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Numerically solve differential equations.
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"metadata": {}, | |
"cell_type": "markdown", | |
"source": "# Exercises Script: IMPRS Introduction Course 2017" | |
}, | |
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"metadata": {}, | |
"cell_type": "markdown", | |
"source": "## A first-order differential equation" | |
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"start_time": "2017-05-23T15:21:30.478951Z", | |
"end_time": "2017-05-23T15:21:30.662448Z" | |
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"source": "%matplotlib inline\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n\nplt.style.use('seaborn-poster') # Set style for matplotlib plots.\n\n\ndef rmse(x, y):\n \"\"\"Calculate the RMSE of two arrays\"\"\"\n return np.sqrt(np.mean((x - y)**2))\n\ndef integrate(func, dt=1, tmax=500, F0=0, **kwargs):\n \"\"\"Numerical integration of differential equations.\n \n Paramters:\n func (function): Differential to calculate the rate of change.\n For robustness, the function sould take an arbitrary number\n of positional arguments.\n dt (float): Time step.\n tmax (float): Integration time.\n F0 (float): Initial value.\n **kwargs: Additional keyword arguments passed to the `func`.\n \n Returns:\n ndarray, ndarray: time, values.\n \"\"\"\n F = np.zeros(int(tmax / dt)) # pre-allocate result array.\n F[0] = F0 # Set initial value in result array.\n time = np.cumsum(np.repeat(dt, F.size)) # calculate time array.\n \n # Start iteration at index 1 to allow using\n for i in range(0, time.size - 1):\n F[i+1] = func(F[i], F[i-1], dt=dt, **kwargs)\n \n return time, F\n \n \ndef g(x, alpha=-1.3, R=3.9, C=100):\n \"Differential.\"\n return (alpha * x + R) / C\n \n \ndef euler(Tnow, *args, g=g, dt=1, **kwargs):\n \"\"\"Explicit Eulre method.\"\"\"\n return Tnow + dt * g(Tnow, **kwargs)\n\n\ndef leapfrog(Tnow, Tbefore, *args, g=g, dt=1, **kwargs):\n \"\"\"Leapfrog scheme.\"\"\"\n return Tbefore + 2 * dt * g(Tnow, **kwargs)\n\n\ndef adams_bashforth(Tnow, Tbefore, *args, g=g, dt=1, **kwargs):\n \"\"\"Adams-Bashforth scheme.\"\"\"\n return Tnow + dt / 2 * (3 * g(Tnow, **kwargs) - g(Tbefore, **kwargs))\n \n \ndef analytical(time, alpha=-1.3, R=3.9, C=100):\n \"\"\"Analytical solution\"\"\"\n return R / alpha * (np.exp(alpha * time / C) - 1)", | |
"execution_count": 1, | |
"outputs": [] | |
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"metadata": {}, | |
"cell_type": "markdown", | |
"source": "a. Use the explicit Euler method based on\n$$ \\frac{dF}{dt} =\n \\frac{F(t + \\Delta t) - F(t)}{\\Delta t} =\n \\frac{\\Delta F}{\\Delta t}\n$$\nwith time step $\\Delta t$ = (1 yr, 5 yr) and compare the numerical solution\nwith the analytical solution (plot and RMSE) for the period 0-500 yr." | |
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"start_time": "2017-05-23T15:21:30.664857Z", | |
"end_time": "2017-05-23T15:21:31.404655Z" | |
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"source": "fig, ax = plt.subplots(figsize=(10, 6))\nfor dt in [1, 5]:\n time, T_euler = integrate(euler, dt=dt)\n T_analytical = analytical(time)\n err = rmse(T_euler, T_analytical)\n ax.plot(time, T_euler,\n label='$\\Delta t$ = {} yr, RMSE = {:.4f}'.format(dt, err))\ntime = np.arange(500)\nax.plot(time, analytical(time), label='Analytical'.format(dt), zorder=-1)\nax.grid('on')\nax.set_xlabel('Year')\nax.set_ylabel('Temperature perturbation')\nax.legend(loc='lower right')\nax.set_xbound(0, 500)\nax.set_ybound(lower=0)\nax.set_title('Explicit Euler method')", | |
"execution_count": 2, | |
"outputs": [ | |
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"output_type": "execute_result", | |
"execution_count": 2, | |
"data": { | |
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"output_type": "display_data", | |
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oX1O7efkayktXU7JmKWtLllOxdhWJsjVQUUK0ci3xqrVkJMrITJSRlSwnx8uJNdD7FgFy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\nAAAjiQAAjCQCADABeB7jlaDxEjoAAAAASUVORK5CYII=\n" | |
}, | |
"metadata": {} | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"cell_type": "markdown", | |
"source": "b. Plot and interpret the numerical solutions of the Leapfrog scheme and the\nAdams-Bashforth scheme with time step $\\Delta t$ = 0.1 yr" | |
}, | |
{ | |
"metadata": { | |
"ExecuteTime": { | |
"start_time": "2017-05-23T15:21:31.409247Z", | |
"end_time": "2017-05-23T15:21:31.891880Z" | |
}, | |
"trusted": true | |
}, | |
"cell_type": "code", | |
"source": "fig, ax = plt.subplots(figsize=(10, 6))\ndt = 0.1\nfor func in [leapfrog, adams_bashforth]:\n init = euler(0, dt=dt) # use explicit-euler for initial timestep.\n ax.plot(*integrate(func, dt=dt, F0=init), label=func.__name__)\nax.grid('on')\nax.set_xlabel('Year')\nax.set_ylabel('Temperature perturbation')\nax.legend(loc='lower right')\nax.set_xbound(0, 500)\nax.set_ybound(lower=0)", | |
"execution_count": 3, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"text/plain": "<matplotlib.figure.Figure at 0x7fa1c8e78f28>", | |
"image/png": 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imOuZ8d4vhJhIRESkawpSJH4T+LiZndRRYUTa8tpjv2Hqkhsb1xcMvZoZV2om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\niEgQBYkiIiIiEkRBooiIiIgE+f+FqgVUDb/3wAAAAABJRU5ErkJggg==\n" | |
}, | |
"metadata": {} | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"cell_type": "markdown", | |
"source": "_Interpretation:_ Both models are initialized using the explicit Euler scheme.\nThis is done to compute the first timestep (computational initialization).\nWithout this, ther leapfrog scheme would become unstable, as the computational\nmode amplifies initial errors." | |
}, | |
{ | |
"metadata": {}, | |
"cell_type": "markdown", | |
"source": "## A first-order system of differential equations" | |
}, | |
{ | |
"metadata": {}, | |
"cell_type": "markdown", | |
"source": "The Lorenz model (1984) of the general circulation of the atmosphere is\ngiven by three first-order differential equations.\n\n$$\n\\frac{dX}{dt} = -Y^2 - Z^2 - X/4 + F/4 \\\\\n\\frac{dY}{dt} = Y - 4XZ - Y + 1 \\\\\n\\frac{dZ}{dt} = Z + 4XY - Z \\\\\n$$\nAssuming $F = 8$." | |
}, | |
{ | |
"metadata": { | |
"ExecuteTime": { | |
"start_time": "2017-05-23T15:21:31.894222Z", | |
"end_time": "2017-05-23T15:21:31.943998Z" | |
}, | |
"collapsed": true, | |
"trusted": true | |
}, | |
"cell_type": "code", | |
"source": "def g(xyz, *args, a=0.25, b=4, F=8, G=1):\n x, y, z = xyz\n dx = -y**2 - z**2 - a*x + a*F\n dy = x*y - b*x*z - y + G\n dz = b*x*y + x*z - z\n \n return np.array([dx, dy, dz])\n\n\ndef runge_kutta(x, *args, g=g, dt=1, **kwargs):\n k1 = dt * g(x, **kwargs)\n k2 = dt * g(x + 0.5 * k1, **kwargs)\n k3 = dt * g(x + 0.5 * k2, **kwargs)\n k4 = dt * g(x + k3, **kwargs)\n \n return x + 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4)", | |
"execution_count": 4, | |
"outputs": [] | |
}, | |
{ | |
"metadata": {}, | |
"cell_type": "markdown", | |
"source": "c. Integrate the Lorenz model using the 4th-order Runge-Kutta scheme.\nSpecify intitial conditions, e.g. $X(0)=1$, $Y(0)=0$ and $Z(0)=1$." | |
}, | |
{ | |
"metadata": { | |
"ExecuteTime": { | |
"start_time": "2017-05-23T15:21:31.947343Z", | |
"end_time": "2017-05-23T15:21:33.454355Z" | |
}, | |
"trusted": true, | |
"collapsed": true | |
}, | |
"cell_type": "code", | |
"source": "nyears = 3 # Number of years to simulate.\ndt = 0.01 # timestep\nx0, y0, z0 = 1, 0, 1 # Initial values.\n\nxyz = np.zeros((int(nyears * 365 / 5 / dt), 3)) # Pre-allocate a [n x 3] result array.\nxyz[0, :] = np.array([x0, y0, z0])\nfor i in range(xyz.shape[0] - 1):\n xyz[i+1, :] = runge_kutta(xyz[i, :], dt=dt)\n \n# Splot ndarray into separate timeseries.\nx, y, z = np.split(xyz, 3, axis=1)\ntime = np.arange(x.size) * dt * 5 # Create time array (in days).", | |
"execution_count": 5, | |
"outputs": [] | |
}, | |
{ | |
"metadata": {}, | |
"cell_type": "markdown", | |
"source": "d. Plot the time series (3 years) of the state variables by choosing a\nsuitable time step. A unit of time is equal to 5 days." | |
}, | |
{ | |
"metadata": { | |
"ExecuteTime": { | |
"start_time": "2017-05-23T15:21:33.459160Z", | |
"end_time": "2017-05-23T15:21:34.279279Z" | |
}, | |
"trusted": true | |
}, | |
"cell_type": "code", | |
"source": "# Plot values of X, Y and Z as a function of time.\nfig, [ax1, ax2, ax3] = plt.subplots(nrows=3, sharex=True)\nax1.plot(time, x, color='#1f77ba')\nax1.set_ylabel('X')\nax2.plot(time, y, color='#ff7f0e')\nax2.set_ylabel('Y')\nax3.plot(time, z, color='#2ca02c')\nax3.set_ylabel('Z')\nax3.set_xlim(np.min(time), np.max(time))\nax3.set_xlabel('Days')\nax3.set_xlim(0, 90)\nfig.subplots_adjust(hspace=0)", | |
"execution_count": 6, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"text/plain": "<matplotlib.figure.Figure at 0x7fa1c84fb8d0>", | |
"image/png": 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4IuF1HKsrZ8GXHxLdVVjTgkdXJ/IL3GK8rLFsZhj0NCQJtzY1wOdTQ7D/2dhO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\nzXQXljt0Ha3HG2dFZ05C4rNnnR439L3ykj7HQF53NV4zyS3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4Pf+OH2rzQBNXgfkib+Yj\n+IPptldfVmlmPLyS6ZSYeuYQv1d+0+Eg6H+KGpdtV/VUsWLx+/DujeyTWR5ynZJPhbow1DIfTntQ\nP//6D7EPqJpj50pllgLQ7ZDGs++5nfWN2tb5/sul61MYhcAD1PXcWXgrXK6MRgT/qCpTDaa//D3M\nfw0+ukPVwPqVLXSkVq3aeyLXk8Aj1qyfpsc9x+7/fsehWtfrZ+BRvJF9F5A8n/saZLRUheA/Wwgn\n/AkOOkfduPc/BY78OVzyBvxiBZz2L2jb19+5eElKqtJh3zjFndX54DZlIxzti47fmAGV08kW3LaS\nSz707/iO1ColTUliQsGV8ZAC87jGVXtWrzg2rxv7ilu9klrFW2F5fY75jR5P/XdsJJ3LP1eGEk5N\nx4jL4JR/hJ+NHnCqlqwWb1KZ8HjGvG53O6zpbZ1sSFWpshqOJoVGxtkvqRUoU5azHtHGKz/8D+a/\n6d/xDnS+/D/3dxCU66cf2cKaSh1ke3Q+lMAj1phfnu4NNFJKz9JNf3avgbKd/szD9GmOlk1jbmcY\nezuc/6ySKl3yGhz/f8qZKi0jOnPwg7Z94erPYOSV+rXpjyn3q2RxvarYrYvoczpDX0PjnN9b39hv\nne+2vfUSZ785nUPvLJ/fS2emxFI3vjEDivqmF2kZekW5xKPvmZnxyOnozT69pNNQJT8FdUMQbYer\nVRPh9ctVfRQoS9XT/xP636CJZSkL7n0OSf+Jr+L5+piy5+7NBR7D9diLRrehsHOlHvuZ8QD1vTz+\nXv38g1thbQxthJOVbYt0pjMtS9n5O3z9R+/vMVz1Hd5Yi0vgEWucwCMlXXXHbghTP7rdJ1lIkbc+\nzQc8aRlw+kOq2NoK/JnNfx3evFKtICQ6y7/Qq52DTt9fatDveD1eM9n74+8tMmw7w5DDpKRqW9ai\n9bC32Lu5Cd5iZjwasgN1goPynd78bZXt0ON4cbSqz/hfs+8mffKD/gX39Vn3Pbx6sa7BG3ganP2Y\nN0YfHYfAsIvUuLI4tjKy5tgQcKiyUqHr6Ka3Na/f0Q48HKlVywIlafObw2+FoReqcc1eePk8WD2p\n6c8IoTHtEfapU8bdCSf9RbvHFW9UEmgvKfE+AyyBRywp2qQvql1GKpvPhuhgyEKC7X8R8lzMzpQe\nO1odqFiW6tp+3jM6Bb30I6XFrKuN7dwiZelHejxwwv7v9zRsNNd+5/3xI3G0cuggBeYJwZ4mMh7g\nvhiWetBHoHS7HkfSE8hPOgxW8iZQ9uRf/M7/Y66fDi+fDzUV6nm/E+G8Z721aD3yZ+wLqKY9Ep+1\nHqU7dCah01BlmtIUrsBjnn/zqo9pyuCnzMrEstSCm2OKU10OL50D3/83+aTGsaB0h2rYCJDRSkm7\nLcud9Zj7irfHLPbWShck8IgtLplVE+las1+EX4WwsZBaHSgcdDZc9AqkZqrni9+HT+5KHNvI+tRU\nwsqv1Tirtdu5xaH7YTrYWuuDjaTL0SrM9G97o8Dcr0yiEDmO1ColveELn+k8ZcoCwsUMPEzr3njj\n+Ht107qFb/mTWXTYMBNeOlfVKYBaYb3gBe8lse0GqAwqqJvmuS97u38v2GS4U3Ub0/z2eV2VDTTA\n1gXRO++7ZFZRrJVMb6Ea7zqd3Otq4IvfwtMnqGtBol734oEfX9Q930Zcpv/++52omk8DrPpGNaX2\nCpfZhgQeiY/ZUKih+g4H8wZpm18ZD0PO4Hdx+YFI/5Pg/Oe07GrW0/DdP2I6pbDZNFutsoKq7Who\nxTOzle7Zsnut97VJ4TYPNHE5W0mdR1xi2zobm9e1YUmPGYyYF8lwKTMzHnEqtQLVT+iYe/TzD2/3\n9obDYeNstWrtSBt7jIWLX2s8Qx8pZlPBGU/G343q5h/1uEsQbouWpa/hFbuhrLDp7b3C5WjVPzrH\ndEhvoUxiDjPsnzfNgucmKJv5b+5TgXLZzvj7/cYzC9/R40Ou0+OUVBgQcLurrXQ3t4wUHzIecdIZ\n6QDFtXJyaOPbZeUqN5c961Qjrdoa75taORmPtBbqgiZ4z8BTVRr6g9vU84l/Vl2YB58R23mFilkw\n6DS4bIjOI/VFevOP7rqPSPFCaiXOVvFP6TalFYeG6zvAXQB+IGU8AEZfo7ICW+Yqx6TPfwNn/Me7\n/a+dAq9eomouQC2QXfJG8/KiSOgyErqMVjeqhctg3dSmzzPRxqzTMAvHm6LdAPXvANixBFpF4Xtl\n9vCIltTKJDUdTv6L6r316S9h1yr1+vbF6sdZeMtqrQL8rFy1gp+Zo2REGa3UAlZGK/V9y8xRq/pt\neirJZSIb0ITDjuW6iXTHofubBQycoDIioHpoHXSWN8f1obhcAo9YUVOlsxetezRf+NVhiAo8avaq\nC0w7D1cw6ur0CnJe1/hp0JeMjLxC/SFP/LN6/t5N6gTSflBs5xUKaw1JR89xjW/XZZTK7ABsnuNt\n4OGF1KpVe1V0Wb5TSRhtW7774bBzlZJ1tB/UcA1GJDRlpevgecYjUFye1Tr+b25S0+CcJ+Hxo1Tt\nxZznlcxx+CWR73vRe6oezZF2dDsMLn1z/15TfnDItSrwAFVkHi+Bh23rxZSMVlAQpISpnXF+37FM\nFwP7SbR6eDRHvxNUzcf819X1wMwYAezdo35CwUpR54Ouo6HrIdD9cJVhT+bz9yIj2zHknP3f7zFW\nmR3Ytd7KLqW4PInYvlif0DuPaH57Uxayw+NC2LLtei5SWO4/R92l7TCrSuG1S+LbOtKkpkp3Y89u\n3/SF13Rp2zTH23l4IbUyJRB793hz03ogUVUGb18HD4+EVy6Afw9VDa28LCJtykrXwcuMh23rwCNe\nC8vr066/6ovk8MHtkdmY2jZMeRDevEpfF3odDZe9FZ2gA1RdnFMXseRDbzJZXlCyRRsYdBoevIWw\n46AHSrUQDZzAIyVNZQliSVoGjLwcfvIt3LFA2S+PvELdLLfqCKkhBvh2nWovsOBN+PRueHwc/Ptg\nlVlZPz055VumW5XZK8shK1ffS+5a5XYqjQRHapXeUteURIhkPGKFGfUHE3iYqVKzaMwLpLA8ulgW\nnPWoujDsWKIyWB/9DM59Ov5XbDb/qF1teh7Z9Hzb9of0bFUPsnmOtxkFR2qVmqGL6sKh/WCdwdm+\n2LNUctJTW6N6Oaz62njRhqkPKW95s8ldJJiOVo3dPHmZ8di7R99sh9qUMpYccp2SAP34kmpa+soF\nqsA31ExB+S54/1ZY9rF+bch56nwVzexPegtVPPv9w6o4+ceX4KhfRO/4jeG6bgcpswJ3Rnt7FAKP\n2hrdrLBNL2+dxyKldXcYdaX6ManeG7BJL1VNMatK1eJGZYl6rCpVf9+71qifwuXqu+5QtEH1tJn+\nmJLRHnINDL/Uv1qkaFJWqB3R2g1s/FzY80idKdwwI/KFZNvW59Scjp5dvyXjEStCDTxMV4pCjwMP\nKSyPPpmt4KKXVboeYOHbMO+12M4pGFwyq7FNb5uSqi/Opdu8sToFdTJ0Mh65YTQPNJEC8/CY+qAO\nOtKztRMRwKT7vbP9bs5KF6BFvnK8gshXxl1WunFe32FiWTDhQS19rCpVLlQ/vhzc6q9tq3PQ/w51\nBx1H/kxJuWIhORt1tR7Pey0+VrE3G/UdwVy3HbLb6QxONDIee9bpm/JYyqxCIT0LcjpAQR913eh5\npDJlOfg8FaQcfguceJ+6bt78Pfx6I1zzBZzwJ/W9t4zrwPZF8PGd8NBw+OExFdQkMqsm6nGf4xrf\nzuwpY9YQh8vePbrGLse7RTkJPGKFGXiYPt+Nkd9HjyXjkRwU9FENBh0++YVepYpX1pmF5U3Udzj4\nYQVdsVv5w0P4heUOUmAeOrtWw3fO99ZSNwIXvgTjnBVpG77+gzfHCqbGIyVFy60izXiUJoijVUOk\nZagsR+/x6nnNXnj/Znjt0saD6tpqWPoJPHU8vHWNlpll5sKFLyvL3kgC+0go6ANdA6YrO1d4L9cM\nB9d1O4SMh2XpOo/yQv+drcz6jmDrUBKN9CzoPgbG3g5XfQR3rVLmLebvpXQrfPZLeGSManqbqJiZ\n5b7HNr6d6bLmxd9LsfdWuiCBR2yo3qtvcvL7QIvWzX+mRWvtsGK6VXiBF3p5ITyGXaSkDKBWKd+9\nKX4bLdVWK/0sqO9iMBaNLomBR7VJpr1fxIHHQD32q0dOsvHl/+lVsEOvV641oLroOrKnFV+4b37C\nxanxSMtquubCCTz2FkXWdK4sgRytGiIjGy5+XXePBpXBePRwePxo+OzXqn5j4l/gjSvggYHw2sVa\nngHQ9wS4aSoMOi3686+P08kcYJ7HjdFCxSwsz8yF/N6hfT6adR47Y2ilGyta5sOoq+CGSXDd19D/\nZP3e7rXwyvnw+mXRszP2CttWvTlA9QJrqvVCbmd9Dt4yV0nuIqHEeytdkMAjNmxbpHSrEFq61qnz\nqNittLheYRYhSeARXSwLTvsX5AUyTRt+0E5Q8cbmubp/R4+xwek9O/iQUXAFyhEGHpk5eiV9x7LI\nT9TJztaFsOQDNW5ZAMcafSQyWsKhP9HPZ0b4Pa6r1eem1t2b/r6Z9RjlEdxYlO7Q40QpLq9Pehac\n8wSc/bj6HTlsmQs/PAJf3QuT/q4amZr/VwV9VSfyS9/03p0sXIacowuPF76tmpfGiuJN+v+r07DQ\nM0F+LMI0RuFyPU4UqZWXdB2tsn/XfaOzZqCMCh49Qt/IJwLbFmmZco8j1Hm2KZysR3V55AGuK+Mh\nUqvEZrORAgsp8PBJbuU06MLyVMcnBElWHpz+b/38q3vd8rd4wVXfEWTRajsfMgpmoBxpxgN0cFRb\nGf9St1jz3f16PPan+7ucjLxSd6xf9G5k2buSLVqn3tyNsNl7qGxH49s1hyvjkaCBh8Owi+Cn8+C4\n/3PbuZqkZcGAU+GCF+GWGepGP54MLlq00Y3RKnbD8s9jN5dwC8sdzABg56rI59MUZh1oLHp4xAtd\nR8E1n8MZ/1X22KBu4l88Gyb+NX7VBSYumVUT9R0Oppvk5gjlVj5Y6YIEHrEh3AI188TlhYzBwXEI\natUh/n3rk5W+x8Owi9W4qlS5XMVDMaWJq74jyMAjK1cbFuxYplaxI8VLqRVoS11QRYlCw+zZoFYM\nQa2kj752/22yC3SNQelWlcEL+3hB1HfsO64hi4pESpGoxeWNkZkD434Ot/wAdyyEK96Hc56Ci15V\n1qa/3ggXv6qamDbUFT4ecM6L4O5lEG1CNYSpj1lr4XWdZn0cqVWLfPU3eSCTkqKsfG/63l2XOOlv\n8NbVkUkzo4GZnenTRH2HQ0ejZjjSxb6SGGQ8LMu6yrMjCZp9JzALOg0N/nN+nLiqyqEiINuKVLYi\nRMZJf9E3UCu/VNKCeKG2BtYHbiJbFrgzGc3hOEfVVCitbaR4KbUCcbYKltnPKv98UFrqxno6DDY6\n5i56L/zjBdPDw8EVeESS8TClVglWXN4crbupoHDo+TDwVHXzHE82q43R5zjIDGTWln+urFVjQbgL\nhg65XZVGH3QXbz+o2K2/xweizKox8rqowPuY3+rXFr8Hz5/mrXTdS6rKYd00Nc7p5F4kawzzehap\nvNmUWpn9kiKkuYzHM5ZlfWRZluhvvKKqXDcAbNtfrUgFiyvw8CjjIYXl8UPLfDj1H/r5F/dAZWns\n5mOyZZ7KxEDw9R0OprbZi6JKr6VWprOVFJg3TE0lzH5eja0Ut9VpfQZO0HKrpR+Hn7kzMx5tmst4\neCS1Mi2fE7G4PBlJy9CF7tXlsZFbmYXlWXmqN0aopKTogvTd61QzVj8QmVXjpKTC0XcraWF6oFZi\n02x4/nR3fVe8sG6qkgCDynYEc93N6aRlZZEupJnF5a2iF3j8HjgeWGhZ1hWeHfVAZusCvWoY6qpJ\nm17aq9qrXh5FRi1BnljpxpzBZ+l0askWmPzPprePFuHUdziYripeSASdYDkty108Gy4FfSEt0GRq\n0+z4k7jFA2Yh8oBTm7bdbpkP3Q5T4+KN4Wdng+nh4eCZ1Cpw85GVB2mZ4e9H8BazU3Ms5FZ71mtl\nQKfh4dfBOHWadq37++0lLkerJLXSjZTBZ8DVn+rrx7aF8OwpkfcB8ppQZVagvptOZqS80C0fDRUn\n45HdzlMZfpOBh23b9wEjgeXAs5ZlfWhZlncVJgcikRSopWXo4GD3Wm9ukIqMjIcXq8dCZFgWnPx3\nvWL8/X/9L0QMhnDqOxzMVbdIM3W2rWs8cjt7UwibmqYL8kq3urOAgmLGk3p8yHXNb997vB6bza9C\nwVXj0bPpbb2QWtm2Li5P9MLyZKP3eL2Ku+JL1c06mmwxZVZhFJY7uFQLPp3XCw9AK91w6DwcrvpE\nr+TvXAEvnqOkavHCSqew3ILexwT/OS/kVrXV+lzqYWE5BFFcbtv2YuBw4G7gWGCRZVlXW5Y1uKEf\nT2eXjLgCj5GNb9cYbXqqx5qKyCJZB7HSjT/a9YcxN6pxXTV89qvYzqe2RutMW7Rp3CGnMcxVt0gz\nHuW7dA8JLwNls+Prxpne7TcZ2DIPNs5Q44J+7qCiMfoYF8nV34Z3XKfGIz1bZVGawovAY28R1Abk\nL4lqpZuspKbDoNPVuGZv9OVW4TYOrI9fzpQmppWuSK2apv1AuPoT7ea5fRG8clF8FJwXbYTCZWrc\neXhoJgHtPahbLNkKBBa3PSwshyBdrWzFA8AIoBZ4CljQyI/vWJbVzbKstyzLKrIsq9iyrHcsy4oT\n4/FmcOzNrFToeHDon3cCD/CoUNcMPCTjETcc/Uu96rriC1j2WezmsnU+VAVWGHuMDd2/vkUbaBnQ\n4EcaeBR7XN/h0PUQPd44q/HtDkTMbMeh1weXZeo8Qlvtrp0cen+U2hqdeWrTo/ljtswHAtuEG3iY\nn5P6jvhjyDl6vDDKcisz8OgSxoKhQzScrZz9Wqnu+wWhYQr6wOXvqusUKCe+t67xxoExElwyqyBs\ndE286J/lk5UuhGCna1lWf+AZoAD4AvhjIz++YllWS+AbYCBwJXA50A+YaFlWtt/Hj4i9xfrGq/2g\n5hvBNITXgYcr4yE1HnFDVi6c8Af9/Mvfxa653dopehyqzMrBcVep2BWZg4hppetloNxFMh4NUr4L\nFrypxunZ7k7STZGSqq0rK4uVhjoUijcqHTwE18wuJVXrtcOt8XBZ6SaZo1Uy0PMo/Tte+aXKUEUD\ns7C8RZvmrZ2bwgw8/HC2qqvVvYjye4k9frC0HwiXvq3OcQDLP4Vv/hTbOa00+ncEW9/hYLpOhht4\nuGzro5zxsBR3A3OBwcDVtm2fYtv2Hxr68XR2DXM90Bs4y7bt92zbfh84A+gB3BCF44fPlnnsS12F\nY8cHPgQegVXF1Ay9Ki3EB0Mv0nK8wuXw44uxmUck9R0OBR7JrVyOVh6eDHM76cB781z/HGcSjbkv\na2nbsAv3bxjYFN0P0+MN00M7rqu+I8hktpOlKNsRXv2b6WiVDD08ko3UNBh0hhrXVkUvC7x7jQ5y\nOo+IrK4sux1kBJws/ajx2LNOywVFZhUaXUfB+c+yL3M65UGY/0Zs5lJXqyWqGTnQ7dAmN9+PFq2V\nfTPA9iXhNUqMVcbDsqyDgOnA34CJwBDbtp/3dAahcwbwg23b+/KUtm2vAaYCZ0a05/JCqNgT2eya\nItIGROBt4GHb+kYut0voEhrBX1JS4AQjiTjxL9G3162rhXXfq3FWa7f1bCi09ajA3Cz8zvW4JsmR\nW9VWKve5A526Wpj5lH5+yPWhfb6bEXisnxbaZ81zW7ByEcdSt64G9oZxHndJraTGIy45yOgRsziC\nHjGh4MV128GydJ1H8SbvawkKxdEqIvqf5FYavH+rcjqMNpvm6HNYr3Hh9dtxbOyry93upcHiynhE\nV2o1ByVjusa27Qm2bW9uZvtocBDQUN5+ESojExKWZc12ftizAd4OwrElXLzQiZoX4Ujt+Cp2qyJ1\nkMLyeKXXOOh/shqXbYdp/43u8bfOV1IZCK++w8FcfYso4+Fx80ATc1XJzPIcqKz4UgcAPca6nVKC\nodMwZXkMsH56aFmIXWv0ONieCWZdRjie/C6plQQecUmPIw251ddKvuw3kRrC1Mclt1od+f5MxNEq\nco64XakNQC1CvXFV9J2uVn6px32PD28f7QbosWk4ECwxrPH4CjjItu3nPD1qZOQDDX0LdgFtIt77\nyi+965FRH6ewPDUj/JXjFm10F9dIMx6uHh4SeMQtx9+r+7dM/Q+UbGtqa29Z850e9xwb/n5cGY8I\n/r5cqzAeBx5OTQLAmkne7jsRmf6YHjsua6GQlgFdRqlxyebQVt3CynhE6GxVZgQekvGIT1LTtLtV\nbSUsj4LcKtKO5fXx09nKzCaL1Co8LAtOf0j/rovWq8xHNPs7rfxKj70IPMJp3Gv2NIlm4BFHWY76\nNPQNCEt4adv2KOdn34s/vhDuvBqnfJe+mHYYEn7Rl2XpLr7Fm6F6b/hzkh4eiUH7QTDiMjWuLoNJ\nf4vesc3Ao9fR4e+nTU/dmySc1RcHx9UqrYV2IfGK9oP1auq6aQd2ncf2pbA60H8jr5tqGhgO3cbo\n8foQ6jxiEXiYWRKp8YhfBhtyq0U+y63q6nTgkd3em7oyP52tXBkPCTzCJj0LznsWMnPV86UfwYwn\nonPsskIltQKVtWoTppmBWWAeTuDhLPKlZXl+rU1EUf9uVNajPm1oOBMSAoHYZe4rqnmKl3ipE913\nIbbD0+45SA+PxGH8b3R37dnPw44Ibt6DpaZK9+9o2dbtDR4qqelaMrNrTXgOXXV1+mSY18Wb5oEm\nKSnQ6yg1ri7TGcoDEfMie8h1aqU5HLqHWeexOyC1atUhePe/bMMcQzIeyUvPcYbc6it/5Va7Vmkr\n8UgLyx3MjIdfUqus1vr/SAiP/F5wpiFt/uIeHRD4yaqJ7FtbDzfbAW6pXaj3C7atpVY5nTy/1iZi\n4LEIVedRn8FAmL5hAbIC0W3ZDu9TuL4EHkQmtyqWwCNhyO0ER9yqxnYtfB0FA7nNc9QNOKhak0jN\nB5wVuLrq8OqTyndqxxa/MnRO4AFuH/UDiZJtys0K1GrXyCvC35erP8qM4D5TsUdrqkPpQ+DKeIRh\nqevUeGTmqRVPIT5JTYOBp6lxbaW/zQS9vG475BuBR6R9jUwq9ujguW1/7xdmDkQGnwmH/kSNa6tU\nDXBVmb/HdNV3hNi/w6RFa92Vfcey0KRie4tUUTp4bqULiRl4fAAcZllWb+cFy7J6AmMD74WPuUIw\n22PzLq8aEIF3gYdkPBKLI27XlsdLP4L1P/h7PJfM6qjGtwuWSC11/WoeaGL6pS/7xJ9jxDvT/qst\ndEde2XzX8KZoma9X3rYtgsqS5j9jBqXBFpaDuyDczF4Eg23rwENkVvFPtNyt/Ag8WrTW53Eve3mY\nsi2RWXnHifdBx6FqvGsVfPl7/45VV6f7d6RlKVOPSHDqPCqL3DUbzeFjYTkkZuDxJLAWeN+yrDMt\nyzoDeB/YADwe0Z6zcvV/8sqv3DfmkWDbuilZektoO6Dp7ZvDs8BDajwSiqxc1dHc4Yvf+Vvw5lV9\nh0OkzbP8dLRyaNNT1WCBstQ1+0kcCJTvgplPq3FKOoy9PfJ9Om5hdl1wUgWXo1XP4I9jLhyFmvGo\nLFar5yAyq0Sg51HQIhAQr/gyuIA2HMzva+fh3u3XOReW7/TOMclczCkQK13PSMuEc56E1Ez1fOZT\n6jvnBxtnqLYOoCSF6S0i25/L2WpZ8J/z0UoXEjDwsG27DDgWWA68CLwMrAGOtW07wibtTwX0AAAg\nAElEQVQHFgy/1DkS/PhyZLtz2L1WN6fqMip8vbSD1xmPzDwtMxPim1FXQX4g2bdxhsp8+EF1hW76\nlttFHzMS2kZoqRutDJ1ZSL3sU/+OE49MfkDL64Zf7M3/c1fDpjgYuZV5TssPIeNhSq3Kdwb/OZDC\n8kQjNQ0G+Sy3qqnSGY/crpDT0bt9uwrMParz2ClWur7RfqByl3R4/xa1SOM1Sz7UY+f7HQkuZ6sQ\nAg9XxkOkVgDYtr3etu1zbdvOtW07x7bts2zbXuvJzh33IFCdoutqI9+n2bW3++GR7y+vm7ZXDTfw\nqK3RXy6/Vo8F70nLgOOMVO9XfwivULs51k7V9RQ9x3lUVBmhm4vL/rlb5PNpjIFG4OG3a075LnWM\nb+6DN66E58+Ap06A506DN66Az38L817zp8txfXaugumBpHFqBoy705v9ms5WG4IJPMLMeGTm6FXJ\nUIvLpbA88Rhs9Av2Q261db7OgnU7pOltQ6XAWMjxytlKHK38ZcyNWnJcug0+usNbxYFtw5JAtYCV\nAgMmRL7PcJ2tio3Aw4eMR4RL70lIfi/oPV61qy/aoCwlI3EWALebS/cxjW8XLGkZagWmaL0KPGw7\n9BvD0q2qSBmkviPRGHyWypxtmq1WuX58AUZf4+0xVhgriP1O8Gaf2e2UPWFlcXg30q6Mh4+BR6fh\nqrZg9xpY/71ynvEi4+NQWQIL31bueRtm0LA7eAPk94Z+J8Gwi7yVfTh88TtV+A9w2E2h3fQ3Rdv+\nkJWnChY3zlQ65qaMCsKx0gV1DsxuqzpChxp4uJoHdgjts0Js6HW0svms2B2QW5VCZivv9m8Gyd08\nuG6b+GGp6wQeVmpotVFCcKSkwFmPwiNHqJqJxe/D/Ddg2IXe7H/rfC3t7X6EN5lXU9YfirNViSG1\nkhqPKGG6uMzxoKfHPv96y+3yEgmOt3NVaeiyAqinl5fAI6GwLDjhj/r5xL+qi65X2LZ2dbNSI3PW\nMLEsbSVZsjn0ObsyHj5m6SxTcokKELygYjd882d4YBB8+NNAJjSUbt6rYfqj8MTR8NiRMPu5yPr4\nmCx4C5Z9rMYt23qX7QB1we4yWo0rdjd/o+VYjKa1CD0IcCx1K3aHlgksE6lVwpGaDgMDq8I1e92L\nJV5gygJNuaAXeB141NXqv5s2PcLvEyY0TV5XmPBP/fyTu2BPBC0NTBYb3khOk8xIyW6ra6HCzXhI\n4BElBp6mf1lLP3Hrf0OlYjfsWKLGHQ5SK39eYK4EmsWYwWLexElheeLR80jof7Ial22Haf/zbt87\nlumVl25jvG0eZHbTDbXA3Ml4tMiHjGzv5tQQwy9mX1+fOS9CTWX4+6qthu8fhn8Pg+/u130BQGUx\nDr0Bzn8ObpoGd6+B326DX66FW2fDRa/C0b8K3PgYWc2tC1Tw8tBQmPwvZaUZLrvXwsdGoHHSn707\nTzmYK8ZN1XlUlekLedt+oWdyWxq9PEJZkHFq8ECkVonE4LP12GtZpJPxSMuCjgd7u28zg+qFs9We\n9VoWJvUd/nLw+bqJZWURvHtD5JL8ujqVPXHwor4D1PnTkVuVF0JZkOfEfeoCS+x0o0ZaJgy7WI3r\nqmHeq+Hva8NMPfYyXesqMA8j8Cg2Mx4+ylYE/zj+Xl3r8/1/3HKRSDB72PQ/yZt9OoS70ldTqW8O\nW0fh+5rXFfqdqMalW3Vfi1DZMAOeGK+aT1UWqdesVBh6IVzzBdw2B069Hw46GzoMVvaz6YFOsW37\nqnqTY34N130Jd62CU/7hvgkq3aZ6ujw4REmlzJWqYKjYA69eDHsDgcuACWpuXmNq5Dc00cG8cAX7\nskCmPjlYwu1e7pJaSeCRMPQ+WjXLAyW38qrHQtEmfY3sPML7DEJ6CyWXBiU7jbRWQBytoodlwWkP\n6kzAuqkw5cHI9rluipLOg6oj8VKF0s4IRIN1tnLmktNJZRY9RgKPxqgvtwr3xLBmkh73OCKyOZmY\nbi9hZTxMvbxkPBKS9oO0JKiqFCb93Zv9+hp4GM2zQqnziEWgPO7nejzlwdBkTXuL4MM74OkTYNtC\n/frBF8CtM+GcJ1S9Vygr+tkFMOYncOMUFbSY7ltVJSr4fGgofHB7cP+3JVvh+dNhe6DvapueqlOv\nH43HuoxmX8bGXIypj+m80i4M23Gze3l5CJa6ZpCSLVKrhCE1XTcTrKnwzt3KDI69kkfXxzkXVpW6\nM27hUGjo9yXj4T8t8+Hsx/Tzb/8KG2eHv7+5xuL2sEvC309DhFpgvrdYXb/At0U+CTwao/1AnaHY\nucJdIB4Kq7/VYy+asDmYxWPhZDykh0dycMxvlBYelOY/Uvejok36u96mV3irzk0RrqVuLJpddj9M\nOXqBkjJM/mfT2zss+wz+dxjMfla/1n4wXPM5nPukO/gKe25j4OJX4ZYZKvhMCaxK1VbBnOfh4VHw\n6iWw6F2oKnd/tqZKyccePUIVNILKsFz8emTNApsiK1f9H4CSnjYmDTMvjGFlPIzAI5ReHpLxSFz8\naCa4drIee+FE2RBe1nkURhiwC6HTezwccZsa19XAO9eFV2tZVqjMRgDSs72r73BoF2KBeRSutRJ4\nNEWkReal2/VqZ4ch3l7QIq3xcLoDWylSXJ7I5HZWDkSgTn5f3RvZ/ha9q8dDzvV+9TvfzHiEcLGN\nReABqt7BSlXjKQ/CmsmNb1u8Bd66Fl69ULuCpLVQkrgbvlOBjNe0GwBnPQI/nQeH36ouXADYqlj8\nzavgb91UMfqLZ8OzE+D+3vDBrboGolUHuOoTtdjiJ6bcatOshrdxZTyiKLVy7HQzcyNv2iVEl15H\n65qk5V94I7dymqdaKdAzwu7RjeFl4LFDMh4x4djfGV3NV8Ond4e+j1nP6vqcEZd668wG9Zytgsh4\nRMG2XgKPpjjobMjIUeNF74VewGl2fu493qtZKVrm65NtqBkP24bdgcAjt4svGj4hihx5hzZDWPIB\nrPom/H05Ky+gAg+vyWyltbGhaJv3RKmHR306DYMjblXjuhp47RJ3FhPUAsM398HDI2HhW/r1nuPg\npqlw5M/8/xvL66KCpJ8thGN+6y6yrqtRxeirvlFaYrO4ve8JcMNkVV/iN65+Ho3IrZwLY2pGeHa+\nrsAjyIyHbWsDEZFZJR5pGW651YovIttf8WYdCHQa7r3RgoMr8IggU23bOuPRsq1/WUthf9Iy4dyn\ntepg7ssqkAiWqnKY8UTgiaV6hXhNbmd9HxtME0Ez8BCpVQzIyIaDz1PjmgpY8GZon1/xpR73Hu/V\nrDSO3Kp0W2irPBW79c1H6x7ez0uILll5cOw9+vnHvwjPZnXbItg8R43bDfLvZtS54FYWBX9zGK3m\ngQ1xzD3677eyGF44UzX5e+9m1ejvX4Pgu39AdUDSlJkLpz8EV37ojawqFFrmw9F3w51L4ZI3lQwr\nv94cslqrRZUrP4RL34ScKPWtMC1JGyowr67QiygF/VR36lAxA65gMx6VJer8DiKzSlQGG3KrBW81\nvl0wmFnNXuMi21dThFvvVp/yneqaDiKzigXt+sMpRn3lJ3fB+h+C++z0R3W2dcAp/lwvLEt/L0o2\nqxqOpojCIp8EHs0RrtyqthqWf6rG6dnK/tRrzALzUDqYOzIrgNbdPZuOEENGXQWdR6rxrlUw9aHQ\n92Gu1Iy83JNpNYhrpS/IOo9YSa1Arahe+JK7RmvjDLW6tXayyiiAkmSNvgZunaV+H34UaQdLajr0\nP1HJsG6fA/dsV65Yd69RVr3nP6f+PdGcY0EfnZnbNHt/C8qtC8GuU+Nwg95wajyksDzx6XOMDjqX\nfxaZBb6pVPCyLrM+rbtDSiC4jkRqZa5ii8wqNoy6EkZdrcZ11fDapVDYzO+0ZCtM+XfgiaUy1X5h\nBqSFzdR5iNQqDug8QttXbp2vLpjBsHaKdgboe5w/uuE2YTpb7TYCjzaS8UgKUlKVxZ9jrzv5gdCK\ntytLYf7rapxq2En7QTjaZudkmJoRm5vDzBy47F045f79uwK36qDqK26dGbBZjMPO12mZ6qa8ZX7s\nAiLLgm6BrEdlscqwmTjZNtBBdKiE42olheWJT2q6toGuq9HnslCxbR14pKT5V1gOas6OnHDX6vB7\nQRRK4BEXnHI/dAvU8ZUXwgtnNH5fZtvw/q3qPAjqu9txiH9zaxdCnYcUl8cBlgUjr9TP90WozbD0\nIz322qXAIT9MZytXxkMCj6Sh83A49CdqXFsJb1+nHIyCYdbT+iQ4+Ex/dcKms1UwgUddrW5o2Lq7\n6oQdC1LTYMwN8NO5cMdCuHEq/GwR3LlM1VdEW1aViJiZ31Vfu9/bZAQeXcIMPDKyIb2lGgcrtSoz\nA484DBqF4BhxqR7PfTk8C/wdS3UPg66H+t+o1FmEqavW57hQMQvL20ngETPSMuCiV7QpRvEmeOo4\nWPe9ezvbhm/+BCsDUvyWBXDCH/2dm8tSt5k6D0dqlZWn3Ah9QAKPYBh+ifpyACz5sPlfXE0lLHxH\njVPSod8J/swr3IyHeYKTjEdycew9ehVty1yY+OfmP1NVrjprO4z9qS9T24eZ8WguHQ2q2LM2EEDV\nzzbEitbd1ApVXtfYSqoSDacpI7hr4AA2BgrOrVTtFBMOTtYjWKmVmfEQqVXi0uEgVQwOqjfN5h9D\n38eyT/V4wMnezKspzHNhuB3MXT08pMYjpmQXwOXv6c705TvhuQmqt9LaqbBumnIanPyA/swZD/uf\nJTczYU3dv1aVa0fGcMw9gkQCj2DIyIbDbg48sd1fmoZY+jFU7FLjgacqj3w/CLfGY7fUeCQtmTnK\nZcOxgJ36kPo+NsXkB/Tq8MDT/E35QujaZjOblx8ngYcQHm3763PO+h+0U+CeDfrGq9MwyGgZ/jGc\n4KGyWC0CNYeZGRGpVWIz4jI9nvN86J93NU89JfL5NIdzgwrhF5g7gUd6S+nJFQ/kdoJrv4IeARtm\nu059F587FZ492d1r5sT7YOAE/+fUurt23mpKauW61vqXwZfAI1gOvR4yA7Z689+ALfMa39Y84ZnF\n6V6T01np8SE8qVVKurY2FZKHrqNh/K8DT2zVW2JjI30Tti6EqQH5oJVqfM5HQtU2m9m8eMl4COFh\nWTrrYdfCyq/U2LQo7nNMZMdoGWKBuSvjIYFHQnPwefoGa97rUL4r+M+W7oANM9Q4v7dbEuoXruxv\nCDV5DpWluv6tbb/YyVAFN07mY/yv9ffRJCsPznlSNyD0m5RUaBv4ru1Zv39TWQcz+PVROizf0mDJ\nyoOxtwee2PDZbxrWkG6eqy+iuV2hd4QX0aZISdFSqT3robam+c/YtqGX76a+kELyMe5OGHSGGtdU\nqOZxqya6tyneAq9fql2ZjrjN/2yHQ0Hgoh6MtlkyHsnFgFP1eO7L6tGUuER6zgy1iaCruFykVglN\nizYw7CI1rqmAH18M/rOL3gEC1/QBp0ZHQmlKYAqD6LFQH9MVUGRW8UVaBoz/leqtdNqDahF6xOUw\n4QG4fS4MvSC689lX52E37iZpyv0k4xEnHH4L5AVkAuumwMyn3O/bNnz9R/f2ft/YOyvAdTVQvLHp\nbUFdZGsCPR5EZpW8pKTAOU9ol43KYhV8vH+LWmWe/Tw8eayW6LUfDEf/Mnrzc3nYNyO3koxHctF7\nvJaErJqoHAAdiUvLtu5Gg+EQqrNVmWQ8kgqzCduMJ4NbkAO3E1a0bgpzOuoGhduD6CpdH/MzUlge\nn2S3VTbrZzwMZ/4XDrkuNk0eXc5WjQS5kvGIQ9JbwKn36+df3ONuFDPvVe3U0qqD8vL3m/wQC8zF\n0erAIb0FXPYW9Dku8IINP74EL50LH96ui8hyu8LFr0amqw8Vl8SgGV9xM+MhZgiJT0qq4RRoq+JL\nOyC3G36JWimMhFB7eTgZj4yc6P4NCP7QfqDOmhVtgPmvNf+ZwpXaKr/dwMjMDULBslSzVlABcCjS\nMIBtC/W4Q5Sy1UJi0jaIwGPXaj2WjEccMeAUHVDU7FU3cTOfgu//Cx8abkAn/SU6F7E2IVrqml8s\nH10LhDghMwcueQOOv7dhrWnPcXDt59H/LrQfpMfbFze+nW3DrrVqnNPZn344QvQ5/Ob9swupGWpl\nMFJClVo524jMKnk48md6POnvzduKz3xSjw8+P7pOde0Nq9PtS0L7rNkLp8NB3sxHSE5clrqNZNec\njEdWnq9ZmTTf9pzMnPw39QtaOxmqSuHjO93vD7sYhpwbnbmEmvEwZS3mqrOQvKSmqQvxyCtVf5nt\nS5VTW++jlfNGLOxgzcBjWxOBR/lOqAw04pT6juQhMwfO/B+8fpnqOQNw8l+9+R2HUlxeWQrVgUJL\nkVklD72PVosqayerGrIfX1ASl4ao2ANzArUgqZn+GsI0RLt6izA9xwb/WSfwyMzzrcu0kCTk91KG\nQnXVDWc8KkuhdGtg2z6+3hdI4BEO6S3gktfhnZ+4GwUCDL0ITn8oejdzodrxSeBx4NIyP/oX1cbI\nClwoizao1Ze6uoYdWcyVGenKm1z0PxFuma5qPDoPh44He7PfUKRWZVJYnrQcew88c5Iaf3MfDDqz\n4d/xjCehukyNh14QfUvl9kGsRDdE6Xb9/e1wkPQTEpomNV3VbexYqpQvNVVuWasZjPh8rZXAI1wy\nsuHCl2DdVFj5tfqj73sC9Dg8uvNo01P1RKirCc4VY19wYskKshBb2g9WgUd1uZIJNlTMZkoPzFSx\nkBzk9/L+PBSK1KrUeF8yHslF98Ng0Omq6W/FbvjkF3D+c+4b9OLN2k4cCw6/NfrzdGU8Qgg8XPUd\nIrMSgqDdABV42LXqftFc7Nm2QI99/j5JjUckWBb0PBKO/z847vfRDzpARbFOEdCuNU1rWW1bBx55\n3UQvL8SWYOo8zBXA9hJ4CEEQiqtV6TY9luaByccp/4DMXDVe/B5M+Zd+r7Ya3r1RyaUBRl4em3NM\nq/a6yfCOEGo8pL5DCJXOI/R4w3T3e1H8PkngkQw4Nnp2rbt4vD4lW3VK2UerNEEICvPk1lidh8su\nclDD2wiCSVqmvtlsLuPhklpJ4JF05HZSPRQcvv4jfHKXshR/9WJYM0m9nt0Ojv19bOZoOluV73Rn\n4ZpiqzhaCSHi2OsDrK8XeETx+ySBRzJg2qQ1Jbdy1XdI4CHEGDPw2Dq/4W2cjEdWa7kxFILHyXo0\nV+MhUqvk5+Dz4Ki79fMZTyg3ypVfqucp6aqLdCxrfFxmGwsb385k3wq15f68IDRG5xHKPRBgg9EK\norZGX4Oz20FOB1+nIYFHMuBqDNNETwSzK6UUlguxpu0ASA9YTm+cpaSAJmWFWirTfpAUTwrB4zhb\nVZdDVVnj2zm9bAByOvk7JyF2HPMbOPE+fdPl0KINXPQK9DkmNvNy6GT0Ddkyr/ntqyu0LCu/N2S2\n8mdeQnKRngWdhqvxnvVQvEWNty/SksNIG7gGgRSXJwOmA0FTzdhM2UpBP//mIwjBkJqmVmDWTVU2\nfsWbIK+rft/UnEphuRAKrgLzQmUG0hAlW/U4VwKPpMWy4IjbYNAZsOgdVVRe0BeGnAfZBbGeHXQa\npsfBBB5bFyhDGYAuo/yZk5CcdDsUNs5Q43VTVUbQbITd/bCGP+chkvFIBtoaQURTxWnigiHEG+ZF\n0+kc7LB5jh53ilInYSE5CNZS11nxwxKp1YFAmx6qp9Gp/4AxN8RH0AHK4S8lXY23zG1+e/NcKYGH\nEAq9x+vxsk/U45rv9Gvd/TdJksAjGcjI1h3Mty9t2NnKtvUKcot8yOkYvfkJQmN0Ha3HG2e533Nd\nXEcjCEETrLNVSSDwaNVeZeAEIRakZeo6jV2rYW9R09ub58aucm4UQqDXUZCRo8bLv4DyXcpsAVQt\npZl98wkJPJIF58tSV91wE6KSrVCxS42l2ZAQL5irdRtnut/bFMh4pLWQ4kkhNEypVen2hrepqdRB\nidR3CLGm83A93tKI2YaDE3ikpIujlRAaaZmqeStAVQm8fjnU7FXPB52uWjT4jAQeyUJzxWkuj2Y5\nUQlxQm4XyOuuxhtnwt5iNd69VtV8gAqqo3AyFJKIVoYrS+nWhrcxe3hI4CHEmk5G4LFpVuPble3U\ntvkdh6iCYUEIhUOu1+N1U/R4yLlRObwEHslCRyM91pA1qdR3CPGIZWlHmboaWDtZjVd+rbfpdVT0\n5yUkNmYgsa+Oox5mYblIT4VYYxb1rpvW+HbOORKi4kAkJCE9Doee49yvdRnlrv/wEQk8koVmMx5m\n4DHY//kIQrD0PU6Pl32qHld90/D7ghAMpkNVSSMZj2Kx0hXiiHaDlMYelMtQXW3D25mBhyzKCOFy\n9uPQMXDf2G4QnPt01CT4EngkC63a64vn1oWqIYzJhoB9WmoGtJeMhxBH9DlW1XEALHoP9myAFYHm\nXll5UlguhI4ZSJi9OkzESleIJ1JStKNQZZFbHm2yxgk8LOhxRFSmJiQheV3ghu/grtVw8zTI7xW1\nQ0vgkUw4hbrVZW65VclW2LNOjTsNE02oEF9k5sDgM9W4qgSeOBpqK9XzoReK25AQOmmZyr0PmpBa\nScZDiDPMQGLd9/u/X7INCpepcaehqgGiIISLZSlL6SibDUngkUz0GKvH66bqsZPtANGECvHJoUax\nW/lOPR51dfTnIiQHuZ3VY9n2/TPAIDUeQvxhXsNNuem+14zat/oafUFIECTwSCZ6GiettYZTweqJ\neiyBhxCPdB0No65yvzbiMqlHEsLHyWLYdSr4qE/RRj3O7RKdOQlCU3QeDi0DPWjWTIKqMvf7Sz7S\n4/4nR29eguAhEngkEx2G6NTr6sBJy7ZVkxgAKxV6Hx27+QlCU5z8dxh7B3Q9VHUXnvBgrGckJDKu\nAvMG5FZ71qvHjByRrAjxQUoq9D9JjWv2ut39Kkt0FqRFflQ6TAuCH0jgkUykpMKAU9W4pkKdtLbO\nh+LAyl73w1WxriDEI+lZcMIf4Lov4fh7IS0j1jMSEpmmLHVrq3WfmNbdpaGqED8MPE2P572qxwve\nUtd1gIETpPZNSFgk8Eg2Bp2ux7OfhVnP6OcDJ0R/PoIgCLEgp4mMR/EmJcECFXgIQrzQ7wTIbq/G\nyz9Xmbm6Opj5lN5m5JWxmZsgeIAEHslGn+O0XnnVNzD7OTVObwnDL47ZtARBEKKKU1wO+wcejswK\nJPAQ4ovUdFXfBmDXwlf3wtyXdS+ujgermjhBSFAk8Eg20jKUPr4+Iy4XHbMgCAcOZuCxZ4P7PQk8\nhHjmiNsgM1eNF74NH9yq3zv29yINFBIaCTySkVFXQ78T9fOOQ+HYe2I3H0EQhGjTuoceO32M9j2X\nwEOIY1rmw8l/3f/1g89XUixBSGCkOikZSU2Di1+DVRNVI7Y+x0nTQEEQDiyycpX7T8Uu2L3W/Z4E\nHkK8M+IyqKmEiX+BqlIYdjGc8nfJdggJjwQeyUpKKvQ7PtazEARBiB1teqjAo3QbVJVDRkv1uhl4\ntOnR8GcFIdYcci2MvkaNJeAQkgSRWgmCIAjJSZueemwGG7vWqMfMXMhqHdUpCUJIWJYEHUJSIYGH\nIAiCkJyYdR6O3GpvEZRsVuO2/eSmThAEIYpI4CEIgiAkJ/m99HjnCvVYuEK/1nZAdOcjCIJwgCOB\nhyAIgpCctB+sx9uXqMcdS/Vr7STwEARBiCYSeAiCIAjJSbuBerx9sXp0BR4DEQRBEKKHBB6CIAhC\ncpKVC3nd1Hj7UqirhS3z9fuS8RAEQYgqEngIgiAIyYsjt6qpgMLlsHGWet6yrdv1ShAEQfAdCTwE\nQRCE5KXLKD2e/hhUl6lx98PE0UoQBCHKSOAhCIIgJC+9x+vx7Of0uNuYKE9EEARBkMBDEARBSF66\njIKMnP1f73109OciCIJwgJNQgYdlWf0ty3rIsqz5lmWVWpa1xbKsDyzLGhbruQmCIAhxSGoaDDzV\n/Vq7gdBxaGzmIwiCcACTUIEHcCJwDPA8cDpwM9AOmG5Z1qimPigIgiAcoIy7E9Jb6ufH/V7qOwRB\nEGJAWqwnECKvAf+zbdt2XrAs6xtgLfBT4IoYzUsQBEGIV9oNgBunwII3oesh0Pe4WM9IEAThgCSh\nAg/btgsbeK3IsqzlQJcYTEkQBEFIBAr6wPhfxXoWgiAIBzSJJrXaD8uy8oEhwJIwPz/b+fF2ZoIg\nCIIgCIIgOCR84AE8DFjAv2M9EUEQBEEQBEEQGiamgYdlWcdblmUH8fNtI5//NXAJcKtt2yvDmYNt\n26Ocnwj+KYIgCIIgCIIgNEGsazy+BwYFsV15/Rcsy7oR/p+98w6votre/zunpPdGekISEgKE0DuC\nAkpAQFBEBPVexcJFxYJiAQtiR1G/l58CNpqoSLHQa+g19BoghfTe2ynz+2Pu7MyBlFNmzpyT7M/z\n+LgnZ8rWnMzM2utd78JHAOaxLPuj2BOjUCgUCoVCoVAo4iFr4MGybA2AK6YexzDMYwD+H4AvWJb9\nUPSJUSgUCoVCoVAoFFGxuxoPhmEmAvgJwPcsy86Rez4UCoVCoVAoFAqldeSWWpkEwzB3AVgL4ByA\nnxmGGSD4uJ5l2dPyzIxCoVAoFAqFQqG0hF0FHgDuAeAIoCeAQ7d9lgEg0toTolAoFAqFQqFQKK3D\nCJqAt2sYhjnl6+vbKzIyUu6pUCgUCoVCoVAoNsepU6fAsixj7vH2lvGQlMjISJw8eVLuaVAoFAqF\nQqFQKDYHwzB3OM2agt0Vl1MoFAqFQqFQKBT7gwYeFAqFQqFQKBQKRXJo4PE/aOdyCoVCoVAoFAql\nRS5bcjANPCgUCoVCoVAoFIrk2F3gwTDMQwzDrGcYJoNhmFqGYa4yDPMxwzDucs+NQqFQKBQKhUKh\nNI09ulrNAZAJ4C0AWeB6erwH4G6GYQaxLKuXcW4UCsXOKKgpwKfHP8WB7ANwVDpiRPgIPN/zefg5\n+8k9NQqFQqFQ2hT2GHiMY1m2ULCdzDBMCYAVAIYD2CPLrCgUit1RUFOAqZunomCrgb8AACAASURB\nVKCmAABQq63F+tT1SM5Kxncjv0OcT5zMM6RQKBQKpe1gd1Kr24IOnhP/+3eINedCoVDsF5Zl8fbB\nt0nQ4aR0gqPSEQBQVFuEZ3Y+g4yKDDmnSKFQKBRKm8LuAo9mGPa/f5tcac8wzCn+H5HnRKFQbJhD\nOYdwNPcoAMDP2Q+bJ23G1klbEe8TDwAoqSvBS3tfQq22Vs5pUigUCoXSZrD7wINhmBAACwDsYlmW\nth2nUChGsfzccjKe02cOAlwC4O/ij6WjliLSIxIAcL3sOj49/qlMM6RQKBQKpW1h14EHwzBuAP4E\noAXwb3POwbJsb/4fUSdHoVBsloyKDKQUpAAAwt3DMTpyNPnM28kbi4YtgoPCAQCwPnU99mbulWWe\nFAqFQqG0Jew28GAYxgnAXwCiANzHsmyWzFOiUCh2wt83/ibjB2IegFKhNPg8zicOr/d9nWwvPLYQ\nlQ2VVpsfhUKhUChtEbsMPBiGUQNYD6AfgDEsy56XeUoUCsWO2HurMYNxf9T9Te7zcNzD6B/YHwDn\nfvXVqa+sMjcKhUKhUNoqdhd4MAyjALAGwAgAE1iWPSrzlCgUih2RV52Ha6XXAABx3nEIcgtqcj+G\nYfDuwHfhpHQCAPx+7XeczKNlZBQKhUKhmIvdBR4AlgCYDGARgGqGYQYI/gmVeW4UCsXGOZxzmIzv\nCr2rxX3DPMIwq8cssv3+kfdRr6uXbG4UCoVCobRl7DHwSPrfv98GcOS2f2bINSkKhWIfpOSnkPGA\noAGt7j+9y3R08e0CAEivSMeyc8skmxuFQqFQKG0Zuws8WJaNZFmWaeaf9+SeH6VpqjXVSCtPQ3l9\nudxTobRzzhaeBQAoGSW6+XVrdX+VQoX3B70PJcMVoP94/kci1aJQKBQKhWI8dhd4UOyLzIpMzN4z\nG4PXDsb4TeMx5NchmLZlGnZl7ALLsnJPj9LOKK0rRXpFOgDOucpF7WLUcZ19OuPxro8DALSsFu8f\nfh86vU6qaVIoFAqF0iahgQdFMk4XnMYjmx/Bnlt7oGMbX9LOFZ7Dy/texsv7XkZFQ4WMM6S0N/hs\nBwD0DOhp0rEzE2cizD0MAHCu6Bx+vfqrqHOjUCgUCqWtQwMPiiRkVWbhhT0vkN4HPk4+uDfiXtIR\nGgB2Z+7Gv7b9CwU1BTLNktLeOFNwhox7+Pcw6VhnlTPeGfgO2f465WvkVuWKNjcKhUKhUNo6NPCg\niA7Lsnj38LuknqNXQC/8PfFvfDH8C/z1wF/4ZOgncHdwBwCklqbiia1PoKi2SM4pU9oJV0qukHGC\nf4LJxw8IGoAJ0RMAALXaWiw8tpBKBm2IlPwUfHbiM5zKPyX3VCgUCoXSBDTwoIjOnsw9OJ53HAAQ\n4BKAb+75Bh4OHgC43ghjo8ZiVdIqdHDpAADIqsrCzF0zUdVQJducKe0DvijcTe2GYNdgs84xp88c\n+Dj5AAD2Z+3HtvRtos2PYj6Hsg/hiW1PYNWlVZixY4ZBkEmhUCgU24AGHhRRYVkWS88tJdtz+86F\np6PnHftFe0VjZdJKBDgHAOBWot888Cb0rN5qc6W0L0rqSlBYWwgA6OTdCQzDmHUeLycvvNHvDbL9\n4bEPqVzQBvju7HdkrNVr8f3572WcDYXSPqjR1GDFxRV4cvuTuOf3ezD8t+GYvmU6vk75GjfKbsg9\nPYoNQgMPiqgcyjmEyyWXAXAvdyMjRja7b7BbML4d9S3c1Zzsal/WPiw/t9wq86S0P1JLU8m4k1cn\ni841OnI0hocOBwCU15dj3sF5NGiWkeLaYpwpPGPws/1Z+2mzRwpFQo7lHsPYjWOx6OQinMg7gcLa\nQhTXFeNs4Vl8f/57PPDnA3hh9wsG914KhQYeFFHZkLqBjGd0mwEF0/JXLNY7Fh8P/ZhsLzmzBIez\nD7dwBIViHsKHX6x3rEXnYhgG7w16j0iujuQewZrLayw6J8V8TuSfuONntdpanC88L8NsKJS2z9a0\nrXhu53MG9Zmejp7knsizL2sfHv77YXx56kvUamutPU2KDUIDD4polNeXY9+tfQC4G9CoiFFGHTcs\nbBie7f4sAIAFi7cPvY3SulKppklppwib/nXytizjAQC+zr74YPAHZHvxqcW4WnLV4vNSTOdEbmPg\nMSRkCBlfKr4kx3QolGbRs3psvrkZnx7/1G77WZ0pOIO3D74NLasFAPQN7Ivf7v8NB6YcQPKUZOx8\naCde6vUSfJ18AXC9j3668BOm/jOVZj8oNPCgiMf29O3Q6DUAgKTIJKiVaqOPnZk4E/0D+wMAimqL\n8N7h9+zyhkyxXYQPvBjvGFHOeVfoXXgk7hEAgEavwdz9c1GjqRHl3BTjOVd0DgDAgMFj8Y+Rn18s\nvijXlCiUO2BZFu8dfg9vHHgDqy+vxsv7XsYXJ7+Qe1omUdVQhVeTXyXP+vuj7seyUcvQxbcLqZsL\ndA3EUwlPYeuDWzEjYQZUjAoAcKP8BqZunmqgjKC0P2jgQRGNnRk7yXhc9DiTjlUqlFg4ZCGx2d1z\naw82Xd8k6vwo7ReWZUnH8gDnAOKyJgav9nkV0Z7RALgH63tHaNBsTXR6HW6W3QQAhLiFoFeHXuRF\nh2Y8KLbEgewD2Hh9o8HPVlxagZT8FJlmZDr/PfNfYqbRM6AnFgxaAJVC1eS+zipnzO41G7+N+43c\nI+t19Xj38LtYeHQhCV4o7QsaeFBEoUZTg5P5JwFwL3YJfqb3SAh0DTRo0Pbx8Y9xq+KWaHOktF9K\n6kpQpeHsmiM8I0Q9t5PKCYuGLYKzyhkAp32m9R7W41blLTToGwAAMV4xcFI5IcorCgCQUZGBOm2d\nnNOjUABwix9fnvySbHf17UrGi08tlmNKJpNWnoa1V9YCABwUDvhg8AdGKRtivWPxy9hfMDFmIvnZ\nb1d/w7M7n6Wy6nYIDTzskLOFZ/Hk9icx9Z+p2JG+Q+7pAACO5h6FVs/pPYeGDjXbqnR05GjcH3U/\nAK44dN6hedDpdaLNk9I+yajIIOMID3EDD4CTbr0/6H2y/cXJL2gTOyshtOyM9uJWVSM9IgFwNWPZ\nVdlyTItCMSClIAU3yrnvarxPPFYlrSL3ojOFZwxq0GyV5eeWE/e+JxOeNOle6qJ2wYLBCzB/wHyS\nkTyRdwJTN0+1i/92injQwMPOyKjIwNM7nsaJvBO4UHwBrya/ahMuUAeyD5Dx0NChFp3rrf5vIdA1\nEAB3s159ebVF56NQDAIPd/EDDwBI6piE6fHTAXDFlHOS5yCvOk+Sa1EauV52nYz5wEP4QiT83VMo\nciGUDk/tPBVqpRqTYyeTn21M3djUYTbDrcpb2JK2BQDgrnbHY10ea+WIpnk47mEsv3c5vB29AQDZ\nVdmYvmU6dmXsEm2uFNuGBh52xpIzS+6wpPsq5SvZNeVHco4AAFQKFQYEDbDoXO4O7lgwaAHZ/ibl\nG9qIiGIRUmc8eF7p8wp6BfQCwJkkzNo9C9WaasmuRwEyKzPJmJdYhbmHkZ/dqqRyTYq86PQ64vjo\npHTCfZH3AeBqIXnL+b239sr+HG+JddfWQcdy6oOp8VMtqpPrE9gHa+9fS2zNa7W1eHnfy/gm5Rva\nD6kdQAMPOyK3KpdIq9zV7ghxCwEAXC65jGN5x2SbV151HpEzdPPtBle1q8XnHBg8kLgFNegb8NbB\nt2ghGsVsDAIPkWs8hKgVanwx/AsEuwYD4Cx85yTPITJEivjkVOWQcahbKAAg3COc/CyzIvOOYygU\na3K+6DzK6ssAAAOCBsBF7QIA8HHyQc+AngC4lX9h9s6W0Og0+PP6nwAAJaPElLgpFp8zxC0Eq5JW\nGdjuLz+/HC/seQEVDRUWn59iu9DAw47YkraFrDhM6TwFs3rMIp9tS9sm17RwuuA0Gffq0Eu0877c\n+2Wycnmp+BK+P/+9aOemtC94RysFo0CYW1jLO1uIn7MfloxYAje1GwDgYPZBfHL8E5tezbRn+EUP\nV7UrWYUNd28MPDIqqdSKIi9CKfJdYXcZfHZ32N1kfDD7oNXmZAp7bu1BSV0JAGBY6DAEuASIcl4X\ntQu+GPYFZveaDQZcXej+rP14dPOjVOXQhqGBhx2xJ3MPGY+LGod7wu+BWsE5SiRnJcuWohQW0fIy\nEzFwUbvgwyEfkhvSsrPLqD2mHdOga8DB7IM4XXDaqi/helZP5DbBrsEm9ZcxlxjvGHwx/AsoGSUA\nzsGFBs7io9FrkF+TDwAIdgsmphZ+zn5wVDoC4DLFFIqcCO1yBwYNNPisf1D/JvezJbbc3ELGD8Y+\nKOq5GYbBjIQZWDJiCbHTz6jIwNTNU7ExdSNdsGmD0MDDTiiqLSJNsiI9IhHlFQVXtSv6BfUjn18u\nvizL3IQZjx4BPUQ9d8+AnvhXt38B4Ap23z74Nhp0DaJegyI9JXUlmPLPFMzcNROPb30cr+1/zWpu\nZcW1xajX1QMAQt1DrXJNABgUPAjzBswj29+c/oZYUVLEIb86nyy4hLiGkJ8zDIMOLh24fWry6ctL\nG0Cj0+D3q7/juZ3PYdJfkzBz10ysv7YeGp1tS3A1Og3OF50HAAS4BBCJNE8nr05wV3Mv3CkFKTZX\n41CtqSaZGC9HLwwMHtjKEeYxNHQofh37K2K8uOautdpavHP4Hbya/CrK68sluSZFHmjgYScIX+6F\nrlGDgweTcUqB9VdLqhqqSEfoGK8YeDp6in6NWT1mkZvR9bLr+O+Z/4p+DYq0fHj0QwP98vb07Vif\nut4q1xbaqd7+0Jeah2IfwvM9nifbHx37CH/f+Nuqc2jLCOs7gt2CDT7jnfHqdfVEX0+xT66WXMXE\nvybig6Mf4FDOIaSWpuJg9kG8d+Q9PPzPwzZtIHCx+CJZ+OgV0OsOq3mlQkkW7CoaKmyuziP5VjLp\nkzMifARRWUhBuEc4Vo9ZTSz1Aa4x8aQ/J2FXxi66gNBGoIGHnSBMwfYO6E3GQmmTMDixFpdLLoMF\ndzPo7t9dkms4Kh3x4ZAPiff3zxd+xpmCM5JciyI+V0quYEfGnf1mlp9fbpXVSuHLqbUDDwB4pvsz\neKLLE2R7/qH5NtN/x95pKajkAw8A1NbYjjmRdwJPbHvCwCCCl98C3GLUE1ufwM3ym3JMr1WEz2W+\nkPx2endofKbbmtxqV2ajze29EfdKfj1XtSs+HvoxPh36KckEFdQW4OV9L2Pm7pnULKINQAMPO6E5\nOVOcTxzpmJySn2L1FQFhzUUXny6SXaeLbxc8k/gMAK4p2NsH30aNpkay69kCLMuiXldv96s8QnnR\nq71fJRrnvOo87M/eL/n1c6qbXxW3BgzD4NU+r2JSp0kAAB2rw+v7X8fmm5utPpe2RkuBBy+1AkDq\nQCj2xc2ym5i9ZzaxpI7zjsOK0Stw5vEz+Om+n4iJQGFtIWbvmY2qhio5p9skxpivCAOPM4W2s6im\n1WtxNOcoAMBN7Ya+QX2tdu0xUWPwx/g/0D+wsQbmUPYhTNg0AQuOLKCLCXYMDTzsgBpNDa6UXAHA\n1Xf4OvuSz1QKFRL8EgAAxXXFVn/AGgQevtIFHgAwI2EGuUZmZSYWn1os6fWsjUanwZ7MPXjv8HuY\n+OdE9P+lP/qs7oMeq3pg1B+jMCd5Djbf3EzS9vZAva4eO9N3AuD86yfHTcYjnR8hn+/M2Cn5HOSU\nWvEwDIN3BryDsVFjAXDBx5sH3iQWlRTzMEZqBdCMhz1Sq63F7L2zUampBAD0D+yPlUkr0atDLygY\nBfoE9sGKpBXo6NkRAOdc9+GxD+WccpNcLuFqLx2VjkQyfDudfToTIwq5ajWb4nzR+cb//0H9JZVZ\nNUWwWzCW37scnw79FH7OfgC4Ws9119ZhzIYxePPAmzhbeNbuF+ekokZTg+O5x1FQUyD3VAyggYcd\ncK7oHLHRbSpVG+cTR8bXSq9ZbV5AY+ChYlSI9YmV9FpqhRofDfkIDgoHAMCvV38ljQvtmeLaYiw+\ntRgj1o3A7L2zsT51Pa6XXSeNIvWsHnnVedievh1vHHgDSeuTsCF1g80VITbFkZwj5MF1d9jdcFW7\nYlDwILioOB/7fbf2Sd6fpaWXU2uiVCjx4eAPMSF6AgAuczf/0Hysu7ZOtjnZOy1ls2jgYd98deor\nYoMd5RmFxXcvJv0vePyc/fDV3V+R+8k/N//B0dyj1p5qs5TVlZHvXqx3LFQKVZP7OamcSPPLtPI0\nm8nmH845TMaDggfJMgeGYTAmagz+euAvPNntSaLw0Og1+OfmP5i+ZTom/DkB36R8g/OF52nPpP9x\npeQKxmwYg6d2PIX71t+Hv278JfeUCDTwsAOEKyBN1VHEeTcGHldLrlplTgDndsHrbqO9ool9pZRE\ne0XjxV4vku13Dr+DyoZKya8rBTWaGnyd8jWSNiThxws/orS+lHymYBQIcw9Dd//u6OTdyeD/bWFt\nId49/C7+s/s/KK0rberUNoPwwTUyYiQA7iE7OIQzRajWVEtukcwHHmqFmqyayYVSocSCwQswOXYy\nAC74WHBkAb498y1dtTODwppCAFw27fZOykKpVWFtoVXnRbGM84Xn8cuVXwBwf7eLhi0iVqu3E+UZ\nhZd7v0y2Pzr2kc28fF4pvULGnX06t7hvvE88AO6ecLXUes/xljicLX/gwePu4I6Xe7+MLZO24PEu\nj5M+SQAXrC0/vxyPbnkUg9YOwoztM/D5ic/x+9XfcTT3KFJLU1FYU9huHDE1Og1eS34NxXXFADjJ\n3HuH3zOok5KTpsPvdkp+dT6+P/89hoUOQyfvTnJPh8DLrIDGm5MQYcbDmjesqyVXSWF5vO+d85KK\n6fHTsSdzD1IKUpBXnYfPTnyGDwZ/YLXrWwrLstiZsROfnfjMQBqnYlQYFjYM46LHoX9gf7g5NN5Y\nNToNTuSdwKrLq4i14aHsQ3h86+NYNmoZgtyCrP7fYQx8RooBY+BX3zewL5FZncg7gUT/REmur2f1\nJPAIdguGgpF/rUXBKDB/wHw4KB2w5vIaAMD/O/v/kF+Tj3kD5jW7KkoxhGVZElD4Ofvd4RYklKQW\n1xZbdW4U82FZFp+c+IRs/6fHf1p9Hk+OnYyN1zfiUvElpJWnYWvaVoyLHif1VFvlSrHxgUcX3y5k\nVfpS8aVmC9GtRXl9OS4UXwAARHhEWNWKvCX8nP3wWt/XMKvHLGxO24xNqZtIqwGAk+gdyzuGY3nH\nmjzeWeUMV7Ur3NRuhv92cIOb2g2h7qGI9oxGnE+cwT3Enlh3bR3JFvJo9BqsvLgS8wfOl2dSAugT\nTkBRXRG+TvmaW4WOTMLbA96WxB7WVPgshpJRItor+o7PozyjoGJU0LJaq2Y8hLZ/wqyL1CgVSiwc\nvBAP/v0garW12HR9E+4Ouxv3hN9jtTmYS0VDBRYeWYit6VvJz1SMCpM6TcJTCU81KwVSK9UYFDII\ng0IGYW/mXrxz+B2U1ZchvSIdj297HKuSVhlIS2yBvOo8cvPr6tvV4G+pb4fGIsWTeScxI2GGJHMo\nri0mVpDBrvLJrG6HYRjM7TsXvk6++Ob0NwCA9anrUVBTgEXDFt0hKaHcSbWmmsgR/V387/jc29Eb\nCkYBPatHUW2RtadHMZPNaZtxrpB7kQx3DzdwhGsOpUKJ2b1m49mdzwIAvjv7HZI6JskexJuS8RDW\nSNpCo9wTeSeInFfubEdTuKhdMDl2MibHTkZedR52Z+7GqfxTSMlPISv9TVGrrUWtttaoe0Kcdxzu\nCr0LEztNRJh7mJjTlwyWZfHb1d/I9pIRS/DqvldRp6vD3zf/xku9X2o2e2gt5F/+s1G2pm/FY1sf\nk/2BVaetQ1pFGgCgo2dHOKmc7tjHQemAjl5cgV1GRYbV9KF8/w4ATQZEUhLmEYY5feaQ7XmH5tm8\nzV5Kfgom/zXZIOjoH9gf68evx/yB842uP7g7/G6sHrOaFErnVefhhT0vEOcXW0FYfzMgeIDBZ9Fe\n0SQQuVB8QTKZkbCwXM76jqZgGAZPd3/awCr6QPYB/Gvbv2hNghEI5VNNSeiUCiW8Hb0BQPb7OMU4\ntHotlpxeQrZf6/sa1ErjCpoHBg0kWYLMykwk30qWZI6mwGc8FIyi1axNnHccsQkWqhzkQtgXrF9g\nPxln0jqBroGYFj8NXw7/Ensf3ottD27DtyO/xRv93sD0+Om4P+p+DAkZggS/BER6RMLP2Y/UirTE\n1dKrWH5+OcZuGItZu2dZdWHXXM4VnSPW0t39uuOu0LswJmoMAC7oOpR9SM7pAaAZDwOiPKPwUq+X\n8MP5H1CpqURaeRqe2fkMVietlm0F8nrZdbLqIJRU3U6cdxxSS1PBgsWNshtI8E+QfG43ym+QcXNu\nHVIyOXYy9mftR3JWMiobKjF772ysGbPG5laLtXotlp1bhqXnlpLfpYvKBW/1fwvjo8ffIRExhgiP\nCKwYvQLTt05HXnUerpRcwfxD8/HFsC/MOp8UCG0khTIrgHvpjveJx9HcoyivL0duda4kgYHcPTyM\nYXz0ePg5++GVfa+gWlONyyWXMXXzVHx191eSSdDaAsJgwt/5zowHwAUkxXXFKK0vhU6vg1KhtNb0\nKGawJW0LsqqyAHA9qoaFDjP6WIZh8FS3p/D8Hq5h5y9XfsGIiBGSzNMYhIuGkR6Rrb7ouqhdEOoe\niluVt5BWngatXitrxuZ0ftMW/rYOwzAIcQtBiFsIhoQMaXFfrV6Lak01qjRVqGqoQnl9OdIr0nG9\n7DpO5Z8iZj0sWOzP2o8DWQcwJW4KXunzilGBixzsymjsuzIhhjMyGRE+AhtSNwAA9mftx+iOo2WZ\nGw/NeAhwVjnjqYSnsPb+tQhwDgDArep/euJT2eYkXPno7N18qlaYcbhd2ycVN8q4wMPT0VOWol2G\nYfDR0I+Il/v1suuYd2ieTbk9ZVdl49/b/o1vz35L5tXdrzv+GPcHJsRMsChI6ODaAUtGLIGr2hUA\nZ0276fomUeYtBrxcggFDLJ+FCOuVpLKQlLuHh7EMCh6En0f/TORyRbVFeHLbk7TLeQvwheVA01Ir\noLHOQ8/qDcwbKLYHv0DDM7PHTJPvj0NChpAFhuN5x3G9VL4u4KmlqeSe35rMiod/jmv0Glm7sQst\n/MPdw2U35ZAKlUIFT0dPhLiFIM4nDv2C+uHhuIfxVv+3sH78eux8aCf+k/gfsrDBgsWvV3/FlH+m\n2GzDyn239gHgnru8/LxfYD84KTm1zMHsg7IbmdDAowkiPCLw3ajvyC9qQ+oG7M+SvtFZUwjlTC3Z\n1UZ4RJCxNQKP4tpilNSVAACiPaNlW2X3cPDA13d/TewUd2bsxOcnPpf9DwsAttzcgof+eog0hGLA\n4OmEp/Fz0s8I8xBHLxrrHYv3Br5Htj8+/rGsDyyeqoYqcmOO9oomwZEQoSEB73UvNrZipWsMnX06\nY+3YtSTL0aBvwFsH38KXp76ETq+TeXa2h1Bq1VLGg4cWmNs229K3EdedHv49DBrHGYtSocQjcY19\ngn69+qto8zMVgxrIFtQKQoTKAX5hTw4uFF2AluWcwewp2yE2ga6BmNljJjZP2owXer5ArPzTytPw\n+NbHDbL6tsCtilvk/S/BP4Hc/5xUTqRJZWl9qdUWp5uDBh7N0Mm7E17r+xrZ/vzE59DopO030BRC\nOVO0Z/N1FJEekWRsDcs04U1RbgewGO8YfDT0I6KPXX15NX66+JNs86lqqMLbB9/G3ANzUaXhOul2\ncOmAH+77AS/2elH0JkyjO47G/VH3A+A0nJ8d/0zU85vDheILxPGsKQto4LaMh0SBh9A1LNDFtorv\nm8LP2Q8/3vcj6fUBAD9d+Akv7n3RJrsyy4lBxqOZwEPoSkPrPGwXlmWx8uJKsj0z0fRsB8/EThOJ\n/fiWm1tka7gqXBGP8owy6hhh4CEMXKyNsL6jV0DT3dbbE84qZzzT/RmsvX8taVhZXl+OZ3c+izMF\nttNp/njecTIeEmwoM0sMaJTtyj1nGni0wEOxDxGJSHpFOn6/9rvV55BWxmlEXdWuCHAJaHa/MPcw\n8uKdXp4u+byEN0VrF5Y3xYjwEXi7/9tke/Gpxfj1ivVXu04XnMZDfz9k0KxnVMQorB+/Hn0D+7Zw\npGW82f9N+Dj5AAD2Ze2TLUPHc77wPBk3JbMCgHCPcJKpkkpqxXdsZcDAz8U+5AIOSgd8MPgDzOkz\nh9j/7s/aj+lbpuNWhfzZLFvBoLi8md+tn1Pjz2ngYbucLzpPFh86eXfCwOCBZp/L09ETd4fdDQCo\n1FTiQNYBUeZoKvYceAhfTOW29bUlYr1jsSppFcke1GprMWv3LANlipyczD9Jxn0C+xh81sO/MXN1\ntvCs1ebUFDTwaAEFo8DcfnPJ9k8XfrJq1qOyoRIFtdyLU5RnVIsrQE4qJyIlyazMlLzOQXhTlKOw\nvCmmdJ6CZ7o/Q7Y/PPYhVlxcYZVra/Qa/N/p/8O/tv2LOCk5q5yxYNACfDHsC8ltmT0cPAyaaH16\n/FPJO4K3xPmixsCjuYyHglEg1puTDxbWFqKsrkz0eeRXcxkPX2df0TNNUsIwDJ7o+gT+e89/SaOs\nG+U3MG3LNNlXq2wFYSDB1+TdjkEvjxYsNinyIrT/fCTuEYulu3wGGIBsdVI3y7jAw0HhYLSxRaRn\nJFlskEtqxbIs6Yvh6eiJSM9IWeZhq3g6euK7kd+RTFBFQwVm752NioYKWefFsiwJPNQK9R0Lft39\nu5PF6QtFF6w+PyE08GiFRP9E0mU5vyYff9+03k0srTyNjPn0XkvwdR612lqy0isVwpuirQQeAPB8\nj+fxWJfHyPaik4vw2YnPJO1ke7HoIqZtnoZl55aRgC/BLwHrxq3DxE4TrVb/Mj56PHnJz6zMlLUw\nmbcddFQ6trjaJ8yW8Q4wYlGvqycFxcIu1vbE0NChWDNmDTFQKK0vxVPbn8L29O0yz8w4zhaexeNb\nH8eIdSPwwZEPRLX65jMeaoW62cBeWONBMx62SVldGbalbQPAZfbHRo21A50L9QAAIABJREFU+JyD\nQgYRK+X92ftRXl9u8TlNoV5XTxagIjwjjHZTc1Q6kr/19Ip0WRaPblXeQmVDJQCgm283m2i6ams4\nqZzw3xH/JTLzW5W3MO/gPFlrS7OrsokNe4Jfwh2tF1zVrgj34L5bN8pvyLowSb9RRvB0wtNkvOrS\nKqt9uUxN1QrrPKQuHuLrSLwcveDt5C3ptUyBYRi81ue1O35nz+9+nhTDi0VVQxU+Pf4pHt3yKJEJ\nKBgFnkt8DiuSVhgU/FsDBaPAS71eItvfnf0ODboGq84B4FaAeDepGK+YFi0hhQG1MNAWA2Hw3ZJM\n0daJ8orCmjFryApbg74Bc5Ln4McLP9qEiUJzXCq+hKd3PI3TBadRUFOA36/9jtf3vy7anItquECi\nqa7lPDTwsH02Xd9EmnyOixrXpBGFqagVamIZqtVrDSxGrUF6eTqpcTNWZsXDL+Rp9VpZelNdLL5I\nxl39ulr9+vaCu4M7vhr+FclI7721F+tT18s2H2GhOy8Fu51OXlygpNVrkVEufS1wc9DAwwh6d+iN\nrr7cH+D1sutW08eZGngIX3Sl/FLVaGqIbMEWu3kyDIMXe72IN/q9ASXDrTQdyjmEiX9OxO6M3Ra/\n+Gh0Gqy5vAZjNozB6surSZYjyjMKK0avwKwes2ST9fQN7Et6ZuRW52Jj6karz+FayTUybs1G0lqB\nh71mPHi8nLyw7N5lSOqYRH62+NRiLE5ZbJPBh1avxdsH3yadxXmSs5KxLX2bxeev1daiUsOtyjZX\nWA4Avk4CqRV1tbI59KzeoHZyStwU0c49OrKxV8GeW3tEO68xCO9lpgYewixwapn1awcuFgkCD18a\neLREuEc4Fg5eSLYXnVwkW/NXoXyqOScyXtoMgPQokQMaeBjJ5NjJZLzu2jqrXJMvLAeMK+AWBgHC\njs1iwzd4AoBQ91DJrmMp0+Kn4duR38LDwQMAUFJXgpf2vYSndz5tlsaxvL4cP174EUkbkvDJ8U+I\njEetUGNWj1lYN26dTVgPPt/jeTJeeWml1a1Yr5Y2dncV3uiaQsrAg6/vALieJ/aOo9IRnwz9xCCb\n99OFn/DJ8U9sqncNAGy8vpHUgXXy7mTwcP7h/A8WB0t8tgNovocHwOmx+cUHsTOeFMs5knOE2H/3\n7tAbMd7iyXYT/ROJ4caRnCOo1lSLdu7WEC4aGiOTFiIMVKxhFHM7BhkPGni0yoiIEUQeWK2pxsKj\nC1s5QhqEv7cuvl2a3IcGHnZGUsck4sCzPX27VTSj/M3L2OK0EPfGfYTBgdgI+0SEutlu4AEAA4MH\nYsP4DaROBwCO5R7D1M1TMW3zNPx+9fcW+17kV+dj883NeGXfKxixbgQWn1psYNE6KmIUNk7YiOcS\nn4OD0kHS/xZj6RHQg8hyMiszsS9rn1Wvz9d3AK371we7BhNvdLEbMrWljAePglGQbB7PL1d+wYIj\nC2wm+NCzegNTh7f6vYXx0eNJ9utq6VXS28ZcDBytWmhuxjAMvBy9AABl9eKbF1AsQ9hnQ9h/QwyU\nCiVxt9LoNTiQbT13K3McrXiExdzWsMYXomf1uFR8CQD3d2XPElVrMrfvXBLkJmcl43D2YateX6PX\nkIaPga6Bzd4Tha0P5Aw8mhdfUwxwUbtgbNRYrLu2DvW6euzI2GGQBRGbel09CR6MLU4TBidZldIF\nHsJz26LU6nY6uHbAtyO+xT83/8E3p78hqdBzReeIe4evky9C3UPh6egJBgzK6suQU5Vj8IIjZHDw\nYMzsMZM0e7M1Hu/6OPFiX3lxJUaEj7DatU3JeCgVSkR4RiC1NBXZVdmo19UTD35LEQaIbe0BOi1+\nGme7e+QDsGCxPnU93NRueLXPq7I18+Q5nHOYvDD1DOhJbB2nxE3B+0feB8At3lhi02lM80Aebydv\nFNcVo6yuDCzLyv7/h8KRW5VLbL99nXwluUfdE34P0d3vydxjIL+SEj57y4AxudbPoBmwlTMe6RXp\nqNFyBhBdfbvSvxUj8Xbyxku9XsI7h98BAHx+8nOsC1rXYn2jmNwsu0n61XTz7dbsfqHuoXBWOaNW\nW0szHvbC+OjxZLw9TVpXmfTydIPaAWNwVDoSW0kppVbCDIE9BB4At/I5Lnoc/pn4D97o98Yd/0+L\n64pxtvAs9mftR3JWMs4Wnr0j6PBw8MDk2MnYNGETvhv1nc0GHQAwPHQ4+d2kFKRYzT5Pq9fieikn\nsQlxC4G7g3urx3T04KQIelYvajGlMPBoKxkPIZNjJ+ODwR+Q7RWXVuDHCz/KOCMOoZva1M5TyXhk\n+Egie9qTucciuZWwULwlqRUAYn6hZbWkLoQiP+uurSPPuEmdJkGtFL8ubkDQAFKsfiDrgFXs8HV6\nHQkYQtxC7nAXag1XtSt5jmdUZFi1hovWd5jPhJgJpCnu9bLr2HR9k9WuLXy+t2QIoGAUpBF1fk2+\nqC6DpkADDxNI9E9EsCvXK+NE/glJXVLMLU7j5VYVDRWS+UrbS41HUzgqHTEtfho2TdiEVUmr8Gz3\nZ9EroBeRYwjxdPREon8i/t313/h25LfY9/A+vDPwHZtomNgaSoXSwFZ47ZW1Vrluenk6caiJ825Z\nZsUjXOFrSfZmKm3F1aolJsRMMJBdfZXylaw2yjWaGuy9tRcA9wLFS10ArkCed1vJrc61aMVN+Ltt\nSWoFwOBvW4peMRTT0eg02JC6AQD3MiSVesBB6YChIUMBAFWaKoPOzlKRU5VD7oFRXqbJrHgiPLl7\nYqWm0qq1SUKZbLxvvNWu2xZQMAq81vc1sr383HKr9X0zpS6H/24B1pfy8dDAwwQYhsF9kfcB4FZn\nd6TvkOxaZgceArlVdqU0WQ9eauWgcLDbFzqGYdAjoAee7/k8ViStwIFHDuDI1CPYPXk3dk/ejaOP\nHsXBRw5i9ZjVeKXPKxgSMkSSFTkpmRA9gdQl7UjfYZUGR0KZVWuOVjzCrJmYgQef8XB3cIeL2kW0\n89oa0+Kn4bnE58j2e4ffM+gcb012Z+4mTlajIkbdsdrLvwQCsOgl0KB5YCv3IL6fA0ALzG2F3Zm7\niTPiXaF3IcgtSLJrDQ8bTsYHsw9Kdh0eS+o7eAzkVhJb4wsRNgZuTSZLuZO+gX3RP5BzlcypzrFa\n3zdjCst5Itxp4GF38N7gAESxhWwOU5sH8ggzEFLIrXR6HTlviHtIm2ou5ObghgCXAAS4BIjiJS83\nLmoXYr9ap6vDlptbJL+mcMUs1se4B5fwOytWbZJOryPOR21RZnU7/0n8DyZETwDA9fl4ae9LKKxp\nuj5JSnZn7ibjMR3H3PF538C+ZHwi74TZ1xH+t7WW8RD2GaIF5raBlEXltzMoeBDp2Hwo55Ck1wIs\nc7TiEfbksubLIW/f66JyQZCrdMFgW0a4CLTs3DLJG/U16BpI9jjMPazZZqo8Bm0XaOBhH8T7xJPO\nomcKzkjmDc+vcjBgSLdJY5C6wDy/Jp90AbeX+o72zEOxD5ExL22QEmHGw1iplUHGo0qcjEdJXQm0\nLPc9bQ+BB8MwmD9wPrr7cZ3rC2oL8Gryq+Rv1RrU6+pxOIdzc/Fw8CBF5ULifOJIw61T+afMduLi\n66+UjJK4yTSHMPAorSs163oU8bheeh2n8k8B4P72BwYPlPR63k7eRH6SVp6GnKocSa9nSQ8PHoNm\nwFYqMC+vLycSxhjvGFpYbiZ9AvugTwfu3pddlY2taVslvd610mvkPt9SYTkPlVrZIQzDkNQtC1YS\niz49qyeBR5BrEJxVzkYfK7S3lcJS1x4Ly9szXX27kgDgcsllg5SsFPAZDze1m1EW0AAnleEbLool\nD2wP9R2346h0xOK7FxOXp9MFp7Hs3DKrXf9Y7jEisxoaOrTJJpoqhQqJAZwpQ0VDhdlmArzUytfJ\nt9Wsq1BqxffeocjHb1d/I+OHYx+2StZcaKcuddZDlIyHwFLXWlKrG2U3yJjvcE0xj2cTnyXjVZdW\nSWoQYGxhOQ+VWtkpw0KHkTFvBygmBTUF5AEuvAEZg9RSK2EWxdZ7eFC4QPnB2AfJ9qZU6Zw2imqL\niG471jvW6BUzBaMgQUpWVZYoDQ/zahq7x7aF5oHGEuASgM/u+oxIS5aeW4qU/BSrXDv5VjIZC3X1\ntyNclbtQbLrbWoOugUimWnO0Ariidh5aXC4vNZoaont3UDjggZgHrHLdISFDyPhQtnSBB8uyJPDw\ndfJtVfbSHMFuwVAxnBWrtV4OU0sbu6THeInXyLE90j+wP6mRuVJyhWT4pMCU+g6Ak5T7OvkCADIq\naeBhN/Ts0BPuas4m9FD2ITToGkQ9v7n1HQDnac97R0shtaIZD/tjTMcx5DuxPX27ZJpToUtRa40D\nb4f/Lmn1WgMbXHNpjxkPnj6BffB0d667uZ7V440Db6CyQVobWZZlse/WPgBcVmNw8OBm9xW6rgjt\nO43FwEq3lR4eAM142BL/3PyHdBAf3XG0QVAoJd38upFn9tHco5LdA4vrisnfmrmOVgCgVqjJImJm\nZaZVJJN8fQdg2GiOYjoMw2B6/HSyvebyGsmuxQceDBijAg+gsc6jvL5cFvkpDTzMQK1QkxWUGm0N\nTuadFPX8wsBDqPU0BqVCSVaPc6pyRO9mbNC13M6sdNsrno6exE2otL4UR3KOSHKdayWNgYepjihi\nF5jnV7ftHh6t8Vzic+juz9V75FbnYvGpxZJe71LJJRTUcsFe3w59W+zf0s2vMeNhjvTPoGu5S8uF\n5QCt8bAVWJY1kFlNiZtitWurFCoMCB4AAKjWVONswVlJrnOzzHJHKx7+2a/Va5FblWvRuYxB6GhF\nMx6WMyZqDFn02HNrjyQKlDptHfnORXpGGm2KI6wblrLZdHPQwMNMhoU1yq32Ze0T9dxCTac5GlG+\n10iDvkH04ndh3YixGn6K/IyNGkvGW9KkcbcSZjxMDTzEttQVZjzaY+ChVqjxyZBP4KTk7GzXXVtn\nkYtUaxgrswI4eRSfhbpcfNnk1VzerQwwLuMh7ONBMx7ycbbwLLlHxPvEI8EvwarXF8qteBMEsbFE\nrXA7QvehtIq0Fva0HJZlSeDh4+QDX2dfSa/XHnBUOmJyHNefRs/qse7qOtGvcbX0KnQsJ002NtsB\n3NZ2QcJm081BAw8zGRIyhHTh3Z+1X9TiIUsyHgCnD+XJqRbXwYN/KQxwCTC5IytFPoaFDiOrIXsy\n90jSsZR/qWDAmLxiJrYpQlvvWm4MYR5hmNVjFtl+/8j7qNfVS3Kt5KzGwEO4KNMcvNyqTldnUIxr\nDMKMhzE1Hk4qJ2LQQTMe8iFsYvpI50es7po0KHgQGUsVeIhRWM4jrO+Uus6jsLYQ5fXlAGi2Q0yE\n5gmbrm8SXeJ3qfgSGXfxoYFHm4fvag1wvzgxG5/xGQ8XlYtZ+nThl0pM68Dy+nKiX6WF5faFk8oJ\nI8NHAgBqtbWku7RYaHQa3CjnXFHCPcJNbtgnVcbDQeFgdoFnW2B6l+lkJSyjIgNLzy4V/RoFNQXk\nARjjFWNUJjTep7Er8vXS6y3s2fT1eIzJeAAglru0uFweimqLsCODa7jr7uCO0ZGjWzlCfAJdA8lC\n3uWSy+RFW0zEaB7IY81+C8K/QRp4iEcH1w5E5lxcVyy6GZFB4EEzHu0DXjMKQDTdfI2mBnnVnCNP\npGekWatCwoyHmF8qoRaQFpbbH2OiGhu6bb65WdRzp1WkEcmMOR1vQ9zF6z/DsizJeHRw7dCu/ehV\nChUWDFpAHHJ+vviz2Ra2zSF8mAod/1oixrvx5UaoLTcGg+JyIzIeQKPcqlJTKXlDL8qd/HHtD3J/\nmBgz0eSFCbHoH8R1ldazepzMF7c2E2gMPFxULhZnWoUZE6l7eQgLy4V/mxTLebBTo6vk+mvrRT33\n5eLLADiVQbxvfCt7N0IDDztmYFBj46MjueIEHsKVDXNkVoB0GQ9aWG7f9A/sT7o8H8k5IurqryX1\nHQDgrHImFn+W3ggrNZXEjrq9OVo1RZxPHKbGTwUAaPQafHbiM1HPb6rMCjBcVRW+9BgDX8QOGJ/x\nMOheTrMeVkWj1xB9OwPGqkXlt8MHHgBwPPe4qOeuaqgi2bgozyiLFzx8nXyJPFbqXh7C4J/28BCX\noaFDyX3qUM4hsrBsKfW6etJ7JcIjwujCcoBbsOH7LEndULMpaOBhAUKLvmO5x0SxvLO0sBzgmg7y\niPmlEmrvacbD/lAqlLgv8j4AgJbVYlfmLtHObYmjFQ+f9SirLyOWm+bQ3h2tmmJm4kwiN0rOShYt\n5V+nrcOx3GMAOPkp3zm9NcLcw+CgcABgutSKLy5XMIpWu5bzUEtd+diTuYcEi0NChhg46libvh36\nkh43/PdWLAxkVhZY6fIwDEPkVvk1+ZLU5fFQqZV0qBQq0q9Gz+qx8fpGUc57reQatCz3zmlKtgPg\n7p28Mia7Klt099NWr2/Vq7UxVAoV+gX1AwBUaaoMOkiai0FhuYnNA3n8XRp7eYhZXE57eNg/Qm31\ntrRtop3X0owHYJips0Ru1d4drZrC3cEdL/V6iWx/duIzUfoPncg70ditPGQolAqlUcepFCrycpZV\nlWXSSxVfXO7r5Evuc61BmwjKxy+XfyHjqZ2nyjgT7nvQ2aczAOBG+Q0D2Z6liFnfwSOs8xCzjlSI\nntWT+rwg1yC4ObhJcp32zMROE8l4U+omUV70hfUdwt5IxsI/bzV6DQprClvZW1xEDTwYhvFnGOYu\nMc/ZzHXCGIb5g2GYcoZhKhiG2cAwjCzLKGLLrYRazo4e5mU8FIyCWOrmVOWI5rhFpVb2T6J/IsmI\nncg/IdqDlw88XNWuZtssCw0LLJFbGQQe7ahreWtMiJlAMhIZFRlYdWmVxec0kFkZWd/BI5R08JKB\n1tDoNCipKwFgfH0HAIPMSEl9idHHUSzjaslVpBSkAOAWqwaHNN9Y0loI5VZiZj2kCDyEcmup5FbZ\nldlk8YBmO6QhzD0M/QO5711OdQ6O51ku87tUYl5hOY+BJF9k99PWaDXwYBhGxzDMfoZhAo04370A\nxLXLuXM+LgD2AOgM4AkAjwHoBGAvwzDGi9xEQmjRJ0aBOe/XzYAxWO0wFT6NVq+rR3GdOL08+FVo\nV7WrgXSBYj8wDEOyHnpWjx3pOyw+Z0ldCVmFjvWONVvbLFbBW15No4aW1ng0omAUeLP/m2R76bml\nBkGaqbAsSwIPJaPEoJBBrRxhiDkF5qZ2LecR9vKgGQ/rseLiCjJ+JO4RYi0qJ/0C+5GxGC+APMLm\ngdFe0aKc0xrOVrSw3Do80OkBMt50fZPF5xNmPPgsnimIpTAwB2PuAgyAIQBOMQwj/3IF8DSAKAAP\nsCy7iWXZPwGMBxAB4FlrTybMI4z8As8VnkNVQ5XZ59KzenJzCXYLtqhPhtgF5g26BlIUFeoW2q6d\nguyd0R0Fcqt0y+VWYsisAENnK9EyHlRqZUA3v26YGMOl/Wu1tfjq1Fdmn+ts4VlyT+gT2AceDh4m\nHW9OgblBYbkJGQ9a42F9cqtysTVtKwDATe2GSZ0myTwjjt4dehOXNykyHg4KB9Ga6wozHlIFHrSw\n3DqMCB8BNzUnY9uVsQsVDRVmn6teV0/qciI8IuDu4G7yOeR0tjJ2+WElAEcAexiGeVHC+RjDeABH\nWZYlfy0sy6YBOARgghwTGhjMya10rM6i7sAFNQUk5WmuoxWP2AXmOVU5YMFJtmh9h30T7xOPcHdO\nmXi64LTFLhtXS66SsUWBh/BGWGn+jVBYXE4zHnfyYq8XyQPw75t/40zBGbPOsz19OxnzpgWmIHzJ\nSS01LvAQdi0PcDb+dyt0taJNBK3DqsurSPHrw3EP20ztgIvaBQn+XNf07KpsUVZ767R15DwRnhFG\n1zq1hrAQXyqplfBvr5M3DTykwlnljKSOSQC4wMGSGssrJVfI35Y5MitAOvdTYzA28NgBoDeACwAW\nMwzzC8MwztJNq0W6/m8et3MRgMm/AYZhTvH/mDshYZ2HJR1RhalacwvLecTu5UELy9sODMMYZD2E\nL5DmIEz5xvnEmX2eQNdAIsWwpHs5n/FQMApiH0xpxM/ZD88lPke2Pz7+scnFjnpWTxrCKRklaU5p\nCoGugcQCUnjvawlzMx60uNy6lNeX449rfwAA1Ao1psVPk3lGhogtt8qoyCALc9Ge4sisAM4UgrcZ\nlzrjoWAUFndbp7QM724FWCa3Ei4W8Y2sTUUshYE5GC24ZFk2A8AgAD8BeATAMYZh5BAE+gBoasmq\nBIAshQf9g/qTF6ajuUfNPo8w5WmpRlQYzeZW51p0LoAWlrc1kiKTyJiXQ5gLH3ioGBXivM0PPNQK\nNQJduFIyS0wR+OaBfk5+RrsetTce7fwoecm4VHzJ5Ifg2cKzJMDrH9TfIKNgLAzDkJe0gtoCo6QH\nQvcVU7JZPo60uNya/H71d5K9Hxc9zuYyj8ICc0ue2TxSFJbz8HUe5fXlogfNGp2GGNqEu4fDUeko\n6vkphiT4JZB73vmi8yZbifOcLTxLxj0Ceph1Dm9HbziruPyBzQYeAMCybD3LsjPA1VnEADjJMIwc\n8qam3kjMKjpgWbY3/4+5k/F09CR2ZukV6WanrYQ6Z0u1lmJnPIQr0DTwsH9ivGOIxv5i8UWzu1lX\nNlQSCUCMd4xFdUlA4ypMjbYGZfWmP2TrdfXkOOpo1TxqpRpz+84l21+nfG2S5vjP63+S8b0R95o9\nD+ECizFZD2H9jinZLHcHd7I4RDMe0lKtqcbKSyvJ9hNdn5BxNk2T6J8IJyV3rzqee9xi50ehK1tH\nL3GzBkL1g9hyq/SKdCLZoTIr6WEYxuKsB8uyJOPhrHI2W97MMAxZoM6rzhOlD52xmGUxwbLsDwAG\ng8sybGAY5kPGetXGpeCyHrfjjaYzIVZhQNAAMjbX3UrMJj7+zoJeHiLo9wykVm5UatUWEPb0MFdu\ndbn4Mhmb4yV+O7wNNGBewFxQ3fhiamurrLbG4JDBGB42HADnTPbd2e+MOq6qoQpb0rYAAJyUTrg3\nUpzAwxhnK6GrlSm/X6VCCU8HTwDWKS4/U3AG3539DisurpCs/4KtsvrSahL8j4oYJXoGQAwclA7o\nGdATAFBcV2y0nXNzCDMeYkqtAGmdrYR/c9RK1zrcH30/lAxXA/T3zb+h0WtMOj63Ope4SHb17Uo6\nkJsDH3joWB1RClgDs73tWJY9DaAXgG0A3gSwHYA1BNUXwdV53E4XAJea+LlVMLDVNaOfh9hNfJQK\nJSkwF6OXB184p2SUCHQzxlmZYusI6zy2ppsnt7pYfJGMu/pZHngIdafm1HkIrXSpo1XrvN7ndfLg\nWnt5rYFRQHNsSdtCZDSjO442y1GFRxh4GPPyx9d4KBmlyZbefJ1HWV2ZaL2Nbker12L+ofl4bOtj\nWHJmCRadXIRxG8dh2bllkl3TlqhoqMCKS5yFLgMG/0n8j8wzah6++S8AHMuzzN2Kz9YpGIVFNvhN\nIWXgQQvLrY+fsx+Ghg4FwC34HMg6YNLxwvoOc2VWPEJljDULzC0y1WZZtoxl2bEA3gNwD4DPxZhU\nK/wFYADDMGQZhWGYSHAZmL+scP0mSfRPJHq5o7lHodPrTDpeiiY+/Opxna6ONN0yB5ZlSeAR5Bpk\nUYRNsR0iPCKII0ZqaapZelODwEOEjIdBE0EznK2EqzZUatU6YR5hRAqjZbWYd2heiytwWr3WoDfD\n5NjJFl1fuDpsTODB13j4Ovua7BzEByoN+gZyrxWbz058dod8Qsfq8H+n/w9LziyR5Jq2xMqLK1HZ\nUAkASOqYZNN9IfiGboBltrr1unoigYrwiICD0sHSqRkgbCQsttTKoIcHzXhYDd7SHDBdbnWmUBB4\n+FsWeMhlqStKNx+WZRcAGAPAfGNi41kOIB3AnwzDTGAYZjyAPwHcArDUCtdvErVSjb6BfQFwRWBX\nSq6YdPy1ssZeCGKtPAijWUsKzItqi1CnqwNA6zvaGsIic3N6elws4gIPtUItige8pTdCoTUwX6hO\naZlnuz9L7LuvlFzBt2e+bXbfLWlbkFnJ1QP1DOiJBL8Ei64tdLbiM77N0aBrIBIeU5oH8ggL4C1Z\niGmO47nHsfbKWgCc0cLsXrMxPX46+XzpuaUWWWjaOnnVeSQoVTAKzEycKfOMWibeNx7uai5bdzLv\npMmLhTw3ym5Ax3LHWmKu0Ryh7qGkPkl0qdX/FpscFA7UrdKKDA0dCh8nrmJgf9Z+AwlpawhbNnT3\n727RPOSy1DUm8OgIoNWQjGXZHQC6gct8SAbLstX/u8Y1AKsArAGQBuAelmXN794nApbIrcSs7+AR\nq8BcKHmhN6e2hbD/wvb07SbJQUrqSsh3I9Y7Fmql5ZkwSwMPYQ8PmvEwDieVEz4c8iF5uVl+fjl2\nZ+y+Y78aTQ2WnG5ctZ+ZONPiRqIGzlY1LTtb8bpmwDQrXR6D7uVmGBe0BMuy+PxkY8L/5d4vY0bC\nDMztNxeze80mP//g6AcmvWTYE4tPLSYLVA91eshiS3ipUSlU6B3IecpUaioNsremIJQnWmIn3hwO\nSgeiXsisyDTZ+ro5ajQ15P4d5RVFHQCtiFqhxriocQC4jOjmm5uNOq6wppDU5XT26WyWm6AQsU2I\njKXVwINl2QyWZWuMORnLsnksyyZbPq1Wr5PJsuyDLMt6sCzrzrLsAyzLpkt93dYQ9vMwtcDcwNFK\npIyHWNEstdJtuwS5BZF0bXpFukmZutP5p8nYUq0pj7+LPxwUnFTBrMBDKLWiNR5G092/u4Ee/82D\nb+J0QePvl2VZfHriU+RUc/eRPh36GBhqWEKUV2PxcUvOVsJ7mLBBqrFI2UTwSM4R8rcT4xVj0Lfi\nqW5PYUT4CABcDcQnxz8R9dq2wJmCM8RwwF3tjlk9Z8k8I+MwWCw00xTmWmmjWsGSBqotEeHJ1XnU\n6eoMnN0sQShtpDIr6yN0t9qYutGoRT+h9bPwfdNc7FpqReHo6Nmxt36LAAAgAElEQVSRvOykFKSg\nRmNUvAagschLyShFa+IjVjRLmwe2bcwtMj9V0Nhzs1dAL1HmomAU5HubU5Vj8uqeUGpFAw/TeLr7\n0xgVMQoAUKutxdM7nsaay2uQWpqKhUcXYkPqBgDcat38AfMtznbwCF96WqrzEMpFzQk8pMx4/Hr1\nVzKekTDDoP6EYRjMGzCPFOFvT99u4MNv72j0Giw8upBsP5f4HJGR2DrCwMPc5r9XSwUZDwmkVgCI\nFBIQr86DOlrJS4x3DLr5dgPAyUwvFDXVF9sQYXA8INjyhR8PBw8idbU1qRXFSBiGwcBgLgrV6rU4\nlW9cM/QaTQ3SytMAcMGLWE18hNaklnyp+MJygAYebZF7I+4F8782ONvTjJdbpeSnkHGvDuIEHkDj\nKoxGrzF5dY/PePg6+Yoi/WpPKBgFFg5eiD4d+gDgimY/Of4JJv01Cb9f+53sN3/AfIMshaUI7VZb\nstQ1yHi4mR54CF+Gxcx4lNeX40A250zj7ejdpL2wn7MfZvVozAJ8efLLNuNy9eP5H8nLd0fPjpja\nearMMzKecPdw8pw8V3gO1Zpqk45nWZZkPDwdPSWz8DZwtioXp85DCpUFxTQmdmosMt9wfUOL++r0\nOhzKOQSAq8kRY7GPYRiy0Jdfk2+yta+50MBDZAzkVkbWeVwqvgT2fz0RxXAG4vF38YeK4XSblhSX\nG0it3KjUqq3h7+JPjBFyqnNwruhcq8dUa6pxuYTr4RHpEWlSM7fWMDf926BrIEXDtL7DPFzULvhu\n1HeYEH1nX1gVo8K8/vMMHpZiIFxtFfZDuB3hPUy4qGIswoyHmL08dmTsIM237ou8r1nXv8mxk8l3\nO6UgBfuz9os2B7m4XnodS89xni4MGCwYtMCuAn6DxUJWa1C4awz5Nfkory8HwGU7pGpnJgw8RMt4\nCOpKxTAGoZjO6I6jyULzPzf+adH0IqUghXw+IHiAxc16efh7kp7VG9RISgkNPERGmP4yVjMqLGrr\n5tdNtLmoFCryApZdlW32ChsfeHg7elvcX4RimwjlVsY475zKP0VkUGJmOwDDXh6mZOqE9R3U0cp8\nHJWOWDhkIVaPWY1p8dMwMnwknur2FP584E9M6TxF9OsFugbCReUCwPiMh1BGaixS1XhsTWuUJ46N\nGtvsfg5KB7zY80WyvfTcUrvOetTr6vHmwTfJKum0+Gmi1XpZE0vkVtao7wCklVq5ql0R6Ervl3Lg\n4eBBFnnqdHXEFa8phE1+hc1/LUWOOg8aeIiMj5MP4n3iAXB/2MZIRXhLUkDcjAfQ+KWq1daapWuu\n0dSQKJsWlrddRoaPJNmx7enbW7WWFK7WilHkJkR4IzSliSB1tBKXRP9EvNHvDSy+ezFe6v0Swj3C\nJbkOwzCkkWBBTQHpA3E7fP2OWqE2q4ZAihqPqoYqYrIQ6BqIRP/EFvcf3XE0qeE7X3Te4sZ1cvLZ\n8c9IQX2Yexhe6PmCzDMyj/5B/Ymjm6kF5peKG3sWS+FoxRPoGkhMN8Sw1C2rKyMucTFeMZJlaiit\n86+u/yLfv7VX1jZZG6zVa7EzYycA7v43PGy4aNcXS5JvCjTwkAA+dQsAyVmtm3xdKOaKilQKleg3\nL0s7U1JHq/aBt5M3+gdzDbUKawuRUpDS7L4sy5Juq0pGiUEhg5rd1xwMVmBMaCJIu5bbL611MGdZ\nlkitglyDyIPaFKTIeBzLOwYty8mshoQMafUFTsEoMCNhBtlefm65KPOwNptvbiZ1P2qFGouGLYKL\n2kXmWZmHp6MnWfBLr0g36Tl5vug8GVva06YlFIyCBP7ZVdnQ6CzT4tPGgbZDmEcYMfUory/Hqkur\n7thnd+ZusgA8OHgwMaoQA5rxaCPcHXY3Ge/J3NPivqV1peTlvpNXJ9G7nlrqbEV7eLQfhM0Ef73y\na7P73Si7QWxVewb0hIeDh6jzMPdGKMx4UOmAfSHsYN5UnUdxXTHqdfUAzCssBwAXlQtZNRarxuNw\ndqM0Z3DwYKOOSeqYRL7jx/OO40zBmVaOsC1S8lMw/9B8sv1639fRxbeLjDOyHOFiobFyK5Zlcb6Q\nCzzc1G6iuVE2By+30rN63Kq61fLOrcC7aAK0sNwWeDrhaWLw8sOFHwyeZSzLYuWllWT74biHRb22\npYvT5kADDwno7t8dvk6+AIBjucdQ1dB8X0NhMZvYWnnAMI1mToG50NGKFpa3be6NvJfIUXZl7jL4\n3QvZlbmLjO8KvUv0eXg5ehHNv0mBB+3hYbcIMx5N1XnkVllWWA5wki4vJ+77XVYnjtSKd5lRMkr0\nD+pv1DFqhRr/7vpvsv39+e9FmYs1SCtPw4t7XyR1HfdH3Y8pceLX/VibISFDyDj5lnGtyLIqs0gA\n282vm1lZOFMQ09nKwNGKFpbLTpxPHCZ1mgSAk8W/f+R9UkO5I2MHzhVyhi+RHpEYHGLcAoexyNFE\nkAYeEqBgFLg7nMt6aPQaHMw+2Oy+x/OOkzHvLCQmln6paA+P9oOzypm8ROhZPdZcXnPHPizL4p+b\n/5DtkeEjRZ8HwzCkwNwUiz+DHh60xsOuaE1qJbx3mdPDg8fbkZNblTeUt1rH1Bp51XlkXgl+CSbJ\nHx7o9AD8nbnu68lZyQbdr22V9PJ0zNg+g7g49Q3si/cHvd8m6gO6+3Un340juUeM6sEldP+TUmbF\nYxB4WFjnQTMetscLPV+Ap6MnAOBA9gG8f+R97M3ciwVHFhjsI3aA6+noCXc1d++igYedw3eqBTh9\nXnPwGQ8GDPHPFxNLu5cbZDxojUeb55HOjxA70PWp61FYU2jw+an8U+Sh1zOgJ8I8pAlGhRZ/eVV5\nrezNQTMe9kuQaxDJcjUVeAidfIQvYKbCZzz0rL7ZInZjEXZ2NzVb7ah0xBNdnyDby8/bdq3HzbKb\neHL7kyio5cxSoj2jsXj4YtGlwXKhVChJ9rZeV2/QIbo5+FVoAK2aCohBpGckGVvibKVn9STw8Hf2\nN6h9osiHr7MvFg5eSCRXG1I34MW9L6KioQIAl5Xja0HEhl+gLqgpsLh+yBho4CER/QL7wU3NWc/u\nu7WvSblVUW0R0TN39ulMol0xCXAJgJLhuuhakvFwUDhI1hyJYjv4OfthQgxn71errcXXKV8bfP7T\nxZ/IeGKMuP0chAhlfcY6W/EZDx8nnzbzQtReYBiGNBLMr8m/IygQvmgJX8BMxcdR0ETQwjoPYeDR\nM6CnycdPjp1M7vk70neQJrK2xtHco5i+ZTpxQYr2jMb3930vyfNKTniVAgDsvbW31f2FaoXu/t0l\nmZMQYcBtyXclpyoHNVouoyOlBTDFdIaHDcf7g94nDpM8XXy74JOhn0iWXeQDDxasgXJAKmjgIREO\nSgfcF3kfAM6feUfGjjv2EVqSGqsPNhWVQkUKbXOqckzyjdfpdSRLEuoeKrmGlWIbzOoxC65qVwDA\nnzf+xKFsTsd+OPsw+c4GOAe02LPAUkwtMDdoHkizHXaJUG51e4G5UNMu7GlgKnzGA7Dc2UpYFG7O\nireL2gXT46cD4B74tlbrwbIs1l1bh5k7Z6JSwwWCnbw74Yf7fhC1YaitMDBoIGnmlnwrmTSFbIqi\n2iJSixTvE2+VrIGPkw+Rg90ov2F2Dxgqs7JtJnaaiHXj1mFa/DTcG3Ev5vadi5VJKyUN9A2et9XS\ny63om6SE8CvHALAxdeMdn/O+zIChE5bY8JroGm0NSdsZQ15NHrGKpDKr9oOfsx+e6/4c2X5l3ytY\nfGox5h6YS372bOKzkmYVTA08DGRWtL7DLhG+BF0pvkLGLMuSjEeAc4BFtq38ixtgWcajRlNDmsdF\nekSa/eI5tfNUEuRvvrnZahrr1qhsqMTc/XOx4MgC8gwYFDwIK0avgK+zr8yzkwYXtQtxtyqtL8Xx\n3OPN7iuUYg0IGtDsfmIT481Z35bXl6O4rtiscwibHtLAwzaJ8Y7BG/3ewBfDv8D0LtNJQCwV1na2\nooGHhPTw70FW584UnjHQhBbXFpObl6+Tr6QaUXMLzDMrMsmYFpa3Lx7r8hixB63R1uDHCz+Spmu9\nAnrhodiHJL2+sHu5Md9Zg67WZroeUeRF2DxVWLhbVFuEKg0nVbVEZgUYZjwscba6WHwROpYrTrek\nW7enoyceiXsEAKBjdfjpwk+tHCE9ZwrO4OG/H8bW9MaO7FPipmDJiCWi9g+wRcZ0HEPGQhON2zma\n0xh4SKVWaAqh7bQwc2EKQkcrKrWiAIbviM25WQJcI8N3D79r8fVo4CEhDMPg0fhHyfayc8vIeEPq\nBpLKTeqYBKVCKdk8zC0wFwYe4e7SdC2m2CZKhRJfDv8Sw0OHG/y8u193fHPPN5LL7oQ1HsYEHsJ9\nhN93iv3Q1a8r0TafLTxLfs53xwYsX6EVK+NxufgyGXfz7WbRnB7r8hiclE4AuMz47YYO1qKioQIL\njy7E41sfJ3VVLioXfDTkI8wbMA8qhaqVM9g/w8OGE5ODXZm7mnS30ul1xKlSrVCbVd9jLsLvf1Mm\nDMbAZzyUjJLUVVHaN8LnLd+jqyl2Ze7ChtQNFl+PBh4SM6nTJAPbxCM5R+7oTim1D7rZGY/KxsDD\nEicZin3ionbBN/d8g59H/4w3+r2BJSOWYNWYVVYpKnVRu5CXRGO6lxsEHu408LBHnFXOiPXhVmAz\nKjJIDcal4ktkn3ifeIuuIVb38ssljYFHvK9lc/J19sWDsQ8CABr0DVh6bqlF5zMVlmWxPX07Jmya\ngN+u/gYWXO1AvE88fh/3O8ZFj7PqfOTEWeWMkRGcRXitthZb0rbcsc/pgtNE5jQgaIBVO7a31u+m\nNep19WRBMdIjkppwUAAYNmVtaXE6rUwcAwwaeEiMo9IRMxJmkO3X97+Op7Y/RVbbRoaPtFg+0Bo0\n40ExF4Zh0LtDb0yLn4a7Qu+yqsEA/70tritGrba2xX1pxqNtIJScni/iukKL+ZLPN8gEQKSD5sBn\nPJSMUhS5yr+7/ptkPf649gdult3ZvV0Kcqpy8Pye5zEneQ6KaosAcM+s2b1mY83YNe1ywWly7GQy\nXn1p9R1F3FvTGiVo90bea7V5AUCMVwwZmxN43Cy7SSSCtL6DwuPh4EFklC0t9IlVg0YDDyswJW4K\nenfoDYB72F0t5ZpFOaucMafvHMmvb1A41EIa7Xb4jIeKURlExBSKNTCl4E14s6SBh/0itCU9mX8S\nLMuSAMRR6WixNESMjEeNpgZpFdzKX0fPjnBSOVk0J4AzRHi86+MAuFqPxacWW3zOltDqtVhxcQUe\n+PMBA3fFgUEDsXH8RsxImEH6+bQ3Ev0TSUPAG+U3DBoAVzVUkdoPR6WjpKYwTeHp6EkUFDfKTHe2\nEhaW0/oOihC+jregtqDZBpqmvD+2BA08rIBSocRXw79Cr4DGJlOualf8957/WuUlKcAlgKxUG5vx\n0Ol1pIdHiHtIu9D3UmwLUwrM+e+1cOWGYn/0C+xHxsm3knGj7AYKarimdQl+CRbfh8TIeFwrvQY9\nqwfA+euLxZPdnoSPE9dnZF/WPhzOOSzauYVcLL6IRzc/ikUnF5FMoo+TDz4e+jGWjloqWVNQe4Fh\nGGJzDACLUxaTesxfr/5KemCM6ThGll4mvNyqSlNl4OZnDELZYpxPnKjzotg3QptyocxeiDGyZ2Og\ngYeV8HLywk+jf8LPo3/G53d9js0TN6NfUL/WDxQBteL/t3fnYVLVd77H399esGmgG2ig2elmU0FB\nQNxRFgPEx+CSmLmaqGNGTTSLGbPMcGOuiYmO9yYxoybRjBjjqBNjJAsxMRG3xLjgggHEyCKbyNJs\nDTQNTS+/+8c5dThdXdVrVZ+urs/reeqpU+f8qvrX3+fU8j2/LT9Y26C1a3nsqN5BbYO3gqW6WUkU\nGi0i2MxMGzX1NcGKymrtyGyDCgcFV5s37N/AI/84NhZuxvAZHX79Hrk9gulr29vi0ajrVwfHnIT1\nyu/F50/5fPD4tldvS3rlsT2qjlZx5+t3csUfrmj0P1w67lKWXLyEC0dfmLYFyjLNvLJ5QYvAun3r\nuGf5PWyo3MADK70V5g3jUyd+KpK6hbtbhVswWiOceKQyaZbMF048wgu2xtQ11LU50U1GiUcnyrEc\nppVOY375/E6fCz3WbaWqtqpVa3k0Gt9RpMRDOl9r1/LYXrU94XMkM80eOTvYDs+gcs6wc1Ly+rFJ\nC9o7q1V4RqsT+p+QkjrFfHzcx4NxLh9Wfchdb93V4dd0zvH0xqdZ8NsFPPaPx4LWmrKiMh6a9xDf\nPuvb3W4V8o7KzcnlG6d/I+gp8NDqh7jodxcFrR0Xj704shaDcBep8IxvLalvqA+6eQ8qHNQtF4GU\n9guP5wov2Bqzs3pnMD6oo5R4ZIm2DjDXwHKJWmsTDw0s714uHXdpMKVpzPh+4xnXNzWDYWPjPA7V\nHuJo/dE2Pz/8Yy/ViUduTi63nX0bPXK82YZ+ueaX/GHDH9r9epv2b+L6pdfz9b9+nV2HvWl6e+T0\n4MbJN7J4wWJOHXxqSurdHU0tncrN025usn9s37GdMjYzmXBLRbgFoyUb928MutaptUPijSo+lngk\navFIVTcrUOKRNdo6wDzcx08tHhKFob2HYnhdP5pLPDYfOHZ1Znif4UnLSWboX9C/0UyAhnHztJtT\n1g0oPM6jrd2t6hvq2bDfm3FqWO9h9O7ROyV1ChtdPJovT/ty8PjWV25ttK5Ja1QdreKe5fdw6ZJL\nG62yffbQs/nNRb/hhlNu0FSqrXD1xKv53rnf48T+J9LvuH5cMvYSFs1dRFGPosjqNKbvmGAl67Yk\nHu/uVTcrSS7c1Sr8nRqTqhmtADRiOEuEV3Nua4vHqD7ZN6WiRK9Hbg8GFg6korqCrQe34pxL+OMz\nfHUm3VNTS+e49uRrGdBzAKv3rGbOyDmcOfTMlL12o5mtavZR2qu01c/9sOpDauprgMZ97VPt0yd+\nmnf3vMtTG56ipr6Gzy79LPfOvpfpg6c3+7za+lqeXPck96+4n71H9gb7B/UcxNdP+zpzR83VOI42\nml8+n/nl86OuRiAvJ4/j+x3Pyt0r2X5oO/uO7Gt0TiezevfqYHtiycR0VlEyUK/8XgzsOZBdh3ex\n6cCmJt+3qUw81OKRJcJdUMJJRTKx6SLzcjSVrkSnvLgc8MYmxWY3irdx/7FFjcqLyjulXpJeZsYl\n4y7hljNuSWnSATQaXxdbu6K11lWuC7bDi7mlmplx65m3BjMhHqo9xLXPXMvdy+/m4NGDTcpXVFew\naNUi5i+ezx3L7giSjlzL5coJV7LkkiXMK5unpKObCK9nEx5z1BwNLJeWxMZ5HDx6MFgkMyZRK0h7\nqcUjS4SvBMeSimRq6muCqXTLiso0la5EZmzfsSzbvgzw5q1PdHU61uJRmFfIoMJBnVk9yUADCo4N\nqt1zeE8zJZt6v/L9YDudLR4ABXkF3Hf+fXzphS+xbPsyGlwDi1Yt4tF3H2Xa4GkM6zWMw3WHWVe5\nLuEg4zkj53DT1JuC5F26j3CLxbt73+WsYWc1W76uoU4Dy6VFY/qO4c2dbwKwdu9aBgw7dp7EupjG\nuj93hH5RZomBPQfSO783VbVVLS57v2n/pmDmk3Re1RNpSfj8W1e5rskXbHVtNTsO7QC8qzW6oist\nCbd4xF/Va0l4teh0Jx4AhfmF3H/+/fz47z/moXceot7Vc6T+CC9/+HLS58wYNoPrJl3HlEFT0l4/\niUZbB5iv2bsmGFg+acCkFkpLtgpPD/7evveC79v6hno27d8EeOMoV7GqQ39HiUeWMDNGF49m5e6V\nVByu4ODRg0kXWotltqDEQ6IV/nEXvtocE27+1fgOaY1GiUcbWzxiiUeO5XRaS0JeTh43Tb2JBWMW\n8PDqh1m6eWmTKdHLi8uZPWI2C8Yu6PDq7tL1je47mh45PTjacLTR2I1kllcsD7aVkEoy4Vn63ttz\nrBV1W9U2jjZ4MwCm4vNFiUcWKSsuY+XulYDXL37SwMRXPsI/8MYUK/GQ6IQT30SJR3hgubqUSGuU\nFLRvjEdtQ21w1W9EnxEU5BWkumrNKi8u51tnfYtvnvFNth3axt4je+mR04ORRSODRRElO+Tn5DOh\nZAJ/3/V3th3axo5DOxjca3DS8m9XvB1sTy2d2hlVlAw0tt9Yci2XelffaJHR9/cf++5NReKhweVZ\nJHzChFs14qnFQ7qKoh5FwbiN9ZXrcc41Oq6B5dJW7e1q9cGBD6htqAWivSCTm5PLiD4jmDxwMieW\nnKikI0tNK50WbL+1862k5ZxzLN/ptXj0zOsZ2cKH0vUdl3sco/t6vxM3H9hMda23YGa4O9/Yfh3v\nYqrEI4u0NvGIXVnOszwtHiiRi3W3qq6rbjKlX3hQbWf0uZfM1/e4vuRaLtC2rlaNxnek4MtXpCNa\nm3hsPrA5SLAnDZhEfk5+2usmmeuEfl53K4dj7b61AKzafWxMx8kDTu7w31DikUVimSzAhsrEicfh\nusNBv/lRRaPIz9WHlEQrPOBt9Z7G/ZljzcEFuQUa4yGtkmM59C/oD9BorYuWdOaMViItOWXQKeSY\n9xOuucTj5W3HJiKYNnha0nIiABMHHJsx7c2db+Kc453d7wDQJ79PMOVuRyjxyCLDew+nZ15PgEb9\n98LW7F1DvasHGs8VLhKV8BWW2AcgeKtOx2a0Gt9/vKZ9llaLdbfad2QfdQ11rXpOZ63hIdIafXr0\n4fh+XrepDfs3sKt6V8Jy4RnQZgyb0Sl1k8x1xpAzgu3Xtr3GxgMbqaypBGDCgAlBstsRSjyySG5O\nbvBBVVFdkXBgpRYZkq7mpAEnBdsrd60MtsMLZ4VbRURaEhtg7nDsO7KvVc8Jd0HVeCLpCsKLa764\n9cUmx2vqa3hjxxsA9C/or+90adHo4tEM6umNq1xesZyn3n8qOHb64NNT8jeUeGSZlub/VuIhXU1p\nr9Lgg3D1ntXU1NcABAsdQePkRKQlbR1gfrT+KFsObAFgZNFIdUGVLmHWiFnB9gtbXmhy/I0db3Ck\n/ggAZw09KyVXq6V7MzNmDPdaxmobanlg1QPBsTmj5qTkb+gszDItJh57vX2G6SqydBnTh0wHvCt4\nsakhY1fyAKYPnh5JvSQztXUtj00HNlHnvC5ZGt8hXcWkgZOC1rvXtr/GodpDjY7/aeOfgu1zh5/b\nqXWTzHXZ8Zc12Te6eHTK1ghS4pFlmks8jtQdCQadlxeXU5hf2Kl1E0nmrKHHVix/5cNXqDpaFYz3\nGNZ7GMN6D4uqapKBBhQMCLYrqitaLK+B5dIV5VgOM0fMBLyr089teS44dqTuCM9ueRbwptE9b/h5\nUVRRMtDEkomcNvi0RvuuPfnalL2+Eo8sU15cTkGut/DV6t2rG62LsHLXymBg+cSSiQmfLxKFM4cc\n68v8501/5pnNzwRXoMOD4URao7RXabDdmsRj3T4NLJeu6YLyC4LtJ9Y8EWwveX9J0AIye+RsXUiU\nNrlzxp3MGDaDEX1G8MUpX+TC0Rem7LWVeGSZvJy8oD98xeEKthzcEhx7fcfrwba6rkhXMrBwIKcP\n8Qa2bTu0jVtfuTU4lsoPRMkOpYXHEo+d1TtbLK8WD+mqpg+eTllRGQArdq3g1W2vUlNfw0PvPBSU\nufyEyyOqnWSqgYUD+cn5P+GPl/6R6yddj5ml7LWVeGSh04Yca0Jbtn1ZsB3uM3/q4FM7tU4iLbls\nfNN+pyP6jGBq6dQIaiOZbHCvwcF2axKP2OKB+Tn5jCzSoqrSdZgZnznpM8Hjb7/6bRa+tJCtVVsB\nmDpoKpMHTo6qeiJNKPHIQuGuKa9sewXw5rNfsWsFAEN7DWV47+GR1E0kmTkj53BSSePZq7489cua\nqUXarKRnSXDe7DzUfOJxuO4wHxz8APAGWGq9GOlqFoxZEEwG82HVhyzdvBSAXMtl4ekLo6yaSBP6\nxs5CJw04iaIeRQC8tPUlDh49yPNbng/Gd8weOTulzWoiqZCXk8eP5vyIBWMWcGrpqdx+zu3MLZsb\ndbUkA+Xn5AcDzFtq8diwfwMObyzc2H7qZiVdT25OLj+c9cNg2nHwBp5/84xvckL/EyKsmUhTunST\nhfJz8plbNpcn1z7J0YajPL3xaX63/nfB8Xll8yKsnUhyJT1LuP2c26OuhnQDpb1KqThcQWVNJUfq\njlCQV5Cw3Pp964Ntje+QrmpY72E88bEnWLxuMZU1lcwrm6cuVtIlKfHIUgvGLODJtU8C8J3XvhPs\nLy8uZ9LASVFVS0SkU5QWlrKKVYA3s1WysRux8R0A4/qO65S6ibRHSc8Srp90fdTVEGmWulplqSmD\npnD20LOb7P/cpM+pz7yIdHuDCo91S2muu9W6ymNT6aqrlYhIx+gXZhZbePpC+hf0Dx6fP/J85pfP\nj7BGIiKdI7yWx45DO5KWi3W1KswrZEivIWmvl4hId6auVllsVNEoFi9YzPNbnqekoISZI2aqtUNE\nskJr1vI4cPRAcGxs37H6fBQR6SAlHlluQM8BfPL4T0ZdDRGRThVuvdhWtS1hmUYLB6qblYhIh+ny\njYiIZJ3hfY6tVRRbpyPeun2h8R2a0UpEpMOUeIiISNYZ2HMgBbneFLrJEo+1+9YG20o8REQ6TomH\niIhkHTMLWj12HNpBbUNtkzLv7nk32I6tDC0iIu2nxENERLJSLPGod/Vsr9re6FhtQy1r9q4BYGiv\nofQt6Nvp9RMR6W6UeIiISFYa0WdEsL3l4JZGxzZUbuBow1EAJpRM6NR6iYh0V0o8REQkK5UVlQXb\nGyo3NDoW7malxENEJDWUeIiISFYa129csL2+cn2jY0o8RERST4mHiIhkpTF9xwTb8YnHqt2rgu0T\nSzSwXEQkFTIq8TCz8WZ2t5mtNLMqM9tuZkvMbHLUdRMRkcxS1KMoWMF8feV6GlwDAIdqD/He3vcA\nrztW/4L+kdVRRKQ7yajEA5gLzAIeBj4G3AgMBJaZ2bQoK7Q974MAAA+QSURBVCYiIpkntiL54brD\nbD6wGYAVFSuod/UATC2dGlndRES6m0xLPB4HJjvnfuCce8E59xtgPnAYuCnaqomISKaZPOBYg/nb\nFW8D8MbON4J900p1TUtEJFUyKvFwzu12zrm4ffuBtcCwaGolIiKZKtyisXzncgBe/ODFYN9pg0/r\n7CqJiHRbGZV4JGJm/YGTgH+08/lvxW6prZmIiHR1Jw84mTzLA+D1Ha+z5cCWYKD5hJIJDO41OMrq\niYh0KxmfeAD3Agb8Z9QVERGRzFKYX8iU0ikAbD+0nYUvLQyOzRoxK6pqiYh0S5EmHmZ2vpm5Vtxe\nTPL8hcAVwBecc+sTlWmJc25a7NaBf0VERDLURWMuCrZX7l4JQJ7lcfHYi6OqkohIt5QX8d9/BWjN\nBOnV8TvM7HPAHcAtzrmfpbpiIiKSHT4y6iN8/83vU1lTGey7YPQF6mYlIpJikSYezrlq4L22Ps/M\nrgR+AvzAOXd7yismIiJZozC/kO+e/V2+8pevUFNfw7h+4/jqqV+NuloiIt1O1C0ebWZmlwAPAYuc\nc/pmEBGRDjtvxHk8d9lzbD24lfH9x5Ofkx91lUREup2MSjzM7FzgF8BK4OdmdkbocI1z7u1oaiYi\nIpmu+Lhiio8rjroaIiLdVkYlHsBs4DhgCvBy3LHNQFlnV0hERERERFqWUdPpOue+5ZyzJLeyqOsn\nIiIiIiKJZVTiISIiIiIimUmJh4iIiIiIpF2mjfFIGzN7C6gzsxVR1yVDxdZj+UektchMil37KXYd\no/i1n2LXMYpf+yl27afYdcyJwOSOvIASj8ZWOudOjboSmchP3FD82k6xaz/FrmMUv/ZT7DpG8Ws/\nxa79FLuOicWvI9TVSkRERERE0k6Jh4iIiIiIpJ0556Kug4iIiIiIdHNq8RARERERkbRT4iEiIiIi\nImmnxENERERERNJOiYeIiIiIiKSdEg8REREREUk7JR4iIiIiIpJ2SjxERERERCTtlHiIiIiIiEja\nKfEQEREREZG0U+IhIiIiIiJpp8RDRERERETSLusTDzMbYWZPmtl+MztgZr82s5FR16urMbPhZnav\nmb1qZtVm5sysLEG5AjP7npltN7PDfvlzO7/GXYeZfcLMFpvZZj8ma8zsP8ysT1y5fma2yMx2m9kh\nM3vWzE6Oqt5dhZnNM7PnzWyHmdWY2VYze8LMJsSV03u5BWb2J/+9+924/Tr34pjZTD9W8bfKuHKK\nXTPM7AIz+6uZVfnvyzfNbHbouOIXx8xeTHLuOTP7U6icYpeAmZ1tZs+YWYV/zi03s8/EldFvlSTM\nbJaZ/c2Py14ze8TMShOUa9f5l9WJh5kVAs8DJwBXA1cC44AXzKxXlHXrgsYCnwT2AS81U+5B4Drg\n/wAXAtuBP5vZKWmvYdf1VaAe+N/AfOA+4AZgqZnlAJiZAUv8418EPg7k452Lw6OodBfSH3gL+AIw\nF1gITAReM7NRoPdya5jZ5cDkBPt17jXvS8CZodv5sQOKXfPM7LPA7/Dev5cAlwG/Agr944pfYjfS\n+Jw7E7jZP7YEFLtkzGwS8CxeLK7Di8sbwINmdkOoqH6rJGBmM4BngEq82N0EnAs8Z2bHhcq1//xz\nzmXtzQ9oPTA2tK8cqANujrp+XekG5IS2rwUcUBZXZrK//5rQvjxgDbAk6v8hwtgNTLDvKj9Ws/3H\nF/mPZ4XKFAN7gXui/h+62g043o/XV/zHei83H6++wA7gcj9u3w0d07mXOGYz/bic30wZxS55bMqA\nw8CXFb+UxPNBoAbor9g1G6c7gKNA77j9rwGv+tv6rZI8fs8C64G80L7pfrxuDO1r9/mX1S0ewALg\nNefc+tgO59xG4GW8oIrPOdfQimILgFrgl6Hn1QGPA/PC2XI2cc7tSrD7Df9+mH+/ANjmnHsh9Lz9\nwO/RuZjIHv++1r/Xe7l5/w9Y7Zz7RYJjOvfaT7FL7jNAA3B/M2UUv1Yws554rUW/d87t9Xcrdon1\nwPteOBy3v5JjvXz0WyW5M4ClfjwAcM69gfede0moXLvPv2xPPCYC7yTYvxqYkGC/NG8isNE5Vx23\nfzXeh8HYzq9Sl3Wef/8P/765c3GkmfXulFp1YWaWa2Y9zGwc8FO8K/iP+4f1Xk7CzM7Ba2G7MUkR\nnXvNe8zM6s1sj5n9T9y4IcUuuXOA94D/ZWbvm1mdma03s8+Hyih+rXMp0Ad4OLRPsUvs5/79PWY2\n1Mz6mtl1wBzgh/4x/VZJrh6vxSheDXBS6HG7z79sTzz6441ZiLcX6NfJdekOmotn7HjWM7NhwG3A\ns865N/3dLcVO5yMsw/vwWwtMwuumVuEf03s5ATPLx0vSvu+cW5OkmM69xPYDP8DrWjob+A7e+I5X\nzWyQX0axS24o3jir7wF34o3PWgr8yMxu8ssofq1zFVABPB3ap9gl4Jx7B6+b5EXAh3gx+jHwOedc\n7EKVfqsktwav1SPgj6UcQuO4tPv8y+tgBbsDl2CfdXotugdD8WyWfxXgd3hjD64JH0Kxa8mVQBEw\nGm/A/lIzO8c5t8k/rvg19W9AT+D2Zsro3EvAOfc28HZo11/M7K/A63gDzm9BsWtODt5V+n92zv3a\n3/e8ebMhLjSze1D8WmRmQ/ES3rvD3V9Q7BLyW8QX4115/xxel6uLgPvN7Ihz7jEUu+bcDTxq3syH\n9+AlGP+F120y3OW+3THM9sRjH4kz234kzuSkeXuBRNOX9gsdz1pmVoA3C8Ro4Dzn3NbQ4b0kPxdB\n5yPOuVi3tGVm9jSwCfh3vC8XvZfj+F2CvoF3xf64uH7Lx5lZX+AgOvdazTm33MzW4g22BMWuOXvw\nWjyWxu1/Bm8mnCEofq3xabwk7uG4/YpdYnfgjd+40DkXGwP4nJmVAHeb2S/Qb5WknHOPmdkJeBf3\nvoGXXPwS+CONu1q1+/zL9q5Wq/H6qcWbALzbyXXpDlYD5f7UpmET8PoMrm/6lOzgd3lZDJwGXOCc\nWxVXpLlzcYtzrirNVcwozrlKvPMp1hdX7+WmRgMFwKN4XwKxG3hfKvuAk9G511bhK32KXXKrk+yP\nXRFtQPFrjauAFc65FXH7FbvETsaLV23c/teBEmAQ+q3SLOfcN4EBeF2ahzjnLse7iPC3ULF2n3/Z\nnngsAc4ws9GxHX4z8Nn+MWmbJXjzOF8W22FmecA/Ac8452qiqliU/LU6HsMb3HaRc+61BMWWAMPM\n7LzQ84qAj6FzsQl/MaMTgPf9XXovN/V3YFaCG3jJyCy8L1ide61kZqcC4/HGG4Fi15zf+Pfz4vbP\nA7Y653ag+DXLP98m0rS1AxS7ZHYAp5hZj7j9pwNH8K7U67dKC5xzh5xzq5xzO81sPt73bXiGunaf\nf+bPvZuV/IXFVuD1AbwF7yrWd/D6pU7K4isGCZnZJ/zNOXjdW24EdgG7nHN/8cs8jvfF8jVgI95C\neRcCZznnlnd6pbsAM7sPL163A0/FHd7qnNvqJyd/A0bgxW4f3kJ5k4DJzrkPOrHKXYqZ/QZYDqwE\nDuD98PtXYDBwmnNurd7LrWdmDrjdOXeL/1jnXgJm9hjeZ9hyvKk4p+DFpRqY6pzbrdgl5y8w9hze\nmgnfADYAn8BbtO0a59zPFb/m+eNgbgCGO+d2xh1T7BLwf6f8Cq9L30/wvhMWAJ8Hfuicu9kvp98q\nCZjZFOCjeJ974M1O9zXgP51z/xYq1/7zL+rFSqK+4fXzW4z3g+Yg8FviFsbTLYiVS3J7MVSmJ3AX\n3lWHI3hXBmdGXfeI47apmdh9K1SuP/AzvCsy1fhf2lHXP+ob3gDpt/B+/FXjzbrx0/j3qd7LrY5n\nowUE/X0695rGaSFesrsfr8/4B3iDLIcodq2OYRHejEI78bqwrASuUPxaFbt8vAt7v2+mjGKXOC4f\nBV7043cQr/X3RiA3VEa/VRLHbiJeQlGJl7QtJ7TQYlzZdp1/Wd3iISIiIiIinSPbx3iIiIiIiEgn\nUOIhIiIiIiJpp8RDRERERETSTomHiIiIiIiknRIPERERERFJOyUeIiIiIiKSdko8REREREQk7ZR4\niIhISpjZTDNzoVudme01sxVm9oCZnRt1HUVEJDp5UVdARES6nf8GlgIGFAMTgEuBa83sCeAq51xN\nhPUTEZEIKPEQEZFUe8M592h4h5ndDCwCPgVUAp+NomIiIhIddbUSEZG0c84dAa4B1gP/YmblAGY2\nz8x+ZWabzazGzHb5j8fFnmtm+Wa208xeSPTaZvagmdWaWan/uMzMHjGzD/zX3GFmz5vZ3E74V0VE\nJAklHiIi0imcc7XAo0AuEEsCrgJ6Aw8AXwAeBuYBfzOzgaHn/TdwnpmNDr+mmRUClwF/dM7tNLN8\n4Bn/9X8G3ADcBewFpqf1HxQRkWapq5WIiHSmlf79eP/+OudcdbiAmf0eeBG4FvgPf/ci4KvA1cCt\noeIfB/rgJRngjScZB/yTc+6JVFdeRETaTy0eIiLSmQ7690UAsaTDPEVmNgBYjTcOJGihcM6tAf4G\nXG1mFnq9a4CdwB/8x/v9+4+aWVHa/gsREWkzJR4iItKZ+vj3BwDMbLyZ/dp/vB/Y5d/6+rewRcAo\nYLb/3FHATOAR51wdgHNuE/B/8VpGdpvZy2Z2q5kdn8b/SUREWkGJh4iIdKZJ/v1aM+sD/AU4D7gT\nb8rducBHgD00/Y76FV5yco3/+Gq8KXt/Fi7knPt34Hjg60AFXhetd8zsulT/MyIi0nrmnIu6DiIi\n0g2Y2UzgBeCLzrkfJTieD7wLlANjgcnAb4F/ds49HCrXE6gCXnLOzYx7jfvwEo6hwFtAhXPuzBbq\n1RdYBgxwzpW09/8TEZGOUYuHiIiknZkV4LVMjAUe9LtE1fuH47+LvpJgX8yDQE/gx8Bo4KG4v1Ps\nJzgB51wlsBEoNrPcDvwbIiLSAZrVSkREUm26mX0arxtUH2AiXjeqwcATwJf8ci/jjef4gZmNxBsk\nfh5wFl5Xqyacc2+a2d+BK4Bq4PG4IrOAn5rZYmANcBiYgTdF72POuXpERCQSSjxERCTVrvJvDXiz\nWG3Bm3XqEefcX2KFnHP7zGw+8H28Vo56vK5aM/37ZB4E7gUWO+cOxB1bgdd9a7ZfB4fX2vE1/zki\nIhIRjfEQEZGM4g8S/y9glnPuxYirIyIiraTEQ0REMoa/hsdbeKudH+/0JSYikjHU1UpERLo8MxsE\nzAHOB6bgrXiupENEJIMo8RARkUwwAfgfYB9wF944DxERySDqaiUiIiIiImmndTxERERERCTtlHiI\niIiIiEjaKfEQEREREZG0U+IhIiIiIiJpp8RDRERERETS7v8DuSHIGJXc7AUAAAAASUVORK5CYII=\n" | |
}, | |
"metadata": {} | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"cell_type": "markdown", | |
"source": "e. Plot the $X$-$Y$ and $Y$-$Z$ phase space cross sections." | |
}, | |
{ | |
"metadata": { | |
"ExecuteTime": { | |
"start_time": "2017-05-23T15:21:34.281480Z", | |
"end_time": "2017-05-23T15:21:34.883207Z" | |
}, | |
"trusted": true | |
}, | |
"cell_type": "code", | |
"source": "# X-Y phase space cross section\nfig, [ax1, ax2] = plt.subplots(ncols=2, figsize=(10, 5))\nax1.plot(x, y)\nax1.set_xlabel('X')\nax1.set_ylabel('Y')\nax1.set_aspect('equal')\n\n# Y-Z phase space cross section\nax2.plot(y, z)\nax2.set_xlabel('Y')\nax2.set_ylabel('Z')\nax2.set_aspect('equal')", | |
"execution_count": 7, | |
"outputs": [ | |
{ | |
"output_type": "display_data", | |
"data": { | |
"text/plain": "<matplotlib.figure.Figure at 0x7fa1c84fb7b8>", | |
"image/png": 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mtq9IZL1v0JsHlSQlWroEeFJFyeXIqumsjxvz/hHM++4M/kljL8xKIGhD4BsH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\noMhLDGNcaiTjBkYyK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}, | |
"metadata": {} | |
} | |
] | |
} | |
], | |
"metadata": { | |
"_draft": { | |
"nbviewer_url": "https://gist.github.com/03d2e7df042d08f2e5ef39d254b4f7bd" | |
}, | |
"gist": { | |
"id": "03d2e7df042d08f2e5ef39d254b4f7bd", | |
"data": { | |
"description": "Numerically solve differential equations.", | |
"public": true | |
} | |
}, | |
"kernelspec": { | |
"name": "python3", | |
"display_name": "Python 3", | |
"language": "python" | |
}, | |
"language_info": { | |
"name": "python", | |
"version": "3.6.1", | |
"mimetype": "text/x-python", | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"pygments_lexer": "ipython3", | |
"nbconvert_exporter": "python", | |
"file_extension": ".py" | |
}, | |
"toc": { | |
"toc_cell": false, | |
"toc_number_sections": true, | |
"toc_threshold": 6, | |
"toc_window_display": false | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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