{ "cells": [ { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import sympy as sp\n", "from sympy import symbols\n", "import matplotlib.pyplot as plt\n", "import seaborn\n", "import networkx as nx\n", "import pydot\n", "import ipywidgets\n", "import pandas as pd\n", "\n", "from IPython.display import display\n", "\n", "sp.init_printing()" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The cython extension is already loaded. To reload it, use:\n", " %reload_ext cython\n" ] } ], "source": [ "%load_ext cython" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Beginning the Exploration - Cobweb Diagrams\n", "\n", "We will use the graph of the logistic map\n", "\n", "$$\n", "x_{n+1} = \\mu x_n (1 - x_n)\n", "$$\n", "\n", "and the diagonal $y=x$. This map expresses chaotic behavior for certain values of $\\mu$. We can examine \"orbits\" of this system by looking at what values the map bounces around to. A cobweb diagram is a good way to see these \"orbits\".\n", "\n", "**Task 1.** Find the parameter values at which the stable period $2^1$, $2^2$, and $2^3$ orbits are first created. Label these $\\mu_1$, $\\mu_2$, $\\mu_3$." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " Cython: _cython_magic_15630965f190cc95eb8319f568d4a71e.pyx\n", " \n", " \n", "\n", "\n", "

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+01: import numpy as np
\n", "
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 02: cimport numpy as np
\n", "
 03: 
\n", "
 04: cimport cython
\n", "
 05: 
\n", "
 06: @cython.boundscheck(False) # turn off bounds-checking
\n", "
 07: @cython.wraparound(False)  # turn off negative index wrapping
\n", "
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\n", "
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       "  goto __pyx_L0;\n",
       "
" ], "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%cython -a -c=-O3\n", "import numpy as np\n", "cimport numpy as np\n", "\n", "cimport cython\n", "\n", "@cython.boundscheck(False) # turn off bounds-checking\n", "@cython.wraparound(False) # turn off negative index wrapping\n", "def cobweb(f, int n=100, int start=0, float initial=0.5):\n", " \"\"\" Generate the path for a cobweb diagram \"\"\"\n", " cdef np.ndarray[np.float64_t, ndim=2] web = np.zeros((n, 2),\n", " dtype=np.float64)\n", " web[0, 0] = initial\n", " web[0, 1] = initial\n", " cdef int state = 1\n", " cdef np.ndarray[np.int64_t, ndim=1] vals = np.arange(1, n)\n", " for i in vals:\n", " if state:\n", " web[i, 0] = web[i - 1, 0]\n", " web[i, 1] = f(web[i - 1, 0])\n", " else:\n", " web[i, 0] = web[i - 1, 1]\n", " web[i, 1] = web[i - 1, 1]\n", " state ^= 1\n", " return web[start:]" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(0, 1, 100)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e8e82fa417cd4fd6a5b49194d2632f23", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type interactive.

\n", "

\n", " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another notebook frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "interactive(children=(FloatSlider(value=3.0, description='mu', max=4.0, min=1.0, step=0.01), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "button = ipywidgets.Button(description='Save as File')\n", "@ipywidgets.interact(mu=(1, 4, 0.01))\n", "def plot(mu=3):\n", " f = lambda x: mu * x * (1 - x)\n", " web = cobweb(f, n=1000)\n", " fig = plt.figure(figsize=(6, 6))\n", " ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])\n", " ax.plot(x, x)\n", " ax.plot(x, f(x))\n", " ax.plot(web[:, 0], web[:, 1], linewidth=0.5)\n", " plt.show()\n", " display(button)\n", " button.on_click(lambda b: fig.savefig(f'logistic_cobweb.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here they are." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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p00i3THyHhoTIeweWlkJ4eMjhlbEG7OWIy+xDswWjEd/t+U5uiIkRokYNeWMg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\ndfj9d642+YSDoacYUGUAFtr7vw4h5M2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EhcGQISZnNJnWmv9ZfwSAkT1a8m58FB7u8iMn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\nxY1gySIvlDK+mbVJSbmFlIW5fH20gP83IpLkx0LNjiSEy5g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HJeBjgc/+Yv9dMw49oKqU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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 100)\n", "web1 = cobweb(lambda x: 3.069946 * x * (1 - x), n=1000, start=100)\n", "web2 = cobweb(lambda x: 3.449945 * x * (1 - x), n=1000, start=500)\n", "web3 = cobweb(lambda x: 3.549946 * x * (1 - x), n=1000, start=500)\n", "\n", "plt.figure(figsize=(6, 6))\n", "plt.plot(x, x)\n", "plt.plot(x, 3.069946 * x * (1 - x), 'b-')\n", "plt.plot(x, 3.449945 * x * (1 - x), 'g-')\n", "plt.plot(x, 3.549946 * x * (1 - x), 'r-')\n", "plt.plot(web1[:, 0], web1[:, 1], 'b-', linewidth=0.5, label=r'$\\mu_1$')\n", "plt.plot(web2[:, 0], web2[:, 1], 'g-', linewidth=0.5, label=r'$\\mu_2$')\n", "plt.plot(web3[:, 0], web3[:, 1], 'r-', linewidth=0.5, label=r'$\\mu_3$')\n", "plt.legend(loc=0)\n", "plt.savefig('logistic_orbits.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bifurcation Diagrams\n", "\n", "We've already noted that the accuracy of finding these bifurcation points was low, let's instead examine a bifurcation diagram. A bifurcation diagram is essentially a probabilistic view of our map for different values of $\\mu$. For the following plots, the $x$-axis is differing values of $\\mu$, and the $y$-axis is a large number of plotted values after the transient." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " Cython: _cython_magic_6398a5bdb96021c52aeef5865e2d7f0b.pyx\n", " \n", " \n", "\n", "\n", "

Generated by Cython 0.27.2

\n", "

\n", " Yellow lines hint at Python interaction.
\n", " Click on a line that starts with a \"+\" to see the C code that Cython generated for it.\n", "

\n", "
 01: 
\n", "
+02: import numpy as np
\n", "
  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numpy, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)\n",
       "  __Pyx_GOTREF(__pyx_t_1);\n",
       "  if (PyDict_SetItem(__pyx_d, __pyx_n_s_np, __pyx_t_1) < 0) __PYX_ERR(0, 2, __pyx_L1_error)\n",
       "  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;\n",
       "/* … */\n",
       "  __pyx_t_1 = __Pyx_PyDict_NewPresized(0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)\n",
       "  __Pyx_GOTREF(__pyx_t_1);\n",
       "  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_1) < 0) __PYX_ERR(0, 2, __pyx_L1_error)\n",
       "  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;\n",
       "
 03: cimport numpy as np
\n", "
 04: cimport cython
\n", "
 05: 
\n", "
 06: @cython.boundscheck(False) # turn off bounds-checking
\n", "
 07: @cython.wraparound(False)  # turn off negative index wrapping
\n", "
+08: def bifurcation(np.int64_t precision=1000,
\n", "
/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_6398a5bdb96021c52aeef5865e2d7f0b_1bifurcation(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static char __pyx_doc_46_cython_magic_6398a5bdb96021c52aeef5865e2d7f0b_bifurcation[] = \" Acquire bifurcation points for varying mu for logistic map \";\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_6398a5bdb96021c52aeef5865e2d7f0b_1bifurcation = {\"bifurcation\", (PyCFunction)__pyx_pw_46_cython_magic_6398a5bdb96021c52aeef5865e2d7f0b_1bifurcation, METH_VARARGS|METH_KEYWORDS, __pyx_doc_46_cython_magic_6398a5bdb96021c52aeef5865e2d7f0b_bifurcation};\n",
       "static PyObject *__pyx_pw_46_cython_magic_6398a5bdb96021c52aeef5865e2d7f0b_1bifurcation(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  __pyx_t_5numpy_int64_t __pyx_v_precision;\n",
       "  __pyx_t_5numpy_int64_t __pyx_v_keep;\n",
       "  __pyx_t_5numpy_int64_t __pyx_v_num_compute;\n",
       "  __pyx_t_5numpy_float64_t __pyx_v_xmin;\n",
       "  __pyx_t_5numpy_float64_t __pyx_v_xmax;\n",
       "  CYTHON_UNUSED __pyx_t_5numpy_float64_t __pyx_v_ymin;\n",
       "  CYTHON_UNUSED __pyx_t_5numpy_float64_t __pyx_v_ymax;\n",
       "  PyObject *__pyx_r = 0;\n",
       "  __Pyx_RefNannyDeclarations\n",
       "  __Pyx_RefNannySetupContext(\"bifurcation (wrapper)\", 0);\n",
       "  {\n",
       "    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_precision,&__pyx_n_s_keep,&__pyx_n_s_num_compute,&__pyx_n_s_xmin,&__pyx_n_s_xmax,&__pyx_n_s_ymin,&__pyx_n_s_ymax,0};\n",
       "    PyObject* values[7] = {0,0,0,0,0,0,0};\n",
       "    if (unlikely(__pyx_kwds)) {\n",
       "      Py_ssize_t kw_args;\n",
       "      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);\n",
       "      switch (pos_args) {\n",
       "        case  7: values[6] = PyTuple_GET_ITEM(__pyx_args, 6);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  6: values[5] = PyTuple_GET_ITEM(__pyx_args, 5);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  0: break;\n",
       "        default: goto __pyx_L5_argtuple_error;\n",
       "      }\n",
       "      kw_args = PyDict_Size(__pyx_kwds);\n",
       "      switch (pos_args) {\n",
       "        case  0:\n",
       "        if (kw_args > 0) {\n",
       "          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_precision);\n",
       "          if (value) { values[0] = value; kw_args--; }\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1:\n",
       "        if (kw_args > 0) {\n",
       "          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_keep);\n",
       "          if (value) { values[1] = value; kw_args--; }\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  2:\n",
       "        if (kw_args > 0) {\n",
       "          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_num_compute);\n",
       "          if (value) { values[2] = value; kw_args--; }\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  3:\n",
       "        if (kw_args > 0) {\n",
       "          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_xmin);\n",
       "          if (value) { values[3] = value; kw_args--; }\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  4:\n",
       "        if (kw_args > 0) {\n",
       "          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_xmax);\n",
       "          if (value) { values[4] = value; kw_args--; }\n",
       "        }\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  5:\n",
       "        if (kw_args > 0) {\n",
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" ], "text/plain": [ "" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%cython -a -c=-O3\n", "\n", "import numpy as np\n", "cimport numpy as np\n", "cimport cython\n", "\n", "@cython.boundscheck(False) # turn off bounds-checking\n", "@cython.wraparound(False) # turn off negative index wrapping\n", "def bifurcation(np.int64_t precision=1000,\n", " np.int64_t keep=500,\n", " np.int64_t num_compute=10000,\n", " np.float64_t xmin=0,\n", " np.float64_t xmax=4,\n", " np.float64_t ymin=0,\n", " np.float64_t ymax=1):\n", " \"\"\" Acquire bifurcation points for varying mu for logistic map \"\"\"\n", " cdef np.ndarray[np.float64_t, ndim=1] mu = np.linspace(xmin, xmax,\n", " precision, dtype=np.float64)\n", " cdef np.float64_t x = 0.5 # unimportant initial x val\n", " cdef np.int64_t i, j, k\n", " cdef np.ndarray[np.float64_t, ndim=2] points = np.zeros((len(mu) * keep, 2),\n", " dtype=np.float64)\n", " k = 0\n", " for i in np.arange(len(mu), dtype=np.int64):\n", " for j in range(num_compute):\n", " x = mu[i] * x * (1 - x)\n", " if j > (num_compute - keep): # we throw away the transient\n", " points[k, 0] = mu[i]\n", " points[k, 1] = x\n", " k += 1\n", " return points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The full bifurcation diagram for the logistic map follows." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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wY3nw1gQ/cY/4+LTlchnFI+0bjH7jsShCOS0vyzJUVYW6rns91B4K+WN+V5um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\nsfcQAxtNwhQNHmPInwzEhroocpfLZVw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VL5jZ77z0YsQu2/9aKgB8LnlKn79HwJ73D9Dn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\nDxLKQgghhBBC9CChLIQQQgghRA//Pw4BWhw05bwFAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "points = bifurcation(xmin=1, xmax=4)\n", "plt.figure(figsize=(12, 4))\n", "plt.plot(points[:, 0], points[:, 1], ',', color='k', alpha=0.8)\n", "plt.xlim(1, 4)\n", "plt.savefig('logistic_bifurcation.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we can plot the bifurcation diagram, let's examine the first several bifurcations." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "mu_vals = np.array([3,\n", " 3.45,\n", " 3.544,\n", " 3.5645,\n", " 3.56875,\n", " 3.5697,\n", " 3.5698925,\n", " 3.569934,\n", " 3.56994316,\n", " 3.5699452,\n", " 3.569945646])" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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8wAfayV8Uta991Ee173/4hwO/+Zu9h7STr20w2sWo2Gw2kxPiOXGbv5PnxrZ76CqcA4oC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\nrVYLnU4HnU6n8LhoW+jFArJnjn1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gk8FX3Vdgeq5Dva+6TwhhSv7qJNMadtjtTqb0Ybgg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ZFjTVLbtqGeDOYaMXBMRIVwPLZphxkHm3hwxBC1XJwqCTh6hX2LoghiCT/jHpGWKHIUOpbF\nPbZH42h8XnmeT1wgWWjhPiD++GdcD6JbfF0QYUi1hJMjPmvHcd55NpGFxanPoGvA4HJ4z26HMTwC\n5jgvil5pF5lOsF4BWIlfGsVybsPc/8eP8rx7eVVVUlVVsFav6zoIOwgt/HHPsiw0bWbL9FhaLjc/\nFnl/lhCFwsQAYi9JkiDwiqIIIiZN0xBpqqoqRK+GYZCyLE+s7jnVEUIJ6YpoHg3rfdRj4bgMRCMW\nYhC105EuNu2AUEO6MjdvhvMh6tpwzu12G/4h1ZJ7+hz+Lz0F0XlZvjrCFUtB/ihLa66QzvxZWHxx\nlsOjiS8Rj4A5zssRa6j6TO5CS+FGuM7jMo5jcEEEm//zf2S32wXxxH/8MRmAEIOToYiECA4bZLRt\nO+nFxWkw4XyHeiaIGNST7XY7GcdRsiwL54Nw6rouRMV44QM9vpAqyaKPUwFxPq5L4ygb7gmfAfcQ\n0y6IuAcINe6RhvOywMK5SqrPw+eHBR3+nHBsjgDq+z7woSp6x3lEvjvKBUfUa7H0WJcKpFhEi8et\na9/Ld+MCzHFeBG2BzalA2npa5NRtyHEeCev3F88AuxU2TROiRyygRI4pdGgiLCITC3g+B9dXQegg\nTRApeF3XhaibdlJkAxCIGI5UsaBj8w2k7vH1YeKi94fw0c88zontYUvP14qIna5TY/HGn19d1yHN\nEM6NGlyP+gwfd0blOGdApP7fb3T+czWs98ISwcZN4B8RF2CO8wLoWhE9gXzF6Jfzeli/4/gDzhEy\n/qMOgYAJAYQOHwvbQBhBhIlIMOPgmjId9YHYQg0Zoly4JhyDF1D4nFwH0TRNiLRBtOHcc+nFEFbs\neohz4b2u6yaiCmhhBuGG62RDDm66zK9hTKrr2k04nKdBC4Q/Rrb7Lh49amTVr36Ee6gZcwHmOE8M\nJjXjOIYUIJHjyjkmTjyZdFHmvBK6pi/LsklRN1IVEcESsVdnu64LUTTUbgFE2ZDOx6mDHG1iB0Od\nSojrYOC2yDWcODb3HsM94dwxG318HnBk5M+EzTlEjkJKbytyrAuBWAPaGRHjixJwjTjOg2JFZCZj\nzNvbonrVrwIGP48Kj12fiX7dWnyJuAmH4zwlm80m1GnsdruQQoRCekx49MSJ9yfcht55Gfq+l3Ec\nw1eIprZtQ1PnNE0nKYRN04Q/6FhdhjiB0QREFW/TdZ0kSRIaReMfTw5g3z6O4yS9D4KMt8XqcN/3\nQYyhno1t6dFEGfBiS5Zlk9os1IKx8OIoFgsxtpZHJA/HxzjE58RXbM+Oj47zSFj9CrVpE/oa3pJr\nRZA+wgebJE/AGPPIqYfABZjjPBmcegSRpeu+ILw4Ksb7q8jXy9nQOw7o+z449MFFEQ0/Ud/F6Yk8\nyWiaJtRCQXzBUAP9yNI0DdG19Xo9WeHVaX44Jo4D50Y849g3y7IQCUPT5zzPQw2arl/j4+O8iJz1\nfT9psIxt8TOPF/w918QBNGPGezgOzm2ZmzjOPTLXk2uuR+StsaLfjwT3OoxxbafHr8JTEB3nCdB1\nGZjIcK0XJlPa/Sy2Ek489ojtOFdCPxvWRIBdFyGuUCzOdVFN00jXdZNnlUUOBFRRFOF1He0qiiLY\nzEOMccofUhNRv8UiTD/raMLMVvd5nstqtZo0ZucaNaQ24mtVVZPoOqJnPM6wAyNH1bIsgxCzff4d\n50acTSsUObqw/vgxf7Az2321ULtllPmS2rNYjdaSY9xDeuESHkMmOo4TBSLLWj1GfddmszkRX9jX\nWr1W23kEzHEMdKoRR8JQm4UoVJqmwYEQLokixx5eHMHiHmD7/V66rgsTD0Th1ut1MOAQkSDGhmEw\nx4KyLGW9Xkue5zKO40ndJzs36oi5NX5gwWccRynLctKsGYYflsU+xhw9FtE1P26BivMULOkL+VV8\n9TkeRZzMXeez9OL0CJjjPChI28GKMk9o2GZarzbz+7wabU2KXqkps+N8Fu6FxcXuWM3ltLzdbhci\nS0hbRNQMNWWoncIxEE1CNBtRKUTScF5E29BLzOoXpp91XJO2x0dkTGTabDqWLoi6M4Dj4bOAQENf\nMYw72O9eUrWc12FRhOub8edgnnEcP/UZVVV1czMSj4A5zoORZZlkWTbp4yVymh6l67tYZOlePryN\nkYZ426phx3kwEHlG3RiiXYhkbbfbYMBRlqV0XRfqx2D0IXIULRxZg6hCamDf90GsYRukAqIOFGmJ\n3PdMjxf4GZE4ncrI4wkaNYuc1n3x2MLpitxMGp8Pp0I/em2K8zjoCJeObrn4ul+uVd91a/El4hEw\nx3kYMNFBrQU3VtXCCTbzWBnXzZVjkS3doPXQSNatyRzng+iUX5HjBCtN08lEgHt6IaWwbdtgby9y\nFHFcb8XRLkS8RCRY2/MxrYi5yNSNEBEuyzJeZBoBYxHFrS0AUhtxTWzewcem2hRXYs5V0YLm1gJr\nDhdf85RXcpG8hz5gHgFznDsHrj9wU8MKEKyhLUMNTKa0fTS+8uozE7Oldxzn8yDtFxNATCbSNA3P\nNU8KiqIIIq3rulB3VRTFJGoEswtmvV5LmqaTCBwMO5qmiUbARCQ0XMY40XXdRDAhjVDkKKR0WrPI\nu9jitEeAfeGIiHqxw35ec+p8inM1XPfIPTkl3jOfMRHh6BkcaG+JR8Ac547RAzIK8ZHqw5Mgq47L\nSkucm3jp1WvHcb4GngjCxZDBz5gk5HkeaqRQM8Z9v7jZMtL92IEQ9WXslqpB9Avv41ww5+DFnCRJ\nwnVvNpvwlWvAWIzhfZHTdhg49wGPgDkX80hRLs13Ca+vPM93RZQ+06qCr+8SR8avwiNgjnOHZFkm\nm83GzE0fxzFMXFDILiLBeUynGepUH10bxt+7+HKc74ejYhqeNLDphsjUpRCRMTRc3u12IWq+2+0m\nkXPdiBnHaJomHLOu68lYw4s8IhLew3VXVWXWctV1HerhcK9n+Hy3VufpOVfH9ShoUcS1kl95nmvz\nXel8bBL0mf/nr/qcL8EjYI5zR2CSA0ezmCuhrrvgSQ0c0nQ0TE+ggJWKiO25L5HjOF8H3BCxMsvf\nc3oi7O2Z3W4XbOkhhJCuDLEG4cV284AjX4iUjeMYRBlvz2OQHlMwOcKYpBeB9HjFvQlxDyLyGD7Z\nzk1gIfFIQksTE0RfYQ7xTKmN1zLruWU/NOACzHHuBExG8P0wDFGxxBMXncbD6UWRvl4nzAm1Zxq8\nHedeQc8wEQkmO2AYhmDQ0fe9JEkS0goxVkA4IeqF/bAPpyjqKBQLKDb80MKKa7usKDqbeMAEiJtP\na/v5siwnYu1w3tvPjJy74llEF/gRSQH+qjS+Sy3befHn0Yl9prc24BBxAeY4N4cbKfPEJAZEFosw\nq88XVoq4NkzktE+PPnbEit5xnC+A67MQ2arrepIiAzE2DEOYSHF0mrfl1+F6CCdE/GzVemIxh3uJ\n4Rh4n2tPeRzR4896vT6JsMG1lccmAAdH7wPmMM8mvJIkkT+KyFvTSGL8jf9KUXCJCLtn8XVpn9J7\nEFoxXIA5zg1B7jqLI7wmcmqKYdV46cmPSLS4PSqq5kw7HMf5GiC+OOok8i56drtdSClkS3i8Hpsk\nWf270HQUwieWxgNxhJ5k2I5dE7ENomBIUYRTIoQW32PTNGFRqeu6sC9SEjnyL27C8fI8o/ACbzdM\nfRvH0TT8+S6uHVn7TImEbvdxC9yEw3G+GRQNbzYbSdN0kt6zXq8ngkyvUlsDDiYyu90uWuPFryMV\nKIZHvxzn60EzZDavgOBp2zbYyHNKISJhVVUFww2kHzZNM2nc3Pd9iEShETJSA/WijV6kwb4AAhAL\nQqjXgs28iIT6MQgt1LBi/6ZpZLVaTVItGTSOFrehd0QezkzDQtvgi7ynH8ZSEC/lIzbq16ih+qh9\n+zWEDs9dPnM89FO9ZbTPI2CO801gJRj1HbrZKSZFOrWQsdKGRMRM68H7S003+H2uA0uSxFekHeeK\nYFKGuizYvaPOK03TEFkSkYmRhohMokyYkOD5hzjC2MC29ThWpOG6VFUVvu52O+m6LkTROOUQ4ks7\nJDJstLHZbEI/MFy7TofCMZ3XBOl5z0AsgjeOo8jb29UEWJ7nFwuIpmlma82W1KHdMq2P5zmX1rYx\nWNw6cJMb8giY43wxmIAgDWe73U5czDDp4NViNEu1sNICrZoLy0HR2td6zSNgjnN9VqtVcDtM01TK\nspRxHKWqKlmv11JVlZRlKXmeB7G1Xq+lLMswHiBCJXK0pReR4HCICRmiYqj70uJGR8CKogjbw45+\nGIaJ6MK2bFdvtbvAWAPhtd1upW3bScSMI/24r2s5nDn3jbaQxyT6rWlumqL3WX6U5YklvsW17tGK\nJIucj1DNCaivFlefbX7M4xjSqz+Cus+b/NK5AHOcLwSGGSy+RN5Xh7lZKfr2oDZiv99HGw5yvZZO\nLdQ29VpcWcJqgdjyZWnH+STsTLjf78O4AEHDCy6IFHEKIY8f/FxzTzCIGy22INQgqlCHBSCQhmEI\nhkDb7VaKojAXg7TTKo9deA3XClHFk1GkM263W9nv92GRCoe/4GN17pyY2LL6WwJENvQ+98yPspS3\nplmcNvmR9EqOZM9xa+OJOZH12WvjRZrtdjtr2z93HeqzvMmY4wLMcb4IXp3mdCFMNPh9kfeBZb/f\nm82SgX6NjydyKqb4Z8usw002HOfr4TTBoigm/f5E3gVN3/dS13UQMyLHZ7brOqnrOtSOikiILpVl\nOanLGsdRuq6TqqqCIOv7Xtq2DZMVpAMCRMBg1oHr5dRHiEVrwYbr13A8EZncC16DuOQ+YXmesyC0\nl/Wdu+cjYiuG3tY69rl/176XuX/fEbm7Rr2S7iH4FdxaAIK567iHaLvXgDnOleDGxUgbAtzrBhMY\nfp/TeSwjDaBf16tBXNth9QCba7qs33czDsf5HJbLoa6bQq1XLJ2GF06QVggBhecfPbdETvsJ5nl+\nUgemU5Zxjt1uF5o383HYqRDijAUUuxxmWRa+h2U9xiU2AME16/ceIdrhxPtDfoVxxkeOeQ0RtvS8\nSZKEuq63Bfv8KEv5909d2TsfETqxtMVH4dp1oofa25sEozwC5jifJMsySZIkrEBjtVqnCIpIWEUW\neZ/0ZFkWJh5s8xxzKtR1FlpY6VXocxGuOWHm4stxPkdd1zKOYxgbRI7P5W63m4gV63njVD2RY78v\n7vEnIiGlUWTqWFiWZYiKYR+kH/L4oieqcFEUeR/f2LADwo/HFqRHor61ruvJ+MO9x3A/WKTCsdbr\nNa7JU57vkGtFtr4L69ou/XfJuRABOxcpu5YBx0f5jgjYV8Jj0Zyb8xxswHFLF0QXYI7zCeBihp45\nmICgwFyvFqO2AiB9iEEaohUij0W12HTDqsMA2M4auFxwOc51QNQH6YZIuxM5puVxlFxHsnmVF6IF\nYALFzzo/82iSzCINdWYix3RETDy4sTNqT6uqCuMETIGw0GSlOXOa4X6/l3Ecw/kgsLjmFXVlkQUk\nrwG7MZZwuGexdS+gBuyzgs6JYy0qX2rsMQxDcJvFS5+/sstxAeY4H2Cz2UiSJJLnuVRVFSYXnGrI\nkyBexWYBpOu9dGG8dV7ej7eNRbO0aEPhO+/Pvcgcx/k4WZZNGh6j5QTcANmAR+T47Op+gHhuEYFi\nkYKeWljF5Weea0n5HNzbC+mIHPnqum4ixtjpEGJxHEfJsiyISL4mjHkQawDb8eIPjmf1JBOfl3wr\nS+u2nM+DSJkWat/JPdQ+fQY91ol8LKo3DENYPJcbjTk+0DnOBUB4wa6ZJ0rcfwcTLaDrPrSFcyyF\nUKMnVbwt/7P2t4QZF8Zbx3QcZzk6miRiR7lRG1bXdUhDxlgCZy+MFWVZBuGCqNIwDNK2bTDN4H6A\nGuzLYgdRKp78YVUYph9sjIFxAfe33+8nYxhH9XDPSEtkcSbyLvQgStu2DenbdJ64rZnzKa5pkuFc\nj++MmM25Bj4ClunYZ9IID/t6BMxx7pV/+tOf5EdZhpoO1EdgxZdTbESODoexXl46VZCxenhprFqw\nj4gnncZovec4zjyr1SoYXcBmnoUFjw/8bGMs2e/3oT4UjoTYls07uIcWwPc64s5R97lVb57sDcMQ\nJmhd102OJ/IeOYMg5LGDxz49GdJjE8TZfr+XqqpCfRpFAT/W2Mc5wcXWY+P/V/PwglMsDXFheqJH\nwBzn3vjll1/kR1nKv/35z/KHg4U0rKBhuIHJA+ossGotcnQpssRWTDRxbcQ5tFA753bI57HqRwAG\nto8WuTrOq5AkSYhGwWZ+tVpNUpN1nWaSJJKmaVi8YTMOjgYhSoT9eaxhy3hE3LAP0hD52YaY4n5d\nDMRQmqYhPQcLSLgGXQCPfxCYu91uUv8lcozAWc3iAcTno6dH3RKv23oN9P/n0t5gz07MERKv3+Pn\n5Db0jmOQJIn8kX7+pz/9Sf4qIl2aSlEUYZKjrZk5F5lXsnX3duw/Fwn7CCyq5mrIGGtShMkbVvId\nx5minwvYw4scnx+u68KznmWZFEUxqRVl8DoLLggYPpaIhNe1qyHXlOnzaFMPBkZBq9VK2raVPM+D\nmQifq23bMLbxvWp3xCRJghDl9Gi+p9VqpfuA3c6W7EH4Tgt4577R6c0i9u/HM/4dv2R+co/2+y7A\nHIfgh3nSWPGvfxX5h3+Q1f/+3yIik6amIqd9dbAirQUNol7XSvezzDjObW9hpTF6CqLj2EDAjOM4\nGTNgkMGCi8USxA/6X4G+70PaMgsnRJdwXNRViRzTGtGvi6NM3A9Qu6PG4CgdjoN7S9NUyrIMIgl2\n+NxWgykP6drof4ZoDN8fJkQ8dqI2zpliTTJdbDkx+HfjGv3Q7pVL7utemkMznoLoOCJmyoYFHMzS\nNJWqqk6K27Msm7ig6XQfSyzx5IgnZXMTpmtEzmLHiF2v4zjvzwRHgJAGhBYTEEksfPg5ats29L9C\nqiAaJpdlGYQJp+TtdruQoqifWTRa5hVePoZ+tlmcabAIAxGHe0M6Ytd1oY8YnBXZDdGqeUWtV5Zl\nQTQi0lbX9aRO7rD//eUKfSPuSuhck2f7veHx7NHvxyNgzkuDP25ICVoC6jWapgkpiHqVmdN9rPct\nwRMr1NfoSJqOqlkTLGsipiNesfM867xu9XwAACAASURBVOqZ41wCR2fSND15xpBup+sw2Rwjy7IQ\nPWLyPD85Hi/GzDUf5bopLPhgXNLRNxZ11jjBUTp+D/VmIsdaCq5b0/VbzcFmGwtUuEdsi5TJNE1D\nGiLOlyTJS4XAPLrlfCc6OvZo6Oi+BepY51iyzVfjETDnZeGVxaXiC41JsfrLgopFji4m50lZkiRh\nUpJlmemCOAen61iiLnYvS1MVPfXQcabgWSuKIkS7+Hna7/dSFIX57GAs2O/3QbDoY3O6MtdTYT8R\nmaQjxiZOqNHixRikPOp6Mx4nOPWQ3+OxZRxHqaoqRNeGYZDdbhciYugdJiKT+4RlPa4N18mujogC\nHnjqRswe3XLuhUf8ndM9FC0sYaUXvm4tvkRcgDkvCiyjLx14tC0z10DoiBQ7CXIaEmyXRY6rwpY7\n4lIhtiR9kKNd+rh6n2uagjjOo4NJMqf5WQsniOTgedemGIBdTrlJscjUBIe/cl0WhCBexzF4AYYj\n8F3XBUEEp0SrBvXcQhDGtr7vpes6qapK2rYN0TYIqu12e+KCyO6MiKRhJRtOjiTa7q9a/kqgjYkL\nLufeePbfx3usLXUB5rwsS6Ne4JdffhGRaQhcr2jz5AbbYOKElWnuz7NkNWcpHIGLFd7H6lL4Glx4\nOY5MHAthr973vazX64nbKdN13Yl44l6BDKcmAn7+OH2Qr0lkGmFH9ChJkvBss9MhVnrPPdc6TZnH\nKHZzFJEgukTexSibiiAFMkmSE1OQpmkmK9GbzSYsSFHkzv5wnwAr/dRx7o1HEWNZli3t83UOb8Ts\nOF9JkiTyoyzlh5EGdI5/+Zd/Cd9jpRsTlqZpJhOs2ESHBZmImCIIr83VgGmsqFcsKmalLF6aAuk4\nzwzEjMi7eEGvPwgy7qkF9DPIz1TbtpPtORpV13WIYkGA4FhsWiFyFGe8gIPzlWUp4ziGY202mxCt\n47o03aCZwbVY4xIiZ/p+ISiGYQj3iOjXOI6y3W6DKREfU7flwGd62PdpI2CO82jcmxjjcSTP88Wp\nhLoP2D0shrgAc54anWv/1jTBXn5pk+FffvlF/t//+3/lL3/5i2muwc5ljBY62viCUw1523Ppgjpd\nyToeiJ1D9x5ijMmZd0d1XgKkwqVpGlJWEO3Z7XahL5YGzwybUrBVPTsF8jOKSQ1qpPhYHGXCtWiz\nC8vwg6+V6qpE5Ojiai2y4Fp4bNDjhB5rcM+YzHC6o8jUsAj3BLHFjaPRTDoWWXQc5/bcgxDjMemS\nxu1tO20vqBxbb7Lo4wLMeUpiBc5gHEdp2/Zsj4yfP3/KMI7yb3/+s/z6668naYuYiKD2gdEW9Foc\nWQLN+qo5Fxmbq/HQ6ZELo11xteY4T0KSJNK2bbB8h+EG0H2rrJRCbcfOz5tuyqz302nKvB2iW7q+\nVBtrsLU97O55fNHHZbj/GKcN6v5kDDIAcO2wll+tVpIkSRgXIbysVEyeRF0yoXIc5zbcUojxHGxu\nIfkcKnJ2k9YXLsCcp4GjXUvC5vy+1XvlR1nKf3VdiJj99ttvUSdB7VTGqUO8Gm70vDk5Viw1MPYa\njsdfeYIYMwPQEzFPPXReEYiFqqqkKIqTpuoiEsSFiJhpgCLHZuvYVgs1mGMgLU/k6ICIZxT7oF6K\nTT1wrTy2NE1zIlqwH6JSPCZw+jOjxyv8zNfJaYQs5jilcrPZBHMOkXfRmmXZ5P7weWJ/1MJRFsFL\n9wFznEfgVhb215qnqNqxNrbdV+J9wJyHRg8CH1mVie7z9japF/v111+l+etfw0QMVtGYiGVZNkkb\nEpkW0qMug40wuD8PYGFk1WfpVCad1qhf08ePiTidKuk4z06SJJKmaYh0sVU6Pzeo+9Q9qyy0vftu\ntwupeBAg2ryHBZU2usDPu91O2radPJu66TM3bIawscYnCDuuL9MmPiyu9PvW9oCvDxb43FuM+4fp\nbbfb7cv1AXOcR+OW/cN0K41z11IURVgQ4t5f9xABcwHmPCT80H1lKPytaeRHWco/iMj/l+fS932Y\nQGhhU5ZlNK0QEy/duFlkmvpzTvwsiWBx+pDej1ewrfN4FMx5BbIsk2EYQsQL6PQ+CA3Yh+P1GNrk\nhhdYmqYJYwQLGH4WdQ0Ub6Mjc9bzb/XvEjn2L8R1WI2fsR8L0JjYZDFnpVnz4g/GaohXkekkSgtD\n8ZpTx7lbbt28mcfrJfMVrv1i0eWNmB3nAmLNK7+at6aRf/vzn+W///u/w6owJhBW6iATM8jQ6Yva\nslpkfnDhFCht4METsbnrsdzOOHLmOM8GHA7xh5d7a7HQYXa7nVRVtdi0h8Eff05hRJSL68U47c96\nBllIcR0XxkK9D6c6c/og6lX1+MDXgxoyfI/PTUfeYlEvXR83jqOsVquQcs2OiSISFrXYiMRxHMeC\nF2/menshxVC7HwKYLR1wG3rHsThnqPFd/OUvfzlJ64uJGK7ZsIQX11DwMXjyMyeEOPo2tyquidWD\nOc6zA+EFcw3099K1kngueDEE6Xz6ebZgMVRVVRBA2BcLODi2bsbOUWrdQwyW+ADmHHz9ItNFHTbJ\nABByfM2o97IWlTi1ei7tmd/nc+33exmGQdq2laIoZLvdTpxj+77n63MrRMe5Q24d/dLExJXIMdrF\nETCu+2qahiNgN9FCnoLo3C3flWZ4KZhwcI0FJkFN04QURWs1HZORWPqfntwtFUk8KcK1sTGIbg4L\ntIuQ1385zwYv3qAmKc/zie27VYOJejB85bpNK1KjUwqzLAviip9FRHogrnTNGF8PbN3xPHMKIQMx\nxcfDuSCeOAXQMhrRdWmxhSUrxRnjiK6DZZHHYhG1d6vVKkyQ2BDJcZz74l6eSx531uv1bBRMY6Uc\n3jIV0SNgzt1xizTDS4FTmV797fs+rOZCECF951zxPh+bvzKWOONJm645EzkVXYyn/DjPCo8jaZqG\nBRE4FIochQP+iOt+XWgOvF6vw3PcdV003RjPH6JJHNHG+bnGipu662Ntt0f7du2wiJ+5fhRftVMi\nLw6hKbRukYFzwkGRrwFNovEazsP74z5QZ8ZClQUh4P5n4ziGSOHhmJMGPY7j3JZ7EV+azywWKzMO\nT0F0XptHEF4WPGkRORbDY4KC1epLxE5sYLFcx6x9Yv0xrElX7Gc35HAekR9lOXEvRZqKVYcJV75x\nHKXrupNmnSJHp0GIC13/BHRqno5SIRUQdvQix9RG3p+PzeLMqvnkCDzbxOvzQhBWVRWiafpZ32w2\nE3GH83M6I59fn0NfGy9QiZxG3dCgmcfOz/T1cRzn+tyb+LqkFldZzQeKotDv3UQLuQBzbs4lvbvu\nkbIsJ/bQnAYoIpP6D5HTnl26OeoS4TMntjD50cQmjfpnF17OI/Lz50/5UZbyd3kufziIGu5JJfL+\nrO12O6nrOvyeI/Wu7/uQpihy6irKzBnuQMhot66+7yfRKZ2irOvROGKGiJLVCF7kKO5Y+OD1vu8l\nz/NJiuHcQoy+Vz1e8XXqz5BFLv6xCONxDvVwqAUjMephece5Az4qvmLCh9/jbea2n+Pc9cVSC9u2\nvbkDoojXgDk3hKNdjww7lLGrmk7D0XVa2rFwrpB9Dl2LoVfMdd2ZVb+mxSPv7zj3DMaRPx5+/q+u\nk//Y7SRNU2maRoqiCP33RN7/+GLM4d5eEEPaBAd1YyLzERo8V2g+PAyDjONo1oIxHMGaM7LQgo7r\nPBGd4+NB4OgxJpaSzKmR1r2xSyJ/Pjye8D1Zfca47o3ryVRBvOM4N4bFDffSWsLcs2z14eLvLz3X\nOXC8qqpCqnmaplKW5UX1Y1+BCzDn27lXc43PolN3dP0HT94s58LY++fQYk6vYMdWzed+VhNAX5F2\n7o6TceTtTUTeI2H/1XXB8ZCd93jSj+cT0XdgLX6wqY7xfIjIUXRoMwvYvvMYwAsisdpQnc6H11h4\n6fPra8G5LJMRDerc2KaehZJeqGGs69F9DWN1sFwj5imIjnN7dGTpmoIoxpyjIXNp3TquncXWMAw3\nF18inoLofCOPWuN1CbyarbEmKVz0f8nAwqmCenLENRs6VWjJcXFMvszFF+Y4X8y5ceT333+Xt0Pk\nC+ILsAjA73hVVeF97ncFq3Z2QbTSEZm2bU9EBD/XXO+12Wwky7KJQOLnlMcGvMeGHBac+seRd0Zb\n2zNlWYZaMj0W6FRCqzZNp1Dqe7Ki/ficadxyG3rHuREsvqx0wa+ibdvwb45rCScl+L5eYRq4AHO+\nhWcXXgy7h/FrFrHC+dgESR8vli6oexpZWPVfnnbo3DOXjCPcTJh7TiFFENR1HZ4XtlDXxxA5pvBZ\nkZrVaiVVVQVxp5uqQ1Dx/jifTkvmc2us59QSRAzGJF6ksY7J2/A98rH5X+y8LHCta2WMBszugug4\nN0BHvjhdcGmEilki3L6q/msJdE+X39wV8BRE50t5ljqvj6BXcmJpS9b3SyZfsVQka/9zgs16zQWZ\nc0/oVMElpGkqdV0HG/rtdhtED3pQoT8Vng0YVyCd14om62j1ZrMJRjxJkkhVVSFyZj2nVmTKGgt4\nG23uIzLtu7U0pRHfW0Y+eB2fgX4/ti8LOOu8env+bHW9rIiUJwdxHOdL0ZEvXcelGxovqdlcug2E\n0NJUx2s5M9LCnNvQO8/FK4svkWnjUXZBtIilCs5FwWKTrLkUKZ4knRNXLr6cZ4KjS5j8o/8U/66j\nhouFlhYY+tmA2cdqtQrjXV3XJymHOsUQ6ZSIePP14TzcBFrk2OsL16rNe/Q5eV8Wg7GxBnVsc+nL\nuj7N6isWi+zr+jIch0xIupMdHcf5MmKRr1jU6xLDnCURriWph+Ca80m6j5toIY+AOVfn1YUX0HVZ\nemWanc2uJYo+4qK4YHs34XC+He1ueCmbzdH6HX/cLRc+MPe8WM8Vvsd1aoOOmPjB+Xl7fX4WP1qo\niBwXX6zIFJ8PKc5s0mMZeeDzQY2bfl/vh7otvGfdC7bVkcPNZhMibJHP32tOHeeb0OKL3QJjogj1\ntUsiYddwN8V5IOYwt/xMJGy9Xt/ciMMjYM5VcfH1Dq/+8gRNT6wwUYlFui6p4eLXY3UXehV+LiVR\nJKzE+4TI+XIQDdImG29NI2/NZWVBv/76a3iu1ut1iHTpeiOOTCF6zFHk7XYrWZaF1/Az3gNpmk5S\ng/l5Y5MdjlBBPHE9FfbhtD6GI2W4Dm2bD7QFPF8Pi6ssyyYr3RBUgMUkW/VzpI2/8nGsMWq73Z40\nqeZ7cxzne+BaWICU7TkgzM6Jq8+Yd/CYxLVoPEaM4/jhc9xafIl4BMy5Ii6+3tETJ6Qi8kQI8Gq8\ntbo+d/y5VXktrGIr/eeiZLDpdpxrY/1enRs7ltaB/cduJ+uDuyHXTiF6w8eB2OJoNNwQsyyTsixD\nZGiz2UzEAyYweI17ATI6IsZROcDRLC1u9DO9Wq1kGAYzsm7VgumIFvcpG4ZBuq47GRd0/ZmGo3/6\nvPqadNSNF6NwP/jcfLxxnK9n7jn7SNTK6t/1meOgPoujbFVVnYxFwzBMonYfxGvAnMfFxdcUayWd\nHdGwDa9S60nWXFSMj2VNnLRA4/cvwVeknWsRi3DxvzmWpp388ssv8geKMmVZFhokIwIFUw4Ru/0D\nVlo5TQ4Ra4iHJEmCiOm67qRZssixJhPPJIQdR+UApwsCrv9C5EqLG+ynxxfL/h5ot8c8z08iWVx/\nJnKsY+VzIfLH4pGjY3wvOqrGx1Wi1VOeHecLOTeGfsTx8Bq9wtI0nUTXdOphXdfmnIQbLH/01B/d\n8TO4AHM+jYuvI5ik6JVeXe/FEzktkHQ0zIKPFUsBmiuej6HTE92Iw/kMnxFcFizCrEnEj7KUYRzl\nP//zP0XkXQxAbKD55na7nRhtoFZK5P25wnHxu48URP2s4nqSJDlJqcN2MOLAsfq+D+dkAcLnw/cY\nR3T6MKLSaZqGei0eT6wxgV0O9bUXRXFi6APRaDlA8vjGDar5GpumORnXeOGIwedD73nKs+N8EefE\nF4ugS4kJoKWCTkfMOPVw7tjo5XhJxI37P4pHwJxHBBMBF1/vxFZ5sXpuTbJ0pEpvtxSdbmjVgVlR\nMZHpJPBcXZjjxNBRrs8KLgs+liXE3ppG/vZv/zb8zBEjtqMHemEEx4cIQQoib8P7Y3IB23mw2WzC\nH3mu3eJIFvZD2h5MQliosFjD8XH/3GyZo+ja0EObjuAZT9NU9vt9SKVEhM5ySrTcDvXnwUKTt+Fj\nWJE2FnGO43wNc+ILAuejPb+wrz6eyDE6FjsuXi+KIiq0cGw9L+m6bpJ+WBTFor81KmXRI2DOY4GH\nWaezvCrWxEfktKfPXGqhtco+t63+nvfVK+tzgsqqISF8ZuREmYtyfSVaiP0oy2DW8fvvv0/SVTab\njYzjKHmeT0SSjkTx9jrKzFEariHDdk3TnESSuPkyjrVarSTLsokJD8xBOBIHkDrJUS6R97RBS3Dp\nscFaiAF930uSJCEiyJE8S/jhmADCTYsyiEkez/S4Zi1GOY7zNZyLfLF4atv2042XtRgriiK6yNK2\nrVRVJW3bhv1iQkyPI2VZTrblLIaPCsnvwgWY8yF+HP5ge+TriF79tr4HVj0YiEWpmNhkhvdd0sw5\ndl2OM8etRJcFzvuH9TqMS7/++qukaRrEjY7CaKv1pmnC5ABRIDRRBjpKwyJnvV6H9MLmIAL1Ygyi\nWyLHVETLtEM3J+Y6NBYq6/V64mLGAlLXZfEzb4mduq7DdWN7q84Mnx2ElV58w/n3+/0k6s99ELXw\n0vWy4gs+jnNVvsvYJpYCmOe5dF03GZNEpmmA2kTDiqax26zIcVxjkw52cey6TqcanhwTp5u/s6/B\nBZjzYVx8TdFRpFjkqa7rE+toyzJ6bkWY040ssTe36m29x4X7xvG8JsO5K9Fl8dtvv4nI++LQfxz+\n0MPdTzsd6sUJTjPkJsSIPom8PzdN00iWZeYfdS1yWMTwc861WhApEChWrRZ+tp7zvu/DPpw2yGmH\nOnqn7d75/88SmPo6IBhjUTfAQs2ypNc2+rSNjzeOcyXmxNclEaI0TWfrsPDPApEtXVt2iXNhURQy\nDMPJYjV+LopCmqaZXIPOeGCUWPQUROcxwCqzc8SKHGHCwX2DkArF28cK/JeYaLAQw8/n0OeyJlPW\n985rcs+iS8P9woZhODGJwO9zlmWh9opf11+R5ify/tzkeS5lWQYzD8DPIaJbOjUYtsossjgKJnLa\n00v/rCcfOO6S1GWrtxeoqspMJbfGG65T4xRE/pzwmXMaI0e7OHo2F5F3HOfzxMZsFkQsrtI0DeMV\nwHhqgW2XmHdooWaJOqQs8rnR+FkvnnHaNos86x5i0bBb4QLMuZiPNEZ9ZngShJ9FjpMma9DSk79z\nqTqx81pfLXhypAVXLDpGr3tK0AtiCa9H4K1pJD1cNzc7FpEgGhDx4j/mEBUsfvj9uq5DGo3+Q66j\nSrpOarvdBsGBCBJSHDnlEFgCDterz4PjWpFtLYBwX3p7PhcvGOlm0RCuiOTh3NgO52uaZuIuyamJ\nsbHHugfHcT6GZVDEY7gWPhwRGobBTCe0mjRzny4Nxkl8xb4s1Kx9rWgZXtdjBsaepmkkTVOpqip6\n/bFo2K1wAeZcjEfApux2uxOntHPRK9SNaM6lAFnRrjlBFZvgxFbMrVo0eeKUoLquT5z7rH5Vr8Sj\nCi/mL3/5ixRFIV3XTSzR8XzpVL/VaiVd15nP32azkbqupaoqyfM8CCh+fvb7/UkNFUQTonD8Gq4F\nYgjCj4Vc5FkUEQnn4ucYdW3YngVbLMrOIB0IaTu63xiEmTWJwXZYceZFJ50dAGHIQk/hCz6O8wmW\n/N2CQEGkaS7FELDYYtdEkfdnX+8PwYbxk4XVufRHvh5e8OLxIkmSSd8wtBrRDow4F4u6ezDocAHm\nXEz6gpPSOXQRvchpxAmvWavOevVc76fhY+vX9X4xMRhLM4wZdzwrVVWdWKXrNLtzAu1ZRNozCC9m\nv99LWZZSluVENJRlGeqwIGTwe6/d/vDsFEURolUxkw3eh99DpAtpi0mSmIJLZCoQ9QINR8yR5oif\ncW3r9ToITi3gYnWjoKqqk4bKfIyyLKXve9NKHt+XZTkxOLGichCG+v+FjjdtquY4zmIu/Xt0LhoF\nIKBi28aiTnitaZrJ35RzTot8PK4V4zEJx9NpjcMwhAWzoiiCyyL4RMPmq3IfV+E8FMODT8yuiVX7\nwBOcmFji9zlNh4tKz61YWwINaUJz22FyFhNn+hpfmTlxdqlIu2eh9kzCi9lutyF1kJ9VTPxhww7x\nwCY0+Io//jhGnufm4geiPizCNpuNtG0rXdeF2k+eCLBI4QgTpwlmWTapE+NzYrzgPl+4Dl33xvcU\nGzuQdonjsbGHtcjEi0j4mSN7fB1adMZSKkXE89sd5wMs+Ruja730e7r+Ct/HDDNiNVwaLM58FmuR\nuG3bUCMmclxMats2jD8cGRuGQdbrtVRVdVMx5gLMWcQjTCJvgRXpsuzotRCzCvi5RiNWB6bNOxhd\n3M6v6Wu2XBdj1+zMs0SkXSrUvvM5Y/H1jOC+drtduFcYRGRZFt7nmifAP8NxMNbLJhb1rqpqIoog\nUvjZRD0Vv8c1pNgvy7KT53UubdlazDmXIo06ObbNx+egF3dwPNS0WunPOh0SzpS8v1q48hx3x7mQ\nj/zN4L5/wzBInufS9/0kKnbOWCPWfJmt44uikLquzx7rUjG0Wq3CPuM4TiJmONd2u52ISmyPzITD\nfMlt6J37wJoM3rv72a3hSc1cobkVEdMiaS7ypFd/ONXISjHiIvy5a3e+nqVC7RZRtWd/rjGpQB8Z\nCApelUWUiQ0lRCTUkm02m8n7GggQy0oeTYkZXIf1upWeiMUV/bzqtEkWf7EG67HzAtS6QTRB5PV9\nH8SZFnXc90tnBrDBCRaI8Jr+PBzHuYxL/g5wfaYWRG3bmosscxRFEaL6EHR5ngcxlOf5xJmQRZbl\ntKhhIaeB86HI+2cAEw6RY93YarUKfchwXXBTpIyHm2ihv7nFSZ37wnp45yZk7oD4jmWGoTlXx8WF\n7pi0sJjTqT96VVlfD7/OKUSX4ILs9iwVRJeKsGcXWnOgFgDPHPcGQ5E4BECSJEF4YcKC1EAWWQyO\nqbfh54nT77APk2XZiVuiNQbwz+yoajV25jEGr1t1q7yAhPo4K/WRDYfmImnA2hZOlGz2ga9Jkvgf\nGMdZyKWLcKhDBRA2eZ7Lfr+fFWCW42HXdSG9D0Ych+dYRI4ir6qqMBYkSTJpmsyGINooAz8jXXzu\nXmDCgYibNt/A9XFd2oHlDcmuiEfAXhBrBd1agY/hLoi20+DSmilO9cHECIOeVTjPWK/xe3wOPfHh\ndKQl1+fcP5dE1cZxnDz3P8rypZ7l/X4vVVWFyT4s5bfbbfhDvV6vJxMAiARODcSxrHS/ruuCCYW2\nYNcggsTPPKcEcT0ob6PF33a7DQ6O3NiZ71tfR0x8cfSPHR91yiDvg7RIiMumaU7SHHmM5DRpFnck\nRt0F0XEW8JEMCH4uIUaGYZCu6yRJkonA0nNBfg9jJl7DcXSzZK4hS5IkzHUgfviYMfF16b1ybzCu\nDcP5iqLQ4/JN/hC6AHtyzqUTelrhx0C6jE750SYcgEUQtuPJB+pLMDnkCJl1HM1cOhHOZ9V9LU19\ndJ4DfuZfsZ8fm9RA7OBZxDPNaSx1XYdnEk6G2EeLGDj7sQkFImF4jnV6MhtucPSMa8PORaRXq1UY\nP7Afp/boqBte058L12mxKyQ+L54AaUdG3JuInPQls2pKcT0QqpcuYjnOq2MJkqXW6lo8ibyPh7q/\nIZ59fdw0Tc16Lsvu3RJATFVVZoPkpZbxmL9aKYoYryG6yrKc1PyS0+JNtJALsCfjs9GtpbzSyrmF\nFlAglo7IqT/W+3w8TkvSKUrnol+xiYx1PZgE8WTKOpbjPBN93weB0rat7HY7aZom9JRhe3Q9XmKi\nYKUgchSJ04G5lkpHobX4EpnWhvG4AWGmm0dznRbXtuE8loiLpSbrRtQwB9lsNlJVVRBzONdms5mk\nLOE1y+2MPxNehPKUZ8dZzlza+RLRst1uT2zZecEpBlu9Y/FKn4Ot5dmREAKIz2WkAZ6cj48bM+jg\nz8K6D75PnAvRvqIo3AXR+TjfJbiYV1s11+haK431uhY51vcxd7JLiImouRXmV+v95UxBauIrUZbl\n5I86NxdF1Au1VTr9z3JCRKQLES2ORuG5xn4sWKyURhZZ2shDm+xwpIojWDwOsCmIFZ1n9FgAYYpj\nQXjxfbLrKgSVbjAdq4+dq591HGfKJQYZbHzB4PnXYsuaB3CT5a7rwjH5qyXCeF+cB6+jNovH3t1u\nFz2OFkl6/IKxxzAMQWCxEQeffxgGSZIkRMKwwCQi8/aMX4QLsAfjFoLL4o3+ML8Sc0JmLj0QEzZr\n8sXfa3exc9dxjqUGIdY5ryEInceA68Nege12G2yL+Q89GneKHNMD8U/vb9VUsTDDa3ANhDhhE4tY\nnSa/B1hc8aoxR8H0eXkb65jnKMsyfB4QkRCnWZZNLPP52iFczy3u6PHUXRAdx0bXZ4nM27brSNMc\nzYL5HI+NIqfphvgZgil2bUhfjBlvWMcfhmHSZ5FBGiFH2iC68BXXgiheXddhvDrc97LczSvjAuzO\nuRfBNXd9rwQKzC+Bt+fVYivVj62cY2k8nCbEr8fglCDLURGvW4LLV6ZfB21//yqkaRruHeICqD/S\nobGnVQPGDYdFjuYUPHHgGlD8zI6JXCOmt+WvbCXNNVQMG13o3lsiyxZxOOqF71EPB0t8LZqw4MSi\nECJUo1MtD4LNVZjjELHxeE5csQughutc547DUSqOgImcpgVyVIxqqwKwq9ev66iadX7cj4g9brHo\ngtMhXsf1s6ArikL2+z03Z/Y+YM79Cy6GJ2yvwI+yDPUQQKcIWa+LzAsZTsXRYswi5mo2V/9lHSsm\nxliwvcr/rfOO1YfsGcmyLNwbxVG5ugAAIABJREFU0lLgYIjoUtu2Ewvl/X4v4zjKdrs1ayU4DZCb\ngPJzpp9DdusSmUbAdJrjufrSpmlOItkQN2VZhveWLqrwtaBmDmMcp2fintj4g90U4XpoCVttSnLg\ntQuMHYf4zBhsiZrdbidlWc7WewEIl6IoTJHGrq0iYpppzF1LVVUTkaXrvjg1HFjjF8QgC0ZE1nD9\n6/U6jEEYq8iS3k04XpFHdyh8FRH2z//8z/KHw8PLzY315OpcJOrcayzEzjke8gq6vpa5c+r3dM0I\nVrpFXrtv1CsTawj9DKxWq8mKKPfBYZEwjqNUVSWbzbEnVpIkwZAixmazkTRNJc/ziZsh3hM5ChQr\noq6fZ133pbfF6xwVQ/qhjmpzPdicEOO0Rgg42OzjuJjQ4BoQEcN7fA38VUQmfYL4ng9Mu7M6zovy\n0TF3LjURfQ/nomP8PRairGOyqBrHcVbU6f1Rb4vGyFVVRc+zJI0SUTeIQu791batNE0Tas2GYdBj\njteAvQLnBNcjMo6jpGn6VJM05tdff5X/+Z//CT9zBCpWNzU3aQKXrEbz8fVExrJ35u3njhXbxlMP\nHRE5GZseWYzhujnlJU3TiXBB/yuRad1UWZYnUSANpyYiZQfPkd5HR7cwOcD5ROwUYQ2idewuKCKT\nSD0mRZZJB8BYBdHEjoxIheRr1o6G1hgES/7YGDiOYzjv0tpXx3kVloyxSOsTmQocFiwxMbZer6Ni\nR5sTxY7J++N6EYnS9WJokizy/uzneT5Z/MJYVp5x2ObIfJZlUlVVONc4jlHbe93DTIlFrwF7Rp5R\ncFn0ff+00bD/2O3kz3/+s4gsSy2cczrkY8yZXJwTQHo/Kwp2bsU8lkoZ29d5bebE2D0/87g+tkXm\n2oCmaaSqqpMaB7ZIh6CAc1bs2YVgqaoqpP2JvAsa1EHxfhBKECsscvS2gAUUok6cNszXgvvlBaE5\nR0LUjfF5cU2YsLDdvcix1o2vDXViOBd+P7SrpKr9ws9eA+a8LJeMp1zHFBNdOk1QxBQgE2BqAfRc\nFeMEZxLgvDDM4JRkfh+L9W3bhmvrui4Y/jRNM9v3i9O4kUqJc61Wq3ANVnojp5VDFC7tnfYVuAC7\nMq8iuGI8mwj7+fNnSD387bffouLKMsyIpQTqY8zVbul9Y5OopVEsXq3WgtBydXMcC2tcuydB9vPn\nz8l1INKFiUfXdSd/oLEdR7qQdpgkSRBE2jgCaOMcbRuPOih+BrWhDo8HOuIUW7iB2OFj4HXehrEW\nXPQ5NOwOydeW57lst+8Nruu6ls1m2qtsu92GfdlR0hKMh/OfNlh0nBfg0nETESCdosc/W7VXeH7Z\nFExT13UYI/V1YZxAiqKOeEHcQcSh7xinCOJ1NEiu63rWkMMC4xTul+vGkN6I6+QxC98j7fFmWDVH\nt/pXVdX4aIjI5N9L0DTv/85wl5/JwmvHtv/Pev2+/Z//PI5NM1ZVNeL3VP++xn5/536vrffOHaco\nikWXP3f8S541EdmOdzA+fMW/RxxzrsYlz8KF6HHxU2PB0utsmvGPIuGfiIxpmo5FUUye2TRNRxEJ\n34/j+zOF7QE/b9ie99Hw7xKe0aqqRhEJ14DX+X1+nmOfEb+uz4Pr4nvkn3Ht1v4xYmMcjsWfKV8D\nPpsl98Xvq8/ax5tX5QvHpC/ngnHK2i42ZvI/jCc8ni7Zj9Fj4LlzYAzVr1nnwXYYE2LvLzlG7H19\nL7Ft+TX9PsYpeq0fbzAeeATsQs65FDpH8Hncw4r4R/kPVbthRZBETley9T5A1zlcWn+lV5cZXlGe\nW8mOHd/TDp1rYf2xETkdPz86LljH+XGoHXhrGknJ4bDrulBfUNf1JBKGeoOu62Qcx2A2sVqtpK5r\nSZJE9vv9JGWn7/uThqi67hMugYj+dF0XemhpU4z9fh/MdMZxnESjsC1WkvUzymmSIscxgNP/dJTv\n3PjC2+hoW1VV4bPkXmTYntMu+XjW9eOz+EgtrOM8E0vHQV1LGmvMzOmDVoodolAxN1eAdD5ds8p1\nYtq5EI6DOLZ+H69ph0N8hY28ZbyRpulknoNzcE8xvkbrerXJyOHn42D2jbgAO8Mj2cLfI9bk6xHA\nhC5dcL2YcJ0TMFy4zq/Nfc+1E1a/HaCbnuoJDddpWO/7JMj5ai4RZdY4cW4cfjsIAggxFKhjsoH9\nmqaR9XodRNVms5FhGEKNVtd14X2RqYiA1bsuFLfcBiGs1ut1uAY8ZxAfGDfYsIONO9gEwxo/+HWR\nd1GjUwT5WnGNVkoi3B41GHeQhol7YZdHbIdr1uYjfB/6WpjDGOYpiM5LcOmciNPl5pwOWfzoFDse\nHyw3V67dwtgB90BtboEURL0/jyNzKX4QWkhDxHHxmr5HLQb1/JvbhvC+2I5rf+GGexBqN2l94QJM\n4YLra3gkIYZre2sa+cd//Mfw+q+//ioitlDiFWfNXBNktoVm9LHQADZWg6ajYrquC8X6mrlImeN8\nNbHUDBGZRLYgqs6Nw29NI29NI8M4ButhrgsoikLyPJ/UgWGykue5dF03cevi97m31RxaAMFBEJMD\nXrWOmV9gH15Y4Qgbj58s/mJ1X1oQ6fFCXwdfCxjHMdRwodEyjgehCUGJ64bQxPvWsY06WDfhcJ4e\naw60xBCCHQr7vo+2xEA9qyXUdrtdsIHXcOQI78O8woo08TWJTE0/rGtj0QYnxK7rzLoxy0CE5yps\nrhQTiKhhYzdEROkoAnaT1hcuwOT8yqpzPe5diOGB5v/3nz9/yr/8y7/Ib7/9NtmWV565z4+VJhQr\nmudUJUsEjeMoSZJIURQT04yYcQdfF684f9Rt0XFugY5sIbq1dLx4OzgbauthOB0iMoaVXfzRZ/ev\n9XotTdNImqZBsMTcvUSOIobFDSYau90uHFen6QGkPXJvP07T43NgfNps3q3j+Tnm5s4QYZwaGUMv\nLEEY8f3wwhHewzH1gtCcMysLQj7XYVyMN1lznCfgR8RqfYkhBMY0pCtjjGKQTq1NL0QkPLOx3lra\nUCN2neM4hmNr0w+IH3Y0ZMt53jbP80k64pIG0YxllX/OGRKCjyJgN+ElBdirOxXeA/cmxOB2No7j\nZBX4t99+k/9SEy6d9oPX8NVyR9PuZryqHavpYqyBmScu+nwi035lMdtsLeQsAek490AsZXEp6/Va\n+r4Pf+QhxlCfJXKcAIzjGF7Tggmuf7HniZ+3qqomUSxdN6VrohBl0uMIHBkhqLjWi8crHlcQidNj\nEwSevn6kV2Jbhs/NQk6Lv7quJ26QOA83cGaBaUUK5UZNUR3nq0FE/81I9f3IsXa7nSkisJiD9hrW\nexYQLajl0u+JvEeoMK4xentcF+YuOmVR16mhdQdHtDiCp1PC5+AaMxwT9cC4Fr4nETkNtX0Df3OL\nk3431h9pF1r3Af8/8P/Td/7/cOTT4q1p5E/GipVOI9Scq8uysGqxuDA/ZiG/5HhaOFrHs95znHtB\nP6Mswv6otv13Y3/k/SMFZbfbhQkB12wBpCNyw+au606ebZF3MZLneYg88SQG7/V9H86BZwzv4fy4\nFkSEuHkyxAtHuazFIBY9IlPhF1vwKcvy5PnXEX6RY30b7ouPWVXVJGqGe8Vnp9MirTHy1otxjvOV\nvDWN/Pz5M/o+pz3z9yLTmi5tdsHg2YcIYzCenEs/3O/3k2eRo0sabt+hrwu1s1zb1bZtmDdhnMQY\n1fd96BPGpj+cTWDRdd1Jry8RCecex1GyLJv0Cbs02nZtnjIC5nVcj0msMP8rwYTg3O/E3//934vI\nNIXGSjliOALFxFbP59jtdmEg0pMtSyhhomZF46zv9Yq4iy/nEbBMOGJst9swSWjb1jSq4YnBer0O\nxdy6t4yVyof0RIg69J7pui70ANMuhavVKrzHKX1s1sHXZ8FGF7xQw8Yf2jTEGn/0og5HqhBRY/El\nIpNz8HEQMdPiCnVhnN5oROS8Bsx5Kngu86MsT7JqGCz44HtQFMXkedI14QzXalmCxXIoZLj3V6yO\ni/cvyfgItbd8D+xCCFiwcWQKY2SapsH0h68zlkbN0TaGxz6kOxqfi9eAfQYXXM9DrBj/K0Au8zn+\n9V//VX7QCjGjayfmDDViKT5LzDBitSMWmOTErlMz587oOI8C6sXemuZk7OdC7KIoguAaD4YdeI8n\nOTx5aA51ZXMgHZAnG1azU6xCc9SLhRRSDsF2u5WyLE/SE9lREREz1FXhfQAzDHZVnIPHEIgpTJRQ\ne9a27STdkCNmur6VnVg5oodI5DlzE8d5NKwyl3MLRZZFu8gx8o7X67oOER29P752XXeSgsjPvRYs\nlmEHC0LAWQSIJLEAgtDRphi4Dz5f27ahXk27NiJNnF9bMk4gpXEcxyA2OSsgVsf73TysAPN+XK8B\n/59eOyqGgXEpf3dY7eWVYZ0HzfVe2ngD74ucdz3U7Pd7aZpmcmxL7M0ZdMQiZXr/JdfjOI8CjyGY\nnLDgWq1WUhRF+IfxhdN3UMyOovLYJADpgVxozs8YC5imaUJUC/VP2kGQo0MsrHAM/IzoOPbD92z4\nwxEoKzquzT74dQAxCcdEXpnW6YvaDRJOrDw+YRV/SR2s4zwSc6UNcyIsZsSB9GaAtGhd/4X9u64z\nXQSBFf2CaELUaM7qvm1bqes6jD1WXzDL4IKNOxDd0pE+ETHvbSnIZOC5Yl3XwXWxLEv9OZ+3n/wC\nHkqAeZTrtQndww/h8c82cr2U33///SSthtMAdBqO5QqmJ1CXwKF0ToFk9Oo4n8c6tw7nXxI1c5xH\nA0YXLMiwwqpXWtmQQ69Ez1HXtez3+/C8opaiaZrJJKrv+0l0jM1zMFZgIgExg0kFixyR49gAAafr\nqzgtcK6+U48pOBaPeTg/16JxxA7n4s9SR774XIiM0Tlu0pPHca6BjnrFWDJnZVdWCB68PudiiG34\nK2BreUtgDcMQntHYMXRki6NuWkDi+rnRMsC2eA9jMMZe3pcXz0Smczg2CAF6nObFtHuJtt+1APMo\nl2PR9/1sI9elfOR3iCc0/JW/xyQIcF2GnnzEolUx2GFtzoWNsa5Vv2ft6+LLeXYsQSYyTVdElApR\nM7hp6WelaZqQrpMkSZjorFYrqapK+r4PDZexasyGHCLTNESR48SCF3qqqppdeOH0RvzM94vrZWIR\nMe7jhdfGcTxJgeQeZxB+3Liae6jBORHHZPF4uK77yA9ynAvhfoVLWLLdnGOhBQuicyUWlk07ZwHg\nZ+tcaZoGUdN13SSqxMKqUS1BdHolei9a14VxI1bfpbfHgpnIaT8yrs01jnUT59W7E2Ae5XIuYa6B\n65wYW9LwcAnWREbk1F7ZqrlgMbUk8jTnUKjNQfh1K21pbgXc+t5xXgEtyHQvMcCrxCLvz4ruOZam\nqWy328nKdZ7nslqtQj0nVmljK7Ko+8L+6E3G44xOI8bxOFKFe8O1itiNmkVOI+WI6OmUah7TMPay\nmEKaIp8brQD43kUkpFcfruMmltCO8xkuFV8ipyUAYC71j9F/o60oE8+D9JwoVqNlWcpjW059ZIGk\nrwVjpxZcuh/YuUgeWDpnS5JEqqqaiKy6rid2+MZxbzLm3JUAwx8ZF1zOR5kTY9eoHdORrZjLYCwt\nkY8TE1G6t451fHwfE1QxQab3ix177jXHeRW2223oDagNODCebDabiWMYLOV5BZZdxfjY2Iat7Tka\nhrov/luIBtI4hsj7eMLjRtd1IVLGtWaWIAOcvsgpjuM4TmrJRKYN5DmFEBGxufGII18s1Gg8+nyT\nJMe5AZf294pFdbRosaJQZVmendPEolex8+jrgkERtoWosqJy+lp4G5h04LpxDi3K0jSdXIseoyxN\ncM4Yybp/43O5yZhzVwIMriWOcw2s6NiPsox2oV+CXgnW6IlKzDWRj6NFm+Waxuho2kdEEoQZpxbx\n9TmOMwViTC/w6IlG27aSZZl0XReED9dvoq6Ln/88z0NaI+qpYEkvMk1rZqMN/CwyTbnhZtFlWUpZ\nlkEwxaJt1jjSdZ0kSXJyTpiG4N5YCFomQRhrsiyT/X4fbPh5oYp6lc3PqBznyYE4YLGiIzeNIfZi\nhhwiR4EUM8uwhMqcqOLjV1UVTIy0mNKRKxyD23vwV6RQDsMgSZKE47ZtG65Hm2vgeDgXG4PwuMjX\nwp+t3GjMuSsB5jhfCSxg35pmNp94KVYkab1eT8SVVeM1FyVbUhPG0TMrtTF2bH6dr1e/Hjum4zhH\nzqXHc/oNJgmojeIm0DoNiUWX3pfTDyHKVqtVsJvGxESvHLNgErFTHtlUg8VbURSTSDuPeVzflSRJ\nuC8cg98TOUa9EEFj4w6Kgn3M+sxxbkSSJBdHv+b+xmLcYJG1NAVPiw7thIhj6zkQCx8WY7Hz8utY\neOJ6rjkHRhZf+nVcGwQcN54uiiIapMnz3LwnNHoWmZaGKHv9m3RkdgHmvCTXiLRals2xlMQ5LhU/\nVhQuFsHiKJd+b+41x3Eug8WYbh4KsiyT3W4XJizopYNmzQA1HNvtNjQkXa1Wk0kNuxP2fS95nod0\nQZHjc63FFnp0MWwSpJ0SOaUQET0WWTgWxlQ0o0a0C5FD3cMMET6jDsZNOJyH4DOlDTFzDcvG3XIX\ntECKYMzhMAYLn1jdq8a6Ht7PitqBmM09v16WpeR5Huq52KXWmr/x9fDnxu/tdrsg6nCfhxTGmziv\nugBzXpLP1INhksLmGlakidOGYqmIsePHhNiSaBf/rOydo+eKHdNxnMtByh6beWDVlydHmBggRVCn\nM65WqyDM2rY167bgoog6MnzFs62jWiJT23jreCLTdGrsh15eEFNWxJ7d0CwDIFwLvuL6adv78Ih2\nHAPLKE5EPlXawFhtLixBZYkbXmxBJItT92LwsdhJEOdmLGFXVdWkFmtO/MFi3oqCwXqe0wO1Hf0l\n6LYi2vZexE7l/C7+5mZndpwbk2XZ2XqrGKjXsEQYF7HzBOXS6Nglwii2rT6/CyvH+X70cxerYUC0\nCxMQbrAsckz5Q81U3/chKoUUPp6E8Ti02+1Cc1a2tcf1cY0ZQJogepnx67Ce1vfH407TNMFqn69J\nb4drPmw3Dc85zh3Av/86AjOOo/z4pMkXolzaTdWyaU/TVPq+P+mFxYIDogWpznPn1OjjcoNmLZ50\nI2URCTWtbB+Pc1mpguyM2DTNxEpf5DgODsNw0ot1CVa92Xa75XYjN4m6ewTMeUnGcQwP86UgFUib\nbcyJm9h7H03/i9lGW9stqSvT18TRO/EJkeNcFW11L3KsGdO29Vzrhece4muz2YT0QzyvSDGESLMc\nDK1VX234geg5jqWbnEJ8IZrGi0xc/wWxx/8AtkPt7GEfj4A5d0GsLVKMpVGwpdtBsIhMo1QwqGC0\no2Fd10F8xa77XFqjFi7cCFqn9/G5WUhqx0HtqigiwdYeC0RIzRaREBFD/ddnxBeuR+R9Ab4oClyD\n29A7zncCi9VLRBhWc9mhTOS039acGNPbflSEcXrjnMjSk57Y+bR1PQ10PiFynC9CuyvyBAqOiSA2\nVnFdlxZXqDHjOgikPGrYSl5kWkfGYwhSEdU4MXFB3O/30vd9iNjF6la5xuyQfnWTegzHAbFetHPA\nhONcul9MfF1iDEbCQUSmNu4sNqx0RnDOvl3XsGr3RI5sAYhFnSpoRb1EjmMVR9VQ6wWxh/EP7rJg\nSR0/R+902rda7PIImON8NxBhS2vCeLLAtVZWBMxKO9Tb6nqvS8SgtoW2LOUZfd18TXg9ch0eAXOc\nb6Lv+0l0jAvQ9SQGdWL8M6cvQgChjxnSD0Vsp8Qsy0K0rWmaILwQBQPaCZEbLWvBiMgWXrdMgXC8\nw7V7HzDn2+Fo10d70bII+0id+dLzsUCJcc41cbfbzYownQ6pbNtF5F3gsMizolsYt/T1FEURjsnG\nHyyWuKHypfVfItNmz4iiAVjnY9OLD34FXIA5Lw/39Jnjx2HVmO2TWWTpCQomNMy5Gq5Lw+s8EdLF\n9nNOiTEi1+ERMMe5AVbvMUyMMF61bRvEEuoxdrud5HkuWZZNIvXr9dqcuCHtEAYaSDHc7/chhVEv\nOIlIEGqoMYNY43EE16CdF/kYIu+C8fCaR8Ccb+OSFMMl6D6BPK+AXX3Mst6ag1j1UixG+HuO9qzX\n61k3Q4wbFlYD6LquT0TUMAym42tRFJOFmDRNT+Y2LCJhtAEhxunNXGM2DMNkHsP/V+es8+u6nohF\npGeeiwR+JS7AHEckrDZbK1c/ylL+6U9/kr87rB7D4UwXvLO4wusYSC6pvwIfqU+LRdaW7DNzPR4B\nc5w7ILYyX5Zl6AUmckw9QkNmrgOzJpgsnFBz0TTNiYBjExDsg3REbMdNpkXeJ01scc/pjeyoSM2q\nfV7ifDnXFl6aOSHGxMSUhWURz/0GOQXRWmjhe0TPLw2LFxhp6PQ9q6YLfbrwGosdq2ZN3yvEYFVV\nISWRo/64jth8xbpOvie+XwhUkTBXu8mY4wOd4xzAarPI+4D5oyzll19+kTRJ5G//1/+S33//XUQk\npOlYFso6gmSl/SmDi5NrAEujYey6uGS7S2rODsf0CJjj3BmWGCvLMriVtW0r6/U6NEjGhENH5QGE\nE9IFy7JkURRAmqHVegPvixwXk8ZxnIx5WZZNBBlve/h5eTGM41zANdIML+XcObS5xhwQVXguWSxB\nfKEP4Tl0KqGOpPF5tCshXycLJV6swTXotD+cxzomeiTi3KiJnYtSnbsuuC/ytel+ZXKjRsxuQ+84\nitDXI0lkGMf3dIG//jW8X5blSXRprhcXb7vUCn6JoBKRyWq0xaXW947jPB4xkx2kDbEFPSYf2s5Z\nG37AppmbO+92O3NhCMfKsiyMj3w97IiIyFqe58HeHhMsbXfvONdgzkL+uxjH8eR3W9vAI/ozB/po\niRxFFB/7o88PxgWOaJ27FpGpwQaPH1rglWUpu93OEj/mz5jbwH0Rzoh63IoZjUCM4vNAmqOVSik3\nyvLxCJjjRHhrGvnDej1xLdJuYJatMtc26JTAc2CleKltPafzXGozP/d+7HyO49w3GGuw8r7f70Pd\nWNd1UhSFWfthrWQXRREmPDDbWK1WkmXZydiAGjIr9RnXIPI+MUL/xc1mE9KKqDm0R9ydq/DVaYYf\n4UdZhjmFFiCchRNDR7dQOpGm6VnjDcaqHWP0tbHQ4cbIeB09y/j4qP1Cfy+OQmkXx6qqJhGvrusm\n4xRqxvQCkBWlZ6t5PgcLRDUGugmH49wbv/32m6RJIv/0pz/JL7/8MnmPH2aRU2GDyQrei6EjaXOp\nh7GGyzoCh2uxxNQ5W3odsXMc57HB5LMsy1CcjwkWT1JRCI/+YdwHTOR9rFiv16EPIl7XNR8YQzjV\nmlef0ch5u92GfmbU2sNrTp1PcY/CS+R89G2z2URThEWmzZYhmOBmiGd6qVugTnfEosjc9lrkcUQd\nizwQXjDowBihI+Oo88KxOdpW1/VJXzOcV89XrIgWPgekOaL+C2PUJZb/X4mnIDrOGf7yl7+I/PWv\n8uNPf5qk2WBiwlEu3Y+La8GslEX0FftId3dGpyGyIGPreytdMWZL7zjOc8HPujYGwCQIaTvou9P3\nvaxWq8nkDqvOGFOQHgTnV7yPejGMc7zqvdvtQiqiiEz2c5yPcA+phud4a5poLzAWJQw/X7hHFj4Q\nLzql0YK3QdTKMsmwQLohm2QAFl14Xdvl67kFR95wDSy4cG18zXq+Eov66ZRKfg33guOLm3A4zn3z\ndrBbxupvLJKkBQ+wDDkwqCLFh4+1RAixwBI5dU60UiT1/hqkAzmO87ywCQEmq2mahokY6jZE3tOP\nsMoOV0MNImK80g2jIu4F1jSNNE0jbduGOrD9fs/i6ybpQM5jc48RrxgxG3oRO6VOxHY1hPiIuf+d\ng4XYEgdGLWa4ATQWUmLXoMcMFl7cwFkLp7n/SxU5P0HfEz4vCFoSZDcJibkAc5wLgFhC1EoLrFit\n17nmyNb359L/rAbQLORi5+TUoNg5VDTOU4Ic58kZxzE0gUbKTl3XkmVZcChDOk+WZaH/F4DBBiJe\nurE7hBhSnRANy7IsTJ4PCz92Vb3jGGhXw0chdq3W32ROF2bW63XUTj4GxAqeP6QunjtG0zQn14x9\ndF2aTlXEmLHb7YIoyvP8RDhaaZC8IGSRJEl0wVhfl27TcWtcgDnOB4hFvvir3m6Oj6T96WvQdVtz\n59YRN5HZvmMeDnOcF2K/30/qxtiggydL2sxjGIaweMOiCpM+GHiUZRkK6nnSddh3uZOA87LoOq9H\nxLrupf0/YaZzadQLYoUjakVRRK3eIaSGYZAsy05s4fF+13WT+i9dq4ZehUCLvjRNJcuyybGt+jKe\nt+x2OxnH0YyAIW0R1vfcQ42dFW+JCzDH+SCcVoNoFBqe6nRCSwzpYlvVC2cRLLxiXe1jaAFniTLH\ncV4bGGUgMoZJS5IkITIGMEFC/x1+D0IMjZuLopAkSSTLsjAR/Ujzeef1eKR0w3PMuQ/GUuiwXZ7n\ni9IHz8G1Wnwsq6ZMG2Z0XReuBe/ztUKMobcgtuOeYNaxtTgax/Ek/Xm9Xod5lP49wHXD0MOKkl1i\nWvIVuABznE8Ae+W6roOIgTATOe0DxsRch9hafg5OQcQkaQlzdWBz7oiO47w2GN8gyEQkRMV2u53k\neS7b7TbUi3RdF8az/X4feoBtNptQVyYiYeHqsO19WJQ5d8czRL00c3+32QkwZrCxJH2QidVLWdGg\nOTGIz78kS30WXxx9gl39drsNoqeu60m9W9/3k3NoUzLLHRLzHsy/dGNq/sr1bszhmt2G3nEekXEc\npaqqyQoLoklWOuBcPRivAJ9LX9TW83r1eKmphyXIljaCdhzndWETj/V6Lev1OtRkYOLDfQ3zPA8T\nzr7vg2jDpHDOgtt5bZ4p6qU5dz+c0sfExBSjBYfOlMFzimPFxBwMeLBoouo2J+dCqmHTNGG/PM/D\n860NPJB+yMdfrVYTR0S4utwNAAAgAElEQVRE+zQ877EcD/X9cGokpVNelj50JVyAOc4VgDkHjDl0\nPy7eLtbLCz12wNIIFI6nI2cs0HSvMF2vpsWc1cfHcRwnBsYYRL8w8WrbNoyLuqcYxqy6rjmNyV0Q\nnQnPFvWysGqwOCJkpcotKTvQwk27LEIMwWTHgs8NC/o0TWUcx0lkiZuta3OQrusmphhIN4Q4w7ZI\nQeTtkeZosV6vw/UjTXoplJp4k/4XLsAc54rosHmsSbIFb3tO+FjHsCJXnAIZM+qICURYSDuO4yxl\nu91OImNpmsp6vZa6rmW324UJFk+0rHoQxxF5DfElYme8sIDRkRy2bP8oLFa6rou6A+qI1TAMUpZl\n6NtlPbtIQeRjxI7fdd1JLRunX7IZhzX3GYYh1IPBGVLfnwYRtYOw8wiY4zwDVpRrzhnRSg8815TZ\nqiuz+pKxmIrZ5M+lGnoaouM4n4FNN2DOUde1VFUVxrC6rrkWxucljoi8jvgCl9ynJcguxYoqsdEO\njgsDDD4vFlA40q0XUhBVq6pKxnGUPM+j5hu6lg3jhTb10HMSRAGbppE8z0/6pcVE2Hq95vu3LSC/\nGB/oHOeLYJF0TnTxtsiTvqSfmH6dxZeVcjhXE+bmG47jXBtY2+MromFYiU6SBBH3046zzsvxauLr\ns1jRsKXpeBBREEIszPI8n9RjMaihgkiDCNLbbrdbSZJEuq4L2+jjcO8wRM1xHKQ1W9dQlmWwmG/b\nVsZxDJE2fS8MatfcBdFxnpTtditZlp2kFOpUP/4654o017h5LsXREnOx5oXGtp6H6DjOVYEQW6/X\nOjXpJqvR30Fd1yfNdJ1TXll8Xeue0bvPwrKu182TAeqvhmGYXBs3ax+GQVarleR5PunZhf3hUIha\nLy2mIP6Qiqjt6DFX0cINwPSnKApZrVbROZR1f4djfi6X84O4AHOcL6YsS1mv1ycuh1Y0imu1Lo1E\nQYTNpRiy2Iv1/TJe80bMjuN8Cdxn7DA+Pa0NPTvIfeTfK/GK4gtco0Ew11AxsILX78ecFjmyxr+D\nelsdbeKaLzSMhsDC+xCC1jVAsLVtO6nr0qBWnbddrVZnbfVxLbG6tO/ABZjjfDGIdrH4suzmdV8v\nvQ+2wVekKlrph5pLBJ3XfTmOc0OeesGHDUou/fdR4faqIu5ROVcDfgk6NVHPA2L27kwsYiYydW/U\ntWOc2ojtOPoFIYjIFsRYmqahx6rIVMDp9jroIQiRtt1uTVF1RpDdRIW5AHOcbwJNTNl+GfbMEFzn\nzDg4goUwu45wxXqOWTVh+pwfibw5juM4X89nxBsiStcQcV8t5l45+nUt5mqbuNaKI06xfaxmz0gz\nZCt8XTvG5+I5i04lZPv6YRik7/vgsIjtIei4dAKZPF3XBRG22Wwkz/MTEaYjdriWw319PuT4AVyA\nOc43U9d1aE6K1EQWRB+xoNfvx+rL8P1cLdlSK3zHcRzncfisgPuKiBz/+1GW8uNgb/7qfFaEavdA\nwH/v2d59vV5LWZYTETYnykCsLstKZ0TWDtxQY+D/H66J6BGIyFgM3JtVs6a5h4VmF2CO883Apceq\n1+LoWAwWaefcDBfWeJ28p67DTTgcx3GcCdcWdG8LGgs7R5Y4+GkhtNlszBS9uq6DoQbvywIrZh/P\nETX+CvEk8i6+EHWCyyGwxBjmSTDjaNv2pIk0X4fIu3BrmiakO84tIiu7+ps4r7oAc5wbgN44S23q\nNRi8dJNnjXVcK0XxTIPmp67JcBzHce4DF2FHzkXBYlGuOawab9jJa1hAibwbiulzcRqjjoaxyCnL\nMgiiYRjM1EVcB9pSsFFITGyy4QZ6jaH/2Jx5B46LW41u9IW4AHOcG7Lb7WabNGsswcZpgyywkCvN\nIivmkGidd0k6pOM4juM41+eSVMxL+1nx9n3fm21p8BqLMy2W+r4PIgfvoTeXiIRGzKjRwn5WNAv2\n87ouDbVhjSHOu64LVvn6GpumiUbacA0Hkes29I7zasTSDbfbrTkgWkYdIkc3IBZSOLa2p7f2t4TW\nknRIx3Ecx7k2r14Hdsn9WyYZcwzDMBFAOJcWcRAviGSxAIJY2mw2YTsIpt1uF3pz7fd7qet6IoTq\nug5RqiX3BTFn9fcqyzJsk2XZpAmzFnks0pqmuXlfPhdgjnNjEGmCIyLEFA9YenuRU4dDdlaM7aO/\nx3Fwrkg0zk68dhzHcZwrw46Nr8hXZp5sNhtJ03SSHoiG6FrE6UXgmMir63rSy0vkKJ70/yHej/Xf\n0lb2OL7Iex2ZtYCM7cqyDNE3buA8x+F37SZayAWY49wB+/1+Ute13++j0S6A9/U2WrhZgznEHh+L\nv4LDNp6U7ziO43wbryrCkiQxHQQ/ypLUxNVqFU3vEzmKIitiBfHF9V8srtI0laIopGmaE0GkRVhR\nFJM+YTjmOI7hNT1H4WNypA7OjjHQ/wzOjLfABZjj3AnnDDNi+2ihxvsgkmb1F7NEV0SYuQui4ziO\n8628mgi79n2ifkqjX9Nuh7wdm2ywOOJzcN8tFmNFUUie50EI6W30dcSiYjDksO4FkTukPDZNY5qF\nWPtR6qbXgDnOq8M9uGLhcyvqFYlcBaE153zIsDAj3AXRcRzH+XZ0A+ln5SvuzRIs2+3WdDLc7/em\nuBKZ9gPjY7L5xjAM0nXdRHDhPUSmUJMFwaavA8eG8NM16HPRvP1+H0QaDD+2260Z2RM5saG/SZaP\nCzDHuUPW67UZPkc6oW6WbAkyLdTw85xLonUsx3Ecx7kV6BMm8pxC7DvvZ7VanaQ4olZLCzYIGsvk\nI03Tk4gVtgUcMeMoFRtlzBGrH+P3d7udVFUlSZIEx0WRd4G1Wq2C6LvUJfI7+JtbX4DjOKdYqYdI\nJ+TIGDsdikzTFjk1cbVanawm6V5ivL+LMMdxHOeesETYuV5Z98wthCTmECx+UHsVg8WLjlJZoC6M\n0wbHcQz1VtzfK2bsMQxD6OWFY2pYbBVFIfv9fiIwEX3DeWbu8yZGY/cnCR3HCSRJIqvVKtir7na7\nIKSsCJcWUxBrLL50LzE4MOpUxZgVvuM4juPcCisi9mhRsY9c77WiOFqEtG07WzMFIaUbP2vxZKUq\nwpFws9lI3/chIlVV1cn+uhl027bBLh7HZVOx7XYbhFnbtpIkiXRdF7bF78g550VxF0THcTTjOIbw\nf9/3YYUn1pCZYWt6tm/VDZbhwBirCXMcx3GcewNC7JHE2I+ylB9GE+IlXNLrK8Z2uzVrvZZGwESm\nAo6vqeu6k8gYFnGbppHNZhOiVVaTZx3lKopiEnETOZ2TjOMYRF5VVZLn+SITDnVPbsLhOM4p/McF\nPbvY/TDWmJlrunRDQj2IWdEvx3Ecx3kE5sTYvQgyXMdbxBjiK9BRpc1mY9Z6ARYmaZpOXA2tCBwf\nn8USG3RAsCGS1XVdiEZZqYUA+81F/pDps16vpa7rkCnUdV2oC2MiwswjYI7j2HCe+263m0SzYmIJ\nAo230WLtXK3X4X23oXccx3EeAhZjtxRk1jm/U3yJ2AIHwsqCxRjSDpHWdy4Cx8fUNWaIjMF+Ps/z\nsL0l+lgosQDUfU3rug6pijpipmu+8jwPP18jmvhZXIA5zoPw/7d390GSXWUdx7/PzMIO07wkbAyC\nCYnBAJ1QwWG6oqJoSFReLHm1NAJKMLEMr4KogLGoAKUmxBLfYqFQQKwCAoSCihiQIMSUFJtUT3rz\nxpCwSVCCSAyIIT3VJHQf/7jn9J6+c2+/Tffte2d+n6qt7b19+97n7PSe7afPOc8J/5F0Op3+NMK8\nEbCsQhzDRrVGVEzUQjAREamkcRKyWSVl6eul77uTKYizkren1jTnhymFWQna6upqfxlFSLLCerN4\n77F4bVk66VtfXx9ImuLq0I1Go5+oxaXt6/V65rTKcUbUiqQqiCIV0mw2++u52u127ghWXM0wTrzS\npefj68KRaol5I2YiIiJVllU5cVgSNk6lxTipyjvfOQeHDi00ARtVWCudSMVTCfOE59IjTqEwRtb5\neQlSuEYYwQojeGH0LL1UolarDSRUYSqic27g3nG7yjD6BRoBE6mcbrfb70TjtWCxeAQsFpetz6py\nmE7qVAVRRER2u/Qo2ajRsvjDfTy9cJxkrehpiLGs/UVj6eQkXq+VFic+YaQrLd6bK14blq6oGMTX\niGONpw8G4bNKGDFbW1vrJ1+NRmMgvpWVlYF7pe6rIhwiMp6sIhqQP2KVN1UxaxQtrpKoKogiIrJX\n5SVmYYRl2rVdZdi/LK9SYHr91dra2rZ1WjCYrKVHm4KwF1eedFIV3zts3BzvB5YWjq+srNBqtfrr\nxJrN5kB8cTGQstAURJEKi6cYpqcbxtKl59PPhdcHody9EjAREZHt4iTqx0MiVmBiNU5hjLR4Vkve\nyFZ6GmE6gcpa6xWv88p7Pr52XuzxveP48pK4kHSl7xsSwvX19YHXhvuGqYrhcObF50wjYCIVlyqY\nse25IN7AOeucMC0xTGlU8iUiIjJaGAEbt6DHLDZiDkUsJhGPJKW3pxl2r2HnxEUystaPhUQqnJ/e\nhDlvJC4+J+z1FWs2m/2qivFm0nEy2EqNTPZ6PdbX12m1WttK9BdNCZhIhcVJE2RPQYz3A4sfZ50T\nXzeiMvQiIiJDxGvA8taNzXIj5nHWZqXFCUleifr0vUI1wmHxxKXjsxKz8Pp4RCqclzW9MF4rFkbh\n8qYQxvcOiVqILUyfjNeitVot1tbWtiVnRdMURJFdoFar0el06Ha7uRUQs6YqZo2cZZStVyUOERGR\nMeRVWZy1vOmH01T5C1PzhpWbD9IVBmH4HltLS0v918dTIMN5WYlQeh+xvGQzPj+d+MVxdzodWj5B\nrtVqbG5uZu4VViSNgInsAu12m263C2RXQMwrzhEnYkM2d9YImIiIyJRC4Y5FVkAcZth0xnRCtby8\nDORPHcx6fRiBykp2wibNsXjKYUi+8taMheuH57MS4PCcmdHpdGi32/E9VQVRRGZj2HTD+Fg66Qqv\nS1VN1AiYiIjIDISpinGp+6LkJVrxXl6jhGQmXaxjmK2trf5IV/oeq6ur2+KKp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_bifurcation(fig, axarr, index, x, y, xmin, xmax,\n", " ymin, ymax, precision, keep, num):\n", " points = bifurcation(precision=precision, xmin=xmin,\n", " xmax=xmax, keep=keep, num_compute=num)\n", " axarr[x, y].plot(points[:, 0], points[:, 1], ',', color='k', alpha=0.8)\n", " axarr[x, y].set_xlim(xmin, xmax)\n", " axarr[x, y].set_ylim(ymin, ymax)\n", " axarr[x, y].set_title(r'${1} < \\mu_{0} < {2}$, $2^{0}$ cycle'.format(\n", " index, xmin, xmax))\n", " axarr[x, y].set_yticks([])\n", " for i, mu in enumerate(mu_vals):\n", " axarr[x, y].plot(np.ones(10) * mu,\n", " np.linspace(0, 1, 10), 'r-', alpha=0.25)\n", " axarr[x, y].annotate(i + 1, xy=(mu, ymax-(0.05 * (ymax - ymin))),\n", " color='red')\n", "\n", "fig, axarr = plt.subplots(3, 3, figsize=(12, 12))\n", "plot_bifurcation(fig, axarr, 1, 0, 0, 2.9, 3.5, 0.4, 1, 500, 100, 1000)\n", "plot_bifurcation(fig, axarr, 2, 0, 1, 3.4, 3.6, 0.8, 0.9, 500, 500, 5000)\n", "plot_bifurcation(fig, axarr, 2, 0, 2, 3.53, 3.6, 0.8, 0.9, 500, 500, 5000)\n", "plot_bifurcation(fig, axarr, 3, 1, 0, 3.56, 3.58, 0.888, 0.896, 500, 500, 5000)\n", "plot_bifurcation(fig, axarr, 4, 1, 1, 3.568, 3.575, 0.889, 0.894, 1000, 500, 5000)\n", "plot_bifurcation(fig, axarr, 5, 1, 2, 3.5695, 3.571, 0.890, 0.892, 1200, 500, 5000)\n", "plot_bifurcation(fig, axarr, 6, 2, 0, 3.5698, 3.57, 0.8903, 0.8905, 1500, 500, 10000)\n", "plot_bifurcation(fig, axarr, 7, 2, 1, 3.56992, 3.56997, 0.8903, 0.89045, 1500, 2000, 10_000)\n", "plot_bifurcation(fig, axarr, 8, 2, 2, 3.56994, 3.56995, 0.89041, 0.89043, 1_000, 50_000, 100_000)\n", "plt.tight_layout()\n", "plt.savefig('logistic_bifurcation_points.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So what are these values that we've found? Let's record them." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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BrmmasgOf8ZL1C/lwOPSSjDRN0yMkjLNL8hBtIru0FH88HstGQKal5mvgPDUy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\nGfbNUt5/X6KO+hptLoyIdDQnnpGNfeIxJ5NRYgz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fcSlMnB7Xz5nafVcLIVgLkajXb8iq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "points = bifurcation(xmin=1, xmax=4, precision=3000,\n", " num_compute=20000, keep=100)\n", "plt.figure(figsize=(12, 4))\n", "plt.plot(points[:, 0], points[:, 1], ',',\n", " color='k', alpha=0.8)\n", "for mu in mu_vals:\n", " plt.plot(np.ones(10) * mu, np.linspace(0, 1, 10),\n", " 'r-', alpha=0.25)\n", "plt.xlim(2.9, 4)\n", "plt.savefig('logistic_bifurcation_fullpoints.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot our cobweb diagrams with these more accurate values." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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7NIMmxlK5REFmDmslRbHIH3ETTMF33wdmQkfcmFLQ9XvwLQTzhnP6/GV6RUSx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\nVtCwi9WR/CIjK4+xsxL4+XA6/x3Zlfu6uO50jx6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vjOrKvZ0a2iFAUemFDzHdKfauKX1f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\nFpnd7a57QYZQFJDWmncXb+WLFTvp26E2zUdORPn6w8+PX3H/AG8jf/0dZ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ikAACAASURB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 100)\n", "fig, axarr = plt.subplots(3, 3, figsize=(12, 12))\n", "for i in range(9):\n", " axarr[int(i / 3), i % 3].plot(x, x)\n", " mu = mu_vals[i]\n", " f = lambda x: mu * x * (1 - x)\n", " axarr[int(i / 3), i % 3].plot(x, f(x), alpha=1)\n", " web = cobweb(f, n=1000, start=800)\n", " axarr[int(i / 3), i % 3].plot(web[:, 0],\n", " web[:, 1],\n", " linewidth=0.5)\n", " axarr[int(i / 3), i % 3].set_title(r'$\\mu = {}$'.format(mu))\n", "plt.savefig('logistic_bifurcation_cobwebs.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could keep recording these values if we wanted, as this will keep going infinitely, and appears to be approaching $\\mu_\\infty \\approx 3.57$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Period 3 and 5 Orbits\n", "\n", "We found all powers of $2^n$, but we haven't found any odd-numbered orbits. Let's track these down." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " Cython: _cython_magic_03f0b3ea9f65dc103568deb6a9e57f68.pyx\n", " \n", " \n", "\n", "\n", "

Generated by Cython 0.27.2

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\n", " Yellow lines hint at Python interaction.
\n", " Click on a line that starts with a \"+\" to see the C code that Cython generated for it.\n", "

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 01: 
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+02: import numpy as np
\n", "
  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numpy, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 2, __pyx_L1_error)\n",
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       "
 03: cimport numpy as np
\n", "
 04: cimport cython
\n", "
 05: from libc.math cimport exp
\n", "
 06: 
\n", "
+07: cdef float map_func(float mu, float x):
\n", "
static float __pyx_f_46_cython_magic_03f0b3ea9f65dc103568deb6a9e57f68_map_func(float __pyx_v_mu, float __pyx_v_x) {\n",
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+08:     return mu * x * (1 - x)
\n", "
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       "  goto __pyx_L0;\n",
       "
 09: 
\n", "
 10: @cython.boundscheck(False) # turn off bounds-checking
\n", "
 11: @cython.wraparound(False)  # turn off negative index wrapping
\n", "
+12: def bifurcation(np.int64_t precision=1000, np.int64_t keep=500, np.int64_t num_compute=10000,
\n", "
/* Python wrapper */\n",
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" ], "text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%cython -a -c=-O3\n", "\n", "import numpy as np\n", "cimport numpy as np\n", "cimport cython\n", "from libc.math cimport exp\n", "\n", "cdef float map_func(float mu, float x):\n", " return mu * x * (1 - x)\n", "\n", "@cython.boundscheck(False) # turn off bounds-checking\n", "@cython.wraparound(False) # turn off negative index wrapping\n", "def bifurcation(np.int64_t precision=1000, np.int64_t keep=500, np.int64_t num_compute=10000,\n", " np.float64_t xmin=0, np.float64_t xmax=4, np.float64_t ymin=0, np.float64_t ymax=1):\n", " \"\"\" Acquire bifurcation points for varying mu for map \"\"\"\n", " cdef np.ndarray[np.float64_t, ndim=1] mu = np.linspace(xmin, xmax, precision, dtype=np.float64)\n", " cdef np.float64_t x = 0.5\n", " cdef np.int64_t i, j, k\n", " cdef np.ndarray[np.float64_t, ndim=2] points = np.zeros((len(mu) * keep, 2), dtype=np.float64)\n", " k = 0\n", " for i in range(len(mu)):\n", " for j in range(num_compute):\n", " x = map_func(mu[i], x)\n", " if j > (num_compute - keep): # we throw away the transient\n", " points[k, 0] = mu[i]\n", " points[k, 1] = x\n", " k += 1\n", " return points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can perform the same process to find the odd-numbered orbits. I'm not doing 9 different levels of this, because they're hard to find, and it's tedious work." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "mu_vals = np.array([3.84, 3.74, 3.702, 3.68725])" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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lqseUjyYAn/1IpREcNSgK1hpiJ7BraC7yRjUiE3m+/qlhYK0vqlcNKA2RRos8\nPe8tt7TSmxQCXDnj7dc0EubpdIwi8htFhiIjwmhGREBUD5RoKVlWYuO6okugSqJ4nyRSuciPtpPz\nif3AvtU6NDROomWF7sGJoinR0Rad6Xqo4xTVrTgXOXsRUe5FHhwnPtrwfvbjPeZAdFybg+p0pBIJ\nThT5SOlyoyOBlsZGB0G9MQI1Q380dDzHPFHYMPK8vb1+H1GIUUPOSo6iqNTd5cGBi8L+9d8kixpx\niQy7RlA8nXrPEdnRKKBGRqJooJLZqN16D+eJXLcl107qquqN3rPqYEQIdb2ebSJx0z6+N/C810F8\nYR/mlohy52/5rfO7C8jTSYuwzdP0KjfiRN8GuK+6P+Lecrr1mY6uS8GpNIKjpEQjKTnvld4uvWnm\nYZk0HJHHzBC9t4fLWDkDEZEp5tFQsxpcl+hcL1IgwWE/acSEURc9T5KiEY6oHl0K5ScJqpIF1zMa\nz6gdUZRESTZ1RqM91CnqWLR8oW2MSJYSdyU+FIkeFRnBUaOVIzVdAVojLW3LYQrsnlfrZ9sUY/xa\nH8eXzsctedrkI43pcJR73BUf7lEoSUlKzcfqUmruMSCI+zlPQxLkE4ig4cCSW4aKCAyNikZeaIx0\nWSEyGFG0h8bWPweCE4sSQxpYJTt+LiIREVmJyo2WAly3vC6S4ogskcho1If5Xacjgk4yQz3WORPp\nHdtD3WafRvockXOvNyLiVhDBiUhMRGrY78SHRzt6k0JwwuWe/f3RY/4Zj66ORbojPtztzzZH5z/h\nWq1Wtt1ubblcNv6Ycnn+08HD4dD4Iy7+sZj/CeHy/OdcI/wRnv85pv9xov/5GP9U0f+Yc7/f2263\ns+12a7vdrv6jw91uV//Znf/hmf/pof85mbeHf5TnZc/nc9vtdrZYLOo/N5zP57Zareo/Wdtut/X3\nQZqyXq9tvV7Xfwj39PTU6L/ValWPr+vNfr+v/zTSx2C73Tb63MX1h3+66TKbzWy1WtlyubTVamWz\n2azxJ5z+B5/808qqqmwymdjT05M9PT3ZYrGodcCvRXLCz5c/9XRd8jkxm81sMpnUc2Y2m9l2u7XN\nZmOHw8E2m83FH+n5n4Bqe7fbbX3frs/b7bZus7fB55S2GX9aevnPfQ8q/JNenlPxP+/l70cT15VB\nLuW9jJ6K/3ntIO8jjkv6Z50fIXep1f9B1MkEDYf/e7KL/0Oy/+PxcrmsFS76F243CmYnhXfjkFKy\n/X5v+/2+Bu3JZFIbPQc3NTJupCaTSeNfYtfrdf0vy5vNpjEx1ut1TZD8Pr3c3W5XG+eqqhrkZ5BL\nccNs9gI0JIdmJ6LiY5nS6V9pyg7iAAAgAElEQVR7x+NxbfRdTwhU/MdxJ1KLxaImQk9PT7Zer22z\n2dhut2v8G7gTYbPmPzw7KXASsN1ua/LgE5gk2T/1H+xTSrX+TPEv35Tn52dbLpf1vxL7XPJ6OYdc\nxuOxTSaTWs/9H+/9vsfjcUNXKYfDoe738/1dVjDIIJ9A3oMUPbJM5d/Iu8pr7tPrygUpXCKHoxe5\nR1got/RjCFul1PyDRKZhXobTWZ4uE1B0X4XZ5avruRyiy1BsUxTC77LvwYX19CaFhJ65HySlyw3H\nmjba75RbpvJyeJ5LGVG5/luXn3I64Pqsy6WuP54utw/H8/k511OWxfvR5SXeZ7RUxaUspmP7ND3S\nFPOYeHT4fZd29CqF4MSjyT3Hv23Z9LVLqm/Zh3ZrPV3SOQ5C5++GD3ePGzG8Pp1O7Xg81lEaX7o6\nHA62WCxqj30+n9ceKr1NZ4aM7NB711DjZrOxp6cnWy6Xtl6v6zJ96Wk+nze8cZfRaNSo1z1hF3rb\n9Kyj9vky3CCX8vT01FiGcnl+frbValUvHZm99C0jK5vNph5HP2/2svzkejebzeoIzvPzs6WU6siR\nRk48mnI8Hutr7n3M53Nbr9dWVVW45OXLmiml+t5ct82sjgT6spMvs06n01pHPIpyPB7rfK6jvsTk\nkSS/z8lkUrfH+81ltVrV0SVPx/Z5Oa7/HtE0s5cOLVCuLTuMRqNXe7r3kkdrzyCXUlWVjUaj+lgu\nlxfj5vOT4nMwXYmStC2b3rKkyiWhaAn3I8VXePqQ6lqHv6rQqkq+T8aBdLvd1gBLI+UA73toPLTu\noX43KrPZzJ6enmqD58sWT09PtQF4fn6uw/SHw8Gen59tNpvVisF75bIBCYjn8XK5pLZYLOrlEaan\nQTGzxpKWl6GG9K7yla+cPr/lW/qr8x2E+2i8T/nbdcjshfi6rjjxWC6XF3rD764XUb1eB/e7sE6X\n/X4fgpjXYWZ1PVxK0/J8LrjOU09UpyJhW30/meurOxLeLz4fzaxBbnwuen96P2w2m01K6XojPliq\nqnp/ALtBnJy+hwEZjUbhsvzdpFCc+EhxjHEjPZ1Oa7vURkBo43wfqeoMMaVPEmD2onvj8fhi78wt\nut12fy7sPzOzlNLdNkHdJYLj+2Tm87nNZjPb7XZ2PB5rz/VwODTIynw+t9FoZIfDoRFJoZes3z0K\n456zkpvJZGLj8bjexJzO+3Xc6/Uokad18HeD6JtGaRDdGEwmk9pbH4/Htl6vbbfb2WazqaNS4/G4\nbtsQwekuathdR3zfk2+WNTuBwPF4tO12a7PZrAEQu93OxuNxI7Jh9rJJnPVwzw/3bXn00aNEHt1x\nEsXonRNfT+c6s1gs6slMkh/tBaOe+F4u/852+jmW7fvIvG5uWPa9PB4B8jnp+XxTsvcjo2GlSpdN\njV03Pral043Lb6kjt0l9kMeRlJLtdrt6XKMHB9rE00U643Pe96P2uTH3eDxaVVVXN+u3RRn9ISDP\nl2s/bfzd5S7rXqPLl/bpPhfudeAeB+5nSOni3RwXeyC4H4Z5ufch1waWHz3S63l0/ZX7ibgvRPcX\n6f6O3qTAtXXdA6Xi57h/hXt3ovHk2PE3x4Vj6OlSunxhINug7YrK0P0u2lY++q77Xzg/qPPRPh7e\nU7SvhvXovGQ6/bSCHhOP9ibcsufgtfsT9LFzvXZreQNOlCG6P45zXfeX3KIX+goJ1U+ev+eemlvL\nzt1TVE60HyiVuAeHoXiyWn9iaj6f236/b4TY/bdHTzya4l7ndDpteJceDnMWrUsCfNLJ6zZ7WZJa\nrVY149xsNrZer+s6DoeDjUajOlrg0R+/l+VyWZfv3q8/zeVPq7hnPDwm3i4eTfGlpHTeI8Moi0fF\nfAz9aSEX7t/ycqKlGE9jdvmklYtH3jzvfr+31WpVj63vDXJ98Hbsdrs6j0cYfT+XR/vYTtcThmt9\nb5FHi/i6Ba/Do53eNl8y9fvyqJffsy69+ZN9fni6zWZT71eygh4Tf6/HvYlTkaeqHqk/salPkvir\nKdryRtKrZzvIq2WxWNhkMrHNZlPv9aIdMbOL/Tn+Sb2gvpid7Jfv/4uEURG1rb4nyL+7vCYK1DUi\nmbuntigP9xb2IvdgTeo50hulh21ggDyXi5DoE1H+PXqqKorCaPSGZV97ykWfvFKPneWyDZHHfHcp\nxDOLPNauEa9o7DRKodGcKLKT0ktUTnUtpcvICOtQXXLdYd0aNdToDnXmNB3TRb3UH0YKOU/YBpbJ\ne2Kf01PkPWMeFBPBee1xzdt+i5f8mgjOgBNlCe3arXrAuevnXLro7bVI0K153uvoEmXSdqR74sM9\nCtWlKDUIVAx9tJbLD0wTkRAqgy4J6BKVp1Ujo4aI4UBd0ogex02paTRoYPzaEHq+LhyraHmJfRgt\n/VGvIjJBYsoyuBSqdZPg5paWqCOehxOZhEiJFtumesP+UDKiRF4JCvuBdUftiPrzMxAcH7f3PBSY\niTc5oCemtIH+4AiVJSTHKaXGfL+mG0o4qBNdiEiwxBOWH+ntPZe2cnXlltw8bSqR4ET7UzRCktIL\neKuX6hIZKBoDfrIcjRKRZKlXzXpYBomUp8kZFq7LRh5xr1IQcGk/5SJkSnp0DHQfjOfT/FFZ2p5o\nf48SICUbzEsdYx4lFEq6CEwk80wTSQSyStTUY/TzkQNyLqvo9+C8BZyVpF7L95Y9C0p+epWCcOKR\nxMdJx10ioI35TKck0h/alTb9Ij5x3vtnm661kY5cGW3prx25Nml5qTSCw+iH32Rk+HXg6c3yvC47\naXRFQVqVi3WRjBD41bONyI0aN71PVf7oei9SIHB1ISguJBfav1FUh2WrLl4jn/TAWb+3WcmDpo+A\ngaTI06TUXJZi29oiLUpM2vLoPUf5cI9FEJyIlLT1/T3ISq4Ntx69Y0WBOPHRwjGnPWGUlZ+eR7Ei\nR3B4Ppc2spG36nUuwtRGtFhnF11vW6Lqi+Dc9Tk034w5nU7r19/zNfOj82Nl3HTkj3X7f/14Wr5H\nhn+54JtKfcPvfr93z87MTpue/LE7f8T4+fm53uzkj3Vzgx//w8rvw9voL1rjY7a+WdPstPlLX17X\n5Z0mX43CF/m56Htw9Pp4PK773183ED3ybfbyFxr+nhzfRO7p/PF+bmj2+vgensViYSklq6qq1mf+\nLQJF35vjerOUF4K5nviGZq/X9Xy9Xtf/scVXJPhjpJ6eeqttX61W9vT0dPHYt78bh3PK6/LXKJhZ\nEW+d83eL6DhEj7yqTIPNkJ5n1LI5k9f872FSSp3fF7IMNoaaXb50cpDHk5RSbZMcf9we+Sbg4/FY\n65a+cJJz0e2Uv4iPdtExbimPnev/I1LnpucNvq5T1G/VTf2PRZfJZGL7/f7iPTxertfJe5zKI+1+\nPjcfrr1a4V3lHqwp51lqCI/hNmV1utyTUtMrJTP2cjXUznQ8zzVAjQTp8gLbErXfy4vax/vuVQrx\nzHIRCf+unxqpyy0Z6v6VXFSI5zSv6q7qDz0c9cDYnmhpNIpAet6oTbm2RjobLU+xfZrO26BRJPsk\ne3Bynmh07dalKWJEl0OXGvTcsERVjnC8cnqjqwmc55GOpdRcAu+iR23Xb40oppTCuqOlt9ycYf6u\n9ad74sM9ClWw1CUogi8H1iXay+JKRSXQ71w+IvnxvGrseD5aB/W2eD1qVKgUqsyq0L1K4cAV6QRJ\nqy7xeFrVheh6jkQxHwkSRUlKSk0djpbCSHoigub1U1eVjFDXVbc515SYaZ8RqJToKImyQpaougL6\nNXCOjjZDo4ZKy4rKpkNHR4vXe5XCceKjJMKInC6o3jGv64naG7WPbToc6VebrrKtbbqtxPta/bps\nRXy8NldSaQSHnisBlUaJwM8OvOaZKhgwH8tRY5FSTFKUKGkZalByHrCWHRG03qQg4NJIB/vUPzWa\nwnFz0TGOIjn+qaSBQpIb1aeRG36SxPhvvU8lQGzbtciT/mab2Xb2iToIqqckXCzXCovgtO11ugbo\nbzmuGZ3IEGh76Zj1KgXhxCOJ2hQXOvPReNOe+KenJWZcIx6vidBEadvIUNf0Ebm5FsWhQ1ckwSFQ\nRwZGWWq0BOR5o2vRUhQ7mYChHjTTkrQo+FOh1DjyO9OnlOpPL5/nepNCgIvjrH2kBIZ9GRFMjVZE\nkQrWGRGkiJAyWhN5VgQqXaYioGk7aNA08kIPX/uJ7VW9jMh/VC/rYP2U0giOHn6vt4B+ZFxyBue1\nxqWtjsERKkNyWMH5F81JtVkpNZ9wjHSDhEjLpO26RUevERC1o9eikyRc6tx1cTxSiQSHRCKK4vAm\no5A8PV0XJT5UEDUm6gErsHMwvEw1DowKeV6mZVtobLS8Abhi4dgqwVFS4RL1JceH487xzBEmFxLV\na540dcx/U4+9PbzOepjHzylpy7UxEtZD4qL3wrblIly4x6IIDklCBL4aaYnIzTXgj0D8FsPRhQj1\nKoXgxKMJ7QJxgzjEg2OcUp54X9OnXN4uRL2LXvLeIhKTI+e04zmyJoSmN4Jzt6eo/E8qn5+fbbvd\n2nq9bvzrrj49xT9RfHp6qvNEwvPH47F+Lb+ff3p6yv7BJf9M0az9z8PW63V2t/d0Oq3/hdp3nps1\n/xTUy3ivV8l/Nlkul/UTTCP5SwI+icSnraJx9bHwP5s0Oz1RxDL1bwz0jw13u509PT3VT/yxbv57\nvJfLJ+y8Df5noKPRqH56wu9tPB43/qphdH5SwsV10v+00+/Hy+CTYqvVyqqqqj/93rwNLn7/Xrf/\nqa1Z81/Y9Um1Ep/641MhIzzR4fNXnwrRp6X8aSi9ruJPkLDOKV5Z7+Vde939MvhTxl5fYT/Iq8Tn\n9WKxsOVyWdue6fkJJj5BSx04cROrn8KcZp488nRmzT/wnEwmF09keT4+0cR8lNFoVKeN9G8qT1zx\nryBG+CPYkTz5539X4vl8nnEuTKfThm6vVquyn6KiJ82oB71GZb70vDVSw+Ul9TxZF68Z2LWumSoD\n16iRLisYPHK2TdN6GraLnn5v8gk8M41m5CJ0On7Ur6icaLkqGn+tO6WXiIjZZVhWdY1jrroXRSup\no2wrPzWsrXlz98D0qqe6zIV+fk4PEKG5dpjlvVETz1G9Uh3LLke030BD7owG5cL80THgRBlCu8Zz\nkb65bhAf1LboSkdKl5Ea4k2kw7ymdjXSsyjC5PXqyormZd0aGSXOcPUjmj+4fj98uEehJBE08rru\nz5vW9clcyF6XutihNDAs1/MyHZUjWrLSTy41qUGKSBjTexm9SSHApSQxIiLR0pIaa83nEhl9Jdw5\nEqHkh/qkk5TGzMvQyc40nl/b3EZUeF96n1pXG2lnn7aROitkiSpHHLxfcuRGjUOX823EJHeOYx8t\nJeiY9yqF4MQjCnUkpXQxpjnS4WkjEqxzNUeqeZ3Oek4n2SZt27XlLbYtIixeTkqXewE93TVyn0oj\nODQiymK9I/zTO1ENCfNrPgK1ArYqExWK5Wq9ZNDCLrMGR713r4tt6R20UioKuNiXOpYuOs5txIeH\nkl69lhOOof9mPupGFE1RHaEeMD3JM/Wc6fy6n/P2UH/ZNp5n/6kRjYi4AGwRBOcWIhIZgS6RlWuE\nJzIUXcqNjEuvUhBOPIooeU0p/usG2hTqSI5s0F5FUUHqIklIFLUh5twyH/weomABCVnXudLVqUgl\nEhwOmA+aKwg7jgNKIxEpTErNx7kpVCBly1F+/66eupIWJSg0dpExzXnIvUqBwMW+zvWZGnxNk4te\nsMyo3LYx13NKYDju1I0oFK060hI9uYi6eFsIjhqVudYfGnH0NPTA0IZi3oPjfZDzUm8hGW2kJZeP\n49tGppg3AvqB4JQhOu9Tyj8tRPKgTojqjmJVRICivG06em0uaBuj61E9Of1VZy03F6TesggOSYp/\njwBdB0GNk3cQB10jI95hJEWR8dFrZNNevqfRa2xnzpDovdKgDMB1XWjkdUz8HPvVxySlvJHW8iPi\nqYRF26Jkmec5STW/LqEqMdf5oOdYDsm8EqTcvHHR+RGRKs4TzLGiIjg5sCfR5HgpGWnzUNuIjhqi\nrsQoyqNO292lQJx4BKFtUYyPMCoiMkooFJNUJ3OkuOtBvYx0XbE0ys/2RuSHeTWgocEK9kkqjeDQ\nI1bioEtBymi1o1yhSG44ECQdVCYFDRqnHMlix+vSQmR4qJQsh8YsMjp3lwKBK0cuXAgm/lsNNY19\nNNbqJalw/FU/FdQ04qMkRsmU6gXb5G2ngWOZbKsSNfZNRK61DiUyKcUvwyyJ4NyyPHSNjBAHukR/\niEu3lBF56IMj9PiixIS/2yIktBkRydB5qcRBI4Btet0WScwdxAKW17YEFrWB93dt/qD/yiQ4jKrQ\nABCQ1WvJATS9VZbpeagcUVSInc5yHaSULNGoeXq2n0rO86yHdfcqBQGXGm9+j6I6HHf1SFwisIh+\na1qKeihRGTqx1duiXqhnFhEz6rfeE/tAAUlJFvvPy2KZOZLEsq2gJaqIKOQMzXsfEcG5ZoRy14YI\nTjlCY55SutAFxSj/TmdYSUxk64gtXQlDTu+vzYGULiM4ahO1bD3PvvDvubrP9dwVZ+5SqBKZKFLi\nouxUDYqKlu2dqPURTDRspgpKJWKdqqwkO1RSGl+m08HuTQoBLjW2JDMahVGiqWkobaRJx5jj58LJ\n6u30TyUJqt8EObaX6XjvSsL1nukBKvnRPoqu6XUl6ewHHlbIY+IR6HPcFHjbDIGnyRmSqAw9R4OW\nS6tt03y9SSE48YhCo+2/U7p87QLHVQmBfk+p+SJQxYQ28nyN1KgT1kZwaE9z+pwjPurQR/cqx11x\n5q4Eh0s2Pni6ZKSdT9LAiEtK8evlCeZKMNRAaEhavV31ujXk32Y0aMQ0+qTG5O5SIHDpWPu5iGTq\neFMvXJTMsHwdS42mKOFSgGH51FMFEaYh8aH3pvcTRVZyeudlaZ/lSB11kW1imS5W8BJVdNzi/d6S\nluS0a346V3quVykQJz5aImPvvzUiExFenfcc/5QuX0tBbLmmU7csXUU66/Xn6lKdjaKXvD/2U9Q3\n6L/7OUB2B+GbYPlm1c1mU7+RMaVUp3t+frb9fm/z+dwmk0n9NsSnpyebTCaNN7uu12urqqp+8+x8\nPq/feuxp5/N5/elvRzY7vWnx+fm5fjvjdru12Wxmu93Ottutbbdb2+12db7j8Vi/YdnfoOtvnF2t\nVrbdbuu33Hp7/M2Wft3s8u3Gg5zE39Cbe3uxj8Nyuaz79OnpyXa7ne12OzM7vVn0+fm5MS4u3u+e\n7/n5udYLs+bbg72spbzh09/y69eWy2X9RtH5fN54Q6e/yfhwONTl+Bu9d7udHQ4HG41GdZ6UUkM/\nF4tF3TbeL9vI+5ue3xDqOuh9ttvt6jnjeuntnc/nNpvN6jeMz+fzukx5g3Exr9U9Ho9Odswsfjs5\n35w6wptYR3gz6whvIdZzKn7e9VDzq6SUGtejN3Ln3r4+yOOI69n0/DZi/t7tdo03Yy+Xy1oXZrNZ\nbfOm06kdDgfbbDY1TiwWi/rN+MSE/X7feHu212Vm4Ru7287TDumbvYm9nsfr8XtV/dxsNtm39LsN\nZtrR+W3Kvb7Z/y6sCR61erkpxU8zabiOEReNyNBrpdej3qqyRnqp0bJSVLefY5vpmXu9Wj9Ff99d\nCvTMor70T0PIM6XLfVoujHL4b0ZQcte8TN07Q13QJSBvs0Yeo8gOdZDXNBKldXt9bfrDstr243hZ\nJh6V6jU8uGIiOLmD95vzbltC5xceeq78KOzf5i3n6h8iOI8vtAfX9INjHy1nRfaJkVbVJ9oo1bNr\nehzpqEZ9ovvQ9rMdim1cffHyorTB/LofPtyjUO8UBVYNt0UhfA3FR0s+NDhRGE/L94GjcaKRVIOS\nM0IkXPwdtZlt610KAS72VY6sKMFIKV1MJIKHLmPqpxKdlJq6EYEMy/f0JMjRkqQe0fKTti9ajlVS\nltMzvT+dNyRASn6i9lvBm4yvGZ22NLcsT7XlaSM/OYM0OEKPLyQ4FDoMkW5ERMHLU4JD3aDN6apH\n10iOLqVT9xwDIj1WO6gkRttDfNZlecHVsgiOGnYlDNrBagh04LWDSV44IDpAkaGKQJ7GhIOWixKo\n50+Fp9fuv3uXwoBLiUXOsPuYRoadukBpIwgpXQIW9Yv6owSYuqFt1zzaDpZDAqf36elyZIft5PzS\nPtH1dab3e9Z+s08QwYnAPff7LYQmt8+hS341Ar1KYTjxKEI7QnsV2RaSCo3Y5cgEr9Np93peo6dd\nvuu9XZsvGgGKnM7o0PtIpREcGhplrBq6p5JwEElM1PBRmVTpUoq9/2gAGDmKDJeSMiVjLlpG1J5e\npRDgaiMAKaWL/tS8OgYaoYkiQEqKCTyqYxHpjYiKRkE44XPEhvcQEelIx6jDSqq0fUq06H0pyVOi\ndq6rWILTBcwjApRbxmr7fS19lzYQ53qVQnDi0USjLS50bCOjrs43xz5HCKIlbuJLLo9iZ1s6bYcS\nl5y+ts2BHFHiPaG/yiI4UUcrG6UiuHK4EtBD9w6lESEY5MJ69NCpED7gPogsI1qWyhk0Kqymjzz7\nXqUw4GojK/zt0rYsqL+pO6pbes3P6/IT9TcHbiTMqrMkO6yLwOd662Vp/1CvNeKl6SJCpqSI4KcO\nwXneFUdwcoB/K0B3OViXGq2cgdLImaYbCE4ZouOYUgrHmzaO2JEjNildvjbllqPL8irb2nXORJGq\ntnSKZdfalUojOBp6IyNU5eAaYwTAnoagQOMRhfddCbUNOhCal8rqZbBcDhaNa5Sek6F3KQi4IsIQ\njUsU4XDRaAWvK6lI6YUgR2OueZVU0DOJInYs1+vRSArLIBBQr1iWlutpPR2XNqLojpJB9ot/16M0\ngqNGwfu/DZAV3IlTXYxMF4OSS6/OHo1Cb1IQTjySUE9SapKSlJp6p5ERpo30LyINbXoUEQglT110\nWtNQP7XdbXW/5kilEhwffO149Wx5LaXLZ/FZDj9dmZSs+HcFDDUoVM4orKYeskaS1CjwHlhH71II\ncEX9o1ERJSKaNiJCJBX6m7qoOsQ8Gslh+dH4ezmqg56OBEhDyJ6G+qqRQpYTEa6oj7QPtN90PpC8\nWyGbjNs80PcA32vlvFcdxLTepBCceCThHKczQnzRqB3PqW2LyNA1XVRS3IVoaBpts0YVc9HIW6JL\nXedGuiM+3OU9OGYvz9zP5/PG8+/L83P/+/3eRqORbTab+hn76XTaeCfKqb+tfnfJcrmsy3NJKdnx\neLTJZFK/z8bfi+Lv3BmPx/Uz+ZPJxGazWf0+kMPhYPv9vn43yWQyqevy99jMZjOrqsr2+339ngJ/\nP8put7P1el2/D2M6ndpsNrPZbFa/y0TeLzLIWfi+BzOr3wPhfTafz+u+1XfmqPDdSz5GfqhMp9P6\nHTuz2cyWy2X9Dho/np+fa51YLBa22+1qffFx9TH3upfLZf2+muPx2GiT2el9T5vNplHXarWy8Xhs\n2+22rq+qqvp9Nv7OHRfvE323ktfl5Xlav0/vQ3/vk7/vyeeD99Py5T1AOytA+D6Pkbyzhu8AWcr7\njSIZZd59E73XxuwFe26RkbyDx2UavGdkkMcTt0lmJ93z+envdlkul/b8/FyncYxwPdlsNqHOHI/H\n2j6q/rmMRqOLvJ5Pz1Pfl8ulHQ6HRhrP5+3e7/cNrNH35DBPm0TzTO9nNBp1mo/vIvdgTfRGyXad\nfSqzy3mo0b4BXedjWi51uUS/Wad6yqzHztEYs8v36Gj4P1oa8HqG0HO76HJPSs1Ntf5bIzJR5CK3\nNEP90HwazdDxVC9Jx1mjRCmli7HXpc1omcv1zdvAul1c7xkNoi57Xu0TlunpoggVIpFFRHAs7xW+\n2sOMlo9uPegBR559VOeAE+UIIzHXln6uRT243OVlR/pC20V8vNaGSKffM/KYm1O5OoLl5Pvhwz0K\n1aUdJSmc0CQpSlo4gCldLiexE2n8lHik1HyhH9uiRk1D+iQ6uozm5zT8qGXklljuJoUDl677qmF2\nUbKhEi1DpnS5qZd66L89HQkI2xMRF01HfdEyqY9tusK0et85nXfR89p2rZ9tKJ3gvAaUXwP6kcN2\nDeTbiFWvUjhOfJREy0QRgWgjHdGSFu1eW75b9ereR1RvbikuSF/ef1FFkRQCrXYAB1U9bUZnokiJ\n7jNQJVDv1tsSgZCnU+Oq5EXJTUqprpcGTI1Xb1IQcEU64t+VkDCNnmMZNNg+LiTOOi7UE4KPX2Ne\nbTvHPaV0oYcROdJIYFQW54HWqffI+1aJollKfKL+s8I2GX8U2EcEx/Hi1rKi8burFIQTjyTq1KaU\nro47dSRHYhTvHuF4yzxiv7TNjVQawaHxcYXQ5QXepBIZP0fQ93I0SuL1qEfLOlJqPokVRYHYTjUg\narx84NQ7piFlPb1LgcDFfvQxUyOuIVodc+ZJ6YWcaLRQCY2W5eV4uyJdpI64KIlmG/y7kgzeK/N6\nXZpHP6P5wUP1jwS8rW+tcIJT4jFEcB5faKB1bncx9j7PSJI+Ut+6EJL3Pj4FwUmpCdq61ECDop1O\nAqKePPNSyVTZaIi6tMWF9VIhqeBehhoutlUNYa9SGHBpH9Hwen+3GWQlATpxc3qXi4Z4+RGxidpN\n0hAthVJnlIip7rFs/WR6OgPaJi8/yqftZn9I1PJTE5xrSwgfZXB6lcJw4lEkMtJtxKEPvfmoeohD\nkS2PytF06Y74cLd/E1+tVrbf7+unOvwJAX96g/+aujzvHD/pjtVPd+iO7c1mU5czn88tpVT/C+pi\nsaj/kdWfhOKu8P1+Xz/dxKdzvL3+VJSXx6e7lsuljcfjOo0/TePfJ5NJ/RTLZDKpnwAys/CJl0Eu\nxZ9MMnv55+zZbFb/o63+Y7j3Kf/N2Z9sOh6P9S796XRa/9v84XCw7Xbb+Ifu7XZbj+Vms7HZbFaX\n77owPT915df4NJc/of+ImCAAACAASURBVGT2ooN8ws6f+nO9M3t5KnC9Xttms6mfenL9pazXaxuP\nx/W9+9Nck8mk8U/mVVXVT6GZWf2EFvNRfG75eX/aytv12aXLEyF9y61PZA3Sr1RVVduU6Ckjl3uN\n4yjzdJXWl0v3VonuazKZ1Od1PuX64VP8m3i0adOsGaExa3rYDP2ZNV+O5OUwLz1iLl15mUyja+VM\nT6+fHjh/e1l+jWnoNUd7POg99yIFe2bab4zucDz8ui4b5vRD99FwOcrLYv2M0LEdLNuFkRtdIoqW\njfTgvbMtGsnSKBL1ty1io/oe6ahGweyTR3Ae9ehVCsaJ18hHLwk9+pFSujlP1Ke3Lr+le+LDPQpV\nYI82C6vR0E+zyz/LTCn+MzDurYgMEyVHbFiPkiM1tKyP7aKiREakNykEuCIy4P0XLVvpBnP97Xl1\nMzj1kEZe26F6pvoVLRFF55VI8X6oa0qUdQlLl1W1z/S36iXTaH7tZ6/fz1nhT1GldDtYP8rRmzw4\nTnz0OJR6lEbkUokERwHYrElYUrrchOvXaCRIKrw83RuhoK6eqkZnSDiiTZxqHKNojn9GJEiJ27AH\nJy9K/jieUaSDJMXTR32ue2G8Lh87Rkai9uRIkUZUlMx7eZpWSQZJup9T0uXXcnsz2CesU/f3aB06\nP5kPRL94gsO9eZFjpNjgfR5Fgnleo7wc48jQKFZRf5jOpS/D8qXz8dEG7orx67VPhuPtRzSPeAR6\nfzd8uMtina9P+n6C3W5no9Go3pNwOBzqt6f624Z9bfNwONR7Cw6Hg83ncxuPx3Y8Huu9Cr62Nz3v\nz/BzKSXb7Xb2/PwcrvP5/gjfc8P9M1VVXbx51s/5Gyafn59ttVrZdDq1qqospVTvq/B9Hvv9vr5/\n3wsUvU13kJNwbwj3NnF/ie+X8r0t/iZgpjez+o3U/iZi3+vi47rZbGy5XDb2ufh6NXWV4u3wtwKv\n1+t67F10Txf3CI3H48YbjlnH4XCw0WhU67X2S0rJVqtVrXc8/I3ErsN88zNlNpvV5ex2u8b+o/F4\n3DhnZnz78+SiUQ8oo/Nb0lNKNp1O6+/j8bh+G/VisbD9fm+TyaR+Y3pKqT63XC4b++jMXt60znq4\np8DfNp1SqrFru93aaDSq23Q8Hus9YNPzm9x3u52Nx+NG2YvFooFlfZHDr2y39pXt9r0J57sKbcO9\n5B7tviYc74+Se7XB7d+1fW697Dm7l1cVheoZITG7/JfSKNTu+QyMj/tp6B3psoCdPQB6TTzn+cky\n6dFqG3nOy9N6I098iOC0S7TcolE1XXZK6WU8NaITRVzaImosU/WNkRRPy/FXfdUIEyMjWr9GIlme\nRiDZZuqjRqhy90XxeqJ7QgSnqD040ZMcuJfQg8ydZ2SHGKNjq/jBfNF4qm57Oh3H3qQwnHgPicZ9\nOD72SPfEh3sUqksCuv6vew40RO6KGC0JRaCk5WmIWZcauH+C4WG2L6X4vSu8L03Pzaaef1iiyku0\nNOi/1QDrsiLDnEoyonFkXiUpFDVeOvZKVLQ+Jbm6BMrfbBeXO7x+XVKlLmmdakCj+1dDG40HCF4x\nBEeXk7zfIgLp14kb0Z4/YoZiDsuNcEFxRvfqaXoAfb9SCE48ouj8UftD3VBb5/l5njaIdVD/csS8\n9COVSHAUyNW7UXB2UQDn4CvgEKxpuBTgNUKgeQlWrqwRSHmZvKYRhTYj1psUAlwcfx4ci5QuIzuc\nHJExVz3g+Yis+pildPmfUZ5GyYt+pvQy/iQr1LdcVEbLp/C3Emm2QaML2vZonnAMtJ9LIjgkEPxN\nvPF7Vd3R8yQ9Xh6vaeSY/am4xHSKS6o3iiW9SCE48WiSc1qpB+o4q/OiRFexIKUUlqG6qTqp0V/q\npdpjEihiluov71VxRO145BB8OoLDQaDxIBCTrBCcORARGCgD5iBw0DS/KoMqpoKdetQ8r8aRSsG6\nqXC9SiHAFZFY7dvI49XoSUQeCDbUISUvXm5k5El6Uoof49Zz1IOITCnQaDRBSZhGZ1hH5BUSsDQv\ny+Q9sY/RlqI2GSsepNPFUD8Un5QoKyFU4hLhFJ0ixRzVTcWnyJD0IoXgxCOK4nrkNEfOjuIBMYpp\nSJKicpRMULf1k8QowkV1AohfESYpzmg6nRs50gNbXBbBUa9RIxsRICmwqMeshkDBhgTJFZDkKVrK\nUNKjderBNmsEgUpOJkzj0ZsUBlyc0DqRXGiUI0OuYWHm80+m5/WIPGsa9VxSit9/k1JTD6i/Oi88\nH/tB28/2KEHRc5o/R7ZyxJFgZ4VFcNRJ8vHx++c1JUXUjVxaPVQ/dAlcCY8uq7qeqHHoVQrDiUcS\njpc6QEpMIozg3CRZUjtDnVE7p6RCI5neFr2u5SjeqX5TLzUqSlzkPGB9bK8SomIJjioAwYSgG/2O\nBs87Plr6IvHhgKmHRKOg3m/kCbJM9c5YlqehYimo9SqFARf7MaWmvqTUHBu/rl7BNQIRESf1NqKI\nB4mALk3ymoKCeniR3ukcUdBQg6hAQyKu5130vnMkivp8vp9iCE7krXJ8VYd0THVZMnJcSKKYRvOp\nZ80xYX4lyr1jRErF4cSjiEbaVK806kH74flVZ2iLtPwoOqPOmpIOYhXrUzupdtfTKMaq7WP5UVs5\nT9QxUDubSiM46jHypiOQ18iJhnD9uxImP69KEIXpOaBkmKyf6TytC5XBfwsLDcN2HyKFAFcuYhIR\nDo5LpD9KAvip0T9tQ26sVDeUtDAy6L/VSLItXl+UTsFGPSUlQFq/1hFFdPS+2GbWfW7Xc3oAAnPt\nUBJyLerCNKob/jvnXOW8XyVU6nBFxkbHWQ1FL1IITjyaKOboHCV+kbwST6hXkW2M7CdxiHOfdeZ+\nk6RTb9VRV8xVXGZ79Z5I0HLERqOcRRMcjXzkJjeZo4DsBUFSQFDPiMBEwKJSKaDnDKkycVU0smpv\nvwKZKkkvUghwRX2aUvOV6lG434XAwAlNwqA6p16EelYkJlqeTuKIaKi3rgZQ20dCrO2m0VXQYl1K\nCAm8bHuURgHRz5USwVHHRkmskg1iSgS26iTpEUWjOU4ppUY5kR4r4YpIai9SCE48krQ5LupwcV7q\nZ2RfmD4iRcQf1XHaW+KPkoqUmhFy6nIUadIyWB8jORGpieYQMel87q57/e5GcDTcxYFRBqlAo2Ch\njBid0xgwAkXU4VHUhmxY61JAyxGdiDVrRKFXKQi4csRBxy+lpu4oiaXo2LAe/05y4ue8DrZJx5b6\nrMRViTLrVU9Ky1UvXomJRkXZV5xr/NR+1nkYtcPzl0JwOL6qLzwXOTFKakg6IvCn3mmETUFeiVLk\noUcOUa9SEE48kqjTQwyhnrhw/JUYEG+obxEJ0Qhv5MzQpiqhyTlUxBneo+p+hInRvFPbrPNN86VS\nCY6yO3YwgVtJkBIPF40M+UBwkJmXg57z4EiMlOQo4dLyvE6y6cijG4ArFiUn3pfqwfg1NT7qKXGy\nKtElsHBCc+yiye91KyCwPLaf7VLCremoZ3pO01Evo37UPtB70LQEUvYvrhdBcDRCS9KhUZMcQYkc\nMh1bNTSKJcS1KHoTtY962Ta+d5NCcOIRJTevlHBHDog66cHcCwm3lkOMVNKsThXTUNfUsSKeel06\nh6LAQWTnWWY0b87f77oUfpdCCQRKCtjh3sHqLVGBIu9HGSU7VomSgh9BRw2ihu21/epFqwfOdqiS\n9SqFAFcuWqOhz9ySixJZTkySh2i8XDSiFxkZjdaol6bjq2XyPNsWtVvbqySc95c7WIfOE+0ftp9z\nrxSCw3kXkYsId9TbVF1T/PJ0Sox0rJXQRNFm71/1pnm9NykEJx5NclE7JTeMoCh+cNXA86iuUZ88\nTeRckfjwIG4yPfXVr2s71EFjOdo23r/mYTkZx6K8JSoFlQhoct9JNhTs29iskhI/p6G8ax5fRGy8\nLg37sT1RWz1d71IIcHGScyJHXk1Kl8udCiQRmVRCSmPm15lOSZR6PRH5jSI8es7vi7odeWBKPHKk\ni9cjkqegpiRHnQYla/cGnvc61Klgv+acLM7paI6TgHg5nON6TR04plGSQ+yhzg6OUDkSRT/U6aGx\npyOmZEedNM+rxElxQDFSyRYJfY5sKP6QgPhvtbsajdS61D5H8459c05XFsGJvPIc6yNR0UnOjtbB\nISCTEapHREOmDJv51HiRCKl3RiMZgZpGF3qXQoBLdUJDmSSTKV1OFhpwv67REZecQWf6yPgrUdGI\nCsc+Ryqi9NpO3q+3KwIwJUPUWy/P8zPqk7vn6H7Oel0EwYkwItKvHMgqQYnmrwI9CQp/6xirceJ5\n5mG+XqUQnHhEyTkvEUaQQNChpm6pk0wdVZukTl5KTT2MCL7qutaltlh1PSI0bJfiXpsDQJwtluAo\nuEZRkojdkfyoR6ZEQ8tT8FGypGUrM1WipGmjwY48RDVKvcuDA5f2Y0QmNayZUrowZBq5oZ7R8EdE\nmsaH51leSpfv5PHrJLksT4lLjlDpOfW0WE7Uf0yrZVDv9D7YBq1HgLcYgsO+9/mbUpPg8P4iUt1G\nfNjfqkskOhq10bGhzqiDxHHpTR4cJx5d1MiTMET6FtkH6pUL9UPtpQv1KaWm/rEcJV6qdzn9vuXg\nnPG2aL8Qs8kP7o0zdyM43sEKvArqkdeTY4wawYkMpHihIUtV1q2kSZluTlFZFsmSKiaVrhd5YOBS\ng8K+TildTDpOCr+ukRE/TyG5ITBQBzUPQUl1Vo0T9ZhRA9atRlcNJkEsmvwkPWwj6yHBpl4r+WMf\nKiDrHDyXUcR7cHJOR6RnxAol0OwLdZYih4vYEHnYPg40AMQu6ltkwHqRB8aJEoRzmEdKl1sn1Na4\nqAPmeahfEV5GadTmEKvUTinZaTtYPrEiN++IOdF8JA6e77ssghOxzbbfNFJUkNwAR52uTFVJj5IW\nHRBlogQ0zaf1EySj/L1HcR4QuNqMjRJYTkx6ySnF776JrunkJnFSkqDgpCScRkjP8zePiPwqWdLy\nlTypcYyIHutUUsN7JOhof+s9nMelyE3GNBb8rQTE0+i8Zf/o2Cth4XfFAcUcjj3xQQlmr/KAOFGq\nRE4MbRJ/qy4pJkWEWx2QyLnzer0M6rina7NpbbY1wiISJHWgaMfVIdC6U2kERz1mDoyeU2+av6MO\niwZEzymj1QiBRgmUrLAebQMHh4oSESgd+N7kgYBLFVzHiH2qkz6KaHBcqDNRmbmx8zx+jaDh5zSf\nkhnqI8vh9QiUvE8IbARCApemzc0VEiI1miwn532xTLSpCIKjOhWRkRxOKAnR8VOcyRmXCD/YHiVf\n2sYPcYJSeiicKE2UkOqYRtikc1P1z4U6xHPqiBEbFH80vTpX1+wnCQxxV50Izcd7zpEnxb5UIsEh\nGKgi6OHpKDpgVCIaANahA5jrYJblg6TGU0FOB1ZZsCr4h4LXAwCX9oMaG46PGpiU4vcjKXngeLsw\nipFS0onUIE0uJD8a6dCoCQkSDSr1yiXyyiNyFJEXtj26FkVe2H8UJVk5wiReVxF7cCKHhXM5mpNK\nrNmfxIhoDnOeaz72teMUCawSsYjU9yoPgBMlitqHaCWA85C6QhsS6V9Kl++NYdlaf0oX87ahWzmy\n3hYUiMgOy4uceyVEvHfVf7/H87m7OlJ3IzgUHXQlP8pI1TviIKrSaHmU3OByIBXoVUnIiCOwVKOd\nq6tX+WDgautv7Tf2r15PKf+UnC4p6PIMjR0JEnXKz9EYeZ1tRINlKXFQUHGJiJrqa46I5ETb6fWw\nn1Q0ChF5eX0Az3sdvF/qSkovehiBN8mrRupIfq4R9UjHIoKlRkcNw1d7pLckUadGHWWOKwkQHXTi\nWzTPHTv4SbLBsiJif02HVSdVnxW7o+iP3lduDnLe+T2j/jJf9JdS+1MBEQOlAnHQ2ohR5L2qAWM7\n1HvyQdBBpzJRgaOBb1MY1tObfBBwRQSlrU91skRGgssqBBQCA8dCCTLTe9kKKhw/z6+Gj9d1Eqte\n+m8FH8+jAKlRFS2fZbtopMrvQ+tWosffrJvnzmNUBMHxucUxyxkVP3S+0igpIYlIkTotxBRGmJmH\n6VRfGBHqVQaC8yqJ7BodGp3H6ugqBnBuKsEmHkVzmfpzzQYpwc6ljTAwmifU7Qhv/F6V7AkZK/cp\nKnYUwTMC1YjIeHqeY6e2KZ6WF3mpBBsat1y0QT2uLsr02QlObgmAkzk3mXSiq3FKqRlhUd3JkQX1\n6vVIKTXIrbeTuqXl+DnPw/tTj0zLUOKteh4RK6anRHOG9SlRUpLGcYuAGsBcxBKVkhAlMpHeRTrL\nPFoGgZ1Y4GMU4UREkCLCFBH83mQgOG8SnT8RwSHx0aiP6gLndc4ZUt1RTMsdnA85nVVd5MH0JF/a\nTnVOI2Lk93i+Xl4EhzetXig7z5WBnzlFUk+VonVFZaq33ObFasQnAicOZg40PzPBiSaPKnWULqXm\n26Q10sMJpZNJDb8SWBeOI8eJoKDXlVxo5IjtU5KVIypsK/NGZTAt743lRtEXBUzmbQsf63xgeec+\nL+Ix8QigCfhKnDVdpFNanhKXyDCxf0mEckRH80dk8+4yEJxXSWQnlPSqYydzq6EPnl/r0CgNdY2k\nqY3U5Ai+6mUUZYx0XzGb7fL8nIPa/iiQkEojOJzcOUNAZfABpfLwe5vn659UNqajwdLycwZFjVyU\nnmHoNjb8mQjONe+A908jy4mQUmpMLv7mhM6BiHoXnGxen+bTqIbqDQHIy9L01EHVNyVkvK4Tm23S\n8rQdBA/qYHQPWre2I0dkOEdIzqygCE5EIrroK9MoSSeRyRkJJVQRmVKDpoZDjVevMhCcVwlJRuQk\nq1OszlJKL3gV2ULFEpccSY/IizqY0cqE6jvbE+mrEnniFYl9SpcRKq0Lc6W8CE7kUUdKoNe8g9U4\ncPD5PfLacwaurZ7ICOSE96AGIweovROddwSutntRb5bpIwKoXi7zqeKT/OjkYr06BpHHowTH9USj\nGASFHKHIlReBEcvw+3GJ2haV7WlZnrdDxyAi6UqQtJ6obef2F0FwlBwryc4Bds4h0WWoqI95jmNB\nnVc9JWlWzzoav15kIDg3C3EupfjhF44p9USXcPyTJNmvs3zVozaikiPiGlXUtC7qaFG31cZF90TC\n5v0RYRrblkokOC66RMBBpIJExMHPe4eoUYnyaX71dlmmtkHL1fR6Xu9FJWLtvRCddwKuXFtzE4sT\nIKXL8CkNBz0bTryU4sgKDUDOeEeEh94Tz2n9qic0XgpiChrRBI70U897XUrINErl90UikqtP87T1\nD8th2ee+L2KJKgJsJTVtERldvosOjcpoXVF5kTHiOJOYEdt6lYHgvFpIQlK63Eyb+805S0dOcVb1\nkelIjCLCrORcyYjir1/zepVg8TvxLlcP7zeKiLINxRIcZWrsoMgbVoBVA6NK4uVReE1JlJIXBfuI\nHGl5ek7vQb9rOyiqiO8qNwJXDth57Vraax6GTniWy/FQr1h1Q5d8VNeiCc0ymY4ERfUwiqpoei/L\nyyZRUj1wuUbGI33IEew2ck+AIVki+SG5UcJjBT1FFYFmpJ80DATdNs9XiUgQYm8QdyVQ1EWtR0m1\n4tndZSA4NwvnTkpNu6CGnec9Lz9Tyu/xjAh6RJip04p96hwp0ciRD5ap99Q213I2IGoz2lveEpVO\ncgVyZbE6sZVUeDpXCD0iL1sNkzLhXLRG20SA899sT2Qcovu9Jm0k42a5Aly31nGN0KgBoKcQER0d\nN51onABefy6fAoz3fUQ81OvifaSULiafGh8dX9VjlhuBIOuIdFvvVUmI6hx1Nke69VpEGnmPSFcE\nwYkMhOpeFHnxfqGXGZGTSO/V4YrqEBC/mCPR9S448a4yEJxXSZtzolES6ljkULfpWoSz19JoZKft\nXKS/UZl0gvS84mr0SbzSeoskOBop8RulUkQkIDIcrjyehmlJUiLiwc/Iq75GrNhGeu9qHCg5o/Na\naVPsrGSA602kKdMendA8H4E/J3VEgjWS5+kUTGikNXpCo8XzucgK00ZEnMaHukPyoXkishuREr1v\nnQfUP22jtkHr8jTRvGEafsd8LYLgtJGYnIFgX0VArSQnIj/qHWsdUVoS9ih97zIQnFeJOj7UKReN\n3Gi05ZbjGhFq0z9GdVRv2S5Nw3vTMkmY9P7VDrO8TDnlvgfHlYCdkQN4grxGRdhhPOdlRKQiIkuR\n90ywVzITGQetM0d4ciTqPSWn8F86HyQzbyU2lJyXq6FIrzcyGJy0nGzqYbBONcwKGhyzaPzpRUSG\nnu0gQFB/aBwj8kEPP2qrfo/0i33C8VMjrMRI+4lApbofESnmuzfwvNeRmwO8/0jnlFTruLcZItXz\nNoLFdDnSo3rWmwwE51XCearj6vOf9u4agaH+ebmRLhFfIoKSq0+Xl3JOaZQnwkKtI6Xmkhjtt7ZR\nMdBKjeAo6WAkxc9FHm4EwC5UHBcF+KjcSDRkyE+2MzJGvEZpK69XAXCpIr6XXPMqSEwjEFBim5vI\nnNBeXs7Y+3UlOtpmpqMXoqSWuqVeeEoxOY6IEwmGelARmaaxI+nXqCTr5r2wjQQViuo123wehyIi\nOARv1XXVqTZ9JfnVZUstM7cUpvrfdl5JEklxbzIQnFdJRAaILddwMaeTioeMROcIeo64sG0uniaK\nwHjbSUzYZm+b4iT11/O1zQuWf25Hmf9FFRkWNWzqXUaRGQVtTRsZMyoKf2tZUR0aalQjEBk41q91\nfogEwHUPktPmnag3kkujzF8NPa/ruLVNPB1vTn6Ojf5W4qVlKSlxIcBp+zSSEumRglG0/EZREs+I\nDkklQTAiNVE7z/1SBMFRMO9iXCKSQeBXvb7m5Wr0RiNBmj83b3qXgeDcLLkxa9O7rphIrFM9VRIR\n6bPiKrFNddnLIalPKcZ0ptW6PY9/En9YX84xtVIjOCnll4kiQ6WgTy+eRiqly03AWmZELNTT1XMa\n0dElEj/v9Uflc7BZVu/SAlzvCaq5Scqycx42J6GSEyU7SlI4sdWLIMlM6XJZKiI0kZEnMWBdqjss\nQwkH70GJGNut5bE+JXlRfarzOk+0T7wMTxMRQitkiSoC0wjwuxqgW/MRK9ra0FamGpneZCA4N0sX\nPep6UBdog9Rxi/AyIhvEXQ0q0F76dS2P9xc5l1Fdkf5H0Wa9B7ETZRIcF4KoC40DAT1aytI8EVjT\n2PE8iQuNRmQQXJTYeFkReYoMhLa3d+kIXLmJd2v6tnIicsOJS2LEqAUnRI7EaMSH4830OcKgBIFE\nS3VFP1WnIhKvBN6F96BtVd1kX7LtLIvt7kKGojZru62g9+BQh6Lv3hc53etKRHitzcDkjrZIkLet\nVxkIzlW5FhV0aRtfJTL6mwQjt3TZpoPqRHo5imskG110k44l64ran2u3Oqx+Dv1Q3iZjnawkJkpk\nctEW/1QDptEcJUXqWVMBWQbzRmTKf0ekJjIOkTw6wYnkVhLTZgS8vDaQUM9XDbGuK7PciHDQQ6Cu\nUY+UJNCbUd0k8Kj+KXhoHSRBSvL5mfOwVC9JlBRE/FCi6BJFPZnX+xYgWEQE5xp5UN3hefaF6tk1\nQ3WtXs6lrqRqiOB8nLwV7zQancO3W/WK+b2dXNkgJnL5KbdsyigKyZaSH13Kyuk7y+L9a/uJlVpm\nuiM+fMHuIMvl0na7Xf17vV6bmdlisajPLRYLG4/HZma2Wq0a6efzuZmZ7Xa7+vt4PLbJZGLz+bwu\nbzab2Xw+t8ViYbPZzJ6enuoyvMzVamXb7dam06mtVqs6L9tB0TTr9dpms1ld/9PTk63Xa1utVvb0\n9FSn9/pns5mZWd2W1WrV6INHl5PuNaWqqpvLORwO9ffj8dgov6oqG41GNplMbL/f19em06ltNhsz\ns/q6y2g0qsfK9cbMbL/f23a7tePxaKvVyiaTSV23645+93wuu93Onp+fbTab1WPr41lVlc1ms/q6\nlpVSqut18fTj8bgef2/7er2u2++ffs3r9Dz7/d5Wq5VtNhurqqoem9lsZofDwZ6fn+ux8fmzWCxq\nvTd70T/X3dVqVbff79Xvw+V87mVCFiDUMbMXPXN9MmuOufep2Um3jsejbbdbMzvpoaf1a5o/V68L\n5wzbcMs9DHIfuQXPqAsu1AmX4/FYn6ct87zH4zEsK6Vk4/HYlsulmZ10xbFvPp/XOjmZTOp2qz7u\n93sbj8f1+aqqbDqd1tem06nN53Pb7Xa23+/ruWF2wmnFWq9juVzWuDMej22xWNTtMbO6zdvttnHe\n7IRDm82mvof1el3PR8f/XvT9HqzJwNRyXqsJq8xJztPVsjW9i6bXurT86Dc9d60jWuqI2tWr3Nkz\n6xKSj8Khmk9ZvpetXoaniaI79GY8P9uoyz5eZrQ0Q73VtWNdbtLlHtbNqEi0H4YRA22btsnzRnUx\nYqPzQ9vHiJK3jeVoNNMK2WTMiB71jOe6LiF1ObqW1TVqo0ev8skjOLf0+Vv0wfNr5KZNB4gDPBdF\nSKLoUKSHink+nxV7UoqfgvX7iKLq/K33wbJYJ/GZ5RBvrORNxi45UNflJ/9UI8Ny/Dw7SuvRcynl\n30cTtSFSBn6ynWxDGwnqVT4AuKIJc2392icVw6n8rktCPK9AoctFOtFp8FV3IpJAsOA4e5tJdJRU\n+HWvR4Vt4n0qELEdClY0hiwnImJKjNSxUDJ0Lr8IgsMxYh9Ql/y+dVyio43o5nT7PQlUr/IJCM4t\nfdu2nNilvGvLTLp0lMsX7RVTIsMy/TvbR/xQIpFSE48jPb92X15Xl7Z7O71eLpNHeaWfyiU4SlrU\nm6bxYOcwraeL9twQvNRDjaIoCoKRMC8Jlk6EiADxWkrx5upe5AGA6y0gTy9FJ1hKl6SUBEUNj5IE\neiP8reRBIyttkZtrpILREX5nm3VuKBApASJwRZElnVfebwQvLYPpraA9OJyvSv4ibIiwJMIslkPD\nwXOR8WgzCtcM/M7kvQAAIABJREFUZa9E5wFwoqu8BU/a+p3O51vK7ZI/t0+H5CYiSPwdEYyoDLWN\n19qjDmRE4BlYuKbTOceSGHhOWybBiYw6DQbJhg8EAScX3SGpUE80ZwAV8AkgUR0qCm45AsV28dpX\nQwSni3QB9hwQUDeUBDMtvRmSBPWASAi0PoZYlZhrBCBKo9dSuiT5JO+R7il59jr9HNtD4PG8bGcU\nWWSfMA3AupgIjusMx037kGPO/mI/qTGhflCvNBrkQr3gEUX4VLdVbjWyr5IPwInXkojofl+btysO\nvbZsJQTRQYelS3tIojj/c6RNSUWURn9rnxJfojIigkTiFvUB24b5Uz7BUSLj55iWwOGfCiKeT8Nx\nLM/zE+yYl23Tur1MbUsEQjxPQ8c25vLdVR6U4ERyDQRyk0+jHtHk0dCtGrrI86fR8U+NciiBoqfC\n9ippYLRACY/fH3VG82m90VxyidJ4m3gPGlnyvPcGnvc6iBGc934fnJcEbAVZHT/tS43mKnZpNFB1\nSImterdvwYnXGmP+pYuSh3u15b3kFsLRpU2v6T/qhBKAKPJ8rY1KDlQ/XLdyUZyIhER1aX0pxdsE\nruEycVijp3QymI7zqw+c6YXgRCAcEQdGOtQr5jktyzswAok24KDy6EHxQWszKjJg4f33JgURHJVo\nokcTNPK0U2r+NQTLiaI0np75VCei67l8avCiCCW/K7FQgpZSfvmLHp3nJSgqwDB/FHXSuqyQJSr2\nBb/7b//Ue6UeKND7p/aV9xEJopIrHTvqc9Tfioe9Sssbz197fJS8tc1vve+IYJA0EHu8vgij2rDP\nr1E3o+gKse1ae3MRIDqIufvhXGEbiVEsK8LqIgkOvZOULievglLkeZJlqrerHi/z5upTAsOy6PGx\nDREg8bq3IfL8IqLUmxRGcNr6qm3CtwGAkgU1RgQ2NVZqwJhPl0LUI48iI2oo2QaNqGi0oI0Iab8p\ncdG5ofqvhEv7Oj0Agbl25Eijn4uukRxqX6q3zLFTEFcdVTxR/KCuECNzjtXd5Z1x4lHIz2tJ2XsS\npK5RkFz05tYjIiu6tEq7Sj0mWVFyw3bmojvESMVFkh3tLzgWZRGcaLLqDbMz/Ya1Y6JDyUsOtL0j\nWZfm08+obr2HqJwIXAeC012i/tbxSKlpqLoAiS4d6YRUg0Zy4PXR8yAYaRme3tsbgYZGErxM1WuS\nJSVWETnXcthHnA9arhplzkErZA8OySp1SJeMqGPEGSV30TXqoBIT1Uvt/4jk8Lxe71V6xom3GPB7\nHm9pH/PqvCLusHzavJTi125QL0hGtI4oSkTykCMkTBNdY/m5ZTBtX5Qmwuk+Ham7ERwlCxEwaKRH\nDQwnvRILnlMjExkNF/XkIkPKdhMAWV7OuOn3z+CZ9SmqDxpd04iJn8sRHZKA3ASP6tPQLMeZJCdH\nkrwsAgRBS4lwFEnQ9DnjqaQr0lOdf8xDrwv3XcQSlXqoPna8f/YXx5iGJ/JgVbfYv95/1BfqUDTG\nJGL+Sf3rXQrCiXsTnPfO37bcFC3d5MhIRFpyZd6SPtdu5olIE/U/R2io6+qYUYpdooqMeuSl4wYv\nwNuFYMNz6ln598izZv38zfORR5cDpqhMAmhksHqVgoCrTUhiXNQbTulyXCIPIpqMEfHhmHOykqx4\n2/Q7DV9EjjVUrOQtIlsaKXDRtqnBVR3WNjGao17g+bOICA77KBex02VF9g/Hi3qgxkfLZznEKF7X\nZUtKNL69yyfBiUjuSYhuIRldiEvXNLekb7seOUjRofjStZ6I4Oh1sfX3wwfrQfSvGPzc8/OzLZfL\n+tXz/tcMKZ1ef++vkX9+fq7zmL38DcJsNrPtdmuz2axxza/zrxvMmn+X4Pk2m83F3yhst9tGe5fL\nZeMvGSiebrlc1n/j4HX7tVL+puFRxP/iQF8N7n+P4f2pf7/g8vT0pITbptOpjUajxqvSj8ejPT09\n2Wh0mgb7/d52u13j1fq73a6+fjwe67+EMLP6L0LMrH61+mg0qst4enpqlOX1efrJZNL4u5Lp+fXq\nXi//RsT/lsR13dvk7RiNRrbdbu35+blun9lJ93a7XUOnN5tN/dcEk8nEFouFLZdLOx6PllLy17bH\nnftgMplMLv4KYbvdNsaef9/hfe6vl59Op3UfeXqWbWZ1X/vfYPhfe1RVZev12ubzuR2PR5vNZvX1\nxWJR5/dPHztiiKcn3g3ydnmNMXyr5P56oO0vCYgtbdevlTkajRr4wb9ecJ32645T+/2+8ZckKaVG\nGT6vvC5ti2NGW1uPx2MDcz2N8oG7yT1Yk0ZHNHKinpB6ulxm0lAvrzlDzJUdRXE0j1lzozKXQHgP\nvNYlQhXV25t8As9MdSi6boj06dhq5ELlNR4QvRGtg3XTY6FOuq7xu0YXWBbngwvbES1Pef0ujGjy\nHO8raocVFMFhJJhznn2pY6n4EPW3LjGyb3P6x3xej+oKMUqxrlf5BDjxEcIxdWnDkvc6utajEUyf\n4/y85eD80fxcvmX9Wh+jw7p8l+6ID3cjOBGxcdG9CwrC7IQIsHLkIVpe0jVyTxctb2ibuyxxUQhe\nuXy9yCcArqi/I1Kpe1qi9Gq4mI9pr03yaC+NrqGn1NynQ2OqyxUkO0qUon0cqlu6bKZ5mZ5Gm8aa\nc0T6oIg9OLwXdX7YnySmignaX9GyOIkg+y7nmGmf5wg726XLWHeXT4ATHyWqJ9HWCto3zjvP3+ZM\nvfcREZG2Q5dobyE/uuTdgbiVR3CiyarAQ0822r+Qy+NgxL0POWKiER5+UhGVdLUZTb2e+6119SYF\nAVeuf3Jj2tafESHK6RINEg0b8+sEVZCIPH0lEDSujLywDPV4UkoNY6xRSc4BT0ej2qa/bWTN05dE\ncJQsRvOQRIZjQPxRIqqGKRq3SKf0U0kU9YxtVkLVixSEE48onF+qP7koqtq+aH+WXyfpphPSByF6\nK5FSDGQadSZTqQRHDU4U3fBOoNGJSI0qlCpCjlTl8mm9/O2ijFzzRu2Iyu9dCgWutvGN9CmXl8Yn\nMnptdemSEMElmpz0VhgR4ZKPTnI1dmqQvR4SI78vrU+NdUT6WRbnodYnS19FLFHlDAH7S8mKX/N7\n97H185HDw/ORXvK6klSNCHFc2Oe9S6E48YjC+UbHKaXLbQ4RBtHWaLn8jHCM9bhEONQnuWmL4HwK\ngsPBzA0qgSkK6TFNFH5WZkwDE0UAmCby9FShaAByyqf3E5Ga3klOwcAVERU9r9/biI/qSBvp4feu\nYxZNZHr5UbSE+zOUmCgBUdLvdbJ8goYukSiYqCFXIPR7tzv/Cd57Hbx3vy+OixoaBXzFiwiTFE8i\n50aJEcvPlaH4M+BEWdKG86pTGsFpK8dF7aFiFkkz9T+a421OXoSZvId7E6FUGsHRkH+0Bp0zSurR\nEBCiwdJBYR7dm+DpcmUogKkSpfSiSHpf2oYP8chcCgWuaKJrn3Ls3ICokChwLNX7ztWr13P1aF5E\nPy4iLyQ4JEG6hKVl0eB6vhzJ12iOtz0iUFGEifdTGsEh5ijAs/8iMpdSahASjcgp+clFaTjGXiYj\nZzqePIYlqnIkcmJdFDf0HHGI1/ipOpVzwEiqOb/9es4RVLtFPGId1Fu990j/XxspSiUSHBU1OC4a\nxiMQKANW74gDHSmAfkYRF36qsYiuRZ5YtL6eU7RepDDguoVs5MYv+n5tvLWOyNAoeejafhpbGj6N\nMmokJwIh1d3IaEeG2OvlPWoEI1eWFbIHR4lCNOY6vmoMonHR9AR7kkgaAyU53vdMH+lQ7/jgUhhO\nPJLomNEGRKSEdo5z3kVtmGIO9YeOk19TnNJDgw7RPeh5dXqozyREbHMUoFBs8jKKJThqSKI9BxqR\n4SCyAzgoyjKjTmN9HExdi9cyWAcHxkXBivegYBnl71UKBC6dyH5O+1ANRDRpleyQmPp5/YzGqo1c\nRXVF0RUtgwaWnpcub6nB1CgAgVIBrG25zEFISaCSeytkD45GaQm6GlFhhIbjxGWsiICwb/x3rgyO\nty5NcrypIxFe9SIF4sQjiBIAitogficJUExQobMR2Re1QywrIvW5eRHpHvFSMU113OuMHAbPozZa\ncO2ujtTdCA471CXytjQspgxXO57lMJ92nne8DhDLYR6NJHk5qjDRfURtazOMd5fCgCvXZxHB1L6/\nZhiiMVPidM2rbjNAEVmiXIv6uL7r+jRJD4FSiTgNM/U9IjfqZeYM9fl6EREc3UujhoXj4Oc1sqXE\nh3pCwujlKVnO4QPrUcPH9BFW9iKF4cQjieK+ziMX2hae83RtNpDEmDbVf5OEqKOuS64Rnirx1vti\nnRFpYjs47yJM8TapXb33UvjdCI4CfUQEvDP85l241yDaR5MjUH49BxgKOBHIsd25cnLkRhXvw6Rw\n4GojH2pEcnlIFHLkI6XUmMBKhiMd1noiw6aiOq/3wc8O69UXyyU8F0VvFISo7xGRP58rYg+Ozl11\ncDhHoygKjQPBm/NYl/PUs430x8fE68jloxc9OEJlCO2SEt3ICY+WrPx8LqrsZUcRGa2XBMLnMvXd\nr6kTz6Vp1qnzISI3xJSIpPFeoygysOqukeK7Epy2wWhjeyQ4ZJL+m4PFjtQytbNz0RoaC21rTvE4\neJpHPe/epUDgyvWVehCU3Lqyjqd6JZonagdJq64159pDUR1pu4eoD9RgR0tYek4BRw/OJwK0kquz\nDhcRwSGB0/kdLUnp3NSoL89rnypJ0oiP18UxUMzTMaCuDgSnTInmcG7bgv8m+Y3KaHNmPB+JjZL7\niHgx6qL4p5FGtlftpN5XVIaWR0wSu15mBCcKu0VhsCjsHhkVGgdlkToQEbvW9BxkBRyWRQXMESb+\nvmZAe5ECgSsH8Drh+FuXIDUfox5RdEYJhUpuIkdpcsaJ9USkPFd/DvhoRNsiPeos0DBHES56Wecy\niiA47AcSkUioA4oHzKtOF/vSCY/uo1HcYb/zmnqwbFfvmFEgTjyCRPaDn9SJXIRGy8g5P1E5UWSH\ngQDPy3JYvhJq6qemj3Ay0v8owpnSC0FTfYfzUeYenJwy6KDostI1I6RAoGE4HbgINKLBVIOiQBkR\nIlXINqXoVQoDrqgvc+ejflXiEE1yJcg8lyNJSphz13Nlazuv6cE1gqdpSWCU4NDwMz3nnd63gFER\nS1Q0ABqNiYiGAy3ne66f/LpGcSKc8fpIICMyHnnKbaTsrlIYTjyS5MiIRhF5LXKYSFa8XLWRjETm\niAjrZh1qa7k6oqTc07OcnD3TVRLiKNuqdWi/nedduQTHB4Lgqp3BjtNBizqYysG8HLQ2gqRsltc0\nmpOLEmg5GuGJjF5v8gmAS8lL1J86EV006hYBSxdCFdWTa6fXF4Vto7y5+q+J1qcg4ueiZSwlAQ5E\n9L6wLl8EwVGyQoKjpI7ERyMr0XIT9U1D6/RQdSyU4NCoECeYlxHr3uQT4MQjCHUwihTr2ObIjufR\n8+qEUdfYhpz9Ynlqf3N2WIlKW9tod6O0xBZ1FIolOJFByp13iVikrmWyAzWUrKBD0qL16SBG4KZK\nFIUTFUyjqMFAcF4nnKC5a6pP0bp05I0QLBjepa5F39vItuqK6l3OU+M9ReXqdY3URMuv/jtavtKQ\nMr+jjiIIjo4TjQ37gumu7cEhqCs4U6d0/LReLhXm0raN/d3lk+BE3xLN61yEMKXUWD5lfs/r5yLS\nzHRqp3IOHue/581hE9Prb3WKSJ54T4o5GsFiHnU0rMRNxspYc4MRgY+Gh5mfnRUBeo6lelnqfXna\ntk8lMrymxvcaM+5NCgauyBBEBMZ/p5R/o3REqNWjiepUIhQBE+uPSHt0D5E+5K5FuhWRs4icKNiw\nrtyeHRr6kvbg8J4JoIxkBaB6gSc6jgrUjA5pmF/3GehyBdNqdHHAifJExyoX4VDbETk3qiNMrzim\ntlGJimKlts31k/rKOtTGRXaa11i/pqeec8lcy7y3I3WXQnXA1cCot6vrdTqg+jvypDQ0Fw1eZEgi\npYiMECWnnKqEqvC9ScHA1UYWcuQgyh95HZEhiUBH64hIVdROptFoJNNF6+hRP/C7AoSChhpO9k+k\nl5yLGdJTRARHvV3eA/tNz6k+qIetxEf38jCdjrUf15bldf9U71IwTny0cNz9d47g6HX+zpGfiLhE\n5FjzRtFFzoGI7Ks9VKcrwjLeJ3U+pXSxZyhamvJ0RRIcBX+CqUq0LBAxRWWd2uk5I9FGdpSJthk7\n9chYd0SSBs/sNonIgvadTkZNw4mrIKCi3k/Unui6lx0tRea+dyVtuXQEDL9PNcJRVIKAEi31Rs4B\nyUB6AAJz7WCkhv3FPiPB45iyP/1To2IEbeKQftfx9n7WPTrR0qmn7R0rCsSJR5DINvh5CqOizEfs\n0KWeKPKX0uV+whyuMK222T9zgQPFVy1H03r7lbTzUx0pv0fM2zKXqCICogMShW5zg8DOoeKo0mhH\nex30wFiPgj7bpudyRIzSRpJ6k0KAq22Sar/pBG+L3rg+RJHEtvFQQhIBVu58rrzc7+g+cvej4KD3\nzrmk57TNNNj8rUb33sDzXgfntobttQ8ItArq7Gslh0yvXirr0eUszavgrnrauxSCE48kjLRFGEV9\ni+Yq7VG0X0znpRJ36o8GAvg9d02XVyPcaCNRahO9XI3gRFsB9DzIX1kER8mLKgM9Lh0IDhzzMowb\ngfT/z967R8vXnGWBT/X5knT6hEwCX0AgJF9gBm3A5Dv2mYgKwkQgyLgQgTUrIAhycQRnGEdxFMVZ\n4bYUlgICy2Hwwk0JEAIudIAZBTIocrGb/r5AaBMCSUhiEMKEgZye5tJd80fvd/+efvqtvXdfdp/e\n/atnrb1O9961q2pXvfXU875Vu49OMt5ElJogPRHDz8CGqB5jKgydIzjNwYNNBaiXzvsc47YtaR6e\nePEmevur5JOqV1UaJZwUmSh0AvQENdsmjx/N14sW8GclqqJdOiNwvGfhdvQETfGMG+e5zTVCZsSu\ndurZHEd7WFCpmEpNGCdDx3jiXOCNF8/uFJzWEwFVQiTlbNl93rzFYt2LOHP0V/NV50qXuCUKU+an\nUU0NFLCtF+m7uUSljcUdqJ3pdZB+5vvUsDRMljIcVsh83Wt4rhuXnRJs3KGeYDopOkxcdQLHS5Mi\nmZS9ef1q8OyjikiqPCbNv0qc2TlveYXPx5gOQevkbPXxogQ6rvhZTxE6PtahkwJPHOpRc1uqF6tE\nrf3L4kcFC7e/Ch3uD76uYtSzm9bRYZ64b6TGn85LMW5vQlYe88QL5+tFEHU8q3hn+9V9Pl5gwEvH\n4iQ19+m8x2NQHQZtuyJ9d3/oj9UfPxwrSx30PPi5Uzm87ClnTwzpxj0VTqqCPcLS+7i+HNnh51Nh\nk4krjdREr+3q3eNF4ey8DiieUDiPurxTXlTVZ7WdlKDxyubQtURUtuzR8wJV0DA5aWjbaxsSAZ0Q\nOB5J8/PpvhpuS7Y1b5+EjnVOq33O6Zjk1X7YBnkCVK46CTrEE+cE5QIWMN4+QbVJFbl8zvLR+Y3H\ntDojKt4tvTdvqYjR8rSe7CRofvzM7JixPavDpvl3NoJTN8l7EwGrRR7w2mmsCpl4dAJQovOMSD08\nK8fuUW/Zqxffp89VN1m3gg4TV0oIeMLDzqtHof2sfau26EVfVKRrPzI5Nal/Kn/7rNEgj6A8MeI9\nN9+vAkfrrvkY2vasjnWoCPTEh11j71ftw1s257FeFQHzJjvdY8HeLbXxxuRzcnSYJ+4TVdzujW+N\nDPJ4V1tUMZDae6c8xnauQQDPAaiam/XZtN52nc+pqFEhY39V3LXNMz20hOl0uvF9PB7j+voaV1dX\nuL29xXg8xmw2AwBcX1/j7u4OALBcLjEejzEajcp7+fNiscBsNkO/3wfWLbpV5mKxwO3tbfn39vYW\nMUYMh0NMp1Pc3t4CAIbDIe7u7rBYLDAejzEej3F7e4vlclmW2+/3MR6PyzJ6vQdNNhqNyrwA4Obm\npsyHYc+WsQ1rP+un8XiMEAIA4OrqqrxmbTocDgH4bWp52bXb29vSxoC1nZndWHmap5XD5Zn9LRaL\nMq/xeIzlcrlR/zrc3d1hNpvh+vq6HA8AMJlMNvK+u7vDzc0N5vN5WRaPF7NPtjN75tlsVj7PcDjE\nzc3NVn3H4zFWqxWurq4wm80wm8022qPJs5wLbAxfX19jMBhsXLu+vsZkMkEIAb1eb8NmptMprq+v\nyzZdrVYAHjy75WffV6sVbm9vEUIo+83SW1/e3t7i5uYGt7e3JU8YB/X7/fKc5TkYDDAejzGdTjf6\nP+P8oVxjMHvi8W3Q+WE+n5d8ZIgxYjweb8wzk8kEw+EQ8/m8vNfy0nJHoxF6vV7JAQw9x5yrY97y\nNtu1c/a8+hzGMwbjruvr67LcxWKxwbE25trEI21lzA9sHb1YLMqOub293SDi29tb3N3dbUxm/BkA\n+v0+hsMhJpNJSWZqRFdXV7i5ucF0Ot0QJ1dXV+j3+xvXrFwmfiN7YG00i8UCIQTEGDfEj3UcG4dN\nXtaJOsFm+OB+vr6+3hCtagPT6bS0LesDa+PZbFbaELApALi/vLK1HM7DPlvfAw/sjNOm+psHuRGE\nnbOJdD6fYz6fYzabIYSA0Wi0IeztXiUirgeAsj3M9m18hBAwGAzK8geDQZnW6mbPXzzDJvOeKUzA\nWFvNZrPynHGETRaWbrVaYTQalTwynU437jeY6Li9vS3FyNXVVdluxgvKQeyALRaLkm+ATWdtPp+X\notu4SO0z4/zA8xM75zaH2ef5fF4613bOxu9isUCv1yvHvIHtFljb7nK5LG3M7jeBrpwwm81wc3NT\njmt29A1m18Zt+gwG4wWro+f4MPeyQ2B2bs6H2TmX1ev1sFqt2uWZNsJCGgLnkJe3lqj7BzTMBwod\nc6hP1yK9MJt+rwqzpfY7eMttkLdX+BmrlilOgo6Gnr3lPW95htPrfhs7H6P/yqSmgSwzektHXjhX\n62l/OT+vXAMvxepSEtskKGRd1V5aRpOlPH0GXhZDR/bgMF/oMhD3HyhsrvtiNHSu6Yv22FjK8vZI\n2H3ap6nlc28/zknRUZ44RyhHeEtUan9mA3aO00O2R+iLLPZXl4J0GcrjE75H9+TpZ12qSm0R4b88\nBrleOtaKdN38HRwlU4au3fHE5RF16q832ekkmcqT01ijaxksrBTe5OaVnbq/VXSMuDwBoagTGjzI\n+B5P1HCaqld0PYHMf1XMpvrdE/lqc5yfvn3A57guVeKb//Izqij3bL+4txMCh8cqv7aq7cltzATM\n93GbKgfYPSp+VNxye+reB25vrpe++XYydIwnzgXK82pP3nUVMAZvL5zn9KT2d2p9VLTHmH6zs8re\nlLM4P36T0PLnc8o56hzwWEDLm4xb2YMzKsJTHNKy8ByHc+/u7rBarcoQru29sHS2jMWhPw67rVar\n8p7xeFwuQcxmszL8Zvdafgor4+7urgz3DYdDXF1dlSG3u7s7hBDK+23vgu2lsPInk8nG2qSG/zJ8\ncFhe14N1nwyfM1uy+9fcsHmP9T0AN8yq+1m8fT+2b8xgYVmrky6xqd0peN3dlqmurq7KNXZdRp1O\np+XeNMtf7d3CwMCDJZkRLYfc3t5iOp1urcPf3d1hOByW46prGA6H5dJTv9/f2Oti+wD6/X45FofD\nIXq9XrkMEGNEv9/HarUq29T615agjGN6vR5msxlGoxHm8zlCCKVN2b7BxWKxEdo3rjIuMZu0/YLX\n19db+xcyzhs2vwDr/uv1eohxvVQ5Go3KfVUMHne9Xg9XV1cIIZRcwMtUMUbM53Msl0tMJhMA2NhL\nZ0ulk8mkHNdWH/6s845xm8L2llkaneeMH1L7HvnZ7Hlsfw1vJ7Gl4dFoxPNiu5vP2lBN7AGZUuO/\n7LmAwnf6Wjjf46lW84x42auubM+jU1XMKljPe0o6dV+dSm4NHfXMvGiLhlO5PUHLARq50f6z83XR\nOO0vb5mh6o0atVcuk21C33LSfL17vMhklffGHqF3X+rZC6+rM29RcTvzsxov8PKReprMIXyeeUK9\naUgEx84Bm29Fea/Lal9w3XMEpxvQsRbj5pwW4/ZPWPD40nHubefgPJjjNMKoZfJ8CoqUaF2Zg7xI\nN5/n8WAH58l2b/d7Y4fHaIzlmOjeEpVHutw5XgN7afV1bW5UvkfPe+mssT0i0aUAnnwYKUHDRpQS\nPidFR4nLm3gN3nmdZOyc139V/aD9FeP2P62sq7MnqNjGtb4GJgcb+HreszUlLX0+bxLmz54Ak0m8\nc0tUzC32bDyeTWDYNRYczDFM5Hy/Z1uWH3OItT3XKcVLnk2cDB3liXOBcpHyhNmGN/dpHnyO50ez\npTpnLSU+dOx7wQO7xrbM9efvPMfyeOLlJ+YeS6dzM1+LXRQ41mjccNrY3FE80PU7d4JOBJaHKmol\nEy9S5Bmgkr8agDdRallc7yxw0vAGdxMRYt95QvYmaU/8cpqmeXv2Zvnw/er9c2TRIx4mMravuuf3\nJknPbqvu8dLxta4IHE9AKJh4mZRZ1CgJqwBRsagRY8vL0vJEom3PwoejPOpQtY6O8MS5wnNeDGqP\najPMTzp++f6U48xC3cC2qILc6kvj21314PRaD3XG+JlYBPGqilcnS1/Yfjd/yZgbjRvR84T0mno2\n2hGpjmZDYDHDEwd3sJIj58MExcbheXGeCPPa4GToGHF5AkP/6uD3RKknJjUPncy95SavD6vEmJaR\nWorwymZxw0KKy+R0nh17xGn3cZ76XJqviLpOLFHx+FbSZ2+SuUYjtkrCStJ2nj+rKNE+0MiPTiJ1\nouwk6BhPnBtUDKij441LFdWah6VXR00FkebLdszcwPbK9VHni8ePznUcnVGHgLlO51ErS9Pxs6CL\nv2TMSpEbPfVXidtTgNZhqYnOvntek6eQdbLRTmFj1clGCZPrw52s+Z8MHSGuOoGSEjgqilPgwc/n\nPFLy7k2c0a6kAAAgAElEQVSl8QStfVZPhcWL2iHblPdcHml4Io4nTj6n48zOa8TIG4ddETgqQr2x\nygJFBShH2lIeKveBkrlOLCx+2BlST5idJI4knxQd4YlzgzcGvSVl5X6Pd3Tu0uVNS6vi3BNFMab/\nkTXzgXKRLimpmNL52J6XxxPbvYolrpc6cZ1dokpNStzgDBYSqUmOG8UjblWTdp5DxzrBsSfHHaoG\nokTmGTl7Zpx3Jq40PLGgUQf7y6JB15sZKQGjeXCZem9qGYvTs63YgFeC4smVyULHgifEUlGbVNSF\n66feY6otvTYrnqdVz+pYB7cvtzG3LbeZRmS0r1gA8Vhmm1SByMJGBRa3NRO815cnR4d44lygduCJ\nCJ3LtM89oeEJGivDzrGdaNk697AQUfHD86FGMLUs5lpP1OjzW5nKz8q9Uma3BA4/mOc9coMwkbBq\nVKLmTuPGUuGRCvsxwenSABuVGoaKIUPqPl228iaT1tFB4koJCvusg7/KO9L7+bonoFWIV4kmtVEN\nAXsTl1eeJ9j4GbyQs9XDu+YJtxg37ZjJiOviEVVXIjhKvuptapiexyvfw+2g/MOCxz6ruNHJwNpX\nha7ynPbbSdFBnjgXeLyemshVOKs4VhtSB4rFgDeHWVkxbv/fKOUty5frxnOs1lX5TZd9dQmY62D5\n2TnmSBJD3XyLShvS6wydGPQ6p2NlzMTuGZQ1rC4nMbRsr3PUsDQiwyLL88wsT1b9J0FHiMvzWAw6\nGXueNKfVQe2JZS4zRU5KXEoMXF9dxmAy8MQL10E9tpRo13biZ1bCYi+M89HwNgt7vpfLaJt4jnWo\n4FARwt4tTw7adtwvnpjRqI8uaVkbKrmrEOJ+U086O0LdhI7lGLeXhbwVCh6znjBJ2aWWY9+9ccyf\nOY0KJ+ZXXQnhNOpQMH/wM+hSFOdj54p03dtkrOuAOtEwAejkxGFcJhPuKO4Qbiz1urSBPc9KDxZF\namRqNF6YjuuZiga0jg4RV1UbexN8SrCoJ5Rqdy2P87Xrei9fUy8mZUsqcnhy1efQQ6HXuL5cjhc9\n5GfWELbXFva5KwJHn93zPPmw9uDPdh+3F/cpX+fz6p0yyXuRIbYDy5NtIvNEN+CNQ29M23md01JO\nCOfPHMI2xOD5RcWFN3/FuLmc5fGOJ+q5fF3S0rI0OsoOhUZ7qF26J3C043lQq3eb6hxLr+TLjeQ1\nvObNnpLBEyWcN5OgN8FyffiaPt+9oIPElfJMGCqGOU2V6PGWaTzB6n22cj2vxssvRShqj1qeJ85S\neSo5eWvdSm5e9FPLF4HWiT04SvLMNSxUmGS9yIt60txWfB8Ttrap58ip3XF0SO3r5OggT5wLeFyq\nA11lBzxHxZiO1qoYVwGtvObZrOWnjpjnzKmNswjxytL5WiOcWoY9k461TkZw+MGtkXlge5EZL+zF\nRKxG5HnIPAGwV6XqkScGFmDckfaZjU072K5xWibbeyGtGDtJXCoWqq7bd40SeqKFbSwlblKRNh3k\nbDOcj9oS2yrblZWVEiFcLteN7ToltpREvbGjZKvtyM5EVyI4zDUaPdEoDvenRlHU/pTYWfx4XOIJ\nWJ44VBCnPOWTooM8cU7QMZaaN+y6jncW3oyqOVDL4nooJ/C2C4288LzHcynPXyq29DwLJ64fPz/P\n+9wGPDZjFwWOF8pXj0cflDtMSYsblBvTGlLJhhtYlamnXJVguA48cahxqrBSo2XjORkugLhYnMS4\nSRbcD6l1X8970shHjNuvVqvtqJBK9b2V6ZGPJ3g4P76u9yoBeiLd0qbsWO1T28Dz+roicJhANcri\nOTicjvuRSZxtgPNS54f5g8Un8x9HkD0+VMF5UlwAT9wHUk6Jt8yktqJzo4HnP51zdG5jzuB6eNES\nzUdtWMeORilVBClv8vhSzrPP6mDwPejq7+Aokas3y0Sg63bWMErIKbHB6lMnCu4cJTFPbHGd2Qi1\nAz0jS00sWeBUQweNhm11cOmgr5rU1QZTwsegHj/bhUblNJTLE5mSldpYinD4mTWN2rl91udU4uV2\nSRGxPlNXBI6OyZRw84ib+4PHuXKS2p7X7tyP1o4seuwcc5E6XCdHx3jinKB9HeP2iysGb/zymLdz\nBuZBLw/Pxr05UvNiW7W/nkNg6XmccB09ca+cy+XqGOP266TA4Qfkh1RvihtSO4/DvZpGQ3GWXj1w\nnUg8kaOkqGFFFWrayRy18SaZTFxp6IDwRIoOjBg3hSwLYvUcPNGp13Qgevam/awC2pv8VNR7Akfr\n7uWlf/lzSvixQPQEHXtSXjsVeXfiNXH2DNkb9aI6Gr3x+pfbJkX86vhYn3ttbPeosLR7WDRnR6ib\nUKdco/aes2JQG7D0fB/nq1zCvGR14DyVP71IptWD52jlPxbkzJWec8Y86UWHeIwV5XdL4OhDcUMr\naXjKlDuJiZjv5c7iTlAR43UQN7YZqJJcSnB5Eymn1wnE0pwUHScu9QZ0MtIJnoWnJ5Q0bwbbqJKN\nno9xW/Rqv3MaTqsCmJ9Noyx6rqpdtC7aVgodM16Ep3juTkRwvGiwihElby+9jm2eGOyzRuk0Uqdc\nxOXopJP6fFJ0nCfuC+qce+LD4yn+HmPcsjF2njXKx2mVBw06h6WEFQt+tT2dK5nfNBKpDhuPM81P\nHQ2KkHbzd3C4s/Sw8+rVckN7xMMiw5tMuPPtM4sqVdfqZfMkxmVafdRYvO86Cd0LOkJc2l4GbnPu\nE76Pz6Umc81PPWwV3kxWTA48qamQsXw9geM9mw5+FSn8fFpffW4mExVNXBZf82zVixx1SeBw26qn\nqJOFtYG2iY5pthGNAHncxO3MwknroHal4vik6AhPnBvUqY1xe2nb0rHDpPNdjNtvj9pndfx1HlQ+\nUBtSbtD68ThQccJ1UJv3nAF1mnQs8HOr0EJXl6i8AZsKW/F1Vb7cEdzZSlhqXJwnG4OqbfVmtcOZ\nKDnErKLIIz0u56ToCHGlPB6DDm67R/9yP3jXefDzgFXvSAcl2x0LXB3IOqitXPZ4NJ2SktqeijIl\nRhVTBk+wewSpQpzboRgjnRA4qf6zvlYhoQJWo4AqdlTYMPdwX1t52v7cn8x3bOua38nQEZ44R2hE\nxhMKLEZ4fOs41rFoeca4/eKK55Bxnmp73nyrgQYW4Dr3sW3q/Ks2bvX3+LbK9mMXBY5OSjrYuaGY\nWDwPLBUxUcPRDve8bauPJ4p0sjEDY2PQiVQNTMvVDj0JOkZcKnB0UlExYfCED+fneVI86XE+2rfa\nh15kh+1On0HFrU7C6qGZXXP5GnHk+3g81QktbhseP57Ip3HXCYGTiq7Ys/Iza1puC49/NBSv93Of\neHXw7rX6WFt7keWToWM8cS5IOe8a/bC0Hpcx11k6Hbs8pj2BrI4al6fCn7krNe9avvZX7ZMdLRZc\nKuC5PhoZdwRU9yI43lIPiwA976lMJRdrLO68GOMGWanHz16sdZqWq1EX9eytDPbwNB0br5IrT8In\nQ4eISwe8koQKWW5P9s41P7uesivrvxgfiAb7zGWoKGIC8Lwx7+BrKtSUxPTZlPT4Hs5Tn53bw/MS\ndQwosaFDm4xT/asTgLWp8o06XV4UVvNlTqpy1NTh8USUJ95Pgg7xxDnBEyIxpqP43M+WTjlKeUCj\nKFy2/VXe8US4d1gdUnbL9fWcIb6P53qNUuk1FlHcPrFrAkeJVgnGHlo9F6+h+a82HhsHf2b1bNCO\n5A5Ro0h5/FZ3fgY2AC8ceXLSirFzxKXt5IliFhwaqWACSA1uT5R6nrmKEBZRGvlRMcbXUzavwoaj\nRioyLB9uF/7MTkCqLT1v05vI1ZbR0QgOE6vZBfeN2oQSv6X3eMgrS50qzVtFknKS57SdDB3jiXMB\nCxUGT+AqHlTE6tym458dLeU6tSfmqRT/KffpX647cxbzMHMh2zY/jzponDd/prm3e5uM9UG1c7nR\ndRJjjyZFKNpg3OmegXl5cSdwB1pn8STA+ejkwB2dMpqToyPEpdGF1GSg13gws914k5HdnxrcBhbP\nMW4OWC9iwvert8Jpve8eMfFzsh1r/bW9WAilhA6nV2GkIrGLAkcdkRQ/pASOF+VJiRu2RRXb2q5c\nJ2/iYTu4F2eoIzzRBSg/8cFpdD70xE+Mccs+NcLjCR0dBxxRUudM519vTuT5TvnLi854ZaXEDY2D\nbv6rBo3U6MSkjaaTmddIKXWqKlnPqeDRaACTnIoWnWiV9LTuPPHdWxSnQ8TF7cNCVImf+9Du44lD\nvR62AxXWXKaKUCYkzZ/rwYKChbGSA4smPqeEpLai93F5LEyUNO2ZNFqkBMn14PpIne9dwNQdSvTq\nMaaELwvDFKd4DosKH253nmjUg1dxrvartncSdIgnzgkqSLmvY9xcOvdEjNpSjJs85Dl6nsDm8lLC\n3bNfHe/8V5045gvPMeP5zxNMfE65lIIV3RI49hAGbih7aBUJ3HjWaXxoJ1SFjTl/FkkqZvjgDlFS\n8ozSC8lxeWokJ0VHiEu9BI1SxOj/BHqTiUgncY2SqHhmceAJISUTFTFKEJxvSsRr1EVJTaM/nJbL\nSUUC+B7vrz4Dn0fHIjjeGFXxpgSsn1OCpoqrPBHDduJNLmwvyj8nRUd44tzAHMDcxM6w2pjdp0Jc\nOcHy4fHJ49gTxymBbmA79oIMKrR4nHhzoTpSyq+eM6b5UF27t8lYRQoTiKdqdTJQ9ceCRj1nJTAV\nH56S5b/a+J5Q8ghPRZcam14/KTpCXJ44VKEQY3T7JjWo+V71gDxSURtTEaG2qh6Let1MPkpGniem\nE6UKEc6fhZF6UEw0PIl6glHHHN9D9eyUwOGxnxrPPB5T3rS2qeav96gD5KXzvNgUp5wUHeGJc4SK\nG28ssy16TkqM6aVwtSWdTzhPzy6rottecIAdPr1XOaVqbCkXefOyE1jolsBJNYAqV2+C8hpfBY2G\ndXfpCI4icXmqZFVQeREfrqvVhfNhtXxSdIS4vEiena8aRDzgVUxqNKPK445xc3+L9hXfz2Sl93li\nxLMLu4+9NS8vLdfaRPPnZ+O8PGiURiM+bOtF/p0ROMobnjDW7zpJeLxTxV/cXt6Y9/hNxTvbYhY4\n3QDbEvOBJz74e4zbPw/gRf68uS4lxj2RovnqtVQe6vSxLafmU3aK1MaJRza4WctEFyM4qUb0GlU7\nwhq5igSYJKwR9Zrlo+WkDETTKnF5BsOTUOp5NCpwEnSEuFQ4VtmHtq1+90KiMT4gIi5Lw6wqKpRY\n+D67h8tNRRRVsPBkynVVIc919CI8SoZKLDaOrE6WVp9bJ2RDca0zAqfJGNcJKEW6qfHujf1U2V50\nRtucy9d+PRk6whPnCB5LMW5Ge9UWvKhgjJtLUepYVXFgKjiQmq84/1RezCl2nzryOl50vlWusnPq\nZGo7xa4JHG+gqmhR8mhyaKOnvCSeaNiAUtGhKnJqWs8UwZ48ehNjZ4irSZ/H6O+PUVuwdDrYlFj4\nfIyb/xaCBYXaj3pUqaiMiiQeCykhnYKWlYrCcD5cJ8/+lVDVSyMC6uTv4LDd1I1Xfv463klNKil+\n4InC4xG2R3aQToqO8MQ5gfvMEyXa3zGmfwzW8tNIsJ1P2TM7UXbeu0dtNCXMOS/mSo1aM1eoc8/1\nZOdf/3rjJV6CwNkHXghsnyNlfKkGbypeUqSVItyT4QyJqyrEWtdv9lnz4MgDp7HyvKiJEgoLg5Qw\nZnJicuHPHJXxhJASWIzbv5WjkSAul+/nz0yi+tycp/eZRQ+3S2HTnYrgpMZk04PboclYV/tscl9d\nlDJHcLoBHn8a1WUxEKP/ezeWRlcJvMifigS1HW+lQdOnIkIs0rh+yrUandIlqbqgg9bLaa+HU+Ac\ngjrBoR2uhphaNtn3OCnOgLh2aRvtJ2/iiDFuTQbshWtfqnjg6zzQWHxYOZyGy2LC0KUuFUbehJUS\nP0yWLNrYU9J28ESTEqfmy+V6JCkE1FmB4xGxZ2869pvwhTdJNK0D3+eNkSxwugEdXzFu/+irCgDP\nweDx3sTuPEc9ZXOpaCGPc+Y95U7P5mP059WUgFdHqmJuzAKnTbAKrQo7H3KcFCckrrpn3re96pYF\nvD5KCQgeoOoRaRRGvZ4YN4WGigWO6vC99uyeCLP7WWRxHlamiiYlVL2m6TkfT2xpXl2M4KTIU22v\nySSyq1PTdGJqOhlY358MWeDsBY56qLNgYE7i/t0lkl1lK5y/ly4V7VYeStnwPhH3fY+YBc75QZc8\ndiHG1nFk4trHaL1QZCqdN8i8AanXdC04Rv//snihWhYp2jcpEmAR4i2fsvfGbWd5ctTHW0piwtIo\nkQoZA6fhOnj5e3lb3WLcihi1+nbDsY5TkfA+9r8n2Z8OWeAcBOOIFH/tEp2xe1JLQSn+2jXfYzvu\nxzhimw4QMvbCcrkEAMQYsVwusVwumxIyQgiNjjbRtA771mO1WjW6d7VaYbFYuOfn83l5bbFYYDAY\noNfrldcmkwmGwyH6/T6WyyVCCJjP55jP5+j1emU+ADAYDDCdTss+MAyHQ/R6vTLv6+trDIdDjEYj\nDIdD3NzcAECZ33A4LMuezWZYrVYYjUYAgNlshtlshhgjrq6ucHt7i16vhxACFotFaTN3d3cbf29u\nbjCdTss6WZmG+XyO8XiM2WxWnru6uio/2732bOPxGJPJBIvFAovFosxvOp1iuVxiPB7j5uYGs9ls\no4/G4zEAoN/vA8jc0ASDwWDju9qdwq5ndBfMi8xRwAN7WK1WJU81Rb/f3xjjKRvi/JtgtVphMpnU\n5nlMDAaDLa41GF+eAiFViUNwe3sbjSwz9se+4uJFxd8na9Lt2vdtiy6FiRmDkYcRiomL8XicrJvl\nwXn1er0NETGZTMqJp9/vY7FY2CQPABuCyYQBC4fZbIbhcIjZbIa7uztcXV2V+SyXS9ze3pZ5cdrh\ncLhxDliLjKurq1IMGUzQWL2snJubm/Ie+wwA19fXmM/niDHi9va2JM7FYoHValW25XA4xHg8Lus4\nmUwQY0QIYRJjvMWZI4RwfAK7R7TBx0k88cT67+OPn67MjuPUHHiJGAwGG8Ivxtheo7YRFnoYlqjO\nGk7oGUcOiTdZo60qd99D17y98nSPjbehzluW0aUjUHhXNx1bvjFu/26NndM9Pt5+H2+fkN2vf71N\nivo8vJdDy9L+03033F7o+GviXT1OigteorrvfszHTjbfHj+0kWkWOPeMhsR1AsPd+Z7UmnbdoW8v\nWF5VG+9i3PzHeJaG33oAtt+ysefS/UG8P4fL1LcX9OByvTccvHqxiGGxZOesProfh797e5m43HgG\nAqbuuA+u4f7Qz02Oc9kH8aLiuO965OPhPg7lgKrjEWQ8tFhzdXPsGp7dJ5zLoUtdojJoiBNYL63o\n2u58Pi/TDgYDzGazrTzv7u7ceq5Wq419MaPRqPx+dXVVLvEMBgMsFgvEGMv9O1yO1Ws6naLf7+Pm\n5qZcD7d7rW62H8mWvmi5CMCD5Slbkru+vi6X02zZ7vb2FvP53G0LW86zNL1er6wv7yMo8m++eeAh\nw67j5mxxz0tUebkno21kgZPRGLsS+9XV1UGb2lL3pjbusSDRtDbBm7gAUAoSTjedTrf2qEwmk/I+\n3SRqAiOEUAoVAKWQsXO6kbjX65X7YUyADQaDsj7T6RSDwQAhBPR6vY3yeU+P7QniOvd6vVJQ2V6d\n0WhUbirmjZD2jLwP6Pr62m3fjIxj4mKE4hnAnJ1TbSLuCrLAyWgNulG2CWwC3uXtA4MObo3WsLhJ\nnbP0Vr6JFIt4mKDg+pkIMoJRIWVRIn3jxhNSJrBijKUwsTpYOuDBmwj2ZhSwbjsWU3d3d7i9vd16\nO4Nh51XkAOi7N2RkZJwd7I3MriGEsE3KR0QWOBlnhV29utvb21IUKOq8GRVRqSUxS2fLVpbGRIa9\nhWVva02n0/L7YrHYeKV0NpttLJuZsLB7LOpyfX29tUwGYOONsdFoVEaPLLLEb5hZJGY4HJb52LKY\nPa8tiZkgI/G2HQ7LyMjI6BCywMnoNHb9OYKqdf8m4V1+1ZyjNHa+3+9vCCeO0thv9AAP9hFxNMjS\n2dKeCR7eJ3N9fV3u97F7ObIEbO9HMlHGv9czn8/Lus5ms3IJy/YE7RNBy8jIyDgnZIGT8VBh1wiR\n/Z6Mosn+IP5RwlQ63txrYoXzth8VHAwGpSDhzcXAg83HXI6JHQtdX19fYzwel1EdE1Mmluzacrm0\n39wp16oyMjIyuoj8s5oZGRW4u7vb6bVE3mdjURiD9yu2KpT4BwYZFv3hJabFYoFer1dGYbz0V1dX\n5S8pW/RqsVhsXLdr9l1/STkjIyOji8gCJyPjiFBBxP/Cw/t3Ht7r3IbUfiD7mXY7eEnJRJT+ywD7\ny5Gf0WiE1WqFm5ubsh70s+55k3FGRkankZeoMjLuEbvsIeJ/p8DwRFFqCY3/95flw29pEbLzk5GR\n0WlkgZOR0RHsuqGaf4eI9/akIkOpt8gyMjIyuojspWVkXCjqlsd0qcyWropoTlY6GRkZnUaO4GRk\nZGxFh0II+XdwMjIyOo0cwcnIyMjIyMi4OGSBk5GRkZGRkXFxyAInIyMjIyMj4+KQBU5GRkZGRkbG\nxSELnIyMjIyMjIyLQxY4GRkZGRkZGReHLHAyMjIyMjIyLg5Z4GRkZGRkZGRcHLLAycjIyMjIyLg4\nZIGTkZGRkZGRcXHIAicjIyMjIyPj4pAFTkZGRkZGRsbFIQucjIyMjIyMjItDFjgZGRkZGRkZF4cs\ncDIyMjIyMjIuDlngZGRkZGRkZFwcssDJyMjIyMjIuDhkgZORkZGRkZFxccgCJyMjIyMjI+PikAVO\nRkZGRkZGxsUhC5yMjIyMjIyMi0OIMR4/0xB+C8Drjp7x6fAogHfcdyUORNefIdf/fvH7Y4zvdt+V\nqEMI4dcAvPmALO67n3L5ufyHufxWeeaRlvJ9XYzxtqW8W0cIYdzl+gPdf4Zc//tFCGF833Voghjj\ncw65/777KZefy3/Yy28z/7xElZGRkZGRkXFxyAInIyMjIyMj4+LQlsD5ppbyPRW6Xn+g+8+Q63+/\n6Hr9m+K+nzOXn8vP5beEVjYZZ2RkZGRkZGTcJ/ISVUZGRkZGRsbFYSeBE0LohxB+OoTwZAjhtSGE\nL3HSPC+E8KMhhGkI4TUhhI+ja18UQnhDCOF1IYSXHuMBdsEh9Q8hfHQIYRJC+Nni70u6VH+5/q4Q\nwheeruZl2YfazwtDCD9R3PuzIYR+V+ofQnhKCOFbi3rPQghfdMq671D/54cQfrio+6tDCM+la58R\nQviF4viM09a+Gg2f7WtCCE8Ux+tDCL9RnH9+COFnivOvDSH8RbrnqSGEbyrS/8cQwifdQx0+pbCb\n14QQfiiE8Oixy6frzwwhvDWE8A10blSU/4YQwteFEMKpyg8hDEII/0fR9q8NIfxdr+w2n5+ufX8I\n4edOXX5TG2yx/JPYXwhhSde+n86/IITwU4X9fVcI4ale+S5ijI0PAAHAM4rPTwHwUwA+VNJ8E4DP\nKz5/EIA30ecnATwNwAsA/CKAq13KP/Q4sP43AN6n+PwhAN52yrofWn+6/j0AXgngC7tUf6x/0uA1\nAF5UfH+PjtnPpwL4zuLzAMCbADx2hvV/JYDPKD6/BMC3F5/fHcAvFX+fXXx+9qlt6JBnk/T/I4B/\nWnx+KoCnFZ+fUfSNjfUvAfDlxecegEdPWYfC7n/VygXwVQBefuzy6dw/APAdAL6Bzv00gA8t8v9B\nAH/yVOUXY+W/oTb6t6csn85/YnH+59ro/5r2b2SDLbX/yewPwLsS6b4bwMuKz9+Igl+bHDtFcOIa\n7yq+PqU4dBNPBPDM4vN/AeA/FZ//NNYE/9sxxjcCeAOAF+9S/qE4pP4xxmmM0Z7ltQCeHkJ4WstV\n3qzYYe2PEMInAHgj1vU/OQ6s/8cAeE2M8ckir1+PMS5brvJmxQ6rfwRwHUJ4BMDTAfwOgN9st8ZS\nsWb1/yAAP1J8/lGsxy0AvBTAv44x/j8xxncC+NcAPrblKjdGw2djfAqAVxT3/k6M8beL80/DZmT7\nswD8nSLdKsaY/FG0luoQiuO6iJw8EzSmj1U+sI7UAHgvAP8XnXtvAM+MMf5kXM8w3wbgE05Vfoxx\nHmP80eLz7wD4GQDPhYM2yi/OPwPAXwHw5RV5tVY+GtpgS+WfzP48FGW+BGvHHAC+FQn7c9FUCZGa\nugLwBIB3AfhK5/p7A/hZAG8F8E4Ao+L8NwD4NEr3TwB88q7lH3rsW39J88kA/s2p635g+z8DwE8U\nf1+Oe4jgHFj/vwzg2wH8n1iT3P/Ssfo/BcB3Avg1AHcA/sKZ1v87APxPxedPxJqg3gPAFwL4Ykr3\nt+/LhvZ9Nkr3fABvB0UAAbwf1hHCOYC/VJx7FoC3APjqwuZeCeC9TlmH4vwnYy2G3w7gx1ARudy3\nfKwF1auxFg+fiQce/C2I6wB8OIB/dary5Z5nYR05fP9Tlg/gawD8GQCPoSKC01L772SDLT1/6/ZX\nnPs9AGMAPwngE4pzjwJ4g4yRyj7gY+dNxjHGZYzx8aIhXhxC+BBJ8ikAviXG+FwAHwfg20MIZ7OZ\n+dD6hxA+GMBXAvjvT1VnxgH1fzmAr4kPFPa94ID6PwLgwwD82eLvnwkh/IkTVh3AQfV/MYAl1ssO\nLwDwV0MI73/CqgNoVP8vBPARIYQpgI8A8Das6332aPBshpcB+J5IEcAY41tijC8E8F8C+IwQwnth\nbXPPBfDvY4x/CGsH4e+dsg4hhKcA+DwUS+RYC6Dk/q0Dyv98AD8QY3xr1fPVoa3yi8jnKwB8XYzx\nl05VfgjhcQAfEGP8vlSZbZaPHW2whec/lf0BwPPj+leVPxXA14YQPiBVTlPs/a8aYoy/EUL4UazD\n1Lzx6rOLc4gx/kRYbwR9FGuifD9K99zi3L1gj/r/alhvuPw+AH8uxviLp64zY4/6/2EAnxxC+Cqs\nvZR61yQAACAASURBVIJVCGERY9zaTHcK7FH/twL4sViEZ0MIPwDgDwH44ZNWvMAe9f9UAD8UY/xd\nrG3px7H2jpNk3SZS9Y/rZdhPBMrQ/CcVad8G4CMpi+di7fGdHSr6xvAyAH8pce9/KjaSfjiAV2Ed\nTfne4vIrse7fU9bhzcW5XwSAEMJ3A/gbLZT/RwB8eAjh87GO8j41hPAurPdk8JJQI94+VvkxRnvW\nbwLwCzHGr60r+5jlY93+tyGEN2E9X75nCOHVMcaPPFH5X4Q9bPCI5b+qyK9t+0OM8W3F318KIbwa\na1H1KgDPCiE8EmP8PeyqG5qGeorw0HMAPKv4/HSsN3z9KUnzgwA+s/g8xHq9LgD4YGxuMv4lnH6T\n6CH1f1ZR/088ZZ2PVX9J83LczybjQ9r/2ViHaAdYE82/AfDfdqj+fx3ANxfnrwH8PIAXnmH9HwXQ\nKz5/BYAvLT6/O9b7t55dHG8E8O6ntqFDnq249gew3sAb6NxzATy9+PxsAK8H8AeL798J4CXF588E\n8MpT1gFrr/ntAJ5TXPsyAH//2OXL9c9E9Sbjjztx+V+O9UTXa8sGqsqn84+hepNxW8/fyAbbKP9U\n9oe1zdsm+0cB/AKADyq+vxKbm4w/v8oONspqmrDI/IUApliHqX4OwP9anP9SAB9ffP4gAD+OtRh4\nAsDH0P1/C+u3p16HxE74No9D6g/gi7HeO/EEHe/ZlfpLPi/H/QicQ+3n07DeIP1zAL6qS/XH2it6\nZVH/nwfw1860/p9ckMvrAfxjI53i2mdh/XLAGwD8+VPX/9BnK76/HMDflXs/urjvyeLvX6Brz8d6\n38FrsI4WPu8e6vAXAcyK8/8SwHscu3zJ5zOxOcHeFvn9ItZ7KVMT49HLx1r4xeL5jXc/55TPT+cf\nQ7XAaav9G9lgi+W3bn8A/ijWexefLP5+Nl17f6xF9huw5tCnpequR/4l44yMjIyMjIyLw9ls/s3I\nyMjIyMjIOBaywMnIyMjIyMi4OGSBk5GRkZGRkXFxyAInIyMjIyMj4+KQBU5GRkZGRkbGxSELnIyM\njIyMjIyLQxY4GRkZGRkZGReHLHAyMjIyMjIyLg5Z4GRkZGRkZGRcHLLAycjIyMjIyLg4ZIGTkZGR\nkZGRcXHIAicjIyMjIyPj4pAFTkZGRkZGRsbFIQucjIyMjIyMjItDFjgZGTsihPCmEMJH3Xc9MjIy\nMgyZl7aRBU4CIYR/FkJ4ewjhN0MIrw8hfE5F2nfJsQwhfP0p63sM7PLMRfrkc4cQ3j2E8H0hhLsQ\nwptDCJ8q9746hLCge1+3Qz33vjcjo23sMY5eFkKYFWPlF0MIH07XHgsh/EAI4Z0hhF8JIXxDCOGR\n4tpF8A5wPm12IC9dTH9cDGKM+XAOAB8M4GnF5z8A4FcAjBrc9wwA7wLwx3cs771O/Hxb5e37zN5z\nA3gFgO8qzn8YgP8XwAdT+lcD+Jw96773vUdquzcB+Kj7Kj8f533sMo4AfDSANwP4UKwdzvcF8L50\n/QcAfAuAPoDfB+BnAXyBk09neeec2uxY3LJvfxxYZuYlOXIEJ4EY42tjjL9tX4vjAxrc+kkAfhXA\nv61LGEJ4Vgjh80IIP431gNTrfyuE8I30/dkhhN8NIfSbPMOu5R3wzAA9dwjhuvj+t2OM74ox/jsA\n3w/g0/ep96EIIbxfCOF7Qwi/FkL49cKj+2shhFdJuq8LIfyDqvucvN8nhPCqIs0bQwhfcIpnyjhf\n7DiOvgTAl8YYfzLGuIoxvi3G+Da6/gIA3x1jXMQYfwXAD2EtBhRH450izdG4p0l5595me6A27314\nqQknFekyLyEvUVUihPAPQwhzAP8RwNux9gzq8BkAvi0WktrJsxdC+JgQwiuw9kI+BsBXAPh4J/kf\nBPAEfX8cwOtijIsdnmGX8vZ9ZmDzuT8QwO/FGF9P15/ENsn8nRDCO0IIPx5C+Mimz7TLvSGEKwD/\nCutnfwxrb+87AfwzAB8bQnhWke4RAC8D8G0193HePQD/sni29wXwJwD85RDCS3d8lowLQ5NxVNjY\nLYDnhBDeEEJ4azHJPZ2SfS2Al4UQBiGE9wXwJ7GesBXH5B3gQO7Zo7xzarNDeKkub36OnXipCScV\n92ReMtx3COncDwBXWC+xfDGAp9SkfT6AJYAXJK7/DwB+GcDPAPgCAI/W5PdaAB9K3/9nAP+8+Pxi\nAD8B4MewXg7aqtuu5e3zzN5zA/hwAL8iaT4XwKvp+x8G8G4AnoY1GfwWgA9oWL/G9wL4IwB+DcAj\nzrUfBPC5xec/BeDnG973JgAfVdTjl+XaFwH45vu223zc/1E3jgC8D9aRijGA9wbwKIAfB/AVlGYI\nYALg94q03wIgSD5H5Z3iHpd7ALwXgH8P4P8G8CMA3vsY5Z1Lmx3CS037o0izMy9V3VNcz7wkR47g\n1CDGuIzrJZbnAvi8muSfDuDfxRjfmLj+AgDPxtozehLAr6cyCiE8FesQ7Wvo9IvwwKt6C4CXxBj/\nONaG/acPKY+x4zMD28/9LgDPlDTPxJosrIyfijH+Vozxt2OM34o1SX1cw/rtcu/7AXhzjPH3nGvf\nCuDTis+fBuDbG95neD6A9wkh/IYdAP4m1pNAxkOOBuPo/yv+fn2M8e0xxncA+GoUtlx44j8E4HsB\nXGM9mT8bwFdKPkfjnaLcKu55B4APizF+BNbRzs8+tDzGfbfZIbxUl7dgH15qwklA5qUSWeA0xyOo\n34/y57A2Thcxxr9a5PFzAL4ewBtDCF8WQvivnORDAG+LMc4BIIQQAHwk1oSBYnDbYP8dAKsDy/PQ\n5JmB7ed+PYBHpJwXYe0VphABhIb12uXetwB4XhHqVfwLAC8MIXwI1p7SP294H6d5Y4zxWXS8W4xx\nV0LMuGy44yjG+E4Ab8XafsvT9PndATwPwDcUE+6vA/hmbE+4x+QdoIJ7CgFiXPNucMb0EXgHuOc2\nk7x35aUmee/DS004ydJlXgLyEpV3AHhPrNc9n4F1yPSlAO4AfHzFPX+0SPNuO5QzwpoA3gHgn8q1\nT0cRHgXwdABfjvVg+0BJ93ysl6qaLCVVlbfzM1c9N9Zrw6/A2ov6Y6C3qAA8q8i/jzWR/dkijw+k\n+78FwLc45dXeK+mvsBaFf6+oSx/AH6Pr/whrT/VHmt6HB6HgK6zD8H+96KMrAB8C4L++bxvOx/0c\nu44jAF8K4D8U9z0b602pX0bXfwnA3yhs/VkAvg/Ad9D1o/JOcb2Se7Dej/NTAF4H4PlHKO8s2uwQ\nXtq1P/bhpQb3ZF7Sdr7vCpzjAeA5WK8x/waA38T6NcPPpes/COBvyj3/O4Bv37O8pwJ4sZz7KgDf\ng7Uaf1thrG8B8K2U5plY78H5/Ucor/KZd31urD2pf1EM9l8G8KlS1n/AmkR/A8BPAvhouf+Htfym\n9zr3PK+oy69jTbJfR9c+DGvy/vNN7wO9jon1noBXYP1a6zuL+uRXNR/SY1fuAPAUAP+wSP8rAL4O\nQJ+uP471q8vvLGzwu0GvWh+bd4rztdxTpPvvAHzjEco7izY7hJf26Y99eKnmnsxLcoSiMTLODCGE\nHwTwj2OMr0pcfwTrV6//fozxh09auZZR7AF4EsALY4y/23JZz8P6rY3fF2P8zTbLysjoAqq4J4Tw\n1Bjj7xSfXwrgpTHGv3LqOt4HMi91D1ngnClCCG8F8DExxp9PXP90rF+H/Nni1P8WY/yuU9XvElBs\nSPxqAM+MMX7WfdcnI+McUMU9IYQXY71EsgSwAPBZMca3n7iKF43MS8dDFjhniBDCswH8ZwDXbXsK\nDyvC+scI/zPWvynxsTHGt9xzlTIy7h2Ze+4XmZeOiyxwMjIyMjIyMi4O+TXxjIyMjIyMjItD3fv0\ne+HRRx+Njz32WBtZZzTBfL7+Oxjcbz0yOovJZPKOGONz7rsedchcc8HIPHbxaJtnWhE4jz32GMbj\ncRtZZzTBE8WPHT/++P3WI6OzCCG8+b7r0ASZay4YmccuHm3zTF6iysjIyMjIyLg4ZIGTkZGRkZGR\ncXHIAicjIyMjIyPj4pAFTkZGRkZGRsbFIQucjIyMjIyMjItDFjgZGRkZGRkZF4cscDIyMjIyMjIu\nDlngZGRkZGRkZFwcssDJyMjIyMjIuDhkgZORkZGRkZFxccgCJyMjIyMjI+PikAVORkZGRkZGxsUh\nC5yMjIyMjIyMi0MWOBkZGRkZGRkXhyxwMjIyMjIyMi4OWeBkZGRkZGRkXByywMnIyMjIyMi4OGSB\nk5GRkZGRkXFxyAInIyMjIyMj4+LwSBuZTiYThBDayDqjAV5U/H3yXmuR0XGM7rsCGRkZGYcgxBiP\nn2kIx8/0IUGv18NyuTwskyeeWP99/PHDK3RkZOHbHcQYz76zMtdcLrKj9nCgTZ7JS1QFBoPBfVcB\nALBare67Cq1iMBhgV1F9qr7p9Y4/HNrIMyPjHBBjbPV4YjrFE9Np6+Wcy2E8NxptBk/5+33OU8cu\n+xTcmNm3wHw+P0k5ecLbhA4aHdzAdt+01YbHEpdcP84zxrh33e2+Nu3n0myz6fOYzR1C4JfWdhn3\nh+l0Wn5O2SSf39VuU7Za53geMkd6ZRbc2OrE2+qovNRBf8hzXXqEpg53d3fl516vt/EdAGazWW37\nNmnD+7S9VP1CCLV1T9Xb7mvTfizvc4lmNkVdm9VhMpmg1+sdROBaVpM2bNtGjyXYLpXHzw2LxQIA\ncHNzA+BB/43H4zKN2eh8Pkev10Ov18NwONzoa3USe73eRnSo3++75d/e3pbpvXyaQu8bDAZb44Ns\nqlWyadVyz2kyP+YgTRlIFerIxoz1YUAIAb1eD6vVCldXV8noRBOCTg3CJraXyt/qscsEUZXWrsUY\n3cHPqKr3LvVJ2RLnkUpzqmjmseC1mbVz04ma87A2qkpvk0bKdrkNU/2W6mvOtwpevnyvF/msy3cw\nGGA0Gm2I3dVqtdeYyNgNJmwsgjOfzzEcDnF9fV2msaUs6wfrJ+7ryWRSfjaeHQ6HW9cU0+l0o3+9\ntLpc5i2f6X3z+dzlueLedsmmjbVEAPFUR6/XO1lZ+5ZvaUajUeU9vV4v9nq9eDCm0/VxhhgMBjHG\nGHu9XhwMBhFA+dfaIMZYfuZrdtj11GHlaDtbfql8vXPWZ/v2P+dp9dLnbcPW7K/3TE3zjWewL6Hu\n2PWZ9uELbdMmR6rdNS8vT+MB7/xoNGrUp/s8n9mod96rT+s4Yx5rC4PBII5Go405w/rb7MLjzSo7\nHI1GWzzm2ZGmsfLsSHFhjNt8nLJhvl6Ufxdb5IdWQgaq7DzsG63QtcdTR4n2qbfV0ZStV2fLd5/o\nUJfAS1KLxQKj0aj0Lnq9Hvr9fhnVWa1WyWhCakMesI4Q6dIXgNKT6ff7W17FaDRyy/K8GL6P+9Kz\nDc4zhIDFYlGGou1+L6TsYRdb9zy7urRd9845qpJqq9TY4wiFRjoqwusllJfMprlenJd56159bm5u\nyuuch6Vl+0nVq0kEz6D9PxqNttpQl00y2sF8Psd4PC7bfjwel2OY7aLX62GxWGxEcxRmAxrRsXPK\nDbwUBqznon6/j9VqhX6/X+ajfGVvxuqYsbqmNkkXY6TdCa8N1YQjehdtHJ6yPLZXZOVUKVk9b3U4\nGGfs+WgEwz6bd2DeBnst2m4xVkdwvP5s6n2nPOeqPPl8XcSn7vohNtzkOerahds2nkGEpu7Y5xlT\n464qYuH1NUcJU/3qecmct37nvLxoD3vv6tnX1aWKh1JRRc/Tt/St44x5rA1YW3P/cUSb7YX7zNJ7\nfciRF7Zhvp8j21XRmiYRHC6D87c0nId9jm3yQyuZJhrgWCKiLvxeR2j7HseanLheXDczsoPREWLw\n2kQHuF7z+qTOrur6P8aYTFOV9y5LRqc8mpaZ6gO6fu8Cpu7QfrJnqpvkVWin0laJpV1EM9ePx70n\nSlRwpcQV31e19MVLW6lnZgejqU21jo7w2DFhDp7ODWZDJizNBuwetQ21Ia9f2VZijEmb0vOah9WH\n0xiPN1iSb3WJ6iQCxx78UIGzD7nsm/8+6fd9PjXOg3HmxGBG7w1gL3qjf2OMrtei+eg5HYR8PUUo\nTWy5TgQxYVTlW3Wk6tw0vRcp8+wwxpKslvEMBEzdUTWOzMZ4wvCe2545Fa2o+szRDPWKuf9TUZqU\nfbKtcN/xHg1PsHiTUlMHwKs7j1OyjeM4YnU4cx5rA9wPXr+zLaXs2YvGqL2lIjTePlF1vPk8i5hU\n4EF4ZWu8xksQOE0GmEdUVaTtHWocTSaTJhGfJiHrpnWruv4wCByeFHhQqeL3JvEYY6N+aiJWOVTr\nTRgp4k/ZW6p/NU2NR7Pzkapfk03tFfm06lkd6zCb8J69LgKSimxURfNYeDAfmV1qXlwPT4x4kZs6\nUZJafvAiQ3wP11/tMVW2x6NH46k6nDmPHRtskzHGDVvjSAyLHeVE62u7X6M8LMbVXixPPthWdPtA\nyvY829U6GtrmmVYFTpUgOcZyVdMlqqqjiszq0jctX6MVqXRmQAfjzIlBByIPGG/C0Qlc80i1Oac5\nhpBIRT+qRBGnt3o3Ed+HRhP3iXZquDmegYCpO7iNvQne6yud4HcZ/5qP15cpIcztq+KG74lxc9mB\nn8Wb9Pi+lL3zxMl1UqHmCTQuW+yjXZw5j7UBa2u2KzuvURzmTW9e4giLNw40Osc2qoKFnYEU79l9\nqbGmXFicG8cW+aGVt6h6tJt6NBq5u7zv7u62zvd2eENpNBol3ybg3f/eWza9ijckgPVO79TbJ5ye\n39ThZ9E3IO7u7rb+vxTXYUBvnelO9ktFj97S4N9omM1m5TlrU+uL5XK59Rsl3v/tUrvi/lhzxYM6\nKEbO76dYfqm+sR/dGo1GZVlmm1U2zW/aaFprG+9+O8fXlsvlxrMtl8vyOj9/r+JNG2nL9A9mnBGs\n3WezGW5ubsrfbLFnmUwmZZ/GGLFYLMr2sPE7kN+dsfFv3GXXYozlG0bD4RCr1arsZ+MztgFDjBHz\n+RzL5XLjf7GZrQPbb9NNp9PSrvgtzNVqVb5daOdHoxFijLi+vi7fLNVrNzc3mM1mG+UvFgvM5/Oy\njXrFD2/yW40M+90qtrOM4+Hq6grAA54xu7m9vS3nu+l0ivF4jOVyWdrebDbbePt2Pp+X985ms5I/\nmRfv7u5KGzK7Gw6H5bjp9/sbdmyfzTYGg0Fp8zFGrFYr3N7ebuQ3n8/LetlYm81miDHi9vbWzm0O\nlmOjDdUERyF663L8XY+q5YAmR9MlpCaRFTieYOpc00PVL3tTB+PMPR9rO/ZC7BxHcLwoTMrr1f5L\nedTszajH74XwPVuKcdNT0Tp711LP4NmnF5Wqs7Vdo4bcvlye9Q86tAfHsxV7Du5Pszn2Ir1lvJSN\nme1YHmxnXJ72lV2jtq20X2+JomrJjT1sbxxwHt4yHdspj1HOk9uJ269VnDmPHRtsS2zTfE2XkPS6\nchwvS7FdqK1wpCfGza0DnI8uy3LkhstUm7byeSmsONe9Jaq6ZZ+m4qPJRFb3+ZD8dz1Sk5W3ydBL\nb0ZwMDpADFXC15uwOG2M22RQ1bdNlhua2IVHCnq/2jh/blIXzqdOoBw6ZmLcJD3HHu9dwNQdqX7k\nUD47EFWcYe2REgyWzhPDOqGoLeuSVspGlAd0HwQvFaREqu6T0GWKlKjTfRcq5PgZrb1aRQd47JjQ\n9vX61NKxUFDh4dko5+0JeLUrrgf3t7f8FeMDHlEOsfItjbMNoVVHqpVM9aGbEG/TI0UQh5ah9W06\n6TWJAJlhKMEpQbEHdRDOnBiYqNlT4AFZFf2LcfstKvU21AOxvGJMb96ri6xUHVX3qhjTic2zKS+K\nU3fUTcqp8cQTXozlOOhMBIfbSe2Bz+sEz2TNaay9eHLQfG2s8nlPlLLdqe16kwrbCeehHrTXpyxG\nvP7Wsabiydtnw9EkrtvRuKoKZ85jbYDtKMYHv/zO49PA6XTss/0ytyqvaoSQVxA8G/but7QqgnWs\nKDcW17sncHSyqhIDXrpUev2+r9ipiqaoUaQmAs2rbiLyJh4VNxom3htnTAyeuOGJhwe4Rj68UKt9\nV29U+1Dz04lLJwjt/5TdeREnJQUN6XMZGt3z8moyHnQpTL/z5Kltmsi/MwKHIw3ah6mom7a3d57b\nqY43tB3VTtUGvcmoygbYU/eWotSOVMTz2NN71T48rlNxyPbcGs6Yx9qCRkr4s0bZuI81Dfev8aaK\ndrVbFrgqvvm7N+epzafGBte9qEP3lqiqSNlrmJRwqRM4VUeqI5ocdelT+aqy9erkPZtOVAfjjImB\nxYuBDV4Fz64RDG8C0YlCJwbuH89b14HuiYKUMGaS4mdXD8vus/aoIg6vjFRdNK2KRs8bK5671bcb\njnWkxCDbG/c997H3/Npfnu3wpKJerMdl1q+078AV2Z4o5r4020gtS9g5vZ9tm8cU2xWPG3Y0LI0n\nBFvHGfNYW2C78pwn7l/lKW8+4n5X0aSOJM89nmiycpU/Y4xbPJWa0znPIn2rPNOawElNTHXnvYiO\n52FVTXApbzp1XomfO8qbJKxDvUmz6vAEjif2DkaHiMGLYnlCRUle+8oGDNuKCiUVMyoyeOJTsZOy\nB++61UkGcoxx8/como4NfpaUQNbvmq7qOVS4dUngcP/qM3G/s8hQotXIYNXEoWJcxSNPIppfyiFK\nLSuynVal4bQs1FL2y544R7z4nLWVijIup3V0iMeOARWhKljVMbLz9teL4rB9c/7KQ2zTqQiP2nWK\ngzQNjy8VXUX67gmcFKE2IV2PtPc9qoi9aiL1OlGXGvR6XXSmqj6eit4bHSAGnlT12ZW4vcHoiVUW\nuDFuTjCcbyoyxJOIF+rlspUE6iIJnAfXrc5etSyeYL1n8MZWlT1qWdROnfihPyZmbiPub29cshC2\ntNxmKVHC19WzTgnNVL56Te1EOUpFCT+zCm5vvHiCih0DFfX8LDxmrZ6towM8dkyo2GSBw23PgkX7\nRm2R+YKFqdqPRmhYBKvw4nGmTqHH68rHfB+6GMHxvI26KEeKrHWAV+WRmiB0svAGOxNDFdmlogCp\nZ9GwNj+XPudRxE2MnSAGHhDcPnxd7Yf7ziNyLxqhfRhjdG2xzrPn+1RccL+prfOEoJOTZ++ejfPE\npu3W5hHPQMDUHTr2PMLmceqNR+437Rfua6/9zVa1z72JKsVRGinRSUbtm23cE/oq9jyh5PGr8hDb\ntecMto4O8NgxocJVBY6l0XlMBT7bCNsXHzE+4DWNzKnQ4vLZlrh+lp8XEWUO5HoV57q3B4cfXolH\nG9Ub8KmoR8orTZ3TSAB/3sVb8+pSVV5VHauiEEzMB+HMiYEHq4ZLDTzxeO3jCRLPY1AxwYPNm2CU\nHLp0HFpnvT+egYCpO3hc1T1/KhKoE4N6rur8eBEWz565DM7T7CzFKzHGjfs0csJjpYqj2PPmiVH5\nR8eHCiCNbutYbQ1nzmNtwPrfi+BwGq9/2c6ZB9Um1aY5P8+uYtz8vRsVTgYWaGr3lieLm+Jc9wSO\nEgo3FDeqegRVBOUJCy964hGddq53D+efijZ5QojLa+pVe+KKyeVgdIQYjjEpP2yHFx3c96iz13gG\nAqbu4DbhcexF2VjMeE6Pim0vuqscYOQd4+b+Ks/J85w6u98TQN7z8KSmz6kRI1kK2LiH68PlqUNg\n1yy9evatoiM8dkxo32pkxltWUtuKcVMgaUTPW0HQ/NiGWOjaoQ56KmDg1V3vj10TOFTxnYiYB5B2\nWt19dQIlxu1/yLfvhJAKiyvZqor10mgZp4jgHNIG9300FZHnWl4qctfkULtORTr3fbYuRnDYS2Xv\nsah/+Zz2ma95y0jq7DSJCvNkwO3KQsAj+Lq+YK+Z77fn1UgR38tLBfrdezaezFRYcaSKJ8fW8RAL\nHI0OcjSH+zIlMrSPNXrncYHa0jG4r8ncH7smcFJEWkfQqQmhSUN66WJMT+a7TA5KYE2PYz7fLseL\niuPY+Z7LcS5Rn33qcS51b3K0STxtcY23rMIiiCcOL7rhRVTtvDpgVX3M6bXfvYgQO0S79BFPXKml\nCuVBz9k6x+PSeezYR5Xj7R0pW6uaN5uWrUEOrtMpHalWMk2F0dUz0EbySKauM/bpwHM/DsY9ej73\n3XY64I4VteO/+ywNpSIBu9wTY/3/fNmnLlpG8bkTb1HV9dux7EjPecvjTdv4mKJC+bXt8tRWWsVD\nEMGpErXH7Lc2hWyT4EBVfWKL/NDKfxPn/7g9mUzK/0o7n8/L/2w6mWz/s2I75/0n79R/966Cd09v\nh/9YnrE76gxuUPz32UPQc/7Tt8Js0Ptv8Sl4eZkNLRYL9Hq98r8v75KH1SOuxX/5H6I9W+zRfwrX\nul9fX2O5XGI2m2E0Gm39N/IR/TfqKnC+Pec/kxfo64lzRo/+4zew7rdUXxhGxX/Q5vs1z9R/def/\n2K3Xte+4HqPiv40PBoPyUHtO1ds7P51Oy3ztmavqMir+Q7rmZ5/1Oe27Xs88ehwsl0vc3d0hxgf/\nqd5s2P6zN7Bub+1btl+DZyMxRvT7/Y2+1M9qF004lud1rqN9TvGlx21t4SRW6j0MN8ahqJoo9Nyp\nGnZXKJFcKubzOUIIyespgmVwH6aE7z7tqHlx2TqhpbBYLJJ1CSHg5uamMh8VZlwHa7v5fI7ZbLZF\nHPy9jpRS5XHSZCXPDIPBoCTwEEIpEkwAGteosJ5MJlitVuX9ljZlc9am1lYsULzrlsbsyq5PJpPS\n2ZvP57i5uSnTVzllfE3LYueQyzchbXmwjXB+Jo7Y7liIs11fOkfdF8bjcWmHwJovRqMRYoxYLpeY\nz+dYLpeuqGFBwbAxAWDDqbJyLP10Oi37mG3S+n4wGGw5UGbzdvC4WK1WpUDTud7SNXXIDkIbYSG0\nFArzjmOG6c9hPfoUm4zPAdbeMW5vlKvb7Kn36N6Dffo+dW0f+6pajtIN503ut/bS+6ueuWm9HYu0\nCwAAIABJREFUdQmOjs78knGT5T9v2byqH3hPjL7JYveZHXK6VF7eq7Opent7ZLy/qfrX7fupGzc8\n9mLc/t0o29PUOjrAY8cEv+mnb7J5n9me2P64//mcvgyjXMTLZVyOlq1cofbGb2N5XK42Gdvkh1Yy\nbUCs2uD3fWiHNp0gjr1OehTyOGNi4A2fNgCsDVOTf9Xm9Bg3Bx0Tv/bhvpvumqbz6qmkwiRyqO2k\nnrPpUfe2YTwDAVN3pOzCe5U61f/6+rS2bUpUpD5zXmqfWr8KgVney+WnxJG+CqybrOvGBNulVxfv\n/tZxxjzWFowfVVyzkLY02u/cf5aHxz2eALb+1FfDOd/U3j+rC9/H9sQcrxv90cXfweHO2GWCOIT0\nzyH6UlUXNs6qNrCoxkHoADGkRA0PgFT7xhhr213bWXfve2Ucy4ZSfevVu2kkkZ9HCcg7do3ueHnF\nMxAwdYc9K08ESsjeM7PI5AhLStjoGNZIiArsKq9VI3CeeKgS53VlWHq2t6qIaJ1teALpKJHmOnSA\nx44Jdm7V0bU+Zx7Tc6noM9tnjJv/t4rtwcrx3r5T8eLxLYsvrlcN33RP4GijegOqrckldegAPaR8\nM0C+t0qwNM3XiORgdIAYlOS5vereDIkxbgzeY9jTLvfvEjHxwvteflV5epMK17OJSGpaZ+6beAYC\npu5gwec5ECmhlxLDZn9eNEc/88TCNtnE/qrETVW/qTfsLUvYX+W6KlHMbci/1aOTqi6dtIoO8Nix\nwX3MIsf6KMbN/1llnKDLitxHPK41GuT1Leer9mH5qC16ESK2YX4G4bzu/S8q9X5Sa3ZtHTqQ67zd\nqsOr+y5ExvlUpWXjOBgdIAZvSUknqdRvD2n4M9WeVa8npjwR7vPUJNfETvhgj0ijm1UTTiqfOttX\nIknllxqXXRI42tep6EiT9vDakm01rgvcGssqeqrstap/uY5WFl9Tr9gbHyrw9Hm9KBEv0XlLFNqu\nlqZ1dIDHjgnuB54L9DMvucpyjxup4bztmo4Lbz8WjysWvnzO8vdWJuy6RuX5PIBl7JrAaULWhxze\nwKvzZJt4ubuUX+d5VZFflbf2sAgcJVZuoxg3f7lT+8nu99qPB2sqDMsiislc+0cnuH3sRYmFBvZG\nn3u25ZFQk8mU89XohKXRNvDqHs9AwNQd3F/qeaaie1Xj2aBLWJa/kHOZhm2Z7+d+06UC5QIvHfed\n2mOd4PWEijcR8TUen96Y4/taRwd47NjgJR4D25il4b5SW/Ty8vaEKdfYNe5fFrMe/+o1jTYz73lj\nFV1dotr12GfySIX2m3rbuyw17PtMXuQm5U0ziR2EMyYG9Sh00jZUtZle90LxMcat/HkS0773JntO\n76Xdx5Y94ZWyz5SNWD673KvXmkQ14xkImLrDe8aUfXj9w2LFa1MVwtqG3j4DdYA8UcresPaFTka6\neZiFlkZ2Us9R5ZR53rs+H9+fIzjtgCMuMg63+kNtyBm7ZR9pBEXvs3zV0WRbYd5S8W31U6dAhThH\ney4iguN5oHUTwC5HE5KuIvtd722yn2LX+mt+vM9ib3SAGHTAeMrfG0wpcXhI31TZZypfnmDq7Myz\n12OMgVQeu9i2kia1fSd+yViFhDeJswjQiJY6SZqHhuOb8AL3jQouFiipPDSqwx675c0ix8uHo8Ge\naE85CKmonnJtFjjtwutnswWNFnr2qPahNqrCWseHJ9Jj3P7JAL2HedHq5kU1+YhdFThtELf3ede8\nvHs9T6oqr328+CaTDoce90YHiIHD7TwINcJR144GJeiqCUTTWj10UKuIqaqXN4lwHbnM1PKZV++U\nIEqJGM0nJd5SY4DStOpZHetgO9K28cSM1x6eUKiKENYJC/7LER79q3aZEvn6XHywbfHhPY8+q3jS\nG2ltjHqChyNMraIDPHZsKEdULVcyf3m8qMLE7rFrOjaMf+06n+P7lJM826pzOEmwd2+TsRJ7aiKv\nmuibHE0Ew76ecmoJICVyqiY4bzLySIg9tYNw5sTAbRxj3JgcPNLVyYjzSNmTpfFE6y7ipMnh2XJq\nQjgk6riPnXt2lrqXJ8yivvcuYOoOfgbzQrnNdewxGXterP1NLR2pOOBJhr1gjwN0ouIlKs3L67sq\nscsToj5TKlrlibyU56+RpxzBOT5YYLCtsY1whF/tQcU12wNzKo8T5ksWMuogsL1W7RVTW40xbvzl\nOa5I3/0lKh2s6kXtM4G0eTSdgOomzl3LYwM7CGdODOp5clt4a/5K1Jr+GP3jrWV7E4lXpkZ77Nk8\n+1Xxlspzl/FhdfVEVeq5qzz34nsnlqhS/aV7vHgSV8+T7Yv7JCWOue1UlOj9mraJYFGxot4884TX\nz/yc7PHrmOPrPHnxs9hnjR4dhafqcOY8dmx4dsJiIPWZ72Xb137ice/xqTqYOlbUNtherC5q/54d\nsVBDFwVOaiI5xh6cVNTk0KNqMuHB7U0sdROPrlPqNTa8Sxc4GurUAeYNPE0X44MBHWPcSqMTidef\n3mRTFVb1bFfrXidS7Ln1+iGibRdbrGoL5/5OLFFpva09zS740HPcpxrF4Lw8O7DP3hIU10kjSx6P\nqL17y7QsRDwb9QQN11dFuGffvByhkRr15q09W8UZ81ibYPtTu+E0LEw98e7ZuhdJ1HnK8mcxZP3t\nORExbov7lLDXz8X93RI4TYi6inD3IWxvQtsl8qOqtyotdygfnmfoXau792CcMTGoRxnjA4Fiql7D\nm177eyTNpM6TVmpCSEVTOBLjlVNnH3zdoMtxnrCx9HqtiW1r/bjtlFCq7J/asXMRHB6/vJfAa5dU\ndM4+10X0UpEcrz4akdE+UfGsNsmCgu1a05nNpkRznUjXcchOl+Xh2XZrOGMeawvqDHPUhPudBSv3\nvfYpR3tUEHlLTJyObceLFOmYsns9DmQb4vPoYgSnivw9Mt01FN807xQxKSlwh9R5yKxwU+l2vabR\niYPRAWJIRVHsmtdGPIi9yYfFE4vMVDi2qm+8EK2d9/LxwrGW3r7b31Q0sMpedNLlMnYZJ3qe8xEh\n1Il/tqmRDbYTjuZYGs8JUfFR145sp9z/3sRS1Rcqtj0BlZqIUnl70awqMcdOgEZxWIxbG3L61tEB\nHjsmuL3ZzmKMG+Ofo3V8ngWQJ6T50D727IzLSNlujHHju0YAWWDxvVTH7m0yrprgvcmm6qhbOmqS\nh+aXirA0qZOWuU+Uqor0eE1zb3SEGNQ74WfX9lbyryLtfBzniGcgYOqOqgneG3NVDgaTPAsh3gvj\nebC6TFAX7UuVp5HLVASpztY1suNNnMyDPN48752vc/1aR0d47JjgSInyYWoPjIoa7WfORyN/GmxI\nRRTZ9jUKzXVUUWTnPUfErsWuCRwdCE0GYooE9Kjy7pvmsUt5VeXWlb+v+Dn0eFFx3EfZ+bico03i\nOSbXKCF75Fq13OSJDC8KSO2yJbht8tD6cJ1ifDBxsdiydN5yqSdqqiLSnB9POpw+1Ra78OUpjsxj\nhx379ucx7aBOAxRpWuOHUJDEURFCOH6mDxEO7pMnnlj/ffzxwytTgaurK6xWq1bLuBT0er2D22o0\nGmE2mwEA5vM5BoMB5vP5UcuIMSKEYJ/DQZmdAIdwzTHa676hNnBKtDF3bOBEPNY2bDwxBoMBFotF\n5+3vGGiTZ3ptZdyo8N69Fn+W6FKbLJfLfTzujWc89+cdjUZHyceIbDAY7Hyv3TOZTLBYLMoJTSe2\nTJa7oWl7pWy01+vtbL/Hsneziabipond7WObGfXwePDu7m6LP41rYowbdsLXlI9GoxF6vV5t3zWx\nO07D+dn5LtrHvc4umZC3celtMhgMsFwuD8rjlKJoMpkcNb99vG2+p9/vbz3/riKsiqg8b/PckRIa\nu5J66jyLU2671WqF1Wq1k9Dh8X2IHc/nc/R6vWTfDwaDjfwXi0WjPDPuD7PZDL1eD7e3t1itVqWw\nub293eAhtsHpdIp+v7+RD0fWTPyY3am9cF43NzdlmsViUebTxGYtn8Fg0CiyR+Uel2AF5+0+nyna\nmmDPPZpxDNzd3W18V0E3Go128hS61GZW133r3Ov1MJ/Pt9psVxFmE1mX2q4KJjQM9lxNnIVUGj7P\n0RJPBLDQaWq7tjzGE04T++D0Nzc3mE6nbjqzk6ZtYWKpTqx10YvvCobDYdlPvV4PV1dXmM1mGI/H\nZRpbou71eogxlqKE7TKEUIqMm5sbLBaLjSgw25DdNxgMyrwnkwlWqxVCCBvCxWxKbTbGuBFVNifJ\n7o0xbtmNLbEDOE6IPIHLYLgTo60oCxPSpUM9TIMNsipw++uA4/x3rU9T7NtHVu997efYdndJ0UIv\n4lI3UZsgsb730vMel6rJP7VkpKLByN68bhanVu+bm5sNe7TJajQabaSfTCZlPt6SAufpXdO628RW\nZRc5ytMuVJDO53NcX19vXDOhcX19jel0uhWd6/V6uL6+xmAwwHQ63epPixQphsPh1liYz+cYjUbl\nX2DbZjnqaw5qr9cr6xVCcCOITaKKh+LhmE3vGU0nxEvY9NgEIYQtDxNAOSgs/J6CXjvGMtIuxN1k\n0rgAdGom85wDPWdiA1j3d7/f34jKeHmwXVSF6tn7ZsGtosFsnzzYrTzH43F5fTAYlBOIRWv4Pvac\nvWgNi6sUv7AXr46Hd26XSFXGblDnDdgUHvzZBIIKYhO9HqdZFFixWCwwm81Ku+v3+6Udc5SQy/Fs\nYDKZuFFmq5PZI4v8NnGRzLwP2pykmoqW1Wp18cRh4VPPG16tVlgul0ki3oVYvUG8a9vyhFjl5Wtd\nlQR4czWHfFM4hi2m8t+hDTpniLwfxiIlLFo0Osg2YpN43VjVKJzlrZEVzjcFFhacpwkaFULGDykx\n7tXdmzBT95pzYfu8bDLkt31YIGYcH71eb0NQ2JuT1i/T6RTD4bC01dVqVb58YKgT7Z6dr1Yr3N3d\nldGa+Xxe2jELEe53+2z8plFEKzvGuCHGVqtVcrn32GjlNfGrq6u4SyTiYYlcNMFR+uOMX6+0cCvg\nv+rsEfix7KPX65Vee1to8truIa/26pJJm+Pm0l8T99CkTTNfnQYvKv4+ea+1yGgbnXtNvEnoib3j\nrpOFp5A9NHmVjwXAJeLu7q7caNzr9TZCrsA6VKp7aiwEq8sNhqbtb55DkwiJ1Wk0GiVfzeR0Bs3f\nizrtuvbsbQoEdov4Xegy2tFxyMbkhw1t/4jjE9MpnphO7/3HJE91pDjl3MfuOa86tNJyKe+UO8rW\npi8BXrjPQxOv/WEJ/fI6rb4GPZ1Ot2yF0+trkIrU2yl8XeEJFWC9/qx7fMbj8cZyAb8twPmrp78v\nUWn5KcFThT3G2sNhiEfCLkuOdROCXj/nCSTjeLA3oobD4cZ5740+YLffYWpTJB0SjW4bJ5WGx/oN\niGNg39/NaBP22wcPA6qM29ZpUxEbe30S2HxFl8Hr2E0m99QgNdJh8B4J/qu/IdPkFWRGE/vr9XqN\nNlUfQh7Fve3vADxz7NKGVZFB7e+6CUEjfOfm9Nw3Tz4ssFf3q+ywyXJq0wh3ClXlc6R7V5zCrlux\nVHvYKoWZer3Xg3W0h30FQWpDXhNS23eA13l5D4u4AR54KfwbD8B6CcvO8c57juosl8vyftvEq31n\nm5XtfkVdP1tfWF1S9udFijStLclV/cAhR3u0vmwXNzc3G9+9Tcve0h9f0x/l0voWxHNxs1hVVI+R\n2khbZzP7RqSr7LQq/X3hFG+/PIwYj8dbPyRp0WsPTeerpisMKfAbfd414EGUmbcSeDzF6GwEx7zn\nut9UaPp6r3W0h6urq90rWIE2382vUqz2ewK3t7etlX9OSP1AmW5CNvT7/dKWrq6uSnvg34ng9NfX\n18nfnUm9Kskwu7L+SNV3Mpk03kt2dXXV2MtncJvMZrMNG/H+bcNqtcJsNnNt2fYhcd78DJy06lnO\nFVWTv/ebMx4OWWLedTkKeCAYDv2dpDrsI4yO9a9KMpqBl6fq2n4wGGwtZylSb/2l8qvCrsvhKS7f\nNb9DcG9vUeU3EbZhBqa/9rszzvgtKsPV1ZX7+mGv18PNzQ0mk8nWG0PAg8EzGo02fsTqUHvi1xo5\nH35N0xBj3OlfGnjRmaplqmO9MaZr97sSShffojp3Xrmkt7Rajzh3gMeOCfuXDIe8ZZnCOdqU1alN\nnjmL/ybeRod2FYPB4KIFjql6+20N/XVWFS4Gb8Nu1YD1ru8zyO2eJjZKA3ZDAPH3JtGeqnpqe7WJ\nLgqcjMtBfk384UDnXhPfFVncPFzgXzHmpR/7XveDZbbnBkiHVb19AnWiwgO/6VUXMtYfajPwMmrd\nsm1dPU8lbroM2/u3z3IRY5flmV1+hLKuXlXf99kgynsivfy5rewz76Xwft0YyK+JH/sYjUaIcfP/\nNvHeF/vM31N9qvaib556e/e8f1vCab1giO0d5XSejdq9XN4plj/PQuBkPMCli727u7uN16n1l1Z1\nE60HFhCp9tp1L1WTN5v2FRfnFhq+RDAhm101eXup6Z6duvT9fj9pcywwYoxb/xFe62W/VKvl2S8z\n8/e6t0H5F2ntmvcLyrxXw37VmCOXvKHV+zcTGcdBCGHjd8Kq9q6YvWk6fmHFHL3U76vZfWaj9o85\nde/OYDDY2h9qYy2EUNqM3aN2qW+eAs3+7+ChyAIn46TQgaZEOZlMave3NPFijyUqzk2ctO31dPVN\nvlQ/pSZia8dd+9dLbxNMKi/bV2GTgf3sfgoaxfQ2kgOb//+qro523svXex4D//Amvwp/6Y7YfeL6\n+hq9Xq8UwiZ4dD/icrnEzc3Nli3d3NyUHHp3d+eOARMj+iOr3k+52L9VsGi7nbdy9fe/+HPq7eAm\nL3ocA2exBydjEwf3yT3twdll423G7jjGxuE68H6hru/B0c3dqR943LcNm749V1WvfbFrvdvYZJo3\nGR8X19fXmM/nW3v4eN+d9ju/HAEc5pClxgv/oGnqf/wdwkOd22R8fX0dbc+CF+bl/4ya2jXubSoF\n1qrVm0h37eCmA56f4Rx3onvIm/MyjoGuC5w6XMLLDV3hpH2QeezhQOc2GeuP/wCbYc/hcFhLLKZK\nOZTc7/eTUQILvzb57QBLDzwIVdsvRuryBz/Dzc3Nxv8h0jxTP/TG4DSpzVgPw+Y83TBnbaOb7LiN\nbROebui0fuN2518AtY2TutGN2183pnJ5lp/3q6K8KZP7kPOxPCwd/3+r+/7RtkuBbrz07ArY3A+j\ne1GsX9gWmBe4/3iPDNs0l8Wbde0+3RjKdsX3q73xfTwOvP0O9oz8Q45cb3Vqddzwd978auet7LY5\nogs81tZh/cAbj5lLrK/Ydtk+2N64D/U+tivdsKx2y/fzeOA0OhbV1k6ONjoHQAQQB4NBtM+po9fr\nbfzd9xgMBo3y4mv82eo6Go3c+3u9Xnne0vLzDQaDjfOaR93zcd4HYzpdH2eItcnFOBqN4mg02mgr\ne3brA+3PXq9XptE+4H7z2l/7yNKPRqPyuvY9f7d0Vr7VzyuL7cKeR+tteesY4efnOje1H/tsbe21\nnzfuuG+K+5bxDIi+7rC2YXswcBtbX3ucNBgMtuzR7tO2Z3uw+7x21rI922BbsLL4utWJ7c0bN8qB\nbDveM3Odte+5nSyd/bXnse+t44x5rA1ou9s4jjFu9KWl5f5gG/K+s3159sbjRvnSs3W2Da4732O2\nZPVnGyP7bZVnWsk0RcY6KaWEhJ7zSIQHcCqPFAFUTRRKQlyHJoKtyeSTOnc04jhzYuDJQ0Wh/uWB\n5tmNJ1CYpJkE+DPnxaRQ139alvabTlIqLLSclE2pSKmrT9X51KH5y/3jeAYCpu5I9UuMm0JRx7AK\naBYHfD+3i9omf7a21D7gSYnLZbtXblEBY3aVslEW6p4g40lIec7qZePSytDxYum4bq3jzHmsLTDf\nqWhgwaAcVzW/6T3qGDA3xRg37En5TcdOjHFrfHAZBuU/yrdbAsebfFKTuRL9LtGXJoTelPQ9YtI0\nOnnVCR4mqDoxx9GJg3HmxKBeAxu8ihmNZrBH69mP9l8TUauDvKofm9qY5+2k7j+G/Val9cS0d/BE\nBuAunoGAqTu4j71+VHHJxFsliJlj1Kli0mfPVCNFGvHwIoZcR+ULjeBoVMjGjoomHivqyXtjw/LS\n8cjfuX4s2lrFmfPYscH9w/0ZY9zoQ/7MYLvyREbKgWTbVDHF9bF6sB2k8lausfpp3dHFCE6KZFMe\nch1R6+BNETWrRy9tlSBpKpa86EFVVKZJ/bxJ5iB0gBjYS1RvIRWx8+xHQ6Q8YemklGpzg9dXVUJX\nI5J8vYmt7mp/3Abq9auNNxXfXnsVRyeWqKwt1JbsPI+5GOPWc2ukUMeoJ3gsrdkd9wvbsKZnoavL\nDXpd7VaFDOerk5+OL52QWDzps6o9cDrmu5OgAzx2bHhRGu0D7Te1fRYdlqcXCeLrnI7rweOB03Hk\nxuMwHnPKS3a+ONeqI3USgbNvFCV1cGN5E0Vq8vC8fs/LqqvHLmKoSQSB0x7FM+oAMXgTNBOnthun\njXEzghNj3GpT9bDrbKQqgqj5q8BRz1aFb1VeVXapaZpED9nT13R1Ql/Od0LgqKfK/c/jXqM2PIlY\nn3ji2q5pFET73bNp77x9V0HJddX0Vgf7a89jeXnRHS+a5E1KXvupqPO8/pOInA7w2LHBUVSeExxh\nsMVDaj8xxi1uSvU5zzt8zWxeIzhsTyy0+LDnMCR4r3sRHB6AdUIgRfK73pMi7aqo0T7CSyfHuslC\n06YElBrNQegAMXAb6QCJcXMTsraV3a/9y20eY9wa+HyvJxbUk1dST0WWmtpPjA+8qpT9VEV7Uu1R\nZ3defk3yimcgYOoOHVueePCeVaMeqagNj031nHXC4OvqtHBatnOzCV0W4nP2ncvQ8cH2XuVUMc9w\nHb3x4j0H5986OsBjx4QKE+5bFRt23u5TnrB7OF8V2SqqNfrJdhDjppDRa944UPtlXu70EpXnsSjh\nNJ0cdj28aE2TqEzdhMF5WYemymtSP4+ELN+D0RFi4GfmwZOaaHiweEs1qcm9SQRNvXOv75v0qx72\nfB5xpNKkDvaO6sr2xKM3yXv1pbF77wKm7rBnY5KOcTNKwuPfi2IpsfN3y4vHrNqKLk+xffJ5jqbo\ncpSKHPXMmXt4gkvZrE5GXp/rOOOJMZWWBVzr6AiPHRMaWTR4YpzvYcHKtsH3sgDynLcYN5dw2c41\n8slprAzmax6HXAfHvru7RMUNmBIeTSehKmL2BFOVB9O0nKaHR6BeGu1gLz17dnujA8SgERXuWy/y\nopNOXd96AtfL99DIoVd3q1+V0FKC0fNqE3UefmqMeHVNORgq3uMZCJi6g8mSn9XbJ8BtokJaeUUj\nGHZdJwD2WuuiJlqWRgn5Gk8YbBNcnidaY9yebKw9dELjduEJUoWY5an5tI4O8NgxofODRvk0IsN/\nY/QjLN5ykZ3j6yyeLK0n0q0uzEtWNtdRx5GdYxsvznVP4FSRa5OJQon6kAhM0wmrSVSp6fPs4vl7\nRHgwzpgYNNypqj81IadEZIwx2X8xRrd/dulfr06ex9TEruy5dxX22kb6fKnn9xwMvV7RDp3Yg2Nt\nouFxe74U6avNqUjy+thsV8WRCtCqiGBqGcDrI/7O5fGkwTau44KvsQjTZ9Vn1Pp5NnUUR6wOZ8xj\nbUBFBEPtj/tRo4N2v35XgaTCmcvVyIxnN2wrdq9GbLwIu9hWqz9H0RrpVB0eAVVNNt5E4jXaIUeb\nAqquHfi49AgODyQeBFV97fWPFw07Rt+rOI8xbpxv0p9VS7IpguC6sG0baXied5Uo966pULT+8J63\n+HzvAqbu0IiKfWavVUP73Bdqj14feJG/FGd4ERXPBrQ+2g/eROVNEGor2s8a4fIiXWqbVRMSi7LW\nccY81haY/71IjXIMiwgvyqtRQc/WNDpXVZbHt17k0bMjtcFTOFL3InBS5LDvoYM0lc46/VjlHvP5\n1Es8CGdMDEqwXjscS7Qe2k9VHnXqqKu7RzRN68lixxNK/H2fKJGNkeJcJyI4Suyp5/WEgJ7Xvzqp\ne23FE4G1nfaPerHchyk70+iRCtwmtqMRHX1+FVkxbi4dqz150aNWccY81gZ4WZWdGr3GwsO+qxOk\n9qwRSU8gx7gZ6dExknKaPNHMy+e6lCr5XY7AuY8oSRePg3FmxHCsdklEGdy0Gv737E8nCW/S8Cah\nfQRYUxHueddKdPbMTeqvZdeVT+3ZmR/60+Unb5JW0lbbqYvGVIkWbueUl2znuEydfOzcLhEjL7LH\n+XtiiSc3b5zw/fzMHHW19msVZ8ZjpwCPbxbBLLbNzj1RkxLLKnBStuHZLUcCNT2PM478aJqqI3ZN\n4HCYiweLrl2zN6CDLbV+7Q3IFGFbw2tYXpdEqhp/l4465VGJHYnhvp/lHI9D+rxqIrIjZbNVUQi7\nnrr3UDtlci1s7N4FTN2Repa6drRrqQiOtqnHN6m86zijyX6/pnbG/dWk7k1tJZUXH63jIRM4nphp\nyjOHRr2r+GZfLvFs1Csvdk3gsJiIMf0qoz24egasUL2GU3Wp65DemqV2ln5Wb0XLZFKLcdszZFHH\nYUYlPVbTlq/lZ/fVoc64XlQcxyDRczuOOTkcM52X3pskUgKlSTl1S091y39eflXX2ySeoxEYNvmE\nnSbjAvtsf9nr1T7xNuLqUo5yEPeHjnHte66vRoVSEZWqfuU8DBrpVM4wvuI6tzlm9z0umcfaOLyI\nYlX61PW6OSYldr3rfD611NUqP7SRqZEBDzYdxF7kRgc4Ews3joZNWSUywTDxsfixeqU2bzIReZ81\nZGv10bAh55da61bDueRNxlUDJB/NDm67Y4m9RL90YomK94NolNc7x3zhORReKF85iu1ZN4VyvzDP\neULL6qd1tHuZ1+weFW+eSGMeYe7hezye030T7CxqHtwOreFMeewY8JY4d+HGlPNflVcXpZaYAAAg\nAElEQVSdQ1O1TLXvEWO1WPr/23v/GGu77q5rXfc85Z3O1P6i1RSKtLWWTlH7jjPWamIiEFNslBp/\nxNcYpJCa1FpINERLGhGFJo0iYDGmAaT4o9pi8UcTEaxAI6i8cN/MCxSGt7y8rQHEGJHa9hkH07m3\nf8xZ5/6cz6x9Zp6Zc83MNc9eyck557r2tffae639Xd+1rmvOrNosj+BU2UlukDSwDWMiQKJSkQTf\n6/P9Px5vbfNP4Dy+N7OdgiSGxjcg5rnqFh3fU5/KSR8sCwQGAyZtxew3xbZKYRAyka6y+2zvQMV2\nHxR8XsqrPQMCc9uLVVOTCe452rZKiJigGA/43b5X+Y7bE8uIB5XPUfeKwLBNhasVATLmeL3YnvvI\n+8rJ4+yyQBx7qNiOKYxTrW2Sc/qlfbTyXfuU7zqwQMH21b7g/mIMYx/eg9R/kQTHwcfBxBmDiYOv\nI7ng+SrosIJSERlXkGgA6sF3f2Z2R7BJfeyA1IU6kATuFDAWAgzOrH3OZJFVQftAbxMyoJi0eJNX\nmzvHo50rcpxCHX1ddXuSQXhb1l1VG6q9Q1/+sBAc7vte1uo9y/3u/Z2230ZuaEMTlXyvqtAk3P5s\nQm5foO8zQND29jFKRdqqfqqASZ+ifrPKQnBsl1L5kj9XhLy1jV8g3yCnVf/0NWNhjsHvHDvfjX3Z\nL8eorhFxXt7v4HAiBltXYkxCWBnhJjRgsT3Bywu5rSLTC5y+DcCydhXMKt15zOO7wtNzpnvLAoDB\ngcHAWgV5t63s46wk2+S523yuItccx2OYhDNT5kY28a30d5ZfEagcn304wHn+DIipA4+ZrK/6nRV4\ndvWiTWmfFNomxcQwrzHJzXPEEtub1xozegkNx3UgqgIIMcPkJM854FQkjnr5uLNs+xzn6TWeTRaA\nY7sWV1JSHHcYu2hHE56KoNuG9PmKBLMtx60wnLpWxQTPZZEEh5N3VuiMwYGEZMXEpTKAr8HC3SA5\n3swc1wZjgKgqLSQt+d2698gLSY/7roDlA8szBobK2Ukusg2/V0SChMP9VeMw8HA8Bx7bwL5mH8y+\nbWf6t/WrAinJd+rPY5x7lXW7H8+Pvu9gzDY4vwiCUwV1f7dPsfrigNJ7OUGhLU2i3T9xyiSbY9iX\n6Me2k+fDd+Nq9e4KYy9Qcm5c616FYKfyjHFsLjG28Lg/+xjtSfuazPrlah/xpkrkeF1rrfSx1CHP\nZ79MGla+ujyC44lUAG1C48qNs1ICO9tX1RACSEUmqmpQ9mvi48oTg4sJEo8ziNhJelleFRDvJQsA\nBhM+BypXQhzcSTiqoG5C5CCSOtAefmUbBhuTd/qzCUqPgFXB1hUsAx2rip4314c+VFUUuBdI+GiT\nJRGcHlHwWvJ4RRJoM9uchKAC/Qq78lr7lqst9GeToar64kSMtpf9bgQ743KVKPQCq6uXbjeLLADH\ndin0WSfsFWHt9eE4Y5LssRyj7BfEqtZu4qeTijznZNF7ajX28n7oryrPVtUZnidIcCNWoG6DGNSd\n1TDTJeDznMHIQYP65jgmZmbNDqDUwddwPg+WZwwMtL3BO8XE1Jso21TEwwDe2iYZ7Y1d+SP1rTJz\ng40DE7Nczs8VAAfGbFNV+LgH6H95jUGMpIZzY7uq77mBZ1evKhGpfKlaF87dIJ7CvrnGJjnsywmZ\n93SVWdPfqXf12T7TI9KuBnH+3DsVoXJ7HmdCN6s8YxybSxw3TVJtQ+OVY43JR2VTYgiFmEf9nNSn\nfr6G+6kiUCt9l1fBqQDfoF8REBqmIj8mQPzsyg0rLiZZrgiQkfI6goODKMHImbTb2aEqkNoZuWlt\nEcDQA83qRXsarFvbDBgGaW70KoMwuTJ5Jsmyf1VZtttyrjm2r6W/EIBIzOx39Hv6ookK15Dfuc84\nBsZeTAXHIG8Qt52c7Bh8Kx8jblX+ZD/0vjbeVPveOpmwOdA4WHh8E3D7gPFxGzE0Hg+CM7/Qv0xi\ne2Qlv5sQtVb/I808bl+s9pC/s/+ej5n45Gdg0vIIjkmJMyBuLIINgcGbr7V2A/BNXJz18jz7JIC4\n+lMFMQcwBxgCi7NJBywHF86LTvggWQAwOHDzuNvYZikkmK6ceZ1JpivQNpFyEEp96AOt3SzF2md6\nRNq6sI0DLn0qx29ts8rjeac4OWCf1IVJyZIqOMaTHpk0CSE22Pcqv/C6VySI9ua7Awr9rOeHFf7Y\nRhVJ6e0b+jz1cvD03nDgynlw3rPJAnBsDumRdZNK29V+Shyr/KzyD4oTMOqW+lWkhXobr43jc+PM\nLJ1WGVEFEvleZUcE5jxXZa/st/rOhXd2WxEpkyJnygbPqppTBSQSOQaxbOPKw4NkIcDg6oNt7U3I\nDW4CWdmwtZt2SmE26nV31a8iF2yX/bW2ubEZOAgKBJw8l9cwcHFN8nNFtL1eOYbXz0SLfXLMVZvF\nVHAM1ARdBoYqwOeaeN1oV663gwX9wNnqNrJioDfxtE9WfubgYr17fdnuTLbsm9uC4uyyEBzbpThm\nca1NkCn0H5MZ42t+rvYGcdOY6HbGX++7Clc8Xsz8g6LzdBr17YaKiJh0EKRIeNinqz0kGTzvvmkE\n91dVXjxWlU2zDTNwkqcUB1hn7DuTZw4MLpVyE1YZAKso9oVsw4DFwNXLKniOm9dVRBOX6rwDKW3v\nLJ7EnroaOCqybt+jHilOIkzi7XPcA1rjRRAcJgjcy9xPXFuDswO7wdjJkq81UXU1JMVByzZ3olON\nYV3dd88fq3lxjVwtyD6JlSY6jyLPHMd2LRVp4LkqRpiEEF98TUVofF3le8Zmkmfr4vjKRI+4lbLI\nCo6zVwJrVR7vlVt9jYOGSY4Jj41dESVncjQCSRZfnB9BycStyuKqCk7ldA+SZw4MFakz4Ld2E5ir\nzWz/MUA4o+0RaNqetqP/UR8HUwMCgwg3Pu1u0sxr7f8OMFXw5ZysK+dg4kWCkPZZ7dEnJzC3vUxg\nnaVyf2cbA73XsLeXeT19sspuTZBJCrb5ocmDsaHaBz1iZl9hP8bIIvDcIM7s51FIzjPHsV1L5UtO\nsCqinmJfqAi4CbCTOMcfJwIch3rRz4l9xmCPs8gKDjeCs08umjNSV1oqUsDP2X+VvbAvAnwaiONy\nLLLTqiJEwzMQcty8tqr0mBG73U5kAcDg7MRg6s1eBQwTJVfp2I8JiQMBg4yJAImGSbft6+oI/SHF\nBNtEp/I/V2LYljpUxJ3r5WDq4Je2mTuz2tXL5C/nmuvnQEDb8HsVMNgv7UeA75EY2so69casiAqv\nsV+R/HIu1iv7po9UCZrb+rz1m10WgGNziUl0RT5s09be+XxrN/+M2/vc/sP+nYhxvDzvd7anj6U4\nhq50WC7BYUBwcCeQM4siqBOwTU6YPTmwebEdAAj2dgj3a1LmUl7VF4ORs/mqKmUW/WBZADBsyxQq\nQmNwrTaes2/apgoM1KMX2LyR6WM9Yk0CYYJjoPE+qXyv8iG2yzbWmz5a6eY10Z5ZxC0q73uul4Ge\na8T1JxnpkaFtwcK25XjGMvuA90ClWw8frFvlXyS0DGwVyTJR9B5JIdmbVRaAY7sW2q7yYbYz1tH2\ntpHbG2tT6Pvs0/7n63v9tXbzl9KVdC3vr6gYwMkQ87OzT1dtuMAmIAZ+X19lvQ4aBh8aPfXkcQYG\nV4IqUON1nIMDtNlutn+wLAgYTAQM7AzIXPvWNjdxtfFIWHMsr3GVybIv6kjfrUiV/ctjV7rYDyq/\nMQBVpJxrSP+z3+U1uX7cTxpjERWcypac423AzDYkmfYf2rgiEVxvJ1oVYWIfHMe2dkBiX062PE/q\n48BlX6BfmdCQZHmPzCoLwrFdif0i32nDak8zPlXE1JhGn8oxKgLlzxyLmEN9q2IGx2BfiyQ4BGln\n2z5eZa0u1zMwVFWVXrbKzMdGIYA5C/eGdrbDQEun4mcGOfdBJzD524ksABh6IJ9CAK42rUmRM47W\nNjeWz5MAUwwkaW9X3jgubU//qwJP6uUgWl1vv6I+XEcTee8BZnnbgq0Sh1lLx7t6eT60Ke1ubOD6\n8f225Id+wUogj9OutD3PV+SY8+BnEytjRUWC7Lv2G35O3bhO2ca4yIA6uywAx3YtFdHI94owOzFk\nrK2woiLm9mF+rohRa+2GP3ofpTghJaatji2P4FTl3lzEivi4YsKgZmJSBRD3xzY0eK9ywgy4qrqQ\nVBEwTKRMyJwpGSzslHaOe8uCgMEkg+DOjMB+wI2d796QBmuvdUUwXYGpxjdhYDCkD/l6vuz3Jvcm\n+VW7bZm194yrkAYyr9XcwLOrVxXQ6Q9OTuhzlX9UhJT7tiKjBn9jH9fZRJf+X5EQJz0cg9cw2BlP\njDkkKa7k9MiSSf+jyIJwbNfS8y3bpbW2gQ3bYgixI/siRrBdtX+oW5UkGHtbu/lAsrnB3JXieTqN\nzVtGDByubhCASVQq0tHLdCqCVBEPGoabnzpxHOvF66wfv7tqU5Eork8VsB8kzxgYnF1XJDiF9kz7\nsB9vTmesVdZJkmx/Y79VBs5xTBTYb45lop1iIsM2Jvau9FE3JwlcU2doVeCv5p1tllLBqYiGs1gD\ndHXOQdx+5XW7jcRaJ9uGtjU28nOlM8W45TmlKGsuky3Ohdewnf1mVnnGODa3VPho0kqhfUy0neT3\n9oT3BdtbB4/lgkPlr8RN6La8h4wJANw83NAGCQJxFfx7hIV9e8P6mmpTVyyWY5DomLy4nQGChrWO\nrhjYgR8kCwEGztWAbrLg9ia8Js5sbxLb2s0H21trG+/e2CaiJkImLFVFiGTF5MZZuLKcci4mRwQZ\nBiwHUVegqurQEgmOCWm1f6vqDW3Ywxe2s33S/yr8oa0YJFJsLxMUBxTbn7o4QNGm7st4yHPEau8Z\nB8ZZZSE4tiupbFgRBSdXJhb0XduKxJS+x77znJO2CpMqUlSNawyDby3vFpUz1wpocrFNTPjZoEsw\n4aZz5cbg4D4I+L6GgFCRKgKHS73Wl4BJEK2ur5zt3rIQYOCGcFbojcR1SzExrrKHKmvg2FWVhkTD\nwa1HLkiE7NfO9h18chz6orMkB3IHI17bO9/r336HdX5yAnPbi3OtSHFKte8rf6AtexWRinTaJ72m\nPQJDP3VFLvVxWwYIkiySNvsqj3NM6+7qE+ds4jO7LATHdinGIeIK7VLZkcezD35mfxWRNs64bWub\n/lNVhnIsk2PPEftxebeouJFdpTGBIPFwpmWwNqlhvzYQDc3FNwHhpnVAdXXATsPzDCQ0cn6mnjzW\nA6sHyQKAwYBbAXmKyTKPmWR4Q9nGObbXvQoWtrn9kH7DedDHUpwFey4EAwZDk2DuKQFFdw24jg6Q\nrmxpnZ+cwNz26gVkzoVkzyTPZMS+wPW179AH6DPuy/qZfFWEgeNzXIuJszNr6uUkwOtQjV+tS/Y5\nuywAx+aSyt4VyU3ZliQbU/nuxI+JXEV0evvA+8T4whio/bO8W1TcnC6N+7irIlwogm8FUmaovC7b\ncFxnezSaiU1V8amOk5SRNFVtVgbdWA+OXQHdvWQBwGDwryo43DwmOLZtlWF4g1noVyY2BpiqYkM/\nq14kJK4U8Tz92X5eBTpnTq4GEVC8V0wkqyC+6m9xt6hMbkxWvD9JGk0MTUy4hvStiixmmxwj15nH\n6WvWo+e/9gF+NtZwvtmuqhizXY8UeU95r84mC8CxXQttzGPb1tsEwn05WarI+zYi7X7ymP2VGJNS\nVZS4VxdJcAisOSGTFRMGvhPoSToM2A6O7NvZDAmPN3VV5naG40BBI7FPk7Qqw3NAomPtJDNaADDQ\nLg4OrdW3jBzEq+wgr2Eb2sMBhpvXgcZEoSKrJOLUk5+zredl0mSS7CBk36kqFDkW596rXDCIZpvU\ncUkVnJwziS7t6iTEhIft6J+0GQkFSUwF7MQPfk8xwaHtbBsTNepX2dhEOj9XJNA2752r9N1JInab\nLADH5pKKqNjvbGP7ncXV2ryO9qyqwN4X7M/9OIZViZRwZpnP4FSbgwG/ClwOMgRvkpjs10DPTWmy\nYiLEYNEjUiQ+bst5OIiaENGoBgfOaWeyEGAwGawIT0UwnRWb6PbIA4mvSY77cuZL29IXch75brJN\nEpHC6wgAFYHjuuRx+p/JEP3dwYu6VKRPCcgiKjhVgPZ8K79r7eb/baqqaJYqYaItaeuKdJkMc1za\ng+1Njmlb+53Hp717/p9rkcK9R/LrCtXsshAcm0PouxU+2RdsH/fRI90mMz1S7feKrBDXevuy2HPL\nq+BUi8Jsk8cYUMgemVmRzDiYmZTkmDxnUKqybr7n9c7a3H+PrJncuELUI0RcswfJAoDBJI/HelmG\nM04HkvzMvhzA6CskLL3s1AGiZ1f6Yc7JwSqPO9vx/OyfDLYEjIqcVyTPSYZJvn1/1fcifgfHlQbu\nW+5fBnivf1Ux41owCJg8cX1pI2ODyS71qD5T7+oa+ybt3euX19D3HQQ5Nn22ajerLADHdikmIPRB\nr3dF5u0/vs62JtGvrnMi1iPYKb0Yx/PmBoskOGZvVfk/F86VGweSigA54Pg6BghnZQQLg56zfZMf\nBiyDWHV9GtXzcbXJ5x8sCwAG+kFV8aDtSB6qTVYFdF5HG7R2M2CZADvo28+qV2vvgMBknv3k+AxM\nqYf1535xdmYiV2XZJkecE9tuWZ8nJzC3vZxMUHJte0SSPlQFB64r9ztxwD5UJTT0m6of62ac7JFj\nzrOnj/eUA6L3SV5fjUNfq6pbO5cF4NgcQhvxGO3TWk0YnGBlu9Y2iUqFYSa42W9VGWICynGpKzGP\nfdLH506kZulUE+hmi95E2d4EhkyTm9xGvI2YGPAYUAhOVYCtnIx9E7CYTbtPs1xn0zvJjBYADL3b\nA9xgVSbOwF4FiorocLPRniatJMWuiJAIUH/2mzqSOPNY6u0Aa+JrspxC36iydVczOV+TRFcg3fdS\nCE5FauxLVYJhMuK1NJFxsDBR6NnWY5kY0I+yTY5j25JsVHOgn1b7qiJd1t+EhgG0R7BmkwXg2K7F\nNkwxqa7W3z5vspJSEfke0XdszOurfWI/MkF3kro6tjyCUxEFZ6wOID3Gmd8ZdNxvLir7zDEqgHdF\nqSJVBifrasMbYBwAqadfDoAPloUAA32B372RuY4kPT7uIFIFIIO+ryFpMsmmD1Ykgn7v6yud+Jl+\nZ5JXAVKuW69a5bGqKlJF4HiuPQMCc9uLvlMBvO3sNrlOPM71r4hk5XcptpUxy/5NG5owm5A5A7fu\n9Dv2bzyuKkzZ1vMwGcp2g+DsXnr7vLVN4lGRB8aT1toNX882+c4+mERV1xEf7TNV8mZdcgzHvdXe\nWPYtKgNotZkdLHJRDcAOGv7sTJtkxO0ILCZg1pEgVWX3DiDWlc5AcDKB2llmtABgqMDVwaiqvpEo\ncP0J5Hm+OlZVVkygK5LLY6mHSYk/2z9yTJMkzpc+QtLG/hlgrF+137jG7INr66A9N/Ds6mUwtp2r\nPdgL8LSd14++mW0rf+Zx+rKB3YHJ2EXsyXbUlzpVhD2F/sBrvE84V8/fa7UznLpNFoBjc4nX1wS5\n8iH6C/vp2czxLvvi+7aqDYsSvs77xLEUvrvMCk4vE3ZVhRvOC0BjbquyGOTTKOy/ysJpqDQCr+G1\nzPAdeDlfBtVKZ7LlXvB8sDxjYLBd8xg3iqsmXleubYozU/qAs2iO56qfx+ZYFRkwibcfeg+QmJCE\nO7D1SBb7T/25hzxfZ1gJPN6fhQ0WSXBog1wf24VA7cBhUmP/zHa0Ia/N9lzTClesg3GD41Y6EiuM\nNVwT+iH90XvD864qP8a82eUZ49gcYjtTekS+IhL0GfsNr3Wiwz7pgz7neEe/tr4kT05iXwzBIbB4\nQVtrNzZOb3G9aCY3FZFikGIbBgPq4T4JOp4DSY+DHsHEhKqn185kIcBQ2ZebwQGEm6W1tnHOAMw+\nbY+KzGT7XsA3Qamy8jxe6Wad3LerglUFy2ScgciBi9fyeu6N1NPrumo760+o7+qVa+XAnH7ljJYk\nINc/5+zztjX9riJQJKvs0zjigOGEinr7XIWD1I3fTWx5nP7C456352dyNassBMfmEBNwk+LW6geB\n7Qvsi6SVduwlQdxPjMl+5XUes7XNveN9tFiC48yTgYXHW9sMMj0SUmVdBv5cQGfd7tfBxEHD59yf\n+676dDWqqiQ5M2dfD5YFAEOuT2s3yUvF9G3r1tqG3Q3eJhXMZKvqhcmpdSDBqUiHrzO5MMGxTxig\nTKipi4nPtrUjsXGmTpLPdqvPi/gz8SqBMHkkuNPfvPd5TR6riKDJhxMivrOd21vHKgGsSIqDGH3N\n/Xkf5RjOvD1e5b8mQrPLAnBs12Ly63MmCBVZNu4RM02gq7hDf/G+SbFPEMN4jrjE/oE5y3wGpwDM\nDZAwUJiNVhvTRMCZOAMOwbwiUQ6C7tdZNPvkmB6nGo+O5nF4bGeyAGDw5nQlwe+t1f9klcKAzTWn\n7baR7qpt9kuCQ5LAYMlrTMiqzKbKogwSBIiK3FX+5IDpoM3v1IWgtxSCY8JJEHbgN7HlulfB3OTC\nOFURcONJteYVATfZMKGofMJkxfY2ITKBNrZyTzmwOdgNgjOf9Igk97ztwTbGmuwr3+2zrd2s1nkc\nV6bzs3G7IkTcU4yt6G9ZBMdVFwd7btQq6JuYuJLDcz3y1CMTzly84Mxu2d7kxUG0mqsrPiZBaXwe\nt8PeSxYADM5EHIxsH4M7g5YC88Ya81oGN9qMOmQ/ton9pCJFrW3+qTkDDjMpz7eqANFPUwxsXiMG\ncPui954Tguw/5xALeQanIqvVfqp8haBM/6oIC32uIrIMCt7bDjS+xoBvEmPywe+0K+dckW+Sn7yu\n0qkKkCb0jyILwLFdiskokw6uOY8bM4kl9m/263GoA/smFnE8+ym/myBRb7/mxplZOiX4ExQcLLgB\nvWkJ8AZ+BxMCnLPp20C/p4uDAIHBfTnIcK6eH68zSNGRHiTPGBicIVdrVAXeqgpT2bIXxL3elQ9Y\nL9qL+nOMqr3JLvvh/HrtCDqci0GM60CgcSBjdp9tGKDZV2trgrOIZ3AqYpnrlsd71QjawMcdACpb\nplT2Yr/2HevrsWGDDV/bRvRJvI0/VcCiXg56KU4CuAaPIs8Yx+YS+x39uGrDV2ttwy9b6z8kzH1R\n7Y/etVWlx0mB8ZF9eIy5cWZWgmMg6WVVNByDDQMQN3jV3zawMrskWeKYvcBZ6cNraPTbiB37cVVh\nJ+SmtWcNDK5O0J4MzFwXtrcNWmsbNuhVx7juVSXO9u3ZvNeH/cykifo6M6v6qPyI8yHYeI84iNpP\nvY9IjvJ9KQTHpIFrXAV0rkGvusLPJBmt3cQsX+f+XRXJPqyDbZvtqnFkpxt4xnPspyLV1Z4xYa4C\n5M6waps8YxybS0iUXSmjD5q0Mq7Rrk7Q2Sdxwde31m7gT15T+ZsTLettgo6YuMyHjLcFAYN49b1H\nJKrg5oBQbWJu4FxgZ3G98d0mDZrjV1UB6tEjTeybDvxgWQAwVGSCgO4NehfyYfJY+Y6v69mGwYYb\nnNdUlSfPzeTGxJckg0BVAVQK+/A+oG8bmBxETZxYBVj1++QE5rZXRUBMJnJOXCf6WVV18bpwj/I8\nj1sHEy/agphCPZmcMRBQT+phEkb/5yttWwUv+5MzdCdu1HdWWQCOzSWOMzxG26dUBMSYsS3O0Hfz\nnX6eYhxh/7zW/sZri6RqWQTHAb9XHamIATdnL4AR9Ctg7wUrA0EucNXeAZLn01jbiJlYavnyOer1\nIHnGwMBNZptuWyuuc2tt43PvOld1XPUwUXEgqLISV514zNkR/bRXGeBc6J8OPj2AIinitQShnGMV\nwPk513N13WIeMiY5oz/QFrYJ58q1rMilK17MXJmZ0hcqv7bdsj39kjpX1aYqcyYJYn/214LAdjGU\n/lJVunaWjG2TZ4xjcwlJcX43WfXa089ozyqxYr/0F553Ncd+Z6xprcYk+k8Vf6HfsgiO2WBO2sTi\ntqrJB3n1iMY2QsVAx+urYFBdv41EVePchRTtJDN6xsDgwHubjXyOG0kB2Zvmxtp73R3oW6v/hNik\nyMHOIGDyRp/IMZz5kwjl2AQeXpvX2c/cH0mX58nzBsxVv4shOFVQoI/QBq5gcS24hgR82s+Bp0c+\n6EMkMM50bXPjDn2S41aY4fbOot228gle7/NVZWBWecY4NofY5q3VZJJ4QZ8iqff3vK6qytAf+e7+\n8r1XsDA22o86uLa8W1S9AJFisKkyVgO6M9lthMJB7rYXHaIiM1VlqCInDqC3XVO9XjLB+aBr0Vq7\n4Qvc+ARur3drN3/r4bYNyetNUrI/bn5nOh7bgagKtr1qi4Ggl7XR99gn5+RKYl6fa0f/Tt1jIX9F\nRWKQa8T50j96wYI4xO953gEea7QxFskk/Z3XpB/bBtmHM9/qxWvt3/QXBkKSOuIyj1frV5ErEudZ\n5Zni2FxC25tsVIma21VVQCdSVeXQWJjXVgmAKzzss8Ih90E/W+2P5RGciqzYcF703satAoGzC2dI\nBBU6g8e9CwlxALgr4bkvweH87y1PDAz3mfNdXgw8t7Wx/1XEpaomudrWWv2XMfZF+moFRNQ5z3ks\n+xx9mf5skGDw8xy4Pyoy5SpUa8u6RWXbGQdsI88/19CE1oGd/aQdUpwc0bfcr30qj1V+aqxjP6k3\n95zta5ykbvTlyheqfhzgZpcPKcFp7SapcKwzUa2wznjo/rw/KkwyrjgZMJlnYmFMcf9ouyyC0yMX\n/M5Nm8ZNqcDb2QXbmEjlu/tiNsZFzvHpQASoHJdz6AXG24755cyeoHVveQRguG1ed2lTEYreulSb\nv9rYFRmtjldjV4DO8RwsPA7JRxWU6Ovb9oZ1oD8b5KgH++mRN5MwZ2OtLa+CkzpvI6Ka2w3gNTYR\nZ2xPnqtISUVYaCfaiHrSlx1Y7Av0t8qPiGHbKpe9ZM1B0GMPgnN/SRvcFh8+SBYFTkEAACAASURB\nVIJszCJWtnaThFsHjkV/oX9mO87BiZfJkosa7BOYuDyCUwUrTtJgUgEDAcbEwwBjEKgM69IZDevA\nkdf6ZQAhMDpLMsjawSrwue11J7kHMHwQHR764nhVEK5IX2/jG3wN3Fxjkwdn0a31Hx43KSeQeA6V\nn5nA9CoMrrZUa+T1Yx/VmM6eqsDNYLl6LeLPxL1mrd38s2gLEx2SC5Igr6evpY2YtXI8kxcmSSSs\nTtpMyu3X9jVeS5zMNWCfqtJt+LB9/oME2J1jWGs7JTiPiW+P8ariho953t7jFfHldSbV6RP0MWOe\ncTV9zTGRvtWWRnBMGlq7+WdoBFxvYm5uk5FeZpZ9GrC4UTlm6kKg62U71JnjZd/si46UxiWQmDxl\nm7vKXZz/q1evOYDnsTdt1cZ6+LqqIlMR0h6Z6hEK9+NgZ12cVXeIRJnN9UheFYQYzLxGBqEeABZg\ntgiCw4Sntfof+pmg5Dv3bF5rgsLjTHTYR+7fqupD8mExAco+jWPUxZjkz9bd+OZ5VGNX5LwixfeR\nD4IH98Wxl/i6Lenj/qZver+7UuP4RCxxDCMGWi8nU/bZPJfHpdeyCI6ZYBW4TBS4cQkKbO8Mh0ap\nMhmSnGxbVYoqYEph8LIRTabYtqcbGSzbPAQ0bsgdMp+5N2RvjG1ZYpUxmvTepjvtXY3XIxlVP/RB\nk+RK1/QX6kufs6/Rj3qgwXMGnIo45XkCDfUwABnk0O8iblExqDNRyPnkPDlfz5945L3sZKkiLiYR\nPGYd+N2ZrYOLCVZrNwla1ZcJiYkZyTgJujHKRG7b/GaRF3KLqsKXh1bHbsPKu1zXw+LU+TYdt2G3\ncTjbVNjZlkZwqsyDAJHHvdGyHTdnHiNAV8DMvvK7gd/jGsiqzD+NQP3yvVcN4lgprh7wZV0eLDMB\nw0M25C5ePYJjEuQNVfXTIzjVLYBtoOBX9ssxelWF6jpnzfa/ipAwSFVzrkrHvTFzjFgIwXHFxSSG\n+z/XjO19HY+7DwZ3k4lsR7uxr95nEwr6mROeHsY4SerhkAnTtgQs2xmrvL6zygshOPcV4oZtb5/z\ncUrPP6u+e1VMJwCO0SbATDaMn0wYFklwuAFYqeDG5QI4k2A7LywzX2dZ3HzVOCRIJBpVMCEIOBuu\nnIYBxkQmpQcqDC47kWcIDA/NWHqv1mriVRGYu+pAksB+XDnZ1rfJOfU00fCtsuqWaurCY670GHSs\nF0HMZLG1zT/Jnxt4dvVyQpPzS3Fli5mliU0ey7YG8yrI90hABf4es8I4kxHOoRe8KuLF9rcFoop8\nVySpFwRnk2eIY48h9qVeG37u3Ub1d5J8+gGPVQWKnj94v7Dfam+ZkMUS/0zcmyaBtloYZkdeXC+m\nQboiMyYtNpZfrgh5ExM4bTzq43EYxEyAsk0VWHYCHAsBBpPFqvxNO89BkG57fRCiRHu7j+rWVdVn\nRagqgkPA6hEiVyV9y4x+XxDGRVRwmIik75gcGHzznZWwKpFKqYiDqzo9cRJD+7v60wtmVTJonb13\nqsDWu7ZqT9zznLcF3p3KQnBs1+KY09pNbKxsxXhUEZNqb/RiXK+fHrFyZYg+SVLlPuZOpGbptFo4\nVnI4uYr4VIHC7V2ZseET2DiuN6hZL6/PsQiE1r0CgyrYbSNjzjB3IgsDBlfJWrv53AHXK49xfXs+\nkN9966ZHRm57maj43Lb+SDK2kaXqGEmwKzDbbsXdpU/79+r4IgiOE5bUP9epCuqu5PCcpRfQt5Eb\nV46d/FRYmN/p35Ufux9iiElLdZ1JlfG30qXSeRCceaSKRfl5G4k3qahIEkm57Uu/IElxgpBSVWgS\nQyrsrXwTe3B5BIcGMxnJ4wRasr9cLN8aMuGxAUggKgLilzNZEzNXashSKTYsyRG/V85XzenBshBg\n8FzpNySMtBevZcDPY1Wf3sApXHfrRZ8gyb1LJWfbiz5Bv6na0nfsp9V5V2zcF9vZL7lfHgN4dvVy\n1ZZkmaStIhy9d+OGg0X6TFUFYR/c05UPmpizr17iVV1PfbaRvWxjEsWxq+q01+3RZCE4tkupiKjt\nTju1tvm/1timIrr5zjjYI+uVf1T+VZFec4DesbkTqdkIjjMQLiony+pMLjRL6dWCsq0N5OBkQlON\naWDyRq/uL/JVAeFtWXcVqKpgey955sBgR+9lG/5ebXRnpM5EUrj+eY7+aPE4tKPJAI9Trx6R2NWL\nfkN/I5m57Xq2E9FaxC8ZM5lhYuJkogL7ClOqwJD2dWLivu2fxsFeMCCOWT+PYb8lVm4jL5wP25GM\nmRRV2F1l7rPJM8exOcQkpfpsnOO1jIeV/W13+47x0D6Rn2+721DhKvVLmRtn3osZ5OjoKF6/fh0R\nEXt7e/H27dsbbS4vL2OapoiIODw8jJOTkzg/P4/9/f14//3319edn5/H0dFRnJ2dra89ODiI8/Pz\nuLq6ir29vYiI2N/fj729vTg+Po6zs7N4+/ZtnJycxJs3b9bv1+t5ff3h4WEcHBxERKz79lhnZ2fR\nWovT09M4Pz+PaZri5OQkrq6uYpqm9bmUs7Oz2N/fj4hr4ri3t7ce6/j4OM7Pz9f6RkS8//77cXh4\nGBcXF2tdPgzy/vvvrz+nn0REnJ6err+nD1xdXcXh4WEcHR3F+fn5+lq2ze9HR0cb45ycnKxtd3x8\nHBGx7vPVq1fx/vvvx+np6br/iHc+wDHoBxGxttU0TXFwcBCnp6dxfHwcr1+/Xl9zenoaZ2dn6+OV\npG5p/9Tn9evXcXh4uF6H3Cc5pzdv3kRExMXFxUZ/veM9cbuc52rvHXUue1aSfkG5urqKiFivYcrp\n6el6z+W1tFdEbODW1dXV+nh+zms4fspt/hix6fvpI6lv4lf2leNQ58SwlMSVvO78/Lyc9+vXr8u5\n557a29tbX5vtjo6O1ljO40Pmk7RjrrdxLuKdz9FHImIdDyu8Sd/P+EObTtO0gasR77AtJfdY2v/4\n+LjULX2YvnJ5eRlXV1exv78fR0dHa5x6DJmF4ETEGpRPTk7i7OwsXr9+HdM0xatXr9bgERHrAB9x\nvRC5cHltSh7PxWFgcSBJ4Dg/P4/W2prM5IbmpnVQssFyo19cXKzBZW9vL169erXR38XFxZqk5ZxS\n//Pz87WDMBByHaqxX7JwA5O4pKRtHXiqPtJG3PC9IJTrvb+/fwOs6T8cj0FnmqaN/gg2lPPz8w1i\nT1unZHDLNUidSbj29vZuEGn6Yc4p55J+yvZJom6Tt2/fkkwtgnHnvrIPJaBHXK9ntuO6RLwjhXl9\nnj8+Pt6wmQlPRGyQE5OFBHP6xeHh4dq3En/29/c3SFTakeMdHh7G5eXlDZvm/NJXMonLMaZpWvuS\n90Oux9HR0UYCln15P/K413DIboTrmutvXGHM8fnT09MNzCF2ZrvEMkrGSPorE3vqk/YndhE36cMR\nN30t4l3i+Sjxbo6yEEubLpX5VgO/87ZP6P61S2osx/M2gEuq1e0nl6er+/ir8tmNEnSK55DjVyVu\nl7qpF+e5M1lIaddldopvFbpM3to7+2QfLun7NqJvY7pkylJtrwzPEm/vNkCvb+pRHa9817fvqtKy\nb4n5lokfEOUaVrdNVn65iIeMq/Wu7vXTnhGbz/3RblwTt+uV6e0THM929TMu9h9fY5xku8pfaFfb\ntMJh7h/OxUL92X5WWQiO7VJ6t6V69qxueVYxqOrLz2VVPluN7xiaUl3jWGtMmxtnZum0etaE4J4L\nEXoWwPcIfX+ZDw/yYUqCO43WAzKTCm9uEieOneLg4EBrcpXX26F8bRUw7yULAYYe6eS5KvCwDZ/Z\nqojJtnva9pFsb/CmH1f3sBk4qyBLPXr3wHm+eq4ifZj92s84l2pd7dPU14nIUggO9XaQ5zHa3ecp\nFQhXCVd+5jv9g/1ZF5Oxyl+tY0Wcqjneph99udeutx97yd5sshAc25WYrFYkItvle88X7Gd5zn1U\nx3s+5L2xjQRlv9Vzj+w/lvg7OL1FdTAhwDvoc/H5YGcF0FU221r9b+S3VZTsGKlHle3yWvdjh3AQ\n5jwdzHYiCwAGgrY3QkVkTHwd8KuAXj0QTKJLf3F1h+NST0uPHNueJjL0RfoE224LJlXQ4n4wAeP+\nqPzY480NPLt63TUIcw2qNtXam4RUL5Ma99dr1zu3bT6t1YTdfu8gZ19wG49bYXJvfrPKAnBs12I7\nUm7DH/pu7yH7bYSE41S+17vGvkSfqZIJvi+S4JCMsErDRXNGlO0q0mPG6E3OgIeFu7HJ8xirP3YG\nByAfrwID9fLc2c6AxOM9h7qXLAgYKvJAm5PsmuiYgObxfOftH/Zdbf6qEtBau0GMDSTZvvK5anM7\nWNmv7ae+xsdJqJz9k1j3AqDXGP0uguBUBKAK/K7A+nhFCCoyU5EJY1SVYFU4VhEc24t+SB/ifvE+\n6CVxtC/7rvqEH5Tj7gSnbpMF4diupCLI+d3korKh+zKJrfo3ga0wt4pdFeGq/M6YLb9eHsGpgj6D\nDY9XRIRAUW287IsBgkHBgFIFBZOdymjU2+DFflInBycHkB5YVkH2QbIgYOCaeU2cnaTQj/I8++Ox\nKgvqBRpeXwUYBzweSztXm9n9UgeXkUms6dvUiSTcz6FVQbHaX9UzJQS3pRAcJx4mOD1iWflK5VOu\nilW+aALJ6h3f2bfJiMko9asSuipzp24VpplI9Qi0AyfPcS1mlwXh2K6khz+3nWvtJk72sM/9VDhF\nqfYU+3Ic51iOp9Zpkc/gVGBAgpAT9fMnfjbGx5KMMIMmAKUYSBiEaHizUbPPCnDMfCtny+O9ZyKq\n8zt92HhBwMD1SKkCBt9ba2XVId+rz7cRTn/3ZrXfckwTnTxWVZb43WSHfW97TsMkOqV3jcGoyr6K\nLG4RBIe2c+DvBQmSAkq1ft632zLpbZjnKvO2MXoBx5l1RYo4d+rGW+HWmS/7LPdP5TezyoJwbBdi\nMl75rX22Ijlsv42sGuOqcz3f7V3XS0p784uIq7Y0gsMNxU1fsb6ceBV82D4/sxLkEj/7rW4hEDwY\nJPK4N7/JFPVjJkQyxLHZp58rYoCqyNmD5BkDQ5VR5/EqiGfbKkOtSI6DDIGbhITnKyJrcMl32r3q\nn/amv1g8Nz6PlevhgOSEgKSrmpvXwf2b7BDElkJwuE6Vb1VAzM++deXqIO3r6nCKbVCtP/d8lczQ\nftnec6p81WNV/l7Nh2NWRNDi8XaCU7fJM8axuWUbkazIwzZfus1WPZ+qbrFnf9U+8PdefKOvLfIW\nFYHZWQwBxGVUb1BnzXneD3I6+6369K0w6uTnZkiU/PwFwc5jVRmRy3cmYyZrO5EFAIM3pEGXQF8F\nsWxLO3GN83wVtHxLzJkO+9i2OZ2d28a+tiJR9E2PY9Cx32/zLc+JPmx9XV5eHVsEwZHON8Cfe9pr\nb/vnOuV1bNerfFCME/Zp6mSiYJ/J+WS/PWJRVXBSQFZv6OtEoQpY9nP6y6PIAnBs12IMa+0m2WXb\nFD/eYdJtnzWOGYOqMfK794Pffdclx3BMbm2hBMfEgNmpAYIExM/ocGF6GX0VDFwtyXe2dWBk+wo0\nK4dhoKFz8VqXlVM/A7Kd+kHyzIHBt1aqjet1tk0cAKqg4wzCZNIAzrErP6zOOSgxcJjgZD8Goyr4\nsF3qnr7mKpF9kLp0QGWjTZVpLYXgONHhWlO4/hZiRPW8C3Giuo1u36kwi9eYcDuRq3S7Cznz3HvE\niFWkHMP2p37b5jyrPHMcm0NsSxNgS5V8208r/zCGWYwbFT6ZhOV7VchgG/a1SIJTZa7eRBX4J3j7\n1hM/M4vFIm2Ah8v9zGR8i4rj+x5+tfH9PEjlWAxEDqTUz7rbke4tCwMGboL8zs1hMHU2U1Xg7Dv0\nH294Z+f5Ofv2bQzq7L5MhHg8pQce7M+E3DrZlyrA8n6hz7od/XHV7yJ+B8fr6FuRla28rvQVVjsq\ncPZ6V3apdKmCgRMjjssAUvlUdZztewSIhJC6ex+kVMeNv7PJwnBsF9IjNbZlZV8SZV+f33uJgIlO\nT4ds64Sf/XC8ap8snuDYKCQtrGqQADB74QblYtpI24DaIJ/jOVj5NhH1zmPOim3MbaSJjrCthL0T\nYpPyzIGhyhp6zwyYcLJtRaSr7xVA97JVBgz7UPWMTEUmfC7bczy+p472M1YCeK0rO55Hbw7VuARF\nAeUiCA4xxPuX68I9x0SK61EFAJKVihBVbWgbB4qK+FRYZb0t1KHCrYpAe3wmksTYikxV+2N2eeY4\nNqeYsJpQ9vY4xUSmIjb2sV5MqoiVSXgKE4DKT1V8WB7B8b3wKtsm0aGheHsr27uq481oslP117uf\nzetoAJMRAxTBzOXrinhVxq/AbyfA8YyBoUcsqs1owKX0SEmPSFSZq4OT29kmrARWGbY3vbMZ6+4x\nXYlJPUjyq1um9Dv6MeduP/daOYlYCsHxPLjWrub51p59pPIZkhX2zXZV8KEuFVbxnI+bIJmo5LW9\nPeC5VHuiunVusZ9Y79nlGePYXEIf6FW1+b1Hgqo9nsfz+mo/VHat+qG48lw911X58GqOy/szcW5Q\nZ6JcLFdPmFVsCwAV2XHZzCQlx0sj0EF4nDo609oWyKyvr7ezGEh7mdq9ZAHAYKJRPeNkkmFg5Trz\nu/tl9ZDn7GfWzQTW56hnfs621a3WbJNS+Wfv2R3uqerZLa+V9UqdfYulmvdKl0U8g2OMcXWrWj/b\n1uBbkRkTXfuiMc++wP565KTCgKqyWc23SgaqPcQ+PV/7jsfeFgRnkQXg2BzSiwPVfq6Iee+xh4oM\nV8Q6P9PHKv+qdPIcjNd5DuRqeRUcLqRv43DxaBBWbsz6WMWxUQjaJCgOLuy/Op99ue8c13pVjmJy\nZmZscPX7zmQBwOCN4szCQboiCgw4POaN2iMnlR5+BoPkubqlys3P2x4V+eJ4FXnzMz2uDFI3+zOz\nPRIl7xMnBtV6rs4vooJT+UoV5FN6pKVaA/oij1WYwb7TXyr/SulVCavbbGxjW1unitz0ntPy3DmH\nCpP8PNLssgAcm0sqMrOtne1WVd9MTOxXtreJTb7bd/O4j1lvx97W2uw4817MIOfn5+t/h354eBjT\nNMWrV68iImKapjg4OIijo6P1v2N/9erVxr9xPzs7i7Ozs3j79m2cnZ3FycnJ+l+uv379et3H6elp\nHB0dxZs3b2J/f3/9r9wjIvb39+Pi4iJaazFNU5ycnGzod3x8vNHn6elpXFxcxMnJyfr75eVl7O/v\nR8S7f/We1+S/l3/z5s01U4yIvb29uLi4iNevX8fe3t56zhHX/2Y+/4385eVlnJ+fr/8FfR7nv7d/\nyXJ4eLiee86ZcnV1tf48TdPaFldXVzFNU0S884OIiIODg7U9zs7ONnzp/Px8bbv0Odvi6upqff3B\nwUFEXPtg+lD6X15nmx8dHcXh4WFcXV3F6enpho+nLS8uLtY6nZ2drT/nHrm8vFz7aO6LlPThvPbt\n27fr/iMi3rx5s9Y7/e74+Hg9h729vYiIePXq1XqPvHnzZt1/jpc2uby8vMWCz1NS/5xL+tbl5eXa\nvjyeax8RGxiRuMJ9eHh4uN7biW055uHh4dqvTk9P4/j4eO2fxJ1pmqK1ttGGcnh4uOG7Edf2zGPZ\n/vT0NE5PT9e+bixJe6Z/5JgcL9eA/XMNcy7E8cSznHO2HbI7Sbuk7XzONrS9It75SdqIfpf+zv7p\nV7Rr4hkl2yampBgTc79FvPP79LP0/Qr7dy5zsCZmmC7XOvNhu2zTy3z5TEIe8xis9JCFsh0rLGaj\nqQ+vJcPN69yO+vRuTaQO7tfPTDxYFpD5VJlxa/WzBK6cZbtARtmrovGcqy6u0iCrKJ/T4Nj2z16m\nH3HzdgarO/QBtmdb7h9LIDv32nLergaEqgCeXyykguMKSuUnvUpIXsO1rTJnYkWV7faeabI/VGPY\nVsQS2qeqHnNOlY1964lj57nq9kNVWfJaPkoVZwE4NpfQJtVaV1Xoym68njHYuFhVbyiVL7NvVq8T\nW9xntS/nxpnZQIcbKN97m7Eqn3LhSWxMVBgo2C/JEsfJVwaxXiDwMz82mvugcTm2y9kGyrxmp8Cx\nEGDgOlUBxDZq7ebzAil3JTEkHFVQIjnlcepKwkGd6Zut3QxMJkEmJxXJcRLA+fAYSZrbGfQ4ptcd\n5H3Wn1Df1atKenpA773O4E65bc18rCIb9tEeuTIubiNa7rMiPQ5slW70X/tlin2V/lgFxFlkITi2\nSyHeVa/W6geOW9tO1qtrqrHcX4WTvRjFdo6nnBvHiCU+g+Mg5ElyMUgevKAMRqx+EJTZ3uDGNuyr\nel7HAMBnG7IdKzYkbgRK6ssARCDmNexzZ6DxzIGhyhh5PKXa1D2pqm0OaO6f7T1m9WxHa5v+WxFf\n9m2i0VuLXqZN/6jWLfUhGSeIeI9kW+rMfcU+l1LB4Vw4H6/TNhKSa2tfdJ+2KdtxvX19rint06vw\nMKmyvpUfWneTGgvn3SMq1MNr5Mx+VnnmOLZrqXyS690j4ymOedX56nNFhE2EKNX+Manalshz7LkT\nqdlAhxuWC+nNaGLABScQ8JaAbxExGyZ5qICHRIPHTHY4jsGfBq0qOAbLqqJAZ6jA5EGyEGAg+fPx\nirDSpq7+mORmP779R5v0yE/Vrtqctht93mPTfz1nXuNxfAuW1/tWWlW1rObpQJz6KYAu4q+oTAB8\nq9HrUO0zroVve9LHUqpAVK1hL9BURMi3PNnOPkY96HfUtyL8sO3GfDyOx9oW4GaVheDYLqVnA9vH\n7StSap9vbZPMVITdY5sQ53X2CY5JvZzEWxZbwfGGMoh7EViZMYhz4QzSLMtnGz+v0LvV5NsRrNaw\njcHIjuMsuiJmKc6y6Cg7ITetPXtgqKpVvUoI7cS2trszF5Oj6lkD27UiVvQ7v1tn+0SvSpDn6a/0\neQdtAgTJPfXrrRf90ccqIoS5LaKC4+yT+83El3NnhcTZptff69wjJzzH9bYQP3rE0zY1eTF+OFmq\n/Nv6magYs7et7c6waps8cxybQ3oYZf+tzm8jK63drOjmeC4sUOyT1qci8Ew67TMF2V4eweEm9Iaq\ngpWBKNvdNYhV2Tyft/Dnqn++qAPbssRfZXokOb51lXN1MKXhdybPHBi8EU0aK78xWchzrd3801rb\nkufcp6uNVSDhRjXJrSpzvpXJsau2VXWn8qsqK6+qC7x96kpEnveYXNdVn4up4FCckFQ+kudSvJY9\nYOb1XDsTGa+1xzMOmOy6H+rg5K0amxjk4ETfNlny3uoFV67nrPLMcWzXQn8xluR529PEYhvWMC62\ndrfHInq+YfE+c6Ei9XG/iyQ42wK2NwYBPL+bwHAjVpkobyVxY3rRGfgMKg6kzoRIsEhczIBpfIMR\nAYZG3im5aW0xwGBwrsA6j1fVkBTavjpuksLrTYJzDNvEAYi+aOCpbmdZb/roNp/ONiaBPsZxqtsp\nFeD0SNKqj0USnB55dMJVERjijINEVb2o1pPrXmXEvI4Bp6rImcwSK6mv5+/KtOfpPnqkzwGzuuU6\nqywEx3YlVWwwZlXEnJ/t4/ZP4lzVn6VH3n2NSUyV+HVwdXkExxuPAaRaYJILAgPbOmNmOwayiqw4\nW0oDMBDl523lY1dyaPAe8XEGTV05LzrLg+WZA0MF/lVp3evmQJ7rTaLBzVf5IPvNPuwb9hcGHtq3\nt4mrKoB9sao0MvhwXhXB4d5x4PFatbYZ7Dm/iuCs+ljELSoDO/2qCtI90DUJdpteUlKRb9sn1592\nMLEwyfB+8J6xLf3Zgcj6mSTdRpJ7gWxWeeY4tmuxz7X2zm8qe7Z285aWY5D7o52JJz1derhc+Tz9\nhnvJPq35LY/gVBmkDWHw6R1LQxDsnZU7SNkwDBYMHi7V9RhyVd1xfzYiSZF15TW+lbUTkvPMgaFX\ntjfIbgssDETVLc5s42zZhLbnfyYnJi20ZephH/AY1dx5q4DH6UPO5OlvJHdVX3xVe8jrkTrFQv5M\n3CDtQGC78zht61ukbGeC7UDTI7IV9rm9j1f+XvlA9tvTt7d/Kv+zHr114PdBcOYR47/xg+3sX/Zx\n9tFaXdExQa8IvI/32qU4ie/tg9W+Wt4vGR8cHKx/xfPo6Cj29vbi7du3sbe3t/5lYP+i6vn5+foX\nVPPXWiPixi8CHxwcrH8Vlr9mm7/8erD6RdeI619XfIVfdY2I9a/WpuRn/nIsf6X44OAgXr16tf5V\n2Gz/avWrsPlLtvnLjKl3yv7+/vrXH3NN3rx5s3FNfvcvVb5UyXXMX7rkL3Dy1y1zzfNXWyPe2en4\n+Hj9C5kpe3t7a3+qfhX2+Pg43rx5E2dnZ3FwcBCXl5frX4NNnzs5OVmPRX89ODjY+MXP/f39tY+k\nrmn7fE9fpZ8eHx+vf7n48PAw9vf317+Yncf5C7h5Pn05f7GbvxB+eXm5nuv5+Xm8fft2/cu7EbHx\na7r5q7Tpf3t7e3F+fr6xjqtfcF7EzxknNvBXiSNu+lTO1X53dHS08au/Ee9+iT33f57jL5z716b5\nC7Rpx4jY+JySPsAx89eNU7gX+EvGnCN/pXZvby+urq42ftU4x08/OT09Xf8aeOJk/mp4jpW/ZJuY\nnWvHsXOsIfMLf/Gd2MhfFL66ulq/5y9Z85eF/QvbEe/sXPlnyrZzqVO2457KmJs+nHPgfy9IvaZp\nOq9735HMwZqqsmkyx9BtIZ9jZszqhp8hcNbD68lMc5yqH2ZH2Rezcma/Hp/CqpArRhXzdZZVVR8e\nJAvIfKpKGb+nVPbkuVzrvK7ql37A49WrVwGhb4aqd6zqBDJ9fnembN1YSbCf2/ey3+yb88pxva7s\nn/vK/om2i7hFletf2THXhX6U86tuy7jiSvv08IOviM1nwIyDPE69qludPT9lH1VG3sMXCn2Hc3dW\nzvY8XlUUZpEF4NiuxXjg4/5Ou/X8j3YLVSJ72Fv5XQ+37Oe+TcYXx1jpo8/UiwAAIABJREFUvLxb\nVFWpfhvoMwBxM5Fw5HEeY0DipktD83u+83N1L5wGoyGpEw3Jfjmu9U7hMQanncozBwYHl9ZaeYug\nB7y3kUdvQAc9bzb3xeP0O75Xty2q8dkXhbY3ubGeXBt+zrWg3iZZ9GfvNycB6mMRBMdr7EBAe+Tc\nU4hTtIPXjX7o/WqCwX6tD9fX/mCymsfc1kGCfVbBLPtxH54n14HrRt0q355VnjmOzSE93+2teUUk\n7Avs15hJf6oIlMdp7Z1fVuSZ2OU9U90qXizBYXZtApCLVG3mXgZlkpL99wJCLqgDkJ+PILDwO3Wn\nk+XYNCjnakdzvw62Drg7kQUAgzdGRWKcFfCc7c3ATsCmLegDJlkVkTUp4LuriOyHvuDNbeKV8+Hc\n7cf0P/fNfUH/clbvyqTX+rGBZ1cvztMV4t6+Mkm07fKzfYWEJ8XkievNdTbOeCz6W6//qlpNG3MO\nPeJjssu5V4mC9ZglIevJAnBsl1L5ZIVRthWvNRb1+uL5bfHHOJTigkP6pQsA1r8g9rMmUu8ebtmh\nXFxcrJ9daNdZVhKfODo62rgHPE1THB4e3rgnHHH9XEM+w3BycrK+vxdx/ZzD5eXl+vXq1as4Ojpa\nf87nGyJi4771/v7+xr3zg4ODOD8/Xz8vdLB61oLPL+QzGUdHR/Hq1av1f1nlPfL8z+X8r9H7+/tx\ncnKy1onj5tittfUc+N9eX7r4P9jyP2yfnp6u7ZL/5X1/f3/d5npfXN/Dzfu7x8fH6+PZx/HxcVxe\nXsbR0VFcXV2t7xPzOam8Z+3/Hp2+k7a+uLhYP38xTdP6eZ581iefdbi4uFjrlD6R/VHfFD4fcX5+\nvn5W5/Lycv0sWz6jxb55b/z09HQ9Ts4hn1E6Pz+P169fx/Hxcbx9+zamaVo//5P3yFtr8f777288\nK7RESey4vLyM169fr+19eHi4fv6GWMPnXPKZhMvLy/V/Sj4/P4/j4+M1ZvC/lfNZB//n51xvHk/7\n5FpHvHsmIW2ZtsvnXfgf79Pn3n///bi6uoqTk5P1fM/OztbX0L9yD6QP8Nmr9NmUvC51OD8/X89z\nb28vXr9+vfbJ7HvIPEKf5LH069yrr1+/Xj8DmJLPTUW8+6/vvb75H8h7z/ocHR1Fa+/+G32eyzh8\nfHy8xtarq6uN58iurq429MvYqP9EPuszOLM8ZBwRG/8q/QQPOZ6fn68fvjxZPXBLMsEHfJNcJCG6\nvLxcB6e8Nvs6ODhYL2ZrbQOo8yFMPqiZRjs/P98gJalzGtAPGu7v72882JWSAJYAQOd6+/btBqjm\nw6sXFxfruXHOHxYhgFcPUuaapK0iYv1Q5cnJyXodc+29WbWRIiLW/WWA90Pm7iPtk4QriUpKgj8f\nPs9xaUsGznzQ8/z8fO2P+UB1+nPqSF2naYq9vb11v3ns7Oxs46FizjEfek3dCEC5R9LfkyQukWSf\nnZ3F6enpem0IyCTTEbEO+PwjhxSuD0k3hb5BUk1CxYcuSRryHPc7E6Z8qD7HyQeD08+yTyZLec3F\nxcUGiWEQo5/n9fQN7plcA5J+Psx828OnQ+4n/iMLEpCId8kW2xILIm4++NuzUz5Inr5VkWPrlu9Z\nPKBvU/d8sPjw8HCdvL1+/XodA/UHIpvZwa5ljrJQlmL9EGiWtlju5K2FwK0HlmFdpg2UmFlyZQmP\n/Xhc3vby7QuXcj1Gr0Tn2yEuR1svtm1txw/uLaC0W5VZOf/qNqXXyPao7GXfYUnXZVTfJrBelQ9U\ntxTYt29teQ3S57fdhvJa+PYG51c94Od5VM+RuV0s5M/EuUZpE0rlW1zDbfudfXjfVj5pDLG/+RYE\nMdC2tK9vm8c2H/EtJ2NQdWuj14f9ZHZZAI7tWtJ/K9ul+FYm440fy8j2eQ2xjbeWqltjxpaU6tYT\nr8l5eC/R7zDfWW9RzQY6XGROigasHrjlwib4E7RJgtw3F9Rtsh8/F5NjmuSQgNhYBiUHFZKzXqDK\neft9J/LMgcEbjxvVbUxWuLG4ZgbpPG9Qz7a0/Tbd6Acm19SZ95/pyxVAcdzK524DCoNbzsV90+cr\n4sc21HHV3yIeMvazTcYRB3faygTEdq8CPfc78YvCsRxMnAD5OZqKELEvjsHPfuYn52mf874i/to3\nUkxqdpaI3SbPHMfmkh7e9cgyMcD4xOvog631n/1iH/QrihME6ut957lx/JX/LYvgVMDBhTRrNJhw\nAWlQGpDEpAo8JEIV4BvYGcTYrwMI58U+XLVhnwZKkikb3Q5xL1kIMPQeSvPmsr1tV67/bVk5CWcV\nFHjcpJrju/JG+3Nu1pFzcsXFZJ/JgPdDivWtQNC+bNDi/uJ82zMgMLe9KrJZ+QbFwdoVDfaV9qXP\nVZUy44EJtd8rLOR+sM7b+nIlvOcv9HFjFMegPryu8vNZZSE4NodUdqTYP/Ia7gf7NPe+K3ZVX3yn\nLxHDevG66rsiV7HUv6Iio6RBCBhmnq6sGFAIRD3m6aDGjeiqTZVRUQdfl2NwHN7m4nzsXHmtK0UM\n3m5/b1kIMJhw5LHWbv51mjdaL1MxeamyFwca6lJVQvjdZNxBjXNyG5P6qppI/7Ff+jvXg8BjYu19\nYtCz363GWMRfUblSZh+p/MDgTpuasHK9/G47GnOMR7QZ19vEjL5TYZxtb7JaERsTfe4v45HHph9v\nC7o7l4Xg2K7FNqQ9ejbP94qQeI/Yz4yBrd38FXj3ax9wvKZeTgQ47tyV4lk6dcZYZSvcNATwbRvL\nlZqKLDFo5KI6A3cW5uoSg4lBhmTGQcrBzAbluvh6O8ODZAHAUAG8N4YDTI/MmMTYdxwcTIJNaF3l\nyHdXm3jONmRQY/vsJ8/Rr5yJk8yQPDlguqrF9XRFgf1XRB/jLeoWFedtcPca0leqJMP714Qg+678\nkedcKan2NrHMlTX7mc+ZdDsQ0Z4WV2lSl7y2R+jcdlZZAI7tUiofqsiL2+Z3EuHWagJse3sM69N7\n0ffcr7GTMZz6rPpZbgXHJKS1tjVjzcVx2d7ExFmHiUoVMAxwzERMTky+eIx6VVWHqoKzbQySqsrJ\n7iXPGBhsZ29Mvhvce1U12r36zGBlIm1CRLts2/gGkyogOtClVJU8k/NekGGA5nWcN9uY8JPsVf1m\nm6VUcEgCDMKcT66HEySTgmrtbNPKZxycuJ/ZJ/3X5MY+RTtTN75XOEN/5Lzp19bdvlqtU1Utm1We\nMY7NLd6vlc153IlSHmM7E9WKHNuHq/OOWezL41YEmv6zyAoOyQTZW5W5Mlhwc5mYVP1xY/MY+yN4\nMDtzgFkt9oZOHNcAwO8kQg40NCpJXhreweelE5zWbj4jUREJA78JJte+tZtEmP0xgDHwmGxyE1d+\n5zG52dNfUpfUm+PaH9nee8KBm1UZz5mk2hVEX5P6UAyM8NUnJzC3vbymKVU2a9v5lWvq4GGw9lqZ\nvPZIQra3fZnZ0qbGJ9qp6s9krUdwvUfyWmIi58/rXGWaVZ45js0htKf90kS+tU1ik+1s42zX2s0/\n2vCY7MvJVXWMe8Nxz3vD8Xrl57P+teYsnTLjJnlwadzBweSkV4FhH+w7P/uYM+M0asVGeZw6WX+D\nh8GJTuT+2G8a3o77IFkIMDgwtFY/KMfPBmr6jAkIgYLBL/si2a38ksSCgYu6UIdsR9vzuPU0mPE4\n++b4JH45xyrT4jxa26yY0YcZuETYF1HBcXJB4Paa5zpUdiPY23YViTEJsr+lj+SYtkt1nckMrzXx\noF/kMY9fBRuQ1w1/Ynv6S0pFoGaXheDYHEI78ljvu/d2SuVTtmPVL+OZcajXdzU2fd37YtXf8io4\nnDgBiAvUC1S9jIobrsqO+e4KCwkKjccgRWZpYmSC5ayImQ11cbCtAiTnmO0eLAsABm8OV9Rop9Y2\nbxmkVKDvwEGyUG1IA7fJjkkusxDqxOtbazfasm/OxwSIxIr9+70izfZbBuqKkPHdazM38OzqZXA2\n0HoduY9tH/tGRX6JTwwCDiL2a9q/p3NFbkxwOL9Kh4rsGldNBHv7xvhl355dFoBju5beupqoVoSz\n8pPbfNOxzPH3NrLsdk4MGePoyzi+TILDRSS5cPCoiAevy8XJd4KXNzeBvWK0POaMNc9TH5ds/dkl\nQwYpjsVATSeyQzqzu7csABi8QUkSTDZy/RgsDLhVtsH1z3Y5NvVwJsQ+SCSok6t6PmYfsv0duDhH\nr4nXinqSYJHsuM/Ktytyw/Vsz4DA3Paibew/VXXD+9TAznVwolRlu/aJFBNrjlORL49PPLAfu18H\nNSduDnQ5NtejR3KIn1xXznU2WQCO7VpIholXXu/Knk60TKxNmBkDHcsovJ7xL9vbfxzrOTf69+r8\n8h4y7i1iRXQcmHqEh0SElRKDBKs8DnTbgo+JiIHTWRCN58zQTkkAIsOtwOnDQnBMGk0+vA6uUlTk\nqALevMabk7apgosJlIOMbVmNR1+3L9jv8toqWLV2k1g5MJroVL7k/eUKhfbbIm5R9UDaBLIiy8QZ\nB3J/J1Bvs5+Jgf3cuhgH6EvOrh3QiGlVEPP8iW357qSTvkL/t+/uBKdukwXg2FzihKNHPmkPk2/H\nFBcMKj8lDlRC/6wIufX1Z76vPi+vgkNy4iqIyQQXlCTB1zqDMYhX7DEN4kDD7yRhJDxm0ASSak49\nAkY98lzqS4NXmfS9ZQHA4HXh+vF8a+2Gf6RU9mCQy2sZwD22fcjHqI8rJiYIJtHUwXNjUOr5pX3e\na8G+vHc4T863mjPtIFs8OYG57UU8MTkkhlTEjtcyQTJhZP9V4mSiQZ92QpPHeb1JlrHJVSD7Ktvb\nf2xr+66JV7YzMeQcdoZTt8kCcGzXUhGG1m7eRqzsUBFz9927xj7ghLAiVcRUvlu3nl+vji+vgkNg\n4abmpjIoE5AM1s6KCVa5qAYsj1GNZ3DymDSMwdBAWM2JoGjQcwb2YSE4VQXEBLa1m//6wBu+RzYN\n0s6QTTDZLo87uFXBhgS48lv6vvtPPVmdqYIv/avysV5A7hF2rqvJk+czd2a1q1eucxWQCbD2LZNe\n72vuXfot/Y4klTYlrlR6MECwHXWrgkFKFTxIeitiZsxh8Kr80UGv6mt2ecY4NqfY1vlOGxqXSFor\njMnv9nnaN8chQaoSPu4d47njPrGZmIR+llfB8QbvEZTecRuvVx3ZFgwq1lgFoAoMPE4vy0mdqoyQ\nQdDB1YBEB3npBCfFG6Bi/Xm+snNr7UYVg9faDlxbkgVn1WxXkU4TUga6yq+reTlwOODRV1u7+cNZ\nnCt9lGOxHUkQ1zb7ph9inoshOAzc9C36B+1d2YJrYbCvyAh9hHayf5kYVL7KwEBbVKTESZN9rGf/\nyodzDF5D/6CPec6D4Mwj28hw1Y5xzH6a7Yw5edzJE6WKfdTLxJtjkGjznddjnOVVcDzx1m4+wOuM\nqXe+CiJVJu3My1luLrwrSAQxE5IKfAxmBh9lwTeCqFm1QdmOdi955sBQZQUVQTFJpl9UAcM+4IzB\nQJ1j0Wec3VfEOa9je34n2FSbnOMyAajIiglVdU2PtHOtewGP82OVZ6XvkxOY217GEBI2rqV9gsTA\na+hgb9uYQPcIqsGcQcZ4Q1JM25mQOQkyjlZEmMeJmfR5kxuvj8nTTnDqNnnmOLZrqXCntTo20E68\ntsJAJ0P8bLsSF3oEt0qKuLccU42/qe+q3TIrOM4ynHUbXFxO71VmGPD8IpPlJqxIh6+zLgY1Ow/1\nZObnPuw8W4LJBnA9SBYCDF5fgqdJAzdLBeaVjXiM9qY/ehPSTqkj7cgNTMLQ2mYJ1qSEgMA2DpDc\nH947bue9Y5ByMGdSwJezrtVr1h/g2tXLxMYgTT8zgbENaEuTocpXUzhehUGVT9Mn7K9VssSAx7mZ\nBKU+9sWKkNmXSNbp6yY1DJSzykJwbJdSEYzW2kbMSDEZznbEPWNBZV8nbxTiBvtxzDLRon9lP4yz\n8KXlVXAcFEgWnFF6kdNI/kwwJogYfOgMzD4qolSRnCpzc8XAejkL81jU2wBXZVgPlmcODK5iOdPg\nxuhlNQ7KXNs8n9IjoxWB4EbO9yoYOLAaKOjD1ofByUSXRItkuBqDOjkzNxF0FdPA42A4N/Ds6lWR\nCAOywd2+RT8xONOvTBZ7/mn7GH8YqIwtqY8JqK83YbNN6Zu9rN5J5zbsMYlzsJ1FnjmOzSGVD/N4\nazd/hLG1m8800h/o49nW3+1nOY6JfupiTHGix+OO5cTZRRKcHpGpiAjPEUT4mW2rrNwVF/bhaxg8\nOQ5BrEe4TNJ4nuNVLNZBpKf/h4HgWCqwZKB3YOKGqogig4XtUJGBKjgQKCpyVI1b+U+VYbE/jmdf\nJ8ixLx7jGjiYeX3sc1UGn7IUgsPAy/Ws7F6RQ/tNRSiqcyaQ9FsSWCc+BHiPXZFoB50KU3ukjPr0\nfMtVGpPy3l7inGeTheHYQ8UkxUlatmnt5s9p9LDB/bC/beTF/uNjrhi1tvkMm5PYPJ/XA9OX968a\neiBbbfiKDZIk+FVVYSpw4AZm8KIhtvXZA8SK9NjwPTJGQDHD5jweLAsABm4ABxIDKu1koK+Ce1Wx\n6613fnfgcPWEfspAyqBV6Zv9V3pXQYZErgp8la9nWwdcr4X3l/emCM4iblGRMHANuNYmhyS26X+u\nhtAP6ZcEevqCXxzL/mbfpa+S6NI2lZ9yDPtVnq8IMNfLfsv1sN9ybQbB2b2YKFu4T00WWmul3elz\nxhlXYPI6t63wr/LVvD7fqwKF/XmxBMckxRUSgoMDQ0U6uEhmnhVYuw+PxT5oLIObSQ4NeBsZq8DL\ngY1OmY74YHnGwMDgy6BB32it3bA7AwLPM0PpBfCKMLkyw0BoMkD7mBRVgcP+xzlRTwdbky6uh/3C\n+6NHrk3YCID+rLVdBMGhD9ku3ne5jiQ0Bndf08OR3vrS7yrMcaJUkWSPw74qLKlwiMEpx6p0sM+a\nKFMX6zq7PGMcm0uYLNNvTVaIhXmslwCS0OY5x8weYbVPVwmW4zrnUSWinEss9RZVtSnvQgLSmLm4\ndyE/FbvsXe+MvDpXtXOwcybPQOvrqwBoZuyA9iBZADA4Y+Ym48bL784oi4C8AQoEBhLhbM8AwXM9\nolAFEmfhFXGxrrR/jmff9jFnUlX2ZRJnEl+RPI6XuuH8IggO7We75Nr3AJl7twroJjq0H/2QQcT7\nnvjWS7KMYSb+zrKpN/2rGssVGr8Td6iDCVOOw7azywJwbJdCgmASSTxhFYZ73HG08u0KY3m8t1eo\nn7Ekz9Gnq6SNfgnfXB7BqbKcCjwMyL3zvSynIiUOKj3i4r56ZKeXFTsA3QYiBCePY/0eLAsABm5e\nA3aVZffsWwGyCRHBwH0R1E1Qqn57drP9toFEa5sl5F41pgKg7LuaKwORg7fnU/kggWjV15MTmNte\nvXVMv8r5OmN1oE77eN9vw4geBpioVISi0jnb0sbWl8erBMtkzMGlqgT5Zb/znPLz7LIAHNuluNJC\nuxoTW6ufhaF/VKTDduQ11IE45UTKSZ3xu8LT1JHJwcoHl0dwtgUAggfZZ0VAfE1FBraRjyp49F4m\nI9Vxgse2vnwexuxmm/z8YHnGwFAxfq5N5RPecNwglS/x3eVVZzhV4LF/2R+sXy/YOUjlmNv2BOdb\n6VBVCKo+rYMTAwNUsVcW8UN/FaaQBDvZqtYh26Z/2q/on/QfVwR7tiTRsa+RWFYJkdvltdt8ib6i\nbLnER69dLzmw780uzxjH5hKSGJKG1toNWxAvTSK8n7nXiV+V/StMrAh2Fd/oN9bDyRj8aFkEx2DS\n24hVpabKLKrzD30RBCsA8BycBdspsq0BtdK3lwXuDDQWAAz0DQeNCrB7ts9rDMpu28t0qsCwzWfc\n77aKYu986lFdU1Vzcp7W/TZ92Z8zv6qdfH0RBKcCZO7Lqlplv3PyVBHnqp3xYdu+dtZbYUFFYnv+\ntA0HHUise1UV8vyrvcq9+CiyABzbpZCA8Htr7Ya/0K+ZpNCW7Ctt5mTaxJX2tY/lsQpbnaSmzkw4\nTJBRsVwWwfEmrTbzNjB4KIm5z/V0IhttW9ttROaDvujQD5IFAAPLq1V53+tCYK6uoT28QZ2pVv5n\nsCcQOOBl38xo6BcOZr3zVcCsXgav6rbHtgpFj9CkPvbtVftFPINT7fse8XNyUu1bkxfbh75R+aXH\nYcLT04999PCl0vuDYM5tY/o4/c17MseeXRaAY7sU44T9gWSF8cJVS94qqhKiimD7rkKFv77OpKnC\nT8+hIPrL+yuqKnj4e2/z32UT7uJVjdsb6zZitisd04keLAsAhl5Abm3zF4GZibBNa5sgUFVj7kqi\ntwF9L2O27/QqT75FxfGqasBtvrQtOFf63yUIdoL8Iio4H2R/9Sond93P9rlqDbcRprvYrBr/Njy9\nzbZ3bd/TtdJnEJx5xH7G2+w+56Rsm8/fNanaRsIrjDMhrhK63p5adAXnPpvxIdfcB1AqQz0EEB6q\n74eJ4OR88zNtwGPVBnFFpaqibQtSdwky7qciFr33irTdBhLbfMLZ/11uU/g2HX2ba+e+sPaLJDh3\nuW13Xyx5rNdTjftBX7P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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_bifurcation(fig, axarr, index, x, y, xmin, xmax, ymin, ymax, precision, keep, num):\n", " points = bifurcation(precision=precision, xmin=xmin, xmax=xmax, keep=keep, num_compute=num)\n", " axarr[x, y].plot(points[:, 0], points[:, 1], ',', color='k', alpha=0.8)\n", " axarr[x, y].set_xlim(xmin, xmax)\n", " axarr[x, y].set_ylim(ymin, ymax)\n", " axarr[x, y].set_title(r'${1} < \\mu_{0} < {2}$, ${3}$ cycle'.format(index, xmin, xmax, 2 * index + 1))\n", " axarr[x, y].set_yticks([])\n", " for i, mu in enumerate(mu_vals):\n", " axarr[x, y].plot(np.ones(10) * mu, np.linspace(0, 1, 10), 'r-', alpha=0.25)\n", "\n", "fig, axarr = plt.subplots(2, 2, figsize=(8, 8))\n", "plot_bifurcation(fig, axarr, 1, 0, 0, 3.8, 3.9, 0, 1, 500, 200, 2000)\n", "plot_bifurcation(fig, axarr, 2, 0, 1, 3.735, 3.75, 0.1, 1, 500, 500, 5000)\n", "plot_bifurcation(fig, axarr, 2, 1, 0, 3.7, 3.705, 0.2, 1, 500, 500, 5000)\n", "plot_bifurcation(fig, axarr, 3, 1, 1, 3.687, 3.6875, 0.2, 1, 500, 300, 5000)\n", "plt.tight_layout()\n", "plt.savefig('logistic_bifurcations_odd.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that at each level of odd-numbered orbits, there's an additional bifurcation series made up of $n \\cdot 2 m$, where $n$ is the number of the initial bifurcation $(3, 5, 7, 9, \\ldots)$, and $m$ is the next number in the series. This is especially clear for $n=3$. In other words, each odd numbered bifurcation follows the same pattern that the base-$2$ orbits do, they increase exponentially, while converging to a number, and the devolve into chaos as soon as you're outside their fixed orbit values.\n", "\n", "This means that for any $n$, there are an infinite number of corresponding bifurcations." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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Y5CQ8CtL4TqSu61HShS3r24thZzkC40Bqvl8UxUi4M4aN+4/bFvZ9H2ZZWnGs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\nCCEEAOD/B2WS7rN5lCjLAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "points = bifurcation(xmin=3.825, xmax=3.859)\n", "plt.figure(figsize=(12, 4))\n", "plt.plot(points[:, 0], points[:, 1], ',', color='k', alpha=0.8)\n", "plt.plot(np.ones(10) * mu_vals[0], np.linspace(0, 1, 10), 'r-', alpha=0.25)\n", "plt.xlim(3.825, 3.859)\n", "plt.savefig('logistic_bifurcation_odd_zoomed.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To show where these values actually occur in the entire bifurcation plot, we can plot our red lines." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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ad5I3vi9FUglLwkn02XaOL4+1Cw9tZPZc6DWzCUBK0WC9D1K6W5CokV3rYqLn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\nucvJQ9t5aFzORbp1BNF032wbH+wsSdWorkbYeY313uU483z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "points = bifurcation(xmin=1, xmax=4, precision=3000, num_compute=20000, keep=100)\n", "plt.figure(figsize=(12, 4))\n", "plt.plot(points[:, 0], points[:, 1], ',', color='k', alpha=0.8)\n", "for mu in mu_vals:\n", " plt.plot(np.ones(10) * mu, np.linspace(0, 1, 10), 'r-', alpha=0.5)\n", "plt.xlim(2.9, 4)\n", "plt.savefig('logistic_bifurcation_odd_full.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems that these odd-numbered orbits approach the supercritical point at around around $3.6$.\n", "\n", "Let's look at the implications of these orbits on our cobweb diagram. We need to rewrite our cobweb function slightly, as it's not precise enough." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", " \n", " Cython: _cython_magic_c09e6ef83b4b75ca34f4baad446d89ac.pyx\n", " \n", " \n", "\n", "\n", "

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+01: import numpy as np
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       "
 02: cimport numpy as np
\n", "
 03: 
\n", "
+04: cdef f(np.float64_t mu, np.float64_t x, int n):
\n", "
static PyObject *__pyx_f_46_cython_magic_c09e6ef83b4b75ca34f4baad446d89ac_f(__pyx_t_5numpy_float64_t __pyx_v_mu, __pyx_t_5numpy_float64_t __pyx_v_x, int __pyx_v_n) {\n",
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       "  __Pyx_XDECREF(__pyx_t_3);\n",
       "  __Pyx_AddTraceback(\"_cython_magic_c09e6ef83b4b75ca34f4baad446d89ac.f\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
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       "
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       "    __pyx_v_i = __pyx_t_2;\n",
       "
+08:         x0 = mu * x0 * (1 - x0)
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       "
 10: 
\n", "
+11: def cobweb(np.float64_t mu, int n=1, int num=100, int keep=100, np.float64_t initial = 0.5):
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/* Python wrapper */\n",
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       "  int __pyx_v_keep;\n",
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       "        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);\n",
       "        CYTHON_FALLTHROUGH;\n",
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       "        CYTHON_FALLTHROUGH;\n",
       "        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);\n",
       "        CYTHON_FALLTHROUGH;\n",
       "        case  0: break;\n",
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       "        case  0:\n",
       "        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_mu)) != 0)) kw_args--;\n",
       "        else goto __pyx_L5_argtuple_error;\n",
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       "        case  1:\n",
       "        if (kw_args > 0) {\n",
       "          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_n);\n",
       "          if (value) { values[1] = value; kw_args--; }\n",
       "        }\n",
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       "          if (value) { values[4] = value; kw_args--; }\n",
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       "      switch (PyTuple_GET_SIZE(__pyx_args)) {\n",
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" ], "text/plain": [ "" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%cython -a -c=-O3\n", "import numpy as np\n", "cimport numpy as np\n", "\n", "cdef f(np.float64_t mu, np.float64_t x, int n):\n", " cdef int i\n", " cdef np.float64_t x0 = x\n", " for i in range(n):\n", " x0 = mu * x0 * (1 - x0)\n", " return x0\n", "\n", "def cobweb(np.float64_t mu, int n=1, int num=100, int keep=100, np.float64_t initial = 0.5):\n", " \"\"\" Generate the path for a cobweb diagram \"\"\"\n", " cdef np.ndarray[np.float64_t, ndim=2] web = np.zeros((keep, 2))\n", " cdef np.float64_t x = initial\n", " cdef np.float64_t y = initial\n", " cdef int offset = num - keep\n", " cdef int state = 1\n", " if num == keep:\n", " offset = num - keep + 1\n", " for i in range(1, num):\n", " if state:\n", " y = f(mu, x, n)\n", " else:\n", " x = y\n", " state ^= 1\n", " if i >= offset:\n", " web[i - offset, 0] = x\n", " web[i - offset, 1] = y\n", " return web" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's an interactive version to play with." ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "scrolled": false }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "cdb7dac047784452bb02074889f891c4", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type interactive.

\n", "

\n", " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

\n", "

\n", " If you're reading this message in another notebook frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "interactive(children=(FloatSlider(value=3.74, description='mu', max=4.0, min=2.5, step=0.01), IntSlider(value=3, description='n', max=5, min=1), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 5000)\n", "\n", "def f(x, mu, n):\n", " x1 = x\n", " for i in range(n):\n", " x1 = mu * x1 * (1 - x1)\n", " return x1\n", "\n", "button = ipywidgets.Button(description='Save as File')\n", "@ipywidgets.interact(mu=(2.5, 4, 0.01), n=(1, 5, 1))\n", "def plot(mu=3.74, n=3): \n", " fig = plt.figure(figsize=(6, 6))\n", " plt.plot(x, x)\n", " plt.plot(x, f(x, mu, n))\n", " web = cobweb(mu, n=n, num=1000, keep=999)\n", " plt.plot(web[:, 0], web[:, 1], linewidth=0.5)\n", " plt.show()\n", " display(button)\n", " button.on_click(lambda b: fig.savefig(f'logistic_N_cobweb.png'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are our $\\mu$ values with $f(x)$. " ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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SqJrzCkQpcPxVTjZ8/SxEv2d6z9w1FcpUs52qcIJKmDs3dbrAZw/AxGth0FzTk8ePpWVm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obeYTuJNdIS3SFG3g+Hd8DBrbaTiGDzVcPmV81CTw+f6tyQNz7fz3fnf87Ivu15ZcZYElrF2o4U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\niS7sSZkMp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QohRC01i/nD3NXY6lhTtAnKT/DqsSReySxk1nUD+fkdw6S4ESKUEifA3jVQ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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 5000)\n", "n = 1\n", "\n", "def f(x, mu, n):\n", " x1 = x\n", " for i in range(n):\n", " x1 = mu * x1 * (1 - x1)\n", " return x1\n", "\n", "fig, axarr = plt.subplots(2, 2, figsize=(8, 8))\n", "for index, i, j in [(i, int(i / 2), i % 2) for i in range(4)]:\n", " axarr[i, j].plot(x, x)\n", " axarr[i, j].plot(x, f(x, mu_vals[index], n))\n", " web = cobweb(mu_vals[index], n=n, num=5000, keep=1000, initial=0.8)\n", " axarr[i, j].plot(web[:, 0], web[:, 1], linewidth=0.5)\n", " axarr[i, j].set_title(r'$\\mu_{}$={}, {} cycle'.format(index + 1, mu_vals[index], (index + 1) * 2 + 1))\n", "plt.tight_layout()\n", "plt.savefig('logistic_N_odd_cycles_cobweb.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can clearly see that we have period $\\{3, 5, 7, 9\\}$ cycles here, but if we plot with $n=3$ we obtain something else entirely." ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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5cPcJfnHzWH63Ez65y6Zmse//Ft7/VesiiGldJf/T5OC0Q3WJHEMxcGI1D+fI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\nQFqiBxHNupnbjN3Wrpt9xPoEYzBKDSLTwDnnwbHTwPG8H6w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fLN7Au+tT+fk13XhiVHcx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\nLiM1XWdwEoCzjQEefnojhUdP8cvPX8bdUwY4bZJG0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 5000)\n", "n = 3\n", "\n", "def f(x, mu, n):\n", " x1 = x\n", " for i in range(n):\n", " x1 = mu * x1 * (1 - x1)\n", " return x1\n", "\n", "fig, axarr = plt.subplots(2, 2, figsize=(8, 8))\n", "for index, i, j in [(i, int(i / 2), i % 2) for i in range(4)]:\n", " axarr[i, j].plot(x, x)\n", " axarr[i, j].plot(x, f(x, mu_vals[index], n))\n", " web = cobweb(mu_vals[index], n=n, num=5000, keep=1000, initial=0.8)\n", " axarr[i, j].plot(web[:, 0], web[:, 1], linewidth=0.5)\n", " axarr[i, j].set_title(r'$\\mu_{}$={}, {} cycle'.format(index + 1, mu_vals[index], (index + 1) * 2 + 1))\n", "plt.tight_layout()\n", "plt.savefig('logistic_n_3_odd_webs.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the $f^{3}$ case, since we're plotting $f(f(f(x)))$, our period 3 orbit becomes a fixed point, and all orbits that are share a root of $3$ become the previous orbit. So in this case our period 3 orbit becomes a period 0 (fixed point) orbit, and our period $9$ orbit becomes our period 3 orbit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Download\n", "\n", "Please download the notebook and run it locally! It's quite fun to play around with the interactive plots. TODO" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.6.3" }, "widgets": { "state": { "3b51ad47f98d45f0881ba32edebecbe4": { "views": [ { "cell_index": 8 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 1 }