NumericalMethods/HW2.ipynb
2022-11-11 04:29:03 +03:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 72,
"id": "ddfbd19c",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.manifold import TSNE\n",
"from sklearn.datasets import load_digits\n",
"from sklearn.preprocessing import StandardScaler\n",
"import time\n",
"\n",
"from scipy.sparse.linalg import svds as scipy_svd\n",
"from numpy.linalg import svd as numpy_svd\n",
"from sklearn.utils.extmath import randomized_svd as sklearn_svd"
]
},
{
"cell_type": "code",
"execution_count": 73,
"id": "28566ca9",
"metadata": {},
"outputs": [],
"source": [
"plt.rcParams.update({\"font.size\" : 15, \"font.family\" : \"serif\"})"
]
},
{
"cell_type": "markdown",
"id": "ac58d544",
"metadata": {},
"source": [
" ### Задача 1"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "fe997d27",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0.28824414, -0.72344481, -0.31466461, ..., 0.48469425,\n",
" -0.48534312, -1.75019397],\n",
" [ 0.97365819, -0.3006159 , 0.23759037, ..., 1.7838543 ,\n",
" 0.98583849, 0.47303252],\n",
" [ 0.97682293, 0.66719562, 0.34751901, ..., 1.08327426,\n",
" 1.34790485, 0.82349545],\n",
" ...,\n",
" [ 0.45672919, -0.83670329, 0.28055832, ..., -1.27079724,\n",
" 0.82394745, 0.08654333],\n",
" [-0.87594766, 0.32259166, -1.46007173, ..., 0.58111975,\n",
" 0.75498419, -0.69455994],\n",
" [-2.75542392, -0.99751411, -1.08212821, ..., 1.93992511,\n",
" -0.38518655, 0.20831918]])"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 2000\n",
"A = np.random.normal(loc=0.0, scale=1.0, size=(n, n))\n",
"A"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "0c04f8c3",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/goloshch/.conda/envs/NPM/lib/python3.10/site-packages/sklearn/utils/extmath.py:368: FutureWarning: If 'random_state' is not supplied, the current default is to use 0 as a fixed seed. This will change to None in version 1.2 leading to non-deterministic results that better reflect nature of the randomized_svd solver. If you want to silence this warning, set 'random_state' to an integer seed or to None explicitly depending if you want your code to be deterministic or not.\n",
" warnings.warn(\n"
]
}
],
"source": [
"#np.linalg.svd\n",
"t_numpy = %timeit -o -q -n 2 -r 2 numpy_svd(A)\n",
"u, s, vh = numpy_svd(A)\n",
"u, s, vh = u[:,:2], s[:2], vh[:2,:]\n",
"A_svd = u @ np.diag(s) @ vh\n",
"\n",
"\n",
"#scipy.sparse.linalg.svds\n",
"t_scipy = %timeit -o -q -n 2 -r 2 scipy_svd(A)\n",
"u, s, vh = scipy_svd(A, k=2)\n",
"A_svds = u@np.diag(s)@vh\n",
"\n",
"#sklearn.utils.extmath.randomized_svd\n",
"t_sklearn = %timeit -o -q -n 2 -r 2 sklearn_svd(A, n_components=2)\n",
"u, s, vh = sklearn_svd(A, n_components=2)\n",
"A_rsvd = u@np.diag(s)@vh"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "c7e12c91",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Error\n",
"_____________________________________\n",
"A_svd : 1995.4380988107664\n",
"A_svds : 1995.4380988107664\n",
"A_rsvd : 1995.6080648210457\n",
"\n",
"Time\n",
"_____________________________________\n",
"Time_svd : 2.94 s ± 46.8 ms per loop (mean ± std. dev. of 2 runs, 2 loops each)\n",
"Time_svds : 563 ms ± 9.18 ms per loop (mean ± std. dev. of 2 runs, 2 loops each)\n",
"Time_rsvd : 121 ms ± 6.46 ms per loop (mean ± std. dev. of 2 runs, 2 loops each)\n"
]
}
],
"source": [
"print(\"Error\")\n",
"print(\"_____________________________________\")\n",
"print(\"A_svd : \", np.linalg.norm(A_svd-A, ord=\"fro\"))\n",
"print(\"A_svds : \", np.linalg.norm(A_svds-A, ord=\"fro\"))\n",
"print(\"A_rsvd : \", np.linalg.norm(A_rsvd-A, ord=\"fro\"))\n",
"print()\n",
"print(\"Time\")\n",
"print(\"_____________________________________\")\n",
"print(\"Time_svd : \", t_numpy)\n",
"print(\"Time_svds : \", t_scipy)\n",
"print(\"Time_rsvd : \", t_sklearn)"
]
},
{
"cell_type": "markdown",
"id": "a37e1433",
"metadata": {},
"source": [
"__ВыводЫ:__\n",
"\n",
"- рандомизированный svd работает быстрее всего, он экономит вычисления за счет приближенного ответа\n",
"\n",
"\n",
"- нормы фробениуса для всех вариантов получились очень большие; думаю, что это связано с тем, что матрицы случайные, в них нет каких-то закономерностей, которые часто встречаются в матрицах из реальных задач(для реальных матриц убывание обычно экспоненциальное)\n",
"\n",
"\n",
"- как видно из графика ниже, сингулярные значения убывают медленно, это не позволяет делать хорошие малоранговые приближения"
]
},
{
"cell_type": "code",
"execution_count": 76,
"id": "14d641f9",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"u, s, vh = numpy_svd(A)\n",
"plt.figure(figsize=(12, 6))\n",
"\n",
"plt.subplot(121)\n",
"plt.semilogy(s)\n",
"plt.xlabel(\"n_component\")\n",
"plt.ylabel(\"nth singular value\")\n",
"\n",
"plt.subplot(122)\n",
"plt.plot(s)\n",
"plt.xlabel(\"n_component\")\n",
"plt.ylabel(\"nth singular value\")\n",
"\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"id": "b7868f15",
"metadata": {},
"source": [
"### Задача 2"
]
},
{
"cell_type": "markdown",
"id": "4369bc2a",
"metadata": {},
"source": [
"- $(A^TA)^{-1}=(V\\Sigma^TU^T U \\Sigma V^T)^{-1}=(V\\Sigma^T \\Sigma V^T)^{-1}=(\\Sigma^T \\Sigma V V^T)^{-1} = (\\Sigma^T \\Sigma )^{-1}=\\Sigma^{-2}$\n",
"\n",
"\n",
"- $(A^TA)^{-1}A^T = \\Sigma^{-2}V\\Sigma U^T$\n",
"\n",
"\n",
"- $A(A^TA)^{-1} = U\\Sigma V^T\\Sigma^{-2}$\n",
"\n",
"\n",
"- $A(A^TA)^{-1}A^T = U\\Sigma V^T\\Sigma^{-2}V\\Sigma U^T = \\Sigma^{-2}U\\Sigma V^TV\\Sigma U^T = \\Sigma^{-2}\\Sigma^2=I$"
]
},
{
"cell_type": "markdown",
"id": "4116a2c8",
"metadata": {},
"source": [
"### Задача 3"
]
},
{
"cell_type": "code",
"execution_count": 349,
"id": "127916f3",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 0.6 -0.8] [-0.8 -0.6] 14.142135623730951 7.0710678118654755\n",
"[-0.70710678 -0.70710678] [-0.70710678 0.70710678]\n"
]
}
],
"source": [
"#Считаю, что собственные значения и векторы разрешается искать не ручками, а в питончике\n",
"A = np.array([[-2, 11], [-10, 5]])\n",
"\n",
"#1) Считаем правые сингулярные векторы V\n",
"res = np.linalg.eig(A.T@A)\n",
"v2, v1 = res[1].T\n",
"s2, s1 = res[0]**0.5\n",
"v = np.array([v1, v2]).T\n",
"\n",
"#2) Считаем левые сингулярные векторы U\n",
"u1, u2 = v1@A.T/s1, v2@A.T/s2\n",
"u = np.array([u1, u2]).T\n",
"\n",
"print(v1, v2, s1, s2)\n",
"print(u1, u2)"
]
},
{
"cell_type": "code",
"execution_count": 362,
"id": "6c037a22",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Right singular vedctors : [ 0.6 -0.8] [-0.8 -0.6]\n",
"\n",
"Left singular vectors : [-0.70710678 -0.70710678] [-0.70710678 0.70710678]\n",
"\n",
"Singular values : 14.142135623730951 7.0710678118654755\n"
]
}
],
"source": [
"# Меньше минусов\n",
"v1, v2 = v1, -v2\n",
"u1, u2 = u1, -u2\n",
"\n",
"print(\"Right singular vedctors : \", v1, v2)\n",
"print()\n",
"print(\"Left singular vectors : \", u1, u2)\n",
"print()\n",
"print(\"Singular values : \", s1, s2)"
]
},
{
"cell_type": "code",
"execution_count": 361,
"id": "38da9e8a",
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x432 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Рисовашки\n",
"t = np.arange(0, 2.01*np.pi, 2*np.pi/100)\n",
"n = len(t)\n",
"x = np.cos(t)\n",
"y = np.sin(t)\n",
"\n",
"x_new = np.zeros(n)\n",
"y_new = np.zeros(n)\n",
"\n",
"for i in range(n):\n",
" x_new[i] = A[0,0]*x[i]+A[0,1]*y[i]\n",
" y_new[i] = A[1,0]*x[i]+A[1,1]*y[i]\n",
"\n",
"plt.figure(figsize=(12, 6))\n",
"plt.subplot(121)\n",
"plt.plot(x, y, color=\"black\")\n",
"plt.plot([0,v1[0]] ,[0,v1[1]], color=\"blue\")\n",
"plt.plot([0, v2[0]], [0, v2[1]], color=\"red\")\n",
"plt.xlim(-1.5, 1.5)\n",
"plt.ylim(-1.5, 1.5)\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.title(\"Unit circle\")\n",
"plt.grid()\n",
"\n",
"\n",
"plt.subplot(122)\n",
"plt.plot(x_new, y_new, color=\"black\")\n",
"plt.plot([0,s1*u1[0]] ,[0,s1*u1[1]], color=\"blue\")\n",
"plt.plot([0, s2 *u2[0]], [0, s2*u2[1]], color=\"red\")\n",
"plt.xlim(-15, 15)\n",
"plt.ylim(-15, 15)\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.title(\"Unit circle after transform A\")\n",
"plt.grid()\n",
"\n",
"plt.tight_layout()"
]
},
{
"cell_type": "markdown",
"id": "76355bef",
"metadata": {},
"source": [
"$||A||_2 = \\sigma_1, \\; ||A||_F = \\sqrt{\\sigma_1^2 + \\sigma_2 ^2}$"
]
},
{
"cell_type": "code",
"execution_count": 360,
"id": "2957d83e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A2 = 14.142135623730951\n",
"AF = 15.811388300841898\n"
]
}
],
"source": [
"# Нормы\n",
"print(\"A2 = \", s1)\n",
"print(\"AF = \", (s1**2+s2**2)**0.5)"
]
},
{
"cell_type": "markdown",
"id": "839a440f",
"metadata": {},
"source": [
"$A^{-1} = V\\Sigma^{-1}U^T$, $\\Sigma^{-1} = \\begin{pmatrix}\n",
"\\frac{1}{\\sigma_1} & 0\\\\\n",
"0 & \\frac{1}{\\sigma_2}\\\\\n",
"\\end{pmatrix}$"
]
},
{
"cell_type": "code",
"execution_count": 359,
"id": "f97fba41",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[1.00000000e+00 3.74700271e-16]\n",
" [7.63278329e-17 1.00000000e+00]]\n",
"[[ 1.00000000e+00 -1.56125113e-16]\n",
" [-1.66533454e-16 1.00000000e+00]]\n"
]
}
],
"source": [
"# Обратная матрица через SVD\n",
"v = np.array([v1, v2]).T\n",
"u = np.array([u1, u2]).T\n",
"s = np.array([[s1, 0], [0, s2]])\n",
"sinv = np.array([[1/s1, 0], [0, 1/s2]])\n",
"Ainv = v@sinv@u.T\n",
"\n",
"print(Ainv@A)\n",
"print(A@Ainv)"
]
},
{
"cell_type": "code",
"execution_count": 358,
"id": "0e1b0097",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([1.5+9.88685997j, 1.5-9.88685997j]),\n",
" array([[0.72374686+0.j , 0.72374686-0.j ],\n",
" [0.23028309+0.65050763j, 0.23028309-0.65050763j]]))"
]
},
"execution_count": 358,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Собственные значения\n",
"np.linalg.eig(A)"
]
},
{
"cell_type": "markdown",
"id": "331d2bf0",
"metadata": {},
"source": [
"### Задача 4"
]
},
{
"cell_type": "markdown",
"id": "5a9196fc",
"metadata": {},
"source": [
"1) $A_{ij} \\simeq h_i \\eta_j \\Leftrightarrow A=h \\eta^T$, по теореме о ранге произведения \n",
"$rang(h\\eta^T) \\leq rang(h) + rang(\\eta^T) - 1 = 1$, т.е. аппроксимация имеет ранг 1\n",
"\n",
"2) По теореме Эккарта-Янга-Мирского лучшим приближением матрицы A ранга r является её обрезанное сингулярное разложение по первым r сингулярным числам, причем $||A-A_r||_F=\\sqrt{\\sum_{i=r+1}^n\\sigma_i^2}$\n",
"\n",
"3) SVD-разложение даёт $A = U\\Sigma V^T$, где $U=(u_1 \\;u_2\\;...), \\Sigma = Diag(\\sigma_1, \\sigma_2,...), V=(v_1 \\;v_2\\;...)$, $u_i, v_j$ - векторы-столбцы, причем $\\sigma_i\\geq 0$\n",
"\n",
"$A_1 = \\begin{pmatrix}\n",
"u_1 \\\\\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"\\sigma_1\\\\\n",
"\\end{pmatrix}\n",
"\\begin{pmatrix}\n",
"v_1^T\\\\\n",
"\\end{pmatrix} = \\sigma_1 u_1 v_1^T$\n",
"\n",
"Тогда $h=\\sqrt{\\sigma_1}u_1, \\; \\eta = \\sqrt{\\sigma_1}v_1$(коэффициенты можно и по-другому выбрать, но мне нравится так)\n",
"\n",
"4) $\\delta_{err} = \\frac{\\sqrt{\\sum(A_{ij}-h_i \\eta_j)^2}}{\\sqrt{\\sum A_{ij}^2}} = \\frac{||A-h\\eta^T||_F}{||A||_F} = \\frac{\\sqrt{\\sum_{i=2}^n \\sigma_i^2}}{\\sqrt{\\sum_{i=1}^n \\sigma_i^2}} = \\sqrt{1-\\frac{\\sigma_1^2}{\\sum_{i=1}^n \\sigma_i^2}}$(доля необъясненной дисперсии фактически)\n",
"\n",
"5) $A_{ij} = \\sum_{\\alpha=1}^K h_{\\alpha i} \\eta_{j \\alpha} \\Leftrightarrow A = \\sum_{i=1}^{rang(A)}\\sigma_i u_i v_i^T$, т.е. $K=rang(A)$"
]
},
{
"cell_type": "code",
"execution_count": 327,
"id": "435bc6dc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"delta_err : 0.7742251888975445\n",
"delta_err_formula : 0.7742251888975445\n"
]
}
],
"source": [
"A = np.load(\"A.npy\")\n",
"\n",
"u, s, vh = np.linalg.svd(A)\n",
"A_svd = u[:,:1] @ np.diag(s[:1]) @ vh[:1,:]\n",
"\n",
"print(\"delta_err : \", np.linalg.norm(A-A_svd, ord=\"fro\")/np.linalg.norm(A, ord=\"fro\"))\n",
"print(\"delta_err_formula : \", (1- s[0]**2/np.sum(s**2))**0.5)"
]
},
{
"cell_type": "code",
"execution_count": 328,
"id": "55837ecb",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[5.00299422e+01 4.99770106e+01 2.54470684e+01 2.45000000e+01\n",
" 1.11272856e-14 9.55930610e-15 8.62751654e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 4.99613766e-15\n",
" 4.99613766e-15 4.99613766e-15 4.99613766e-15 3.65548473e-15\n",
" 3.20651151e-15 1.21059206e-15]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.semilogy(s)\n",
"print(s)"
]
},
{
"cell_type": "code",
"execution_count": 117,
"id": "480b8e58",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"delta_err : 3.2502455784278293e-15\n"
]
}
],
"source": [
"u, s, vh = np.linalg.svd(A)\n",
"A_svd = u[:,:4] @ np.diag(s[:4]) @ vh[:4,:]\n",
"\n",
"print(\"delta_err : \", np.linalg.norm(A-A_svd, ord=\"fro\")/np.linalg.norm(A, ord=\"fro\"))"
]
},
{
"cell_type": "markdown",
"id": "0f89340f",
"metadata": {},
"source": [
"__Вывод:__\n",
"\n",
"- По сингулярным числам видно, что ранг матрицы равен 4, ошибка такой аппроксимации это по сути ошибка вычислений\n",
"\n",
"\n",
"- Задачка забавная, я бы за неё больше баллов ставил"
]
},
{
"cell_type": "markdown",
"id": "a8688c28",
"metadata": {},
"source": [
"### Задача 5"
]
},
{
"cell_type": "code",
"execution_count": 91,
"id": "4a205d41",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.0\n",
"16.0\n",
"[ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.]\n"
]
}
],
"source": [
"digits = load_digits()\n",
"A = digits.data\n",
"y = digits.target\n",
"\n",
"print(A.min())\n",
"print(A.max())\n",
"print(np.unique(A))"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "98116264",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x432 with 9 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6, 6))\n",
"for i in range(1, 10):\n",
" plt.subplot(3,3,i)\n",
" plt.imshow(A[i].reshape(8, 8))\n",
"plt.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "fefcb6e8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 9 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Такой вариант нормализации работает так себе\n",
"#(вычет среднего+деление на стандартное отклонение)\n",
"ss=StandardScaler()\n",
"ss.fit(A)\n",
"A_transform = ss.transform(A)\n",
"\n",
"plt.figure(figsize=(6, 6))\n",
"for i in range(1, 10):\n",
" plt.subplot(3,3,i)\n",
" plt.imshow(A_transform[i].reshape(8, 8))\n",
"plt.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 143,
"id": "31c0c6c0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x432 with 9 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#min-max нормализация\n",
"#То что надо\n",
"A_transform = 2*(A/A.max()-0.5)\n",
"\n",
"plt.figure(figsize=(6, 6))\n",
"for i in range(1, 10):\n",
" plt.subplot(3,3,i)\n",
" plt.imshow(A_transform[i].reshape(8, 8))\n",
"plt.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 159,
"id": "0cbf466b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"((1797, 64), (64,), (64, 64))\n"
]
}
],
"source": [
"u, s, vh = svd(A, full_matrices=False)\n",
"v = vh.T\n",
"print((u.shape, s.shape, v.shape))\n",
"\n",
"n = 2\n",
"u, s, v = u[:,:n], s[:n], v[:,:n]"
]
},
{
"cell_type": "code",
"execution_count": 145,
"id": "71184634",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1797, 64)\n"
]
},
{
"data": {
"text/plain": [
"1332.574288788176"
]
},
"execution_count": 145,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A_new = u @ np.diag(s) @ v.T\n",
"print(A_new.shape)\n",
"np.linalg.norm(A_new-A)"
]
},
{
"cell_type": "code",
"execution_count": 199,
"id": "11ed6e84",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 9 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6, 6))\n",
"for i in range(1, 10):\n",
" plt.subplot(3,3,i)\n",
" plt.imshow(A_new[i].reshape(8, 8))\n",
"plt.tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": 200,
"id": "a5282d4e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x7fa5e040db10>"
]
},
"execution_count": 200,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"X = u@np.diag(s)\n",
"\n",
"plt.figure(figsize=(6, 6))\n",
"\n",
"plt.scatter(X[:,0], X[:,1], c=y, cmap=\"tab10\")"
]
},
{
"cell_type": "code",
"execution_count": 201,
"id": "dd4293dd",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/goloshch/.conda/envs/NPM/lib/python3.10/site-packages/sklearn/manifold/_t_sne.py:780: FutureWarning: The default initialization in TSNE will change from 'random' to 'pca' in 1.2.\n",
" warnings.warn(\n",
"/Users/goloshch/.conda/envs/NPM/lib/python3.10/site-packages/sklearn/manifold/_t_sne.py:790: FutureWarning: The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.\n",
" warnings.warn(\n"
]
}
],
"source": [
"u, s, vh = svd(A, full_matrices=False)\n",
"v = vh.T\n",
"\n",
"n = 64\n",
"u, s, v = u[:,:n], s[:n], v[:,:n]\n",
"X = u@np.diag(s)\n",
"\n",
"X_embedded = TSNE(n_components=2).fit_transform(X)"
]
},
{
"cell_type": "code",
"execution_count": 202,
"id": "2d10f578",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, '64 признака - максимум')"
]
},
"execution_count": 202,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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isZsYdkwuVrsJTQ/vj9brlnz/SQkWm4mmehdl2+o6PD6zf8LBr3MGJpOSFdnphMfMVLNYKkogKsn3UYZhUFlaT9XexlbD/zctLuOb1zbjbg7/CFavR7Ji3k7KttZ2eJzJojF0cuueLjmDkiP23EA3CTRN/SorSiCquaaP2bu1hnnPrqOuxbqu9gQzZ9wwhuwBSSx+bzseV3gW9Q7k2ze2cM6vx3d4zEW/m4LQWj8YmHBqEVuXl+N2Hvrw0XQRlp41xZOy25SnKIqPqv70ISs/38Wbf13eKsEDOBrcvP335Tib3DRUOyMag5Sw7fsKUnLiAu6fcelQkgOs9JSSHcc5/zee/GGpmCwa8alWpsweiDUutHqGyaIz7cIhIV1DUWKZqsn3Ec2Nbr59c0u7I1y9boPNS/eTmhNHxa6GiMayf0cd5982kbf//j3lJfWAb176iacXMmJq+yNPMwsSmf2rca225Q1O4d2HVyDxzTzZ1buQIZN9ywgqihKY+uvoI/ZsqvE3SQTO8lL6pgw+9tzBfPD4KjzdmCIgGEITZBQkYLGZuOD2SbiaPTibPCSkWLvVZJIzMJkrHjyOktWVuJo9rP26lPKd9cggwx97UkGXy1SUI4lqrukjzDYd0UEOFRrkDk6mYHgaZ9wwmqzCxIisxmEya4w58VBitdhMJKbZQmoTN1t0Bk/IYsTUPE6/bjTJmXGYrTpmq97haF5boonUnPhul6soRwJVk+8j+g1JwWTW8TgDV3Ez+yeSPzQVgPxhaZx/exr/+vkXrUejdkLovnVXA++ErP6JHP/joSQFaHMPl/gUKz/+wxT2bqmloaaZrP5JfPLMWip21dNymiXNJBh3UmHE4lCUWKGSfB+h6Rpn/2Is7/zze1zNnoPJWNMFo2fkc/QPBiEOq+qbbTrehuCH++smjfTCBMp31mH4T9NMvrb2CacOQOuhHixCCPKKUw6+PuWakbz5l+W4nV4Mr/TftaQwZqZqqlGUzqhZKPsYr9egdGM17mYv/YakYktof+GMFZ/uZMEbW9psb6/rotmqM/umsTRWu9iyfB9mi87wqXnkDEwO63voDq/HoGR1pa92X5REdlFSmw81RTlSdTQLparJ9zG6rtF/RHpQx46ZWUD57no2Ld538HltQqqFCacNYMHrm9v0ZLHYTWT1T0IUCQaO613r7eomrdfFpCh9gUryMUxogpOvHMkxPxhMxe56EtNtpOclIKVk/446Ni3ZB4CmCTRdcMbPRqtBRYoSY1SSPwIkpFoPLpQNvjbvEy8bztiT+7NnUzW2BAtFo9IxWfQoRqkoSiSoJH8ES8uNJy1XdUFUlFim+skriqLEMJXkFUVRYphK8oqiKDFMJXlFUZQYppK8oihKDFNJXlEUJYapJK8oihLDVJJXFEWJYSrJK4qixDCV5BVFUWKYSvKKoigxTM1do/Ru9ftg8VOwaxFkHwVTfwlJudGOSlH6DJXkld6rfBM8eTy4m3yvd3wNi5+ES9+EgSdENTRF6StUc43Se8298VCCP0B64aULwAi81q2iKK2pJK/0XrsWB97udcL8+6G2FFbNgU2fgNcNbgesmwvfvwQ1u3o2VkXppcLWXCOE0IGlQKmU8kwhxADgFSAdWAZcKqV0has8JcYZBgfXLAzkqwd8/w7QraCZQGi+2r70wrG/gBPvCk8sNSVgTYL44JZeVJTeIpw1+V8C61u8fgD4u5RyMFANXB3GspRY1lQFz5xEh0n+cF4nuBvBVe9r4vE4YeFjsP2r0GLZ+BH8bSg8cSw8NAxePMcXn6L0EWGpyQsh8oEzgHuBm4UQAjgR+LH/kOeBPwBPhKM8JQaVLIIP/w8qtoDX5auJh8rdBMuehwHTgzteSti5CMpWQ0IWVGyCLx8Ew33omO1fw0vnwzWfhR6fovSAcDXX/AP4DZDof50O1EgpPf7Xu4F+YSpLiSUVm2HOZbB/XUQu7932ORXbX0Tak0hPn47ZnNr2oK2fwxf3w55lYHja7m/JcMP+tbB/PWQNj0jMihJOISd5IcSZwH4p5TIhxAndOP9a4FqA/v37hxqO0pc018IzJ4OjOnJlOKpomP9rdg3IQGIwdMgfycs7/9D+la/Ce7/0PbQNlmaGuj3BJ/nmWij5Fqp3guGEym1QXQKJ2TD5Gug3oWvvSVG6IBw1+anA2UKI0wEbkAT8E0gRQpj8tfl8oDTQyVLKJ4EnASZOnNiFRlilz1s1x9d2HkG6hKJdDkr6NyGFYOOm35OSMpm4uEIwvPDxba0SvAR259nYnWfDqwkyK1wM3NmE2dPiV9PrhJzR7RfqqPF9CKT0h9WvwYe/9vX+aUPAurfh+Nth5GxIKQQhwvTOFcUn5AevUsrbpZT5Usoi4CLgcynlxcAXwHn+wy4H3gm1LCXGlG9s2w8+AjQDzG5fv3opDfbte9e3o2E/uFqXv3ZYAlsGxNMUZ8Jp0ynNs7F4fAreA38pJpsvGc+9Eda81bogrxve/SX8dYjvDuXBgfD+ze0keADp+4CZ9zt4dAo8Mh5Kl4fvjSsKkR3xeivwihDiHuB74JkIlqVEQaPXy/yqOuZV1LPL4WRkop10s4m55TU4DckPslK4riCLeJMe+AJ548Ac7+sVE2Ga11cTl9KD1+uvuduSadmDp8muUZ5uxdAP1aalJnCZNfZm28iv1H0fChWbfP82fehL0NcvBGsCvHwhbPU/kPV28Q7F2wxV2+D5s+FXqyAuLZS3qygHhTXJSynnA/P9X28DJofz+krv8WJpBb/dUkqzcShJflPbOln/vWQf7+yvYd6koVi0ADeNR50Ln98T8SQvAbfZV74mNTIzZ/p2WOJgzI987fIeB3WJZoSUQOsmE0MXVOfmkF+2izbdOmt2+mr1g2ceSvChMDyw5g1fW72ihIEa8ap02dLaRn53WIIPxCNhc5OT18vaebBqtsO4Szk8qYaTAezLMOPVBZrXIKcKkpLGHTrgtAfhqB+CbsHaTuVboGO3F7bfrXPdXPj8z+EJ2OOAqh3huZaioJK80g3P7C7H0UmCP0ACz5aWt3/A+vfo0qCnLvKYBPWJZvrtbWbMmnqGVeciWj7cNFnhB4/Br7eScum3WBMGAK2blzTdSr4+ov1CpAca9oYv6I3v+x4KK0oYqCSvdNl+Vyd9yQ+zuqGZAV+u5OYNO6n3tEheTZVQvjbM0bVm8UiGbG9i2JZG0prMiGN/EfhAWxIiYzDjJ/yPlJQJCGFB06zYbAWMGfMfbKOu9E2ZEEi/Sb6eNOFSvR3e/Gn4rqcc0dRUw0qXHZ+WyIKahi6d4zAkr5dVs6bBwccThvhq04t6cAC0bvXNZTPy3A4Ps1qzmTD+f7hcVRhGM1Zri5r/tP+Drx5sfYLJBtNvgW8f9/V9D9NdiVz3NtUlpyGS8klOnoCmqT9VpXvUb47SZVsbmrt1nktKtjY5+a62kaNTEny9SSItMRdO/ysMmObvTRMciyVA75YT7/R9SHxxD9TugoEzAAmv/BhkeKc+NqSbXctuozo9Dk2zMnbMMyQljQprGcqRQTXXKF2ypr6JV/d3f4SqISWbm/wfEh0NKOqMyeabFfLKj+CEO33JvNUDXAETroCb18PwM7uU4DuUPRwuegl++hWM/TEsfDzsCR5AkzB4UwXCWYfbXcn3Ky7HMNQkrkrXqZq80iW/2xxw4HLQNCEYHGfzvSg+Feb9vosXMMGo82HQiTD8LF8PncJj4ITfgNcD5et9fdmzhoMtKaRYAdj8qW/5wbrdkD8Zxl4MaQMgPgPWvdN68rIwEoDdaTBoeyMbixOR0ktl1ddkZsyMSHlK7FJJXumS9Y3da6oBsAjBALuVo5PjfRtS+oGmd60nieHxJfDRF7Tdp5sgJ4xNGp/9Cb595NDApn1rYdmzIHQYeDzkjuv4/BBpEvL2OnHYdMry7Xg89REtT4lNqrlG6ZJsa/D1AosQFNjM6IBVE8zOSuGNsYMOPci0JsLgWb7aeVdkDOna8d1RtxcWPBx45Kr0wtYvYOMHvsnKIkgDBpY0MWnxHlJtwyJalhKbVJJXuuSmwpygfmnidY1RiXa+nDyc3SeMYcf00TwyopBk82EJ/QePQ/aoriX6wSd3KeZuKVkAgUbpHiR9TUPDzmi/a2WY6AZY3GBb9lpEy1Fik0rySpecnZXCNfkZHR6jAy+OGsh744uJ0zWEEK0HILUUlwY/nQ/XfA79j/U1hXRkwAxfs0yk2VOD6w259XPfsRHu4qgZXlj0GDhVk43SNSrJK10ihOD3gzte/yXTYuLY1IT2E3sguWPgyg/g0jdh7CUw5NTDmkI0Xw+Zs/7evcC7asDxYInv/DhnnW9QV2eLjYSDuxnevyXy5SgxRT14VbpME4JJSXEsqQs8TfBtA3O7d2EhYOAJvn/gG1y0+EnfqlH5k2HSTyAhs3vX7irdBFe+D0+f7Fs3tleQsPYtmP0Y6JF9FqDEDpXklW55aFh/Zi3d2GYOmzMzkrkoNz08haQWwin3huda3ZE1HG7f5etR8+VfoT607qNhYXh9a+CqJK8ESSX5KCgvL+ett96irKwMTdMoLi7mrLPOIi4uLtqhBa043saSY0byxM79zK+qI9tq5ubCHCamBNHE0ZcIAYl50FzVdp8lwbfoRzgWHQ9W1vDgmpEUxU9I2XtW3Js4caJcunRptMMIK8Mw8Hq9mEwmhBBUVlbyyCOPBDx2xowZHH/88T0codIhKeGh4VB/2CyTQoOkfr7pDXqEAHMcXD4X8if2UJlKXyGEWCalDPiLoWryEeL1evn8889ZvHgxbrebuLg4CgoKKC9vf9rd+fPnk5OTw9ChQ3swUqVDDfvBEaAWL40eTPAAArKGqQSvdJlK8hHy4YcfsnLlStxu37D3pqYmNm7c2OE5UkoWLlyoknxvYk3w1eZbqE42sb1/HA67TlK9hwElTSQ0RbrJxoD962HvSl9PJEUJkupCGWYNDQ188803LF++/GCC74rGxsivd6p0gSUehp/tm6oY2JduYcVRyVSnWmi26exPt7B0XAr18Z307w8HocH+DZEvR4kpqiYfRps3b2bOnDkYhoFhdG9mQlWL74XOfhic9cjtX7KpOL7VQt9oAq+UbBkQz7g1dZGNQxqQURzZMpSYo5J8mNTV1fG///2v28kdKUkTGlNGjgxvYEroLPFw8Rw8letxr/wBcNjAJyGoS+qBP6XsoyAvspOiKbFHJfkwqKur4/HHH+9ygk9KSqKpqYnsmhqmLPoOS10dpW+8gX3sWPL++lfM2VkRiljpDj11EEIzIQOMbrW4wj+nfOsCEn2jgbsyilhRUEm+SxwOB4sWLWLjxo3ExcVxzDHHUFxczGeffYbTGWC2wk40NDQwbvhwBt93PzQ1HZwqpWn5ckouu4xBH36AOGySrJXlK3lq1VOU1JUwJnMM14y+hsKkwjC8O6Uzbk8dNls+TU1bWm3XvJLCnY7IFp6Y45u1U1G6SCX5IDkcDv71r3/R2NiIx+OryZWUlFBQUMCePXvozngDwzBYsXYtiWmpZDe1mCLA68VbXk7TkqXET5l8cPP8XfP59Ze/xul1IpHsqt/FpyWf8tLpLzE4dXCob1HpgMfTwJIlZ+N0Vhy2R6co9Uxya+eAxQxed+DpiUMhNCg8NrzXBJqb97B798vUN6whMXEUhf1/itmcEPZyosHh8X3o2k32KEcSfSrJB2nJkiWtEjz4+sLv2LEjpOt6pWR7v3yyd7ceMi8BT9mhAThSSu5ddC/N3uYW53pxeBw8tOwhHj/p8ZDiUDq2d++buN11QOuukkKYyBx+PWLsfVDyLexbA1/cB+5w9ZLyD4I67qYwXc+npmYp36+4DMPwfSBVVX1NScnjDB92P3l554e1rJ5U2lDKXd/cxff7v0ciGZUxivun3U9+Yn6n51Y5qvjP2v9Q6ajk5MKTOT7/eMod5SRaEok3991RxirJB2nz5s2tEnzYCIGhB+jJ6vViO+qogy/rXHVUNle2OUwiWbF/RfjjUlqpqV2GYbRtktE0nYb6dSTEF8OgGb7ZK5c8DdUOoLvt9DpY433t7/2PgZPv9i05GCZSStauu+Vggm9p/YbbSE4eT3z8oLCVF2mlDaV8vONjGlwNvLrxVepch3o5rSxfyTnvnMPbs9+mX2L7s6fO2TiHPy3608HX7217Dw0NkzDhkR4SLYmMyxrHlUddyfjs8Qfv3Ls002qUHFFJ3uPxsHbtWjZs2EB8fDwTJkwgNze4GROTksKwXmggUpKzZw9eTUM/8ODWaiXh+OOxDjr0h2Y32dHaWZwi1ZYamdiUg+LjBiCEBSkPW0xbgtXaInloGlzxAbx2OexZ0fU1YHWrr2nmR//zrV8bAS7XfpzOve3u/27x6Uyc8BpJSSEstN5D3t36Ln9c+EcMaeAxPMgAiwA0e5s59c1TGZg8kAenPcj729/nvW3v0eBuYGT6SGb2n8kDSx5oc56Bgcv/86511TJ/93y+Lv0au26n0eO7UytOLeaeqfcwPH14ZN9oCI6YuWvcbjfPPvss5eXluN1uhBDous4ZZ5zBuHGdd0vbuXMnL7zwQkRq82ank6PWrCV/9268us6ukSM595mnEabWn8F3L7ybuVvn4mzR5msz2bh10q2cN+S8g9v27t1LSUkJdrud4cOHY7FYwh5zX9fUtIPy8o8ByMw8hbi4og6Pb3aWsWjRyXi9LZ6dGDqWpmwGrnyQ5JMKiT86t3XNrn4fVG2Dub+A6m2+Njhp+FaTmnEnfPcErH/Xd2zeBBg5G/In+aYviCC3u4avvp5IR6uimM3pTDtuIaKzRVyiqKa5hhmvzcDTE3P5d+LKkVdy88Sbo1Z+R3PXHDFJfunSpXz88cdtRqGazWZ+/etfY7FYMAwDt9uNxWIJeBv2yiuvsGFDz4w47NevH6NHj2b8+PGYzb5pZZ1eJ79b8DvmlczDoltwG24uG3EZN467ESEEjY2NPPvss1RUtH44OGvWLI49NvwP7vqqnTufZuu2h5DSd+ckhMbAgTdT2P8nHZ5XV7eKtet+jaOpBGkYxFWOIHftNZhcSXjia9BmNJE8aghJSWPb/v5UbIamKt9C45bozza6cNHJNDVta3e/rsczZswzpKZM6sGouubaT65l4d6F0Q7joJvH38yVo66MStlqgjJg7dq1AacZkFKyatUqGhoa+Pbbb/F4PMTHxzNr1ixGjRrV6thwTjkwfvx4li9f3u7+0tJS9u3bx/Lly/nJT36C2WzGqlt5YPoDVDdXs69pHwWJBQcfCNXX1/Poo48G7Mr5ySefkJyczEg10IqmphK2bnuoVXu0lLBt20NkZpzUpkYvpaS2bjlVld9gMicxfvxL7HrqA/ZnvYIjbT3bj70dc1M2rsRdiCYTYoXAas1h3LgXsVlzDl2ol41UHTvmv3y78Djaf24gArbZ9xa76nexuGxxtMNo5aHlD1HjrOFXE37Vq9rqYzrJ7969m0WLFlFXV0dTU+BVjDweD++9916rbfX19bz55puYTCaGDz/U1paQEL7uZStWrOj0GI/HQ1VVFatWrWLChAkHt6faUtu0w8+fP7/DvvrvvPOOSvJAecUnGAFu7w3DTXn5JxQWXntwm5QGa9b+koqKLzCMZoSwsHXrX5BDDKTmBgFS9+A0b/N9jRu84HCUsHr1DUya+MbBa+3a/SJbt/4Nr7cBXY9n4MBf0b8gOrU+ALs9m+OmLmbxkjNxucraHiANUpIntN3eSyzbtwxd6Hh7ci7/IPxn7X+obK7knuPuiXYoB8XsBGUrV67kueeeY82aNezcuZPq6uounS+l5LXXXqOpqYklS5bw9NNPd/kaHQl2dKzb7Q6qiWjdunUd7ne5XO1+0B1JvJ4mDu8G6WNQWbmAhYtO4osvhrNw0Sls2foXysu/8PeqkUjpxDCcBxP8QYdV2qT00tCwnubmPQDsKPkXmzb9Aa+3HpB4vQ1s3nwP27Y/HJk3GSSrNZWpx84nNfUYdN3XhCSECU2zMWzYfeh67+1jvrFqIy7D1fmBUfDO1ndodjd3fmAPicmafENDA2+//XarAUpeb9c/8Q3D4OGHH6a5Obo/MJvN1uF+r9eLw9H5iEuHw9GnVp+KBI+n/fVaq2u+Ofh1U9MWdu7cSsCHk0HciQuh4/E0ALBt2z8CHrNjx+MMKLoxqrf2mmZm3Njnqaj4goqKzzCb08jLO4+4uPB12Qy3lftXMmfjnGiH0aG/Lvsrdx19V7TDAGIsye/atYuvv/6abdu2dWsEaiDRTvDAwRG1gZLB2rVreeONNwKc1Zqu66SkpHT6cDnWOV3tL9rSVvd/hwzDzf7yT9D1OKQM3I1SSjeG0Rz1GrMQOpmZJ5GZeVJU4+iMIQ1u//p25pXM67W1+APe2vwWt0y8pVeMuA05yQshCoAXgGx8fxVPSin/KYRIA14FioAdwAVSyvC1d/ht3ryZL774grKysu7PANnL1dfXs2vXLvr3799q+9atW3nttdeCusbkyZP55ptvWLBgAR6Ph7i4OE4++WTGjDlyFqCQ0qCpcUvnB4alLDclJY+zc+fT+Kr+gT4wBJrW8V2acsgnOz7hi11f9PoED2DWzGys2sjYrLHRDiUsbfIe4BYp5QjgaOAGIcQI4DbgMyllMfCZ/3VYrVq1ijlz5rBnz56YTfDgazaqrGw92rW5uZmXX345qPOTk5Mxm8188803uFwuDMOgoaGB9957r1V7v1dKnti5nwnfrmXI16v5yZrtlDh6bw+Lrtq//0OaHCURu76mta61GYbT3w4fuC6VkTHziLyb6q43N795cE6a3s4rvaRYU6IdBhCGmryUci+w1/91vRBiPdAPmA2c4D/seWA+cGuo5bUol08++aRbqy/1NV6vl+zs7FbbFi9eHNRzhsLCQs477zweeeSRNt8rt9vNMx98xOoGQa3by85mV6tHkh+U1/J1dQNfTx5GltUcjrcSVXvL3go4NUG4tH/ttr+jSUnjGXXUE2GPYUftDupcdQxLG4ZFj51BcE6vk31N+6IdRtAGJA+gKLko2mEAYW6TF0IUAeOA74Bs/wcAQBm+5pywcTgcQT1sjAWappGXl9dq26ZNmzo8x2KxcNlll5Gfn09TU1O7Hwj7zHZW1Af+PhqAw2vw9O5y7hiUF/CYniINg4b5X+JYuQL76NEkzJjRZhrmzvSe0ZuC+vq1VFcvID19WliuWNZYxs8/+zk76nYgEAgh+O3Rv+WsQWeF5frRVNVcxY/f/zHlTV15ngIaGka35w8KTVljGf9Y9g8uHn4xmXGZUYnhgLAleSFEAvAG8CspZV3L21AppRRCBHyKJYS4FrgWaNPm3BGr1Yqmad3qNdPXJCcnt9nWUZ99s9nMLbfcgtXqW5fUZrNhsVjafCgawPyhHU/p4JKSxbXRXXfWXVXFtjPOxGjRhVUkJDDo448wp6cHfZ283POprPwaKaPdBOXrjrli5VUce+yX2G2hfYBKKbnmk2vYUbej1fY7vrmDNGsaU/OnhnT9aNlUvYnn1z7P17u/ptrZ9cd5uqZHrRm32lnNM2ue4b/r/8sD0x5gZuHMqMQBYeonL4Qw40vwL0kp3/Rv3ieEyPXvzwX2BzpXSvmklHKilHJiZmbwn3i6rjNxYsBRvFGh65GrJU6ZMqXNtmOOOebgdActmc1mbrrppoMJHnx3AjNnzmwzF055QgpuU8ef8zowJL5nHg66du9m969uYuPkKWw+cSaVzz6L9HrZdd11rRI8gGxoYMvU4yi99TaqXngR9/6Av14AeL3NNDZuISlpHKKdSd6iw2Dlyo6nUgjGuqp17K7fHXDfdZ9dR6Or7y0O/9rG1zh/7vnM3Tq3ywleQ2Ng0kDcXZ0crgvXD5bT6+S2r2+jyR29MSoh/8YLX5X9GWC9lPKhFrvmApf7v74ceCfUsg5XXFzcKx5cCSHC1mXzcImJiUya1Hb+kMLCQmbNmuWb7sBqxWQykZOTw4033hiwL/zEiRNJnjaDGnsCbk1nX2Iq3xSPRnaS9CxCcG1B5G83PeXlbP/hedR/8glGXR2ePXso/+fD7LnjDpyrVrd7Xt0777DvwQfZevIsaj/4sNU+KSXbdzzBl19NYNF3Z/DNgskRbZPvjqamrezb9z4NDR03v3WkylGFR7Y/SdcJc05g8d7eNQVARxrdjdy76N5uN7X8cMgPmVU0K6QYdPR2k3lX49I1Papz7ISjuWYqcCmwWgixwr/tDuB+YI4Q4mqgBLggDGW1Ulpa2vlBEWYymZg2bRrz58+PyPVHjx6N1k7b86RJkxgzZgxlZWXExcWRkZHR4bXOnTyRqTIed5CfRxkmnadGDWBwXORr8lUvvYR0OKDF7bVsbqbunbmdn+zxID0e9t5xBwnHTUX3Twu9t+wttm9/FCmjP9ahPVJ6WLf+NsAgPn4QY8b8B6SktnYZZnMKKSmTOn2WMDK94+kqmr3NXP3J1YzLGse/TvoXcebePSBu2b5leAOOSg7OmQPPJD8xn6dWP9WtaQ90ofObSb9BR+eexaFPT+A1vIhgRtBFSDh613xD+2MAI9oQlZiYiK7rkVnMIwg2m41p06Zx7LHHsnPnTrZu3Rr2Mr777jumTZvW7qhXi8US9LOM/nYrvx+Ux11b9nR4nEUI7hiYw7X5me1+wISbY9lypCu0/s9C12j4+muSzzgDgJKSJ6Ke4M3mDIoKf07JzidwuQL3DjEM3618ff0GliyZjctVge/G0EAICynJE/AajaSnTaeg4DLM5tbzFn25+8ugYvl+//dc9+l1vHD6C6G8pYgLZQCRSZiIN8eTFZfFHVPuaLUQSLCy7FkMSxvGTz4JvSkNwG24OTr36LBcqzt6UwNllw0fPjxizSSdSUpK4tZbb2Xq1KlIKSO2qIimaWzZEr4BPD8pyOKTiUM6PGbDtFFc1z+7xxI8gGXQQAjxuYY8+B8fl+vw9Vh7nttdwZat95KWehxCdFan8uJ0liGlB9/wEwMpm6muWUBd3Qp2lPyLRd+djsvVeszEZzs/CzqeVRWrKKmL3FiBcBifNR5Tp9+rwDzSwyUfXMKC0gU8/P3D3brOvqZ9/Gzez8LWpj8geUBU7576dJK3Wq1Rm4ulsLDw4POARYsWsWbNmoiVFe7nDqMT43hyRGHAfbOzkokLtBxhhKVddjki1MVNPF4Sph/qkpiUNDa064WJlG7K9r3hT96hXMeF211Nyc6nWm3Pjgu+d7JAsLNuZ0hxRJqu6Twwve1KTcFq9jZzx9d3UO+s7/BZRXsMjIMrP4XKolk4a2B0u7H26SQPwc/mGG5Tpkzh+++/Z926dSxYsCBig7KklAwaFP71Ns/OTuWJ4f1JMflqz2bgJ/0yeGJEUdjLCoZ14AD6P/lvzIWFYDL5/gXoPRSQ2YywWsn9870H2+MBBg++FTeWEGag6X2kdFNR8XmrbVcddVWX2nyLU3vX3PaBzCqaxcfnfsyswlkMThlMui34rrIAVc6qqPWRbynJmsT5Q6O7MHqfXxnqmWeeYdeuXRGKKDBN0zAMA13X0XUdV4htyeCrrScnJ1NXV3ewDIAf/vCHrea0jwSPIdFFx3cMe5pdvLqnktp1VRTt8TBheAajprW/MHJ3SSkx6uoQNhv7H3qI6uc7aD82mYifeiwJxx5L4qmnYj5sVPC6Bgc/WfoZlxiPMoTNXX70JQlqwskel5I8iQkTXmm17Y1Nb/DHhX8MuMbpAQLBKUWn8Jfj/xLpEMNuW+02Zr89O9phdNkn531Cbnxw60iHIqZXhjqQFHvSgbsHr9cblsFYB9aaHT9+PPv372fz5s2YzWZGjBgR1oVK2mPSOk5lX1XVc/3izVz1Xg0ZHmgAvlxeyVcvb+ScW8aRNzh8C4kLIdD9g79cO3Z0fLCUxI2fQNrll7fa7HDsYsuWB9hX+TU3GxY+YyZD2Nxp2S2Tugsz6xmBjWaGsrHrbyRChLDRP8AyhQe6Dd4y/xaW7VvWZhIvu27nshGXcd3Y63oq1LAamDwQHT3oXjcmYepWU004TcmZ0iMJvjN9Psn3takNzGYzN9xwAxUVFWzZsgW73c6oUaNIS0sDICsri6ysrChHeYhXSq5ft4Pz59Vi9RxWs5Xw9t++59p/Ho/JEv7BYM7NHT9wFmYzCcdPb7XN5apg8ZIf4PHUITBIBc7i7U7LqiCNSjIpZhMurMznRF7hUsy4eYKrMBH9xaIBkpPHtTslcKIlkX+d/C9e2/QaL617iXp3PdP6TeOGsTeQHR/WWUWiYkT6CFZXtj9moqVkazKGNLo1UjYcBILc+FwMaaBFeQBen0/yubm5lJREv7fAgSacYCQkJJCSksLgwYMjHFXo1jc48DoNMhpkwKYLKWHzkn0Mnxr+uW0sBQV49rTf3TPlvB9iGzas1bbdu1/C63XQcu1SK268CDQCvweAN7iIr8QMkAIdL3E04kHHhIe1HMUYVoT+hoD09JOorJwXYE970xG31tCwvsP9mtC4cOiFXDj0wu4F2IvdOuVWrvjwijY1dIHAoltwep3YdBua0Pj7jL/j8Dj46ac/DeraAtFhU1dXSSQf7fiIoWlDuWTEJWG7bnf0+SQ/a9YsnnvuuTYPPiM5CrU9JpOpwz77mqZx9NFHY+pkKoHexKxpaN6Ov4/1VZHpi55x3U/ZtXw5MsBD7cybbiL92mvabK+pXR5wbhonNjYwjDGsRMNok+yd2BASfsgrnMp76HhxYuUtzsNF6LM5mkwpDB16NznZZ1C27z02bfojbncVQpjJzT2PPXteJZgkf2C1qSPRmMwxvHrWq9z33X2srliNQDAuaxy/mfQbqp3VLClbQpotjdMGnEay1dfkNyBpANvrtre6TqCEHs4Ef0Czt5mXN7ysknyo+vXrx9VXX838+fPZu3cv6enpTJ48mYqKChYvXhyWNnshBGazGbfbHfCDw2Qycdppp7Fo0SIqKio6/HCZMWNGyPH0pCFxVpKSLLh1sLTTHJo/LHxt8i3FH3MMOffew767/4TR2AhSoiUnk3fffSSeGPj7mBBfTE3Nd21WY7LjYCwr0Nr5Yz6GBRSyg1N5Dyu+9mwLbi7h+QAfCV0jhIWszNNIShwBQE72meRkn9nqmLKyNzGMYCZO6/Md4kIyJHUIz576bMB9k3IOTf8hpeSi9y5qk+DBl9Btuo1mb/cqJ7p/BHIwo2kbXNH/UO7zSR4gJyeHiy66qM32efMC3RZ3zmQykZiYSH19PSkpKcycOZPhw4dTVlbGyy+/jMPh8PUCMQyGDh3KiSeeSGZmJiNGjODtt99m48bAD+qklD06wCgchBA8N2oAN09t5PSvfOujtkx5aXnx5A5OiVj5KWefTfIZZ+CpqEBPTETrZFxEQcFllO55pVWSF8KCwOiwn/okVuJmJWZaP7DUkK0+GISwkpN9Jropid27n4cguulJ6WLP3v+xt+xNRgx/gJyctv2ms7LOZN++ue0uFXhAfHz4u9PGonsW3cO6qvYXt+9uggdfcteFjl230+xtbvcuQBc6x/U7rtvlhEtMJPlQHGhiOTDR18CBA5k+fXrAeWBycnL41a9+RVlZGR6Ph7y8vFZNL3a7nfPOO4977703YFmRGhUbacPi7bx90QTeH7aHPa9ugzoPuklj5LQ8jj13cMQniRO63qZ7ZHvs9v6MH/cC6zfcQVPTNkAjK/MU4hOGsWPHo4dNUOZbfi8r60wGFF3PwkWdr3GakTGDwsLrWbzkDIJJ8C1J6WTDhjvIzDypzbquQ4rvor5+DQ7HTgyjmfaabvL7/ahLZR5pnF4n9313H29s7nzd41B4pRchBHcdfRfJ1mTKGst4ZPkjeKQHr/Ri0S3Em+L5xfhfRDSOYMRsku/sIagQgp/+9KdkZ2cf7PMejEALeLRkNpsZP348y5cvb7PvrLP67gIOFk3jnPH5MD4/2qF0Kjl5PEdP+QiPpwFNM6NpVl8TmvRSsvPfSOlBCBOFhddRVHj9wec3QuhI2fHvja7bqaya3/3ghE5N7TLS01rX8MzmJKZMfo/q6oU0NG5h9+4XcDhKObSqlMBqzSE397zulx3jpJT8bN7PWFK2pEfKa/I0sbVmK7dPuR2A4/OP56X1L7GjbgcTsidw4dALSbVFpimzK2I2yXs8ng4fvp522mnk5OQA4Z8L/qyzziIlJeXgmqpJSUmceeaZfaI3TSwxmQ6NMRBCMGDADRQWXovbXY3ZnIqmmVvtT0s9jsqqLzq9rrO5DMPobpdKA72dxbuF0EhLm0pa2lTycn/I1m1/o6zsHaT0kpk5i+LBt6Lr1oDnKrC2ci0ry1dG5CFqIFbdSl7CoQpfUXIRdx59Z4+U3RUxm+QtFgspKSlUV7ftJ5uQkBBwjvZwEUIwffp0pk+f3vnBSo/SNDNWa+BxCEOH3s23C9tfjk8IKzU1S2lu7v4Ia6/Xweo1PyczcxYDB/wSiyXwcH2TKYGhQ37P0CG/73ZZR5r1Vetxe3tuzWdd6H1iecW+9RSwi84888w23RVNJhOXXHJJr1hsROkZzc172F36Mnv2zMHlqmr3OJut49GJUjpDSvA+Bi5XOXv2zPEP2up7qzb1VvkJ+T06D8WD0x8kzZbWcwV2U8zW5AEGDRrEVVddxddff01FRQV5eXlMnz6d9C6sC6r0bTt3Ps3WbQ/h6x2tsXHTHxgx/G9kZ5+GYbgpL/+E6prF2Ky55Ob+EE2z98jqUVK6cburKSt7h/z8H0e8vCPBlNwppFhSqHK2/0EeLknmpF7RcyYYfX6CMkVpT0PDJpYsPcffW+UQTbNyzNHzWLnqWhyOErzeJoSwomk6GRknsW9fEKtRhUl21lkcddQ/eqy8WLenYQ/nvHMOTZ7IramqofHbY37LeUN6z0PwjiYoi+nmGuXIVrZvLkaAhR+E0Nm46W6aGrfh9fqSgZROvN4m9u//lISEUfjWpo8sISzExQ2IeDlHkryEPOZfOJ9bJtxCVlxWt5fd6+i8KblTelWC74xK8krM8g0satslUkqD2trvMQJMfyClg6amzQwaeBPp6SfSeYumwGRKAbreQ0vTTOT1i705ZqLNbrJTlFxEvau+2z1t+iX0CzixmN1k59zic0MNsUepJK/0WY2N29iy9a9s2PhbKisXtOkum5V5GlqA7opSelt1nzycYTSzZeuDVFZ+Dp3MPimEmfS040hKGosQZoSwYLcP7DR2IayMG/siNmtOp8cqXffcmudweLr3bEUguGnCTcwqnIVNP/T7Y9WsFCQWMLN/RJeuDruYfvCqxK7S0jls3PTbg1MVlJa+THz8EKZMfh/hr4ElJ48lL+8C9uyZ42+XF/jWTTVwOveGJQ4pXZRXzCMr63TGjnkSQ3owm1L4Yv7QDs8bM/oJkpPHhiUGpa2N1d1fA0AIwejM0czsP5M3N7/Ja5tew+l1cvqA07l0xKWY9cg35YWTSvJKn+N217ZK8Ac0Nm5i+fJLKR5yOxs3/p76+nUIoZGYeBR2W3/K9r3jPzL0hV5aMoxmysreYtDAm7HZcv3dNDueOnhHyb9ITz8+rHEoPk3uppAevJo0E/NK5nHJiEs4f+j5UV++L1SquUbpc6qqFrQ72VhN7SKWLJlNXd0KpHRhGM3U1i5l3/53CXdyb03y7cITqa9fi67H0Vn9qbb2+wjGcmRzep0HZ4rsDq/hDWkCs95GJXmlD+p6j4nOZncMByldrF5zI5pmJTvrVHzLowfWcsoFJbxSrCkhLbtn1sxMz4+d0eoqySt9Tnr6CdEOoV1OZxnNzbsZNuxe0tKOJlCvG02zkd/vsp4P7gghhOBPU//U7fPPGXwOQ1KHhDGi6FJJXulzTCY7uTkXRDuMgAzDTZNjByZTPOPGPsfRUz4iJeVohLCg64lowkJ29pkUFf0s2qHGtPHZ4zkh/4RunZthbzvNeF+mRrwqfdLqNb9g//4P6eqc7j1B0+yMG/scKSmHBiA6nftocuwkLm4AVktsJZHeqsnd1O7qUB3Jjcvlk/M/iVBUkaFGvCoxpalpOxUVn9EbEzyAYTjYsPG3rbZZrdmkpkxSCb4HxZnjeGv2WxQlFaF3YbBarE1eqJK80ufU1a1GhNB7oic0Nm7BMFydH6hElK7pvHLmK1x+1OVBn3PR0LZLifZlKskrfY7NlkdHfdB7A02zIIQahtIbxJvjuWnCTVi1zhdcGZo6lEtGXtIDUfUcleSVPic5eQI2Wz+iOZZP1xP8SVzj8C6dmmYlL++CgyNvld7h4hEXB5x4LM4Ux3F5x/GPGf/gtbNew9zBlBd9kapqKH2OEIJx4/7L2rU3U1OzGF+tXgTRF77lH3j7dwL9+l1Mbe0ympv34vHUBThWJzPzFIYN/QOG4WbLlgco2/cWmrBiSBcZGSdSPPi2br233qp50yYcy7/HlJFOwvTpCIsl2iF12Q1jb2BLzRYW7lmIQGBgMCx1GE/NeooES+yOW1C9a5Q+ze2uwzCcWCwZLPj2OJzOsjbHmEwpHHP05xhGI2ZzCroex759H7Jm7c/bHKvr8Rw/fcXBWviKlddQXb0Awzg0Y6Wm2Zg08S0SEg71pXa5Kmhs2o7dXhBTk44Zbjd7bruNhnmfIQ0DoetocXHk3H03ppRkbCNHotnt0Q6zS7bVbGNzzWYKkwoZljYs2uGERUe9a1SSV2LG7tKX2bz5z61WdtI0O4MG3kz//le1OX7Hjn+xddvf8fXSkVgtOUyc+Kq/KcjH63WwcdMf2bdvLlJ6sNv6M2zYPaSmHt0D7yjyPFVVCE1DT0lptb1x0SLK/nQPrq1bA58oBNjtCCnJvvNOUs/7YeSDVdoV1SQvhDgV+Ce+oX9PSynvb+9YleSVUEgp2bnrGbZvfxQpnQhhprDweooKr2u3W5zH00B9w3qslowOF/AwDDeG4YyZ6QiaN2xgz69/g2vHDiRgH3UU/f7yF8z9+uFYs5aSSy5BNgc5f4vVStF/X8Q+alREY1baF7UkL3z93DYBJwO7gSXAj6SU6wIdr5J87DGcTiqffBLnps3ETZ5M6sU/RmiRfSBpGB48nlpMpmQ0TT12Amhet46aN9/CcDQRf9xxlP3u9xj19YcO0DRMWZkMev99tl94Ea4tW7p0/aTZs+n3QLv1NyXCOkrykf4LmAxskVJu8wfyCjAbCJjkldjiWLuWHRdcCF7f7I/1n37K/oceYtC8TzFHcDF1TTNhsajF2gF2NbtY+va7JDzzFPmlu8AwqH1nLhiHDSQzDLx19WyaelzwNfgWnJs3hSliJdwineT7AbtavN4NTIlwmUovsevqnxxM8AdIh4Nd1/6UgW+8HqWoepanspLq//0Px8pVWIcOIe3HP8acl9etazm3bafu44/A6yXx5FnYhrY/iZbbkPx8fQkflddgSsrB/X9/ZPSWjdz974ewu9ouewggm7o/B7tr126klDE3WjQWRP1eVghxLXAtQP/+/aMcjRIunupqvDU1Afc518XujZzR1IRj5Uqkx0PDggVUv/hfX61ZShoXLqT65f9R+MIL2I8a2aXrVj73HOV//wfS6wUpqXz6GdKvupLMX/wi4PH/LCnj44panBKc9ngAVg0exqMXXM6v//tkyO/zcNLpxLV9B9aBamHyoEgJ276EhY9C1XbIHgFTfwn5AVtcQhLpJF8KFLR4ne/fdpCU8kngSfC1yUc4HqWneDpYG7UX9egKp5q33qLs7j+BlIGbPDwepMdD2e9/z4Au3Mm4S0t9Cd55qAYuvV4q//Msiaeeim1I2xr9c6WVNButv88ui4VPJ0/l5v8+2Y1lxzsmNA3D0f07gZglJdTuAq8blj0Pq18DjxPMNqhrkQqrtsD6d2Hqr+DkP4Q1hEgn+SVAsRBiAL7kfhHw4wiXqfQCpsxMRFxcwCYA84DYq+01b9xI2R/vDqo9u3n9egyXCy3IAUX1n30ecLt0u6n/5JOASb7RG3gVLK9uwmsyoXf0IdwN0u3GNrTjdW2POLuXwpzLoG4PbQbUBVxjXMKCv0NSDky5LmxhRLSbg/St0fZz4GNgPTBHSrk2kmUqvUe/hx7y9aduSdcpePyx6AQUQdWvvIJ0BTkhmZQIvQt1ab2dP1MhoJ3rTE1JCLh+1sDSnVjCnOAB8HoxHAEz15HF3Qzf/RsengBPz/TX1rt45/rJ78DZELaQIj65hpTyAynlECnlICnlvZEuT+k9Ek84nkGfzSPxtNOwDhtGykUXUrzwW6wxWJP3VlW37bHSHim7lBATTzo54Hah6ySdemrAfX8s7keiScfi/5A1A3avh5tfejrocrtE06j74MPIXLuvcDvh8aPhw9/4ml+6SzNB6bKwhRX1B69KbLPk5ZH/94eiHUbEJZ44g4Yvvgi6Nh/0cVJizs4i53e/o+zuu321d/8zjaybb2r3A3NQnI2vJw/j6d3lbNpZyvTNaxnxxquklOwIqtwuMwzcZXsjc+2+oGE//GsaNLSdVqNbbMnhuQ4qyStKWCSddhpl991Po9CoSEklq6oSm7v9RG5KS+vwes0bNlD2x7txrFiBsNtJOe88Brz7Lo3ffA1eg8QTZ2Du16/VOUZzMw1ffoW3rpb4o48mu6CAn372PhWPPgomU0hdJINhzo6dOXu67K3rw5fgE7Mhd0x4roVK8ooSFobZzGNX/Yy3C4eiG14MIbjw0/e54v3X27aNd9Ie7y4tpeTHF2P4k7JsaqL6hReo++ADiv77IpaiojbnNCxYwO7rf4Z0uw+WkXjyyYfuLoJ9XhACx5o1pHJhxMvpdZwNsH1+eK6VmAuXvNH2WVYI1ITXihIGD2zby9wBw3BZLDhsdpxWG3NOPoN3pp/U5tjks87q8FpVL7yIESApeysq2Hr2bBxrW48z8NTWseuaa33JXErfP4+H+g8/bNXtMtJc27u2lmrMMNwgw7EUpQY3LIG0gWG4VqurKooSCkNKnimtoNnUerGJZquN/50yu9U2y/Dh5Pzh9x1er3n9+vbHGbhc7LjgAmrfmXvw4W3FY4+2/9C3p8Yk6Dpx48b1TFm9jT0VrEmhX0fXwRT+efpVkleUELmlxOENnGRrEnx//OaCAvIfe5RBb72JZrN1eD3byJEdN+l4vey59VY2Tp7CnjvuxLFyVbdjDxctLo7USy+NdhjRM+OO0K+hmaCxPPTrHH7ZsF9RUXopKSXvlFUx6du1FH+1iotWbGFrY9cn4zqcVdMosAWugRXv2k7Kj37E4E8/IXHmzKCul3bZpcGtvOR2U/vmmzRv3tzxcaYIP3rTNDJ+dj3m7KzIltObTboGBs+CkJYOFBCfGbaQDl5VLRqixLrSZhe3btzFvKr6NvsE8KvCLC7rl0Gutfu3yvMq67hmzXYc/qkEhJRYpeTVYXlM6df1XiflT/yLin/+s9vxtKLrB+fPiRRhszHgzTeP7LlrDAO2zIN174AlDkaeC7uXwPcvQkUns3SabHDsL+DEO7tVtFoZqheo2lPKsg/epnL3LopGj2HcqWdjjYsPeKzb5WTBKy+yZv48vG4XhaPHMensH7Jn0wZcjiYGjJ1IbvFQNeNfEBq9Xo5ZtJ79ro5HeVo1wR0Dc7miXwbWbs53v7imgYd27GNzUzOjEu38X1EORyXGdetaJT+5hqZvvunWuVFhMpF25RVk33JLtCPpnVa+4utmSYBmPVsqTLsZjr2x271qVJKPsh0rl/Pm/X9EGofmEzFZrFz59ydIymh7i/vaPXdRumEtXnfrhamFEEgJJquFIVOmcurPblKJvhMv763kt5tKaQxyNKoOHJ2SwEPDCii0WyMbXADNGzdR9/571M/7DNe2bT1efihSLriA3Lv/GO0wei+PC77+K6x7FzQNRl8Ik37iq/WHKJqLhhzxpGHw3j8fbJXgATwuJ2/8+fdc+dATrbaXl2xnz8b1bRI8+NqUATxOJ5u/+5Zhx05nwLjwT00aSzY0NAed4AG8wMKaBs5Ytpnvjh7OhxW1PFdagcMwmJ2ZytUFGcR3Zd6ZLqh46mkqHnvM19e9nQnGeisRF0fCiTOiHUbvZrL4HtCG4yFtV4rt0dKOIK5mB+u++oKty77D2Rh4sqGq0l24m5upEjrrGhykW0zoO0uCWh7P7Wxm3TfzGTBuIh6Xi+0rluJyOOh/1BgS0zPC/Xb6pB2NzWxuasYswN2FG1YDaPIanLdiK2samg6eu7WpjLf3V/PRxCFYwryEoWt3KRWPPtqj/drDRdjtxI0fT8L06dEORQlAJfkIqC3fz0u3/wqnowmjgxn/PLqJS5Zv5GunPNhSZyWFMwqKGbS5825xhtfD4rmvs+j1VwDwetxIw6D/qLGcffPtWOxtbwN3r1vDik/ep7mxgeLJxzLy+JmYgpzytq+QUnLK0k2sauj+rIhNhsH39a2nAWg2JDscLt7dX8MPczqeliBYRlMTnqpq6j/9xLcgSF+jab7uoY8/FvG1e5XuUW3yQZJSUrpxHduWL8HjctLc0IirqYHC0eMZecJMLDY7ANu/X8rbf/kTRhB/sJ8edxYrRk5u87BFM7xc9s7TZO7b1c6Z+M4Rot1BMHHJKVzx0BPYExJpbmygpmwv25YvZsm7b+JxugCJyWolvV8BF939F0zmULp+RV+Dx8vSukbiNY3bNu5kbVPgYfwaYNMEZiFo8BpIAj4K69CZmck8fVRovUikx8O++x+g5rXXfIuM9MC0A5Ei4uLI//tDJBx/fLRDOWKpNvkQeD1u9m3byqK3XqVk1QoMT+u28pI1K1n2wdtcct8/MLxe5j50X1AJ3hAaq4eND/g03RAa62fMJuvVx2j3Q1jS4VDqprpa5v7tz1TsKqG5oR5NN7WJ3eN0Ulm6iw3fzOeoGYGns+0LXtxdzh1bSvHKzhP2OdkpPDaiCIANjQ7eKqvmv3srqfV48QRZ31le2xhSvAD7H/o7Na+/3iebZw4nm5po+OorleR7KXV/1YEtSxbxxDUX89qf7mT78iVtkiT4EmVdeTlL5r7B5u++JeBKDQF4dBOG1s4DPCFozuvP9U+9hGZqW8NOSEun04UIpGT3utU019f55i8PEPuB+DcvXhhc0L3Qqvombt9cijuIBA9Q7T70ATws3s7tg/JYePQILslNJ9mkk6hrnf5R7HV5cHbhYe7hpNtN9f/+F9QqUn2C2YyekhrtKJR2qJp8O6r3lvL+w3/B087K9i1Jw8vit18jLiUVT5A1M4vHRVJ9DbXJAdp2DYNJVo3PnnmibXIWgsbamqDKCIYQAntSGObdiJKnd5XTlXWOfpR76Ptd7/Hy8t5KPq2oxaJpPDAkn5PSExny9ZpOr3Ng+VQpJV4JJi34rqxGUxMyEqszRYnQdZLPOSfaYSjtUEm+HSs+eR9vB/OBB9JUU92l40/56m1eP/0yDKGBpiH83SytbheXJKfxwXcL2p4kZVgf0OlmC2NOPi1s1+tpO5uDb+5I1jXOzEwBoMrt4aTFG9jn8nDgu/l5VT1pZh2rAEcHN0pjEu2YhOCPW0p5vrQSh2EwJM7KfUMKODY1odM4tKQk9JQUvOXhn6ekW+x2CHKlKi0u7uA9pNA0kJLc++/Dkt+vw/OU6FFJPoC6inJWzfuo/fbwMCks3cYlb/6LxWOnUZmaRe6+XUxa8TVDBg2kiYnIEJoEOqOZTBheL0kZmTjq6iJWTiSsb3Cw3+VhVKKdUzNTWFQb3GIYzVJS5faQbjHzcMm+Vgn+gCp3xx+gcZrGEyOKuGXjTt7dX3NwGoONTU4uXrWV9yYMYWSC7yF8g8fLxxW1NBkGx6cm0t8/uEoIQfZtt7H3zjt7R5NNsEsRCkH6tdeQfs01OFauRLpc2MeNQ7P2/KAxJXiqd00Ab/z59+xYuZwuL8AbTpoW/JqhXSB0E7a4uFbdO81WGxPPOodjz7847OWF036nm/NXbGW7oxlNCAxD8rPCLJ7eXUFDO7NAHu645HheH1/M0QvXsaM5+Ds1AVySm8YfBvfDYUgmLFyL02j9+6EBZ2Wl8O+RRXxTXc9lq7cj8E1FbADXF2Ry28C8g8c3LFjAnltvw1tREXQc0STi4uj3t7+SOEMNeuptVO+aLjAMLyWrvyeqCd4XSEQuKwBXc3Or/vtuZzOL3ppD2dbNJGflMHbW6aTn949I+aE4delG9hyYg8ZfOXm8ZD/XFWQxZ18VZZ3MTwPwbW0jFS4PpiCng7AK0ITgrkF5XJ3vmyFwU10TFiFwHvY7YuAbYdvsNbhi9XaaDvvg+feucmakJTElxdekkzB1KoM//4yNY8dF7OcdNrqOOS9PDXjqg1SS78M03YQlLs7XgyZIhtdDmzYKQHq9bP/edxe15otPOO3ntzBkytRwhRqy9/bXHErwLbiAR3ftD/o6Fk2wtLaBUmdwtfgMi5n/JRmsf/Up/ldbzaDxkyk68VRcAe6AdQGjE+18Vd12tkvwDab6396qg0keQLNYDs0S2YulnH8+WTffhIjQlA5K5KgulIfRNB29lw0Mam8SMpPFQs6gIWEvz+Ny8fET/8Tbi3qAvFZW1e4+g+AHNLkNyYZGX3NPMMqbnfz2o09ZtWoFezauZ+Hr/2PuXTdxYWYS9sN61FiFxi+LsnG30wQqIWDXS+ugQe0HEMxoZJMJc//+xJ8QgX7quk7S6aeT+4ffo/fhXlhHMlWTP0x5yfagu0H2lPaem3jdLkpWLY9ImR6Xk/Id28gZHP4Pke5wG+FpPjOAOo+X5iDb8F0Ivhw/g6/HHs/Ako3szB+I22RhaGkZlxQW8E55DTVuL+OT4vhjcT8Gx9nIspjxBPiZxWka52S37U+e89u7KLn8ijZL/iWcdhoNH3/cNiizmYSZM2lasgSjshI8Hty7duHeuze8z3LsdkxJSWTddmt4rqdEhUryh/nundejHUJQNF2PaE3b8Hox2+zUle9n4ZuvsHP1ShJSU5n8g/MZNGFKxMptT4IpPM0EEnh6d3mgFqvA/DV+Q9fZMmD4wdcbhI0NpRXYhODMzGT+WNyPTIvvDjDJpPPAkHxu3bQbj5R4pC/Bz0xP5KT0trXhuAkT6P/Uk5Tddz+urVvR01LJ+NnPqPzPs4ETtpTEjR1Lw6efttqG2+1L8qGKjyf13HOwDR9B0mmnotntoV9TiRrVu+Ywb/z5d/6eNb2XZjJjMptwBdv1rZtmXHEtXzz/VKsVhUxWK8dddBkTTp/dwZnh95uNu3hhT2WPltkVdk3wzvhiRrdYJGRbk5PXyqqo83o5LSOZqSkJQc//762vZ9OkyYF3CgFWK0So+6V94kSK/vtiRK6tREZHvWtUm/xhijt42Hj6L35DfJiGbweaIfJwWoCHXGabnXNv/X3EEzzAF8892WbJOI/Tt2qVO4iRwOF0QlpisDNGRIXDkJy+dBNrWsxcOTDOyq0Dc7m3OJ/jUhO7tMCL9HjaXyVIyo4TfAgLyQi7nfSrr+r2+Urvo5L8YYYfdzyJ6W0X080eVMzwqdOZfsmVYSknNa8f1vj2R0em5Re0bYsXgsS0dPofNRp7UnJY4ugWIajeU9qjRc5KT6a/vXdPiewBbt7QwcyhXWBKTcWUnd2tc+0TJyK6OUAp/YafqX7wMUYl+cOYrTYuffBhxp9+NnHJKSSmZ3Dcjy/nx3/6KwAjpp1I1oAOekMEQwiSs7I5+Zob2p2Du2bvnjYjXoUQTLv4SqrL9oRWfog8LmfY7miCZdIEI+Ptvbo2D7AmhDnsD5f/+GNdPkeLjyfvvvsoePJJbCNHIiwWtPQ0hNWKsNk6brMXgvRLLw0hYqU3Ug9eA7AnJDLj8muZcfm1Afef/9s/8/TPr8LZ1L0pZ01mCxPPOIfc4qHUV5bz9cvPt5meONB0xdIwWPPFJ5Rt3RzVqQjiU1J7PMkDfFZVF/EhahowNSWBhTUNXZr47AAD3wjXYLtodsQ+YgSYTG163bTHNmoUBU/+G1NqKpb8fgx441AnAul207joO+rmzaN2zpw2zXAA5oICNUVBDFI1+W6wxcdzxd8eZ/i0GVjj4tH04D4rzTY71rh4Zl37c3KLhwIw8cxzufH51xk08eigrrP9+6W4mhqJ5ojc5sYGPAHWoI20nqjFG0CKWe/yQiIH2DQRlgR/gH306KCPzX/0EUypgT98hdlMwrTjyL3rTmyjRrXdb7GQ89vfdjtOpfdSNfluSkhL5/Sf3wLA/h3bePmuWwIuvn3AoAmTOe6iy0jNy0c3tf62l6z6np2rV/hGo3bC8HqDWpQkkgyPh+q9pezdvIFty5eQkJrGmFlnkNm/KGJlSimJ0zSajci/93fLa7t1ngbcUJAV1liy77iDHRdfDJ2M3bAOHYo5iDZ8YTZT9Oor1LzxBlXPPoe3qgrbiBFk/vIXXfpAUfoO1YUyTJZ/8A5fvfwcQmit5qDXTCZSc/vxo7sfxBoXH/DcuQ/dx+ZA0wr3Ypquo+km33sVAk3TGDvrDKZfclWbD7FwWFbbyHnfb8HRi35fD3dGRjJPHlWEHsaaPIBz2zb2/+0hmhYvRrpch5YKlBI0Dc1uZ8Abr2MpKgpruUrfoSYo6wHjT5/NsKnHs2PV9+gmE0Jo1FeWk15QSOFRYzpZ5Dj0xKXppqDuBMKl1R2FlBheL8s/nMu2Fcu4+J6/YUvofF71rtjSdPh0YL1LhtkUkQQPYB04kILHHj342rl5M5XPPotz6zbixo4l7corMOfkhL1cJTaoJB9GcckpjJjW9e5nI6bPZMeK5bid3R/c0pMJviO1+/ayYM5/mXnVdWG7ptuQDLRb250Tpje4t7hfRBJ8INbiYvL+/OceKUvp+0J68CqE+IsQYoMQYpUQ4i0hREqLfbcLIbYIITYKIU4JOdIYNmjCZIqnHIvJakVoGiaLBd1s5sSrrqdg1Nhoh9cl0jDY8O1XYbnWrmYXF6zYQtGXK5n9/eZuPwztCdnW3jWpnaIcEGpN/lPgdimlRwjxAHA7cKsQYgRwETASyAPmCSGGSCmj+8SwlxJCcNoNNzPulDPZsep7LPY4hh07jbjkFI6aMZNHLr8goqtEhZuzsQHD6w04YjdYDq/BGcs2URlg9abexiRoNZ2BovQmISV5KeUnLV4uAs7zfz0beEVK6QS2CyG2AJOBhaGUF+tyBg9pM+tj+Y4dmMyWkJpyepoQGluXfkfxlGO7fY33ymto9Bq9PsED3FucT5yueiMrvVM4fzOvAj70f90PaDm+e7d/WxtCiGuFEEuFEEvLe8vCxr2IlBKhhbGtV3TvR97xg+PWDK+H0k3ru1XOAduanDQGOR1wNJmF4PJ+GdEOQ1Ha1elfrhBinhBiTYB/s1sccye+qTte6moAUsonpZQTpZQTMzPbzhlzpMsdPARNC99qPJom6OqwIrPVxvDjTgh6vhyTxUpKVmi9PYYn2IkL54dbhKSZ1UpJSu/WaZKXUp4kpTwqwL93AIQQVwBnAhfLQ53uS4GCFpfJ929TukjTdSbNPq/zA4Ngtto4/pKryBlUTLCJXmga9qRktq9YjqPusEFCmhaw3V036QybGtoqRadlJJPchQQqgGik2/MCLAKiKL1JqL1rTgV+A5wtpWxqsWsucJEQwiqEGAAUA4tDKetI1VhTzcI3/hfydcxWGwUjRzH21DO5+M8PkV5QGNR5/Y8aQ3NDPY66mjb7Tv7JDVz50L/IHjgY3WRGN5tJ61fABb+/P+R+8mZN8MbY4qB/QQUBl66NKA34RWH3ZopUlJ4Sau+aRwEr8Kl/ruxFUsrrpJRrhRBzgHX4mnFuUD1rumf5h3PxukPrAx+XnMKp1/+KojHjD7ate92dLGQtBPbEJCaedQ5v3Pu7gIcsfP1lRs88hUvu+weNNdVIwyAhLT2kWFsaGGflqn4ZPL+nAncnXeR7uvVeAL8ekEOyWQ01UXq3UHvXDO5g373AvaFcX4Hd61YjQ5ivxWy18eN7/kZyVusaZ+HosdTuLwvYNVM3mUkv6M+Zv/wNO1Z93+61mxsaDn4dqVkp7xiYywt7KiJy7e6yC8Ejwws5Mzsl2qEoSqdUNaSXS8nJY+/mTUjZNhlb7HYMrxev231wgRHdbCYxPRNrfDwDx01k0tk/xGy1tTl38uzz2bjgK5wOx8EPEZPVyqSzf8iYk047mLQ1TefzdmJLLyhoZ0/4LKptxKppuCLU0+bAk4lgx9LaNMGW6aN7bHSrooRKJflebsIZP2DTogWtJz3TNHKKh/Gjux+kZl8Z3875L7vWriYuOZnJPzifocdM6/S6SRmZXPrgwyx6cw471/gX6Z59PgPHT2p1XHJ2DnlDR7Bn47rDriCYde0vwvEWO+SJ8FQGV+WlY9Y0nt1TgVkIvFLiMNov8/SMZJXglT5FzULZB2xbvoRPnnwEZ2MD0pAUjR3PqT+7CVsHyweGk5SSz//zL9Z88Sler4fkrBxO//ktB+fEj6RGr5ejvlnTYeLtLqsQbJw2CpuusafZxeLaRuJ0jWvWbMcZoDiTgE8nDmV4gj3ssShKKDqahVIl+T5CGgb1VZVY4+LanbI4Vr27v5ob1+/EkOAK0+9rsd3KC6MHMCCubVPWq3sruXXTbppbfLDYNcGLowZyXFpiWMpXlHBSUw3HAKFpJGUcmYPFzspKZVxSPG/tq2ZrYzNv7a8OWNMORpymcd+QflyY234voAtz0xmVGMeLeyqocHk4JSOZs7NSsHRh1K+i9BYqySt9Qr7Nwo2F2exudvF2eU3ANUrB9yD1weJ+3LllT5tav10TDI23cW52WqfljUiwc9+QyD9YVpRIU0le6VPybRZGJcSxvK4x4OCne4r7cWl+Jhf3y2BrYzPf1DQwd38NDsPgh9mpXJqXgbkPTJegKOGikrzS5/xnVBGXrtrG+gYHXukbbTfAZuHxEYWMS/Y9r9CEoDjBTnGCnSvzj8xmLkUBleSVPijTYuajiUPZ1NjMfpebUQl2NfJUUdqh/jKUPmtIvI0h8W17xyiKcojqLqAoihLDVJJXFEWJYSrJK4qixDCV5BVFUWKYSvKKoigxTCV5RVGUGKaSvKIoSgxTSV5RFCWGqSSvKIoSw1SSVxRFiWEqySuKosQwNXeNoihR4a1zYTg96MlWvLVO9AQLwqThWFuBu9yBOSce+4g0hK7qoqFQSV5RlB7lrXdR+dJ6XLvrQQJe6VtAVwJC+FZ+cRsIq05NnImkGf3RbDq2IaloNpWyukp9xxRFCTspJa6d9Ti316LFmYgblYmw6ThL6qh+eQPeepcvqR/gOfDi0Ebp9CKdXmre3oww62BIUi8cStxRGT36Xvo6leQVRQkraUgq/7se5+ZqpMcAXaPm3a2YUu14qprBY3TtgoYv4QNUvbIB622T0RMsEYg8NqkkryhKWHgqHdR/tZvmjdV4a52HKuX+pO7Z3xSGQiSVL64j85rRCJNqqw+G+i4pihIyd1kj+x7+nsYlZXhrnK2bYsLMtauB6rc2R66AGKOSvKIoIat5b5uvSaWLLTHdYkiaVpZjODw9UFjfp5prFEUJmvQaOFZX4FhXiRZnJn5yDpa8BFwldT0ah9A0vPUuNLtKYZ1R3yFFUTolpUS6DSqeWYN7bwPSZYCApmX7SD5zIMJmQrpdPRePx0vzxio0m46eZO2xcvsileQVRWmX0eSm+p2tONZUgCFbt7VLkG6Dmne3kXh8P+o/29WDgUHtxzuo/WgHyacPIHFqv54ru49RbfKKogQkDcn+f6/CsbrCN2CpvYepHqNnE/zBciV4JbXvbqPsb0tx7Wno+Rj6AJXkFUVpw3B4qP9yl69fuxHBrjJh4il3sP/fKzGa3NEOpddRzTWKorTS8G0pNR/sAGSLkah9gNOg5qPtpJ07JNqR9CphqckLIW4RQkghRIb/tRBCPCyE2CKEWCWEGB+OchRFiSznzjpqP9zhG8DUlxK8X9Pifao2f5iQk7wQogCYBexssfk0oNj/71rgiVDLURQl8hq/K/NNRdCHNSzcE+0QepVw1OT/DvyG1o9lZgMvSJ9FQIoQIjcMZSmKEkFGkzuio1V7gmu3egDbUkhJXggxGyiVUq48bFc/oOXj9t3+bYGuca0QYqkQYml5eXko4SiK0k2+6X/X0byxKtqhhEx6JQ2L9+KpdEQ7lF6h0wevQoh5QE6AXXcCd+Brquk2KeWTwJMAEydO7ON1CEXpe6THYP/jK3yTikWrpUYXvm6aLZkEwqYjG7o2fYFzUzXObTWAIOGYXJJPH4AQImyh9jWdJnkp5UmBtgshRgEDgJX+b2A+sFwIMRkoBQpaHJ7v36YoSpRJj0HT6gq8dS7ixmTg3FaLt9YVvQQP4JUIq078lBw8Fc1It5e4UZnULdiNt4tJHvA/NJY0LtqLdXAK9qFpYQ+5r+h2F0op5Wog68BrIcQOYKKUskIIMRf4uRDiFWAKUCul3BtqsIqidI80JA3f7Kbui11Ih/fg9roPt/tWZeoFfeGl00vDV6VYipJIv3Q4VW9sxrsvtCYX6TZoXFymknwEfACcDmwBmoArI1SOoihBqP1gGw2L9gbuFtnLukq6dtRR9telBxcKCZV09+3eQqEKW5KXUha1+FoCN4Tr2oqidJ/R7KFhUVlkkrkJiMCMvy3vNkIhLBpx47I6PzCGqRGvihLjPJXNCF0gw52MBeTedQxGg4uKF9fjrWiC8OTmsDFlxxM3OjPaYUSVmrtGUWKcKdWK9EagyUJC1csbMKXbSTt/CKaMuPCXEaL4ydkI/cjtWQOqJq8oMU+LMxM3LhvHiv1hb592bqqmdl4JjV+X+uaY700EmNLs0Y4i6lRNXlGOAKk/GEz8sXkIi+7boAEmgXVwCtn/NxFTVveTYcOXu3vnVAhmDeuA5GhHEXWqJq8oRwChC1JOG0DyqUVg0KYJI+WcYir+vap7Fw/mga6g56dLOMJ71RygavKKcgQRQgRso7b2T+z+RU1BtHlHo5emBE+FmtpAJXlFURC6hmVAsq/G3RVmDXO/hIjEFA6ONRXRDiHqVJJXFAWAtB8Wo9lNQSd6EWfCVpyCuxfP+miEaUBVX6aSvKIoAJgy7OT8ZhIJ0/p1nOgFaPFmkk8fQPP6qrYTi/UWusA+Ij3aUUSdevCqKMpBms1EyukDiRudSe3HO3xzs5sEms2EbPYiDQP78HRsg1OoemVjtMPtkCkrDksozxpihEryiqK0YclPJPPqUe3u3/OnRT0YTTfogtRzBx/RUwwfoJK8oihdZjR2vI5qnauSPY4t6MJEYfxILLqthyLzz1czNgtrQVKPldmbqSSvKEpYraz6ks11S5HSQAiN/vEjIl6miNOxDUtHCEHcuEysg1IiXmZfoZK8oihdZi5IwL2rba+ayuY9bK5bitc/G5oJHbNmiXg8aRcOO6LnjO+I6l2jKEqXZV41Ci3B3GZ7SeM6vPJQt0WPdOM2nBGPx5QU+Q+SvkrV5BVF6TLNbiLvrqNxbKzCubUGS0ESzTtqkO/4lt1raXX114xNOxGT1vZDISx0gXu/A3Nu7x2UFU0qySuK0m32oWkHm0niRmUwNm022x9bjdd76MHs1voVGEgmpc9CiPA3HghdoKdaw37dWKGaaxRFCZvCqRMYc8oZmCxWhKahCR1dmMi05kckwaMJTOl2LAWqP3x7VE1eUZSwmnH5Txh5/IlsW74Eo8JFxvYM4mRoTSnCrIFJI/6YXByryvFW+9r5rYNTSLtgqOoP3wGV5BVFCbusooFkFQ1Eug323r8Yo8nduqneqhE/IZum5b6FTDS7CaMhcN97LdNO5mUjMKXZEbog+eRCjEY3wqSh2VQK64z6DimKEjHCrJF5/RiqXl6Pe1/TwdWa0n40DEtuPKlnDwag5oNtNHxVGvAalnQ75sxDSwsKIdATVG+aYKkkryhKRJkz7GT/YjzeehdIiZ7U9iFp4vEF7Sb5pFmFkQ4xpqkkr0RVeX0zn6/fz/qyegZnxTN7bD8SbRHqaqdElZ7Yfu1bjzeT9uNhVL2yAQ4s6CQg6ZQiLHmqa2QoVJJXwqKkspG/z9vEFxv243B5sZo10uLM7G9w4XIbDM5K4K4zRzCtOBOA91bu4fY3V1Pv9By8hlkT/Om99Vx6dCFXHTeAvBS1CPORJG50JrahaTRvrEJ6JbYhqejx6gM/VELK3jMX9MSJE+XSpUujHYbSRdvKGzjr0W9o7GSBBrMueP6qyThcXq5+vvOfc26yjTNH53LZMUUUpMV1eryiHKmEEMuklBMD7VM1eSVkf/l4I01BrMDj9kru+2A9++uDG+a+t7aZp77eznPf7uCXM4v5+YnFoYaqKEccleSVkH23vSrodZo37WvA5TE6P7AFt1fy6BdbsJtNeKXB0Jwkpg3OQNPa9o2ubXLz3uo91DS5OXpgOuP7p6g+1MoRTSV5JWQZCRaqGl1BHZsSZ6a2yUWzp2vNhM1ug/s+XIchQUowaYJLjinkppOHkOR/ULt4exVXPLsYKSVOj4HVpHP8kEweu3g8eoAPBEU5EqhpDZSQ/eyEwVhNwf0qzRqRw3HFGd0qx2PgS/KA25A8/+0OfvDYApweL15D8tMXl9Lk8uJwGxgSHG4vX2zcz9yVgbvmKcqRQD14VUImpeSRz7fw9083ddpsYxIQqBIvOHzuwuDoAgrT40m0mVi1uzbgNZLsJr769QxS4tQAGiU2dfTgVdXklZAJIZgyII3hOZ1PEtVeK42uCfRutKh4JWyraGRlOwkeoM7h4Ypnl3T94ooSA1SSV0K2YEsFlz+7mHVl9d2+hseQeNvJ0v3T7ITaor6xrJ71e+tCvIqi9D3qwasSsj+9t45md9d6zHTFzipHyNdwuL1c9O+FOD0G+Wlx3D17JAWpcXy1uZwEq4mThmcTb1V/DkrsUb/VSsg27+t+Db4n1Tb7Rtdu2d/Aj5/6DpMmMOkCXQjuYDXPXDGJowemRzlKRQmvkJtrhBA3CiE2CCHWCiEebLH9diHEFiHERiHEKaGWo/Q+NU0urv/vsnabWXo7jyFpdhs0urw0urxc88JSnJ7OB3UpSl8SUk1eCDEDmA2MkVI6hRBZ/u0jgIuAkUAeME8IMURKqf6CYoSUkh89tYgt+xqiHUrYSAnfbq1kxtCsaIeiKGETak3+euB+KaUTQEq53799NvCKlNIppdwObAEmh1iW0ossK6mmpLIJt9FHq/HtcHdxNK6i9HahJvkhwDQhxHdCiC+FEJP82/sBu1oct9u/TYkROyqboh1C2Lk9Xo4ZpNrkldjSaXONEGIekBNg153+89OAo4FJwBwhxMCuBCCEuBa4FqB///5dOVWJouG5ifSicXRhcdmxRWoueyXmdJrkpZQntbdPCHE98Kb0DZtdLIQwgAygFChocWi+f1ug6z8JPAm+Ea/Bh65E08i8ZCYWprJ4RxXOGGniuHBSQecHKUofE2pzzdvADAAhxBDAAlQAc4GLhBBWIcQAoBhYHGJZSi/x9velTPnzPBZuq8Bq0rCb9WiHFLJ4i87grM5H7CpKXxNqkv8PMFAIsQZ4Bbhc+qwF5gDrgI+AG1TPmtjw+Pwt/OrVFeyrc+IxoK7Zg8Pt5drpA0IelRotmoC/nD8m2mEoSkSE1IVSSukCLmln373AvaFcX+ldpJQ89MmmgPteXbKbgjR7WEan9rSThmdx+qjcaIehKBGhRrwqQSuvd+Jpp8tkrcNNrcPdwxGFx/q9fWPErqJ0h5qgTAlaoi026wQNLRYTV5RYo5K8EjS7xcTQ7IRohxF2/VLt0Q5BUSJGJXmlS1677hj6pdiiHUbYmHXBNdO6NLRDUfqU2Lz/ViImyW5hwW0z2VhWz/ur9vDw51uiHVK3WU0as0Zkc9bovGiHoigRo2rySrcMzUnkp8cPinYY3SaA44dk8siPx6OpRb6VGKaSvNJtcRad5D46DYAEtlc0RjsMRYk4leSVbhNCcPvpw6IdRrvMmiDO3P6vuMWkfv2V2Kd+y5WQzB7bj97a2uE2JE0dLEtYkBrXg9EoSnSoJK+ExGbW+uTMjZqA44rVtMJK7FNJXgmJEIIbTxzc5yYpM+saPxiXH+0wFCXiVBdKJWRXHzcAgEc/30Ktw01vny9aE/DHs0eSYFW//krsUzV5JWRCCM6fUMA54/oRZ+ndNfo4i85xxRmcP1HNHa8cGVRVRgnZ5xv2cfVzS7tdgzfrArc3vPX//BQ7+xucWE0aDreXvGQbw3OTOHtMP049Kge9tz4tVpQwU0leCYmUkuteXB5SE024E/zMYVk8fsl46hweSiobKUyPJzPRGtYyFKWvUEleCcnSHdW4vJ0v/ycAIaCdmYrDwqIL/nPFJI4rzgQgM1FXyV054qk2eSUkLm/nC35pAm47dWhEV46Ks+jMHJ7N1MEZESxFUfoeVZNXQjJlQDq6EHhl2yp6ZoKFiyb355KjC8lOslHX7OGx+VtDKs9q0phYmMqq3TUIIUiLt1CQFscFEws4Y1QuQqi2dkVpSSV5JSQmXeOec47i9jdXt9puN2t8fNN00uIPNZf8+tRhfLe9iqUl1V0qQwhIsZsZlpvELScPYWJRWlhiV5QjgUrySsh+NLk/k4tSeeCjjeypdXDCkCxuPHEw1gADpO6ePZIzHvmGABX/gHKTbTx9+URG5iWHOWpFOTKoJK+ExaCsRJ68bGKnx43IS+ammcU8/PkWvIZE4nsom2gzkZ1k4/oTBjEoMwGX18uofinY+thIWkXpbVSSV3rcL04awuxx/Zi3fj9mXXDqyByykmJntSlF6U1UkleiojA9/uB0CIqiRI7qQqkoihLDVJJXFEWJYSrJK4qixDCV5BVFUWKYSvKKoigxTCV5RVGUGKaSvKIoSgxTSV5RFCWGqSSvKIoSw1SSVxRFiWFCBjsdYA8QQpQDJdGOoxsygIpoBxFBsf7+IPbfY6y/Pziy32OhlDIz0Am9Ksn3VUKIpVLKzqdg7KNi/f1B7L/HWH9/oN5je1RzjaIoSgxTSV5RFCWGqSQfHk9GO4AIi/X3B7H/HmP9/YF6jwGpNnlFUZQYpmryiqIoMUwl+RAJIW4RQkghRIb/tRBCPCyE2CKEWCWEGB/tGLtLCPEXIcQG//t4SwiR0mLf7f73uFEIcUoUwwyJEOJU/3vYIoS4LdrxhIMQokAI8YUQYp0QYq0Q4pf+7WlCiE+FEJv9/0+NdqyhEELoQojvhRDv+V8PEEJ85/9ZviqEsEQ7xlAIIVKEEK/7/wbXCyGO6c7PUCX5EAghCoBZwM4Wm08Div3/rgWeiEJo4fIpcJSUcjSwCbgdQAgxArgIGAmcCjwuhOhzK277Y34M389sBPAj/3vr6zzALVLKEcDRwA3+93Ub8JmUshj4zP+6L/slsL7F6weAv0spBwPVwNVRiSp8/gl8JKUcBozB9167/DNUST40fwd+A7R8sDEbeEH6LAJShBC5UYkuRFLKT6SUHv/LRUC+/+vZwCtSSqeUcjuwBZgcjRhDNBnYIqXcJqV0Aa/ge299mpRyr5Ryuf/renzJoR++9/a8/7DngR9EJcAwEELkA2cAT/tfC+BE4HX/IX39/SUD04FnAKSULillDd34Gaok301CiNlAqZRy5WG7+gG7Wrze7d/W110FfOj/OlbeY6y8j3YJIYqAccB3QLaUcq9/VxmQHa24wuAf+CpYhv91OlDTolLS13+WA4By4Fl/k9TTQoh4uvEzNEUwyD5PCDEPyAmw607gDnxNNX1aR+9RSvmO/5g78TUBvNSTsSmhEUIkAG8Av5JS1vkquz5SSimE6JNd64QQZwL7pZTLhBAnRDmcSDEB44EbpZTfCSH+yWFNM8H+DFWS74CU8qRA24UQo/B90q70/+HkA8uFEJOBUqCgxeH5/m29Unvv8QAhxBXAmcBMeai/bZ96jx2IlffRhhDCjC/BvySlfNO/eZ8QIldKudffhLg/ehGGZCpwthDidMAGJOFrv04RQpj8tfm+/rPcDeyWUn7nf/06viTf5Z+haq7pBinlailllpSySEpZhO8HMl5KWQbMBS7z97I5GqhtcXvVpwghTsV3S3y2lLKpxa65wEVCCKsQYgC+h8yLoxFjiJYAxf5eGRZ8D5PnRjmmkPnbp58B1kspH2qxay5wuf/ry4F3ejq2cJBS3i6lzPf/7V0EfC6lvBj4AjjPf1iffX8A/lyySwgx1L9pJrCObvwMVU0+/D4ATsf3MLIJuDK64YTkUcAKfOq/Y1kkpbxOSrlWCDEH3y+dB7hBSumNYpzdIqX0CCF+DnwM6MB/pJRroxxWOEwFLgVWCyFW+LfdAdwPzBFCXI1vttcLohNexNwKvCKEuAf4Hv9Dyz7sRuAlfwVkG75cotHFn6Ea8aooihLDVHONoihKDFNJXlEUJYapJK8oihLDVJJXFEWJYSrJK4qixDCV5BVFUWKYSvKKoigxTCV5RVGUGPb/OHRo9Gl6+ZwAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6, 6))\n",
"\n",
"plt.scatter(X_embedded[:,0], X_embedded[:,1], c=y, cmap=\"tab10\")\n",
"plt.title(\"64 признака - максимум\")"
]
},
{
"cell_type": "code",
"execution_count": 203,
"id": "e69350cc",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/goloshch/.conda/envs/NPM/lib/python3.10/site-packages/sklearn/manifold/_t_sne.py:780: FutureWarning: The default initialization in TSNE will change from 'random' to 'pca' in 1.2.\n",
" warnings.warn(\n",
"/Users/goloshch/.conda/envs/NPM/lib/python3.10/site-packages/sklearn/manifold/_t_sne.py:790: FutureWarning: The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.\n",
" warnings.warn(\n"
]
}
],
"source": [
"u, s, vh = svd(A, full_matrices=False)\n",
"v = vh.T\n",
"\n",
"n = 8\n",
"u, s, v = u[:,:n], s[:n], v[:,:n]\n",
"X = u@np.diag(s)\n",
"\n",
"X_embedded = TSNE(n_components=2).fit_transform(X)"
]
},
{
"cell_type": "code",
"execution_count": 204,
"id": "27756893",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, '8 признаков')"
]
},
"execution_count": 204,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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lDuOXXb+EHB+QOCBse13qbKna0mx/c3bO4abvbwrrNz87fzabKzY3fF5ctBif7msxRUKkUawOi4MT+pwQUVsTk/2BKfImXYIiV1HY3C5FrlD7diSUe8oDbo9hzC8Av+7elyxMFWq7cuBYFEvDZm2MJYbDex7Ou6e+a9rdTboUpneNSZdgVfGqsMdr/bVRH0sVKk6rk6K6ItyamwmZE0hxpOB3+fEbfhyqA1Wo1Gl1Ya+3KlYuGXoJd04I+O1LKc1gpkZIKan75Rf8u3bhGDqUmNGjD/SUDmlMkTfpMlgVa4uZGqM1RrI9mUWFi/jrwr+iKiqpjlSeOeYZPt78MTtrdjIpaxKDkgdxzTfXhFwfo8aQFpvGtaOubThmCvw+pJTsvud31MyejdQ0EILUq68m5aor0YqKsGZnoya0PamcSfsRXWmTaMKECXLJkiUHehomB4AqbxXHfnBsSEqCSFBRI84xrwq1YeW9N5hJFSrjM8bzyomvBLV9e93bDbVeFaFw5fArGZk2ksOyDyPGEtPmeR4KuFevZvvFlyD9TR7WViuK3YbUdHr+40kSjjnmwEywmyKEWCqlnBD2nCnyJl2F19e8zpNLnzwgYyfbk/n5wp9Djtf6ail2F5MZm0msNfYAzOzgQauoYMe11+Fds6bFdsLhYODcn1Hj4/fTzLo/LYm8ufFq0mU4f/D5pDnS9vu4Cgq5CaG5bQDibHH0S+xnCnwE7Lz2Orzr1rXaTqgq/t2798OMTMAUeZMuRKw1lk/O/IQLBl/AsJRhWJXwRT2ihVWxEmeNI8mRxKNHPNr6BSbNotfU4NmwAYzWa+8aHg/WrKz9MCsTMDdeTboYSY4k/jDlD0gpG9L7RqMwR1McqoPXT3odn+FjcPJgc6XeQYTdDpGafoWIvK1JhzFX8iZdEiEE/zz6n/z9yL9z7chribXERlz9qdW+ETx8+MMMTxvO2B5jTYGPAorNRuo114DD0WpbYbOhlZfvh1mZgCnyJl0YIQTTc6Zzy7hb+OG8H5iWPa3DfdpVO5MzJ3NinxOjMEOTxvS4/TZ6Pva3wEq9BYTVijU7ez/NysQ015gcFMzdPZfFexa3+3qrYmVE2gjOH3w+J/c5uSFS1aRjVH/3PXsefRTD6yXx9NMRitKqKUa6XNTMnk3i6acHHXevWMHu+36PVlpKzNix9Hzsb1iSk3EtW0bZq68FgqtGjCD5wguIGT68M2+rW2G6UJocFPxz6T95Zc0rIcdVoQZK8oXJGT8qbRR1/jpcmouT+57MzWNvxqKY65r2UrdoERXvvguKSuoVl+PZvJmiPzwQ3EhVQQ8Ts6AoQZuywuGg78cfY+/XFwB/YSFbTz0N6XI19CPsdtT4eLTS0uA+rVZynn6a+GMiT2jX3WnJhdL8jTc5KOid0JsYSwxuLZCLRiAYnDKY1058DYfqYMp/p4QEUk3tOZWbxt50IKbb7aj79Vd23nAj0uMBoPb775G+MMVYwgk8hIg8UuJZvw57v75Iw6Bq5ufB53Ud6XKhucJsuvv9FD3yiCnyEWK+s5ocFJzR/wzGZ4wnxhJDnDWOBFsCf5v2N+JscVhUC3894q8NNVcFglRHKpcOvfQAz7r7UPrCiw0CDyC93vBmmebs8U1cK6XXy57H/87W005n64knUfLcc0H9t4ZRG/2cRt0VcyVvclCgKirPH/s868rWUeevY2jqUOJt+yImj+9zPO/Ev8PcgrnEWmI5c8CZJNoTD+CMuxdSiyzVsrVfP/x5ecGiLkRY/3l9zx70PXvaPhmLBee0jm/CHyqYIm9y0CCEYHha8xtuw1OHMzzV3JDrDJIvuxTPunWBFXwL+LdtQ9jtwSv9KOz7KUlJGDU1oCjEH3ssPf/8SIf7PFSImsgLIVRgCbBLSnmaEKIv8D8gFVgKXCalbL6isomJSZcl8ZRTKPrLo62KPFK2yewSEYrCwJ9+RLGHFoAxaZ1o2uRvBdY3+vwY8JSUcgBQAVwdxbFMTEz2M0ZFxYEZWFWo+uwzqr74kk3Tj2TD2HHkX3Qx7lXhaxCYBBMVkRdC5ACnAi/XfxbAMcCH9U3eAGZEYywTE5MDQ0cDmOxDh6Kmp6OmphIzZkzA4yYSdCPgQ3///ejFxUi3G/fy5eRfdDHV35hF01sjWuaafwL3AHt3wlKBSikbCmMWAGF/Q4QQ1wHXAeTmhs8EaGLSLagrheXvwMIXwVUKErDFQsZwOPM5iE0BTxUkZIOiHujZhpDzzL/YfsWVAfdGnxep6RElJANAUej3ycdAYBO37KWXcK9fD03NP01dLQEMA9/2HaFtdZ2iP/6RhBOOb98NHSJ0WOSFEKcBxVLKpUKIo9p6vZTyJeAlCARDdXQ+JiZdAl2D3ctg6w+g2iBzFHxwBfiauP55fLB9Hjw7AQwNEAGxv+Z7SOl7QKbeHI4hQxj4w/d4t22j5rvvKXv55YivFQ4H/j3FiNgYtl94Ib5duwOiXe9yKex20m65BaOygrKXXwkRevfKlWH71aur239DhwjRWMkfDpwhhDgFcAAJwNNAkhDCUr+azwF2RWEsE5OuT9UuePUEqCqI/Bpj70uvBFcZPDMeRp4LJz8OMUmdMct2oTidxIwcSdkrrzYf+BQG6XKx5bjjUByOgJfMXoTAMWIEGffeizU7m+pvZgeSnDUNgmrB/77qyy9JPPXUdtzNoUGHbfJSyvuklDlSyj7AhcAPUspLgDnAufXNrgA+6+hYJiYHBR9f2zaBD4fUYfWH8OYZkZtE9iN1ixa1/SK/P1jgAQwDYbFQ88MPbD3+eEr+8VSowNdf2xyF9/3eXNG3QGdGvP4OuEMIsYWAjT408YiJSXekqOXydxEjdSheD1U7otNfFBGRbpq22pFATUmh4p13kD4f0u0ObWKztbhJK/1+qj75JDrz6YZEVeSllD9KKU+r/36blHKSlHKAlPI8KWXbKzSbmByMRNO8YmjQyRWy2sOus8/DYwv4rcv6r6b4VAtlCUkt9qPExwU8bcKYfuJPOYXU3/6Wnk8+QfyppwQKk4RDSvTaujbN/1DCjHg1MYk2o86Hn/8enb6cPSChZ3T6iiJ3TT6G0XUaxy36hbqYWBJraxiWtxlFyobSLjZdI95Vy4LhY5iydkVoJxaVvjNn4tu8hXDZcGtmz2bo2sBbUdyRR7LH6aTq8y+QdU0EXVGIm26mOWgOM0GZiUm0GX4WqFGIzlQscN7rrRbhOBD4JHx1xDHccccfeeD6u7jl7od4/tzL8FqC3zp8Fisz7/0jIlzFKE2n4IYbsfbOxdozzINM19Hro2cVm43MBx4Ia84BcIwY0eF76q6YIm9iEm0yhsO5r4I9oW3XCRVGXwKDT4ahp8NVX0PvqZ0zxw5yXmYyjkbPHsUwGL15PXbN32C68VitvHr6eRiajiUjI2w/3nXr2H7JpSSeNSP0pBCoDgc1c+aw8/ob2HnDjeE3oQ2DinffxbdzJ2Wvv0752++glZV1+B67C2bREBOTzsJTDU+PBncr9UxtcXDqkzDy/MijQA8wupQ8tGUXLxWUAnDed19w1ecfEFOfY14XgmWDR/DA9XfyL4fO4Vs3UPJ4MyYsIej39VfsvO7/8O/Yt8nc4/f3YUlNo/D++1vNh+MYNgxvfj5S0xCANAzUxETsgwbS8y9/Cf+m0I0wi4aYmBwIHAnwm9nw8rHgbcHFTwjod9RBI/AAqhBc2jONdwrLqdMNRm7Z2CDwAKqU5O7ZzYOvP8+g5YsoacnkJCXCaqX/rK+p/OADqmd/gyWjBzEjRlD4xz+1nvBMCPyFhQ1VpfYuW/WyMlyLKsm/+BJ6vfwf1Lg4rJmZHbzzgw9T5E1MOpP0QTDiHFj2FsgwOdmFGjDLxB984tM7xkasouDSDXZk9MRrsWLX6v3ZhSDTVUvG8np/+pYsBqqKNTMTo7qa0mefQ6usBE2j5utZiLi40OYZGeilpYE+FQXFbkdJSEBvkkBNFwJV19H27CHv7HMQgPPII8l56h8Iy6EjfYfOnZqYHCiOuhc2fAl1xaHn0gZB5sj9P6coYFcUPh47gKtW5/Hfk2cwfe0KcipKURUFJSYmMru4ouAYMwbX4iW4li5Bq6iA+gIl0uMJu4rX9+xBxMcTO24c0udDr65GKy4OynsjCbxNGIAiJfh8SAJlC3fedBMiJpa6uXNRYmPJ+uMDxB93XPR+MF0M0yZvYrI/cFfAj48FkpPtNSgIFX47N7BR2w2QPh+uZcuRfj/2fn3ZcmwbhDNcYrI2siU7l5ziQux+P23yR7JY6PPuO8SMGtWh8Q8kLdnkDx4joInJwUxMMpz8N1yXvMbSwwby6+G92XruLcgeww70zKKGsNlwTplM3LQjcK9bB20xiUQhdYNF83P+o8+hqW3M4KlpVH7cfSNmTZE3MdlPeDyFzN95D5WWCtxqHfl73mLFyu5ZS0ex2QLpCPYjWaUlHL1kPgtGjMVX/4DRG2341sQ62ZzThypnqJ3fqOu+hcFNm7yJyX5i8+Y/A8Er1vLyn5BSIrpgwFNHiJ0yBWtmJv6CAqRv/1T9tOsaQ/K34FdUhCHRhQjY44G5oyfwl6tuQjV0dFXlrrde4rglvzZcmzhjxn6Z44HAXMmbmOwn3J7dYY9rWk3Y4wczit1On/ffI+Wqq7APGwaRmlD2Puza8dDzWG247Q6mrl2B1dBR61MsSOBvl/8Wr92OKyYWr83OE5ddR3lCIgCxhx1G3OGHt3m8gwVT5E1M9hPpaSeEPW61tjEy9iBBjYujx+23kXTO2WFdFoXTGYiEVVWE3U76nXeSeNFFYLO17HLZ0IFAS0mlzu7AZbezoU9/1gwYgt4k3kAKQUKTfDcWXadkwiQy7v89vV/t3glyTXONicl+om/f6yku/praurUNx4YOeewAzmj/kHDiiZT86xmk379vg9ViQbpcaG431l69yHzkYWIGDSLv/AsgUvOOxcILl1zDJnsMXquNLTm9ySgvxWI0ymgpBJbMTCp79AhKlak7nUx56klS7F0vw2e0MV0oTUz2M9XVq6hz5ZGSfBh2e/qBnk6bqfriC6o//wIlMYG066/H3jd8mUKpafgLC1Hi4pAeDyXPPEv1V181H8FqsQTMNE0LhAgRfmVvtfLOWRfy8tGnBB0+Zf0q7nn1GaTLhbVXL3Jf+jdfORK4bcMOrELgl5K/Dczhwp6p7bn9LomZ1sDEpAuRkDCKhISD0ye7/K23KP7HU4FskIpC7fc/0Pezz7DlZAe18xUUsP3yKwJRqJpG8hVXkPWXP1P16afNd66FiQgGUq65huQLzmfHVb/Bv3Nnw3FhsdBv8CBiFIHbCDwEYqTBjYk2ki+6EPuAASSecQZCCGYAhyfHke/2keuwkXEIrOD3Yoq8iYlJxJS99J996X4NA8PjoeqzT0m/8cagdgW33opWVNRgnql45x2cEydgzcrCv6sN5Z6FwKiuwpaTQ87T/2T7lVeBYSA1jYRTTuHyi86mKK+ID/dUECME/3r1XziXLKLc7UbY7dTNm0f2448DkG6zkm47dMR9L+bGq4mJScTIpkFLUiLDVHXybdkaFOAkvV486zeQdsvNkXva1Pdv1G+aOoYNY8AP35Ny7TU4p03D0iMdUV3N7/v3ZNlhw/k+1YJz8cKGh5D0eqme+Tm1v/4atmufYeDWu1793GhjiryJiUnEJF90ESImpuGzsNtJPPXUkHZN88cLux2kpOhPD4Yt9dcsFguG241r6VIAKt97j7IX/03tt99S9vIrbJtxFnp9cXCjti6s7b7ooYcbvpdSsrKqlhMXb6D3T6vo//MqLl65FVc3FntT5E1MTCIm7cYbSL/1FhzDhxM7ZQq933wDe//+Ie2yn/oHSnw8SlwcIiYG5xFHUDNnTutpg+vZWzdW6jq13//Ajquvofqbbyh59rl95iK/H72qippvvgHAMXhQWP96f0EBem0t1ZrOcUs2cuKyLays9SAJhKbNrajhT1vaYEI6yDBt8iYmJhEjhCD1yitJvfLKFtvFDB9O/29m41m3DtXppOjvT+BZvTrycQiIvKhfmUuPh+K/PxFww2xM/b4AgOJ0kn7HHRT/9a/BK3rDIP+CC/n73/7FutrQh4xfwryK7pvWwFzJm5iYdAqW5GScEyey+49/wrN0aWQBTvXoYVbkhttN/PHHBUw/9UjA2qtXw15BymWXknTeucEXSolWVMTi0kqam4FF0G1NNqbIm5iYdBrVs7/Bt3176AkhUHv1CtmENWw2XHYHpUnJwUXBHQ4STjuVnn/7G4lnnomanh5IT+z1UnDd/7Fx4iS827cjhCD99tvBGuxFU6eo+L3Nm4p2eHwct3gjdVob9gsOEkyRNzExiTpSSmrnzqXmhx/Cb7RKiUJgFY4QIAQJ556D/c23+d1df+LSh5/mkWtuoaBHJhVJySRfeAEZd92FYreT9fBDqAkJwd47dXXsuPIqANSkJGLHjGnIgrm6/2DOe/Apim0xofOox2NIdnl9vLW7+xUAN23yJiYmUUVKya7bbqd27tyAwDcT5OQvKNh7AQA1n39Bev8B3H36Wdy0bjvzR0+gZOrhvD2qH5kx9qBrfY0Kfu9FKyxsyOjZ68UX2PPYY1QvW8HvbroXt93R6ry9hqTEF36uBzOmyJuYmEQV1+LF1P788z4vmOZoYqOXXi/Fjz3GoFmz2PD2WxiqBasSPhulJS0VrbAo6JgSF9eQsllxOsl6+GHw+nD/ui6ieccogukp8RG1PZgwzTUmJiZRRS8rQyjtlxbPypXknX5GswIPkPP888GVp1SV7GefCWm33eWNeNwH+vXkyG4o8uZK3sTEJKo4Ro4MjoIVIrBJ2oYgKH9+Pv5du7BmB+fEkYZB+Rtv4N20iYw/3A+ahvRrOI85Gq2ggLply4gdPRpRv6H79I4wxdPDoAK/6XXwJYuLBFPkTUxMoootJ4ee/3yCdb/cjHukl9i5FhK+bnsREL22lsY+MlJKtp16Gr68PACqPvmU+OOPI+3WW8k77fSG7JVqejoDZs9CiY1lSVVdmJ5DEYDfkC2+PRysmOYaExOTqLM762fcRwiMeIj7QUAbfdCVuDhsffoEHav+6qsGgd9Lzbffsf3Sy4LSE+slJey+9150KamNcFwFeGHHHibNX8uk+et4Or8IowulYe8IpsibmJhEnZLiWRhGvV96BA4r1iGDEU4nqArWXr3o+/FHKPbWPWoA9KqqkGPudetRhcCphkpcONHzA4/mFbHD42eHx8ff84q4f1NB6xM/CDBF3sTEpMP4Cwup+e47XMuXI6VEUff5pLsnGhjW5lfFEnjpsGOx/DyXoWvXMuDbb7Dl5oa0izvyqJBjhhDsSusRcnxvPp0nB/fC3ih6ViHgRRNuDo3RgNd3l/HfwoPfb94UeROTKLKxfCPnzDyHw949jKtnX02pu/RATylqSKlTW7uJ2tqNSLlvE7X2l3lsPeVUdt97Hzt+czW777qbgQPuR1ECvumVFwoqp1vZmNuTzZkpFCU4Q0T1qwHDOGLRRp5ctQEpZUMwVdnrr1M7dy5SSmKGDSXtjtsbrjGEwp+vvoVHrr6ZOoeDOkcMmqKgxMeR/eQTVPo11te5SbaqWIA4VeHsjCSUZpMbNLlf4HcbC9CMg9tsY5b/MzGJEpWeSk786ERcmqvhWGZsJt+c+02D//bBiqbVsWz5xdTVbQXA6ezPuLHvUPvVDxT+7t4gn3cRG0vO00+jj3Ly6/Yv+LzUh/Gdm97bt2LV/Fh0g+yKGkbsKkUCSwaP4J7b7gfAovm4a+dqLtxdSOVHHyN1HaGqJJ19NpkP/AEAw+tFLy1lzKZiygj8XJOrKxm2bTNJcU7+c9X5uBAcuXA9uzoY3GQVgtWHDyfJ2rV9VMzyfyYm+4Fle5YFCTxAkauIdWXrGJ42/ADNKjps3foEtbWbkDJQZLumfA3L75xM3OwwG5uGgb9wN8nTzudFLY4tFXlctv0FrFpgc1RXFQpSEuhVXseCEeN4/Irr910qFDbl7aB05md8eMRxrBkwmN6FBVwy83PiTziBkqeewpufjxofT+y1d1CWlgFCUJGQxLwxEwGYWVaDS9cjFvi9GS/DYVMEiZY2FDnpgpgib2ISJTxG+ARYq0pWHfQiX1O7tkHgAbCCqPYT8DAPxTEscL9WRWD3eTCaBEepsbG88sQzfKEEm25UXSelvJiHr7yBhUNH4bU7WDh8NAtGjeel225DqaoKpBeurOTeV5/lxnseCRn7+7LqNt3bmPgY1tS48Yc5l6yqlPj8+CRk260H5RuZaZM3MYkS07Onhz3+7fZv9/NMok983DCE0UjQ/SCaSeqYcc89xIwIiPztvTOoSctEV1Qa1vxCYIuJ4blpE7m/XxaqrmP1ebH6vGQXbSfOW8v8EWPx1ueb8Vtt7E7twdrs3kFJyYZs34bN76Mp/WLt4WqHNMuGWk+z7Xf5/Iz5dR1HLFzPiUs2UeU/+HLbmCJvYhIl4mxxZMRkhBxfV7aOjeUbD8CMooOUkozMM7FqieANiLulEBxrFapjnbhtNvyKgsdi5Y3b7mP9yac1XHt4cjzvTBxGyVW340/PQrHZ6dGnHxc++Bg2m42bemfwzcB0ZiyazXk/vM8F3/yXIceeiGIJThWs2gNjNEaRkrvffgm7z4tSH02bZbNya24PBsY6iFTn3VLia8Zes7d6lMeQbKjzcN9B6FZpbryamESJdWXruPjLi9FlaPi+gsKkrEn8bdrfSI1JPQCzax9S6qxafT3l5b8iUDBqXCS9oeBYq7Cm3xAeuO52Dl+1FKfHxbIhI9ma0xuAe/tkcFvfrIjH0TU/lXuKiImLJyYhkVOXbWZNjRuflKhAus3K+//9N8a8uUh3o1cIRWHroCH88OCjDE1N5ursNL4oqeKWDTvwG5K9/xIKEC4syimgrg0SaBXw86Sh9I21t954P9LSxqsp8iYmUeL1Na/zj6X/QLbgopdgS+CzGZ+RFpO2H2fWfnbv/oCNmx7CMPZmlBTE1KWT/lQsHw0dzQtnXIDXFip4CvDL5KH0a6cY1mg6f9hcwNJqF/1j7Px1UA5ZVpXKjz7Cs2Ejvm3b0EpLseXkkPGHP2DLCeS4qdZ0Rs1bg6eR26MCzOiRxCfFoZWhrBDWFt8SPawWlh02HEsXSoFgeteYmOwHEuwJCESLIl/rq+V/G/7HTWNv2o8zaz91dVsaCTyAxJ/oY+AP85lcVs1La/KD7OSNWVBZ226Rj7eoPD20d8jx5PPPb/G6v+cVBgk8BFbwM8MIPBBInhZmoZtkUdAkYdMiFPs1Ll61hRyHnVFxMVyWnYbahTdkTZu8iUmUOKXvKSitpNg1MKjx1eynGXWcuPihKMq+6FUhVJzOgQAclRLPWRlJ2MLVYwV+t2knm+uaL7nXHFLTKHvtdQpuv52SZ59rKNTdGr9U1PBaQfjgs+a2S/3NWDLcutFi3pufK+p4t7Cch7bu5rq1+XQli0hTOizyQoheQog5Qoh1Qoi1Qohb64+nCCG+FUJsrv9vcsena2LSdXFYHByXexyqaN6v2qE6OK73cftxVh0jM+NMevQ4CUWxo6qx2O2ZjBj+DwCEEDw5JJfZEwZxampCyLV+Ceet2NLmMXfdfgclTz9NzdezKPvPf9h++RXIZqpLNWZ5tSuSNDkR0dxGbFPchuS7smp2ekK9fLoK0VjJa8CdUsphwBTgRiHEMOBe4Hsp5UDg+/rPJibdmgemPsCQlCHYVTtWxcpxuccxo/8MkmxJZDmzePiwh5mYOfFATzNihBAMH/YEU6d8x4QJHzN1yvc4HD2D2gyNi+GVUf3ItltDrm9rOT3/nmJqf/oJWb96l14v3i1b8KxZE9SuyOtnQWUthd594prjsLUoaFZp4HS1nnpYofngqHCowFaXl/W1bnzNmK4OJB22yUspC4HC+u9rhBDrgWzgTOCo+mZvAD8Cv+voeCYmXZkEWwL/PfW/7HHtwapYDypPmpZoKuzhGOp0sMsbvI0ZGyYLZEtIvy9QYKQRQhHIRqmE3yss556NO1EEaIZkRkYyg5wOpiXHMS4hliXV+6KOFcBS74d/5TczOWXObO6//i5WDG4+OK2tMu0xJFetyUMVghSrhZnjBpBlt7Wxl84jqhuvQog+wFhgIZBR/wAAKAJCHYhNTLohQggynZkHehr7nX8NzWX8/HW46zc+BfDcsNDN06ZIKdFkIDrW2rMntj598G7dGsgRr6oozjgcI0YAUOLzc/fGnfikbFhuf7CnoqGviQmx/GVANt+UVZFitfDbkgLsd9/SUG92fe/+ZJSVBDZbo7RZutePHiQe3cdt63fy3pj+Uek7GkRN5IUQccBHwG1SyurG4b9SSimEaGZzW1wHXAeQGya9qImJSddDr6mh6JE/4165EltuLlkP/omU7GxWHT6CdwvLqPHrnNYjiSFxMS32835hGfdsKsBrSDJsFp4f3pvJr79G4UMP41m7FlvfvmQ99CBKTKCfXR5/QOCbYXG1C03CV+MHIoSg8qNl7C33vXLAEH5307147fawHjXRQAc21LVSwHw/ExWRF0JYCQj8O1LKj+sP7xFCZEkpC4UQWUDYYotSypeAlyDgJx+N+ZiYmLQPt3snW7b+HZ+vhPS048jKOpea2nVYLPHExw1HCIGUkh1XX4N3wwakz4e/oIC8Cy6k/6xZxMc5+b9eofndmyKlzoKSPO7eWIu3/q++yKdxzvKt3NEng6MffIQJic6Q63o5Qu3+TVlb66bMryOA0tzeDYL+2unnBQQeGlbxKgGTTlt95ZtDFTAw1hGl3qJDh0VeBJbsrwDrpZT/aHRqJnAF8Lf6/37W0bFMTEw6D4+nkIWLTkXXXYCkunolW7Y+gaLYkFInJXkqo0a9iFZS1iDwAOg60uPBvWIFcUcc3uo4fn8Vy5ZdzMeuofi4iMZJziTwVP4eXthRwmXZqTw0ILiQd6rNSo7NQkELG7oGktd2lfDM9mKsipWzTzuXSz/9H257qM++AUReXrxlYhWFJKvKP4d2LYtENLxrDgcuA44RQqyo/zqFgLgfL4TYDBxX/9nExKSLIaUkL/9F5v06HV2vY6+x2zC8SOlD12sxDDflFfMpKvoUYbWG+oVLA2FtfZUNsHHjn6hzbSVBlhDOiGsALsPgzV2lYU0fn4wfRB+HDQsBu39TEdMkPJm/B5+U1OkGbx17Kuf+7QVKklJCzDTtNR2EWx2fmp7Ir5OHkuPoOpuuEB3vml+g2VxAx3a0fxOTxhiGQV1dHQ6HA2uEotIZ6JWV+PcUY83ORo0LNSuEw++vxuXOw27rgcMReV6XaCKlpLZ2PT5fGfHxQ7HZ0thZ8Bbbtj1Ja34lhuGmtm4rFZWL8Y41sK0AxQeGBWS6im3UYDye3eRvfwGfr4z09JPIyjwjpJ/K6nWUyTiKSUNBx5BK2E1QqxDs8WoMafLj7eWwMX/KUKo0Haeq4peSx7YV8nJBSbOr8hpnXGQ/oAgYFx/DHp8W5EmkAD3tNhxt9CbaH5hpDUwOGsrLy3njjTeoq6tDSsnxxx/PlClTOm08z6ZN1M37FeGw45wyBXvfvgBUvP8BRY88EhAmIcj519PEH3lk+D42bsK1cAFutZjNGW+AVUFKP3373EKfPr/ttLkDeDy7KSn5FiFUevQ4CV33sWHjA1RU/IoQFoQQjB71Ktu2/YPIHAcFFRULqK1dj7zcR2xvBdtWgZYhqTuhHM+GG6mtWY9fqwF0Ssp+4ovdG6lKvpTR8bG4DYlHN/id9894UTBQG4m7pOla0WUYzfqdCyEaqjVZEYyKj8GhKtS1EKUaDRTgmaG9mVtRy0Nbd+E2JAKIURUuzErp1LHbi5mgzOSAYxgG1dXV2Gw2YmNjG45rmkZdXR1xcXGoqspzzz1HSUlJw3mr1crll19Oeno6eXl5CCHo27cv9jC219bQNA0hBGXPPkfFW29heD3QJHe488jpZPzuXradcQY0icCMmTIF7/r1CCFIvvxy0q7/LbU//siu2+9AGgYGPvQ0g5J7NLCBojiYMP5D4uOHtnmukVBbt5klS87FMPYFCwXqsgavdS2WJDStmshEXiEgxC1ZsYNTftXh5DrxJgAOoKUEBdOT4vi5sjbomEPAU0NyOSuzZQH9qbyG36zOo66Tg5GSLSprjxiBIgSf7inng6IKEiwqt/fJZJDzwG24mgnKTLoshYWFvP3223g8HgzDYPTo0QwZMoSff/6ZwsJCFEXBYrFwwQUXBAk8gN/v58cff6S4uBiv1wuAw+HguuuuIy4ustdzr9fLe++9R15eHv03b2bsqtUovvAh6nU//UyRJETgAdwLFjR8X/af/2BJSab0uecbIjcVgFJB7CIF1xEGQqi4XNs6TeS3bP5rkH29OTStEiHsSOmNoFdJYJO0JZEPFlmlUdvWMtDMbyLwAB4Jv9+8q1WRn5Ycx9TkOH4sqw5KbSDqvzoq/QoQowjeGd0Ppf7tY0ZGCjMyuubqvTGmyJt0OlJKhBDs2bOHzz77jKqqKjIyMhg+fDhffPFF0CbeihUrWLFiRcNnXdfRdZ133nknbN9bt25tcOuDgPB/+eWXXHDBBRHN7fPPP2f79u1IKcnZsbNZgd+Lu9HcmkO63ZS/+SZadXAZOqGBUq9jUurEOjsvYMbnLyOSbcXIBZ76/pp3NhTCipT7znuxMbch6L11muvZFYEJRhGCN0f2ZWZxJX/asotqTcciBJqUIVkpI0UAfWNs5Lt9WETg0ba2xs24hMj2YLoKpsibdAp+v59vv/2WFStW4PP5goQYYNu2bWzbti3i/nS9+dVj436llKxfv55FixYxadKkVvvNz89v6NvjsGPQistZVjx43OBr2bPal78dNTk50Hf9yl9aBNpQB4qi07fvbcTHDWl1fu0lLe046uq2NkkT3AQJscXJeI1StMyOp/YKFngrKxnDW/ymQ31aCKzSI0ERghkZyZySnsiiqjq+LK7i3d2l7fagERhscwce+j4JSMn9m3dxeo+khv2Ag4GDZ6YmBw2GYfDmm2+yc+fOhmP7e+/nm2++YejQocTHxwOBh8qiRYuwWCwMHjyYtLQ00tPTiYuLo7Y2sLxeM3IkWYVFWKUM5EhvZN+VdknZzRr+fnlY8xRSn1YRPhHYKrRaQdeD86obBkZtLTEjRuBeswYlJoaM399Jr2OHYbf3wG7v3CwfffvcgN9Xxu7CD5ASYhzZuNxbgxtJiH2xjPgyhYprBN6R0fs3suNnNCuZyi/MY9+mdIbNwqi4GL4tbz3dsgCOTU3g2QhSIzTGpigckRzPNWvyifQdZUisnQ2u4NaGFGH9Bot9minyJoc2xcXF7N69+4DOQVEUqqqqiI+PZ/bs2cyfP7/h3Jo1a7BYLDidTk455RQ++ugjpJT4UlNZePFFHJOcyosFpazJGU6CVsllyU8Sk1GHqF/i+/saFP3DwFIIqf4p9BtzF1p1FbtuuRUamXukYSANg7Tf/pa0665F2Paf/7QQKoMHP8jgwQ82HFu16reUlf+MoXsRPnCsEKjVUH22htFy9oF2YcfLKcxkHkdiE4IXh/VGEXDVmvzw7YXAW78YiFEEr47oy9FhUhhHSnO54kPGVQSXZ6fhEIJ7NmxH8fsxVBUJ6JZQN92u5gffGqbIm0SdvXb0zkBRFLKzsykoKGjx7cDv9xMXF8frr79Ofn5+yHlN06iurmb+/PnceOONbNu2DZvNRv++A3jrfxvIqSgjtwxUYac0/Vp69XiGoA1HBbRsKFVXM2LcWAyfD0tyMlpJyb4Vvd+PZ9UqvJs24Vmzhl4vvhDdH0az915BVdUKVNVJYuIYioo+o7DwIxAqWZnnUD1/Lup3u3GsEpTc70dPJuAU0yqCuLih1Naui3gudiEZEGvnvn5ZnJKexKh5a8KaT5yqwsP9e/JWYRmqENzaO6NDAg9wZo8kPtlT0ZAwrTm8huSZ7cV8OX4gv5v3KZuqqkmqKufX8UezfuBIDHXfD+evg3LanFnzQGOKvEnUSUpKavG8w+HAE6baT48ePSguDpviqAGbzUZSUlKQKSgc/fr1Y86cOezYsaPZNlJKSkpKSExMZOzYsQB88dxyfGvKscr693Rpw1UygPJNx5M6dFZIH0IE/oQUm40+777DrrvvwbtxI4bb3SD20uOhbt68wAMgNRmBQFWaLyzSHqQ0yMt7noJdb+D3lwNWhFBRFAu6vs9rpbJyCWq8JH2Vgm+AxIgnQoEHUHC7W/65B80J6JF2PD+NGIIqBHW6Tmkz6Qj+O6ofk5LiuCQ7erVv/zYoB6eqMqu0Co+uU+JvfuGxx+fn6jX5PDB0CMbMj9F8Xk6YOxNVCPIGjSLB4eAvA7M5KT0pavPbX5gibxI1PB4Pn376aYsbqqqqkpOTw7Zt2zCa+DS3JvBOp5MBAwawdu3aVucyYcIEvvrqq5AxGiOEID09veGzq7aGHWtLQTYRYMOOpyK8XTg9bV+VJ2t2Nn3efYe6BQsouPEmjLpGBSoUwQM/3MBXno0IIThn0LncP/l+FBGdVeG69fdQVPRJoyN+pPQT+kKloadA5WUSx8rwNufm0dH1tpUufKy0D3fNW0O6zUpPhxWLCK269Kf+PZmUFL2I1L3YFIVHBmbzyMDsQA76DTuatdEbBBKbTTn7QqqK97D+lx+xSoO7VRfHHTUW0UpZx66MKfImUePDDz8kLy+vRVONruts3bq1XRuxXq+X1atXtyjce1m7di2xsbHU1IQXJavVSkxMDDNmzGg4tqf4C6QMV+RDothrAAUhYpCyrtE1X5KZOYOUlMMajsWMHo2SmIjh9YKmIex2CrMlsz3rMFBASj7b/DG943tz+fDLI739FgkW+NbxTDDwhA2daQ6Ftnqb66i4pIViv06xX2dtnQebENiFRBECCRyeFMdve6W32ldHOTczmTd2lbKsxtVsm3SbBUVVOfnGOzjx+lsBUKL8xnUgOHgfTyZdivLycrZu3RqRLb69njaapkUk8AAbN25k8ODB2Gw2LBYLVqsVu92OoihYrVYMw+Coo44KNi0p5cRlrQ44tAchcO0ZSnra8UgZLBKG4WH5isv4/of+zPlxOGVl81BiYuj7/nvEn3AC9qFDiTltGv+8QMff6M/Na2j8suvnsHN3ufJYv/73rF5zK6WlcyK638hpe6GM+LhRJCdPa/N1fqzsJifomE9KTktP4i+DcnhlRF/eGtUPESZvTbRRheB/o/vhDGNPj1METlXh+UZePIqidguBB3MlbxIFdu/ezeuvv77f3SSb+t43xu/3U1VVxfXXX9/w8Pn2228xDKPhQfHVV18xZMiQhlQKyclT6HX4VeT9cD2eskE0FkTdk4QjpuUSeIbhYcXKy0lLPRZFcZDzwMXkJE+htHQOzh9+RLglsr5PBUmPmOBoSSkNams3sGTphRhGIN1vael3DBnyKFmZZ7Y4tqrGBdnew6EodrJ7XkKdK4/y8p/Zu5GsKDGMHPEMQljZuPFB3J68oOvqXJsZNuxxqqsXo+te9m1AB2z+KSnTKS//GcPYZwwxAB92fISmmEixWbg4a/+XRUywWvhk7ACuXpPPLo+P3jE2bsnNIMGqMi4htkuV7IsmpsibtBmXy8WOHTtwuVykpqbyww8/4GslUrSjqKoa9JZgs9nQNK3FB8vq1atxuVycffbZlJSUoKoqWqOUBKqqUlVV1SDySYnjGTrsIVzFH7Djlz5IfW+BCQ17cj47d75FJFGkpWXfA1Bc8iUxMbkMHfIYZyZ52eq1ocmAzDsUhVvH39VwTXHxbNasvbk+v8w+DMNDXt7TrYr8uHHvsmTJOUEBSftQSEmZxtgxrwKgaTWsWn0DFRULEEKlX99b8HgL2bTpEaQM9+8ocDiymTTxc/bs+RKA9PTjURQ7DkcmmuZm6bLzcLm2AxJFjWetHMm/jUsRGMhGbzAxijggAr+XUfGxLJ467ICNfyAwRd4kYvx+P88//zwVFftqau41hXQmqamp6LpOVVUVVqsVi8WCxWKhuknagKYYhsG2bdt4//33Oeecc0JMSYZhhHgCZWWdxWkXncV38gs2ztURwsAWv4fsqS8BbY8Kdbt3sHLVtaRZJL/PdLPBoyKAKRkjSYsJ2KI9nj2sXnMTzdm8DaP1ukUJ8cOZPm0xNTXrURQb6zc8gMeTDyioaixDh/y5oa3FEs+4sW9hGP6GbJQ//jSmGYEHqzWeOOcQVNVO3743Npmbl+UrLsPtDsRFCGFlyOA/0c9XwvCtN2NInY/luXwpzmFEfAKPDsphaCslAU2iiynyJhHz3nvvBQk87LOTWyyWhlVy4+9bYtiwYaxb17rPdXl5OVJKVFUlOzubiy++mOeeey6iOeu6Tn5+Pk6nkxkzZvDpp5+iKApSSs455xxiYsILzshjBaTfia4JVFttMzWfI9uM3GtGiVNhgjPwoNHq1lJWNoe0tGOoqlrSbD+KEkN2zwsjuNOAeCcnB1I5TJr4MVXVK5CGj4SEMVgsoflWFGXfw7mxqaUxQlgYMeJ5VDV8Zs/i4lm4XHlIGXCJlVJnw4b7AydlYBfiPPEx1yUXMnbM6xHdh0l0MUXeJGJ27doV9rjVaqVv374NrpNxcXHU1dU1ZIYMh6IozJgxg02bNrX6QNhrktF1nR07duD3+5kwYQI//vhjRA8Tq9WKEIIRI0bQv39/qqurSUxMxOEInxq2tHQO69bfg2LREWpLq2gDqzUJRXHg85XV28VrkLL1OUmps27d3Wh6bbMpDuz2LHrlXE5u7rWt9tcURbGSnDQx4vZpqUdRVv5TiNgLYWX58ovJ7XUt/fvfHnKd319B0wdUIF/OvqeilBpVVcuYWVzJrJJKHIrCb3LSGBEfi0nnY4q8ScQ4nU7c7vAJr84880wcDgf//ve/KS4ubtjcbG5zVFEUdF1vsK2HI9y1uq7z+OOPRzxnq9XKSSed1PA5JiYm7Oq9oqKCbdu2IWUl5RU3oaqR7THYbOlMmbwvSGrPnq9Zv+HeCNL8Gvi1SgA8nl00fSuw2TI5bOqcoNV2ZzJs2BOsXXcXlZULUNUk/P5yDKO2IcHZjp2vkJZ2FImJY4OuS06eSmNBF8JKTEwvPJ7dGMa+gLfPxfl8uC6/oWj3u0XlnNUjieeH9d4v3jWHMqYLpUnEnHfeeSF/kHa7nUsuuYSYmBhcLhclJSVBbo7N/QFrmsZ//vOfsAU+hBANro8dITc3l0svvZRx48a12K6goIDnn3+eWbO+5quv5rBs2cloWiRjq/Tvd3fQkYyMkzly+jJSUsJXimoeg4weZ5KYOJ7s7Es5bOp3URd4w/Cya9f/yMt7loqKhY2O+1i95mbKy3/CMHzYbAkYRl3I9XV1W0OOxcUNZviwf2BRExDCQmLCeMaNfRencxCK4kBR7Ajh4BP9pAaB38uXJVV8tKcipE+T6GKu5E1C0DSNDRs24PF4UBSlIUo1IyOD2267jUWLFmEYBuPHjyctbV8YusfjCdncbMn7pby8POghsDdDZFFRER6PB5er+cCV1rBarUyfPp3evVvPYPj555/j9+81y1jwepwU7h5Mr9y9kbV7y0U3jQHQWb/hd8THz8Th6Imm1SClZMvWx+pdFNuGM24gI0b8I9Cz7qKoaCaG4SEl5QgcjpbdNxvj9RZTXb0KRbVTVPQ5NTWriInpg8e9A5d7B4bhRVHs9M69huqa1dRUr8WvVTSYmWprNyGELSTPvDNM/nufr4wNG+9H02sQQqG2bj3lFfOxWpPqq1IFHvgvcQFlpPEP7mW7CJRR9EnJmlo357b5J2XSFkyRN2mgsrKSL7/8kq1btwatxlVVRQjBeeedx+DBgzn++ONDrq2oqOCll14KOS6lbHEjtvFDQAjB7t27qaqqijjoqTmOPvpoBgwYEFHbvamG981JxevbZy8ePOgRqmtWUVj4fsi1fn81mzb/GU2rpbJyIVLunXdb5y+QUmfz5kdxu3dRVbUE3XA1FFwZN/ZdEhJGttpLRcUiVqy8EsPQCXgDCUDWr8Ile01IhuEmL/+ZsH1I6SMmJhefrwKQSOknt9fVQaaaTXUensor5ISSS4mXFYFRpI6mVbFu3R00NVUJII1S7uNBbpEv4RN2HEIc0JJ5hwqmyB/iuFwuVq9eTU1NDQsXLmy0ot3H3tX5xx9/zH333QcETBylpaWkp6eTnZ3Njz/+GHajVVEUjjvuOH799dcQl0dFUYLE3O/3U1lZGST8FosFKWWbslrGxcVx2GGHtd6wnn79+rFu3bqGMRRFIzm5EEVx0DPrXHJyLqKmZhR79swMsjMH0CkpmR3xWM2jkJ//XLNujBs2/oFJEz+jpOQ7qqtX4XD0JDn5COz2NFR1n1CuXPV/TTZP9/4sI3/oCGEhPn4EQ4c8isuVh82WFvQmke/2cvLSTahaBWexJ0wMbfNvbxapkyl3U6RnM6mqlAuOHBXxvEzahyny3Ry/38+8efMoKSkhMzOzIfOi1WqlvLy8ofRdJHi9XnRd58cff2TBggUNG6PTpk2jri7UhgsBX/TGwVJCCLKzsxk6dCjfffddSPumcxFCcMIJJzBr1qwQW/9RRx1Ffn4+eXnBEZo9e0Zu2gA47bTTcLvdbN26FUVRGDlS0K/fMFJSjiA7+2IAVDWWlOSplJX/GmTGEIZE0SW6tWPbW4qwYsjmq6D6fCVs2fI4OwvebFTtSUEIC0MGP0zPnucBoOstxw60hqo6sVqTGTToT1gs8SQkhIrw/wrLcesGMShtrroUo7n53X9ewlGuM8iqoJ5/Sofma9I6psh3U0pLS9m5cye//PILFRUVGIYRUfbGlrBarbzzzjts3749aGX9448/cuyxx4bNLAkERcNKKdm1a1fIij0cFouFrKwsJkyYwKBBg5g3b16Dz/tRRx1Fnz596NOnDwUFBQ1vIFarlSOPjGzT0zD8eL2FCGHlkksuaTCNNN0sdrnyWbT4THQ9kGoAVAQSDJ1eu9y4HCqlaTaacaaPbC4tCLyi2ElKnMSOna80cc80kNLHxk0PkpA4hjjnQFovtB0eIRz0SD+BnJxLiI8f2axffGCuEgnUiXiWyMlMYBGWSN4UDIj7RqHnmnxQFGwRlGc06Thif+cbaYkJEybIJUuWHOhpHPRs2LCBDz/8EF3X91s+GUVR6NWrF9u3b49Kf3s3TqdOndqql82uXbtYunQpQggmTpxIZmZmi+1r6zazcuU1eDwFQMDtLzX1SEaOeA5FCR1r0+a/sHPnazQ2Q8R4BVMXliCAkmQrq0YkdEjkAxud4VMKpKZMY9Cgh1i46KSwQUuK4mDo0L+RmXE6a9feSdGez4gk/cJeLJZE+vW7g5zsSyJyZ9xQ5+aUJZtxGQaK1JkhZnK8YxNDkvvTM+sC1q2/E5cr1BPHustGj386A+YdVaXPe//D3rdvxPM0aR4hxFIpZdi8ouZKvhvyySefRBQkFCmRRLAahsH27ds5/vjj+eGHHzpcGUrTNMaMGRORG2V2djbZ2dkR9WsYfpYvvxSfr7ThmJR+ysrmsnPn6/TufU2Ya7w0Fc19qcaihSAp6QgqK38JPipsWG2pxMT0wuHICSuehuElxhG4/6FD/4ZqiWP37g9CvGOao2fWufTKuTTimQ5xxvDh2P78dVshNZrOuIybmJGT1vCAmDrlG7blPUde3j8aXWVl3KmfILMKkH4/sZMnY0lJCT+ASVQxRb6boet6i5Gm7aEtD4yVK1e2mMc9UhRFieqDai9ebyG6Frp/IKWX6urlYa/JyjyLwsKPGjZdFSWGbPswsM4FvwuLLgPPgA6ofr++t+Dzl1FVtSDIJCOll+LiWQwf9gTjxr7NosUz8Pn2BF2rKA4SE8fVf29lyOCHyMw4neULfkPa1rOwunrgSllPRZ9ZIJqu8BV69rykzfMdl+DkgzGh3kuFhZ+yLe9fgE7Pnhdi6F6s1mRyc3+Dw5EFxw1p81gmHcMMhupmqKq6r9qRBKSI+M09GpGHxcXFbRb4vUnHGs8jOTmZxMTEDs8ndKxkjDBpB4Sw4owbFPaaxMSxjBr5IvHxI3HGDqBf31vofeR/4bCbIakP5dk9QYnsZydEaICTotjJyjqL0tLvw6ZEUJRACly7vQfDh/0dRdnnTSOEjazMGSHXJMSOpe+iR0ksOJK4slGkbZ1B5pqrQ9qVk8GLK57nh5Ji9A6a9rblPcu69Xfi8WzH4ymgsPAjEhJGMmjQ/QGBNzkgmCLfDbnkkkuw2+wkVA4nsXwUQqphhd5mszUU07BYLOTk5IQ2agYliuXQhBAcf8wx9MrKIi4ujgEDBnDllVdGdYy9WCzx9Ot3R5BQgkp8/DB65/5fs9elpk5j0sRPmTJlNr17X4dQVTj693DbSioGRJq6VmXAgN+RnX0ZQthR1XgUxcHAAfdjt2dgs4VLwavSv9+dDZ9SUg5n8KAHsVqTUdVYMjJOY9CgB0Ku8m6pxKIlocjAQ0Ux7CQUTUXo+3Kmb2QId/F3nvGdydVrd3Deiq1orRS9bg6/v4K8vKeCjknpp6Dg3Xb1ZxI9THNNNyQpKYlTD7uYn/+3CYFKSskkahI24XOUB72u+3w+7rzzTiorK4mPj29IJRzJZu3eAKm22t7tdjvp6ekUFRWhaRpCCCxSEnPLrRyuaQibjV7/fpHYuOjX/NxLn97XkZw0karqVSA1EhLHk5gwEiHaXglISonPWxJha53du99jyuRZ9M69Bpc7n9iY3sTE9AJg0KA/sWzZRRiGBhgB98gwBUN69jyvwWWyhYkhhIJs4mnjsPfCTzmaVsHz3IJX1OfxkbCiuo6Piys4P7PttvKqqlXh79gIn+vIZP9hinw3pbbcjyAgWoq0El89mErLcnTrvj86RVGwWCz06hUQmXCFNZrD7/czfPhw1q9f36boVK/XS1FREaNHj6aoqIjEmBgGPPsc1tragHXJ42Hndf/HwF/mooTJaxMtEhPHhiTbaguG4aeubhM7dr6F2xPOoygQadoUv78KgJiYHGJigt+cEuJHMHnS15SWzUERVnr0OBmrtX0mK3v/JIRVQfp1MECqGkbPGiYf/hkbN/6Joj2fUyWTgq7xGpJCT+u568Nhs6WFPZ6ZcXq7+jOJHqbId1PSe8VjsSlovoAAK1iIqxlIVUpgxSWEID09PSjdrtfrbZNdfteuXe1KPyCEIDc3l9NPP53aX+axS9OCvKylrqMVFWGLIO/MgcDnK2fxkrPx+UrCRMAGEEIJqfIkhI30tOOa7VfXXbhcW4mN6U1S0qSgSNa2ojgs9LhpDJWfb0Mv92Dvl0jiSX0RqsKgQQ9Q59pK35p8ttAfo14GbIpgXEL70v8mJAzH6RxCXd2GhmOqGk/fvre0+x5MooMp8t2UARN6ULCxgo0LClFUBUeclakXj+Xr7wuora2lZ8+enHvuuUGi3qNHjzb51VdWVrZrbn6/H5stYBu29sxCNn1z0DTU1PArw67A0mUX4vHsbPa8EFZSU6ZTXvYTBlq9541Cjx6nMGjQH8Je4/WVsnjxWWhaNUgdq9vDxDU+bBnj4OL3wNL2txpLkoO0y0L3CyyWeCaM/5C3a3dz2bpKtrk1JJK7+mYyLSW+zePsZdLEz9m27QkqKhfjdA5k0MD7Wwyq6s4Yho40JGoHM6lGgwM/A5NOQQjB0ZcOYdJpffF5NBLSY1BVhYHDm19Z7a/gqcZRpfZ+/Uj9zVWUvfoawmJBahqZDzyAGhdayagrUFW1DJdrWwstBEOHPkbmqiXsyauj2qHjdOv0LFMR1/0fKOFFb/PmR/F5i5H1JQYNq2RrT42hm+fAc5Ph1hVRvQ8hBLnx2fw0OZsqv0aMqmDr4Ea3oigMGHBPlGZ4cCKl5Od3XmPZV58hpaT/+Emcess9WGwHrki4KfLdHGeSHSd2dM3A0A0Utfk/5IKCgv0i8qoK+fkvIJRU+va5kfRbbiH+xBPx79yJfcAAbH36dPoc2ovLlUe4tMNC2HA4shgx/F8kJIyA128h01NDQ+ytUGHdZ3Dk3YSga7h3fou0NfKPVwSumPqN4Io88NWBrXMefIlWUwaixZo537Limy8x6h0Sti5bzCePPcRpt9/bUHbS4ew8p4JwmP+63ZydG8r58tmV6FpAvFWr4KTrRtJnZKg5xOfztTvF797VeWvXCwGK4kIos9m1C0pKZjFl8mwcgwfjGDy4XWPvT5zOgQhhDbG3S+nD4yliw8bfM2H8h2HSIwgoWQ/f/BHSB8Hoi0CpF/HZvyeppJTanjEYauANR9ElSVX+xgN04l2Z+L0eVn03i5qyUnoNH0X/8ZHl1Vnw8fss+Pi/6JpG1oDBOJOT0RoFI0pdZ8ealbx43aX1uZEUeg4awthTzsRitZKa3YvEHuHLP0YLM3dNN8ZT6+fVu+eG6INigYv/NIXE9H2bbFVVVTz//PPtjpbt168fubm5zJ07F0VRiImJYdq0afzwww9BJQPT0vPo128pdnvgmKLEMnTIX8jMPKNd4+5vpJQsX3EFFRXzwp4XwsqI4f+kx7Y8+P5h8LsAAUIJfBn+wOfEXnDTIrDGwINJ6EKyangCFUkBv/bUch8j19egSAJtb1+z3+7xUEPz+Xjn97dTUVSI7vdhsduZcvaFTJ7Rspvqqu9m8+1/gnPyKxYLRhsitVXVwtTzLmLyWRe0a+57MXPXHKIUbKoIvwCUgqJt1UEiv3DhwqBskW3BarVyxhlnkJSUxJQpU/B4PCQkJFBcXNzEHdNgyJB5iEa++gIwmsmh3hUpKvqUqqplzZ6X0k9NzVp6TLkTnD1g8X9g5yKQeuAr0AqqdsDj/eCEPwMSVcLYNdX4LYGVvFUXYHFC1ii49OPOv7FDmG3LF1NVsgfdH/g91Lxefv3gHSadcQ6ihX2KpV9+EnKsLQIPoOsav7z3Nq7qasafOoOEtPS2TT4CzIjXbowtppngHiGJjQ/eCPJ6ve2yx/fu3ZvbbruNpKQkABwOB0lJSQ2FuoNdMhXKy/ogxN7NR4EQKqltrod64Cgt/a5RPvfwiPo0BIw8B+pKG4l7E/wu+Cm4KLlVk1g1CYfdAvfvht/MAlv73BpNIsPvCXWDNTSdNT9+y66N65u9TqhtD54Li5Qs++ozXr75ar5/5YWo74uZIt+NyRmUTHxaqDdHzpAUcoYkBx0bPnw4VmtkhaMlEr/wM6fXHJKOSMLpDL8hmJGRQVxcXEN6AlVVKS09neyeF+GMHUBK8uFMmPARdnv0Vy+dhc2WDjT/x60odhLiR+w74Cpttm3gfHn44/Ofg09+Cx0sg2jSOr2GhyurKPn25ed5/+H7+OntV8Ned8RFl0d1HtIwWPvT92xbtiiq/Zrmmm6Moipc/KcpLJy5jV0bK7DHWhhxZDb9RvdANEmo1a9fP84880xmz57dYoIxXejkxeexNWErtZZaHl34KIOSBzE8bXhDm927dzNz5kxqamrIysoiLS2NsrIyMjMzOfXUU4mNPXhXpn363MCe4i/R9bqGjTQpJYoS2IxNTz6K1DoHuBdB1hjofQRsng16MyYpRQ1fmc/wB7xxeh8O4y7rxDvq/uzetIH5H76L3+tl1LEnMmz6MUHnE9J6cN4f/sLsF5+mtrwMryuQpVTqOhJY+uWnjDr2RJKzgtNZp/bs1aZ5KKoFQ2/ZnKP5/ZTu3EH/8ZPb1HdLmCLfzbFYVQ4/Z2BEbUeMGMGIESMoLCxk/vz51NbWkp+f3+Axo6oqC1MWUhBX0HCNlJIVJSsaRL6mpoZXXnsdze9DANvy8sju2ZObb7456ve23zF07N/+lSmrt1OcZkFmjSZt+jMIm5OamtU4qmuI+++NCO2tQHtbHFz2KXgqYPuvgAqqBbRG5h6tBdOP3wUFi02R7wB78rbywZ/vb/B42ZO3Bb/Py+jjTg5qlzVwMFc++TxLv/yUH998OeicNAxqyktDRL5w8wYixRYTQ+aAwaRk5bBhwS94qivDNxSQ0jOy2giR0ukiL4Q4CXiawDvuy1LKv3X2mCYdIysri7PPPhsI+M7PnTsXXdeZOHEis5fPhiZ1ohXXPqvfm8tX4zYM9lr8DV2noKAAn8/XEOV60DL3SVj5X2x+Lzm7vLDrV1hzHNwwH0f6CfDGoGDR9tXCK8cFfOTHXAKn/ROK18F/jgYjgg06RYX0ru9W2pVZ/cPsIJdGzetlyeefhIj8XtRmfkdXfjuLXkNH4vd6MAwDhzOOjP6RLZ4AfG43O1avYMfqFSgWC87kVFxVFcgm5jip66iWyMymkdKpIi8Caf2eA44HCoDFQoiZUsp1nTmuSfTIycnhoosuavj8qPNR7vzxTnQtEB2b6E1ky6wtLBTLqOs9gPdKqjkipIpS4C3goMXngp//DotfBn+TlbenAj6/BS56D2r3hL9e6rDqPUjpF/iKdGMtvidMvLZjcz/ECZeJqaX8TFkDwtcU2LJ4Pm/ddytlO3cAkJCe0WDWaSuGpuGqrCBzwKCwbwM71q6i37iJ7eo7HJ298ToJ2CKl3CYDBSz/B5zZyjUmXZjDsw7nHNc5jCodxaTiSRyzfSKZ27az7N8vcfOyjWxJ6kG1w4lWv9nqV1TiRo87eEXe0OGN0wMbod7q8G1KNoKigCOp+X50X+BNILlP+PP2JtkmVTtcNQssB/nbzwFm1HEnY2mUzdRiszPpzHObbZ/euy+2mJiQ44amUZKfj6HrGLpOZdFu3NVV7Z6XlEaz5p6EtB7t7jccnS3y2UDjTE4F9cdMDlIWLVqEr8hHn9o+DCiO59Qvv2bywoUcPm8eTz1yDzFeD5+MPZJFfYexKrsfvwwdzxnHH3+gp91+Fr8Cu5aA3lyQmAIZ9d40F78fMM00h98NRaswptwQ/K4jlIBpR1gC4j7wBLhpMSRFXsTFJDzpvftywZ/+Rv8Jk8kdMZoTf3srI44O/n00pMSj12drVVQOO7+5erfNv4GpFmtUzCyxiUmMOfGUDvfTmAO+8SqEuA64DiA3N/cAz8akMRs3bmTevHkIITj88MMZNGgQu3fvbtiIHb90CVafr2GlkFFeykWzPuPlsy5ifc4A+sTa+dugHAY5258y94BSsR2+DZ81soGkXgGfdm8t5E6GuzbDxq/AXQHfBldsklKneO0/WZNdQ+KYVIZU9SJOxgeCpfY+RAxA80Jy10yzfDCS2X8gM+4OrZ4F8OKOYv6yrRBDSsYkxPLGiN7Nuky2hFBVpNGB4vVCMO7kM5h+yZUoSnTfejtb5HcBjf2McuqPNSClfAl4CQJpDTp5PiYRIKXk66+/ZvHixQ2BGbt27eKCCy4gMzOT9evXo2kazjpX0KugTdPoWRqwS5+Zkcyzww5OoTJ8OjU/7kTJ+5I4aUHQzCpesUBdCbxzTsDuftZLMOyMfd4wm2bB9uD0B2lbtzLI5WBbn1gWJ5UxuSKX2PxG/UsNilZ30p11f6SmUf31LLQ9RcSMHk3sxOZt2z+X1/BYXiH++t/xVTUuLv1xMce3sdoZgOYNX1cgUhxxcRx9Refsv3S2uWYxMFAI0VcIYQMuBGZ28pgmHWTevHlBAg+gaRozZ85kwoQJ5OTkYLVaKc7IQGtka3fb7KwYNBwVOCUt+kW49wdSNyh5YSU1PxfgzS8BrbnNtfrNO78rYGrxu+Hja6G2USnAI38XZL4RBFzMsos8TF1cwaT5Bdg2fBt4WDTGXQ7/ng6VzeesNwlF6jo7rrmWwj/+keJ/Ps32a66l9OWXQ9tJSXH+Nr7dsg1Po5q2fgnrm0kFHXUabf5abHamX3xlpw3VqSIvA6XnbwJmA+uB96WUaztzTJOOM3fu3LCh1TU1NcyZM4fLL78c5aQzeejKG1kxcCiaoqArCt9OOoLPpx2LKgRHdaD4xIHEm1eNVu4BzSDF9kILLWWoG6TmhcIVAXGuKwuYckKyUYIiA+kLnF6Jxeuu76dJu8JVAaHf8KWZgTJC6uYvwL1qFdLtBk0Dr5fiJ55kweFT2bk8kPhQGgafPfFn3rn/DnbM/hxVCw5SS4jEtTUCWsp5A2BzOFCtNoYecRRn3v0HRh5zYlTGDUen2+SllF8BX3X2OCbRIS8vr8VMlCtXruTEE0/khRodX2omd996Pw6PB01V0KwBTxApJS5DclDGte7dgKMSgYc2VEMEJHx0TUDspQ5jLobMUbBrcUjLxt1qCuzom4jbppFU7qHnHi8CGVjRf3Q1jLkUTn2iQ7d1KKBXVdL0H0wAceWVbLzpJpwffEThpvVsXboIpGTYusWsGDSWiuR0LPbAvtHTQ3NZ44jB74m8AHmgYLpseBhb7HaOvuI6fvnvG3jdrkDSMiEQioKsNwX56jOzlu7cTp9R7a81HAlm7hqTIH788ccWz2uaRoVPI7XMT26xn2R/JTa7B62RZ4EBxKhtUscug613AsKqYIh2FujwVAYConQfrHof7KEFIhqvyw0BS8YmkZ8lKEq3smmAk039G43td8OyN6GqIKQfk2Bix4wJm+tHlZBUU0f+yqVsW7F0nxgbOpd8+m9O+e49/qSX80rddob6arn00aeYcNrZTDrrfJIyewb1JYSCoqrYYmJQrVYGHzad0++8r96/PiDkI485kd6jxoAQ+7JSShn2jay6tDjKP4VQDrh3jUnXoqKiosXzSUnJzHluNZdvrSau53IWTK7lG04KWkH1i7Hx/I5ijk9JYExi1yzj1xyKw0KPG8ZQ8ckWXIWnE6t9DoQPqmkVvytgirHGBAVRNe6rPMmKx64g65dbhqqwK8vBgLw61L16pVrBXQmJpktlS1izs+n14ovkX3MNwu9v+DkbgMdqIcFmxx4b/PuoGgYDt2+k/JWtVAArpEQaBhabPeBf30SYpTToP/4whhw2nZTsHNJz+1BVvIfyXQUgAuagVd9+xYrZX4RGszZ9AAmFHn36R/eHEAZzJW8SRHJycovnh6RPpTSvGjte+kx8mVXKaPwieLNqs9vHk/l7OGnZZv6RV9SZ0+0ULCkO0q8egfMPbyNm/Bsx6BToMx3U0CCZVknoBX2mgTUW7PE0fVwYSvjHh2xsdpBG89kqTYJwTp5ExZ03UWe3oikCvyLQVIW1uZn0Hz+ZnWtWhr3O0DR0TcOor3Ps93pwV1fhdbtC2pbt3M7gqUcQn5rGNy89y7sP3BWIfq1/IOiaFiroYYhPTuGUm+/q2A1HgCnyJkFMnz692XPHHHMMFi0WzW9gcVQBgmQqELLxL3Twyufv+UXUah3wHz7QjLkQLv4vTLsDRDs2QDfMDKQ8uOY7uPQTsAQ/EJOq/IFu6wVCGJBY7ceiNxrL74L/XgCz7+/AjRw6jDnjHJaMG8qKPpms7tWDucP7cuTdv2fL4l+prWjbwzJcEZCKwl2s+n42L/72clZ/PxtXZctvv+Gw2Oyceus9xCWntPnatmKKvEkQ/fv355hjglOx5ubmcuWVVzJ9+nTSe8djsSloniSkhMt4jRjc2KQHBY2mK1UJ7PAcPJWfmqXfUeAMrYvbKr462LkQMoZDbRE08eawaZIJK6pIqvLj8OhklHgYvTZMqme/KxB9W7a1ffM/hIhLSeWyf7zAgN9cS85lV3DOX55kyGHTcFdXN1R/ipTmCoN8/+oL6D4fLUXBNofFZqfnoKH0HDSkzde2B9MmbxLC9OnTmTJlCpWVlcTHxxPTKJfH0KlZ7N5UyZaleyhadBNZk5/lSeu9LGcktUnn8W5lsLlHAD1s0c2qd0AQAgYcD0tfa9t1Fnsg+rVkI7x/BeGSxzvdOuNXNZMXpzGqFWqKILXz7bgHO3HJKUw996KgY72Gj0L99AM0XxvqGIfRcNViQW+mzF9MQiK5w0exdelCQASNpVqtDJx0OL2Gj2DEUce36mYZLcxC3ibtoq7Ki9+rE5uk4/XtwmHPwGpN5rdr8/m0uBIICPz9/bK4qXfnVqPfb2z5Ht4+u40XCYjLDFSIMvwdG9/mhNvWQGznv+J3V9b++B3fvfpimyJUFVXFYneg+bz06NsfQ9Mozgt+oxKKQuaAQVz00OMIRcFTV0vZzh388Nq/Kd6RV+/1I7DHxXH10y8RExfdOBKzkLdJ1HEm7rMt22z7XjtfHN6HW3u7yXN7GRjrYODBmrcmHCn9AgnEmk1WFg4JtYWRNxcKIAL/tTgC/vaaB+wJcOG7psC3A0PXKd25nZqyUlb98A2G1raHraHrJGVk4q6pJiYungETp/LDqy+i7+1HCAZPncbhF1xK0dbNJGVmUVtexqd/fwRPbWPTm8RbW8Om+XMZfXx0k5C1hCnyJlFnaFwMQ+Pa4YnS1UnuA9njYfeygPB2BtkTYfL/wae/BV8jgUjuBxnDOmfMbkq5X2PX+rX8+uJTuKqrMPztf5Pau3KvKS0hb/kShGpBKAqKonDqbffirqrk9TtvbDDlKBYL/jCeOQBr5ny3X0Xe3Hg1MYkUIeCyj2HStdBrSiB/vBLl/YY9a+D7B0NrwhYug6dGBtIlmLSIRze4aOVWRs1dzYnFft6ceCJ+PboF0aUecJM0dJ2lX3zCnDdeQvf78Lld6H5fswIP4GvhXGdgiryJSVuwxsAJf4arZ8OtK2D0hQGzSrSQGnibKaTuq4WfHoveWAchUhr4fGVI2bxb7mN5hfxaUYMmBIZqYXt2f+aPO6rFfkM3QSMLf5NSsnvT+ob0262hqCo9B+/fNzJT5E1M2ktMMpz5LDjT29lBOCFRoN/RzRQfkVB16GamrKhczM9zx/PLvCP46edxlJf/Grbdwso6vI38STSrjYKsltNep/fp1/C9UBQSemSgWqxY7Y5A1a8WkIYR1p8+HKk5uRx95f4t6WiKvIlJRxl5HqhRKtN3+C1w9n8CbwhNsThgwHHRGecgQ9NqWbnyajStGil96Hotq1b/H35/ZUjbvrH2oM1GRddIrmrZzFW8bUvD99IwcFdXctKNd3Dxn5/gxlf+S/aQYR12eYxJSOSSR5/C5ti/+1WmyJuYdJRj/hAouN1S6b+wSAIZ5gnY9vsdBUf/HlQLzHge7twEPcfR4G0z/kqY8JuoTv1gwe3eTuibj4LLlRfS9sEBPcmwW3EKsPm9xNdVc+Sib9s0npQSKQ3ScvvgiHVywYOPcfod9zHmhFNR2lGvODkrm9889SKqZf/7uph+8iYm0cJdAbN+Dyv/R7igpxAUW73vvARE4PMFb8Lgk4Lb6f6AyEe5LNzBhNdXyq+/TsMw9m1IG5pg04eD6dl/EqfcfDf22H3Jret0nUWVdQgB42NsFK1axlfPPoHmizzi9YKHHiNnyPCQ45sW/so3Lz4dyFfTFCEQQiANA9VmY/ypMzjs3IuiUv+1JVrykzdF3sQk2rw5A7bNad+1qh3uLwwWdL8nEDnbtuT23QYpJWt/+o68bf8mJncVQljZpOfyeeWZeMttTFi/lEkZqfQdOxFd8zNgwmSSs7JD+slbsZQ1c77F6nCwZ9sWSnfkNzumYrFwwnU3M/zIY5tt8+Jvr6CuItgMNPyo4zB0HVdVJQMnHcao405C7Id/NzMYysRkf+Jue8KqBnQvVO8OVJUq2QTvnBvYbLU54dzXYODx0ZvnQcLSLz9h3vvvoHm9OFJyKezbi9fHXo+WboN02NhvBP4vXiP/jZcA+PX9d7jgT38lc8Cghj42LZzH7Bf+ic/jIS0nlxn3PMDqH75h88JfKd8dmqvf0DRUa8ur78sf/xdv/e4WassDQp87cgzHX3vTATHJtIRpkzcxiTYDTwBLC5trNickNJcbXkBdMexZB6+fApU7AqmGvTXw/uWHZPGQxTM/RquvVuYpd/Bd5iloln0b3ZrVxsKx0xsKc2g+L9+9sq90Y1nBTr565slANSYpKdu1k08ef5gjLry8+UGFIDUnt8V5xSYk8n8vvMEtb3zILW98yHl/+HOXE3gwV/ImJtHnyN8FxHj1e4AS8L4ZdFIgSjY+EzJHBlbrr50M3iaJyRQLvHNeoMiIv0nQjKLC7hWHXvGQJiZlTQ2VrabHivO28MljD3Pi9beycf7coOyT0jAo27mDwi2bcNWETwynqCrxqZFlHbU6unbqDtMmb2LSWewNkGnO9c5bA7N/DyvfC3jUGEZgle8qI2z6Q2ssXPEF5IzvtCl3ReZ/+F8WzfywYTW/vv8IZh11dkNNYYvfx2nff8DA/PVB1wlFJaVnNu7amrA53y02O5n9B1K4ZSN6o5QHqsXKERdfwYRTZ3TeTUUZ0yZvYnIgaM2v2h4PZzwTcL8s2wLpg+HFIwgv8E4YdiZkj+uUqXZlppxzIXank7U/fU9x/jaGbl2DoagsHn0EAJOX/xQi8ADS0Kko3I1hhI+O1XxeaivKyRk2kh2rV6AoCgMmHcbE088mo9+ATr2n/Ym5kjcx6Uo83q9+Jd8YBc5/HYaecch62ADUVpTz8s1XB626o4HdGceMu/5A9tDh+8UTpjNoaSVvbryamHQljnkg9JiiwqCTD2mBB3AmJZOe2zfq/Xrravnk8YcCG7PdEFPkTUy6EuOvhEGnBFIYqPZAQrTjHwJLlNImHMQIIRg09YhOetgJKot2d0K/Bx5T5E1MuhJCwEXvwnlvQJ/DQfPCtw/Aa6eAp+pAz+6AY7FaO8VNUdf8OJOSW294EGKKvIlJV0OIgPvkjgUBH3lDh4LF8PltAXfCFe/CG2fA/y6BPWsP9Gz3KwMmTcVitUbNdm6x2rDY7Ew992LiUlKj0mdXw/SuMTHpiuT/Euwnr/tgx6+w8N/w/UP15wRsnQP/9zOkdR9vkJaIT0nj4r88xdx3X6euopzCLRvb3ZdisXDMNdfTo3c/Mvp23+Lo5krexKQrktgrYJNvTHxP+PFvjcRfBr5f8e5+n96BJKVnNmfedT8XPPwY1pC0veFX+IrFgtLIzCMUhVNvupORRx3frQUezJV8REgpyS9z4dMM+qc7sajms9Gkk5l8Hax+Hyp3kJ+lkpdjQSoFjKutJtHTWMpkwKRziKH5/bz3p3vwe4I9YhxxTjS/vyFwai8ZfQdy+AWXsPCT9/G56hhxzAkMmjptf075gGGKfCv4dYNr3ljCwrwyFCHITHTwwf9NJTXO3vrFJibtxeaE635kz5onySt/EwM/PUrcxNXooWvV5JarHnVHln31GUVbN4cc99TWhm1fVrAdV3UVhVs2oqgqP739KqU7d3Dc1dd39lQPOOaStBXu/WgVP28qweM3cPl0tpfWcfv7Kw70tEwOBSx2Sm3lGPiJcesM2lKLGi528Yvb4NFs+PsA+Pg68IXJc97N2LludZva65qf2S88jeb14nO50LxeVn33NZsXhi8h2J0wRT4MHr/Oy3O3ceyTP/LRsl1BQea6hJ83lTLm4W9Ys8t0aTPpXOy2HghdMm5VFTa/bL68tK8W6kpg7SfwYfevHpXYI7NN7XW/PyhJGQQSlX393D9wVXfvv2NT5Jug6QYX/Hs+j83awNaS5ldElS4/Zzz7C3M27NmPszM51MjNvYY4r4rNZzQv8I3RfbD525DMjd2J2qpKtiyOzgpc8/tZ9e3XlO3aiTS6596GKfJNWJhXzpbiWvx6638khoTfvr3UXNGbdBo2WwpjYy9GdF/NbhPLZ33Bv6+7lLqKDhRmaYQ0dOZ//D/evu82/vvA3fg9nqj025U4pETe5dPw6y0/rd0+vU2BFl5N8uXqwo5OzcSkWaxahKv4vcQkh+ai7waU7MhnTn31p2hiaBqa10vx9m3M/d8bUe//QHNIeNdUuf1c/fpilu+sRAA3HDWA244byEfLCli+s5IB6XFcOqU3NovC+N7JqIpAEDbhawiqInBYDqlnpcn+RPPB0jdbaBDmN9VVCk8OhdvXgCOhM2e3XyncvKFTTSq638+ebVs7rf8DxSEh8rf9bwXLdlRg1P8tvPDTFr5cvZtdlW48fgOHVeGr1YWMzU0iv9TF+RNyWJRXTkGlm7La0OruigiYahQBTrvK+RN7AQF/+ld+yeOLVYUkx9q49+QhDM6M35+3atLdyPsJvJUtNJAQlwm1RcGHvVWBtAdXft6Zs9tv+H1eln75WVT7bPp4VC1W0nv3ieoYXYFuL/LVHj8/bSpuEHgAvy6DNlU9foMl2ytYsj1g5xNAj3g79540hAdnrqXOF1x0IDHGisunM7BHHC9cOp6sxEDU3RPfbOSVX/Lw+AOrjTkbi3nw9GFceXj006OaHCIseKH1Nk0Ffi875kd3LgeQRZ9+QFVxx5wchKJw7v1/ZsE7L1BdsJkMew2l3lhqNAdYY0nK7Mm0i66MzoS7EN1e5GetKWqzo4EE9tR4uf+T1YQLk65wBYoWbC2p473FO7jrxCEAvL1ge4PA7+XBz9eRmejgpBFZ7Zm+yaGKqxyWvw3bfmx/H9YWiokfZJRszwtxgQxBCISigJQhZh2Lzc7JN91J7ohR5OauAvsaIPBGXuJNgJHnkn7hEyiq2lm3cMDo9sZkn2ZgtbQvY52vFQ8bt1/n0xX7clA39zD569cb2jW+ySHIhq/g8QHweN9AimEZvnRd64hAHvpuQka/gVhsreTUlxKp6yEC74iL57LHnmbQ5MMCB3z7omIVARmOajLi/N1S4OEQEPmjh/TA2oFcMwkxLf/DWxXR4LFz+dTw4eVV7uiWKzPpphSuhI9+A66SjvfVaxJM6D5BUZPOPIfswcPadI1itWKLjeWc+x4ipWfOvhMjzgl+y7HEwPCzojTTrke3Fvl1u6tZXVDFU+ePYWKfZHJTYslKdKCKwBO8NQRQ7W55JbW7ysPRT/xIYZWbO08YzJDMuJA2lS4/nywraOddmBwybPsRdC06fR31++j000VQLVbOuf8Rhh91LKrVGtE1KZk9ufbZV8kcMCj4xNH3B4qnO9MD2T7P+BcMOLYTZt016JY2+UqXj3Ne+JWtJXUoAiyq4JEzR3DBxNyGNm6fxrhHvsXtD++SJYALJ/bi4+W7WhzLqxkUVrq58/2VvHvtFL6+dTqD7v+Kpt3e/eEqJHDkoHR+2VKKVVU4clA6Tnu3/CcwaQ+OJFAtYLT85pfnyObGofeTH5PNkNo8XlrzR9KM6uBGm7+B/kd12lQPBEIIjr/2ZhTVwoZ5P4EMpBD21oUmJRNCkJyVjcMZuuhCUeGERwJfhwAdUhghxN+B0wEfsBW4SkpZWX/uPuBqQAdukVLO7thUI0NKyXkvzm/wnjEk+DTJHz5dwykjs4izW/j3z1v5z895LUa12i2CTXtqMCLYtdUlbCyqAQK/XEmxNkqauF5qhuTej1chJdjqzUdJsTa+uPkIkp1m/U4TYOR58OszULkTdC/hIjXqFAenj32WcksihqJSaE8lyahB0sRFYPF/4KRH99PE9x+qxcIJ193MCdfdDICnrpYPHr6f4vx9/u2KxYLVZmfaxVccqGl2KTq6jPwWuE9KqQkhHgPuA34nhBgGXAgMB3oC3wkhBknZ7l2kiCmu8ZJfFppzxjAkpbU+vlpdyD+/3YxHazmowqNJlu4IBE+JeofaluQ+K8nR8P2NRw/gwc/XhbTxaYEe/Lpe/9nDv37YzPVH9ufOD1ayvrCaPmlOnjxvNL1Tna3eq0k3wxYL//cTrPwvuCsgZzLMvBmqd4MRWDSsi+uPV7FhKIG9ouPLF6AQJnGZ7oNZvw/Yn3PG79/72I84nHFc9tjTaH4/dRVlbFu+BKRk4KTDum05v7bSIZGXUn7T6OMC4Nz6788E/iel9AJ5QogtwCSgUxx3a70aN7+7jLmbS7GoIuwKXZeQ5rTy2KyNrQp8Y2TD/7XMpj213P7eCv5x/miuPLwv87aU8t364hYv9RuSHWUuzvv3fAoqXOgGlNcFTE0/3X20aco5FLE5YeI1+z7/di4sfR2K18HGr3Ai0cQ+ZwBNWJr/HVvwHCx+GaZc3608bcJhsVpJ7JHJ2BNPO9BT6XJEU0V+A7xX/302AdHfS0H9sRCEENcB1wHk5uaGa9Iqd32wknlbytAMiWY0L6uT//o9bl/nhEX7NIOvVhfisCos3V5BpcvXamoEqwI/by4JeigZErx+g7W7q5nUN6VT5mpyEOFIgMNvCXyvawytKeTwfA/zqly4Dck3Gcdy//bXcPqrw1+ve2HBizD2UkgbuP/mbdJlaFXkhRDfAeGSN98vpfysvs39gAa809YJSClfAl4CmDBhQrty7c3bUoqvlcRjAK5OEvi9eDWD9xfvJIIElgD1m7Ph3joksbbu6bNr0g7yfoEPrgR3OQLJGxYn/5v0IJv6nMSI+FxiJy+E7x6EtZ/W2/KboHtgzcdw1O/288RNugKtiryU8riWzgshrgROA46VsmGXchfQq1GznPpjnUJijJUaT5RczzpIpALfHBZFMC43mWFZ3SexlEkHKNsGb5xG48WA6q/hkoX3Q+EXULIRaveAUCBnAuxYCIRZzMx9ImAGcpp26kONDvnJCyFOAu4BzpBSNs5tOhO4UAhhF0L0BQYCizoyVkv89eyRqJE4vh8A2jqriX1SeO2qiShd9H5M9jMLXySs0U/zwLY5ULM7EBVr+Otz1TTztqprUJHXmTM16aJ0NBjqWSAe+FYIsUII8SKAlHIt8D6wDpgF3NiZnjXTBqZz23EDu6TQt3VhPzQrvkMRuiZdD8PwkZf3DCtWXsOWLY+j623I9a5Ga9vMgNriKPVlcjDRUe+aAS2c+wvwl470Hwk+zeCdhdtZv7v6gJQ825t2eC+R5qFvrq+kWCvLdlRgVQXDMhNQTcE/qJFSsmrVb6moXIhheKio+JXy8l+YMOFjFCWCP78pN8L856Izmc9vgSGnRKcvk4OGg9pHTzckl7y8gBU7KyMq1xcOuyrwdsCQ3vTdoSOPmRSnjTfnb+ef323GkIG+HzpjOJcf1qcDvZocSLzeQioqF2AYgQ1Rw/DicuezoWQlz5am4jIMLuuZypSkOB7csptFlXVk2S08OCCbIXExkJgNoy6AVe8Fd2yLB90f2FSNlLrSwDVqZGkBTLoHB7XIL99Rwbrd1e0WeACvLhnTK5GVO6vaJdCNh1YVgd6CC2dLpDpt9E93sjBvX+1KCTz8xVqG9kxgYh/TnfJgJGClDF4K1BixXLbOwE8lALNKq0mzqlT7dXzARhcctXgjSRaVqYlOHh57Hb3WzwS/O9CBNRaOvAcciYHVeaQk5pgCfwhyUNsCXD4dpQ31WJtjRTsFvjGKgOkD00hpZ4oCiyLYXuYOOa4ZsCivvIOzMzlQOBzZOJ0DECLweyGEhe84Gr8MXl+V1gt8Yyo1na/Lqjl2p43SCz+EPtOg5zg4/mE47GYYfwVMu6uVGShgi4PYVLj4vVbamnRHDuqV/OheSVjUUJHviF28vRgSftxYgsPavufmnhovKbGhqyyLIkiPt3d0eib1rJ+3m18+2IyuGWT1T+TUm0ZjsXZeTIIQCuPGvs26jY9QUrkC6ejHnLoZoLehWLwh+dQ+mKuv+Jw3d5Xy4s4Sqn5Zw/jEWP52+O/I9tXA4ldAsQT2pTJHBLIrjr0MsscFzDTJvcFi/h4digh5ADYrm2PChAlyyZIlbbpma0ktd763gvVFNWi6QYxVxW8YeLWuc19tQRX7TEACGJwZx8ybpmEzi4V3mPzVpXz53KqgYz16x3PefRM7ddxir5+Tlm6iWgs4mOlS4m6DWc8G/HFgNuU+jX9u3xPkJOlUFRZPHUZKbQGUbYWUfpBilps81BBCLJVSTgh37qBXjv7pcXx60xG8dfVkVFWh1qd3isArtN3nvT0EFRZWBDvK3azZXbUfRu7+LP9mR8ix4u01nT7uQ1t3U+zzU6sb1OoGmpQktsFryq4ITktP4oUdxSFe8HW6wYdF5ZDcJ5AT3RR4kyYc9CIP4NN0rnh1Eb5WEo9ZVZg+KA2bKrAqok2i3bkJERqN00jlNUPi8unc8d4Kvlu3h+/X78Hl6xqRvQcjShjT3v4gz+Wl8brDL2Gg04Etgv2keFXh20lDyLRbMZoxQhZ5zcpjJs1zUNvkIZBC+OwXfsXtbz3Wymm38tJlE6jzavh1ycK8Mm5/bwWRvjkfKAPQ9jIXt723HAkkxViZedMRpMaZ9tXmqCn34HVpJGXEBNnbJ53el4INFUFt+41N6/T5TElysq7Ojaf+F82hCCYlOllZE7rR3pS/DsqhT0zg3/rCrFTe2F0W0ub09KSozteke3HQi/xHywpYsyt8Bj5VQJzDQrVbIyvRwctXTMRhVXHU/+H7NAO7RWm2OlQkqApYFaVN6YvbigRqvYGHmNdv8PjsjTx2zqhOG+9AI6WkvHwuXm8xWl1/ln8J7hofNoeK5pck9Yjh8PMG4ky0h1z34zsb2bigCKGAUATJGbE44qxMOKUvWf2TOPO2Mfz47kb8Hp0B43sw7YJBzcwilMo9LnauL8dqV+k/rgdWe2Qbtvf0zWJDnYe5FYEKRkelxHNvvyzy3T6+Kg1vihPA1CQnZ2UkNxx7dFAOZT4fX5TWNLS5sVc6YxPN2gMmzXPQi/zMFbvDHlcFvHDpeE4YnolfN8KmCujfI67NPvZKvevOXknXDRiXm8glk3K575M16IYMmxFTEbTrgaIQbCrS6nPQd1eklKxafT0V5fOQUqL5darqLqdm1+SGNiU7ati8pJjUnDiOv3oYqVmBEm/bVpSwaVEReqMH7l6b+66NlRx5ySCS0mM5+67xxCYEXBp1zeDn/21i67JiVKvC4ecMYNCkQNLV3Vsq2b25EofTSlVpHSu+LWBvCaYFn23l4genYHO0/ifkUBXeHd2fCr+GAJKsgWuuzUljdmkVTd9BFeDRQdlc3jMtyEVYFYKXR/anwONji8tDrsNOv1jzjc6kZQ56kU+IDb0Fi4DlfzqBeEfAJbG5XDDjcpPJSLCzqzI0atAiINz+bVqcjZKaYI/mxfkV3Hn8IJb/8XhKarw8+8Nm3lsSXLjbkIGvSX2SWZxfEbHp55IpuXywtABP/cPBYVWY3K/7BkaVV8yjomIeuhF4kCkWyJr4BjU7J9J0C6msoJb3HlnEOfdMIKNPAuW769CaSSetawY/vLEBxSJQFMGoo3PIX1VGTYUHzacj6y+b89YGnIl2ivKrWPhZHjKcLU9CXaWPmf9cwRm3jYlI6AGSrcHtxiY4ybZb2dHEpp5sVTk/M7XZGJAch40ch1ky0iQyDvqN1ysP64vNsu+PQRFw10lDGgS+NZr7Q1KaeTDYLGpYgb781UUM++MsTntmLpP6pvLipeOwNdnos1kUrp7Wj2FZ8RHN7eZj+vOH04YxbUAaFkVgUQTHDOnBjUc3mzLooMfnDU2iJRQdoYbfXJQG/Pj2hkC7CPZVDU2i+QyWzd5BeWEdfs8+gQfQ/Aabl+5h4Wfbwgt8I/bkV/PBX5fg97Uv955DVfh6wmBOTE0gRhFYhWBEnIPPxw0i1sxZZBIlDvqV/MQ+Kbx8+USe/m4zXl3n0sm9uXBS5BWm9tSEz/1htyhouhGyKTu5bwq7KnaFCL2v3uxT5da4/9PV/OeyCVhVBZ++TwD8usGwzHjyIjC3WETgAWa3qPznionUegNeNXHdvCRgQsJoZCPVlYbAX5eG1Js3S7hqfOSvKmXJV/kdHl9RRf1mbWQhdbUVHvJWlDSYeNpKqs3CG6P6tetaE5NI6BbLhemD0vnohsP44uZpbRL48jpfQ3HtptR6NFJig1+JRf1YNx7dv8V+PX6DBXnlPHH+aBpnPx6VnchDn6/F1WTlpwpwWIOXoZqEP362puFznN3S7QUewOnsz7ChT6AoMYCCRclh58+3NX+BgJzBycz7aAt6B+MjFIvA4bQy9sTciDdVAfzeTq9Pb2LSbrqFyLeXJ2ZvbPacBErrgm3vqgI2VXDXiUN4/aqJxDVTos+mCpJjrbz2S35Q9uNF+RV8t6EkpL1FVUiKCbWxzlq7J7Ib6WZkZJzMUUeu5qgjV5Mi3sbw9mi2bXJGLEdePBitnSaTfRi4S5+itvhf5C37hexBiRFfmTOk++6RmBz8dP+lYQvkldW1qb3NojaYZWatKaI2jLAIICPRwfkTcnj0q/URbbAeNTidTXtCIy+7XgmU/YcQAlV14PNo6C14QO3d+Bw4MYNVcwrQ2+kOK6WOlBKf28X3r32CPf6cVq+x2lVOv3k0iekxEY0x971NrP6pAGlARt8Ezrg18k1bE5P2ckiv5Kf0TcEeYU4YQSDNwNT+gRqZM1eGum4K4JLJucy6dToJMTacttb/gAVw1OAe3H3C4JBzZ4zuGdHcujO9h6eGfdjZYlTOuG0scUkOACaf0Q9LO5PDBRCo9vEASMNBuEJmw6b1JHdECmm94hhzXC+ufmIaWQOSIup96ax8Vs0paNjk3ZNXzRfPrezAfE1MIuOQXkbccPQANhTV8O26gFkk3mGhwhXsxRFvV0mMtZGV6OAvZ42kR3xAVAJumcFC4LAq3HXiYJz1tvM/zxjB7e8HR9Q2rSSVlejgjNE9cdot/MuAv369Hp9mMGNsT/5w6rDo3/RBRnpufMBtpkkiPZ9b5/N/LafXkBRO+u1IPLV+tA4EtQlhQbH0QvcuQYgKmr5HxSXbOeriwYh2prZe/VNByLGireGD+ExMoskhLfJWVeGFS8dT7fEjZUDQL31lEQu2lWFVFZw2lfd/exgDesSFXHvzMQN44puNDf7rqiJ48+rJJNVv1vp21TI9z8XMIbn8obScjZVukmOt/PmsEUAgLXGv5Bgumty74aFwxpienDHGXL03RVECQWdNkQYUbKpg1r9XM3BCBka4RhEipYaUVVjtDhJ7OJh09mB+encLEklMnJXTbxnTboEHwpZxVA9QLh2TQ4uDPtVwZ7CjzEWV28+AHnHENLO5CvD5yt3MWltEqtPG9Uf1JysxYJv17qim9D+rkfUPAGFVSLt2JPbchP0y/+7GB39bTHF+C9kiBVhtKpqm01K5eItVoUefeAq3Vof4wEtpIPX19BuTwYnXzcBis2HoBj63jt1p6ZDAA2xeWsw3/1kTdGzqWf0Zd2LvDvVrYgItpxo+pFfyzZGbGhtRu9NH9+T0MHbzmh92NAg8gPQb1Hy/A/tVI6I2x0MFaUhi4luJ7pSRuTFKoKLIRTj/dyEUhGU4Pm8iFltgPEVVcMRFZ9tq4PgeKIxgweeBIKtxJ/Rm2BHmW5tJ52OKfCdghAmtNzpgLz5U8bk13v7TfNzV0Umlq/uNVnMHuWv8FG+vZsW3O9A1gxFH5tBraHRcJPuP70H/8c27g5qYdAamyHcCzsmZ+HfWBJlrnJPbFxF5KPPl8yujJvAAQiEohUE4FFXhkyeXNeTA2bG2nBOvHUGfUZ2fktjEpDMwRb4TcI7ugfQb1NZ7VMRNz8E52lzBtZXiHbVR7a81gQeoKnEFJTnT/AaLv8wzRd7koMUU+U4ibkImcRPM1XtHcMRaGvLoRxuLTWH0cTmsnrPr/9u78+i4qjvB49/fq1VSad8t2ZY3eccLYCA2hDUEksbJGWjICQkkzKGbIR26O0s3oeefmaYn052l04eE04Smh/QkzTZpcAI0hCVsAQzYGK8y3i3Z2qyttNX27vzxHrKW0laSLKn0+5zjg+q9V/XupaRfvbrv3t+PaM/ZcyTLYtlc28m//tWbrLm0ggs+VzXhm7BKnUtzejGUmtmuum3llJTsE0u4/NYV1NW0Dwjww7EThu72KDtePM6HL50c83mO7mrihYf38Ptf1dDRPHoVKKWmggZ5NWNVrijg5r/ZxKduXErZ4hxk0G9rIEktgbHw+i2MbWg8Nr7FSPGozcF368d07N43T/Hiv+zl0PuN7H2jjsfvf49wi5Px9PThdmrerae5dnKHo5RKRodr1IxWUJ5FQXkWy84v5fH7txOPJDA4KYG/+O2NPPOjnfR0jnJzVpxFs07aA+H8zy7k0PuN2OOsCgbgC44tO+V7vz16dujHQCwSZ/8fTtFwNMzJ/S2ION8oNt+4lLWfrhx3O5QaK10MpWaN3s4Yh3c6wbnqvCKyC4K89dTH7H6tlkRs+N/jS764hPzyLN7+j0N0tkbc4GvGdCN2ADfFvD/DyzVfX0XV2uFvxj7ynTfoCQ/88LE8YA8aHbK8wh0/uFQTlakJGWkxlA7XqFkjGPKx+tIK1l5eia+5h8YHd7H4dJjq5flkhHxk5fmHpO70+ARjDC/8fA+tp7vdSlApBHjoW0MV7Ynzws/30NY4fPGXlZvn4RlUI2BwgAenuYM/DJSaTHr5oGad3sNtnPm3fX3rEJb7LC76UjVZ55dyZGcTLz68x6m37YGCshBnTnWNmIK4cmU+tQdax1IIqo+I0HC0g7yS5KujL75hMZ0tvRzcPnJNAMtjESpwql5Fe+K0N/WQmesnK1cLdKvJoUFezTpd754ekjai8606ss4vZfGGYm6670JOHWwjmOUjvzyTx//2vRFfr3Z/a0rtyMw5m24h2hPnD78+RNOJMAXlWVz0hSWs3Dxv1CC/4pIyutujdDT18OyDHyE4c/MXry+meEE2lSvyKVmoOY9U6jTIq9nHSjKtst+2wnkhCuc5mUNfGJQULGUCHq8AgmUJFdV5VC7PB5z8Ok//eCdn6sLYCWg8HubAO/X4AhaWF+z48C+7+7U69r5xChFDot9xhz5o5NAHjXi8wlW3r2LZBaWT0w8152iQV7NO9pYKeveeGZA2IufK5LV9I92TN9695cZqEMjKC1C1phCxhETMZsfvjtNcGx4yzh+LjGHg3zDiLJ9E3PD6Ywc1yKuUaZBXs46/MpviO88j/HotJmEIXVxOsDo/6bHVm8o4fbh9wErWvLJM2hu7x3fz1cDu12vZcPUC3nrqY15+dB8l87MJt0Zoaxj+Buxk6J3EDyo192iQV7OSf342hV9eOepx+avzqF8QIPtYD36PRfX6YoKZHormhzj8QdPAvPLuFMnhtNR18fKj+/sen6wZ383alNlw7KNmzZ+jUqJBXqWtzkicrQ+8RXNnlHjI4LeEqt0n2NrtzFwJZHpZtK6IRMxmxSXlNJ/sZPuzR0accz/AOVxi8u5vj2iQVynRIK/STrQ3zu5Xa3n92Bnau2PE3av1qG342GeIYvAjRLrjhPKDXHTDYgDmryogmO2j5p3TdLVHaW+cQflmZtCiRTW7aJBXaaXldCdP/2gnPeEYx70JEln2kAVS/X3w/DF2//4kXp+H9dcsYN1V81m1eR67XjnJm098fO4aPgKxYP1VyW8sKzUaDfIqbex9s47XflXTd0N1YdzCbyAO2AJeA4tjFv5+Ud8YiHQniJDg3W1HCGT6WPmpcuqPtI96PssDucWZbknBqRHI9LL5xmUsv7h8ys6h0psGeZUWesJR3nj84wEzZvwIXwkHeS0YI+wzVEYsLokM/ysfj9rUvFuPxyscer8x+UEC/qAHAyzfVEZPODqlQX7hmkJWfkoDvEqdBnmVFjpbI1geITFotmHICDfEgxQUZ9F0Ijzq6/iCHl75twPD7hdxioZ7fR72vXVqXG1ccUkZlkfY99bpMd+0Xbi6cFznUGqwSUlQJiLfEhEjIkXuYxGRfxKRQyLykYhsnIzzKDWcnOKMgdMhXWLB4vVFtNZ3jfoaXr/Fuivnj3iT09jOv1gkgR032PGxRWuvz2Ll5nlccetKtt6zfkzPWbKxiGqtDawmaMJX8iIyH/gMcKLf5uuAZe6/i4AH3f8qNSUCGV6u+5O1PP/QHoxtSMRtcosyWP+ZBXS3R4iPkKDsE+VLc6lYlkcg00d3R3TAPssSAlleoj1xEmMM7JZX8Ac8eP0eNt+4lHlL8wCnGMqWm5byztNHBrTL8ggXbV1MaVUO2YVBcgozxv4/QKlhTMZwzY+B7wLP9Nu2FfiFcZLVvyMieSJSbow5PQnnUyqpBasLueMfttDZFiErL4DP7xT4OLqrCY9XRp3/XlvThgFuuGc9237yIb3dMUSEq29fydLzS6mtaeXZn+4i2ViLWAMLhXt9Fld8ZQXVm5Jfia+7agEZ2X4Obm8gkOnlvCsrKZ6fjeXR7N9qck0oyIvIVqDOGLNrUHHjCqB/Mcxad5sGeTWlvH7PkPS/VecVsXBNEUd2No34XJMwPPjfXiUz18/N//1CRIRAhrcv8FZU57HiknIOvH0ayyMYG9ZdNZ+OM72E8gKs2lLO4R2N9HbFqVpbyLxlyVMtfKJ6U9mwHwJKTZZRg7yIvAQk+028D/gezlBNykTkTuBOgAULdC6wmnwiwrILSjm5r4VYZPTC3d3tUZ78X+9z299tHvI6n/7SctZcVkF3R5TCitCAdMMAG6+tmsymKzVhowZ5Y8zVybaLyFpgEfDJVXwlsENENgF1wPx+h1e625K9/kPAQ+CU/xtP45Uaq7LF48vJ3tkSGXZfYUWIwoqJtkipcyPlAUBjzG5jTIkxpsoYU4UzJLPRGFMPbAO+6s6yuRho1/F4NZ1C+UE+/43zyMoLYHmEgoosLM8IS2HVjGd3xwj/4RQdr5wg2jS1mUBns6maJ/8ccD1wCOgGvjZF51FqzOYty+f27ztDMIm4zcN/+fqwudxLqrLPZdPmDGMMiTO92DEbX3EG4k3tOjPW0kPDP34AUef963jxOAVfXUnmKk3iNtikBXn3av6Tnw1w92S9tlKTzeO12HLTMn7/y5oh+wors9j65xumoVXpzdiGM/93P70ftyICVpaPkj9dh2ec9Ww7Xj5Ox0snhkxyavn3GjL/pwb5wXTFq5qzVl9aQUdzD7tePonltbBE+Nzd51HuzmdXk6vrvXp6P26FmI0BErEILU8dpPiOtcM+J1obpu03h4k392IwSNCD3RJJvmJ4DGsh5iIN8mpOu+SLS1l7eSU94Ri5JRn4g/onMVVidZ0DA7GB2Ah5f+Jnemh66CNMv6pepmuEgrl6iyUp/Y1Wc14oP0goPzjdzUhb8ZZeEp1RPEVBxGf11eYFZxFZ7+FWPDkBvAUZSL+b4T37WjAj1L8dwjhDQpKs0PscpkFeKTVl2v/zGOE36xCPYIzBV55F7FQnuKkhEu1Rmn++B3wWnhw/RV9bjelNYIV8iFecjHDjKcGl8X0IDfJKqSkROdZO+I1aSBiMO8oSb+7BW5BBvHHQME3MJnGml4YffoD4PZi4ja8yBIlxjLML2OEYnkEL1OY6DfJKqSnR/WETDBpuMd1x4j0jjKsbMO6q5Njx0VND9yc+CzsSx8PZIG+MYVDKlTlHg7xSakpE6zqT75iKde0CVqYPb4Fzb6X1N4fp+iTfv18ouWsD/vKsKTjxzKcp75RSU8KTO8XDJp9EL0vwVWZT/CfnIR6LjjdqzwZ4gKih8YEdmDlaDF2v5JVSY9K1s4GOF49j4jae/CDe3ADBNYVkrStJenzOFQuI1LQOmE0zUZLpxVuYgWR48RVnkHleMf4F2X1DMtGTYTqePzr0iQlIdEbxZo9v4VU60CCvlBpV184GWh8/2PfYDseIEab3QAt2e5TsyyqHPMdfEaL4rnW0/OoA8eaeSWmH6Y4T6wk7c+yPtmO3Ryj48koAYg1dNP7zLhjmM8UKzM1wp8M1SqlRdbxwPOl2E7PpePUkxjZJ57T754Xw5KV29SxBD775oSQnPXvunv0tfR8gXTsb+6ZmDuZbmI3lFpGZa+bmR5tSalyS1c/t2xdNUPc3b4ExZKwpouDm5X2Jx4wxBKqyiRxrHzYA9ycZXnKuWUjm+mJipzsBoeWxGuxwNPkTEob254+Sc+UCIkfbkx6SsaGYwptXYEcS9B5qxe6OE1xZgDc0N6ZaapBXSo0qtGUeHc8dG7rDI2Cbvqvrnv0ttP/nUfI+v4TYmR6aH9lDojVytji6QHBNEbGTYRJtSXL2J2w636oj/NpJJ7B/MvQywpqo3n0t9B5sHXZ/wX+pJtERpeEnH2D3S4uQ+4UlZF88byzdn9U0yCulRpVz2XxMxCb8ei3YNlbAi5XlwxhI9B9vj9v01rTS1LiHyMHWAa8hPoui/7qG6PGwE5STMFFnUdTQHSB+a0AemwGG+ZbgKQgiXovWZw8PCPAA7dsOk1Fd0DftMl1pkFdKjUnuNQvJvWbhgG1nnqqh50zP2atogUR3nPiZoUHcYOh6r56eXc0pZYzMWF+CleGl87Xa0Q92r/wTbb20PXuEeEOSRGjGuVmb7kFeb7wqpVISPd1J767mgcMklmC6YklnuIgIscae1KZUWuAvzyLvukXk/tFi8IoTyIe7l/pJm2zo/EMdkpHkelYk7QM86JW8UioF8eYeGh/4cEjaAka4QeurysGT6SV2YgzpCjwy4LWtTB+ZG5z5+NmbKwhdMo/oiQ6aHt7NqEtoExA72jFwm0Dosgp8pem/ClaDvFJq3FqePDg0wMOI8TZ6sG3sJxj02nZvnN6PW8lcWwyAWELkWEfyNowiY10ROVcumBMBHjTIK6VSED8zOYubxn5CQ9vTh8lYUUjrbw47K2mNSSkPTqy+e84EeNAxeaVUCnzzQuc8d7sdSdDyZA3dOxpJtEewO4aZOz8KKzC3FkVpkFdKjVvBTdV4izIQnwXnohKTRwgsyaXno2aITywXjic/SOu2w3S+fQoznnz1s5QO1yilxs2T7af0L84n0dpL23NH6d17ZgpPJgSX5WPGOzbjs5JO1ezZ1eT84BV69jRTdMfatC4ZqFfySqmUiCV4CzPwZI8zPcBY46mAf1EOZX95PtlXzCdyIPkCqmHZo1ylxw3Rk2GiteMrTjLb6JW8UmpCQlsq6Hr39Nhvgo7juOjxMA0/2ZF8nvtoEmNriomO4cBZTK/klVLjZuI28TM92L1xoic6pqbaE4BtMFF7xJusgVUF5N+4LLUbwbbBX5mdevtmAb2SV0qNS6y+i6af78bEEpi4Dd6pv1YUn+WslE3yYRI50ErOpZVY2f7hPwy8QJLSsqFPzcMKpncY1Ct5pdS4NP/rXuyumJMszAaGSxrmEr+FpzQj5fOJzyLrknn4yrKclbCD2Ya2bYcJbSpLvt8rBNcWJX/tVIaBZhkN8kqpMTMxm0RHkhTBwxEQr+WkGx4PcT4cJOAha1MZuddWUfLNDZR998KkhyfCUbyVIbI2lQ3dGTf07mxO+rzOV07StaNhfG2bZdL/Y0wpNXm8ggS9mJ4kYx/9+OaHiDf34i0MkrGmiPArJ8Y3bG/AW5RB6Tc3DtjsyfFDwILIwG8PdmeMll/sG7b037Cnidl0f9BA1sbS8T1xFtEgr5QaMxGh8NaVnHl0r5Nxsjf5zJTSuzf0/dz9UVNK50p0xgY8NnGb7g+byNpYStf2+iTJ0VI6DZFjHTT8dCcFN6+graue5x74IeHmJkqqFnP9N79DKL8gtReeITTIK6XGJbgkj7LvXEisvou2Zw4Rb05S5KP/8SsKsEJ+Eu2RsScUs4TA4ty+hyZh0/TPHxGr73JXqU7i4qWEIXayk/ofvMe2Ez+jN9EJQO2BfTz5P77H7T/8GWLN3pHt2dtypdS08WT7CS7LJ+faRUP2BZbmDXhs+T2UfmM9oS0VYz+BMfhKMvse9u5vIdbQ5cywsRkxpXGqjLHJ8529QWvsBB3NjXS2tUz6uc4lDfJKqZRlri0i/6ZqJNOL+C0y1hZRdPvqIcdZmT7yrltE/peWD406Ar4Fg+aqG+h6r77vod0Tn7q5+P0aEjMDp2Dato0/mPrMoJlAh2uUUhOSdX4pWeeP7cZl1roS/KVZdO9tJtEawVuSQXBpPt07GoYUE+mfT8a/KNdJLTyZvOJ8cLhDSILgFR8e8ZIwcbxeP+uuvZ5A5uxOS6xBXil1TvnKssgtGxg4xWfR+c7pAQW5PYX9SvMlki+ESplA6T0bidZ2Ev79SeIN3YgIl5X9MUc7d9OZaGPJzZey/PLLJvGk00ODvFJq2vmKM7ECXuz42Rk1kaPtdO1oIHNdCc3/Z29KVaCGJc4QUtaGEjLXF9PyRA09O5uwxGL5kospvH01voLZPUzzCQ3ySqlpZ2yD3TVwyiQxQ+uTB2l/7ujQfRMUurQST5YPcKeF3rwCbl4xqeeYKfTGq1Jq2okleHIDQ3cYZ6HTpA7VeC2y3KLgc4EGeaXUjFD41VVOLpmxRqWUq/gZJDh3SgBqkFdKzQj+ihDl924idPG8sT0hhTTw4rfIXFeMNy84+sFpQsfklVIzhuX3kHPdIjq310+4lusAHiG4soDMNUVkrCuevNedBfRKXik1o1g+i9K/2Ii3aHKutiXTR97WJRTduorM9SWIpG8912T0Sl4pNeP4CjMo+7aTVjj8Zh3tzx5J7earzyL32oWENpVPbgNnkQlfyYvIn4nIARHZKyJ/32/7vSJySERqROTaiZ5HKTU3ZW+poPD21SlFKxHSvvLTaCbUexG5AtgKrDPGRESkxN2+CrgFWA3MA14SkWpjTHpXzFVKTYmM5QUEluUTqWkdsN2TF3CqVMXc8XuPgDFgnGIl3qJMMlYXTkOLZ46JfsTdBXzfGBMBMMY0utu3Ao+524+KyCFgE/D2BM+nlJqjcq6YT/OR9r6ALj6LvK1LiJ3uovPtUyBC9qcr8VeEiBztwBPykbmhBDkHNWhnsokG+WrgUhG5H+gFvm2MeQ+oAN7pd1ytu20IEbkTuBNgwYIFE2yOUipdBapyKfr6GsKv12JsQ/bmCoLV+WSsLCTnygVDjlWOUYO8iLwEJCmcyH3u8wuAi4ELgSdEZPF4GmCMeQh4COCCCy6Y8mSiSqnZK7Aol8AiDeDjMWqQN8ZcPdw+EbkL+LVxcoBuFxEbKALqgPn9Dq10tymllDqHJjpY9TRwBYCIVAN+oBnYBtwiIgERWQQsA7ZP8FxKKaXGaaJj8o8Aj4jIHiAK3OZe1e8VkSeAfUAcuFtn1iil1Lk3oSBvjIkCtw6z737g/om8vlJKqYmZ23OLlFIqzWmQV0qpNKZBXiml0pgGeaWUSmMa5JVSKo1pkFdKqTSmQV4ppdKYOGuXZgYRaQKOT+EpinBW5KardO8fpH8f071/kP59nI7+LTTGJK1rOKOC/FQTkfeNMRdMdzumSrr3D9K/j+neP0j/Ps60/ulwjVJKpTEN8koplcbmWpB/aLobMMXSvX+Q/n1M9/5B+vdxRvVvTo3JK6XUXDPXruSVUmpOmRNBXkT+TEQOiMheEfn7ftvvFZFDIlIjItdOZxsng4h8S0SMiBS5j0VE/snt40cisnG625gKEfkH9/37SET+Q0Ty+u1Lm/dQRD7r9uOQiPz1dLdnokRkvoi8KiL73L+9e9ztBSLyOxH52P1v/nS3dSJExCMiO0Xkt+7jRSLyrvs+Pi4i/ulsX9oHeRG5AtgKrDPGrAZ+4G5fBdwCrAY+C/xMRDzT1tAJEpH5wGeAE/02X4dTlWsZTrH0B6ehaZPhd8AaY8x5wEHgXkiv99Bt909x3rNVwJfc/s1mceBbxphVOHWg73b79NfAy8aYZcDL7uPZ7B5gf7/H/xv4sTFmKdAK3DEtrXKlfZAH7gK+b4yJABhjGt3tW4HHjDERY8xR4BCwaZraOBl+DHwX6H+TZSvwC+N4B8gTkfJpad0EGGNeNMbE3Yfv4NQMhvR6DzcBh4wxR9xiPI/h9G/WMsacNsbscH8O4wTCCpx+Peoe9ijwhWlp4CQQkUrgc8DD7mMBrgSecg+Z9v7NhSBfDVzqfn16TUQudLdXACf7HVfrbpt1RGQrUGeM2TVoV9r0sZ+vA8+7P6dT/9KpL0OISBWwAXgXKDXGnHZ31QOl09WuSfCPOBdXtvu4EGjrd1Ey7e/jRGu8zggi8hJQlmTXfTh9LMD5ungh8ISILD6HzZsUo/TxezhDNbPWSP0zxjzjHnMfzhDAL89l29TEiEgI+H/AnxtjOpyLXYcxxojIrJziJyKfBxqNMR+IyOXT3JxhpUWQN8ZcPdw+EbkL+LVbYHy7iNg4uSXqgPn9Dq10t81Iw/VRRNYCi4Bd7h9PJbBDRDYxi/o40nsIICK3A58HrjJn5/3Omv6NQTr1pY+I+HAC/C+NMb92NzeISLkx5rQ7fNg4/CvMaJuBG0TkeiAI5AA/wRkW9bpX89P+Ps6F4ZqngSsARKQa8OMkD9oG3CIiARFZhHNzcvt0NTJVxpjdxpgSY0yVMaYK5+vhRmNMPU4fv+rOsrkYaO/3NXnWEJHP4nwlvsEY091vV1q8h673gGXuzAw/zg3lbdPcpglxx6f/BdhvjPlRv13bgNvcn28DnjnXbZsMxph7jTGV7t/dLcArxpgvA68CN7qHTXv/0uJKfhSPAI+IyB4gCtzmXgnuFZEngH04QwB3G2MS09jOqfAccD3ODclu4GvT25yUPQAEgN+531beMcb8qTEmbd5DY0xcRL4BvAB4gEeMMXunuVkTtRn4CrBbRD50t30P+D7OsOkdOFln/3h6mjdl/gp4TET+FtiJ80E3bXTFq1JKpbG5MFyjlFJzlgZ5pZRKYxrklVIqjWmQV0qpNKZBXiml0pgGeaWUSmMa5JVSKo1pkFdKqTT2/wFI4zQcIDWyfAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6, 6))\n",
"\n",
"plt.scatter(X_embedded[:,0], X_embedded[:,1], c=y, cmap=\"tab10\", s=20)\n",
"plt.title(\"8 признаков\")"
]
},
{
"cell_type": "markdown",
"id": "97f13c17",
"metadata": {},
"source": [
"__Вывод:__\n",
"\n",
"- Разложение по 2 компонентам грубовато. Видно, что есть какие-то зачатки кластеризации, но компонент явно недостаточно\n",
"\n",
"\n",
"- Разложение по 8 компонентам даёт хороший результат. С помощью t-SNE можно \"спроектировать\" признаки в двумерное (латентное)пространство, построить кластеры\n",
"\n",
"\n",
"- SVD/PCA помогают снизить размерность задачи "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.0"
}
},
"nbformat": 4,
"nbformat_minor": 5
}