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      "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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      "Ensemble Kalman Filters"
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      "#format the book\n",
      "%matplotlib inline\n",
      "from __future__ import division, print_function\n",
      "import matplotlib.pyplot as plt\n",
      "import sys\n",
      "sys.path.insert(0,'../code') # allow us to format the book\n",
      "import book_format\n",
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     "source": [
      "> I am not well versed with Ensemble filters. I have implemented one for this book, and made it work, but I have not used one in real life. Different sources use slightly different forms of these equations. If I implement the equations given in the sources the filter does not work. It is possible that I am doing something wrong. However, in various places on the web I have seen comments by people stating that they do the kinds of things I have done in my filter to make it work. In short, I do not understand this topic well, but choose to present my lack of knowledge rather than to gloss over the subject. I hope to master this topic in the future and to author a more definitive chapter. At the end of the chapter I document my current confusion and questions. In any case if I got confused by the sources perhaps you also will, so documenting my confusion can help you avoid the same.\n",
      "\n",
      "\n",
      "The ensemble Kalman filter (EnKF) is very similar to the unscented Kalman filter (UKF) of the last chapter. If you recall, the UKF uses a set of deterministically chosen weighted sigma points passed through nonlinear state and measurement functions. After the sigma points are passed through the function, we find the mean and covariance of the points and use this as the filter's new mean and covariance. It is only an approximation of the true value, and thus suboptimal, but in practice the filter is highly accurate. It has the advantage of often producing more accurate estimates than the EKF does, and also does not require you to analytically derive the linearization of the state and measurement equations. \n",
      "\n",
      "The ensemble Kalman filter works in a similar way, except it uses a *Monte Carlo* method to choose a large numbers of sigma points. It came about from the geophysical sciences as an answer for the very large states and systems needed to model things such as the ocean and atmosphere. There is an interesting article on it's development in weather modeling in *SIAM News* [1]. The filter starts by randomly generating a large number of points distributed about the filter's initial state. This distribution is proportional to the filter's covariance $\\mathbf{P}$. In other words 68% of the points will be within one standard deviation of the mean, 95% percent within two standard deviations, and so on. Let's look at this in two dimensions. We will use `numpy.random.multivariate_normal()` function to randomly create points from a multivariate normal distribution drawn from the mean (5, 3) with the covariance\n",
      "\n",
      "$$\\begin{bmatrix}\n",
      "32 & 15 \\\\ 15 & 40\n",
      "\\end{bmatrix}$$\n",
      "\n",
      "I've drawn the covariance ellipse representing two standard deviations to illustrate how the points are distributed."
     ]
    },
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     "input": [
      "import numpy as np\n",
      "from numpy.random import multivariate_normal\n",
      "from stats import (covariance_ellipse, \n",
      "                   plot_covariance_ellipse)\n",
      "\n",
      "mean = (5, 3)\n",
      "P = np.array([[32, 15],\n",
      "              [15., 40.]])\n",
      "\n",
      "x,y = multivariate_normal(mean=mean, cov=P, size=2500).T\n",
      "plt.scatter(x, y, alpha=0.3, marker='.')\n",
      "plt.axis('equal')\n",
      "\n",
      "plot_covariance_ellipse(mean=mean, cov=P,\n",
      "                        variance=2.**2,\n",
      "                        facecolor='none')"
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W/by1tQaOHAlg6VLbayvwV6VLSkz09GhoadFRUGBF7Ca3fr1YWFdTI8JyVpbl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\nEREREUW0/w9rsNLD90my1QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6b1d7c240>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Algorithm"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As I already stated, when the filter is initialized a large number of sigma points are drawn from the initial state ($\\mathbf{x}$) and covariance ($\\mathbf{P}$). From there the algorithm proceeds very similarly to the UKF. During the prediction step the sigma points are passed through the state transition function, and then perturbed by adding a bit of noise to account for the process noise. During the update step the sigma points are translated into measurement space by passing them through the measurement function, they are perturbed by a small amount to account for the measurement noise. The Kalman gain is computed from the \n",
      "\n",
      "We already mentioned the main difference between the UKF and EnKF - the UKF choses the sigma points deterministically. There is another difference, implied by the algorithm above. With the UKF we generate new sigma points during each predict step, and after passing the points through the nonlinear function we reconstitute them into a mean and covariance by using the *unscented transform*. The EnKF just keeps propagating the originally created sigma points; we only need to compute a mean and covariance as outputs for the filter! \n",
      "\n",
      "Let's look at the equations for the filter. As usual, I will leave out the typical subscripts and superscripts; I am expressing an algorithm, not mathematical functions. Here $N$ is the number of sigma points, $\\chi$ is the set of sigma points.\n",
      "\n",
      "**Initialize Step**\n",
      "\n",
      "$$\\boldsymbol\\chi \\sim \\mathcal{N}(\\mathbf{x}_0, \\mathbf{P}_0)\n",
      "$$\n",
      "\n",
      "This just says to select the sigma points from the filter's initial mean and covariance. In code this might look like\n",
      "\n",
      "    N = 1000\n",
      "    sigmas = multivariate_normal(mean=x, cov=P, size=N)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "** Predict Step**\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\boldsymbol\\chi &= f(\\boldsymbol\\chi, \\mathbf{u}) + v_Q \\\\\n",
      "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi\n",
      "\\end{aligned}\n",
      "$$\n",
      "That is short and sweet, but perhaps not entirely clear. The first line passes all of the sigma points through a use supplied state transition function and then adds some noise distributed according to the $\\mathbf{Q}$ matrix. In Python we might write"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    for i, s in enumerate(sigmas):\n",
      "        sigmas[i] = fx(x=s, dt=0.1, u=0.)\n",
      "\n",
      "    sigmas += multivariate_normal(x, Q, N)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second line computes the mean from the sigmas. In Python we will take advantage of `numpy.mean` to do this very concisely and quickly.\n",
      "\n",
      "    x = np.mean(sigmas, axis=0)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now optionally compute the covariance of the mean. The algorithm does not need to compute this value, but it is often useful for analysis. The equation is\n",
      "\n",
      "$$\\mathbf{P} = \\frac{1}{N-1}\\sum_1^N[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$$\n",
      "\n",
      "$\\boldsymbol\\chi-\\mathbf{x}^-$ is a one dimensional vector, so we will use `numpy.outer` to compute the $[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$ term. In Python we might write\n",
      "\n",
      "    P = 0\n",
      "    for s in sigmas:\n",
      "        P += outer(s-x, s-x)\n",
      "    P = P / (N-1)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Update Step**\n",
      "\n",
      "In the update step we pass the sigma points through the measurement function, compute the mean and covariance of the sigma points, compute the Kalman gain from the covariance, and then update the Kalman state by scaling the residual by the Kalman gain. The equations are\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\boldsymbol\\chi_h &= h(\\boldsymbol\\chi, u)\\\\\n",
      "\\mathbf{z}_{mean} &= \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h \\\\ \\\\\n",
      "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
      "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} \\\\\n",
      "\\\\\n",
      "\\mathbf{K} &= \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}\\\\ \n",
      "\\boldsymbol\\chi & = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R] \\\\ \\\\\n",
      "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi \\\\\n",
      "\\mathbf{P} &= \\mathbf{P} - \\mathbf{KP}_{zz}\\mathbf{K}^\\mathsf{T}\n",
      "\\end{aligned}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is very similar to the linear KF and the UKF. Let's just go line by line.\n",
      "\n",
      "The first line,\n",
      "\n",
      "$$\\boldsymbol\\chi_h = h(\\boldsymbol\\chi, u),$$\n",
      "\n",
      "just passes the sigma points through the measurement function $h$. We name the resulting points $\\chi_h$ to distinguish them from the sigma points. In Python we could write this as\n",
      "\n",
      "    sigmas_h = h(sigmas, u)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The next line computes the mean of the measurement sigmas.\n",
      "$$\\mathbf{z}_{mean} = \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h$$\n",
      "\n",
      "In Python we can compute that with\n",
      "\n",
      "    z_mean = np.mean(sigmas_h, axis=0)\n",
      "    \n",
      "Now that we have the mean of the measurement sigmas we can compute the covariance for every measurement sigma point, and the *cross variance* for the measurement sigma points vs the sigma points. That is expressed by these two equations\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
      "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T}\n",
      "\\end{aligned}$$\n",
      "\n",
      "We can express this in Python with\n",
      "\n",
      "    P_zz = 0\n",
      "    for sigma in sigmas_h:\n",
      "        s = sigma - z_mean\n",
      "        P_zz += outer(s, s)\n",
      "    P_zz = P_zz / (N-1) + R\n",
      "\n",
      "    P_xz = 0\n",
      "    for i in range(N):\n",
      "        P_xz += outer(self.sigmas[i] - self.x, sigmas_h[i] - z_mean)\n",
      "    P_xz /= N-1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Computation of the Kalman gain is straightforward $\\mathbf{K} = \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}$.\n",
      "\n",
      "In Python this is the trivial\n",
      "\n",
      "    K = np.dot(P_xz, inv(P_zz))\n",
      "\n",
      "Next, we update the sigma points with\n",
      "\n",
      "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
      "\n",
      "Here $\\mathbf{v}_R$ is the perturbation that we add to the sigmas. In Python we can implment this with\n",
      "\n",
      "    v_r = multivariate_normal([0]*dim_z, R, N)\n",
      "    for i in range(N):\n",
      "        sigmas[i] += dot(K, z + v_r[i] - sigmas_h[i])\n",
      "\n",
      "\n",
      "Our final step is recompute the filter's mean and covariance.\n",
      "\n",
      "        x = np.mean(sigmas, axis=0)\n",
      "        P = self.P - dot3(K, P_zz, K.T)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Implementation and Example"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I have implemented an EnKF in the `FilterPy` library. It is in many ways a toy. Filtering with a large number of sigma points gives us very slow performance. Furthermore, there are many minor variations on the algorithm in the literature. I wrote this mostly because I was interested in learning a bit about the filter. I have not used it for a real world problem, and I can give no advice on using the filter for the large problems for which it is suited. Therefore I will refine my comments to implementing a very simple filter. I will use it to track an object in one dimension, and compare the output to a linear Kalman filter. This is a filter we have designed many times already in this book, so I will design it with little comment. Our state vector will be\n",
      "\n",
      "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x}\\end{bmatrix}$$\n",
      "\n",
      "The state transition function is\n",
      "\n",
      "$$\\mathbf{F} = \\begin{bmatrix}1&1\\\\0&1\\end{bmatrix}$$\n",
      "\n",
      "and the measurement function is\n",
      "$$\\mathbf{H} = \\begin{bmatrix}1&0\\end{bmatrix}$$\n",
      "\n",
      "The EnKF is designed for nonlinear problems, so instead of using matrices to implement the state transition and measurement functions you will need to supply Python functions. For this problem they can be written as:\n",
      "\n",
      "    def hx(x):\n",
      "        return np.array([x[0]])\n",
      "\n",
      "    def fx(x, dt):\n",
      "        return np.dot(F, x)\n",
      "        \n",
      "One final thing: the EnKF code, like the UKF code, uses a single dimension for $\\mathbf{x}$, not a two dimensional column matrix as used by the linear kalman filter code.\n",
      "\n",
      "Without further ado, here is the code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.random import randn\n",
      "from filterpy.kalman import EnsembleKalmanFilter as EnKF\n",
      "from filterpy.kalman import KalmanFilter\n",
      "from filterpy.common import Q_discrete_white_noise\n",
      "\n",
      "\n",
      "np.random.seed(1234)\n",
      "\n",
      "def hx(x):\n",
      "    return np.array([x[0]])\n",
      "\n",
      "def fx(x, dt):\n",
      "    return np.dot(F, x)\n",
      "    \n",
      "F = np.array([[1., 1.],[0., 1.]])\n",
      "\n",
      "x = np.array([0., 1.])\n",
      "P = np.eye(2)* 100.\n",
      "enf = EnKF(x=x, P=P, dim_z=1, dt=1., N=20, hx=hx, fx=fx)\n",
      "\n",
      "std_noise = 10.\n",
      "enf.R *= std_noise**2\n",
      "enf.Q = Q_discrete_white_noise(2, 1., .001)\n",
      "\n",
      "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
      "kf.x = np.array([x]).T\n",
      "kf.F = F.copy()\n",
      "kf.P = P.copy()\n",
      "kf.R = enf.R.copy()\n",
      "kf.Q = enf.Q.copy()\n",
      "kf.H = np.array([[1., 0.]])\n",
      "\n",
      "measurements = []\n",
      "results = []\n",
      "ps = []\n",
      "kf_results = []\n",
      "\n",
      "zs = []\n",
      "for t in range (0,100):\n",
      "    # create measurement = t plus white noise\n",
      "    z = t + randn()*std_noise\n",
      "    zs.append(z)\n",
      "\n",
      "    enf.predict()\n",
      "    enf.update(np.asarray([z]))\n",
      "    \n",
      "    kf.predict()\n",
      "    kf.update(np.asarray([[z]]))\n",
      "\n",
      "    # save data\n",
      "    results.append (enf.x[0])\n",
      "    kf_results.append (kf.x[0,0])\n",
      "    measurements.append(z)\n",
      "    ps.append(3*(enf.P[0,0]**.5))\n",
      "\n",
      "results = np.asarray(results)\n",
      "ps = np.asarray(ps)\n",
      "\n",
      "plt.plot(results, label='EnKF')\n",
      "plt.plot(kf_results, label='KF', c='g')\n",
      "plt.plot(measurements, c='r', label='z')\n",
      "plt.plot (results-ps, c='k',linestyle='--', label='3$\\sigma$')\n",
      "plt.plot(results+ps, c='k', linestyle='--')\n",
      "plt.fill_between(range(100),results-ps, results+ps, facecolor='yellow', alpha=.3)\n",
      "plt.legend(loc='best')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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U3YhuDZoxplcMN3b0w2oxoe4+jv/r8wDInTQao25glcYMF5kg6NEwbzmMzzs/\nAOC8swdGndKvP2/eOl544UvS0nIAaNu2LbfdNqzKYz2fJM7V5IUXXkBVVd58882aDkUIIYT4wyso\nKGDFihUsX76cZcuWcfjwYTp3bs8PP3yMouRiMmViMuUCGuHhx+nUqQlmsxmLRcVsVrDZLAwe3AEA\ntTCZO1tv+HyumwsT50WbKHjhNuC8xPmmkqv9YVbxdG2GNWE75hW7cY3oXmX37NTcJH+ygE5OD8ui\nYVr6lsKEuT3q8Z7cfG0DBt3oQ+Q2G2xbw/WqjWc63kG+0yDfqRMdbmZYLz/qh5yXDjrd+D8yFZPT\ng+OeXrgHtSs7gErQmtT3ThBMTse8+RDq9iQsy3ZhWZ6Ikl0AgGFWKXh4YBktmAkOvoa0tBzat2/P\nU089RZ8+fSo39rocJHGuBl999RU//fQT33zzDZmZmUXbQ0JCsFjKVxxcCCGEEOVz8OBBBg4cgMPh\nLNrm42PF19eJqu4okUx17NiExYtfLLM9c+HwAa2UxNndsyV6oA/m3ckoB09hBPthXrsPw6LiLqzb\nXPKcFlgTtmNZtafSiXN6QS4JSduZu2cTK47vZM1UFwCftDHBifY0cvRhdO8o7nrOn7pB3t5ypXE0\nvAJROek8d2fwRdu3fr8e885jaI3rkvfqXZWK9aJUBU/raCxr9xE08NViu7TYerj7tsI5ojv6NREX\nnGhG0xqh6w3p3t3GggVN6dChQ7UnzOeuLqrchg0byMnJ4ebz1rM3mUzMnj1bxjoLIYQQl6mgoAC7\n3X5ekuRBVTNp1sxDUJAvcXENuOWWLgwa1J7o6JCisckVdXb4wNlxuMVYzbgHtsE2Zy3WHzdj1AnA\npBu4+rTECPQttT332XrOFRznXOBxcTjzNIeyTrM/4xSLDuxg65kDGOgA9EyC9qcg1W4hK348C26I\noXucrUQSqTcIxTCrKKcyocAFPqUvGQ5gWe1drMVxfz8I8KlQvBXlGnAtlrX70IN8cfeKw92nFe4+\nrdCjzxVTcLs9fPPNKm6+uRPBwS0Kk2bv52wyQceOHas1xgtJ4lwNJk2aVGodZyGEEEKUn9vtZuvW\nraxatYqVK1eyadMmli37gdjYYBQlE0U5A7gBWL/+3/j52QgM9I6Hzc7OvqxrmtJyUI+ewfC1opXo\n7fRyDe7gTZwXeRNnANegUoZpFNKujUYP9EE9kopyPA29cAluwzDIcOSRlJ3K0ZwzHM0+w5GsFA5l\nnmZf+imdNUCzAAAgAElEQVROF2SUbExXIDMWa1ZzXl93CNiL9cGBTH+qZdk3pSroUWGoh1NQk1KL\nKm+UxrzhIACeLk3LPKaqOB4bhOu2LugNQs+V8Cuk6zrz56/njTe+5/Dh0xw4YGbChFurPaZLkcRZ\nCCGEEFedKVOm8N///pf09PSibSaTicTEBTRr1rnE8X5+tiq57tlhGp7W0cUnBp7H1bc1ht2CZeNB\nDKs3lXJdbCywquDo0hTfJTtY8vlXzLpW52j2GZKyU8lzO8s+T1fAEQIFoZAfho8rihtjW3P7oDD6\nh+VT74ufMcwq2kP9LnlfWkw46uEUlMMpZSbOpoxczPtOYNjM3vuvAr//vouxYz8mLS0XVVVQVQWz\nWeGaayJJSPgneqP6xY7fsyeZ3r0noGl60baYmBjatCn5d14TJHEWQgghxFVGIyvrOOnp6cTG1qN3\n7zh69YqjR48WhIb6V+uVzduSAPC0uUji6GfDfX1rrIs2Y3J5cHdsglG/+NjhI1kprE7ey4ZTB9l4\n6gCDTMm8A+Qt3cxP569B4rF6k2NHsPdVEAIFYYSa6xJfvy7x0T60irYQF22lRZQFi9k7DMP3lYWY\nNB3n7V3KtSKh3jgcAPVISmEffSn3vrGwt7ldDFirJkVs1qw1Ho+CYRh4PBoej4bTCfn5ZpzOXoAB\nmIpeHs/+oqQ5KiqKJ598kuHDh2M2Xx0p69URhRBCCCH+dDRNIysri9DQUABMJgeqegpVPc7YsW24\n6aYJdOrU9IpN/AJQtx4GwNM25qLHOW9uf141jXO9zck5aby+dh7f7V1d7HhbtALo9D1ghcQhkB8G\njmDCfP1o1tBK84aWolfLaGvRxL5S5Tmxfb4cAMfYAeW6L+28xLks5g0HAPB0qophGiY0LZbQ0MYs\nWZJAvXr10DQNTdPQdR3DMCgtDW3atBlHjx5FUZQr+vdeXpI4CyGEEKLa5efn88ILL5Camlr0SktL\nIyDAn71716AoJ1CUU4AHgIiIECKquOZxeZydGFhaRY3zuQe2wTCrmDwarkHtyXEV8MHmxXyw5Sec\nmht0FdKugaxGkN2QbTn1ybBMonFuAVO6tiKqYwTNGloIC6z4BEbbnDUomXm428fi6dDk0icAWmPv\nhDvlSGqZx1jWeRNnd+drKhxTcb54PC3RNO9Y7sjISABU9dL3ajKZynVcTZHEWQghhBDVSlGy8fVN\nY968eei6Xmyf2Wyg66uviq/iTanZqMnpGH42tCb1L3qsEeJP7odjIDOPT1z7eP2zeaQ5CickprSC\nQ/0Is9ahR5ydHq3s9Iy34TuhBSzewijzcZxxF+/RLvvCBvZpCQA4Hupf7tP0mMIe58Nl9Di7PZi3\nHAK8KyRWVFpaDlOnJvDMMw+h63EYRtWMOb/a1PxTKoQQQohaaePGjSQnJ5Obm0tOTg6ZmZmsXbuW\nmTOnUbeugsmUgaqeAXIAgw8/HENwsC/h4UGEhwdRp04AFsvVk4oUmxh4QZWHCzk1Nwvbmvnnql85\n9NsJ78ashnBwIN0bXsNj4wPp384HRTk33MDTswW2xVuwrNyDc+R1lxWjZXki5j3J6PWCcd3Sqdzn\naYUl3pRjZ0DTS9yfuus4pnwXWmy9MlfqK8uuXccYOfJdkpPTsVrjeOyx6lk05Wpw9TytQgghhKgF\ndBSlANB49923+e23lSWOWLHiY0aMKFkFYfjwblcgvstnvsiKgQBuzcP/9u7k8+1rWZ+2Dafh8O5w\nBMGhAQyO7cTjzwfRoVnpva3unt6SceZVe8AwvIWIK8g+tbC3+f6+FZvA52tDrxeMcjoTJTkdvVGd\nYrstG84O06jY+OalS3fwwAP/JTe3gPbt23PrrbdV6PzaRhJnIYQQQpSQnZ3NL7/8wsKFCxk58m4G\nDeqMyZSGqp4G8gGDHj3qERjYCX9/O/7+Pvj722ndOoo+feJrOvzLUtTjfF7ifCrDzeRft5FwYgNJ\n+g50teDcCTn1UVPbcHezPjz+jzCaRFx8dWCtZQP0UH/U5HSUI6lFwyfKSzmcguWXbRhWM457+1To\nXAAtpq43cT6SUiJxNq+v+MTAWbN+4/nnv0DTdIYOHcp//vMf7HZ7heOqTSRxFkIIIQTgXZBj8+bN\nzJo1ix9//BGXy7ucs79/HkOGlOwdHTdu8JUO8dKS0zBtOwI9Kz7BTT1vxcCUTI2X5u1kbsp3GP4n\nvNXSVDDl16Wh3oa+kR3p3zmKri1thAaUczKbouDu3hzbwk3Ypy8l/7W7KtTrbJ+egMkwcNzRFaNu\nxYZTgLeyhmXtftTDKXh6xRXbV1RRo5w9zh6Pxty5G9E0nSeeeIJnnnkGRbn48JY/AkmchRBCiD8h\n9dgx/D/6iILBg3F18w6h+PHHHxk7dizgrW7Qo0cLhg7txM03d6jJUCtEvfddlBWJWL4ah3tgm3Kf\nZzqViXoyA83PzrMrNGYdnIZWfz34G9j0QHrW6cbIVl24Ob4xZvXyy6Q5/9oX6+It+Hz8C9jN5L84\nrFzJsymnANuXKwBwPFS+EnQX0ssoSaecSEc9noYe6IPWPLJcbSlKFNOmfcWKFasZOnToZcVTG0ni\nXI3eeecdFi5cyPHjx7Hb7XTo0IEJEybQrFmzmg5NCCHEn5Vh4PPddwS99BJKbi4+c+eSmpAA0QHc\ncEMDYmLqMWRIB0aP7ktUVJ1Lt3cVUZJSUVYkAmD7dlWFEue81YcIBVb4BTA9402IyMVkKAyL6c/b\nA27H31o1QxDcfVqRO/Vh/B/6CJ/Ji0AzyJ84/JLJs+2bVSi5DtzdmqO1blShazqdbmw2S5kl6YoN\n0yhHr7GmxeLxxBIaqvypkmaASvep79ixgx49ehAUFESLFi34/vvvAe/68g888ACBgYFER0cze/bs\nSgdb20RHR/Pqq6+ydOlS5syZg9Vq5a677sLhcNR0aEIIIf6ElDNnyBk5ks+feorM3Fy0unVRcnII\nffJ+zKa1+Punsm7dv3jppeG1LmkGsM1dW/Sz9actmLLzyzzWMAz2J7v5aGE2I147zaz/tw6AjU1S\nwZZLXHAsy+5+mf/ePLLKkuazXEM7kTvjEQyzis8Hi/F96VvvZMEyKCczsE9dAoBjbHlL0CkYRn00\nrQl33/0+N930OlN3HuUMJXucS1v4RNd1du06xtSpS7jvvveZPv1XDCMUTYvH42lKFaSQtVKle5xH\njRrFiBEjWLVqFQkJCQwdOpSjR48yY8YMdu3axfHjx9myZQuDBw+mW7duNGzYsCrirhWGDRtW7P24\nceMYOHAgBw4cID6+dk6cEEIIUbsYhkFiYiIJH37IkoUL2aJpAPjcO5g7JgwhuNezWNbuwue9HykY\nP7j2jlM1DKxzvImzEeKPKSMX68JNxcq+ZeZqrNrlZOnWApZuzSHZlQQhhyH4MOOMowDsamTlP31H\nck/cdSim6vssXIM7kjPzUQIemILPf38GXSf/tbuL9Tyru49j//AnbHPXYnJraNF1cd1YstSbruss\nX76biIhgmje/Bk2LRNfroet+5OTksHnzYXJzc1m//gDPAzckHmfovLUMGdIRi8WMZf25ihqJicd4\n7bW5bNhwgIyMvKJr5OT4MmpUx2r7PGqLSifOe/bsKUoQ+/fvj4+PD4cPH2bOnDmMGzeOwMBAevfu\nTbdu3Zg/fz6PP/54pYOujXJzc/nyyy8JDw8nNja2psMRQgjxJ/HUE0/w3bx5Re/9VYXr+8ZTf1g8\nRh0ruR88QOCI/+Dz5ve4+rRCa3eZC3PUMHXnMcz7TmDUCaRgwp34PjWNjKkrecMdz+5jDnadTCfF\ncQaCjkHwYWhxFFRP0fkdT3r/fPFvzxIcV/EFQC6H+6b25Mx6jID7P8Tn4yWgG+T/ayTmlXvw+XAx\n1oQdABiKCefQTuRPuB3MKgUFLnbsSGLHjqNs357EqlV7OHIklREjhjBp0r3AucmKAQEBbN68mZ9/\n/pl5c+eyfNkyftR01r/wDUOG3ISea0LdcRRDUXBeeyM5e4/xyy/bAIiIiKB79+50796dbt2u7lKC\nV0qlE+cbb7yR2bNn8/zzz5OQkEBgYCDx8fHs3buX5s2bc8899zBkyBDi4uLYu3dvVcRcQoMGDUrd\nnpycXCXHV8bq1au57777KCgoIDo6mjlz5uDr61u0/+uvv2bGjBmkpKSQnp5OkyZNsFgsfPPNN9Sp\nU/u+JhNCCHH1UEz5PLp9A78DQxQTg/7Siy6v343d91ydYff1rSkYOwCfj5cQMPZjMn97BfyujlXf\nTJl5GFYz+F48Ho9mkDV1BcHAV/Wi+du6/ZxWTDTYuY/vD/yTE3VzIFgrcV7L0Ib0imrJAFsUEbkz\n0QN9CG55ZTu33De2JefTxwi47wN8piVgXbQZNTkdAN1uwXlPLxwPDyya2Acm1qw5zIgRbxRrJzIy\nkmbN2nB+0nyWn58ft99+O7fffjt6v37M37OHnNtHoOsdMW9ai8mj4W7VCo9PC2JiIvjoo4+49tpr\nadSoEabLqDX9R1bpxPmdd95hwIABvPzyy9jtdubPn4/dbicvLw9/f3927txJhw4dCAgI4NixY6W2\nERYWVur2jIyMyoZX49q3b09CQgKnT5/mww8/ZOzYsfzwww/4+PgwadIk0tLS+PnnnzEMg1tuuYXX\nXnuN9u3bV0ssZrO5zM/6amKxeOtg1oZYxZUhz4QojTwXZdN1BybTEdQ9K+h94BjHQv3h19cgLqr0\nE96+H2PlXtRdRwn55xy0/z5yZQMuzakMzB2fg5h6eFa/Aeq5hNAwDJLPeFi6OYefNuSydPtxdvzi\nrTjxYZcdZDWC/zWHYbvh7gOZvFMP6vgE0yQknNbh0fRp3JrejVpRzz8YANOXv3sbbt+EwKCgK36r\n3HEdHj8/frvjDX5NTmev1cyeQF/s9UNY8/4EfPADfDEMPyCALl360Lr1j7Rt25Z27drRtm1bunTp\ngqpeuiyeOS6Ox/fswd29O3pYGOquXQAoPXsSFhZGWFjYH/Kb8bP/v6isSiXOBQUF9OvXj0mTJnHr\nrbeyerW3JMnmzZvx8/MjLy+PrVu3AvDkk08SEBBQajuvvvpq0c+9evWid+/eFYqjoj3F1dGzXBa7\n3U50dDTR0dG0bduWuLg4vv/+ezp27MjcuXNZvnx50Xiyhg0bcvz48WpLnIUQQvwxpaamMmnSJMaN\ne5y6dQtQ1cOYTA6U5d6v3NWB7dDKSpoB7FY8nz6JuftzKDMS0G9sjzG0yxWKvnTZHywhLDMPthxi\n5sj5zI3twOkMD6mZHlKzPHgMN4Tthfpb6RN4gIb5cCgYdsX6MzquG1abDi8s5dXkSF58+m38yprg\n59FQ/zUHAGN4jyt4h+ecPJnBTS98zi53Ya+4ywNnsrHnutC0LpjN3nTtbOdvvXqBbNiw4bKuZRQm\nxaZDh7x/rvWOC9e7dq3EHVydfv/9d5YvXw6Aqqr06tWr0m1WKnHeuXMnOTk53Habd3nFHj16EBsb\ny+rVq2nWrBm7d+8uSgITExPLLFny6KOPFnuflpYGgMfjKe3wWstkMmEymXC5XCxdupTevXsXJc0e\nj4dt27bx8ssvV9v1PR5P0Wd7NTvbe1QbYhVXhjwTojTyXHj/HZ45cybff/89TqeT7OzdvPHGiKL9\n/glbUYH8zk1wZmdfvLHGodhfGo7fi1+jjJ1CZssIjPrB1XsD5zEMg22HXCzeUMAvG3JZ8O3PnP0u\n4cbFP/JkfzPOwHQIS4FGpyHgNKhOAEatMgEGebd15MT/PY1VtZDdJQ39jTX4JJ7Aufkg2WX84mD7\ndBmW/SfQYuuReXtHuNTnVOUUbLYoXC4z9erVY8SIEbRs2ZImTZoQGxtLVlZWlV7NNzycYMC1ezeZ\nZ85Qf/VqANJbtkT7g/23FB8fX1SMISwsjJUrSy4PX1GVSpxjYmIoKChgwYIF3HLLLWzcuJHdu3cT\nFxfHiBEjeO+99xg8eDBbtmxh7dq1fPLJJ5UOuLbIz8/nX//6F4MGDSIqKoqsrCymTJmCqqpcf/31\nrFmzhtOnTxcd/8knnzBq1CgiI8tXeFwIIcSf186dO5k4cSJrC3sLTSYTAwe2YeTI83qJdR3L6j0A\nuHu2KFe7jof6Y0nYjnXZLvz/Ng3HEzeBw43J5fH+6XSDy4PWtH6JlecqyjAMjqZ42HbIxYqdDn7a\nUMDJdG+P68DM3cQ4MjkWZCHLrhF/OpuH3Z8z+YJlENrUbcxfYrty338WAAVEPXgbVrXwK3mbBdfQ\nTtg/+x3bnLXkv1RK4pzvxPetBd4fJ9wOlupb3sIwDE6dysQwDCIjQwEbmtYQXY9A132ZNeszGjRo\ngNVqrbYYADzR0QCoSUmoBw+iZGai1auH9ieqelYZlXpC6tSpw7fffsuECRMYNWoU4eHhTJo0iWuv\nvZa4uDj27NlDVFQUISEhzJw5s8xJeX9EqqqSkpLC+PHjSUtLw9fXlzZt2vDNN98QFRVFgwYN+Pe/\n/82XX35JXl4eoaGhJcrXCSGEEKXx89NYu3Yt/v52/vKX63jggX7ExtYrdoy6JxklLRctIgQ9JryM\nli6gKOS+/wDBvV/C+nsi1t8TSz3MMJnIWvUaWrPydfacTZK3HnSx7ZD3tf2Qi4xc/bxruwlufJCg\nmEQe/tZbTeKjDm621YOFX8PEVQrZd3UmpmFjWoY1oEVoAyL8Q7D+uAk1uwBP60Yl4nEO7479s9+x\nzl1L/ot3lFjcwz51CcrpTDxtG+O6pWpLrZ08mcHGjQfZvj2p6JWams3YsbfzyivPoWnhwLkkOSbm\nylQz0Ro3BsCclIR10yYAXB06VGjp7z+zSv9qNWTIEIYMGVKyYbOZGTNmMGPGjMpeolay2WxMnTq1\nzP2KovD3v//9CkYkhBCitlPVdFT1GC1apPDZZ49z3XUtCQjwKfVYyypvJStPzxYVSoqMiBBypz2M\nz38WYqgKWM0YdkvRn+qeE1g2H8I+fSl5b40qsx2n22BNooNfNhXwy6YCjpy+YPil4iKofhqRUemY\nQg9x2LOTTM2JPRsG7wGPApEP38bQdp1wHZxJyPoDfLC7HgVDbijWzNnazc5hJculebo0RYsKQz2W\nhnnNPjw9zvW8m9Jz8XlvEQB5Lw0v14p5FbF48W6efXZasW1BQUFoWiiaVnO9u1pEBIbFgpqSgq1w\n/K+ro9RnLi9ZclsIIYS4ShUUFOBwOAgJ8cNiOYyiHAW8K8zddNPFJ5KbV+4GwN2jfMM0zufu3Qp3\n71al7lP3JBPc80Vs364i/+93YASdK7F6Mt3Dr1scLNlcwG/bCshzGN54fdLxbXSC8Mg0lIBUcpRT\nnHGmk4VBFoB3qDJtwxvzTlIAFn0Hzpvbc9f1t3g/h38Mxzrk3/h8+DOO+6/HqBMIgCk7H+svWzFM\nJly3lzKZUVFw3tEV33d/xDZ7TbHE2efdhSjZBbj6tKrUsJOcnILzfnkJRNPCMYwwBg5sy+LF3gXP\nWrduTevWrYmKiqr58m6qihYVhfnQIew//QRI4lwRkjgLIYQQV5h15Upsa9aQM24clFEma/369Tz1\n1FO0bBnDp58+jMmUV+pxpdJ1LKu9Pc7lHd9cXlqLBrh6xWFdnsjRt37lu3Y92XbIxdaDLk6kaWDS\nwP8k1DlGQMRxNP+j5Bs55ANHANzediyKSpPg+jQPjaRN3WiGNO1ETEAdgt94DgDnvX2Krunp1gxX\n/2uxJmzHZ9KP5L9+NwDW/23E5PTg7tkCPSKk1Hhdw7vh++6PWH/YQN4b94DdgnI8DfuMpQDk/6Pi\nwyRPnEhnwYINLFiwgSNHUtm27XtUtT6aFgh4E+O6deGLL76ocNtXgqdxY8yHDqE4HBg2G25Zzbjc\nJHEWQgghrrCgl1/Gsns3nsaNKRg+vNi+/Px83njjDWbOnIlhGNjtbrKyUggO9it3+2ricZSMPLQG\noejRdask5jNZGr9uK+DXLQ4CtbbMIJHAT5fyZnIQekAqhJxGiT4NASfQTd7sOAfAgDo+AXSq35RW\ndaJoGdaQFqGRxAbVw6IWT0Msv+1EPXoGLSoMd5/iPd75L96BNWE79lm/4nh4AHpUHaxz1wGlD9M4\nS2veAE/rRph3HMWasA3X4I74vPU9JqcH562d0do0LvdnMGvWb8ydu4a1a/cXbfPx8SExUSMurgbq\nP1+msxMEAVzXXgu2q2PBm9pAEmchhBDiSnK5MO/3Jl5+n39eLHH++OOP+eijj0hJSUFVFcaNG8xT\nTw3BZrNgXrOPwGFvkz9xBI6HBlz0EpZV51XTuMyhAZpmsOWgi4QtBSzdUsDWgy4MNR/q7UC59jB/\n36kQm5XJzf4z+V9z7zlnp/o1Ca5P14hr6BJxDZ0jrqFJcL1yDVGwfeZdiMQ5qjeoxccca/GNcN7e\nBdu8dfi8vYD8F27HsmI3htWMa8jFhxo4h3XzJs6z16A1jcD2zSoMs+qtpFFuvixcmMjatfux221c\nf30/hgwZQv/+/YutCFwbaOcnzp061WAktY8kzkIIIcQVZD58GFPhOgXWTZsw79qFp1UrFCUHt/s0\nKSkpxMdHMXny/bQ5rzfUt7CX1OfdH3GM7nvR0mmWld7E2XMZ45sPnnQzY3EOc1bkkZ6jAzqEHkRp\ntQXC9mKYNHTg/a4w6Wd4YbMN2y3tiAtrSMuwhrQNj6Gub2CFr2s6nYV18RYMVcFxd89Sj8l//jas\nP2zE9s0qUBRMhoFzYJti46xL47y9C74vf4d1yXaU7AJMuoHjr73RL6hEUpKCrtdH1yPRtGAefvj/\nGDbsDAMHDsTf37/C93i1OL/H2S3jmyvkqk6cDcNA1/WiRULE5dN1HcMwajoMIYT40zu5ahV7gesK\n3/t/NYWC/3cvkM3Ikc25/vqXaNu2cbEeWnXHUSwrvJP9lJQsrD9tLbuXVdcxr9kHgLtny3LFpOsG\ny7Y7mLooh4TNBd6N9nSC4rfjqbOFPLLQAcVkol+j1tzatDNtbwpHX/Efuu1zMi3qZrSWlasUYft6\nBSaPhuum9hhljFfWY+vhHNUL+6zfsH9RWBFi2KVXvDMiQnD3aon190RvL7Wvlfz/u6XEcXv3JvPx\nx0vw9fXjlVeeK6yxfG6ITFWsPHc1OFuSDgpL0Ylyu6oT55CQEFJSUggPD5fkuRJ0XSclJaVolS0h\nhBBXXnp6Ou+//z6fTJ9OfWDHDR0I/HkTPrN/omDiQAjwISIihIhSkkafKd7qB1pkCOqJDGyf/FZm\n4qzuPIaSmYcWFYbeqM5FY8op0PluWR7TFmdz4IQHTBqW+vsIa7GZU+zn7Jp1jQPrMjLuOu5q0YNI\n/9Ci81139cA+81fs0xLI+89fy76QYaAcSUWPrlN62Tddx/65NxF23NfnojHn/98t2L5ZhanAhR7o\ng6t/m4seXxTrsG5FdakLHrkBo965McmbNh3kzTe/59dfdwLg6+vLU0+9i59f+ceV1yaexo1xt2yJ\nFhGBXufiz4go7qpOnC0WC2FhYZw5c6bmy7fUYoZhEBYWhqWMmdtCCCGqT0FBAdOnT+fDDz8kJycH\ngJ5A+sB4fLJysKzdh23eOpxlJIzKiXSs89djKCZyvhxH0KDXsP6eiHLodKlDDc6Nby67t/lEmoep\ni3L4dEkOOfkG2LLwb7kFIjaTq2dzCvAxW7mlSUdGxl1Ht8hmKKaSCa9jTD/sM3/FNnsN+f8YhhFS\nyvAFtwf/x2Zgm7sWd/tY8l+9C0+Xa4rHvHw3alJqqZMCL2TUD6Zg7AB83/0R19DOYC/fv22uwR3Q\nJ34LFjOOv90IgKbpPPTQRyxYsAHwTvQbPnw4DzzwwB82aQbAaiU1IaGmo6iVrurEGbzJc3h4OVc8\nEkIIIa4yY8aMYdmyZQD07duKt/aeoOOJDDI7N8Xha8Oydh/2T37DeW/vUify2acmYPJoOId2Qmvd\nCOdtXbB/vRL757+TP3FEiePPjW9uXmLfriMupvwvm7kr8/BoBoQcIuTaTWTZ95CLDjpcExLBX+P7\ncGfzHgTbL548as0icfVthfW3Xdi+WIHj8UHFD3C4CXhgCtaft3pj23yIoJv/hXNoJ/JfGl5U8cP2\nqffzKW1SYGkKnrsVLS4Kd//Wlzz2LCPAh8zf/wlmFSPQOyZaVQMwm8Ow2+2MGTOGhx9+mJCQ0oeJ\nCAG1IHEWQgghagOPx4PZfP4/qxqqms1DD/UlI+MIL700jN4dmxLa+BEMs4rWpD5aTD30v3+FecdR\n1C2H0drHFm80pwDbZ8sAinpJnff1wf71SmxfrSD/+dvAdl6Pq6ZjXlNYv7lwYqBhGCzf4eCDBdn8\nts0BgCkwmbC2CaQph8kAzIrKkNhOjI6/nh4NmlfoW17HQwOw/rYL+4ylOB4ZCGbVuyPXQeCo97Cs\n2I0e4kfOrMewrNiNz5SfsC3YgHXxFhxjB+D4S69LTgoswWIufcGTSzg3dtqGpjXG42nAhAlNeOEF\ng4iIiAq3J/58JHEWQgghLkNKSgrr169n/fr1rFmzhvr16/HVVx9iMmWjKJmYTOmAkwEDoujf/x8o\nioK65TAm4/+zd+dxWZX5/8df55x7Y99BQGRXcVdUFDXKXHKpzDRtcapp32uyZpqapqZpmmmdvmVl\nM5YttriMUz81SzP3HXdZBAEFRBGQ/V7POb8/bkQRUFTcmuv5ePgI7vss11HSNxef63PpuBI7gMn9\nT7D91qF4zFiK5bOV1J0SnC1z1iBXW3EOSsTV8J4rOQ5X9ygMewsxLd7WJEAquw8iV1tRo0PQooLZ\nnGXj+dnH2J7rcF/Pt5LIASvZr+6gHAi0ePNA75Hc0S2NMK9z60PsvLYnamwoSn4ppqXbcYzvj1RZ\nh8/UdzBu3Y8W6kf1gumoSR1xDe2K/TdX4fnXBZjnbcDjvR+wfPAjkqqddlHgWY3H6WL37gPs3p3H\ngQNHyc8vpaDgKFVV9axc+Q9UNQJVjULX3b2LO3TocN73FP53iOAsCIIgCGehqKiIKVOmUFBQ0OT1\nw5/tiesAACAASURBVIcPIssbmi1mlySpcQbXkFkEgNr1RAcK22/S8JixFPN/NlH/l6knWqu5VCwz\nfwLA+vB1J18Q251X4/3sF1g+W9kkOB+vb67u35kH3y1j/hr3boPBQXbiB21km3UN+1UXZsXAA71H\n8WTyOHzN59mDWJax3TcCrz9+heXj5ThTOuM7+U0MewpRo4KoXvBMk1psLTKI2g/vx3rfCLz+9A3G\nTe6e1mdaFNhWNTUqqal/QNO0Zu8dPdobX98rZ6MS4fIjgrMgCIJwURhycjBt3Ur91KnnvClHW+m6\njqqqwIngenKAPdXu3buprq6mpqaGw4cPU1JSQklJCe+88w6K0lB6gB1FqaVjx3pKSw/j5WWmf/94\nBg3qzODBXejfP/6MHaCUzGIA1KTIxte0+A440rphWpWBee56bPeNAMC0KB2lsBw1NhTn6D5NruOY\nPBj95bkY12Uh55SgJbrLDJSGlnXP7AtjfnkdJpOTwSP3sMO1jE119QBM7jKYP6ZMJMq3/bop2G8d\niuer/8G4Phu/kX9BKSpHje9A9X+mo0W23NFJ7RdH9aLnMP6wHbmilvphXdEdLkymk6OJ+/f+1Vfn\nsnXrfkJCfAkJ8SM01BeLxci0aWl4enqi6/5oWiC67oefXwyTJk2iurqa6OhooqOjiYmJITo6Gm9v\nn3Z7ZuF/kwjOgiAIwkXh++KLWFavRg0Px3711RfsPi6XiwEDBlBaWtrsvc2bNxMZGYl7jzsNcCHL\nOnfccTtlZeXNjv/znycRHu6FJFkBO6BiMMDPP79IbGwohuP1vG2kZLlnnF1dI5u8br/rGndwnv0L\ntnuvBcDywY+Au3XaqQvmdB8P9yLBL1e7SzxemcrSjbXcsCobC/Cjd0d6pe7liN9yVtUdA2BYxyRe\nSr2F3qExZzXmttB9PLDdNhSPfy1HKSrH1SOK6nnT0UNa3wjF4XCxYUM2S9dksnFjDtnPfsHMmc8w\nbtxoNM0T8EJVPQCJ9PSZrGn4puBk8fHDuOqqoY1lFwCSZOTzzz+nvLz5n6cgnC8RnAVBEISLwpCb\nC4Bpy5bzCs5Wq5WdO3eSkZHBfffd1/CqE0WpA2oxGmsJC/OirMw9u6zrNG4AZTZvwmwOwh2a9cZf\nAwZ0oqoqGG9vS2Mv5YiIALy9K5AkW7MxJCae20IyQ+OMc9PNQhzX9UEL9cOQfQjDxhyQ3B0otEBv\n7FOHNLtORY3K9sGDGfHlapyz19K/ZBAhhSXc4bST7+uNftO37Ko/AlboHhTFC4NvZkR0rwva2tV2\n/0gsX63F1SOKmjlPoPu33pHjww9/5PXXv6Omxtrk9fx8I05nYrPjX3nlbxQXF3P06FHKysooKyuj\nqqoKiyWiSWgWhAtNBGdBEAThwnM4UA4fBsC4bdtZn/7zzz+zcuVK0tPT2bt3L66GLat79fIjNbUT\nklQDuBqP/+676fj4eDQLiu4AbW92/S++ePysx3S2pGO1yIcr0T1N7o1ATmY0YLtjGJ5vL8Iy+xck\nq3sxn+3ua8DTHQw3Zdn4ZGkN6TkOCo64AA+2eIfTv7aEodm7ifU4CMDP8bUU19cS4xvCH1JuYmLn\nlBZ7MLc3LTaUiox/goex5U1OALCgaaH4+CRRU/MNXbp0YdSoUVxzzTV079691W2sExISSEhIuHCD\nF4Q2EsFZEARBuOCUkhKkhsVaph07QNNOE65O5WThwq9ZuPAHAGRZomfPTgwZ0o2ICCeSdKzZGb6+\nLS94u5SbaTXWN3eJbPHZ7dPS8HhnMabvt4BLQzcZsN49nNW7rby9oIq1e04Efg+TROeEOlYGdKT/\nwhIet/0/yhq+mdjWxYPX0yZxR7erMCkX+Z95LzNWq4N167JYvnwXiqLw178+hKYFoeuBqKovoHDd\ndZGsWzeCmJO2fhaEK4EIzoIgCMIFpxw82PixXF2NIS8P10kziNXV1axZs4bg4GBSUlKQ5Tok6RiK\nUoEklTNpUme6drUwYEACffvG4uPjga+vb+O5VwIlyx2cXUmRLb6vRQXjHNEL07KdAORdM4Bb37Ox\nOdu98bW3t4MhaXlo/vlkVOWys7acXD+43wQDC1zYG8qtn3/2RSydLm6LNZvNyaJFW1m4cDOrV2dg\nbZgx9/Hx5rnnPm62c62Pjw8+PmKhnnDlEcFZEARBuOAMRUVNPj+8bBnzli1j9+7d7Nq1i/z8fADG\njr2KYcOeQpKqcdchu40e3YfRp3SWuNK01IruVFW3pxHSEJyvr+hLht2On7+VHkO2s8e5lh/r6sHd\nYQ5/sxeDYhPZN6qW/otyMaugxoVd9NAM4HRKPPHEp9jtTgB69uzJ8OHDGT58+EldSQThyieCsyAI\nwiXi+emnANTfffclHsmFpxQWAqD5+iJXV3N4yzr++uMvje+bTAb69o1l2LAoJKnyUg3zgmqpFR1A\ndZ3GT9usLN5Uzy/bAvhnh74Um304HGNmQMpydls3s67OPYM7oEM8ExMHMTiyM92COiJLMkr0QVj0\nZ+DEboEXSm2tDVmW8PQ0Awq6HoqqhmIyBfLww48SFBTEmDFjxKYiwq+WCM6CIAiXgFRbi/8LLwBg\nvflmdN/W23ZdySoqKggMDEQpdJdqOMYOwPLNz/QvzOGee4bTq1c0vXrF0KVLxCn9e39ldP2kUo2O\nVNaqLNpUz6JNVlbvsuI4sa6RN29KxRy/kaq6d9lS6551HxndmyeSxzIoonOzS6s9OuHsH49x636c\nad3addhlZdVs2pTDxo05bNy4j127DvDuu79j0qRb0LTgJh0tpk+f3q73FoTL0a/4bylBEITLl6Gh\nNAHAmJ2NY8CASzia9pednc3777/PkiWLWbt2LiHF7h68jht6Yp73CwHZh/jH0hcaO0b82smHK5Er\n63D5efHHJSpfriimzuZukSfJGj16H8E/Jpt81x6y6sqgFhRJ5pYuqTzWbwxJQa2XdwDUznwA48q9\nOG7o325jfvPN7/n73xc2eU1RFA4ckFDVluu0BeHXTgRnQRCES0DJy2v82JCRccUE54qKCvLy8hg4\nMAlJqkPXLei6GV038fPPK/jwww8xGAysWbMGAINBYfPmRfQ5eAQAtWskalIkhj2FGHYewDW4+Qzq\nlcawPhstMhAtOqTVYw6syCcAWC8FM3NJLUgq3fsW4RudzT7bbvbYasC9BpAQD18mdk7hwd6j2ry7\nnxYdgr2dtqwGC6rakbi4NCyWJfTt24+UlBRSUlJITk7Gy6v1/syC8GsngrMgCMIl0GTGOSvrEo6k\n7TZu3MgjjzyCw17PNn8PwgYlUvfePbi3RTaSm7ucDRs2AGA2G7njjmE8+ugYokL9kB/5N7oio0UE\n4EqOdwfn9P1XfHA2/rIH38lvocZ3oHLDq03azNXUa2zMsvPB99UM+CGbPsAerxBSrtrHQe+f2Ftf\nBg3l3NG+IYyN68e4uH4M6JCA0uZWfefH6XSxc+cB+vePR9f9UdWOqGooYGDEiEgyM2/EZDJdlLEI\nwpVABGdBEIRLwFBQcOLjyzw4q6rKu+++yzvvvIOmaQyMCUHOP4K5pIK6d+8GGUBl6tR+9O4dytGj\n1Qwb1o2wMD8A5P2HkXQdNTIIDAqu5Dj4bCWG9LzT3vey53Th+fzXACj7D/P9m9tZ4RPD/hIn+w+5\nKK1UGw+9z+be/vto6n42yVuhHuL9OzAxMYVx8f3oHhR1UXtM67rOggUbeeWV+ZSWVpOevoygoETg\nxBjM5v+NMhpBOBsiOAuCIFwCzWacdR0u4eYcrSkpKeGxxx5jw4YNSJLEU0+N56+bcvAsOAo2J3JR\nBVondzlBaKgfoaF+za6hFJYD7j7FgDs4A4b0/RfpKdqXruvsPeCk8u8/cOO+Q42vy5+t4cukE6UV\nFpNEfLiB1IHHGPC6+5ujZd7HCPcK4A8pE5jadehFm1k+WUZGIb///Rw2bMgG3LvyFRbWExR0+X39\nCcLlRgRnQRCES0BpCM66yYRcXY1y6BBq5OW34KqoqJDNmzcTGurHhx/exzWJ4Xj8c3Hj+8q+Q43B\nuTXygaMAqA3HqYnhaD4eKIeOIZccQwsPuHAP0E40TWdbroNFm+pZvKmemoNV5Gxy72T4XNJoXsv8\nkVsrMjg4ZRymcBcmrxrscjWbDucwK3sz/3Q31GDcuBuYNnQcHoZLU/7wxRermD79c1RVIzAwkBde\neIHJkycjX4IALwhXIhGcBUEQLjKpuhqlvBzNYsHZty/mDRswZGZeZsFZQ1EqGTLEg48+uo8hQ7oS\nGuqH6b0fkHS98SglpwTniF6nvZJcWOa+4vGALcu4+sViWpWBIX0/jvHt1wmivVTVaaTn2Nm6z076\nPjvpuQ4qa09syDL70C/4q3b29Ahj9WMFrP+HQmqekwNL/sas5KbXSqpS8HSpuDr4c//VN13kJzmZ\ngZSUkRiN3zBt2lSeeeYZ/P39L+F4BOHKI4KzIAjCRXa8TEONjcXZrRvmDRswZmZiHzHioo+lrq6O\nRYsWsWjRIqZNu4MxYwYgy+XI8hGgHoCbbkppPN68wL34zzksCeOaTJSckjPeQznoDs7qSTPTruS4\nhuCcd8mCs92pc6jcRXGZ2vjfvMNO0nMc7CtyNju+Y7BC2gAHnV0bmPbCVpwyTE47QlbJET7qBal5\n8MAuhS3XdaSDlz/hXgF09AningJv4DO0bqdvKXch6XoYLlc80dHebNq0ieDgtnXrEAShKRGcBUEQ\nLrLjwdkVG4srKcn92kVeIJiXl8fs2bOZO3cuNTU1APj727n++tbrXJXMIgx7CtH8vbA+OModnPed\nOTjLDcH5eI0zgKtfPEC7LxDUdZ2DpS625jgoLHVRY9WoqdeoseoN/9Wortc5csxFaaXW6nVMBugd\nZ6ZHokpA+GEcHkVsOrqHOSW5rJwNsg4zBskkpPTldwkDGDQ5Cm35Kww4YGNV3/tRO0c0Xstj1fcA\nqEkXLzjX1dmxWu0EB4ejqom4XKGN74nQLAjnTgRnQRCEi0w5KTg7u7q3SL6YLemWL1/OnXfe2fj5\nwIEJ3HJLKuPGJZ/mLDDPd882O27oj9ojCgAlt+0zzlp00xlnAMPOAnCpYFDO6hmOq7dprM+wsTXb\nzpZ9dtJz7KcNxE3GJUOHQIWOwQYighTCgnTMvhXgW8QR9QDbj+Yxu6IEPfdEacrtWQppB1Ss/hZu\n/ORVbgsJbHzPcVMKli9WYf5qLfUv3XLiPhlFQPOtti+UH37YznPPzaFnzyT+/e8vANFOThDaiwjO\ngiAIF5mhYfMTNTYWV5cu6JKEITcXHA64wD1zZbmOYcPCCAvzZ8SIntxzz7X06hV95hM1DdOCTQDY\nJ6eihQege5mRy2qQKmrRA71bPs/qQC6tQjcqaB1OLALUQ3xRo0NQDhxFySpG7dGpTePXdZ3Mg06W\nb7OyYudRNmbW42rs+qaD5RjeUYcJ7liKt48DX6MHfmYvAiyeBHp6EezpRbCXF7qxhgpXGQXVR8ir\nOsLWyiMUVVegV+tN7meUFXqGRJMcFseQwFhu/9cCoAL1T1PwOik0A9hvH+YOznPXUf/8RDC6/4lt\n3Gq764WdcS4qKue55+bwww/bAfD3r6S62oavrwjOgtBezjs4W61WnnzySebPn4+madx2223MmDED\np9PJgw8+yLx58wgICODNN99k8uTJ7TFmQRCEK9rJpRq6pydqdDSGggIMubm4unU7r2tXVFSQnp7O\n1q1bSU9P57333iMy0hdJqkVRSpGkIxiNGtu3v4HJ1PZ/Agwbc1CKylE7BuFKSQBZRo3vgGHXAZSc\nElwpiS2eJxc1tKLrGOSe4j2Jq18cyoGjGNLzThuc6+0aa3bbWLbNyvJtVorKGpKyqQYpuIDgiCMY\n/Q9TKRVj1azUArUAjoZfdW17RkWS6eQbQp/QWPp3iCM5LJ4ewZ2wGIwAeLz+XwzFFbh6dsJ+x1XN\nznclx+HqHIFh3yGMy3fjHNMX7E6U/UfQJQm1c3jbBnIKm83J6tUZLFmyjVtuGUJqahJwPOC7//vv\nfy/jxRe/xeFw4e3tzTPPPMNdd92FwSDmxwShPZ33/1FPPfUUeXl5ZGRkEBoaSmZmJgDvvPMOe/fu\npaioiO3btzN+/HgGDx5Mx46XbnGEIAgCAJqGITsbV9eul6R38snBGcCZlIShoABjVtY5B+cXX3yR\nJUuWUFLStHRi166viInpxYmg5XY2oRlOKtO4OaVxdzy1c/gZg3PjwsCo5nW1ruQ4zAs3YdiW12S7\n6GM1Kpuz7WzKcv/anmvH4QIkFXyL8EzKxRS2n0oOIWlQJjc8nu7errp3aDS9QqIJ9fSjyl7f+KvS\nXuf+2FFPsMWHOP8wYv3CiPMPI84vjE6+wZiUln9f5KJyPN5zt5+re/W2Zt8EACBJ2G8diuHluVi+\nXotzTF+U/YeRXCpqbCh4tn1DkcrKOn76aSc//LCdFSt2U1dnB8BgiCI5+b6GL1sdSdIAnQMHVuNw\nuBg/fjwvvfQS4eHnFtIFQTi98wrOVquVzz//nG3bthEWFgZAt4a/9OfNm8dTTz2Fr68vaWlpDB48\nmIULF/LYY4+d/6gFQRDOg+ecOfj/4Q/U3n031X/960W9t3TsGHJlJZqXF1qoe8GWKykJfvgBQ8PE\nw6mcTicbNmxg8eLF3HrrrfTt2xVZtgM2JMkOOKivL6SkpASLxUjfvnEMHBjPgAGJDB4cz6mh+azZ\nnZi+3+r+cHJq48tqojucna6zxvEezlpUULP3XP3dCwSlzfuZv6aO9Rk2NmXayT65o4W5CkL24x+V\nh9UrF7tuAwfctA0eTpfocRSW3NcT613X0Dskmg5e/u2/A5+u4/XHr5CsDuw3DsCV2qXVQ+23pOL5\n1/kYf9qJVFqFktlQpnGWHTUWLdrFk0/+q/Hznj17Mnr0aMaOHQuYOd4R8Ph/77rrAaZOvZOEhISz\nuo8gCGfnvILzvn37kCSJhQsX8u677xIUFMSrr77KhAkT2LdvH126dOGOO+7g+uuvp1u3bmRnZ7fX\nuAVBEM6ZZelSALw//RT7VVdhHzXqot27sRVdTEzjbHdLCwRtNhurV69myZIlLFu2jMrKSgB8fGpI\nSZkINF0A9+yzI5k+fQQREQEYje3743njz7uRK+tw9YhC7XpigVtjcD5NZw3leA/n6JDG15wunS37\n7KzZ68OrsoIx5xDPvFVEjcECsgNjyAGCYwuwe+dSoR0BoBLocRie3e3JpG0OPOpdHP+GYOKMXdjq\ngqj7W48L8hMEz7/Ox7RkG7qXhfqXp5z2WD3MD+fIXpiW7sA8bwPSsVoA1Fbqm2trbXh7Wxo+80JV\nw9D1QK65pjdDh2YwevRoRo8eTeQZenyLn+YKwsVxXn+7VldX43A4yM/P5+DBg6xfv57rr7+enJwc\n6urq8Pb2Zs+ePSQnJ+Pj40NhYWGL1wkKaj4TIfzvMhrd9YTi60I4rl2/Jux2TJs2NX4aOH06ji1b\nICLiNCe1H/moewZW7tKl8XmkwYMBMGdnN742Y8YMnn766cbzunbtyE03DWLy5CH4+jZfiNe9u+8F\nG7PyX/dss3T71fj6nnSfvu7yDGPekaavn3xuSRUAps4dWZYJn/xwjF921FJT7w7+k7xDGVhdwoSo\nFWzoU81B+34cmpMSAA18DGZePBTBbWvqidh9ore0NqgL3D8aVA3p0ZlYZv+Caf8R1G+mQ0jzbb/P\nlfzRUpR3l6ArMuo30/HuFnvGc6R7R8PSHXh+sw491v3TWFO/BIwNv0cVFTXMnbuOuXPXkpVVTF7e\nTxgMEUhSECAjSRL+/u7uJ8LZE/+GCC05/nVxvs4rOHt6eqKqKk8//TQmk4mrr76azp07s3HjRry8\nvKirq2PHjh0APPHEE/j4+LR4nVdeeaXx46uuuoq0tLTzGZYgCEKrpE2bkKxWtKQkiIxEXr4c4z33\n4Fy8uLF294LePzcXAD0+vvE1PS4O3cMDqbgYrTwfKdDJ9deH8eWXcUyYkMKECYNIuog9gJuoqkNa\nvBVdktCmDGv6XkI4uixDfinYHGBpoXtDQSkAv1vi4r3SfPAqBb8i/LoeRvEvZlN9CQM3Q9SRzXxh\nBQmJ5PB4RsT2ZlRML4b9Yw3GWT8DoPt4oN2ehnbvSOgVg6K4W9ip3TqiTPoH8poMpNTf45r/B+gd\nc96PLn23CfmJf7vv8dFD6KP7tuk8fUw/9FA/pMwiyHPPmOvdO7F06TZmz17BokVbcDhcAJjNZvbu\n1enbN/R0lxQE4RysWrWK1atXA6AoCldd1XxR79k6r+AcFxfXYi2Zrut07tyZzMxM+vXrB0BGRgY3\n3nhji9d5+OGHm3xeXl5+PsMSrnDHZwnE14FwXHt+TfgsWYIJqE9NpfbRRwkZMQLll1+w/e1v1D30\n0Hlf/0z8MzIwADsMBmY++iibNm1i6dJ5hHSJxrgjC0f657hSOxMYCMuW/anxvOrq6gs+tpaYv1qN\n0e7EObQr1b5GOGUc/jEhKHlHqNuRg9otqsl7R46pdMwswReYX1GFPGAhmpe7rKMKQIOtURJs1plc\nHUz0qJu5Oqo7QR4+7rri33+J8ZMV6BYjda/cin3yYDhe1lBd3TjLXd0lDOmnP+Fz5/sYt+VhSHuO\n2vfvxXHDgHN+bsOWXHynvYOk69T/fgLWm/o3e/bT8Zw8GI8ZS5HsTnSjQnWYD28/+TkrV25DkiTS\n0tKYNGkSI0eOxMfHR/x9147EvyHCcT169KBHjx6A++ti7dq1533N8wrOAQEBpKWl8fbbbzNjxgzW\nr1/Pvn37GDx4MLfccgv/93//x/jx49m+fTsbN25k9uzZ5z1gQRCE82FeswYA+7BhaKGhVL79NkF3\n3onv3/+OIzUVZ+/eF+zemqaxYudOPgSWvPZa4+s7dnzB8G7BGHeAklmIK7XzBRvD2TLP3wiAfdLg\nFt9XE8NR8o6g5BxuDM5Wu8ZHi2r4eN5RSuvqsMsSR1LnoMkQ6unLkMgkksPiSA6Lo89oD1jwAr0O\nOIhKTHHXKOs6ns9/heWTFehmAzVfPI7zmh6nHaceHkD193/A6+nZWL5dj89vP6D++ZuxPjX+rJ9Z\nzj2Mz+3vItmc2KalYZ1+Q4vHOZ0ufvhhO998s46ionLq6uzU1tqYMmUor94+HI8Z7lp6V2IsDv1q\n7rnHxODBGUycOJGIi1QaJAhC+zrvFSSffPIJd911F/7+/nTs2JEvv/ySDh068NRTT5GVlUVUVBQB\nAQF88sknZ1zcIAiCcCFJNTUYd+xAVxQcgwYBYB8xgtrf/hbvTz4h4JFHOPrjj+heXhfk/g8++CCL\nGxYHmk0GJk0ezF13XUOfPjGo292bohgyirBfkLufPbnkGIa1WegmA47r+ze+XlalMvunGg6Wuphc\n7ccEYMGsHD7Z3gm7U6fgiIvSSpVuxm0AHPDXQZF4qPcofj9wAt4my4mb6DpaoDfy0Wrkg2VonYLx\n/NM3eHy8HN1koGb2o2cMzY0sRurevxe1Ryc8//wtnq8uwD4xpcnCxDORjlThO+Vt5IpaHCN7U/fG\ntFYXHP773yv405++bvZ6ebkP9TG349nvG0zbtuHs0hNdtzB8+HCGDx/e5rEIgnD5Oe/gHBMTw8qV\nK5tf2GBg1qxZzJo163xvIQiC0C5MGzciqSqO5GT0k9ZcVD//POYNGzBmZuL74otUvfVWO99ZR1GO\nMWpwFDsWw8MmA5N2vUVQ8IkFdcfblSkZLS+ivqh0Ham8BvMnK5B0HfvoPuh+npRWqsz4vppPf6yh\n3u7uaGGq8GcCYMotYY3J5j7fVI3PgB+JKd4LQFmYhWWTf0/v0Jjm95IkXP3iMC3fhSE9D8PsX/D4\n6Cd0o0LNJ4/gHHmWPwGQJGwPjcaQnof5v5sxLUrH9sh1bTu31obvbf9EOXAUV99Yav79UCtbgXuj\nqhFMmNCNb77ZxdSpUxk4cCDe3t6NvwBqH36YgPvuwzZy5Nk9gyAIly2xpZAgCP8zTi7TaMJi4diM\nGYSMHYvXN99gT0vDdkPLP55vi/r6ejw9PQEVRTmKohxEkiq5rZcfDwFS10iqgpt2oVAbFv8pmcXu\n5rwXaWMWqaoe82e/oOw/glxUjlJUgVxcjmQ70Uu59LqB/G12BZ/9VIvVoUFIBt5d1+AyVpFfqEI2\ndFMy8BnxBpIkYVVt1GguutQYABd9+6dQ31JobuBKdgdnz5e+RTl0DN2gUDPrYZzX9Tnn53Jc378h\nOG9tc3D2fOM7DDsLUGNDqf7qSVxmA+tXZ/Djjzt5+eVbUZRwVLUDqurufhEYCD/99FOr17ONGUNJ\nfj6002p+QRAuPRGcBUH4n2Fetw4A+9Chzd5zdelC1Ysv4v/HP+L/+99TOnQoWmDgWV0/MzOzYb3H\nOjZunI+PTylQc+L+heUYAXtcWLNz9RBftFBf5NJq5MJytE7Nd9prd6qGz2/ew7guq9lbmp8n9vBA\n0n0jGbMwmFpXDfgexC9lOVXKQfeW1hrsbPgtSizTqHXUoTc0Jhkb14/ninyAVWjRp38WV3IcgDs0\nKzK1/3oQ59h+5/Vojmt7oluMGLfsRy45hhYecPoTXCrmeetxAYvuvZaFr/2HJUu2UVbm/vMbPnwa\nQ4f2PPuBiNAsCL8qIjgLwpXI5W5lhUH8L9xWcmkpxqwsNIsFR7+WQ1n9b36Dx8KFmLdswbR+Pbbx\nZ15Ylp2dzfr161mxYgUrVqwAwGBQSE//nquv7t7kWKWhNZka3zw4A7iSOmIqzUDZW3hRgrPHW99j\nXJeFFupL/TMT0KKCqA4K4P8VmZmzVWN9ht29M52xjLBBv3DEsJcq3NtaP5sygQkJA5CQcH3yHF5H\na8gZ82eckYEYZQV/ixfe82YAoHU6fY2xq18cuskALpXaj+5vUk99zrwtOIf3xLRkG6bF6djuHXHa\nw40r9yKXVjPJy8LC50/ULcfGxjJ+/Hg6dRI78gmCIIKzIFyRAh56CNPGjZSuWYPu73+ph3NF9iGY\ntQAAIABJREFUOD7b7Bg0CMzmlg+SJBypqZi3bMG4a1ebgvOsWTOZM+dbACwWI9OmpfHww6OJimoe\nfJX9DcG5hRlnaCjXWJWBIbMI55i29Qw+V4Y1mXi88T26JHHs/fv5wSeW+avrWLq1HrvTCoDJq5rI\nfhs4YNjEEV3D02Di4b7X8Ujf6/AxeTReS0+MgKPZhBTW4EyMaXxdOdiwa+AZvgnQ/b2onvs0GBVc\nKYnt9oz28cm4lmxj/7fr2RffgeLiioZf5aSldefmm4eh6z7oug+mb74CIG3IMHbn5TN+/HjGjRtH\nUlJS+2/hLQjCFUsEZ0G4whhyc/FYsgQA465dONqhofv/AlND/86WyjRO5uzdm2PAttWr2RwZSVZW\nFtnZ2YwaNYoHH/wtilKHJNUgSTXI8jFGjQrF5UolOTme8eOTCQ1tfde64zPOWmvBubu7nZuSUXQO\nT9h20tFqvB+ciaTr/PfqEdzzhS8VNe4dDTHWk5CcgxS2h9z6XPLRkZGY1i2NZwfeSLh385IHNTEc\n4/pslJwSnMNPlDPIB93XVFv4JuJUrqFd2+fhTuIcncyn8r95Yns+TG664NPhCGL8+DRARqqpwbzU\nXf8++c8vMSk6WoRlQRBaJIKzIFxhPL/5pvFjQ16eCM5toeuNCwMdZwjOH2Zk8ALA7t3uXw1CQsBs\nTgTUJsePG9ePcePaUI+r68h5p59xdh1fIHiBgrNL1Vm/u56Ehz4g8EgVq/yimaQNRq23EtEtF69O\ne8m3Z5Orq1APJtnAdbF9eHbgBLoGtd5OVO0c7h73vpLG16QaK/KxOnSLET30wmwHXl5ew9Kl21i5\nchfh4QFMnz4VTQtE03zRdR80ixdRPXqSsGsX4fHxhPXtS0REBBEREfTq1QtwF2RblixBstmwDx4M\nMTGIyCwIQmtEcBaEK4nDgce8eY2fGhp6AgunpxQUYCguRvP3x9ndXXes63qTWUVZtiJJFQweE43l\nTegOdB6fTNLARJKSIunWLYpTQ/PZkI5WI9fa0Pw80QO9WzxG7RKBLkso+w+D3Qnm819YdqjcxfoM\nO+v22vhhcz2/3bOam/KyKTN68OTYAST0XESBaw+HNCfYQJYkronqzk2JKYyLT8bP7HnGe6iJDcE5\n50RwlhvKNNSo4HbtEGKzOfnxxx3Mm7ee5ct343K5/0wSEuJ47LH34JTYe81vfkPO9OnYoqKoePfd\nFq/pOX8+ANabb263cQqC8OskgrMgXEEsy5ejlJWhyzKSpmHIy7vUQ7oimI+XaQwZArLMt99+y5w5\nc1i0aA6yfAxZPookHQM0evXy4ujIXngv20XNDQNwTExplzE0KdNoLUh6mNDiwlByD6PsK0Ht2ems\n7qHrOnmHXWzIsLEx086GDDsHSl2N7w+uOsir+T8D8MhtsCN2Pjjc76WEJzIxMYUbEgYQ4nl2M8SN\nwTm3eXBu70WOpaV13HPPB+57yDLXXnstKSkpDBw4kFNDM4Bt9Gj03/8e89q1SJWVzdYEKMXFmNev\nR7dYsI4b165jFQTh10cEZ0G4gnh+7V7tXz9lCl5ffy1mnNvoeHCuT03l5Zdf5uOPPwagqOh7YmOb\ndnyQJAm5Xxws24Vhe367B2c1NvS0x7m6dXQH54zCMwZnTdPJKnSyIcPO+kwbGzLslFY2nRX38oAe\n3Sro4J/FB2/9jEHXeT0V5sZaiffvwJSuqUzqPJhOvucecLXIQHRPE3JpNVJlHbq/F0rhuQXn2lob\n+/YdIiurmDFj+hIQ4A0o6HoQqhpGWFgg06ZtIzExkTvvvJOwsDDKy8tbH1tgII5BgzCvW4dl2TKs\nkyc3ed/jP/8BwDZyJLrvhSkpEQTh10MEZ0G4QsjFxZhXrkQ3Gqn53e/w/OYblIMHwekUvWJPR9Mw\nrVtHFTBl0SJ+3rABg0HhH/+4o1loPs7VJwYAw46CdhvGmeqbj1O7RcH3WzFkFB2fDAbcs8klFSr7\nipzsKXCwMdPOxiw7lbVak/ODfGX6Jbnw75RPpSmHnccy2VxbxcIvIaIStnSSyXsijZ96DKVvaGz7\nLIKTZdT4Dhh2H0TJKcE1IAH5wEmlGmewbNlOvv12Pdu25XGwYaYa4Ntv3yMtbQCa5omun+iE8ve/\n/939rEFBbRqedexYd3BesqRpcNZ1PBYsAKB+0qQ2XUsQhP9tIjgLwhXCc+5cJE3DOnYsWkQEakQE\nhuJilMJC1Li4Sz28y5YhI4OSY8cYZTCQuWEDgYHefPrpIwwZ0noXB1fvGPe5uw6AqoEin/c4lDYG\n5+Nbb1dsPMAHC6rYV+Qkp9hJ7iEndTa92fHhQTK9u9UT3PEwqlcxeyqzWVZ2EBqaZKDDrOUmbsx2\nYPcxE73gJV6N7XDez3MqtXNEk+Dc9hlnA19+uYXFizcDYDQaSUhIoHPnznh6xqCqZ9i4pA1sY8ag\nv/ACllWrkGpr0Ru2xDbu2oUxJwc1KAh7Wtp530cQhF8/EZwF4UqgaXh+6+4VXH/bbQCocXEYiosx\n5OWJ4Hwa5rVr8QE8fb3oEuLFnDlPEBNz+nIJPdQPNTIQpbgCZf9h1M4R5z2OxhrnFjY/cbp0tu6z\ns3KnjZw1Jr4DpN2F/O3ryibHBflCp6h6AjqUYQ48RLVSRGZlAUtttXCivBiLYmRwRGeuierBb78u\nInL9OnSTAfsnj6JcgNAMJ9U5N3TWkBuCs9picJYaSi9C0bQQfvMbE336XM2IESOIjY3F2M4/QdHC\nwnD07495yxbMP/+M7cYbARpnm60TJoif2giC0CYiOAvCFcC0di2GwkJcHTtiHzYMAFdsLOY1azDk\n52O/xOO7nJnXrMYCfPuH61Emp+Lj43HGc8BdrqEUV6DsKDj/4KzrKPmlwIkZZ03TWbC2ju/W17N2\nr41aq3s2WdK9qFWMRDhqufmqDOpCa7AqRyl1HqGg+gjbXQ53c4+jJy4f7OFD39A4+obFMKBDAoMi\nOuOhGPF4dQGen65DNyrUfPoIzmt6nN9znMapnTXkA+4Bap2C0XWdzz9fxaFD1Tz77NNoWiia5tV4\n7tChQxl6hjaB58s2dizmLVvwWLLEHZydTjz++19AdNMQBKHtRHAWhCvA8d7N9VOmgOwuG3A1zDKL\nBYJNOZ3OxhlL2VWOefNGAALG9UdvY2gGcPWNxbx4G4Yd+ThuST2vMUmHK5Hq7GgBXugB3mQXOnj6\n4wo2Zp74lic2po5OnQ/g8M0jK0+lfyGUHZjLqlOqREI9/UgMCKdPaAz9wuLoGxpLlE9Qs1plj9f/\ni+c/F6MrMrX/fgjn6D7n9Qxn0tjLOacEqaoeudqK7mkir9rKU/d+yNq1WUiSxPXXP0FiotcZrtb+\nbGPH4vfyy5hXrACrFfPatSjl5TgTEnD26nXRxyMIwpVJBGdBuMxJFRV4/PADuiRhnTKl8XVXbCyA\naEnXoKysjNmzZ/Pll1+yaNFnxMXJGNNXIdXbcXWNRA9rfUe/lqh9Gn5/22GB4PEyDWdMGH/7+hjv\nfVeN0wX+EYV0G7CPYm0f+TVHyHcAZbA9BPoXwlS1I3369SIxIJzEgHASAsLb1FfZ8s9FeL7+Hbos\nUTvzARzjks/7Gc5EjQ1DlyXkglKU3BJU4G1vC39OexGr1UFQUBCvvPIKCQkJF3wsLY6vY0ccvXtj\n2rkTy6pVJ2abJ01q1z7TgiD8uongLAiXOc///AfJ4cB2zTWokSd2bzs+46z8CmecdV2nuLiY9PR0\n0tPT6Waz8dT332P86iuc/U7s0ldUVMSqVavYuXMn8+fPx253z+AuXvwpjz8+FuPqvQA407qd9Rhc\nvaMBMOw+CC4VDMo5P8/x4Lykwoe3F1QDOn2Gb2Kn9iPrq9wlGj4mD4ZGdiUtqhsj1CrYtoi7qztQ\nmzr5NFduzvLBj3j9dQG6JFH7/r04Jgw853Gf3Y2NaNEhKPmlGFfu5S/AX0qrAZg4cSIvv/wygYGB\nF2csrbCNHYtp5048v/kG8+rVAFgnTrykYxIE4coigrMgXM50/UTv5qlTm7ylRkWhKwpKcTHYbGCx\nXIoRtqvs7GzefPNN0tPTOXLkSOPrg3w8+V1NPV6rvqR+kBFdN6HrRnbsWM2zzz7feNzo0X149NEx\nDBqUCIBxdQYAzmFnH5z1AG/UmBCUgqMo2YdQu0ed0zPlHnJSMreACcB2KYAu0TohKf+PtaXbkJB4\nsPcobkjoT7+wOAyyO5wr5mL0vy3B/P1W1Le+x/r0DW26l2XmT3i96C7rqfvnXeddYtIWNTXWxrpx\nNTHcHZxXZPAo8F1gIL975x1GjBhxwcfRFtaxY/F97TUsy5YBYB88uMk3o4IgCGcigrMgXMaMO3Zg\nzMpCDQzENmrUKW8aUTt1wpCfj+HAAVxdulyaQbYbDZOpmiVLlgAQEOBFcnI8A3pHM/KfiwGQCwuR\npJLGn6x36lTPbbcNxcfHg7vuuobEhgVqANRYMWzLR1dkXEPO7ffG1TsGpeAohh35bQ7ONofOhgwb\ny7ZZWbbNSv5hFwtyDgMQPzwApe8s1pYW4W20MHPUA4yObV57rHaJpPaj+/F+YCaery1ENxmxPTbm\nNANV8XzxGzw+Xg5A7evTsN9+1dk/8Bnous6+fYdYuzaLtWuz2LmzgIMHy8jJmYevbwec8b0xsRPD\nlhxCgJUPP0z9ZRKawd2JxpmUhDEzExC9mwVBOHsiOAvCZez4bLN18mQwmRpfP3r0KD///DPluk4x\nkPvggxy0Wrnnnnu47747AVPLF7wsuVCUIxgMRXTpUsmMGffSr18cCQkdkCQJ4/Jd+KruTT6UwqY7\nxA0YkMCAAS3XzBoyi5BcKq5e0We1KLDJyPrEYv5uC4YdBa0GUV3X2V/iYu0eG8u3WVm920a9/US/\n5QBvmf6yu63c555LySi3EucXxpfjHqdzYOvdOhw3pVDrcOH96Cy8Xp4LFiO2+5qHUKmqHu/7PsS0\nYg+6UaHu7buw33phOlSMGPEXdu4saPKaxWIhJ8eL3r3jcMa7F9lJmvvPS+t0dluGXwzWsWMxZmai\nWyzYxBbbgiCcJRGcBeEyJdXVNS5gqr/11ibvPf7446xuqNEEYN8+AAoL12M2x6OqCbhcl19o0XWd\n5cuX8+GHH/Lqqy/Ss6c/ilIIWAH3dtdTpgxpco5xVUbjx8d7A7dF4851Z9ji+nRa2kGwyTbXGTY2\nZNoorWy6e1+PGCMj+3kwsp8H/eIMBMa4W7Nt9bZybaeefDz6wTYt8nNMGUKdzYn305/h9dwcdy/m\nO68+8Yx5R/C5/V0MOSVoQd7UfPYYrkGdz/l5m5MAX1Q1CF33JSGhDyUl9aSmpjJkyBCSk5OJj4/H\nYHD/U+I8ZeGfejkG50mT8J41i/rJk9F9fC71cARBuMKI4CwIlynLokXIdXU4+vfHlZjY5L1//esP\nPP+8g7hjdST+vJvw4T0Iee12IiODcM/gZgEqLlfsJRn7qXRdZ9myZbz99tvs3r0bgM8+e4N33rnz\njOcer1MGkA8da/NCPeVgQx/h6Ja31W6L4wsEpd2FvDGnjG0HNLbsa77NdYifzKAkC9f0tjCirwWn\nqZLNJVnMK8nhjRWZrHColHrCnaljeGHQJBS57TsR2u+8GsnuxOuPX+H99GdgNmCfOhTDmkx8fjsD\n+VgdrqRIar584ryeVVU1VqzYzZw5axg7NoWbb57S0G/Zt/GY1157HU9Pz1a36XbFxzf9vGPHcx7P\nhaJ26sThvXsv9TAEQbhCieAsCJcp86ZNAFhvaLowzGAoJiiolI8+egDjyr34/rwbp9VJdXzTHeEU\nJQdQWbHiEEFBQXTv3v1iDb2JjIwMnnrqKfbs2QNAWLAPj95xFXc8ceYfk0ulVRj2FqJ7mMDbgnS0\nGrnkGFrUmbZxBvlgw4xzG449Wfo+O0u21LMrz8GufAdrPYLoai3np89z2O7jLq2ICFJI7WZhcDcz\n3eNd1BtL2FOWwS+Hc/nH97kcqT+x49/VDU1PtPgw/px6y1mN5Tjb/SPB7sLr5bl4Pf4Jhs25mL9a\ni+RScYzqTc3MB+AcylGcThc7dhSwbNlOvv56HSUlxwAoLZW58cbnmx3v5XX6/st6YCBqUBBKeTma\ntze6v/9Zj0kQBOFyJoKzIFymDA3lF86kpBOvGY6iKBmAu4ZWbdi++Xi7s1Pt3fsLv/3ta5hMFr78\n8kv6ndTK7WIJDfUkN3cfYWH+PDVxII99tgrLrBVUPjoG/QznGte4F3HpQ5OgxuYOzoXlbQrOyvGd\n66LPfKyu66zPsPPW/CpW77Y1eW9XYCRdi8v5XdxRcm8Owux3lCPOEvaWF/JmUSEl2ceaXS/A7MWA\n8ARSwhO5Wa0FluLfLZ66M46kdbbHxiDZnXj+fSGWz1cBYH10DPV/mgRK22ewT7ZnTwljxrza+HlM\nTAxTp05l8uSza4F3MldiIkp5OWpUlOiPLAjCr44IzoJwOdJ1DDk5ADgSE9E0DaOxEkXZDSfFTS0y\nEN1sQD5SCTXWZrOOXbpEcM013VmyZBtTp05l9uzZpKZe+BZlALJch6IUEhlZxNy5v6O/xUjYLW8j\n17t7LZu+34r9N2mnvcbxMg19eC+kHfmwMbuhzvnMXTIaZ5w7tV6+oOs6K3faeGt+FRuz3OPy9Ksk\neVAhPgFVOI3HOPBDIcwH6/6FvJzV/BqeBhNJQR3pHhxFclgcA8MTSfDv0FjO4Pn9twBoDVttnw/r\n09cDYPn0F+qfn4j9tmGnPd7hcJGenseOHfk89NBowISuB6Bp/ui6L507X0Xv3gvo1asXN954I4MG\nDWq1DKOtXPHxmDduxBV1bu37BEEQLmciOAvCZUg+dAi5thY1MJC/fPghZWWHeP/9yYB6yoEyamwY\nhqxilPxS1F7RTd42m43MmvUQjz46iwULNjJt2h08/fR07rrrLjw9z7w4ra1sNhtz584lKSmJlJTO\nKEoxsnwIcNcCDw3xxe+GvyNX1qFGBaEUlmOeu/70wVnXMa5016Jqw3shV9QCzTtrtMilIhdXoEsS\nWlRQC5fW+THdytvzq9iW6wDAz0ej11Vb2Gxbzhq7E9wd5Kj3gWeAAYcg3r8D8f5h9AiOontwJ7oH\nRRHrF9pqzbJhdQbmuesBUBPCWzzmrEgS1uk3YJ3eel/n9PT9rFmTyZo1mWzenIvV6n6+MWPuITy8\nC3CiPtxgoLH9X3tx9ugB0KwuXxAE4ddABGdBuAwZG8o03vDxYebMmRiNCg880Id+/eKaHavFhUFW\nMcr+w82CM4DRaOCDD+7D09PMF1+sYsaM97j77rvOOIb9+/ezZcsWpp6y8cpx5eXlGI1G5syZw8cf\nf0xpaSlpaX1ZsOAJTp4Vlw+W4XvzG8hHq3Fc3Z3amQ8Q0Gc6xo37kA+WoXVquZRCzjuCUlyBFugN\nvWNga6779TZ01pCLK5BUDTU8AMzGJu+VVak8/kE5P6W7O3kE+8qMHVXKOucC1lSVADA2rh99QmOI\n8gkmzuCL/tlb9C6T2XTzy+DRhlZ/Thce//gvHu8uQdJ1nIO74Liueb/m9qfw5JNfkJl5oPGVLl26\nMGTIEFTVl5ND84VSf8staH5+2K+++oLfSxAE4WITwVkQLkNKdjb/Bzx3wB2AZsy4r8XQDGeucwZQ\nFJm3376TMWP6UlZWjb//blyujqhqKOAOlg6Hg02bNrF8+XKWL19OQUEBAGlpHejUKQhd90DXzYAH\nmmZiyJAh1NTUNN6jZ89OTJs2CF3XGn/cL5Ucw3fi6yiHjuEclEjNZ4+BlxnHdX0xL9yEed76VnfF\nO96GzjksCVmW0Rs6RigH2xCcG445tb555U4rD79XTmmlip+XzEM3KeR6LObzHPescLx/B964ehpX\ndWy606DaOQJDVjGGjEJcyU07R7R0b+/7P8K4dT+6LFH/zI3uZzzHOuTW6Lre8PssoesBqGoHNC2E\nCRNuIzm5kCFDhpCamkpw8NktjjxvFgu2G2+8uPcUBEG4SERwFoTLjMPh4I9z5vBZw+evvnorEyem\ntHq82lA7q+xvPTiDu0fyqFG9Gz6rwmCowmDYj6pGomnhTJgwiZ07dzYeHxDgxbXX9sTlOogsO5pc\nq6bGisUiUVMDgwZ15qmnxjN8eI8m9bFSeQ2+k95EKTiKq3cMNV89CV5mAOy3DHYH57kbsP7u+hYX\nkTVul53WHTOgN9Qqy0VnLtVobEXXcI7DqfPq15XM+L4agJQkE9eNz+L/di3gmL0Os2Lgqf7X81i/\nMZgVY7PrufrGusthdhScNjibvtuC11OfIldbUSMCqP3oAVyp57ej486dBbzzziJkWUKWZWRZ4tCh\nY1x7bTKPP/4ImhaMpp3oR/zoo4+e1/0EQRCE1ongLAiXGUmSOHC0FA/g/aev58YHRp32+OPBWT7N\njHPrbCjKfhQlnyFDonA4yhk1qhejRvUhOTkOQyv9kn18PMjMfBeXS23xGKm6Ht/Jb2HIPoSrayTV\n855G9z1RU+28pgdaiC/K/sMYtufjOnU2XdUaO2o407phBog+KThrGpymF/KJhYHB5B5ycv8/y9iV\n50CR4YlJZrK85vHylm0ApEV14/W0acT7d2j1eq4+MfD1WvcOgi0dYHXg9fxXjd0uHGP6Uvvub9ED\nvVu9JsDevYUsW7aTnTsP0KFDAK+9dh+a5oeu+6LrnoBCcXEdixalNzu3utrAww9fHn26BUEQ/leI\n4CwIlxkPSwlzNSdFQPS9I87Ysk1t6N+s7D98HnfVePHFCfzlLzef1VmtBWvPv8zHsOsAamwo1fOn\nNw+QBgX7xBQ8Zi7DNG9Ds+Cs7CxArqpHjQk5samHhxktxBf5aDXykSq08IBWx3W8Fd2aWh8mPlNC\nvV2nU6jCn+/TeSPzfbLyi/E1efB62jRu7nzmThJq4w6C+c3ekwvL8LnzfQy7DqCbDdT9ZSr23w4/\nbSs2Xdf59NNfeO65OagN24l36hTFSy8NaXZsjx6pfPzxx2ia1vjLbDYzdOiF2VZbEARBaJ0IzoJw\n2VAxGvdjKEknoM5OUJA3x0J8z3iWHuaH7mVBPlaHdKwWPeD0s5ytaS0Enwvj8l0A1Mx8AL1Dy5tg\n2Cen4jFzGeaFm6j/yxQwnvjr6OQyjZOpUcHu4HywrNXgbHPo2HYdIRL420Yj9f46Nw/15IaxJTy+\naiZV9no6B0TwxbjHTjvLfDJXtyh0g4KSfQjq7I0lJ4Y1mfjc+wFyeS1qTAg1sx9F7XH6baY1TeOZ\nZ77gs89WAjBx4kSGDRtG7969Wzw+LCyMcePOvFmMIAiCcOGJ4CwIl1BJSQkmk4ngYC+Mxkwk6ag7\nnAFq58i2XUSSUONCMew+iJJ3BFfyuQXn9iIfLEMpKkfz80TtHdPqcWrvaFydIzDsO4RxxR6co090\nnTAdXxiY5l6kl3HAxk9bapjs6UcMDZ01Upq2O6up1/j0pxo+WlTD9gL3jLPaMYiP7gnisNca7l42\nD03XuS62Dx+OvB8f01nstOdhQk2KxLD7IIbdB3ClJGL56Cc8X5qLpGo4hvegduYDbfqmRZZljMYA\nzGYzb7zxBjfffHaz/IIgCMKl027LvNesWYMsy8yaNQsAp9PJPffcg6+vL9HR0cybN6+9biX8yun6\nmYoTrmzFxcX861//YsKECfTv358HHrgbSdqMJLnDnpLVEJy7RrT5mo11zmdYIHgxGDZkA+Aa1Pn0\nnSQkCfstgwEaex0DUG/n/7N33uFVlOn/vmfmlCQnvYckJJQECKGFGqryo4h0kbaAi2UVGwgi4qor\nsOra8avoLrqIImJBRQQRG016LyEJJCGEJKT3enLOzPz+OElIJCEVwXXu6/IyZ2bed56ZnEM+85zn\n/Ty6Q3GogsD5jh154M0set0fx5L30vkiySZ233gjgXHPpvPUmlw27Cjm+U/y6DEvhRXr8ynMKadN\nRTGKJLL+3Q78XPYJy/Z/gaKqLO47gXW3P9o00VyJtfIhQH/gPI4Pvofp2c8QZIXSx8ZS9OnCRmb6\nRWS5C88++ybbtm3TRLOGhobGH4xWyThbrVaWLl1Kly5dqmsFV65cydmzZ0lJSeHEiROMGzeOyMhI\nAgICWuOUGv+jiGIRcJHy8hDOnj1L165dGxzzRyEnJ4e5c+dy/Pjx6m1Gox43N5Xk5CTaV7ljnEsF\nwNq5kRlnQO5YVed844Wzfr9NOFsa4SZRcWckpue/wrD9BEJhKaqzA/rD8QgVVi74BdBvWSGKAnqd\nwB1DnLETvCAZfIvyORhj5mBM7aV6g7oaeaa3Ar9CqZ8TE759iTPZlzDpjbwz4j7GdejT7Ouy9gyG\n9Xuwf/FrBFVFNRkpfvteKib0beQMdlit4ciyOzoddO7cudmxaGhoaGjcGFpFOL/99tuMGzeOH3/8\nsXrbxo0bWbhwIc7OzgwbNozIyEg2bdrEo48+2hqn1PgfRJJy0OmiKC62Mn78PKKjk9iyZQsdO3a8\n0aG1AjJeXlYyM1Ows9MzYkR3Jkzoy8iR3XH6TZvsK6UaTc84t2yBYOvQFOGsBHhgGdQZ/b5YDN8e\nJX70QFLePMo44AtdEKIAs0Y48sxdfkj2Rbh3DIKdMKtDOe7PeBOVWMHpxAoMOoF7bnOid4iB6E+3\nAHBQX8CZ7AKCnb1Yd/ujhHm2rAW0tZfNwUJQVeR23hStexS5y5VEQHFxOadPJ3H5ci6XL+eRnp7H\n5ct5+Pm58eKLD2O1dkVRTC2KQUNDQ0PjxtJi4Zyens6HH37I4cOHawnn8+fP06lTJ2bPns348eMJ\nCwvj3Llzdc7h4XF1S1yNPw4HDhzAzs4OFxcXXF1dcXFxQZIat9AsOjqaZ555hrVrl+PqmoogGBEE\nO3x8HDh4sJD77ruPPXv24OZWv4PCzYyqWlDVywhCIpJUwqZNT9Khgw+OjvWUCqgquvO27nUOfTuD\nc8OLAwGE7jZvYUNSNs6NHHNdSM1BSsxEdbLHNCgcGrHgMH/yULz2xRL/6m56fxvE4ZMLtljfAAAg\nAElEQVS2fyeEkT2Ieq4TqZY4Zmx7lhPpF+ifZ8dBoCIpmaDQEiYMCUYURFRVZXvCccZu2kjv7XEM\nBdI89Tx/yzQe7D0GJ2PTSzOuIrIryuhe4OyAsup+TDVKM1RV5Ny5VCZMeOmqYZ07h+DoOAJBuNof\nWqNl6PW2e6r9DdGoifa+0KiLqvdFS2mxcF68eDFPP/00RqOx1vaSkhIcHR2Jioqid+/eODk5kZyc\nXOcc//znP6t/Hjp0KMOGDWtpWBq/E6qq8NxzT7Nnz/5a252cnHj33Xe5884767X6+vHHH5k1axZF\nRUW89JKOl1/+K2BbPLVu3WMMHryUM2fimD17Nps3b0anu/nXsiYkJPDKK6/QrVtXHn54AoJwEUkq\nqd7f4xqL5QBIzbWVLHg4QSMcNapQO/rZfoi7DKp6TSu064lQ6YahDup8TdF8LtnMN3sL2Ly/kPNn\n3UkXdfRMvUCEfxq9StJRDHqmPNeJpQfe4qvYAwDY6wycdSi3/ZxWSP81T+Bm78iQtmGkFuVwLC0B\ngLuKDUAFd94+Cd3AO1rt2rLzSzj84BhiY1NY6OqEqtijqh6oqhvgRmBgKQMGrCcgIIA2bdrg7++P\nv78/QUFBmmjW0NDQuAHs3r2bPXv2ACBJEkOHDm3xnC1SIvv27SMxMZFp06YBtkVdVQu7TCYTJSUl\nnDx5EoAFCxbg5ORU5zwPPfRQrdc5OQ13BtP4fVFVlbKyMhwcbE0sRLEIUcxGkjKYPbs7eXkpFBSU\nUlBQSmFhGUVFRajqWYqKvFBVF1TVEVl2BAysXbuW+Ph41q1bh6IoTJzYl0WLxlJYaOvq5uzsjL29\ngXXrHmHkyBX88ssvLFiwgBUrVrTKtaSkpLB27VpGjRrJgAG9KttIN4/c3FxWrVpFYmIiFy9eJD4+\nHkVR8PNzZ/Zs9yZbvOmPxqIHrKFtKKzRzrrhgeDmakLML6EoPgXVx6VpF9JKmH45gQ4o69eB8srf\nZxUWq8o3+0v499YiTl+40onQwWTP0dAwhsSeZm/ZdkRV5XwXF7qvexyzbMVeZ2Bx5GQeHzCRpMzL\nlL/zNPaFZiJw43h5Ht+ePwyAl70zj0SM4e6jccBxrG3cKf1NDE1BVVXWrPmFo0cTOHbsAomJmdX7\nxo6dh7t7W6DqAcWMJEl89dVXdc6l/Zt2fajKKGr3V6Mm2vtCo4rw8HDCw8MB2/ti7969LZ6zRcL5\n6NGjHDhwALFGB689e/YQFRVFaGgoMTExREREALav5CdOnNiyaDVuCDt27GDZsmVERvbltdceQ5Iy\nEIQ8qGzNcccd/Wu1hFYUheLicgwGPaKYBthKD3Q6CVV1Yt269zl/PgmAxx8fz5NPTqr1HqoiMNCT\njz56lEmTXiY19RIWi6XZX7Woqsrhw4f573//y/bt21EUhYsXjzF06KOoqjuy7IWieKGqRvbs2YO3\ntzeBgYFcuHCB+Ph40tPTefDBB2vMaEYUy7Gzy2f16tXVW3U6iZkzh7Bgwdhm+SI3x1GjCrmDD+Kx\nC0gJ6VhvkHCuqm+2Dryy8K2oVOHjX4pZ/V0hqdkyAK6OIqN72zO2vwO39LDDZdetMOs0xjO298UH\nntmYZbgjpD/PDZxKF39bfbG/kwe6YF84ncSOgQ+TEOLMvpRYACaF9MNBb8SQfAjgSuOUZmEAXFm9\neheJibbFmnZ2dvTo0YO+fftitdpzRTRraGhoaPxZaJFwXrBgAQsWLKh+feuttzJnzhzuueceXn31\nVd566y3GjRvHiRMnOHjwIB9++GFL49X4HcnJyeG5555j06ZNAOh0ZUjSqAa7rImiiHON9spXkBGE\nfBYuHE1U1CUGDuzE6BrevXXRv38I33//DN269cBqbZ5QiY+P55FHHuHMmTMA6PUSU6ZEcv/9Iytj\nykKnywIkFMWDv/99CYmJV5cV3XffYEwmGUEoBsyAjJsbrFgxA39/d9q186Z9ex8cHe2aFSdccdSQ\nOzVDOLf3QX/sAke3XULwDaZH++Zn0mti9+8fUB3tMM+5dgmVkFGAFJ+OajJi7RFEWo6V97YV8dFP\nRRSW2h6yQvx1PDzBmTsGO3CpOJ1DaVEs+TWeY2nn2esA3qW2uZL7+LFtyt308wu56jxyoAe600mI\nl7IJ6t2BoLDaAlm8VOnh3NazGVcrIcsdsVoDAIl58+ajKAoRERF06tSp1WrkNDQ0NDT+mFy3otGF\nCxcSGxtLYGAgbm5ufPDBB/j7N95eS+PG8uWXX7Js2TLy8vKwtzfw5JOTmDevYdHcGKZOjWTq1MhG\nH9+zZzBQgCCcx2LpQlMzfQEBJpKSLuDh4cTcubdy99234ltnNzuZ8vJkBg9uT35+HsXFZXTo4EtI\niB8dO/oiywkIwtUPBA89NLpJ8VyLKkcNa6eGPyvlFSqnLpg5FGPm0DkzQ0/b83fgyHdJPBefzr/n\nezJxYMtcHMS0PEzPfoYqCFhu6YoSWL8Y1Vf6N+eFt+fh/+Tz9b4SLFbbvoFhRh6e4EynjiW8euQz\nlq07Rb65pNb4r3pIPHhAptzJyJsLVyDWU9NeFYOYfPXXsEJRGWJeCaq9AbWRNeI5OUWcO3eZyMhI\nrNZQFOXKuNmzZzdqDg0NDQ2NPwetKpx37tx5ZWKdjjVr1lQ3RNFoHlFRUZSWltKvX79rHldeXs7J\nkyc5cuQIDz30UJ2uFtOnTycnJwdHR0dCQ0Pp3LkzXbp0oVevXtjZ1c6S7tz5I3l5eQwbFsbrr/+V\n4GDvVr2u5iCKKRgM5ciyP7Lsydq16+jYsSODBw+uQ9CrSFIukpSC0ZjJl18uIiwsEDu7a2cMHRyM\nrFw5l9dfvwtVBelaDTxaG1W9YkV3jYyzoqg8vTaPj34qosJ6ZburaHMeGaDLp8IK963MJiNP5v6x\nzXfZkM5cAmwWbMb1v1L21OR6Y0rffBYn4PVMPz7fXYIowsRIBx6e4Ez7QCtvHP2Wuzf8QoViC7qN\noxv9/ELo7xtCP7+OdB8uot72AkwbVK9oBlAqM8lScvZV+8SkymxzoGejFkhu2XKUJUs+pqJCZefO\nKfj43EBHEg0NDQ2Nm56b36bgT0ppaSmvvvoq//3vf3nhhSVERnZGlu2w1V7aOHr0KDt37uTQoUMc\nP34cs9nWDGLkyGB69PAEZEACRFRVIC4umoyMXACOHDlSPc+hQ/sJCAiqfCWj06Xyr3+NYdSoNkyd\nGtkqWebWQhCy0emyKSiwsGLFcioqLHTo0IHZs2eTnJzMoEGRjB3bB0m6hCDkVo+LiGjfpPPUVXN9\nvRHT8hCLylDcHevNlqqqypNrcln7QzGCAGFt9YR3MuPln0lgVi48AX7l5+h1+3ZOfD+Sv6/N43Ku\nzD9muSKKTf896s5eKVmx+2QPZU9MqOWWUWZW+GJPCf/ZWsjXv8QAcNg7mAfGOvG3253w84QPzuxg\n2sdbqjPMUztFsrjvBDq4+tY+mTfkRv8f2Bu4FnKAbeFPXRln8ZJNTCsNlGlkZhbw1FOfsHmz7XNg\nyzb/b3es1NDQ0NBoOZpwvgnZtWsXS5cuJTk5GVEUaN++Ap3uYOViMwcUxRFVNfH++2+zdevP1ePC\nwgKIjAzFZMoDate3CgJ8++0TlJVVkJtbTGxsKtHRKSQmZtK+fTyQgao6IwhFCEIeXl4mpk0b+Lte\nd1OQpAoWLRrHRx/tIiEhgeXLlwNw/PhuJk585gZH1zxqNT6p42FFVVVWrM9n7Q/F6Hxi6T7oDCnl\nKXxRWgAXwdEMTwJts6ycLD5I7wkVnNw6llWbC0nPlXnrIQ8M+qaJZynqUvXPYno+mRuOsaddV6Iu\nVnD2YgXH4ysoKFHwqCghvDQLi17P6o/74exmYHP8Ee784UsuFtqywIP9O7N80HR6eAfXf8JG1IdX\niWKxjoyzVJlxVoLqF85btx5l/vy1FBaW4uDgwNNPP81dd911Qx6WNDQ0NDT+WGjC+SaitLSUpUuX\nVltadevWlpUr766s8QVbBrmosi01dO3qSGDgaCIjQxkwIBR3d8c6562iQ4crGb6hQ8Nq7JGBfAQh\nv9Wu5Xrj6mpi8eIJPPbYWH744SRffLEfV1cTDzww8kaH1myk2MqFgfW02l75dSFvby5E9I5B7vIF\nx3NtGVJHvR3hXm3p7tmWEvd9mHLL6FRm5Jh4nMF3SBzfcjtf/lpCVoHMh0944WTfOIGoKCrWY0kY\ngW9DIpgQd5yLz//EvO4+tY7r0d7AK96psB/Ufu3ZmxfF6z9t4XSWzSGjk3sbnhs4jZFB3Vvl24uq\nGmcpOfsqz+qqjLPctn5HjcDALhQXlzN8+HBeeOEF2rZt2+KYNDQ0NDT+HGjC+SbCzs7IpUtx2Nnp\nWbJkEg8+OAq9vv5f0RNPaPZ+Op3E2LG9GTu2d73HCAWliJdzEbKLELMLEXOKELKKEHOKUO0NlD4z\nBYw33i3hinC+ur75ve8KefHTfHBNROz6FVZV5ZFeY7ir6zCCXbwQBZsYNoRegoPn+SjkDoZnbWJv\n1hFG3CFy8rsx7D5dzoR/ZLBoijOdAw2089Whk2oLWVVVOZNoYdO+En7clUt0SiYVgsgDnrcyKv4U\no3MTmNupDO8evoQHGwgPNhDoJeHw9A4A3ne6zCPfrwLA28GFJ/tNYlbYEHRi06356kN1cUBxtkcs\nLEPILbY1i6m6h9fMODtjtXakc2dPfvihE126dLmpypA0NDQ0NG5+NOF8kyAIpdjZxbFq1UwEQaB9\ne5+GB2k0iO7geZwnvYJgles9xhrRjorJ/evd/3shna901AitLZw/+aWYv6/NA8c0jBGfYVas3Ntt\nOM8NnHqV8JM7+KA/eJ6wfB2fj1/I9C1v8PPlQ4ybJBL1wxjOJFZw92u2rKxeBx3b6OkUoKdzoB5Z\ngW/2lxCXalu8F1lwGRHI9PNl9Usdsazsi903B3nHdJayaTafZqsi8+X5gwz9bhdhwJc+RfiZ3FjQ\n+3ZmhQ3FXnfteuXmogR6Ip5NRryUjVxDONfMOFutMsXF5bi6uiDL7bFaA7HV/ENYWFhd02poaGho\naFwTTTjfFJgxGE4BRbXKKTRajn5vLIJVRvF2Ru7gh+LlhOrhhOLpjO7URQw/nkJ3OunGC2dVrdH8\n5Eqpxjf7S1i4OgfsczD1+4QSxcykkH78a+isOrOlcgfbA5eUkMGANsP5dNxCZmx5g61JB5gyTmJy\n7iSiLsqcS6ngUqZMzCULMZcstebwdBaZEOnAY1mlcAIM/X3INUaxdbgLM78Bywc/Mq9HBpmWEhLy\n0ynJyiUnFcwSTPzLX5jW8xaM0vXN4CuBHnA2GSklB7mXrTkKqoqUnE0F8NHB87x5zzv07h3OqlWr\nUZSW2fJpaGhoaGiAJpxvAhQMhnNAE9orazQa8aKtTXLp0jsw31W7gYfhu2MYfjxVbbl2IxHT822O\nGm6makeNH46WMu//slF0RbgO3EC+XMwtgV15d8TfqkszfotS+U2FdCEDgIH+ndgwbiEzt67kq/i9\nzA4TWT/jr0iiSHGZwvlUC+eSLcQmWygzK9zW14Gh3ewotpRSPO8YAC+WnuD/tp8AFXp4Qlh2BfJ3\nR9hTmbS9N9sZkUKEPh2Z07v1a8wrKqwsWrSGdet2ERrqx6RJ/VhU5eV86coCwfLUHN4pMfOyIJDy\n9w0A6HTJlJZK2DW/J42GhoaGhkY1mnC+QRQUFPDmm2+ydOkdGI3pNzqcBtHtP4fcxR/V7doLEG82\npIuVvr7BVy8Ws3a3WfDpziRdtcjs96a6vrmTPwgC24+WcvdrWViFMjwGf0qOnEMv73Z8OOYRDFL9\nH1u5SjgnZlRvGxzQmU/GLuAvW99kffQevok7TE/vYCJ82hPh046hfdox4xZ3VFT2JMfw0M+/8t2F\nY+w+YSvZiAs0MKZdVzztnTk3KYuw/0bzZlIAM5+chqeDM/3e2g/8iHVQ57pCahEZGQXce+87HDwY\nB8DRowkEBXVA7mH73YkpNks6i8XKwNEvcAlAVenUqRPz589n3Lhx6K7hCa2hoaGhodEUbtq/KKqq\nYjabr2rM8b+ALMs88sgj7Nixg5yc06xe/cCNDuma6I7E4zLhJSz9Qyjc+tQNFZhNpaohhlJHAxcl\nwAPF1YSYU4x4ORfF3+P3Dq+amo4a2w6Xcu8bWVgUC363bCRNuUxHV18+G78QR8O1Pw9V1yCk13ZI\nGRoYxoZxj7Fo54dcLMxib2ose1Njq/d7O7igE0UuF+cBoJOhZ6YAqLy3+CXsPG3NVYRexagfLyTw\ncCpO+KJ4eWE88CEA1oGtK5xlWWHSpJeJi0ujTZs2rF27lrS0NDw8PKhISwPWICZVoCjBSJLA6C7d\nOJ7xK4sjIhi8ebNmL6ehoaGh0erclH9Z8vJyeOihe3jggQdQ1f+9pgSvvvoqO3bswM3Nkb///Y4b\nHU6D6CqzffpDceh3R9/gaJpAWQVSWh6qTkJp43b1fkFA7mazIpNO39hyjSoP59N2njbRTBltbv2M\nNOUCfiY3vpy4GA97pwZmAdXZHtWoQywuhxJzrX1DA8M4etcrnL37TdaPXcDjfcZza2BXXIwOZJYW\ncLk4j7ZOnjzZbxKnhyzGaFGRAzyqRTOA6uZIxcR+tk6CH+9GKCpDOp2EqpOw9O3YuvdEcmTp0iUM\nGDCA/fv3M2zYMEaOHElERARyYCAAYnIWFksoFksI/+zTnyPAuL59NdGsoaGhoXFduCkzzhZLHLt3\n76WgoJQNGzYwa9asGx1Sq7F161befvttRFFkzZoHCQqq32/2ZkFXowmG/aubsQwL+0NknataMiuB\nHrW63dXE2q0t+l9j0J1JwjKm1/ULxmwBi1xvgw/pnC3j/PQheyze+bgN+pTLcga+Jle+nPg4AU6N\nzIYLAoqPK9KlbMTMApR2V2fafUwu3NauJ7e16wnYvt25UJBBobmMHt5BiIKI4etDAMjhgVeNL79r\nGMYv9mO34VesvTsgKCqWiGAwGa86trmoqicWSxduu20wo0bdiZdX7c+JHBAAgJSSUl1m45iWhgBY\nA6+OWUNDQ0NDozW46dIykpRPYGAxr7wyB4Bly5aRmJh4g6NqHeLi4li4cCEAy5dP+00TktZDvJSN\nyy3/wLD5SMMHN4Kq7nGqJKI/FIdub2wDI24OxGvUN1dh7VZV53wdM85WGZfbnsct4gmkmJSr96sq\narQt43zGQ8Vh4AfkKRl0dvdn+53P0Mm97oYo9aF4uwAgZjSuoY0gCHRw9aWXT7vqRYdVD0vW8Kub\ng1j7h2Dt1AYxsxCH57+0bRvYqUkxVqGqKikpOXz//QlOnrxoi18JoqKiO6pqb7uOOrLHipsbioMD\nYlERQkEBAFKyrT24rAlnDQ0NDY3rxE0mnC3odLGAwpQpA5g8uT+lpaUsWLAAq9V6o4NrMQEBAYwb\nN4SpUyOZN2/UdTuPYdMhdFHJ2K3d0fLJyiqQ4tJQJZGy+bcD4PDaty2f93dAqnTUUIKuzrpWUbXI\n7Ho6axg2HUZ35hJibjFO095ATM2p3meVVb7/9jKGkjJy9AZyB31OqVrIIP/OfDfl743PNNdA8akU\nzpkFzY656mGpqpSlFoKA+a+3AKCrLDGxNEE4Hzhwnqef3sCECS/RseMj9Oy5mDlz3uLjj09jtfbB\nYulEg1+GCULtrDOgu1QZs9YJUENDQ0PjOnFTCOfS0lI2b96MTpcAFFZvf/XVOfj5uXHs2DHWr19/\n4wJsBUSxBGfni7zzznTeeuue69qxTHfa1upYOl3pFtECpJgUBEVFDvGj/NExKM726PfFott/rjVC\nva5ULQyUr1EOI3fwRXUwIKXkIOQWt34QsoL9G1sAKHdzRkrLo2z0a9z/3EX6z08l4C+X+Oj/bPcy\n2q8Ci1DB5JD+fDFhES5Gh2adUq3OODdfOFdnnLvWnb01TxuIamfzalZFAWv/kEbOLJKUZGH16p/Y\nv/8cBQWluLu7M2TIEEJD+yDL7o2OsUo461JSQJaRUisXWGoZZw0NDQ2N68RNIZyff/55HnroIVas\neLXWdldXE6tW3cv9949l+vQ76x2/Y8cOSkpKkKS86x1qo4mOti2iE8Uy9Prz6PUHEcVkBEG4Zhvt\n1qBKOIuFZdXisdlzRVV+/R0eiOrsQPkDtky5/es3f9a5yopOuUapBpKINcwmtHRnklo9huy1B9DF\npXHRzpW2Xe4n2sGTNunpzF//ISmpRVjt04hw3gfAWS94NGIMq0fd36IGIoqPKwBCMzPOQkYBYmYh\nipM9Stu6WleD6mrCPLEvAHL3IFQn+wZmdUCWQ7BYBjJmzIMsXbqUjz/+mGPHjnH69Gk+++wz5s6d\n26Q4qwSylJKCmJ6OYLEge3mh2jcUi4aGhoaGRvO4KYTzRx99hF4vMXVq5FX7hg3ryosv3omzc9pV\n+3Jycnj44YeZM2cOr722BJ3uKDrdjXVHiImJYcaMGYwcOZITJ75Brz+AKF4E6m/53JoIhaVIiZnV\nr1tau/vbWtfyB0aiONph2B2N7nBci+a+3lQ1P5HrsKKrSWs7ayiKyo/HSpm6PA3Lis0AvNC+D469\nU1lwf2fSnfUMK0hifdbLiBGr6Vh6AYCOkX14buC0epubNPr8Taxx/i26s5UlD10D4RruFOWP3o4c\n7EX53bfW2l5QUMp//vMjo0b9k+JiJ6zWHpjNkVit7VAUB+zs7Hj00UcZPnw4vr6+zf72pbpUIznZ\nlnVGyzZraGhoaFxfbhpXjaVLJxNex0KkKkTxIpLkhix7oqoqmzdv5tlnnyU3NxcHByPBwQ6AiiSd\nA+yxWn9/t4qcnBymT59OTk4OTk72pKScAq5+GLie/LZWVzqdBOP7NH++39S6qq4myu8fgcMbW7F/\nfQtFny9qfrB1UWFF2HQQdUxEy+ZRVaQqD+egq7OmWaWF/PPARn5NiWGBbOBxIOPACQr/2pcAJ48m\nizlZVknKtLLjZBnvbSviQpqVKTknCC/NIsVFYt0dP1Ohg0Rg5Cz49QO4MxrW7nKgb6EAlNB3+K20\nRiV/S2ucq37n1rrqm2sgd/Yn/+gr1a+jo5NZs2YHGzceoLTUZoW3aVMy06Zdn8+AtUo4p6YiVdY3\nW7X6Zg0NDQ2N68hNIZz79evII4+MaeAoFZ0ulrKy7tx//3x++uknAIYM6cLKlXMJrs4qqkhSFCkp\n/mzbtpd77rnnusZek6effpqcnBwiIzuxbt0juN2ALntVZRqKtzNiZmH162ahKOjO2ko1ata6ls8b\njf3qnzD8cobzP+7mZ69ygl286ObZtlmiswpZUbi8Yg0e/zlI0pLbcFwyvdmhCxkFCOUWFHdHVOcr\ntcKKqrA++ldW7N9IvrkEgA128DhgPh5Hr3VP4KgzEeQQSDtTEJ1d2tHVtR0+js4YDQL2BhFJgqQM\nKzGXLMQmVxCdZOF8ioWyChVEC3icx77XaZ7dYKtdfmGwjGDUMSIgjHDPQDq7+3NxQAU9/raeu/aU\nolbeL7lT09wz6kNpYY2z7syV8pzG8vzzX/Lmm99Vvx40aBBz585l1Kjrtwi2ZsZZc9TQ0NDQ0Pg9\nuCmE8zvv/A1JaszX06WYTMk4OYk4OdmzYsV0Zs8eepVQKysrYeLEqaSkZGNvb8/MmTOvT+A12Lp1\nK1u2bMFkMrJq1b03RDTDFeFsnj4I+7e/t71uZjtpMTETocSM7OeG6ulcvT1OKKZkTCDDv4wne9mH\n/OMvV8a4GB3o6hFIuGcg4Z5tCfdqSxd3f/TXaBOdXpLPJ9F7WHd2N5s35wJwfMt2tg+w8tSAO3Ay\nNL1mVaqjTCM6O5nFu9ZxOD3eFmtFRwqihhEl5WMRvqZTtopDiR3FphLOFsZytjCWrVUVQmVuUBgA\nhf5Q5A+CDMbCyv+KIKQQvakIxT4TWahgVAz0yIAsNx3dFs0mtku/2tfRCYrftcfxb/9BUFUUVxOq\n95V73BJUX1uNc3OFc3XGuWtjsrciiuJL//7jMZl2MXXqVP76178SGhrarHM3hSqRrEtJ0Rw1NDQ0\nNDR+F24K4dyujiYN9SGKqbz00jiWLRtFmzZ1r8C3tzfw+OPjWLjwQ5YuXUpQUBADBw5srXDrxNfX\nl/bt/Zk3b/gNbWoiVQrnivF9MH60CzGrECE9H9Wvjs55DVC9MLBrIFmlhXwTd5iN5w9wPOMCXsGQ\nqIfx5+FpYy/2eVcQlX2J7LIi9l8+x/7LV1w3jJKOrp5t6eEVRE/vYHp6tyPUzY8Daef58MxOtiWe\nwKrI+BZB70qhGpYJd5z+ma0XjvHysDmMade05iTVrbaDvCixmHn18Gb+ffIHZFXBSXKmInY0Balh\nmOxEvFzakeC6j8556fwlYS5ng50pN6ZSIKaQK1yiUEpBsc8D+zzwOVPvOS2V/+/lFcx/1hcAeTg8\nOZ3pPYbVeXzFpH6UZuRjevpTrH3at7ipTEmJmZ9+OsW2747RB1iSVQCyAo16KK2k1IyUkI4qicid\nr86Aq6pa+aAqoiiByHIAimJi8OAwjh+/FUfH3++BUfH0RLWzQ8zPRxcTA2jNTzQ0NDQ0ri83hXBu\nKu7uDf9xnjNnGHFxabz77g/87W/3sWXLVtq3b3/dYhowwJ/du/+B0XgDb2mJudpz2RoWiNw9CHFv\nLLrTSViaIZyrMo8x/noGfLSYctkmDU16O0b06cPlGeWEfHyUf/wqULRuMaqqklFaQFT2JaKyLnEm\n+xJnsi5xoSCD4xkXOJ5x4crcgoisKtU/j20fwWOnPABbCU7HHIH2gj8XilOY891bjGvfm38NnYWf\nY+Ouo8pR46K7wIgNT5NSlIOAQJvySC4fGQayHZMHOfDyfe64O0mYHukAn6Wzsn8x5nv7A12q57Iq\nMjE5qRzNSOBYegJnsi7hoDfQxtEdP5MbbRzdaePoRhtHNwKdPGm7Lwnn+P9D8XGlfHbdormK8gdG\nYe3bEbke94rGsnjxOr74Yn91bfHXwFEV3ryUjUMTHkx1sakIioq1Sxuwu+LsUeYPA1sAACAASURB\nVF5uYf363bz//i98++0q3N27oyim6v2iKP6uohkAQcDq748+IQH92bOAVqqhoaGhoXF9+UMK58by\n3HPTSEjI4IcfTnL//ffz008/XRf/ZEEoQ5LOY29vaPW5m4IuOtkmeroGgJ0ea7cg9Htj0Z25hGV0\nz6bPV7nQ8MWyY5TLcGtgV/4SNoTRwT1x0BshPB/r56cwbDvOmleiaHNre/qEOjEiqDsjgrpXz1Ng\nLuV0VhInMy9yMjOR01lJJBZk4mdyY07XocwJG0ZSsj2lS96uHiOh4rjldtoMSiXX05Z53pV8lmci\np3BX11swXKP0A4DEDABezjpIShEE2AWSe2wMl7Pa4OEs8sp97kwceEX4yd3awmf70J1Owvzb+yBK\ndPNqSzevttwdfivXRFVxePUtAMoeHVNLfNaHNaIlD3R6FMULs9mZ0lIzERERDBkyhA/ffpskRUHK\nKoQmCOeqxaVy5ULdwsJSPvtsH2+//T1paTa7x08/PcmDD/6+i17rQw4IQJ+QgKCqqKKI7N86deIa\nGhoaGhp18T8tnCVJZPXqBxg37kUmTrwFQVCB1hbOKnp9HFwlt35/qso0rN2DSC7Mpm14APbQ7AWC\nZSfjMADHfWBp/8k83md89YNHUoaFJf81M8GrF/NTD+Py8S7mHHYCINhHR+8QA31CjQzqakdYkAND\nArowJOBKFre4ohx7nQFJFPlqbwkL37pMWpat9tjaox26U4kMFXNZdaov2IUQOPAHki0xLN3zCe+c\n2M6C3mOZ2WVwnX7HUdmXcDp2nAggyV2kQ/kIEnb3B1Xi9n72vHa/B96uUq0x1u7BQMvt+/S/nEF3\n8iKKtzPld10729wy7JDlUKxWd8DAo48+yYIFTxFYmXG9e/9+PI8cwSHfGxmJxtoh1mx8snHjARYt\n+pCysgoAunTpwqJFi7jtttuuxwU1i6oFggCynx/om+9/raGhoaGh0RD/08IZwNHRji+/XIyLiwM6\n3Qms1hAUpXUWYQHodOkIQnrLJqmwojt10ZZ5bEo96m9jqRTIe9xLGb3uCSLy9BwDzMfOkVNWhIe9\nU6PmUVWVN7av58XsMor18LeJs7i35wjA1iL631sLeeXzAsoqVAo79Gd+6mH+mhvFV6Hj2X9J4GKG\nlYsZVr7aWwpAt3YGZg03MWWwCTcnm2B1NNjZzvNVAS9+ms+wvEs4yxVYQ/0QxvaGU4k837cUOjrz\nn62QvGMazkHncOi8k+SiDBbvWsfKo1tZ0Hssf+kyBDudHllReOfkdv518GuSsmxCMa9gJgkXQ3Ax\nifzrXjemDjHV+a1DlYOEFJsKFis0p0mNqmL/qs23uezhMeBgbPocDZCeno+vry8WS89a7+OgoKBa\nx4UEBeFw5Ah5aVas1gh0uiigrMH5qxcGhnels0coZWXvMXDgQObOncuYMWMQr+HrfCOoJZy1hYEa\nGhoaGteZ/3nhDOBZ7QiRg16fjyy3x2oNRFUlrFYr+mZkqbZt28b+/XtYtuxWTKZmZrFVFf33JzA9\n9zlSYiZl82+n9B9TmzcXV4TzitLjAJx0sVCiB6eMEtqvmk/H9iGMbteLUcHdCXHzq7PRhqwoPL7r\nI9J+3ANAcWefatF8PM7MotU5RF201TpPHuTA83MDsMwOwe5QHF93TaLkn0OITbZw5JyZo+fN/HCs\njDOJFSxdU8E/Psrj9n4O/GW4IwPD7Fjyfg4bdpYgCPBim2Q4BZaRPdCH2QSQfcJlli13Y9pQE0+8\nn8uh2M4UJoXStW885X67SCi8zJLdH/PG0S3M6zGKHy+eYv/lc9hXgF8xVAgip3I70DvUwNrFXrTx\nqP/trjrZI7fzRkrMRDp3ubpUoSnod0ejP3YBxcOR8rkNlHQ0g/37zzFz5kqWLn2ce+4Zes1jZR8f\nAKTMTGTZDVXtjU4XRWZmEjExKWRmFpCenkd6ej7p6fm8/fZ9mOxN6M7a2laXhU4m1MODQ4cOEVBD\nnN5s1Kxp1uqbNTQ0NDSuN38K4VwbGUmKQxQz2bTpAq++upply5YRGRmJ0dhwhlBVVaKjo3nqqafI\nzs6mZ08ds2ZdW8TUhRR1CdOzn6H/NaZ6m3HtTkoXjQdHuybPh9mCGJOCIsApX1g+aDoTO/Yl/6uX\nMZ3None6yA/2cRxMi2P5/i8w6e0I9wykm6etdjfcsy3tXX2Y/8sHbEk4ytIs29f7rn27klOhsmJ9\nHu9/X4SqQltviVfu82BEhM1ezTx7KPpDcRjX78E8ayjhwQbCgw3cPdqJ8gqV7UdL2bCjmJ2nyvlm\nfynf7C/FwShQalaxNwisfsyTfotsLhwVI7qjC/Kz3aNzlwEICzKwZYUPG3YWs+zjfM4eCcXOEMK0\n8ZeI4ieic1JYtv8LALzsnZlZPAL4mkQ7N6YPd+LVv3lgZ2j44cbaPQgpMRPd6aRmCWe7t7YBUPbQ\nbWBq3WzzgQPnmTlzJSUlZk6fjqvhblE3ipfN2UXMtNnyKYoD5eU9ePzx19i+fd9Vxy9d+jztZSNC\naTmyry+KhwfATS2aoXbGWWt+oqGhoaFxvfkTCucq8lm79n3i4uKYNWsWRqORHj160K9fP2bPnl1d\nK1pFamoqy5Yt4+DBg+Tm2ryGBw3qzMyZg5t0ViGzAIcXv8b4ya/V/r1lSyZi+OYw+sPxGL/Yj/me\n4U2+mvj9R+hvVYj1gLv6j+bhXrY6VNOAbnB2BxsCJrD5tjZsTzzJnpRo0kvyOZQWx6G0q9tmOxvs\neURqD5wlv0MAU1ZkcCjWjCTCgxOceWKqCya7K9lq84S+ODz1CfojCUixqbVszOwMApMGmpg00ERq\ntpXPdhXz6c4SLmZY8XIR+eQpb/oYi9DFpqI42mHtHwLOTqg6CfFiFpSawcGIKArM/n9OjOrtwDMf\n5vL13lK++CqI8HbzWD45he/Td+Bt50bR6VEkbrddk66jN2891PiGLNZubTFuPnJV98XGIMWkYNgT\njWoyYm7lbPPBg+eZMeMNSkrMTJkyhddff73Ba5K9bQsCpcwr7dcvXEgmJ6eCyMhIfHx88PHxwdfX\nFx8fH9zcgtDv3g2ApWvXVo3/emKtWaqhZZw1NDQ0NK4zf1rhLAgCGzc+zttvb2PLlqPExKRy+PBh\nDh8+zJQpIwF/wCYORbEMd3czP/ywHVlW8PV1ZdiwMJ59dupVNZ9iXBqGn06DVQZVRZAVm5eurCAU\nlWH85FfE4nJUnUTZvcMpWzwB1c0RxdsF/eF47N7/GfPdtzbJ0zchP53PPltHfyC7kwfLBk2r3mft\nbqt9NZ29zISFE5nQsS9gazkdlX2JM1lJnK60j0vIz6CNoxufjFuAz7r3AHhgpwOHrGb8PSU+esKL\nnh3qyKSajFRMGYDdR7swrt9D6fN1N5zx99Tx+J2uLLzDhZMJFbT11uHpIqH/wJYBtdzSFQw6MOgh\nxA8hJgUpLg25R3D1HN6uEu895sW0oWU88X4OUYlWot/05d7RD7D7TDnnUywsVfJt5+vrR0kT7qNc\nea90Z5q+mNLuvZ8BMM8YhOri0MDRjefw4TimT7dlmu+44w5WrlyJJEkNjlMqhbNYQzh37NiRb775\npt4xVZZulrCwFkb9+6H4+KDq9QgWi1bjrKGhoaFx3fnTCmcAOzs9TzwxkSeemEh+fgmHD8dz7FgC\nXbtmI4q/oqouCEI5UIyrq8LatQ/TpUsAwcFe9Wb8nO77d3Wb6vqoGNWDkuXTUUL8rmwbG4Hs54Yu\nLg397mibiGwEGSUFTPv2DZYk2Vw9uo+8FUuN2mVrtyoxWDuL6uXgzK1tw7m1bXj1thKLGXudHrHc\ning+DRmBH80e9Agx8MlTXvi61f92KZ891Cacv9hP6bN3grH+unFRFIgIuSLADT+fBsAy8oqFnRoW\naBPO5y7XEs5VjIiw59c32vDyF/ms/q6I978vAqBTgJ7H/MwQXbtrYGO4cq+SQVGgkQvhhNxijBv3\nA1B234gmnbMhXF3dcHAwMXr07bz55puNEs1QI+OcldXoc+mjo4E/VsYZUcTStSv6mBgsHTve6Gg0\nNDQ0NP7H+VML55q4upoYNaoHo0b1qNxiRhAyax1z++0R156k3IIUk4IqCpTPGwWSiCqJNqcMQQBJ\nxDIgFOuQLleP1eso/utQXF7aTOH/fc16tzQuFmZxsSCTYks5wS5edHD1paOrLx1cfQh28aZCtjJj\nyxskFWYxOMcImFF7tCMtx8qqbwspNas4iva8JUnoEtJ5//NMJFd7XE0iESEGgrx1tR4ATHqbmP15\nfTzTFYWzDl4Mj3Tm3/M9a5Vm1IXcMxhreCC6qGQM35+gYlK/hm559T2rqvOuGN6terMa1ha+OoAu\nNpWKeoY62ov886/uTBls4rl1ebTx0PHK39xxuzvHFlNw0zo4ql7OKL6uiOn5iImZKB18GzXOuG4X\nQrmFihHdaj0MtRwd7dvfznffDcPX17fRohlqZJwzMhrdcr064/xHEs5A7scfI+TlobrX3UlUQ0ND\nQ0OjtdCEcysixachKCpyB19KV8xo9LjdyWdZvGsdxdZMkiVo8+sF3tt8gcQaOmBfamytMaIg4Ki3\no7CijBBHb8Irm1P8Knlz9xNpZBcq1cfea+9N7+I0vns/lr2uV2zLfNwkBnQ2MqCLkf6d7ejSVs/L\nn+dTtDaW6UBp50A+XOyFKDai3EEQMM8eim7pJxjX72m0cNbvj0Uoq8DarW2ttuBqWKU9XExqg3P0\n7GBk8/IrIrdmu+2mYu0WhCE9H92ZS1Q0RjhbrNit2QFA+f0jm3y++hGQ5a7Isiv+/q5NHq06OqLY\n2yOWlSGUlKA20NVPzMlBSk9HcXBADg5uZsw3BsXdHTTRrKGhoaHxO9Ai4Wy1Wrnnnnv4+eefKS0t\nJSIiglWrVhEWFobFYmHevHls3LgRNzc3XnvtNaZObb7V2h8BKdYm8qyd2zR6zIHL55n93VuUWSuQ\nnES2ROi584iZdy8EcGBcJO2cvXE02JFYkElCfnrlfxkkFWZRWFGGj4Mr34TPRix/gzwPdyb+XwmK\nAkO72TEh0oHyChXVEgT70pgflEvH/l1Jy5U5cs5MRp7M5gOlbD5g81s26sFsgVUlNl/qsPEdKW+M\naK7EfGckDsu+wLDrLGJSVqOEq/4nW5lGRY0yDaghnM81LJxroShIl2zCWW6OcO7eFsNPp9CdTmqU\n+DdsPYaUloc1xA/LreENHt9YZDkEq9Wn+RMIAoq3N2JSEmJGBnIDwllXmW22hoU1ukRFQ0NDQ0Pj\nz0aLhLMsy4SEhPDSSy/Rpk0b3nzzTSZNmsT58+dZuXIlZ8+eJSUlhRMnTjBu3DgiIyNvenurllBl\nn1bTVeJaHM+4wMwtKymzVjArbAivDbsLu0EpMGI5o/bk0HfV8Gprut/6NFTIVpIKs/Cyd8Zp4wkA\ndgg+KAosmuLMk9NckSSb6DVmhsC+g4y3z2b4/TabMVVVib9s5UB0OYdizRyKNXMxw4qTg8B011xI\nrWxD3QRUVxMV4/tg3HgA44a9lD01uYEBKoafTgE2/+ZadPRF1UtIl7KhuLzRFn1iej6C2Yri5dws\nW7+qBYJSIxcI2r33EwDlfxvRpAWddaGqKocOxdGv3wis1qCGBzSA7O2NLikJKSsLuUOHax5bXd/8\nB1oYqKGhoaGh8XvTotSS0Wjk2WefpU0bW4Z17ty5xMfHk52dzcaNG5k/fz7Ozs4MGzaMyMhINm3a\n1CpB36zoKjPOcmjDGeeYnBSmf/sGxZZyJof0541b5qKXdMg9g7H07YhYWMbp53cx/51sZryQwfKP\n89i0r4SENAuKomKQdIS4+ZGSrmfrv201wtHubfhkqRd/n+lWLZqhhltEjdbbgiAQ4q/nrpFOvPOo\nJ0ff8efs+wHEvOePx8XKzHnXptt7lc+2eVobN/xqcxa5BmJCBtLFLBQ3k61rYk30OuSOtlIJ6fzl\nRp9fvNj8bDP8ZjGlql7zWOn4BfRHElBcHDBPH9Ss89Xk3Xd/YNy4f/Gvf31La7SGr/Zyzsho8Ng/\nan2zhoaGhobG70mr1jgfOHAAf39/PDw8OH/+PJ06dWL27NmMHz+esLAwzp0715qnu+moKtVoKOOc\nkJ/OlM2vkmcuYXRwT94dcR+xl6zsPVvOwRgzfmovVhOP94YdbOjbGQSBn0+UV493chDoFmygQxs9\nG/eUsD3Ddt4Zi8Jw73O1FZo1LABVFGwZ8bIKsDfUGZePm4R4IQOhpBzF1xXVq+mtya0DO1V34NPv\niMIyqke9x1a7aQzvVmercbmTP7qYVHTnLiP/VljXg1RV39zEhYFVKIEeKK4mxOwixPR8lBp117/F\nvjLbbJ49tMUNT7ZtO86yZbYmLqGhnVs0VxXV3QMb4ayhr/xsWjq3zrk1NDQ0NDT+F2k14VxQUMBj\njz3GG2+8gSAIlJSU4OjoSFRUFL1798bJyYnk5Lpt2pydmy7QbjrKzIgXs1AlEVNEaL12bEkFmdz5\n7etklhYyPLgbG6c9yftbCnn832nVx+gcOrPMzomupVl8PrgAdXh3ohLLOR5Xxsn4Mi7nWNkfbWZ/\ntBlBVehbbssoBt/eA+q6l85AJ3+EmBRckvNR+9Rv2yUk2DKP9Grf/N/LfaPg6fU4frYf+c4h9R4m\n7bKVB0jj+9c6V5V7hNijPXxzGPvELIyNjEW8XACALjSg+fH3bAe7onCKz0LtVE/JRFoeus1HUUUR\n3WMTGzzXtTr9HT+ewLx576GqKsuXL+fuu+9uXty/QQqq9PAuKsKushNgnSgKugsXAHDu1w/c6n9Y\nuFHo9bbPk8e1rkPjT4f2vtCoC+19oVEXVe+LltIqwtlsNjN58mRmzJhRvQDQZDJRUlLCyZMnAViw\nYAFOTk51jv/ss8+qfw4PDyc8vPUWWf1uxKYiqCpqB796RXNacR5jNiwnuTCbyIBOfHXnUmISZZa+\nb1uMN3O4K8N6mBgUbsJr3e2w/HPuPLUP+bkh3DHEpXqe9FwLJ+PLOX2hjD5SAQ67y22OFL71Cx61\nV3uEmBSEExeuLZxPJdqO7x7cjJtgQ5lzC+I/NiB8dxTS8+qOq7gMYc9ZVEFAHdWz7pgrFwgK0df2\nxa6JkGh7iFDbN39hnVopnIUTF1DH9qnzGHH1dgSLFWVSfwiq2y/aVrN8nnXrdhIdncLPP7+JIKiI\nogxYAVAUmQEDlgAwZ84clixZ0uy4rzq/r63URUhPv/aBKSkIZWWo3t43pWjW0NDQ0NBoDrt372bP\nnj2ALSk3dOjQFs/ZYuEsyzIzZ84kNDSU5cuXV28PDQ0lJiaGiAib93F0dDQTJ06sc47bb7+91uvC\nwsKWhvW7Yzgehx6oCPWjuI74C82ljP3qReLz0unuFcT6MfMpzC/nLy+kYbGq3HubEy/fVyWOzRRO\nj8TtX18hfHeU4jMJtRwqHHQwsDMM7GyH4ZvKcofwthRd477ZdWmDCbAciqVk+oB6j3M6Fo8ElIb6\nUtHc34ODhNPonhi2Hafiv9spnz/2qkP0247jXGHF0rcDhQagxrmqsrfFQe64AWrUpUa/J5zjLyMC\nJd5OWJsZv6GTH06AfDSu7ntabsHtvR8AKLrn1qvOc/lyLl98sZ9PP91HQsIV0XrggI7OtUohFEpL\nbY1bhg8fzooVK6rbubcGRgcHPABLcjK5OTn1H3f0KEagon17cq5x3I2kKnN0s8ancWPQ3hcadaG9\nLzSqqJmM9fDwYO/evS2es8W+Uw888ACiKPLuu+/W2j5t2jTeeustCgoK2LVrFwcPHmTy5AZcFv7A\nVNmmyZ2urm+WFYX7f1xNTG4qoW5t2DjhcVyMDjzzYR4Jl610DtSzbE5tr17V24WKSf0QVBW7D3bU\ne96qBX9VrbXro3rR2+lru0VIUbYOg9bwpi8MrEnVIkG7NTswfrwb6dRFqLBW76+ubx7Rva7hACjt\nvFGNOqSUHISiskadV7qYWT22ucjdbW4iuv3nsHtrG+qReCxl5ur9xk2HELOLsIYHYo0MvWr8jBn/\nx/PPf0VCQjre3t489NBD7Ny58zeiGUDEzs6JY8eOsW7dOgyGumvPm30dVTXOmZnXPE6XkACAtQHn\nDQ0NDQ0NjT87Lco4JyUl8cEHH+Dg4ICLy5VSgu3bt7Nw4UJiY2MJDAzEzc2NDz74AH//xtm0/RGp\ndtSow8P5hYNf8XPSadztHPl0/GN42Dux5WAJH/9cjFEP7z3mib3x6meYsvv+H8Yv9mNcv4eyReNR\nXa5e+CdVCece1xbOVdZyUkwKWKygv/pXL2QXIqXloZqMLRKeAJbh4cgBHkgpOTgu/BAAVS8hdwnA\n2iMYww82C72KawhnJBE5xA9dVDLSuctY+zQg7IrKELOLUI06FB+Xax/7G8rLLcTEpNCrVzusHToj\n+3kjpWViWrGRQ8A4oLeriT5dA+l3MZNMoOuI7vQSRMAOVXVFUZxQVSdmzLiXI0eOMm3aNIYOHYpO\nV//HTBRFfH0b16GwqVS7ajQknOPjAU04a2hoaGhoNESLhHNQUBCKotS7f82aNaxZs6Ylp/jDUJ+H\n85fnDvDW8W1Igsia2x4iyNmLyzlWFv7H9pX8sjluhAXVnWmUI9pj6R+C/lAczhNfovDzx1FrCkJV\nrc4gN+S5rLo4VLtdSOfTkOuwmtOdtdUSW7sGtrwJhk6icNMSDN8dQ3c6Cd2pJKSEdNvPlTEr3i4N\nxi138rcJ59jUBoWzdCnbNqatV6PjT0rK4sMPd/LJJ78iy3DixE6MxjZk/vgLdrt3Y9i/nzPbt1OW\nm8ve/BL27rvSwfGBIifCLQNRFAdq2sfde+993HvvfY06//VE8fREFUXE3FywWKCehRFaxllDQ0ND\nQ6NxaC23W4PSK44aco02zScyEnlsx1oAXhzyF4YEdEGWVR58K5v8YoUREfbcN6buBZNVFP/nfpzv\nfB1dVDIuY1+gcOPi6myweDkXMbcYxc2EEtDw6mFrt7ZIiZnoTifVKZylM7YyDTm8aY1P6kNp5035\nI2OqXwtFZUhnLqE7nYQUk0LF7RENCtyqB5Eqq79rUV2mEdxwtlxRFJ599nPee+8n1Eq/5vDwcFJS\nyujQAVR3d8omT6Zs8mSmvvoqI86eJerLLzm+dy9nkpLwCA9nwODRKIqpwXPdMCQJxcMDKSsLMTsb\nxc+vzsOqhXPH+heNamhoaGhoaGjCuVWQ4tIQVBVre18w2G5pRkkBd217m3LZwpywYdzTbTgAq74t\nZN9ZM96uIm8/7FGvRVkVSqAnBd89hfOMlehOXrSJ588WIXcPQjpVo765EV3rrN2DMH571NYVb+bg\nq/brquubW0c4/xbVyR7rwE5YB3Zq9BhrJ1vpS2Nab1c3P2mEh/Mzz3zKe+/9zP9v787joq73PY6/\nZoYZQDYFQQXU3FBxySVRNC21Mj1tXjVLsyxtuWXrtZPZveVyK8tjpXb0qKeTx+MpvVl6OmaruZua\nW2ouuIC4gCCgyDozv5n7B0KagCDqsLyfj4ePh/zmN7/5DH4f+J4v39/na7Vaueeee3jkkUfo1KlT\nif8eddq0oWebNpTcXK9ycoWFYUlNxZKaWmxwNmVnY0lKwm2zYTSs2Lp2ERGR6q7CNwdWa1l5l939\nDi5dppFvOBj59UySsjPo1qAF79zyECaTie2H8nl70RkAZj5Tl9AgS5nKcNcN5OzSP2K/JRpzSiaB\n90zBa/3+35ZpXObGwELF7SBY8ALugpngLefXulbwxsCr6bcZ58vvHli0+UkZdg0cPvxBIiMj+ec/\n/8mMGTPo3LnzZT/EVEVG2PnfTpSwe2Bh/2ZnkyZgKdt4FBERqak041wCc0IKtW95nfx7u5A9Y1Sp\n5xbdGNgyHLfbzcurF/Bz8mEi/IP5uP8YbBYv4o47eOL90zgNePIPAfTt6Fu+ggJ8OffJC/g/81e8\nl20h8P5puMILeu5erqNGod+2kz4GhguvnfHY/r0N21fbsMQXLHNw17JhtI4sX23XkKtxKG4fK5ak\nDExnc4q9QbKQ+fxSDeMySzUMoznNmzdh3bo+V72TRWXjOh+cS9o9UDcGioiIlJ2Ccwls/96GKTsf\n76VbyH5nRInbVMPFW23/dddKPtm3Hl8vGwsGPEuITwBzvspk8j/PkGd3066Jjf8ZfoWbTHhbyZr7\nJK66Afj+dSWW80sTyhqc3aGBGA3qYEnKoE67FzGn/NZ/2BUaiH1AJ/KH9yz1vV53hZ01didiOXAC\nZ0yLkk9NuNx22yYMoxVOZ8GMenUPzQBGYWeNkmacC9c3Ny3bluYiIiI1mYJzCWw/7gbAlGvHuikO\nR++SdzMsXKpxoqEfEzf+FYDpfR4jxBTJoEkprNuTB8Cw3n68+WgwPrYKLAkwm8l5ezjuuoHUmrIU\nV7B/uVrHOTs1wfJVBuaUTIzwOtjv6oz9rptwdm0Blsq5csdoFVEQnPefLDk4Gy7Mxwq7atS96KG0\ntHOEhNTGMNrgdF6b1m+Vlauwl/PlZpx1Y6CIiMhlKTgXJysPr01xRV9af9hdcnDOzseceBq3l4X/\nTlpFnuHgvuYxOE62oef/nuRcjpu6gWbeeyqEATElLzMoF5OJ3LH34OzSDFdgrXK1jsuZ9ADOmBY4\nu7XA2bFJxdvOXQfO1hF4A5b9x0s8x3wyHZPDwFWvNtTyLjr+66/HGDjwXV566RkefbTvdai2cjEu\n08tZrehERETKrvKnJg+wrt9fEMICC9YhW8/PPhensKNGVqM6fJ6wDR+LjXN7+vLMh2mcy3HTv4sv\n694Pv3qh+QKOW9pgdGxSrue4GoeS98ydODs3uyqh2eVycfBgUqn9vCuqcDfG0m4QLK6jRlJSBg88\n8D7p6VmsXr3tmtZYWblK2z3Q5cJSeHOggrOIiMhlKTgXo3CZRt7jt+EK8MXrYBLm85tr/F5hm7SN\nQTkA+KXczMpN3vj7mpj5TAgL/hha5u4ZVU1WVh4PPvgBsbHjuemmV3jnXmzA7gAAIABJREFUnWXk\n5ORf/oml+L//20hU1NM0bjyaTp1eZvny7RitCm5W9Cqll/PvO2pkZeUxbNh0kpIyiImJYc6cOZir\nwOz61VbajLPl5EnMeXkYoaG4g8q306KIiEhNVPOSxOW43VhXFgRnxx034rglGih51rkwzG0MysHf\nVIe0X7vRPNyLde+F82Bv/2rZ4gzg9OlMBg58l5Xnv1eJiaf59NNN+Phc2Y2PbrebadO+5Omn55GQ\ncIqkpAwSE0+Tnd2U/Pr34PL1xZxyFtfpcMCM83dtAs3ng7PROBTDcPH4439h9+6j3HDDDXz00Uf4\n+PhU6P1WVRd11Ti/0UshrW8WEREpHwXn3zEfOYXlaCquOn44OzTB0acdALaVxQdn196Cbar3hkLW\nnr5YzTbmvFCXhqHVe/n49Okr2LEjnoYNG7JmzRoWLVrE669PxuHojtN5Ey5XQ6D4LZ6Ls2bNXt5+\neykmk4lp06Zx5MgRNm3axG23DcCFP86oKABMe7M5fLgusbGv8eMFH2YK2+kZTcI4fjyNnTsTqV27\nNv/4xz8IDg6+qu+9KnH7+eHy88OUl4cpM/Oix9RRQ0REpHyqTbozpWfhP+av5I24BUf/jld8HduP\newBw3NoWLGYcfQtuCrSu3Qd2Z9HOgIVydx/CD4jzC4eENowbXpsbm3r//rLVjIVXX51ITk59nn/+\neerVq0fzC2YtDSMYwwgGmuHldYolS/7OwYOJPPfcAAIDi1/r3avXnTzzTDYdO3bmoYceAsDb+7fv\nozMqCtsvv+B14AALVh4nPv4UDz74AVOmPMSjj/a+aKlGo0atWb58OadOpdFUoRBXWBjm+Hgsqak4\nL1iSoRlnERGR8qk2wdl7yU/YvvsFy+5EztzWDqxX9taKlmmcD8yuiBCcrSLw2n8Cry2HcN7cqujc\nQ8fi6ZqSh90Me1MG0K21D2PuCaz4m6nUvHE622GxBPPWW29d5lwbOTn1mDz5C5KTT7FgwRrGjr2H\nkSN7Y7vgA4hhNMfpbML48f9d4pUcLQu26faKi2PcpEmYzWZmzpzJyy8vID7+FB8Ubn7SuCl2ezSR\nkT5ERt5Q0TdbLRhhYXjFxxf0cr4gJKujhoiISPlUm6UaXhsPAGBJysD25dYru0ieA+uG/QD8emMI\n0X97nj6LJ7CnQ8Gv+m0rdxWd6na7+fsXCwGIC/LBl4bMerYuFkv1XNNcoBYOR8fzs8llY7PZmDt3\nHl27diU9PYvx4z+he/fxLFu2BbfbdL63clOg9O9b4VIN64EDmM1mxo0bx3vvvouXxcysWd/yQEY2\nLh8r9uCeQM1cz1ySknYPLArOmnEWEREpk+oRnN1urD8dKPrS9y/fXXIjVFlYN8VhyrVjb9uQh7cv\nJCUnk12pR/kvW8Es9JnlGzidW7BO9LuEX8jZVdDK61dbY94ZFUyjsGozgX+RtWv3kp1tw+HoiMtV\n/hn1zp078/nnn/Pxxx/TokULEhJSmT79OxyO9jidEWW6hrNwxvnAAazbtxM0fjzPvf023xkuagM9\nTSZyHx6Ky+1f7vqqO+N8cL5w90BTVhaW5GTc3t4YkZVni3UREZHKrFokPUvcScxpWbjCAsHpwmtH\nfMGyiq4lb89cnMJlGt80cxOXcZKWweE8deMdzA/8nuxPT9AgPpMeM/6LHl26s+HEfp46P4FnRDVi\nSC+/q/22KoVvv93Jww/PpFOnjixe/BneV7h822Qycccdd9CnTx8WL15M06ZNcbvrlfn5RkQELj8/\nLGlphN59d9Hxm1u3ZnO/fgQMH87Z8PArK66aK27GuWi2uUkTsFTPdokiIiJXW7UIzl4bC3b5c/Ro\njXFDKLXeX47PnO/I7NKc7Dw3WXkuLGYTYbVLDwiFLeem1TmOr5eNF1uNpr67AbP7xJIR8w5+G45w\n6wEnH/utBaBNshVw0PvB5tWy7dyGDfsZNWoWhuGia9fYi27Wu1JeXl4MHz68/E80mbDHxOCzahVG\nWBi5991HzuDBONu0wR8o/+8Xao7iejmro4aIiEj5VYvgbD2/vvkvZxvw6ZEo1plW4PXlNrrc/QtH\nfX/rK9zvJl9eHhJEh2aXBkDz8TS8Dpwk0xt+ioTw03fx1FtmoODX2/+Z0opZHOG+nS1YHhVMqukI\nbZJyAQc+HRtS3fak27EjnuHDZ5CX52DEiBGMGzfO0yWRMWMGXkeP4mjXDryqxdC9LorbPVA3BoqI\niJRf1V/j7HZjOb++ec65cDafrcXi0DZYcDPmxBb8fApmmn1sJr7dmsttryQzfEoKOw//boe7H3YC\nsLIJONLacXRnO+oGmunW2pumDbxYF16w7KPnyWOkb7kDv59Gc0NuFm6rBVeTsOv6lq+UYbjKtO10\nQkIKQ4e+R1ZWLvfeey9vvvlmpZhRdwcH4+jYUaG5nIpmnC9cqqFWdCIiIuVW5ROI6cgpvJLPkGqt\nRVaUH988X5vmJ+6Fgbt56exOHp09AgJ8ST1r8OG/MvnbN+f4dmsu327N5c6bfHn5/iB8bWbO/HUF\n/YFvGtXC/9jdPPtAbZ78QyD+voWfLSJwxNSjzpFTrHsgl1y3GdaD0bw+eFWuNaL5+Q5stjDcbl9M\nJgNwYjI5WbVqCw88MIU6dfzo2bM1t99+I337tiMs7OLtlsPDQ+nRI5bsbIPp06dj0RrYKq1wxvnC\nmwM14ywiIlJ+VT44b563i/7A+rC6HG/xJ+5c4SbCP5gVUX60j8tm3/SFuJ66kxZ1GjDx4To8c08g\nf/6yIEB/szWXb7bmYq27i9T4dABsNz3IjsebUifg0rDovK0d1rmnuPHwAVyNC2bxjJZl6wpxvWzY\nsJ9nnvmImTP/TExMl4seO3cuDYCMjGy+/HIrX55v2/fYY314990R588yYbHcyJ//fBsOhwOrtey7\n/0nl5AoOxm2xYMnIALsdvLzwio8HFJxFRETKo0oH583780hbvheAbR0zcOPGYjJzIiudCR3gizio\n//eNtAzciMliplFgXZrVrk+zJvV5+YVQdu4O5NvNDrrU+jdB+ZASGciEl24u8fUcfdrhO/cHbCt3\n4+he0B7NaFV5gnNy8hkef/wvpKScZeXKdcTEXPxeBgwYwLFjxzh27BirVq1i5cqVbNy4gYYNO2MY\nLTGb03C56uF01sNiQTPN1YXZjCs0FEtyMubUVEwuF6a8PIywMNyB1X3DHhERkaunUgZn70XrsS3Z\nRNbsJ3CHFv8fe3KGk0f/dJpNZ44CsDziHE2Cwlj74GSOn0tjf0oi6WsW0PxUDqOPBzGvUSbxZ1OI\nP5vCD0d/28iE9nDnyoK/BvyhKzml1OXo0Qq3jxWvnQlFbRyMVpWjBZrTaRSF5tjYWF5++eVizzOb\nzTRu3JiRI0cycuRIcnNzMQwDp9MfaHx9i5brxjgfnC2pqZgzMgDNNouIiJRXpQvOplNn8XtlIabs\nfHz+upLcVwdeco7d4WbUtNN4J6fRJO8MZ3xgdz34uPv9+HrZaFGnAS3qNMB7zBn4n0V8eKABr781\nlYSzKRw+k3z+zykOn0nm0JlkBibkAQ4cfduVXpyvDUf3lth+3IPXLwkAOCvJUo033/ycn346QFhY\nGLNmzcKrjDfQ+fr6XuPKpDIo7OVsTknBKzERUHAWEREpr0oXnGv96V+Ysgs6Xrg+Ws2O+/rRqqkP\nvt6/NQB5Y0EGm/fn84zzGADrGkHXyJYMaNrpomvlP9QL33eWYd2wH799SbRq14hWIRcHXVPKWYJf\neQG3jxVHbMvL1ufo0w7bj3sAcNu8KkVHjYMHk/jww2+wWCzMnj2bsDDP1ySVS+HugZaUFHXUEBER\nuUKVqh2d+VAy3gvWYGDiuK8v/mcymfXUGm4YcYxeL51kzIenee3jdOZ9fQ6rFzwbVrBMY01jmHzz\nA5e0THMH+JI/vBcAPn/5ttjXtK7+FShYhoGv7bI12i+YlTZaNLgqHTW2bz+C3e4NePP7f5KkpAzy\n8hylPr9Fi0b84x9zmDRpEt26datwPVL9uC7YBEUdNURERK5MpZpxtk1agslw8XF7G7vDc5n+DbyU\nvo1/1Ytmb6KDvYm/Bci3HwvG/6WCnf68e7WjQ9gNxV4z7/G++Mz9Hu8vNuOu44+7lg18bLh9bLh9\nbXgv3QyAo0/bMtXoal4fo1FdLImnMVpWfH3zsWOnGThwKg0bNuKLL5ZSp443JlMOkIPZnMtjj73D\njh0Hadu2IV26NOemm5rRpUtzGjYMOf9BwYRhtKZ37/oVrkWqL+OCTVCKgrNmnEVERMql0gRn88+H\n8FuxjRwvE2/cZifHClN+gJuTDhP3qZtDtgbsOmJnV7yd5uFetK8XR0RyPlk2eOCBESVe13VDGPa7\nOuP97634/uW7Es+z97nM+uZCJhOO29tj+ehHnO0qdjOd2+1m7NgFZGfn0bRpc4KCalOwP4kvEIJh\ngNPpi8vlZufOBHbuTGDevB8A2LDhbVq2rI/LdQNOp0KzlK5wxtnr8GEsp07h9vbGiKgc6/NFRESq\nisoRnN1u0p9dRB3gg25uMkN8+fC2x1j2w1we3OZgw/9+QLePJ3NTVAAALreLP41bzO3AibahhNcJ\nLfXy2dMewXFLNKasPEx5DsizY8p1YMrNx5TnwNm2Ea4WDcpcbs74QRjN6pP3UK8KvGn47LOfWLly\nN0FBQbz55pvFnrN8+XKysrLYuXMn27dvZ9u2bRw6dIjGjYfgdOZgGLUrVIPUDIVrnG3btwPgbNoU\n1G5QRESkXCpFcN45cwt9Dx0mzRfeuRlm3T6aAU07cepVNwyexYANZ7l18Vv8c9BYIgNC+DxuMw13\nFWwfHHZ7LJfbRNod7E/+yN5XrV53UC3ynri9QtdITc3ktdc+BeCNN94o9YY+f39/br75Zm6++eK+\nzIahjhhSNoVdNUx5ecD54CwiIiLlUiluDmzw/hIA/rcXPNStX1F3jHq33ERudAR1c+HGjckM+PxN\ndqYkMPmnz7il4L5AzD3beKrsCvn00/VkZGTRs2dP7r//fk+XI9Wc63cfzLS+WUREpPwqxYxz9LnT\nxNeGn+9uxpLYwb89YDJhPNYXxi7g5V0+fNI+gzs+m0TtbDftUsDtY8XZsYnnCq+AMWOGU7duD7p0\n6XpJNxCRq83t64srIADzuXOAOmqIiIhciWs643z8+HFuvfVW/Pz86Ny5M7/++muJ577Tz4e/3PUM\nVsvFWT5/UDfcfj50OJTH45YoXG43Pc/PNjs7NwNv67V8C9eIBcNoyaBBQ2jUqJGni5Eawrhg1lnB\nWUREpPyuaXB+4oknaN++Penp6QwdOpShQ4cWe96O+nDHH5+hgX+dSx8M8CX//lgA3o+PYFzXgbzq\nLNioxBEbdc1qv5YMowkuV/FbiYtcKy4FZxERkQq5ZsE5MzOT77//nnHjxuHt7c0LL7zA0aNH2bNn\nzyXn7hjTnVsal9xHOe+RWwHw/WwTY6P70flgwQ1Oju6X3+mv8gnC6axYGzuRK1E442zUq4c7IMDD\n1YiIiFQ91yw4Hzp0CB8fH/z8/OjZsyfx8fE0a9aM/fv3X3Lu3U+OKvVaRttGOLo0w3wuF5+/r8ay\nJxG31YLzpqoza5aamklCQipOZxSgNmBy/RX2ctZss4iIyJW5ZjcHZmdn4+/vz7lz59i3bx8ZGRkE\nBASQnZ19ybm1gy7fi9j01AD4eSa1pizF5HLj6tqcwPql92+uLPbtO869975FSkoms2fXK3HJihSw\nWgvWrYeEhHi4kurF0qIFAF7t21e5763GhBRH40KKo3EhxSkcFxV1zYKzn58fWVlZREZGcvr0aQDO\nnTuHv7//JecuWrSo6O9t27albdtLl224B8fiHvsxpoysgq9vjr5GlV9dq1fv5v77p3LmTDadO3fm\nlltu8XRJUkMZw4ZBairGqNJ/wyMiIlIdrFmzhrVr1wJgsVjo1atiG9fBNQzOzZs3Jzc3lxMnThAR\nEYHdbufw4cO0bHnpuuQBAwZc9HVmZmax16w1tHvRttnZNzXBUcJ5lcWiRet58cX5OBwGd955Jx9+\n+CFWq5W0tDRPl1apFc4S6Pt0lZnN8OKLBX+vYt9bjQkpjsaFFEfjQgpdOBkbEhLC+vXrK3zNa7bG\nOTAwkH79+jFlyhTy8vJ4//33ady4cbGzyWVVeJOg28uCM6Zyb+CQnHyGP/5xIQ6HwRNPPMHcuXPx\n9dVOfyIiIiJV1TXdAGXOnDk89NBDBAcH07p1axYvXlyh67laNODc7CfA2wt3QOUOofXqtWLmzBkk\nJ59m5MiRni5HRERERCromgbnyMhIVq9efVWvaR8Se1Wvdy24XDfgcDTjzjvbe7oUEREREblKKsWW\n29WJy9UAh6MFoG20RURERKqTa7pzYE3idBpAAA5HFArNIiIiItWPgvNVkJZ2jptv/h8WLtyP223z\ndDkiIiIicg0oOFeQ2+1mzJiPOHQoiX/8Yykul8vTJYmIiIjINaDgXEGzZ3/H99//Qu3aQcyaNQuL\nRdtpi4iIiFRHCs4lOHEijQED3mTUqFn89FMcbrf7knO2bz/CpEmfAfDee+8TGRl5vcsUERERketE\nXTWKkZ/vYOTIP7NjRzwA//rXz7Rr14iFC58jIqJgRyKXy8Vzz/0Np9Ng1KhR9OvXz5Mli4iIiMg1\nphnnYnz55VZ27IgnIiKCZ599luDgYNLTHYSGtqXws4bZbGbOnCn8x3/8B6+99ppnCxYRERGRa04z\nzsUYPPgPZGc3o3XrtnTo0IEXXniBhIQE3O5WOBy5mM3JmEw5NG/empkz+3i6XBERERG5DhScL+GD\n0xnNgw/e9NsRHx9atWoFgMvli8vVxFPFiYiIiIiHaKnGRUw4ndG4XLU8XYiIiIiIVDIKzhcwjBYY\nRl1PlyEiIiIilVANCc5WDKMtLlckYOXcuVzWrPkVwyjYrGThwrXs25eP09nYs2WKiIiISKVVrdc4\n5+U5yMuzExAQi9NZHwgHmrNs2XxefPFP1K9fm9tua88nn6zH1/f/WL++K2FhYZ4uW0REREQqoWo9\n4zxu3EL69n2LX35Ju+CoDbM5mMaNG5OcfIaFC9ficrkYNWqUQrOIiIiIlKjazjgvXLiWhQvX4uPj\nfcmuf4MHD2bQoEFs3bqVZcuW4evry9ixYz1UqYiIiIhUBdUyOO/cmcArrywE4K233qZt27aXnGMy\nmejSpQtdunS53uWJiIiISBVU7ZZqpKdn8dhjfyY/38Hw4cMZOnSop0sSERERkWqg2gXnFSu2k5h4\nmg4dOjB58mRPlyMiIiIi1US1W6oxbNhQfHy60qlTJ7y9vT1djoiIiIhUE9UsOAficLTk7rvbeboQ\nEREREalmqtVSDaezOWDzdBkiIiIiUg1Vm+Dsdodqu2wRERERuWaqfHA2DBfx8akYxg2eLkVERERE\nqrEqH5w//3wT3bqN4913/+bpUkRERESkGqvSwdludzJlylIMw0XDhg09XY6IiIiIVGNVOjgvWLCa\nxMTTREVFMWjQIE+XIyIiIiLVWJUNzllZeUyb9m8AXnnlFSwWi4crEhEREZHqrMoG57lzvyc1NZOO\nHTvSr18/T5cjIiIiItVcld0AZejQW0hIsDJw4GBMJpOnyxERERGRaq7KBuf69TszdepgT5chIiIi\nIjVEFV2q4YvTGeHpIkRERESkBrni4Pzuu+8SFRVFYGAg7dq148svv7zo8RkzZlC/fn2Cg4MZP358\nhQu9UMFmJ9paW0RERESunysOzlarlaVLl5KZmcmcOXMYMWIE8fHxAGzevJmJEyeyatUq9uzZw6JF\ni/jss88qXGxurh23Owins0GFryUiIiIiUh5XHJxffPFF2rRpA0D37t1p2rQp27dvB2DJkiUMGjSI\n1q1bEx4ezujRo1m0aFGFCv3ii83Exr7Gvn0BVOGl2SIiIiJSRV2VNc4ZGRnExcXRtm1bAOLi4mjZ\nsiXTp09n7NixREdHc+DAgSu+/ooV2/nP/5zL8eOn+eGHdVejZBERERGRcrkqU7dPPvkkI0eOpGXL\nlgBkZ2fj7+/P3r17OXr0KP379ycrK6vE5wcGBpb42Pff72T06NkYhouxY8fy6quvqv1cNWe1WgEI\nCQnxcCVSWWhMSHE0LqQ4GhdSnMJxUVGlBucJEyYwadKkS47fd999fPHFFwCMHz+ejIwMPvnkk6LH\n/fz8yMrKYvr06QAsXboUf3//El/nwmUcbdu2LZq5Xr9+L4MHv4vd7uTpp59m8uTJCs0iIiIicllr\n1qxh7dq1AFgsFnr16lXha142OE+YMKHEx99//32+//57Vq9ejZfXb5eKiopi//79RV/v3buXVq1a\nlXidAQMGXPR1ZmYmABs3xpGbm88DDzzAq6++Snp6eqlvRqqHwlmCtLQ0D1cilYXGhBRH40KKo3Eh\nhS6cjA0JCWH9+vUVvuYVL9X4+9//zpw5c1i3bh1+fn4XPTZkyBD69+/Piy++SFBQEH/729+YMmVK\nOV/ByujRr3DDDf3o1asXZnMVbTktIiIiItXCFafRiRMncvToUZo2bUpAQAABAQFF4TgmJoY33niD\n3r17065dO4YOHcqQIUPKcXUvnM72GEYdevfujcViudIyRURERESuiiuecT5y5Eipjz/33HM899xz\nV3BlC05nOwxDi/pFREREpPKoNOsfjh9P4+DBZAyjHYYR6ulyREREREQuUil2EklOPsPAgVPJzLSz\nZEk3oqLCPF2SiIiIiMhFKsWM86BBU4mPP0WDBhHUq1fP0+WIiIiIiFyiUgTnAwdO0rJlSz799FOC\ngoI8XY6IiIiIyCUqRXBu0qQJixYtIjg42NOliIiIiIgUq1IE58WLFxMWpnXNIiIiIlJ5VYrgHBER\n4ekSRERERERKVSmCs4iIiIhIZafgLCIiIiJSBgrOIiIiIiJloOAsIiIiIlIGCs4iIiIiImWg4Cwi\nIiIiUgYKziIiIiIiZaDgLCIiIiJSBgrOIiIiIiJloOAsIiIiIlIGCs4iIiIiImWg4CwiIiIiUgYK\nziIiIiIiZaDgLCIiIiJSBgrOIiIiIiJloOAsIiIiIlIGCs4iIiIiImWg4CwiIiIiUgYKziIiIiIi\nZaDgLCIiIiJSBgrOIiIiIiJloOAsIiIiIlIGCs4iIiIiImWg4CwiIiIiUgYKziIiIiIiZVDh4JyR\nkUFoaCgjRoy46PiMGTOoX78+wcHBjB8/vqIvIyIiIiLiURUOzuPHj6dp06aYTKaiY5s3b2bixIms\nWrWKPXv2sGjRIj777LOKvpTUIPv27fN0CVLJaExIcTQupDgaF3KtVCg4b9u2jYSEBAYMGIDb7S46\nvmTJEgYNGkTr1q0JDw9n9OjRLFq0qMLFSs2hH3ryexoTUhyNCymOxoVcK1ccnN1uN88//zzTpk27\nKDQDxMXF0bJlS6ZPn87YsWOJjo7mwIEDFS5WRERERMRTvK70iR999BHt27cnOjr6omUaANnZ2fj7\n+7N3716OHj1K//79ycrKKvFaISEhV1qGVENWq5U+ffpQu3ZtT5cilYTGhBRH40KKo3EhxbFarVfl\nOqUG5wkTJjBp0qRLjt96660kJiby008/AVwy4+zn50dWVhbTp08HYOnSpfj7+5f4OuvXry934SIi\nIiIi15PJ/fvUWwa//PILHTt2vOR4hw4d2L59Oy+//DJnzpxh3rx5ALz55pvs2LGDJUuWVLxiERER\nEREPuKLg/HsTJ07k8OHDLFiwAIAtW7bQv39/1q1bR1BQEL169WLKlCkMGTKkwgWLiIiIiHjCFa9x\nLk1MTAxvvPEGvXv3xuFw8NRTTyk0i4iIiEiVdlVmnEVEREREqjttuS0iIiIiUgYKziIiIiIiZXBN\n1jiXRVpaGjNnzuTw4cOEh4czZswYGjZs6KlyxAMMw2D27Nns3r2b/Px8mjRpwqhRo4iMjMTpdDJv\n3jw2bdqEn58fI0aMIDY21tMly3W2b98+JkyYwJNPPkmfPn00Lmo4u93O/Pnz2bRpE263mx49ejB6\n9GiNixouMTGRefPmkZiYSJ06dRg2bBgxMTEaFzXIzz//zLJly0hISKBHjx48/fTTAJcdAytWrGDp\n0qU4nU5uv/12hg0bdtnX8lhwnjt3Lo0aNeK1115jxYoVfPDBB0ybNs1T5YgHuFwu6tevz7BhwwgO\nDuarr75i6tSpTJ8+na+++orjx48ze/ZsEhISmDJlClFRUdospwYxDINPPvmEiIiIomMaFzXb/Pnz\nOXXqFO+99x5BQUGcOHEC0Lio6WbOnElsbCyTJ09m165dTJ06lVmzZvHjjz9qXNQQfn5+3Hvvveza\ntQu73V50vLSfDQcPHmTJkiVMmjSJWrVq8frrr9OkSZPLfrjyyFKNnJwcdu3axX333YfVauUPf/gD\nqampJCYmeqIc8RCr1crgwYMJDg4GCjbWSU5OJjMzk02bNtG/f39q1apFdHQ0UVFRbNmyxcMVy/X0\n9ddf06lTJ4KCgoqOaVzUXHa7nbVr1/LYY49Ru3ZtTCYTkZGRgMZFTXfy5Em6desGQPv27bHZbKSk\npGhc1CDR0dHExMRcstleaWNg06ZNdO3alcjISIKDg+nTpw8bNmy47Gt5JDgnJydjtVrx8fHh9ddf\nJyUlhXr16nHy5ElPlCOVRFxcHMHBwQQEBHDy5EnCw8OZMWMGGzduJDIyUuOjBjlz5gxr1qzhrrvu\nuui4xkXNdfLkSUwmE1u2bOHxxx/npZdeKvoPUOOiZrvxxhvZtGkTLpeLnTt34uvrS8OGDTUupNQx\nkJSURHh4OCtWrGDBggVERkaSlJR02Wt6JDjn5+fj4+NDbm4uJ06cICsrC19fX/Ly8jxRjlQCOTk5\nzJ8/n4cffhiTyVQ0Ro4dO0Z6ejo+Pj4aHzXIggULGDhwIFar9aLjGhc1V25uLk6nk5SUFGbPns2o\nUaP48MMPOXPmjMZFDffwww/z448/Mnz4cN577z2eeOIJbDabxoVKGdkkAAACyUlEQVSUOgYKHzt1\n6hTJycllzqEeWePs7e1NXl4eISEhfPTRR0DBD0UfHx9PlCMe5nA4mDp1Kj169ChaW1Q4RqZOnQrA\nxx9/jK+vryfLlOtk//79pKam0r17dwAubDWvcVFzeXt743K5uPvuu/Hy8qJNmzY0aNCAuLg4jYsa\nzG63M3nyZB555BG6dOnCgQMHmDp1Ku+8847GhZQ6Bgofe/TRR4GCXa/LkkM9MuNcv3597HY76enp\nQMFdj6dOnSI8PNwT5YgHuVwupk+fToMGDbj//vuLjoeHhxfd+ANw/PhxjY8a4siRI8TFxTF06FCG\nDh3Kvn37mDNnDvPnz9e4qMHCwsJKfEzjouZKTEwkNzeXmJgYTCYTrVq1IiwsjAMHDmhcSKljoEGD\nBlc0PjwSnGvVqsWNN97IsmXLsNvtLF++nNDQUBo1auSJcsSD5s6di8lkYvTo0Rcdj42N5euvvyYn\nJ4dff/2VgwcPEhMT46Eq5XoaMGAAixcvLvoTHR3Nk08+yciRIzUuajB/f3+io6NZvnw5hmGwd+9e\nkpKSiIqK0riowcLCwrDb7fz888+43W4OHTrEiRMniIyM1LioQVwuF3a7HZfLhcvlwuFwYBhGqWMg\nNjaWLVu2cPz4cdLT01m1alXRbzpL47Ettwv7OB86dIiIiAj1ca6BUlNTGTNmDDabDZPJVHR8/Pjx\ntGjRgrlz56r/pjBx4kR69uxJnz59MAxD46IGS0lJYdasWRw+fJiQkBCGDx9Oly5dNC5quK1bt/Lp\np59y+vRpAgMDue++++jbt6/GRQ2yevVqZs+efdGxIUOGMHDgwFLHwJX0cfZYcBYRERERqUq05baI\niIiISBkoOIuIiIiIlIGCs4iIiIhIGSg4i4iIiIiUgYKziIiIiEgZKDiLiIiIiJSBgrOIiIiISBko\nOIuIiIiIlIGCs4iIiIhIGfw/F5L+IYh7XOUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd68d6a6cf8>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It can be a bit difficult to see, but the KF and EnKF start off slightly different, but soon converge to producing nearly the same values. The EnKF is a suboptimal filter, so it will not produce the optimal solution that the KF produces. However, I deliberately chose $N$ to be quite small (20) to guarantee that the EnKF output is quite suboptimal. If I chose a more reasonable number such as 2000 you would be unable to see the difference between the two filter outputs on this graph."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Outstanding Questions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All of this should be considered as *my* questions, not lingering questions in the literature. However, I am copying equations directly from well known sources in the field, and they do not address the discrepencies.\n",
      "\n",
      "First, in Brown [2] we have all sums multipied by $\\frac{1}{N}$, as in \n",
      "\n",
      "$$ \\hat{x} = \\frac{1}{N}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
      "\n",
      "The same equation in Crassidis [3] reads (I'll use the same notation as in Brown, although Crassidis' is different)\n",
      "\n",
      "$$ \\hat{x} = \\frac{1}{N-1}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
      "\n",
      "The same is true in both sources for the sums in the computation for the covariances. Crassidis, in the context of talking about the filter's covariance, states that $N-1$ is used to ensure an unbiased estimate. Given the following standard equations for the mean and standard deviation (p.2 of Crassidis), this makes sense for the covariance.\n",
      "\n",
      "$$\n",
      "\\begin{aligned}\n",
      "\\mu &= \\frac{1}{N}\\sum_{i=1}^N[\\tilde{z}(t_i) - \\hat{z}(t_i)] \\\\\n",
      " \\sigma^2 &= \\frac{1}{N-1}\\sum_{i=1}^N\\{[\\tilde{z}(t_i) - \\hat{z}(t_i)] - \\mu\\}^2\n",
      "\\end{aligned}\n",
      " $$\n",
      "\n",
      "However, I see no justification or reason to use $N-1$ to compute the mean. If I use $N-1$ in the filter for the mean the filter does not converge and the state essentially follows the measurements without any filtering. However, I do see a reason to use it for the covariance as in Crassidis, in contrast to Brown. Again, I support my decision emperically - $N-1$ works in the implementation of the filter, $N$ does not.\n",
      "\n",
      "My second question relates to the use of the $\\mathbf{R}$ matrix. In Brown $\\mathbf{R}$ is added to $\\mathbf{P}_{zz}$ whereas it isn't in Crassidis and other sources. I have read on the web notes by other implementers tthat adding R helps the filter, and it certainly seems reasonable and necessary to me, so this is what I do. \n",
      "\n",
      "My third question relates to the computation of the covariance $\\mathbf{P}$. Again, we have different equations in Crassidis and Brown. I have chosen the implementation given in Brown as it seems to give me the  behavior that I expect (convergence of $\\mathbf{P}$ over time) and it closely compares to the form in the linear KF. In contrast I find the equations in Crassidis do not seem to converge much.\n",
      "\n",
      "My fourth question relates to the state estimate update. In Brown we have \n",
      "\n",
      "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\mathbf{z}_{mean} + \\mathbf{v}_R]$$ \n",
      "\n",
      "whereas in Crassidis we have\n",
      "\n",
      "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
      "\n",
      "To me the Crassidis equation seems logical, and it produces a filter that performs like the linear KF for linear problems, so that is the formulation that I have chosen. \n",
      "\n",
      "I am not comfortable saying either book is wrong; it is quite possible that I missed some point that makes each set of equations work. I can say that when I implemented them as written I did not get a filter that worked. I define \"work\" as performs essentially the same as the linear KF for linear problems. Between reading implementation notes on the web and reasoning about various issues I have chosen the implementation in this chapter, which does in fact seem to work correctly. I have yet to explore the significant amount of original literature that will likely definitively explain the discrepencies. I would like to leave this here in some form even if I do find an explanation that reconciles the various differences, as if I got confused by these books than probably others will as well."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- [1] Mackenzie, Dana. *Ensemble Kalman Filters Bring Weather Models Up to Date* Siam News,  Volume 36, Number 8, October 2003. http://www.siam.org/pdf/news/362.pdf\n",
      "\n",
      "- [2]  Brown, Robert Grover, and Patrick Y.C. Hwang. *Introduction to Random Signals and Applied Kalman Filtering, With MATLAB\u00ae excercises and solutions.* Wiley, 2012.\n",
      "\n",
      "- [3] Crassidis, John L., and John L. Junkins. *Optimal estimation of dynamic systems*. CRC press, 2011."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}