Seasonal_ground_temperature_variation.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "7jiG2sbP2xnj"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "h0m2JnTe2xnm"
      },
      "outputs": [],
      "source": [
        "temp = np.loadtxt(\"Temp_Aachen_2018.csv\", delimiter=\",\")[:,1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "Xir1D6ln2xnn"
      },
      "outputs": [],
      "source": [
        "# Define some helper variables\n",
        "n = 1000\n",
        "days = 365\n",
        "z = np.linspace(0,20, n)\n",
        "year = np.arange(days)\n",
        "\n",
        "# Define parameters of function\n",
        "Tm = np.mean(temp)\n",
        "Td = 9\n",
        "omega = 2*np.pi/days\n",
        "phi = np.pi * 0.85\n",
        "\n",
        "T_s = Tm + Td * np.cos(omega*year + phi)\n",
        "\n",
        "# Calculate fit\n",
        "RMSE = np.sqrt(((T_s - temp)**2).mean())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "a4KbBwQY2xno",
        "outputId": "c1dc92d8-2586-4eb0-dc2a-f3eea79adc84"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f19dc1dd7d0>"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Visualize result\n",
        "plt.plot(year, T_s, label=\"Cosine fit\")\n",
        "plt.plot(year, temp,'.', label=\"Measurements\")\n",
        "plt.xlabel(\"Day of the year\")\n",
        "plt.ylabel(\"Temperature (°C)\")\n",
        "plt.title(\"RMSE = %.2f\" % RMSE)\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "94kWeKfb2xns",
        "outputId": "5f276079-a32a-410b-cb3f-4a37563b99c0"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PolyCollection at 0x7f19dbc94cd0>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "kappa = 0.5e-6 * 60 * 60 * 24\n",
        "mt = []\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "for t in year[::90]:\n",
        "    T = Tm + 0.03*z + Td * np.exp(-np.sqrt(omega/(2*kappa)) * z) * np.cos(omega*t - np.sqrt(omega/(2*kappa)) * z + phi)\n",
        "    mt.append(T)\n",
        "    ax.plot(T, z, label=\"day = %d\" % t)\n",
        "    \n",
        "ax.invert_yaxis()\n",
        "mt = np.array(mt)\n",
        "ax.legend()\n",
        "ax.fill_betweenx(z, np.min(mt, axis=0), np.max(mt, axis=0), alpha=0.1, color=\"k\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Yon6f-52xnu"
      },
      "source": [
        "### References\n",
        "- Carslaw, H. S., and J. C. Jaeger, 1959: Conduction of Heat in Solids.\n",
        "2nd ed. Oxford University Press, 510 pp."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OaWeK9ui2xnv"
      },
      "source": [
        "To make the problem suitable for optimization, we need a function with parameters and a return value that should be minimized."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "aHITiBLA2xnw",
        "outputId": "debe174f-ef29-4f5b-e238-abf584e3f0e2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f19dbc53650>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "def func(params):\n",
        "    Tm, Td, phi = params\n",
        "    omega = 2*np.pi/days\n",
        "    T_s = Tm + Td * np.cos(omega*year + phi)\n",
        "    RMSE = np.sqrt(((T_s - temp)**2).mean())\n",
        "    return RMSE\n",
        "\n",
        "from scipy.optimize import minimize\n",
        "params = Tm, Td, phi # initial guess\n",
        "result = minimize(func, params)\n",
        "\n",
        "Tm_opt, Td_opt, phi_opt = result.x\n",
        "T_s_opt = Tm_opt + Td_opt * np.cos(omega*year + phi_opt)\n",
        "\n",
        "plt.plot(year, temp,'.', label=\"Measurements\", alpha=0.5)\n",
        "plt.plot(year, T_s, label=\"Cosine fit (trial and error)\")\n",
        "plt.plot(year, T_s_opt, label=\"Cosine fit (scipy.optimize)\")\n",
        "plt.xlabel(\"Day of the year\")\n",
        "plt.ylabel(\"Temperature (°C)\")\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "mSapc3MX2xny",
        "outputId": "8317450c-d595-40c2-890c-28244e8106a2"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib.animation as animation\n",
        "from IPython.display import HTML\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "x = np.arange(0, 2*np.pi, 0.01)\n",
        "line, = ax.plot(x, np.sin(x))\n",
        "\n",
        "def animate(i):\n",
        "    line.set_ydata(np.sin(x + i/10.0))  # update the data\n",
        "    return line,\n",
        "\n",
        "# Init only required for blitting to give a clean slate.\n",
        "def init():\n",
        "    line.set_ydata(np.ma.array(x, mask=True))\n",
        "    return line,\n",
        "\n",
        "ani = animation.FuncAnimation(fig, animate, np.arange(1, 200), init_func=init,\n",
        "                              interval=25, blit=True)\n",
        "HTML(ani.to_html5_video())\n",
        "plt.clf()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 653
        },
        "id": "VySG0veB2xny",
        "outputId": "3e644f45-641c-4129-c14d-46687ae82efd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<video width=\"880\" height=\"320\" controls autoplay loop>\n",
              "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAFxA21kYXQAAAKuBgX//6rcRem9\n",
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              "MA==\n",
              "\">\n",
              "  Your browser does not support the video tag.\n",
              "</video>"
            ]
          },
          "metadata": {},
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 880x320 with 2 Axes>"
            ],
            "image/png": 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SyVnsVWCK2CRZ0diWMm2Cr9HWHGKbIj7mXEcSKHs/EMxK7HVkmnP+iQeex/a3WuUssxq4SESOc85xj2Nrj6rEOW++ATwsNiFJC2xfcVPJW3dR9lpZ4+NeBQ+JSLJz/XwaWzu2tBbXnKpcC4Pd96zHBmn+h54DsFmAK1PT+xYVAhqghcck4HNjzAJjzC7XTzq2o+kkAGPMbuyJ/0JnegljzF+xbZFnYJswbcf2mXE/QSHgPYewzcoeEpFD2D4s7wUs9ho2IPwA2IftUPtPnGxyThX7Wdj+cytE5CC2U+mllH/yvAsbaOZgm4ls51jNU228g21CtkNsFqrTjTFbsG3kz8LWKOzHXnxPqoPtzcYmTdmPvSDdboz5CsAYs8rZ5q3Y/cvCdnou74mkX4XHxtgsfw8CLzn7+IIz6yFsTdtW7E15YLPUMmr42dXWJOA1Y8wPAd/15cB87JPNn7EXodecMr2KvTi7y/6is8yz2GOVDlQn6L4X26n9Peznt8lZX42HOnD+Xz+ldBPG+7FPrW+TY1m2SrJvOp7iWIf/LGyGx3Od/0+/ddi+gSOcdR51tuV3MfZpbYazP09g+5987lrmFuxNg1KqAsb6wglags1fAYwHfo89/7yH7b/zV2d+LjZx1PnY/+k3sLVy7nVU+5od4Brsuf4z5zy5Dnu98desPIG9bi/CXkOisAkmKlunYJs5foM9J0P52WP915ELsU0QM7Dn4ghsAjN/E7xnnLL+5JQzgyo24Xb5Lbbf1/fYAOR7jtUkludPwMXOtfK/Tnlre9wr8jK2X9lubAuPX7paTFT7mlOVayHB73sOYh/s34a9L3iMYw8PylWL+xYVAmJMfd2XqaZCRL4F3jHGVJq2t6kSkYXYppMPhbssquEQm1b5C+DEgAArrMT2Y7jLGDM63GVRSjUOTs3LN8Bx5TT1VNg0+9j+XL2MMRkVL61UzWgNmipD7HggsU6zqt9iE4oE1rQp1ewZYzKNMd0bUnAGYIz5QIMzpVRFnGbWg+RYX+CpwAINzpQKPw3QVDC3YpsS7MUOon2xPiVSSimlmpR47HiOB7FNEvdh+w0rpcIspE0cReRTbKpzH/aEcJcx5hunI+Sr2D4VudhxLn4of01KKaWUUkop1fSEOkBLMMbsd/6+FDuA4i9EJA2bSGCOiIzHDnp7coUrU0oppZRSSqkmJqRNHP3BmSMeME667yEcy1QzFzueSGrg+5VSSimllFKqKYsI9QZF5DVgjPPyfGxK6p3+1KTGGCMiW7BjJGm/J6WUUkoppVSzEfIAzRhzA4CITMCO2/GHqr5XRO4B7vG/9nq9nTt27FjnZVRKKdVwbN++vcAYEx3ucoRCdHS0adeuXbiLoZRSqh5Vdl0L6zhoInIU6I4d6LCNMaZIRATYCZxeWebA5ORks21bXYx3rJRSqqESke3GmORwlyMU9LqmlFJNX2XXtZD1QRORBBE5zvX6Euyo5XuAr7Hp3AHGAds0rbtSSimllFKquQllE8d44D0RicWm2d8LXOj0OfsVMEdEHgQOADeGsFxKKaWUUkop1SCELEAzxmwGTiln3jpgWKjKopRqnHw+H+Fslq3qh4jg8YQ0qbBSSinVYIU8SYhSSlVXQUEBW7ZsobCwMNxFUfUkMjKSrl27EhUVFe6iKKWUUmGlAZpSqsHbsmULrVq1IikpCZtHSDUlxhiysrLYsmULqak6BKZSSqnmTQM0pVSD5vP5KCwsJCkpiYgIPWU1VUlJSWRnZ+Pz+Rp0c0cR6QW8CrQFcoGJxpgfgix3M3A/NhlXGjDZGKNVwEoppSrVcK+CSqmQKfYZpqWlc82s5UxLS6fY13D6efn7nGnNWdPm/3wbQR/DmcCLxpje2LE85wQuICI9gEeAEUAq0AG4LYRlVEop1YhpgKaUYvrCDJ5Ly2BpZhbPpWUwY5GOcqFUIBFpDwwB3nAmzQW6iEhgu8zxwHxjzC5jI84ZwNWhK2nD5WtAD3+UUqqh0gBNKcXSzCzyi3wA5Bf5WJKRFeYSNWzdu3enffv2pZKWLFiwABHhN7/5TRhLFn7z5s1j+fLl4S5GfekC7DTGFAE4wdcWoGvAcl2Bza7Xm4Is0yy9vWorv/jjp1zwt6+47bXV/OkfPzJ78UY+/WEXP+zIJfeotgJVSint0KGUYnhKEms255Bf5CM6wsNpqUnhLlKD17VrV+bPn8+4ceMAePnllxkyZEhYy1RUVBT2fnrz5s1jwIABnHrqqWEtR2MhIvcA9/hfx8fHh7E09S8+NpI+HVuxPecoP+08QLAKtVYxEXROiCU5MY7kxFjXj30dHxupTZ6VUk2aBmhKKSaNTkUElmRkcVpqErePCp5Jr9hnmL7QNoUcnpLEpNGpeD0N80apvst64403Mnv2bMaNG0dubi7Lly/n6quv5uDBgwA89dRTvPvuuxQVFdG+fXtmzpxJt27d+OKLL3jooYfIy8ujoKCAe+65h5tvvhmAl156ialTpxIVFUVxcTEvvfQSQ4cOpXv37iWBD8CQIUN46qmnGD16NKNHj6Z///6sWrWK2NhY0tLSyt32ww8/zI8//sjRo0dZt24dvXv35vHHH2fKlCls3LiRwYMH8+abb+LxeDh48CD33HMP3333HXl5eZx66qlMmzaNqKgoRo8ezZAhQ1ixYgU7duzgrLPOYsaMGXz88cfMnz+fzz77jDlz5nDnnXcyatQoJk6cyKFDh/D5fFx88cU8+uijdfY5hNhWoJOIRBhjisRGCV2xtWhuW4AU1+vuQZYBwBgzFZjqf52cnNyk2wBe0L8TF/TvBEBhsY9duXlsyznK9v1H2ZZzhG059vf2/UdZsG5P0P6wLaP9AdyxwK1zYixdEuPo2iaO+LjIUO+WUkrVKQ3QlFJ4PcIdY3pxx5heFS7n76uWX+RjzeYcRKj0PeFS32U97bTTeOGFF9ixYwfz58/n8ssvx+v1AvDWW2+xbt06li1bhtfr5fXXX2fy5Mn861//YtCgQSxevBiv10t2djYDBw7knHPOITk5mSlTpvDzzz/TqVMnCgsLyc/Pr1JZ1q9fz5dffklkZGSF2wZYvXo1a9asISEhgdGjR3PLLbfw2WefERsby5AhQ/jkk0+44IILmDJlCiNGjGDWrFkYY7j11lv561//yu9+9zsAMjMzWbBgAYWFhZxwwgksW7aM888/n4suuogBAwaUNPW8++67ufDCC3nggQcAyM7OrrPPINSMMXtE5GvgOmxykHHANmNMYKfNucBiEXkY2A3cDrwdwqI2CpFeD13axNGlTVzQ+UXFPnYfzGdb9hEngDsWxG3ff5Qv0/dSWFw2gIuPjaRbkl1vtzY2aOuaFEe3pBZ0bB3TYB8qKaWUnwZoSqkqC9ZXraEGaKEo6/XXX8+cOXOYN28eb775Jm+++SZgm/mtWrWKwYMHA1BcXFzynqysLG6++WbWr19PREQEWVlZrF27luTkZMaOHcv111/PL3/5S8477zx69+5dpXJcd911REZGVrptgLPPPpvExEQABg0aRHR0NK1atQJg4MCBpKenl6xn2bJlTJ1qK3eOHj1aEoACXHnllURERBAREcGAAQPIzMxk2LBhZco2cuRIfve733Ho0CFGjRrFmWeeWaV9asB+BcwRkQeBA8CNACLyEjYxyHxjzAYR+T9gifOehdjsj6oaIrweOifE0jkhNuj8Yp9hz0GnBi7nKFuyj9ifLPv7v9tyy7wnyushOTGWrklO4NbGBm7+v2OjvEG2pJRSoaUBmlKqyhpTX7VQlPWGG25g0KBB9O7dm169jgV/xhgeeOABbrutbGb122+/nfPPP5+5c+ciIgwaNIi8vDwA5s6dy5o1a1i4cCHnn38+jz76KFdddRURERGlAi3/8n4tW7as0rYBYmJiSv72er1lXhcVFZWsZ+7cueUGieW9L9C4ceMYPnw4n332GdOmTePZZ5/l448/DrpsY2CMWQeUiUSNMbcEvJ4FzApVuZojr0foFB9Lp/hYTu5edn5eYTHbco6wOcv+lARw2UdYmpnFwnV7y7ynfavokhq37kkt6N62BT3b2t8to/WWSSkVGnq2UUpVWVX7qjUEoSjrcccdx2OPPUbfvn1LTb/kkkt4+umnGT9+PG3atKGwsJC1a9cycOBAcnJy6NatGyLCl19+yXfffQfYBB+bNm1iyJAhDBkyhH379rFy5UquuuoqUlNTWbFiBYMHD2blypWsW7eu3DJVtO3quOSSS3jiiSeYOXMmERER5OTkkJWVRWpqxcexdevW5OYeq7lIT08nJSWFG264gVNOOYXhw4dXqxxK1VRMpJfU9q1Ibd+qzDyfz7DnYD6bsw6zOfsIW7OPBXEb9h1m9eacMu9p3yqaHm1b0LNdC3q0bUGPti3p0dbWvkVFaFJspVTd0QBNKVVlVe2r1hCEqqw33nhjmWnXXnstWVlZjBkzBrDB10033cTAgQN5/PHHmTx5Mo888ggDBgxg6NChgG2KeNNNN5GdnU1ERATt2rXjlVdeAeDRRx9lwoQJzJw5k2HDhtGvX79yy1PRtqvjmWee4f7772fAgAF4PB4iIiJ48sknKw3Qrr/+eiZOnMi8efO444472Lt3L2+88QZRUVH4fD5mzJhRrXIoVR88HqFjfAwd42MY2rNs7frBvEI2Zx1h477DJT8b9h3mx50HWLGxdD9Kj0CXNnFO0GZr3Hq0bUn3tnEcFx+LR/u8KaWqSewwLo1TcnKy2bZtW7iLoZSqR8XFxaxfv57evXuX6gOlmpaKPmcR2W6MSQ5T0UJKr2sNmzGG7MMFJQHbxn2H2bjX+Z11mAKn36tfbKSX1PYt6dW+JakdWtKrfSt6tW9JlzZxmqxEqWassuua1qAppZRSSlWBiJDUMpqkltEM6d6m1Lxin2Fn7tFjNW57D5Ox5xDpew7y/fbSCUuiIjz0bNuCXh1swNarfUt6dWhJt6QWRHq1uaRSzZ0GaEoppZRSteT1iDOYdhwjerUrNe9AXiEZew6RsdsGbOl7DpG++xD/+G5HqeUiPEKPti3o1aElvTu0om/H1pzQqTXJidpUUqnmRAM0pZRSSql61DomkkFdExnUNbHU9MP5RWTutcFahv/3noN8snYXH3+/q2S5ltER9OnYir4dW3F8p9Yc36kVfTq21sySSjVR+p+tlFJKKRUGLaIj6J+cQP/khFLT8wqLSd99iJ92HeCnnQf4eedBftp1gDUB2SW7tonj+E5OTdtxrTmpczyd4mMQ0do2pRozDdCUUkoppRqQmEgvJyXHc1JyfMk0Ywy7D+Tz084DTuB2kJ93HuDzn/bwnx92lyzXtmUUJ3WOtz/JCfRPjqdD65hgm1FKNVAaoCmllFJKNXAix4YGGNO3fcn0vMJiMvYc4ocduXy/PZfvt+WyJCOLBa6BuNu3iqZ/cjwndo6nf3I8J3VOoF2r6HDshlKqCjRAU0pVqNhnmL4wg6WZWQxPSWLS6NRmnx66qKiIP//5z/z9738nIiKCiIgITjnlFJ588kkSEhIqX0GAW265hWuvvbZk7LK6MHPmTJ555hliYmL417/+xVVXXcVXX30FwMMPP8z9999PTIw+VVeqsYuJ9HJiZxt8XXmynVZQ5GP97oP8d5sTtG3fz8J1e/n8pz0l7+vSJpbBXRMZ3C2RgV0T6duxFRGaQVKpBkHHQVOqmassAJuWls5zaRnkF/mIjvBw19jUkA5U3RDHQZswYQLZ2dm89tprJCYmYozh/fffZ/DgwfTs2TPcxQPg+OOPZ/bs2QwbNqzMPBEhJyenRsFkfdFx0Cy9rqn6kldYzLpdNuX/t1v38/WWHDbsPVwyPy7Ky4AuCQwqCdoSSIiLCmOJlWq6dBw0pVSFpi/MKAnA1mzOQYRSAdjSzCzyncFX84t8LMnICmmA1tBkZGTw3nvvsWXLFhITbUY2EeHyyy8vWeYvf/kLc+bMwePx0L9/f1544QXi4+P5xz/+we9//3s8Hk9JLdzFF1/M6NGj+c1vfsMll1zCxIkTiY6OJiMjg61bt3LiiSfy9ttvExUVRWFhIX/4wx9IS0ujoKCA3r17M3PmzJJy+I0fP57MzEwmTpzISSedxFNPPcWAAQPYv38/t99+O1Z1mGAAACAASURBVAAjRozA6/Xy6aef0r59e5RSTVtMpJdfdEngF10SuO7UbgDkHC7gm605rNlsf77Zsp+lmVkAiEDfjq05tWcbhvVMYmiPJOLjIsO5C0o1GxqgKdXMVRaADU9JYs3mnJIatNNSk8JVVOutqyBnY/2sO7EHXPN2hYt8/fXX9OrVi7Zt2wad/8knnzB79myWLVtGQkICt912G/fffz/Tp0/noYceYubMmQwbNgyfz8eBAweCruPbb79lwYIFREdHM3LkSObOncvVV1/NX/7yF1q0aMHKlSsBeOSRR3jooYd4/vnnS73//fffp3v37rzzzjsMGDCATZs2lcybMWMGM2fO5KuvvmpQNWhKqdBLbBHFGX07cEbfDgAUFfv4eddB1mzOYdWmbJZvyOaVJZt4ZckmROCETq05tWcSw3omcXKPNsTHasCmVH3QAE2pZqzYZ/CIfVJqDEEDsEmjUxGBJRlZnJaaxO2jUsNU2sbh888/58orrywJfiZNmlRSuzZ27Fjuvvtuxo8fz9lnn82AAQOCruPSSy8lLi4OgFNOOYXMzEwA5s2bR25uLnPnzgWgoKCA7t271/MeKaWaiwivp6Q/24Th3THGkLn3EMs2ZLM8M4vlG7J4efFGXl68EY/AwK6JjO7djlF92nHicfE6mLZSdUQDNKWaqWKfYcLsFSzOcJqzAKd0TywTgHk9wh1jejWcZo2V1HDVt0GDBpGenk5WVhZJSZXXJrrHI5o6dSo//PADCxYsYMKECVx77bX8z//8T5n3uJN3eL1eioqKAJtm+7nnnuPss8+ugz1RSqmKiQip7VuR2r4V15/aDWMM6XsOsXxDFovT97E0M4s1m3N4+rP1JLWIYmTvdozu044RvdrRpoX2X1OqpkIWoIlIDPA2cAJwFNgDTDLGZIjIQqAbkOss/qox5plQlU2p5mj6wgyWOMEZgAGKnZxB09LSNWtjOVJTUxk3bhw333wzc+bMISEhAWMMH3zwAQMHDuTMM89kypQp3HPPPbRu3ZqZM2eWBFQ///wz/fr1o1+/fkRERPDpp59Wa9uXXHIJzzzzDKeffjpxcXEcOXKEjRs30q9fv2qtp1WrVuTm5moTR6VUtYgIvTu0oneHVtwwrDsFRT6+3pLDwnV7WbR+Lx9+s50Pv9mOCJzcrQ3nnNiRc0/sSOeE2HAXXalGJdQ1aC8CnxhjjIjcCbwEjHbm/dYYMy/E5VGq2VqamYU7h6sInJaaVG7SEE23f8zs2bN59NFHGTp0KBEREfh8PkaOHMnYsWM577zzWLt2LcOGDSuVJATgwQcfZN26dURFRREXF8f06dOrtd377ruP/Px8hg4dWlIzd99991U7QJsyZQpnnXUWcXFxmiREKVVjUREeTu2ZxKk9k7j/vL7sPpDHovV7SftpD4vW72Xlpmwe+eeP9E+O55x+NlhLadcy3MVWqsELW5p9ERkCvG+M6e7UoD1b3QBN0xErVXPT0tL52xfpFBQbBDg9NYk5Nw3l+pdXlGTxApsk5K1bTw1buv2GmGZf1T1Ns2/pdU01FUcLilm0fi//+WEXn/+0m4N5tqn28Z1aM25QZy4acBztW+lYjKp5ashp9u8GPnK9flxEHgF+BB4wxmwIT7GUah6CJf/weqRM1sZhKW2YlpbOrK82aLp9pZRSVRIb5eVcp4ljQZGPpZn7+OT7XXy8dieP/usn/t/HPzGiVzsuG9SZc/p1JCZSH8Ap5ReWAE1EHgRSgbHOpOuNMVvFttm5A/gntq9a4PvuAe7xv46Pjw9BaZVqmspL/hEYuPl88NyCjJLgDIJne1SqqauoL3XAct2BTOB71+RxxpjM0JRUqYYlKsLD6D7tGd2nPX+8uB9pP+/hg6+3lfRdi4+N5IohyVw7tBvd27YId3GVCruQN3EUkXuBq4AzjTH7y1kmD+hsjMkKNt9Pm4IoVb+KfYYxTy1gS/bRkmnxsRHcNrJnSY1bvZdBmzg2C42hiaMToJ1B6b7U440xowOW6w58a4ypdhYWva6p5iTrUD4ffbuDN1dsJnPvYQBG9m7HhGHdOKNv+1JZcJVqShpUE0enBuxqXMGZiEQAScaY3c7rccDuyoIzpVT9m74wg+05x4Izr0e4bWTPkDZt1At089KQP29jTB7wsWvScuDeMBVHqUYvqWU0N53egxtP686yzCxeX76ZT3/czZfr99K3YysmjU7hgpM6EeH1hLuoSoVUKNPsJwNPAxuABc5FOB/7NPJfIhIN+IB9wEWhKpdSqnxLM7NKUu8DdE6ICflA1SKCiFBYWKg1aE1YYWFhyWfdiAT2pXZrISKrAC8wD/izMaY4ZCVTqhEREYantmV4alt25h5l9uKNvLliC3e//S1TP1vPnWNSuWxQcrPNHKyan7BlcawL2hREqfoVrsyNgXbt2kV+fj6dO3dubDfwqgqMMWzfvp3o6Gg6duxYZn5DaeLo5vSl/iUw1hhzJGBeNBBvjNkjIm2Ad4DPjDFPBllPYN/qzvv3B239r1SzknO4gDlLNzFn6SZyjxbSt2MrHjj/eEb1bhfuoilVa5Vd1zRAU0qVq9hnmLEoo0ymx1Dz+Xxs3ryZvLy8kG9bhUZMTAzdunXD4ynblKmhBWhV6UsdsPzVwDXGmF9Wtqxe15Qq7UBeITMWZvLy4o3kF/kY2bsdj158Il2T4sJdNKVqTAM0pVS1NdRBqX0+H435nKWCE5GggZlrfoMJ0Jwar2uxwVlOOcu0B3KMMYVObdobwE/GmP+tbP16XVMquB37j/LUp+v44OvtxER6mHJWH248rbv2T1ONkgZoSqlqayhNG5WChhOgOX2pt2L7Uh90JucbY4aKyJ+AHcaYGSJyGfAnoBjb1zsNuNcYk1/ZNvS6plTFlmbu44EPvmdz1hEGdU1g2jWDOC4hNtzFUqpaNEBTSlXbNbOWszTzWCLV4SlJvHXrqWEskWrOGkqAFgp6XVOqcnmFxfzlP+t4efFGEuMiefaqgdo3TTUqlV3XtF5YKVXG8JQkoiPs6aExDUpd7DNMS0vnmlnLmZaWTrGv8T6AUkopFVxMpJc/XHgCL14/mCKfYeIrK3lzxeZwF0upOhPScdCUUo3DpNGpiFAqOUhjMH1hRknTzDWbcxBBm2YqpVQTdXa/jvyzYytumL2S33+4lv1HCrljTOO4XilVEa1BU0qV4fUId4zpxVu3nsodY3o1iAQhVbE0M4v8Ih8A+UU+lmToePdKKdWUdUtqwXu3D+P4Tq35y3/W8cqSjeEuklK1pgGaUqrJaKxNM5VSStVc+1YxvHXLUHq2a8Gf/vkj/167K9xFUqpWtImjUk1UQ02VX58aa9NMpZRStZPYIopXbzyFS19Ywu/e/47+yfGa3VE1WprFUakmSlPlq6ZCszgqpapqwc97uHHOKk5LTeKNm4ci0rQfTKrGqbLrmtagKdVEBeuP5Q/Qyqtdc08/tWcbBGHZhuZTA6eUUqpxG9O3PVcMSebd1dtI+3kPY4/vEO4iKVVtGqAp1UQNT0lizeackho0d3+sYNkObx+VyoTZK1iSmYUxsGJDFogN2jQjolJKqcZiytl9+OjbHTz96XrO6Ntea9FUo6MBmlJNVEX9sYLVrhljl/U3ei42gNMEOrAGTimllGqoOrSO4YohXXh9+Wa+25bLgC4J4S6SUtWiWRyVakSqMxBzRanyg2U7XJp5LDhzr8O9jFJKKdUYXHlyFwDmfbM9zCVRqvq0Bk2pRqSuBmIOVrtmDKzelE1BsUGA01LaMLRnW5Zt0IyISimlGpd+x7WmQ+tolmbuC3dRlKo2DdCUakQqSvxRHf7aNfd7gwVtXo/w67HarFEppVTjIiKc0iOJf3y3g4N5hbSKiQx3kZSqMg3QlGrAArMtDutZfuKP2goWtCmllFKNVc+2LQDYmn2UE47TAE01HhqgKVWJcA74HNik8c4zUrhrbGqVBmJujgNVK6WUUn6dnYGqdx04ygnHtQ5zaZSqOg3QlKpEXfX7qq5in+Hd1VtLNWl8b/U2khPjGJ5yrAliReX+2xfpFBQblmVmsXxDFrMnnsKLX2ZWO2jTYE8ppVRjEx1pk2EVFJWfUEuphkgDNKUqUVf9vqpr+sIMtuccLXktwPb9eWzJPlqlQHFpZhYFxfaiZIAlmVncNGclqzblVDvYDFeQqpRSStWWMRqgqcZF0+wrVYlgKelDYWlmFsWua0pUhKckrb4/UKzI8JQk3HVcxlASnFV1He6y1OR9btUZIkAppZSqrf1HCgGIj9P+Z6px0Ro0pSpR0YDP9Wl4SumEICd3TywJsKoSKE4ancryDVksybSDUHsFCpwgC2xSkKoGm4FlqW6QWuwzTJi9oqQsjbUWTpt6KqVU47HvUD4ASS2iw1wSpapHAzSlKlFf2Q0ru9kPDAxvHZHCrK8yqxwoej3CqzcNZcaiDJZkZLEt5whbso81meycEFPlYLO2Qer0hbYM/jqzUDYVrUva1FMppRqPzL2HEIFuSXHhLopS1aIBmmpwmkstRWU3+8ECw+oGiv513D4qlQmzV7A152hJbZq/DFU5vrUNUpdmHgvOAEQIWVPRuhSu/oiq4RCRTUA+4H/a8Zgx5p0gy90M3I/tSpAGTDbGFIaqnEopWLfrIN2TWhAT6Q13UZSqFu2DphoUf1O4pz9bz9LMLJ5Ly2DGooywlaU++0zVtF9XTco1fWEGKzdm4+8n7QO2ZB+t0fGtyfaHpyQR5USFApyeErqmonUpXP0RVYNzpTFmgPMTLDjrATwCjABSgQ7AbSEuo1LNWu7RQjbuO8wJnTS9vmp8tAZNNSgNqSlcYA2XwWAMvL9mGwCXD+7C5DE1r92rqF+Xuxbx1J5tEIRlG2yNojEwbYEt14oNWby7eitXDOlSqiYssBbSndERKAnUanJ8a9LML1gTyfqqFS32GZ5fkF5nn5NbuPojqkZnPDDfGLMLQERmAA8Cz4e1VEo1Iys3ZuMzMLRnm3AXRalqC1mAJiIxwNvACdimIXuAScaYDBFpD7wGpGCbjkw2xnwZqrKphqMhNYULrOF6b/U2tuccLcms+OwX6Xg8Ne+DVNHNvjsIWrEhC0Qo9hnWbM6hQ+voknIVm2M1Ye5AKTCIOrl7ItERHvKLfLZ5o7O+mtQC1aSZX3314wtm+sIM/vp5ep19Tm6h3A/VoL0mIgKsBO43xuwNmN8V2Ox6vcmZppQKkWWZtlXKsJ7a0kE1PqGuQXsR+MQYY0TkTuAlYDTwOLDcGHOuiJwMfCgiPbS9fvMzPCWJ1ZuyKSg2YW8KF1jDBZRKe1/sM7Wq3avoZt8dBBUbSqq8/NP8wZafO1AKNsB1sc9w19hUlmRkMSylDRjh24wtnNvxAJe1+wFWLoTD+6DgEBTlQ3EBeCIgIgYiYyCuLbRsD606cmYXL2s2C/lFNsAbltKGaWnpJbV1t41MqdFg2HUlcHiC2n5OSgUYaYzZIiKRwKPAq8D5NV2ZiNwD3ON/HR8fX/sSKtXMGWNI+3k3HVpHk9q+ZbiLo1S1hSxAM8bkAR+7Ji0H7nX+vgLbTh9jzCoR2QGMAj4PVflUwxDKpnDVLYvPB89+vr7k5t+dpr6uE5u4g8PAGq/LhyTjEeGdVVvZvj+vTE1Y4ADXHoF4c5Cj3y/n3rhMBm7ZhOxLh0O7YCfwTfXKdhNwTUwrNnu6UJjUlx27B/DYD4lsLLJlXr4hq0aDYQdTk+M6PCWJFRuygn5OStWWMWaL87tQRJ4F1gdZbAu2RYhfd2dasPVNBab6XycnJ+sAgUrV0vrdh9iUdYQbhnXDVnYr1biEsw/a3cBHIpIERPrb6js2oc1BmqWG1IQssCzFPgNieG/1sb5N/tq96Qsz+NsX6RQUG5ZlZrF8Qxav3jS0xkGaOzj013gt21A6aL19VGpJCn13E8mlmVkY42OIrOcs7xrOjPiWlJ3b7YqzocAbR1SHvtBzNLTtBYndoUU7aNEWoluBNxq8kWB8UJQHBUfgyD44tBsO7IB964nZu54++9bBzh85cecHnB0B271JLCk+kcXbhkLRCUBUmZq96gZbNe3vZgj+OSlVGyLSAnu92u9MuprgjzjmAotF5GFgN3A7tom/UioE/r3W3lKe269jmEuiVM2EJUATkQexNWZjgdhqvE+bgjQjDSndvr8syzKzyyTkAEol4TDAkswsZizKqLPmj8U+UxKwGUPJ9ksFs8bAluX8vng6HaPTSJIDAOyRJD4sOo3Vvj6s8vWhXY/+vHnb8GqWqHfwyfu38uknH5L90yKG8CNXRCziChZxODqaRb5f8DGn06/nFUDNgq2a9nf79Rm9+fUZ5ZS5hhrS91GFTQdgroh4sQlJNwA3AIjIS9jEIPONMRtE5P+AJc77FgIzw1BepZodYwwff7+ThLhITumhCUJU4xTyAE1E7gUuA840xhwBjohIkYh0dNWidSdIcxBtCtK8NKRBgSsry/CUJJa5EpwYQ532e6pw+4f2wndvwdevQ1Y6/YCslil86LmQwl7nsTuuL9MWZpJfbPvSXdyrXZ2UCYCELoy98tfMWHQe/5uRxXmdj3J16+/JXfk+5x5YxfmsxHz9OviuYUPGL8gvigGqHmxVlOky1BrS91GFhzFmAzCwnHm3BLyeBcwKRbmUUsf8sOMA63Yf5NqhXYnw6mhSqnEKaYDm1IBdjQ3O9rtmvYdtAvKwkySkM7AolGVTDU9DGBTYX2sy66sNFZZl0uhUlm/IYkmmreGq62Ai6LE4CVj6HHz3d5vUI7YNnDoZBl5PUocTuNS1Dx6v1Ftq+LLNUsdw3Ol3wYGd8N1byNevwZK/MhW4KGogzxf+kv96j6/S8QnWJzFcNVkN4fuolFKqYnO/ts3bxw1ODnNJlKq5UKbZTwaexjYJWeB02sw3xgwF7gNeF5F0oAC4TjM4qoZQe+KuNfFzlyVwvLKTu7cpuTj4fHZ+XQQP7mMxOGIjj+TPgmkLAQPJp8Cpk6DvBRARXea9YevX17oTjJhC8fDfMP+jdzlu/RuMzFvC6Ohv2Nm6P+073g8m1Y6lUI5gZZ+Wlh60Jqu+A7fAxC3bco4wLS1dmzoqpVQDUVjsY/63O+jZtgUDuySEuzhK1Vgoszhuw7bZDzZvN3B2qMqiGodwDgocrOYMID42gttG9iyVHCRwvLHdB/LJL/IxbUFGnY2/NWl0KolHN5H6/V8ZmvcV7IONbUbwmucSknqOYtIJDTNIKPYZJryyiiWZrTFmMn0iLmNql6/ot+df8M410HkwnPlH6DEi6HuDBVzl1WTVdxNE//fxnVVb2ZZzlC3ZR3n60/W1TgijlFKqbixct5eswwXcdHoPzd6oGjVtnKsaLH/tyVu3nsodY3qF9AbYf7Ofe7SoZFp0hIfbRvYsVZbAYOH77bllgodaO7gL7z/v4trVV9rgrM8FvDX4bc7dcwevbOvEc2kZzFiUAdigZlpaOtfMWs60tHSbeTKMpi/MKElsArCuqCN/9twOd/8XTvkV7PwvvHohvDEedq0t897n0myA5t7H4SlJJePSuWszgwVudcn/fUxOjMN/WN0JYZRSSoXX3DXbEIFLB3YOd1GUqpUqB2gicoKInC0iI0RE641Vg1ebYMV9sw+25uyusallavECg4WTOscT5bXBm2DHIKtxkFRcCMueh+eGwNevQddT4ebP4Oq3+OeuxKDBSHlBTbgsdSVOAdua8bTUJNv88fwn4c6VcOJ4yPgMZo6Aj/8H8nJL3htsHyeNTuWusakMT0kq9ZmUF7jVteEpSaWaAvgTwiillAqf7MMFfPHzboanJHFcQpUThCvVIFXYxFFEWmEHk74VOIIdzyUGSBGRlcATxpgv6r2UStVAbZq8BfZ/89ecBQocr8zng++351JwtAgDrNqUU7N0+5uWwMf3wp4fIaErXPYi9DmvpL9Wef3zQpXIoqr9vYanJLF6UzYFxQYBTk8JaKrapieMfxmG/xo+/h2snAk/fAjn/JnhPQcE3cfy+tTVZ5PYwL6Gw1OSWLqhfhLCKKWUqr75326nsNhw+eAu4S6KUrVWWR+0BcBrwECnnxgAIuIBRgC3i0iqMUbHd1ENTm2Clare7LuDhWlp6bywsHRCkWoHSfkH4dOHYM0cO2D0qPvg9N9CZOmngf7yLU7fh9cjJc0Ih/UMTWKVqga/wY5j0Kaqxw2Am/4D374Jn/8ffHArd/QYRevTpvDvbdFVCrjqMxlK4P7eeUYKw1OTwtI/UimlVFnvf72NVtERnKODU6smoLIA7TRjTH7gRGOMD5sGf5GIlE0bp1SYFfsMHrEVTjWp5ajJzX5gs0io5nY3LISPfg25W9iacDJToyeRYvozyRuDt5zyGUOZwOGusan1HjhUNfit1nH0eGDQ9TYb5ecPI1+/yg3b13DDOX+GQRMqzPZY3wL3d1lmdknfSKWUUuH1084DrN1+gKtP6UJsVOAVU6nGp7IArZ0zgPRq90QRGQLsNMZsDxbAKRVu0xdmsHJjNsbYvmCndE+s91qOwDTsnRNjufLkLpVvt+CIrTVb/TJEtmBh6v3c/nN/8oogentGhU0zwxU4BDaxHJbShmlp6TVKcR+0ueRFf4MTLob5d8E/7oYfP4KLpkF8eDp+N4QhH5RSSgX3/ho7vM14HftMNRGVBWhPAC8Fmd7SmXddnZdIqTqwNDOLgmKbnsIAxYY6zwIZGFjcNjKlas353Hb/AO/fBHt/hu4j4OJpvPj+LvKKbNKJyppIhitwCGy66PPBcwtq1t+v3OaSqWNh8lL4z4PwzRsw4zSKL3qB6Tt7hXyQ6nAO+aCUUqp8hcU+5n2znR5tWzCoa2K4i6NUnagsQOtjjFkQONEYs1BEptVTmZSqtVAELuUFFlUKTIyxNWb/+T34iuxYYMPvAo+H4SmFVS77pNGpGAzvra77wbErEth08ZpZy2vc36/C5pIx8XDx89DnApg3Ce87V9PSdx6rC66ql7HOoPwEKGEZ7FsppVSFdOwz1RRVFqBVlKdU/wtUgxWKGo8aJyHJPwjzJsNP822GxvGvQPKQGpXd6xEEqZfBsasjsHnntpwjTEtLr1INV5WC6b7nw6Ql/Pz8FUws+ITBUT8xufBu3lkVXbWaymqoagKUqmayVEopVX/eW70VEbhskI59ppqOygI0n4h0MsbsdE8UkeMAXznvUSrsQlHjUaNaun0Z8PY1sG+d7WN10XO2lsilumUPVWr9iviDyndWbWX7/jy2ZB/lubSK+88FvrfSgDQ+mS+GvsznCx5nsvcj5kf9gbty72LGoi51ur9VPZ61GcZBKaVU7WUdyift5z2cntqWTvE69plqOiobqHoG8L6I9PFPEJG+wDvAi/VZMNX81GZg6XAob8Dkcq37N8waA1npcNYjcPmrZYKzmgjVAM0V8QeVyYlxJZ+be3DpqrzXn9ykolqo28f05d3WE7i58F68FDMn4jESvplhm4zWkaoez/IG0lZKKRUaH327gyKf0eQgqsmpsAbNGPO8iLQHvhERf7bGKOApY8xz9V461azUVY1EqJqeVbmmy+eDL/8CC/8fxCbCdR9Aypg6K0dDSmBR333/vB7hiiFdeC5tMBcXPMqsqKlce+AlmLvf1kZGxdV6G1U9nprZUSmlwmvet9t17DPVJFXWxBFjzP+JyBNAP2fSj8aYw/VbLNXUVCVoqqumerUN9Oo0wCs8Ch/cBj/NZ2+L3jza8vf02pzMpB51l8ijoSSwKPYZfMbQoXU0xhi6JMbxzqqtvLNqK5cP7sLkMWWPY3nHuqLP4FhilGjuNE/yfNwsUta+b5uNXvMutD6uVvtR1ePZkAJjpZRqbrblHOG/23K5dGBnYiJ17DPVtFQaoIlILGCMMatCUB7VRFUlaKqrGonaBnp11rfo0F54+2rYtor0dmcxfud15GZFVjq2WWM1fWEGzy/IdCUKycPf8PDZL9KDJi8p71hX9BmUTowiXHDwNl5L6c0pm1+EWWPh2veg44n1vr8NJTBWSqnm6N9rdwFw7olae6aangr7oInIROBT4N8icmNISqSapKr013H36brzjBR8PmrUH622fbLqom9R8Z715E4bBdtWsabLRB6OvIfcosiSdb745YZG09euPIF9Bt3HrdiACVg22HEs71hX9hm45+cVwbNF4+Cyl+DIPph9LmR8Ude7q5RSqgH599pdxEV5GdW7XbiLolSdqyxJyK+B0cAZwJ31XhrVZFUlaHInixCEaQtsE7fn0jKYsSijytuqdvKOGpS1QpuXUvjiWFoc3ckDhTdzzcZzEY8Hr6t1X+7RIpZmZvH0p+uZMHtFowzS/LVc/s/II5QcN6+UHofD65Ggx7G8Y13ZZxB0fv/L4foPweOBNy+Hr1+v611WSinVAOw5kMeaLTmM6dNemzeqJqmyJo7LgcexKfW1iaOqser216lNM8XaNj2rVd+iHz+CubdgfF5uKbyXhb4BgI9in6FzYixbso+WWtwASzKzmLEoo9E1lQv8jIp9hrvGprIkI4thKW3w+WDu13YA7csHdwl6HIMda3dftvLeG/i+W0ekOLV4EVxw4ktckzEFmX8n7N8CYx4EHbxU1QERSQLc1bNxQE+gvTEm27VcdyAT+N617DhjTGYIiqlUk/fFz3swBs7u1yHcRVGqXlSWxfEOETkL+zD8s9AUSTVF1Q2aatofrSZJJyp6f7UGQf76NfjH3dCiHR/1nsqylV7w2fKf3qstxlDSr8rNGMIydlltBX5Gp/dqW+YzvvvM3hWuI9j3YlpaeklftugID0jwz879vmlp6a4+ax7yR8zips33w5dPwtEcOO9JW7OmVC0YY7KAAf7XInIvMModnLkcNMYMCDJdKVVLX6XvRQRt3qiarKpkcdTATIVcTWuxqpJ0YvWmbJZvyMJnKLnh97/33dV2oOVin6legpAlf4PP/gAJ3eCGeVyeK1bBPQAAIABJREFU0IOsVhllyi8Ci9P3sWP/UbbkHMWY8I1dVlvHsinaWjKfzwa4tc1OGVgz997qbU5CkPKTtgS+5/MtcNOEf8Dfr4ZVsyAvFy55AbyRtSqbUgFuBh4IdyGUak6KfYbF6fvon5xAQlxUuIujVL2oMEATkf8B/maMyStn/mCggzHm4/oonGq+atpMsbymke7pBcWGJZlZGEPJDX+w2q3ymlaWqmXr2YbJvr/jWTIV2p9gxzhr3QkvBC2/f1qxzzBjUdkArjEpnU3Rx7QFGUEzNVZXYM0cUGlz16A1rtGt4Nr34f2b4Pt3If8AXD4HImNrVT6lAERkOJAI/LOcRVqIyCrAC8wD/myMKQ5V+ZRqqr7btp8DeUWM7NU23EVRqt5UVoN2GPhBRBYDK4DdQAzQBzjXeX1XvZZQqWoor2mke7pgAzIonSEwsOlheTVb/tq4gqIifrn1L3g8n0PyyXYMrrg2VSpnU0nRXpu+guU1Ow2sPfX5YNqCjAqbu5Zb4xoZA1e8BvPvhO/+Dm+Mh6v/DjGt62T/QzUoumqQbgZeM8YUBZm3E+hsjNkjIm2Ad4ApwJOBC4rIPcA9/tfx8fH1VFylmoav1u8DYEQvbd6omq7K+qA9LyIvA+Ox2RyTgSPAf4GbjDFr672ESlVDeTfq7ukegVWbSgdx/to0/xhenRNjufLk4IktlmZmUVhUxBMRs7jCs4hVnl8w6LoP8ca0CvXulhKOYKE2Y9eV1xw1MHgt9hk8noqbu1YY8Hoj4OIXILo1rJwJr18K138AMVW7Ea7ouNbZmHmq3ohIlDGmoI7X2RK4Ajg52HxjTD6wx/k7W0RmA9cQJEAzxkwFpvpfJycnN76UrkqF0IqNWcRGehnYNSHcRVGq3lSlD1oe8Ibzo1SDVt6Nunt6ec0LAwO78oKb03omMH7Lo1zm/Yq04gFMzv8NQ974oVSftnDUooQjWKhuX0F3sLMt50iVat9qWttYJrA653G8US1g8VQbpF33AcRWfoGv6LjWdlB0VT9EZDRwOzAWSBKRImAt8D4wo5ykHtVxJfCdMebncrbfHsgxxhSKSDRwGfBNLbepVLNX7DN8t3U//ZPjifRq4ifVdFUaoCnV1JR3w1+lIMBXzKT9T+PxfsXnxQOZXPgbCogs06ctHDfp4QgWqhs8uYMdr1CSYbM+EqUEDazG/i+IB756Cl6/xI6bFptY4XoqOq61qUFU9UNEPgbygLeB3wG7sE3zj8c2zU8TkfuNMf+uxWZuBmYFbPdPwA5jzAzgdOBPIlKMvc6mAX+uxfaUUsC6XQc5XFDMoG4Vn7eVauw0QFOqqoqLYN7teL5/jw1JI/nN7lspwBu0T1tNA6PaNFNsDMGCO9gpNtA1MYbkxLh6SZRSbmB1xkPg8cKiJ+C1S+CGeSVBWrDjX9FxrdWYeaq+3GeM+T5gWiGwElgpIo8BPWqzAWPM8CDT/tf19wfAB7XZhlKqrK+35AAwuKsGaKpp0wBN1bvGkkihwnIWF8GHt8HaudD3QrqNm82kxVvK7dNWU7VpptgYgoXAYOfKk7vUWy1fuYGViDN4tQcWPgav/X/27jw+qvJq4PjvzAQSIIgQF5SAaAJaq1YUEHBhU9tqtVZUFJe6oaBC32Lbt/ra1bebbalVLCB1raIo7ktdWZRVcKu2r5JFhOBKwioBkpnz/nFnwmQyazLLnZnz/XzygVly58zNneSe+5znPN+Fi5+Err0i7v9Y+zVfmr3kkwjJWfjjTcCaDIVjjEmhd9ZvBrD5ZybvJZygiUgnoJ+q1qQxHpOHcqWRQtQ4/T54fCL8+3H42hlwzj14vZ3S0jK/I2WKuZAsREt20pHEx3+tUfzgoAaO+3i2k6Rd8lTU/e/2/WraEpEDgP8CBhDyt05Vz8xaUMaYDvngs6303quEstLibIdiTFollKAFJlzPBZqBfiIyBPiBql6U6AuJyG3AmcBBwCBVfSdw/1pgF9AYeOrvVHVeots17pcrjRQixjmyAp6e0io5C1/sOJWJUS6UKXZEtH2VjiQ+odcqGs19lcKwtbPgwXMYedB03vzYk7f7v8A8DryJswaZrT9mTI7z+ZWqz7cz7BD7vWzyX6IjaL8HTsTpgIWqrhKRQUm+1nycFsNLIjw2PpiwmfyTK0lHmzgresE/fwzvPAgDToVxd7dJzlItF8oU0yGTSXz4a93W9D2GndQdXvsjV3lvgFG3sPijrwpq/+epbqp6XbaDMMakxtr6r9jV7OfQ3tld0saYTEg0QfOqao1Iq5KjpNaVUdXXAMK2YQpAriQdreKs6MXkpn/Aqr/DwSc5ix0XdU57DLlQppgOmUziI77WqP+B3V8hK/7G1Z1+wdWXPQRFVkKT494UkQGqWpXtQIwxHffhZ9sAOHR/S9BM/ks0QdsZWJhTAUTkSPaUJKbC/eJkbm8AP1XVL1O4bZNluZJ0tIpz0R9g+W3Q9zg4/yHo1CXb4eW1TCbxEV9LBL75W9i9Hd66H+ZfDufem/YRU5NW04FlIlKF03YfAFUdk72QjDHt9dHGrwCo3K80y5EYk36JJmg3Ay8BfUTkAeBkYEKKYjhJVdcFmpD8L3AfcFqkJ4rINGBa8HaPHj1SFIIpFMEGEUurN+L1SOTFpZfdDot+Cwd8Ay58FIo79scgtAHGsEN6IQjLa6M3w8iVrpepFEyOJ42sZOaiai6+a2Xa3nvUCwYi8J1boakR3nsUnpwM35vttOQ3uegBYCawGpuDZkzOW9+wA4C+vbpmORJj0i9ughYY2XoPuBBnkU8BfpGqbo6qui7wb5OI3EqM9seqOh3nqigA5eXlmooYTOEIbRAR1Kopxep74KWbYN+vwUVPQEnHLwKEvubK2noQZ3HmaM0w2tMwI1+Suqx3/PR44axZe5K0Tl3gjNuc5M3knNC1yYwxua1uUyNdO3vp2dUqG0z+8yT4vJdV9SNVnamqf0tVciYi3UQkdDGLC4C3U7FtYyIJbRARFGxKwX+eguemQc+D4ZKnoFtq5kGFL87s82vL6y6p2siMBVVMmLOCGQuq8Pk1YsOMeIKJzbKaem5fUM2sxdUpiT3T2vPefX5tsw87xFsE59wNFWOdcsdXf92x7ZlsWSoiR2c7CGNMaqzftIO+PbtaLwNTEOKOoKmqikidiOyjqhvb+0IiMhs4HegNvCgi24BTgcdExIszMlcLXNLe1zC5K1MjQKENIoKKizycV/YRPDYVuu0LFz8B3ffv8GsF31Pdph14Pc6omVdoGUErLvLg9UibEaP2NMzIlaUMgqL9vNvz3tMy6lZUDOP/AfedCUumO8fF8Gs6tk2TaScCV4pINa3noB2TvZCMMe3h9yufbG7kpAH7ZjsUYzIi0Tlo24F3ROT5wP8BUNVp0b+lNVW9OspDybbrN3koU6VtwQYRS6o2UuQRfApn7P8lp717PTv8RTw18C+ct3d/UjHrKPQ9eQX69erCuYPLQZ05aMdXlrG0unViNW/Vevrs3YUh/XviVxJumJErSxkERfp5TxpZiV+V/fdyuieee2zfVu89WlKXtuS0czdnDuLd34IXb4Bu+8BR53V8uyZTrMW+MXli047dNPmU/fYqyXYoxmREognae4EvY9IiUyNAbRpE1NewY9YFaPNuLtv9U955w0ND9+qUvHZ4aWN5z65MGTMQgCljne2r0pJYeQU2bN7JuoZGios8TB1bmXAcubKUQVCkn7cq3LGwpiXJ9HhoNYoantQpiir8+5MtLc9JeXLatRdc/DjcdarTNKRLTxhwSuq2b9JGVRdnOwZjTGps2uGs7FTWLf3L3RjjBgnNQVPVX0X6SndwpnCMqCijuMg5HNt7kp30XKRtn8MDZ1PStJkpTdexUr+W8LynRCTyniaPqmTq2EpGVJTRp2eXVvPTkokjmHjOnTiMa0cPcH2DkEj7Jt78s/DHH11dx19fqWJLY3PLc4b275n65LRHuVP2WtwdHrkE1q9K7fZNSonI30SkPMpjIiLjRCRVXYiNMRlQv91J0HpZgmYKREIjaCISsROWqtrseZMS0UaAkpmbllSZ5M4t8MA42LSWRQNuYvH/HQH+1JYHJjKqFTqiN2NBVUv8uVCm2BGR9k3oaGL4+/f5FY84zRRVaUnufGE5uE9JaXK65/jbxPcO/Qvn/PsaZO65cNkLsN9haXid3O7C6RLPAc+LyCZgJfA5UAIcChwPPA9Yd0djckjDV4ERtFJL0ExhSLTEMXTZ9hKcdcqWpz4cU6iirU2VTNKVcJlk0054aAJ8/h6M+RkjT7ieqYurU14emOwC3blWptgRkfZNrPc/c1E1b3zUgKrTTWho/54MPbiMW19Z05KkeT2S8qS29fFXQsmg33PGv6fBA2fD5S/C3n3T8DpZWF4gj6jqc8BzInICMAoYAOwAFgDTOtLsyhiTHfVf2QiaKSwJJWiq+uPQ2yLyS+DeNMRjTCvJzE1LqFGG3wePXQEfL4HjJsOJ1+OV5BKpdEk2ocs3sd7/spp6dgcyMcUZKbtmdCWI8ujqOqBtU5FUCD/+Hmo4lDPOmgWPXwkPnguXvwBd9o6zleRfx+1dOHOBqi4BlmQ7DmNMx23b6ZSy71Via6CZwpDoCForqlovIoekOhiT3yKVcQExS7uS6U4YdwRKFV74KXzwLBxxDnzzt7YAcY6IdBx4PcKUMQNbGq9k6nU5ahhs/8xZ0HzeRXDRY05b/lS/jjHGGAAam3wAdO2cih7LxrhfonPQpobc9AJDgc/SEpHJWzMXVXPbq1Xs9inLa+pZUVvPcQeXMWNh9NKuZMr+4o5ALb8D3rgT+p8IZ80ET6LrtJtsy1b5Z9TXHX4dbF4Pb8yGJ6+Bs+d06HgqpPJWY4xJVuNuZwStpJMlaKYwiGqcTneAiNwTcrMZqAbuVNVN6QosEeXl5VpXV5fNEEwSJsxZwbKaPZ35RKBvzy6sa2hsuW9ERRlzJw5L/Yv/+wl49FLY9zBn7lAKytISYc0f8pjfhz5yCfLBszxdeh7rjvmJ/XzTREQ2qGrEzoz5xv6uGdPWTU++xwMr1rH6ppPZp7RjFQvGuEG8v2uJXvL9sapeFviaqKp/gJSs5WsKyIiKMkJPXYPXBjraXj+udSvg8auhtDdcOD9jyRnsaf6wrKae2xdUM2txdcZe26SZx8ussp/ylg7gzO2PUL/wb/bzzRMicpuIrBURFZGjQ+4fICLLRGSNiKwSka/H2MYVIlIlIjUiMkdEbPKMMe3UuNuZo2sljqZQJJqgvZTgfcZENXlUJcdXlrVM+you8nDu4PKWdcCmjq1MfWnXxmp46HzwFMGFj6Ss616i4q3tZXLb62u/4opd11Pr781NnntofO/ZbIdkAkTkGBF5IZBM1Qa/Evz2+cAJwMdh98/GqR4ZCPyBKM2yRORg4GbgRKAS2B+4qh1vwxgD7AzMQSspsgTNFIaYc9BEpDNOW32viHSHlgGQHkC3NMdm8ozXI9x3+XHMCrS0H17RC1RYGij/mzQyxeVh27+EB8ehO7fyzNen89AzO/B6VuBXMlZuaM0fckd7ylGDP99Lm/6bJzr/gh9s/h3UnQjlgzMei2njPmAGzpIwvmS+UVVfA5CQJkIish8wGDg1cNdjwAwRqVTV8KHTc4CnVfWzwPfOAm4E7kj+bRhjfH6n5MZjvwdNgYjXJOQG4Bc4na23hNy/FfhzuoIy+avNwswxGoTEEvcEdvcOeGg8bFrLwgH/w4/f2Z9dzQ0tD2dqrSlr/tCWW5OP9qxFtufn25MF+93GOe9Nhrnj4YqXoKwio7GYNnyqOjuF2+sLfKqqzQCqqiKyDuiHMy87VD9aj76tDdxnjGkHRa3psikoMUscVfVXqurBKenwhHztrao3ZyhGk6fCy//ufK2WGQuqWq6URePzK9+/eyV/fnlN5Lldfh88diVseBP/CT/ilxsGt7xOUKbKDYMJ6dyJw7h29ABXJCLZ5tZ5ee0pR/V6hEkjnRLdJ744gOcO/Q3a2IA+eA5/f+ENJsxZkdAxnYpYTBtLRaRjQ5kZICLTRKQu+LV9+/Zsh2SM66iC/fU0hSShOWiqOjndgZjCM6KirKVBCMCWxuaETthnLnJKJINNRlqdwAbXOvvwOThqPH+T8WzY1NhmG1ZumD1uTT5Cj8dkjo/QhPP6dw9kceVPkIZajl1+DW/VfNKuJLS9sRgQkbdF5C3gJGCZiPxHRN4KfnVg0+uBA0SkKPA6gjMqti7Cc9cBB4Xc7h/leajqdFUtD36VlpZ2IERj8pPSuuTYmHyX6DpoA4DbgG/gzEkDQFV7pSkuUwCC5WF3vlbLlkZnjZPgCXt4OVdoWVzdph2EjkeIwPCKXsxYUMXe79zJRVvvRPufiJw5g2X3vIUv5Mk9uhTx9QN7uK7c0K1lf+mQzXl5sfZze8tR24wE7xjNltKP+O72edzWaQaTmn4Y8ZiOxUpjO+S/0rFRVf0ikOBdhNMcZBxQF2H+GTjz05aIyC+Bz4FJwMPpiMuYQmAjaKbQJJSgAXOAmcDPgfOBKTg19ca0W7D8T5WW+TbRTthD5+SE/pIW4ISKMlChatED/NV7J1VazqI+v2ZiUec2ycBVJx3iyrk8hTTnKJvJR6z9HHeh8ygiJZzr/dfzzOI6zvAu5ZfyANsqkqsIb28sBlR1MYCIXK6qd4c+JiKXA4vjbUNEZgOnA72BF0Vkm6pWAlcD94rIjThzsS8L+Z6/4zQGeVpVa0XkF8DSwMOLcDpAGmPayQbQTCFJNEHbS1XnichNqvqeiFwNrAR+m8bYTIFI5IQ9dJQiOCAmwAmVZdx7+XHc/Le7ucVzB5/r3nx/10/ov3Y3ExPcthtEKvvL15PzbCYf6djP0Y6xO/kj/1k5iUt2v4C/5ERgYEfDN8m5Drg77L5rI9zXhqpeHeX+D4HhUR67Muz2HJyLm8aYDvJ6oNmvqKqVOpqCkGiC1hT4d5uI9Ac+A/ZJR0Amc9JVVpfsduOdsPv8ikecq2caUq6ogE/B21DDTzf/imY8XL77J9QX7ceFgVG4XBmJsHb8mRFtP3fksxDtGJs89usw4mm465t4XroJepTD189K+XtKRiGU0orIUJwkal8RmRryUA+gODtRGWM6onORF1UnSevkza/fWcZEkmiC9pqIlOGsKfMmsBurp89pwU6IS2ucZhupLKtLdbnezEXVvPFRQ0tyFkzUios8nNxP4MFxFPu28+yR0+mx6TCmunikLJpcGenLddH2c9pKTLv0hIvmw99Phsevgu4HQL/jOr7ddkjnZ95lDgCOBroCg0Lu3wpcmo2AjDEd09nrNE3a3eynkzeh/nbG5LS4CVqgU9V0Va0H5orI60APVX0/7dGZtGnphBi4ncqyulSXkS2rqWd3SKePvj27UN6zKyMP7sZltT+ATWuRM/7KGcdeyhkdjj47cmWkL9dF28/hx+ySqo2okpqRpr37wYR5cM/p8ND5cOUrEddICx/duuqkCu58rSZlo13p/My7iao+BTwlIt9W1X9mOx5jTMd1LtqToHWzcXBTABIdQXsZOAJAVdfjtBs2EeRKCdGymvo2nRBTVVaXSLleMvspfHvjh/Tl2pGHwLyL4ZM34cTr4dhLk47TLT8rt8RRyMKPMa9HUjuiduAgOPdeZ/H0B8Y5SVq31lXi4aN4K2rrWbV2U8piSOdn3qUWiMhPgZNxKqJfBv6qqruyG5YxJlnBZUd2+/xxnmlMfoiboKmqBhbQ3EdVN2YiqFyWK934RlSUsXptA7t92tIJMVVldYmU6yWznyJu78XAWmdHngtjftauON3ys3JLHIUs/BhbWp2Gpi0DT4XT/wzP/hDmjofvPwOdu7Y8HD6K996GLSmNIZ2feZeaBZQBtwduXwYcBlyetYiMMe0SOoJmTCFIdARtO/COiDwf+D8AqjotLVHlsFzpxhcp6UnVqE0i5XrJ7Kc221v+N1g5Cw46Ad8ZM5i5sH2jT275WbkljnyU6Ohk+DEWnKPVkaYtEV978OWweR0s+Qs8PhHOux88XqD1KF5wDrzXI/j8mpLGMen8zLvUcOBrqs7sVRF5Fvh3dkMyxrRHcA7aLkvQTIFINEF7L/Bl4siVbnzZnPMU3pUxqf30n6fhxRthn0Ph/AeYuWQ9t71axW6fsrymnhW19dx3+XEJnXi65WflljjyUazRyXQsWp3Qa4/5OWxeD+/Phxf/B779+1avOW/VejZs3smWxma8Av16dWH8kL4dHu0qwHmO9UAXYEfgdjFgVSDG5KBgieOuZl+WIzEmMxJK0FT1V+kOJF9YN774QrsyCjC0f8/E9tP6Vc6oQ7d94cJHoUtPltV82NJARIGlNfXMWlyd0EmoW35WbokjH0UbnYzX0TAVyUzUkVGPB876G2z7DFbOdJqIDL+m5TWXVtezrqERcJaRKO/ZNS1JVQHMffwAWCkijwRunwOsCrbeV9XbshaZMSYpXYud09XG3ZagmcKQUK9SEekrIs+KyDuB20eLyA/TG1puCp5kzZ04jGtHD8i3E56E+fzKjAVVTJizghkLqvD597QnCO3K2LKWWbz91FDrNFgQj9MRr+dBgDP6FPqdqk6ikwi3/KzcEkc+GlFR1nLlNXR0sqWjYeCwDCZQmXhtAIqK4fwHnJHgF290RoYjfF9nr+ARIn6OOio4wrespp7bF1Qza3F1yrbtEh5gNXBI4OstwIvTev/oLMZljElSabFTCr59V3OWIzEmMxItcZwNzAV+HLj9PvAP4C+JvpCI3AacCRwEDFLVYLI3ALgPZ+HrLcClqmrzBHJcrNKypEv6djTAA+dA4yY4fy70OablocmjKllRW98yEpJsiWABjCIUtGijk4l0NEz22PD5lTsWVjH/zToAxh1TznWjK1leG2VktEtPZyT47yc7I8Pde0Pfoa1i9ggp7eQYKt/nPqrqZdmOwRiTGt0CI2iWoJlCkehqf/up6gOAH0BVm4FkPyXzgROAj8Punw3cqaoDgT8A9ya5XdMBsUa6OiLSyV/Q5FGVTB1byYiKMqaOrYxd0te0Ex66ABpq4Nu3wKHfbvWw1yPcd/lx/OjUgYltL8zMRdXc9moVy2rq+fNLa/j+3StTOkphsiva6OSIijI6BzpxROtomOwI08xF1fz1lSrWNTSyrqGR2xZU4/EQe2S050HOiLB4nM6O9TWtYvYrUT9HHRVzhC8PiEgPEZkhIs8Ebh8uIhdkOy5jTPKCCdpXlqCZApHoCFpzYMFqAESkJ5DUMIOqvhb43pb7RGQ/YDBwauCux4AZIlKpqnlXb+NG6WrxHmuULOH5PX4/PDkJ1q+A4dfB0IkRn9aR+ULh5ZbJzGEzuSHSSFgiHQ2THWFaVlNPyHrq+Pya2KhUn2PgnHvg4QvgwXPgipdb1khLZwOZApj7OBun2mNU4PZHOJUgD2UrIGNM+5S2jKDZHDRTGBJN0B7F+WO3l4hcCUwC/p6C1+8LfBoYkQuuubYO6AdYgpYB6SpzinXyl3Dp2Ku/hH8/AYd/F065ucMxRTKioozlIeVuwTlslqDlj2gXIeIl9ckmRyMqylhZuydJ83ok8YTq0G/BaX+C56bBQ+c7a6R16tLhJCrWZ629FzZyqCx4oKqeLyLjAFS1MfRCozEmd3TrbCNoprAk2sXxz4HSkB44o13TVXVuWiOLQESmAS1rr/Xo0SPTIeSddF2hj3Xyl9Co3aq7YOlfoXwofG+20/kuDTo6h824X7yLENESjmSTo8mjKlGUR1c7c9DOPTbJ1vhDrnDWSFt6qzMn7dz78Hq8TBpZ2XLhQJWkEqJ0jJDn0MLqu0NviEgXkqz8MMa4Q6mVOJoCk+gIGqr6kIg8HPh/qibprAcOEJEiVQ2WUfYD1kWJYTowPXi7vLzcJgt1UDbKnOKO2q15EZ7/EfQ6BC54GDp1SVsswTlssxZX53OpV0GLdxEiWsKR7AiT1yNMGTOQKWMGtj/Ysb+ALevh/cfgpZ/Bt37boYQoHSPkOdRcZKGI/A9QIiInAz8EHs9yTMaYduhmXRxNgUm0zX4/EXkRaAQaReSfItKvoy+uql/gtD6+KHDXOKDO5p9lTjZavMdsTvDJ2/DoZVCyN1w4H7pFH81KVYMTa3Of3+I1pYnV0CbjPB44ayYcdDysuANWzOxQfPEagbTnM5RDzUV+htPYaivwW2ApkJ5aaWNMWlmTEFNoEh1Bux94DjgPp0TkysB9oxJ9IRGZDZwO9AZeFJFtqloJXA3cKyI34vwhtdbIeS7qqF1DLTx4Lvib4YInoKwi5nZyqNTKZFEwAZ80spKZi6q5+K6VrUoZ09mII1k+vzLztXW8u/u/uKVLHXu/cAMXHX4Lbxb1bVd88UbI2/MZypXmIoG5zb8LfBljclhxkYcij1iTEFMwEk3Q9lXVP4bc/pOIXJrMC6nq1VHu/xAYnsy2TG6LWDq2/Ut4YBzsqIfz7od+x8XdTg6VWhkXiJaMuCnhCI3xnKLreabLL/n2mp+xY8hMHv/iwKTj83ok5hy29nyGOtI1NVNEZAjwI+DrgbveB/6kqquzF5Uxpr1EhNKSIrbvasp2KMZkRKIJWrWIDFTVNQAiMhCoSl9YpqDs2g5zz3VG0E6fDl87I+LTwps5DD/EPSMfxv2iJSOpSDhCj81hh/RCEJbXRu9yGK0xSWiMNc378Ju9f8VvNv8353z4I8654uW4o8qRpHTR+BwgIsOB54FZOC31BRgKvCQi31bVldmMzxjTPt1Liti200ocTWFINEErBd4VkWWB28OBZSLyOICqnp2O4Ezui9uS29cEj1zizD076SdOJ7sowk80rxtTwdSxla4Y+TDul85kJPTYXFlbDyL4/Bq1bDBa0hQe44GHD4cD74aHJzjlv1e8HHNeZiSxRsnaO3ro8lb7PwEuV9UnQu57QkRWADcAZ8X6ZhG5DTgTOAgYpKrviEgJ8DBwOM66ful4AAAgAElEQVRc7C+AyZHmS4tIf6AGeC/k7nGqWtPud2SMoXtxJ0vQTMFIZg7a/WG3jYkr5hwXVXjqOqh5FY65BEbfGHNb4Seay2saWhp7GBNPpGQkVYlG6LHpU5xjm+hlg+HH8pKqjYEyxI0M6d8Tv7InYfIMgG/f4nQ2feh8uOQp6Nw14dhSsmh8GJfP//x6WHIGgKo+JSJ/jPQNYeYDtwBLwu6/E/hnYL3O63DWAh0VZRvbVPXoJGI2xsRRWlLEZ1t3ZjsMYzIi0XXQ7kt3ICZ3xSrvijnH5ZVfwr8ehoHfhtP/AnHWkM3HciyTGeGJ2KSRTiI2Y0FVShKN0GPTK7SMoEU7TsOPZa9HWuIoLvIwdWxl6ziGToQtdc4aaY9cAhc8BN5OCcWWjjl2Lp//uSPGY1/F+2ZVfQ2cOS8h9+3EKZsMWoEzx80YkyF7lRSxbWcTqtrq82lMPkooQRORA4D/AgaEfo+qnpmmuPKGy0uBUiJWedeQ/j0pLvK0TapWzHRONsuHwjl3gzf+oeimZg4mt0Qb8UlVohF6bA6v6AXqXKSIdpyGH8tLqxNYTNtzIUd0/Q+jql/C/+Q1eBJcwD0dTT1cfrGkWESOJPKi1CUpeo0fAE/FeLybiKwCvMCTwG9U1drPGdMB3Us60eRTdjX7KenkzXY4xqRVoiWOjwNv4vyhsT8ySXB5KVBKxCrv8vm17Tyx9x+DF26AfQbChHkJl2vlQvc4407RSgrrNu3A64k92pWISMfmlLHRj9Pw56sSfzHthTU0N1/M7M4NnPzeI9C1DL71u7gjz+ng8oslXYCnozzWvsUSQwSWhKkExkZ5yqdAH1X9QkR6AfOA63HKJiNtbxowLXi7R48eHQ3RmLxUGlgLbdvOZkvQTN5LNEHrpqrXpTWSPOXyUqCUiFXedcKAfVqfuNYshCcmQffecNFj0LVXVmM3hSFWSaFXoF+vLowf0jfliUaiI+jxEp49v0e8XLv7Op7c6898beVM6LYPnJT5Srt47fuzSVX7p2vbIvIj4GzgZFWNWEqpqrtwmoigqg0icjcwgSgJmqpOB6YHb5eXl3c4iTQmH3UvCSZoTezbvTjL0RiTXokmaG+KyABVtdb6SXJ5KVBKJFzetW6l042uUxe4cD7s3S97QZuCEquk0KdQ3rNrWi6cJDqCHm90OPT3CEUlLBlyO1+rngILbnZG0gZflvLY4ymE6oBQgZGuC3CSs80xnrcfsElVm0SkGCeheztDYRqTt7qXOPNurZOjKQSJJmjTcdrqVwEtLXRUdUxaosogn1+5Y2EV89+sA+DcY/tyzejUXQl2eSlQSiRU3vXpv5w24Qhc+Bj0PiKzQZqClmxJYaqkY47b8ZVlXD6yEoY9Bnd/E56b5oxEH/7dVIcfU75WB4jIbOB0oDfwoohsw+nW+GegFlgYaFCwS1WPC3zPr4FPVHUWcALwaxHx4fyNXQD8JtPvw5h8UxoYQdu+yxI0k/8STdAeAGYCq8mzOWgzF1Xz11eqnLlTwK2vVuHxpO5KcL7Nm2pX05ON1fCP70FzI1z4KPQdkplgjYkiUxdOUjWCHvH3SPf94eInnCTtsSuhpAccMiolcSciX6sDVPXqKA9F/UWnqj8P+f/jOPO2jTEptFdIiaMx+S7RBK3VH6B8sqymviU5AycByZcrwemQdFnT5vVw/3ehcROM/0dGTyCNiSZTF07Sngj2OhguehzuOQ0eusBJ2PoNS+1rRBHvvRVCB1tjTOYE56BttRJHUwASTdCWisjRqvpOWqPJghEVZays3ZOkeT2SN1eC0yGpsqbtXzjJ2dY6+N6dcNjpGYzUmOzLSCLY+win4c4/zoIHzoHvPw19jmn1lFjJUqKJVKTnxXpvhTZHzRiTXqXFzhy07ZagmQKQaIJ2InCliFTTeg7aMdG/JTdMHlWJojy6es8ctHycJ5aqq9kJlzU1bnLKGhtq4LQ/wTfGd/AdtGVX6E0uCj9urzqpgjtfq+nYcdx3iLNkxQPjnM/dpc+1mucZK1lKNJFKNuHK1zlqxpjs2NPF0RI0k/8STdDytsW+1yNMGTOQa0YNaDlpEmlfy2g3JwypupqdUMnWzq1OQ5DP34exv4ChE1PwDtqyK/QmF4Uv7D7n9Vq27/K1LO7e7uO4/wlw/oNOqeM/zoJLn4d9BwKxk6VEE6lkE658naNmjMmO7jYHzRQQTyJPUtXFwDKgTlUXB7/SG1pmBU+altXUc/uCamYtru7QNv7y8hpG/2khMxZU4fNnd1kbn195ZPX6NidX7REs2Zo7cRjXjh7QqkxqxoIqLp+9gE//djrUrYITpsGJ0+Jssf0inTAa43bhC7tvaWxu+R3R4eO48mQ4917Y0QD3nwkNtYCTLBUXOb/uw5OlWI+FSvR5QZNHVTJ1bCUjKsqYOrYyLysTjDGZ0z1Y4mhdHE0BSGgETURGAXOBZqCfiAwBfqCqF6UxtowKP9lfUrURVZIaDQs/8VrX0MhfXl7DI6vXc97gvlkbUZu5qJq6TY0tt0Vg+CFtT646MgI4c1E1dy94j9me33GAZw1v9b2EY8amt6+MXaE3uajVmmZhUnIcH3Y6jJvjdHa877tw2XMxR74TbWQSXg7u9zu/M6L9jsi3DrbGmOwqtRJHU0ASLXH8Pc48tPkAqrpKRAalLaosCD/Z93ok6fK5SCdewUTt9gXVWSvBW1ZTT+ggniogbUf1OlIy+GZVHbM8v2eIZw2zmr/Da74JzJX0JqOFsMacyT/B43beqvVs2LzTSXIE+vTswvghKZoDe8Q4aNoJT10L95yO99JnoiZLXo8waWQlqs5nSTVyibfXIwjC51t3savZz4yF1SldksQYY2LxeoRunb1stRJHUwASTdC8qlojrU+4d6chnqwJP9lfWp38BPdIJ15Bu5r9zFu1nqXVmZ+fNqKijOU19YSmZMtrGpgStsx4snNMgiNub1bV8d/1N3GY50PubD6dv3AhUwfsk4Z30ppdoTe5KHjcThpZyazF1a0uMKT0d8KgC53h8ievgXu/43R37HUI0Ha0XBVmLIx/ccYafxhjsql7SScrcTQFIdEEbaeIlIJzji8iRwKNsb8lt4Sf7KuSdPlc+IlX+BXyDZt3sq6hMeMNLSaPqmRFbT1La5yr49HeT7ySwUgndXctfJ/Znt9zmOcD/ll6Nov2uoqpA/ax0Sxj4sjIBYajJ4B44clJgSTtGSiraDNavv9exQklXlZWbIzJptKSIitxNAUhZoImIg+p6gXA/wIvAX1E5AHgZGBCBuLLmo6Uz0W6Ql63aQfrGpycNtNXnr0e4b7Lj2tztT5cvPccflJ3SPdm7vT8jqGeD7m7+Vu8stdVzL1qeEbekzEmtj0XVA7i+4f+mlM//Dly7+nw/WfajISBc+EmXuJlZcXGmGzqXlLEJ5vzanzAmIhENXqHQRF5W1UHBf5/MPAtQIAXVbUmMyFGV15ernV1ddkOA4jfYGPGgqqW5Ka4yMPUsZWuKg1KpEHIhDkrWFbjdJjbm2083PUWDvPXMKf5NP7ExUwd23o0wM3LDhiT78J/59x25Ed884OboNs+PHjYDH69wtfy2HVjKvCIpKzcMtWffRHZoKrl7d5ADnHT3zVj3OaSu99g9doG/vPrb2U7FGM6JN7ftXglji3Zm6p+BMxMVWD5Jl6DDTddeY508hS+NlOkzpPB8qa9mut5sPh3DPTX8cZBE1nYNC5iWaOtU2ZM9oSPkt239Ri+ee49MP9yJvxnMkVDb+Wpz/dtlZCl6vNpn31jTDp0Ly5ix25fzA6yxuSDeAnaUSLSEOF+AVRVe6UhppwUb/K8mxpaRDp5irREQHjnycmjKtlr16ecunoavX2f4D/lZoYeP5W5UV7HGgoYkz0R54sdPgzO+wfy6KWMf38y4yc8DP3jfyaTHRGzz74xJh2Ci1Vv39lMj66dshyNMekTL0H7EDgtE4HkulyaPB/p5CnSEgHhJ1be+iou+b/JqO9TFlbewJz/DGXYzjUIwvLatiduubRPjHG7ZJOkqKP2h50GFz8Oc8+Hf5ztLGx9WOxf88mOiNln3xiTDsEEbevOJkvQTF6Ll6DtUtWPMxJJjgs/GZp4YgUzFlS5cv5VpJOnSSPbLhHQ6sRq3Up4aDzs3MrLh/6KKf8eyK7melbW1oMIPr+2OXFzU1mnMbku2SQp2qi9z6/MrN2fDT1+z88230SXeRch353hdHyMItkRMfvsG2PSobTYScqs1b7Jd/ESNHdkFGmQyNXoZK5Yh58MhU7Qd9scjEgnT7HWZuL/noXHrnDadU+Yx72LurOr2WkW4lMCK19HGHFzUVmnMbkuVWWDexK9nrxV9DPmd7uF7k9Ohq++hBFTnbXTwiQ7ImaffWNMOgRH0KzVvsl3MRO0YAfHTBCRtcAu9qyv9jtVnZeu15u5qJrbXq1it09ZXlPPitp67rv8uFYJWEcmui+t3tjqZGpJ1UbXnKzEOnlq89gbc+CfP4GuZTDhEehzDCPWV7F6bQO7fU5iJkLM9dWMMR2XqrLB0ETvw+be/LTnn7nD97/w8s+h4SM47U/gbf2nwUbEjDFusCdBa8pyJMaklyfbAYQZr6pHB77SlpyBc5ISTDAUWFpTz6zF1W2eE37FOlHhI21FLilvjMTnV2YsqGLCnBXMWFCFz6/g98Mrv4LnfwQ9+8MVL0OfYwDnZG3owb1aLrR7gH69ujB1bKWduBmTJpNHVTJ1bCUjKso69FkbUVFGcZHzq7+4yMPhhx4KV7wIh4yCN+9pKWUOClYSBOeqdrQFvzHGtFdLkxArcTR5Ll6JY94aUVHG8pr6lnUEVGlTMhR+xXp4Ra+E55X5w5aX80Vfbi7rwkcKO/t3cNXGW+CDZ6HPsc7IWbd9Wp7v9Qh+balsxKdQ3rMrk0ZW2rpnxoQJLZUedkivqE114klV2WDE0TCPwIXz4dkfwtv/gHu+DRPmQY9ya5lvjHGN7iXOHLStVuJo8pzbErT7RUSAN4CfquqX6XqhyaMqWVFbz9Ka+pbyvPAE7KqTKlqdyPj9cPvCxE5UcqmLWehI4T7Nn/PNFTdA80dwxDg4cwZ07trmeyK9PzuRM6at8DUGozXVyZSoiZ63E5x5O/Q6GF79NcwZC+fPZVlNU8G1zBeR24AzgYOAQar6TuD+tSRYii8iVwA/xSkyWABco6pWl2VMB1iJoykUbipxPElVjwKOATYC94U/QUSmiUhd8Gv79u3tfjGvR7jv8uP40akDW0qGUOH2Bc6V7tsXVDPn9RquHT2AuROHce3oASyvbV3yOG/VeqccMILQcqTrxlTg99O6hDALIpYysqfkabB8wNPFP+Og5o9gzE0w7q6IyRlELrfqSEmoMfkqfI3B4OfOlZ8RETjxejjnbti5Ge75Fld0fb1VSaSbLzal0HzgBCBSF+O4pfgicjBwM3AiUAnsD1yVrmCNKRSlxXvWQTMmn7lmBE1V1wX+bRKRW4E1EZ4zHZgevF1eXt6hTCf8SvKEOStaJRh3vlaLKi1lSCMqylhZW99Srri+oZHRf1rIeYP7tilVCt32jAVVCY+8pVO0Ea7JIyv4+mdPcOKaP6CeTvjOfRDv174Tc1uRrsLn0qihMZkS+rnwCi0jaK7+jBwxDnpVwLyLGVv1vzzW92xukcs4bsABBTHPVFVfA5AIHS0TdA7wtKp+FtjOLOBG4I6UBGhMgQqWOFoXR5PvXJGgiUg3oJOqbg7cdQHwdqbjCF+seUtjM7cvqN6TyIyq5JHV61nX4FS3KLCuobHVcyJJVXvsjooYx/EH4n12GqPXPAx794PzH4LeR7Rr+9bpzZi2Qj8Xwyt6gTpz0FK9XmKyC1nHdeDRcPVimH8ZR9Q+zv3l6+HY+535aoUtkVL8frQefVsbuM8Y0wFW4mgKhSsSNJzyj8dExIuz9lotcEmmgwieSN35Wi1bGp2rM6EJldcjnDe4b8soVFC8pMstI0vhcXzngC0wZwx8+QEM/BacNRO69mr39m3tI2PaivS5mDI29eslpmUOaNdecNHjzpy0pbfC7JPge7Og8uSo35LyRNFdTlLVdSLSCfhfnFL80zqyQRGZBkwL3u7Ro0fHIjQmjxUXeejkFeviaPKeKxI0Va0FMrbmWjTBEylVWk50OnsFjzjlj6GNQ+atWs+GzTsTKlVyy8hSSxxVG7mi+zLGvPsnaN4FJ//KWaDWE3tKYp6feBmTcakcXU/bSL3HC6f8yllm46nr4IFxMPw6GPsLKOrc8rTg74dHVu/53ZhvzYISKcUPWAdUhNzuH7gv0jZTWrpvTD4TEbqXdLIujibvuSJBc5vQhMojsGrtpjZXpSeNrGTW4uqEkq6OjCylMinyeoRJg/fmW+//mIpPFrK98350uWQ+3oOPT+j7rUujMamVytH1tI/UH/5dOOAb8NhEWD4D1r6O7+y7mPmekxyG/q4Myqeuj0mW4j8GLBGRXwKfA5OAh9MepDEFoHtJkc1BM3nPErQIQhOq8MYhoeWOmSjnS2lStOYldj46iYqmep7xDePmHVfy/bX7ce3BiX27W+bSGZOLIl1sSeXoenBbS6o24vUIS6vrWzU5Some/eGyf8Li38Nrf8I/83i2No1nRdOpKB7Ch35c3QglBhGZDZwO9AZeFJFtwKnEKMUXkb/jNAZ5WlVrReQXwNLAw4uA2Rl8C8bkrdLiIrbaHDST5yxBiyPb88dSkhR9VQ8v3QTvzgXpxtTd1/K0fwQgSW0v2/vCmFwW7WJLMhd6fH7ljoVVzH+zDoBzj+3LNaOdBCxSiXYyF3USHq33FjnLcBwymoZ/XMGN3vs5VVbwk6ar+IgDUQWvQJ+eXRg/pG9ONgtS1aujPBS1FF9Vrwy7PQeYk8q4jDHOCNqGzY3xn2hMDrMELY5szx/rUFKkCv96BF68AXbUQ8VYHi37IS8u2w7+5LeX7X1hTC5LxcWWmYuq+esrVS1Lfdz6ahUez54EzOdXHlm9vl2vk/Roff/jeWLYI3R5/bdcLC/wfOcbeLrHRTxbejbHDTiAq0+q4F8b3+GZ2qfo170fg/Yb1JG29cYYAzit9rftbEZV7XeKyVuWoMWR7c6E7U6KvvgAXvhvqF0EXfdxFp0+YhwXK3zVJbG5c+GyvS+MyVU+v+IRZx1o1faX/i2r2bMOY3C7oQnYzEXVbNi058qy1yMJv057EsiJY49kVtHN3Pzvk5n61V85b+s9nFf0Gp/s81O+9/Q0NmzfQJGniGZ/M31K+zD7lNkcWHpgku/aGGP26F5chM+v7Gzy06WzN9vhGJMWlqC5XNJJ0fYvYdHv4M17QX0w6CI45eaW9vnekLIqY0xmzFxUzRsfNaDqTF4a2r9nu0agR1SUsbJ2T5IWnoCFJ3B99i5J+HXaM1of/P3E6AHQfDEsvwN97Y9cveLnrO/cCR/Q5Hfmiqzftp5JL0/iqbOesqvexph2C10LzRI0k68KO0FbciscNAL6Do35tJxoL79rO7xxJyz5C+zaCv2Gwzd/A32OTcnmc2IfGONSy2rq2R3InBTwKe36/EweVYmiPLp6zxy00ARs2CG9WhI4r8C5g8sTfp0OlzAXFcOJ03i7z+FseP0n+MJahvjUR932Ot7+4m2O2f+Y5LZtjDEB3Us6AbB1ZzP77ZXlYIxJk8JN0LZ+6iy+qj44ZBSc9BPof3zERCTb7eVjJkc7tzqJ2fI7oLHB6bL23RnwtTOdeqoUyfY+MCaXparBjtcjTBkzkCljBkZ8XAipoxQBTfx3gNcjTBpZiSod6gC5zr+ToqISmprbTuLv5OnEum3rLEEzxrRbaWAEzRarNvmscBO0vQ6Aycvg9T/D+/OduVoHHc8/S8/mjncPoLGZlkQk2+3lIyZHx3SFN++BN+bAzs2wdz84+RfwjQmtFo9NlWzvA2NyWaYa7Cyvrcfnd0aufH5leW09U8Ym/jlNxYWYft370eyPfOLU5G+iX/d+SW3PGGNChZY4GpOvPNkOIKv2OwzGzYHrVjtztdav5Dv/vp6XvVO5xvsUpc2bWFrtjFp19jpXkQXwCC0nQZmwJzlSBvnfZ/DK/4Jbj4TX/ghdesKZM2DKW3DspWlJzsAZASgucg4Xa7FvTHKCc7XmThzWso5iOoR+Tr0CdZt2MGNBVcK/ryJdiEnWoP0G0ae0D15pPTfEK17KS8sZtF/UTvXGGBNXsMTRFqs2+axwR9BClVXAd++A0f/DG/On0//jR/lJp3n8sGg+G3YMo1+vi3n3oP145aOdqMKqtZuYtbg6MyNIqpyxfz0j18/jNJbR1/Ml7AQqxsLQq2DAKeBJ/yRZa7FvjPsFP6fzVq1nw+adrGto5PYF1QmPhKWiFFNEmH3KbK5++Wo2bN9AJ08nmvxNlJeWM/uU2dYgxBjTIcERtO2WoJk8ZglaqL0OZMVBV3Fx1YmMldWcX7SQEzatwPPkUu6gE4uLjmSJ/0iW+I5gadXe6UvQdn8FHy+DmoVQ/TIXbFwDHqj37MNzXcfxatfTOKTPN5g8IHONOqzFvjHuF/ycLq2uZ12DMwcsmZLkVF2IObD0QJ4+62ne/uJt1m1bZ+ugGWNSpnuxc+q61UocTR6zBC3MitoGdmkRz+swnt89jG/29zJ78Cd88fqDjN78Fqd43wLgq4374H/kRFbuOJDXt/Vm38rBXHLqMLzeJKtGm3fBxjXw6b/gs3/Bp++idauRQGvqrzqX0WXwlXiOHMdD1WXcvrCWXRv9FH+S+FVxY0z+idU8qL0jYam8ECMiHLP/MdYQxBiTUlbiaAqBJWhhwk9sjjq0AgZ/iwOOuYy7X32HLf+3iFO6fMBRu99F/vMEw4HhAPXQtKoEb69+sFcfZ25YyV7QuXTPxv3NTtfFnVvgqy9h8zrY/jmEtqMu3ouPewxh7sYKFjUfwcfN/ZjabQDXHjSAZS+tsEYdxhggdkMPK0k2xuSr7tbF0RQAS9DCRDux8XqEiacMglMG4fMrdyyq5oEv/8OBu2o53PMxX5N1HNltM0exDepWwe7t0V9EvNC1DPbuC/2GQVklHHAU9D4Kevbnxr+vZFlTYHJ+s7YkYqlq1W2MyX3hDT1ue7Uavx+uGV1pJcnGmLxVal0cTQGwBC1MIic2e65cF/EZA3nLN5DiIg9Th1VyVPD7fE2wa1vrRE28UNIDOneLuUZZtETMroobY4JGVJS1LEoNTpJ266tVeDxW+myMyV+lnYsQsRJHk98sQWuH0CvXAD26FHHVSYe0Tpi8naBrL+crwOdX7lhYxaOr17N1ZzM9Sjpx7uC+LVe8g2KN4tlVcWMMOL8nHlm9vqUZCDi/Y1JZ+hxrnpsxxmSDxyOUdi6yBM3kNUvQ2iF8hOvKEw9GFS6+a2XMk5iZi6r56ytVLVe8tzQ2R7zibYmYMSYer0c4b3Bf/vLympbfKbBnncZUJFKpWLjaGGNSrbSkiG02B83kMUvQ2iF0hGt4RS9W1DSwrLYeVWKexCyrqW91IgWpv+JtjCkck0dVoih/f/0jtjQ6JyupXKcx0sLV9rvKGJNt3UuKbA6ayWtJ9oQ3sGeEa+7EYQjCshonOYM9JzGRjKgowxt2UdvrEWv2YYxJis+vzFhQxcV3rUQQvn5gj5bHYv0OStaIijKKi5w/E9EaEwVjmTBnBbe9uobbX3X+P2NBFT6/tnm+McZ0VPeSTlbiaPKajaB10LKa+tAm+YgQNeEKXu1+ZFXrOWixmn3YHBBjTLjw0sMh/XtSXORJeYfXRBoThcaysrYeRPD51UoijTFpU1pcxHZL0EweswStg0ZUlLF6bQO7fYoAJ1RE767o9QhTxgxkypiBCW8//OTnkdXrOefYcgRhea0lbcYUovDSQ59fmTq2MiUdXiNdFIqVZIXG4lMIlhNYSaQxJl26lxTR2OSjyeenk9eKwUz+sQStgyJdYU5FshQ8SZrzem2rk591DY389ZUqu0ptTAELb1R0woB9UtZYKNnGIKEXqcCpIlCNXhLpdiJyG3AmcBAwSFXfEZEy4NWQp3UFDgH2U9WGsO/vD9QA74XcPU5Va9IZtzGFpHtJJwC272ymZ7fOWY7GmNSzBK2DUt1xMZiYPbJ6PXWbGok0hcOuUhtT2NK5JmKyjUEmj6pkRW09SwNzcT1An15dGD8kdvm2i80HbgGWBO9Q1Xrg6OBtEfkRMDI8OQuxTVWPjvKYMaaDugcWq96+yxI0k58sQXOZ0KvX4YJXpgVa5r3l6lVqY0z7pXMpjvDRuXi/X7wewa8t14zwKZT37JqzF41U9TUAkZiVEFcAN2QkIGNMG92LndPXrdbJ0eQpS9BcJnwR7FB9e3YBoG5TY0uiNrR/z1y9Sm2McaH2jM4lm9TlMhEZAfQEno3xtG4isgrwAk8Cv1FVXybiM6YQBEfQrJOjyVeuSdBEZABwH7APsAW4VFX/nd2oMi/0RCd8pGz8kL4sra5nXUMjBB7zKWltEGJdJI0pLO0ZnUtnyaULXQHcr6rRzgw/Bfqo6hci0guYB1yPUzbZhohMA6YFb/fo0SPS04wxIboFRtB27LYEzeQn1yRowGzgTlW9V0TOAe4FhmQ3pMwLXwQbdbo1Bk96gothZ+pKdbINA4wxhSedJZduIiKlwHnE+NukqruALwL/bxCRu4EJREnQVHU6MD14u7y83BaPMyaOrp2d09evdtnAtMlPrkjQRGQ/YDBwauCux4AZIlKpqtXZiyzzIp3oTBm75/+ZvlKdbMMAY4zJY+OBd1X1g2hPCPw926SqTSJSDJwNvJ2pAI0pBF2LvQA07rYEzeQnVyRoQF/g02DJiKqqiKwD+gEFlaDFk+kr1YU0t8QYY0RkNnA60Bt4UUS2qWrwStgVwJwI3/Nr4BNVnQWcAPxaRHw4f2MXAL/JSPDGFIhuwRE0K3E0ecotCVpCrFY/8yaPqkRRHl1dB4Df78xLs3loxph8pMefJyMAABYaSURBVKpXx3hsRJT7fx7y/8eBx9MQmjEmoGtnZwRth42gmTzllgRtPXCAiBSparM4/Y37AetCn2S1+pnn9QiC8PnWXexq9jNjYTUej81DMyaf7W72c/m9b/Dehi0c2acHd186lM5FnmyHZYwxwJ4E7atdNoJm8pMr/uKq6hfAW8BFgbvGAXWFNv8sHXx+ZcaCKibMWcGMBVX4Iq18HUekeWjGmPx1+b1vsKS6ni2NzSyprueKe9/IdkjGGNNiTxdHG0Ez+cktI2gAVwP3isiNwFbgsizH42qJtr9PRRdGm4dmTGF5b8OWVrf/FXbbGGOyaU+Jo42gmfzkmgRNVT8Ehmc7jlyRaOKVii6MBbbGkTEF78g+PVgSMlJ+VB+b72uMcY+WNvs2gmbylCtKHE3yEi07HFFRRnFg7kh7R7+CnSPnThzGtaMHWIMQY/Lc3ZcO5YSKXhQXCT26FDG4f692lUcbY0w6eD1CcZGHHTYHzeQp14ygFZpESxSjGVFRxuq1Dez2KQJ4JHJ3RRv9MsYkq3ORh2EV+7Dq481saWzmb4tqKPKKNQcyxrhGt+Iim4Nm8paNoGVJsERxWU09ty+oZtbi5PqhTB5VydCDeyECCqxauyniNmz0yxjTHtYcyBjjZl07ey1BM3nLErQsCT/5mbdqPbub/Ql3XPR6BL+CBp5iJ1DGmFRKRXm0McakS7fORbZQtclbVuKYJSMqylhZW48vkGBt2LyTy+99g1VrNyXccdG6Kxpj0sXKo40xbtals5ctW5qyHYYxaWEjaFkyeVQlfXp2abnt8yvvbdiSVEnR5FGVXDemgr49Syjp5GHeG+u5/dX2rXUWSSrWUDPG5CYrjzbGuFm3Yq+12Td5yxK0LPF6hPMG921VQnRknx5JlRR5PYIgfLJ5J1sam1m3qZFbX61Kej5bNB2dJ2eMMcYYkw5dOztNQlTt4rHJP1bimEXhJUQTT6xgzus1SZUULavZUyYJzqhXe9Y6i7btjq6hZowxxhiTat06e2n2K7t9foqLvNkOx5iUsgQti4IlRKFJT/jteMLnsnk90uG5aMElAOo27cDrEXx+tTluxhhjjHGNLoHFqnfs8lmCZvKOJWg5bvKoShTl0dV1AJx7bN8OT+YPljbuavbjFejXqwvjh3R8u8YYY4wxqdCts5OU7Wjy0TPLsRiTapag5TivR5gyZiBTxgxM2TZDSxt9CuU9u1ppozHGGGNco2txcATNGoWY/GNNQkwbIyrK6Ox1OrYJ4BGsg6MxxhhjXCM4gvaVLVZt8pAlaFnmxlb2k0dVMvTgXoiAAqvWbrIOjsYYY4xxja7BEkcbQTN5yBK0LHNjK3uvR/ArBDvXJrImmzHGGGNMpnQNNgmxETSThyxBy7JIrezdYERFWVJrshljjDHGZEq34mCJo42gmfxjTUKybERFGW9+vIldzX5XJULha7RZB0djjDHGuIWNoJl8Zglalrk1EYq0RpsxxuQ7ESkBHgYOBxqBL4DJqlotIvsB9wMVwC7gGlV9Lcp2vgP8CfAC7wGXqurWDLwFYwpCcA7aVzYHzeQhK3HMsmAiNHfiMK4dPQCvR7IdkjHGFLo7gUNV9RvAU8DfA/f/HlihqgOAy4C5ItIp/JtFpBS4Czgr8NxPgJ9lJHJjCkRwBK3RRtBMHrIEzRhjjAlQ1Z2q+rxqsE0SK4D+gf+fB8wKPG8VTuI1MsJmvg28raofBG7/DbggbUEbU4D2zEGzBM3kHytxdAmfX5m5yOnmOKKijMmjKm00zRhjsu8HwFMiUgZ0UtXPQh5bC/SL8D39gI/DnneAiBSpqtVjGZMCe+ag2UfK5B9L0FzA51e+f/dKltbUowpvfrwJEZKa/xUpwQMs6TPGmHYSkRuBSmAs0CVNrzENmBa83aNHj3S8jDF5Z68uRfz+7CMZ2Lt7tkMxJuUsQXOBmYuqWVpdT7CeJthuP5kELbie2q5mf0uCp0qb+6zphzHGxCciPwLOBk5W1R3ADhFpFpHeIaNo/YF1Eb59HXBKyO3+wKeRRs9UdTowPXi7vLxcw59jjGmruMjL+UMjDWAbk/tsDpoLLKvZk5wBiJB0u/1I66m5dY01Y4xxs8Co1gXAKaq6OeShR4FJgecMAfoAiyNs4gXgGBE5LHD7GpzOkMYYY0xclqC5wIiKMjp7ndJDAU6oSL7dfqSFpW2xaWOMSY6IlAN/BvYGForIOyKyMvDwfwMjRKQKuBe4SFWbAt/3axGZBKCq24ArgSdFpBooB27O7DsxxhiTq6zE0QUirYWW7FyxaOupuXGNNWOMcStVrcO5Vhbpsc+BU6M89vOw208DT6c8QGOMMXlP9nQSzj3l5eVaV1eX7TBcybpCGmPyhYhsUNXybMeRCfZ3zRhj8l+8v2s2gpanIjUNsQYhxhhjjDHGuFvW56CJyC9F5MtAnf87IvJgtmPKB9YgxBhjjDHGmNyT9QQt4EFVPTrwdWG2g8kH1iDEGGOMMcaY3GMljnkqWtMQY4wxxhhjjHu5JUE7V0RGA/XAzaq6MNsB5TqvR7h29ACbd2aMMcYYY0wOSXsXRxFZDkTLEgYBTUC9qjaJyPHAE8AQVf04wramAdNC7uoNfNbBEEuB7R3cRrbkcuyQ2/Fb7NmTy/Fb7O2zr6oWZ+m1M0pEmun437VMyaXj2WJND4s1PSzW9HFLvDH/rrmuzb6IvAjcqaqPZej16nK1fXMuxw65Hb/Fnj25HL/FbuLJpf1ssaaHxZoeFmt65FKskDvxZr1JiIiUh/x/AHA08F72IjLGGGOMMcaY7HDDHLTfiMixQDPgA65V1TVZjskYY4wxxhhjMi7rCZqqfj/LIUzP8ut3RC7HDrkdv8WePbkcv8Vu4sml/WyxpofFmh4Wa3rkUqyQI/G6bg6aMcYYY4wxxhSqrM9BM8YYY4wxxhjjsATNGGOMMcYYY1yiYBM0ERkgIstEZI2IrBKRr2c7plhEZK2IfCgi7wS+xgfud937EJHbAvGqiBwdcn/UWN30PmLEH/FnEHjMFfGLSImIPBmI410ReVlEKgOP7SciL4hIlYi8LyInhXxf1MdcEvsiEfkoZN//0E2xB+J4SUT+FYjvdREZFLg/V477aPG7/rjPNYnuNxG5InBc14jIHBHplOE4o34mw57XX0R8IcfIOyJSkclYA3FEPVbDnpft/VoWtq/WiEiziPQKe15W9muMv4EJf94ztY8jxZrocRt4bsb2cYz9mtBxG3huNvdrQsdt4LmZ3K/tOu+JsJ3viMgHgec+LiJ7pSPehKlqQX4BC4BLA/8/B1iV7ZjixLsWODoX3gdwElAeHnOsWN30PmLEH/Fn4Kb4gRLgNPbML70OWBT4/93ALwP/HwLUAZ3iPeaS2BcBZ0X5vqzHHnjtvUP+/z3g3XjHhluOmzjxu/64z7WvRPYbcDDwCdAbEOBpnC7HmYwz6mcy7Hn9gc0u2K9Rj1U37dcIMf0IeMYt+5V2/A3P1j6OFGuix22m93GM/Rr3uHXDfo3wnIjHbRb2a7vOe8K2UQp8DhwWuD0D+GMm4o/6vrL54ll707AfsBUoCtwW4DOgMtuxxYi5zYfE7e8j7Bdm1Fjd+j4S/SXq1vgDsQwG1gb+vx3oHfLYG8DJ8R5zSeyLiJ6guTH2S4F3cvG4D40/8P+cO+7d/JXofgN+DMwKuX0asCTLsbd8JsPu70/uJGhu3K//F+n3W7b3Kwn+DXfDPo71s4923GZrH4fHmshx69L9GvG4zdZ+jfTzJsHzA+Bc4IWQ24cDddmIP/hVqCWOfYFPVbUZQJ2fxjqgX1ajiu9+EXlPRO4SkX3JrfcRK9Zceh/hPwNwd/w/AJ4SkTKcq0afhTy2FugX67GMRRnZD4CnQm7/PrDv54nIIeCUXOCi2EXkfhFZD9wMXEyOHfcR4g/KtePezRLdb/2Aj0Nur43wnEwL/0yG6hYoe3tLRH4uIt5MBhYi0rEaylX7VURGAD2BZ6M8xS37NZnPu6v2MbGPW3DHPo533IKL9msCxy1kb7/GPe+J8D2R9u0BIpK15cgKNUHLRSep6lHAMcBG4L4sx1OIcupnICI34ozU3JDtWJIVIfaLVfUw4CjgdWL/UcgaVb1EVfsCNwF/yHY8yYoSf04d9yY94vw++RToo6pDgJOBE4HrMxheUC4eq1cA9wcTnzBu2a85K4G/g27Yx/l23EKW9msun/eEK9QEbT0hmbGICE72vC6rUcWg+v/t3WnMXFUdx/HvDypUW6W0SrE0UAvaQthcSpSIUtmUF7UWFUUlIItF0aAS4AViWRJCLAaQpRRKkAiUNUgCaVlsKArSQvcNKKuNCAECYksJhb8vzpn2djpzZ56HduY+9PdJbp577nLu/545c89z7jbxYv77LnAJqbL3pf0oi7VP7EeTzwAqGL+k04EJwLciYk1EvAask7RzYbERwItl8zoVb1F97AAR8a/8NyLicmCkpCFVi70mIv4MjCXd797n6n0t/lzGfabe9xHtltuLwG6F9IgGy3REo+9kUUS8ExGv5PHXSc99HFS/3JZWUleLqlSuA4Hvk8prE1Up16wn3/dKlHGregvVKOM26y1Up1xL6y10p1x78n9Pg9Uble36K8bdsFV20HKlmQf8OE86inSv6cruRdWcpAGSBhUm/RCY35f2oyzWvrAfzT4DqF59kvSbHN9hEfFGYdZtwMS8zBhgF+ChNuZ1TKPYJfWTNLSwzFHAy/ngCxWIXdIgScMK6fHAa0CfqPcl8a/tK/W+r+hBud0BjJO0c/5neCIwvXORJiXHk+IyOym/TU7S9qR/kuZ3LsryY3SdSpRrdjTpZTwrGs2sQrnW9PD73vUybqfe5uW6WsY9qLdQgXLNSustdL5ce/l/T9EM4AuSRuf0z+necSHpyQNrH6YBGAU8CjwFPA7s0+2YSmIdSarYi4DFpHupR1R1P4CrSVcO1pHeirOyVaxV2o9G8Zd9BlWKn/TWpQCeIb2kYgHwWJ43FLgPeBpYCowtrNd0XrdjBwbkMl0MLAQeBParWOy7kR4+rsX4ABserq98vW8Wf1+p931taFZuwLXAuMJyJ+XvwzPANDr/ZtWy48l5wMQ8PgFYkuvOUuBPwPYdjrWsnaxUuRbieAQ4vm5a18uV3rXhXSnjRrGW1dtulnGTWFsdYytTrmX1tsvl2tv/e9bHm9PjgBX5c7kL2GFLxNvuUHslpZmZmZmZmXXZVnmLo5mZmZmZWRW5g2ZmZmZmZlYR7qCZmZmZmZlVhDtoZmZmZmZmFeEOmpmZmZmZWUW4g2YGSHpe0pOSFkpaKemvkg7s4PZ3lzRP0nxJx9fNGyFpYoN49+9UfGZmVk2SFuRhmaT3Culbuh1buyRNktS/Q9s6VdJZeVySrsxt70/rlvuFpCWSluf2+WZJu0rqL+kJSTt0Il7bOvk1+2akDg8wPiIW5PQE0i/fHxERj3Vg+2cCIyPiZw3mHQxcEhH7F6ZtFG8VSeoXEeu6HYeZ2dZA0ghgQUQMarFoR0naBiAi3i9ZJoAdo+RHpXubd93yHyX9HtY+EbFa0uHAEcBZwCxSm79a0rnA4cD3ImJVXvcQ4K2ImCPpNGBwRJzTk3jN2uUraGYNRMSdwBTgdEgHZkmP5rNsSyWdkKcPk/SypI/V1pV0k6RT6vOUNFDSdfmM3BJJv8/TjwV+DUzIZz33qlt1CjAqz7u7MH1Cjuk5SWcXtrOzpFslzZG0WNIFjfYxzzuwkD65dsa1LA9JkyXNzfHMljSqMC8knStpLnBhq3I2M7MtQ9IRkv6er/bMkTQ2Tz84t0FXSVqUj/H7Sro+jz8maZe87HGS/ibp7nyFbnbuCNa2cXrOe56kGZJ2y9MnSbpD0kzSDxZ/ulnbIWlKzu7hPG+nHMtphe1MljSpJO+G+9rAd4F/RMTqWtbA+6QfOo6c/wDgDOCEWucMICIejIg5OTkdOEmSev7JmLWhm7+S7cFDVQbgeWD/umnfAZbl8R2BbfP4YOAFYHhO3wicnMeHAq8AAxts46K87DbAAGA+cHSeN4l0laxRbAeTzorWx3tZHv8k8CawS07PBL6ex/sBM0hnAevzPQm4qZBeCBzUKg/gU4V1fgDMKKQDOKfbn6cHDx48bG0DMAJ4I4+PBB4FPpHTewAvAdvnNmUd8MU873zgVWB0Tl8B/CGPHwe8A+yZ02cA9+XxY4BrCm3jT4B78vgk4N/A0EJ8rdqOQYX09cBphfRkYFKjvMv2tUEZTQNOLaS3Aa7O7fGJedoBwJttlPezwN7d/tw9fDiHfphZM8UzY0OAaZI+R2rYhgB7A6uAS0mN1FRSp+fmiPhfg/wOBX4b6VaM1ZJuAA4DevucwE0AEfGqpGeBz0h6AzgEGFo4sTcQGNVg/b8A50kaCnw2ZRUP57OHZXkcJumXwMdJjdvgunyv6+X+mJnZ5vFNUkdlduE4/j6wax5fGRFP5PHHc3pFTs8hnaCseSQilufxqcAFkrYFxgNjgCfyNrati+HeiHi5kG7VdvREMe+yfX26br3hpBOOwPpbIzd5tKBN/8n5Lenl+mZNuYNm1twYNhx4pwD3AkdFREiaB/QHiHQ/+pp8S8XJpI5YOz7oA6BrC+Pvkb7PtdbpyxGxdtNVChuPeFvS9aTGaU/SWVPK8pC0K3A5MCYinpG0LzC7LutGnVMzM+scAfdHxDGbzEi3L9a3H43ak3a2cWFETG0yf31b0GbbUbSOjTt8/dm4bSmON93XBtbkvMosA7aTtFdELCtZrj/wdhvbNOsxP4Nm1oCkbwOnABfnSTsCL+TO2deA/epWuRS4AVgeEU81yfYB4AQlA0i3g9zXRjj/Bdp6W1S+cjeL9MBzbV+GSRreZJUrSJ3Kb5Buv2yVxw7Au8BL+d77U9uJy8zMOmomcGjuCAEg6YBe5vUVSaPz+InArIh4D7gLmChpcM7/I5I+3ySPVm3HW2zczq0k3WqIpCHAkSXx9WRfF9H4jpL1chs4Gbim9ixeznNsLd98BXF3YHFZXma95StoZhvcImkt6fmwZcCRseENjmcBV0r6HbAAqH+z4+3AVaQzhM2cD1zGhgP6bRFxaxtxLQKWSloCPBsR41os/yPgj3n5AFaTrpKtql8wIlZJmg88FRFrWuUREQslTSe9Bes1UgNtZmYVEhErJR0DXK30EqvtSM9ZtXOVqd4jwEWS9iAd94/N27gxd55m5VsL+5FucZ/fIJ7FLdqOi4H7Ja0hvT1xKnC7pOWkZ73+uZn29fYc49kN5hWdQ3oub2bujAWp7T8zz/8qMDciXm+Rj1mv+DX7ZpuBpC+RngkbHW2+7rcK8pW8J0kvB3mu2/GYmVl1SDqO9JMu47sdy+Yi6R7SC0fmfoA8pgPTIuL+zReZ2Qa+xdHsA5J0LXAn6c1QfalzNhFYAVzpzpmZmW0lfkV643KvKP2g9kPunNmW5CtoZmZmZmZmFeEraGZmZmZmZhXhDpqZmZmZmVlFuINmZmZmZmZWEe6gmZmZmZmZVYQ7aGZmZmZmZhXhDpqZmZmZmVlFuINmZmZmZmZWEf8HWxDQ3w1BXUgAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# First set up the figure, the axis, and the plot element we want to animate\n",
        "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(11,4), dpi=80)\n",
        "ax1.set_title(\"Average air temperature in Aachen (2018)\")\n",
        "ax2.set_title(\"Modelled ground temperature\")\n",
        "ax1.set_xlabel(\"Day of the year\")\n",
        "ax1.set_ylabel(\"Temperature (°C)\")\n",
        "ax2.set_xlabel(\"Temperature (°C)\")\n",
        "ax2.set_ylabel(\"Depth (m)\")\n",
        "ax2.set_xlim(0,22)\n",
        "ax1.plot(year, temp,'.', label=\"Measurements\")\n",
        "ax1.plot(year,T_s, label=\"Cosine fit\")\n",
        "vline, = ax1.plot(0, T[0], \"o\", color=\"tab:green\", ms=6)\n",
        "ax1.set_ylim(-5,30)\n",
        "ax1.legend()\n",
        "\n",
        "T = Tm + 0.03*z + Td * np.exp(-np.sqrt(omega/(2*kappa)) * z) * np.cos(- np.sqrt(omega/(2*kappa)) * z + phi)\n",
        "line, = ax2.plot(T, z)\n",
        "ax2.invert_yaxis()\n",
        "\n",
        "# initialization function: plot the background of each frame\n",
        "def init():\n",
        "    line.set_data(T, z)\n",
        "    vline.set_data(0,T[0])\n",
        "    return line, vline,\n",
        "\n",
        "# animation function. This is called sequentially\n",
        "def animate(i):\n",
        "    t = i\n",
        "    T = Tm + 0.03*z + Td * np.exp(-np.sqrt(omega/(2*kappa)) * z) * np.cos(omega*t - np.sqrt(omega/(2*kappa)) * z + phi)\n",
        "    line.set_data(T, z)\n",
        "    vline.set_data(i, T[0])\n",
        "    return line, vline,\n",
        "\n",
        "fig.tight_layout()\n",
        "\n",
        "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
        "                               frames=365, interval=20, blit=True)\n",
        "HTML(anim.to_html5_video())\n",
        "#anim.save(\"animation.gif\", writer=\"imagemagick\")"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.8"
    },
    "colab": {
      "provenance": [],
      "collapsed_sections": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}