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@fredcallaway
Created October 10, 2017 19:57
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"\n",
"from demo_utils import *"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Learning a resource-rational search algorithm\n",
"> This notebook demonstrates an RL algorithm that learns a metalevel policy to select\n",
"nodes in best-first search, in order to minimize the sum of external and computational costs.\n",
"\n",
"**Author:** Fred Callaway <fredcallaway@berkeley.edu>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Lava world\n",
"Our agent has found itself in a rather unfortunate predicament. It lives\n",
"in a 2d gridworld which is covered in lava of varying temperature (lighter is hotter).\n",
"The agent needs to find the goal state while minimizing the total heat it experiences.\n",
"The best path from the starting position **A** to goal **G** is shown below."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x10b99eef0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from gridworld import LavaWorld\n",
"np.random.seed(10)\n",
"size = 9\n",
"base_env = LavaWorld(size, rewards=-np.random.random((size,size)) - 1)\n",
"base_env.render()\n",
"plot_line(dijkstra(base_env))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Search as a metalevel MDP\n",
"\n",
"Dijkstra's algorithm is fine when computation time isn't a concern. But when you're\n",
"standing on a tile of lava, you may want to minimize the time you spend thinking. On the other hand,\n",
"not thinking at all could lead you into an especially hot area of the board. There\n",
"is an inherent tradeoff between the cost incurred while constructing the plan and the cost\n",
"incurred while executing the plan.\n",
"\n",
"Navigating this tradeoff is an example of *metareasoning*: reasoning about\n",
"how to reason. We can formalize a metareasoning problem as an MDP just like\n",
"the object-level problem (LavaWorld). The states of this *metalevel* MDP reflect the\n",
"internal state of the planning algorithm, i.e. the search tree. Actions reflect computations,\n",
"i.e. expanding a node on the frontier. Costs include both *computational costs* incurred while\n",
"planning and *external costs* incurred while executing the plan.\n",
"\n",
"**N.B.** My work is mostly in RL, where we speak of maximizing rewards rather than minimizing costs.\n",
"In the text, I use both terms (perhaps an unadvisable choice). In the code, rewards/costs are always\n",
"expressed in units of rewards. LavaWorld is a shortest-path problem, so all rewards are negative."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"initial frontier:\n",
"[Node(state=(2, 2), path=(), g=0)] \n",
"\n",
"frontier after expanding the initial node:\n",
"[Node(state=(1, 2), path=(0,), g=-1.9533933461949364),\n",
" Node(state=(2, 3), path=(1,), g=-1.1421700476015268),\n",
" Node(state=(3, 2), path=(2,), g=-1.6010389534045444),\n",
" Node(state=(2, 1), path=(3,), g=-1.7145757833976907)]\n"
]
}
],
"source": [
"from search import SearchMetaEnv\n",
"# We set `cost=-0.2` which means that the agent incurs a reward of -0.2 every\n",
"# time it expands a node during search\n",
"meta_env = SearchMetaEnv(base_env, cost=-0.2)\n",
"\n",
"frontier = meta_env.reset()\n",
"print('initial frontier:')\n",
"print(frontier, '\\n')\n",
"new_frontier, reward, *_= meta_env.step(frontier[0])\n",
"print('frontier after expanding the initial node:')\n",
"pprint(new_frontier)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see above, we represent the search tree by the frontier nodes. For each\n",
"node, we store the relevant `state`, `path` (the sequence of actions used to get to that state), \n",
"and `g` (the sum of costs incurred on that path). Note that `g` is negative because I'm representing\n",
"costs as negative rewards."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Best-first search as a metalevel policy\n",
"\n",
"The next step is to create a policy that interacts with the metalevel MDP. Here, we'll consider\n",
"best-first search algorithms, which can be represented as a\n",
"metalevel policies that always expand the node $n$ in the frontier $s$ with highest priority $f$:\n",
"\n",
"$$\\pi(s) = \\arg\\max_{n \\in s} f(n) $$\n",
"\n",
"Best-first search algorithms differ in how they define $f$. For example,\n",
"$A*$ defines $f(n) = g(n) + h(n)$ where\n",
"\n",
"* $g$ is the sum of costs incurred on the best path to $n$, and\n",
"* $h$ is an admissible (optimistic) heuristic that always underestimates the cost from $n$ to the goal.\n",
"\n",
"More generally, we can define arbitrary best-first search algorithms by defining $f$ as a linear\n",
"combination of node features:\n",
"\n",
"$$f(n) = \\mathbf{w}^\\intercal \\phi(n)$$\n",
"\n",
"For example, $A*$ has $\\mathbf{w} = [1,\\ 1]$ and $\\phi(n) = [g(n),\\ h(n)]$ whereas Dijkstra's\n",
"has $\\mathbf{w} = [1]$ and $\\phi(n) = [g(n)]$.\n",
"We'll see why this formulation is useful when we address learning."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"from base import Agent\n",
"from search import BestFirstSearchMetaPolicy\n",
"\n",
"# By passing rewards as a function, the cost at each tile is\n",
"# randomly generated for every episode. The rewards fall between -2 and -1,\n",
"# thus the negative manhattan distance is an admissible heuristic. \n",
"base_env = LavaWorld(size, rewards=lambda: -np.random.random((size,size)) - 1 )\n",
"meta_env = SearchMetaEnv(base_env, cost=-0.2)\n",
"\n",
"def manhattan_distance(s1, s2):\n",
" (row1, col1), (row2, col2) = s1, s2\n",
" return abs(row1 - row2) + abs(col1 - col2)\n",
"\n",
"def features(node):\n",
" \"\"\"Returns [g(node), h(node)], Φ(n) above.\"\"\"\n",
" return np.r_[node.g, -manhattan_distance(node.state, base_env.goal)]\n",
" \n",
"def test_weights(meta_env, name, weights, N=50):\n",
" \"\"\"Returns summary data for `N` rollouts on `meta_env` using the given `weights`.\"\"\"\n",
" agent = Agent()\n",
" agent.register(meta_env)\n",
" agent.register(BestFirstSearchMetaPolicy(features, weights))\n",
" df = pd.DataFrame(agent.run_many(N, pbar=False)) # run N episodes\n",
" df['name'] = name\n",
" df['agent'] = agent\n",
" return df\n",
"\n",
"df = pd.concat((\n",
" test_weights(meta_env, 'Dijkstra', [1, 0]), # 0 means Dijkstra ignores the heuristic\n",
" test_weights(meta_env, 'A*', [1, 1])\n",
"))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below, we plot the performance of Dijkstra and $A*$. Note that both algorithms are guaranteed\n",
"to find the best path from start to goal. Thus the difference in return is due entirely to\n",
"the difference in the number of computations (node expansions) that each algorithm performs."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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qnoYPH15mWELM53zcuHHIzMxEQEAATp8+jZUrVwo/+tTX18e2bdtga2uLRYsWYeLEiUhP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\nBDo6OjA1NUXv3r3x6aefCp+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"text/plain": [
"<matplotlib.figure.Figure at 0x10bc2aa20>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_performance(df)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Learning a best-first search policy\n",
"\n",
"Above we see that $A*$ performs better than Dijkstra because the heuristic allows it\n",
"to expand fewer nodes. However, it still might spend too much time planning in order to \n",
"ensure that it finds the best path to the goal state. Perhaps, rather than fixing the\n",
"feature weights, we can learn the weights that tradeoff best between computational\n",
"and external costs.\n",
"\n",
"*Policy search* would be the most direct way to learn the weights, directly optimizing\n",
"the average return (e.g. through stochastic gradient descent). \n",
"Note that the return includes both computational and external costs.\n",
"\n",
"However, policy search can be sample-inefficient.\n",
"To develop a more sample-efficient algorithm,\n",
"we note that the priority function $f$ is analogous to a Q function, which \n",
"gives the value of executing an action (in this case, exapanding a node) in a state.\n",
"Thus, we can redefine the $A*$ policy above as a standard max-Q policy, where $Q(s, n) = f(n)$.\n",
"\n",
"Recognizing this parallel, we can now apply a standard Q-learning algorithm. We simply\n",
"regress the weights on the empirically observed value of expanding a nodes, i.e. the sum\n",
"of all rewards (both computational and external!) that are received after expanding that\n",
"node. We plot the performance of the learned search policy below."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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DJBFnZ2fs3bu3UrupqSlWVuNxKiJtxV1kREQkCQYMERFJggFDRESSYMAQEZEk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\nRJJgwBARkST+D5rkezJSfXHBAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c2573c8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df2 = pd.concat((\n",
" df,\n",
" # weights=None means the weights are be learned\n",
" test_weights(meta_env, 'learned', weights=None)\n",
"))\n",
"df2.name = pd.Categorical(df2.name, categories='Dijkstra A* learned'.split()) # fix order\n",
"plot_performance(df2.query('i_episode > 10'))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we plot the performance (return) and weights as a function of episode.\n",
"We see that the learned policy reaches a high level of performance very quickly."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"final weights: [ 1.444 2.427]\n"
]
},
{
"data": {
"image/png": 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JqUjBiJEQuzCGeY5gf8EeduRupa9rfyxllrdcb3MwarWU7NpF4ebNyKyt8Xv5ZSybuHGE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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c24f748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"policy = df2.query('name == \"learned\"').agent.iloc[0].policy\n",
"fig, ax = plt.subplots(1, 2, figsize=(8,4))\n",
"pd.DataFrame(np.stack(policy.saved['weights']), columns=['g', 'h']\n",
" ).plot(ax=ax[1], title='Weights')\n",
"print('final weights:', policy.saved['weights'][-1])\n",
"df2.set_index('i_episode').groupby('name').return_.plot(ax=ax[0], title='Return', legend=True)\n",
"None"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Searching in a structured environment\n",
"\n",
"The benefits of learning will be greatest when there is something in the environment\n",
"to learn about. In the \"pathway\" version of LavaWorld, there is a ring of low-cost\n",
"tiles on the edge of the board. The manhattan distance heuristic does not know about\n",
"this structural regularity; thus, it will be a less useful feature and should receive\n",
"a lower weight."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x10c257cf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"size = 14\n",
"min_cost = -1\n",
"extra_cost = -10\n",
"mean_cost = min_cost + extra_cost / 2\n",
"\n",
"def basic():\n",
" return min_cost + extra_cost * np.random.random((size, size))\n",
"\n",
"def pathway():\n",
" R = basic()\n",
" R[:, -1] = R[0, :] = R[:, 0] = R[-1, :] = -1\n",
" return R\n",
"\n",
"base_env = LavaWorld(size, rewards=pathway)\n",
"base_env.render()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll now test each of the three search algorithms on the two types of environments\n",
"and at two different computational costs. The algorithms with pre-specified weights\n",
"will do well in some environments but not others. The learned search algorithm adapts\n",
"to each environment and eventually matches or beats the competitors."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"all_weights = {\n",
" 'A*': [1, min_cost],\n",
" 'Dijkstra': [1, 0],\n",
" 'learned': None\n",
"}\n",
"\n",
"def data():\n",
" for rfunc in (basic, pathway):\n",
" for cost in (0.05, 0.5):\n",
" for name, weights in all_weights.items():\n",
" base_env = LavaWorld(size=size, rewards=rfunc)\n",
" meta_env = SearchMetaEnv(base_env, cost=cost)\n",
" df = test_weights(meta_env, name, weights, N=200)\n",
" df['cost'] = cost\n",
" df['rewards'] = rfunc.__name__\n",
" yield df\n",
"\n",
"big_df = pd.concat(data()).set_index('i_episode')"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x10c935390>"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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VFxc4nNmRiOucpxUXo6gqenk5Zn29uxjw9+uHsXcvdjyO0p5ALlIi0mm0UKjA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\nlFoEo4P3oqJSQMpNRp5fZHBfD8oLg6nef8nf4cNX/PT3YkhDdkYM3wF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ptTX4+p9M34PqXwurqGP3ALi1FCwxH+7p6cdjWjXAQ4BeNRW1HD9gQvl3V5VUXg5ZDHCD+p0gcI\nSKEkCVQSDIdRhIdg9usF5PIheg+bjh0tR+LxlW3gEAsJWvL03MLBEciuaCWHGD3MBeHrdB5ZUrZU\nItpkVrF+QgEErmzOIs4v1P7iWPvLe7Fz4E+VRX5gWPh+QcbWjcWI/MkcpjsMdrQ4mDrJQ8hDtDYx\nZFsdNGVZbM0UyvKxwl0OEUoBABKgOcsQWygBsqY90YI35RFweAYkaNHXyxwGlzn47dGt2DXdj4n2\n+rIMLiOxSnslR1j4vs8BYtRYIHIERLn0hZXMA2Upq+GF4P4BDCj+14QvFl1lEupYBguKCGRqIQBk\nCuKDVdkDZV5GEAYAKJqnyHK9PIrhq/dN+d0L6H/+eRnOYFDZHCbhK4L3vFB+vrL4kdze78tFYeAj\npARPHxYnpTTl/kjhZz/7GT7wgQ9g+fLl+PCHP4znn39ev/bYY4/h9NNPx7Jly7Blyxbs2LFj1MZR\nL3Y98AAQhjjw5JNx0V0N6zvo7dUdKKnvp+5T0S3PEARawrcYz2g4wgciwRMPy8L6NglfTZDg4EEg\niZPACOYDAByZZF8p2iMgA8WYxcy5LM0LAJxizs48CIDdR80ByllwMFmvn4OWXASBbDnLQ4SOSfhR\npXTKo9JzysKPE77cjxCEZRchQlmrnYBwLhYCtIxCWMB/7X5ULC5ik33UZCdwRDU3GC59RcyMUZRV\nPQNCwCiRrXwJss2uDIlEx9WVDJWHQbEwDRDrT2vsT4gkMt05D2DwYmVkqUPhUSXKAwJwfZK+HAM1\nCu9AqvQJIfBdSAvfGJ/UaBA9yKhCIjU/I6cAmWUJv2jE8LmK4SshYmiI9iIo3ULAyyjzAIRTZH2h\nFlQldTmNVPoEBGE+L7MWomsfUGl0oQcU20Sowg/l585kGEV8kJrwuViAPLeoGfd9sDOqIskwKsq9\nZ599Fp///Odx3XXX4be//S3e//7349Of/jQAYNeuXbj00ktx5ZVXYtu2bVi7di0uvfTSmsT6niCl\nIA4x8uRNqLh8aa9RfKlUqtjP3BcAuFLpy3vkdnenvsfCYjygMQlfjTooA6EQ6GlLU4JwSfjSbRp/\nDchK1yhNxvABkIKqX68sfEN6zkWlu9Ah4C0ZEBDwck4flwXSKuAc+WKA3f1lcC4IyikFsqgN8Otn\ne9HbJyaUIBQx9WJRLk4QESohQGnAwe9f3o8ij8bUn8sCJERvuyu7tPEKEReR6X1KIa/S8oDIDncc\niiCx6Am5KBurFlamOF+RXlTl1lEnQ0gqJ8iQABnmiwwDAFymOzg8ExM1McbgqNK6XJxHnVYv8AxB\nW1FqBjw/OqYYh7LwVXcADk4cGS4BkgawIm2vyNUAJZkSmGmIQexvNS5RPbAcCgvfoUyEYVjkFTFV\n+moBQtUCCAQBBQK1c0jBgwwmtbr4i+M75AEoQiK6NIIAhUxULVHXQCAEJbm445QAPF7idSTw/e9/\nH+eccw6OOeYYUEpx0UUX4cYbb0QYhti6dSuWLFmCjRs3wvM8XHLJJXj77bfx9NNPj/g48jt2YM8v\nf1nXvmrBQQiJx9RTFiJhXjTiiinw6yB8VUtfhX+8KVPqGpuFxVigIQlfTaA0EOosgkjNrFyiBBxQ\nhA8gojgp0pLebYbEap8T0IGi3E+8N+TQaX6qih8ngCNd8XxATM6EA37o6vcVimX0BRz9A6Eoy8q5\n7sqHkGLX3gEc6C9j+1sD6MuHIv9eNfshxs/Axf6+InpLoT52vjmLny5biSc3deoubZElKfcqlQEo\nhTw04RMeVfOjLHLp68+Xi/rgSogHAOSto0H6urRrXvJPtNCi5YSFLy1cQpBlWanm5wgdca5M2Baz\nvCij8FhE+GpKdRyK6ZPFIorT6F4qlb7nSJe+Xo/pZYIOO4AzhDJJniQYP9CErzQdFBzCmxCo1EdI\nz4Ss9qeOMACCP+0awBvv5hHwQH8fYOwTkmjBEmkfCTih+Pmmw3H/BzoRGguWEBQZj2LWNFddkEg5\nJQT5rGoRLD0LlMQLGEGeKzg4wi+Xy9i/f3/Fv97eXjz77LPI5XK44IILsHr1anziE59AU1MTKKXY\nvn075s+fr4/DGENPTw+2b99+UOOohTfvugt7H30UpT17Bt/ZtPCNGH4yDx8AAkn4vBbhqwVnWqU9\n+V0mjoPsggVoXr683kuysHjP0JAqfTGBcrAAOvUsSMTwlWhPCd9Ml76omion+JQ8fGcgSInhR6Iu\nxgX5MOWW3XUEXP5/mJWdhVcQ1fMvOwT5rGx168oxqzg+Z2AU6CsECEHRV5CLjIRLX6WWgYQ65x0A\nuEuwv53DdylCGiDkHGVGECuQWyqBggrrlPMKlX5IKBxGtEtfYecZSzBjr49i0+t6DKR/CtA7FSH5\no9wmBhJyB0AIUQKQQPvIzQ8bipQ4QrcAIIvmcAZAn9W7McbgSgs/lB6R/e0O8rNysuIglKBfxvCJ\nEMERDubGqwxyHoUSAI4QFEEQJ12FNMIHD0XxH2oSPjGuQ+w5IKve7csXESDUhE8oBeEOUMqBB1l9\nHK3LIMDKwzrw1pQW7Ol7K3ZMDqFNKIeKbIQLnxKC/iwTYkYejUX8KbMnOBfCzuDgHutt27bhoosu\nqtg+Y8YMMMbw/e9/H7fddhsWL16Mr3/967jkkkvw4IMPIp/PozkhcMtms8grq3kUUKtYjt7HLLaj\nHhyT/A2EhUL8PSnnoJkMwny+wqUvmmBFX6ypH/1o3ddhYfFeYlQt/FtvvRXr1q3DMcccg49//OPY\nuXOnfm04Ih/VhpSEHDSIx+51XJhzlN59FxTCCsr4BFM7RJUzkRKmRHuVMXxnQNXNjVz6SrRHOIVD\nBOE7ykLlHjw0YVHTIrgQbPPHRc144MSFKHoUYQiU5Bzc+vYAjntyL5wSEJQDmbFOZDnUyIJXEK0B\nArFgoVQvCMpeCfD6RPofJeAIjfrs4p8gfEe69AEeevJlsfjghIiytwnCf6eToLAystiI+tC5sjBN\naaQs5sNCwwKPwAkQoKxz2ENvACg2weOtgBHHZi6FL9Py+vKi6t3/nNKN7cd2RMfSHgGOoivYLuAB\nqCMm3TDkKOoaBWGUlsddBNqln4jDSwGoN2BY+JyI2LtaJJJAE76+Rk5QlL/2F0VWh6ssfCpIG+Us\neKk5CoMY9/YjJ03DnO4mUGJqEyAInwAl1eOBE7jBACghyDc5kuvFDQ5ljQPAqGnADt6lv3btWrzw\nwgsV/x555BF4noczzjgDRx11FDzPw6c//Wm8/vrr2L59O7LZLAqFQuxY+XweuVzuoMZRF+rRB5ga\nGbPBUoqFn+bST0K1gI4tBMplsQCwOfcWDYBR+5Y+8sgjuO+++/DDH/4Qjz/+OGbNmoVrrrkGwPBF\nPsptK4rQKAtfute19Ipj4LXXQCSpMAp4LsWkFgcOBTiqVNrjQHF/SZe9BYRLv7W4F22F3QCImFMp\n4LAojEBAgDBEuRi50csZMQmGJQ8lV1jVx/1mH3reKGDR628iKAfS801FMRASufQViKjTKgVvVFqg\nDAWvFzyzF+CRy7jkEBxoVtX0xMTEwLRnIG7hi1NRiooY/oHyAZRlb3iXutJ3rwhfH0JcmyR85gTa\nAk9cAAJeFoREywhpCNI3FaUSB2j0BsaYdumXAnEXW3LxA5rEWHLFZx7wEITJDIyAI69qHRCxlBL3\nj6KsRXuQxZQEzLx1l7ig3NGOFm3hk1DoI0LHIFmKslLOl4RbQ42fUBrF8KWHRXwUxr1lohUyTbjk\nufweq8/fDPEUciwmHIy58tWChBEgHHnH3dy5c1EsGiWMZelozjnmzZsXW7AHQYDXXnsNCxYsGPFx\nDAkpVn1FPF8iTHHpJ6FV+ymV9myRHYtGwKh9S1955RWEYYgwlF3FGENGrpCHK/LRYrIAoKGycOJM\nRDhHYedOgBAMtPlQjVEcJu1baeEzbq72pftU5llzHtlkHfldOH7nLwBO4EAsOnQMX1pl4BzlUhlK\n9AVPtEdFkEFROBdAiYhLgxMEQSiJV3gBQCKXfiytnAgFPJeWOgIPJR+A1wsOGO5mgp9unIztK9sB\nEISlEihxRGtZznVanroqTqLQholCkEc+EBOgT4UwkRHHsPCjkINw6QsLP4zKCGhwQjC7aY608EV5\nYAy0YqAUghhk6zgMHoss01yGRQV/KiBd10R4JwgzrkHP5ybhMwSlSLRHSlm9u6p/78DHZH8KQB1w\nLtoy/W7HAdEfQFr4ZKBVu9HBI/V9UZZ4dh0zhq8+Y4qiT/H0kmZQJyJiQggYYbKTYCQIFd8loi38\nnC91FyAoNksLn0f3W98H5WxyRofwzzzzTNx333146qmnUCqV8LWvfQ1z5szBokWLsGnTJjzzzDPY\nunUrisUibrvtNkydOhWHH374iI9Do47yuAomyccEuAZ0DL/GcbWFn6bSt3XzLRoAwyL8WiKf0047\nDYwxnHjiiVi2bBl+/vOf45//+Z8BYNgiHzW50ZCDqvKxJGpWIgZXwsAbb8CfNg3cc41ympHLF1AW\nPgEKHUC+HZybOdmIEdhkt4gzj58qDHEKMEX4REy8PAhAuXDLcxV7B0DKPooejR0rIK6w8CEWDGJH\nI4wgx0kJwGkgxstkJ73ARdmT5+bAgQGRdheSuHWJMJQWPhFpeTrcIXYouB5oCuEDwJ8LooNYjgm3\nrENcgFN5XSr8ELn0KS3HBGUKmQOHY33nSfp9IREx5kIxrHTps4iofLfyq5kU3AFAgABghogKRHgj\nVLMkQsBDB+WyYWWXDcI3UuYAoOznAE7QVwyxr1DCrn1FiBa2nqiHwAhAAEJolBUhiwzlPLlgodTI\nYhDX8dzCZjgLZ8fGzgiTojvD3Sz3L8miUhuOnoSZnb5w87c4Wt0/pc1DU7NRg9+w8Emqq2V4OOmk\nk/CFL3wBV111FVatWoWnnnoKt9xyCwgh6OzsxK233oqbb74Zq1evxmOPPYabbrop7tEYYdSyxCsQ\nSzMJ0136Mvd+qC59beGP4rVaWIwUhmUK1BL53HXXXVixYgXuuOMOdHZ24l//9V9xxRVX4Hvf+96w\nRT5qcqOJGL7OuQcQ7t4FFobwZ84Ee+H/tIUvU7RBywE4DzVBm5a1qwvkCEtNka9HOaa2uniHSwtf\nicmkTgCci+PxqJyqyN1ydFU2yBGGxEFYFkWANOEj1OPwCtMwI5vDvr5XAFIGB0NIRUU8hC6m+AtB\nDgygLduGP+WfRbkcRpO+MfdQ4kQufU3GBL9bNwmvvXE8zmYhUtoJ4K3CmwCAYyevxrsDu/FQ0Azw\nA1EqGERcmZfaALwL6oQIKZfqgAhOuQs5NyM/D1kJLnSQL4cgzEzLo3ANC7jFz4AjPS1Kf44ECMIA\nIS2Jz42EsrQurXDpl8oEcKRLXxK+6PIX91gEfg60nwAOQchEOWC4ATj3Ac6iOgIkctVHhC+9Hcbk\nb+bbJwu5MOnSj9IKReVCCqAkXfqMipS8gBOUWhzwYgBwEVYiDkEoc/i1hU8BNgoWPgBs3rwZmzdv\nTn1tzZo1eOCBB0blvGmoZYlX7Mu53p8bpXBj+0hFfj0WfgyByGixnfEsGgHDmhmUyCcNF198MTZt\n2oQ5c+YAAK699lqsWLECL7744rBFPtqtHHAoA5UwoXovq5mvLB5g4nmgRJSeNYvpvP8Hb+AN534E\nbQMxhuKcwJNx4KzHUCxDv04AkFIAEoqKca7SDRAqFgZhqD0GOt4cCstY1V1XYAFHEIjCtGGocvcd\nzdaknMVH51yI//fuv2Ef7QVCggBUeyN7mo4GfbkFHR0HsN17Du9M8vBOe4fwNCByKVPCBKFwGiP8\nAY9hwKcVFn6HNwl7iu/qv2fnZuPItqPwU/YyEMhcdFZCCI4m1oRQCcRogLdWzUD7Q3vx2owMZv2p\nAICIdDvq6c8jpOIzGSiGWl8BqEp70d+fWvR3eGrfU/ivd0TO9arJaxCUCV6e/Q76s1KXQRz0lg8g\nI69PE35AIUr3iA8rCB2US5LwCQFkgyNGSUT4aqGYaQIFZB4+116aIMyIz1B+94fpEtQAACAASURB\nVBghhkhSnKclK7UBSrQHRIWJAFA/ThgVLn0AqnZ+Wbr0qVwMEhCUWx2Eu4UFKqoXSs8NIs8Wdwic\nUuOSz77HH0eYz6Nj48aa+w3Jwg+CyI0vCbrieIrwa6j/0whfW/juyNc+sLAYaYxaDP+NN96IiXwo\npaCUwnGcYYt8CBEPHg2hXfpgTryKWiAeXEIpmC7oEif97oGXZUW06H2ci054lBL4brKSDQEtBaCh\nsFRdU7RHAIQhprQwQdqKvAIX4ASlhIXPQo5QqvTJG8eC7J0N8sYxyLhSBKcarhBHi/YCEhVdcXLC\nSg2KPkAIfnnCJOyYukCmIBpDZgz0ubNAnzsrsvy5DDmwEpLV8bozUaUwAgKfCXJ0KBEWrrhQgBBk\nWQZqzUhZgHfnNONHZ83AW5MjlzmlFIwwLbQMiXC5F4pRsRIuK/xlZJiCUqDJbdZpegCwqGUxpmen\n47dHt+K5Rc36s+kP+kVkgKtjAWFINQmL28JQKOpbKGLcgSf6BlCiQxHEcUA80fwoAEfIQsCRwkue\nBUImCwIRUEorGtU0qXi7KdqrYeFTIpoThazSpa9Ee5RQTD7tNDSvOgbwma62SAlBmoCPG9/3RsSB\nJ5/E/ieeGHzHOtLyFFTqnP69hoVfSxuQRvjl/ftFSp8V7Vk0AEbtW7p+/Xrceeed2LlzJ4rFIm68\n8UYsXLgQc+fOHZbIZ33XBjQPLBGDN2L4hAn3KAgRlqyh0FWx9hBhzFoHVJtbuaswj0EDIHBkUVmT\nPAEQ2XyHUwJGRRhBifZ4GOK0VZMwpc0H9eS4Qg/gDEWfxg7kSAsfHODlVtCd60BKTThidjNyPsXS\nuS1iV+4I0R6Ey14tT5wmMfmUChGJ8FBUeIsJ/R0HpJwDCTJG6IBo1TxofOL0aHS85R0r9N9MpiYQ\nRnRtAwoGUEVyAUphCQ7x8eaULPpyYuFTbmqV1mjUZAehi+OPbI9K10IQX7PvoLvDw7RJvrwfhgcA\nTCx+DPg0o25cFJIBkWV0uSb9IKAoFDnAmSR8BgSunqMDKgiUZjIgjgOAoEwIgpa3I8IvN2nRIoEs\nQUzj4WEnmZaHyGIHAJZi4YvPRpBMe5OL968UldqUaI8SitZjj8WUU08V4yAAuLgHXC84CHggvGOc\niWyDRoHqO6/Ay+X6cuyHaOFrq94gfxOqjG5NlX4K4edfekn07LAxfIsGwKgR/mWXXYaTTz4ZW7Zs\nwbp16/Daa6/hlltuAaV0WCKfw1oPByGCEEjIwaRKf8Gs5sjCJxGhE0JAq1j4gNLJyRQ9Kt5Muark\nRmKFWggBaCmQoXYCKgvXcFXcJwzhUw7PoaBqMg6ES7/s0ViPd58ThKHK94/QnHExpc2L3MOcCSuc\nhghAdN93R5JHKZ8F/dNq0JdORRjK6zZU4mZsUVnZBAQhCDgrAQmXvkMY3te5Ad2ZqVjXuT7azsRK\ngnkUriMWQoQQEBq59EthEQ51kfczeOikKXhg4yz0TuqR55aLLkrwkRNn4qwTOnXTIC4XTqI2PtXe\nDWqQJSUsIlR5FR3OFH1fVNN5TiCq6hEOtItFU8CFSJCBic+FM5DA0983YakLwqeuCKsEBChlJPGU\nMwgHpggPBxOCPY9RNLe6aMlGixAmr5GQ6AsYdU9IJ3xKIwufMYKmrPhul8K4S199Fl2TfDRlHfE+\npfXc1wPeP01cPyMxz8h4x95f/CL2N5d57YPF6IdC+LFiOlWOzQ+S8BWSCxcLi/GIUZsZPM/DVVdd\nhauuuir19eGIfCiaxM9A/Js2yUPnnBY8+JIS0RnrGOlSLgFauGeCBQkLX07QgUdBCkqAFe1DSmVQ\n2YaUQBB+AGlxyfr9FBTZJmGtvr1PED6lBOUMRXsxA496yJSyCIP9ghCMhQBTJTrlts7WLF7pBUBL\nCMDAeVmEFnJZAL3oLwQg7y4UYw52gBESF+0ZQjgdw+cEXLT2A0m49BlxcNyUtThuytr4dgoZwxZ/\nq9oDRJEcDVDiJWFdclE4p+D5cLTlrbIoxDVRSrTqXrm9uzNT0ZObhaPalhr3Q42LwTFU/OAEk9xO\nvFPcAV0YAeL2hQBAy3jijBn44+v9CN50kB8IQImo2ERCBh54kVCPASQgoNksaNlBCFHad3eHXMwE\nvliwyBg+AQCHoq3Zxf7+yBrVlRcpNdLyDAs/QRgOcWThHVUEiuj0rrJh4QPR9yHjUmTlYpBT0b64\n9wAT4kBZk8GhjWPhJxvUKOuel0ogVbrVAUMkfKOjHa9i4dcl2qsxHguLRkDjmAIGGBWET0IOEgq1\nPHUcHTbnhoUFSsFYVLI1aVErgZ7cVWWboewRoJBw6ROAFOTEIN3AjBKUCNUxfN2whxJ4DgFCT7jC\nCVDMUNASRYZl4CNAGITxxQkiwleWXVvWR0+nj7f3lqBa7xAATkZMPv0DxsSnmv1E6xbAqbTwIY8D\nWq7Iw0+6zaNxiYMq0VroSLc+ZcK6ZsKl79IcSFgS4wyZzmSAtuYJMq700CifOlFCOIYts8/X56Qm\nWRIKx3Dxg1NM8brwQlGFYlS2BkDk5/3n0lso+6JQUW8+kBa46LCI0IslECqXPiswhCAoE47eJlXL\nl4jCTiET2kASEXNThqG/EKC92RG1CtR1qbWVcX+TFn4yhk8IEfF3blj4pNIJRygFCQlCRtCac7B2\nxRTkf7UfKLag1ZmC9mBWyh0cn0gSrCJyXioBI0T4sVS8aml5auFR7biEVCX83JIlyC1aVP94LCzG\nCA2pNFGET0MOUXNFdChTLv2oRp4U7cmJOERo2uoAgGwhRFAWPcwpjQLgAVNu5vi5yYAifDEZu9Id\nTCAmL12/n4n4LNWET1DKMD0uF2XwMIy5+YEoDqysW4c4ehwBpZFLXxJ5/4AxeUmiEyEN6RZn6RZ+\nKOITFaI9FnObG+NiMkwgV1WBIz0TDgW4A9AyAh7AY552r4MbhK/uAQEyTBYA0oVq0r+GzIzhk6ib\nnrrWTl/2HpfeB3GNAHnz6FhnOsIZgpBrl7sS7RECIPBkVEMQvuMLkaUoFBQtkHKlXuHSlzF87shM\nAUowdZKPjMeQYUpTYMbwTcKPxIzqmgglQhwI9VZZbVCK9kjKI0pZtHgS18jgZ1wg8HDclE3INJJi\n3Cxiw7m28JOWf2HnThz47W+jfQchfFOJz8vluIV/EC594rpVhXldH/4wWmyzHIsGQEMSvkNkHnXA\nwQLZuS1p4asYtiHai6XjKMNzIIsylwsIk3uZcLGabmVCCJTcmxMCCgrHkb3NpYWvJhPHEaTmwANC\nB5RAKvXF8Twu3IwcScJXaVhU/h2Vyg1BEYbiehWRqraoclBCPGiO2XDp0+gDEgsfVgYn8QmuqoWv\nag7I8XGXSrW6sHxDJsRtU5qzaMn60rsRVcsLFeFTgoz8bKg6VhXCT8bwKYkWTOAEHZ7sUmjcb04I\nyIGZaOo9XJ6D6AWIvjZOQXYtxiwcC5KfBCqFm9T34eRyAAiKrtBvPLuoGeAEezOThGiPEVAQcFY5\nZk34hBiEH12Dk6kkfDE8VcefaDKPXPqVuhalfVDrKkYoli9qQ1e7h67JObhO4zzWsWeyRqe6P995\nJ3b96Eep+6bCeD22eDBT9MxxJF36ic+d+n5F+Vy/pwetq1dbwZ5Fw6AhXfpElmAlYdQtj7iunhxj\nJEopmNw/TInhA0CZuvBRiMXwVfpThUpfE74Qb2nRnhHDBwDmeACKcImPUtG08MUBXZQBzmPkDAAu\nM4RfiEiKEFHERbj0iempNz8ZuA5NxPCZjmIwx1CyE6Rb+KSKha9WQyoV0XWAohQFhgwB7Qfgoj2X\nxfJ5BE/++S2UQgZHNqch8jo4SHSNSlBYpYSu6c6mRGgxoCQVnMJzGI6bfDyct15DQJ9DCO2g0Qp+\nKtMJxTUoC5+BFCZhIVuMP4avy0wNkZbnLDwa//1iiN3tj4IR4JnFTfjTgVOx358E8Gd1SV+eQqoZ\nKgg97tJnaMowZH1ahfClSl9+9SILv4ZLnzkASlEBKjC4noOMR0GYOF/DoEp3usGU+oNZ+CbJc7MH\nQJpLn5BogSGPS1w39j7qeRWLgGkXXWRr6Fs0FBrz2yrd1DTkcNSC3Iny8FWpW/ECieXho4JbCELC\n8NisTQg7puitnBD4n/wIXj/lY8aeAAYk4VNh4buMRCEE6dIHANcR8T6X+sBAKwgB9nX7IFKF7fAy\nRA2/+C1wEjF8JcBSDVvkJenGPTFwKixr06XvGipyRbBcqsdpqX4LX362by1ow84jWpGfIr0sjIHw\nyPL2qAuHOrLyIIsWCqr1LSJPDNUx/GoufRb7Pb4YEWr+93Wtx9KOo6EiB4rwMyQn34fIwlchAVn/\n33UImnwfNBTXRxwHmaYM3mqeCXDp8ucu9mcmy45rVNbSJwhrWfimS59QTG51kfMZHDe90p6w8GW6\nn2ogpAvvVJJ3pUufak8OYQxrlrSlfp7jEdXa0ZoWfmgQb9q+qcc1Xo+Rf4qFT31fn0M9vzQRFiGe\nV0nu1rK3aDA0JOETR7jGaQgw2fXOdOmbBEJYFPvlCI0WqxJcuOTfbu0BJndFjEEBr2MSWIsxeRKA\nSws/lOItxkSsl1ASiw86rnBb+5LwKQF2zc6BXPYROG1tcEJRdz/RHC9y6adY+DSIisnk/DTCF0JB\n02tAEy59oo/AwJvfwp8KO2KHYIO49Ac6cthxTLuuLEYcKixmeUqXeEJ3AABhZQyfI3LzRxZ++tfQ\ndJUqwtcubk70mECEWt0svJR15ILEsPBdw8IHAJcRHLd4ElwC+C4ThO9RvY8QYorrZFSIEDkjIKDp\nFr4k/Fg/A7lIYYRVpHVRiHNwI4avFqdlaeGzlMUQ1S59oo+tyCh2DQ2AaoRvknR5797K9w0WwzcX\nD6aFnwgVAILwky79ZOU86vtxgifEuvItGg4N6dKnVJSJpQGHIzuVEceJyCDxYCq1t2nhG1FuhESk\nzQkhnPQSMNEa1nPNPQHIJhs6hi8nXUopgv370X/gAADAc8Tk7hIfJMgYBM5AXBcs7BPirwoLX4r2\nlIVPVLc0wAmiy8t4YsxhaForMoc96dJX45dExDkQENHG9/m+Z2JxYqeGaA8Qor4QysrkIp5sWPgu\ndeGErrSOHUOlLwmfROJKwlLulwFmxvBBhVufAkEIgEf5+iAEWZ/BC10dM8+xJhQgIxCGhR8CWuDn\nMIpmPyOseyn8jAhfeCmIJPxywKEL7xCC1mwHgH2x8epCQEYdBECJMBmo62LqBRfAaRciUVV4hzuh\n9OgbFr4kfJJG+MxRUQ15bBp1a2NsSFXoxhyJHHn9u0n4e/ZUvG0ohB8OQvjE88D37RNkr1z6nhfb\nh3pebGFqXfkWjYiG/NZSIkiahByMyInRjSqnxURrlEYuUNlW1YSKjTMaxbjVCw5x4Jld2wiAvBCn\nCZU+wcwpPqa0eSCMorx3r56clGgvI0vT6rUIKKjngYVlEM5jKn1KiRYY6gWC8fe7rcJNvbvnSBBC\n0JyM1aoKbAbnMzfNwucV2QEKg8XwlcWp1P/UEc2B1Ald6sKlIrMAIdNW+IH2Drw6I4s3OiOPCdOu\n6fRzKrKjsjESMxcLZrhAXku7Oxl4S6ilm13xWZkWvupXr9rHMgoc0XYksiwnwhCMISsJn4QOKAgY\nNyZ+rix8gpZMBy5fdCXWdZ6oX9YWvtlIhSoLXxw3O28e3EmT5DbxWnOzGeYQC4wSl6V101T6KRY+\nk30oWDZbsf94Rozkq7j0S+++iwoMVpinSgw/LTxgdsFTFv6gLn1L+BYNiIb81lIqrfIQIHJiNGP4\nsZgwpZGFD15hTepYNyVwXWa49EUBE7NNK0Hk0hfiLYozT+jCtefNiU0GxHHQ2tYNRhiaWYs6HACg\nL+gVFj4vR536JFwWZQVocZ+y8AnQl8ni/sUfxVtHCJJpykbEctLySfjAMUKDYGYpmC59R4ZCOIC2\nvuX6mkw4VcqyZv0oDQ0A8vO70Lx0KQbaOqWFL8dLXThEWfgRKXMviydWtqG3uSn6nCTLpbW9BSKS\nZIZbXFv1+Ul6zo1S8KLrbvJy0bYwQfhc1ewnmJadjoUf/QTcSZPRvHQp/ISF78Ag/L4u5Ohk+NQH\ncRxkWTa2QPJVWWJDQ6LEimkLKbXN88VCRpTsFecvhzVU+vI6zBh+2wknYNrHPganrXHi9wCEcFXV\nua9C+KkW/hBEfYNZ+FRa87xU0u8zLXy/pwdNRxwRmzushW/RiGhMlz4BwqAZNNwPP98GYL906csq\nXUkLn0ii4xy84jkl2O93gBKic9sByG54DjwngJouCKPgBeXSj6wvUTWO6v7rs6++GjMox1FTVuCh\nPw0A2IcTWzfjZf44FrUsxj73j3AZhROWUHAii8xhRKuy1U+dlkfEScvMlcQNNBuEf8baKfjfva/j\nj29CK76BuIXf05kFIUCpzNG7cwlody9I187Yp1HNwj/l2Mk4Yk4THhngQAkIutrRufIs0B//CSgl\nYvi0MobP1MKFRwsK5XmpJtrTnwWin8oSJr3dUQxVL5Kie98iLXxRIVCcZ6rXA8/rxetlqeCXb29a\nsgRNS2R/Bl1zXRC+S33dpJeUmjCreSUc+ri2AM0FkhpPjAyMxUoSapv2OhGAOeJ4qgS0qdL/5IJP\n4UDpACh7GGVEpXUpGFg2CzarcQruxBCGAGNVY/ilg3HpmxZ+CsmbIAbhI0W0N/W880AzGZR2747e\nZAnfogHRkIRPiGhmwvbn4KINIPvjor1EWp4qdcrBYx3G/rioGbtazsTu3ZPQSgHHjfLklYXvuRz7\nMh3wywMgngs+0C9fT6RMKXW954E4DlwA7V4Hsp6osb2wZTE2dB4NADjgeXAdAicsgpOoJbDDSKwd\nKhCJ9sSwo9gzgJhLX9T9Vw57Y1jGImbO9CxKMubfXwzBy/E4pXm+JJoyDIt7mvDzl8SE6EnXs8MI\nMBARvkelaI8gQfjS0jUJ31Fleavl4cctfFGJTrlKoq5+mvBJlJLZ5LsQDh0CnzkoAjiqZSUWzFiH\ny7lo6UxTPAt6ERGK+PqyuR14pzeHedOz+Mm23TrrQaniUxdIlOrPQ2UipO2nvj9RVeAooyT6DKL3\ntbntaHPb8YYKhejPtrHJhwcBCGNVY/hhopW2ek/NY5oegJS8exPKpR+aFr7p0lffTxvDt2hwNCTh\nix7iDDQI4HCRwyxi+BFZK2irSxK+uRbgBGCZHHhMtAchbFMxfKeMn8/dDAD4zMCPwYt5AFEt+Yrz\nJMpvrlvajtYmB9MnR9uJ62riMmsGOIzE4taAIdojRDODJ3PbTQtfvCcav26eY7j0507L4SUp2uMg\nQFBZKrSaha8QcpmFIAlfxcjVVeScnAhbCPk5POmNcFQbXRiEnzKRpl2PWWJXx/BLUWggInwCLkMy\nGY8BA3JMvo9iHhXq9SqRBAEuFi2TmnI49y978Po7Bfz62f2Y1C41GfJzddIa1RiFd6AXbHVY+AAo\nS6jDUwvvyFoIhku/oaFc+qZVblr7Uigbw1AIfxAM5tLXmoyEGNjCotHQkDMFJUBIGCgP4agYvmqP\nK/YwdqY6hYZzrq0iQoCmJoZNyzoBiNi061KoQvQqFOC7ROxMCJgxCahueRpyUqAJdW9nm4f3r5gU\nsyZN68EMPziMaGtNW/hGpT2lL5jZKUinKUn46rqrVNrrnuSjq91DZ5srahUElRZ+tdK6CgEXE6JD\nlPKdxER7M7Iz4RIXWZ9i1aJJOGqe6l0vFwiGhU+0f74a4VdasO9vPwf0/z4Y24+YFr78PWukLTbL\nPvVZP7lAqjFpB4LwVVx+ZmcG//LX89A1WRbX0few0no00/JUVTyWkk+vCD+MWfhJwk/3IIj3ker7\nNBB0/fwqFj5Py8MfKcInJObS52EotsWEl0prYkV7Fo2NxrTwpUqf8UAK30TMjaVZ+LKmvWgJG7fw\nPZdh5uQmAH2gFGAyLY8gmqhNlT71DKKmcQW1Fo55lSRaMX65j3BBR8dwWNRlTR2vzW3X+yrCnztV\nkE5Spa8FfwkB4dnv60LGY6CUwvcYwDm+eOF8vNwX4Jd7/xA7RjWXvoKqVqjIymEEcPIgAFzqwaUu\npmVnYIo/BafMW6SrvinCN/P8dVYESyde5c42vQ6L2uaB5F+J7xgjbmnhuxTHTlqFV/tfRTGbwevo\n04uAvz5lOv77mb1YMKOGop07ICDwWdwLoohALaRU+lx84MZ9pJXXoJBm4cc6AiJdpa/uLzdK6zY0\nVJ37KjH81MI7Q4jh1wQhOl6vYviERXUNIFs3q9/12yzhWzQgGpPwKRAQKi18+eAbzXOSKn2VF53m\n0neZisUKqz7jURRJJCiLqfSdSI2uVPpJ1GrpqfeRhN/W5ODdIBqQ6wjV+MxsD2blZgMA2k3Cl+ee\n0iYmqGQJVe1xIPEFz/uWdhgnF69NbvXQ57QAiZom1QrvKCiXvna3i+40IITg8FZRv747042/nf/J\n2Ps8IlzwbhhpFtRnXG3y1CmABlm25NJd6ArKws/4FBvbNgEA/tw2gFWHtSEnLfwVC1uwYmFL1WsU\nKYXiPB6NL+B0RTtN+JWWpFmQpR6VviJ8UUs/QfhpZJ608FO8B40EnkL4w7Hww1IJfc8/X9e5CaXa\nW6Nj+DSqaxBbPCeeKwuLRkNDLlMJEeVwCQ9BeRnEcaRoTe8Q29dcpQfU6KJFI/GZWBcQdLV7cBjV\nuc4qXg4AzHX1goGTuEtYTVb1WPhqgmnNOVi2sBWH9QgyZJSgzW3HeXMuQHdmqh5/p98pwpz+vuia\nUOmi1p3VzEkqMTERuQACgCyLLFxFbM4g7mHl0tcaA0ZA/rwCi93VOKn75Krva0U36P99EM39i/U2\npkR7VV36ldZxWoVBcyJWmoisEa+fNsnH8gXVCb7yvJCEz+HR+AJOtUilMt+92REhC3W/xIuRaI/U\nFcNXF1K5X1o1t+zcufBnzhStf9H4MXzt0k+ppc+DINU9X4vw3926FfmXXqrv5AbhK5e+aeGbz0/s\nWbIxfIsGRMNa+CGhIOBwgrJ+YCMLP6HSRxQTLxOuM6s5iM7NZpRESnsQOLIWvhez8I1Ws8QgWEQu\nyGo9s02YE4fnObo4jVvFtT2naS7eKryN5tYS/vqMmXq768T3j9TsFJCud3PMYoBRnXfV7AUAPOqj\nGBYHtfD1uRDF8Ek5hyOza+Em4s8mHEpB8pPhtJsufaM6XAoUkZmETwjBSSsmocXULxgLHEX4Ge/g\nLTBKCUi+HZS76PQ7Y69l589H17nnIjt/PgDgsNYlKIYDWNAS9UOPWYVUVMVLV+nLGD4xLXxRQlgt\nrNJi/21r16Jt7VrguS+LfRqc8NNc+srCT3PnA6haTTDI59H7u9/VfWpiuPRD5dKnNLXsM/FF/QVe\nLtsYvkVDojEJnxAEysIMiyAsnlcdi+FL614RfmB2hyPQhU4ojWpjd3iTMGOSKExjkjBxnJhL35xo\n1QSVLMmZBpOECSE6dc2pQvgndL4P/UE/jpm7ClOzkTq9u12cS3kIIvFaDQufEN1PwLTwfeajt3xg\nUJW+gs6Rl7tXG7uC0lcw496oSnvVapIzkm7Bbl7bmbY7gMilP9h4aoFSgPTOwPKBj6Mr0x17jVCq\nc/bV2JZ1rIgfwCi8Q6no9pBGyhUWvj5mRPjVvB/J/RsZaRa+WkCnufPN9yTR9/TT4EGAjk2b0LJ8\nOd78zndQfPPN6idPWvhBIBagyY6OkM9qWxtKu3fbGL5FQ2LUvrXlchlf/epXsW7dOqxevRrXXHMN\n+vr69OuPPfYYTj/9dCxbtgxbtmzBjh07ahwtDqXSBwAnKGkCTY3hS4W9dukbLXI5jd7DKPSq3aUu\nWrzW+DGRsPBp5DUQG6Ke6oMhqQBWJOg46STlUR+nT9+Mqdlpse2tTQ6+/LH5+NvTpotD6W566WNW\n54vK9kavtbltyLDMkAl/+mQfrkPR2V57oaOvMSaopLGfSRBdcGeQMRmT71nruvEP586uvf8g0CmT\n4cEtGojhRaHEBwFBluUq9jNj+OZ3yVwc1Mwk0Ps0OPkoCz9Fpa8s/OT3uBrhqzK82blzwXK5OGEn\nnwXEY/i8WBQufUpjoj0TrLU1NmYLi0bCqM0U3/rWt/CjH/0I3/72t/Hoo48iDEN8/vOfBwDs2rUL\nl156Ka688kps27YNa9euxaWXXqpLbA46aFlaFwBYUNIPLEtx6auYdeTSNyYVGfd3HSpcwIOk3WjB\nFoh8b+U+Q4nhq/G5g1j4tdCSc+A6cUs4Zn0k3eWEpF7b6dM348I5H69qbSehyGrZ/Bb8f59YgK5B\nCJ9q7310/GxG5rI76YTuUhfLO1ZiafvSusYEAM05BzM7M4PvWAOfOG0GZnZmcNKKSQd3AEMn4dAM\nzptzAdZ3bajcjciCUInbYS660lT6FcdpTCmORi3RnrLwaaJHQDXC1/urhbfxXae5ykUXCAFrEh6y\noK8vUumnWPgA4EjCDwzjxcKiUTBqM8XWrVvxt3/7t5g/fz4ymQw++9nP4mc/+xn279+PrVu3YsmS\nJdi4cSM8z8Mll1yCt99+G08//XR9gybQhA/AsPDVDnHiJkaaVGC8xIlYPFy6eSbOfl/XoCpcc5uw\n8A9SpZ8Q/ygSNK3fg0FqHn6KSz9NcJRlWbR77fWfy/j8WR3jZqYnRaKjzUd3u4d5M5qqvAs4eeoH\ncETbUTWPTZILvGFi3rQs/uHc2ZjUUl2TUBOGhU8oxYzsTOSc9GukhKZY+Abh1+FxafQ2ramiPWXh\ny6I71Qi/8Oqr2PXgg3rRoD0Cqn2z8f1naYRPqe4/UFYd81i0+E9+n5glfIsGxrBi+OVyGf39/RXb\nKaUIggBZ4yElhCAIAuzcuRPbt2/HfCl6AkQst6enB9u3b8fSpYNbc0qlL343CN+ouKbqoZBEnDjW\nf17+PneaGOe+WA30aMePvn8aSuUQ5PUd+o0VhXfUtddD+GYMn0Ytdqu5SbXAMAAAIABJREFU9OuF\njqvTysVQtBMFMTwpfznjQzhQ3l/3OXzqYyAcQC7FRV0L2qVvejEohe9R0bRoOKhy38YKxKi0RwdZ\ngGRZDn00/vmbFns9Lv20hWdDoUYeviJ+ls0illkvCf/P3/oWAKDpyCORnTMnWiDI59Ak/JiFTwjA\nRTopzeVAHEcQfsLCT3rIlIVvYdGIGBbhb9u2DRdddFHF9hkzZuCss87CnXfeiZUrV2LKlCn46le/\nCsYYBgYGkM/n0dzcHHtPNptFPp+v67xKpa8QufTVhojwdQzfENsp8MRkGldXR7+vOkw85O++GVW9\nS6blJcdSC5UxfPHrsC38FJd+haciYeEvbj1sSOc4f85f47n9z2JRy9DepwifJgSVcuOQjlUT44Dw\nISvtcZDUev0m5jTNxTOl/9UFjQDEUgHrybEfB1c8LCRd+sR167bwFdTClicsfPO7ZVr4LJcTVrrU\ntDhtbQj2749U+tUs/MS8ZWHRSBgW4a9duxYvvPBC6mvFYhF9fX3YsmULPM/Dxz72MeRyObS2tiKb\nzaKQaIiRz+eRS3O5pYCaFj4iUtMEXKXwDhBXRPPkTJmSzhd7OZaWR1Itq2Qf7TTErG5C4ErGT6bZ\nDRXReKqL9qjvD0twNNmfghM63zfk96lFTcz9X2VSHSqqLdTGCkq0xwkdNNwxr3kentn3VGxb1snq\nPgD1CPJIo1N+orQua2oS1jbn2kU/aAxf/h0Wi7He9TELPxNpO6gkfLUfk+p78Ue6Sh8AWEv99Rws\nLMYbRi0t7+2338ZFF12Eq666CgDw8ssvIwgCzJkzB/PmzcNPfvITvW8QBHjttdewYMGCuo4di+GT\niGTV5EooAeR8oFbrkUvfsPCTk/EgxBE9/EJolTYZD9XCJ5SmCtoOBno81YqFAOg888xBu4eNBtJc\n+u7kycjMm4fswoUjd6LxZOETMqjzYk7T3IptZrpkXS798XDNw4AS6yoLn7W0oLx3r1DNK8LPxIWY\nPAi0Z8B8Ly8WY8LZZJlpBZbLiRCBElfKOD6AitK6Jsz9LCwaDaNmDt1///343Oc+h76+Prz77rv4\n8pe/jA996ENwHAebNm3CM888g61bt6JYLOK2227D1KlTcfjhh9d1bGao9AlSRHskQdwJC19Zwlkn\n7lGoqW43zkNIZSqV3qcewk+03nQHKbxTLxQ5xGr8Jyx8f/p0+DNmDOs8B4O0PHzqeZh2wQXIDZfw\nx1kXMxXDr8eln2U5bOh6v+6ZILYZhF/XIzr21zwcJEV7jrSig/5+beGzhIWPIEDQ2xsdQ743HBiI\n62gSi2v9u3qW5bYY4VMavZ6M4be0oPPsszHjk/HS0RYWjYBRI/y/+Zu/wbRp07BhwwaceuqpmDdv\nHv7hH/4BANDZ2Ylbb70VN998M1avXo3HHnsMN910U92WiutELn2AVObh0wQBJGL4lFBM8Ttx6owz\n4gceRO0dkSdBWEW0N2QLnxDD+h3e7dDx3kSxoPEAmqLSH8GD61/HhbVLKQAi2i7XMZ5Vk1fHSN7M\n2a+v8M44uObhIBHDV3Hyff/zP9j7q18BSHfpl/ftiw5h5O2TFAufOE562q0ifEOMR2qo9AGg+cgj\n4U2dWrHdwmK8Y9TYwPd9XH/99VVfX7NmDR544IGDOnbGozGXfqTSl5vSYvjEtPBFVziPJRqjDKL2\njvLwxX8xNbXvIxwYgFOHqCcp2hus0l690Cp91PZUjAVG6hrTEDvieInhE1Eyt94FDmtq0ipyk/xr\nlc39UM+H8eL+F9Dld1fdpxHAzcI7lILKvPgDTz6p90kSPgCUZZEdIKqDX+HSV7F4160IpZk/Y676\nGip9C4tGxvgw/4YI36Vx0V6yln6N0rphLWFeLXV7YlvSwp952WUo7dlTl4o3mZbHRozwlYahdnWx\nsUCqaG+kMM7S8tQirqPVx/wj6ov59vz93+vfMzGXfnXCWdC8EAuaR1D/MFZQLv2SqJpZ4b5Hiksf\nQGnPHv07L5dTy1urxQRx3XRRrorhT4qKLMWa54yDBaSFxUhhfLDBEBGz8BGRmhbt1bTwCZRNmHT/\nklqLASDm0hfNc4xiKc3NdafsJFX6C2fksGhmDgum1+jPXgdSS+uOEwtFx/BHwcI3MS4maPn5d0/y\nMWt6fZkn5rjNGgcNXza3DphpecRxUq35eiz8MFllD0YXSyPVT3XXFC+kx/CrqfQtLBoZDUn4nksR\nmBZ+RaW9RCyeEE2GyqUff4Paub4YPpHnONh4cYzwKUVXu4dL/7LnoI4VO67Ow6+u0h8rTJ/so7Pd\nw5zu4ZW9TcV4sOoNaDfyQS4+TJd+w6fc1QEeBBh4802Udu+GP316/YS/PypYxMvlSNFvWviK5F1X\n5/QT162I0RNKZYEPUWlvVGpEWFiMMRqS8DMuRUnF3wn0Qxm5tBMuXln3nsgKeZryEw9zMraeRKQV\noPCcYRDXKOWNq3gvSfF+jDUmtbr4wkcrU9BGArHPcDxM0Op7eJCLrRjhj7PFzKggDLHnF78AOEf7\nhg0x9z1rbkbLihXx/hOyRa1Z3jYslSJCNwg/NAjfrLNPEi59AHA7OlDavRt8YKBqLX0Li0bGOJgd\nhw7Ppfhzcw96ZUc71fwieoa1ei+Wg08JE654kthPoU4Lv81txxk9Zx30+AcTBx70cRG3WtT1TySM\nB4JMI5OhwIzhTwTwMMTA66/DnTwZuQULYtZ82/HHo2Pjxtj3WOXkJ9PyUl36poWvqvB5XrQoMyvx\nqZr6e/dWqPgtLA4FNOS32XMIQsrws3l/ibdWn4HmI48EALBEXM5gdvm6aFSiu/LVcOmnWvi6oh9F\ni19/o5laGElCdqmL1ZOPw9KOo8WxJ4p1Mt4s/GGShU8H78dwKIGXSgjzeV3FziR8tS2tYl5olOLm\npRJ4ioWvCJ86TnxBkHKP3HbxTJf27tVhgXp6Y1hYNArGwew4dCg1fkgZCtPmVuThE5pYveuCNAyc\nQtctT5LtYCVak21tRwQjTFDruzZioayPP17c+aOOcWDVmxiuwns8eCneSwQHDgAwPHUGySohbIzw\nU+L5MQu/Sgy/9dhjAQBtxx2X6oXxe4SOxp08Ge7kyej80IfQtnbt8C7OwmIcoeEZwUzzYvoZTqze\ntUufghOCgIex7RqDWIppebzDxmhM7sOMITcaRro97rCRpiWxqIpygvDNz01V3UOKSx8Q33EeBFVd\n+n5PjxADzpiBpiVLMOfaa0EcB/kdOyrO1bxsGQDoUs/NR9Vuy2xh0WhoeMKPh8PjE63+qVz6lMmG\nOYO79GtX2kt570FiNEghVl1sImC8ldYdgfjvxfM/hTIvD77jIYBAqu3T0lq1hS+zbcB5vAlOUxOC\n/furuvQnf/CDyC1ciNySJeI1XR67UrhLCEHL8uUjeGUWFuMLDW+CmNZdRVpe0sKncQKsyMOvu3kO\nRs4VP4pW4IQk/PFgVQ9TtAcA7V47pvhTRmhA4xtJCx+I8uJNa11raAzCVy1vq7n0qe+j6YgjKp9n\nW1jHYgKi4RnBLNyWLLyTjNM51AEnpegNNVT6qS79UYjhj0q8Vo1tArr0xwOSniaL2tAxfMPCn/Gp\nT1W2cVbpt6aFn80ChAgLP6XSXjUMN5PCwqIR0bAzkiL3UhC1etW19FncwlcTsOdkcET7UZjsCcup\nlmjvPYvhjwYpTLAY/mChmPccE2zBNWzIrBlqWPjU8ypa4qrvs5mnTz1P5+Wrqnp1ebbsosxiAqJh\nv+2uIwm/HBG+qkWfjN2b6XkLWw+DS934doXBCuKYE/hITeajYGEQ1SFwIrr0x4PFlvz+HSK49dZb\nsW7dOhxzzDH4+Mc/jp07d+rXHnvsMZx++ulYtmwZtmzZgh1SFDcUmC79NKS59Ikk/LBU0m1261ro\n2jx7iwmIhv22u44YeimI3H5zp2ax/ugOzO6WFkDCbUdIohxu0sIfTLQ3GpZk0m05Qpi0aRPaTzhh\nVI497jDOLPw0QVij45FHHsF9992HH/7wh3j88ccxa9YsXHPNNQCAXbt24dJLL8WVV16Jbdu2Ye3a\ntbj00kujehd1YjDCT3Xpe56oolcuR4Rfx0LXuvQtJiIadkZKs/A9l+KsdV1oaRIWfMVDrZS+EtWE\nPAAGt+BHaDLno0T4bWvXIrd48agce7yBjFcL/xAi/FdeeQVhGCIMQ3DOwRhDRhLv1q1bsWTJEmzc\nuBGe5+GSSy7B22+/jaeffrru4xPPi4ntUvdJsfCp5+nGONqlPwQL/1C6RxYWg6Fhfb6esvDLKVYE\nSY/hq7r6Fful/D3YRDDeLfwJhXFG+I3aeKVcLqO/v79iO6UUp512Gu655x6ceOKJYIyhq6sL3/ve\n9wAA27dvx/z58/X+jDH09PRg+/btWLp0aV3nHtS6RxWXvu+LGH5fn26zW8+zeSh6YSwsBkPDfttd\npiz8FMJMrt4N4q/llh9SjfvhThSqXa8l/OHDvKfjgPAb1Xrctm0bjj322Ip/Z5xxBorFIlasWIGf\n/vSn+M1vfoMTTjgBV1xxBTjnyOfzyCaq32WzWeSN0reDoZ7W0urzpL4fpdq6biTaG4JLv1HvkYXF\ncNCwFn6aS1+h6uo94dIfsmgv7RwHCcKYcEFawh8+xlkefoVYtEGwdu1avPDCC6mvXXzxxdi0aRPm\nzJkDALj22muxYsUKvPjii8hmsygUCrH98/k8cjJHvh7UY+HrMBuloL6PsFDQoj1TpV+PoNbG8C0m\nIsZ+djxIHDVXWASHzUqZVJKr92ou/RqivVEnDnl8a+EPHzaGP/p44403UJSFbQDh5qeUwnEczJs3\nL6bKD4IAr732GhYsWFD38Yfi0ieU6lx7JdoDELXHrSeGb9PyLCYgRuzbft111+GGG26IbauVqvPs\ns8/i7LPPxrJly7B582b84Q9/GNL5NizrwN+fMxsnLZ9U8VqaK1//rEe0V6OtrDt58pDGWQ2apCzh\nDx/jzKWvvzuHUB7++vXrceedd2Lnzp0oFou48cYbsXDhQsydOxebNm3CM888g61bt6JYLOK2227D\n1KlTcfjhh9d9/Lpc+qaFLwlfWfgAEBYKNZ/daseysJgoGPa3fc+ePbj66qtx9913x7bXStUZGBjA\nJz/5SZx11ln4zW9+g/PPPx+XXHIJ+vr66h84JZjdndEd8mIwCd74G8m0vGou/RqkMeNTn8Kca6+t\ne5xVIScca+GPAMaZhc9aWuC0tcGfPn2shzJiuOyyy3DyySdjy5YtWLduHV577TXccsstoJSis7MT\nt956K26++WasXr0ajz32GG666aYhLb6G4tInBuFT348s/EKh/mJTDRp2sbAYDoYdw9+yZQtWrFiB\nU045JbbdTNUBgEsuuQR33XUXnn76aezZsweUUmzZsgUAcPbZZ+Ouu+7Co48+ilNPPXW4Q6pQ6cd+\n1hLt1eHmI5SOiFVgLfwRxDiL4VPfx8zPfGZceBtGCp7n4aqrrsJVV12V+vqaNWvwwAMPHPTxhyLa\ng+HSj1n4AwNDJvwJU43SwgJ1EH6tVJ3m5mZ8+9vfRnd3N66++urY67VSdfbu3Rt7DQDmzp2L7du3\nH+x1xFCtH3nSpV/Vwn8vSMNa+CMGfV85HzcW26FE9qMK1cmyDgs/M2sWgt5eUN/XTXVUHj4A8FIp\nVp635mkV0dv7ZDGBMCjhb9u2DRdddFHF9hkzZuCRRx5Bd3d36vvy+TyaE6t2larT399fkcaTyWQq\nlL4HjWQevumqr0H4eqHwHqz6p5x2Gt665x60rV496ueaSLBE22BQhF+Hhd/+vveh/X3vAxB10aOZ\nTKypVd26iWTYz8JiAmBQwq+VqlMLtVJ1CoVCxWuFQmFIaTy1UM3CB6W1y+O+h8rd3OLFmPvFL476\neSYMxpmFb1EfdEOcOi1zhbYTToA/cyac1tZY3n29i/VDUVhpYTEYRo3ZaqXqJF8DgB07dgwpjacm\nkjH8Kir9irc1aIU0C3vvGhVENnkiRt/7euB1daF11SpxjIMg/EO1wZGFRS2M2uxYK1XnuOOOQ7FY\nxN13341SqYQf/OAH2LVrF04YqWYvCQu/qkt/kPdZNB7sBN5goBQ0lxvWfTNd+vV2iLSFdywmIkaN\n2Wql6nieh29+85t46KGHsGrVKnz3u9/FbbfdNnIu/SqV9kiy0l7lG1PfZ9EAsBN4Q6L5qKO0pX6w\niFn4dT67/vTpyMyejczcucM6t4VFI2HESutef/31Fdtqpeocdthh+P73vz9Sp48jmWNrFtSp5dJX\nfeQt4TcuLOE3FNqOPx7tM2cO6xjUFO3VaeE77e2YliJGtrA4lHFoMlsN0d6ghECItfAbEPXUULA4\nNHFQMXwLiwmIQ3J2TLr0h1JrnVBqSaMRYV36ExaW8C0s6sOhyWzV2uPWYeETz9NVvCwaEJbwJxxi\noj1L+BYWVdGw7XFroWp73EFi+ADQfe65oJnMKI3MYrRAbJrVhIUlfAuL+nBIEn41C7+eGH5m9uzR\nHJnFaMOGYyYcYql4lvAtLKri0Jwdq8RzByu8Y9HAsN3PJixiMfw6VfoWFhMRhyTha8W20U5TvmAJ\n4VCF9N5Yl/7Eg3XpW1jUh0OT8OUqX6/2DevPEoKFxaEFalX6FhZ14ZD0f3nTpmHyaacht3ix2GDm\naFvCPyRBbMGkCYuDKa1rYTERcUg+HYRStB57bPS3Gd+1hH9owt7bCYtYe1y76LOwqIqJ8XRYwj/0\nQamd7CcoiHHvrUvfwqI6JsYMabTHtTH8QxP2vk5sVOh2LCwsKjChCL+uWvoWjQkbw5/QUA10rIVv\nYVEdE2KGtDH8CQB7byc0tIVvCd/Coiomhv/LuvQPebSuWoUwnx/rYViMESzhW1gMjglF+Nalf+jC\nzMqwmHjQSn1L+BYWVTHxXPqcj+1gLCwsRhyK8K1oz8KiOiYE4bPmZtBsFl5nJ7glfAuLQw7WpW9h\nMTgmxHKYZjKY9bnPgVCK4jvvjPVwLCwsRhiW8C0sBseIWfjXXXcdbrjhhtTXHn74YZx77rmxbTt3\n7sT555+P5cuX45RTTsGjjz46UkNJhU7Zsha+hcUhB5uWZ2ExOIZN+Hv27MHVV1+Nu+++u+K1UqmE\nO+64A5/73OdirnTOOS6//HKsXLkS27Ztw9VXX40rrrgCb7755nCHY2FhMQGhY/eW8C0sqmLYhL9l\nyxYwxnDKKadUvPbFL34R//3f/42LLrootv3FF1/E9u3b8Xd/93dwXRcbNmzAihUr8PDDDw93OIPD\nWvgWFocciLXwLSwGxaAx/HK5jP7+/ortlFI0Nzfj29/+Nrq7u3H11VdX7POZz3wG3d3duPfee/HE\nE0/o7du3b0dPTw88z9Pb5s6di+3btx/sddQN6vujfg4LC4v3FjSTET/t821hURWDEv62bdsqLHQA\nmDFjBh555BF0d3dXfW+11/L5PDLyAVXIZrPYs2fPYMMZNpz2dnR9+MPwaozbwsKisdC6ejW8ri64\nnZ1jPRQLi3GLQQl/7dq1eOGFF0b0pJlMBgMDA7Ft+XweuVxuRM9TDU2HH/6enMfCwuK9gdPaiuaj\njx7rYVhYjGuMSR7+/Pnz8frrr6NUKultO3bswIIFC8ZiOBYWFhYWFoc8xoTwFy9ejJ6eHtx0000o\nFov41a9+hd/+9repwj8LCwsLCwuL4WPMCu/ccsst+OIXv4jjjjsOnZ2d+NrXvlZTD2BhYWFhYWFx\n8Bgxwr/++uurvnbOOefgnHPOiW3r6enBt771rZE6vYWFhYWFhUUNTIha+hYWFhYWFhMdlvAtLCws\nLCwmABqmeU4QBABgy+9aWAwC9YyoZ2Y8wj7PFhb1YSSf54Yh/Hdkl7vzzjtvjEdiYdEYeOeddzB7\n9uyxHkYq7PNsYTE0jMTzTHiDNIgvFAp45pln0NnZCWbrZVtYVEUQBHjnnXdw5JFHVlS0HC+wz7OF\nRX0Yyee5YQjfwsLCwsLC4uBhRXsWFhYWFhYTAJbwLSwsLCwsJgAs4VtYWFhYWEwAWMK3sLCwsLCY\nAGgIwn/22Wdx9tlnY9myZdi8eTP+8Ic/jPWQhoQ777wTRx55JJYvX67/Pfnkk9i3bx8+9alPYeXK\nlVi/fj3uvffesR5qVTz11FM44YQT9N+1xl4sFvH5z38eq1atwtq1a3HbbbeNxZCrInktTz/9NJYs\nWRK7P7fffjsAgHOOG2+8EWvWrMGxxx6L6667blzntzcCGvl5PhSeZcA+zxP2eebjHIVCga9bt47/\nx3/8By8Wi/zee+/la9as4b29vWM9tLpx5ZVX8n//93+v2H7ZZZfxz372s7xQKPD//d//5atWreK/\n//3vx2CE1RGGIb/33nv5ypUr+apVq/T2WmO//vrr+YUXXsj379/Pd+zYwTds2MAfeuihsboEjWrX\ncs899/BPfOITqe+5++67+emnn87feust/vbbb/MzzzyTf+Mb33ivhnzIodGf50Z+ljm3z/NEf57H\nvYX/61//GpRSbNmyBa7r4uyzz8aUKVPw6KOPjvXQ6sZzzz2HJUuWxLb19fXh5z//OS6//HL4vo+l\nS5fi9NNPx3333TdGo0zH7bffju985zv45Cc/qbcNNvb7778fF198MVpaWjBnzhx89KMfxX/+53+O\n1SVopF0LICzOww47LPU9999/Py688EJ0dXWhs7MTF1988bi4lkZFoz/PjfwsA/Z5nujP87gn/B07\ndmD+/PmxbXPnzsX27dvHaERDQz6fx44dO/Cd73wHxx9/PD74wQ/iBz/4AV599VU4joOenh6973i8\nrg996EO4//77cdRRR+lttca+b98+7N69GwsWLKh4bayRdi2AmMR/97vfYePGjVi/fj1uuOEGFItF\nAMD27dsrrmXHjh3gtnzFQaGRn+dGf5YB+zxP9Od53BN+f38/stlsbFsmk0GhUBijEQ0Nu3btwsqV\nK/GRj3wEv/zlL/GlL30J119/PX75y19WVE0aj9fV1dUFQkhsW39/f9Wx5/N5AIjds/FyXWnXAgAd\nHR3YuHEjHnzwQdx999144okn8PWvfx2AmOTNa81mswjDUE8gFkNDIz/Pjf4sA/Z5nujP87ivpZ/N\nZiu+XIVCAblcboxGNDT09PTgu9/9rv77mGOOwebNm/Hkk09iYGAgtm+jXFc2m606dvUwFQoFNDc3\nx14br1CCHgDI5XK4+OKL8ZWvfAWf/exnkclkYteaz+fhOA583x+LoTY8Gvl5PhSfZcA+zxPpeR73\nFv68efOwY8eO2LYdO3bE3DLjGX/84x/xjW98I7ZtYGAA06ZNQ6lUwhtvvKG3N8p1zZ49u+rY29vb\nMXny5Ng9S3Pjjhfs27cPN9xwA3p7e/W2gYEBPQHMnz+/4lrmzZv3no/zUEEjP8+H4rMM2Od5Ij3P\n457wjzvuOBSLRdx9990olUr4wQ9+gF27dsXSMMYzcrkcbr75ZvzkJz9BGIZ4/PHH8dBDD+G8887D\nSSedhBtvvBH5fB5PPfUUHnzwQfzFX/zFWA95UDQ3N9cc+xlnnIGbbroJe/fuxSuvvILvfve72Lx5\n8xiPOh0tLS342c9+hptvvhmlUgmvvvoqbr/9dpx11lkAxLXceeedePPNN7Fr1y7ccccd4/ZaGgGN\n/Dwfis8yYJ/n8Xoto4KxThOoB8899xw/99xz+bJly/jmzZvHZbpLLfziF7/gp59+Oj/66KP5ySef\nzB9++GHOOed79uzhl19+OT/22GP5iSeeyO+9994xHml1/PrXv46lvtQaez6f51/4whf4mjVr+HHH\nHcdvu+22sRhyVSSv5aWXXuIXXnghX7FiBV+7di3/t3/7Nx6GIeec83K5zL/yla/w448/nq9atYp/\n6Utf4uVyeayGfkigkZ/nQ+FZ5tw+zxP1ebbd8iwsLCwsLCYAxr1L38LCwsLCwmL4sIRvYWFhYWEx\nAWAJ38LCwsLCYgLAEn6dsFIHC4vxDfuMWowmDoXvlyX8QbBv3z585jOfqcgdHgnk83n80z/9E9as\nWYNjjjkG//iP/4gDBw7UfM+Pf/xjLF68uOLff/3Xf434+BoJ559/Pq644or39Jw33XQTjj/++FE9\nxxNPPIHFixfj5ZdfHtXzNDLsM9oYGItndKTwve99D3fccYf+u1GvZdxX2htrPP/883j44Ydx2WWX\njfixv/CFL+Dxxx/HNddcA845brjhBuzbtw+33npr1fe88MILWLRoEb70pS/Fto/XQhgWw8MRRxyB\ne+65BzNnzhzroYxb2GfUYrTxzW9+E6eeeupYD2PYsIQ/Rnj11Vfx4IMP4vbbb8f69esBAN3d3bjg\nggvw0ksvYeHChanve+GFF3DUUUdh2bJl7+FoLcYKzc3N9l6PEewzanGooeFd+uVyGV//+texYcMG\nLFu2DH/1V3+F3//+9/r13t5efPnLX8aGDRuwdOlSbNmyJfY6AHzjG9/ASSedhP+fve+Os6K6239m\nbt+7vcIuTYq0pSwsS1cBEQtCVDRGjdGYGHx/SKzRJMb4JtYXjSgoikYRwQqxASpYQAGlI73uAtvr\n7WXq+f0xM+fO3LIFV5F4n8/Hj8vcKWfOnHOebz/FxcWYNm0arZe9ZcsW3HjjjQCASy+9FAsWLIjb\nhsmTJ8c14fXv3z/hNVu2bIHFYjGYhMvKypCWloZNmzYlfN8jR47g3HPPbV/nnCaqqqrQv39/LF26\nFOeddx7Kyspw4sQJAMDKlStx8cUXo7i4GJdeeik+/vhjAIAsyygrKzOUHv3ss8/Qv39/rFq1ih5b\nunQpzj//fAAAz/P417/+hQsvvBDFxcUYM2YM7r//floWM1E7BEHAY489hjFjxqCsrMxgatOwcuVK\nXHLJJRgyZAgmT56MBQsWQJblVt830X9btmxptb/eeustTJw4ESUlJbj77rvR0tJCf2vrHQHgyy+/\nxBVXXIGhQ4diwoQJePjhh2m9+Xgm/VWrVmHGjBkYNmwYpk2bhpVJ66OcAAAgAElEQVQrV7bavjON\n5BztfCTnaPvm6IIFC3DllVfi3XffxcSJEzFy5EjcddddcLvd9Jy23nHy5Mmorq7GSy+9hMmTJ9Pr\nJEnCE088gTFjxqCkpAT33HMPfD7fD9LPs2fPxi9/+UvDuwWDQQwfPrxD2zCf9Rr+I488gvfeew9z\n587FgAED8Oabb+J3v/sdVq1ahfz8fNx8882ora3FHXfcgdzcXCxbtgw33ngj3nrrLQwePBjvv/8+\nFixYgL/85S/o06cPNm3ahH/+85/o3r07Ro4ciQcffBD/+Mc/8PTTT2PEiBFx27Bw4cKEuy116dIl\n7vGKigoUFhbCYrHQYwzDoLCwECdPnox7jd/vR01NDXbv3o0LL7wQtbW1GDRoEB544AEMGzasgz3X\nNhYvXowHH3wQwWAQvXr1wttvv42HHnoIN998M8aOHYuvvvoKd955J2w2GyZPnoyxY8di27ZtuPXW\nWwEA27ZtAwDs3LkT06dPBwBs3ryZllF95JFHsG7dOtx7770oLCzE3r17MX/+fBQUFBj8Y9Ht+Pvf\n/46PPvoI99xzDwoKCvDcc8/h8OHDuOiii+hzH3jgAdxxxx0oKSnB/v37MW/ePOTk5OC6666Lec/8\n/Hy8/fbbCfuhtZroLS0teOGFF3DfffdRk++cOXPwxhtvtOsdT548iblz5+K6667D/fffj1OnTuHR\nRx+FzWbDvffeG/O8NWvW4O6778b111+P++67Dzt27MBf/vIXZGZmYsqUKa1+zzOF5BxNztEzOUdP\nnDiBZ555Bn/605/oHL399tvx+uuvt+sdFy5ciFtvvRXjxo3DTTfdRO+7bt06nHfeeXjyySdx4sQJ\nPP7448jMzMQDDzzQ6f08c+ZM3HHHHaiurkZRUREA4IsvvgAhBBdeeGHCd4/GWU34brcbb7/9Nu67\n7z785je/AaDsYHXFFVdg165dsFqt2LNnD9544w2MHDkSADBx4kRceumleO655/D8889j586dKCoq\nwrXXXguGYVBWVgaLxQKHw4HU1FQ6kPr3759wYRg0aFCH2x4IBOB0OmOOO51OBAKBuNccOXIEhBDU\n1tbib3/7G2RZxssvv4zf/va3WLNmDQoKCjrcjtZw1VVX0QkqyzKeffZZXH311fjTn/4EQOlLt9uN\nZ555BpMnT8aECRPw+OOPQ5IkmEwmbNu2DQMGDMDOnTsBKJre1q1b8eijjwIAXC4X/vznP9Oa3aNH\nj8aOHTuwY8eOhO1wu91499138de//pUuDMXFxQay27VrFxwOB26++WZYrVaUlZXBZDIhPz8/7nta\nrdbTNr/Ksoz58+fT6zMzM/G73/0Ou3btQklJSZvvuG/fPvA8j1tuuQX5+fkYPXo0rFYrRFGM+7zF\nixfjwgsvxIMPPggAGD9+PE6ePInt27f/JAk/OUeTcxQ4s3M0EAhg0aJFGD16NAAgIyMDf/jDH7Bn\nzx4MHTq0zXccNGgQrFYr8vPzDeMoNzcXCxYsgNVqxYQJE7Bt2zZs374dADq9nydPnoy0tDSsXr2a\nChGrVq3C5MmT6S6G7cFZTfjfffcdJEnCpEmT6DGr1YrVq1cDAJ544gnk5eXRhQQATCYTpk2bRqXF\n0tJSvP3225g1axYuueQSTJkyBXPmzOlQOyRJSpiywbIsWDbWcyLLcty9nAEkPN63b1+8+OKLGDVq\nFF2IysrKMHXqVCxZsgT33Xdfh9rdFs455xz6d0VFBZqamnDeeecZyGjixIn48MMP4Xa7MWHCBPj9\nfhw4cADnnHMODh06hEcffRR/+ctf4Pf7cejQIYTDYYwbNw4A6B7VtbW1KC8vx9GjR3H8+HFkZWUl\nbIf2zc877zx6rKCgwKA9jRgxAsFgEDNnzsRll12GKVOmULNvIiQiWEAZM4m+SV5enmEhmjBhAiwW\nC3bu3ImSkpI233Ho0KGwWq245pprMH36dEyePBmXX3553DETDodx8OBBXH/99YbjTz31VKvvdiaR\nnKPJOQqc2Tmam5tLyR4Azj//fDpHhw4d2u53jMbgwYNhtVrpv4uKirBv3z4A6PR+ttlsmDZtGtas\nWYNbb70VHo8HGzduxDPPPNNqG6NxVhO+x+MBAGRnZ8f93ev1Ijc3N+Z4dnY2ldBnzJgBQRCwfPly\nzJs3D/PmzUNJSQkef/xx9OrVq13tmDp1Kqqrq+P+NmfOnLjRw2lpaQgGgzHHA4EA0tLS4t4rPT2d\nBg9pcDqdKCkpwZEjR9rV1o5A368ulwsA8P/+3/+Le25TUxP69u2LPn36YOvWrWhpaUFubi4uueQS\nPPDAA/juu++wY8cODBs2DOnp6QCA7du34+9//zuOHTuGzMxMFBcXw263xyzM+nZ4vV4AiJmMOTk5\n9O/S0lI899xzeOWVV/D8889jwYIF6NevHx599FEMHTo0pu1VVVWtasdLly41LBiJ2gYoRJCZmUlT\nt9p6x+7du+PVV1/FCy+8gCVLluCll15CUVER/v73v1P/noa2xvtPEck5mpyjGs7UHM3LyzP8W5uj\n2ths7ztGw+FwGP7Nsiy9pmvXrp3ezzNmzMCKFStQUVGB7du3w+l0GoSq9uCsJnxt0rlcLoNZY+fO\nncjOzkZ6ejqamppirmtubkZGRgb991VXXYWrrroK9fX1+Pzzz/Hss8/in//8J/7973+3qx2LFi1K\n6B9MZKLq2bMnamtrqckHUAo71NTUJFzEDh48iP3792PWrFmG4xzHISUlpV1tPV1oA/Oxxx6LG52s\npY1NmDABW7duhcfjwciRI2Gz2TBkyBDs3LkTmzdvpgPU5/Phtttuw4QJE7B48WLql7rjjjsM+3JH\nQ/tuzc3Nhm/u8XgMi86UKVMwZcoUuN1urF+/HgsXLsS9996LTz/9NOae+fn5WLFiRcJn6rWXaETn\nZMuyDLfbjezs7Ha/Y2lpKV5++WUEAgFs3LgRL7zwAu688058++23hntrGqO2sGsoLy+Hz+f7QXzE\n3xfJOaogOUfP3BzViF2DLMtwuVwdmqOng87u57KyMhQWFmLdunXYtm0bpk2bZogvaQ/O6ij94uJi\nmEwmbNiwgR7jeR5z587FmjVrMHLkSDQ2Nhr8TZIkYe3atdQM+9BDD2Hu3LkAFLPTddddh2nTpqGu\nrg4A6ERvDf3798eQIUPi/pfIZzdmzBiEQiFs3ryZHtu6dSt8Ph/KysriXnPw4EH89a9/NURsNzc3\nY+fOnQaT6A+B3r17IzMzE01NTYb3O3z4MBYvXkxNouPHj8eOHTuwfft2lJaWAgBGjRqF9evXY+/e\nvZg4cSIAhaS8Xi9uvvlmOsDD4TB27tyZMFIXAEpKSmCxWLB27Vp6zO12Y8+ePfTfL774Io1ozczM\nxC9+8Qtcc801qK+vj3tPq9Wa8PsNGTKkVR9ZTU0NysvL6b+/+OILCIKA0tLSdr3j+++/jylTpkAQ\nBDidTkybNg2///3vEQgEDJH8gJKi169fv5gCLvPnz8fTTz+dsI1nEsk5mpyjwJmdo7W1tQbryvr1\n6yGKIkaNGtXud4zn8mkLnd3PDMNg+vTp+OSTT7Blyxbq7+8IzmoNPy8vD7NmzcJTTz0FWZbRp08f\nvP322xAEAVdddRVycnJQXFyMP/7xj7jzzjuRm5uL5cuXo7q6GvPmzQOgfIC77roL8+fPx9ixY3Hq\n1CmsXr2a+kk1DeXzzz+HzWbrtAIovXr1wtSpU3Hvvffi/vvvh8lkwhNPPIEpU6bQlB6/349jx46h\nR48eyM7OxrRp07Bo0SLMmTMHd9xxBxiGwcKFC5GVlRWTstHZMJvN+MMf/oD58+dDEASMHDkShw4d\nwtNPP40ZM2ZQX1ZZWRk4jsOOHTtoYNnIkSPx4osvIjs7G8XFxQAUiTwlJQXPPPMMbrnlFvh8Przy\nyitoaGhIaC4FlO9x0003YcGCBbBYLOjVqxcWL14MSZLoOaNGjcL8+fPx4IMP4pJLLkFzczOWL1/e\noWjW9sJms9Hx5fF46DccNGgQvF5vm+84cuRINDU14a677sK1116LUCiERYsWYcSIEXHN4LNnz8Y9\n99yDRx99FBdccAG2bduGdevWxU17+ikgOUeTc/RMz1EAuP3223H33XcjEAhg3rx5uPDCCzFgwIB2\nzVFAsZ5899132L17d7uDB3+Ifp45cyYWL16MwsJCKkR0COQsB8/z5MknnyTjx48nw4cPJzfccAM5\ncOAA/d3lcpE///nPpKysjAwbNozccMMNZMeOHYZ7LF26lFx00UWkuLiYTJw4kTz11FNEEARCCCGS\nJJE777yTDB48mPzv//5vp7bd5/OR+++/n4wYMYKUlZWR+++/n/h8Pvr7t99+S84991yycuVKeqyq\nqorMnTuXjB49mpSUlJA5c+aQ6urqTm1XZWUlOffcc8mGDRtiflu+fDm56KKLyODBg8mkSZPI008/\nTXieN5xz0003kdLSUiJJEn3PgQMHkrvvvttw3oYNG8j06dPJkCFDyAUXXED+9re/kWXLlpFBgwYR\nl8uVsB2SJJH58+eTcePGkZKSEvLwww+TuXPnkjvuuIOes3r1anL55ZeToUOHkjFjxpAHH3zQ0Led\ngWeffZbMmDGDvPrqq2TMmDFkxIgR5G9/+xsJBoPtfkdCCNm0aRO5+uqryfDhw0lpaSm58847SUND\nAyEkMgaOHTtG7/nee++Riy++mBQXF5PLLruMrFmzplPfq7ORnKPJOXom5+i4cePI8uXLyZgxY0hZ\nWRl56KGHSCgUavc7am0dNWoUKS0tJYIgkBtuuMHwLoQQMm/ePDJp0iTDsc7qZz3OO+88Mm/evNPq\nD4aQ/4IdAZJIIokkkkgiCgsWLMBbb73VaqGkswnHjx/HpZdeijVr1pxWqeaz2qSfRBJJJJFEEv/t\nKC8vx5o1a7BmzRqMGzfutPdlOKuD9pJIIokkkkjivx2yLGPJkiUwm834xz/+cdr3SZr0k0giiSSS\nSOJngKSGn0QSSSSRRBI/A5w1PvxwOIx9+/YhLy+vXXm3SSTxc4UkSWhsbKTVun6KSM7nJJJoHzpz\nPp81hL9v376YGuJJJJFEYixfvvz0cnV/BCTncxJJdAydMZ/PGsLX6iEvX7484Y5YSSSRBFBXV4fr\nr78+pob4TwnJ+ZxEEu1DZ87ns4bwNbNfly5dOq2SVhJJ/Dfjp2wqT87nJJLoGDpjPieD9pJIIokk\nkkjiZ4Ak4SeRRBJJJJHEzwBJwk8iiSSSSCKJnwGShJ9EEkkkkUQSPwMkCT+JJJJIIokkfgZIEn4S\nSbQB0etFw4oVEH2+M92UJH5AEFmGe8MGCC7XmW5KEj8yAgcPwrtlS9zfiCxD5rgfuUUAIQQt69Yh\nfOJEp90zSfhJJNEGmj74AIF9++Bat+5MNyWJHxDBQ4fg+vJL1Lz44pluShI/MhrefhvNH38c97em\njz7Cycceg+T3/6htEl0ueDZtQuP773faPZOEr0O4shJCU9OZbkYSPzHwjY0AACJJ9BiRZXi3bYMU\nCnXoXp5vv0WovLxT25dE50IOh890E5I4DUh+P2RB+F73ILIcc8y/axcAIFRR8b3u3VH8EOMwSfgq\niCyj9t//RtXChWe8HR2B4HKBiGLkekLQsnYt/Hv2dHbTfraQg0HlD4ahx3w7d6J59Wo0vP12u+8j\nhUJo+eQT1C1d2tlNTCIKgsuFlnXrIPN8u6+JFug6C/49e+DetCnub4LLheDhw532rNOBzHGd+r5n\nAjLPo2rBAoMVLrB/P7jq6g7dR7+WRoOvrz/t9p0OkoT/AyF4+DCChw6d6WbAv28fTj76KELHj7fr\nfCkQQNUzz6D6xReh7XIsB4PwbN6Mxv/8p8PPJ7KM5G7JRsg8TxcB0eulxyX1747416RkDMCPhvo3\n3oBn0yb4tm9v9zV6P63Q3NxpbWn8z3/gWreOWor0cH3+OerfeqvDlqJoEFGE55tvOkwSUjCIk489\nhubVq7/X88805GAQMseBq60FoAhvDStWoKWDbji90KfBlJ4OAOCqqgzHQ8eOoebf/6bfTvL74dqw\noVWhoSP4IVwIP3vCJ6KI+jffRMM770SOfQ/SI6II8TQ+lOjxoHHFChBRRPDo0XZdoy0gQmMjggcP\nKn+3tHT42RoaV6xA5ZNPKsQvipACgdO+V0fRkUlCZPm0NBL3pk2oWrAAMs8jePgw6t94I6EJUDuH\nVxcQAJA8nsgJccpcyhyHmpdeQuDAgbj3TBL+jwfNNdcRAiQ6wufr6r53G1zr16Pl88/pv33btsWc\nI4fDACGnrc0RWUbgwAG4Pv8cLZ9+isYPPkDLunUG4bQ1+L/7Tmnbjh3tOp9vbKSk2l4E9u9H9Ysv\nGgQqrqYGtUuXQtKsZ98T2jzW5pjWr+25v34tIa24BLiaGsO5dcuWgausRGDvXgCKr9/95Zdwffnl\nab1DNDqrb/T42RN+PHL+PqaUls8+Q9WzzxokdjkcRqANC4LerysFAgkJjYgiWj77DFx1NURdNLFv\n504AgBiH8JvXrEHL2rWtCjLawiEFApB8PjStXo1T8+ZBdLvpOXxDA4JHjrT6HqcDrrYWJ//v/+D+\n+ut2nV/5r3+h7rXX4v6mCSuh48fRvGYN/Pv20d9CR49CaG6G2NIC386dCB45knBh9+3Ygfo330Tt\nkiX0mOjz0e8i64QhrV+56mpw1dVxCd+3e7eh75KWlNMHX1cHbxzyNEDr33bWHyeEGAmpg6bgmPtJ\nEtzr18Pz9ddgrFYACrlGC7YawbRGNK3Bs3kzGt55B55vvgEABA8eVCwbqt+51TYSQtcNk9PZruc1\nvP026t98s0Nt1ARnvUk8cOAAwuXlCJ861aF7RUMWBNS/9RYlXcnnM3zL9qzl+r6Pp3ho9yA8HzfG\ni1HHmCZsRFsCOgrN0vpDKFxnzeY5PxTimU0kvx8mh6Nd18uCAMJxMKWmAlBMvITnIXo89B61r7wC\nvqEB2RddhNDx48ibNQuszQaGjchbsk5ACB4+jJOPP46MMWOQOWkSGIZRTHabN0P0euHbvh3+Xbvg\nOPdceg1fWwtCSExKkej1wrt1KwDAnJmJ9LKyuO+hJz6hpYUGqni+/RY5F18M365daPrgAwBA4a23\nwlZY2GbfCC4XGt99F7kzZsDapQtkjgNjtYLR+cI1CwvheXi3bUPG2LFoWLECKf37I62kJOaeotcL\nye+n3y107BgIgJS+fQEoVgquuhpElpUJuG0bUvr1U65V+0b0eMA3NCh/t7QA3bvHPIerqVEbSGDJ\nz4clKwvBw4ch+f0wp6cbJqPk88Gcnh65f5xv0BQVaUt4HozN1mYfav0oh0Lt6vOfA9wbNyKwbx+c\nAwfSeZcITDsIn6urQ80LL1DTLaAIh7j44tNuo57cNEKROQ6h48eR0r9/5DeVYE437SuR60Fuh3Yo\n+XwQNDdDO/pJCoUgNDWBMXeMNjSlyjBn1GPyaboy+MZGWLKy4N+1C8FDh6hLlkiSYt5XSbo9hK/v\n+xiBTJZBdHEgQlMTrPn5xhuofaeNRVFvCewgpFAIp554AmmlpcAPEFfxs9LwiSyDb2gwBPLEJfx2\nSlZEllH/+uuoWrgQcjgMIkl0AsmBAIJHj6Ju6VJKLu6NGxE6fhwtn3yCk489hpDO/2sYdDwPwvNw\nf/UVlVx9O3fC9cUX1CcpBQKUlG2FhVQz12v4UihkCAhyb9wY/z0IMWifgf376d++nTshc5zBF8pV\nVSFUXo6al1+O8T3qNdfgoUPgamoUab6yEiefeAIBncYNAOFTp6g/HADCVVUIHjoE94YN8H/3Hbgo\nDZwSMRSze92yZahftow+O3DgAESPJ2I+JwR1y5bh5GOP0YkoNDdTy0Xg0CG0fPppTHCXdr39nHOQ\nP2sWzNnZACJ+fP240dwognpPvVUEQFytoCM+28aVK1H7yisJFy/frl1KwNIXX5zVwVdSINAuvyVd\nzNU5I3o88O3eHfdcvVCdCG7VBKuNQ0t+PoTm5u/lxzdYCAgBqwr/0Za+aA1faGmBd/v2dluAzBkZ\ncY/riZTIMlzr18fEEOjHZXuIkVfnHhHFDo0z7ZvqTdSU8E/Dmiq4XKh+7jm4v/46rvtT9Hrp2CA8\n32ZbDWtvlKVF+00THOPFYWgCgaS+i+j1GgSHjmQOaOu3b/v2pEm/owhVVNAPJoVCqFq4ENXPPw/X\nZ5/RcxJp+O2Bd8sWhE+doiZ7obmZBn1IwSDcX35pMNVrUrf/u+9ABAF1S5ZETMTqYGGjLAvhykoQ\nUTSQdcaECRHNhmWpps/X1Rl8+JVPP02DcSx5eZC83rjFY5pXrYJ7/Xr6by3C35KbC8LzCB49Cq6m\nhraNq6pC3dKl4Kqq4NcttKGKCpz6v/+jgowm6PCNjYr/UpbBVVYa309n0pO8Xiqpi243Gt97D3Wv\nvgoiy6h+8UU0qNq7BoMWJcsxRGvt2lVpb9QzQ+Xl1OQbPHgQnm++QfOaNYZzhJYWmNLT0fU3v4E1\nPx9mVfuT4hG+unBqmr0UCBgDwOIQvjYWAvv3txqkKXOcYrEQRQSPHQNXUwO/KgRqCOzfD6G5Ge6v\nvvpJBJ+eLk7Nm4dTTz7Z5nnaAqv1ce2rr6Lp/fcROnYs9tx2xIZE+6RThwwBgO8VPR9t1nX07g1T\nWhqChw4ZyFzWNHz1nTwbN6J51aqI5t0GEgk0eoEyfOoU3OvXo/q55wAoWnDd8uUGXzPh+bgBa4Z3\n0gnbHXFBUL96J2n42hwUXS6E46TKSV6vQZBoS6jQa/DR40W71qZu4Rzvu1D3gfZ+sowTDz8MrrZW\nsdY+8kjcsRm3LbpvoCmeHbWotIb/WsLnampQ99prcH/1FQCFZDXpST8Z45G7HAggePhwwrxLrrpa\nCY759FN6LLB/v8Es3pofXg9tsdcGjbVLF8PvQnMz/Hv3QvJ6kT5mDHr++c/ImjIFKZo5X5ZhU4mN\nr601EL42kC25uXAWFyttr6wEV1NjXBBOngQAeg7heYBlkXnBBQAAz9dfA4QgrbQUrM1mIF3GZAJf\nX4/GDz6Ad+tWyKGQIshIEgSVkPV+7WiXg0b42rOjA5tkjoN361bwtbUI7NuntEXrO90kksNh2v+m\n9HSkl5XB0adPbIdHXafBv3s39ffLggDJ64VF1eoBUMKnGr5u8dI0H73AIbpcEJqaIPN8XE1RDoVA\nZBkN776LutdfhxQKxdXquKoqKpwE9u9HzeLFaFy5EpLfT33ZeoHCu3Xrj14gpDPQ3iAzIEKO2v+1\nfo8XsNqWdiWHwwYLEwA4Bw4E8P38+HpyBADWZoO9Z0/IoZAh+FMjGKolquMqUYAnV1uLmn//m2qR\nCYNOdSRnSNuVZQhNTQgdPUoFYVNaWsw1bb1TewmfiCIl9c7S8LVr+IaGuAKd6PMZBO62hAq9dS9G\nw1efZS0oAGOx0LmmJ2ZqaYr6Znx9PZpWrQKguEa5mhpUPPQQDZRs7d2AyFhoSxDrCP5rffgaqXOV\nlZHgFJaFyeEA39CAumXLIIfDdLHIu+IKAEDje+8hXFmJgFp1qdeDDyqauyjC1rWrEl362msgPA9T\nejq6XHcdGt9/H6Hjx2HJyqLPl4NBCC0tMGdlIfeyy1Cnmp2jETp+HCn9+tEPbUpJAaAQKet0Qmhq\ngmfjRoBlkTFuHFjV72vv3ZsG3GiabKiiIsZ3Z83PR/4vf0kXQy0bgXU40PXmm2HNz4fk88GSn4+8\nX/yCmtzt3bsrvm+GoZq0o08fcNXVCOusFqLPh+pFi5R/6HzzwcOHqflLv6BqWjBfXw9zdja4qipY\ncnNh69YNgX37QCQJ1q5dlWwHjweE59HyySfx+05H3FIgQNuZe/nlSOnXL2HuczRMqamQeR6NK1fC\nlJpKv4ElJ4eew6pBTXIwqCxi4TDsvXqBq6lB+ORJhKuqDNJ/uKoKzatXg7XZDL5h2t5QyLAA+rZt\nQ7iyEqLbjbwrr4RN7QO6ODAMzcTQ+q9u+XLq57P37AmYTAiXl8P7PYuPnAnoNTVCiCHOIxrUDB7l\nhonnB2+NmCS/H7Wvvmo8yDAw5+SAtdmohUoP0esFa7eDVQPxvDt2wJKRAYcaQ0LvHeUWZGw2WDMy\nEIBi8TJnZhrap5GONiY0QuTq6uD95hvkTJ8OqLVCiCii4Z13wNXUJIzrkKOChjU0ffQRVRA02IqK\nEDx0CHI4HBO817JuHRizGVmTJhkEIFkQ0J5wSP0Y5xsa4N2xA2klJRHB5jQ0fGq1TSDYSl4vWHUO\nA/GFCkIIQAgYljVq+FHkqj2LdThgyc2F0NioxAfpvq/McUr6Ls/D0acPUktK0LhihSJMqkIAa7dT\na2jzmjVIHTYs/rvp2krds50Y4PtfS/iatsfV1UFobITQ0IAUVXIPHjwYo+U5+vWjk0TvZw4cOIDm\njz6CzHHIGD8egQMHQAQBeVdcAefgwWDMZth79ABfV2fwffMNDSA8D2vv3nD07QvWZjMsSObsbEhe\nL83j1n6z9+iBwP79cA4dqpisTpyABCBtxAiqZQKAc8AAhEeMgHPQIJjS0mByOiM54QxDB0nKwIGw\nqAuYBltREbjqatQtW4auv/kNZI6DLTUVjNkMU2oqJL+ftpm12yGHQrAWFMDevTtsRUUGwtdr3PqB\nGTp2zLjYMgxMaWkQ3W6ET55E7auvwlZUBMLzsPfoAWtuLj01vawMaSUlEL1eVD79NEAIbN27I++q\nqxDcvx+yKML95ZeGBUgKBOg3txYUAFAmWSIwJhOd3GkjR8LRuzdqlyxB03vvIWvyZAAwaPiaEKD3\nM5vS0mDv0QOhY8dQ+/LLhvuHjh6l6VbxFpzGlSsNk967fTsVjOrffBPd77gD9W+8QV1CuTNmoGXt\nWjpG+bo6Q1CPJTcXrMOBcHn5WVktUh/P0lZAIzWhagu1Ot6pRtTONCv/nj0QmpuROnQogkePQg6F\nwNrtYBgGlvx86kphzGYEjx6FOS0N1S+8AFtREQp//3sQWZH1n1cAACAASURBVEbzRx8BAM556KHI\nM+Ok2bE2GyxqsBff0EADSaM1fFmX0w0ANS+8QI/r42wkv19xkUVZEmgf6QlfR7r+XbtiNExNUYk3\nTj2q0Jw2cqRBcI8WthJBb6kIl5cjXF6uuCG0uiHfQ8NP5OMWfT6YdUGI8QTBmsWLQXgeaaNGGayK\n0RYTrR9Zux3WvDzwtbVo+eQTGggNKOmc2tgzpabStVbPMWJLC8yqJaU1jf2HrvL4X2fS5+vrleA8\nVdsjPE8HuKNPH1h0xKIHa7fHTU1pXLECshqF79m0CaLLhfTRo5E6bBj1rVjy8gAoZKCl4GjmMk1L\njA6useblwdatG/j6ekihEORwGIzZjLRRo5B/zTXIvewyg4aZGhWxzpjNyJ0xA46+fcEwjMEVYO/V\ni/6tmetMqamw5OWBsVrR5cYbkTV1KiSvF7WvvEJ/BwCzOvkd6oKUfeGFsBUVoeD668GYTLCrvqxE\n0PpEC6bR7uvo00cheFGk6XcaYaeVlsKitt+Sl4fU4cOVtqSno8v11yPvyitRcO21sGRmImP8+LjS\nseT3Q2hqAutwRN65lUyLlP796TexFhTA3rMn0kePhujx0MmsHyva2JCCQcPktvfoYbivps1HF+Rh\n7Xak9O8fidAmxBD/IEUV9QmVl1MSzJ46FWklJeh+553o+rvfAYit+mXJzaUCztm4yQ+ni+Wg/uxv\nvkHThx/Ct3s3mtesiRSXUn/XSEdbYLU+bC0ISw9NmMq68EI6FjTN3ZqXB8gyhJYWCC4X6pcvR7VK\nvtq4TWQqJoIQE2HNWq00ultzdRFCIlH6mqavEX4gYAyAjUqH5fweNHNNkCT1/aJ8+VIggKaPPoJ3\ny5ZYTTi6beo8iQnA1Z1H0/xUy4vo87VrnMXTwvVZLNEEJ7rdqH3ttVYDJun3TeAylbxeEPW+XsGL\nI43GqqOEEMX92dyMlk8+MTwrkUmftdvpGhudEipzXEQJSE0FY7EAMLpABJeLHm8truSsIfyHH34Y\nTzzxhOHY5s2bMX36dAwfPhzXXXcdKnRmuwMHDmDWrFkYPnw4Zs6cid0Jomw7guDRo6hetAhNH3xg\nWBC1D2Tv3t2gSaaNHEn/ZljWoFV0veWWyHmjRqFo9mxYcnNhzsxE1qRJhudqhA+AEoBGCpTwVROe\nBnNGhkLMhCBcXg6Z4xTtgmXhHDQIjNlMI8MBRStvDYkIX5MqAaDrb3+L7nfeCdZmQ8a4cbD36BEh\nL/W89NGjkV5WRrXktJEjUfj731PrQqJ2aNc7evdW3l9dDDLGjYM5OxsZEyZQjTl07BiNek0ZMAC2\nwkKYU1PR7fbbUfSHPxjMuY6+fZE6dKhBGDPHMZHLgQBEtxvmzEx6vV7DN6WnI/OCC+h9nIMHo8uN\nNyJ72jSkDBigPEv1+WsLukXtA0BdFBkGss6SYE5LU65lGMUqUVqK/KuuUs5TF6WCX/0KzuJi5Eyf\njoJf/QqZ558f03b9+NFiGVyffw7IMtLLypAxfrzSBqsVtsJCMFZrjH9ZT/jt1b5+KiCEGOIftPa3\nfPopfDt3wrd1K7xbtyqBZYTQRTl07BiaP/mEkp2WhWEI2FLP5evqUPXcc3RxJ6KI8IkTsOTlwZye\nTi04WoqVXhtPROwGP7nepxtn0WZtNpizssCYzeAbGtDwzjs48b//SzVd7d30Jv3WAvfCYT8EIoCX\nlb7qcdddtM0afDt2oPnjj+H6agO8ghfWG38Rsw6ljRhBx42+3YLbbYwNUXeS09wB9cuWofKpp2K0\nZ0KIoS/i1TnRf+vovg0ePYpwRUWrdUvaIkXR64UUDoOAICgFsLvOuAue3EoWVkzQnmbSt9lg1dwn\nUSZ2veler+HrS3LLoVC7BKTo/uzMgD2gE0z6LpcLTzzxBN577z389re/pcebmpowZ84cPPnkk5gw\nYQIWL16MOXPmYNWqVeB5HrNnz8bs2bNx9dVX44MPPsBtt92Gzz77DM52FoDQQysr6dm8GUCkepQ5\nI4P6gRmrFZa8PEOAhrO42FBhimEYFNxwgxJg0707siZNgiyKyJo0CQzLouh//gdEFKkWoMGqW7Ct\nXbuCq66mA1kjbZOmQTgckEMhmLOyYO/VC+716xE4eBBEJXw9NGKzdu3aZnqR5sdnzGYDKev9x3qN\nV7MKaEFzmiaeWlyMVJV04sGUmkr7VX/M1q0bggcPwlpYiHBlJX3/lIEDkTFuHABjhGvGhAmwFRbC\nptOQ9RaN1sCwLOy9e4OvrYW9Z08EDx2iATz6BU3fn86BA5F1wQVI6ddPiZsYOBAMyyJj7Fh6jl5o\nYh0Og1WGYVmYUlIg+nxKxgTLwjl4MMwZGejxpz9RUzCgWEk0/5slPx/5s2ZF7qvzLerb5lb7Jn30\naIQrKmiFP1uURYVhWVjz82OiwC25uWdkC8/OgBQKoTnUAAYMsqzZMbXdheZmEELg9zcjNS03EsQY\nVeCIEr4+JU0l/ODRoxAaGxGqqIA5IwOhigoQUaQCqhajoS34mjbO19cndA0ZgtB8Pjr2aDxOejq1\nOjBq3Q1LXh6ExsaYgk9EEGh1OEAh/NbKNstE6R/NCsBYLAa3naFfZBFBKYBDQjkGZWVRwu02dy7M\nmZnUhanvt7qo2AaNvLS4FQ2+HTvo/CaEoPHddxE+dQrd/vhHsBZL3ODD1tIBteDN6Iwb7bfKf/3L\nECsUD5LPp1RNVHnZzMsIiAE4zU54t2xptRppoih91m5XhB2du5SeE23Sj+IHLfaLTxAEqr1XzqWX\nxvRHyoABwLfftvq+HcH31vCvu+46mEwmTJs2zXB87dq1GDhwICZPngyr1YrbbrsNDQ0N2Lt3L779\n9luwLIvrrrsOFosFs2bNQm5uLjZs2HBabfB99x1cn38OORRSTNc5ObDk5SFn+nS6aJvT0pTFsqAA\npvR0ZIwfTxdTp47gUvr2hV0txJJ5/vnInjKFki3DsjEfE1DMvZrmaC0oiGgLDBPRlIcPR8rAgdQc\nbc7KgrVLF5izs5WCLoFAzMLiHDwYOZdeii6//nWbfaBJ3pa8vMjzYdTwo2EwWbdyXsyzorR8c2Ym\nJUtLTg5d+Bir1UCaGqEzVisyJkxASv/+7S5wFI2uN96IHn/6E7KmTAEQ0coNhK+7t/a3ragImeed\nF1eAMqWmRr5j164xgWNsSgpElwuiy6XEVKjvZnI4DOfSwhwME2ONiPe+KYMG0fOtBQVIHzOG/maL\nUxRIH6iVNnIkut5yCyxZWQkX/J86TjQeAC/z4OSIb15vCpY5Dk18E5YeehFCOHFusuT304BKDRrh\na8JA8MABnHjkEdQvXw4ASB06FADAquZWqNqp5tqSvN6ERWz0z6mcP5+mdmrHDWNR/TaW7Oz41dw4\nzkC4UiAQNxZDCw6UoRI+2iZ87ZywRY60iWEUaxjL0rlBK8qpAbPRBWTM2dkxFgK9LzuwZ49SrdPv\np4QdnQEBAHwrhK99d9HtBlddrUS1q2moNOW0lSA2NiVFCcb2+eh7m3kZteEaBA4dQvPHHyfc9157\nd8HtRriqKlK8CwrhszabIa6HvkO0ST9aIdSyqHRBoP7vvqMCuia4Nq9ZY+gP1uFodwXE9qJNDV8U\nRQTjDHiWZZGamoolS5agoKAA999/v+H38vJy9NGlRZlMJnTv3h3l5eVwu92G3wDgnHPOQflpbhuq\nBUeYs7ORf9VVBkKy3Hgj6t94AxkTJijttlrR46676O+9Hnggxv91OrDk5kIKBGAtKKAmLXvPnnSB\ntxUVoeCXv6RRvimq7905aJAShQ/ETFiGZRNWxouGOSsLaaNGwd6zp5Ho4miU+jZraKtimR5ppaWQ\nwmHw1dWQOY5W8GNYFs6BAxE4cAB8bS2seXkGYrX36oX8q6+GvXfvyAL7PcAwDJ0Q1MyuEzD05Gpq\npR/097MUFEAqL4+JZNbuoXn49NXSomEtKEDw0CGYMzJiKr0xVqsSPCrLNM/bWlAAc1YWTA4HWKsV\nGWPHwr1hg2JliFpgAShWEXWhtXbtSgXU1oIUf8rYW70FXQDILAOJSCAcF6PhSUSEmZMR5loviiV6\nPHEJX1u4QxUVlDBSS0roWqGZTjUypjEbfr9Bkw9LIZgZixKYF2WO9m7datDSzBkZ0Gwu2tyO9z21\ndurvJ/i8CPsbDBoZa7cj7xe/wKknn4xo+CBgTCaFuOMQPmu3gwTCIADCJgmWLEUYNakKkHYOECHf\nsM+j3BeKEOscNAiOc8+FvWfPGKuD6Hajzl8NH/EjVRcMKHm9QF4euNpaQ4AsoIu9UK2dsiDQ9UDS\nafiaMNGybh1ShwyhPvBoMBYL/c6WnBxwwSCEpiYD4deFamH7uO39AoggoGr+fACKMK1ZgLU+shUV\nQWhuRt4VV4BX9zCRw2ED4cdYgKNSrQElGyxj3DhkX3SRUbhVv0GXG2+EtaCAWq07C20S/tatW3Hz\nzTfHHC8qKsIXX3yBAp2fU49QKITUKBJxOBwIhUIIBoNwRGk6drsd4dMIWCCShHB5OcxZWeg+d27M\n75acHHS7/faE13eWjyRjwgTYunWDJSeHLlZ6X7oGc3o6stT8du0cSvjfY8FmWBa5l10GwBh805or\nQE/45g4QvqN3bzh698ZJNWaDtdlgcjiQOXGici91UYv2KTKqGbwzwdrtisCmmoD1qZGM1UpNcNEF\njRLB1qULwuXlVCrXQy9tx5TX1EGz6sRb3BmGQcEvfwmZ43Dyscfosa433xyxJJnN6H7nnQnT0/SB\nk3oB52wl/IBHcWcEM8yQAhJkno/rp7XwMrhw637Q8MmThkI6cpSGr5F9WmkpsqdOpedpgplGTKzV\nCsZqVbIyVHOtTGS4BWVu94kiaD3iavgqCZh149NwDc8bBAuXtw419TXoLTlgNynflXU4aJwR0Wn4\n2hoWj/DNWVkgARdEKwseAn2+fr5TwldrQbyy/1mUcc3ItirarL1XL6SpgbR8nKyANw+9DN5pxq9c\nkfmh1Qng6+th69oVtqIigzUAUNYfTnX/UcJXBTPR7aau0raUA5PTSddcS3Y2vaee8BtaTqCoHSVv\n9VH6+oJY2tzPnDwZ9t694Rw6FKkMg3BFBUS3O27QHn1PnctXj+CRI0rwtOYOcDpp8LbmavrRffjj\nxo3D4dOoOOVwOGIIPBQKISUlBeFwOOa3cDiMlHZoYRq4ujrUL1+OtJEjIXMcnGp1rDOFlH79aKpN\nxtix8HzzDTUXtgY9cbS3tnpbaK9pV2/G74hJX4MmVccMcHWha40UOwuab51OuCi/u5ZW2F7CTy8r\nAxgGTjWQTw9WR/jxcus1WFVfX2vvz9psyDzvvMgCHG36b8WUpycSvcvmbCR8IstgA8paEEq3QPZL\ninlbvzmRtnBzMrhwfA3f0a8fQkePounDD433jyZ8FZnnnWecJ5qGr9NETU4npGCQmvQ1MzqgEFOi\nXTH1Gr4GbW5bEmj4MscZ2siLHBxeBiEpSAnf5HAoBMCyVMMHIXT+RZuSAWVcyWr/cTJHx5vXJiKF\ndyPTmkktYXI4DE/5YWTUhyESAQ1cPRgwyLACQTGAFLMz7jMsnAw+hUDwuKlFQvJ6FcFLlmErKkL2\ntGlIKy1F9fPPR65TCT9w4AC1EGqBbUQQaH9o7xctBIakEKysFbYowqdwOgAOsIRleGuUmBd7z560\n0FjXW24BCKGZSoAx+0UzuRfNnh1xyWRmwqIKP4Ayj4kkQfR4lNopaiwPY7VSS4Y1QWaY0NSkBG6q\nMKWlQQ6HDeOyswn/B0vL6927tyEqX5IknDp1Cn379o35DQAqKirQN6p4RWsI7N0LyeejJWHjLdBn\nCllTp6LHfffF9fdEw/QDLNgMy6Lg+utROHt26+fptMd4E7kt2M85B0CsycpZXIy00tJ2CTydAb2f\nOzr9UevT9sYKmDMzkT11atyJpjfVtVYYxpKVhcLf/x6ZUdkc0ciaPDnuBkHtgebL1WuMZ6MPv/7N\nN2AJKGb0ULoZIpGUXcn0kdwquZl5GXw4Psna48Q6AKqpnOeN2jjDxLiwtAyNtNJSeszkdBpM+vo0\nuaoFC4w1KLTnSVJcwqcm/QQaPldZiWa1KpspLQ1W1gK7X4TfIlDCY9VYEdZmM5r0td+jg34zMmBK\nTwchBCaRgJd5WPPzIRdkYUtmJV4/8Sq9TiQiOL8HDcvfQJ9tuowJEPyn8UMsOKqYuaOFe5nIsHAy\nbEEJRJKoVU/0+Whcja2oCIzJZLAosg4HnZMtn3yCcHm5oSofoBCiTGRUctVo4hoNQakhKQSP4IZH\ncBu+pTknBwQELr4FzZYQJDODrNow+n56EjKRDenNtm7dYmJkDOmhakxYPJO8Bk2QE5qbwTqdkQwh\nTQizWJTjuvVElEXUhWsRlowWIsZsVghf9x3PGsKfOnUq9u3bh7Vr14LneSxatAhdunTBoEGDMHbs\nWPA8j9dffx2CIGDFihVoamrCBNXP3q6G6zrFnJUFu2oC+SmAUSv6tetcPem2cyvP9iClXz/YWhmo\nGrrfcw+6/fGPrRJYIuRdeSXyZs2KyYs3OZ3InT690wNOEiFHt6tZdL9r/24tlqG90Bb+9lgLbIWF\npx2Q2B4UXHstetx3n1EbsFg6JR7lxwTf0IhuB30wMWaE0s2QiGLS13K1OSkMn6hofWZOBs/FN6Oz\nDkekdsS0aeg2dy6sXbsqZZKjIsVNTmeMq8vRqxe63X67cSw5nYAsKxkXDAP2wjFwdVVTHxE/cEzm\nOEPVTE2Qpib9jIw2o8w1EzBDANHKQrKZ6DsCinAeCdqLkLD2jNRhw5Axfjy63HwzTA4HCAhYmYCX\nObBWK4K/ugB156YiKCnjOcwIqCXNqD65D5IQm9Ip2iJ9pRGZTGTIFhNEIsISlmD3iSCE0LRkoaUF\nvh07QEAoqerjDEypqQbhR/T7Y9LWZI5DQPTDJXvwn6p3DRp+SCVLURYRshEqAFmysiATGZzMocXk\nw3cXFyCQobRZJCLsPXvCVlgIe+/eiiYe9S2iAyrbEqJpKqwgGNwk9LvbbEqskarYWXJy4Mk1Y/+k\nXFTmGPua8DxNz6b3OVsIPy8vD88//zwWLlyI0aNHY/PmzViwYIGSDma14qWXXsLq1atRVlaGZcuW\nYdGiRR0y6es/fvqoUe3aFeunCk1CTVQ/+4eEOTXV4PfuCEwOB1KLi09LWOhMmDMyUDh7Ni1Koweb\nkqJodJ1A+NRlo+bFn0kwZnOMQMEwzFln1teIy8KYEUqz0KA9TbhyCS6qCVl4GUKCoD3W4UDuzJnI\nnTkT6aNHw5KdTYO5os35pvQ0HPQegESMi7slJweEZfB14wY0c82RgNDGRrB2O4ThfeDuouZYk4h5\nP+eyy6iLR0/4rN2umHjNZuwPHMTGxq+U79aG+8yam0sFCtHKQowifFgjWjYhMmSTqlWq5MSmpKBl\nbC+Q9BSlD1TLhJazXxc2bhZU7j8G3mEC4cIxfaK1AQAkIlHhopFrRLm5ngZT2gISCAisXbqAsVgQ\nLi9Hc80x7Orph5gRmy1jSktDWkkJ0tW0WH0uu97nLYPAzMvI3l1HayjIRKbvwjAMtoR2wy/6lNol\nGRmQiOKWqRqUBn+OFS2l3ej7S6l2FN56K7reeCN9RuEf/oD8a66J+y3aJHzd7wZrrfYtov5vzspC\n5ZXFaO6RghOXn4u0UaPoNVIoBFkUUC5W4oBHqdr6k8vD1/D444/HHBszZgw+jPKpaRgwYADeeuut\n036eNqlyZ85MWJf4bIFz8GB4t2xJWAWwvQiKQdhMVpiY/9qKyQmRyJqRNWUKUocP7xRzt3PQIHSb\nMwfmdtYLOBM42whfIzaWMSmxGKRZqUvOcco307ltzZyMUMgLhyzCzBrHOGuzwZyaanCRsBYLQAjq\nli5VDqgBnF6bgA+r38O0LpdgeNYIw30OePdjc9NG7HRtx6+dqq9WlmFKSQEnhSFZFPKTiQwToxBx\nWmkphKYmeLdsMZRSZm02WHJyINntWF2jrIM2kw0pqUCKV9WSiQQzGyFwR+/esPfqBbJRR/hWBlZE\nrFWyNWIJDMsc9gcPosW1E33VMd5I3Pig8h30Se2Li+y9aR8LsoA97t3Y61HS3LQo/GP+o7CkmOD0\nCBBJbNlXjfDDUhhWrVocZITT7OC9ArKrCFJdPAgylfRQux2SIMBl5XB8VCFcfAscDiUbgrrYVDN3\nSr9+8H7zjZLaphJ+yrnnwqPWpSBERqpLQMb2JoRsEcFDS7KXiATBzkAkIurERtSH98BZ2h8HzYfh\nKlL6K2XgAPh3VaM+Q8bemhW4rqeS5ryl+RvwMo+JXc+PWwNEJjLC5tY3QNNbMfV/M1YrCCH0ffVV\n9jTLitPsROqwYbS0r+TzQZJFtCCITTXvY1DG4ISZCaeLs1YtpoVd+vU7q7V7QDFB5l9zzffSHCUi\nYvHx5/FpbfyNZn6usHXt2mohoY7Ckpt7xi0arcF0lhE+cjPRUmiHOLA77I5UyESim5GY0tNBdF1t\n5mUcbzmEJr6Ranga4n0Tw2LJMNRC43coZNHIxW6OExQVC0JYCoNNccAv+iHIAtiUFITlMCU/vYav\n+dWBWA0//5pr0PU3v6HnflH/Gb4Y4kX6pAvgFlxo4psgyiJkIqN2WDY2TrIBaalUKxdtLASV6GgJ\nXIt+vSOQzQw+r18HW1ERTOnp8HZVzjvuP4bUYcMQ7JOL3RcrmSMf166GoPYdAUFICuG4/zh4hyJE\nCHJik35IChriWEJpZnBSGDnVIcWHTwjMmZmUuOv7OkFU68OpwEmsrHwHsEdM+kBE8yVq7jwAWk1S\naaPax2AQlkKQiUwzFABAMjGQzCx4WUCYEXDMfwyusb3QeE6EfAtSumLn9AIcPi8HlcGIj36nazt2\ntChkG0+TdgsuHOAOIyAmTgU1lDHXmfQDTBj1XB2CJiVoVHOFEJ6nY8zO2mHv1g3d7riDZvbIIHSM\ntfDNZ49J/4eGflKd7aDldL+H4BKSwuBkDm7B1fbJSbQJQgjcfGy1r586mLNsPsgg2Dc1H+IlY2C1\nOUFAIPMcZI4DY7PSxQ9QCN8kKou9V/Aa/Ojx6kjoCb/HvfdSX7LfpmixlcFKrKx8F01cpAKkqDNp\nn0Q9/KIPbsEFU0oKwlKE8CUYNWF9LruWWsWYzfjC8xVWu9dSawAABDMtYAecQ4UWj+BGE9eEI6Za\nHPcfg8saMpj0OfU1NMIXrUbhRjaxii89K0spsdsjUoeEtVpRf9EAeAviW7iO+49CkHlK+GKUSV8y\nMyCs8rygFDT0aSjdbMhcIA6l0FbG+PEghKC2v/JNeJnHm6eW4Zj/KNxspCIdAIOgRMvTpqdHNprR\n+oGIcAtuBKUAZF3wpGRhIZkZaIKPS3DBIxjnrdOUioEZSjowA4YKa5zEgZM5yEQ2rL2M1QqRiOBl\nHoKFwYlA4vowvhwLvIJHCYzUjUE/o/CTRviaACPzPNXwtb62ZGZGxg+RqYB1yHswSfga9JMqCYBX\nq5RFaz5JnB4O+Q7gxePPoTpU1fbJPyGcbZH6hFEWbxtrg82uEkTAB8gyZDMLQfVfyywDCyeDFTQC\nECDJEnJnzkSXm26CuSAfYSlqhzodOZlSUmiQWEuqstA2cg045j+Cj2tX0/MknUn7qHRSPSbDkp2t\nEr5CfnoNH9ARVygEzu+FpJrdj/oO45D3ICQiIcOSgS52pb5D0CRQ15tABMiQaByA2xyiooxgZcFZ\nlGdpJn0xaslTCC9inYgm7eg1YWqXaRibo1gTD3iUKm8ZWbF1JwAYBK6QGFIiydV3D6dFGtLYMwXC\nLdOVrXSnTEHaPbeCc6rvJ+s2pLErpu4Ws9JWTUA1EH5aGiVPOcrFIBIJxGGDN9dK3526WUwMAqIf\njZxxDwIza8aMoivQL60/CAg+q1+LTY1f08qOnMyhMlhJx481Ly8SFGhhcSKgZJS5eRf2efYasjVW\n1a1CUAoiIPkN5aA51RUgWICAGMCu/GZIRIS9eBB9jv670NRDyNSis7lpI5qlzlXgzlrCl6LSF/4b\nUROqMSxArYGXlMGjEb8GURbjBuIk0TqaOSVAyMUnrrv9U8TZNickVUO0mWxwWJyQTAwEn7rrncUE\nzmmCzDIIp5lVDT+y2IpEhDk9HY5evfBZ/ad45shTOOjdj3dOvQVOiswDTTN2DhqEgl//GicKjfNB\nT5CiHPm7ltUWWwLn+LHgZE7nw5eQNnIkci6/XHmG2u9NH36IxsZyHHTU45PaNQhJEW290FGEAenK\nFt0BkwDqhx7YE3mDRmLiCCVwrEV2Q7QyYMFCtLHwFNjAOhw0PYyPInxZJfyqkLJDp7YWKO2UIRAj\n4adbMuA0K4RaEVCKy/TI01eOVO4XdpoRdkYeFpKCyv7xars1q4CJMcOfbYFgUa5jWBYuRAKQ9cTG\nOhwISgGs83+NmlB1RFDSmfTNqalwqim9UpRgFU6zgL9tJmr7p4IBC8nC0KBFrR8awsadJM2qYJVi\nUgJ3d7l2YGPTV5F7SiG8cXIp3IILBASW/Hzq2mDsNpwIVIAQghVV72B1zYc4Hohse+sXfTg8Phth\nVqSbcAEAZ1LWbd5MUO4/hu+6utFy/UTIowfRc/TuE81VQohi0h+WWQKJSPjWnbgM8OngrCP82ldf\nBd/YSPeujoZX8GLBkadx1NfxYkE/JVQGT+H1E69it2tXu87XJpV+oQOApSdewTNH/oWjviPxLksi\nATQpPFprjHceaaW294+FgBjAMd9RpfZDJ8QY/Fi7X9J0KtYKh8kBycJCVAlftDA4NjoL0qxJ6F9Q\nAjMvw8JJNNhMJCLVjHa5dgIAPqx+HxWB49jp2qFUQCMSmu1hSlZSjzyIUeZ4vQYaliNpf8FMCyqL\n07H7kgJ4zCFwOpO+SCTkXn450tUdNzXiEiQegRQGhydm44B3n0GYcJgclGiDJAiZyDAzFow8/zr0\nvfFWZDuU6HQX3wLezoJllB08G7rb0PO++2hev2A2edjd+AAAIABJREFUjjdJJTw3r2QjcDqh3yt4\nYzT8NHManOaIjzvHmoO83F7K92AZmMePwOHx2dh7UR56X3sTZhZdobRZNUVr30zrCytrRSDLahAs\nXHxEM9X3rzz4HPiGFMJTYIOLb4kUElI1fDYlRdkmfMQIFNxyM2r7GjNRBFYCL/OQTQzMjAmyWSF9\nfT9Ew6IGRerfWQ/9HJeJrNQqIEpp4dy0rvCLftSEq9HMKXsAHPMdpedyMof6vqn48lcFEFJ18Q0m\n5btzFpn2mz/DhBpdhoRBw9dM/qpJf3DGEPRJ7Yt6sTHGYvN9cNYRvujx0E0G4uVD73LtQFAK4j9V\nK9p1vz3u3agOdsxsWxeuxZEogaKiNoQvdnWeNlgfVmrDN3L1kImMna7t8IuJ0/a4OCZ9URbRyDVC\nkAV8Xr+23c92826cCpxM+DshJMakebbBJ3hxyHsw4e/awt8a4TdxTXj2yL+wT416PlOQiIiFR+dj\nZdU7kEaeawgS6yhcLhfuv/9+vP7664bj2u6Xd911F7Zu3Ypx48Zhzpw5IISA4zjMnj0bV155JbZt\n24Zf//rXuO222xBoZRtSDZoP2MbaVMJnIIsiCJERMgkIZVhg69kDjq7KhkE5p0IwO1Oxb0oePIPy\nYevWLW5Q1f6GE9h15Dv4BD+qLW4srXgVhBAc9R5FICwZhDQ376JWsJBkLNDTOLobvPk2NHKNinBn\ns8DMmMHLHJZWvIotzd8op6rKBydz8BTYINpMRlM2ALvJQUnHJ/mV/HiGoa6HVHMqQEwob2kA52DB\ngIE5JQVNXCPmH36SxpSEVRO/ZvrVNFstfdFI+J6YdqSa05RnqeiX1h9pGQVgwYJ1piBr0iTU901F\nKN2C7NzuyFJL7Gp9owXNae4NG2tFINMCQRbQxDViv2cftZABMAgCQlYK6sb3ADEx8Iv+SCGhcBii\n10t99wzDQOiSSV06GiSBp5YWE2OCZI7V8KMR0fDbSfh5eZCJDJZhUZSp1HfZ696DArtiYakMKmtj\nM99ELbAExOD+C7NKn4dNEu23oBTAfq+yVlhYi+G7aBq+ZtJ3mOwYnjUCspkxjsnvibOO8AFAaGhQ\n6qOrk6yuhcPchYex+7gPAlE60dyO1LSwFMbHtaux7ORrHXr+xzWr8V7VCnzVuJ4ee3rlKby/qREu\nn5D4Qh1komzokEg71EzJbsGNo74jWFf3Kd469UbC+2mTXCQiJCLBxbvQxEd8WR7BE6P9J8L6hi/w\nduUbcc/3CV68fmIJnj48Dz4hdiesswX/qVqBD6r/g3L/8bi/a4sAJyfus9pQNQgIasPxt738vqgL\n1eJk4AR8go9qF/GwXY00BgCP7E+4QUt78GPvfhlQtR+rSviilYUMGU18E/aHFKHaYXIgfcwYEEYx\nNptLh8DTPRXHxuaAYdm4QVXHAkewtcQMlzmMihEZcAtuvFe9Eu9WrEKzV4DDNQIMGKSYUtTKbIpG\nGhKNi2uRQwn0OxU8ibAchtnugOkXU7B9RhfUhmuwvuELABENn5PCCGZacI4zthCYw+SA06QQbYs6\nvxmwkcI5DIvaGiuONdUhaFU3c3Io53Myh2P+I2jhm+HunY7afqlw91a341UJLyxrvuHImPUInhgN\n32FyGAi/LGc0LOnpyLPlo0f+ANjZiOXUxtrhUE3h9eE6uHk3DZrLSckHM2YYLIWF4FJNEGQer5S/\nhFU1H+CoP6IQ6YmNlwVKYJqgxtrt4L0eeIPNYFJT6DXr6j6JCVBkRRlewQPRDPACA94UiWGQTRE6\n6582kP7dpoavs+pIRFK2moYMBiy6ZPRAqjkNB737qUDVwrfAI7hRr7oOuqcoxYa0gGlCCAKs0uch\ns4igqIzxmlA1qoKV6JHSEznWXMPaQtP2iAzRysLGOPDtFidCIgtRbh+ntAdnJeFrmw1ohL/5gBvE\n0YxXPqmmPjh9bmsitKYxt4YGTvnQ3zRtitEAebFt864oi1h64lW8duIVnAyeiPltc9NG1ISUTSrc\nvJtGETdzTQk1a/2k9ot+LD7+PF6reMVwTlNUMEsi+EQvZCIjJMXukritZStqwzVK3mu4Ls7VERBC\nUBOq+UlaA7TiI20RfmsavraRilcVfAgh2O/ZaxCERFnEW6eWY7dqcu4IXjvxCt46tRyraz/E6yeW\nJOzHCh3htTWmRVGE1+uN+c+v1oVfsmQJHnnkkZgiWK3tfllRUXHau18G1UW0qk5GYzMDwW6CIEoQ\nJImaah0mByxZWajrmwreYULKyBHItubQ+XDMfyzmvpJE0JBrxWczuiCkVlo76jsMSTCBPT4NgZOD\n8KeBf8HoHKXwS5MqUEWP+Z7OnkgxpWCPezdcfAvsJjsGll4CKUfVRMEY8q1FIsKal49sa2xet93k\nQKpKOi28ogGzDGMsuxpMBVgJwVQzAAayMxKE+UX9Z3jp+As4KJ/A0XHZYNPUHf2iNXydoO7iW2JS\n7ViGRbolAwPSB+GywsvhMKWAtVqRM20asi6YRGv3K222w2FSLKmVwVNYUvEyfGN6o7ZfKkbljMWY\nX/wPMn97PcAw4GUhshWvOm+CYQlrd9VBlrVaAJG0tICojDnWZkMo6EFA9KOa/H/23jtMjus88/1V\nVVd1np4cMBGDnEiAIEEAzBSDKIGUBFNcmRIlK1nSWr7ySt69u7oOa1/7euVrr31tmborXcuSKStZ\ngaJIU6IkUkwQCBJMIHKaASaHns6h4v3jVFV3zwwCSZAWpH6fZx4MprurK5xz3u97v3ByOI7Didxx\njueOIc1bTmXTYbY8S8mRKJUl0oaDFdXQQwpmq3gmzVqzv/EPVHn4gcWbb2WNqt3qHBsnFsFUJWRJ\nJhAKMxgbRLd10kalgVPGyPgqrGdcpFyjsWyXybQE0MMKc02SP6Y8o3JlfBWaHBRdJb05rarkzJyo\nDAjK6OUAew5myWbjv96SfjV0Db516uvkIoewlz+Mvexh32pUz8PDz5mVB32+ssl8eWxyHumV9DMn\n2TmOg2Ha7Enu9j/3UuoF/ubw/81EURDQi6nneXL6cZ+QMkaasdKoyGzNGrw4trjUXm3VH54nVXuS\n3GJ1x4uh7E7Wxe5JNaGci1wOZg5w39A/8XLq/OK554Mvn/gi3zn9rUVfezWxdG9RO5E/xv6hHH/1\n7WHypcqz87ylsn0WwncncMZdCA5k9vPg2AP8cOwH/ntGiqcZzg/x44mHz/vc5mOkcFpIxcbiu31N\nlyrPNWuc/Zns2bOHK664YsHPHXfcAXDW3S/n73B5IXe//MrDU3z/8Qx6SCZdMDAtG9Ml/JDrYR7d\n1sQzdy4h0dBGS7AF0zGZ05McWyQ/xbK9f8WYWN0gkqXajUuRCm2UDfGG9pC43hfmnneN3Nox36Am\neP/SDxELxMgUTAplh7AS5qPLPsFgbBkODnkr7/e3d3BQ21oXJZewEiakhJGQSLqSt4RcW2lkCBIf\nWhNn8o4NTEYr51NdhhhSQsiaW8OueI1xKlnnHkaKpxesWSBI/x3d72J9orLfRWL7dtGSW3Zr5SUF\nVVZ9D9k79mOD0xzd3uzPIe/1+d/TE+llJmMwU0yRLbpJbI7uqzoz5Rn2zD6DFAxiY2PbDs/NZDkw\nnCdvibV5INhHtEqKV0yh/uhBCWyZclCmLbaE3e9egr51NR9b9jt8YOmHUOVKPN1z/jx1ZT7Srmf+\n3Du6SP/GFkpOyU2aFJ0ro4GFnyuYBX8NXxlfCcCcG3LJmTky7UF239XNTGMlhg9ijTp0NIBjiVCF\n56hlpDw5MyuUhXCIsi7Gfj7bCBcwReiiJvyD5WMM5U9y2Pk5AE446UtJsrTw0hzH4ZX0y8JCtEo1\n9Zrnm43teXPepJgojfuLCkCxfGZv9tnDWX7/i0d5drri7R3OHEK3dfbOPce3Tn19wXk4CGu3qNvk\nihZffvq5Bde0a+apGk91f/qVmvcMRAeAsxP+7gNpHvyF8HI8sistQnbVC2K2ivAN2+BI9nCNF7ov\nLfbHPpw9VPO+Z2Z/4d/Hs+Fnzyf58bOzZNzNVWzHZro8zfFFPLrP33+aP/rKuT1K7xw8D2ROn2Pv\n8BinpkqMTFeu97V4+IcyosQpqc+i2zoPjH6fJ6Z+fl7ndDZ4ccLFxmjezFOwCjSqQt7NnsMI83a/\nnP/z6KOPnvVzZ9v9crHXznf3S3/m2CqYQUqaBF6M2CUyz8NEEjXhsUCceEB4cy+mXsB0TPrdMe7B\nm5OmJf69tfM2dix5B922SLLTXcLvi/SzPLaCo+kT/NOJf6xZnEHM84SaoE9dSypncmRaGOLRQJTW\noEiyS+lzSKrql5CFmtoWlY9DSghZkokGor7XJkmSv4eGYdpgCaIyVAmrt42bO99Kg5pYcKywEsGJ\niDVIioSRJdmXpst2maAcopxJsHfsGCXjzE7IsdHCgjBk0CXyak/fdhxsx6E9WDEIvdc1l1Dn1793\nh4TUjZqnUBatd8tW2VcipsqTPDb1U1JSzjWWoBg1GJ0p++tMW/vSmrV8cjAqVIJogMf7b+NQ6BZ2\nLLmDllArS6ODNGqNaHIQrZrwz+Hhp400ZcNmKigx2xakaBWxVJE0KQeDNeEPDzkzx1Rpkiatmbja\nQEgJ+5J+vsqRdHB8xwCgZNjsftFmYqaieABkqIy7oBahpLt5GmYLp1ZeuD1JLuoidtHEIejLRQCW\nBQFl8YX6VGGYh8Z+SFAWGxpUvyepJ1kS7l7wmfnwvLlgoZ8xfT/j8TGywYrkUtTPTPhDE0XsyDiz\npRTrW1ZyMn/ct9pfSb8s3pM/uehnY7QywzgEszX7pE+Xp3lyujZW6oUcPPRG+nlx7gWmylOcchNO\n+iL9/uvDkyW+/qiwVm/a3FxFdgs9/OoFsdqb3DXzFLtnd3F127Vc1XoNeTPPcH4IEFKgbpfR5CAP\njv2AI9nDzJZneduSHWe8V5m8yQ92Tfvn99s7umuMjbJVJqhU5M4jI+5GILpFSDv7JkTzFyYhtTWS\nL1We3WLy6HxUS3glq8Sp/ClmMwZNDY08Nf0EB10DwIOXCHQ+WMwrm9VnCBVDTJenuLRRtJCdLE5i\nOw6DsWU8P7dXqC5vQCPAwcFBfvSjShfH6t0vZ2Zm+NrXvlbz/pMnT7Jjx5mfrwcb4UlKjoJjaeQV\nCWS3MYr7GD3C/+1ln2BOnyMaiPpe1343YfKSxEZ/vDmOg+USvWU5qLJKSAmxLrGeQ4owesuGzehM\nma5mjUsCt/LYyQx6zyjxSO2S6I2xHmkD8ATSdKWsqkkVdf0pY46eSC+W29c+HmxYNEHMu45oIEbO\nzPH82zvYZq3xW7ImswZYXq9+UT++Ir6SFfGV/MPR/6dGkQwrYUqDzbx88zRWTwMhyanknVhlTD3A\n1GgjTsskAcViSbSNWX22Zo0rli3+7vuilO/vPlkpy1MlFQmpJpY/8cwN2I7Nth2Gv774Hr4kyHV+\nyDCki9p+Ry1gmA6m6fjrZzUychHNsXAcyDbqpPImsjv/ops2UrCKPN1wkKZigNm4myTnwHS4G6kg\nE5Mb+ciy2p1BtSpVQnXbMIfkkG8ABqoy+lNGimTWwDAdnpoboyeQoaxISG6VRNSpEH4sECdnZhkv\njVG2yywNiVBWk9rEZHkC27F95VNCwsGpWTNtGzCiFAoSahzKtk4cSJP3ydjGoVgW1ykVGzmy/MIR\n/kXo4YsHZjs2edVwf3dfsjQMV8sr2+UFNewvp17yX5tvEHgxtXPBk1UnRhrJ5wKM5MdI5y2cYAon\nMeRbZoshlTNx4iNYtsOVLVvPufhXJx4mdNEWFLXAXLZiYCw2geYjoTbSqDUxXZriByPf4/sj32Wq\nNMW4myfw4O4ZnEABJ5gimS/6921fah8Pjj1QE9csmgW/nrVa0vcW22dnn8FxHI7njuLgEA3EsByL\n4fwQo8URv7rhXB0Bp9P6gt8LVh7DtLFs54yfn0ievfGQbuu+UeXFWb3rOFk4yr8M/TNpI+XfgzNJ\n+rpdrpnIR7NHSBby5EsW+8bHeC65Z8FnzhQ2OlUYZqwoEv/SRoqUnlrU2JrTk9w39BV+NP5vvpz4\ns4MnGJsp06b2oMrqOSX914o3avdLB9Ak13CzgqRlCSTXu1EqMXwQoalGu49Dp/K+11W0ihTKFg8+\nZvvJZLZTUQ5M2yFYRVy626nPtBw+980hfvZCkmxORj59jU+21fBIzyiGkV95D9JEpVd/QhOqyitz\nB/nLH7zEkzfeyC/u6iYWiC3q4XvXEQ80YNkOc40qgY2V5LKZtIFkujK946AQIJUTa1xCrU3EjCgR\nAqpGakkISVEIKSEKZp5nZn8hNpKxNaSc8MYtyyFQbuOurt/iP/T9JlMpnZJu16iR1eEwSZLY2rqd\nzc2VjV2cfCtSoZ2OYKVBT0h2N8KRFCQkP5SwKr6aq1qvITsjzlkJFv3nkjIWdq8cLWfJFk1sx2G2\n1WE2l/fHf0SNom1chxWUiXcv9Vv1YitILn0lswtj3JqrwEpIyCj+dY1NKIzNlmvCIxk9jeHmXuUC\nI/x/h/+Z2YAEqiY2CKvy8FuCYs046SqqHW5IqFFrxHZssmbGT8hsDS7cG8Vxy/3yeXHunoefojZU\n6j+bUhO6ceEs+IuO8Of0lGgmkQgx2ROmULaEh28GkYrNGKaDbto4jlND6iWrxOHsmcuwkuWzE/7u\nA2meeHmOjCkItpAJIRVbSJZTTOeyOJ0vYvc9Rbp05gU3nTchMotliSYcniw5H4ZlM314NZcHdiIh\nsbZhPeHMWjBDOGqB4+MVMkjqsySzBoXyvFafVcZERInQFmyj7JJUVs/zP1/8Ep/f90/ols7pqRL2\nqgewVz7IVLYitZ/MH2d/eh/3DX3VJ8CiVXQlrBBZM4ttO5yeKvpec9kuc2D2BD986RCm5XC5u2hM\nliZ5aa4Sy6+u010M0+mKh5vKia03f/ziGONJnZm0USNvV4dUHp4UCW45M7vA4xgpnOZ/HbuXR8ZF\niaKXXZu3MjjBNHuNHzJSPO3XdMOZJf35bXeP545iuN6DrYhmK9WZwgCpcorPfXPID52AMBy+Mfw1\n7hv6CqcLp/nnkyKZM7mIfD9brvzNy4s4nRsXBm+h0fc+3gi8UbtfOoAiuXuHI1GQVZDEWDNlle2t\nV9eM5S//aIx7HxhhLlkxhmdmFU6PSX5c3vPuQXiCKhXCL+u1AdHnj+Z8byqWWy/I0KgQoefhz2VN\nJCfg9wCAioe/Z+wAw43f4UX5CSxNJh5Y3MP3DI+2YBvjyTLjSR3JrkjPsxnDl/RtBw4Olfmjr5xg\naKJIo1ZL+GElguyei4xMSAlTtst+1YBjqZAT5FwybJ47Nsvel1X0ssL/+MYQD++ZqbnOdL6WNK9t\nu54uZz2zGaNmfiWkhZK+JEk1cf51iQ1c3XYtYzPimCF//4FaedtDxsyKZ+6IBMRZfYaCWy0RVsJ+\nDtJAdKn/GcmpfN9sZqEa5p1PQFZr9lmQD70L+dhtPsEDlNxGRXIVr76wPs7UjpuRAoF5PQsEiXvG\nfkdQlOo1amIsjBVH/fK8wdjyBeeFI4yPXEEke+5J7ialp0jatY6bpxRLtoZ14pqFx3mNuOgk/aKh\nM76hj+xlyzh1uhJ3lPQ4lJrIFydJ5UxiYYWiVfAf1lD+BJZjEVLCC7yneCDO8dwx8mZ+Ucu8bNi+\n5H3zu9LYjkMpHwatGdOaZjQ/hhMURDlpjnA4k2NVg+i6NFue4UBmP1c0X8mMM4QTThLQW1FllQY1\nsWgiVr5kUx5byXdHbBpiO+m/tpsTmRRSJIITSrHv1DT7tX9lc9PljGanyRUtckWL7lYZxR21PeFe\nX76PBqK0Bzs4kj2Mg8NMyvDJ6aHTPyEfCoAsJudw7vQCSXhOT5LUZ2lUmzAdk4gSwXIsMkaabz0+\nwa5TB2jdmCMWFD2odw0fZrw4RmNJZKQ+PvUYU+VJhvInaVATNGvNDOVPUjSLPH+ozJr+KM1xsY3n\n0zNP0h9dynOZ57E7CwRT6yiXgqTzJs8cmYQ+8Tyqyc9TVZxQkmH9IE1FlS8c+zy2Y/OplZ/xF6an\nZ57k9FyKfMliSUuQ/mg/L6VeoEQWp/mIHxqqluK9Xtse6UyXp/j68H1+SKQz1MVEaZwT+ePobttX\nrzqoJ9LDLZ1vZV/6JX4+9Shj2TlGZ1RGZ8rs2NbKl/fdzxyn/Vn49eF/9r93sSS/kWJl44/96Ve4\nseMmstIEWBpmIUY8FGdOT553d8az4c3a/TJGG6viW/GKuMpKJfkv5qzhmrbrat5/akoYYE+/pOOs\nEjKxZMTBDmBZbkMe9zmKDuuC/HTDRlNlP3bvIRqSfWN58vAKzAYILc1C0wkkJFRJY2S6xNjswtBO\ng5pAcgKUjRKYYWRVrCtxtbaxzZKwCEd5Y6hJbcXrwlrIK+AmlM+kK5K+48CxER0JeOFYlvbVlaxz\nEGTr5Y7IklwTbwewTRXJVpGP7MDufwI5NcCYVSaTtzAth5m04RtIAKenyzTGqrfddfiLbwzjOA5/\n8L4K0RrFyvNRa2RzzU9A89SIVNaCpgBaAPIIOdtZJAMtnjVBski51RRpa5aiVRBJg5JGR6iDDy79\nKC3BFp6Z3SXI1qpQ12KE7+VYVSdv27bwrh0zSKFsowXcJkruWtgabBO19baDrsm8OB3iyAMjRMM2\nTrcIozZpTb5UDxUPf23DenbP7OKxyZ+RLGVIJyNoidpnBiDZbvmdpWJaDocyBzmQPoCSyrLaUZFk\nm1s738b0CTEmO5uDnBx67WW283HRefgAL8p5jsyKWJyUFQ050GNIkxswZweQMj3ki1aN5HoiJxK6\nrm69dsHxtrZux3RMds/uWvT7XjlZiZ2lymk3DhNBKrZgmA7j5XHQxHsO8iPuH/2uHyJ4fu45ds08\nxf0j3yPX9VOQbJyCkIW8ZBwvU9iDIksiiQnI5CSefiVNMmsQJEYg4PBi+WeMFcb51+MPcipd8WKz\nhYqV3h0Re0CrsoZMgGZVJBiZluOTPcBzs89h9z2F6pb2jJZOL7j+km7xvWeGyOnifoaVCPFAA2Wr\nzNNTu7AHfk7ZsNnSshWAMX0IJ5SCUhONqpggR7NHMGyD9YkNtLnJTq+Mj/Gtn0/y4+cn+OLxe/nu\niX/jyakneHDsfoad53HaDhBduRsHh0OnCjiByqI7mql4yQU3u95pO4hpVkI+AN8Y/hrfOf0tDNtg\nojROPhNBHrqBDnsdy2LLcRwHXcpDOIntSDSqjcyVa7336pLHfamXKFklPzRxefMV2LbDyGyesmEj\nFVqFpOyIcEYkEKHR9QTHsxUjpWyV2Zvcy4nkFA4OW5q3EpACNKgJGtTEggS91mCbu52qg2U7lO0y\np3Kj6HIGqdBKMmsRC8RFDfBZdvf6ZUPIaWFZaIP/f12O+h5ZQQ/ys+eT/OE/Hefvv3+6ZnyPjEtY\nliMqK/SIu5CLxd3zSFU3y39mVuL3/9dRhieLNSQHYq4VSp4yANLcCqyCkHA1WSOdt/jLbw3zwrGK\ncuLJ37Iks0W5C/ngTqRUv//cY4G4m92uISHx7t73sFbfySPPiTWhnG3wj5XJVfJNTk4Uqzx8h1hQ\n/D6bMbis6XJu7XybvwmPg4PtdgyUJcWX1z1YhrgXLcE2lCN3IGX6mZyrqBeFsk25Kvz4pYdG+cne\nypjLFCrNib7180pOUDpv8bauHVzTcgN7DmV4+UTOvVcVlaZRE+taMmMSkFRk1wmpDhtsatpMW7CN\na9uu5/CaOIYq89wl4r4UpSQFs0BYCYtcK93i4ScsJmdN4qp77+wze/jTaR3TFPepujzbX/esICXX\nyIsoEZ/w14eu4R2d7yHutgweHnU4dCrP3sNFZFdRCCsRIq4xFwvE/d9bg61sadlK1sySzBoU55rZ\n+1wDjuOQK5osCYn1uNu4UtwnO+CfT75kUTYcSsUAbcF2NjZt8iX9dQMXLn4PFyPhOzLFwCzTpVlA\n8mUrzRYys3z6Ksh34AD/8MPj7Nqf4vmjaY5kjhFWwmxs2sjqhrU+ORXKFi3GahJqgr3JZxfturf3\nSGWyJ8spVCeC5ChQaMG0bCbNk37c0VO/vBKZkzNpxpNljmeG/GPoGUEACZfwNyQu4b+s/mylHMbW\naqTDw6dFJm1UiRMLK1jx08xmDGZTcGSmUhaYK1q+l9rjNgyJKBH+8pvDPPS4SdmwyeTFQFcDEjgV\n7ybk9gifNivXb1g2+ZLFVMrglZFJjk6KBSEcCBNXYxR1G6dJGFKmCesS62kPdpB2JkFyKKWakCW5\nRo7sjfT52c0/nPkXnPAs44UJZkpJfj7yDOm8ScbIYFoOkgRmZBx7zXf58cz3Qc2jujG88XwlBFNw\nJ4cTG0c3HX9hyRRM9k+d5ljuqN/XXCo0I2W7ic5uQ5ODqFIIR83jhOdQ9ARaYYDRmXJNiKRklZjM\nZPmXn00wkasYA52hLlY3rMEyNUEkRhj0GI4jxkHMDdk0uIvUVL7y2bFcxVAL6Z0Epjbz9sRH+MDA\nh/yOXh4CUoCNjWLf9tm0wdhICMt2eG7aDZHk20lmTSanAozOlJkpnDuv45cFpgVlo0IEZRJ+Z+Cs\nEeTZwxnSeZOjowWeOVRV2WFpFIoSmYKFZAiCtkzhNYX0DqTsEhoUMe5m58QBj44uJPxMwaQwr5S2\nUBBzIaSEaowMD9UG8+xUFMmMELfEgm7ZFe+yUW2kQU0QUkL8fG+BB3fPYJg2U5MVbzydFudWLFuc\nmioTcRUOx4GY28xnNmO6a9cmv9ysoJcZmixgO47r4dfmH5RNQYK9bZXvyhZMPyO/pFs1kj7A4y/N\nMTJdIpkxanJhjo5UHKdUzmBD46UceWEpX/vpOP/48Bi27fhGcU+kV9SY2w6pvElQ0XypvCoywOqG\nNXxo8Lfpi/Qz16bx/dvamXNbCxNKk9MLaJK4F/uH8uw9kmH3wTTxgJhLtqXUnJOHTN7kf3xjmAef\nFnOtOg/KV3fsALohovsJrdEn/LZYlO2DS2lLEZY+AAAgAElEQVT0NgWyKuEWFUG8onmS+L0z1Mne\nIxk++4/HSGYM2oqbGZ020A0bqdDC1KyDUYySzJqcHo7wn1b9PrGi22/fUv2wwrr8+5iafh8n45fS\n9aEPARVJf/1A1FdtLwQuPsK3Aui2ToYJFDOKlO5FKjYRLQ/Q3OBamW7iS8Eq8I3HR/jysa8wPJtk\nMLYcRQrwju53cW3b9bSpncweXsdff3uU2zpvx8Hh8enHxNc4puj2dPx59rnJfg4OaT2DaruxdzOM\nrYfIUiFdL3HICxtMZrIYpkO+7A5KPUZppgvDtOmPDKDJGn2RfhEHI8x0SscoVwZa9TETaoJoSEHC\nlbEDJQiI7wnIErYDOdfbbQ+1U8yGmZ6IMp4sM3w6wOSsRT4vI6WWsjy6EvnYWzHSQm3w4mw5e86X\nq2bTBrPTIg7raHlOJcWCG1EiNKrNwrMOZsCIED/2fpq1Fnoivf4EKifbSOUM38N1cMgnE4yeimPZ\nDqbl4HQ+z5w+J35HqA8O4rVoaanIpg2UmOY4TtsBIiEx0UdyY4wlxbWfzo/gNJyGQAmrHCGVE4t0\nKmdSLNsojsaBzCtCmSmK6z02Kj4bkmLiGmQTudRMckgYSjNpA9nV2v/19Df4u6P/k18Uv88zI4cq\nHkFiA4oUIGIIlSkWs+lpFguSaTl+so9n2E3oo/69HUq5CtXkJRx/eiv/+vgk3/xJmkggQpMbDwS4\nrv0G3t33Hn/TlaJuQ7aHQtniiJuTIuXbSGYMUikV24HR1MXTAdG0nBqZ3bIakBBx4VRR858l4Leu\nvmxFHAmJVEo8n1su7UVTZbJZibHZMlOnW1FPvYXOmHjWekmsC1Nz+gLCT+ct38P3kCuIDWKCcmhB\nbgxAqSrZ7eR4EVmWWNcmZG+7qoLmnT07ubP3LhzHYc69jomkzt7DFQUmmaoYI47jsGHAnSsOSI64\nvmTW8I3YDW7d/OmhBCfGC6TzJifGSjz8iyxzVe8rkEaWJZa01BoCXkikULb9+37ZijiKLJErCjXj\nT+47yeTc4tUpXj7NgeGce55CZcno4v/LYyuZzRg8uS+F4zgEFc29HxKaXclZagiIOdGoNeE7/noM\njAhOaI65YpGXjug8vT/lh1Mm53QyKQ3LdnDMiueeLVSe0bOHMximzdFTBrbjEJArhO8ZOBKSIHNL\npSPY6c/n9oaoUBWQiIYUsILcslmMIcUS62B1e+T2UAeHThXIFS0Onsrz070ZnIN3wNQGSC0lnTdp\nnbkNKdPD+JGlaHKwMv4cWZRhAmMTASQnyL7eqwn1ibwiz8NvaVD5yNuWLPosXgsuPsJ3VAxLyJqN\nahMhGpCPvZ0Y7TTH3UHgZboqZUgM4URmMOa6uKH9Lf5hFEnhxtjdyNPrASjMtpJwpdSnhw/x1/v/\nhm+f/gYPTdyP3fsLWjb/DGfpzzBtG9kUD1xCwsi2oJuOb4UVyzYTyTKpkpgA/laI7sOVD9+BZIZJ\n5Uz6ov38p1X/2Zf0J6YkirpNJlN5LG+9otKxqyOeQJElwkEZKVUpq5NKCRqiiv/9AKoTZnbvTUy9\nfLl/rsr4FaiTW+jM3cAHVr0HqdSMlBRlJUGX8Atli/FZXSzEpoOUd61uNc/onCCSsBJmILyMom4T\nUCSalU6mUzol3WJ5eB1WKYY0fhlkejk1VfI9/LLu8L9+MM3DT5gMpu9C1htwYpOk5dP+pLMsB9sG\n25Hosbb499XRxYSLhGSkdB8FQ+dvn/4hx7PH+En669j9j9MYCxArLyVbtDFMG2lqPdL4Zq4I30am\nYDI6U0ZyCX86pbNrfwqtquTGLjRRzlXkVo8oknoSqxzEiY9hopOZbOWe3o+ysfEyXjyexU6KZ7G5\nfS3tUbGoWXaF8COBKCviK0nZE9AsegicTruEX2j143rJjEG2YDI0XMnO7osM0BfpJxqI0uJWFUiZ\nJRRKNkWrDI4MxRZmswblvPDm5soXD+EbNjUkLBkRP4dENzQKZYsul7RybvOWTcvdLndmGEWWWNHe\nSlMsUJHDzQC97SESITdp0P37dFqvURNAyKnVDZcALEPGtkXCXmGRvhp/891TPPbinAjlTJfpaQ3S\nGosiD1/HNZE7+enzSR59IUmz1kJrsI1cyfIX9688Ms50Smeteg2BfA8zSXGxXlnppYOuB+s4mIaY\nk8L7F+vI9e03cnvrezn8cjtINtmCxVzGwnYcskWLvHe+uXbiYYXmeG2a1tBkyT+ml/tyyWCcy1c1\n+I6F4zhMzgmPva2x1vlI5UxSObOmGumLD40yOqOTLZgsiy3nb797iu89KcZ3OKAhy0A5jmRXMuc9\n1SuiRCqEbwWRSgkIlETvDVPjod0zjM4Iwj94Ks/eAyazGQPTCBBUZSJBxW/q4zgOuw8KdcsyFUq6\njSpVNQ1yzzmoykjTa+m0NtIRqiJ8t3Ph9tar2dixgv/rt9bQ3eaesxl2zzfMzKzMyEyJhNzOlFtB\nNDRZIhFVkIwo8uSl/pyemQ4iD1+PpMcxLce/b7IsYVoOmhTi9JS4PsO0Rb8Cp1KWF9IUOpsv3JbX\nFx3hh5QgjrsgtIabibnxlkhQrgxu9+GgFnCaheQsjV6JZIUYnizxxMtzzKR1plIV2WrXgTRB4syV\nsnzj+HcYmcsynDuFYTqENBknPIMTm8CyHayyWEh62kI4yX4s20FTJV+K1E2Hl4ZnsBwT3RGepG44\nwqJsFItyddxpKqXzxQdHyWRdmcpN3PnzDy/jbVe28tm7B/jUzl62rhBSbyysIOUq5THSzBoURUKR\nJSxbNMhIZi0kK+gPvI++vZvfve4G/uydN/F7O3uJh917ZcSIhRXkqkxW03L8eyMVWkVyi5ZnMpuh\npFv8+Bd5dr8o4TgQDsq0h4RRcHpaEKpy+B0ssTchITE8WfLLYqoX2+mpMMHkRnG5DUP+gmjZohuh\nVGpkaWMnt7bfgXzsNqRcBwFFQlVkEqYwUvIN+/j60Df8hUqRJVY290C5gWzRQppeizyzBifdQ26s\nTxiCxWau2dBIJKjwzccmyaUrk6mYamJyTicyvAMpuwQ5K6xtCQn50E4UWSIWVshngxw+pnJguMiX\nHx7j1JF2gqdv4o6+22iKuDE3q7ZD2c0db8UyAtjt+3CwmSyKkERXtI3feUcvt20R2b8HhvO8sF9I\n1abloDiVBfc9vb+FfPA3oNxI2bDRDQep2IwiqSQzBrm0eK/nbV0MyJcsDp+uanajxxhfGmG2I+gT\ndV97iIi7icra/ihr+tx7bIbRVImEmmAqZYDlKny2xmBXmIagmKeSO58m54Tc2tkc5INvXcKGwRiO\n4zA1N6+U01IpGzbFguxnr3e3BlnRLY43mzF46pUUmYIg2pYGlXhYQcr0EjG6eWDXNPc/Pe0v2tVl\ntNMpnVhY4be33ERv7q1Mpwxs2/G92BXdFUlfNyrL8//8zmnGZsvIkszUWEKQpBtGlCWFy9e648RU\neU/fe7FGNxILB/xEvBZX/Rx2Cb+k275sHNJkupprif34mFi3VvbUVlrM5cwFCYzDkyXko7eRPrAV\n1UzUZPwrqoksgVRu8BPtGtSEn8AoSZI/fzE1granBgJWiLLhMDZbtaucEcEwHSxTIRxUiEUUMm7Y\nJVuwmJzThdLrKATy3QzGKi2fvbbny5aEkWfWoiU30BnuxLKFwxZVxb2/pu067h54L/GwSsLdHril\nvJEb2t9CQm3k4P4ETiFBfqaF6ZTh34NMldIw0CmOVa1QDU8WKek2siTRFViOPX4JN8ffV7l+4PRU\nmf/jyyc4eCqPJEkE1QvbVOOiI3xNlXHcCdzVrKG5sWc1IFU8/LKwHp34GE5kGinXiWREeWpfir/+\n12G+88QU//KzSabmKqR76FSefYdtxpNlHKWMZTu+R7Fc3kqX2zUqlTM5OSS+86p1CciI2F1QlWtI\n86Xik/zdkb9Bl0X837IdsIKsXyq8vmOjRV48nkU3bf7++6d5ZSiHpXv1yGLyRdwGMp3NQZYtiTAQ\n62N1w1o+uPwDvH3TYCW2k+9AliQURZD1+KzOvT+oxOLvvLadDUtjrOiOEAsHiLlk//YrW7mkp0t4\nR4CU7vU/41m9W5Z1sbKjlWi8RKacJ523GJ2Ex16YQ55bRjSosL5NbBTywtGsbyhcsUp4YcOTJbrC\nQpLS0qIFZSSkMDJdJjfRJTxUKsaAXWpANVpgboCuFo3NbRvQjDakfIeQ2YDPvHWLb9wVy7YfG5Ql\nWNW2BHl8E/njm/ySpwd3z2APb0M+tBPJVrliVQMfdmWyE/v6kWZWIY9sxcq24jgOV/QP0DR9CxOH\nB2k11/AbrR8lV3BYWdxJX0MH0uxKTk+XGJupLHxtSj+hQJhmd7MTyXR7FRRNLMuhVAhizy4FtQAN\nI8zps2ArbFvexareCP0dwhD8wa4ZnLI4xthsmT/76hifv/80YzNlnj9UFJ6GK0cWyxbk2xnsCovx\nmhXjJ29cPEl7hunw85eqSrWMKAevamHvW1r9edAUD3D3Wzq5YWMTH75tiT/npXQvbeoSWoNtvPOq\nNvBK3CyVJS1B4lpEGOHucXJFk0LZIqTJbFoep8klw8z8OL0dYCZt8MKRsu+p7tjaWkN+0ymdcZf4\nEtEAUdfxGE9WxsSBYfEc5neyG+gIowZkWhOaH+uemtNpiquENBGys20HU5doblC5ZkMjjiMy6wFy\nLrFs6diIIku8fcUW1rlS/5LSVXRqfRi6TDyiMNgV4vJVDezYKgzK6iZlHjEHVWmBFzk2W6YpptI+\nz8NPZg2fgPvaK/kBUqkZKT3AyydrjU1DzgpJ34hiWsIZ8ZSvbMHkJ3tnsS2XhiSH9lB75cNmEMO0\na2L0GFHUgISlK4SDMvFwgELJwrIc/3rWD8RojKrkD17Hlc1XkcoZIjHONXD6OkLIssTIdIlWrQ3b\ndlDk2qoDDx7hm7lGtrRsFZ0RU0uRj96ObWjkil6opsxEUkeWJG7f1sYtl4sMfc+RATgxXqKs24Q0\nmSXNQZyJDUxNie/0wtEvn8j6xwxrck1J4YXARVeWFw3KXB69idHOg9zYs51Tz4tJZVpOJYbvBECP\nIgVztDSorG5axy9OioXfw/Gxgv8w1g3E2D+Uwy5EIOZuJ57uJY3IWL+89TLM6CgvT7rta40ojTGV\nTSvifPtxFWdqPR0tc2SSOdCEpGRYFnm9VDPBJCvItrUJHn0hySN7hYfXEAlUFhyzQviaKqPM2985\nIAf8vam711g898RqJoc6kPQ4VzffyMHJMIfGZ3D0OOmSOOZ/uL6Dq9YvXtZx6xUtWE4jf31IxCwv\na7mMl+wRmhsCwmMCepsaGQ0kUEJzEMxSNmxkM8Q7r2pjWfe7UeMpOoJL+GnkBM8fzfrZ/v0dYdoa\nNU5NlVgdW0ukN8o/PKHT0aTR3Rrk+aNZQELKdeDEx/14olRoJZx9C/JMkSWtQdSAzP/2rh6yVpSH\n0iJJrTkSY3v7Nh7MPkm+ZPmJfLIscUl3N9/O6jWVhYZpE5BlrtnQzIFTeZa0BFEDEgOdYYYmQBq/\ngnBQoehmPfe0BinrNs8eNnnp8XUc1kQC0Nq2Pq5feSn/5fFjjE6X/dIqb/wBdCWEoVMuBPn5i3N8\n/+lpLl0W4/DpAjYr0NqOYLQeIu+kkPQ40bAYs33tnmxtAlVelaVxZKTAP/5ojGnXmOpqDjGmx7GV\nJI10sbw7zLHRgqtsSRSsi8fDD4fmLUFGBEWWRO6GR/gxlUsGY1wyWNviVEoNcnvrtaiyyvWXNlJs\n6+KFuTGWhtvYvCLOicISFEnGLjXVfC7oGgwNkTN0ZLRcIjMqhBYJKoSCtf7RS26GeiIa8JVGz4MG\nePlEjs0rG2o8fID+TnHclgZx7WMzZTIFk9W9bqhQFh5u2bJp0hQ/8c7LJ/DydG5ZuoWdDZtEn/+8\nifzKbxJc1ug7KrGwghqQef/NXQvKEQFSWY/wZZriC+/F0q4QjbHK82lv0pia09lzSKxxK7ojfqjB\nw5P75jXWkU3hCOkxZovjSDNl+rvF9fz1d06RzBhYa1QIWKAYrIqv5pT+c/FZp3K/A4qQwCm0Ei+s\nITkzQKRJ9p9htmiRdtfRRFRh3UCMXftTnBwv8nffP01QlXnvTUIhjQQVWhMqMxkD25KxbQnZ3Sxn\nPrzje+29qysNqvuhgJi7PW0hbt7cvOC+AIzPlinpNqGgTIerqHjq1rKuMMmMwcFTVS121Qvvj190\nHr4kSdxyySCfWPUxWoKtfi2lbjqs7Imwui/KJYMxpHKCgCwRCSps6VvmS4IreiLc/Rbx4E9NldBU\nmctXujFBQ9SDdzZrhAp9SKVGpEIrqzpbGGioJE5cuWwJ/+U/9BEJKqzoDqPNbOIjKz6KU3YnrMs2\nhuXUZKaqhOlo0nx5DYR34VmRmO4CYwYJa2d/NIqksMJ5C1JWKAzb27fSE+lFyvQjlSr1n03xhVbr\n/ON4pS53b11PV6tGUJORJi4V197eRUJLENIknIYRsDQ29i7hxk3N9LdHWRLuRpElrljVQKFssfug\niB+3N2r0t4co6TZjszrPPBtBN2CwK0xPVeZw1BbPwgHkEzchTWzi5HgRRZZoT4hJ0d8RZl1XF72R\nPq5o3gLAbT23cKlyG6blUNRtpHQvWxtvoCGs+c/67hsr2e5r+6PsvKadP3jvUjRVWM7vuaGD1oSG\nGpBpb6zcp+XdEbavS9CaUFnTF6Wk26zpi7JtbcJPhJqY0zk1JSZ8b1uIO68RnklDMIoWkMhmNL73\n1BSO4/DisSzFssXN6wZZ3dKHE53CdAzIdRFxSSQWDtDdKkj/ukuaCWkyAUXi6vWCrKarwk/rBqIi\n+dAOsKyx3/e0JCQwwmSs89sX4pcB6rxFTXIUFNltfWqLedEYXeiXfOCWLtb2R30JXJIk+mI9xLQw\nd1y2HEWRWB5bSd/kh5DKtb3oPZm0YZHjNkQCUG5guXEryuw6/++RkLJgTr58Qqh3jbGAHyIbmqiQ\ngBeXn8vN9/DF8/IUyUPuot/eJMa7LEnYNpiWSUiTfUPDy8/xcg6iYcX3lqMh0Z447/bkAPzyMhDK\nqBqoPX/vvIKaTFMswOq+aI2KsWFprObe33yZWFcm53SCqkxvlYfvSdie6vH2ra28/cpWViVWIEkS\ngWIHBEo4DpQKGsmsQdINa0pJ0UVUynXQ2xJHO3Y7UqYHKTXgH39Nv7u2OgqBiSuh2ERYU/xWyLmi\n6Xv4iWiADUvF+x9/2W0IZth+mCKkysRCCsWyTaZgIh94N+vyH2AxqAGRJ+DJ9d69hUrYwwv1QGWs\nLrZ+j86WKRk2QVWmw33Wx7xjuPd9pqrD6ALl6QLgovPwgRqZw/MoDdMmGlL4j3f0sPtgmhf3N6Io\nEyiSwkCii//+AZmjowUGOkKoAZkHds2QK5oEFImVveJmxwMJomEZCYkdlw3y3Z/00BxXaYgGiNiV\nNolXLuvyZfF7bu4iWzCJBBWkuWVgBwi3j4g613lWdVwTkyIWVpjNGKwfiPG+mzsJazL/4xvDjFlB\nEbuyK6R1NngTWpYk10pf+DirLfQzYSA6wERxgqAc5O7+e5gpTxNvWMuJ8SKdjSEG5EFeSe1DDpg4\nc70M9i2sDV3VG+HRF5IUyxZBVSYRVejrCPHckQxf/tEYsxmDWFjhitUNNZ7xjjWb+ObYC0izK5Dy\nFYLubNZqFA5Jkri7/56a7/yNK1Zy9IUfUyjbSOOb2fqWSwH42I5uklmDzSsb/IZJXqJXNZa0BPmD\n9w5gWg4/e2GO4ckSN25qpr1Ro71R44/uEaGKYtkiXPU8etqCDE0UmUkbDHSG+fSdff5rbaE2OuVV\njCSFIdbVHGQ8WUaSJK69pIlXcut4eVI0RJLmBvyqA4BP7ezDtGxi4QA3lT+NaVsMnQrw9Cu1XtOy\nJWGe3H8F5ckNrLiqib4qA0oywlic3zbIvwzQ5pFQOKhwecsWckaeaUnGcZxKmVQVNq9sYPPKhpq/\nrU9sYH2iUtMvSZIgcKCrJeiTkRcSaG1YaAz3tYe46/o+GiKr+JPRk8wZgpQiQXnBHg3e4l/t4Vf3\nas+XLHJFc0HrV48ofcI/JVRKz+iM5FaRDR9CKjYTbJL8tcDLCfAk32jVmFQUiZAmkytZPvHN3xcg\nFlKYy1Umn1c5EHIN4P94Rw+5osln/1EomesGojXtdy9bEefhZ2dJZgzec0MlxAYivOoZO2pA5toN\njYSDCrr9LlJ6mr/dlSWtCDIrFYI1SoA0eQnLoivYumkpG5fFeeiZVmaGr68593tu6uSBX8zw1L6U\nr5iEgiJsAfD//nDUd5waIgGWLRFhk5eOV0qqH3dDR5oqEw0pIn8jZSDZGk2hxXfSA2EYevd0pqoD\nqBequXxVA0dHhdHmrbfheWpQX3uIkekytuPQ2azR6RK+pzIvWxImElL8niJQ20H0QuGiJPxqdDYH\nOTCcr/GaE5EAUrmBgCLREepEkQIomrBYPXxqZw9f+rcxLlsRJx4OcM/NXcihCD8tPAHAlYO9rLhL\n9rumBeQAakDCMB2WdVQ8hkQ04A+0NpYzc6qfcO+33LKX2gfWEBREeee17dz/9Ax3XtfuT+a7rm/n\n8z/MYqQmkFL9RNrPLb74CYshRXSBWsSbbzoPwr+tq7LJSV+kX3SRa6pYrivjq9CUIGHNpJjrZLAr\ntOAY1fG89kZRirNxWZxHnptlNmPQmtD4b7/ZjxoQi/jdN3ayui9CNKTw4NN3UsjXnnt/R3j+Vyy8\nNq2ZaFCjUNLBiPqTbGlXmKVd4vNXrk7wzKE065cu3sBCliU0WeKGjU0MdoUWJCkBNWQP+J44CPm/\nGooU4PrGHfxLXhgaH7ili899a5jVvREaYwEu0dbyTelhnFIDlJp9Dx+80kjx/8agGGN6y8LyqKaY\nSm9LjONjMks7Q7Weqvz6u+y9maj2Oq+9pImuZo2rOkRL0hfjJ0hmDD/W/lqQcElv+ZKwT/hezwnP\nKwUhn5YNm3hU8RPdEtGAv6hHgkrNIp6oIoFELEBYEzk8XgLWuoEYLx3PMjqjMzJdIqBIfGxHN6mc\n6c95LwTp5b14Xl9L9ipyJ0Smd0hT/DHiVQzkihaRkOI3tPEQCwsP34t5z5/70bBSozZ45FItHcfC\nAVZ0R2hr1AhpCqpSeU2E10TZbXujVrO7ZDwc8Ofah29b4s8ZTQ7SHmonpOXJjG/G6dqLleznmbFK\nJYmERLvWxbZ1je69VWuIVVOFsXXXdR0cPl3w1a5IUPGdnkzB9D3iRCyAGpAZ6AzV9BDwEFQl31iZ\ncHMu5htH1UhEA0wky+iGXdPy28PKngiNMZVUziDhEX6VcRhUZXraQr7MH1Jl2hJazXhpjAYY7Azz\nytAbG467OAm/ysN/+5UthIMyV1fFqZd2hVne1EM69HzNrnDV6GgK8gfvrbSMvGJVA7od4qeHRalI\nWAnTPW/vgz/a9J/RLWPBRPPwqZ19zGYMvpX0EtHmtfF0t2fs7wjzqZ29Na8tWxLhbz62gS891Mw+\nM1czYM4Eb5BGQ+L7mhch/Plk9VqgyRobEhvQzee5+vLLFiXjaEihNaExk9b9Up7GWICP7ejm/qen\nuX1bm7+4S5LE1rUVo2nr8i4ee7G2x/aNm2rjrotBlmQub7mcH52YEW1QAwuNpPfc2MGd17WfMx4W\n0mRW9Z5fV6t1/TEGOjPMZQ0uXbbQMxhcIu7Pyp4IS1qDfPrOXv/ZNGgJOufeyuSU2HDkXEpOe1Pt\nwgDivt6yuZkjHaEFddYiYXX0vK7jlwHVkv41Gxp90gPYtCzO6GzZ7xHxWuDNkd72kN9a1xsLAUXy\niVtzCb96DiWqDClFkWpk2lW9Efa4jYAS0QCyLNHTFvQX9dW9EV46nuWffjRGoWyxfV3jgvE1X5Hz\nrj2kKn51TUiT/TnsxfDzJcs39qsRDSkks2VfUZi/Hiz2GUmSfJXUw+++q7I2zc8jqj5mtYcfCyvc\nekUzd2xvXZQ8VUUSFTMzqzmKBJhcs6HR9/Sr8yM8Q2WgM0xIk7ljW2Uhrn4G8Yiy6Hc1+EZexCd8\nz6DzfvfOfdxtMBRf5N548Lz2ZNaokdxBPJ/meID+jpDoOeKOGUUR65FhiiS9aichpIn8rLZGVVQF\nBRXfQPEIv71R45pLLlxLXQ8XJ+HLtVbnrZe31Lwc0mQ+9bZLGSu20hZsn//pM0KTNbrDPf5mDfPR\nHFl8sxsPnrcvpyRkmRrpGqAlem5CibkS1XxJaDF4g9QbvPNrbi8kbmi/iSuaty7YxKMa/R0hZtI6\n7U1q1d/CfGpn3xk/A3DblhYm53Q2r2zg+09Ns2EwuiA7+EzY0Xcrjzxw+IyvK7J0QTtVgVgAqmX8\n+WhLaPy3uwf8xXG+gTQQXcqUWyt/ruccUCQ6mjTGk2XefV0HUymdSFBmTX/Uj2sCfPrOPp4/mmX/\n6FUMT0eBh17j1b25qDbS5pcgveOqttd9/PUDUfYP5VjdG6EtoTE6U/Jb7oJQ/Z56JcVAZ4jtaxMs\nW1JReBLzYvzVhsdAZ5g9hzJEgooflrjr+g7+6tsiXOMZYoWyRVNMFVUE81AdzuhpC/nKQlCrVX0i\nVTF823bIl+xF50c0pGDbju+1zjcoYqGFpBZUpXNmgv/h+5ay2Fuqw1HxiCCtxYxuqNoMpiqd9qr1\nFcKvUU9cgu1pDXLX9bVtx6sN5EQksGjipXe/VnSHeRhxP/vbQ35ORVCV/aoKr9/A2Tx8zxCbSul+\nSaIkic1vultDSJLEuoEoLx3P1nQ2jARl0qZNUBNKnAdvHHU2B5mc0/3rrTbeq/cvuJC4OAn/PHE+\n+9vPx/sGFk/eeLVQFZmyy/jNMQ0bm3U9Lef4FH7yz/l45pUeBJ6RoHDPzV20N2o89uJcjVX5ehGQ\nA2clexBxqL1HMjWD/nwQ0hQ+fruIeV+2Is6r5ec///Cyyn6ovyToOkuzjOoSqDMtkNXYeU0bczmT\nrWsSZ3zPQGeYgc4wV8018pNdFk++uqMoGRsAACAASURBVNP9d0O18qK9AVnJve0hfv8uofJ1NKmM\nzpR8SR/gnVe1EdREzHl+SGx+/kv1nPQS7xJV7+lrD/GJ23sIarKfgAdw9YbEOVWKK1ZV8hGq70lQ\nlUWjGEmiULZEO2vH8QmrGt56MDJdrslfmP96Nc4nE3x+8x0PWkDys+cXO3Y1ivM6Fq7sidSqU1Xz\n1/PwF0uqrDYMGqKBRVVNz4Dp7wgR0mT6O8J+rB/EOIv5Hr4r6Z/l/D3janLO4MR4iUQ0QKFsY5iO\n37/gytUNbFgaq1E9QppMOi8k/Oq12JvzHe5xPcNybX+Umy5rXlCNciFxURL+ha5NvNBo1lqYVSbw\nuuk2BGPYSoGIeu64tGexRkLnnoitCY0VPZGaAeItHL91a9eZPvaGYdvaBG0JjZU9577OM+G1eON+\nE6GLBJ3N56deeDjfUAMIb+T6S5v4P1/tSf07IVBNbudh/LweeAv3fCPjHdsXVxLmk1g0JAzTtkbV\nreYJ1mRoAzWqi4ctq89sqF21vpGnX0mxeUVFPaw2SEKajCyLcEKxbPsJe2eS9EHEs5vi6oLQ42JG\nQvB1hEskSXIz2M1zzkFPTl/TF0VTZe66TiivXpiluqPhYFcYWZJY2rlwHamW/htcSf+P3z/IqakS\n//SjsZr3qgGZ/3xXPyFN5tGqkGFQlfx74dXmx89UookwFAH2D+XIFU0uWxF3y4oryoAkSTVkDxUD\nMeTW07c1akyndF+B8dYBj/BlWeKOM4zFC4WLa6X08EtO+Hf338P+4CjfGv4mpmOyomGQ4dKx8wov\neF5G4iwSk4eAIvG77+w95/veLCiyxKrec++B/uuOs3n/v24Iqgq4hvH8ePGFxqreCI/sTdLTdn73\nfzHvd20VoX/27oGzfv4Dt3RRNuwFoYFq3HlNO7dva62RqqsNQk8ZCAdliuVKyd1i8ny1EbBYsu5i\nnwm9TlUlGnIJ/yyECYLMbNvhksFYTV+Q9QNRnj+apa2qLLanLcTf/s7KRY8Tqcpt8rvgNag+JbQm\naj1+T52oXk+rY/geYmcxWFoaRBLyCbfufmlXmJCmsGt/qmY8zEfYf3biu962pYWvPjLuO2iDXaKS\noFruf6NRJ/w3ANFAlC09K1nR/rsczx1lc9MV561KrOuPcs/NXVz6Bso6dfz7wluMVyxSEfDrBjUg\n+YT/RmPZkgh/84kV5z0Xvdjtqw1ReZhfNrgYFEUiotSSz2BXbfUAiLDdxJzu1+AvRlDVJLZYxU61\nAeM10anuif9a0BQPkMwaCwh0Pv7Tb/Ty1CtptqyuvSd3v6WTdQOxGoXjbKj28Ku/szmu8pl3958x\nj6k6PKDNI/xISBF9H86AgCKJ63T7BizrCrN9bYKbLmuiNXFmtc4LP3hG1eaVDfR3hPwwRHODyl9+\ndHl1StobjouT8C8SNGlNXO42ijlfyG4Tmzp+dSHLEn/98RUXPJnwYoSivImrHa8uHLikJchn3t13\n1kX9jUB1bLvawxdtZt0a/EUItjpmv5iHH6jKxt++NsH9T0/X7CfyWvCeGzrIl+wzVi556O8IL1rd\nowXkV7XeVSsh87/Ta0+9GBLRqp4FsuRXNgGLhg4W+94kBmv7o3S3BpEk6ZzjwvPsq8Mm8z/zRqta\n8/G6Z9u9997L9ddfz+WXX84999zDkSNH/Nd27drFjh072LhxI3fffTcnT570Xztw4AB33nknGzdu\n5B3veAcvvvjieX+n9GaaRHXU8QZADcjnXCR/LSBJ3Lalldu3vbGxy9eK/o7wOb3XC43qceG15vbI\nw2vnW90Z0sOq3ghvu7KVFT2RRRtNeZ5lIhrg6g2NrBuI8b6bXl+uT2NMvaDJwefCay3RnJ8AWG04\nLNZ7Yz52Xt3GtZc08aG3Ljlvo9E719dTVnqh8brO5Hvf+x4/+MEPuO+++9i9ezfbtm3jYx/7GLZt\nMzMzwyc/+Uk+/elPs2fPHrZv384nP/lJHMehXC7z8Y9/nJ07d/Lss89yzz338IlPfIJ8/uLZ9KOO\nOuq4AJAkbtvSws2bFy+F/XXFu6/roCES8BtIeUm8R0cKom31It6sGpB56xUt/O47e2va3nroaw/x\n2zu6+cy7+9ECMh/b0b1AYv9lh/Maq3Hm50RVG1Vee+azYXl3hDuvbX9VlSReeeCvDOHPzc3x8Y9/\nnN7eXgKBAO9///sZGxtjYmKCRx55hDVr1nDjjTeiaRqf+MQnmJqaYt++fezevRtZlrn77rtRVZU7\n77yT1tZWHn/88fP74l/yGH4dddRRx+vBNRsa+bMPLfPVhepktW1rE6+5Umn9QOy82m3/suK1Lv1n\nI+oFzasuEDxV5lz7oryZOOeTN02TQmFhe0JZlvnwhz9c87dHH32UxsZGOjs7OXHiBMuWVfYiVhSF\n3t5eTpw4QSqVqnkNYOnSpZw4ceL8zrpO+HXU8SuBenju/OC14R3oDJ9x98tfB2xaHufISKGms+r5\n4n9/z0BNV8H//v5BLMd5w0Jrq3sjDHaFf6kql85J+Hv27OGDH/zggr93d3fz6KOP1rzvj//4j/nT\nP/1TZFmmWCwSi9VmmofDYYrFIoVCgXC4VkYJhUKUSgu3FFwUdcKvo446fo1w1boEK3sitDeqv/R9\nSN5IBBSJ976l89xvXATzcw2aF9k86UKiNaHxe79x9i6jbzbOSfjbt2/n8OEzty4FuP/++/mTP/kT\n/vAP/5Dbb78dEOQ+n8CLxSKRSIRSqbTgtVKpRCRyfpbQr/OAr6OOOn79IMtSzT4DddTxWvC69bR/\n+Id/4C/+4i+499572blzp//3wcHBmqx8y7I4deoUy5cvX/AawMmTJ1m+fPn5fWmd8Ouo41cD9blc\nRx1vGl4X4X/3u9/lq1/9Kl//+tfZtm1bzWs333wzr7zyCo888gi6rvOFL3yBzs5O1q5dy7Zt29B1\nnfvuuw/DMPjOd77DzMwMV1999eu6mDrqqKOOOuqoY3G8LsL/4he/SD6f584772TTpk3+z/Hjx2lr\na+Pee+/l85//PFdeeSW7du3i7//+75EkCU3T+NKXvsRDDz3Eli1b+NrXvsYXvvCF85b039TWRHXU\nUccbhnp4ro463jy8rvqMH//4x2d9fevWrTzwwAOLvrZ69Wq++c1vvqbvrS8RddTxK4K68V5HHW8a\nLs7ZVvcK6qijjjrqqONVoU74ddRRx78f6nO5jjreNNQJv4466qijjjp+DXBxEn4dddTxq4G68V5H\nHW8aLkrCr7fjrKOOXxHUCb+OOt401JmzjjrqqKOOOn4NcHESft0rqKOONwx/9md/xuc+97mav/3p\nn/4p69evr+m3MTY2BsDIyAgf+MAH2LRpE7feeiuPPfbY+X9ZfS7XUcebhjrh11FHHYDY7vq//tf/\nyn333bfgtQMHDvBXf/VXvPDCC/7PkiVLAPjUpz7FJZdcwp49e/jsZz/LZz7zGd8YOCfqc7mOOt40\nXJSEX+/OVUcdFx533303iqJw66231vzdtm0OHz7MmjVrFnzm+PHjHDlyhN/5nd9BVVWuu+46tmzZ\nwkMPPXRe31mfyXXU8ebhoiT8uldQRx2vHqZpkslkFvzkcjkAvvKVr/Dnf/7nC1pcDw0NUSqV+Nzn\nPsfWrVt55zvf6cv2J06coLu7m1Ao5L9/6dKlnDhx4vxOqj6X66jjTcPraq3774b6IlFHHa8ae/bs\n4YMf/OCCv3d3d/Poo4/S0dGx6OcymQxbtmzhIx/5CBs2bODxxx/n937v9/j2t79NoVAgHA7XvD8U\nCi3Y/vqMqM/lOup403BxEn4dddTxqrF9+3YOHz78qj+3ceNGvvrVr/r/v+mmm9i2bRv/f3t3HxZV\nmccN/MvwOqgrGBhKVDC0iZmAEDBEpbCaFsguC5eKay5rCiRrq9mLmJppl7ptrAUCvtUaYApUgrIp\nWyq1DyKyioq22ONMvkRAbIIBMwwM5/nDx9lmeRec4cx8P9fFdcl9n5nzu9Xf+c25zz3nHD9+HO7u\n7l2Ku1qt7v+DsFjwiQyGU/pE1KsTJ050edBVW1sbbG1tIZPJ8N1330Gj0ej6lEolPD09+/fmzGUi\ngxFfwbew4KI9IgOysLDAli1bUFFRAa1Wi4MHD+Ls2bOYNWsWZDIZPD09sXXrVmg0GpSUlODkyZOY\nOXNm/977LsdORP/FKX0i6lVQUBCSk5ORnJyM+vp6uLu7IzMzU3fNPzU1FWvXroVcLoeTkxNSUlIw\nbty4/r05P7wTGYz4Cj4PEER31ebNm7u0xcTEICYmptvtXV1dsXv37rsdFhENkuim9DmdT2RCmM9E\nBiO6gs8DBJHp4Ad4IsMRX8EnItPBgk9kMOIr+Hw0LhER0YCxehKR8fAMn8hgRFfweXggMiEs+EQG\nI7qCzwMEkQlhPhMZDAs+ERkNV+kTGY74Cj4RERENmOgKvgVX6RMREQ0YqycRGQ+n9IkMRnwFnwcI\nIpPBa/hEhsOCT0TGw3wmMhgWfCIyHuYzkcEMquBrNBq88cYbCAoKgp+fHxITE1FXV6frLy0tRXh4\nOHx8fBAbGwulUqnru3jxIqKjo+Hj44PIyEhUVlb2a588PBCZEBZ8IoMZVMHftm0bLl++jMOHD+PE\niRNwcHDAhg0bAAANDQ1ISkrCihUrUF5ejuDgYCQlJUEQBLS1tSEhIQFRUVE4deoUFixYgMTERLS0\ntAzJoIiIiEjfoAr+smXLsHPnTjg4OKClpQUtLS1wdHQEABQXF8PLywuhoaGwsbFBYmIi6uvrcf78\neZSVlUEikSA2NhbW1taIjo6Gk5MTSkpK+t4pzwiITAYX7REZjlVfG3R0dKC1tbVLu0QiwciRI2Fp\naYm0tDSkpaVh7NixyMnJAQAoFArIZDLd9paWlnBzc4NCoUBjY6NeHwC4u7tDoVD0HTEPEESmg/lM\nZDB9nuGXl5fjscce6/Ize/Zs3TaLFy9GZWUlZsyYgUWLFqG9vR0qlQpSqVTvvaRSKVQqFVpbW7v0\n2dnZQa1W9xkwb7xDREQ0cH2e4QcHB6O6urrXbWxtbQEAr7zyCvbt24dLly5BKpV2KeAqlQr29vZQ\nq9Vd+tRqNezt7QcaPxEREfXDoE6XV61ahb179+p+12q16OzsxC9+8Qt4eHjorcrXarW4evUqPD09\nu/QBgFKphKenZ9875RQgkcngjB2R4Qwq2yZPnoz3338f169fh0qlwltvvQU/Pz+4ublh+vTpqKqq\nQnFxMTQaDTIyMuDi4oKJEydCLpdDo9EgKysL7e3tyM/PR0NDA0JCQvreKQs+ERHRgA2q4M+dOxe/\n/vWvMW/ePEybNg0qlQrvvvsuAMDZ2Rnp6elIS0tDYGAgSktLkZqaCgsLC9jY2GDnzp0oKipCQEAA\nsrOzkZGR0b8pfRZ8ItPBfCYymD6v4ffGwsICSUlJSEpK6rY/KCgIhYWF3fZNmDAB+/btG/g+B/wK\nIhq2WPCJDEZ8F9B4gCAiIhow8RV8IjId/ABPZDDiK/g8QBCZDq7SJzIY0WUbb8VJREQ0cKIr+DzD\nJyIiGjgWfCIyHuYzkcGw4BMREZkB8RV8IjIZXJNDZDjiK/g8QBCZDq7SJzIYZhsR6aSnp2Pq1Knw\n9/fHggULcOnSJV1faWkpwsPD4ePjg9jYWL0HYF28eBHR0dHw8fFBZGQkKisrjRE+EfVCfAWfZ/hE\nd8Unn3yCgoICZGVloaysDHK5HPHx8ejs7ERDQwOSkpKwYsUKlJeXIzg4GElJSRAEAW1tbUhISEBU\nVBROnTqFBQsWIDExES0tLX3vlPlMZDAs+EQEALhx4wYSEhLg5uYGKysrPPfcc6ipqUFtbS2Ki4vh\n5eWF0NBQ2NjYIDExEfX19Th//jzKysogkUgQGxsLa2trREdHw8nJCSUlJX3uk9fwiQxnUA/PMQoe\nIIjuWEdHB1pbW7u0SyQSLFq0SK/t6NGjcHBwgIuLCxQKBWQyma7P0tISbm5uUCgUaGxs1OsDAHd3\ndygUirszCCK6I6Ir+Cz3RHeuvLwccXFxXdpdXV1x9OhRve3WrVuHN998ExKJBCqVCiNHjtR7jVQq\nhUqlQmtrK6RSqV6fnZ0d1Gp13wHxAzyRwYiu4PMAQXTngoODUV1d3es2Bw4cwPr167FmzRpEREQA\nuFXc/7eAq1Qq2NvbQ61Wd+lTq9Wwt7cf2uCJaFB4DZ+IdLZt24ZNmzYhPT0dUVFRunYPDw+9Vfla\nrRZXr16Fp6dnlz4AUCqV8PT07HuHzGcig2HBJyIAwMcff4w9e/Zg7969kMvlen3Tp09HVVUViouL\nodFokJGRARcXF0ycOBFyuRwajQZZWVlob29Hfn4+GhoaEBIS0uc+uWiPyHBEV/B5gCC6O3bs2IGW\nlhZER0fD19dX93P58mU4OzsjPT0daWlpCAwMRGlpKVJTU2FhYQEbGxvs3LkTRUVFCAgIQHZ2NjIy\nMvo3pc98JjIY8V3DJ6K74siRI732BwUFobCwsNu+CRMmYN++fXcjLCIaIqI7w+cZAZEJYT4TGYz4\nCj4RmQxeoiMyHPEVfB4giEwH85nIYERX8HlGQERENHCiK/g8IyAyIcxnIoNhwSciGgIvv/wyJk2a\nhLq6Or32oqIibN++3UhREf0XCz4RGY+J5HNTUxNKSkrw9NNP6309ce7cuSgsLMTJkycRHh4OlUpl\nxCjJ3Imu4PMaPpHpMJV8PnDgAPz9/TF//nzk5uZCo9EAAD744AM0Njairq4O77//fpeHDBEZEm+8\nQ0TG08+Cf+D//IAz//enuxzMLb6eo/Drx50H9Jq8vDwsX74cU6ZMwZgxY3D48GHMnj0bFy5cwJQp\nUzB+/Hh8+eWXiI6OvktRE/WNBZ+IaBBOnz6NmzdvYurUqQBuTePn5ORg9uzZ8Pf3h7+/v3EDJPr/\nxFfwJaK7CkFEPelnPv/6cecBn3UbSm5uLm7cuIEnn3wSANDR0YHGxkZUVVVh0qRJRo6O6L/EV/CJ\nyGSI/Qr+Tz/9hM8++wx/+9vfcP/99+va33rrLWRnZ2Pz5s1GjI5I35CdLufn5yMwMFCv7dChQwgL\nC4OPjw/i4+PR0NCg6ystLUV4eDh8fHwQGxvb5XnaPTGVRT5EBNGv0i8oKMADDzwAPz8/ODs7636i\no6NRVFSEH3/80dghEukMScG/du1al0+y//73v7Fu3TqkpKSgrKwMTk5OWLVqFQCgoaEBSUlJWLFi\nBcrLyxEcHIykpCQIgtD3zkR+gCCinxF5Pufm5iI8PLxLe3BwMBwdHZGXl2eEqIi6N+gpfa1Wi1de\neQVz5sxBfn6+rv3gwYMICwuDt7c3AGDlypWQy+VoaGhAcXExvLy8EBoaCgBITEzEnj17cP78eUye\nPLn3HYr8AEFEpqOnxwVLJBJ8+eWXBo6GqHd9nuF3dHTg5s2bXX6am5sBADt27MBDDz2kW7Bym0Kh\ngKenp+53R0dHjB49GkqlEgqFAjKZTNdnaWkJNzc3KBSKoRoXERER/UyfZ/jl5eWIi4vr0u7q6or3\n3nsPhYWFyM/PR1VVlV6/SqWCnZ2dXptUKoVKpYJKpcLIkSO77euLBVfpE5kM5jOR4fRZ8IODg1Fd\nXd2lXa1WIzo6Ghs3bsSIESO69NvZ2UGtVuu1qVQq2NvbQyqV9thHREREQ++Or+FXVVXh2rVriI+P\nB3DrWr5KpYK/vz8KCwshk8n0Vt7/+OOPaGpqgkwmg4eHBw4fPqzr02q1uHr1qt4lACIyA1yTQ2Qw\ndzyf5u/vj7Nnz6KiogIVFRXIzMzE6NGjUVFRgfHjxyM8PBzFxcWoqKhAW1sbUlJS8OSTT8LR0RHT\np09HVVUViouLodFokJGRARcXF0ycOLHvHfMAQURENGB37QKal5cXNmzYgNWrV0Mul6O+vh6bNm0C\nADg7OyM9PR1paWkIDAxEaWkpUlNT+/cdexZ8ItPBa/hEBjNkd9oLDAzEyZMn9dqeeeYZPPPMM91u\nHxQU1ONXWnrDG+8QERENnPg+XrPgE5kO5jORwYiv4BOR6WDBHxBBEHD9+nVjh0EiJb6CzwMEEQ0T\nDz/8MLy9veHr6wsfHx+EhIRg7dq1aGpq0m3z/PPPY//+/QCAZ599VncHvtDQUBw7dmxA+/vzn/+M\nnJycoRsAmRXxPS2PBZ/IZJjCmpy8vDz88pe/BAB8//33eOONN7BkyRJ89NFHkEgk2LVrl27boqKi\nQe3rxo0bcHR0HNR7kPniGT4R0RAZN24cUlJS8M033+D48eMAgAULFiA7OxtAz2f1mZmZCAsLQ01N\nDW7evIkXXngBAQEBmDZtGlavXo22tjZ88MEHOHjwILKysrBs2TJcv34dfn5+eO211+Dv74+CggJc\nu3YNCQkJeOqppzB58mTMnTsXly9fNuRfAQ1j4jvDJyKzc6zuC/z7p68Nsq8Jo7ww7d6wO379iBEj\nMGXKFPzrX//SPSCsN1lZWcjLy0NWVhbGjx+PrVu3wtLSEv/85z+hUqmwcOFCFBYWIi4uDtXV1XB0\ndMSrr76K69evo7m5Ga6urigtLYVWq0VCQgIeeeQRpKWlQaPR4KWXXkJmZibefvvtOx4PmQ7xFXye\n4RPRMDd69Gi96/g9OXDgAD7//HMUFRVh/PjxAABbW1tcuHABRUVFeOKJJ/DJJ59A0sv9CiIiImBj\nYwMA2Lx5MxwdHaHValFTUwMHBwd89913QzMoEj3xFXwiMjvT7g0b1Fm3oTU2NuoKeG8qKytx//33\no6ioCEuXLgUALFmyBADw/vvvIzk5GX5+fti4cSMefPDBbt/DyclJ92eFQoG3334bdXV18PT0hIWF\nBQRBGPyAyCSI7hq+KSzyISLT1dzcjNOnTyMgIKDPbVevXo2NGzdi+/btumvt33zzDSIjI3Hw4EEc\nP34c99xzDzZs2NDje9w+Jmo0GiQlJSEhIQEnTpxAVlZWv2Ig8yG6gs8pfSIarq5du4aXXnoJkyZN\nQkhISJ/bW1tbw8/PD5GRkVi9ejU6OzuRm5uLdevWobm5GY6OjrCzs4ODgwMAwMbGBs3Nzd2+V3t7\nO9ra2iCVSgHcmj3Yv38/2tvbh26AJGos+EREgxATEwNfX19MmTIFCxcuxIMPPojt27cPaDZy5cqV\nuHr1KnJycrB8+XKMGDECYWFhCAoKQlNTE1atWgUAmDlzJo4cOYJFixZ1eY8RI0Zg/fr1eP311+Hn\n54f169djzpw5uHLlCjo6OoZsvCRe4ruGz4JPdFekp6cjNzcXzc3N8PLywpo1a3TfL3/zzTeRm5sL\na2tr3fa3F5pdv34dq1evxrlz5zB27Fi89tprmDZtmrGGYVDV1dV9bpOVlaX7syAIugV4R48e1bWP\nHj0apaWlut+3bt3a7XsFBwejvLy8x/3HxMQgJiZGry0pKanPGMk88AyfiPDJJ5+goKAAWVlZKCsr\ng1wuR3x8PDo7OwEAFy9exF/+8hecOXNG93N7UdqLL76IyZMno7y8HMnJyXjppZdQU1NjzOEMO1qt\nFnV1dbhx4wbuueceY4dDZkp0BZ+L9oiG3o0bN5CQkAA3NzdYWVnhueeeQ01NDWpra9HZ2Ynq6mp4\neXl1ed3ly5dx6dIlLF26FNbW1njqqacQEBAw6DvKmZoLFy7g6aefhlwux8SJE40dDpkp8U3pE9Ed\n6ejoQGtra5d2iUTS5Zrw0aNH4eDgABcXF3z77bdQq9XYsmULTp8+DRcXF7z44ouYNm0aFAoFXF1d\nYWdnp3utu7s7FArFXR+PmEyePBmVlZXGDoPMHAs+kZkoLy9HXFxcl3ZXV1e968nl5eVYt24d3nzz\nTUgkEty8eRMBAQF4/vnn8eijj6KkpAR/+tOfkJubi9bWVt2q8Nvs7OygVqvv+niIaGDEV/A5pU90\nR4KDg/tcZHbgwAGsX78ea9asQUREBADAx8cHe/bs0W3zq1/9CnK5HMePH4e7u3uX4q5Wq2Fvbz/0\nAyCiQRHfNfxebjFJRHdu27Zt2LRpE9LT0xEVFaVrP3HiBPbt26e3bVtbG2xtbSGTyfDdd99Bo9Ho\n+pRKJTw9PQ0WNxH1D6snEeHjjz/Gnj17sHfvXsjlcr0+CwsLbNmyBRUVFdBqtTh48CDOnj2LWbNm\nQSaTwdPTE1u3boVGo0FJSQlOnjyJmTNnGmkkRNQTTukTEXbs2IGWlhZER0frtefn5yMoKAjJyclI\nTk5GfX093N3dkZmZiXvvvRcAkJqairVr10Iul8PJyQkpKSkYN26cMYZBRL1gwSciHDlypNf+7m7o\ncpurqyt27959N8Ia9q5fv46wsDCcPn0aI0aMMHY4XWRnZ+PIkSN6N/8h88UpfSIiIjMguoLPG+8Q\n0XBUXV2NBQsWwN/fHxERESgpKdH1Xbx4Eb///e8REhICb29v/OEPf0BDQwMA4LXXXsPy5csxbdo0\nRERE4MSJE4iIiMCmTZsQEBCAJ598Ejt37tS9V01NDRISEhAYGIgZM2bg448/1vU1NjYiKSkJU6ZM\nQXh4OC5dumS4vwAa9kRX8DmlT0TDjSAIWLRoEWbOnImysjK8/vrrePnll6FUKgHcuv1wWFgYvvrq\nKxw/fhw//fQTsrOzda8/deoU9u3bh71790IikeDSpUu6++uvWbMGKSkpqK2thVarRUJCAh566CF8\n9dVXeO+99/DXv/4VZWVlAIC1a9cCAL766iu8++67OH78uMH/Lmj4Et81fCIyOz8WF6PlwgWD7GvE\nI49gzIwZA3rNF198gTFjxmD+/PkAgMDAQISFheHTTz/FihUrsHv3btx3331QqVSoq6uDo6Mj6urq\ndK8PDAzULYIEAEtLSyxevBhWVlaYPn067O3tce3aNdTW1uL777/H8uXLIZFIMGHCBMydOxd5eXnw\n9fXF0aNHkZ+fjxEjRkAmk2HevHl6D+Uh8ya+gs8zfCIaZq5du4bLly/D399f16bVajF9+nQAwLlz\n57B48WK0tLTg4YcfRlNTE8aMeta8BwAAClpJREFUGaPb1tnZWe/9Ro0apfdkQisrK3R2dqKmpgbN\nzc0ICAjQ288jjzyCxsZGtLe3631wcHV1HfKxkniJruDzGj6R+RkzY8aAz7oN6b777oOPjw9ycnJ0\nbbW1tbC1tUVtbS1effVV7N27F97e3gCAVatWQRAE3bb9Pa6NHTsW9957r95UfUNDAwRBwOjRo2Ft\nbY2amho4OjoCgN4sAhGv4RMRDVJAQAAUCgUOHToErVaLy5cvIyYmBp9//jlaWlogCALs7OwgCAJK\nSkpw+PBhtLe3D3g/3t7esLOzw65du9De3o7a2lrExcUhJycHNjY2mDVrFlJSUnDz5k18++232Lt3\n710YLYmV+Ao+EdEwM3r0aOzatQsfffQRAgMDERcXh3nz5iEmJgYymQwvvPACFi5ciMDAQGRkZGDu\n3Ll39ERBa2tr7NixA+Xl5QgJCUFUVBQCAwOxdOlSAMC6devg4OCAqVOnYvHixQgNDR3qoZKIWQg/\nn1caxm7f4OJgRgZ+yf/ERD26nStffPEF7rvvPmOH0y0xxEg0HAxlrvAMn4iIyAwMuuCHh4fD29sb\nvr6+8PX1xbPPPqvrKy0tRXh4OHx8fBAbG6v7Tipw60YU0dHR8PHxQWRkJCorK/u1Pz4tj4iIaOAG\nVT3VajUUCgWOHTuGM2fO4MyZMygqKgJwa+VoUlISVqxYgfLycgQHByMpKQmCIKCtrQ0JCQmIiorC\nqVOnsGDBAiQmJqKlpWVIBkVERET6BlXwL126BCcnJ73vk95WXFwMLy8vhIaGwsbGBomJiaivr8f5\n8+dRVlYGiUSC2NhYWFtbIzo6Gk5OTnq3oiQiIqKh0+f38Ds6OtDa2tqlXSKR4OLFi7CyssKcOXNw\n5coVTJw4EatXr4ZMJoNCoYBMJtNtb2lpCTc3NygUCjQ2Nur1AYC7u3u/Vq1ySp+IiGjg+iz45eXl\niIuL69Lu6uqKJUuW4NFHH8XLL78MJycnpKenY/Hixfj73/8OlUqFkSNH6r1GKpVCpVKhtbUVUqlU\nr8/Ozg5qtbrPgG3Gj+9zGyIiItLXZ8EPDg5GdXV1j/1z587V/Xn58uXIycnB119/DalU2qWAq1Qq\n2NvbQ61Wd+lTq9Wwt7fvM2CJnV2f2xAREZG+Qc2P79+/X+/BDFqtFh0dHbC1tYWHh4feqnytVour\nV6/C09OzSx8AKJVKeHp6DiYcIiIi6sGgCn59fT3eeustfP/991Cr1di8eTM8PDwwYcIETJ8+HVVV\nVSguLoZGo0FGRgZcXFwwceJEyOVyaDQaZGVlob29Hfn5+WhoaEBISMhQjYuIiIh+ZlAFPyEhASEh\nIYiJiYFcLsfVq1exbds2SCQSODs7Iz09HWlpaQgMDERpaSlSU1NhYWEBGxsb7Ny5E0VFRQgICEB2\ndjYyMjL6NaVPREREAzeop+VZW1tj1apVWLVqVbf9QUFBKCws7LZvwoQJ2Ldv32B2T0RERP3E77gR\nERGZARZ8IiIiMzCoKX1D0mq1AIDa2lojR0I0vN3Okds5Mxwxn4n6ZyjzWTQF/4cffgAAzJ8/38iR\nEInDDz/8gAceeMDYYXSL+Uw0MEORzxaCIAhDFM9dpVarUVVVBWdnZ1haWho7HKJhS6vV4ocffsCk\nSZNgN0xvVMV8Juqfocxn0RR8IiIiunNctEdERGQGWPCJiIjMAAs+ERGRGWDBJyIiMgOiKPgXL15E\ndHQ0fHx8EBkZicrKSmOHNCC7d+/GpEmT4Ovrq/upqKhAU1MTli5dCj8/P0ydOhV5eXnGDrVH586d\n03u4UW+xazQaJCcnIyAgAMHBwcjIyDBGyD3637GcP38eXl5eev8+mZmZAABBEPDOO+8gKCgIjz32\nGDZu3Disv98uBmLOZ1PIZYD5bLb5LAxzarVaeOKJJ4ScnBxBo9EIeXl5QlBQkNDc3Gzs0PptxYoV\nwq5du7q0//GPfxRWrlwpqNVq4ezZs0JAQIBw5swZI0TYs87OTiEvL0/w8/MTAgICdO29xb5582Zh\n4cKFws2bNwWlUilMmzZNKCoqMtYQdHoay/79+4UlS5Z0+5qsrCwhPDxcqKurE+rr64Xf/OY3wo4d\nOwwVsskRez6LOZcFgfls7vk87M/wy8rKIJFIEBsbC2tra0RHR8PJyQklJSXGDq3fvv76a3h5eem1\ntbS04PPPP8eyZctga2uLyZMnIzw8HAcOHDBSlN3LzMzEhx9+iISEBF1bX7EXFBQgPj4eo0aNwoMP\nPojf/e53+PTTT401BJ3uxgLcOuOcMGFCt68pKCjAwoULMXbsWDg7OyM+Pn5YjEWsxJ7PYs5lgPls\n7vk87Au+UqmETCbTa3N3d4dCoTBSRAOjUqmgVCrx4Ycf4vHHH8esWbOQn5+PK1euwMrKCm5ubrpt\nh+O4fvvb36KgoACPPvqorq232JuamvCf//wHnp6eXfqMrbuxALcO4qdPn0ZoaCimTp2KLVu2QKPR\nAAAUCkWXsSiVSgi8fcUdEXM+iz2XAeazuefzsC/4ra2tkEqlem12dnZQq9VGimhgGhoa4Ofnh3nz\n5uHYsWPYsGEDNm/ejGPHjnW5a9JwHNfYsWNhYWGh19ba2tpj7CqVCgD0/s2Gy7i6GwsAODo6IjQ0\nFIcOHUJWVhZOnjyJ9957D8Ctg/zPxyqVStHZ2ak7gNDAiDmfxZ7LAPPZ3PN52N9LXyqVdvnPpVar\nYW9vb6SIBsbNzQ3Z2dm63/39/REZGYmKigq0tbXpbSuWcUml0h5jv51MarUaI0eO1Osbrm4v6AEA\ne3t7xMfHIyUlBStXroSdnZ3eWFUqFaysrGBra2uMUEVPzPlsirkMMJ/NKZ+H/Rm+h4cHlEqlXptS\nqdSblhnOLly4gB07dui1tbW1Ydy4cWhvb0dNTY2uXSzjeuCBB3qM3cHBAffcc4/ev1l307jDRVNT\nE7Zs2YLm5mZdW1tbm+4AIJPJuozFw8PD4HGaCjHnsynmMsB8Nqd8HvYFXy6XQ6PRICsrC+3t7cjP\nz0dDQ4Pe1zCGM3t7e6SlpeHw4cPo7OzEiRMnUFRUhPnz5yMsLAzvvPMOVCoVzp07h0OHDiEiIsLY\nIfdp5MiRvcY+e/ZspKamorGxEd9++y2ys7MRGRlp5Ki7N2rUKPzjH/9AWloa2tvbceXKFWRmZiIq\nKgrArbHs3r0btbW1aGhowPbt24ftWMRAzPlsirkMMJ+H61juCmN/TaA/vv76a2HOnDmCj4+PEBkZ\nOSy/7tKbL774QggPDxe8vb2FGTNmCJ999pkgCIJw48YNYdmyZcJjjz0mPPXUU0JeXp6RI+1ZWVmZ\n3ldfeotdpVIJa9asEYKCggS5XC5kZGQYI+Qe/e9YvvnmG2HhwoXClClThODgYOHdd98VOjs7BUEQ\nhI6ODiElJUV4/PHHhYCAAGHDhg1CR0eHsUI3CWLOZ1PIZUFgPptrPvNpeURERGZg2E/pExER0eCx\n4BMREZkBFnwiIiIzwIJPRERkBljwiYiIzAALPhERkRlgwSciIjIDLPhERERmgAWfiIjIDPw/s9pE\n+YTavuUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ca23f28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, 2, figsize=(8,8))\n",
"axes = iter(axes.flat)\n",
"for (c, r), dd in big_df.groupby('cost rewards'.split()):\n",
" ax = next(axes)\n",
" dd.groupby('name').return_.plot(ax=ax, alpha=0.8)\n",
" ax.set_title(f'cost = {c} rewards = {r}')\n",
" ax.set_xlabel('')\n",
"\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at the weights, it seems that the search policy learns to heavily weight the heuristic\n",
"in all cases but the low-cost pathway-rewards setting. In that setting, the policy discovers\n",
"the outter ring somewhere around the 50th episode, and quickly learns to down-weight the heuristic.\n",
"\n",
"We don't see the same effect in the high-cost pathway-rewards case. It is possible that down-weighting\n",
"the heuristic leads to so many more node expansions that the benefit of taking the pathway is negated.\n",
"It's also possible that the high computational cost discourages the policy from exploring adequately\n",
"during the initial stages of learning. This could be addressed by introducing noise into the selection\n",
"or evaluation of nodes."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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zmK2lWxifMLFFliGEEKLjardFe3neUpbnfYJNb2NkzGiiTTFUeisYHjOSUGNY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"text/plain": [
"<matplotlib.figure.Figure at 0x10bb97e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, 2, figsize=(8, 8))\n",
"axes = iter(axes.flat)\n",
"for (c, r), dd in big_df.groupby('cost rewards'.split()):\n",
" policy = dd.query('name == \"learned\"').agent.iloc[0].policy\n",
" pd.DataFrame(np.stack(policy.saved['weights']), columns=['g', 'h']\n",
" ).plot(ax=next(axes), title=f'cost = {c} rewards = {r}', ylim=(0,10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conclusion\n",
"\n",
"In this demo, we saw\n",
"\n",
"* how search algorithms can be framed as metalevel policies acting in metalevel MDPs\n",
"* how an agent can learn to tradeoff between computational and external costs via RL\n",
"* how a learned policy can adapt to the structure of the object-level environment\n",
"\n",
"Future work might explore\n",
"\n",
"* learning to search in more complex environments with richer features\n",
"* learning planning algorithms for stochastic environments (e.g. MCTS, RTDP)\n",
"* learning policies that can transfer between different environments and computational costs"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.1"
},
"nav_menu": {},
"toc": {
"navigate_menu": true,
"number_sections": true,
"sideBar": true,
"threshold": 6,
"toc_cell": false,
"toc_section_display": "block",
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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