{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "HLZRySda6U-g"
},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LGVnPDHJw9_I"
},
"source": [
"# 特異値分解と情報削減\n",
"\n",
"このノートブックでは、行列の特異値分解と、その応用例として画像データの\"低ランク近似\"について説明する。\n",
"\n",
"関連する線形代数の知識、とくに諸定理の証明については、適宜線形代数の教科書等を参照すること。\n",
"\n",
"*純然たる*(≒形式的な?)線形代数の教科書には意外とSVDは載っていなかったりするので、工学であるとか数値計算など、応用を意識した教科書を参照するのが良い。\n",
"\n",
"Webで無料のものが良ければ、Mathematics for Machine Learningもいいかもしれない \n",
"※[著者らのページのリンク](https://mml-book.com)からPDFがダウンロードできる。\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "aakEipnQ6lik"
},
"source": [
"## 特異値分解 (Singular Value Decomposition, SVD)\n",
"\n",
"特異値分解は、線形代数の中でも応用上非常に重要である。 \n",
"本ノートで説明するような画像処理や情報削減の方法として用いられるだけでなく、量子多体系(物性や素粒子・原子核などの物理学,量子化学などが対象とする系)の計算手法である密度行列くりこみ群(DMRG)法など、自然科学分野の理論計算などの根幹にもなっている汎用性の高い手法である。\n",
"\n",
"\n",
"**特異値分解定理**: \n",
"任意のランク$r=[0,\\min(m,n)]$の$m \\times n$行列$A$は\n",
"- $m \\times m$のユニタリ行列 $U$\n",
"- $m \\times n$の対角行列$\\Sigma$ \n",
"- $n \\times n$のユニタリ行列 $V$\n",
"\n",
"を用いて$\n",
"A = U \\Sigma V^\\dagger\n",
"$\n",
"と分解できる。 \n",
"上は$A$が複素行列の場合の表記で、実行列の場合は、$U,V$は直交行列であり、随伴操作(複素共役かつ転置)$\\dagger$は転置$T$となり、対角行列$\\Sigma$の各成分は非負となる。 \n",
"\n",
"以下では、特に断らない限り実行列の場合のみを考える。 \n",
"$\\Sigma$の各対角成分を**特異値**と呼び、慣例的に$\\sigma_1 \\geq \\sigma_2 \\geq ... \\geq \\sigma_r \\geq 0$となるよう並べられる。 \n",
"※一般の$m \\neq n$の場合は長方行列となるので、上での\"対角行列\"は正確には、対角ブロックとゼロ行列ブロックを含むような行列を指す。\n",
"\n",
"$m (3, 3) (3,) (3, 3)\n",
"特異値 => [15.52961563 3.39284204 1.82199376]\n",
"USVd => [[1. 9. 6.]\n",
" [2. 4. 6.]\n",
" [3. 8. 3.]]\n",
"USVd@rank2 => [[2.27571625 8.70200595 5.94787683]\n",
" [1.22318899 4.18145497 6.03173892]\n",
" [2.04499401 8.22307947 3.0390196 ]]\n",
"||A-USVd||_F 1.8219937599763407\n",
"USVd@rank1 => [[2.27747026 8.71226915 5.9321303 ]\n",
" [1.46888535 5.61909622 3.82600794]\n",
" [1.84748528 7.06739811 4.81214776]]\n",
"||A-USVd||_F 3.8511087217022104\n"
]
}
],
"source": [
"import numpy as np\n",
"from scipy import linalg\n",
"from numpy.linalg import svd, matrix_rank\n",
"\n",
"# 適当な3×3行列(rank(A)=3)を作成して表示\n",
"A = np.array([ [1,9,6],[2,4,6],[3,8,3] ])\n",
"print(\"A\\n\",A, \"\\nrank\", matrix_rank(A))\n",
"\n",
"# SVD(特異値分解)を実行\n",
"U, Sigma, Vd = svd(A)\n",
"print('それぞれの行列(U,S,Vd)の形状を確認 =>', U.shape, Sigma.shape, Vd.shape)\n",
"print('特異値 => ', Sigma) #Sigmaは対角成分のみをベクトルのように持っている事がわかる。\n",
"\n",
"#積がもとのAと一致するかcheck\n",
"print(\"USVd =>\", np.dot(U, np.dot(np.diag(Sigma),Vd) ) )\n",
"\n",
"#Sigmaをrank2で近似してみる ≒ 行列の(2,2)成分を0にする\n",
"Sigma[2] = 0.0\n",
"USVd = np.dot(U, np.dot(np.diag(Sigma),Vd) )\n",
"print(\"USVd@rank2 =>\", USVd)\n",
"print(\"||A-USVd||_F \", linalg.norm(A-USVd,\"fro\"))\n",
"#Sigmaをrank1で近似してみる ≒ 行列の(1,1)&(2,2)成分を0にする\n",
"Sigma[1] = 0.0\n",
"USVd = np.dot(U, np.dot(np.diag(Sigma),Vd) )\n",
"print(\"USVd@rank1 =>\", USVd)\n",
"print(\"||A-USVd||_F \", linalg.norm(A-USVd,\"fro\"))\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "tvke5nx56FZ-"
},
"source": [
"確かに特異値分解ができているが、これだけではどんな恩恵があるのか、 \n",
"なぜ低ランク近似を考えるのかあまりピンとこないだろう。\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "xC5Pil9881f6"
},
"source": [
"## 画像データの特異値分解\n",
"\n",
"では次に行列として、より具体的なもの、画像を考えてみよう。画像データは\n",
"- 縦横に並ぶピクセルの数を行列の行と列の数に対応させる\n",
"- 各ピクセルの画素値(8ビット,グレースケールで表現するなら、0が黒255が白の256階調)を各\"番地\"での行列要素の値に対応させる\n",
"\n",
"ことで、自然と行列とみなすことができる。\n",
"\n",
"適当な写真をもってきて、簡単のためグレースケールに変換した後、特異値分解をしてみよう。\n",
"\n",
"宇都宮大学オリジナルキャラクター「宇~太」の写真を用いる"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "9vB1BQQd_QpL",
"outputId": "63d0181d-6f6e-4020-bba3-7f7b5c00a8c3"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--2022-10-11 06:41:42-- https://raw.githubusercontent.com/SotaYoshida/Lecture_DataScience/main/notebooks/pic_for_notebook/u_ta.jpeg\n",
"Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.110.133, 185.199.108.133, 185.199.109.133, ...\n",
"Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.110.133|:443... connected.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 146087 (143K) [image/jpeg]\n",
"Saving to: ‘u_ta.jpeg’\n",
"\n",
"\ru_ta.jpeg 0%[ ] 0 --.-KB/s \ru_ta.jpeg 100%[===================>] 142.66K --.-KB/s in 0.008s \n",
"\n",
"2022-10-11 06:41:43 (17.1 MB/s) - ‘u_ta.jpeg’ saved [146087/146087]\n",
"\n",
"sample_data u_ta.jpeg\n"
]
}
],
"source": [
"import requests\n",
"from PIL import Image\n",
"from IPython.display import display\n",
"\n",
"!wget \"https://raw.githubusercontent.com/SotaYoshida/Lecture_DataScience/main/notebooks/pic_for_notebook/u_ta.jpeg\" -O u_ta.jpeg\n",
"# ls コマンドでファイルを表示\n",
"!ls "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 280
},
"id": "A_fIQBqfL7de",
"outputId": "f8be541c-5c2e-4712-f514-9ea89f42657d"
},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#画像ファイルを読み込み\n",
"img = Image.open('u_ta.jpeg')\n",
"gray_img = img.convert('L')\n",
"gray_img.save('u_ta_mono.jpeg')\n",
"gray_img = gray_img.resize((gray_img.width//3, gray_img.height//3)) #画像をリサイズ\n",
"gray_img "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "6-AHTquvMIVx",
"outputId": "af1d319f-76c4-4282-8631-bbd3164d9b90"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"full rank => 196\n",
"rank 9 Fnorm 3371.396392985502 # of m.e. 4743\n"
]
},
{
"data": {
"image/png": 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KYkp0MGXC6DEld6oagTSOdBuGxAle4jCiWgMELLpWf8jwn2j9kAmpwXLKRBYcR4TllasS5Jiw0z2mophNCygAhrYfNSQymTWNWegyYdsu24TdrgdLnIVJJKkww4auIcGF4yRM00gf4WWrBjVxBehOYjrsGx1/dilgtqpZ8AQh1bIkroShFiIeKelTup7oMRXNYBShMIoCCN0mhhhB16Zp1EK7aRu1sG1MRUS7bQ83kSzGIFElm4NOa13cMI3CSUf4KCRERVWtBJncnRzC2O1H94KLqaqZWRDSNWeCKMgSnFst1oqyU3F/9KpkrRWEC5oTuULbxxAT6BYyYX0bTEMXhPRk1jRIHlXzBhd3yfvNGVrXqJgGJMWgPuWsGBEVyWijk3ROgzL4LDukLFkmTAtSWowiOa7YXFF2RNgJJyLDhxn2MCghCP2WcUWYtX0bVK1V0JNQQ0AYsogh6e6CXF3KdiNx6oKPysDRfLLqf2RP2Mu2iQdlgHsWATkiap5XTKVsI+b/uFqeRTyeYsPP6LEZR4bl8EfTbyWmBNJCaFSt7VpTtaAxChjENoCpFT9KUlJ6SsmTNz2SBZ0OCBLGxidXcy+pYsUaJMkpiTfiM0QjaiSppIvCj8PPPGK8I8N/RVg8JaykOjglItfvNmfN5E5xWjBT0aYJGUAao0e3x9tA7N361t3p0mMahv3+8fHx7mZyIOn+dyHg0/04Re2/6ruu7bq2bYN4SnEiIFGaaQqsUQmIAmJNytkG7mo6g1MzCxZ4oFpHJ9j94YTSzP1pHF0sblREsLGYJphMSUWUyD6uiHXtSDW+u4ZuznbbJqiAcZoeHm/vbu/u7u8fbp2M97e3//sUHv9x2Idts/3r1tSsCSFYCG23vdi0m/7q8utN5PtUUX0Cpg3T5BqEcdSmAEuomVwresr/ydfLdmoEMxtnKU5JwpjRLpFsAKxCr9lr0VahxlFD2Ox2TQP3NA3X+/ub24eHh8fH/WF/iD4epuFuaOIUztut+bXVmD00tP3u1a472758pW9UNafJSYVroDlilqGtjAARJYGgLt+8Usca+ok/lkWOBQ8AVQgiAgihVcsBEcliQsV6iw6TCNHgw32M4zj+x8fHm+vrm/uH/WEcxk/3orKPFtzksoVL3E85mCHQ0LZdvz9s2t3mw8cwhA5SgnBz7nBwJgAZomUBFGrMvYIYz6LCJ0gw5jCfwVOJfAcJZl2jkaplF2Yh01h0ignhOh0Ojw8PDw/39w8fP93c74cY3TFOwUI77g20y/MujdPdEFNMTkLC2A77+9sm9F13Od1tz1+EapZk1oCaTiAkDS7uyd1TTUw9GvHMR58ljKC4iHpKmMbDkPLiB+36VlzUREUsJ15KckV0auMpDuPDzfXNzd3d/f3h8fFwmCIdQCKJBoetijbtJR9HefDCU6IGTMMN1MK0ubt78brrRc2MsKqZTJEcSp/M3T158iNbsV6CYgt+lrCMmjtT5LQfR3eSoqIWgrpm80a16AUPIjH5sH94OOxvrj9+url7eNzHGKeYnBQK3Wnd8NjAPR5GjVECmZ8ppozTsI8UuWvOXoz4q2JUFBhRKDShi5pBNJsPWHbXEWUidrzHTkyqmqNq4CCahCAMnlIaICqmWSSqCMTjIXmKCOPj7acP3//w7sP13cNh0s2mazdt24Ygj4Nqq7fjuabm6zd//XKg/JjECaaU4ri/v7/V/Til/ePfPL5C24uYqpnVsJcFFRVp4zC7mNm4XIWacgqInq7Y7pSw7EUbcPHzo9CT88DNBglsTIOaipioAjo8SpqmwbqbH9//9M+/+8O7j/f7kbp91Ww3GWK066HpXv15bP7bzV6/ab5u3u3l9wxqjak2DQ+ffv7nf/fu/vZuc/OHf//p5n9pIWpiZoCTTKLqh0l2BoSM3aaUUsxINDAnJUFEQnskCJ8IDycEahA07a4bPTnZvHhx1YEh5PlyeALJ/b6d9vv99Ok//d37Dx8/3A1TbLdNv7natBZCs9ldXPyPb87Ovvrz9qYLt590urX9/dlrJ6Giodu08vqbb199eLi7/Z/f/+tLGe8bFqbS7BIbYJZEKUGyr5lzDdxZHe1CmSP5ESlPwkgkHJ4mery7yvBX6Dd9YzlPzZltJdJ5/z4N+/1+uP7d727uHkbpJXSbvz67uLy8PNv1/abfbL560bYvvnrd3fLhhtP2xUV/Hgu7i5i4anPBzWb7YujOtru+JZcAv6iqhi4KVQU5+y47U5IN0RVhMpeUzISd0pV1OVOK6WOjo9M9dFAyAxgFaHR3+u0/3Nw9PO7T+OH9ftTtWdttdxeXly+/fX111gUVAFudYthvdYqR491gzQQ1s6YxFVFEjW23AWT6sNPpfLMrbmS2/k1UnSlFSpPSjAwQkuNmnLMHCm38AmEzge4+qipcRNq+7wwUoWfNlhft/vff/3z3sA/duPem7TZnZ+cXL64ur766OuuMMcUYRdzTJM3vI4IMnCyOriE0XWNmwbTpd1ftMB0umpCG2LSeESlRUTFTEWlHZXJNU8XeUBGr1ZI9xUufszyADIwLQ0giIqHbdI3V+EZJyqH74ed/+v7mcb/9qt+FbndxfnlxeX51eX7+YtcbpnFAEjOnjxExouk8mtn+oGZNl2O5khg2tk3T1aZBnHENwLWWlaiJj9QYK+ItWIqaMBNV8sq+QFgGuAWi0KC5jKENVr3PjAcZDRA+XH+82Q9X7at+s724vLg4P9+d7zbbs76RZCAjTcG4v9z/Poa+DbFt5G5UNWcysyaoxyhBm2bbiINxStXOzdiigE7GlMxjRb9nx+oo+vIEGzgFTKtDoKYpWEYZLdicS6dwQDSk5N6KO0X6t3/54mx3drbbbjZd37ZdYyopm6qMcYK+vx4Y2m3jojkJOjtukfA4RBISJLn6cPBSiZGDmhkS8TSk7MQV86GkM60DSfJkyZ7GoAWSC6liaznN2Eyzus8mgZY0KN/1bbfZjH/+27/9+rzv+6YJwVQZJ5lkitGTe/IhjuPdYTQPbdCU0LQWQmhCxhZLZJRNs4dg2BMQZEgkpxGSyeMUc7pHWTBky+cY9zh1oU/jY7NfqorWsrJWYdLMpTlTRkF64ub84rEdpzfffPfNWduEjG+5uzJJybVMSNGTDiZqgMWYkIH7YKIgKjrb9JGNTSMhKp7TFnNmkyenLwnJJUtiRttWa3Z8nYA5KyxBNEiOgwk8Kz/JodYcyxHY5uyimabL3aZvm2CQjE8zCsVTSl7NOncDPDrilDwbZVLR9sxW3dbZ9HQKXHQOQEByIVJN8EBhxYWwFVEnEPfJgi1IgqamyXhXTkRBqdBM7sxQb6r1X1nBqQqUpNAhnl0ThREJU0rSU+BirZvmUCxAijVKkC/fbmJzEbRUGTBnCWeH1kyzbyxzpRqWDL/PLdkzYE7+qeIXZzFAgH4bGEsYzj3mLHx3Du1mF5LvAjxZUgmmOcsgIht1MBHj9DAdonX7i02nZucqCiSqgoS0fWMi+O/Orgd9uQs14kBHTigTsbafqq6aIxDr0FF+g/DjPXYsFZnT2ymqMgqyy3y2DSmllLNWPLnTskPL+9uJOIQXr7aBUBMwJSdNcr3VNF3vH8frHz7tYZuv/9VXLy92nezFRNTMEKcIsUZU5Oqrjt3FpVStm8U3IapAfNSUU62L9Fuc3WzZC0TgJ4SdoFRukGIw3vs4mahKt5WRLjlFoXybJBQPNxGyTU0bNCYo6B5dGzMKk0+Pj58+3Ox/+Pvvb6jb7/72t7/57tUre9Quozlwn5IbGhF16/uzs/PZNQEy0qKqYikk5JrIZTvNUQtRKcktfkRKSMesKYCKOJ0+pkMMaiox5upD94qYGEUU7fn53QTtA/YJyXMmqZhtN5oG9/Hx9vbdTzePf/j9+xtiMw7f/8Nv3r65HNtt226kMQUkes5ZkdD3XSM5vVqKFGOJW1mIgjRvKRZgt8yAC3N1YopHKFU8IYw0FYKJkganJpP9PpCA5hBYwTDdZXPx8mGknvUWHaSG7G+EbevTcPfp5tPHm5/e3Q0/fowB2kzff/jd37949c3l7ny7Ob9w7fumT8k1a0+ZHmUsRs88QIJgcjgareSWoESWMTUNFUKfjtbo1G3JZUdKqDdDxuAxTSpiSlEVoTtF6U6E0IXoUEmjCHISgSkU0+Hu08f3H64/3Hx8/5huDs0O1rTp4f7+/U8f356d73aXV1fDRa9mTCmzkU+DJFsFUmolJd2RckdHlsSBOZetbEeUKMARYU8MY0JUBYn9EIrxw5zpmVyEjlxFTIIalC6cDpNqCBqa1kyc+8PNh5/f/fT++tP9w90o+2mzoQQzvxsf7/afttvt9vLFyzevLrddG4TFRTlMSbXWTxedqaW+KyGXgRIs0u9IyhfE7liPPcF7pGxNdH02PWiqShGIQ+pdCVDa3Y5JNoEOFWuaJpiS482n9z/+9OO7D7d3g48IZu02Qg14GD3J0LVdf3716tOnV5dnZ31IGlSbDUAjMwIkmOHPHA5zb1e8yVotnVmseGV/lLAc6VCiO+sMABhkDra5e/L8kwgvfoOHpJevekoIOZ00xvHhDz/9+MNP797fPh7Yadg0cbM7AEDTTD4e0qNZ2Jx/+Pjh9curq/NeQhNCc2ltt3XWUgmKiEKYCFKspPVlg0S5NpCW5Tim4yQGnbH7vGxNIw0AwNIeVJXJQabkquIksPmbr64HWvN6e3DTRpKPHof97T/+8w8/fPh4t4/eWLfZOfqejOPYx8kRNLnD+vc///jyxdWrq7Oubdvm4tVufJR7VuipVEl4cohot5k6mQljsekqXRVN+GIYqRifLipAa4EA0XfiVMvrRdIpToKh2cSeZg0CzEIQpml4uP/wT7/7/t2n+8G12X59ebbjj5M+xihnby4G0obxMI5J2s3u/OrFm9cvr7Z933U7aXqPEcUXEaioKJNDFUCKM2GY8wbWxn0top7JOV0xASRn0hmaLiSQ2G45uRk1pZhyHoaThE+jE0CyNgQRidNhf3/z6ad//w8/Xx+SdbuLV3/1zdkW//DD/Y3o9i/+6w7iN//h5ub29m64hzS7yzdfffXt+Xa7gU+teEpALd5VVSuvmBAP2d8quSzFtNJZn1Xr87MrliMdiXTjflOs+76PCaopl2bn9BkSVErXisLQBKRp2j/c3X/6eP3zf/z+bpD2/PLly6/+5pttFx9//Phu5Mvu699edvpz9/P1hw8fb7vDwySbq3c/319utttxPLw987IoAASeQzwCUWprqe6xauOraK4u0mp/pS/Db9loUlW736B1EWqK45SNxOQOzbFSgm1gp9CYPEg8PNzdfvp0+/HjzfX7vWz7i1evX71689s3nR0u5e5h5OYQz785a67evfz04f37jzdvPt0O9+/PBzlv+/7w+NC2XhLii7grdYCikP4wnUAB86U1vHyKeZwYwSI5Cweid+3Yiwh0jzhWzRyMlVtggo0B0xiRxofr9x8/fPj08dP949h1u8tXb1+/enH19bl62sohOTgdwuV5f/eb8/vXbz98/PD+3Zvb/XS3Cxtrmuvvv5PJshUv0JxmpFAi0Yl+4yAgLgX2XxysuZHEKSueIMFSMhkIPDRTEhXRvaYYXDzH3IBazYPkonCI+Phw+/7Hdz//fHN9t09yfvXy9duvXr843122aULAIVH8cJtCt3v5b1/s724/XX9498Plb673k78cqfbw8f511/V5y6iKKnIcMBPWdHsQhLL0o6nWBoC5PoRfZEUqmUsZeHigmKjYYPSMG3nOWGIJADAR9BjHuL95/+Mffvr5w+3tfgqXr99+9farty8vNm3rUxwcE0Ti3buPD49XzevztH+8v7l+9/rqxbtv7/0McRrdN5/uYqeZuSrEXZtdaNM1XpVzdWwqZ+bwKHKywucJy1uM7smng2hQFduLiKWSdKwilTCCSTwOw/7h7uP7P3z/7uP1wz6if/H1t9+8ffvqYtsgDfvDo7cdXMLjzz/8FN+/6DuJ0/B48+bNqzc/vLve2zRMcXx4uL/n65DdEMupnqAozAFtutbn1L6aTyt1zbLtWOVKJQynhOXsUQolThGi6oNZcHWvHFCi9+JMB/PpcX/34dOHn3/46ePt/ZCk2b366uuvX7083zQS9w+Ph4e0uRycHD7887eHx08MoaePl1cvrl69/fH97bTfD8OjGacY2qy/MmEQF5UEgVjbphkBLrkhdY8hB114skLPpKdDRJUOKcXk8KRZ0gsoLvASH0AcRonx5vr9H64/Xn+4fjhM2rSbV1999ebl1a5vtMQt+zfffErTfrj+wx/SeH6hEBMfQ7B2e/7y9vC4Pxxu7asX277vsCioDEipC4SB3VQ2Uk4c9lnul9VgBaIqfU+zBgRQEK6h6VsVVQkWsjtEpoz0OUBCsSdi/PjD9/9wfftwf2DTtf3u7NW3b16cbVoFidBrg/arb+MgDwN++CGkr3pwEGWUZnvB5uxxOhyG4aF9/ZdvbdNw3jI1S8gApVjjdafkKPuc/FpBj5p4X+l5tomCoFFBu71sqKrYdU0LF9CTJ08ppUTPsip6Su9//7u/u9lH2qbfnl9cXFy9eXnemUcouNnFtL2bvv1xwnAfv/9hh4crnwiB+8T2vHtJ8ymO2F283o0mdczItodQTMSiQ2e0NzduceU6hxbgiXg/RYLrUpIOBHNVhaqZA+L0lGKKGeQlm/g4puifPnz4cD9J02zPLi5fXF1eXl3u+q5RU6INKXk8vwgq8Pj4MBz2B8tNBnwaJmqrPZJHnp1ftuqAF18Pczev3LxHUOv9Sg+YUzcFs0p7lrC6ngVF1JrlqLkUUL3inCSZhsMQY9oPY6I2/dnFxeXVy6vL88uzTdcYsvgkzbpNN6SuCUxx2u9LWyjGMSaKBTGGqMrEo9DCDLJVMGDug5G90COyimb/PGEnRJa5qXbLYskAADwNhyn66Np00u4uXl5eXb28vDg723aNycoWsLZpvG8M0zg87K3s5DglF9WgFB+DIdc+1eDDLHtBr31S5gIJ5gy9E6vp6NXnCRNd5wHyaBpznaykbFc2m/NONmcXLy6vLq8uznfbvjGtTE+QsNCwC4o4DvvBSk1znBIFlkWECumEM+XTJgQuXmqemXIbjqM5z5hzJelp4dWzgT/SY5ycXvueMOea16qMCrlrbzH50HdnqT27vLq6uLi4ONv0oXi+JNWQGgNSTHRhnIbrc811VnEcEkK7fdVpo2mzEUikF5mXE6YIdystlsTnTQYI1KvrNgORXySslpeM9w9jc/DfOADepbZN1tiUIdhcim0g+z/TFP3nn79vw4vvvn15udttdq1hHA4RzsSJhw2TqNjDR9z8ICHdSfw27Q/Dfv9wdzcwtGcvfnvZX2795X//5/lAkBytgqpaaHyMRNIgamlKTGTp4JAL6PI6zmmPx4SdZuYUyCvFJIkvDAAseGQj6i5NUFI8gSKIslV3bv6H3zJcvH3RBRGROFLVSHocHw7vpmlMw4d//IdP7f0thzc/yB4SYxynOE0Pk3/f7L4+7y638QLDdnthogoVy+FBAxiTJElBUi6oI6nuRanWP9UeObbuTzJzsthzTZxketz3ILIOaVsb3UyDaIaXVWKckgP2r34bdHPeMY7TlKaRGx8Pw2F/f39z/bsfD6On+3S/771jd/GAO+QM6V6/GlOcXHePE4dx/+FW+vOmpv4UHCOm5HTA4c6S4AGxnF9bA+0FYpTjffZs0Y4iaJtwOGxakgwmql2n5qaiIibFGg44kLAtSIwxDcMwjMN+GB7ubu8fHh/3j/ufb6gBU9+K8VW40nF6uK/aSUOzUdXQNJu+PeslppX/mOWLmiYSPkVjytV0TsQF4lh213HE7Pm2FwKVXjE1oQsk2XeQ0LcSWPIVSwJT1+oYXcSncfLHYX9/f//4+HD/+On27u5wiJGOAU3bjvt7jdT+xc6m6fwuxlwNaVAVUXga0fSmjU5Y0vpYIijuANJgko0Cz3U8K2ARs1l1vMeOX5JF2IjRFXlXlp5RJXIlBfuCNJdtSo7p/vHT/X5/e/vp9u7xYf843D8eDjEBphZdVM0H9cnPdxe76Ff9FKfSfjGoCOMke9vuRjSaS9VXcy+mgGjwmI2FJCg1LpWwbCcuoNXnCJsXTcRneeMRRk/wnGklUT3zYrtNacPbT//0u4/397e39w+P4zRNfhinMTmUQR1iTTNamtLj3UsV4cU0pZgoYqFpTBgP0YFmd3a26/u2qElUq8qCUdtG3EselSatKbQ5wjrTddqG8CSMxNJkJCBdh00Of/fQ0Ku7gCKOXMlIyIYf99H5h8fpp3/+8fufbg9jEg2hay/EU3JoCPvY73zaei+v3uPRzrrd/3TWtNZstmeXl9sGPt7/eHu43198ffl6l0KJCHvBoyiixqZlckcpxUildn5dbFXgnONoy2kH5Fws0zSaNu0mUiAIDF0n0QUOd8/1jE6EwzRN0e9+/k//9vc//PjxQIS2s26T+/0yNP227c4uxPUm4ue/id/Zy832z15ZsNBtz19eXfSNpv2PN/u7+/O31tiBnnG96stCrUSJFCyha4+mmlLJK678+MR4fIoEM3lSS1ES2YZBIHDtz3tJFEmee2rlMHSUF2ka4+O//3f/zx8+3H5g0zb92dmun0QRrOl3Fy//5jcvLlu1v//76d2/+6cpbnaNvVV3YmB8uP6nvtV0I9q0wjSmBzN6KezWXNFlkiIsBDLl0A/psY0ppZxDy1ns55z9hR1PCKuAx0ifYtuGSUTERBuH56PEUu4aQYfHIaqFCfc3D4dkvfb97u3V1dXl+dm269vQtl3/zYtNJw1+br2zmxu7Omuab7qcsGcqMuzT+Lg/7B8ffNMCkNwwIvdRqv2ERGwn4ygVIgtNyiFxHivp2Td5nhWz1OM0DRqnTcriUJoIB4QEvUTZwWm/lzg97B8PkeHc+rP/6vLq9euXL7++2LSNOkl2cT/p+e7ly0d5wU9jO/S/+2/OQmM5iUc4TUnU2jQe2uS+CVgVDeTUJCPEcve8gt7kph+xtKigP2d3PE+YAK4ijevSoMdzWJSlOBQAkA4t4xQn6a8kddvzy8sXV69fX12+3ASRNE4xpoxS9D+97Lu3F/1w1z5+/34Ibds2obEmKK3dtVMaD925H7TI8YxflPp5AilxKcAUmKi6asrNWuh0uvgTwk6w+7IbxQM6V8stLC0oah4CVGvbO0Nkomx/M109ot/tzs7Ozi7Od5uzQPcJYII4kPzjJ222L1+8ZEN/eAyNpxTDlMugIUHZ9tYMjr3OskBFXJRZDBNJYg1PCwARg+TKM589ghNb8WTBaqDUxDovCRUMRuSmvhm/UssbtQsMzmDf/O3Ipm2atmnatmkarQ2LGaPIAfcPI8P55cuApslNuIKZCmM2IhxsOB4mP+SwbekSmkOoIkgTU/AlLUdAQMUzZkChqAuOpf1nOjuXZgYzMuRei4FWCSZ5cZUamhZsmhAsVx3WmAKdTpGUO043TTCvbR9WOOCMg+aNKzWMJ0cITAZAssXz1Ap8xi58kiSG9XeLRqkBt+KFlvyZ2biiz9mEBQ3kjFa4KAW55xYqWFK8/urdz95x1bVLHkcdj5QO7U9MwjrwuisXwo7eL9vo5HVZf0FdJqk/5+fOb5bHzHORnXp3n/N4CynLI6pjX3I2ym5GMUxnaqSSWL+ybtknT7MGPjMFWEjIasehzOC3L1Yq50Ad6ySsBoESnqF7dMQY07ysq8eIkCqgHpdJVZIENaHvaGSFO3jalfDLhAnnqatJBArkkjgloKXytlQrIadLZN4D6SUFtcopT9PkmHKz+CNu4tL4kKIupSdJZUeUhuZH/ftORpopO/XGns8wlZkrypJp6flamfKE90S0VLuU4a4kr0BAT5FMzpLkMJM1A+6re8+MLovuOQ6bF3rA2onlT1uxetsFSVRoVjhzc7sZJveyYqJcpGHRLGXUIqCn5HCIzv0TamecLCe4rPg8H6hLJ6WF3pqyNSHziv3RrrPLPwsEUDVpYaQSywbA5CBcNLgXCzUpEDUzYqZT4mG6uSNuH0cPGppSqyUAc5VLDjRLYNKlXVg112tZWNEEZYjFRJzRTj4Vl0/T+hQlF/axt9x+drdVZVrlKpY/kh4nEUnhwsZsGCRPk1pqSsaWxzTG9O7d3fe3rh/+r8f2xe7sRdd2bWiCKadhdNjWCJw1aSfjFCUbv4X5SRELyj1TSgsyXSGcImUlNxKmH6f1nQQptMwzwLEFIaLWb8AoAOkCgQN0EIA/jCrqFxsZxxQddEDErKQre5qmh2H6539897sb2t3veHWh/ZlZCCGEID7GMbJpCIj1qW0PH3MWXXWjCUItBB6EKc2bvM5r1fI58kXBcaj2dAnzumXxPZsZdE+OcgACc6tFQD1FVTrMzKiZOWTdJZZxOEz7/eN+pMXcGa7R4rQoTGWGrgm1g6msrjLksnfmDbRg3TMzlpDEl/SYVL1RWX0lw+o9ydIhfE4YY1bCWRyKpLTkoQDFMhGqtW3btbkWJ/MFF6OjrNJsDsxTjPLRVTvPNWWfu55valcnkSKiYuYodlK9bbaJUoyWezMXlDOnJExWOlCrNa1LY0iRdO3e7M7Odm3IsiijF6WpPjK6Mg/9iKtAwn02s/Lgln+eGlOfIYx0ILdcZu5Zr6FJUTQrjdLVP9eexGyETBPFIJGeHO4cYKZiatbu+v14//NP/pBClO7y9VdfXbXGGA/wuL+9fYy6edOL2XkQa5oS6kPRMnkXZRXtPtt382JibcWcauinSDBJJk/uo0swM7PQwHPtB0k4HbnwOziaoDYeYAJtg/uUQPrjFJq2bYI4m7g/2OPHfhoDmhff/Pm/evumxRTHYTjcf3r/6YHh8i/OQtv22GgT/o0vo5TcRSN3TteUnZIjw3XRdqUa52iTnWa/qVb9A7VguToNAojm3Ba6s8RTI3MLlf2+NWsUIgZXjeMYWodJI3am48Eebz487IP+5i/+8i9/+/Ki8Tg+Pjw8fPr486cDen8tDXE4hJRqMgJy0ZBnDL8kKVQOzOd0oHiki0FSTm9fCOtOVkzopNIc1msQAf1+jNNEYczdAx3z0UISTMTSKBJCo2BK0zQNhwnhsJn6rm3dXN5O+uZvDyGEb7796lU3xOHw+HB7f3dzfT8hNIFO4kE9/Dh9P/MXgaQUMLmrR0lLerNn0hbRW1w6aeQLKyZCV1KpkE2fMwbxsE8pQplYCEP1HbadQnQfoRZaA1MUcBweojT9drPdbG1CuET4s78aLYRXF13r47C/f7i/vbu/eZyk7Xe7xkKwOOw/3fuY+xuyMiPg0Al0xBpTAXPn4NlClFlby5fKhcvpFaJBjbugCSBa9Rhyz8CYUi4BAEENTRAIggp9giBN02G/v/27DweG/uzi8vLln3dN0J+FKSXsXpxZiM3h/ubTzfXt/d3jKJ0htH3X9VfnfSMxRhCeAxKiorkBkDBNgy7dtFWOlJFUePEE8zjVBCQFEiwE3zScSCKYi4q6e6xSq8qrrF7EPU1uTNO4f3j4+Pvv70frzi9fvv56ux16daiooz/vHSneXX+8vv5w+7AfvA3abTebvu/Pr4xMKaEcwpPRFQrgUE/DvlkczmqDoGo81oGvpcdTwgCohaZpvG1SymEINVHJYWjXzN35eyk33MiNoJlSStO4v/7pes9md/XqZrjapfv+XdJGptBtZJgO9x8/fvh4/fHuMHrQbndxcX7W991uh2HKrWCzoeRazKVc3zvAjq3/msJQ5cosXr6wYhDR0LQNzagU0kXEVEsfy0QIHEIHU4wu5p5ECBVVM1MM99c3k/QXH2+Hq25/tbuL7SaNTR/2tw/3P37/4cP19afHyBC63eXLl+e7vm/7xuM+Vj8Li2DPftA4NnMefrWgBDlrtryeXY7PEyZQMzMTRk9M7sksO5+sFmpWB+JxHJI2ykgEpWhg241tg7h/nGxzcbvfxDevXjw2l1seLMRP319f//j319c3d3cT2mZz+ertm1e7Td+2HPl4AzHUAFH22yUDhz7Fuig5ua/afgsnypPuEMdui2TTRsAk7WGSyVPyKI2ZBTg8JYeUvHuiaUZ3NmaTg0pRM1Mbv72Jsb/f7384u9v//u3rN+HPdlsJ06f7//Affnx//fHx/jAk7bevvvvuu+/eXiC0QQ9Rbz80G1s8b4GoojQ5dTSNAizdFlH2+MxjuXnBsVTcHy+YwAwa4aNiGHKfPrHEpFESAUJhljeAhXF/oNrl5UMUQcrdvmz7Xex377652cfbrvs3l1eb9N1fnem4f0x///tP+66no9nuLl9/8+03b99cdZPSY9c2F27FmsLMUwREwaSNqZa2uSSrVqg5swBcJE1HhJ2UWUFF3SMIOXgSAyCbVkhRODMaktMdIMabjwNseHHuExMTAcYpcvtyTKH96uGQJHr3GG8v/v1G4jSFdw9RX/VBLfRnV2/evj5vJafas+maqxb7CibUreRqFEn7ACQWIzt3UV1tp4q/ePpj/lj22pFizGmQkwgIReQMLGRjxmNMQKKUIjYRqLWbl1DrN9vbx1cX7cH7KRFBFeMwJRfbtW3T7i5evHnz+vL8rLcJCkyHNIwmM4RXNGWV8KUnNEqW0aoT0DKYY7jnKXaf75ucHONkjUCQUsbJElVLHkJGQ2pZpKoSdIqAYv3Ltt9eXF7d3D3utZUmPcTJAY7jRAnfvdhsus3Z5YvXr67O+i4QdPjoMZK1ZY3M6GqG/yRYyBIrA3izGbKQJzgtPj31ZERyTWvikGISKbVwJCWxtkFjaSMpBrEQQuOoJ00ATX9+cfn67ceb29u7oEnCI8Zo8HFPCRev/ux8u92eX1y+uNy1mkusSTjFlFykPIpxJSIiLQIK2g7NCRFVhszXacrRKWGq2SdLaVCnK1VM4Mkd7mamWfALRaG2oWloQuNMrA2IbBu25y/f3t7d3d7028E/XITxYDIOqX+9vfrrf31+ttnuznZnG2Vu7U1Hq9IF3i3+P0v9LqEq2uXU2EyP+rwHj+g6ybs/JizHQ50ulLjbpFbN9LIdx3zgD7S4ZApAbLoflJr2A1UlJ9Y6abFX2XQXcTzs/+L9fvzhd+9uDzB5cf7Vd6/e/OXbvgsWQtB42O+j28Ygst1ytx1vpuqM5NVxQsXMqT6V865mvbXaWfkL6ZgV5X87ZUSpP8cmxMwI5kvIF06IKQjw8EiI2PnGUNjV3elT9o7MVD059zd3o4iY7Hbbru0DkDy5e4zRVduNCaTBKMEPvnj7KEaQKNKQ2wAsUO2asHnFTop2Tt2WBYHdeALokBEgWB/qc1s5xwYAgwzlIN2ynrlPfo5ZS6PduXS9gAeQKT32qEUmIZRWTcBhmiJ1Zh+Zd1GpgZgd5LqiK+OwWPeQI1Ke5lLN7ltFSDPyOjeDIqnkkosBoCQ/gSXcVx0qwN3Fo8eowCiKxQDP2Mnc7FjETqJfxetaXtSgYMVx1mocfCI8TgmT6oIL8uFHRcrOhBWuyJOUZ5CLG1gDgPNeqf5Exq2I0omkDEnoXkzP0/zXOdJY53c2kcv9Z6n4pxFWyMv3Lg553j2ohIkriVKRWh0HrghjrYxdwYMCzBZTdetZD40tcOdRXcdiDq5icKsgIZaPFsPqi25LhXBFBOL55B6Wevx8S6doYt3c8wTIHD3O5y2XhEoXSUepCvPhPyw5OC4LVFMWY57PbAvwdNBH/sks+b/sQR+9dOaeMmlVTVIPhs4TnBvXLft6rpYvTrbn+iwt4CAIcSnH6awfVV0h1FEWgY+ctrWGgXHMsgtdX16xYzbPj8rjqCtGAl75Ije4W01WAbursUfP+YEiYGmWv3rGkqOiK6+8AlXZ9ypiZtlgdblWcuVZwo7pWr8py3lcOdMzCzsHkBuN5pAPdPbP6zQXh1Zy6CvbTGu/ft79hGdW5OwLz0mxWQxJmd68dnWP1eetZccxXc9IRWCeFV89gnWGq7idgb71qIv3W3kLddJXL12WpALMm57JgdOxACv9UIX9At/MC/EnrFg9KKNK/fo9qdsHxbPI3uBM7nr3Z7k+G+fLyFjFA2Q5raRwO1NxSVbFpItwLAss858VWZyfe0TJacOt+pLZtJj3WOYHmeVvhfNmcuZ5K1phhkYKKbM1UfHBKn9dAOaz5AUnW6d8JHNHRX/XMnEWHX+cFZfv6DJnJ1fNVSg3XKI4RcnMGqym7WYrIwk8S/lsoDiKd4XcFGrBqPJsLfPH1QZcZaock/WnErZSHwTqETBS+TFvaxeppkC90Up3rmY22xgkmbQYXjlFNLdmYko8afTL5e+1Wj5KyTmS9X8iYaVRwoou4MhPwFxkt9pGeRMscbjylicXTz5HHEiiSiSUD5S2YmuRuUxwHdPpIP+lhGVS1qy4UoqzgMkV7jXDYwkVF/kAQVFQ9CSSUpJ6Gvj8dcqsUYp9VbJwWKUGUJGO58dZefFPEPeVB2T+e+aEtYBb++/HlM9rUi0u0EU8pRyMJVhSkpz5dCAs7mJmt9O9vU7xWLbh0R47+jye6w6xcuXyobH5TGrMltQcMD1C01lr8LIrSlKokt0bpiiSkhdXIDukXg4WhkjJwqhHxq5FkQCsBZTFZVgeWsT/nH30Rwib6eKyedb/wonjVGZ0JTMcQlclJZUz0gTlhFuUMwlyBplIzbxREPns3ZMB1byx+S85eXtOFDuplHg6wvqv1couHoMcfYzVGTvSQMXJyCNfBUUWZq6yQ2YNVfId8j2XSr7ylPmZa0asbz3RzZmwpwp6rds522Xl60fPLGZV3R+LBVe2vovPBlRmzkUeZptqdj+5lhBrDp8nsPwlWKa3/v2cIvvcka5FKlYWmymrjMVlx8vsxGUycx7VvDbiTnfJKAByqtYq2yaLs4LWHJPF1Y8lT/hoNVeDO7k+m2HKFeMdm9WoAnieZF8NZ142shw0oyiHmhe57KyH4c2GRzHU5sGe7uFlUMfK7GjST8T95whbX7KoSEghaiUu8tCW4GKVnkXQLFtvlpuZEx2z5MtSdqapKsoTmp5S9vnrs5ZHPpVmSRY71oA8UVuYhVceUd3/+ZvMnQoWymYQYzXmz1yfG9/81p++x5ahczHh66IXk+BYcK2YFHXYDqAcmMwqGkQA5O2Wqy2rCC3e/5NhV8tj9hBXmXXrUf1xVuTz7C3HLDBrk+VeRzLYQdHcdqG4/5W+IumrI7To3Sx25GiFlj3HRTx/ViqeXE9OjOMyzmVB5tlaa8ziZh6hGJXTqkeaTxNaT0aGKCuVlZK8fPqZeSXryBbHbCGNzxL3GVZkzVKp9GJesSOhxPLRMt0rHzCv8aKcq1mmM3NmSZTJy1ARn53XOvy6YmXJVsrguUX7LGC6cvqq+lq9e6prFpm4PDFvJBF6OX0WOetWClUsGxmgnERfj+aYdZowq+ljFbdM8Zqwk7us2fcYgTzds8sMACsxSaB0S+YC5HqCpMR8WGD1n50Q6gy9zYvwZDWK9KjDm/n1ZI99ccVWvCRruk4nk+slI2e7v2xuYl6N2TMrwt8d5WwZR66+yEe7Vrx7qR7gajFmyXu0xdab7E/cY8sNK8H1lfA4V/gIgij7KOur2lSJZM4hztvuCCAhPIlAUlrDJKfDWBbsP3vF1tdiSEshTVYv6p2rJF7GNatfVvPYkSCpHoeJ4o/lNDsU9jw26Ncjx0qMyWdX7HghntljC10r6AxLCckqH6LeT9bGchF6WodTCzhYb7eIe1LgFcCcUy2qizWzIheFkeVYffy/bI+taDzasrMzJatPzbDqgjiCdCeY5QIpdYLccxwm5Ygm8ylHKklEkKJKbvS2bN85qXstAo+h4M8v2Jex+1We9JrijAysUkkclRXriqHYVABKWtqM4rh4BQYgtSQwOVVq34cVsPE5FOeIrOfo+qJ1Xz/KI8q4QB759cqGnTmxBC0JiJbeajnDsqxYkYp5ggSSgZ7CDSvnYGH/GeCZ/eBjuk6vz0MDQFUucgTb1J70wJIgOOdrzU4/kE/MpHpJw06JGQaR2R0TaPbJkGJYl0nN2mMuEFtN3tqgXOg6Je2z57bMxC30zpV3p8n7mbQs2cHc75aiDvV84jEWwUnPhC2ooohgishR/5rou9IhM7V1Fo/Nnufpeu7M9flrK8gmR1cEOFoxIG+oEnks2yvX/Ypk8D+HPFk8EzgrK+ZzInJHVIlRRF1WZK1Y/xSAWiy9P50VV9/GDMTOVOR5k5lT5hng+v3qDmfBLpQsRzwRQmeUgg0QkNyRWBGjMYP3S5qK5BHMdB2byGvp9ZyQeaYkv5I1QzTHI1/hKpUqrwFJVuugfJ3uko/1oBQH2hPmYkfJuW1QTDEQUD1iRMnHU0ippDkKR2C1Yidjf5awORDEMvj54B2ppscxVxSLFlkHySykM9go0UU0V727wwFPE+YVkwyYiktMRD59ceaHMlOunIMwT7zsWZ0faddM2Mnn1oYfIKWy88iGOsI7CNDT7OEWC5BFJSG5COnqDo9CCD2VkHbOe88n3oAQMzVdS3sA4qIuyL0BniFrRdnp9bTf/TzkvDycE2kW9LDqFEFuX0BfZo3ihXcpgLuIJCIm+CRG8VTy9dw9980NCuaWR0HzSTSY/855kajh92zWrY3oShnWYNIzK7YyZ1C5Iuev5uBC0VQlu6boVyLr2jyqXGXG0hffU05dmhLSqNpoJax0ySvZZWLSNjmL9Iilil1YrZpFPj5vkcxWJJ7p7LwWcOWOuUZNimzw+WPMzSqZ+6bOBQBe+gxDIJGiTtcpIk6qVE/KfFSKU9SsdJJprOu0kTJk1uezBuhPqHmezY6kyXO2IosynQkTqeG9/HZtTZk3QKInINcwQ+BCT1ORDWQ+tywlTqMhBXfzFD05HZJP5TQNpqFrczVRDQuuDG0BqKxRlZmuEwnJL7HiLI6gQLJy8HwjVQMXEVgND0k5exgCeCxJUUz7MTpzLqZTFXHgYyStbzctfEpxijG5O1VE1IKahbbrTYNUfVsVl4jQSEHiKh5b/1q242I8foawBYmqJlBVuGv7uezaEkLKRvrcRYFpiskBJZib3sYpjZHeei5QF0ByxxsxC7lE34Lm2sI6irowM9Z4LInnf3xW9j2zYllmaE42L8awo+qsxenLlBE05vTTigPEmAoqJYlUutPgGkITVNRoLFa/aAhW885deUJBVi75zie/nUf7GSTyM52dM32rk0S53G3OJ1rsOkut1+pNd/cp5goYAMnFOE0QhbRt15qIKNWI3FenduYjU1KcJvjVyaqtgxdu5ELVZ5btc7aiIJdbZ1oUBOZe85XmqkjMKorhyVMi3HMWGcRU1RUQUbWmCSpQ1pMICNVCXTDBqodxteOLivHc6o2F4JlnVobQUQrjM4TVIAkIJORyyEpBZcM5L5SlUsIhsIB8VKOn1E9OiJqaukOSMkVAPE6hEQ/ZkEq1DWuT1010bj60GkmJVeSBCBdSZnqWzx9T9mzXWRTHqqi8Jf9iuUd+bP7hLsJcaWDuIUnj+bALVXcgKqYh5TgSICG3UMxHY0kK2YLPm2wN83KxqiGaT/jBbHCdcN9Tc+tZVqyh4mKtlBMGF7JnVCBvipTzurPZIcht3dRMc3PqJJw0CVMwM6GWtmC5yrXciMkjvNpLhT6ZEcqyXIUHjwl71gb5XAy6Srj8ypV1qRdTTQBKtUnW85GfrZqNWgLqSZiEo5lmH6Qe85dpoos4YiwpR3UFUBymk97H9eFPhswTVjx+KZi3KDB7mqzxzJq+MBt1AkJyyxmpw8yWvapaLi5Un9xVnU0TAsQyQqfFHsuiHh4jTBeBhDyLRYHMENd6Hmea6o9jBS1PP7XIU6zpW2ifI0NaFEM+s4MrbildVhWAe0MkJZomGGCkublH0Vn3k5JSnaf1eIoqOxn2+iMr2/Lo959JEuPMDFjE8BGB2Sw3gNVMzHOSTQbVXNwiAGDBYeoxHxKvNBrdzXK+YuERd895VYt7OxPGah0DdVsuQqYO+eQXnxEe9SeLhpiNuJVDM1f4lK5Fc8RaIGrzgmVNhQLSAyI0eu6h76j4Y2a4OQVIZnhoJmyZ0DnP53OC41nCuAgPHGN4VQpijb8JIXPvHiBPskg9NhGz/587ykhBKeshoaUDiTo1orZLn13HYmmszN8sK+fMpTrbIE6JfBqU4BwGmGWIrlSjLITVAFiuOpvNfyK3INUi1pHNKCmdjevHC13iEDI6jAhAdSbXtm/duqwziTUTLWP+8ootCED9a459YI7vrfLfKhqKEpvNwaPcnzknf5VEt4LziEDUzZOpzbLBU7Kkte2ErGKFa3jti0D+6fWkRRoX3l2rhvXWqpsruy2lrhLMxdgZs5aiqDyRzlQa3tRIEdTV1JLm3v3iOkVp1MrJVDNdM1OUznVHWPDRgq1W5HnC1uYFWCGAeXnKUpX+/rM1pyqQJZynpS0AhbnJKN3Kd7N9BJirmTHHZAhPKcW8gsd5e+Rqj5VtzzqiE9L+GCvWzTsDumu6Zf5Zsh8qnctAKDVfoAYo6nklOZdUhQDNzQIgLiYQCawbcP2cZainiuaP51M97da3IEHPf0Nm06OUoVTLinVDWV15Flb0su6SC2KgoOWsgeRzwuxM+8yLNVUn55FUxXM8xXVEeMKKT4ZfMS5ZicV6vxLyy4e3oljosHzAkJd+y2WbOpSc8uH2EkQxMRcUFBMMGmKKnnPWmeIkNu/E40SSgirzaK65/mtlh32OMKkLQaF5TvFf3ZElNF0tA0fpQkDm4wPyatIFcBGMI0FJC/fUOVNQLOTDFEAkCW0TzEpcp0CZBJD9VFCWFZHVaOuufMKbzx5NXkxQpSzQbDVDnBTJQKcXj7OAOKIQdRBw0rMeiwlwjxpEGCUBMC0ixMQ1kDnNeZcklLr7WdIXI0FnubGSYfO6VWtZcKLInmHF1Y/l3zOELWRlxeKoodES9a/H/wBOJV0RI8Rz24ZyYAk9W8vlJLNiP5VD1QtdR1Kr6rpTNnzm5ZER/GTFpP50Za5Qrxhw0fxlkgsGksEROMTzQVNkYi5y1DJKd0/5DGFCTGsUMD8lC8Otu+S+m1jkRQ49SgYV1/P9ZCme0dzPo1SoJJQZ8eJTI6ellFLAqsCzrZGbKjqZi+NLSj2FgIagQM79SGFR/Nm9KdpWZt24suWLfpL1uE7oI2bL8oiwLykE1jyGFV1lP+XbZ0dSSuC54o6zwCLcIRQNTeY/mbdlHVxR2p4oIrbiwdlzKUNfbTAe8+n8sGOp+Dw9mCMpVd+vfl0nV7OHbAYyeUqeVRYTgXIGIakCzS0tsgtgKmtbrZhl7hRdBiPFk1nGvs7YOvY4jn6sCDv+jcwZEFg2HACpCYuVrvqB8qvi4WcjOBIQhVG0MVG6B1VS1AQwkwIOFSOw3IlgOQ1HllvWH8tRVnJKw0m66ULYMSvO6DkI8bn4FDOoKKXXAAB4PmcVCaCYWPFZcs6AqIphnERcJZiII0EcCTkTP+v2HFCHlBTHeYctCyKUHAiWkyHOxDxv9H8uKCErI5tlp52Sv7IPluiOw6eUz+/QoK6q9Aw65uZWTDXPA0D10WjJmftgrnPAZq5zrpnj5HrWBv4MxM0TVGUWw3Xr5icvrFKoJalwFl1npkpVJlr2KpnLWUvYeGF4iJdSTVk9YzVlR4bDKVWn2QTPEjbv0FprX789Y0UyK5h5X89bIw9XxZGRK5PoUvN5mPu2wIRajxRgyadCPjSlTllhiAplrlJLThk128oFLzii5PRIiWfJ/Nyvvqgq+AzXrN6uFtN8o89bFv9Z1xcJ+yVfvxL2S7t+JeyXdv1K2C/t+pWwX9r1K2G/tOtXwn5p16+E/dKu/2IJ+38BsZFCexPmc1YAAAAASUVORK5CYII=",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"rank 19 Fnorm 1837.5080112082685 # of m.e. 10013\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"rank 39 Fnorm 883.9820242926976 # of m.e. 20553\n"
]
},
{
"data": {
"image/png": 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eO1VmWhlUp6S8q0B1pjQSyGRRrep6r+M+OhBShxTQxb4bul3SaMfR6geoMI1mkFuGZilaEDtLOONOrdx1Pah6TBDcVtwZqpmlWO5f/dbrb5yN2yh9b26r1eCFBFzrXU2tsY0YPvCpj3/wFPviRZNRCUMqpz620WkYY91PKaONyKQLiTLt3Fkik+lem7mkD6UoJ6pGsiBazJQhtcr0AWKct6AgwmiP1MduOOg0NyFTrk3miozdw+9965v3tqEkBuv61apkArLiYFFg77CnPvGJlzZWzcAhIi58UN3nyebbf/O1761+8Wc+eObTiu/xKd9JnYfgJS7KkMJZ30dMOfRblM5hzsIY72XUNFSLILD33kPWqpktp24ZczYUgUkjrzMgboZUwuTmlkgSJab9xdn9r3/nvI7wvvSFPph1LklgpazQtvGhT77w7MnaM71zhXpOMTKLd2/9V3/5xnu7v/mf/u9WD8bSHfPColdft9kNm93Y+RQlw+XdfmJXoqX+5ifA3YC3zEkCTaXtrEw1f0QjCVuwD8Es9ATBrFjAACO5Re4e3L17prtvlX6F4r52L13Nml0RFKVM+9GPnvvQj77YSexC3nGsZcPc74fB4/ybf/Q2Tk/ufvmdI5Zpe+R1m9uTLmOCdz1zH5KlSfSRA6MlWSk7OrmfZhKTFNwVwSVX81YTmUG7huHOgMY1wa5vMHP3zIAlc8p3dvUCx2u9W6Oz4t6VrpSu4XGAx0Nb3brz3I9+PCeu3AkzoZjXCU4EMuv9/fFg91797ssdt0W7warHLjtjiBFlxZphqPuuL3XLDmhl9O7W3scUBFVnEgibQRCw7aycsYKZwJE30rGbVjFrQxUKMyy+Pz3z9GrVP3v+6n35qrfibolCi2pmfcbxRz/ywTsryDfrHFk6z/TOxv3QMyOB9XDmPk3vvPspUH1eVPYlwkqXVS3ipmdlBoYyVbeQ0swTq+ftvYs0CtUwsYTxUJIjGyAJqs57jKTfLNXeiESWsrMC1mn97LDqvH/x7akvbk4zU2djzXT66tnnP3Tn5HjNhxoK0gqRMFbkuigqrJRnXniwr9nFmYWtMvp9P0REwlIyR2wNbklnmaaygls0NCpV1g+BlMHDjBUNT9JiFWe1W4wH7Vq32WNWDCTRMEpTWZVNPzhPn7/tjvRCKlII9P1qdXT60qdXIzjFqo+smAvwcGSI5lKiO/Fx5BD3pyBqGRKZoEICZmZAtnqeT7IRBQ1KTLBfXUgsVqsNdZQoCWo2Y85Alsh3qS49MYO2GXFjkugDChDPfPz1+xPdACn2Gu48+9TpZnN051gdjOgKs2Sg4zRhKMwRg9sU6X5MCwj3A1LRLgvKBAKWNVGs1V6cLjGgfRQuNm59Wh+EICtG65AzcwXU1VhpLt9dLbi+nyoKsDSzTONqX3IKw8nHu+/er4gw81W1p1566fnTVVd8n2YGRy1FGe425ZzvUZEws6NqDtW76UivNSwtQeRcksqgZ8oZCQNGwQEozVhOsl5MFU5VWCvOtwRlLkySi9EH5irlNcGuO+ioISM9KWTnXREBDk/Xau9F3Zb16vbm1gc+eHq86syy5qpnRi1ETUdlGhDwLlORJPyZQAfo7f2aGtEx5CQiaQ5kq6Ar4UK1IoPghBIiy2ZzkWmNBVEvGR0LhDqXbGZ0+JC3LPr4COWo8ZhaWpZDSYFm/XOlxIWiDE998IXnnzomLdLQZWeCOSaq76ZddhvWba6HmFreW15cbasXPtitabveNSo6ZSTcmEEWVENSCcc0FgjuNVRBsqwt6EwhkWWuq7XaxFIcF2aboUPfKh4vGN2BGerneH4rQ/AUVk9P9WI7rJ/5wAc/9MzGlJmSl9EAWBeTaGQmSts8GWlOqdw+Giu8Pnx43AM5JZihFAyRCJWi5oACBqhDKplqPC7rO8tAaC6RzRvpoGLCvHBzwE/iCqBzTRU1o8AmyFW2e6sipS5Qnr/TP3jr1u1bx0dFStDEkg4pWSawxy6K2Z5ZErtgQUKW/VPT+ZSr9/7yw0f17GI3jfvzPtmvh35zcudoQAK1661WYr86TiEqYE5zZvZ36nbkUqmYjYayMeOwwImXi3LJUMVN4yFJRlRF9tzz1h1IRFcT+/Wtp9/Z3DpedZQEMqhaCEvHNLG3OtE7jCMG35uBCFrc/eaWR2fnm3f/Tyvc7x4+vG1jgkYlhvVq8/SLH/vUCwPhE8x2eubBSIDO2Xd3T42A0REjI1J0IwWaKQ6E0yvCPNlBK2GgY6+iHLpMMSYDuzvHow2rrgtJRrmURCLT9wWZWAFjqO9yjGnV1+3F3e9+7VuvvHuru7Xdep5zm8f1qK+7kb1nHafpXmVR/4FP/+iHfuS5W74fSz3cJBlBy1zdjzQpC9BoumSrllimtMS/c8Z5Q7DrchkShJGGKaZdTjTIkWMpR9YdleKWNDemIkq3m9wHhYVEJCDLiVEvXn3tW19/5fX7tjpda9TxtNrmcGf09XkY19Ik9Dmhd9P0zW/1Jy9+9As/dVysFYjaekE04uThxb6nu8IkKNMIJmeUkOIjVv5SsKvujnO9mmZkX/YoJojjVKwbeh9UBodgSEqiD+cTVuv7YMTK9lPXo24fvPndr3ztnfNdsrvd931m5ubsvq3Suu16L/b7SaXklB3HqfMy1Lj33t/+wY/+7D/+kftsKRctMyPlhlXPki6JaymjBmlAamHQ2kEJhSeFVJYhIxRh2VkCpDJysESRd7nqm3sMALD9bt1Zfc+Jk2ka0Q/71/7+S1997f4EW90qquiPh7en0h3X7SZ3KljvduvV1GWke0a3yWlyRWU/TH/zd//+c//wxxwCOhdkhTREX+qUU4fJRIBuMGZmikYANuMFkv4j0T2koBlUe8ux52ReQpr81u2+eIeaSoAJp9l+u+5j2j/VveW99fvv//3f/PV3z3zwTcdxOxwdJSa4bNzbeq9SENucbEpGIESPC3VdUco7m/rpL7778MUjM2AsJjMDzXB8+52pTJFTx6SZIzLFRpj0FrwsQCOv41TXUSrACzOVcjOhywRoZY/VneMS8Axy5dNelgT9eF+89/M8Utz92l/89bcels2tBAxTFFPYilsz2dluA/rpyXDr2aNNqasup/Hswf27755d7HbqDROn3h7mV89Xac7IVoWzDtYf3w9x8kFwGo0+hVqdq4VfvCy63FDFm60SyqR1lhXDKBQlGEN0xyUvitcACOtqwqiT/RZJ9XV85ff/7Otn8lXpmCFDV8b9UPJh7O/c6TfPH//oS9MzL9auoMSuKwyZWb0Y6/1vfO2b33vzbLdb8Qx5byJSSC/uIHKsKxtYAZhRRCJAqaa5OZX1ED8Cl6TeRbCb0T2AjMjsc6oDR3jf40G3ctSgsTe6Muik8WzcVCgffvvf/v4398Ma6UNe6PRkd/EQ3bDvP/jyS888c3rn+KROF0asdBZhm7qvgkrXdznc+cRvnL326re+/u2/sed253flAE3InbNOLJalnEw7rpM1w9xIuHlm1sCMECyyPUJPv/59XfIaCw3WYUVqF3V9p3M7idEgKeUpSBiN/fju67/9L98pw2mO6C2jZ30Qq5c+/JGPfPiFO33Jh31X3wYDlNb9dLrdW6JYRkUNYYS99NFfePDa//Hr42hbL4IySaZ1ltS215qjdyX76GgmZQrmStDQAmjN1LcnJ5rWoq9MJs9j8A61Tt2qO7JaTYWEJaItPfwovva1//DNr752fOLnU1lpqvDVc5/42c88v+kUdTwrA0MKq+vJJyX9jGSnrOaxK0NO5FTEk5c/8u29TzKfJHMokgMIWfraaQxBpoqFAGqWElv+rAVs1JMcNA3ZXm/cT51pmqq8DCaUJBOoGZluMKM/+P7v/fHfv9s9P91f2dpiO568/POf+/Ct4YRn96JfdYptwZT0uu8sy74vkYxKdyRKpynNSoRbrrFbr/vdLhu8YKUB2IWG471p79UAZQM3SDZCHWyJVA7V28sg+BFowLIKZuIqIqYa7ICToSQU0ZoIGMUSoXf//Z/9u9fP827/zHuTZV39xOe/8MlnrNbtwzKcYNw7XRC6vW0q68Xat6t+X8Z0JUWKHTLDLC92D3WCccoAzTJpDsKMktR7raKDImU+e2goowEFlwbkak365oplAKSbaapd9oSR3K9v25gmMyFzzDJQzIhX/quvTSjdnXKR26OPfe5n/8HzvLiP4iUNVexZpw60MESOw1F0UTtGn1LSTDVLB1SSDu2tq6crQpH0zDAURpgSq36bAzwIKBWO2txWYSxc6CX1fN89JhhoBExpNcWdWJwZhhJ1NBPAXgoos+qNb9wrHTvX/dOf+8c/8+ESF9MeqxXHKW2j7c76tdcgSi3oK8qY2IXHTGCiGUMZKsVyuzsNKytPwkRXok6ucDffDCyEKYHMVLg1r2zWHdRsdtJXy5rXrSKlFJ1mJXv1XVgxTblypqyXRSYmltI6NqaQlVDe/pVf+uzzfnZmpSuZD+VHxrFW61gnN8sL20x7nuxHj97eKx3MmQ248OJ1LLZ5ttxf93dKCkgFZo6pEaI1HpMMCVKRbnCS5qZIzdRrmh0KTI8RrClqMmjw6sVSSecK6V7VePKuSAkyO86K8PKL/+xjz2xiN8LcEhHGwqhZDHU0z5R152VATZZhtH7uc6QhE4CtkGP9wOmDqdyxpf4qStHK6GmD7Sh1lFE+s4uIORfXlU6QJ2L3DkDKDNoEQUk3W/chTtGqAJ6T3ADBt6tVdMPP/crFdCEUoga8s8i0qDA0jAAynwqbalUfplY3CbhbClkFKx/9wMP95vbMd3OZsXUiGNJ6kiUvLftlIjb7Z7QM+cYeuxFShUBJAUd0rZhRh+NSJ0u2FsOqll0Aw2aPGjnt0WMXfaeY6MaonmHmObHrdhPg/ZQ1lCxjJYwhmE/JErtc2ziWo6PP/cx7uw99fLXojNLcKEKRXelrZFSg8SivAALi3O7QVu2JgKlnpAALKQZrZbfeGoFfSohIspgi6sknvnTBlX9ve7SVuqJQQaT3dXQjMo0IIHRxn71BWiGsA5SyhBFVfQaKNPpL/8t/cv/oU8Oouf2USlkKKXo5ndBYoDRjNjhnSVNmQB5XZ641weL6ihlNkuBuhv3evSvsNcLTgOqGhMI7UwK3XvoKTLuvvvpj64fJWpDJ4jRBweKRE7v9e69/9a/urV/+0IefPnoaOp96D6UxgoON7GsJo3YP73xi+4DBmaMHUcrMVGGoC4pDIyMpQ+Y+R/OzUhppzOmaKOU6xTTHAgKZZrjQ6a6a537FPYplSSkUdMOWJq6e/cQf7HKvV773sqIrdbSSVPgUJjDG5NDv/+qv//5bU3f/y8e3X3j+kx//6DANkw0TOHB84Cs33esGZlh5sM0uQFBJq9XcZFaLo1DDmLlna1RWBjNILiHSzB4zmi0tYMBjIo9Gvy0GKLdTpxrZm7fqGisUOLQcdh++/VZ2/e7trfqCDC8dxr11fRPfsXvrr3//P9y1F8+fivHVN/TfvPyFz70IHkmR0a9se9F3MawQmaaRa4xz6cGGFVursqpB5kFUzhznrsPMpHUs6HA2RuzV0OOGKgppaqFY36U4UTCvaE3DZYoMsMABIfTBZ7+Tpou7RdxZr8xJlZ2NoxfQ8N4X//QvL/D07q4+OL7HUdN3Xv3tj3zmRz76wVvT+UWsbKU8H+5cjJP1oBxTYwQFgkjAhC6pClhtQC6MbO0imtsJWlsH2LoOr6nijSkKiV41SVJVlWmk1utdUp5h1gCyaHu23H7+aF/H/YPoJ0BZQSuo7DCps/PXvvQ7X67rLm8V3rs/DZvtGrvXXvviyz/2Uy8/t1mNe2HotEuwpwcQyg4yp8W0M3MTvVSlaIM1MJggEZq5vc3Gz9IRNxPN64qYsZv6lJU+c6JhgDJSxA7F3ZCJMbyEQFhZv3RUK7vjbTUrmkY/6upZHbjam97889//8ntHt1TTdoOvfbpIrvbeXfz7b/z27Zf/0T98rtvvxu60nm1YA0lmZ5MhK43F4R0lyqJLeo/JvFFyci63tCIZ2aDG1v7zxHzMFbWXJnQFUmcZSSjdlzxVZrAI0JJHn/zAu1t97B8c7WhIdK5d9aHePXnq4Zf+7R++5qfDlOZDI9NNGKa+Smbjq9/8w5/4ws88NyAeHvW7HoTGDWsshTyTkEhFK1TSA94lkEhdElcWv6XZNPiTwBz3ISI7i3HnMTgUoVJKhTJlxQuM07gVYGLikz+/f2v4z/5RN7kutHJta9dVe37/d3/we1+52GxKdkwEJpeb3M97RRf71e3p4Z988Ud/9qc/ejsfWo2+7+2NXO2OonXLoTFTZBTMzDT00YPKyFZZyLk8a8aGVCmbdbiqfNdnmGbSUqU49/XuZiMK9JdOzakRNd2VTNRRZt4pNT3Yre6kCTGVY1zsbHD5+Tf+7e++hp7R3/L7vOXn5dbbU9hu83Cz2alM0W2G7Vvnpx/7iX/4k8+vchLY71blnVslD8FvC2srCXrU7227BvQ0OyDxsjgmNDIEWoPP++wx1XRHDdH7bgV5pPmKjkk0FSLGyr6TSOZEz9vs9HATgX41bXPVZ+DuH//ZX73RH6mWsr84/dRPlt96o08VfeRn7375fmjfre3igfqVv/qtf/Hp3/hPb3lWRKdx7THHgNECgLTWr2rFKxd+PTJzgexnClJz1zcijZvVFijoSZdhd+t4N1ZY101RMhs0mx4CPQFFxolXhq8maeB59bVGTK/+u3/+5e4W91wN+wdP/dNf/cTDf/f9+2fc8MX//fFX/vKPvn33wdEmt3ZkD6aV/vob//xnv/DRZ/r7LLk66wqNCYiMyYhiMZSA2ebtGBovQMqWOGuOqlomZhCqDuzFR41Hv1EIUGf7aX82FetgytU+zWOq4aV4V8edkxT6Xfbbvda5u1XGrTpOZvf/4r/927dX/QWO1rs3N5//Z194ug4fChGTv/2dH/nIp/4nX//jv/q71/202wW5u3X62nc++Gef+dynPtCdY3XcCjnIHA1OmkJjzSJbb6x1cDY0BqlZsoWY6UaUvAoG3+AEZ6AChh3KwM0qagZQO7OujpN1RJ0SYIPBrb/fDYPON329yFV3MQ3lzf/Xf/2t7I923ZHe2n/4N/9Hn84zTS+sN77v9N1vvIjx6Cc/9T/46z/+2r2otb+9e2vz3Iv7r3z9917+5V84QsEECYXy1jnOagWVXioq90kzs6Z/PkO/i7qpFQTzKq3venRPOoJQBnton0Ln61Vot5eDXWv9kIoZhL3BgwzV0dZlj/X+b//4t7/FwcfjvHv2zC//5s/fPt9b1/+DF17tuZ+GN+Pk/K6dfOLHfvWvf+fL78bkq5OHHI5t/+qrf/r5X/8VPnRT6/WAMxUAU8AodevdKhcY26BGD2m92Tpw4a6lmjfBHIlIcVDUfXTGROz26/BKQpEQgSKjUkD0RxcXPIndUXd+3h+/9Qf//G/3R0Cx7Xv2mV//5Y/ygXpqd/zUt49yV8v3S6h0Z2ebD/zTn/7bv/rrb9712+uLrYFH3P7Bd5/66VWGpLCSFMwNMoQBQue1kFAmzIwtg9cV3jMB15McdKbcJCU6WJpzHCfbWvTH2k4WYgKFOQGCdeXh/X6lwCqkVXzx3/7uV3FnHdNZ4kM/82uffWo8L30NP7p4bjorvW+/9+Yd3Nr1+eDh6fPP/+Qv/e2ffOkd74+4iwmr+uZXPnlkaBxcZ6tehgoTzkAbljT3rDYDobn7rxk96sbApkfoEFENxSYRQ68onXcontsdw7rC3EekIcmOZbro9l5qDNN2fXL+5//3Pz87PcoLqY+P/PqvfsIe7Es3Vcpuffpfbk84lbe++YXdPXTrzfZs23Wf/olf/+K//ot3sxgDmfGmdykTrU2MwFQJy2RRyDcPuNTAxAZrtw7mg2CPwG83wJwCUuGD57g/78jS9yydalhhTpaiE+gBqIasC4nVTvDtv/pv/3o8tr33F/vjn/5nP3/rbCxHuc0jv3jz1rN3Hk7jnq9845fX3+u7nZsH17o4+bV//JU//v1vyjvG/uiDlprb05M0JWSoFcE068FySCytTWu6ZC22GtHcSPFYVZw5PCGw1rOTFakdGaWupmmUdWbO6jkXZHwYyrTPYft0/av/5x+9vrrFGru6/vRnf/PHh104J1mHqaywPro7Hp/s969+8+nb1mOcsusz8ux884XP/+Zvf/Hbb4+ndudTq/VeCbrHSMitkChFKOi47qsys5kBtsA3lyFHM13iiaqYEaK5527aGW9hqsEyvTP0nsHikhg79wqwZ+FDlIHT7Xd/91996WFhXfdn50f/8H/8T04fvldK7m1da41+6J/1i6HLsnsNVqYzI7oeVV3V9LC++F++9qe/9zd3n/0vPr+6OxQkKBg4TUVOlY4hG10oOY9ucsxfCJgHcwlsPPb3F0ytSx6oNlmMmuRdKaYd0HeQpClCSjea8Z4NydL//W/9m1f8uMT47rT57C/+/CePL2wVe7grKJ+qnXz0G1a3vb354IWzQrjHLr2Lceinba4//sxPvzI9/eFu7BSGqGYmL9VM1CjRIhzlAqS1dm9pNpAHQjfIzIVU9bg91li2lIDd2e5iawBqrceKSNaW21lPGBEVGcer7YS3/m+/+04/oEbo5Md+7Vc+jPso08ihj10OUOaue/n3zzhkPvzej6/GosnkbkUYzVbjG77+0AecZ7t1X5cpJstNkzSjenXH52xWUAv9l7b06reEKuehUo/dYyB8fnWyp/UClHXH3mskGpMQqmwVuNMczfHVP3mvOy778+3RRz/zjz77AkfFjsOAaQynQlbLR27tYVX7t7a9OTLgCKjkWLzPGI0Xg0Nng7WW8tYpWZxAQWsB6UkkgksL86GUiWXsyGU32eNUcZ79wIjdyAiSUihdkTRQKWWjrtOF/sF+gF5/vQwW4254+Rd++ceOtmfZC2XF7QX6PqZaPMtLT783QVbfvnALa+3wyZ7TFLbOTOy6YRy33WFaWQsMW3YbDLHhpDO7ef5qQU75qFiP7rGZO6zpYjtq2xVaMjuLLVcdmRExTcVby7+2+57MztCN2/rMT/3S5z92NE67tFJ0PqnrqV0C6Ty9UyaQunux8pCZAa6a69VYJ0kOq9nFunUXmVrnAzJNFVQaWWbqJua5Oa01okE5bTiE3TAe15g5C7pf4+zBw+j2MJOilhSocDaQea7YWO6HI0760Auvj1N99ud/9TO34h7SpHU8uLCjNba1jTuIzbF5CRvfeOvEpv2uQozp4bnWm+PCyZ5abWJfpvWMypskOKUgSDjIMnQBCWlccpNlMMiyZkIue+4xe8xdKYkXr94/61fbVU3AIvfquoxKAL7ua4UEZPGVxvTP/6/+r9/YfPqf/OZHcb6DYy3czzwu3Meem6wIjuNYylk5qV/+Pz/XPXhwbxtTx7ioEE82hvLC7c/+xMf203ormJO0gMK8J1NhBQRWR/ciQUTSjcqMeZ/NWy1pB2/96IphnhUVdQxfE/feRem73mtaccO+uhkoBbxBr3VUb+v/2Qe/uXr5J26fnWFgjXSb2JWY0A/TuLvY3r337tf/6qIw69H2i0hMNpR9usOYu4vBuP/67rc//7/9VD/BUByRBrMMFKspMC0sp9vcR2ZG0Iq11oi2eWaKJXm9BYT/6qbxgJRxfu/tOshfeqoY6vGHYCAY1QADaihhxTNNmXJsfD8RGVHcp4schhj32+352Xdf/97d/f7di77m9mjtWzL7mGTFklnZR5V1UbP4uPrf/BdDm3HU9IZIGQQrloINmfvtdr+faiTpxrly1AL7ZlPySYApWg3VNjZNXbVSDAlN60wMkw3RiBWWpAFj3pm24eWcFikV11RXnY/bi9e+9a1X3z2r24iOBlauDAqkGb3SHYYZ1mUAxnJx9iCmGJgQyDZriUKXolX0GfSVESlYKivNDl1/y6iqG+H9o5xgUpmw2+p3OO6V4FQleDbTk4BkLijAC3rxaqRK1DSM5w9e++orrz94uJvozrANpzrwwvqhau/DnnPpnJleMszENGeNtU1rLmnIPGvJkB5KkMiuiHTfTTUisvFnLytiEuYBkO8rGABaUam3ZZt+0ylsmvZrGZJsVdpQ1xGZmVLx2NejsdK4e+c7X/27V+/tzpPu7ODGLmRm6WWSG5S2Ppd7F5G0gqytSNQpJnvpU6eYe/YIZraJsGBRGkXJJZh3F7ukUVKatwFPs4teUpj3sYpkKtm0gG4aoQSUcgNTGYf5LIiRqzoWt4llnN79uz/80ncvSlcEd1nBNKnrilkRL9brvRcNebHp64jOuuJOI027C1jmlB/5x587fhhLfmxukDsLqK31DhglWKFpamlLYy9rCaguPfTjWQOYwjqHUl3RqNKsUt8rSmY6nVlJMVI17VgXHaR1Gb/8J1/5+3e61Wkq6clBVeyZlUNk2Y9PTS6v++OzHDY/8/JTT2/69dB1zjzbM9+7f/Fw+5Mv39nXVW2D75BVcKTkhSmzKUvNAnf3sjo/36dcUE5oUy6boc98giqShEKZ9FQJn0wE497zgxtqsVFwR6qC7CitNKr045/8X751FuveEwnvpJroGClwPDp5qtt8+Ck++LM/v7PfHq8/+n846gaNIgTPIwzuiqkeTTWrDWy8SsvMKSANg/XM1ota2m5YHW8fnI1TrTnbOTMaCDF1jXJ0TTCxKCDQYQoPhbH1nIydlRYwZtCKURnbst4lyIsv/qUfd9PIYiZUWBjN+pPnPvzCiy88/exRN52ev7t+ZfQ79/bPyM7ul85QQy6zbRskecaKVZeSKCRAT5Is2huTvSpscqM7wKHvz7f7w4hFZRse68vkxseqIulEpmIsVjgJoCm49Yyx5NSAvQhHZoTbjj3ivIZF9KVmo2f46qmXX375A8cnJ6u+brtSo97vjz7ywe9O62H31rd/3DJDBFtdwybvPEa3qbQJyMCC9JKTA0mbumKmbGRZWHdEM4ucffQc5V/3z49ygitozgRD3TLfb5rAAJrXjKQrJYNyQIzTZnj+mfd2ZViPNbo7H/rEy598/vaqr9tAbMfwTPrUdx944Xvjbtg+/N4nSgFAm9SZpCyeILjqtiicQcJWXxAsjVI2Xh+VbgLh3dqLTzUic7GIM637imA3Es02sA8yoykNSBixq72QmWwDCaP50TW2mbYaysc+Ol3ETkcvfPLTn/7w0912jPO9iTmKKx+jrjT1L33iS1X9avudBKAIK8YIuFdZstOEss1yCNKZotHSDaJqyy0TchDee9d3u/0YNTPRbiZvTBu4WdFMyIwCqimsUypTpU4MM5g3AoYFALd+2nYDY3f0mX/6b751/Omf/omXTnzc3TPrMO1LZ7HPjdWx2JRxtvnIOJS91W9nFxGimyJhzqIUh2m/qX1zNM6MNKPaoFqQGbWPlinBkXLvhmG8OB+niIgZ7JC1QR+PV8U2M7cl5SmOcEMQ09g1HKXFMSkYrWwrvYPO8fSv/9x4dGvN2GrugwQyoNahLtv3Ap8dtt0oe+d8kzDBPMfJCnOCd92YnrAy9/xaJjLlNDejCTE6kgARbOad3lu3341TnVpP2Nye/358xStgfxti0OJ9TRWXXUwpQchaW3Ny7lZHnTpONWVelFnbKM/mXgLFMFl/63g7wfPhrppnxNgtnbAkFfSsNOrAN5faNpZJqnP/UWuqbeFRI5OZ0SLzBkPsMYIBwEzXnNNwUVRUzASqbB3xUCLlCCSyQlkBQElrY+clzhmjlIqp+LrHlIXbKQ4dzEC2uWVKs2il1nk28ELakGTKbGNlOdfISKDNGKO5eURepjEHwR41HlgKajRCARBd53OC2h6VACgSzpQsayuStsljADNbeA5VBahEUA1+R52hFyRaG7g3YtQCVrflaLwAzNNxkFRr6F46x0gQBaK5TVEjYgn2318VlxK1gMLIlFu3Ol5NtdFmMPMNIclNVTK1URmHcs5cUoDapHyDajAyK5U5LTKZGkRj7clzLiHrMNNiVkyIymah58cnUaBo3pnXUmqdJuSNUSWPjNMFc7lxOjIr3de3jspWMY/U1Ty9WJI1HnIYfcmKUo341ub+arKOWaNqDFOb0SsIZsxAZ7IgM9tU+7mIItEwx/AwAVK4sEjWWLCtpdYys9Y6uiFv6OKjKzbzmZCc2/u9rI8HlPEAT84Dx5VYJcBhX4vNLeSiLTltSsUQQGROoSkKkmIhmaApqkltLJPgGGUlWgOZ2mxkC82k88bu0IL0zhLQZJJKrWbIuM44ejQfE5YchwDM4f16s+rSvWHIDaFqn+w+tVaunMc0kwKyCrTMlJnSLaNW5FSLQeyOujJTRefQiZGiZxsvOhvkBQ+dlStjnkfX2qqENv54HttHStX9Jvx2M6Ra+Ds02URj6Tanm6GEt+gUaK0XQiY6lwSUqEaDZLM1bJ8WCResTNs3H97u8/4uzGTrwlYQk7fCj0AwI8yxNLcl3cnFqAgZU7b6w9IwdjnrHzRzK8UtnzSGUHBPpuidzn0fHfvV6TOlUAkF3akZDsoMxgQXQ8aRZg5G0oRUGzxZoww28Pu/95ff+tALP/rgFel4NM86OHJXy1FOk3mfKKF9GQz7OYFHhpOmNnU85ak6dpZGminBOVHBDJ00HD9vgDk3BJttukLKOlSsjk7XmoTKPkdByYC51Nok9yhgBdRb1ixogWuyMCMwWFwMOf3x/+Ot8fX1F8eHp3Zxdufz60oTO6/nnUMMGQgYMsKsHQTijJwJR4SAbSYVsnn6Z2PxwWhka1Aq3bAa3q5PFCxyHsirDuzs+NZJD0YGrNTa7BEYbbRzrT2pLBmlNc2k3C3TwWUX5fbi269nyenhtDZVrT+6ccwhrTuVoSTmgeqc2fNUNr03KMm6M/e26eZ9JDCZbdq0kYB5N1xjHN3olJhnYRNUoiSt3xwfWbUA6LYcndJQZjOG5pMLok0Hz5jHE5skIEFn3T2cVkUax0Gp7s5Lm5ozUN2G8hlEMNtMrdkuKRsE1zxnjt08ZsvazprzsPborBEVrVw/kebG1NkW6xiACiKtDMPAIrUwiLpkujdejARlwIoWQz8pWVATZpFkj9VRHx1ynNYhnnzoxdV5iFTSsasWvVWZI1Rm5zzHVch5hgeQqcyWqdkCTjW5CKbR5nDlWt7yaMef6B41o5iiv31UspQG7yUtYITC3dq5H6tIJCYffMySO/Qlduo3OJus9xQwmp1+9kvfHC29mEV94edupXutATtZvfIXX8unf+bTFgmkJQ2JJA1pxRLZeMhCBQ/nCNgyKNGW2qDafsvpegPZYwVDTTphcXqnR3gRraQ8NKIrhshCKYGee3MCxBQyV2SFTxkwyyieExzCz97/nW9P6fU99C//xq9i29DOolf+69/6+7jz9//lC25Z1UfO3UVCetclMxM1wNyNBRNauBOcOXHAorUt9Jx2cS1YvDkiLQjmVN0Y+6MPPw/ltC+McKabYYyhp6mm4E7sRfOE5eg2Wefj3teruIdbR/vd1sU4sd12/Z//3G/9v98+75Mf+V/8+rPf7wgCBd/61//qjVu3d3/6T1+02JlHRRGtsSynajCai4yCZGqXXmyuNlM0n2MCzfObYpyCT/BjiTYOwjLZP/2BYRKnHc0Lcp9pls0k5ySD0fvQNMYq9wZkeiHqbt0Puz0cexuO8yFWJ3t86H/9i3/37Qe3PvHZ51dvnuynsM7LO3/yL795vJni7MHWuyNNk2ksbGTRwhoApeKDkOF5ZqYI+pztKGPeV3SDoJxkN0KqR8pIrgkEs3/u+CIHS2rfI6d9Tcn7YOaIriQRdRxWsdt3ga4mTHs3yx1P1m9/w5+/c2e/3a2PRgQDx7/wmTHieLPf8z7FMsRrf/l7b/Z2kd3Hn0fWPuModnBEiK5QGqnMhCvi4txXQyGEtIaL2pxsWpuqooiqWq8hpjeqLSS0n4YCdMe3hmKQEs5apxQo61Qji1ovvOnMhFISGrtiu7Ff9bav737jX/zp+OO/+IUPDhfVEZ1PU92aedZ7W9twLO771/7kd74YJ77L25//0BoxIrdRSkAAFxs4pxp0t9iinRJlnJ22UWgdcsoaETDdoM7exDwsbOUJP35qo/A0mDmjyi1r1qlO3rUxIgpz5j7krKVnFQYf0zb89m/90dvTvVe+8yufvfPwLNfmNmqCdW7TaCXLkT/4yr/549dzgzGPP/eFI0qTgaXFhkuegJgPIIOS+9K3VC8b7OgU22wdKOdpUJHXzf11VTRBvdfwzTO3TakK1dpADrGNHQ1TcbVIfBA9kilv3UJdTNvunT9/c3NnfOWdV1//6efyweiuAEPKzYD9tjuxN778O7/79q1b4zb6T/7GZ4Y6Thg4ps/pksFSciTUYGL4GN6XOeDPBjculXC0ID+m8XoKfQPilqYoU9rxs7eHStQkpDZNUgnA3cfRgDbScAwUWZuA4xtsz4d1f35W++NpN9y693vf/Llf+bFTaBdl6ntgt+9OTXzvlT/8o69tbx/Hdrf+5G98/tZuN2nV19EKQCpnQGV2UaKUiF2ueze2wVlSNFPBpcjSatK6ev7CTZKYhwF+9OydXpGKWrqux0UN0jKy1nRmIcUErOyjFA+aYapaD9N53jq92915F+N+OI03/sXf/syvfOQIAa+Rth53p9Pb3//qf/h3r+N4k7t996l/9ivDW7JVwcPs1vXCaW4SxI6ZMpqUqqG4SFQ3QmwZDU3EzAqRICkNSz/R4/ZY7sNhqzvHSuo4z/fTznjEYcoJmVYiKtAPUQXABp+iuCardI77bt3Xe8Otl3959/2woK+2//7rX/7cJ567c7v3YH2Yuzf+wx/+bUz1eOB+2m0+92s/v7kY12uNWx1ra/OcFYDFEUnRKiX4Sju/MDN3kFa4HNDXhnNHZESaW8FVXLFeFwwE+qefGmyyNbZjb1mn+24UQprYJVkjaop07P1omoKQVNz2I7tud9bf+Z9v/puvxOaoPsSx/c1XTlfPPnP7g0fcfuf1u9sHO2xKhrqLB3d+6T/7iZNpd0sPkNax7vqhQlWtYcjavBRFQjVW66fReto10x+YmrPsiMhAWdl15v0Nc2/Wcbj9zAZJPMR8qI/XcFpmrQm5ALgiiCgbTFUd+27aj9YRu0hT3vkFf/Yrb4zrVdTVCtP4JiYOve39oa3v5FaO8YKf/M//hz+13p0n9yqFufchsh1lKWTKWrOw6IANt6ajCkUisq3UHG9kZmSC1nkpN+C3G2Uk93J6pwvBMyd0RjNOAglDqIYpUfvBx6qo1F4la6+EIryLHLlZ7d85/rVP/v7vfG1/a73f71eGsh41ba1bc+piCreYyqd//Zc+gIs9b+3HFRFj38fFWAS2Xsx2dktmUJomaN0XKkNRM+cq2nyaQIJWStfhxsSVR+bd2/FpibROUy2qDT4UYpKIziMVdcpCVxK62K07nVd/COs17dl1MSb6FT7+9Mv/5k/fHO70UZm1TJ1tt12ebKezTQY3H/3p//SnTh9eTLq1eru3Guj9HCuOiUw6uZyjIheRntanzMyVRRGhirmx22nu7k67iXHfUMVuc/TsWjDmfoT2qKAPNu33ISlIFlG7h8c9kWC/rxX0umJAHTPQdTjvnhnv1ZN//Imf+81n3u2NZh12Vvrh9vbhVFlx62P/4HOfeWb71sh+5e9Oa5QiTmPXyBbFTTUcQbi1Q+gyrPW9EEZ41GgejvR2lhHZAKtrunedmTMc3bndGTBNZolJY6QZx1TJMSZKSJ/OxxfKuI/sTu9ZV3y3u52RaeaaKldlzOwUOfRnX/rDP3+DZT8YMnqbpsLMlz77E5/5ke7snM5u2N9frcNStXRbWqu4Ghp5gTRMyUk19tE3WBMAFDFzFOfhEC3BzYwnjJYRzMY0r2GWEe1YWuxHWZDmE2mou/MYzfpE2U7HCGFzEaVXxgTfYLzI9e3xQS3Vjv+Tn3/rq1/77jcv7tXax8T+Ax//8Ec/e7vDRYj0Ie9Pm16xoxeHtUMz1SasNORFE0Ewx34pdQIEy9zDyDnlp5GGGK9ZRf72NcE2t9aDGxKg9l5ijJBhl+5ZW4VNu4szvLTJyFSwC6BwZ9ZYul3HOibWpU5pTqKs68X2vdd3+9KV8sydo95rtJ4FEjUaO4dmI81z3/Ewcy+ScIQcMU3B2thuwCHWWOoXc/jxyEyxmyPS2h1KAZQYzVKZE5BsRahERq1GIwOhIgmuhGMubkk0pawkoMypqp48+5EBIMfQWHFBt2KRbTKUeacx3NGmqGMBodCOxVBCUatQEDO6ujgyNEEJzFxh3GhlvC7Y/GapADLBrDUpJBQZQKqB5ClgRkZFFFM429iU+V3mk+FAZEw438GMtfHlZ4phM9nZ+j5TbEcjtJ8u5x21FgLyEO4uq7Y8AB5+JtystlxfQCnDkJkJWICKSAbboMiGF437sYRI0LzVQkQa2rllQuQl3WJu/88Z4VXE0pQtgJZxIE9RapBHqx1gYUklla1z8fDQrtztUpzVo7+6Gd2jxZQpCJlURBWrYa6rKSP2u32bsE+pHbGZImxuPGn7MGf8H6KnAZaHH7l4OJBq7vkFEXKlDqNloQTyMPq3FWh0KJ5Lj8ztf+S6uWIZWAYdWbCxwtI4z8GPWuv2YvSUNX7rXHZkA0vaDD+0Qt6h0bAdtYKZzEtpPgIhl4fV6m4C05a59QSItLZ2y0l+hyP9AFwWla4vy/utWFb40vOOtIpIKQpzTANYp2m82GabQjqDmzm2ozLD3BSgI5TOdmKw2rl+IMiU1EaAzWzl+chOLtVoNBs/1+Aa2bWZvhmCxrJm8yj/AwbXVO0JxoMKNRSLgpLZ4kz3mMIp1HGq4+Q+s3e6CibqnKWnq4aczOByLvHM5pElQpIiWi8RL5/5nBum2MqYs6otRVMuYHC7wQN74GBEZr24qZo34bdqsPnkW2oWLCsyaipRa01431OZc/3eUGHtlNl29Ddo9dB3ggDbS3MuztvhRrisjNT6F1uxtBEVEgQa6wbNcjZ5MMtwWdk8GKonCoZcxi0IaAy/VE45RZsARC9r71auDGRUAZJpdt2RLVRpvYjNULdD5TQTGwyYZ4U109een9iQ2hl+sAWk4dxAMAs/Hxx0kO/KJT5iTR7TjSRr6iwqFZmZOU1jGgE3MEvpvY1lFZGZnHvJjchEQ5baTdNn3WlcItKQafONtrpYgym4VNTnskc2c3+d4qBF/xZaAS+X7FEj+YhggGWrFKWpKjMyIusevZmZBJf77O2amcplNMp8bB0hmDMyqak4s3ongHNNvlHaW6tFtB4WQgpvR2kvI96lhWVBa2fCLvfIZatdnc36iGSP6W2Za0WZlpERkTVQq3tPb5YAUjawCAZapFOErMWYIFrNRMtWF2ySaa7wXo5CVGYjb80Gg3MRejljVaSiub2rUi2h1EGm9qMbQ0wfYQ1wDpyRqcRUayKiWFe6TjQwzaCZvWQRhGS2mGjabOYa1Y45l8cVzMZ0iXZgaV2KesrWnURTO9tSCqEdPcy5rjwD9teFa1HKIcrRTfPxiCoqGwsss4o2jlMay6qAnbe41d2ZtTVJtvN4lW0wWLMH6eXyjGNOWZgIQVAbWmNCSm5MZaufE1C2CWiNnWKmgBHZWKPmzX3MI95wZeDgFQDuJl/xuoHJbACJFDkhHZHkajUgCbSYgWZo/IfWprEMds9Zl5jtLOEIyBWkWVQKMETrCDPmHFvSDLUdzk3JEq3hTmI7qwAgaeay2XDwcrlwuUaLlr0/Egw1lC4iIzOjH4biPBrGaX5cgqxQlZC7dZga3B4HhgepiEZpENKLVNEIbt5r5GAYZ+4fNB/DBUAGq1FmThMUXpSRhAt0ZrrjYCiWL+aNuEh7c+DWDaSARpXMqCHAu2LGpFkB0Ixf4yJYS3CsZCaVVMzMi5x9VhuSokTWUO+7SR0gRavfzEgMMkFv8eMBtGh+XS3YaDMR1VbzINQVEzgnBDM97apg17dcO+JdmEcYgoJcY16JWjJmYK+2ozPaUVOphSJpRCrbmVyYSCn2CUPuzRxBS9X2fI2YGW8I1VZrbktwSeNsjYuKedDxZdixLNfVVbkm2HVVvHwpFw5hm9B7ZfHZuA9qI9iatctGF543SzRgXTN30lubyuyYeePD5uwrD98v2UqzQAcpFkXklVt5wnVzj80hZvtbLfjJZRbemiEzIaW1Bl1FG6I0s+1EzWQrwUQhMz1FZvMC1iL6Q7C0PKnLPaKrUfsSFV+Po5aY5f2Fezx1dpFu/lwdcqvme1o3vM2fNt9X2yoxTzRvWb2UM4AgRIIOmmlhiCwgpyhlo8Ne3kDDdNiCxCv3z8M/N64bQj5WsPkZzW+xTLcCISYsWwuxmS8uBLnE58som5ZzzBEDm7dqWpWXsfo1XsYykO5S1kMocfk63Rwl/v7X4/eYrng/HJR62b6tMCehTVQiaW3yN5cooUk80xeuGLG2VEsHorRUTGTzmcE3bPrBBGr+7/JecH2NeHPJHnti3KLkLU+YiQazzoMLEzOZs1FoZFvpINrSjzhPsWmZcVCk0ptNafvw8LbzMMgrPurwLK6Fvzdv9lrA+GTBLu3ivLd41R9eftohfJuhlQPGZIAaXRSZizXEHJcsWze12JC2wloi4WULzMayLdQVpeXVW7wqz39kjx0s0sF24BBhNl9Gm/PaNpBnNhLG1r/VJJ350o0DkGK0pNg4F8DUsv7FXDS5dAglMKviYUPdWA++38/eX7ArKzurJIFLVlobtoHD8LW5a2FOwzgvgpoLmD18wwVa4NN41Fq2MNlQydnaNjN5Xbnm/XC4gUsZrodQj+6x65IeNFrgwagdnuDc17/sMs0SthG81nD3xd7Pj+GQmEkCIqBL3zH7pxkVJpBoSX7buTjkktINGQ6SX26Tm6v2fub+8LJlgzSlJ2VCLk5tjnwh0dgQj/lOlqfRhJ8tfaudt7D9ED7lbO2yrZgO22FplLh8DJfeDQcTfWkrnxxS4YoRuozJrtrrQ7mj5dpAi6QECDN01d5GC0QIKGezGVjmtrVaM+YkteGrOW/uGcG63GC8hOne13jcuB5vPBa5Fg1vjeIHovH8sKNRkxGANSSOcwvW1YAPrQ+n9VBoTupmobNpWetKawlu854zxVJXNgNvSqHDrx4r2CMyP+I1Zuz18EacXRnmaNEWQH3eS40ZOMeZUiaZ80BOn7vYLjdN83NKWREWjPiwzy9tNK9EhldTykvpbgjyiCpe2dqwzCWJu2ko554IMza320Ru2VabGgXMnfVIy+Di6VpkeMCJNa/afMJag86ba+PNuPCKP3/M9WQ/pisneMmsneo7H1rcgLV5lx26M9BI1CJaDwp4GBG4oJwS8xAKNh7lHCtlC0oAUJkKiDnr+ozLccZJl1t/XDz/WHV8/CG8nFGwBv7Pmja/95VwrRn9+YBXw1Koa4kJgQy6UGf/ZKqoYrIdAqR2GpwdoptY3mZxNFo+oS2hDrdyUL0rhvvJgl3azavVjAOAzNkOcl67lpC1qorYyviSQGWTk0tDqNSOFpFqaz0gpIDgLZIk0GiHxKwNTd95WKrLBTvY/oOlXwzm1dW82bSzSHe5Iu0TcFAJEWy9cDq4K7ZbV84zelqMmEtOE2pH3SGzkY5pBDPVQK52ow29X+5hvg4iXC6YgMv9cnUXXsffHmfuD4lztjPcG7R9JVZtJ3FAqnZIuSTjXNRDO/dlDnZB1TndpEW0U9yJzGiARhUFmjKWAVoU6S1e4xx0zs7m0og9et1QyJshFRcjS8xngoDW5lxz2UYzayQttNQg1QD5OeRYOL3GmjLDaA6LCGM7uK3VHEAo0up8QkBtU5RAA604F0fN2Xs8ziJed3BPijy4wBCwFjA1y6RsY/ShnDnHIpnzeJRmGtuwHdBQA2CIbqgJWE4DkNG+rkwk3EBVEaZIA+SoodIoKWZenJCsmRYtsxXJKybjivJx3jNXF/NmDXp2IS0ynOcMI1HD2E5Pna1HWzhLJQwhm3f6/Nv5QSbmiYUIoUbIW9kLJqUUIIKhJBmo0YY1uxuLOyU55pLUvEEOS9M2GRdGaSu7X1/QxzR4X2ZB82G+y0hoLXtsCR0atRVSS8baOy9lPUJV1YmMRNt7qtk628GMBuckI9mGsiZ6p7k54b5MHNQViPRStMYguMKUvUIGfh/BgKVqI6a8BbCCyTBPEcHcG0rLbC+MmIFWzCj63JZPCkGaECHLkChN7eE3WCpDFByMiZO4KrTGZXMDsBDrtQSOV4OpxRtdxiNPFmxx7u3pN4JKwhGcmxQOgTEU4e05qs3ZafI2QKBFw/AQIm0nWCBoCdQW68/nS1kBpKzyrjtee6tdiwtUumjisjo6fDpwWeK8EfI3wR4VVlcz8pmfccVht92UlvAuKgi5K2wOeUVaLO4tMsnZpmS1SqtQbcAByGwniygmRn+8Kr0tzost9ppVes4WDjc4L+CikMtPr2Wjjx2igMVdte2mmS9zwNFm1UDpt5FSFqVphknbnGEtuKJVKS0RRGZwCi1I6txNnVET7sOtk2JXXc9coW614yV6vrkEly750eV5bAY92yAu3ATjISleJBMk8z7HVPGJRM5wIxRqlBqqpkJiJlKcGiqcauXabKUNutiths1xBy86rMzyCGcMcqFcHRZnWbjZix1CpCuCPZK9NZyCbEeNCWjTz2xOwpZdKBLsUzVtSS6zhYiz/22tUAKyEgntMtUJprrfVZGl8zSjebdar8p8DNTBzuX80Yc4agkaloD48oaXxbiRttyIPKSQmUqHNt1ZmUx5880tjSEYastZ2bnGIKKaMyoZIa8GgBqrd6laDRGhGKdt/+NPbXTx8I3vb1k6t9D62Nh3wzBElI45t6K3DokWbBqVFFtChxlTOGz4JUoHgMP0h/dRRbbovSEuMzNxQYI1B8SX71AoaRc14O5tkDfmlYpIZmRGKPYTUCNzWPdUXa92AXpPrtfQMhN9PjvhEH1fxelmlFNLzekyqMTi1HRzxW7KhRZCibSZx9GOrTsE1TyEpDMA3JVpv63hhIxK5FSMcyE7IkKpUV3psrAozfrN+jwjWRxUMcx+5JBUz7qnA8yfEq+Aetcx76sm7ap5eXyiKaXPNJJDwL+UqmZUYom8JNiq32RO+30lBWOFm2oN5TRl69uWWYFYqEC3PjrPSnNXRrFl1+fVKpJmxGu+oysA/hLqHTyQru6z9xVs5h8uIERDaObux7nxjPP8cs7MNCqLyTmsa1WdqmKs7YRyRsqNRWN7Hn3DRsv65HyaUY9lYP1Mw1kQlwZ+6KqJOAwZuQyxZjkfWcfHrhhpM/FsLgu0Q/9wwDmh5QEQAm0J+2gsLWadzlg4VXYe+2qNAzlGyUM3TrdaOeZ6+sx0CXlRYm7aFqiZgDHT1eYSwRIqNOd9GUaAV85inwW7YRUXvDLRYBVc/vVlgr5otVljlmbb7C0fdaf32O1t6PNiolLaV9JBNg6ilb4vbe7KMlVmjgKynQKpdhd2WEEeUsxZ4RqwqUPwd4kmPEEVD4cALuO7be4an6G3y+HKoFoHI7MFfq1ggc49C8pQamcWSS+TGyurMWFgf3RrV/fT5O7ImffXKEGCGqGDODAGsETyamU3XkF1lg0m6hFVvG4kydm4H9LVlrjMTLT5gemwkCSFtHlaraWE9EJVeVcgd5uq9TnIWDNtjhD6zfHFVKfOnRIiqqUy2rm6MiIbWHVZo76STpFXV2YJ+HVlRR+7YhDBnI2NLcM2wEzOLEbMeRpahmaNbm1sUxQgwTqMwVIUgd4gWDc04LW4yZT0zZ1pPNu5F1ctGRbKitqwV8xMpssg9YolvxqdH57zIcJ6gmBqfbhz4LkApqDlJWKkw5tzBhGt0elBOmcKojljkhd6J9eGqiBXhckMYriVUx337o5aKEk5MazdfyM/LiXBw8deBoez/7789Yz3XN9jN2PFRV3m+dYtYndzHhgByxxsgUkDJpgx25EktAKrZu4+F/pAWDGf9gL6GUaRrW5HfWdk6RmCMmbIBrPtvYxwdNg+l3vhkjugmc6txYS/vyo2KgmW3K0x34W5wyEX+zGnXpAZJ5gRjZc+52re5oaZIzO9VHSIHNNElyGEsr69292b9kPJGWBpaswGn9rlOiwh1JW9xcstdbVb5IYq3jT3AGzG4LXEiEvqd/WbJlgaqbkM5AqRbllh3paBymTnE43uRkuWRmZX2dx+eL7f9as2zMZcU52TymUiyiwtrptyXbvbK5WGJx9v0t7DWgqhNsjroOVsG/Cg53OiNB/rPYdXxWp7NgkzpMiCaqB3iSKWmo0U3R+d3tuPF1ZCsPSEatpc17Y2dWcJ73BZe1mK8IuMurzrG0v2uBWjH2qtl8VzQH4YBbV8poeS7lElOqM111jX5t2AzjZ7a/QCI9wz5wXJ8OHWU/V8Z5tqBmtA2CHUMbPmLgkw54E/B9d1WZSYDdileO+/Yg1M85g7gOYy+sx/4JWUZXYsAqxkBAoEpyEkKmhoB/2kkFGZCaGU2hDuRKb50Z39tN97MXMUjSpm1rq2zdjqHQ3t4MKIPqSdTbIlkNCSnj1hxVJizrx/2TKcqwVNaLZdsjY0e9nD9OZyQl4Q4ezG6t6IY9IcS2ZWdn3GBMksoeRwe7zY11pdonFKIi/pFW3MkZr2kw2WXLTq0l7w8j8+ccUgNG1BmC1tW8u+nDX+kP2h2V2WBAw13C2lYJ9gpopzqm4WlZQiSuddykLFPJNmR3cuthfbvpTizqF2SxDYSPeQZAfQnld86KKJ19bJliVdBLux5xqbwTxbI14ShhbrcGakzXJRYGq2zVbaDouEhSKNGd4xJnWWY5UiEhR6VarKzKRAuYP62q5z6wzm2ZLpBWxpEqitlKu13c3cgTmq07VV4mXh4jErxlb/n7vAMrPNs4q0eSpnm7E553lsJa1kFxlp82CzumdhBRIhd9UdokuVjsgipafCacpguaP+vbGOzE5jDetIazNW2pgVeisSIJFaOtObtTz42ktVuwEN3LCKhyKpSQo0bV8iNF16TWYzSEuOtQ8oUu1k2YJI1SBMU2aAU0ZfCrKGGheVBlDJ09Wz7+yEVGBTytqW1majATicV8UF7GhJ4BJo6XKLidflfBwSjHljyjyN5KGVSy1GXYyGrPXfpIrLQ/NIBzMxGk9sJqlPnXZC5wjAEWbKlnpl2NG6u6iJ44GuFnjPx8bOuXTDlZY8pUmopbZ/sBvLlr8q2A2JgNlvEcziCYDz8e7LzFq1J8e5nUFJY9qKiIgK71yKSAGIpCUSfrG1vljGKnPfrBxYGgG33Dre73bnuw0nO3Zy4U2IsJY1NCLxHMXrMpe6voduxlSPQ4KFmbdW5wmzzhTgB6LaXLRlmiEToquqX3W5HwN1autqqhNWmUnWLUrvsqRnFBFk1rkLBGbdJpmw9HmhmGpTDpeRb6Lm8Zea4Wbykqk8+7YnR/cLv0ImIvd0kA6xjeaJBgHmEpa0UZhhDB+m/b5bH93KOk4Zav0vHRkp1F2cbtYmGiLaWeqEsnCulZkx6YZ5AiLaXMWmOVji4Ia8zB7hsFsuQ0jpyao4hyfXmtYgtJ4cttWynJNy86aINdmVOu4uymrT9bYXlEazmlMaosbqdNUB8pjUW6ZEMyKrDKwojdnNXPC9eWNJ4GVt9UBjaf8sITKu/PRJqphqUgkiS5KteJKBOV7LlC0j9KsZlaCIid26nt1/S/1q6AwakwRjZ12J0h1vEHRTreY5Py5NbQc5kZAbpvlOl1KSUgtthXNPux3W5UYNgmhzQd9fMABUYwc4vIhQNNJDY1rKkJdvm26ZQWdQATuycu+eb257NtJHvz4dg75ar9nGZOYclcGQgb7Mx8VHGn0KszmgkBr1sX1N5Gz9GzZxzQ8fNO0/EivO6zJzT7JQEtxFogpJGgsiW1MIC1RblYCWCdlRv7mYiG4o3gDqOk0o654lw3JEKRjbVCYYlQFRlXCzHNXG083epI1miuayDGXeaThsukNaM2sabgSLj8SKLXpuL7J2IG47itNbsfuyNQBEyMxTqgANqrCjo7o/v7DipSsYx9od9e30AIKumSdiraSjYMLVCiBp3sYUtVy3SbCcR5bzqI7rYe8Tr0esombR2xsvTh/zF1yAo2b3fe5PZwsDKMFKOcppnMbJrKx7kok2zFZzdKckrAXbsFb8BOC4nI84O0peySWX27sh0DXjcX2P3RT80hFiNqe8NEDXUlWqlTHnOGfeHgnAhqH9RXMdsJwhl7kVZH7p7O/n3Pjw8ysCXCZ/S+511cQffs9r/2vXDcT7+mN4dJO+z6Wb3y61hmufxuv//H9zPfk+9JgXPU6w/15cPxTsB+36oWA/aNcPBftBu34o2A/a9UPBftCuHwr2g3b9ULAftOu/t4L9fwAdDmU52M1JSAAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"rank 58 Fnorm 513.8683243934796 # of m.e. 30566\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"rank 196 Fnorm 8.531916171225453e-11 # of m.e. 103292\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# SVDを実行\n",
"a = np.asarray(gray_img)\n",
"u, s, v = svd(a)\n",
"fullrank = matrix_rank(a)\n",
"print(\"full rank => \", fullrank)\n",
"\n",
"# 陽に必要な行列要素の数を計算する関数\n",
"def num_of_me(u,s,v,rank):\n",
" m,n = u.shape\n",
" return m * rank + rank + rank*n\n",
"\n",
"#低ランク近似を得る\n",
"for factor in [0.05, 0.1, 0.2, 0.3, 1.0]:\n",
" rank = int(factor*fullrank)\n",
" ur = u[:, :rank]\n",
" sr = np.matrix(linalg.diagsvd(s[:rank], rank,rank))\n",
" vr = v[:rank, :]\n",
" b = np.asarray(ur*sr*vr)\n",
" img = Image.fromarray(np.uint8(b))\n",
" USVd = np.dot(ur, np.dot(sr,vr))\n",
" print(\"rank\",rank, \" Fnorm \", linalg.norm(a-USVd,\"fro\"), \" # of m.e. \", num_of_me(u,s,v,rank) )\n",
" display(img)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "YOB6BFXV58Th"
},
"source": [
"幾つかのrankについて元のグレースケール画像との差分(フロベニウスノルム)と、陽に必要な行列要素の数、近似後の画像を表示させてみた。\n",
"\n",
"元の行列(rank=196, 行列要素の数103292)に対して\n",
"rank=39, 58などでの近似を用いることで、大体2-3万の行列要素で画像を表現できる事がわかる。\n",
"\n",
"今の場合は一枚の写真のみでサイズもたかがしれているものの、例えば画像認識タスクを行う機械学習モデルの訓練の場合には、一般に大量の画像データ(とラベル等)が必要になるため、近似で削減できる情報が数分の1スケールだとしても馬鹿にはできない。\n",
"\n",
"実際にはSVDを計算するコストも勘定に入れなければフェアな評価は難しく、SVDを陽に用いたアーキテクチャがやりたいタスクに対して最適である保証はないが、実際に画像認識モデルを作り学習を行う際には一考の余地はあると言えるだろう。"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "zTJqCqNnU5hR"
},
"source": [
"### 練習問題\n",
"\n",
"上では、`numpy.linalg`にある`svd`でSVDを実装し、`scipy`の`linalg.diagsvd`関数を用いて低ランク近似を計算した。\n",
"かんたんな行列の例を参考にSVDの結果得られる$\\Sigma$の行列要素を書き換えて、もとの行列の低ランク近似を計算し、ライブラリの出力と一致するか確かめてみよう。※SVDや行列積などはnumpyを用いて良い。"
]
}
],
"metadata": {
"colab": {
"collapsed_sections": [],
"provenance": []
},
"kernelspec": {
"display_name": "Python 3.9.13 64-bit",
"language": "python",
"name": "python3"
},
"language_info": {
"name": "python",
"version": "3.9.13"
},
"vscode": {
"interpreter": {
"hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
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}