From 2c3784cc13f653879bd5195c14bec6609096720a Mon Sep 17 00:00:00 2001 From: Daisuke Oyama Date: Wed, 16 Sep 2015 22:00:47 +0900 Subject: [PATCH] Revise DiscreteDP solution notebook --- solutions/discrete_dp_solutions.ipynb | 363 +++++++++++++++++++++----- 1 file changed, 300 insertions(+), 63 deletions(-) diff --git a/solutions/discrete_dp_solutions.ipynb b/solutions/discrete_dp_solutions.ipynb index 015fcb9a6..ca15c0d3f 100644 --- a/solutions/discrete_dp_solutions.ipynb +++ b/solutions/discrete_dp_solutions.ipynb @@ -51,6 +51,7 @@ "import numpy as np\n", "import scipy.sparse as sparse\n", "import matplotlib.pyplot as plt\n", + "from quantecon import compute_fixed_point\n", "from quantecon.markov import DiscreteDP" ] }, @@ -65,10 +66,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Consider the following problem:\n", + "To recall, we consider the following problem:\n", "$$\n", "\\begin{aligned}\n", - "&\\max_{\\{c_t\\}_{t=0}^{\\infty}} \\sum_{t=0}^{\\infty} \\beta^t u(c_t) \\\\\\\\\n", + "&\\max_{\\{c_t\\}_{t=0}^{\\infty}} \\sum_{t=0}^{\\infty} \\beta^t u(c_t) \\\\\n", "&\\ \\text{ s.t. }\\ k_{t+1} = f(k_t) - c_t,\n", " \\quad \\text{$k_0$: given},\n", "\\end{aligned}\n", @@ -84,7 +85,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We let $f(k) = k^{\\alpha}$ with $\\alpha = 0.65$, $u(c) = \\log c$, and $\\beta = 0.95$." + "As in the lecture,\n", + "we let $f(k) = k^{\\alpha}$ with $\\alpha = 0.65$, $u(c) = \\log c$, and $\\beta = 0.95$." ] }, { @@ -105,8 +107,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "Here we want to solve a finite state version of the continuous state model above.\n", "We discretize the state space into a grid of size `grid_size=1500`,\n", - "from $10^{-6}$ to `grid_max=2`." + "from $10^{-6}$ to `grid_max=2`.\n", + "\n", + "The grid size in [the lecture](http://quant-econ.net/py/dp_intro.html#computation) is 150,\n", + "where the value functions are approximated by linear interpolation,\n", + "while we choose a finer grid since we fill the gaps with discrete points." ] }, { @@ -151,7 +158,13 @@ "Thus the state indices and the action indices are both `0`, ..., `grid_size-1`.\n", "Action (indexed by) `a` is feasible at state (indexed by) `s` if and only if\n", "`grid[a] < f([grid[s])`\n", - "(zero consumption is not allowed)." + "(zero consumption is not allowed because of the log utility).\n", + "\n", + "Thus the Bellman equation is:\n", + "$$\n", + "v(k) = \\max_{0 < k' < f(k)} u(f(k) - k') + \\beta v(k'),\n", + "$$\n", + "where $k'$ is the capital stock in the next period." ] }, { @@ -160,7 +173,8 @@ "source": [ "The transition probability array `Q` will be highly sparse\n", "(in fact it is degenerate as the model is deterministic),\n", - "so we formulate the problem with state-action pairs, to represent `Q` in sparse matrix format." + "so we formulate the problem with state-action pairs, to represent `Q` in\n", + "[scipy sparse matrix format](http://docs.scipy.org/doc/scipy/reference/sparse.html)." ] }, { @@ -233,7 +247,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "(Degenerate) transition probability matrix `Q` (of shape `(L, grid_size)`):" + "(Degenerate) transition probability matrix `Q` (of shape `(L, grid_size)`),\n", + "where we choose the [scipy.sparse.lil_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html)\n", + "format,\n", + "while any format will do\n", + "(internally it will be converted to the csr format):" ] }, { @@ -252,18 +270,52 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Discrete growth model:" + "(If you are familar with the data structure of\n", + "[scipy.sparse.csr_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html),\n", + "the following is the most efficient way to create the `Q` matrix in the current case.)" ] }, { "cell_type": "code", "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "# data = np.ones(L)\n", + "# indptr = np.arange(L+1)\n", + "# Q = sparse.csr_matrix((data, a_indices, indptr), shape=(L, grid_size))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Discrete growth model:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "dgm = DiscreteDP(R, Q, beta, s_indices, a_indices)" + "ddp = DiscreteDP(R, Q, beta, s_indices, a_indices)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Notes**\n", + "\n", + "Here we intensively vectorized the operations on arrays to simplify the code.\n", + "As [noted](http://quant-econ.net/py/need_for_speed.html#pros-and-cons-of-vectorization),\n", + "however, vectorization is memory consumptive,\n", + "and it can be prohibitively so for grids with large size." ] }, { @@ -282,21 +334,22 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "res = dgm.solve(method='policy_iteration')\n", + "res = ddp.solve(method='policy_iteration')\n", "v, sigma, num_iter = res.v, res.sigma, res.num_iter" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": true }, "outputs": [ { @@ -305,7 +358,7 @@ "14" ] }, - "execution_count": 12, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -314,9 +367,18 @@ "num_iter" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that `sigma` contains the *indices* of the optimal *capital stocks*\n", + "to save for the next period.\n", + "The following translates `sigma` to the corresponding consumption vector." + ] + }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": { "collapsed": false }, @@ -328,7 +390,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "metadata": { "collapsed": false }, @@ -345,9 +407,16 @@ " return (1 - ab) * k**alpha" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us compare the solution of the discrete model with that of the original continuous model." + ] + }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "metadata": { "collapsed": false }, @@ -356,7 +425,7 @@ "data": { "image/png": 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mTp06PPbYY9jY2DB8+HCcnJxo1KgRXbp0MWw3QIMGDZgwYQKmpqYMGTKEgIAA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\nHEjmrbcmU6hQOQYObJndlxcREfFMcjJMmrSP1q2f4aefplC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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -401,7 +470,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "metadata": { "collapsed": false }, @@ -412,7 +481,7 @@ "121.49819147053378" ] }, - "execution_count": 16, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -423,7 +492,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "metadata": { "collapsed": false }, @@ -434,7 +503,7 @@ "0.0038595076780651993" ] }, - "execution_count": 17, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -452,7 +521,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "metadata": { "collapsed": false }, @@ -463,7 +532,7 @@ "0.0013020872868430011" ] }, - "execution_count": 18, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -482,7 +551,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 20, "metadata": { "collapsed": false }, @@ -493,7 +562,7 @@ "False" ] }, - "execution_count": 19, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -505,7 +574,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, "metadata": { "collapsed": false }, @@ -516,7 +585,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 22, "metadata": { "collapsed": false }, @@ -527,7 +596,7 @@ "521" ] }, - "execution_count": 21, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -538,7 +607,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 23, "metadata": { "collapsed": false }, @@ -549,7 +618,7 @@ "0.00065355751082307734" ] }, - "execution_count": 22, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } @@ -567,7 +636,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 24, "metadata": { "collapsed": false }, @@ -578,7 +647,7 @@ "True" ] }, - "execution_count": 23, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } @@ -594,6 +663,13 @@ "## Comparison of the solution methods" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us solve the problem by the other two methods." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -603,20 +679,20 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "dgm.epsilon = 1e-4\n", - "dgm.max_iter = 500\n", - "res1 = dgm.solve(method='value_iteration')" + "ddp.epsilon = 1e-4\n", + "ddp.max_iter = 500\n", + "res1 = ddp.solve(method='value_iteration')" ] }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 26, "metadata": { "collapsed": false }, @@ -627,7 +703,7 @@ "294" ] }, - "execution_count": 25, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -638,7 +714,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 27, "metadata": { "collapsed": false }, @@ -649,7 +725,7 @@ "True" ] }, - "execution_count": 26, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } @@ -667,18 +743,18 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "res2 = dgm.solve(method='modified_policy_iteration')" + "res2 = ddp.solve(method='modified_policy_iteration')" ] }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 29, "metadata": { "collapsed": false }, @@ -689,7 +765,7 @@ "16" ] }, - "execution_count": 28, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -700,7 +776,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 30, "metadata": { "collapsed": false }, @@ -711,7 +787,7 @@ "True" ] }, - "execution_count": 29, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -729,7 +805,112 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 31, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 loops, best of 3: 2.83 s per loop\n", + "1 loops, best of 3: 201 ms per loop\n", + "1 loops, best of 3: 204 ms per loop\n" + ] + } + ], + "source": [ + "%timeit ddp.solve(method='value_iteration')\n", + "%timeit ddp.solve(method='policy_iteration')\n", + "%timeit ddp.solve(method='modified_policy_iteration')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As is often the case, policy iteration and modified policy iteration are much faster\n", + "than value iteration." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Replication of the figures" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using `DiscreteDP` we replicate the figures shown in the lecture." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Convergence of value iteration" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us first visualize the convergence of the value iteration algorithm as in the lecture,\n", + "where we use `ddp.bellman_operator` implemented as a method of `DiscreteDP`." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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vvDOEt98elI2DNps1uOYaGkE3NVmZoLOIi1Lki3lgIIhAoLhtWYyWa2rMqK21\noLbWjJoaM+vstY4QBIJwWJTu5CIOBlMzlrBer5QJeLKy0agq6tzJ2qwZjFVEIpHGqVMjePvtIVy4\nMC5FfzqdCtdcU4kdO6pZL27QNj+3O4y+Pj/6+wPo76dyLjU8SqtVoqbGLBNzVZWJRctrFEEgUtXz\nVFFwMJgqWbtSCqNRBYuFytZiUaGsTJ0tq/P2q6FSLf1c6kzWDMYSIQgEFy6M4+23h3Dq1AgSCdpu\nqlDwuOoqF3burMGWLeXrVi6ZjIDh4RD6+wPo68uJOZUqFrPNpkNtrSVPzmY4HKxtea2QSGTg9yfh\n8yXg9yezZXkeCs1OwlS8Kpl4czKm2yt5BTkmawZjkRkcDOLYsQH88Y/DsqrapiYbdu2qwTXXVMJg\nUC/jFS49ophFKff1+TE0FCopZqfTgPp6C+rqLKivL0NtrXnd/bzWCoQQhMPpSUUs7o/FSk8sU4jJ\npCoSblkZrYIW95vNqhUt4ZnCZM1gLAKRSBJ//OMw3nijX9YO7XIZsXNnNXburIHDsT7m4hYEArc7\nhN5eP/r6phZzeblBknJdHRU0G7e8OkinBQQCyUkjYTGl06VXDMtHpeJRVqaG1UrlS8saqSwKeS1I\neKYwWTMYC4QgEHR0ePDGG/04fXpUkpHBoMaOHVXYvbsW9fWWNV1VKy5Y0dPjR0+PTxK0WOWfj8tl\nzIqZSrm2lol5pUIIQSBAxTsxkSjKJyYSCIVSmEmfYYNBWSRfuZTV0OuVa/r/ZC4wWTMY88TjieLN\nNwdw7NgAJibohCUcx6G93Ynrr6/D1q2uNdsOHYul0NcXkMTc0+Mv2Svb4dCjoaEMDQ1lUlU2W0Rk\nZSCOGy4lYJ8vmU2JaXtK8zyHsjLVlCIuK1OzFcPmCJM1gzEHUqkM3n3XjTfeGMDFi9I6NnA49Lju\nulrs3l0Lm023jFe48KTTAoaGgpKUe3v9GBkJo3AIpsGglsTc2EhzNlRq+UilBJl8Swk5kZi+jdhs\nVsFq1cBmU2fzXNlqpe3D6330wmLCZM1gzIKRkTBee60Px44NIhKhUweq1QpcfXUlrr++Di0ttjVT\nfRcKJdDd7UNXlw9dXRPo6wsUtTMrlTxqa6mUGxutaGgoYzN+LTHxeBpeb0KWJiZy5VBo+lm0tFpF\nVr5UvIW51apZluFKjBxM1gzGNKTTAk6dGsHRo32yKLqhoQzXX1+HHTuqVn2VLiEEbncYXV0Tkpzz\nZ1ATcblNrqhUAAAgAElEQVSMUrTc2GhFTY15XXXyWQ6iUVHGcUxMJOHxxGUyjkRKr5MtolBwJSWc\nX9bpmApWOuw3xGBMgscTxWuv9eGNNwYQCtHVrdRqBXburMGePXWory9b5iucO/F4Gr29fknO3d2+\noiUf1WoFGhutaGqyoqnJhsbGMjZkaoEhhCASSZeMiEVBTzeMSaXiYbdrCpIWdjutprZY2IIjawEm\nawYjD0EgOHNmFEeP9uHcuTFpf3W1GTfeWI9rr61elVG03x9HZ+cELl/2oqvLh6GhYNGEEjabDk1N\nNknONTVm1ga5AKRSArzeODyeBMbHae7xxDE+HofXm0A8PrWMNRpFCRlrsjLWwGRSMRmvA5isGQzQ\ncdGvv96PI0d6pR7dKpUC27dX4YYb6lfV+tCEEHi9MVy+7MXly1TQhVXaCgWPhgaLJOcNG6ywWtdW\nh7ilQlwAolDEYtnnm3pZRJ1OIUXC+RK22zVwODRsGBMDAJM1Y50zNBTE4cM9ePvtIanzlMtlxA03\n1GP37ppVUe1LCMHISFgS8+XLE7I1rwE6b3Zzs01K9fVlbAjNLEgmM/B65ZFxLlKOI5mcfKIPnuck\n8TocWjidWqnMZLy2EQSCaDSDcDiX5gqTNWPdIVZ1Hz7cI+swtnlzOW6+uRGbNjlX9M1TEAiGhoIy\nOYtt6iIGgxotLTa0tNjR0mJDba2FVWlPQyKRwfh4HGNjcYyNxTA+nsDYWAyjo3EEAlNHxwaDMith\nKuB8IdtsGvazXyOkUgJCoQxCISreUCidzeVCFlMkkpnRRDEzgcmasW6IRlN44w1a1e3xRAHQiHP3\n7lrcfHMDXC7j8l7gJIiR88WLXly86MHFi15p2JiIxaJFS4sNGzfa0dJiR2WlcUU/cCwXkwl5bCwO\nv39yISsUYnQsj4ydTlp9rdezW+lqgxCCZJIgFEoXCLi0iEOhDBKJ6adKLcRgUMBozKW5wtazZqx5\nvN4oXnqpG2+8MSBNe+l0GnDLLY3YvbtmRXYY83qjuHjRi44ODzo6PEWzgtlsOrS2OqTomY1tzjEf\nITudWpSXUwm7XDppm0XHKx9CCGIxYVLhlpJxKjU7BykUHEwmBUwmKl6TSZnNczLOLxsMCraeNYMx\nHX19frzwQhfefdct9Xxub3fillsasXlz+YqSWyiUQEeHRxL0+Li8Q5jZrEFrqwNXXEGT3a5bUde/\n1AgCwcREAqOjMYyM0KpqmseYkNcQmQxBOJxBMJhGMEgFS/PifeFwZtopUQtRq3lJsDkBlxaxyaSA\nVssv2/8dkzVjTUEIwblz43jhhS6pPVqh4LFrVzVuu60JNTXmZb5CSjKZwaVLXpw/P46ODg+GhoKy\n4zqdCq2tdknQ67VaOx5PY3Q0LklZTGNjcaRSpaskmZBXNqmUMK14xX2z7ZCl1fKTCjdfuuJ+jWb1\nTOjDZM1YE6TTAv74xyG88EIXhodDAGh79A031OOWWxqXfVgSIQRDQyFcuDCOc+fG0dk5IZu6U61W\noLnZhiuucKC11YG6uvXTIYwQGiXnR8gziZItFjUqKnSoqNDB5aJSrqjQMSEvA/F4RiZZuYDl+2Kx\nmbf7chxgMilhMilgNlPJms0KmM3K7HZun9GoWNNTojJZM1Y1yWQGr7/ejxde6JKGK1mtOtxySyP2\n7Klb1vbocDgpyfn8+XFZuzPHcWhoKEN7uxNtbU5s2GBd89N2CgLB2FgMbncMw8NRuN20PDYWm3To\nk1LJy0TscmmzuY5NkbnIEEKroAOBNAIBKlqxTHOagsHZdbxSKDiZeKmIcxIWo2CzmUa/7MGLwv7a\nGauSeDyNV1/txYsvdkvDlqqrzbj99iZs3161LOLLZAR0d/tw/jyVc19fQLYilcWiRXu7E5s2UUEb\njSt/DPdcyGQEjI3FszKOYniY5qOjcaTTpW/qFotaJmIxYmZR8sKTTgtF8i0UsRgVz7QNWKXiYLEo\nJclOJWC9fvnafVczTNaMVUUkksQrr/Ti8OEeafhSQ0MZ7ryzBVde6Vrym0AkksS5c+M4c2YU586N\nIRrNza+tVPJoaXGgvd2J9nYnqqtNa+omlS9lMVIeHo5idDQ26U3ebtegslKPqiodKiv1qKykcmZD\nn+ZPKiXA50vD70/nRb45+YrlSGTm7cAGgwIWixIWCxWtWKY5lbHFolzWjlfrBfYfwlgVhEIJvPRS\nN44c6UU8TodfNTfbcNddG9HW5liyG4W4OtXZs6M4c2YU3d0+2RzbLpcRmzY5sWlTOVpabNBoVv+/\nmNimPDgYxdAQTdNJ2eHQorJSh8pKHaqqqJQrKnTQalf/z2OpEQRaHS2KWJRx/rbfn0Y0OjMJ8zwn\nSVbMC+UrSnmtN82sJth/DmNFEwol8Ic/dOHVV3uRTNKbUXu7E3fe2YKWFvuSXEMqRXtunzkzirNn\nx+D1RqVjCgWPtjYHtmwpx5YtLpSXG5bkmhaLeDyNoaGoTMxDQ5FJV34SpSwKuapKj4oKHTQaNpXp\nTIjHMwgEMvD5UnkizsDvT0v7ZlodrVBwKCtTSqmUfFk78OqFyZqxIolEknjxxW4cPtwjTWSydWsF\n7ryzBQ0Ni780ZTicxJkzozh9egTnz49LDwoAYDJpJDm3tztXZbQodvYqFLPHEy95vtmsQnW1HjU1\nBlRX65mUp4EQgmhUwMRECj5fOptyQhaj4nh8Zh2zjEaFTMSlktGoYFXRywSdDQ2IRgWEwwSRiIBo\nlCASoeVIhGS3Zz8Dmsjqu8sw1jSxWAovv9yDl17qltZX3rLFhXvuaUVdnWVRP3tiIoZTp0Zw6tQI\nLl/2yqq3a2stuPJKF7ZsKUdDw+pZgQug0fLgYBQDAxH090ekauxS45RVKh6VlTqZmKur9TCb12Zn\nuLkSj2cwMZGTcKnyVIt7iKhU3LQStliUa3pI0kqCEIJEQpRsaemWEnAkQpBOL+6MnGy6UcaKIJFI\n45VXevHCC11Sx7H2difuvrsVGzZYF+1z3e4QTp0awcmTI+jr80v7FQoera12XHVVBa680rXs47Rn\nSiiUwsBARBLzwEAEY2OxkosJ2O0amZCrq/VwuXTrvopU7KiVHxUXlmcyVlin42G1qmCzKWG1KmG1\nqopEzHpGLw5ipBuJ0Eg3HC6Wa6F8RSnPdhY0EbWag8HAQa/nYTBwMBp56PV0n8HAZ49xuOYaLZtu\nlLH6SKcFHD3ah9/+9rI0BGvjRjvuuad1UdqkCSHo6wvg5Ek3Tp0awchIWDqmViuweXM5rrqqAlu2\nuKDXr7w5w0XETl+ikMVUau1khYJDdbUetbUG1NUZJEGvx3HKYvW015uS0sREWsonJlIzmjVLpeJg\ns4kiVsFqVRaVtVrWRLAQTCbecDi3LVY952/Pdt5vEY1GLlexXCjdwv0q1eI+dK2//1bGioAQghMn\n3Pif/+mQ5sHesMGKe+5pxRVXLGzvbkIIBgaCOH58GCdODEsrbgF0Kckrr3Rh27YKtLc7oVKtvBss\nIQQ+XxK9vWH09dHU3x9BJJIuOlerVaCmhkq5tpamykrduunVSwhBKJTBxEQKXm9aJmWvl8p4unZi\nhYLLRsLKoshYLBsMrH14LiyleFUqDkYjjXDzRSsvF0e/SuXK/L0yWTOWnIsXPfjv/76A3l5a7VxZ\nacKHP3zFgo6TFqf3FAU9NpZbGMNi0WLbtgps21aJjRvtK67aNxRKobc3LJNzMJgqOs9oVKGuTi7m\n8nLtmpYIIQSBQHpSEXu9qWlv7FotD7tdlU1KqSxGxmYzE/FMoStdEYRCBKGQkE1UsuK+QhHPV7xG\nIxXrZNtiFbRajTX1e2SyZiwZQ0NBPPtsB86eHQVApXnPPa247rraBRPm8HBO0PlV3GazBldfXYnt\n26vQ3GxbMf/EsVg6K+SIJOiJiUTReQaDEg0NRtTXG9HQYERdnQFlZeoV8z0Wkng8A48nhfHxFDye\nXBofpzKeriOPwaCQRGyzqeBwUBGLUtbpWDvxZIjyDYfl8pVLOF/Es2/jnY14xe21Jt65wGTNWHT8\n/jh+85sOHDs2CEIItFol3v/+Zuzd27ggk4ZMTMTwzjtDePvtQWkRDwAwGtWSoFtalj+CFgSCwcEI\nenrC6OoKobc3jNHRWNF5Go0C9fUGScwNDUbY7Zo1c7MSBAKfL50n4aRMyNO1GZvNSpl8C6XM2orl\nJBIEgYAgybVQwoX7ZitfnY6DycTDZKJypWX5Pibe+cNkzVg0UqkMXn65B7/97WUkEmkoFDxuvLEB\nd97ZApNJM6/3jkZTOHnSjbfeGsSlS15pv8GgxrZtFdi+vQqtrY5lFXQolEJ3d0hKvb3houE8SiWP\n2lq9JOb6eiMqKlZ/j+xEQsDYWFIWHYtlrzc1pRBUKg5OpxoOBxWw06mSyna7alUta7hY5As4GBQQ\nDJJsXrydTM5OvlptTrSidHMSpmWzObdvpbbxrjQIARLFlWYzhsmaseAQQnD69Ch+/evzUuexq66q\nwL33ts9rhq90WsC5c2N4++0hnDkzKi0xqVIpsHWrCzt31mDTJicUiqW/mQsCwdBQFN3dIXR1UTmP\njxdPMOJ0arFhgwlNTSY0NBhRXa1ftZ2/kkkB4+MpjI0lMTaWy0dHkwgEiju/5WOxKCUJ53Iq6PXa\nZpxITC7cYJBGvYHA7AWsVlO55sTLw2ym0W5+BGwy0X2L3at5NZNKAbEYEInQPBqlaSb7YjFAmPuc\nKEzWjIVleDiEX/3qHC5cGAcAVFWZcN99m9DW5pzT+xFC0Nvrx1tvDeL48WGEw3RoEsdxaG11YNeu\nGlx9deWSzyIWj6fR3R1GZ2cQnZ00ak4k5NW3ajWPhgYjNmwwSclkWrnDwUqRSpUW8thYEj7f5EJW\nKjk4nVTA+ZGx00mjY7V6dT6gzBZBoJ2v/H4BgYA8zUfAdJUrKlizmc9LxdsaDbcuH35KQQgVbjRK\nRRqJ5MqiZPNToXBTxf08Z4VWO/fXsklRGAtCNJrCb37TgaNH+yAIBAaDGvfc04obbqifU5VuKJTA\n228P4Y03+mXt0FVVJuzaVYNrr61e0olKQqGUJObLl4MYGIjIZjgDclHzhg1U0DU1hlVRnS0IBBMT\nKYyMJDEykpPx6GgKPl+q5IQqAB3iRIWsQnm5Gi6XGuXltGy1KlfFd58rmQyNeql4iSTgQimHQqTo\n72QyVCpuUuEyAcsRhJxI82Wbn092bD7CVSgAgwHQ6QC9niadrnhf/rH8bZ6ngQabFIWx5BBC8Pbb\nQ/j1r88jFEqA5zncfHMj7r57IwyG2U1RKQgE58+P4403+nH69CgyGVpnZDZrsHNnDXburEZNjXlJ\nblJebxyXL+fkPDIi7wjG8xwaG41objajudmEpibzio+aEwkBo6NJSco5OScnHU7D81xWxlTCYu5y\nqWCzqdackNPpnIT9floVXSoqDoWESR9iCjGZeFgsPMrKqGxpLkbG9Nh6FXAqVSzWqQScn88VpZLK\n1WCgAhXzwnIpCatUwHL9ipisGXPG7Q7h4MGzUgevjRvt2LdvC6qqTLN6H48nijffHMCbbw7A56NS\n5HkOW7a4cP31tbjySteit0N7vXF0dARw8WIQly8Hi4ZPqdU8GhtNaGmhct6wwbQiF7EQxyGPjNDI\nOF/KExOThxRWqxIVFTQ6zo+Q7XYVFIq1IZBEgsDny8DvF+Dz0eT3C9I2lfPMGhU5DrBY+JKprIyH\nxZKT8XrogEUIEI9TkYbDNInizd/Oz8Ph+UW5+YItFG+pXCwvp3DnA5M1Y9YkkxkcOnQJL77YjUxG\ngMmkwZ/8STt27qyecWSQyQg4fXoUR4/2Se3bAOB0GnD99bXYvbsWZWXzaOCZhkAgiYsXqZw7OgJF\nq03p9Uo0N5vQ3GxGS4sZdXWGFdURjE43msbwcALDw0kMDyckKU82Q5dSyaG8XI2KCnlyuVSrergT\nIXROZ1G4hTktZxCLTR8K07WeuaJIWC5kWi291moVRAQhF8HOVLyRCJCZ2XLaMiaLcktJNj/X6WiV\n8nqCyZoxK86cGcUvf/kePJ4oOI7DDTfU43/9rytmXOXt98fx2mt9eO21fgQCVJAqlQJXX12J66+v\nxcaN9kWpCoxEUrh4MYiLFwPo6AgUVWvr9Ups3GjGFVdYsHGjGVVV+hVRJUkIgd+floQs5m53EolE\naSkbDApUVubLmOYOx+qrthZFPDEhYGIig4mJ0hHxTGbFUqk4WK1UvpPla03C4nChUIimcLg4LxRx\nNIoZV/Hno9Xm5Go00lRqOz+nY64X/nsvJ5lMtkNaDIjFsx3V4rl9c4XJmjEjQqEEfvGL93D8+DAA\numTk/fdvmdGKWIQQXLrkxZEjvTh1akTqcFNRYcSNNzZg166aBV80I5US0NkZxLlzfnR0BDA4GJHd\ngDQaBVpaqJxbW83L3hlMnNN6aIiKOF/Mk63wZDYrUV2tRmWlBlVVaknQRuPq+bdOpWhEPDGRyeb5\nicp5Jr2k9fpi+YplcVuvX/1twoTQm78o28kEnJ+npx5FVxJRslOJtjBXrp4/uykRh2dFReGK0i1R\nFoWcf36yeC2dBYH1BmdMCSEEf/zjMH75y/cQDiehVivwoQ9dgVtuaZxWbrFYCm+9NYgjR3qlqT95\nnsO2bZW48cb6BY2iCSEYGYnh3Dk/zp/349KloGy9ZpWKR1OTCa2tVM4NDcZlGY8N0AcJtzuJwcGE\nLEUipesRjUYFqqqokPNzg2FlV10TQqetzBdvoYhn0kas03Gw2RSw2Xgp5SSsQFkZD41mdUqYEBrV\nTibewn3h8OyrmzUawGSiQi3M81O+oFdrFTMhVJZTyTRWGPHmlaOxuT3c5MPzgE6b7aSmLS5/7CNz\n6w3OZM2YFJ8vhp/97Kw0l3dbmxMPPngl7Hb9lK/zeKJ4+eVuvPnmAOJx+pdvsWixZ08d9uypX7C2\n6EgkhY6OgCTowuUh6+oMaG8vQ1ubBU1NZqhUS38HCgbTGBiQS3lkJFlyOI9er5Ai5OpqDSorqZRN\nppU5SYgoY683A69XgMcjwOMRy1TG01VP8zytms4Xcb6YrVYeOt3qMocgUKkGg1SywWAuldqe7UQZ\nWi2VrZhKSTg/V89uUMaKIJUCIuJ456xkI5FcORrNHi9xbL6yVSgAgyhXHaDXFQg3u0+vo78LsazL\nnqfRTF21z4ZuMRYMQghef70f/+//XUAsloJOp8JHP9qO666rnVQahBB0dfnw8svdOHlyBOKDWGur\nAzfd1ICtW+ffo5sudRnB2bM+nD3rQ1+ffKyz2axCe3uZJGizeenuUoJA4HYnMTAQl6Q8NJREMFh8\n5+B5DhUVatTUaFBbq0FNjQbV1RqUlSlXnJTp2s85CYtlj0eA15tBIjHdohq8TLyFEbLFsjraiDOZ\nXKQ7nXzD4dkJWKcDzObSoi21b7VUN6fTcqkWylcm3PxzYvPrJa5S5QQqCjZfpmJZlHC+fHU6+vNd\nYf+GAJisGQX4fDH8+MenpR7aV11VgX37tkwaDWcyAt59142XXuqWlrxUKHhce20N9u5tRG2tZV7X\nk0xmcOFCQBK035+LnhUKDq2tFmzaRAVdU7M0ncIyGYLh4QT6+xPo64ujv58KulQUqdPxqKnRyFJV\nlWbFzOCVThN4vQLGxjKyqJjKWEA0OrV1dDoODocCDgcPu12e22w8tNqV8T1LQQitEg0EaAoGc2Ux\niTIOh6d/v3wMBipgUcJiuXDbZKJyWcmI0g1HqEzDEfl2/r5InoDn03arVOYEajDklcUJRkoc0+vp\n8ZX28xQEIJ4AYgla1T5XmKwZAHJt0wcPnkUsloLRqMa+fVtwzTWVJQUYj6fx2mt9OHy4BxMTtIuj\n0ajGjTc24MYb62GxzL2qe2IiIcm5oyMga3u2WtXYssWKLVusaG21LPpY53RawPBwEv39cfT1JSQx\nl1qm0elUobZWKxOzzbb80XIiQTA+nsH4eAZjY4JUHh+nbcdTtUap1VTGdjsPh4PPK9Ncr195Mhbb\ngQMBwO8vLWExzVQoHJeLdCcTr7htMtGq1JWG+HAiCTYsl21EnJSkYDs+x8UnFIpikRaVSwhXr1s5\nvcQLRRvLlqOxXFnaHwfiSfl54r6FgMmagUgkiYMHz0o9vbdurcCDD15ZcmWscDiJw4d78MorPYhG\naV1VRYURe/duwK5dNVCrZ3+XIoRgcDCKkye9OH3ah8HBiHSM44DGRiOuvNKGLVusixo908U4Eujt\njWcj5gSGhkqLubxcjbo6Derrtair06CuTgu9fvnu0JGIIAmYSjlXDgQmj455noPdzsPp5KUIOV/I\nRuPK6UFNCBWM30/TZAIOBGbeCUujASyWyZMoY6NxZXW6Eh9IwhEgFKZ5OJITcDjbhhuO5M6LznEh\nCZ6ncjXoAaPYCW2SbTHyNeiXX7iEAMkUEM12IovE5HIV9y+2aDkO0KqzVe7zWGyQdTBb55w7N4Yf\n//g0AoE4tFol7rtvU8m2ab8/jhdf7MLRo31IJumdsKXFjve/vwmbN5fP+oZOCEF3dwgnT07g5MkJ\n2aQkWq0C7e1l2LLFis2byxal7Vkcv9zTE8+mGPr6EkVLWAKAy5UvZi1qazXLIuZEgmB0NCNLopQj\nkcnvwkolB4eDR3m5Ak6nAk4nD6dTgfJy2n68EmbYSqdzkbDfD/h88lwsz1TCev3UEhbTfBZWWEhS\nqTzx5sk3X8ShUG7fXMWr05aQrT63L3/baMi14y6XdNPpnFijsWwu9uAuSIX7YnEgM49VroBi0eo0\nk5Sn2Kct6HDGOpgxZkUqlcGvf30eR470AgCam234sz/bBodD3tN7bCyCP/yhE8eODUpzdW/Z4sId\ndzSjudk2q8/MZARcuhTEyZMTOHVqAoFA7rHVbFZh2zY7tm6l1dsLPVtYPJ5BX18CPT0xSdCllnF0\nOlVobNShvp5Gy3V1miWd3UsQaBtyvpBHRqiUfb7J7zxaLZcVsQLl5bxUdjrpEKfl7MSVSBTLtzAP\nhWY2EYfBAJSV0TSVhJez3VKsbg4VSncyCYfnts6xKFejETAZs+V8ERvlEa/BsPTV84TkJCpWH0cn\n2S4l3OQ8V7lSqwC9liadJvvwMQ/RLidM1uuQkZEwvv/9ExgaCkKh4HHPPa24/fYm2Q19bCyCQ4cu\n4Z13hiAIBBzHYfv2KtxxR/OsOo1lMgIuXAjg+HEPzpzxIRLJCdLh0GLbNhu2bbOhsdG0YEIhhGB8\nPIWurhg6O6mc3e7i4VJ6vQINDVo0NtLU0KCFybQ0/xKRiICRkZyIR0aomMfHhZLV7oA4XagCLhcP\nl0uBigqFFC2bTMtTXZ1OU+FOTBQnUcaxGczaxPM5CZeVAVarPBfTcg1DymSoVEMhIBjKlsOly8HQ\n7MdCKxRUuPnSNRqyvcDFcv6xJa6WT6epPCOxXC6maKxgO++8aHxus6GJKLJjlg1ZyUri1ebKRdu6\nnJwXq+d8OpOtKk/mUrwgjyVz58RTtByfx8MHk/U649ixARw8eBbJZAbl5QZ8+tPXoK4uJ1+PJ4pD\nhy7hrbcGIQgECgWP972vFrff3gSXyzijzxAEgsuXg/jjHz14912vTNBVVfqsoO0L1v6cyRAMDMTR\n2RlDVxfNC4dMKRQc6utzYm5s1KG8XLXogguFBLjdmWxKS+Wp2pGtVl4ScUWFAi4XTTbb0kbIYhux\nKN9SUg4Epn8flaq0gPNzs3np24QTiUmEG5KLNxii7cCzQavJiTZfslI5T8wm4/RjcxcCQoBUOivV\naAnpTrIdjc2v7VaSbJ5EJ9vWabJizopXvcCLbhCSFW0SiCZoEqUaTcilmi/bQgmn5zAP+nxhbdbr\nhEQijYMHz+KttwYBADt31uD++7dAq6XPa15vFL/7XSfefHMAmYwAnudw3XW1uPPOlmknQQFoNNvT\nE8bx4x4cP+6VVXFXVemxY4cDV19tQ0XF9O81HfF4Bt3dVMpi5FzY1mwyKdDUpENzsw4bNuhQV6dZ\ntElR6FShBMPD6TwxZzA8nEE4XFrKajWHykqFFCGLQi4vVyzZbFyZDBWwxwN4vaWlPN14V56nsrXZ\ncnl+2Wql7cdLFfSn01SygaA8BUO5XJTwbIYW8XxOrGZTidyU2zYZF78aXhCoTMNRmiKxXFlMpeSb\nmuOEIQqeSlSfjXIN+ryyTl7O39ZpF/YhjBAgkcrJNpYv3GSuLB7L3yeWF0K0Ch7QqbNV5arSZZ2a\nJm1BXutkbdaMSRgYCOAHP3gXo6NhqNUK7Nu3Bbt314DjOAQCcRw6dBmvv94vSXr37lrcdVcLnE7D\ntO/tdkfx1lvjOH7cK+sk5nRqsWOHAzt2OFBVNT9BR6MZXL4cw6VLUVy6FMPgYKKoStvlUktybm5e\nvKg5EhEwNJTB0FAaQ0M5MU/WwUurpVKurFSiqkqRLdMoebGjekGgka8o4/zc46HV1NN1UjIYigWc\nnyyWxY+IxcUophKwuC8cmf79RFSq0uLNl65YXswpOAUhJ9TJ5Cttx3IinkusI7bhTilZffFxzQL1\n7BYEGrXORLSljsUSQInJ/2aFUgHoszLV50k1X7Ay+ZaQsFIxu58HIUBaYNXgjCl4801a7Z1KZVBd\nbcanP301KitNiMfTeOGFLrz4YheSyQw4jsPOnTW4666Waau7I5EU3nnHg7feGkdvb262CKtVje3b\nHdi+3Y76euOcZRSPUzlfvEjlPDAgl7NCwaGxUYvmZp0k6IVua85kaM/roaEMBgfTUj5ZJy+djkNV\nlVKScWWlAlVVdN7qxZIyIbTKtlDE+flUbaccR4Vrt8vzfDkvZm9pcVEKfyCXJPFmJyMJZLdnGgXz\nfE64FrM85YvYbFqcqmexQ1UoCoQipeW7UOI16ACjHjBmc2k7m/Ta3H5RugsR8RNCq4SjCSCSyFUn\nRxNAJC7P88+JxKlw54tGJZesVNaU2K8B9AXHVLO8VQgCEEvRFEwAo+FstXg6+wCRylabp+Tl/H2x\nJIMif7QAACAASURBVJCZ70PG/F7OWKmk0wJ+9atzePXVXgDA+95Xh49/fDM4jsMrr/Tg0KHLCIVo\nF9Rt2yrxoQ+1orLSNOn7ZTIC3nvPj2PHxnDmjA+Z7F+eTqfA9u0O7NzpRHOzaU5iSiQEdHaKco6i\nr69Yzs3NOrS26rFxI63WXqgZwMQq7HwhixFzqY5eajWHqioFamqUqK4WpayE2bw4HbwEgVZHj48D\nY2M0F8sez/QSM5sBh4OK2OHIlUUxL1oHnDSVbL6I85Mvm890Wkm1OivdSSQs5gvd8YoQIJGkUg1G\ncgIORXJCLizPZbjQdOLN3xaj3vl8T0KAZHp6wRbuF9N8oltRpFNKtmB//vHZ9GhPie3TScAbBaL+\nGci1QMDJBWqfVnD0+ucKa7Neg/j9cTz11HF0d/ugUimwb99mXHddLd59141nn+3A+DitK2xutuEj\nH2lDU9PkQ7CGh6N4/fVRvP22B+EwvbPyPIf29jLs2uXEVVfZZt0WLAgE/f1xnD8fxYULUXR1xST5\nA1TODQ1abNxIBb1hgw4azfzvwITQYVH9/elsymBgID3pyk9OpwLV1Tkx19Qo4XAsfCevdJqKN1/E\nYtnjmTo6NhiKRZwv5IXuPS0OS/IHAJ8/K98SUg6GZvZ+Oi1QZsmlfPnmlxcywk+lqHink65Ynm07\nr1YNmAw05Qt4MgnPV7ypNBCOU6mKuaycoFF8YZQ7nzHIWjWNWA3anHj1Gvm2QVN8TKee+XclBEik\ncwKNZlM8nStLx/IkK+1PUVnPF57LVoOrcnl+OX+fTg1olXn71LlzVNmHDDbOmgEAuHTJix/84ASC\nwQRsNh0+85ntIAT41rfeQE+PDwCdcezDH27D1q2uktFgKiXg+HEPXnttFF1dubtuVZUeu3c7ce21\nDpSVzW4qHp8vhfPnozh/PoKOjijC4dx/Ec/Tam0aOevR3Dx/OQsCwdhYBv39GUnOAwOZknNd63Sc\nTMjV1bQKeyHntRaFPDpKkxgZj43RyHmq51arFSgvB5xOmsSyw0EnrFhIEgkqYZ8fmPABE9lc3PbN\ncIpOnqeSlURslkvZWkZzzTxmdMpHFHAwLM8DISrdQCgXGc+2Z7NaBZj0OQGbsqI1G2leeGyuVc2E\n5EQ6lXQjBeck59hpTK2cXrSTyXcm0a0g5MQaS9KHuHyRzkS4822fVnD0ukWZ6tVygc5EwOoSC3uk\ns98tngZiBXkwDYxGi4+L5bkyZ1lzHPc1APcAIAC8AB4ihAxkjz0G4GEAGQB/TQh5Ye6XyJgJhBC8\n8kov/uu/zkEQCNranPjoR9vx0kt0qUqALlN5990bcf31dSWjw+HhKF57bRRvvTWOaJT+VWm1Cuzc\n6cT115ejrs4w46reVErAxYtRSdBut/wO6XCo0N5uQHu7Hq2t+nnNCEbXss6gtzctyXlgIF1yRSiz\nmUddnTKbFKitVcJuX5h2ZbENeWQkJ+WRkVykPFlnLp6n4i2UcXk53b9QPYsFIRcRT/hyMs7fnskQ\nJa1GLtxSyWyaf3V0JkPlWijhQLh4OzaLSUWUipxYxejXnM3zpSuW5zJ8iJCcUEMxKtlQbGrxRhNz\na7tWKqiQjDp5btACRi3NDdrcPlG4M2m7JSTbISwJRJKAL5gri7KNJKhopXL2eGyeE5oAgFpBBatX\nlxauviDXqQF93jlKXv67Ezt6xcSIPZ2XUsBEHIiFSx+L5Yl3ISL22TLnanCO40yEkFC2/AiArYSQ\nT3Ec1w7gIIAdAKoBvARgIyFEKHg9qwZfIDIZAT//+Xt47bU+AMCtt26AyaTB7353GfF4Gkolj1tv\n3YAPfKBFGqolkkoJOHHCg6NH5VF0Y6MRe/a4sH27Y8aLZfh8KZw9G8HZszR6zh9OpdXyuOIKPdrb\nDWhr08PpnHtvbb+firm3N42enjT6+tKIxYr/lmw2BerqFKirU6K2lsrZYpm/mFOpnIxFIYvlySYA\n4ThaLV1RQSUsJqeT7l+ImaVSKcA7QZMnm+cL2R+Yvve3UkklbCsDbNZcslqyedn8q6STKRrp+kNU\ntP5QtiNZnoQDYVpNPVMUPI10zQaaW4xUtBajfL8pu2TibP8E0plsh7BJBJxfDsWogOcSFerU00vX\nmCdfo6505JeP1D6dkst0KtmK5843us0XbKFQdaUkXHA8f1VdUbTRVGmJFm1PUp7vFKQArRrXqWiV\nt04pz6fbt8G6xNXgoqizGAF4suUPAfg5ISQFoJfjuE4A1wJ4a66fxZicaDSFp546jo4OD1QqBd73\nvlqcPTuG0VHaS3vr1gr8yZ+0o7xcPgzL70/g6NFRHD06ilCIPgKLUfSePS7U1k4/bIsQgt7eOM6e\njeDMmTAGBuThTX29Fps3Uzlv2KCDQjF7ScbjAvr7M+jpEeWcKtkj22rl0dioQn29AvX1VM5G4/xC\nu2QScLtzaXiY5h7P5BGQXg+4XFTKLleu7HTOP0JOp3My9vqyUvbmyoHg1K/nOFo1bbPmZGwtkwvZ\nZJp7D+l0mko2EKbt2JKIC7ajM1wmkOOoXEXZWkx022LKydecFbJ+lvNXp9JAMDq5bPP3hWJz68Ws\n1wAmHZWrSZdtu54k2hX3TVcbkUxT0YbjwHgU6PVno/UkEE7QPJIolvF8eiJrldn26WzPaoM6J9/C\n7fyyTiX/PoTQzlqibCOpXNmfAoZD2YeGRRatks8+FGQFKisXbhccE8ULAHEBiGWAeIbmYornJV8G\niMdz58TnEZHPq82a47j/C+BBADFQIQNAFeRiHgSNsBkLzNhYBN/73jvS+GmXy4hXXukFQNul77tv\nEzZtKpe9pqcnhMOH3Thxwit16qqrM+DGGyuwY8f0UXQyKeD8+QhOn47gvfcispnC1Goe7e16XHml\nEZs3G2CxzO7PS+wA1tmZQmdnGt3daQwPp4vEqNNxaGhQoqFBKQm6rGzuoelspczzNCrOF7IoZaNx\n7rITBBoJe7y5yDg/SvZPM1uYQkGl67ABdjHlCbnMMrfe34TQ6mhfMBcF+wsiY39o5pGwggfKTDRZ\nxNwol7Al2x48m85I8WROwFIek+8Ty7OVL8/lZFtKwGLZlE2Gadp1xeFAomDHJ7KiTebkKwk4kSvP\ntfpVrcjJVq/KK5fYLpRxfnQrEHrd+aKNZsveGBAN5rZlx/9/9t48yK7rvu/8nHvf2u/1vqOxryQI\nEIQokiIlkaA0shVTUuzJH9FMJk6Ny5XUjFOp/DGeTMVTduy4EidxjZ1UKk6skqvsSlyTOClXxo4s\nU1KsjaBAUuACAiD2vRtAo/ftLffeM3/8zrnn3NevG90AZUsuHNbhue/1u8t73Xif+/3+fud3zPiw\nsM2H7UFa2gBoy3kohhKbTeEarQZuLYZJk0VeW8mCeCUSSD/sNKwHaev+01VKfQ0YafOjf6i1/iOt\n9S8Av6CU+r+A3wT+1zUO1fat/aN/9I/S7WPHjnHs2LENXPKjBvDBB/f47d/+PouLdbPes+LGjTlK\npRyf+9x+Xn55V7oYRhwnnDw5zTe+Mc6VK6K4g0Dx9NP9fOpTo+zZs/6Uq1ot5tSpJU6eXOT995cy\n9nZ/f54nn6xw+HCV/fvLm8oMlzKhERcvRly6FHHpUnNVGc4wVGzbFqZw3rkzx8hI+EBWdhyLZX3r\nlvT7QTkMBcKjo9K3bJE+OPjgU56aTYHx5BRM3jPdbN+bXj/zOwgEuv29AuKB/ux29wOU7PRBvFaf\nXdhY1adAmalVVQfgnq7VjysbVME24cqHbAa8LY83k2gVBtDVsRq8nZ76teCtlkUlr3XNSeJgulCD\nO/dk21e6rdvLjTW+FO/T8qHAtFKEatFsF8y2/1yLCs55Nw6JNsq7CYseeBebcHdJpjdZdbscZeFb\ne4gEKZCbhnIeKgakHXnTvW0L1o4W4OZDaGgHWB+u/vasrdu9tPo19Q9BmQPklbmu0PWS6a2PT7/+\nTd49/k1CBTxEBO5DmbqllNoOfEVrfciAG631r5mffRX4Ja31iZZ9HsWsH7CdOHEzXdZycbHB4GCF\nMFQ89dQIX/ziIXp7JUW4Xo/57nfv8LWvjTMzI1KiUsnxiU8Mc+zYCH19a6fiLi5GvPvuEm+/vcDZ\ns8uZOcc7d5Y4erTKk09WGR0tbBictVqSAfOVKxGNRvZvoFoN2LMnx549efbulUSwfH7zf+ELC3Dz\npkD55k3p4+PtYfhhQ7lWE/jebYHx5JTEjtfN/O6BwX6njH2V3NuzORhrLWp3ek6Au9a4ERBXytDX\n7SnialYZ93RuXAknicB1bhnmlmScXZLt+RX33MLK5kpDFnIOwOlotv3nuzokHrrWn20UO9gu1MxY\nb/NcTZ5fbjxYXLfDB20LgC18W7f9+LSN36awbbjHafegbH/2MIlfSjmgtgOt/7jc8nwhhKYWaC5H\nsBx72wbAy/Ea25Hs+7BNsRqo7bZ9EKdJaqYnQASsJMYKN3a4fWyfq7U8tmr8tw/8OceslVL7tNYX\nzMO/Crxttv8/4PeVUv8PYn/vA9540PM8aq5prfna1y7zB39wmqtXZ1FKsXNnD319Zb74xUM89ZSY\nIIuLTf7sz27zZ382kS6isWVLB5/61CjPPTdAodDen1taijl5coG33lrg/PmVtDCJUrB/fwdHj1Z5\n6qkqfX0bC75aOJ8/3+T8+SbXrsWryoSOjITs2ZNnz54ce/fmGRraXAJYHEtilwWy7WstMDE4CNu2\nOSA/KJSbTQHw7btw5y7cmZQ+eU9qT6/VgkBU8NAADA4ImP1xM3HtJBHlOzUr4J2ac9v3ZuVnGwVx\nb9f6vbCB62pGMLPoIDy75LZbIbzR+/RSYTVwU+iWsxAurpG13Yzl/It1uLcicV4fuD6MF2oPBjML\n1c6SGdsoXX+74s03jowyX2oB70wEN+ezzy95UH5QlRsY4Fby2dFul9cAcCkHWjmQrkSr4TobwYRZ\nocsH7nIMbZaK31QLVVbJtkJ1laoN5DNWCjCfdQzUtIs3+8BdSOCujUM3HYTXWATvwa7/IdJoHiZm\n/U+VUgeQ938J+N8AtNZnlFL/CTiD3ID8748k9MM3rTV/8Adn+MM/PMv581OMjnaybVsXL7+8iy98\n4QClUo6pqRpf//oE3/3undSq3rOnk89+dozDh3vbQrBeT3j33UXeeGOeM2eW0zh2GCqeeKLC0aNV\njhyp0tV1/z+Vel1z8aKA+dy51XAOQ5UB8+7dOTo7N/7XG0Wijq9fh2vXZLx1q30VrFIJxsZg61bX\nt2zZXCaz1hIntjC+fcdBeWqdudGFgijiocHVMO7r3Xjmd7MJ0/MGxB6ELZhn5++v6O4H4p5Oqfu8\nXksSgfDsIswsyThrYJwq5GXJgN5IU0rg2t0B3RUz+ttm7OpYe3pRvQnzNem3FuCDSfd4oea251c2\nD7VAZcFr4Wuf84Fsf27Bay3mRQNV28frsLjgPef9/GGgWykIYH3wVvJrP99hbmiWY1jyQLoUSV+O\nBLhLNVhelOessq09JGwDBKQdOdND97gcmsc5qBjYhoHcHCglY6RhxSjzmnawtaBdScw8bU/Rfhjk\nsZAtB+ZGwGzbsRxAUWlCc2OgFKjAhDnMtSdKnIHaQ1zPowpmPwItihK+9KXv84d/eJZbtxY5cKCf\nI0eG+Vt/6yl27uzh3r0a/+2/3eTEickUtocP9/LZz46xd29X2+OdPr3MG2/M8957LgYdBIrHHuvg\n2Wc7OXKket+5z3GsuXw54uzZJh980OTq1ShTiSwIJBFs//4cBw7k2bMnv+EVpSyYr13Lgjlq88U2\nMJCF8tat8txGBXqzKSCeuLMaymsVAAkCAfDwEAwPwsiwqOWhQYkdb+TcSSLgnZyBezMC4nszAuLp\nOUneWq8pJXZ0fzf094hN3d9tRvP4fiC2atjCt3V7ZlGAvBGb18aB24G3FcKtdrk2iUs+aBc84C7U\n3fZ8bXMlIEMlKtwHbrW4Wgnb7Q5jkWvtVG4Gvt72UsvzSw+QNR4G7SGbAW0h+7iUE5VkletSG+gu\ntfnZciQ27oM0hQfbVtC2PhfI+1IGuBjY1rRR5QksJ9ntFfPYbn8YeCj5UA2zgC0HUDKQDQxgrdWN\nEtgmSuLkNeRGoabNzYB2j2sa2pR0WLP99lDwQDb4I1j/kLdaLeJXf/Xb/MmfXKDRiHniiSH++l9/\ngs99bj/z802+8pVbvP76XeJYEwSKZ54Z4Md+bAtbt2anXmmtuXatxvHj87z11gJLS+7bbs+eMs8+\n28nTT3euuyCG1prJyYQzZxqcOSPquVbLwnnHjpADB/Ls3y8KeiNVwJJEEr2uXIGrV9cH8/Aw7NgB\n27fLuG3bxqt4+VAev23GCUnsWmv+cWfVwXh40MF5oH9j1vlKTSA8OW2gbIA8OSNqeT0IBkqAa+Hb\n37Ld27X+NdSbML0A04tODc9448zSxtSwUmI191agtwo9FegxYwpnU1az9SYlSQS0cystvZZ9vLDJ\nTOd8CF0l1zu9bQtmu13OZ+G70PB6Hea97YUW8G42Fq2UwLRaMN3fbn1s4KuVgHTR9KWWsR2MHyZR\nqhRAxajbiukdYXYshxJjxkIMiJWo1VVgNaO/vZI8fPWxkgFshwFrR5gFbVFpAgNaAqfAQSAbAw2M\nGk/MqB1o7fMfRs6ZAkpKutwEmG0FeaXJKU2oNIGC/6mSfwTrv2xtYaHOz/3cV3jrrXHy+ZCXX97J\n3/t7z9HT08FXvnKT48cdpJ97boCf+ImtDA1lyTU/H3HixDzHj88zPu7mQW/bVuSZZ7r46Ec76e9f\nOyC5vJxw7lyTM2ek37uX/UYdHQ05eLDA44/n2bdvY3CenxcwX7kCly+Lcq61QEMpAbOF8vbt0jdi\nY28WylYlbxmFkSEH5ZEhmTe9XtNakrTuThkozwiY7fbSGkVSbOvtgsFeGOiBATNaIPesUwVMa4kB\nTxv1O7XgwGzHjYA4DAS6FsKtY09FFHGuxWSJYoHb7PLaALYQ3uiXdjG3Bnz9x2UZiybRqh6thu9C\nQ1ZHyjzf2Ny12NaxSfAmxmJebLYHbyuUl6IHywoPlQOrhWxHC3grOWcn+8lRNQ1LBrZLHnSXjDVu\nn3vYWG3RA+wq4CpNMczaxr5lHCNqdS3A2uc+jFYwUC17sC0ruRnIG8AGShMGGqWkozRaaRKlxaJH\nU1OaGpo6UNOyXUPTbPkN/0bY9wjWf5na1auz/J2/80dcvz5PuZzj7/7dZ/mrf/UxXn11gu98504K\n6WefHeCVV7KQjqKEU6eWeP31eU6dWkrjxp2dIR/7WBfPP9/N2Fj7THCtNXfvJrz3XoP33mtw8WKU\niTtXKgGPP57n4EHpvb3rW+VRBDduODBfuSJTpVrbwADs2gU7dzrFfD8way3zkm9NwM1xuHlLxsmp\ntaE8NCBQHh12fWR4fYVqs6rvTku/MyXdPm6sk5BUyAuAB3sFxhbMg32ijtdKKGs0PQgvrgbx9ML9\n56zmQ+jrFPCuBePOFjWstSRazSxLnzXjXM2A2QB5cRPlPatF6ClDt+0lb9v0zqIkiGkzNWe+Ln3O\njK3q1wJ5sysideShs2CUtxk7C9leNZazCgRei01YaAfdZha8yw84B7pi4FrNy3Y1D9WcdAvdvJ8o\nZeKfVs0uxatHC92VhyjCkTeQrawB3KLShB5wrd2dwhaB6nICy1r6irf9YSRuWfVqAesgC6HS5AJN\noDQq0AQIZAlIQZugaSgMZDUrWqfb9Qe6jVrdAhQloISiqBT/Z9D9CNZ/Wdp//+9X+If/8BvMzcli\nHP/8n3+G2Vl49dVxarUYpeCZZwb43Oe2MTzsID011eQ735nltdfm02IlYag4fLjCCy90c+hQpW0V\nsTjWXLjQ5NSpJu+91+Du3ewiG3v25FI4b9+eW3fVqZUVuHQJLlyAixfF1m61s4tFgfLu3QLoXbtk\nKcf1WrPpoHxr3MB5HJbbKNd2UN4yImp5PSjX6lkI2+07U+tX3eqqCIQH+7IwHuyVkpft4tdRLMCd\nWoB786v74gZUcWcZ+qoC5L5Ot91vtltt6SQR2PoQnlmG2RX33OyKZCffrwVKQNcK3e4S9HRkIZwL\n5ZhzNYFuK4Rbn9+sHd5ZgK5W6HqPu4oCwCAUeC148F1ouscLBr4LBsSbtUcDRN36oPXHal5AFwak\n0E2UAGwxdn3Jjh6Amw/o1SolkLXQ7Qi9baUphPK7DALQgQjwxLg5DQxYjZJtBe5m4rTtWk5Bh+2B\njCWlKQUC2tCo2CBwSjaFrNJEaOoKVoyCrXtq9sMgi0IAW0JRUooCkEd+dSGaHKDQyD1UgjbbCRrQ\naDSx6XWlqZNQR/N/q22PYP2j3ur1iC996SRf/vLb1GoRu3f38LM/+zyvvz7N3Jxkrhw50sdP/uR2\ntmwRfzZJNKdPL/Gtb83y/vtLaVLGli1FPv7xLp57rqttHLpWS3jvvSbvvtvg9OlGprZ2pRJw6FCe\nJ58scPBgno6Ota3tuTmBsoXzzZurE0NGRwXIFs5btqw/H3dpCa7dgOs34YZRy3fvtVfL1QpsG4Ot\nW2BsVMbRkbWhrLXUn564BxOTcPuebN++t35CV7kIw/0w1Cfd3+5oEzO3NvVaMJ5dWt+SDYMsgPuq\nBsJmu7eanU4VJwLb6eXVqtgCeX6D9aorBQFub9mMHS3K2EBYKYkBz9WzvZ0q3kziVSkngO0uurEV\nyNU8hDmZDpQC9kOGb0cInXnozGXVru3lUG4AAAhMwlcreJMsgJcfMJbrq1w7VlKVq8mZaUp+glSs\nzHxg7aC7ZCzwJS39YSpxBTjIdijP3m5RtRa2ytrGgSjapgfaZQPaFQTCD9uKBrJFFCUlkA2R6U8B\nCXK/pAnAoF17/0FMkoFsjWSVnf2g7VfUjkew/lFut27N8xu/8T2+8Y3L1OsJjz8+wv7925melm+5\nnTur/LW/toP9+7sBWFiIeO21Ob7znTnu3RMfNpdTPP10Jy+91MPu3aVVU7WWlhLefbfByZMNzp5t\nZgqdbNmS48kn8xw+XGD37rXV88wMfPABnD8vgJ6czP48DEU1793r+npxXx/M127KeG9q9euCQGLI\nW7d4fUxWd2qnXLWWBK6JSbg9JaMF9ForNOVzq0Fst9sp5CiGqXm4MwuT83B3Fu4ZOE/Nr68QAyU2\n9EDX6t7fKXFi/3y1JkwtwbTty95jEze+HwQUEu/t7chCuLfDPddjFoZoxjBTE+DO1mDWjmZ7zowb\nVcFhILDtKmQh3OUDOS+/g4aGOQPcuQbMN70eue3NgqYVvp0597gSmji4AV6MQG4hXhu+Sw9oMXcY\n0FZD1ysGujYzOTRKV9tEKQ3LrAauhfCDfpMWFFSUAb9RuCWbEGVgS5CN02pP2a4YC3lFa5YNeOOH\nhFoORdnAtqwEsKJotYGtRhnQYkALcgNglWxTaWokqZpNPgTQKqCAokBAHp3CPzRdmetSZjt7A6BJ\nSEjQ/G114BGsf1TbG2/c4ktfOslbb42TJIqRkWG2besnDAMGB0v81E9t5yMf6UcpxcREnW98Y4bv\nfW+epinpMzCQ58UXe3jhhdUqen4+4Z13Gpw8WefcORd/DgLF3r05jh4t8OSTBQYG1iqUAufOCaA/\n+EAKkPitWIQ9ewTK+/YJqAtrTBdqBfO1GzJfubUVCqKWd2yF7VvXV8tayzSnW3fh5h2nlm9PrR1L\nrpRhpB9GB6Xb7b7ujQH57pz06YX1AVktrQ3jvk6XtJUkonp9+LYC+X6FOgIlirevw8HXh3Jvh4Ba\nKVG7PnTbQXl5g4VBynnoKZo4tIVxSUYL52JegLMQtYDX63NGEW+mSlU5hC6jeFMI5+S5SigK3U4d\nij27eaGl2+c2azUrA7mKD10D4VJgMpV9e1lBpASwSwksalg00F1MHi5hqmyvxYxlpSkGuCzkIBHg\nWks5sPasqNtlEla0KNuVhwRbvgW2TtXqFGqBAZhqAVqEJlKaFaNm6x8KZuWaiijyKHIp9J26DnCA\npQW0orKl1w1wH6b9H+rwI1j/qLUoSvgv/+UMf/InF3nnnTs0m0Wq1S4OHx6iWs3zhS9s58UXhwlD\nxblzy3ztazO8//5Suv/hwxWOHevhiSey60wvLyecPNngjTfqnD/fTG1pmUed5+jRAk89VaCra7UX\nXa+LYrZwbrW1SyXYvx8OHBA4b9vW3tKOY4kxX7kGl6/KeGdy9et8MO/YJnAeGW5/zOUVgXLa78hY\nW8Ni7a46GG8ZclBuVclJImr49oxAeHJuY0AOlEB3qFv6oOn9nQLlkrlp0VpqQt9bgnuLXjePp5fu\nrxILIfRVoL8iQO6rZB/3dMj1LDRgekUAPFOT7emaezy3QSs8F0CPAXBPSYDcU3LbFsI1DbMNgW3r\nOGdAvJnKVaVAYNuud+TkuhID4FqShW1r3yx8CwF0Geh2ml71FK9qiTU3EfD6wF00IH4Q8AZkgdth\nk6UCAW4YmmQpo24JNIkSu7amYNnYycsGuA8KFQWUUXQQpLDNQwo5pyAd2OIfIGxLBOSRmLFcg0pB\nG5qjqzTIoc07l/8nxs5uktAwzz9M02gClPk8IEQRtgA/SK8nC//EXNHfUh97BOsfpTY7W+O3f/v7\nnDlzlxMn7tFsFunrq/Dkk8O89NIoP/mT2+noyPHGG/N8/esz3Lwp3m0+r3jhhW4+/elehoedhG02\nNe+9J4A+daqZFifJ5RQHD+b5yEdEQVcqWQpqLXOc339f+sWL2frZ+bzEmh97TPrOne1BOjuXBfO1\nm6sLimwUzHEs6thC+aaB8swaS0B2VWBsCMaGYYunlltjybWGKOTbM6bPOkCvVZazFchDPTDYBcM9\n0N/l1HEzbg9i2+9Xpaqr5CDcb0CcQrlDCnXUYg++BsgpiM3j+yWHKSUxXwvd7hL0WigbO7pckEzd\nOWNDz7YB8Wxj4yq40ArgnNuu5FzxjEQJ5OZj6XORQNeOm7Wd84EAtxXAxcBkMRvo2+lCNQ3z23+f\nIQAAIABJREFUnuK144MkUoXGXq4GUFVQCTQlBblAk1OJTAMKjK0ciK3cJGHZQHdJJ6mt/KCtiKLD\nxGxLKGMn6xR0vsL1bVqxtwW2tR8AbK1tbFUtJKnCJr0Wp2gbJEQfwmxobUBvlb7fVeZaBLbag6z/\n38O2n1WfeATrH5V2+fIMv/Vbb3Lr1hKvvz5DGBbo7S3z+c/v5qd/ei9jYxWOH5/nq1+dZnpa/Miu\nrhwvv9zDiy92U62KH5wkmnPnmpw4UefttxtpgZIgUBw4kOO554o89VSBcktB2loNzp6F06cF0DMz\n7mdBIFOnHntM1PPevaunF2kt85YvXoHzF+HyNZlC1dqGB2HXDti9U8ax0dWlNptNGJ+E6xNw/baM\nt+5KZa3Wls8JjC2Yx4akd1Wz1za35EDsg3lmnQSyviqM9K4P5OUG3F2QPrkAdxYcjOfuk71dzsNA\nFQYqZqy6x/1VUYxzdVlmcGoF7i3L6Cvj+gbKUlYLAt++soz+dk8RCMWOnm3AdKM9hDdacKMUQHcB\nevLZscuskKTCrALOADiW+PPiJgAcKAFvV86Bt9NTvhjbOTG2d00LcBdMOcoFs93Y5NdOqCxwHXgL\nJoEqDNz8W5QmCRK0krm1S0qz5KndB0lQClBUjK3sVK42qhKTiWwh5xRlhKahElaQ/jBJWyUCCqma\n1Gmc1kIfT2U77AtsIxKapj9os1nWOSSe3RondtC3KjbJXEuc3oYkqAdc9soHt72WkMBkhvtZ4aSf\nh06vI/GuJeZ/UZ97BOsfhfbGG7f43d99h8uXa5w9u0ixmKe/v8Qv//JzvPjiCN/97jyvvjrN7Kx8\nM4+MFPjxH+/j2Wc70yUvp6Zijh+vc/x4nelp9223c2eOZ58t8tGPFunuzgL6zh1499326rmrC554\nAg4dgscfh0q2+BlxLHHmi5fhwmUZl1rWLi6XBMi7dsDuHbBzu6zt7Ld6Q1Ty9QkH54nJ9vOFB3th\nqwfksWF5zlfh88swPg3jU3Br2mxPr22L50MB8UiPgNn24R6xdEFqC1sg312Au4tue725xaESFTxY\nFWU82JmFczkvWdGtMLZ9egNTpkq59hC2IA5yoj59EPvjXGNjGdGFQMDbUxD122NA3JUztbqVxGFX\njPqejQS+s2Z7Id54xrNSTv125WTsDDRFY3lb2zk2tnMKXw/Cm7Wc8wo6A+g0o4VvEGhyQYLy4rqR\nSmigWVCaJS3wfVCLOW/A26FE9VqlGxrg+MCz9m1EQs2zlR+0uZitS9iy9q1vaydG5foWcp34Q4Ft\nAWVgq1PYC+gS896dovX1bESMAPDBQZsYcNrzOis9/RNriVknKWwT80koFAFq09dhP03rF/wN9T8+\ngvUPc9Na80d/dJ7/+B/Pcu5cnbm5iFwuYM+eCv/qXx3jwoWIr31tmoUFoejWrUV+4if6OXq0ShAo\nokjzzjsNXnutztmzjTSOPDAQ8rGPFXn22SLDw6F3Ppnj/M470m/fdtcSBGJtW0Bv25aN4TabYmVf\nuAwXLsGlq6st7d4e2Lcb9u2BvbskAcw/RhQJmK/cgqvjcPUW3Gmz+EWgJON6+6jpIwJp38JeqTsQ\nj0/DrSkZF9aoDlYteTD2wNxvKoI1Y4Hv7Xm4M5+F88I6QC6EMNSZ7RbOPWWZwzu5LD0Fsbd9Pxh3\nFaG/vLr3lGSa0nIs6vdhQNyVh76CALjPQjgPRSNVtFGkc7EH4sg93mgGdtWDb1cI3Tmxn3NeCctE\nyVzeRWM/z2uYMwDeTKJZqBx4OwOZP5wPpAdB4ubpBgmxkmIXS0qzqDVLiN282VZGUTEx3SJWcWYt\nZhenhIiEhkpYRvqDZEzbeb8+dH07OVilKp2V3CShzkNUSDGKOu8p28CDn8DUxWl92MYPoWqtHnVq\nthWyLgNbt5zfGfua0EB2M9fgZkoLZMHGqMXxaD1/VlE7QIMmIDCgD3hFffERrH9YW6MR8zu/8zZ/\n+IfXuHmzSRAocjnNk0928VM/9RFee20pLWKyc2eJV17p5/Dhisn+jvj2t+ucOFFnaUm+jvN5xdGj\nBT7+8SIHDuTT5LIoksztd94RFe0vE1mpwOHD8OSTop796VRJIvOZPzgPH1wQSLeuZDUyBHt3O0D3\n9To4ay31rq/ccnC+cXu1lR0GopK3jTg4jw25xSaSRJK7btyTfnNKVPP0GvZ1uQBb+qSP9Usf7YVO\n896W6gLk2/MwMee27y2uPdWlEIoqHqquBnNXSazqyWW4u+zAbPv9MrY7W2A8YMbestxELMYw1YDp\nuoxTdQHxdH1j8GoH4u68sfFNYta8UcDTHohno41Xk6qE0JMT+PaE0BlKYQ1lK1kFkvGcAtjrm1HA\nJQVdge3aWN3SCRKxnFVCHIi9vGiU7yLJprOZrdXcoaCMAClPkipPCyKLXxvTtRbzg6rsEq7QhlXX\nFoJ+lrRFTpP4oeK3ypynQGAsZQd5F6+1eEtS29Y+82CwTVLrOMyAXpn3aZW1tZod5Kx1bUG38XP6\nkJUukFW0KmlnnyfQcn6r5oP0v/WvwV1/TBby2rxfOf9n1c8+gvUPY1taavBP/slxXn31DisrUKnk\nqVYT+vqqjI7uoF6XP5ddu0p8/vMDHDzYgdbw3nsNvvnNGmfPOgJs25bj4x8v8txzxbRQSRRJ1vab\nbwqgVzy12dcHTz0lfe9eFy/WWtZd/uACnD0P5y6strXHRuHAXqec/QpjtTpcvin96rgAerFlf5Ak\nr11bYdcY7NwiYLbTr5qRKOSbU3B9Em4aONfbAC8fwqgBsg/nHmPXTy/BhAHxbQ/Ka6nkQIkiHumC\n4a4skKtFsaRbQTy5LGshrzevuJSDwQ7pAx0Oxt0lIBCL2ofwVF36zAZUcTUH/UXo3QSIpw2MN2JJ\nd4TQ7YG420DYxoKTQApsLBr1O2v6wiYWQsh7AO5UAuBCYLOcEwic+l1RmkU0Czphgc0VyrDwrSgo\nYe3XJJPJjFGdiVGdy0qzTPxAcWVbgMOqXQFS1tp2CIwlnvyA1rJVidbKblW5NlmrVV1a6G7ewpVr\nFmWtvOQwGy9vbx9b0MtrNg5bFxuOU9DJOdWqc6r0/fo2sw94d+b13nf2JiFOeytkFQ7yynu/zjJP\nDNzDDOJpOf8nHsH6h69NTS3z9//+Nzl5co5CIceWLRXiOGJ6usTu3SN0dxfZsqXIF77Qz1NPVVla\n0rz2Wp1vfrOWxqILBcVzzxV58cUS27fbxDIpSvLmm/D22zJ/2batWx2gt2516rdeFzifOgOnP1id\nEDbQD4/tc72z0/1sbgEu3oCL16XfvLMaAF0VA+UxGXeMOit7pS5Avj7pVPPtmfYQ6a3C9kHY2g9b\nB2CsT6ZDBYEsjzg+B7dms+NaiVfFnADZ9tFuGQcqspLRnSXXb5vx3n2Wg+wqOiCnYC6Lyq9puFeX\nPumNs437F63ozguM+wsGynmzVKOxixcTmHlAEHfloNf0nlBTyQnkbQGQSEnBjdlEQDxjxo1Y3gqx\nnrtN7wg0+SDJABiVEAViPy+qBwNwCUWnsZ0LQMGDr81otrZr4yHgaxWvWNutsV0XT7UWc2Ts5c2q\nXTsFyClrW13LQd5PUPKRu9n4rcZZs6GJG7sEMWtjO8i79LDNK1s/l1t7kJfz+NCzwHOKNjFqNEhR\nd3/rOgtYq2STFLLKfLaQtaqzcWmbAR62QbxqOZ+95sicK86M7j1mbXIXJkh4Vv3SI1j/MLWzZ6f4\nuZ/7NhMTNSqVAs88M8zbby8yPx9y8OAg+/d38fnP9/Pcc11MTia8+uoKJ07U00Ing4Mhx46VeOEF\nUdFayyIYb7wB3/++rFxl25Yt8Mwz8NGPwtCQPKc13J0UOL9/Vqxtv0Z3tWLAvB8e3y+wtvvdmTJg\nNoCebAF7GIiFvWebgHnXmCso0owExtfuwlXTb7fJFA+UxJG3DZhuAF0tS7Wu8TkYnxUg3zLbaynl\n7hKMGBCPWjh3C+zuLmehbPtalrVSkrjVCuS+kiRwLcYwWWsBck0yntdqAWJNDxRFFfebsWhkUYzE\nhKcjmGrCVATTzfWPaVsriDvsVKjQqeE5LSCejgXEG82GrhgA99gkrCAhH2qUsaF1kBApAfCcTljY\npAXtA7gIxnqWcpAKPERpVlTMIjJvdzNN4BtQRKcJXavju05hP4jitWo3j7XQ/WxtByVfcW42juvn\nNlul6RSnbgGDvamI08/Qwev+53MTpxIgXmUhr45RZxOoNqpqs4o2SveXG7CgJS7tK3irZkXQZM/n\nEN/uXJi0Pbd/ZK6ZFO6tjoF7n3IjoDLnstthurdOrzMy+0T4gD+i/vkjWP+wtK9+9Rq/8AsnWF6O\nGRjo4OjRHXzjG5Mkiebw4QH+9t/eybFjPVy/HvPqqyu8845LGDt0qMDLL5d44gmJRc/MwIkTcPx4\ntnrY0JAD9JYt8lwUiaV96gy8/4FY3bYpJVOoDj0OTzwmc5ztGr+T03DuKnxwBc5fg3lPqYMU99i9\nFfZuh33bRT0X8qLwx6ezYL41tTq7OxcKiHcMOTiP9cvz00twfQZuzsCNGYHzvZbz21bOw5ZuGOtx\n41iPKMSJRRhfkHFiUZTy9DrLU1YKMFzJ9oGyAHm6AXdq0i2Qp+vr273lEAaLMFgSKA8UpGynCiWT\neTYWEFsgT0f3L9pRCqA/D305GauhzA8mkGzsppJY8EwCMwbEG4kLF5UA2EK4aJRwLhAlnBgreukB\nIJxD0Y2iomSlIcn8TTLK1AE4YZF4U1nOUopS4GurUVnL2U+uEtUb0zBx3o02C15f8drj+9OULMws\neDejdv2kKTmHyhT6cDFyG7eNjaVskbAR4Lr0Mu0B17ewXRZ21ga2CVHhGuDzz5GN0frq0ilb6xS4\nJLA43a+dbbwxNRulx3FQVx7Y7e8kwcJdYfO5w1WwJdXd9vrs8ePMeSHyVHM2i9zeKCliSI8ftowB\nu9SvPYL1X3RLEs2/+Tfv82//7WmiSDM83M+OHSO8/fZd4jjhx35sgH/8jw9z9arm1VdXOH/e1fR+\n/vkin/lMmeHhkGZTksSOH5f50PZj6u6GZ5+VbjO463Wxtd85Be+dhhVvvm+1ImA+9DgcPOCmUs3O\nC5jPXYUPrkq5Tr91VwXMe7fJuNUULlmuw+XbcGkCLt2GK3eg0WJBKyVJXjuHYOewjGP9oqRvzwuY\nb5h+c6b9Ag/5UNSxD+SxHoHf7SUH5nED5tk15jiHgajiEQ/IQx1SnGUpFhBbKN81anmtr3WFxIt9\nIPcam5pQpitNRTDZlD61ARhXQoFwfw56c5pSzuQVKIgCiQ/PJDBtYLyyQRD3BtBrp0AFCWEoGdE6\nSIgDyX6eUwmzeuOZ0DkUXSiqSqUqOEfWgrblGBdVzPImABkixTvyiMKWFY38qUx2Ck9Cg2jT8LVZ\n1H482Sp4cMlIco6IzSRT2XdupwPljNINU3Bkla42cLd42ujxNREKTUhgbh6UAbtVnv57sXZykBq7\n6wG3Fbak17eWbe2UbeABz1e2refIAtZtu4pfVtnqlnNZNeugrtJ3Zmeau3NkQXs/yMqeFugO8D5g\n3Tmdeo7IqubYe86+L+tAuBsIe65R9f8+gvVfZJuba/Crv3qSr3zlKo2GYnh4hL17B3n33duUyw0+\n//k+/spfOcIf//EKN24I4cplxUsvlfjUp8p0dweMj8O3viVK2iaK5XJw5Ai88AIcPCjQXFoSML99\nCs6cy2Zuj43CU4cF0Du3y+vrDYHz6YsC5zstC2VUO+DATumP7ZKFK0Aysy95cB5vU8d7oMuA2cB5\n+6Ao5vFZuDIF16eNYp5rn5zVWYRtvbC9T8axHqnYdXsZbs7DLaOWx9eBciGEkSqMVmGLGXvLojzv\n1hyQLZTXyqxWiEU9XIKhIgyV3LrGUSAxYwvjyabEjNdrXTkBcX/ewDiUVZqsKl7UMJXAVCxAvl/G\nd15Bn1HEnaHY0rkwEVs60MSBZCfPKc2s3pgaDhElXE2VcGLUpJtjGiNzfDcD4cAAuIitXCUxZhsb\ntfNem0b9bnRakT9nN2/UdVb5yhevi/HGG4avve1QaK/4hjK2fFaBWsUrVbHWhmH22Fmlm8PFcV0y\nWuKdIzaAdshd69hrKVw/MSubGBWn57FTisIUTFk1nYWtBWDWPl5tV1v4WRA6u9gfV9vGDni6Dfza\nJXk52LaC1Yeuoh3MW7eVudbVqjkb2yY9tvktavO5aXOzoeVcSkegIxRxOnYW/+gRrP+i2pUrC/zy\nL5/kxIkJlpeLjI0N8sQTA1y8eJfe3gW2bu1jYOAxbt2SL6Tu7oDPfKbMJz9ZJJcLOHlSIH3xojvm\nrl3w/PNic1cqUnXs7ffgzbclg9tfLnL3TnjqEBx9EoYGRYlPTML7F+H0JbhwLWtNlwqwb4eA+bGd\nUnBEa7Gwz92CC+Nw+Y4UHfFbLoQdg7BnFPaMSK+WYXIRrk65fn2mPZgHKg7K23phaw8QCJBvLsCN\neRnvrrF8ZCuUt3RKwlfdQHlixfSaZFiv1bryAmQL5a6iQLSJxHXvNKRP3iduHCoB8WAe+nOaSt4U\nbTHW94IWEE8ZdXy/hK1qAP0B9IZaErVyCUGQiC0dJCyRMG9AvJEylHkU3QRUlDZqWCxjlcJMkrEW\njR29kSaZ1gLLIjoDSldBS6znmoHZxppuyaj2s6ljbKx3M8rXXkuQwteB0dryfuZxklq46ytep3ad\nCnULQyjsVCQXI03SY6+ndH3oygQxUdMOP34WtA9cCzOXINWqcLNWsoOhJvJuGPyKaBa22Tht4EFw\nfdg6qGOgbm8BXDzYAjDGpmRZyAYGiHI+aKdeW7fdbYb9+0jI3jhkgwHptpZ9Aq1BJx5YIw+2EehY\nfrcalNlHaen2M/KzCSBE6cAkygvI0RD2/pdHsP6LaMeP3+U3f/MU3//+DLVamX37+njssT5yuXnG\nx2eYmupn9+6tFAoh3d0Bn/1smU9+ssT8vOLb34bXXoOFBTlWqQQf+xi8+CKMjYliPnVGAH3qjFPQ\nYQj79wicjxyCnm6ZTnX2ssD59KWstR0oSQJ7Yi88vlsytYPAwfn8LbgwAUstyrWzbKBs4LxjSEpu\nXp2Cq9MOzu2s7OFO2NkvcN7eK5nYcw0H5JsLopwX2+wbKIHy1k4Y6xQ4dxahpkQd3/agPL9Golhe\nwUgZRgyU+4pSWCRRkul8pwF3mzKuV/KyIxQYD+ShLyeVtTAx45oSEE/GcC++fw3prgD6Q+gx9nQh\nhbGo4gVjTc9y/2UGCwbEVYVJnrKLGohaiowlPa82FhMOsCsluSIfIS4r2erU+iZUMGijqknHgGwc\nMU6jvvdPtnJZzTpTnKPVOnXw3ZjdrFOTPfayslXm2ALExEDU2tFrx3TlWiNP6UbmqzxIgehiq85W\nzkI3XHV83Qa4ZKDuK08HK2cD20/EQtEHbozcskbeORxsszAEa2Nb5evg2k7VRut2Z4dLZNv9PmOy\natYDrg4MZOWTyYLVU7MpeJWAFgxgQWl77f7EtJyBq4DWQlZpQMegE9ARJJF5LOexUE7/6Zr90uKo\nSo4dbP+TR7D+82xJovnP//kqv//7l3jzzUWgyOOP93Ls2AgDAzG/93t3mJsrc+TIMGNjJX78x8u8\n9FKJW7cUX/sanDzp1PHWrfDSSxKLLhYlSex7b4mSrpkMaKWkIMkzH4Gnj4janl+E987DO+cE1P5i\nFF0VgfMTe+DgbplGNTENH9yE8+PSW+Hc3wkHxmD/mMB5oEvizJfuwaVJuDgpKrq1dZVgV7/AeWe/\nqOa5Blyfh2tz0m8utFfbHXnY2iVg3mqKkagQ7tTh1jLcXIZbK7C41vSsAEbL0keMSiaEGnDHwPhO\nU7Kr12rFAIYLMJSHvrxU2QpMNvWChnsGyNPx+klmlQAGjTIuh86ijoOEKBBVPKMT5jcAz04CupWi\nhKaQKtjEICCmTsKcijeUHZ0DKgQUIT1WLkWfALNBzAobKD4OWBXsVkGy8V9rmsdERlFuHMCJWWTB\n6h5bsMJNyXHzdtdPerLZxQmx9xVsi3D4cWR/Lm+Ywrf9MSOvZ2O6/nxqX+1a4Fr4rm8tR0AzA113\nvRbosXkcZqBrY7e+es4q3CzQ/TELXN8+Fr8g2BRsW1Vt1jrOAjeXUbRiG7cq2Qilmyhio2YDuQHJ\nqFkBYApabT49q2QTC9nEQTaFa2yAqwED2bRrMpDV9vjm54nKvlaDSgy4k9iDeWKAbbJ5tUY9feIR\nrP+8Wq0W8e/+3Xm++tXbvPXWMpVKjscf7+NnfmY3ly9H/N7vjZMkmiNHBviZnxnixRdLnDun+PrX\nZX40iDp++mk4dkxKf07PwOtvwvE3sms879gGzxyFjx6VEp93pwTO73wAl2+55DOlYPcYHNoHh/ZK\nlbClGpy9CWeuw5kbMNuSZd1XhQNbDaC3COCvTjkwX763WjUXcwbKfTLu6JfVoK7POzjfmIdGGzAP\nVWBbl1PMlaLMHx5fgZsrAue7tfZA7Ag9KJtYMqEsTXi7CRMNuN1Ye2WmUIlCHi6IZV2W1exJQokd\n343hTixTnNZqCkncGgg03aGmmJPkLaUSolCU8bRRxutVtQpQ9KDoNKrY2tPgSkMuqHhD1nQOqBoQ\n53GJWRbDTWJqBp33bzq1t8U2TjKwSIwNfT8V7Be7FFvbn9ebnVcbpzbs/QAckRgo5AhS29mqx9XZ\nyME68LWgtsf04ZtVvDZByUIxbGsx+2o3QmqqxV68WGeu1cZOfdiuhq4FYRNnKTdTVevAiMAso0Jz\n2Hiqs5QDUZqpcm6uOofvE/jXmoWtO/b9YKt0M1W4SiujgDGwba9onZpVkOismk0iA1nbY7G4VkFW\nAblUyYradXY0ic7uk8Ry/Sm8DXAxr08Vsj2u+etLaHNc8/pEmzFxxzNd/fibj2D959FmZ+v8y395\nlldfneHcuRV6ekKOHu3ls5/dz4kTDd54Y4JmM+Izn+ngV37lAO+/H/Cnf+pqc5fL8MlPwqc+JdnZ\n75wSQJ8978Db3wfPPwPPfgSGhyQh7K3T0se9NaFzodjaTx2AJ/dDpSyxZgvna5PumADdHfCYgfOB\nrVJD+9I9OH9X+rWp1XHV3g7YMwB7B2HPIHSV4cocXJ6FK7MC53ZgHuyAHd2wvVvgXCjAZAOuL8EN\no5ZX2uwXKoHxWAeMlcT+1qFUyrrdFCBPrLMyVEcIowUYyWu6C3JTpANYUWJV345FKa8VP84pUcf9\noaYSJuRyCaGJGzeChFkD5PWStxTQjaJbKVO+0qpisZPrxMxvIFkrQEAs1rSfwWwxl7Bi8Lle02iT\naS1qODRfxO6abCx4IxCW89uSla48pgN6TOQBZW0A27isZFL71rNvDVsl61C5+lhWSbs4by61m/0b\nhBg7NScgZ/Ru1mp2itdCsokm8m42VPo78K/TB27WXrZK10HSQt3FiP2M7gSX5OSrW9uhHWjttp9d\n7TKQY1zMNoevnNFKYEviQKubKJretsRpA20s6rawNWtimTVHnarVRl16ILSwTWSKU/rnqw3sMqD1\nYajsfZ55bWLUrDlWW6XcCu8weyytSP88zDU72FrAmuNbK9QHt42JafOJJzgr3L4fC25zXPXF1x7B\n+gfdxseX+Wf/7DTf+tYS4+Mr9PQEPPPMEGNjO5idTTh16g75/AzHjuX49Kef5dVXA+6Zuc59ffDp\nT8MnPgGLS/Ct1+C1E67MZz4PRw/DC89KoZLpOQfo694iHOWigPmpA3Bwj0Dn9HV494qMK54SzoWw\nbxQOboeD22TFqcsGzufuwJV7WWgpYGuvwHnPoFjbywlcnhE4X56VCl+trb8DdnQJnMc6IV+Aew24\nvixwvrncPtO5Kw9bywLmQbNYRVMJlG/W4VajPdBBMq1HCzCc13TkxbaOAykActtAeb05x30hDIWa\nLqOQgyBGhwkrKmEK6etV2Cqh6FU22UrmEtss5DoxcxuIFVt7umRgmksBJXOEa0T3LdAh2ciY5Kxs\n7BpjHTcNPNc7hlWbqyHsLOP7Qdif4azMdeWwtqudO+wUcOiZz6uP5ZKsBJatSVY2ecu3sUOcbeuu\nyULXjX4Ws8siV20Vb64FvE2ycV1j0+Inafnq2drWFpK+tRx7x8t2v0BHFuRWOdtc9RClBeKBToxC\nbLYo26ZAN43ZWuDamzN7PIGjfd2HB1sPsj4YLWwztnFMush4BrRmubek5XgaT8XiqdnIA23iVDQK\nt8Cmdyxfoac3A/6xzXF9eKe89erBWVjbm4XEU+bmeOrvfu8RrH+Q7cKFeX7pl07z9tt1Zmdr9PXl\n2L17mNHRUZSCpaUZms3LhGEfo6NHWVyUiSojI/ATPyFZ3R+ch2++Jsli9q1v3woff06s7gR4830B\n9KWb7tzlIhx9DD76hGRwTy3Ae1cF0BcnspnTo70OzntHZD7y2Qn44I6A2l/5KVCS/HVgWPqWHri5\nCBem4ZJRza1x5lIOdvbA7h7Y2S2LcEw24dqSwPnWcvtFIQaLsKMC28pif+tQLOdbdemTa8SUqyFs\nK8JIQaCMgfJMAhMGymtV5KoEAuReA+RcmJAEMVGQMKMS7umE+jpA7iagR0EHpJawNop2yQB5Pbu7\ngKKKLV2ZkMfZw00TI15PFWujpiXW7Cd9uRhufJ84s1/1qoCflCWwE1XdXNeKzkI48eLKDiQ2mUq+\nWq2yzB5DbmayAPatYpXJbtZGS+cy8d6s8m2m8PXLZzr71qrowEDXZRpnE6p8kDdbFK9VupKxvBq6\nOXM+H+IOuipN7LJKN/GO6UM3Z6CrDXQtbH3wNlHaTLXSpMAFnV6TANJ8qonNQNYoqxRTKEaQNA2I\nfSs5Ia1wrvJrwNaCzKhxCzDtxWjTRCurQE3sN8EAbC1Fm3hK1oOi1vIbSW8CvOP450taj2fed+xZ\n0fa9KvMXo81vR6uW44iTINfsQ1tnbG35AvaOk5i//bbWu0b94+8/gvUPqr333gw///OsIXuDAAAg\nAElEQVRnuHo1Ynm5RldXmZ6efg4eHKZSUTz1VJP/+l8vcu3aMPv3b6O7u8ToKLzyiixB+fqb8M3v\nwh1jYedyAudjn4BtYzLF6vg7cOqCm2JVyMOR/fDMIXh8F0zMwslLAugJr3xnGEi8+cmd8OQuOfaZ\nCTg9AWdvZ2POVjkfGIYDQzDqwfnCjGRnt06ZGq7A7l6B80BFMqCvLcGVRbi61N6OHi4JmLeW5UYj\nCeBuBNdqopjbTYfKKVHKYwVNV8H8uw5hxijlO/Ha85B7AxjJiUou5GKCMCEKY+ZUwh0dr1v4o0JA\nr4KOVJWKldsgYV5F61rVCqggVncBGy+2trLAeL1YsbWnJVnLJZFZqDXvY007EGtT5tIBxlrIUapK\nV2dEr4awjW5mk5oSE89cC8IWvglNbEEQmyCFgbA2qjz01OpqADewAFa4ylT2ehQ2q9kq3xyhAfBq\n+Fq7uZlR0fZ6MLFtC8wgndylUClwG2TBG+MUb3u1mwJYKwNdnSpbgW3DWMtRGsd1KlfjVG5eoKtZ\nrXIzsLXbyim9VOHmRZHq0INQ0KIYE1R6PAtyVitbq0Z9mzfxXpdCzFPhSZSBlFOgoXcT4EPbHtM/\nVmJA66tZRVYZ+8BW7kvMh6x/zPR4pP9i1rSy/RuKuOXaEi3HimLSwINWq68L7z0mGvXldx/B+gfR\nXnttkp//+XNMTyfUahGlUoXOzg6OHBnh4x8vsXNnnl/8xRvcu1dgx45unn++h1degX37REV/6zVn\ndff1wksviJJeWBFAnzjlynsGCg7vg2cPS5LY3Xn4/kX4/iUpUGJbRxEObYcjuyT+fGte4Hx6Qsp1\n+m2wCgdH4fERB+fz0wLo8YXsa8NA1PK+PhlzBcmmvrIIlxelDGdrGyjC7ips7ZDM7mYo2dfX6wLm\nRhvW9eZhawGGC5q8IcySEqV8M1q7UldfCCOhphomFPIJKohphqKS7+qYxhpgLKHoVwEdaAok5qtd\n1O28illYJ5Erh2Rmi1VtLVOZbFQnoraOsnUwxtSNtkBxMF7vX6zMzXXx4SAFn12lOL4viGOaqR0d\nescghfTaSrgdhMXAtWCxhTFUCk57HB/AOoVdgm89O8VqredcCnN5la9Y7XEaZn+VnskeR6XwtTcE\ndma1O4a/ba9HvmZbFW/eU7vKzcHVDQPahoFvE6XjFrUb4+xlk2KnAwfcRIldnYhl7aAbrwZEBrih\ng1IKInB2sq+aE5wVq+UYykA38ezaVis51rJ/bGHrK1s3f9jBrFWNtqhae11x7N6fD1rjAGSh23qM\nFjUb2+P4qjhouSazv8a8J7KQTRKpz5wqaA/WrQob77OO3U0OcSLWY2yUNS37288/vRGRY6g/Of0I\n1h92++M/HucXf/ESy8uaej1PLlegWs3x8stb+MIXunnnnTz/6T/dZWamxuhojl/5lS3sP6D4+rck\naczOi967C/6HY1Ly8+QH8K23ZFlJ27YMwgtPwbOHYL4Gb7UBdFcHfGQ3HN0j5TvP3oF3bsLpcah5\nvCiEopyfGIX9wzAfwZl7cPaeZGn7LR+KYt7XB9u7QOfh2jJcXBBAtyrZUgA7q7CzQyqE6VAU85Ua\n3Gy0L685kIdtBe3mORu1fDOSDOx2fwGdAYzlNL1hQj6foIOYWhgzrRImdbKmWq2i6FOKMtrY1qJy\nF+9jWefMvrKcok28EpN5+T5WtUJTxs1NdvuKql3rX6Svip09Ld8OVu2CzOdtv69A1E13ctN8tMkp\nFzVsU638/W3OeZOAJKOE7f7WPg6NFd1OBVslbLRSGwWs7gPgpncMu8CGcwYEwHZfC9/QKN8seO0x\n3Dxgl1iVgjeFb5BazVm1K2NgY7s6MYpXUuBEMZsbgATUKrXrgTeFHA6wqbXs27h4wDQqN2m2qFxI\nbWBbsdzPcE48mzUxoPPhHTfbK+VUifpw8kAZa1ILObaWOTjY+mrUe6+rYskebGPvRiKxNvQacWN7\nQ+KrdgvZOJEvoAwkWzLD/euwXSNKOI7NF5YLeLgbABtn9j4T7zg6SkyP0Nr+tZk6d5r0r09rhU60\nvZ9Ca00SJ/S/d+ERrD/M9ru/e51f//Wr1GoBUVSlUIgpFAJ+5me2MTDQx/HjAdeuzXHjxhT798/w\nK7/6BCe+X+LNt0mTBo8cgh//FPT0CqBfe8et+1wuisX9whEpavLmRXj9g2xJTwvop/dCbyecmoB3\nb8KFu9nEsC3dcGgLHByBYkks7bP34GJLJbF8CHt74UA/jHaKCr6yCBcX4cYSq5C0pSyqeUsZcnlY\nAK7WBM7tCokM5mF7UdNXgCAvJTrvJHA9kgUnWluoYCSEoTChnE8IczFJGDOrEiZ0vGY8uRdFj4Gy\nta2bxMytY1sHSPy4A1le0cYz7wdkSeDSlFGmbrVLbJK9rIpavV9CbBS1WwwCY0/H69rT8o4UcRof\nDr19Jd67Ojva1Xm2ICZFpIWoqzGdS+PBdl9Ryk4JWwUrMW4bA24ipTVyBsR2oUprHdc9BWyXV3TK\nVSBuAZz34r4WwNmeLWVpAd5e+Wbh20hVcDv4prXStGQwK6t6Eu0Bt4GL6yrvS9zkr6u8U7tJi9pN\n4ix4dQu8bVyYgDRpKgUUcs7YJjQ1BZb+lCOVN7EiT8m1Zkv7kEuVcuKB39rR7ZK22hwjha3ZP4W1\np9T9+Kw9VuzD2tjQUSIx41XxYt8Wtzce3jVERs0m3v6+IkZ5atj+PuQ4Oo4Fss0ErRMDWm+JFgte\ny3UDWK0hiRPiKCGJEmIdo7WS1wQBiQrQSpm3rjIfQRwnxElClCQkSUKsNR+7cfMRrD+MprXmt37r\nGv/6X19neblAsdiFUiuUywl/82/uYWKij/l5WFqqc+fOGQaH7nHo6HPcmOgiSWSq0HNPw2eOwdwK\n/Nkb8N4FXELZCBx7Bo4cgDM34Xvn4OwN0jBLtSRw/uhe6KrCyRvSb3hx6kDBviF4aivsG4a7K3Bq\nEt6fXL2M5PZueLwfdvaKqr24CB/MS/UvvwVInHlPFfrLEIVw26jmiYa7fts6c7CrqBksSiZ7FMDt\ndcBcCWBbTtMVJuTyMYQxK0HMXRJm1wBlJ5Jxbe3rBKmeNauiNTOtC8iCEyVkoQlrWddorll5SyPl\nOF3s2C64sL46tksIFs1XfwjYQhf+/OHWc/n2dFYVR0ZRJ6k17StaB+IGftHEwEDQlY7MkUv1sgVx\nI1XDKrXPrR6QObIuEcuHcIwFp04BqtPzZlV0vgXCbl+nhBsZBe0UsA/gnOgdazvrJkrX020BszLw\njY3aNrdFOjTwBUmsalG9SdOpJgukjOI14EnVqj2Gt38mu9hOPPP2teDMqNRWpWv3b82a9mKmqUr2\n4qOJsag1pLFb38ZNfNjhgTMx0PTUrVXn7azoVcrWHsOAP7YqPXDH8W9G0puOlvfQjEUZWyVNK6z9\n/S3xEk/NxubSbQZC4FSs4XKawK4hjuMUtHGcCHyVEsBiRkUa2El/XUlCrBPiRAtwtRZlDALmICBR\nyhxLtbxl87rEeHlKoYIAlIIw5JXz5x/B+mFbkmh+8zev8qUv3WRuroP+/ipJskxnZ4PDh/cRBLLC\nxa5dCdduvMW5SzlypR3s2tVPEMi0q89+Gq5MwKuvww0z5SoXwtMHBdJhAb5zWpR0zcSAw0Dizx87\nACP9Ym+/dU1qbNtWysETW+DIGAx2w+U5AfSF6Wzd774yHBwQaztfgBs1gfO1FuVcCGCXgXO1BI1A\n4swXa2Kd+y2nJCN7W0lTzEMcwpSGK+uAeWtO051LKORjdCg29Djt1XIBxaBSVNDkDQAb94FyCUUV\nKOGmTTVpskzU1u7W5p91By4728ZtI9qnolu7WTKy7YIRVpELVNsV3pB4csN+DRvsCdTWsqdd4Y8G\npJnSNknLFJxAkyPfYksnKUS1icPafQWCEZItnUtBLNnQ7SDcmtBlpx7lPRBbG7qOg3Adm3yV3dcm\nXOU9BZwY+DYMgC2IrTq2MV8b7y24eG+iPeXbAt9VcV4LX6tYHZxVqjIbZK1mvN+YUa2+Yk6hY2zh\nNGsZp3YtPDNTjNooxNhC20DTqtx20E33TbL723O3Jmz5+4OANbb0stC0St23on1Y+/LQqlMftp6S\ntbDnPrBtRuhYkyTawDZMFW2CSgFrYZuCtumpWUCrkKQFkhpFouXYUZKQaE0Ux/Kc/+dhIRsEKXjd\nn442r9dtIavyeVQu58YwlG62aX0ulyPI58lVq2kPy2We/Af/4BGsH6Y1mwm/9mtX+Q//YYLp6Qrb\ntlXQeoliUVOtbmP37gG6uuDzX4CvvHqdP/7TmGKxwNNPj/LCswGffgku3ISvfw+mTKy5uwovPwPP\nHIZz4/Dt07Lms227huH5x2D/Vjh9WwB9xVsRq5SDI1vh6W1QLItyfu8u3PEqkQUK9vbBEwMw0g13\nG3BmXuLOfsw5VALnfZ1QKUlW95U6XFpZnZ3dlYO9JU1/EYIcLAVwLYJbkfv3b5sFc1c+Jp/a2DG3\nSWi2gWYPil5FamFHxCwRMaPaJ2qVjX1d8hRvk4glItovEqEpQbqCVJDu06RdZrW1q3PY5RkxceeI\nOM0kXp18lZhpOrZGtYWqWMAJec9iln0SEqOKbZzYnUuymMVcdvNwbXxXUzcgjlpALLFlZ0nnDS4t\niOto6igvJmwVvBiA+bQ7K7qe7os5pyhuC2A/AauA0iFhOtWonkIYXSdIs52t/Rx6ABagqARP/Rrb\nOWl46jJBbiHMCtM2szl2AFQ+eJOGp04xADUJWgmectaePWvsat9qtnN7EwteMsCXfT1r2KpdrcSe\n1hZggUcKvOtOSDOT46Z5jaeSW6c3+bC3544ik4ncYidbcKb7tu4XGyvZg21rVrVPOA+2SawlDqts\nYEeJ9UtW0SaJ9qzjmDjR7nICMwFRZauXx4l4VVEUk1jr2F6GUiRBkMLWvTXtRqNoM5ANAgdYC1kL\n1zAkyMm6tD50LWTDapVcpSKgrVTIdXQQlkqE5TJhqUSuXE637fM5+9hsq1wOpbLfOUqpR7B+0NZo\nJPzTf3qVf//v7zIz08GePWWKxSYLCyGFQjdPPjnMxz+u2LEHfv8PVnjtuBD3b3xxkL/x1zs4exW+\n9j1YMstajvTDj70AO7bCax9ILNoWK+koCqCfPwCTK/D6FXh/nNQGL4QC6I8YQJ+6C2/fyS4PWSkI\nnB8bkIztS8twanZ1tva2DjjQCT1lqAdwqQ4XV1ZnaA/mYXdJUy1CkoNJo5qXWl4XIIlfQ/mEUj5G\n52JmVMQ47QuI9BHQozQl80VfJ2ZaNdtCPAS6CCiTGHWd0DBKeT0ol7FzoMVCbpdhbYtvBsaydnCN\nTGyYVYlcdu0oycZWqToWGzpK06ayNrUsn2HLbApyRRVbqFoY23PoFKpiL7tErSgFZWjywbOK2Aex\nTRCzAM+CWBS8BbB0fz9lPj8H4byBMC0qWCAcapm/G6TzfAtmn5wBsFXA1n5ueADGASEFsG89kwVw\n3CCTrEUo+5BzvmNCCwSNarV2c4JTvX58uJ3VHHnQBpxFHbSoXV8tW/CarGcs4EMyyVext6+9UYgt\ndCMD3JbELwvd1FI2+6SZyIk7n7I3CLj3l94gaHScoBuxsZItcBWJDky8ljSkrY39K8rWwFbLemdJ\nEBpVq8xHosz9iyZOYuI4SdVtos2iowa2SWDsa6W8t2VK2yQJWimBWxA40BYKWTVrgeuB1x9DA9i8\nVbQtkM1A1T7vA7hUIigUVkH2w2qPYP2ArV5P+Bf/4hq/8ztTzM0V2bOnxMBAiStXYorFHJ/61Ah/\n5ZUcb70Hl64kfP/kBPlgnp/+n4vsO7ybV193SWO7t8KPPQ/lKnz9XTh1zZ1n9wh88iAM9cNb1+GN\nq24OdKgkQeyZnVAoib397h2Y9+LPfWV4ekQWyVjQcHoOzi9kC5B05eFgF4xVBbrXG/DB8up62WNF\n2FnSdBQkyWwigcvR6uzv7gC25hMq+ZgwJxnZt4hZatHXCug3YC4am7hOxLSK2oK5ilT+KiLxypiI\nZZprJHlpOrDZ1gKjiCaxiZNmXymILZrXu8zsJqCxhSXd6xOjnhPz9W/nzgr48yZy7F4v9nZCA7fW\nsUDfxnxz5NNYs8BYoEoaZ7ZxYgfw0EBVmiRpCYxrKcCttSxQLnjWtMKHMNS811noIyqYPIHOozSE\nRgnjgTjQEGh/qUBRz+i8UcB48VsL4GZWAaYAzhmQWSBql3AVW/s5II0Zp9AOyEA40c4yTprGzoXU\nrk5Vb7AahFb1RjZOHZAuyrCWco098KZ2r43rtoLe28e3l2PjBmgfvHgWs3bWdJxAw2Q3p/OQPcD7\n1xgnAtxmLElSSSKgVS5um9jYrXXMDXCjZkycJC6EHIQkuHiteysmISqO2yrbNE7r/Yp8ZbsKtvm8\nwNazhfGB2wLfsFQi19lJvrOTXGenKNpymbCjQ6BrQGu3U/DaXiz+wCD7YbVHsH6AVqvF/Pqv3+DL\nX55hfj7Htm0l9u4d4PTpeZSCn/7pfrbsrHL8Dfm3PjF+FxWdo29LN307DrO4LJ/3nq3wykuyMtTX\n34XrpvhJPpQ49Mceg9tL8K0L2Tj0tl742E7Y0g+np+DNCZjzFPRgB3xkBMZ6YDKCd2alrrZtCthZ\ngce6oVSU5RrPLMO9lhBsfx72lDWVoiSO3UrE1m6tjz2a04zmE8r5mGYuYlJF3G0D0CqKQQVFA5CG\nUczt1HUnEosuGHDauHJr08hyih3Y+cyRSfBqrgHlJkUCM9XKqeTVQNbYOLCdr2yLdGgi8mZyknt9\nbCLrzbTIiIWrJiFHnhy2iKZvU9cJTOJWaCApsee86Tnz6TSAmlHFEie2trYAPzQQLhg7vImsIbYx\nEAtwI5SuGQjXUEnTWNLWjs55EG6xopO6QFhHTu3aODAFBzpPVarYAtiCW5Mq4FSRegrRt3/jBhnr\nGWM963bQthBtkCZI2d+SVhArD7yQScyyqtfGh1N7uyUmnSreGJqRKfkXsDoRy7+uVnsZZ2dbG9yf\n2mRAraOEpBGhY/F9tHYpf3Yqrx+/jZsxcWopqzQTOVmlcBMim4UcxdmPMQxF3SpXFDWxCVFGCWcs\nZAtbYyMHuRzkcs4+blG5uY6OLGwtYL0xha8/GugGeXvT+pe3PYL1Jpso6ht8+cvzzM/D0FAHhw6N\nce7cJNDglS90EIejzM3LTeLB/Qv892+9y/W5YR4/tINKpcCuMfjsJ2C2AX96EqbN8pGdZXj5MOzf\nBidvitW9YgBaLcJzO+GxUVnM4sQtmPCWnRyqwEft8pRNeGcG7noKuxTAoR7YVoU4J9b2+ZXsHOdq\nCPvKmp6iCJxbWpSzD+cAiTUPFBKK+YhGLmKceNXyjXkUQ0pRISGHpGNN06CuVv/uugioGBtbE5sM\n7NVgVqlatnHoJk1jR/vNZkDbFaUsZP9/9t411q70vO/7veu+9u2cfe4kDw/JIWc4MxxJo9FYF9tx\nJLdOiiLoJ390ChlIYLhA8iFAAaGxUcOFUdd1ECCAUaSp26BA2tqJZTdNAlStbcWVY1uypBlJo7lo\nOJzhnTz3fV1rvbd+eN+1zj4k56aRPJzRfoCFfVv7wkPy/Pb/ef7P87g09P2bjzQVoU9bhx6k9bnH\nU9ZugrdTyLPGMWcai2dMXE4dF406roeLHKWpBSEJITE06eYCS+FhLGaUsbwnPR1QQ7i+dO1O9RcE\n7dVt+h5A7N3MuvIgLo+ncmdrwQ1UHUxEk4aehXB0/Hw348WDbgbA9eAK62u/NbS1h38NRm2OUtbG\nvLn61dA4mhtHsle+DeDvSTnPglRbkJU3Sz3IkGWPv4fSbkNN/cXD+gzLsRYp9+ewSjdq12jbKN06\nvXys3VgZB1zvTnbJB59abuq4RypXao3SRzVfA9jAnW+FL3o0zzkySDV123tTybN121m16wEskoS4\n2yXu9YgXF52y9fXa+nigyvWp5iA8+uI7jwfHHNbvIpQy/OZv3uCf/bMBBweGxcUeTz99gps399Bm\nn81HclY2ziAQnD8HP/4Zw6/+4ytcuxuxtdXjx3+sz9/6rNvZ/KXnYN/D9kQf/qOPuTT4n7zqlmXU\ncX4FfvICiAT+7Aa8PGMk6yQO0FvLcEvCX+7B/kz9uRPBRxdhuQ1DAS9O3GSxOoSAM4lls+Uc4HvA\nK/L4JLAA2Ioty4kmihVFqLiBvm97VMur5pZPOY99OvveaAFdnLq2qAdO86qXTDhl7ZSgouLe3uQj\nk5erQ4dvoZRrp3Xdvxx4RXpv2rpW1IYSt79ZzABZEZHMKOQ6XV1wBOS6jqsJiYm8Lne/MgtqINdq\nunZeu68Fia8zB8259XG0V7l2WicurW0jQmsdhE2BsAWBLQnM0QrCWkHfl5bWXg2b8kgJG3Ag9mpY\ni8bV65Rw6aDaQPtNINzArn6OV7R2puWoSV3b4zCtFTDBzLmzKruGtk89K+lTzz4dbOpacf3aHE8f\nK+n/TH7Jg51Vyvd8nvvgW4N6xgDWKF6NKXUDXmNnjFQzitcog1LqqKYLGBE26eKmm9+nlrWxSKWa\n8roVAh2GTftPA9z6sla5QeDMUHGMSNPjjuTZY+a+qNNpgBvPGKSiVuvoervdgHfWQPWwp5E/6DGH\n9TsM1551k3/6T4dsbyva7T7PPrtCUUwZTq5S0uMjHzlNpxPyn/4NuDWA3/03B7z++iGLPcGv/pen\nEHnIl74Jhz4lvbkMf+MZKAX8vy/BHT/GM428ij4Jrw3hz2/AyEM2DuHpdXh0BQbA1/eO9z73Ewfo\nhRx2gW+Pj7dUtUJ4LLcsZFCG8Kp2KyBnYzW0nEqPlPM11H1w7iPoexPYm6nmELfysdWkvSumDwBz\niPW1aHeepOReB3Y9fGNWLasmHXzcPa0offK1ngzmljbETa32uEque52dAq8Iify5gVfps0CuV0U6\nyNZAdjpYAdNGHYeIGaWrPYxTgsZBXQBTYOpfszZ7WQK/mNLBWCNM6UFcIExt1tJ+hnSCsCnCBghd\np6YrD+PyeJHQ/wSxgQcxMynpGt61Kcu3MunwSKU20KuOIGzwKjg+UpDGQ76B9iyEawU8025kuR+o\nSh2dW7c1zdSyUfWl9i1FcDSs4550+DH41u0JsxO9jn8RsMrNbjaVV70+d1HDtx5+UbuWlTSNK9kE\nIVocdZMba9HWorRLLyvr+m8deAOXYq6hK8QxpWsfpHSTxAF4tiXIXw/imCBJiBYWSBYXiRcWjkPX\ngzZ+AHCjVsu91zweypjD+h2EG3hyh9/6rQE3b2rStM/HP95lfSPixVevMJjmfPQja/zYMzlPfAT+\n8Guwsyf55jdusNHZ5uf/zqO8sLPIjh/beXoFfvpjsC/hy99zo0IBllrwuYuQt+Avbrle6DpO9+DH\nToJNXQ36ykwbVieCp/tu7/S2gW9Pjq+IXI3hsbYlTp16fkke3zjVCWArNrRTiYoUt8X9ae0+AUvC\nkOCWTeyK6j4TWBtBF0vSmL8q7h3xKTB0gdgrUEkF94C5dmBnCN/X7JT1bAq7VsAC7Xct13VgRXJs\nwtZRLfkoze2mZrk6cuxVssYyxTIlwHjnt/JAjnzKulbIU2rFW3d9OnUMAakHcjhz3hRBydF8bEXg\nTViBTXwLU4UwUwI7JTCVT127fcCCFGyCMMFMetqDWJczZiK/a8u7q2u4Cl2BLmZAXNdsYwfAWj2b\nGRCrkqMBFgmYuvWJe+A3Uz9uwDpbn5451xifUjZHKeUGwMwo2rr2K9373Zt+rlPVxrracA1gPVvv\ndVX5Ro56g5VTvgbXAPgm8NUGVUmUL12busbbqFiBalLNXv3iFe9Mm1Bd19UPSjHX0L03zezru/V9\nYZ6T9PtO6fZ6xHV6uXYtz97218M8n6vcD2HMYf0O4nd+Z4df+7UDrl83hOEiTzyR8syzXb72revs\nHVjOnO7w859f5o09uHzNwf3O1dcR6jrxqQssnToBwMkl+JvPwK0pfPmVo9ncW334a4/CCPiTa7Dv\nW7nSCH7sBJxagtemrg5dO6+zwCno1Q7sWHh+fLzv+WRiOdMGYrhu4do9GelTkWU91YSxZDdU3OG4\nvO4gWBGW1Ju79sTxTVAWywKCDpbAq+b709mGHGf+CtEoyvtS2cYrVAdmi52pF8/WihWFr5K693N1\n46M2KAfvEkPp7UbWm6w0sQetO096KBeE1BurXNrapbhT/8lK8PCuO0MD3y/sUtWpN3LV6nhC0PRX\nz6rjlMAGBEZ5VTxF2AmhtQSm3prklbEJXIpa1+1HBc2WH2vB1unpAHTQQPAIxnUPrId2nWZWgmZc\no668wrU0M6PrdHdTd/ZqVUvviIam51jPKGFlj15XSV9v9qMwtVe3szXgRtlKGjPYbGtTDexZADdf\nQoKj9535nA7AygFYOAAbGzSLl4yxaGWQlXK1XnCqV8x2gFuUsSilkEofldOFOKZ6m/u9gm5SzVFE\nkKb3wzeOjxRwHBPXardOMc8A9s3g+6NgnJrHO4s5rN8m/v2/H/D3//5dbtwQWNvj3LmAn/zrfV66\ncsAbV4esLFn+7i+e5qsvhkgFvTacWd3m//jSLYaizyeePclKL+RvPuNap/54BtJPbsDHz7opYV+9\n6UpjACc68MlNkDF8bQ+2vVFMAI934eyi2zb13OR4insrdYBWMbym3XrIOhIB52JDJ5WoWHFDHE9t\np8CGgAy32Wn/nrS2ABahSWkXVFT3AD7ANOlsS4X0Rqk6rIdxi4CIeinEcTC72nLhq6z3q+W6L1lT\nEDYK2KWvIyJikhkoT7AU1MsuRDP3OiEi8Sp5gm2Ur3utADWjkCMEFTWQ6/OEV/8BGcImhDYgsBJh\nJgR26lPVEBi3GUqQIWzs09TWp5ELMMVRypjE/U3Y0HvWLCiF0F5BN+5nb+7SwRFBmr7bwkHTACJ1\nivjetLTWDtjaQ1PE9yvnWlaqOn0t/Dmzhi+OgN2kosXRa9Wp6NqApaxzSpeKY3W9qn4AACAASURB\nVDOijW/F8pmAIwD72i+hF9LCT7ICrQ2yVH6kI5gwwIjQf3zhTFY1gM2RIUvfC9+mp/cIvsLXeAOv\nfu+FrohjgjQlWVw8Ur3eyRx3Oo2rOe50nLvZg3ieYp7He4k5rN8iXnhhwuc/f4vr1yOKos2JE5pP\n/eQyU6X41rfu0O8P+YmfeYTDogXApz8KnWXNr/9PN5mUhqeeWOLn/pMuIoM/euXI2f3kBjxzDl7Y\nh2/ePnq/Sytu89U1Cd/Yp3FhLyXw0T4EmUtxb8+0WK3FlrMdVy68Yo7Xn9uB5ZHUkKaSg1By6x64\nLgtBHwNIhkgm4kiaWyw9BB2fti2ojvUzuzWO1o/6dKnmWdVcL5N0G6mcC1rfk8o2fhjIEZgrZmvL\ns2rZ1ZXdZ3UWpYSQ0Ju8plgmhBivgt3krYjUQ1lTQzloasl1zTklICNEAGNgAsfUtPJmrpTAhoRG\nIezUQdkUM0COfN048kDWvqY79erYq0eRgUncbQUY7ZSxmlXGPkWtgxloe7OWKjharZccpbGbdLN1\ncJXVkavaPgjYNdylh2a9AvEofe5A7JWwmkldz6rh+rWk8t9CZyA868jW1k2yKiTGuPqvU8HCzwZx\nClhJ5eq/M+lnLYT/EbiRkEprpDYYrAdw1IyRdG9lMfWgjNpklWVHAPZ13VkQB2lK3O+TLi01yrcB\n7QNAHLVa81TzPP5KYw7rN4m7dyU/+7PXuHIlZjBosbYueeJjPdZP5jz33E2y9g69U6fZPL1Erw1/\n7VPw9avw59/c5+q1AY+vV/zi373AH70q2PeGsic24CNb8N19NwIUnGHsU6dgqQffGsLr9Y5q4COL\nsN51w0demNAMR1qI4GLbEqTwmnErI+voBZatTJMkkt1QsjMD2BinnvOZ1PbsPOwcWMASoSkojyln\n18/slHOEQlIyW2t20FS0EL7X2c24PnJZ16ls68Hs6sFJUzO2GAoMla9BG6+WQ2IS/ykqDGNE08vs\nXuN4+nqMZYKg8FpceyxkPn1tcUAeI3wqPGjMXTmBjQmtITDTo5S1sb6uLJxCNvGRkUtP/eGVqI2A\nzKlLN9UTtESoumaMb+fJHIwbOPr6ryx8TfcBMK7hqaojyBIdqec65ax8alqWvo4bzpwjuC8lPduW\nZIKjOq/yyrpUfopO9CYQ1h7COFezDXwrtfDeMu3S0KpWwaGz3Al3nrQGqfSR49nXfmt3tJ6p+zYA\nrlPPaeoua/U7Y8CKul2SpSXS5WWXgu71jtqL6sNDeF7nncfDHt8vrKMfxod5WEJKwy/8wi3eeCPh\n8LDF6ppkZbPFxmbO3TsHhO0DxuEKj59a5COPQXsZ/u3zMJ1K9m7tcLa9y/lPfYzf+5b7uW714ZPn\n4dv78LuvuPdII/j0JsQt+Oo+DLzCbofw9DKQwren8Lx3iIcCnmxbei24A3y13iwIdAPLmUwTphXb\ngeLKDKBzBGveGDai4kBoDvxjAljCkvmU9ARJPTvFtU8ZulhCD+c6iadwxi1nAoPwHtVcD/0QqKZN\nylLR8S1Ss4rZ9RO7x2Nv+HLv79LYAdq7vys/9sO5pI/6jGsVrH07VJ2+zqmV8lGKW+GWS2YENiYy\nqU9bTwhMSWj2ENaBHZsQaIHQLZeu1n7ylp54SOYOzCoE3TlSx3Vq29bquIZ24s5VhYOtlTQwNj6d\nrfx5snTn4GvAjeKt1a5wdWhZucKsDWa+HPhzlHHzYZUvBltz9D51mlsqVxdW/h9DMwITmrnOhcIo\njSFEW93Ug42xGGWRlUQp527WQYQRpnkLqTVV3e87k4Z23wUs2qoGwiIMIcsdeLPsCMBJQhTHxL4e\nHHW7pMvLJEtLJAsLx6Hb6zkg+9thWn+Bm8c8PhghpWQ8HjMajY5djsfjt3/ym8SHFtbWWr7whbt8\n4xshBwct+suSpJfw5KUOSSq5drDLpOrwzMeX+OmfCPjObdh5xW3AigdvkLcnFCcuMCSn34KfeNRt\nsPpXr7rXz2MHaZvBn+9C4XutT2Xw2LJza//ZxHEBYCO2bHZhEsLLfqASQCIsj2SGLK3YDuUxQHeB\nFeFqtAdU7M3UnjOceg6QTClRWOrZKgJDB0vi3dfuN3s9NVoRYPxYUIVFElEvjjBASYD1g00qvzep\n9j9LtIdqncqeVcw1mF0N2hAgCQmJyHALHEZYxgR+PWTdlxyREdBCMMFN6ZrMgDv0SjkiNCDMmMCO\nCUxFWPcg0/Iq2Sll9NSnowtHG2ZT1jno2CnkGtx+iAgmcPBUqb8sQE28yvb14FrRqsjDtHRpbVGr\n52BGYQuQwkPdHBnK6rSz8kdl/DmRhzEe+DO1YWU9iHkAiCVGua9driZsm3HVqlLISjr/mBDowPnl\nNc4BXWlNpTxs8bXgwPo/pjoyYYUhxMlRGnrGiJV4FRzmOcnKCtnamqsDLyw4JbywcEwJJ73e3HA1\nj4cyasjWgJ2F7L3QfdA59fWqqt7+zd5lfGhh/c//+QFf/KLi8LBLuycJWgEfe7rF6gnBf3h+j0kV\nc+5Myk99NufLXiVvLkM3O+S3nw8g7vOZ831++iKMQvh3V51gSUL49GmQKXxlD6RXzI924cQCvCbh\nj/2Xp1DAUx1LK4dXDfyl/yUcAI+kmk4qGcSSazNp6i6wJpyBa5+KHQ9oi22MYYaKKRJvNsdgaHtl\n7XYWu7nZDs4OmjkCgcQgif14TWcCK/0QEHWPaq4XWUivZiUCQ0KKG+tRg1l5x3blu5rdVG6Xxh4R\nonxzjSIkIyTzZrUxMCJs0tvaQzkhNBnBMSgbAhsgbG3uShFKOHWsSw9lr5JNBCoBHTkgqynoIe6f\neq2K8Qp5Fsg+Xa1n+pZVrY5LsIqm/nwMtiFUhYdseAT0WhUrA6X2UzR8Tbnpc7ZOEZfKP+YvfWra\nKo0tFabSaBti8MsRjMBoi5IKWSqUsWgR+ky728MrtaFSGqmdK1oHASYM0MKirGpakRolnGXH6sFB\nkhDNQDhdWSGdgXAy0/9b3446nXkKeh7vS2itG3A+SM3ee/tBIB6Px5Rl+fZv9g4iDEM6nQ7tdpt2\nu33s+te//vXv6zU/lDXrr399ys/93C63b3fJWoZ0wXD+fMwzn+5x+faYF1/cYWVxyk/9rQvsjCMC\nAZ+5BNcnlt//w9uMRhV//aMtPvtTq/zpDefuDgP4xEkIW/C1fZoFGpcW3SrM78zsge5Glkc6MInh\n8sxayX5oOZVLqqTixsxUsAzBunBrEg+omsU5YFnA1aYrStQxY5mmhyVCoWZS2/Xwj9zXnB2cA6+M\nnUM7w6WSQZL4R92yygkR2k+xrkh8qxRoX2Oe+nR4ncrOfKW7BrM5BmanqEtghPCPOyjHBDYntILA\nFARmRGAmXim79LUwKUJbhPIpa105yNW1ZF1DVyHk1KtkcK1OsQcmrlYrC5dqJnRtU3omHS2NB7L0\n9d5oBtgetrJydWE7U1dWzMB41rhVfy6OUtSNYWvGIKZ8v3ChMMp6p7RA28CZtKShKhVKabQIXNqZ\nAGVtUxeWxqKsxUSRg7EQKGuboR71jt2g1SLwarhRxGlK4CGcbWyQ9vtNS1IN3/r23IQ1jx92lGXZ\nAHQ4HDaX9fV777/3vveSXp6NMAzvg2t9+83gO3u7vkzfYqHIvGbtY29P8w/+wT537nSIM4g6sLho\nuPixNvuV4cqVfRZ7Qzae2mJnHNFvw1OPwV9cg+u3JsjRmMcWJvQfP80fX3Wv+dQaLCzC1w+g8INP\nnlqEThueL2Bap8BTy3oHbgp43tcuQwHnU02WldwOJVe8ESwG1oUlRnFIeSzFvYQh9eYwjWHCrDHM\nqWe8enaVTEmCIcGgKRs413Otnev6Xji7lHbQqGNFQoZbw1hgGBMzJET5erMzduEd2wGlX02picg9\nmAtcbXlMyL4Hc0poM6+WRwRmRGgUofFzrG2LQAcInTuFq0undm0AtL2TOgcVIdTEq+ACl9qOXL1f\nJy7dLKegR7gasodurX5l6IGt3WOzQ0SkcK9T147rxxTeIW2dOm5S0DNGMWVce4D27VjWNq9rK9XA\nWNcDu+p25sogqwqlLToInSJGoKym9DBW1iliHQq0cYq4AXEUQxwT5F4VexAnHsZhq0W2vk66tka6\ntESyuEja7zdtSkm/T9LrzduQ5vGew1rLZDL5vkE7HA5/IGnjGqizYL338kGwnT3/rSD7fseHCtZa\nW37pl/b4zndyRBQQtQztdsmFjy2i4pCb1w9I8gGqt0x/pcuFU2By+P9ed0ab6Y1rtNoK8fgj7BUB\nG204fwKeH8HITyF7tAvtLny3gMp/mTudWxZacMW6jVbgzGKbrYppWnF7RhEvC+giGVNx6Fus3GAS\nS4ai9PVn5e9P0bTQaD9lyxUunbGrBQikB2ZIPQ3MwdXVnLveS10r58AbzWIMKRk0vcwjEoYzqjn3\nqrkEJkQc+pR4TEROQAIMvGKuH8sIbOYNXyMCMyQyBwTGpbiFSREqc/3GauxNXCNX+DeJayzXIUJO\nXOrZSI5UtPBpaZxSNiOnkk1IM1hExq7+KycQpKCCGRXs68eyAquPnqe8ulbWQddar57xwDYutVIq\nmjWLTZrcOvd0pVya2mpn0FIWrTRV4aZnqSBEC7+s01hKqZDaOaZ1GDrvmrBufKUxbkBH6tLSjSrO\nMuI0JU1Tok6H7MQJl5peWiLp94+BOO335ynpebyrsNYyHo8ZDAYMh0MODw8ZDodve7sGrjHm7d/k\nLSKKIrrdLp1O577L+vrs/e12+9h9rVaL8EO+RORDBet/8S9G/P7vB2gbkndDegsTlrZyljYyrFHs\njrcZhG2ePr/IM48LXtqH6cQt0gim2/x5mJD2emydbPPMaXhdwZ96y/WZNiwvOEgX9f7qtiX19ehr\n/t/qemRYapVsxxVXvYpOsawJg0EyEJJdHIjdMgw3qtPh2NWfcww5Cu3dz+DsYQGKzKvnpEltKwxT\nb9iqaBN4cGsUU4SHc4Qi9ZVr66d6OQBXRCS+1lz4OnThU9oQ0XagZQhNDVoSkBDalgfzeAbMxpnF\nTOLA3NSNC6doaTmIqhwhKw/toTN42dQBVMYeyhP/WOLd2LV7OoFqCmYyA2w8eAWUxr1fk9LGAVta\nKPwyh1oB1+nsSrnRcdZvi/LtWsfUMa79yGhQyqJKSaW0+5sJnXFLGndfKV3RQoUhOnDjX+rWJREE\nkLadKp5Rxqm/TJaWyE6eJFtZIV1eJl1acoe/PgfxPB4UtcKdhepgMGiOt7o9HA7fE3DzPH9TyN4L\n2wcB+GFWtA9LfGhg/corkl//9YpJEZP2YrrdAaYd8eiTHaIErtzdY2ASNlZSPvVszjfvuuedXwMZ\na37nD0uUCPmPP9rhzJbgz7xxrJ/A2SW3xeoND+mzLUvacpDWXjSfyRRpXnIrkI0re1FYFlAMKDnw\nae4Qy6JPZSsUBfVgEk3bT/SKmmlhLgWdNDOw617nyrdTuYEgqW+T0lQISm/YUrTJ/LQwp5xjr4Bj\nP2SkrjVHaK+MI2JaBMTAoU+R77qhIrZFZBNCowj0hNAceONXjjAJgcocIJV3YtsYbO7B3PVq2fco\nW9+bLHEpblm4FLZV7nmqVrweynoyA2z8YwGUpVfCkVfeuH3CpXFq2dqZ+rN16rhQvkXKNqq7BrJW\noPE9xdqilKGaVkjj0tHKtzNVSlP6mrEWAh0JN1sag6qVcatF4NcIiiwjzDLiLHNmrbU18hMnyFZW\nXP/wDIjTpaV5q9KPeNTQPTg44PDw8E2PBylepe7fkPdOo9Vq0ev16Ha79Hq95nir2zVso+hDg5KH\nNj4UP+GytHzhCyNu3oogSVhanlAmERcfS2l3Q6ZRyRu3pqSh5OM/foIXdyAQ8NQZ+N4YXn5phK0q\nntwAfarLi0OIBVxchhvAN32d+kRmydrwhnFDqgSWM7lCZCXbgftPIoB1YQioGCHZE/UUMUOGoqBE\n4u4LUXR8XdmtIhCAapQwfjynG8xZeOe0pIUgJsKg0Uz8yMyK3O9hpoHzgLBxaWe41qkBEZoQ7SeD\nZQg/gjNs3iMltDmRSQj0gNCMCc0ugY0QJidQCUJZUMP7wSw7HsxTsCWQO7CqCKrU1Q609KnvGtgh\nVL7mXNeUayUsAyjrISSzULZQWGcMM3amPm1g4nuOrR9wonH7hqcSLa03Ywu0dkausqhQ2qlgJQzS\nuJamQkpn2ApC14aNRtU1Y9/GFLRajTpOsowsy0hXV2mdPk22uuoMXCsrLmW9vEyyuDjf+fsjFEop\nDg8P3xa89x7fL3SzLHtHkH0QdOfAfbjjQ/G389u/PeErXwlRQcypk5JpBIvLltNn27AA3/vOIWlU\nsflknzEJ3QxOrMO3DkBpzej6bbKOJX7yLKURnOs59nzHu/hXEku/C5d972ogLGdyicpKdoST1hGW\ndaEpKZtxnyGGxWaEp/GzwhQ9tB/wYXyLlfIKWZEhif1WKNUMCqnoEPo5XhK3JcoQouj61LahIOSQ\nqOl9zhGUWMZEVD59nfphJBNcSnuPEE1Ii8AmxFoS6CGh2ffO7DZCR041qxGoAegxLpUdHoFZTsF6\nxSwDV3uuLFQTMMqlt5UHs4x9Cns6YwLDp6+tb8XSR+q60i49rdVMHdk6BV0o9zyr3V+MtNhSoacS\nbd3wDzdQzFIVFVKaBsjKGiptKCvpvy+EbgymT1dbIVxLk19BGOQ5kQdy1O2Sb26Sb2yQrawch/Ly\n8lwZf0ijqir29/c5ODjg4OCA/f39Y4B9EJC/X5dylmUsLi6ysLDwpscseGvgJkny9i8+jw9kfOBh\n/fLLkn/yTzRjGdJbhirRpG3FmQs9bE9wMCgZDgfYXsLqyT4rPbAteOXQObX1eI+9XkJvMefkSsaJ\nPrymwJSQhZaNLtwKYMcAWDZbEp0V7Hggp1iWhGJMyUC4xqkMQxtJRdWo6BhJC4nxE8LcROSSzBvB\nEkLcyJJ6J3JF14/wVJR+8pciJSQmBiosQyL2/f0t7+QeEjL1EK7T2goYE3mHdmjbLqWtK1dr1vt+\nr3KbQCYIpV0DuS7AuClgVCkoHJz1ofs2oyOoYgfUanoPmIV/rDieqq6MA3rlF1ro8GgwSGmPNjQp\nb+KqU9fN+EwHa1tI1FShiWYWRjmVLK3w7dSaShmmpVsDqkXgxLdPVxsh3JStGSDHeU6a5yTLy7S3\nthyQ19aOgLy6StztzutrH/Cw1jKdThv47u/vN8csjGcf/37AGwQBvV7vLcF772O9Xo90/oVvHvfE\nBxrWxlh++ZcLbt0NCNOQxRMaGUq6/YjlsylhBLfv7FK1I7Y2e5w5GbJroSyg34Kkq/mDVwqMCPjM\nEx2iRXhVAsKy1YW9GF637j/2RqYI8oL9wCnpHMOih/RIuLGLi2gCKgzKL5lUtFFA6XuXASpiPyks\n9faxoxR3DWh3n3NaS3JiIiIMEwLGxKgZ9VwBAyL2CLHEdAiJgTGhb8sKaROZmFCXhPqQyOwR2JjA\n5AiZIdQY5NhN/qINMgLZRVRDp6Zrt7YUUGVQ1qaw1LVEKaCMXL+yrQEsXN24FH62tZ5R18YZvbT0\nY7bq+5QfICKatLaZSHSpj+aIKJCloigligAVGBSWUmqmSjoYx7HbU+x7jkWaunR125m6ojwnyXPi\nxUVaZ87Q2tggW18nW1sjX1sjW18nbrf/yv4dz+O9h7WW4XB4H3TvhfHsfe92AEYURSwuLjZHv99v\nQPtmQO50OgTz9rh5/ADiAw3r3/3dkq/8B+dn3tzSFKIiii2nL3VIEkGhp9yaSsIo5NmP97jpRnqx\n0YdhAs9fGWEqydn1kNFaG6Ggl1jyDly17txerGi3Cwahw2+MYVFICipGTT1aYb1VTOPGg7aRfqpX\n4NPcFXGzuEKgmulgbmpYQOAV9JAQ6c1hIYYhIQdESJJm+9SEkLGvbdep7QLBIRF33aQwmxHrkEAf\nEuk9QhsTmBaBzEHOpLRtDee2h/MB0HIQrlKvmseAPpr+VcZQTjyYa8Vsj9LYKvaw9op5Wqewg6Oe\n5anyrmtfUy4VeizRRrgWJr86sSyVm04eCCrjepALpV1FPwqaGrNTyTlhp9Mo5SzPibpd2mfP0trc\ndDD2UM7W1uYK+SEPYwyHh4fs7e2xu7vL3t7efddnDynl27/oTNSp5hq89TEL4tnL7vzfyzzex/jA\nwvrgwPCP/pFmfxzS7muCLsSion0qY309QeTw0suHWODxS212bIi1cHLdbb/SpWH3+g5BF3pPrBEK\nWO1Z7gYwsBAHhpVOwWFcMcDVn/tCUlJRCABDD4WhaDqfHYwLv40KNCURmhhJ2qyBHBP58Z8xERqJ\nYEiApEtKRIhhQMSBH1SS+xWSB4TsEmFJGvU88PdBaDvEJiHUY0K9T2gEgekQqBRRSZADXydue5e1\nQcja7JVDFYDM3JBzPQTtHdtVCIVwqtskRxAuvRvbWK+Yrast18NDajAXFUz9ykhjoLKYqURVbiym\nMtalryeV95NFSByUp1WFEgEyipDaQdkGAaKdEXa7hF4pt1ot4n6f9rlztE6dIt/YoHXihEthr67O\nB388RKG1Zn9//03hW1+vlbCu2y3eQbTb7WPQnQVtfX32dp7nP8Q/6Tzm8YONDyysf+M3Sl67FiBi\n6JwMEcEhVTviicdbmAQOi4LBYUG7b1ncXCQIYGkVbnl1XQ0OGHVCegsZW2sZ1m/BsljWWyXTvGTg\nRlKxJCQVJaVwfdA9KtzOZqelEypCClJfizZMSVG0qVX0tElz56T+nJHvm458X/SIkH3fD932KymH\nROwSIohpEwKCAyJ2CEmITEakIdL7RHqbwHYIVIiQEVS+5mzb3tTVQlQjB2ed+5R26hSytqB9y1Sj\nmoWf+oVzapfedV3fV6tjjUt7S1xqu172rQNsqTGTCiUF2mqUFlSFdGpZhEihKY1lWlVUxqKiCBU4\nKGshEK22g3KnQ9RqkbTbZOvrDsonTpB7IOcnTpAsLMxVz/sY0+mUnZ2dtzx2d3c5PDzk3YwZ7vV6\nLC0tsby8zNLS0lten9d55/Fhjg8krF97TfMvfw+GZUD3hGV1VXJHRpw+IYh7MSaDa68PCLuG1TNL\nxGlAugg72rXA5l3DX3xvggkEjz/WYdByr5vFirwzZRxoLJaucPVmKdxssLajFAGgkORIAkpSAj+3\ne0KCJPMq2viac5uIEJBMEAxI/fQwN7Zz3yvvlgf0gIhdIiISWggKAg4IuUNkOySNet4lMoFTz1UG\n1QGonRk4txHVwJnBjFfOZeqUszVOXUtcrbn0iyhU6I1ewt/n69Slhonf06yNu6+oYOrt8dpiK4MZ\nVSjtRmZqZSinFaXUyDBCYiiUZlJJpBDI0CLRKGtdG1Sn06jlrN0mWVqic/487dOnaZ065Y6TJ4k7\nnffpX92PXtT9vjVst7e3j8F3e3ub3d1ddnZ2GI1Gb/+CuLnI/X7/LeHb7/eb2/F8O9c85gG8B1gL\nIf4b4D/DVR53gc9ba68JIc4CLwIv+VP/zFr7X7zHz3ksfu3XKu7sB8RdWN2E7UqRtRXLpxehBeNJ\nxWE1IUgiTm91EQswBbIYdBteuzuhqiSLKxHJyTYWy1KnoExLKiBGk4kChNPAGYqQgggH6ZiKFhUJ\nAdLXpnMkGTGuEWhIjCQnwaAQDAiQLNLyW6IPiKlIyYiIsRwQsUtM4N3bUwL23FIN2yXWIaHeJ1Y7\nhLZNoCJEFbvUti7dH6pqIcqRu4+WS1NXdVrbuPnZFVBEbgiJ9unryjjoqsr1Qkvr+pRL7VdG4oaM\njNXRUBJp0SOnmJXRbp3yVDZgrqyiUJqpUsggdKsYrXZqud0mWlgg7HRI221a3S7tRx6hs7V1BOVT\np0iXl+dK+YcYUkq2t7e5e/fusWMWyNvb2xT1MPy3iTiOWVlZYWVlhdXV1eZ6fSwvL7OyssLi4uKH\nfizkPObxw4j3oqx/w1r7ywBCiL8H/NfA3/GPvWqt/fh7/XAPiq99TfGlPxKUBlp9S2dZU1aa9lJM\nbyMhiuC17QE2EmycbhMsh2gBSQZF5tLct24fQA82HlkkiiWtzpQqcM1UPVEACissIZKMggQ3ECOk\nIKMkI6Si8uM9NQmhX1h5SAdIiLyKPiBHkJD4OvQeMZCSA0NC9oh9DdpNHdslwjgFrUNCtU+kdx2g\nqxRRlSD3nFKuU9vl0DuqUygTp3jVyNWcK+GUczE9qi2X1tWQdeWVtIWJdWlubZ3anmiX0rYSlMBO\nFGriFksobSgLRVEqZBBRoplKRSEVVRCgjKGyFiMEQbdH6MGcdToky8t0L16kc+YM7dOnaZ8+Tb6x\nQTAfxvADjel0egzAd+7caUBcX9/b23tHr5Vl2THoPgjEKysr9Hq9+Zereczjhxjf929Ja+1w5mYH\n2HnvH+ft49f/O8XeKCBctJzasuxUijjRrJ3rkqUwQLG7P8amsP54DwuEORQpgGVQThkEiiSN2Dob\nErTGaCyxUOQUBMINLnGQNriJ0AUtSnIPaSjpYokJkIwQVCz4VLfmEIFkgYwAsOwQo8h8zRl2iNEk\ndIgQCHaJuEtkO6Q6JFJ7RHrXpbdliiinIHfBdqDMEKWGauCMYlXgAT12aewqdHCejp2hS/q09tS6\nxRgycip5YnCrI607xtKpbg22tJhxhZTOlS0rTTGpqAioAsNUGSZVhRQBMrKU1mBFgFhYIFxYIOp2\naXU6pOvrdB97zIF5a4u2n+g1/4X+3mI6nXLr1i1u377NnTt3jgG4PobD4du+ThiGrKyssLa21hyr\nq6usra0dA3Nrvh5zHvN4KOI9SRohxK8BfxuYAJ+eeeicEOKbwCHwS9bar7yX96njq1/V/NlfBsgQ\negsG0wuIZUGwlLF1KmYYwv7uEBPDyrk2rTwm6DjvlBGWpAtXXxhAZHj0iYioVaIwdERBjEYLg6Cg\njfRbnAtyCloIJArLkA7Wp78HCCoWSfwyyh1CNF1a3iy2S4IgI/MjPneJIG6UgQAAIABJREFUSUhI\nCbhNxA6RbZPo2BnE1C6h6XgFfegAbTpQthDFANShS3eXoftp6zGozCnlInCpbZUcKWVZ+hGfODgX\n1g8ZsS6l7SeE2VKjRxJlQqSiUc1VEFEYydibv6pIUAlfY261iRYXCbtd8m6XbGOD3pNP0j171oF5\na4tkcXH+S/5dhrWWvb09bt++3Rw1mOvrh4eHb/s6SZIcg/D6+noD4vX1ddbW1lhaWpqno+cxjw9Q\nvCWshRD/D7DxgIf+K2vt/2Wt/YfAPxRCfAH4x8DPAzeB09bafSHEM8AfCCEu3aPEv6/4739TMSgC\ngh4snBKIsKCMYz5yNuZQCDotw/OvTrDdgFObXVQbRAwysERdGBaSQTmis1xw6vQCloqWKIkFKEpy\nSnKgoiJiSg/n9taMaaHJiHCNXCV9MtyU6bskQEaC4ZCIbTJyv4xjmxhNSs8PJ9kmshGpSYnUgFjv\nEBqf4q4VtO5BmSOKQ9ADB+QihenALbSoYld3LiZOPVeB32Ip/SSwwMG8kA7OFTBSXjkLbKFRQ4Wy\nEVJbinFFIQ1VKCi0YlRJKhFQhS6dTZwQ9HpECwsk3S7tfp/eE0/QPX+e7rlzdM6dm9eX32FIKbl7\n924D4FkQ18fbDeqI45iNjQ1OnDjRwPdeGC/MnfHzmMeHLt4S1tban3mHr/O/Af/OP6fpa7LWfkMI\ncRl4FPjGvU/6lV/5leb6Zz/7WT772c++6Rt8+9uGP/1qQBVBry/JliKGSpN3LNFKRtaBG3sTVG5Y\n7EYkaylxAlVkoQ0isNw+3CHtTthYbxFFJTkKKzRQ0EMhMGjGLKCIEUiGZChaRChHQBZ9Bdtyi8yv\nwjBsE1OS0SVAEXKdhIiEhIA7TlXbNqkSROo2kU4IZYYoA6j2vILOEFPv3pYZTFOYjo6AXPjaszKu\nFl2rZxm5GvRY+elgwhnECuXqzaVBDyukiaikpJhICm0pA81EunpzGYZUxqCshVabqN8nWlig3evR\nOX+e3sWLdM6do+v7mOc15gdHrYxv3LjBjRs3uHnzZnP9xo0b3L17923XEPZ6PU6cOMHGxkYD5dnL\nfr8/n4g1j3l8gOLLX/4yX/7yl9/z64h30/N47IlCPGqt/Z6//veAT1pr/7YQYgXYt9ZqIcQjwJ8A\nT1lrD+55vn037/2ff77ii18SVB1YelRz6kzFnUpz5mzMiYsd0tzy7Wt3KScFZz6+wtnNNtPIErYh\nDAwmH/Pd515HhZpPfmyBtTyiECU5UzoIKqb+ekDFhISCDhGKMRFjumS4fc8H5IS4cfk7fvlGC8Fd\nYqYkdIiZeBUdk5qYWN0lVhWB7hCWFRQH3sEdwXSEkBp0y0F3OnJmsSqESQmV9OYxA+OJb7kKYFw5\nE5iMHZhHlZscJnFwlgKpQ4pJxbQylGHMWComNZyFQAFBq9XAOer3Wbh0id7Fi/QuXKB7/vy8Veqe\nmEwm3Lx5k5s3b3L9+vVjUL558+ZbuqeDIGBtbe2BIF5fX2djY4P2fMzpPObxoQ4hBNbad536ei8S\n6b8VQlzEJVsvA7/o7/8p4FeFEBI3y+oX7gX1u427dy1/9BVBGQvaK5K1EwG3CksnlbRP9ejkcMtU\nVJMCs5qydbLFMLLEbRChge6YyfYBJlJs9CwrrRDJmB7SL5oc0ccQYJAcsEBIgEWzTZeQmADNHXIE\nKRFwhxRDTgvYI+YuGV2/jvIKse2QqYBY3iI0OWGVIIqxc3KrNkwzV4fWHShiB2VduHarSeCWX8jE\n1ZknfrNUCQwNSOmMY2PlW64EdiKRY+PGcRaayURShhETrRlXkjIMKbVCCUGwsEC8vEy6uEh3bY2F\np55i4bHH6F64QOfsWcL51h5GoxFXr15tjmvXrnHt2jVu3LjB/v7+Wz53YWGBkydPcurUqWPHyZMn\n2djYmPcNz2Me8/i+4r24wX/2Te7/IvDF7/sTPSB+639QHJYCcku4KAg7lnQiERttNldD7kQwuTOg\nWEx4bCNlmEDaBkJN0BvTizTf29+nZSdsrvXRDOgjKCmImNAjpPS90a66vEeCISdCsUOIoUeC5Q4p\nmpwUwR1idshoETIiYpfUdEmUIpZvEOoeYZFAuQ+66wF96MZ1lhGMADlxyngSuKlhMnXO7Yn0g0cs\njLS/DgyUWxFZudR2VQVUUjKZSAojKFAMi4qpEFTGUAFBt0u0tESyuEhnbY3+xz/OwuOPs3DxIu3T\np39kR3GOx2OuX7/ewHj28q2AHMfxMRjfe73b7f4V/inmMY95/KjEQ198LEv4nd+DMhIky4aVNcu+\n1OhWwKOnQu4KWGppvqs0mZBkm6skLdCRIu2N6YaG26N9gsMhWRdWlxULCCoOWUATYZDss0iMpcQy\nok+GZoCgYJEcuOOHnOQItkmaVqwdYnZIdU4ih8Rqj1B1CKZAtQuyA5PYu7vbMEmcMazKoAhhWvgx\nnd6hXdaAVi7VXRgYulq0LSxyoJEmoCg0k4miCCPGUjNWmjKKKLCQ50TLy0T9Pr2lJfpPP83Ck0+y\ncPEinbNnf6TqzVprrl+/zuuvv87rr79+TCnv7Lx5p2GWZWxubrK1tcXp06fZ2tpic3OTzc1NVldX\n5zXjecxjHn/l8dD/5v43/9Zw80BgWpZowSL6EaIcI9ox2UpK1oHXhgVhqEg22rSWQkysCLtjOqFm\nKsbIGweEbcmZ1YS20EgOWSGiYkxISYcQxQ4dAmIshhv0aBNQEHGXNh0CdonZJid3kLZ7pCYlrbaJ\n9AFRmSCmQ2cAK2LEdApqCtMQxhpUAdPAXZelW47RQNnCUDtYTw2MXB+0nRjkSFPpgMlYMlGWKYph\nUTIVAaUxSBEQ9ntEq6vOqf3kk/SffprFJ56ge+HCj0Raezqd8sYbb3DlypUGzFeuXOHq1asopR74\nnCRJ2NzcbGA8ezkH8jzmMY+HLR56WP+P/7OhigTBgqG9aIhiw0Gc8Mi6oMwFeQoH21NMGrCymRPF\nCtEd04sUEzFmVWleU4e0q5L1lYyQQxYQlOywSIgzjY1ZIkdxx/dGBwS8QZsWESUR2+R0iTgktjvk\nOiWR20Q6JiwSxHQXVAcm3tGt2jCO3XCSKnNp7qJwSzLGfhNVEboadKUcrA80KIEZK+TYUCrLZKyY\napggGZQV09BNDLNZTrSyQrS0ROfECZaefZb+Rz7C4qVLpP3++/1X9kOLw8NDLl++fAzIV65c4fbt\n22/6nI2NDc6dO8fZs2c5c+ZMA+S1tbV5n/E85jGPD0w81LC+dQu++ZKb9ZH2LPFqxNhMSGOF2Vhg\nrQfXjaQsCuxqzMn1GNUdsxIppmLMSSxvHG6TD6csb1gWk4IM5ZV1SsU2HQISFJYb9Mmx3CQn8MB+\nnZw2CVMiu0euM1K5S6RSB+liH2QXxpkb+1nmMPIGsSJ0armqXL15JJ1JbKRh7FZFOjVtsRNLNdSU\nEqegjWCkNUOpKKKIEgvtDsn6OvnSEr1Ll1h65hn6Tz1F9/z5D11quyxLrly5wquvvsrly5d59dVX\nefXVV9ne3n7g+VEUsbW11UD57NmznDt3jq2tLVqt1l/xp5/HPOYxjx98PNS/5f+X/1UzNgK6kPUN\nCz3BHSPoLEecWgu5HoA+GDFdSTi/JJh0x5z0ivoEhgGHyGuHpIsTzi50iJgQUtIFFLdZIkNzm5SI\nDEnIXTrkhNwkJSEDIt4g1x3S6pBYDRykJx7Sk8hBepq62nJVuVT3pIAqgWG9zzmAgU9zDxVMLLY0\nqENJqSImY8VYWUbGMqgU0yiiAsTCAvHaGu2VFfrPPMPyJz7B0tNPk6+vv89/Mz+Y0Fpz48aNBsaX\nL1/m8uXLXL169YH9yFmWcf78+QbK9eWpU6eIPmRfWOYxj3nMYzYe2t9w1sLv/oFjnugYRFdQJJpM\nKbL1FuNUsNK2fPXQ0C6npOc7nEgUh2LEaSwDccDCSHMrO6A31nT7roc6YELoe6udms6Am7RJSHzK\nu0VGxDUy0yKvpsRqQNRAugMjVzdnGrv+5iqAYeAMY2XkXNulcICe4urQAzdFTB9KiiJgMjWMS8MY\nxWEpmYYhpQCxuEi8vk53fZ2lT32K5Weeof/Rj5IuLr7ffyXvKcqy5PLly7z88su8/PLLvPTSS7z6\n6qsP7EsOgoCzZ89y4cIFLly4wPnz57lw4QKnTp2a15LnMY95/EjGQwvrl16C1++CWRC0Fg2LyzCQ\nBhYjntwIkQncVpKwnBKcFZxfgAMxYhPDUBxyEsEboxtkBxWr5zUrQQvFDm0CIsZEVLSxBFyjR0rA\ndXJyUgYkdkhLCpLqGlHZJpiMnWt7FCOKEUxSGE29UgaK0o34HEnfYmVgqhygJ2AnUI0M01IxGilG\nhBxWkrEIKISBbpdkY4PO2hrLn/40q5/+NEtPP030AU3hjsdjXnnllQbKL7/8MleuXHmg2Wttbe0Y\nkC9cuMDZs2dJ0/R9+OTzmMc85vFwxkML6//9X2qmgYC2JeiB6AlCo0hagv1OxMmO5XuHBWJZc3rB\ncijGnPag3gTGZht1Y0R7aci59gqKW03au0NCzB4ZkDMlZpc2gtC+TltnpNVt4qpFONau/3nsnd6T\nzAF5Krw5rHKp7pGCMc7FXSg4cKYxdSApypDxWDJSMNCKoTJMQoHJcuKNDdpra/SffZbVz3yG5U98\ngqTXe59/8u8uiqLgxRdf5IUXXuC73/0uL730ElevXr3vPCEEZ8+e5fHHH+fixYvNsbCw8D586nnM\nYx7z+GDFQwvrf/1/uwmcQdeStC0mslRZxPKJgOU23IlBFock3SmdtZQ1oRmIQ04BU3ZJDkri3iGL\nVUDc3mGZBMNNlkgQXGWBFhE3yEjI2Cc1Ae2qIJYjonHozGOTHDEewjR3ZrCpdJCeShj51ZIjCwMJ\nEwGHGlsY5IFmUlqGI80Qy0GpmIQhZRAQrq2QnjxJ99IlNj73OVY++Umy5eX3+8f9jkJrzZUrV3jh\nhRf4zne+wwsvvMDly5fRWh87L4oiLly40AD58ccf59FHHyXP8/fpk89jHvOYxwc7HkpYX34NrmwL\nzDJkC4Z0JaQICuJQEy13GefQ0lNuL0nWQslKllCKIevAlB1OILha3SYdSNYeMSyRY7lNH0HIdXoI\nQq7SJSKy1+iohLS8SVS2CEdDKDowVIhSwqF140CHFqaVg/OocunvkXH3DwxmZClHlvFUMyw0B1oz\n0IZxKKDXIzl5koXNTdY/9znWf/In6V648NBvRtrd3eX5559vwPzd736X6XR67JwwDLl48SKXLl3i\nySef5IknnuCRRx6Zj9WcxzzmMY8fYDyUsP69/9NShEDHEnYsUVswSgXpcsjacsA0tdxRA7rFiN7Z\ngJgxC2gqdtkApnobc3dMpzdgs90lYJcuUxKmdJiQUNFiSmpKutWUqBoTjXDzuweRG2gyjGBceChX\nMPZO7kPjVPYIGFrM0DAdWoZjw0BZ9ivFUASUUUS4tkK+ucnSJz/Jxuc+x/KzzxJl2fv7w32TsNZy\n9epVnnvuuea4du3afeedPHmSS5cu8dRTT3Hp0iUuXrw4V8zzmMc85vFDjocS1v/6SwbdEgQdCDsQ\ndgxhoMkXEnYzWOuU7N44JFxSnGknxKICDlkFSnaIDwvyfMBKomglU3IOaGPJ2KZFQMYdWiqmVd4l\nnqYE4yFMchiOEKMUhgWMExhWzuU91A7ah9qZx4YWPTBMRpbhWDPQgt1KMQpCdJYTnzxJb2uLjZ/5\nGU789E/TOXPmff6J3h9SSl566SWee+45nn/+eZ577jkODo7vW8nznP+/vbsPkqOu9z3+/vX0PE/P\nzG4SliS7SQiQIDmB4GYxbjgQeZKHhIcIQeogit7KRRA8wgVFEKowFlpacup6i3suSM4xdfBcFMsj\noocgFKEQSoQYwkVEyIUk+7yzszM90/M83b/7x6y5PISQh93MLPm+qlLsdHemf71dPz75df8eli5d\nykknncSSJUtYsmQJ7e3tTSqxEEIcuVourCsV+OtuhdcOZszDZxk4posXM0gc5SMZdskYBcxAkbZK\nFRXyiOIQx6XGGLPQDJdHiHpFZll+IoxioQgyTAyTgB4kXvUIVscx86BKRcgpVKHaeORdqDVCuVhv\nzCqW8xqf84130q7tUXA0OaeO7SnGqy6Oz4e24gS7umg78UTmXHABHStX4m+hRR1c1+X111/npZde\n4sUXX+Tll19+37CpmTNncvLJJ7Ns2TKWLVvGokWLZJYvIYRoAS0X1k8/05gEjBiYcYjM0JRVDRXQ\n1JM+6rEiAcemrqrEj6ozS7n4KKPIMANw3TEMxyaoy3QkHBL48DNIHI+glyZecfCXFWa+DIUQ5Cqo\nfADyFbBptKZtr9HDO+NCDsh6uDlNMeeRc1zG64pM3cPx+VDJJMH580kuX07XRRcxc/nylljJyvM8\n3nrrLV588UVeeukltm7diuM47zpmwYIFnHLKKXvCec6cOS3/Hl0IIY5ELRfWv3pcUw2CjoCKatyo\nwo0aRGdCe7xOIFhl3HGIUmRO0E+dHBYOCTQwhpG3CegSs9tytPuiBBgmTpGIWydaHidQ8GE4Bcj7\nUU4ZMl5jOFa23mg9Z+uQ1Y1e3+k6Xg5KtsZ2PDI1SNddHJ+JMWMG4QULmPn3f0/nhReSXLKk6UGX\nTqf5wx/+wPPPP88f//jH9y312NnZSU9PDz09PXR3dzNjmvRCF0KII13LhfUzL3roqIFheRgxUCEP\nFdCYbSaVWJkoeQJ5h2CgSjhapp0KQaoo0iSoMl6waQ+Nc3TIR5BRLPLEalUi5QwBRzUC2vZQOQ/s\nKmRVY+hV1m20rMddyHroHJTTLjlHk65CuubimCa0tRM+5hiOOuss5l1yCdbChU37Xbmuy6uvvsrz\nzz/Pc889x+uvv/6u/bNmzaKnp4fly5fT09PD7Nmzm1RSIYQQh6KlwrpQgAFbQafGiGkCSUXV70JM\nM2NWHctfoVRyCITLdAQqJJVCkyeITZI6PjdHyB0lXC0zI+YR1zmsWp1wOUPA9hqdxewq6m8BnamD\nrRot6XEXssC4Sy3jkctrxosuqbrGVgYkEgQXLmTWGWcw/zOfIX788U35Hdm2zbPPPsvvf/97Xnjh\nBfL5/J59wWCQ7u5uent7WbFiBfPnz296a18IIcSha6mwfvZ5KPtBR8EX12BBNaAxLYWRqOEzC1C0\nMWtFkm0uBnkSlLCo4WMcszxGuFZiVtwhadRIVKuESg7+bAVyflSuCuMeZDTkdOPncd0I6zEXL6Nx\nMh7jBY+xemNXPRwheMwxzDj9dBasW0fihBMOewAODg7yzDPPsGXLFrZt2/auRS7mzZtHb28vvb29\ndHd3yzSdQgjxEdRSYf2fT2vqYcACFQPTAi+isdpqxANlgrqCUy8QDTrMikCCGgGK+EmTJE/FyZEI\nZDk6XCZRcQmXSpjZCmQVKjvRks7QCOmshpQL4xo97lFJe2TzmtGyx5irKQUC+Ds7mdHdzcKrr2Zm\nT89hC2mtNW+++SZbtmzhmWee4a9//euefaZpcuqpp3L66afT29tLZ2fnYSmTEEKI5mmpsH5um0Zb\nCsIaIwb1sMaLQai9hmEWMKo2Uc8h6a8S9nmYZImQI0mJiFfAc0exlM3Rho9woYSZbbyTVuNe4zF3\nZqIlPeZCGhhzccc88lnNWMFlpKqxfT6MjqOIn3gi8668ks7zzsN3mFqrO3fuZPPmzTzxxBPs2rVr\nz/ZIJMLKlStZtWoVvb29WC00JEwIIcTUa5mw1hreHgPdqTESGhVXeEGXYLRCMlolqspQdgiZRRLR\nMmFKxClhUSJEFrOawvJsZnolYhUDM1OBcY0aV42gTnuQ1pDyYKzxcyXlkc56jFY8Uh5Uo1FCxx3H\n7DVrWPgP/3BY5uweHBzkd7/7HZs3b+aNN97Ys72trY1Vq1axatUqli9fLo+3hRDiCNYyYf32LnAU\nkFAYMQ/TAjfoEbYqhMNlAhShliHmFZgZqBKlTIgcEdJYZFDFcQI1hxlGHTOjIK1RE61n0l7jvylg\nxMNLezhjHqmcy1AdbJ+J2TmbGT09HLd+PTM+/vEpfeRdKBR44okneOyxx9i+ffue7bFYjDPPPJNz\nzz2Xnp4emZBECCEE0EJhveX5xipbhDXKAh3TGFadWLRK1CgT8grUawUivhJWsEyQLBY2cfLEdZ5K\nIYtVLhBTJtgGKjXRik5rGPVgxIOUpj7iMj6uGSl5jLhQiUYJL17MvCuvZMG6dVO2hrTneWzbto1H\nH32Up556as/sYaFQiDPOOINzzz2XT37ykwQCgSk5vxBCiOmrZcL6uZc0bkQ1OpdZoCIQiJSIhcuE\nKOCr2YQMhzZ/EcsoksDBIkeMHKHyOP5SjnC+jl+bqJTXCOiUC6PAcCOsK6MeqYxmoOySVo13022n\nnsoJ//iPtJ900pRcVyqV4tFHH+XXv/41/f39e7Z3d3dz8cUXs2rVKiJT9A8EIYQQHw0tE9Z/elND\nTEFMQxSI1QlEK8SCZcIUCFTzRCjQFigTxSFGlihZYu44ITtDPVsj4BiowkRApzwY8mDYQw+5FEZh\nxPbor3nkAyGCxx7L7IsvZtH69QTi8Um9Fq0127dv5+GHH+bpp5+mXq8D0NHRwerVq1mzZo304hZC\nCLHfWiKstYa+ceAEIAZGHFS4SthXJO4vEVEOZi1HxHBIBhtBHSNLXNskSg7VVAUj4xIs+Bo9vkc0\nDLowpNHDGnvYYzCvGXShErOILl3KohtvZM4550zqu+lyuczjjz/Oz372sz2dxXw+H2eeeSZr166V\n99BCCCEOSkuEddaGvE9BBIyExoho/JEi4WCZqFEk7DqYbh5LFWg3C8TJYWmbRNkmaJcoj1bxjWn8\nFWDEhUENAx7eoEdmxKPP0QxpBTNn0tbby5JvfIPE4sWTVv5MJsPDDz/Mz3/+c2zbBhq9udeuXcva\ntWvp6OiYtHMJIYQ48rREWL+wFeohDXEFYfAlXIKhMpZZIopDwM0R8eVpMx0so9GqTtRtIk4Rb7SK\nMebizyiMvAuDHvSD218nPaLZXdSMKgNj7lw61qzhxJtvJjhJazIPDg7y0EMP8atf/WpPh7ElS5Zw\nxRVXcPbZZ0tnMSGEEJOiJcL6j6+AF2u0rFUSfJEKYV8RyywSVg7Beo4IjVa1hU3Cs7EKDuZ4ldJQ\nDSPl4R83Gx3K+jRuv0dq2GNXUTNmmpjzF9B11VUsvu46fJMQoLt27eLBBx9k8+bNuK4LwGmnncbn\nP/95li1bJvNxCyGEmFQtEdbb3pjoVBYHFdYEY0XCZom4r4iFQ9C1SfhytJl5LJ0jXrIJZGuoMRd3\nsI4aAzOtod/DHfBIDWveLnqkzQDB44/nmGuv5dirrjrkdaYHBwf58Y9/zGOPPYbnefh8Pi644AKu\nvvpqjjvuuMn5ZQghhBDv0RJh/caAhjmNnuC+hEvALBNRBeI+h5B2CLt54jpLm2mTrGcI50sYaRdv\nxIMRF2MEfCmN2+eSGtS8XdKkzSDBxYs54etfp3P16kNq7aZSKTZu3Mgvf/lL6vU6Pp+PSy65hC9+\n8YvMmTNnEn8TQgghxPu1RFgPFwELiIEZqxLyF4ipAjGjSNS1sZRN0ueQVDksp4A5XoOUxh2oo0Y8\nzCGFHvJID2reLmjS/gDBE07gY7ffTud55x10ucrlMps2bWLTpk2Uy2WUUpx//vmsX7+erq6uSbt+\nIYQQYl+aHtaeB45qTIaCBcFYmbBRIm4WiKk8AS9PApsZpk2iahOwq6iUhxrReEMexqCHb8ggM+Dy\ndgHSPj/BxYs58Y47mPvpTx9UmbTWPPHEE/zoRz9ieHgYgE996lNce+21HHvssZN49UIIIcSHa3pY\nD41APQJYYMRcgqESMcPBMhwi5Im5WeKGTZvKEc05GGkXRlz0MHi7Xej3KAwqduYhpUwCxx7L4m98\n46CDeseOHXz3u9/l5ZdfBmDx4sXcdNNNdHd3T+JVCyGEEPuv6WH9yl/AiwJR8CXqhM1i4321kSdG\nHktnSWib9moeM1tHjXqoEQ93oDGWujII/TmPYW1iLpjPwhtuoGv16gMuR6VSYePGjfzkJz+hXq/T\n3t7O9ddfz+rVq2UiEyGEEE3V9LDe9joQA+Lgj1QJm0ViKo+liljaJuZlacMmVijjS9VhhMbMZLtc\n3H6P4QwMaB9qdgfzvvCFRq/vA+xMtnXrVr7zne+we/dulFJcfvnlXH/99cRisam4ZCGEEOKAND2s\nX3ubPZ3LgrESEaNATBeIGzlink2bytBWzTc6lY1o1JCGAXB3e4yOePTVfXjtCTpWr2bx9dcf0PCs\nSqXCfffdx0MPPQTAwoULuf322zn55JOn5mKFEEKIg9D0sH5rVMN8UDGPYKBMTOWJqzyWkceqZUhq\nm6hTxRh1G63qAY23W5Md8NhZ0lSsCG29vfzdHXcc0IQnO3bs4I477mDHjh34fD6+9KUvcc011+D3\n+6fuYoUQQoiD0PSwHsg1phk1LJdooIil8kQnlr+MkyFRzhPM1GBUNVrV/R7lPo9dtiajTBKLF7H0\n7rsJzZixX+fTWvPII49w7733Uq1W6erqYsOGDSxZsmSKr1QIIYQ4OE0P66wHRMAXqxLxFYhSIKFy\nJMgQr2eJ5Ev4xlwY8cGgxuvTDIx6DHmKWnImx331qyQ/9rH9Ole5XOaee+7hN7/5DQCXXnopX/va\n12Q9aSGEEC2t6WFd8itINMZXRw0HizwJ5RDXuca46mwNY1ShBlzog+yQZncFSmYY/2lnMf/yy/fr\nPAMDA9xyyy288cYbhEIh7rzzTs4999wpvjohhBDi0DU1rF0X6mEgpgmGSkSVQwyHhGET9zJYTgFf\nSjfeVfdpqrs1u2yFjUk22cXK/3Yrxn4Mq9q+fTs33XQTtm0zb948vv/978vkJkIIIaaNQ1vZ4hCN\njYOOgYp7RCbeV1vkSJAlWcsQyNQwRhs9wHW/ZmS4sVx1MWCx+6SD7pamAAAJQ0lEQVSLWbR80Yee\n46mnnuLLX/4ytm2zcuVKNm3aJEEthBBiWmlqy/qtfiAKhuUSNouNR+DYtKks8aKDOeaiRoA+KPVr\ndhWhGggzOuckIr1nEQzuu/g//elPuffee9Fac9lll3HLLbfIBCdCCCGmnaaG9Wv/F4iDGa0R8xWI\nKoc4ORLaJpwrQwqMIdB9HgNjkFU+qu0d7Fp2GZ84ftY+v3vjxo3cd999ANx444187nOfk3WmhRBC\nTEtNDes3J1rW/miFqMqTIEcCm2Q1i5muTQzVgsIADFQURKLklp5JOTmXhQvb9vqdWmvuv/9+Hnjg\nAZRS3HnnnaxZs+bwXpgQQggxiZr6zvqtUSAOwXCpMcUoedpVBqvoYIx6qOFGWPeNaRwMAgsW8Ob8\nswA+MKwfeOABHnjgAQzD4O6775agFkIIMe01NawHsxpimnCwiKUc4tgktE0oU8EY1qg+TbFfM1Rt\ntKpnXfE5xuthwmE/s2a9f2z0I488wv33349hGGzYsIHzzz+/CVclhBBCTK6mhnWqpFGWJjLRuSyp\nsiRrOXxjdZh4BD6UhiIGgfnz0addCMC8eYn3vX9+8skn+d73vgfAN7/5TRlDLYQQ4iOjqWGdqYOy\nXKKmQ1zliesc8XIeX8qDIaj0w2AFCIWYu24dQ3YjoOfPT7zre7Zv3863vvUttNZcd911XHLJJU24\nGiGEEGJqNDWsiyb4rDpRVcAiRxvjRDIlmHhXPZqCvFaYR89mwRe+wO7dNtBoWf/N6Ogot956K7Va\njXXr1nHNNdc063KEEEKIKdHUsK4GwYxViSqnMb7atfGP11GD4PbBYBEw/Rx14YVE58xh1653h3Wl\nUuHWW28lnU7T09PDzTffLMOzhBBCfOQ0NazdqCIYrhJXjclQErV8Y3rRfsgNgO0pVDzBgmuuIZ+v\nkMmUCIVMjjoqCsAPf/hDXn31VWbPns0999wjE54IIYT4SGpqWHsRCISKxCbC2nKKqGGN7odBG+qG\nQWzpUtqWLt3zCLyzM45Sii1btvCLX/yCQCDAD37wA5LJZDMvRQghhJgyTQ1r4hAOlIiTI6kzBDMV\nGIJaH6SqoAJBuq6+GqUUfX05AObPTzI2NsaGDRsA+MpXvsLixYubeRVCCCHElGpuWEc1UX+BOHna\n3Cz+sToMQGYEihp87TOYe9FFAHta1l1dcb797W+TzWZZsWIFn/3sZ5t5BUIIIcSUa25YW5qIr0Bc\n5UjUchijGvpgKAdaGbStWEFw4vH2wECjZb1z55947rnniMVi3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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "w = 5 * np.log(grid) - 25 # Initial condition\n", + "n = 35\n", + "fig, ax = plt.subplots(figsize=(8,5))\n", + "ax.set_ylim(-40, -20)\n", + "ax.set_xlim(np.min(grid), np.max(grid))\n", + "lb = 'initial condition'\n", + "ax.plot(grid, w, color=plt.cm.jet(0), lw=2, alpha=0.6, label=lb)\n", + "for i in range(n):\n", + " w = ddp.bellman_operator(w)\n", + " ax.plot(grid, w, color=plt.cm.jet(i / n), lw=2, alpha=0.6)\n", + "lb = 'true value function'\n", + "ax.plot(grid, v_star(grid), 'k-', lw=2, alpha=0.8, label=lb)\n", + "ax.legend(loc='upper left')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We next plot the consumption policies along the value iteration." + ] + }, + { + "cell_type": "code", + "execution_count": 33, "metadata": { "collapsed": false }, @@ -738,37 +919,81 @@ "name": "stdout", "output_type": "stream", "text": [ - "1 loops, best of 3: 7.2 s per loop\n", - "1 loops, best of 3: 467 ms per loop\n", - "1 loops, best of 3: 488 ms per loop\n" + "Iteration Distance Elapsed (seconds)\n", + "---------------------------------------------\n", + "1 6.924e+00 9.756e-03 \n", + "2 4.107e+00 1.951e-02 \n", + "Iteration Distance Elapsed (seconds)\n", + "---------------------------------------------\n", + "1 6.924e+00 9.754e-03 \n", + "2 4.107e+00 1.950e-02 \n", + "3 3.866e+00 3.034e-02 \n", + "4 3.673e+00 4.010e-02 \n", + "Iteration Distance Elapsed (seconds)\n", + "---------------------------------------------\n", + "1 6.924e+00 9.911e-03 \n", + "2 4.107e+00 1.975e-02 \n", + "3 3.866e+00 3.082e-02 \n", + "4 3.673e+00 4.225e-02 \n", + "5 3.489e+00 5.175e-02 \n", + "6 3.315e+00 6.115e-02 \n" ] + }, + { + "data": { + "image/png": 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8cN1118HT01Or6W7evBk33ngj/P3921ynEOLyddnVdA4ePNhVm27VpVxbMiMj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ZNPPplwjx4R2UzLgM3IyMDPf/5z5OTkICoqCgUFBViyZIndOldddRXKysoQHh6Obdu24a9//ava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\nmtQsFguqqqpQWFiIg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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "%timeit dgm.solve(method='value_iteration')\n", - "%timeit dgm.solve(method='policy_iteration')\n", - "%timeit dgm.solve(method='modified_policy_iteration')" + "w = 5 * u(grid) - 25 # Initial condition\n", + "\n", + "fig, ax = plt.subplots(3, 1, figsize=(8, 10))\n", + "true_c = c_star(grid)\n", + "\n", + "for i, n in enumerate((2, 4, 6)):\n", + " ax[i].set_ylim(0, 1)\n", + " ax[i].set_xlim(0, 2)\n", + " ax[i].set_yticks((0, 1))\n", + " ax[i].set_xticks((0, 2))\n", + "\n", + " w = 5 * u(grid) - 25 # Initial condition\n", + " compute_fixed_point(ddp.bellman_operator, w, max_iter=n, print_skip=1)\n", + " sigma = ddp.compute_greedy(w) # Policy indices\n", + " c_policy = f(grid) - grid[sigma]\n", + "\n", + " ax[i].plot(grid, c_policy, 'b-', lw=2, alpha=0.8,\n", + " label='approximate optimal consumption policy')\n", + " ax[i].plot(grid, true_c, 'k-', lw=2, alpha=0.8,\n", + " label='true optimal consumption policy')\n", + " ax[i].legend(loc='upper left')\n", + " ax[i].set_title('{} value function iterations'.format(n))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Dynamics of the capital stock" + "### Dynamics of the capital stock" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let us work on [Exercise 2](http://quant-econ.net/py/dp_intro.html#exercise-2),\n", + "Finally, let us work on [Exercise 2](http://quant-econ.net/py/dp_intro.html#exercise-2),\n", "where we plot the trajectories of the capital stock for three different discount factors,\n", "$0.9$, $0.94$, and $0.98$, with initial condition $k_0 = 0.1$." ] }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 34, "metadata": { "collapsed": false }, @@ -777,7 +1002,7 @@ "data": { "image/png": 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vt9lg0CBITIThw63nAQPgiy/UVS4iHc9ZE71pmitaMI4OzxsWZiV6gPh4/3Vf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\njWY2zsz+ZWa7zeypCxz/jJltMLMmM/tBKnVbfHg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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -798,16 +1023,28 @@ "ax.set_ylabel(\"capital\")\n", "ax.set_ylim(0.10, 0.30)\n", "\n", + "# Create a new instance, not to modify the one used above\n", + "ddp0 = DiscreteDP(R, Q, beta, s_indices, a_indices)\n", + "\n", "for beta in discount_factors:\n", - " dgm.beta = beta\n", - " res = dgm.solve()\n", - " k_sim_ind = res.mc.simulate(init=k_init_ind, ts_length=sample_size)\n", - " k_sim = grid[k_sim_ind]\n", - " ax.plot(k_sim, 'o-', lw=2, alpha=0.75, label=r'$\\beta = {}$'.format(beta))\n", + " ddp0.beta = beta\n", + " res0 = ddp0.solve()\n", + " k_path_ind = res0.mc.simulate(init=k_init_ind, ts_length=sample_size)\n", + " k_path = grid[k_path_ind]\n", + " ax.plot(k_path, 'o-', lw=2, alpha=0.75, label=r'$\\beta = {}$'.format(beta))\n", "\n", "ax.legend(loc='lower right')\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] } ], "metadata": {