"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"make_video(M - low_rank, dims, \"figures2\")"
]
},
{
"cell_type": "code",
"execution_count": 554,
"metadata": {
"hidden": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████▉| 600/601 [00:00<00:00, 858.48it/s]\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 554,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mpe.VideoFileClip(\"videos/figures2.mp4\").subclip(0,10).ipython_display(width=300)"
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true
},
"source": [
"### Speed of SVD for different size matrices"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"import timeit\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"m_array = np.array([100, int(1e3), int(1e4)])\n",
"n_array = np.array([100, int(1e3), int(1e4)])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"index = pd.MultiIndex.from_product([m_array, n_array], names=['# rows', '# cols'])"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"pd.options.display.float_format = '{:,.3f}'.format\n",
"df = pd.DataFrame(index=m_array, columns=n_array)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"# %%prun\n",
"for m in m_array:\n",
" for n in n_array: \n",
" A = np.random.uniform(-40,40,[m,n]) \n",
" t = timeit.timeit('np.linalg.svd(A, full_matrices=False)', number=3, globals=globals())\n",
" df.set_value(m, n, t)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"hidden": true,
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" 100 | \n",
" 1000 | \n",
" 10000 | \n",
"
\n",
" \n",
" \n",
" \n",
" 100 | \n",
" 0.006 | \n",
" 0.009 | \n",
" 0.043 | \n",
"
\n",
" \n",
" 1000 | \n",
" 0.004 | \n",
" 0.259 | \n",
" 0.992 | \n",
"
\n",
" \n",
" 10000 | \n",
" 0.019 | \n",
" 0.984 | \n",
" 218.726 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" 100 1000 10000\n",
"100 0.006 0.009 0.043\n",
"1000 0.004 0.259 0.992\n",
"10000 0.019 0.984 218.726"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df/3"
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true
},
"source": [
"### 2 Backgrounds in 1 Video"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"We'll now use real video 008 dataset from [BMC 2012 Background Models Challenge Dataset](http://bmc.iut-auvergne.com/?page_id=24), in addition to video 003 that we used above."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"video2 = mpe.VideoFileClip(\"videos/Video_008.avi\")"
]
},
{
"cell_type": "code",
"execution_count": 394,
"metadata": {
"hidden": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[MoviePy] >>>> Building video concatenated_video.mp4\n",
"[MoviePy] Writing video concatenated_video.mp4\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████▉| 1600/1601 [00:02<00:00, 751.90it/s] \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[MoviePy] Done.\n",
"[MoviePy] >>>> Video ready: concatenated_video.mp4 \n",
"\n"
]
}
],
"source": [
"from moviepy.editor import concatenate_videoclips\n",
"concat_video = concatenate_videoclips([video2.subclip(0,60), video.subclip(0,100)])\n",
"concat_video.write_videofile(\"concatenated_video.mp4\")"
]
},
{
"cell_type": "code",
"execution_count": 321,
"metadata": {
"hidden": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|█████████▉| 500/501 [00:00<00:00, 563.14it/s]\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 321,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"concat_video.ipython_display(width=300)"
]
},
{
"cell_type": "code",
"execution_count": 395,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"scale = 0.5 # Adjust scale to change resolution of image\n",
"dims = (int(240 * scale), int(320 * scale))"
]
},
{
"cell_type": "code",
"execution_count": 396,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"N = create_data_matrix_from_video(concat_video, fps, scale)\n",
"# N = np.load(\"low_res_traffic_matrix.npy\")"
]
},
{
"cell_type": "code",
"execution_count": 209,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"np.save(\"med_res_concat_video.npy\", N)"
]
},
{
"cell_type": "code",
"execution_count": 385,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
"(19200, 10000)"
]
},
"execution_count": 385,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N.shape"
]
},
{
"cell_type": "code",
"execution_count": 386,
"metadata": {
"hidden": true,
"scrolled": true
},
"outputs": [
{
"data": {
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xJsxn5ubNm4msT8cO92XbPRs7P1X6xXvE62NfqA2XInmOgWVRmWZFRUXFCjgX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\nXgDzMz4wLwwn42WcOs+jcgwu0xlXy20pQXrhhRfwO7/zOwB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uQKcMCEgdZxp15eYBd241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\nWQAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(N[:,200], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 397,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"U_concat, s_concat, V_concat = np.linalg.svd(N, full_matrices=False)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"This is slow, so you may want to save your result to use in the future."
]
},
{
"cell_type": "code",
"execution_count": 329,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"np.save(\"U_concat.npy\", U_concat)\n",
"np.save(\"s_concat.npy\", s_concat)\n",
"np.save(\"V_concat.npy\", V_concat)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"In the future, you can just load what you've saved:"
]
},
{
"cell_type": "code",
"execution_count": 331,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"U_concat = np.load(\"U_concat.npy\")\n",
"s_concat = np.load(\"s_concat.npy\")\n",
"V_concat = np.load(\"V_concat.npy\")"
]
},
{
"cell_type": "code",
"execution_count": 398,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"low_rank = U_concat[:,:10] @ np.diag(s_concat[:10]) @ V_concat[:10,:]"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"The top few components of U:"
]
},
{
"cell_type": "code",
"execution_count": 513,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 513,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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h4nudyTlDu6e+LwDAZ36V13jyDF6b3s61tbUZwbBew+206+vrHVua217X1tY6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\npplZARdNM7MCLppmZgXeAKsulXs9mDBQAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(U_concat[:, 1], dims), cmap='gray')"
]
},
{
"cell_type": "code",
"execution_count": 511,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 511,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Oqn2rNusrV64kXm9cH/qm0WhUDFNDcHGeu3fvJm3GtmCPLJvSOlqqjDGbq0Q0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\naAZBEDTBnzJAEJu8JEV0AAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(U_concat[:, 2], dims), cmap='gray')"
]
},
{
"cell_type": "code",
"execution_count": 514,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 514,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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jjx4yzhRg/N0fJmvGLjjDhpjsGcdIVk7GmCIGbI/ZXosj+9/Ozs7UXpsdGWegx9o0Mt8w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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(U_concat[:, 3], dims), cmap='gray')"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"Background removal:"
]
},
{
"cell_type": "code",
"execution_count": 399,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 399,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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oootmTDPu3ze/+c25eq6vr8/8sXo/o94hFfrUpz6FL3zhCwB2++lFF10EYDcw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\nTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape((N - low_rank)[:, -40], dims), cmap='gray')"
]
},
{
"cell_type": "code",
"execution_count": 401,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 401,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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H9WSGIK9zZ2enM6Y+zyaTSWp87TtiI3vHtQ/+6QYn/S2amxlp8L6sra2FWfnn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\nuKt1R4YIv1cNQbOMbdoub2fkupS5h2m7oqNwvRzvlyPqp9/TlyNRxU/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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape((N - low_rank)[:, 240], dims), cmap='gray')"
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true
},
"source": [
"### Aside about data compression"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"Suppose we take 700 singular values (remember, there are 10000 singular values total)"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1341719.6552, 10527.5148, 6162.0638, 4234.9367,\n",
" 3174.0389, 2548.4273, 2138.1887, 1812.9873,\n",
" 1557.7163, 1345.805 , 1163.2866, 1000.5186,\n",
" 841.4604, 665.7271, 0. , 0. ,\n",
" 0. , 0. , 0. , 0. ])"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s[0:1000:50]"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"k = 700\n",
"compressed_M = U[:,:k] @ np.diag(s[:k]) @ V[:k,:]"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"hidden": true,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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4ikxBiqIgFAoZ7swbCbOyREyM/d5pOCn0mtXBSRBHQADo6uqqEagJeEIxC55W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hW4CG0ZHByE0+kEAHoiaWlpKXJzcxNoACski4RJth3C4TD6+voQDAbR09ODD33oQwnvsc+yY0NU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\n/VUtIzf/VMtetSMOUpj08oM9Fz/LwhLRTbPob1BtvdFopnSr9JdhhsUj9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cTjcRw8eLCi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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 12))\n",
"plt.imshow(compressed_M, cmap='gray')"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"image/png": 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AZ/1IKgOMOmVUpAygs1ug2lB0pge6dq5ImBzNfplcx1mMhiv2sTNvryNiTH12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\nSUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(compressed_M[:,140], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.allclose(compressed_M, M)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
"2.864899899979104e-09"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.linalg.norm(M - compressed_M)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
"((19200, 700), (700,), (700, 6000))"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U[:,:k].shape, s[:k].shape, V[:k,:].shape"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"space saved = data in U, s, V for 700 singular values / original matrix"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"hidden": true,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"0.1531310763888889"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"((19200 + 1 + 6000) * 700) / (19200 * 6000)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"We only need to store 15.3% as much data and can keep the accuracy to 1e-5! That's great!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Now back to our background removal problem:"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"### That's pretty neat!!! but..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Downside: this was really slow (also, we threw away a lot of our calculation)**"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 5min 38s, sys: 1.53 s, total: 5min 40s\n",
"Wall time: 57.1 s\n"
]
}
],
"source": [
"%time u, s, v = np.linalg.svd(M, full_matrices=False)"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(19200, 6000)"
]
},
"execution_count": 52,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The runtime complexity for SVD is $\\mathcal{O}(\\text{min}(m^2 n,\\; m n^2))$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Let's create a smaller version of M"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Idea**: Let's use a smaller matrix!\n",
"\n",
"We haven't found a better general SVD method, we'll just use the method we have on a smaller matrix."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def randomized_svd(M, k=10):\n",
" m, n = M.shape\n",
" transpose = False\n",
" if m < n:\n",
" transpose = True\n",
" M = M.T\n",
" \n",
" rand_matrix = np.random.normal(size=(M.shape[1], k)) # short side by k\n",
" Q, _ = np.linalg.qr(M @ rand_matrix, mode='reduced') # long side by k\n",
" smaller_matrix = Q.T @ M # k by short side\n",
" U_hat, s, V = np.linalg.svd(smaller_matrix, full_matrices=False)\n",
" U = Q @ U_hat\n",
" \n",
" if transpose:\n",
" return V.T, s.T, U.T\n",
" else:\n",
" return U, s, V"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 3.06 s, sys: 268 ms, total: 3.33 s\n",
"Wall time: 789 ms\n"
]
}
],
"source": [
"%time u, s, v = randomized_svd(M, 10)"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": true,
"scrolled": true
},
"outputs": [],
"source": [
"U_rand, s_rand, V_rand = randomized_svd(M, 10)"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"low_rank = np.expand_dims(U_rand[:,0], 1) * s_rand[0] * np.expand_dims(V_rand[0,:], 0)"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
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FyTOIKPWafh9B+1m0UgBiJxvZGh2hZH9knNrfyCy5CqKTJ7LXR/f2jne8AwDw0ksvAUCb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\nHFzBPYAG1gAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(low_rank[:,0], dims), cmap='gray');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How do we get the people from here?"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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nhhlh6ZdmKeUVAB6utf5tKeUlXppaay2luNy5lHI9gOsB4MSJE/vWn3o3RZ3T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\nAzzHpqSehRHGAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(M[:,0] - low_rank[:,0], dims), cmap='gray');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### What this method is doing"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rand_matrix = np.random.normal(size=(M.shape[1], 10))"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(6000, 10)"
]
},
"execution_count": 80,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rand_matrix.shape"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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DPafLQHESm41KabkvI/HMsjCrwvuW9x73nHuTu+J0IViGzc8XQ0IoZmsLLu91OGoKf/gd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\npvCH3+GoKfzhdzhqCn/4HY6a4n8B1InzrWaCG4YAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(rand_matrix[:4900,0], (70,70)), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(19200, 10)"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"temp = M @ rand_matrix; temp.shape"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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0GeoKxFmtevP12O3t7Srk0MfdZDLpx9errx7vYfjaa6/NtOHpp5/u7/9Xv/pV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\ngfbSbGhoaFgC/x8KpxT2Z1sHjQAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(temp[:,0], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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oSxwDHwvC3dFY/tbWVttWrtz8TlZ+fHycrdhkC9r/UkxRZ8Kz2VlGR5dLKYsr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\nmpJUwaIpSRUsmpJUwaIpSRXeAcP6frOgkavdAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(temp[:,1], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(19200, 10)"
]
},
"execution_count": 85,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Q, _ = np.linalg.qr(M @ rand_matrix, mode='reduced'); Q.shape"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-3.8163916471489756e-17"
]
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.dot(Q[:,0], Q[:,1])"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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0GeoKxFmtevP12O3t7Srk0MfdZDLpx9errx7vYfjaa6/NtOHpp5/u7/9Xv/pV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\ngfbSbGhoaFgC/x8KpxT2Z1sHjQAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(Q[:,0], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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z+YxGo6kXBHTDKdV1hoNFtzPAtFsRy3N3Fv7Q19fXO1sY34apoYX3UvnuxpDj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\nKioqFkCdNCsqKioWwP8PyALLgCQcFfsAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(Q[:,1], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(10, 6000)"
]
},
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"smaller_matrix = Q.T @ M; smaller_matrix.shape"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"U_hat, s, V = np.linalg.svd(smaller_matrix, full_matrices=False)"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"U = Q @ U_hat"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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ZZkVFRcUUmAmmCXTDDp1tEJpIgisOnXF9xdawMl9VMh2W3jNaCTNDiOtbJtEh\n9iE6JzMcTOukyzaQtXMVJrPoK7OPtU2CjKlGjvmZXqrPiVyfnTu+ezmllE7+TH/mHEOllFZ37vpw\nvY/3j+pEeY27oDmr1fyTHi3Hc1ju6upqOqb1HeI93ADKe9GZ/N57723ryszoul8V28Z3je5J6rIE\n7LiinT59GsDoncsYuv7mmahUQmQ9MszPz6d94NmThsPhFWc5qkyzoqKiYgrMBNMsZSdDtVq91dUA\nQMexWPWLnhGaq1UU3uc6HEWmy4vCtDL90bSuONm9IotzloSgzyIduWXwf9/FUFfcrB2T3MuhyTP6\n9mXJWOgkrLSvrpmrljrJe1Z3XqPWdQ+DdTapvzlT1d0Q3Zrvek8yIHWJ8r3WWc8DBw50dtv0eq2v\nr6fuSCyH9bz11lvbc7m3OZ3m2aajR4+2+l3Wh/Uku1xfX+88N8/sr33MurteV928Mk8QHQvZTqGR\n14Cz5UlRmWZFRUXFFJgJprm4uIjbb7+9N/Ce33XvY+pPuJr4/imanNidjAm3wOn/Eaty3Yun99JV\ncBKndv+t73imR4ws4g5dgbl60w8vYqyT1Iff97JST+uXSvQlFJnEZ9XDHSN9Ho/xk7o5Mi8mqAW6\nVmSXMubn59t7cmy6Tm0wGHSCLzxRh451t5r797W1tY5els+aksT+/ftbJuhMmHvxaEJeT93GEEem\n97vhhhva3xjm6Hreffv2dcpxtqys0p+1p4jTPX38nVM7Qqbj9n2Tmqa5YqY5E5PmYDDA8ePH2wdw\n5syZ1jXAY4xVROLA9kHoL8fW1laaZzISF/uc0rMoHxex1LCViZuTRiX0GU/0nlE5vEaV6JmTtg78\nvYxL2rbMYVrbuVdMMJAbdbxcdcB2aL0penpGJBX9+BJxYuBEo+41wI4Yy7KZ2ScyBGXbjfAFXVtb\n64jlLsrzXDV2elYofVae04CTlW4R7BOql/fEE08A2JlEfZtlfteJ1d8n1pkYDodtHV215ttd6Lvi\nE6xmCMuCACKjsbsn+fPQXBdUP0yKKp5XVFRUTIGZYJqXLl3CX//1X4chZh5qRjFD3R54nWc9UvHc\nV3eyD12lubKSdfjqrJmLspWsLyyzTwx2Jbdem4mifczMWaSybxdr+KmuK5HaIvqubcjcxCaF95Mz\ni75sQt7OwWDQMk2vM5+9nuNuWBRb+b2UUeZ2stEoa3zm2hbltvSYbBou+fu+ffvavnAR3EVf/V9F\nZLbNDSLugPwSAAAgAElEQVTef+qUzj4hA2O4I6/R3KL+jFQlkuWRdVFZjWz+qaqLLM+Ajv9MVeT3\nvHz5cmcvq0lRmWZFRUXFFJgJptk0TScTjef7c72I5l90pkOdExnj+vp6GBIJYIytcqUnY3UW4nob\n/c31U5qtXJXPfm/eQ/vCy8/CxiIdjyvUo1Xe9WJRiKNmI9dz/Tkp64h2SnS4w7ked6bp7ECfvesK\n+UkWeODAgbYcD5PjmDp37lzr7MzraEwky1K25uzO26vtcilFJR1e78Yify6rq6udvuTYViOo619d\nt7m9vd1xDKfxgzs7svxLly61YY+EG9QWFhba8eHjge1VnSGv95BQZa57JaVRF0PCQyQ3Nzc7UhcZ\nNPuGxs8LFy60z7ov41mEyjQrKioqpsDMMM2NjY0xxkP9ouuN1Iru6bLcIZl6qVJKyySyVUWZhFv5\nyBi5agEjRuKpsYjhcNjWwz/Vkdct9L4L3/Lycvu/r6yeV3AwGHTYXcRkva7KDlhP13f67pRRghXX\nm0V9HaU/c3j9XM+l7JvPxq95+eWXw/A/bdOhQ4da5kZ4wgjNp8nnRybGa1mHhYWFVBesz57PyK3l\nzjgvXbrUtsGtypSitra22vLOnj0LYMSklaXdeuutAMaZMzDKVM93RevtrkGEBgW4U7q2wd3yHDoW\nsqQ2kQ4201eq9wJ10e973/sAjPSyv/zLvwxgx1XKPXImRWWaFRUVFVNgJpjm4uIi7rrrrjGrqa88\nHlyv+gu3sHvqqVJKayHjCk2WoCzGGZ3qXHhPrmBkwtR/UgfGlVf1n7yXs8CVlZUxvzGF6pHYZtfx\nOXONnPjd2r+0tNRJaEKoJZ+M0tOXRT522Yqt/eheBlFS2Gy3QncQV99E9o3Xs2ma9tmQGbrec//+\n/R2dI8eJP8eNjY0O62P/qa7Tde99Ket8P3DtC3661MPvZIbr6+vtc/M9htQbhHUl4+J4dY8TTfbr\nOv0+K3WUDMX71r0i+tIF9gVMZGnyVF/PfdnvvPNOAMDv/d7ODuMMDWXoNhDbKvpQmWZFRUXFFJgZ\npnn8+PExxkQ2wFWIqzwZ0MWLFzs6Pa6mvuIqK3VdjOqK3Boa+Yplabx8tVLmynq57m8wGLT/a0IH\nrfv8/HzbZk8lRmid9toDfmtrq2VGZGBu3XzppZfaiCzWhwzbQ1ej9jmjUE8C132pRKG7JwKjZ66h\ns7zGGavr3/bt29f212c+8xkAI50f++TAgQN417veBQD45m/+5rE+Yb2UBfJ/sjWWr/fmuHUWr2PR\n9fOePEPZH8vms2H9uJfO6upq6wFASzhDQVUH61ZlH6+um1Q4Y9zc3OzoiaOx6Qw1Y5p6zDGJD6aW\nwT584xvfCGA0XjmGbr/9dgA7UU2+nc2kmIlJc2NjA88888yY8p3GHXdn4Qu1urqKu+66C0B3HxU3\nfhw+fLgj0nJgqtHCJ2oiUkK7S4SLMoPBoFUFuDOzDjh3NI9CI3ldtm2t9hv7Rx2ktdzt7e3O5ORh\nlUtLS+09eT3bouGArBvv5aF5mgOA/c1nxHP0RWc7uIB4v0XiOctzsbVpmnYC4MTISfOxxx4DAHzt\na19rJ0DW75lnngEwyruoW8qyf1gPtlcXTu8vf8E3Nzc77WM5Hv64trbWUc1wcqPL0JEjR9p2MgyZ\nn+ybwWDQawD18n0yj2LtfbJkOXyGpZS2HJ9go8xbrp7yMTkcDlP3N9bz8OHD7eLObEsPPvggALSb\nvNEgtrm5ObaV9jSo4nlFRUXFFJgJprm9vY319fUxtpU5NqsYwRWfbIEiJc/VzO1urHBxUd1/fKtW\nYmlpqeOYm4X86f80LkSZkfweUVgm6xg5/Oq5Chd/+xJwRGzZw/acQbFOly9f7rj/EOog76Iay2e5\nBw4cwLFjx8bq4fkllel5yCHLJXNVuKM6jQTf+q3f2oqyHq7IOrznPe8BAHzpS19qk1q4UYYZ3Q8d\nOtQJPPAdGTc2Ntrx6v3khjDN3M4MQ2yDqljosE327+UuLCx0DFPZzgVRpiA3zOm1UaixXhvdw7/r\ne+DvPftEAxSiDPc8h+8aVTJ8Vrye42NxcbEyzYqKioprgZlgmqWUzszvSlo3CiwuLnZC/Txcjmxk\nOBy2+kpnFFydFxcXO07ZrtvRVGI8h/opMhNd9Xk9761uPyzX9a9RLlBvu+uRuPIuLCx0QvPcPSNK\nihIlAPF+4gru7lwHDhxo+4JM3/f4vnTpUlsPrvQnTpwY+76ystJx8mZ5UQb2LFmLGoLcrYy5MWlM\nGQ6Hrc6SjPMd73gHgBF7YRn3339/qy9zpqMBChyD1EWS5aqu25N66BgE0GZFX1lZ6dyTelnqbnXM\nq7uVfi4sLHQMZa7TZx+vrq52Qi7dkLO4uNh5Pz05hxqLHH3pED1ju4a1si88qIBj84knnmjH2c03\n3wxgFJDy1FNPARjPrZoFIuyFq2aapZT5UspnSyl/tPv9plLKg6WUx3c/u/JSRUVFxT9QvBpM86cB\nPArg0O73BwA81DTNh0opD+x+/7m+Ara3t3Hx4sUx52MyALILrozqnuGJE5TB6bXq2uP6Cw9d02Pu\n1qL7WvPTne7Vudz1Pc5cV1ZWWsZF9kN2xdX00qVLHRcVtpu6NLUkU+foulZee+nSpY5u1T0LtO38\ndOs5y7vhhhtaBsC6kwWR6R88eLBlT1z5qaNT1xfXe7pbmCZA8d9cn900TctW2E9k/HxmJ06c6DBz\n3oPXPProo+19lP0DI4aj7MXHjO/Bo2xU9Wt6Dn9/4YUXOs/Px7GOM7K8SAfp50Tjnr+7TcDDFTXt\nW5SIWc8Fut4obkVXPaqH66oNQXXHwMgiTva9uLiI17/+9WPtJNP391RdyaZNZXhVTLOUcgLAfw3g\nV+TwewF8ZPf/jwD44au5R0VFRcUs4WqZ5r8G8C8AHJRjtzRNc3L3/1MAbtmrkAMHDuDd7353+z3a\nbsFXJ3V25crjektC/SH70uC7HjCqgyfN8HpFzr1kaQRXuQsXLuALX/hC2wfAiGWQpW1sbLRsyO/J\nc9Xqrem79FxlYFlyX93fhsfcX9b9BjVJBf0DCbLJI0eOdOpDNsq+obTBNrN/9F5qzfVkLSxPEwzz\nf9eNsp6bm5vtmKHPL9kLmf/b3/52ADvPhxZZSj1kNep877spsn3ug6rX8V7PP/982z7C0x1GW7D4\nuZ7YOvrNpQw/D+g61uu48zHj7VaPCZcgCJUWPCzW94vf2trq+AEz2Qj7+MiRIx0PGE+Tx2e3trbW\nsYFMiiueNEspPwDgTNM0D5dSvis6p2mappQSct9SygcAfADYaey+ffvGJrIsM7c+9Cx7SpTh3K/3\niWdjY6Oj8HYRUDPU+CTgkThLS0vtOe7UzpdkZWWlI2LzoVKM3b9/f2fi821ctW0urvpA0wHPSYUT\nB7G2ttaJs2YECicy3nN1dbUVj+67776xPlGDmr/k7tY1Pz/fcVRnf3FCVEd0rx/bx3YvLy93nKh9\n8YoMjhRJeS5VD0tLS62r0smTJ8fO5efGxkZn3ypfiE+dOtUZX9mYUlchz7oUxfUT0cTq1/k9IxWU\n9hMwvnhFuwVoe5sm3/zO67u9vd1REbFcLhYbGxudXKdU+WjGJ+9Tj6aL8sJO63J0NUzz2wD8UCnl\nvwKwDOBQKeU/ADhdSjnWNM3JUsoxAGeii5um+TCADwPAnXfeeWX7I1RUVFRcY1zxpNk0zQcBfBAA\ndpnm/9o0zftKKf8SwPsBfGj38w8mKU9FX34Huu4AKlq6USbbQ0RXPTfGqNLbc1r6Kto0TZhxHOiu\naECXqfqKe+7cuZa1cPVkmJeKP1wdybRc5FBjiivSnWnqtrVkUZ69/PLly3j22WcBjFgefyMz5up+\n/Pjx1imdrIBt0vBPzUupfUFmqBmCyKo8T6ru18M+8OxS6vLiOQnoVvTmN78ZwA7r8MxH/M0Nahcv\nXmzbd/z48bHf9DlTinAHcR1T2TbSnsdAXXucaaqhz3MwRBn+XVR2t7oo32efu1q2ewChDDgLAFHJ\nkv/zOfBTs02xD3yXUULfezdmeU5W3dF0FpzbPwTge0spjwP4nt3vFRUVFf9J4FVxbm+a5s8B/Pnu\n/+cAvGfaMnynwcwBVs/LFMuRi0Nm3FHdUN+9/Ls6+gIjZqJZk5xR8BoyqM3NzfZ/MjA1FAA77JK/\nUZ/Ia9ydQplwxtC1b6iLJAMjk3vsscfaspkVhmyS7SWjevTRRztKfEJzUfK+ZMve7vn5+ZbFsg0s\nj2xBM9awb9lfrIMyFXf3oYsP73P+/PmOnlgNU9qPq6urbZuz/aZU1+d6RR0LbqzIcoxqzkdnmEQ0\nJqN9obxsnhNlIMokpKgN/q4pO43CLvW76hedaVK3rwbIt7zlLQBG45ZjSdvibnnuaqX6T7cjTIoa\nRllRUVExBWYijBIYd4XpSyqhK+ukSSnUItjnyBpln/Y6+PXZary4uNjrHgLsrH5M8eVpx5Q5OSvw\nbPG6i6bXJ9qTR3c7BEZMk0z2xhtvxN133w1gFO7I/qO7Dq3pm5ubnb51xqNMg2yRrFZZkXsDEJHD\ntLs+8TuZp6ZCc+d4Qu/prjfKklk++5sMkeVpSkHvd9elKXskPEWfBkNkrnfK9FwH71n7h8NhJ/gi\n6lOWEbn3AeMsMmKfCn1PPayWiPLdep5Pfr/pppvwfd/3fQCAv/zLvxwrVz0osnfNXa1014TKNCsq\nKipeQ8wU0yRKKXtmU1ZmSmR6PC3PVxw9x1dWLzeql+tG9XffQTBa5TPLnTqau46KVlwyRNWJZYw6\n8rHL9u/WPeV9rxzqBe+44472Grfm+46Auosn4ZZL1aW5HspZloYi8pMskH2jWfapwySrVyu1J7nw\n3Ro1cYTvFOrW7rm5uY4l23V/KvV4CrxoZ1IPoXUGG41bZ7IbGxudJL9RAIjWQeHPVetDuE+sMtbs\nXtEx3xOen3fddVfr5cFj7ntZSukkwM70z4uLi51dOydFZZoVFRUVU2BmmKZCfTYz/WK0Z0iU4gwY\nZ057lRtBz8ms035cGZ2j7xxPcqwMIdPH6irqejFnEJubm50EIt5fCwsLnYgbX/lVn+SJK3zvHE1/\n55Zi1WX5HvJkTB4pNBgMWn2ib++hiTGc0RHUYalPIhmqR6ZomKXvU+X1UjiL9z7X/iJYF91DynWH\n/nwnkbhUQvJ68Fq2Ra91P0tCI7x8z60ozDmK0Mvqx7HEEFU+q8XFxdanl8/Tx6iGWvIePMefr/qR\nZinsMszMpKkdFw2EaF8Rz0LtSuQo1KvPATibWPUzEzn8ntGE2GcgyRyANcQsmzR1wO5lFFMlvotE\n2gYX9fjd66LO1S4u6XbL7jDt6hF1NPdJzvs8CqH1TPOaid9FNR5/wxve0MmMRRGQ7iw0fA0Gg3Cb\nYK3vxYsXOwuRh2nqJnM04PHTM6XPzc11tk4mfIKNoJmIXMzv2/Y6M7DqxN2nluJ3zU+g50STvOdk\nffrppwGMVDznz59vY/N5Dsth/2k73Lijuzjw2kkIU4QqnldUVFRMgZlhmltbW2MKbM3dp1D2mLn/\nRNdEjsj6XeEMNhLzXeTwcofDYUccybK96PVRQoW+8FD/dLHe66Xt8nbq94zVRs7QXq5nYFfW4UYP\nZWa+ZbIzRRdNgW64I9ltFFzgSVqefPLJNmyV96R4yGxHfu+o7tr/zjSdyeq9st1TdUtkd7p35rq6\nutrZG8jH//z8fCfTvWdnJ5aWljpt9jGpuyb4rqBah6jtQNe5fTAYdFgtmT4zZTVN0z4TwlmyXp/l\nFtU+6XM/7ENlmhUVFRVTYCaY5tbWFi5cuDC2ku21u9329naHjbqeK8oe3acD8hXVVyKtQ2ZQiowC\n3hYtN9NBal94OyMm4fVz6G9Rmj09RxNiZK4oykacKbmDviaM8DR3ygi8v91JO+p/f/aRXpzs05/R\n9vZ2m1zEda6uW9akI0SUId37zRNtKAP2pBKRXtt3T3UW7v2ifaLPyDOXOztlueri5qxZDS+uD3cJ\nRANBMn296oR9R1OWq6Gr/J/SgCeT0b3ps/lDdfO+8+WkqEyzoqKiYgrMBNNcXV3Fww8/3K4O+/bt\na1cPurh40ga1JvI3Z2JR6qdMRzqJJU2ZUGYZ13MzXU5Wl6juQNf6mLFStYxnbDn6zR2x3ZMhqmvk\nCpVZXTXtmzNCbXeUsELbr4wg0wFrXzhDcrasDs4MC6X1nA75njhC6xMl9XCrdmQpzpi+X6vs1veA\nVwblumnXuaokwPeHQQoeTql2BXcnUhbt11FPrM737iaVjan5+fl0L3Nic3Ozza7vGeXJml9++eVW\nciCyYBStx7S6zco0KyoqKqbATDDN7e1trK+vj+1Lw/RPqtsDxpOK8n/6cjFcjqspV9jBYBCyTiBm\nV3v5YAJdFptZHPVYxCiyRAxRHTNn6MgPNVthIxbp16hl0dvjzEf3WifbcH2l+v65dV/b7b6b3v5I\nYnBGF/ndup6SOjHVUfJ/3w2UEo+mOssCHEopHb2n7xOvOmpnmq5b05BL9q17GJRSOv6d3l4NO+1L\nws3vnuCESVBUB8h76nVah1JGW6+4Dy09AdzSrfXyAILPfOYz7f9veMMbAABvetObAACf//zn2zpQ\nUqCE4AyWUJ/racMoZ2bSXF1dDSvvL5LGkvL8U6dOAegaDjQixPfD4Scfup7jTsw66WUT6yTxte4G\npC82naj5G+PKI0NQZPTQz+j+Ufx8tjjogCJctaBleCy2i4UaV+4TtLYtU6v4ZLKwsNCZSKOcjdlv\nvI+qeNgGiuuRO5fXwxc8zbLvhpK+qCiPQvKYe73Go640L6RnWtd6Zoa9SIR3IuBGKDXasZxoq+Js\nwfVNzzQPJsF7qeP/E088AWDkDsaoIQ0W8Nh8V83ou81yPFZ/L1TxvKKiomIKzATTBLrOwy66EEqp\nnSl5xmni8uXLrdjF1cVDw4CuCoBihLJRdc0ARquU718SOeq7qDA/P9/Wiysqz2HI2LFjx9qs6V5O\nn3juxhhlKnsZvZSZuKtWFJrqseKR2J8ZlPSeXi/dvlXLV1bq6hstw7PzRGF9rgrwcEUXh/Ue/E3d\ndyJ3H7/e6+FMMeojN3ZGob0Zg1Uxn33qzt9RkELmHrawsNCRGPxZ6Z5bmZM826Tivr9XVA2srq6m\nqp177rkHwM7ulNzb6qmnnho7x9+9aJvkSVGZZkVFRcUUmAmmWUrp6Aszh3Vd5fcy2ERZy/0cTSDB\n/6nXYiiXsltPoOA6IWUmrn9yndWhQ4c6WYPIMKmn3djY6Ox+mLlKRK4TUWISos8tyd1Y/Bo1JLgz\ntOcw1L5wlqzGgL3apzpEPzcKzctCB1Xn7e3hc3SnaA248PGkOljX9Tnjj4ySvGek885cyHRsO9OP\nnPh1l079ZL3IljVs11mz3sf7gs9cJYosGCMKkY6yhAGj90L12G4HoH3i8OHDuPnmmwGM3s/HH38c\nwHhSD7bJpYpJUZlmRUVFxRSYCabJ9GJRcgTCnaO3t7v7nvv1qs9wJtKXRCMLU5ybm+u4UWQO56pr\nyhJPvPLKK63e9LnnngMwcofhNU888UR7DpMX0B3G9ah9usqIbWe6nChElYiYj7Mf1x8pA/N+U/2i\nW22z/Wcit6zoXNc9qo6Pv2f5Lt26r6GD2T7j2heZLn5+fj5lcmRrhKZMy1L0AaPn70xM6xexT62D\nXuv1irwGMj2qMlnVQes92E7PfanlRN4pGiyh9yabPHDgQJudn/fmDgOPPfYYgJFbonodTBLYoqhM\ns6KiomIKzAzTVL86dXR2XZjqcnzVzHaGVGdtt1xG6csIZxv6uzMx1/uovswZFFe48+fPt6stdS5R\nIt5HHnkEwMiySIuih/wdPny4o1uNGFSmy5xE3xmFhrru1v3y5ubmOswkcix2RuJ6uMga7Nf6mNBy\nnHEqA8t0rVG4ouuoiT7pItJ7+r0JtVo7E3ZvjcuXL3esydRPqs+pO5JnjE53wCSiJBiRblXL1Xt6\nu/w9aJpRSr0o3Z6X5+8uHdmff/75NiiGHifulaISiUsMk6IyzYqKioopMDNMc3Nzc2xVyRIxRKF+\nzuiIvjApZ4iahCBbaaNgf78mSqefReCoHtd9RDUKw1kPdUL0OWWKrH379rUhpdR7shx+P3DgQKsj\n9VVdGZ2zdreQR88qYx+qP3JGov3n1t+MqWiS5D4PiihZhl6jia8zyUb7nuW5T6KyeNenE2y/Rr6R\nLfZZ47OdKv056G/+Ply+fLltp1ul+UlWum/fvk6/R9KG97szWX2fMl9fLS/TAfvWItq+SL9Ljxf3\nx2Z59Ive3NwMd9mcBDMxaQLd/XIiwwUw7jrjdL9Poetijl+rk1wmqvE8PeYPRQdsJkJyYN14442p\nqKYimg94v4bfX3nllXYrWxfnKMrfcMMNbYYbDxtVscezzHiIqiJ6SfVT45n93EhU9j71SVlVAn5O\ntFUxEbkyuaiXZebRCdEzr0eBA9m9NceCj1cXnTc3NztbKHuY4OLiYsd4xU91ofP9kaL+4qeL+57B\nSNuZuYdp2UTWXlW1ef20r6LACmA8BJb35HvA7FXuNE/jc1SvvXBV4nkp5cZSyu+WUh4rpTxaSnlX\nKeWmUsqDpZTHdz8PX809KioqKmYJV8s0/w2AP22a5r8tpSwC2A/g5wE81DTNh0opDwB4AMDP7VVQ\nxsoi1wN+usN2lrldV0+e43uazM/Pd0S1yME7c9OJQgcjMSRrg9YDiLPYZI7cfQp6fqeC/OzZsx3G\n62GjBw8ebF0zPK9p9DwyMZhQJtHXf33uJnshCvOM3GC0vMXFxbafvS9dLCyldFyW3FCl7DZS6fAc\nN4S4lBK5anlosLJyD5GMwkc9YQU/aTRShpwZY5yB+nXaJ8vLy+kW0S6lNU3TMVjyM9rLKDPCDofD\n9v7OLKnC4ufRo0c7+0tNiitmmqWUGwB8J4BfBYCmaTaapnkZwHsBfGT3tI8A+OErvUdFRUXFrOFq\nmOZdAM4C+HellLcBeBjATwO4pWkapk8+BeCWSQrT1Us3o/fVSlfwLOM1Ee0R5IxHdZ0RK/C6Zauc\nf6qbTd9KHe3cqOdoX2QGkkhJ7m5Y0flkJGQb3IMFGLFOujeRefJTDU2eVd/3mFY4yyU0jNIliL4Q\n0Og3b6cbs/TaLKN8n4O4PytNvOGskdDUeNkumTxH9XuTGMX4P91rfB+g1dXVzjjjs4p0w+rQr78R\nfcEiWo6PRd+XSPvY7+HjQyWuKAkKMJ7t3Z859fiaUIRuSUzuMSmuRqe5AOCbAPzbpmneAeASdkTx\nFs1Or4ROUKWUD5RSPl1K+fS0GxtVVFRUXC9cDdN8DsBzTdN8cvf772Jn0jxdSjnWNM3JUsoxAGei\ni5um+TCADwPAwYMHG/ut404QWSO54niSVCbw1UQI7iBNh1jNKu0rY5+rUuR8q58RE3bmpDqr6Hr9\nHv1GRDqZTBemyHbsGw6HrfWR/USdKPuYTPPGG29snevJQj18Tj0AMv1z3+6KUdtcBxlZWzMPh8gD\nIEsuoVKMnxOxP2dn7sKkdfX+92u1PHfQ1z2DOIbpTuO6zfX19U4SaGdpEdPMXMj0N+8ntbj7GHY9\npfafJxBxj4DBYNAZF86a9Zh7G3jI5ubmZptGjqHLk+KKmWbTNKcAPFtKedPuofcAeATAHwJ4/+6x\n9wP4gyu9R0VFRcWs4Wqt5/8LgN/YtZw/AeB/xM5E/DullJ8A8DSAH5mkoL4EB0B3xVYHWw/f48pB\nR+/FxcXOdhcEV2NNxtHnFL2Xw7rWM9t5sc9RN/J7ixhqVIeIzUSszfst8sPLdMn+/eLFizh9+jSA\n7n4x7P8TJ060bJQMwH1P++oZMX7XJxKqa8sCJLwMAB3/VrLmyIMi89JQSzbhQQFRnfv8U/mbhwPq\nvj2sO5lmpEuOWKzeW6UMr5+3d25ursMWo7HuHiu+i6SOUU0Bp+Xqu+3PPHKod2aeOckPh8NWioos\n9H24qkmzaZrPAfiW4Kf3XEFZ7f+RuBkp8yPXBWAkUmrWmMwJV908sklOB3XfBAiMD3jP3+gLgIoc\nWaSMurFkxoVJoO3faxJpmqYjLhH+Qg6Hw078PNvJqIzTp0+3eQ6ZdYYqlMh1xh2d+9yJ2MfeF2q4\n8YlBRXuWo/kk/RzvKzcoqbjtE4OLi+qi5c81U/1ofXwr38Fg0Brt6E4TXeOO6p7BXdU5mXFNn4e3\n3cVhfZ8In+TY55ubmykB8KAXoN+Ym+WC8Dypm5ubbZ3VADoJaux5RUVFxRSYiTDKpmnG4mOV3Tiz\niXaO85UxY2Z6ThSu6GJJ5LKSZZKPxNjMhUmV8F4fX903NzfTezo0Q42v1CriZ/HRkfEpc6SPQtrc\nMVlFeLJ/ZttmNnrmCD169GgndJNlk8GqMYriqe/5ogzdmatntdH+cpc0fy5RIEJk6OD4jFQevI8/\nE5eitP3ZPklaBssm4yTzZ59rOTregfEdQ1lPv0f0PvF6N7DwmuFwuGeosfa178Xk2/6y77QcQsdi\nFhTjUotKBZpRbBJUpllRUVExBWaCaQJdXU+UkQYYd6dwZuP7lWvZ/n/k7O4rva/O6k/qekqCbdCy\nnJWxnI2NjTQ5iLIYD4vL2O1gMEgdr7UfM9ebvmwvWXim9q3XT1mgu8PQePH0008D2NnDmnpPz0xP\nQ9PJkzsxE8eOHeuwM9eDRnvUR7kks373Pora6f2lOu++sOC9jIhqtHB2xf7T/cWdwfnOldFumdE4\n2wu6ayav8zBUItLdOqtXHae2R8vT+mXhpn0GQ9d/Rgw92yEgQ2WaFRUVFVNgJpimWmv1GNBdRbhS\nHDhwoNVruQNrpjOKoEws0ovpvdXxN1s1VX+TpbKKEh44w+lzS/IVVh28vX6+OkduSe6OEunvvO6R\ng7dbaHUlj5yfgfF8jmfO7MRBkGnSwk5dHb8fOHCgdR3z/o9crTLPiUkcubV8lzgiPXTmQhU916g+\nCgufdJkAACAASURBVE0ik0kXWi/2ge8MuX///o6DOZmd74SpcKd7zcGZ6eKVeWY7KXh7+2wFfe+w\nzw2DwSDMMwp0n4fuulmZZkVFRcVriJlgmqWUsf1QdM9qt5Iqw+FKQSuhO237Kq2ImFSmr1NG5ytg\nlGQBGHeu9nsqq8n8RqPrMlarLCTzX4wc193JWHXE3s6MgbGtCmcNS0tLLXtkZm2/VpkJgxOYQJbX\nMkBh3759nSCFPobuuqsoAUumw9S+d0YXhfZmeyBFurQs6Ys+j8wJPdqvyvX0eq3vWBnpgFmW1yNi\n45TqXGJQazx1qdn+Rlq/zC+2T+KK/Izdc8OhwRWs315hu47KNCsqKiqmwEwwTVrGuMqodY5soy/M\n0Fmjsz+NvHHmpBbBzBIeRaI4g3A9ksKTSkRsIYtGihKJZJE8USIK14Nq1ESWbkyjQrJ9wfXaKPwv\nqqf+5r6AvK/ey1Od6Q6MjH5heCbZqKZ6cwbnbYqkgb4QWr/e26u6+cx7IZIufEypROIRRhF79kgb\nZ4iLi4t7jh0dk5l0oXXwMRwlQPZQS17DZ+XROlqfSF/v774zT31X9npH1IthWqY5E5MmGxDFgftA\nil5ab7RnZ4/yHPpAm0SEjwwkUYif18vFai1/L1Gtrz6TTFKRqNU3ybLczKDhE0d2veLChQutCsWz\nnWt5mcGG5+oCRRGebkg0Emn+T3ddIrR8toPivo8PrWdmYOxbKKOFOBLZ9Z5qmMictVX8z7Ilqcjs\n7m6RuxTr60bDzN3M6wqMh0a6oYVjwI1RGtqbTWBaHs/1MOXI5Stz64oWr0lRxfOKioqKKTAzTFPd\nDlRUn2Q18AwmESPIVh4VYTSpQnSursIZE1O25E7Q7owf1StaKb0ekVuNf3emo2Vk6oJJxBR3Oo6c\nvomIMTlbVsnBGWVmIFlfX28ZE0V4Mk+Wt7Ky0oZoMkM3sy5FGb7JNJ0J65jKjHZav8xpXPuJx+i0\nz3HHHUMJfR6ZCmo4HKbBHFoXdx6PmDQ/vV2RtOLZqsj6yCZVivLsV75/j5bt/R4ZTV090jfOMtWW\nhjln7nUZKtOsqKiomAIzwTSpQFcjgSvQHX0ha4QyTl/xo328ox0qtfytra1wnxmvF5E5pSvj9EQC\nhLIM74uMUff1gYbWuREs0qlljNzr0Hdv3md5eTk0fml5yuRc3xw5bXv9aCxiGaurq+0xhnBS78n9\nYg4dOtRJ2kDGyWsiHbW3OXInipgSP9mORx99FMCICXsOT30nvA6RM3o23jTrvIedRu5T2ZjWcej3\nZ7+R+QPd3KnsYzJ+dYvLWG1UD5eetC6ZA330PZoDJkFlmhUVFRVTYKaYZt8+MX2OxR466IiSB5Bl\nqSU5S2Wl986cliNL9l6rZ5/FOHKodxYT6RWdubquSO+ZWd8jnXLkSeD3JtxrIAodjFiR192fkbYx\nCzJQfRcd6aln43da1W+44YaWIZF9RunjvH59euy+fiGYpORTn/oUAOA7vuM7xn6PdMsZY9rc3Gzr\nnLnZaJIW1/VllvyovMj9iqCekn28sbHRkS6c1Ufs1tmjjpdMWtEyMrdBf3cib4hJUZlmRUVFxRSY\nCaYJ5Alx3cpH6D7ZWRINP18RrVbOkFx3omX0pVEj+pzHgXH9S8Y0o7C2zJk5qrPXJWKlfZZw149l\nXgj62yTWeA084Kc/a09w2+fT2ScVkInRh5B6t3PnzrX6NbaHjJPJkslEDxw4kOoMdT8ar0ekdyPT\nvfXWWwHs7KEUtSVi6F7+1tZWmLBXzxkOhx1dPuEeHpG+ktBkGJkvrVrGo4Q3Wi/VkWpgC4AOe1Zm\nGDnbAzsMNko+o3XQuSHbE2wvzMykCYzHSXu2En8BVXmcDQSdXFz05sPVF8EfQuQu4pOHiwzahswx\nnOeur693lNGRgSnbFz4y1rixiSJRFCvel8szM/j4ZyQqe1/3uXTo5OwiNsU4lh/lIc0WIo2xd6hr\nE69nfk++rE8++eRY3U+cONG6BLmLjxrm9hIPt7e326xNt99+OwC0eUSjBc/HYDQBZaK33jtbZAhd\nOP2caMxnQR46+WWqnSjjkL9P3t5INebn6mSetU8XBM3aNA2qeF5RUVExBWaKaSoz2MvROlJG629a\nxsbGRihi+z2d3UauPZkLSLSfSua6ETHXbOc+XWEzcULZqrOraRzXFXvtdKnMzrdLjZhr1k9RLLCr\nXVzk0v89S7myEHchc7FanwPvQXcgivL83Nraal2DyBTdYLWystKK3i4F6Zj07YI1nFDLVcNSxq70\nOv9NjYlExLiyc12M1vciC1LQLEPu1pQ5zeu9CA9YUWd5r7PmG8hc96IAkWl2c1VUpllRUVExBWaG\naaoOSle7TDnepySP2FtmJNIwskw3FxllfMWODFWZAjxSbmeO66pjytxY1KXDWTaNKX3ZiSJG4OW4\nHlTZb8Ye9V6ayIH9wzqz3ZmhhdC+d11t5N7krNuZuur6MjcnuittbGy0BiQai/y5Hjx4sL2ebJSG\nJGXC2U6QPpYi1peNTT0nQqZfjpJyZIEb6nLlz8od2TVTVhasEO30Gbm/+Tl9Ll9+zO0UqnPNWOhe\nqEyzoqKiYgrMBNNUlwNHlvZNQxCJzCqsOjXqrAhlLJkjbORU6yttX8q6SMfn5zrjUUthphPyumj/\nZFZcDVf01TzSo2YpxDT7u++tFFnRM48ErZe7zjh70b72/uZvqsfMmJLWwfud8Ge0sbGB8+fPA0Cb\ny5Pn0BPjlVdeaR3XyUZpIWfykMFg0N6TYZPuNK9tyqze+pyzAAn9njlyO3tbW1vr6GOjoAzCmRz7\nQp8DdbZsL8/luzgJ01SPmsyzQ9ljxkZ1N1SGylbreUVFRcVriJlgmkxioPqGzG8xCvXrK1evjY5l\nq7RCda2ZbjWzqvO6qC0Ri4wsu5muyhlndF7ESrMQ1eh610uxnZogw1dxt34DSNPuqeSw1/4ummzC\nHdcjvepe/ab6WLIe91SgTnNxcbHDCPkbr923b1+rpzx79uxYP7Gex44dwxe/+EUAo6Qg99xzD4AR\nI9NEwd4XPt5U/0xE4bH833W2HlDw5JNPdpzv/d6RN0S0572nRHTPFbUD+LvsUkff2Nax6bp83sP3\nSFpcXGz7e1rPkqtimqWUf15K+XIp5UullN8qpSyXUm4qpTxYSnl89/Pw1dyjoqKiYpZwxUyzlHIc\nwD8FcF/TNGullN8B8KMA7gPwUNM0HyqlPADgAQA/N03ZqgMjIh1FtiVGZHV1XZxDI4wI14GpzsTv\n4YlANGoiS/KhkRB+L/3MVsJIh+grq7dJ+zbz69ve3u54A7gOMdpnx++pqdx4ne+3rVKAPxvXXRGL\ni4utr2PWF5H1NnpGhO+q6BEuGnnjyXSVeTJhhesDv/rVrwIAPvnJT+ITn/gEgFFKuLe97W0AgOPH\nj49du7Cw0Enfl0Wk6TluOT5//nybpNnHIrcHYVtuvPHG1vKfSVPaF840iSiyyHXdOuazd4+I/DQz\nvTvQ9c7wHTrn5+c726BMiqsVzxcA7CulDAHsB/ACgA8C+K7d3z8C4M8xwaTpD99D1QjtOH/Z+wwm\nrrCO3Fv8obiIED04rbN+qnHLX16tV2Yg0fZGk7ciEuUzJ18doC42aV0ykT1SH2RuLLo4cLLky+nO\n0HqvaBLXz9XV1c6C6eK+bgmc9Y2+2BSfOelFE2v0jIGuKw0wekYU0zmeX3zxxfZ/7m/0hS98Yaxe\nnEzVhczDf3VCyiYurS+v81h71oWfKysrnQz6Xt729nanL6LgDv+tL1+DL4w+RqPsXK4yGg6HnXv4\n4uxj6kpwxeJ50zTPA/hXAJ4BcBLA15um+TMAtzRNc3L3tFMAbomuL6V8oJTy6VLKp6/UM7+ioqLi\nWuNqxPPDAN4L4C4ALwP4v0sp79NzmqZpSimhhaVpmg8D+DAArKysNJEbye554aeK3ERfiF7m6Kyh\nens54arI7QzAmXGUYMCvUXbbZ1Ca1LldRW9PWhJdu1d4ph6L8hvyu9ed9+Qqr6GWzuyUMUYGDC2P\nZQyHwzTfJ5+z7kCqW/8CsdM43YiYqOOll14CML7njRuzIubvrJ3PgVmT1tfXWwMLRfZnnnkGwGgM\n0bXp6NGjLTN0Q4aOG3Xd0TaxfjfddFMaIuz9oM73mXpExXNnfy7RaR9k5KjPAKnfM2lR3/fsfXJp\npc/wuxeuxhD0PQCebJrmbNM0QwC/B+DdAE6XUo4BwO7nmau4R0VFRcVM4Wp0ms8AeGcpZT+ANQDv\nAfBpAJcAvB/Ah3Y//2DSAnU1yJygI8dw1xlGuk1fzSKWupeTq7qdZKu6rtKZEy6heh/vA/2eOS17\nIovItSpy9I9cn7x+WeIPfw6llNAh3+uTuZBELDrSd2oZ6ioUOWfznIzZ0B1lbW1tLNkDMEoR5yG9\nangk+yTUoMA6uiGC9bvhhhvac+jaQ9ZNxkmjzUsvvdQaZbi/ET91T3e/h7O+KCgjM7RG756/Kypd\nZIZM/S0LIIic+L1+ytj7Qqm1DtFvhI7VK2WbVzxpNk3zyVLK7wL4DIBNAJ/Fjrh9AMDvlFJ+AsDT\nAH7kSu9RUVFRMWu4Kut50zS/AOAX7PBl7LDOacrB1tZWGAKXuRGpfjFzLVEXkcxFiNA9YDIrXbRi\ne3mTJE2IXC2yhAq6IjqDiKz7kVdAdG895uVH+s8oiYS33RMBR8lQssQfqo/y8tyVSfst+1SW6myb\nWFhYaMccP515KotzKSNybfP2kdXy+8GDB9t7ZfucMzHIcDhs60MrPK+hq9Dhw4fbkM1Ir85P729H\n5DnRN4YyxqqsMhvTRF+dMulK//frVIry9yrSaWaMdS/UMMqKioqKKTATYZTAuIVbWUIfm8zYo+tQ\nIh2Mr36ZZVp/K6V0/AMzx+koRDJy0M/uy3Koo4vu6RZRdb7PfDA1RNUdp8mAouQIWV9vb2932J2H\n7Gk7s2TLyhIczkiiwAGvb6S7JaLx5c7PrjdWv1uXQNjOaEdN+n2yvJdffrnVU/p4J3vUUECyTvUK\nAEYhmGfPnm0t7EwKwsQYTEsX1Suzfmsf9rG9rP/0uD9rZ6yql57Equ1jKHqvMst65HN6zXWaryZK\n2cmPqIPRGx+JhZmzse+Toy9jRu37oC9LJlJEm7FlLkeRmN834ftkSTEsM6oo9IXmuS5GR6KMX5fF\nAA8Gg86mWJHRLcqxqedqpm83ongfRRvSRWK/Z26PkLkuRS4vUeCBQkVbz43JCXFxcbGtF12F2B6K\n8jp+fYKhO5K6xfEY3aQ4aXLvoSNHjrQiPA1JXIxp1PIFFJhs8swWplJKR63SFxiSuQrpu91HbLJz\nJnnf9yrXUcXzioqKiikwM0xTM9fQMKSInFWz+OpIZMtcXPpWMmdOGpqXZRV3MUjrEbHRjC0q83ED\njbMqdXfKVnNd7V0p7uxKcz5mBi7NdO7GE4cyMD3m9XM3IjfgaF2iLP/RNUDXMV/jyinCuhrD+0Qz\nDjmz1u9kbB6DruI/x63vb0QoK/c6e1DA9vZ2K8I741TXpaNHjwIY5fdku4nI7Sx7Zn2ibfZcImj5\n2biNzu9z4fN3JAsMiaTPSVGZZkVFRcUUmAmmub29PeYw3OekGq0cmb4tcm7u01n59WQCumo5W3Rm\n6W5AWg9vi57jhojI+JSFK0YOwBlr1jpnhiplyZFzvF7b96wit5TsHHU5inS/CmVgffrczHgVuc74\nnkPefysrKy2joxHGXb/UbY76ydtuuw3AKNFGpM+mftGTmUTuZm5w0Z1WWR/e+4UXXgAAnDt3rv3/\n1KlTAEauSzRK8d779+8fy1uq5WpfZ/0e6QczJqf5NX3c9rG/7Nnr+xu5IwGTuQ/uhco0KyoqKqbA\nTDBNQi14UfIOYJwV0froYWSRk3oWGqZsyI+5BXkwGHT2+I6coAlnbq4fjHa3dN2SMsS9HOojB+DI\noTtz/FWL716hdMrWMsu4IqtP1J7MYZ1Q3ZWzIO2LTBrQ3SDdZcafPbGxsdE+e4YwktHp83TWGO3L\nznHL6+kyFIXxeqZ1TyajrJtgfXifS5cutZIcda1sA+9NHeehQ4dw5MiRsWOeXk1Zmj8zfQ59qeCA\nOPSyj2H2Wd/5me2F5PWd9J5hPaY6u6KiouI/c8wM01Q2qAwsS0m2sLDQSTnlekFdmTLrmepQqI/y\ncDS16mbO0O4TqA7dbplVZraXbkhTYmnZfg7r6UzJd3TUfsiYne7Z7g7dkVdD5p+pOsWMGUbJpl2v\n6Owq0pG6X2QUOOAJLNRJ3vV4rpvWDPVExL7J7mit1iQjPCdLLMMxpM/X2XLkWZBJZVEKPH7Sss6U\neJq5ncecWbNNi4uLe1q7VXLLEEmCk4Q2ZhII0JWe+gJLJpF+IszEpMkXL3ITISIxUTem109/IVXh\nT7hjsebz9IEaidweAdTnakS4072KwVmcuxp3/CXjtbotcTQ5Rt+jtuhxX4h84tIBlzkQ62LjaoxJ\ncnj6d3X5yaKPovZ6xBLLeeWVVzpbO/gkp8/BXaJUzAd2xGA/5i/m5cuXQ1FW76WZkliOj21tX6Ye\n0fHrizrP5dih2L62ttZmeuJESsPXmTOjLI90lqcDvef7jN45os/hfJpJM/qe9UWfe9K0qOJ5RUVF\nxRSYCaYJjDssR2FaURyrH+sTnyZxS3KRO2K7vKczCXUwZ/0ylx7d6jZjtZFy29vp7dVsTv6bZ/HR\nPokcgrNtVyN3Jx7judGeMF6Ob3gVOUNH4rjf0xlmX7Z+Z/q6zay7CvEcDVn1WHO/98WLFzt78Lha\nQv93R3WVGIBx1x6XQPS4j6tIFM0MeVGW9nPnzo3Vi32gMe3sp9OnT7fHALRGpMOHD3ekniyYoi+w\nQcd6ZiCcJCQ6cpGbxKE+LOuKrqqoqKj4zxQzwzSBWF9Dlw1X0CtLcFblCS368v+pbi3TaxFRooi+\nXTP9XlGyisxtSBlTpNOL2hI5a3t9daXV/W/801l3pjOMDBHqouXneH2IpaWljm7Pdbc8PhgMWlbl\nRovMKKLX631cqvA+5n30eXrf0Ol9fX29NZr4fkTKvrPnqXsg8XjmwK1tcP18lPwiY2Mu3W1sbHSk\nJtaH4ZmvvPJKO77oJO8GyHPnzrW/Oft2SWT//v2p26C2N3Nqn0QPSqhtJGKfk6AyzYqKioopMFNM\nM9JBUncSwVfWzGKmOSRdl0Mmq3oV16/oCpdZ3NxFRVe9yArvdSQiPU1kUVeoVdjZt+sSlek4s9PE\nG65LdstupGt2Jtbn3kRmQZak7eU9nAVFllmyGQ1l5DVZGjqFW7dpMXaWq+WxXs52Dx061LlnNJZc\nL+weGCx3fn6+k7LNdeARu3KpajgcdvLAeiIRZb0+hpyJDYfDMcd5YPQeUe+5vLzcvrs8xzPM8z4v\nvfRSa4X331TqyMZ/H9P056h9U63nFRUVFdcAM8M0VX+j+iPXdagOMgvKj76732GUgNePRSnY3Arv\n/oeRLi2z0mn9fUXUvnAdpjtBK+POfP+U1exlNYz2VMpYnz6rKACB33k+s4u/7W1vG6vnkSNH8Pd/\n//cAgE9/+tNj7fTyVL/q+kV9ZplDuLM1PacvJJRjiKGS9GfUQAIPuMgypmtfECzXs71rfTwsMwqz\ndSlDGavXz8dxlALPM/1H/UNWyYQgi4uL7TtBX1g61JPN8/ejR4+23ii8h+/lHnnURHrePsd3L+dK\nUZlmRUVFxRSYGaapflhRiJOvtLrCZv6QytacIUZbIURWXz2uepDMqqnMbi/rucLrpSyS9eFnZjXc\n3u7umxQxV6+XW6sXFhbafs6SLUcRQX5PBXWP3/u93wsA+OZv/mYAIxZSSmnTqD3yyCMARuzF9bIa\nsRQxEX536cLbq1Fgbj135qnRWwR1dbSY6zgjnPlof7JdqsPUuuhzcn9W1ZFmkViqq86eo3+PktJE\nvrCeFs8lrdXV1bZ/GEnEfuLWH2SXX//613Hy5MmxPiE4PpaXlztRaV73UrpbzDh03F6pTnMmJs1S\nCgaDwdiE5JNQRMVdjOiblLIY3iyUkPUCYof1zO1HkblG6ELg9/V6qeEmM3ixHxYXF1PXFO3bzGCm\n2856KKpPTpFKINu0q5TSGksefvjhsXPuvfdeADsvECdJvlSeRUhf3mhi8b5xlU6U1cmfTdbe+fn5\nTtgqz9GJP+tb7eMsV4JnwI8yUvlir++Bn6uO9a5yItygtLCwkIb2ats44bmblPe13pPqjBdffHGs\n/UeOHGn3LnLRXfNB8Hye4+3UhcHVI5Fh70pF9SqeV1RUVEyBmWCawPgqHTGwSRJQZKuKHvPVOHIA\nzsL3lCX46haJTb6SRc77WcYbNXhF7hdRezXLkSdQ0BA7V+zz3rxG9xrKnKLVBSnLmxipUD73uc8B\nAL74xS8CwNh2tsp02Xb91HZm2aG0Lh7q6vVUiYZwFyjNguSZ0SPXqiwgIlKhuMjsY3J9fT3M+K7n\nqvomY06R+xuhYjm/Z/eK+tzF8mi3BMJVTzR8nTt3rh2LVAvx2VHqOHjwYFtHXufG4n379nWYc5/0\n6eNqUlSmWVFRUTEFZoJpUmkf6U76Vq7MRcgZSqSg9zKU6fjKo+U4o/TPPj1JlJvS3Wo8qcRgMGhX\nYWc/3k7V0bHfPAx1a2ur4+Ac6a4yJ+qob10H5gx2YWEhzEoOjBzD9fk4E3Y9o0ol7kITOWlnkkOU\nVIVwVjUcDtv/PaO5GvH8OUY6Zs9x6uNCE5+4S5A/e623s8jo3fFz2EcMqVX3MDegESqV7aUj1Tp7\nBnhNWEI3KzfGMnRz//79Letk/7N+HEPAaF931TNHn8rQs3Zm2JNpllJ+rZRyppTyJTl2UynlwVLK\n47ufh+W3D5ZSvlpK+Uop5R9NVZuKioqKGcckU+yvA/g/APx7OfYAgIeapvlQKeWB3e8/V0q5D8CP\nAngzgFsBfKyU8samaXo3C2manazpERvMrNSq63O9kR+PVpLIzSbbEVKxV8im6lMzR9tINxelxeM5\nmfXcQ+zU8hmFY/LajA0re3Aml+mC+/aB0SQQhLMq/c0ZJc9xHZb+n/UNxxTQn96O7McTnESJrb0v\nnVWxnlp3DwZYXFxM94nnd0oHw+Gw0+9R+7NwR2Xde3mYKCN2zwv/3NjYSB3gowQbmZ6X16yurrZ9\n52GdHOOrq6ut1Z2uSwzL1Pf82WefBTDqw2PHjgHoWvs1tJqhn5NiT6bZNM3/B+AlO/xeAB/Z/f8j\nAH5Yjv920zSXm6Z5EsBXAXzrVDWqqKiomGFcqU7zlqZpTu7+fwrALbv/Hwfwt3Lec7vHOiilfADA\nB4Cubm33dwDxPuKEr/Sui9FV2q+PLIK+UkcW/Cw5QBSG51s6RKF+GWP1+yqyfZO0Hn5txFicgWtf\nuJ+bs7WoPE+uqyzadXMe6qfI2KOzP2+7f8/CO/VZ7RUCGlmMM68I9TpwZqf1ikJbFbqTpTt0e3KP\nqJ3uKxn5F3tbdCy4dOHBHhpmGyVKIdxp39vgiWKAkWeCp9bT/vNEIJQSlpeXW10mryeD5XHVi/K5\n0bF+Uly1IahpmqaUMrWXaNM0HwbwYQBYXl5u1F0milqR69rPKFchrwfi/XL8msgZmogmimyg+2DW\niSIzGs3NzXWyBnnGdHVRycSdCNlmZCrC+0DXhSRzNfIXVMVzdwFRw5C7Uvk1UU5Dn7jUod7v7+VO\nIpLqfbM+6cs74GqEaBKeJKDBJ2EV37MIJYX3d5+7Tdb/iiirETC+txUnxL58DS6Gu+GFE5vmCcic\n5lUl4L+x3aurqx2DEo1GvFbVAOyf8+fPd/qgD1fqcnS6lHIMAHY/uePS8wBuk/NO7B6rqKio+E8C\nV8o0/xDA+wF8aPfzD+T4b5ZSfhE7hqB7AXxqkgLV1UEzHrlINYmzarTlrbMEZ2DTOrj6roraDm9D\ntK8Lz8nES213lCEnq7szJd2Rk2V4n7rorKuws6lMNI3qFYVaEs6wm6ZJXT+iAADP0hOF1Dm77ROV\nnVn65/z8fMewGMW7Z4YbQvvB6+7O/fqs3HgUOdS78SSqVwZtS5SDNUMWjqzub24s8japi5sb5NSY\nF21xrOWq5MYdNOmOxPh3iuc333xzZyfSSbHnpFlK+S0A3wXgaCnlOQC/gJ3J8ndKKT8B4GkAP7J7\n8y+XUn4HwCMANgH8k70s5xUVFRX/kFCuNGj91cTy8nJzxx13jB3zldpXd2WPe0ENQb7qRXvKOCNR\npuMOtlyF6bZAncr6+nrrMNznGJ7pqiIDS5QIQ89VhujK/D5G7ax+MBj06mH1Gs2/qPonYGTQUOd2\nZ396z0yvGxk6eI8sIEHZi7dPGRB1aHsx6oitRUEGbsCMjE+ZMcZ3pYwCAqIMXF5X79toXGQhhMpu\nnW1ryGSmA1a4hNQXQODvZd9+Tn3JaDz7EvuS7J3lHzx4sN27iGPpoYceerhpmm/pNMRQwygrKioq\npsBMhFEC8Z44QJ7KTeEsyHUnEYuMVivXkXBlpYPs29/+dnzjN34jAOCuu+4C0LUIMjv11772NTzx\nxBMARqsm94hmhnL3GABih/Coj6Jr1KHYoSzLneKjwAG3fGbWYP0/c9nSvs0s9sDell1lXhlzzhzH\n9d5aF009FpWr+r1Ib6ffo7pH13jfutSjFnNnex6qqu5E2XugOuW+8cVzs/dHXYj2CnJYWFho+9TH\njIcOl1I6/RS1wcegj2NlyR6qyu+U/s6fP99KhVmIb4bKNCsqKiqmwMwwTfXNVH/IbAc61Q05G3W9\niDId12GqDyB1HLye4Vo/+ZM/CQB461vf2vF/9Hry94MHD+Id73gHgNFK+Fd/9VcA0DJQ3SWQK6Fb\naC9fvtyWydAwItKREpkv4cLCQqvHc92Z9rGzISJKgsH6sVwNA+S9WV62T/z29nZHD+XW12gsZJZZ\nbbOzKmXdmY4vCrgg3A84Ch106Bh1HbD7QerYzHSGfm89J+o3Z3CZb6f2QRbyqnpswpmi+l56+Xqu\nSgAAD2JJREFUH0RSyyRBHo7I+yMKWgFGY5Ofly5davWclWlWVFRUvIaYCaZJthKFA2bWzFK6yVJd\nb6Z6F65ynjKN+y2/853vxLvf/W4AI8v4V77yFQDA3XffDWBndc/8+bgKP/744wCAj3/84+25TPP/\n5S9/GcDIkre0tNTxPfN66j2cLXjfRNE5zpx0CwVncMTi4mIndNHvrb6PbtGNEmR4CKTrIlW/G+lY\nvd2Zf6XqNJ09ZsxV65Uh6jdn8croIvbu3/05uq4vinrjubo/uI93f0bKqDO9v467rM4RG818o0vp\n7h21V+pFv97vkz1zQr1R+JtLLdp/zo4nxUxMmnypVPHsA77POdczrvhgBkbGnPvvvx8A8PrXvx7A\njsgNALfddls7mVFB/Pa3v32snJdffrkV2d0YQAPQc889BwD45Cc/ORYmpvXzQQ2MXjJOsFFoXtYH\nGsoWiUmOzOlbRVJ30XBRS8X3bPJVA4KHvPmzilzIsjaoOOcLh+7fk7lJqciW5eOMgisyQ5ee633h\neQL0f58EonBRfzYe3x/1D+vgk7Be71CjSjahRuqRbMJR41OWESkaz1lf6CTsBiBCiVS2QOoY6AtN\n7UMVzysqKiqmwEwwTYcabohoVcnEVRcdtre3W6b54z/+4wB2dsADRszk0UcfxdNPPw0A+NKXdvIt\nHz++k6DpB37gBwDsGIbOnj0LYBT4TxH+wQcfBAA89dRTAMYzfbtxRw0AziSi0DPN5K3tzLI66bmR\nW9Jeoam6CmcOyYQyioytqaI9yuzNc1x0z9yJlPV58gYVATMGpv3m1zsj1jZ4Vh3fMZFlRv2kahIf\np87+lAFlzNfHUlR3LccTzTgDVvbnBkLfb6qvfdE9M/ekyPBIOKucJFNTVC+i75oo01YfKtOsqKio\nmAIzwTTJLDN2A8TKYnefcMakjIJGmF/5lV8BMNpLhOzhs5/9bKvHIxga+dGPfhTAjr7xa1/7GoAR\nQz137lz7m9ZzMBh0nHudiWl4WxQm6m33XQcznZH+FoVeZiGlERvqczbWaxRRurYsGYeWn+WwdIai\n6fL8nlo/1ymTMWn9XP+dhVPqrptklp4vUq/LsL293dk3PWOcUdvdPUYlhz6da5YuzsfQYDDoBGxE\nOtgocEShfZulmlO26+OMUMOOs2yXTNRt0Z+DM2ptQ+YGl6EyzYqKioopMBNMk9ZzXZGyFSeCJ0SN\nWA1Xt4ceeqi9JxAnfCU+9rGPARjXa7nTt+trIqfwzFoYpQmLnKw9CUSfnitjiLrq+70iNul6Sm8L\nWZuWkwUXqCuOuyfpvV3X5Xq3yEXIf4tYXxTswGszpukp9fQ3d/rW312P6yxycXGxEy7Jc3yfdmW3\nkduVlgvkwQ/b29utDt6lC2+D6tmz4Am1ZGdJoNWFMEstpwwvY+g6Vt1WESXwzoJXiOh5VqZZUVFR\n8RpipphmFILljE6vyXQmUaosv95XraZpOla0SAfpeihfrdSPznWafm9dsf1T+yLzz+zz38zCPC9f\nvpxuPxAxgywULnKkj0JTiYiJaHu1HGcLrruKrKXOvIbDYXuMDCy63hN1OAvU+maMmlAfx8xHNEqe\n0RdC6P3te2ZpIIJDdf0M2Mis5zruPEWdSxfKqH0MRuPW9aaZnlzh5UeI9Ot7zQXKPPvK7sNMTJql\nlI5IneWD1Gv8/0wRHj2UyODiDzeLsABGg88nHn1JPOY5eoGye/t9ontl2XK0XS6eDAaDzrE+J+1M\nTaIinGfO8U3ZNN7d8x1G+UwzkUqPuwHN263t9EldFwefGHxy17b03Yvl+sRA6OTs/eUTYTQ+fOHw\nhQ/IY/YjN7Modt3LIXgORfy+iT+afKN+13ZH7kn+3vdlj9c+cfVWXzamaA6YBFU8r6ioqJgCM8E0\n6XKgq4uvEC4qa4hZlt0lWkH8N11pMyqvjMVF7syYEtW5LzdoFq6ocdvZiqi/Z23Xevpq3Bc3nBkO\nNGY+E+FVGvDynL1rnsnM2bvPFc3VENF1UfBDFjDg2N7e7mSi8jGg++I4g1PJyVlPFGcNjBseNdZc\nEeUYZf/RnS5z91JEoZZ90kCmfoi2Ao4CIvSe8/PzqcFRn+te75H2hWf/j97tvqzzfahMs6KiomIK\nzATTBGKHZaC7CuhK5itWtoJHehs3AGxsbOwZuK86MF9po4zh2WoX6eZcd6juFNw1T+uq51BfqM69\nhBs4Ikdi7zd1/8n0n6ozypKrKCPIjB1R+70cv1ZZiddP2+nuMN43S0tLqRtYxGo841PE4CJHfIcz\ncR+/yu4jaYf1IfryhbL9Pva8HDVkqq5R26ntdoOZt0ndzPYy/ERJQiLjUaQL9fLYTr6nrp9VXXim\nt98LlWlWVFRUTIGZYZrKDHQFz6xn0eqQMR3VI0X3ZXl+XaSvzML3omQJXndnZHp+FvalrlhsM62Y\nzmSHw2HKutXivldKrFLKWHIMb1eGzH1KrZpZfs6FhYWO10LGIrX/9tKbaTv93K2trdSx2dnV1tZW\nmlZNpZbMVSaSMjL3GLXY+zFv38LCQutS5Tr0yEUo0w9Pw7q0Ltk40/8znbz2VaZ/1rHk7NaTrCwt\nLaWSkb+fS0tLE+l6I1SmWVFRUTEFZoZpRtY7xSSJS/usYL6CuQ+Zrvp9PmHZb86g1tfXW12T6+3c\nCgugk8FddZHOIHx/F2WemSO3OjU7q4gY3F564ih9mUNXfQ+RdEbmmftZtp4b6SYj9q7HtX3eb1Ho\npofDuqVcr4/GkluwowTKnhzYdYfE2tpaR2dI/bYi28VTGXvGwCKdZKbr1jIy5qvvYuStoJ/6Trql\n3vtCdZqEB6NoO93WQPBd2dra6tR5UlSmWVFRUTEFZoZpbm9vh/oU9xHTVSoL8nfWodY+12+pH5iv\nhL7qacSH1jv7dJbC32jRU4u9Mi6vu+tG3XobhSt69FAUCZFtt7CystKu/J7+rM8DwBmFMrGMTSmy\nFd+lhOy5a/l9LDKy1Gf1ivSnhCfY0OioKCoHiHc+dF189Dw9tFHZpLNG1y9qGHH27LVeWVSN6kiz\nJNfax66b9vdSy3Aduvf1wsJCynyjLTH8vYqkFN/9dFLMzKSZxYFmzuNRnG8Wp6sTYt8k7B08yUvq\nIYP6cPxliCYVF3P6MjV5O30iUpEoE6cVfXu3UMx3kTYyuER9qeVtbW21ky/L9fJ0oytvr9ddAyGI\nKAY6W/zUyJCpfbyv9Z5ZuK0+80kmE7+nh1M2TTfnI39jf6pI6hOhjwH9313kor2HvA/6YrXdYKVi\nvqMv1j4LuYzeYX9fI7Weq2b0/V9dXU2v60MVzysqKiqmwMwwzQy+mkdiXsYEo3MyUXdubpQ5PMrw\nzXMzN5jIpYFwBqF18MQfzii0Db4LnzOfyLDk4vry8nLKAFieui55/kuiz0E/S6YR3UsNYBmzjFzI\nvB7uoqL3z9QHGqLqRju/Vp2hvV1ahubN1Hspm3FVh4uUep4aFrVc7RMPbeV3FXmzseL160ucoiwy\nyvav3zc3N9PsVJ4HM+qTiI27tBm56bn6I8sbqglY9F2dBJVpVlRUVEyBMq25/TWpRClnAVwC8OL1\nrovgKGarPsDs1anWpx+zVh9g9uo0S/W5o2ma1+110kxMmgBQSvl00zTfcr3rQcxafYDZq1OtTz9m\nrT7A7NVp1uozCap4XlFRUTEF6qRZUVFRMQVmadL88PWugGHW6gPMXp1qffoxa/UBZq9Os1afPTEz\nOs2KioqKfwiYJaZZUVFRMfOYiUmzlPL9pZSvlFK+Wkp54Drc/7ZSysdLKY+UUr5cSvnp3eM3lVIe\nLKU8vvt5+BrXa76U8tlSyh9d7/qUUm4spfxuKeWxUsqjpZR3Xef6/PPdZ/WlUspvlVKWr3V9Sim/\nVko5U0r5khxL61BK+eDuGP9KKeUfXaP6/MvdZ/aFUsr/U0q58XrWR3772VJKU0o5eq3q82rhuk+a\npZR5AP8ngP8SwH0AfqyUct81rsYmgJ9tmuY+AO8E8E926/AAgIeaprkXwEO7368lfhrAo/L9etbn\n3wD406ZpvgHA23brdV3qU0o5DuCfAviWpmneAmAewI9eh/r8OoDvt2NhHXbH048CePPuNf/X7th/\nrevzIIC3NE1zP4C/B/DB61wflFJuA/B9AJ6RY9eiPq8OmJnlev0BeBeAj8r3DwL44HWu0x8A+F4A\nXwFwbPfYMQBfuYZ1OIGdl+67AfzR7rHrUh8ANwB4Ers6cDl+vepzHMCzAG7CTijwH2HnJbzm9QFw\nJ4Av7dUnPq4BfBTAu17r+thv/w2A37je9QHwu9hZeJ8CcPRa1ufV+LvuTBOjF4B4bvfYdUEp5U4A\n7wDwSQC3NE1zcvenUwBuuYZV+dcA/gUADZq9XvW5C8BZAP9uV13wK6WUletVn6Zpngfwr7DDVE4C\n+HrTNH92vepjyOowC+P8fwLwJ9ezPqWU9wJ4vmmaz9tPs9A/E2EWJs2ZQSnlAID/COCfNU1zQX9r\ndpa/a+JqUEr5AQBnmqZ5ODvnWtYHO2zumwD826Zp3oGdkNcx0fca989hAO/FzmR+K4CVUsr7rld9\nMsxCHYhSyv+GHTXUb1zHOuwH8PMA/vfrVYdXA7MwaT4P4Db5fmL32DVFKWWAnQnzN5qm+b3dw6dL\nKcd2fz8G4Mw1qs63AfihUspTAH4bwHeXUv7DdazPcwCea5rmk7vffxc7k+j1qs/3AHiyaZqzTdMM\nAfwegHdfx/oosjpct3FeSvnHAH4AwH+/O5Ffr/rcjZ2F7vO7Y/sEgM+UUl5/nepzRZiFSfPvANxb\nSrmrlLKIHWXwH17LCpSd/FO/CuDRpml+UX76QwDv3/3//djRdb7maJrmg03TnGia5k7s9Mf/2zTN\n+65jfU4BeLaU8qbdQ+8B8Mj1qg92xPJ3llL27z6792DHMHW96qPI6vCHAH60lLJUSrkLwL0APvVa\nV6aU8v3YUfP8UNM0q1bPa1qfpmm+2DTNzU3T3Lk7tp8D8P+3b8cmCMRgGIbfzlpdRKwtbL01HOMq\nt7C3sHUAR7AQsVBUcA8bi0QEC+EXSRTeB1JdcR8hfEcSbpjXV5X5+UjtQ9X84WtIN3sXoK3w/hFp\nG7UDtnk0QJ90GXMC1kCvQrYxz4uganmAAbDJc7QCupXzzIADsAcWQKd0HmBJOlO9kQpg+i4D0OY1\nfgQmhfKcSWeFj3U9r5nn5fmVfBFUIs+3hn8ESVLAL2zPJelvWJqSFGBpSlKApSlJAZamJAVYmpIU\nYGlKUoClKUkBd3xDuPwTlavJAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(U[:,0], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"reconstructed_small_M = U @ np.diag(s) @ V"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And the people:"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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RWC/6sZhmKeU6AP8VgPfT4bcD+MD8/x8A8I7jtJFIJBKrhOMyzX8K4B8CeA4d\nO1trfWT+/0cBnO2rZH9/HxcvXnTtlQZNScb2RQ1O9ZJ9eOyTUUrp2EYjr7DWzWU5/k1j9ax+bkdn\nXw0ir7V2WK2xGWOulqjhqaee6iSbtb/Pf/7zARzE+xnTUvunjSMvFzV5rB5jwmwTsj7rkj9mKMyu\ngS5T5/upae3sNyfONcZl19iYWFzjzs4Ovv3tbwMAzp07t9Rfi3l87LHHFn2w/hiz0wQU3Jbu+mjH\nt7a23BSBXGZzc3MxPtYHW0Z51VUHliy7VzfccEPHnmtgVqnxorp4AYj3LPLiF20MDKrRnT59enH/\nVC720kdJOLxk31EinFbgumcbjXwDrWD5sTjyR7OU8jYAj9Va/6yU8kavTK21llJcKUsptwG4DQCu\nueaaJXWb178adOA9Z5HCU70VHLqhbeiDxmpEZLDm+jRcygu6N6hKy/VHqxzs5edwD3VsaQA7r1pR\n9YsdTBpKYtDJYW1tbaESax5Hu3Z7e7vjsFEVfDKZdF56DSXjFSn24bF67CW2OthBYo4VL6OUTsZ6\nH/nDb3JZWypXKWVxnangat644oor8D3f8z1LspojyFYC3XjjjQAOJihVp23iYHU9CvbmD4ddr8+i\n9mV/f3/xrGhWd34fdFWbt0dWtGWvp3prGYW3uEBlYSeWyuOtNjtqlqPjMM03APjxUsqPATgF4Lml\nlH8J4BullHO11kdKKecAPOZdXGu9C8BdAHDTTTcd//OfSCQSlwFH/mjWWu8AcAcAzJnm/1Jr/dlS\nyj8G8C4Ad87/fmRIfWzonc1mnaBeDbWYt7soH8i4qFuvUcY6nU4Xs5GnOtq1UfCt12ZkYGajvDKd\naE8kIN4xkTPYRAHwFhqyvr6+6J+qaBZCs7m5ucTYACxUXZP9mmuuWfTXzAN2vam9xkI4I5XeR2O3\n29vbnXXtGnLEZhhjbroc0Pq2vb29MFWoesn3Xu+RXa/se21tbVGfspZWRiv7awybcyxYfWY+MNOH\nsehrrrlmcW9tbNV8s7a21tGI1AS1vr6+6Iddr5oNa0heOBjQ1SCsvDdubG7RJZLee6HnWhmSouWY\nXn/0Gfd2dRiLSxHcfieAN5dS7gfwo/PfiUQi8Z8FnpXg9lrr7wP4/fn//wrArWOu18BVtoeoHYR/\n9y0Z9LKBqzG6tYeyBgRzIhFlhmoT297e7jg0bKbma5X9qDNqY2Oj43jQgHMv8UGUyGJvby9MjqAM\nm6/X8WdC6mHFAAAgAElEQVRmYSxGnVDWzyeffHLBmNRBpayZoeyDM9Wr7VFZqbfkUjUSb9kdM3I+\nfubMmQU7i1jLzs5OZzmssiq2pdl15vjR+3H+/PmOs06XvG5vb3fs7Gr3vOKKKzqhRdFYrK2tLcpq\nCBovUNDgfV3csbm52Xn2lN16tkR9dli70vKetqf3RsffS7TTSrrjIZdRJhKJxAiszDJKb3kf0F2C\nxUvDlA1Ewa8tewhfqzOg2tKY0aotTb2ROzs7HRaqIUfsEdSs7mwbNfYT7bPNiRQ82y/Xx97zaB8g\nPmf2NbVp8jUalmSeY2M8Fy5c6MzwGqa0ubm56IeNobEYrZ9DyNR2aGnWTp8+3VkS6UUEaMiXJmfh\nAPkoTMd+P/XUU4t+ato+9rTb/eR0cQBw//33L8niLURQb/f29nYnSYiG7aytrXXGQjUSL3BdIyUM\nbKM2efS9unjx4kIe07D0nvPy4kjjaoX5qf2SbdRaJlpiehQk00wkEokRWCmmyQGuLZuQ93+gy648\ne1nENPf29jpsz2MWUeIJjQ+rtXYYqmZy55Rdej3bZDRxrDJDzpptfVAbIqcfUwahDPbBBx9cLN20\ngGvz3ho4eJv3q2Ewc1cbprePkCYXMahdb29vb8EajaUpM97c3Fyc+9rXvrZUj6c56POm935nZ8fN\nNg8cjvVTTz3V0YzUnsdxt/q8Gpvn9Hkap+mlW1P7vMHGZGtrq7MsVFmb7pAAHI4te/5NPl3Kq7ZS\njgzRsVAtjZ9b7acXATMkZlsZpvct8CJUhiCZZiKRSIzAyjBNXW0TxRt6s4KXJIN/c2xca8WBoc9z\nz8eiuE32QqpHnD186r23GZc9xRovF+19w6xDbaXMoLRf1t8vf/nLAIBf/uVfxqte9SoAwB133LF0\nvSefsVGD1v/kk08ujmnCXR5rtbFGkQ211gVjMlamK404AYyOrf3d2dkJbV3qvfVifTWWlZ8zY5/W\nX1v1w8t1OY0a94WfLbWLW72s0ZgdV8fU09zsOrXv8rMarYzj8dQoEoPnida4YH2/tre3O7ZyZfze\nKkG9R15Mc2TbbK0w6sNKfTSZbg9ZKxotg2oFz6oB2HMEqcrhyeKpDXqNhsWokZszyuiHlVUafQm0\nf6wuap5EXVbJuTJ13Ew1q7XiuuuuA9B1LnBIicnC//fw8MMPd/Y10n6y6cM+MPqS8QRl50xmXW99\n8eLFxRhYIL6ZGHhNdN9kyuqrt1SQ5eS155qhnvf4sXP68bRllM95znMW1+pLrw4Y/rDaGNv1Gljv\ntakOFw7/s3M2xnyvrLyNu9XHJig7Z33XvLL29+LFix3TiffMqyPJy0JmiBax8HgedRllqueJRCIx\nAivDNIHlUB+dPZReczZ2ZZGq1q2trXXov4KXfQ1hrhEL5dk4UjV4do/qYcdBn8rt5Xw0KINllmYh\nPV/96lcBAI88cpCc6id+4ifw2te+dlGnycFts9zKHNRpVGtdOIvMwWROD2MYZ86cWbAnTS5h17La\nbv0x1qbL+M6cObMob8zLxsKY7O7ubuho1LAzvp+6PNCuufLKKztJUJTJcbZ4dV4Z+Lj1S/c34nAe\nK2/PjGah52Wxhujd2d/f77BR0yQMOzs7izHUIHlmk7qfkTo5OemHslCTy9gqm5UMXuic3hN9B71E\nONEy7AjJNBOJRGIEVoJpcsgBsJziSYOimelomILOJmxz0tmtZQRWe4pXts9mwterbY4N2urU8Wyu\nasvU/rLtVO2nKiezK2MLH/nIQU6Vr3/96wAO8nPauNs+NlE4EAc+q5PBGOKZM2cWbWp6NdYK7Jw6\nvDS4+vz58x3HFI+Xta3LTo15mY1uZ2cnHCd9ltbX1zvaijEwq3d9fb1j8zUnDT8nZtdV2S0XqI45\n0NWiONWf7rapdvbz5893Auq1n/wcakC+ajheGQ3jms1mCy3AWG6UCX5/f39xTgP1WatSlq1jwukY\n9b3UZc+cIChDjhKJROISYiWYJnAw+2igLdD1PHvebg2I1aBVZq5euy2ZgG4SAEYULM/98WQHlncJ\nNHgzZWT31FmUQ16UbXPiDV2ueN999wE43F/nqquuWng8f/iHfxjAYXZ4q4eDpXVZnLLnU6dOLerT\nZYDWh4sXL4ZeeK3PS/DcihLQYHROcqxeX00abODdBLSf1uapU6c6yS40ez8zTbWNaqD+xYsXO2FS\niu3t7Y4WoFnjn3zyyc4eT1qGnyWNROClria32rqV/T3++OP47Gc/uySXhbHZs+QlNTao/X99fb0T\nFG9MVrVQPhbZrCeTibvIYQiSaSYSicQIrAzTZEbFnsoo8e7u7m4nsW0Ui8nXqQd0CLjskOB4+x3F\ne3rX6czYWi46RIYoYcdsNuswemM+d999N4ADlmB48MEHARza21S+vb29DntRRsD2QC3L9i31nqsN\ny4sv1b2CuKzaxa1eS/a7t7e3iBiwsuZpVwblpRnkxBr2V22Emg5we3t7aS8mrsfkYruxPcvG8tTm\n14oH9mzdfUtVp9Pp4pzaqM12u7W1tWCLais1PPDAA/jkJz+51L8vfvGLAICf+qmfAnAYPzudTjt2\nf/Vo80IE+6vxmtxPZZ+ePVQjQYZiZT6a3ocSiFeHqMrFUAcMryaIgpn397vb/HrqtX7E1UnjBehH\nHz0uMyRTdStQV9uJAndrrZ29bSyfI4cn2f8fffRRAF1DP8trTglV+y306OLFi2Emfu6Tbj+sKrz3\nfESrwDj7v2Y5MgeVZx7RLYF5S16+jutl84g+B/bRZAeMrmSxFVX2IeI+RGExvALKxtSO6Uo0llE/\n2N6HVtVy3mYZOJhkOSs/98/qu+GGG/Dyl78cAPAHf/AHAIDPfOYzAA4nh3e842CjWg6EV4cNT3w6\nmapDdHNzM/wARquR+NxQpHqeSCQSI7BSTJOZUovt8V+gnQkaWA6Gjpw6HrtVeEwiklfb9/rCfY6C\njVtB915oVB8r9Y55qrL9/6GHHgJwyCS83I2aU9FbhmfHOFSG4bE+Dc3hUCF1eqh6/swzz3ScOiYn\ny2vsLNoXipdr8n5BQHcL39OnT3fUX2/dvLJtk8H6y8+ism4D79cTPV+cW1UdXmo+YPaszNzCpr7r\nu75rcY1uxaw7kZ45cwY33HADgMOQNrt/v/d7vwcAeMUrXgEAuOWWWxaLHjzZ+TjLqk5O3i1Bnw9l\n1tPptBPCNxTJNBOJRGIEVoJpGuPi2SRidB6rjFgVO2Ja4UhadyvYVeWJQhpaZT0m6y0Tjc612jRE\n7JR/W3D7Aw88sFRmZ2dnsVe45aIcYlNWm6H1YWdnpxMErSyBWbeG7SiL5OQN2ra3pE5Dg5hpGjNS\n+50m1djd3XVDWxjevkRqk5zNZos27Ji1ZbY+fp6trPZPQ624fQvvYvuzjoU6A83Jw5n4ldF576cy\nOuv3/v4+rr76aldWk88y1b/uda8LnX3MPHUs1bnFGeDZzsn91lAr7dcQJNNMJBKJEVgJpsm2OD4G\ndFkjM80oZZqW5SzShiEes5ZdsI8JM3OKluiZbIDv1TOot1XlG9MHXj5mjMuC2tmjrem8rG21jXGY\njZdV3PprrNFYqGeHU3uuhotwALYGwns2Ow2ZMTAjNLmipXnW5re//e3FObPtaVIZXkZp8OzGVreN\n/1//9V8DwIKZ2RhdvHhxEYGg4Uk8tppF3ernYHQrr+Nm9XF+Tb2PxkK9sCtlchxuph5xjRThxC6q\nDWjijlJKJ5GLLu7g/LTRzqhcts8XEiGZZiKRSIzASjBNBQfsRizSS72mjM7L0twKDI884FzvEFuh\nya1tertntmItuS6+LkqW7CVh9by3Vs7iAn/yJ38SAPC+970PwIGX0+xsmjE88vZ78jKb1EBwK6P2\ns1Y9Bl6iqunGDJwOUPdm4np0L271KnOKPl0CqjGYfExlNpRS3GgFHgv2rmsAt6Zt29nZWXieo714\nOBs7993k4d/MytWTbfbVjY2NTkyovnOces2eIWW51petra3FOQ2S5wgITTai0QecGlFt8PqX0zKq\nfbwPyTQTiURiBFaSaXrwGE3LVuiVA4btZBe17dleW572SD4vJjRaNcSMui92lfugzM1LAWaz+803\n37x07Qte8ILFKpXPf/7zAIA/+ZM/AQC8+c1vXqpnNpt1mI0y/+l0urAxaUo3k/P8+fOdhMnq6fRS\nkymbMcxms5Dt8RLJaPdDtb+xrPbXllxyn5TBeWnWbCyMpantz8ARAAZNLLK7u7s4pnGjzKyVCXI8\nJeB74XUFDjNtvSc6NqWUxTOkbdmYsA1Xl27qqjX+v8mhyVCm02knWbNB3/u9vb2lxNBjsPIfzb4P\nIp9rqbjRh2fMEqrWGlV9KD1oW56JQcsOcT5xX1rLRLVNXV9t9dx666149atfDQD4xV/8RQCH69Lf\n+MY3LvWTP068lTCw7CzQh1mXVfIyuZbx3uRVZ4WCsxzpOHF/NTA/+nBPp9OOCUCXJu7u7roOEf67\ntra2+HgYoj5sbGwsPrBRRp/ZbLbIFWAfEbuG831aG7y3EMvOS0Kj9e7eFsamGpvqzOYOk8P+Whib\nXW+hbhcuXOhsjGfgtnTHAr1nbBKLJkw1FRwFx1LPSynPK6V8uJRybynlnlLKD5VSri6lfLyUcv/8\n71X9NSUSicR3Bo7LNN8H4N/WWv+bUsoGgC0APw/gE7XWO0sptwO4HcB7h1TmBawPCeSOmKa3XLEv\nEN6Th6/tMwGwYT1yPnlBwlGbGvTv1ectozR4uSg9pxpwmO/wJS95CV760pcCOAy4ZocIsBxuowxO\n2dt0Ol0wGTun++IAfqIJlk/7y21o+JkXHmPg/J/qaFF1mBm1BtlreMzm5mbI9I3hcFiS7v/DWwub\n3FG2Hu6vMn1Ti62d9fX1xVJI25vJxtTuL2cOMlarWbDMccjhfryHD7C8KMCSvWjIl/XPZDl//nwn\nu5SBHXTK2tUJuLu723kO1NnGjF+TxgzFkZlmKeVKAD8C4NfmDe/UWp8A8HYAH5gX+wCAdxy1jUQi\nkVg1HIdpXg/gmwD+eSnl1QD+DMB7AJyttT4yL/MogLNDK/SWNuls4i1TVLbRYmYtu+dQxxKX0fo4\n1KGP3XoyazgG22kiVqrL3bTP3jUsq7EQ2+v87NmzC8Zw4403AjjMfeglPFGWZuFJHF6kNkgNVOac\nm5puTMFsJAqlqbV2HCsaXsTLOxVe2JQyc5WXc1GqnZLtcRGb1XumDI1hY7O7u7tge+ZYufbaawEs\nP1tWt+6/ZHLycXU2eUlIdMGFaiCcMEX3/zGm+f3f//0AgJe+9KVLCwSsXzw2zKj1PphcPP5R6kY+\n3nq/WziOTXMK4LUA/lmt9TUAzuNAFV+gHtwp9+0tpdxWSvl0KeXTtgY6kUgkVh3HYZoPAXio1vqp\n+e8P4+Cj+Y1Syrla6yOllHMAHvMurrXeBeAuALj55purepKVPXosK5pFvGWHautSJsA2yBa0rb5w\nID7m2eaipZGe11x/t+SN2uRxs+tt5ucgfLM3WYJi2yHRyhoT3dzc7DBeY0icwFdZggVKe4xV75+G\nnzBzijLecz91iSU/A8q07HpdmrixsdEJTdEy/Nzqvkncxyjdm5ep3uySdo2Nm/3e2tpaeKfNLujt\nkR7Zi42x8vOsNmDNlM42alsCavZZZtSmcWjyEytjXv/ZbNZhpSYXR054oWw8XrPZrBNAr6nrVEsA\nLmNquFrrowAeLKW8fH7oVgBfAvBRAO+aH3sXgI8ctY1EIpFYNRzXe/4/A/jg3HP+nwD8Dzj4EH+o\nlPJuAF8F8NN9lXheXz4HxEskvbKenSpK2OHZAVvssRVYHkFlZoYcsWWD5+WL6lNZ+S+zy8gOxXuS\nWxnznNo53WLAs5F63n09ZuyDGZ7a2RR8P6Jx42eAkyCzfMbM9vf3O/Y7jVv0npMoAJu959x3Bnvs\ndWdPjUO8cOHCgvXp7pasFWgcq7Er6/fGxkYn4F1ZuLeFiPadNQi1F+vSUAD43Oc+B+AwMccb3vCG\npXruvfdeAAcxwK95zWvc8eJ9fJQleluAKEvW54Pt7roEdCiO9dGstX4WwC3OqVuPUy8PXLSFL28Q\nNkR91Rday7AaFX2YC62h9l4mbbMv/IczDkUOKs6iriqu9rfVJo+VXm8fRPuY7Ozs4Ny5cwCA7/u+\n71s6pxuj7ezsuFsbc58mk0knMNq7rxpQHoFNKVEQ82Qy6Xw09cPoZYvX9dvswNJsS946eu2Dfsw9\nB0Rk3uB6ohC5/f39pXXoDJ5sI2ep3U+WRU0WBnZy6nW6Quhb3/rWYiM1c0y95S1vAXD44X7/+98P\nAPjjP/7jRZZ3zaDPq5PMNKGruHjyV/VcHcqavZ/LDkWuPU8kEokRWKlllJ4jKGJgTNejmdtbOhjN\nKrV2Mxh5JgFlJpFTpsX+mJ1G2dgNY5Z5srqiDjSu3xiXlTFW+SM/8iMAlpcMfvd3f/dSWV1S5y0c\n0IwyrE5H26byGEV5Ur2yHJrF1wJdls376iisrKrl3I6uVdZ8mrzNbMQ0Z7NZZ3moMiZm6DbeJruF\nh/H4RzlAWd1XBmyszdsFVXMIqDpssvB1On5/9Ed/tHD0vPWtbwVwEMrG43bTTTcBAD71qU/he7/3\ne5fKWL3mkHz66afDXJvWz9OnT3cWuhhUTZ9MJmH2qz4k00wkEokRWBmm6TlZgDhIlcupfTHana8F\nL8RHmVPLNuQxnchxw2gF26vsfUs4PfbthVipXMYczNlQSukwuMje6PVJZ3uPjerMz/kXIzuewdvP\nW22c+/v7i3PWP7V3ra+vd1i3gZODWH2alchDn9bD91MDsb3+mr3S5LSwIs6sb+XNuWZgB58XngMc\nMkPPIWd/rV5vB0yr5+tf/zqAw91Lf+d3fmcRvP76179+SS6rz5Zl3n333Ys90c1ZZPfKbI8cFqSh\naWx71RyqaofmHJq6b9JQJNNMJBKJEVgZpgn4jDBiYt6+P4Yhyx89D3Rky2zZQyN7lAcvY3cfe+Q6\n+8KmJpNJyMz5r7Iebw94L8s818NsMMpFyfVGTJPbVNmj5BceM/DGUW2HGuA8mUw6adp0LJh1eUvx\noj4oA2b7rjeGQDdXZimlE5jPwfbAssfc2Ke1ZYk7eNmj2gHNRsp2X+2nRh1wJIGO0z333APgwE5u\nrNGSghhrNFvnC1/4QgAHXnWzq6vdkrWWvuiR7e3tzjJMg94zZsvpPU8kEolLiJVhmmzTZKjX1eAt\nv4tYjMdg+7zpfM5jen1B6UC8f42XBEJlZNYWnVOwd7/l1fcCkSP0sXm+b1HiCc8O3Rcd4ZVt2W49\nr6kyOs/ey4HuQFdjYJuYyaF2Ri8hs7WpjIyD0U0OtSHyeY1vtWvM5sdJgy0e1dgn2ys1akF3zeQx\n1iWNxsaZaeoOAcYab7nlIGz7B37gBxbpBXWMrb7rr79+Iad58w26n/rTTz8dsmy+r/rs6fh5Ma3J\nNBOJROISYmWYpseS7DiD2UZkSxuzLKpV1pMnYn0t22F0LZdpMc6+WFBlLECcMo0R2T15q4hofLjf\nEdNszeDKwLz4yoi5su02ktNrmxOI2N/ITmxgG2CU1o5Xw7B9jctydIWOu7JcY4zee6DLKFvaBa/6\n0eWYmviYoXs+aT85HlVXD/F+U/w8sXzGKnlLkIj58vYomgLR00C8fZa8v14yn6FYmY8m0A77URXZ\nU1sN3svmhcFw2ZY8HBbTp65ycLPeDC9jU8upoHXr75ajyguXUkTneGz7VG92ZkUPpjfBecHtGugf\n3V/PmaV94qw4uu7YC7+KXjZv0y0Nt/Emcl1fzm3qR0T7rWon0A3M57KaVd8zLWjIkX24NKcAf2C1\nTXauaD4E3Q9oMpksAtOjZ5EnFjun+T4NGxsbnfAwHQvOceC1wX/39/fDDGp9SPU8kUgkRmAlmCar\neMAye2nlrYzCWPR3iyEyG+oLMfIyIimYRShLUXY0NOSoz9wQhSRpW/Y7Ch/isdZwDK2bl+xpPerY\n4GvVFMB9iEJAvLAdDWvyHEoR09dFEPx/u0Z3k/SgoVEsa3Qdj606jYZoA7qIYn19vTc4m5N6qIlB\n7xGzNc3vaeCdQ5Whc/5P+79mg9KlpjbWfEzhmZ48NV3HVvvNzra+JcwRkmkmEonECKwE0wS64QI6\nC6tN0rOBRQzFC0VQtFgfz/KRg8W71gsa577t7u52jOWerS+yx6p8XkIRj4V4QfH8l21XLWZoxyN7\np7djZcTEWizZc/ZEdt5WeJNeM51OO8vsDJrqjM/rPeeA9j4the2eau/UsCJmcZr7VHen5DJ6P9i+\n2xeWx2W9c3rM2rcgeVvmCXQTm0QB53zvI3braXns0DOo3VrHmu+ZpwkNQTLNRCKRGIGVYZpqG/Ps\nRcCy3dLznnnw2IeG6bCNNJqVuR5lkRZszPVFyS48xtiy+ygLUu8r16ezpzc2aofyWHLELA3ePjt6\nrhWg742p7ukdeUm5rtY9ihg1X6u2y8gbz3bxSNvga9V+zWE7+my3NKVI4zJMp9OFl1tDcth+5+2b\nxfWx91qZbpTsg/tnSyNt6ebW1tbinI0x7+fO9XAyaGX49l7VerhcV59/lk/3bVLZmdXrQoGhSKaZ\nSCQSI7ASTNOYCLOGyGvY8p7rbOUxnZbdckggd5TsorX4P4rH410aW7Y+TZwQ2ZzYAx2NGwd0e3Zi\nbdMQ2Zi84Oro3vE5r17tl/aF2Zbec/bAWpsttm2IvNJqs2s9b7qsEvBtoVafBvarJsJ21r4lrxzQ\nrePOiUp0+wj1YPM1yjC9+6L1GCz+c3Nzc+E9N9umLivme69RC57Ntm/xxGw2W9oDHThcKGD1872K\n0gL2YSU+mi20ApwjQ7+nokYvB6tG0UvBbeoLqAPeclp4D2r0cfPU6Sj421PvvCzgfJzr9VS2aAy0\nT95k48nVV4aDjaPAdc4CFE0c/FfHzZvYokUF+iHzyqg6vLa2Fn4suU+Rk6LlDIucFuxYUnAYkaqt\nppJq0PdkMum8G+qo2t3d7XwAr7jiiiV5t7e3O9sPR/v38OSgpiPPUReZ5dhUZPXYh1FXgwH+woUh\nSPU8kUgkRmBlmKaGEEUG+SGB4UPCdjxmEq1z99R8DbhusVKtj//qMsohyx7telWROIyipfbb9d5W\nx4aIQetvLwN2a114K7RHZVVmyKqqllWVlI8pW/FCZ/oWGbBpxsChRlE/+5aPemD5tE1VmT1TlmYg\n2t3d7TgatX5mkdofZaO8E2zLKWaqsS7V1C2VSykd05OGJzGiML319fXQaarysVYwFsk0E4lEYgRW\nhmlGAeiR3TI6BvhOo1aokVeHB7ZHjWGRyni8+lpB82ocV1alzMyTp8VcvUxLEbPUsBvP4aLXMLQM\nB3RrNp3Irsq2q0iD4P97z4PKEtnJIpuuJ58XfsUy90HZG++bFDllZrNZZ9GEtulpSGbjU3vq/v5+\nJxBcmSaAjsPFsrJbPZubm53nXwPPWQOI9uvxtE99Tvh+qi0/2jmUnXZjsxwl00wkEokRWBmmCfie\n4xZ7GeJFtvr0mBeo3MciubwyktbStZYddQh09o28/Fyfemi9kCOtj5lONAYRA7XrvDaj8lzWsxlG\n1+7t7YXRC2xXHWJ3azFxk8uu8ezWfC2PmRdWY2W8SAavD6WUDuvW52xvb6+jNekzub/f3fNJvcyc\n6s3qU1skj7kGn+vOlc997nMX/TEb5qOPPgrgMCyJ5VUWqWF2k8mkw4AN3k6Vyr51TNiemcsoE4lE\n4hJiJZgmz77Asq0v8joye+yzpfH5IYxJ2/SSU2hZlcVjt57ds4/pcPtR28wqdWbVMszo1NvN+7J4\nyXO1Le6LJ5+3FHZIoHnERpllab+85A19SxC9LOoK9USzfKqt8NhqvWyTjJZstlK8RdEMe3t7S9nN\nuU2OcIjuue5zxH1VeyeXVbuiJuXgZ9GYpjFMjfHkWFMvVR3X742TV49GBej+S57mMBTHYpqllH9Q\nSvliKeXuUspvlFJOlVKuLqV8vJRy//zvVcdpI5FIJFYJR2aapZQXAfh7AF5Za71QSvkQgHcCeCWA\nT9Ra7yyl3A7gdgDvbdXFdhSqf+kvlwWG2SE8G53G93mMp2XT7LP1eTa+lq2vz5bGdq2+ZYEtW6S3\n7NHgpSaLloV6K2SiZWgeM2zZcyPWrv1mhu6xPeuT2q8i1tyCp2VEzxLvEaT3iBmUttuKAomeIc9j\nHsUocpvK0DWG1YvWUGbcGn/P8x+9a559MYoEYLtlFF3BtlF9pnVMOBHOWJvmcdXzKYDTpZRdAFsA\nvg7gDgBvnJ//AIDfR89H0x5IVacYQ9TpyNmzt7fX6zzxQhpYPmD5pig8NU/Lei+dyuGpuF4uQAav\n043UfVYPNchbH1Qvn6b2wQuz8VRkLWPQh5tf7CEhTNH99D6EUdv8/2hdM4+Rvvyq9ntmA82D2Vpr\nr/Ky3PpRYnNBlD2LnT+qcuszxR9VXSvuTXSa+1PHi80GkTrtjZsu2OBnMnq+rMzGxkbn3tg5zWQ0\nmXTzKwzFkdXzWuvDAP4JgK8BeATAk7XWfwfgbK31kXmxRwGc9a4vpdxWSvl0KeXTTzzxxFHFSCQS\nicuK46jnVwF4O4DrATwB4P8tpfwsl6m11lKKS81qrXcBuAsAXv7yl1cv48m8HW3Xrg+XjylbYBYb\nqXx8Xau+SIX0Zs8o8YHnPInCkjh0qS/EisOJorCi/f39UL3hv33ONS9sR8t6yzu1TMSeGS3Nw3Ou\n2Xkro3k6WT5tX+9RazmfshpmL5FTxzP19GlBXpseIpWWzQZROBjLpYswoveMy3qmEG9HSa9+fq8i\npr63txfubuBpAwatt5WJfyiO4wj6UQB/UWv9Zq11F8BvAXg9gG+UUs4BwPzvY8doI5FIJFYKx7Fp\nfg3AD5ZStgBcAHArgE8DOA/gXQDunP/9yNAKecaNHEF91zE8I35kO+RwkZa9LHJ6aLCwZ5RW5sNl\nIkyj/KYAABvoSURBVLbGoUuRzXdI6AQz7WicuL/ahv7mfkahRszioryjHuuOGD+zwcjR0sqN6NUX\nhVbpfWHHRpRRnh1oBi/IPdIGVAbWHFoOoNbySeAgY7plTW/lRbVr9Zj3Hugz6fkc9DlQVu89t5FW\nNp1Ow2eS36so0F/b4mzxYxN3HPmjWWv9VCnlwwD+HMAMwGdwoG5fAeBDpZR3A/gqgJ8+ahuJRCKx\najiW97zW+ksAfkkOb+OAdR6n3pB5DQlV8Y63rtfjfWFADJ1pW1599Sa22uSZP7L/eTO32my8ZB6t\nCIJW/z14YU4G7ueQult2Ni0Xhf8wm4zsnixfFL6l4PpaXv6W7Vf7FbXJ9UdM2BsbPWbsku270X1g\nu3grpEeh7M889uzJ7nue+PmI9ofy+qd9YptmZMv0wuDGIpdRJhKJxAisxDJKYHkm58BTL+DXykdM\nJPK48/+HzDIRE2M5ot9cNrJBenJ5CXg12DiKr2SoLayVmMTb3VLtd9FyQ7YXt+IOW8svgeX7oSyj\nFXsZRUyU0k0C7ZWJ4voMXrC2MijPjtp6BrXuqJ+8A2YEtkF6dkX9f5S8JLoO8L3p0TNtfdjZ2elE\nHkTysY20FSMdxSu3WHyrL/rODcVKfDTtxfNeqGgVAd+0KDO3F37S+mi2VBb7HdWjKjhvUKX18wvf\nF3rDzgUrq3uteA4XVev4Q+QFTwPLG7d5qqyOhY7JkI+4PtR8XMc0ktOrd8iHtbVqxdBSX72VMUPB\n9enE2FpR1TfJc5nICaL98GTnFUv6cYoch3zOq1efwejjxB9N7hejta031+8501Qu+91ySLWQ6nki\nkUiMwEowTaDfCeAxPC+0hct6ISqGyJFg5T0ZhsjL10Q7CLIqqNcpS2DZrU1vbyArG7EyL3QmUgu9\nJWZjzBpDynqzfF8oFN/naFGAx1z7HFVcj8HbTlf3sRliEmix5Mih5GlIhpbZRct6GZ/6ZBmi0vM5\n/WvOJy+0zXPcGCJzRovVexpJn+bG9R/F8Qkk00wkEolRWAmmaTOqFyIU2R04vMCzYfJfth22Zrso\nYw7P0pGNxMAyaBtRgDfLpXYbZlVRog4v3KnFLHQWVjtxaxbWUKbpdNoblO6xrZZNObLJcf06Xp4D\nIHLYeDZlracVhB89m55W4PVNxzuqz7OhexpYy8Gi6NPouA+RBtfyObRYt/7m523IwhLtg/oc+P2I\nNFUe6zE2aUYyzUQikRiBlWCaNvty6q3IFsGzjLf43ivrHWuFCOlspwxFywNt9qhlPLmUjTILaYXy\nMIZ449kL6TFUvSZij61+emwrsrdx/S2btMrVF8TMmb4j1uLZsbUPrSDrVj+H2OLUa95iZpHsLftu\nS2aDPnfeMx4l8OD/D9FstC/eNdHzy9ELUV88Zh7JkkwzkUgkLhNWgmkaPHbZCoaOmKA3E0WeypYN\nzLPJqc0xsqe2mCv3V+tRMAOLWEKrDrumlRLLs+tFdiyNPfUSPCg8BuzJ2ccOuL+a7k1Tk3l1tbL1\n92k23rGWfdCL9hgKL3mGtuGx5MguqLK1yg7xxvO7F937liai/fQ87YpSujtzav383A4Z96HLPBUr\n9dHklyN6yXgw+rL9cH1RSE/req2Hy+jLGr1IHvjm68ZWrcDwSC4vWDtSiVgt0YfGfnvbD/TJ4B2z\nemezWSdMqqVaqcy6cZhn8Pcy80SbiPFHphWypIjk8z440TVDHErcJ+2D9/GL2h/y4dLzQ+TjFXtD\nVngpWmUjR9AQ2T0TT1SWw/3GItXzRCKRGIGVYZr81We11eDN2H0hLjxLRwZmL/tPlF+PmUnkDODj\nrbAJYFmdjgzyrdmwFdKjrIMZY6SWeGYNHS9d/+6FROm2qV4uSg3tYfOI9kHZOGsZLcbf9wy1njMd\n21YY1hDHl8dCo/A1LwxOtYDWElN9Fvf3u9n69V63VHr9O4SleQtKvDIRWky/pX1G467Hh8gXIZlm\nIpFIjMBKME2zP/Gs0GcjaRm5vePK+rxZS9mAZ1dp2bwYrWBcrjcK+LV2dnZ2Qpk1LMZblunNtF4S\nj6hP0Zgwi1QmaPCYq9kneadE71rAd17Z78gB5N0rg9pVOTN6hBb7boWtRVqGx1ijelqO0VabLedO\n1DZf22dX9OyFHivVcYrGzXPqer6DaFmt92zr7+i9iPrTQjLNRCKRGIGVYJqGsQv4+8IKvFAEhTcz\nevJYmWjmsr+cVqvlKdbjEeubTCa9oRY8A/f1gb2tVu/W1hYAYHt7u3ON7jao7BY4TNIQ2ag4G7jX\nd4PeI2OjmvqPw0/Mo67wPKmtcBTPDuhdy+e8vkTagJ5neNEGgM+EPfamdvDI6+21H9nkuT4vSqXl\nqTdEy5FbbUXvFdfn7WZpf8fYnY+KZJqJRCIxAivFNFszdgt9MXbMwCLvuWcj9TzsUdb0FoMaEv+p\nyUf4Go3Vi+yMLFckA7MEDfa2Mru7uyFDUpsmEEcbMKNVr6+yBQ7kVs+4Z4czFhrdD77nUeTEEM/z\nEDY0hD0ya+t7tvk+92Xp97Qzz6YZ2UKHMC99NrkPkfbD0SN94+YtafSSq+g5b+my3lttm88flXUm\n00wkEokRWAmm6dkTx8SB9cVremW8WS/yOHuzUxT/xTanyGPf8thGXk0g3r/Gi/dT+XgnTJ2pPbZs\nnmaTw2yHfStUVGarQ5P6qh309OnTYX+8uFsdE4/Z9dk0h9qxDZFt2YPagr2EGNqGN26GIfGjel3k\nrfba8u5jS9sYYq9vta8wTUSfC9YoWnbmCJGNlFdbjWWcK/HRtEBk7lCfQd4LZDW0wm1aYQ99S7A8\nNaJVtu8Yf6ij3IocUK/16IOwtrYW7u/iZfFurZvXY/px4r6oqs3947/A4UugH+zt7W2cOXNmqe5W\nSE7fmHghJRruxCqkfoyGOCu8PX4i1bultmoZ73c02Q8ZC37OohwMfK+i98f7sA7J99DXB158Eu2r\n5e04YGg5jdQEpZOYV18fUj1PJBKJEVgJpmlhEzyTROr0kJAjT7XtUxV4xo4ofUuF8bLGRGoTM7wo\nUUdrdm+pVspmra2LFy8ujtlulqyyA1jaclWZSMQaaq0dxqpbt5bS3cnR1P1WViKvfyabmhiUSUwm\nk3BHTq43Yi8Gvq99wfv83Eb98Z5JBdermoLn4Ig0JO8eRctrW3J4fehz8nhy6G8vc/uYd1nLeKYK\nz5xhv8c4w5bqHFU6kUgk/oZjJZgm0G849phnX9C3Z1eMnEdcR2Rg9sJYtN5WW961LQan9XpJKbgO\nNpa3xtLOGduzMsoQuc2IUU+n0w7r84KQhzj2olAgvZ9ra2tuCAn/ZfvzEKdVxHS8oHY959keI8bp\nsaGWbb7Pbt+6nmWIdkbtqyMC33++nu+H55zj3yyTjqWXIrFlJ7bfkdPPs1l79u8h6C1dSvn1Uspj\npZS76djVpZSPl1Lun/+9is7dUUr5SinlvlLKW0ZJk0gkEiuOIUzzXwD43wD8X3TsdgCfqLXeWUq5\nff77vaWUVwJ4J4BXAXghgH9fSvmeWmt70+U5WvYLj9n1sQNlRVxWZylvtvFmX8+ONRSejXSMDawV\nkmJ1aPC42kyn02lvZIKXNkt/M0swhup5Re2vhg2pfXE2m4XhTFFWe+6D3j8OKYnAzETLtlL0tZ6v\nvggMz9btlQEOxqTPC+w9Qy22O+R5jbzc3HakqbGcKo8uzuB6tZ6W/XnIMlZDpL0MCYOK0Ms0a62f\nBPDXcvjtAD4w//8HALyDjv9mrXW71voXAL4C4HVHli6RSCRWDEe1aZ6ttT4y//+jAM7O//8iAP8f\nlXtofqyDUsptAG4DgLNnz9qxxfloJvDSx0V2PJ6JIqbErGiIB3uItzCS2YMymlYQdAQryzFu0YwN\nxDGXnCDDY1EMz9an9i27dm9vr8NqhyTEsPqUZa2trS3FWvI5rYPr8cZB73lLg+izV7bu2RA7+xAG\n20JrLFpxmXwN24Kj/g2RxbOvGzw/wpj4VgWXGRod4LHloTi2I6jWWksp41o9uO4uAHcBwM0331w1\nzKhPPRxryO37CHg3sBWMPsYpoH1guSMTg3ddn6Nkd3e3sybb60PkOOOPqYYC6Zh4D7mq3qxa9n18\na+2uMolW57A6px9EM0uwU2vISxE5jTxTUeTgG3I/eQIf4uTRY+p0i2RVeXkCa9XLTqPo/eIVXlF9\n3rHoHWSzUus+ROF5Xj/7PsLanzE4asjRN0op5+ZCnQPw2Pz4wwBeTOWumx9LJBKJ/yxwVKb5UQDv\nAnDn/O9H6Pj/U0r5FRw4gm4C8B+HVurNmJGR2wtT6Lumr61IdTGwmqPwmFjEmFrwZupWyAywrIJH\nTh7v2sgpU0o3R6NiiLOOz0ehIFxfpP56jiqDMWtjlhyGZuuYIzXTM9tE8NRDlY/l0nr5uRnqCDrq\nOU9TUgY3RJuKWJunrWg7QJwj1rvPkUmAy0QmLO97ETmzWkx4KHo/mqWU3wDwRgDPL6U8BOCXcPCx\n/FAp5d0Avgrgp+eCfrGU8iEAXwIwA/B3h3rOE4lE4jsBvR/NWuvPBKduDcr/IwD/aKwgatfos0G2\nWJ9nUI/CFTxDc8Sy2GYVsVwveNagZb09fTxEjNBjk1EfPMapOS75nC6x1D54rC8ywnPmdr0P3nJA\nDU/SjDfr6+sdp5OXsSnK/M4y92kl3vEhmkNLC+rTjLjNSK6Wvdhjk5HMXoYrj32qXIbWM97HRlvs\n27NnRzbNqH3+7dnij+oIymWUiUQiMQIrs4xSmVm0RJJnjL4Zf0yYBrevySU8lhYxTC91XeSR5foi\nbzyATuIJ7RezQmNXkfeb62mFcCiD8zzFdrxl29M2oz2H9P/ctjKw9fX1zr0y+6WBk3pEdl4gzt3p\nsZBo/HlMIrsdM/+hNjSPibV2CojabrFbhafltWyQkUbI7FZtkZ73e4i9eOxyR5PDk28su1yq88hX\nJhKJxN9ArATTVNboefC8v5G9zvut3lVuy8pGnmYvIYbCiz2LZPfaidhaK0pAl6VxWZ1h2a4XpVVj\nuYypagZ3lcVbLqd7mjNLiOxlvLggYh2GnZ2dTnymJR9hhtyK54vqjljk3t5eeB9azNFjZEeJGVb5\nPLui3gdvYUPEuLi+KB7YG78obtdbGhnd35aNlBHtXODVFb1PrBX0LbONkEwzkUgkRmAlmCbQtVlE\ns6e3M6RhTOxZ32zv1deyobaYptp0hsSKsT0oYqzqMfZ2CYzYJPfL29VP5fJsmVqfjg/fnyiBiKEV\nH+jZn5RReHvMRKuiVCauZ8gWIENWcRki5uq10YqHjBh66xjL21qiyb95eWErnVx0b/hZilhfa1WZ\n1sP3w9PC+Lf3DEVgJjwWK/HRZHXQfke0mg3qkcoY/QXaD8IQOSOVpeUs8j74er2n0qrskaOK1e3I\n0eKpdUMC4PtUUi+gW/cpWl9fD1Ur76Ok8BxMfcs8+f7qy+U561Tdb718YxwaHvo+lgaWr7VWX+F9\nqLWNaALmY1GImyer1/bQfqqsUdvRR9hrO5KT350hY+kh1fNEIpEYgZVgmuoIajllmF31bcHJM1Ir\nEQPghzR4qnyU29EzIygb8hhxpAoxOxrSP/4NHLI9T93UUBDFECM5z9J97KrFIluzfNQ/dnhF6iYH\nfXNQPHDo3JpOp2HyE0+WSLPxMjRFz5Kn9bQcmFFWLa+dMeYMhfdct8xSkarsaQ6R44fr7zOB8Tts\nGGLGicwQx0EyzUQikRiBlWCaCjboeufsb196Ns+43TKA6zEvjEKD7j17G3DAYiKbide3iKGw7dZg\njMnQClFRJ9RsNuvY8ZRVsm00cs60+qIMmx0uUbAxy6DXe+Ej0V7rLVukx7CjfinzHxKUzowp0pCY\ngalTTNnW/v7+4pyFVI2xTXv2de2319+oLPctCunha/rqMXiB8C27bCsEr8/u6fkIxjqEkmkmEonE\nCKwk0wTimZFn41agutYRzSYeA43sXLXW0AscMQuuL/L0MrwZu29W98oaPHk95gAsL9dUmTW5B7Ob\nyDvqeakj72gppRMepfbdlj3Q2LcXkhY9S7V2A/2V7Xl7wev985idZw83RKFZ1pbdh+l0utijXse/\nZb9rPf/ah+gdYrRsmi1vvLbR0lZaUR58PLrejrfeQ/7d0j77kEwzkUgkRmAlmKYypJaNoTVjtzyL\nfTY5j7mOCWYfkrBD4XkEFZ69J/KMs/xRLCczusimWUrpzPgaSM8sMEpywXJpqjkvQa0e0yTCastl\nOUyG7e3tTp+ifnr2u6gP7D3XmFr+G6UVHGJftL4Yu+T93Yeg5V1uLazg4y1bZAs6Fi1m6EWy6PPq\n2XsjVszPX2vnUm1zTP8YK/HR5A+M/j5KgK0G7PLLEWW1aTkHWg9U5EDg1TmRfNouY0iGG3XyeHki\nFfxgseqpZSKHWUstNJm9FzRS0Vrqpt57XuHDYUNAnJmK++md63N0MYasyhmy+MF7Pr2/nOuglWch\ncix5ckaOMn6mIjPXEAfTkLa8iUkn/iEr2bycr8dZvDIUqZ4nEonECKwE07SZpmWYbTl5+mZPrx4t\nww4SVRFY9W4F0qoskbnAM9D3zcZAVz31wpO0Ps1wvr+/32Fn3trziDGZDK0la0PW/nuw69TpwfWY\nvFFweyRD1F50Pz1G7K119q7xruffkdnGM4m09sPR+lSb8q7pC6/xHI+qFRz3/fQC2SOnGmsoGgZn\n4PfCnmXNQWvPlKfBjUUyzUQikRiBlWCaBp6tokB1zw7iGeT5Gs8G4zkr+hwaY+ypng3Gs0tF9kmu\nr8+J5f1W+yIfj+xj3nLRVkYZ+xvdI76H0Xh5ZdSepZjNZh3moMzay2CkbXptDAlRUXg275ZGEtnp\nPXbfcigponvF91zHK1ogwrK3lmwqe/RYpI6BnWMNJ3rfo7CxSD6rR0PQPEdVMs1EIpG4DFgJpmls\nhWfByNbn2YYUyjBbDMCzcbRY0VDPYmunyZbt0JuVW7ZC7y+3wYHSVkcrlMquVeag0FleZeZreVYf\nEi0Q2fw8xtMKzu5LAuH1Y0iijYj5e6y7haHPbwusibTqURavZfraAJbHOrKx8nFljxE7ZUYdRTN4\n796Y1IZDnoGhSKaZSCQSI7ASTNPgeSojr7LHRtW7xna5aLYzcJlodvJsmhHjbNkOPTsee0wZHpOI\nYve84PbIVsRlvL5EqeG0rSGRAHyvtA8cWxgtU+R67LwG+nvsL2IXzGr62JCn2bTYstqCowgKr18t\nNu4l8+BrWHZDlCxZ+xW1ree8epTpsz26T1v03jNduMHXtGzm9rePNfL5yBvfh2SaiUQiMQIrwTSV\nTTHTadk0+5asDbFnDIkb9GYvZXJjbF98fohdJtp7PFrW58nFYxCNB8/YUb9aXuGorFc+Yure9d6Y\nRGPr7boZXeOxociW63myvSV7QyI4tGzE+jzm1NpbKWKjXLdB++exSH3+vbjKqC+endJbGmnXRqui\nWolhvGcqei5a7+lYrMRH0+AZrvscLt4xK8v021ONtd6+AeXjGjQefRS8672M89HH25Mlch7xR0D3\nvNGgX75O1Th2YnEezkie6N54fWrlfoyCp1tjq+Er9tcLeNaXldd2q1y61xK/2JFcLFsUosWOPX12\nhjjQWi97FHLUksebmCKTTiucSNtuTSit90zrYzmjbwFDP8zaT+5DZALsQ6rniUQiMQIrxTRZrVBH\nwxijb4sBDIEavj1WOyZ0I2JenhlCkxGws0JZx5AQC88B4y0pi6AMs8XiFa1lfGPuh7LJ9fX1kI3y\nElFlLR7Di1Q+z6yh99ESgXgqvY47yxKxPQMvAYyC+FvMUzUa7x613qvIfKPPKMvh3U/VYLzrrY6I\nEXraWMv0FOW71TqY8feF4CmSaSYSicQIlOMYRJ81IUr5JoDzAL510rIQno/VkgdYPZlSnjZWTR5g\n9WRaJXleWmu9pq/QSnw0AaCU8ula6y0nLYdh1eQBVk+mlKeNVZMHWD2ZVk2eIUj1PJFIJEYgP5qJ\nRCIxAqv00bzrpAUQrJo8wOrJlPK0sWryAKsn06rJ04uVsWkmEonEdwJWiWkmEonEymMlPpqllLeW\nUu4rpXyllHL7CbT/4lLKfyilfKmU8sVSynvmx68upXy8lHL//O9Vl1mutVLKZ0opv33S8pRSnldK\n+XAp5d5Syj2llB86YXn+wfxe3V1K+Y1SyqnLLU8p5ddLKY+VUu6mY6EMpZQ75s/4faWUt1wmef7x\n/J59vpTyr0spzztJeejcz5VSainl+ZdLnmcLJ/7RLKWsAfjfAfxtAK8E8DOllFdeZjFmAH6u1vpK\nAD8I4O/OZbgdwCdqrTcB+MT89+XEewDcQ79PUp73Afi3tdabAbx6LteJyFNKeRGAvwfgllrr3wKw\nBuCdJyDPvwDwVjnmyjB/nt4J4FXza/6P+bN/qeX5OIC/VWv9PgBfBnDHCcuDUsqLAfyXAL5Gxy6H\nPM8ObCnZSf0D8EMAfpd+3wHgjhOW6SMA3gzgPgDn5sfOAbjvMspwHQ5eujcB+O35sRORB8CVAP4C\ncxs4HT8peV4E4EEAV+NgKfBv4+AlvOzyAHgZgLv7xkSfawC/C+CHLrU8cu6/BvDBk5YHwIdxMPH+\nJYDnX055no1/J840cfgCGB6aHzsRlFJeBuA1AD4F4Gyt9ZH5qUcBnL2MovxTAP8QAC+MPSl5rgfw\nTQD/fG4ueH8p5cxJyVNrfRjAP8EBU3kEwJO11n93UvIIIhlW4Tn/HwH8zknKU0p5O4CHa62fk1Or\nMD6DsAofzZVBKeUKAP8KwN+vtT7F5+rB9HdZQg1KKW8D8Fit9c+iMpdTHhywudcC+Ge11tfgYMnr\nkup7mcfnKgBvx8HH/IUAzpRSfvak5ImwCjIYSim/gAMz1AdPUIYtAD8P4BdPSoZnA6vw0XwYwIvp\n93XzY5cVpZR1HHwwP1hr/a354W+UUs7Nz58D8NhlEucNAH68lPKXAH4TwJtKKf/yBOV5CMBDtdZP\nzX9/GAcf0ZOS50cB/EWt9Zu11l0AvwXg9ScoDyOS4cSe81LK3wHwNgD/3fxDflLy3IiDie5z82f7\nOgB/Xkq59oTkORJW4aP5pwBuKqVcX0rZwIEx+KOXU4BykCPq1wDcU2v9FTr1UQDvmv//XTiwdV5y\n1FrvqLVeV2t9GQ7G4/dqrT97gvI8CuDBUsrL54duBfClk5IHB2r5D5ZStub37lYcOKZOSh5GJMNH\nAbyzlLJZSrkewE0A/uOlFqaU8lYcmHl+vNb6jMh5WeWptX6h1vqCWuvL5s/2QwBeO3++TmR8joST\nNqrOJ74fw4Fn7wEAv3AC7f8wDtSozwP47PzfjwH4Lhw4Y+4H8O8BXH0Csr0Rh46gE5MHwH8B4NPz\nMfo3AK46YXn+VwD3ArgbwP8NYPNyywPgN3BgU93FwQfg3S0ZAPzC/Bm/D8DfvkzyfAUHtkJ7rv/P\nk5RHzv8l5o6gyyHPs/UvVwQlEonECKyCep5IJBLfMciPZiKRSIxAfjQTiURiBPKjmUgkEiOQH81E\nIpEYgfxoJhKJxAjkRzORSCRGID+aiUQiMQL/P1pmXjM/OBaRAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(M[:,0] - reconstructed_small_M[:,0], dims), cmap='gray');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Timing Comparison"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn import decomposition\n",
"import fbpca"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Full SVD:"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 5min 38s, sys: 1.53 s, total: 5min 40s\n",
"Wall time: 57.1 s\n"
]
}
],
"source": [
"%time u, s, v = np.linalg.svd(M, full_matrices=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our (overly simplified) randomized_svd from above:"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 2.37 s, sys: 160 ms, total: 2.53 s\n",
"Wall time: 641 ms\n"
]
}
],
"source": [
"%time u, s, v = randomized_svd(M, 10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Scikit learn:"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 19.2 s, sys: 1.44 s, total: 20.7 s\n",
"Wall time: 3.67 s\n"
]
}
],
"source": [
"%time u, s, v = decomposition.randomized_svd(M, 10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Randomized SVD from Facebook's library fbpca:"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 7.28 s, sys: 424 ms, total: 7.7 s\n",
"Wall time: 1.37 s\n"
]
}
],
"source": [
"%time u, s, v = fbpca.pca(M, 10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I would choose fbpca, since it's faster than sklearn but more robust and more accurate than our simple implementation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are some results from [Facebook Research](https://research.fb.com/fast-randomized-svd/):\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Time and Accuracy vary with k"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import timeit\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"U_rand, s_rand, V_rand = fbpca.pca(M, 700, raw=True)\n",
"reconstructed = U_rand @ np.diag(s_rand) @ V_rand"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.1065914828881536e-07"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.linalg.norm(M - reconstructed)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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S31WWx61yPb5/aWmps2LzdoxWn30OHJcfunNsfX09fc/HoTLNioqKiikwE0yT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\nR9pymFnewzNLGSbYoJPJ+6+y6Mx5El0/u0+gKwN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R+TmqTbOioqLiDcRMMc0oKUGWEEPT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\nAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(reconstructed[:,140], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"pd.options.display.float_format = '{:,.2f}'.format\n",
"k_values = np.arange(100,1000,100)\n",
"df_rand = pd.DataFrame(index=[\"time\", \"error\"], columns=k_values)\n",
"\n",
"# df_rand = pd.read_pickle(\"svd_df\")"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"for k in k_values:\n",
" U_rand, s_rand, V_rand = fbpca.pca(M, k, raw=True)\n",
" reconstructed = U_rand @ np.diag(s_rand) @ V_rand\n",
" df_rand.set_value(\"error\", k, np.linalg.norm(M - reconstructed))\n",
" t = timeit.timeit('fbpca.pca(M, k)', number=3, globals=globals())\n",
" df_rand.set_value(\"time\", k, t/3)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df_rand.to_pickle(\"df_rand\")"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" 100 | \n",
" 200 | \n",
" 300 | \n",
" 400 | \n",
" 500 | \n",
" 600 | \n",
" 700 | \n",
" 800 | \n",
" 900 | \n",
" 1000 | \n",
"
\n",
" \n",
" \n",
" \n",
" time | \n",
" 2.07 | \n",
" 2.57 | \n",
" 3.45 | \n",
" 6.44 | \n",
" 7.99 | \n",
" 9.02 | \n",
" 10.24 | \n",
" 11.70 | \n",
" 13.30 | \n",
" 10.87 | \n",
"
\n",
" \n",
" error | \n",
" 58,997.27 | \n",
" 37,539.54 | \n",
" 26,569.89 | \n",
" 18,769.37 | \n",
" 12,559.34 | \n",
" 6,936.17 | \n",
" 0.00 | \n",
" 0.00 | \n",
" 0.00 | \n",
" 0.00 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" 100 200 300 400 500 600 700 800 \\\n",
"time 2.07 2.57 3.45 6.44 7.99 9.02 10.24 11.70 \n",
"error 58,997.27 37,539.54 26,569.89 18,769.37 12,559.34 6,936.17 0.00 0.00 \n",
"\n",
" 900 1000 \n",
"time 13.30 10.87 \n",
"error 0.00 0.00 "
]
},
"execution_count": 117,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_rand"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"df = pd.DataFrame(index=[\"error\"], columns=k_values)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"for k in k_values:\n",
" reconstructed = U[:,:k] @ np.diag(s[:k]) @ V[:k,:]\n",
" df.set_value(\"error\", k, np.linalg.norm(M - reconstructed))"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df.to_pickle(\"df\")"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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PP5Y4TqkCbj3bbtB1QQRcGcDuz07T+JkQHCLWzPpKuUj8D/Fl7nPUc5x1f52QOmfdX+Z5\nHQ569uxJz549iYmJYebMmYwYMYKwsDDCw8NZtmwZn332WZnLmYC1cnNycjKtW7cuUi4iDB8+nKef\nfrpEHW9vb+caXgV0KRR1vty6ZWaMIeKZCLIPZJPy2Gbo1s1axFMpN7F9+/YiXYOlLYVy3333ERER\nQbNmzUo9R0ZGBuPGjWPAgAHOhTkL9O7dm3nz5nHo0CEAjh49yu7du8uNKyAggMDAQOdinh9++KGz\nlaZUaaq0ZWYMyUA6kAfkitDJGIKAOUBLIBkYLMKxqozjbAKuCCBkUAg52V6QkgKTJ1srUmsLTbmB\njIwM7r77bo4fP46npyetWrXirbfecu6/6aabuOeee3j55ZdL1O3VqxciQn5+PgMHDuSRRx4pcUz7\n9u158skn6dOnD/n5+Xh5efHqq68WSZhlmTlzJn/961/JzMwkIiKC999//8IuVtVqVboEjJ3MOolw\npFDZs8BREaYZwyQgUIQHz3aeC10CpjySL9YIx/feg9Gj4fPPYeDAKvt5ShXQJWBUZdElYC6+/kDB\nanMzgQEuiKGIgqH6J9sMJOvSrvDQQ1DB51yUUkq5XlUnMwEWGcNaYxhjlzUSIdV+fwBoVFpFYxhj\nDGuMYc3FeC4y+0g263tvJLn5FNi2DT75pOp/qFJKqUpR1cnsShHigD8A443hqsI7RRCshFeCCG+J\n0EmETp4XYcxlnZA6NB3XlAPLvDn15CwoNmRYqapSE1Z7V9XbBf0NGZOMMZswZgPGrLHLgjDme4zZ\nYb8GFjp+MsbsxJjtGNO3UHmCfZ6dGDMdYw88MKYuxsyxy1diTMvzD7ZsVZrMRNhnvx4CvgA6AweN\nIRTAfj1UlTGci+b/aI7Dz8Gu1bHg4+PqcJQb8Pb2Ji0tTROaOm8iQlpaGt7e3hdyml6IxCHSyf48\nCViMSCSw2P4MxrQHhgBRQD/gNYwpeL7ideAvQKS99bPLRwPHEGkF/At45kICLUuVtXmMwRfwECHd\nft8HeByYDwwHptmvX1VVDOeqTkgdwiaGkfxIMideWkTAJw9Z6575+7s6NFVLNWvWjJSUFA4fPuzq\nUFQN5u3tXeajE+epP9DTfj8T+AF40C6fjcgZIAljdgKdMSYZqI/ICgCM+QBrPMRCu85U+1zzgFcw\nxlT2v+CqsgOvEfCF3dD0BD4W4RtjWA3MNYbRwG5gcBXGcM7C7gvj4KyDZKXnEbBqFbz0EpQy5Fip\nyuDl5UV4eLirw1DuTYBFGJMHvInIW0AjREob29AUWFGobopdlmO/L15eUGev9ZMkF2NOAMHw+yj3\nylBlyUyEXUCHUsrTgN5V9XMvlMPXQectnTEOA+sHwnPPwdixEBLi6tCUUuqchICn8z6Y5S07WRV2\nJSL7MOYS4HuMKTrruohgTLXvB3frGUDKYhwGyReOXPMIkpEJ06a5OiSllDpnRyAXkU6FtuKJDET2\n2a9FxjZgTCiA/VowtmEfEFaodjO7bJ/9vnh50TrGeAIBQNqFX11RmszKkPZ1GpvHn+DQlY9aC3ju\n3+/qkJRSqnIZ44sx/s731tiGzfw+tgGKjm2YDwyxRyiGYw30WGV3SZ7EmK72KMZhxeoUnOtGYElV\njHhy64mGzyb4umD84v1ISr6ahu+3xyM01NUhKaVUZWsEfGFP3+cJfIzINxizGpiLMUXHNohswZi5\nwFYgFxiPSMEME+OAGYAP1sCPhXb5u8CH9mCRo1ijIStdlU5nVVmqejqrshz99igb+22k1fRWNLu7\nUkcKKaVUlXOn6ay0ZXYWgX0CadCrAbuf2E3j9Hl47toM77zj6rCUUkoVo/fMzsIYQ8TTETj8HWTt\nzoZ334W1a10dllJKqWK0m7ECJE8wp9IhIgISEuDbb10Wi1JKVZQ7dTNqy6wCjMOQ5+XL0Rufhu++\ng6VLXR2SUkqpQjSZVVDSI0lseq81pxvHwz/+ATWgRauUUu5Ck1kFhd0XhnEYkts/B//+t65ErZRS\n1Ygmswqq27QuTe9pysGlDjK827s6HKWUUoVoMjsHzSc1xzPAk10P7oA77oCPPnJ1SEoppdBkdk68\nAr1oPqk5uelC3tqt8PDDcOaMq8NSSim3p0Pzz1F+bj7GYTDffw99+8L06XD33a4OSymlSnCnofma\nzM7Tmf1ZZN8wEv+9S+C338DPz9UhKaVUEe6UzLSb8TyICJv+uJltR/+KHDpiLeCplFLKZTSZnQdj\nDM3/0ZzMJOHArTNh2DBXh6SUUm5Nk9l5avjnhvhf5k/yj5eSd0nT8isopZSqMprMzpMxhohpEZzZ\ne4b9UzfA9dfDvn3lV1RKKVXpNJldgMCrAwnqF0TWAeD77+Hxx10dklJKuSUdzXiB8nPy8fDygHvu\ngddeg61boXVrV4ellFI6mlFVnIeX9SvMGHg/2XUbw6OPujgipZRyP5rMKkH24WzW9ksmud00mDMH\n1q93dUhKKeVWNJlVgjoN6xA6OpTUxGZk/u0FaNXK1SEppZRb0WRWSVo82gJTx4Pk/f3A39/V4Sil\nlFvRZFZJ6jauS7P7mnFo9iHSpy+E4cN1AU+llLpINJlVouYTm1O3eV1ObTgOH3wACxa4OiSllHIL\nVT403xgcwBpgnwh/NIYgYA7QEkgGBotw7GznqM5D84vLz87Hw+RBVBTUrQsbNoDD4eqwlFJuSIfm\nV657gW2FPk8CFosQCSy2P9caHnU8EE9Pjg2ZhmzeDJ984uqQlFKq1qvSZGYMzYDrgXcKFfcHZtrv\nZwIDqjIGV0j7TxqJTwRxpOUw67mz7GxXh6SUUqUzxoEx6zFmgf05CGO+x5gd9mtgoWMnY8xOjNmO\nMX0LlSdgzCZ733SMMXZ5XYyZY5evxJiWVXUZVd0yewl4AMgvVNZIhFT7/QGgUWkVjWGMMawxhjW5\nuVUcZSULvj6Yeu3rsStvJPmPTNVuRqVUdVZq7xkiRXvPjGkPDAGigH7AaxhT8OX2OvAXINLe+tnl\no4FjiLQC/gU8U1UXUWXJzBj+CBwSYW1Zx4ggQKk37UR4S4ROInTy9KyqKKuGcRgi/hnB6b1wIPca\nTWZKqerJmHPpPesPzEbkDCJJwE6gM8aEAvURWYE1COODYnUKzjUP6O1stVWyqkwT3YAbjOE6wBuo\nbwyzgIPGECpCqjGEAoeqMAaXCb4hmPqX1yd5ajKN0ubg8POCu+5ydVhKKVVYQe9Z4YdjGyFSWu9Z\nU2BFoeNS7LIc+33x8oI6ewEQycWYE0AwcKTyLsFSZS0zESaL0EyEllhN0yUi3AbMB4bbhw0Hvqqq\nGFypYIkYgMyvN8HDD8PRoy6OSinlTkLAE2PWFNrGOHca80fgECJl9p7ZLa0a8cCsKzrwpgFzjWE0\nsBsY7IIYLooGVzWg666ueGz3g7gZ8OyzMG2aq8NSSrmJI5CLSKcydncDbsAYZ+8ZxswCDmJMKCKp\ndhdiQe/ZPiCsUP1mdtk++33x8sJ1UjDGEwgA0irh0kq4KA9Ni/CDCH+036eJ0FuESBGuEaFWN1c8\n6nqQ3zaaE33ug+nTYf9+V4eklFIgMhmRZoi0xO49Q+RsvWfzgSH2CMVwrIEeq+wuyZMY09W+Hzas\nWJ2Cc91o/4wqaenpDCAXwa5Ju0j84QbOZNeHJ55wdThKKXU204BrMWYHcI39GUS2AHOBrcA3wHhE\n8uw647AGkewEfgMW2uXvAsEYsxP4G1X4XLEuznkRnE46zao2q2jc6Qhtng6BHj1cHZJSyg3oDCCq\nUvmE+9BkbBNSVwWT2fgyV4ejlFK1jiazi6TFQy1w+DjYNXE73HuvNWejUkqpSqHJ7CKpc0kdwv4e\nRtaebPI+mAMPPgj5+eVXVEopVS5NZhdR88nNSVjXGcfjD8F338Ho0ZCXV35FpZRSZ1XDJoqq2Tzq\nWP92yLnlTrK3n8H31Ylw+jR8+CF4ebk4OqWUqrm0ZXaRiQiJ12xk67Ie5D7+PCxZAnv3ujospZSq\n0TSZXWTGGMKfDOfUtlMkLuhJzvLNEBEBIrpUjFJKnSdNZi4QfH0w0Z9Fk7Ehg8Qb95B9ONta96xf\nP8jIcHV4SilV42gyc5GQ/iHEzI8h85dMdj2wC9q0gWXLrIR24oSrw1NKqRpFZwBxsRPLT1CvXT28\nGnjBvHkwdCjEx8M330BQkKvDU0rVYDoDiLpoAi4PwKuBF3mn89g2P4rMV76AxETo00eH7SulVAXp\n0PxqImt3Fmlfp3FsURAdXl2Ar+8RXaFaKaUqSFtm1YRvW1/il8WDwIbJ9Uhv90drx8KFsGePa4NT\nSqlqTu+ZVTOZOzJJ7J1IXnoesV+0ov7gWKhXz3oeLSLC1eEppWoQd7pnpsmsGsrancXWIVtp814b\nfE9vh2uvBR8fWLzYGvWoap2cnBxSUlLIyspydSiqBvL29qZZs2Z4FZtJSJNZNeNuyQysmUKMMYgI\nmf9JxPcvfcEYWLQIoqNdHZ6qZElJSfj7+xMcHGwv1qtUxYgIaWlppKenEx4eXmSfOyUzvWdWTRV8\noe1/bT9rbjrBkSnfgacnzJnj4shUVcjKytJEps6LMYbg4GC3b9XraMZq7pJbLuHABwfYfM8x2r+6\nlEvGtLJ25OZayU3VGprI1PnSvx1tmVV7XoFedPi+AwFXBLB13D5SZx6A336DqChrxhClqqmWLVty\n5MiRCz7P/PnzmTZt2gWfp2fPnqxZs6ZE+YIFC4iPj6dDhw60b9+eN998k2XLlnH55ZcXOS43N5dG\njRqxf/9+RowYQXh4OB06dKB169YMGzaMlJSUUn/uSy+9RGZmpvPzddddx/Hjxy/4elRRmsxqAM/6\nnsR+E0tg70B+HfMrWWme4OEBf/iDtS6aUpVIRMivRgvH3nDDDUyaNKlKzp2Tk8OYMWP4z3/+Q2Ji\nIuvXr6dnz550796dlJQUdu/e7Tx20aJFREVF0aRJEwCee+45EhMT2b59O/Hx8Vx99dVklzJZePFk\n9vXXX9OgQYMquR53psmshnDUcxA9P5rY72Lx7tzCapVFRsKf/gT/+Y+rw1M1XHJyMm3atGHYsGFE\nR0ezd+9exo4dS6dOnYiKimLKlCnOY1u2bMmUKVPo2LEjMTEx/PLLLwCkpaXRp08foqKiuOOOOyg8\nuOzFF18kOjqa6OhoXnrpJefPbNu2LSNGjKB169bceuutLFq0iG7duhEZGcmqVasAmDFjBnfddRcA\ncXFxzs3Hx4dly5Zx6tQpRo0aRefOnYmPj+err74C4PTp0wwZMoR27doxcOBATp8+XeK609PTyc3N\nJTg4GIC6devSpk0bPDw8GDx4MLNnz3YeO3v2bIYOHVriHMYY7rvvPho3bszChQuL7Js+fTr79++n\nV69e9OrVy/n7O3LkSIWvv6zrq3WMcWDMfeddX0Sq/VavXj1RRR36/JAkTd4q+QmdRDw9RRYvdnVI\n6gJs3brV+f7ee0V69Kjc7d57z/7zk5KSxBgjy5cvd5alpaWJiEhubq706NFDEhMTRUSkRYsWMn36\ndBERefXVV2X06NEiInL33XfLY489JiIiCxYsEEAOHz4sa9askejoaMnIyJD09HRp3769rFu3TpKS\nksThcMjGjRslLy9POnbsKCNHjpT8/Hz58ssvpX///iIi8v7778v48eOLxDt//ny58sorJTs7WyZP\nniwffvihiIgcO3ZMIiMjJSMjQ1544QUZOXKkiIgkJiaKw+GQ1atXl7j20aNHS8OGDWXIkCEya9Ys\nycvLExGR1atXS1xcnIiIZGVlScOGDZ2/k+HDh8unn35a5Dz33nuvTJs2rcT5W7RoIYcPHy7xuaLX\nX9b1FVf4b6gAcEqqwXd4hTdYdb51y22ZGUNrY1hsDJvtz7HG8PB5Z09VKY4uPEry0wfZdeVM5K9j\noXNnV4ekargWLVrQtWtX5+e5c+fSsWNH4uPj2bJlC1u3bnXuGzRoEAAJCQkkJycD8OOPP3LbbbcB\ncP311xMYGAjAzz//zMCBA/H19cXPz49Bgwbx008/ARAeHk5MTAweHh5ERUXRu3dvjDHExMQ4z1vc\njh07mDhxInPnzsXLy4vvvvuOadOmERcXR8+ePcnKymLPnj1F4omNjSU2NrbU873zzjssXryYzp07\n8/zzzzMWSvWaAAAgAElEQVRq1CgAOnXqREZGBtu3b2fhwoV06dKFoLNM/i3n8ZhTRa6/rOurpf6H\nMa9gTHeM6ejcKqAiw+HeBiYCbwKIsNEYPgaePP941YVq/UZrjKdh77/3k3/X3bSq54vJyLCeQxsw\nwNXhqQtg98JddL6+vz+OlJSUxPPPP8/q1asJDAxkxIgRRYZ+161bFwCHw0Fubu55/8yC8wB4eHg4\nP3t4eJR63oyMDAYPHszbb79NaGgoYCWRzz77jDYXMKFATEwMMTEx3H777YSHhzNjxgwAhg4dyuzZ\ns9m2bVupXYyFrV+/nt69e5/Tz63I9VfG9dUgcfbr44XKBLi6vIoVuWdWT4RVxcrO/69XVQrjYYh8\nNZJm9zdj3yv72D5mO/L0NBg4EF55xdXhqRru5MmT+Pr6EhAQwMGDB0vcCyrNVVddxccffwzAwoUL\nOXbsGADdu3fnyy+/JDMzk1OnTvHFF1/QvXv384pr1KhRjBw5skj9vn378vLLLztbRuvXry8Rz+bN\nm9m4cWOJ82VkZPDDDz84P2/YsIEWLVo4Pw8dOpRZs2axZMkS+vfvX2pMIsL06dNJTU2lX79+Jfb7\n+/uTnp5+7hdbzvXVSiK9StnKTWRQsWR2xBguxcqOGMONQGp5lYzB2xhWGUOiMWwxhsfs8iBj+N4Y\ndtivgRUJVJVkjOHS5y6lxaMt8PT3hEcehv794e674bnnXB2eqsE6dOhAfHw8bdu25ZZbbqFbt27l\n1pkyZQo//vgjUVFRfP755zRv3hyAjh07MmLECDp37kyXLl244447iI+PP+eYdu/ezbx583jvvfec\ng0DWrFnDI488Qk5ODrGxsURFRfHII48AMHbsWDIyMmjXrh2PPvooCQkJJc4pIjz77LO0adOGuLg4\npkyZ4myVAbRr1w5fX1+uvvrqIi1XgIkTJzqH5q9evZqlS5dSp06dEj9jzJgx9OvXzzkA5FyVdX0X\nzBhvjFmFMYkYswVjHrPLgzDme4zZYb8GFqozGWN2Ysx2jOlbqDwBYzbZ+6Y7H3wzpi7GzLHLV2JM\ny3JiCsCYFzFmjb29gDEBFbqe8m6qgUSALALJBNkH8jNIywrUMyB+9nsvkJUgXUGeBZlkl08Ceaa8\nc+kAkPLl5+eLiEjm9pOSd+NQERB57DERu1xVb6XdvFfqXJzzABAwAn72ey+BlQJdBZ4VmGSXTxJ4\nxn7fXiBRoK5AuMBvAg4pGLhh1TUCCwX+YJePE3jDfj9EYE6Z8VjHfCbwmECEvU0R+PysdSo6AESE\nXSJcAzQE2opwpQjJFagnImTYH73sTYD+wEy7fCagN3gqgTGG3PRc1vfaxOb0B8m7ZSS8/jqkpbk6\nNKVUdWRlgXP5ju4PzEbkDCJJwE6gM8aEAvURWWG3ZD4oVqfgXPOA3uVMV3IpIlMQ2WVvjwEVWi6k\nIqMZGxjDPcATwFPGMN0Yplfk5MbgMIYNwCHgexFWAo1EnN2UB4BGZdQdYwxrjGHNBdxfdiue/p6E\nPx7O0e+OsWn/3eQuXQkhIWC101wdnlLqIgsBz0JddmswZkyRA6xnu5zf0YisBBohUtp3dFNgb6Ha\nKXZZU/t98fKidURygRNA8FlCPo0xVxaKrxtQ8gHBUlRkNOPXwApgE3BO0wKIkAfEGUMD4AtjiC62\nX4yh1G9ZEd4C3gLw9S39GFVS6OhQPHw82DZsGxtHCjFfh+L1+ANw+jS89po1c4hSyi0cgVxEOpV5\ngEgeEIcxDYAvMCa62H7BmIv5/ftX4INC98mOAcMrUrEiycxbhL+db2QAIhw3hqVAP+CgMYSKkGoM\noVj/IlCVqNEtjfDw8WDrzVtJfiSJyPo+1njvrCx4911wOFwdolKqOhE5jjHO72iMCUUk1e5CLPiO\n3geEFarVzC7bZ78vXl64TgrGeAIBQOn3PozxANog0gFj6ttxnazoJVTkn+kfGsNfjCHUHokYZAxl\nPznojIuGdosMY/ABrgV+Aebze6YdDtTSuVlcq+HAhnRY3IHwaRHw1FPw+OMwcybceivk5Lg6PKWU\nqxnT0G6RgTEV+Y6eDwyxRyiGA5HAKrtL8iTGdLXvhw0rVqfgXDcCS8p8ulwkH3jAfn/yXBIZVKxl\nlg08BzwEzu4+ofybcqHATGNwYCXNuSIsMIblwFxjGA3sBgafS8Cq4hp0t/5OczNy2fHrjYT/IwDv\nf94L+fkwd66Lo1NKuVgoMBNjnN/RiCzAmOXAXIwp+h0tsgVj5gJbsZ41Hm93UwKMA2YAPsBCewN4\nF/gQY3YCR4Eh5cS0CGP+DswBfl+RWeRoeRdT7krTxrAL6CzCha/lcJ7ccaXpypS+IZ0NPTbgGehJ\n3IhN+HRoaD1craqNbdu20a5dO5fG8NRTT/Hxxx/jcDjw8PDgzTff5JtvviErK4unn37aedyGDRsY\nOnQo27Zto2XLlvj7+wOQl5fHoEGDePjhh/H29i5y7uPHj/Pxxx8zbtw4APbv388999zDvHnzLt4F\n1nKl/Q3VuJWmjUkqpVQQKXdEY0W6GXcCmeUepaot/zh/4pbEkZeex/q3oznVro+14/vvISPj7JWV\nW1i+fDkLFixg3bp1bNy4kUWLFhEWFsbQoUOZU2x18+Kzxy9dupRNmzaxatUqdu3axZ133lni/MeP\nH+e1115zfm7SpIkmMlWUdc/sNkTCi22VMzQfq6m3wRjeLBiWX9Gh+ar68E/wJ25ZHJInbLhqAxmL\nkqzlY/r2hRMnXB2ecrHU1FRCQkKccwOGhITQpEkTWrduTWBgICtXrnQeO3fu3FLnKfTz8+ONN97g\nyy+/5OjRor1CkyZN4rfffiMuLo6JEyeSnJxMdLQ1cG7GjBkMGDCAa6+9lpYtW/LKK6/w4osvEh8f\nT9euXZ3n+u233+jXrx8JCQl0797dufSMqiWse2bnPRdfRe6ZfWlvqobzi/Yj/sd4tt2+DY+WjWDW\nLBg6FK65Br79Fs4yI7i6eCZ8M4ENBzZU6jnjGsfxUr+yZzDu06cPjz/+OK1bt+aaa67h5ptvpkeP\nHsDvk+126dKFFStWEBQURGRkZKnnqV+/PuHh4ezYsYMuXbo4y6dNm8bmzZvZsMG6ruIz4m/evJn1\n69eTlZVFq1ateOaZZ1i/fj333XcfH3zwARMmTGDMmDG88cYbREZGsnLlSsaNG8eSJUsu8DejqpnF\nGPNn4PNzXYag3GQm4nx6W9UC9VrXo+OKjhhjkEv/zOmXv6DevX+GXr2sbsdLLnF1iMoF/Pz8WLt2\nLT/99BNLly7l5ptvZtq0aYwYMYKbb76ZK664ghdeeKHMBSoLO8fvIAB69eqFv78//v7+BAQE8Kc/\n/QmwZrPfuHEjGRkZ/N///R833XSTs86ZM2fO+eeoau9O4D4gD2OyAIN1z6x+eRXLTGbGMFeEwcaw\nCUo8tCwidLiQiJXrFMwms/fZvSQ/Vp/ox/9L0GM3wMcfw4QJLo5Ona0FVZUcDgc9e/akZ8+exMTE\nMHPmTEaMGEFYWBjh4eEsW7aMzz77jOXLl5d5jvT0dJKTk2nduvU5/ezylkLJz8+nQYMGzpadqrUC\ngFuBcEQex5jmWKMuy3W2e2b32q/bgD8V2m4Atp9/rKq6aDyiMT6tfNg0xYsjL62Ee+3/5PbSHcp9\nbN++nR07djg/l7YUyn333UdERATNmjUr7RRkZGQwbtw4BgwY4FyYs8CFLoNS0H356aefAta/phMT\nE8/7fKraehXoChQ0/9Op4H20MpNZofkTW4mwu9CWDLS9gGBVNVGnUR3ifojDL8aPLeOPcmjeYdiz\nBy69FCZPBu3GcRsZGRkMHz6c9u3bExsby9atW5k6dapz/0033cSWLVtK7WLs1asX0dHRdO7cmebN\nm/Pmm2+WOCY4OJhu3boRHR3NxIkTzyvGjz76iHfffZcOHToQFRXFV1/pfAu1UBdExgPWSrAix4CS\n6+qUosznzIxhLNaDcBHAb4V2+QP/E+G2Cwj4nOhzZlUr90Qum/64ifS16XRJjKLuMw9a017FxMAH\nH0BcXPknURekOjxnpmq2WvKc2UrgCmA1Ih0xpiHwHSLlLoB3tm7Gj7G6FedTtJsx4WImMlX1PAM8\nif0mltiFsdSNDEbefpu8eQvg8GG47DJ48kmddV8pdTFMB74ALsGYp4CfgX9WpGKZA0BEOIE1Xf/Z\nhy6pWsHh66BBD2v6q0OfHGLXpCDavLqCoE8nQVISnHUJIqWUqgQiH2HMWqA31kjGAYhsq0jVijxn\nptyMT6QPDl8HG/+cRJOxjxHxVHPrD2XDBli61BoookvJKKWqgsgvWBMenxP9RlIl1L+sPgnrEmj2\nt2bsf2M/azpt4PjPx+HDD+Fvf4Orr7Zaa6pSnc/zWUqB/u2AJjNVBoePg1YvtCJumTX4I+dgDjz/\nPLz3HqxbB7Gx8Pbbei+tknh7e5OWlqZfSuqciQhpaWklJnd2N+XOml8d6GhG18rLysPhbS3omToj\nlXoBJwl4ZRwsWQIzZsDwCi0Eq84iJyeHlJQUsrKyXB2KqoG8vb1p1qwZXl5eRcpr3GjGC6DJTFVY\nfnY+q6NXc/q30zR/IIyWkf+Hx203Q506cOAANGqkA0WUqkbcKZlpN6OqMI86HiSsTqDxiMbsmbaX\ntS+1JX3LGWvW/U6d4KabrOH8Sil1kWkyU+fEM8CTtu+2JWZBDDmHc1h3+TrOpNeBu++G//wHoqNB\nZ2ZQSl1k2s2ozlvO0RyOfneURkMaAZD9QyJ1JgyHxETrPtobb4Cb35RWypW0m1GpCvAK8nImsuPL\njrPiDyfYM/hz5B8PW92NhWZCV0qpqqTJTFWKeu3qEXRdELse2sP6JQPJfGGONRhkzx7r2TRtWSul\nqpB2M6pKIyIc+uQQO+7aQf7pfC598VKaen4NY8ZYM/HPnAndurk6TKXchnYzKnUejDE0uqURl22+\njAa9GyA5An/5izUFVl4edO8ODz4I+iyVUqqSactMVQkRAQHjYTj06SFyUzMI3TQN887b8NBD1kz8\nSqkq5U4tM51oWFUJY4w15zVweN5hDs89zOG+42nz4Z/x/lNXa8e+fXDJJVBs1gKllDpX2s2oqlz7\n2e2JfC2SEz+dYPVd9Uj9IhPJyYE//MG6h7atQis8KKUqmzFhGLMUY7ZizBaMudcuD8KY7zFmh/0a\nWKjOZIzZiTHbMaZvofIEjNlk75tu/YsWMKYuxsyxy1diTMuquBRNZqrKGWNoOrYpl228DL9YP7aP\n3M6JFafg0Udh1y6Ij4cXX4T8fFeHqpS7yQXuR6Q90BUYjzHtgUnAYkQigcX2Z+x9Q4AooB/wGsY4\n7HO9DvwFiLS3fnb5aOAYIq2AfwHPVMWFVFkyM4YwY1hqDFuNYYsx3GuXBxnD98aww34NLO9cqnbw\nudSHuB/iiFkQQ4PuDeDGG8mcvw769oX774deveDQIVeHqZT7EElFZJ39Ph3YBjQF+gMz7aNmAgPs\n9/2B2YicQSQJ2Al0xphQoD4iK+ylHz4oVqfgXPOA3s5WWyWqypZZLnC/CM6MbwzOjC9C0Yyv3ILx\nMARfHwxA5q+ZrL46iS11/0n2yx9Yz6U1aODiCJVyU1b3XzywEmiESKq95wDQyH7fFNhbqFaKXdbU\nfl+8vGgdkVzgBBBc2eFXWTITIVWEdfb7imR85Wa8I7xp+WhLjnx5hNVPRHD43k+tGfiPH4cRI6wB\nIkqp8xYCnhizptA2ptQDjfEDPgMmIHKyyD6rpVXth71flHtmxtCSQhlfhNIyvnIzHp4etPhHCxLW\nJFC3SV22DNrCLyN/QdashU8/tSYt/ugjXQBUqfN0BHIR6VRoe6vEQcZ4YSWyjxD53C49aHcdYr8W\n9P/vA8IK1W5ml+2z3xcvL1rHGE8gAEi74IsrpsqTmTE4M74IRTK+CGVmfGMYYwxrjGFNbm5VR6lc\nyS/Wj44rO9Li0RbUaVIHc01v2LAB2reH226DG2/Ue2lKVQXr3tW7wDZEXiy0Zz5QsOrucOCrQuVD\n7BGK4VgDPVbZXZInMaarfc5hxeoUnOtGYElVLKlepQ9NG4MXsAD4VoQX7bLtQE8RUo0hFPhBhDZn\nO48+NO1+jv1wjEMfH+TSsAV4PvkQDB1qrWqtlKqwch+aNuZK4CdgE1AwnPgfWL1oc4HmwG5gMCJH\n7ToPAaOwxkVMQGShXd4JmAH4AAuBuxERjPEGPsTqnTsKDEFkV2VeJ1RhMjMGg3VP7KgIEwqVPwek\niTDNGCYBQSI8cLZzaTJzP3tf2MtvE3+jbvO6tH20LoE9G0BEBGzfDlu3woABuqq1UuVwpxlAqrKb\nsRtwO3C1MWywt+uAacC1xrADuMb+rFQRYfeHEf9zPB51PEgcfZJfX8wl52gOvPIKDBoEV10FK1a4\nOkylVDWhczOqai0vM49dk3ex7+V9tH6rNU1GXALvvWc9cH3woHU/7emnoVUrV4eqVLXjTi0zTWaq\nRji15RQ+bXzw8PTgwKwD5B8/TeNDH+DxwrMwdiw8/7yrQ1Sq2tFkVs1oMlOFbRqwibSv0qjXth7h\nExsQMrAhJjDQWmpm1Sq45x7w8XF1mEq5nDslM52bUdU40V9EE/VFFABbRu9n/XVJnFx9Er7+GiZN\ngjZt4MMPda5HpdyIJjNV4xhjaDigIZ02daL1263J2pNF7vFceO45ZMlSa1mZYcMgIQGWLXN1uEqp\ni0CTmaqxPDw9aHJHE7r81oWga4MA2LUwjG1RH5L179lw7Bhs2uTiKJVSF4MmM1XjObwdzvcedT04\nNOcQKx9ozM4B35Jz4yhrx3vvwejROt+jUrWUJjNVq4Q/EU6XHV1odEsjUl5OZUWbtRz+4jAcOGDd\nR4uMhEcegfR0V4eqlKpEmsxUreMd5k3b99py2cbLaNCrAfXa1YN//IOcFVvI/9MAePJJuPRSazJj\npVStoMlM1Vq+Ub7EfBmDb1trZPL2f55hdeK9HJ72P6RtO6hXzzowJ0dn5leqhtNkptxG49sbY4xh\ny6Rs1mW/yHG/K6wdU6dCjx7WM2pKqRpJk5lyGyH9Q+i0qRNt3mnDmZQzbOiZyP639ltTYW3fDl26\nwJAhsKvSJ/RWSlUxnQFEuaW803nse2UfjUc2pk5IHTKWH8Rz9rt4v/OU1e342mtwxx2uDlOpC+JO\nM4BoMlMKWH/Vek6uPEnT4QE0P/0OdSaOgdhYSEsDX1/w9nZ1iEqdM3dKZtrNqBTQ7qN2NLqtESnv\nHmfl/JvZvSCAvFN51jyPbdvCRx/p9FhKVWOazJTCHs7/blsu22QN5096KIkDMw/AqFEQFAS33QaX\nXWZNZqyUqna0m1GpUpxYfgL/jv541PXg8OeHkB9+ouGXf8Ps3QMvvwx33eXqEJUqlzt1M3q6OgCl\nqqOAywOc7/e/lcqxb4Px7zSPiOvWEnjjAGvHL79AQACEhrooSqVUAe1mVKocsf+Npc17bcg+kEvi\nm23ZOPIQGZszrEVBW7WCv//dWvVaKeUymsyUKodxGEJHhtL5185EPBfByZUnyfotC955BwYNgn/9\nC8LD4f77rTkglVIXnd4zU+oc5Z7IxVHfgTGG5MeTObP5EM1zP8Dnq9fh2WetpKZUNaD3zJRSZfIM\n+P1/m/zT+RyYf5rUnBtp9Mfbad7zUnwBPvnEmh7rgQf0nppSF4G2zJS6QGdSz7D3hb3sf30/+afz\niXg2gubp78JTT4GXF4wZAw8+CE2auDpU5WbcqWWmyUypSpJ9JJuUl1JoOLAh/gn+nP5hO9kvvEfA\nwhfA09Naeubvf3d1mMqNuFMy0wEgSlWSOiF1iHgyAv8EfwD2fmpYv+APJHb9meO9/4a0aGkdmJ6u\nK16r6sGY9zDmEMZsLlQWhDHfY8wO+zWw0L7JGLMTY7ZjTN9C5QkYs8neNx1jjF1eF2Pm2OUrMaZl\nVV2KJjOlqkjEMxFc+vylZOzMY8PXfVj/7wiOfncUpk+HiAgYPx727nV1mMq9zQD6FSubBCxGJBJY\nbH8GY9oDQ4Aou85rGOOw67wO/AWItLeCc44GjiHSCvgX8ExVXYgmM6WqiKefJ2H3h9E1qSuRr0Ry\nZs8Zjsw/ArfeCsOHI2++ZT2nNm6cJjXlGiI/AkeLlfYHZtrvZwIDCpXPRuQMIknATqAzxoQC9RFZ\ngXXf6oNidQrONQ/o7Wy1VTIdzahUFXP4OGg6vimhfwkl/3Q+BHhy/LZn2fHjcJo3XcYlbz+O2b0b\n/vtfV4eqapkQ8MSYNYWK3kLkrXKqNUIk1X5/AGhkv28KrCh0XIpdlmO/L15eUMf6l5pILsacAIKB\nI+d4KeWqspaZMbxnDIeMYXOhsiBj+N4YdtivgWc7h1K1iUcdD+ewfskVxOHFtiVXsCpsEandniA/\nJx/27LFmFtm928XRqtrgCOQi0qnQVl4iK8pqaVX/UYJUbTfjDMroixWhaF+sUm4m8OpALtt0GVGf\nReFo4M32h06y/or1yM//g3ffhchIuPNOTWrKFQ7aXYfYr4fs8n1AWKHjmtll++z3xcuL1jHGEwgA\n0qoi6CpLZiKcS1+sUm7HeBgaDmpIwtoEYv4bQ7MJzTC3DEV+3cn+K54m7/1Pfr+nVgMeoVG1xnxg\nuP1+OPBVofIh9gjFcKyBHqvsLsmTGNPVvh82rFidgnPdCCyhip4Hu9j3zBqJUFpfrFJuyxhD8HXB\nzs/Hdvjx67IEkoIW0CxyI03P7MCz4J75gQPQuLGLIlW1jjGfAD2BEIxJAaYA04C5GDMa2A0MBkBk\nC8bMBbYCucB4RPLsM43D6o3zARbaG8C7wIcYsxOrcTOkyi6lKh+aNoaWwAIRou3Px0VoUGj/MZHS\n75sZwxhgDECdOr4JZ87oQ9PKfZz4vxPsfmo3R78+iiPAQbO7m9H82kM4el8Jw4bBQw9Zw/uVOgt9\naLrqHDSGUAD79VBZB4rwlgidROjkqWMulZsJuCKA2P/GkrA2gcBrAjk87zAeEWEwbhz5s+ZA69Yw\nciTs3OnqUJWqFi52y+w5IE2EacYwCQgS4YHyzqPTWSl3l5eZh6Oeg9yMXFa3XkHIJb8S9stUvP0y\nISUFvL1dHaKqhrRlVgmM4RNgOdDGGFKMYTRWX+y1xrADuMb+rJQqh6OeNdFC/ul8Aq8LYf+WS1mZ\n/wHbL5vN6X1iDRB5+GHYscPFkSrlGjrRsFI1UNaeLPY+t5f9b+9HcoTO8wOpd9PlcOaMNcPIww9b\nXZHKrblTy0yTmVI12JnUMxz5/AhNxzeFgwdJHTYbv2Vv45/7C9xzDzzxBPi6xXdZjZSZac05nZJS\ndCtcNncuXHXV+Z3fnZKZDq1QqgarG1rXSmRAXkAIuxI7kXOmA0HN9xHx2dv4/dNRzhlUVTl5smSS\nKp6sjhZ/EhcIDIRmzawtPh4aNCh5jCpJW2ZK1SK5J3LZ9+o+9j6/l9wTuTT5axPCJzXC69EJ1nD+\nVq1cHWKNJ2IlobISVUGySk8vWfeSS35PVIW3pk1/f63MhrQ7tcw0mSlVC+Wk5ZA8NZnUd1Lp9J6D\nenf+AbKzYfJka9VrHf1Yqvx8OHiw9K6/wokqK6toPQ8PayHxgqRU2hYaCnXrXtzr0WRWzWgyU+r8\nZB/Opk7DOrB/P7/1/pQGv3xMcKuj8Oqr0KePq8OrctnZkJZW/nb4sJWk9u+H3Nyi5/DyKr0VVXhr\n1MhaTLy60WRWzWgyU+rC5J7IZe1lazm94zRB9TZxabul+K7+DKpmaalKJ2J121UkMRVsR45ARkbZ\n5/TxgeBgawsJKZqkCr8PCbFaXjWRJrNqRpOZUhcuPzuffS/vI/nxZPIz82gyvinhY33w/PZzazLj\ni9S0yM2FY8d+TzgVTU45OWWfs0EDK+kUJKezbQXH+fhclMt1KU1m1YwmM6UqT/ahbJIeSeLI50fo\nPH4lXo/dDx06wOuvw+WXn9O5cnOtwRAFSenIkd+3wp8Lvz9+vOzzeXmdPQGVtgUGVs8uvupAk1k1\no8lMqcqXeyIXz/oO5LMv2DZ8G40zv8Dntnj2jpvGwdzgsyangs/HjpV9/nr1fk9CISGlJ6TiZX5+\nNabns0bQZFbNaDJT6tzk5VktprJaR4U/56dmcd+e9TTKP0MQ/8cqjvEXnityPh+fogmp4H1Zn4OD\nrWSmXEuTWTWjyUy5m6wsqzvuxInze01PL3s9T2/vosknJAQaNsinw44Uwn/ahcmD/IHNCB1whqBL\n8qnfLUYTUw3lTslMe5qVqmR5edbsD+eSgIqXZWef/Wd4eFiDHgICfn+99NKin8tqPZWemDyA5pw5\n0Iikh5I48b802mb+E49v/wsTJsCUKeDvXwW/LaUqh7bMlNsTsebnzcj4fUtPP/vngrL09NJbReXx\n9S2aeIq/nm1fgwZW/aq8t5SXmYfj9HHy/v4wW2a0ICxkMYFv/BUGDdKbWjWIO7XMNJmpGqd44qlI\n8invc/EHZctijDVIoWDz9y8/8RR/rV/fGrVXE2RsymDT/7d35kFWVXce/3xf791AQyMygC00i0tr\nBBFR45KMiEt0nKDGaDRRKxmdqpmKS9UYiLPoOMmYjDUTHUczVkziYMYFddAiOiqDlks0gigGUIxi\n2+xbgDaIrL/545ymL00vPJa+93X/PlW33nnn3OX77uvX33vOPff3mziHLavgEF5mxI9HUPE3V6Qt\ny9lL3MwyhptZ92fnzhCFobERliwJr8nyypUtBtTR80atSRpPs/nsz/vKyp7XMdmxeQdL/uUTGn/Q\ngFFE7U21DLtiK7lRdV0fn8nJCzezjOFmVvh8+unu5tTWa+v7RBUVcPjhYRk0KPRo8jGfysrCjdyQ\nRbYs28LiKYvZsmQzoxsuQSXFISzWxIlpS3Pawc0sY7iZZZtt20Jcu/Z6VUuW7PmgbC4XQgbV1gaz\nan5Nlmtqel4vqBDYuXUnuZdmsuW6W1jYcCV1Z35M36k3h0i7TqZwM8sYbmbpYRaG/9ozqcZGWLFi\nz5jFlkIAAA09SURBVGngNTV7mlPydfBgj9pQ6GyctYYFk+aytamMAcWvMOLZSZSfdWzaspwEbmYZ\nw83swGEW7jtt2ND20tq4li7dM91FeXnbJtVcrq315MY9hR2bdtA4eR5LfroeikuovbmWYd/tg/r3\nT1uag5tZ5nAza8EMNm1q34yal/Xr22/bubP9/edy4f5Ue0N/tbXhWSUf/nOSfN74OYsnLybHFo56\n9ky49FLshz90U0sZN7OM0Z3MrNmMmp9J2hdD2rGj42NUVYUp4Pu6+PCfs6/YhiZ0+200/eRZPsxd\nz4jJfaj+x8v86iclOjUz6VzgLqAI+Blmd3SVtgONm1kemMFnn7VEbGi9JKM5tNfe1NS5GVVW7p8Z\nFcozTE73Zd29c1h0w3K2buvDoQPmMfw3V1M+sjptWT2ODs1MKgI+ACYCS4HZwOWYLew6hQeOHmNm\nZrvHu9tXQ+rs4dpcLkwhT0ZyaL0kH6Dt2zeksGguV1dDael+fVTHyQTbm7bRePkMljzXB5WVMOzW\nYRx+0xAoKkpbWo+hEzM7BbgVs3Pi+ykAmP1zV+k7kHTrAaXbb4cHH2wxos4etpWCESWNZ/BgOPro\n9s2pdb2nsHCcQHGfEob/ehKDPt7M4u8tZucnK2DQODb1OZYFS/+iZcXBg6GiguGXbuCQx26kafPh\nvL/8Wy3tQw6D8jJGfW0F/aZ9nw2bRvLBysta2mtrobSUoy5ZTJ/Hb2fdp8fw0epJLe1Dh0JxMfUX\nLaDXk3eyuul4Gtac39JeVwe5HF/46ptUTL+PlRtOonFd4tm5ESMAGHPBLEpnTGXZH05n2fovhTYJ\nhg8HYOzZT1H8/HQa105g5caYF66oCIYNA+DEP52KXpxFw5qvsLppbDxJxTB0KLmKHONG3wdvvMFH\nq77Kuj+GWaGDztlB7VNX7vN30AlDgCWJ90uBkw7WwQ423drMBg+G8eM7N6DmpXdvf8jWcQ40FXUV\nHPPYMdjcubDhbHJ/KKXq88RIy8hiqK6ieMBWqK+nqKkfVVsT7UeUQK8qigb0Cu3rB1C1PdleBpWV\n5A7tA/X1FK8dSNXORPuR5VBWRm5g39C+agBVlmg/qgKKi8kNrAnty2uoUqL96BD2RX8yAOrrKVna\nl6qi2J7LQX3o+GjIIKivp/ST3lQtj+0lJbvaOaw2tC+upGpVbC8vh/oqVKZguk1NlJWUU7U2tJcO\nqdmfU88hUIw0J1F1P2b379dOM0qPGWZ0HMfpafSkYUbvhziO4/RMZgOjkOqQSoHLgKdT1rTPpGJm\nEudKLJL4UGJyGhocx3F6NGbbgb8GngPeAx7DbEG6ovadLh9mlGhzOqgZ7U4H9WFGx3Gc/OlJD02n\n0TMbD3xoxmIztgKPAH+egg7HcRynm5CGmbU1HXRICjocx3GcbkJmp+ZLXAtcC/4QseM4jtMxafTM\nlgG1ifeHxbrdMON+M8aZMc5jBTqO4zgdkYaZzQZGSdRJFPx0UMdxHCd9urzPY8Z2add00CLg52Z0\nOB30s88+M0mb9/GQxUAnERVTwXXlh+vKD9eVH1nVBfunreJACskyBREBZH+QNMfMxqWtozWuKz9c\nV364rvzIqi7ItrYs4RFAHMdxnILHzcxxHMcpeHqCmWU1QrTryg/XlR+uKz+yqguyrS0zdPt7Zo7j\nOE73pyf0zBzHcZxuTsGbmaSfS1otaX6irkbSC5J+H1/7JdqmSPpQ0iJJ5xwkTbWSXpS0UNICSddn\nRFe5pDclzYu6bsuCrsSxiiS9LWlGxnQ1SPqdpHcUEx1mQZukvpIel/S+pPcknZK2LklHxvPUvDRJ\nuiFtXfE4N8a/+/mSHo6/hyzouj5qWiDphliXuq6Cw8wKegHOAMYC8xN1PwYmx/Jk4EexXA/MA8qA\nOuAjoOggaBoEjI3l3oQsAfUZ0CWgVyyXAL8FTk5bV0LfTcB/AzOy8D0mdDUAh7SqS10b8CDwnVgu\nBfpmQVdCXxGwEhiati5C/NePgYr4/jHg6gzoOhaYD1QSniebCYxMW1chLqkLOEB/EMPY3cwWAYNi\neRCwKJanAFMS6z0HnNIF+p4ipLzJjK7445kLnJQFXYSwZv8HnEmLmaWuK+6/gT3NLFVtQHX856ws\n6Wql5WzgtSzooiXAeU00jRlRX9q6vgY8kHj/d8DNaesqxKXghxnbYaCZrYjllcDAWO7yiP2ShgHH\nE3pBqeuKQ3nvAKuBF8wsE7qAnxB+xDsTdVnQBWDATElvSbo2I9rqgDXAL+LQ7M8kVWVAV5LLgIdj\nOVVdZrYMuBNoBFYAG83s+bR1EXplp0vqL6kS+Aohdm3augqO7mpmu7Bw+ZLKlE1JvYAngBvMrCkL\nusxsh5mNIfSExks6Nm1dki4AVpvZW+2tk+b3CJwWz9l5wF9JOiPZmJK2YsLw+n1mdjywCXbP2p7y\n334pcCEwrXVbSn9j/Qh5E+uAwUCVpCvT1mVm7wE/Ap4H/hd4B9iRtq5CpLua2SpJgwDi6+pYv1cR\n+w8EkkoIRvYrM3syK7qaMbMNwIvAuRnQdSpwoaQGQrLWMyU9lAFdwK6resxsNfA/hASzaWtbCiyN\nPWuAxwnmlrauZs4D5prZqvg+bV1nAR+b2Roz2wY8CXwxA7owswfM7AQzOwNYT7jHnrquQqO7mtnT\nwFWxfBXhnlVz/WWSyiTVAaOANw/0wSUJeAB4z8z+NUO6BkjqG8sVhPt476ety8ymmNlhZjaMMDQ1\ny8yuTFsXgKQqSb2by4T7LPPT1mZmK4Elko6MVROAhWnrSnA5LUOMzcdPU1cjcLKkyvj7nAC8lwFd\nSDo0vh4OXESYBJW6roIj7Zt2+7sQfjArgG2Eq9VvA/0Jkwl+T5gdVJNY/xbCDKBFwHkHSdNphGGB\ndwnDBu8QxsLT1nUc8HbUNR/4+1ifqq5WGr9MywSQ1HUBwwmzx+YBC4BbMqRtDDAnfp/TgX4Z0VUF\nrAOqE3VZ0HUb4eJtPjCVMCMwC7peIVyIzAMmZOV8FdriEUAcx3Gcgqe7DjM6juM4PQg3M8dxHKfg\ncTNzHMdxCh43M8dxHKfgcTNzHMdxCh43M+egImmYEhkN8tz2OknXSBoj6T/z3LZM0swYuf3re7H+\nhZImd7Zevki6WtI9B3q/HRxvn8+34xQyxWkLcJwOOB34B+AC4OU8tz0ewEIYqk4xs6cJD6SmiqRi\nM9uetg7HKTS8Z+Z0GZKGx6C4J3ay3o0xGPIkQkiw24BbJP20jXVrJE2X9K6kNyQdFyMqPAScGHtm\nI1pt812FXHPvSnok1u3qQUn6paS7Jf1G0mJJl8T6nKR7FfKHvSDpmURbg6RDYnmcpJfa0Ppnkn4b\nz8FMSQNj/a2Spkp6jfAwb3KbRySdn3j/S0mXxB7YK5LmxuWLbRxvt16hpBmSvhzLZ0t6PW47TSGO\nKJLuSJybOzv6nhwnS7iZOV1CDLv0BHC1mc2WNFjSM22ta2b/Rgi1NSv2rD4ws3oz+8s2Vr8NeNvM\njgO+D/yXhRiK3wFeMbMxZvZRq20mA8fHbdraJ4S0G6cReoV3xLqLCOmG6oFvAqfszWdP8CpwsoXA\nwI8QsgQ0Uw+cZWaXt9rmUeBS2BW8dwLwa0KsvolmNhb4OnD33oqIpvu38XhjCVFEbpLUn3ABcUw8\nN/+U5+dznNTwYUanKxhAiC13kZktBDCz5YQQX+0xFpgnqQ+woYP1TgMujvucpZBKo08net4FfiVp\nOiEMVFtMN7OdwMLmHlQ81rRYv1LSi50cpzWHAY/GwLGlhHxkzTxtZpvb2OZZ4C5JZYSg0C+b2WZJ\n1cA9ksYQoqwfkYeOkwnm+VoIU0gp8DqwEfgceEAh2/eMvD6d46SI98ycrmAjIdDraZ2tKOnQOMT4\nC+AbhASio9saLtwPzgf+g2CYsyW1dVG3JSlrL/a5nZbfU3k76/w7cI+ZfQG4rtV6m9rawMw+B14C\nziH0wB6NTTcCq4DRwDiCIXWkKalLhFx2Y+JSb2bfjvfqxhMi8F9ASEniOAWBm5nTFWwlDF99S9I3\nOlrRzFbHocW5hH+sDwHXtDNcCCFI6xUA8X7QWmuVOy6JpBxQa2YvAt8jZGzutZef4zXg4njvbCAh\nKHIzDcAJsXxxO9tX05Ku46p21mmLR4FrCBNimg2mGlgRe4nfBIra2K4BGBP11hLOJ8AbwKmSRsKu\nzABHxPtm1Wb2DMEsR+eh0XFSxc3M6RLMbBPhav/GOA2+3XtmkoqA/ma2lpBz6tUOdn0rcIKkdwn3\ntjoziSLgIUm/I2QQuNtCbre94QlCZoaFBJOdS+h1Qrh3d5ekObRKrthK6zRJbwFr9/KYEBI3fgmY\naWZbY929wFWS5gFH0XbP7jXCUOZCwj21uQBmtga4Gng4nrfX4z56AzNi3avATXlodJxU8aj5jpMH\nknqZ2R/jZIk3gVMt5BZzHCdFfAKI4+THDIUEp6XA7W5kjpMNvGfmOI7jFDx+z8xxHMcpeNzMHMdx\nnILHzcxxHMcpeNzMHMdxnILHzcxxHMcpeNzMHMdxnILn/wEKXyZlzRapbQAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax1 = plt.subplots()\n",
"ax1.plot(df.columns, df_rand.loc[\"time\"].values, 'b-', label=\"randomized SVD time\")\n",
"ax1.plot(df.columns, np.tile([57], 9), 'g-', label=\"SVD time\")\n",
"ax1.set_xlabel('k: # of singular values')\n",
"# Make the y-axis label, ticks and tick labels match the line color.\n",
"ax1.set_ylabel('time', color='b')\n",
"ax1.tick_params('y', colors='b')\n",
"ax1.legend(loc = 0)\n",
"\n",
"ax2 = ax1.twinx()\n",
"ax2.plot(df.columns, df_rand.loc[\"error\"].values, 'r--', label=\"randomized SVD error\")\n",
"ax2.plot(df.columns, df.loc[\"error\"].values, 'm--', label=\"SVD error\")\n",
"ax2.set_ylabel('error', color='r')\n",
"ax2.tick_params('y', colors='r')\n",
"ax2.legend(loc=1)\n",
"\n",
"#fig.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true
},
"source": [
"### Math Details"
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true,
"hidden": true
},
"source": [
"#### Process behind Randomized SVD"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"Here is a process to calculate a truncated SVD, described in [Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions](https://arxiv.org/pdf/0909.4061.pdf) and [summarized in this blog post](https://research.fb.com/fast-randomized-svd/):\n",
"\n",
"1\\. Compute an approximation to the range of $A$. That is, we want $Q$ with $r$ orthonormal columns such that $$A \\approx QQ^TA$$\n",
"\n",
"\n",
"2\\. Construct $B = Q^T A$, which is small ($r\\times n$)\n",
"\n",
"\n",
"3\\. Compute the SVD of $B$ by standard methods (fast since $B$ is smaller than $A$), $B = S\\,\\Sigma V^T$\n",
"\n",
"4\\. Since $$ A \\approx Q Q^T A = Q (S\\,\\Sigma V^T)$$ if we set $U = QS$, then we have a low rank approximation $A \\approx U \\Sigma V^T$."
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true,
"hidden": true
},
"source": [
"#### So how do we find $Q$ (in step 1)?"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"To estimate the range of $A$, we can just take a bunch of random vectors $w_i$, evaluate the subspace formed by $Aw_i$. We can form a matrix $W$ with the $w_i$ as it's columns. Now, we take the QR decomposition of $AW = QR$, then the columns of $Q$ form an orthonormal basis for $AW$, which is the range of $A$.\n",
"\n",
"Since the matrix $AW$ of the product has far more rows than columns and therefore, approximately, orthonormal columns. This is simple probability - with lots of rows, and few columns, it's unlikely that the columns are linearly dependent."
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true,
"hidden": true
},
"source": [
"#### Why M ~ Q Q.T M"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"We are trying to find a matrix Q such that $M \\approx Q Q^T M$. We are interested in the range of $M$, let's call this $MX$. $Q$ has orthonormal columns so $Q^TQ = I$ (but $QQ^T$ isn't $I$, since $Q$ is rectangular)\n",
"\n",
"$$ QR = MX $$\n",
"$$ QQ^TQR = QQ^TMX $$\n",
"$$ QR = QQ^TMX $$\n",
"so...\n",
"$$ MX = QQ^TMX $$\n",
"\n",
"If $X$ is the identity, we'd be done (but then $X$ would be too big, and we wouldn't get the speed up we're looking for). In our problem, $X$ is just a small random matrix. The Johnson-Lindenstrauss Lemma provides some justification of why this works."
]
},
{
"cell_type": "markdown",
"metadata": {
"heading_collapsed": true,
"hidden": true
},
"source": [
"#### The QR Decomposition"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"We will be learning about the QR decomposition **in depth** later on. For now, you just need to know that $A = QR$, where $Q$ consists of orthonormal columns, and $R$ is upper triangular. Trefethen says that the QR decomposition is the most important idea in numerical linear algebra! We will definitely be returning to it."
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"#### How should we choose $r$?"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"Suppose our matrix has 100 columns, and we want 5 columns in U and V. To be safe, we should project our matrix onto an orthogonal basis with a few more rows and columns than 5 (let's use 15). At the end, we will just grab the first 5 columns of U and V\n",
"\n",
"So even although our projection was only approximate, by making it a bit bigger than we need, we can make up for the loss of accuracy (since we're only taking a subset later). "
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"#### How this is different from random mean"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
"(4800, 2)"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"test = M @ np.random.normal(size=(M.shape[1], 2)); test.shape"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"Random mean:"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"image/png": 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W4dIM3bIJTkcEhhqMW/pAdSa3qmFv9UGn8TltdUo5M3dNVz6stwSFW9lRcTGH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\nQh6OIYQwQh6OIYQwQh6OIYQwwv8HsXDOfE53XhEAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(test[:,0], dims), cmap='gray');"
]
},
{
"cell_type": "markdown",
"metadata": {
"hidden": true
},
"source": [
"Mean image:"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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z8v1UVbr5mlmDzO2coggAZ5xxxnibK5NzSFCGU1mVFqzKkP3yl7/s9K1bt67T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\njsYY08P/A0CPiyl1YEmVAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(M.mean(axis=1), dims), cmap='gray')"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"image/png": 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Uq6zcSv/rE8Z5rDaIVy5CrWzaSuNTc8v3s88ui+q5ze22stJnlpJN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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(test[:,1], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": true,
"hidden": true
},
"outputs": [],
"source": [
"ut, st, vt = np.linalg.svd(test, full_matrices=False)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"image/png": 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h+JkeUsVIhbKpe68qdg+pPqRClIDatVeyRGtOOBbhQ35zNMaYDjw5GmNMB54c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\nDjw5GmNMB54cjTGmA0+OxhjTwf8HdZ+QVOXxnJAAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(smaller_matrix[0,:], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"image/png": 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Lw46ybsf2cehMvv84PCfPC2t6q1bVyXJ5JcDWioyqariCQ42yvZze2Be/ORpj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\ngR+OxhjTgR+OxhjTwf8D/quBcijsO+8AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(smaller_matrix[1,:], dims), cmap='gray');"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"hidden": true
},
"outputs": [
{
"data": {
"image/png": 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4dJKGyiY/uI1DYokxxhxmeHI0xpgePDkaY0wPMw8fzLpZ1jE4dGnSecDBepFy\nh1FhYi0ZqBUtabRY18l6pLqvmk2qXVVX0yPVvbT0UW6H71OFgrF97FKSy/v27evUZT3ynHPO6dSp\ntGms0zF5DKnx9cgjj3Tqzj///E5ZpdKadmdAfl5KD6xdQ2nl+ZnVQm3zufw9r7npZabdOXFaHdNv\njsYY04MnR2OM6WHmy+qhriEt0StqUx5eIqmsHy0MzbQDdJcyyn2o1jcqS7Ja2qulci3DuZIhVP+p\naJra0i+7+tSW/bnMGeJzpE0tQiZH7fASnCNJsksO1+V7OfXUUzt1nCFnWtRStCW7kMoSxLRka1Lf\nT0Yts9nlqyX7eD532i2h/eZojDE9eHI0xpgePDkaY0wPMw8fnOS6orSlWlYZpbOw3qB2PMzUtC6V\nqbzWVibrKrX7VO4wKqtRy4b1qk+4L5W9bI8KP+N2lO3KpURpVGxP3mgeAHbs2DE+ZpcgzvaTs21z\nlqCsM3IGGpV1/bXKYs7n5n5ocdti8vOsZTFXY2ra+67tJpnv05qjMcYcQjw5GmNMD54cjTGmh5n7\nOU7SCpTewZpKy7lqlz7WwVr8/5TmobQ4pWXW/MVaQr8yrLepdlRmZr5nFfbHWqHSqPia2TeVr8H6\n0VC9+YUXXpDtKI3queee65Rz5vInn3yyU7ewsDA+3rJlS6fu4x//eKecU5bxfSqdjsd/1k/ZVpWa\njX2AOa2bosXPV32vVCipGv/cP7WdFKdh8JtjRBwZEfdExM2j8sqIuDUiHh39/+RaG8YY83qhZVn9\neQAPpfL1ADaVUtYB2DQqG2PMYcGgZXVEnAngXwL4jwD+zejPVwN4/+j4RgC3A/hSra1Jr+BqeVRz\nOVAuQS3ZjpV7jgqBaskovhSJQG2yzvblz/IyXy2Vl+JSoiSLbF+LaxbbpzIpqczpvNzkLN152c22\nczm3y5nKt27dOj7euXNnp27VqlWd8oYNG8bHHFrIWcPzNVsydnM5uyUtxQVNhecN/VwfKoN3vu/a\nsjqXf/KTn8hrTrRl4Hl/BuCLAPLoWyilvDrCdgNYOOhTxhjzOqU6OUbExwHsLaXcPemcsvjPQe8/\nCRFxXURsjojNNcdNY4xZLgxZVr8XwCcj4mMAjgZwQkT8JYA9EbGmlLIrItYA2Nv34VLKDQBuAIAV\nK1Ycmt1zjDHmNaY6OZZSvgzgywAQEe8H8G9LKX8YEf8ZwLUAvjr6/3cGtDXxp3qVxqqmU+Q2lSYF\naO1Gha2A5H2jAAAQFklEQVSxnpV1s5Y0USozs3K5AdoylQ/d9Jz1P96FT2UUVyGBnD5MhYNyXyv3\nJuVOxHXZxYUziB84cKBTzs+FnwPrf6pPsr0nn9x14Pj5z3/eKec+Wr16daeOM5VnvZLtUTsTtmTa\nbnEzm3Re7dwWlmJ7Hv933XXXVNdfihP4VwF8OCIeBfChUdkYYw4LmpzASym3Y/FXaZRSDgC48tCb\nZIwx88fhg8YY08NcU5ZlnYd1KLWdAWtLSgNi7W2oFsfaG2uFuV6l3OIyn6tSSLG21LL7mvKFy9es\n+brlvua+UztGtqS/UjtG1vQsFVKmfOaUnqu2eOAya5m5rpZu7Zlnnhkf520agIN9JE844YTxMeuR\nucw6J/dXHrdDtyypUfNDbkkNqNpp8Wfev3//+Piiiy7q1LGP68TrDzrLGGN+z/DkaIwxPcx0WQ1M\nXm61hESpcD1+3W7ZMF6FJykXIV7mq9A5hdpZD5g+1FAt81vckFpoyc7OqFBD9cxUu5zNW7kPsaTC\nzze74PC5eVnLoYWcfXzFihXjY74vdoXK4Y+cCWj79u3j47Vr13bqTjvttE45961yxQK0ZNGSlSdT\nG+Pq+9lynZytff369Z26W265ZVAbfnM0xpgePDkaY0wPnhyNMaaHmWcC59CsV2FdTumILT/xK7cC\nvqba3U+5grS4rbDGonQfpSPWGKpPtvTtUtxqWmzN12zZyY71ydwOZ71WKd7YhUrtXMg7DGYtk7OP\n1/TwDI8LleYth0LmLOXAwfeSwxB550R2A8r30pKxeykpy/IYU+OilvovP29+9kPxm6MxxvTgydEY\nY3qYuSvPUNcRtYxQmYf5cyqaRi2t1DKCqWUNV8v1bF8tMiPfZy3yZ6hLRG2Zn9upbbClMoErGUJJ\nKoyq42ef7WO3GrW8q2VHz/W8rM6uPbwcVy5CvPxVy0blmsXfjWeffbZTzpE4TzzxRKfu+OOP75Rz\ndnLOYp5dZVQkF6D7elr5peYel/uhJbt953pTfcoYYw5zPDkaY0wPnhyNMaaHmbvyTNKeWnaVU/oa\n6wusQ+Wy2iCetSTW0JTLgXKjYf0l28Malcq8XdNRhrqJcDtsg9IROQQvwzpUfkY1nSlfs7b7oNJE\nc19z6J5yYeI+Yb1SuZTkMVULk1QZmXgM5baU3sZ9wO3ketYjeYfGvXt/t/MJ65GnnHLK+Jj1SD43\nc+KJJ3bKPKby2FAafO23i9xuLUxyEn5zNMaYHjw5GmNMD54cjTGmh5n7OWaUNqfC/FifUfqDSm/G\nupjyI5zWV4pRupjSX9iGWiZkpdmqXRZb4D7KKbg+9KEPderOPffc8fFtt93WqduyZcvEa9TsU36i\nGZVpHujeC+uTXM66mfKJzP0BHBxOmDW/nOkbODjkbaiGXPPPzf3AfcDn5nvjsMRs+44dOzp12QcS\n6PpLKr9joPudVPa1hCHaz9EYYw4hnhyNMaaHmS6rjzjiiMEZMvLSTy0vmVpYUc6wzMtq5eKiNjyv\nuaYom/JnObxM9VVLhhzlzlFrd6irDNBdfj700EOdurykZNcYRi2VW9ykVGZ3Jbfwuby0b8lUlFGh\nrdxOzQ1oErXQzHwvfJ88/jL8HPJn2f1r3759nXL+Xi0sLHTqeAme3YJ4/GfbVSZ3xstqY4w5hHhy\nNMaYHjw5GmNMDzMPH8xaylAXnNqG7C2ZuLPuo9xfarukKVTYE2tAWVfhz7W4MrToYir0kVEhW6xZ\n5fIDDzzQqbvvvvvGxzW3GmVfy26JLbsY5nHJ53IoqQrlU25S3G5uR2nafJ2aC44iX7OmTyrdM3+W\nbef+ylr0448/3qnjnRSzS1N2AQK6vxFwiCKHMGad05nAjTHmEDLozTEitgF4DsArAF4upWyMiJUA\n/hbAWgDbAHyqlPLUa2OmMcbMlpY3xw+UUjaUUjaOytcD2FRKWQdg06hsjDGHBUvRHK8G8P7R8Y0A\nbgfwJfUBtfsg0xLilrWSWnoipWVm7aQWntSyE5rSybJ+pLZQYFi/UmnTlC9ei+01P8dsv9JA1XYG\nfM2l7OyYqemcmdp9Zlp2a+S+Pu644ybapzRIpU3X+ivX11IBZlRoIcP3kr+T3E72Owa6adP279/f\nqcvhmKwj8s6JuTx0zmGGjrwC4PsRcXdEXDf620IpZdfoeDeAhb4PRsR1EbE5Ija3bC1qjDHzZOib\n4xWllCci4lQAt0bET3NlKaVERO8/r6WUGwDcAADHHHOMfh0zxphlwqDJsZTyxOj/eyPiWwAuA7An\nItaUUnZFxBoAe2UjFVQWnNqufAq1i6HaeY9f0/k1Poda/fKXv5T2ZRvUxvMtYYgq/I1RWa+X4iqj\nXHDYDUTZriSCFntaXFpUqGFNsphWJuFr5jHEoXtq3C4lW5NadreELCppRmXfz1ICcPDyPC+Bud1c\nl3dRBPROinzNoVSX1RGxIiKOf/UYwEcAPADgJgDXjk67FsB3prLAGGOWIUPeHBcAfGv0r9NRAP5X\nKeUfI+IuAN+MiM8C2A7gU6+dmcYYM1uqk2Mp5ecALu75+wEAV74WRhljzLxZNpnAlWbGOgm7iSgN\njdvN7gAcnvSJT3xifLxx48ZOHesWOexp586dnTrOdL1169bxscrUrHYmZJQbEsNaUj5XXQNoC8FT\nIWUZzqyt9GauUy45KpxR6WBAW0Z0pbdNun7fNXM77G6iMowPzaDfZ1+ub9FSW7Ks19zg1Gdzme8l\nj2NON8hjPGuSrEcOxeGDxhjTgydHY4zpwZOjMcb0MHPNUYVXDUX5bp111lmduvXr13fKl19++fiY\ndaa3ve1t42NOiZTDmgDgjjvuGB/ff//9nTrWOLIPG4c3qh0PVTgXa1JKm1Op2Wr6kNKoWC/K1+F2\n1XVq9zItyu+S9azsx8rPqGWnwgz3u/IjrH0X1DNT/d6yrQSjtplo2fEz0/KdV/3FY4TtqYURD8Fv\njsYY04MnR2OM6WHmy2rlXjGJlhCyvDQGgEsuuaRTvuuuu8bH/Nqel84HDhzo1PHS+eGHH57Yjlr2\nqF3wahlVVH/xNbNriHJ/qYWMKfecmktOJi+dayFueUnELhvKXUfJErUs11n6aLkvldmmthRVz17J\nAMpdTWU453NrmcAVyg1PueDUsiMp1zGVlZ5tz9nIX+usPMYY83uFJ0djjOnBk6MxxvQQLaE+S+Xo\no48u2dVGpfJS+pva1a0WJpY1jqGaZ589ud/YbaBlV8MWlHuCcp3hz6nMzCr9VE1byp9V4XgtWaVV\nFnOgq2fxNfN9tuhptZ0Ah55ba0e54LRkR8/lWhZzpd+rnRQ5pZoaXy1uP0qHVZ/jFILqO8dueLff\nfvvdabuXifjN0RhjevDkaIwxPcw1K4/6aV4tI9RSobasyEsvdnPIn1WbBAHdJRIvOVSGbLW0YtvZ\njWXopllAd2nTcp9qk69aFhe1lG7J6pJpyWytMoHXMmLncs3dJNvE18z9x89zaAbxvnIef/w8W5bK\nuV12WeJ2lbSVr8njX51bu08lsWR7VKZ5bqfFFbBzvak+ZYwxhzmeHI0xpgdPjsYY08PMNcdJrkNq\nRzXWPlp2mattID8J1ilYC1H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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(np.reshape(M[:,140], dims), cmap='gray');"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"heading_collapsed": true
},
"source": [
"# End"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}