{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Building an alternating current sine wave in Python\n",
"### Experimenting with wave properties amplitude, wavelength, and frequency "
]
},
{
"attachments": {
"1200px-Types_of_current-2.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"![1200px-Types_of_current-2.png](attachment:1200px-Types_of_current-2.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Figure 1) In this lesson, we'll be seeing how sine waves represent periodic oscillations, like the green alternating current above. Today's example represents AC current, so the X coordinate is time (t), and the y coordinate is current (i) or voltage (v). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The sine function is a trigonometric function of an angle. Let a line through the origin intersect the unit circle, making an angle of θ with the positive half of the x-axis. The x- and y-coordinates of this point of intersection are equal to cos(θ) and sin(θ), respectively. Remember the unit circle is a circle with a radius of one, and sine and cosine are defined in terms of periodic movement around the circle."
]
},
{
"attachments": {
"Sine.jpg": {
"image/jpeg": 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}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"![Sine.jpg](attachment:Sine.jpg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Look what happens if we animate our sine function at each point in the circle below. We have a sine wave! "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Given what you know about the sine function, what do you think the AMPLITUDE of the wave generated by the sine function is??"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, both cosine and sine waves are periodic, which means that after a certain time, the period, they look the same again. Also, both waves look alike, but the cosine wave appears to start at its maximum, while the sine wave starts at zero. Now in practice, how can we tell whether a wave we observe at a given time started out at its maximum, or at zero? Good question: we can’t. There’s no way to discern a sine wave and a cosine wave in practice, thus we call any wave that looks like a sine or cosine wave a “sinusoid”, which is Greek and translates to “sinus-like”. An important property of sinusoids is “frequency”, which tells us how many peaks and valleys we can count in a given period of time. High frequency means many peaks and valleys, low frequency means few peaks and valleys"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that you know what a sine function is, and how a sine wave represents, let's code one out in Python. Use the np.arange function to choose your sample size (from 0 to 10) and 0.1 your frequency. You can play around with these numbers in the binder too. Amplitude of the sine wave is sine of a variable. We'll use time, which you'll notice we just used in the [In] above. If we were making a sine wave to represent an image instead of alternating current, the x axis variable might be \"space\" for both the line above and this one. Note: Since the sine function varies from +1 to -1, the amplitude is one."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To get started, we'll use an import statement to call two modules, numpy and matplotlib, that will let us build the sine wave."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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P+fjVU+kfMPx+X+D1slTjs/FIHZ29du5b6h9XA0PWFqYTHRbMswFwZayJwAW99gFePFhNcX4aCVGhVofjVrNSYliak8Cze87qDGbqsp7bc5ZZKdEUTZtidShuFRkazJ2LMthYUuf3M5hpInDB9rIGWrv6ufcq/7oaGPLxq6dy9nxXwPWyVGN3rL6DA2dbufeqbK8faXci7ls6lT67g5cO1lgdyqTSROCC5/eeIzM+gutmJlkdyqRYXTB4paM3jdWlPLvnLKFBNu5e7Ju96a8kPyOOwqw4nt1z1q9vGmsimKBzzjPlj16V7TOjjI5XWHAQdy/KZGdFAy1601iN0NM/wEsHa/58wuCv7ls6leMNnez345vGmggm6IV957AJfHiJf54JDfnQkizsDsOGw5caUFYFqq2l9bR193PvUv8sjQ65ozCDyNAgv244oYlgAgYcg61pbpqdTEZ8hNXhTKp56bEUZMbyh/3++yVQE/OH/dVkJ0SwLMe7p2N1VVRYMLcVpLOppI7uPv+ctEYTwQT86UQT9e09fKTIv8+Ehnx4cRZlte2U17ZbHYryEnVt3ew+2czdi7L8tjQ63IeWZNLZa2d7eb3VoUwKTQQT8NLBGuIiQrh1nn/0JL6SdQszCQmSgJy5SY3upYM1GAN3Lx51Vlq/sywnkcz4CL+9MtZEME6dvXa2ldWzdkE6YcFBVofjEQlRoSyfm8rLB2voH3BYHY6ymDGGFw/UcNX0KUxLjLI6HI+w2YS7F2eyu7KZ+rYeq8NxO7ckAhFZLSLHRKRSRB4bZf3NItImIoecP98Y677eZktJHT39Dr9tLncpH16SRcvFPt441mR1KMpiR6rbqGzsDLjvwN2Ls3AY/LJPgcuJQESCgCcYnHw+D7hPRPJG2fRPxpiFzp9/Gee+XuPFAzVMT4xk8dR4q0PxqJvmJJMUHcof9gfGaIzq0l48UE1osI0189OtDsWjcpKiWDJtCi8eqPa7PgXuuCJYClQaY6qMMX3Ac8B6D+zrcTWt3bx3qoW7FmX5ZS/KywkJsrF+YSavHW2krSswxmhXH9Rnd7DhcC3FeanERfjPAHNj9aHFWZxo7KSkps3qUNzKHYkgExh+mljtXDbSNSJyWES2iEj+OPf1Ci87b5DdtchrQ5xUdy7MpH/AsKW0zupQlEVeP9bIha5+PhRgZaEhty9IJzTYxosH/Ks85I5EMNqp8cjrpgPANGNMIfAj4OVx7Du4ochDIrJPRPY1NXm+Tm2M4aWDgzfIpiZGevz43qAgM5YZSVG8fMi/vgRq7F4+WENSdCg35PrnsCpXEhcRwvK5KWw8UofdjxpOuCMRVAPDG9RnAX/RDdUY026M6XQ+3wyEiEjSWPYd9h5PGWOKjDFFycnJbgh7fEpr2qls7OSuRYF5JgQgIqxbmMH7p85T19ZtdTjKwzp6+tl1tJHb56cTHBS4DQ7XL8ygubPXr2bwc8dvcy+QKyI5IhIK3AtsGL6BiKSJs6guIkudx20Zy77eYsPhGkKChDXzfXs+VletX5iJMbDxsJaHAs32sgb67A7WLcywOhRL3TwnhZiwYDYc8p9hV1xOBMYYO/AIsA2oAF4wxpSJyMMi8rBzsw8DpSJyGPghcK8ZNOq+rsbkbg6HYeOROm7MTSY+0n8H1xqLnKQoCrPitDwUgF45XEtmfASLp/rXvAPjFR4SxKqCNLaW1tPT7x9DTrjl+s4Ys9kYM9sYM9MY823nsieNMU86n//YGJNvjCk0xiwzxrxzuX29zb4zF6hr6wn4M6Eh6xdmUlbbTmVjh9WhKA9p6exld2Uz6xZmBFyLudGsK8ygo9fuN/1qArfQNw6vHq4lPMTGinmpVofiFdYuSMcm+NWlsbq8zSV1DDgM6wr1ZAjg2pmJJEWHsuGwf1wZayK4AvuAg80ldSyfl0pUWLDV4XiFlNhwrp2ZxCuHa/2uY40a3YbDteSmRDM3LcbqULxCcJCNtQsy2FXRSEeP7/er0URwBe+cbKHlYh93LNAzoeHWFWZwpqWL0hodkdTf1bR2s/f0BdYVallouDsKM+i1O9he1mB1KC7TRHAFrx6uJSYsmJvneL7Jqjcrzk8l2CZsLNHykL/b6JyU6A4tC/2FxVPjyZoSwatHfP87oIngMnrtA2wtq6c4P43wkMAYaXSs4iNDuT43iU1H6rQ85Oc2HqljQVYc05MCY6TRsRIRbp+fztsnmn1+2BVNBJfx5rEmOnrs3FEYWINrjdXt89OpvtDN4Wr/GndF/a+zLV2U1LRxe4ANMDdWty9Ix+4wbPPxCWs0EVzGltJ64iNDuG5WYHanv5LivDRCgoRNfnBprEa32TmuVKCNNDpW8zPjyE6IYNMR3+5gqYngEnrtA+wsb6A4L5WQAO5OfzlxkSHckJus5SE/tulIHYVZcWQnBOb4WlciIqyZn87uymZau/qsDmfC9C/cJfzpeDMdvXY9E7qCtQvSqW3r4eC5VqtDUW7257LQAv0OXM7a+RnYHcanWw9pIriEzSV1xIYHc+1MLQtdzoq8VEKDbD5/aaw+aKgsdFuBJoLLKciMJTshgo0lvvsd0EQwil77ADsqGijOTyM0WP+JLic2PIQbZw+WhxwOLQ/5Ey0Ljc1g66EM3qls5sJF3ywP6V+5UeyubKajx64tJcbo9gVp1LdrecifaFlofG6fP9h6aLuPth7SRDCKTUfqiQkP1tZCY3Tr3FRCgoStOnOZ39Cy0PgUZMYyNSGSTSWaCPxCn93BjvJ6VualallojOIiBpvYbimt19ZDfmJLiZaFxkNEuK0gjXcqfbNzmf6lG2H3yWbatSw0brcVpFF9oZuyWh17yNfVtA52ElytVwPjsrogDbvDsLPC91oPaSIYYWtJPdFhwVwfoHOyTtTKvDSCbKIT2/uBraWD5Y3VBYE9G994FWbFkx4XztYy3ysPuSURiMhqETkmIpUi8tgo6z8uIkecP++ISOGwdadFpEREDonIPnfEM1H2AQc7Khq4dW4KYcE6ttB4JESFcnVOgpaH/MC20nrmpsWQo2MLjYvNJqzKT+Ot401c7LVbHc64uJwIRCQIeAK4DcgD7hORvBGbnQJuMsYsAL4FPDVi/S3GmIXGmCJX43HF3tMXOH+xj9v0TGhCbitIo6rpIicaO60ORU1QY0cPe8+c16uBCVpdkEav3cHrxxqtDmVc3HFFsBSoNMZUGWP6gOeA9cM3MMa8Y4y54Hz5HpDlhuO63bayesKCbdykQ05PyKr8NERgi4+2nFCwo7wBY7QsNFFXTU8gKTqULaW+9R1wRyLIBM4Ne13tXHYpnwG2DHttgO0isl9EHrrUTiLykIjsE5F9TU3unyfU4TBsLa3nptnJRIbqTGQTkRIbzpKpU/Q+gQ/bWlpPTlIUc1J1JrKJCLIJK/PSeP1oo09NbO+ORDDalEWjFolF5BYGE8FXhi2+zhizmMHS0udE5MbR9jXGPGWMKTLGFCUnu/+M/XB1K/XtPXom5KLVBWkcre/gdPNFq0NR49Ta1ce7J1ucV3Y6E9lE3VaQRlffAH860Wx1KGPmjkRQDWQPe50FfGBcYhFZAPwcWG+MaRlaboypdT42Ai8xWGryuK1l9QTbhOVzdYJ6V6zKH0yk23yw5USg21nRiN1h9B6Zi66ZmUhseLBPXRm7IxHsBXJFJEdEQoF7gQ3DNxCRqcCLwAPGmOPDlkeJSMzQc6AYKHVDTONijGFbaT3XzkoiLjLE04f3K9kJkeRnxGoi8EFbS+vJiAtnQVac1aH4tJAgGyvyUtlV0Uj/gMPqcMbE5URgjLEDjwDbgArgBWNMmYg8LCIPOzf7BpAI/GREM9FU4G0ROQzsATYZY7a6GtN4HWvo4HRLF6vz9UzIHVblp3HgbCuN7T1Wh6LG6GKvnbdONFGsZSG3WJWfRlt3P3tOnbc6lDFxy11RY8xmYPOIZU8Oe/5XwF+Nsl8VUDhyuadtLa1HBFbmaVnIHVblp/FfO46zvbyB+5dNszocNQZvHW+iz+6gOF+/A+5wY24y4SE2tpXV+8SYZdqzGNhW1kDRtCkkx4RZHYpfmJ0aTU5SlJaHfMi2snqmRIawdHqC1aH4hYjQIG6ancz2sgafGJ494BPBufNdVNS1U5ynZSF3ERGK81N592QLbd2+NwBXoOmzO9h1tJHl81IJ1mlZ3aY4b3B49iM1bVaHckUB/1sfOmvVS2L3WpU/OADX60d9q4dlIHqvqoWOHvufW3wp91g+L4Ugm/jElXHAJ4Lt5Q3MTYthWqKOq+JOC7PiSYkJ+/MAZsp7bS+vJyIkiBt0oEW3io8MZdmMBE0E3q6ls5d9p89TrGdCbmezDZaH3jzeRHef7/SwDDQO56TrN81OJjxEB1p0t1X5g+NvVXr5+FsBnQh2VTTiMLBKy0KTYlV+Gt39A7xd6Ts9LAPNoepWGjt6WVWg34HJMHTv0duvCgI6EWwrqyczPoK89FirQ/FLy2YkEhMezHYv/xIEsm3OHvW3ztFEMBnS4sIpzI73+u9AwCaCi712/lTZrOOqTKKQIBvL56aws6IBu4/0sAwkxhh2lDWwbEai9qifRKvyUzlc3UZ9m/d2sAzYRPCmdqDxiOL8NC509bP/zIUrb6w86mRTJ1XNF7U0OsmGykM7vHgKy4BNBNudHWiKpk2xOhS/duPsZEKDbWwv994vQaDaVjb4O1mhPeon1ayUaGYkRXl1eSggE0H/gIPXjjayQjvQTLrosGCun5XE9nKdwtLbbC9voDArjvS4CKtD8XsrvbyDZUD+Fdxz6jztPXYdW8hDVualcu58N0frO6wORTk1tPdw+Fyrfgc8pDhvsIPlG146hWVAJoLtZfWEh9i4IVenpPSE5fNSEIHtZVoe8hY7nKU67UPjGYuy40mKDvPaEmnAJQJjDNvLG7gxN5mIUO1A4wkpMeEsnjqF7eXeWyMNNNvLG5ieGEluSrTVoQQEm01YmZfKG0cb6bV7XwfLgEsEpTXt1LX16JmQhxXnpVJW2071hS6rQwl47T39vHuyWece8LDi/FQu9g3wzsmWK2/sYQGXCHaU12MTuHVuitWhBJShxLvDSy+NA8kbx5roHzAU6/0Bj7p2ZiJRoUFe+R1wSyIQkdUickxEKkXksVHWi4j80Ln+iIgsHuu+7ra9vIGrpieQEBU62YdSw+QkRZGbEq33CbzA9rJ6kqJDWTRVm057UlhwEDfPTWFHuffNUeByIhCRIOAJ4DYgD7hPRPJGbHYbkOv8eQj46Tj2dZszLRc5Wt+hZSGLrMxLZc/p87R29VkdSsDqtQ/wxrEmls9NJcimZSFPK85Lpamjl0PVrVaH8hfccUWwFKg0xlQZY/qA54D1I7ZZD/zaDHoPiBeR9DHu6zZ/bimhl8SWKM5PY8BheE3nKLDMe1Xn6ey1a496i9w8J4Vgm3jdlbE7EkEmcG7Y62rnsrFsM5Z9ARCRh0Rkn4jsa2pqmlCgvXYHV+ckkJ0QOaH9lWsWZMaRGhvmdV+CQLK9rJ7I0CCfmEfXH8VFhHDNzER2eFkLOnckgtGuL0cWwC61zVj2HVxozFPGmCJjTFFy8sTa/3/ullk8/9fXTGhf5TqbTVgxL5W3TjTR0+99Tej8ncNh2FnR4JxYXZtOW2VlXionvWyOAnckgmoge9jrLKB2jNuMZV/lR4rz0+jqG2C3zlHgcUdq2mho79WykMVWzBv89/em1kPuSAR7gVwRyRGRUOBeYMOIbTYAn3C2HloGtBlj6sa4r/Ij18xIJCYsWMtDFtheVk+QTbTptMUy4iNYkBXnVeUhlxOBMcYOPAJsAyqAF4wxZSLysIg87NxsM1AFVAI/A/72cvu6GpPyXqHBNm6ak8yuow0MeFkTOn+3o7yBq3MSiI/UptNWWzkvlYPnWmls9445CtzSj8AYs9kYM9sYM9MY823nsieNMU86nxtjzOec6+cbY/Zdbl/l34rz02ju7OPAWZ2jwFOqmjo50dipg8x5ieL8NIyBnRXe0YIu4HoWK+vdPCeZkCDxqhqpvxv6t9ZE4B1mp0YzLTHSa8pDmgiUx8WGh3DNzCS2lekcBZ6yo7yB/IxYsqZo02lvICKsnJfK7soWOnvtVoejiUBZozgvlTMtXZzwoiZ0/qqpo5f9Zy/o1YCXKc5Po2/AwZvHJtYvyp00EShLDP1R8ubp+/zFzooGjIFVOrSKV1kybQqJUaFs84LvgCYCZYnU2HAWZsd77UQd/mR7WT3ZCRHMTYuxOhQ1TJCzg+XrRxvpszssjUUTgbJMcX4qR6rbqG3ttjoUv9XZa2d3ZQvFeTr3gDcqzk+lo9fOe1XWzlGgiUBZpjhP5yiYbG8ca6RvwKFlIS913awkIkODLC8PaSJQlpmVEs3M5CidwnISbS9rICEqlCXTdO4BbxQeEsTNc5Itn6NAE4GyVHF+Gu9Vnaetq9/qUPxOn93B60cbWTEvRece8GLFeWk0dvRy2MI5CjQRKEsV56Uy4DDsOqrlIXd7r6qFjl67loW83C3OOQq2WTj+liYCZanCrHhSY8Msr5H6o20694BPiIsMYdmMREtLpJoIlKVsNqE4L403jzfR3adzFLiLw2HYUd7ATbN17gFfsCo/laqmi1Q2dlhyfE0EynKr8tPo6Xfw1gnre1j6i0PVrTR26NwDvmKlswWdVeUhTQTKclfPSCAuIoRtpVoecpdtpfWEBAm3ztVE4AvS4sJZNDWerRZ9BzQRKMuFBNlYPi+FnRUN9A9Y28PSHxhj2FpWz7Uzk4iLCLE6HDVGq/LTKKlpo/pCl8ePrYlAeYXV+Wm099h5v+q81aH4vKP1HZxp6WJ1gbYW8iVDrbusKA+5lAhEJEFEdojICefjB3qtiEi2iLwuIhUiUiYiXxy27psiUiMih5w/a1yJR/muG2cnExESxNayOqtD8XlbS+sR0bkHfE1OUhRz02IsaUHn6hXBY8AuY0wusMv5eiQ78KgxZh6wDPiciOQNW/89Y8xC589mF+NRPmqoh+X2Mmt7WPqDbWX1XDU9gaToMKtDUeNUnJ/G3tPnaero9ehxXU0E64FnnM+fAe4cuYExps4Yc8D5vIPBuYkzXTyu8kOr8gd7WB6ysIelrzvVfJGj9R2s1k5kPmn1n6ew9Gx5yNVEkGqMqYPBP/hAyuU2FpHpwCLg/WGLHxGRIyLy9GilpWH7PiQi+0RkX1OTNjP0R7fMTSEkSCxrOeEPhsoK2mzUN81Lj2FqQqTHvwNXTAQislNESkf5WT+eA4lINPBH4O+MMe3OxT8FZgILgTrgu5fa3xjzlDGmyBhTlJycPJ5DKx8RFxHCdbOS2FJap1NYTtC2snrmZ8bplJQ+SkRYlZ/KOyebaev23PhbV0wExpgVxpiCUX5eARpEJB3A+dg42nuISAiDSeC3xpgXh713gzFmwBjjAH4GLHXHh1K+a01BOufOd1NW237ljdVfqGvr5uDZVlbp1YBPW12QTv+A4TUPjr/lamloA/Cg8/mDwCsjN5DB2TB+AVQYY/5rxLr0YS/vAkpdjEf5uJV5qQTZhC2l2npovIbKCbfNT7/ClsqbLcqOJy02nM0lnisPuZoIHgdWisgJYKXzNSKSISJDLYCuAx4Abh2lmeh/iEiJiBwBbgG+5GI8ysdNiQrlmhmJbC6p1/LQOG0pqWduWgwzk6OtDkW5wGYTVhcMjr/V2Wv3zDFd2dkY02KMWW6MyXU+nncurzXGrHE+f9sYI8aYBSObiRpjHjDGzHeuWzd041kFttUFaZxqvsixBmsG4PJFje097D1zntsK9GrAH6yZn06f3cFrR0ettrud9ixWXmdVfhoig2e4amy2ltVjDKyZr81G/cGSaVNIjgljS4lnzo01ESivkxwTxlXTE/Q+wThsLqkjNyWa3NQYq0NRbhBkE1bnp/H6sUa6+ia/PKSJQHmlNQVpHG/opLKx0+pQvF5TRy97Tp3Xm8R+Zs38dHr6HbxxbPL7TWkiUF5ptbPW7alLY1+2raweh5aF/M7SnAQSo0LZ7IHvgCYC5ZXS4sIpmjaFTZoIrmhLaR0zkqOYo2UhvxJkE1YVpPHa0UZ6+id39j5NBMpr3b4gnaP1HZZN3+cLWjp7ea/qPGsK0hnssqP8yZqCdLr6Bnjj2OS2HtJEoLzWmvnpiMCrh/Wq4FK2ltUz4DCs0fsDfmnZjMHy0KtHJvc7oIlAea3U2HCWTk9gU4mOPXQprx6uZWZyFPPStSzkj4KDbKyZn86uigYuTmLnMk0EyqutLcygsrFTO5eNoqG9h/dPnWftggwtC/mxtQsGWw/tmsTOZZoIlFdbnZ+GTWCjloc+YHNJHcbAHYVaFvJnV01PIDU2jFcP107aMTQRKK+WHBPGNTMT2XikVstDI7x6uJZ56bHMStGykD+z2YTb52fw5rEm2nsmZ2hqTQTK661dkMHpli4dmnqYc+e7OHC2lbUL9GogEKwtTKdvwMGOSZrYXhOB8nqr89MIsgmvHpm8S2NfM9S/4o4FGRZHojxhUXY8mfERk/Yd0ESgvN6UqFBuyE3i1UO1OrG908YjtRRmxzM1UWciCwQiwtrCdN4+0cyFi31uf39NBMon3Lkwk9q2HvaePm91KJarauqktKadO7QsFFDuWJDBgDHsmYTvgEuJQEQSRGSHiJxwPo46+byInHZOQHNIRPaNd3+livNTiQwN4uVDWh565VAtIoM9r1XgyM+I5b2vLmdVvvvHlHL1iuAxYJcxJhfY5Xx9Kbc4J6UpmuD+KoBFhgZTnJfKpiO19Nond9wVb2aM4eVDNVw7M5H0uAirw1EeJCKkxoZPynu7mgjWA884nz8D3Onh/VUAWb8ok/Yeu0eG5fVWB862cqalizsXZlodivIjriaC1KHpJZ2PKZfYzgDbRWS/iDw0gf0RkYdEZJ+I7GtqCtw/BIHshllJJEaF8sqhGqtDscxLB6sJD7GxukCHnFbuE3ylDURkJzDa/7p/GMdxrjPG1IpICrBDRI4aY94ax/4YY54CngIoKirSpiMBKDjIxtoF6Ty79xztPf3EhodYHZJH9dkdbDxSx8q8NGIC7LOryXXFKwJjzApjTMEoP68ADSKSDuB8HHUwDGNMrfOxEXgJWOpcNab9lRqyflEmfXYHWwNwPuM3jzfR2tXP3Yu0LKTcy9XS0AbgQefzB4FXRm4gIlEiEjP0HCgGSse6v1LDLcqOZ1piJC8erLY6FI976WA1iVGhXJ+bZHUoys+4mggeB1aKyAlgpfM1IpIhIpud26QCb4vIYWAPsMkYs/Vy+yt1KSLChxZn8V7Vec62dFkdjse0dfezs6KROwozCAnS7j/Kva54j+ByjDEtwPJRltcCa5zPq4DC8eyv1OV8aEkW39t5nD8cqObLK2dbHY5HbC6po8/u4O7FWhZS7qenFsrnZMZHcP2sJP64vzpghpx4fu855qTGMD8zzupQlB/SRKB80oeXZFHT2s27VS1WhzLpjjd0cOhcK/cUZekENGpSaCJQPmlVfhox4cH8ft85q0OZdM/vPUdIkHD34iyrQ1F+ShOB8knhIUGsK8xgS2n9pE3W4Q367A5eOljDyrxUEqJCrQ5H+SlNBMpn3VOUTa/d4dfTWO6saOD8xT7uKcq2OhTlxzQRKJ9VmBXH7NRonvfj8tDze8+RHhfOjbnJVoei/JgmAuWzRIT7lk7l8LlWSmvarA7H7Wpbu3nrRBMfXpJFkE1vEqvJo4lA+bS7F2cRHmLjt++fsToUt3th3zmMGWwhpdRk0kSgfFpcRAjrCjN4+WCtX9007h9w8Lv3z3LT7GSmJUZZHY7yc5oIlM+7f9k0uvsHeOmA/wxPvb2sgcaOXj5xzTSrQ1EBQBOB8nkLsuJZkBXHb947gzH+0dP41++eJmtKBDfPueQUHUq5jSYC5Rfuv3oaJxo72XPK9ye3P1bfwfunznP/sml6k1h5hCYC5RfuKMwgNjyY37x/1upQXPY/750mNNjGR7TvgPIQTQTKL0SEBnFPUTZbSuqoa+u2OpwJa+/p58UDNawrzNCexMpjNBEov/HJa6djgF/tPm11KBP2x/3VdPUN6E1i5VGaCJTfyE6I5LaCNH73/lk6fLApqX3AwS/ePsWSaVNYkBVvdTgqgLiUCEQkQUR2iMgJ5+OUUbaZIyKHhv20i8jfOdd9U0Rqhq1b40o8Sn32hhl09Np5fq/vDTuxqaSO6gvdPHzTTKtDUQHG1SuCx4BdxphcYJfz9V8wxhwzxiw0xiwElgBdDE5gP+R7Q+uNMZtH7q/UeBRmx7N0egK/3H0a+4DD6nDGzBjDk29WMSslmuVztcmo8ixXE8F64Bnn82eAO6+w/XLgpDHG/8YDUF7jszfOoKa1m82l9VaHMmZ/OtFMRV07D904A5s2GVUe5moiSDXG1AE4H690KnMv8OyIZY+IyBEReXq00tIQEXlIRPaJyL6mpibXolZ+bfncFGYkRfGzt6p8poPZk2+eJDU2jPULM6wORQWgKyYCEdkpIqWj/Kwfz4FEJBRYB/x+2OKfAjOBhUAd8N1L7W+MecoYU2SMKUpO1iF51aXZbMJf3zSDkpo2XjvaaHU4V3SkupV3TrbwmetzCAsOsjocFYCumAiMMSuMMQWj/LwCNIhIOoDz8XLfutuAA8aYhmHv3WCMGTDGOICfAUtd+zhKDbp7cRZTEyL5/s4TXn9V8OPXKokJD+a+pVOtDkUFKFdLQxuAB53PHwReucy29zGiLDSURJzuAkpdjEcpAEKCbHz+1lmU1LSxs8J7rwoOnWtle3kDn71hBjHhIVaHowKUq4ngcWCliJwAVjpfIyIZIvLnFkAiEulc/+KI/f9DREpE5AhwC/AlF+NR6s/uWpTJ9MRIvrfjuNdeFfzntmMkRIXy6etzrA5FBbBgV3Y2xrQw2BJo5PJaYM2w111A4ijbPeDK8ZW6nOAgG19YnsuXXzjMtrIGVhekWR3SX3inspm3K5v5x9vnER3m0ldRKZdoz2Ll19YVZjAjOYrv7zzOgMN7rgqMMXxn+zHS48K5f5kOJ6GspYlA+bXgIBuPrpzD0foOr+pt/NrRRg6ebeXzt+YSHqIthZS1NBEov7dmfhpX5yTwnW1HaeuyfgyiXvsA395cwfTESO4p0vmIlfU0ESi/JyL80x35tHX3872dx60Oh5//6RRVTRf5p3X5hATpV1BZT/8XqoCQlxHLx66eyv+8d4Zj9R2WxXHufBc/eu0Eq/PTuEWnoVReQhOBChiPrpxDdFgw//xqmWXNSf/51XIE4Rt35FlyfKVGo4lABYwpUaH8ffFs3jnZwnMW3DjeVdHAzooGvrgil4z4CI8fX6lL0USgAsrHr57GdbMS+dbGck43X/TYcc9f7ONrL5WQmxLNp6/TzmPKu2giUAHFZhP+855Cgm3Cl1445JE5C4wx/P3vD3PhYj/f++hCQoP1a6e8i/6PVAEnPS6Cf71rPgfPtvKTN05O+vGe3n2a14428rU1cynIjJv04yk1XpoIVEBaV5jBusIMfrDrBG+faJ6045RUt/H4lgpWzEvlwWunT9pxlHKFJgIVsL59VwG5KdE8/Jv9VNS1u/39a1u7efg3+0mKDuM7H16AiM48pryTJgIVsGLCQ/jlp64iOiyYT/1yL3Vt3W577+bOXu7/xfu0d/fzs08UMSUq1G3vrZS7aSJQAS09LoJfffoqLvba+dQv99LS2evye7Z19/OJX+yhtrWbpz91ld4XUF5PE4EKeHPTYnnygSWcar7I+id2u9TzuLa1m0/84n1ONHbw5P1LuGp6ghsjVWpyaCJQCrhuVhIv/PU19Nkd3P2T3eyqaLjyTiO8cayR23/4JyobO3niY4u5WYeQUD7CpUQgIveISJmIOESk6DLbrRaRYyJSKSKPDVueICI7ROSE83GKK/Eo5YrC7Hg2PHI9M5Kj+atf7+PLzx/ibEvXFfdr7uzl25vK+eQv95IaG86rn7+e4nzvmgRHqcsRV8ZcEZF5gAP4b+DvjTH7RtkmCDjO4FSV1cBe4D5jTLmI/Adw3hjzuDNBTDHGfOVKxy0qKjL79n3gUEq5RXffAN/feZxfvXOaAYfhnqJsivNTmZ8ZR1J0GMYY2rvtnGzu5Lk9Z3n5UC19dgf3XpXNN9fl6/wCymuJyH5jzAdO2l2dqrLC+eaX22wpUGmMqXJu+xywHih3Pt7s3O4Z4A3giolAqckUERrEV9fM4zPX5/Dj1yt5ds9Znt1zFoDkmDC6+wbo7LUDEB5i4yNFWXzquhxmJkdbGbZSE+aJiVIzgeEjfFUDVzufpxpj6gCMMXUicsmiqog8BDwEMHXq1EkKVan/lRIbzr+sL+D/rJpDWW07JdVtHK3vICY8mMz4CDKnRHDtzETiI7VpqPJtV0wEIrITGK3g+Q/GmFfGcIzRLhfGXY8yxjwFPAWDpaHx7q/URMWEh7BsRiLLZiRaHYpSk+KKicAYs8LFY1QD2cNeZwG1zucNIpLuvBpIBxpdPJZSSqlx8kTz0b1ArojkiEgocC+wwbluA/Cg8/mDwFiuMJRSSrmRq81H7xKRauAaYJOIbHMuzxCRzQDGGDvwCLANqABeMMaUOd/icWCliJxgsFXR467Eo5RSavxcaj5qFW0+qpRS43ep5qPas1gppQKcJgKllApwmgiUUirAaSJQSqkA55M3i0WkCTgzwd2TgMmbm9B7BeLnDsTPDIH5uQPxM8P4P/c0Y0zyyIU+mQhcISL7Rrtr7u8C8XMH4meGwPzcgfiZwX2fW0tDSikV4DQRKKVUgAvERPCU1QFYJBA/dyB+ZgjMzx2Inxnc9LkD7h6BUkqpvxSIVwRKKaWG0USglFIBLqASgYisFpFjIlLpnCPZr4lItoi8LiIVIlImIl+0OiZPEZEgETkoIhutjsVTRCReRP4gIkedv/NrrI7JE0TkS87/36Ui8qyIhFsdk7uJyNMi0igipcOWJYjIDhE54XycMtH3D5hEICJBwBPAbUAecJ+I5Fkb1aSzA48aY+YBy4DPBcBnHvJFBoc9DyQ/ALYaY+YChQTA5xeRTOALQJExpgAIYnDOE3/zK2D1iGWPAbuMMbnALufrCQmYRAAsBSqNMVXGmD7gOWC9xTFNKmNMnTHmgPN5B4N/GDKtjWryiUgWcDvwc6tj8RQRiQVuBH4BYIzpM8a0WhqU5wQDESISDETyvzMg+g1jzFvA+RGL1wPPOJ8/A9w50fcPpESQCZwb9rqaAPijOEREpgOLgPctDsUTvg/8X8BhcRyeNANoAn7pLIn9XESirA5qshljaoD/BM4CdUCbMWa7tVF5TKoxpg4GT/qAlIm+USAlAhllWUC0nRWRaOCPwN8ZY9qtjmcyichaoNEYs9/qWDwsGFgM/NQYswi4iAulAl/hrIuvB3KADCBKRO63NirfE0iJoBrIHvY6Cz+8hBxJREIYTAK/Nca8aHU8HnAdsE5ETjNY/rtVRH5jbUgeUQ1UG2OGrvj+wGBi8HcrgFPGmCZjTD/wInCtxTF5SoOIpAM4Hxsn+kaBlAj2ArkikiMioQzeUNpgcUyTSkSEwZpxhTHmv6yOxxOMMV81xmQZY6Yz+Dt+zRjj92eIxph64JyIzHEuWg6UWxiSp5wFlolIpPP/+3IC4Ca50wbgQefzB4FXJvpGwW4JxwcYY+wi8giwjcGWBU8bY8osDmuyXQc8AJSIyCHnsq8ZYzZbF5KaRJ8Hfus80akCPmVxPJPOGPO+iPwBOMBgK7mD+OFwEyLyLHAzkCQi1cA/AY8DL4jIZxhMiPdM+P11iAmllApsgVQaUkopNQpNBEopFeA0ESilVIDTRKCUUgFOE4FSSgU4TQRKKRXgNBEopVSA+//xwZkd3KSZ0QAAAABJRU5ErkJggg==\n",
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