQEiNVQ0BikqBExreh4hAnI/jxiOLduNfa46oPv7ugeV4ZEgP5a6KeYCieCCp8UFAseF8ATAh8TiezJgqLQ0VmpyLxnmYgmFrRvv378euXbtw+PBhMAyDZGjKwYMH8cILL+Dll1/GHXfcgXvvvdeoJlEoACSsj+FmwQFWjgBiJYuwlbGcwCuA3+3AY5d0x+JTitFnbqesytBihRB9XBSP75gJp0jBNsfB3cbGFdhkYncc3A2w8azfWX+RLveRb+PGLe9uxcJdjaqO9TLAO1KrIBRZK0FyY2h4FZte56Hgr3dIrpSkruhpOW5rdS6rJHGwE7oqIvX19Zg3bx5qamqwfft2AADHcejTpw+qq6vxs5/9DMuWLcN//vMfrFy5Ei+88AK8Xi/uuOMOPZtFoaQhZV2M9h8G18avVQlSdhGQiccmAm+SoRXFmPPzfhjzjhshmR4qkgXb1nwBz8JXDc9gZfmJvXXFFM08grLDCbZzheaXzKdxY+Knu1QrIQO7FODdG8+kqyBaIJbhbtZjCD7yetbKSKZiwzcG89E252o5bmt8LpJX0O2GZlmzkrAsiy+++AI1NTVYvHgx4vE4OI5DYWEhrrrqKowZMwZVVVVZx73zzjt47LHH0KNHD3z66adaNimvoVmzpJGVVaRqiGpBKh+y26RhZs0VjTOWGJohh4eWKIvb52/HIhmCmlS2rWi/i+Fe/5XgdlMyWGmJTv3OrMxfdh03jgaj+H9L9uGb/U1oCMVxOKgumcr/DemKey/sqnHrpDF7TNALqX4evnwCopeNE9zeRjQMz4KZ8CyfL7hL1jej5bhtYNYqu/YFtajNmqXZisj27dtRU1OD+fPn4+jRo22uVwMGDMCYMWNw5ZVXimbKuvHGGzF9+nQcOHBAqyZRKLKQZX3MwUJieYuwAkwXnmxmyfK7HXjz+l74ZMdx3PrBdsREzEa7HGWi5wrFWAg7dlk77kDPfmdWvIYdx41/rjyE332+N6dzXHpqMf5x1WmJxAwUzZDqx+4v30b0kmrp/uf2IjLy13CtXyJ/RU/Lcdtmc0A+oNmXfPXVV7fFfpSWlmL06NGorq7G6aefLvscgUAAjY3qlmgpFNUkl3RnPQZHSpAvikoRukUjt558GBxJKl5nM352ejvsuO9cvLmuDr8VEOSksm09uq8zXha5hmXjDnTud6bGa9hk3AhG47h3wU58uL0hp/Pcf0EnPHpxD41aRUlFqh87WlccZfVHm7nKZtH6LKKRY2DKuwI9Blr/nkxEU5PC4MGDUV1djcsvvxxut5jtjZ+33noLsRiteUGhWBGaqlhf/G4Hbj+3EwJeJ+7/eHfW9hDjRnWxcLatDa5OmNq8kFdRsXLcgd79Lp/iNdLQwNUtGI1jxopD+MvyA4ipKQgCIOAEBnYrwvNXVKJLkYJ6ORRFxKqGgPP4eOuNJFGy+mfHFT0gffU1Ka0W2MBl0kw0U0Q+++wzdOvWLadzdOpkj0JMFIuRtKimroYAwAlqyVdCPqYcNYwUofDmsi644o5BGP3eLmw8ki40fO/ujj5lkwSzbfEpKvFAO4QtbKXUvd+1WncL3vgD0Fjf9rNs666ZMVMqydXVbV9DGLe8vw0bjggLtXK44rQSvHbdGTmdgyITtxeRS8bCu0i4srji1T+brOi1QVf9dUEzRSRXJYRCMQviLPkWFFyA/Es5ahR8QmHXwlJ8Of5xfBzphlve34HU0JEQ48Yc3zm85xJSVEat82BaZ5as7EMyvwMj+h3bozd8T9Ygvmoxmnbvkv1dmh4zpYYchK19DWGMnrMZexqjOTdjfP/2mD5cXlVtTbHo+KsF0Uuq4V72QbZRDgpX/2z6DImTFWwCjfai5D0kWfItKbi0krcuLHoiIRT+7OHXsPv+c/HsNz/i+e9+RFSG+wufojJn01HM2XQUhW4G797YG+d0KdTyLhSj5Dswqt8xHh9cg0YgeprMDDkWtZ6qFbZ+99kP+OfqutyvzwD/vrYnfnZ6u5zPpRQrj7+a4PYiNOFPOcV22PkZkiQr2AmCzF8UijkQY8mXEFwQDRvTDrW0urCwhaVpP9smQNEEXGu+kBQK/W4HJv+kG7bfey6eHVGByyvUF3ZrinK4dvZa/H76q4gvfB2u1bXG9zul3wGh/U6OQE8iSoWtYDSOG9/ZnLMS4nMxeGRwV+y471xTlBDLj78akYztCI2djPDwCQiNnYzgw6/JUyJs/gyJkRVsBl0RoeQ9pFjy7bDsa9cARTNw7N0C7/wXRPdJFQr9bgd+0a8DftGvA576ej+eWabcOjcwuu9kDMkXid/qXUVouvmPKOvdT/H51KDmOyCx31nVeipH2ApG45iz8QheWXkYe4+ewDXhjXiEJyZJDr3be3H3eV0wuneZqa6BRI6/Zrk4qYztIPIZaggpsoLdoIoIhSKQahDFZQjd/EfDhBkpwcS14mMAMF3AksRuAYpaoUSoaLUsimWwAYSFxkcGd8P4s8pRPXcLttXLs0L6uGhWIDsAlMVOIDrr//DU8Gl45Kfy07GrRbUAT1i/s6r1VEzYigfa4U/HTsWzz60Ci4TiuiEzS1tzIkvb9+7ukte6+7xOmDK0NR1vJATXKvPiCkhTHK3o4kTaM9QcAVmB8wUQGvco2fMywVBFhEJBtkW1sKISzgFD0dSQe9ClXKQEE9eO1XDtWE38ZETJRqlQIWZZTD1ezALXpciDpb88C4t3N+Dm97chHBdv46jwBt7UvgDQiWvC3q8/x0/3tOCy09qhTwc/RvYs1cWCbVUBPhPLWk8FhK16VxFGu27CipWJ34QU105cE+Y2voY+ZZN4V0aK3Az6dwpgxsjT2tLxkiB0G9bv5BgkLBpfZJdvVwy2R2+EbnoUvln/B0e4GQDAhJrhmz2VzssqoYoIhZIkxaLqKk/62RuniIgJLqmQPhlRMlAhVEhZDlmPT3b8w9CKEmy951ws2H4MNZuOYtEu/qKxlWw97++p2+ccCWHDkYMAgEL3brx5fS9c2F19TAoflhXgM9GjqJtBrjpNnXti1hXTsWdJLfyNh7CTx+VKSnEdFd6QlRSBtyAhIUK3Ef1OrsJlVRcn23y7YkTD8L05tU0JSULnZfVQRYRCIQUhFzEeSJ6MKOmoESqkLIeRUfcosrz53Q7c0Kc9bujTHq+uPIjJn+/L2meXo0z0HJnbm6IcRr29BT2K3WDAoKKdV5uiczaqyqxl7IoRqwb7GsK4bf4OrDkUbE0JXQUUVPHuK0dxTXJ+lwL885qevH2DGKFb736nQOGyrIuTjb5dIYjprzaCKiIUCkGkCi6uFR/DtWO14L7ETkZ2JAdLtBqhQtKy2H+YrGvzcdu5nXFdnw54cOEu/HdHQ9vv87xVONRcyGvlPsQUYp6XXyDd21ozYk9jBGfPXIuRPdvhHyNPk3bbEnmmJAafq0aL2BWdVg2C0Tje31KPBduO4+u9jWiKctIHtSJHcfU6gHm/6IMBnQOC+5EkdOvZ75QIsFKGCOZEfSIDFYHfg62+XR5I6q92gSoiFIpa9HKTSHURE1FE7OBvawXYXRtR8OxE1ZZoVX7TOlsWS/0uzBp9BlqiLGZ8dxDPLD+AENy8ldcPMYngY7mZkBZsP46K51aizOfE6WVeVJUHMHlIN5T6T043sqz7hAWfG07K+MKcqBcVYj0fzQRXXCZ7HDoajOKe/+5E7W6ZNVF4kFJcO100DFsvllZIiYsr0KnfKRFgpdx0Pcvnw7V+CbkxCTb+donrrzaA4ThOvgmEYjkikRgaGlrMboblKG+NEamr45+oDQmujIZR8PR4Qas49UXVgQzlsuSiYQj/301AY7Ybiux3kMt7jIYNsywu3t2AW97fDsQiWZXXlaRjFaJzwImHLuqGMWcUof1fb82tX5uQ1lRqTNASvvFFLnzjUDAax5wNR/DWhqP44XgI9SEZlS9lkJbuOXktXwnCEx6Hu6KPvJNYbJxT2w9cq2vhe/tJwe2hsZPThHc5fYDE52N7LNZfjaSkxA+PR/n6BlVEbA5VRNSRNdmkCj4lHeD57ytwNB/POk7rgYiEbDL5Au/E7w8ALc2Cx2QKD0rOzRaWIvSLR+FoOGxaytJMWqIsFmw/hkU7G/De5npoI66m8/PQarzaNEdwu9QzNeubMEwRERF05MIWlmLfva/g0aWH8PGOBjRF9HiTCXxcFBMLd+CeSg7eTt1U9WFN3qlByml5eRG4cAjHF3+s7FpqBNhoGJ4FM+FZPl/wtHLHIIp20HmZH6qIUHihiog6UoUOpdZJzScGA63ieUtzAwLTbgUTFlY6+AgPn4DopePk7ZzxHtl25fDNnqr9ZKaRQNYSZfHY53vw2roj6tvCwyPBWvwhuEhwu+gzNdEaaZQiImU5l8uthWOyslZphZMBuhd5cMmpxXj04u5pbneqyWGcM1IwbN+0F+HnJ6Wtksq9lpp2umtnw/vpLMFzKhqDSMas4o1qiYZRuvd7cHUH0OQtI7+9BqBWEaExIhSKGAJBomJoHqxmtr+t1SYIhTj2boHvlcmKlRBAoT9w6nsUEKhzDT7WUiDzux2Y/rMK/P7i7pj46W4s2H4ccQ3MVlJBzncua8G7a1ZgQKfsTEv5kLFGq/EjNWuVn4tgVHgjKnJ0tzunox+/HNARo3u3176GjNpxzsj0v9FwlhKi5FpqArnzISbBkisMbi9cg0YAAGIGuGvaGaqIUCgiyCksl4kdJoYklpwglJAUYlQoIbnkxVckUMtVBLUSyDKuV1o1BK+M6omWKIv3txzF3I31+Gb/Caj19pGTnSvGAt/9GMTZM9eCQcIC36nQjVmBbRgscm47ZKyRGj9e8g3CQUcROsVP4K7wN4L7JRU+vjgOJdXP23kduKZXmXYrHxpjpHLq2rCUN15M0bUUKly2r81BSB0ZinmQN6pQKAShVLCxxcSQJA8mCLmKJusNpCkrgtmrIiG41n4B55bvAADx3hcgdvYwxQULk9uVKIJaCGRi1/P36I1f9CvHL/qVJ7JtrTiI5775ES0Kl0lCjLLsXByAGAfsPxHFzDqnqCJiByNAY68LEfcWIxDOLjx5iCnEbwMjEWLc8HFRXBfhLyqYVOjUVj9PcueAcvzp0lNzvykdMTKdqimpW21emyMfVjkp4lBFhEIRQYlgY5eJIUk+TBCyBIfiMgQfmAnX1hWi7hSOvVvg/9fvwLScXKZ3r/8K7IKZCP3yiTTFQZa7hZgiOOsxREbcBubE0bb25CwkKVA8/W4HHrqoK+4+rzMWbD+GJXsa8Z8NR2W7bn3v7o4+ZZMUZ+eSWk0553M/grUrUOhhcHqZH16nA73a+7PSB5tNMBrHgu3H8e2+E3h/yzEEo3FwHBDnABbAQN/NmBsRV9TkKHRjQqsVVz/3uxic0ymAF686LffilAZgpOuSWW5SlqnNocKNl9bloJAzMlMoBCK6LB5oh8gVt4NpPELuxJADxE4QGsasSAoO/gC8901DU0GxuNIVDcM367E0JSSJo+UEfLMeQ/CR19vaKcfdQlQRbD4O37t/STsmeuEo0VuRulc1imdqxfYnLj0Vb66vw/RlB3C0JS56LSAhSCsNppYSvhvYhJB+LMxhxY9BAMDSfU3415q6tn2dTMLdyONk0BBhEWc5oFUJcDkZnFLsweujz0BlqU9Wm5JKxY76FuxpCGPZviYcDUYRZROrOa2nV4RcRU1qP7nVz70OYMqwHripX7n2sR86Y6TrUqxqCFBcJpjOW9fVcLNjBSVQ68ZriHJn8zhHq0MVEQpFDIllcVvESQhAYpCk1jErokKMNwD/n2vgKCwBJIIRXRuW8qZzbmt38/F0QV6Gu4USRc/RdAzuZR+ADbQTTCstJSTlqnj63Q7cPqATbh/QCcdaYnh40W58tO04YhrnZVS7mpIkzgFHBepoxGIcttaHMejV9W2/uRjA5wTcTgbBGIdwio7lAHRJcQzIV9TE9pNKDHCsoCMWj++LPuUFqtpIBEa6Lrm98N43TTBrFon1bwwhBzdevRVJ28c52gCqiFAoElhmWVxjiAuS1CNmRUKICRSWyDqNHKUhcx+pfqVU0XM0H0f48glwL5+nSiDTUvEs9bvw8jU92/4+1hLDk0v3Y+vRFgSjLDYfCULGookgalZT+JCTTSrGAU2x1v9koF91Dm0Qc2VjC0sx9f5f2GIcM3KMdlT2he/JGhxfvFDRtewsEOfkxqunIpkHcY52gCoiFIocUpfFIyG41i+xhlUrFwscYUGSesWsaCHEyBHSefcRcbcQUwQFYaD6XkQVT48PiEeBaFjVey/1u/DU5SeDnpOFE99ZfwS1e8xJfZlrNikrwDnd+GPPX+O5A6/ClbJSZlo8m54rAga6LjEen7Jr2VwgznU1VS9FMh/iHO0AVUQoFAXkbNUycGleCwscSatBusas5CjExKqGCLpFAYl4IsUrSAKKoBhcWRf19yJyPUckBN/cZ8B+/KomFtzU2JJjLTFM/WofvtrTgP2NUcRUxFQoJddsUiTicQAMw6BjwIX/GdgJ487q2BbvEYr+1PRv2M4rAlLYXSDWZDVVB0WS2DhHShpUEaFQ5JKjVcvQiVhLCxwhQZIkxqy04fYiNOFPWVmzAID1FyE04U+qBL8sRbCkAzz/fUV1HIjs6635At75L4CJhNK262HBLfW78MzPKtJ+a4mymL3uMGZ8dwg/NkWRgxcXL6PC/GlvAeFsUiTiBDCwawAvX326eIYrs79hm68ISGF3gZg4N95WiJ4zKG1QRYRCkUlOVi2DJ2I7WuBIneza2tCjN5p/+2aijsjmbwEI1xFRRIYQyXas0Nddzu0FXO4sJSSJEf3H73bgV+d2xq/O7QwAbcUUF+5owJ6GMHYfD6Epqn7dRG42KRJgABR6gDPbB9CvYwFxqYjlYMfxSAm2F4gJc+NNQvqcQUlgrdGMQjGRXKxaRk/EtrTAkTbZCbjZxQaOQGzgCN0ua4S7HGn9x+92tBVTTNISZfHmujrM+P4gjrXE4HI4EI2ziMQ5uB1AUGQZRSqblNR2rXExCYWDba0j0s7L4MFBXXHrOZ0sl06XD9L6k9Hkg0BMkhtvG6TNGRReqCJCocgkF6uW0ROxZhY4wtJNkjLZme7vrrOrjRUsuH63A7ef2wm3n9uJd3syU9e6w0FsPdqCxkgix5WTAZaWnIW64AKUs8JVyXPBwyQUCg6Al43gmozMXJzLjQu7FuL6vh0wuneZLZQNMRT1J8LGHE3IF4HYbBdAHkiZMyjCUEWEQpFJLlYtowU7LSxwpgvbQpg92eWBv3tO/YcQQTIzU1cmjr1/BpvxHhvcxbi9dDzC7MlAdRcD+FyA25FdR8QFgHEkVjKKvQ48eEFn3HpO5zbFgvcbQilCY+0foJ2K3P5E7JijAVQgNhGz5wyKKAzHcXonKKGYSCQSQ0NDi9nNsBzl5UUAgLqMQnaqJ8poGAVPjxeciPUQXnOa1E1oL4nw9QPX6lr43n5S8JjQ2Mm2mPTU9B/LCZLRsGzBUGhMEDs3/YZOItk3LPK8FPcDim2hfSGdkhI/PB7l6xt0RaSVYDCIRYsWYd26dVi3bh02b96MlpYWDBs2DC+99JKqc37zzTcYP3686D5vv/02zjmH/OwslASqrVrJpflZj6VlPGID7XRbms/FApfvwaViSLrZ1e2Fa9Vnpq8I5Iri/mPFlSIdLaX0G0pHqj/R50Wh5CdUEWnlhx9+wKRJk3Q5d4cOHXDxxRfzbisrMzYokqIBVlrmVdnWvAkuVeFGJOVG5176Phzh5ra/iV4RkEJB/6GCZDp58w0pQaQ/0edlMwhx0aSQD1VEWgkEArjhhhvQr18/9OvXDxs3bsQf/vAHTc592mmn4cknhV05KDaDbwAGEtbijPoPjubjRFqLrRCsnBORENxfzYXnyzlpaWrlKA1i/u4cw6QpIQDhKwIaQgXJdDT5hrQQ5iwiENp+zMkjZLloWqRfUvSHKiKtnHLKKXjiiSfa/t6+fbuJraFYFaEBOHrhKEtZi+2cbtKxd0uWi1zbNjlKg0AGHM4XABNq5j1E83dM4CROBcl0cv2GtIi3sVLMjp3HnLxChoum4+Bu8/slgWNovkIVEQpFK0QGYM+Xb4seSpy12K7pJpPviEcJSSJHaeDzd2fq9sJbO1vwGK3eManCJRUkM8jlG9Ii3sZqMTt2HXNIREchXNJFc+0X8Hz8qqn9ktQxNF+hiogBHDlyBH//+99x6NAh+P1+9OrVC5dddhlKS0vNbhpFQ8QGYKEq1UlItBbbMd2k2DtKRZbSkOHv7lpdK7q7Ju+YZOGSCpJZqP2GtIi3sWLMjh3HHNLQWwiXGjudm781t1+SPIbmKVQRMYCdO3fi+eefT/tt6tSpeOihh3DLLbeY1CqK1kgNwKzHBwePQkK0tdhKgfkykLsqoUZpMGJFgHThkgqSPKj4hrSIt7FszI7NxhyiMEAIz9Xgone/JH0MzUeoIqIjRUVFuPXWWzF8+HBUVFTA7/fjhx9+wJtvvomamhpMnToVPp8PN954o25t8HhcbbmuKcpR8uxiFZWIimz3XHkLYp/XAI31J38sLoP/vmkIdO2gvpE6wYVDiK9aDO7IATDlXeEcMBSMx2d2s3JC6h0BAIrL0G7oiLR7ldcPisA+MB3h5yfp9o6j4XrERLYXhuvhNv17LwK6XmtyG/TDiPFUqp8WVlTCJdEOLc5BEcaK82rsm68RFRHCS/d+D9egETldgxs6AqH/zkwfA5MUl8F//iWIrf9K8PhA925gdnyt27yjxxhqxb5AErZQRJ5++mnU1oq7RfAxa9YsdOrUSYcWJejbty/69u2b9dvUqVPRu3dvTJ06FdOnT8e1114Lj8ejWzsoxuAcMBTR4jLBAdg14ia4RtyUEO7ryBbu2V0bswTqaHEZvPdNg6Oyr8iRZCP6jgCgqBTe+6apfieOyr7wPVmj2ztmyrvmtJ1iDaTGEueAoVk/ZxoOHFUXAgrPQbEucgxHXN0B8XNIbJcD4/HBe980XoOM975pYLqdhljNP/j7ZaAYsbn/AE6cVJa0nnfoGEoetlBEDh8+jF27dik+LhqVtI3qxrhx4/DCCy/g2LFjWLNmDc4//3xdrkMrq6tDbcVUx81/5Pe/vfmPaGpo7W+nDQZOa93YEAUiJ8jK3hENo+DZidnL1431aHl2ojV9aFOCM3HBNXAv+yC9sKTHh+glYxG9pBpNbi/Q+t5VV87NfMfS6zDy6DEQBSLuX8d6DGxrO1HYIEON0VWUpceSk31KyO8/MuJ2eBa+IuscqrDBe1UKidW0+d5/mCfuw+Utg5hJpMlbhpgW91XYA5g4K8tFs8ntBRqi/H070A4MGwfTrPO8o+EYSmJfMJO8rqw+ffp0TJ8+3exmKMLhcKCiogLHjh3DoUOHzG4ORSOU+siTmL3Dbj60vM840A7hyycADKwlQFktILy1Xov7yzlp8VFm93ErIHssEcvWt/AVBH/zMlxbV2ges0Pi2JWXKIj7MDSznUisD1/fRjwK39xnePd3NB2D56OZ4IrLcu/DVhtD8wBbKCJW5dixxEdQUFBgcksomiIWbJlqQSzuAM/Hr2QXOTQ5e4dlg1z5EJqkm4/DvXyets/YIOuwVQLCc67XQpEVuC1pONi6QnvDAYmZh/JwdQZQaDgiSQjP6NtukdTnAOD5Zn7b/3NVeK0yhuYLVBExic2bN2P37t1gGAb9+vUzuzkUA+CzIArua+LKg50K0xm1usMndLOBdghN+JM+1mHSMwtpVK+FIo2k4aBur+bXJG3VNKfVGYsrMEoNR6QK4UrmFU0UXtLH0DzCYXYDrM7atWtxxRVX4Iorrsja9tprr7WteqSyatUq3H///QCAkSNHomPHjrq3k2IyAhZEMcxaeUgu3/NBdKphHgxZ3YmG4fvX77JXtpqPw/ev3wHRcO7XsBia1muhiCIlwHm+fh+OvVs0vSZRq6YSqzNi359j7xYUTJsA35yn4P10FnxvP4mCp8dr/rz0RJXhqFUIj146LiGMm7F6teozuGtnJ+ovRcOi8w4fSYWXYn3oikgK99xzD+rq6gAA9fWJjA4rV67EmDFj2va5++67MWzYsLa/W1paBAPln3vuOTz11FM488wz0b17d3Achx9++AFbtmwBx3E499xz8fjjj+t3QxRikCuYpdI2gRhtsSNl+V6D+zZidce15gs4WviDFR0tJ+Ba8wVi5+WWEtNq6FmvhZKOmN8/ADChZs3dpRR9VzqPX6pXZ4x2L9PpORga96EBYqtXfPOOGNSQYQ+oIpLCpk2bsH///rTfGhsbsWbNmra/kwqKHO666y6sWLEC27dvx+7duxEKhVBSUoIhQ4bgqquuwrXXXgun06lZ+ynkonTATE4gZgWEmr18r9V9y56kcxASnFu+ldyeb4qIHAWDRCHJkiQNB69MhiPczLuL1u5Scr8rFuM82gAAIABJREFUI8YvtaszRrqX6focBAxHnC+A0LhHTXe5SkOG8pc67zAn6uFZPl/gZNSQYReoIpKCmlokgwYNwpYt/Mu4v/rVr/CrX/0q12ZRbICSAbNt5QEwNyBUTx9aMcFfarJ6cGYiC5AcpUHG6o6YkIDy8zS/9XxAykrPBtrRDDUawvbojeiQ6+CtfUNwH02tx3JWTQ1acVC76mmYe5kBz4Ht0Ruhmx6Fb9b/tSmjTKgZvtlTicpiJlf5a5t3omG41i+xzGoPRR1UEaFQDEDUghhoh8iVt4NpOJImWLtW1xoXEGqg+5eUdVBqsgpMvxVMqJn3WD5EV3ckhASu37uSxQjjZ14At0il4PiZF4geb0uErLQeHyKt9VqoEqItXHl38e0aW4+lVk2NWnFQu+rJFXcQPa9Wz8uQ5xANw/fm1KwVMdKy0ylW/khxE6boClVEKBQjkBhQ+YRozS12AsqGoRmfZFgHJe87JGOy5blXvsleSkiIr1oM1yBxt6pY/2HgPpoJhidOhPMXIdZ/mOjxdsVs9758w5RYAZFVU8NWHNSuegbagfUX8cZ3afm8pLKWafEcSMtiJoSa1Ss6jtgfqohQKAahdEDVMtBacBVi3KPwvzYlS4h2NB+H/1+/Q/Nv3zQ8sFSNJTJ1slXijy0lBHB1B6Qv7vai5ZdPCCpzVgh41Q2aItM4CLMeG5kGXNWqZ/NxcP4isIF26d+ths/LsXcL3EvfF91Hi+dAVBYzEVQry3QcsTVUEaFQjETBgCo2aHMMA7akXN41RVYh/P9+DEw4yHsY03ICrrVfIDZQu0BrORNm9OJq0fgC0XMr9MeWEgKY8q7iF01RDCJX3A4wyHKx0wpdA16tpuBQeCHJemz4Co3A2Cpm/GBaTiBc/RDgdGv/vJJjkUACAUC752CZ2k+EKcsUMqCKCIVCKm5vYsVi5kQwHJe2ieE4+N6cKsv3V3QiFlBCkjg3f5ubIqLGL1tosvIGRCd1rqyLYhcFKWHJOWCo4PUMzWimY8CrWZnZKDpBivVYC6FTAwVZ0vjRcATRS8cpOqccpFK2c76AZsK3lVL4kqQsU8iAKiIUCsE4jtdlKSFt22T6/pq1LJ+LXzbvZNXrPBT89Q7Rydb91VzRNikNhgwIBaobXINANx9wo2spUPKKXIROrRRks1YLpMbdyODR2in6VltpIEVZphABVUQoFFKJhOCUqBwrR8nIZaKN9xbJ+CSVgjcjZgJQ6JfNM1lJTbZ6BENy4UQV4NT7NDo4VBcf8EgIngUvWyLIlRfqTmYN1AidGirIZq0WSI5F5T00vZ6hKw3026NoCFVEKBQC4bMG8iFHyZBKHYx4DI5QU/Y2fxFiZw+T3b5Ua6X7y7lZSkgSSb9skUlOarLVOhiS3bUR4ecnwdd4spApW1iKWN/B/OdJ3qPGq1CyFSyZAoLc/kVKkGsm1J3M3miq6Ju0WkBaFjOtoN8eRWuoIkKhkIaANTAT2ZOZ1EQMKMv4JGWt/M3LcH/5tmiThPyyZU1yYpOtlkJHNIzw85OAFCUESNyne+0Xoodq7e4hR6iRLSDI7F8AQUGuqVB3Mtuj9QqgKXEJVnOXkgP99ig6QBURCoUwpIIcAeWTmdREHHzkddmTtJS10vPpLDgiIdH28Aq4Gk1yWgkdrg1Ls5SQJEyoWTB4Xq+MQJLKpMxnJ6d/Jc9NUpBrEqvUTKCoR5e4DhPiEuwWmE2/PYoeUEWEQiEMKWtftN/FCI95WP5kluGuE72Yp6o1xyX+adA+h0QBL87j4xVwtXbHyHVClLrP2NnD4Nr4tWHWTjGhxrW6Vvazk2NNJtlqa5WaCbpglG++yTEAVsoCJYmNArPz+tuj6AZVRCgUwpCy9sUVCAVy3HWU+vxKtY8t7wHsWC24PXLJWN72kzbJSd5n5VkIXn2X4e4efEKNkmcndV+RC69BZOSviVRCAAvVTNAYo3zziYgBINWtKRJCbPnX4I4cgMtbZunVDTXk67dH0ReqiFAohKGZNVCOqxPku/TIbV9k+AS41i8RDI6PXlLN21zSJrlY1RCguIzXPavtPRBi7VTy7CTfH8FKCGAza7lcjPLNJygGgDS3pqSCFm19Nj7kX5C2ad8ezdJlaxxmN4BCoWTQag1kC0vTflZqDZTj6iRnH8XtKygW3i4UAI+TkxwfpgiYbi+8901LKCMZbSHNbUnRs9Oof5mG1duvAlXfKcHXkY3bi1jfweBKO4Op/zFx/WjY2DYAkgoaouGEsLzqM7hrZ8O1utacduqNCd+eY+8WFEybAN+cp+D9dBZ8bz+JgqfHw7F3i+bXopgDXRGhUAhEC2ugFq5OQvtItU9V+wl0x3BU9oXvyRocX7yQCKusIAqfHWnWZqVYvf1KMcptkTT3SCLcxCCtoLm/nAv38nmmt9MINPv25KxyELRCR9EPqohQKKSSo9uPFq5OovtItU9oew51QsyA8fiIcL+SQvGzI8StTDVWb78CNHNblBD+iHKPJEgIlVLAPF++DSYjU6CtheUcvz1JBbO1nzozkoGknYNm6bINVBGhUGyKXH9eI31+c64TIod89ifOI+E8n9DCN1/Ot0dS/A1JqWKlFLBMJSQJFZZ5kFAwQzc9Ct+bU2WlGKdZuuwBjRGhUOyKHH9eI31+5fhZ5wj1J1aJFf3brdhmteT6ncr99giKvyHJTUw0BsvjEz2WCsvpSCmYvlnyiq0CNEuXXaArIhSKjZHjrmOUO5TuFk6CXDmsBCl++EqwYptzJZfvVMm3R4p7JFFuYiIxWLE+g+H57iPBQ6mwnI5kHSqeIrF82DZDXh5CFREKxe7IcdcxwKVHbwsnSa4clsGKypsV26wVcr/TDPdEpm6f6O5Z3x4BLn4kuYkBJxW00r3fg6s7gCZvGWK9zkPBX34lfEygHRWWM9BCMbNzhrx8hCoiFArFEPS2cJLkymEVrKi8WbHNRsK7WuQNiB5DpNWewCx6cHvhGjQCABCrOwHX6lo4mo8L7h696FoqLGcQ63UeOIYBw3FZ2zgAjMix0X4XI141JL/i/vIAqohQKHaHkOBtvS2cRLlyWAQrKm9WbLNhCK0WhZsFhT+SXVxIcRMTQrKviUnVekLImM+Ha+sK3n4IJB4X6w3wumexhaUIj3mYmPugaAdVRCgUG0OUL71SC6fCyZQ0Vw5N0FmgsKLyZsU2G4XYahHDceB8ATChk0KeJVxcCHATE4LEvmjImJ/DuCSlvMXOHgZXRtpeS/RTimqoIkKh2BUCfenlWjhVTaYkunLkgBEChRWVNyu22SikhLzI4NHgynsQubpgRYjriwaM+bmOS1LKGVt5FoJX30XsKhhFe5xTpkyZYnYjKPoRj7MIh2NmN8NyBAKJQS8YjJjcEvW41n0J96pFvNuYSAhsx1PBdq40uFUAnC6wnSvBVvZPXN+ZYQ+JhuGfcX/WZMpEQnBuWo7oRaOyj2mFK+mA6EWjwHY8FfGupyN2/pUIX/cAuNJOqppqWj/I4RkowulCvLI/nJuWp9VCSAoWap+brpjUZiuMCY6GI3BtWCK4PXbBVYidc6nwt5ckEoJr7WI4Ny2Do+EI2PZdtelvNiCtH+jVF1U+f8kxv31XsF17qmsToMm4xLbvCtd3H/PWXmELSxG+7gHA7RWfIwjBCmOCkfh8bjidyquCkPl2KRRKzljVlz7nYGSCXTnkYmRANul++HxYsc1GYFThQ8pJtO6Lsp8/j3uUZAX4eS+A7Vih+j1qMi7ZbOWakjtUEaFQbAqJ/stysKoCpSWGPwMrKm9WbLPe5CrkEejOaQm06osyn7+QshK9cJTo6R2RUE7vUatxiRoSKKlQRYRCsSnE+S/LxKoKlJbQZ0BRi1GFDynaI+v5Vw0RVFbcyz4AG2gnmlI4l/eo6bhEDQmUVpQ7c1EoFGvQah1lC0vTfiZ9CTypQPFBsgKlJbGqIWAD7Xi35cszoORAq5AXvXRcQtjTKKNRPqxGmkYkBOeGpaK7MPU/iisrzccRvehacB6f5HnUoGhsjoTgWvUZ3LWz4VpdC0TDqq5JsT90RYRCsTGWXAKnPsRwHNwNho1n/c76i/LmGVCMh67EmQOfqxUfXFkXWbVLwtfcA1/NM6LnUYXMsZnGGVGUQBURCsXuWHAJ3JIKlFa0+okzLSeytzmcYDtXGN4kSn5gVXdOTTG6GKBAXEgmrLcATN0+MMEG0f2SbWYXvir9HlXcq+TYTOOMKAqhigiFQklHzUSsx+RtQQVKC6RcL6ifPkU38nw10gxLvtj3noRjGDjCQXhr32j7m686eZuSIeM95nSvImMzjTOiKIUqIhQKpQ01k5Nuk7fRlklCoH76FDPJ29VIkyz5Ut8z53KDiUXTj+G4LGWkTcngOLhWfQbm2EFERtwGMADTcCT9Pep4r3T8oiiFKiIUCiWBmslJpwktn32MqZ8+xXTycDXSLEu+1PecqYS0/c5xiFx4DbiisjYlw3FwNwqmTZAcN/W8V664g/h2On5RMqBZsygUCgB5k5MWx0giodzYPfsKzRpGIYY8ynxkliVf9HuXyH7FFZWdzIwGyB43Nb/X1n7iee9ZeD/8h+BudPyi8EFXRCgUCgB1k5Mek3fe+xjb0U8/T93srEy+rUoauhKZ8T2Exj0K3+ypvAUKvYtmyWqTknFTy3uVm/GLDbSz7vhF0RWqiFAoFADqJic9Jm/qY2wvP/18E2htgVyXSxIVTJVtMipjmOD3cNOjcDTUpX/vANzL58lqk5JxU7N7lZnxCwAiV95Ov3cKL1QRoVAoAMQnJ84XQKzXeYqOUTt50xiJVvT20zdCiKSpPC2JHOs6274bcQpmrpmgdF+JFPse3pzK+z3IbZOicVPoXr0BhG56VPa9ysn4lYRpOCJrP0r+4ZwyZcoUsxtB0Y94nEU4HDO7GZYjEEgMxMFgxOSWGIjThXhlfzg3LQcTCaVtYmJRuJfPA1g2MaE7XaLHJCdKrrST4maw7bvC9d3HWW1Injd83QMnr68zpvaDSAiutYvh3LQMjoYjYNt31ey+HXu3wP+PB+BetQiunWvg2rAEru8+RryyP7gS8WBTJe12bVgC1841vLsxkRDYjqeC7VyZ2/UMwvZjQsp7c+5cC+fhPYK7xjtVwLtgZpYQykRCcG5ajuhFowz7RtuIhuGfcX9ObeJKOiB60SiwHU9FvOvpiJ1/JcLXPZA2juXSD1zrvoR71SLebULfg5w2AcrHTa6kA+KnnJkwRrQGxDPxKJxbvpM9Djg3fi34fWcSO/9Ky3zrcrH9mKAQn88Np1N56DldEaFQKG2wPXoj+JuXUfD0BDjCzWnbmEgI3kWz4F72AUIT/tRmYdTcjUgryySJbiMy0dWdScdVCrn+4knywc3OCih+b8EG4uK4NIst03ElUrXbqZw2KR03o2H4Zk8FE0of55WMA3JXp2mQOkUMqohQKJQ0XFtXZCkhqTiaj2dPVBpP3rkqN5aOS9DZnUm3ZAAK/MWTWMnNjguHEF+1GO4fdllOsRVF4XtjC0vBFRSL7mOGgmmF2DK93U6VjJtajAOxqiFgvQHR+YLzBWiQOkUUqohQKJQ05EzYhlg91So3Fo9L0DtrmF4CmxJ/ccBaVlLH3i0IvfEHoLEeyZ5jGcVWAiXvLXnPjqP7RfdjTtQn0sUa+J1ZIbbMkIB4meOmJuOA24vQhMfhf3kif6V3bwDBSbMACcWVkt/QOiIUCiUNuRO2rhbGHOoX6FLbxED0tuzqJbApaZelUhG3KrZorE/72S51baTeW7TfxQgPn4DQ2MkIPvwa2B69RWtfAIBn+XwUPHUL3J+9YVgNEiPr73BhleNTq/tUZjs5bwCxvoMTY5NB/UmrcYCtPAstv54OzhdI/72wFKHbn6RKCEUSuiJCoVDSELPapeL4cSdcq2s1d1HJ1a3KCi4aYvErelt29bLKSrUrswq0JZQQ2L+ujdR7i1cNyb4/gXiEVBzNx+Fd9Frb37qvIBlUf4fdtRHh5yfBl6KYKrm3VPcpx651cK35Ao5wMzzffgR8+5FhK21ajgNsxVlo/t1/bJFunGI8NGuWzaFZs9SR19kwkpmwNi4DE83OwNK22+E9yrItyckCpUHmG0fDEbg2LBHcriR7ix79QCpjle5Zw3TIdAZIZ+0J3ToVbM8BiWdvdEalHJDKDBTvejrYyv4Gtkhb1Pa3ZDYntDTBuW+r5HWMyKglN8OUaqJhOP92d9bqmOJ7c7rAtu8K7/vPwdHSmNu51KL1OOB0ge1cCbayv+W+cbXktZzAg9qsWVQRsTlUEVFHvg8wyQmdc3rg2LcFTFy4D8mZOOWmi1WT3jITLQX5rH6Qa0pdOYqW26uLopCKLgKbTgqO2Wip2BJJLu/N6YLjwHbZKVwNSdmso0DsWvclXCs/5d2m9N60GOtUkTKGMeAQvvousF1O00dxszn5LidkQtP3UigUbXF7Eb1sHKKXVMO1YSmcG5bCvf4r3l1FXVQUBI9rFkCpg4uGbJcxEbcruW4+hlRWFwpqzSHtsZ0qwicxquK2meTy3pS6ChLhGqkSLd0+zXAhFR3DLOxeSLE2VBGhUCjitAqsTP2PgIAiAghPnEp87DULoNRaIJapTEkpK4qED70rq/OgSdpjE9qtK62KbUFr1qwklgq4l6NcqnxvcmPKkpCQvUoSgeelZfyW4Vm+LJ5NkGJfqCJCoVBkITUxCgWvKxG+NbU+aygQy1KmqoZITvREpxilgoogbI/e8D1Zg/iqxWjaba06IrrX1JERuJ56XdJXkMSeV6xqCFBclhUjktxHyb0ZvdJm96QLFOtC0/dSKBRZSKXsdK//Cr63n0TB0+Ph2Lul7XdFwrdAekuzrc9ylCm5yopRKUaVYvW0x3rDeHxwDRqB6KXjEgKbBZQQKeVSq1SxyRXI0NjJCA+fgPDlE8AG2qXvY4UVJKnnBcB737SEMpKCqnszeKyzRDZBSl5CV0QoFIo8ZFo+My3oSi1/JMYZyFGmZE30BqUYVUwkBKeEokEFFethqBU8YwUyGVvG1O0F09wILlACx9H9YDtXEKuMyHlejuHXwvdkDY4vXpjz+GTkWEf0aiwlr6GKCIVCkU3qxCk7eF2N8E1YnIEcZUpqxSA50ZOmaPG5ovBBBRXrYaoV3O0F274bfB+9pJ9bmMbIfV6Mx6ebAqcX+ZB0gWJNqGsWhUJRRuvEyXY5TXQ3Z0qV4EzXjdQqzZZAhhuFIrer1mdoupuPgCtKJlRQsSamWsENcgvThEiiUrrjx52iu1laGSfU7ZVCoSsiFApFFVKTsnv9V3Bt+//t3XlgE2X6B/Bv0qRJ2tKTUo4qLdqWU8utgigiy6H8qILLLreCiAgeSNH1Qlzk7LIrKyi6LJbLRTnWVRAWrAis5ShQ2lKLQGkBFWjpRZsmTZr8/igNPXJM7qT5fv6CzGTmycwknWfe933ek9Dc+zB0sT2gNTZDs7eoUUFcfAWafo9BpCyHPiAY+sg7GrdkeGq3KzPMdUWp58nxk3nufAruLYOjhbYItoRk3NNaY4kAJiJEZCMhZTtF6ir4H9sFHNvl0V0yzNFdzEXAB/MEJRfe9ofeUlcUTfcHof79fI+NnyxwY3LsFYOjrWgR9PhkvGnJ4bjekPyc0bxks4d1eyViInJLfn4+Dh48iEOHDuHs2bMoLS2FXC7H3XffjREjRmD8+PHw9/e3edtr1qzBkSNHUFZWhsjISAwaNAgvvPAC2rRp4+BPQuQiVpTtBOqegirWvY6aAUnNWxNsZcfke0K2rT18AJrP/wqxurrRIrMlbb3oD72lVq1aD06iSBh3JcfeMDjaUougpvuDqO02wKMfJgDGW3X0IhFEer3h/zp/OTSDxkEzaKxHfxbyPSK9vsGV6sMGDRqEa9euQSaToXv37mjbti2Ki4uRmZkJtVqNrl27Yv369QgNDbW8sQaOHTuGZ599FiqVCt26dUPHjh2Rl5eH/Px8hIeHY8uWLYiNjXXSpwJqarQoL6+2vCI1EhnZCgBQVHTTzZF4AY0asi+Wmxy4boq9LSTOnB9BaHcN1bjXvSbpMEqjriu3bKLrji/PHdIUfxOs5AXXljRtM2T7Uk0uVw+dAs0jExq95nHXgZnjbIwuMBSqKX/2upZpT+Rx14KbhYQo4O9vffsGB6vfEhsbi/fffx/p6enYsmULVq5ciQ0bNmD37t2Ii4tDbm4ulixZYtU2lUol5s6dC5VKhbfffhs7duzAX//6V3z77bd45plnUFJSgldffRXMBcmrSWV1T86tZNegVWcOhBXYXQPwkO4l9uAAVnIWL7i2PKrV5taAeWnaZkgy0wT/hgkZ59WQuKrM84oFkE9j16xbUlONPxWJjo7Gu+++iwkTJuDbb7/Fn//8Z8FdtHbs2IGioiL0798fEydObLRs3rx52L9/P86cOYODBw/ioYcesvsz2EOn00GpvAmVSgmtVgPAt5Oj4mI/AIBWW+vmSLxEVCeIf/8noNb88RLpaiGtKEbQlbMIPn/C5kGrzhwIa80fdk/oXmIvbxvXQt7D068tTylpa0/rri0PQzypWAARExEBunbtCgBQq9UoKysTPK5j//79AIBRo0Y1W+bn54eRI0fi448/xv79+92aiOh0OpSWFkGjUbktBk+j1ercHYJ3EYmgi4oFamvM57B6HWoj2kEdFQNl21i0PbzN+j+kTp58T+h7W0IVHQMvGtdCXsYZ15ajxoZ5QqU7C627lrqw2fowxOtbc6nFYCIiQGFhIQBAKpVaNUbkp59+AgD06NHD6PL613Nzc+2M0D5K5U1oNCqIxX4IDg6Hv78cYrFv99qTSOo+PxMSK+l0gKoSInU1RNU36/7fcLFejBp/OcqlMlQDqLi7N+RW/CF1xeR7Qt7rSd1L7OLMwf7kWDxXABw/NszprTYWzpu9rbtCqhca0xJac6llYCIiwCeffAIAGDx4sOBuWZWVlSgrKwMAdOjQweg67du3BwBcuXLFAVEa5+8vMQyoMqWyshgikQhhYa2hUAQ4LRZvVJ+QkFBiwD8UQCigbwu98iagqYG+ogTQ6SAWAXIAeohQqmiFytgeaPvQMIj85Ra3rK9RQbVkAWDpD25wOEIFbtPofh4aBtW3nwAVJc0XyhSQjJ8LSd9HEWjj9j2F7mIu1H9Pbvw5g8Mhm7MC4tiu7gvMw1n6PXUGnqs6pn4DxJWlCNi0APKl22383rcC2o+26h1CrgMh502jLoHWzDaC1CWQmt1XK+heSmm+H3Ps/I2kxtzxm9CS8C7Lgh07dmD37t1QKBR45ZVXBL+vqqrK8G+FQmF0nYCAgGbruoNarYZeD8hk/FEiBxKJIAoMhii0NURRdwJ+foZFMgDwl6M2rqfgP4a1p36w/If21h95e/7AivzlkM1ZAQSHN9/2vA8hHfC41/8B19eojN+4VJRA/fdk6GvYTdNTePu50qtV0B7ZC80366E9uhe6yrJG/7cmfrO/ARUldcs9hNDzJopsb3Y79cubHseGx00c2xXypdshffZdSJJmQPrsu5D9bQ/8kp4FZE3uPxzwG0nkSC2iRWT58uVIS0uz+n2pqamIiooyuTw9PR3vvPMORCIRFi5ciE6dOtkTplsIKd+r0dQ9j9Hp6saLELtmOZyfPxAVW9dtS6uB3k8CVJRBIxJe+lBacBHmOkvUT75XKZUB9pZTDLoDmJeKsMsnoC/6FZWycGi7DXDMtj2AJDMNcjM3dGU/7OWYkSbcVarTm8+VkPkt1FZ0q/I/fRzm+iRUFlyEppNzz4/Q60DwebujNwLMDJgvvaM3xCczmh1Ho8et0wNA/W1KNYD+TwG9/q9Zt7OW8jvmbizf25it5XtbRCJy/fp1XLx40er3aTQak8syMjIwa9YsaDQavPXWWxg92rpm28DAQMO/q6ur0apV86Y7pVLZbF2iFkssBgKCoQcgAoCbZVa93eWT70llkPQfBgDQtrA/NF4x6zUB8OJzZWIQtqhJuXqhg7KhUUNy+oDZXXrSuAfB583SgHnArsHsLERBnq5FJCIpKSlISUlx2PZOnjyJGTNmQKlUIjk5GZMmTbJ6G0FBQQgJCUF5eTl++eUXdO7cudk6v/1W90NkagwJEd3mKaU2WwKPmj+BzPLWc2VNGWwhg7IlZ/4Hsdp0N2a9PNCjfgOsOW/mBsxLMtOcVqqcyBNwjEgTmZmZmD59OqqqqvDyyy9j+vTpNm+rvuxvdna20eVZWVmN1iMiM7xggjRvUZ/UGcOkzrN467mytqXG3pYfzT0Pe9RvgNXn7VbLheaRCXWJxa3P4rUtYkQCMRFpICsrC9OmTUNVVRXmzJmD559/3q7tDRkyBADw9ddfN1tWW1uL3bt3AwCGDh1q136IfEX9k0PVuNehHjoFqnGvQzl/g01lO30akzrv4aXnytqWGntbfnSxxsvku42Dzpu3togRCdUiumY5QnZ2Np555hlUVlZi1qxZmD17tqD3ZWVlYf78+QCAPXv2NFr25JNPYu3atTh69Cg2b96MCRMmGJalpKTg0qVL6Nq1KwYNGuS4D0LkJGfP5iEj4yjy8n5CXl4ufvvtVwDAP/6xAZ07u7BVj32eHcLTZ72m27zxXFkzv4WQlh1v7JrpiPPmjZ+byBpMRG6ZNm0abt68ieDgYPz22294/fXXja43f/58hIffLutZXV1tcqB8YGAgVq5ciWeffRbvvfcetm/fjpiYGOTl5eHChQsICwvDX/7yF4hEIqd8JiJH+uyzT3HokOeUx2yEk73Zhkmd9zB1rjz12jcxCLtp1SzBLQSeMAu6Lez9jnnr5yYSiInILeXl5QCAiooK7Ny50+R6s2fPbpSIWNKvXz/s3LkTq1evxpEjR/Dzzz+jdevWGDduHGbPno02bdrYHTuRK3Tr1gOdOt2NhIQu6Ny5C2bNmo6rV93UP7nBzRf0gDT9K4irblfhsmemZWe4HePUAAAgAElEQVTE6FE3iK7G4+A0jp5l3GEanPOa4c8AekBUUVx3/uP7QPJzhk0tBN7YMgTA7u+A135uIgFEen2TWnrUogiZR+Tq1UIAQNu2HV0RklfgPCKWjR07Clev/mZz1yxbrztjN1/G6ILCLJe2tMDWOvEee4PoYk49Di5OcDxuzgCNGgHLJ5vssmPvtW8rl137bkpwrb0O+FvQcnncb4Kb+fQ8IuSdlJpa7D5fhkvlanQMkWHk3WFQSD2zfsLAgX0AAIcPZ2D37q+xffsXKCy8iICAQNx//wDMnDkHYWFhUKvV2LTpM+zbtxfXr19FaGgYhg0biWnTnoNE0vjrVlpain379uDIkR9x+XIhbtwohlQqRceOsRg2bCSSksbAr8Fs5PVyc3OwZctG5ORkobS0BHK5HKGhYejSpRtGjUpC7959Deuq1Wp88cXn+P77fbh8+RK0Wi2Cg4PRtm179O7dF1OmTINM5kVP1UzMTWCM20pbmohRcN3/lsKJx4E3d+bL41p17Tvyht5F177XnH+hx4OthuTDmIiQW5y6WoWJO8+hSKk1vBYZcBmbnohDz7aeO8HjmjWr8OWXnyMxsRf6978fOTlZ2LXrP8jL+wkffbQOr746GwUFBUhM7IXo6GhkZp7Exo3rUVZWhtdee7PRto4dS8eqVX9BmzZRiI6+A127dkdJyQ2cOZON3NwcZGQcxeLFKY3GEB0/fgTJyS9Dq9UiPj4BPXrcC61Wi6Ki6zhw4DsEBgYaEhGdTof581/GiRPHERQUhMTEXggMDEJpaQkuXSrEhg3/xJgxv/eqRMSauQkA95S2dNgNopdz2nFgogfAMWVdHX1Db/M5t+ZG3IvOv5DjoYvo4B1JFZGTMBEhl6vW6JolIQBQpNRi4s5zyJh+j8e2jOzZswvr129BTEwsgLoxRTNnPo0LF85h5synERTUCl9++R8EBQUBAM6dO4vp0yfjm2/+jSlTnkHbtrdLLSYkdMHatZ+hW7fujfZRXFyM5OQXcejQD0hL24chQ35nWLZx42fQarVYsGARhg4d3uh95eVlhkkyASArKxMnThxHfHxnrF79KRQKhWGZXq9HdvZpBAYGOe7guIC1iYU7Sluy7n8dZx0HJnp17C7r6oQbelvOubXJkEvPv7EECa0Ev93i8Si6DPmutV6RVBE5i2fe7VGLtvt8abMkpF6RUovd54U/8Xa1adOeMyQhABAcHIykpDEAgIKCi5g//01DEgIAcXEJuP/+AdDr9Th16kSjbcXExDZLQgCgdevWmDXrRQDA999/12hZSUkJAOC++5qXbAwJCUXnzl2arXvvvT0bJSEAIBKJcM89iZDL5ZY/tAexJrFwV2lL1v2vI/g41KggOfUdpGmbIclMAzRqs+9jolfH3okOhdzQm2TinFl97VtIhoxdC646/+LLZxGwYgrkXyyDbF8q5FuXImD5ZOgu5grehqXjIVJW2H4OiFoItoiQyxWWm7/RsLTcnfr3f6DZax063AEAiIpq1yhJqRcdfSeAupaOprRaLU6ezEBOThZKSm6gpqYGer0eSmUVAODy5UuN1u/atRsKCvKxcOGbmDz5GXTr1sPoOBIASEjoDD8/P3zzzVe444478fDDjyA8PMK6D+xhhM5N4M7Slqz7X0fIcbClaxATvVvsLOtq6w29uXNm7bVvS+uGS86/mQRJ/fdkyJduF7QZS8dDHxBi9v2+klSTb2MiQi7XMcT8H0hLy93JWLnl+tYGU6WY65fX1DROsC5dKsQbb8xDQYHxeWgAGBKSes899wLOn/8ZR478iCNHfoRcLkfnzl3Rq1cfDBs2Eh06RBvW7dAhGnPmvILVqz/AypXLsHLlMrRv3wE9etyDgQMfwqBBg00mMR7L1M1XYCg0948GRHD/YE/W/a9j6TgANnUNYqJ3mz1lXfXBrc0vN3ZDL6A7lzXXvi3JkE3n38rB4GbHolWUoPbUD0Cn5g+lmpHKUDNkMmRffYCGs4XpRSLUDJsGSMzfgvlMUk0+jYkIudzIu8MQGXDZaPesyAAJRt5tvLuBJxCLTfdmtHZiyrfffg0FBRcxcOAgjB8/GTExsQgMDIKfnx8uXSrE+PFj0LS6dkREa/zjHxtx6tQJHD9+FNnZp5Gbm4PMzJNITV2H5OQ38Pjjow3rjx37Bwwe/CgOHTqArKzTyMrKxN6932Lv3m8RFxePDz/8xOvGiXhDTX2bY2xh1XPMHQdJZpptff2Z6DVmw4R54stn4b9nncnlpm7ohbZgCL32bWrdsPL8i/OzId/wNsRqZbN1TbW6WUqQ9EW/Ap3MrHDreyzOPw1pxh40/csg0uvhv3cdlK98yqSafB4TEXI5hVSMTU/EGamaJcGmJ+I8dqC6IxUWFuDChfMICwvH+++vaNYy8csvl02+VywWo3fvvobqWNXV1di+fSs+/vhDrFy5HIMHD2mUXEREtEZS0lgkJY0FAJw79zMWLXoH5879jE2bUvHccy844RM6mTfMCG5ljA6rYORpyYyJ42BPX39vSEY9Vn2rRoMJQBvSBYaaTOgEnzOB176trVtCz7+4IBuKf8xrNJM7YLnVzeLYjsj2JpcJnedIXFkKyc8ZTKrJ5zERIbfo2TYQGdPvwe7zpSj0gnlEHK2iohxA3cB0Y92j/vvfPYK3pVAoMHHiVOzY8SWuX7+GS5cK0aVLN5Prx8XF46mn/oClSxfh/PmfrQ+eHM9BFYy8Yn6F+qfFv+WbXc1itxRvSEY9kKUS2DUjprlufI49rVuWzr9GDUXqO82SkHrmWt3MjkULDodfz4eAco3RfQqd5wioS9x0VrQgEbVETETIbRRSMcZ08e7B07aKjr4TYrEY+fkXkJl5EomJvQzLdu36D/bv32v0fVu2bMSQIUMRFdW20et5ebm4caMYYrEYbdpEAQBOnDiOmho1+va9r9FkirW1tUhPr6vGEhXFPsiewCElSb1gfgWhT4vZLcV5LLZqlDcvqlHPGeNznNW6JTnzP4hUVWbXMXkszCRIijkrIPKXA2ieiFg7z5EhcWNSTT6MiQiRG4SFheGJJ8Zi+/Yv8OKLM5GY2Avh4RHIzz+P/PwLmDTpaWzcuL7Z+zZsWIc1az5ATEwsOnaMgVTqj+vXryEnJws6nQ4TJ05FRETdINQLF85h1aqVCAoKQnx8Z0REtIZKpUJubg5u3ChGREQEJk6cIjjmH388jM8++4fh/zdu1N2wLF68EHJ53YD8iIjWWLIkxZ5D4z52zhlgD0FdXix0ufL4+TUEPi1mtxTnsqtVw1njcxx1I97gO2KpxQ0w81lrVBAXX4Gm32MQKcuhDwiGPvIOaLsNQGB704P8ralypZMFMtkmAhMRIrd56aV5uOuuOPz739vw009n4OcnQUJCF6SkvISOHWOMJiJz576G48ePIi8vFydPnoBarUZERGsMGPAgnnjiKfTrd59h3QEDBuHmzZs4ffoUrly5jJycLCgUCkRFtUVS0hgkJY1FWJjwwgBlZaXIzc1p9np+/gXDvxtO2OhNTHVpqp31PvQl1yEtvOjULhMWu7TogYAVU8x2ufL0+TUsPS3WdH8Qtd0GsFuKk2nj+0AvEhntsqQXiaCN72P2/Z46Pkdoa1s9vVRm9LOa695o6TMK7ZqmF4mgmsJkmwgARPqmZXmoRamp0aK8vNrsOlevFgIA2rbt6IqQvIJEUjdWRavVuTmSlstjrjuNGgHLJxu/gRGJgAY/kU4bb2EmBl1gKAAYHVysCwozdLmSZKZBvnWpyV2oxr3u1hYRadpmyPalmlyuHjoFmkcmuDAi60RG1rWOFRXddHMk9vH068Qm5r7DZjT7Ppv7Ht76rkXeahExeh0IiEMvD0T1lPegi+lhVazkeVrKb4KjhIQo4O9vffuGb4wMJiIyweyTehPVdizN/m21W11ems6UrZMFQBcVY7LCUcPZl+2dadvZOBGhZ3B7y5mJWdntYe3YjHpNv892zTYPmPkeB6Km32NQjXsdVW/8i0kIUQPsmkVEPs3aGy9njbdo2OVFfDEb0qwDEKuqIM7PNPu+hiVTPbkUKCci9AzuTAhtquomoBy1pe+wNjoBkitnjcfU4PvsiCTNU7uuEXkqJiJE5NNsufFy2lNjqQzabgMQsGutxYo/9RrG79E3QR6eKPkKtyWENlR1E5q4WEyuQtsAJhIR4Pb32WFJGqtgEQnGRISIfJrZOQNMcOZTY2u6mRi9cfTgmyCPTpR8hZsSQqurulmRuFhKrmoT+kGac8hkbPXfZ7baEbkex4gQkW8z0a9bLxIZXd3ZNyRCW1u8tiXhVqKkeWRC3Y2nt8XfAtQnhKpxr0M9dApU416Hcv4Gp056aW23J6vGa5gam3HrO6K992FD0YemGn2fLWyH1yqR47FFhIh8nrEn9brQSAR8/j5QUXJ7PRfckFhqbWGZW3IIF7ecWdvtydrExVxrm/jyWUBX23yfilbNvs9stSNyLSYiRESA0Rsz+dLtqD31AyoLnDuPSEOWuoeofz+fN0W+QsBAbW9hbbcnm8ZrGEuu6rt4VTcvsaoX+0HXNkbYdojIKZiIEBGZIPKXQ9J/GDSdXFgnnoO6CTZWmPJkVl7XjhqvYbaLV1WZUyrgEZFwTESIiJzJhqfa7B7i42yoMOU0DmyV0d2RAOXLn8B/3waIiy9DF3kHaoZOAQKCm6/soITc7fOmEJFZTESIiJzErqfa7B7is6yuMOUkjm6Vaba9C5mQ5Bw2uT1HJOScSJPIs7FqFhGRM1h4qu3w2dmpxfCIp/iOvn5t3Z6dVdbqu3gZw5K8RO7HRISIyAmsKj9KnqFGBcmp7yBN2wxJZprlm21r1xfIE57iO/r6ddv3gSV5iTwau2YRETmBRzzVpjoCxjlY2w3J2Pp6fzlqBo2DZtBYu25wPWFiPUdfv+78PnDMFZHnYiJCROQEbn+q3YJKv9pDUIIhZHA4Wt1eYGJ9UY0Ksv2pkKZ/BdWUP9te3coDKqc5+vp1+/eBY66IPBITESKySKVSISPjGI4c+RFZWafw22+/QqvVIiKiNe69tyfGjRuP+PjO7g7To7jzqXaLK/1qK4HVpwR1G2o/2vCaufWBurKw9la3cvdTfEdfv57QykNEnodjRIjIon379uD11+fi3//eBqVSiT59+mHAgAchkUiwd+9uPPvsFPznPzvdHaZncWXf9IZjFTL2Qp76NgfJQ/i4BGu7DQnpRuSQcQ92DtS2d98OvX45VoOIjGCLCBFZJJFI8Nhj/4cxY37fqOVDr9dj69bN+PDDv2HlymVITOyFO+/s6MZIPYsrnmoba/0wua4LS796AqEJhrXdhoR2IxJfzAY89VgL6Lrn0Ou3RgVx8RVo+o2ESFkBfUAI9JHRPttlkIjqMBEhIotGjHgcI0Y83ux1kUiEP/xhItLTf8SJE8eQlrYPU6dOd0OEHsyZfdNNdD0yx5cGyQtNMKztNmRu/YakWQdQ8/hMj7vRtth1z8Hji8ztz9OODRG5FhMRch8vGkw7cGAfAMDhwxnYvftrbN/+BQoLLyIgIBD33z8AM2fOQVhYGNRqNTZt+gz79u3F9etXERoahmHDRmLatOcgkTT+upWWlmLfvj04cuRHXL5ciBs3iiGVStGxYyyGDRuJpKQx8PPzaxZLbm4OtmzZiJycLJSWlkAulyM0NAxdunTDqFFJ6N27r2FdtVqNL774HN9/vw+XL1+CVqtFcHAw2rZtj969+2LKlGmQyew/5vHxCThx4hiuX79m97ZIOEtjFYzxpQncBCcY1g4Or18/9W2Iq8pM7l+kqjLdAuWu3z8L42ZUE96CfPMix40v0qiNHie3zBJPRB6HiQi5hbcOpl2zZhW+/PJzJCb2Qv/+9yMnJwu7dv0HeXk/4aOP1uHVV2ejoKAAiYm9EB0djczMk9i4cT3Kysrw2mtvNtrWsWPpWLXqL2jTJgrR0Xega9fuKCm5gTNnspGbm4OMjKNYvDgFIpHI8J7jx48gOfllaLVaxMcnoEePe6HValFUdB0HDnyHwMBAQyKi0+kwf/7LOHHiOIKCgpCY2AuBgUEoLS3BpUuF2LDhnxgz5vcOSUSuXLkEAIiIaG33tkg4a1s3fG5QsBUJhrXdkHR3JED52kbIP3sbkvxMkyEYO0fu/P2zNG5GkfoORKqqZq/bmjRID24zmaz5WldBImqOiQi5nsBKNp5oz55dWL9+C2JiYgEAFRUVmDnzaVy4cA4zZz6NoKBW+PLL/yAoKAgAcO7cWUyfPhnffPNvTJnyDNq2vf00OiGhC9au/QzdunVvtI/i4mIkJ7+IQ4d+QFraPgwZ8jvDso0bP4NWq8WCBYswdOjwRu8rLy/Db7/dvunJysrEiRPHER/fGatXfwqFQmFYptfrkZ19GoGBQXYfkwsXzuPHHw9DJBJh0KDBdm+PhLOmdcPurjBe1ILZULMEI7g1oNfD71wGxDd+afw5rO1GJ5VB23e42USk2Tky9/uX+jaUr2106nG1OG6mSRJSz2LSYOz6AOB/cKtd8RBRy8ZEhFxOSCUbT31CNm3ac4YkBACCg4ORlDQGq1atREHBRWzYsNWQhABAXFwC7r9/AA4fPohTp040GmfRcDsNtW7dGrNmvYhXXpmN77//rlEiUlJSAgC4777mT7VDQkIREhLabN177+3ZKAkB6sZ23HNPojUf3SilUomFC99EbW0tHnvs/xAXF2/3Nkk4s12PAkNRM2IaROXFdicOgp/ge2qycivBcEZLhLXjS8z+/lWVQXpwGzRDJtgUixD2dM0zlTQYPa7+ctTG94WoRuW0eIjI+zERIZfz5hmn+/d/oNlrHTrcAQCIimpnNLmIjr4TQF1LR1NarRYnT2YgJycLJSU3UFNTA71eD6Wy7qnk5cuXGq3ftWs3FBTkY+HCNzF58jPo1q2H0XEkAJCQ0Bl+fn745puvcMcdd+Lhhx9BeHiEdR/YDK1Wi7fffh35+RcQFxePl19Odti2SSALXY/s7uZTo4Lk5H74f/MRxLWaRouatmB6fHdLZ7VEWDm+xNLvm/TgVtMzszsg0TObOMkCIVYbbxEBTCQNpo5rjQrinENmY9H5y32rqyARNcNEhFzO7TPs2qFNmzbNXqtvbTC2rOHymprG8zdculSIN96Yh4KCiyb3V5+Q1HvuuRdw/vzPOHLkRxw58iPkcjk6d+6KXr36YNiwkejQIdqwbocO0Zgz5xWsXv0BVq5chpUrl6F9+w7o0eMeDBz4EAYNGmwyibGkrnvYn3D06I+IiYnFypUfNmt1IddwVolg8eWzUKx/A6Lqm6bXqW/B7DbA8d0tHdy6YrEl4vt/QR8ZbdP+rDkHln7fxLc+d9NWYYcleuYSp/FvQb5lkckWNmNJgy0FE+ppBo3zjBYzInIbJiLkct48w65YbHoO0IaDyoV4++3XUFBwEQMHDsL48ZMRExOLwMAg+Pn54dKlQowfPwZ6vb7ReyIiWuMf/9iIU6dO4Pjxo8jOPo3c3BxkZp5Eauo6JCe/gccfvz0D9Nixf8DgwY/i0KEDyMo6jaysTOzd+y327v0WcXHx+PDDT6weJ1JbW4v33nsbP/zwPaKj78Df/rYGYWHhVm2DHMzRJYJvVToyl4TUE5X85vDuls5oXbHUEuH//WY0/AZbvT+B50DbbQD0/nKzXZaaxWrNuDo75wdRTX4P8vVvQNzk3It0tRBfLWh2PGxtwdYFhta1/BCRT2MiQq5nbanMFqiwsAAXLpxHWFg43n9/RbOWiV9+uWzyvWKxGL179zVUx6qursb27Vvx8ccfYuXK5Rg8eEij5CIiojWSksYiKanuj/65cz9j0aJ3cO7cz9i0KRXPPfeC4Ljrk5C0tH1o164DPvjgI7RuHWnNRycvIDnzP7NlaRvSh7dzbHdLJxWzsNQS0fQxgtOKZ0hlqBk0DrL9qSZXaRqr0ETPqgTOROKkaxsDiJu3lIqqbxo9Hra0YPvSbz0RmWf68S6RE9U/kVONex3qoVOgGvc6lPM3eEZfcheoqCgHUDcw3Vj3qP/+d4/gbSkUCkycOBVt2kShpkaNS5cKza4fFxePp576AwDg/PmfBe9Hp9Nh0aIF+O67/6Jt23b4+98/RlRUW8HvJ+8hNHGob8G0eJNfUQJp2mZIMtMAjdrsupZuumVfLBe0naa03QZA5y+36j31N/mOphk0FrrAUKPLjLUKC0r0LCRwQo+XuSTU2PGob+G2pOa+UT75W09E5rFFhNzHmTNOe7jo6DshFouRn38BmZknkZjYy7Bs167/YP/+vUbft2XLRgwZMrRZApCXl4sbN4ohFovRpk0UAODEieOoqVGjb9/7Gk2mWFtbi/T0upuJqChhTzN1Oh0WL16Iffv2ICqqLVat+rhRKWJqWYQ85dbJAg1Ptc11t9SLRPA/+vXt91no8mRxMHfOIUhzDkEvC4Tm3oehi+0hbDyHVAaNhZYIW+KxiVQG1fi3Id/wNsRqpeFlUy0FQsbVOap7nNWtWwImd9QFhaFm5Ay2gBBRM0xEiNwgLCwMTzwxFtu3f4EXX5yJxMReCA+PQH7+eeTnX8CkSU9j48b1zd63YcM6rFnzAWJiYtGxYwykUn9cv34NOTlZ0Ol0mDhxqmFSwQsXzmHVqpUICgpCfHxnRES0hkqlQm5uDm7cKEZERAQmTpwiKN7t27/Anj27AADt23fA+vWfGl3vnnsSMWpUko1HhTyFttsA6AJDTd5Y6mUBUM5PBQKC614w0d1SLxJB1GSck6UuT0K7+ojUVfA/tgs4tkvweA7NoLGQpn8luNuZNfFYQ3z5LOSfL2qUhOjlgVBNeMvoZxAyrk56aJvZfQpNqGwpJlI/uaP04Db4H9zaaPwLu2ERkTlMRIjc5KWX5uGuu+Lw739vw08/nYGfnwQJCV2QkvISOnaMMZqIzJ37Go4fP4q8vFycPHkCarUaERGtMWDAg3jiiafQr999hnUHDBiEmzdv4vTpU7hy5TJycrKgUCgQFdUWSUljkJQ0FmFhlrtUALe7kgHAqVMnzK7LRKQFkMqgmvJno1WzdIpWUD29+HYSUv96kwHQopsl8D/yNYwx94Te3E23KYLHc9z6XEISJsBJxTNMdKESqaog37zI+GcQMK7OUdUIbS4mIpVBM2QCNIPGOryCGxG1XCJ907I81KLU1GhRXl5tdp2rV+vGFLRt29EVIXkFiaRu+JRWq3NzJC2XN1x3kZGtAABFRZarR7VIGjUkWQfgl3cMAFCb0A/aex8WdGMpTdsM2T7T3aDUQ6dA84jxifuMDboWQjXu9ebJjYkZvxveLOtCIpuVrW3ayuKoa0GSmQb51qUml9fcN8p0NyaN2vRNvkaNgOWTTSYQ1gy69/g5YdzI538TyIDXQmMhIQr4+1vfvsEWESIiMk4qg7b3MGh7D7P6rfY8oW/YuuJ35n+QWpgYr17T7kfmbqibJizOmItFSIxN+R/5GpKcw1ZVuqpf5qhqhM6am4aIqCkmIkRE5HB2zxd066Zb220A/ApyBLWONEpurC0D7KLiGUK6SNlaOtihCYQPFxMhItdh+V4iInK8W0/om5Z2tfoJvYntNNU0uRFSRcodhJa7tTnGWwmE5pEJdYkEWzGIyIOxRYSIiJzCUU/oG25HfDEbktMHIFZX3V5uJLlx6CSLjmSiC5UxbouRiMhFmIgQEZHzOKqLT/12Eh9BzeMzLSY3jqoi5Qz1iZX/7k9MVhYD3BsjEZErMBEhIiLvIiC5sXuMirNJZagZOQOSnMOeGyMRkZNxjAgRuRyrhpPTOWqMijN5Q4xERE7EFhECIAKgh16vh0gkcncw5FN4vZHzeEMZWm+IkYjIWZiIEMRiP+h0Wmi1Gkil/u4Oh3yAVqsBUHftETmVN5Sh9YYYiYicgF2zCDKZHACgVivdHAn5ivprrf7aIyIiIt/DRIQglwcAACorK6BU3oROV8s+/ORwer0eOl0tlMqbqKysAHD72iMiIiLfw65Zt+Tn5+PgwYM4dOgQzp49i9LSUsjlctx9990YMWIExo8fD39/67otHT16FJMnTza7ztatW5GYmGhP6HaTyRQICAiGUlmBiooSVFSUuDUez1A/doEJmbMEBARDJlO4OwwiIiJyEyYit0ydOhXXrl2DTCZD9+7d0a9fPxQXFyMzMxOZmZn46quvsH79eoSGhlq97datW+PBBx80uiw8PNze0B2iVatQSKX+UCpvQqOpga/fgEskdY2FWm2tmyNpaUSQSv0RENCKrSFEREQ+jonILbGxsXjxxRcxYsQIBAYGGl6/cuUKZs6cidzcXCxZsgTLli2zetudOnXC0qVLHRmuw4lEIigUgVAoAi2v7AMiI1sBAIqKbro5EiIiIqKWiWNEbklNTcXYsWMbJSEAEB0djXfffRcA8O2336KmpsYN0RERERERtSxMRATo2rUrAECtVqOsrMzN0RAREREReT92zRKgsLAQACCVSm0aI1JcXIwPP/wQ165dg0KhQHx8PIYMGYKwsDDLbyYiIiIiaoFEetZpteiVV17B7t278bvf/Q5///vfBb/PXNUshUKBV199FZMmTXJUmEREREREXoMtIhbs2LEDu3fvhkKhwCuvvGLVe1u1aoWpU6di6NChiImJgUKhQGFhIbZs2YLt27dj0aJFkMvleOqpp5wUPRERERGRZ2oRLSLLly9HWlqa1e9LTU1FVFSUyeXp6el49tlnodVqsWzZMowePdqeMBvZuHEjFi1ahNDQUBw6dMjqOUqEqqnRory82inbbslYNYsAXgd0G68FAngd0G28FhoLCVHA39/69o0W0SJy/fp1XLx40er3aTQak8syMjIwa9YsaDQavPXWWw5NQgBgwoQJWL16NUpLS3H69Gn07dvXodsnIiIiIvJkLSIRSUlJQUpKisO2d/LkScyYMQNKpRLJyclOGcchFosRExOD0smBkg8AAA+KSURBVNJSXLt2zeHbJyIiIiLyZC0iEXGkzMxMTJ8+HVVVVXj55Zcxffp0p+2rtLQUABAQ4LwZpiUSP4SEKJy2/ZaOx44AXgd0G68FAngd0G28FupIJH62vc/BcXi1rKwsTJs2DVVVVZgzZw6ef/55p+0rLy8PBQUFEIlE6N69u9P2IxaLbOqzR3V47AjgdUC38VoggNcB3cZrwT6c0PCW7OxsPPPMM6isrMSsWbMwe/ZsQe/LysrC8OHDMXz48GbLNmzYYGj1aOjUqVN48cUXAQAjR45EmzZt7AueiIiIiMjLtIiqWY7Qr18/lJeXIzg4GEOGDDG53vz58xEeHm74f8O5Qs6ePdto3T59+qC6uhqdO3dGdHQ09Ho9CgsLcfbsWej1evTq1QuffvopgoKCnPOhiIiIiIg8FNuTbikvLwcAVFRUYOfOnSbXmz17dqNExJyZM2ciIyMD58+fR0FBAVQqFUJCQjBgwAA89thjGD16NPz8bOtTR0RERETkzdgiQkRERERELscxIkRERERE5HJMRIiIiIiIyOWYiBARERERkcsxESEiIiIiIpdjIkJERERERC7HRISIiIiIiFyOiQgREREREbkcExEiIiIiInI5JiJERERERORyTESIiIiIiMjlmIgQEREREZHLMREhIiIiIiKXYyJCREREREQux0SEiIiIiIhcTuLuAIi8QX5+Pg4ePIhDhw7h7NmzKC0thVwux913340RI0Zg/Pjx8Pf3d3eY5GRKpRL79+9HdnY2srOzkZeXh+rqajz88MNYu3atu8MjJ/j666/x+eef4+zZs9DpdIiNjcWYMWPwxz/+EWIxn+X5gvz8fBw6dAjZ2dnIyclBQUEB9Ho9PvjgAwwfPtzd4ZELaDQaZGRk4IcffsCxY8dQUFCAmpoahIWFoWfPnpgwYQL69+/v7jC9EhMRIgGmTp2Ka9euQSaToXv37ujXrx+Ki4uRmZmJzMxMfPXVV1i/fj1CQ0PdHSo5UWFhIZKTk90dBrnIwoULsWXLFshkMtx///2QSCRIT0/He++9h/T0dKxatYrJiA/4/PPPsWHDBneHQW50/PhxPP300wCAyMhI9O3bFwqFAhcuXMDevXuxd+9ezJo1Cy+99JKbI/U+TESIBIiNjcWLL76IESNGIDAw0PD6lStXMHPmTOTm5mLJkiVYtmyZG6MkZwsMDMSYMWPQvXt3dO/eHbm5uViwYIG7wyIn2Lt3L7Zs2YLIyEhs2rQJMTExAIDi4mJMnjwZ+/btw8aNGzFlyhT3BkpOFx8fj2nTphm+92+++SaOHTvm7rDIhUQiEYYNG4bJkyejT58+jZbt3r0b8+bNw5o1a9C/f3/cd999borSO4n0er3e3UEQebOMjAxMmDABMpkMGRkZ7KLlQ3bs2IE//elP7JrVAj355JM4c+YMli1bhqSkpEbLjh07hkmTJiEyMhIHDx5kq4iPmTRpEo4dO8auWWTw5ptvYtu2bRgzZgwWL17s7nC8Cn89iezUtWtXAIBarUZZWZmboyEie129ehVnzpyBVCo1eqPZr18/REVFoaioCJmZmW6IkIg8Sf19wLVr19wcifdhIkJkp8LCQgCAVCrlGBGiFiA3NxcAEBcXB7lcbnSdHj16AAB++uknl8VFRJ6poKAAQN34EbIOExEiO33yyScAgMGDB7NbFlELcOXKFQBA+/btTa7Trl27RusSkW8qKirCzp07AQC/+93v3ByN92EiQmSHHTt2YPfu3VAoFHjllVfcHQ4ROYBSqQQAKBQKk+vUF62oqqpySUxE5Hm0Wi2Sk5Nx8+ZN3H///XjkkUfcHZLXYdUsavGWL1+OtLQ0q9+XmpqKqKgok8vT09PxzjvvQCQSYeHChejUqZM9YZKTOes6ICIi37RgwQKkp6ejXbt2WLFihbvD8UpMRKjFu379Oi5evGj1+zQajcllGRkZmDVrFjQaDd566y2MHj3anhDJBZxxHVDLFBAQAACorq42uU59S0jDct5E5DsWLVqEbdu2ITIyEp999hnHh9iIiQi1eCkpKUhJSXHY9k6ePIkZM2ZAqVQiOTkZkyZNcti2yXkcfR1Qy9WhQwcAwK+//mpynatXrzZal4h8x9KlS7Fx40aEh4fjs88+M8wzRNbjGBEiK2RmZmL69OmoqqrCyy+/jOnTp7s7JCJysPpSnOfOnYNKpTK6TnZ2NgCgS5cuLouLiNxv+fLlWL9+PUJDQ7F+/Xrcfffd7g7JqzERIRIoKysL06ZNQ1VVFebMmYPnn3/e3SERkRO0a9cO3bp1g0ajwZ49e5otP3bsGK5evYrIyEj07NnTDRESkTukpKRg3bp1CAkJwfr169G5c2d3h+T1mIgQCZCdnY1nnnkGlZWVmDVrFmbPnu3ukIjIiWbMmAGg7sajfq4gALhx4wYWLlwIAHj22Wc5qzqRj/jrX/+KTz/9FMHBwfjnP/9paDkl+4j0er3e3UEQebp+/fqhvLwcwcHBGDJkiMn15s+fj/DwcBdGRq72wgsvoKioCABQUlKCy5cvIzg4GLGxsYZ1Zs2ahYcffthNEZKjvPvuu/j8888hk8nwwAMPQCKRID09HZWVlXj00UexatUq+Pn5uTtMcrIzZ84Ykk8AOH/+PKqqqhATE4OQkBDD61988YU7wiMX+O677zBr1iwAQPfu3REXF2d0vU6dOhkeYpAwHKxOJEB5eTkAoKKiwjBxkTGzZ89mItLC/fTTT/jll18avVZRUYHTp08b/l9SUuLqsMgJ3n33XfTu3RubN2/GsWPHoNPp0KlTJ4wZMwZ//OMf2RriIyorKxt9v+vVz6ZNLV/9PQAA5OTkICcnx+h6/fr1YyJiJbaIEBERERGRy/FxDhERERERuRwTESIiIiIicjkmIkRERERE5HJMRIiIiIiIyOWYiBARERERkcsxESEiIiIiIpdjIkJERERERC7HRISIiIiIiFyOiQgREREREbkcExEiIiIiInI5JiJERERERORyTESIiIiIiMjlmIgQEZFPqqmpwZAhQ9C7d29UVFS4bL8ff/wxEhISsGnTJpftk4jIEzERISIin/Svf/0LV65cwcSJExEcHOyy/U6YMAGtWrXCRx99BKVS6bL9EhF5GiYiRETkc6qqqvDRRx8hICAAU6dOdem+W7VqhYkTJ6K4uBipqaku3TcRkSdhIkJERD7nq6++QklJCYYOHYqwsDCX73/s2LEAgE2bNkGr1bp8/0REnoCJCBER+Zxt27YBAB577DG37D86Oho9e/ZEcXExDhw44JYYiIjcjYkIERF5nJUrVyIhIQH9+/dHUVFRs+V6vR7Tpk1DQkICnnzySWg0GsHbzsvLw5kzZxAcHIwHHnjA6DqTJk1CQkICduzYgcrKSixfvhyPPvoo7rnnHgwZMgQffPAB1Gq1Yf309HRMmzYN/fv3R2JiIiZMmICMjAyzcQwfPhwAsH37dsGxExG1JExEiIjI48yZMwddu3ZFWVkZ3njjjWbLN2/ejMOHD0Mul2PFihWQSqWCt/2///0PAHDPPfdYfF9FRQXGjh2LdevW4caNG9DpdLhy5QrWrFmDl156yRDL008/jR9//BFarRbV1dXIyMjA1KlTceLECZPb7tWrFwDgyJEjqK2tFRw/EVFLwUSEiIg8jlQqRUpKCuRyOQ4ePIjNmzcbluXn52PFihUAgHnz5uGuu+6yatsnT54EAHTr1s3iuh9++CGAumTj1KlTOHnyJBYtWgSJRILvv/8eq1evxpIlSzBjxgwcPXoUJ06cQFpaGnr27AmNRoMlS5aY3Hbnzp0hlUqhVCqRm5tr1WcgImoJmIgQEZFHuuuuuzBv3jwAwIoVK5Cfnw+tVovk5GSoVCoMHDgQEydOtHq7WVlZAICEhASL61ZXV2Pt2rXo06cPAMDf3x9PPfUURo8eDQBYtWoVRo0ahblz5xpKAHfo0AF/+ctfIBKJkJ2djV9//dXotv39/REbG9soJiIiX8JEhIiIPNbEiRMxcOBAVFdXIzk5GatWrUJOTg5CQ0OxePFiiEQiq7an1+tx48YNABBULWv48OHo2LFjs9cbji157rnnmi3v0KGD4X3nzp0zuf36GK5fv24xFiKiloaJCBEReSyRSIQlS5YgNDQUOTk5WLt2LQBgwYIFiIqKsnp75eXlhvEYQiYxjI+PN/p6REQEAEAmkxlNVBquU15ebnL7ISEhAIDS0lKLsRARtTRMRIiIyKO1adMGc+fONfx/+PDhGDlypE3bqqmpMfxbyAD3yMhIo6+LxXV/Plu3bm2yVcbPzw8AzM4T4u/vDwCNKnAREfkKJiJEROTRamtrsXPnTsP/8/LyoFQqbdpWaGio4d83b960OzZ7VVRUAGgcFxGRr2AiQkREHu2TTz7BqVOn0KpVK7Rr1w4FBQVYunSpTdvy9/dHQEAAAPNdplylPhFxx+zuRETuxkSEiIg81pkzZ7B69WoAwFtvvYWlS5dCJBJh69at+OGHH2zaZn2lqitXrjgsTlv98ssvAIBOnTq5ORIiItdjIkJERB5JpVIhOTkZGo0Gw4YNQ1JSEu677z5MnToVAPDmm2+ipKTE6u3WTySYk5PjyHCtdvXqVcOs8b1793ZrLERE7sBEhIiIPFJKSgouXLiAyMhIvPfee4bX586di7i4OBQVFWHBggVWb7f+pj87O9thsdqifv+xsbGGCltERL6EiQgREXmcw4cPY9OmTQCAxYsXNxrM7e/vjxUrVkAqleK///0vduzYYdW2H3roIQQGBuLixYu4dOmSQ+O2xoEDBwDA5gpgRETejokIERF5lPLycvzpT3+CXq/H+PHjMWjQoGbrdOnSBXPmzAEAvP/++1aN9wgICDDc/O/atcsxQVtJo9Fg3759EIlEePLJJ90SAxGRu4n0er3e3UEQERG5UnZ2NsaOHYu4uDh88803Lt9/Wloann/+eQwcOBDr1q1z+f6JiDwBW0SIiMjn9OjRA4MHD8a5c+dw8OBBl+//n//8JwAYWnWIiHwRExEiIvJJc+fOhVgsxscff+zS/WZkZOD48eMYMmQIEhMTXbpvIiJPInF3AERERO4QHx+PRYsW4ddff0VFRQWCg4Ndst+bN29i9uzZGDVqlEv2R0TkqThGhIiIiIiIXI5ds4iIiIiIyOWYiBARERERkcsxESEiIiIiIpdjIkJERERERC7HRISIiIiIiFyOiQgREREREbkcExEiIiIiInI5JiJERERERORyTESIiIiIiMjlmIgQEREREZHLMREhIiIiIiKXYyJCREREREQux0SEiIiIiIhc7v8Bbvsxpz5qP38AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "width": 401,
              "height": 270
            }
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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f/Sp/93d/l//9v/93Hn744VRVVfXgGQEAQOkpqSDw3HPPZd68eamurs5jjz2WUaNGJUk2bdqUyZMn5+c//3keffTRfPGLXzyo9RobG3P33Xenqqoqc+fOzUc/+tEkyfbt2/Pf/tt/y69+9avce++9+du//dueOiUAAChJJbVHYM6cOUmSW265pSMEJMlxxx2XmTNnJvn9J/y7d+8+qPUeeOCBtLe357rrrusIAUkydOjQfOc730m/fv0yb968vPPOO912DgAA0BeUTBDYsGFDli5dmoEDB6a2tnaf8fHjx2fEiBFpbm7O4sWL/+h6O3fuzIIFC5Ik/+W//Jd9xj/0oQ/lYx/7WNra2vLLX/6y6ycAAAB9SMkEgaampiTJqaeemsGDB+93zhlnnJEkWbZs2R9db/Xq1Wltbc3RRx+dk08++QPX2/PaAABQFCUTBNatW5ckOeGEEw44Z+TIkXvNPZj19jxnf/a81vr16w+6TgAAKAcls1m4paUlST7wDj5Dhw5N8vvNvt2x3pAhQw56vUNVWTkg1dVH9tj6dI3elA+9LC/6WT70srzoZ3kpmSsCAADA4VMyVwT2fDrf2tp6wDl7Prnfc2Wgq+vtuWpwMOsdqp07d2Xr1gPXQO/Y84lGc/O7vVwJXaWX5UU/y4delhf9LG3DhlWlsrLzb+tL5orAiSeemCR54403Djhnw4YNe809mPXefPPNA87ZM3Yw6wEAQDkpmSAwbty4JMlrr72WHTt27HdOY2NjkuQjH/nIH11vzJgxGTx4cLZs2ZLXX399v3OWLFly0OsBAEA5KZkgMHLkyJx++ulpa2vLs88+u894Q0NDNmzYkOrq6px55pl/dL3Kysqcf/75SZJ//ud/3mf83/7t37J48eIMHDgwF1xwQZfrBwCAvqRkgkCSTJs2LUlSV1eXtWvXdhx/++23M2vWrCTJ1KlT06/fv5f92GOPpba2Nrfddts+602dOjUVFRX5n//zf3Z8+p/8fq/B3/7t32b37t35whe+kKOOOqqnTgkAAEpSyWwWTpLa2tpMnDgx8+fPz2WXXZbzzjsvAwYMSH19fbZt25aLLroo11xzzV7P2bx5c1avXp3q6up91vtP/+k/5eabb05dXV3+8i//Mp/4xCdy5JFH5le/+lXefvvtfPSjH81Xv/rVw3V6AABQMkoqCCTJzJkzc9ZZZ+Xxxx9PQ0NDdu/enTFjxmTChAmZOHHiXlcDDsbUqVPz4Q9/OA899FAaGxvz3nvv5UMf+lAmTZqUKVOmpLKysofOBAAASldFe3t7e28XUc7cPrQ0uQ1a+dDL8qKf5UMvy4t+lrY+f/tQAADg8BEEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAb0dgH/r1WrVuVHP/pRXnzxxWzZsiXV1dU5//zzc+ONN2b48OGdWmvdunW58MILP3DOPffck89+9rNdKRkAAPqckgoCDQ0NmTp1anbs2JHTTz89Z599dpYvX56///u/z7/8y79k3rx5GT16dKfXHTJkSD7zmc/sd+ykk07qatkAANDnlEwQaGlpyde+9rXs2LEj3/zmN3PNNdd0jM2ePTsPPvhgbr755jzxxBOpqKjo1NrHHHNMvvvd73Z3yQAA0GeVzB6BJ598Ms3NzTnnnHP2CgFJcsstt+Tkk0/O0qVLs2DBgl6qEAAAykfJBIHnn38+SXLZZZftM9a/f/9ceumle80DAAAOXcl8NWjZsmVJkjPOOGO/43uONzU1dXrtlpaWzJkzJ+vXr09lZWVGjx6dCy+8MMcff/yhFwwAAH1YRXt7e3tvF7Ft27acddZZSZJFixblyCOP3GdOU1NT/ut//a85+uij89JLLx3Uuh9016CBAwdmypQp+cpXvtLpPQcAANDXlcQVge3bt3f8XVVVtd85Q4YM2WfuH1NZWZmrrroqtbW1+Y//8T9m2LBhef311/PP//zPefjhh/M//sf/SJJ89atf7UL1AADQ93TLFYG77rorL7zwQqefN3fu3IwYMSIbN27M+eefnyRZunRpBgzYN5+sWbMmn/nMZzJw4MC8+uqrXS05L7zwQm644YYMHDgw//qv/5oRI0Z0ec392blzV7Zube2RtTl01dW/v+rU3PxuL1dCV+lledHP8qGX5UU/S9uwYVWprOz85/vdckXgrbfeyurVqzv9vLa2tiTJ0KFDO461trbu96tBLS0t+8ztij//8z/PuHHj0tTUlPr6+nzuc5/rlnUBAKAv6JYgUFdXl7q6ukN+/hFHHJFhw4Zl69atWb9+fcaOHbvPnDfffDNJcuKJJx7y6/y/xowZk6ampmzcuLHb1gQAgL6gZG4fOm7cuCRJY2PjfseXLFmy17zusGXLliT/vv8AAACKomSCwJ67+zz99NP7jL3//vt55plnkiQXX3xxt7xec3NzFi1alOTAtywFAIByVTJB4Iorrkh1dXVeeumlPP7443uN1dXV5fXXX8+4ceM6NhXvsXHjxtTW1qa2tnafr/j85Cc/2e/XflauXJkbbrghO3bsyJlnnpmPfexj3X9CAABQwkri9qHJ7zcB33PPPZk6dWruuOOOPPHEExk1alSWL1+e3/72tznmmGNy991373PP/7a2to6Nyns2H+/x+OOP51vf+lZOO+20jBo1Kv3798/rr7+e5cuXZ9euXRkzZkz+7u/+7rCdIwAAlIqSCQJJMn78+Dz11FO5//778+KLL+Y3v/lNjjvuuFx11VWZMWNGhg8f3qn1rrnmmixcuDArVqxIfX19WlpacsQRR+TMM8/MxRdfnKuuuiqDBw/uobMBAIDSVRK/LFzO/I5AaXI/5PKhl+VFP8uHXpYX/Sxth/o7AiWzRwAAADh8BAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABvR2AXu0tLTk+eefT2NjYxobG7N8+fK0trbmggsuyJw5c7q09qpVq/KjH/0oL774YrZs2ZLq6uqcf/75ufHGGzN8+PBuOgMAAOg7SiYIrF27Nrfeemu3r9vQ0JCpU6dmx44dOf3003P22Wdn+fLl+fu///v8y7/8S+bNm5fRo0d3++sCAEApK5kgMHTo0EyYMCE1NTWpqalJU1NTbr/99i6t2dLSkq997WvZsWNHvvnNb+aaa67pGJs9e3YefPDB3HzzzXniiSdSUVHR1VMAAIA+o2SCwMknn5xvf/vbHY9XrlzZ5TWffPLJNDc355xzztkrBCTJLbfckueffz5Lly7NggUL8md/9mddfj0AAOgrynqz8PPPP58kueyyy/YZ69+/fy699NK95gEAQFGUdRBYtmxZkuSMM87Y7/ie401NTYetJgAAKAVlGwS2bduWLVu2JElOPPHE/c454YQTkiTr1q07bHUBAEApKJk9At1t+/btHX9XVVXtd86QIUP2mdvdKisHpLr6yB5bn67Rm/Khl+VFP8uHXpYX/Swv3RIE7rrrrrzwwgudft7cuXMzYsSI7igBAADohG4JAm+99VZWr17d6ee1tbV1x8vv19ChQzv+bm1tzZFH7ptgW1pa9pnb3Xbu3JWtW1t7bH0OzZ5PNJqb3+3lSugqvSwv+lk+9LK86GdpGzasKpWVnX9b3y1BoK6uLnV1dd2xVLc54ogjMmzYsGzdujXr16/P2LFj95nz5ptvJjnwHgIAAChXZbtZOEnGjRuXJGlsbNzv+JIlS/aaBwAARVHWQeDCCy9Mkjz99NP7jL3//vt55plnkiQXX3zxYa0LAAB6W58PAkuWLEltbW1qa2v3GbviiitSXV2dl156KY8//vheY3V1dXn99dczbty4nH/++YerXAAAKAkldfvQG2+8Mc3NzUmS3/3ud0mSl19+OZ///Oc75kyfPj0XXHBBx+PW1tYDblQeOnRo7rnnnkydOjV33HFHnnjiiYwaNSrLly/Pb3/72xxzzDG5++67U1FR0XMnBQAAJaikgsCyZcuyfv36vY698847eeWVVzoe7wkIB2v8+PF56qmncv/99+fFF1/Mb37zmxx33HG56qqrMmPGjAwfPrxbagcAgL6kor29vb23iyhnbh9amtwGrXzoZXnRz/Khl+VFP0vbod4+tM/vEQAAADpPEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAIa0NsF7NHS0pLnn38+jY2NaWxszPLly9Pa2poLLrggc+bMOaQ1X3rppUyePPkD5/zDP/xDPvaxjx3S+gAA0FeVTBBYu3Ztbr311h5Z+7jjjsunPvWp/Y4de+yxPfKaAABQykomCAwdOjQTJkxITU1Nampq0tTUlNtvv71b1h4zZky++93vdstaAABQDkomCJx88sn59re/3fF45cqVvVgNAACUN5uFAQCggErmikBP2rRpU374wx9m48aNqaqqymmnnZYLL7wwxxxzTG+XBgAAvaIQQWDVqlX5wQ9+sNexO++8MzfffHMmTZrUo69dWTkg1dVH9uhrcOj0pnzoZXnRz/Khl+VFP8tLWQeBI488Mtdee20uvvjijBo1KlVVVVm7dm3mzZuXJ554InfeeWcGDx6cK6+8srdLBQCAw6pbgsBdd92VF154odPPmzt3bkaMGNEdJezXuHHjMm7cuH2O3Xnnnfnwhz+cO++8M3V1dbn88stTWVnZIzXs3LkrW7e29sjaHLo9n2g0N7/by5XQVXpZXvSzfOhledHP0jZsWFUqKzv/tr5bgsBbb72V1atXd/p5bW1t3fHyh+Tqq6/O/fffn82bN+eVV17J2Wef3Wu1AADA4dYtQaCuri51dXXdsdRh069fv4waNSqbN2/Oxo0be7scAAA4rAp9+9DNmzcnSYYMGdLLlQAAwOFV2CCwfPnyrFmzJhUVFampqentcgAA4LDq80FgyZIlqa2tTW1t7T5jjzzySMen/n/o17/+dW666aYkyaWXXprhw4f3eJ0AAFBKSur2oTfeeGOam5uTJL/73e+SJC+//HI+//nPd8yZPn16Lrjggo7Hra2tB9yofN9992X27NkZO3ZsTjrppLS3t2ft2rVZsWJF2tvb8/GPfzx33HFHz50QAACUqJIKAsuWLcv69ev3OvbOO+/klVde6Xi8JyAcjOuvvz6LFi3KypUrs2bNmuzYsSPDhg3LJz/5yXz2s5/N5Zdfnv79+3db/QAA0FdUtLe3t/d2EeXM7wiUJvdDLh96WV70s3zoZXnRz9J2qL8j0Of3CAAAAJ0nCAAAQAEJAgAAUECCAAAAFJAgAAAABSQIAABAAQkCAABQQIIAAAAUkCAAAAAFJAgAAEABCQIAAFBAggAAABSQIAAAAAUkCAAAQAEJAgAAUECCAAAAFJAgAAAABSQIAABAAQkCAABQQIIAAAAUkCAAAAAFJAgAAEABCQIAAFBAgst3AUcAABDGSURBVAAAABSQIAAAAAUkCAAAQAEJAgAAUECCAAAAFJAgAAAABSQIAABAAQkCAABQQIIAAAAUkCAAAAAFJAgAAEABCQIAAFBAggAAABSQIAAAAAU0oLcL2GPVqlVZsGBBFi5cmBUrVmTz5s0ZPHhwTjnllFxyySX5whe+kMrKykNe+0c/+lFefPHFbNmyJdXV1Tn//PNz4403Zvjw4d18JgAAUPoq2tvb23u7iCQ5//zzs3HjxgwaNCg1NTU5/vjjs2nTpixevDjvvfdexo0bl4ceeihHH310p9ZtaGjI1KlTs2PHjpx++un5kz/5kyxfvjyrVq3Ksccem3nz5mX06NE9dFbJzp27snVra4+tz6Gprj4ySdLc/G4vV0JX6WV50c/yoZflRT9L27BhVams7Pzn+yVzRWD06NG56aabcskll2To0KEdx9etW5frr78+TU1N+c53vpPZs2cf9JotLS352te+lh07duSb3/xmrrnmmo6x2bNn58EHH8zNN9+cJ554IhUVFd16PgAAUMpKZo/A3Llz8xd/8Rd7hYAkOemkkzJz5swkyc9+9rPs3LnzoNd88skn09zcnHPOOWevEJAkt9xyS04++eQsXbo0CxYs6HL9AADQl5RMEPgg48aNS5K899572bJly0E/7/nnn0+SXHbZZfuM9e/fP5deeule8wAAoCj6RBBYu3ZtkmTgwIGd2iOwbNmyJMkZZ5yx3/E9x5uamrpYIQAA9C0ls0fgg/z4xz9Oknz6058+6DsHbdu2rePqwYknnrjfOSeccEKS3+9D6CmVlQM6NthQevSmfOhledHP8qGX5UU/y0vJXxF48skn88wzz6Sqqipf/epXD/p527dv7/i7qqpqv3OGDBmyz1wAACiCbrkicNddd+WFF17o9PPmzp2bESNGHHC8vr4+3/rWt1JRUZFZs2ZlzJgxXSmzV7h9aGlyG7TyoZflRT/Lh16WF/0sbb16+9C33norq1ev7vTz2traDji2aNGiTJ8+PW1tbfnGN76Ryy+/vFNr/+Hdh1pbW3PkkfteymppadlnLgAAFEG3BIG6urrU1dV1x1JJkpdffjnTpk1LS0tLbr311kyaNKnTaxxxxBEZNmxYtm7dmvXr12fs2LH7zHnzzTeTHHgPAQAAlKuS2yOwePHiXHfdddm+fXu+8pWv5LrrrjvktfbcdrSxsXG/40uWLNlrHgAAFEVJBYElS5ZkypQp2b59e7785S/nhhtu6NJ6F154YZLk6aef3mfs/fffzzPPPJMkufjii7v0OgAA0NeUTBBobGzMl770pWzbti3Tp0/PjBkzDup5S5YsSW1tbWpra/cZu+KKK1JdXZ2XXnopjz/++F5jdXV1ef311zNu3Licf/753XIOAADQV5TM7whMmTIl7777bo466qi8+eab+eu//uv9zrvtttty7LHHdjxubW094EbloUOH5p577snUqVNzxx135IknnsioUaOyfPny/Pa3v80xxxyTu+++OxUVFT1yTgAAUKpKJghs3bo1SfLOO+/kqaeeOuC8GTNm7BUE/pjx48fnqaeeyv33358XX3wxv/nNb3LcccflqquuyowZMzJ8+PAu1w4AAH1NRXt7e3tvF1HO/I5AaXI/5PKhl+VFP8uHXpYX/Sxth/o7AiWzRwAAADh8BAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABAEAACggQQAAAApIEAAAgAISBAAAoIAEAQAAKCBBAAAACkgQAACAAhIEAACggAQBAAAoIEEAAAAKSBAAAIACEgQAAKCABvR2AXusWrUqCxYsyMKFC7NixYps3rw5gwcPzimnnJJLLrkkX/jCF1JZWdmpNV966aVMnjz5A+f8wz/8Qz72sY91pXQAAOhzSiYIXHvttdm4cWMGDRqUmpqajB8/Pps2bcrixYuzePHi/PSnP81DDz2Uo48+utNrH3fccfnUpz6137Fjjz22q6UDAECfUzJBYPTo0bnppptyySWXZOjQoR3H161bl+uvvz5NTU35zne+k9mzZ3d67TFjxuS73/1ud5YLAAB9WsnsEZg7d27+4i/+Yq8QkCQnnXRSZs6cmST52c9+lp07d/ZCdQAAUF5KJgh8kHHjxiVJ3nvvvWzZsqWXqwEAgL6vZL4a9EHWrl2bJBk4cOAh7RHYtGlTfvjDH2bjxo2pqqrKaaedlgsvvDDHHHNMd5cKAAB9Qp8IAj/+8Y+TJJ/+9Kc7feeg5Pd3JPrBD36w17E777wzN998cyZNmtQtNQIAQF9S0d7e3t7bRXyQJ598Mn/zN3+TqqqqPPnkkxkzZsxBP7epqSk//elPc/HFF2fUqFGpqqrK2rVrM2/evDzxxBPZvXt37rzzzlx55ZU9eAYAAFB6uiUI3HXXXXnhhRc6/by5c+dmxIgRBxyvr6/P1KlTs2vXrsyePTuXX355V8rcy6OPPpo777wzRx99dBYuXHhIVxoAAKCv6pavBr311ltZvXp1p5/X1tZ2wLFFixZl+vTpaWtryze+8Y1uDQFJcvXVV+f+++/P5s2b88orr+Tss8/u1vUBAKCUdUsQqKurS11dXXcslSR5+eWXM23atLS0tOTWW2/tke/x9+vXL6NGjcrmzZuzcePGbl8fAABKWcndPnTx4sW57rrrsn379nzlK1/Jdddd12OvtXnz5iTJkCFDeuw1AACgFJVUEFiyZEmmTJmS7du358tf/nJuuOGGHnut5cuXZ82aNamoqEhNTU2PvQ4AAJSikgkCjY2N+dKXvpRt27Zl+vTpmTFjxkE9b8mSJamtrU1tbe0+Y4888kjHp/5/6Ne//nVuuummJMmll16a4cOHd614AADoY0rm9qHjx4/P1q1bc9RRR+XCCy884Lzbbrstxx57bMfjl156KZMnT06SrFixYq+5f/qnf5rW1taMHTs2J510Utrb27N27dqsWLEi7e3t+fjHP54HHnggRxxxRM+cFAAAlKiS+UGxrVu3JkneeeedPPXUUwecN2PGjL2CwAe5/vrrs2jRoqxcuTJr1qzJjh07MmzYsHzyk5/MZz/72Vx++eXp379/t9QPAAB9SclcEQAAAA6fktkjAAAAHD6CAAAAFJAgAAAABSQIAABAAQkCAABQQIIAAAAUkCAAAAAFJAgAAEABCQIAAFBAggAAABTQgN4uAErBqlWrsmDBgixcuDArVqzI5s2bM3jw4Jxyyim55JJL8oUvfCGVlZW9XSYHoaWlJc8//3waGxvT2NiY5cuXp7W1NRdccEHmzJnT2+VxAE8//XTmz5+fFStWZPfu3Rk9enQmTJiQiRMnpl8/n1n1FatWrcrChQvT2NiYV199NWvWrEl7e3u+//3vp7a2trfL4yC1tbVl0aJF+eUvf5mGhoasWbMmO3fuzDHHHJMzzzwzV199dc4555zeLpNuIAhAkmuvvTYbN27MoEGDUlNTk/Hjx2fTpk1ZvHhxFi9enJ/+9Kd56KGHcvTRR/d2qfwRa9euza233trbZdAJs2bNyrx58zJo0KCce+65GTBgQOrr63PHHXekvr4+9913nzDQR8yfPz+PPPJIb5dBF/3qV7/KX/3VXyVJqqurc/bZZ6eqqiq//e1v89xzz+W5557L9OnT89//+3/v5UrpKkEAkowePTo33XRTLrnkkgwdOrTj+Lp163L99denqakp3/nOdzJ79uxerJKDMXTo0EyYMCE1NTWpqalJU1N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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "width": 385,
              "height": 255
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ax.get_xaxis().set_ticks([])    # enable this to hide x axis ticks\n",
        "ax.get_yaxis().set_ticks([])    # enable this to hide y axis ticks\n",
        "# initialization function: plot the background of each frame\n",
        "def init():\n",
        "    line1.set_data([], [])\n",
        "    line2.set_data([], [])\n",
        "    line3.set_data([], [])\n",
        "    line4.set_data([], [])\n",
        "    line5.set_data([], [])\n",
        "    time_string.set_text('')\n",
        "\n",
        "    \n",
        "    return  line3,line4, line5, line1, line2, time_string"
      ],
      "metadata": {
        "id": "2pWgZgotGE5a"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# animation function.  This is called sequentially\n",
        "def animate(i):\n",
        "    # Motion trail sizes. Defined in terms of indices. Length will vary with the time step, dt. E.g. 5 indices will span a lower distance if the time step is reduced.\n",
        "    trail1 = 6              # length of motion trail of weight 1 \n",
        "    trail2 = 8              # length of motion trail of weight 2\n",
        "    \n",
        "    dt = t[2]-t[1]          # time step\n",
        "    \n",
        "    line1.set_data(x1[i:max(1,i-trail1):-1], y1[i:max(1,i-trail1):-1])   # marker + line of first weight\n",
        "    line2.set_data(x2[i:max(1,i-trail2):-1], y2[i:max(1,i-trail2):-1])   # marker + line of the second weight\n",
        "    \n",
        "    line3.set_data([x1[i], x2[i]], [y1[i], y2[i]])       # line connecting weight 2 to weight 1\n",
        "    line4.set_data([x1[i], 0], [y1[i],0])                # line connecting origin to weight 1\n",
        "    \n",
        "    line5.set_data([0, 0], [0, 0])\n",
        "    time_string.set_text(time_template % (i*dt))\n",
        "    return  line3, line4,line5,line1, line2, time_string\n",
        "\n",
        "\n",
        "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
        "                               frames=Nt, interval=1000*(t[2]-t[1])*0.8, blit=True)"
      ],
      "metadata": {
        "id": "ovAiEGd-GFFZ"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import HTML\n",
        "HTML(anim.to_html5_video())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 309
        },
        "id": "_Z-zgRrWIrRe",
        "outputId": "d7dfc8bb-a759-463d-9fa5-38466e6e9cbb"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAMvhW1kYXQAAAKuBgX//6rcRem9\n",
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              "<IPython.core.display.HTML object>"
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          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ENnpSZtADnb4"
      },
      "source": [
        "### Neural Network Prediction\n",
        "\n",
        "Now let's show a neural network part of the data from this harmonic oscillator and have it try to predict the rest."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iS_fKzAIDnb-"
      },
      "outputs": [],
      "source": [
        ""
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Teaching Physics to a Neural Network - Coupled Pendulum",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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