{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "# Run-and-Tumble" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "tags": [] }, "source": [ "In this notebook, we will simulate the \"run-and-tumble\" model of bacterial chemotaxis, and see if it allows bacteria to move up the concentration gradient to find nutrients. The run-and-tumble model assumes that a bacterium swims by alternating between periods of straight motion (\"run\") and abrupt directional change (\"tumble\").\n", "\n", "For simplicity, we will treat the bacterium as a point particle, and model the run as a spatial step in a chosen direction and the tumble as a random choice of a new direction for the next step. So far the description may sound just like a random walk (or Brownian motion). The special feature of chemotaxis is that the bacterium will sense the chemical concentration and modulate the tendency of tumbling. In particular, bacteria like _E. coli_ use *temporal* sensing, i.e., they check if the concentration has increased over time as they swim. If it does, then they will be less likely to tumble, which means they tend to run for a bit longer. Importantly, the run length does *not* depend on the absolute concentration at any given location, but on the history of concentration along its own path of swimming." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "To model such behavior, let us assume that the running speed is constant, but the duration of the run depends on whether the concentration is increasing or not along the running trajectory. In the simulation, we will let the bacterium run for a default duration first, then check if the concentration has increased, and if so, we will let it run for some extra time proportional to how much the concentration has increased. Note that, in this implementation, each run will potentially have a different duration, so the simulation will not proceed in uniform time steps. In this case, it is necessary to keep track of the total time lapsed since the start of the simulation.\n", "\n", "To simulate this run-and-tumble model, we will again define a Python class. Let us consider motion in 1D for simplicity. Since the bacterium is swimming in a chemical environment, we need as input the concentration profile as a function of spatial position." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [], "source": [ "class RunTumble1D:\n", " \"\"\"\n", " simulate the run-and-tumble motion of a bacterium in 1D.\n", " \"\"\"\n", " \n", " def __init__(self, dt=1., speed=1., x0=0.):\n", " \"\"\"\n", " initialize the simulation by setting the initial position of the bacterium.\n", " inputs:\n", " dt: float, default time step size.\n", " speed: float, each time step the particle moves a distance dx=dt*speed.\n", " x0: float, initial position of the bacterium.\n", " \"\"\"\n", " self.dt = dt # default duration of run; actual time step will be modulated\n", " self.speed = speed # speed of running, assumed to be constant\n", " self.t = 0. # current time since the beginning of the simulation\n", " self.x = x0 # current position of the bacterium\n", " \n", " def run(self, T, concentration, alpha=1.):\n", " \"\"\"\n", " run the simulation until time T (total time since the very beginning).\n", " inputs:\n", " T: float, total amount of time since the beginning of the simulation.\n", " concentration: function of spatial position, can be called as `c = concentration(x)`.\n", " alpha: float, proportionality constant such that (extra time) = (concentration increase) * alpha.\n", " \"\"\"\n", " c_old = concentration(self.x) # concentration at current position\n", " while self.t < T: # run simulation until time `T`\n", " r = np.random.rand() # draw a random number uniformly from between 0 and 1\n", " if r < 0.5: # move left\n", " direction = -1 # direction of running\n", " else: # move right\n", " direction = 1\n", " self.t = self.t + self.dt # advance a default time step\n", " self.x = self.x + self.dt * self.speed * direction # move a default distance in given direction\n", " c_new = concentration(self.x) # concentration after moving a default distance\n", " if c_new > c_old: # if concentration increased\n", " extra_t = (c_new - c_old) * alpha # extra time for running\n", " self.t = self.t + extra_t # add extra time\n", " self.x = self.x + extra_t * self.speed * direction # move extra distance\n", " c_new = concentration(self.x) # concentration after moving extra distance\n", " c_old = c_new # update current concentration" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Let us test this class by running the simulation in a constant gradient of chemical concentration. First we need to define a function to describe the concentration profile, which will be a linear function of position." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def const_grad(x):\n", " c = 1. * x # constant gradient = 1.\n", " return c" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "Now let us run the simulation in this concentration profile." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "current position = 380.0\n" ] } ], "source": [ "rt1 = RunTumble1D() # create an instance of simulation\n", "rt1.run(1000, const_grad) # notice how we passed a function as an argument\n", "print(f'current position = {rt1.x}')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "It looks like this bacterium managed to move up the gradient to a position with higher concentration. Note that one bacterium could have moved in the wrong direction just by chance. In order to see a general trend, we need to simulate a population of bacteria and look at their average behavior. For that, we can make $N$ simulations and look at the distribution of their positions after some time $T$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "N = 10000 # number of simulations to run\n", "T = 1000 # number of time steps to run\n", "results = [] # collect results from every simulation\n", "for n in range(N):\n", " rt1 = RunTumble1D()\n", " rt1.run(T, const_grad)\n", " results.append(rt1.x)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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bWCR5NXAD8JGqegq4AjgBWAvsAj61t+9ZVZuqal1VrVu+fPl8litJS9pYwiLJQfSC4gtV9ecAVfV4VT1bVc8Bn+WFQ007gWP7Nl/Z2iRJIzKOq6ECfA54oKp+r699Rd9q7wS2tfktwPokBydZDawB7hxVvZKk8VwN9YvArwH3Jtna2v4DcF6StUAB24EPAlTVfUmuB+6ndyXVhV4JJUmjNfKwqKr/A2SGRbfMsc2lwKVDK0qSNCfv4JYkdTIsJEmdDAtJUifDQpLUybCQJHUyLCRJncZxn4WkJWbVxpv3edvtl509j5VoXzmykCR1cmQhYP/+5SfpwOfIQpLUybCQJHUyLCRJnQwLSVInw0KS1MmwkCR1MiwkSZ28z+IA4X0SkobJkYUkqZMjC0kLms+VWhgcWUiSOi2asEhyRpIHk0wm2TjueiRpKVkUh6GSLAP+CPhlYAdwV5ItVXX/eCubX56klrRQLYqwAE4BJqvqEYAk1wHnAAsuLPzAlxaOcf7/eKCdL1ksYXEM8Fjf6x3Az09fKckGYEN7+bdJHhxBbVOOAv56hL9vGOzDwnEg9ONA6APsYz/yO0OoZN8N2od/PtuCxRIWA6mqTcCmcfzuJBNVtW4cv3u+2IeF40Dox4HQBzgw+jEffVgsJ7h3Asf2vV7Z2iRJI7BYwuIuYE2S1UleAawHtoy5JklaMhbFYaiqeibJRcBXgWXA5qq6b8xlTTeWw1/zzD4sHAdCPw6EPsCB0Y/97kOqaj4KkSQdwBbLYShJ0hgZFpKkTobFAJIcm+SbSe5Pcl+S32ztRya5NclD7ecRrT1JLm+PJrknycnj7cGcfbgkyc4kW9t0Vt82F7c+PJjk7eOr/gVJDklyZ5LvtX78p9a+Oskdrd4vtgshSHJwez3Zlq8aaweYsw9XJnm0b1+sbe0L7u9pSpJlSb6b5Mvt9aLZD/1m6Mei2hdJtie5t9U60drm9/Opqpw6JmAFcHKbPxT4K+BE4HeBja19I/A7bf4s4CtAgFOBOxZwHy4BfmuG9U8EvgccDKwGHgaWLYB+BHh1mz8IuKP9N74eWN/aPwP82zb/YeAzbX498MUF3IcrgXfPsP6C+3vqq+2jwDXAl9vrRbMfOvqxqPYFsB04alrbvH4+ObIYQFXtqqrvtPkfAw/Qu6v8HOCqttpVwLlt/hzg6uq5HTg8yYrRVv1ic/RhNucA11XV01X1KDBJ77ErY9X+m/5te3lQmwp4K/Cl1j59X0ztoy8BpyfJaKqd2Rx9mM2C+3sCSLISOBv44/Y6LKL9MGV6PzosyH0xi3n9fDIs9lIbPp9E71+DR1fVrrboh8DRbX6mx5PM9cE8UtP6AHBRG45unhqqsoD70A4ZbAV2A7fSG/X8TVU901bpr/X5frTlTwKvGWnBM5jeh6qa2heXtn3x6SQHt7aFui9+H/ht4Ln2+jUssv3Q/D4v7seUxbQvCvhakrvTe+wRzPPnk2GxF5K8GrgB+EhVPdW/rHrjuwV/HfIMfbgCOAFYC+wCPjW+6gZTVc9W1Vp6d/KfAvzMeCvae9P7kOT1wMX0+vJzwJHAvx9fhXNL8ivA7qq6e9y17I85+rFo9kXzpqo6GTgTuDDJW/oXzsfnk2ExoCQH0fuQ/UJV/Xlrfnxq+NZ+7m7tC/LxJDP1oaoebx9czwGf5YVDTQuyD/2q6m+AbwL/gt5Qeuom0/5an+9HW/5PgB+NttLZ9fXhjHaosKrqaeDzLOx98YvAO5JsB66jd/jpD1h8++El/Ujyp4tsX1BVO9vP3cCN9Oqd188nw2IA7djq54AHqur3+hZtAS5o8xcAN/W1n9+uOjgVeLJvODgWs/Vh2rHKdwLb2vwWYH27imU1sAa4c1T1zibJ8iSHt/lX0vuOkwfofeC+u602fV9M7aN3A99o/8oam1n68P2+/7FD7/hy/75YUH9PVXVxVa2sqlX0Tlh/o6r+DYtoP8Cs/XjvYtoXSV6V5NCpeeBt9Oqd38+n+TgTf6BPwJvoDeHuAba26Sx6x1xvAx4Cvg4c2dYPvS9rehi4F1i3gPvwJ63Ge9of0Yq+bT7W+vAgcOa4+9BqegPw3VbvNuA/tvbj6YXZJPBnwMGt/ZD2erItP34B9+EbbV9sA/6UF66YWnB/T9P6cxovXEW0aPZDRz8Wzb5o/82/16b7gI+19nn9fPJxH5KkTh6GkiR1MiwkSZ0MC0lSJ8NCktTJsJAkdTIsJEmdDAtJUifDQhqBJD/XHkp3SLvj9r72PChpUfCmPGlEkvwXencyvxLYUVX/dcwlSQMzLKQRSe9b4+4C/gH4hap6dswlSQPzMJQ0Oq8BXk3vmwoPGXMt0l5xZCGNSJIt9B6DvZreAxsvGnNJ0sBe3r2KpP2V5HzgH6vqmiTLgP+b5K1V9Y1x1yYNwpGFJKmT5ywkSZ0MC0lSJ8NCktTJsJAkdTIsJEmdDAtJUifDQpLU6f8D2ALMhVvYmq0AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "nbins = 20 # number of bins to use\n", "plt.figure()\n", "plt.hist(results, bins=nbins)\n", "plt.xlabel('x')\n", "plt.ylabel('count')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "Bravo! The bacteria have indeed moved up the gradient, as their distribution has moved to the right of the origin." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "We would like to see how the distribution changes over time. Because the distribution has a single peak, we can characterize it by its mean and variance, even though the distribution may not be exactly Gaussian. To see how the mean and variance change over time, we will run the simulation for different periods of time and collect the results at each time point." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" }, "tags": [] }, "source": [ "You may have already noticed that our codes above are almost the same as for the [random walk](./random-walk.ipynb), except how we defined the simulation class (and that the `run` method for this class takes an extra argument). This is the advantage of using Python classes (a.k.a. object-oriented programming), which makes our codes rather modular and easy to reuse. In the following we will continue to use codes that are simply copied (and slightly modified) from the [random-walk](./random-walk.ipynb) example." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "outputs": [], "source": [ "rt_list = [RunTumble1D() for n in range(N)] # create and save N instances of the class\n", "T_list = [0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000] # time points at which we check the distribution\n", "xmean_list = [0] # list to store the mean of the distribution at each time point above; first value is 0 at T=0\n", "xvar_list = [0] # list to store the variance of the distribution at each time point above; first value is 0 at T=0\n", "\n", "for T in T_list[1:]: # we will not check the first time point T=0\n", " results = [] # list to store results from every simulation\n", " for rt1 in rt_list:\n", " rt1.run(T, const_grad) # run each simulation until time T\n", " results.append(rt1.x)\n", " xmean = np.mean(results) # calculate the mean position at given time point\n", " xvar = np.var(results) # calculate the variance at given time point\n", " xmean_list.append(xmean)\n", " xvar_list.append(xvar)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(12,4))\n", "ax[0].plot(T_list, xmean_list)\n", "ax[0].set_xlabel('T')\n", "ax[0].set_ylabel('mean')\n", "ax[1].plot(T_list, xvar_list)\n", "ax[1].set_xlabel('T')\n", "ax[1].set_ylabel('variance')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" }, "tags": [] }, "source": [ "Notice how the variance increases linearly with time, just like for Brownian motion. This means that the process is effectively diffusive. Moreover, the mean of the distribution also increases linearly with time, which means that there is a drift. Therefore, the population of bacteria is on average moving to the right, that is, up the gradient! The drift velocity is proportional to the concentration gradient, and also depends on the parameter `alpha` in our model." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [] }, "source": [ "```{admonition} Exercise\n", ":class: tip\n", "\n", "How does the drift depend on `alpha`? Try to figure it out yourself by running simulations with different `alpha`s and plotting the drift versus `alpha`.\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```{admonition} Solution\n", ":class: note, dropdown\n", "\n", "See below.\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use a nested loop to repeat the above calculations for a set of different `alpha` values." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "alpha = 2.9999999999999996\r" ] } ], "source": [ "xmean_all = [] # list to store `xmean_list` for each `alpha` value\n", "xvar_all = [] # list to store `xvar_list` for each `alpha` value\n", "alpha_all = np.arange(0.3, 3.1, 0.3) # range of `alpha` values to use\n", "\n", "for alpha in alpha_all:\n", " print(f'running alpha = {alpha:.1f}', end='\\r')\n", " rt_list = [RunTumble1D() for n in range(N)] # create and save N instances of the class\n", " T_list = [0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000] # time points at which we check the distribution\n", " xmean_list = [0] # list to store the mean of the distribution at each time point above; first value is 0 at T=0\n", " xvar_list = [0] # list to store the variance of the distribution at each time point above; first value is 0 at T=0\n", "\n", " for T in T_list[1:]: # we will not check the first time point T=0\n", " results = [] # list to store results from every simulation\n", " for rt1 in rt_list:\n", " rt1.run(T, const_grad, alpha=alpha) # run using specific `alpha` value\n", " results.append(rt1.x)\n", " xmean = np.mean(results) # calculate the mean position at given time point\n", " xvar = np.var(results) # calculate the variance at given time point\n", " xmean_list.append(xmean)\n", " xvar_list.append(xvar)\n", " xmean_all.append(xmean_list)\n", " xvar_all.append(xvar_list)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the mean and variance curves for different `alpha`s on the same plots." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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bN4PS0hhcXAYSGvImpqZXLqGUmZnJypUryc3NpVWrVgwZMgQrK5lTLdWSY7YkNU5mRSYzd87kWP4xRgePZlanWVgYW3BsbRx7V2VgTindi37B7PhJTFoE4/Ht21i0qV+eVBgMHNu8nt1Lf0KnqaHb2AmE9RvMps2bOXXqFFbGNgytaY+VsKfAxaZJ70EG0zcwvV7Pk08+yaZNm/D29iYqKoqRI0cSHh5e79hp06YxePBgfvvtNzQaDVVVVdehx5J0/fy9yDDtCosMhRBkZi4hIfH/MDIyJjz8I9zdRl2xoL9Wq2X79u3s3bsXa2tr7rvvPkJDQ5vrdqSbkByzJanhDMLAL6d/4ZOYT1ApKt7v9T5DAoZQVVrD6rkbSUs1wdtwjKDjf6GqKMX5iSdweuxRjExN67WVn5rMpu+/JDvhNL6t2nDHlCdIycnlm2+/RVOjIUIfSEe1L0fsTOjyYBsi3GUwfVM4deoU06ZNIy0tjYkTJ5KXl8ekSZOIukRuz8VER0cTHBxMYGAgAPfddx8rVqyoNzCXlpayc+dOFixYAICpqSmmF/mfTZJuRRdbZNjlEosM1eos4uJmU1S8G0fHnoSF/h/m5h5XvEZqaiorVqygqKiI9u3bM2DAACwu8nhRunnJMVuSrp20sjRe3fsqMbkxdPfszmtdX8PD2oO0Q2fZ/FMcGq0xrYt/x/nYViwiIvB4Zz7mISH12tGq1ez9bQkxa/7C3MqaIU8+i0tYa1auXk1qaipOKkeGq9tRgAWxfTwZPSgYITTo9TVNumfArR1Mr5sFOSeatk331jDk3cseolarGTt2LMuXLycwMJDQ0FA6dOhwwaDcs2dPysvL65374Ycf0r9/f6D2cbKPj8+597y9vTlw4EC9c5KTk3FxceHBBx/k2LFjdOjQgc8++0w+epZueQ3dyVAIQU7OH5w+8wZgICTkTbw8x11xNrqmpobNmzdz8OBB7O3tmTRp0rlASWoGcsy+2ruUpJuC3qBncdxivjzyJSZGJrzZ/U1GBY3CoDWw++s1HDtmgZ2hiLanfsaqPAeX55/DcfJkFOP643rSkYNsmf81Zfl5tOo7kO73TSTm2HF+/+YbVKjoqg3FT+3BNmcTRkxph7ejJcUlB4mPfxEX5wEEB89osvu6tYPp62Tz5s1ERkYSEREBgEaj4bnnnrvgmF27djXZ9XQ6HYcPH+aLL76gc+fOTJs2jXfffZc333yzya4hSTeaVXklPH86Ha0QfBrqw73ujhcNjms0BcTHv0RBwWbs7aIID38fCwvfK7afmJjIqlWrKC0tpXPnzvTr10/OHt6i5JgtSc0vqSSJV/a+wvH84/Tx7sMrXV/B1dKV4sQUNn4dTUGlM/5lu/E7+hvWkW3weOsbzAIC6rVTUVTItgXfcebAHhy9fLj39XcxWNny089LyM/Px1dxp0d1MNFGKkoHefNYn0D0+gri418mM2sp5ubeODg07fqEWzuYvsJsRHM5evQokZGRAGRlZWFtbU337t0vOKYhsxxeXl6kp6efey8jIwMvL69653h7e+Pt7U3nzp0BGDNmDO++e33uXZKaW6VOz8uJmSzNLqKdjSVfX2Ynw7y89cSffgW9voIWwS/i4zMZRVFdtv2qqio2bNjAsWPHcHZ2ZsqUKfj6Xjn4lpqAHLMl6ZajM+hYcGoBc4/OxdLEknd7vsvQgKEoikL88lXs2KpCZTCj7envcS49jeuLM3EYPw7FyOiCdgwGPcc2rWP30p/Q63R0v3cirQcOZfuOnRw8eBArlQUDNW0xMjiy2N2YhydF4uNoSV7eBk6feR2NpgBfn6kEBk5HpZJ1pm94pqamZGZmAjB79mw0Gk29YxoyyxEVFUVCQgLJycl4eXmxbNkylixZUu84d3d3fHx8OH36NCEhIWzZsuWiC14k6WZ3tKyKJ2JTSa6u4RlfV14I8LjoIkOttpTTZ14nN3clNjatiQj/ECur4Cu2Hxsby5o1a6iqqqJnz5706tULExOT5rgV6QYix2xJah6ni07zyp5XiCuKY4DfAF7s/CLOFs5oigvY+dlfnM4JxLE6kbAjP+DYMQL3N1Zh6l3/F9C8lCQ2ffcFOWcT8GsTSb+pj5NTXMo3335HRXkF4QYf2qkD+M1I4DPMl9e7+6PR5nL8+LPkF2zCxjqCtm2+w9a2dbPcpwymm8H48eMZNWoUISEhPProo9TU1DB9+nQ+/fTTRrVjbGzMl19+yaBBg9Dr9UyZMuXcY0iAoUOHMm/ePDw9Pfniiy+YMGECGo2GwMBAfvzxxya+K0m6fvRCMDctj/eSs3E1NeG3dkF0d7j4auzCwh3Exc1Goy0kMGA6fn6PYWR0+YC4vLyctWvXEhcXh7u7O/fffz8eHldemCjdGuSYLUlNS6vX8v2J7/n++PfYmtnyUe+PGOg/EID8vVvZsDSXMo0/AVnrCcjYgvsrs7AfM6Zeqp5GXc3e5Us4vHYFFja2DH36eTxbR7Ju3Tri4+NxNLJlZE1HkoUlH3uaMmt8O/ycLMjMXELi2fcRQkdw0Ex8fKZgZNR8Ia8ihGi2xptbx44dxaFDhy54LS4ujrCwsOvUoxuf/Hykm02WWsPTcWnsKalguIsdH4T44HCRRYY6XQUJif9HVtYyrKxaEB7+IbY2rS7bthCCY8eOsX79erRaLX369KFbt26oVJdPBWkKiqLECCE6NvuFbiByzG48+flIN5tThad4Zc8rJBQnMCxwGLOiZmFvbo+oqeTEvB/Yc6IlpvpKwk4swNPfCs/338P0Iql0Z2MOsGX+N5QX5tOm32B6jHuAE3FxbN68Gb1WT6TGHy+9D18baek0OJAHewRSXZ1IfPxLlJbG4OjQnZCQN7G0bLoNWi41bsuZaUmSblhr8kt4Lj6dGoPg41Afxl1ikWFxcTSxcTNQqzPw832EwMDpGBldvuxRSUkJq1evJjExER8fH0aOHImLi0uj+qcrrKZkbTL2QwIwdpal8iRJun3V6Gv45tg3/HjyR5zMnfjiji/o49MHAHXCQbZ+t4/k8lY4l8YRGrcIr0cfwOnhh+tV6igvLGDbgu9IiN6Lk7cv9815HxNHZ5b8+ivp6el44kS3mpZsFCp+9jbmrXs7EuBkQkrK56Skfo1KZUV42Ae4u4++6M+LfI0WIxScTJsuBJbBtCRJN5xKvZ5XEzL5ObuINjYWfB3uR5Cleb3j9PoakpI+Ii39BywsfOjQfhn29pef7DUYDMTExLBp0yaEEAwZMoSoqCiM/rXY5XKEzkD5jgzKtqWjGClo21fKYFqSpNvW0byjvLr3VZJLkxkdPJrno57H1tQW9Fqy//iajdvcqNSHEpz0B0Gqs3gt+h6L1hfmLxsMeo5uWMPuZYsQej09xj1Au8HD2bN3H7t//Q1TjOmtCUePKzOUGkYODmBxz0DKy2I4EP0SVVWJuLmNpGWLly66m63OIFiQVcB7SdkMc7Hn07CmW1jerMG0oigpQDmgB3RCiI6KojgCvwD+QApwjxCiWKn99eEzYChQBUwWQhxuzv5JknTjOVZexROnUkmqruEpX1dmBLhjepFAt6zsOKdiX6CqKhEvrwkEB83E2PjydXoLCwtZuXIlqampBAYGMmLECBwcHBrVP3VCMSUrzqIrqMaijTP2wwJR2TVd8X9JkqSbRbWumi+OfMHi2MW4W7nzbf9v6ebVDQCRG8/hbxZxILsP5poSOpz4CN/h3XB74X2MLC+sppGblMim778iNykB/7bt6Tf1CUqq1Xz33TwKiwoJ1rvTztCC7w16UrxUfHZPNwKcICHhVTIzl2Bu7kXbtvNxdupz0X4eKq1k1pkMTlZU09vBhqf9XJv0c7gWM9N9hRAF530/C9gihHhXUZRZdd/PBIYALer+dAa+rvtbkqTbgEEIvk7P592kbJxNjVneLogeF1lkaDBoSUmZS0rqV5iautCu7QKcnHpetm29Xs/+/fvZtm0bKpWKkSNHEhkZecVNWy5oo7SGkjVJVB8vwNjJHOcprTBv2bhAXJIk6VZxMOcgr+19jfTydO4NuZfp7adjbWoNBgOV2+exeUU1GTX9cM2PITxvPb4fvIJNnz4XtKFVq9nz62IOr12Jha0tw6bNwLddRzZv3szhw4exUSwYrGnHGSN7HhTVTB7Ugo96BVJUtIn9++dQo8nHx2cKgQHTLzqZUqDR8XZSFkuzi/AwM+H7CH+Gu9g1auxviOuR5jEK6FP39U/AdmqD6VHAQlG7InK/oij2iqJ4CCGyr0MfJUm6hrJrNDwTl8au4gqGOtvxYagPjhdZZFhRmUBs7POUl5/E3f1OWrZ4FRMTu8u2nZuby4oVK8jKyiIkJIRhw4Zha2vb4L4JvaBibxZlm1IRBgO2A/yw6eWNYtLwtJAbiaIoPwDDgTwhRKu61xr9xFBRlAeAl+uafUsI8dO1vA9Jkq6PSm0ln8R8wi+nf8Hb2psfBv1AlHvdbqEl6aT/9C6b4vtRo7ciJOFnWoZZ4Pn9cowdHS9oJ+XYYTZ9/xVl+bm06V+7wPBsSipfffkVVVVVtNb54q8K4k1DNRo3FQvv6U6gYzWxsU+Sn78Ra+sw2rT5BlvbNvX6qBeCn7MKeScpmwq9nid9XXnWzw0r4+ZZXN7cwbQANiqKIoBvhRDfAW7nBcg5gFvd115A+nnnZtS9dkEwrSjKI8AjgNxIQZJuAevyS3g2Ph21QfBhiA8TPOovMhRCT1r6jyQlfYRKZU3rVnNxdR102XZ1Oh27du1i165dmJubM2bMGCIiIho1I1GTUkrJX2fR5lRiHuKA/cggjJ1u+tzoBcCXwMLzXmvUE8O64Ps1oCO143yMoigrhRDF1+wuJEm65vZm7WXO3jlkV2Zzf9j9PB35NJYmliAE+iO/EL3sAIdLR2NVnUfU2XkE/28KdnfffcG4W11exvaF84jduRUHT2/uff1drD28+WPFShISEnAWNvTXRbFOZcFLmkoe6x/ME30Cycv9lX3730MILUFBM/D1mXLRsqdHyqqYdSadY+XVdLO35v9aehNiVX/NTVNq7mC6hxAiU1EUV2CToijx578phBB1gXaD1QXk30FtmaWm66okSddSpV7P64lZLMoqpI21BXMj/Ai+yCLD6uo0YmNnUFJ6EGfn/oSGvo3ZRRaXnC8zM5MVK1aQl5dH69atGTx4MFZWl8+nPp++UkvpumSqDuWisjPD6f4wzCOcmvzR4PUghNipKIr/v15u1BPDumM3CSGKABRF2QQMBpY2d/8lSbr2yjXlfHToI35P+B1/W39+GvITka61u4ZSWUjZby+x8WAbcnUj8MjeQ1uLeHyWfI2p3z9l6YQQxO/dybYF31FTWUGXu+4latRYjhw7xubfv0LoDHTWtsDcyp/HakpxcFHx29juBNgXcPzYBEpLD+Hg0JXQkLewtPSv18dirY7/S8pmUVYhrqbGfB3ux52u9tdk3G7WYFoIkVn3d56iKH8CnYDcv9M36gblvLrDMwGf8073rntNkqRbzInyKh6PTSWxqoYnfFyZFVh/kaEQgsyspSQm/h9gdNlSR3/TaDRs376dffv2YW1tzfjx42nZsmWD+yUMgqpDuZSuT8ag1mPd2xvbO3wxMmv+utPXWWOfGF7q9Xrk00RJurntzNjJnH1zKKgu4MFWD/JE2ycwN66b+DizgaSf57EldxJ6vYqIhAVE3NMF50d+uqDkXVlBHlvmf03S4YO4B7dk4KNvg4UVCxctJiMzA2+9E51NIvjWFNZVlPJ43yCe7OtLduY8DkTPRaWyICz0PTw87q73M8AgBMuyi3grKYtSnZ6HvV14IcAdm2ZK6biYZgumFUWxAoyEEOV1Xw8E3gBWAg8A79b9vaLulJXAU4qiLKP2cWKpzJeG9evXM23aNPR6PQ899BCzZs266HGfffYZ33//PUIIHn74YaZPn35tOypJDWAQgm/T83knKRtHExW/tg2il2P9RYbqmhzi42ZTWLQTR4fuhIW9i7m552XbTk5OZuXKlRQXF9OhQwcGDBiAuXnDH+1pMisoWZGIJq0c0wBbHO4MxsSt4bPZt4qreWJ4hfZuq6eJcsyWbhWlNaW8G/0uq5NWE2wfzGd9P6OVc91GWDUV6Na+zJ4dxpxUP45NWSqRpRsI/vxFLNr8k8NsMOg5tnEtu5YuRAgDfSY9TJuBQ9i7dx87d+zExGBEb0045S6+jM0txMfVmj+mdMPP9izHjoymsjIBN9fhtGj5ykWfSJ4sr2LWmQwOlVXR2c6K/2vpTbj1tU/Fa86ZaTfgz7rfIIyBJUKI9YqiHAR+VRRlKpAK3FN3/FpqF7kkUrvQ5cFm7NtNQa/X8+STT7Jp0ya8vb2Jiopi5MiRhIeHX3DcyZMn+f7774mOjsbU1JTBgwczfPhwgoODr1PPJam+3Botz8SlsaO4nMHOtnwU4luvaL4QgtzcVZw+8xoGg4aWLV/H22sCinLpxX5qtZpNmzYRExODg4MDDzzwAAEBAQ3ul0Gto2xjKhX7sjCyMsHhnpZYRrreEikdjdDYJ4aZ/JMW8vfr269BP29ocsyWbhWbUzfz1v63KK0p5bG2j/Fw64cxVZnWvpm6j5JfXmFd8jiKRAA+6Vvo0NEUj5k/XFDyriA9lY3ffUH2mXj827an/0NPUqHVMe/7+eTm5RKod6OjWTgfGhvYnlfII72DeKqPBxlpHxOT8DPmZh60bTMPZ+e+9fpXqtXxfnIOP2YW4GBizGehvtzj7nDdxu1mC6aFEElA24u8Xgj0u8jrAniyufpzrZ06dYpp06aRlpbGxIkTycvLY9KkSURFRTW4jejoaIKDgwkMDATgvvvuY8WKFfUG5ri4ODp37oxl3f/EvXv35o8//mDGjBlNd0OS9B9sKCjlf/FpVOsNvN/Sm4me9fOPNZoiTp9+lbz8ddjZRhIe/gGWlpcPik+fPs3q1aupqKigW7du9OnTB1NT0wb1SQhB9bF8StYkYajQYtXZA7uBfhhZ1l/Qchto1BNDRVE2AO8oivJ3bcCBwOxr3OcmJcdsSYIqbRXvHHiHFWdXEOYYxjcDviHUMbT2TV0NbHuH+E1H2VH6HIpOS7vMxbSZORGbvv8EvDqtlui/fuXAn8sxtbRkyFPPEdy5+7kUPAvMGKBpQ4WTF3fnF+DhYsXyid3wtTzE0cNTqanJxcf7AQIDn61X7k4IwW+5xbxxNotCjY4HvJyZFeCO3UWqP11Lt/QOiO9Fv0d8UfyVD2yEUMdQZnaaedlj1Go1Y8eOZfny5QQGBhIaGkqHDh0uGJR79uxJeXl5vXM//PBD+vfvD9QuovLx+WdSyNvbmwMHDtQ7p1WrVrz00ksUFhZiYWHB2rVr6djx8rvASdK1UKU3MCcxk5+yComwNufrcH9aXmRVdX7BFuLjX0SrLSMoaAZ+vg+hKJfOd6usrGTdunWcPHkSV1dX7rvvPry8Lpqye1HavCpKViRSc7YUE29rnB+IwNS7frrJrUhRlKXUzio7K4qSQW1VjndpxBNDIUSRoihvAgfrjnvj78WI/4UcsyXp+oktjGXGzhmklaXxSJtHeKztY5j8XS0j9xSa5U+x43QPzminYV+aQJRDAoE/f4Cxk9O5NrLOxLHx2y8ozEgjtHtv+k5+hLyiYr755huKiooIMXjRXhXC5xZ61hUU8FCvQJ7qbU9K0sscP7sea6sQWreei51tvblY4iqqmX0mg/2llbS3teTnNoG0sbGsd9z1cEsH09fL5s2biYyMJCIiAqhdFPXcc89dcMyuXbua7HphYWHMnDmTgQMHYmVlRbt27VCpbvkFU9IN7lRFNY+dSiGhqoZHfVx4MdADs38tMtTpyjmT8BbZ2b9hbR1GZLuFWFuHXLJNIQQnTpxg3bp11NTU0LdvX7p3746xccOGMoNGT/m2dMp3ZqCYGGF/ZxBWnTxQjK7+0WBpXg62zq4ojdiO/HoSQoy7xFuNemIohPgB+KEJu3bdyDFbup0JIVgUu4hPDn+Co5kj8wfN/6dutEEP+76kYMMi1uU9S5lwJSBrI53vb4/jPR+ce8Koqa5i19KFHN24BhtHZ0bPeg3PsNbnUvBsjSwZqomkyt6NsUVFODtb8uvErniabeVIzNsYDGqCAp/H1/eheuXuynV6PkzJYV5GPnbGKj4K8WGchyNGN1Aq3i0dTF9pNqK5HD16lMjI2pIxWVlZWFtb07179wuOacgsh5eXF+np/yyYz8jIuOTs29SpU5k6dSoAL774It7e3k1yL5LUWAYh+D4jn7fPZmNvomJZ20D6ONbfJKWoaC9xcTNR1+Tg7/cEAQFPY2R06RSN0tJSVq9eTUJCAt7e3owcORJX14ZvCVsdW0jJyrPoS2qwbO+K3ZAAVDYNSwm5GHVFBfv/WMqR9WsY9Pg0wnvWz+uTGkeO2ZJ0bRVWF/LKnlfYlbmLPj59eKPbGziY12VvFacg/nic46fs2Fv5NsaaSjprVtPmy/9dUPIu6fBBNs+bS3lRAZGDh9Pj3okkp6Xz1VdfUVFeQWuDH+0MQXxjrue34kIe7hXIEz2tSD77LHFFu7Cz60h42Lv10vqEEKzIK+G1xEzyNDru93RidqDHRTf0ut5uvB7dAkxNTcnMrK3qN3v2bDQaTb1jGjLLERUVRUJCAsnJyXh5ebFs2TKWLFly0WPz8vJwdXUlLS2NP/74g/379/+3m5Ckq5BXo2VafBrbisoZ6GTLx6G+OP9rkaFeX03i2ffJyFiIpWUAHTssx86u3SXbNBgMxMTEsGnTJoQQDB48mE6dOmHUwJlgXZGaklVnUccVYexqicsjrTELtL/qe9TrdBzbtJZ9vy2lprKSVncMwK/1pfsv3fjkmC3djvZl7ePF3S9SVlPGi51f5L6Q+2pnmoWAI4tQr32TzVkPk2roiFPxKbp3M8H7qQ/PlbyrKi1h20/fE79nB07evox74wPsvHxYuWYtJ0+exNHElhE1HVDbOnFvaTG2tpYsn9QFN+O1HD38ASAuucj8TKWaF89ksLukgjY2FvzYOoD2tjdudSUZTDeD8ePHM2rUKEJCQnj00Uepqalh+vTpfPrpp41qx9jYmC+//JJBgwah1+uZMmXKuceQAEOHDmXevHl4enpy9913U1hYiImJCV999RX29vZNe1OSdAUbC0r5X3w6lXo977b05oGLLDIsLT1CbNwLVFUl4+39AMFBL6BSXbqMUUFBAatWrSI1NZXAwEBGjBiBg4PDJY8/n9AZKN+VSfnWNADshgRg3cMTRXV16RhCCJIOR7Nj0Q8UZ2fi27odfSZOxcWv4ZVDpBuTHLOl24nWoOWrI1/xw8kfCLAL4Jv+3xDiWJdeV54Lq54h63gyG4repRpbQoq30e2lu7Fs1w6oHQtjd25l+8J5aNXVdLtnAlEj7yYu/jSLv/oKdbWaDgTRqtqPBeYGFpYW8VDPAJ7oaUZSwpOcKT2Io0MPQkPfxsLiwicylXo9n6Tk8m16PpYqI96tW7CuuoFSOi5GqU2Juzl17NhRHDp06ILX4uLiCAsLu049uvHJz0dqatV6A2+czeLHzAIirM2ZG+5fb+tWg0FDcvLnpKR+i7mZO2Fh7+Ho2O2Sber1evbt28f27dsxNjZm0KBBtGvXrsFlj9SJJZSsSESXX41FhBN2I4Iwtje76nvMS0lix6L5pJ08hqOnN70nTiUgsuN/KsOkKEqMEOK2WnUmx+zGk5+P1JTSy9OZuXMmJwpOcHeLu5kRNaN2O3CAU3+hX/U8+zMGc0w7CjN1MV280gl7+fFzJe9K83LY9P1XpB4/gmfLMAY++jTGNnasWbOGM2fO4GbuSI/SFqit7JheUYKZsyXvjwnHxWgFSUmfYGRkRovgl+ptviKEYE1+Ka8lZpJZo+U+d0deDvKs92TzervUuH1j9VKSpJtKbEU1j8emcrpSzaPeLrwYVH+RYXlFPLGxz1NREYeHxxhatngZY+NLV87IyclhxYoVZGdnExoayrBhw7CxaVilDX2ZhpK1SVQfzUflaI7T5AgsQh2v+v4qS4rZvWwRJ7dvwtzahjumPEabfoNRNXDBoyRJ0o1ibdJa3tj/BkYY8WHvDxnkP6j2jepiWDuD/OgDbCx6lRKVNx6lx+g9uS1Og2sL+xgMeg6vXcmeXxejKEb0m/I4bfoPJubwYTYtXIzQG+hqFEpomSfLzAx8V1HMgz0CeLyHQlLCoySWH8fZuT+hIW9gZuZ2Qb/OVql5OSGTbUXlhFuZ83W4H53sra/1x/OfyJ8IkiQ1mhCCeRkFvJWUha2xiqVtAunrdOEiQ4NBR1raPJKSP8XExI42bb7DxblewYhztFotO3fuZM+ePVhYWDB27FjCw8MbNPsr9IKK/VmUbUxF6AzY3OGDbV8fFJOrq5Cg1dQQs/ovov9ajl6no8OwO+ky+l7MrW+uAV6SJKlKW8X/Rf8ffyX+RTuXdrzX6z08ret2lE3cguGvZ9h/phtH+RBjfTWdnU4R+f5UVLa1Y3p+ajIbv/2cnLMJBLaPot/UJ9AqRvy0cCGpqan4WLnRtTwIjYUVUw1l6K0tWPZAR5z4hWNH5mJsbEOriM9wdR12wXhepNXxcUoOCzILsDAy4q0WXkz2dMb4P1RXul5kMC1JUqPka2p3MtxWVE5/J1s+CfXBxfTCUkZVVcmcin2BsrIjuLoOJaTlHExNLz1DnJaWxsqVKykoKKBt27YMGjTo3IYWV1KTVkbJn4losysxa2GP/ahgTJyvbjtZYTAQv3cnu5b8RHlhPi06daPnhMk4uF9+K3NJkqQbUVxhHDN2ziC1LJVH2jzC420fx9jIGDSVsOlV8reuY1PRcxSbBeBWncAdj3TEsfsoAHQaDfv/WMbBlb9jbm3D8OkzCe7Ujf3797Nt2zZUioreJq0JKnJhpZmBz6tKmNQjgEe7akhKfJDkytO4uY2kZYtXLhj/awwGfsgo4NPUXMp1eu73dOKFAPd6P0duJjKYliSpwTYXljE9Lo0KvZ53WnjxoJfzv/LeDGRkLiYx8T2MjMyICP8EN7cRl5xdrqmpYcuWLURHR2NnZ8f999/f4C2V9ZVaytanUHkwB5WtKY4TQrFo5XzVecyZ8bFsXzSPnMQzuAYEMeSpZ/EJb31VbUmSJF1PQggWxy3mk5hPcDBzuLB2dHo0ht8e5cCxdhw1/RgjlY4u/rlEPvsgRnU7yGbEnmTjd19QnJ1JRO/+9J40ldKKSubNm0d2djZB9j50yvVDZ2rBk6KcCmtzfp4UiYNhEcePzcPM1KXe08i/86LfPJtFqlpDX0cbXgv2JNTq6iY/biQymJYk6YrUegNvns1ifmYBYVbm/BYRVG8AVKuziI2bSXHxXpycehMW+n/1cuPOl5iYyKpVqygtLaVTp07069cPM7MrLxIUBkHVoVxK1ydjUOuw7umFbX9fjMyubjgrzcth55KfOLNvF9YOjgx+4n+E9+x702zCIkmSdL4idREv7365fu1onQZ2vEv+imVsLn6GIquWuBky6f9sD+zDa6sSaWvU7FryE0fWr8LO1Y0xL72FV3grdu7cye7duzE3M2eARQd8c+zYbGrgg5oSxvUI4JHO5SSdnURqVTKeHvcQHDwbE5N/Uv8Ol1UyJzGLA6WVhFqZXzQ18GYmg2lJki4rrm6RYXylmoe9nXkp0BPz88rLCSHIzvmdM2feBAShIW/j6XnvJWeIq6qq2LhxI0ePHsXJyYkpU6bg6+vboL5osioo+SsRTVo5pv62ONwZjIn71dUeramq5MCfv3J47QoUlYquY8YTNeIuTMzrb3cuSZJ0M9ifvZ/Zu2bXrx2dewr9skeI3h/IMeuPUMwFXdtqaPfohHM1+7POxLF+7icUZ2fRfshIetw3iey8PL755hsKCgoIdw2mfYYnepUpz1NBro0ZC+5ui51uHidPLMbc3IvIdgtxdPxnw6MMtYZ3krL5I7cYZxNjPgzx4T53x5syL/pyZDAtSdJFCSGYn1nAm2ezsFGp+LlNIP3+NZNQoykgPv4lCgo2Y2/fifCw97CwuHRgHBsby5o1a6iqqqJnz5706tULE5Mr58kZ1DrKNqZSsS8LI0sTHMa2xLK961WldBj0ek5s3cCeX3+muqyUiN796H7fRGwcnRvdliRJ0o3gkrWjDXrY8wU5i+exvfQxCu3CcTUpZsBzvbD3dwFAp9Wyb/nPHFz5BzbOztzz6ju4BoeweetWDhw4gK21LcPsuuKRZskeUwNva0oZ0z2ATzsVkHR2AhnqTLy9JxEU+BzGxrWTG+U6PV+k5vJdRj4A0/zceNrXFWvjq1sUfqOTwbQkSfXka7RMj0tnS1EZ/Rxt+TSs/iLDvLz1xJ9+Bb2+ghbBL+Lj82C9Xaz+Vl5eztq1a4mLi8PDw4P7778fDw+PK/ZDCEH1sXxK1iRhqNBi1dkDu4F+GFle3UKVlKMxbF80n8KMNLzDWtFn9hzcAhuWoy1JknQjumTt6KIkNAsf5tAON044vYuwMaZrd3Mi77/r3EREbvJZ1n/1MQXpqbTuN4g+E6eSlZvH3LlzKS0tJdIngtYprhiEilepJMnGlHl3tcJa8zWxp5ZjaRlIh/bLsLevLb2sMwiWZBfyfnIOBVodY9wcmBXogbe56fX8iJqdDKZvcFOmTGH16tW4urpy8uTJeu+np6czadIkcnNzURSFRx55hGnTpl2Hnkq3ii2FZUyLS6Ncr+etFl5M/dciQ622lNNnXic3dyU2Nq0ID/8Qa6sWF21LCMHRo0fZsGEDWq2W/v3707VrV1SqK89OaPOqKPkrkZqkUky8rXGeFIGpT8PqTf9bYUYa2xfNJ+VoDPZuHox87kWCo7r+p01XJOli5JgtXUsXrR0tBCJ6Hllffs7u6gcpcGuLi1UVA5/tir2XHQB6nY7oFcvZ//syLGztGD3rNXxbR7J9+3Z2796Ng70Dd7n0xjHBmCMmBuboyhjZ3Z83O2aQdPY+KrSF+Pk9RoD/M6hUtWtdthWW8frZLE5XquliZ8Wi4EAibRtWlelmJ4PpG9zkyZN56qmnmDRp0kXfNzY25qOPPqJ9+/aUl5fToUMHBgwYQHh4+DXuqXSzU+sNvJ2UxfcZBYRambM8PIgw6wsXGRYW7iAubjYabSEBAdPx93sMI6OLzxIXFxezatUqkpKS8PX1ZeTIkTg7XzmVwqDRU741nfJdGSgmKuzvDMKqkwfKVeTYVZWVsvfXnzm+ZT2m5hb0njiVyMHDURnfvCWYpBubHLOla+GStaPLslF//xCHt1hz0uMt9BbmdO7nRPu7+2JUN4YWZqSx7qtPyE1KILR7b+6Y8hgV1Wrmz59PdnY2bXzCaJ/ugdAovE81x21M+PKuEKzVnxMftxpr61DatvkOW9vaakdxFdW8cTaLbUXl+FuYMr+VP0Od7W6ryQoZTDeTU6dOMW3aNNLS0pg4cSJ5eXlMmjSJqKioRrXTq1cvUlJSLvm+h4fHucflNjY2hIWFkZmZKQdmqVHiK6t54lQqsZVqpno583KQJxbnLTLU6SpJTPw/MrOWYmXVgjZtvj03kP6bwWAgOjqaLVu2oCgKw4YNo0OHDucWuVyKEAJ1bBElq86iL6nBsr0rdkMDUFk3/vGgTqvlyLqV7P/jF7Q1atoNHEaXu+/D0tau0W1dSW5yGc4+1qiMZfWPm5kcs6WbxaVqRxsOLiHj/fc4oJ9Anm9HnOz0DJzeFUeP2s2m/t7FcPeyhZiYWzDif7No0bk7hw4dYsOGDZgYmzDEqQteCVbEGQteN5QzsLsvi9qfJTnpPvJ05QQGTMfP71GMjEzJ12h5PzmHn7MKsTFWMSfYkwe9nDG9DSsh3dLBdM4771ATF9+kbZqFheL+4ouXPUatVjN27FiWL19OYGAgoaGhdOjQ4YJBuWfPnpSXl9c798MPP6R///5X1beUlBSOHDlC586dr+p86fYjhODHzALeOJuFlUrF4jaB9P/XIsPikoPExr6AWp2Br+/DBAb879xjvX/Ly8tj5cqVZGRk0KJFC4YPH46d3ZUDWF2RmpKVZ1HHF2HsZonLI20wC2x84CuEIOHAHnb+/COlebkEto+i1/1TcPLyaXRbV5KXWkb0qmRSTxbSZ0IIET29mvwatxs5ZkvSpV2ydnRVERWfTOH4VhWn/OagNbWm0yBPOoxsiVHdpEhJbg7r535CZvwpgjp2ZsDDTyGMTVi6dClnzpzB38mbrvkBmJSZ8jHVHLE14aPRQVhUf8yZ05uxtW1LWOi7WFu3pFpv4LuUXD5Py6XGYGCqtzP/83fH0eSWDikv6/a982a0efNmIiMjiYiIAECj0fDcc89dcMyuXbua9JoVFRXcfffdfPrpp9ja3jq1G6XmU6DR8b/4NDYVltHX0YbPQn1xNfsn/UGvryEp6SPS0n/AwtzngkUm/6bT6di9ezc7d+7EzMyMu+66i9atW1/xMZ/QGSjfkUHZtnQUI7AbGoB1d08UVeNnNrITT7N94XyyTsfi7OvPmJfewq9Nu0a3cyX56eVEr0om5XgBZlbGdB0dRIuoS9fTlm58csyWbnRF6iJe2fMKOzN2XlA7WnvgNzLeeJvDJmPJadEFR0eFAU90xNm7dn2JEILjm9exY9EPKEZGtXX0e91BYmIif/31F2q1mu62bQjNdOaYkYF3RQUj+/izIOI4Kcn/o9qgITh4Nr4+DyIw4vecIt5JyiazRssQZzteDvIgyFKWE72lg+krzUY0l6NHjxIZGQlAVlYW1tbWdO/e/YJjmnKWQ6vVcvfddzNhwgTuuuuuq++4dNvYVljGM/FplGr1vBnsxVRvZ4zOC3zLyo5zKvYFqqoS8fIaT3DQrHMlj/4tMzOTFStWkJeXR6tWrRgyZAhWVleu/axOKKZkxVl0BdVYtHbGbnggxnZX3rTl38oK8ti9dCFxu7djaWfPgEeeplXf/hgZNW0JpsLMCqJXJ5N0JB8zS2M6jwykTV9vTC1u6WH0mpJjtiTVF50dzaxdsyitKT1XOxp1OcUv3k3cLj2xwS+jMbOnwyAfokYEnUs5Ky8sYMM3n5F6/Ah+bSIZ+OgzWNjZs27dOqKjo3G2dmSgpjVW1Va8RzXpnpZ8M7IFuqK3SUzYib19Z8JC38HS0p8DJRW8lpjF0fIq2lhb8EWYH90crK/zJ3PjkD8FmoGpqSmZmZkAzJ49G41GU++YpprlEEIwdepUwsLCePbZZ5ukTenWpdYbeCcpm+8y8mlpac4vbYMIP2+RocGgJSVlLimpX2Fq6kK7tj/i5NTrom1pNBq2bdvG/v37sba2Zty4cYSEhFyxD/rSGkrWJFF9vABjJ3Ocp7TCvKVDo+9FU11F9IrfiVn9JwCdR99Lp1F3Y2rRtKvHi7IrObg6mcSYPEzNVUQN86dtPx/MrrI8n3TjkWO2dCPSG/R8c/wbvj32LX62fnzd/2tCHENQb19Oxutvc9JmNJkRPbF3NGbEI+1w8699wiGEIG7XNrb++C16vY5+U5+g7YAh5OTksOi778jPz6eNZRDtC3w4rAg+M65i8tAWvBh0nISEpzEYtLRs+RreXveTqtby5slk1uSX4mFmwudhvoxxc7hg8kWSwXSzGD9+PKNGjSIkJIRHH32Umpoapk+fzqefftrotsaNG8f27dspKCjA29ubOXPmMHXqVACGDh3KrFmzWLRoEa1bt6Zdu3YAvPPOOwwdOrQJ70i6FZyuVPP4qRRiK9VM8XLmlX8tMqyoTCA29nnKy0/i7nYnLVu+ionJxfOWk5KSWLVqFcXFxXTs2JH+/ftjfoWdA4XeQMXeLMo2pSEMBmz7+2LT2wfFpHEpHQaDnpPbNrPnl0VUlZYQ1qMPPcZNwtbZtVHtXElJbhUH1yRz5mAuJqYqOgzxo11/X8ytZBB9q5FjtnSjya3MZdauWRzKPcTIoJG81PklzNUa8p4eTeJBHfGhL1Jt7kS7/j50HhWIsUntk7iq0hI2ff8liQf34xUazuDH/4etqxt79+5l69atmKvMGKSLxKnYkXepRtPSnoXDW1Ca8w5xcRuws2tPeNj7aEx8eP1sNj9kFGBipDAjwJ3HfFyxvIoUvNuBDKabgbe3NzExMU3S1tKlSy/53tq1a4Ha30Il6VKEECzIKmROYiZWKhWLWgcwwNnuvPf1pKX/QFLSx6hU1rRuNRdX10EXbau6uppNmzZx+PBhHB0dmTx5Mv7+/lfsQ01KKSV/JaLNqcI8xAH7kUEYO1lc8bx/Sz1+lB2L5pGfloJnSDh3zngFj+Arz4Y3Rml+FYfWpHD6QA4qEyMiB/gSOdAXi6uoKiLdHOSYLd1Idmbs5OXdL6PWq3m7x9uMDBpJxcpFJLz9Eaedh5Peti+2TqYMmdIaj2D7c+clHNjLpu+/RKOupvf9U2g/bBTl5RUsWrSI5ORkAkw96F4WzEEUXrVU88yoVnTyOM7p+CfR6SoIDpqJj88Ufskt5Y3EOEp0esZ5ODIzwAM3MzmJcDkymJakW1i+Rsuz8emXXGRYXZ1GbOwMSkoP4uzcn9DQtzEzvXgt6Pj4eFavXk1lZSXdu3enT58+V9wKXF+hoXRdClUxuajszHC6PwzzCKdG1x8tzExn5+IfSDp8EDtXt3MlnZqyjmlZQTUx61KI25eDkUqhTT8f2g/0w9JWBtGSJDU/rV7L50c+Z8GpBbR0aMkHvT/A39SDnKfuJeVAGfERM6g0d6d1H2+6jg7CxKx2NlpdUcHWH78hbvd23AKDGfzE/3D28ePUqVOsWrUKnUZHD10oHjUevIMa5w5uLB3kRW76/3Hy5ApsbCIID/uQApUf9x5PYVdxBZ3trHinpTcR1o2f9LgdNXswrSiKCjgEZAohhiuKEgAsA5yAGGCiEEKjKIoZsBDoABQC9wohUpq7f5J0q9paWMa0+DTKdLU7GU7x+meRoRCCzKylJCb+H2BEeNgHuLuPvmhwWlFRwbp16zh16hRubm6MGzcOL6/Ll4ETBkHlwRxK16cgavRY9/bGtp8vRqaNWxRYVVbKvt+WcmzTWkzMzOk14UEiB4/A2LTpAtzyIjUx61OJ25MFCrTu7UX7wX5YXcViSEmSpKuRUZ7BjJ0zOFFwgntD7uX5js+jxB0n+am7OWPWm+T2D2HlYMbIya3wCXU8d17ykUNs/PZzqspK6TZ2Ap3uHItOr+evv/7i6NGjuKjs6VMdxkFhwmcOBmaP6UBL+5PEH3+ibvOtaXj7Psa8zBI+SI7HWFF4v6U393s6ybzoRrgWM9PTgDjg79o/7wGfCCGWKYryDTAV+Lru72IhRLCiKPfVHXfvNeifJN1Szt/JMMTKnF/bXriTobomh/i42RQW7cTRoTthYe9ibu5Zrx0hBMePH2f9+vVoNBruuOMOunfvfsWtwDWZFZT8lYgmvRzTADsc7gzCxO3K1T3Op9NqObp+Ffv/+AWNupo2/YfQbez4Jt10pbKkhpj1qZzanQkCwrt70mGIH9YOt2+ZJ0VR/gc8BAjgBPAg4IGcAJGkZrMpdROv7XkNgeCj3h8xwG8AJV+9Qer8tcSGPkKxXQgtOrrSe0IoZnXVgzTVVWxfNJ8TWzbg5O3LnTNexS0wmPT0dP74/Q9KSkpop/MnoMafD9AQ3seTpb09SE99j2PHfqndfKvtd6QRyPAjyRwvr2aQsy3vtvTGw0w+jWusZg2mFUXxBoYBbwPPKrXTXncA4+sO+Ql4ndpgelTd1wC/AV8qiqIImVwmSQ0WV1HNE7GpxF1kJ0MhBLm5qzh95jUMBg0tW76Ot9cEFKX+gpKSkhJWr15NYmIiPj4+jBw5EhcXl8te26DWUbYplYq9WRhZmeBwT0ssI10blYohhCAhem/tpiu5OQREdqT3/VNw8vZt3AdxGZWlNRzZkMbJXZkIvSC0mwcdhvhhexU53LcSRVG8gGeAcCFEtaIovwL3AUOREyCS1ORq9DV8cPADfjn9C62dW/N+r/fx0JiReW9/kjKdiO/4MsLcin7jwwjp4n5uLE2PPcH6uZ9SVpBH1Mi76TZ2AopKxfbt29mxYwdWmDOspj1HhSW/eKp4dWwX3M1jOXbkUdTqLPx8H8XD72k+TStmbvoZHIyN+S7CnxEut9cW4E2puWemPwVmADZ13zsBJUIIXd33GcDfz4u9gHQAIYROUZTSuuMLzm9QUZRHgEcAfH2b7gesJN3MhBD8kFnAm2ezsL7IToYaTRGnz7xGXt5a7GwjCQ//AEvLgHrtGAwGDh06xObNmxFCMGTIEKKioi67FbgQgurj+ZSsTsZQocGqswd2A/0wamTpuJzEM2xfNI/M+Ficffy4+8U38G/bvlFtXE51uYbDG9M4uT0DvV4Q0sWdjkP8sXO5vYPofzEGLBRF0QKWQDZyAkSSmlxKaQrP73ie08WneSD8Aaa1n4Zm2xoSZr9OvPtIMlv3wcXbkoEPt8Herbbcp1ZTw+6lCzm8dgX2bh7c9/p7eIWGU1RUxB+//0FGZgZBendCtC340thAr8GB/NTZjZTkjzgctwALCz86dFhGrCGESTEpJFXXMM7DkVeDPHG4jXcvbArN9ukpijIcyBNCxCiK0qep2hVCfAd8B9CxY0c5aEu3vXyNlulx6WwpKuMORxs+C/PFxfSfQLagYCtx8bPRaksJCnwBP7+HqV3K8K928vNZuXIl6enpBAUFMWLECOzt7S97bW1+FSUrzlKTWIKJlzXOk8Ix9bG57Dn/Vl5YwK6lPxG3a1vdpitP0arPAIyukE7SUOoKLUc2p3F8WwZ6jZ4WndyIGhpw7geUVEsIkakoyodAGlANbKQ2rUNOgEhSE1p1dhVv7n8TM5UZX/X7ip5uXcl/+QnSNiZwqtWzVFh407a/D11HBaGqKx2anXiadV99QnFWBu0GDaPX+AcxNjPjyJEjrFuzFnSCvpoIThkc+SHYmrfubo2N0WliYh6mqioZb+9JuPg9y9spJSzKSsTP3JTlbYPo6di48Vq6uOb8VaQ7MFJRlKGAObU5058B9oqiGNcNzt5AZt3xmYAPkKEoijFgR20eniRJl7ClsIxpcWmU62sXGU71cj73mE6nKych4R2ysn/F2jqUdm0XYGMTVq8NvV7Pnj172LFjB6amptx55520bdv2so/7hFZP2bZ0yndkoJgYYT8qCKvOHihGDX9EqFFXc3Dl7xxa9SdCGOg8+h6iRo7BzLJpglx1pZZjW9I5tjUdbY2eFh1c6TgsAEePxuVv3y4URXGgdrY5ACgBlgOD/2u7cgJEkmpVaat458A7rDi7gg5uHXi357s45hSTMrQ7Z3VtSOw4C1Nrc4ZPaY1fhBNQu35k329LOLjid6wdnRjz0lv4tWlHVVUVf/7yK7Hxcbgb7AnXhPGTuTGjRofxaCtHklO+5HTqt5ibuRPZbhH79eHccyiVfI2Ox31ceCHAQ9aMbkLNFkwLIWYDswHqZqafF0JMUBRlOTCG2gUtDwAr6k5ZWff9vrr3t8rHhZJ0cWq9gbeSspiXUUColTnLwy9cZFhcfIDYuBdQq7Px83uMwIBnMDKqX50iKyuLFStWkJubS0REBEOGDMHa+vJbxFbHF1Gy8iz6IjWWka7YDQ1AZdPwBSsGg55TO7awZ9kiKkuKCe3em57jHsDWpWk2XdFU6zi2NZ2jm9PRVOsIau9C1LAAnLzk1rdX0B9IFkLkAyiK8ge1kyJyAkSS/qPTRad5YecLpJSm8Fjbx3i0zaNULprLmU8XEBc0njzn9viEOtDvwfBzlYRyk8+yfu4nFKSlENGnP30feBgzSyuSkpL487c/qKiqJEobRILeg/XtnPloZDgqfQKHDj1EReVpPD3uwdZvBi8klbAmP4UIa3MWtgmkrY18KtfUrkeSzExgmaIobwFHgPl1r88HFimKkggUUbvw5bY3ZcoUVq9ejaurKydPnrzkcf7+/tjY2KBSqTA2NubQoUPXsJfStRRXUc3jsanEV6p5yNuZlwM9Ma+bYdDr1ZxN+oj09B+xsPClQ4dl2Nt1qNeGVqtl+/bt7N27FysrK+69917CwurPWp9PV1JDyaqzqE8VYuxqgfPDrTEPsm9U39NOHmP7wnnkpybj0TKUkc+9hGfL0Ea1cSkatY4T2zM4sjGNmiodAW2d6TQiAGdv+RizgdKALoqiWFKb5tGP2rKm25ATIA0mx2zpfEIIlp9ZzvsH38fG1IbvB35PR+swch+6i9RTBmLbv0iNqQPdRgfTrr8PipGCXqcj+q/l7P9jGRY2ttw541WCOnRCp9OxYd169h3Yj53Bki7aDvxhY8UD97SmS6A9qalfk5zyJSYmDrRpPY9N2jbMiclAbTDwUqAHj/m4YtKIp4dSw12TYFoIsR3YXvd1EtDpIseogbHXoj83k8mTJ/PUU08xadKkKx67bds2nJ0vvuGGdPMTQjC/bpGhjUrFz20C6XfeIsOysuOcin2BqqpEvLzup0XwTFSq+jMQKSkprFy5kqKiItq3b8+AAQOwsLj0IjyhN1CxO4uyLakgwHawPzY9vFCMG/6IsCgrgx2LfyApJhpbFzeGT59Jyy49mmTluFajPxdEqyu0+LV2otPwAFz9bK98snSOEOKAoii/AYcBHbWTHd8Ba5ATIA0mx2zpb+Wacubsm8OGlA108+zGOz3ewfLYcZL+15MEuztIiRyGjZM5wx9ug5t/7XhVkJ7K+rmfkJuUSGj33tzx4KNY2NiSn5/P8p9/Ia+kgFCdF5k6P0709OGzgS3Ra5KJiXmYsvLjuLmNwNTnRR47W8aeknS62FnxUagPQZa3b8nPa0Eu32wmp06dYtq0aaSlpTFx4kTy8vKYNGkSUVFRjWqnV69epKSkNE8npZtGvkbLtLg0thaV08/Rlk/DfM4tMjQYtKSkzCUl9StMTV1o13YBTk4967WhVqvZvHkzhw4dwsHBgUmTJhEYGHjZ69YklVK8IhFdbhXmYY7YjwjC2LHhg3J1eRn7fl/KsY1rMTY1pef4ybQfMrJJNl3RafSc2pVFzIZUqss0+IQ70ml4AO6BTVeL+nYjhHgNeO1fL98WEyByzJaa0smCk7yw4wWyK7OZ3n46k8MfoOT92cT/spu48Mcptm1JSGc3eo0LwdTcGINBz6FVf7L318WYWlgy4tnZtOzcHYPBwJ4du9m6fSsmBhVtta3Y4eTGI+PaEuZhRVr6jyQlfYRKZUVoxBf8qe7Ah0eyMVEUPgjxZoKH3HzlWrilg+ldv56hIL2iSdt09rGm5z0tL3uMWq1m7NixLF++nMDAQEJDQ+nQocMFg3LPnj0pLy+vd+6HH35I//79G90vRVEYOHAgiqLw6KOP8sgjjzS6DenGtKmglOnx6VTq9bzTwosHz1tkWFmZyKnY5ygvP4m72520bPkqJib1g8kzZ86wevVqysvL6dq1K3379sX0MgGtvkJD6dpkqg7nobI3w2lSOBbhTg3us16n5eiGNez7fSmaqmra9B9Et7ETsLSzb/T912tba+DU7ixi1qdQVarBK8SBTo+0wjP4v7fdWEKjoWzdOqz79EFlJ4P4/0qO2dLNTgjBothFfHL4E1wsXFgweAEROicyR/clpciL+E4vgpkV/SeEEdLFA4CirEzWz/2Y7ITTtOjUjf4PPYGlnT0FBQX8uex3Mguy8dU7U6APonRQCB/1DKBGnUbM4YcpLT2Es3N/dN6vMflsOScqshnibMf/tfTG3axx5Umlq3dLB9PXy+bNm4mMjCQiIgIAjUbDc889d8Exu3btatJr7t69Gy8vL/Ly8hgwYAChoaH06tWrSa8hXVvVegNvns3ih8wCwqzM+ToiiFCr2nQMIQykpy/gbNIHqFRWtG71Fa6u9QsvVFZWsn79ek6cOIGLiwv33HMP3t7el7zmBduAa/TY9PHB5g6fBm8DLoQg8dB+di7+gZKcbPzbtqf3xKk4+/hd3YdwHr3OQNzebGLWpVBRXINHsB0Dp0TgFeLwn9tudF9KSij+5VeKFy9Gl5+P++uv4XCfzHK4WckxW2oKJeoSXt7zMjsydtDXpy9vdn8To3UrSZzzIad9R5PZqhcuvlYMfKg19q6WCIOBI+tXsWvJTxibmjL06ecJ7d4bIQR7d+1hy9atGBsUWmnDiPHw4YkJ7fB2sCAzcwkJif+HkZExgSEfsbg6im+O5+FkYsy8CH+Gyc1XrrlbOpi+0mxEczl69CiRkZFAbbUEa2trunfvfsExTT3L4eVVW/rV1dWV0aNHEx0dLQfmm9j5iwwf9nbmpfMWGVZXZxAbN4OSkgM4O/cnNPRtzEwvzLsUQnDy5EnWrVuHWq2mT58+9OjRA2PjS/+T12RWUPxXItr0cswC7bC/MxgT14av+s5NPsuOhfNIjz2Bk7cvd82eQ0C7+osfG0uvN3B6fw6H1qZQXqjGLcCWOyaF4R3qcM1/YNQkJ1O8aBElf/6FqK7Gqnt3PN55G6sePa5pP25VcsyWY/bNKiY3hpk7Z1KkLmJWp1nc538X+S88RPqebGLbvkCFuSeRA3zpPCoQlbERJbk5bPjmUzJiTxIQ2ZGBjzyNtaMThYWF/LnsdzLys/DRO1NqCEI/Iox3uvhRU5PN0aOPU1S8G0fHnhR7zGFcciUp1fmMr9t8xV5uvnJdyE+9GZiampKZWVs9avbs2Wg0mnrHNOUsR2VlJQaDARsbGyorK9m4cSOvvvpqk7UvXTtCCOZlFPBWUha2xiqWtAnkjrpFhkIIsrOXcybhbQDCwt7Dw/3uegFlaWkpa9as4cyZM3h5eTFy5Ejc3NwueU2DWkfZxlQq9tVuA+54bwgW7VwaHKhWFBWye9kiTu3cgoW1Df2mPkGbfoP+86YrBoMgITqH6DUplOVX4+pnQ+9xIfhGOF7TIFoIQVX0QYoWLKBi+3YUY2NsR47AcdIDmIdcn+BPalpyzJault6gZ96Jecw9Nhdva28WD11MUHY1KYO7k6TqSGLHmZjZmDNiSit8w50QQnBs01p2LPoBxUhh4GPP0KrPAIQQ7Nuzj82bN6MyKLTWhnHEw4fHJ0biaWdOds7vnDnzJmDAI/ht5lV2Y0lsEf4WpvzWLogeDrJq0fUkg+lmMH78eEaNGkVISAiPPvooNTU1TJ8+nU8//bTRbY0bN47t27dTUFCAt7c3c+bMYerUqQAMHTqUefPmoVarGT16NAA6nY7x48czePB/3mtBusbyarRMi09jW1E5A5xs+Tj0n0WGNTX5xMe/SEHhVuztOxMe9gEWFl4XnG8wGDh8+DCbNm1Cr9czcOBAunTpcsmtwIUQVB/Lp2RNEoYKLVZdPLAb6I+RRcOGBW2NmkOr/iR65W8IvZ6Ow0fT5a57MbP8b5uiGAyCxJhcDq5OoSS3Cidva4Y+3hr/Ns7XNoiuy4cu/OknamLjUDk44Pz44ziMH4exrMBwS5FjtnQ1CqoLmLVrFgeyDzAkYAivdH4F3bzPOfPdn8SF3E++Yzt8wx3pNzkcS1tTygry2fjt56QeP4Jv63YMeuwZbJ1dKSoq4s9ffic9NxMfvROVhmB0w8N4s6sfanUGR4+9QlHRLuztokh1e4tnUtUUaot40teV5/zd5eYrNwDlZi4L2rFjR/Hv2pxxcXFXrJd7O5Ofz43p/EWGrwV7MdnT6VzgmJu3jtOnX0GvryIo6AV8vB9AUS4cPAsLC1m1ahUpKSkEBAQwYsQIHB0dL3k9bV4VJSsSqTlbiom3NQ53BmPawHrMwmAgbvd2di39iYqiQlp27k7PCQ9i7+Z+9R8AtfnaZ4/kc3BNMkVZlTh6WtFpRACBbV0atbPif/XvfGjToCAcJz+A3YgRGJk3XXkpRVFihBAdm6zBm4AcsxtPfj43pr2Ze5m9ezZV2ipmd57NSIeeZD85gfQUM+JaT0Zj6kDXu4Jpe4cPKHBqxxa2LfgOYTDQ6/4ptB0wBCEEBw9Es2njJhQDhOlacNTNl0cnReJpZ0p6+k+cTfoYRTHC1m82X5R3Zl1BGa2sLfg41Ic2cvOVa+5S47acmZak66hab+CNs1n8mFlAuJU5c89bZKjVlnL6zOvk5q7E1qYN4eEfYmUVdMH5er2e/fv3s23bNlQqFSNGjKB9+/aXnME1aPSUb0unfGcGiokK+zuDserk3uBgNSPuJNsXzic3KQG3wBYMmzYD79CI//QZCCFIPlZA9KpkCjMrcHC3ZOBDEQS3d72mQfTl8qHlYh5JkgBq9DV8GvMpi+MWE2wfzPyB8/E4HMfZcf1IdBlIauRgbF0sGPlwG1x8bagoLmLTd1+QdPggXqERDH58OvbuHhQXF/PnL7+TlpOBt96RGn0wumHhzOnmR2XlGQ7FzKas7Bj2jncQbTeTj9Oq0IpyufnKDUoG05J0nZyqqObxU6mcqVLzqLcLLwZ5YFaXklFYuJO4uFlotIUEBkzHz+9xjIwu/Oeak5PDypUrycrKIiQkhGHDhmFre+mNSqpjC2u3AS+pafQ24CW5Oez8+QcSDuzF2smZIU89R1j33iiXSCFpCCEEqScLiV6VTH5aOXauFvR/MJwWUW4YXaMfFOfyoX/6iYpt226qfGilNsKfAAQKId5QFMUXcBdCRF/nrknSLelM8Rlm7pxJYkki40PHM73NU5S/OYPTa44R1/ppSqyDCO3qTs97W2JipiJuzw62/vANupoa+kx6iPZDRiKA6APRbNywEUUvaKML4birHw8/EImHrRFJyZ+SmvoNxsa26Py/YmahPydTKujjYMM7Lb0JtDS73h+DdBEymJaka8wgBN+l5/NOUjb2JiqWtQ2kj2NtEKzTVZJ49l0yM5dgZdWCNm2/w9am1QXn63Q6du7cye7duzE3N2fMmDFERERccvZUV6Su3QY8rghjN0tcHmmDWQM3NlFXVnDgz185sm4likpFt3sm0HH4aEzMrj7dQQhBelwR0auSyU0uw9bZnDsmhRHS2Q2ja5T7JzQaytavp3DBgps5H3ouYADuAN4AyoHfgcbtMiJJ0mUZhIGf437m05hPsTG1YW6/uXTWuJE5qj9p1UGc7vwSmFsy4P4wWnZyp6qslA1z53LmwB48gkMY9MR0nLx8KCkp4c9f/yA1Kw1PvSNC3wLdsDBe6+ZHaWkMB6JfpKrqLBau9/Kr8iDLUivxMNPzfYQ/w2W5uxuaDKYl6RrKqandyXBHcTmDnW35KMQXJ9Paf4YlJYeIjXuB6up0fH0fIjDgWVSqC2ch0tPTWblyJfn5+bRp04bBgwdjaXnxvDmhM1C+K4PyremggN3QAKy7e6I0IGA16PUc37yevct/prqinIje/ehx70SsHRu+ccvFZJwuJnpVEtmJpVg7mtH3/lBCurqjukZB9Ll86J9/RpeXh2lQEO5vvtHk+dDXSGchRHtFUY4ACCGKFUX571tLSpJ0Tl5VHi/vfpl92fvo492HOd3nYPznbyS+9yRn/O8mM7Anrn42DHyoFXYuFiRE72XT919RU1lJj3EPEDXiLhQjIw5FH2TD+g0IvaCtLoSTrn5MeSASN2s9Z87MISNzMaamniR4L+KzXBvK9JU87uPCc/7uWBv/t8pIUvOTwbQkXSPr8kt47nQ61XoDH4R4c79H7SJDg6GGpKTPSE37HnNzL9pHLsHB4cLdmzUaDVu3bmX//v3Y2toyYcIEWrRocclrqROKKVlxFl1BNRatnbEbHoix3ZUfDwohSDkaw/ZF8ynKTMcnvDW9Jz2EW0DQFc+9nKyEEqJXJZF5pgQrezN6j2tJWDdPVCbXJoi+aD7022/d7PnQWkVRVIAAUBTFhdqZakmSmsCW1C28vu911Do1r3R5hbu9h5E3fQpnDpcRHzmbSjNX2g/yo9PIALTVVaz94kPidm/H1T+Isa+8jYuvP6Wlpfz56x+kZKbiqXdA0bdENzSUl7v7U1i4nf0HXqGmJocq16f5UD2II5lqutiZ838tvQmztrjeH4HUQDKYlqRmVqnX83piFouyCmljbcFX4X60sKqdBS0vjyU29nkqKk/j6XkvLYJfxNjY+oLzz549y6pVqygpKSEqKor+/ftjZnbxwFhfVkPJmmSqj+WjcjLH+cEIzEMuXdXjfAVpKWxfNJ/U40dw8PBk1PMvE9Sx838KNnOSSolelUR6XDGWtqb0uKcFET09MTZp/pmWmzkfuoE+B/4EXBVFeRsYA7x8fbskSTe/Km0V7x98n98TfifMMYx3e72LZ2oRSUP6cNqqL6mRA7F2MGXU5FZ4hzqSdOQgG7/9guqyUrqOGUfn0fdipFIRcyiG9evWI3QG2ulacsrFn8mTI3GxrOJU7LPk5q5EWLZmvesXLMlXcDTR8UWYL2Pcrv2GVNJ/I4NpSWpGx8qreOJUKknVNTzp68rMAHdMjYwwGHSkpn1LcvIXmJg40LbNPJyd+15wbnV1NRs3buTIkSM4OTnx4IMP4ud38W25hV5QsS+Lsk2pCL0B2/6+2PT2QWnAzG9VaQl7fl3MiS0bMbW0oM+kh2k3aCgqY5Orvu+81DKiVyWTerIQCxsTut0dTKveXpg0cFvy/+IWyYe+IiHEz4qixAD9AAW4UwgRd527JUk3tRP5J5i1axbp5elMbTWVJ9o+QeX3n3Lihw3Ehj5NhZU3oV3d6XFPSxAaNnzzGSe3bcLJ25fRM17FLTCY0tJSVvz2F0npyXjo7THVt0Q/NIzZ3fzIzVvJ/hNvodVVcNrlbb4ujaAgX89kL2dmBbhjJ3cwvCnJ/2qS1Az0QjA3LY/3krNxMTVh+Xk7VFVVJXMq9nnKyo7i6jqM0JA5mJg4XHB+XFwca9asobKykh49etC7d29MTC4e3NakllHyZyLanErMWjrgMCoIY6crPx7UaTQcXreSA3/+gk6jod3gYXS9exwWNpeuCHIlBRkVRK9KIvlYAWaWxnS5M5DWfbwxNW/+oUZfUkLxr8tr60Pf/PnQV6QoShfglBDiq7rvbRVF6SyEOHCduyZJNx29Qc/8k/OZe3QuLpYuzB80n/ZmwWQ+cBen8oNIbj8Tc0sVQx9sQ0AbZ1JPHGXDN59RUVhIp1Fj6Dp2AipjY44cPsK6NWsx6PS01bXgjEsAEydH4mBWxPHjUyks2kmx1QAWWjxBdIGBSBszFrf1pq2sGX1Tk8H0DW7KlCmsXr0aV1dXTp48ecnjPvnkE+bNm4eiKLRu3Zoff/wR81swgLgZZKk1PBWXxt6SCoa52PFhiA8OJsYIYSAjYxGJZ9/HyMicVhGf4eY2/IJzy8vLWbduHbGxsbi7uzN+/Hg8PT0veh19pZbSdclUHcpFZWeK0/1hmEc4XfHxoBCCM/t3s/PnBZTl5xLUsTO9JjyIo6f3Vd9zUXYlB1cnkxiTh6m5ik4jAmh7hw+mDdxN8b/QpKRQtHDhP/nQ3brh8dabWPXseas/Kv0aaH/e9xUXeU26xuSYffPJrMjkxV0vcjjvMEP8h/By15cxjjnMyZl3c9x7PGWBgQS1taP3xNaoVDo2z/uKY5vW4eDhxX1vvI9ny1DKyspY+ftfJKYm4W6wx0rXEjEkjBe6+5CZuZgDxz5CLczY6vA1S0pdsVYpfBDizQQPJ4xu7XHqttDgn3SKonQD/M8/RwixsBn6JJ1n8uTJPPXUU0yaNOmSx2RmZvL5558TGxuLhYUF99xzD8uWLWPy5MnXrqMSAKvySnjhdDoaIfgk1If73B1RFAW1OovYuBkUF+/DyakPYaH/h5mZ67nzhBAcO3aM9evXo9Vq6devH926dUOlqp8WIQyCykM5lK1PwaDWY93bG9s7fDEyu3IKRXbCabYt/J7sM/G4+AUw5uW38Gvd7qrvtySvioNrkkmIzsXYVEWHIX606++LudXVp4g0hBCCqoMHKVpwy+ZDN4QiztvCVghhUBRFTpBcZ3LMvrmsTlrN2/vfBuCdHu8wzH8ohe+/zIHNRSSGzMDYTGHApNr69+mnTrDhm88oK8ijw7A76X7fRIxNTDl69ChrV61Fr9PRTteCROcARkxuh51JBjGH76O07Ajx1lOYrx1BdomBcR6OvBToibOp/Od6q2jQf0lFURYBQcBRQF/3sgBkMH0Jp06dYtq0aaSlpTFx4kTy8vKYNGkSUVGNKwHbq1cvUlJSrnicTqejuroaExMTqqqqLjmbKTWPCp2elxMyWZZTRDsbS+aG+xFoaYYQguzs3zl95g1AEBryNp6e914wY1pSUsKqVas4e/YsPj4+jBw5EhcXl4teR5NZQclfiWjSyzENsMXhzmBM3Kyu2L+y/Dx2Lf2J+D07sLJ3YOCjzxDRpx9GRleXw1xWUM2htSnE789BpVJo19+XyEG+WFg3b2W2v/Ohixb8hDo29pbNh26gJEVRnqF2NhrgCSDpOvbnpibH7NtLmaaMt/a/xbrkdbR3bc87Pd/BtcKIM2Pu4rDpIIpbDMDHX0W/x7pgYm5g64/fcHTDGuzdPbj39XfxDo2gvLyclUt+JSHlLG4GO+x0IRgGh/K/7p6kpn5LdOrXFKgCWWa9iL2VloRbmfJdKx+i7K48Zks3l4b+WtQRCD9/FuRmsG3Bd+SlNu3PFle/QPpOfuSyx6jVasaOHcvy5csJDAwkNDSUDh06XDAo9+zZk/Ly8nrnfvjhh/Tv379RffLy8uL555/H19cXCwsLBg4cyMCBAxvVhnT1DpdW8kRcKqnVGqb7ufGcvzsmRgoaTQFx8S9RULAZe/tOhIe9j4WFz7nzDAYDBw8eZPPmzSiKwpAhQ4iKisLoIrsKGtQ6yjamUrEvCyMrExzuaYllpOsV0xg01VUc+Gs5MWv+QkGhy133EjXybkwtri4/r6JYzaF1qcTtyUJRFNr08SZykC9WDSi791/cbvnQDfQYtRU9XqZ2cmMLcPnB6QYnx2zpWjiYc5CXdr9EXlUeT0c+zdRWU6nasJI9n6wi3vcRFGMVve/xI6JvIBlxJ9nw9aeU5ufRfshIeoybhLGpWe1s9Oq16LU62umCSXIKZOSD7bA2iufgoScorkxlq9Usfq1uh4naiDeDPXjQyxljuQ34LamhwfRJwB3Ibsa+3DI2b95MZGQkERERQG2N4Oeee+6CY3bt2tVk1ysuLmbFihUkJydjb2/P2LFjWbx4Mffff3+TXUOqTy8EX6Tm8kFKDu6mJvwRGUxX+9qydnl5G4g//TJ6fQUtgl/Ex+dBFOWfIDk/P5+VK1eSnp5OUFAQI0aMwN7evt41hBBUH82nZE0ShkotVl08sBvoj9EVcpENBj0nt21izy+LqSotIaxnX3rcNwlb54vPeF9JZWkNMetTObUrEwSE9/Ckw2B/rB2aN4iuzYdeRMmff/6TD/32W1h17/6ftjK/FQgh8oD7rnc/bgVyzL49aPVavjr6FT+c/AEfGx8WDVlEK7sQ0mY9z/4kPwoC78fdsZL+/7sDSxuFbT99x5F1q7Bzc+feV/8P7/BWFBYWsvL3JaRmpeFqsMNRF4IYFMrT3VxJSv6Q+IyFnDK5g4Vmb5NRpWK0qz2vBXvhbta8qW/S9dXQYNoZiFUUJRqo+ftFIcTIZulVE7nSbERzOXr0KJGRkQBkZWVhbW1N9+7dLzimKWc5Nm/eTEBAwLnUgLvuuou9e/fKgbkZpas1PB2byv7SSu50tee9lt7YmRij1ZZxJmEOOTl/YWMTQXj4R1hb/bO5il6vZ8+ePezYsQNTU1PuvPNO2rZte9EZZm1eFSV/JVKTVIqJtzXOkyMw9ba5Yt9Sjh9hx6L5FKSl4BUazugZr+IefHV5xNXlGg5vSOXkjkz0ekFYV3c6DPXHtgHVQq6WzIdumLpNWh6m/lqWKderT/+VHLPlmN1ckkuTmbVrFrGFsdzd4m5mRM3AOCOHfY88wUmHEeidzOk2wJp2o/uSefoUv735GSW52UQOHkHPcQ+gGBuzY+t2du7ahZEBInUtSXHyp+eD7TA3HCQ6+gEyarT8ZvE5u9SetLA047dw73NVnKRbW0OD6debsxO3GlNTUzIzMwGYPXs2Go2m3jFNOcvh6+vL/v37qaqqwsLCgi1bttCxY8cma1+60J+5xcw8k45BcEGB/cKi3cTFzUSjySfA/xn8/Z/AyOif2YisrCxWrlxJTk4O4eHhDB06FGtr63rtGzR6yremUb4zE8VUhf3oYKyi3FGu8HiwMCOdHYvnk3zkEHZu7ox4djYtOnW7qooW6kotRzalcXxbBnqNnpad3Yka5o+dS/OVbxIaDWUbNlD04wKZD90wK4BdwGb+WcsiXQU5Zt+6hBAsP7OcDw5+gJmxGZ/2+ZR+fv3I//kndv6RQ47beBxNCxj0fE9s3CzZvmgeh9etxM7FlXtefQefiDakpaWx4tc/Kawoxl/vgloEYTwqgsfaWpKY+AoZuavZbPIAv6mGgMaIlwLdedTHBdPb/OnZ7aRBwbQQYkdzd+RWMn78eEaNGkVISAiPPvooNTU1TJ8+nU8//bTRbY0bN47t27dTUFCAt7c3c+bMYerUqQAMHTqUefPm0blzZ8aMGUP79u0xNjYmMjKSRx65qVMnb0hlOj0vnsngt9xiOtpa8lW4H34WZuj1VSQkvkdm5mIsLYPp2OFrbG3bnDtPq9WyY8cO9uzZg5WVFffeey9hYWH12hdCoI4tpGRVEvqSGiw7uGE3xB/VFRb1VZWVsu+3JRzbtA4TM3N63T+FyMEjML5EXerLqanWcWxzGse2pKOp0dOigytRwwNwcG++BTPn8qF//hldbm5tPvQbc7AbOfKmyIeu0lZhqjLF2Oiar8y3FELMvNYXvRXJMfvWVKQu4rU9r7E9YztdPbryVo+3cMaaI4/P5JC6M1pnTzq0LiXqsTHkJJ7mr5mfUJydRbtBw+g5fjJ6ASt+/ZMjscewEmaEaluRGRLIlDERqMvWciD6HY7pfPjZ9AdStFYMcbbjjRZe+Jg370Js6cajNGRNYd3mAF8AYYApoAIqhRBXv7tDE+jYsaM4dOjQBa/FxcVdNFCRasnP5+ocLK3kidhUMtUanvV3Z7qfG8ZGCiWlMcTGvkB1dRo+Pg8SFPgcKtU/AWBqaiorV66ksLCQyMhIBg4ciIVF/RQJXWE1JauSUMcXYexmicPoYMz87S7bJ51Wy5H1qzjwxy9o1NW0HTCErmPGY2l7+fMuRqPWcXxbBkc3pVFTpSMw0oVOwwNw8qo/c95ULpYP7fjg5JsiH9ogDBzKOcSKsyvYlLqJ93u9Tx+fPo1qQ1GUGCHEVU9HKoryFrBXCLH2atu41uSY3Xjy87k6uzJ28cqeVyjTlPG/Dv9jQtgEKo8cZ9u7a0l37IKtIZeBT7bDMSyQPb8sJmbNX9g6uzDosWn4RLTh1LETrF29lmqtmmC9NwlmAQwZ35Zw13xOn3md1NJEfjWZzg5da3zNTXm7hRcDnBs/9ko3l0uN2w2dSvmS2oUuy6mt7DEJuGzyoqIo5sBOwKzuOr8JIV5TFCUAWAY4ATHARCGERlEUM2pL7XUACoF7hRApDeyfJDULnUHwSWoOn6Tk4m1uyor2LYiys8JgqCHx7Oekpn6Hubkn7SN/xsGh87nzampq2Lx5MwcPHsTe3p6JEycSFBRUr32hM1C+I4OybekoRgp2wwKw7uaJorp0MCmEIOHAHnb+/COlebkEto+i14QpOHn7XPKcS9Fq9JzcnsnhjamoK7T4t3ai04hAXHybJ89PCEH1oUMULviJiq1ba/OhR4zA8YGbIx86uTSZVWdXsSppFTmVOViZWDEkYAie1telrNk04EVFUWoALbVbiovrPckhSdeTWqfm45iPWRq/lGD7YL4d8C0tHVpy5pPv2XPMjmqHTrRyjqf7y1PJS0tm0cxpFGdl0HbAEHpNeJBKdQ2Lvl5AUl4qTgYbTHVhFPcI4YU73MhI+5wDBxezSzWcn1Uz0OiNedbflad93bC4zJgt3foa/FxSCJGoKIpKCKEHflQU5Qgw+zKn1AB3CCEqFEUxAXYrirIOeBb4RAixTFGUb4Cp1NZJnQoUCyGCFUW5D3gPuPcq70uS/rPU6hqejE3lUFkVY9wc+L+W3tgYqygvjyM27nkqKuLx9LiHFi1ewtj4nxnchIQEVq1aRVlZGV26dOGOO+7A1LT+Yz91QjElK86iK6jGorUzdsMDMb5CibnsxNNsXzifrNOxOPv6c/dLb+LfJrLR96bT6jm1K4vD61OpKtPgG+5I1IgA3AOaZ2ZFaLW19aH/nQ897j6ML1FT+0ZRoi5hfcp6Vp1dxfGC4xgpRnT17MqzHZ6lj08fLIybbzHm5Qghmvw3HkVR7IF5QCtqy+1NAU4Dv1C70DEFuEcIUazUJuN/BgwFqoDJQojDTd0nSWqo00WnmblzJmdLz3J/2P1M7zAdiirZOPVDEk0isVQVMnKEGo+BD7Hn18XErP4Laycnxrz0Ft4Rrdm7eRc79u0CAX66IE64BPD4uNZY6TcRc3Ai6VpzFpnN5ajGha72VnwY4kOQ5Y2fiiY1v4YG01WKopgCRxVFeZ/aEnmX/TWsriZ1Rd23JnV/BHAHML7u9Z+oXdz4NTCKfxY6/gZ8qSjKBTt8SdK1IITgt9xiZp/JwEiBr8P9GO3mgMGgIyXla5KSP8PExI62bb7H2fmOc+dVVVWxfv16jh8/jrOzM1OnTsXHp/5ssb6shpLVSVQfL8DYyRznKa0wb+lw2T6VFeSxe+lC4nZvx9LOngGPPEWrvgMavemKXmcgbm82h9amUFlSg1eIPYMeaYVnsH2j2mnw9UpLKf71V4oX31z50Fq9ll2Zu1h1dhXbM7ajM+ho4dCC5zs+z9CAobhY3hi/ACiK4gC0AM59mEKInf+hyc+A9UKIMXVjviXwIrBFCPGuoiizgFnATGBI3bVbAJ2pHcc7X7xZSWo+Qgh+jvuZj2M+xs7Mjm/6f0N3r+6krd7B1uWZVFp0IJiD9H33fgpLK1g08xmKsjJo3W8Qve+fSn5eId98+BX51UV46J1IFAEEjWzNa6FlnEmYSlLZcbaYP84yfV/MDUZ8FOLFOA9HuQ24dE5Dg+mJ1AbPTwH/A3yAu690kqIoKmpTOYKBr4CzQIkQQld3SAbgVfe1F5AOIITQKYpSSm0qSMG/2nyEuo0JfH19G9h9SWqYUq2OmWcy+CuvhC52VnwR7oePuSlVVcmcin2BsrIjuLoOJaTlHExNHYHagTw2Npa1a9dSXV1Nr1696NWrF8bGF/7zEnpBxb4syjalIvQGbPv7YtPbB8Xk0r+XatTVHFzxG4dW/YlA0Hn0PXQaNabRm64Y9Abi9+dwaG0K5YVq3APt6P9gON4hlw/ir5YmPZ2inxZS8scfiKoqLLt2wePNN7Dq0eOGzYcWQhBbGMuKsytYl7yOkpoSHM0dGRc6jpFBIwlxCLmqyijNRVGUh6hN9fCmdnfaLsA+aicsrqY9O6AXMBlACKEBNIqijAL61B32E7Cd2mB6FLCwbsJjv6Io9oqieAgh5H4E0jVTrC7m1T2vsj1jO328+/BG9zewMbJm++z5xBb6YqoyY2DYIQIem86+35dycOUfWDk6cvfsOXiEtWLjsjUcTj6OuTDFWhtKQkgwz470pizvKw7FLCXVOJIfzReRUGPGMBc73mnhjZusGS39S0OreaQqimIBeAgh5jS08bqUkHZ1jw7/BEKvqpcXtvkd8B3ULmb5r+1J0t8OlFTwZFwq2TVaZga484yfG0YI0jMWkpj4HkZGZkSEf4Kb24hzQVVZWRlr164lPj4eDw8PJk6ciLu7e722a1LLKPkzEW1OJWYtHXAYFYTxZWo1Gwx6Tm3fwp5fFlFZUkxo9970HPcAti6ujbong0GQcDCXg6uTKc2vxtXPhj7jQ/AJd2yWwLDqyBGKflxA+ebNoFJhN2wYjpMfwDz0P//TbzY5lTmsSVrDyrMrSSpNwtTIlL6+fRkZNJKunl0xMbphf3BOA6KA/UKIvoqihALv/If2AoB8atP42lI7ETINcDsvQM4B3Oq+PjcBUufvyZELgmk5ASI1l4M5B5m1cxbFNcXM6jSL8aHjyT+ZzrJP11JqEoB3dTQDnu1Emc2dLH7xfxRmpNGq7wD6THqIxGOJfPHep1Toq3HTe7LPzJ/J41oTYrOdxJOPUaGrYb3Ne/xWEYSryoQfW3kxxMX+et+ydINqUDCtKMoI4ENqK3kEKIrSDnijoZu2CCFKFEXZBnQF7BVFMa6bnfYGMusOy6R2xjtDURRjwI7ahYiS1Kx0BsFHKTl8lpqLj7kpKyNb0MHOCrU6i7i4WRQV78HJsRdhYe9iZlYbRwghOHLkCBs2bECv1zNgwAC6dOmCSnVh2oW+UkvpumSqDuWisjPF6f4wzCOcLhvIpp44yo6F88hPS8GjZSgjn3sJz5aNC0aFQXD2SD7Rq5IozqnCyduaoU+0wb/15a99NYReT/mmzRT9+CPVx45hZGeH00MP4TBhAiZujQv+r5UqbRVb0raw8uxKDmQfQCCIdI3k1a6vMsh/ELamN8UaPrUQQq0oCoqimAkh4hVFCfkP7RkD7YGnhRAHFEX5jNqUjnOEEEJRlEZNYsgJEKmp6Qw6vjv+Hd8e/xYfGx++7PclIQ6hRM/dwOFjCiqs6WnxJ2HvvsSB9RuJXvEpVnb23DXrdRy9glj+3S8klqRha7CiRNsak+6hfNC1htSkx4nPOsFZq3v5zuheMioEkzydeDnIE1vjxqXUSbeXxmza0onax3sIIY7WVeW4pLrdubR1gbQFMIDaRYXbgDHUVvR4gNqNBwBW1n2/r+79rTJfWmpuqdU1PBGbSkxZFfe4O/B2C2+sVUZkZ//BmYQ3EEJPSMibeHmOOxeEFhUVsWrVKpKTk/Hz82PkyJE4OTld0K4wCKoO5VK6PhmDWo91L29s+/liZHbpAbkwM52di38g6fBBbF3cGD59Ji279GhU8CuEIPlYAdGrkinMrMDBw4pBD7ciKNLlipu+NJa+opLSP36naOEitBkZmPj64vbKy9iPHo2RZfNt7nK1/l3OrlpXjZe1F4+2fZQRgSPwtb3pZk0z6p76/QVsUhSlGEj9L+0BGUKIA3Xf/0ZtMJ37d/qGoigeQF7d+39PgPzt/MkRSWoWOZU5zNw5k8N5hxkZNJKXOr+EOrOaX1/5lUKDC67lR+k/Uo+m8zMseetNCtJTiejdn14Tp3B440GWrPgKgzBgofPngEsAL432w6TqW04eW47axJ8/7ReyutSKYEtT/orwoYt985UHlW4dDQ2mtUKI0n/9UL9SoOsB/FSXN20E/CqEWK0oSiywrK5G6hFgft3x84FFiqIkAkXUluKTpGbx70WG34T7caebAxpNASdiXya/YBN2dh0JD3sfS0s/AAwGAwcOHGDr1q0oisLw4cNp3749Rv/KAdZkVVDyVyKatHJM/W1xuDMYk8tselJdXsa+35ZybNNajE1N6Tl+Mu2HjMT4IhVALnc/aaeKiF6VRF5qOXauFgyYEk5wRzeMmjiI1ubkULx4McW//IqhvByLDh1wnTkDmzvuQFHdeLM3/y5nZ21izdCAoYwIGkGkayRGyo2Zw30lQojRdV++Xvfkzw5Y/x/ay1EUJV1RlBAhxGmgHxBb9+cB4F3qT4A8pSjKMmoXHpbKfGmpOW1L28Yre19Bo9fwTo93GB4wnEM/7OBQtBojvRVRmsW0e+NhDh45y4GXnsPSzp7RM1/D1NSZnz5fQK62CDuDA3sN/gwaFM77/vtISZmOTl9FvNPLfFXWnrIyA//zc2Oanxvmstyd1EANDaZPKYoyHlApitICeAbYe7kThBDHgXo1u4QQSdTOcv/7dTUwtoH9uS2kp6czadIkcnNzURSFRx55hGnTpl302ClTprB69WpcXV05efLkNe7pzaVMp2fm6XT+zCuhs50VX9YtMszL30B8/MvodBUEB8/C12cKtb8LQl5eHitWrCAzM5MWLVowfPhw7OwuLCNnUOso25RKxd4sjCxNcBjbEsv2rpecWdbrtBzdsIZ9vy9FU1VNm/6D6DZ2ApZ29g2+FyEEGaeLiV6ZRE5SGTZO5twxKZSQzu4YNfEPAnVsLIU/LqBs3TowGLAZNBCnBx/Eok2bK598jV2snF03z2482+FZ+vr0xdz4xq0kciWKotgKIcoURXE87+UTdX9bUzsZcbWeBn6uq+SRBDxI3WSIoihTqZ35vqfu2LXUlsVLpLY03oP/4bq3BDlmN48afQ0fH/qYJfFLCHMM4/1e72NXYsOvTy+nQO+MS1k8fTslIEY8z7Lv5pKflkJ4rzvodvckdv+5nUM5azHFmFJtC9KDg3lngJ6i7GdJTIxFYzuIH40eZ2eRnva25nwU4kOY9fUpdyndvBoaTD8NvERt7eglwAbgzebqlFTL2NiYjz76iPbt21NeXk6HDh0YMGAA4eHh9Y6dPHkyTz31FJMmTboOPb15RJdU8MS/FhkadOWcin2RnJw/sbGOIDzyA6yta1NPdTodu3fvZufOnZiZmXHXXXfRunXrCwJkIQTVx/MpWZ2MoUKDVWcP7Ab6YWR58YVrQggSD+1n5+IfKMnJxr9te3pPnIqzj1+j7iUroYQDK5PISijB2sGM3uNDCOvmgcq46YJoYTBQsXMnRT8uoOrAAYwsLXGcMAGHiRMx9fa6cgPX0M1Szq4JLAGGU7tAUFC3Wct5fwdebcNCiKPUbsz1b/0ucqwAnrzaa92K5Jjd9JJLk5mxcwbxRfG1taMjp3NiUTTr91eiGCzpWP0T7WeNJSbJg32vzcbCxpY7X3gZdYEJ87/5gTKqMNW7sdnUn2dH++JvuoC0hD8wNvXgqPt8vsx3RFEEb7Xw4kEvZ1Q3UMUe6ebR0GA6vO6Pcd2fUcBI4MabkrpBnDp1imnTppGWlsbEiRPJy8tj0qRJREVFNbgNDw8PPDw8ALCxsSEsLIzMzMyLDsy9evUiJSWlqbp/y9EZBB+n5vBp3U6Gfy8yLCraQ2zcDDSafPz9nyLA/0mMjGrTKzIzM1mxYgV5eXm0atWKIUOGYGV1YbqGNr+KkhVnqUkswcTLGudJ4Zj+f3t3HR5XlT5w/HvHIjNxd23T1N1doJoChaJtYWHht8ACi8MuttgKuwvry7JLBS+wNKlB3d29jbtObCYZP78/JjXqbdJIz+d5+jS5ub1z7tzk5O25733fmAv30ijLyWLd/I8oOHyAwKgYbnvxdRL6XFlH6bKcOrZlZFNw2Ii3r44Rd3ai6/BINNrmS7FwWSzULkrHOG8etuxsNOHhhD73HP4z70Dt0zLdEa+GEIJDVYdIz0o/q5zdXSl3MT15Ol0C224VkaslhJja1DBllBAiv7XH01HIObttEUKQnpXO29vexkPtwV/H/pVeojvf/SKDSkcgwfXHGdtjO7p7fsXX//0vxccOkzJkBAMm3MWqjJUctxTgJbw4aO9CyoAu/KPXLooLXqTMZcUe8Sy/M41mX5mVcYEGfpsSTbTn5afVSdKPXW4w/SnwLHAQcLXccJpXTUYWtmJzsx5TF6nHf9q5baHPZLFYuOOOO1i4cCGJiYl06dKFfv36nTUpjxgxgvr6+nP+7Xvvvcf48ePP2Z6bm8uePXsYNEj2RLhSZ3YyvCM8gHc6ReOt2Dh2/HUKCxfg7Z1Iv34L8fPtBYDNZmPt2rVs2bIFg8HA3XffTUrK2UUSXDYn9WsKqF9fiKJV4T89Cf2giAs+5GeqNrLxi/kcWrcKT4MP437yM3qOn4jqCnKMK/Lr2Z6RTe6BKjwNWobelkz30VFodc0XRDuqqqj+7HOqP/8cp9GIZ9euRP7+9/hOvBlF23ZKxJWaS1mcvZj0rHRyanPQqXSMjR3LtKRpDI0cikZ12c1d26WmqhpLgB6tPZbmJOdsCcBsN/PW1rdYnL2Y/mH9eXfYuxR+fYIvNm8H4UU/81z6PzGWo5Y5rH7tFRRFYdLDT2PMs/PfrxZgx4nZGc1m/0TemOJCVfcyBbnHMASMZrnXM/y71Iafxsk/usZxS6h/m6ofL7VPl/sbp0IIkdGiI+lAVq5cSZ8+fejWrRvgDs6eeeaZs/bZsGHDZR/PZDIxY8YM3n//fXx920XJrjbj61IjL/7oIcPa2j1sO/wsjY25xETfT1LSc6jV7hza3Nxc0tPTMRqN9O3bl5tuugnPH3XqazxSRU16Fs5qK959QvGbnIDa5/yrGnarhZ2L/8eORd/gdDjoP/VWBt06E0/95T8hXlVkYvviHLL3VODhrWHQ9ER6jolG59l8AaM1Kwvj3LnULkpH2GwYxowh8IH78R4woM38ommwN7AibwUZWRlsL92OQNA3tC9zhsxhQvyE9lLOrjntVhRlgBBiR2sPpL2Tc3bbcajqEM+ve55CUyGP9n6UO/3vYOXLa6mwBxJkymRs5xX4PPQOS79K58T2r4nu2p0BI+9m5fr1FIsqtMKXlY447hoXxazQL6goycDTIxJr4r95tTSCrBorM8MDeD05ikBtx/5Pt3T9XO530muKonwErMKdNw2AEOLbFhlVM7nUakRL2bt3L336uJ+9LC4uxmAwMGzYsLP2udxVDrvdzowZM7j33nu57bbbWnbgHUidw8mLxwv5tqz61EOGUTrIzHqPvLx/4ekRTp8+nxAYMARwr0ytXLmSnTt3EhAQwJw5c0hIOLv6o6PaQk1GNpbDVWhCvQj+aQ88k/zP+/rC5eLopnWs/3wepqpKOg0aysh7HsA/POKyz6G61MyOxTmc2FWO1kPNgCnx9Bofi4dX8/wCEELQsHUrVR9/jHn9BhQPD/xuu5XA2XPwSLxo5cvrxulysr10OxlZGazMX0mjo5EYnxh+1vtnTE2cSozPue3abyCDgHsVRckDzDTlTAsh2m36nZyzb1xCCBYcXsCfdv+JIM8gPprwEarvrXy1aYd7Ndr0MQMe7EFB8Ct8+/bvaKyrY8Tt91NXoeWztYsAhRxHPNaYRN4feYC6ijeorLQTFPskC+zT+DSnllhPwZe9khgV2HZS1aSO4XJ/Kz+Au3uhltNpHgJo08F0a9HpdBQVucutvvTSS9hstnP2uZxVDiEEDz74IKmpqTz99NPNPs6OanuNiceO5FNstfF8QjhPxIbR2HCMHfufxWQ6QkTEHXTu9Es0GveEevz4cRYvXkx9fT1DhgxhzJgx6M4oSyccLuo3FlG/yp2e6jcpHsOwKJQLPOhXdPQwaxd8RGnmccISk5ny+LNEd+1+2eOvrWhk55Icjm0rRa1V0femOPpMiMXT0DxpFsJmo27ZMqrmzsN65AjqoCCCn/g5AXffjSagZdqLX6msmizSs9JZnL2Y8oZyfLQ+TEmcQlpSGr1DereZ1fJWdnNrD6CjkHN26zJajLyy6RXWF65ndMxono97li3v7qTCFkCQOYuxMd8S8MrvWLdmF3s+eoOg6FhGTv4/1uzeRgW14ApgjTaZpyc7CRVvUV2aRVDQGLKDnucXeTYqbLX8LCaEZxPC0bfB8p1S+3e5wfQAIcS1dNa6odxzzz1Mnz6dlJQUHnnkEaxWK0899RTvv//+FR1n06ZNLFiwgB49etC7d28A3nnnHSZPngzA5MmT+eijj4iMjOTuu+9m7dq1VFZWEh0dzRtvvMGDDz7YzGfWtjlcgj/llfKnpocMF/XpRD9fT/Ly/kV2zvtotX707PkhIcHuwgRms5nly5dz4MABQkJCmDlzJtHR0Wcd05JVQ82iTBzljXh2C8J/WiIa//OXVastL2X9Z/M4vmUDhoBAJj76C7qOGIOiurzqGvVGCzuX5nJ0cwmKWqHnuBj63hSHt2/zPBjjrKmh+suvqP7kExwVFeiSk4h46018p01D5eHRLK9xLYwWI8tylpGelc7hqsOoFTXDo4bz/IDnGR0zGg9164+xLRFC5AEoihIKtN9af22AnLNbz1ktwQe8ROqOWJZ8fhiEF31NHzPwrjAqu/2VT//8V6oK8+k3/hbMZl++3rUCNRqOO5LpNSSeD2IXUlW5GJdnDGGpH/GHyniWnailu8GL+T0T6eXT9hpJSR2HcjlNBhVF+Rj4vRDicMsP6fL1799f7Ny586xtR44cITU1tZVG1PZ11PfnzIcMbw8L4N3O0aht+Rw+/By1dXsIDZlESsqv0ekC3RUgDh1i6dKlWCwWRowYwYgRI9BoTv/f0llvo3ZpDg17ylEHeuKfloRXl8Dzvra1oYFt333F7qWLUBQVA9JuY8C0GWg9Ly++MddY2bUsl0ObigHoNjyKfhPj0Ps3T/Boy83FOH8+Nf/7DtHYiH7YMALvn4N++JV1V2wJVqeVdQXryMjKYGPRRhzCQWpgKmlJaUxKmESQV9ClD9JOKYqySwhxZaVczv73acAfgEjcXQnjgCNCiG7NNMRmJ+fsK9dR3x+Hy8E/9/2TD/d/SJxvHL/u/DqZ/8ql3BZAYN1RxkZ8Qsj//Zqdh2vY9OUnePv60m/EfWw8vp8axYTLGUxBdHeeGJVDXfmfcTotxMY+wkbdnbydU4FdCJ6ND+eRmFC0zdy4SrpxXWjevtyV6cHAXkVRcnDnTLf73Dyp4zj5kKECp57OLir6lBOZv0Gl0tKt658IC5uGoijU1dWxZMkSjh07RmRkJNOnTycsLOzUsYRLYN5aQu33uQiHC5+xMfiMjkF1nooZLqeTA6t/YNNXn9BYV0vXkWMZfvdsfAKDL2vcDXU2dv+Qx8F1RQinoMvQCPpPjscn8NoXGYUQNOzYgXHuPExr1qBoNPimTSNw9hw8Uzpf8/GvdWz7KvaRnpXO8tzl1NvqCfEKYVbXWUxNmkrngNYdXzvyJu65eaUQoo+iKGOA+1p5TJJ0SSWmEl7c8KK7JXhiGrdkjWfb++WAN31M8xg0xYV55FwW/ve/FB45SJd+o2kkjCXHN6NBR56mG3feEkmw432Mxbvx9x+EJvZ1ns1X2FpbxjB/A++lxJDgLe9mSdfH5QbTE1t0FJJ0Fc58yHCgn56/psYSqhjZu/d+jNUbCQwcQWrqb/D0CEcIwe7du/n+++9xOp3cdNNNDB48+KxW4Nb8Omq+y8RebMajkz/+aUloQ85/azB3/x7Wzf+IyoI8orp0Y/SLrxOe1Omyxm0x29nzQz771xbitDlJGRRO/ykJ+IVce9ctYbdTt/x7jHPnYjl0CHVAAME/+z93PnRI6zYtKawvZHH2YjKyMsivz8dT7cm4uHGkJaYxKGIQapXMZbxCdiFElaIoKkVRVEKINYqivN/ag5Kki1mVv4pXN72Kw+XgzZTXsX8m2G4TBDbkMjb4P4Q+/hxHakNY9eqvAEH/MT9hR8kJTEoWDlc4fkP780LSSoqLfkWDxofElPf4wjKIvx+sQK9W8acuMdwVHtjqd92kG8tlBdMnc/Mkqa3YUWvm0cN5FFttPBcfzhOxoVSWL2LbiTdwuRykpLxJVOTdKIqC0WgkIyODnJwc4uLiSEtLIyjodPqA02yn7vtczDtKUfnoCLynC149gs87GVcVFrDuk/+Qs2cnfmHhTHv6JToNHHpZE7e10cG+lfnsW1WAzeqkU79QBkxNICBcf8l/eynO2lpqFi7EuOATHGVl6BITCf/1G/ilpaG6zHSTllBvq2dF3grSs9LZVbYLgIHhA/lpz58yIW4Ceu21n/sNrEZRFAOwAXcL8HLcVT0kqc2xOq38Yecf+Pzo56QGpPJ4+RyO/EfBhUJv03wGjynHPuUTlixcxLEtC4jr3J8Gj2jWlO5HJ7ywhQ5m1hQwFj9DUWEhERF3UBT0BHdl1ZBnKef2sABeS44kRNd26uFLNw5ZZFFqV873kGFPLwtHDj9ORcX3+Pn1o2vq7/H2jsPlcrF161ZWr16NoihMnTqVvn37nlqNFi5Bw64yapfl4LI4MAyLwndCLCqPc38sGupq2fL15+xbsRSthycj7/sJfSZOQ3MZjUxsFgcH1hay54d8rA0OEvuEMHBqAkFRl19r+oLHzs/HOH8BNd9+i2howHvIYCJ+/Qb6ESMu+8HH5uZ0OdlaspVFWYtYnb8aq9NKvG88P+/zc6YmTiXSENkq4+qA1gB+wJO40zv8gF+36ogk6Tyya7N5ft3zHKs+xv3hs4lbEs8BmxcBDScYG/B3wu9/kDyfESx/610aamtJ6T+TQ6YiLPZCUMcwdMYAgpR/U5y9FG/vJKK7f84fK0JZdKicJC8Pvu6dxPAAWe5Oaj0ymJbajbxGK48fzmdHnfnUQ4aW6tVs3f9LHI56kpOeJzb2IRRFTXl5Oenp6RQWFtKpUyemTp2Kn5/fqWPZik3UfJeJLb8eXZwvAbcmoz3PCrHTYWfP8sVs/eYLbI2N9Bw/kaEz78Xb1++cfX/MYXNyYF0Re37Io7HeTlyPIAZNSyQk9tomfSEEjbt3Y5w7l/qVq0CjwW/KFALvn4Nnl9Zrn51ZnXmqnF1FYwW+Ol9uSb6FaUnT6BncU952bX4a4AfACHwJfCmEqGrdIUnSaUIIvsv8jne3v4uHyoN3G16m6Gs/KlDRy/QJQwYdQcyYy9o1O9m15BXCorqhChvETnM2HkJPZO9R3NQ/k5ycWVQKG3Hxv2Cddga/OVqBTdTyXHw4j8eF4tFKCweSdJIMpqV24ZumhwzB/ZDhtCANx4+/SEnptxgMXenbZwEGQwpOp5ONG9exfv16dDodt912Gz169DgVyLksDupW5GHaXIzKW0vA7Z3x7ht6ThtwIQSZO7aw/pOPqSkrIb53P0bd9xOCY+IuOVan3cWhjcXsWp5LQ62N6C4BDEpLJDzx0gH4xQi7nboffsA4dx6WAwdQ+/kR9MjDBNxzD9rQ0Gs69tWqtlSzNGfpOeXs0pLSGB0zGp26ecr6SecSQrwBvKEoSk/gTmCdoiiFQohze1tL0nVWb6vnra1vsTRnKSO9hjFqwxjy7CEENGYy1u/PhN8/nYrk51n6wV+oLCggMnUquaIKu6jAxyeFW+/uRFXx22Rm7icwYBj26Fd5PM/F3voyRgYY+E3nGBLlA4ZSGyGDaalNO99DhobGXWzd9jxWaxnx8Y+REP84KpWO4uJiFi1aRFlZGd27d2fSpEno9e7VZiEEjfsqqFmSg8tkQz8oAr+b4lB5n5umUZadydoFH1F4+CBB0bHc9tIbJPTud8mxOp0ujm4uYefSXEzVViKS/bj5oW5Edrq2RijOujpqFn6N8ZNPcJSUoIuPJ/z11/CbPh2V17U/tHil7E476wvXsyhrERsKN+AQDroEduH5Ac8zOWFyhy5n10aVA6VAFdA6/6uSpDPsKd/Di+tfpMxcxrNVD2M5kkgVanqZPmNI7y2obv87Ow9XsfHVF/HzTcArZRzHKMVb8WXIxLFEBS0l9/hraDT+xKe8z9yGPvznYCWBWg1/7xrHraH+8k6X1KbIYFpqs7bVmHjsSB4lVjvPJ4TzWLQvudm/4UThfLy9E+jfbyF+fr2x2+2sWrWCzZs3YzAYuOuuu+hyRrqDvbyBmkWZWLNq0UYZCJ7dFV3MuakWJmMVG79YwKH1q/Ay+DDuwUfpOe5mVJfomOVyuji+vYwdS3Koq7QQluDL2FmpRKcGXNOEbyssxDh/PrVff4OroQHvQYMIf/UVDKNGXfd8aCEEh6oOsShzEctyl1FrrSXIM4h7U+9lWtI0UgJv8J5OQsB1/uWuKMqjwEwgBFgI/LSt9QKQbiwOl4N/7f8XH+7/kGQSeGDnc1TZI/C3ZDHW9wMibh9C3aB0lv/3PxQePkRgwliKdHW4qCU+qg83T/MkK+tx8gtKiIi4i0z/x3gyp5pSayWzIoN4OTECf60MW6S2R35XtmEFBQXMnj2bsrIyFEXh4Ycf5sknn7zg/k6nk/79+xMVFcXixYuv40ibl90l+GNuKR/klRHjqSO9TyeSOcHunffR0JBDdPQckpOeQ632Ijc3l/T0dIxGI3379mXChAl4Na3WumxO6lcXUL+hEEWrwv+WJPQDI85J6bBbLOxc/D+2p3+NcDoZMO02Bt06Ew/vi1eaEC5B5q5yti/OoaasgeAYA1Me60lc96CrDqKFEDTu2duUD70SVCr8pkwmcM4cPLt2vapjXotSc+mpcnbZtdnoVDrGxo5lWtI0hkYORaO6QacQSx3kboSs1e4/U96DpLHXexQxwFNCiL3X+4Wl87tR52yAgroCXtz4Ivsr9jPHfBd+e3pSrejoaf6SIV2Wo7n1jxytDWblqy/jqQlD02kUuepq/NVBTL1zBA2Wf3L48Ar0+s74d/qAd0sDWHG0nG4GTz7qFk8/P1n5R2q7btDfhO2DRqPhD3/4A3379qW+vp5+/foxYcIEul4gqPrggw9ITU2lrq7uOo+0+eQ0WHn0cB576hu4MzyQN5NCqCj4Ozvz/omHRxh9ei8gMHAoFouF5cuXsGPHDgICApg9ezaJiYmnjtN4uIqa9CycNVa8+4biNykBtc/Z+bvC5eLwhjVs/GI+JmMVnQcPZ8Q99+MfFn7RMQohyNlbybaMbIzFZgIj9Ux8pDuJvUOuPoh2OKhfsYKquXOx7NuPys+PoIceIuDee9Ce0VTmemiwN7C6YDXpmelsLdmKQNA7pDevDnmVm+Nvxlfne13H0ya4nFC853TwXLgDXA7QekP8cNBc//KDQoiXrvuLShd1I87ZQggysjN4e+vb6JwevHz8RYxVEeishUz0ep+Ym6Kx3LSS7xd+x/HNn+AbO5xiLzMqGhjUfRjdBhaQnTMbIZzEJb7AMqbxxyMVKIqJ15Ii+Wl0CBrZwVBq42Qw3UIOHTrEk08+SX5+PrNmzaK8vJzZs2czYMCAyz5GREQEERERAPj4+JCamkpRUdF5J+bCwkKWLFnCL3/5S/74xz8223lcL0IIvig18ssTRWgVhX91i2OcdzmH9s7EZDpMRPgMOnd+BY3GhxMnTpCRkUFdXR2DBw9m7Nix6HTuQNlhtFCTnoXlqBFNmDchD/fE4zwP/hUePsjaBR9Rlp1JWGInpjz5PNFdLt6FWQhB3sEqtmfkUJFfj3+YNxMe7EpyvzBUVznZO00mahZ+TfWCBdiLi9HGxRL26iv433ILKu/zN4xpCS7hYlfZLtKz0vkh9wcaHA1E6iN5uOfDpCWlEesbe93G0mZU550OnnPWgaUWUCCiFwx9wr0SHTMQNPIhqI5AztlXrtZay1tb32J57nLGusbTe/sYjC5vEqtXMCZxLp5TX6DAfwyLf/02WqcfSqehFKjrCfeKYNrd3Skq/S0nMg8RFDQKU8SveCjXxlFzGRODfXmrUzTRnvIBZql96NDB9LJlyygtLW3WY4aHhzNp0qSL7mOxWLjjjjtYuHAhiYmJdOnShX79+p01KY8YMYL6+vpz/u17773H+PHnPoyfm5vLnj17GDRo0Hlf86mnnuJ3v/vdeY/Z1lXbHTx/rJCMihqG+Ov5S5doHOXz2X7ofTQaH3r2+BchIeNpaGggPf1b9u/fT0hICA8++CAxMTEACIeL+nWF1K0pQFGB3+QEDMMiUdRn5xbXlJaw/tOPObF9M4agYCY9/gypwy6egyyEoPBoNdvSsynLqcM32JNxc1LpPDAMlfrqcpftRUUYF3xCzcKFuMxmvPv3J+yXL2MYPRrlEjnazSm/Lv9UObsiUxHeGm9uir+JtKQ0+oX1Q6XcQCWnLHWQu6EpgF4Dxiz3dt8oSJ3mDp4TRoNePmDZUuSc3X7sLN3JSxtfosps5KmKZ7CeiMZprWGM7c+kDi7Fccs3rN54hAPL3kQfM5giLzMeip3Jw0fjF7uOo5nvodMFEdPlr/yrrhufHjIS5aFlbvcEJoZcW+UjSbreOnQw3VpWrlxJnz596NbNvdJps9l45plnztpnw4YNl308k8nEjBkzeP/99/H1PfcW++LFiwkNDaVfv36sXbv2msZ+vW2srueJI/mU2+z8MjGC+4MbOXZ4DrW1uwgJuZkuKW+i1QZy6NAhli5dSmNjI6NGjWLEiBFoNO5vX8uJamoWZeGobMSrRzB+UxPR+J29Wmgxm9j67ZfsWZaBWqNh2Mz76Df1FrQeF789X3yimm3pORSfqMEQ4MHoe1PoMjQC9VUG0Y3792OcO5e6738AwHfiRALvvx+vHt2v6nhXo85Wxw+5P5Celc6e8j0oKAyOGMxjvR9jXOw4vLXXb0W8VTkdp1M3stdAwXYQTtDq3akbAx92B9DBna77w4XS9SXn7Mtnd9n5x95/8NGBj0hRujNr38+pbzAQYdzB2JC/4T95DPnJv2bxH/6Dh8MPR6cBFKpMJPvHM+oWP/IKX6awsJyoyPvY6/Mw/5dtpMZh5P9iQnguPhy95votJkhSc+nQwfSlViNayt69e+nTpw8AxcXFGAwGhg0bdtY+l7vKYbfbmTFjBvfeey+33XbbeV9v06ZNpKens3TpUiwWC3V1ddx333188sknzXhWzcvmcvG7nFL+ll9OopcHi/t2Irh+Ebt2vouiqOna9Q+Eh03HZDLx7bdfcvToUSIiIpg1axbh4e6cZmetlZol2TTur0QT5EnwT7rj2fnsMnROh4P9q5azeeFnWEz1dB89nmEz78MQePHVxdKcWranZ1NwpBpvXx0j7uxE1+GRaLRXPtELp5P61asxzp1H465dqAwGAufMIXDWfWibbgm3NIfLwZbiLaRnpbM6fzU2l40EvwSe7PskUxOnEq6/eJ54h1Gde3rl+czUjcjeMPwpd/AcPRA08vZya5BzdtudswHy6vJ4cf2LHKw8yCzLw/juTaHRbqOf8SP6d1+N4+Y3WHbAQuZ3H+AVO5ACj3r0KsHtE4bj0H/B8ew1GAyp6Dv/nV8WGdhUUk5fX2++Skmim+H6l/mUpObSoYPp1qLT6SgqKgLgpZdewmaznbPP5axyCCF48MEHSU1N5emnn77gfu+++y7vvvsuAGvXruW9995r05NyZoOFRw/lsd/UyKzIIF6KUZN3/DGOGTcQGDCc1NTf4OERzt69e/n+++9xOBxMmDCBwYMHo1arEU4Xps3F1K3IR7gEvhPi8BkZjaI9vVrsfkhwJ+vm/wdjcSExXXswavZDhCUkXXRs5Xl1bF+cQ96BKjwNWobOSKb7qCi0uisPol1mMzX/+w7j/PnY8/PRRkUR9vJL+N02A7Xh+jyZfqL6xKk0jsrGSvw8/Lit022kJaXRPbh7x6/VelbqxmowZru3+0ZDahokjZGpG5Kcsy/hzE6GBoc/z+W8TX2ZAd/qY4xU/42ocXoyO3/A8rnp+OjisCb3oUpVT4+wZHqNr6Wg6CkUu0Js4i/51nUzfztciae6gd92jmZWZBCqjj4PSR2eDKZbwD333MP06dNJSUnhkUcewWq18tRTT/H+++9f0XE2bdrEggUL6NGjB7179wbgnXfeYfLkyQBMnjyZjz76iMjIyGY+g5YhhOCTkipePVGEl1rFf7vF09e1jgM7X8flspPS+Q2iou6lpqaGr75aQHZ2NnFxcUybNo3g4GAArLm1VP8vE0dZA54pAfinJaEJOntFoyI/l3UL/kPe/j0EREQy/dlfkdR/0EUDx8rCerZn5JCzrxIPbw2Db0mkx+hodJ5X/iNiLyuj+pNPqf7qK1y1tXj16kXo00/jM34ciqblf+SMFiPLcpaxKHMRR4xH0CgahkcPZ3rSdEZGj+zYXQnPTN04WXXjZOpGwggY9H+QOEambkhnkXP2hdVaa3ljyxusyFvBeNd0uu4cgdkOKSXfMjT+S1zDZ/JdXhglCxbjHT2AXI8afFQq7pjcB5PrQ/IKjhIcPJ6K0JeYndtATmMFt4UF8HpSJKEe5zbNkqT2SBFCtMyBFSUGmA+EAQL4UAjxgaIogcCXQDyQC8wUQlQr7kjnA2Ay0ADcL4TYfbHX6N+/v9i5c+dZ244cOUJqamozn03H0VrvT5XNwbPHClhWWcuoAB9+n+RDbe6vKa9Yhp9vH7p2/T2ennHs2LGDlStXoigKEyZMoF+/fqhUKpwmG7XLcmnYVYbazwP/tEQ8u55dz9lcU83mrz7lwOof8PD2Zsjtd9PrpsmoNReesKuKTexYnEPW7gp0Xhp6j4+h19gYdF5XHvRajhzBOHcutUuWgsuFz4QJBN4/B++m28ctye60s65wHYuyFrGxcCMO4SA1MJW0pDQmJUzq2F0Jawoga1VT7vPaM1I3+rjTNpLGtMnUDUVRdgkh+rf2OH5MURQ1sBMoEkJMVRQlAfgCCAJ2AbOEEDZFUTxwz/H9cHdfvFMIkXuxY8s5+8q15vuzvWQ7L298mVpTPT+teg57ZiAGUyED6/5Dp37ZHE58lLUr9xLg242SAC0NipVe8UmkDDpKSemXeHiEEZT4On+p7sy3ZdUkeOn4TecYRgWe2zRLktqDC83bLblM5gCeEULsVhTFB9ilKMoK4H5glRDiN4qivAi8CLwATAI6Nf0ZBPyj6W+pnVtnrOeJI3lU2528kRzJLZ4HOL7vZez2WpISnyMu7qdUVhr5/POPKSgoIDk5malTp+Lv749wCUzbSqhdnouwOvEZHY3P2FhUZ6RdOGw2di1dxPbvvsJhs9Fn4lQG3343XoYLT9jVpWZ2LMnlxM4ytB5q+k+Op9e4GDz1V7ZSIlwuTOvXY/x4Lg3btqHy9ibgnrsJnDULXVOlkZZyvq6EwV7B3Jt6L2nJaXQO6Nyir99qbGbI3XQ6gK487t7uE9lUdWMcJI4G78BWHWY79iRwBDj55NxvgT8JIb5QFOWfwIO45+cHgWohRLKiKHc17XdnawxYal52p52/7v0rHx/8mJ6uQdxz8A4aTSpii1YyNHA+ytgUvq68nfqVmeijh5GlNeKr1nDH1HCM5r9RUlpFZNQctnr/hJ9kVmFx1vB0fBhPxIbheZUPb0tSW9ZiwbQQogQoafq4XlGUI0AUMB0Y3bTbPGAt7mB6OjBfuJfKtyqK4q8oSkTTcaR2yOpy8U52Cf8qqKCztycLuoWjKXmPgycWYjB0oXfveXh7dWLjxs2sXbsWnU7HrbfeSs+ePVEUBVuRiervMrEX1OOR6If/9CS0YadzjYUQHNu8ng2fz6Ouopyk/oMYee8DBEZGX3BMNeUN7Fyay/Ftpai1KvreFEefCbF4Gq4siHZZLNQuSsc4bx627Gw04eGEPvcs/nfcgfo8T+83pzJzGYuzF5OelX5WV8K0pDSGRA7peF0JXS4oO3g6eM7fCk4baLwgfhj0u98dQIekyNSNa6QoSjQwBXgbeLrpjuFY4J6mXeYBr+MOpqc3fQzwNfBXRVEU0VK3O6XrIqc2hxfWv8DRqmPMMj+F/kAcLks1A4sX0L3rRg5E387WnUZCgiMwxodgoZr+KXFEddlAafU6fHy6IRL/xZPFnuwvrmCYv4HfpkST7H39GxtJ0vVyXX7rKooSD/QBtgFhZwTIpbjTQMAdaBec8c8Km7adFUwrivIw8DBAbOwN2EiinThqbuTRQ3kcNlv4SVQwPw8qJPvww1gsJcTH/YyEhCcoK6vi00/+TWlpKV27dmXy5MkYDAZcFge1P+Rh2lKMSq8l4M4UvH/UXbD4+FHWzv83JSeOERKXwO2/eou4Hr0vOJ66ykZ2Lsvl6JZSVGqFnuNi6HtTHN6+V3br31FZSfVnn1P9+ec4q6vx7NqVyN//Ht+JN6NoWy7/r9HRyOr81aRnubsSuoSrY3clNJW7K25krXL/bS53bw/rDoMecQfPsUNAK39BN7P3geeBk7d1goAaIYSj6fOT8zKcMWcLIRyKotQ27V953UYrNRshBN+c+Ibf7fgdgdZwnsr5HY0VWkJLtzPQtQDtIFhYn4brkBZ93EiOaavw0xmYNElDVe171NapCEp4nY8tI/jyWA3hOgf/7BrH9FD/jv+gs3TDa/FgWlEUA/AN8JQQou7MHyohhFAU5YpWMYQQHwIfgjv/rjnHKl07IQQfF1Xy66xiDGo187pFk1D7Tw7v+xgvr3j69/sSb+8erFmzno0bN6LX65k5cyZdu3ZFCEHD3nJqlmTjMtnRD4rA7+Z4VGfkL9dVlLPh83kc3bQOvX8AN/3fE3QbNQ6V6vzVNuqNFnYtz+PIpmJQoPuoKPpNjEPvd2Vd66wnTlA1dy516RkIhwPDmDHufOgBA1rsF4UQ4nRXwrwfMNvNROgjeKjHQ6QlpRHnG9cir9sqHFb3inPWancAXXrAvd07qCnvuemPzw1Swq8VKIoyFSgXQuxSFGV0Mx5XLoC0cTWWGl7f8jqr8lYxxXov8fsHYLda6J79CT3iVnIwvD/7sr0IC+9FdqwZK0YG9QohIHIJFdXHCAiawA7fZ/ljYSNmZw2PxYbyi7gwDLJmtHSDaNFgWlEULe5A+lMhxLdNm8tOpm8oihIBNC05UQScmWQa3bRNaicqbHaeOlLAKmMdYwN9eCvaRNmJeyhoyCI6ehbJSc9TVFTJggX/orKykt69e3PzzTfj5eWFvaKBmkVZWDNr0EYZCJ7TDV306ZxnW2MD275byK4l37mbjNx2JwPSZqDzOn+DEXOtlV3L8zi0oQgEdB0WSb9JcRgCLn8lUwiBefNmjB/PxbxxI4qnJ363zyBw9mw8EhKu+f26kIL6AjKyMkjPSqfIVISXxosJcROYnjSd/uH9O0ZXQiGgKhMyV7mD59yNYG8AlQZiBsO4V93Bc3gvuEh3SqlZDQPSFEWZDHjizpn+APBXFEXTtDp95rx8cs4uVBRFA/jhfhDxLHIBpG3bUryFX238FQ31Nh4rfwdnnh7f6qP0Lv8Ej+5lfGsZjndFPF4JsRzWVBHo7c1N46uprlmAwxGGPfEjni2P4HCuiZEBBt7uFE0nvbxjJN1YWiyYbsq1+w9wRAjxxzO+lA7MAX7T9PeiM7Y/rijKF7gfPKyV+dLtx8qqOp46kk+908lbyeGMsX1B7v6/o9OF0Kf3fPT6/vzww2q2bduGn58f9913H8nJyQi7k9ofcqlfV4iiVeE/PQn9oAgUlXu11+VycnDNCjZ9+QkNtTWkDh/N8Ltn4xscet5xNNTZ2P19HgfXF+FyClKHhNNvUjy+wZffEMBls1G3eAnGuXOxHj+OOiSYkKeexP/OO9EEBFz6AFfBZDPxQ94PLMpcxO7y3SgoDIwY2LG6EjZWQ/a602XrapuyugKToM997uA5fjh4yCf9W4MQ4iXgJYCmlelnhRD3KoqyELgdd0WPH8/Zc4AtTV9fLfOl2w+b08afd/+ZeYfnMdA6jkFHpuFscNIp62tSfJZxtGssmVUDCYsayQnvKuyKkaEDPPHy+x/VNRV4RfyUT1wz+DbHRJSHk4+6xTMlxE+mdEg3pJZcmR4GzAIOKIqyt2nby7iD6K8URXkQyANmNn1tKe6yeJm4S+M90IJjk5pJo9PFm1nF/Leokq56T+YnaHDkPkxu/SHCw2+lc6dXyc+vYP78f1BTU8PAgQMZN24cHh4eNB41UpOehdNowbtPKH6TE1D7nM5hztu/l7ULPqIyP5fIlK7c8vwrRCSnnH8cJht7fsjnwNpCnHYXKYPC6T8lHr+Qyw9CHdXV1HzxBcZPP8NZWYlH585EvPsuvlMmo9I1f1k1h8vB1pKtp7oSWp1W4n3jeaLPE0xNnEqE4fp0R2wxTgcU7z69+ly0C4QLPHwhYSSMeNodQAfEt/ZIpYt7AfhCUZS3gD24F0lo+nuBoiiZgBG4q5XGJ12h7JpsXtjwApkV2TxQ8xIex8PxMBfRI3s+ms75LHV2J9jRF11SEAfVZYT6aeg/LJN602bU2h4cCPsnfy1RsLnMPBUXxs/jQtGrZUqHdONqyWoeG4EL/Rd13Hn2F8BjLTUeqfkdNjXyf4fyON5g4eHoIO7T/kDRofdQqw306PF3fAwjWbr0B/bs2UNQUBAPPPAAcXFxOGosVH51GMuhKjShXgT/tAeeSf6njltVVMD6T/5L9u4d+IaEMfWpF+k8eNh5VzwsZjt7V+azf3UhdpuTTv3DGDAlnoDwy+8waM3JwThvHrXfLUJYLOhHjCDogfvxHjKkRVZZjlcfJyMrgyXZS6horMBX58stybcwLWkaPYN7tu+VndrC08HzmTWfo/rCiGcheRxE9Qd1B6s40sEIIdbirrSEECIbGHiefSzAHdd1YNI1EUKw8PhCfr/j90Q1JPNo9u+w1UBs/g8k2pZxIsVAuW0wYVHDOOJZhktlZMQQCyrdYhoaFWqj3uWNmh4cL7QyLtCHtzpFkeB9Zc+fSFJHJH+jtWEFBQXMnj2bsrIyFEXh4Ycf5sknnzxrn2PHjnHnnadLu2ZnZ/PrX/+ap556qsXG5RKCfxdW8HZWCf5aNfO6+BBc/BwFtTsICZ5Aly5vkZVVwfx5f8NsNjN8+HBGjRqFRqWmfl0hdSvzAPCdGI/P8CgUjTsntrG+js0LP2PfiqVoPTwZcc/99J2UhuY8q8LWRgf7VhWwb2U+NouTpL6hDJgaT1Ck4bLOQQhBw44dGD+ei2ntWhSNBt/paQTNmYNHp07N92Y1qWysZGn2UjKyMzhqPNpxuhLaGiBv0+kAWtZ8lm5gbXXOBqi2VPPq5ldZl7+eW2ofJPxod1T2Wnof/C/E5LHOP45IryGIKD371cVEhjrp1nsHFssJnH5pfK5+mCXFVmI9BfN7JDAhyLd9/8dfkpqRDKbbMI1Gwx/+8Af69u1LfX09/fr1Y8KECXTt2vXUPikpKezduxcAp9NJVFQUt956a4uNqcxq58kj+aytrufmIF+e89tJ5fE3qUdF19TfYzBM4LvvlnH48GHCwsK45557iIyMxJpdS9mipjbgqYH4T0tCE+h+SMXpsLNn+WK2fvsFtoZGeo6fyNA77sHbz/+c17dZHOxfU8jeFflYGxwk9Apm4LQEgqMvL89W2O3ULf8e49y5WA4dQh0QQPDPfkbAPXejaWpZ3lwsDgtrC9aSnpXO5uLNOIWTbkHdeHHgi0xKmESgZzsMMIWA8sOng+e8LeC0gsYT4oZC3znu1eeQLrLms3TDaYtzNsDWkq28vOFlnDVqHi36Dc4yD8LKdxBb9g2ZSZ5Y1EOIiBrIQV0xKk0lI4eVI1iFzRXJ9vC5fFjhh8DGc/HhPBobipdsvCJJZ5HBdAs5dOgQTz75JPn5+cyaNYvy8nJmz57NgAEDLvsYERERRES482Z9fHxITU2lqKjorIn5TKtWrSIpKYm4uJYpmfZ9ZS2/OJpPo9PFO4m+9Kl+m7KstQQEDCW1y284fryS+fP/js1mY+zYsQwbNgwanRi/OkbD7nLU/h4Eze6KV1d3a2shBJk7trD+k4+pKSshvnc/Rt33E4Jjzh2/3ebkwNpC9vyQj8VkJ65HEAOnJhAad3n1lZ11ddQsXIhxwSc4SkvRJSQQ/sYb+E1PQ+XZfE+eCyHYU77HXc4u9wfq7fWEeodyf7f7mZY0jST/pGZ7revGXAXZa04/OFjf9FxwSCoMeAiSx0LcMNBe/kOektTWdMQ52+6085e9f2HugbmMqJtG9xPjUNltpBz6CLtfFttiI0kMGkWtn8I+dT7xsfUkdtqE3V5FSfAz/L1hJNlldiYF+/B6ciRxXjKlQ5LOp0MH08ePv0m96UizHtPHkErnzq9cdB+LxcIdd9zBwoULSUxMpEuXLvTr1++sSXnEiBHU19ef82/fe+89xo8ff8723Nxc9uzZw6BBF+6w/sUXX3D33Xdfwdlcngani9czi5hfXEV3gye/Ds3GnvcralxWOnd6FR+fNL75ZgmZmZlER0czffp0goOCMe8odbcBtznxGR2Dz9iYU23Ay7IzWTv/IwqPHCQoOpbbXnqDhN79znlth83JoQ3F7Po+j8Y6GzFdAxk4NYHwRL/LGrutsBDj/PnUfv0NroYGvAcNIvz11zCMHInSjCXXCuoKyMjOICMrg0JT4alydtOSpjEgbADqC9TBbpOcdijccXr1uXgvIMDTH5LGuFM3ksaCX9QlDiRJV0bO2c0nry6P59c/T25JIQ+UvoquKBB/UyZRmfPJitOh8xpMdGRvdmkL8PA0M3JwFkLsoVY7jK8MT7OiChK9VHzWM5GxQR2sKZQkNbMOHUy3lpUrV9KnTx+6desGgM1m45lnnjlrnw0bNlz28UwmEzNmzOD999/H9wKtqm02G+np6bz77rtXP/DzOFDfwKOH8zjRYOWRKB/SrH+mJmsxvr59SO3yW44cMbJgwT8QQjBx4kQGDhyIo6SB8n/sO90G/JZktKHuqhr1xko2fbGAQ+tX4+Xjy/iHHqXH2JtR/ehJcKfdxeFNxexalou51kZUZ38G/rQ7kZ38L2vcDXv2YJw7j/oVK0ClwnfyJILuvx/PC6wQXY06Wx0/5P5AelY6e8r3nCpn92jvR9tfObvq3KbgeTXkrAdrHShqiO4Po19yp25E9oH29J8CSbpMHWnOFkKwKGsR72x7h0Rjbx7I+inCIkg88SVWj8McSIggJWwMx30tnFDl0KlTCZFRm7EJHZsD/8y82mgUq8LLiWE8EhOCh6zzLkmX1KGD6UutRrSUvXv30qdPHwCKi4sxGAzulIczXO4qh91uZ8aMGdx7773cdtttF3zNZcuW0bdvX8LCwi64z5VwCcE/Cyp4N7uEIK2Gf8fX4lf4MLWOOpISn8NguI2FC5eQl5dHQkICaWlp+Hn5ULc451Qb8MA7U/BqagNut1jYkfENOzK+RTidDJh2G4NunYmH99lVN5xOF0c3l7BzWS4mo5WIJD/G/6Qb0SmXru8snE7qV6zEOHcujXv3ovL1JejBnxBw331om+l9sbvsbCneQnpWOmvy12Bz2Uj0S+TJvk8yNXEq4fp20qHPanI3Ssla5Q6ijVnu7X6x0P0298pzwijw8m/VYUo3FjlnX5s6Wx1vbnmT1ZlrmV76MEEFSejNhUTnzCcrEgJ8hhMV3pnNmnwMvtWM7LsfIfI4bvgJ/7FNI7/aRVqoH68lRRLl2U4fipakVtChg+nWotPpKCpyNwl76aWXsNls5+xzOascQggefPBBUlNTefrppy+67+eff95stwtLrDaeOJLPhmoTE4P0PKKaR0PO53gYUunV82MOHKhm7doPUavVpKWl0bt3byz7KyldstPdBnxwBH43uduAC5eLQ+tXs/HzeZiqjXQeMoKR98zBL/TsoNPldHFsWxk7l+ZQV2khNN6XMfd1ISY18JJPjDtNZmq//Rbj/PnYCwvRxsQQ9stf4n/braj0l18i70KEEBw1HiU9K52lOUsxWoz4e/hze+fbSUtKo2tQ17b/VLvLBaX7T+c9528Flx203u5GKQMfdq8+ByXLBwelG057n7MBdpft5sUNL6Ip8eXBnDfBrCEmbzFCs4PjcTEkR4zhsHctNdoTdOmaTVDAToyarnzl+Rnr6z3o5K1lYa9oRgTKpkmSdKWU9tywqn///mLnzp1nbTty5AipqamtNCK3wsJCpk+fjslk4pFHHmH79u2Eh4fz/vvvX9FxNm7cyIgRI+jRoweqpltt77zzDpMnTwZg8uTJfPTRR/j5+REbG0t2djZ+fhfPJb7U+7O0ooZnjhZgcQleimwktewZ7PZy4uL+Dy+vO8hIX0pJSQldunRh8uTJeFk1p9uARxsIuCX5VBvwwsMHWTP/35TnZBGe1InRs39KVJez0yxcLkHmzjJ2LMmlpqyB4BgDg6YlEtcj6JIBqr20lOpPPqH6y69w1dfj1bcvgffPwWfcOJRmaCBQ3lDO0uylLMpaRGZNJlqVltExo5mWOI3hUcPRqrXX/Botqr70dPCctQYaKt3bw3q4c5+Tx0HsENDIh4pag6Iou4QQ/Vt7HNeTnLObf852uBx8uP9DPtr7H8YUzyQxvz9ejZXE5s8nN9RKsN9wrKFRHFUXEhxSQmq3PViEmbW+r/GlqQsalcKz8eE8GB2MTqZ0SNJFXWjelivTLSA6Oppdu3Zd83GGDx/Oxf6zs3Tp0lMfV1VVXdNrmZ1OXjtRzCclVfQ0ePC892KUgn+i8U6kW9cv2Lu3ho0bP8bLy4s77riDLskpmNYWUra+qQ34LUnoB7rbgFeXFrPh07mc2L4Zn6AQJv/8WboMPfuBP+ESZO2pYPviHKpLzARF6Zn0SA8SegdfMohuPHQI48dzqVu+HFwufG6+iaD778erV69reg8AGh2NrMlfQ3pWOltKtuASLnqG9ORXg37FxISJ+Hlc3oOPrcJugfzN7uA5czWUH3Jv14e4A+eksZA4Bnya77ayJHUE7XHOBig2FfPihhfJzynn/qxXUJt9iShag1q1ntyoeGIiR7Lfqxy7x3F69TiMQX+U/R4zWCDuoageZoT580pSJOEebXxhQJLaOBlMS+yta+Cxw3lkN1r5aZiL8TVP4CjLJibmAXTaO/nss++prKykV69e3HzzzSi5jZS/vxtntfWsNuAWs4mt33zBnuWLUWs0DLtzFv2mTEfrcbr0nBCCnH2VbM/IoarIREC4Nzc91I3kvqEoqgsH0cLlwrR2Hca5c2nYvh2VtzeB995DwKzZ6KKvraqEEILd5btPlbMz2U1E6CN4sPuDpCWlEe8Xf03HbzFCQMXR0w8O5m0ChwXUOogdDOPfcAfQYd1BrjhJUoeyPGc5b25+k675w5iZNxutrZ7Ygr9RGFRPSMBE1ME+bFHnERmVR3LyLkoJZa7Xf9na6Eeq3pO/dotmiP/lNbmSJOniZDB9A3MKwd/zy/ltTgkhWg0fhOwgqPR3aDwj6dJ9Lrt21rN9+6f4+flx3333ER8YTc3CLCxHjGhCvU+1AXc6HOxZnsHmrz/HYqqn++gJDLvzPgwBp5uSCCHIO1jF9owcKvLr8QvxYvwDXek0IAzVRYJoV2Mjtd99h3HefGy5uWjCwwl97jn8Z96B2ufacvsK6gvIyMogPSudIlMRXhovboq7ibSkNPqH90eltMEA9FTN56a6z/XF7u3BnaHfA+7gOX4Y6K49V1ySpLbHbDfz7rZ3WX1oIzOO/wxPcyRB5TvwZDnFEcmERk5iv0cJOn0WA3ruQ9GVkOH5FN9YB+FhU/FmcgQPRAWjuci8K0nSlZHB9A2qyGLj50fy2VxjYmKAwr2WV1GV7yMy8k7Uqrv47NNV1NbWMnDgQMaOGoNtewVl89y3Qf0mxWMYFgVqhezdO1i34D8YiwuJ7d6TUbMeIjQ+8dTrCCEoPFLNtoxsynLq8AnyZOzsLqQMCkd1kS5a9vJyqj/7jJrPv8BZW4tn9+5EvvcevjffhKK9+luS9bZ6VuStYFHmInaX70ZBYVDEIB7r/VjbLGfnsLlrPmetPrfmc+Jod/CcNBb8Y1p3nJIktbiDlQd5Yd0L+J6I4r7cl1A77EQX/5dyvyq8g6bQGKBmjzaX2PhMYqJ3s089kk/Uv6PYouH2sABeTYokVKZ0SFKzk8H0DSijvIbnjhVgcwl+GXScrlWvoNMGkpjyN7Zvb2Tfvm8JDg7mJz/5CaE2H2r+eQhHRSNe3YLwm5aIxt+Tivxc1i34D3n79xAQEcUtz79CYt+BZ+U7Fx2vZlt6NiWZtRgCPBh9bwpdhkSg1lw4iLYcPYpx7jxqlywBhwOf8eMInDMHr379rrpihtPlZGvJVhZlLWJ1/mqsTivxvvFts5ydEGDMPv3gYM56sJmaaj4PgDEvu4NnWfNZkm4YLuFi7qG5fLT1Y6YdvgffhhT8qg+jd/wPY1gqhogR7NaW4udfzsDuu6lWw188/sRWWxQpXp582y2aoQEypUOSWooMpm8gTiEw2h389FAuPfUqHhXv41O5jrCwNITrTj77bAMNDQ2MGDGC4X0GY/q+gMp9eagDPQl6oBteKYGYa6pZ8+FHHFj9Ax7e3oy5/2F6TZiMWnP6W6kkq5Zt6dkUHavG20/HyLs603VYJGrt+YNo4XJh3rCBqrlzadiyFcXLi4CZMwmcPQvdNbTZzazOJD0rncXZi6lorMBX58stybeQlpRGj+AebaecnaXWHTRnrXbnP9fkubf7x0HPmU01n0eCZxt++FGSpBbhdDl5+IeHqd5n5r6s51GEjsiyL6gxlKCKSKPC10KDLpfkTkcIDDnKcu0c/ueciMap5rWkcB6KDkErUzokqUXJYPoGYXY6yW+00eB08YB/CWNrnsND40lc0u/ZssXG0aPLiYiI4L577sOQ46Lyg30IpwufcbH4jo7GKZxs+24h27/7CofNRp9J0xg84y68DKfzlsty69iekU3+ISNePlqG39GJbiMi0ejOv4LqslioTU9350NnZaEJDSXkmacJmDkT9SXKRV2I0WJkWc4y0rPSOVx1GI2iYXj0cNKS0hgVPQqdug00InA5oXjP6eC5cAcIJ+gM7qB56M/dAXRQUmuPVJKkVlRnraOyoZLY5Un0aRyEd30Ofo4vMYf0RAnrxW5tOaEhRXTvsotDqk78SfNfCh3epIX680ZyJBEebWC+k6QbgAymOzghBOU2B6U2O1oF/BUz442PExw8DrvtLj77bBtOp5Px48fTL6o7dV9nU1tixqNzAAFpSaiDPDm+dSPrP51LXUUZSf0HMfLenxAYebqCRkVBPdszcsjdX4mnXsuQW5PoMToarcf5g2hHZSXVn31O9eef46yuxqNrKpG//x2+N9+Morvyyd/utLO+cD2LshaxoXADDuEgNTCVFwa8wKSESQR5BV31+9dsagtPp25kr4XGakCByN4w/Bfu4Dl6AGjkLz9JutG5hItScylmkxlvqw9BDQMIr1yE2SsfETONfEMdeObQrct+XH61/EP7PFscqSTrPPiqWzQjZeMVSbquZDDdgdlcLvIbbZidLnzUTgJdheSIRmJjX2PLZkF29nri4uKYMn4Smm11VC0+gNpXR+C9qXh1D6I06zhrP/iI4uNHCIlL4I5X3ia2++lazlVFJrYvziF7TwUe3hoGpSXSc2w0Os/zf1tZjh/HOG8edekZCLsdw5gxBD5wP94DBlxxyoUQgkNVh1iUuYhlucuotdYS7BXMfV3vY1rSNDoHdL6m9+6a2RrcpepOrj5XHnNv94mAlMmnaz7r20CgL10Rq8NJXlUDWeUmsipMZFeYmT00nt4x/q09NKkDsDgsFNYX4lXviZ8Io0bUEl77BxzBfWkMHUW2uoKoqBxikvbyvWoa/2MGuDS8nBjOIzEheMgymJJ03clgug2zWCyMHDkSq9WKw+Hg9ttv54033jjvvsuXL+fJJ5/E6XTy0EMP8cgzz1JocbfEDVPV4u2sRK3Woyj+fPXlVhRFYcrkKXQRUdR/nIPN4sQwMhrfcbGY6o0s++sfOLJxLd5+/tz0yBN0Gz0OVdMDb9WlZnYszuHErnJ0HmoGTImn17gYPLzPfUpcCIF502aMc+di3rgRxdMTv9tnEDh7Nh4JCVf8npSaS1mcvZiMrAyya7PxUHswNmYsaclpDI4YjEbVSt/SQkDZIXfFjazVkLcFnFbQeELcUOg72x1Ah6bKdt3thNFsawqWTWRVmE8Fz/nGBlxn9OWI8PPkpm7hIAuq3PCuZc5+4YUXMFqMVNca8bUEgqJF46gDGnDETea4ZzXehhx6d91NnlcQv1L/mUJXAJOD/fh1pyiiPeVdLUlqLTKYbsM8PDxYvXo1BoMBu93O8OHDmTRpEoMHDz5rP6fTyWOPPcaKFSuIiIqi34ABdB47ge5dUwgWxWiEHa02DJNJobGxjPj4eG7uPwbXynJqC7LQxfsScEsywl/Flu8+Y2fG/xAIBt06k4HTb0fn5S4XV1vRyM4lORzbVopaq6LvzXH0mRCLp/7cINpltVK3eDHGuXOxnshEHRJMyFNP4X/nTDQBAVf0PjQ6GlmVv4r0zHS2lmxFIOgT2ofXhrzGzfE346NrpVuapgp3ysbJANpU5t4e2hUG/tQdPMcNBa1X64xPuiSH00VhdSNZFe5AOavcfOrj6gb7qf10GhWJwXq6RfqR1iuSpFADSSEGEoL16D3kNCq5Xc2cHR0dTf8B/ek/tj+p4Z3xdYWiCCdqVxlo9Lg0Oo7pS4mJO44+Jp/5qofYLAYQr9PxaedoxgX5ttLZSpJ0kvwt0EIOHTrEk08+SX5+PrNmzaK8vJzZs2czYMCAyz6GoigYDO5yRna7Hbvdft50iO3bt5OcnExYbBy5Fhvjb53BtqX/Y1yXO9GovXE6g6mutqAoCt7e3kw2DMI8NwuVXkvAzM549griyPo1bPxyAeZqI12GjWLE3XPwDQkFoN5oYeeyXI5uKkFRK/QcF0Pfm+Lw9j13JcRhNFL9+edUf/Y5zqoqPLp0IeI37+I7eTKqK8iHFkKwq2yXuyth3g+Y7WaiDFE80usR0hLTiPFthWVAhw0Ktp0Onkv2ubd7BULSmNM1n30jr//YpIuqt9jJrjCfEzTnVpmxO08vMwcbdCSGGJjYPYKkEL07aA42EBXghVpWROjQWmPOTkxMxGQzcfPUCaxduJaejw9E7TKBYsWl88WmOFFUDnoOXMV63WD+p3oel6LjubgwHosNxfMitfolSbp+OnQw/cqJQg6aGpv1mN0NXrzZKfqi+1gsFu644w4WLlxIYmIiXbp0oV+/fmdNyiNGjKC+vv6cf/vee+8xfvz4U587nU769etHZmYmjz32GIMGDTrn3xQWFhIcGUVmoxUtgpQoA/t27kSrCcFkUuFwWPDy8sKg9aYqrwzz1hL0gyLwuymOopwjrHn5bSpys4nolELa0y8T2bkLAOZaK7uW5XFoYxEI6DYikn6T4tH7e5wzBmtWlrs+dHo6wmrFMGqUOx960KAryof+cVdCb403N8W7uxL2C+t3fbsSCgFVWacbpuRsALsZVBqIGQRjfwVJ4yCil6z53Aa4XIKSOsupdIyT+cxZFSbK6qyn9lOrFOKCvEkKMTAuNeysoNnvPKlK0vVzo8zZRUVFREdHU2oqwVVlJT6oE7v37kLjrEBovLGrPRGKHQ+PRtA5ecfzNfJFBOMDfXm7UxRxXufOwZIktZ4OHUy3lpUrV9KnTx+6desGgM1m45lnnjlrnw0bNlzWsdRqNXv37qWmpoZbb72VgwcP0r1791Nft7pclFrtNDpd+ChWAl3F6BQX4E1NjQuVCgL8/NE0gDDbQKUQ+lhvzJp6Mv7+WzJ3bMUnOITJTzxHl6EjURSFxnobu7/P48C6IlxOQerQCPpPjscn0POssQkhaNi6laq5czGvW4/i4YHfLbcQOGc2HomJXC6TzeTuSpi1iF1lu1BQGBgxsHW6EjbWnK75nLUKavLd2wMSoPfdTe26R4CnvLXaWhptTrIr3XnMZ+YzZ1easNhdp/bz9dSQFGpgRKcQkkIMJIXoSQwxEBvoje4ijYOkG8/1nLPBXYHIbK1HXa6gUgeiCDsKNpweBuyKA63GjtrTQjUB1NCASxfMvM7R3BTk23bq40uSdEqHDqYvtRrRUvbu3UufPn0AKC4uxmAwMGzYsLP2udxVjpP8/f0ZM2YMy5cvPzUxV9sdFFpsBIRHYCzKIdhViFodSG5uNUFBoXh7e6PHE1FtR6gU1P4eqGo1bF79BXuWL0Gt1TL8rtn0nTIdrc4Di9nO3hX57FtTiNPmpPOgcAZMiccv5Oxg1mWzUbdkqTsf+tgx1MHBhDz5BP533XXZ+dBOl5NtpdtIz0pnVd4qLE4L8b7xPNHnCaYlTbt+XQmdDijefbpsXeHOpprPPu6az8OedAfQgZf/nwPp2gkhKK+3uleZK81nVc4oqjm9cqkoEBPgTWKIniFJQSSFGEgM0ZMYoifE4CEDj3amo8/ZQgiqLdXodRrK8isRKk/UzkpKyksIjYrEqbLh4dlAo9qLaqIRigpfTQXrB6XiLVM6JKnN6tDBdGvR6XQUFRUB8NJLL2Gz2c7Z53JWOSoqKtBqtfj7+9PY2MiKFSt44YUXcApBkcVGtd2Jp8rBhL7BvJKdTU5OI35+dr77bhELPp6Hd6MW4bSj8tai8tVhMddhqjaya2k63UdPYPhds9D7B2BrdLB9cQ77VuZjszhJ7h/KwKkJBITrzxqPo7qami+/xPjppzgrKvHo1ImIt9/Cd+pUVB6Xd9sxuzab9Ex3V8KyhjJ8dD6kJaWRlpxGz+Ce1yf4qck/XbIuZ527AyEKRPWFEU+7Uzei+4Na3vJvaVaHk9zKhqYV5rNXm01Wx6n99Do1iSEGBsQHcFdIDIkhBpJC9cQH6fHUyhQb6dq09JwN4HA5KK0pwqNGQ/+e48jOfZbCwkOERMXwTcZ3fPivP6LSWygnDBs6DBoVUR46cjRqGUhLUhvXYsG0oij/BaYC5UKI7k3bAoEvgXggF5gphKhW3BHUB8BkoAG4Xwixu6XG1tLuuecepk+fTkpKCo888ghWq5WnnnqK999//4qOU1JSwpw5c3A6nbhcLmbOnMmYiZM4ZrZgdwmeun0a//jLy+ijOvPWW+9y6613IYTggbvn0D0yBUUF6kAv7A4rNSUFOGw2VGo1s37zAaHxiditTnYtz2XPinysZgeJvUMYOC2BoCjDWeOwZudgnD+P2u8WISwW9CNGEPibOeiHDr2s4LfWWsvynOWkZ6Wzv3I/akXNsKhhPDfgOUbHjMZD3cL5f1YT5G48nbpRlene7hsFqWlNNZ9Hg3dgy47jBiWEoMpsO/0AYLmJ7Er3xwU/KjMX6edJUqiB2/tFn0rLSAoxEOYrV5lbmqIoMcB8IAwQwIdCiA9uhHm7JefsqVOnYrKZqC0v5f77fsYff/cXokIc/Patd7h99ixcLif33HcbEb16U4IvWhXEeejw06jl97wktROKEOLSe13NgRVlJGAC5p8RTP8OMAohfqMoyotAgBDiBUVRJgM/xz0pDwI+EEKc+9TGj/Tv31/s3LnzrG1HjhwhNTW1mc+m9QkhKLPZKbM60CougkUJXooTh8OPxkaBRqPBV6tH1eC+nmpfHS6doN5Yia2hAY1WiyEomJz8Ajoldebg+iJ2f59HY72duO5BDJyWQGic71mv17BtO8a5czGtXYui0+E3Pc1dH7pTp0uO1+6ys7loM4uyFrG2YC12l51OAZ2YnjSdKYlTCPYKbqm3ClwuKN1/OnUjfyu47KDxgvjh7uA5eRwEd5Y1n5uR3eki33iymYn5rNXm2sbTZeY8NKqmIFl/Ki3j5N/euhvnZpmiKLuEEP1bexwnKYoSAUQIIXYriuID7AJuAe6nmebtG2nOBncnw4r6UlSVDoTKD4QFjdqBXa3CqTjReViwaLVUE4QLFSE6DWEeWtRnzEsd+f2RpPbmQvN2i/3mEkKsVxQl/kebpwOjmz6eB6wFXmjaPl+4I/utiqL4K4oSIYQoaanxtSfWpk6GDU4XBqWBIFGGWtFjNutxuQQGLz2eVg2YXai8NCg+Gsy11TSU16JSq/AJCsHbzxeEgs3i4JNXtmCutRHdJYBBaYmEJ/qdei1hs1G3bBlVc+dhPXIEdWAgwY8/TsDdd6EJunS3vmPGYyzKWsSS7CUYLUYCPQO5M+VO0pLS6BLYpeVWWupLTwfPWWugodK9PawHDHnUHUDHDAat58WPI11SbYOdzDObmTQFzflVDTjOWGYO9fEgKcTA1J4RJIYYSA51B9CRfl6oZJm5Nqdpvi1p+rheUZQjQBRy3r4qVoeVqvJCdBYfXCo9alGH0OqwKKDVWsDDSYUShA0P9GoV0Z46WepOktqp670MFHbGRFuK+3YiuCfsgjP2K2zads6krCjKw8DDALGxsS030jbCaHdQZLEBghAq8KEBu8OfBovizs3TeKEyCxQNqII8sVjrMRVVgxB4+/ljCAhEUamwmOyYa21YzQ58Q7yY8GA3ojqffljQWVND9ZdfUf3JJzgqKtAlJxHx1pv4Tpt2yXzoqsYqluYsZVHmIo5VH0Oj0jA6ejRpSWkMjx6OVtUCucf2Rsjf4s57zloD5Yfc2/Uh7lXnpHHu1A2fsIseRjo/p0tQdGYzkzPymStNp/NJtWqF+CA9nUN9mNQ9vGmF2b3K7Ospc87bq6aFkD7ANq5x3r7R5mwhBDUNRhxldWhUQbgUGxpVAza1BtRWtB5WatW+mPFBo0Cspw5/mdIhSe1aq91TFUIIRVGuOMdECPEh8CG4bxleYJ92PzE5haDQYqPG7sRTsREiStAqOkwmP0CFj4c3HhY1IFD56rArNkwVRTjtdjy89fgEBaPWarGa7ZhrG3E6XKi1Krx8ddz6TNdT748tNxfj/PnU/O87RGMj+mHDiHjnHfTDh130PbQ5bawrXEd6ZjobizbiEA66B3Xn5UEvMyl+Ev6e/s37hggBFUebgufVkLcJHBZQ6yB2CIx/w736HNYdVHJ153KZrA6yz6jHfLKhSU6VGZvjdJm5QL2OpBA941PDTqVlJIUYiA7wQiNX0zoURVEMwDfAU0KIujPngauZt2+UORvcDxlWVhSgNXki1AGoaUDo1FgUJzqdhQadBzVEgKIiVKsh9EcpHT/WUmmYkiQ1r+sdTJedvA3YlJ9X3rS9CDizpV1007Yr5unpSVVVFUFBQe12cjY5nORbbNhdggCq8Rc12B0+1FvU6LQeGFweqBpB8VQjvKC2phy7xYJG50FARBQ6Ly+sDQ5qK8047S40OjW+wZ7UN9Ri8HGXuTNv345x7jxMa9agaDT4pk0jcPYcPFM6X3BcQgj2VewjPSud73O/p85WR6hXKLO6zWJ60nSS/JOa940wVza1625K36hvWvAKToF+D7hXoOOGgk5/0cPc6FwuQVFNo/uhv6Z6zNkVZrIrzJTWWU7tp1YpxAW6y8yNTmmqzRyqJzHYQID+8rtXSu2Xoiha3IH0p0KIb5s2t+i83RHmbACTpZ7GknLUBOJU29GqrVhUoNY2oHgIypRgHOjw0aiI8tThcYn/9AshqKqqwtNTpqZJUlt3vYPpdGAO8Jumvxedsf1xRVG+wP0gS+3V5t1FR0dTWFhIRUVFc4z3uhIC6pxO6h1O1LgwUEsVCsVWLVCPp1qH2q6gqBTwUGGzNWC3WlFUKjz0erQedkqMdVgbHLicApVaQeetQatVQw146nT4Hj1G7rPPYTl0CHVAAME/+xkB99yNJvjCDwQW1BewOGsxGdkZFNQX4KXxYmzsWNIS0xgUMQh1c3X/c1ib2nWv/lG77gB3ysbJdt1+rVOLtq2ra2qZfXKl+WTQnFNpxuo4u5lJYoiBYcnBp4Ll5FA9sYF62czkBtZUneM/wBEhxB/P+FKLztvtec4Gd9BrNtegNIJL5YGKClxqBZfiQKV10KjywooHWqUef40Gq1pF9mUe29PTk+hoOd9JUlvXkqXxPsf90EqwoiiFwGu4J+OvFEV5EMgDZjbtvhT3E+GZuEssPXC1r6vVaklISLiGkbeO3EYrjx3OY1edlVHKRmaLjykt6cfx4xF0iezEgNJoPCx2vAaGcaR+Czu//w5FUdF/2q30n3YbJZkNbP8uh4r8evxCvRg4NYHk/mGoVArO2lpqFi7EuOATysvK0CUmEv7rN/BLS0N1gVWPWmstP+T9QEZWBnvK95zqSvhIz0cYHzcevbYZVoOFgMrjp4Pn3I1gb/hRu+6xENFbtutu4nC6KKxuPBUon8xjzq40U1F/dsvs2EBvEoP1jOgU7M5jDna3zQ7S69r1CqDUYoYBs4ADiqLsbdr2Mi08b7fXORsgp+wYq155GbU5DZeXDf9AO8f1ZQTGH2FXdBeWqqahU1Q8kxDGT2NC0ckUNEnqkFqsNN71cL4yS+2NEIKFZdW8dKwAhIUHXH9lsKuEXbt6oVYiGKHtTlSZHm2sDxXhpaxftoDGulq6jhjDsDtnUVOhZntGDmU5dfgGe9J/cjwpg8JRqVXY8vIwzl9Azf/+h2hoQD90CIH3349++HCU80zqdpedTUWbSM9KZ13BOmwuG0l+SUxLmsaUxCnN05WwwXhG6sYaqCt0bw9KPr3yHD8cPHyu/bXasZoG21kNTE4GzHlVZuzO0z+zAd7aU4FyomyZ3a60tdJ410NHmLPBPW8vXfIXGj48SmXoOCI8CykOcGIPOURVZw0LdTOpVoK4LcSbVzslEO4hH8aVpI7gupfGky6txu7gheOFLCqvIVU5zv+53sdRmsTG40PpEdKFPkUReHp6YhuoYuWmD6lal090andGvfg6DkcwK+dlU5JZiyHAg9H3ptBlaAQqlULjrl1UzZ2LadVq0GjwmzqVwDmz8ezS5ZwxCCE4VHWIjKwMluUso9paTaBnIDNTZjI1aSpdA7te2yqmwwaFO06vPhfvAQR4+kHCKBj5LCSNgYD4q3+NdsrmcNdlPhkon07PMGM0n10xIzbQm8QQA+NSQ5se/pO5zJLUGmpMlWT86nGUkuGI8L6EBFZwzK8AXecivguYxjGlK129XMzrksxAf8OlDyhJUrsng+lWsqXGxGOHcymz2pgpPmeyYxv79w5ARzzTNCmEFfig7qpne/4SMr/chn9YBGnPvIx3QCpb03MoOlaA3k/HyLs603VYJCqc1C1fhvHjuVgOHkTt70/Q/z1CwN13ow0NPef1S0wlLMlZQnpWOjm1OehUOsbEjiEtKY0hkUOuvpydEFCVdUbqxgawmUBRQ/QAGP2Se/U5sg+oO/63nxCCCpP11AN/JwPnnEoz+cYGnGfUZQ426EgMNnBT17BTTUwSQwzEyIoZktQm7Nr8Lbnvfos1ZDrhEbVk+1VRk7CP/TG9WK3cg6/aye+SIrg3KvSiVTokSepYOn4008bYXYL3ckv5c14pYUoFr4k/oS81sD1zNL30XehVEYlHqJ5M3wPsWPodOm8vRs9+iPBOI9i1LJ+CI3vw8tUx/I5OdBsZiWJpoGbBPIwLFuAoKUEXH0/466/hN306Ki+vs17bZDOxIm8Fi7MXs6N0BwJB39C+zBkyhwnxE/DV+V5g1JfQWA3Z606nbtTmu7f7x0HPme7gOWGkezW6g2q0OcmpNJ9RKcPk/rzCTL3VcWo/D42KhGA9qRE+TOkRQUKw/lTQ7OclbwVLUltks1tY8ubPsR+IR4keiyGglhOheyjq4s13up/RoOiZE67nxeQk/LXy16ok3WjkT/11lNNg5WeHc9hbb2GUWM29ju84sb8ndlcKabZkQpx+VMdVk7H17zjsVvpMnErywCnsW13J1ox9eBq0DL0tme6jo6CilKr3fk/N11/jMpvxHjiQ8FdewTB61Fn50A6Xg60lW8nIymB1/mosTguxPrE82vtRpiZOJdrnKp4Ud9qhcCdkr3EH0EW7QLhA5wOJo2D4k+4AOjCxGd+91udyCYprG89aYT5ZLaOopvGsfSP9PEkMMXBr3ygSg/UkNOU1R/nL7n+S1J7kHtzCvpd+jyloOsGJTk4E5GBKLWZRwBTylEQG6B38rmsqqQavSx9MkqQOSQbT14EQgi9KjfzyeAGKq4EnxN+JL6vlQNYY+qhS6V4XiTNSYeXxT6k8mk9S/8H0GD+TY1stpP/5GB56DYNvSaTH6Gicxw9T9sKfqP9hBSgKvpMmEThnDl7du531mseMx0jPSmdpzlIqGyvx1fkyPXk605Km0TO455XlQQsBxuzTK88568FWD4rKna4x4ll3zeeofqBu/6urFyoxl1tlxmI/XWLO4KEhMUTPgPgA7gyJObXKnBCsx1snf7QkqT1zOZ2s/eAl6laBKn46SmA9hxN2szGuL1tUMwhVW/lH5yhuCQuW1XEk6QYnf+O3sBq7g+eO5ZNRUUeqOMjDjo8pO5xMvWUw083J+Pv4sF+1niObNhEan8TNM1+h8Kg3y/9ViM5Lw8BpCfQcFYl1y3qKH/wVjbt2ofLxIfD+OQTedx/aiIhTr1XRUMGS7CVkZGdwvPo4GpWGkVEjSUtKY0T0CHTqK3hYrbHaHTSfzH2uOZm6EQs9ZpxO3fAKuPhx2qgLlZjLqjBTaTq7xFxMgBeJIQaGJweT0PTgX1KInhAfD/lLVJI6oKrcY2x9+lkafNMwdNNyPGIPR1MNLNX9FJei5fEoT36R1AO9WpbslCRJBtMtakuNiZ8dzKLC7uBO8TmDKg6QlzWMvpaupDqjKPHOY8X+f+Dt78eIex+luiyadZ9XovWw0H9yPD2HBdO4PIOCGfOx5+WjjYoi7OWX8LttBmqDu85zo6ORNflrSM9OZ0vxFlzCRc/gnvxy0C+ZGD/x8tt6n0zdOFV1Y/fp1I2EkTD0idOpG+0ogDxZYi6rwnRWesaFSsyNSQlxl5oL0ZMUIhuZSNKNRAjB3v/+gdKFWWg6z8QcXMK+bgVkBEymTIlgjI+Vd7t2J95bdiWUJOk0GUy3AIdL8F5uCX/OKyOUUl5x/B370RAaa6dzi6kTisHJ8uMf0YCJXhNvw27vxc5lRtS6avreFEf33l40/u9L8t/+EldtLV69ehH6i6fxGT8ORaPBJVzsLN1JRnYG3+d+j9luJkIfwYPdH2Ra0jQS/C6jAcLFUjei+sHI5yBxDET3b/OpG3ani7wqWWJOkqSrZ6mqYMMTD2HTTETpPZA9nbaxJr4v+1Q3Easx8WmXKMaFhLT2MCVJaoNkMN3M8hut/N/BE+w2ORgp1pBWtZzSrEH0q+tBgjaU3XUryMndT+dBo9Hph3F0eyMqdQ29xsXQNdFG45f/pvDVpeB04jN+PIH334933z7uY9flk56VzuLsxRSZivDWeHNT/E2kJaXRL6wfKuUSK6gXTd24vSl1Y0SbTN0QQlBltv3o4T93Wsa5JeY8SAzRc3O3MBKDZYk5SZIuLvP7r8l6fxnqlDsojD7O5u5erNTNQae4eCnGg58l9pTdCyVJuiAZTDej/5Uaee5YLk6XhUdd/ybkuB1X2S2kWVMot2eyKPtzQjulkNr9KfIOqlBUFnqMiiLFvwTLl+9SunkLirc3AXfeSeCc2ehiYqi11vLVsa/IyMpgb8VeFBQGRwzm8T6PMzZmLN5a7wsP6EKpGx6+7tSNYU+6V5/bUOqGw+luZHIyNSOr3OT+u8JMbaP91H46jYqEoNMl5k4GzAnBelliTpKky+K0Wln74sPYKvti6zeATb32kxF0M9VKENN8TbzZbSDhnvKulSRJFyeD6WZgdjh58Vg2C8vNJIsTzK5fgPloD7rX9icILesLFkCgjvhBsyjK9KfGqJA6NIxO4giWBe9RlZmFJjSUkGeeJmDmTFw+3mwu2kz62vdZW7D2VFvvX/T7BVMSphCmDzv/QM5K3VgNORvOSN3oDyOfd3cbbANVN05WzDgdLLsD5h/nMof4eJAUomdqz4hT7bKTQgxE+nuhliXmJEm6SqUHtrP75b+iThrH0SFHWNa5C/vV95CormZu9ygGBcqUDkmSLo8Mpq/R/voGfrr/CPk2heniW/pmH8c7bzKjnMkcLl/LPlc24V0nUFEcT/EJFSn9Akmq24rtH69QV1WFR2oqkb/7LT4338wxUzb/OfZPluYsxWgxEuARwB0pdzAtadqF23o31kDOuvOkbsRBzzvcK88JI8HL/3q+LYC7LnNJneXsgLncveJcXn+6YoZGpRAX5E1SiIEJTd3/kmQjE0mSWoAQgs1/eInavSGYBvRhRZ98vtffigK8EOXi58mj0cj/qEuSdAVkMH2VXELwj/wi3s0ux1dU83Tjf/A8HEWP6rsR5nJWVP6HgIR+aGrmUF7oSaduehKKV+H485c0Wq0YRo0i8IEHMPWI5385y1i0/C4yazLRqrSMjhnNtMRpDI8efm5bb6fD3STlZPBctPPshilDn3DXfL6ODVMsdnf3vzOD5ZPVMxrtzlP7+XpqSAo1MLJzyKmAOSnUQGygN1qZyyxJUgurL8ln/VO/RIkcxa4JmSyKGUqhEsswj0r+1HsIsd761h6iJEntkAymr0K51c6jBw6xsR76i+1MKVqN/4nRdLNEsLfsexwBPqj976Smyp/EBDXxWRnwlyU4PDzwmz4d73tnskmbR3rWx2z5pqmcXUhPfjXoV0xMmIifx4/ablfnQdYqd/CcvR6stU0NU/pet4YpQgjK662nguSsMxqaFFY3IpoyMxQFovy9SAoxMCghiKRQfVPgbCDYoJN1mSVJahV7v/g7hYvrqOjXlSW9Gtmou4tAUcO/OumZHt27tYcnSVI7JoPpK7SiwsjPD2didsIs+6ckHhL0qryL6spDbGIPwnsYwhJLbLid2EOfoluzGXVgIP6PP0be+FQ+q1rHD7sevHg5O2u9O9/55OqzMcu93Tcauk2HpHHu1A3vwGY/P4vdeVbXv5MVM3IqzZisjlP7eWnVJATr6RXtz4y+0acC5oRgPV462chAkqS2wWauZ8VTv8Dp14+10xvJCBqLGQN3+xl5s8dIDFr5a1CSpGsjZ5HLZHW5eP3oET4usxMjSni4aiExBwcTVe3Nobql2Dy6IZhJtK+F2D3/wmvtfnRJSfDyk3yfYiG9cDFF2/6Ft8abCXETmJ48/XQ5O5fzjNSNNVCwDVwO0HpD/AgY+LB79TkouVmqbgghKK2znBUsn1xpLq49vcoM7lXmxBA9M/pGNT0A6C41F+7riUrmFUqS1IZlbVjCoX/vIn9gLF938eWoeghJlPK33l3oHdCvtYcnSVIHIYPpy3Dc1MCD+/ZywubNOOf3DD+SR4/CaRRVbGe3YgDdrYR7WYjd9Vd8Ko7jMXggxx64j898jrC36m8oR93l7B7r/RjjYse5y9nVFsGeT5tSN9ZCo9H9YhG9YOjP3avPMQNB43HV4260OcmuNJ1qlX3minOD7XQus7dOTWKInn5xAcwMiWkqM6cnIViPt05+i0iS1L64HA5++NWz1CtxLLnDi5X60Wix83K4hce63IxapptJktSMZKR0EUII5hXk8FpWJVrh4OH6D+m5rzO+JUnst2zDqRlCqMZJ3O6/42fOxzJ2AN8NHMnXYic2224SHYk81fcppiROIVzrA3mbYdWbkLkKKo+5X8QQDp0nuleeE0eDPviKx1hWZz2jWsbp4Lm41nJqP0WBSD8vkkIN9I8LPFUtIynEQJivh8xlliSpQyjPPMDmtxZyYFQg38SlUKpEMlTJ42+DxhPhJR8wlCSp+clg+gJq7A4e3bOV1WYDXV1HuTV7G12P9qfAeIBiVTdCVOHE7Z9PgKuUrNHJ/DYlkEztDvw0ftwWfxvTE6fRzSFQstfA1z+F/K3gtIHGE+KGQt/Z7o6DoamXlbphdTjJq2o4q4nJyeDZfMYqs16nJinUwMCEwLPSMhKC9XhqZS6zJEkd19o/vEmuWce3d0Wz3WMgIa4KPuqkY2rM9NYemiRJHZgMps9jU2Upjxw4QbXw4hbLt4zfrUedF8JBu5FAV2/6Hf0OL48yVo/14ovERpweRxkeNZzHokczssGCLmcdbJgB5nL3AUO7waBH3MFz7BDQel3wtavNtrOamJwMnvONDZzRMZtIP0+SQg3c0T/mVCOTpFADoT5ylVmSpBuLqaqUZb/8C5vG+JARMgwLntyuzuV3I6birZG/5iRJallyljmDwyX49cEt/LvSkxBMPF78Lb12xZNXXYOXI4q+2d9jDSxi7jgz25JcpARF8GTAcCabLQSd2AQb5rsP5B3kDpyTxrqbpvhGnPU6TpegsLrhnLrMWRVmjGbbqf10GhWJwXq6RfqR1iuSpNDTFTP0HvLSSZIkbf/kQ7aUV/DV7b3JUneikz2bv/UfSM/A/q09NEmSbhAyImuSZ65jzo4tHBVhDHZsZuZuI67j/hRb1aTmHyEv9H/8YZqDmvgApuh78mxtDSkHNoN9Jai0EDsYxr3qfnAwvCeoVJitDndN5qyiszoA5lSasTldp1472KAjMcTAzd3CTpWYSwoxEBUgW2ZLkiSdj8PSyBe/epPvR4azOvJmvGjkF57FPD/6Vnl3TpKk60oG08D84zt4rdCOwIdZxm8YvF6PscqTuJI97I3eyzszNfQICuLpqjKGHtuPhv3uMnV97kMkjaUyaAAnanGnZew0kVWxg8xyEyVnPACoVinEBXqTGGJgdJeQM4JmPf7eulY8e0mSpPblwIoMvs49yNeTx1ClhDDUvJd/jr2VUG+/S/9jSZKkZnZDB9P1NiuPbMhgtSqZBJHP7AMH8NqjR112mKzE3WweoWFiQy0Lq834mow0RA3nWPzD7NH0Ya/Jj8wcE1nbTdRbtp065skHAIckBjWlZehJDjUQG6hHp5EtsyVJkq6Wy+XiP2+/xrcDktiTPIkIZwnvBVRz35j7W3tokiTdwNpUMK0oykTgA0ANfCSE+E1Lvdbq47t5Or+cMlUiN5tWM2FFI+Tnsj95J9G963i4oRFPU2d2a0fwqmc3vq+NwnL4ZDBcT6iPjeRQA7f0jiK5KZc5KdTdzETeYpQk6UZxvebto1s38tecbSweNgknGtKqNvHnW36Kp0be2ZMkqXW1mWBaURQ18DdgAlAI7FAUJV0Icbg5X8dmt/Psog/5NnAgBpWOx04sIWJtARUJa+k8SNDT3JVNFb34yNUNs9mHuCBvksINPNDTHTAnh7pLzfl6aptzWJIkSe3O9Zq3//DXt/mqSzfywsfRzXqEX0bEM3bsY835EpIkSVetzQTTwEAgUwiRDaAoyhfAdKDZJuWqykru3PkDB4OG0ct6gFtX7sWi20xh576UBvyagvAUksJ8mB5i4JlQvUzNkCRJurgWn7cf+PovLO86EV/q+Un+St6e/Yy8+ydJUpvSloLpKKDgjM8LgUE/3klRlIeBhwFiY2Ov6AWCgoMJsdRyR+VKBtsV4h96mqSIt2UHQEmSpKtzyXn7WuZsgEBTAyO1O3kxuid9xj57DUOVJElqGW0pmL4sQogPgQ8B+vfvLy6x+zk+v+VnzT4mSZIk6fyudc7+w/0vNPuYJEmSmlNbymEoAmLO+Dy6aZskSZLUNsl5W5KkG15bCqZ3AJ0URUlQFEUH3AWkt/KYJEmSpAuT87YkSTe8NpPmIYRwKIryOPA97hJL/xVCHGrlYUmSJEkXIOdtSZKkNhRMAwghlgJLW3sckiRJ0uWR87YkSTe6tpTmIUmSJEmSJEntigymJUmSJEmSJOkqyWBakiRJkiRJkq6SDKYlSZIkSZIk6SopQlxxDf02Q1GUCiDvKv5pMFDZzMNpKzryuUHHPj95bu3X1ZxfnBAipCUG01bJOfu8OvK5Qcc+v458btCxz+9qz+2883a7DqavlqIoO4UQ/Vt7HC2hI58bdOzzk+fWfnX082ttHfn97cjnBh37/DryuUHHPr/mPjeZ5iFJkiRJkiRJV0kG05IkSZIkSZJ0lW7UYPrD1h5AC+rI5wYd+/zkubVfHf38WltHfn878rlBxz6/jnxu0LHPr1nP7YbMmZYkSZIkSZKk5nCjrkxLkiRJkiRJ0jWTwbQkSZIkSZIkXaUbKphWFGWioijHFEXJVBTlxdYez9VQFCVGUZQ1iqIcVhTlkKIoTzZtD1QUZYWiKCea/g5o2q4oivLnpnPeryhK39Y9g0tTFEWtKMoeRVEWN32eoCjKtqZz+FJRFF3Tdo+mzzObvh7fqgO/BEVR/BVF+VpRlKOKohxRFGVIB7tuv2j6njyoKMrniqJ4ttdrpyjKfxVFKVcU5eAZ2674WimKMqdp/xOKosxpjXNp79r7vC3n7Pbzc/9jcs5uP9eutefsGyaYVhRFDfwNmAR0Be5WFKVr647qqjiAZ4QQXYHBwGNN5/EisEoI0QlY1fQ5uM+3U9Ofh4F/XP8hX7EngSNnfP5b4E9CiGSgGniwafuDQHXT9j817deWfQAsF0J0AXrhPscOcd0URYkCngD6CyG6A2rgLtrvtZsLTPzRtiu6VoqiBAKvAYOAgcBrJydz6fJ0kHlbztnt5+f+x+Sc3X6u3Vxac84WQtwQf4AhwPdnfP4S8FJrj6sZzmsRMAE4BkQ0bYsAjjV9/C/g7jP2P7VfW/wDRDd9048FFgMK7i5Fmh9fR+B7YEjTx5qm/ZTWPocLnJcfkPPj8XWg6xYFFACBTddiMXBze752QDxw8GqvFXA38K8ztp+1n/xzWdegw83bcs5u2z/3Z5yXnLPb2bVrzTn7hlmZ5vQ3zkmFTdvarabbLH2AbUCYEKKk6UulQFjTx+3tvN8HngdcTZ8HATVCCEfT52eO/9S5NX29tmn/tigBqAA+brod+pGiKHo6yHUTQhQB7wH5QAnua7GLjnHtTrrSa9WurmEb1aHeQzlnt6ufezlnt99rd9J1m7NvpGC6Q1EUxQB8AzwlhKg782vC/V+qdlfzUFGUqUC5EGJXa4+lBWiAvsA/hBB9ADOnbzkB7fe6ATTdCpuO+xdQJKDn3FtuHUZ7vlZS65Bzdrsj5+wOpKWv1Y0UTBcBMWd8Ht20rd1RFEWLe1L+VAjxbdPmMkVRIpq+HgGUN21vT+c9DEhTFCUX+AL3bcMPAH9FUTRN+5w5/lPn1vR1P6Dqeg74ChQChUKIbU2ff417ou4I1w1gPJAjhKgQQtiBb3Ffz45w7U660mvV3q5hW9Qh3kM5Z7fLn3s5Z7ffa3fSdZuzb6RgegfQqelJVR3uRPv0Vh7TFVMURQH+AxwRQvzxjC+lAyefPJ2DOy/v5PbZTU+vDgZqz7jt0aYIIV4SQkQLIeJxX5/VQoh7gTXA7U27/fjcTp7z7U37t8lVAiFEKVCgKEpK06ZxwGE6wHVrkg8MVhTFu+l79OT5tftrd4YrvVbfAzcpihLQtAp0U9M26fK1+3lbztnt8+deztlAO712Z7h+c3ZrJ4xfzz/AZOA4kAX8srXHc5XnMBz3rYr9wN6mP5Nx5y6tAk4AK4HApv0V3E/DZwEHcD+52+rncRnnORpY3PRxIrAdyAQWAh5N2z2bPs9s+npia4/7EufUG9jZdO2+AwI60nUD3gCOAgeBBYBHe712wOe48wjtuFeoHryaawX8pOkcM4EHWvu82uOf9j5vyzm7/fzcn+ec5JzdTq5da8/Zsp24JEmSJEmSJF2lGynNQ5IkSZIkSZKalQymJUmSJEmSJOkqyWBakiRJkiRJkq6SDKYlSZIkSZIk6SrJYFqSJEmSJEmSrpLm0rtI0o1DUZSTpXQAwgEn7payAAOFELZWGZgkSZJ0DjlnS22BLI0nSRegKMrrgEkI8V5rj0WSJEm6ODlnS61FpnlIkiRJkiRJ0lWSwbQkSZIkSZIkXSUZTEuSJEmSJEnSVZLBtCRJkiRJkiRdJRlMS5IkSZIkSdJVksG0JEmSJEmSJF0lWRpPkiRJkiRJkq6SXJmWJEmSJEmSpKskg2lJkiRJkiRJukoymJYkSZIkSZKkqySDaUmSJEmSJEm6SjKYliRJkiRJkqSrJINpSZIkSZIkSbpKMpiWJEmSJEmSpKv0/xxDudzxu+p6AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(12,4))\n", "for i in range(len(alpha_all)):\n", " alpha = alpha_all[i]\n", " ax[0].plot(T_list, xmean_all[i], label=rf'$\\alpha={alpha:.1f}$')\n", " ax[1].plot(T_list, xvar_all[i], label=rf'$\\alpha={alpha:.1f}$')\n", "ax[0].set_xlabel('T')\n", "ax[0].set_ylabel('mean')\n", "ax[0].legend(loc='upper left')\n", "ax[1].set_xlabel('T')\n", "ax[1].set_ylabel('variance')\n", "ax[1].legend(loc='upper left')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Furthermore, we can plot the drift (slope of the mean curve) as a function of `alpha`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "tags": [] }, "outputs": [], "source": [ "drift_all = []\n", "for i in range(len(alpha_all)):\n", " xmean_list = xmean_all[i]\n", " slope, intercept = np.polyfit(T_list, xmean_list, 1)\n", " drift_all.append(slope)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(alpha_all, drift_all)\n", "plt.xlabel(r'$\\alpha$')\n", "plt.ylabel('drift')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }