From 8918d3efcd6702a474cc589e7f21d54d7c855076 Mon Sep 17 00:00:00 2001 From: theking90000 Date: Tue, 3 Dec 2024 20:04:03 +0100 Subject: [PATCH] Ajouts des questions --- QUESTION10.ipynb | 250 +++++++++++++++++++++++++++++++++++++++++++++ QUESTION11.ipynb | 133 ++++++++++++++++++++++++ QUESTION12.ipynb | 136 +++++++++++++++++++++++++ QUESTION13.ipynb | 49 +++++++++ QUESTION14.ipynb | 157 ++++++++++++++++++++++++++++ QUESTION15.ipynb | 124 +++++++++++++++++++++++ QUESTION16.ipynb | 235 ++++++++++++++++++++++++++++++++++++++++++ QUESTION17.ipynb | 129 ++++++++++++++++++++++++ QUESTION18.ipynb | 147 +++++++++++++++++++++++++++ QUESTION19.ipynb | 146 +++++++++++++++++++++++++++ QUESTION2.ipynb | 177 ++++++++++++++++++++++++++++++++ QUESTION3.ipynb | 128 +++++++++++++++++++++++ QUESTION4.ipynb | 162 +++++++++++++++++++++++++++++ QUESTION5.ipynb | 163 ++++++++++++++++++++++++++++++ QUESTION6.ipynb | 122 ++++++++++++++++++++++ QUESTION7.ipynb | 174 ++++++++++++++++++++++++++++++++ QUESTION8.ipynb | 258 +++++++++++++++++++++++++++++++++++++++++++++++ QUESTION9.ipynb | 220 ++++++++++++++++++++++++++++++++++++++++ 18 files changed, 2910 insertions(+) create mode 100644 QUESTION10.ipynb create mode 100644 QUESTION11.ipynb create mode 100644 QUESTION12.ipynb create mode 100644 QUESTION13.ipynb create mode 100644 QUESTION14.ipynb create mode 100644 QUESTION15.ipynb create mode 100644 QUESTION16.ipynb create mode 100644 QUESTION17.ipynb create mode 100644 QUESTION18.ipynb create mode 100644 QUESTION19.ipynb create mode 100644 QUESTION2.ipynb create mode 100644 QUESTION3.ipynb create mode 100644 QUESTION4.ipynb create mode 100644 QUESTION5.ipynb create mode 100644 QUESTION6.ipynb create mode 100644 QUESTION7.ipynb create mode 100644 QUESTION8.ipynb create mode 100644 QUESTION9.ipynb diff --git a/QUESTION10.ipynb b/QUESTION10.ipynb new file mode 100644 index 0000000..ea6ea21 --- /dev/null +++ b/QUESTION10.ipynb @@ -0,0 +1,250 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 5, + "id": "6c549f44-d375-49c4-9b4f-8a576c81ff2a", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.linalg import hilbert" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "91cfb434-788e-44e0-bf36-7da87016e895", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def getAb(n):\n", + " A=hilbert(n)\n", + " b = np.ones(n)\n", + " return A, b" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "a6e789b3-494c-4fe7-b6fc-922eff00cd6f", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def forward(A, b):\n", + " n = len(b)\n", + " x = np.zeros(n)\n", + " \n", + " for i in range(0, n):\n", + " x[i] = b[i]\n", + " \n", + " for j in range(i+1, n):\n", + " x[i] -= x[j] * A[i, j]\n", + " \n", + " x[i] /= A[i, i]\n", + " \n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "2c362bf6-3f7d-4c1e-9411-13f298a73179", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def gsseidel(A,b,x0,maxiter=10**3):\n", + " \"\"\" méthode pt fixe Ax=b\n", + " Avec A = B+C\n", + " <-> (B+C) x = b\n", + " <-> Bx + Cx = b\n", + " <-> x = (B^-1)b - (B^-1)Cx\n", + " <-> x = (B^-1)b - (B^-1)(A-B)x\n", + " <-> x = (B^-1)b - (B^-1)Ax + x\n", + " <-> x = x + (B^1)b - (B^-1)Ax\n", + " <-> x = x - (B^-1)(Ax-b)\n", + " \n", + " Jacobi : B=diag(A)\n", + " GaussSeidel : B=trigInf(A)\n", + " \"\"\"\n", + " \n", + " B = np.tril(A)\n", + " Bi = np.linalg.inv(B)\n", + " \n", + " err = np.zeros(maxiter)\n", + " x = x0\n", + " \n", + " for k in range(maxiter):\n", + " x = x - Bi@(A@x-b)\n", + " err[k] = np.linalg.norm(A@x-b)\n", + " \n", + " return x, err" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "id": "d57bd138-7784-43e9-9a31-4d2931a232ad", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def grnormal(A,b,x0,maxiter=10**3):\n", + " \"\"\"\n", + " Méthode du gradient normal\n", + " Direction : -(Ax-b)\n", + " Pas optimal : -dT(Ax-b)/(dT A d)\n", + " \"\"\"\n", + " \n", + " err = np.zeros(maxiter)\n", + " x = x0\n", + " for k in range(maxiter):\n", + " d = -(A@x - b)\n", + " pas = -d.T@(A@x - b)/(d.T@A@d)\n", + " err[k] = np.linalg.norm(A@x-b)\n", + " \n", + " x = x + pas * d\n", + " \n", + " return err, x" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "id": "d76b3894-3ad1-49c3-9d7f-6f4e294bec1a", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def grconjug(A,b,x0,maxiter=10**3):\n", + " \"\"\"\n", + " Méthode du gradient conjugué\n", + " Direction : -(Ax-b) + ||Ax-b||/||Ax(k-1)|| * d(k-1)\n", + " Pas optimal : -dT(Ax-b)/(dT A d)\n", + " \"\"\"\n", + " \n", + " err = np.zeros(maxiter)\n", + " \n", + " x = x0\n", + " g = A@x - b\n", + " d = -g\n", + " \n", + " for k in range(maxiter):\n", + " step = -d.T@g/(d.T@A@d)\n", + " x = x + step * d\n", + " \n", + " # Nouvelle direction\n", + " gn = A@x - b\n", + " d = -gn + ((gn@gn)/(g@g) * d)\n", + " g = gn\n", + " \n", + " err[k] = np.linalg.norm(A@x-b)\n", + " \n", + " return x, err" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "id": "99db6da4-471b-472b-92dd-adf0d9565444", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-7.99999949e+00 5.03999972e+02 -7.55999963e+03 4.61999980e+04\n", + " -1.38599995e+05 2.16215992e+05 -1.68167995e+05 5.14799985e+04] [1. 1. 1. 1. 1. 1. 1. 1.]\n" + ] + }, + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "A, b = getAb(8)\n", + "x0 = np.ones(8)\n", + "maxiter = 1000\n", + "\n", + "x, err = gsseidel(A, b, x0, maxiter)\n", + "\n", + "xs = np.arange(0, maxiter, 1)\n", + "\n", + "plt.plot(xs, err, label='Gauss-Seidel', color='b')\n", + "\n", + "plt.xlabel('Nombre d''itérations')\n", + "plt.ylabel('Erreur ||Ax-b||')\n", + "plt.yscale('log')\n", + "\n", + "x, err = grnormal(A, b, x0, maxiter)\n", + "plt.plot(xs, err, label='Gradient', color='orange')\n", + "\n", + "x, err = grconjug(A, b, x0, maxiter)\n", + "print(x, A@x)\n", + "plt.plot(xs, err, label='Gradient conjugué', color='green')\n", + "\n", + "plt.legend(loc=4)\n", + "plt.plot()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "37aa7820-c174-41d4-ba43-43011688b7af", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION11.ipynb b/QUESTION11.ipynb new file mode 100644 index 0000000..31a92e7 --- /dev/null +++ b/QUESTION11.ipynb @@ -0,0 +1,133 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "eaa5c617-eab9-46fe-b681-70758e02b349", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "81126b39-6eeb-4c59-9f49-b5d2f7c65901", + "metadata": {}, + "outputs": [], + "source": [ + "def grnormal(A,b,x0,maxiter=10**3):\n", + " x = x0\n", + " iterations = np.zeros((maxiter+1, len(b)))\n", + "\n", + " for k in range(maxiter):\n", + " d = -(A@x - b)\n", + " step = -d.T@(A@x-b)/(d.T@A@d)\n", + " \n", + " iterations[k+1] = x = x + step*d\n", + " \n", + " return x, iterations" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "id": "f8e03c1b-437f-477c-b1d0-b5a18a2fdbbe", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def grconjug2(A,b,x0,maxiter=10**3):\n", + " g = A@x0 - b\n", + " d = -g\n", + " x = x0\n", + " \n", + " iterations = np.zeros((maxiter+1, len(b)))\n", + " \n", + " iterations[0] = x0\n", + " for k in range(maxiter):\n", + " step = -(d.T@(A@x-b))/(d.T@A@d)\n", + " \n", + " iterations[k+1] = x = x + step*d\n", + " \n", + " gn = (A@x-b)\n", + " d = -gn + (gn@gn)/(g@g) * d\n", + " g = gn\n", + " \n", + " return x, iterations" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "0bd3228a-40aa-42f8-8e80-c73f2106e855", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "A = np.array([[1,0],[0,50]])\n", + "b = np.array([0,0])\n", + "\n", + "x0 = np.array([30, 1])\n", + "\n", + "x, it = grnormal(A, b, x0, 30)\n", + "plt.plot(it[:,0], it[:,1], label='Gradient', color='blue')\n", + "\n", + "x, it = grconjug2(A, b, x0, 2)\n", + "plt.plot(it[:,0], it[:,1], label='Gradient conjugué', color='red')\n", + "\n", + "plt.plot(*x0, 'om', label='itéré initial')\n", + "plt.plot(0, 0, 'og', label='Solution')\n", + "\n", + "plt.legend(loc=2)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "def6fc4c-8bb7-45da-9abd-823943669f46", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION12.ipynb b/QUESTION12.ipynb new file mode 100644 index 0000000..2d56241 --- /dev/null +++ b/QUESTION12.ipynb @@ -0,0 +1,136 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 8, + "id": "c5dc3dd5-c340-4aa6-a898-b467845121e6", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.linalg import hilbert" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "id": "073124ba-d6bd-4f82-9431-fe81bdc77c21", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def decompoQR(A):\n", + " \"\"\"\n", + " A = QR\n", + " \n", + " Q = Matrice vecteurs orthogonaux (colonnes)\n", + " R = Coéfficients des projections sur les vecteurs (triangulaire sup)\n", + " \n", + " \"\"\"\n", + " m, n = A.shape\n", + " Q = np.zeros((m,m))\n", + " R = np.zeros((m,n))\n", + " \n", + " for i in range(m):\n", + " # Vecteur ligne de A = \n", + " v = A[:,i]\n", + " pr = 0\n", + " \n", + " # Retirer projection sur v des autres vecteurs\n", + " # proj A sur B = A@B/(B@B) * B\n", + " for j in range(0, i):\n", + " av = Q[:,j]\n", + "\n", + " pr += (av.T@v)* av\n", + " v = v - pr\n", + "\n", + " # normalisation vecteur\n", + " Q[:,i] = v/np.linalg.norm(v)\n", + " \n", + " \n", + " R = Q.T@A\n", + " \n", + " return Q, R" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "id": "e35d7cf5-cbbe-4948-98ed-a241643110d0", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-4.393707619954057e-14\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(2, 201)\n", + "y = np.zeros(len(x))\n", + "\n", + "for i in range(len(x)):\n", + " A = hilbert(x[i])\n", + " Q, R = decompoQR(A)\n", + " y[i] = np.linalg.norm(Q.T@Q - np.identity(x[i]))\n", + " \n", + "Q, R = decompoQR(hilbert(8))\n", + "print(Q[:,1]@Q[:,2])\n", + "#print(y)\n", + "plt.plot(x, y, color= 'b')\n", + "plt.xlabel('dimension n')\n", + "plt.ylabel('Erreur ||Q\\'Q - I||')\n", + "plt.title('Perte d\\'orthogonalité')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ea75b7ed-f555-46b7-af0c-6549d09ffe82", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION13.ipynb b/QUESTION13.ipynb new file mode 100644 index 0000000..31c0410 --- /dev/null +++ b/QUESTION13.ipynb @@ -0,0 +1,49 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "349bd8d2-2bc8-45e3-9f8a-7d60f7dedd39", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "885fccca-d36b-4d94-ba40-03eb06df2c57", + "metadata": {}, + "outputs": [], + "source": [ + "def getA():\n", + " pass" + ] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION14.ipynb b/QUESTION14.ipynb new file mode 100644 index 0000000..21af47f --- /dev/null +++ b/QUESTION14.ipynb @@ -0,0 +1,157 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "e4411a89-e2d3-4fa7-b003-04ccff1d8b0a", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f9ae855c-d325-4200-8adf-20cb102d984e", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def fglasser(t):\n", + " return np.sin(t* np.sin(t))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "dfea9591-86f9-412d-bd65-815d3ff15145", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 20, 500)\n", + "y = fglasser(x)\n", + "\n", + "plt.plot(x,y)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "5cc72b40-1a39-4a6c-9bd5-01d2094aa248", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def integrNC(fct, a, b, N, m, n, r, coeff=None):\n", + " # Schéma élementaire\n", + " A = np.zeros((n+1,n+1))\n", + " bx = np.zeros(n+1)\n", + " \n", + " for j in range(n+1):\n", + " bx[j] = m**(j+1)/(j+1)\n", + " for i in range(n+1):\n", + " A[j, i] = (r+i)**j\n", + " \n", + " coeff = np.linalg.solve(A, bx)\n", + " \n", + " h = (b-a)/m/N\n", + " I = 0\n", + " for k in range(N):\n", + " # Ajout d'un shéma élementaire\n", + " Ie = 0\n", + " \n", + " Xk = a + h*k*m\n", + " for i in range(n+1):\n", + " Ie += coeff[i] * fct(Xk + (i+r)*h)\n", + " \n", + " I += Ie * h\n", + "\n", + " return I" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "e6b107d0-e80d-4c70-8098-81656c149a66", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N=100\n", + "m=1\n", + "n=1\n", + "r=0\n", + "\n", + "def G(x):\n", + " return integrNC(fglasser, 0, x, N, m, n, r)\n", + "\n", + "x = np.linspace(0, 20, 5000)\n", + "y = G(x)\n", + "\n", + "plt.plot(x,y, color='r')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d3a53969-8d84-455f-8df3-4c8426789ac1", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION15.ipynb b/QUESTION15.ipynb new file mode 100644 index 0000000..a49cc77 --- /dev/null +++ b/QUESTION15.ipynb @@ -0,0 +1,124 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "fcdc8220-ff32-44a6-a1aa-008c9d2ab047", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "f6807c1d-c008-4661-a888-5244338ff765", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f(x):\n", + " return x**-2" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "b1095809-d35b-475a-887e-728695022470", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def integrNC(fct, a, b, N, m, n, r, coeff, tol=1e10):\n", + " h = (b-a)/m/N\n", + " I = 0\n", + " for k in range(N):\n", + " # Ajout d'un shéma élementaire\n", + " Ie = 0\n", + " \n", + " Xk = a + h*k*m\n", + " for i in range(n+1):\n", + " Ie += coeff[i] * fct(Xk + (i+r)*h)\n", + " \n", + " I += Ie * h\n", + " \n", + " return I" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "36508cd9-143a-4174-bc98-6c01634f1fcd", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.998686802598624\n" + ] + } + ], + "source": [ + "I = 0\n", + "a, b = 1, 5\n", + "N=100\n", + "m=1\n", + "n=1\n", + "r=0\n", + "coeff = [.5, .5]\n", + " \n", + "while True:\n", + " Ie = integrNC(f, a, b, N, m, n, r, coeff)\n", + " \n", + " \n", + " d= b-a\n", + " b += d\n", + " a += d\n", + " # print(I, abs(Ie), abs(Ie)<1e-10)\n", + " if abs(I+Ie) - abs(I) < 1e-5:\n", + " break\n", + " I += Ie\n", + " \n", + "print(I)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d52567ea-6629-4433-9df9-e3f93de1c36c", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION16.ipynb b/QUESTION16.ipynb new file mode 100644 index 0000000..8080716 --- /dev/null +++ b/QUESTION16.ipynb @@ -0,0 +1,235 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 82, + "id": "cd435d88-7613-4888-b731-2563dfe481c7", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "id": "a8ddf0ad-fbc5-481b-ac44-3fef2dfb56db", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f_edo(t, y):\n", + " return np.sin(t) - np.sin(6*t) - 3*y" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "id": "06b3136b-a310-46af-940c-fa4ab2cff33c", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def euler_expl(fct, a, b, y0, h):\n", + " y = y0\n", + " t = a\n", + " \n", + " N = int((b-a)/h)\n", + " r = [(t, y0)] \n", + " \n", + " for k in range(N):\n", + " y += h*fct(t, y)\n", + " r.append((t+h,y))\n", + " t+=h\n", + " return r" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "id": "dbbb8ea1-116f-4f27-8ad7-ee42a0ab5556", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def RK2(fct, a, b, y0, h):\n", + " y = y0\n", + " t = a\n", + " N = int((b-a)//h)\n", + " r = [(t, y0)]\n", + " \n", + " for i in range(N):\n", + " k1 = fct(t, y)\n", + " k2 = fct(t+h, y+h*k1)\n", + " \n", + " y = y+ h*(.5*k1+.5*k2)\n", + " r.append((t+h,y))\n", + " t+=h\n", + " return r" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "id": "b398c503-919f-4d4f-9cfe-0449b7c48a86", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def RK3(fct, a, b, y0, h):\n", + " y = y0\n", + " t = a\n", + " N = int((b-a)//h)\n", + " r = [(t, y0)]\n", + " \n", + " for i in range(N):\n", + " k1 = fct(t+0*h, y)\n", + " k2 = fct(t+2/3*h, y+h*k1*2/3)\n", + " k3 = fct(t+2/3*h, y+h*k1*1/3 + h*k2*1/3 )\n", + " \n", + " y = y+ h*(.25*k1+0*k2+.75*k3)\n", + " r.append((t+h,y))\n", + " t+=h\n", + " return r" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "id": "e8aa9ef5-61d7-46a6-a41b-72fea746ccf3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def RK4(fct, a, b, y0, h):\n", + " y = y0\n", + " t = a\n", + " N = int((b-a)//h)\n", + " r = [(t, y0)]\n", + " \n", + " for i in range(N):\n", + " k1 = fct(t+0*h, y)\n", + " k2 = fct(t+1/2*h, y+h*k1*1/2)\n", + " k3 = fct(t+1/2*h, y+h*k1*0 + h*k2*1/2 )\n", + " k4 = fct(t+1*h, y+h*k1*0 + h*k2*0 + h *k3*1 )\n", + " \n", + " y = y+ h*(1/6*k1+2/6*k2+2/6*k3+1/6*k4)\n", + " r.append((t+h,y))\n", + " t+=h\n", + " return r" + ] + }, + { + "cell_type": "code", + "execution_count": 93, + "id": "63cbd3c9-1026-4d59-9fdf-d268a487ad51", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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/f8VuRFxCumnKoX9MMFmaTACU3BZYs2ThPCGEqMn69evH7t272bJlC48//jhDhgzh8ccfL7XP4MGDyc/P57XXXrvqeTZu3MjQoUMZNWoUaWlpVV1+vSEtI+UQ6GkiOSAQ7zTI9YrhwI9v0fb+Gc4uSwghqo2LzoUtY5zzJImLzqXcx7i5udG4cWMAZs6cSb9+/XjppZd45ZVXSvYZMGAAkydPZuTIkdhsNt57773Lnqdx48Z07dqVJk2a8PnnnzN16tSK35AoIWGknKLbBcHyNLK9GpG4Zj5t73d2RUIIUX0URSl3V0lN8sILLzBs2DAefvhhQkNDS7YPGjSIxYsXM2LECOx2O++///4Vx6eoqorZbK6OkusF6aYppz4dQjGrZ1EVLWpaNKo539klCSGEuEZ9+/alVatWZXbJ9O/fnyVLlvDll1/y6KOPoqoq+fn5PPPMM2zevJmEhAR27tzJAw88wKlTp7jjjjuccAd1k4SRcmof7s1hV8dsrEUubYj/4xMnVySEEKI8pkyZwqeffkpSUtIl7/Xt25elS5cyb948Hn74YTQaDYcPH+a2226jadOm3HjjjaSnp7Nu3TpatWrlhOrrJkVVVdXZRVxNTk4OXl5eZGdn4+np6exyeOrjrTTclYfWWkSU6U2Gvr/a2SUJIUSVKCoq4uTJk0RHR2MymZxdjqiBrvQ9cq2f39IyUgFdOgRjU3Ox6UwUxfuB3ebskoQQQohaS8JIBfRtHsgxvQUAu6YNmbt+cXJFQgghRO0lYaQCAj1M5IQ6JsbJ9GvN3h8/dXJFQgghRO0lYaSCYtoFoapmLEZvsg7anV2OEEIIUWtJGKmgvi0DSdVmA6CxtKYoYaeTKxJCCCFqJwkjFdQu3JuDHj4AnPNpw94fpl/lCCGEEEKURcJIBem0GsJa+oFqI9+9ASlbZZ0aIYQQoiIkjFyH3jHB5CgZji9yWmDPTnFuQUIIIUQtJGHkOvRpGsBOkzsAeZ5tOPyzdNUIIYQQ5SVh5DoEeBhRwr0ByPJqzInVzlnJUgghhKjNJIxcpy6tAzGrGaBosKZFg0UWzhNCiJpg/PjxKIqCoijodDoiIiJ4+OGHOXfuXMk+UVFRzJgxo+RrVVV56qmn8PDwYNWqVZecc+LEiSiKUuoYcf0kjFynvs0C2GfUAWAxtuH0n587uSIhhBAXDB06lJSUFOLj4/nss8/49ddfeeSRR8rc12azMWHCBObOncuqVavo379/qfd/+ukntmzZQmhoaHWUXq9IGLlO7cJ9SPR0jBs569uSA0t/cm5BQgghShiNRoKDgwkLC2Pw4MGMHj2a5cuXX7Kf2WzmjjvuYMWKFaxdu5ZOnTqVev/06dM89thjzJ8/H71eX13l1xs6ZxdQ22k1Ci1b+mNfnQhaT/LjfcFmBa38pxVC1D2qqqIWFjrl2oqLC4qiVPj4EydOsGzZskvCRF5eHsOHDycpKYkNGzYQERFR6n273c7YsWN5+umnadWqVYWvLy5PPjErQd9mgazdGEdTK6hqG3L2LcWz3U3OLksIISqdWljIkQ6xTrl2s507UFxdy3XM4sWLcXd3x2azUVRUBMD06aWffHzllVfw8PDg4MGDBAYGXnKON954A51Ox+TJkytevLgi6aapBL2bBrDH6Ak4Fs7bvUgWzhNCiJqgX79+7N69my1btvD4448zZMgQHn/88VL7DB48mPz8fF577bVLjt+xYwfvvvsuc+bMua5WGXFlFWoZ+fDDD3nrrbdISUmhVatWzJgxg169el12//nz5/Pmm28SFxeHl5cXQ4cO5e2338bPz6/ChdckAR5GvCLdUQ/kYjF6kXHABqoK8o0rhKhjFBcXmu3c4bRrl5ebmxuNGzcGYObMmfTr14+XXnqJV155pWSfAQMGMHnyZEaOHInNZuO9994reW/dunWkpaWV6rqx2Ww89dRTzJgxg/j4+IrfkChR7paRBQsW8MQTT/Dss8+ya9cuevXqxbBhw0hMTCxz//Xr1zNu3DgmTJjAgQMH+P7779m2bRsPPPDAdRdfk/RpHkiqxvG4mFLUmuJTu51bkBBCVAFFUdC4ujrlVRktEy+88AJvv/02ycnJpbYPGjSIxYsXM3v2bB599FFUVQVg7Nix7N27l927d5e8QkNDefrpp/n999+vux7hUO4wMn36dCZMmMADDzxAixYtmDFjBuHh4cyaNavM/Tdv3kxUVBSTJ08mOjqanj17MnHiRLZv337dxdckfZoFssPkDUCWTxv2/TjDqfUIIYS4VN++fWnVqlWZXTL9+/dnyZIlfPnllyWBxM/Pj5iYmFIvvV5PcHAwzZo1c8Id1E3lCiMWi4UdO3YwePDgUtsHDx7Mxo0byzyme/funDp1iqVLl6KqKmfOnGHhwoUMHz78stcxm83k5OSUetV07cK9yfDSg2qlwC2ExG2ycJ4QQtREU6ZM4dNPPyUpKemS9/r27cvSpUuZN28eDz/8cEkLiaha5RozkpGRgc1mIygoqNT2oKAgUlNTyzyme/fuzJ8/n9GjR1NUVITVauWmm24q1Sf3d9OmTeOll14qT2lOp9UodGsWQHbqAbwIxZ7dCnvWaTTeDZxdmhBC1Etz5swpc/uYMWMYM2YMQJljPnr37k1ubu5lzyvjRCpfhZ6m+Xu/naqql+3LO3jwIJMnT+Y///kPO3bsYNmyZZw8eZJJkyZd9vxTp04lOzu75FVWeq2J+jYLYLvJA4A8j7YcX3r5wCWEEEIIh3K1jPj7+6PVai9pBUlLS7ukteSCadOm0aNHD55++mkA2rRpg5ubG7169eLVV18lJCTkkmOMRiNGo7E8pdUIvZsG8JxBx4BCO7meURz582uajHF2VUIIIUTNVq6WEYPBQGxsLCtWrCi1fcWKFXTv3r3MYwoKCtBoSl9Gq9UC1Lm+OH93I00ivChSHWGtKL0xmC/f1CeEEEKICnTTTJkyhc8++4zZs2dz6NAhnnzySRITE0u6XaZOncq4ceNK9h8xYgQ//vgjs2bN4sSJE2zYsIHJkyfTuXPnOrnYUJ9mgew2GQAwG9tyZv08J1ckhBBC1GzlnvRs9OjRZGZm8vLLL5OSkkJMTAxLly4lMjISgJSUlFJzjowfP57c3Fzef/99nnrqKby9venfvz9vvPFG5d1FDdK3WQBfLnenqwWyvRuzd+l0Bg0oe4VIIYQQQoCi1oK+kpycHLy8vMjOzsbT09PZ5VyRza7S8dUV3JeUgVYbTGDGXO5Y8CloZZVHIUTtU1RUxMmTJ4mOjsZkMjm7HFEDXel75Fo/v2Vtmkqm1Sj0bhrAIaMVAKvSjvwDMkufEEIIcTkSRqpA32YBbDP5ApDl04Jdi75wckVCCCFEzSVhpAr0bhJApk5BtWVg1+hJOWxyLJwnhBBCiEtIGKkCfu5G2oR5kaTLBsBa3Abb6d3OLUoIIUSliYqKYsaMGVV2fkVR+Omnn677PFVdZ2WRMFJF+jYLZL1LIADZ3jHs/+kDJ1ckhBD1w4gRIxg4cGCZ723atAlFUdi5c+d1XWPbtm089NBD13WOyjRnzhy8vb0v2V7T6rwcCSNVpG+zAE7rdSi2bGw6F45tk8nPhBCiOkyYMIFVq1aRkJBwyXuzZ8+mXbt2dOjQ4ZL3VFXFarVe0zUCAgJwdXW97lqrWm2pU8JIFWkT5o2Pm550jWM2Vkt+K9SsU06uSggh6r4bb7yRwMDASxbKKygoYMGCBUyYMAGA1atXoygKv//+Ox07dsRoNLJu3TqOHz/OyJEjCQoKwt3dnU6dOvHHH3+UOtfVuj9Wr15N586dcXNzw9vbmx49epQKR7NmzaJRo0YYDAaaNWvGvHmXnyDzQp1ZWVkl23bv3o2iKMTHx7N69Wruu+8+srOzURQFRVF48cUXy6wzMTGRkSNH4u7ujqenJ6NGjeLMmTMl77/44ou0a9eOefPmERUVhZeXF3feeecVFw6sDBJGqohWo9CnaQDrXf0AyPVsS8Lyj5xclRBCXB9VVSk225zyutZpsXQ6HePGjWPOnDmljvn++++xWCzcfffdpfb/v//7P6ZNm8ahQ4do06YNeXl53HDDDfzxxx/s2rWLIUOGMGLEiFITel6J1Wrl5ptvpk+fPuzdu5dNmzbx0EMPlSwou2jRIv7xj3/w1FNPsX//fiZOnMh9993Hn3/+eY3/CqV1796dGTNm4OnpSUpKCikpKfzzn/+8ZD9VVbn55ps5e/Ysa9asYcWKFRw/fpzRo0eX2u/48eP89NNPLF68mMWLF7NmzRpef/31CtV2rco9A6u4dn2bBfLLrmSUvHyKDR7sWXWEqFHOrkoIISrOarHzyT/WOOXaD73bB71Re0373n///bz11lusXr2afv36AY4umltvvRUfH59S+7788ssMGjSo5Gs/Pz/atm1b8vWrr77KokWL+OWXX3jssceueu2cnByys7O58cYbadSoEQAtWrQoef/tt99m/PjxPPKIY3buKVOmsHnzZt5+++2SWsvDYDDg5eWFoigEBwdfdr8//viDvXv3cvLkScLDwwGYN28erVq1Ytu2bXTq1AkAu93OnDlz8PBwrEI/duxYVq5cyX//+99y13atpGWkCvVuGoCqgTwcaTr/bFMoynZyVUIIUfc1b96c7t27M3v2bMDx1/66deu4//77L9m3Y8eOpb7Oz8/n//7v/2jZsiXe3t64u7tz+PDha24Z8fX1Zfz48SUtKu+++y4pKSkl7x86dIgePXqUOqZHjx4cOnSovLdZLocOHSI8PLwkiAAl93jxtaOiokqCCEBISAhpaWlVWpu0jFQhXzcDbcK82VzgzgAzFLi2I3Pzt/j1nejs0oQQokJ0Bg0PvdvHadcujwkTJvDYY4/xwQcf8MUXXxAZGcmAAQMu2c/Nza3U108//TS///47b7/9No0bN8bFxYXbb78di8Vyzdf+4osvmDx5MsuWLWPBggU899xzrFixgq5duwKUdNlcoKrqJdsuuLDy/cVdTsXFxddcy9Wu8fften3p5UsURcFut5f7euUhLSNVrF+zAPaa/FHsFswmP7YtrlifoBBC1ASKoqA3ap3yutyH9eWMGjUKrVbL119/zZdffsl99913TedYt24d48eP55ZbbqF169YEBwcTHx9f7v9W7du3Z+rUqWzcuJGYmBi+/vprwNFls379+lL7bty4sVRXzsUCAgIASrWu7N69u9Q+BoMBm812xXpatmxJYmIiSUlJJdsOHjxIdnb2Za9dXSSMVLG+zQKxKlBsPwHA2dNhYL32dC2EEKJi3N3dGT16NM888wzJycmMHz/+mo5r3LgxP/74I7t372bPnj2MGTOmXC0DJ0+eZOrUqWzatImEhASWL1/O0aNHSz7wn376aebMmcNHH31EXFwc06dP58cffyxz0OmFesLDw3nxxRc5evQoS5Ys4X//+1+pfaKiosjLy2PlypVkZGRQUFBwyXkGDhxImzZtuPvuu9m5cydbt25l3Lhx9OnT55KuquomYaSKtWngha+bgd3nFzIs0rfHfHi5c4sSQoh6YsKECZw7d46BAwcSERFxTce88847+Pj40L17d0aMGMGQIUPKnJfkclxdXTl8+DC33XYbTZs25aGHHuKxxx5j4kRHF/3NN9/Mu+++y1tvvUWrVq34+OOP+eKLL+jbt2+Z59Pr9XzzzTccPnyYtm3b8sYbb/Dqq6+W2qd79+5MmjSJ0aNHExAQwJtvvnnJeS7M6urj40Pv3r0ZOHAgDRs2ZMGCBdd8b1VFUa/1WSknutYliGuqJ77dxdKdSTyRZUTV6GkdMo/eL8jieUKImu9Ky8MLAVf+HrnWz29pGakG/ZoHYtFoUazHAUg65iML5wkhhBDnSRipBr2aBKAocMiYD4BZaY/91PWtiyCEEELUFRJGqoGvm4G2Yd6s9GiIYrdR6NqAXT9+5eyyhBBCiBpBwkg16dcskHyNCZ0lDoCje8v3iJoQQghRV0kYqSZ9mzmeE08yZQBQYG0D5y5dUVIIIYSobySMVJPWDbzwczOwzC0SVBtFLhEcXSJdNUKI2qEWPHgpnKQyvjckjFQTjUahd9MA0vX+mAqPAbBrfaaTqxJCiCu7MDV4WZNoCQF/fW/8fRr58pC1aapR32YBLNp1mgyXVNxpRl5hDGTEgX8TZ5cmhBBl0mq1eHt7lyyU5urqWu5p2UXdpKoqBQUFpKWl4e3tjVZ7bSsql0XCSDXq3SQAjQKL3CMZm2enyCWKI4s+odmDbzm7NCGEuKwLy9JX9cqtonby9vYu+R6pKAkj1cjHzUDbcG92JYLBfAKLqTG7NxXSbIIdNNJjJoSomRRFISQkhMDAwAqtFivqLr1ef10tIhdIGKlm/ZoFsisxi7Pe2bgXQYGlHfaEjWiiezq7NCGEuCKtVlspHzxC/J38OV7NLjzi+4trFKh2CtwbsnfhZ84tSgghhHAiCSPVLCbUC393A6ftruitiQAc3muC4iInVyaEEEI4h4SRanbhEV+AnEBH36vZ1gHbwcXOLEsIIYRwGgkjTjC0lWPU8W+mcADyPBqydeE8Z5YkhBBCOI2EESfo3TQAd6OO44UqOvUUKBoS4wKh4KyzSxNCCCGqnYQRJzDptQxsEQhATrDjn8BCLIVbZXp4IYQQ9Y+EEScZ3iYUgN8050OJV2O2/LzImSUJIYQQTiFhxEl6NfHHw6jjRGExWuUMKBrSEhtB5nFnlyaEEEJUKwkjTmLSaxnYMgiA7FAjAMX6jpxdK3OOCCGEqF8kjDjR8NYhAPyuegKQ5dWY7b+tBlmqWwghRD0iYcSJejU931VTYEarSwdFQ05aWzi1zdmlCSGEENVGwogTGXVaBp3vqjkX7mgdKXKJ5fTvHzqzLCGEEKJaSRhxsuFtHF01y8x6UO1kezVi99rDYLU4uTIhhBCiekgYcbKeTfzxMOlIKDCjcz0HgOVsB9Sjvzu5MiGEEKJ6SBhxMqNOy+CWjunhM8P9Acj17MjRJbOcWZYQQghRbSSM1ADD2zjCyLI8G6h2cj2jOLr9HBSec3JlQgghRNWTMFID9GwcgIdJR2KBGZ1nLgD2vE7Ydi90cmVCCCFE1ZMwUgMYdBqGnF/JNyPMMT18lncsexd/4cyyhBBCiGohYaSGuDAB2m/ZhYCNPI9wkg4qcC7eqXUJIYQQVU3CSA3Ro7E/niYdpwrMGHzNAChFnSnaMs/JlQkhhBBVS8JIDXFxV01aSAAAmf4d2fnb9zI9vBBCiDpNwkgNcmECtMXncgEb+W4hZB73g9M7nVuYEEIIUYUkjNQgPRr74+WiJ6XAjCnY7tho60jWus+dW5gQQghRhSSM1CB6rYYhrRxr1aQE+ACQHtCBXStXgq3YmaUJIYQQVUbCSA0zvE0oAIszs1EUK4WuQRQmhsOxlU6uTAghhKgaEkZqmO6N/PB21ZNaYMElXA+ATdeR5JWfOLkyIYQQompIGKlh9FoNQ86vVXPKxwOAtIAOHNiwF4qynVmaEEIIUSUkjNRAF56q+TXtHIrGSpGLP/aUxqgHfnZyZUIIIUTlkzBSA3Vr5IePq560QgvuDd0AKHLtzLHf5akaIYQQdY+EkRrI8VSNo6vmpKcRgDOBHTi+KwWykpxZmhBCCFHpJIzUUBe6an5JPYdWX0yxwRNtRgy2Xd84uTIhhBCickkYqaG6NXR01WQWWPBs7gdAjlcn9i37WqaHF0IIUadIGKmhdFoNQ2McrSNHXBz/TOn+bUk+bIGUPc4sTQghhKhUFQojH374IdHR0ZhMJmJjY1m3bt0V9zebzTz77LNERkZiNBpp1KgRs2fPrlDB9cnw1ue7apIyMLhaselM6HPaY94qK/kKIYSoO8odRhYsWMATTzzBs88+y65du+jVqxfDhg0jMTHxsseMGjWKlStX8vnnn3PkyBG++eYbmjdvfl2F1wddG/ri62bgXGExXjGOaeLP+nVi14rFYLM6uTohhBCicpQ7jEyfPp0JEybwwAMP0KJFC2bMmEF4eDizZs0qc/9ly5axZs0ali5dysCBA4mKiqJz58507979uouv6xxdNY6navbpbABk+rbi3AlXOLHaiZUJIYQQladcYcRisbBjxw4GDx5cavvgwYPZuHFjmcf88ssvdOzYkTfffJMGDRrQtGlT/vnPf1JYWHjZ65jNZnJyckq96qsLXTWL4zNw81VRNVq05o5kb/jCyZUJIYQQlaNcYSQjIwObzUZQUFCp7UFBQaSmppZ5zIkTJ1i/fj379+9n0aJFzJgxg4ULF/Loo49e9jrTpk3Dy8ur5BUeHl6eMuuULtG++LkZOFdQjPv5uUfSAzuye+1mMOc6uTohhBDi+lVoAKuiKKW+VlX1km0X2O12FEVh/vz5dO7cmRtuuIHp06czZ86cy7aOTJ06lezs7JJXUlL9nejr4q6anaoFUMnybkJRYgAc+tW5xQkhhBCVoFxhxN/fH61We0krSFpa2iWtJReEhITQoEEDvLy8Sra1aNECVVU5depUmccYjUY8PT1LveqzCxOgLT2Rju/5lXxVpTOpf0pXjRBCiNqvXGHEYDAQGxvLihUrSm1fsWLFZQek9ujRg+TkZPLy8kq2HT16FI1GQ1hYWAVKrn+6RPvh724gq6AYUzNH6DsT1JH9249DTrKTqxNCCCGuT7m7aaZMmcJnn33G7NmzOXToEE8++SSJiYlMmjQJcHSxjBs3rmT/MWPG4Ofnx3333cfBgwdZu3YtTz/9NPfffz8uLi6Vdyd1mFajlHTVbCkuAMVOnnsY6ulI1L3fObk6IYQQ4vqUO4yMHj2aGTNm8PLLL9OuXTvWrl3L0qVLiYyMBCAlJaXUnCPu7u6sWLGCrKwsOnbsyN13382IESOYOXNm5d1FPTC8dSgAvx1NJ7SZBwBml84cX/GVM8sSQgghrpuiqjV/oZOcnBy8vLzIzs6ut+NHbHaVLq+tJCPPzLvdm3JqaRKmokwa5D3D0Pd/hODWzi5RCCGEKOVaP79lbZpaQqtRGHa+q2ZDQT4arY0ikx/6tKbYd37t5OqEEEKIipMwUotceKpm2eEzRLULACDXqxP7Vv4EdpsTKxNCCCEqTsJILdIpypcADyM5RVaskY5xI2mBHUiJU+HkGidXJ4QQQlSMhJFa5OKumjXnctEbbRTr3dFnt8W8VQayCiGEqJ0kjNQyF9aqWX7oDE17OKbJz/Tvwu61q8GS78TKhBBCiIqRMFLLdIzyJfB8V01hqCsAGX4xnI33gsNLnFydEEIIUX4SRmoZrUbhhvOtI38kn8PdT0XV6NBYOpOzYa6TqxNCCCHKT8JILXQhjCw/mEqrvo0BOBPUhd3b9kNu2asnCyGEEDWVhJFaqGOkD4EeRnKLrGT66gA7uZ5R5J+KhH0LnV2eEEIIUS4SRmohzUVdNb8fTyewkREAm7YrZ9bKUzVCCCFqFwkjtdSN5ydAW3HgDK37NgEgNbgz+/alQdohZ5YmhBBClIuEkVqqQ4QPwZ4mcs1WEo0qGq0Fs9EHS1ob1N3fOLs8IYQQ4ppJGKmlNBqFYa0dE6AtO3SG6Fh/AArcunJy9fdgtzuzPCGEEOKaSRipxUq6ag6eoWWvRgCkB7TlaJwGEtY7szQhhBDimkkYqcXah//VVXPYYsbgUohda8SW3Qn7DlnJVwghRO0gYaQWu/ipmt/2pxLTz9E6kuXTlQPrfgdLgTPLE0IIIa6JhJFabvhFXTVNuoaDqpLl05SExCA4stTJ1QkhhBBXJ2Gklmsf7k2ol4k8s5Wd6bm4BxYBYC/qhmW7PFUjhBCi5pMwUss5nqpxtI4s2ZdCx2FtAcgI6MKuLdsgL92Z5QkhhBBXJWGkDrjQVfPHwTNEtAlEoZhC10BSU1rC/h+cXJ0QQghxZRJG6oD24d408HYh32JjY8JZApo4/lmtdCd3y3wnVyeEEEJcmYSROkBRFIbFOCZAW7I3hW7DYwFID4hl5+5USD/qzPKEEEKIK5IwUkdc6KpZeegMftGeaLW52HQuZJ7tBnsXOLk6IYQQ4vIkjNQR7S7qqlkTl0HDbo7p4QtdepC2YYFMDy+EEKLGkjBSRyiKUtI6smRfCt2HdwTVTpZ3E3YcdYfETU6uUAghhCibhJE65MJsrCsPnUHnrsPFMwOA3IK+qHtkzhEhhBA1k4SROqRtmBcNvF0osNhYfSSN9je2ASDbuysn1y+D4iInVyiEEEJcSsJIHaIoSslKvov3ptCmZ3M09lwsBk92n24LR5c5uUIhhBDiUhJG6pi/nqpJw2JT8Y7IBaDA3hv7LumqEUIIUfNIGKljWjfwIszHhcJiR1dN73sGApDt1YrdWw5CfqaTKxRCCCFKkzBSx1z8VM3ifSk0iArGoCaBouFoZj848KOTKxRCCCFKkzBSB93YOhSAVYfSKLBYCe5gAiBP3wPz9q+dWZoQQghxCQkjdVBMA0/CfR1dNX8eTqf/PSPQ2AoxuwSwfo8eMo87u0QhhBCihISROkhRFIafbx1Zui8FNzdXTMYTAJzO7w+7vnJmeUIIIUQpEkbqqAuP+K48fIYCi5XGNzQEIM+1PZlrvwVzrjPLE0IIIUpIGKmjWoV6EunnSlGxnVWH0+gxdBiGotOoGj3rTneDHV86u0QhhBACkDBSZymKUjI9/NJ9KWg0GlxCUgDItPbBvuF9sJqdWaIQQggBSBip04afDyOrDqeRb7bSe+KtKPZiilzC2XTcD/Z+5+QKhRBCCAkjdVqrUE+iLuqqiYhqjFHvGMiakDUINrwLdpuTqxRCCFHfSRipw/7eVQMQc2tbAHLcO3M0Lh0OL3FafUIIIQRIGKnzLszGeqGrpnP/bmjtmdh0JvamDIT174CqOrlKIYQQ9ZmEkTquZYgn0f5umK12Vh5OQ1EUGnR1AyDP2IfUI/vg5FonVymEEKI+kzBSxzkmQHO0jizZmwzAwFEDQS0m3z2MbUkdHK0jQgghhJNIGKkHLowbWX0knTyzFRd3A97hBQAUFfcl9+BaSN7lzBKFEELUYxJG6oEWIR40vNBVc+gMAH3v7ANARkAsWxIawPoZTqxQCCFEfSZhpB5QFKVkIOuSvY6nakIb+WBwzcWu0VN4rjeWPb/IAnpCCCGcQsJIPXEhjKw+6uiqURSF2BtbA5Ae2JOtpzwd844IIYQQ1UzCSD3RLMiDhgFuWKx2/jjo6KqJ6R6BohRT6BpEQVJb7Lu+gZwUJ1cqhBCivpEwUk8oisKNbUIB+H5HEgAGk45GXQIByPbuze7TRtj8gdNqFEIIUT9JGKlHRncKR6PAhmOZHEvLAyB2YGMA0v3bci4uFHXbF1B4zpllCiGEqGckjNQjDbxdGNAiCICvNicA4B/mgU+YHlWjpcjYi6Mpdtj2mTPLFEIIUc9IGKlnxnWLBOCHHafIN1sB6DSkKQDJIT1JOuINmz8CS4GzShRCCFHPSBipZ3o08ifa341cs5Wfdp8GoGH7AAyuKhajF1pzLKdScmH3fCdXKoQQor6QMFLPaDQK93R1tI7M25SAqqpodRra9m8IwOkGfTh8zAs2zARbsTNLFUIIUU9IGKmHbu8Qhkmv4XBqLtsTHINVW/UKRdGoZHs1wi01mnMpyXBgkZMrFUIIUR9IGKmHvFz13NyuAeBoHQFw8zLSqINjcGtyaB92nvR2LKCnqs4qUwghRD0hYaSeutBV89v+FNJzzQC07R8OQFpQRzyP+VB06hDELXdajUIIIeoHCSP1VEwDLzpEeFNsU1mwLRGAoGhP/MPdsGv0ZAR0Z2uij6N1RAghhKhCEkbqsbHnH/OdvyURq82Ooii06RcBwOnQ3hgPumA7uQkSNjmzTCGEEHVchcLIhx9+SHR0NCaTidjYWNatW3dNx23YsAGdTke7du0qcllRyW5oHYKvm4GU7CJWHk4DoEmnQIxuOswmX8yubdiR7AUbZji3UCGEEHVaucPIggULeOKJJ3j22WfZtWsXvXr1YtiwYSQmJl7xuOzsbMaNG8eAAQMqXKyoXEadltGdHONELgxk1em1tOrlGNyaFNYXy0FX1CPL4MwBp9UphBCibit3GJk+fToTJkzggQceoEWLFsyYMYPw8HBmzZp1xeMmTpzImDFj6NatW4WLFZXv7i4RKAqsP5bB8XTHejWt+zRA0UCWd1MMxREcOOMOG951cqVCCCHqqnKFEYvFwo4dOxg8eHCp7YMHD2bjxo2XPe6LL77g+PHjvPDCCxWrUlSZMB9XBjR3rNx7Yb0adx8TjWMdj/kmhvUn/Yg77FsI5xKcVqcQAk5nFbIt/iwn0vPIKSpGlUfvRR2hK8/OGRkZ2Gw2goKCSm0PCgoiNTW1zGPi4uL497//zbp169Dpru1yZrMZs9lc8nVOTk55yhTlNLZbFH8cSmPhjlM8PaQZrgYd7QaGE7ftDGmBsTQ+8RPxZ7OI2vQ+3PCWs8sVot7JKSpmxoo4vtwUj83+VwAx6DQEuBvxdzfg7250vDwM+LkZ8fdwbA84v93LRY9GozjxLoS4vHKFkQsUpfQ3tKqql2wDsNlsjBkzhpdeeommTZte8/mnTZvGSy+9VJHSRAX0auxPlJ8r8ZkF/Lw7mbs6RxAY6UlIYy9SjmVzqkEfMo+eJSpgLvT+P3APcHbJQtRJ1mIb5gIrxUU2is02LEVW1hxO46ttSWQUmgkhDU93V5JsXuQW27BY7ZzOKuR0VuFVz63TKPhdFFr8Lgoq/h4XhRl3I75uBrQSXEQ1UtRytPNZLBZcXV35/vvvueWWW0q2/+Mf/2D37t2sWbOm1P5ZWVn4+Pig1WpLttntdsd6KFoty5cvp3///pdcp6yWkfDwcLKzs/H09CzXDYpr89m6E7y65BAtQzxZMrkniqJwYnc6v320D11xPt02PUfIDacJuOEJ6P+cs8sVolYryi8m9UQ2GafyyEkvJDu9kOy0AvKzLdd2AtWO1mDBLdATo48bdjcdZk8dOS4KGcVWMvIspOeZycgzk5FrJqfIWq76FAV8XQ2lgkrbMG/GdotEr5UZIcS1y8nJwcvL66qf3+VqGTEYDMTGxrJixYpSYWTFihWMHDnykv09PT3Zt29fqW0ffvghq1atYuHChURHR5d5HaPRiNFoLE9p4jrdHhvGW78f4WBKDjsTzxEb6UtUG388A1zISYczwV1IP76KAVs/gR7/AKOHs0sWotYoyLGQsD+TlONZpB7P5lxqwRX2VlHsZnTFRehtRSh2G3aNHpvWgF1jwKY1oGp02IpN5Jy2wOm/AowGaOxvoke0Fw1aBhEZ44+7jxGL1U5mvpmMXAsZeeaLgorj64w8M5l5jv9/tsCCqkJmvoXMfAtHzjjO/fPuZBbtOs07o9vRONC9Sv97ifqn3N00U6ZMYezYsXTs2JFu3brxySefkJiYyKRJkwCYOnUqp0+fZu7cuWg0GmJiYkodHxgYiMlkumS7cC5vVwMj24Xy3fZTzNuUQGykLxqNQtv+YaxbEEdSWD9id6wnr9lZ3HfMge6PO7tkIWq07PRCTuxO5+SedFKOZ8Pf2qBdvVQ0JKM5exyPlHhCzqTiUpiBzlqAcn7nIj1kBNtRAooJ9CiiiWcBZy169qeGQmooRosvhS5+FLiGkOUZSZFrMDkZReRkFBG37QxwBP9wd6Ja+xPVxp+YSM8yu9QvZrXZOVtgKRVUkrMK+XTdSfadzmb4zHX8e1hz7u0WJWNQRKUpdxgZPXo0mZmZvPzyy6SkpBATE8PSpUuJjHTM5pmSknLVOUdEzTS2axTfbT/F0n2pPHejGX93I827hbDllxMUEkSOdyu2xxfRd9MH0Pkh0EnrlRAXsxRZidt2hoPrk0lLyC31nqtnEbriOFySd9Pg+D688/IvOT7TWyUvyIarn4VIn0KauZnRaACDOwS2gqCWNDh7kgYea1Ebx5OYayTutCehJw20PKxSrHMh1yOSNL9o0hu0p1gJJSMpj4ykPLYvjcc7yJUW3UNo1iUYN++yf351Wg2BHiYCPUyltt8eG87TC/ewLi6Dl349yMpDabx1RxtCvFwq7b+fqL/KNWbEWa61z0lcv5s/2MDupCyeHtKMR/s1BmDjj8fYtTwR73NHaH5kJm2Gp6C/bSZ0GOfkaoWoGdITc9m/7jRxW89QbLad32rHqJ7C+8w2ok/uxNWcVeoYsx7SA+3YA634+RbR1LMQN4OdHLcovKLaoQlqBUGOAIJXBI5Ucl5OMuz7HvZ+B2f2o6pwPMvEyRRvvI5r8ch3/Fq36N1JCo0hNbozxdom2G2OcygKRLTyo2XPUKLb+KNcYwuHqqp8tTmB/y49RFGxHU+TjldujmHk+VXAhfi7a/38ljAiSvlhxyme+n4PDbxdWPt//dBqFHLPFjHvuY2odui0/XVsrY7QraM/PLoVNNqrn1SIOkhVVU4dOcfWX+JIPfFXK4ep8AxhpzcQfGYLhuK8ku1nPVWyg+2Y/C2EexcR4uvKfmso+6zhHFHDCW4Sy9gRgwny8ylfIan7Yd93sPd7yE3Gbocj51xJSvHB95iKW5FjN6vWxPHIDqRF9aPYHlpyuHeQK+0GhtOsazA6/bX9PB9Pz2PKgt3sOZUNwI1tQnj15hi8XQ3lq13UeRJGRIUUFdvoNm0l5wqK+WRsLINbBQOwYvYBjm49Q2DadsKSvqDLsGQ0d86FlpcOXBaiLlNVlRXvf0zCPlcsmjAAFLuVwPRdhKZswDsrjmItpAWpFAcU4xNgo0nDBvg3bAtBrYhTInlpC6xPcbRGNA/24KWbWtGlod/1FWa3QcIG2LsADv4C5hzsNtif6caZFF/8j9kwFTt2LXAJJK5hD84G9kJVHd01Lh562vQLo3W/cIwuV+/BL7bZ+eDPY7y36hg2u0qQp5E3b29Ln6by6L/4i4QRUWHTfjvEx2tO0KuJP/MmdAEg41QeC17dCqqdrlteQtP5JO07NoYH/3S0+QpRD8RtO8bqjzdh0Tm6JTQ2C6EpG/E6u4J830z0oXpCG4fRtG03DGFtISgGfBuCRktmnpk3lh3mu+2nAPAw6pgyuClju0aiq+zHZYsL4chvjm6cYyvAbqXYqrAvw4PMFB+CjhWjt4FVayQlpDsnI/tj1fsCYHTTETskitZ9G6AzXL2lZE9SFk9+t5sT6Y7WoXHdIpk6rAUu13CsqPskjIgKSzpbQO+3/kRVYdVTfWgY4HiM79f39pB4IJMGp9fhm/UNvfqnoNz7MzTs69yChahi51LzWf7RSjJSHT8LWmsRbtb1hEbE0aJLe0LbDITAFmU+8m612Zm/JZH/LT9SMt/H7bFh/GtocwI8qmEQeH4mHPjREUxObQXAXKywJ9OXnFMeBJ2woFE1pAV0ID5yKAVuIQAY3RW6jWxKi+4haK4SlgotNl7/7RBfnl9ws6G/G9NHt6NduHeV3pqo+SSMiOty/5xtrDqcxoSe0Tx/Y0sAkuPOseh/u1DsxfTY9DyufRJp0rkLjPvZydUKUTWK8ovZ8lMc+9clAxoU1YZf+noibyim64T/XrVVcFv8Wf7z8wEOpTiWtGgV6snLI1sRG+lbDdWX4ewJx9iSvd86/j9QYNGwJzOQggQXAhOKSQvqzMmo4ZhNjhp1hlxibw+nY+8OVz39urh0/vn9Hs7kmNFqFB7r15jH+jeWidLqMQkj4rr8eSSN+77YhqdJx5ZnBuJi0KKqKj+8uYMzJ3OITPgdV+tP9O+R6uiqaXD1X1RC1BaqqhK3/Qxr5x/AXOQIHP4ZezHYF9P7f2/hF93+isen5RTx+m+H+XHXaQC8XPT8c0gzxnSOqBnTrKsqnN7hGF+y/wcoyAQgu1DL3qwwLCf02OydiY8cSrHB0dpjKj5Aryn9aNrqynNEZRVYeP7nA/y6JxmANmFevDO6HY0CZKK0+kjCiLgudrtK37dXk3i2gDdua83oThEAJVPEa60F9Nj0PH6DTxPabSiMmuvkioWoHDkZhaz5+hCJB7MAcMtPIfr4dxQNMjLohW/RaC7/V36xzc6XG+OZ8UcceWYrigJ3dgrn6SHN8XWroU+a2Irh+CpHMDm8BKyOx28yC3TsyW5O2rlBZPr0BEWDxmYmqHUhIx++Ga3+yq0dv+xJ5rlF+8gpsmLSa5g6rAVju0bKRGn1jIQRcd0+WXuc15YeplWoJ4sfd6xXo9pVvnl5C+dSC2h0fBF60zIGxKbDY9vBv7GzSxaiwlS7yp5VSWz5+RjWYlDsxUQlLMOU/wfBrz1Hy96jr3j8puOZvPDLfo6ecTzO2zbMi5dGxtSucRNFOXB4Mez5Fk6u5cK0sfuyW7A9YwIFbo0A0OmzuOnJfoQ0vPJjyCnZhfzfwr2si8sAoFcTf966vS3BXqYrHifqDgkj4rqdy7fQddpKzFY7Pz7SnQ4Rjl88hzYms2ruYQzmLLpseYHIG5Px6jkGbnrPyRULUTG5Z4tY+cV+Tsc5xnZ4Z8XR7MjXJLex0++9n/DwvPxjt6nZRfx36aGSbgkfVz3/GtqcUR3Da3crQE4y7Ft4fmK1fRRaFJYev4lMt9scXTeqnWa9fek7qu0V5yex21XmbU7gtaWHMFsdE6W9ektrbmobetljRN0hYURUin9+v4eFO05xS/sGvDO6HQA2q515z20kP8tC88NfofFfQ7822fDEXvCUXzCidjm6NZU18w9iMYPGZqbJsR/wOruR3Mdvof8D/73scRarndkbTjJzZRwFFhsaBe7uEslTg5vWvcm/Tu2ARQ+hZhxjTWIEadljSQ/sCIDJ08bwSZ0Jbuh1xVMcS8tjyne72Xt+orQRbUN5ZWSruvffSpRyrZ/fMsRZXNG4bo41h5bsTSEzzwyAVqeh3UDHGJKEiMF4HzFRVGSFzR86rU4hystcUMzyT/eyYrYjiHhmn6Dz9mnYdNvw+/aLKwaRjccyGPbuWl7/7TAFFhsdIrz55bGevFJXZyENi4WHVqO0GUXfyEQ6RPyP6OOfYDBnU5Sj5Yc3t7Pl1xPYbfbLnqJxoDs/PNydfwxoglaj8OueZIbMWMu6uPRqvBFRU0kYEVfUJsybtmFeWGx2FmxPKtnesmcoRjcdha6BZPnGsj3RG7Z/AYXnnFesENcoLSGH717eQNyODFBtRJ9cTLvd73Cqvz99f91IwxZdLnvs8gOp3PP5Fo6n5+PvbuDtO9qycFJ3YhpcuWWg1jN6wK2fwE3v0dgfenX6nfAzrxJ0ZiugsH1JPAvf3EpORuFlT6HXanhyUFN+eLg7Df3dOJNjZuznW3nh5/0UWmyXPU7UfRJGxFWN7RYFwPzNidjsjl49g0lH+0GO1pH4yKHoD7liK8yDbZ85q0whrkpVVfb/Gc8Pb2wlJ8uOqTCDjjv/h0/mMnLeeJyR//sRo8ntssdvjz/L49/swq7CTW1DWflUX26PDavdY0PKQ1EcC2Q++CceoU0Y3OkYfm6f0OLgbLTWQtITCvj65Y0c2ZJ6xdO0C/dmyeReJS2vX25KYPh769iTlFUNNyFqIgkj4qpubBOCt6ue01mF/Hk4rWR76z5hGFy0FLgGU+jWgV3JXrD5I7AUOLFaIcpmKbLyxwfrWbPgBHa7Bv+MPXTa8TppYVlE/vQjPW6adMXj487kMuHL7ZitdgY0D2T6qLZ4ueirqfoaJqglPPQnmnZj6Nc4k6C2K2m1/zW8so9jsyj88cVB/phzkOIrtHa4GLS8PDKGL+/vTKCHkRPp+dw6ayMz/jhK8RW6e0TdJGFEXJVJr2V0x3AA5m1OKNlucLm4dWQYRYfcUfMzYPd8p9QpxOVkJZ9j4X9+4+j+YlBtND7+I80PfUL83Z0YtnA9oWHNr3h8SnYh987eSnZhMe0jvHl/TIfKX0+mtjG4wS2z4OZZtAqGVn0PEZw2g+iTi0G1c2RzKt+9toVzqflXPE2fpgEsf7I3w9uEYLOrzPgjjttnbeR4et4VjxN1Sz3/aRLX6u4ukSgKrDmaTnzGX79cWvcLR2dSyHcLwaZtx6EzbrBhpmMiJSFqgKS1W1j43w2cy3HDYM6iw+53MRWsxjbrFW6a+jE67ZVXqM0uKGb87G0kZxfRMMCN2fd2kkXgLtZuDDz4J77hTenX4xQGn59pv2cmBksOWalFLPjvFuK2n7niKbxdDbx/V3vevbMdniYde05lM3zmOuZuiqcWPPApKoGEEXFNIvxc6Xt+afD5W/5qHTG66Gg/wNHvGx85lDNHvSE7EQ4sckaZQpRQLYXsmfUJv36dg9nmimf2CTrteIPUFgW0/nU5HXrfftVzFBXbeHDudo6cySXQw8jc+zvjU1NnUnWmwObw4Cq0HccxsHkGLh12ELN3Gt5ZR7EVw/LPDrB2wVFsV+h+URSFke0a8PuTvenR2I+iYjv/+fkA983ZRp7ZWo03I5xBwoi4ZmPPDzb7bvupUiPf2/QPR2uAPPcwtJbWJJwzwfp3HOtfCOEEtvht/PnCu6zf0xgVLcGpm2lx8F2SH+nHzV+sxNf36vPh2OwqT3y7m63xZ/Ew6vjy/s6E+bhWQ/W1lMHVMfHhrZ/RPgwaDjhOSPJ7RCb8DsC+P0/x0zs7Kcy1XPE0IV4uzLu/Cy+MaIlRp2H1kXTu+2KrBJI6TsKIuGZ9mgYS7utCdmExv+5NLtluctPT7nzryMnIYRyL84a0gxC33EmVinqruIiixS/x8/82cehcZ1DtND62EPfc73CbN5MbJr2OcpWVdsHx1M2Lvxxg2YFUDFoNn4zrSIsQmXDxmrS5Ax5aQ1BUc3r2OYXB5Qda7/sYrbWI1GM5fPPqRjJO5V7xFBqNwn09ovluYjc8TDq2xZ+TQFLHSRgR10yrUbi7iyN0zNuUUKovt92ACDQ6lTyPCHTZ7cjM0ztaR4SoLknbyHlvBN8tiSalOAattZC2ez8kr9Vpev66hhZt+l3zqT748xjzNiegKPDO6HZ0a3T56eBFGfwbwwMrMHS5n8Ft0jG22kibvW/jUphOYbad76dt4fjOtKuepm24N/Mf6FISSMbPlkBSV0kYEeUyqmM4Bp2Gfaez2X3RnAAm94taR6JvZPcJX0jcBAmbnFSpqDeKC2H586R9NJFvjzxMrhqG0XyOZoffwTylB7e9+zNurtc+Idl325N4e/lRAF64sSXD24RUVeV1m94FbnwHbv+CLlEqYb33EXXiTXzOHsJu07Dsk/1s+vkYqv3K3bltwv4KJNsTJJDUVRJGRLn4uhm48fwv54sf8wVoPzgSjc5GvnsD1LNdyC/SwIYZTqhS1BtJW+GjXsQtX8fC9FcpVrxxyzuN39lZRM99iwF3PFWu0606fIapP+4D4JG+jRjfI7oqqq5fYm6FiWuIaNKC7r2P41s4k/CkVQDs/C2Rn9/bgqXoyuHiQiDxlEBSZ0kYEeU27vyMrIv3pnA2/6/BaCY3PR2GNQQgMfJGtsX7w9FlcOaAM8oUdd2u+TB7KGuONGJ57rOoGhPe5w7j1vBPbli4mKiG7ct3usRzPDJ/Jza7ym0dwnh6SLMqKrwe8msEE1Zg6vEQQzqk4hM0j6ZH5qHYizl9qID5L64i92zRFU/RJsybrySQ1FkSRkS5tQ3zonUDLyxWO99dtF4NQPsBkWh0FgpdAig42wdrsQIb3nVSpaJOUlVY/w72RY/wfcJY9lsngqLF++wWIie4ccfLszHqTeU65fH0PO6fs42iYjt9mgbw+m2tr2mgqygHnRFueBNl9Dx6NVGJbr+UxkdnYDBnU5ClY/7zqzgTn33FU0ggqbskjIhyUxSl5DHfrzYnlKxXA441azqOaARAcoNhbD3lB/sWwrmEMs8lRLnY7fD7s9iWv8w3CU+QZhgJgLt5Df3fG03PwfeW+5RncooY9/lWzhUU0zbMiw/v7oC+vs+uWpVa3gST1tK4eUu69dhMaNrruOWdxmYz8cO0TezfGHfFwx1dNl1LAsm9EkjqBPmJExUyok0oXi56Tp0rZM3R0qPi2/dviEZbgNnoQ1rmUFSbDTa976RKRZ1htcCih7Bu/Jj5Cf8my6UPqHa8/LZy92fPExLUsNynzCkqZvwX2zidVUiUnyuzx3fCzXjlGVlFJfCJgvt/x6PXJIZ1PEwD5TV8zh5EVQys+TKB5XNXXPHw1mFeJYFkhwSSOkHCiKgQF4OWUR3DAJi7qXSrh06vpf1NjoF/aYGD2ZniDzvnQl56tdcp6ghzHnxzJ+bdP/NV4n/IdemEYrfiG7GTe/7776tO6V7mKa02Js7dwaGUHPzdjcy9vwt+7sYqKF6USWeAodPQ3PUNg1oV0Dr4dfzT1oOiIW6jlq/+M/eKM7aWFUhyi2QZitpKwoiosAtzjqw5mk5CZunFsDoNbIFGk0WxwYMTmSNRi4tg3f+cUaao7fIz4MsRFB7ZxPxTr5Jvao3GZsG/yW7uevb/KnRKu11lynd72HQiE3ejjjn3dSLCT2ZXdYrmN8CkdbRu05yBTWfgn/EjANlpYXzx6Odknc287KF/DyTjv9gmgaSWkjAiKizK340+TQNQVZi/JbHUe1qthpgRjpaTTN8BHMwIgi2z4OjvzihV1FZZiTB7CHkJx5mfPI1CYxO01gICY/Yz6umKBRFVVXl58UGW7E1Br1X46J5YYhpc+zwkogp4R8B9v+HX/1FubzmPkPxZaGwWzDRi4ZTFHDuw97KHXggkXi56CSS1mIQRcV3Gdr2wXk0SRcW2Uu/1HNIJHSnYdC7szh7n2LhoEmSfru4yRW105gB8PpislHN8k/o6ZkMEeksuwR2Pcts//lnh03689gRzNsYD8PYdbenZxL+SChbXRauHwa+gvec7bo3ZTkv9a+iKczGbwvnz7UPsWHX5cSSOQNKlJJBIl03tI2FEXJd+zQNp4O1CVkExv+5JLvWeolFodpNjpd9sty4ctfeBwrPwwwSwyWAzcQUJG2H2MDIyYEHam1j0wRiLzhLSK56bJ02p8Gl/3HmK1387DMBzw1swsl2DyqpYVJamQ2DSevp0dKWv93MYzOlYjAFsn1/Ayq/nX/awmAZ/BZKdiVkSSGoZCSPiumg1Cnd3jQAcj/n+XZ9hgzAUH0RVtGxOvAFV7+GYJv7P/1Z3qaK2OLwE5t1CWrY7P6S/hlXni6nwDA0GpTLivn9U+LRrjqbzfwsdzf0P9W7IA73K//SNqCZeDeDexTQbegvDg/6NqTABq96Do3/68tP0mZc9TAJJ7SVhRFy30R3DMWg17DmVzZ6L1qsBx5wkjUaFotht5Jqa8mfOGMcb66dD3B/VX6yo2XZ8CQvuITU3gEUZ/8Wq88alIIWIETkMu/uxCp9276ksHv5qB1a7ys3tQvn30OaVWLSoElodDHqZ0LumMTrieVwKD2DXGkk+0oJv/z0Nu73sJ20kkNROEkbEdfNzN5YsJvb39WoA+g+5Fb23YyKjxNMxpPg5Jqpi0UOQk3zJ/qIeUlVY+xb8Opnk/HB+yvwvVp0XrvmniLrdwqDbJ1b41PEZ+dz3xTYKLDZ6NvbnzdvbotHI7Kq1Rts7cX/wB8Y2fw/3oo2oipbMrC7Mf/S/mC2FZR4igaT2kTAiKsWFGVl/3ZPMuYvWq7ng9qn3oNgLyXcPY8cyE8U+raAgE354QMaP1Hd2O/z2f7DqVU7lR/PL2Vex6TxwzU+k4Rgt/W+6r8KnTs81M272VjLzLcQ08OSjsbEYdPJrr9aJ6IL+4T8Y23EJfsWLAchRe/DtQ++SnZVR5iF/DyTjJJDUaPJTKSpF+3BvWoV6Yrba+X5H0iXv+/h40migDwApgUPZuDcIDO6QsAHWvF7d5YqawmqGH+6HrZ+QkN+ExVmvYNO545oXT5N7Xekz7O4KnzrPbOW+OVtJPFtAhK8rX4zvjLvMrlp7eUegeXA5dw44TThzQbWTZ+rMose/5nT8kTIPuTiQ7JJAUqNJGBGVQlEUxpWsV5OI/aL1ai4YcEsXtC5mLEZv8k435pDpFscba9+G46uqs1xRE5hzYf4dcGARJ/JbsTTrJWxaN1zzTtL8IR96DhxV4VNbrHYe/moH+0/n4Odm4Mv7OxPgIbOr1npGD7jza266NZyW+ndR7MXku8Ww/Pn1HNq2rsxDygokORJIahwJI6LS3NS2AZ4mHYlnC1gTd+nU7zq9loFjYwFIiBhI1rd7yY64DVDhhwchN7WaKxZOk5cOc4bDyTUcK2jP71nPYde64Jp3nJaPBNGt9y0VPrXdrvJ/C/ewLi4DV4OW2eM7Ee3vVonFC6fSaGHwK/S7fxTdPF5Day2gwC2aje8nsenX78s85O+B5F4JJDWOhBFRaVwMWu7oGA7AvE1lr9LbqH0AwU3dUTV6EiLvYO93h1D9W0FBhmP8iN1W5nGiDjl7EmYPhpQ9HCnqyopz/4dda8ItL442/4ikS/cbr+v0ry87zE+7k9FpFD68uwNtw70rp25Rs3QYS/vHX2Ng8Gvois9S5BLMvh+1/P7pB2XufiGQeLtKIKmJJIyISnXP+RlZ/zySRtLZgkveVxSFAXfHoGhUMv1aoeZGsCWxCejdIH4drHmzuksW1SllL8weAmdPcNDSn1WZTziCSO4R2j/VhNhOg6/r9J+tO8Ena08A8ObtbejbLLAyqhY1VVQPGk+Zzy3NZmGwnKLY6M3JLVH88NIrqOqlXcUxDbz4asJfgWTc5xJIagoJI6JSRfu70auJP6oKX20pu3XEO8iV9oOjAIhrcjvui3eREHL+iYk1b8CJ1dVTrKheJ9c5umbyzrDPNpw1GROxa4245R6i49TWtG3f/7pO//Pu07y65BAA/x7WnFs7hFVG1aKm840mcPKPjOmxFJPlMDadC2dOd+Xbyc9gtV4aNC4OJLuTJJDUFBJGRKUb1y0KgO+2XbpezQUdh0Xh5mOkyORHQsRg0mb9QlHjUfw1fuRM9RUsqt7Bn+GrW8Gcwx7uYN2Ze7FrDLjl7qfzfzoSE9Pzuk6/4VgG//x+DwD39YhiYm+ZXbVeMXnhdt98xt2SiLt1C6pGy9niQSx48EXy87Iu2f3iLhsJJDWDhBFR6fqfX6/mXEExS/amlLmP3qil1x1NAEiIGITG6sO2XxJQA1pAfhr8+KCMH6krtn0O390LNgs7NfeyIfkOVI0et9y9dH+5By2bdbmu0+8/nc3EeTsotqkMbxPC88NboigyqVm9o9GiH/E64yYG46/+BkCWcQCLJr5Hekr8Jbu3CpVAUpNIGBGVTqtRGNPFsV7N3DJmZL2gYfsAwlv4oGr0HGlyB357k9iT3wP0rnByDaz7X3WVLKqCqsLq12HJFEBlu+FhNp+60RFE8nbT67/9adoo9roukXS2gPFfbCPPbKVrQ1+mj5LZVes7pdN9jP73CKIM34JqJ9ujB789tYgTB7Zesq8EkppDwoioEqM7nV+vJimLvaeyytxHURR6jW6KRqdwzrcVZwI7of1yKelNJzt2WD3NMc5A1D52Gyx5yvFvCGwxPcXW+P6oGh2uebvoO20YjaLaXNclsgosjJu9lYw8M82DPfhkXEeMOm1lVC9qu+jeDH/hX7TxmYtiLybXsy1rp+1h16pfLtn174FkrAQSp5AwIqqEv7uRG1oHA5d/zBfAJ9iNTjdEAXCo+R3YNe4ce28htuajQLU7HvfNu3TOElGDFRfB9+Nh++eAwka3Z9lxopsjiOTvZOBbI4kKb3Fdl7DZVf7x7W5OZuTTwNuFL+/vjKdJXynlizrCrxG9XphJr4bfo7EVkO/eiF1z8ljz1SeX7Noq1IuvH+iKt6uePRJInELCiKgyF9ar+WVPMlkFl65Xc0H7IZH4NXBH1bixv8UdeKcVsHltDgQ0h7zU8+NHyl6hU9QwRdkw/3Y49AtoDWxwf5ldx9qjarS45u9g8Nu3ER7S+Lov886Ko6w5mo5Jr+HTcR0J8jRVQvGiznHxpvXTH3Fjt/Xois9S6BrM0ZUBLH7jlUt2bRnqeUkgudLvLVG5JIyIKtMhwoeWIefXq9l+6rL7abUa+o9rjqJAlm9H0vxb47tqL0dNN4POBU78Cetl/EiNl3vG8ehu/DoweLDW5WV2x7UERYtL4XZumHEnDYKir/syvx9I5f0/jwHw+q1taBnqed3nFHWYVkf4/a8z6s5M9MWnsBi9OBUXy8IpU7D/7Y+cvweS2z/aRHJW2SsDi8olYURUGUVRSlpHvtqSUOZ6NRcERnrSbpBj0OuBmLuxak3kv/cVubH/cuzw52sQv6HKaxYVlHncMatq6j5wC2S14T/si2sCigZT4TaGv3sPQX7h132ZY2l5PPXdX4/w3ty+wXWfU9QPPoMmMvbJUEy2w9h0JtLyhvHdhClYCktPztgy1JPvJnYjxMvEsbQ8bv1wI0fP5Dqp6vpDwoioUiPbheJh0pGQWcDaMtaruVjnG6PxCnBBxYOdbW7DVGRnz/s/ora6MH5kAuSXvVy4cKKEjY5ZVc/Fg08Uq/gXB+IagqLBaN7KzTPvI8g79Lovk1tUzEPztpNnttIl2pdnbri+cSei/nGJGcj4VwbiqWxH1WjJNN7E9xNeIys9udR+TYM8+OHh7jQOdCc1p4jbZ21kW/xZJ1VdP0gYEVXK1aDj9ljHTJjv/BGH7QqtIzqDln5jmwOQ59Wd5IBm+B3PYPt+E/g3hdwUWDRRxo/UFKoKmz6EOTdCfjoEt+GPwskcOhblCCKWLdz23oP4eV3/lOx2u8pT3+3hRHo+wZ4m3h/TAb1Wfn2J8tMGN+WetycQ4vonAFme/fnlHwtIOrK31H6h3i4snNSN2Egfcoqs3PPZFn4/IIt5VhX5aRZVblKfRrgbdexJyuKbrYlX3LdBUx9iejua3o+0fYBinSuuC/7gVPhDoDPBsT9gw4xqqFpckSXf8aTT71NBtUHrO/j97H0ciY92BBHrFu744GF83P0q5XKz1hxn+cEzGLQaPhobS4CHsVLOK+onxc2PW9/6Dy3CVpY8+vvHqzvY9+dvpfbzdjUw/4EuDGwRhNlq5+GvdjD/MstciOsjYURUuSBPE/8c3BSAN5YdJi236Ir7d7+tMd5BrqhWVzZ1vRcFSH7tfSw9/uPYYdWrkLCpiqsWl5V5HD4bCPsXgkYHQ19n2cFuHEuMAsBg38zo9x/Fy8W7Ui63+kgaby8/AsDLI1vRTlbhFZVBq6f/s6/Sves+tNZcCtwi2Ty3gLVfflZqN5Ney0f3dODOTuHYVXh20X7eWXG0zIX4RMVJGBHVYmy3KFo38CK3yMp/zy9mdjl6o5ZB97dEo1Gw6mI41KgbHtkWtn22FDXmdsdf4j9MgALpw612R36DT/pB2kFwC0S952d+XljM8dOOp2QMbOau9ybjYaqcJ1wSMwv4x7e7UVW4q3MEd3aOqJTzCgGAotDu/n8y/E4zeksqFqMPB9Y34Nf/vl5qN51Ww7RbWzO5v+Ox9HdXxvHMov1X7HYW5SNhRFQLrUbhtVtao1Hg593JrI+78kDUwEhPOt/k+IA7E30XOW7++O44wf4z0eDXGHJOw6JJMn6kuthtsOq/8M2dYM6G8C4Uj1nKD6+s5lReDAB63WbunvkE7kb3SrlkgcXKQ/O2k11YTLtwb168qWWlnFeIvwsfOIpR/2qCyXwYu9ZIYmJHvpn8KjartWQfRVGYMrgZr9wcg6LAN1sTefirHZddDFSUj4QRUW1ah3mVrOj7/M/7r/pD3H5wJKFNvFGtWnZ2fxi7okGdNZ/MNlNBa4S432HTe9VQeT1XcBa+HgVr33R83fkhcvvOZNGUrzlj7A6AwW839818GleDa6VcUlVV/v3DPg6n5uLvbmDWPR1kqndRpbybdWLs9FtxL94Aioazlu58NX4mxzcuK7Xf2K6RzLq7AwadhuUHzzD28y1kF8hsrddLwoioVlMGNyXQw8jJjHw+WnP8ivtqNAoD72uJwUWHvTiYbR1GoLfC0RffwNbvZcdOf7wESZcugCUqScpe+KSvY+CwzgVu+YRkr2Ese/p70n16AeDdMokH/zsFvabypmP/fP1JftmTjE6j8MGYDoR4uVTauYW4HINPMPd+/C8CXZag2IvJc2/H2lmZLJ5yN9aiv+YjGRoTwtz7O+Nh0rEt/hx3fLyRlGyZHO16SBgR1crTpOc/IxzN7R/+eZwT6XlX3N/D10TfMc0AyPccTEJoc7xT8ti6cBO0utUxfmTh/TJ+pCrs/gY+HwRZCeATBQ+s4MDuDDa8vZW0wB6g2onsa+HuyfdW6mU3Hs9g2m+HAXh2eAu6NKycJ3KEuCY6A3e88z+6D8lAa82iwC2E0zl3seS2ezm69IOS3bo29OP7Sd0I8jRy9Ewet324kTiZHK3CJIyIaje8dQh9mgZgsdl5/uf9Vx2V3qRTEC17hoIKJ1pOpMDoi/eyrRxXu4NvQ8hOgp8eccx7Ia6f1eJYcfenSWAtgiaDUSesZMvMTzjwi5m0oM6g2mh3ux833jm0Ui+dnFXI41/vwmZXuaV9A8Z3j6rU8wtxrdrddjf3vDEYF0MKVp0rp8ImEvfuMX57oDvm9HgAmgd78sPD3WkY4EZydhG3f7SJHQnyh1FFVCiMfPjhh0RHR2MymYiNjWXdussv8/7jjz8yaNAgAgIC8PT0pFu3bvz+++8VLljUfoqi8PLIVhh1GjYcy+SXPclXPabX6CYERnqgWg1s7fYwNo2O7GnvUtDzddAa4OhvsOmDq55HXEVOsmN9mW3nH2/s82+swz9l3YMTOH6sOekB7QArfR5oQo9B7Sv10kXFNh7+ageZ+RZahnjy2i2tURSlUq8hRHm4+7lz7/S7iG6jAUVDfPQIcrJGseGW29j32eNgsxLm48oPk7rTPsKb7MJixny6hRUHzzi79Fqn3GFkwYIFPPHEEzz77LPs2rWLXr16MWzYMBITy57Mau3atQwaNIilS5eyY8cO+vXrx4gRI9i1a9d1Fy9qr0g/Nx4//5jcK4sPXnUAmE6vZchDMZjc9NgJZUfb0bgU2tj14jTUga86dvrjBTi1vapLr7viN8DHfeDUVjB5wZjvyIu6g42330K85hbO+bYApZjhk9sT0ymqUi+tqiov/HyAPaey8XbV8/HYWFwMMmBVOJ9Wp+GGR/rS955mKIqNDP82nGg8lfxPjvPb3e3J378MHzcDXz/QlQHNAzFb7Uyct51vrzLBoyhNUcs5c0uXLl3o0KEDs2bNKtnWokULbr75ZqZNm3ZN52jVqhWjR4/mP//5zzXtn5OTg5eXF9nZ2Xh6ygqddYXZauOGd9dxPD2fe7pG8OrNra96TNLBs/zy3m5QoeGx+USd2kjh2BF0aJIKB38GrwiYtBZcfKr+BuoKVYXNs2D5c44xOEExMHoeyQeOc/L//svhpg9T5BKAxlDMrVO6ERRV+T+D87ck8Oyi/WgU+PL+zvRqElDp1xDieqUn5rJ01i7yzllRVBsNT/yCR9YfmG6OJnbyF1hdA3hm0T6+O79K+ZRBTXm8f+N63cJ3rZ/f5WoZsVgs7Nixg8GDB5faPnjwYDZu3HhN57Db7eTm5uLr61ueS4s6yKjTlgSQ+VsS2ZV47qrHhLf0pctNDQE40eROcjwiMX71K8mBdzgGWWYnws+PyfiRa2XJd0wgVzKt+yiYsIJDPy0m4am3OdDiSYpcAjB42rnr2V5VEkR2JJzjxV8OAPD0kOYSRESNFRDhwV3/6U6TjoGoipbjjW4hKeoRdN+ms+ye3uQtf4M3bmnJY/0crb7TVxzl+Z9lcrRrUa4wkpGRgc1mIygoqNT2oKAgUlOvbQGh//3vf+Tn5zNq1KjL7mM2m8nJySn1EnVTt0Z+3NYhDPX8NMtW29UnMYsdEkl0W39Qtexo/zBmox+npj5P8eCZjvEjhxfDlo+qofparmRa9x8c07oPexP1pg/Z9vwUMj/9kz1tn6DY4IFniJ4xz/bCO6hy5hC5WFpuEY/M30GxTWVYTDCT+jSs9GsIUZkMLjoGTWhF37ubodUpZPq1Ykun53DNaMfRZ+ay+elOPNU0jZduaoWiwFebE3l0/k6ZHO0qKjSA9e9NTqqqXlMz1DfffMOLL77IggULCAy8/Eqe06ZNw8vLq+QVHh5ekTJFLfHMDc3xctFzMCWHORvjr7q/cn7+Ef9wd1SNBzvaPYIpV8vW199BHfSKY6flz8PpHVVbeG128bTu7kFw72KszUaz6e4R5G0qYG/rR7BpjQQ39WD0v7rh5lX5C9NZrHYenb+TMzlmmgS689Ydbet1c7aoPRRFoVWvBtwxtRN+DdwoNniwr/VETkXcg/vvCssfnsANh6by6c0NMGg1LDuQyrjZW8kulMnRLqdcYcTf3x+tVntJK0haWtolrSV/t2DBAiZMmMB3333HwIEDr7jv1KlTyc7OLnklJSWVp0xRy/i5G5k6rDngaNZMzrr65EEGk44bH22Lu48RiymYPa0n4rXtOIf2F0KLEWAvhu/vg8KsKq6+lrHbHAsNXpjWPaIbTFxLrtWPbSMHkp3VjIMtx6NqtDTuGMDNk2MxmHRVUsprSw+xLf4cHkYdH4+Nxd1YNdcRoqr4NXDnjn93ov3gCFAgJaQbWzo9g0dWc5Le3Y3hs9tZ1mkXPkbYevIsoz/eRGr2lRcKra/KFUYMBgOxsbGsWLGi1PYVK1bQvXv3yx73zTffMH78eL7++muGDx9+1esYjUY8PT1LvUTdNqpjOLGRPhRYbLz868FrOsbN28iNj7fF4KIjx6sxh5qPpXjGZ2Q1fQS8Ix2Tdf0i40dKlEzr/pbj6y6T4N5fSd6+myN3jCLZ51ZONBwJQNuB4Qy+PwatrmqmIvpx56mSVrDpo9vRMKBy1rMRorpp9Rq639qYW6Z0wNPfhNnkx652T5AQdRfemzw58d6XLNI8xzC3oxxOzeW2WRs5lnblyR7ro3L/ppkyZQqfffYZs2fP5tChQzz55JMkJiYyadIkwNGqMW7cuJL9v/nmG8aNG8f//vc/unbtSmpqKqmpqWRnZ1feXYhaT6NR+O8tMeg0CssOpLLy0LU9p+8X6s6wiTFotAppgR1JjBjJwaenYL/pY9Do4dCvsPgJyD5dtTdQ06XsKT2t+62fwrA3ODT7PVKfeJ7DzR4lNbgrKCp97mpKz9uboGiqpstk/+lspv64D4DJA5owqOWVW1WFqA1Cm3gz+rnOtOwVCkByaE82d/4POktHsr4v4o64mXzu+h62rFPc/tFGdiRcfcB+fVLuR3vBMenZm2++SUpKCjExMbzzzjv07t0bgPHjxxMfH8/q1asB6Nu3L2vWrLnkHPfeey9z5sy5puvJo731x7TfDvHxmhM08HZhxZTeuBquren+yJZU/vjC0aISFb8U/9bZdLm9I/z2f44dNHpoeyf0fBL8GlVV+TXT7m8cgcxaBD7RMPorVL9m7Jj6KOqqY+xtPYkiF390JoUbHmpLeMuqe9LtbL6FEe+t53RWIf2bB/LZuI5oqij0COEsyXFZrJ5/mHOpjvVs/DIP0CTuO3I80wntmMcil+HM19zIjDGdGdCibofxa/38rlAYqW4SRuqPAouVQdPXcjqrkEl9GvHv82NJrsWelUms/z4OgOiTS2jxeBeim/vBuumQsN6xk6KBliOh5xQIaVMVt1BzWC2OR3YvzKbaZDDc+gnWItj24Ggsqb4caj4Wm84Fd38jNz3WDp9gt6orx2Zn/BfbWH8sgyg/V35+rCdeLpW3uJ4QNYmt2M6O3xPYsSweu1VFsRcTfmoN4Ym/kRGTTXgjA68xnuE3382oTnX3IQ0JI6LW+uPgGR6Yux2dRmHJ5F40C/a45mN3LI9n848nAAg7tYQhn07BFNIAErfA+ulw9KLlwBsPhF5PQeTlxzvVWjnJ8N29jtlUUaDvv6H3/5F77AgHHriXdPf+JEY45gsKbeLFsIltMLlXbTC40Orlotfy06M9yvXvKkRtdS41n3ULjpJ0yNEto7fkEh2/BGPheoI6n+WEZwxnur3AvcN61smnySSMiFrtobnbWX7wDJ2ifFjwULdyNeX/+fNuDv7mWKwqOG81t375Aor2/NTiZw7A+nccc2uo5+c0Ce8KvaY4Wg7qwi+D+PXw/XjIT3dM637rZ9B0MMl/LCHp3y9zvNF4zvk4VkJuNzCcbrc0QqOt2jUzl+xN4dGvdwLw/pj23NgmtEqvJ0RNoqoqCfsz2bDwGFlnHF03rvkpRCf8hiVgC52aZbMj8l763fcKWoPJydVWLgkjolZLzipk4PQ1FFhsvHlbm3I3Yy74eBEZu7wAaGDfwdB/3Yap0UUTap09ARtmwu75YLM4tgW1hp5PQKtbQFML10UpyoYdc+CPl0pN6676RHP4o7c5N+dPDraYgNnkg0avMmh8axrHXn6+n8py9EwuN3+wgQKLjYd6N+SZG1pU+TWFqIlsNjsH1p5myy/HsRQ6/hhyzU8lMO03whutIriBF963TsfQonJXw3YmCSOi1vts3QleXXIIb1c9K6f0wc+9fBNvffzMW1jPxgIQkryOyNDjtHrqeUxNmvy1U04KbP4Atn8BlvOP2/lEQ49/QLsxoKv8yb4qjapC+hGIW+54JW4Cu9XxXpvRcOMMVHRsf/oR0g97ER81FFXR4uav46ZHYvENrbrxIRdkFxZz8wcbOJmRT4/Gfnx5X2d0VdwKI0RNZy4oZs+qJHYsO47d6vjDx7XgDO6WFQyIXkpRv6mEDv6Hk6usHBJGRK1ntdkZ8f4GDqXkcHtsGG/f0bZcx5ttZubM/Azr4WagaPDP2EPzQ19i7d6CFk/9B9fmF/2FXngOtn7qWDCu0NHFg0cIdHsUYu8DYw2ZB8NS4OiGifvdEUCy/rYyqF8T6PYIxN5H8blzbHzwQZIMQ8n2cjxBFBXry6B7YjC4VP0EY3a7yoNzt7PycBoNvF349fGe+LoZqvy6QtQW5kIrW5YeYv+KJFQc3TNaawHJ2mQSWrbirgGNGNQyCG0tfuJMwoioE3YmnuO2WRtRVfj2oa50behX7nPs2XKS9V8eA7sW97xTtNk3C5M5i/xuMbR46j+4xVy0WrAlH3Z8CRvfg9xkxzaTN3SZ6JgkzNUJCzyeS/ir9ePkWscjuhdojRDVE5oOgSaDwNfRFZVzaD8b/vkOCSG3YtO5gKaY/uNiaNG1QbWVPeOPo8z4Iw6DTsMPk7rTOsyr2q4tRG1iKbSy9ItfSNtupdjgX7I9Xmcj1VtL737hjO4Rhaep9j19JmFE1BnPLNrH11sSaRzoztLJvTBUYFbQ1BPZLPlwD0V5VhR7Lm32fo5fluMx4PzOLWg+5Xnc27X/6wCrBfYugA0zIPOYY5veDWLHQ/fHwLMKB2BaLZC02RE+ji6HjCOl3/cMg6aDHQNuo3uDoXR3y7GffmHb1yc46+t4dNngW8CoJwfgFeBSdTX/zcpDZ5jw5XYA3r6jLbfHhlXbtYWorXJyz/LnvIVYLR1JOZzFhfYQGypJBhXfFt7cNrwJTSNqT7CXMCLqjOyCYgZMX01GnoWnhzTj0fPLc5dXTmYhSz/cR+bpPEBFn7+Y7tt/R3v+RyC/QxOaPvU8nrGd/jrIboNDvzjmKknd69im0UO7u6DHE5U3gVpuKsStcASQ43+CJfev9xQtRHR1hI8mgyGwRZlP/dhy81j19rccPx3iaA1RrYR20zBybP8qf1rmYicz8rnp/fXkFlkZ1y2Sl0fGVNu1hagrstMLObg5hT0bk7Gds5RsV1EpdNMS1cKXTl1CCW3sXS3drhUlYUTUKT/tOs0TC3Zj1GlY8WQfIvwqtpx9scXG2q+PcHizY7FHXUAO2rh36LonDe35n4S8tg1p9uRzeHbt9teBqgrHV56fQG2DY9v1TKBmt8Hpnee7X353TNd+MbcAaDzI0fXSqD+4eJd9P2fOkPL7r5xcsZ5Ea3dyvBxBTWNLpOeTnWndsmX56rpO+WYrN3+wgbi0PDpG+vD1g10r1JIlhPhL5uk8Vi2PJ35vBq7nn8K5mLuvCb8GbviFuuEb4oa7jwmThx4XdwMmd32ZUyNYiqwUZFvIzzaX/G9024BKb0GVMCLqFFVVufuzLWw8nkmfpgHMua9ThScIUlWVQxtSWLfgKNZiOwZXLfqYk1j+eJduu4vQnf9Zz2sVSZMpz+LV/W+TEZU5gdogx1wlV5pAreAsHF/lCCDH/oCCzNLvh3ZwtHw0HQwh7UFz6Ye4qqoUHT5M4tIfyF71B8bEAk5E30hySHdQNCg2M6r3Rsa8/BQ+lwkwVUVVVR79eidL96US6GFk8eM9CfSsW3MmCOFsB46fZdHvx0k+mkUDi4K3/SphXwGDUYvK+TVD7Sp2VcVuvfSjf/ADrWjSsXKnp5cwIuqc4+l5DJuxDovNzod3d+CG1iHXdb5zqfmsmH2Q9ERHl0iD5l4UNN5O7oKP6bazEL3NsV9e8zAaPfFvfPr0Lx1KUvc7JlA78OPfJlB7ytGiAXBm/19jP05t/Ws/AKMXNO7vCCCNB4J72XN+qBYLOVs3E7/ke6xrN+GamY9NoycprD8JEYOx6Rwf+LqQs3S9pyVtGrZwykyOH685zrTfDqPXKnz7UFdiI50w2FeIeiKrwMK325L4Zl08tiwL/jaFILuWJi5GfLVa7EU2zPnWK55Db9Ti5m3E1dOAm5eBmD4NCG3iU6l1ShgRddL0FUeZuTKOIE8jf0zpg8d1ji632ezsWp7I9iXx2Kx2NDqFmH6hJPus4ezcT+i+LR/DhVDSOIToJ/4PvwFDSn/YlzWBWkBzKMr564mcCwJbOoJKkyEQ3hm0Zddvy84m888/SPrtB3Rb92EodPxSsWqNJDboTkLkQFStNwC+4S70GdWC0Cbe1/Xf4nqsj8tg3Owt2FV45eYYxnaNdFotQtQnxTY7vx9IZfb6k+xMzCrZ3iXal/u6R9Ej3Beb2YaiwfF7S3H8r9FVh8FU9WNNJIyIOqmo2MbQGWuJzyzgvh5RvDCiVaWcN+tMAWu+OcKpw471I0zuetoMbECC62rS5syi+9Y8jOf/yMiLDiT6H0/jN/gGlIu7UsqaQE3nAg37nB98Ogi8Iy5bgyUpiZRlP5O2fAmuB+LRXNSIku7lzoGWA7C79gGbYyI2d18j3W5uRJOOQShOnIfgSGoud36yiXMFxdwRG8abt7epk2tsCFHT7Uo8xxcb4lm6LwWr3fHRHu7rwvju0YzqGHbdf7xVhIQRUWeti0tn7Odb0Sjwy2M9iWlQOY+5qapK/L5MNv7w1/oRJnc9LXuFkOK9meSv3qPH5hxMxY798yP8iXh8CgE33PTX2jfgGBtyZCm4BzvmANGXPW5Ctdsp3LuXhKU/kPfnn7gnlR5DkhCgcKxVW7TBwyAjrGRyVa9AFzoMjqRZl2C0eucODt1/Opuxn2/hXEExbcO8WDCxGyZ9LZxKX4g6JCW7kHmbEvh6ayJZBY5fWO5GHXd0DGN89ygi/ap+9uULJIyIOm3yN7v4ZU8ybcK8WPRIj0qdodBus3N06xm2LY0nJ70QAI1WIbKNH7kBcaQtn073jWdxPd8jk9/Ah7DHniTopltLh5Kyzl1URM6GdcQvWYi6YSum7L8mMLMpcChCIaV1DK7hI9GkhlN47q8+38BIDzoMiSS6XUC5Fg6sKjsSzjJ+9jZyzVbahnvz5X2d8HaVGVaFqCkKLTYW7TrN7A0nOZbmaK1VFBjYIoj7e0TTtaFvlbdiShgRdVpabhED/reG3CIrL49sxbhuUZV+DbvNzondGexZmUTqieyS7QYXHfoGeeQe/5UO23fjm5sFQH6IN6GPPE7ILaNQdH/1xVozMkhfuYzkZT9j2H4QXfFf/S8FBtjbxIPcmN54BfVBSfUlN81c8r7epKVxbCDNu4YQ0tirxnR/bDyWwQNzt1NgsdE52pfP7+3olCZgIcTVqarKurgMZm84yeoj6SXbW4R4cn+PKEa0Da2yFk0JI6LOm7cpnud/PoCHUcfKp/pU6WOkGadyObw5laNbz1CYYyn1nso5fM4m4pWbjEthBrhYCL5pKBRmkbVuFS4nUkHRYtW5UKxzI8Pbh1MNgiCgBQYlDEuWAhf9FGo0CmHNfWjWLZjotgHoDTWr2+PPw2lM/GoHFqudXk38+WRsR1xqWI1CiLIdS8tjzsaTLNxxiqLzfxj5uxu4u0sk93SNJMCjchcHlTAi6jybXeXWDzew51Q2I9qG8t5d7a9+0HWy21XOnMwhfm86pw6fIz0xl8r4CfIOciWksRcRLf0Ib+mLsYbOqPjbvhQmf7uLYpvKoJZBvD+mPUadBBEhapusAgvfbE1i7qZ4Us53F/97WHMm9amkWaXPkzAi6oX9p7O56f312FWYe39nejcNqNbrW4qspCXkknk6j7PJ+SQmnSI3KROd2YBNa0LV6FE0oNFoMbnpMbrqcfcx4uFnwjvAFf8wd/zD3XHxqPljLRbtOsVT3+3BrsKItqFMH9UWfTVOMy+EqHzFNjvL9qfy9ZZEZt3TodLHfUkYEfXGy78eZPaGk0T6ufL7E72d/jSHqqoczzqOn4sfPqbKnUDIWb7eksizP+1DVeGO2DBev61NrV7WXAhRPa7181v+rBG13pTBTQn2NJGQWcCHfx5zdjkoikJjn8Z1Joh8tu4EzyxyBJF7u0XyhgQRIUQlkzAiaj13o44XRjgWhJu15njJI2zi+r2/Ko5XlxwCYFKfRrx4U6sa8VixEKJukTAi6oShMcH0axZAsU3l+Z/2Uwt6H2s0VVV5c9lh3l5+FIApg5ryr6HNasyjxUKIukXCiKgTFEXh5ZExmPQaNp3IZNGu084uqday21Ve+vUgH64+DsBzw1sweUATCSJCiCojYUTUGeG+rkwe0ASA/y45RFaB5SpHiL+z2VWm/riPORvjAXj15hge6NXQuUUJIeo8CSOiTnmgZ0OaBLqTmW/hjWVHnF1OrVJsszPlu90s2J6ERoH/3dGWe2T1XSFENZAwIuoUg07DqzfHAPDN1kR2JJx1ckW1g9lq49H5O/l5dzI6jcJ7d3XgttgwZ5clhKgnJIyIOqdLQz/uOP9B+uyi/RTb7Fc5on4rtNh4cO4Olh88g0Gn4eOxsQxvE+LssoQQ9YiEEVEnTb2hBT6ueg6n5vLK4oOYrTZnl1Qj5ZmtjP9iK2uPpuOi1/LF+E4MaBHk7LKEEPWMhBFRJ/m6GXhuuGPukbmbEhj5/gYOJGdf5aj6JbugmHs+28KWk2fxMOqYN6EzPRr7O7ssIUQ9JGFE1Fm3xYYx6+4O+LoZOJyay8j3NzBzZZx02wCZeWbu+nQzu5Oy8HbVM//BLnSM8nV2WUKIekrCiKjThrUOYfmTvRnaKhirXWX6iqPc+uFGjp7JdXZpTnMmp4jRn2zmYEoO/u5Gvn2oK23CvJ1dlhCiHpMwIuo8f3cjs+7pwLt3tsPLRc++09ncOHM9H605js1ev2ZqPXWugFEfb+JYWh4hXia+m9iV5sGy+KQQwrkkjIh6QVEURrZrwPIne9O/eSAWm53XfzvMHR9t5ER6/VjL5mRGPqM+2kRCZgERvq58N7EbDQPcnV2WEEJIGBH1S5Cnic/v7cibt7fBw6hjZ2IWN8xcx+z1J7HX4VaSI6m53PHRJpKzi2gU4MZ3E7sR7uvq7LKEEAKQMCLqIUVRGNUxnGVP9qZXE3+Kiu28vPggd326mcTMAmeXV+n2n87mzk82kZFnpnmwBwsmdiPYy+TssoQQooSEEVFvNfB2Ye79nXn15hhcDVq2nDzL0HfX8tXmhDqz6u+OhLPc9clmzhUU0zbMi28f6oq/u9HZZQkhRCkSRkS9pigK93SNZNk/etM52pcCi43nftrPuNlbSc4qdHZ512XjsQzGfr6VXLOVzlG+fPVAF7xdDc4uSwghLiFhRAggws+Vbx/syn9ubIlRp2FdXAZD3lnLd9uTamUryZ+H0xg/ZxsFFhu9mvjz5f2d8TDpnV2WEEKUScKIEOdpNAr394xm6T960T7Cm1yzlf9buJcHvtxOWk6Rs8u7Zr/tS+GheduxWO0MbBHEZ/d2xMWgdXZZQghxWRJGhPibRgHuLJzUnX8NbY5Bq2Hl4TQGvbOWn3efrtGtJKqqsnDHKR79eifFNpUb24Qw654OGHUSRIQQNZui1uTfrufl5OTg5eVFdnY2np4yQZOoPkdSc3nq+93sP50DwLCYYF65OaZGDAJVVZUTGflsPpHJpuOZbD5xlow8MwB3xIbx+m1t0GoUJ1cphKjPrvXzW8KIEFdRbLPz4Z/HeW9VHFa7ip+bgVdvjmFY65BqrUNVVRLPFrDpeCabTmSy+UQmZ3LMpfYx6TXc2z2Kfw1pjkaCiBDCySSMCFHJ9p/O5p/f7+FwqmNdm5vahvLyyFZV+oTKqXMXhY/jmSRnlx67YtBp6BDhTbeG/nRr5EfbcC/plhFC1BgSRoSoAmarjZkr45i1+jh2FQI8jLx+a2sGtAiqlPOnZhex6URGSQBJOlv68WK9VqFduDfdGvrRtZEfHSJ8MOklfAghaiYJI0JUod1JWTz13W6Op+cDjjEaz49oiWc5H59Nyy1i84mz58d8ZHIyI7/U+1qNQpswL7o19KNbIz9iI31wNegq7T6EEKIqSRgRoooVFdv43/IjfLb+JKoKIV4m3ritDb2bBlz2mMw8M1tOni1p+TiWVnqRPo0CMQ28Slo+OkX54m6U8CGEqJ0kjAhRTbbFn+Wf3+8h4fy6Nnd3ieCZG1rgZtSRVWBh84mzJU+8HDmTW+pYRYEWwZ50a+RHt4Z+dIr2xctFJicTQtQNEkaEqEYFFitv/HaYLzclAI51b7xc9BxKzeHvP2HNgjzo1siPrg396NrQV6ZoF0LUWdf6+S3tv0JUAleDjpdGxjCkVTBPL9zL6axCTp9f26ZRgNv5lg9/ujT0rRFzlAghRE0iYUSIStS9sT/LnujFz7uT8TDp6NbQj0BPk7PLEkKIGk3CiBCVzMOk556ukc4uQwghag1Zm0YIIYQQTiVhRAghhBBOJWFECCGEEE4lYUQIIYQQTiVhRAghhBBOJWFECCGEEE4lYUQIIYQQTlWhMPLhhx8SHR2NyWQiNjaWdevWXXH/NWvWEBsbi8lkomHDhnz00UcVKlYIIYQQdU+5w8iCBQt44oknePbZZ9m1axe9evVi2LBhJCYmlrn/yZMnueGGG+jVqxe7du3imWeeYfLkyfzwww/XXbwQQgghar9yL5TXpUsXOnTowKxZs0q2tWjRgptvvplp06Zdsv+//vUvfvnlFw4dOlSybdKkSezZs4dNmzZd0zVloTwhhBCi9rnWz+9ytYxYLBZ27NjB4MGDS20fPHgwGzduLPOYTZs2XbL/kCFD2L59O8XFxeW5vBBCCCHqoHKtTZORkYHNZiMoKKjU9qCgIFJTU8s8JjU1tcz9rVYrGRkZhISEXHKM2WzGbDaXfJ2Tk1OeMoUQQghRi1RoAKuiKKW+VlX1km1X27+s7RdMmzYNLy+vkld4eHhFyhRCCCFELVCulhF/f3+0Wu0lrSBpaWmXtH5cEBwcXOb+Op0OPz+/Mo+ZOnUqU6ZMKfk6OzubiIgIaSERQgghapELn9tXG55arjBiMBiIjY1lxYoV3HLLLSXbV6xYwciRI8s8plu3bvz666+lti1fvpyOHTui1+vLPMZoNGI0Gku+vnAz0kIihBBC1D65ubl4eXld9v1yP02zYMECxo4dy0cffUS3bt345JNP+PTTTzlw4ACRkZFMnTqV06dPM3fuXMDxaG9MTAwTJ07kwQcfZNOmTUyaNIlvvvmG22677ZquabfbSU5OxsPD44rdQeWVk5NDeHg4SUlJ9eYpnfp2z3K/dZvcb90m91v7qapKbm4uoaGhaDSXHxlSrpYRgNGjR5OZmcnLL79MSkoKMTExLF26lMjISABSUlJKzTkSHR3N0qVLefLJJ/nggw8IDQ1l5syZ1xxEADQaDWFhYeUt9Zp5enrWmX/4a1Xf7lnut26T+63b5H5rtyu1iFxQ7jAC8Mgjj/DII4+U+d6cOXMu2danTx927txZkUsJIYQQoo6TtWmEEEII4VT1OowYjUZeeOGFUoNl67r6ds9yv3Wb3G/dJvdbf5R7AKsQQgghRGWq1y0jQgghhHA+CSNCCCGEcCoJI0IIIYRwKgkjQgghhHCqOh9GPvzwQ6KjozGZTMTGxrJu3bor7r9mzRpiY2MxmUw0bNiQjz76qJoqrRzlud8ff/yRQYMGERAQgKenJ926deP333+vxmqvX3n/fS/YsGEDOp2Odu3aVW2BVaC892w2m3n22WeJjIzEaDTSqFEjZs+eXU3VXr/y3u/8+fNp27Ytrq6uhISEcN9995GZmVlN1Vbc2rVrGTFiBKGhoSiKwk8//XTVY2r776vy3nNt/51VkX/jC2rz76xrUafDyIIFC3jiiSd49tln2bVrF7169WLYsGGlZoi92MmTJ7nhhhvo1asXu3bt4plnnmHy5Mn88MMP1Vx5xZT3fteuXcugQYNYunQpO3bsoF+/fowYMYJdu3ZVc+UVU977vSA7O5tx48YxYMCAaqq08lTknkeNGsXKlSv5/PPPOXLkCN988w3Nmzevxqorrrz3u379esaNG8eECRM4cOAA33//Pf/f3v2FNPnFYQB/1G1kQkFFNhwUgWZeJNVYNQkhxKCgq0gowiChEREVFbuITAiCIi8s60rsRksShC4q9KIkqYuUCdGCQisYZbEiWFqU+u0i9Nd09Nt59/7pvDwf2IXHM3geXv169jrY06dP0dDQYHNydePj46isrMTVq1ez2q/7vALUO+s+s1T7ztB5ZmVNXCwUCkkkEklbKy8vl2g0mnH/6dOnpby8PG3t0KFDsnnzZssymkm1byYVFRXS1NRkdjRLGO1bV1cnZ86ckcbGRqmsrLQwoflUO9+7d08WL14snz59siOe6VT7Xrp0SVavXp221tLSIoFAwLKMVgAgPT09f92j+7yaK5vOmeg0s/6k0lfnmZUt194Z+fHjB4aGhlBbW5u2Xltbi8ePH2d8zpMnT+bt3759OwYHB/Hz50/LsprBSN+5pqenkUqlsGTJEisimspo3/b2doyMjKCxsdHqiKYz0vnOnTsIBoO4ePEiSkpKUFZWhpMnT+Lbt292RM6Jkb7hcBiJRAJ3796FiODDhw/o7u7Gzp077YhsK53nlVl0mllG6TyzVBj6bBodJJNJTE1Nobi4OG29uLgYY2NjGZ8zNjaWcf/k5CSSyST8fr9leXNlpO9cly9fxvj4OPbs2WNFRFMZ6fvq1StEo1E8evQIHo9+P/pGOo+OjmJgYAALFixAT08PkskkDh8+jM+fP//z7xsx0jccDqOjowN1dXX4/v07JicnsWvXLly5csWOyLbSeV6ZRaeZZYTuM0uFa++MzMjLy0v7WkTmrf3f/kzr/yrVvjNu3ryJc+fOoaurC8uXL7cqnumy7Ts1NYW9e/eiqakJZWVldsWzhMo1np6eRl5eHjo6OhAKhbBjxw40Nzfjxo0bWtwdAdT6xuNxHD16FGfPnsXQ0BDu37+P169fIxKJ2BHVdrrPq1zoOrOy5aaZlQ3XHrWWLVuGgoKCea+gPn78OO/VxIwVK1Zk3O/xeLB06VLLsprBSN8ZXV1dOHjwIG7fvo2amhorY5pGtW8qlcLg4CBisRiOHDkC4PcfahGBx+NBb28vtm3bZkt2o4xcY7/fj5KSkrSP8F67di1EBIlEAqWlpZZmzoWRvhcuXEBVVRVOnToFAFi3bh2KioqwdetWnD9/3lV3C3SeV7nScWapcsPMUuHaOyM+nw8bN25EX19f2npfXx/C4XDG52zZsmXe/t7eXgSDQXi9XsuymsFIX+D3q4sDBw6gs7NTq/+rq/ZdtGgRnj17huHh4dlHJBLBmjVrMDw8jE2bNtkV3TAj17iqqgrv3r3D169fZ9devnyJ/Px8BAIBS/PmykjfiYkJ5Oenj7WCggIA/901cAud51UudJ1Zqtwws5Q4875Ze9y6dUu8Xq+0tbVJPB6XY8eOSVFRkbx580ZERKLRqOzfv392/+joqCxcuFCOHz8u8Xhc2traxOv1Snd3t1MVlKj27ezsFI/HI62trfL+/fvZx5cvX5yqoES171w6vjNdtXMqlZJAICC7d++W58+fS39/v5SWlkpDQ4NTFZSo9m1vbxePxyPXrl2TkZERGRgYkGAwKKFQyKkKWUulUhKLxSQWiwkAaW5ullgsJm/fvhUR980rEfXOus8s1b5z6TizsuXqw4iISGtrq6xcuVJ8Pp9s2LBB+vv7Z79XX18v1dXVafsfPnwo69evF5/PJ6tWrZLr16/bnDg3Kn2rq6sFwLxHfX29/cENUr2+f9L1F1u184sXL6SmpkYKCwslEAjIiRMnZGJiwubUxqn2bWlpkYqKCiksLBS/3y/79u2TRCJhc2p1Dx48+OvvoxvnlWpn3WeWkWv8J11nVjbyRFx275KIiIi04tr3jBAREZEeeBghIiIiR/EwQkRERI7iYYSIiIgcxcMIEREROYqHESIiInIUDyNERETkKB5GiIiIyFE8jBAREZGjeBghIiIiR/EwQkRERI7iYYSIiIgc9Qug7TSg1y0ZsAAAAABJRU5ErkJggg==", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a, b, y0, h = 0, 1.5, 1, .1\n", + "\n", + "def plot(edo, label):\n", + " r = edo(f_edo, a,b,y0,h)\n", + "\n", + " x = [x[0] for x in r]\n", + " y = [x[1] for x in r]\n", + "\n", + " plt.plot(x,y, label=label)\n", + " \n", + "plot(euler_expl, \"Euler\")\n", + "plot(RK2, \"RK2\")\n", + "plot(RK3, \"RK3\")\n", + "plot(RK4, \"RK4\")\n", + "\n", + "x = np.linspace(0, 1.5, 200)\n", + "y = (29*np.exp(-3*x) + 9*np.sin(x)-2*np.sin(6*x)-3*np.cos(x)+4*np.cos(6*x))/30\n", + "\n", + "def ff(x):\n", + " return (29*np.exp(-3*x) + 9*np.sin(x)-2*np.sin(6*x)-3*np.cos(x)+4*np.cos(6*x))/30\n", + "\n", + "\n", + "plt.plot(x,y, label=\"Vrai solution\")\n", + "\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "b=5\n", + "def plot(edo, label):\n", + " r = edo(f_edo, a,b,y0,h)\n", + "\n", + " x = np.array([x[0] for x in r])\n", + " y = np.array([x[1] for x in r])\n", + " #print(label, y)\n", + " plt.plot(x, np.abs(y-ff(x)), label=label)\n", + " \n", + "plot(euler_expl, \"Euler\")\n", + "plot(RK2, \"RK2\")\n", + "plot(RK3, \"RK3\")\n", + "plot(RK4, \"RK4\")\n", + "plt.yscale('log')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "635c32ce-ab45-4083-87d8-4b312f79dbdc", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION17.ipynb b/QUESTION17.ipynb new file mode 100644 index 0000000..0e70c4e --- /dev/null +++ b/QUESTION17.ipynb @@ -0,0 +1,129 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "6a47bb60-4ac8-4627-8d8f-ba95f775e6ad", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "cafc7c60-9128-48d0-af9a-66d2d12f0c6f", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f_edo(t, y):\n", + " l = 1\n", + " g = 9.81\n", + " return np.array([\n", + " y[1],\n", + " -g/l * np.sin(y[0])\n", + " ])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a7bb3d49-334b-4afe-9901-775872baf2f4", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def AdBash4_RK4(fct, a, b, y0, h):\n", + " t = np.arange(a, b, h)\n", + " y = np.zeros((len(t), len(y0)))\n", + " \n", + " # initialisation\n", + " y[0] = y0\n", + " for i in range(1, 4):\n", + " y[i] = y[i-1] + h * fct(t[i-1], y[i-1])\n", + " \n", + " for i in range(4, len(t)):\n", + " y[i] = y[i-1] + h * (55/24 * fct(t[i-1], y[i-1]) - 59/24 * fct(t[i-2], y[i-2]) + 37/24 * fct(t[i-3], y[i-3]) - 9/24 * fct(t[i-4], y[i-4]))\n", + " \n", + " return t, y" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "1a7b1862-4c30-405c-8621-5a2b35164d67", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0, 'Temps [s]')" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a, b, y0, h = 0, 100, np.array([1, 0]), 0.1\n", + "\n", + "t, y = AdBash4_RK4(f_edo, a, b, y0, h)\n", + "\n", + "\n", + "plt.plot(t,y[:,0], label=\"Adam-Bashforth 4\")\n", + "plt.legend()\n", + "plt.ylabel('Angle')\n", + "plt.xlabel('Temps [s]')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f0e79f18-4569-472f-a4e6-213fc7c2609d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION18.ipynb b/QUESTION18.ipynb new file mode 100644 index 0000000..9db9779 --- /dev/null +++ b/QUESTION18.ipynb @@ -0,0 +1,147 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "23bf2de4-1ad7-4bcc-b8a4-75737b31ec3a", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "87e8765d-2b61-478d-9ad1-2a8d4cb925a3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f_edo(t, y):\n", + " return 1/(1+y)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "b342537d-ad37-42db-aef3-b33ac342695e", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def ptfixe_eulerimp(fct, x0, h, ti, yp, maxiter=10):\n", + " x = x0\n", + " for k in range(maxiter):\n", + " x = yp + h * fct(ti, x)\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "be078e7a-bfaf-4b71-82c7-3609dfed1ad3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def eulerimplicite(fct, a, b, y0, h):\n", + " t = np.arange(a, b, h)\n", + " y = np.zeros(len(t))\n", + " \n", + " y[0] = y0\n", + " \n", + " for i in range(1, len(t)):\n", + " y[i] = ptfixe_eulerimp(fct, y[i-1], h, t[i], y[i-1]) \n", + " y[i] = y[i-1] + h*fct(t[i], y[i])\n", + " \n", + " return t,y" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "fcd619b9-0f98-4dfc-9413-58f430c5991f", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a, b = 0, 25\n", + "h = 0.1\n", + "y0 = 0\n", + "t, y = eulerimplicite(f_edo, a, b, y0, h)\n", + "\n", + "plt.plot(t, y, label='Euler Implicite')\n", + "\n", + "def f(t):\n", + " return np.sqrt(2*t+1)-1\n", + "\n", + "plt.plot(t, f(t), label='Sol analytique')\n", + "\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "plt.plot(t, np.abs(f(t)-y), label=\"Erreur\")\n", + "plt.legend(loc='upper right')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cd3c87b5-2624-4270-aa03-0a52c6ad2495", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION19.ipynb b/QUESTION19.ipynb new file mode 100644 index 0000000..d788f01 --- /dev/null +++ b/QUESTION19.ipynb @@ -0,0 +1,146 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "7a5c0139-3d42-4163-87e0-2c545af4a54a", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "84f76ae7-f53b-4a7e-af5f-6a979dcedfa9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def fexamen(t, y, alpha = 1.1, beta = 0.4, gamma = 0.4, delta = 0.1):\n", + " y1, y2 = y[0], y[1]\n", + " \n", + " return np.array([\n", + " alpha * y1 - beta * y1*y2,\n", + " delta *y1*y2 - gamma * y2\n", + " ])" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c3165e93-6475-40f7-b8c9-f72ad24c9793", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def RK2(fct,a,b,y0,h):\n", + " t = np.arange(a, b, h)\n", + " y = np.zeros((len(t), len(y0)))\n", + " \n", + " y[0] = y0\n", + " print(y0)\n", + " \n", + " for i in range(1, len(t)):\n", + " k1 = fct(t[i-1] + 0 *h, y[i-1])\n", + " k2 = fct(t[i-1] + 1 *h, y[i-1] + 1*k1*h)\n", + " \n", + " y[i] = y[i-1] + h * (.5*k1+.5*k2)\n", + " \n", + " return t, y" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "c36ba389-8ab4-4af1-a27d-c1c756e54274", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[10 10]\n" + ] + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a, b = 0, 60\n", + "y0 = np.array([10, 10])\n", + "h = 0.01\n", + "\n", + "t, y = RK2(fexamen, a, b, y0, h)\n", + "\n", + "plt.plot(t, y[:,0], label='y_1(t) - Proies')\n", + "plt.plot(t, y[:,1], label='y_2(t) - Prédateurs')\n", + "plt.legend(loc='upper right')\n", + "plt.title('Evolution des population')\n", + "plt.xlabel('Temps')\n", + "plt.show()\n", + "\n", + "plt.plot(y[:,0], y[:,1])\n", + "plt.title('Orbite')\n", + "plt.xlabel('y_1(t) - Proies')\n", + "plt.ylabel('y_2(t) - Prédateurs')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "70f5eab2-dede-4497-a69a-52389cdb9562", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION2.ipynb b/QUESTION2.ipynb new file mode 100644 index 0000000..af43ec8 --- /dev/null +++ b/QUESTION2.ipynb @@ -0,0 +1,177 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "f5d42618-1e03-4591-b1a6-afa1eab8f660", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "4adf5389-da9f-42e1-bd07-4e349cdc70db", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f(x):\n", + " return np.sinh(10*x)/np.cosh(10*x)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "28afeaef-022b-41c7-be84-dd1556612f2f", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def InterpolLagrange(xp, x, y):\n", + " g = 0\n", + " \n", + " for i in range(len(x)):\n", + " s = 1\n", + " for j in range(len(x)):\n", + " if i != j:\n", + " s *= (xp - x[j])\n", + " s /= (x[i] - x[j])\n", + " \n", + " g += y[i] * s\n", + " \n", + " return g" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "8de6efdd-e0da-4b92-a380-914d0f99dbf0", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Fonction tanh(10x)\n", + "x = np.linspace(-1, 1, 500)\n", + "y = f(x)\n", + "\n", + "plt.plot(x, y, color='r', label='Fonction tanh(10x)')\n", + "\n", + "# 5 points\n", + "n = 5\n", + "px = np.arange(-1, 1+(2/n), 2/(n-1))\n", + "py = f(px)\n", + "plt.plot(px, py, 'og')\n", + "\n", + "# Interpolation sur 5 points\n", + "x = np.linspace(-1, 1, 500)\n", + "y = InterpolLagrange(x, px, py)\n", + "plt.plot(x, y, color='g', label='Polyn d''interpo avec 5 points')\n", + "\n", + "plt.legend(loc='upper left')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "a5e65db9-8f11-46e6-b856-21101b5a6765", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Fonction tanh(10x)\n", + "x = np.linspace(-1, 1, 500)\n", + "y = f(x)\n", + "\n", + "plt.plot(x, y, color='r', label='Fonction tanh(10x)')\n", + "\n", + "# 5 points\n", + "n = 5\n", + "px = np.arange(-1, 1+(2/n), 2/(n-1))\n", + "py = f(px)\n", + "\n", + "# Interpolation sur 5 points\n", + "x = np.linspace(-1, 1, 500)\n", + "y = InterpolLagrange(x, px, py)\n", + "plt.plot(x, y, color='g', label='Polyn d''interpo avec 5 points')\n", + "\n", + "# 10 points\n", + "n = 10\n", + "px = np.arange(-1, 1+(2/n), 2/(n-1))\n", + "py = f(px)\n", + "plt.plot(px, py, 'ob')\n", + "\n", + "# Interpolation sur 10 points\n", + "x = np.linspace(-1, 1, 500)\n", + "y = InterpolLagrange(x, px, py)\n", + "plt.plot(x, y, color='b', label='Polyn d''interpo avec 10 points')\n", + "\n", + "plt.legend(loc='upper left')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "54fa3df7-6029-4724-99d3-198f8c3eb924", + "metadata": {}, + "source": [ + " " + ] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION3.ipynb b/QUESTION3.ipynb new file mode 100644 index 0000000..7d5c921 --- /dev/null +++ b/QUESTION3.ipynb @@ -0,0 +1,128 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "c40b6070-62d4-4327-ab1d-3a69870cb158", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2d6f97b3-f882-4692-980d-f72d789d1fad", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f(x):\n", + " return 1/(1+np.exp(-2*x))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3e5f9704-47ff-419a-b13e-d94011ab82e4", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def InterpolLagrange(xp, x, y):\n", + " g = 0\n", + " \n", + " for i in range(len(x)):\n", + " s = 1\n", + " for j in range(len(x)):\n", + " if i != j:\n", + " s *= (xp - x[j])\n", + " s /= (x[i] - x[j])\n", + " \n", + " g += y[i] * s\n", + " \n", + " return g" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "5efc3a03-b2e6-4d2a-8dc5-cfec903e84f5", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-4, 4, 500)\n", + "\n", + "n = 21\n", + "xp = np.arange(-4, 4+(8/n), 8/(n-1))\n", + "yp = f(xp)\n", + "\n", + "errN = np.abs(InterpolLagrange(x, xp, yp) - f(x))\n", + "\n", + "plt.plot(x, errN, color='g', label='erreur interpol normal')\n", + "\n", + "xp = np.zeros(n)\n", + "for i in range(n):\n", + " xp[i] = 4*np.cos(np.pi * (2*i+1)/(2*n))\n", + "yp = f(xp)\n", + "\n", + "errN = np.abs(InterpolLagrange(x, xp, yp) - f(x))\n", + "\n", + "plt.plot(x, errN, color='m', label='erreur interpol Chebychev')\n", + "\n", + "plt.yscale('log')\n", + "plt.ylim((1e-7, 0.5))\n", + "plt.legend(loc='upper center')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "11ad8748-993f-4c27-a75a-400394e14b68", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION4.ipynb b/QUESTION4.ipynb new file mode 100644 index 0000000..70eaa48 --- /dev/null +++ b/QUESTION4.ipynb @@ -0,0 +1,162 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "e0d4ef4c-0dc9-47e3-814d-43e0ceb90583", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "07f35ceb-c355-4ca7-8af0-9e3e0c858500", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 50\n", + "lb , ub = -1 , 4\n", + "delta = 0.3\n", + "dx = np . random . uniform ( low = -1 , high =4 , size =( n ,) )\n", + "dy = 2 -3* dx + dx **2+ np . random . uniform ( low = - delta , high = delta , size =( n ,) )\n", + "plt . plot ( dx , dy ,'ko')" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "cc3e1932-2337-4dce-b8d9-ac0825192202", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def RegressionPolynomiale(x, y, m):\n", + " A = np.zeros((len(x), m+1))\n", + " \n", + " for i in range(len(x)):\n", + " for j in range(m+1):\n", + " A[i, j] = x[i]**j\n", + " x = np.linalg.solve(A.T@A, A.T@y)\n", + " \n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "df4c6c2c-4fe6-40a0-9dc3-af4a9d208c8d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.99659294 -2.99847341 0.99997957]\n" + ] + }, + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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oEPvzSvkyK8fqckREpAlauzeP7YcLCQ22cW0//zoKozoFi3MQGmxnwok+7v/RJk4RETkPVZ02r+ndiig/611RnYLFOaq6OmTRxoPklZRbXI2IiDQlpeVuFmZW9a5IsLia+qVgcY76tYumW8sIyio83sYmIiIi56JG74pE/+tdUZ2CxTkyDINbT6TMqs03IiIi56LqfeOmQe2w+2HviuoULOpg4sC22G0Gmdm5bD9cYHU5IiLSBNToXeGHLby/T8GiDuIiQ7i8ezygTZwiInJmLpeLOXPm8JPHMvCYMCghmk5+2ruiOgWLOrp1SGXafHvNPircHourERGRxiglJQWn08m0adNYmx8GwGcvPE5KSorFldU/BYs6urx7PDHhDo4UlLH0xNSWiIhIlZSUFNLS0nC73Thad8MR2x5PeRkFm5aRlpbm9+FCwaKOHEE2JqqnhYiInIbL5SI9Pd17P6L/1QAUb1mO6SoGID09HZfLZUl9DUHB4jxULYd8tvkQx4r89y+HiIjUTUZGBm63GwAjOJTwHqMAKFz3iXeM2+0mIyPDkvoagoLFeejZOoo+baMod5u8m7nP6nJERKSRyMrK8v7Z2WMUthAn5cf2U5a9odZx/kbB4jxV9bTQcoiIiFRJTEz0/jmi31VAzdmK043zNwoW52nCgDY47DY2Hchnw748q8sREZFGICkpCbvdTlCLdoS264XpcVO04bMaY+x2O0lJSRZVWP8ULM5TM6eDsb1bAjB/5R6LqxERkcbA4XCQnJxMRL+xAJRkrcRddLzGmOTkZBwOhxXlNQgFiwtw+9D2ALy7Zj8lLrfF1YiISGPwxz/9mfih1wM1l0HsdjszZswgNTXVqtIaRJDVBTRllyS2ICEmjOxjJXyw/oD3BFQREQlcn313iDLDQXykg18m3cHOHcNITEwkKSnJr2cqqihYXACbzeC2IQk88clW3li5R8FCRCRAuVwuMjIyyMrKYn3zUUA4Nw9OIPmaq6wurcFpKeQC3TokAZsBK3cdZ/vhQqvLERGRBla9ffe8f85nZ1llC+9d/3vd4sqsoWBxgVpGhTKmR+XBZG9oE6eISECp3r4bIKLvlRiGjdI963km7fd+3777dBQsfKBqE+db3+7DVaGDyUREAsH323eDQUTfKwEoXLsI8P/23aejYOEDo7vH0TIqhGNFLj7ddMjqckREpAFUb98NENqhH0HNWuEpLaR465eA/7fvPh0FCx8Istu8nTjV00JEJDB8vy131YFjRZuWYFa4ah3n7xQsfOQHQyqDxRfbc8g+VmxxNSIiUt+qt+W2hUbi7DocgMJ1n9Y6LhAoWPhI+xZORnaJxTThP6uyrS5HRETqWVX7boDw3qMxgoIpO7gd16GTMxT+3r77dBQsfOi2oZWzFv9etZcKtzZxioj4s6r23YC3hff3Zyv8vX336ahBlg+N7d2S5s5gDuaXsmzbEcb0aGl1SSIiUo9SU1M5RiT/tXXCU15G8aYlQOVMRXJyst+37z4dzVj4UEiQnZsGVXbfnP+NlkNERAJBi2ETAOgVWUbSz+5m9uzZFBcXB2SoAM1Y+NztQxP4+xc7+WzzYQ7nlxIfFWp1SSIiUk/yS8tZuHY/AL+fdDXDOt1hcUXW04yFj3VtGcngDs1xe0ze/Hav1eWIiEg9enfNPkrK3XSJj2Box+ZWl9MoKFjUg6pNnG+szMbjMS2uRkRE6oNpmrz6dWXvojsvao9hGBZX1DgoWNSD6/u1JiIkiN1Hi1mx46jV5YiISD1Yk53L5oMFhATZuGmgTreuomBRD5yOICYMaAPAq9+oE6eIiD967cRsxfX92hDtDLa4msZDwaKe3HlRBwAWbTjIkYIyi6sRERFfyisp5/11lZs2f3hRe4uraVwULOpJrzZRDGrfjAqPyb/ViVNExK8s+HYvpeUeerSKZFD7ZlaX06goWNSjqlmL17/Zg1ubOEVE/IJpmrx2Ypn7h9q0eYoLChazZs3CMAymTp3qo3L8y3X9WhMdFsze4yUkpz3PlClTmDNnDi6X6+xPFhGRRmn17uNsPVRIWLCdiQPbWl1Oo3PewWLlypU899xz9OvXz5f1+JXQYDsti3cC8Po3e5k7dy7Tpk3D6XSSkpJicXUiIlIXLpeLOXPm8ODcNwG4rm9LokK1afP7zitYFBYWcuedd/L888/TvLkagtQmJSWFxS/8AYCwxCHYI+MAcLvdpKWlKVyIiDQRKSkpOJ1OHpr5W/ZS+bv8b8k/1O/x0zivYPHAAw9w3XXXceWVV551bFlZGfn5+TVugcDlcpGenk7FsX2U7FqLYbMT0X9sjTHp6elaFhERaeRSUlJIS0vD7XYT3mcMRpAD16EsSvdt1ofE06hzsJg/fz7ffvsts2bNOqfxs2bNIjo62ntLSEioc5FNUUZGBm63G4DCzA+BE8fq2uzeMW63m4yMDEvqExGRs6v6kFglcsA1ABRkfux9TB8Sa6pTsMjOzubBBx/klVdeITT03A7XmjlzJnl5ed5bdnZgXHqZlZXl/XPxtq9xFx4nKLIFYV2G1TpOREQal+ofEkMS+hDcIgGPq4SiE8ejgz4kfl+dgsXq1as5fPgwgwcPJigoiKCgIJYuXcpf//pXgoKCvC9+dSEhIURFRdW4BYLExMSTdzwVFK77BIDIAeNqHyciIo1K9Q9/VbMVRZuWYrpKah0X6OoULK644grWr19PZmam9zZkyBDuvPNOMjMzsdvtZ/8mASIpKanG61GwdhGm6SGs0yCCmrUGwG63k5SUZFWJIiJyFlUf/mzOZji7jwCgYM2HtY6TOgaLyMhI+vTpU+MWHh5OixYt6NOnT33V2CQ5HA6Sk5O99935hynZsRqAiBOpNzk5GYfDYUl9IiJydlUfEiP6j8WwB1O67zvKD++oMUYfEmsKsroAf5aamgpUbuxxu90UrvkQZ+JQIvpexT1D40hN/YvFFYqIyJk4HA6mJiczv7AXAIXffnDKGH1IrMkwTbNBe03n5+cTHR1NXl5ewOy3cLlcZGRksD0ri6WRV1DgCWbObQPUsU1EpAn4eMNB7ntlNe7iPPZmTAJ3BVA5U5GcnOz9EOnvzvX9WzMWDcDhcHjbnj/92Tae/HQr/1qxW8FCRKQJeGXFbgDuv7o/zs5pZGVlkZiYSFJSkmYqTkPBooHdNiyBv/5vG6t3H2fDvjz6tI22uiQREalF1pFCvtieg82AH1/SiXbXTbW6pEZPp5s2sPjIUMb1qbwq5F9f7ba4GhEROZOq39NjerSkXXOnxdU0DQoWFph0SeVx6u9k7iO3WN3aREQao2JXBW+t3gvAXcM7WFxN06FgYYFB7ZvTu00UZRUe/r0qMDqRiog0Ne+s2U9BWQUdWzgZ1SXW6nKaDAULCxiGwY9PpN9/rdiN29OgF+aIiMhZmKbJy1/tAuBHF3fAZjOsLagJUbCwyA392xIdFkz2sRKWbj1sdTkiIkJle4A5c+bwo6m/ZfPBAkKDbdw6ODAOz/QVBQuLhDns3Da08i/rP7/UJk4REaulpKTgdDqZNm0an+wsBeDo6kU8/tgjFlfWtChYWOhHF3XAMGDp1iPszCmyuhwRkYCVkpJCWloabre7xrkg+d++T1paGikpKRZX2HQoWFiofQsnl3ePB3TpqYiIVVwuF+np6d77VeeClO3bjOtQ5aml6enpuFy6iu9cKFhYrGoT539WZ1PsqrC4GhGRwJORkYHb7a68Y9iIHDAOgIJv3/eOcbvdZGRkWFFek6NgYbFLu8bRsYWTgtIK3lmz3+pyREQCTlZWlvfPzm7DCYqKw12US9GW5bWOk9qppbfFbDaDu4Z35A/vb+KfX+7k0Jdvs2OH+tCLiDSUxMRE758jB98AQMHaj8FdXus4qZ1ON20E8krKGfTYR7gNOwdffZiyvRuBwDs5T0TECi6XC6fTiT22I61/8hSmu4J9z9yDu/CYd4zdbqe4uDigP+yd6/u3lkIagccffYTctZ8AEDn4eu/jbrdbu5FFROqZw+EgOTmZyMHjASje8kWNUAGQnJwc0KGiLjRjYbGqpGyLSaDNPXMxPW72PfNT3AU53jFKyiIi9SunsIxhf/gEj2HjwMvJuA5sBTRzXJ1mLJqIqt3I5Ud2Ubp7HYbNTuTA62qM0W5kEZH69drXe/AYNvq1jeIvKfczefJkZs+eTXFxsUJFHWnzpsWq7zLOX/UuoR36ETHgGvK+nI9ZUeb92ssvv8zUqVMtqFBExL+5Kjy8sqKyl9BPR3VmwoBRFlfUtGnGwmLVdxmXZK2k/PgB7GGRhPceXWPcmjVrtNdCRKQefLThAIcLyoiPDGFcn9ZWl9PkKVhYLCkpCbvdXnnH9FDw7XsARA6ZcMpYdX4TEfG9F5fvAipPMXUE6W3xQukVtFjVbuQqhes+xVNWjCO2PaEdB9YYq70WIiK+tWbPcTKzc3HYbdwxrL3V5fgFBYtGIDU1lQEDBgBgukooXP8pAFGnmbX45z//2ZCliYj4tZe+3AXA+P5tiIsMsbYYP6Fg0UhMmjTJ++eC1e9hmh7CEocQFNO2xri1a9dqOURExAcO5ZfywboDANw9oqO1xfgRBYtGIikpCcMwAKjIPUjJ9m8AiDrRsKWKaZpaDhER8YFXV+ymwmMytGNz+rSNtrocv6Fg0Ug4HA7vcghUXnoKEN7nSmwh4TXG6iAcEZELU1ru5tWv9wDwk0s6WVyNf1GwaER+/OMfe/9ctmc9rsM7sTlCieh/dY1xOghHROTCLFy7n6NFLlpHh3J175ZWl+NXFCwakRqXngL5qxYCEDnoejAq/1fZ7XaSkpIsqU9ExB+YpsnfP98JwKRLOhJk11uhL+nVbES+f+lp0aYluIvzCIqOx9ltOKCDcERELtTn23LYcqiAcIddl5jWAwWLRiY1NZUZM2ZUzly4yylY8yFQeenpjBkz1LNeROQCPf/5DgB+MDSB6LBgi6vxPwoWjVBqairFxcXMnj2bWwe2woZJSLte3DnlV1aXJiLSpG05WMDn23KwGXDPCG3arA8KFo2Uw+Fg6tSpPP/XJ5g4sB0AL3yx0+KqRESathdOzFZc06cVCTFOi6vxTwoWTcC9ozoD8OH6A2QfK7a4GhGRpulwQSnvZu4H4KcjO1tcjf9SsGgCerWJYlTXWNwe03tYjoiI1M2/vtqNy+1hUPtmDO7Q3Opy/JaCRRPxsxOzFvNX7iGvuNziakREmpYSl5tXVuwGTv4+lfqhYNFEjOoaS49WkRS73Lz2zR6ryxERaVLe+nYvx4vLSYgJY2zvVlaX49cULJoIwzC8KfvF5TtxVXgsrkhEpGnweEz+cWLz+z0jOmG3GRZX5N8ULJqQ8f3b0DIqhMMFZSxcu9/qckREmoTPNh9mR04RkaFB/GBIgtXl+D0FiybEEWTj7hPXXT+/bAemaVpckYhI41d1iekPL2pPeEiQxdX4PwWLJuaOYe0Jd9jZcqiAZdtyrC5HRKRRW783j693HiPIZvCTSzpaXU5AULBoYqLDgrltaGVv++eX7bC4GhGRxu25E7MV4/u3oXV0mMXVBAYFiybo7hEdsdsMvtiew8b9eVaXIyLSKO05WswH6yr3o907Su27G4qCRROUEOPk2r6tAXjhc7X5FhE5nec/34HHhEu7xdG7TbTV5QQMBYsm6mcn0vd7a/ezP7fE4mpERBqXnMIy/r0qG4D7LlNDrIZUp2Axb948+vXrR1RUFFFRUQwfPpyPPvqovmqTM+jXrhkXd46hwmPy4nLNWoiIVPfPL3dRVuGhf7tohnduYXU5AaVOwaJdu3b8+c9/ZtWqVaxatYoxY8YwYcIENm7cWF/1yRn84tJEAF77Wm2+RUSqFJVV8PJXle2777ssEcNQQ6yGVKdgMX78eK699lq6detGt27dePzxx4mIiGDFihX1VZ+cwejucfRoFUmRy83LX+2yuhwRkUbh9W/2kFdSTqfYcLXvtsB577Fwu93Mnz+foqIihg8fXuu4srIy8vPza9zENwzD4P7RlbMWL365ixKX2+KKRESs5arw8PcT7bt/fmlnte+2QJ2Dxfr164mIiCAkJIT77ruPBQsW0KtXr1rHz5o1i+joaO8tIUHtVH3pur6taR/j5FiRizdW6nAyEQls72bu40BeKXGRIdw4sK3V5QSkOgeL7t27k5mZyYoVK7j//vuZNGkSmzZtqnX8zJkzycvL896ys7MvqGCpKchu4+eXVu54fv7znZS7dTiZiAQmj8fk2RONA+8Z0YnQYLvFFQWmOgcLh8NBly5dGDJkCLNmzaJ///489dRTtY4PCQnxXkVSdRPfumVwO2IjQtiXW8LCTB1OJiKB6bPNh9l+uJDIkCDuvLi91eUErAvuY2GaJmVlZb6oRc5TaLCdn46s7Gsxb2kWHo8OJxORwPPM0iwAfnhxe6JCgy2uJnDVKVj86le/4vPPP2fXrl2sX7+eRx55hCVLlnDnnXfWV31yju68uD2RIUFsP1zIp98dsrocEZEGtXLXMVbvPo7DbuOnI9S+20p1ChaHDh3irrvuonv37lxxxRV8/fXXfPzxx1x11VX1VZ+co6jQYO4a3gGAjCVZOlJdRALKM0sqZytuHtyW+KhQi6sJbHU6mP7vf/97fdUhPnD3iE78/YudrM3O5asdR7kkMdbqkkRE6t2m/fl8tvkwhgE/G6X23VbTWSF+JC4yhB8Mqbycd96J9C4i4u/+tmQ7UHn5fee4CIurEQULP1PVEObzbTms36sj1UXEv20/XMiH6w8A8MDlXSyuRkDBwu8kxDgZ36/ySPV5S7dbXI2ISP2atyQL04SrerWkZ2u1M2gMFCz80P2jK1P7RxsOsv1wgcXViIjUj+xjxbyTuQ+AyZqtaDQULPxQ91aRXNWrJaYJf1usvRYi4p/mLc3C7TEZ1TWW/gnNrC5HTlCw8FO/HNMVqOybvzOnyOJqRER860BeCW+u2gvAlBO/76RxULDwU33bRXN59zg8JmQs1l4LEfEvzy3bgcvtYVinGIZ1irG6HKlGwcKPTbmiMsUvWLOP7GPFFlcjIuIbOYVlvP5N5WnOU8Zob0Vjo2Dhxwa1b86orrFUeEwy1NdCRPzE37/YSWm5h/4JzRjZRY0AGxsFCz9Xtfb45ups9ueWWFyNiMiFyS128fKXuwCYcnkXDMOwtiA5hYKFnxvWKYaLO8dQ7ja9J/+JiDRVL325iyKXm56to7iiZ7zV5chpKFgEgKorROavzOZwfqnF1YiInJ/CsgpeXL4LgAcuT9RsRSOlYBEAhie2YEiH5rgqPDy7bIfV5YiInJd/frmLvJJyOseFM65Pa6vLkVooWAQAwzC8V4i8+vVucgrLLK5IRKRuCkrLee7EB6NfjumK3abZisZKwSJAXNo1lv7toikt9/D855q1EJGm5aXllbMViXHhjO/fxupy5AyCrC5AGoZhGPzyiq789J+r+NdXu+G7T9m/cxuJiYkkJSXhcDisLlFE5LTyS8u9H4h+eYVmKxo7zVgEkDE94mlmFlDscpO68Fvmzp3LtGnTcDqdpKSkWF2eiIiXy+UiLS2NkSNHMvLu35BfWkFiXDjX99NsRWOnYBFAHn74Yba+NRuAyEHjsTmbAeB2u0lLS1O4EJFGISUlhdDQUFJSUvhyVSa5LQcC8PULv2Xm/z1scXVyNgoWAcLlcpGenk5J1jeU7d+KzRFK9EU31xiTnp6Oy+WyqEIRkcpQkZaWhmmaAEQNnYAtNALXkV0Ubf5CH4KaAAWLAJGRkYHb7QYg94tXAIgYeC32iJOH97jdbjIyMiypT0TE5XLx5JNPeu/bQsKJGjIBgLzlrwOVYePJJ5/Uh6BGTMEiQGRlney6WbrzW0r3bsIWHELUxbfWOk5EpCFlZGTg8Xi89yOH3YgtJBzX4Z0Ub/nS+7jH49GHoEZMwSJAJCYm1rif93nlrEVk/2uwR8bVOk5EpKFU/2BjC40gavANAOQuf42q2YrTjZXGRcEiQCQlJWG32733S/eso3T3OoygYKIv+QEAdrudpKQkq0oUkQBX/YNN1NAbsYU4cR3aQcnWFWccK42LgkWAcDgcJCcn13gs94tXAYjoexVB0S1JTk5WPwsRsUxSUhI2mw1bWBSRg8cDp5+tsNls+hDUiClYBJDU1FRmzJjhnbko27uRkp3fYtiDGPGLP5KammpxhSISyBwOBw899BBRwypnK8oObqdk26mzFQ899JA+BDVihll1TU8Dyc/PJzo6mry8PKKiohryR8sJLpeLjIwMsrKycCb04o1j7bHbDP6bfBmdYsOtLk9EAtjh/FKGP/4JbsPO4Td/T0nWN96vGYbB9OnT9SHIIuf6/q2W3gHI4XAwdepU7/0jL63kf5sP89R/tzLn9oHWFSYiAe/p/23HbdgZmBDN8J/fwsKFwQBMmDCBBx98UDMVTYBmLIQN+/K4/ukvMAz4ZOqldG0ZaXVJIhKA9hwtZsyTS6jwmMz/+cVc3LmF1SVJNef6/q09FkKfttGM7dUS04T0T7daXY6IBKjZ/91KhcdkVNdYhYomTMFCAHhobHcMAz7acJC12blWlyMiAWbzwXzeydwHQMrVPSyuRi6EgoUA0L1VJDcObAtA6qLNFlcjIoHmiUVbMU24tm8r+raLtrocuQAKFuI17cpuOOw2lm8/yufbjlhdjogEiG/3HOe/3x3CZkDyVd2tLkcukIKFeCXEOLnz4vYA/OXjzXg8DbqvV0QCkGmapH28BYBbBrejS3yExRXJhVKwkBomX96FiJAgNuzL58MNB6wuR0T83Bfbc/hqx1EcdhsPXtnN6nLEBxQspIYWESH8bFRnAJ5YtIVyt+cszxAROT+maZK2qHK24kcXd6BtszCLKxJfUIMsOcVPR3Xi5a92setoMW+szOZHF3ewuiQR8RPVO/962vZnXW5rnA47SZfrUDF/oRkLOUVESBBTxnQB4KnPtlHicltckYj4g5SUFJxOJ9OmTWPu3zJ4J6sCgI5lO4iNCLG4OvEVBQs5rTsuak+75mEcKSjjH8t3Wl2OiDRxKSkppKWl4XZXflCJ6DeW4BYJuIvz+HjODFJSUiyuUHxFwUJOKyTIzkNjKzdSPbM0i9xil8UViUhT5XK5SE9P9943HGE0G3knAHnLX8d0FZOeno7Lpd8z/kDBQmo1oX9berSKpKC0gnlLsqwuR0SaqIyMDO9MBUDUsBuxRzSn/Nh+CjI/BsDtdpORkWFVieJDChZSK5vNIOWaymY1L365i73Hiy2uSESaoqyskx9M7BExRA29CYDcpS+Bp+K046TpUrCQM7q8ezwXd47BVeHxXhYmIlIXiYknr/iIHnknNkcopXs3Ubz1y1rHSdNVp2Axa9Yshg4dSmRkJPHx8UycOJEtW/Rm488Mw+DX1/XCMODdzP1k6oAyEamjpKQk7HY7wbHtieh7JQC5S/5RY4zdbicpKcmK8sTH6hQsli5dygMPPMCKFSv49NNPqaioYOzYsRQVFdVXfdII9Gkb7T2g7PEPNmGaavUtIufO4XCQnJxMs9F3Y9jsFG1ZTtm+mocdJicn43A4LKpQfMkwL+Bd4siRI8THx7N06VIuvfTSc3pOfn4+0dHR5OXlERUVdb4/WhrYgbwSLn9iCaXlHp750SCu6dPa6pJEpAn5cnsOP3zha0x3Bfv/nkTF8f1A5UxFcnIyqampFlcoZ3Ou798X1HkzLy8PgJiYmAv5NtIEtI4O42ejOvP0/7bz5482M6ZHSxxB2qIjImfn8Zg8/uF3APz4kk60aDuDrKwsEhMTSUpK0kyFnznvYGGaJsnJyYwcOZI+ffrUOq6srIyysjLv/fz8/PP9kWKxX1yWyOvfZLPraDH/WrGbn47sZHVJItIEvLt2Hxv35xMZEsS0sT2ICe9ndUlSj877I+fkyZNZt24dr7/++hnHzZo1i+joaO8tISHhfH+kWCwiJMjbNOuvn21T0ywROavScjdPLNoKwP2XJxITrtkJf3dewWLKlCksXLiQxYsX065duzOOnTlzJnl5ed5bdnb2eRUqjcMPhiTQvWUkeSXlPP2/7VaXIyKN3N+/2Mm+3BJaR4dyzwjNcgaCOgUL0zSZPHkyb7/9Nv/73//o1Onsf0lCQkKIioqqcZOmy24z+NV1PQEqT0DN0RVBInJ6h/JL+dviyg8gD1/Tg9Bgu8UVSUOoU7B44IEHeOWVV3jttdeIjIzk4MGDHDx4kJKSkvqqTxqhy7rFcWm3OMrdJn/5ePPZnyAiASn14y0Uu9wMat+MCQPaWF2ONJA6BYt58+aRl5fH6NGjad26tff2xhtv1Fd90kg9cm1PbAZ8tOEgX+84anU5ItLIZGbn8ta3ewF4dHxvDMOwuCJpKHVeCjnd7Sc/+Uk9lSeNVfdWkdw+rD0Aj723CbdHTbNEpJJpmvz+vY0A3DSoLf0TmllbkDQoNSKQ8zZ9bHeiQoP47kA+81fusbocEWkkFq7dz7d7cnE67Dx8TQ+ry5EGpmAh5y0m3EHyVZWXnz6xaAt5xeUWVyQiVit2VTDrw8q9V0mjE2kZFWpxRdLQFCzkgvzo4g50axnB8eJyZv93q9XliIjFnlm6g4P5pbRrHsa9ozpbXY5Y4IJaeosE2W08Or43d77wNf9asZs7hrWne6tIq8sSkQbicrnIyMggKyuLuI7defV45dHnv7q2py4vDVCasZALNqJLLNf0boXbY/K79zbq9FORAJGSkoLT6WTatGnMnTuXp5dlU1bhIc7MZVyfVlaXJxZRsBCfeOS6njiCbHyZdZRFGw9aXY6I1LOUlBTS0tJwu90AhHboT3jPSzE9bta+9BsefvhhiysUq1zQsennQ8em+6/0T7bw1/9tp22zMD6aMpx/PP+sTjAU8UMulwun0+kNFdiCaHPP0wS3SCB/9Xsc/++z2O12iouL9e/ej5zr+7dmLMRn7hudSOvoUPblltDhmnu906PTpk3D6XSSkpJidYki4gMZGRknQwUQNWQCwS0ScBflkvv5KwC43W4yMjKsKlEspGAhPuN0BNHh+LcARF10C0HNTq6xut1u0tLSFC5E/EBWVpb3z/bIFkSPuB2A40v+gVlWdNpxEjgULMRnXC4Xb6bPpGRXJkaQg+ZX/uKUMenp6bhcOm5dpClLTEz0/rn55T/F5gijdO8mijYsrnWcBA4FC/GZqunRY5/Ow3SX40wcSljX4TXGuN1urrnmGosqFBFfSEpKwm6319iweezTecDJLXt2u52kpCTrihTLKFiIz1RNe1Yc20f+128BEHPlzzCCa3beW7x4sZZERJowh8PBg8kPEXPVfQAUfPsB5Yd31hiTnJysjZsBSsFCfKb6tGfeV/+hIvcgQVHxRF9y+yljtSQi0rR1u+7nJzdsfvGq93G73c6MGTNITU21sDqxki43FZ/5/iVoYYlDib/lUUx3BQde+iXlOTUPKps9ezZTp061oFIROR9VXTY37NjH0vBLKTdt/PnG3hz86h1dWh4AdLmpNDiHw0FycrL3fknWSoq3foVhDyLmqvtPGa8d4yJNR/Uumwv3hVJu2ijbu4nVb2UwdepUnn76aaZOnapQIQoW4lupqalcfvnl3vvHPnsOj6uU0PZ9Ce99eY2x2jEu0jRU77IZ1nU4zq4XY7rLOfrx0zyhy8jle7QUIj7ncrkIDQ31nhkSddHNNB99N+6iXPa/cB+e0kJ15RNpIqovcRqOMNrcO4+gyFjyvpzvbYalf8+BQUshYhmHw8H06dO99/NXvosrZzf28GY0v/weQDvGRZqK6l02m426i6DIWMqP7Sfvq397x6jLplSnYCH1IjU1lRkzZmC328FTwbGP5wIQ0W8sP57xuHaMizQRW7ZsAcDRuhuRg68H4Ngnf8OsqHlVl/ZMSRUFC6k3qampFBcXM3v2bH524xX0C8sFYFfccErL3Wd+sohYLiUlhWeffRYMGy2unoxh2Cjc8D9Kd689Zaz2TEkV7bGQBpNfWs5V6Us5lF/G/aMTefiaHlaXJCK1qNqwCRA17EaaX/5T3CX57H/+Pjwl+TXGao9FYNAeC2l0okKD+cOEPgA8t2wHm/bnn+UZImIFl8tFeno6APaoeKJH3AnA8cUvnhIqQHumpCYFC2lQY3u3YlyfVrg9JjPfXofb06ATZiJyDqpv2GxxzWRsjlBK96ynaP2nNcYZhqEum3IKBQtpcL+7oTeRoUGs3ZvHS1/usrocEfmeqo2Y4X2vJKzTIDzlZRxdNPeUcffdd59ChZxCwUIaXHxUKDPH9QTgiUVbyD5WbHFFIlJdYmIi9ogYYsbcC0DeF69ScWzfKeO6devW0KVJE6BgIZa4fWgCwzrGUFLu5lcL1tPAe4hF5Azuv/9+Wlw9GVtoBGX7t5K/8p1TxuhYdKmNgoVYwmYz+PPNfQkJsvH5thxe/ybb6pJE5ISPv8shrMuwyrbdHz0FpueUMdqwKbVRsBDLdI6LYMbV3QF4/INN7Dycx5w5c5gyZQpz5szRseoiFsgpLOOxhRsB6GPsxXN8b42v61h0ORv1sRBLuT0mtz37Fat2H6d0VyaH3vi192t2u53k5GT9AhOpZ1XHoWdlZbG5xQi2lUbSs3UUCyePwHRXeL+mY9ED27m+fwc1YE0ip7DbDOJ2LsLj7k9oxwFE9L+GwrUfA5XnD1Q16FG4EKkfKSkppKen43a7cXa7hLgbr8H0uGm3bzHB9lFgdzB16lSry5QmREshYimXy8Xz6Y+Tu+xlAJpffg/2qPgaY9LT07UsIlIPqh+HbguLImbs/QDkr3iTF9Ie1XHocl4ULMRSVY14Cla/R+nejdhCnLQY98saY3RyoojvVe+uCdDi6snYw5vjytlN7pfzAYV6OT8KFmIp74mIpoejHz6Fp7yUsBNLIqcdJyI+Ub27Znjvy3F2vwTTXUHOe0+CuxxQqJfzo2Ahlqp+ImLF8f0nl0TG/JSgZq1OO05ELlxVWLdHxhFz1X0A5C5/jfLDO047TuRcKViIpZKSkrDb7d77Baveo3TPemyOMGKvnw6GTY14RHzI5XIxZ84c1qxZAxi0uHYqtpBwyvZtJn/Fm6eMV6iXulKwEEs5HA6Sk5OrPWKS80E6nrIiQtr2IHr4D9SIR8RHUlJScDqdTJs2jeXLlxM5eDxhHfvjcZWS80H6KY2wFOrlfChYiOVSU1OZMWOGd+bCnX+EY5/MA6D5yDv54ZRfWVmeiF+ofgUIQFCLdjS7bBIAx5f8g4rj+095jkK9nA81yJJGo3qTns6dE9kWN5IPNxyiU2w4H/xyJE6H2q6InA+Xy0VoaOjJM3lsdlr9KI2Q1t0o2bGaw/95tMZ4NaeT01GDLGlyHI6ajXjyistZk72MnTlF/PGD7/jTjX2tK06kCbvmmmtqHPTXbMQdhLTuhru0kKMf/dX7+IgRI7jlllvUXVMuiJZCpNGKdgbz5K39AXjt6z38d9MhiysSaXpcLheLFy/23g9J6EvU8B8AcGzRXNyFR71fGzhwIFOnTlWokAuiYCGN2iVdYrl3ZCcAHn5rHUcKyiyuSKRpqd6HwhYaSez4hzAMG4XrPqF48xc1xuoKEPEFBQtp9KZf3Z0erSI5WuQi+d+ZeDwNui1IpEmr3oeixbhfEhQZS/nRbI7999ka4wzD0BUg4hMKFtLohQbb+esdAwkNtvH5thyeXbbj7E8SEVwuF3v3Vh57HjHwWpzdhmNWlHNkYRpmec3Zv9GjR2sJRHyizsFi2bJljB8/njZt2mAYBu+88049lCVSU7eWkTw2vjcAT3yyhdW7j1tckUjjVtWz4p133iE4tgMxY+4F4PjSF0/prmkYBh9//LEVZYofqnOwKCoqon///sydO7c+6hGp1W1DExjfvw1uj8kvX19DXnG51SWJNErVe1YYQQ5ib0jBCHJQnLWSglULTxk/ffp0zVaIz9T5ctNx48Yxbty4+qhF5IwMw+BPN/Zh3d5cdh8tJuWttTzzo8EYhmF1aSKNxvdPLW0+5mc44jrgLjzO0Q/n1BirfhVSH+p9j0VZWRn5+fk1biLnKzI0mKfvGEiw3WDRxkP8a8Vuq0sSaTRcLhe33XbbyVNLe40mcuA4TNNDzgdP4inO846dOHEixcXFChXic/UeLGbNmkV0dLT3lpCQUN8/Uvxcv3bN+L9xPQH44/vfsXF/3lmeIeL/qu+pAAhukUDM1ZMByPvyDUp3ZdYY365dOy1/SL2o92Axc+ZM8vLyvLfs7Oz6/pESAO4Z0ZEre8bjcnt44NVvyckrYs6cOUyZMoU5c+bgcrmsLlGkwXz/HBAjOJTYiTOxOUIp2ZVJ3vLXT3mOelZIfbmgs0IMw2DBggVMnDjxnJ+js0LEV44Xubj+6S/Yl1tCybYVHH77caDyr7PWjiVQuFwunE6nN1QAxF4/nfDeo6koOMqBl35ZYwkEKv99FBcXa8ZC6uRc37/Vx0KarObhDnoe+wKzopywrhcTdfEt3q+53W7S0tJISUmxsEKR+peRkVEjVEQMGEd479GYHjc57/7llFABOrVU6ledg0VhYSGZmZlkZmYCsHPnTjIzM9mzZ4+vaxM5I5fLxUvpv+fYp5VHrDcb9SNCO/SvMSY9PV3LIuLXqnfWdLTqQswVPwfg+JKXKNu3qcZYu93OjBkzNJMn9arOwWLVqlUMHDiQgQMHApXJd+DAgfz2t7/1eXEiZ1L1Sa1w3ScUrvsEw2Yn9oYU7JGx3jFut7vGWQki/qZqr4QtNIK4Cf+HERRM8davKFi5oMY4XQUiDaXOwWL06NGYpnnK7aWXXqqH8kRqV/2T2rFPn6Hs4HbszmjiJs4Ee9Bpx4n4m6SkJOxBwcROeJigZq0oP36AnNP0q3jjjTe0/CENQnsspMmqvqvdrHCR884s3CUFhLTp7p0O/v44EX/jcDgYk/w0YR0H4nGVcOTtP2KWFdUYoz0V0pAULKTJSkpKwm63e+9X5B0i5/0nME0PkQOvJaL/1djtdp3YKH7trdV72Wq0A+D4R09RnnOyaZz2VIgVFCykyXI4HCQnJ9d4rHTHavI+fxWAmKvu567k3+mTmvittdm5zFywHoApY7pwdO1nzJ49m8mTJzN79mztqRBL1PmsEJHGpOqXZnp6uveSu7yv3sAR3xFnj1GsDR9G9rFiEmKcVpYp4nOHC0r5xb9W46rwcGXPeKZd2Q2bzWDq1KlWlyYB7oIaZJ0PNciS+uByucjIyCArK4vExETuvvcX/OjF1azfl0f3lpG8fu8QXv77c96vJyUlaSZDmqyyCjc/fP5rVu8+TmJcOO88MILI0GCryxI/d67v3woW4rcO5JVww9zlHCkoU2dO8RumafLwW+v496q9RIYG8e4DI+gcF2F1WRIA1HlTAl7r6DD65X2FWeEirOvFNBv1I+/X1JlTmqp5S7P496q92Az46x0DFSqk0dGMhfitqjMUQruPInb8dABy3nuCok1LvGMMwyA/P5+ICP1ylsbv/XX7mfzaGgB+d0NvJl3S0dqCJKBoxkICXlVnzqJNS8hb8R8AWlz7ICEJfb1jTNMkKipKMxfS6K3efZzkf68F4O4RHRUqpNFSsBC/Vb3jZu7Slyna/AWGPZj4mx4hOLa992umaWpZRBq1PUeL+fnLq7xXgPz6ul5WlyRSKwUL8Vs1O26a5Lz/JKV7N2ILjSD+1sewR8TUGK8Dy6Qxyisu5+6XvuFokYvebaJ46vaB2G2G1WWJ1ErBQvzW9ztz4i7nyFt/pPzoXoKi4om/5VEMR9jJL+vAMmlkyirc3P/qarKOFNE6OpR//GQo4SFqPySNm4KF+K3Tdeb0lBZw+D+P4i46jqNlInET/g9sJ8OHDiyTxsLtMUl+Yy1fZh0l3GHn75OG0jIq1OqyRM5KwUL8WmpqKjNmzMAwTk4dV+Qd4vCbv8fjKiWs82BaXP2A92s6sEwaA9M0+e27G/hg/QGC7QbP3jWEXm10FZ00DbrcVAJCYWEhUVFRVP/rHpY4jLibHsGw2cn7+i0KPn+Z4uJideSUBvf9zrEVPa5m7pIdGAY8fcdAru/XxuoSRc75/VuLdRIQIiIimD59Omlpad7HSrK+4diiubQY9yDRF93MyKEDFSqkwT300EPMnj3bG3ojBl5Hi7FdAfj9hD4KFdLkaClEAkbVskj1DZ2F6z4ld8k/AFhv68y/vtplUXUSiIYNG0Z6ero3VDh7jCLmql8AkPvFq6x/+29WlidyXrQUIgHn+9POSUlJPL1kJ0//bzsAc24bwLW9404Zo9kM8aXk5GRmz57tvR/aaRDxN/8Gwx5M/ur3Of7fZ7Db7Vqek0ZDh5CJ1IFpmjy2cCP//Go3hmlyZMHjFG1b4f26Di0TX3K5XISGhnpnKkI79Cfu5t9iCw6h6Ltl5Lz3BJgeAGbPnq2j0KVRUEtvkTowDINHx/emg3kQ0zBocUMKoR36e7+uQ8vElzIyMryhIqRdb+Ju+g224BCKt31Nzvvp3lABugRamh4FC5ETKirKWZ5+P8Vbv8IIchB3829qhAtQd065MC6Xizlz5vCPf1Tu63G06UH8LY9ic4RSsmMVR96dBZ6KGs/RJdDS1ChYiJyQkZGBu6KcIwv/QnHWSmzBoZXhon0/7xi3282YMWOYM2eOAobUSUpKCk6nk2nTprF+/XocrbrS8ge/wxbipGRXJkcW/AncNUOFYRgkJSVZVLHI+VGwEDnBO+XsruDIgsdPhotbflsjXCxfvpxp06bhdDq1NCLnJCUlhbS0NNxuNwCO1t2Iv+0P2ELCKc3ewJG3/4BZcWpQnTZtmjZuSpOjYCFyQo0p57OEC9C+Czk3LpeL9PR07/2Qtr1oedsfsYdGULp3E4ff/B1medkpzxs6dChPPvlkQ5Yq4hMKFiInnHpoWQVHFvypWrh4lNDOQ055nvZdyJlkZGR4ZypC2/cj/ge/xxbipHT3Og7/+7eYrpIa4w3DYNq0aXzzzTdWlCtywRQsRE443aFluMsrw8X2b7AFhxB/069xdh9Rc4hORZXvqdqkOWXKFN58802gsk9FXNVGzZ3fnpipKPU+p2/fvsyePZvS0tIaMxwiTY1aeotUU9WnIj093fspszJcPE7sdcmE97qM2BtSOPrxXIrWf+p9ni4JlCopKSk1//4AYV0vJu6GhzGCgine9jVH3v0zuMtrPO+ee+5RvwrxC5qxEPme1NRUiouLmT17NiNGnJid8LjJef9JCjI/xrDZib32QSKH3OB9ji4JFDh1kyZARL+xxE2ciREUTNGW5Rx5Z9YpocJut+vqD/Eb6rwpcgYulwun01njjaLZ6LuJvuhmAPK+nE/Bl6+Tm5vLCy+8oBbgAex0f1eihv+A5pf+GICCtYs4tuhvNZpfVZkxY4a6ukqjp9NNRXygat9F9VNRc5e8iFlWTLNL7yL6kttp2akHzWJicVfb2T99+nS1AA8w1TdpgkHzK39O1ODxQGUAzf38lVOeo1bx4o+0FCJyFqc7FTXvqzc49vHT4PFQ2noALW58BMMR5v161aWogwYNUjOtAOHdZ2MPJvaGGUQNHo9pejj26TM1QsWIESOYPHkys2fPpri4WKFC/I6WQkTO0fdPRb333ntpNXAMMeNTsDnCcB3aweE3H8NdeOyU5+qTqf+bM2cODz3yO+Jv+jUhbXtgusvJ+WA2xd8tqzFOh4pJU6XTTUXq2Zw5cyo7I7ZMJP6Wx7BHNKci/wiH3/oD5Yd3nPY5Wkv3Xxuyj3HNn94hKLol7pICjrzzJ8r2rK8xRsegS1Om001F6lnV1LfrUBYHX5lO+dFsgqLiaHVn6im9LqqomZZ/Wrr1CLe/sJKg6JaUH9vPwX89dEqoAEhOTlaoEL+nYCFynqpfYlqRd4gD/5pOyY7V2ByhxE2cSfSIHwJGjeeomZZ/MU2Tf3yxk3teWklhWQXDOsVwS7OdmPmHaoyz2+2arZKAoaUQkfN0ussLMWw0H303UcNuBKBoy3KOfjC7RofFyZMn8/TTTzd0ueJjJS43//f2Ot7N3A/AzYPaMeumvjiCbKfsx9Hlx+IPdLmpSD073aWomB6OL/47rpzdtBj7AOHdRxDcIoEj7/yJiqN7ATXT8ge7jxbxi3+tZvPBAuw2g0eu7cndIzpiGJUzVA6HQxs0JWBpxkLkAqWkpPDEE0/w/X9KIW17EDthJkGRLfC4Sjj68VxKNi+jtLRUn16bsMVbDvPg62vIL60gNsLB3344iIs6t7C6LJF6p6tCRBpQYWEhUVFRp4QLm7MZseNnENaxPwCd3Xv5aNa9hATZNV3exLgqPDz5yRaeXVZ5xc/A9s2Yd+dgWkWHWlyZSMNQsBBpYFXnRJzCsBE94g6aXXI7GAZ92kbRLvu/vJD+eI39Gep1Yb3awt7uo0X88vU1rN2bB8CPh3fgket6EhJkP8t3FPEf2mMh0sBOezIqYGByz9B4brhnGNPeyGTDvnzWufsR1ncshZkfecdVdeus/r2k4ZzuVNLp06dzc/Kf2RjWl8KyCqLDgvnLzf24pk8rCysVadw0YyHiY2da4tiTk8+wyU8T2nEAAMXbv+HoR3/FU5zrfb6aKDW808022UIjibnyF4T3Hg3AsI4xzLl9AG2ahZ3mO4j4Py2FiDRCld06k4kcPJ7mo3+CEeTAXZTLsU8yKN76pXec2j43nNNdNhzW5SJaXD0Ze0RzTI+bghX/Zu+iF3CGaT+FBK567byZkZFBp06dCA0NZfDgwXz++efnXahIIKns1mlSsHohB/45DdfhndjDmxF346+Im/gr7OHNq42rfNObM2cOU6ZM0WFm9aT6qaS20AhaXJdM/M2/wR7RHFfOHg6+MoPjn7/Kc88+Y3GlIk1DnfdYvPHGG0ydOpWMjAxGjBjBs88+y7hx49i0aRPt27evjxpF/Eb1HhblObs58HIyzS65jaiLbsHZ/RJCO/Tj+OJ/0LlzYq1r/trg6VtVIc7Z81Kaj7mXoIgYTI+b/G8WkPvFq+AurzFORM6szkshF110EYMGDWLevHnex3r27MnEiROZNWvWWZ+vpRAJZKft1gkEx3WixbgphLTuBkCc5zhrX/w15Tm7T/t91B7ad377xN94dlWe95Lg8qPZ5Hw4B9f+LTXGaXlKAl297LGo+qX4n//8hxtvvNH7+IMPPkhmZiZLly495TllZWWUlZXVKCwhIUHBQgLWmS5LjRwygbjLf4LbsFeu7X/7AXlfvIqnrKjGUG3wvHAlLjdzF2/juWU7KHebeMrLyP/q3+R98xa4K2qM1estUk97LHJycnC73bRs2bLG4y1btuTgwYOnfc6sWbOIjo723hISEuryI0X8TmpqKjNmzMBur9kDwW4zuG90F34ct4eiLcsxbHaihtxAm58/R0T/a8A4+c9Vh5mdP7fH5N8rsxn9xGL+tjiLcrdJa/MoB/6eRN5Xb5wSKkCnkorUxXn1sajqh1/FNM1THqsyc+ZMkpOTvferZixEAllqaip//OMfT3tZ6pQpU8h5Zy6FHfrT/Iqf44jrQItrJhM5ZDy5y16hZNtXQM01f3XxrHSm18E0TZZuPcKfP9rM5oMFALRrHsZvru/F2F4tedjccMqeFjUtE6m7OgWL2NhY7Hb7KbMThw8fPmUWo0pISAghISHnX6GIn6rtoKqqDZ6lu9dy4MUpRA68luiRd+KI7UD8TY9QdmAructepnPnynHa5FnpTK/DLff/H099tpXl248CEB0WzJQxXbhreAdv98wzhT0ROXfntXlz8ODBNaZhe/XqxYQJE7R5U8QHTrfB03A4iRp2I1FDJ2JzVDZoGtqhGaE7l/FK2q9q/V6Bssmztn0rIe370uySOwjt0A8Ah93GpEs6MPnyrkQ7gxu6TJEmrd4aZL3xxhvcddddPPPMMwwfPpznnnuO559/no0bN9KhQwefFSYSyGp7o7Q5o4m++FaaDbkBz4k9F65DO8j7+i2KN38OpqfGeMMw+MUvfkH37t399tP3KUHMsBHWeQhRF91MaEJvAEx3OXdc1JEHxnQjIcZpYbUiTVe9nRVy2223cfToUX7/+99z4MAB+vTpw4cffnhOoUJEzk2t546UFXLv4OZMnXklD/z1LVbnhuJo2Zm4G2ZQceld5H/7AUXr/4untHIPgWmaPPNMZWOnprg84nK5eOqpp3j33XcBmDBhAg8++GCNgFTV4MoICSei75VEDrqe4OatATArXBSsXUT+12/Rqu0jJMQMsOI/QySgqKW3SCN2ps2IU6ZMIeOFl4gcdD2Rg8djd0YDlW+mRZu/oDDzI8r2fXfK96xteaQxbQB1uVxcc801LF68+JSvGYbB9OnTSU1NxTRN7pr6Gz7afJzw3pd7l4ncJQUUrvuEgpXv4C46DsDkyZN5+umnG/S/Q8Sf6KwQET9Xee7INACMoBDCe48mYsA4Qlp18Y5x5eymaNNSir9bRkVu5abr0/VkON3Gx4a8IqJ6qNm4cSNLlizhTL+a7BEtGHf/o5S06sf2w4Unv8+R3RSsXkjRpiWY5WU1nqMGVyIXRsFCxM/V1sXT0aorkQPH4ex5Kbbgk4dmle3fStHmZZRs/Yq0x/7P+yZba8OuE+prA2hVmHj55ZfJzMw8Y5AACIpuSVjXi3F2vZiQdr0wbJVXc4QE2Ti+fjEFaz+hdPfa0z5XDa5ELpyChUgAOFMoMBxOnN0vIbznpYR26O99IwYI9xTxg1G9Gdm5OVcPSsTtKq31Z9THm/LpZkhOqT8ohJC2PQht34+wLsNwxHeq8fXS7I1c3zuW9OS7+ONvH7EkHIkEEgULkQBxLm/SNmc0zu4jCe8xssanfajck1F2cBtl+zZX3vZ/h6cot8bzfbmMUFsYsoc3J7hlIiFtuhHavh8hrbtjBJ28JNT0uCnL3kDxthUUb1uBO/9IjX0TVi/niPg7BQuRAFK1rLB161aeeeaZMy4rBIVF8vbyjXyRdZx3v9lGqS30lDEVhccoz9njvV1/2TD+/NsUWkaFEhpsP813PTdFJaXEtEvEFhlHULNWBDVrhSO+E474ROwRzU+toyCH0t3rKN21hpKslXhKC2t8/fuBpzFtQBXxNwoWIgGqLnsmZs+eQ8of0ghp24OQtj0JaduT4Nj2GEbtxwg1cwbTKiqU6LBgwkOCcDrsOB12QoLsuE0Tj8ekwmPi9pgUlFaQW+wit6Sc3OJyjhaWYnL69v+mx035sX24DmVRlr2B0t3rqMg9UGsdNpuNkpISBQeRBqJgIRLAznVZ4PRdPsMIbpFAcGx7gmPbExLXge6DR3KooIzS8poNuM6Hp7yMirxDVOQepCLvEOU5e3Ad3kH54V2YFWVn/wYnaN+ESMNSsBAJcOe6LHCuMxymaZJfUsGB/BIO5ZdRUFpOsctNcVkFRS43ZRUe7IZBkN3AZhjYbRAREkxzZzDRzmCaOx28/do/+fX0B4Hz/7VTvY+FiDQcBQsROWcNtfGxtktkz0Xbtm158MEHT+m8KSINQ8FCROqkoTY+nm2GBCr3T1x22WX07t1bmzBFGgkFCxFptE43Q2IYBv3792fSpEkKEiKNkIKFiDRqujRUpGlRsBARERGfOdf379ovVhcRERGpIwULERER8RkFCxEREfEZBQsRERHxGQULERER8RkFCxEREfEZBQsRERHxGQULERER8RkFCxEREfGZoIb+gVWNPvPz8xv6R4uIiMh5qnrfPlvD7gYPFgUFBQAkJCQ09I8WERGRC1RQUEB0dHStX2/ws0I8Hg/79+8nMjISwzB89n3z8/NJSEggOztbZ5DUI73ODUevdcPQ69ww9Do3jPp8nU3TpKCggDZt2mCz1b6TosFnLGw2G+3atau37x8VFaW/tA1Ar3PD0WvdMPQ6Nwy9zg2jvl7nM81UVNHmTREREfEZBQsRERHxGb8JFiEhITz66KOEhIRYXYpf0+vccPRaNwy9zg1Dr3PDaAyvc4Nv3hQRERH/5TczFiIiImI9BQsRERHxGQULERER8RkFCxEREfEZvwwWjz/+OJdccglOp5NmzZpZXY5fycjIoFOnToSGhjJ48GA+//xzq0vyO8uWLWP8+PG0adMGwzB45513rC7J78yaNYuhQ4cSGRlJfHw8EydOZMuWLVaX5XfmzZtHv379vM2ahg8fzkcffWR1WX5v1qxZGIbB1KlTLfn5fhksXC4Xt956K/fff7/VpfiVN954g6lTp/LII4+wZs0aRo0axbhx49izZ4/VpfmVoqIi+vfvz9y5c60uxW8tXbqUBx54gBUrVvDpp59SUVHB2LFjKSoqsro0v9KuXTv+/Oc/s2rVKlatWsWYMWOYMGECGzdutLo0v7Vy5Uqee+45+vXrZ1kNfn256UsvvcTUqVPJzc21uhS/cNFFFzFo0CDmzZvnfaxnz55MnDiRWbNmWViZ/zIMgwULFjBx4kSrS/FrR44cIT4+nqVLl3LppZdaXY5fi4mJIS0tjZ/+9KdWl+J3CgsLGTRoEBkZGfzxj39kwIABzJkzp8Hr8MsZC/E9l8vF6tWrGTt2bI3Hx44dy5dffmlRVSK+kZeXB1S+6Un9cLvdzJ8/n6KiIoYPH251OX7pgQce4LrrruPKK6+0tI4GP4RMmqacnBzcbjctW7as8XjLli05ePCgRVWJXDjTNElOTmbkyJH06dPH6nL8zvr16xk+fDilpaVERESwYMECevXqZXVZfmf+/Pl8++23rFy50upSms6MxWOPPYZhGGe8rVq1yuoy/d73j7o3TfOUx0SaksmTJ7Nu3Tpef/11q0vxS927dyczM5MVK1Zw//33M2nSJDZt2mR1WX4lOzubBx98kFdeeYXQ0FCry2k6MxaTJ0/m9ttvP+OYjh07NkwxASg2Nha73X7K7MThw4dPmcUQaSqmTJnCwoULWbZsGe3atbO6HL/kcDjo0qULAEOGDGHlypU89dRTPPvssxZX5j9Wr17N4cOHGTx4sPcxt9vNsmXLmDt3LmVlZdjt9garp8kEi9jYWGJjY60uI2A5HA4GDx7Mp59+yo033uh9/NNPP2XChAkWViZSd6ZpMmXKFBYsWMCSJUvo1KmT1SUFDNM0KSsrs7oMv3LFFVewfv36Go/dfffd9OjRg4cffrhBQwU0oWBRF3v27OHYsWPs2bMHt9tNZmYmAF26dCEiIsLa4pqw5ORk7rrrLoYMGcLw4cN57rnn2LNnD/fdd5/VpfmVwsJCtm/f7r2/c+dOMjMziYmJoX379hZW5j8eeOABXnvtNd59910iIyO9M3HR0dGEhYVZXJ3/+NWvfsW4ceNISEigoKCA+fPns2TJEj7++GOrS/MrkZGRp+wPCg8Pp0WLFtbsGzL90KRJk0zglNvixYutLq3J+9vf/mZ26NDBdDgc5qBBg8ylS5daXZLfWbx48Wn//k6aNMnq0vzG6V5fwHzxxRetLs2v3HPPPd7fF3FxceYVV1xhfvLJJ1aXFRAuu+wy88EHH7TkZ/t1HwsRERFpWE3mqhARERFp/BQsRERExGcULERERMRnFCxERETEZxQsRERExGcULERERMRnFCxERETEZxQsRERExGcULERERMRnFCxERETEZxQsRERExGcULERERMRn/h8j0KjPQ/8/LwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 50\n", + "lb , ub = -1 , 4\n", + "delta = 0.01\n", + "dx = np . random . uniform ( low = -1 , high =4 , size =( n ,) )\n", + "dy = 2 -3* dx + dx **2+ np . random . uniform ( low = - delta , high = delta , size =( n ,) )\n", + "plt . plot ( dx , dy ,'ko')\n", + "\n", + "m = 2\n", + "a = RegressionPolynomiale(dx, dy, m)\n", + "\n", + "x = np.linspace(lb, ub, 500)\n", + "y = np.zeros(len(x))\n", + "\n", + "print(a)\n", + "for i in range(m, -1, -1):\n", + " y += x**i * a[i]\n", + "\n", + "plt . plot ( dx , dy ,'ko')\n", + "plt.plot(x, y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3b432d7f-8e74-4629-bec4-84d7d8c20fb0", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION5.ipynb b/QUESTION5.ipynb new file mode 100644 index 0000000..b521214 --- /dev/null +++ b/QUESTION5.ipynb @@ -0,0 +1,163 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 9, + "id": "32325121-b5c7-40fc-9ef2-e09b561fd5bb", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "8bcd6e56-07dc-47fe-8fb5-3d107a463f3d", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def fouriergeneral(dx,dy, n=3):\n", + " A = np.zeros((len(dx),1 + 2*n))\n", + " for i in range(len(dx)):\n", + " A[i, 0] = 1\n", + " for j in range(n):\n", + " w = np.pi * (j+1)\n", + "\n", + " A[i, 1 + (j)*2] = np.sin(w * dx[i])\n", + " A[i, 2 + (j)*2] = np.cos(w * dx[i])\n", + " \n", + " a = np.linalg.solve(A.T @ A, A.T @ dy)\n", + " \n", + " return a" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "ff9aba98-48df-4c92-929d-152f74382589", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def fourierparticulier(dx, dy):\n", + " return fouriergeneral(dx, dy, 3)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "3b5cd02c-7599-46cf-8024-8dba07ff1376", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "dx = np . arange (0 ,2 ,0.1)\n", + "dy = np . concatenate (( - np . ones (10) , np . ones (10) ) )\n", + "plt . plot ( dx , dy ,'ob')\n", + "\n", + "\n", + "a = fouriergeneral(dx, dy, 3)\n", + "x = np.linspace(0, 2, 500)\n", + "y = np.zeros(len(x))\n", + "y += a[0]\n", + "\n", + "for i in range(3):\n", + " w = np.pi * (i+1)\n", + " y += a[1 + i*2] * np.sin(w * x) \n", + " y += a[2 + i*2] * np.cos(w * x) \n", + "\n", + "plt.plot(x, y)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "d2cf6462-d6fa-4ac6-897c-9d851a2c464f", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "dx = np . arange (0 ,2 ,0.1)\n", + "dy = np . concatenate (( - np . ones (10) , np . ones (10) ) )\n", + "plt . plot ( dx , dy ,'ob')\n", + "\n", + "n = 8\n", + "a = fouriergeneral(dx, dy, n)\n", + "x = np.linspace(0, 2, 500)\n", + "y = np.zeros(len(x))\n", + "y += a[0]\n", + "\n", + "for i in range(n):\n", + " w = np.pi * (i+1)\n", + " y += a[1 + i*2] * np.sin(w * x) \n", + " y += a[2 + i*2] * np.cos(w * x) \n", + "\n", + "plt.plot(x, y)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "faf237f8-27dc-4219-a7bf-2e83cbbcc346", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION6.ipynb b/QUESTION6.ipynb new file mode 100644 index 0000000..dc90048 --- /dev/null +++ b/QUESTION6.ipynb @@ -0,0 +1,122 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "id": "4948da38-6b41-4090-b0f9-a5ab509809d1", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "3a0c01e6-6655-45da-be0e-75a81f494976", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f(x):\n", + " return np.sin(2 * x)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "b438251c-2f39-4003-9569-35496cd8773e", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def bissection(fct,a,b,tol=1e-6):\n", + " m = (b-a)/2\n", + " k = 0\n", + " while abs(b-a) > tol:\n", + " # milieu\n", + " m = (a+b)/2\n", + " f = fct(m) \n", + " if f * fct(a) < 0:\n", + " b = m\n", + " else:\n", + " a = m\n", + " k+=1\n", + " if k >= 100:\n", + " break\n", + " return m" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "ad6f3b5e-a979-47da-95e7-d25e0c4fb9b1", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(-5, 5, 500)\n", + "y = f(x)\n", + "\n", + "plt.plot(x, y, color='b')\n", + "\n", + "h = 0.12\n", + "xi = np.arange(-5, 5, h)\n", + "for x1 in xi:\n", + " x2 = x1 + h\n", + " if f(x1) * f(x2) > 0:\n", + " continue\n", + " x0 = bissection(f, x1, x2)\n", + " plt.plot([x0], [0], 'ro')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "582faece-8f7b-4af0-8911-7218283dfb3d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION7.ipynb b/QUESTION7.ipynb new file mode 100644 index 0000000..152ebc2 --- /dev/null +++ b/QUESTION7.ipynb @@ -0,0 +1,174 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "83556834-6ac7-4721-8121-4189de0b13d0", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import math\n", + "from matplotlib . colors import ListedColormap\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "a151b08e-688f-4a07-95c1-c0ad95232e0e", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def f(x):\n", + " y = np.array([\n", + " x[0]**5 - 10*x[0]**3 * x[1]**2 + 5 * x[0] * x[1]**4 - 1,\n", + " -5 * x[0]**4 * x[1] + 10 * x[0]**2 * x[1]**3 - x[1]**5\n", + " ])\n", + " \n", + " J = np.array([\n", + " [5*x[0]**4 - 10*3*x[0]**2 * x[1]**2 + 5 * x[1]**4, -10*x[0]**3 * 2 * x[1] + 5 * x[0] * 4 * x[1]**3 ],\n", + " [-5 * 4 * x[0] ** 3 * x[1] + 10 * x[0] * 2 * x[1]**3, -5 * x[0]**4 + 10 * x[0]**2 * x[1] ** 2 * 3 - 5*x[1]**4]\n", + " ])\n", + " \n", + " return y, J" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "214d1930-4c0e-4aab-ae5e-bdc44dc3cd90", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def NewtonRn(fct,x0,tol=1e-6):\n", + " k = 0\n", + " x = x0\n", + " f, df =fct(x)\n", + " # f, df = fct(x)\n", + " # print(\"f=\",f,\"df=\", df, \"|f|=\",np.linalg.norm(f), tol)\n", + " while np.linalg.norm(f) > tol:\n", + " f, df = fct(x)\n", + " dfI = np.linalg.inv(df)\n", + " x = x - f@dfI\n", + " \n", + " k+=1\n", + " if k > 10:\n", + " break\n", + " \n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "59abd31c-26b5-4a71-9668-ecef255d54a4", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.30901699 0.95105652]\n" + ] + } + ], + "source": [ + "p = np.array([1, 1])\n", + "\n", + "# print(f(p))\n", + "\n", + "x0 = np.array([1,1])\n", + "xroot = NewtonRn(f, x0)\n", + "print(xroot)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "4370d5c6-b098-484b-a577-9ce86ada4f02", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Erreur pour x0 = [0. 0.]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# fonction a utiliser si on souhaite tracer les bassins d’attraction d’une fonction f\n", + "def plot_newton_fractal (f , roots , h =0.007 , domain =( -2 , 2 , -2 , 2) ) :\n", + " colors = ['b', 'r', 'g', 'y','m'] # Liste de couleurs\n", + " xmin , xmax , ymin , ymax = domain\n", + " nbpixelsY = math . ceil (( ymax - ymin ) / h )\n", + " nbpixelsX = math . ceil (( xmax - xmin ) / h )\n", + " image = np . zeros (( nbpixelsY , nbpixelsX ) )\n", + " for j in range ( nbpixelsX ) :\n", + " for i in range ( nbpixelsY ) :\n", + " x0 = np . array ([ xmin + j *h , ymin + i * h ])\n", + " try:\n", + " r = NewtonRn (f , x0 ) #On appelle la methode ici !\n", + " if r is not False : image [i , j ] = np . argmin ( np . linalg . norm ( roots -r , axis =1) )\n", + " except:\n", + " print(\"Erreur pour x0 = \", x0)\n", + " plt . imshow ( image , cmap = ListedColormap ( colors [: len( roots ) ]) , origin ='lower')\n", + " plt . axis ('off')\n", + " plt . show ()\n", + "# Definition des racines et trace des bassins d’attraction\n", + "roots = np . array([[ -0.809 , -0.587] ,[0.309 , -0.951] ,[1.000 ,0.000] ,[0.309 ,0.951] ,[ -0.809 ,0.587]])\n", + "x = plot_newton_fractal (f , roots, h=0.05 )\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c3811318-c08f-4fcc-8e6a-f35d9958548f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION8.ipynb b/QUESTION8.ipynb new file mode 100644 index 0000000..d6c47ad --- /dev/null +++ b/QUESTION8.ipynb @@ -0,0 +1,258 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 9, + "id": "cd0f878e-2083-45d6-9537-13801b9f4ee9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "2aa18b72-6f8f-4512-8fe4-c29a3c3b17c3", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "relax=1/10" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ee56c13e-1946-47d3-8bdc-3045dc591009", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def fexamen(x):\n", + " f = np.array([ \n", + " x[0]**2 + x[1]**2 - 9 , \n", + " -x[0] + x[1] - 1\n", + " ])\n", + " J = np.array([\n", + " [ 2*x[0], 2*x[1] ],\n", + " [ -1, 1]\n", + " ])\n", + " \n", + " return f, J" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "ca6950a5-a648-4654-98c2-b692750c30e9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def NewtonRnRelax(fct, x0, tol=1e-6):\n", + " k=1\n", + " x=x0\n", + " listX = []\n", + " fx, Jx = fct(x)\n", + " \n", + " while np.linalg.norm(fx) >= tol and k < 1000:\n", + " listX.append(x)\n", + " # JxInv = np.linalg.inv(Jx)\n", + " # x = x - (relax * np.dot(JxInv, fx))\n", + " x = x - (relax * np.linalg.solve(Jx, fx))\n", + " \n", + " fx, Jx = fct(x)\n", + " k+=1\n", + " \n", + " listX.append(x)\n", + " return listX\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "id": "3c9a95c9-40d7-4efa-93d2-01067473e8b8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.56155298 2.56155289]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x0 = np.array([10, 0]) \n", + "l = NewtonRnRelax(fexamen, x0)\n", + "print(l[-1])\n", + "theta = np.linspace(0, 2*np.pi, 40)\n", + "r = 3\n", + "x=r*np.cos(theta)\n", + "y=r*np.sin(theta)\n", + "plt.plot(x,y)\n", + "\n", + "# tracé droite\n", + "x = np.linspace(-5, 5, 40)\n", + "y=x+1\n", + "plt.plot(x,y)\n", + "\n", + "plt.plot([x[0] for x in l], [x[1] for x in l], 'or')\n", + "\n", + "plt.xlabel('x1')\n", + "plt.ylabel('x2')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "e5402726-5acd-4c1a-9a1d-c6cebc91da0c", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Intersection du cercle et de la droite: [1.56155298 2.56155289]\n" + ] + } + ], + "source": [ + "# Intersection cercle et droite\n", + "\n", + "print(\"Intersection du cercle et de la droite:\", l[-1])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "2be93022-5a6c-436a-bcaa-c88cb1b89501", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-2.56155291 -1.56155295]\n" + ] + }, + { + "data": { + "image/png": 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509BttKabxBIqNSIiUnUuF6z8D3z3JBhOqHsOjJoNDTpYnUx8mEqNiIhUTX4mfHor7P7WHHe6Bgb/B4LCrc0lPk+lRkQ8gstlcKywhKz8EvKKSwnwsxMUYCfQz05QgB9B/nYC/e3mP/3s2DT9UTP2roBPxkF+BviHwOBnIekGTTeJW1CpERHLuFwGRwtLyMp3kJV3/J/5DjLzHGTmO8jKLyErz3zsSEEJTpdR6ff+reSYhad8HOBH0PFC9L/PiQoNoHm9MJrHhtO8XhgxYYEqRye4nPD9M7D8aTBcENvG3N1Uv63VyUTKqdSISI3IKy5lc1ouGblFZOWVmCXl92Ul38HRKhYVgOjQAKJCAihzGjjKnDhKXTicLkrKXCc9z1HmwlHmIo+yM/7fEBUSQPPYMJrXC6d5bBgtYs3C07RuKEH+fmf8vh4n7xDMGwd7vzfHSTfCoH9DYJi1uUT+h0qNiJy1MqeLHYfySU7NJjn1GMmp2ew8nI9Ryb4SExZIvfBA6oUH/fYRYY5jI4KIPf5YTFgggf72Ct/D5TIocboocbrMolPmpOR4sXGUuXCUOn/3ORclTudv/17morjUSVa+gz1ZBezJLCAtu4icolLWp2SzPiX7pK9lt0F8ndCTCo9ZesKpHxHkXVd3dn8H88ZDQSYEhMEV/4HO11qdSqRCKjUiUmUZOcUkpx5jfWo2ySnZbErLobDE+YfnxdcJoWnd0PJSUi/iRGn5rbDEhAUS4FdxUakKu91GsN2P4AA/CD7rt6OoxMnerAL2ZOWzJ7OAPZn55YUn31FGytFCUo4Wsmx75kmvCwv0o3lsOM3qmUWnZf0IzmseQ93woLMPVZucZbBsKqx4DjCgfntzuim2ldXJRE7JZhiV/buU58vNzSUqKoqcnBwiI3UolEhlFJaUselAzvGrMObHwZziPzwvPMifzglRdEmoQ1JCNJ0ToomN8LBf5JVgGAaZ+Y7jRef3ZSeflKOFVDSbZrNBx8ZR9GsVS//WsXSOj8a/GopcjclNNxcD7//BHHcbA5dNhYAQa3OJz6rs72+VGhEp53IZ7MnK55eU4wUmJZvth/L+sO7FboPWDSJJSoimS0I0XZpE0yI2HLvdi6ZdzkBJmYuUowXs/l3h2Zyey68Hc096XmSwPxe0jKVf61j6tYolLrIaLi1Vl51fm9u1C49AYARc+QJ0HGl1KvFxKjUVUKkR+aO84lK+2JzBok0HWbf/GHnFf1xYGxcZZF6BaRJNUkI0HRtHERak2evKOpxbzPIdmSzfkcmKnVnkFJWe9Pm2DSPp18osON2a1jnluqEa5SyFb5+AH14wxw06mdNNdVvUfhaR/6FSUwGVGhGTo8zJsu2ZLEhO4+tfD5+0cyg4wE6nxubVl6SEaJKaRNMwStMO1cXpMkhOzS4vORsPZJ+0oDo8yJ/eLerSr3Us/VvXp3F0LXzvcw6Yd9ZOXWOOe4yHgU9AgBtdQRKfplJTAZUa8WUul8HqvUf4LDmdxZsOkvu7KzItYsMYltSYAW3q06ZBhHuv9/AyR/IdrNyVxfLtZsk5UlBy0ufPqR9O/1bmVFWPxBhzIXR12r4E5t8ORccgKAqGvgzthlbv1xA5Syo1FVCpEV9jGAZb0nP5bEM6nyWnk5H72wLfuMgghnRuxNCkxrRvFOld25A9lMtl/v+1fMdhlm3P5JeUYyctPA4J8KNXi7oM7tiQKzo3PLuzcspK4JvH4MdXzHGjrjDyLYhpdnb/I0RqgEpNBVRqxFekHClkQXIaCzaks+twfvnjkcH+DOrYkCFJjejZrC5+Pr6w193lFJbyw+4slm0/zPIdmRzKdZR/rl54INef24Qbzmta9YXGx/aZ001p68zxeXfAxY+Bf2D1hRepRio1FVCpEW+Wle9g0caDzE9OO+mwuEB/Oxe3rc/QpMb0bx3rWyfhehHDMNh+KI+lWw7x/pqU8qtu/nYbgzs1ZHTvRLo0qfPnb/TrQpg/ERw5EBwFw16DNoNrOL3I2VGpqYBKjXibfEcZS7dksCA5nZW7ssq3Xttt0Oecegzp3IjLOjQgIjjA4qRSnUqdLpZuOcSsVXtZu+9Y+eOdE6IZ0zuRQR0b/nEHVZkDlv4DfnrdHMf3MKebopvUYnKRM6NSUwGVGvEWqUcLeeXbXSzYkEZx6W87lzrHRzE0qTFXdGpIfXc6+0RqzOa0HGb+sI+FG9IpcZo/C7ERQdzQswk39GxqHoB4dA/MGQMHk80X9b4bLnoE/FR2xTOo1FRApUY83cGcIl75dhcf/5xKqdP8T7d5vTCGJjVmSFIjmtXTDQZ9VVa+gw/WpPDO6v0czjPX3gT42Xg4cRs3Hn4Ov9J8CImB4dOg1aUWpxWpGpWaCqjUiKfKzHPw6rJdvLcmpfxMmQta1mPSxS3p2qSOdi5JuZIyF19syeC9ldu58uDL3Oj/DQBbA9qTdtEr9O+RVC332hKpTZX9/a0jQUXc2LGCEl7/fg+zV+2jqNS8YeS5iTHcN7AVPZvXtTiduKNAfztDGhcyxP4P8N+ECxvTnEN5rvgqnPMPEvftUW46rynXndvE826yKfIndKVGxA3lFpfy5oq9vLVyL/kO85C8pIRo7hvYivPPqacrM3JqGz+GhZOgtABC68GI6RyO68MHa1J5d81+Mo9PTQX62xnSuRF39G9B89hwazOL/AlNP1VApUbcXYGjjFmr9jH9+z3l9wdq1zCS+wa24sI29VVm5NRKCmHJ/bD+HXOceAFc9SZENPjtKWUuFm86yMwf9rLhQA4AgX52buvXnDv6n0NIoLb7i3tSqamASo24q+JSJ++u3s9ry3aXH5Pfsn44ky9pxaXtG/j83a/lT2Ruhzmj4fBWwAb9/gb97gf7qUvK+pRjvPD1TpbvyAQgvk4Ijw1pz0Vt42ons0gVqNRUQKVG3I2jzMlHa1N55dtd5TtWEuuGcu8lrbiiUyOd+Ct/Lvl9WHQflBZCeByMeAOa96vUSw3D4MstGTy2cCsHc8zD/C5pF8ejV7Yjvk5oTaYWqRKVmgqo1Ii7KHW6mPfLAV76Zhdp2UUANI4O4Z6LWjKia2PdUFL+nCMfFv8fbPjAHDfvbxaa8PpVfqsCRxkvfbuTGSv2UuYyCA6wc/dFLRl3fvM/HuInYgGVmgqo1Ig7+HJLBlMX/8q+I4WAeWPJOy9syTXdE/QLRCrn0BZzuilrB9jsMOBBOP8+sJ/dz8+OQ3n8Y/5m1uw9Cph3b//n0A70PqdeNYQWOXMqNRVQqRErFTjKeHzhVj76ORWAumGB3DHgHG7o2YTgAC3QlEowDPjlbXNBcFkxRDSEq2ZAYp9q/BIG85PT+NeiX8nKN9d3DU1qxEOD2uqUarGMSk0FVGrEKhsPZHPPh8nszSrAZoPb+rbgrgvPISxIR0VJJTnyzK3am+ea43MuMU8HDquZqyg5RaU8t3Q776zej2FARJA/kwe24qbzmmp6VGqdSk0FVGqktrlcBq9/v4fnlm6nzGXQIDKY569JolcLHZwnVXBwoznddHQ32PzM+zb1vvusp5sqY9OBHB6ev6l8C3i7hpE8MbwDXStzR3CRaqJSUwGVGqlNGTnFTP44mVW7jwBweYcGTB3RkejQQIuTiccwDPh5BnzxIDgdEBlv3lm7Sc9ajeF0GXy4NoV/f7G9/Pyka3sk8LfL2lAnTD/PUvNUaiqgUiO15YvNGfx93kayC0sJCfBjypB2XN09QYfnSeUV58Bnd8PW+ea41eUw7FUIjbEs0pF8B08t2cacdQcAqBMawN8ua8PV3RN0lpLUKJWaCqjUSE0rLCnjn5//ygc/pQDQsXEUL16bpGPopWrSfoG5Y+DYPrD7wyWPw3l3gJuU4rX7jvKP+ZvZlpEHwKXt43j+miRCA7VGTGqGSk0FVGqkJm1Oy+HuD9ezJ9NcDHxr3+bcd0lrbdOWyjMMWPM6LH0YXKUQ1QRGzYT47lYn+4NSp4vZq/bx7y+2U+J00aFxJG/e3IMGUdohJdVPpaYCKjVSE1wugzdX7uGZL7dT6jSIiwzi+auTdLaHVE3RMVhwJ2z73By3uQKG/hdCoi2N9Wd+3neU295Zx5GCEupHBPHmX7rTKT7a6ljiZSr7+9tj/go5depUevToQUREBPXr12fYsGFs377d6lji4w7lFnPzWz/x5OJtlDoNLm0fxxf39FWhkao58DNM62sWGr9AuPwZuOZdty80AN0TY5g/sQ+t4sI5nOfg6td/ZMmmg1bHEh/lMaVm+fLlTJw4kdWrV/PVV19RVlbGwIEDKSgosDqa+Kivth7ishe+Z+WuLIID7Dw5vCPTbuym3SBSeS4XrHoZ3roUclKgTjMYuxR63uo262cqIyEmlE9u703/1rEUl7q4/b1f+O93u/ChiQBxEx47/ZSZmUn9+vVZvnw5ffv2rfA5DocDh8NRPs7NzSUhIUHTT3JWikud/PPzrby3xlwM3L5RJC9e24Vz6msxsFRB4VH4dALs/NIctx8OV74IwVHW5joLZU4X/1r8KzN/2AfAiC6NmXpVR4L8dWK2nB2vm376Xzk55kFQMTGn3t44depUoqKiyj8SEhJqK554qaISJ7fMWlteaG7t25x5d/RWoZGq2f8jTDvfLDR+QTD4PzBypkcXGgB/PzuPXtmeJ4Z1wM9uY976NK5/Yw1Z+Y4/f7FINfDIKzWGYTB06FCOHTvGihUrTvk8XamR6lRYUsbYWT/z454jhAX68dqN3ejbKtbqWOJJXC744Xn49l9gOKHuOTBqFjToaHWyardyZxZ3vLeO3OIy4uuE8NboHrSKi7A6lngor75Sc+edd7Jx40Y++OCD0z4vKCiIyMjIkz5EzkRhSRljZq7lxz1HCA/y5+2xPVVopGryM+G9kfDN42ah6Xg13LrMKwsNwPkt6/HpxD4k1g3lwLEiRry6imXbD1sdS7ycx5Wau+66i88++4zvvvuO+Ph4q+OIDyhwlDF65lrW7D1KRJA/b489l25Ndd8bqYJ9K83ppt3fgH8IDHkZRkyHIO++ctEiNpxP7+hDz2Yx5DvKuGXWWmb+sFcLiKXGeEypMQyDO++8k3nz5vHtt9/SrFkzqyOJD8h3lDF65k/8tPcoEcH+vDOup27kJ5XncsKyp2H2lZCfAfVawfhvoevNHrW76WzUCQvknbE9uaZ7Ai4DHlu4lYfnb6bU6bI6mnghjznTeuLEibz//vssWLCAiIgIMjIyAIiKiiIkJMTidOKN8opLGTNzLT/vP0ZEsD/vju1J54Roq2OJp8g7BPPGw97l5jjpBhj0DASGWZvLAoH+dp66qiPn1A/nySW/8t6aFPYfKeS/N3QlKiTA6njiRTxmofCpbgQ4c+ZMRo8eXan30InCUll5xaX85a2f+CUlm8hgf94d11OnpErl7VkGn4yHgsMQEGrubkq6zupUbuGrrYe458P1FJY4aR0XwZzbexEZrGIjp6fbJFRApUYqI/d4oVmfkk1USADvjetJh8aevdVWaomzDJY/Dd8/AxhQv525uym2tdXJ3MrW9FxGz/yJw3kOLmhZj5mje+Dv5zGrIcQCXr37SaSm5BSVctMMs9BEh6rQSBXkHoS3h8L3/wYM6PoXc/2MCs0ftGsUyVujexAS4MeKnVk8+tkWLR6WaqFSI3JcTlEpN89Yw4ZUFRqpop1fw7Q+sH8lBIbDVTNgyEsQoPV+p9KhcRQvXpuEzQbvrUnhreOnEIucDZUaESCnsJSbZqxhw4Ec6oQG8P6482jfSIVG/oSzFL6eAu9dBYVHzDNnbl0OHUdancwjDGzfgAcvbwvAE4u28s2vhyxOJJ5OpUZ8XnZhCTfMWM3GAznEhAXywa3n0a6R1lzJn8g5ALMGw8rnzXGPcTD2a6h3jrW5PMy4C5px3bkJGAbc9cF6tqbnWh1JPJhKjfi07MISbnhzDZvTcqkbFsgH48+jTQMVGvkT278wD9NLXQNBkTBqNgx+DgKCrU7mcWw2G48P7UCfc+pSWOJk7Oy1HM4ttjqWeCiVGvFZLpfBXR+sZ0t6LvXCzSs0rRt49wmvcpbKSuDLh+CDa6DoGDTqArd9D+2HWZ3MowX42Xn1+m60iA3jYE4x497+maISp9WxxAOp1IjPmrVqHyt2ZhHkb+fdcT11sz05vWP7Yebl8OMr5rjn7XDLlxCj082rQ1RoAG+N7kGd0AA2Hsjh3o+Scbm0I0qqRqVGfNL2jDye+mIbAA8NbqspJzm9XxfC6xdA2s8QHAXXvAeXPwX+QVYn8ypN64Yx/ebuBPrZ+WJLBs8s3W51JPEwKjXicxxlTu75cD0lZS76t47lpvOaWh1J3FWZAxbfDx/dCMU50Lg7TFgJba+wOpnX6pEYw9MjzTuXv7ZsNx//nGpxIvEkKjXic55buoNtGXnEhAXy75GdTnkLDvFxR/fAjIHw0+vmuPddcMsXEN3E2lw+YHiXeO6+0NxF9uC8Tfy4+4jFicRTqNSIT1m1K4s3VuwB4OmrOlE/QrtVpAKb58G0vnAwGULqwPUfw8AnwE/3KKot917Siis6NaTMZTDh3XXsycy3OpJ4AJUa8Rk5haVM/ngDhgHXnduES9rFWR1J3E1pMXx+L8wdAyV5kHCeOd3U6lKrk/kcm83Gs6M606VJNDlFpYyd/TPHCkqsjiVuTqVGfIJhGDw4fxMZucU0qxfGP65oa3UkcTdZu+DNi+Hnt8zx+ZNh9CKIirc2lw8LDvBj+k3daRwdwt6sAh75bIvVkcTNqdSIT5ifnMaijQfxs9t4/pokQgP9rY4k7mTjx/B6Xzi0CULrwo2fwMWPgp9+TqwWGxHEtBu7YbPBwg3p/LzvqNWRxI2p1IjXSz1ayCPzzb/hTbqoJUkJ0dYGEvdRUggL7oR546G0ABIvgAk/wDkXW51MfqdjfBTXdE8A4PHPt+r8GjkllRrxak6XweSPk8lzlNGtaR1u79/C6kjiLjK3w5sXwfp3ABv0+xvcvAAiG1qdTCpw38DWhAf5s/FADp+uT7M6jrgplRrxatOW72btvmOEB/nz/NVJ+PvpR16A5Pdhen84vBXC6sPN82HAg2D3szqZnEJsRBB3Ht/m/fQX2yhwlFmcSNyR/oQXr7XxQDbPf7UDgClD2tOkbqjFicRyJQXw6e0w/3YoLYTm/eH2H8x/itsb0yeRJjGhHM5zMG35bqvjiBtSqRGvVFhSxqQPkylzGQzq2ICruja2OpJY7dAW8+rMhvfBZocBD8ON8yC8vtXJpJKC/P14cJC5c3H693s4cKzQ4kTiblRqxCs9t3QHe7IKiIsM4l/DOurUYF9mGLBuNrxxIWTtgIiG8JeF0O+vmm7yQJe2j+O85jE4ylw8tWSb1XHEzajUiNc5VlDCe2v2A/DUiE7UCQu0OJFYxpFn7mxaeDeUFZu7miashMTzrU4mZ8hms/HIFe2x2eDzjQe1xVtOUqVSs2HDBp544gleffVVsrKyTvpcbm4ut9xyS7WGEzkT763ZT3Gpi/aNIunfOtbqOGKVgxvh9X6waQ7Y/ODiKXD9HAirZ3UyOUvtGkVybQ9t8ZY/qnSpWbp0Keeeey4ffvghTz/9NG3btuW7774r/3xRURGzZ8+ukZAileUoczL7R/MqzfgLmmvayRcZBqx90zwd+OhuiIyHMYvh/HvBrovT3mLyJb9t8Z6nLd5yXKX/C58yZQr/93//x+bNm9m3bx/3338/Q4YM4YsvvqjJfCJVsiA5ncw8Bw0igxncSeeN+JziHJgzGhbdB04HtLocJqyAJudZnUyqWWxEEHcd3+L9b23xluMqXWq2bNlSPr1ks9n461//yvTp0xk5ciQLFy6ssYAilWUYBjNW7AVgdJ9EAnQmjW9J+8W81cHW+WD3h4H/gus+gNAYq5NJDRmtLd7yPyr9p35QUBDZ2dknPXbdddcxY8YMrr32Wj799NPqziZSJSt2ZrH9UB5hgX5cd24Tq+NIbTEMWD0NZgyEY/sgqgnc8iX0vhM0/ejVtMVb/lelS01SUtJJa2hOuOaaa3jzzTe5++67qzWYSFW9sWIPAFf3SCAqJMDiNFIrio7BRzfCF38DVym0uQImfA/x3a1OJrXk0vZx9GpeV1u8BahCqbn99ttJS6t4MdZ1113H7Nmz6du3b7UFE6mKbRm5rNiZhd0Gt/RpZnUcqQ0HfoZpfWHb5+AXCJf/G655F0LqWJ1MapHNZuMfV7Qr3+K9OzPf6khioUqXmuHDh/P888/z9ddfV/j56667jmuvvbbagolUxYm1NJd1aEBCjG6H4NUMA1a9DG9dCjkpUCcRxi6FnrdpuslHtWsUSd+W5vENizcetDiNWKnKKykHDx7MfffdR0lJSfljmZmZXHnllTzwwAPVGk6kMg7nFbMgOR2AcRc0tziN1KjCo/DBtbD0YXCVQbthcNv30KiL1cnEYoM7mrsdF2/OsDiJWKnKpeb7779n4cKF9OjRgy1btrBo0SI6dOhAfn4+GzZsqImMIqf19qr9lDhddGtah65NNPXgtVJWw7QLYMcX4BcEg5+DUbMgOMrqZOIGLmkXh5/dxq8Hc9mbVWB1HLFIlUtNz549Wb9+PZ06daJbt24MHz6c++67j2+//ZaEhISayChySoUlZbx7/JYI487XWhqv5HLBiv/AzEGQewBiWsC4r6HHOE03Sbk6YYH0blEXgMWbNAXlq87oII/t27ezdu1a4uPj8ff3Z9u2bRQWaiud1L5Pfkkju7CUJjGhDGzfwOo4Ut0KsuD9UfDNY2A4oeMouG05NOxkdTJxQ+VTUCo1PqvKpeapp56iV69eXHLJJWzevJm1a9eWX7n58ccfayKjSIVcLoO3VpoLhG/pk4ifXX9r9yr7VsK082HX1+AfDENehhFvQFCE1cnETQ1s3wA/u40t6bnsP6IpKF9U5VLz4osvMn/+fF5++WWCg4Np3749P/30EyNGjKB///41EFGkYl//eoi9WQVEBvszqrumPr2GywnLn4HZV0LeQajXCsZ/B11v1nSTnFZMWCC9mptTUIt0tcYnVbnUbNq0icsvv/ykxwICAnjmmWdYunRptQUT+TOfbTB3PF13bhPCgvwtTiPVIu8QvDMcvnsCDBd0vh5uXQZx7axOJh5i0PEpqCWbtAvKF1W51NSrV++Un+vXr99ZhRGpivUp2QD0axVrbRCpHnuWmdNNe5dDQCgMew2GvwaBYVYnEw8ysH0cdhtsSssh5YjWevoa3fFPPNLhvGLSsouw2aBjvLb0ejSXE757Et4eBgWHoX478+pM0vVWJxMPVC88iPOOT0Et3qwpKF+jUiMeKfn4VZpW9SOICNZ9njxW7kGYPQSWPw0Y5rqZcd9AbGurk4kH+20KSqXG16jUiEdan5oNQJcm0ZbmkLOw62uY1gf2r4TAcBjxprnDKVC3uZCzc2n7BthtsOFADqlHNQXlS1RqxCOtTzkGqNR4JGcZfD0F3r0KCo9AXEe4dTl0GmV1MvESsRFBnNssBoAlmoLyKSo14nHKnC42HsgBoItui+BZcg7ArMGw8nlz3GOceTpwvXOszSVe58RBfIu0C8qnqNSIx9lxKJ/CEicRQf6cExtudRyprB1fmrubUldDUKR536bBz0FAsNXJxAtd2qEBNhtsSM3mwDFNQfkKlRrxOMnH19N0SojCrlOE3V9ZCXz5ELx/NRQdg4ZJ5q0O2g+3Opl4sfoRwXRJiAbgp71HrQ0jtUalRjxO+XqaBE09ub1j+2Hm5fDjK+a45wQYuxRimlubS3xCYj3zjKODOcUWJ5HaomNYxeNo55OH+PVzWHAHFOdAcBQMfRXaXmF1KvEhDaPMqc1DuSo1vkKlRjxKTlEpuw7nA5B0/NKyuJkyB3z1CKyZZo4bd4eRb0GdptbmEp/TICoE0JUaX6JSIx5lw/GrNE3rhlI3PMjaMPJHR/fAnDFwMNkc97oTLnoU/AMtjSW+qUGkeaUmQ6XGZ6jUiEc5cb+nLrpK4362fAqf3Q2OXAipY967qfXlf/46kRpyYvopQ9NPPkOlRjxKcqq5SFhTT26ktBi+fBB+nmGOE86DkTMgKt7aXOLzGhwvNVn5DkrKXAT6a2+Mt1OpEY9hGMbvFglr55NbOLIb5vwFMjaZ4/PvhQEPgZ/uxyXWiwkNJNDPTonTxeG8YuLr6BYc3k6lRjxGVn4J2YWl2GzQtmGk1XFk01xYeA+U5ENoXRg+HVpebHUqkXJ2u424qCBSjxaRkaNS4wtUasRjGIYBgN1m02VkK5UWwZL74Ze3zXHT8+GqNyGyobW5RCrQIDLYLDVaV+MTVGpEpPIyt8Oc0XB4K2CDvn+Ffn8DP/1RIu7J3NZ9TDugfIT+JBKRykn+ABZNhtJCCKsPI6ZDiwFWpxI5rRM7oHRWjW9QqRGR0yspgMV/heT3zHGzfjDiDYiIszaXSCXorBrf4nELE1599VWaNWtGcHAw3bp1Y8WKFVZHEvFeh7bC9AFmobHZzZ1NN32qQiMeo4HOqvEpHlVqPvroIyZNmsRDDz3E+vXrueCCC7j88stJSUmxOpqIdzEMcyHwGxdC1naIaAh/WQj97ge7n9XpRCqtvNToSo1P8KhS85///IexY8cybtw42rZtywsvvEBCQgKvvfaa1dFEvIcjD+bdCp/dBWVF0OIimLASEs+3OplIlZ1YU5OWXcSRfIfFaaSmecyampKSEtatW8ff//73kx4fOHAgq1atqvA1DocDh+O3H+Lc3NwazSji8TI2mbubjuwCmx9c+DD0mQR2j/r7j0i5mLDf7jt2MKdY94zzch7zJ1VWVhZOp5O4uJPn8uPi4sjIyKjwNVOnTiUqKqr8IyEhoTaiingew4C1M+CNi8xCE9kYRi+CCyar0IhHO1ZQWv7vcccXDYv38rg/rWw220ljwzD+8NgJDzzwADk5OeUfqamptRFRxLMU58DcMeZ2bacDWl1mTjc17WV1MpGzdmKBcKOoYGIjdJXG23nM9FO9evXw8/P7w1WZw4cP/+HqzQlBQUEEBemHWOSU0tfDnDFwbC/Y/eHiKdDrTjjFXxREPE1GThHw24Jh8W4ec6UmMDCQbt268dVXX530+FdffUXv3r0tSiXioQwD1rwOMwaahSaqCYz5AnrfpUIjXuXEoXsqNb7BY67UAEyePJmbbrqJ7t2706tXL6ZPn05KSgoTJkywOpqI5yg6BgvuhG2fm+M2V8DQVyBEdz4X73NiK3eDyBCLk0ht8KhSc80113DkyBEef/xxDh48SIcOHVi8eDFNmza1OpqIZziwDuaOhuwUsAfAwCeg5226OiNe68SVmoa6UuMTPKrUANxxxx3ccccdVscQ8SyGAT/+F75+FFxlUCcRRs6Exl2tTiZSo04sFI5TqfEJHldqxHed2OXmMgxKnS4C/DxmSZi1Co/C/DtgxxJz3G4YDHkJgqMsjSVSGzJ0pcan6LeCeIy6YYFEBvtjGLA9I8/qOJ4hZQ1Mu8AsNH5BMPg5GDVLhUZ8gmEYv1tTo1LjC1RqxGPY7TaSmpiLWdenHLM4jZtzuWDl8zDzcsg9ADEtYNzX0GOc1s+IzzhaUEKJ0wXo4D1foVIjHqVLQjQA61OyLc3h1gqy4P2r4espYDih4yi4bTk07GR1MpFadWKRcL3wQAL99evOF2hNjXiULk2iAVifmm1pDre17wf4ZCzkHQT/YBj0DHS5SVdnxCcdytUZNb5GpUY8StLxKzV7swo4VlBCnd/drM6nuZyw8j/w3ZNguKBea3PtTFw7q5OJWOagzqjxOboeJx4lOjSQ5rFhACQfyLY2jLvIPwzvjoBvnzALTefr4dbvVGjE55UvEo7S7XJ8hUqNeJwkrav5zZ7lMO182LMMAkJh2Gsw/DUIDLM6mYjlfjt4T1dqfIVKjXicLtoBZU43ffckvD0U8g9B/XZw6zJIut7qZCJuI+VoAaDt3L5Ea2rE45zYAZWcmo3LZWC3+9gi2NyDMG887FthjrveDJc9DYGh1uYScSNZ+Q7W7Tf/4tMjMcbiNFJbVGrE47RpEEFwgJ284jL2ZOVzTv0IqyPVnl3fwLxboTALAsPhiheg0yirU4m4nS+3ZOAyoGPjKJrUVeH3FZp+Eo/j72enU3w0AL/4yroaZxl8/Zi5ILgwC+I6wq3LVWhETmHJpgwALu/YwOIkUptUasQjnTivJtkXzqvJSYPZV5hbtgG6jzVPB653jrW5RNzU0YISftxzBIDBHRtanEZqk6afxCP5zMnCO76ETydA0VEIjDBvRNlhhNWpRNzal1sycLoM2jeKpGld7QT0JSo14pFO7IDanpFLgaOMsCAv+1F2lsI3j8Gql81xw87mYXoxzS2NJeIJFm86CMAgXaXxOZp+Eo8UFxlMo6hgXAZsPJBjdZzqlZ1i3ojyRKE59zYY+5UKjUglHCsoYdVuc+pJpcb3qNSIxzpxtWbFzkyLk1SjbYvMw/QOrIWgKLj6HRj0b/DXiagilbF0qzn11LZhJM3qaerJ16jUiMe6opP5t7APfkqhqMRpcZqzVFYCS/4OH14PxTnQuBtM+B7aDbE6mYhHWXx819OgDtr15ItUasRjDWzfgISYEI4VlvLJLwesjnPmju6FtwbCmtfMca87YcwXUCfR0lginia7sIQfdmUBMKiTpp58kUqNeCw/u41b+jQD4K2Ve3G5DIsTnYEt8+H1vpC+HkLqwHUfwqX/An/dfVykqpZuPUSZy6BNgwhaxIZbHUcsoFIjHu3q7glEBPuzJ6uAb7YdtjpO5ZUWw6L7YM5fwJELCT3hthXQ+nKrk4l4rCXa9eTzVGrEo4UF+XN9zyYAvLlij8VpKunIbphxCax90xyffy+MXgTRCdbmEvFgOUWlrDwx9aRThH2WSo14vNG9E/G321iz9yib3H1796a55nRTxkYIrQs3fAIXTwG/AKuTiXi0r7YeotRp0Cou3LfuBycnUakRj9cwKoQrOzcC4A13vVpTWgSf3Q2fjIWSfGjaByashJYXW51MxCto6klApUa8xNjzzQXDizYdJD27yOI0/yNzB7xxEfwyG7BB37/CzZ9BZCOrk4l4hZ2H8li2wzyvSqXGt6nUiFfo0DiKXs3r4nQZzFq1z+o4v0n+AKb3g8NbIKw+3PQpXPgw+HnZbR1ELGIYBo9/vhWny2BguzhaxWnqyZep1IjXGN/XvFrzwZoU8opLrQ1TUgDz74D5E6C0EJr1NaebWgywNpeIl1m2PZMVO7MI8LPx0OC2VscRi6nUiNfo36o+LWLDyHOU8fHPFh7Gd/hXeONCSH4PbHYY8BDcNB8i4qzLJOKFSp0u/rloKwC39GmmO3KLSo14D7vdxtjzzZs+vrVyL2VOV+0GMAz45W2YPgAyt0F4A3PtTL/7we5Xu1lEfMA7P+5nT2YBdcMCmXjhOVbHETegUiNeZUTXxtQNCyQtu4gvtmTU3hd25MG8W+Gzu6CsCFpcaE43Nbug9jKI+JBjBSW88PUOAP7v0tZEButYBFGpES8THODHjec1BeCNFXsxjFq4dULGJpjeHzZ9DDY/uOhR8/yZ8Nia/9oiPur5r3eQW1xGmwYRXN1dB1eKSaVGvM5NvZoS6G9nQ2o2q3YfqbkvZBiwdoa5XfvILohsbJ4MfMFksOs/LZGasuNQHu+tSQHgkSvb4We3WZxI3IX+5BWvUy88iGt7mH9zu3/uRnJrYidUcS7MHQOLJoPTAS0vNe/d1LRX9X8tESlnGAb/PL6F+9L2cfRuUc/qSOJGVGrEK91/WRuaxISSll3Eowu2VO+bp683b3Ww5VOw+8Ml/zTvrh1Wt3q/joj8wXfbD5dv4X5wkLZwy8lUasQrhQf58/w1nbHb4NP1aXy2If3s39QwYM10mDEQju2FqCYw5gvoc7emm0RqQanTxROf/wpoC7dUTH8Si9fq1jSGOweY2zwf/nTT2d0+oSgbPr4JlvwVnCXQejBM+B4SelRPWBH5U2//uJ89WQXUCw/kTm3hlgqo1IhXu+uilnROiCa3uIz7Pt6Ay3UGu6EOrIPXL4BfF4I9AC57Cq59D0LqVH9gEanQ0YISXjy+hfu+ga2J0BZuqYBKjXi1AD87L1yTREiAHz/uOcKbK6twF2/DgB//C29dCtkpEN0Uxn4J590ONu22EKlNLxzfwt22YaS2cMspqdSI12tWL4xHrmwHwDNfbmdreu6fv6jwKHxwHXz5ILhKod1QmLACGner4bQi8r+2ZeSWb+H+xxVttYVbTkmlRnzCtT0SuKRdHKVOg3s+XE9xqfPUT079ydzdtGMJ+AXCoGdh1GwIjqq9wCICmCcHT3hnnbZwS6Wo1IhPsNlsPDWiI/XCg9h5OJ+FDZqbU0gnPjp2BJcLVr4Ab10GOakQ0xzGfQ3njtd0k4gFHGVObnt3HfuOFNI4OoQnhnW0OpK4OX+rA4jUlrrhQTwzqhN928T9sc1v3gx+fvBopDnucBVc8QIER9ZyShEB85C9B+dt5qe9R4kI8mfmmB7ERgRZHUvcnEqN+JQBbeIwgFNed3ksF36eCV3/oqszIhZ6ddluPvnlAH52G6/c0JVWcRFWRxIPoOkn8R3HS8qfVpXRz6nQiFho8aaDPPPldgCmXNmOfq10c1ipHJUa8Q1NmlT+uZs311wOETmt5NRs7v0oGYDRvRO5qVeipXnEs6jUiPfr2hVSU61OISJ/Ii27iHGzf8ZR5uLCNvX5xxXtrI4kHkalRrzbkCGwfr3VKUTkT+Q7yhg7ay1Z+Q7aNIjgpeu66DwaqTKVGvFeH3wACxdanUJE/kSZ08Vd7//Ctow86oUHMWN0D8KDtI9Fqk6lRrzTnDlw/fVVfpkB7N5zsPrziMgpPbHoV77bnkmQv503/9KdxtEhVkcSD6VSI95n3jy4+uoqv8wANsSdw7Xvb2bX4fzqzyUif/DOj/uYtWofAM9fk0RSQrSlecSzqdSId3E64eabz+ilrvpx/P3vM8jMc3Dt9NXsOpxXzeFE5PeW78hkysKtAPz10tYM6tjQ4kTi6VRqxLtcdx0UFFT9dYMG4Xcog/fHn0fbhpFk5ZvFZuchFRuRmrA9I4873/sFp8vgqq7x3NG/hdWRxAuo1Ij3uHeSuZamqiZNgkWLAIgJC+T9cT1p1zCSrPwSrp2+mu0ZKjYi1WnX4XxumbWWPEcZPZvFMHVER2w68FKqgUqNeIeJ4+CFF6v+usmT4fnnT3qoTlgg74/vSftGkRwpKOG6N1azLSO3moKK+LYVOzMZ/uoPpGUX0bxeGNNu7Eagv34VSfXQT5J4vjEj4NUZVX/d5Mnw3HMVfio6NJD3xvWkY+MojhaUcN301WxNV7ERORvvrN7P6JlrySsuo3vTOsyZ0Is6YYFWxxIvolIjnqusBB4aDrM+rfprT1NoTogODeTdsT3pHB/FscJSbnhzNVvSc84wrIjvKnO6mPLZFv4xfzNOl8GIro15b3xP6obrrttSvTyi1Ozbt4+xY8fSrFkzQkJCaNGiBY8++iglJSVWRxOrHNsH0y+BZ+ZX/bWVKDQnRIUG8PbYnnROiD5ebNawOU3FRqSycotLuWX2z+Xbtv96aWueG9WZIH8/a4OJV/KIUrNt2zZcLhevv/46W7Zs4fnnn2fatGk8+OCDVkcTK2xdAHd2h3u/h9IqvrYKheaEqJAA3hl7LkkJ0WSr2IhUWurRQq56dRXf78gkOMDOtBu7MnHAOVoULDXGZhiGYXWIM/HMM8/w2muvsWfPnkq/Jjc3l6ioKHJycoiMjKzBdFIjSoth6cPw9qvwcVHVX38Gheb38opL+ctbP/FLSjaRwf68+ZcenNss5ozfT8Sbrd13lNveWcfRghLiIoN48+YedIyPsjqWeKjK/v72iCs1FcnJySEm5vS/UBwOB7m5uSd9iIc6shtmXAJrpsPC2i80ABHBAcy+5Vy6Na1DbnEZ107/kf98tYMyp+us3lfE23yy7gA3vLGGowUldGwcxYKJ56vQSK3wyFKze/duXn75ZSZMmHDa502dOpWoqKjyj4SEhFpKKNVq01x4vR9kbIRVdqhqp6mGQnNCRHAAb99yLiO6NsZlwEvf7OTq138k9Whhtby/iCdzuQz+/cU27puzgRKni8s7NODj23rRICrY6mjiIyydfpoyZQqPPfbYaZ+zdu1aunfvXj5OT0+nX79+9OvXjzfffPO0r3U4HDgcjvJxbm4uCQkJmn7yFKVF8MXfYd0sc3yoGby+EaryIztqFHz8cY3E+2xDOg/N20Seo4zwIH/+Oaw9w7vE18jXEnF3hSVlTP5oA19syQBg4oAW3HdJa+x2rZ+Rs1fZ6SdLS01WVhZZWVmnfU5iYiLBwWbLT09PZ8CAAfTs2ZNZs2Zht1ftQpPW1HiQzB0wZzQc3gLYwHY5TPmwau8REwOHD4Nfze2ySD1ayL0fJfPz/mMADEtqxOPDOhAZHFBjX1PE3WTkFDPu7bVsTssl0M/OU1d1ZERXFXypPh5RaqoiLS2NAQMG0K1bN9599138zuAXlUqNh9jwIXw+GUoLICwWhr4Gva+DI0eq9j6ffAIjRtRMxt8pc7r473e7eenbnThdBvF1Qnjx2iS6NdUiYvF+mw7kMO7ttRzKdRATFsj0m7rRPVE/+1K9vGqhcHp6Ov379ychIYFnn32WzMxMMjIyyMjIsDqaVKeSApg/ET69zSw0iRfAhJXwwaqqFZrIyForNAD+fnbuubglH9/Wi/g6IRw4VsTVr6/mha+1iFi8l9Nl8O7q/Yx6fRWHch20rB/Ogol9VGjEUh5xpWbWrFmMGTOmws9VJb6u1Lixw7+a002Z2wAb9P879P0rfDIPrrmm8utoIiMhMxMCrTl6Pbe4lEfmb2Z+cjoA3ZvW4flrkkiICbUkj0hN2HQgh4fnb2LDAfO8pn6tYnn5+i6adpUa43XTT9VBpcYNGQasfxcW/xXKiiA8Dq56E5r1hblzzYW+VVGLV2hOZ/76NB6ev5l8RxkRQf48MbwDQ5MaWx1L5KzkFJXy3NLtvLN6P4YBEUH+TB7Yipt7JeKnBcFSg1RqKqBS42Yc+bBoMmz8yBw3HwAj3oDwWJgzB667DpzOyr2X3Q4ffQQjR9Zc3ipKOVLIpI/W80tKNgAjujTmsaHtidDfZsXDGIbBp+vTeHLxr2Tlm7enGZrUiIcGtaV+pLZrS81TqamASo0bydgMc/4CR3aBzQ4DHoLzJ5vlZN48uOqqqr3fo4/ClCk1EvVslDldvPTtLl75dicuA5rEhPLitUl0aVLH6mgilbLjUB4Pz9/MT3uPAtAiNox/Du1A73PqWZxMfIlKTQVUatyAYcC6mbDk7+B0QEQjGDkDmvY2P+90QmIiHDhQ+fesWxcOHarRrdtna+2+o0z6MJm07CL87Dbuuaglt/ZtTnCA+2YW31bgKOOlb3YyY+VeylwGwQF27r6oJePOb06gv0fsMREvUtnf3/61mEl8XXEuLLwHtswzxy0HwrBpEFb3t+f8619VKzQA06e7daEB6JEYw+J7LuDh+ZtZuCGd/3y1gw9+SuGuC1syqns8AX76JSHuwTAMvtySwWMLt3IwpxiAge3ieOTKdsTX0YJ3cW+6UiO1Iz0Z5o6Bo3vA7g8XPQK97jKnm8C8QvOvf5nTSJXl5wcffuhW62j+jGEYLEhO5+kvtpX/wkiICeGei1oxLKkR/io3YqH9Rwp49LMtLNueCUB8nRAeG9Kei9rGWZxMfJ2mnyqgUmMBw4Cf3oClD4GzBKISYORbkHDub8+ZNw/uvhvS0qr23h9/XPXdUW6iuNTJhz+l8Mp3u8nKN2/l0Tw2jEkXt+KKjg11tLzUquJSJ9OW7+bVZbspKXMR6Gfntn7NuaP/OYQEuvdVUPENKjUVUKmpZUXZ8Nld8Otn5rj1IBj6Xwj93eFc8+aZV1qq8mPogVdoTqWoxMnbP+5j2vLdHCssBaBNgwjuvaQVA9vFYbOp3EjNWrb9MI9+toX9R8ybsp5/Tj0eH9qe5rHhFicT+Y1KTQVUampR2jqYMway94M9AC55HM67HX7/S/pMFgWDR1+hOZV8RxkzV+5l+oo95BWXAdCxcRSTB7aif6tYlRupdr8ezOWlb3ayZLN5MntcZBD/uKIdgzs21M+buB2Vmgqo1NQCw4DVr8FXj4CrFKKbwqiZ0LjbH5/7+ONVW0MD8Nhj8Mgj1ZPVDeUUlvLmyj28tXIvBSXmGT3dmtbhvoGt6N1CW2jl7DhdBl9tPcSsVXtZvcfcou1ntzGmdyKTLmlFeJD2joh7UqmpgEpNDSs8CgsmwvbF5rjtlTDkFQiJ/uNzz+Qsmvh42LfP7Xc6VYcj+Q5e/34Ps1ftw1Fm3j+qV/O63Dewle6tI1WWXVjCR2tTefvH/aRlFwFmmbmsfQPuvPAc2jbUn4fi3lRqKqBSU4NSf4K5t0BOKvgFwqVPQo9xJ083nXAm0042m3nbBDe4BUJtOpxbzKvLdvP+mhRKjt8cs1+rWO4b2IpO8dHWhhO3t+NQHrNW7WPeLwcoLjV/fuqEBnDduU248bymNIoOsTihSOWo1FRApaYGuFzw48vwzePgKoOY5jBqFjTsfOrXfPMNXHxx5b9GfDy8+KLPFZrfS8su4pVvdzLn5wOUucz/ZAe2i+Oei1vSvlGUxenEnThdBt9uO8ysVXv5Yddvd7dv0yCCMX0SGZrUWIc+isdRqamASk01KzgC8yfAzqXmuMNVcMULEHya7+28eTB+PBw9Wrmv8dhj8NBDPjHlVBn7jxTw4jc7mb8+jePdhnYNIxnWpRFXdm5Ewyj9zdtX5RSVMufnVGb/uI/Uo+YUk90GA9s1YHSfRHo2i9ECYPFYKjUVUKmpRvtXwdyxkJcO/sFw2VPQbXTF000nVHX7tpcvCj4buw7n8+I3O1my6WD5lRubDXo2i2FoUmMGdWhIVKhunOkLdh3OY/aq/XzyywEKjy8ujwoJ4NpzE7jpvKY6BVi8gkpNBVRqqoHLBSv/A989CYYT6rY0p5sadDj960pKzGmkzMzKfR0fWhR8No4VlLB480EWrE/np32/Xf0K8LPRv3V9hiU15qK29TXd4GVcLoNlOw4z84d9rNiZVf5467gIRvdJZFhSYx2aJ15FpaYCKjVnKT8T5o2HPd+Z407XwuDnIOhPDumaNw9uuw2ysk7/vBN8dFHw2UrLLuKz5HQWJKexLSOv/PHwIH8ubd+AoUmN6N2irm7F4MH2Hyngq62HeHf1fvYdPyzPZoOL28Yxpk8ivZrX1RSTeCWVmgqo1JyFvd/DJ+Mg/xD4h8DgZyHphtNPN0HVp5zq1jVvUKlCc1a2Z+SxIDmNBcnp5Vt4AeqFB3FFp4YM69KYzvFR+gXo5opKnKzec4Rl2w+zfEdmeZEBiAj259oeCdzcK5GEGE0xiXdTqamASs0ZcDnh+2dg+dNguCC2DYyaDfXb/Plrz2Tr9tdfw0UXnXFcOZnLZbAu5RgLktNYtPFg+a0YABLrhjIkqTHDkhrpSHw3YRgGuzPzWbY9k+U7Mlmz9yglx88pAvC32+ieWIfBnRoxoktjwnRYnvgIlZoKqNRUUV6GeXVm3wpz3OVGuPwZCKzk3wqrsnXbZjPX0ezdq3U0NaTU6WLFzkzmr0/nq62HKCp1ln+uY+MohiY14qK2cSTWDdUVnFqU7yjjh11ZLN+RyfLtmSddWQNoHB1Cv9ax9GsVS+8WdYkI1gJw8T0qNRVQqamC3d/CvFuhIBMCwuCK56HzNZV/fVW3bmsdTa0qcJTx9a+HmL8+je93ZuF0/fbHQHRoAJ3jo0lKiKZLE/Of0aGBFqb1LoZhsC0jj+U7Mlm2/TA/7ztWvoMNINDPTs/mMfRrFUv/1rG0iA1XyRSfp1JTAZWaSnCWwbKpsOI5wIC4DubupnotK/8eVV1HExsL06ap0FjkSL6DxZsOsnDjQTakZpffluH3mtULIynht6LTpkEkgf5acFxZOYWlrNyVxfId5tqYQ7mOkz6fWDf0eImpT8/mMYQGalpJ5PdUaiqgUvMnctLM6aaUVea42xi4bCoEVOFAt6quo4mNNZ8bqCsB7qDU6WLbwTzWpx4jOSWb5NRs9mQV/OF5gf52OjSKJCmhTvnVnPg6IT5/RcHlMjiYW8yezHz2ZBawJzOfzem5JKdmn3Q1LCTAj14t6tK/dSx9W8aSWC/MwtQi7k+lpgIqNaex8ytzuqnoKARGwJAXzROCq6qq62g05eT2sgtLSE41C87640Unp6j0D8+rFx54/EpOHZISoukUH+W16z/yikvN0pJ1orwUsDszn31HCsrvsfS/WtYPL78a0z2xjs4OEqkClZoKqNRUwFkK3/4TfnjRHDfsDCNnQt0WVX+vqqyj0dZtj2UYBvuOFJKceqy85GxNzz1pXQiYnfWc2HCa1g0lNiKIeuG//wg0H4sIIiLI3y2v8JQ5XaQeK2Lv8eKy+/iVlz1ZBWTmOU75ugA/G03rhtGsXhjNY8M4Jzac3ufUo7FuHilyxlRqKqBS8z+yU807ax/4yRyfeysMfAL8g6r+XlVdR6Ot216luNTJlvSc8pKTnJrNgWNFf/5CzKms2N8Xnd8Vn3rHxycejww+fQEyDIMyl0FJmQtHmQtHmRNHqYsSpwtH6fFxmev4553Hn3P8o9RJZr6jfNoo5Wghpc5T/zzHRgTRvF4YzWPDaRFrFpjm9cKJrxOiAw5FqplKTQVUan5n22KYfzsUZ0NQFAx9GdoNPbP3qso6Gm3d9hmZeQ42pWVzMKeYrLwSsvIdZOY5yMo/8VFCvqOsSu8Z6GenXnggkSEBlLmM8tLy+6LiqsY/0YL87TSrF0aL2HCztBwvLs1iw4j00qk1EXdU2d/fWmLva8pK4OspsPq/5rhRVxg1E+oknvl7rlhRtQP2XnhBhcYHxEYEcWGbuNM+p7jUWV50zH+W/K70OH4rQ/kO8orLKHG6SM8pJj2nuFIZAvxsBPn7EeRvJ9DfTpC/nSB/v9/+PcBOoJ/5WFCAnaiQgPKrL81jw2gUFYLd7n5TYyJSMZUaX3JsnzndlLbOHJ83ES6eAv5nufMoLa1yz9M6GvkfwQF+JMSEVuqY/+JSZ/kVntyi0vJiEni8qAT9rrScKCsqJCK+RaXGV2z9DBbcCY4cCI6GYa9Bm0Fn/77z5sGkSZV77kcfaR2NnLHgAD/i64QSX0f3ORKRiqnUeLsyByx9GH6abo7jz4WRMyC6ydm/d2UXB59YR9O//9l/TRERkVNQqfFmR3bD3DFwcIM57nMPXPgP8KuGBY5OJ9xzT+UKDWgdjYiI1DiVGm+1eR58djeU5EFIDAx/HVoNrL73r+zi4Hr1dAsEERGpFSo13qa0CL54ANbNNMdNesFVMyCqcfV9DafTPDm4Mp5/XoVGRERqhUqNN8naCXPGwKFNgA0uuA/6PwB+1fh/87x55rRTZbdwN67GMiUiInIaKjXeYsNH8Pm9UFoAofXgqjegxYXV+zWqcmrwicXBF1xQvRlEREROQaXG05UUwpK/wvp3zXHiBXDVmxDRoHq/TmUXBoMWB4uIiCVUajzZ4W0wZzRk/grYoN/foN/9YK+BIlGVU4Pj481Co7U0IiJSi1RqPJFhQPJ7sOj/oKwIwuNgxBvQvF/Nfc3Knhr88MMwZYqu0IiISK1TqfE0jnxYdB9s/NAcNx8AI6ZDeP2a+5pVOTX4ootUaERExBIqNZ4kY7N5mF7WDrDZYcCDcP59YLfX3Nes6qnBWhgsIiIWUanxBIYB62bBF3+HsmKIaGiePZPYp2a/rk4NFhERD6JS4+6Kc+HzSbD5E3N8ziUwfBqE1av5r61Tg0VExIOo1LizgxvM3U1H94DNDy56BHrfXbPTTSfo1GAREfEwKjXuyDBg7Zvw5YPgLIHIeBj5FjTpWTtfX6cGi4iIB1KpcTdF2bDwbti6wBy3HgRD/wuhMbXz9XVqsIiIeCiVGneSts68d1P2frAHwCWPwXl3/LYQt6bp1GAREfFgKjXuwDBg9Wvw1SPgKoXoJjByFsR3q90cOjVYREQ8mEqN1QqPwoI7Yfsic9z2ShjyCoRE136Wgwcr9zydGiwiIm5IpcZKqWvNw/RyUsEvEC59EnqMq73ppt9zOuHQoco9V6cGi4iIG1KpsYLLBT++DN88Dq4yqNMMRs2CRknW5KnsbictDBYRETemUlPbCo7A/Nth55fmuP0IuPJFCI60Jk9VboMAWhgsIiJuS6WmNu3/EebeAnnp4BcElz8N3UZbM90EVdvtpIXBIiLi5lRqaoPLBT88D9/+Cwwn1G0Jo2ZCg47W5qrsbqfnn4e77tIVGhERcWsqNTUtPxM+vRV2f2uOO10Dg/8DQeHW5oLK73aKi1OhERERt6dSU5P2roBPxkF+BviHwOBnIekG66ab/lfDhtX7PBEREQup1NQElxO+fxaWPwWGC2LbmLub6re1OpnJ6TSnntLSIDYWsrIqXlej3U4iIuJBauF2z9XL4XCQlJSEzWYjOTnZ6jh/lHcI3hkGy540C03SjTD+W/cpNPPmQWIiDBgAN94ImZmnLjSg3U4iIuIxPK7U3H///TRq1MjqGBXb/R1MOx/2fg8BYTD8dRj2XwgMszqZ6cT27cosDo6Ph7lztdtJREQ8hkdNPy1ZsoSlS5fyySefsGTJEqvj/MZZZk41ff8sYED99uZ0U2wrq5P9pjLbt2NjzZ1OjRubU066QiMiIh7EY0rNoUOHGD9+PPPnzyc0NLRSr3E4HDgcjvJxbm5u9QdzlsI7w2HfCnPcbQxcNhUCQqr/a52Nymzfzsw0C03//rUSSUREpDp5xPSTYRiMHj2aCRMm0L1790q/burUqURFRZV/JCQkVH84vwBo2BkCI+CqGXDlC+5XaKDy27cr+zwRERE3Y2mpmTJlCjab7bQfP//8My+//DK5ubk88MADVXr/Bx54gJycnPKP1NTUmvkfctGjMGEFdBxZM+9fHbR9W0REvJzNMCpzRn7NyMrKIisr67TPSUxM5Nprr2XhwoXYfne+i9PpxM/PjxtuuIHZs2dX6uvl5uYSFRVFTk4OkZEW3WvJKk6nuespLe3027f37tVaGhERcSuV/f1taamprJSUlJPWw6Snp3PppZcyd+5cevbsSXx8fKXex6dLDfy2+wlOLjYnyqJ2O4mIiBuq7O9vj1go3KRJk5PG4eHmLQZatGhR6UIjmIVl7lxzF9TvFw3rZpUiIuIFPKLUSDUaMQKGDjV3Qx08aK6h0fZtERHxAh5ZahITE/GAWTP35eenbdsiIuJ1PGJLt4iIiMifUakRERERr6BSIyIiIl5BpUZERES8gkqNiIiIeAWVGhEREfEKKjUiIiLiFVRqRERExCuo1IiIiIhX8MgThc/UiVOIf39zTBEREXFvJ35v/9ndBHyq1OTl5QGQkJBgcRIRERGpqry8PKKiok75eZvhQzdRcrlcpKenExERgc1mszqOpXJzc0lISCA1NfW0t3GXs6fvde3Q97l26PtcO/R9PplhGOTl5dGoUSPs9lOvnPGpKzV2u534+HirY7iVyMhI/QdTS/S9rh36PtcOfZ9rh77PvzndFZoTtFBYREREvIJKjYiIiHgFlRofFRQUxKOPPkpQUJDVUbyevte1Q9/n2qHvc+3Q9/nM+NRCYREREfFeulIjIiIiXkGlRkRERLyCSo2IiIh4BZUaERER8QoqNXISh8NBUlISNpuN5ORkq+N4lX379jF27FiaNWtGSEgILVq04NFHH6WkpMTqaB7v1VdfpVmzZgQHB9OtWzdWrFhhdSSvM3XqVHr06EFERAT169dn2LBhbN++3epYXm3q1KnYbDYmTZpkdRSPoVIjJ7n//vtp1KiR1TG80rZt23C5XLz++uts2bKF559/nmnTpvHggw9aHc2jffTRR0yaNImHHnqI9evXc8EFF3D55ZeTkpJidTSvsnz5ciZOnMjq1av56quvKCsrY+DAgRQUFFgdzSutXbuW6dOn06lTJ6ujeBRt6ZZyS5YsYfLkyXzyySe0b9+e9evXk5SUZHUsr/bMM8/w2muvsWfPHqujeKyePXvStWtXXnvttfLH2rZty7Bhw5g6daqFybxbZmYm9evXZ/ny5fTt29fqOF4lPz+frl278uqrr/LEE0+QlJTECy+8YHUsj6ArNQLAoUOHGD9+PO+88w6hoaFWx/EZOTk5xMTEWB3DY5WUlLBu3ToGDhx40uMDBw5k1apVFqXyDTk5OQD6+a0BEydOZPDgwVx88cVWR/E4PnVDS6mYYRiMHj2aCRMm0L17d/bt22d1JJ+we/duXn75ZZ577jmro3isrKwsnE4ncXFxJz0eFxdHRkaGRam8n2EYTJ48mfPPP58OHTpYHcerfPjhh/zyyy+sXbvW6igeSVdqvNiUKVOw2Wyn/fj55595+eWXyc3N5YEHHrA6skeq7Pf599LT07nssssYNWoU48aNsyi597DZbCeNDcP4w2NSfe688042btzIBx98YHUUr5Kamso999zDu+++S3BwsNVxPJLW1HixrKwssrKyTvucxMRErr32WhYuXHjSLwGn04mfnx833HADs2fPrumoHq2y3+cTf0ilp6czYMAAevbsyaxZs7Db9XeLM1VSUkJoaChz5sxh+PDh5Y/fc889JCcns3z5cgvTeae77rqL+fPn8/3339OsWTOr43iV+fPnM3z4cPz8/Mofczqd2Gw27HY7DofjpM/JH6nUCCkpKeTm5paP09PTufTSS5k7dy49e/YkPj7ewnTeJS0tjQEDBtCtWzfeffdd/QFVDXr27Em3bt149dVXyx9r164dQ4cO1ULhamQYBnfddReffvopy5Yto2XLllZH8jp5eXns37//pMfGjBlDmzZt+Nvf/qapvkrQmhqhSZMmJ43Dw8MBaNGihQpNNUpPT6d///40adKEZ599lszMzPLPNWjQwMJknm3y5MncdNNNdO/enV69ejF9+nRSUlKYMGGC1dG8ysSJE3n//fdZsGABERER5WuWoqKiCAkJsTidd4iIiPhDcQkLC6Nu3boqNJWkUiNSS5YuXcquXbvYtWvXH8qiLpieuWuuuYYjR47w+OOPc/DgQTp06MDixYtp2rSp1dG8yokt8/379z/p8ZkzZzJ69OjaDyRSAU0/iYiIiFfQCkURERHxCio1IiIi4hVUakRERMQrqNSIiIiIV1CpEREREa+gUiMiIiJeQaVGREREvIJKjYiIiHgFlRoRERHxCio1IuI1Dh48yPXXX0/r1q2x2+1MmjTJ6kgiUotUakTEazgcDmJjY3nooYfo3Lmz1XFEpJap1IiIx8jMzKRBgwY8+eST5Y+tWbOGwMBAli5dSmJiIi+++CI333wzUVFRFiYVESvoLt0i4jFiY2N56623GDZsGAMHDqRNmzbceOON3HHHHQwcONDqeCJiMZUaEfEogwYNYvz48dxwww306NGD4OBgnnrqKatjiYgb0PSTiHicZ599lrKyMj7++GPee+89goODrY4kIm5ApUZEPM6ePXtIT0/H5XKxf/9+q+OIiJvQ9JOIeJSSkhJuuOEGrrnmGtq0acPYsWPZtGkTcXFxVkcTEYup1IiIR3nooYfIycnhpZdeIjw8nCVLljB27Fg+//xzAJKTkwHIz88nMzOT5ORkAgMDadeunYWpRaQ22AzDMKwOISJSGcuWLeOSSy7hu+++4/zzzwcgJSWFTp06MXXqVG6//XZsNtsfXte0aVP27dtXy2lFpLap1IiIiIhX0EJhERER8QoqNSIiIuIVVGpERETEK6jUiIiIiFdQqRERERGvoFIjIiIiXkGlRkRERLyCSo2IiIh4BZUaERER8QoqNSIiIuIVVGpERETEK/w/LhHEQ8K9QkUAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Autre intersection (autre x0)\n", + "x0 = np.array([-4, -4])\n", + "l = NewtonRnRelax(fexamen, x0)\n", + "print(l[-1])\n", + "\n", + "theta = np.linspace(0, 2*np.pi, 40)\n", + "r = 3\n", + "x=r*np.cos(theta)\n", + "y=r*np.sin(theta)\n", + "plt.plot(x,y)\n", + "\n", + "# tracé droite\n", + "x = np.linspace(-5, 5, 40)\n", + "y=x+1\n", + "plt.plot(x,y)\n", + "\n", + "plt.plot([x[0] for x in l], [x[1] for x in l], 'or')\n", + "\n", + "plt.xlabel('x1')\n", + "plt.ylabel('x2')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "95ad5b3c-ad20-42d8-9db3-8cbfe0e12e96", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0 0]\n", + " [-1 1]] det= 0.0 Pas inversable :(\n" + ] + } + ], + "source": [ + "# x0 posant problème?\n", + "# (0,0)\n", + "x0 = np.array([0,0])\n", + "fx, J = fexamen(x0)\n", + "print(J, \"det=\", np.linalg.det(J), \"Pas inversable :(\")\n", + "\n", + "# l = NewtonRnRelax(fexamen, np.array([0,0]))\n", + "\n", + "# print(l[-1])\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ac961713-f133-4254-8065-226906413cc0", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/QUESTION9.ipynb b/QUESTION9.ipynb new file mode 100644 index 0000000..1803ec8 --- /dev/null +++ b/QUESTION9.ipynb @@ -0,0 +1,220 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "0ae8d8f4-2f60-4ef3-bf50-eae61169de5d", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d984aa22-593e-48ea-a27d-beeb3b6377d8", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def getAb(n):\n", + " A = np.zeros((n,n))\n", + " for i in range(n):\n", + " for j in range(n):\n", + " A[i,j] = (i + 1)**(n-1-j)\n", + " \n", + " b = np.random.rand(n)\n", + " return A,b" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8835175c-38bc-42cf-8af5-ec9a13c7410f", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def backward(A,b):\n", + " \"\"\" A matrice triangulaire supérieure\"\"\"\n", + " n = len(b)\n", + " x = np.zeros(n)\n", + " \n", + " for i in range(n-1, -1, -1):\n", + " x[i] = b[i]\n", + " for j in range(i+1, n):\n", + " x[i] -= A[i,j]*x[j]\n", + " #print(A[i,i])\n", + " x[i] /= A[i, i]\n", + " return x" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "94e34e9e-d397-4010-8b0a-d51d79ae52a4", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def GaussianElimination(A, b):\n", + " \"\"\" Descente \"\"\"\n", + " n=len(b)\n", + " A = np.array(A)\n", + " b = np.array(b)\n", + " for i in range(n-1):\n", + " pivot = A[i, i]\n", + " #print(A, 'pivot=',i,i, '=', pivot, 'b=',b)\n", + " for j in range(i+1, n):\n", + " if pivot == 0:\n", + " pass\n", + " # print('pivot is 0', 'ij',i,j, A[i,:])\n", + " c = A[j,i]/pivot\n", + " b[j] -= c * b[i]\n", + " A[j] -= c * A[i]\n", + " #print(A, b)\n", + " return backward(A, b)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "6834425f-f943-4c17-906d-5409e0f90413", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "def GaussianEliminationWithPivoting(A, b):\n", + " \"\"\" Descente \"\"\"\n", + " n=len(b)\n", + " A = np.array(A)\n", + " b = np.array(b)\n", + " for i in range(n-1):\n", + " # Pivotage : on échange la ligne avec abs(A[x, i])\n", + " pmax =A[i,i]\n", + " lmax = i\n", + " for j in range(i+1,n):\n", + " if A[j, i] >= pmax:\n", + " pmax = A[j,i]\n", + " lmax = j\n", + " \n", + " # print('Pivot max = ', pmax)\n", + " # print('échange ligne', i, lmax)\n", + " # switch lmax and i\n", + " # print('bef switch', A)\n", + " # print(b)\n", + " A[i], A[lmax] = A[lmax], A[i].copy()\n", + " b[i], b[lmax] = b[lmax], b[i].copy()\n", + " # print('after switch', A)\n", + " # print(b)\n", + " \n", + " pivot = A[i, i]\n", + " #print(A, 'pivot=',i,i, '=', pivot, 'b=',b)\n", + " for j in range(i+1, n):\n", + " if pivot == 0:\n", + " pass\n", + " # print('pivot is 0', 'ij',i,j, A[i,:])\n", + " c = A[j,i]/pivot\n", + " b[j] -= c * b[i]\n", + " A[j] -= c * A[i]\n", + " #print(A, b)\n", + " return backward(A, b)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "556548f6-bc0c-4f04-8cad-8f0be037e8d2", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\theking\\AppData\\Local\\Temp\\ipykernel_35980\\378739895.py:13: RuntimeWarning: divide by zero encountered in scalar divide\n", + " c = A[j,i]/pivot\n", + "C:\\Users\\theking\\AppData\\Local\\Temp\\ipykernel_35980\\378739895.py:15: RuntimeWarning: invalid value encountered in multiply\n", + " A[j] -= c * A[i]\n", + "C:\\Users\\theking\\AppData\\Local\\Temp\\ipykernel_35980\\378739895.py:13: RuntimeWarning: invalid value encountered in scalar divide\n", + " c = A[j,i]/pivot\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "en = np.arange(3, 21, 1)\n", + "e = []\n", + "epivot = []\n", + "for n in en:\n", + " A,b = getAb(n)\n", + " x = GaussianElimination(A, b)\n", + " e.append(np.linalg.norm(A@x - b))\n", + " \n", + " x = GaussianEliminationWithPivoting(A, b)\n", + " epivot.append(np.linalg.norm(A@x - b))\n", + "\n", + "plt.plot(en, e, label='||Ax-b|| sans pivoting')\n", + "plt.plot(en, epivot, label='||Ax-b|| avec pivoting')\n", + "plt.yscale('log')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f03a740f-35bb-4bac-8cfe-c6d497151a83", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d19b8b72-c5b0-4685-ba7c-f041af75bde8", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.11.5" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}