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"\n",
" \n",
"\n",
"*This notebook contains an excerpt from the [Python Programming and Numerical Methods - A Guide for Engineers and Scientists](https://www.elsevier.com/books/python-programming-and-numerical-methods/kong/978-0-12-819549-9), the content is also available at [Berkeley Python Numerical Methods](https://pythonnumericalmethods.berkeley.edu/notebooks/Index.html).*\n",
"\n",
"*The copyright of the book belongs to Elsevier. We also have this interactive book online for a better learning experience. The code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work on [Elsevier](https://www.elsevier.com/books/python-programming-and-numerical-methods/kong/978-0-12-819549-9) or [Amazon](https://www.amazon.com/Python-Programming-Numerical-Methods-Scientists/dp/0128195495/ref=sr_1_1?dchild=1&keywords=Python+Programming+and+Numerical+Methods+-+A+Guide+for+Engineers+and+Scientists&qid=1604761352&sr=8-1)!*"
]
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"source": [
"\n",
"< [CHAPTER 24. Fourier Transforms](chapter24.00-Fourier-Transforms.ipynb) | [Contents](Index.ipynb) | [24.2 Discrete Fourier Transform (DFT)](chapter24.02-Discrete-Fourier-Transform.ipynb) >"
]
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"source": [
"# The Basics of Waves"
]
},
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"There are many types of waves in our life, for example, if you throw a rock into a pond, you can see the waves form and travel in the water. Of course, there are many more examples of waves, some of them are even difficult to see, such as such as sound waves, earthquake waves, microwaves (that we use to cook our food in the kitchen). But in physics, a wave is a disturbance that travels through space and matter with a transferring energy from one place to another. It is important to study waves in our life to understand how they form, travel and so on. In this chapter, we will cover a basic tool that help us to understand and study the waves - the **Fourier Transform**. But before we proceed, let's first get familiar how do we actually model the waves and study it. \n",
"\n",
"## Model a wave using mathematical tools\n",
"\n",
"We can model a single wave as a field with a function $F(x, t)$, where $x$ is the location of a point in space, while $t$ is the time. One simplest case is the shape of a sine wave change over $x$. "
]
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"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"plt.style.use('seaborn-poster')\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
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"outputs": [
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0, 20, 201)\n",
"y = np.sin(x)\n",
"\n",
"plt.figure(figsize = (8, 6))\n",
"plt.plot(x, y, 'b')\n",
"plt.ylabel('Amplitude')\n",
"plt.xlabel('Location (x)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
}
},
"source": [
"We can think of the sine wave can change both in time and space. If we plot the changes at various locations, each time snapshot will be a sine wave changes with location. See the following figure with a fix point at $x=2.5$ showing as a red dot. Of course, you can see the changes over time at specific location as well, you can plot this by yourself. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
}
},
"outputs": [
{
"data": {
"image/png": 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yyOr9Ly52j32axG6/PfZ4+e1v/fWYZq5t26Z6+umxn8Ho0V5H5V+PPBL7UOOJJzasPjZDoZrDgTSUC8j6mDAhtk1f//6uo9mgyFWCsyGcXCwF/gLsns7y2XgB7wLTE8yfCkzNdP3ZTnAS/VDfd19WNxEYW7aoDhlS/TmIqD78sNdR+UsopHrNNbHHy1VXNcwf6spK1QsuiP0sbr/d66j851//iv2MGkpNX7xQyI2/Fv1Z/O53DevCIBXPPhtb03f00cGr6ctVgtMMGAFMCic6VcA04Kxs3B5KMYafgTEJ5t8PrKznOudEXtlMcLZuVT3hhOoDyara3Q9v/PAC//qX11H5Q1WV6iWXxH42t9zSMJObiFDIJXjRn8k11zTszyQiFHKDUjbkmr5E7ror9jMZObJhJnyJxD+9e/LJwazpy0mCE7Mg7AqMAhYCoXDtziPAIfVdZ4rb3Qb8NcH824DKeq4zJwlOKFR9a6pxY9UXXsjaqgOtqkr1ootif4Qa+pV5RYXqWWfFfiZ33+11VP4QCqneemvsZ9PQr8xDoZrjSv3xj5b4RTz4YOyJ/JRT3AVnQxaf+J15ZnATv5wnODErgYHAS1G1OvOBq4E22Vh/3La2AXckmH97fROc6Fe2b1FVVqqec47Ph17wQKIf6IZ6z3zrVtWhQ6s/BxF3pWVi3X137PFy1lnB/YHORKI2fbff3jC/O3V5+mk3AnnkM/rVr4Ix9la2hUKqN9xQWBcIeUtwgMOBscCmcE3OR8CM8L9XAQMz3Ubc9pZn+xZV9MvL0cQbmlDI3YKJ/uJdemmwv3jpKitTPfbY6v1v1Mj9MJvE4qvYhw5tWFfmW7fWHDTTbvHW7pVXYnuLP+ywAHeoWg9VVTUHzfzzn4OfDOc0wQFKgZvCj2ZXAauB0UCPqPf0Dj/K/Xl9tlHHticB7yeYP8WPjYxNcvFVp2ef7a5SC93ataqHHlq93yUl7gfZ1C3+yvzYY12iWOg2b66ZDD/+uNdR+d/EibHjnf3iFw1jJPKKCtf+KPq39c47vY4qO3LVyDjSwLgynNhMAn4DNKnl/WcDFelsI4UY/hDefreoeaVABXBlpuu3BMcbY8bEXpmfemowG7+latkyN/ZYZH+bN3c/xCY18Vfmhx9e2Ffm69apHnJIbDL80kteRxUc06fHDmq8337uO1ioystVTzqpen9F3G9sochVghOKekR8txTe3xd4LJ1tpLDOFsACXOd+Q4ATgE/DjZ1bZrp+S3C88+STsVfmAwcGq2+GVC1cGDtYYNu2btxSk574K/NevQrzpLV8udu3yH62aKH6zjteRxU8H38cOxL5brupfvut11Fl36ZNrpPHyH4WF6s+84zXUWVXrhKcE4BG6SyTixfQBRgXfnJrI/AyUJqNdVuC462XXortgOqAA1R/+snrqLJn3jw3kF1k/3baSfXzz72OKrjefz/2yry0VHX+fK+jyp7vv48d4blt28IYEdwrX37pvnORz7NDBzcwaaFYsaJmr/Gvvup1VNmXaoKT1lhUqjpeVavSWSYXVHWJqp6iqq1VtZWqnqiq33sdl8nciSe68Yi2285Nf/op9OsH8+d7G1c2vP02HHIILFvmprt3d4Mg7ruvt3EFWf/+bmyznXZy099/DwcfDDNnehpWVnz4IfTtC99846Z32AGmTq0ekNSkLzLW0p57uumVK93YZ6++6m1c2fD113DQQdXHfqtW8OabcPzx3sblpUAOtmkK26GHukE6O3d204sXuxPZtGnexpWJ//wHjjvOjZIN0KuX+6EtLfU0rILQowfMmOFOXlA9qOv48d7GlYlx4+Dww2HFCjfdtas7Xvbf39u4CkFk5Pp+/dx0WRkMGQIPPeRtXJmYOtUl9gsXuulOndwgq4cf7m1cXrMEx/jSfvu5k9Y++7jpyElrzBhv40pXVRVcfjlcdJH7N7jRnqdMcT9CJju6dHEJQP/+bnrLFlcbePvtrrI+KFTh73+HoUOhvNzN69fPjfq8227exlZItt8e3n3XHSPgRiK/4AK44gqorPQ2tnQ9+SQcdRSsXeum99nH1eL06eNtXL6Qyn2shvSyNjj+snq1e0Imvjv6IPR9sm6d6uDBsbFfcknD7JwuX8rKXPfz0Z/5Kae4wV79rqzMdQoaHfuwYQ3jEXivVFa6Tu+iP/MBA1zDbr/btq3mMCZHHOG6nyh05LMn40J6WYLjP9u2qV58cewX+bDD/P0j9NFHqt26VcdbVGSjYedLVVXNnlv32091wQKvI6vd/PmqPXrExvznPzesTi+9Egqp3nNP7BOcu+zivsN+9eOPsd0GRHr2DsKFXzZYgmMJTsEZMyZ2FNzOnVUnT/Y6qlihkOtZtnHj6jhbtVJ97TWvI2t4XnxRtWXL6nJo29affcc880xsnE2aqD72mNdRNTyTJ7unqqLL4aGH/Nfr7zvvxMbZqJHrwM9vceaSJTiW4BSk996L/XKLqF53nT+uXNasUT3xRI25qurVS/Wbb7yOrOH6/HPV7t1jy+TCC11fIV7bvNndbo2OrXt31blzvY6s4VqyRLVPn9gyOflk1VWrvI7M1WTfeGNsh6g77qg6darXkeWfJTiW4BSsJUtqVs/26KE6Z453Mb30Umz/NpH2Nlu2eBeTcdasUf31r2PLpls31Xff9S6mKVNiO3sEN8ZUIffGHBRbttRsC9Wpk+rzz3tXS/LJJ6o9e8bGNHCg6s8/exOP1yzBsQSnoFVUqN50k2vbEl1V+/vf57eR3cKFNRu1tmmj+sIL+YvBJBcKqd53X2wnkuDG6slnR5I//1zz5FlSovrvfzesWwxB8OyzsZ1IguqQIarffZe/GNavV7388tj2QUVFrta6IYzXV5uCTXCAK4AJwDJAgVHZXL8lOMEya5bqPvvE/gh16ODaweSy9mT1atVrrql5whw0SHXRotxt12Tmiy9ie3oF1/7l1ltzW3uycaPqX/6i2rp17LZ/8QvVzz7L3XZNZhYvVj366JoJ6dVX5/a2VXm5eyihU6fYbe+xh+oHH+Ruu0FRyAnOV8As4AFLcIyq+zG46aaaycbOO6v+85/ZrdH54QfVP/0ptlEoqLZrp/roo3YVHgSVlap33+0af8eX4c03Z7faf8UK1dtvjx0DKZJU/f3v1mVAEIRCqk88UbMMW7Rwj2kvWZK9ba1f747NLl1qJlXXXWddBkQUcoJTFP5bbAmOifbdd7Ej6Eb/EJ1zjupbb9XvhLJxo+r//ueqp6NviYF7qusPf3DtPEywLFvmjovoRpvgnoAbPlz15Zfrd0IpL1edMEH1//4vdsTzSKP4ESNUly7N/v6Y3Fq7VvXKK2OfkIzcMho82P1GbNiQ/norK117sHPPrZl0g2s/Zg8qxEo1wRH33uARkWKgArhZVUdla719+vTR2bNnZ2t1xgMffgg33ghvvVXz/9q0gcMOc2NC7bMP7L6769W0dWuoqHA94C5d6ro8//hj+OAD16371q2x6ykuhjPPhD//2XqYDbovv4Rbb4XnnnOnlGgtWrjekQ85xA0JsdtubkyoFi2gqAg2bnTDKXz7LXz+uetN+f33YdOmmtsZOhRuusn10m2Ca+FC+OtfYexY95sRraTEHSv9+kHv3m5YiJ13hmbNoHFjd7ysXu2Oly+/dL8tU6fCunU1t3PkkXDbbW58KRNLROaoatK+mi3BceuaE/l37969D7QEpzDMmwejR8NTT7nEJRs6doRzz4ULL4Rdd83OOo0/fPMNPPAAPPYYrF+fnXW2agVnnw0XX1w9wKMpDD/84IaOeeQR+Pnn7KyzaVMYPhwuuwx69szOOguRJTjprcsSnAK2caMbLfj552Hy5MRXS3Xp1AkGD4aTT4ZBg9xVmilcW7a4UZjHjXN/V69Ob/ntt3djA516qht3rFmz3MRp/KGiAiZOhJdfhgkT0k922rSBAQNcDd+QIS4pNnULRIIjIoOAiSm8daqqDohb1m5RmbRVVbmanblz4euvYdEil/Bs2OCqkJs1c7U03bq5K+5+/dy/RbyO3HhBFebPd4MXfvstLFgAa9bA5s1ugMbWraFtW3frao89oG9f2Gsvd/vKNDyq7jdl1ix3C2rxYli2zA2cum2bS17atnWDw+67LxxwgKupadTI68iDJdUEpzgfwdThA2DvFN5XlutATMPQqBH06uVexiQj4hKWvfbyOhITBCLugqhbN68jMeBxgqOqZcDXXsYQb86cOatEZHGWVxtJ4r7K8nr9opD3r5D3DWz/gq6Q96+Q9w1s/zKRUgtIr2twfEdVO2R7nZE2PqlUqQVRIe9fIe8b2P4FXSHvXyHvG9j+5UPgEhwR6QOUApG73PuIyNDwv18P1woZY4wxpgELXIIDXAKMjJo+NfwC6Ap8n++AjDHGGOMvgX1M3BhjjDGmNvYwozHGGGMKjiU4xhhjjCk4luAYY4wxpuBYgmOMMcaYgmMJjjHGGGMKjiU4xhhjjCk4luAYY4wxpuBYgmOMMcaYgmMJjjHGGGMKjiU4xhhjjCk4luBkQER2EZEXRGS9iGwQkRdFpEuKyzYVkb+LyDIR2SIiM0TksFzHnCoRGSoi40RkcTi++SJyh4i0SmFZreXVMx+xp0JEBtQS47oUlvV12QGIyJQ6yuHNJMv6qvxEZGcRGR3+nMvCsZQmeF9G5SIi54vI1yKyNXy8/zab+1HLNpPum4j0EZEHw7GVicgSEXlKRLqmuI3ajoU/5GKf4radatlldMx5UXbh7aZSfqPq2L/yFLbhSfmleg4QkbYi8rCIrBKRzSLyjojsn+I2ikTkWhH5XkTKReRTETklW/sQxME2fUFEmgOTgK24wT8VuA2YLCI9VHVzklU8AhwPXA0sBH4HvCUi/VT1k9xFnrKrgCXAn4EfgV7AKGCgiBysqqEky48FxsTN+ybLMWbD74GPoqYrU1jG72UHcDHQOm5eP+CfwPgUlh+Lf8qvO3AaMAeYBhxdy/vqXS4icj5uf+8A3gGOBO4XEVHVB7KyF4mlsm/DgX2Be4EvgM7ADcBsEempqj+ksJ15wIVx876vZ8zpSLXsoJ7HnIdlB6nt38NA/EVFi/C8VL6L4E35JT0HiIjg9qErcCmwFrgWdx7sqao/JtnGreHtXIf7DIcDz4vIYFV9PeM9UFV71eMFXAZUAd2j5nXFnSCvSLLsAbiE6OyoecXAfGC81/sWjqdDgnlnhuM+IsmyCtzm9T4kiXFAOM5BaS7n+7KrI/ZHcAl5uyCVH1AU9e/zwvGVZqtcwu9bATweN/9RYBXQ2ON9S/Rd3BUIAbeksI0pwPt+LbtMjjkvyy6d/Uuw3Ijwe4/3a/mlcg4AhoSnB0a9pw2wBrg3yfo7hn+Pbo6b/y4wLxv7YLeo6u8EYKaqLojMUNVFwHRcoSdbtgJ4LmrZSuBZ4BgRaZL9cNOjqisTzI7UdHTOZyw+4/uyS0REmgGnAhNUdY3X8aRDk9cWQmbl0g/oADwZN/8JYHvgkLQCTkMq+5bou6iqi4GV+Py7mGLZZcKzsoOM9m8ksBx4K4vhZFWK54ATgJ9UdXLUcuuBCSQ/Dx4DlFCz7J4E9k/1FmxdLMGpv32BzxPM/wLYJ4VlF6lqWYJlS3DVnn50ePjvVym896Lw/fAyEZkkIofmMrAMPCUiVSKyWkSeluRtqIJadicDrYDHU3x/UMovIpNy2Tf8N/77/EX4b7Lvc96JyN64K+BUvosAvcS1FawQkXkicm4Ow6uv+hxzQSy7nYGBwFPhJDwVfim/+HNAXefBLiLSso517YurwVkQNz9rZWdtcOqvHe5+Y7w1QNsMlo38v6+ISGfgFuAdVZ2d5O1PAq8CP+Gq0q8GJonIUao6JaeBpm49cBcwFdiAu7/8Z2CGiPRS1RW1LBe4sgs7E1eV/0YK7w1C+cXLpFwi/xe/vC/LVESKgf/ganAeSWGR94CncO1ZtsMdCw+LyI6qelvOAk1PfY+5QJVd2Ahc5UKqFxu+KL9azgHtSNwWKPL5twU21bLKdsA6Dd+XSrBsxmVnCU5m4gsGQFJYTjJYNu/CWfgruPZFZyd7v6qOiJqcJiKv4LL828hxlXGqVHUuMDdq1lQReQ/4ENfw+PpaFg1U2QGIyE7AIOBnUMrjAAAgAElEQVRfqVwxBqH8EsikXCLvSbS8H90HHIxrv5EoqYuhqjfGzXpFRF4CrhORe1S1thNQ3mRwzAWt7MAlKHNVdV4qb/ZD+dVxDsj0e5fT31K7RVV/a0mcYbYl8ZVktDV1LBv5f18Qkaa4VvLdgGM0eav4GlR1I/Aa8Issh5dVqvox7iqprjgDU3ZRziC9K8YYASm/TMqltivGdnH/7zkRuQO4ADhHVd/OYFXPAE2BlB7nzbc0jrnAlB2AiPQF9qKe38UoeSu/JOeAZN+7us6Fa4C24SexEi2bcdlZglN/X1B9/zfaPsCXKSzbNfyoefyy26h5T9ITItIYGAf0BY5T1c8yWR3BuMpKFmcgyi7OmcCnqvppBuvwe/llUi6Re/7x3+dIG4Bk3+e8EJHrgGuAy1T1iUxXF/7r5zJN5ZgLRNlFGYmrBXk6w/XkpfxSOAfUdR5ckqR26QugCbBbgmUhC2VnCU79jQcOEpFukRnhDp76k7xvg/FAY9xTLZFli4FhwNuqujXbwaZLRIpw932PBIao6swM1tUa1z/JrCyFlxMi0gfYg7rj9H3ZRQvv075kcMUYkPLLpFxm4B4p/r+4+WfgriKnZzfU9InI73G3a65T1dFZWOVvgC1AJhctOZPGMef7sosQkRJcPy+v1/KEUjpyXn4pngPGA51F5PCo5VoDvyb5efBN3MVHorL7PPxUckasDU79PQRcgrsfej0uk74V+IGozqpEZFfgO1x/FbcAqOonIvIccE84Q14EXITrRye+sL3yb9zJ4nZgs4gcFPV/P6rqj4n2TUSuAvYEJlPdYPAqYAf8s2+IyFO4z/1jYB2ukfG1wFJgdPg9QS27aGdSyxVjkMpPRIaG/9k7/PdYEVkJrFTVqemUi4gsABar6pEAqlohIjfgOodbiuss7gjgHOBSVd3m5b6JyHDgHtwJYVLcd3GDqn4Zta6YfQs/iXQN8CKuMWgbXC3CCcA1mrxD0oylsH8pH3N+K7twTHXuX9RbB+Nu59R6seGz8kt6DsAlMTOAJ0Xkaqo7+hPgb9ErE5FKXH9F5wKo6goRuRu4VkQ24n6Lh+HKL9kj5qnJRmc6DfUFdMFV320ANgIvU7OTrlJc8jMqbn4zXK+yPwPluCuVAV7vU1R834fjTvQaVdu+4TL36birqgpgNe5L0NfrfYrbv2txvYOuD8f5A/AgsGPQyy4qzsa4J20m1PL/gSm/Oo7FKemWS/jYnpJg/oW4NlhbgW+Bi/2wb7gefpPuf6J9wz0e/wYucd+Ke6LlA+B0v5RdOsec38ou1WMz/L5XwvtWUse6fFN+pHAOCL+vHa5jxTVAGa6jvgNq+ZzGxs1rhHugY3F4/+YBQ7O1DxLeiDHGGGNMwbA2OMYYY4wpOJbgGGOMMabgWIJjjDHGmIJjCY4xxhhjCo4lOMYYY4wpOJbgGGOMMabgWIJjjDHGmIJjCY4xxhhjCo4lOMYYY4wpOJbgGGOMMabgWIJjjDHGmIJjCY4xxhhjCo4lOMYYY4wpOJbgGGOMMabgWIJjjPGciAwQERWRUV7HAiAizUXkShF5WkTmi0goHN92XsdmjElNsdcBGGOMD3UE/hH+9yJgPWDJjTEBYjU4xhhT0yrgKKCdqnYDPvU4HmNMmkRVvY7BGNOAhW9L3ZTo/1RV8htNYiIyBTgcaKuq6zwOxxiTArtFZYzx2hSgFBgJTA1PG2NMRizBMcZ4SlWniAi4BGeKqo5KdVkR6QmcmMbmPlHVl9OL0BgTRJbgGGOCrCe13N6qxeOAJTjGNACW4BhjAktVxwJjPQ7DGOND9hSVMcYYYwqO1eAYYwLL2uAYY2pjCY4xxg+qwn8bpbmctcExxiRkCY4xxg/WhP92Tmcha4NjjKmNJTjGGD+YDywDhovIZmApgKr+1auAROQfQPvw5F7hv/eLyLbwv69S1VX5j8wYkwrrydgY4wsicjBwJ9ALaAHe9mQsIt8Du9bxlq6q+n1+ojHGpMsSHGOMMcYUHHtM3BhjjDEFJ3AJjojsLCKjRWSGiJSJiIpIqddxGWOMMcY/ApfgAN2B04C1wDSPYzHGGGOMDwUxwXlPVTup6nHA814HY4wxxhj/Cdxj4qoayuX627dvr6WlpbncRK1UoaICqqrcvwGKi92rKIipqMkpVaisdK/I8dKoETRubMeLqSnR8VJUBCUldryYxCLno6oqd4yIuN+XRul2x5llc+bMWaWqHZK9L3AJTi6IyJzIv3v37s3s2bNzvk1VmDsXJk6EDz+EOXPghx8gVEv61qUL7Lcf9OsHgwZBnz4u8TENgyp8/TW8+SbMmgUffwzffVf78dKpE/TsCb17w9FHu+OmpCS/MRtvLVwIb78N06bBvHnu+KmsTPzedu3ggAPc78rAgTBgADRrltdwjceWLIFJk2DKlOrjZcuWxO/dbjvYe2846CDo39/9xrRqlb9YRWRxSu8L8mPiInIe8BAZ9kcRl+AcmMsE54sv4OGH4fnnYenS+q+nfXs47TQ44wx3kIlnvYWYXPruOxg7Fp56ChYtqv96WrWCk0+GM890Jy+7Yi9MP/zgjpUnn3S/NfXVrBkceyyccw4cc4xdTBWqlSvd8fLMM+5Cu75KSuDII2HkSDjppNxfTInIHFXtk/R9luDE6tOnj2Y7wVGF116DO++E999P/J5mzWD33V1NTbt27gCprITVq10i9NVXtWfTvXvD5ZfDsGH2Q1QIVGHqVPjb3+CNNxK/p7gY9twTdtkFOnZ01caqsGYN/PSTu/rasCHxsnvsAVde6ZKdpk1ztx8mfz78EO66C154IXGtXlGR+33ZdVfo0MH93lRVuWNk6VJYsABW1dInc+fO7vflwguhZcvc7ofJjy+/hH/+0yXCW7cmfk/XrtC9O2y/vbtAqqyEzZvd8bJwISxblni5Dh3goovgssvcuSwXUk1wUNXAvoDzAAVKs7XO3r17a7aEQqrPPqvao4eqO/1Uv4qLVQcNUv3Xv1Q/+US1oqLudVVVqX71leq//616wgmqJSU117n77m57VVVZ2wWTZ9Onq/bvX7NsRVQPPVT1jjtUP/xQtby87vWEQqrffaf66KOqp56q2qJFzXXuuKPqmDHJjz3jX59+qnr88TXLFlR791a96SbV999XLSurez2hkOrixapPP616xhmqbdvWXF/btqp33qm6ZUteds3kwLffqv7mN+73JL58995b9dprVSdOVN24Mfm6fvpJddw41fPPV+3Uqeb6WrZU/eMfVX/+Ofv7AczWVHKEVN7k11cQEpyDD66ZhPzjH6orVmS27jVr3Mlp//1rHli/+IXqRx9lZx9MfixerHrKKTXLsnNn1Vtvdf+fiU2bVP/7X9V+/WpuY6+9VN95Jzv7YfJj5UrVc8+teaJq1071mmtUv/46s/Vv3ar6wguqRx9d83jp0kX1uefc75sJhg0bVK++2l1YR5dlixaql1ziLrIzKc/KStU331Q96STVoqLYbdx1V/b2I8ISHB8kOKqqr73mPuVevVSff94dCNkUCqm+/XbNE5eI6sUXuwPb+FdFhfsBiK9h6d5d9bHH3Ikm26ZPVz322JonrtNPV12+PPvbM9kTCrlauXbtYstuhx1UR492iWy2ffKJ6rBhNY+X445TXbQo+9sz2fXyy6o77RRbdtttp3rbbapr12Z/e99+65Lv4mLV9u1zc0wWdIIDDA2/HggnOBeFpw/PdN3ZTnBCIdXJk3N/tRMKqY4f72qIog/k0lLVSZNyu21TP99+WzMxbd9e9b77VLdty/32J092tzGit9+hg+qLL+Z+2yZ9S5e6pCL+Cvz223NzEok3Z47qwIGx22/ZUvXhh602x4/WrFEdMSK2vBo3dreNcpHYxFu82NXq5EKhJzhay2tKpuvOdoKTb+Xl7gevadPYA/v667Nfe2Tqb+zYmrU2552nunp1fuOorHTtutq0iY3l3HOTt9sw+fPGGzVrbU45RfWHH/IbRyik+swzqh07xsYyZEj+j11Tu48+Ut1119gyOuKIzG9d+kVBJzi5fAU9wYmYP1/1oINiD/BBgzJv+2MyU16ueuGFseWy666uNsVLS5fWvG3Vq5fqwoXextXQVVa6hsLRbW3at3ftY7y0Zo1rjBx9vHTt6m5nGe+EQu6CJfohlJYtXXvNQqplswSngSc4qu7H8ZZbYn8cO3d2bTBM/i1Zotq3b+xJYcQI1fXrvY7MCYVU//Mf1SZNquNr29a1IzP5t3Kl6jHHxB4vxxyTm6dS6ut//3PtOSLxNWum+sQTXkfVMG3cqDp8eOzx0rt3YV6kWIJjCc7/N3Giu+qLHPTFxa6dh8mfd9+NLYOSEv9eVc2Z49puRTdYv+km634gn2bPdk8rRZfBzTf7swy++071gANiT6yXXpqfdmTGWbDAPeYdXQYXX5y8O4mgsgTHEpwYP/xQs0Hr5Zdbu5x8eOgh1UaNqj/3nXdWnTXL66jqtnp1zQatw4ZZHyj5MH68avPm1Z97u3a5a6yZLZs317xlNXBgfhqzNnQffBB78dSihepTT3kdVW6lmuBYh+0NxM47uzFGfv/76nl33w2nngplZZ6FVdBU4YYb4PzzXa+xAEcc4caR6tvX29iSadcOJkyAm2+uHgbkuefgqKNcb8kmN/79bzjxxOrvZJ8+7ng55hhv40qmeXP4739h9Ojq3tQnT4ZDDnHDR5jceP5595sS6YV6993ho4/gN7/xNi7fSCULakivQq3BiXbffbGdMfXta/2fZNvWrTUf0bzoomD2GjxuXOxTeXvu6W5LmOypqlK98srY4+Wkk1zNSNBMnRrbE/JOO1nj42wLhVyv0tHHyyGHqK5a5XVk+YHV4Jja/O538Mor7qoL3Dg2Bx3kxqMxmVu/3g1U+MQT1fP+9jd3dR7EscJOPtmNMty+vZueP9+NTv7RR97GVSi2bnXjyN11V/W8yy93V+eR72iQHHYYTJ/uxr0CNzbaoYfCxInexlUoQiFXE/+nP1XPO/109/luv713cfmRJTgN1ODB8N57sMMObnrRIvcj9Nln3sYVdCtXwsCBLiEAN2jqM8/A1VcHe8T3fv1gxgw3+B7AihWuanzKFE/DCrzNm+HXv3aDZII7Ru691w2E2KiRt7FlYu+9YeZMOPBAN71xIxx3HPzvf97GFXSVlXD22XDffdXzrrvODZppA+fWZAlOA9a7t/sR2nNPN/3zz3D44a5Gx6Rv6VL3+c2d66a3285dVQ0f7m1c2dK9u0ty+vVz05s2wa9+Ba++6m1cQbV+vWtbE6nZaNoUXnwRLr3U27iyZYcdYOpUV5sJ7uR8+unw6KPexhVUkZq+//7XTYvAmDFw221utHhTUyA/FhHZRUReEJH1IrJBRF4UkS5exxVEu+4K06ZBr15ueu1aOPJI10DQpG7RIlc1/9VXbrpTJ1dDdthh3saVbe3buxPyUUe56a1b4aSTXANkk7qVK10N2PTpbrplS3jjDdfAuJC0bAnjx8OIEW46FIJzz4V77vE2rqApK4MhQ1wCDO5W99NPwwUXeBuX3wUuwRGR5sAkYC9gJDAC2B2YLCItvIwtqDp0qH7iAdyV+bHHuqdoTHJff+1u7y1c6KZ32cUljfvv721cudKihTs2TjrJTUeuzB96yNu4guKnn1xN38cfu+m2beGdd2DAAE/DypniYhg7Fi6+uHre5ZfDrbe65rGmbpGavrfectNNmsDLLxdOzXBOpdIS2U8v4DKgCugeNa8rUAlcken6G8JTVLXZvDm259RGjQq/P4VMzZ3rBqiMfGbdu7tB5hqCioqaT4rddZfXUfnbwoWq3bpVf16dOql++qnXUeVHKKR6zTWxx8tVV/mzs0u/WLFC9cADqz+vli1t8GTVHD1FFb4tdJyIeFnzcwIwU1X//zM/qroImA4M8SyqAtC8uatOHjrUTVdVwRlnwH/+421cfjVzpmtQvHKlm95vP3dbqksDuVkauTL/3e+q5115Jdx0k12ZJ/LVV66WNLqm7733oEcPb+PKFxG44w74y1+q5/3jH3DRRdX9RJlqkTZ98TV9Awd6G1eQpJuoHA1MAH4Qkb+IyO45iCmZfYHPE8z/Atgnz7EUnJISePZZOOccN63qfoD+8Q9v4/KbSZNg0CBYt85N9+njnijacUdPw8q7oiLXudu111bPu+UWl+hYklNt7lzXHuunn9x09+7w/vuwxx7exuWFa691x0zEmDFw5plQUeFdTH6zcKG77R3dpm/KFPjlLz0NK3DSTXA6AWcB84E/AV+LyDQROSuP7V/aAWsTzF8DtK3PCkVkTuSVUWQFolEj157iD3+onnf11TBqlJ20AF57zT3yunmzmz70UHj33YbbB4WIuyr/61+r5919t2sAaVfm8MEH7qo70tvs/vu7NloNpaYvkUsucbV/kad/nn7a9apeXu5pWL7w5Zeupm/RIjfdpYs7XhpKTV82pZXgqOoWVX1CVY8AugG3Ap2BR4FlIvKIiBySgzhrhJJgXoB7GfGfoiLXF8eNN1bPu/lmuOqqhp3kPP+8e9Jl61Y3fcwx8Oab0Lq1t3H5wZ/+5DozjHj4Yff0TEO+Mo88cbZ+vZvu29ddiUf6n2rIRo50/eI0buymX3nF9QkUuXBoiGbPdjV9y5a56d13d8nN7l7cKykEqTTUSfYCBgIv4Rr/VuFqeK4G2mRj/XHbWg6MSTD/fmBlputvyI2Ma/O3v8U2DLzggrhBOsvL3VgPhTp0bdijj8YOcXHSSQW/y/Uydmzs5zRkSMMcpPOFF1QbN67+HA4/XHXDBq+j8p/XX48dCuTggxvmIJ1Tpqi2alX9OfToofrzz15H5U/ka6gGETkc97j2UbhalI9xt4vuBL4TkWw3ifoC1w4n3j7Al1nelsHdnoq+Mn/wQXf1VTlthut5qlUrd5O4VSv37OLMmd4FmyP33uvaJYVCbnrECHf12aSJt3H50ciRrl+chnxl/thjcNpp1bVXxx/v+rlp1crbuPzo2GNdLWjLlm76gw9cH0GRxvsNwWuvuU4zN2500/36uZq+Tp08DSv4UsmC4l9AKXAT8B2uxmY1MBroEfWe3rjGwJ/XZxt1bPsPuEfCu8XFUwFcmen6rQandtFX5uczRiuJukyPfhUVqY4Z43W4WREKqd5wQ+zu/fa3bnBEU7f4K/P+/VXXrfM6qtz75z9jj5fTT1fdts3rqPxv1qzYQTr33lv1xx+9jir3nnlGtbi4er8HDVLduNHrqPyNFGtw0k0uRuA62asMJzaTgN8ATWp5/9lARTrbSCGGFsAC4DPcY+EnAJ8CC4GWma7fEpy6/e9/qoc0+qD25CY6yZkxw+twM1JZ6UYAj96tP/7R+u1Ix+TJru+OyOd34IGFW+0eCqneeGPNZDjmdq6p07x5rm+gyOfXtWthj1w/ZoyqSPX+nnhiw7ydm65cJTghYCnwF2C3FN7fF3gsnW2kGEcXYBywAdgIvAyUZmPdluAkt/TQ0+pObiKvYcO8DrXetm514Ufvzp13eh1VMM2cqbrddtWfY7duqt9843VU2VVVpXrppbHHy7XXWjJcH/Pnq+6yS/Xn2LGj6uzZXkeVffFtG88803WeaZLLVYJzAtAonWWC9rIEJ4ny8tiWk3W9GjcOZCvcDRtUjz66ejeKilQfftjrqILt009Vd9ih+jNt397dkigE5eWqv/mNJcPZ9P33rlfwyOfZooXqG294HVV2VFaqXnZZ7PFy6aV22zsdqSY46T4mPl5VrWeLhmz9+tSf+62ogA0bchtPli1ZAv37w9tvu+mSEnjhBTdAoKm/Hj3cSOSRketXrXJ9w7z+urdxZWrVKtfh49NPu+nICM9//KO3cQXdrru6xsZ9+7rpzZth8GDXeDvINm+Gk0+Gf/2ret7117tpGxE8++wjNelp06b68ZhkGjcOVAcxH37oflA/+8xNt27tnnyJDCppMlNa6kbP7tfPTZeVwQknBHcokG++cfvy/vtuukkT9/SYjfCcHR06uB7DBw9201VV7knGm28OZl9cP//shl4YP95NFxXB/fe7QUfFenHLCUtwTHqaNEn5jK8nnRyY56hfeMH9+Cxf7qZLS6sfVzXZs/32bjydIeFR46qq3FAgF15Y3XliELz3nktuFoRHxOvQASZPdr3xmuxp0QJeeskdHxGjRrnx8iKPVAfBZ5+5YRbmhPvKb9ECJkxwx77JHUtwTPouvzxpfWoVRVy99A//vwdXv6qqcj+Y0d3EH3QQzJoF+ybqbclkrHlzGDfOddcf8eCDLpmM9ODqV6rudsKgQbBmjZu3116u66dIzZTJruJieOABuO226nkvvui+p99+611cqXriCZfcLFnipnfaydX6HXect3E1CKk01GlIL2tknKIxY2K7q416VVKk5/Gggupee6l+9ZXXwSa2dKnqgAGx4Q8bplpW5nVkDcfDD6uWlFR//jvt5J668qO1a13v1dHHyxFHqK5Z43VkDceLL8Z2O9CmjeqECV5HldiWLarnnx97vPToofrDD15HFnzk4imqhvCyBCcNM2a4jCDyVFXjxqrDh+v0u2Zo69bVX+rmzd0wB356ZPatt1Q7dKiOUUR11Ch7ksELM2ao7rhjdVk0buyeQvJTWXz0keuTJfpk9fvfu+4ETH59+aXqnnvGlsWf/uSvsliwQLVXr9gYR4xQ3bTJ68gKgyU4luDkT3m56ooVMY+Ef/11zR+hoUPdkFVeKi9Xveaa2Lg6dVJ95x1v42roli5VPeig2HI54gj3uLCXKitV//732Fqm1q3dOFPGO+vWqZ5wQuzxcuCBql984W1coZCrlYy+wGvSRPXBB/11gRd0luBYguO5DRtUR46M/RFq31716ae9+bJPn+66f4+OZ9Cgwu1ZN2jKy1WvuCK2fFq0UB092pvegD/7TLVv35on0QUL8h+LqamqSvX221UbNaoun5IS1Ztv9qY2Z+FC1WOPjT1eunZVnTMn/7EUOktwLMHxjSefjO3JFlzbl3nz8rP9pUtrJlqNGqneeqt1o+9Hb74Z2ylgJLGYNi0/21+71nXEFn3iBNVLLrFu9P1o1qzYTgHB1R5PmJCfC6nNm93t7ehx18CNQdYQR0XPh4JNcIArgAnAMkCBUdlcvyU4ubF0qergwbE/AEVFqmeckbtu+1eudN3lt2gRu92ePe2qyu/WrFE966zYcgPVIUNUP/44N9vcsMHVCLRrF7vNbt1UJ03KzTZNdmza5Gr/4p97OOII1alTc7PN8nJXuxifjHfsqDpuXG62aZxCTnC+AmYBD1iCEyyhkPvid+lSM9E5+WTVKVOyc8X12Wfuajs+sWnVyo3/YiM7B8fEiTVvK4Lqr37lrtCzUQO3aJEbRDU+sWnSRPX6661haJB8+KHqL35R83g55BDVZ5/Nzsgxy5a522DRg4JGfscuucSeqsuHQk5wisJ/iy3BCabNm93toTZtav4Qde3qnoh4//3U76NXVal+/rnqHXck/nErLla94AJraxNU27ap3nuvuzKOL9uddnLj+Lz7buqP94dCbkDHe+9VPfTQ2NGcI0/UDRtW2KNYF7KqKndbPP5CKtIG8PzzVV97Lb3EddEi1YcecmPUJeod4/jj3XhrJj9STXDEvTd4RKQYqABuVtVR2Vpvnz59dPbs2dlananD2rVwzz2uu/JVq2r+f7NmcOCBriO10lLYbjvXA2h5uevFdPFi19HXRx/BunU1l2/SBEaOhGuvdcubYCsrc8M63HUX/PRTzf9v3Bh69XLHy267Qdu27nipqHDHy48/uuEVPv64usfqaMXFrofc66+3Th4LwbZtrpO9v/61usfpaEVFsP/+7lVaCp06QdOm7v/WrXPHyNdfw7x51Z30RRNxw0hccw0cfHBOd8XEEZE5qton6fsswXEfVuTfvXv3PtASnPwqL4dnnoHHH3dd4Gd6SO69txsc86yz3NAAprBUVLhu7h980A37UJXh8L/dusEZZ7gxpDp3zk6Mxj9CIZg40Q2C+tprLvHJROfOMHw4/Pa30L17dmI06bEEJ711WYLjEz/95AajmzLFJTupdN3ftq3rJv+ww9wYR3vtlfMwjU+sWeOOl0mTXPf3ixYlX6Z58+rjZfBgV+tjgx02DBs2wFtvuUF0Z86Er75KvkyTJtC7Nxx5JBx1FPTvbyN/ey0QCY6IDAImpvDWqao6IG5Zu0XVAKxZ46qJly6F9ethyxZXjdy8OeyyC3Tt6q6o7AfHgLu18N13LtHZsAE2b4aSEmjVCjp2hD32gJ13tuPFOBs2wMKF8P337rdm61ZX49O2LbRrB7vv7m5fNWrkdaQmWqoJTnE+gqnDB8DeKbyvLNeBRMyZM2eViCzO8moj+5jC9UIgFfL+FfK+ge1f0BXy/hXyvoHtXyZ2TeVNniY4qloGfO1lDPFUtUO21xm5BZZKxhlEhbx/hbxvYPsXdIW8f4W8b2D7lw9WUWuMMcaYguP1Laq0iUgfoJTq5GwfERka/vfr4VohY4wxxjRggXuKSkTGAiNr+e+uqvp9/qIxxhhjjB8FLsExxhhjjEnG2uAYY4wxpuBYgmOMMcaYgmMJjjHGGGMKjiU4xhhjjCk4luAYY4wxpuBYgmOMMcaYgmMJjjHGGGMKjiU4xhhjjCk4luAYY4wxpuBYgmOMMcaYgmMJTgZEZBcReUFE1ovIBhF5UUS6pLhsUxH5u4gsE5EtIjJDRA7LdcypEpGhIjJORBaH45svIneISKsUltVaXj3zEXsqRGRALTGuS2FZX5cdgIhMqaMc3kyyrK/KT0R2FpHR4c+5LBxLaYL3ZVQuInK+iHwtIlvDx/tvs7kftWwz6b6JSB8ReTAcW5mILBGRp0Ska4rbqO1Y+EMu9ilu26mWXUbHnBdlF95uKuU3qo79K09hG56UX6rnABFpKyIPi8gqEdksIu+IyP4pbuMOZ3IAACAASURBVKNIRK4Vke9FpFxEPhWRU7K1D4EbTdwvRKQ5MAnYihv8U4HbgMki0kNVNydZxSPA8cDVwELgd8BbItJPVT/JXeQpuwpYAvwZ+BHoBYwCBorIwaoaSrL8WGBM3LxvshxjNvwe+ChqujKFZfxedgAXA63j5vUD/gmMT2H5sfin/LoDpwFzgGnA0bW8r97lIiLn4/b3DuAd4EjgfhERVX0gK3uRWCr7NhzYF7gX+ALoDNwAzBaRnqr6QwrbmQdcGDfv+3rGnI5Uyw7qecx5WHaQ2v49DMRfVLQIz0vluwjelF/Sc4CICG4fugKXAmuBa3HnwZ6q+mOSbdwa3s51uM9wOPC8iAxW1dcz3gNVtVc9XsBlQBXQPWpeV9wJ8ookyx6AS4jOjppXDMwHxnu9b+F4OiSYd2Y47iOSLKvAbV7vQ5IYB4TjHJTmcr4vuzpifwSXkLcLUvkBRVH/Pi8cX2m2yiX8vhXA43HzHwVWAY093rdE38VdgRBwSwrbmAK879eyy+SY87Ls0tm/BMuNCL/3eL+WXyrnAGBIeHpg1HvaAGuAe5Osv2P49+jmuPnvAvOysQ92i6r+TgBmquqCyAxVXQRMxxV6smUrgOeilq0EngWOEZEm2Q83Paq6MsHsSE1H53zG4jO+L7tERKQZcCowQVXXeB1POjR5bSFkVi79gA7Ak3HznwC2Bw5JK+A0pLJvib6LqroYWInPv4spll0mPCs7yGj/RgLLgbeyGE5WpXgOOAH4SVUnRy23HphA8vPgMUAJNcvuSWD/VG/B1sUSnPrbF/g8wfwvgH1SWHaRqpYlWLYEV+3pR4eH/36VwnsvCt8PLxORSSJyaC4Dy8BTIlIlIqtF5GlJ3oYqqGV3MtAKeDzF9wel/CIyKZd9w3/jv89fhP8m+z7nnYjsjbsCTuW7CNBLXFvBChGZJyLn5jC8+qrPMRfEstsZGAg8FU7CU+GX8os/B9R1HuwiIi3rWNe+uBqcBXHzs1Z21gan/trh7jfGWwO0zWDZyP/7ioh0Bm4B3lHV2Une/iTwKvATrir9amCSiBylqlNyGmjq1gN3AVOBDbj7y38GZohIL1VdUctygSu7sDNxVflvpPDeIJRfvEzKJfJ/8cv7skxFpBj4D64G55EUFnkPeArXnmU73LHwsIjsqKq35SzQ9NT3mAtU2YWNwFUupHqx4Yvyq+Uc0I7EbYEin39bYFMtq2wHrNPwfakEy2ZcdpbgZCa+YAAkheUkg2XzLpyFv4JrX3R2sver6oioyWki8gouy7+NHFcZp0pV5wJzo2ZNFZH3gA9xDY+vr2XRQJUdgIjsBAwC/pXKFWMQyi+BTMol8p5Ey/vRfcDBuPYbiZK6GKp6Y9ysV0TkJeA6EblHVWs7AeVNBsdc0MoOXIIyV1XnpfJmP5RfHeeATL93Of0ttVtU9beWxBlmWxJfSUZbU8eykf/3BRFpimsl3w04RpO3iq9BVTcCrwG/yHJ4WaWqH+OukuqKMzBlF+UM0rtijBGQ8sukXGq7YmwX9/+eE5E7gAuAc1T17QxW9QzQFEjpcd58S+OYC0zZAYhIX2Av6vldjJK38ktyDkj2vavrXLgGaBt+EivRshmXnSU49fcF1fd/o+0DfJnCsl3Dj5rHL7uNmvckPSEijYFxQF/gOFX9LJPVEYyrrGRxBqLs4pwJfKqqn2awDr+XXyblErnnH/99jrQBSPZ9zgsRuQ64BrhMVZ/IdHXhv34u01SOuUCUXZSRuFqQpzNcT17KL4VzQF3nwSVJape+AJoAuyVYFrJQdpbg1N944CAR6RaZEe7gqT/J+zYYDzTGPdUSWbYYGAa8rapbsx1sukSkCHff90hgiKrOzGBdrXH9k8zKUng5ISJ9gD2oO07fl1208D7tSwZXjAEpv0zKZQbukeL/i5t/Bu4qcnp2Q02fiPwed7vmOlUdnYVV/gbYAmRy0ZIzaRxzvi+7CBEpwfXz8notTyilI+fll+I5YDzQWUQOj1quNfBrkp8H38RdfCQqu8/DTyVnxNrg1N9DwCW4+6HX4zLpW4EfiOqsSkR2Bb7D9VdxC4CqfiIizwH3hDPkRcBFuH504gvbK//GnSxuBzaLyEFR//ejqv6YaN9E5CpgT2Ay1Q0GrwJ2wD/7hog8hfvcPwbW4RoZXwssBUaH3xPUsot2JrVcMQap/ERkaPifvcN/jxWRlcBKVZ2aTrmIyAJgsaoeCaCqFSJyA65zuKW4zuKOAM4BLlXVbV7um4gMB+7BnRAmxX0XN6jql1Hritm38JNI1wAv4hqDtsHVIpwAXKPJOyTNWAr7l/Ix57eyC8dU5/5FvXUw7nZOrRcbPiu/pOcAXBIzA3hSRK6muqM/Af4WvTIRqcT1V3QugKquEJG7gWtFZCPut3gYrvySPWKemmx0ptNQX0AXXPXdBmAj8DI1O+kqxSU/o+LmN8P1KvszUI67Uhng9T5Fxfd9OO5Er1G17Rsuc5+Ou6qqAFbjvgR9vd6nuP27Ftc76PpwnD8ADwI7Br3souJsjHvSZkIt/x+Y8qvjWJySbrmEj+0pCeZfiGuDtRX4FrjYD/uG6+E36f4n2jfc4/Fv4BL3rbgnWj4ATvdL2aVzzPmt7FI9NsPveyW8byV1rMs35UcK54Dw+9rhOlZcA5ThOuo7oJbPaWzcvEa4BzoWh/dvHjA0W/sg4Y0YY4wxxhQMa4NjjDHGmIJjCY4xxhhjCo4lOMYYY4wpOJbgGGOMMabgWIJjjDHGmIJjCY4xxhhjCo4lOMYYY4wpOJbgGGOMMabgWIJjjDHGmIJjCY4xxhhjCo4lOMYYY4wpOJbgGGOMMabgWIJjjDHGmIJjCY4xxnMiMkBEVERGeR0LgIj0FJHbRGSWiKwUkXIR+UZE7hKR7b2OzxiTnCU4xhhT03+APwMh4Gng38AG4Apgjojs4GFsxpgUFHsdgDHG+NCTwOmquigyQ0QEuBe4BLgRuNij2IwxKRBV9ToGY0wDFr4tdVOi/1NVyW80dRORHYGfgC9UdT+v4zHG1M5qcIwxXpsClAIjganhab/aFv5b6WkUxpikLMExxnhKVae4uz+MBKao6qhUlxWRnsCJaWzuE1V9Ob0IY5wV/jsxg3UYY/LAEhxjTJD1pJbbW7V4HKhXgiMi+wGjgJXA3+uzDmNM/liCY4wJLFUdC4zN9XZEpDPwKlACnKyqK3K9TWNMZizBMcaYOohIJ+BdoDNwmqra7SljAsASHGNMYOW6DY6IdAQmAd2B36jqS2mGaIzxiCU4xhg/qAr/bZTmcjlrgyMiHXA1N3sBZ6rq/9KMzRjjIUtwjDF+sCb8t3M6C+WqDU54OIZ3gH2Bc1T1qWxvwxiTW9bRnzHGcyJSDCwBtgMeAZYCqOpfPYpnCnA4MA9IeFsqncfZjTH5ZwmOMcYXRORg4E6gF9ACvOvJWES+B3at6z1+62XZGBPLEhxjjDHGFBwbTdwYY4wxBccSHGOMMcYUnMAlOCKys4iMFpEZIlImIioipV7HZYwxxhj/CFyCg+tw6zRgLTDN41iMMcYY40NBTHDeU9VOqnoc8LzXwRhjjDHGfwLX0Z+qhnK5/vbt22tpaWkuN2EaiMpKKCuDbdugogKqqkAVRKC4GBo3hqZNoVkzKAripYbJqqoq2LIFystrHi+NGkFJCTRpAs2b2/Fi3PFRXl59vFRWVh8vRUXVx0uzZu73ppDMmTNnlap2SPa+Atvt+hGROZF/9+7dm9mzZ2d1/VVV7gfKFLayMnjrLXj9dZg48f+xd95hUlRZH37PwJAlBxVEUJBkQEFFDARzjogJE2bXsK6sYthFV9e85pxzTpgTAgYMoIIERbIkyRmGmenz/XG7v+nq6ZnumQ5V3XPe56lnpqqrbp1b51bd380wd25y1xUUwC67wCGHwGGHQd++loHVBIqLXTr56CP49FOYPj2560SgWzc46CA44gjYbz8nlo38JhSCsWNh5Ej48kuYONEJmmTYYQfo3x+OPhoGDnQFq1xGRJL6uub0PDgicg7wONBRVeekEE60wNktnQJn2jT3Ibr4YjjvPGjePG1BGwHhxx/hscfg1Vdh7drUw+vYEYYMgfPPh623Tj08I1j89hs8+CC88gosW5Z6eG3awOmnw7nnQufOqYdnBIt58+Chh+D552HhwtTDa9zYfV/OOw923jn18PxARCaoau+E55nA8dK7d29Np8C54AJ49FH3f4MGcNZZMHw4tK3SijtG0FB1pe5bb4XRo8v/XlgIu+3mtq5dnb+bNXM1M8XFsHQpzJ8Pv/4K48e7TC9eGKeeCldfDV26ZDxKRoYZNw5uvhk++KD8bwUFsOuu0LMn9Ojh0kvLlu54SQksXw5//ukKTD/+CJMnly+9i8Dxx7vvy267ZSdORuaYMgVuvBHefNO1AsTSowfsvrurzWvfHlq0cDUzRUWwerWrQf7jD/jhB1fbEy+Mgw+G666DffbJfHzSSbICB1XN2Q04B1CgQ7rC7NWrl6aLUEj1+ONV3aeobKtXT/Uf/1BdsSJttzKyyA8/qPbvX96v9eurnnaa6jvvqK5ZU7Uw//xT9fHHVQcMKB9urVqq552numBBZuJjZJbJk1WPOqq8XwsLVY89VvXVV1WXL69amEuWqD73nOqRR7r0ERv24MGqM2dmJj5GZpk7V/XUU1VFyn8HDj5Y9emnVRcvrlqYq1e7dHbSSap165ZPLwcdpPrrrxmJTkYAxmsyGiGZk4K6BV3gRJg61WVQ9ep5E1WrVi6xlpam/ZZGBli2TPXss8t/HDp2VH3gAfcRSQezZzsBvMUW3vs0aqR6992qxcXpuY+RWdauVb3yyvICZKutVP/7X5ee0sHChao33KDaooX3PnXqqF53nerGjem5j5FZNm1SvekmV1CK9mOLFqrXXKM6f3567rNsmepdd6m2a+e9T0GB6kUXqa5alZ77ZBITOAESOBEWL1a95BJXcotOWP36qc6albHbGikSCqm+9JJqy5Zev3XooPr885kTHCtXql5/vWqDBt779uyp+ssvmbmnkR4++aR8BtKmjRPCmzZl5p7r1rmMq1kz7307d1YdMyYz9zTSw/ffq3br5vVbkyZO8Kxdm5l7FhWpPvaYatu23vtuvbWrhQ4yeS1wgBPC28NhgXNheL9fqmFnUuBEmDWrfJV1w4YusYVCGb+9UQWWLVM98cTyvrrjjsxlVLEsXKh6xhleGwoLVW+5RbWkJDs2GMmxbp3qBReU99U112Quo4plxQrVv//dW3MkojpsWPbSrJEcxcWq117rak+ifXXBBemr4UvEunWqI0aUb2E466yqN7Vni3wXOFrBNjrVsLMhcCKMHFlePZ96qktwhv989135UvhRR6nOm+ePPWPGqHbt6rXngANcfwzDf37/XbVHD69/9ttPddo0f+z5+WfV3r299uy6q9UWB4WFC136iPbPzjurjh/vjz1//KE6cKDXnu23V50wwR97KiOvBU4mt2wKHFXXDHH66d5E1aOH6m+/ZdUMI4pQSPWRR1wfhohPGjd2nTr9rmHbsEH18su96WWbbVwVt+Efb77p7TNVr57rL+V3/7riYtX//Ee1du0y25o1U/3oI3/tqumMGuWaLKP7v1x/vWs28pPIty+6WbxePfftCxImcHJE4ER4/nlvomrUyPV6N7LLhg2qZ57pFRB77KE6Z47flnn59FNvn6DCQtWHH/ZfgNU0iotdR+LYPi+TJvltmZcff3Sd4aObQf7zH/8FWE2jtFT15pu9TVJbbqk6erTflnn57TdX2xedri+9VHXzZr8tc5jAyTGBo+qG6XXp4k1Uw4fbRyhbzJtX/qW+4ILg9luYO1d199299p55pv+lwJrCihXlpws47rj0jaZLN8uXqx5yiNfeo44Krr35xoYNqoMGeZ9///6qixb5bVl8Nmwo37qw335VH6KeCUzg5KDAUXWdumJfgsGDbahnpvn5Zzd6ILpa9umn/bYqMZs2le/UOnCga/o0MsesWd7+ULVqqd55Z/Br0EpKXFNIbL+PdA1BNuKzZInqXnt5n/s11wR/yodQSPX++71NnO3bq06Z4q9dJnByVOCoukR1++3el2HvvbPXq76m8fHHrkkw8qy33Vb1p5/8tqpqPPOMt89Qjx6uhsdIPz/8oNq6ddmzbt48eE0MiRg50vUri8ShXbvcmugtl/jtN9Xttit71vXrq771lt9WVY0xY7xpvmlT1bFj/bPHBE4OC5wIr7/uHbrXubPr6W6kjyee8A6n7dUruFXGiRgzxn14InHZaqvcE2pB5513vBOxbb+96vTpfltVPSZPdh3UI3Fp0sR1fjXSx9ix3nmJWrfO3QEB8+ap7rhjWVzq1lV94w1/bElW4NiaxQHmhBNg1Ci3Jg24dUX69oVffvHXrnxAFUaMgHPOKVuj5fDD3bpSW27pp2XVZ7/94NtvoUMHt79okTv2+ee+mpU3PP44HHssbNzo9vv0cetL5eoClz16OPsjCy6uXu3WJnrpJX/tyhfefx8OPBBWrnT73brBd9/BHnv4a1d12WYb+Oortyo5uDWvBg2C++7z1azKSUYF1aQtSDU4EWbMcLU30SWtr7/226rcJRRSveyysucJquefH/z28GRZtMjVREXiVqdO8GcmDTp33eVNL8cf7zph5gOrV7v5lKLj99BDfluV27zyirffyoAB+bP24KZNbk2r2P5E2ex/hjVR5Y/AUVVdutQ7aVeDBm46eKNqlJSoDh3qfTlvvjn4nUOryrp1qoceWhbHWrXcVARG1QiFVP/9b296ufji/BvZWFRUfsTMbbf5bVVu8thj3oUyjzsuuCMxq0tpafnpES69NHvvRV4LHGAb4A1gNbAGeAton46wgypwVF1Jq1+/sgRVp46bYMxIjs2by5c88rmkWlTkHZEnkt/xTTehkOoVV3jTS7ZLqtmktLR8zea11+ZvfDNBbE3f6afnT81wPO64wxvfs87KzvIxeStwgAbAH8Bk4BjgaOBXYCbQMNXwgyxwVF21+OGHlyWoggI3gsaonI0bVY880vvcgjY7ZyaIV2N1661+WxV8SkpUzznH+9xuucVvqzJPKFR+GHk2S+a5Sk2p6YvHI494a6wGDcr8XFwZETjhWpPDgIKqXJfODbgMKAU6RR3rCJQAV6QaftAFjqpLPIMHe1+m++7z26rgsnat6v77lz2rwsKaVfMVCpVf3mH4cCuZV0S8mr4HH/TbquwSO01FtkrmuUgo5BY3rSk1ffF4/nnvaNTDD89sH7VMCZw1YXGxAPgv0Lkq16djA74AvolzfAwwJtXwc0HgqLqPzXnneV+qm26qWS9VMqxc6Z1gq169mrkOT00uYVaFeDV9zz7rt1X+4EfJPNewGtIy3n7bOxfXgAGZW408UwKnPjAEGBUWOqXAV8CZ6WgeStKGxcCjcY4/BCytZpgTIluuCBxVl2kNG+Z9ua66ykROhCVLVHv2LHs2W2zh5oqpyfzvf970csYZ+d1HoCqsXetdTbmm1fTF44UXvCXzQw/Nn9FjqVJUpHriiWXPxvq4uTXyotdU3HPPzIwey3gfHGBbYAQwCwiFa3eeBPapbphJ3nczcGuc4zcBJdUMMycFjqoTMzfd5M20rGTupp7v1q3smTRr5magNdzkhtEl8xNOsJL5ihXemr769d0M14abYiC6ZN6vX+ZK5rnChg2qhx1W9kxslGIZX33lnSX76qvTf4+sdjIGBgBvR9Xq/A4MA5qkI/yYe20Gbolz/ObqCpzoLdcEToS77/aKnDPPrLkl81mzvCsnt2kTvNWd/SZ2no6aXDJftMitxxRd0+fnNPRB5LPPvCXzPfZwi3fWRFavdotORo9mffttv60KFhMmqLZo4friZKLwlKzASXkmYxHpB5wBHAgI8BOwArgNmCkiA1K9RwwrgeZxjjcL/1YjufxyN9OqiNt/5hk45RTYvNlXs7LOtGmwzz4we7bbj8y+udNO/toVNAYPhrfegrp13f5HH8Fhh8Hatf7alW3mzoV994VJk9x+ixZu9vB99/XXrqBxwAHw6afQuLHb/+EHN6PtX3/5albWWbYMBg6EsWPdfoMGbsbiY47x166gsdtubpbs11+HOnX8s6NaAkdEOojIv0VkJq4/zpHA00BPVd1dVfcCdsf1l7k/bdY6pgA94hzvDkxN871yinPOgRdfhFq13P7rr8Nxx8GmTf7alS0mTHBLEyxc6PY7dXLiJlen0s80Rx4JH3zgPtLglqmInlo+35k2DfbeG2bMcPtbb+0yrt69/bUrqOy9N3z5ZdnSMb/+6oTgvHn+2pUtFixw35cJE9x+06ZuGZQDD/TXrqDSuTPUr++vDVUSOCIyRERGATOAfwFzcZ2Ot1bVS1R1UuRcVZ0A3AV0SaO9ACOBPiKyXZRdHYC9w7/VaE4+Gd58s0w1f/CBW2Mp30vmX34JAwa4EhbAjju6zGrbbf21K+jsvz989hk0aeL2v/++ZpTMI2J4wQK3v/328PXX0L27v3YFnd12gzFjnBgEtz7evvuWicR8ZeZMVzM8bZrbb93aFQj22stXs4wEVLUG51mcYLkd2EFVB6rqS6paVMH5U4AXUjEwDo8Dc4B3ReRoETkKeBf4E3g0zffKSY4+2lWbRtTzqFEu88/XTOvtt+GQQ8pE3J57uo/PVlv5albO0Levd1HXSZPcx3zWLH/tyhRjx3rF8E47uZq+jh39tStX6N7d+7zmzXMiJ18XAZ482b0Pc+a4/Uiz9y67+GqWkQRVFTjH4JZEuEZVZyY6WVV/UNWzqmdahWGuBwYC04HngReB2cBAVV2XznvlMgceCJ98UtZmPmGCy8jyraT11FNu1fVIX6ODDnLVxi1a+GtXrhEpmUdE4YwZrnQaqY7PFz74wK2YHRHDffqYGK4O223nMvmuXd3+4sX5uXL9uHEuXosXu/0ddnA1fTvs4K9dRnJUSeCo6khVLc2UMVWwY56qHq+qjVV1C1U9RlXn+G1X0Nh3X1dajXy8Z81yImf8eH/tSgeqcNNNMHQohELu2ODB8N570KiRv7blKt27wzfflPVZWrIE+vVzQjkfePRRV7sZ6ZMWaZ5rHm/IgpGQtm3d96VXL7e/di0ceii8kO46e5944w3XoTjSJ61nTyfq2rf31y4jeVIeRWUEm112gW+/hS7hnlBLl7o+Fh995KtZKVFUBGecAddfX3bswgtdB2s/e+znAx07uvSy555uf/16OOIIePZZf+1KhVAIrrwSLrgASsPFs2OOcc24JoZTo1UrVwN26KFuv6QEhgyBW291hZBcRBXuuAMGDSoTw/vs4/r5tW7tr21G1TCBUwPo0MFVq8ZmWnfdlXsfoWXL3JDV558vO3bDDfDgg2Wjx4zUaNkSvvjCpRFwmdaZZ8Lw4WUCIVfYsME1Yd51V9mxv/3NjTCsV88/u/KJRo3g3Xfh7LPLjg0fDuef7wojuURJCVx0Efzzn2XHTjrJ1fQ1beqfXUY1SWaynJq05epEf8mwbp3qEUd4JwQ87bTcmeBt2jTV7bcvs71uXdWXXvLbqvyluLj8itqHHJKZqdczwfz5qr17l9kuonrvvX5blb/EW+9sr71UFyzw27LkWLZM9eCDvfZfc43NCh9EyOZMxvm05bPAUXWLw/3zn96XePfdXWYQZF55xc0wG7G5VSvVb77x26r8JxRSve0279IOnTqpTp7st2WV8/HHqi1bltncsKHqyJF+W1UzePJJ79IOW26p+vXXfltVOd99p9q+fZnNtWq5JU2MYJKswLEmqhpGrVpw222uv0qkiv7HH11HwS++8Ne2eGzc6PpOnHRS2ciX7t3dfC19+/prW01AxFXXf/hhWRX9jBlu9NHrr/trWzxKS13frEMPLRsGHpnA78gj/bWtpnD22d65chYvdv3+HnooeE3iqvDAA94JC5s1c30Uhw711zYjDSSjgmrSlu81ONGMH6/arp16qvCHD1fdvNlvyxy//eZdIyiyMOSqVX5bVjP54w/VHj28/jjnHNf0GQQWLlTt399r34EHqv71l9+W1UwWLVLdZx+vP4491jUFBYFVq1QHD/bat8ceqnPm+G2ZkQisBsdIRK9ervamXz+3rwq33AJ77AETJ/pnVyjkOg336lW2RlDduq4E+NprZbPuGtmlUyc3L8jxx5cde+IJN3w2sjaPH6jCSy+5CftGj3bHRODGG11J3Ea++MOWW7pa4YsvLjv29tvOTyN9nnP+k0/cbOevvlp27JJL3DBwm/08j0hGBdWkrSbV4EQoKVG98UbVgoKykkzt2q42Z+3aJALYtMkVkzdtStmWyZPLl/o6d1b9+eeUgzbSRCik+vDDqvXqef10wQXZX2F65szyHefbtFH94ovs2mFUziuvqDZt6vXToEHZ74C8aJHqkCFeOxo1cvYZuQP52skYuAJ4D1gEKDAineHXRIETYdw41S5dvC9/27aqzz3nRFA5vv1W9cQTVQsL3cmFha7Od9y4Kt97yRLViy7yiixQPeMM1TVrUo6akQEmT/aOUgLV5s1V779ftagos/detUr12mvdSLro+x99tMvEjOAxb57qwIFefzVs6ApX69dn9t4bNqjefrtq48be+++3n+qMGZm9t5F+8lngTAO+Bx42gZN+NmxQveoqV4MT/SHo1s0Nyf7//jmPPlpejUS2ggL3exIsXqw6bJj70EUHse22biSMEWyKi13GEVub07696iOPqG7cmN77rVihetNNqs2aee/XsqXqyy+72iUjuIRCbpRVbG1OmzYuHaW7MLN2rep996lutZX3fo0bOyFuQ8Bzk3wWOAXhv7VN4GSOqVNVDzigvHZp21b1qXO/1VBF4iZa5FRQk1NSojpqlOpJJ5VV/kS2+vXdXBpB6bhqJMecOa4yLzYZtGjhpiWYNq36YYdCLimde65LH9Hh16qlPeyobQAAIABJREFUevnlqitXpi8uRuZZvNj5M/Yz0rixq8n96afqi9VQyDVpX3GFapMm5dPkkCFWy5fr5K3A+X/DTeBknFBI9aOPyjdDvEKcnCzeNniwqjpB88cfrqlr6FA3h03sqYWFqued56qxjdzl669V998/fnLo3t2JnZEjXQZXUQZWWuoE0yuvqF54oeo225QPS0T1lFPcSDsjd5k40TUrxksvHTuqXnaZ6htvqP75Z8XpJRRyv7/7rjs/tpk9sh12mBNORu6TrMARd27uISK1gWLgBlUdka5we/furePzYTXKNKIKH38M990Hoz4uYi1bUIfihNcVSyE9t1vLjD/r/v9q37E0beqWAfj7320Ru3zi66/h3nvdqJmKlnfYYgs3YqVxYzcn04YNsGoVzJlTtgZQLA0auLWOLr3UzYdk5AeTJrn1n15/veLlHRo0cOmlaVM3qnLzZrcQ5oIFsGZN/Gtq13aL8F52Gey+e+bsN7KLiExQ1d4JzzOB4x5W5P9evXrtZgKnYmZ/v4SOfdokfX4rlrCMVp5jdevCgQe6NYIGDXIfLiM/WbDArS795ptuSoLqUFAAAwa4tDJ4sK0JlM+sWOHSyxtvuJXtQ6HqhdOnD5x8Mpx4ohuubuQXOSFwROQA4LMkTh2jqv1jrjWB4wdFRa7oXZy4BmczhbQoXEvb7eqy/fZuXpu+fWHvvV0QRs1iwQI3z8g338CUKW5G5AULvJlYnTrQrh3ssIObp2S//Vx6ad7cP7sNf1i61M2v9N138NNPrmZv3jy3IGaEOnXcPEfdurkavb33drMmt2pVUahGPpArAqcBkEzDxAZVnRdzrTVR+cXgwW7GvQSUDhpMwauvIJIFm4ycRNVp5o0bXU1e3bp+W2QEmVDINU0VFbnmpwYNsO9LDSQnBE4qZErgiMhSYG66wgvTLfx3WprD9YUtoOEO0DXRedPht7WwPhs2ZZC88l0cLH65TT7HL5/jBha/VNhWVRPW09XOwI1zmmQeWlWJNIElozhzkaj49fLblnRTg3xn8ctB8jl++Rw3sPhlg5wTOCLSG+gA/7+OVncROSH8/4equsEXwwzDMAzDCAw5J3CAvwFnRO0PCm8AHYE52TbIMAzDMIxgkbN9cAzDMAzDMCqiIPEphmEYhmEYuYUJHMMwDMMw8g4TOIZhGIZh5B0mcAzDMAzDyDtM4BiGYRiGkXeYwDEMwzAMI+8wgWMYhmEYRt5hAscwDMMwjLzDBI5hGIZhGHmHCRzDMAzDMPIOEzgpICLbiMgbIrJaRNaIyFsi0j7Ja+uJyB0iskhENorIOBHZL9M2J4uInCAib4rI3LB9v4vILSKyRRLXagVbz2zYngwi0r8CG1clcW2gfQcgIqMr8cPHCa4NlP9EpJ2I3B9+zhvCtnSIc15KfhGRc0XkNxEpCqf3C9IZjwrumTBuItJbRB4L27ZBROaJyIsi0jHJe1SUFi7PRJxi7p2s71JKc374LnzfZPw3opL4bUriHr74L9k8QESaicgTIrJMRNaLyOcislOS9ygQkeEiMkdENonIRBE5Pl1xyMXFNgOBiDQARgFFuMU/FbgJ+FJEdlbV9QmCeBI4HBgGzAIuBj4Rkb1U9ZfMWZ40VwLzgGuA+cCuwAhggIj0VdVQguufAR6NOTY9zTamg0uBH6P2S5K4Jui+A7gIaBxzbC/gf8DIJK5/huD4rxNwIjAB+Ao4qILzqu0XETkXF99bgM+B/YGHRERU9eG0xCI+ycTtJKAHcB8wBWgLXA+MF5GeqvpnEveZBJwfc2xONW2uCsn6DqqZ5nz0HSQXvyeA2EJFw/CxZN5F8Md/CfMAERFcHDoClwArgeG4fLCnqs5PcI//hO9zLe4ZngS8LiJHqOqHKcdAVW2rxgZcBpQCnaKOdcRlkFckuHYXnCA6K+pYbeB3YKTfcQvb0yrOsdPDdg9McK0CN/kdhwQ29g/beUAVrwu87yqx/UmcIG+eS/4DCqL+PydsX4d0+SV83hLg2ZjjTwHLgEKf4xbvXdwWCAE3JnGP0cDXQfVdKmnOT99VJX5xrhsSPvfwoPovmTwAODq8PyDqnCbACuC+BOG3Dn+Pbog5/gUwKR1xsCaq6nMU8J2qzogcUNXZwDc4pye6thh4NeraEuAV4GARqZt+c6uGqi6NczhS09E2m7YEjMD7Lh4iUh8YBLynqiv8tqcqaOLaQkjNL3sBrYAXYo4/D7QA9qmSwVUgmbjFexdVdS6wlIC/i0n6LhV88x2kFL8zgL+AT9JoTlpJMg84Clioql9GXbcaeI/E+eDBQB3K++4FYKdkm2ArwwRO9ekBTI5zfArQPYlrZ6vqhjjX1sFVewaRfuG/05I498Jwe/gGERklIvtm0rAUeFFESkVkuYi8JIn7UOWq744DtgCeTfL8XPFfhFT80iP8N/Z9nhL+m+h9zjoi0g1XAk7mXQTYVVxfwWIRmSQiQzNoXnWpTprLRd+1AwYAL4ZFeDIExX+xeUBl+WB7EWlUSVg9cDU4M2KOp8131gen+jTHtTfGsgJolsK1kd8DhYi0BW4EPlfV8QlOfwF4H1iIq0ofBowSkQNVdXRGDU2e1cBdwBhgDa59+RpgnIjsqqpLKrgu53wX5nRcVf5HSZybC/6LJRW/RH6LvT6QPhWR2sAjuBqcJ5O4ZCzwIq4/S1NcWnhCRLZS1ZsyZmjVqG6ayynfhRmCq1xItrARCP9VkAc0J35foMjzbwasqyDI5sAqDbdLxbk2Zd+ZwEmNWMcASBLXSQrXZp2wCn8X17/orETnq+qQqN2vRORdnMq/iQxXGSeLqv4M/Bx1aIyIjAV+wHU8vq6CS3PKdwAisjVwAHBvMiXGXPBfHFLxS+SceNcHkQeAvrj+G/FEnQdV/VfMoXdF5G3gWhG5R1UryoCyRgppLtd8B06g/Kyqk5I5OQj+qyQPSPW9y+i31Jqoqs9K4ivMZsQvSUazopJrI78HAhGph+slvx1wsCbuFV8OVV0LfADsnmbz0oqq/oQrJVVmZ874LorTqFqJ0UOO+C8Vv1RUYmwe87vviMgtwHnA2ar6aQpBvQzUA5IazpttqpDmcsZ3ACKyB9CVar6LUWTNfwnygETvXWV54QqgWXgkVrxrU/adCZzqM4Wy9t9ougNTk7i2Y3ioeey1mynfJukLIlIIvAnsARymqr+mEhy5UcpKZGdO+C6G04GJqjoxhTCC7r9U/BJp8499nyN9ABK9z1lBRK4FrgYuU9XnUw0u/DfIPk0mzeWE76I4A1cL8lKK4WTFf0nkAZXlg/MS1C5NAeoC28e5FtLgOxM41Wck0EdEtoscCE/wtDeJ5zYYCRTiRrVErq0NDAY+VdWidBtbVUSkANfuuz9wtKp+l0JYjXHzk3yfJvMygoj0BnagcjsD77townHqQQolxhzxXyp+GYcbUnxqzPHTcKXIb9JratURkUtxzTXXqur9aQjyFGAjkEqhJWNUIc0F3ncRRKQObp6XDysYoVQVMu6/JPOAkUBbEekXdV1j4EgS54Mf4wof8Xw3OTwqOSWsD071eRz4G6499Dqckv4P8CdRk1WJyLbATNx8FTcCqOovIvIqcE9YIc8GLsTNoxPrbL94EJdZ3AysF5E+Ub/NV9X58eImIlcCXYAvKesweCWwJcGJGyLyIu65/wSswnUyHg4sAO4Pn5OrvovmdCooMeaS/0TkhPC/vcJ/DxWRpcBSVR1TFb+IyAxgrqruD6CqxSJyPW5yuAW4yeIGAmcDl6jqZj/jJiInAffgMoRRMe/iGlWdGhWWJ27hkUhXA2/hOoM2wdUiHAVcrYknJE2ZJOKXdJoLmu/CNlUav6hTj8A151RY2AiY/xLmATgRMw54QUSGUTbRnwC3RwcmIiW4+YqGAqjqEhG5GxguImtx3+LBOP8lGmKeHOmYTKembkB7XPXdGmAt8A7lJ+nqgBM/I2KO18fNKrsY2IQrqfT3O05R9s0J2x1vG1FR3HDK/RtcqaoYWI57CfbwO04x8RuOmx10ddjOP4HHgK1y3XdRdhbiRtq8V8HvOeO/StLi6Kr6JZy2R8c5fj6uD1YR8AdwURDihpvhN2H848UNNzz+I5xwL8KNaPkWODkovqtKmgua75JNm+Hz3g3HrU4lYQXGfySRB4TPa46bWHEFsAE3Ud8uFTynZ2KO1cIN6Jgbjt8k4IR0xUHCNzEMwzAMw8gbrA+OYRiGYRh5hwkcwzAMwzDyDhM4hmEYhmHkHSZwDMMwDMPIO0zgGIZhGIaRd5jAMQzDMAwj7zCBYxiGYRhG3mECxzAMwzCMvMMEjmEYhmEYeYcJHMMwDMMw8g4TOIZhGIZh5B0mcAzDMAzDyDtM4BiGYRiGkXeYwDEMwzAMI+8wgWMYhu+ISH8RUREZ4bctACLSRUSeEJFfRGSZiGwSkVki8pqI9PLbPsMwEmMCxzAMozw7AccA84BXgHuAH4EjgB9EZLCPthmGkQS1/TbAMAwjgLwHvKmqGn1QRLoDE4A7gVf9MMwwjOSQmPfXMAwjq4Sbpf4d7zdVlexakxgR+QnYFainqkV+22MYRnysBscwDL8ZDXQAzgDGhPcDiYhsD3QBZpi4MYxgYwLHMAxfUdXRIgJO4IxW1RHJXisiPXF9ZZLlF1V9pwrhdwdOBAqB9sDRgAIXVuGehmH4gAkcwzBymZ5U0LxVAc8CSQscoHtM+EuAIar6eRXCMAzDB2wUlWEYOYuqPqOqUoXtzCqG/0a4H1A9YEfgfeAjEfl7BqJjGEYaMYFjGIaRAFUtUtUpqjoU+BC4Q0R28NsuwzAqxpqoDMPIWTLdB6cCPsPNh7M3MD3FsAzDyBAmcAzDCAKl4b+1qnhdpvvgxGPr8N+SFMMxDCODWBOVYRhBYEX4b9uqXJSpPjgispeI1IlzfGfgAmAzMKoqthqGkV2sBscwjCDwO7AIOElE1gMLAFT1Vp/suQXoJiJfAXNxhcEuwMGAAJeo6gKfbDMMIwlsJmPDMAKBiPQFbsPNEtwQ/JvJWEROAAYDvYA2uMLgIuAb4H5V/c4PuwzDSB4TOIZhGIZh5B3WB8cwDMMwjLwj5wSOiLQTkftFZJyIbBARFZEOfttlGIZhGEZwyDmBA3TCrQ2zEvjKZ1sMwzAMwwgguShwxqpqG1U9DHjdb2MMwzAMwwgeOTdMXFVDmQy/ZcuW2qFDh0zewjAMwzCMajJhwoRlqtoq0Xk5J3AygYhMiPzfq1cvxo8f76c5RpZYuRK++QZ++gkmTYL582HRIti40f1ety5suSW0bQs77gg9e8K++0KbNv7abfjD+vXw1Vfw888uvcyZA0uXwurVUFAAhYXQujW0awddukDv3rDXXtC+vd+WG35QVATffQfffw9Tp8L06bB8ufvuqEK9etCkCXToANtvD7vvDn36uP/Fl8kRcgcRmZvMeSZwjBrFokXw4ovwzjswbhyEEtQHzp8P48fDu++WHdt1Vzj6aDj9dOjYMbP2Gv6yYgW89prbvv4aiosrP3/BAieA3nuv7FiPHnDEETBkiPvfyF/WrnXflldegVGjYNOmys+fPx+mTPEe69gRjjkGTjwR9tzTxE4q5PQ8OCJyDvA40FFV56QjzN69e6vV4OQXqjBmDPzvf/Dhh1BaWvG5TZpAo0buo7J+vSttVUb//nDFFXD44a4Ub+QHEya49PL665WLmoYNoVkzl8aKilwJvbJP6p57wt/+BiedBLWteJk3TJsG990Hzz0HGzZUfF79+i69FBQ48bNyZeXfo513hgsugDPPdNcaDhGZoKq9E55nAseLCZz84rPP4PrrXTVxLNttB4cc4poRdt3VlZwaNPCeU1QEc+fCxImuuvmTT8qXuAC6dYMRI2DQICtx5TI//ADXXANffFH+t3bt4MADYb/9XMbTpYsTONFs3uxK5RMnurA++8yJpVg6dICrr4ahQ03o5DJTp8K//gVvvln+t9at4YADoF8/2GUX6NrVFaCiKSlxtX5Tprhv1Jdfumbz2JrlNm3gyivh4otN6EDyAgdVzdkNOAdQoEO6wuzVq5cauc+kSaoHHaTqytNlW5s2qsOGqf76q2ooVL2wZ85UHTFCtUOH8uH37q361VfpjYuReWbPVj3++PL+bNpU9eKLVb//vvrpZcEC1TvvVO3WrXz43bqpvv9+WqNiZIG//lI9+2xVEa8/69dXHTpUddQo1ZKS6oW9ZInqI4+o9upVPr1ss43qiy9WPy3mC8B4TUYjJHNSUDcTOEYs69Y5AVOrlvfD0LWr6lNPqW7alL57lZSovvGG6h57lP8QnX226tKl6buXkRmKilRvvtllTNH+a99e9d57VdeuTd+9QiHVTz9VHTCgfHo55hjVP/9M372MzFBaqvrgg6pNmnj917Kl6i23qC5fnt77ffed6lFHlU8v++2n+vvv6b1XLpHXAgc4Ibw9HBY4F4b3+6Uatgmc3GXsWNWOHb0fgnbtVJ9+uvqlqWQIhVTfead8Cb1VK3fcCCYTJ6ruskv5jOqee9IrhOMxerSr7Yu+9xZbqD7xhJXOg8rMmar9+nl91qiR6n/+o7pmTWbv/dNPqgMHeu9dt67qrbdm9tsWVPJd4GgF2+hUwzaBk3ts3qz6z396q4sLC1WvvVZ1/frs2VFcrPq//6k2bOj9EJ15pqtZMoJBKOSajAoLy3wkonrhhaorVmTPjtJSJ75btPCml6OPds0URnB44YXy7/XJJ6vOn589GyIFqW228dqx336qc+dmz44gkNcCJ5ObCZzcYuFC1b339r7we+yhOmWKfzbNm6d6yCFem3bcsWZXKQeFVatUjz3W65suXVTHjfPPpqVLVU891WtTu3au34/hLxs3qp5/vtc3bduqfvihfzatWaP6t795bWraVPWDD/yzKduYwDGBk/eMHau65ZZlL3mtWqo33uhqUvwmFHIdBRs0KLOvcWPVt97y27Kay8SJqp06eTOGyy5T3bDBb8scr72m2qxZmW116qg+9pjfVtVcZs5U3W03b3o5+WTVlSv9tszx2WeqW29dZpuI6k03uZrBfMcEjgmcvCUUcv0katcue7m33DKYo5d+/VW1c2fvR/Kqq4IhwmoSzz3n7UgcVLE5b175TuvnnONqEozs8f773o7EdeqoPvxw8PpHLV+uevjh3vRyzDGqq1f7bVlmMYFjAicvKSpSPf107wu9zz6uqSqoxGsWOfjgzHdMNFxp9qqrvM9+p51Up0/327KK2bRJ9bzzvDbvvrvqokV+W1YzuO8+1YKCsmffoYPqjz/6bVXFlJaq/utf3vTStWt+N4mbwDGBk3esWlV+JMHll7tOxkEnFFK97Tbvh7NnTzdHipEZNm5UPekkb3oZMiS7Hc9T4Ykn3EiZ6Ix22jS/rcpfSkrc9yQ6vRx+eHY7nqfCO++4kXgR21u0UP32W7+tygzJChybXN7ICf78E/bZx63vAlCnDrzwAtx9t1vkMOiIwD//6WZCbtzYHfvlF7e43uTJ/tqWjyxf7mYdfuUVty8Cd94Jzz5bfrbqoDJ0qFv/auut3f6cOdC3rztmpJf16+H44+Gee8qO/f3vbg26Zs38s6sqHH20mz27Sxe3v3w5DBzoXUevpmECxwg8Eye65RQiQqBpUzcF/qmn+mtXdTjgAJdBtWvn9v/8E/beO/7SAEb1mDXLKwTq1XNrSv3jH7m3jEbv3m5R2MginStXujT0+uv+2pVPLFsGAwaUCYGCAnjgAbcWWa1a/tpWVbp2dell333d/qZNcNxx8PDD/trlFyZwjEAzdqx7WRcscPvbbgvffuvWA8pVdtrJrWu1yy5uf80aOPRQy7TSwZQprqZv+nS337Klq/U7/nh/7UqF9u2dWOvf3+0XFcHgwXD//b6alRcsWOC+JT/+6PYbNnRC5+KL/bUrFZo1g08/devigVvX6qKL3Bprqv7alm1M4BiB5eOP3WKYa9e6/d12c6WTbt38tSsdtG3rxNvBB7v94mK3wvTTT/trVy4zYYJb2HDRIrffqZNLL3vt5a9d6aBpU/c+nHKK21eFSy+Fm2+ueZlWupg1yxWepk1z+23auHfyiCP8tSsd1Kvnmmcvv7zs2C23OKETu5BnPmMCJwuUlPhtQe7x1ltw1FGwcaPb339/GDMGttrKX7vSSePG8N57ZZlWKARnnw333eevXbnIV1+5Zobly93+Lru4VZk7dfLXrnRSty48/7xbVTrCdde5VclN5FSNqVNdTd/s2W6/fXuXhnbbzV+70klBgeujeNddZcceeQTOOKPm5Ek5KXBEZBsReUNEVovIGhF5S0Ta+21XPNatc1XLVp2cPM8/Dyee6Go1AI48Et5/Hxo18teuTFBY6OJ7/vllxy67DG66yTKtZPnkE1cTFqnp69MHvvwSWrf2165MUFAAt9/u0keE22+veSXzVJgwwTVLRWr6Ond24qZzZ3/tyhRXXAFPPeXSDrjBGSee6Jo6855khloFaQMaAH8Ak4FjgKOBX4GZQMNUw0/nMPGiItX99y8btnfzzcGbKCpoPPSQd5jmSSflxjDwVAmF3Hpa0XG/8kpLL4l4803vmlIDB6Z3BfAgc++93vRy2mk2gWQixo51kzxGntnOO6suXuy3Vdnhtde8k6MedFDuTJkQC5mYBwd4AzgMKKjKdencgMuAUqBT1LGOQAlwRarhp1PghEKq//iH9yN01VWWaVXE7bd7n9XQoTVrpdxQyIng6Gdw3nk16xlUhWef9c4rdOSRNW/G36ee8j6DY47J/EroucpHH3lns+7TJ3fmuEkX77/vnVtpn33c/GK5RqYEzpqwuFgA/BfoXJXr07EBXwDfxDk+BhiTavjpnugvFHLrI0VnWhdeWDPWC0mWUEj1uuu8z+jyy2uuELzvPu+zOPnkmlGLVRUefND7jGpKTV88XnvNW4t14IG2en0sb7xRc2v6Yhk1yrsyeq9ebsHXXCJTAqc+MAQYFRY6pcBXwJnpaB5K0obFwKNxjj8ELK1mmBMiW6ZmMr77bu8HecgQq05WdSImdvbQ66+vueImwjPPeEvmRx9d82onKuLWW73p5ZxzrJbrww9V69UreyZ7752bJfNMEPsu1cSavljGjXMrkEeeSffuuTWrekYEjudC2BYYAcwCQuHanSeBfaobZpL33QzcGuf4TUBJNcPMuMBRdVOvi5QlqmOPrdnVySUlLnOKzqxuv91vq4JDbP+SAw6o2SXzUEh1+HBvevn7300MRxg9WrVRo7Jns9tuuVcyTzex/ZSsNrSMX35RbdWq7Nlsv73q7Nl+W5UcGRc4nkBgAPB2VK3O78AwoEk6wo+512bgljjHb66uwIneMr0W1SuvlO/oVRMzrc2bvesEibjVeg0vH31kJXNV16R74YXezGrECBM3sXz/vWqzZmXPKNdK5ukiXtcA689Wnt9+U23XruwZtW2bG+udZU3gAP2AZ4B14ZqcH4Fx4f+XAQNSvUfM/f5KdxNV9JaNxTbff79mZ1obN7pq4kj8CwpUn3vOb6uCS00vmW/erHrKKd7M6q67/LYquEyapNqmTdmz2m471Vmz/LYqe4RCqldc4U0vw4aZGK6IOXNc7U3kWbVqpfrTT35bVTkZFThAB+Df4aHZpcBy4H5g56hzeoWHck+uzj0qufco4Os4x0cHsZNxRXz5ZflMa8mSrNzaV1atUu3XryzehYWuKcaonJpaMt+wQfWII7xi+Mkn/bYq+Pz+u+o225Q9t1wpmadKSYkbfRktbv77XxM3iVi4UHXHHcueWZMmqt9847dVFZOpTsaRDsYlYWEzCjgFqFvB+WcBxVW5RxI2XB6+/3ZRxzoAxcA/Ug0/WwJHVfW777yZVrdu+Z1p/fWX6q67lsW3fn3XBGMkx8SJqq1blz2/7bfP75L56tXlxfDrr/ttVe4wZ45qp05lz69VK9Wff/bbqsxRVKQ6aJBX3DzwgN9W5Q7LlqnuvnvZs2vQQPWzz/y2Kj6ZEjihqCHi2ydx/h7A01W5RxJhNgRm4Cb3Oxo4CpgY7uzcKNXwsylwVF2mVROqk2fPVu3cuSyeTZuqfv2131blHr//7m0z33LL4FcnV4elS1V79/Z+bD/+2G+rco/Yknnjxm6YcL6xfr3qIYeUxbNWLWv2rg6rV6vut1/Zc6xTxw2xDxqZEjhHAbWqck0mNqA98GZ45NZa4B2gQzrCzrbAUS1fnbz11q6He74webKLUyR+W23l+gkY1SO2ZL7FFsEtaVWHuXNdbWauVJcHnWXLvGKxTh3Vl1/226r0sXSpat++3vi9/bbfVuUu69erHnpo2fMUUb3nHr+t8pLVUVT5tPkhcFTdRz26hqNRo/xovvnsM5dBRTerzJzpt1W5z19/eTOt2rVVX3jBb6tS58cfXa1UJF6tW+eX2PeL1avdBIDRzTd33JH7fVOmT/eK/YYNVT//3G+rcp+iIu8oV3Adt4MyQa0JnBwTOKpuTZToPiq1auX20OlHHnFxiMRnl11UFy3y26r8Ye1ab0kL3CR4uZppvf22dyr9Dh1cBmakh6Ii1dNP96aXSy/N3aHTX32l2rx5WVxatXL9Go30UFrqRp9Fp5dBg4IxSaIJnBwUOKou04oeNQJuPaugKOe4bNrkqhTCsxaWlJQfpnnIIa4UaaSXzZtVzzrL+6xPOSW3FtELhVTvvNM7Ceaee9acRRCzSSikes013vRy6KG5tybTSy+5pqhIHLp2zc++i0Hg/vu972bfvq5vl5+YwMlRgaPqBMIll3g/Qocfrrp8ud+WxfDtt6onnlg23W5hoRYdN1iv3Gecx/a//c2WpcgkoZBb3iL6me+6q+urE3Q2bCg/rHfQIHfcyBwPP+xdvmD77VV//dVvqxKzeXP5WoX+/XNPoOUab73lnbttyy39HSRiAieHBU6Ee+/1foTatw9QFeyjj3qNi9pKKNBzeVQLCtzCkUate/OZAAAgAElEQVR2ePllbxNPy5ZuvqWg8vvvqjvv7E0+V18d8NrKPOKjj7zrETVs6BbuDCoLFrjVr6PTy+mnu6Y3I/OMG+cGiET3+7vvPn+axE3g5IHAUXWzHkfPlVNY6ISPr/0svv22QnETLXK+uWucj0bWTH7+WXXbbctcUauW6i23BK+fxcsveye6rFvXJvDzgxkzVHfayfv6/uMfwRMNn3/unQOqVi23bl2u9jfLVRYuLC8yTzst+yuzm8DJE4Gj6uaQiZ6ACVSPO87H6fpPPLFScfP/2+DBPhlYs1m6VHXAAK8rBgxQnTfPb8vcumsXXOC1rXNnGynlJ+vWuVc1tolz6lS/LXNC6/rrveWprbZSHTvWb8tqLps3u87p0emlUydXw5MtTODkkcBRdf13Y/vltGrlZnbNailm0ybvEteVbYWFNXu5dB8pLla98kqvO7bYwo1s86sJaNQo1Y4dy2tg63zuP6GQGzYevRBw3bpumQO/Vt/+6Sc38jI6vQwcaJ3Pg8ILL3ibxAsKVP/5z+wMcDCBk2cCJ8Jrr7nZSGNHQWRtOO1ffyUnbiJbTVhgK8B8+ql3Xhlwi7tOmJA9GxYsUB0yxGtDnTqqDz1kTQxB44cfvPNxgesnNXp09mxYudINTIiutSkocDU5QWtqrelMnaraq5c3vXTsqDpyZGbf7bwVOMAVwHvAIkCBEekMP+gCR1X1zz/Lz39SWOiqDTM5z8zixarDLt2kRVgNTi6xdKlrJ492jYgbXp7JobWrVqmOGOE6r0bfu0+fYDR/GPFZu1b14ou9Q4NB9dhj3azkmWLDBjddQMuW3vt26+YWmzWCyebNqv/6l7f2D9zotvHjM3PPfBY404DvgYdrqsBRder4uee861iBqzK85JL01ujMmKF6+eVl1ZGvYH1wcpH33y/fRFS7thM66ewDM3++K21Hj9ABV/N4991WCs8Vvv1WtUeP8q/1cce539JVQl+2zDWFRY/QATcs+YYbgjGxnJGYyZO9S2ZEtnvvTf+98lngFIT/1q7JAifC6tWur0XduuUT1gEHqD7xRPXmz1m2TPWpp8pP7w6qe9cap6VS+SgqLSjIbq8zIyk2bnSZSfQIpsi2115uUq/qrGi/dq0bGXXMMd7ZqyNJYehQ6zuRixQXu6bE2FoVcIt43nmnKwBVlY0bVd991y0HEN2PI7KdcIJN3JeLlJaqvviim9IE3Lfgt9/Sf59kBY64c3MPEakNFAM3qOqIdIXbu3dvHT9+fLqCyxoLFsB//wtPPAGbN3t/E4Fdd4V994UePaBLF2jZEpo0gdJS2LgRFi2CWbNg4kQYNw5++sn9Fk2dOnDOOXDVVdD+48fgwgshFCpvTEEBPPIInHtu5iJspMSyZfC//8H998O6deV/33FH2Gcf6NkTtt8ett4aGjaE2rVh7VpYvhz++AOmTYOvv4Yff4TiYm8YBQVw8slw/fUuzRm5y5o18NBDcNddLu3E0qUL7LUX9O4N220H7du79FKnjktfK1bAzJkwdar7vnz7LRQVlQ/niCPgxhvd98rIXTZtct+WFSvgllvSH76ITFDV3gnPM4HjHlbk/169eu2WiwInwpIl8PjjTl/Mn5+eMLfZBs47D4YOha22ivrhu+/gnnvgrbdc7lZYCMcfD5ddBn36pOfmRkZZuRKee85lXtOnpyfMli2dEL7gAth22/SEaQSD9evhxRfhscdgwoTE5ydD48Zwyinus9G1a3rCNPIbEzhVCytvBE6EUMiVkl57DT7/3JW0q0LnznDYYXDssa4kX6tWJScXFbkiXuPGULduSnYb/qDqMqw334QPPoDJk92xZOnYEfbfHwYNggEDnNY18ptff4V33oGRI12Nb7zK3IrYemsYOBCOOw4OPRTq1cucnUb+kRMCR0QOAD5L4tQxqto/5lproqoCixe7j9Dvv7uq4pUrYfVq1+RQvz60aOGaIjp3hj32gNat/bbY8JNVq+D7712tzsyZrlli3TooKXE6tkkTJ2o6d3bNEtts47fFhp+sWwfjxzthPHcuLFzomr43b3ZNVc2aQdu2rol8p52gUyfXdG4Y1SFZgVM7G8ZUwrdAtyTO25BpQyJMmDBhmYjMTXOwkThWsR4lZ8jn+OVz3MDil+vkc/zyOW5g8UuFpBq/fRU4qroB+M1PG2JR1VbpDjPSBJaM4sxF8jl++Rw3sPjlOvkcv3yOG1j8skGBXzc2DMMwDMPIFH43UVUZEekNdKBMnHUXkRPC/38YrhUyDMMwDKMGk3OjqETkGeCMCn7uqKpzsmeNYRiGYRhBJOcEjmEYhmEYRiKsD45hGIZhGHmHCRzDMAzDMPIOEziGYRiGYeQdJnAMwzAMw8g7TOAYhmEYhpF3mMAxDMMwDCPvMIFjGIZhGEbeYQLHMAzDMIy8wwSOYRiGYRh5hwkcwzAMwzDyDhM4KSAi24jIGyKyWkTWiMhbItI+yWvricgdIrJIRDaKyDgR2S/TNieLiJwgIm+KyNywfb+LyC0iskUS12oFW89s2J4MItK/AhtXJXFtoH0HICKjK/HDxwmuDZT/RKSdiNwffs4bwrZ0iHNeSn4RkXNF5DcRKQqn9wvSGY8K7pkwbiLSW0QeC9u2QUTmiciLItIxyXtUlBYuz0ScYu6drO9SSnN++C5832T8N6KS+G1K4h6++C/ZPEBEmonIEyKyTETWi8jnIrJTkvcoEJHhIjJHRDaJyEQROT5dcci51cSDgog0AEYBRbjFPxW4CfhSRHZW1fUJgngSOBwYBswCLgY+EZG9VPWXzFmeNFcC84BrgPnArsAIYICI9FXVUILrnwEejTk2Pc02poNLgR+j9kuSuCbovgO4CGgcc2wv4H/AyCSuf4bg+K8TcCIwAfgKOKiC86rtFxE5FxffW4DPgf2Bh0REVPXhtMQiPsnE7SSgB3AfMAVoC1wPjBeRnqr6ZxL3mQScH3NsTjVtrgrJ+g6qmeZ89B0kF78ngNhCRcPwsWTeRfDHfwnzABERXBw6ApcAK4HhuHywp6rOT3CP/4Tvcy3uGZ4EvC4iR6jqhynHQFVtq8YGXAaUAp2ijnXEZZBXJLh2F5wgOivqWG3gd2Ck33EL29MqzrHTw3YPTHCtAjf5HYcENvYP23lAFa8LvO8qsf1JnCBvnkv+Awqi/j8nbF+HdPklfN4S4NmY408By4BCn+MW713cFggBNyZxj9HA10H1XSppzk/fVSV+ca4bEj738KD6L5k8ADg6vD8g6pwmwArgvgThtw5/j26IOf4FMCkdcbAmqupzFPCdqs6IHFDV2cA3OKcnurYYeDXq2hLgFeBgEambfnOrhqoujXM4UtPRNpu2BIzA+y4eIlIfGAS8p6or/LanKmji2kJIzS97Aa2AF2KOPw+0APapksFVIJm4xXsXVXUusJSAv4tJ+i4VfPMdpBS/M4C/gE/SaE5aSTIPOApYqKpfRl23GniPxPngwUAdyvvuBWCnZJtgK8METvXpAUyOc3wK0D2Ja2er6oY419bBVXsGkX7hv9OSOPfCcHv4BhEZJSL7ZtKwFHhRREpFZLmIvCSJ+1Dlqu+OA7YAnk3y/FzxX4RU/NIj/Df2fZ4S/pvofc46ItINVwJO5l0E2FVcX8FiEZkkIkMzaF51qU6ay0XftQMGAC+GRXgyBMV/sXlAZflgexFpVElYPXA1ODNijqfNd9YHp/o0x7U3xrICaJbCtZHfA4WItAVuBD5X1fEJTn8BeB9YiKtKHwaMEpEDVXV0Rg1NntXAXcAYYA2uffkaYJyI7KqqSyq4Lud8F+Z0XFX+R0mcmwv+iyUVv0R+i70+kD4VkdrAI7ganCeTuGQs8CKuP0tTXFp4QkS2UtWbMmZo1ahumssp34UZgqtcSLawEQj/VZAHNCd+X6DI828GrKsgyObAKg23S8W5NmXfmcBJjVjHAEgS10kK12adsAp/F9e/6KxE56vqkKjdr0TkXZzKv4kMVxkni6r+DPwcdWiMiIwFfsB1PL6ugktzyncAIrI1cABwbzIlxlzwXxxS8UvknHjXB5EHgL64/hvxRJ0HVf1XzKF3ReRt4FoRuUdVK8qAskYKaS7XfAdOoPysqpOSOTkI/qskD0j1vcvot9SaqKrPSuIrzGbEL0lGs6KSayO/BwIRqYfrJb8dcLAm7hVfDlVdC3wA7J5m89KKqv6EKyVVZmfO+C6K06haidFDjvgvFb9UVGJsHvO774jILcB5wNmq+mkKQb0M1AOSGs6bbaqQ5nLGdwAisgfQlWq+i1FkzX8J8oBE711leeEKoFl4JFa8a1P2nQmc6jOFsvbfaLoDU5O4tmN4qHnstZsp3ybpCyJSCLwJ7AEcpqq/phIcuVHKSmRnTvguhtOBiao6MYUwgu6/VPwSafOPfZ8jfQASvc9ZQUSuBa4GLlPV51MNLvw3yD5NJs3lhO+iOANXC/JSiuFkxX9J5AGV5YPzEtQuTQHqAtvHuRbS4DsTONVnJNBHRLaLHAhP8LQ3iec2GAkU4ka1RK6tDQwGPlXVonQbW1VEpADX7rs/cLSqfpdCWI1x85N8nybzMoKI9AZ2oHI7A++7aMJx6kEKJcYc8V8qfhmHG1J8aszx03ClyG/Sa2rVEZFLcc0116rq/WkI8hRgI5BKoSVjVCHNBd53EUSkDm6elw8rGKFUFTLuvyTzgJFAWxHpF3VdY+BIEueDH+MKH/F8Nzk8KjklrA9O9Xkc+BuuPfQ6nJL+D/AnUZNVici2wEzcfBU3AqjqLyLyKnBPWCHPBi7EzaMT62y/eBCXWdwMrBeRPlG/zVfV+fHiJiJXAl2ALynrMHglsCXBiRsi8iLuuf8ErMJ1Mh4OLADuD5+Tq76L5nQqKDHmkv9E5ITwv73Cfw8VkaXAUlUdUxW/iMgMYK6q7g+gqsUicj1ucrgFuMniBgJnA5eo6mY/4yYiJwH34DKEUTHv4hpVnRoVlidu4ZFIVwNv4TqDNsHVIhwFXK2JJyRNmSTil3SaC5rvwjZVGr+oU4/ANedUWNgImP8S5gE4ETMOeEFEhlE20Z8At0cHJiIluPmKhgKo6hIRuRsYLiJrcd/iwTj/JRpinhzpmEynpm5Ae1z13RpgLfAO5Sfp6oATPyNijtfHzSq7GNiEK6n09ztOUfbNCdsdbxtRUdxwyv0bXKmqGFiOewn28DtOMfEbjpsddHXYzj+Bx4Ctct13UXYW4kbavFfB7znjv0rS4uiq+iWctkfHOX4+rg9WEfAHcFEQ4oab4Tdh/OPFDTc8/iOccC/CjWj5Fjg5KL6rSpoLmu+STZvh894Nx61OJWEFxn8kkQeEz2uOm1hxBbABN1HfLhU8p2dijtXCDeiYG47fJOCEdMVBwjcxDMMwDMPIG6wPjmEYhmEYeYcJHMMwDMMw8g4TOIZhGIZh5B0mcAzDMAzDyDtM4BiGYRiGkXeYwDEMwzAMI+8wgWMYhmEYRt5hAscwDMMwjLzDBI5hGIZhGHmHCRzDMAzDMPIOEziGYRiGYeQdJnAMwzAMw8g7TOAYhmEYhpF3mMAxDMMwDCPvMIFjGIbviEh/EVERGeG3LfEQkUIR+SVs4y9+22MYRmJM4BiGYSTmWqCT30YYhpE8JnAMwzAqQUR2Bq4Jb4Zh5Aiiqn7bYBhGDSbcLPXveL+pqmTXGi8iUhv4AdgE7AOUAhNVtaefdhmGkZjafhtgGEaNZzTQATgDGBPeDwrXAN2BXVU1JOKr3jIMowqYwDEMw1dUdXRYOJwBjFbVEcleKyI9gWOqcLtfVPWdJMPeCdf35j+qOq0K9zAMIwCYwDEMI5fpSQXNWxXwLJBQ4ISbpp4BfgNuq5ZlhmH4igkcwzByFlV9BidE0s3VwC5AH1UtzkD4hmFkGBtFZRiGEYWI7ABcD/xPVcf7bY9hGNXDanAMw8hZMtQHpztQBxgmIsPi/L6LiCgwV1U7VOHehmFkERM4hmEEgdLw31pVvC4TfXDmAE9W8NtQYAXwNrCsCvc1DCPL2Dw4hmH4joj0ACYDT6vq2X7bUxHhmhubB8cwcgCrwTEMIwj8DiwCThKR9cACAFW91VerDMPIWawGxzCMQCAifXFDsncFGoL/MxnHYjU4hpE7mMAxDMMwDCPvsGHihmEYhmHkHTkncESknYjcLyLjRGSDiKiIdPDbLsMwDMMwgkPOCRygE3AisBL4ymdbDMMwDMMIILkocMaqahtVPQx43W9jDMMwDMMIHjk3TFxVQ5kMv2XLltqhQ4dM3sJIgdJS2LwZSkog0j++Vi0oLHSbBGrMjeE3paVQXOy2SHopKHBppU4dSy+Gl1Co7PtSWurSR0EB1K4NdetaegkKEyZMWKaqrRKdl3MCJxOIyITI/7169WL8eFt+JgiEQjB+PHz0EYwbBz/9BEuXVnx+7drQrRvsthsccAAcdBC0bp09ew1/UYVJk+DTT2HMGJg4EebPr/h8EejSBXr3hv32g8MOg7Zts2ev4T/TpsHnn8OXX8LPP8OcOZWfv+220KcP9O0LRxwB222XFTONGERkblLn5fIwcRE5B3gc6Kiqc1IIJ1rg7GYCx19+/RWeeQZefBH++iu1sPr3hzPOgBNOgEaN0mGdETRmzIBnn4UXXkicQSVi993hzDPhlFOgadN0WGcEjYUL4emn4eWXYcqU1MLacUcYMsSlGStMZQ8RmaCqvROeZwLHS+/evdUETvZRhU8+gdtug9Gj45/TuDHsvDO0bw9t2rgmBoCVK2HxYvj9d5g+vawpIpqmTeHCC+HSS2HLLTMWDSOLfPUV3HknvPdefJ83aOAyoO22g1atnMAtLYX162HBApg1y2VwpaXlr61fH4YOhX/8A6zFOj/45Re44w547TXXBBVL/frQtSvssAO0bOm+N6WlsHGjE0WzZ8Pkya4JK5bCQhg8GK65xtUiG5klWYGDqubsBpwDKNAhXWH26tVLjezy5Zequ++u6rKpsq1WLdVDDlF94AHV339XLS1NHNa6daqffKJ6xRWqHTqUD7NePdWrrlJdsSLj0TIyxPjxqgceWN63oNqvn+pdd6lOmpRcetmwQXXsWNXhw1W7d4+fBs87T3XRooxHy8gQU6eqnnBC/PTSu7fqf/+r+v33qsXFicPatEn1u+9Ub7xRdbfdyocnojp4sOrMmZmPV00GGK/JaIRkTgrqZgInt5k9W/XII8t/JDp0UL3zTtXFi1MLv7RUdcwY1VNOcRlV9D2aNVN9+OHkMkEjGPz1l+rpp5dPL23aqN5wg+rcuamFHwqp/vijEzT16nnv0bCh6s03qxYVpScuRuZZtUr18svLv/tNm6peeaXq9Omp32PqVNW//121SRPvPerUUR02THXt2tTvYZTHBI4JnMBSXKx6222q9et7Pwpdu6q+9FJyJamqMmeO6sUXqxYWeu+5556utG8El1BI9fHHXcYU7btttlF97DHVjRvTf8/Fi12tToMG3nt276769dfpv5+RXt56S3XLLb2+a9HCFZzWrUv//VatcgK4eXPvPdu3V/3gg/Tfr6aT1wIHOCG8PRwWOBeG9/ulGrYJnMwyfbpqnz7ej0Dr1qqPPpoZYRPLjBmqgwZpudLWrbeqlpRk/v5G1Zg/3zVTRvtriy1U77gjM8ImloULVc85xzU9RDdDDBvmmiuMYLF8uerJJ5d/v6/9v/bOPEyq6ljgvxpWRVbBgAub4oKJKCguoAIqbhFNjIq473sMRqPoM65BzVNjlKhEUVTUEEVRgzvIElBQVFQURBRRUWSRRdZhpt4fdfv1Mj1093T33O6e+n3f/Wbu6XPPrXPrdN86W9V1qitX5v/+y5fb9HhiR+qMM1RXrcr//esKpW7gaDXHxGzLdgMnfzz6aNUe8QUXhLMe5vXXVXfaKV6Wgw7ytRaFxCuvVO0Rn3SS6nff1b4s06erdusWL0u3bqpz5tS+LE5yZsxQ7dAhXkf9+6vOm1f7ssyZo3rggfGydO5s63ec7ClpAyefhxs4uWf9ejNkYr/sHTqoTpwYrlxr16pefnm8XG3bqk6ZEq5cdZ1Nm1RvuCF+1KRNG5t2CJPyctVbb1WtXz8qV9Omqs8/H65cdZ3KStuI0LBhvF4eftg+C4uKCtX774/v1DVooPrgg+HJVCq4geMGTkGwcKFqz57xRsRpp9XOcHG6jB8fP19fv77q3/4W7o9jXWXJEtXDD49vL0ccYQuMC4V331Xdeed4Ga+91qc4w2DVKtWBA+N10aOH6pdfhi1ZlLlzbbdWrIznnutTnNngBo4bOKEzfrz1vGPnwh98sDANh0WLVHv3jv8ROvHE/CxIdJIzc6Ytyoxd63LTTYW5023lStXjjotvL/37qy5dGrZkdYf581V32y1eBxdfXJiGw4YNqhddFC/rvvvaGjMnc9I1cIox2KZTBDzyiIVKiIRW2H57c8x2wQWFGc+lXTuYMAEGD46m/fvf5gk5W2/KTmrGjbNwCQsX2nmrVhai489/tlhAhUazZjBmDAwdGm3Pr78O++4L8+aFK1tdYPp0C5nw2Wd23qQJPPUU/OMfFjOq0GjYEO6/Hx5+OOqgdPp06NEDZswIV7ZSpgB/OpyiY8MG+PFH2LABVbjhBvMCG/EQ26+fxZHq2TNcMVPRoAHcfTeMHm0/mGCxsPbbD+bMCVe2UuaBB2DAAPMwDPaj//77cPjh4cqVirIyGDIEXn3VDDKA+fMtTtE774QrWykzZox1PCKdpx13hHffhZNPDlWstDjnHOvoRWKeLV4MffvCf/4Trlylihs4Ts15+23zT960KfziF2jTpszoPJDXbo7+up9/voVgaJMy7mvhcOKJMHlyNKTDggX20poyJVSxSo7KSrj6arj4YvsfzNCZNMmCGhYL/fubIbzLLna+dKm9tMaODVeuUkPVQnOccAKsX29pEWOymMIj9OwJM2fC/vvb+dq1cOyx8NBD4cpVkqQzj1WXDl+DkybDh6uWlcVPKgfHJsr0PIbr0KGFud4mXRYsiHff37Ch6ujRYUtVGmzYUHVx6GWXFfdC3WXLVHv1il9DdN99YUtVGlRUmFfiRJcBteELKV+sXVt1Hdf11xf3b2ZtgS8ydgMnb0ybVq1xEzkqpEz17bfDljRrfvpJtW/f+JfW8OFhS1XcrF2reuSR8c+0VHatrVtXNe6Rv7SyY9Mm1bPPjn+mQ4YU5uLzTNm0yRZGx9btnHOK29CvDdI1cHyKysmce+6JzilUQ5lWWr4ip0ULW2Nxyil2rmoLpe+6K1y5ipVVq+DII20BMdiCy2eegT/8oTAXn2dK48a2hit2sfott8AVV1jbcTJj40ZbW/PII3YuYot1hw4tzMXnmVKvHgwbBrffHk0bMQIGDUoetdzJkHSsoEI7gB2AZ4GVwCrgOaB9Lsr2EZwUrF9f1Q95dUeDBoW5Z7MGVFSoXnqp98yzYdmy+KjxW26p+sYbYUuVP26/3Xvm2bBmTfxIX716qqNGhS1V/nj88fjAoEcfbaOdTlUo1REcEdkSmADsCpwBnAZ0Ad4SkSZhylYnWLkSysvTy1tebl32EqCsDO69F669Npp2yy3WU08xmOUAP/wABx9su10AmjeHN96AQw8NV658cvXVtm05wogRNhLoPfPUJBvpGzMmOpJaipx2mo1mRraRjxsHRx8NP/8crlzFTNEZOMB5QGfgOFUdq6ovAAOADsAFoUpWF2jenMr6DdLL26CBOQwpEUTgL3+BO+6Ipv3973DuudEt8U5Vvv4aDjwQPvnEzlu3hrfesh0wpc7FF8Pjj9tUBNj01W9/C+vWhStXIbNsGRxyiO1kBNhyS3vZH3tsuHLVBr/5Dbz0EmyxhZ2/9RYcdhj89FO4chUrGRk4IvKsiBwlImEaRgOAd1T1i0iCqn4FTAXqwFcgXGbMasQL8pv0Mv/2t4XpdStL/vQn890SWTPy6KMwcKD3zJPx+edm3HwRfFu33dZeXHvtFa5ctUl1PfPVq8OVqxD5/nsb6XvvPTuvCyN9ifTvb04jI33Dd94xtwM//hiuXMVIpoZKf+Al4BsRGSoiXfIgUyp2Bz5Jkj4b6FrLstQpJk+2ntUd5YOpSNV0ysps5WiJcuGFMGpUtGf+7LNw3HHeM4/lo4/MuPnmGzvv1An++9/i8lmSK6rrmS9fHq5chcSCBdZeZs+28zZtYOLEujHSl0jv3uZZfeut7XzWLPP0/e234cpVbGRq4PwCOBOYC1wNzBGRKSJyZi2uf2kFJBuwWw60rEmBIjIzcmQlWQnz6qtwxBE2Hzyd/biz8wNoddsYysrgwQfNBXAJM2gQPPdcdJDqlVds3YD3zM0N/cEHR3udu+1mjhI7dQpXrjBJ7JlPn249cw8FYp7Ce/c2T9BgoV0mT4Y99wxXrjDp0cOcXkYcjs6dG/+MnNRkZOCo6jpVfUJV+2HrYG4BtgMeAb4XkREi0jsPclYRJUlaCWwyLUzGjDEPs5HRiUMOgUtmnY9MnWqejBsEa3IaNLC5mqlT4bzzwhO4FhkwwKYcIqEdJk2y4fS63DOfMMHayIoVdt69u72sIu7p6zK9e9voTaRn/tFH1jOPjHLVRd5/30ZuvvvOznfc0Ub6dt01XLkKgd13t45BxLN3ZD1bZJTLSUE6W61SHUBf4HmgIjjmAlcBzXNRfsK9FgPDk6TfDyzJtnzfJh7PY4/F+/Q75pgk3kPXr1f98ceS2RJeE6ZOVW3ePPqc9thD9Ycfwpaq9hk7VrVRo+hz6NVLdcWKsKUqPGbPVt122+hz6tBBdd68sKWqfaZMUW3WLPocfvlL1UWLwpaq8Fi4UHXnnaPPqVUr1XffDVuq8KC2tomLyMHYdu3DsFGU97HpojuA+SLSN9t7JDAbW4eTSFfg0xzfq05z//1wxhnRbdADB9poTuPGCRkbNbIJ8xJcUJwuBxxgIxetW9t5XeyZP/EEHH+8xV4FC5b52mu2UHvKcEUAABnGSURBVNSJp2tX65l37GjniTvN6gKvvmrTdhFPEj172ghou3bhylWI7LCDtZdu3ex8+XILYhzZaeYkp0YGjoh0FJEbRGQ+5pPmGOBRYE9V3UdV9wf2AX4A7suZtMaLwH4i0jlWHqBX8JmTJapw881wySXRtHPOsUW1DdLcIV4X6d49/gc6soOoLsyZDxsGp58e3S5/wgnw4ovRqTunKp07x0/FRHwFRXYQlTLPPBM/7d23L7z5ZjQqu1OVbbax6c1IkM7Vq21d5KuvhitXQZPOME/kwJzqTQA2YVNRE4BBQKNq8p8FlGdyjzRkaAJ8AXyMbQsfAMwCvgS2yrb8uj5FVVFhQQ9jPbAOHuweezNh/nzVjh2jz69dO9VZs8KWKj9UVqreckt8e3GPvZmxeLHqnntGn1/TpqqTJoUtVf4YMSKNaW+nWlavVj3kkOjza9BA9dlnw5aqdiEfwTaBSuA7YCiwYxr5ewKPZnKPNOVoD4zBwjSsBsYCHXNRdl02cDZuVB00KP5l9Ze/uHFTE775RnWXXaLPsVkz1QkTwpYqt1RWql5xRXx7+eMfvb3UhJ9+Ut1//+hzbNSoNF9ad98d315OOcV+d5zMWLdOdcCA6HMsK1O9//6wpao98mXgDADqZXJNsR111cBZtapqhOcHHwxbquJm8WLV7t2jz7RhQ9V//StsqXLD+vWqp50W/7K69VY3brIhsWcuonrPPWFLlRs2bbKR4Nj2cuGFpRERPCw2blQ9+eT4Z3rNNXXjmebFwKkLR100cBYutF0/sUOe//532FKVBqtWqfbvH/8jdPfdYUuVHcuWqR50UHydhg0LW6rSYP36qi+tK68s7pfWmjWqxx0XX6err3ZjOBds2qR6+eXxz3bQoNLf0OoGjhs4afHuu6pt20a/HE2blnaE5zDYsKHqaMellxbn0Py8eapdukTr0bCh6lNPhS1VaVFRoXrVVfHt5aSTijOy9Pffx0eQLytTve++sKUqPRKn/vr0UV2+PGyp8ke6Bk4xBtt0csRzz9lW5h9+sPP27WHatLoV96U2aNgQHnsMrrkmmjZsmG2RXbIkPLky5b//NefU8+bZeevWtjX+5JPDlavUKCuDv/7VotdH4p2NHg29elk4g2Lh44+tvUQiyG+5JYwdC5deGq5cpcjgwdZGIvHOJk60bfd1ye1AMtzAqYNUVMANN5jPksg2zX33Ndfxv/xluLKVKiJw223mW6h+fUubOBH23hs++CBU0VKiCvfcY343li2ztF12sSCAvXqFK1spc9lltp064nfqgw+svYwfH65c6fD44/ab8vXXdt6unflxOeaYcOUqZU480bbatwwCFn3xhelg9Ohw5QoTN3DqGIsW2QjNzTdH00480fwrRGKeOPnjoovsR6hNGztfuNCMhCefDFeu6lixwgzhwYOhvNzS+vSBt982l/pOfjn+eBtVjbjqX7bMRv7uvNMMz0Jj/Xo4/3xzEBrpPP3qV2YMd+8ermx1gQMPjO+orl1rDlr/+EfYtClc2cLADZw6xGuvWfC6iRPtXARuvBGefjoa5djJPxFnbpEf/HXr4NRTzZnizz+HK1ssERmffz6advnl1o5a1iisrVMT9trLdBGZOq6shKuusgjlS5eGK1ss8+ebE7qHHoqmnXqqGcPt24cnV12jSxczKAcOjKbdfbfFh1u4MDy5QiGdhTp16cjHIuOwFweuW1d10WLbtqrjx4crV11n7VrVU0+N10uXLhbXKkzKy1XvuMMWEMf68SlFvyzFRHl58u/xyy+HK1dlperw4apbbRW/+Hz4cN8pFSaVlbb4uF69+O/xE08Uv17wXVSFYeAsXKjaurV5ew3DW+fkyfFB2kD1sMPqZiDIQiTycthii6h+RMyb9KpVtS/Phx+q7r13fHvp3l31iy9qXxYnOc88o9qiRbyOTjnF4t3WNvPm2e9JrCydOqnOnFn7sjjJmTjRvKnH6uioo1S/+ipsyWqOGzgFYuCceGK0UXXurPrCC7VjPS9cWNUrcf365pm4mH1qlCqffqq6117x+mrbVnXkyNrR19KlqhddFO9CH1R//3t3o1+IfPONar9+8bpq2VL1b38ztwT5ZtUq1euuix/lixhapbw9uVhZulT1hBPidbXllqo33aT6889hS5c5JWvgAFcALwHfAwrcmMvyc2ngbNpk3jpF4hvWAQeovvlmfgydRYvMY2jjxvH37NHDeudO4bJxo+rQoeamP1Z33bqpPvdcfgyd5ctVr7/ehq5j77nTTjb65xQuFRXmbTyZ7kaOzI+fpTVrVO+6y0alE43xsWNzfz8nd1RWqj79tOo228Trrl07800U9lKKTChlA+czYDrwQKEbOBHef9+MmthGFRn6Hzky+4ZVWak6Y4bq2WdXNWxatLBeXXl5buri5J+5c1WPPrpqe+na1TwGr1yZ/T0+/dScDTZtGn+PLbawXl0x/djVdb79VnXgwKrtpUMH1dtvt5Ah2bJggeqQIaqtWsXfo14961Dlok06tcPy5aoXXFB1tLZNG9UbbjBdZ8uiRap33mmBd/NBKRs4ZcHf+sVi4KiaEfLUU/FeYCNHkybmnv1f/0p/bcz69arTptkwcdeuVcts2NBeYEuW5KU6Ti3w8svxUaYjR+PG5vr+8cdtKjIdysvNa/XQoVWnwiIeZs84Q/Xrr/NaJSePTJum2qtXVd02aKB6xBGqDzxgke7TGTmuqFCdNcsWqSbrnIHq8cerzp6d/3o5+eGTT2wtTqJeRVT79rWO8Zw56bWXykrVzz+3Dlj//vHGUz7W76Vr4IjlLT5EpD5QDtykqjfmqty9995b33vvvVwVV4VNm2DUKNu29/HHyfN06gS77WZ+Rlq2hCZNYMMG20K8cCF8+SXMmmVpiTRpAmefDVdfDdttl7dqOLWEKrzwgjkJnDEjeZ4ddoCuXa29bL21tYFNm2D1avj+e/j8c/NommwLeqNG5ol4yBDYeef81sXJP6rmBuLWW83LdDLatIFu3aBjR3PA17ixeU9escI8a8+dC7Nn23ki9eqZb54//Ql69MhnTZzaYsYMuOMOcweRzBxo0cJcFXTsCNtuax6p69Wz35cffzSHgh99FHUCmsiwYXDJJbmVWURmqureKfO5gWMPK/J/jx49uufTwImgCpMmwYgR9gJbvTq78vbZB846C045BZo1y42MTmExcyYMHw5jxsDy5dmVtcceMGiQ+d5p3To38jmFxZw55pPmySdh8eLsyurSxQzhc881g9opPb76CkaOtCNbfznbb2/volNPzY93fDdwMiur1g2cWNatM/frb71lRs8nnyQfnYmlfXs44ADo3RsGDPAfnbpEebm1k/HjLT7UzJlRr7HV0batOWE78EA46igLteDUDSorrZc+bpw53ZsxI3WHapttzMljv37mYHDPPaNxsZzSRtVmCMaNs9+Xd9+tfnQmQqtWNirYrx8cdpiFFKlXL38yFoWBIyKHAm+kkXWSqvZJuLYop6jSoaLCYrh8+y2sXGlTC40bm7fh7bazKayttgpVRKeAqKy0qagvv7T2smaN/bg0a2ZTVjvtBM2bhy2lUyhUVtrUwldfmSfkDRvsN6dFC3tRde5s7cZxwAyexYvhu+8s1M/GjdZemjQxQ3jbbe2oTQM4XQOnfm0IsxmmAbulkW9tvgWJMHPmzKUi8nWOi43U8bMcl1solHL9Srlu4PUrdkq5fqVcN/D6ZUOHdDKFauCo6lpgTpgyJKKqbXJdZmQKLB2Lsxgp5fqVct3A61fslHL9Srlu4PWrDTzYpuM4juM4JUfYU1QZIyJ7Ax2JGmddReR3wf8vB6NCjuM4juPUYYpuF5WIjATOqObjTqq6oPakcRzHcRynECk6A8dxHMdxHCcVvgbHcRzHcZySww0cx3Ecx3FKDjdwHMdxHMcpOdzAcRzHcRyn5HADx3Ecx3GcksMNHMdxHMdxSg43cBzHcRzHKTncwHEcx3Ecp+RwA8dxHMdxnJLDDRzHcRzHcUoON3CyQER2EJFnRWSliKwSkedEpH2a1zYWkf8Vke9FZJ2IvC0iB+Vb5nQRkd+JyBgR+TqQb66I3CYiTdO4Vqs59qwN2dNBRPpUI+OKNK4taN0BiMjEzejh1RTXFpT+RGR7EbkveM5rA1k6JsmXlV5E5DwRmSMiG4L2fmEu61HNPVPWTUT2FpF/BrKtFZGFIvKkiHRK8x7VtYU/5KNOCfdOV3dZtbkwdBfcNx393biZ+q1P4x6h6C/dd4CItBSRh0VkqYisEZE3ReRXad6jTESGiMgCEVkvIrNE5Phc1aHoookXCiKyJTAB2IAF/1TgVuAtEdlDVdekKGIEcDRwFfAlcAnwmojsr6of5k/ytLkSWAhcC3wL7AXcCPQVkQNUtTLF9SOB4Qlpn+dYxlzwe+DdmPNNaVxT6LoDuBholpC2P3A38GIa14+kcPS3E3AiMBOYAvSvJl+N9SIi52H1vQ14EzgEuF9ERFUfyEktkpNO3QYCuwP3ArOB7YDrgfdEZE9V/SaN+3wEXJCQtqCGMmdCurqDGra5EHUH6dXvYSCxU9EkSEvnuwjh6C/lO0BEBKtDJ+Ay4CdgCPYe3FNVv01xj1uC+1yHPcOBwDMi8mtVfTnrGqiqHzU4gMuBCmCnmLRO2AvyihTXdsMMorNi0uoDc4EXw65bIE+bJGmnB3L3S3GtAreGXYcUMvYJ5Dw0w+sKXnebkX0EZpC3Kib9AWUx/58byNcxV3oJ8v0IPJaQ/giwFGgQct2SfRc7AJXAzWncYyLw30LVXTZtLkzdZVK/JNedFuQ9ulD1l847ADg2OO8bk6c5sBy4N0X52wS/RzclpI8HPspFHXyKquYMAN5R1S8iCar6FTAVU3qqa8uB0THXbgL+BRwuIo1yL25mqOqSJMmRkY7talOWAqPgdZcMEdkCOAF4SVWXhy1PJmjq0ULITi/7A22AUQnpTwBbA70zEjgD0qlbsu+iqn4NLKHAv4tp6i4bQtMdZFW/M4DFwGs5FCenpPkOGAAsUtW3Yq5bCbxE6vfg4UBDqupuFPCrdKdgN4cbODVnd+CTJOmzga5pXPuVqq5Ncm1DbNizEDk4+PtZGnkvCubD14rIBBE5MJ+CZcGTIlIhIstE5ClJvYaqWHX3W6Ap8Fia+YtFfxGy0cvuwd/E7/Ps4G+q73OtIyK7YT3gdL6LAHuJrRUsF5GPROScPIpXU2rS5opRd9sDfYEnAyM8HQpFf4nvgM29B9uLyFabKWt3bATni4T0nOnO1+DUnFbYfGMiy4GWWVwb+bygEJHtgJuBN1X1vRTZRwH/ARZhQ+lXARNE5DBVnZhXQdNnJXAXMAlYhc0vXwu8LSJ7qeqP1VxXdLoLOB0byn8ljbzFoL9EstFL5LPE6wtSpyJSH3gQG8EZkcYlk4EnsfUsLbC28LCItFPVW/MmaGbUtM0Vle4CTsMGF9LtbBSE/qp5B7Qi+VqgyPNvCfxcTZGtgBUazEsluTZr3bmBkx2JigGQNK6TLK6tdQIr/AVsfdFZqfKr6mkxp1NE5AXMyr+VPA8Zp4uqfgB8EJM0SUQmAzOwhcf/U82lRaU7ABHZFjgU+Hs6PcZi0F8SstFLJE+y6wuRYcAB2PqNZEZdHKr654SkF0TkeeA6EblHVat7AdUaWbS5YtMdmIHygap+lE7mQtDfZt4B2X7v8vpb6lNUNecnkluYLUnek4xl+WaujXxeEIhIY2yVfGfgcE29Kr4KqroaGAfsk2Pxcoqqvo/1kjYnZ9HoLoZTyazHGEeR6C8bvVTXY2yV8HnoiMhtwPnA2ar6ehZFPQ00BtLazlvbZNDmikZ3ACLSE9iVGn4XY6g1/aV4B6T63m3uXbgcaBnsxEp2bda6cwOn5swmOv8bS1fg0zSu7RRsNU+8diNV5yRDQUQaAGOAnsBRqvpxNsVRHL2sVHIWhe4SOB2Ypaqzsiij0PWXjV4ic/6J3+fIGoBU3+daQUSuA64BLlfVJ7ItLvhbyDpNp80Vhe5iOAMbBXkqy3JqRX9pvAM29x5cmGJ0aTbQCNgxybWQA925gVNzXgT2E5HOkYTAwVMvUvs2eBFogO1qiVxbHzgJeF1VN+Ra2EwRkTJs3vcQ4FhVfSeLspph/kmm50i8vCAiewM7s3k5C153sQR12p0seoxFor9s9PI2tqX4lIT0U7Fe5NTcipo5IvJ7bLrmOlW9LwdFDgLWAdl0WvJGBm2u4HUXQUQaYn5eXq5mh1Im5F1/ab4DXgS2E5GDY65rBhxD6vfgq1jnI5nuPgl2JWeFr8GpOQ8Bl2Lzof+DWdK3AN8Q46xKRDoA8zF/FTcDqOqHIjIauCewkL8CLsL86CQqOyz+gb0s/gKsEZH9Yj77VlW/TVY3EbkS2AV4i+iCwSuBthRO3RCRJ7Hn/j6wAltkPAT4DrgvyFOsuovldKrpMRaT/kTkd8G/PYK/R4rIEmCJqk7KRC8i8gXwtaoeAqCq5SJyPeYc7jvMWVw/4GzgMlXdGGbdRGQgcA/2QpiQ8F1cpaqfxpQVV7dgJ9I1wHPYYtDm2CjCAOAaTe2QNGvSqF/aba7QdBfItNn6xWT9NTadU21no8D0l/IdgBkxbwOjROQqoo7+BPhrbGEisgnzV3QOgKr+KCJ/A4aIyGrst/gkTH+ptpinRy6c6dTVA2iPDd+tAlYDY6nqpKsjZvzcmJC+BeZV9gdgPdZT6RN2nWLkWxDIney4sbq6YZb7VKxXVQ4sw74EPcOuU0L9hmDeQVcGcn4D/BNoV+y6i5GzAbbT5qVqPi8a/W2mLU7MVC9B256YJP0CbA3WBmAecHEh1A3z8Juy/snqhm2PfwUz3DdgO1qmAScXiu4yaXOFprt022aQ74Wgbg03U1bB6I803gFBvlaYY8XlwFrMUV+3ap7TyIS0etiGjq+D+n0E/C5XdZDgJo7jOI7jOCWDr8FxHMdxHKfkcAPHcRzHcZySww0cx3Ecx3FKDjdwHMdxHMcpOdzAcRzHcRyn5HADx3Ecx3GcksMNHMdxqkVEzhQRFZE+YcuSikKSVUReCQIi1uTaJ0VkUuqcjuNsDjdwHMcpGkSko4jcKCJ7hi1LdYjIIcDhwE01LOJWoLeIHJM7qRyn7uEGjuM4xURH4AYgmYHzBObNeHJtCpSE/wGmqOqHNblYVT/DQg5cl1OpHKeO4QaO4zglgapWqOp6Va0MSwYR2QXoA4zKsqgngX1FZI+shXKcOoobOI7jZIyIdBGR0SKyVETWi8hsERksIpIk764i8pSIfC8iG0RkoYg8ISLbxeS5WETGB3k2isgCEblbRJrE5DkTC8gI8Giw3kZFZGTk82RrcNKVVUQmBnnaBvKuEJGfRWSsiGyb5qOJBF58JaHswYFslySk7xPU99mEciLX/w7HcWqERxN3HCcjRGRH4B2gMTAMC1R6LBbochfgwpi8+wOvY4H2HgLmYlGij8ICCX4XZP0jFnDxFWAN0Au4HNgDODTIMxkYClyLBUadEqTPz4WsAQ2BCVhk4yFAV+BioClwSKpnAxwILFaLtBzLPUB/4E4Rmaiqs0VkKyzK+w/AebGZVXWJiHwFHJzGPR3HSUZtRVz1ww8/iu8AzsSMkz4xaaODtINj0sqwaMkK9AjSBPgMWA3smKRsifl/yySf3xCUt29MWp8g7cxcyhqkTwzS/pxQ7n1B+q5pPK+vganVfPYLYDEwC2gEPAZUxMqWkP8NYGnYbcAPP4r18Ckqx3HSRkTqAUcD01T1/7cyq617uSM4PTb4uxewKzBcVauMsqiqxvy/NlK+iLQQkdZEp6N61oKssdybcB6RY6c0btsG+CnZB6q6GDgLG5WaAJwO3B4rWwLLgFZBPRzHyRA3cBzHyYQ2QBPg0ySfRdI6BX+7BH9npSpURI4QkWnAOsxAWAJEXvwta0HWCCtUdUVC2vLg79Zp3FOxkavkH6q+DDwMHADMxEapqqMsKM9xnBrga3Acx6kJyV68upnPqkVE9gPGYdNZg7FpnvXAdsBIsu+IZSJrxWbKqdZwiWEJmzHIgkXTkXU1O2BG0+JqsrcEflLVzcnkOE41+AiO4ziZsARbBNw1yWeRtAXB38+Dv6m2Op+E/Rb9WlX/oar/UdU3ge+T5M3EeMpE1lzxKZufyroX2BFbQN0c2w1WneG0IzA7t+I5Tt3BDRzHcdImGE0YB/QSkQMi6cFL+k/B6QvB3w+BOcAFIpI4FUTMiz0yQiExn5VhO6sS+Tn4m3LaKkNZc8VkoI2IdEz8QESOB84G/ldV78V2aR0JXJYkbxts+ixsp4WOU7S4geM4TqZci62TeU1EbhORS4HXgOOAf6rqTPj/RcTnAvWAD0XkThE5T0SuFZGpwEFBeZEdTeNE5HIRGYxtGW+d5N6fYkbOxSJyvogMFJF9s5U1h4zB6nJEbKKIbI9tbZ8JXB8k3xPIcoeI/CqhnCNjynMcpwa4geM4TkYEO6L2w3zWnA/cBWwPXAFclJB3KrAv5gvnDMwXzQWY75p5QZ4pwMnAJuB24EpgOrbLKPHe64BBwFps+/bTifesqay5QFXnYbuuTomkBaNRj2NbwwepanmQV7Gt7auBp0SkcUxRg4AZWsNwD47jBH4oHMdxnNwgIv2A8UB3Vf2gBtfviq29+Y2qvphr+RynruAGjuM4To4RkZeBjap6XA2uHQW0V9WDUmZ2HKda3MBxHMdxHKfk8DU4juM4juOUHG7gOI7jOI5TcriB4ziO4zhOyeEGjuM4juM4JYcbOI7jOI7jlBxu4DiO4ziOU3K4geM4juM4Tsnxfyu39dvxQ/miAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
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"source": [
"fig = plt.figure(figsize = (8,8))\n",
"\n",
"times = np.arange(5)\n",
"\n",
"n = len(times)\n",
"\n",
"for t in times:\n",
" plt.subplot(n, 1, t+1)\n",
" y = np.sin(x + t)\n",
" plt.plot(x, y, 'b')\n",
" plt.plot(x[25], y [25], 'ro')\n",
" plt.ylim(-1.1, 1.1)\n",
" plt.ylabel('y')\n",
" plt.title(f't = {t}')\n",
"\n",
"plt.xlabel('location (x)')\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
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"source": [
"## Characteristics of a wave\n",
"\n",
"We can see waves can be a continuous entity both in time and space. But in reality, many times we discrete the time and space at various points. For example, we can use sensors such as accelerometers (can measure the acceleration of a movement) at different locations on the Earth to monitor the earthquakes, which is spatial discretization. Similarly, these sensors usually record the data at certain times which is a temporal discretization. For a single wave, it has different characteristics. See the following two figures. \n",
"\n",
" \n",
"\n",
" \n",
"\n",
"**Amplitude** is used to describe the difference between the maximum values to the baseline value (see the above figures). A sine wave is a periodic signal, which means it repeats itself after certain time, which can be measured by **period**. Period of a wave is time it takes to finish the complete cycle, in the figure, we can see that the period can be measured from the two adjacent peaks. **Wavelength** measures the distance between two successive crests or troughs of a wave. **Frequency** describes the number of waves that pass a fixed place in a given amount of time. Frequency can be measured by how many cycles pass within 1 second. Therefore, the unit of frequency is cycles/second, or more commonly used **Hertz** (abbreviated **Hz**). Frequency is different from period, but they are related to each other. Frequency refers to how often something happens while period refers to the time it takes to complete something, mathematically, \n",
"\n",
"$$period = \\frac{1}{frequency}$$\n",
"\n",
"From the two figures, we can also see that blue dots on the sine waves, these are the discretization points we did both in time and space. Therefore, only at these dots, we have sampled the value of the wave. Usually when we record a wave, we need to specify how often we sample the wave in time, this is called **sampling**. And this rate is called **sampling rate**, with the unit Hz. For example, if we sample a wave at 2 Hz, it means that every second we sample two data points. Since we understand more about the basics about a wave, now let's see a sine wave more carefully. A sine wave can be represented by the following equation:\n",
"\n",
"$$ y(t) = Asin(\\omega{t}+\\phi)$$\n",
"\n",
"where $A$ is the amplitude of the wave, $\\omega$ is the **angular frequency**, which specifies how many cycles occur in a second, in radians per second. $\\phi$ is the **phase** of the signal. If $T$ is the period of the wave, and $f$ is the frequency of the wave, then $\\omega$ has the following relationship to them:\n",
"\n",
"$$\\omega = \\frac{2\\pi}{T} = 2\\pi{f}$$\n",
"\n",
"**TRY IT!** Generate two sine waves with time between 0 and 1 seconds and frequency is 5 Hz and 10 Hz, all sampled at 100 Hz. Plot the two waves and see the difference. Count how many cycles in the 1 second. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
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"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# sampling rate\n",
"sr = 100.0\n",
"# sampling interval\n",
"ts = 1.0/sr\n",
"t = np.arange(0,1,ts)\n",
"\n",
"# frequency of the signal\n",
"freq = 5 \n",
"y = np.sin(2*np.pi*freq*t)\n",
"\n",
"plt.figure(figsize = (8, 8))\n",
"plt.subplot(211)\n",
"plt.plot(t, y, 'b')\n",
"plt.ylabel('Amplitude')\n",
"\n",
"freq = 10 \n",
"y = np.sin(2*np.pi*freq*t)\n",
"\n",
"plt.subplot(212)\n",
"plt.plot(t, y, 'b')\n",
"plt.ylabel('Amplitude')\n",
"\n",
"plt.xlabel('Time (s)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
}
},
"source": [
"**TRY IT!** Generate two sine waves with time between 0 and 1 seconds. Both waves have frequency 5 Hz and sampled at 100 Hz, but the phase at 0 and 10, respectively. Also the amplitude of the two waves are 5 and 10. Plot the two waves and see the difference."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# frequency of the signal\n",
"freq = 5 \n",
"y = 5*np.sin(2*np.pi*freq*t)\n",
"\n",
"plt.figure(figsize = (8, 8))\n",
"plt.subplot(211)\n",
"plt.plot(t, y, 'b')\n",
"plt.ylabel('Amplitude')\n",
"\n",
"y = 10*np.sin(2*np.pi*freq*t + 10)\n",
"\n",
"plt.subplot(212)\n",
"plt.plot(t, y, 'b')\n",
"plt.ylabel('Amplitude')\n",
"\n",
"plt.xlabel('Time (s)')\n",
"plt.show()"
]
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"< [CHAPTER 24. Fourier Transforms](chapter24.00-Fourier-Transforms.ipynb) | [Contents](Index.ipynb) | [24.2 Discrete Fourier Transform (DFT)](chapter24.02-Discrete-Fourier-Transform.ipynb) >"
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