Randomise_Orbital_Simulations_160924.ipynb

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      "metadata": {
        "id": "view-in-github",
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        "<a href=\"https://colab.research.google.com/github/liamhall64/Habitable-Exomoons/blob/main/Randomise_Orbital_Simulations_160924.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "code",
      "source": [
        "!pip install pytransit celerite emcee corner"
      ],
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        "id": "7veXbo1Z-WKM",
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          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from pytransit import QuadraticModel\n",
        "# from pytransit import UniformModel\n",
        "from scipy.optimize import minimize\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from astropy import units as u\n",
        "from astropy import constants as const"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KwuYBf-Zo52b",
        "outputId": "ee99301c-a2a2-4cf0-cbbb-09e58ed48500"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/pytools/persistent_dict.py:63: RecommendedHashNotFoundWarning: Unable to import recommended hash 'siphash24.siphash13', falling back to 'hashlib.sha256'. Run 'python3 -m pip install siphash24' to install the recommended hash.\n",
            "  warn(\"Unable to import recommended hash 'siphash24.siphash13', \"\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Orbital Simulations\n",
        "######Randomising the angle at which the Moon is observed around the Earth"
      ],
      "metadata": {
        "id": "tHbOcCqi-Aty"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def barycentre(Mp, Mm, dpm, moon_period):\n",
        "  dp = dpm/(1+(Mp/Mm)) # DIST BARYCENTRE TO PLANET\n",
        "  dm = dpm/(1+(Mm/Mp)) # DIST BARYCENTRE TO MOON\n",
        "  print(f'Planet-barycentre distance = {dp:.3f}\\nMoon-barycentre distance = {dm:.3f}')\n",
        "  return(dp, dm)"
      ],
      "metadata": {
        "id": "PKcdXW1N-QKu"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# PARAMETERS\n",
        "Mp = 1*const.M_earth\n",
        "Mm = 0.0123*const.M_earth\n",
        "dpm = 0.3844e9*u.m\n",
        "moon_period = 27.322*u.day\n",
        "P = 1*u.year\n",
        "P = P.to(u.day)\n",
        "\n",
        "dp, dm = barycentre(Mp, Mm, dpm, moon_period)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1aCQBvXuAfgW",
        "outputId": "ea4fe73e-e605-4925-bb14-fe767d8ecf3d"
      },
      "execution_count": 109,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Planet-barycentre distance = 4670670.750 m\n",
            "Moon-barycentre distance = 379729329.250 m\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "transits = 2 # HOW MANY TRANSITS YOU WANT TO OBSERVE\n",
        "t = np.linspace(0, transits*P, 1000)\n",
        "\n",
        "# BARYCENTRE\n",
        "ab = 1*const.au # SEPARATION\n",
        "Pb = P.to(u.s)  # PERIOD\n",
        "wb = (2*np.pi/Pb) *u.rad # ANGULAR FREQ\n",
        "alphab = wb*t\n",
        "xb = ab*np.sin(alphab)\n",
        "\n",
        "\n",
        "\n",
        "for _ in range(50):\n",
        "  angle = np.random.uniform(0, 2*np.pi)\n",
        "\n",
        "  # PLANET\n",
        "  wp = 2*np.pi/moon_period *u.rad\n",
        "  alphap = wp*t + angle*u.rad\n",
        "  xp = dp * np.sin(alphap) + xb\n",
        "\n",
        "  # MOON\n",
        "  wm = 2*np.pi/moon_period *u.rad\n",
        "  alpham = wm*t + np.pi*u.rad + angle*u.rad\n",
        "  xm = dm*np.sin(alpham) + xb\n",
        "\n",
        "\n",
        "plt.plot(t/P, xb/ab.to(u.m), label = 'Barycentre')\n",
        "plt.plot(t/P, xp/ab.to(u.m), label = 'Planet')\n",
        "plt.plot(t/P, xm/ab.to(u.m), label = 'Moon')\n",
        "\n",
        "plt.title('Position of a planet, moon and barycentre')\n",
        "plt.xlabel('Time (Years)')\n",
        "plt.ylabel('Position W.R.T line of sight (AU)')\n",
        "plt.grid(True)\n",
        "plt.legend()\n",
        "\n",
        "#plt.ylim(-2e8, 2e8)\n",
        "plt.show()\n",
        "\n",
        "# TEST TO SEE IF THE ANGLES ARE RANDOMISED\n",
        "i = 59 # RANDOM VALUE TO TEST\n",
        "alphap[i], alpham[i]\n",
        "a = alphap[i]-alpham[i]\n",
        "print(f'\\nStarting angle of planet and moon = {alphap[i].to(u.deg), alpham[i].to(u.deg)}\\nAngle difference = {a.to(u.deg):.0f}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 524
        },
        "id": "q3CIn1N3FA4O",
        "outputId": "6dc6b391-c555-4c3b-8b95-e3541d7ac646"
      },
      "execution_count": 143,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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jxpU7HjezH3u466672Lp1K88++yzR0dF4enpiMpkYOnRohdmvPxNVSq1Wc++99zJ//nw++eQTtmzZwpkzZ/i///u/GmUp3d8zzzxj+XD3T//8kGeL1/KfbSrN8c033xAQEFBu/euHShFsQ7yiQp0TEhKCyWQiOTnZ8gkbIDs7m5ycHMsdYaVuueUWbrnlFt544w2+//577rvvPpYsWcJDDz1U4farK8L+meXYsWPlliclJVm+f7P8/Pxwd3evdD8qlarc2QxrLFu2jBYtWrB8+fIybS79BGyN0k/S1z//+PHjAJXeiXfw4EGOHz/O4sWLGT9+vGV5fHx8DVvwP+Hh4fz999/07Nmzwj+G16vJ8bWHmhzP2nh/gfm9MGHCBN577z3LsqKiohsemLU0V3JycplLjefPn6/RGZPSMyTXO378uOW9dfnyZdauXcvMmTOZPn16lc+rzvjx43nvvff4/fff+euvv/Dz8ytT8ISHhwNw6NAh4uLiKtxGaVu1Wm2l69yImr5nS7P6+/vbNIdQOXEZTqhzhg8fDsC8efPKLJ87dy4AI0aMAMy/SP/56Sw6OhqgyktxpWOUWPOHYvjw4ezcuZNt27ZZluXn5/PFF18QGhpKZGRktduojlqtZvDgwfz2229lLj9kZ2fz/fff06tXL7y9vW9ou1D2E+yOHTvKtKU6Z86c4ZdffrE8zs3N5euvvyY6OrrCT7SV7VeW5XK3X9fEXXfdhdFo5LXXXiv3PYPBUOZYenh4KDo6e02OZ228v0oz/fNn5cMPPyw3PIO14uLi0Gq1fPjhh2W2+8+f2er8+uuvZfr47Ny5kx07djBs2DBLbih/Fqam+wGIiooiKiqKL7/8kp9//plx48aVOQPTqVMnwsLCmDdvXrn3T+n+/f396devH59//jlnz54tt49/Dq9grZq+Z4cMGYK3tzdvvvlmhf01bzSHUDlxZkmoczp27MiECRP44osvyMnJoW/fvuzcuZPFixczevRo+vfvD5j743zyySeMGTOG8PBwrl69yvz58/H29rYUXBWJjY0F4KWXXmLcuHFotVpuvfXWCgd6e+GFF/jhhx8YNmwYjz/+OA0bNmTx4sWkpaXx888/22y079dff534+Hh69erFo48+ikaj4fPPP6e4uJh33nnnhrY5cuRIli9fzpgxYxgxYgRpaWl89tlnREZGkpeXZ9U2WrVqxYMPPsiuXbto0qQJCxYsIDs7m4ULF1b6nDZt2hAeHs4zzzzD6dOn8fb25ueff67RGYd/6tu3L//617+YPXs2+/btY/DgwWi1WpKTk1m6dCn//e9/GTt2LGA+vp9++imvv/46ERER+Pv7W8bxKj1jUVV/K1uw9njW1vtr5MiRfPPNN/j4+BAZGcm2bdv4+++/adSo0Q1tr3QsrNmzZzNy5EiGDx/O3r17+euvv2jcuLHV24mIiKBXr1488sgjFBcXM2/ePBo1asRzzz0HmG8o6NOnD++88w56vZ5mzZqxZs0ay3hsNTV+/HieeeYZgHKX4FQqFZ9++im33nor0dHRTJo0icDAQJKSkjh8+DCrV68GzP0te/XqRYcOHZg8eTItWrQgOzubbdu2cerUKfbv31/jXFW9Zyvi7e3Np59+yv3330+nTp0YN24cfn5+ZGZm8ueff9KzZ08++uijGucQqlD7N+AJ9Vll4yz9k16vl2fOnCmHhYXJWq1WDgoKkqdNm1bmdt3ExET5nnvukYODg2WdTif7+/vLI0eOlHfv3l1mW/xj6ABZluXXXntNbtasmaxSqcoMI/DPoQNkWZZTUlLksWPHyr6+vrKrq6vctWtX+Y8//iizTumt3UuXLi2zvPQW6etvK69MYmKiPGTIENnT01N2d3eX+/fvL2/durXC7VkzdIDJZJLffPNNOSQkRNbpdHJMTIz8xx9/yBMmTJBDQkKqfX5ISIg8YsQIefXq1XJUVJSs0+nkNm3alGtjRUMHHDlyRI6Li5M9PT3lxo0by5MnT5b3799f7rWYMGGC7OHhUW7fpbeB/9MXX3whx8bGym5ubrKXl5fcoUMH+bnnnpPPnDljWScrK0seMWKE7OXlJQNlbslu3LixfMstt1Tb9r59+8rt2rWr9DX5J0D+z3/+U2aZNcdTlmvn/XX58mV50qRJcuPGjWVPT095yJAhclJSUrn3e2U/nxUdY6PRKM+cOVMODAyU3dzc5H79+smHDh2q8Gfon65/H7/33ntyUFCQrNPp5N69e8v79+8vs+6pU6fkMWPGyL6+vrKPj4985513ymfOnCn3c136njl//nyl+z179qysVqvlVq1aVbrO5s2b5UGDBsleXl6yh4eHHBUVJX/44Ydl1klJSZHHjx8vBwQEyFqtVm7WrJk8cuRIedmyZZZ1avJaVvaere735fr16+UhQ4bIPj4+squrqxweHi5PnDix3O9A4eZJsqxAjz1BEOq80NBQ2rdvzx9//KF0FJs4cuQI7dq1448//rBcyhXqlwsXLhAYGMj06dN55ZVXlI4jOBDRZ0kQhHph/fr1dO/eXRRK9diiRYswGo3cf//9SkcRHIw4syQIQoWc7cySUH+tW7eOI0eO8Morr9C/f3+r5jcUhOuJDt6CIAiCU5s1axZbt26lZ8+efPjhh0rHERyQOLMkCIIgCIJQBdFnSRAEQRAEoQqiWBIEQRAEQaiC6LNkAyaTiTNnzuDl5aX4VAuCIAiCIFhHlmWuXr1K06ZNqxwEVhRLNnDmzJkbmrtLEARBEATlnTx5kubNm1f6fVEs2YCXlxdgfrFvZA6vyuj1etasWWOZ2sEZOXsbRfscn7O3UbTP8Tl7G+3ZvtzcXIKCgix/xysjiiUbKL305u3tbfNiyd3dHW9vb6f8AQDnb6Non+Nz9jaK9jk+Z29jbbSvui40ooO3IAiCIAhCFUSxJAiCIAiCUAVRLAmCIAiCIFRB9FkSBEEQ6hWj0Yher1c6hs3o9Xo0Gg1FRUUYjUal49jczbRPq9WiVqtvOoMolgRBEIR6QZZlsrKyyMnJUTqKTcmyTEBAACdPnnTKsf5utn2+vr4EBATc1GsjiiVBEAShXigtlPz9/XF3d3eawsJkMpGXl4enp2eVAys6qhttnyzLFBQUcO7cOQACAwNvOIMolgRBEASnZzQaLYVSo0aNlI5jUyaTiZKSElxdXZ22WLrR9rm5uQFw7tw5/P39b/iSnPO9qoIgCILwDwaDAQB3d3eFkwi1rfSY30w/NVEsCYIgCE5PlmWg+sEHBedji2MuiiVBEARBEIQqOFSxtHHjRm699VaaNm2KJEn8+uuv1T4nISGBTp06odPpiIiIYNGiReXW+fjjjwkNDcXV1ZVu3bqxc+dO24cXBEEQBMEhOVSxlJ+fT8eOHfn444+tWj8tLY0RI0bQv39/9u3bx5NPPslDDz3E6tWrLev8+OOPTJ06lRkzZpCYmEjHjh0ZMmSIpfe8IAiCIChp4sSJSJJk+WrUqBFDhw7lwIEDSkeziYkTJzJ69GilY1TJoYqlYcOG8frrrzNmzBir1v/ss88ICwvjvffeo23btkyZMoWxY8fy/vvvW9aZO3cukydPZtKkSURGRvLZZ5/h7u7OggUL7NUMQRCEOsNgMpBryiVPn6d0FKEKQ4cO5ezZs5w9e5a1a9ei0WgYOXLkDW+vpKTEhulqh5IDiTr10AHbtm0jLi6uzLIhQ4bw5JNPAuY3y549e5g2bZrl+yqViri4OLZt21bpdouLiykuLrY8zs3NBcwH0pYHs3RbzjTSrGwycWR3PMmHf+ZqfjLIxZQYVSw7/QMhbW4l5pbRaLQuSse0GWc8htdz9vaBc7Yx+1wmPyS8xbbC/aRpCjFI8M7SdwiUfBjZYjQTOk3GXescd42VHjeDwYAsy5hMJkwmk8KpakaWZVxcXPD39wfA39+f5557jr59+5KdnU3jxo2ZMWMGf/31F6dOnSIgIIB7772XV155Ba1WC8DMmTP57bffePTRR5k9ezYZGRksWLCAp59+mlOnTqHT6Sz7GzNmDF5eXnz99dcA/P7777z++uscPHgQT09PevXqxfLlywHz38OXX36ZJUuWkJOTQ/v27Zk9ezb9+vUDYNGiRUydOpUffviBqVOncvLkSXr27MmCBQsIDAxk5syZLF68GPhfR+y1a9cSGhpKeHg433//PZ9++ik7d+7kk08+YeLEiXz55Ze8//77pKWlERoaymOPPcYjjzxS6etnMpmQZRm9Xl9u6ABrf66duljKysqiSZMmZZY1adKE3NxcCgsLuXz5MkajscJ1kpKSKt3u7NmzmTlzZrnla9asscttqfHx8TbfZm0zySb2Z68ixbSVI64yJToJdNevcRgp8xCtkt8k3NSBzk3uwEXtPEWTMxzDqjh7+8A52qgvzOXUma9Z5X2K01oNmP+OopJlTJLEWfkK81MWs+zYd4zQjaGNV0dlA9vQ1q1bCQgIIC8vz3JWRZZlivS1Xzi5alU1ukNLr9djMBgsH8zz8vJYuHAhLVq0QKvVcvXqVby8vPjwww8JDAzk8OHDPPnkk2i1Wp544gnAXNScOHGCn376icWLF6NSqQgPD+eJJ57gxx9/tFwGO3/+PCtXrmT58uXk5uayevVq7rvvPp5++mk++ugjSkpKiI+Pt2R54oknSEpKYv78+QQGBvLHH38wfPhwtmzZQnh4OEVFRRQUFPDOO+/wySefoFKp+Ne//sWTTz7J/PnzmTx5MgcPHiQ3N9fSxaZBgwZkZWUB8MILL/D666/z4YcfotPp+PLLL5kxYwbvvPMOUVFRHDhwgCeeeAKVSsU999xT4etXUlJCYWEhGzdutAwhUaqgoMCqY+DUxZK9TJs2jalTp1oe5+bmEhQUxODBg/H29rbZfvR6PfHx8QwaNMjy6cARJZ7axcx1j3PStfRsnISHSUVjtS86tRsFhXnkqfPJURk45ipxjMPsyDnKs7EzGBx5q6LZb5azHMPKOHv7wHnauPPvxfx68m1WNXIFNDQwQH+pJbE+XSg6cwVftwKSr25ihVcRZ7TwveEn7tNf4KlR7ykd/aaUHr8ePXpw9uxZPD09cXV1BaCgxEDM27VfBB96dRDuLtb/+dVqtaxevZrmzZsD5v67gYGBrFixAl9fX2RZ5plnnsHLywtJkmjfvj2nTp3ixx9/5JVXXgFAp9NRUlLCd999h5+fn2Xb9957Lz/++CPjx48H4KuvviI4OJjhw4cjSRL//e9/ufvuu5k9e7blOT179gQgMzOT7777jvT0dJo2bQpAx44d2bBhA8uWLeONN97A1dUVvV7PF198QXh4OACPPfYYr732Gt7e3nh7e+Pl5YXRaKRly5aWfeTlmS8LP/XUU9x7772WgnDkyJHMmTPHUhh16NCB9PR0vvnmG/71r39V+PoVFRXh5uZGnz59LMe+VGnRVx2nLpYCAgLIzs4usyw7Oxtvb2/c3NxQq9Wo1eoK1wkICKh0uzqdrswpy1JardYuv0zttd3a8EPiYt45MAeDBryMJnqbgrlv0Gt0CI5FkiT0ej0rV65k+PDhnM7J4Ns/XybBeIBsDbywbwZHLhzkmQHTHX5sFEc+htZw9vaBY7dxxeInmF+ymnQvV1Qy3NqwPy8Oewt3rbvlZ7D/8OEM1mrpsW0FCxJfJsETvslfT8k343hp4lIkBx8ZWqPRIEkSKpXKMgq0UqNdX5/BGpIk0b9/fz799FMALl++zCeffMKIESPYuXMnQUFBLF++nK+++oqUlBTy8vIwGAx4e3tb9iNJEiEhIeWupDz88MN06dKFs2fP0qxZMxYvXszEiRMtl6v27dvH5MmTK8x7+PBhjEYjbdq0KbO8uLiYRo0aWdrp7u5ephBq2rQp586dK5Ot9Nhc/xoBdOnSxfL7v6CggJSUFCZPnlymMDIYDPj4+FT6mqpU5jN5Ff0MW/sz7dTFUvfu3Vm5cmWZZfHx8XTv3h0AFxcXYmNjWbt2reUUpMlkYu3atUyZMqW24zqdL7d+xH+TPwcJeubrmdjxdW7pObbS9UP9Inh54hLuPLSVhesn86e3iq9PLaNgTSEzhrxVi8kFwTnIJhNLFjzAZ6qdXHLR4mtyYU7cR3QL6l7pc2K638Z7nQbzyje3s1J7kh/Vx3H7cgxTH/rF4Qumf3LTqjkya4gi+60pDw8PIiIiLI+//PJLfHx8mD9/PsOGDePhhx/m1VdfZejQofj4+LBkyRLee++9ctv4p5iYGDp27MjXX3/N4MGDOXz4MH/++ef/sl6bLqQieXl5qNVq9uzZU64vkKenp+X//yxIJEmyDBJqTbuv3x/A/Pnz6datW5n1bnQaE2s5VLGUl5fHiRMnLI/T0tLYt28fDRs2JDg4mGnTpnH69GlLp7R///vffPTRRzz33HM88MADrFu3jp9++qnMG2Hq1KlMmDCBzp0707VrV+bNm0d+fj6TJk2q9fY5k5VHf+PD45+BJDHmioGHRyyjeXh7q57bun0PpgWupfE3w1jcwMCyrD9puiWQyT2fsHNqQXAui755lE/UuyhSqQnCl8V3L8fP3a/a57noXHnrwT/Rfz+OeMMRvnFJofHCB5nw4MJaSF17JEmq0eWwuqT0TExhYSHbtm0jKCiIF1980XJ2JSMjw+ptPfTQQ8ybN4/Tp08TFxdHUFCQ5XtRUVGsXbu2wr+JMTExGI1Gzp07R+/evW+4LS4uLhiNxmrXa9KkCU2bNiU1NZX77rvvhvd3IxzqY8Lu3buJiYkhJiYGMBc6MTExTJ8+HYCzZ8+SmZlpWT8sLIw///yT+Ph4OnbsyHvvvceXX37JkCH/+yRx9913M2fOHKZPn050dDT79u1j1apV5U5VCtZLuXiCV7e/jEmSGHZVz3/G/GF1oVTKp1EAD49fzb055scfJc9nR/oW24cVBCf10+9v8qlpE0UqFe2kAJbdu9qqQqmUJEm8d+8SuqnDMEoSC6QdrFkx146JhaoUFxeTlZVFVlYWR48e5bHHHiMvL49bb72ViIgITp06xZIlS0hJSeGDDz7gl19+sXrb9957L6dOnWL+/Pk88MADZb43Y8YMfvjhB2bMmMHRo0c5ePAgb7/9NgCtWrXivvvuY/z48Sxfvpy0tDR27tzJ7Nmzy5yUqE5oaCgHDhzg2LFjXLhwoco71GbOnMns2bP54IMPOH78OAcPHmThwoXMnWvf96ZDFUv9+vVDluVyX6Wjci9atIiEhIRyz9m7dy/FxcWkpKQwceLEctudMmUKGRkZFBcXs2PHjnKn9wTr6U16nvrtfgpVEFWkZ3Lfr2gSFH5D2/Ju6M+Dd/5B3zw9JknipbVTyC8WY8EIQnW27vuL989/R6FKRaTBm8X3/XFDQwFIksSH434kyOTBJbWaL7M+J+nAJjskFqqzatUqAgMDCQwMpFu3buzatYulS5fSr18/brvtNh555BEef/xxoqOj2bp1q6VjtzV8fHy444478PT0LDc4ZL9+/Vi6dCkrVqwgOjqaAQMGlJnlYuHChYwfP56nn36a1q1bM3r0aHbt2kVwcLDV+588eTKtW7emc+fO+Pn5sWVL5R+MH3roIb788ksWLlxIhw4d6Nu3L4sWLSIsLMzq/d0ISbb2wqFQqdzcXHx8fLhy5YrN74Yr7fzsKB1LZ/82le9z4vEympgVOIW4YZWPfQHWtXHPjhU8f+h5sjUaBqpbM+//ltkjul044jGsCWdvHzheGy/nXeTeJf04pYWWJRoW/18CXm4+la5vTfsyczK5+5eR5KlkbsuFVx7ajqtb+f4vdVFp+wYMGMCpU6cICwsrd0eUozOZTOTm5pbp0F1TAwcOpF27dnzwwQc2TnfzbrZ9RUVFpKWlVXjsrf377VBnloS6LSlzP8svrQHgDn14tYWStWK73cY9LgMBWG9IYsP+ldU8QxDqJ1mWefKnOzmlhcYGE7PjFlRZKFkr2DeYl7uYx5Zb4Q3ffi36dDqLy5cv88svv5CQkMB//vMfpePUWaJYEmzmrdWPUqSSaFsEj9z/nU23Pene/3JLgRaTJPHBjhcxGp1nNGVBsJVFG/5Lovo8GlnmEf/7aR0WY7Ntj2g/hkGesQB8pznEju2/2WzbgnJiYmKYOHEib7/9Nq1bt1Y6Tp0liiXBJpb9/RF7XHJRyzIPtnsOd3cvm25fpVbz2IAPcDOZOK4z8snPT9t0+4Lg6C7kn+fL1K8AGFnQkLtufcHm+3hz1GcEGnVc0KhZnPgKRoP40OLo0tPTuXLlCs8884zSUeo0USwJN62kuIilKZ8B0Evvx5Be99tlP1GtezFYZb6r7o/ctVy6fM4u+xEER/TiL5PJVUN4sYFHbvvKLvtw1bjyaq93UckymzxkFv74lF32Iwh1jSiWhJu2aPnzHHGVcDHJPDXyU7vu65k7PsXXKHNGq+LzZRUPbS8I9c3ujO1sM6YAcLf7EJo2b1nNM25cj1b9GaCJBODHwnVkncus5hmC4PhEsSTclNzci/yRZ55baYCmHeGBbap5xs3x9WzIbY2GArBGdYz01P123Z8gOIJ315kvufXNMzH2rrftvr9Zd3yJnwGytGre/V18aBGcnyiWhJuy6OcnSXNR42mUeX70h7Wyz8dHvIGfQcUFjZqvV4u+S0L9tvrwbxxRXUQjy9wa8hBal/LzVtqal5s39ze5C4B16pPsS95q930KgpJEsSTcsEvnTrNOvxuAQV7daezlXyv71Wl03Bk8DoC1Lmc4fnRXrexXEOqiL3aYzyQNztMweHjtTQk0cfhLRBWpMUgSHyY8X2v7FQQliGJJuGE//f48KToNbiaYOuKdWt33QwOfwc+o5pJGzS/rxS9qoX7aeCye4+qraGSZ4ZFP1epEt5JKxf+1eRxJltnpksPGI2tqbd+CUNtEsSTckKtXLrLeYD6rNMCzK77uDWp1/1qVltHBdwIQrztLxokDtbp/QagLvtzyJgC9CzT06Wefu1CrMqzvA/QudAHg0+2v1fr+BfM0Xw0bNlQ6htMTxZJwQ5b99jJHXLW4mGSeHjZbkQz/6v8MvkYV2RoNy9a+qEgGQVDKwZOJ7FOdB2BwyMRaPat0vTERj6CSZQ6pc9ieIuaNs4eJEyciSRKSJOHi4kJERASzZs3CYDAomumf88g5M1EsCTVWXJRPQkECAL107fDzrJ2+Sv+kU+sY6T8EgL/VKWRnnVQkhyAo4cu1M5AliS4FMHzoY4rlGDjwQXoVmP+UfLpxpmI5nN3QoUM5e/YsycnJPP3007z66qu8++67SseqN0SxJNTYL7+9TqKbBrUsM3XoW4pmmTJoOl5GOKXVsORP249YLAh1UU7eRXaY0gDo7X8rKrVasSySSsXQIPMlwL1SFkfPHlQsizPT6XQEBAQQEhLCI488QlxcHCtWrCi3XkpKCqNGjaJJkyZ4enrSpUsX/v777zLrhIaG8uabb/LAAw/g5eVFcHAwX3zxRZl1Tp48yV133YWvry8NGzZk1KhRpKenA/Dqq6+yePFifvvtN8sZr4SEBHs1vU4QxZJQI7LJRMLFPwDoqgolpGGYonk8dJ4M9OoGwBZDIoX5uYrmEYTasOCvmeSrJQL1Ju4d+YrScRgx7CluKTAiSxKfrp+ldBzryTKU5Nf+lyzfdHQ3NzdKSkrKLc/Ly2P48OGsXbuWvXv3MnToUG699VYyM8sOHvree+/RuXNn9u7dy6OPPsojjzzCsWPHANDr9QwZMgQvLy82bdrEli1b8PT0ZOjQoZSUlPDMM89w1113Wc52nT17lh49etx0m+oyjdIBBMeycfMStrnLgMS/+yj/SxpgypDX+PPnQRx11fDbX28zbuwbSkcSBLvamJMALtBd3Radzk3pOKg0Gnp49mO7aRPbipO4WpSLl6u30rGqpy+AN5vW/n5fPAMuHjf0VFmWWbt2LatXr+axx8pffu3YsSMdO3a0PH7ttdf45ZdfWLFiBVOmTLEsHz58OI8++igAzz//PO+//z7r16+ndevW/Pjjj5hMJr788kskSQJg4cKF+Pr6kpCQwODBg3Fzc6O4uJiAgIAbaoejEWeWhBr58/AnmCSJtgZPOoV2UzoOAE28A+kqhQCw9vwfCqcRBPtauflrUlxktLLM+LhXlY5jcfuwGYSUGChSwZfr5ygdx+n88ccfeHp64urqyrBhw7j77rt59dVXy62Xl5fHM888Q9u2bfH19cXT05OjR4+WO7MUFRVl+b8kSQQEBHDunHm+zf3793PixAm8vLzw9PTE09OThg0bUlRUREpKil3bWVeJM0uC1TIyjrBJdxlQMbbNA0rHKePBXtPYsuURdroZ2bzjF3p1G6N0JEGwi5WHvwBXiC3xITyovdJxLHwaN6GHMZgMzrDqzB88Kc+0nJWos7Tu5rM8Suy3hvr378+nn36Ki4sLTZs2RaOp+M/3M888Q3x8PHPmzCEiIgI3NzfGjh1b7pKdVqst81iSJEwmE2AuuGJjY/nuu+/Kbd/Pz6/G2Z2BKJYEq32/dgZ5ahWBBhVjezyodJwyukT0ov16dw65FPDzvv+KYklwSllZaex2MX9gGdZ2ktJxyrm1+/P8mvgYZzR61h1ZycB2I5SOVDVJuuHLYbXNw8ODiIiIatfbsmULEydOZMwY8+/AvLw8S8dsa3Xq1Ikff/wRf39/vL0rvpzq4uKC0Wis0XYdmbgMJ1hFry9hg+kIAAN9+qCS6t5bZ3SL+wDY6nKes+fFTOiC8/kp/g3yVSr8DDC6V906uwvQoeMAul0bpPLn3Z8onKZ+atmyJcuXL2ffvn3s37+fe++913LGyFr33XcfjRs3ZtSoUWzatIm0tDQSEhJ4/PHHOXXqFGC+o+7AgQMcO3aMCxcuoNfr7dGcOqPu/cUT6qQl8e9xWqvC02ji4SEzlI5ToTv7/YemeihQqfh2jRjvRXAussnEnvwdAHRz7VAnP7AAdPEzj32WaMqgSF+ocJr6Z+7cuTRo0IAePXpw6623MmTIEDp16lSjbbi7u7Nx40aCg4O5/fbbadu2LQ8++CBFRUWWM02TJ0+mdevWdO7cGT8/P7Zs2WKP5tQZ4jKcYJV1p34FHXQzBtLAq7HScSqkUqvpoevIMtN+Nhfs4lmlAwmCDe3Y9Tv7XM13ot7X5zml41RqzJDn+HrpCrI1ar5L+IAHB4m5G2/WokWLKv3exIkTGT9+PLm55mFTQkNDWbduXZl1/vOf/5R5XNFluX379pV5HBAQwOLFiyvdr5+fH2vW1J/5AOvmRxOhTjlx6gh7XfIBuK3jIwqnqdr/9X8RrSyT6iITv2up0nEEwWbW7DXfiRqhd6V9ULTScSrl5d2Qznrz7eTr039VNowg2IgoloRqfZPwJkZJonWxxICudygdp0rhzSPpXGS+02T5gS+qWVsQHENBXi571OZ+eP2aDlM4TfUGtTP3pzqkvUrm+VSF0wjCzRPFklAlk2xia9F+AHp41I1xlarTv5n5LpDdqrNcLrikcBpBuHl/xc8j1UWDVpaZ0P8ppeNUa0DPe2lVLGOUJL79W5mJtgXBlkSxJFTp9x3fkqUFD5OJe+NeUjqOVe4Y/CQhJUaKVBJf/y0GxxMc39azfwLQUQ7E162BwmmqJ6lUxOg6AJB4dbfCaQTh5oliSajSn0e+BaBbkRcBTUKVDWMlF50bMbJ5RO8t5/6uZm1BqNsuZJ9it+4qACPa3qdwGuvdeot5Ko7jLnqSUhMVTiMIN0cUS0KlCksK2C+ZR7e9JWCowmlqJq69edDMJE0BGRfq5/D8gnNYsf49LmnUeBthVFfHKZY6tu5Bq2IVsiTx85Z5SscRhJsiiiWhUku2fE6BSiJQb+TWuCeUjlMjfW65nfZFJmRJ4puE95SOIwg3LPHSBgBi1GFoVdpq1q5bot3NE7ruL9inbBBBuEmiWBIqtS71VwBi9Y3x9Kr7/SSuJ6lURKvbALA1Z7vCaQThxmSmH2GPWzEAozo9pHCamruj55MAJOlMHEjarGwYQbgJolgSKnQ5/xKH1RcB6BFyu8JpbszQTv9GK8uc1OrZl7lL6TiCUGN/bJpLnkpFI4PEwPYjlY5TY5FhnYgo0SBLEr9v/0jpOIJwwxyuWPr4448JDQ3F1dWVbt26sXPnzkrX7devH5IklfsaMeJ/kztOnDix3PeHDnWs/jn28O2G/6KXJMJLDAwe8LDScW5IVPRAOhfIACzZJn5RC45n/1Xz77dY17Z1dnqT6nTyigXgUPEh5BrOUSYIdYVD/fT9+OOPTJ06lRkzZpCYmEjHjh0ZMmQI586dq3D95cuXc/bsWcvXoUOHUKvV3HnnnWXWGzp0aJn1fvjhh9poTp226Ww8ANGGZuhc3RVOc2MklYp2rlEAJOYdUDiNINTM8aRd7HEzz+p+Z7dHFU5z4+7q/SQAh3Ww98BaZcM4qNIP9f/+97/Lfe8///kParWaRx913PeII3CoYmnu3LlMnjyZSZMmERkZyWeffYa7uzsLFiyocP2GDRsSEBBg+YqPj8fd3b1csaTT6cqs16CBY/XPsbXL+Zc4rjbPM9Qz4i6F09ycwV0fRSPLnNUY2J+xR+k4gmC1lTs/plilIsCgolt4H6Xj3LDWzdrTokSLLEn8vbfi39VC9YKCgliyZAmFhf+bnLioqIjvv/+e4OBgBZPVDw4zkW5JSQl79uxh2rRplmUqlYq4uDi2bdtm1Ta++uorxo0bh4eHR5nlCQkJ+Pv706BBAwYMGMDrr79Oo0aNKt1OcXExxcXFlselExjq9Xr0en1NmlWl0m3ZcpvW+GHjJxgliRYlBnp0v8eu+7d3GyNa30LHzRJ73GD5to+IbFq7U6AodQxri7O3D5Rr496CveAGnV0iMRgMdttPbbQvyjOK1JI9HCk+XOuvY+n+DAYDsixjMpkwOdjlQFmWiYmJITU1lWXLlnHffeYhJJYtW0ZwcDChoaGW9QoLC3nuuef48ccfyc3NpXPnzrz33nt06dLFsr0NGzbw/PPPs3//fho2bMj48eN57bXX0GjMJcGAAQPo0KEDrq6ufPXVV7i4uPCvf/2LGTNm1HrbS9tV+u+NHDuTyYQsy+j1etRqdZnvWft+dJhi6cKFCxiNRpo0aVJmeZMmTUhKSqr2+Tt37uTQoUN89dVXZZYPHTqU22+/nbCwMFJSUnjxxRcZNmwY27ZtK/eilpo9ezYzZ84st3zNmjW4u9v+klV8fLzNt1mVTWdXghu0KmzI32vXVf8EG7BnG4NLgtnjlsme3H2sXLnSbvupSm0fw9rm7O2D2m1jTt4ZDrgaAYlgVedaed/as32BckdgDwd1Jpb8MB9vn2Z221dltm7dSkBAAHl5eZSUlADmP75FxqJaz+KqdkWSJKvX1+v1GAwG7rnnHr766ituvfVWAL788kvGjRvH5s3mOw2vXr3KCy+8wIoVK/j4448JCgrigw8+YOjQoSQmJtKgQQPOnDnDyJEjueeee/joo49ITk7miSeeQJIkXnjhBcBcWC5evJj//Oc/xMfHs2vXLh599FGio6Pp37+/7V8QK129evWGnldSUkJhYSEbN24s98GjoKDAqm04TLF0s7766is6dOhA165dyywfN26c5f8dOnQgKiqK8PBwEhISGDhwYIXbmjZtGlOnTrU8zs3NJSgoiMGDB+Pt7W2zzHq9nvj4eAYNGoRWWzvjqxSWFPDaTy8BEt1CbmX48OF23V9ttDEgUcuvR58jQ2cgsmsrQhtH2GU/FVHiGNYmZ28fKNPG93/8NwZJIrRE4qF7H7frvmqjfbIss/ybRWRrTOSQyLjhk+2yn4qUtq9Hjx6cPXsWT09PXF1dASjQF9BnSe1f4tw2bhvuWus/WGu1WjQaDQ8++CCzZs3i8uXLAOzYsYOffvqJ7dvNw6OoVCoWLFjAggULuOMO86TnCxcupEWLFixdupRnnnmGd955h6CgID7//HMkSaJz587k5OTwwgsv8Prrr6NSqdBoNHTs2JE33ngDgJiYGBYsWMD27dsZNWqUjV+N6smyzNWrV/Hy8qpRkVmqqKgINzc3+vTpYzn2pUqvDFXHYYqlxo0bo1aryc7OLrM8OzubgICAKp+bn5/PkiVLmDVrVrX7adGiBY0bN+bEiROVFks6nQ6dTlduuVartcsvG3tttyLLtn9PsUoiQG9g2IB/19p+7dnGrl2G0m7fMxxyVbN8+xc8P+Z9u+ynKrV5DJXg7O2D2m3jgfy94ArRurZO8TMI0NGlFWtMSRzN26PIe0Wj0SBJEiqVCpXK3F239N/adn0Ga5Teqd2kSRNGjBjB119/jSzLjBgxAn9/f8t6qamp6PV6evfubdm+Tqeja9euJCUloVKpSEpKonv37mWunPTq1Yu8vDzOnDlj6f8UFRVVJmNgYCDnz59X5DUrvfRWevxqSqVSIUlShe9xa9+LDlMsubi4EBsby9q1axk9ejRgfgHXrl3LlClTqnzu0qVLKS4u5v/+7/+q3c+pU6e4ePEigYGBtojtcBJO/AoqiNL74uHlq3Qcm5BUKtpJYRwik90XrevfJghKOXn2BId1JYDECAcciLIyQ6PvZ03iS+xzLSHrTCoBTVsoHQk3jRs77t2hyH5v1AMPPGD5m/fxxx/bKlI5/ywiJElyuL5etuRQd8NNnTqV+fPns3jxYo4ePcojjzxCfn4+kyZNAmD8+PFlOoCX+uqrrxg9enS5Ttt5eXk8++yzbN++nfT0dNauXcuoUaOIiIhgyJAhtdKmusRoMnJQNs8FF+2n3HVpe+je0nwHZLImj5yCSwqnEYTKLd/4AQZJIqgEbmk/SOk4NjOg3Qi8jXBVrWL1Rvv9ka8JSZJw17rX+teNXEoqNXToUEpKStDr9eX+ToWHh+Pi4sKWLVssy/R6Pbt27SIyMhKAtm3bsm3bNkunaYAtW7bg5eVF8+bNbziXs3OoYunuu+9mzpw5TJ8+nejoaPbt28eqVassnb4zMzM5e/ZsmeccO3aMzZs38+CDD5bbnlqt5sCBA9x22220atWKBx98kNjYWDZt2lThZTZnt27/Cq6qwdNoYnjfqs/WOZq+ve4lqMSIUZL4ZfOXSscRhErtzTGf/YzShCucxLbUKjXt1UEAHLi0SeE0jkutVnP06FGOHDlS7iYkDw8PHnnkEZ599llWrVrFkSNHmDx5MgUFBZa/gY8++ignT57kscceIykpid9++40ZM2YwdepUxS5LOgKHuQxXasqUKZVedktISCi3rHXr1mUq6Ou5ubmxevVqW8ZzaOsOmgfjbFfiSiO/pgqnsS2N1oU2psac5DI7M1czieeUjiQI5Vy+eoFDLoWAxMC29ygdx+YGthrL1uPvc8DlKlevXMLLp6HSkRxSVTcSvfXWW5hMJu6//36uXr1K586dWb16tWX8wGbNmrFy5UqeffZZOnbsSMOGDXnwwQd5+eWXayu+Q3K4Ykmwn6PFx8EF2nhGKx3FLmKaxhF/aSlHpWxMRiOqSoaGEASl/LzxE4pVEoF6EwO7jFU6js2NjL2bd5LmkqXV8PemBYwZ+YzSkRzCokWLqvz+L7/8Yrmry9XVlQ8++IAPPvig0vX79u1b5VRhFZ14+PXXX62J6rTEOTcBgIzsFFK15vEnBsVMUDiNfYzo/W9cTSYuaiQ27vtN6TiCUM72s+bpQDqYmjhlMe/u4kFbk/ls0u5TfymcRhCsJ4olAYAVWz9HliRalMh0bOe4UytUpaGvP21LzGNsrD/8k8JpBKGsEn0xB9UXAbilmfNO5t0toB8AR1RnMRmNyoYRBCuJYkkAYP/5rQC0lpz7boi2Hh0BOFJU/ajvglCb/trzIwUqiUYGI8P61N6gjbXtzt6PoJJlTujUbN+9Quk4gmAVUSwJ6PUlHNWYR4TtEuy8n2gBBsXcD0Cyi4Ez5zMUTiMI/7P+2HIA2pd44OnlvJN5N/EOpKXefIY34cgPCqcRBOuIYklgzc4fyFWr8DCZGN7beQbBq0jndv0JLpExShIrtnymdBxBsDhsSAMg0ruzwknsr4NnFADHio/V2j5Lxzaq7O5owXnZ4piLYklg8/FfAGhb4omHm6fCaeyvtWQeFuHAuS3VrCkItePgyb1kaUxoZJnBXZ33Elyp4Z0nAnBIZ+TkqeO1sk+Nxnzzt7UTpwrOo/SY38w0O2LoAIFkfSroINInRukotaJT8zjis7/hmPoiRoMRtcb57joSHMuKHeaBUtsXQUTLTgqnsb/OEb3x2wjnNRJ/bf2ch+96z+77VKvV+Pr6cu7cOQDc3W9uJO26xGQyUVJSQlFRkVMOLHmj7ZNlmYKCAs6dO4evr2+5QTxrQhRL9VzGqSROuJgAiWFdyo9y7oxu7fUQc5d9zTmNis2JK+jbdYzSkYR6bn/ObtBCa7VzjdpdGUmSaKcKIoGTHLq0tdb2WzrpemnB5CxkWaawsBA3NzenKQCvd7Pt8/X1tRz7GyWKpXpu9bYvMUoSgXpoH95F6Ti1wsezIRF6HUddSthy+CdRLAmKyi28wnFNPiBxS8TtSsepNd1DhpJwcj6HtVcw6PVobuISibUkSSIwMBB/f3/0er3d91db9Ho9GzdupE+fPjd1qamuupn2abXamzqjVEoUS/Xc0YvbwQ1aqZopHaVWRXq056g+kRPFR5WOItRzv+38BqMkEVRioG/Pu5WOU2tu6z6RuRlfcE6jZu2OJQzpdX+t7VutVtvkD2hdoVarMRgMuLq6OmWxVBfa53wXNwWrmYxGjqsvAdA5OE7hNLVrQJT5j9JRnZ6LF7IUTiPUZzvSzfNTtjH4oHVxVThN7fF086aN3h2ALcm/KhtGEKpxQ8VSZmYmmzZtYvXq1SQmJlJcXGzrXEIt2Jm4kkwXNZIsc+stzjnFSWV6Rg7B0yiTp1KxbuuXSscR6rFjhkwAWns7f8fuf2rveW2QWH2KwkkEoWpWF0vp6ek8//zzhISEEBYWRt++fRk2bBidO3fGx8eHQYMGsXTpUkwmkz3zCja09chSAMIMLjTy9FM4Te1Sq9S0khsBcOBsgrJhhHor5dxxsjQm1LJM35jauwxVVwyNGQ+YB4k9eS5V4TSCUDmriqXHH3+cjh07kpaWxuuvv86RI0e4cuUKJSUlZGVlsXLlSnr16sX06dOJiopi165d9s4t2EBywWEA2ri2VDiJMjo27gZAMmcVTiLUV3/sWARA62ITrdt0UzaMAqLb9ia0RMYkSazYNl/pOIJQKas6eHt4eJCamkqjRo3Kfc/f358BAwYwYMAAZsyYwapVqzh58iRdutSPO6scVUFeLkddCgE1vVqPUjqOIkZ2m8jC1X9xTCdx4vgeIlrFKh1JqGf2n9sKGoggEMkJx8exRls5kHSySDwvBokV6i6rfjpnz55dYaFUkaFDh3L77fXn9ldHtX7Lt1zUqNGZZAZF189b51sFRNLEIGGQJNbtWax0HKGeMckmjkkXAWgf0FfhNMqJbTYIgCTVJUyy6MYh1E3186OMwN7MVQBEGL1w1bopnEY5rVXNAUjK2a1wEqG+2X5sPblqcDeZGNT9AaXjKGZIz0l4mEzkqiU2HvhT6TiCUCGri6UGDRrQsGHDcl9hYWEMGTKE+Ph4e+YUbCzl2qSd7XyilQ2isC4h5iETkjWXMRoMCqcR6pO/9/8AQNtiDY39myucRjm+vn60KXYBYP2hpQqnEYSKWT0o5bx58ypcnpOTw549exg5ciTLli3j1ltvtVU2wU6yTqVw2NUEqBjS6T6l4yjqtm7jeT9zAekuGnbs/p0et9TPS5JC7TuSexBcIEJbP6Y4qUpL11bs4QhJ+UeUjiIIFbK6WJowoepxeKKjo5k9e7YolhzA2h2LKFSp8DZC5xY9lI6jqIYejQk16EjVlrDt6M+iWBJqRVFJISeuTXHSucVIpeMornurMSxJPkKySxF5RVfxdPVSOpIglGGzPksjR44kKSnJVpsT7OjIuU0AtMIflSS6rbV1bQVAcpH4VCvUjr8Tf6ZYJdHAYKR/93uUjqO43p3H4G8wopckVu78Qek4glCOzf5SFhcX4+LiYqvNCXYim0ykqMwzbscE1O+zSqX6tBkNwFGXIvKv5iiaRagfdiSvBKCl3g2da/29waKU1kVHmxJPAHakr1I4jSCUZ7Ni6auvviI6OtpWmxPs5PixHSTpzIf91i7jFU5TN8R1HI3OJHNJo2bj9u+VjiPUAymFxwFo4dZa4SR1RyvPDgAklaQpnEQQyrO6z9LUqVMrXH7lyhUSExM5fvw4GzdutFkwwT4S9i3BKEkEGFSE+dXPkbv/yUWrI8LoyWFVPokZaxjGo0pHEpxYcUkRJ7RFgESXiOFKx6kzekXeyZeHdpKpNZB15QwBPk2VjiQIFlYXS3v37q1wube3N4MGDWL58uWEhYXZLJhgH8eu7AE3aK1qpnSUOqWNV3sOF+0gVS8+1Qr2tW73MgpVEl5GE30736F0nDojJnoQLfcYSNZp+H3XN0yOe17pSIJgYXWxtH79envmEGqBbDJxXH0JUNOpWT+l49QpfSNv5+fEHRzRGcjJOYevr7/SkQQnteuEub9ShN4NnU70VyqlUqtpaWhIsi6XPac2MBlRLAl1h036LMmyzF9//cXYsWNtsTnBThIPriPDRY0ky9x6i+ivdL3e7QbjYZLJU6tYJ/otCXaUeq2/Urh7K4WT1D0Rvp0AOGE8rXASQSjrpoqltLQ0XnnlFYKDgxkzZgxFRUW2yiXYwcbDPwHQQq/BzztA4TR1i0aloaXBG4D9p9YqnEZwVsXFhSRrCwHoEi76K/1Tr6hxqGSZbI2JjIvikrhQd9S4WCouLua7775jwIABtG7dmjfffJOpU6dy7tw5/vjjD3tkFGzkWO4BAFpqQ5UNUke19ekIQKohQ+EkgrNK2LWMXLUKN5PMwC7iTPw/tYnsTssS82S6q3aJM7xC3WF1sbRnzx4effRRAgICmDdvHqNHj+bkyZOoVCqGDBmCt7e3PXMKN8loMJCsvQpA5+CBCqepmwZE3QlAks7IxUtZCqcRnNGeFHN/pXCDGzqtq8Jp6h5JpSLU2AiA/Wc3KZxGEP7H6mKpW7du6HQ6tm/fzq5du3j88cdp0qSJPbNV6OOPPyY0NBRXV1e6devGzp07K1130aJFSJJU5svVtewvKFmWmT59OoGBgbi5uREXF0dycrK9m1Hrtu9byTmNCo0sM7Tb/UrHqZO6te6Pj1GmSKUifvvXSscRnFBaaX8lNzFsR2VaNewMwAnjWYWTCML/WF0sDRw4kK+++opZs2axatUqZFm2Z64K/fjjj0ydOpUZM2aQmJhIx44dGTJkCOfOnav0Od7e3pw9e9bylZFR9hLLO++8wwcffMBnn33Gjh078PDwYMiQIU7X/2pL0i8AhJe44OPhq2yYOkqSJFoZfQHYfyZB0SyC8ykuLLD0V+rWUvRXqkzfmPuQZJmzWhOZF1KVjiMIQA2KpdWrV3P48GFat27NI488QmBgIE888QRg/iNTG+bOncvkyZOZNGkSkZGRfPbZZ7i7u7NgwYJKnyNJEgEBAZav68+GybLMvHnzePnllxk1ahRRUVF8/fXXnDlzhl9//bUWWlR7kvMOA9BSJ8bCqkqkbwwAqcZTCicRnM3mXT9zUaNGK8sM6iTGV6pMq4hOtCgxfxj/a8c3CqcRBDOrx1kCCAoKYvr06UyfPp34+HgWLlyIRqNh1KhRjB07lrFjx9KpUye7BC0pKWHPnj1MmzbNskylUhEXF8e2bdsqfV5eXh4hISGYTCY6derEm2++Sbt27QDz3XxZWVnExcVZ1vfx8aFbt25s27aNcePGVbjN4uJiiouLLY9zc3MB0Ov16PX6m2rn9Uq3dbPbNOj1HNfmAypig+NsmvFm2aqNttI/6i4Wb0/guM7EqTOpNPELuqnt1bX22Zqztw9s18Y9J/4ENYTp3VCjqTOvWV08hi3kxqRwiQPZ2246V11sn605exvt2T5rt1mjYul6gwYNYtCgQVy+fJlvv/2WBQsW8Pbbb2M0Gm90k1W6cOECRqOxXD+pJk2akJSUVOFzWrduzYIFC4iKiuLKlSvMmTOHHj16cPjwYZo3b05WVpZlG//cZun3KjJ79mxmzpxZbvmaNWtwd3evadOqFR8ff1PPP3VhL5c0KlxMMvLlRqxcudJGyWznZttoK7Is42eQOa+R+HrFu7QLHGqT7daV9tmLs7cPbr6NqYXHwBMCDE3Ez2A1GuqDwPUSJ4xnbPZa1aX22Yuzt9Ee7SsoKLBqvRsulko1aNCAxx57jMcee4zExMSb3ZxNde/ene7du1se9+jRg7Zt2/L555/z2muv3fB2p02bVmauvNzcXIKCghg8eLBN7wrU6/XEx8czaNAgtFrtDW/n3R+WgQwReh2jbx1js3y2YKs22tJfi+ZynstcVKcyfPjN9S2pi+2zJWdvH9imjSXFRXy85AVAQ/+o2xnete70WaqLxzAsqQE/Jv6HMy4yMT2iCPRtfsPbqovtszVnb6M921d6Zag6VhVLmZmZBAcHV7te6SW406dP06yZbecea9y4MWq1muzs7DLLs7OzCQiwboBFrVZLTEwMJ06cALA8Lzs7m8DAwDLbjI6OrnQ7Op0OnU5X4fbt8Ua92e2eKDwGrtBS16LO/iDZ67W7Ee0admZrXjyp8lmbZapL7bMHZ28f3Fwbt+/6jbNaDWpZZmjsXXXytapLx7BDu1602G4k1UXN2n1LmTTouZveZl1qn704exvt0T5rt2dVB+8uXbrwr3/9i127dlW6zpUrV5g/fz7t27fn559/ti5lDbi4uBAbG8vatf8bXdlkMrF27doyZ4+qYjQaOXjwoKUwCgsLIyAgoMw2c3Nz2bFjh9XbrOuMRsO1/krQJSSumrUFgIHR9wGQ6mLi9DkxirBw8/YkmwfsDTG44OnqqXCauk9SqQi5dmfqgdOblQ0jCFh5ZunIkSO88cYbDBo0CFdXV2JjY2natCmurq5cvnyZI0eOcPjwYTp16sQ777xz05cuKjN16lQmTJhA586d6dq1K/PmzSM/P59JkyYBMH78eJo1a8bs2bMBmDVrFrfccgsRERHk5OTw7rvvkpGRwUMPPQSY75R78sknef3112nZsiVhYWG88sorNG3alNGjR9ulDbVt4/4/uaJW4WYyEdf1XqXjOIR24bE0Xy9zSiuxZvd3TBr+stKRBAeXWnAU3CHCRdyNaq0WXu1Zb9hGmv6k0lEEwbpiqVGjRsydO5c33niDP//8k82bN5ORkUFhYSGNGzfmvvvuY8iQIbRv396uYe+++27Onz/P9OnTycrKIjo6mlWrVlk6aGdmZqJS/e9k2eXLl5k8eTJZWVk0aNCA2NhYtm7dSmRkpGWd5557jvz8fB5++GFycnLo1asXq1atKjd4paPaemwFAK1KXPBw91I4jeOIMDbklPYy+7O2KB1FcHAmo5FUTS6goVNwf6XjOIxubW7jq0PbSNfquVp4BS83H6UjCfVYjTp4u7m5WYYIUMqUKVOYMmVKhd9LSEgo8/j999/n/fffr3J7kiQxa9YsZs2aZauIdUpS3hFwgXAxH1yNtPHtRELRWo6bzigdRXBw+w+uI8NFgyTLDOtS8XAkQnldOw6l0b7nuahRsXb3Mkb3flDpSEI9VuOJdAXHYTQZSdaY54OLaT5A4TSOpU8H8zxxJ7Umsq+cVjiN4Mi2HTGPnh9k0NDQo7HCaRyHWqOhhcE8FMue9L8VTiPUd6JYcmJbk/4mXyXhaTLRr6v4RFsT7dt0J6TEPGbY6l1LFE4jOLITuQcACNfc+O3v9VUL1wgA0gpPKJxEqO9EseTENh3+DYBWxWp8ff0UTuNYJJWKMKO5j8S+0xsVTiM4KtlkIk11CYCOgb0UTuN4olsMBiBFU4DB4JyjUwuOQRRLTuz4lYMAhKhvbsqO+irc0zwtTkpJpsJJBEd1LHkXKS7mX7NDutyjcBrH07/znbiaZPLUKrbs/0vpOEI9VuNiaePGjRgMhnLLDQYDGzeKT+B1hSzLpKhyAIgMEJ9ob0TXVrcCkKHVc7XQulFeBeF6m/YvRZYkAvUSzRuGKB3H4Xi4edJCbx40cMex3xVOI9RnNS6W+vfvz6VLl8otv3LlCv37i9ti64qDGXvIUYOLSaZfZ9Ff6UZ0jRlGgN6IUZJYk7hM6TiCAzp+eQ8A4VKTatYUKhOmNReZKVcPK5xEqM9qXCzJsowkSeWWX7x4EQ8PD5uEEm7eun1LAWhZAgGBYiC8G6HRuhB+7W6c3WnOPUGlYB+ZnAMg0r+rwkkcV/tmvQFIV19BNpkUTiPUV1aPs3T77bcD5nGJJk6cWGZuNKPRyIEDB+jRo4ftEwo35MjF3aCBEMQn2pvRQteSLRzihLgbR6ih06eTOa4zf7AcGHO3wmkc15Cu9/LOrws5o1VxJHkn7VrfonQkoR6y+sySj48PPj4+yLKMl5eX5bGPjw8BAQE8/PDDfPvtt/bMKtRAKucBaNWos8JJHFt0mPlunFRNISX6YoXTCI5kw64lGCSJBgZo26yD0nEclp9vIEF685+qTQd+UjiNUF9ZfWZp4cKFAISGhvLMM8+IS251WMb5FLI1MpIs01d8or0pvbvcgW/qu+So1SQcWsngmDFKRxIcxNFzW0EH4XLDCrsuCNYLUzUhkyySL+9TOopQT9W4z9KMGTNEoVTHrdljHkSxRYmJiBYxCqdxbG4e3rQqcQFg6/E/FU4jOJIMk3nk99YNohRO4vjaXDtDnnHtjLkg1LYaF0vZ2dncf//9NG3aFI1Gg1qtLvMlKO9g1jYAwkwNQXyivWmhGvPdOMm5RxROIjiK3NyLHNeZR4Dv3W60smGcQN+O5j6zKS4y586L6YeE2lejiXQBJk6cSGZmJq+88gqBgYHi9HIdlGI4DVqI8Bb9JGyhfbO+/HQulRRNLkaTEbVKfCgQqrZh11LyVSrcTTK3tOqndByH1z60Mw3Wy1xWS2zYs4Q7hz6tdCShnqlxsbR582Y2bdpEdHS0HeIINyun8DInNXpAosu1QRWFm9M7dhxuf35FvkrFvrTtxIb3VDqSUMcdyFwPKgg3eIji2gYkSSLU6M1l9VWOnNkMiGJJqF01vgwXFBSELMv2yCLYwN97f0GWJJrrDXTqGKd0HKfQ2L8pLUvMZ1A3HfpN4TSCI0grTgEg3C1C4STOI8KjNQAZJRkKJxHqoxoXS/PmzeOFF14gPT3dDnGEm5WYtg6AML07Gq2LwmmcRxD+ACRd3KtwEqGuMxoMnNAWANA5THxgsZXYiEEApGqL0BcXKZxGqG+sugzXoEGDMn2T8vPzCQ8Px93dHa1WW2bdiqZCEWpPauEJ0EKQroXSUZxKeIMYKFxDmumc0lGEOm7nwTVc1KjRyDIDO92hdByn0b/jKNRH3uSiRs3O/avo2XW00pGEesSqYmnevHl2jiHYgkk2ka7OAyQir00RINhGt8hRsGcNZ7QmLlw9R2Mvf6UjCXXU9iTzhK8tSjR4unkrnMZ5uOs8CNVrSXExsOf4n6JYEmqVVcXShAkT7J1DsIF9qdvJV0m4mkz0ir1L6ThOpX3bnjTfbuSUVs3axGXc3fdRpSMJdVTy1UOggzBNc6WjOJ1QbXNSSCc1TwzjIdSuGvdZys3NrfDr6tWrlJSU2COjYKXSzsfhJRKNGgconMa5qNRqQg3mwVj3ZW5UOI1Ql6WqLgPQvkl3hZM4n3YB5nnhMq+9xoJQW2pcLPn6+tKgQYNyX76+vri5uRESEsKMGTMwidmha92xC+bOx8GIS0T2EOxqvrMprShV4SRCXZVy8jCntdcmz40dp3Aa5xPX6U4AUl1UpKUfUjiNUJ/UeJylRYsW8dJLLzFx4kS6du0KwM6dO1m8eDEvv/wy58+fZ86cOeh0Ol588UWbBxYql2HKBqBFg2hlgzipDsH94OQh0jQFYnBKoULr9poneg0pkQkKCFc4jfMJ829FIwNc1Ehs2buUsND2SkcS6okaF0uLFy/mvffe4667/tcn5tZbb6VDhw58/vnnrF27luDgYN544w1RLNWiy3kXOak1AhK3RN6mdByn1Dv2DtwyPqBApWLnsQ10bztA6UhCHXPk/E7QQJjcSOkoTitUbshFLpF8fqfSUYR6pMaX4bZu3UpMTPnJWWNiYti2zTwnWa9evcjMzLz5dILV1iUuQ5YkAvRGOkb2UTqOU/LxaUx4ifls0tYjvyucRqiLUk1nAGjp21HhJM6rlW87AE4axRxxQu25oRG8v/rqq3LLv/rqK4KCggC4ePEiDRo0uPl0gtX2ZSQAEGLwQFLV+LAKVgpRmTvOH7+8X+EkQl2Tk3eJDK158twebcXZXXvp0dY8jVOyzkBerujoLdSOGl+GmzNnDnfeeSd//fUXXbp0AWD37t0kJSWxbNkyAHbt2sXdd99t26RCldILU0EHIW6in4Q9tWwUC1f/IIMLSkcR6pj4PT9hlCSaGIzEthOXaO2lZ5s4tDtlctRqtu3+hUEDHlA6klAP1PgUxG233UZSUhLDhw/n0qVLXLp0iWHDhpGUlMTIkSMBeOSRR5g7d67NwwoVMxmNpGvyAOjQvK/CaZxbrw5jADitlTl7WVwGEP4nMWM9AOF6T3F21460ai2hRjcADmSsVTiNUF/U+MwSQFhYGLNnz7Z1FuEG7TuxlRy1Cq0s07+LGIzSnlqFd6b5hmuDU+5Zyv/FPal0JKGOSC1OBRcIc2updBSnF6YLJdmURGZhstJRhHrCqmLpwIEDtG/fHpVKxYEDB6pcNyoqyibBBOttOfQrAGElKny8xV049iSpVAQbvTmlzefw6c3Ak0pHEuoAg0FPmqYQkIgKEZfg7C06uA9r0pPI0F7FZDSiUothPAT7sqpYio6OJisrC39/f6Kjo5EkCVmWy60nSRJGo9HmIYWqnbi0D1wgWGqidJR6IdS9JVtN+8gsTlc6ilBH7Dq+gcJrUw31jr1d6ThOLy7mdt5J/4JUrZpjSTtp206Mli7Yl1XFUlpaGn5+fpb/C3VLhnwegJaNyg/pINhex9D+fJ+6jzRNofhUKwCw7cgfALQoUePlJe4EtrdA72b4GSTOa2DHkV9FsSTYnVW9EENCQpAkyfL/qr7s7eOPPyY0NBRXV1e6devGzp2VD0w2f/58evfubZmSJS4urtz6EydORJKkMl9Dhw61dzNs5mJONhku5qllenUYrWyYeqJvpzvQmWSuqlVsO7xO6ThCHZBy2dw9IUgl5mSsLWFSYwBOXEpUOIlQH9T4lo3Fixfz559/Wh4/99xz+Pr60qNHDzIyMmwa7p9+/PFHpk6dyowZM0hMTKRjx44MGTKEc+fOVbh+QkIC99xzD+vXr2fbtm0EBQUxePBgTp8uexfT0KFDOXv2rOXrhx9+sGs7bClh91IMkkRDg0yHCPHpqjZ4ePgQpjefTdqV9IfCaYS6IPPaUBIR4uxurWl1beDPk3KWwkmE+qDGxdKbb76Jm5v5ts1t27bx0Ucf8c4779C4cWOeeuopmwe83ty5c5k8eTKTJk0iMjKSzz77DHd3dxYsWFDh+t999x2PPvoo0dHRtGnThi+//BKTycTatWVvN9XpdAQEBFi+HGlAzUOnNwEQavSwnP0T7K/0DELqlapveBCc3+Xc82RqzWd3e7QbpXCa+qNX5AgAjruYuHrlosJpBGdX46EDTp48SUSEefb1X3/9lbFjx/Lwww/Ts2dP+vXrZ+t8FiUlJezZs4dp06ZZlqlUKuLi4izTrFSnoKAAvV5Pw4YNyyxPSEjA39+fBg0aMGDAAF5//XUaNar8rrLi4mKKi4stj3NzcwHQ6/Xo9fqaNKtKpduqapsZRangCiGuYTbdd22xpo11UUTDGOKvniGDC1Vmd9T2WcvZ2wfVt/HvXT9hkiQaG0y0CY11uNfCUY9hTFgPXLfJ5KlVbN69nLg+Eytcz1HbVxPO3kZ7ts/abda4WPL09OTixYsEBwezZs0apk6dCoCrqyuFhYU13ZzVLly4gNFopEmTsnd8NWnShKSkJKu28fzzz9O0aVPi4uIsy4YOHcrtt99OWFgYKSkpvPjiiwwbNoxt27ahrqTj7uzZs5k5c2a55WvWrMHd3b0GrbJOfHx8hctlk0y6pgBQ4VHSnJUrV9p837WlsjbWVdqCZgBkamV+/mUJbjrvKtd3tPbVlLO3Dypv445Tq8ATgkpc+WvVqlpOZTuOeAyDSnQku5aw7cjvlOT5V7muI7avppy9jfZoX0FBgVXr1bhYGjRoEA899BAxMTEcP36c4cOHA3D48GFCQ0Nrurla89Zbb7FkyRISEhJwdXW1LB83bpzl/x06dCAqKorw8HASEhIYOHBghduaNm2apUgE85ml0v5Q3t5V/9GsCb1eT3x8PIMGDUKr1Zb7/qHj2zi/W4VKlpk0ZioNvP1stu/aUl0b6ypZlvn2m8+4pFGhaXCJ4f3GVbieo7bPWs7ePqi+jb8uMA/QG+rawvL70JE48jHc8sM3JMvHuKjJrvS1d+T2WcvZ22jP9pVeGapOjYuljz/+mJdffpmTJ0/y888/Wy5X7dmzh3vuuaemm7Na48aNUavVZGdnl1menZ1NQEDVd6DMmTOHt956i7///rvaQTNbtGhB48aNOXHiRKXFkk6nQ6fTlVuu1Wrt8katbLs7jpk72ofoVfg3amrz/dYme7129hRq9OSSpoAjZ7YyVvtEles6YvtqwtnbB5W3MUNzFVDRrnlPh34NHPEYRjXvxV8nj5GhuYpGra5ymhlHbF9NOXsb7dE+a7dX4w7evr6+fPTRR/z2229lbrGfOXMmL730Uk03ZzUXFxdiY2PLdM4u7azdvXvld4G98847vPbaa6xatYrOnTtXu59Tp05x8eJFAgMDbZLbnpIv7gUgmMYKJ6mfQlxbAJBeJMYeq6+Ope3lvEaFJMv063Sn0nHqnbhrr3mGi5pjJ/YonEZwZg412+PUqVOZP38+ixcv5ujRozzyyCPk5+czadIkAMaPH1+mA/jbb7/NK6+8woIFCwgNDSUrK4usrCzy8syTzubl5fHss8+yfft20tPTWbt2LaNGjSIiIoIhQ4Yo0saayJTNZ9kifDsonKR+6tC8DwAZmnxkk0nhNIISNh38BYBgvUSTRs0UTlP/BPg2I1Bvvgt466FfFE4jODOHKpbuvvtu5syZw/Tp04mOjmbfvn2sWrXK0uk7MzOTs2fPWtb/9NNPKSkpYezYsQQGBlq+5syZA4BarebAgQPcdttttGrVigcffJDY2Fg2bdpU4WW2uiS/MI80rXlqmW6tHa+fhDMYEHsHKlnmnEbFkRM7lI4jKODYefPZjGDZcYYbcTahmLuCHL8oziwJ9lPjPktKmzJlClOmTKnwewkJCWUep6enV7ktNzc3Vq9ebaNktWtj4i8UqyS8jCa6tqu4b5VgX418/AnSq8hwkdlyeAXtWolBQeubk8YzoIEw70ilo9RbLX07sC1/PZkmMTilYD9WnVlasWKF047f4Kj2p5un2QjVu6JWO1zN6zRCrn2qTb4gplyob0pKiknTlgAQGx5XzdqCvXRvbR6cMsXFQH6+dXc2CUJNWVUsjRkzhpycHMB86aqy6UWE2pOWfwyAEJcghZPUb+E+5v5imWLKhXpn24E/KVCpcDOZ6NXxVqXj1Fu3tB2Au0mmQKViU6LotyTYh1XFkp+fH9u3bwfM48uIaTWUl6Eyf4KKDLhF4ST1W7c2wwBI1RooKMxTOI1Qm3afMA+QF6p3wcWlbvdxdGYajZYwvXnsvH3pYmJrwT6sKpb+/e9/M2rUKNRqNZIkERAQgFqtrvBLsL/008c4rTUXrP1ixO3KSrql3SA8TCaKVCo2J/6mdByhFqXlHgEgSF33hxlxdqG6EADSCo4rnERwVlZ1dnn11VcZN24cJ06c4LbbbmPhwoX4+vraOZpQmQ37lgHQXC8TFBCucJr6Ta3WEKZ35ZCuhH3paxnc8z6lIwm1JFO6BEDrxrEKJxE6BPbkz7PHSVeLPkuCfVjdM7hNmza0adOGGTNmcOedd9plDjTBOkfP7QQVhJh8lY4iAMHaIA6RQlreMaWjCLXk/KUzZGhlQKJ3xzFKx6n3BsTeyVt/LOSMVkVy+n5ahnZUOpLgZGo8ztKMGTNwd3fn/PnzbN68mc2bN3P+/Hl7ZBMqkaE/CUCYZxuFkwgAkU26ApChuqJwEqG2JOxZikmSaGSQaRvaSek49V5goyCCzDcmsnH/MmXDCE6pxsVSQUEBDzzwAE2bNqVPnz706dOHpk2b8uCDD1o9e69w4wwGPemaYgBiwsT4SnVB32tTLpx0kcg4Lc4u1QeHz2wBINTooXASoVTpMB7Hzu9WOIngjGpcLD311FNs2LCBFStWkJOTQ05ODr/99hsbNmzg6aeftkdG4TrbD60hT61CZ5LpHXOb0nEEIDSgJQF6GYCN+35WOI1QGzKL0gEIcWuhbBDBIsK7HQDpprPVrCkINVfjYunnn3/mq6++YtiwYXh7e+Pt7c3w4cOZP38+y5aJ05/2tvP4XwC00GtwcxWfauuKENkHgGPZYtoTZyebTGRo8gGIujY/oKC80mmfUrUGCoryFU4jOJsbugxXOhfb9fz9/cVluFqQcuUwAMGqAIWTCNdr4dEagMxr/ckE53X4xE7OaVSoZJn+sXcoHUe45pb2g/EymihWSWzc+6vScQQnU+NiqXv37syYMYOioiLLssLCQmbOnEn37mJuLHvL5AIArRqLTqV1SWn/sVRtMQaDQeE0gj1tPWQeT6u5XkVDb3+F0wilNBotLa4NTpmY+rfCaQRnU+NJxf773/8yZMgQmjdvTseO5tsz9+/fj6urq8NOSusoLuRkkXntduUe7UcrHUe4Tt+YUWiPzeaKWsWuQ/F0jx6mdCTBTk5c2gtaCL7WoVioO0K0weznBKn5YnBKwbZqfGapffv2JCcnM3v2bKKjo4mOjuatt94iOTmZdu3a2SOjcM26xGWYJAl/g4l2LTorHUe4jrurJ6F682ePXcdWKpxGsKdMo3kewHAf8fuurmkXaL66kaYWw3gItnVD09W7u7szefJkW2cRqnHo1GYAQg2eSKoa17mCnYWoAkjmNClXDikdRbCTwsJ80lz0gIqurYYoHUf4h/6d7uTtv77mnEbixKlDRDRvr3QkwUmIv7gOJKMoFYAQV3G7cl3UqlE0ACev9SsTnM/Wfb9ToFLhZpLp0X6o0nGEfwhsEkaI3vz/9fuXKxtGcCqiWHIQsiyTpjbfDtu+eW+F0wgV6dVhFABpLjIXc7IVTiPYw77UtQCE6l3QaLQKpxEqEmJqAFybFkoQbEQUSw7iYMoOLmtUaGSZfp3F7cp1UfsWt+BrlDFIEht2i8EpnVFa3lEAgrXNFE4iVKaFVyQA6YYzCicRnIkolhzElmu3K4eVSDT0KT/OlaA8SZIIM5gnmD50epPCaQR7OKnKAaCtf1dlgwiV6hw+GIB0bQlFJYUKpxGcxQ0VSzk5OXz55ZdMmzaNS5cuAZCYmMjp06dtGk74n2MX9wIQRGOFkwhVCXENAyDzWv8ywXmczU4n/dqVtz4dxygbRqhUt+gR+BqN6CWJjQf/VDqO4CRqXCwdOHCAVq1a8fbbbzNnzhxycnIAWL58OdOmTbN1PuGaDNO125V9OyicRKhK1LX+ZBnqPGSTSeE0gi1t2f8LJkmikUGmpbjLqs5y0bkSUaIDYOeJNQqnEZxFjYulqVOnMnHiRJKTk3F1dbUsHz58OBs3brRpOMGsoCiPDK15VOhuLcVgh3VZ/9ixSLJMllbFkZQ9SscRbCgpezsAISYvhZMI1QlWm/uUpVw9qnASwVnUuFjatWsX//rXv8otb9asGVlZWTYJJZS18cDv6CUJX6OJzh0GKR1HqEJjnwCC9BIAWw79qmwYwaZOlWQAEOYeoXASoTqt/LsAkCHlKBtEcBo1LpZ0Oh25ubnllh8/fhw/Pz+bhBLK2p++HoAwvQ615obGERVqUek0GCcuJiqcRLAV2SSTrjV3Fu4Y0k/ZMEK1unccgyTLnNfAqYvpSscRnECNi6XbbruNWbNmodebR/6SJInMzEyef/557rhD3NJuD2nX5jkK0QYpnESwRsS1aTBOGsWty87iYm4K5zRqVLLMgJjblY4jVKNFSAdC9OY+gxsO/KpsGMEp1LhYeu+998jLy8Pf35/CwkL69u1LREQEXl5evPHGG/bIWO9lXJvnqE2TWxROIlijdBqMVBcDhUUFCqcRbOFs/gEAmuvV+Hg0UDiNUC1JItjoDcCRs9sVDiM4gxpf0/Hx8SE+Pp7Nmzdz4MAB8vLy6NSpE3FxcfbIV+9dLsomWyMhyTJ9osWZO0fQvf1Q3Pa+SIFKxbb9fwCeSkcSbtJ5UxoAISrR1cBRBLtFAPvJLMmkp9JhBId3wx1gevXqRa9evWyZRahA5pW9oIMQvUxQs1ZKxxGsoNG4EKZ34YhOz/70dbT2uk3pSMJNytZcBiDcVwwZ4Cg6BPeDzP2kawoxyWIYD+Hm3FCxtHbtWtauXcu5c+cw/WMsmQULFtgkmGCWbTgBOgg2+SodRaiBEG1zjpBGev4xWos7zR1afv4V0nQmQMUtbYYrHUewUq/YMbimv0++SsXZvBSl4wgOrsZ9lmbOnMngwYNZu3YtFy5c4PLly2W+BNvKVptnsA/1aK1wEqEmSqfDyLw2PYbguLbt/Z0ClQpXk0y31v2VjiNYydu7EWEl5j9xp/MOKpxGcHQ1PrP02WefsWjRIu6//3575BGuYzDoyXTRAxLRoQOUjiPUQL+OtzN37Y9kauFqwUWl4wg34dDJBABCDTo0Gq2iWYSaCZL8Oco5zpvSlY4iOLgan1kqKSmhR48e9shilY8//pjQ0FBcXV3p1q0bO3furHL9pUuX0qZNG1xdXenQoQMrV64s831Zlpk+fTqBgYG4ubkRFxdHcnKyPZtgte1JaylUSXiYTPTsNErpOEINhDWPxN8gI0sSp67sVTqOcBMyC8y/D4LF0B0Op3R6qLMacdVDuDk1LpYeeughvv/+e3tkqdaPP/7I1KlTmTFjBomJiXTs2JEhQ4Zw7ty5CtffunUr99xzDw8++CB79+5l9OjRjB49mkOHDlnWeeedd/jggw/47LPP2LFjBx4eHgwZMoSioqLaalaldievBqBFiQZ3d9HxxdGEXrt1+byhbhTfwo3JVJmH7ohs0lXhJEJNdWlt7mN20sXE1aLygykLgrVqXCwVFRUxd+5c+vbty2OPPcbUqVPLfNnT3LlzmTx5MpMmTSIyMpLPPvsMd3f3SjuV//e//2Xo0KE8++yztG3bltdee41OnTrx0UcfAeazSvPmzePll19m1KhRREVF8fXXX3PmzBl+/fVXu7bFGidyDwMQpApQOIlwI8I8WgJwTl1xMS/UfSdPHiPdxTx9Te+o0cqGEWqsU7sBNDSYMEoSm/b9rnQc4Qa9E/8KG3L/5nzhecUy1LjP0oEDB4iOjgYoc4YGzKN520tJSQl79uxh2rRplmUqlYq4uDi2bdtW4XO2bdtWroAbMmSIpRBKS0sjKyurzBhRPj4+dOvWjW3btjFu3LgKt1tcXExxcbHlcen0L3q93jKyuS1kYu7r0sK3o023W5eUtssZ29chqA8/piWS6VJcJ85U2oMzHz+ATYlLMUkSjQwyzRuEOmU7nf0Yhup1XNLo2ZexnuG33Kd0HLtw5mNokk2syP6DApVEv50dGNZ3kk23b+1rVuNiaf369TUOYwsXLlzAaDTSpEmTMsubNGlCUlJShc/JysqqcP3SCX9L/61qnYrMnj2bmTNnllu+Zs0a3N3dq2+MFYxGI+0KJLxci9FJzcr1tXI28fHxSkewuWK9BxpZ5pJGxXfLPyPQ13nHyXLG4wewP3MjeEMzvYfTtrGUs7avsaExcJbU3CTxe9QBnclPpUAl4WoyUXTJ0+bHsKDAulkWxKysN2DatGllzljl5uYSFBTE4MGD8fb2ttl+huqHsmrlHwwZOhwXnc5m261L9Ho98fHxDBo0CK3W+e40+n7RbFJcTBTrTjF8+JNKx7E5Zz9+K74yfyjyl5s6bRud/RjmrDzImpwfOe2Sz/DhzjlOljMfw0//eBn0EFYiMfLu0TZvX+mVoepYVSzdfvvtLFq0CG9vb26/vepJJJcvX27VjmuqcePGqNVqsrOzyyzPzs4mIKDiPj0BAQFVrl/6b3Z2NoGBgWXWKb3UWBGdToeuguJFq9Xa/ECqtTpcdDqn+wH4J3u8dnVBsORHCtmk5R5yyvaVcsbjZzQYSNMWAWoC3SKdso3Xc9b29Y65gznrfyRbK3H6QjqhgS2VjmQ3zngMT1w+AGpoovexS/us3Z5VHbx9fHws/ZF8fHyq/LIXFxcXYmNjWbt2rWWZyWRi7dq1dO/evcLndO/evcz6YD5NWbp+WFgYAQEBZdbJzc1lx44dlW5TEGoiwjcKgFMo1zFRuDF7DsZzXqNGLcuEeEcpHUe4QUGBEQSVmGea2LB3mcJphJo6aTwLQCNJ2aE7rDqztHDhwgr/X9umTp3KhAkT6Ny5M127dmXevHnk5+czaZK5w9f48eNp1qwZs2fPBuCJJ56gb9++vPfee4wYMYIlS5awe/duvvjiC8DcIf3JJ5/k9ddfp2XLloSFhfHKK6/QtGlTRo8erVQzBSfSve0I5u+OJ01rIvfqZby9xIz1jmLXMXPfiGC9Ble1q8JphJvRVO/JSZcCjmbvUDqKUAPFJUVkaA2ARBO3dopmcag+S3fffTfnz59n+vTpZGVlER0dzapVqywdtDMzM1Gp/neyrEePHnz//fe8/PLLvPjii7Rs2ZJff/2V9u3/Nxnmc889R35+Pg8//DA5OTn06tWLVatW4eoqfjkKNy8qvCfeO0zkqlUk7FnObf0eVDqSYKWUKwfBFYJVTapfWajT/ORmQDKZ+pNKRxFqYPPBP9FLEt5GE018IxXNYlWxFBMTY/WwAImJiTcVqDpTpkxhypQpFX4vISGh3LI777yTO++8s9LtSZLErFmzmDVrlq0iCoKFSq0mpETHQTc9BzITuA1RLDmKk9eG7mjdMFrZIMJN83dtCySTpinCZDSiUquVjiRYYc8J8919oXotarWy53as2ru4JCUIN66J0Z+DnCaj8ITSUQQrXbqcRYpOBiR6RN7GqaQLSkcSbkJzn47orv5GnlrFjiNr6d5hsNKRBCuk5R4FF2imbqp0FOuKpRkzZtg7hyA4rSYuLYHTZKrFdAuOYuOen9FLEj5GmQ5hXTiV9JfSkYSb4KLVEapXc0xnYlfSSlEsOYiTXAIgomGMwkluYLoTQRBqJsgnFoAzWhXJ6QcVTiNY4+DpTQCEGjzsOjOBUHuCVP4ApOSIn0FHcCkni5NaGYBb2t2mcBpRLAmC3XnqGtBcb/6h33jAPuOQCbaVUZQKQJhbC4WTCLYS7tsRgExZDOPhCBL2/IxJkmhsMNG2RSel44hiSRBqQ4jJPGTA8fO7FE4iVEc2mUjX5AMQFdRH4TSCrdzSdgQA6S4mrly9qHAaoTqHrp3dDTF4KJzETBRLglALWni2AeCk4bTCSYTqHEreQbZGhUqWGdDpDqXjCDbSIbw7PkYTBkliQ+IvSscRqpFZmAZAsFuYwknMrC6WWrRowcWLohoXhBsR02IgAKkuJZSUFCucRqjK1sO/ARCkV9HI21/hNIKtqNRqwgzmic4PZiYoG0aoVqY6D4DIpj0VTmJmdbGUnp6O0Wi0ZxZBcFo9OoxAZ5LJV6nYsl/cWVWXJV/cC0AojRVOIthasC4EgPSCFIWTCFVJTt3HWa25POkfWzfO7orLcIJQC1xcXGmhN4/UkXhitcJphKpkyFkAhPt2UDiJYGuRgeY5P8UwHnXb1oPmG2Ga6qFJg2YKpzGr0ZCYq1evrnay3NtuU/4WP0Goi4LVTTnKSVKvHlE6ilCJ/MI80rRGQKJ76xFKxxFsrH+nO3nrz0Wc0apIST9IeKgoiOui5POJoIUgue7MpVmjYmnChAlVfl+SJHGpThAq0cavE6svn+SkdEnpKEIlNuxZTrFKwstooku7AUrHEWysaeNgmunhtBY2HVguiqU66pThNGihhVdbpaNY1OgyXFZWFiaTqdIvUSgJQuV6R40BIEMrk3VB3BVXF+1LXwdAC4Or4nNRCfYRJPsCcPzcbmWDCBXSFxeRpjXfBNMpfKDCaf7H6mJJjGIrCDendWgsjQ0mTJLEhsRlSscRKpBWcByAEG2IwkkEe2nhaT5bcdJ4SuEkQkX2HIznkkaNWpbpE1V3LoVbXSzJsmzPHIJQL4QZPQE4cmaLwkmEiqSrzB1/213rCCw4n9jwOADStCXoS0oUTiP8057kVQAE6TW46+rGgJRQg2JpwoQJuLm52TOLIDi90GvTZ2QUpysbRCgn9dQRsrQSkizTt9OdSscR7KR3x5FoZZkrahU7Dog7U+uatNxDAISoAxVOUpbVxdLChQvx8vKyZxZBcHpRQX0BSNfkYxJ9/OqUhP3mS6NBemjmH6psGMFu3HTuhJQO43HtLIZQd5zEPPh1a78YhZOUZbNxluLi4mjRQkw6KQhV6R97B2pZ5qJGxf7k7UrHEa6TlG2ety+kDt2uLNhH8LWzFqm5hxVOIlzv4sUsUl3MXX56tatbwxDZrFgaPXp0tUMLCEJ95+PlR4jefLPE9iO/K5xGuF7GtXn7SjsAC86rVSPzWYtT0gWFkwjX25r4M0UqFR4mmY5hXZWOU4bN7o2dMmWKrTYlCE4tmMakcoHkS3uVjiJcU6IvJlVbAkjEhg9WOo5gZ706jOKzTb+TpoWLl7Jo1DBA6UgCcPjUJlBBqMEDlVS3JhixWZrly5cTFRVlq80JgtNqeW0ajZOmLIWTCKW2HFhJkUrCw2SiZ8xIpeMIdhYV1hUvo0yJSmLTnp+VjiNck1mUCkCYa5jCScqrUbH0+eefM3bsWO6991527NgBwLp164iJieH++++nZ8+6MTuwINRlXVsNAyBNayS/ME/hNALAzhNrAAgvccHFxVXhNIK9SZJEqNF8W/qRUxsVTiMAyCYTmRrz78OooF4KpynP6mLprbfe4rHHHiM9PZ0VK1YwYMAA3nzzTe677z7uvvtuTp06xaeffmrPrILgFLq0j8PLaKJYJZGQ+KvScQQgJdc8X1+wuqnCSYTaEuoaCkBmcZqyQQQAjp/YTYaLGoAB0bcrnKa8Gg0dMH/+fHbv3s1ff/1FYWEhW7du5cSJE7zwwgs0aCDuIBEEa6jVWsL0OgD2p61TOI0AkHFtvr7W/p0VTiLUlg7NzWcvMtV5yCaTwmmE7Yd+A6CJQaKJb9370GJ1sZSZmcmAAeaJJXv37o1Wq2XmzJl4eNSdETYFwVGEuAQDkJ5/XOEkwtmLmZzRmv/fK+oOZcMItWZAJ/OxPumi5ljyHoXTCCcumI9BCA0VTlIxq4ul4uJiXF3/dy3fxcWFhg3rZqMEoa6LDDDfFpupzlE2iMDaa/P0BZWYiAgVN6nUF018mhJQOozH4V+VDSNw0nQWgAjvdgonqViNhg545ZVXcHd3B6CkpITXX38dHx+fMuvMnTvXdukEwUn1ixnL26t/4LRWIu1MMmFNWyodqd46dG2evhCjt8JJhNoWTEOyuMiJC4lKR6nXCgvySHXRA2q6tqqbQ3dYXSz16dOHY8eOWR736NGD1NTUMutIkmS7ZILgxJoHtKKZXua0VmLD3p8Ja/qC0pHqrbSSTHCBUPcIpaMItSzcJ5KdBZs4ZTqjdJR6bee+lVxWq9HIMj0jHbxYSkhIsGMMQah/Qkw+nCaXY9li2hOlGE1G0jWFgERUcH+l4wi1rGvLIfywfxOpLnoKC/Jxcxd9cJWwP/VvAIL1Lrhq3RROU7G6NUSmINQjYR6tAMjUn1Q4Sf2183gCBSoJd5OJ3p3r3u3Kgn31ajcYjSxzWa1m574/lY5Tb2XkmYfuCNHWvbvgStmsWPrtt9/4+uuvbbU5QXB6MWHmu0vTtEUYDUaF09RP2478AUB4iRpPT19lwwi1zlXrRpDBBYAD185uCLUvQ3UZgEj/LgonqZzNiqXnn3+eSZMm2WpzguD0+sSMRmeSuapWsf1QvNJx6qXjlw8CECT5K5xEUEqoxnw2o/TshlC7Tp05QYqLub/zgOixCqepnNXF0owZM9i4cSMlJSUVfj8pKQmj0X6fji9dusR9992Ht7c3vr6+PPjgg+TlVT5VxKVLl3jsscdo3bo1bm5uBAcH8/jjj3PlypUy60mSVO5ryZIldmuHIJRyc/MiVG8esXbnsb8UTlM/pcvnAYhoEKNwEkEpbfzMA5GelC4rnKR+2pT4EwZJopEBWgZGKh2nUlYXS19//TX9+vXD19eXgQMH8vrrr7NlyxYMBoM981ncd999HD58mPj4eP744w82btzIww8/XOn6Z86c4cyZM8yZM4dDhw6xaNEiVq1axYMPPlhu3YULF3L27FnL1+jRo+3YEkH4nxBVEwBScg8pnKT+uZR3gdNa88jNt0TeqnAaQSl9Oo4G4ISLxJkzqVWvLNjc4extALQw+dTpO+qtvhsuLS2N9PR01q9fT0JCAl9++SXTp0/Hw8ODnj170r9/f/r370/Xrl1tHvLo0aOsWrWKXbt20bmz+VPAhx9+yPDhw5kzZw5Nm5bvFNa+fXt+/vl/s0mHh4fzxhtv8H//938YDAY0mv813dfXl4CAAJvnFoTqtGoUzZrcs5y6doZDqD1r9y4HoLneSLs2YhLw+qpds474GGWuqCW27F3GnU2fUzpSvZJhOAkaaOlVd88qQQ0HpQwNDWXSpEmWvklpaWmW4unNN9/kpZdessuZpm3btuHr62splADi4uJQqVTs2LGDMWPGWLWdK1eu4O3tXaZQAvjPf/7DQw89RIsWLfj3v//NpEmTqqxwi4uLKS4utjzOzc0FQK/Xo9fra9K0KpVuy5bbrGucvY3Vta9b6xF8tOsv0l1MZF/MoqF3o9qMd9Mc+fjtTV8PQIjeHaPJhLGS+cEcuY3WEO2DMKM3+9RXOXx2K6Md8HVw1GNYXFxAsoseUBEbPrjS/PZsn7XbrFGxdL2MjAw2btzIhg0b2LhxI3q9nj59+tzo5qqUlZWFv3/ZDpgajYaGDRuSlZVl1TYuXLjAa6+9Vu7S3axZsxgwYADu7u6sWbOGRx99lLy8PB5//PFKtzV79mxmzpxZbvmaNWssI5zbUny883f+dfY2VtY+2WSiocHEJY2Kxcvn0trfMc9wOOLxO5GfDG7QyBDAypUrq13fEdtYE/W5fX6GJuBylfSSdKveC3WVox3DzAu7ydeocDPJ5J6ElWeqfu3t0b6CggKr1rO6WMrMzCQhIcFyJunChQv06NGDvn37MnnyZLp27YqLi0uNQr7wwgu8/fbbVa5z9OjRGm2zIrm5uYwYMYLIyEheffXVMt975ZVXLP+PiYkhPz+fd999t8piadq0aUydOrXM9oOCghg8eDDe3rabMkGv1xMfH8+gQYPQarU2225d4uxttKZ9vy54k0uaIvJdTjF8+PBaTnhzHPX4mWQTb337EiDRpdUwhg+o/HV31DZaS7QPVDtziD8xh1RXPYMHDULjYK+Dox7DOUt+AROE63WMunVUpevZs32lV4aqY3WxFBoaSnBwMI888giPPPIIsbGxqNXqGw4I8PTTTzNx4sQq12nRogUBAQGcO3euzHKDwcClS5eq7Wt09epVhg4dipeXF7/88ku1L3S3bt147bXXKC4uRqfTVbiOTqer8HtardYub1R7bbcucfY2VtW+UNdQ9pBEZlGqw74Gjnb8dh/fTJ5awtVkol+3u6zK7mhtrKn63L64zmN59fi7XFarSExaR89OI2s5nW042jFMLTgGrhCmDVHsZ9Da7VldLN11111s2LCBt99+my1bttC3b1/69+9PTEzMDfdg9/Pzw8/Pr9r1unfvTk5ODnv27CE2NhaAdevWYTKZ6NatW6XPy83NZciQIeh0OlasWIGrq2u1+9q3bx8NGjSotFASBFtr37wPP59KIkNzFVmW6/QdIc5i87VZ5sNLVPj6Vv87SHBubjoPwvQajumM7Di+0mGLJUeTpskFVLRvWve7H1g9dMCSJUs4e/YsW7duZdiwYezcuZPhw4fToEEDRo4cybvvvsuuXbvsErJt27YMHTqUyZMns3PnTrZs2cKUKVMYN26c5U6406dP06ZNG3bu3AmYC6XBgweTn5/PV199RW5uLllZWWRlZVnGg/r999/58ssvOXToECdOnODTTz/lzTff5LHHHrNLOwShIv1j70Qly5zXqDhyYqfSceqF45f2ARAkNVE2iFBnhKrNf0tOiGE8asXR1N1ka1SoZZkBsXcrHadaNe7g3aZNG9q0acMjjzwCwJEjR/j+++95/fXXmTZtmt3GXfruu++YMmUKAwcORKVScccdd/DBBx9Yvq/X6zl27Jils1ZiYiI7duwAICKi7GziaWlphIaGotVq+fjjj3nqqaeQZZmIiAjmzp3L5MmT7dIGQahII98AgvQqMlxkthz8hXYtKz9bKthGhsl8WV8MRimUauvXhdWXT5KmEoNT1oaEA8sACC2RCGjcXOE01buhu+Gys7NJSEiwdPg+fvw4Op2O3r172zqfRcOGDfn+++8r/X5oaCiyLFse9+vXr8zjigwdOpShQ4faLKMg3KhgGpPBeZIvJiodxeldvHqOk1oTINGjw2il4wh1RL+oO5i3YTmntHD6fDrN/EKVjuTUjl5IBC2E4hiXwa2+DPfTTz/x6KOPEhkZSdOmTZkwYQKHDh3irrvuYu3ateTk5LB+/Xp7ZhUEpxXeIAqAkybrhsIQbty63cuQJYkAvYn2rborHUeoI8JDowgqMY+19XfiTwqncX7pcjYALX07KpzEOlafWfq///s/OnfuzJgxY+jfvz89e/bEzc3NntkEod7oHnkri3atJcXFSN7VS3h6NVQ6ktPaf3IDAKEGDySVzeYSF5xAmNGbk+RxKGub0lGc2qWr58nQGgGJnu1GKx3HKlYXS5cvX8bDw8OeWQSh3urWph/uO2QKVCo27VnOsH4PKR3JaaUXpYEOQt0iql9ZqFfCPFqz0bSH1JJMpaM4tfg9SzFJEgF6Ix3b2q/7ji1Z/bFKFEqCYD9qlZpQg3n09wMZ6xRO47xMRiNpmnwAokL6K5xGqGs6hQ4CIE1TTLG+SOE0zmt/pvnsbrjB02HO7jpGSkGoB0J1YQBkFpxQOInz2nNsE7lqFS4mmX6dxyodR6hjune6jQZGI3qVxMbDq5WO47RSilMBCHVrqXAS64liSRDqiKigXgBkaPKQTUaF0zinrUd+AyBMr8LLs4HCaYS6xs3Di4hi84jO24/9qXAa56Q36knVFAIQHTxA4TTWE8WSINQRAzuZz3RkuKg5cnS7wmmc04nL+wEIUVU9TZJQf4VoggBIvnpE4STOaWvSWopUEp5GE70736F0HKuJYkkQ6ogAn0D8DeapTnZcm45DsK0MzgPQslEnhZMIdVXbAPPUG6mqK9WO1SfU3NajfwDQqkSNh5evsmFqoMbFUn5+Pq+88go9evQgIiKCFi1alPkSBOHGtZD8AUi+vEfhJM7nwuWzZGjNf/x6d7hd4TRCXdUr9m5cTDJX1HD45D6l4zidYzkHAQhVNVU4Sc3UeATvhx56iA0bNnD//fcTGBgoJv0UBBuKbBTL9pyVpHNO6ShOZ93unzBJEn4GE+0iuiodR6ijmjZtQUSJzBFXiXX7ltI+WEyJYyuyLJMmXQKglZ9j/QzWuFj666+/+PPPP+nZs+7PEiwIjmZA1O0s2LiSZBeZ7OyTNGkSpHQkp3H49GaQINTgpXQUoY4Lkf04wkWOXtitdBSnknL+OJc0oJFlenZ0nP5KcAOX4Ro0aEDDhmJ0YUGwh6jQrvgYZYpVKjbs/lHpOE4lvTgNgFB3x7ldWVBGhG80AKmmbGWDOJm/95onz21ZbCIktIPCaWqmxsXSa6+9xvTp0ykoKLBHHkGo1yRJItzoA8ChrE0Kp3EeRoOBNK35duWYUMe5XVlQxi3txgBwRmviXK6Yr9FWDp01TyMTbGrgMINRlqrxZbj33nuPlJQUmjRpQmhoKFqttsz3ExPFrOmCcDNaebUlsXgHaQYx5YKt7D68jstqFRpZpl+s6NwtVK19ZC+CtxvJdFETv+cn7uv/uNKRnEKK4TRooYVXlNJRaqzGxdLo0aPtEEMQhFK3tBzGkkM7OKEtobCwADc3d6UjObxtR34FIEyvwcvdR9kwQp2nUqsJNXiR6VLAvpMbuQ9RLN2snPxLnNboAYkurW9VOk6N1bhYmjFjhj1yCIJwTZ+OI3E7MIM8tYqExF8Z1vNepSM5vJTcg+AKoepmSkcRHESYeys2so/U4nSloziFNft+RpYkgkoMxETHKR2nxm74ouGePXv49ttv+fbbb9m7d68tMwlCvabV6IjQ6wBITBXzU9lChsp8u3K7gO4KJxEcRUzYYADSNEViUl0b2JO2FoAwgwcarYvCaWquxsXSuXPnGDBgAF26dOHxxx/n8ccfJzY2loEDB3L+/Hl7ZBSEeif82qS6KQXHFE7i+FLTD5KuNY8HFxc7TuE0gqPo0XkMvqWT6h5cqXQch5dSlAJAqGsrhZPcmBoXS4899hhXr17l8OHDXLp0iUuXLnHo0CFyc3N5/HFxXVcQbCE6qD8AKZqrmIxiUt2bsWHvj8iSRIAeQppEKB1HcBBu7p60LDafAdme/JfCaRxbib6YNLX5btSokIEKp7kxNS6WVq1axSeffELbtm0tyyIjI/n444/56y/xhhIEW4jreg9aWeaSRsWeowlKx3Fox8/vBCCMxgonERxNiDYYEJPq3qzNSWsoUUn4Go306uJYg1GWqnGxZDKZyg0XAKDVajGZTDYJJQj1nY9nQ1qUqAHYcuQXhdM4tgz5LACtG0QrG0RwOG0DegBiUt2bteXa5LktS7QONXnu9WpcLA0YMIAnnniCM2fOWJadPn2ap556ioEDHfP0miDURWHq5gAcy9mvcBLHdfFiNsku5g9xfaLE+EpCzfSxTKorcThTjCF4o5JzDwMQrHbc6ZtqXCx99NFH5ObmEhoaSnh4OOHh4YSFhZGbm8uHH35oj4yCUC+1a2KefzFFdVnhJI5r0+4lFKlUeBplYiPEfJZCzQQEhhFRYv7/uv3LlA3joGRZJlV1BYDIwF4Kp7lxNR5nKSgoiMTERP7++2+SkpIAaNu2LXFxjjdugiDUZYO7/h/vr/yes1qJo2l7aBsWq3Qkh3Po1AbQQAuTFyrJsaZXEOqGYPw4wgWOnheT6t6IQ5mJXFGDi0mmT+xdSse5YTUulsA8f9WgQYMYNGiQrfMIgnBNU/9gWpRInNDB3/uWiGLpBmSWpIEGwj1aKx1FcFAt/7+9O4+rsk7/P/66z8IBBERTQRQ3XFBScSVMUxMRNdPGSU1zG5ep0ZrGprKZyszJrOk3TfZ1atq0xaUyl3LccEHTUBH3jYQwLUVzZRUO53x+f6CnCETQc7gPh+v5ePBQ7vM59/2+uA9wcZ/7/ty1OrI2bz3pSm6qeys277t289wCCK7fTOc0t65czdLcuXOZPHky3t7ezJ07t8yxMn2AEM4TpgWTSgZHLiTrHaXKuZqXTZpXPmCka4s4veOIKqp7+2G8tWM9P5kVZy7+SP3aDfWOVKUcPb8bTNCIenpHuS3lapbeeOMNRo0ahbe3N2+88cYNx2maJs2SEE4UUfcu1l1ZQSoy4WtFJSWv4pzJiFEp7m1X9e5FJdxD6xZdCN1q55SXgfW7FjI27hm9I1Up3187Iteydkedk9yecjVL6enppf5fCOFa93YexZsblpNh1vjupyO0bNBG70hVRnJa0bxvjQot+HrV0DmNqKo0g4Em9kBOkcmh09sAaZbKK+PyT5w2F0250KPd73VOc3sqfMbjSy+9RG5ubonleXl5vPTSS04JJYQo0rhhOGHXrsaJT16ob5gq5vvcowC0uHbrGCFuVVhAWwDSC0/pnKRqWbOr6GdWkwIbLVt01TnN7alwszRz5kyys7NLLM/NzWXmzJlOCSWE+EWYqgvAoWszUYubsxcWkmrKAqBz43t1TiOquug2gwFINxeSmS1TeZTXgZ++AaCprRaaoWpfjVrh9EopNE0rsXz//v3Url3bKaFKc/HiRUaNGkVAQACBgYFMmDCh1Kbt13r16oWmacU+HnnkkWJjTp48ycCBA/H19aVevXo89dRTFBYWuqwOISqq9R2dATguV+OUW/KBDZzyMmFQirhOw/WOI6q4u+6MpabNToFBY9Ouz/SOU2V8f+1IXFhAO52T3L5yTx1Qq1YtR8PRsmXLYg2TzWYjOzu7RCPiTKNGjeLMmTPEx8djtVoZP348kydPZtGiRWU+b9KkScXeHvT19S2We+DAgQQHB/Ptt99y5swZxowZg9lsZvbs2S6rRYiKuCdyBG9uW8NZM3x/LpVm9eRmsDfz7ZFlADQqNFOrxh06pxFVncFopFmhH3uNuez/YSNDcN3vOk9xKes8P5gLAY1uEVV/9vxyN0v//ve/UUrxhz/8gZkzZ1KzZk3HY15eXjRp0oTo6GiXhDx69Chr164lKSmJzp2L/sp+6623GDBgAK+//johISE3fK6vry/BwcGlPrZ+/XqOHDnChg0bCAoKIjIyklmzZvHMM8/w4osv4uXl5ZJ6hKiIsLCOtNho55i3kTXJi5jS/wW9I7m9tOyD4AMtrt0IVYjbFVajFXsL93IiP03vKFXC+qSF2DSNIKudzm2r/q3Qyt0sjR07FoCmTZvSrVu3Um+m6yqJiYkEBgY6GiWAmJgYDAYDO3fu5IEHHrjhcxcuXMinn35KcHAwgwYN4vnnn3ccXUpMTKRt27YEBQU5xvfr149HH32Uw4cP06FDB9cVJUR5aRph6g6OcZkDGd/qncbt2W020oxXACMdQuV8JeEcXZr3Z+mxvaR55VOQfxUvi7fekdza3pMJoEGYLaDKn68E5WyWMjMzCQgIAKBDhw7k5eWRl5dX6tjr45wpIyODevWKT2hlMpmoXbs2GRkZN3zeyJEjady4MSEhIRw4cIBnnnmGlJQUli1b5ljvrxslwPF5WevNz88nPz/f8XlmZiYAVqsVq9VaseLKcH1dzlynu/H0Gp1VX4uASLAmkGo/41ZfK3fcf3v2rueklxFNKfp2ePC2s7ljjc4k9ZVPjzsH4nXkZS4ZDWzdtZSed7nPuXDuuA+/LzgBFgir0dqtvwfLu85yNUu1atXizJkz1KtXj8DAwFJP8L5+4rfNZit3yOnTp/Pqq6+WOebo0aPlXt9vTZ482fH/tm3bUr9+ffr06UNaWhphYWG3vN5XXnml1Cv/1q9fX+ycKGeJj493+jrdjafXeLv1WaxhGNVmzpnsfLLiI+7wquukZM7hTvtv/8lPIQBCrSZ2bk1y2nrdqUZXkPpurlGBF6neVrbs+4Kci/5OSOVc7rIP861XSTNbAY0ahc1YvXq1U9brivpKmwqpNOVqljZt2uS40m3z5s23nuo3nnzyScaNG1fmmGbNmhEcHMy5c+eKLS8sLOTixYs3PB+pNFFRUQCkpqYSFhZGcHAwu3YVvxz77NmiK47KWu+zzz7LtGnTHJ9nZmYSGhpKbGysU4+sWa1W4uPj6du3b6W+7VmZPL1GZ9Wn7HZWLniXY95G8v1OMyBmrBNT3jp33H+b3n8FgBbmxgwYMOC21+eONTqT1Fd+2xcvJFUd5bzptFNeW87ibvvwq63vU5CjEWizM3HkXzEYjbe1PlfWd/2doZspV7PUs2fPUv9/u+rWrUvdujf/Czk6OprLly+TnJxMp05FNxPdtGkTdrvd0QCVx759+wCoX7++Y70vv/wy586dc7zNFx8fT0BAAG3a3HimZIvFgsViKbHcbDa75IXqqvW6E0+v0Rn1NbP/ct6Su32t3GX/2W02vjddAUx0atTbqZncpUZXkfpuLqpZLGvSjnLcKwcNhcnsXhcBucs+3H9qE2jQvNAPi7fzzu1yRX3lXV+Fz7pau3Yt27Ztc3w+b948IiMjGTlyJJcuuWayrtatWxMXF8ekSZPYtWsX27dvZ+rUqYwYMcJxJdxPP/1EeHi440hRWloas2bNIjk5mRMnTvDVV18xZswY7rnnHtq1K5rzITY2ljZt2jB69Gj279/PunXreO6555gyZUqpzZAQempR69p8S/bTOidxX8n71nPCy4SmFHFdHtI7jvAw/ToPx6gUZ01GdiSv0juO20q/dsVgc99WOidxngo3S0899ZTjsNXBgweZNm0aAwYMID09vdhbU862cOFCwsPD6dOnDwMGDKB79+68++67jsetVispKSmO9x+9vLzYsGEDsbGxhIeH8+STTzJ06FC+/vprx3OMRiOrVq3CaDQSHR3Nww8/zJgxY+S2LcIt3R350LUf1IoT54/rHcctbTu6FIAmVjN1/YNuMlqIivHz9qeZteho0s7jX99kdPWUl5fLca+iC6CiWt2ncxrnKffUAdelp6c73qL68ssvGTRoELNnz2bPnj0ufQ+3du3aZU5A2aRJE5RSjs9DQ0PZsmXLTdfbuHFjp518JoQrhbfsTIst1+Zb2rWQRwe8qHckt5OSfQh8INxL7gcnXKO5V1OO8x2pOYf1juKWEpK+IMdgwNeu6NlhsN5xnKbCR5a8vLwcR2+uH7mBomamvCdKCSEqTjMYaHrtPnH7Zb6lEmyFhRwzF90CKappP53TCE/VpVnRayvVlE2htUDnNO4n+fu1AIRZfTCbPOd0lgo3S927d2fatGnMmjWLXbt2MXDgQAC+++47GjZs6PSAQohftLqj6M7dx9WN5wGrrrYkL+eCyYDFrujfdZTecYSHiutS9HZ4htnIt7tW6B3H7aRfLTpFoLlvC52TOFeFm6X/+7//w2QysXTpUt5++20aNGgAwJo1a4iLi3N6QCHEL3p1HIVRKc6ZFMczbn0OMk+0/buVALQssODr7adzGuGp/L39aVJYdIVX0rXXnChyNS+H77yKJqyOaj5Q5zTOVeFzlho1asSqVSWvAnjjjTecEkgIcWNhYZG02Kg4ZtFYl7SQFoP+oXckt5GSlwIWaOXtWX/RCvfT0rs5abbDpOcd0zuKW0nYuYTLRgPedkVMx9/rHcepKtwsAdhsNlasWOGYXTsiIoL7778f421OPCWEuLlmqh7HOM/Bczv0juI28q7m8J05D9CIbu45V+AI93RXywGsOXqY41655OVk4VPD/Wbz1sPu71eDEZoX1sDi5TnnK8EtvA2XmppK69atGTNmDMuWLWPZsmU8/PDDREREkJYmd2MWwtXa1IkGIJWzOidxH6t3fkqeQaOWzU7vrsP0jiM8XL/2v8OoFKfNJrbv+FzvOG4jraCoB2jlF6FzEuercLP0+OOPExYWxqlTp9izZw979uzh5MmTNG3alMcff9wVGYUQv3Jvl9HXzluCY6cO6h3HLexKXwNAuNUPs5vNqiw8Tw2LH2GFNQDYnS5TzwBcunSOY5aim9L2unOozmmcr8LN0pYtW3jttdcc94oDuOOOO5gzZ0655jUSQtye0EataXHtiuX1yQv1DeMmUqwnAAj3j9Q1h6g+IvzuBCDNmqpzEvewOfETsg0GatgVPSI872KvCjdLFouFrKysEsuzs7Px8pK/6ISoDM20ovsbHj4v5y2duXCKdHMhAPe2lykDROWIaTccgMOWQi6cl6k89v+4EYAWtkCMBs87f7nCzdJ9993H5MmT2blzJ0oplFLs2LGDRx55hPvvv98VGYUQv9EmuAcAaZzXOYn+Vu2Yj13TaFRgp33r7nrHEdXE3eF98LMpsowGNiZ+pHcc3aXbTwFwZ60OOidxjQo3S3PnziUsLIzo6Gi8vb3x9vbm7rvvpnnz5rz55puuyCiE+I3Yu/6ASSnOmjUOpGzVO46u9p0pqr+FqotmqPCPNCFuidFgpJW96HSUA2c26ZxGX6d/TOWYxQ5AbMeROqdxjQpPHRAYGMjKlStJTU11TB3QunVrmjdv7vRwQojS1a/bkLACEykWG/F7F9Gu1T16R9KFUoqjWtFVge3q3q1zGlHdtL2jC8mZ6zmuftI7iq427/qYPIOBABtENrlL7zguUe4/w+x2O6+++ip33303Xbp04f333ycmJoZBgwZJoySEDlqYmwBw5Mo+XXPoKTltOz+bwMuu6B89Ue84opoZ0GUMACkWSP+h+t5Y9/C5bwBoSV00TdM5jWuUu1l6+eWX+dvf/oafnx8NGjTgzTffZMqUKa7MJoQoQ9emRbcTSDFnYa2mN/Rcu+dTACLyDdQPbqpzGlHdtG7YnmCrhk3TiN/5od5xdKHsdo5fO7rbOchzj+6Wu1n6+OOP+c9//sO6detYsWIFX3/9NQsXLsRut7synxDiBuKiR+Jjt3PFaGDjrs/0jqOLA5n7AGhpkkZJ6CPcUHR/1MMXq+eVqYcOJZBiKWol7r/rDzqncZ1yN0snT55kwIABjs9jYmLQNI3Tp0+7JJgQomw+lhq0shZNjJdYDW/omZOfTaopG4AuTeQWJ0IfXRvHAnDUdIlCq1XnNJUvYf9ClKYRajUSeofn/tFS7mapsLAQb2/vYsvMZjPWavjiEMJdtPZrC0BqQfWbGG9V8hKsmkaItZB7okfoHUdUU0O6/QEvu+KM2cjmndXv1ifHsvcD0Nri2TewLvfVcEopxo0bh8Xyy83xrl69yiOPPEKNGjUcy5YtW+bchEKIG7q3/QgW795Filch5y6cod4d9fWOVGm2Hf8KgDYF/nIjU6Ebf5+ahFt9OWDJY9t3y+jbvfpMjJqddZHDXrmAkZ7hD+gdx6XKfWRp7Nix1KtXj5o1azo+Hn74YUJCQootE0JUnqg2MdxRqMg3aKzbXn1OMFVKcbjwBwBa1+yicxpR3bULKJqI8Uhh9TrCu+mbj7lgMuJtV/SL/J3ecVyq3EeW5s+f78ocQohboGkarVQdvuUCB89sBv6ud6RKceinffxssmNWij5dxusdR1RzAzr/gU+3f8t3XjZ+OP0djUNa6h2pUiT/uBYs0MoWiMXsffMnVGEy3a0QVVy7oKJbfKRpp1HV5OrUVbuKjqJFXFWEteyscxpR3bVtHkXjArBrGl8l/lfvOJVC2e2kqKJbnLSvE6VzGteTZkmIKm5Q9AQAjnsZOHwoQd8wlWTfxd0AtDB47tU3omppo4UCsO9C9ZhC4NCxbzlqKZqAcmi3yTqncT1ploSo4hrVaUoDqwmlaSTs/VjvOC6Xk5/NcVMWAF2bDtI5jRBF7mpSNLXOEdMV8q1XdU7jeuv3FN3AukmBkWb1Wukdx+WkWRLCA0R4F50jcTRnv85JXG9V0iKsmkZ9q42ed1efK4+Ee4vrNpZAm51so8aaXYv1juNyB6/9rGlrqR7nZ0mzJIQH6Nu2aJ6hA975XDrv2RPFbkv7GoDWVn98fP10TiNEEV9ff+4sKJpG55vjy3VO41oXM89z2CsPgL5thumcpnJIsySEB+jT9j5q2OCy0ci6re/qHcdllFIcvTZlQJvArjqnEaK4OwOLTnQ+VHgCpZTOaVxn5da3uWowULfQTs8Onj2/0nXSLAnhAcwGM22oC8D+s5t1TuM6h07t46xJYVKKmK4T9I4jRDH3dfsTZqU4bVYkH9+mdxyXSTqzAYAIezAGo1HnNJVDmiUhPER0wz4AHDOe89jbEH298z0A2lyFsLBIfcMI8RuNG7Wm7dWi5uGr3e/rnMY1CgutHDKcByAqNE7nNJVHmiUhPMQD3SahKUWqxcT2xC/1juMSBy4XTRnQ0uzZ96ESVVeEdwQA+3IP6pzENdZ8+wmXTAZq2O0MueePesepNNIsCeEh6vjVI6zQB4DEFM+7oeeFrHOkmHMBuKeN3DhXuKe+keMxKEW62cr3577TO47TJRwv+kMsoiAAP98AndNUHmmWhPAgHQI7AnDMlgIedoLpsq1vU6hpNLDa6dn193rHEaJUke36EHG1aCb9L7a/rXMa51JKsY+TAHSp013nNJWryjRLFy9eZNSoUQQEBBAYGMiECRPIzs6+4fgTJ06gaVqpH1988YVjXGmPL1mypDJKEsLphkb/CYAD3hqHj3jWCaZJpzcB0KYanVQqqh7NYKDNtZnlky4m6pzGuTbvX8U5E3jb7TzQ43G941SqKtMsjRo1isOHDxMfH8+qVavYunUrkyffeIr10NBQzpw5U+xj5syZ+Pn50b9//2Jj58+fX2zckCFDXFyNEK4R0aA9oVYThZrG+t2ec48qq7WAI8aik0q7Nup/k9FC6Ktb2IMAHDdmcz7nZ53TOM//DhTdISDyqoWgeqE6p6lcVaJZOnr0KGvXruX9998nKiqK7t2789Zbb7FkyRJOny59Aj6j0UhwcHCxj+XLlzNs2DD8/IpPZBcYGFhsnLe3Z989WXi2SN+2ABzMO6BzEudZnfgxV4wG/G12BvV8RO84QpSpe/cRtMy3Ytc0PtvmGW/FKaXYZy06ByvSv/rdvLpKNEuJiYkEBgbSufMvOygmJgaDwcDOnTvLtY7k5GT27dvHhAkl52aZMmUKderUoWvXrnz44YcePZmY8HwPdC26QmWft53UtL06p3GObceXARBhDaCGj8zaLdybl8WbCFt9ALb/GK9zGufYmZrAOZMdb7ud/t2m6B2n0pn0DlAeGRkZ1KtXr9gyk8lE7dq1ycjIKNc6PvjgA1q3bk23bt2KLX/ppZe499578fX1Zf369fzpT38iOzubxx+/8fux+fn55OfnOz7PzMwEwGq1OnV+m+vr8tQ5c8Dza9SjvvaNuhCSYOC02c6q7fOY0sh1f9lWRn3KbueI/SSg0e6ObpX+WpHXaNWmV32dQ+9n+YUPOWa8xMWsC/h7u+7Kscqo8ctdRW/rR141ERraplK/nq6sr7zr1LVZmj59Oq+++mqZY44ePXrb28nLy2PRokU8//zzJR779bIOHTqQk5PDP//5zzKbpVdeeYWZM2eWWL5+/Xp8fX1vO+9vxcd7xl8mZfH0Giu7vubWBpw2n2J/dhKrV692+fZcWd+Zi4c46aVhVIpatjsrpZ7SyGu0aqvs+gqtDQgtKOSUl4l/f/4CnerEunybrqpRKcWevCNghkbW5h71PZibm1uucbo2S08++STjxo0rc0yzZs0IDg7m3LlzxZYXFhZy8eJFgoODb7qdpUuXkpuby5gxY246NioqilmzZpGfn4/FYil1zLPPPsu0adMcn2dmZhIaGkpsbCwBAc7768FqtRIfH0/fvn0xm81OW6878fQa9arvjhQLW5OfYr+vjeltm9IstLVLtlMZ9c3+aD4YoKXVm+GjHnbJNsoir9GqTc/6dr7/f5zyusQpDvP8gH+7bDuurnFn2lbO7VR42+08GDu90mfPd2V9198Zuhldm6W6detSt27dm46Ljo7m8uXLJCcn06lTJwA2bdqE3W4nKirqps//4IMPuP/++8u1rX379lGrVq0bNkoAFoul1MfNZrNLXqiuWq878fQaK7u+uyP60SjxaU56wcrEuTzdzLW3XnBVfcpu55DtOJgNdK4VretrRF6jVZse9XUNvY81Fz7hsOE8hcqKj5fz33n4NVfV+FVy0c+PyKtGwsO7OH395eWK+sq7vipxgnfr1q2Ji4tj0qRJ7Nq1i+3btzN16lRGjBhBSEgIAD/99BPh4eHs2rWr2HNTU1PZunUrEydOLLHer7/+mvfff59Dhw6RmprK22+/zezZs3nssccqpS4hXEXTNLp43wnA7pzdOqe5dTt3f80xbwOaUgy/5896xxGiQgb2fpRgq408g8bn297VO84tUUqx5+oRANr5dtI5jX6qRLMEsHDhQsLDw+nTpw8DBgyge/fuvPvuLy8+q9VKSkpKifcfP/zwQxo2bEhsbMn3i81mM/PmzSM6OprIyEj++9//8q9//YsZM2a4vB4hXO130U+gKcVRi41Dx7/VO84t2XBgPgAtrN40rtdc5zRCVIxPDX8irXcAsCV9pc5pbs23x7dw9tpVcAPurl4TUf5albgaDqB27dosWrToho83adKk1Ev+Z8+ezezZs0t9TlxcHHFx1eeuyaJ6ade8K202mjjsbeOzxDe5s0W3mz/Jjfz6LbgutaP1jiPELYlqOJC1Fxdy0PAz2fnZ+Fmq1tQXS5OKrqbtfNVEWPMOOqfRT5U5siSEqLgu/kXn9CUVHKly84cl7lzBYe+iH1Ej7nlC3zBC3KKB904hxGrjqkFjyea39I5TITa7jeT8oivSI2t01TmNvqRZEsKDjej9NBa74iczbEhernecCtl8sOgtuOZWb5rUDdM5jRC3xqeGP+1tRVdtbzu1Suc0FbPuwHIuGRUBNhv9ez6pdxxdSbMkhAdrUD+Mjvk+AKw84Nor4pzJWpDPAZUKQFSdHjqnEeL29GzxEAAHTVe4cOWszmnK7+t9HwLQ+aovjRqH65xGX9IsCeHhetQrurhht3aSnPwcndOUz4aN73HE24RBKcb2rt5/0YqqL+6e8YRY7RQYNJZsfF3vOOWSb73KXvtJADrV7atzGv1JsySEhxsa+1fqW23kGDQ+2fKm3nHKZVv6EgAibLWoX7OBzmmEuD1Gk4lIQzMAkn7erHOa8vl8+3vkGDXqFdoYHDvt5k/wcNIsCeHhfP1qcVdh0U0940+5/+XLl86fYbfXBQBimz+ocxohnKN/5CQADliucuLHYzqnublNqUsB6FhwBzVr3nxCZ08nzZIQ1UBMm8kYlOI7Uy5HTu/XO06Zvo7/J6fNJnztMOLuyXrHEcIpenYYRKMCDaum8dnmOXrHKdOlrJ85YCz6g6VHM/mDBaRZEqJa6H73g3TOK5o64MMtr+mcpmw7Lm0EoJOxKd4mb53TCOEcmqYR5Vs0T1FSXjLKbtc50Y0tWPcPCgwaoQV2Btz7qN5x3II0S0JUAwajgS6+dwGQmHcQq82qc6LS7U5aTaKvDYDRd8l5EsKzPNzn7xiVIsUCm7Yt1DvODW2/uAWAzsZwTB58v8CKkGZJiGrigZi/U7fQRqZRsSTxA73jlGrVnjco1DSaWS1Et+yldxwhnKpZcEvutAYAsP6Ie07lsX3fGlIsNoxKMfyeZ/SO4zakWRKimghq0Izo/EAAvkr5WN8wpbh06RzfGn8CoF/DwTqnEcI1+oYVnQO02/wzF8+f1jlNSSt2zwWgbb43Ec2r96zdvybNkhDVSJ9WkzAoxTFTFod+2qN3nGKWrJnJGbMRP5ti/L0yt5LwTCN6PIq/Dc6ZjHy59h96xykmO/syu7WiuZV6NRiocxr3Is2SENVIr15j6Zpb9P93N7nPD2q7zcaG7K0A3GO+Ex8vX50TCeEaFrM3UV5Fs2EnZm3BbrPpnOgXn61+ifMmAzVtilF95S24X5NmSYhqxGA00K1mHwASC7/jSt5lfQNd88WGuXxnAYtd8WjfWXrHEcKlJvd5AYDdPhrx69/WOU0RZbez7UI8AF2MLfC2yB8svybNkhDVzIP3zaBpQSFXDRpvr39Z7zgAfHXiUwC6FQbRJLiFzmmEcK3W9dtyp602StPY/P18veMAsGHzhyT7KDSlmHjvi3rHcTvSLAlRzfjVrE13mgOw8fx67Erf+V427PqCA94FRfeBu/sFXbMIUVlGdpoKwFafqxzcvV7nNLD+2HsoTeNOWyARoe31juN2pFkSohp6sM8/8LPZyTDZ+fKbd3TN8vH+fwHQJd+PTm166ppFiMoysN1Qgm1eZBkNLNs1W9cshw9uY7tPNgDD2/9J1yzuSpolIaqhps3ac1dBHQBWHNPvbYAth9ew1ysbg1KMbCuTUIrqw6AZGNZ0JAAbvc+R9t1u3bKs+OY5sowGggpNDOo0Qrcc7kyaJSGqqQfvehaDUhywXCV+11JdMszbUXQyd49cL+7tNkyXDELoZXzPP1Ov0Mglo5HFG6frkiH16A7iLecA+F2TkRg0aQtKI18VIaqpbpFxdM33A2Dx3tcrfftr9n3JUVMWJqUY2uYvlb59IfRmMpgY2ng4APFep0k5tqPSMyzd/DcumIzUsRmZ1PuJSt9+VSHNkhDV2KiOfwVgtyWbb3Z+WWnbtSs7/0l+FYA+Od707jW60rYthDuZ1PuvBBUauWgyMn9z5c5t9N3RncRbzgAwtNFwzAa5D9yNSLMkRDXWq8vvaZ9fA6VpfLFnNihVKdud/+08TpjyqGG38/sOz1bKNoVwR2ajmfEtJgEQ732BHXvXVNq2F26axjmTiTtsRib1lnMGyyLNkhDV3JguRc3KNz75rN/wnsu3l2PNYX5K0U1EB2XX5K5uQ12+TSHc2cgef6JNgTcFBo13dz6Hsrt+Oo+tWxayxvcyABNaTsZitLh8m1WZNEtCVHOxHQZzp60WhZrG0uNvUViQ79Ltzf7fU1wx2mloLWRE3zddui0hqgJN03jsrlkYlSLJp4B3//eiS7dnLyxkyeFXyTMYaFHox8N3P+rS7XkCaZaEEDxz7+sYlCKxBiz5zHWH49POH2fN5aJ7wA22tSEsvIvLtiVEVdK9bRxxtiYAfPLzMs5cOuWybb3zxZ/5pobCoBRP3fMKmqa5bFueQpolIQSRTbrS3dwagJV5GzmZdtjp21BK8bevJ2LVNDrlWRnxe/e4J5YQ7uKZoR/StMDGFaPGU8tHo1xwDuGR1CQW5SUAEGe6k+gWvZy+DU8kzZIQAoAZg+fha4djFjML/zceZXfu3dA/SPgXRwwX8bIrhjWYTOAd9Zy6fiGqulqB9fhDg0mYlWK/8QL/b51zb/9jLSxg1qZHuGI00LjAwEvDFjh1/Z5MmiUhBAD1/OrxSMvJACz1z+XLT50399Gpn9P5ML1opvD7c2sxYJBceSNEaYYM+AsjcoIA+DRjOTvStzlt3U8vHskhSwE+djtPd5qFxcvbaev2dNIsCSEcxnWbSltjQwoMGh8WxJOUuPK212m32Xh++UiyjBrN8m088ruPnZBUCM81efin9Mq2YtM0nt48lYzsM7e9zv+Lf5kN9hQAxnr14J6O99/2OqsTaZaEEA6apjFv6ELq2EycMpv494HpfJ+697bWOWfROJIt2ZiUYlLLaQTVb+qktEJ4psA69flD5/9HswIrl4w2/vDlg+Rac295fQuTPuDdnxYDMCSnJn966D/OilptSLMkhCimlk9t3uj7Lr52OOBt4vkNoznxY8otreuzpc+x1FbUbA01RnJfr4nOjCqEx+oQNZBJ/g9S22bjFFeYtGQoVru1wutZeXAprx1+A6Vp3Jdp568PrUAzyK/+iqoyX7GXX36Zbt264evrS2BgYLmeo5TihRdeoH79+vj4+BATE8Px48eLjbl48SKjRo0iICCAwMBAJkyYQHZ2tgsqEKLqiAztwpyur+FjVxzw0Xh07VC2HlpdoXWs+mIm8zKXYdU02hfW5m8jP3JRWiE8033DX2KyrTNedsUB+49MXvQAhfbCcj//o6R3eSF5JnZNIzbLymP3L6NmrTouTOy5qkyzVFBQwIMPPsijj5Z/8qzXXnuNuXPn8s4777Bz505q1KhBv379uHr1qmPMqFGjOHz4MPHx8axatYqtW7cyefJkV5QgRJXSO6I//+zwCnUK7fxo1nhs99M8u/JPXMm/Uubzrubl8Nk7I/lX5hIuGY00LvThnYdXYTAaKym5EB5C0xg5YQGP5LfCpBS7bT8w4cPeXM48X+bTCu2FPPfV47x+5C3sGgzIKmBK7wWENG5VScE9T5VplmbOnMlf/vIX2rZtW67xSin+/e9/89xzzzF48GDatWvHxx9/zOnTp1mxYgUAR48eZe3atbz//vtERUXRvXt33nrrLZYsWcLp06ddWI0QVUPPyEG83ftTuueAXdNYdfkbYhbfw4wN00m5mFJsHphCawE71rzHvP925XXLfn42mQhRfiwY8T/8LP46ViFE1aUZDEyc/AWPqM6YlGKP+TLjl/Ti65WvUWgtKDE+6UgCw+d3Z+WlzQAMu2zn8QHLaRZxV2VH9ygmvQO4Snp6OhkZGcTExDiW1axZk6ioKBITExkxYgSJiYkEBgbSuXNnx5iYmBgMBgM7d+7kgQce0CO6EG4lvFkH/t+YbXz68cOsN31HisWLZT/9j2U//Y9Au4mQfG/WfTAHq7rEAW8jubWK/gZra2nGf3/3Kf5e0igJcTs0g4E/jl9A4JrXmXtmPqkWAzMufcyOd94nwt4YX3M9fsz7mb++O4NvahRiNWn42u2MzW3EmPGL8AuopXcJVZ7HNksZGRkABAUFFVseFBTkeCwjI4N69YpPjGcymahdu7ZjTGny8/PJz//l/lmZmZkAWK1WrNaKn4B3I9fX5cx1uhtPr9FT6jNbfBk/aRndkjey+9tZ7LdksKWGD5cNhVz2uX6OnxmAOsqHSe2n8vuIEWiaVuVr95R9eCNSX9Xxu5g/0z4jlpkb/swhw3m+CrDwFRlABtS4Pkqj/VUz48OncU+34UDVr92V+7C869S1WZo+fTqvvvpqmWOOHj1KeHh4JSUqn1deeYWZM2eWWL5+/Xp8fX2dvr34+Hinr9PdeHqNnlRfrbCn6ZZzkc7nD3GpMJ0MUw45RhNmSzANa7alkbkJ2kmNNSfX6B3VqTxpH5ZG6qs6htf6M12saezKSuBHzpCnWalpN9PAXpf2Pt1oHtSW7Msaq1dX7KIMd+eKfZibW74pGXRtlp588knGjRtX5phmzZrd0rqDg4MBOHv2LPXr13csP3v2LJGRkY4x586dK/a8wsJCLl686Hh+aZ599lmmTftlBuLMzExCQ0OJjY0lICDglvKWxmq1Eh8fT9++fTGbzU5brzvx9BqlvqrP02uU+qqyxwFPr9G19V1/Z+hmdG2W6tatS926dV2y7qZNmxIcHMzGjRsdzVFmZiY7d+50XFEXHR3N5cuXSU5OplOnTgBs2rQJu91OVFTUDddtsViwWCwllpvNZpe8UF21Xnfi6TVKfVWfp9co9VV9nl6jK+or7/qqzNVwJ0+eZN++fZw8eRKbzca+ffvYt29fsTmRwsPDWb58OVA0E/ETTzzBP/7xD7766isOHjzImDFjCAkJYciQIQC0bt2auLg4Jk2axK5du9i+fTtTp05lxIgRhISE6FGmEEIIIdxMlTnB+4UXXuCjj36Z1K5Dhw4AbN68mV69egGQkpLClSu/zAHz9NNPk5OTw+TJk7l8+TLdu3dn7dq1eHv/cvPAhQsXMnXqVPr06YPBYGDo0KHMnTu3cooSQgghhNurMs3SggULWLBgQZljfj3nCxQdXXrppZd46aWXbvic2rVrs2jRImdEFEIIIYQHqjJvwwkhhBBC6EGaJSGEEEKIMkizJIQQQghRBmmWhBBCCCHKIM2SEEIIIUQZpFkSQgghhCiDNEtCCCGEEGWQZkkIIYQQogzSLAkhhBBClEGaJSGEEEKIMlSZ2524s+u3WcnMzHTqeq1WK7m5uWRmZnrsnaQ9vUapr+rz9BqlvqrP02t0ZX3Xf2//9nZpvyXNkhNkZWUBEBoaqnMSIYQQQlRUVlYWNWvWvOHjmrpZOyVuym63c/r0afz9/dE0zWnrzczMJDQ0lFOnThEQEOC09boTT69R6qv6PL1Gqa/q8/QaXVmfUoqsrCxCQkIwGG58ZpIcWXICg8FAw4YNXbb+gIAAj/wG+DVPr1Hqq/o8vUapr+rz9BpdVV9ZR5SukxO8hRBCCCHKIM2SEEIIIUQZpFlyYxaLhRkzZmCxWPSO4jKeXqPUV/V5eo1SX9Xn6TW6Q31ygrcQQgghRBnkyJIQQgghRBmkWRJCCCGEKIM0S0IIIYQQZZBmSQghhBCiDNIsVbJ58+bRpEkTvL29iYqKYteuXWWO/+KLLwgPD8fb25u2bduyevXqYo8rpXjhhReoX78+Pj4+xMTEcPz4cVeWUKaK1Pfee+/Ro0cPatWqRa1atYiJiSkxfty4cWiaVuwjLi7O1WXcUEXqW7BgQYns3t7exca42/6DitXYq1evEjVqmsbAgQMdY9xpH27dupVBgwYREhKCpmmsWLHips9JSEigY8eOWCwWmjdvzoIFC0qMqej3tatUtL5ly5bRt29f6tatS0BAANHR0axbt67YmBdffLHE/gsPD3dhFWWraI0JCQmlvkYzMjKKjauq+7C07y9N04iIiHCMcad9+Morr9ClSxf8/f2pV68eQ4YMISUl5abP0/t3oTRLleizzz5j2rRpzJgxgz179tC+fXv69evHuXPnSh3/7bff8tBDDzFhwgT27t3LkCFDGDJkCIcOHXKMee2115g7dy7vvPMOO3fupEaNGvTr14+rV69WVlkOFa0vISGBhx56iM2bN5OYmEhoaCixsbH89NNPxcbFxcVx5swZx8fixYsro5wSKlofFM04++vsP/zwQ7HH3Wn/QcVrXLZsWbH6Dh06hNFo5MEHHyw2zl32YU5ODu3bt2fevHnlGp+ens7AgQPp3bs3+/bt44knnmDixInFGopbeV24SkXr27p1K3379mX16tUkJyfTu3dvBg0axN69e4uNi4iIKLb/tm3b5or45VLRGq9LSUkpVkO9evUcj1Xlffjmm28Wq+vUqVPUrl27xPegu+zDLVu2MGXKFHbs2EF8fDxWq5XY2FhycnJu+By3+F2oRKXp2rWrmjJliuNzm82mQkJC1CuvvFLq+GHDhqmBAwcWWxYVFaX++Mc/KqWUstvtKjg4WP3zn/90PH758mVlsVjU4sWLXVBB2Spa328VFhYqf39/9dFHHzmWjR07Vg0ePNjZUW9JReubP3++qlmz5g3X5277T6nb34dvvPGG8vf3V9nZ2Y5l7rQPfw1Qy5cvL3PM008/rSIiIootGz58uOrXr5/j89v9mrlKeeorTZs2bdTMmTMdn8+YMUO1b9/eecGcqDw1bt68WQHq0qVLNxzjSftw+fLlStM0deLECccyd96H586dU4DasmXLDce4w+9CObJUSQoKCkhOTiYmJsaxzGAwEBMTQ2JiYqnPSUxMLDYeoF+/fo7x6enpZGRkFBtTs2ZNoqKibrhOV7mV+n4rNzcXq9VK7dq1iy1PSEigXr16tGrVikcffZQLFy44NXt53Gp92dnZNG7cmNDQUAYPHszhw4cdj7nT/gPn7MMPPviAESNGUKNGjWLL3WEf3oqbfQ8642vmTux2O1lZWSW+B48fP05ISAjNmjVj1KhRnDx5UqeEty4yMpL69evTt29ftm/f7ljuafvwgw8+ICYmhsaNGxdb7q778MqVKwAlXnO/5g6/C6VZqiTnz5/HZrMRFBRUbHlQUFCJ986vy8jIKHP89X8rsk5XuZX6fuuZZ54hJCSk2As+Li6Ojz/+mI0bN/Lqq6+yZcsW+vfvj81mc2r+m7mV+lq1asWHH37IypUr+fTTT7Hb7XTr1o0ff/wRcK/9B7e/D3ft2sWhQ4eYOHFiseXusg9vxY2+BzMzM8nLy3PK696dvP7662RnZzNs2DDHsqioKBYsWMDatWt5++23SU9Pp0ePHmRlZemYtPzq16/PO++8w5dffsmXX35JaGgovXr1Ys+ePYBzfna5i9OnT7NmzZoS34Puug/tdjtPPPEEd999N3feeecNx7nD70KTU9YixG2aM2cOS5YsISEhodhJ0CNGjHD8v23btrRr146wsDASEhLo06ePHlHLLTo6mujoaMfn3bp1o3Xr1vz3v/9l1qxZOiZzjQ8++IC2bdvStWvXYsur8j6sThYtWsTMmTNZuXJlsfN5+vfv7/h/u3btiIqKonHjxnz++edMmDBBj6gV0qpVK1q1auX4vFu3bqSlpfHGG2/wySef6JjM+T766CMCAwMZMmRIseXuug+nTJnCoUOHdD0HrrzkyFIlqVOnDkajkbNnzxZbfvbsWYKDg0t9TnBwcJnjr/9bkXW6yq3Ud93rr7/OnDlzWL9+Pe3atStzbLNmzahTpw6pqam3nbkibqe+68xmMx06dHBkd6f9B7dXY05ODkuWLCnXD1699uGtuNH3YEBAAD4+Pk55XbiDJUuWMHHiRD7//PMSb3f8VmBgIC1btqwS++9Gunbt6sjvKftQKcWHH37I6NGj8fLyKnOsO+zDqVOnsmrVKjZv3kzDhg3LHOsOvwulWaokXl5edOrUiY0bNzqW2e12Nm7cWOzow69FR0cXGw8QHx/vGN+0aVOCg4OLjcnMzGTnzp03XKer3Ep9UHQFw6xZs1i7di2dO3e+6XZ+/PFHLly4QP369Z2Su7xutb5fs9lsHDx40JHdnfYf3F6NX3zxBfn5+Tz88MM33Y5e+/BW3Ox70BmvC70tXryY8ePHs3jx4mJTPtxIdnY2aWlpVWL/3ci+ffsc+T1hH0LRVWapqanl+oNFz32olGLq1KksX76cTZs20bRp05s+xy1+FzrlNHFRLkuWLFEWi0UtWLBAHTlyRE2ePFkFBgaqjIwMpZRSo0ePVtOnT3eM3759uzKZTOr1119XR48eVTNmzFBms1kdPHjQMWbOnDkqMDBQrVy5Uh04cEANHjxYNW3aVOXl5bl9fXPmzFFeXl5q6dKl6syZM46PrKwspZRSWVlZ6q9//atKTExU6enpasOGDapjx46qRYsW6urVq25f38yZM9W6detUWlqaSk5OViNGjFDe3t7q8OHDjjHutP+UqniN13Xv3l0NHz68xHJ324dZWVlq7969au/evQpQ//rXv9TevXvVDz/8oJRSavr06Wr06NGO8d9//73y9fVVTz31lDp69KiaN2+eMhqNau3atY4xN/uauXN9CxcuVCaTSc2bN6/Y9+Dly5cdY5588kmVkJCg0tPT1fbt21VMTIyqU6eOOnfuXKXXp1TFa3zjjTfUihUr1PHjx9XBgwfVn//8Z2UwGNSGDRscY6ryPrzu4YcfVlFRUaWu05324aOPPqpq1qypEhISir3mcnNzHWPc8XehNEuV7K233lKNGjVSXl5eqmvXrmrHjh2Ox3r27KnGjh1bbPznn3+uWrZsqby8vFRERIT63//+V+xxu92unn/+eRUUFKQsFovq06ePSklJqYxSSlWR+ho3bqyAEh8zZsxQSimVm5urYmNjVd26dZXZbFaNGzdWkyZN0uUH2HUVqe+JJ55wjA0KClIDBgxQe/bsKbY+d9t/SlX8NXrs2DEFqPXr15dYl7vtw+uXkf/243pNY8eOVT179izxnMjISOXl5aWaNWum5s+fX2K9ZX3NKlNF6+vZs2eZ45Uqmiqhfv36ysvLSzVo0EANHz5cpaamVm5hv1LRGl999VUVFhamvL29Ve3atVWvXr3Upk2bSqy3qu5DpYouk/fx8VHvvvtuqet0p31YWm1Ase8rd/xdqF0LL4QQQgghSiHnLAkhhBBClEGaJSGEEEKIMkizJIQQQghRBmmWhBBCCCHKIM2SEEIIIUQZpFkSQgghhCiDNEtCCCGEEGWQZkkIIYQQogzSLAkh3Na4ceNK3EG9Mo0ePZrZs2frtv2bWbt2LZGRkdjtdr2jCOHRpFkSQuhC07QyP1588UXefPNNFixYoEu+/fv3s3r1ah5//HHy8/OJiIhg8uTJJcY9/fTTNG3alKysrErPGBcXh9lsZuHChZW+bSGqE7ndiRBCFxkZGY7/f/bZZ7zwwgukpKQ4lvn5+eHn56dHNAAmTpyIyWTinXfeASA5OZno6Gi+/vpr+vXrB8COHTvo0aMHGzZsoGfPnk7dvlIKm82GyWQqc9y8efNYsGABSUlJTt2+EOIXcmRJCKGL4OBgx0fNmjXRNK3YMj8/vxJvw/Xq1YvHHnuMJ554glq1ahEUFMR7771HTk4O48ePx9/fn+bNm7NmzZpi2zp06BD9+/fHz8+PoKAgRo8ezfnz52+YzWazsXTpUgYNGuRY1qlTJ/7+978zYcIELl++zNWrVxk/fjyPPfYYPXv2ZNu2bfTo0QMfHx9CQ0N5/PHHycnJcTz/k08+oXPnzvj7+xMcHMzIkSM5d+6c4/GEhAQ0TWPNmjV06tQJi8XCtm3b2L9/P71798bf35+AgAA6derE7t27Hc8bNGgQu3fvJi0t7XZ2hxCiDNIsCSGqlI8++og6deqwa9cuHnvsMR599FEefPBBunXrxp49e4iNjWX06NHk5uYCcPnyZe699146dOjA7t27Wbt2LWfPnmXYsGE33MaBAwe4cuUKnTt3Lrb873//O8HBwTz++OM899xzaJrG7NmzSUtLIy4ujqFDh3LgwAE+++wztm3bxtSpUx3PtVqtzJo1i/3797NixQpOnDjBuHHjSmx7+vTpzJkzh6NHj9KuXTtGjRpFw4YNSUpKIjk5menTp2M2mx3jGzVqRFBQEN98881tfmWFEDekhBBCZ/Pnz1c1a9YssXzs2LFq8ODBjs979uypunfv7vi8sLBQ1ahRQ40ePdqx7MyZMwpQiYmJSimlZs2apWJjY4ut99SpUwpQKSkppeZZvny5MhqNym63l3js8OHDytvbW3l5eamkpCSllFITJkxQkydPLjbum2++UQaDQeXl5ZW6jaSkJAWorKwspZRSmzdvVoBasWJFsXH+/v5qwYIFpa7jug4dOqgXX3yxzDFCiFsnR5aEEFVKu3btHP83Go3ccccdtG3b1rEsKCgIwPEW1/79+9m8ebPjHCg/Pz/Cw8MBbvjWVV5eHhaLBU3TSjzWpk0bhg4dSt++fR1Hnvbv38+CBQuKbaNfv37Y7XbS09OBonOeBg0aRKNGjfD393ec43Ty5Mli6//t0axp06YxceJEYmJimDNnTqmZfXx8HEfShBDOJ82SEKJK+fVbUFB0Vd2vl11vcK5fTp+dnc2gQYPYt29fsY/jx49zzz33lLqNOnXqkJubS0FBQamPm0ymYideZ2dn88c//rHY+vfv38/x48cJCwsjJyeHfv36ERAQwMKFC0lKSmL58uUAJbZRo0aNYp+/+OKLHD58mIEDB7Jp0ybatGnjeO51Fy9epG7dujf8mgkhbk/Zl1kIIUQV17FjR7788kuaNGly0yvLrouMjATgyJEjjv/fbBtHjhyhefPmpT5+8OBBLly4wJw5cwgNDQUodpL2zbRs2ZKWLVvyl7/8hYceeoj58+fzwAMPAHD16lXS0tLo0KFDudcnhKgYObIkhPBoU6ZM4eLFizz00EMkJSWRlpbGunXrGD9+PDabrdTn1K1bl44dO7Jt27ZybeOZZ57h22+/ZerUqY6jVitXrnSc4N2oUSO8vLx46623+P777/nqq6+YNWvWTdebl5fH1KlTSUhI4IcffmD79u0kJSXRunVrx5gdO3ZgsViIjo4uV1YhRMVJsySE8GghISFs374dm81GbGwsbdu25YknniAwMBCD4cY/AidOnFjuyR7btWvHli1b+O677+jRowcdOnTghRdeICQkBChqvhYsWMAXX3xBmzZtmDNnDq+//vpN12s0Grlw4QJjxoyhZcuWDBs2jP79+zNz5kzHmMWLFzNq1Ch8fX3LlVUIUXEyKaUQQpQiLy+PVq1a8dlnn7ntUZvz58/TqlUrdu/eTdOmTfWOI4THkiNLQghRCh8fHz7++OMyJ6/U24kTJ/jPf/4jjZIQLiZHloQQQgghyiBHloQQQgghyiDNkhBCCCFEGaRZEkIIIYQogzRLQgghhBBlkGZJCCGEEKIM0iwJIYQQQpRBmiUhhBBCiDJIsySEEEIIUQZploQQQgghyvD/ASCc3e6LjgBsAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Starting angle of planet and moon = (<Quantity 896.96535657 deg>, <Quantity 1076.96535657 deg>)\n",
            "Angle difference = -180 deg\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "_6zpXjdZBD4P"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}