{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
},
"tags": []
},
"source": [
"# The *lac* Operon"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"In this note, we use the *lac* operon in the bacterium *E. coli* as an example of gene regulation to study common phenomena in dynamical systems with feedback control, including \"all-or-none\" transition and bistability."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"The *lac* operon is a group of genes in *E. coli* under the control of a common promoter. These genes encode proteins that are essential for the utilization of lactose, including a permease (*LacY*) that helps transporting lactose into the cell and an enzyme (*LacZ*) that helps catabolizing lactose. The promoter is repressed in the presence of glucose and in the absence of lactose, resulting in low levels of expression of the genes. However, when there is no glucose and the amount of lactose crosses a certain threshold, those genes turn on quickly to enable the cell to utilize lactose. The transition happens because lactose produces a molecule, the \"inducer\", which blocks the repression of the *lac* operon, thus facilitating the expression of the genes. Then the products of these genes further increase the uptake and breakdown of lactose, forming a positive feedback. It is this positive feedback that results in the all-or-none behavior of the gene expression. \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"We can simplify the description of the above processes by modeling only the inducer and the transporter, the latter representing the general expression level of genes within the *lac* operon. In the simplified description, essentially, the inducer promotes the production of the transporter, and the transporter in turn helps increase the amount of inducers in the cell. \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"Let us model the dynamics of the inducer and transporter as follows. Denote the abundance of the inducer by $X$ and that of the transporter by $Y$. We can write:\n",
"\\begin{align}\n",
"\\dot{X} &= g(Y) - \\gamma X \\\\\n",
"\\dot{Y} &= f(X) - \\mu Y\n",
"\\end{align}\n",
"In the first equation, the function $g(Y)$ describes how the transporter increases the amount of the inducer, and $\\gamma$ is the rate at which the inducer is degraded. In the second equation, the function $f(X)$ describes how the inducer promotes the production of the transporter, and $\\mu$ is the degradation rate of the transporter. When there are not too many inducers, the uptake rate of inducers is roughly proportional to the number of transporters; therefore, we have $g(Y) \\approx \\kappa Y$. Moreover, we will assume that inducers can be added to the cell externally, which can be represented by an additional source term in the $\\dot{X}$ equation, $\\xi$. Finally, we assume that the production of the transporter depends on the amount of inducer in the form of a sigmoidal function, such as the Hill function, $f(X) = \\lambda X^n / (X^n + K^n)$ for some coefficient $n$. This function starts from 0 when $X=0$, increases monotonically, and saturates at the level $\\lambda$ when $X \\gg K$, where $K$ is the half saturation point (see figure below)."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"Therefore, our dynamical equations become:\n",
"\\begin{align}\n",
"\\dot{X} &= \\kappa Y - \\gamma X + \\xi \\\\\n",
"\\dot{Y} &= f(X) - \\mu Y, \\qquad f(X) = \\frac{\\lambda X^n}{X^n + K^n}\n",
"\\end{align}\n",
"Without loss of generality, we can set $\\kappa = \\lambda = \\mu = 1$ (by rescaling $X$, $Y$, and time). Then we are left with 3 parameters, $\\gamma, K, n$, and one control variable $\\xi$. That is,\n",
"\\begin{align}\n",
"\\dot{X} &= Y - \\gamma X + \\xi \\\\\n",
"\\dot{Y} &= f(X) - Y, \\qquad f(X) = \\frac{X^n}{X^n + K^n}\n",
"\\end{align}"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"We are interested in the steady state, where the time derivatives vanish. We will first solve for steady states using a graphical method, then verify the stability of these states by numerically solving the dynamical equations. To start, let us program these equations, which mean defining the time derivatives (right-hand side of the equations) as functions of the variables."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def equations(XY, t, gam, xi, K, n): # calculate time derivatives (time t is kept as a parameter for later use of `odeint`)\n",
" X, Y = XY # parse variables\n",
" dXdt = Y - gam * X + xi\n",
" dYdt = X**n / (X**n + K**n) - Y\n",
" return [dXdt, dYdt]"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
},
"tags": []
},
"source": [
"## Steady states"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"Setting the time derivatives to zero, we have the equations:\n",
"\\begin{align}\n",
"Y &= \\gamma X - \\xi \\\\\n",
"Y &= f(X) = \\frac{X^n}{X^n + K^n}\n",
"\\end{align}\n",
"which both describe $Y$ as a function of $X$. Since they have to hold simultaneously, the solution would be given by the intersection of the two curves representing these functions. This can be found by plotting these functions on the same figure. For the parameters, let us choose $K=1$ and $n=2$, and vary the value of $\\gamma$. We will first consider the case $\\xi=0$, i.e., no external source."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"outputs": [],
"source": [
"def func1(X, gam, xi): # first function above\n",
" Y = gam * X - xi\n",
" return Y\n",
"\n",
"def func2(X, K, n): # second function above (Hill function)\n",
" Y = X**n / (X**n + K**n)\n",
" return Y"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"K = 1.0 # half saturation point for Hill function\n",
"n = 2 # Hill coefficient\n",
"xi = 0 # external source, set to zero for now\n",
"gam_list = [0.4, 0.5, 1.0] # values of gamma to plot\n",
"\n",
"x_array = np.arange(0, 3, 0.01)\n",
"f_array = func2(x_array, K, n) # Hill function\n",
"\n",
"plt.figure()\n",
"for gam in gam_list:\n",
" y_array = func1(x_array, gam, xi) # linear function with given gam\n",
" plt.plot(x_array, y_array, label=r'$\\gamma=%.1f$' % gam) # plot straight lines with different slopes\n",
"plt.plot(x_array, f_array, 'k', label=r'$f(X)$') # plot Hill function\n",
"plt.ylim(-0.1, 1.1)\n",
"plt.xlabel(r'$X$')\n",
"plt.ylabel(r'$Y$')\n",
"plt.title(r'$\\xi = 0$')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"It can be seen that, for a large $\\gamma$ ($\\gamma > 0.5$), there is only one solution at the origin, whereas for a small $\\gamma$ ($\\gamma < 0.5$), there are three solutions, one at the origin, another on the plateau of the function $f(X)$, and a third one in between. The latter case will be considered below (see [Bistability](#Bistability)); here we focus on the case with only one solution, e.g., $\\gamma = 1$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"source": [
"With this choice of parameters, the only steady state the system will go to is $X=0, Y=0$. That means both the inducer and the transporter are \"off\", because the inducer is being degraded too fast and cannot sustain the positive feedback loop. Let us now study how the solution changes with the external source $\\xi$. We expect to see that the genes are off when there is no external source, but will turn on when the external source increases to a certain level."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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WA1/Urad4slE9BEWREJ6QweLDIQxs4kZ9d4leB9aO0F5O6ehNwZvwT/BnfJPxWJnpr7ial5hI3C+/YNuhPXZt20qIEI6tD8JE02jVT04RwODT3ly9eJ7Wg4ZhZSth+a/iiUYlBEWRMGVHACYaTJDldXBlJ4QcgA6fgbX+3bQZuRnMPT2X+s716VWll4QAIW7eTxgzMig7YYIUvWvByQT6xNCoWyXsSutPWIa8PA4s/43S5d1o2E3OOSuebFRCUDx2Tl9NZNO5KF5vV5XyDtb6BQ25sPNLcKoOzUfr1wOWXFpCTGaMPK+D4GASV67EccgLWFbXX1JCCMHhVVewKWVB4+5yvA7O79lOYlQEHV55DVMzNXqsUAlB8ZgRQjBpsy8u9pa80UH/OD8Ap/6AuMvQ7X9SvA6up1/n90u/071ydxq7NtYfHxAzZSom1ta4vPuuFL3AUzFcD0mhZb+qWFjpv3hnpadxdNVfVPJsQNUmLSREqHgaUAlB8VjZciGa01eTmNC9FraWMrwOkvK9DjzaQS05wxxzz8wlz5jH+KbjpeilHz1K2v79OL/5BmZO+ov25eUaOLY2CCd3O2q3lrMK6MS6f8hKS6XDK2OU18ETRlZWFpmZmY9FW/UTFY+NrFwDP27zp075Ugxq6i5H9NB0yEiAHnK8DnzjfdkYtJFR9UZR0b7iwz/wEITBwPXJUzB3c6P0K6/o1gM4vzeC1IQs+o5oJKVEeNK1aM5s24hnx664ekhyqFNIIScnh4iICMLCwggPDyciIoKIiIg7nsfFxbFo0SJGj5YzXHo7KiEoHht/HA0lIjGTP8c0wFSG10FCCJz4BRq9DOX121gKIZjmMw1HS0fGNJDjdZC8bh3ZAQG4zZyBiaX+4nAZKTn4bAvFo4EzFWuXkRAhHPrrDzRTU+V1UAxkZGRw9epVwsLCCA0NJSws7I7nUVFR5BeA/n/KlClDxYoVcXd3p1WrVri7u9O0adPHEp9KCIrHQnxaNj/tDaRLbVfaVpezm5bd/wUTM2leB/vD9+N9zZsvWn5BKQv9a/qN6enEzJ6NdaNG2PfsqT9AwHtzCHk5RtoMlDP/EuF/icsnjtDmhZexKyPJg0Jxi7y8PMLCwggKCiIwMJDg4OA7Lvp3e8GbmZnh7u6Oh4cHXbt2pXLlyrceN5OAjY3+Yo0FRSUExWNh1u4rZOQa+NyrjhzBqyfAdz10/BxK6R9Hv+l1UMWhCoNrDtYfHxC/eDGG2DjKzp0rx+sgKo1LhyLx7OBO6XL6S14Io5EDyxZjV8aJZn0G6NZ7VsnIyCA4OJigoKBbF/6bz0NDQzEYDLfaWlpaUrlyZTw8PGjUqNGti72HhweVK1emQoUKmErYsCgLlRAU0rlyPZW/Tl5leMtKVHeV5XXwOdiXhzbv6dcD/rn8D2EpYfzU5SfMTSSUjo6OJv633ynl5YV1o0b6AwSOrgnC3MqM5n08pOj5Hz3ItcDL9Hz7A8yt9O9jeJrJy8sjJCQEf39//P39CQgI4PLlywQFBREVFXVHW0dHR6pXr06zZs148cUXqV69OtWqVaNatWqUL18ekyeocqxKCArpfL/VDxsLU8Z1rSlH8NJaiDwF/X8GC/13ysnZycw/O59W5VvRzq2dhAAhdtYsMBpx+fBDKXpXL8Vz9VI8bQZVx9pOf4nw3JxsDv21BNcq1ajbrpOECJ8OkpOTb13wb178/f39CQwMJDc391Y7V1dXatasSffu3W9d7G9e+MuUkTO3UxJQCUEhlYOXY9kXEMtErzqUsZXgdZCbmT93UL4hNBiqXw9YcH4BqTmpfNzsYylDO5kXLpK8YSNOY8di4a7fm8BoFBxZE0gpZysadJSzOuv0lg2kxsfS690Pn0mvg9TUVC5evMjFixe5cOECFy9exM/Pj2vXrt1qY2ZmRvXq1alduzZ9+/aldu3a1K5dm1q1alG69LPhLa0SgkIaBqPg+61+VCpjw4g2leWIHp8PyeH5vQMJF7KrKVdZ4b+CATUGUKuM/jIaQghiJk/GtEwZnN54XbcegN+RKBKi0ukx1hNTc/3nnJ6UyIn1q6jevBUV69aXEGHJJScnB39//zsu/BcuXCAsLOxWG1tbWzw9PenVq9cdF/2qVatibq5/+PBJRiUEhTRW+YTjfy2V+S83wdJMwkRZWgwcmgm1ekMVOUM7M0/NxNzEnHcbydlBnLp7Nxk+PpT779eY2umfL8nJyuPExmDKV3OgWhMXCRHC0X/+xJCbQ/uXny6vg6SkJM6ePcvp06c5c+YMZ86cISAggLy8PADMzc2pXbs2bdq04fXXX6d+/fp4enpSuXLlJ2pcvyhRCUEhhbTsPKbtvEyzyqXp5VlOjui+7yEvE7p9K0XO55oPu6/u5t1G7+Jio/9iK3JyiJk6DYvq1XAcLGel0untYWSm5tL77RpShrNir4ZyYe9OGvd6ntLl5VhtFgfXr1/nzJkzty7+p0+fJjg4+NZxNzc3GjduTP/+/fH09KR+/frUqFEDCwsJw5bPECohKKTwy/4g4tKyWTSymZxSCNd94fQSaPEGOOsvDmcURqb6TKWsTVlG1BuhPz4g4a+/yL16lYoLf0WTUBwuJT6Ts7vDqdmiLGWryPI6WIyljQ2tBsmZfykKkpKSOHnyJMePH8fb25vTp0/fsbKnWrVqNG3alLFjx9K4cWMaN26Mq6trMUb89KASgkI3kUmZLDwUTP9GFWhU0VGO6M4vwbIUdPhEityW4C34xvvy/XPfY22mv+JqXmIicfN/xva557BrJ2c46/j6YNCgVX85m9BCz54i7PwZOo4Yi7WdvRRN2eTm5nLhwgVOnDjB8ePHOXHiBAEBAQBomkbt2rXp0qULjRs3pkmTJjRq1AgHBwl+Gop7ohKCQjdTt/sDMKFnbTmCV3ZD0B7o8QPY6F/Sl5mXyezTs6nnVI/eVXtLCBDifv4ZY1oarp/I8Tq4HpLCFe/rNO1VGfsy+vcIGA0G9i9bjGO58jTq4SUhQjnExMRw+PBhjh49yvHjxzl16hRZWVlA/tLOli1bMmLECFq2bEnz5s0pVUp/T0lRcFRCUOjiXHgS689G8U6narg5yvA6yIOdE6FMVWgup77Q0ktLuZ5xncntJ2Oi6Z9MzA4JIfGvFTgOHoxVTf17LYQQHFl9BetSFjTpIWd11vk9O0iIDKfvxxMxNSuelTNCCEJDQzl06NCtx827f0tLS5o0acKbb75Jy5YtadWqFZUrV1aVV4sZlRAUhUYIwaQtvjjbWfBWR/3j/ACcWQqx/vDicjDTPyEYmxHL4ouL6VqpK03LyikIFjNtOiYWFri8L2fXdNDpWKKDkun4ci0pXgfZGekcXfUn7nU9qd6slYQIC4YQAj8/P/bv338rAURGRgL5u3nbtm3Lq6++Srt27WjatCmWEor/KeSiEoKi0Gy/eA3v0ER+GFgfOxleB1kpsPc7qNwWavfRrwfMOzuPXGMuHzT9QIpe+vETpO3Zg8sHH2DmrL9onyHXyLF1gTi52VKnbQUJEcKJ9avITE2hYxF4HYSHh7Nnzx52797N3r17iY6OBqBChQq0a9fu1sPT01Mt9XwCKJKEoGlaT2A2YAosEkL8eNfxSsASwPFGm8+EEFuLIjZF4cjOM/DDNn9ql7NnSDP9PgIAHJ4BGXHQY7UUr4OAhADWXVnHK3VfoVIp/baT+V4HkzGrUJ4yI+WsVDq/L4KUuCz6vi/H6yA55hqnt6ynXvvOlK0qqdd2G/Hx8ezbt489e/awZ88erly5AuSP/3fu3JkuXbrQqVMnqlatqoZ/nkAee0LQNM0U+AnoBkQA3pqmbRRC+N7W7EvgHyHEz5qm1QW2Ah6POzZF4Vl6NIyrCRksfa2FHK+DxDA4Nh8aDoMK+m0shRBM9ZlKKctSvN5Azg7i5A0byfbzo8K0aZhIKA6XmZbvdVDZ04mKdWV5HSxBMzGl7VA55jwGgwFvb2+2bt3Ktm3bOHXqFEII7Ozs6NChA2+//TZdunTB09NTJYCngKLoIbQAAoUQwQCapq0E+gG3JwQB3FxO4ADcWU5QUaJISM9hzt4rdKzlQvuacnbTsucb0Eyg83+kyB2KPMSJ6BN81uIzHCz1L1M0ZmQQO2sWVg0aUKq3nFU73ptDyc020GagnDv5qMt+BBw7RKtBw7AvU/jhrLi4OHbs2MG2bdvYvn078fHxmJiY0Lp1a/773//StWtXmjdv/syXeXgaKYqE4AaE3/Y6Amh5V5v/Ajs1TXsPsAW63ktI07TXgdcBKlXSPwSgKBxz9lwhI8fARFleB+HecHENtP8EHPTvps015jLNZxoepTwYUmuIhAAh/rffyYuJwW3WTCl3wonX0rl4MJJ6z1WgTAUJXgdCsH/pImxLl6F534GP/NlLly6xfv16tmzZwokTJxBC4OzsjJeXF15eXnTv3v2pquqpuDclZVJ5GPCHEGK6pmmtgWWapnkKIYy3NxJC/Ar8CtCsWTNxDx3FYyYwJo1lx8MY1qIiNcpK2OwkBOz4AuzKQttx+vWA1ZdXE5IcwpxOc+R4HVy/Tvzixdj37IlNkyYSIoSjawIxtzCheZ8qUvQCjh0i+koAPd4ch4XVw5f/Go1Gjh8/zrp161i3bh1BQUEANG/enK+//ppevXrRrFkzNRH8jFEUCSESuH3W0f3Ge7czGugJIIQ4pmmaFeAMxBRBfIpH4MdtftiYmzJemtfBOog4CX3ngaX+4nApOSnMPzufFuVa0LFiR/3xAbGzZkNeHq4fyfE6CPdLIPRCPK0HVMOmlP6ltXk5ORz66w9cPKpSt0Pn+7bLzs5m7969rF+/ng0bNnD9+nXMzc3p3LkzEyZMoG/fvpQvr9+NTvHkUhQJwRuooWlaFfITwVDgpbvaXAW6AH9omlYHsAJiUZQojgTGsdsvhs961cbZTsIa8tws2P01lK0Pje7+lSgcC88vJDk7WZrXQZavL8nr11PmtVexqKh/NZXRKDiyOhB7JysadJbkdbBtIymxMbzw5jhMTO6sMpubm8uePXtYuXIl69atIyUlBTs7O3r16sWAAQPw8vJSpSAUt3jsCUEIkadp2rvADvKXlP4mhLikadq3gI8QYiPwEbBQ07QPyJ9gHiWEUENCJQiDUTBpix9ujtaMauMhR/TEL5B0FUZsABP95bLDU8P50+9P+lbrSx0n/fMbQgiuT56CqYMDzm+8oVsPwP9YNPGRaXQfUw8zc/3nnJGcxIl1f1O1aQsqeTYE8lcGHT58mBUrVrB69Wri4+NxcHBg4MCBDB48mC5dumClLDQV96BI5hBu7CnYetd7X9323BdoWxSxKArHmtMR+EWnMHdYY6wkXMhIj4ND06FmT6jaUb8eMOvULMxMzHivsZwdxGn79pFx4gRl//MlphJq6uRk5XFiQzBlq5SielM51TmPrvqLvJx8r4MTJ06wcuVK/vnnH6KiorCxsaFfv34MHTqUHj16qJ3BiodSUiaVFSWY9Ow8pu0IoHElR/o0kDTGvP8HyEmHbv+TIncm5gw7w3bydsO3KWtbVreeyMkhZvIULKpWpfQQOSuVzuy8SkZKDr3erC9lOCsuPIxDG9cRaWFHm85duXz5MhYWFnh5eTF06FD69OmDra3+FUyKZweVEBQPZcHBYGJSs/nllaZyNh/F+IPP79B8NLjon5w2CiNTvafiau3KyHoj9ccHJK78m5ywMNx/+RlNwnr71IQszu66So1mrpSrqm/MPjMzkw0bNjD5qy85FxiMEIL27dvz6aefMmjQIDUnoCg0KiEoHkh0cia/Hgzi+YYVaFJJktH4rv+AhR10+EyK3LaQbVyIu8CktpOwMbfRrWdITibup5+wbdMauw4dJEQIJzYEI4Q+r4NTp06xcOFCVq5cSXJyMqVtrBn94mA+m/QD1arJ8VBQPNuohKB4IFN3BGAU8EkP/Yb0AATugSs7ofsksHXSLZeVl8Xs07OpU6YOz1d7XkKAEPfzLxhSUnD99FMpPaKYsBQCTlyjSY/KlHJ+tBLh6enp/P333/zyyy94e3tjbW3NoEGDKJ+VTPVyLrw24xfM1I5hhSTUrhPFfbkQkcza05G81rYKFcvov/PGaICd/4HSHtBCTn2h5X7LiU6PZkLzCVK8DnLCwkj4808cBg3Eqpb+JJjvdRCItb05TXsW3Ovg0qVLvP/++7i5uTF69GgyMjKYO3cu0dHRTBj5MmVNjHQc/ppKBgqpqB6C4p7c9DpwsrXg7U6ShiPOLIeYS/DCEjDTv+IlLjOOhecX0qliJ5qXay4hwHyvA83cHJf335eiF3I2jqgrSXR4qRYW1g/+c8vLy2Pt2rXMmzePQ4cOYWFhwQsvvMCbb75J27Zt0TSNnMwMjvyzHLfadanRoo2UGBWKm6iEoLgnO32vcyIkgUn9PSllJeEuNDsV9k6Ciq2gbj/9esBPZ38ix5DDh03l7CDO8PYmddcuXMa9j7kE03ZDnpEjawMpXd6Wum3vvzorOTmZRYsWMWfOHK5evUrVqlWZMmUKo0aNwsXlzuKBJzesJiM5iQGffKWqiyqkoxKC4l/k5Bn5YasfNVztGNpcltfBLEiPgWErpXgdXE68zNora3mp9kt4OHjo1hNGI9d/nIxZuXKUGTVKtx7Ahf0RpMRm0ue9hpiY/ns4KygoiDlz5vDbb7+RlpZGhw4dmDNnDn369MHU9N97PVJiY/DZvI467TpRrrqk0iEKxW2ohKD4F8uOhxEan8EfrzbH7B4XskcmKRyOzYP6Q8Bdjo3ldJ/p2Jnb8WbDN6XopWzaRNalS1SYMhkTa/3e0FlpufhsDaVS3TJUrnfn5PnRo0eZOnUqGzZswMzMjKFDhzJ+/HiaPKRw3qEVS9DQeG6oHHMeheJuVEJQ3EFSRg5z9lyhXQ1nOtaSs5uWPd/m/9vlqwe3KyCHIw9zNOooE5pNkON1kJlJzMxZWHl6UqqPHOtO760h5GTm0WZQvteBEILdu3fz3XffceDAAZycnPjiiy94++23qVDh4daZ0YEB+B85QMsBL1LKWZIHhUJxFyohKO5gzp5AUrNymdhbktdB5Cm48A+0+wgc9Q8/5RnzmOY9jUr2lRhWe5iEACHhjz/Iu3YNt6lT0CSUe066nsHF/ZHUea4CpcvbsH79er7//nu8vb1xc3Nj1qxZjB07Fhubgq3cyvc6WIyNgyMt+g3SHZ9CcT9UQlDcIjg2jaXHQnmxeSVql9Nfuyff62Ai2LrAc3JM7tdeWUtQchCzOs7C3FSC10FMDHELF2HfrRs2zeWsVDq6NhBMjYRmneT9hi9w8eJFqlatyq+//sqIESMeuabQlRNHiArwpdvr72FhLWH5r0JxH1RCUNzix23+WJqZ8GE3SROWfhvh6jF4fjZY6jfTSc1J5aezP9G0bFM6V7p/3f9HIXbOHERuLq4ffyRF76pfPKvW/MNe/z+5Oi+UunXrsnz5cl588UXMzB79zy0vN5eDf/6OcyUPPDvd00hQoZCGSggKAI4FxbPT9zoTetTCxV5CVcy8bNj1FbjWg8ZyDN8XXVhEQlYC87vOl+N14O9P8pq1lBk5EovKBd80di+EEKxft55xb08g/HoQnp71WTNnDf3799flOnZm+yaSY64zaOL//uV1oFDIRu1UVmA0Cr7b6oubozWjn5Nj6cjJXyExFHpMkuJ1EJkWyXLf5fSt1pd6TvV06+V7HUzGtFQpnN8q/EolIQQ7duygRYsWDBw0kOysbGZM+plz584ycOBAXckgIyWZ42tWUqVxMzwaNC60jkJRUFRCULDuTCQXI1P4pGctSV4H8XBgKlTvBtXkDO3MPjUbE81EntfBgQNkHDuO8zvvYFrI6qDe3t507NiRnj17EhsTy2u9PmP2hFWM/+INKV7Ex1b/RW52Fh2Gv6ZbS6EoCCohPONk5OQxdUcADSs68nyDhy9/LBAHJkNOWn4BOwmcjTnLttBtjKw3knK25XTridxcYqZMxcLDg9LDhj7y50NDQ3nppZdo0aIFfn5+zJs3j+WzttOkUjc6vFhbynBWfGQ453Zto0HXXji5V9Ktp1AUBDWH8Iyz8GAI11KymPdSY0xMJJRCiL0M3oug6Shwra1bTgjBVJ+pOFs785qnnDvlxH/+ISc4GPf5Pz2S10FSUhI//PADs2fPRtM0Jk6cyCeffIKJwZI/vz5GtSaulK/uKCXGg8t/w9zSijYvyPGafprJzc0lIiKCrKys4g6lRGFlZYW7uzvmj/A7rhLCM8z1lCx+ORBE7/rlaeZRRo7orq/AwhY6fi5FbkfoDs7HnufbNt/K8TpISSFu7jxsWrbErlOnAn0mLy+PBQsW8PXXX5OQkMArr7zCpEmTqFgxf1/FniW+GI2C1gPkFAEMO3+W4NPetHtpFDallNnNw4iIiMDe3h4PDw9V3+kGQgji4+OJiIigSpWCzwuqIaNnmGk7AjAYBZ/21H8nD0Dwfri8LX8Tmp3+3bTZhmxmnZ5FrdK16Futr/74gLgFCzAkJ1P2008KdPE4dOgQTZs25d1336VBgwb4+PiwZMmSW8kg9moq/sev0bBTRRxc9Je8MBoNHFi2iFIuZWnSS845P+1kZWXh5OSkksFtaJqGk5PTI/eaVEJ4RrkUlczq0xGMautBJSdJXgc7vgSHStBSTn2hP/3+JDItko+bf4yphJVKOeHhJC5dhkP//ljVrfvAttHR0QwfPpz27duTlJTEmjVr2LNnzx31hoQQHFlzBSsbc5r20rds9SaX9u8h9moo7V8ehZmFhRTNZwGVDP5NYX4mKiE8gwgh+G6LH47W5rzTqboc0XMr4PoF6PZfMLfSLRefGc/C8wvp4N6BVuVb6Y8PiJk+A8zMcBk/7r5tcnNzmTFjBrVq1WLVqlVMnDgRPz8/Bg4c+K8/sNDzcUQGJNHi+SpY2ujfNZ2TlcmRv5dRvmZtarZ6TreeQvGoqDmEZ5A9fjEcDYrn2371cLCW4XWQBnv+B+7Nod5A/XrAz+d+JjMvkw+bSfI6OH2a1O3bcX73XczLlr1nm6NHjzJ27Fh8fX3x8vJi9uzZVK9+74RpyDNyZE0gpcvZULednNVZ3hvXkJ6USN+PJqo7XkWxoHoIzxi5BiPfb/Wjmostw1pIWs54dA6kXYMeP0jxOghMDGTV5VUMqTWEqg5Vdevd8jpwdcXptVf/dTwlJYV3332X5557jrS0NDZs2MDmzZvvmwwALh6MJDkmkzaDqmMqoUR4SlwsPpvWUbttByrUlDSno1A8IiohPGP8eTyM4Lh0Jvaug7kMr4PkSDgyBzwHQUU5xeGmn5qOrZktbzV8S4peypatZJ0/j8sHH2ByV4XRTZs2UbduXebPn8/777/PpUuX6Nu37wPv0LPSc/HeEoJ77dJU9nS6b7tH4cjKpQhhpN2wkVL0FEXPgQMHcHV1xdTUlCpVqjB9+vRH1ti+fTu1atWievXq/Pjjj7rbPSoqITxDJGfkMmvPFdpWd6KTLK+Dvf8DYYQuX0uROxp5lMORh3mj4RuUtiqtW8+YlUXMzBlY1a2LQ7//X7Vz/fp1XnzxRfr27Uvp0qU5duwYs2bNws7O7qGaPttCyc7Io+3gGlKGdq4FXcH30D6aevWjlIuk70VR5Fy7do0XXniB+Ph4QkJC+OijRyuYaDAYeOedd9i2bRu+vr6sWLECX1/fQrcrDGoO4Rli3r4rJGfmMtGrrpwx6qgz+ZPJbcdDaf2rbAxGA1N9puJu5y7P62DJUvKioqnww49oJiYIIVixYgXvvvsu6enpTJo0iQkTJmBRwBU9STEZXNgXQZ025XF2f3jyeBj5XgeLsC7lQIv+Q3TrPet8s+kSvlEpUjXrVijF188/vH7W0qVLGTNmDA6FLIVy8uRJqlevTtWq+cOkQ4cOZcOGDdS9a0VcQdsVhiLpIWia1lPTtABN0wI1TfvsPm2GaJrmq2naJU3T/iqKuJ4lwuLT+eNoKEOaVqRuBVleB1+CjTO0kzPxuy5wHYFJgXzQ9AMsTPUvucyLiyN+wQLsunTBtmUL4uLiePHFF3n55ZepXbs2586dY+LEiQVOBgDH1gVhYmZCy7765zYAAr2PEel/ibZDhmNZQMMcRcnkvffe45VXXsHR0ZG//rrzEtauXTsaNWr0r8fu3btvtYmMjLy1vwXA3d2dyMjIf/0/BW1XGB57D0HTNFPgJ6AbEAF4a5q2UQjhe1ubGsDnQFshRKKmaarfLJkft/ljbmrCR90leR34b4Gww9B7Bljp302bnpvO3DNzaezamG6Vu0kIEGLnzMWYk4Prxx+xefNmxowZQ0JCAj/88AMTJky4p5H9g4i6kkjwmVha9q2CrYP+EuGGvFwOLv8dJ/dK1O/cXbeeggLdyT8O/P39+eSTT9i0aRMdO3b8Vw/80KFDxRLXo1IUQ0YtgEAhRDCApmkrgX7A7YNeY4GfhBCJAEKImCKI65nhZEgC2y5e46NuNXEtpX+PAHk5sOs/4FIbmsiZBF18YTEJWQnM6zxPjtfB5cskrV6N2eBBvPPddyxevJgGDRqwY8cOGjZs+Mh6wig4vCoQu9KWNOwqZ3XW2R1bSLoezcDPv8HkEZOTomSxYMECPvzwQzrdpxxKu3btSE1N/df706ZNo2vXfOMjNzc3wsPDbx2LiIjAzc3tX58paLvCUBQJwQ0Iv+11BNDyrjY1ATRNOwKYAv8VQmy/W0jTtNeB1wEqVVIVIAuC0SiYtMWXcqWsGNNOzjAH3osgIRheXgOm+n+FotOiWeq7lN5Ve1Pfpb6EACFmylTOAl8sWcLViAg+++wz/vvf/z6yfeVNLntfJ/ZqKl1frYu5hf6Ld2ZqCsfWrMCjYROqNGqqW09RvGRlZXHt2rX7Hi9ID6F58+ZcuXKFkJAQ3NzcWLly5b+Gnh6lXWEoKauMzIAaQEdgGLBQ0zTHuxsJIX4VQjQTQjRzcdFfK+dZYMO5SM5HJPNJz1pYS7iQkZGQX966WmeoIcfScfaZ2QCMa3z/HcSPQvL+/czYsJ5XAvzRTE05ePAgP/zwQ6GTQW6OgePrg3CtbE/N5vfe1PaoHFuzgpyMTOV18JQwYcIEdu3ahaenJ926dSM6OvqRNczMzJg3bx49evSgTp06DBkyhHr1/n8IzMvLi6ioqIe200NR9BAigYq3vXa/8d7tRAAnhBC5QIimaZfJTxDeRRDfU0tmjoEp2wOo7+ZA/0ZyupQcnArZKdK8Di7EXmBL8BbG1h9LebvyuvWiwsN5YfBgjsbH8+ILL7Bg4cJCr/q4ybndV0lLzKbba3XRJJQIT4iK5NzOrdTv0h3nSh669RTFT9WqVdmzZw8AI0eO5PTp0/Tu3fuRdby8vPDy8rrnsa1btxaonR6KoofgDdTQNK2KpmkWwFBg411t1pPfO0DTNGfyh5CCiyC2p5rFh4OJTs7iy9515HgdxAXmW2M2GQFl5dhYTvWZShmrMoyuP1q33vbt22no6cnphATmfvABK/7+W3cySE/O5tSOq1Rt7EKFGvr3RQAc/PN3zCwsaPPCy1L0FCWHzZs3k56efmte4EnjsScEIUQe8C6wA/AD/hFCXNI07VtN027uFNoBxGua5gvsAyYIIeIfd2xPMzGpWczfH0TPeuVoWVXOblp2fw1mVtBpohS5XWG7OBNzhvcav4etuW2hdXJzc/nkk0/o1asXZfLy2NS7N+9Mny5lcvrExmCMeUZpXgdXL54nyOc4Lfq9gK2jnASjKDn06dOH1atXF3p4srgpko1pQoitwNa73vvqtucC+PDGQyGBGTsvk2sw8lkvSXVxQg6B/2bo8hXY6V8VnGPIYeapmdQoXYMB1QcUWicqKoohQ4Zw5MgRRrVuw/txcdT+4UcpySAuIhW/o9E07FIRR1f9ewSMRgP7ly3C3tmFJr376dZTKGRTUiaVFRLxi07hb59wRrT2wMO58HfetzAaYccX4FARWr2tXw9Y4b+CiLQIPm5WeK+Dm+Y1Z86cYdm8n/g0LY2yAwZg7SlnOOvI6kAsbcxo1stDtx6A78F9xIYG0+6lUZhbPJl3kIqnG5UQnjJueh04WJvzfucackTPr4Rr5/PrFZnrdwVLzEpkwbkFPOf2HG0qtHnkzwshmD17Np07d8be3p6TJ0/SKSgITExw+WC87vgAwi7GE+GfSPPeVbCy1V8iPDcri8Mrl1K+ei1qt2kvIUKFQj4qITxl7A+I5XBgHOO61MBBgmkLOen5XgduTfMrmkrg53M/k5GXwcfNPn7kz6anpzN8+HDGjx9P79698fb2pkpODilbt+L02quYlyunOz6DwcjRNYE4lrXBs4Oc1Vnem9aSnphAhxFjlNeBosSiEsJTRK7ByKQtvlR1tmV4KzmWjhydB6lR0ON7MNH/6xKcHMw/Af8wuOZgqjk+2kRtUFAQrVq1YsWKFXz33XesXbuWUqVKEfPjZExdnHEarX+lEoDvoSgSr2XQZmA1KV4HqQlxeG9aQ83W7XCrVUdChArF40FVO32KWHnyKkGx6Swc0UyO10FKNByZBXX7QyU5NpYzfGZgbWb9yF4H+/fvZ9Cg/B7Ktm3b6NGjR36IW7eSee4c5b+bhImt/vmS7IxcTm4Kwa2WIx4NnHXrARxZuRxhMND+JeV1oCjZqB7CU0JKVi4zd1+hVdUydK0jy+tgEhjzoOt/pcgdjz7OgYgDjG0wFifrgi+FXbRoEd26dcPV1ZWTJ0/eSgbG7Gxips/AsnZtHPr3lxLjqW1hZGXk0naQHK+D68GBXDq4h8a9+uLgqn84S6F4nKiE8JTw075AEjNy+LK3JK+D6PNw9k9o+QaUqaJbzmA0MM17GhVsK/BynYJtyDIYDHz44YeMHTuWLl26cPz4capV+/9hpsRly8iNjKTsp5+gSSgOlxybybl94dRuVQ6XSva69YQQHFi2GGs7e1oOUF4HipKPSghPAeEJGfx+OJRBTdzxdNNfihohYOdEsC4N7R594vdebAzaSEBiAB80/QBL04cvuUxJSaFv377MnDmT999/n82bN9+x6zgvPp64XxZg17Ejtq1bS4nx2LogTEw0WvaVswkt6NRJwn0v0OaFl7Gy1W+moyjZFIWFZnh4OJ06daJu3brUq1eP2bNnywj9FmoO4Sngx+3+mJpofNy9lhzBy9sh5CB4TQNrR91yGbkZzDkzhwYuDejh0eOh7UNDQ3n++efx8/Pj559/5s033/xXm9h58zBmZuL6yQTd8QFEByYRdDqG5n2qYFdaltfBYsq4VaRB154SIlSUdG5aaH733Xc4Ojo+8udvWmPu2rULd3d3mjdvTt++fe9wQjMzM2P69Ok0adKE1NRUmjZtSrdu3aS4pYFKCE88p8IS2HI+mvFda1DOQYLXgSEXdn4JzjWh6Sj9esBvF38jLjOOWZ1mPXQ46/Tp03h5eZGdnc2OHTvo0qXLv9pkBwaS9Pc/lB42DMuq+kt6C6Pg8OpAbB0saNxNTln1c7u2kRgdxYBPv1ZeB0XJts/g2gW5muXqQ6+HG9kXhYVm+fLlKV8+vwikvb09derUITIyUlpCeOiQkaZpw6X8TwrpGI2Cbzf7UbaUJa+3l+R14PMbxAfmVzM11b+P4Vr6NZZcWkIvj140dHmwMc3OnTvp0KEDlpaWHD169J7JAOD61KmY2Nri/O47uuMDuHLqOjGhKbTqXw1zSwleB2mpHFv1F5XqN6JK42YSIlQ8CRSVheZNQkNDOXPmDC1b3m0vU3gK0kN4RdO05sCHQgiDtP9ZoZtN56M4F57E1MENsLGQ0NnLTIT9P0CVDlBDjqXj3DNzMQoj45o+2Otg6dKljB49mnr16rF161YqVKhwz3Zph4+QfuAgrhMmYFZaf3G4vBwDx9YF4VzRjlot5awCOrF2JVkZ6XR8ZbTahFbUFOBO/nFQ1BaaaWlpDBo0iFmzZlGqlASP9BsUZFK5F5AJ7NU0TbnSlBCycvO9DupVKMWgJu5yRA9Og8wk6PEdSLiQXYq7xMagjQyvOxw3u3vv+BVC8P333zNy5Eg6dOjAwYMH75sMhMFAzOTJmLu7U/oVOR3Xc3vDSUvIpu3gGlK8DhKvRXFm+xbqd+qGS2X9q7MUTwa3W2je6yagID2Eglpj5ubmMmjQIF5++WUGDhwo9TweelsphDACn2maNhA4pGnaDOAscFEIkSE1GkWB+e1ICJFJmUx9oYEcr4OEYDixABoPzx8z1cntXgdj6o+5ZxuDwcD777/P/Pnzefnll/ntt9+wsLC4r2bSmjVkX7mC26xZmDygXUHJSMnh1LYwqjR0xr2WnFLUh/78A1MzM9q++IoUPcWTQVFZaAohGD16NHXq1OHDD+UXhy7QslNN0/oAY4AcoAkwDQjXNC1QekSKhxKbms38fUF0q1uWNtXk7KZl19dgagGdv5Qit/fqXk5dP8U7jd7B3uLfa/qzs7MZMmQI8+fP55NPPmHp0qUPTAaGtHRiZ8/BukkT7HvIGc46sSkYQ66RNgOrS9GL8L3IlZNHadFvsPI6eMYoKgvNQ4cOsWzZMvbu3Xurl3G7k5peHtpD0DQtBPAFZgohdt11TNJYheJRmLn7Mlm5Bj6X5XUQdhT8NkKnL8Fe/zh6riGXGadmUM2hGgNr/LtLm56ezoABA9i1axezZs1i3LiHeynHL1qIIT6esj/PlzIuHx+Zht/hKOp3csexrH6vA2E0sn/ZIuycnGnap79uPcWTRVFaaObbxzweCjIT2UsI4X+vA0KICMnxKB5CwLVUVp68yojWHlR1kbDZ6abXQSk3aC1n1c7KgJVcTb3Kz11/xszkzl+xpKQk+vTpw7Fjx/j9998ZNWrUQ/Vyo6JI+P0PSj3/PNYNGkiJ8eiaQCyszWjeW844v9/h/VwPDqTXux9hbilh+a/iieRJt9AsyBzCPZOBonj4fqsfdpZmjOsiyevgwiqIOgMDFoCF/jvl5Oxkfjn3C20qtOE5t+fuOBYbG0uPHj24ePEif//9N4MHDy6QZszMWQC4yvI6uBTPVd8E2g6uLsfrIDuLQyuWULZqDeq07SAhQsWTSp8+fejTp09xh1FoVOmKJ4j9ATEcuBzL+11qUNpW/6QqORmw5xso3wjqy6m188u5X0jLTeOjZh/d8X5ERATt27fH39+fjRs3FjgZZJ4/T8qmTZQZNQrz+6w+ehSMBiNHVgfi4GJN/Y5yRjxPbV5PWkI8HUeMRpNQIlyhKC7UTuUnhDyDke+3+uHhZMOI1h5yRI//BCmRMHChFK+D0ORQVvqvZGCNgdQsXfPW+0FBQXTt2pX4+Hh27NhBu3btCqQnhOD6j5MxdXLCaexY3fEB+B6JJjE6nV5v1MfUTP85pyUmcHLDamq0aIN7HU8JESoUxYe6nXlC+NsnnMvX0/isVx0sJFzISL0Oh2ZCnefBo61+PWDmqZlYmFrwTqP/n4u4fPky7du3JzU1lb179xY4GQCk7txF5unTuIx7H1M7/V4HOZl5nNwUTIUajlRpJMnr4O/lGPLyaPfyKCl6CkVxohLCE0BqVi4zdl6mhUcZetQrK0d03yQw5EDXb6TIeV/zZm/4XsY2GIuzdf7FNiAggI4dO5Kbm8v+/ftp1qzgZRyMOTnETJuGZc2aOA6SY915ansYmam5tB1cXcpKpZjQYC7u30Xjnn0oXU7/cJZCUdyoIaMngPn7g4hPz+H3V+vIKYVw7SKcXgat3gYn/aWejcLIVO+plLctz/A6+TuIAwIC6NSpEwaDgX379t2xnrogJC7/k9zwcCouWiTF6yAlLpNze8Kp1bIcrpX1b/W/6XVgZWtHq4FDdespFCUB1UMo4UQkZrD4cAgDG7vRwN1Rv+AtrwNH6CCndPSmoE34Jfgxrsk4rMys8Pf3p2PHjoVOBnmJicT9/DO27dth95yc4azj64PQNGjZT04RwJAzPly9eI7Wg1/Cyk55HSieDlRCKOFM2R6AiQYf95DkdXBlFwTvhw6f5Rvg6CQjN4M5p+dQ37k+var0ws/Pj44dOyKEYN++fYUqyxs37yeMGRmU/eQT3fEBXAtO5opPDI26VcK+jP49Aoa8PA4sW0zp8m407NZLQoQKRclAJYQSzOmriWw8F8Xr7apSwdFav6AhN7934FQdmo/WrwcsubSEmMwYJjSfgL+fP506dQIodDLIDg4mceVKHIe8gGV1/SUlhBAcXnUFm1IWNO4ux+vg/J7tJERF0H74a5iaqVFXxdODSgglFCEEkzb74mJvyRsd5Fg6cuoPiLsM3f4nxesgJiOG3y/9TvfK3bFNsqVz585omsb+/fupU6dO4TSnTsPE2hqXd9/VHR9A4KkYroek0LJfVSys9F+8s9LTOLrqLyrWa0C1pi0kRKh4WigKC83bMRgMNG7cWOpGuCJJCJqm9dQ0LUDTtEBN0z57QLtBmqYJTdOeeVeRLReiOX01iY+718TWUobXQVK+14FHO6glZ5hj7pm55BnzGOQ8iC5dumA0Gtm7dy+1axeuxlL6sWOk7duH85tvYObkpDu+vNx8rwMndztqty6vWw/gxLp/yEpLpYPyOlDcxU0Lzfj4eEJCQvjoo48e/qHbuGmhuW3bNnx9fVmxYgW+vr73bT979uxC33jdj8fe39U0zRT4CegGRADemqZtFEL43tXOHhgHnHjcMZV0snINTN7uT+1y9gxuWvHhHygIh6ZDRoI0rwO/eD82BG6gv0t/Xun3Cunp6ezbt6/Qv6DCYOD65CmYV6hA6VfklI4+vzeC1Pgs+o5vJKVEeNL1a5zZtpF6HbpQtoqkXptCKpNPTsY/QW61ndplavNpi08f2q4oLDRvEhERwZYtW5g4cSIzZswo1P93L4qih9ACCBRCBAshcoCVQL97tPsfMBnIKoKYSjRLjoYSnpDJl73rYirD6yAxFE78Ao1egvIPtrEsCEIIpvlMwybbhr8//JuYmBi2b99Ow4aF105ev55sf39cP/4IE0v9Jvf5XgeheNR3omLtMrr1AA799QeaqSnPKa8DxT0oSgvN8ePHM2XKFEwkl0opihkxNyD8ttcRwB0moJqmNQEqCiG2aJp237WQmqa9DrwOUKmSnAnCkkZ8Wjbz9gbSpbYrz9WQ5HWw+79gYibN62B/+H6OBR0jY24GMVfzk0GLFoUfTzempxMzaxbWDRti30vOcJb35hByc4y0GSTH6yDS35fLxw/TevBL2JXRP5yleDwU5E7+cVCUFpqbN2/G1dWVpk2bsn//fmm6UAI2pmmaZgLMAEY9rK0Q4lfgV4BmzZo9vqLgxcis3VfIyDXwuZekscGrJ+DSOuj4OZTSv5s215jLlMNTiJ4dTUZoBhs3bqR9+/a6NOMX/4YhNo6yc+dKGZdPiErn0uEoPNu7Ubqc/pIXt7wOSpeh+fNyLQsVTwe3W2jei3bt2pGamvqv96dNm3arVHZBLTSPHDnCxo0b2bp1K1lZWaSkpDB8+HCWL1+u+zyKIiFEArcPhLvfeO8m9oAnsP/GxaAcsFHTtL5CCJ8iiK/EEBiTyl8nr/Jyy0pUd5XldfA52JeHNu/p1wOWnV3GwW8Pkh2UzZo1a+jRo4cuvdxr14j/7TdKeXlh3aiRlBiPrg3E3NKU5n08pOj5Hz3ItcDL9Hz7A8ytlNeB4t8UlYUmwA8//MAPP/wAwP79+5k2bZqUZABFM4fgDdTQNK2KpmkWwFBg482DQohkIYSzEMJDCOEBHAeeuWQA8P1Wf2wsTOV5HVxaC5GnoPN/wEL/nXJsaiwfvfYRGZczWLp0Kf363Wsq6BE1Z84CoxEXSf6wV33jCbsYT7NeHljb6S8RnpuTzaG/luBapRp129377k+hKCoLzaioKJlh/zuGx6oOCCHyNE17F9gBmAK/CSEuaZr2LeAjhNj4YIVng0NXYtnrH8MXXrVxstM/qUpuZv7cQbkG0HCYbjmj0Uj3wd1JOpfE/2b9j5deekm3ZuaFiyRv2IDT2DFYuP+7a/zoMQqOrA6klLMVDTrJ8To4vWUDqfGx9HrnA+V1oLgvRWmheTsdO3akY8eOj/z/3I8imUMQQmwFtt713lf3aduxKGIqSRiMgu+2+FGxjDUj23jIET3+MySHQ//5ur0OhBCMfns0Z3eepctbXfhynP7JaSEEMZMnY1qmDE6vv65bD8DvSBQJUen0GOuJqbn+i3d6UiIn1q+iWrNWVKwnx7pT8XTzpFtoqlueEsAqn3D8r6Xyea86WJrpr+xJWgwcmgG1ekMVfRO+AN9//z1/LPiDsr3K8tfUf49pFoa0PXvI8PHB5f33MLW3162Xk5XHiU0hlK/mQLUmLhIihKP//IkhN4f2L78qRU/x9NOnTx9Wr16NpYSl08WBSgjFTFp2HtN2XqZZ5dL08iwnR3Tf95CXCd2+1S21cOFCvvzySxxaO/D1d1/jauuqW1Pk5HB96lQsqlfDsYBWmg/j9I4wMlNyaDu4hpSVSrFXQ7mwdyeNuvemTAX9w1kKxZNAsS87fdb5ZX8QcWnZLBzRVE4phOu+cHoJtHgDnPWtwV+7di1vvvkm5ZuWp/Z7tRlVf5T++IDEFSvIDbtKxYW/okkoDpeakMXZ3eHUbFGWslXkeR1Y2tjQarD++ReF4klB9RCKkaikTBYeCqZfowo0rqS/FDUAO78ES3vooK909IEDB3jppZeo0aAGpV8vzQctPsDaTH/FVUNSErHzf8a2bVvsHsFO80EcXx8EQKv+cspJhJ49Rdj5M7QaNAxrO/3DWQrFk4LqIRQjU3cEAPBJz8IVg/sXV3ZD0B7o8T3YFL5cw9mzZ+nbty9Vq1XF5X0XyrmUo3fVR18xcS9i58/HmJqKqySvg+shKVw+eZ2mPStL8TowGgwcWP4bjuXK06jHvVd7KBRPK6qHUEycC09i3ZlIxrSrgpsUr4O8/N5BmarQfGyhZUJCQujZsycODg6MmDmCBJMEJjSbgImm/1clOySExL9W4Dh4MFa1aurWE0JwZPUVrO3NadKzsm49gAt7dxAfcZX2L7+KqZn+EuEKxZOESgjFgBCCSVt8cbaz4K2OcmrtcGYpxPrlTySbFW5DVkJCAr169SInJ4e/N/7N2ti1dK3UlWbl5FQjj5k+HRMLC1zel7NrOvhMLNFBybTsK8frIDsjnSP//Il7HU+qN28tIUKF4slCJYRiYPvFa3iHJvJht1rYyfA6yEqBvd9B5bZQu3BmGdnZ2QwYMICQkBA2bNjAjowd5Bpz+aDpB/rjA9JPnCRt9x6c3ngDM2f9RfsMuUaOrg3Eyc2WOm3112gCOLF+FZkpyXQcMUZ5HSieSVRCKGKy8wz8uN2fWmXtGdJMzm5aDs+AjDjoPqlQXgdGo5FRo0Zx8OBBli5dims9V9ZeWcuw2sOoVEp/VVlhNHJ98o+YVShPmZEjdOsBnN8fQUpcFm0GVZfidZAcc53TW9ZTt31nylaV1GtTKJ4wVEIoYpYdCyMsPoOJvetgZirhx590FY7NhwZDwa1JoSQmTpzIypUrmTx5MkOGDGGqz1RKWZbijQZv6I8PSN6wkWxfP1w/+BATCcXhMtNy8NkaSqV6TlSqK6cU9aEVS9BMTHluqJyEpXj2KEoLzaSkJAYPHkzt2rWpU6cOx44d0xP6LdQqoyIkIT2H2Xuu0LGWC+1rytlNy+5vQDOBLv8p1McXLFjAjz/+yFtvvcWECRM4FHmIE9En+KzFZzhYFs756XaMGRnEzpyJVYMGlOotZ9WO9+ZQcrMNtJXkdRB12Y+AowdpNWgo9k6SPCgUzxw3LTS/++47HB0dH/nzNy00d+3ahbu7O82bN6dv3773dEwbN24cPXv2ZPXq1eTk5JCRkSHhDFRCKFLm7LlCRo6BibK8DsK94eJqaP8JODz68NPWrVt5++236d27N3PmzCFP5DHNZxoepTwYUmuIlBDjf/+dvJgY3GbNlFIcLvFaOhcPRlLvuQqUqSDB60AI9i9dhK1jaZr3HaRbT1G8XPv+e7L95FpoWtapTbkvvnhou6Ky0ExOTubgwYP88ccfAFhYWGBhob+yL6ghoyIjMCaNZcfDGNq8IjXKStjsJATs+ALsykLbcY/88VOnTjFkyBAaN27MypUrMTMzY83lNYQkh/Bh0w8xN9G/5DL3egzxixZj37MnNk0KN5x1N0fXBmFuYULzPlWk6AUcO0T0lQDaDn0FCysJy38VzyxFZaEZEhKCi4sLr776Ko0bN2bMmDGkp6dLOQfVQygiftzmh7W5KR9007/+Hsh3QYs4CX3ngeWjmemEhYXRp08fnJ2d2bx5M3Z2dqTkpDD/7HxalGtBx4odpYQYO3s25OXh+pEcr4Nw/wRCz8fRekA1bErpvyPKy8nh0F9/4FK5CvU6dJEQoaK4Kcid/OOgKC008/LyOH36NHPnzqVly5aMGzeOH3/8kf/973+6tVVCKAKOBsax2y+GT3vWxlmK10EW7P4aynpCo0fzJUhKSsLLy4usrCz27NlDuXL5BfUWnV9EUnYSHzf7WMqSyyxfX5LXraPMq69iUbHiwz/wEG56HdiXsaJBZ0leB9s2khIbw+AvJ2FiIqHKrOKZpSgtNN3d3XF3d6dly3xr+sGDBz9wAvpRUAnhMWMwCiZt8cPN0ZpX23rIET25IH910Svr4REuZDf3Gly5coVdu3bdGpuMSI1gud9y+lbrSx0n/fMbQgiuT56CqYMDzm/KWankfyya+Ig0uo+ph5m5/ot3RnISJ9b9Q9Umzalcv5H+ABXPNEVpoVmuXDkqVqxIQEAAtWrVYs+ePfeceC4Mag7hMbPmdAS+0Sl81qs2VhIuZKTHwcFpULMnVCu4paMQgjFjxrB//37++OMPOnTocOvYrNOzMDMx473GcnYQp+3bT8aJEzi/9y6mpfRXH83JyuPExmDKVilF9ab6y28DHF31F7nZWbQf/poUPcWzTVFbaM6dO5eXX36ZBg0acPbsWb6QNVQmhHgiH02bNhUlnbSsXNF80i7R/6fDwmg0yhHd/KEQ/y0tREzAI33syy+/FID47rvv7nj/zPUzwvMPTzH/zHwp4RlzckRgj54isJeXMObkSNE8vjFIzHtjj4gOSpKiF3s1VEx/8Xmxe/HPUvQUxYuvr29xh3AHI0aMEJs3by7uMIQQ9/7ZkG9dfM/rqhoyeowsOBhMTGo2Pw+X5HUQ4w8+v0Pz0eBS8MnpRYsWMWnSJMaOHcvnn39+632jMDLFewqu1q6MrDdSf3xA4sq/yQkNxf2Xn9HM9a9USkvM4uzOq9Ro5kq5qvr3RQAcXP4bFtbWtFZeBwrJKAtNxT25lpzFrweD6NOgPE0rS/I62PUfsLCDDp8V+CM7duzgzTffpGfPnsyfP/+OxLQ9ZDsX4i7wXpP3sDG30R2eITmZuHnzsGndCrvbhqT0cHxDMEJI9Do4d5qQs6doNfBFbErJSTAKxU2UhabinkzdEYBRwKeyvA6C9sKVndD+Y7AtWLmGs2fPMnjwYOrXr88///yD2W3uZFl5Wcw6PYs6ZerQt1pfKSHG/fwLhpQUyn76qZQeUUxYCgHHr9GwizulnPXvETAaDRxYthiHsuVo1PN53XoKxdOGSgiPgQsRyaw5HcFrbatQsYz+O2+MBtjxJThWhpYFW7UTHh5O7969KV26NFu2bMH+LiP75X7LiU6P5uNmH0vxOsgJCyPhzz9xGDQQq9r6k6AQ+ctM870OPHTrAVzct4u48DDavzQKMwnDWQrF04aaQ5CMuOF14GRrwdud5AxzcGY5xFyCF5aA2cO7osnJyXh5eZGWlsaRI0eoUOHO8tBxmXEsurCIThU70aJ8CykhxkyfgWZujsv770vRCzkXR9SVJDq8VAtLa/2/pjmZGRz5ezkVatWlRsu2EiJUKJ4+VA9BMjt9r3MiJIHx3WpSykrCXWh2KuydBBVbQd1+D22ek5PD4MGD8ff3Z+3atXh6ev6rzfyz88nOy+bDpnJ2EGf4+JC6cyfOY8dg7qp/Waghz8jRNYGULm9L3bblJUQIJzesJiM5iY4jRiuvA4XiPqiEIJGcPCM/bvOnuqsdw5rr350LwOFZkB6T75P8kAuZEILXX3+d3bt3s3jxYrp0+Xc5hiuJV1hzZQ1Daw/Fw8FDd3jCaOT6j5MxK1eOMqNG6dYDuHggkuTYTNoOro6JhBLhKbEx+GxeR53nOlK+ei0JESoUTycqIUhk+fEwQuLS5XkdJEfAsXlQ/wVwb/rQ5t988w1Llizhm2++YcSIe9f1n+4zHVtzW95s+Kb++ICUzZvJungR1w/GY2Ktf+I3Kz0X7y0hVKxbhsr1JHodoPHcMOV1oFA8CJUQJJGUke910K6GMx1leR3s+Tb/3y5fP7Tpb7/9xjfffMOrr77Kf/5zb2+Ew5GHORJ1hDcbvCnH6yAzk5gZM7GqV49Sz8tZteO9JYSczDxpXgfRgQH4HzlA0z79KeUsZ5ezQvG0UiQJQdO0npqmBWiaFqhp2r8W0Wua9qGmab6app3XNG2PpmmViyIumczZE0hqVi4Te9eRM0YdeQrO/w2t3wHHBw8/7dixg9dff50ePXqwYMGCe/7/ecY8pvtMp5J9JYbVlrMhK2HJEvKuXaPsZ59K8TpIup7Bxf2R1HmuAk5uj1bB9V4IIdi/dDE2Do606DdYt55C8bTz2BOCpmmmwE9AL6AuMEzTtLsrMZ0BmgkhGgCrgSmPOy6ZBMemsfRYKC82r0jtcvpr9+R7HUwEWxd47sEm92fOnLm112DVqlWY32c55dorawlMCsz3OjDVP9mdFxtL3K8Lse/WDZvmzXXrARxdG4ipuQktn68qRe/KiSNEBfjS9sXhWFhLWP6rUDyAorTQnDlzJvXq1cPT05Nhw4aRlZWlJ/RbFEUPoQUQKIQIFkLkACuBO5bLCCH2CSFuesAdByS5zxcNP27zx9LMRJ7Xgd9GuHoMOn8Jlvc30wkLC8PLy4syZcrcc6/BTdJy0vjp7E80LduUzpU6Swkxds4cRG4urh9/JEUvMiCRkHNxNO1VWY7XQW4uB//8HedKHnh26iYhQoXiwdy00IyPjyckJISPPnq0v42bFprbtm3D19eXFStW4Ovr+692kZGRzJkzBx8fHy5evIjBYGDlypVSzqEo9iG4AeG3vY4AWj6g/Whg270OaJr2OvA6QKVKlWTFp4vjwfHs9L3OhB61cLXXbyBPXjbs+gpc60LjV+7bLDExkV69epGZmcnu3bv/tdfgdhZdWERCVgLzu8yX43Xg70/S6jWUGTECi8r6R/eEUXB49RXsyljSsLOc1Vlntm8iOeY6gyb+T3kdPEMc+ucyceFpUjWdK9rRbsjDb/aKykIT8k1yMjMzMTc3JyMj44F//49CiZpU1jRtONAMmHqv40KIX4UQzYQQzVxcJE3c6sBozN+EVsHBitHPybF05ORCSAyF7pPu63Vw09cgKCiI9evX31Ei924i0yJZ5ruM56s+Tz3n+7crKEIIYqZMwbRUKZzffku3HkDAiWvEhafRun81zCwkeB2kJHNi7d9UadQUjwaNJUSoUDycorLQdHNz4+OPP6ZSpUqUL18eBwcHunfvLuUciqKHEAncftvnfuO9O9A0rSswEegghMgugrh0s+5MJBcjU5g9tJEkr4N4ODAFqneD6ve2dDQajYwaNYoDBw7w119/0bFjxwdKzj49GxPNhPebyNlBnH7wIOlHj1H2iy8wLeSd0O3kZhs4viEYV49S1GhWVkKEcGz1CnKyMunwymgpeoonh4LcyT8OitJCMzExkQ0bNhASEoKjoyMvvPACy5cvZ/jw4bq1i6KH4A3U0DStiqZpFsBQYOPtDTRNawwsAPoKIWKKICbdZOTkMXVHAA0rOvJ8AzndNQ5Mhpy0/N7Bffjss89YuXIlP/74I8OGPXi10LnYc2wL2cbIeiMpZ1tOd3giN5frk6dg4eFB6WFDdesBnN19lfSkbJ4bXB3NRP9wVnxkOOd2baVBl544uZeMYUXF08/tFpr3GpYtSA+hoBaau3fvpkqVKri4uGBubs7AgQM5evSolPN47D0EIUSepmnvAjsAU+A3IcQlTdO+Jd+oYSP5Q0R2wKobP8yrQgg5JTgfEwsPhnAtJYt5LzXGRMKFjNjL4L0Imo4C13sXh5s3bx5Tp07lrbfe4pNPPnmgnBCCqd5TcbZ25jVPOa5giatWkRMcjPv8n6R4HaQnZXN6RxjVmrhSvrqj/gDJ9zowt7SizQuP5jWtUOihKC00K1WqxPHjx8nIyMDa2po9e/bQrFkzXfHf4n7OOSX9UZyOadeSM0XtL7eJt5b7yBP980UhvnMTIjXmnof/+usvoWma6Nu3r8jNzX2o3LaQbcLzD0+x5vIaKeHlJSeLgFatRegrI6S5v+1e4ivmv7NXJMVkSNELPX9GTBvSW5xYv0qKnuLJoCQ4pgUFBYnOnTuLevXqia5du4qoqKhC6WzZskXUqFFDVK1aVUyaNOmOY7169RKRkZFCCCG++uorUatWLVGvXj0xfPhwkZWVdU+9R3VMK/YLe2EfxZkQJqw6K2p8sVWExqXJEQzaL8TXpYQ4NOOeh7dv3y7MzMxE+/btRUbGwy+eWXlZosfqHmLghoEiz5AnJcRrU6YI39p1RMbFi1L0YsJSxLw394jDq69I0TMY8sSSCe+KX995TeRmZ0vRVDwZlISEcDtPsoVmiVpl9CRwKSqZVaciGNXWg8pOtvoFjQbYOREcKkHLf6/aOXHiBAMHDqRevXps3LgR6wLUC/rT708i0yL5uNnHmEpYcpkTEUHi0mU49O+P9QNWNBUUIQRH1lzBysacZr3kbEq/dGAPsWEhtHtpJGYW+vcxKBSF4Um30FR+CI+AEILvtvjhaG3OO53k1Nrh3Aq4dgEG/wbmd+5j8PX1xcvLi/Lly7N9+/YCrW9OyEpg4fmFdHDvQOsKraWEGDN9OpiZ4TJ+nBS90AvxRAYk0X5oTSxt9M9F5GRlcmTlMsrXqEWt1u0kRKhQFI4+ffrQp0+f4g6j0KgewiOwxy+Go0HxjO9aEwdrGV4HabDnf+DeHOoNvOPQ1atX6dGjBxYWFuzcuZNy5Qq2Smj+2flk5mXyYTNJXgenz5C6bTtOo0djXlb/slCD4YbXQTkb6raTszrLe+Ma0pMS6ThirPI6UCh0oBJCAck1GPl+qx9VXWx5qaWk5YxH50DaNejxwx1eB7GxsXTv3p3U1FR27Nhxa+fiwwhKCmL15dUMqTWEqg766wHlex38iJmrK06vvapbD+DSwUiSrmfQZlB1TGV4HcTF4rNpHbXatKdCTUn+1QrFM4pKCAXkrxNXCY5LZ6JXHcyleB1EwpE5+T2Div9fHC4pKYlevXoRFhbGpk2baNCgQYElp/tMx8bMhrcaytlBnLJ1G1nnz+MyfjwmNvqLw2Wl53JycwjutUtT2VOO18GRlUsRwki7YSOl6CkUzzIqIRSA5IxcZu2+TNvqTnSuLamm/t5JIIzQ9b+33kpJSaFnz56cP3+eNWvW0K5dwcfDj0Yd5VDkIV5v8DqlrUrrDs+YlUXMjOlY1q2DQ/+HW3cWBJ9toWRn5NF2cHUpQzvXgq7ge2gfTbz64eAqZ5ezQvEsoxJCAZi37wpJmblM9KorZ4w66gyc+wtavQWl81fZpKWl4eXlxalTp1i1ahVeXl4FljMYDUzzmYabnRsv1ZGzISth6TLyoqIp+4kcr4Pk2Awu7IugTpvyOLvfv4JrQRFCcGDZYqxLOdCy/wu69RQKhUoIDyUsPp0/jobyQlN36laQ5XXwJdg4Q7v8id+MjAyef/55jh8/zooVK+jX79HuyNcHrudK4hU+bPohFqYSSkfHxRG/YAF2Xbpg2+pBhWkLzrG1QZiYmdCyrxyvg0DvY0T4XaTtkJextJGw/FehUKiE8DB+3OaPuakJH3WXZM7uvwXCDkOnL8DKgaysLPr168fBgwdZunQpgwc/mrNXem46c8/MpbFrY7pVllP3P3buPIzZ2dK8DqKuJBF0JpamPSph62CpW8+Ql8vB5b/j5F6J+p17SIhQoVCASggPxDs0gW0Xr/Fmh2qULSXD6yAHdv0HXGpDk5FkZmYyYMAA9uzZw2+//cZLLz36cM/iC4uJz4pnQrMJcrwOLl8madUqSg8bhmUV/SW9hVFwZPUVbB0tadhVzuqsszu2kHQ9mg6vjMbEVHkdKBSyUAnhPhiNgkmbfSlXyoqx7eQMc+CzGBKCofskUjMy8fLyYseOHSxcuJCRIx99lcy19Gss9V2KVxUv6rvUlxJizJSpmNjZSfM6uOx9nZiwVFr3r4q5BK+DzLRUjq9ZSeUGjanSqKmECBUKOciw0HzttddwdXXF09Pzge0KarX5qKiEcB82noviXEQyn/SshbWECxkZCbD/R6jWmSTnZnTv3p1Dhw6xbNkyRo8uXN3+2adnAzC+yXj98QFphw6Rfvgwzm+/hVlp/SuVcnMMHF8fhEsle2q20F9+G+D46hVkZ2QorwNFiUOvhSbAqFGj2L59+wPbFNRqszCo0hX3IDPHwOTt/tR3c6B/o3/XIy8UB6dCdgqxTT6ke+fOXLp0iVWrVjFgwIBCyV2Mu8jm4M2MrT+W8nbldYcn8vKImTIF88qVKFOIoat7cW53OGmJ2XR7ra4Ur4OEqEjO7txC/c7dcankoT9AxVPHvj9+JSYsWKqma+WqdBr1+kPb6bXQBGjfvj2hoaEPbPMoVpuPikoI92Dx4WCik7OY9WIjOV4HcYFw8lfC3PvTc/DrhIaGsnHjRnr27FkoOXHD66CMVRlG15dzp5y0eg3ZVwJxmzsHTUJxuPTkbE7tCKNqYxcq1NDf2wA4+OfvmJpb0GbIy1L0FAqZvPfeewwePBhTU1N+/vnnO+YE27VrR2pq6r8+M23atEcuhHcvq80TJ04UPvDbUAnhLmJSs5i/P4ge9crSsqqc3bTs/prT103oPX8rWdk57Nixg/bt2xde7upuTsec5uvWX2Nrrn/JpSEtjdg5c7Bp1gx7SVUaT24MxphnpPWAalL0rl48T5DPcZ4bOgJbRzkJRvH0UZA7+cdBUVpoPk5UQriLmbsuk2sw8lmvOnIEQw+zbdM6XlhnwMmlHHv27tPVtcsx5DDDZwbVHaszoHrhhpvuJn7BrxgSEnBdsEDKSqW4iFR8j0bTsHNFHF31l7wQRiMHli3G3tmFJr3l7JpWKGRyu4XmvZDZQyio1WZhUAnhNvyiU/jbO5xX21ahirMMrwMjC798lbdWZtKgQUO2bN1G+fL6xvtX+K8gIi2CBV0XSPI6iCRhyRIc+vXFuv6DVzYUBCEER1YHYmljRjMvD916AL6H9hETGoTXex9jbqF/H4NCIRsZFpoFpaBWm4VBrTK6wU2vg1LW5rzfuYZuvdzcXN57qRev/xlI9zaNOXjosO5kkJiVyIJzC3jO7TnauLXRHSNA7MyZYGKCy/jxUvTCLsYT4Z9I895VsLLVXyI8NyuLwyuWUK56TWq3Kfwwm0LxOJkwYQK7du3C09OTbt26ER0dXSidYcOG0bp1awICAnB3d2fx4sW3jnl5eREVFYWZmRnz5s2jR48e1KlThyFDhlBPgnEVqB7CLfYHxHI4MI6v+tTFQadpy/Xr13lh8EAOHT7KR90q8uPm41JcvH459wsZeRl83Oxj3VoAmWfPkrJlC85vv4W5zmQF/+914FjWBs8Ocrqw3pvWkpaYQJ/xn0mpqaRQPA6qVq3Knj17ABg5ciSnT5+md+/ej6yzYsWK+x7bunXrredeXl6PVO+soKi/MCDPYOS7rX5UcbZleCt9lo4HDhygadOm+Hh78+dAa6Yt+kdKMghODubvgL8ZXHMw1Rz1T9QKIbj+42RMXZxxKuQ+iLvxPRRF4rUM2gysJsXrIDUhDu9Na6jZ6jncautfUqdQPG6edAtNlRCAFd7hBMak8Xmv2liYFe5HkpeXx1dffUXnzp2xsbLk6JhSvPTiYKjUSkqMM31mYmVmJc3rIHX7djLPnsV13DhMbPXPl2Rn5HsduNV0xKOBs4QI4cjK5QiDgXYvjZKip1A8bvr06cPq1auxtHwy57qe+SGjlKxcZu66TKuqZehWt3A19S9fvsyrr77K0aNHGTVqFHN7mGN3Zd0dXgd6OBF9gv0R+xnfZDxO1vqXwhqzs4mZNh3LWrVwKOTGuLs5tS2MrPRc2g6uIWWl0vWQIC4d3EOzPgNwLCtnl7NCoXgwz3xC+GlfIIkZOXzZ+9G9DnJzc5k2bRrffPMN1tbW/Pnnn7zUyRMWtIc270IZ/TWQbnodVLCtwPC6w3XrASQuX05uZCSVfluMJqE4XEpcJuf2hVO7VTlcKsnzOrCys6flgCG69RQKRcF4poeMwhMy+P1wKAMbu+Pp9mjbzQ8cOEDz5s354osveP755/Hz8+OlYcNg50SwLg3t5Ez8bgzaiH+CPx80/QBLU/3d0LyEBOJ+/gW7jh2xbSNnpdKxdUGYmGi07CtnE1rQqZOEXzpPmxdewsrWToqmQqF4OM90Qvhxuz8mJjChR8G9DgICAujXrx8dO3YkISGBtWvXsmrVKsqVKweXt0PIwXyvA2tH3fFl5GYw98xcGrg0oIeHnLr/cfPmYczMxPWTCVL0ooOSCTwVQ+PulbErLcvrYDFlKrjToEvhSnsoFIrC8cwmhFNhiWw5H80b7atRzuHhXgfnzp3j5Zdfpl69euzbt4/vv/+egICA/y9OZ8iFnV+Cc01oOkpKjL9f+p3YzFg+af6JlHH57MBAEv/+h9JDh2JZVf9wljAKDq+6gq2DBY27yfE6OLdrG4nRUXR4ZTSmZs/8iKZCUaQ8k39xQgj+t9kXV3tL3uhw/wtjdnY2mzdvZuHChezYsQM7OzvGjRvHp59+iqur652NfX6D+EAY9jeY6t+QdS39Gn9c/IOeHj1p6NJQtx7A9alTMbGxwfndd6ToXTl1nZjQFDqPqIO5pf65iKy0NI6tXkElz4ZUadxMQoQKheJRKJKEoGlaT2A2YAosEkL8eNdxS2Ap0BSIB14UQoQ+rng2nY/mbHgSUwc3wMbizh9BSkoKBw4cYPPmzfzzzz8kJSVRvnx5vv/+e958801K38snIDMx3+ugSgeoKWdoZ+6ZuRiFkfFNx0vRSztyhPQDB3GdMEGK10FejoFj64JwrmhH7VaSvA7WriQrPY0Or4yW0iNSKBSPxmNPCJqmmQI/Ad2ACMBb07SNQojbHR1GA4lCiOqapg0FJgMvPo54UtIzmbTqOB4WOVTVYtm50w9/f3/8/f05c+YM3t7eGAwGbGxsGDBgACNGjKBLly6YPmg1zsFp+Umhx3cg4UJ2Kf4SG4M28prna7jZ6d/xKwwGYiZPwdzdndKvyFmpdG5vOGkJ2XQZKcfrIPFaFGe2b8azYzdcPSQ51CkUikeiKHoILYBAIUQwgKZpK4F+wO0JoR/w3xvPVwPzNE3ThBBCdjAjPvgK74XTAGj2v/9/39HREU9PTz7//HO6dOlC69atC7a5JCEYTiyAxsOhnH4bSyEE07ynUcaqDGPqj9GtB5C0di3Zly/jNmsWJhJ2TWek5HBqexhVGjrjXktOKepDf/6BqZkZbV+Uk7AUiuLgo48+Yvfu3bRo0YLLly+zd+9eTE1N+eWXXzh37hw///wzAF9++SVhYWEsXryYrl27snfvXsxKwJxZUUTgBoTf9joCaHm/NkKIPE3TkgEnIO72RpqmvQ68DlCpUuEmMccO7Y+1rS1eTaphb29PmTJlqFmzJmXLli3cMMWur8HUAjp/Wah47mZv+F58rvvwn1b/wd5C/5p+Q1o6sbPnYN2kCfY9ukuIEE5uCsaQY6TNwOpS9CJ8L3Ll5FHaDhmOXekyUjQViqImKCiII0eOcO7cOX766Sc8PT1vjSyMGDGCWrVq8cMPP3D48GG2bNnC0aNHsbCwoEuXLvz999+8/HLxGz8Vf0p6BIQQvwK/AjRr1qxQvYfendvSu3NbOQGFHQW/jdBpItjrH0fPNeQyw2cG1RyqMbDGQAkBQvyihRji4ig7/ycp4/LxkWn4Ho6ifkd3HMvK8TrYv2wRdk7ONO3TX7ee4tlm/PjxnD17Vqpmo0aNmDVr1gPbBAQE0LVrV/Ly8mjcuDEA69atu3XcxsaGYcOGMXHiRLZt28auXbuwtrYGoH///nz++efPTEKIBCre9tr9xnv3ahOhaZoZ4ED+5HLJxWiEHRPBvgK0fleK5MqAlVxNvcr8LvMxM9H/1eRGR5Pw+x+U6tMH6wYNJEQIR9cEYmFtRvPeVaTo+R05wPXgQHq98yHmlg9f/qtQlERq1arFyJEj8fDwYMSIEVSqVAkPD4872rz22mvUqVOHDRs2UK3a/2/i9PT0xNvbu4gjvjdFkRC8gRqaplUh/8I/FLjbxX0jMBI4BgwG9j6O+QOpXFwNUadhwAKw0H+nnJydzC/nfqFNhTY85/achAAhZuZMAFw//ECKXtileK76JtB2cHWs7CR4HWRncWjFEspWrU6d5zrqD1DxzPOwO/nHyYULF+jXrx9xcXE4Ojr+6/i3336Li4sLeXl5d7xvamqKhYUFqamp2NvrHybWw2PfmCaEyAPeBXYAfsA/QohLmqZ9q2la3xvNFgNOmqYFAh8Cnz3uuHSRkwG7/wvlG0F9ObV2fjn3C2m5aXzU7CMpQzuZFy6QsnETZUaNwrxCBd16xhteBw4u1tTv6K5bD+DU5vWkxcfR8ZUxyutA8cRz6dIlPD09sba2Jisr645j06dPJysri3/++YfZs2f/67PZ2dlYWRV/D7lI5hCEEFuBrXe999Vtz7OAF4oiFikc/wlSImHgQpBwIQtNDmWl/0oG1hhIzdI1devd8jpwcsJp7FjdegC+R6JJiEqn1xv1MS1kifDbSUtM4OSG1dRo0Qb3uvqtOxWK4iQ1NRVzc3Osra2xtrbGYDCQlZWFlZUVe/fu5ffff+fYsWPY29uTkpLC2bNnadSoEQDx8fE4Oztjbq6/160XdVv2qKReh0Mzoc7z4CFncnrmqZlYmFrwTiM5O4hTd+4i89QpXMa9j6mdfq+DnMw8Tm4KpkINR6o0kuR18PdyDHl5tHt5lBQ9haI4uXjxIp6e/39j0717dw4fPszVq1cZM2YMq1atujUcNG7cuDuGtvbt21cod7XHgUoIj8q+SWDIga7fSJHzvubN3vC9jKk/Bmdr/RdbY04OMdOmYVmjBo6DBkmIEE5tDyMzNZe2g6tLGc6KCQ3m4v5dNO7Zm9Ll9A9nKRTFTevWrVm1atWt1++88w5LliyhUqVKBAcHU6dOnVvHRo0axR9//HHr9V9//cUbb7xRlOHelydq2Wmxc+0inFkOLd8CJ/2lno3CyFTvqZSzLccrdV+RECAk/vkXueHhVFy0SI7XQXwm5/aEU6tlOVwrl9Ktd8vrwNaOVgOH6dZTKEoiTZo0oVOnThgMhgdWOcjJyaF///7UrKl/qFgGqodQUITI9zqwcoAOckpHbw7ejF+CH+ObjMfKTP+EUl5iInHz52Pbvh12z8kZzjq+PhhNg5b95JSTCDnjw9WL52g9eBhWdsrrQPH08tprrz245A1gYWHBiBEjiiiih6MSQkG5sguC90OHz/INcHSSkZvB7NOzqe9cn15VeumPD4j7aT7GjAzKfvKJFL1rwclc8b5Oo26VsC+jP2EZ8vI4sGwxpcu70bCbl4QIFQqFTFRCKAiG3PzegVN1aD5aiuQS3yXEZMQwofkETDT9X0N2cDCJK1bgOOQFLKvrLykhhODI6ivYlLKgcXc5Xgfn92wnISqC9sNfU14HCqmU9G1LxUFhfiYqIRSEU39A3GXo9q0Ur4OYjBh+v/g73Sp3o7FrY/3xATFTp2FiZYXLu3J2TQeeiuFacAot+1XFwkr/xTsrPY2jq/6iYt36VGvaQkKECkU+VlZWxMfHq6RwG0II4uPjH3lvg7pNexhZybD/B/BoB7XkDHPMOzOPPGMeHzSRs4M4/fhx0vbtw+WjDzFzctKtl5dr4Pj6IJzc7KjduryECOHEun/ISktVXgcK6bi7uxMREUFsbGxxh1KisLKywt390TaRqoTwMA5Nh4wE6D5JiteBf4I/6wPXM7LeSCqWqvjwDzwEYTBwffIUzCtUoIykyanz+yJIicui77hGmEjwOki6fo0z2zZSr30XylaVUyFVobiJubk5VarIqa31rKOGjB5EYigc/xkavQQVGumWu+l14GDpwNgGcnYQJ6/fQLafH64ff4RJQfwbHkJmag6ntobiUd+JinXklKI+9NcfaKamtB2qvA4UipKMSggPYvd/wcRMmtfBgYgDnLh2grcbvU0pC/1r+o3p6cTOmoV1w4bY95KzUunk5hByc4y0GSTnTj7S35fLxw/T/PlB2JeRs8tZoVA8HlRCuB9XT8ClddDmfSilfzdtrjGX6T7T8SjlweCagyUECPGLfyMvNhbXzz6VMi6fEJ3OpUNReLarQOly+kte3PI6KF2G5s/L8XdQKBSPD+1JnZnXNC0WCCvkx525y43tCUadS8lEnUvJRJ0LVBZCuNzrwBObEPSgaZqPEKJZccchA3UuJRN1LiUTdS4PRg0ZKRQKhQJQCUGhUCgUN3hWE8KvxR2ARNS5lEzUuZRM1Lk8gGdyDkGhUCgU/+ZZ7SEoFAqF4i5UQlAoFAoF8JQnBE3TemqaFqBpWqCmaZ/d47ilpml/3zh+QtM0j2IIs0AU4FxGaZoWq2na2RuPMcUR58PQNO03TdNiNE27eJ/jmqZpc26c53lN05oUdYwFpQDn0lHTtOTbvpOvijrGgqJpWkVN0/ZpmuaradolTdPG3aPNE/HdFPBcnojvRtM0K03TTmqadu7GufzLu1fqdUwI8VQ+AFMgCKgKWADngLp3tXkb+OXG86HA38Udt45zGQXMK+5YC3Au7YEmwMX7HPcCtgEa0Ao4Udwx6ziXjsDm4o6zgOdSHmhy47k9cPkev2NPxHdTwHN5Ir6bGz9ruxvPzYETQKu72ki7jj3NPYQWQKAQIlgIkQOsBPrd1aYfsOTG89VAF61k1mYuyLk8EQghDgIJD2jSD1gq8jkOOGqaJqcGt2QKcC5PDEKIaCHE6RvPUwE/wO2uZk/Ed1PAc3kiuPGzTrvx0vzG4+6VQNKuY09zQnADwm97HcG/fylutRFC5AHJgH5DAfkU5FwABt3oyq/WNE1/be3ioaDn+qTQ+kZ3f5umafWKO5iCcGPIoTH5d6O388R9Nw84F3hCvhtN00w1TTsLxAC7hBD3/V70Xsee5oTwrLEJ8BBCNAB28f93DIri4zT5dWMaAnOB9cUbzsPRNM0OWAOMF0KkFHc8enjIuTwx340QwiCEaAS4Ay00TfN8XP/X05wQIoHb75Ldb7x3zzaappkBDkB8kUT3aDz0XIQQ8UKI7BsvFwFNiyg22RTke3siEEKk3OzuCyG2AuaappXYGuCappmTfwH9Uwix9h5Nnpjv5mHn8qR9NwBCiCRgH9DzrkPSrmNPc0LwBmpomlZF0zQL8idbNt7VZiMw8sbzwcBecWNmpoTx0HO5ayy3L/njpk8iG4ERN1a0tAKShRDRxR1UYdA0rdzNsVxN01qQ//dWEm84uBHnYsBPCDHjPs2eiO+mIOfypHw3mqa5aJrmeOO5NdAN8L+rmbTr2FNroSmEyNM07V1gB/mrdH4TQlzSNO1bwEcIsZH8X5plmqYFkj85OLT4Ir4/BTyX9zVN6wvkkX8uo4ot4AegadoK8ld4OGuaFgF8Tf5EGUKIX4Ct5K9mCQQygFeLJ9KHU4BzGQy8pWlaHpAJDC2hNxwAbYFXgAs3xqsBvgAqwRP33RTkXJ6U76Y8sETTNFPyk9Y/QojNj+s6pkpXKBQKhQJ4uoeMFAqFQvEIqISgUCgUCkAlBIVCoVDcQCUEhUKhUAAqISgUCoXiBiohKBQKhQJQCUGhUCgUN1AJQaGQhKZpb2qa9vNtrydpmrasOGNSKB4FtTFNoZCEpmk2QABQH3gO+B/QRgiRWayBKRQFRCUEhUIimqZNAWyBXkA3IURQMYekUBQYlRAUColomlab/MKC/W7UmVEonhjUHIJCIZevgFie4sKRiqcXlRAUCklomvYRYAUMAf5l7K5QlHTUXYxCIQFN0zqTXw66tRAiVdO0UpqmNRJCnC3m0BSKAqN6CAqFTjRNq0S+S90LN0zdAWYD44stKIWiEKhJZYVCoVAAqoegUCgUihuohKBQKBQKQCUEhUKhUNxAJQSFQqFQACohKBQKheIGKiEoFAqFAlAJQaFQKBQ3+D+pzaxEC+f+HgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"gam = 1.0 # keep gamma fixed\n",
"xi_list = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0] # vary xi\n",
"\n",
"plt.figure()\n",
"for xi in xi_list:\n",
" y_array = func1(x_array, gam, xi)\n",
" plt.plot(x_array, y_array, label=r'$\\xi=%.1f$' % xi) # plot straight lines\n",
"plt.plot(x_array, f_array, 'k', label=r'$f(X)$') # plot Hill function\n",
"plt.ylim(-0.1, 1.1)\n",
"plt.xlabel(r'$X$')\n",
"plt.ylabel(r'$Y$')\n",
"plt.title(r'$\\gamma = 1$')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"source": [
"For all values of $\\xi$, there is only one solution, which will be the stable steady state of the system. As $\\xi$ increases, the solution moves up the plateau quickly, indicating a sharp transition."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"To visualize the transition, we would like to plot the solution as a function of $\\xi$. For that, we need to find the solution numerically for a given set of parameters. This can be done using the `scipy.optimize.root` function. We have already defined the time derivatives in our function `equations` above."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"import scipy.optimize as opt"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"xi = 0.200, steady state: Xs = 0.266, Ys = 0.066\r"
]
}
],
"source": [
"xi = 0.2\n",
"\n",
"x0 = [0.5, 0.5] # initial guess of solution, 2-d vector (X0,Y0)\n",
"sol = opt.root(equations, x0, args=(0, gam, xi, K, n)) # find root of equations(x)==0 with initial guess x0\n",
"Xs, Ys = sol.x # unpack solution vector (Xs,Ys)\n",
"print(f'xi = {xi:.3f}, steady state: Xs = {Xs:.3f}, Ys = {Ys:.3f}', end='\\r')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"Now we can find the solution for different values of $\\xi$ by repeating the steps above. Then we can plot the equilibrium value of $Y$ as a function of $\\xi$."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"xi = 2.950, steady state: Xs = 3.888, Ys = 0.938\r"
]
}
],
"source": [
"xi_list = np.arange(0, 3, 0.05) # list of xi values\n",
"Xs_list = [] # steady state of X for each value of xi\n",
"Ys_list = [] # steady state of Y for each value of xi\n",
"\n",
"for xi in xi_list:\n",
" x0 = [0.5, 0.5] # initial guess of solution, 2-d vector (X0,Y0)\n",
" sol = opt.root(equations, x0, args=(0, gam, xi, K, n)) # finding root of equations(x)==0 with initial guess x0\n",
" Xs, Ys = sol.x # unpack solution vector (Xs,Ys)\n",
" print(f'xi = {xi:.3f}, steady state: Xs = {Xs:.3f}, Ys = {Ys:.3f}', end='\\r')\n",
" Xs_list.append(Xs)\n",
" Ys_list.append(Ys)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"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(xi_list, Ys_list)\n",
"plt.ylim(-0.1, 1.1)\n",
"plt.xlabel(r'$\\xi$')\n",
"plt.ylabel(r'$Y_s$')\n",
"plt.title(r'$\\gamma = 1$')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"We see that the steady state of $Y$ turns \"on\" sharply near a value $\\xi \\approx 0.5$. That means, if the external source is below this threshold, the *lac* genes are largely off; yet when the external source crosses the threshold, the expression of the *lac* genes will be induced. In the latter case, the expression level quickly saturates as a result of the positive feedback. Therefore we observe an almost \"all-or-none\" response."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
},
"tags": []
},
"source": [
"## Stability of steady states"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"By definition, a steady state is such that the time derivatives of the dynamical system vanish. Therefore, once the system is at such a state *exactly*, it will never change. However, this does not necessarily mean that the steady state is *stable*. A steady state is stable if the system perturbed away from the state will return to it; otherwise, the steady state is unstable. Therefore, to check if a steady state is stable or not, we need to examine the *dynamics* of the system, not just the stationary solutions that we studied above."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"source": [
"The stability of a steady state can be analyzed by expanding the dynamical equations around the steady state (we will do this in class). Alternatively, we may solve the dynamical equations numerically and see where the trajectories flow starting from various initial states. If trajectories converge to certain points as time goes to infinity, these points will be stable steady states."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"Let us use this method to check the stability of the steady states found above using the graphical method. To solve the dynamical equations, we may use the `scipy.integrate.odeint` function that we used for solving rate equations before. Let us look at an example where $\\xi = 0.2$, which is below the threshold, so we expect the genes to be off."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"import scipy.integrate as intgr"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"outputs": [],
"source": [
"gam = 1.\n",
"xi = 0.2\n",
"\n",
"num = 10 # number of trajectories to test\n",
"X_init = np.random.rand(num) * 3 # random initial values for X between 0 and 3\n",
"Y_init = np.random.rand(num) * 1 # random initial values for Y between 0 and 1\n",
"traj_list = []\n",
"\n",
"T = 50. # total time to integrate the trajectory\n",
"time_points = np.arange(0, T, 0.1) # time points to evaluate solutions\n",
"\n",
"for i in range(num):\n",
" X0, Y0 = X_init[i], Y_init[i] # initial values\n",
" traj = intgr.odeint(equations, [X0, Y0], time_points, args=(gam, xi, K, n))\n",
" traj_list.append(traj)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x_array = np.arange(0, 3, 0.01)\n",
"y_array = func1(x_array, gam, xi)\n",
"f_array = func2(x_array, K, n)\n",
"\n",
"plt.figure()\n",
"plt.plot(x_array, y_array, 'k--', lw=1, label=r'$\\gamma X - \\xi$') # plot straight line\n",
"plt.plot(x_array, f_array, 'k-', lw=1, label=r'$f(X)$') # plot Hill function\n",
"for traj in traj_list:\n",
" plt.plot(traj[:,0], traj[:,1]) # plot trajectory\n",
" plt.plot([traj[0,0]], [traj[0,1]], 'b^') # blue triangle marks initial state\n",
" plt.plot([traj[-1,0]], [traj[-1,1]], 'rx') # red X marks final state\n",
"plt.xlim(0, 3)\n",
"plt.ylim(0, 1)\n",
"plt.xlabel(r'$X$')\n",
"plt.ylabel(r'$Y$')\n",
"plt.title(r'$\\gamma = %.1f$, $\\xi = %.1f$' % (gam, xi))\n",
"plt.legend(loc='lower right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"We see that, no matter where the trajectories start, they all converge to the same point --- the steady state we found above using the graphical method (intersection of the black curves). It confirms that, in this case where only one steady state exists, the steady state is stable."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
},
"tags": []
},
"source": [
"## Bistability"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"Let us now look at the case where $\\xi = 0$ and $\\gamma < 0.5$, e.g., $\\gamma = 0.4$. According to the graphical solution above, we now have three steady states. It turns out that the one at the origin and the one on the plateau are stable, but the one in the middle is unstable --- with any small perturbation the system will leave that state and go to either of the other two steady states. The existence of two stable steady states in a dynamical system is called \"bistability\"."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"Let us make a similar plot of trajectories to visualize this bistable case."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"outputs": [],
"source": [
"gam = 0.4\n",
"xi = 0\n",
"\n",
"num = 20 # number of trajectories to test\n",
"X_init = np.random.rand(num) * 3 # random initial values for X between 0 and 3\n",
"Y_init = np.random.rand(num) * 1 # random initial values for Y between 0 and 1\n",
"traj_list = []\n",
"\n",
"T = 50. # total time to integrate the trajectory\n",
"time_points = np.arange(0, T, 0.1) # time points to evaluate solutions\n",
"\n",
"for i in range(num):\n",
" X0, Y0 = X_init[i], Y_init[i] # initial values\n",
" traj = intgr.odeint(equations, [X0, Y0], time_points, args=(gam, xi, K, n))\n",
" traj_list.append(traj)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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zh6MoRjly5DXOnJ1Hp44rsLMLKXcfKSVfffUVw4YNw9nZudxEUKovZVvSNpYeX8qqU6soKC0g1DmUu5veTReXLuzeupv169ezefNmDhw4QLNmzejUqROdO3emU6dONGrU6LoZ5WNuapRRPRDaygOPwLJWQgdvtKqVoDQAISGTOJv0G8dPfEJki4+v2p6ZmcmECRM4ffo0AwYMuKwWkZSSg+kHWXp8KctPLCe9MB1HS0d6ePXA/Zw7CSsSeHvK2yQmJtKlSxe6d+/O//73P9q1a4edXe3NlFYqphJCHRFC0HFwI5Z+sY8jW5Np3sXP3CEpyjVZW3sRGDiOkye/Ijj4QRwdIi5uKy0tpUuXLvTu3Zt58+ZhbW0NwPHM4yw7sYzlJ5ZzKucUFsKCUH0oLgdd2L94P7MyZtGtWzd69OjBxAcmEhUVZdQIJKX2qVehDgW3dMcr2JGdSxNo2tEHrYVqJSj1X3DQRBITf+TUqW9p0fx/SClZt24dPXv2ZOnSpYSEhJCUm8TyuOUsP7GcwxmHEQics5wp3VBKytYUwm8Kp2fPnrz1x1s0a9aswZV0uFGohFCHhBB0uK0RSz7by6HNSUR29zd3SIpyTZaWzvj43EFS0nx8vCfzyCPPc+TIEf5a9RfbCrfxyrJX2J1qGGutSdGQviGd5prm3Nr1Vvq81IdWrVqpBNBA1ElCEEL0Az4BtMC3Usp3r9geBPwAuJTt84KUclldxFbXgpq74dPIiZjlCTTr7IvWUr1RlHrqQieulPj5DefMmbk4eYXwsx7GLRrDwL8Gohd6ipOKsUuwo7t3d4b0GMJNj92EjY2NeWNXqqTWE4IQQgvMAPoCicAOIcSfUsrYS3Z7GZgvpZwphGgOLANCajs2cxBC0GFwI/78ZA+xm87Ssmfdr1ClKKYosLTglwWjuHVGChZ6ONHbnrjT23FP82NI2BBG3T/qhi/5cL2oixZCByBeSnkcQAjxCzAEuDQhSODCoGJn4GwdxGU2ARGu+DZxNrQSbvLFwkpNoVfqn/c++QGbXZsY88evRH6yl6B/8zgxzInjk7x5W2NJZIsX8fTsa+4wlRpUFwnBHzh9ye+JQMcr9nkN+EcIMRmwB/qUdyAhxERgIkBQUFCNB1pXLow4WvTxbg5uOEur3oHmDklRAFizZiMLD55lW4AXp1tGISIj8T93mjuXL0cCjRZk4VtwhgMHHmXf/oeJiHgLf7+7zR22UkPqyw3skcBsKWUAMAD4UYirV9GWUn4tpYyWUkZXtvZqQ+Df1BX/pi7ErDhJSbHO3OEoN7CTJ0/y0tvfcOfspUwotWJBZDi5Vpb0OxLPyol3MWz5cqCsCpcQ2Nr607btPNzdunH48BRSUpaYNX6l5tRFC+EMcOlX4ICyxy51H9APQEq5RQhhA3gA5+ogPrPpMKgRf3y4iwPrztCmb8Nt8SgNz+nTp/l+9s8kOoazP9CZhM7t0ej1NEtNo93pM2jT43jzvXfQABkOdrjn5P3XySwEWilp2fIL9uwZz8HYp9Fq7fHwuNms16RUX120EHYAYUKIUCGEFTAC+POKfU4BvQGEEM0AGyC1DmIzK78wFwKbubL7n5MUF5aaOxzlOpeWlsbMmTMZ/+jrPPHPfua078FfrUJJt7Olf9xxXo/bS+rbz3BmzyqmvPwSWiDLzobZA3uRfuY0XFHmRqu1pVWrb3BwaMqBg4+Rk3vYPBem1JhaTwhSylLgUWAFcAjDaKKDQog3hBC3le32NPCAEGIvMA8YJxtqkSUTdRjciIKcEvb/m2juUJTrUE5ODj/++CMDBgzglU//YqFzE1bcMZhNob745eTxwu5VbNP8y6wH7iAl7QyPPvooc+fOxcHBAaTEKikZC0srtv7+i+GAUl6WGCwsHGkV9Q0WWkf27ZtIcXG6ma5UqQmquF098Ndne0lJyGLsmzdhZavmCirVo9PpWL16NbNmzWLN2vXc/vwMdoW4cNrFBcvSUtqcTaNVTgZv6N5DOvgxeVcj7rnnHrp06VLu8Tb+Modtf8xn5LT/4RceUe4+2dn7iNk1AkfHlrRt8yMaTfmVThXzq6y4XX3pVL6hdRgcSlFeKfvWnr72zopSgWPHjjF16lRCQ0P56Isf0PQcjcv3v7G4dQhZ1tb0OnqGW04tZNZd7Zk2/hbE+QSm/32Ec+fOERkZWeFxO9w+HHtXN9b+8DXyyrVhyzg5RdGs2XtkZe3kyJFXaahfNG90KiHUA94hToREebBn1WmK8kvMHY7SgOTl5TFnzhx69uxJp06dKNC70f61r4h95AlWh/vjWFTM7ftOEXjmNXT+c5hx7yu427ojC7MAaNnxZubPn4+zs3OF57CysaXbyHtJjj/KoY3/Vrifj/dgQkIe4WzSfM6evfbiOEr9oxJCPdFhUChF+aXsXa1aCcq1xcbGMnnyZAIDA/n111/pO2wSnT6cyy83d2NTiA+NMrIYs+Mo//aIot3NKZyzOsu0LtPQ6DW89957FErDOsl9u3Uwap2B5t1uxqdxGBt+nk1xYUGF+zUKfRw3t24cjXud7JwDNXa9St1QCaGe8AxypFFrT/auPk1hnmolKFcrLi5m/vz59OzZk969e+Pq6srzH/xE6T2PM6N5E2L8PWmeksGYf7cyK9yVD567Cwc3N/5N/Jcojyissqzo2rUrW7ZsodjCCSztIOO4UecWGg09751I7vkMdixeUPF+QkuL5h9haenO/v2PUFKSVVOXr9QBlRDqkfaDQiku1LFn1Slzh6LUI6dPn2bq1KkEBwczc+ZMHnnkESa/OZv1LbrzcagPB73daJeYyr3LVzFi50JeeXw4oW3aXXx+3Pk4whzD6NSpEyNHjuSPP/7A2cUF/NrA6W1Gx+HftBkRXXqw48/fOZ905VSi/1hZudEy8jOKilKIjX0GKcvvd1DqH5UQ6hGPAAcat/Vi35pECnKKzR2OYmbbtm3jrrvuonXr1mRlZbF69Wr6j3mJL3SufNrIm+NuznRNSOGRtWkM2DSP0IJD3P3qOzi6/1doLqcgh4LSAgJcA9i5cydPPvnkf7eIgm+CpL1QmG10TD3H3o+FlTWrvptZacexs3Mbwpq8SFr6Gk6e/KrK/wZK3VIJoZ7pMDiU0mIdu1acNHcoihnodDoWLlxIly5dGDFiBF26dCEhIYGQdkOYvPcMH4V4EO/uTNfjSTz8TyZ3nHShU3gy+VlpDHj0aexdXC8e6/Tp09zS9xbDcfU6AgKuqKzbuBdIPcT9Y3R89i6udB0xllP793B48/pK9w0IGIu31yCOHf+IjPNbjP9HUMxGJYR6xs3XnqYdfdj/7xlyzxeaOxyljuTm5vLZZ58RHh7OBx98wJNPPklcXBwWnq0Y+tdWPgh046inKzedTGamsGTgUUcCbRwY/FgksRv+oUn7TgQ0+2/oaExMDO3bt+f2wbdjZ2FHVnE59/IDO4GjLxxYaFKsUX374dM4jH9/+IbCvNwK9xNCEBHxNnZ2oRw48DhFRSkmnUepeyoh1EPtB4UipWTHsgRzh6LUstTUVKZMmUJISAjr1q3jxx9/NHT6Wvoz6Jc1vOnjxCEvVzqdSmGm1oKF4/tjddKSovxS+j/UktSEgxTmZNOy162AYZ3j5ORkwsPDWbhwIc8//zweth4k5yVffXKNBlrcAfEroSDT6Jg1Gi197n+EguxsNv7yY6X7WljY07LlDHS6fA4cfBIpVSHH+kwlhHrIycOWFt38ObQpicxz+eYOR6kFZ8+e5amnnqJp06akp6ezbds2FixYQInWjWGzlvOsvRX7fN1pf/oc04slf4zrx6CbW5N6Ooe4HSm06h2Iu78DiYcOorWwIKhla86ePUvv3r15++23cXR05KabbgIg3DWcuPNx5QcSeSfoiuHA7ybF792oCW36DWLvymUkxR+pdF8H+zAimr5OZuY2EhJmmnQepW6phFBPtesfjFYr2P7XCXOHotSghIQEHn74YSIjI5FSsn//fr788kuEpQOjv17KvVnZbArxpdm5DF7PyOPPe/tx54D2F59/YN0ZLKy1tL01GICMM6dx8w9k/YYNtGvXjj59+vDxxx9fds4ItwhOZp8kq6ic20b+bcGnJez47qridddy012jcXBxZdU3X6DXVf7N38dnKN7et3Ei4VMys2JMOo9Sd1RCqKfsna2J6hVI3M4U0hIrvk+rNAwnTpxgwoQJtGvXDldXVw4fPszHH3+Mi4srE79YQr8Dx1gV5o9vTi6PHE9h1T19eWB498uOIfWSY7vP0aiVB9ZlNa/ysjKxc3ahtLSUuXPnMnXqVLTay1fga+/THolkR/KOqwMTAto/AOcOwinTOn6t7ey4edxEziUcY8+KytdEEEIQ0fQNrK39OHjwSUpKjB/ZpNQdlRDqsTa3BGFlY8G2P42bPKTUP2fPnmXSpElER0cTEBBAfHw8b7/9Nl5eXkz5chk3rdrJn80CsCnVMSr2DJvu6MnU+24t91gZyXkU5ZUSEOEGQEpKCnFHjpCUco5bbrmF3r17l/u8lh4tsbWwZWvS1vKDbDkcbJxh+zcmX19Yxy6Etm7Hxl/nkpORVum+FhaORLb4mKKiZA4fmaLqHdVDKiHUYzb2lrS5JYiEfWkkH1czPhuS1NRUnn76aSIjI7G3t+fw4cO88cYbuLq6MvePzfSet5LvmvqRZ2XJbYfOsLFnOz58ZCAaTcVvyfNJhv4kj0AH1q1bR7t27bCzd8DXx7vSWCy1lnT07ci/p/9FX94kMSs7aD0aDv0J2UkmXacQgl4THkbqdKyd/fU193d2bkOj0Cc5d24ZSUkVz3hWzEMlhBqWlAQ9ekByOYM6jNl+paibA7B1tGTromPqG1UDkJ2dzdSpU4mIiKCoqIgDBw7wwQcf4OnpyeH4RO76bhkvOFpx2NONrseTmB/kw9eTBuLkZHfNY+dlFgHg6GbD77//zrfffkujsCYUF1x74EHf4L6k5KdwIK2C+kId7jfMSdj6hUnXC+Di7UOnYSOI27aZ+B0VtEIuERw8EVeXThw5+jp5ecdMPp9Se1RCqGHTpsHGjYY/q7L9SlY2FrTrH8KZo5kkHj5fc4EqNaq0tJSZM2cSHh7OqVOniImJ4fPPP8fPz4/ioiImffEXg+NOs76RH2Fpmbx2Pp8F9/WnbYtQo8+RmWG473767Ek+/fRT+vXrh6O7Fzmp115ptkdADyyEBatOrip/B7dG0GIo7Pwe8jOMjumC6MFD8QwKYfV3X1CUn1fpvkJoad7iQ7RaGw4cfAK9vsjk8ym1QyWEGpSUBN9+L9HrYdasq1sBSUkwa9aF7dLoVkJkN38c3KxVK6EeklKyZMkSWrZsyYIFC1i+fDk//PADISEhAEyfu4quS7ewsFkgNiWljD10hrUj+vDA8G4mnWfTpk3MnGkYshkU+N/6206enuRmnqe0uPJSJ87WznT268yyE8vQ6SsYEdT1SSjOrVJfgtbCglsefIy8zEw2/PzDNfe3sfahWbP3yM2NJf7Y/0w+n1I7VEKoQdOmwYX1Q0p18qpWwLRpUFq2vURnfCtBa6mhw6BQzp3M4cSeyjvulLqze/duevfuzfPPP8+HH37IqlWraNOmDQCHjpxi2KzlvO/rxjkHO/odPsPqm6J4f9JAk89TUFDAxIkTGXzbIAA04r9RRB6BwSAlaaevXepkSJMhpOSnVNy57BMJ4f1h20woMn1km0+TcNoOGMzelctIPHzwmvt7evQmIGAMp09/T1r6vyafT6l5KiHUEMO3f9CVGAqHlRSLy1oJF7aXFhu2lxYLk1oJTTv64OJtx9Y/j6PXq1aCOaWmpnL//fczYMAA7r77bvbu3cuAAQMQQiCl5MmZSxhy7AybQnxpmZzGh1gw++GBeHlUvAhNec6fP8+bb76JtbU1+/bto22HVgDkZ/93i8W7URgAyccqmHh2iZsDb8bZ2plF8Ysq3qnb01BwHmJmmxTrBV3uGoOTpzcrv/rsmq0WgCaNX8TBvimxsc9SVJRapXMqNUclhBpyaevggktbCeVtN6WVoNFq6HhbI84n5RG33cgsotQonU7HjBkzaNGiBc7Ozhw5coQHH3wQCwvDnIAFf2+l5/zVzIsIwFKv457Ys/x9T1+G3dLW5HNt376dtm3bkpaWhk6nQ6vVYu9iWKc4L/O/D1onTy9sHZ1IPnb0mse00loxMHQgq0+tLn+SGkBgewjpBps/g1LT7+1b2tjQ9/5JZJxNZNui+dfcX6u1pkXkJ+h0+apUdj2gEkIN2bIFrvxCVFIs2Ly54u2lxYJNm43/tt+4jSeeQY5sX3ICXal649SlTZs2ER0dzYIFC1i7di0ffvghTk5OAGTm5DHm26U8aWHBMXcXesadZVGzJnz0yACjViO70oEDBxg0aBAffvgh06dPx9LSsLqZo5sNANnp/61YJoTAr2kzEmP3G9W/NDRsKCX6kmu3EnKTYdcck2MHCGndjubdbmb7ot9IPZVwzf0d7MMIC5tCxvmNnDr9XZXOqdQMlRBqyO7dhpn/F37eij+Lz5o9/LKxsNzti1LO471mD6/+nWn0OYRG0HFII7LTCondeLaWrkS5VEpKCvfeey933303zz//PGvWrKFFixYXt3/6y0p6rolhZWN/gs9n8fipbH6ZOICwxj4mnysrK4v169fTokUL9u3bx9ChQy/b7uxpi9ZSc9XM9eCoNpw+WUzXm4qveQuyqVtT2nq1Zd7heRV3LjfqCUE3wfoPoLhqtbR6jL0fazt7Vn71GfqKznMJf7+ReHreyrFj/yM7e1+VzqlUn0oIteTBQC9stRqmJ5T/Dh3s6UKEvQ0fJiSjM2HkUFBzN3ybOLNzWQIlxapyZG2RUvL999/TsmVLvLy8OHToECNGjLj4jf9sSgZ3f7+Mdz3dybaxZuC+RH7v2Z5nJ/Sq0vl27dpF27Zt+euvvxBC4ONzdULRaDW4+9mTdvryhBDSqi0rY0ewZZuVUbcgRzYbyZncM2w4s6H8HYSA3lMhNwV2mD7iCMDOyZmbx00kKf4Ie1Ysveb+QgiaRbyNlZUHBw4+QWmpKtdiDioh1BJ3Kwsm+Huw6FwmcXlXr2ugEYJnQnyIzy/ijxTj5xcIIeh0e2Pys4vZvzaxJkNWysTHx9O7d2+++OIL/vnnHz744AMcHR0vbn//xxXcsv0g60L9aJ6SxlPper57fBDenk5VOt+iRYu49dZbeeutt/jggw8q3dcjyJG00zmX3R4qlH7sTOiLlKLc4c5X6h3UGy87L34+9HPFOwXfBE36wMaPobBqs+QjuvQwlLWYN4dsI+ZKWFq60KL5xxQUnObI0deqdE6lelRCqEUPBXpho9Ew/WT5C4MM8HSmhYOhlVBqwsghvyYuBEe6s2vFSYoKSmsq3BteaWkp77//Pp06dWLQoEFs3bqV1q1bX9x+4sw5hv6wnI/9vSi0sKTf7kRm9b2JR+/pXKXz5eTkkJ6eTnR0NBs3bmTEiBHXfI5PqBNF+aVknP1v8te0aSDL3sq6coY7X8lSY8ld4XexJWkLx7MqqZPV62XDiKMtps9eBsOXlz73PwLAqm9nGNXH4eragdCQR0hO/oPk5MVVOq9SdSoh1CIPKwvG+3vwR8p54vMrbiWcKChmQYpps0M73taIovxStdRmDdm1axcdOnRg1apVbN++naeeeuri6CGAd35czoA9cWwO8qXVmVSGnSzi68cGEOjpUKXz7d+/n/bt2/Pzzz8TEBBA06ZNjXrehcJ2F2atXxzOrDPEWlxsXCvhzvA7sdJY8WNsJQvc+LWBZrfBls8hL92o+K7k5OlF15FjObEnhsOb1hn1nJCQR3F2bsfhI69QUHCqSudVqkYlhFr2cJAn1hoN0xPKbyX083CmpYMtHyekUGJCK8EzyJHwDt7sXX2anAy11GZVlZSU8Nprr9G/f3+eeOIJVqxYQaNGjS5uTzp3nrtmL+NTfx90QkPv7aeZHB7Bew/1wMqiam+fOXPm0KtXL6ZMmcLkyZNNeq6jmw3OnrYkHjZ8gShvOLPOiOHM7rbuDGkyhMXxi0nNr2T8/81ToCQfNn1c8T7X0PrWgfg2acra2V+Tn33t208ajQUtmn+MEKKstEVJlc+tmEYlhFrmaWXJOH93Fqac51g5rQQhBM+G+nCysJjfkk1sJQxpBBK2q/LYVRIbG0vnzp3Zvn07u3fvZuzYsZcNE/3y9zX027qf9cF+tExKxX9LBs+P7MbAjkGVHLVixWXjjm1sbFi3bh1jxoyp0nECIlw5E5eJXqcvdzhzcTEXhztXZlyLceikjrmH5la8k1cERN1tKGdhYiXUCzQaLbc8OJmi/DzWzfnWqOfY2voTEfE22dl7OX5iepXOq5hOJYQ6MCnIC2uNqLAvoa+7E60cbfn4ZArFV37dq4STuy1RvQI4vC2Z1FM5NRVujTG1smtd0ev1fPzxx3Tv3p0HHniApUuX4ufnd3F7fn4h4779i2kuzmRbW3PzrtNw2oKfnu5FVJBLlc556NAh2rRpw6ZNm7jrrrto3rx5leMPbOZGSaGOpGNZVw1nvvCze/e1jxPkFESfoD7MPzKfnOJK/v/0fAH0OsMw1CryCAqhw+3Did2wloQ9xq2Y5u01AD/fuzh58isyMjZV+dyK8VRCqAOeVpaM9fdgYcp5TuRfPfvT0Erw5XRhMb+a2Epo1y8YGztLNi+Mr3eF70yt7FoXEhIS6NWrF7///jvbtm3jwQcfvKxVMH/lNnot38LfjQNplJ5J4IZz5ODE/Me64udiW6Vzzp07l+7du/PUU09dXOe4OgKbu6G11HBsd/VLPUxoOYHckly+2bSk4uTtGgJtx8KuHyC96uWqO95xN25+Aaz8dgbFhQXXfgIQHj4VO7tGHIx9huLiqvVjKMark4QghOgnhDgihIgXQrxQwT53CSFihRAHhRCVjIdrmB4J9MJSVNxK6O3mSFsnO6YnpFBkQivB2s6S6IEhJB4+z6mDppctri1JSfBdJZVfzeGnn36iffv2DBgwgHXr1tG4ceOL26SUPPrNnzyDhjNOjtwWe5bkmAKcPVz46eGbcLGzqtI59Xo9q1atYvXq1dx3331Vmrl8JSsbC4Kau3F81zlkNetatXBvQSffTnz4jh0bN1YyQqnHc6C1hlWvVflcFpaW3PLgY2SnpbLh59lGPUertSOyxSeUlGRy6PCL9e5Lz/Wm1hOCEEILzAD6A82BkUKI5lfsEwa8CHSRUrYAnqjtuOqal7UlY/08WJCSQUJB+a2E50J9OFNUwrwk0z7YI7v74+xpy6bf49Hr6kdJi5emllJcVl7DmKGQtSkvL48JEybwxhtvsHLlSp577rnL1h3eFXuC/j+vZEGTILzy8nh523l2nBH4utnxwwMdcbazNPmcR48eZeDAgeTk5DB79myioqJq8pJo3NaLvKxiUhKqvzbxbZ4PkvTvrej1lYxQcvSBLo8bVlU7adray5fyj2hO236D2bNiKYmxFSzWc+WpHZvRpMlzpKWtJvFMJaOilGqrixZCByBeSnlcSlkM/AIMuWKfB4AZUsrzAFLKa89iaYAeCTK0Ej6poJXQw9WR9k72fHIyhUITPti1Fho639GY80l5HNpctY4/qLl7/klJ8MtPFqAzfOgWm1jZtSbt27eP6OhodDodMTExl80rkFLy7pzljD5+hj2+nnQ/eZZZOwW/FerRWWn4fnwH3OxNbxnMnz+frl27Mnjw4Iv1jmpaSJQHGq3g2K7qv1WWfd0OLYakV+kIpZseBUdf+GeKoaOiirqOGIuzlzcrvvqEkiLjRsgFBozD3f1m4uPfISf3cJXPrVSuLhKCP3D6kt8Tyx67VDgQLoTYJITYKoToV96BhBAThRA7hRA7U1MbXqlcb2tLRvu5Mz85g5OVtBKSikr4Kcm0+6WN2nji08iZ7X+doLiwapPVXnuuqPLbBkYqbyhkcYnkjTfqrrkvpeTLL7+kd+/evPjii/zwww84OPw3ZyA5I4f7vlnCZ/5eFFlYMOlUEtNPufKzhY740lI+GdGGJl6mzzE4c+YMb7zxBn///TcPPfRQjdwiKo+1rQWBzd04tiu1WrdRkpJg9mxBacmF5F3JLT4re+g1Fc7EwIHfq3xOSxsbbnnwcTKTk9g0/yejniOEoHmz97CwcObAgcfR6Yzrg1BMU186lS2AMKAnMBL4RgjhcuVOUsqvpZTRUspoT0/Puo2whjwa5I1FJa2Erq4OdHK259OTKRSY0EoQQtDlzibkZxezZ6Xpk3lObMzkh18sKr9tYKTyhkLqSjX8+U/dLJWYmZnJ8OHD+fLLL9m4cSNjx469bPtPq3Zz98ptLAsLJCQji589HJl43puD+lLmFRYwulMQN0d4mXTO48eP88EHH+Dv729Yu6Ct6SWvTRXWzoucjEKS4jOrfAyT5zG0GgHeLWHV61BS9fkvQZFRtOrbn11LF3P2qHHf+K2s3GnR/EPy849xNO7NKp9bqVhdJIQzQOAlvweUPXapROBPKWWJlPIEcBRDgrju+FhbMsrX0Eo4VUEr4dlQH1KKS5l71rRWgk8jZxq39WL3ylPkZZn24fv+T85Iafg2W917/lcOhdTpJE/P34vFnav5dkPtzpm4MAPY29ubrVu3XjYDOCu/hKdmLuK1kkLiPNzof+IMawZ3IfykFSUpeXzuqMfT0ZoX+jcz6Zx//PEHnTp1wsrKCiklGk3dfM9q1NYLSxtttW4TmjyPQaOFW9+ErFOw/asqnxeg2z3jcXBzZ8WXn1BaYtzkMze3LgQHPcDZs79w7tzf1Tq/crW6+J+7AwgTQoQKIayAEcCfV+yzCEPrACGEB4ZbSNftbKvJwV5oEHx6svz7v11cHbnJxYFPT6WQpzOtomnnOxqh10mTJqtduG1QrDP8d6jpe/4ajeC9YVEMjPLlzaWH+GZ97by08+bNo1evXrz66qvMmDEDGxubi9v+2XeayXP/Zl7TIDRSMiUjg1kTBiIT88nbkcyOFs7sTc3l2Vua4mBtUclZLrdkyRKefPJJlixZwuOPP15rt4jKY2mlJaydF/G7Uqt8m7BK8xga9YSwW2H9h1UuaQFgbWdH34mPknHmNFt//8Xo5zVq9CROjlEcOvwihYWqDHxNqvWEIKUsBR4FVgCHgPlSyoNCiDeEELeV7bYCSBdCxAJrgWellNftoGNfaytG+bnzS3I6pwvLX2bwhVAfUotL+T7RtDWUnT3taNkzgEObk0g/Y1wJ4XJvG5TW7PwBrUYw/e7WDIzy5a1lh/ho5dEaG0JYUlLCU089xcsvv8yqVasYPXr0xW1ZBSU8N+tf3j10hH/CAglPy2BxuB+PDO+D1OnJ/CMeC3cbfsnLw9/FlmHtAow658mTJ9mxYwf9+vVj9+7ddOjQoUauxVQRN/lRWqSrkc5lk/R9A4pzYd271TpMaOt2tOjRh+2LfyPlhHFzHDQaK1q0mI6UOg4efAq9XhV4rCl10raVUi6TUoZLKRtLKd8qe+wVKeWfZX+XUsqnpJTNpZQtpZTGf11ooCYHGVoJn1XQl9DBxYHebk7MOHWOrBLT/sNHDwjBytaCzQuNe4OVe9ugRLBpY80OYbXUavh0RBvuig7g09VxPLdg38WhqVWVkpJC3759OXz4MDt27KBVK8O6w1JK/j6QxDMz/mSJpyWHPN259eQZVt3enYgmIQDkx5yjNL2QpC4+bE84z7ibQtBqrv0Nf8mSJXTo0IHdu3djYWGBq6trta6hOnwaOeHibVet20ZV4hUB7e6Fnd9D2rXXc65Mz7H3Y+fkzIqZ09GVGnfryM4umKZN3yAzawcJJ6tWjVW5Wn3pVL7h+NlYMdLXjXlJGSRW1Epo5ENmqY4vT5s2osrG3pJ2/UM4dTCdUwev3dC68rZBcVIep1/ayKqnD9f4RCCtRvDu0Cge6x3GbzGJjPp2K8lZVeuc3LZtG+3bt6dHjx4sWbIENzdDJdATaXncO2sHC/7dxvLWwRRaWvDkuXP8MG4gllaGYaRSpyd7zSmsAh1ZlZOHViO404jWwfTp05k0aRILFy5k4sSJVYq7JgkhiOjsQ1J8FpkpVVvdrMp6vgQWtrDy1WodxsbBgT73P0LqyRNsX7zA6Of5+tyOj/ftnDjxGZmZO6sVg2KgEoIZTQ72BuDTCloJLR3tuM3Lha8SU0ktNq3iY1TPAJy9bNkwPw5diWnfwi197HG+NYTC2HTyY8qPrTo0GsFTfcP5ZERrDpzJpv8n6/n7gGkdFj/99BODBw9mxowZvP7662g0GjLzi3nv78MM/XgVmRbpLGkRgk9OLrNcbXluxK2XPb/wyHl0mUU49gxg9aFztA9xxbWSOQdnzpyhoKCAfv36sWvXLrp06VKla68NEZ18EQIObanjVoKDJ3R9Ao4shYSN1TpUk/adaHpTd7b+/itpRqzDfEHTpq9haxvAgYNPUFJStYV8lP+ohGBGAZe0Es5U0Ep4LtSHQp2ezyrogK6I1lJDt7vDyUzJZ89q04ehOnT1x7qRM5l/Hqe0lsprD2ntz5LHuuLrbMtDc2N4YM5OEtLyKn2OXq/nlVde4eWXX2bNmjUMHjyYrIISPlkVR7f31rJh23407V3YHuhL58RkVvVqR48OV88SzotJQeNgyXlfWw4n59CnmXeF51yxYgXR0dH8+++/RERE4OHhUe1rr0n2LtYEt/Tg0KazJif/auv8CDgFwIopV3dEmajX+AextrNjxZefoDdyMIWFhSORLT6huDiVQ4dfUqUtqkklBDO70Er47FT5H/hN7Gy429eN2WfSKry1VJHgFu6EtvJg57IEk9dMEBqB613hICDj1yNIXe280Rp7OrD40S680D+CjXFp9P5oHU/8spsdCRnor6jTk5+fz4gRI1i9ejWbNm8h28aHF37fR8e3V/HxqqPc6lnAoY6BnHOwZ2zCGf4Y0w8XZ8erzqkv0lF4OAO7Vp7EJhs63ttUUMX01VdfZcKECcybN4/+/fvX+PXXlJY9/SnIKSG+rjuXLW2h9yuQtAf2/VqtQ9k5OdNrwkMkH4sjZukio5/n5BRF40ZPkZr6N2fPVi+GG51KCGYWaGPF3T5u/Hw2nbMVfOA/FWJYcP3jBNPHgXYdHoaUsPn3eJOfa+Fig+sdTSg+mU32qtpbmc1Sq+GhHo1Z91xP7u0cwqpD5xj+5RY6vL2aCbN3MG1JLB/8tZv246aS6NmR4Hv/R7+v9nLPt9tYtOcMt7fy4/bGknnNArHQ63mrKI/3xw+s8HzFJ7NBJ7Fp6saRFEPZ53DvyxNHYaEhgYaEhLBr1y569uxZa9dfEwIj3HDxtmP/v2ZYZ7vlcPBrayh8V1S9MuxNO3ejSfvObJo/l4yzxl9LUNADuLl24WjcNPLyTP+/rhiohFAPPBbshR7J5xW0EgJtrBjr784vyRnlLrJTGScPW9r1CyY+5hynD5teDdWutRd20d7k/HuawqPnTX6+KbwcbXhlcHO2vdSb6Xe3pmsTd85mFvDjlgRmbDpLXqNepLk2J6dIR/9IX74c3Y51kzsTn5/EL00CCMjKZl6IJ2MH9qj0PEUnskADVsFOHEnOIcDVFkeb/wrYrVmzhqZNm5KYmMj48ePx9q74dlJ9ITSClj39STmRXSMF70yi0UD/9yE3GTZ8WK1DCSHofd/DWFpZs+LLT5FG3oYSQkPz5v9Dq7XjwMEn0OnqZlb89UYlhHogyNaau33c+CkpnaSi8lsJjwd7YyU0fHDC9FZCm1uCcPKwYcMvR9FVYZiny22NsfCyI+PXI+iya/+NZm9twe1t/Jk+og1PRORz/utxvNk6n7i3+nNkWj/+mtyV9+6Mwr84m6Hrd7Ex0If2iUms6NOets2vPcG9+HQOln4OaKy1nMspxNfZMIFNp9Mxbdo0Ro0axXfffUdAgHFzEuqLiE6+WFprzdNKCGwPUSNgy4xqrZkA4ODqRs97H+DskVh2r1hq9POsrb1o3ux9cnMPEX/svWrFcKNSCaGeeCzYG52UFXYee1pZMjHQk0XnMjmYa1phLwtLLd3uCud8cj771pj+YaGx0uI+qhmyREf63EPIas4dMNacOXMYN24cixcvYvSI4VhqNRdnAs9fsJ7hSamccHXh9pOJ/DWmPy5OxhWjK80oxMLdsNhNTmHpxdZBfn4+x44dIyYmhj59+tTORdUiK1sLIjr5ELczhfxs0/qbakSf10BjCf9MrfahmnfvRWjrdmyYN5vMFOO/BHl43ExgwDgSE38gLW1NteO40aiEUE8E21ozwseduWfTKxxx9HCgJ84WWt49bvrwwpAoD0JaurNj6QnyMk3/lm/pZYfr8KYUn8rh/KLaXZ1NSsl7773HK6+8wtq1ay9bZUzqJO9+vZynnW0pttDyTFY6X44bZPyx9RJdZhEWrtaAISEUZGcwaNAg7OzsmD179mXLaTY0LW8OQF8qid1khpIOTr7Q/RnDMNRj1fswFkLQ54FH0Wg0/PPVp5w9K40uzd6kyXM4ODQj9tDzFBVdl5X0a41KCPXI4yHeSKiwEqqLpQWPBHmxMj2bHVmVD88sT9e7wtDrJJuq0MEMYNfSA8degeTvTCG3lj5w9Ho9TzzxBD/99BObNm2iWbP/Cs2VZhfxxHfL+aSJD64FBXzlZsNTQ/uadHxddjHoJVoXG/R6PefOZ7NhzUoeeeSRyxbNaahcfewJiHDl4Poz5lksqfMj4BoKy18AnWlzZ67k5OFJj9H3cfrgPp546LTRy7FqNNZEtvgEna6Ag7FPI2X9WDSqIVAJoR4JtDHUOPo5Kb3cSqgA9wV44GFpwdvHz5r8Ld3Z0442twQRtyOFxCp0MAM49QnGpoU7WUuPk7/ftDpL11JUVMTIkSPZu3cv69evx9//v2UzMo+kcs8f//JrmB+h6Rn81SGcvu1bm3wOWWQoA6Kxs2DHjh2UFBYw5I6h9XpIqamibg4g93wRx/fU7OtjFAtruPVtSDsCO76t9uFa9r4Vx+AuLFrmbdJyrPb2jQkPn8r585s5eeqbasdxo1AJoZ55LMgLrRB8XEErwV6r5YkQb7Zk5rHuvOlD/Nr1C8bZ05a1cw9XqUKm0AjcRzTFKtCRjF8PU3Q80+RjlCcrK4t+/fqh1+v5+++/cXFxAQy3j+JWxHL73n2sD/Km7ZkkVg/uQrCPT9VOVJZDV65cSceOHQny90FY2lT+nAYmuKUHTp627P7npHkmajXtD41uhrXvQF71kpIQgm3nHkMvDR9Vla7VcAU/37vw8uzP8eMfkZW9t1px3CiumRCEEKOvtY9Sc/xsrBhTtqraifzyWwlj/NwJsrHijfiz6Ex8w1tYaek1thnZ6YVsXVS1MtTCUov7vS2wcLUhbfZBihKqVzIgPT2d3r1707x5c3755ZeLZav1haVs/HYTw4vSOOLhRt/E0ywb3R9bm6p9gEsp+fGHOQC4uBkK0tlba8kvNq3EeH2n0Qja9A3i3MkczsZl1n0AQkC/dw3VUNdUr2RuUhL8/Ks9Or2h47/SFd2uCkMQEfEW1lZeHDzwBKWl1ZsjcSMwpoUwRgjxiRCi4d9gbSAeC/LGSgg+Oln+/3prjYaXGvkSm1fIb8mm3/rxC3MhqmcA+/9N5Gxc1eYWaO0t8XygJVona9K+P1jllkJycjI9e/akT58+fP755xfv4xedzOb3z9cyPkBLmp0d96Yn8eOYwVU6xwXTp0/nn39WAtCho6FctZ2VBXlF11/55IhOPtg6WrJrhellS2qEVwR0mAgxP0DSviofxuQV3a5gaelMixYfU1CYyJEjr1U5jhuFMQmhP1AArBFCNMx1K69QU4vJ1xYva0vu9ffg9+TzxOWVPxFtiJcLbRzteO9EMvlV6DzsdHtjnDxsWD3nMCVV/IasdbI2JAUXK1K/O0D+PtOqsp46dYru3btz991388477yCEQJbqyV51km8WbOapVq5IBK/IPN4dPqBKMQLs3LmTo0ePMnHiRL6b9R3AxVIcTjYWZBVUr/OzPrKw0hJ1cyCnDqaTlmjcuhg1rucLYOcGy583lNGtApNXdCuHi0s0oaGPkZyyiKSkP6oUx43imglBSqmXUr4AfAJsKFvovoMQwq72w6sd06Zh9IgFc3k0yBsbrYaPKihXIYTg1SZ+JBWV8I2J5bEBLK219BrTjOzUArYtrvoKZlpna7weaoVVgCMZPx8mc/kJo+oexcfH0717dx5++GFefvllhBAUncom5bPdfHDkEG+18ca5IJ9vfe2Z2LfymccVkVIyY8YMBgwYwIkTJ7C3t8fa0TD/QJb1n/g625KcXTvF+8wtsoc/FtbaKq2xXSNsXaDXVDi1GQ78XqVDVGlFt3KEhkzCxbk9R46+Sn5+QpViuREY1akshBgE3A8UA22B/wGnhRANrmhIUhLMmiVNGrFgDh5WFtzn78Gic5kcqmAiWicXB/p5OPHZqRSTy2MD+Dd1JbKHP3vXnK7WQu0aO8PtI/uOPuSuS+TcF3sormS1ttjYWHr27MlLL73Ek08+SUlaAenzDpMycw9THc/xTXMfAs5n8Gd0E25u3bLKcU2aNIlvv/2WzZs3c+utt5bFalgeU59vSAh+LrZk5pdcl7eNbOwtadHFj7gdKSYXN6wxbceCb2tDNdTCOi6pcQkhtLRo8RFCWHDg4BPo9WaYuNcAGNOpfAJ4GPhYShklpXxIStldSulO2TrIDcm0aaAvNrz5q7uYfG17OMgLe62GDyspavdyYz8K9Ho+TKjaugWd72iMo6sNa36s2qijC4SFBtc7wnAb1QxdVhHnPttN+s+HKDqZjbykaunu3bvp3bs3773zLmN73UX6L4dJ+Wgn2bFpTGpRwF+NfQk/l8KqWzvRqIoTxI4ePYper+fhhx9my5YtNGnS5L84rbQIK83FEhyBboYWw8n0Ol5cpo606hMIwN5Vp80TgEYLAz801DlaZ95yEjY2fjSLeIecnP0cP/6xWWOpr4zqQ5BSDpRSrrxyg5TSDEVTqs7QOoDiiyMWRL1uJbhZWvBAgCdLUrM4kFP+B1YTOxvG+Hnw49k04k0sfAdgZWNB73ubkXUun39/OlLtYYp2LT3weToax54BFB45T+rMvSS9s43Ub/cT/9VWdry9jFWT59IzrhFp3+6n8HAGhVFOjI4sYKe/N22TzrBmWG+cHexNPreUkq+//pouXboQGxtLVFTUxRFLFwgh0Dpbo8syJIQmXoZyF/GpZrrPXssc3WwIa+/NwU1nKcwzU19JQLShpbDtSzh32DwxlPHyuhV/v5GcPPU16RnVW9TnemRMH4J5X8EaVP6IhfrdSngw0BMnCw3/q6SV8HSIN7YaDW8dq9qKWf5NXekwOJS4HSkc3FD9GcgaWwuc+4Xi+1IHXIeHY9PElbzzOeQcTKFX8y54OLlh19YLt3siSLrNk+FW5znm5Umv5NMsu2cgFhYWJp+zuLiYMWPG8Nlnn7FhwwYiIyMr3FfrakPpeUNCCHG3RyMg/tz1mRDAUNywtEjHgXVm/P7W+zWwcoBlz1S5g7mmhIVNwd4+jNjYZyguvvYSszeSG2piWvkjFoRJIxbqmoulBQ8FevF3Wja7sssvV+FpZcnkIG+Wp2WxNbNqH2zt+oUQ1MKNDfOPknqqZsZra6wtsG/nzZnmxXT+aBjx3Ypp8npPvB9tg+vtTViVdpqxZ5JJcXZieMZpfh5ZtWGl+fn5WFpa0qNHD7Zt20ZERESl+1t62FKaWoCUEhtLLSHu9hxOMt/97drm7u9AcKQ7+9YmUmquORf27tB7KiRsgIMLzRNDGa3WlhYtplNamkXsoefUKmuXuKESwpUjFk5OuJ8jnbsQs6l+3z+eGOCJm6WWdyopavdAoCe+1pa8Fn8WfRX+gwuNoM/45tg5WvH31/spyq+Z2wsHDx7k1ltvZfr06QwfPvzi418v2MhTRUXk2Ngwufgcnw2rWjKYPXs2kZGRFBYW8sADD2Bnd+3BbxZetshiHfqyiqAt/J05cOb6Xo+37a1BFOSUcLiu112+VLvx4NvK0MFczYV0qsvRIYImTV4kPf1fTifONmss9ckNlRCu5PHII+gyMjj/63xzh1IpBwstTwR7s+F8Luszyn8j2WkNk9X25OTzaxUmqwHYOlhx6wOR5GYUsWpW7FVLWJoqNjaWvn378uGHH3L33XcDoNdL3vluJW85WaEXgmm2BbzYv5/Jx87Pz2f8+PG8//77/PXXX9ja2hr9XAtPQ9IoSTF8EYjyd+ZsViFpudfvoiq+TVzwDnUiZsXJKq2JUSM0WhjwIeQkwbr3zRPDJQL8x+Dh0Zv4+PfJyYk1dzj1wg2dEOzatsGucyfSv/sOfYFpawzUtbF+HvhbW/JWJUXt7vR2pYOzPW8eSyKrpGojhnwaOdP1rjAS9qez8be4KjenDx8+TN++ffnggw8YOXIkAMWFpbw8cwVfBLliVVrKDD8LxnXtXqXjnz9/Hjs7O7Zv306LFi1Meq6Vr6HDuvis4fZaywBnAPYlZlYploZACEH7gaHkZhRxZKsZR1EEtoc2o2HrF5B6xHxxYPg3aRbxLlaWrhw4+Dg6Xf2+U1AXbuiEAOD5yCPo0tLI/O03c4dSKRuthmdDfdibU8DS1PJvbwgheDvMn/MlpbxfhZXVLmjZM4BWfQLZvzaRmOWmr6V8/Phx+vTpwzvvvMOoUaMAyErN55mZ//BDU0/siwqYE+ZK/6hok4/9888/M2bMGPz9/ZkxYwYODsYtinMpjZ0lWjcbSsrmSkQFOGOhEexMqN0lQs0tqIUbXsGO7FyegM4cpbEv6PM6WNnDsmfN3sFsZeVG8+b/Iz//BEeP1uPRJXXkhk8IdtHR2HXoQPo336Ivqt+3DIb7uBFuZ8O7J5IoreB2TqSjHWP9PZh1Jo1YE1dWu1SXoU0I7+jNtj+Ps2uF8UnhzJkz9OnTh6lTpzJ27FgATuxL45k5a1kQ5YNLQS6/RQXQOazZNY50ucLCQh588EFee+01nnnmGZOeWx4rP/uLk+fsrCxo4e/MjoSq3WprKIQQtB8USk56IUe3mbGVYO9hmMF8Yh3ELjJfHGXc3G4iOPghzibNJ+XcMnOHY1Y3fEIA8Jg0idLUVDJ/W2DuUCqlFYIXGvkQn1/E/JSKP7yeD/XBxVLLS0cTq3zLR2gEvcc2Iyzaiy1/HGPz7/GXTTArT1paGn379uWhhx7iwQcfpLREx6YFcby6eht/tfHDMzeLJR3DaBkUanI8ixYtIisri507d9KqVasqXdOlrAKd0GUUossxdCx3CHFl7+ksCkuur8qnVwqOdMczyJGdy0+aZwGdC6IngE8U/P0SFJl/yG+j0MdxcmrN4cMvUVBwxtzhmI1KCIBdxw7YRrcj/Ztv0F85LrWe6e/hTBtHO/53IpnCCt7QrpYWTGnkx9asPP44l1nlc2m0GvpMaEFkD392rzzFkhn7KlyrNzs7m379+nH77bfz3HPPkRSfyfy3dvBp8lH+ae2PX046K3pEEepl2uzj3377jfnz53P33Xczb948nJycqnw9l7IKMRyn+KRhuGmHUHeKdXr2nM6skePXV4a+hBCyUws4ur1qs9trxIUZzDlnYf0H5ovjQjgaSyJbfIyUkoOxT6DXX3+lTIyhEgKGN4nnpEmUpqSQ9XvVinDVFSEEUxr7craohNlnKl58ZKSvG60d7Xg9/gw5pVX/1qvRCLqPCKfHPU1JPJLBvNe3sWfVqcvKXBQUFDB48GA6duzIEw+9wLKZ+1jwvxh+9c9gXQt/grNSWNunMz4u7kaft6ioiMmTJ/PCCy/QuHFjhBAIIap8HVey8ncAC0FRgiEhdGzkhlYj2BhnhlXG6lhIlAcegQ7sXJ5g3lZCYAdoPQq2zIC0OPPFUcbWNoiIptPIytpFQsLn5g7HLFRCKGPXuTO2bdqQ9vU3yHreSujq6khPV0c+PZXC0URduaW8NULwTngAqcWlTDtWvdnHQggiu/tz90sdcA9wYNOCeH54cTN/f7WfrX/F89z49+je5C66eo/lt7d3cvJIBku6F7OtiR/hmWdZ178HzvamlaJ48sknSUxMJCYmhnbt2lUr/nKvyUKDVYDjxcV9nGwsaR3owob46z8hCCFoPyCUrHMFxO008yL0fV4HS7t6MYMZwMfnNnx9hnIiYQbnz283dzh1TiWEMkIIQ19CUhKZixaZO5xreqmxLxklOu7/K6XCUt5tnOyYGOjJnLPpbKzCcptXcvOz5/Yn23Dn89GEtvIg9XQOMUtPEeHSnQD7Ftg6WNL5zkb80qOAvb6+RGYksnZQX2ysjV/hbMmSJaSmpvLuu++ycOHCi0tp1gbrxi6UnMlFXzYJr2sTD/YnZpJVQ5Py6rPQVh64+zuwc1lCteebVIuDJ/R6GY7/a/YZzBeEh7+KrW0gB2OfpKQk09zh1Kk6SQhCiH5CiCNCiHghxAuV7DdMCCGFEKaPR6wB9l27YBMVRfpXXyNL6veHQpSjHYOcXDnSKBW8iios0vd8qC+NbK158vBp8qpx6+hS3qFO9L63Gdsyf+aPuHe59/2OTJzeg1sfjeSRvKMccfGlXcZJVgzph9bS0qhjlpSU8PTTT/Poo4+SlJSEk5NTjd4iKo9NExeQUHTc0EroFuaBXsKmYzdAK0EjiB4QQmZKPvExZuxLAGh/n6FE9t8vQaH5Z4xbWDgQ2eITiovTOXT4xRuqtEWtJ4SypTdnYFh5rTkwUgjRvJz9HIHHgW21HVNFhBB4PjKJkjNnyPrzT3OFYbTSn31BD473J1VYpM9Wq+HjiEASC4t5q5LSF6Z699132bBhA78v/A0HJ3vySorp9vcGTjh50Tn9OH/dPgitkUXqpJTceuutHD16lF27dhEVFVVjcVbGKsgRYaWlsGwtiNaBLjjbWrL6kJlvo9SRxm08cfOzZ+dSM7cSNFoY9DHkpsCat8wXxyWcnFrSuPHTpKb+w5mz88wdTp2pixZCByBeSnlcSlkM/AIMKWe/acB7gFmXr7Lv3h2byEjSvvyqXrcSkpLg1y+syPvVC5temcgm+RW2Ejq6OHBfgAffn0lj8/nqD/GbPXs2X3/9NcuXL8fZ2ZmMggK6rNxCooMbPVPj+f2OIWi0xi3BfeDAAYQQfPTRRyxevBg3N7dqx2csodVg3ciZorKEYKHVcHNTT9YeOYfOnB+QdeRCK+F8cj7Hdpk5Cfq3hfb3w45v4Owe88ZSJijwPtzcuhEX9ya5uUfNHU6dqIuE4A9cujpHYtljFwkh2gKBUsqllR2obPnOnUKInamppi8baQxDX8LDlJw+Tfay+jtJ5UIp7/xfvdClWeDw8Bl0pboKS3m/2MiXEFsrHjl0krTiqg+pW758OS+88ALLly/Hz8+PpNxcuq3dQaqtE7emxTFv+DCjkkFpaSkvvvgi/fv3Jy0tjdatW6PR1H2Xlk2YC6VpBZSmGSbx9W7mTUZeMXtOX9+zli9o3NYLVx87di5LuOY8k1rX62Ww84AlT4Le/PNBhNDQvNkHaLUOHDz4BDpd/Z64WhPM3qkshNAAHwFPX2tfKeXXUspoKWW0p6dnrcXk0LMn1mFhpH/7LfLKBRTqiQulvGWhltzvfbFqkY/oks3mTeW/qe21Wr5pEUJGSSmPxp6sUkXU7du3c++99/LHH38QERHByexsem7YS6aVPYPSj/LDXXcZdd8/IyODXr16sWvXLnbt2oWHh4fJsdQUmwhDi6TgsGGiX/dwTyw0glU3yG0jjUYQPTCEjLN5HNtdO1+yjGbrAre+DWd3wc7vzRtLGWtrT5o3f5/cvCPEH3vH3OHUurpICGeAwEt+Dyh77AJHIBL4VwiRAHQC/jRXxzKA0Ghwf+B+iuLiyV23zlxhVOrSUt65y9xoYVFE5HNb2fTNDxU+p6WjHW+G+fPv+RymnzStIzEuLo4hQ4bw3Xff0blzZw6fP0/vLQfJt7DijvNH+fquEUYdJzc3FycnJ8aNG8eyZcuozcRuDAt3Wyy87Di5NZsePaAgy5IOoW6sijVzR2sdatLOG1cfO7YvOWHevgSAlndCaA9YPQ1y6sdr4OHek8DACSQm/khq6ipzh1Or6iIh7ADChBChQggrYARwscdWSpklpfSQUoZIKUOArcBtUsqddRBbhZz698fCz5f0b78zZxhG0QrBtMjmJNr48tnROCjIrHDf0b7u3OntygcnklmWWvF+l0pJSaFfv35MmzaNwYMHs+VcOv12xFEqNNydGc/nw0de8xg6nY5XX32VXr16odVqmTBhAloj+xlqm00zN96f58zGjYaO+X6RPsSdyyX+nHlr9tcVjUbQYXAjziflEbfDzB/CQsDAj6C0AP552byxXKJJ42dwdGjBocMvUFhUT9fcrQG1nhCklKXAo8AK4BAwX0p5UAjxhhDitto+f1UJS0vcx0+gICaG/JgYc4dzTTe5OnKnE3zuczvxaypeQFwIwXtNA2jrZMdDB09ec35Cfn4+gwcPZsyYMdx///0sSkzmzv0JWJWWcE9WHP8zIhkkJydzyy23sGHDBv78889aH05qqkw3d+bv80avN6yx3cbTByFg2f7r941/pcZtPPEIdGD7X8fNt17CBR5NoMsTsH++YX5CPaDRWNOixXR0ukJiDz6NlObv46gNddKHIKVcJqUMl1I2llK+VfbYK1LKq8Z2Sil7mrt1cIHLncPQurqS/s235g7FKK+2bIGtkLxYFIhM2FLhfvZaLXOjGhFqZ829+0+wpYJlN/V6PaNHj6Zp06a8/MorvHP0JA8dTcIjN4uxOfG8PXz0NWOSUpKcnEzXrl1ZuXIlPj4+Vb6+2vLeLEckhiSl08GXH9sQHezKsv1mXF2sjgmNoNOQxmSnFXJocz247m5PgWsILH0aSutHZ669fSOahr/G+cytnDz5tbnDqRVm71SuzzS2triOGU3uv/9SeLT+DzvztLLkxUb+bHCNZvH6uZW+kVwtLfilVSN8rS0ZvieeH8+mXTUB5/nnnyc9PZ1XPv+CobuO8smZ84SnnGZ0/klevvveSmPR6/W8+eabPP/887Ru3ZrXX3+93twiulRSEsz+QVBcangrFBfDrFnQNdiXw8k5HE81fyXOuhLUwg3fJs7sWHrCfGsvX2Bpa1hdLT0eNn1q3lgu4es7DC+vgRw/8TFZWbvNHU6NUwnhGtzuuQdhZ0fGd/W/LwFgbLAfUZYlvOI1lPMbZlS6r6+1FUvbhtHN1ZFnjyQydE88a9OzKdTp+eLLL/kjZi/tP/+O3ruPsSszl16HYhgm0nh25PhKj5uamkr//v1ZsWIFjz/+eE1eXo27MHz3Ujod7F1qaMksP3Dj3DYSQtBpSCPys4rZ/289KAEd1gea3w4b/gcZx80dDWD4N4po+ibW1r4cOPgkpaXXVz+TSgjXoHVxwXX4cLKWLKXkTD14k1yDVgg+bNWCDCsXXkwVkLy/0v2dLS2YG9WId8MDOJpXxMh9xwlZv483wtqTO/V95qXlEpBxlpHbV9HZVfD4iAnXjOGbb76hTZs2rF27Fn9//2vub04Xhu9eqrgYdm+ypV2wK3/trV5hwIbGL8yVoOZuxKxIoLigHpSA7vcOaCzqxepqF1haOhHZ4mOKis5y+MjU66q0hUoIRnAbPw40GtJnVzyksz5p6WjH0wGuLPK8mcX/fAHFla8VqxWCcf4e7OjcnGmOAv38HxhmoeP9UHcGHdrELfu2ExzqxeSRFScDvV7PBx98wPr163nxxRd59913sTCydIU5XTp899Kf3bthSGs/DifncDg529xh1qmOQxpRlFfKntWnr71zbXPyg5unQPwqiF1s7mgucnZuS2jo46Sk/EVycv0oylcTVEIwgqWPD86DBpH522+Unm8YM1gnNwmljVUpL/iMIGmlcfVhMlOSeXPYbXzSvQPvtA1jx5KF+J5LxSs8kEcrSQYZGRkMGTKEhQsXEhISUu9GEVXVgJa+aDWCxXturFaCV7ATjdt4smfVKQpy60Ep+A4Twacl/P0CFNWfWzQhwQ/h4tKRI0dfIz//hLnDqREqIRjJ/f77kIWFnP9xrrlDMYqFRvBZm0iKLOx5oKQZRXt+rXT/vLw8Bg8ezMSJE+nX72ZemPMj7mnn8QkPYNI991X63BEjRhAWFsa6desICgqqycswKw8Ha7qFebBgfRrdu8ty60RdrzoMbkRpkY5dK06ZOxTQWsCg6ZCTTNLvn5W7/oc5CKGlRfMPEcKKAwcfR6+vB8mzmlRCMJJ148Y49OnN+Z9+Qp+XZ+5wjNLEzoZPmoWw0zmSl2PjkCc2lbufXq9n1KhRREVFMeG+u3lh3gK8UjPwbxrMgyPLTwZSSmbPnk1BQQELFy7ko48+wsrKqjYvxyyGtPbj8PKACtecuF65+dkT3tGH/f8mknu+Hgz7DIiGduOY9rEXGzeUX9nXHGxsfGne7F1ycg6yZcvMepOsqkolBBN43H8/uqwsMuv5MpuXGuzrwWN+TvzoO4gPNv4JJ6+enzB16lQyMjJ46pl7eW7RGnzPpRHYrDH3jxhX7u2fzMxMhg0bxueff8758+dxcHCoi0sxiyhXH/IOBCKlqLCa7PWqw6BQpF6yc3mCuUMBIKnFa8zaMxq9FMyaVX9abJ6effH3H8V777lfnO3eUKmEYALb1q2xbdeOjB/mIHUNZ6biC+GhjHSz5qOAkby6YRklO2ZdHGv5888/s+DXn7j/pVG8uuUUjZPP0rhZGBPuGl1uMsjLyyM6Oho/Pz82bdqEn59fXV9OnfrwfQvExUlrDfvNbionD1uad/Xj0MazZKUWmDscpv3PBb0wLLhU314LB/uXWLFieNls9/qTrEwlGuqQqejoaLlzZ91PaM5euZIzkx/D/5NPcLr1ljo/f1XppWRKbDyzzuURlXOESVnr8dBYs2zfUQ53Hk5+li2dTsTSNLIFI4bdeVUykFKyZ88e2rRpw4EDB4iMjDTTldSdpCRo1AgKL1mhw9YWjh+HejjhulbkZRUx9+UtNG7rRZ/xV61rVWfq+2sxaRJ8952e4mINVlaS++8XzKh8GpDZCCFipJTlFg9VLQQTOfbqhWVgIBk/NIwhqBdohOCdFmF81SyI886hPBTwAHf6jeX7fm8is63odCKWyJYtuXvosKuSQU5ODiNHjuSBBx6gpKTkhkgGUPGktfr0zbS22Ttb0/LmAI5sTyb9rPlmbdfn1yIpyTC7vbj4wmz3hnt7USUEEwmtFrcxYyjYtYuCvXvNHY7Jhvi4saZ9JF4z3qVf3B4+s8yn1fEjREREcMftt1+1SE18fDzR0dE4OzuzYcMGLI1cI/l6UNGktc2bzROPubS9JRgray3b/zTf0Mr6/FrU52RlKpUQqsB56FA0jo4mtxKSkjD7KAQpJRPvu4+W1lqe7NiGg6v+oUmTJtx5552X1RqSUpKVlYWXlxdvv/02X331Fba2tuYL3Awqm7R2I7FxsKR13yCO70klJcE8k/Tq82tRn5OVqVRCqAKtgz0uw4eTveIfSs4aP2lp2jTMPnzx7bff5tixYzz33HMsWrSIkJAQ7r777stmFefm5jJ27FgefPBBnJycGDZsmPkCVuqFVr0DsXGwZOuiY+YOpd6pz8nKVCohVJHb6FEAZMz9yaj9DfcZJXo9ZhuF8McffzBz5kw+/fRTFi9ejL+/PyNHjrzsNlBsbCwdOnRAq9XyXQMp6KfUPisbC9r1Cybx8HlOx2aYOxyllqiEUEWWfn443Xormb/9hi732hPVpk0zDJUDKC2t+yFz+/btY+LEiXzzzTesWrUKb29vRo0ahbW19cV9pJScOnWKZ599ltmzZ2Nvb1+3QSr1WsseATi627BpYTzS3EttKrVCJYRqcBt3L/qcHLIWVl7c6sIohJISwz93SYmmTkchnDt3jttuu4333nuPXbt24erqyujRoy/2CRQUFHD//fczc+ZM+vXrx/jxlZe3Vm5MWksNnW5vRHpiLke3N8AhNMo1qYRQDbZRUdi2bUvGnMonqpU/CqFuWglFRUUMGzaM0aNHc+7cORwcHBg7duzFb/9Hjx6lU6dOFBQUMGbMmNoPSGnQwtp54xnkyNbFxyktaTiTMxXjqIRQTW5jx1CSmEju+vUV7lP+KARR66MQpJRMmjQJX19fXF1dsbCwYOzYsTg6Ol7c55NPPmHSpEnMnTv3sscVpTxCI7hpWBNyzxexb22iucNRaphKCNXk2Ls3Fl5enP95XoX7XDkKYd68X3jvvffZvr2kVmP75JNP2LdvH126dKGkpIQxY8bg6upKYWEhTz75JEeOHGHGjBk8+OCD103JaqX2BTR1JTjSnZjlJynMrd3/w0rdUgmhmoSlJS5330Xehg0UJyQY9ZwOHTqQn5/PgQMHai2uFStW8MEHHzB+/HhycnK455578Pb25tixY9x0000kJibWywXvlYah8x2NKSksrTeF75SaoRJCDXC96y6wtOT8vF+M2j80NBRPT0+2b99eK8vvHT16lDFjxvD6669z7tw5hgwZQlBQEKWlpdx2222MHz+e+fPn4+zsXOPnVm4M7v4ORHT2Zf+/iWSnmb/wnVIzVEKoARaenjj17UvmwoXo8ytfrhIMC3V36NCBpKQkEhNr9j5sVlYWt912G6+++iqJiYm0b9+epk2b8uWXX6LRaNixYweTJ09Wt4iUauswuBEajWDr4uPmDkWpISoh1BDXUfcYhqAuWWLU/lFRUVhbW7Nt27Yai0Gn0zFy5Ej69OmDj48PNjY2hIWF0a1bN5YvX05BQQF2dnY1dj7lxubgak2rPoHE7Ujh3Mkba93p65VKCDXEtm1brCMiOP/zPKNuA1lbW9OmTRtiY2PJyamZdWJffPFFCgsL+eijj4iPjycwMJBu3bpx1113sWjRIjXRTKlxbW8JxsbBks2/x9fK7U+lbqmEUEOEELjeM5Kiw4cpMLKISfv27dHr9dTEug4//vgjv//+O7/99hslJSUUFBQQHBzM+vXrefrpp9UtIqVWWNla0H5gKGeOZnLyQLq5w1GqSSWEGuQ8cCAae3syf1tg1P7u7u6EhYURExODrhorsG3fvp2nnnqKxYsXU1BQQP/+/S9ua9q0aZWPqyjGaNHND2dPW7b8cQy9KmnRoKmEUIM09vY4DRxI9t9/ozPyNlDbtm3Jzc3l2LGqVZE8e/YsQ4cO5dtvvyUrK4vo6Gj69++PlZUV2dnqvq5S+7QWGjrd3piMs3kc3pJk7nCUalAJoYa5DL8TWVBA9tJlRu0fHh6OnZ0du6tQK7ewsJA77riDBx98kJ49exIcHMz8+fN58cUXcXd3JzU11eRjKkpVNG7riXeoE9v/PE5JkSpp0VCphFDDbCIjsW7alMwFxt020mq1tGrViiNHjpCXd+2qqRdIKZk4cSLe3t6sWrWK//3vfwQEBNC9e3cAAgMDSUxMrNatKEUxlhCGkhZ5WcXsXX3a3OEoVVQnCUEI0U8IcUQIES+EeKGc7U8JIWKFEPuEEKuFEMF1EVdtEELgcuedFB44QOGhQ0Y9p3Xr1uj1evbt22f0eT788EO2bNnC9u3b6d27N6+99tpl20NCQigpKeGsCQv4KEp1+DVxIbSVB7v+OUl+dvG1n6DUO7WeEIQQWmAG0B9oDowUQjS/YrfdQLSUMgpYALxf23HVJufbBiOsrMhc8LtR+3t7e+Pv78+uXbuMGrq3bNkyPvroIyZNmsRPP/3EK6+8ctnylwDBwcEIIYiLi6vSNShKVXS+ozGlxXp2LkswdyhKFdRFC6EDEC+lPC6lLAZ+AYZcuoOUcq2U8sIU361AQB3EVWu0zs449OpF9vLlyBLjin+1adOG1NRUkpIq75TbtGkTt99+O08//TRPPvkkvXv3Lnc/e3t7goODOWRkK0VRaoKrjz3Nu/pxcP0ZMlOuPWtfqV/qIiH4A5feVEwse6wi9wHLy9sghJgohNgphNhZ3ztMnW8bjC4jgzwja1w3b94cIUSlH+BLly6lZ8+e3HLLLTz++OPXPGazZs1ITU0lLS3N6LgVpbraDwxBY6lR6y83QPWqU1kIMRqIBj4ob7uU8mspZbSUMtrT07NugzORQ9euaJ2dyfrLuFIWdnZ2BAcHc/jw4XK3l5SUcN999zFgwACWLFmChYXFNY8ZEREBGNZJVpS6Yu9sTZu+QRzbnUry8Sxzh6OYoC4Swhkg8JLfA8oeu4wQog8wBbhNSllUB3HVKmFlhWO/fuSsXo3eyNFDERERpKamkp7+34zPtLQ0xo8fz0MPPUSrVq34/Xfj+iUAnJ2dCQgI4MCBA6qsgFKnWvcJxM7JSpW0aGDqIiHsAMKEEKFCCCtgBPDnpTsIIdoAX2FIBufqIKY64TRwALKggNwNG43aPzw8HIDjxw3VIzdv3kzbtm1JTExky5YtzJ8/36iWwaVatWrFuXPnrtk3oSg1ycrGgg6DQ0k6lsXxPfX79q7yn1pPCFLKUuBRYAVwCJgvpTwohHhDCHFb2W4fAA7Ab0KIPUKIPys4XINi17YtGmdncteuNWp/V1dXbGxsSE5OJiMjg3vuuYcJEyZw4MABli5dWqX1CyIjI9FqtezZs8fk5ypKdTS7yRc3P3s2LzyGrkR/7ScoZmfa180qklIuA5Zd8dgrl/y9T13EUdeEhQUO3buTu349UqdDXDE09Kr9hcDNzY39+/czePBgfv/9d/r168eiRYsIDQ2tUgy2trZERESwf/9+brnlFpNbGIpSVRqthi7DmvDXZ3vZvy6R1n2CavV8JSUlJCYmUlhYWKvnaShsbGwICAjA0tLS6OeoT4da5nhzT7L/+ouCvXuxa9u20n137NjBzp078fLyIikpiTvvvJPp06fTpUuXasXQqlUrDh48SFxcHM2aNavWsRTFFEEt3Alq4caOpQk07eSDrYNVrZ0rMTERR0dHQkJCbvjqvlJK0tPTSUxMNOnLZL0aZXQ9su/aFSwsrnnbaNOmTQwaNIigoCAiIyMZOnQoY8aMYdSoUdWOoXHjxjg4OKjbRopZdBkWRkmRjh1LEmr1PIWFhbi7u9/wyQAMdxvc3d1Nbi2phFDLtE5O2LZqRd727eVuz8rKYt++fXTs2JE5c+ZQWlrKmjVrCAoKuqocRZVj0GqJiooiLi6uxhbjURRjufnZ06KrHwfWnyEjyfh6XVWhksF/qvJvoRJCHbCNiqLo0GFk8eX1XXbt2kW7du1YsGABycnJ7N68GZucXPbv28fs2bPRaGru5Wnbti16vb5KVVUVpbo6DA7F0krD5oXx5g5FqYRKCHXAtmUksriYwkvqCv3yyy/ceuutvPnmm0y67z72Tp7M4Pm/MWTpUub4B6BNr9nVpzw8PAgNDSUmJga9Xo34UOqWraMV7QaEcHJ/OqdjM8wdjlIBlRDqgE2LFgAUHT5MTk4OBQUFREZGsnHjRnpGteLEqNGEHjrMP3od2vsmoE9MJGHkSEpquFJpdHQ0WVlZxMerb2lK3Wt1cyBOHjZsXBCnVlarp1RCqAMWPj4AJB44QPv27VmwYAGRkZE4FhaSeO+9OGRm8pZOR7effiL82WcJmfsjsqCQxEcno6/BIXQRERHY29vXyBrOimIqraWGznc0IeNsHoc23Vhl2b/88ksefvjhi7+//PLLjBkzpsrHW7duHV5eXmi1WkJDQ/nwww9rIkyVEOqCxtoanZUlv38/iylTpjBmzBjO7NxJ8oT7sCwq4sWSYkZ/+gnR0dEAWIeF4ffB+xTGxpL66Wc1FodWq6Vt27bExcWRlaVqzCh1r3FbT3ybOLPtz+MUF5SaO5w6M3bsWJYsWUJmZiZLlixh6dKlfP3111U+XnJyMsOHDyc9PZ0TJ07w9NNP10icKiHUsov36/WS4XfdxZgxY0jcvJlzD0xEo9PxCpKhzz9P//79L3ue48034zJ8OBmzZ1Owf3+NxdO2bVuklOzatavGjqkoxhJC0HV4GAU5JcT8fdLc4dS4uLg4QkJCLt6WLSkpoXXr1qSnpzNy5EimTJnCY489xoIFC7C1ta3yeebMmUOfPn2qVL2gMioh1KJDhw7Rpk0bDu3ahba0FK8mTTi9bh1pD08CIXjD0oL2d93FhAkTyn2+13PPYuHpSdKUl5GlNfNtytXVlbCwMGJiYtTymopZeAU70bSjD3tXnyY7raDWzvPaa68hhLj4ExMTQ0xMzGWPXRja7efnd/Gxdu3aATBx4sTL9jVm9cGwsDAmTpzIihUrAPj888+57bbbCAwMZMKECXzxxRdMnz6dxo0bV+vaJk+ezJgxY3BxceHnn3+u1rEupRJCLZk7dy7du3fnscceIzDfsFBIamEB5x+djN7Sknfs7WjUowdTpkyp8BhaR0e8X55C0dGjZP72W43FFh0dTW5uLkePHq2xYyqKKTrd3gghYEstrpnw2muvIaW8+NOuXTvatWt32WMXEsLZs2cvPhYTEwPA119/fdm+fn5+Rp03MjKSI0eOkJGRwXfffcfzzz8PwBtvvIGnpyelFXy569OnD5GRkVf9LF68+LL9Dh8+zHPPPcdff/1FZmYm99xzTxX/ha6mSlfUgsLCQn799VdWr15NVFQUZ55+hgwvL5y+/oZiR0c+dHTAKTiYDz744JqTRxz79MGuY0dSP/kUp4ED0To5VTu+sLAwnJyc2LFjhyploZiFg6sNbW4JYsfSBFr2zMSviYu5Q6ox4eHhzJgxg9dee41nnnkGe3t7PvzwQwoLC5k/fz6vvvoqQ4cOvep5q1atMur4X331FU899RQ333xzTYeuWgg16ejRo4waNQohBH/99RdRUVEU7N3L8a1bcUlNpcDNjc98vNG7ufHVV18ZNZNQCIH3iy+gy8oi7YuZNRKnRqOhXbt2HD9+XK2mpphNm1uDcXC1ZuP8OOR1NAy1cePG7Nq1i+3btzN27FjWrFnDrFmz+OGHH+jZsyfZ2dnVKiNTWFhIcnJyzQV8CZUQasj8+fPp2rUr3bp1w8rKUMBLl5nJzuefxz09nRw/X2b6+ZJaXMyPP/6I9hqVTy9lExGBy513kjF3LkUnTtRIvO3atUOr1bK9gpIailLbLK20dL6jMamncji89fpZr8PS0hInJyfeffddEhMTuf/++/ntt99wdHQE4PHHH2f69OlVPv6zzz7LypUriYyMpG/fvjW61olKCDUgNjaWKVOm8Pfff/PQQw8hhEBfWMiWMWPxSDhJVnAwn7u7k5ydzcKFCy8mDFN4Pv4YGisrUj/5tEZidnBwoEWLFuzZs4eioga/QJ3SQIW198ankTNbFl1fw1BLSkro0aMHQUFBHD9+/LJbs+PGjWP27NlVPnajRo1YvXo1Bw4cwM/Pr0ZHDKqEUA3Hjx/nhx9+oHnz5hw8eJC2ZeWtS/Py2HTHUNzj4sho3JhPHR3IyM3ljz/+wMbGpkrnsvDwwG3cOHL+/puCgwdrJP6OHTtSXFysqqAqZiOEoOtdYRRkFxPzd4K5w6kRCQkJBAcH13qhvSVLlpCXl0efPjW3nIxKCFX0xx9/0KlTJ7KzswEufuvPT0pm66DBeJw4QUbLSKbbWJNdUFCtZHCB2/hxaJ2dSf3kk2rHD+Dv74+/vz/bt29X9Y0Us/EOcSKikw97Vp8mKzXf3OFUW0hICBs2bKj18wwaNIgFCxZgbW1dY8dUCaEKfvrpJ5566imWLFnC5MmTLz5+fv9+9g4diltSEpnduvJBcTEFRUUsXLiwRl40raMj7hMfIG/9BvJrqPxEx44dSU9Pv7iOs6KYQ6fbG6PRati0QNXZMieVEExw8uRJ4uPjue2224iJiaFDhw4Xt51ZsYJj48bjmJVF7rChPH/kCHb29jWWDC5wveceLDw9OffxdKSs/siM5s2b4+DgwLZt22ogOkWpGnsXa6L7B3NibxqJh1U1VHNRCcFIS5YsoUOHDmzZsgVHR0fc3Nwubjv06aekPvscFiUlFE18gPv/+os2bdowd+7cKnUgV0Zja4vHpIcpiIkhb+PGah/PwsKCdu3aERcXR3oNl9xWFFO06l1WDfW3OPQ6dQvTHFRCMMLbb7/NpEmTWLhw4WUVCnU6HVsffAj9zC8psbRE98zTDP/0U+655x6mT59eowvcXMpl2DAsAwI49/HHyBq49x8dHY1Go2HHjh01EJ2iVI2FpZabhjYh/UwesRtvrGqo9YVKCJVISUlBr9fTq1cvYmJiLlvsvjgzky2DBuO8bh2ZXl7kPP8cA597jilTpvDCCy/U6ggDYWWF5+RHKYo9RI6Rsxsr4+joSPPmzdm9e7cagqqYVaM2nviFubDtzxMU5pWYO5wbjkoIFVixYgWtW7dmy5YtdOrUCU9Pz4vbUrdtY1f/AbifOEFGVEv2Dr+TkZMn89NPP3HffffVSXxOAwdiFRxM2hcza6SV0LFjR4qKiti7d28NRKcoVXNhGGpRfgk7lyaYO5wbjkoIV9Dr9UydOpUJEyYwb968y1oFAPvffpszD0zEPjub/Dtu5ycPDz7/4gs2bdpE79696yxOYWGB+8MPUXT4MLlr1lT7eAEBAfj5+bF9+/Ya6axWlKryDHSkWVc/9v+byKG9+fToAbVUqUG5gkoIl9DpdAghcHBwYNeuXfTs2fPitpKcHDbeMRSLOT9SbGNDybPPMPGff0hKSmLLli00adKkzuN1HjQIy+AgUr/4otof4kIIOnToQFpaGlu3nlRvQsWsOg5uhIWVhqcfyWfjRpg2zdwR3RhUQiizZs0amjdvTmZmJs8//zze3t4Xt53+awkxfW/B/dAh0ps04fiDD3Lrs88yfvx4Fi5cWOOLVBhLWFjg8eBDFMUeInft2mofLzIyEjs7O155pUS9CRWzsnOyIrhTY1ZtdUWvh1mzGtYXlKeffppWrVrxwAMP0KNHj4trj1S0lGZxcTHdu3evsDR2XbnhE4JOp2PatGmMGjWKzz//HFdX14vbSvPz2Tx2LFnPP49tXh5Ztw3mM3s7XnnvXVasWMGjjz5a69PTr8X5tsFYBgaS9vmMarcSLCwsCA29iX//DWmQb0Ll+rLwX38khveXTtdwvqAcO3aMTZs2sXfvXlq3bs3QoUMvFrOsaClNKysrevfuza+//mrW2G/4hJCamsru3buJiYmhb9++Fx9PWPA7O3v1xnX7DrK8vTky7l5unzOH4OBg9u7de7FukbkJCws8HnqQwthYcv/9t9rHW7GiPVI2vDehcn1JSoIffhCU6gwfUcXFDeMLypEjR+jZsycnT56kTZs2fPvttwwZMuTidjs7uwqX0rz99tv56aefzBW6waUrAjWkn3bt2snqWL9+vRw/frzU6/WXPZ55+LDcMGiwPBDRTO5uGSXXPjxJ9ujWTbZs2VJu3769WuesLfriYhnXu488PuzOq67HFGfPSmljIyX892NrK2VSUg0GqyhGePhhKa2sLv+/aGUl5aRJFT8nNjb2st+BGv8xxpQpU+Q333wji4qKpLe391XbDx06JAG5ePHiyx4vLS2VHh4eRp3DWFf+m0gpJbBTVvC5esO1EPR6Pe+99x7Dhw/nzjvvvHjLpzAjg63330/CncNxjY8nPTSUWc2acc+iPxg1Zgy7du2iffv2Zo6+fMLSEvcHJ1J44AB569dX+TjTpsGVI1hVK0Exhy1bDK2CSxUXw+bNxh+jog+96vwYY//+/bRq1Yq0tDRcXFyu2l7RUpparRYrKytycnKMv8gadsMlhGXLlrF48WJ27NjBgAEDKEhNZev99xPbqzfOGzeR6+TE700aM3T7NlwimnLkyBEeeOABLCzq92qjLkOGYOnnx8H//UyPHrJKTeuaeBMqSk3YvfvStsF/P7t3mzuyazt48CCRkZHY2tpSWFh42bZLl9L8pJyqxUVFRdWuilwddfIpJ4ToB3wCaIFvpZTvXrHdGpgDtAPSgbullAnVOmlEBPTqBV98AcDWrVvxeu01BiYk0O/AAc4uW8bGyZNxPH4c5+ISMtxcWerkyLcnT/Lk8Ds58fPPF1c4agiElRXuDz7I1Ad1bMw2fKufMcO0YzSEN5ui1Gc5OTlYWlpia2uLra0tOp2OwsJCbGxsLi6leaEe2oWlNFu3bg1Aeno6Hh4eWFpami3+Wk8IQggtMAPoCyQCO4QQf0opYy/Z7T7gvJSyiRBiBPAecHe1TtyrF8yciZSSj8PC8Hv1VTrk5hLfMoqMm7rglJ2NixCkuLvzV1YmmeHh3HPPPbzYq1e9bw1UpKDT7fyRI9FLwaxZkqlTBT4+5o5KUW4cBw4cIDIy8uLvt9xyCxs3biQ8PJz777+fpUuXXrWU5oXV09auXcvAgQPNEfZ/auM+2xX33DoDKy75/UXgxSv2WQF0Lvu7BZAGiMqOa0yncmr//rJUo5Ep7h6yRKuVCYGB8kBEM7mhQ0f5U48ectqDD8rly5fL/Pz8ax6rIXj4YSmtLErLOuD0lXbAKcr1prwOVHOLiYmRo0ePNmrfO+64Qx45cqRGz29qp3JdfBX2B05f8nsi0LGifaSUpUKILMC9LDFcJISYCEwECAoKuuaJi59+hvQdO/BKSyPN3YO4YcPwv/12OnftSlcTFrlvCJKSDMPyiksN11VcLJg1C6ZORbUSFMVM2rZty80334xOp7s4F6E8xcXF3H777YSHh9dhdFdrUJ3KUsqvpZTRUsroS4vNVcTv9wV4paVBYCAe6Wn0KSqiWY8elb4wDZUaIaQo9dOECROu+ZljZWXF2LFj6yiiitVFQjgDBF7ye0DZY+XuI4SwAJwxdC5X3aRJMHMmPPwwnDpl+HPmTMPj1yE1QkhRlOqqi1tGO4AwIUQohg/+EcA9V+zzJ3AvsAW4E1hTdq+r6tasMSSBslFGF/+sgcqg9ZEaIaQohj5Rc5eTqS+q8hFa6wmhrE/gUQwdx1rgeynlQSHEGxg6N/4EvgN+FELEAxkYkkb1HD589WMXkoKiKNcdGxsb0tPTcXd3v+GTgpSS9PR0k+c0iOp+ETeX6OhouXPnTnOHoShKPVFSUkJiYuJVk8FuVDY2NgQEBFw1r0EIESOljC7vOQ1zwL2iKMoVLC0tCQ0NNXcYDVqDGmWkKIqi1B6VEBRFURRAJQRFURSlTIPtVBZCpAInjdzdgytmPTdw6nrqt+vteuD6u6Yb+XqCpZTlzuxtsAnBFEKInRX1qjdE6nrqt+vteuD6uyZ1PeVTt4wURVEUQCUERVEUpcyNkhC+NncANUxdT/12vV0PXH/XpK6nHDdEH4KiKIpybTdKC0FRFEW5BpUQFEVRFOA6SghCiH5CiCNCiHghxAvlbLcWQvxatn2bECLEDGGaxIhrGieESBVC7Cn7ud8ccRpDCPG9EOKcEOJABduFEOLTsmvdJ4RoW9cxmsqIa+ophMi65PV5pa5jNIUQIlAIsVYIESuEOCiEeLycfRrM62Tk9TSY10gIYSOE2C6E2Ft2Pa+Xs0/1PucqWluzIf1gKKt9DGgEWAF7geZX7DMJ+LLs7yOAX80ddw1c0zjgc3PHauT1dAfaAgcq2D4AWA4IoBOwzdwx18A19QSWmDtOE67HF2hb9ndH4Gg5/+cazOtk5PU0mNeo7N/coezvlsA2oNMV+1Trc+56aSF0AOKllMellMXAL8CQK/YZAvxQ9vcFQG9Rv4umG3NNDYaUcj2GtS4qMgSYIw22Ai5CCN+6ia5qjLimBkVKmSSl3FX29xzgEIb1zi/VYF4nI6+nwSj7N88t+9Wy7OfKUUHV+py7XhKCP3D6kt8TufqFv7iPlLIUyALc6yS6qjHmmgCGlTXdFwghAsvZ3lAYe70NTeeyJv5yIUQLcwdjrLJbDW0wfAu9VIN8nSq5HmhAr5EQQiuE2AOcA1ZKKSt8faryOXe9JIQb1V9AiJQyCljJf98MlPphF4a6Ma2Az4BF5g3HOEIIB+B34AkpZba546mua1xPg3qNpJQ6KWVrDGvTdxBCRNbk8a+XhHAGuPTbcUDZY+XuI4SwAJyB9DqJrmqueU1SynQpZVHZr98C7eoottpgzGvYoEgpsy808aWUywBLIYSHmcOqlBDCEsOH509SyoXl7NKgXqdrXU9DfI0ApJSZwFqg3xWbqvU5d70khB1AmBAiVAhhhaEz5c8r9vkTuLfs73cCa2RZz0s9dc1ruuLe7W0Y7pE2VH8CY8tGsXQCsqSUSeYOqjqEED4X7t8KITpgeL/V2y8hZbF+BxySUn5UwW4N5nUy5noa0mskhPAUQriU/d0W6AtcuXh8tT7nroslNKWUpUKIR4EVGEbnfC+lPCiEeAPYKaX8E8N/jB+FEPEYOgJHmC/iazPymh4TQtwGlGK4pnFmC/gahBDzMIzo8BBCJAKvYugUQ0r5JbAMwwiWeCAfGG+eSI1nxDXdCTwshCgFCoAR9fxLSBdgDLC/7D41wEtAEDTI18mY62lIr5Ev8IMQQoshcc2XUi6pyc85VbpCURRFAa6fW0aKoihKNamEoCiKogAqISiKoihlVEJQFEVRAJUQFEVRlDIqISiKoiiASgiKoihKGZUQFKWGCCEeEkLMvOT3N4UQP5ozJkUxhZqYpig1RAhhBxwBWgJdgWnATVLKArMGpihGUglBUWqQEOJ9wB7oD/SVUh4zc0iKYjSVEBSlBgkhIjAUGRxSVltGURoM1YegKDXrFSCV66RwpHJjUQlBUWqIEOJpwAa4C7hqQXdFqe/UtxhFqQFCiF4YSkF3llLmCCGchBCtpZR7zByaohhNtRAUpZqEEEEYVqwbXraYO8AnwBNmC0pRqkB1KiuKoiiAaiEoiqIoZVRCUBRFUQCVEBRFUZQyKiEoiqIogEoIiqIoShmVEBRFURRAJQRFURSlzP8B2vH03+Hb118AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x_array = np.arange(0, 3, 0.01)\n",
"y_array = func1(x_array, gam, xi)\n",
"f_array = func2(x_array, K, n)\n",
"\n",
"plt.figure()\n",
"plt.plot(x_array, y_array, 'k--', lw=1, label=r'$\\gamma X - \\xi$') # plot straight line\n",
"plt.plot(x_array, f_array, 'k-', lw=1, label=r'$f(X)$') # plot Hill function\n",
"for traj in traj_list:\n",
" plt.plot(traj[:,0], traj[:,1]) # plot trajectory\n",
" plt.plot([traj[0,0]], [traj[0,1]], 'b^') # blue triangle marks initial state\n",
" plt.plot([traj[-1,0]], [traj[-1,1]], 'rx') # red square marks final state\n",
"plt.xlim(-0.1, 3.1)\n",
"plt.ylim(-0.05, 1.05)\n",
"plt.xlabel(r'$X$')\n",
"plt.ylabel(r'$Y$')\n",
"plt.title(r'$\\gamma = %.1f$, $\\xi = %.1f$' % (gam, xi))\n",
"plt.legend(loc='lower right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"You may see some trajectories that go to the origin and others that go to the steady state on the right, but no trajectories that go to the middle steady state because it is unstable."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"source": [
"Another fancy way of visualizing potential trajectories is to make a stream plot. This is like plotting field lines of electromagnetic fields. We first pick grid points where the vector field will be evaluated. The arrows will be automatically drawn and joint together to form field lines by the `streamplot` function."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x_points = np.arange(0, 3.1, 0.1) # grid lines for x-axis\n",
"y_points = np.arange(0, 1.1, 0.1) # grid lines for y-axis\n",
"x_grid, y_grid = np.meshgrid(x_points, y_points) # generate a grid of x, y values\n",
"\n",
"x_flow, y_flow = equations([x_grid, y_grid], 0, gam, xi, K, n) # vector fields (set t=0 as equations do not depend on t)\n",
"\n",
"plt.figure()\n",
"plt.plot(x_array, y_array, 'k--', lw=1, label=r'$\\gamma X - \\xi$') # plot straight line\n",
"plt.plot(x_array, f_array, 'k-', lw=1, label=r'$f(X)$') # plot Hill function\n",
"plt.streamplot(x_grid, y_grid, x_flow, y_flow) # plot field lines\n",
"plt.xlim(-0.1, 3.1)\n",
"plt.ylim(-0.05, 1.05)\n",
"plt.xlabel(r'$X$')\n",
"plt.ylabel(r'$Y$')\n",
"plt.title(r'$\\gamma = %.1f$, $\\xi = %.1f$' % (gam, xi))\n",
"plt.legend(loc='lower right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"From the figure we see that, for initial values near the lower left corner of the plot, the system will flow to the origin, whereas for initial values in the rest part of the plot, the system will flow to the steady state on the right. That means the expression of the *lac* genes can in principle turn on and off stochastically: Suppose the genes are off initially. If there happens to be a fluctuation that pushes the system to the upper right region, then the genes will turn on, and will remain on under small perturbations. However, if there is then a large fluctuation that pushes the system back to the lower left region, then the genes will turn off again and remain so until another large fluctuation. The fact that the genes can turn on automatically by chance makes this situation sound unbiological. Indeed, it does not seem to happen for the native inducer. However, people have shown the potential for such bistability in the lac operon using synthetic inducers."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
},
"tags": []
},
"source": [
"## Hysteresis"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"When there is bistability, what happens if we add external source of the inducer, i.e., increasing $\\xi$? Consider the case where $\\gamma = 0.55$, just above the critical value such that there is no bistability at $\\xi = 0$. Let us make a similar plot as above to find how the steady states change as $\\xi$ increases."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"gam = 0.55\n",
"xi_list = np.arange(0, 0.17, 0.03)\n",
"\n",
"x_array = np.arange(0, 2, 0.01)\n",
"f_array = func2(x_array, K, n)\n",
"\n",
"plt.figure()\n",
"for xi in xi_list:\n",
" y_array = func1(x_array, gam, xi)\n",
" plt.plot(x_array, y_array, label=r'$\\xi=%.2f$' % xi) # plot straight line\n",
"plt.plot(x_array, f_array, 'k', label=r'$f(X)$') # plot Hill function\n",
"plt.ylim(-0.1, 1.1)\n",
"plt.xlabel(r'$X$')\n",
"plt.ylabel(r'$Y$')\n",
"plt.title(r'$\\gamma = %.2f$' % gam)\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"source": [
"We see that, somewhere between $\\xi = 0.03$ and $0.09$, there is bistability where we have two stable steady states, ON and OFF. Let us denote these two critical values $\\xi^-$ and $\\xi^+$, respectively. For $\\xi < \\xi^-$, the only steady state is OFF, whereas for $\\xi > \\xi^+$, the only steady state is ON. But if we are in the bistable region $\\xi^- < \\xi < \\xi^+$, the system can in principle be either ON or OFF."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"source": [
"What determines whether the genes are ON or OFF in the bistable region? That depends on the history of the system. If we start from below $\\xi^-$, so that initially the genes are OFF, then when we enter the bistable region, the genes will remain OFF since the OFF state is locally stable. If we continue to increase $\\xi$, then the genes will eventually turn ON when $\\xi$ reaches $\\xi^+$, because at that point ON becomes the only stable state. However, if we start from above $\\xi^+$, so that the genes are initially ON, then the opposite happens as we decrease $\\xi$, i.e., the genes will remain ON until $\\xi$ reaches $\\xi^-$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"source": [
"These two processes can be visualized by the following plot of the steady state $Y_s$ as a function of $\\xi$. There are two branches of steady states that coexist within the bistable region. We can make this plot by solving the steady state equations as above, only that now we have to be careful about the initial guesses of the root. When we increase $\\xi$ from below, our initial guess should be near the OFF state, whereas when we decrease $\\xi$ from above, we need to use an initial guess near the ON state."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"xi = 0.000, steady state: Xs = 0.000, Ys = 0.000000\r"
]
}
],
"source": [
"gam = 0.55\n",
"xi_list = np.arange(0, 0.15, 0.001) # list of xi values\n",
"\n",
"Xs_incr = [] # steady state of X when increasing xi\n",
"Ys_incr = [] # steady state of Y when increasing xi\n",
"for xi in xi_list:\n",
" x0 = [0, 0] # initial guess of solution, near the OFF state\n",
" sol = opt.root(equations, x0, args=(0, gam, xi, K, n)) # finding root of equations(x)==0\n",
" if not sol.success: # did not find root near initial guess\n",
" x0 = [1.5, 0.7] # try again with a different guess near the ON state\n",
" sol = opt.root(equations, [1.5, 0.7], args=(0, gam, xi, K, n))\n",
" Xs, Ys = sol.x # unpack solution vector (Xs,Ys)\n",
" print(f'xi = {xi:.3f}, steady state: Xs = {Xs:.3f}, Ys = {Ys:.6f}', end='\\r')\n",
" Xs_incr.append(Xs)\n",
" Ys_incr.append(Ys)\n",
"\n",
"Xs_decr = [] # steady state of X when decreasing xi\n",
"Ys_decr = [] # steady state of Y when decreasing xi\n",
"for xi in xi_list[::-1]: # reverse order in xi list\n",
" x0 = [1.5, 0.7] # initial guess of solution, near the ON state\n",
" sol = opt.root(equations, x0, args=(0, gam, xi, K, n)) # finding root of equations(x)==0\n",
" if not sol.success: # did not find root near initial guess\n",
" x0 = [0, 0] # try again with a different guess near the OFF state\n",
" sol = opt.root(equations, [0, 0], args=(0, gam, xi, K, n))\n",
" Xs, Ys = sol.x # unpack solution vector (Xs,Ys)\n",
" print(f'xi = {xi:.3f}, steady state: Xs = {Xs:.3f}, Ys = {Ys:.6f}', end='\\r')\n",
" Xs_decr.append(Xs)\n",
" Ys_decr.append(Ys)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"slideshow": {
"slide_type": "subslide"
},
"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(xi_list, Ys_incr, label=r'increasing $\\xi$')\n",
"plt.plot(xi_list[::-1], Ys_decr, '--', label=r'decreasing $\\xi$')\n",
"plt.xlabel(r'$\\xi$')\n",
"plt.ylabel(r'$Y_s$')\n",
"plt.legend(loc='upper left')\n",
"plt.title(r'$\\gamma = %.2f$' % gam)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
},
"tags": []
},
"source": [
"Such history-dependent response, or \"hysteresis\", is very typical of bistable dynamical systems. "
]
}
],
"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
}