notes

commit d15be9da1c4ba20b46373578c42a8d1a2bdca271
parent dfd6eed9e56fc33f14565b1ed3394d0a96589dc2
Author: miksa234 <milutin@popovic.xyz>
Date:   Fri, 22 Dec 2023 12:36:52 +0000

finished summary

Diffstat:
A
ricam_sem/code/.ipynb_checkpoints/ip_gauss_newton_snn-checkpoint.ipynb
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304
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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ricam_sem/code/gn_coeff.png
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0

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ricam_sem/code/gn_loss.png
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A
ricam_sem/code/ip_gauss_newton_snn.ipynb
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304
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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ricam_sem/code/lw_coeff.png
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ricam_sem/code/lw_loss.png
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0

M
ricam_sem/summary_talk/cite.bib
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13
+++++++++++++
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ricam_sem/summary_talk/main.tex
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+++++++++++++++++++++++++++++++++++++++++++++++++------------------------------
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ricam_sem/summary_talk/pics/gn_coeff.png
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ricam_sem/summary_talk/pics/gn_loss.png
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ricam_sem/summary_talk/pics/lw_coeff.png
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ricam_sem/summary_talk/pics/lw_loss.png
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ricam_sem/summary_talk/preamble.tex
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5
++++-

13 files changed, 753 insertions(+), 77 deletions(-)
diff --git a/ricam_sem/code/.ipynb_checkpoints/ip_gauss_newton_snn-checkpoint.ipynb b/ricam_sem/code/.ipynb_checkpoints/ip_gauss_newton_snn-checkpoint.ipynb
@@ -0,0 +1,304 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 703,
+   "id": "df0578d0-70b1-457b-bf63-72bf37b4d7e3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "import numdifftools as nd"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8d3d12a3-f227-486c-a7be-4d7a49871320",
+   "metadata": {},
+   "source": [
+    "# Gauss-Newton iteration"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 704,
+   "id": "e6109fee-4d3b-4f89-9da0-99e3c9bfe31e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def sig(x):\n",
+    "    return 1/(1+np.exp(-x))\n",
+    "\n",
+    "def network_2d(x: np.array, p):\n",
+    "    return p[0]*sig(np.inner(p[1:3], x) + p[3]) + p[4]*sig(np.inner(p[5:7], x) + p[7]) \n",
+    "    \n",
+    "def gauss_newton(x, b, p_0, p_dag, eps):\n",
+    "    p_k = np.array(p_0)\n",
+    "    psi_k = network_2d(x, p_k)\n",
+    "    \n",
+    "    jac = nd.Jacobian(lambda p: network_2d(x, p))\n",
+    "    psi_k_dag = np.linalg.pinv(jac(p_k))\n",
+    "    \n",
+    "    p_k_s = [p_k]\n",
+    "    psi_k_s = [psi_k]\n",
+    "    psi_k_dag_s = [psi_k_dag]\n",
+    "    while True:\n",
+    "        p_k = p_k - psi_k_dag @ (psi_k - b)\n",
+    "        psi_k = network_2d(x, p_k)\n",
+    "        psi_k_dag = np.linalg.pinv(jac(p_k))\n",
+    "\n",
+    "        p_k_s.append(p_k)\n",
+    "        psi_k_s.append(psi_k)\n",
+    "        psi_k_dag_s.append(psi_k_dag)\n",
+    "\n",
+    "        if np.linalg.norm(psi_k - b) < eps:\n",
+    "            break\n",
+    "\n",
+    "\n",
+    "\n",
+    "    return p_k_s, psi_k_s, psi_k_dag_s\n",
+    "        \n",
+    "        \n",
+    "p_dag = [1.0, 1.0, 0.1, 0.1, 0.3, 0.1, 1.0, 0.8]\n",
+    "p_0 = [0.8, 0.9, 0.05, 0.1, 0.7, 0.3, 0.5, 0.5]\n",
+    "x =  np.random.uniform(low=-10, high=10, size=(100, 2))\n",
+    "\n",
+    "\n",
+    "\n",
+    "p_k_s, psi_k_s, psi_k_dag_s = gauss_newton(x, network_2d(x, p_dag), p_0, p_dag, eps=0.001)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 705,
+   "id": "3025397e-3758-41ac-9ad4-7fdb713c0232",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 3 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(1, 3)\n",
+    "\n",
+    "ax[0].plot(p_dag, c='r')\n",
+    "ax[0].set_xlabel(r\"$p^{\\dagger}$\")\n",
+    "ax[0].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[1].plot(p_0, c='r')\n",
+    "ax[1].set_xlabel(r\"$p^{0}$\")\n",
+    "ax[1].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[2].plot(p_k_s[-1], c='r')\n",
+    "ax[2].set_xlabel(r\"$p^{k_s}$\")\n",
+    "ax[2].set_xticks(range(0, 8))\n",
+    "\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./gn_coeff.png', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5fccea2d-1f55-4689-97c4-35fb8eb43f97",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 706,
+   "id": "20985f08-3c1c-4e52-92d1-2bf6630b4ade",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "loss = []\n",
+    "res_loss = []\n",
+    "psi_dag = network_2d(x, p_dag)\n",
+    "for psi in psi_k_s:\n",
+    "    l = np.linalg.norm(psi - psi_dag)\n",
+    "    loss.append(l)\n",
+    "\n",
+    "\n",
+    "for i in range(1, len(loss)):\n",
+    "    res_loss.append(np.log(loss[i] / np.linalg.norm(psi_k_s[i-1] - psi_dag)**2))\n",
+    "    \n",
+    "fig, ax = plt.subplots(1, 2)\n",
+    "ax[0].plot(range(1, len(loss)+1), loss, c= 'black')\n",
+    "ax[0].set_xlabel(r\"loss\")\n",
+    "ax[0].set_ylim(0)\n",
+    "\n",
+    "ax[1].plot(range(1, len(loss)), res_loss, c= 'black')\n",
+    "ax[1].set_xlabel(r\"residual loss\")\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./gn_loss.png', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1bcca449-5e38-4dad-9c9a-e3df39c6d663",
+   "metadata": {},
+   "source": [
+    "# Landau-Weber Iteration"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 710,
+   "id": "4cdd2405-bb58-465d-8357-6704832ded3c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def landau_weber(x, b, p_0, p_dag, λ, eps):\n",
+    "    p_k = np.array(p_0)\n",
+    "    psi_k = network_2d(x, p_k)\n",
+    "    \n",
+    "    jac = nd.Jacobian(lambda p: network_2d(x, p))\n",
+    "    psi_k_dag = jac(p_k)\n",
+    "    \n",
+    "    p_k_s = [p_k]\n",
+    "    psi_k_s = [psi_k]\n",
+    "    psi_k_dag_s = [psi_k_dag]\n",
+    "    while True:\n",
+    "        p_k = p_k - λ * (psi_k_dag.T @ (psi_k - b))\n",
+    "        psi_k = network_2d(x, p_k)\n",
+    "        psi_k_dag = jac(p_k)\n",
+    "\n",
+    "        p_k_s.append(p_k)\n",
+    "        psi_k_s.append(psi_k)\n",
+    "        psi_k_dag_s.append(psi_k_dag)\n",
+    "\n",
+    "        if np.linalg.norm(psi_k - b) < eps:\n",
+    "            break\n",
+    "\n",
+    "\n",
+    "    return p_k_s, psi_k_s, psi_k_dag_s\n",
+    "        \n",
+    "        \n",
+    "p_dag = [1.0, 1.0, 0.1, 0.1, 0.3, 0.1, 1.0, 0.8]\n",
+    "p_0 = [0.8, 0.9, 0.05, 0.1, 0.7, 0.3, 0.5, 0.5]\n",
+    "x =  np.random.uniform(low=-10, high=10, size=(100, 2))\n",
+    "\n",
+    "\n",
+    "\n",
+    "p_k_s, psi_k_s, psi_k_dag_s = landau_weber(x, network_2d(x, p_dag), p_0, p_dag, λ=0.02, eps=0.001)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 713,
+   "id": "70b7fc5a-c9ff-4675-a475-09be8739a04e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 3 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(1, 3)\n",
+    "\n",
+    "ax[0].plot(p_dag, c='r')\n",
+    "ax[0].set_xlabel(r\"$p^{\\dagger}$\")\n",
+    "ax[0].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[1].plot(p_0, c='r')\n",
+    "ax[1].set_xlabel(r\"$p^{0}$\")\n",
+    "ax[1].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[2].plot(p_k_s[-1], c='r')\n",
+    "ax[2].set_xlabel(r\"$p^{k_s}$\")\n",
+    "ax[2].set_xticks(range(0, 8))\n",
+    "\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./lw_coeff.png', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 712,
+   "id": "9ff0a6fc-9c0b-404a-ba7d-28b72b05ad83",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "loss = []\n",
+    "res_loss = []\n",
+    "psi_dag = network_2d(x, p_dag)\n",
+    "for psi in psi_k_s:\n",
+    "    l = np.linalg.norm(psi - psi_dag)\n",
+    "    loss.append(l)\n",
+    "\n",
+    "\n",
+    "for i in range(1, len(loss)):\n",
+    "    res_loss.append(np.log(loss[i] / np.linalg.norm(psi_k_s[i-1] - psi_dag)**2))\n",
+    "    \n",
+    "fig, ax = plt.subplots(1, 2)\n",
+    "ax[0].plot(range(1, len(loss)+1), loss, c= 'black')\n",
+    "ax[0].set_xlabel(r\"loss\")\n",
+    "ax[0].set_ylim(0)\n",
+    "\n",
+    "ax[1].plot(range(1, len(loss)), res_loss, c= 'black')\n",
+    "ax[1].set_xlabel(r\"residual loss\")\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./lw_loss.png', dpi=300)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "venv",
+   "language": "python",
+   "name": "venv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/ricam_sem/code/gn_coeff.png b/ricam_sem/code/gn_coeff.png
Binary files differ.
diff --git a/ricam_sem/code/gn_loss.png b/ricam_sem/code/gn_loss.png
Binary files differ.
diff --git a/ricam_sem/code/ip_gauss_newton_snn.ipynb b/ricam_sem/code/ip_gauss_newton_snn.ipynb
@@ -0,0 +1,304 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 703,
+   "id": "df0578d0-70b1-457b-bf63-72bf37b4d7e3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "import numdifftools as nd"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8d3d12a3-f227-486c-a7be-4d7a49871320",
+   "metadata": {},
+   "source": [
+    "# Gauss-Newton iteration"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 704,
+   "id": "e6109fee-4d3b-4f89-9da0-99e3c9bfe31e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def sig(x):\n",
+    "    return 1/(1+np.exp(-x))\n",
+    "\n",
+    "def network_2d(x: np.array, p):\n",
+    "    return p[0]*sig(np.inner(p[1:3], x) + p[3]) + p[4]*sig(np.inner(p[5:7], x) + p[7]) \n",
+    "    \n",
+    "def gauss_newton(x, b, p_0, p_dag, eps):\n",
+    "    p_k = np.array(p_0)\n",
+    "    psi_k = network_2d(x, p_k)\n",
+    "    \n",
+    "    jac = nd.Jacobian(lambda p: network_2d(x, p))\n",
+    "    psi_k_dag = np.linalg.pinv(jac(p_k))\n",
+    "    \n",
+    "    p_k_s = [p_k]\n",
+    "    psi_k_s = [psi_k]\n",
+    "    psi_k_dag_s = [psi_k_dag]\n",
+    "    while True:\n",
+    "        p_k = p_k - psi_k_dag @ (psi_k - b)\n",
+    "        psi_k = network_2d(x, p_k)\n",
+    "        psi_k_dag = np.linalg.pinv(jac(p_k))\n",
+    "\n",
+    "        p_k_s.append(p_k)\n",
+    "        psi_k_s.append(psi_k)\n",
+    "        psi_k_dag_s.append(psi_k_dag)\n",
+    "\n",
+    "        if np.linalg.norm(psi_k - b) < eps:\n",
+    "            break\n",
+    "\n",
+    "\n",
+    "\n",
+    "    return p_k_s, psi_k_s, psi_k_dag_s\n",
+    "        \n",
+    "        \n",
+    "p_dag = [1.0, 1.0, 0.1, 0.1, 0.3, 0.1, 1.0, 0.8]\n",
+    "p_0 = [0.8, 0.9, 0.05, 0.1, 0.7, 0.3, 0.5, 0.5]\n",
+    "x =  np.random.uniform(low=-10, high=10, size=(100, 2))\n",
+    "\n",
+    "\n",
+    "\n",
+    "p_k_s, psi_k_s, psi_k_dag_s = gauss_newton(x, network_2d(x, p_dag), p_0, p_dag, eps=0.001)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 705,
+   "id": "3025397e-3758-41ac-9ad4-7fdb713c0232",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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vvoivfvWrMd+ns7MTLS0tfb5ieugh4NQpYN48YOZMY/+wWBg/ROYwhuTikVEjFnYDYVDJJdGJqwAwfDgwdao43rLF+jYloLm5GT09PcjLy+vzeF5eHhobG6O+5oYbbsB9992Hyy+/HCkpKTj77LMxZ86cAYdiKysrkZOT0/tVUFAQu1EjRwKZmdb31gGMHyKzGENyMVLY6aNGr78u7mTlABZ2A2E3uFyMBBXg6duLVVdXY+XKlfjd736H2tpa/PGPf8QLL7yA+++/P+Zrli1bhuPHj/d+HTx4MPYbrFwJ/OMf4WX5VtI/p9ZWMYePiBLDwk4uRjoXJk8GRo8GTpwQd0JyAAu7gXDxhFyMFnaRXeEubhuQm5uLpKQkNDU19Xm8qakJY8aMifqa5cuX46abbsKtt96Kiy66CN/85jexcuVKVFZWIhSjWEpLS8PQoUP7fA1o+HBD/55B6e+raUBbmz3vQaQyLkCSRygkLlKBxHJQIOD4XG8WdgPh1ZJcjCyeAIDLLwdSUoCDB4FPPrG+XXFKTU3FtGnTUBXRcxgKhVBVVYWSkpKor+no6ECw3102kpKSAACa7HtbpaeLnzvAGCIygjlIHm1t4Y4ByUeNWNgNhEElF6M9dpmZ4vYugOvDseXl5Vi3bh2eeuop7NmzB0uWLEF7ezsWLVoEAFi4cCGWLVvW+/z58+fj0UcfxYYNG/Dpp5/i1VdfxfLlyzF//vzeAk9agQBjiMgMxo889M8gJUVctCZCHzV6801HRi+SbX8HL2NQycVoYQeIwNq2TRR2//qv1rYrAQsWLMDnn3+OFStWoLGxEcXFxdi8eXPvgor6+vo+PXT33nsvAoEA7r33XjQ0NGDUqFGYP38+HnzwQbf+CYnJyQGamxlDREYwB8kjMv8EAom99swzgTPOAD77DNi+HfiXf7G+fRFY2A2EQSUXIxNXdVddBVRUiJWxoVB4408XlJWVoaysLOr/q+53h4zk5GRUVFSgoqLCgZbZgDFEZBzjRx5m8k8gIDoX1q8XnQs2F3Ycih2I/gF2dIi9vshdZnrsZswAhgwRvUe7d1vbLoqNk7+JjGP8yMNM/gEcXUDBwm4gkR8gA8td3d1iuThgLLBSU4ErrhDHHtz2xLPY40BkHONHHlYVdu+8Axw9ak2bYmBhN5CUFCAjQxwzsNwVWVgb6QoHpLu9mC8wMREZx/iRh9FdGXT5+cCkSWJlrc2b5bOwGwwDSw76z3/IEHH/PSP0lUlbt4oeQLIf44fIOMaPPMz22AGOdS6wsBsMA0sOZiau6oqKgBEjxHLzt9+2pl00MMYPkXGMH3lYkYMcum8sC7vBcPKqHKy4WgoGgblzxTHn2TmDiYnION7WUh5W5KArrxR5aO9eoKHBmnZFwcJuMExMcjA7v0Hn0BUTfYkXRkTG6X/vOjvFF7nHisJu+HBg6lRxbONwLAu7wbCwk4MVQQWEC7sdO8KrbMk+jB8i4yKH/Xhx5C6rOhccuL0YC7vBMDHJwarC7txzgXHjgK4u4I03zLeLBsb4ITIuKQnIyhLHjCF3Wd258Npr4XvPWoyF3WCYmORgxcRVILwDOMDhWCcwfojMYQzJwarCbtYssZXawYPAvn3m2xUFC7vBcPKqHKwKKqDvFRPZi0mJyBzmIDlY1bkwZAhQUiKObcpBLOwGoycmzm9wl5WFnT7H4e23gWPHzJ+PYotcPGHTsAOR0piD5GBH54JNo0Ys7AbDHgc5WDVxFQDGjwfOOw8IhYBt28yfj2LTP69Tp7hYhcgI5iD3aZq1OUjvXNiyReQhi7GwGwyDSg5WXi0BjqxMIoiJ38Ev/8wwhogSxxzkvhMnxMUpYE0OmjFDDMk2NwO7d5s/Xz8s7AbDoJKDVfMbdFxA4YxAgHOEiMxgDnKf/rMPBMKrlM1ITQVmzxbHNuQgFnaDYVKSg9U9dvodKN5/H2hqsuacFB0TE5FxjB/3RXYsBALWnNPGRXws7AbDiatysLqwGzkSKC4Wx1wday/efYLIOMaP+6zOP0B4OtDWrUB3t3XnBQu7wUUWdjZMcqQ4WTlxVcfhWGewx4HIOMaP++wo7IqLgREjgLY2sUODhVjYDUb/IDVNfADkvFAIaG0Vx3YUduyxsxcTE5FxjB/32dGxEAyGpwRZ3LnAwm4w6elil2iAgeWW1tbwHmhWLZ4AxOTV5GTg00/FF9mDiYnIOMaP++zosQNs252Bhd1guKrPffrPPTVVFNpWycoCZs4UxxyOtQ8TE5FxjB/32VXY6aNGO3ZYus8nC7t4cAGFu+wKKoDDsU7g5G8i49ix4D6rt9vSnXceMHYs0NUFvPGGZadlYRcPXjG5y475DTq9K/y113jLK7swfoiMY8eC++zqXAgEbOlcYGEXDyYmd9nZY3fppUBGhtjL7oMPrD8/MX6IzNDjp60N6Olxty1+5UTngoXTgVjYxYOJyV12FnZpabbuAE5g/BCZEfl3j7127nBiOtDbbwPHjllyShZ28WBicpdd8xt0vG+svRg/RMZFLhpjDLnDzsKuoAA491yxrde2bZackoVdPDj52112BhUQvmKqrg7f6JmswzlCROZwAYW7PNa5YKiwW7NmDQoLC5Geno6ZM2di165dAz5/9erVOP/885GRkYGCggLcddddOHnypKEGu4I9Du6yu7C7+GJg2DBReNTW2vMefsakRBbzbQ7ixZE7nOpcsGgBRcKF3caNG1FeXo6KigrU1taiqKgI8+bNw5EjR6I+/9lnn8U999yDiooK7NmzB0888QQ2btyIX/ziF6Yb7xgWdu6yc+IqACQlAXPmiGMOx1qP8UMWYg4ix9mdg/T88957YiGfSQkXdqtWrcLixYuxaNEiTJo0CWvXrkVmZibWr18f9fk7duzArFmzcMMNN6CwsBDXXHMNvve97w16hSUVBpW77L5aArifnZ30z+3kSbFfE5EJzEHkOLtz0KhRQFGROLYgByVU2HV1daGmpgalpaXhEwSDKC0txc6dO6O+5rLLLkNNTU1vEO3fvx8vvvgivvrVr8Z8n87OTrS0tPT5chWDyl12z28AwnMctm8XBQhZJ/JzYwyRCU7kIOnyD8Ac5KaurnBOsLNzIXJPVZMSKuyam5vR09ODvLy8Po/n5eWhsbEx6mtuuOEG3Hfffbj88suRkpKCs88+G3PmzBmwG7yyshI5OTm9XwUFBYk003pcPOEuJ3rsLrgAOOcc0SXe3Gzf+/hRUpK4fRvAxESmOJGDpMs/AOepuinyZ56dbd/76KNG//iH6VPZviq2uroaK1euxO9+9zvU1tbij3/8I1544QXcf//9MV+zbNkyHD9+vPfr4MGDdjdzYLxacpcThV0gAHz0EfDSS8D48fa9j1/x4ohckmgOki7/AFw84SY9/wwZAiQn2/c+V18NNDSIHGRSQq3Mzc1FUlISmvpN7mtqasKYMWOivmb58uW46aabcOuttwIALrroIrS3t+O2227Dv//7vyMYPL22TEtLQ1paWiJNsxcLO3fZPXFVFwjYe34/y8kBDh1iDJEpTuQg6fIPwBzkJic6FgCxV+HYsZacKqEeu9TUVEybNg1VESsHQ6EQqqqqUFJSEvU1HR0dpwVOUlISAEDzyr05I4PKK21WiVOBRfbxS2L69FPgt7/lPE2bMAcpHj8ycqpjwUIJ9yuWl5fj5ptvxvTp0zFjxgysXr0a7e3tWLRoEQBg4cKFGDduHCorKwEA8+fPx6pVq3DxxRdj5syZ2LdvH5YvX4758+f3Bpf09A/01CngxAkgM9Pd9viJpjmzeILs5ZfEtGwZsHGjmIvzgx+43Rol+ToHqR4/MvJgx0LChd2CBQvw+eefY8WKFWhsbERxcTE2b97cO5m1vr6+z9XRvffei0AggHvvvRcNDQ0YNWoU5s+fjwcffNC6f4XdhgwRw3SaJqp3FnbO6egI3/jaQ4FF/fglMdXXi+9797rbDoX5Mgf5JX5k5IfCDgDKyspQVlYW9f9VV1f3fYPkZFRUVKCiosLIW8khGBS9RcePi68YcznIBnpQJSWJApu8yS+LJz7/XHz/7DN326E43+Ugv8SPjDw4YsR7xcaLV0zu0P+QDR3KxQ1e5pf40Qu7AwdcbQYpxi/xIyMP9tixsIsXA8sdHgwqisIP8dPVFf73sceOrOSH+JGVBxdPsLCLFwPLHR7sBqco/BA/kRtbHzoEdHa61xZSS+Q+dl5ZyasKD3YusLCLF3f+docHg4qi8ENhpw/D6mTY2JbUoMdPKAS0tbnbFr/xYA5iYRcv7vztDg8GFUXhh8nf/Qs7zrMjq2RkiAVkgNoXRzLy4KgRC7t4+aHHQUYenN9AUfghfvoXdpxnR1YJBNi54BYPdi6wsIuXHxKTjDwYVBSFH+KHPXZkJz/EkIw82LnAwi5eDCp3eLAbnKLwQ/ywx47s5IcYkpEHOxdY2MWLiyfc4cGgoij0z6+tLXwnEdXohd3554vvLOzISizs3OHBHMTCLl6c3+AODwYVRRHZ49ra6l477KQXdtOni+8ciiUrsXPBeT094VXIHho1YmEXL14tuYOFnRrS0sQXoG4M6YXdJZeI7w0NwKlT7rWH1MLOBedF/qw9lINY2MWLhZ07PDhxlWJQPYb0wm7yZCA1VVzt/+Mf7raJ1KF6/MhI/1lHXph6AAu7eDGo3MEeO3WoHkN6YZeXB0yYII45z46sonr8yMijHQss7OLF+Q3u4KpYdaicmHp6gKNHxfGoUUBhoTjmPDuyisrxIyuPdiywsIuX/sGePClu9k3O8GhgURQqzxH65z/D9/AcORI44wxxzB47sgoLO+d5NP+wsItXZI+RiolJRp2d4RupeyywKAqVe731YdgRI4Dk5HBhxx47soofbssnG4+OGLGwi1dyMjBkiDhWMTHJKPIPWHa2e+0ga6jc46AXdqNGie/6UCx77MgqKsePrNhj5wMMLGfpP+fs7PANsMm7VI6f/oUde+zIairHj6y4eMIHGFjO8mg3OMWgcvzE6rE7eFDdO22Qs1SOH1mxx84HOMfBWR4NKopB5cUT/Qu7sWNFL3N3N3D4sHvtInVEFnb6Qh2yl0dzEAu7RPCKyVkeDSqKwQ+LJ/TCLjkZKCgQx5xnR1bQ46e7O7yojOzl0VEjFnaJYGHnLI/Ob6AYVI6f/oUdwHl2ZK3sbCAQEMcqxpCMPNq5wMIuESonJhl5NKgoBpXjJ1phx5WxZKVgMLw7gIoxJCOP5iAWdolQOTHJyKPd4BSDyvEzUI8dCzuyisoxJCOPjhqxsEsEF084y6NXSxSDyklpoB47DsWSVVSOIRl5NAexsEsEg8pZHg0qiiHywkilVX2hENDcLI7ZY0d2UnkBkow8moNY2CWChZ2zPNoNTjHon2MoBLS3u9sWKx07Ft6rLjc3/HjkHDuVCllyj8pbBslG08I/Z49NB2JhlwgWds7y6NUSxZCZGb6DiEoxpA/DDh0KpKWFHx8/XqxiPHkSOHLEnbaRWpiDnNPWJi5CAc/lIBZ2iWBQOYuLJ9QSCKgZQ9Hm1wFAaiowbpw45jw7soKK8SMrvbcuKUlclHoIC7tEcH6Ds9hjpx4VE1Oswg7gPDuylorxI6vI/KPvH+gRLOwSwfkNzmJhpx4VY0gv7CLn1+m4STFZiZ0LzvFw/mFhlwj9A25t5Y29neDhwKIYVExMA/XYcZNispKKF0ay8vBUIBZ2iYgsMFpb3WuHH/T0hFdOsrBTh4pDSfEMxbLHjqygYvzIysMdCyzsEpGWFl71xsCyV+QVqQevmCgGFRMTe+zIKSrGj6w8vN0WC7tEqTiUJCP955ueLlYXkhpUTEzx9thxLzsyS8X4kRV77HyEcxyc4eGgogGoGD8DFXYTJojv7e3A0aPOtYnUxMLOOR7OQSzsEsXAcoaHg4oGoGKP90CFXUYGkJcnjjnPjszi/cqdw8UTPsLCzhkent8wmDVr1qCwsBDp6emYOXMmdu3aNeDzjx07hqVLlyI/Px9paWk477zz8OKLLzrUWoupFj+aNnBhB3CeHVlHj5+ODqC72922qM7DnQss7BKlWmKSlYeDaiAbN25EeXk5KioqUFtbi6KiIsybNw9HYtxyqqurC1/5yldw4MABPPfcc9i7dy/WrVuHcfodDbxGtfhpbQW6usRxrMKOK2PJKpG9R+y1s5eHc1Cy2w3wHBWHkmTk4W7wgaxatQqLFy/GokWLAABr167FCy+8gPXr1+Oee+457fnr16/H0aNHsWPHDqSkpAAACvUeoBg6OzvR2dnZ+98tMiUA1Qo7vbcuIwMYMiT6c9hjR1ZJSRG3t+roEDE0cqTbLVKXh0eN2GOXKBUnf8vIw1dLsXR1daGmpgalpaW9jwWDQZSWlmLnzp1RX/OXv/wFJSUlWLp0KfLy8jB58mSsXLkSPQNskF1ZWYmcnJzer4KCAsv/LYapFj+DDcMCvK0YWUu1iyNZeTgHsbBLFIPKGR4Oqliam5vR09ODPH0y/Zfy8vLQ2NgY9TX79+/Hc889h56eHrz44otYvnw5HnnkETzwwAMx32fZsmU4fvx479fBgwct/XeYolqPd3Oz+D5QYaf32HEolqygWgzJysM5iEOxiWJh5wwPd4NbKRQKYfTo0XjssceQlJSEadOmoaGhAf/5n/+JioqKqK9JS0tDmr6RtmxUix/22JHTVOv1lpWHpwOxsEuUaolJVh6+WoolNzcXSUlJaGpq6vN4U1MTxowZE/U1+fn5SElJQVJSUu9jF1xwARobG9HV1YVUr23erH+eXV3AyZNiA2ovS6SwO3ZM/F4r9DtNLmAOsp+meToHcSg2UQwqZ3j4aimW1NRUTJs2DVVVVb2PhUIhVFVVoaSkJOprZs2ahX379iEUCvU+9tFHHyE/P997RR0AZGcDgYA4ViGG4inssrLCk9zZa0dmMQfZr7MzvJ0MCzsf4AaRzvDw1dJAysvLsW7dOjz11FPYs2cPlixZgvb29t5VsgsXLsSyZct6n79kyRIcPXoUd9xxBz766CO88MILWLlyJZYuXerWP8GcYFAUd4AaMRRPYQdwyxOyDgs7++k/20Ag/PfKQzgUmygGlTMULewWLFiAzz//HCtWrEBjYyOKi4uxefPm3gUV9fX1CAbD11sFBQV4+eWXcdddd2HKlCkYN24c7rjjDtx9991u/RPMy8kRRZ0KMRRvYVdYCNTWsseOzOPiCfvpP9vsbHEx6jEs7BLFws4ZihZ2AFBWVoaysrKo/6+6uvq0x0pKSvDmm2/a3CoHqZSY2GNHTuPiCft5fCqQ90pRt0UGlaa52xaVcVWsulS6OEqkxw5gjx2Zp1L8yMrjHQss7BKlf9A9PUB7u7ttUZWmhQs7j14x0QBUSkzssSOnqRQ/svJ4xwILu0RlZgL61hPsCrdHWxugrwL1aGDRAFRJTCdOhC/u2GNHTlElfmTGHjufCQTUmiMkI/3nmpws7sFJalFljpDeW5eSMnjPst5j19zMnn4yh/nHfizsfIhXTPaKDCp9zzNShyqJKXIYdrDf02HDwn832GtHZqhyYSQzLp7wIRZ29vL4/AYahCrxE+/8Oh3n2ZEVVIkfmbHHzocYWPby+NUSDUKV+Em0sOM8O7KCHj+treG5yGQtFnY+xLtP2MvjQUWD8Gthp/fYsbAjM/T40TRR3JH1PD5qxMLOCFUSk6xY2KlNlTlCRnvsOBRLZqSnA/p9opmD7OHxHMTCzggWdvbyeFDRIFRcPBEP9tiRVThqZC+P5yAWdkawsLOXx7vBaRCqxA8XT5BbVIkhWXl8njcLOyMYVPbyeFDRIFSJH6NDsY2NwMmTtjSJfEKVGJIVe+x8SJWhJFl5PKhoEPrn2tEBdHe72xYzEi3sRo4Ud64BgPp6e9pE/sDCzl4eHzViYWeEKpO/ZcXCTm2RPbFeXtWXaGEXCHDLE7IGCzv7dHeLi07AszmIhZ0RDCp7sbBTW0pK+FZxXo2hrq5w2+Mt7ADOsyNrcNTIPpEdNh6dDsTCzggWdvbyeDc4xcHrMdTcLL4nJQHDh8f/OvbYkRU4amQf/W9SRoa4CPUgFnZGeD0pyY49durzegzpw7AjRwLBBP6MsseOrOD1+JGZAvmHhZ0R7Aa3F1fFqs/riSnR+XU69tiRFbwePzJTYMSIhZ0R+gfe1QV0drrbFtVomhJXTDQIrw8lGS3s2GNHVmBhZx8F8g8LOyOys8PHDCxrnTwZ3gLDw4FFg/B6YjLbY3fokLgwJDKCo0b2YWHnU0lJ4eKOgWUt/ecZCABZWe62hezj9cRktLAbPRpISwNCIeAf/7C+XeQPXu/xlpkCU4FY2Bnl9R4HWel/qIYOTWxSOnmL1+PHaGEXDPKesWSe1+NHZn7tsVuzZg0KCwuRnp6OmTNnYteuXQM+/9ixY1i6dCny8/ORlpaG8847Dy+++KKhBkvD6z0OslLgaoni4PXEZLSwA1jYWcD3Ocjr8SMzBQq75ERfsHHjRpSXl2Pt2rWYOXMmVq9ejXnz5mHv3r0YPXr0ac/v6urCV77yFYwePRrPPfccxo0bh88++wzDhg2zov3uYVe4PRQIKoqD1+PHTGGnz7PjAgpDmIPQt7DTNDF1hayhwKrYhAu7VatWYfHixVi0aBEAYO3atXjhhRewfv163HPPPac9f/369Th69Ch27NiBlC83+yvU/7DF0NnZic6I1aYtMv7x5xWTPVjY+YPX44c9dq6xOwd5Iv/oIxo9PeL2V0OGuNselSiQgxIaiu3q6kJNTQ1KS0vDJwgGUVpaip07d0Z9zV/+8heUlJRg6dKlyMvLw+TJk7Fy5Ur09PTEfJ/Kykrk5OT0fhUUFCTSTGd4PTHJSoGgojh4fSqDXtjl5ib+Wm55YpgTOcgT+ScrKzwHWcbC08sUyEEJFXbNzc3o6elBXl5en8fz8vLQ2NgY9TX79+/Hc889h56eHrz44otYvnw5HnnkETzwwAMx32fZsmU4fvx479fBgwcTaaYzWNjZQ4FucIqDl+Onpwc4elQcmxmKZY9dwpzIQZ7IP4GA9y+OZKXAPO+Eh2ITFQqFMHr0aDz22GNISkrCtGnT0NDQgP/8z/9ERUVF1NekpaUhLS3N7qaZ4+XEJDMFgori4OX4+ec/xbwmQNxSLFF6j93Bg6JITEqyrm10mkRzkCfyDyBi6Ngxb8aQzBTosUuosMvNzUVSUhKampr6PN7U1IQxY8ZEfU1+fj5SUlKQFPHH64ILLkBjYyO6urqQmppqoNkS0AsPdoNbS4Ggojh4ubDTh2GHDzd2k/CxY4HkZODUKbFRsYxDfZJiDorg5RiSmQKjRgkNxaampmLatGmoqqrqfSwUCqGqqgolJSVRXzNr1izs27cPoVCo97GPPvoI+fn53g0ogEFlFxZ2/qB/vq2tYrNeLzGzcAIQPXR6Mcd5dglhDorAHGQPBXJQwvvYlZeXY926dXjqqaewZ88eLFmyBO3t7b0rlBYuXIhly5b1Pn/JkiU4evQo7rjjDnz00Ud44YUXsHLlSixdutS6f4UbGFT2UCCoKA56j7emAW1t7rYlUWYLO4Dz7ExgDvoSR42sFwqJi03A0zko4Tl2CxYswOeff44VK1agsbERxcXF2Lx5c+9k1vr6egQj7hhQUFCAl19+GXfddRemTJmCcePG4Y477sDdd99t3b/CDSzs7KFANzjFIT1dDGN2d4sY8tKcSisKO66MNYw56EvMQdZrbQ3Pn/XS36R+DC2eKCsrQ1lZWdT/V11dfdpjJSUlePPNN428lbwYVPbg4gl/CAREDDU3i8/cS/PM2GPnOuYgMAfZQf9ZpqSIi0+Psn1VrLLYDW4PDsX6R2Rh5yUq9NhpGrB/v1jAYbUxYxi/TmBhZ73IESMP382DhZ1RDCp7sLDzD6/eVkyFHrvycmD1anvO/X//L3DTTfacm8KYg6ynSP5hYWeU/sG3t4ur3mT+KC2hSGBRHLy6waqVPXaffSYmbAcTXsdmnKYBf/iDOB461Pp99Ly80tRLvBo/MlMk/7AaMSryg29pAUaMcK8tqujuBk6cEMceDyyKg1d7HKwo7MaPF8VcVxfQ1ATk51vTtnh88onYPy81FWhsBDIynHtvso5Xe7xlpkhh5+BlomJSUsJ/EL2WmGQV+QcqO9u9dpAz/FzYpaQA48aJY6eHY7duFd9nzGBR52VejR+ZKbJ4j4WdGewKt5b+c8zMNLajP3mLFxOTpokFH4C5wg4Iz7NzegGFXthdeaWz70vW8mL8yI49dsSucIspElQUJy/Gz7Fj4v6ugPnCLnKenZNY2KmBhZ31FNlHlYWdGQwsa7Gw8xcvxo8+DJudDZi9UbwbW54cOADU14vFXpdd5tz7kvU4YmQ9RXIQCzszvJiYZKZIUFGcvJiYrJhfp3NjyxO9t276dGDIEOfel6yn/53s7BRfZJ4iOYiFnRks7KylSDc4xcmL8WNlYedGjx2HYdUROcHfS9MZZMbFE+TJHgeZKRJUFCe/F3aRPXb6/Snttm2b+H7FFc68H9knKQnIyhLHXoohmbHHjjw5+VtmigQVxcmL8WNlYaffH7ejI7zS1k4NDWIPu2AQuPxy+9+P7OfFiyOZKTJqxMLODAaVtVjY+YsX48fKwi49PbwxsRPz7PRh2IsvZq+4KrwYQzJTJAexsDODQWUtRYKK4hQ5lcGpoUizrCzsAGfn2XF+nXr0GPJSr7fMFMlBLOzMYGFnLUW6wSlO+ud86lT4VnKys7qwc3JlLAs79TAHWUfTlJnnzcLODC6esJYiQUVxysoS870A78SQV3vsGhuBvXuBQACYPdve9yLnsLCzTkdHePNxj3cusLAzw4uTv2WmSDc4xSkQ8N5Qkld77PTVsFOmAMOH2/te5BwWdtbRf4bBYHi1sUexsDODQWUtFnb+46UY0jTv9thxGFZNXoof2ekXl0OHiotOD2NhZwaDylos7PzHS9MZ2trCO/zb0WNn5wISFnZq8lqPt8wUyj8s7MyIHIoNhdxtiwq4eMJ/vHRxpPfWZWRYdzuuCRPE95YW4Ngxa87ZX3Mz8P774pgbE6vFS/EjOxZ2BCD8C6Bp4mqejAuFgNZWcczFE/7hpcRk9TAsIArE3FxxbNc8O31+3YUXht+L1OCl+JGdQov3WNiZkZ4OJCeLY3aFm9PaGh6KUuCKieLkpcRkR2EH2L+AgsOw6vJS/MiOPXYEQEywZGBZQ//5paaKgpn8wUsry+0q7OxeQMHCTl3MP9ZRaCoQCzuzGFjWUOhqiRLgpcUTXuyx++IL4N13xTHn16nHS/EjO4VyEAs7s1jYWUOhoKIEeCl+vNhjt327mOJw/vnAmDHWn5/c5aUeb9kplINY2JnlpcQks8g9hMg/vBQ/Xuyx04dh2VunJj1+2trCd00gY7h4gnpxHyFrKHS1RAlgYWdvjx3n16kt8u8lc5A5CuUgFnZmeSkxyUyhoKIEeGkoye7C7ujR8JY/VmhpAWprxTELOzVFLjZjDjKHiyeoFws7a7Cw8ycvxY9dhV1ODjBsmDi2cjj2jTfE/pBnnQWMH2/deUkuXEBhDYVyEAs7s7yUmGSmUFBRAryUlOwq7AB75tlxGNYfvNTrLTOFchALO7NY2FmDiyf8ySvxc+IE0N4uju0o7OyYZ8fCzh+8EkOy4+IJ6sXFE9ZQ6GqJEqB/3idPAl1d7rZlIHpvXUqKPX/4re6xa28H3n5bHLOwUxsLO2solINY2JnFoLKGQkFFCYgskmS+OIochg0ErD+/1T12O3YAp04BEyaEi0ZSE3OQeZ2d4gtQIgexsDOLQWUNFnb+lJQEZGWJY5ljyM75dYD1PXYchvUP5iDzIi8qORRLDCqLsLDzLy8soLC7sLO6x46FnX9wOpB5+t+erCxxselxLOzMYmFnDYX2EKIEeSGG9MIuN9ee8+uF3ZEjYqGGGSdOALt2iWMWdurzQvzITrGOBRZ2ZkX2Nmiau23xMoVWJFGCvJCY7O6xGzEiPCRdX2/uXG++KRaijB0LnH22+baR3LwQP7JTLP+wsDNLD6pTp8TKPkqcpil3xUQJ8MI+XHYXdoGAdcOxkcOwdiz0ILmwsDNPsfzDws6srKzwH08GljEdHeEbWCsSWJQALyQmuws7wLoFFJxf5y9eiB/ZKTYViIWdWcGgNyZ/y0z/uSUlAUOGuNsWcp4X4seJws6KHrvOTjEUC7Cw8wsvxI/s2GNHp+EVkzmRd53g0JH/eCF+vNJj99ZbYkrI6NHA+edb0iySnBemMsiOhR2dhldM5ig2cXUwa9asQWFhIdLT0zFz5kzs0lcwDmLDhg0IBAL4xje+YW8DncbCTrCix04fhr3iCl4k+YUX4kd2iuUgFnZW4BWTOYpdLQ1k48aNKC8vR0VFBWpra1FUVIR58+bhyJEjA77uwIED+OlPf4rZs2c71FIHyR4/XV3h31HZe+w4v85/IuOHOzMYo1gOYmFnBV4xmaNYUA1k1apVWLx4MRYtWoRJkyZh7dq1yMzMxPr162O+pqenBzfeeCN++ctf4qyzznKwtQ6RPX6am8X3YFBsS2IXvcfu0CFj983t7ha3EgNY2PmJHj+hENDW5m5bvIqLJ+g0sicm2fmksOvq6kJNTQ1KS0t7HwsGgygtLcXOnTtjvu6+++7D6NGjccstt8T1Pp2dnWhpaenzJTXZpzLow7AjR4rizi6jRwPp6aLX5eDBxF9fUwO0t4vi88ILrW8fySkjI3y3BFljSHaK5SAWdlZgYWeOYkEVS3NzM3p6epCXl9fn8by8PDQ2NkZ9zfbt2/HEE09g3bp1cb9PZWUlcnJyer8KCgpMtdt2ssePE/PrAPN72UXOr7OzACW5BALyT2eQnWI5iNFvBdl7HGQXuSqWerW2tuKmm27CunXrkJvArayWLVuG48eP934dNNL74yQWdmFm5tlxfp1/yR5DslNs8USy2w1QAq+WzFHsaimW3NxcJCUloampqc/jTU1NGDNmzGnP/+STT3DgwAHMnz+/97FQKAQASE5Oxt69e3F2lFtGpaWlIS0tzeLW20j2pORkYWe0x+7UKWD7dnHMws5/ZI8h2SmWg9hjZwUGlTmKBVUsqampmDZtGqqqqnofC4VCqKqqQklJyWnPnzhxInbv3o26urrer+uvvx5z585FXV2d/EOs8dI/97a28B1IZOKFHru6OqC1Vfwsp0yxulUkO+YgcxTLQeyxswKDyhzFgmog5eXluPnmmzF9+nTMmDEDq1evRnt7OxYtWgQAWLhwIcaNG4fKykqkp6dj8uTJfV4/bNgwADjtcU+LHP5obQW+/DdKwws9dvow7OzZ4Yn05B+cDmRcT49YdAQok4NY2FmBhZ05PirsFixYgM8//xwrVqxAY2MjiouLsXnz5t4FFfX19Qj6beJ7Wpr46uwUvwuyFXb6didOFnaJ9thxfp2/cTqQcZE/M0VyEAs7K7CwM8dniyfKyspQVlYW9f9VV1cP+Nonn3zS+gbJICcHOHJEzhhyYyj2H/8Q8+aS4/gT3dMDvP66OGZh50/MQcbpP7P0dCA11d22WMRnXQM20QsSXi0Z46MeO4pB5sTkZGGXnw+kpIhiraEhvtfs3g0cOwZkZwMXX2xr80hSMseP7BRbEQuwsLMGg8ocFnYk81CSk4VdMAhMmCCO4x2O3bZNfJ81K74ePlIPc5BxCuYfFnZW0H8hTpwQt/WhxCgYWJQgWRNTTw/wz3+KYycKOyDxBRScX0eyxo8XKHY7MYCFnTUiu3AZWInp7BRfgFKBRQmSdVXf0aPhG6uPHOnMeyay5YmmhXvsrrjCtiaR5DgdyDgFOxZY2FkhORkYMkQcy5aYZBf5hyg72712kLtk7XHQh2GHDxdz35yQSI/dBx+IVbsZGcD06bY2iyQma/x4AQs7iolXTMboQZWVxf23/EzWxOTk/DpdIj12+jDsZZcps6KPDJA1fryAiycoJgaWMQpeLZEBsi6ecKOwS6THjvPrCGD+MUPBHMTCzioMLGMUDCoyQNb4cbPHrr4e+PLewFFpGgs7EiLjR58TSvHh4gmKSdbEJDsWdgTIu3jCjcJu3DgxLaG7Gzh8OPbzPvoIaGoSd+2YMcO59pF89Pjp7gZOnnS3LV6jYA5iYWcVFnbGKBhUZICs8eNGYZecDIwfL44Hmmen99ZdeqnYNZ/8KzsbCATEsWzTGWSnYA5iYWcVWXscZOez24lRDCzs+opnnh2HYUkXDIZ3FZAthmTHwo5iknXyt+wUDCoyQNb4cauwG2xlLOfXUX+yXhzJjqtiKSYGlTEs7AiQN35k7bHbv1/cSzYlRQzFEskaQ7JTMAexsLMKg8oYBYOKDIjcB1KmVX1uF3axeuz03roZM4DMTGfaRHLjdCBjuCqWYmJhZwwLOwLCn39PD9De7m5bdJom7uoAuDcUG6vHjsOw1J+s0xlkpmks7GgAvFoyhosnCBC9TvqdR2SJoWPHgFOnxLFbPXb19dF7MPX7w7KwIx07FxLX1hbeK5KFHZ2GV0vGsMeOALFVg2wxpA/DZmeLveKcVFAgfiYnToTboauvFz15SUniVmJEAAs7I/SfVVKSuN+yIljYWYVBZQwLO9LJFkNuza8DRCGZny+O+w/H6sOw06eLeywTAfLFjxdE5h99H0AFGCrs1qxZg8LCQqSnp2PmzJnYtWtXXK/bsGEDAoEAvvGNbxh5W7kxqIxhYUc62WLIzcIOiL3liV7YXXGFo82RCXNQFLLFjxcoOL8OMFDYbdy4EeXl5aioqEBtbS2Kioowb948HDlyZMDXHThwAD/96U8xe/Zsw42Vmv6L0doqJoBTfFjYkU62eapuF3axtjzx+cIJ5qAYIleWU3wUzT8JF3arVq3C4sWLsWjRIkyaNAlr165FZmYm1q9fH/M1PT09uPHGG/HLX/4SZ5111qDv0dnZiZaWlj5f0ouc/N/a6l47vCRyBSQXT5BsPQ5uF3bReuwOHQL27RN3Grj8clea5Ta7c5An8w8gX/x4AQs7oKurCzU1NSgtLQ2fIBhEaWkpdu7cGfN19913H0aPHo1bbrklrveprKxETk5O71dBQUEizXRHejqQmiqOvfKHwG2RPyfFAosMkC0xuV3YReux03vriot9GTNO5CBP5h9AvvjxAgXvOgEkWNg1Nzejp6cHeXl5fR7Py8tDY2Nj1Nds374dTzzxBNatWxf3+yxbtgzHjx/v/Tp48GAizXQPAysx+s8psigm/5J1VaxMPXY+H4Z1Igcx//iIoj12yXaevLW1FTfddBPWrVuH3NzcuF+XlpaGNKe3F7BCTo5IBgys+CgaVGSQbInJ7cIussdO08SqPZ8XdokykoM8nX8AeeLHCxTNQQkVdrm5uUhKSkJTU1Ofx5uamjBmzJjTnv/JJ5/gwIEDmD9/fu9joS83A0xOTsbevXtx9tlnG2m3nBhYiVE0qMggLp7oSy/s2tqAL74AuruBDz8UBZ6qCwAGwRw0AC6eSBxXxQKpqamYNm0aqqqqeh8LhUKoqqpCSUnJac+fOHEidu/ejbq6ut6v66+/HnPnzkVdXZ135i7Ei4VdYnjXCYokW/y4XdhlZACjR4vjAwfCd5u46CJgxAh32uQy5qAB6PHT0SEuAmhwinYuJDwUW15ejptvvhnTp0/HjBkzsHr1arS3t2PRokUAgIULF2LcuHGorKxEeno6Jk+e3Of1w4YNA4DTHlcCr5gSo2hQkUEyFXaa5n5hB4heuyNHxDw7DsMCYA6KKfICuaUFGDnSvbZ4haI5KOHCbsGCBfj888+xYsUKNDY2ori4GJs3b+6dzFpfX49g0Kc3tJApMXmBokFFBsm0eKKtDejsFMcJzA+2XGEh8NZboseOhR0A5qCYUlLEPZc7OsTfVhZ2g1N0VayhxRNlZWUoKyuL+v+qq6sHfO2TTz5p5C29gYVdYljYUSSZ4kfvrUtPB4YMca8d+jy7mhrgvffEsY/vOKFjDoohJydc2NHgFM1BPryssZFMickLFA0qMkimxRORw7Bu3kNS3/Jk0ybxfdIkd4eGSW4yxZAXcPEEDYqFXWIU7QYng2SKHxnm1wHhHruODvHd58OwNAiZpjN4gaKdCyzsrMTFE4lR9GqJDNJ/D7q6gJMn3W2LLIWd3mOnY2FHA5Hp4kh2msbCjuLAoEqMokFFBmVnh4c93b44kqWw03vsdJxfRwNhDorfyZPhbWEUGzViYWclBlViWNhRpGBQFHeA+zEkS2GXnR3es+7cc4H8fHfbQ3JjDoqf/jMKBMJ/dxTBws5KDKrEsLCj/mSZ/C1LYQeEe+04DEuDkSV+vEAfFcjOFheVClHrX+M2FnaJYWFH/ckSQzIVdpddJr5/85vutoPkx8UT8VM4/7Cws1Lk4glNc7ctXsBbilF/LOxO9+tfA7t3A1/9qtstIdnJEj9ewMKO4qL/gvT0hLcnoOg0jati6XSy9DjIVNhlZgKq3f6K7MHCLn4Kb7fFws5KQ4YASUnimIE1sLY2IBQSxyzsSCdLYpKpsCOKlyzx4wXssaO4BAKcvBov/eeTnAxkZLjbFpKHDInpxAmgvV0cs7AjL5EhfryChR3FjYEVn8igcvOWTSQXGS6M9N66lBQl/+iTwrhJfvwUngrEws5qMiQmL+DCCYpGhgsjvbDLzeVFB3mLDPHjFeyxo7jJMvlbdgoHFZkgQ/xwfh15lR4/ra3hOcwUncI5iIWd1XjFFB+Fg4pMkCF+mpvFdxZ25DV6/GiaKO4oNq6KpbjJkJi8gIUdRSND/LDHjrwqPR1ITRXHzEEDUzgHsbCzmgyJyQsUDioyQYY5qizsyMtkiCEv4OIJihuDKj5cPEHRyHBhxMKOvEyGeapeoHDnAgs7qzGo4qNwUJEJLOyIzJEhhrxA4RzEws5qDKr4KBxUZIL++9DRAZw65U4bWNiRlzEHxYeLJyhuDKr4sLCjaCL/yLrV683CjryMOWhw3d3iDjOAkjmIhZ3VGFTxYWFH0aSkhG8x51YMsbAjL+M878FFXjSyx44GxaCKj8Ld4GSSmxdH3d3AsWPimIUdeRHneQ9O/9uSmSkuJhXDws5qDKr4KLzUnExys7DTNycOBoERI5x/fyKzOGo0OMVHjFjYWY1BFR/FA4tMcPPiSB+GHTlSFHdEXsMcNDjF8w//cllN/0Xp7BRfdDpNUz6wyAQ3ExPn15HXsbAbnOJTgVjYWS07O3zMwIru5EkxlwlgYUenc3OeKgs78jrO8x6c4h0LLOyslpQULu4YWNHpP5dAAMjKcrctJB/22BEZx3neg1N8jjcLOzvoV0wMrOj0n0t2Nucx0elY2BEZx6HYwbHHjhLGwBqY4kFFJsmweIKFHXkV88/gFM9BLOzswMAamOJBRSaxx47IuMj40TR32yIrLp6ghHm5sHvsMeC3v7X3PVjY0UBY2BEZp8dPT4+457KXdHQAd90F7Nhh7/sonoOS3W6Akrxa2B0+DPzrv4rjr34VOPtse95H8aAik7gqlsi4IUPE3OVQSExnGDLE7RbF7/HHgdWrgW3bgJoa+96HiycoYV5dPPHaa+Hjqir73kf/uSjaDU4msceOyLhAwLtbnuh55513gKNH7XsfxTsXWNjZwas9dpHFnJ2FneJBRSa5tXiipwf45z/FMQs78jIv5qBTp4DqanGsacCWLfa9l+I5iIWdHbwYVJrWt5jbskV05dtB8aAik9yKn6NHw5PNR4509r2JrOTFHFRb2/diLnIEyWpcPEEJ82JQ7d8P1NcDKSlAZqYYknrvPXvei4UdDSSyx86ui4to9GHY4cNFHBB5lRdzkN6xMGxY3/+2g+I5iIWdHbwcVJdeClxxRd/HrKZ4UJFJ+lW0pgFtbc69L+fXkSq8OMdOzzc/+YlY/LF3L9DQYP37hEJAa6s4VjQHsbCzgxeDSu/2vuoq8RX5mNUU7wYnk9LTwz1mTsYQCztShdduK3byJPDGG+L4W98Cpk0Tx3bkIL2oA1jYUQK8FlShUDiArr5afAHA1q1iQqvVFF9qTiYFAu7EEAs7UoXXRo127hTFXX4+cMEF4c4FO0aN9J9Jaqq4iFQQCzs7eC2o3ntPJLXMTGDmTKC4WMwzam0F3n7b+vfjUCwNxo0YYmFHqvBaDoocMQoEwp0LVVXW3z3DB/mHhZ0dvBpUs2eLq5hgEJg7Vzxm5xWTwoFFJrlZ2OXmOveeRHbwWg7S84zeUzdrlshF//gHsG+fte/lg6lALOzsoAdVe7s9Q5lW04NKv0qKPGZhR25wY54qe+xIFV6a593SAuzaJY71vJOZCZSUiGOrc5AP8g8LOztEXgnIPs/u1Ckxlw6IXtjt2AGcOGHd+3V3h8+n8BUTmcShWCLjvDTP+/XXxebgZ58NnHFG+HE9B1m9gMIHc7xZ2NkhclKm7IH19ttiLt3w4UBRUfjx884Dxo4FOjutvSFz5M+DhR3FwsKOyDgvDcX2H4bVRe7OYOV+luyxI8O8Elh6UM2dCyQlhR/vP4HVKvrPIzPTt5vArlmzBoWFhUhPT8fMmTOxSx+GiGLdunWYPXs2hg8fjuHDh6O0tHTA5yuDq2KJjPNK/gGiTwUCgBkzgKwscZu/d9+17v1Y2JFhXgmsWEEV+ZiVXeE+CKqBbNy4EeXl5aioqEBtbS2Kioowb948HDlyJOrzq6ur8b3vfQ9btmzBzp07UVBQgGuuuQYNdmzcKROn40fTgOZmcczCjrzOK/nn88/DRZu+YE+XkhLeLN+OHKTwiBELO7t4IbBOnAgPs/bvBo987K23rPt3+LywW7VqFRYvXoxFixZh0qRJWLt2LTIzM7F+/fqoz3/mmWfwox/9CMXFxZg4cSIef/xxhEIhVNl5ux0ZOD35+9ix8EInFnbkdV7IP4C4JzkAXHQRMHr06f/fjv3sfJCDWNjZxQurknbsEHPoxo4Fzj//9P9fUACce66Y37BtmzXv6YOrpVi6urpQU1OD0tLS3seCwSBKS0uxc+fOuM7R0dGB7u5ujBgxIuZzOjs70dLS0ufLc5xOTPowbFaWspuWko/of187O8WXrAYaMYp8fNs2sfDOClw8QYZ5YVVS5N0mAoHoz7F6np0PgiqW5uZm9PT0IC8vr8/jeXl5aGxsjOscd999N8aOHdunOOyvsrISOTk5vV8FBQWm2u0Ktwo79taRCryyM0NkDopmyhRg5Ehxz+i33rLmPdljR4Z5oSs81mqkSFZ3hfsgqOzy0EMPYcOGDdi0aRPSB+hVWrZsGY4fP977dfDgQQdbaRGnL4xY2JFKkpJE7zMgbw6qrxebDyclhefS9WfHZvk+yEEs7Owie2F3/Hj4Cmigwk4PqvfeA5qarHlfQOmgiiU3NxdJSUlo6vdzbGpqwpgxYwZ87cMPP4yHHnoIr7zyCqZMmTLgc9PS0jB06NA+X57DHjsic2TPQXpv3SWXDDw1x+pRIx9MB2JhZxfZg2rbNjF37pxzgAkTYj8vNze8v50+0dUMHxd2qampmDZtWp+FD/pCiBJ9l/Uofv3rX+P+++/H5s2bMX36dCea6j4WdkTmyJ6D4hkxivz/O3cCHR3m39cHOYiFnV28ElSx5jZEsvKKyQdXSwMpLy/HunXr8NRTT2HPnj1YsmQJ2tvbsWjRIgDAwoULsWzZst7n/+pXv8Ly5cuxfv16FBYWorGxEY2NjWhra3Prn+CMyMVHVt8EPBoWdqQaPYZknGOnafHnoHPPBcaPB7q6gDfeMP/eLOzIMJmDCjBW2Fmxl5CPF08AwIIFC/Dwww9jxYoVKC4uRl1dHTZv3ty7oKK+vh6HDx/uff6jjz6Krq4ufOc730F+fn7v18MPP+zWP8EZ+u/HqVPW3tIuFhZ2pBqZOxf27gUOHwbS0oDLLhv4uVZulq9pvshByW43QFkyB1VTk5gzBwBz5gz+/NmzgeRkYP9+4MABoLDQ+Hv74GppMGVlZSgrK4v6/6qrq/v894EDB+xvkIyyssTE6VBI/CHOzLT3/VjYkWpkzkF6gTZrVnzbC111FfDUU+Y7Fzo6xH1pAaVzEHvs7CJzUOlz5YqK4ktk2dni9i6A+SsmFnYUj0DA2b0gWdiRamTOQYmMGEU+r6ZGbCZulP6zCAaBIUOMn0dyLOzsolJQRT7X7BUTCzuKl5MxxMKOVCNrDurpAfSRiXhz0LhxYhP9UCj8WiMi53jH2rtVASzs7CJrUAHh4myw1UiR9Oe+9pq5yew+XzxBCXCqx07TWNiRemS9+1FdHfDFF6J906bF/7rIHGSUTzoWWNjZJXLxhBOr+uJ14ICYK5ecHHtTyGhKSoCMDKCxEdizx/j7+ySwyAJOXRy1t4dvu8TCjlQh692P9BGjK68UeSheViyg8MHCCYCFnX30XxxNE7dDkYUeFDNmiLlz8UpLAy6/vO85EhUKAa2t4ljxwCILOJWY9N669HSl592Qz8g6ajTYbcRimTNHDJ9+8IHoYDDCJx0LLOzskpERvhqRKbCMDMPqzN5eTC/qAOUDiyzgVGKKHIZVeN4N+YyMhV1XF/D66+I40Rw0ciRQXCyOjQ7HsrAjUwIB+QJL04xfLUW+pro6vGQ8EfrPITU1viXu5G9uFHZEqpAt/wDA3/4mthwZNQqYPDnx15sdjvXJHG8WdnaSLbD0Luz0dODSSxN//dSp4t90/DhQW5v4631ytUQWcWryNws7UpGMiycibyNmpHfc7O4MPslBLOzsJNvdJ/RguPxyYz1mSUnhDY2NXDH55GqJLMIeOyLjZFw8YWSrrUiXXy6mOOmLABPFxRNkmmw9dmaDKvK1Rq6YfBJUZBGnF0+wsCOV6PHT1mZs6ozV2tuBN98Ux0ZzUFZWeLTJTOeC4jmIhZ2dZCrsIjeFNLJwQqe/dvv28BYR8fJJUJFF2GNHZFzk31kZeu1ef13c+/mMM4AzzzR+HjP72fkkB7Gws5NMhV1trWhHTk5im0L2N2kSMGaMuDG7fvUVL58EFVmEhR2RcZGL1GTIQZEjRmZWn0eOGiW6R6xPpgOxsLOTTIWdHlRz5oi5ckYFAsa3PWFhR4ng4gkic2TKQWZ2ZIh06aViO7EjR4D33kvstT7JQYYKuzVr1qCwsBDp6emYOXMmdu3aFfO569atw+zZszF8+HAMHz4cpaWlAz5fKTKtSjKzf11/Zgs7xa+WyCLssaMYmIPiJMsCvqNHgXfeEcdz55o7V2oqMHu2OE50OJaFXXQbN25EeXk5KioqUFtbi6KiIsybNw9HjhyJ+vzq6mp873vfw5YtW7Bz504UFBTgmmuuQUNDg+nGS0+WVUmdnWJOHGD+ainyHLt29d10eDBcPEGJYGFHUTAHJUCWHrstW8Sw6aRJQH6++fMZ3c/OJzko4cJu1apVWLx4MRYtWoRJkyZh7dq1yMzMxPr166M+/5lnnsGPfvQjFBcXY+LEiXj88ccRCoVQZeZ+b14hS1Dt3CnmxOXlicAyq7AQOOssMRFW30U8Hj65WiKL6L8nJ0+KHevtcPJk+JZ/LOw8gTkoAbLkIKuGYXX6ebZuFXkoXj7JQQkVdl1dXaipqUFpaWn4BMEgSktLsXPnzrjO0dHRge7ubowYMSLmczo7O9HS0tLny5NkCyqjm0JGY2Q41idBRRaJHLK362+A3luXksLfSw9wIgcpk38AeXJQ5MbEViguBoYNE38Xamrie01nZ3gnB8VjPaHCrrm5GT09PcjLy+vzeF5eHhrjvCnv3XffjbFjx/YJzP4qKyuRk5PT+1VQUJBIM+UhW1BZdbUUea5E5jiwsKNEJCWJfasA+2JIL+xyc3mfWA9wIgcpk38AOXJQQwOwdy8QDIY3uDcrKSk8Vy/ezoXIn0F2tjXtkJSjq2IfeughbNiwAZs2bUL6AHc+WLZsGY4fP977dfDgQQdbaSEZFk+0toq5cIB1V0tAOKjq6oDm5vhew8UTlCi7Y4jz63wlnhykTP4B5MhB+sX/1Kmil80qiXYu6D+DrCxzO0N4QEKFXW5uLpKSktDU1NTn8aamJowZM2bA1z788MN46KGH8Morr2DKlCkDPjctLQ1Dhw7t8+VJMiye0DeFPPNMc5tC9peXF76J85Yt8b3GJxNXyUJ29ziwsPMUJ3KQMvkHkCMH2TFiBIQ7Kt54Q8yVHYyP8k9ChV1qaiqmTZvWZ9KpPgm1pKQk5ut+/etf4/7778fmzZsxffp04631msiklOhGilaxK6giz5noFZMPAossYndiYmHnKcxBCXJ7KFbTrF84oZs4UaywPXkS2LFj8Of7KP8kPBRbXl6OdevW4amnnsKePXuwZMkStLe3Y9GiRQCAhQsXYtmyZb3P/9WvfoXly5dj/fr1KCwsRGNjIxobG9Gmr0RTmf4L1N0d3xWFHayetBopkQUUmuarwCKLsMeO+mEOSoDbhd2+fcDBg2LvuVmzrD13IJBY54KP8k/Chd2CBQvw8MMPY8WKFSguLkZdXR02b97cO5m1vr4ehw8f7n3+o48+iq6uLnznO99Bfn5+79fDDz9s3b9CVllZ4QnZbgRWczPw97+LYzsKuyuvFBNiP/5YBO9AOjrCN6L2QWCRRVjYUT/MQQlwu7DTL/pLSoDMTOvPn0jngo/meCcbeVFZWRnKysqi/r9q/UbzXzpw4ICRt1BDMChW37S0iF+qQeaAWE6f+zZ5spgTZ7WcHOCSS4C//U1cMd18c+zn6kEVDAJDhljfFlITF09QFMxBcXJ78YRdw7A6vbB76y2RZwcq2thjR5Zxc/KqncOwunivmCKvlritBMWLPXZExrmZf0Iha29lGc0ZZwBnny1Gg7ZtG/i5XDxBlnGzK9zuq6XIc7/22sALRHwUVGQhLp4gMs7N/PPuu8A//ymmJM2YYd/7xHt7MfbYkWXcCqyDB8Xct2BQzIWzy2WXAWlpYhPKjz6K/TwfBRVZiD12RMZFXhg5vTOD3rFwxRXizi52YWF3GhZ2dnOrsNN/yadPt/cXOSNDFHeR7xmNj4KKLGRn/HR3A8eOiWMWdqQiPX5CofA9kZ3ixFQgILxZ/u7dwJEjsZ/noxzEws5ubhV2TgzD6uJZcu6jFUlkITsnf+t3TAkGgeHDrT8/kdsyMsJ3WXAyB3V3h+e82Z2DRo0C9A2nB9os30c5iIWd3fRfIicnr2qac1dLke+xZYu4MozGR1dLZCE7L4z0YdgRI5S/xRD5VCDgzgKKt94SPYQjR4aLLjvFMxzroxzEws5ubvTYffQRcOiQmPtm9aaQ0VxyidjW5ejR8L55/XHxBBlhZ1Li/DryAzdykF5gzZ0resTtpncuDDRq5KMcxMLObm4G1WWXia54uyUnhxdoxLpi8tHVElnIiR47FnakMjdykJNTgQCxQCMpCfjkE+Czz6I/x0c5iIWd3dws7JwYhtUNtp+dj4KKLKT/vrS2hu9cYhUWduQHTuegjo7wvVudykFDh4a3VInVa+ejHMTCzm5OB1UoFJ5A6tTVUuR7vf460NV1+v/3UVCRhSInOre2WntuFnbkB07noDfeEDlg/Hjg3HOdeU9g4M6FU6eA9nZxzMUTZJrTiyfq6oAvvhBz3i65xJn3BMRty0aNEsGza9fp/99HK5LIQmlp4guwPjGxsCM/cDoHRQ7DOnmXocgFFP337Iv8t/ugc4GFnd2cvlrSr1auuELMfXNKMBjeTyjaFZOPJq6SxexYQNHQAGzeLI7z8607L5Fs3MpBTk4FAoCSEiA9HWhsBD78sO//0/92pKcDqanOtssFLOzs5nRQOT1pNdJA+9lxKJaMsjqGDh8WFyEHDgBnngl897vWnJdIRk7moGPHgJoacex0DkpPD+8C0b9zwWf5h4Wd3ZwMqq4u5zaFjEZ/z507w/MZdD4LLLKQlTHU2Ch6Ej7+WNxAfMsWIDfX/HmJZOVkDtq6VczzPv98YNw4+9+vv1j72fks/7Cws5v+i3TihNiN205/+5tYkZSbK+a8Oe2ss4AJE8S/8403+v4/nwUWWciqxHTkiPjD/+GHQEGBKOrOOMN8+4hk5mRh59YwrE5/3+rqvqvofTbHm4Wd3bKzw8d2B5Y+BHrVVc5sCtlfIBD9iqmzU3wBvgksspAVtxVrbgZKS4EPPhA9Ca+9JoZhiVRn5235+nNzKhAATJsm/r3HjgHvvBN+3GcdCyzs7JaSAmRmimO7VyXpxZRbQRX53pGFXeQfFBZ2lCiziyeOHhVF3e7dYqHEa68B55xjXfuIZObULcUaG4H33xcX+HPm2PtesSQnh987Mgf5bPEeCzsnONEV3t4OvPmmOHarGxwIr4ytrRXbrgDhoMrK4j05KXFm4ueLL4CvfEXc6i4vTxR1551nbfuIZObUUKzeW1dcLO4R65Zotxdjjx1ZzonA2r5dzG2bMAE4+2z73mcwY8cCF1wg9hGqrhaP+SyoyGJG4+f4cWDePHGRMWqUuIKfONH69hHJzOnCzs0Ro8j3f/318BQgn+UgFnZOcCKwIietOrkpZDT9dwD3WVCRxYzET0sL8C//Arz1lug9qKoCLrzQnvYRySwyfvpv3GsltxdO6C68EBg9WixY1EexfJaDWNg5wYnJqzLMr9P138/OZyuSyGKJxk9rK3DtteKP+ogRIjYuusi+9hHJTI+f7m7g5El73mP/frEvZHIyMHu2Pe8Rr0Dg9OFYn+UgFnZOsHvy6tGj4RVAbl8tAWLyaiAA7NkDHDrku6slslgiPXbt7cB114mbkA8bBrz6KlBUZGvziKSWnR0exbErB+kF1KWXirnUbuu/iM9nOYiFnRPsHoqtrhZd7BMnijlubhs+HJg6VRy/9prvViSRxeK9MOroAL72NTG3ZuhQ4JVXwr+HRH4VDIa33bIrB8kyDKvTC7u//Q1oa/NdDmJh5wS7CztZJq1GihyO9dnVElksnvg5cQK4/npxkZOdDbz8MnDJJY40j0h6duYgTZMvB515JlBYCJw6JS70fJaDWNg5we7CTqb5dbrIrnCfBRVZbLD4OXkS+OY3xe9aVhawebMYEiIiwc4c9P774q4uGRlyxZ2PcxALOyfYuXiioUHcIikQAK680vrzGzVrlticub5ebDcB+GbiKllM/71paTl9VV9nJ/Dtb4seusxM4MUXgcsuc76NRDKzMwfpHQuzZwOpqdaf36jIBRRcPEGWs3PxxJYt4vvUqWIFoCyGDAFKSsTxtm3iu0+ulshi+u9NT49YHKHr6gK++11RzGVkAC+84P6KPCIZ2ZmDZBuG1emFXV0d59iRDezsBpdxGFant0m/GbNPgooslpkZvmOJ/ge6uxv4//4/4K9/BdLTxXe3bmNEJDu7ctCpU+GN6GXLQWPGiD3tNC3c0++THMTCzgl2BZWmybcaKVL/NvkkqMhigUDfGDp1CrjhBmDTJiAtDfjzn+VLKkQysSsH1dSIi61hw8StxGQTmYOSk0XPvg+wsHOCXUH1ySfAwYNiLtvll1t7bivMmCGGZHUs7Mgo/Xfn6FHgppuA554T83n++EfgmmvcbRuR7OzKQfow7Ny5ct4HPPKCLyfH/bsyOYSFnRPsCiq9t+7SS/sWULJITe0758knE1fJBvrvzm23ARs2iIuZ554DvvpVd9tF5AV25yAZR4wAsaAw+GWZ46P8k+x2A3xB/4VqbRU9DkGL6ulXXhHfZR6Guvpqsf0EwB47Mk7/3fngAzGksnEjMH++u20i8go9BzU3A198Yc05u7uBN94Qx7LmoGHDgGnTxD2jfZR/WNg5IfIXauRI688va1ABp3eFExmh/+4kJQH//d9i3zoiio8eP3/5i/W7J+Tni7seyerqq31X2HEo1gnp6eKm5HaYOhWYOdOec1uhqEgMx5aU2FPUkj987WvAqFHAM88A3/mO260h8pbLLxfxY7VAALj9drnnrn3/+yL3fO1rbrfEMeyxc8oLL4iua6ulpMgdVMGg2MdO0+RuJ8ntttuAxYv5O0RkxJlnAo2N4a2nrJSSYv05rXThhcDnn/vqbwcLO6cEAnLtyu00HwUV2YS/Q0TGBYPWze/2Gp/97fDpp0xERESkHhZ2RERERIpgYUdERESkCBZ2RERERIpgYUdERESkCBZ2RERERIpgYUdERESkCBZ2RERERIpgYUdERESkCBZ2RERERIpgYUdERESkCBZ2RERERIpgYUdERESkCBZ2RERERIpIdrsB8dA0DQDQ0tLickvIr/TfPf130UsYPyQDr8YQ44dkkEj8eKKwa21tBQAUFBS43BLyu9bWVuTk5LjdjIQwfkgmXoshxg/JJJ74CWgeuHwKhUI4dOgQsrOzEQgE+vy/lpYWFBQU4ODBgxg6dKgl78dz8pz9z6lpGlpbWzF27FgEg96awcD44TllOKdXY2ig+AHU+Xx4TrnPmUj8eKLHLhgMYvz48QM+Z+jQoZb9cHlOnjPaOb3UyxCJ8cNzynJOL8ZQPPEDqPH58JxynzPe+PHOZRMRERERDYiFHREREZEiPF/YpaWloaKiAmlpaTwnzyndOWXnlZ8jz+nPc3qBV36WPKd/zumJxRNERERENDjP99gRERERkcDCjoiIiEgRLOyIiIiIFMHCjoiIiEgRLOyIiIiIFOH5wm7NmjUoLCxEeno6Zs6ciV27dhk+17Zt2zB//nyMHTsWgUAAf/rTn0y3r7KyEpdccgmys7MxevRofOMb38DevXtNnfPRRx/FlClTenenLikpwUsvvWS6rbqHHnoIgUAAd955p6nz/Md//AcCgUCfr4kTJ5puX0NDA77//e9j5MiRyMjIwEUXXYS3337b8PkKCwtPa2cgEMDSpUtNt1V2VsYPYH0MeTF+AGtiiPEjP8YP40fG+PF0Ybdx40aUl5ejoqICtbW1KCoqwrx583DkyBFD52tvb0dRURHWrFljWRu3bt2KpUuX4s0338Srr76K7u5uXHPNNWhvbzd8zvHjx+Ohhx5CTU0N3n77bVx11VX4+te/jvfff990e9966y38n//zfzBlyhTT5wKACy+8EIcPH+792r59u6nzffHFF5g1axZSUlLw0ksv4YMPPsAjjzyC4cOHGz7nW2+91aeNr776KgDgu9/9rqm2ys7q+AGsjyGvxQ9gbQwxfuTF+GH8SBs/mofNmDFDW7p0ae9/9/T0aGPHjtUqKytNnxuAtmnTJtPn6e/IkSMaAG3r1q2Wnnf48OHa448/buocra2t2rnnnqu9+uqr2pVXXqndcccdps5XUVGhFRUVmTpHf3fffbd2+eWXW3rO/u644w7t7LPP1kKhkK3v4zY740fT7IkhmeNH06yNIcaP3Bg/YYwf61gRP57tsevq6kJNTQ1KS0t7HwsGgygtLcXOnTtdbNnAjh8/DgAYMWKEJefr6enBhg0b0N7ejpKSElPnWrp0Ka677ro+P1OzPv74Y4wdOxZnnXUWbrzxRtTX15s631/+8hdMnz4d3/3udzF69GhcfPHFWLdunUWtFb9XTz/9NH74wx8iEAhYdl7ZMH4EK+MHsD6GGD9yYvwIjB8548ezhV1zczN6enqQl5fX5/G8vDw0Nja61KqBhUIh3HnnnZg1axYmT55s6ly7d+9GVlYW0tLScPvtt2PTpk2YNGmS4fNt2LABtbW1qKysNNWuSDNnzsSTTz6JzZs349FHH8Wnn36K2bNno7W11fA59+/fj0cffRTnnnsuXn75ZSxZsgT/9m//hqeeesqSNv/pT3/CsWPH8IMf/MCS88mK8WNt/ADWxxDjR16MH8aP1PFjYQ+ioxoaGjQA2o4dO/o8/rOf/UybMWOG6fPDhm7w22+/XTvjjDO0gwcPmj5XZ2en9vHHH2tvv/22ds8992i5ubna+++/b+hc9fX12ujRo7W///3vvY9ZMRTb3xdffKENHTrUVJd9SkqKVlJS0uexH//4x9qll15qtnmapmnaNddco33ta1+z5Fwyszt+NM36GJI1fjTNmRhi/MiD8cP40ckYP57tscvNzUVSUhKampr6PN7U1IQxY8a41KrYysrK8Pzzz2PLli0YP3686fOlpqbinHPOwbRp01BZWYmioiL85je/MXSumpoaHDlyBFOnTkVycjKSk5OxdetW/O///b+RnJyMnp4e0+0FgGHDhuG8887Dvn37DJ8jPz//tCvDCy64wHQXOwB89tln+J//+R/ceuutps8lO8aPdfEDOBNDjB95MH4YPzoZ48ezhV1qaiqmTZuGqqqq3sdCoRCqqqosGeu3iqZpKCsrw6ZNm/Daa6/hzDPPtOV9QqEQOjs7Db326quvxu7du1FXV9f7NX36dNx4442oq6tDUlKSJW1sa2vDJ598gvz8fMPnmDVr1mnL9T/66COcccYZZpuH3//+9xg9ejSuu+460+eSHeOnLzPxAzgTQ4wfeTB++mL8SBY/pvv8XLRhwwYtLS1Ne/LJJ7UPPvhAu+2227Rhw4ZpjY2Nhs7X2tqqvfPOO9o777yjAdBWrVqlvfPOO9pnn31muI1LlizRcnJytOrqau3w4cO9Xx0dHYbPec8992hbt27VPv30U+3dd9/V7rnnHi0QCGivvPKK4XP2Z0U3+E9+8hOturpa+/TTT7U33nhDKy0t1XJzc7UjR44YPueuXbu05ORk7cEHH9Q+/vhj7ZlnntEyMzO1p59+2lRbe3p6tAkTJmh33323qfN4idXxo2nWx5BX40fTzMcQ40dujB/Gj6zx4+nCTtM07be//a02YcIELTU1VZsxY4b25ptvGj7Xli1bNACnfd18882GzxntfAC03//+94bP+cMf/lA744wztNTUVG3UqFHa1VdfLV1QaZqmLViwQMvPz9dSU1O1cePGaQsWLND27dtnum1//etftcmTJ2tpaWnaxIkTtccee8z0OV9++WUNgLZ3717T5/ISK+NH06yPIa/Gj6aZjyHGj/wYP4wfGeMnoGmaZr7fj4iIiIjc5tk5dkRERETUFws7IiIiIkWwsCMiIiJSBAs7IiIiIkWwsCMiIiJSBAs7IiIiIkWwsCMiIiJSBAs7IiIiIkWwsCMiIiJSBAs7nyosLHS7CUSe9Pzzz+P888/Hueeei8cff9zt5hB5xp///GfceeedbjdDecluN4CIyCtOnTqF8vJybNmyBTk5OZg2bRq++c1vYuTIkW43jUh67777LoqKitxuhvLYY+czt956K4qLi3Ho0CEUFxdjxYoVbjeJyDN27dqFCy+8EOPGjUNWVhauvfZavPLKK243i8gT9MKupaUFX//61/HYY4+53SQlscfOZ/Sho8LCQtTV1bnbGCKPOXToEMaNG9f73+PGjUNDQ4OLLSLyjj179iAjIwPXXnst/uM//gNf+cpX3G6SkljYERERka1OnDiBhoYG3HDDDXj66adx4YUXut0kZXEoVjGNjY0IBAL4zW9+g4svvhjp6em48MILsX37drebRiS9weJn7NixfXroGhoaMHbsWLeaSySNwWLnvffeQ0lJCUKhEJKTw31K+/fvx2233Yaf/OQnqK2tdav5SmFhpxh9eHX9+vVYvXo16urqMGHCBNx4440IhULuNo5IcoPFz4wZM/Dee++hoaEBbW1teOmllzBv3jx3G00kgcFi591338Xs2bPx+9//HjfccAPa2toAAB988AFycnLws5/9DFOnTnXxX6AODsUq5u9//ztSUlLw5z//uXdLkwceeADTp09HQ0MDCgoK3G0gkcTiiZ9HHnkEc+fORSgUws9//nOuiCXC4LHz7rvvorS0FFOnTsWPfvQj/PCHP8Qf/vAHfO1rX8OZZ56Jm266Cc8//zzS0tLc/YcogIWdYurq6vCtb32rzz51Q4cOPe15kyZNcrBVRN4QT/xcf/31uP766x1uGZHcBoud3/zmN73Ht9xyC2655RYAwN13341Tp06huLiYRZ1FWNgppq6uDjfffHOfx3bu3Inc3Nw+q/lefPFFp5tGJL1444eI+jIaO7/61a/sbprvcI6dQk6cOIGPP/4YPT09vY+FQiGsXr0aN998M4JBftxEsTB+iIxh7MiFP22F7N69G4FAAE8//TR27tyJPXv2YMGCBTh27Bjuvfdet5tHJDXGD5ExjB25sLBTSF1dHSZOnIhf/OIX+Pa3v43p06ejp6cHW7duxbBhw9xuHpHUGD9ExjB25BLQNE1zuxFkjaVLl+KLL77As88+63ZTiDyH8UNkDGNHLuyxU0hdXR2mTJnidjOIPInxQ2QMY0cuLOwUoWkadu/ezeAiMoDxQ2QMY0c+HIolIiIiUgR77IiIiIgUwcKOiIiISBEs7IiIiIgUwcKOiIiISBEs7IiIiIgUwcKOiIiISBEs7IiIiIgUwcKOiIiISBEs7IiIiIgUwcKOiIiISBEs7IiIiIgUwcKOiIiISBH/P3da/ZUg5IWTAAAAAElFTkSuQmCC",
+      "text/plain": [
+       "<Figure size 640x480 with 3 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(1, 3)\n",
+    "\n",
+    "ax[0].plot(p_dag, c='r')\n",
+    "ax[0].set_xlabel(r\"$p^{\\dagger}$\")\n",
+    "ax[0].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[1].plot(p_0, c='r')\n",
+    "ax[1].set_xlabel(r\"$p^{0}$\")\n",
+    "ax[1].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[2].plot(p_k_s[-1], c='r')\n",
+    "ax[2].set_xlabel(r\"$p^{k_s}$\")\n",
+    "ax[2].set_xticks(range(0, 8))\n",
+    "\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./gn_coeff.png', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5fccea2d-1f55-4689-97c4-35fb8eb43f97",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 706,
+   "id": "20985f08-3c1c-4e52-92d1-2bf6630b4ade",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "loss = []\n",
+    "res_loss = []\n",
+    "psi_dag = network_2d(x, p_dag)\n",
+    "for psi in psi_k_s:\n",
+    "    l = np.linalg.norm(psi - psi_dag)\n",
+    "    loss.append(l)\n",
+    "\n",
+    "\n",
+    "for i in range(1, len(loss)):\n",
+    "    res_loss.append(np.log(loss[i] / np.linalg.norm(psi_k_s[i-1] - psi_dag)**2))\n",
+    "    \n",
+    "fig, ax = plt.subplots(1, 2)\n",
+    "ax[0].plot(range(1, len(loss)+1), loss, c= 'black')\n",
+    "ax[0].set_xlabel(r\"loss\")\n",
+    "ax[0].set_ylim(0)\n",
+    "\n",
+    "ax[1].plot(range(1, len(loss)), res_loss, c= 'black')\n",
+    "ax[1].set_xlabel(r\"residual loss\")\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./gn_loss.png', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1bcca449-5e38-4dad-9c9a-e3df39c6d663",
+   "metadata": {},
+   "source": [
+    "# Landau-Weber Iteration"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 710,
+   "id": "4cdd2405-bb58-465d-8357-6704832ded3c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def landau_weber(x, b, p_0, p_dag, λ, eps):\n",
+    "    p_k = np.array(p_0)\n",
+    "    psi_k = network_2d(x, p_k)\n",
+    "    \n",
+    "    jac = nd.Jacobian(lambda p: network_2d(x, p))\n",
+    "    psi_k_dag = jac(p_k)\n",
+    "    \n",
+    "    p_k_s = [p_k]\n",
+    "    psi_k_s = [psi_k]\n",
+    "    psi_k_dag_s = [psi_k_dag]\n",
+    "    while True:\n",
+    "        p_k = p_k - λ * (psi_k_dag.T @ (psi_k - b))\n",
+    "        psi_k = network_2d(x, p_k)\n",
+    "        psi_k_dag = jac(p_k)\n",
+    "\n",
+    "        p_k_s.append(p_k)\n",
+    "        psi_k_s.append(psi_k)\n",
+    "        psi_k_dag_s.append(psi_k_dag)\n",
+    "\n",
+    "        if np.linalg.norm(psi_k - b) < eps:\n",
+    "            break\n",
+    "\n",
+    "\n",
+    "    return p_k_s, psi_k_s, psi_k_dag_s\n",
+    "        \n",
+    "        \n",
+    "p_dag = [1.0, 1.0, 0.1, 0.1, 0.3, 0.1, 1.0, 0.8]\n",
+    "p_0 = [0.8, 0.9, 0.05, 0.1, 0.7, 0.3, 0.5, 0.5]\n",
+    "x =  np.random.uniform(low=-10, high=10, size=(100, 2))\n",
+    "\n",
+    "\n",
+    "\n",
+    "p_k_s, psi_k_s, psi_k_dag_s = landau_weber(x, network_2d(x, p_dag), p_0, p_dag, λ=0.02, eps=0.001)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 713,
+   "id": "70b7fc5a-c9ff-4675-a475-09be8739a04e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 3 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(1, 3)\n",
+    "\n",
+    "ax[0].plot(p_dag, c='r')\n",
+    "ax[0].set_xlabel(r\"$p^{\\dagger}$\")\n",
+    "ax[0].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[1].plot(p_0, c='r')\n",
+    "ax[1].set_xlabel(r\"$p^{0}$\")\n",
+    "ax[1].set_xticks(range(0, 8))\n",
+    "\n",
+    "ax[2].plot(p_k_s[-1], c='r')\n",
+    "ax[2].set_xlabel(r\"$p^{k_s}$\")\n",
+    "ax[2].set_xticks(range(0, 8))\n",
+    "\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./lw_coeff.png', dpi=300)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 712,
+   "id": "9ff0a6fc-9c0b-404a-ba7d-28b72b05ad83",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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JEodfiYiISGs3btzAoEGDcO7cOZiZmWHlypWYNGkS758TkSRDHf/CERERld+BAwfg7++PzMxM2Nvb46effkKXLl3ELkvytB5+PXbsGPz8/ODs7AyZTIbIyMgXto+JiYFMJiuxpKena7Rbs2YNGjRoAAsLC3h4eCA+Pl7b0oiIiEiPBEHA0qVL8eabbyIzMxMdO3ZEYmIiA10loXWoy83NRZs2bbBmzRqtvnflyhWkpaWpF3t7e/W2nTt3IigoCPPmzcOZM2fQpk0b+Pj44P79+9qWR0RERHqQk5ODESNGYM6cOVCpVHj33Xdx7Ngx1K1bV+zS6P/TevjV19cXvr6+Wh/I3t4eNWrUKHXbV199hQkTJiAwMBAAEBYWht9++w0bN27EnDlztD5WWXGiBBER0cv9888/GDRoEM6fP48qVapg9erVmDhxIm9nqmQqbParu7s7nJyc0Lt3b5w4cUK9Pi8vD4mJifD29v6/okxM4O3tjdjY2Ioqj4iIiEpx8OBBdOjQAefPn4ejoyNiYmLwv//9j4GuEtJ7qHNyckJYWBh2796N3bt3w8XFBd27d8eZM2cAAA8fPkRhYSEcHBw0vufg4FDivrsiSqUSCoVCYyEiIiLdKXr+XN++fZGZmQkPDw8kJiaiU6dOYpdGz6H32a9ubm5wc3NTf+7UqRP++ecffP311/jhhx/Ktc/Q0FAsWLCg3DXxtwsiIqLne/r0KSZOnIitW7cCAAIDA/Htt9/CwsJC5MroRUR5+HDHjh1x/fp1AICdnR1MTU1x7949jTb37t2Do6Njqd8PDg5Gdna2eklNTdV7zURERFKQmpqKLl26YOvWrTA1NcWqVauwYcMGBjoDIEqoS0pKgpOTEwDA3Nwc7dq1Q3R0tHq7SqVCdHQ0PD09S/2+XC6HtbW1xkJERESv5s8//1S/5qtWrVo4ePAgPvjgA45wGQith19zcnLUvWwAkJycjKSkJNSsWRP16tVDcHAw7ty5gy1btgAAVqxYAVdXV7Ro0QLPnj3D999/j8OHD+OPP/5Q7yMoKAjjxo1D+/bt0bFjR6xYsQK5ubnq2bD6wtmvRERE/woLC8MHH3yAgoICtGnTBpGRkWjQoIHYZZEWtA51CQkJ6NGjh/pzUFAQAGDcuHEIDw9HWloaUlJS1Nvz8vLw4Ycf4s6dO6hatSpat26NQ4cOaexj5MiRePDgAUJCQpCeng53d3dERUWVmDxBREREupWXl4cPPvgA69atA/Dv/ydv2LAB1apVE7ky0pbWoa579+4v7OEKDw/X+Dx79mzMnj37pfudMmUKpkyZom05REREVE7p6ekYNmwYTpw4AZlMhtDQUMyePZvDrQaK734lIiKSoISEBAwaNAh37tyBjY0Ntm/fjjfffFPssugViDJRgoiIiMTzww8/oHPnzrhz5w6aNWuG+Ph4BjojwFBHREQkEQUFBQgKCsLYsWOhVCrh5+eHuLg4NG3aVOzSSAckHeo4+5WIiKQiIyMDffv2xddffw0AmDt3LiIjI/lYMCMiyXvqiIiIpOTcuXMYOHAgkpOTUa1aNWzevBlDhw4VuyzSMUn31BERERm73bt3w9PTE8nJyWjYsCFiY2MZ6IyUJEMdZ78SEZGxU6lUmDt3LoYNG4bc3Fx4e3vj9OnTaNWqldilkZ5w+JWIiMjIKBQKvP322/j1118B/PuigKVLl8LMjP+3b8z4vy4REZERuXbtGgYMGIDLly9DLpdj/fr1GDNmjNhlUQWQdKjj7FciIjImBw8exIgRI5CVlYU6deogMjIS7du3F7ssqiCSvKeOiIjImAiCgFWrVsHX1xdZWVnw9PREQkICA53EMNQREREZMKVSiQkTJmDatGkoLCxEQEAAjhw5AkdHR7FLowomyVDH2a9EpA/z58+HTCbTWJo1ayZ2WWTE7t+/j169emHDhg0wMTHBV199hY0bN0Iul4tdGolA0vfUERHpWosWLXDo0CH1Z842JH1JSkrCwIEDkZKSAhsbG0RERKBv375il0Ui4tWGiEiHzMzMOOxFerd7926MHTsWT548QdOmTfHLL7/Azc1N7LJIZJIcfi3C2a9EpGvXrl2Ds7MzGjZsiNGjRyMlJeWF7ZVKJRQKhcZC9DwqlQrz58/HsGHD8OTJE/Tp0wenTp1ioCMAEg91RES65OHhgfDwcERFRWHt2rVITk5Gly5d8Pjx4+d+JzQ0FDY2NurFxcWlAismQ5Kbm4sRI0ZgwYIFAIAZM2bgt99+g62trciVUWXB4VciIh3x9fVV/9y6dWt4eHigfv362LVrF959991SvxMcHIygoCD1Z4VCwWBHJdy6dQsDBw7E2bNnYW5ujrCwMAQGBopdFlUykgx1nP1KRBWhRo0aaNq0Ka5fv/7cNnK5nDMV6YWOHz+OIUOG4MGDB7C3t8eePXvQqVMnscuiSojDr0REepKTk4N//vkHTk5OYpdCBur7779Hz5498eDBA7i7u+P06dMMdPRcDHVERDoyc+ZMHD16FDdv3sTJkycxePBgmJqawt/fX+zSyMAUFBRg2rRpmDBhAvLz8zF8+HAcP34c9erVE7s0qsQkOfxahLNfiUiXbt++DX9/f2RkZKB27dro3LkzTp06hdq1a4tdGhmQR48eYeTIkernHS5cuBCffvopbx2il5J0qCMi0qWIiAixSyADd+nSJQwYMADXr19H1apV8cMPP2DIkCFil0UGgqGOiIioEjhw4ABGjBgBhUKB+vXrY+/evWjTpo3YZZEB4T11REREIhIEAatXr8abb74JhUKBzp074/Tp0wx0pDVJhjrel0BERJVBfn4+Jk+ejKlTp0KlUiEgIACHDh3ifZhULhx+JSIiEkFmZiZGjBiBQ4cOQSaTYenSpZg5cyY7HqjcJB3qOPuViIjEcO3aNfj5+eHKlSuoVq0atm3bhoEDB4pdFhk4SYc6IiKiihYTE4MhQ4YgMzMTLi4u+OWXX+Du7i52WWQEJHlPHRERkRi+//579O7dG5mZmejYsSPi4+MZ6EhnGOqIiIj0rLCwEB9++CEmTJiAgoICjBo1CjExMXB0dBS7NDIikgx1vAmViIgqyuPHjzFo0CB89dVXAID58+dj+/btsLS0FLkyMja8p46IiEhPbt26BT8/P5w7dw4WFhYIDw/HyJEjxS6LjJSkQx1nvxIRkb6cPHkSgwcPxv379+Ho6Ii9e/eiY8eOYpdFRkySw69ERET6tG3bNvTo0QP379+Hu7s74uPjGehI7xjqiIiIdESlUuHTTz/F22+/jby8PAwaNAh//vknXFxcxC6NJEDSw69ERES68vTpU4wbNw4//vgjAOCjjz7C4sWLYWLC/hOqGJIMdZz9SkREunT//n0MHDgQp06dQpUqVbBu3ToEBASIXRZJjCRDHRERka5cunQJ/fr1Q3JyMmxtbbFnzx5069ZN7LJIgiTdJ8zZr0RE9CoOHz4MT09PJCcno2HDhoiNjWWgI9FIOtQRERGV16ZNm+Dj44Ps7Gx06tQJp06dgpubm9hlkYQx1BEREWlBpVLhk08+wTvvvKN+5Vd0dDRq164tdmkkcQx1REREZfTs2TO89dZbWLx4MQDg008/xbZt22BhYSFyZUTlCHXHjh2Dn58fnJ2dIZPJEBkZ+cL2P//8M3r37o3atWvD2toanp6eOHDggEab+fPnQyaTaSzNmjXTtrQy4+xXIiLS1oMHD9CzZ0/s3LkTZmZm2LRpExYtWsRHllClofXfxNzcXLRp0wZr1qwpU/tjx46hd+/e2L9/PxITE9GjRw/4+fnhr7/+0mjXokULpKWlqZfjx49rWxoREZFeXL58GW+88QZiY2NRo0YNHDhwgI8soUpH60ea+Pr6wtfXt8ztV6xYofF58eLF2Lt3L3799Ve0bdv2/woxM4Ojo6O25bwSzn4lIqKXiYmJweDBg5GVlQVXV1fs379fr6NJROVV4X3GKpUKjx8/Rs2aNTXWX7t2Dc7OzmjYsCFGjx6NlJSU5+5DqVRCoVBoLERERLq2efNm9OnTB1lZWfD09ERcXBwDHVVaFR7qvvzyS+Tk5GDEiBHqdR4eHggPD0dUVBTWrl2L5ORkdOnSBY8fPy51H6GhobCxsVEvfKceERHpkiAICAkJQUBAAPLz8zFixAjOcKVKr0JD3fbt27FgwQLs2rUL9vb26vW+vr4YPnw4WrduDR8fH+zfvx9ZWVnYtWtXqfsJDg5Gdna2eklNTa2oUyAiIiOXl5eHgIAALFq0CADw8ccfY8eOHbC0tBS5MqIXq7DXhEVERGD8+PH48ccf4e3t/cK2NWrUQNOmTXH9+vVSt8vlcsjl8nLXwtmvRERUGoVCgaFDh+LQoUMwNTVFWFgYxo8fL3ZZRGVSIT11O3bsQGBgIHbs2IF+/fq9tH1OTg7++ecfODk5VUB1REREwJ07d9ClSxccOnQI1apVw6+//spARwZF6566nJwcjR605ORkJCUloWbNmqhXrx6Cg4Nx584dbNmyBcC/Q67jxo3DypUr4eHhgfT0dACApaUlbGxsAAAzZ86En58f6tevj7t372LevHkwNTWFv7+/Ls7xuTj7lYiIAOD8+fPw9fXF7du34eDggN9++w3t2rUTuywirWjdU5eQkIC2bduqH0cSFBSEtm3bIiQkBACQlpamMXN13bp1KCgowOTJk+Hk5KRepk2bpm5z+/Zt+Pv7w83NDSNGjECtWrVw6tQp3pBKRER6d+TIEXTu3Bm3b9+Gm5sbYmNjGejIIGndU9e9e/cX9nCFh4drfI6JiXnpPiMiIrQtg4iI6JVt375dPcO1c+fO2Lt3b4lHbhEZCr7bhIiIJEcQBCxduhSjR49Gfn4+hg0bhoMHDzLQkUGTZKjj7FciIukqLCzElClTMGfOHADAjBkzsHPnTlhYWIhcGdGrqbBHmhAREYntyZMneOutt7B3717IZDJ8/fXXGvd4ExkySYc6zn4lIpKOBw8ewM/PD3FxcbCwsMDWrVsxdOhQscsi0hlJhzoiIpKG5ORk9OnTB9evX0fNmjXxyy+/wMvLS+yyiHRKkvfUERFVhCVLlkAmk2H69OlilyJpZ8+eRadOnXD9+nU0aNAAJ0+eZKAjo8RQR0SkB6dPn8Z3332H1q1bi12KpMXExKBr165IT09H69atcfLkSbi5uYldFpFeSDLUcfYrEelTTk4ORo8ejfXr18PW1lbsciRr9+7d8PHxgUKhQLdu3XDs2DG+fpKMmiRDHRGRPk2ePBn9+vWDt7e32KVIVlhYGIYPH468vDwMGTIEUVFR6ldTEhkrSU+U4OxXItK1iIgInDlzBqdPny5Te6VSCaVSqf6sUCj0VZokCIKABQsWYMGCBQCAiRMn4ttvv4WpqanIlRHpH3vqiIh0JDU1FdOmTcO2bdvK/CDb0NBQ2NjYqBcXFxc9V2m8CgsLMWnSJHWgmzdvHsLCwhjoSDIY6oiIdCQxMRH379/H66+/DjMzM5iZmeHo0aNYtWoVzMzMUFhYWOI7wcHByM7OVi+pqakiVG74nj17hhEjRuC7776DTCbDt99+i/nz5/MeapIUSQ+/EhHpUq9evXDu3DmNdYGBgWjWrBk++uijUnuM5HI55HJ5RZVolLKzszFw4EAcPXoU5ubm2LZtG4YNGyZ2WUQVTpKhjr+5EZE+WFlZoWXLlhrrqlWrhlq1apVYT7qRnp6Ovn374uzZs7C2tkZkZCR69OghdllEopBkqCMiIsN38+ZNeHt7459//oGDgwOioqLg7u4udllEopF0qOPsVyLSt5iYGLFLMEoXL15E7969cffuXbi6uuLgwYNo1KiR2GURiYoTJYiIyKAkJCSga9euuHv3Lpo3b47jx48z0BGBoY6IiAzI0aNH0bNnT2RkZKBDhw44duwYnJ2dxS6LqFJgqCMiIoOwb98+9O3bF48fP0aPHj0QHR2NWrVqiV0WUaUhyVDH2a9ERIZlx44dGDx4MJ49ewY/Pz/s378fVlZWYpdFVKlIMtQREZHhCAsLw+jRo1FQUIDRo0dj9+7dZX5jB5GUSDrUcfYrEVHltmTJEkyaNAmCIGDy5MnYsmULqlSpInZZRJWSpEMdERFVToIgIDg4GMHBwQCATz75BKtXr4aJCf9vi+h5JP2cOiIiqnwEQcD06dOxatUqAMAXX3yBmTNnilwVUeXHUEdERJWGSqXC+++/j++++w4AsHbtWrz33nsiV0VkGBjqiIioUigsLMT48eMRHh4OmUyGDRs2IDAwUOyyiAyGJEMdH2lCRFS5FBQUYOzYsdixYwdMTU2xZcsWvPXWW2KXRWRQJBnqinD2KxGR+PLy8uDv74+ff/4ZZmZmiIiIwNChQ8Uui8jgSDrUERGRuJ49e4Zhw4bht99+g7m5OX766Sf4+fmJXRaRQWKoIyIiUTx58gSDBw/GH3/8AQsLC0RGRsLHx0fssogMFkMdERFVuJycHPj5+SEmJgZVq1bFvn370KNHD7HLIjJoDHVERFShcnNz0a9fPxw7dgxWVlbYv38/OnfuLHZZRAZPkqGOs1+JiMRRPNBZW1vjjz/+gIeHh9hlERkFSb9vhbNfiYgqzpMnT9C/f38cPXoUVlZWOHDgAAMdkQ5JOtQREVHFePLkifoeuqJA98Ybb4hdFpFRYagjIiK9evr0KQYMGIDDhw+jevXqiIqKgqenp9hlERkdhjoiItKbokAXHR2tDnSdOnUSuywio8RQR0REevH06VMMHDgQhw4dQrVq1fD777/Dy8tL7LKIjJYkQx1nvxIR6ZdSqcSQIUNw8OBBdaDjY0uI9EuSoa4IZ78SEeleQUEB/P39ERUVhapVq2L//v3o0qWL2GURGT1JhzoiItItlUqFwMBA7NmzB+bm5ti7dy+6du0qdllEksBQR0REOiEIAiZPnoytW7fCzMwMP/30E7y9vcUui0gytA51x44dg5+fH5ydnSGTyRAZGfnS78TExOD111+HXC5H48aNER4eXqLNmjVr0KBBA1hYWMDDwwPx8fHalkZERCIRBAGzZs1CWFgYZDIZfvjhB/j5+YldFpGkaB3qcnNz0aZNG6xZs6ZM7ZOTk9GvXz/06NEDSUlJmD59OsaPH48DBw6o2+zcuRNBQUGYN28ezpw5gzZt2sDHxwf379/XtjwiIhLBwoULsXz5cgDA999/j1GjRolcEZH0aP3uV19fX/j6+pa5fVhYGFxdXdX/2F977TUcP34cX3/9NXx8fAAAX331FSZMmIDAwED1d3777Tds3LgRc+bM0bbEl+LsVyIi3Vm+fDnmz58PAFi5ciXeeecdcQsikii931MXGxtb4p4KHx8fxMbGAgDy8vKQmJio0cbExATe3t7qNvrC2a9ERK9m06ZNmDlzJgDg888/x9SpU0WuiEi6tO6p01Z6ejocHBw01jk4OEChUODp06fIzMxEYWFhqW0uX75c6j6VSiWUSqX6s0Kh0H3hRET0Qvv27cOECRMAALNnz8bHH38sckVE0maQs19DQ0NhY2OjXlxcXMQuiYhIUk6ePIkRI0agsLAQ48aNw5IlS8QuiUjy9B7qHB0dce/ePY119+7dg7W1NSwtLWFnZwdTU9NS2zg6Opa6z+DgYGRnZ6uX1NRUvdVPRESaLl68iP79++Pp06fo168f1q9fz3uViSoBvYc6T09PREdHa6w7ePAgPD09AQDm5uZo166dRhuVSoXo6Gh1m/+Sy+WwtrbWWIiISP9SU1Ph4+ODzMxMvPHGG9i1axeqVKkidllEhHKEupycHCQlJSEpKQnAv48sSUpKQkpKCoB/e9HGjh2rbv/ee+/hxo0bmD17Ni5fvoxvv/0Wu3btwowZM9RtgoKCsH79emzevBmXLl3CpEmTkJubq54Nq2v8jZKISHuPHj2Cj48Pbt++jddeew379u1D1apVxS6LiP4/rSdKJCQkoEePHurPQUFBAIBx48YhPDwcaWlp6oAHAK6urvjtt98wY8YMrFy5EnXr1sX333+vfpwJAIwcORIPHjxASEgI0tPT4e7ujqioqBKTJ3SNs1+JiMpGqVRi8ODBuHTpEurUqYMDBw6gVq1aYpdFRMVoHeq6d+/+wjBU2tsiunfvjr/++uuF+50yZQqmTJmibTlERJXG2rVrsXbtWty8eRMA0KJFC4SEhGj1bM/KSBAETJw4EceOHYO1tTWioqI4QY2oEjLI2a9ERJVR3bp1sWTJEiQmJiIhIQE9e/bEwIEDceHCBbFLeyWff/45tmzZAlNTU+zatQstW7YUuyQiKoXen1NHRCQV/33X6eeff461a9fi1KlTaNGihUhVvZodO3Zg7ty5AIBvvvlG49YZIqpcGOqIiPSgsLAQP/74I3Jzc587k7+yi42NVU9YCwoKwnvvvSdyRUT0IpIMdZz9SkT6cu7cOXh6euLZs2eoXr069uzZg+bNmz+3fWV9Q87du3cxZMgQKJVKDBw4EMuWLRO7JCJ6CUnfU8fZr0Ska25ubkhKSkJcXBwmTZqEcePG4eLFi89tXxnfkKNUKjFs2DCkp6ejVatW2Lp1K0xNTcUui4heQtKhjohI18zNzdG4cWO0a9cOoaGhaNOmDVauXPnc9pXxDTnTpk1DbGwsatSogT179qB69epil0REZSDJ4VciooqiUqk0hlf/Sy6XQy6XV2BFL7ZhwwZ89913kMlk2L59Oxo1aiR2SURURgx1REQ6EhwcDF9fX9SrVw+PHz/G9u3bERMTgwMHDohdWpkkJSXh/fffBwAsWrTI4J+vRyQ1DHVERDpy//59jB07FmlpabCxsUHr1q1x4MAB9O7dW+zSXio3NxejRo1CXl4e/Pz8EBwcLHZJRKQlSYY6zn4lIn3YsGGD2CWU2wcffIArV66gTp062LRpE0xMeMs1kaGR9L9azn4lIvr3AcObNm2CTCbDtm3b+E5XIgMl6VBHRCR1d+7cwaRJkwAAn376Kbp16yZyRURUXgx1REQSJQgC3nvvPWRnZ6NDhw4ICQkRuyQiegUMdUREErVt2zbs27cP5ubm2LRpE8zMJHmbNZHRYKgjIpKge/fuYdq0aQCAkJAQtGjRQuSKiOhVSTLUcfYrEUndxx9/jEePHsHd3R2zZ88Wuxwi0gFJhroinP1KRFIUHx+PjRs3AgC+/fZbVKlSReSKiEgXJB3qiIikRqVSYerUqQCAMWPGwNPTU+SKiEhXGOqIiCRk165diIuLQ/Xq1bFkyRKxyyEiHWKoIyKSiIKCAsybNw8AMHv2bDg7O4tcERHpEkMdEZFEbNu2DVevXkWtWrUwffp0scshIh2TZKjj7FcikpqCggIsXLgQwL+9dFZWViJXRES6JslQV4SzX4lIKvbs2YMbN27Azs4OkydPFrscItIDSYc6IiKp+PrrrwEA77//PqpVqyZyNUSkDwx1RERGLi4uDrGxsTA3N8ekSZPELoeI9IShjojIyH3zzTcAAH9/fzg6OopcDRHpC0MdEZERUygU2L17NwCwl47IyDHUEREZsR9//BFPnz5Fs2bN0LFjR7HLISI9kmSoK3qkCWe/EpGxCw8PBwAEBATwcU5ERk6SoY6ISApSUlJw/PhxyGQyvP3222KXQ0R6xlBHRGSk9u7dCwDw8vJCnTp1RK6GiPSNoY6IyEhFRkYCAAYPHixuIURUIRjqiIiMUEZGBo4ePQoAGDRokLjFEFGFYKgjIjJCUVFRKCwsRKtWrdCwYUOxyyGiCiDJUMfZr0Rk7A4fPgwA8PX1FbkSIqookgx1RETGrijU9ezZU+RKiKiiMNQRERmZ5ORk3Lx5E2ZmZujcubPY5RBRBWGoIyIyMkW9dG+88QaqVasmcjVEVFEY6oiIjMzx48cBAN27dxe3ECKqUAx1RERGJj4+HgDg4eEhciVEVJEkGeo4+5WIjJVCocClS5cAAB06dBC5GiKqSJIMdURExioxMRGCIKB+/fpwcHAQuxwiqkAMdURERqRo6LVjx44iV0JEFa1coW7NmjVo0KABLCws4OHhob6IlKZ79+6QyWQlln79+qnbBAQElNjet2/f8pRGRCRpiYmJADj0SiRFZtp+YefOnQgKCkJYWBg8PDywYsUK+Pj44MqVK7C3ty/R/ueff0ZeXp76c0ZGBtq0aYPhw4drtOvbty82bdqk/iyXy7UtjYhI8s6fPw8AaNWqlciVEFFF07qn7quvvsKECRMQGBiI5s2bIywsDFWrVsXGjRtLbV+zZk04Ojqql4MHD6Jq1aolQp1cLtdoZ2trW74zIiKSqLy8PFy7dg0A0KJFC5GrIaKKplWoy8vLQ2JiIry9vf9vByYm8Pb2RmxsbJn2sWHDBowaNarEAzFjYmJgb28PNzc3TJo0CRkZGc/dh1KphEKh0Fi0wdmvRKQPoaGh6NChA6ysrGBvb49BgwbhypUrFXb8q1evoqCgANbW1qhbt26FHZeIKgetQt3Dhw9RWFhYYkaVg4MD0tPTX/r9+Ph4nD9/HuPHj9dY37dvX2zZsgXR0dFYunQpjh49Cl9fXxQWFpa6n9DQUNjY2KgXFxcXbU6DiEgvjh49ismTJ+PUqVM4ePAg8vPz0adPH+Tm5lbI8S9cuAAAaN68ufqXVyKSDq3vqXsVGzZsQKtWrUrMyho1apT651atWqF169Zo1KgRYmJi0KtXrxL7CQ4ORlBQkPqzQqFgsCMi0UVFRWl8Dg8Ph729PRITE9G1a1e9H78o1HHolUiatOqps7Ozg6mpKe7du6ex/t69e3B0dHzhd3NzcxEREYF33333pcdp2LAh7OzscP369VK3y+VyWFtbayxERJVNdnY2gH/vLa4Ily9fBgC89tprFXI8IqpctAp15ubmaNeuHaKjo9XrVCoVoqOj4enp+cLv/vjjj1AqlXj77bdfepzbt28jIyMDTk5O2pRHRFRpqFQqTJ8+HV5eXmjZsuVz273qPcLF3bhxAwDQuHHjcu+DiAyX1rNfg4KCsH79emzevBmXLl3CpEmTkJubi8DAQADA2LFjERwcXOJ7GzZswKBBg1CrVi2N9Tk5OZg1axZOnTqFmzdvIjo6GgMHDkTjxo3h4+NTztMiIhLX5MmTcf78eURERLywnS7vEU5OTgYAuLq6lnsfRGS4tL6nbuTIkXjw4AFCQkKQnp4Od3d3REVFqSdPpKSkwMREMyteuXIFx48fxx9//FFif6ampvj777+xefNmZGVlwdnZGX369MGiRYv09qw6zn4lIn2aMmUK9u3bh2PHjr10Fqqu7hFWKBR49OgRAIY6Iqkq10SJKVOmYMqUKaVui4mJKbHOzc3tuQHK0tISBw4cKE8ZRESViiAI+OCDD7Bnzx7ExMSUKVzJ5XKd/AJb1EtnZ2cHKyurV94fERmeCp39SkRkzCZPnozt27dj7969sLKyUj/qycbGBpaWlno9dtH9dOylI5Kucr37lYiISlq7di2ys7PRvXt3ODk5qZedO3fq/dg3b94EwFBHJGXsqSMi0hEx79O9e/cuAPBNEkQSxp46IiIjUDTUy0dBEUmXJEMdZ78SkbFJS0sDgJc+CJ6IjJckQx0RkbEp6qljqCOSLoY6IiIjwFBHRAx1REQGLi8vDxkZGQAY6oikjKGOiMjA3b9/HwBgZmaGmjVrilwNEYmFoY6IyMBlZmYCAGxtbUu8ppGIpEOS//o5+5WIjElWVhYAoEaNGqLWQUTikmSoIyIyJgx1RAQw1BERGbzs7GwADHVEUsdQR0Rk4NhTR0QAQx0RkcFjqCMigKGOiMjgMdQRESDRUMfZr0RkTIpCnY2NjbiFEJGoJBnqiIiMSW5uLgDAyspK5EqISEwMdUREBu7Zs2cAAAsLC5ErISIxMdQRERk4hjoiAhjqiIgMHkMdEQEMdUREBo+hjogAiYY6zn4lImPCUEdEgERDHRGRMWGoIyKAoY6IyOAx1BERwFBHRGTwGOqICGCoIyIyeAx1RARIPNRxogQRGYOnT58CYKgjkjpJhjrOfiUiYyEIApRKJQCGOiKpk2SoMzU1BQCoVCqRKyEiejVFgQ5gqCOSOkmGOhOTf0+7sLBQ5EqIiF5N0f10AEMdkdRJMtSxp46IjEVRqJPJZKhSpYrI1RCRmCQZ6op66hjqiMjQFZ/5WnS/MBFJk6RDHYdficjQFYU6S0tLkSshIrFJMtRx+JWIjAWfUUdERSQZ6jj8SkTGgqGOiIpIOtRx+JWIDB1DHREVkWSo4/ArERkLvk2CiIpIMtRx+JWIjAV76oioiKRDHYdficjQMdQRURFJhjoOvxKRvhw7dgx+fn5wdnaGTCZDZGSkXo/HUEdERSQZ6thTR0T6kpubizZt2mDNmjUVcjyGOiIqUq5Qt2bNGjRo0AAWFhbw8PBAfHz8c9uGh4dDJpNpLP+9+AiCgJCQEDg5OcHS0hLe3t64du1aeUorE95TR0T64uvri88++wyDBw+ukOMx1BFREa1D3c6dOxEUFIR58+bhzJkzaNOmDXx8fHD//v3nfsfa2hppaWnq5datWxrbly1bhlWrViEsLAxxcXGoVq0afHx8NF5UrUscfiWiykKpVEKhUGgs2mCoI6IiWoe6r776ChMmTEBgYCCaN2+OsLAwVK1aFRs3bnzud2QyGRwdHdWLg4ODepsgCFixYgU+/fRTDBw4EK1bt8aWLVtw9+5dvd2LwuFXIqosQkNDYWNjo15cXFy0+j5DHREV0SrU5eXlITExEd7e3v+3AxMTeHt7IzY29rnfy8nJQf369eHi4oKBAwfiwoUL6m3JyclIT0/X2KeNjQ08PDxeuM9XwZ46IqosgoODkZ2drV5SU1O1+j5DHREVMdOm8cOHD1FYWKjR0wYADg4OuHz5cqnfcXNzw8aNG9G6dWtkZ2fjyy+/RKdOnXDhwgXUrVsX6enp6n38d59F2/5LqVRCqVSqP2s7XMF76oiospDL5ZDL5eX+Ph8+TERF9D771dPTE2PHjoW7uzu6deuGn3/+GbVr18Z3331X7n2+6nAFh1+JyFiwp46IimgV6uzs7GBqaop79+5prL937x4cHR3LtI8qVaqgbdu2uH79OgCov6fNPl91uILDr0SkLzk5OUhKSkJSUhKAf28xSUpKQkpKil6Ox1BHREW0CnXm5uZo164doqOj1etUKhWio6Ph6elZpn0UFhbi3LlzcHJyAgC4urrC0dFRY58KhQJxcXHP3adcLoe1tbXGog0OvxKRviQkJKBt27Zo27YtACAoKAht27ZFSEiIXo7HUEdERbS6pw749wI1btw4tG/fHh07dsSKFSuQm5uLwMBAAMDYsWNRp04dhIaGAgAWLlyIN954A40bN0ZWVha++OIL3Lp1C+PHjwfw78zY6dOn47PPPkOTJk3g6uqKuXPnwtnZGYMGDdLdmRbD4Vci0pfu3btDEIQKO15RqLO0tKywYxJR5aR1qBs5ciQePHiAkJAQpKenw93dHVFRUeqJDikpKerQBACZmZmYMGEC0tPTYWtri3bt2uHkyZNo3ry5us3s2bORm5uLiRMnIisrC507d0ZUVJTefvPk8CsRGQv21BFREZlQkb9S6olCoYCNjQ2ys7PLNBQbHR0Nb29vtGjRAufPn6+AColIDNpeGyoDbWvu2rUr/vzzT/z4448YNmxYBVRIRBWtrNcFSb771czs3w5KDr8SkaEr6ql7lceiEJFxkHSoy8/PF7kSIqJXU/TMToY6IpJ0qCsoKBC5EiKiV5OXlweAoY6IJBrqqlSpAoChjogMX1GoMzc3F7kSIhKbJEMde+qIyFgw1BFREYY6IiIDxlBHREUkHeo4UYKIDB0nShBREUmHOvbUEZGhY08dERWRZKjjRAkiMhYMdURURJKhjj11RGQMCgsL1Q9RZ6gjIkmHOpVKxfe/EpHBKn5fMO+pIyJJhzqAvXVEZLiKhl4B9tQREUMdQx0RGazioa7oXmEiki5JhrriFz+GOiIyVMVvHzExkeTlnIiKkeRVgD11REREZGwkGepMTU3VPzPUEZGhEgRB7BKIqBKRZKiTyWTqYMdQR0SGqijUyWQykSshospAkqEO4KvCiMjwMdQRUXGSDXV8qwQRGQuGOiICJBzq+FYJIjJ0vKeOiIpjqGOoIyIDxeFXIiqOoY6hjogMHEMdEQEMdZwoQUQGi8OvRFSc5EMde+qIyFBx+JWIipNsqOPsVyIydAx1RFScZEMde+qIyFgw1BERwFDHUEdEBov31BFRcZIPdZwoQUSGisOvRFSc5EMde+qIyFAx1BFRcZINdZwoQUTGgqGOiAAJhzr21BGRoeM9dURUHEMdQx0RGSgOvxJRcZIPdZwoQUSGiqGOiIqTfKhjTx0RGTqGOiICJBzqOFGCiPRlzZo1aNCgASwsLODh4YH4+Hi9HIf31BFRcZINdeypIyJ92LlzJ4KCgjBv3jycOXMGbdq0gY+PD+7fv6/zY3H4lYiKY6hjqCMiHfrqq68wYcIEBAYGonnz5ggLC0PVqlWxceNGvR2ToY6IAIY6TpQgIp3Jy8tDYmIivL291etMTEzg7e2N2NjYUr+jVCqhUCg0lrLi8CsRFSfZUGdubg7g34swEZEuPHz4EIWFhXBwcNBY7+DggPT09FK/ExoaChsbG/Xi4uJS5uNx+JWIipNsqLOwsAAAPHv2TORKiEjKgoODkZ2drV5SU1PL/F2GOiIqzkzsAsRSFOqUSqXIlRCRsbCzs4OpqSnu3bunsf7evXtwdHQs9TtyuRxyufyVjstQR0SAhHvqii6i7KkjIl0xNzdHu3btEB0drV6nUqkQHR0NT09PnR+P99QRUXHsqWNPHRHpUFBQEMaNG4f27dujY8eOWLFiBXJzcxEYGKjzY3H4lYiKK1dPnTYP1ly/fj26dOkCW1tb2Nrawtvbu0T7gIAAyGQyjaVv377lKa3M2FNHRPowcuRIfPnllwgJCYG7uzuSkpIQFRVVYvKELjDUEVFxWoc6bR+sGRMTA39/fxw5cgSxsbFwcXFBnz59cOfOHY12ffv2RVpamnrZsWNH+c6ojNhTR0T6MmXKFNy6dQtKpRJxcXHw8PDQ6/EY6ogIKEeo0/bBmtu2bcP7778Pd3d3NGvWDN9//736HpPi5HI5HB0d1YutrW35zqiM2FNHRIaO99QRUXFahbryPFjzv548eYL8/HzUrFlTY31MTAzs7e3h5uaGSZMmISMj47n7eJWHdRZhTx0RGToOvxJRcVqFuvI8WPO/PvroIzg7O2sEw759+2LLli2Ijo7G0qVLcfToUfj6+qKwsLDUfbzKwzqLsKeOiAwdQx0RFVehs1+XLFmCiIgIxMTEqHvKAGDUqFHqn1u1aoXWrVujUaNGiImJQa9evUrsJzg4GEFBQerPCoVC62DHnjoiMhYMdUQEaNlTV54Haxb58ssvsWTJEvzxxx9o3br1C9s2bNgQdnZ2uH79eqnb5XI5rK2tNRZtsaeOiAwd76kjouK0CnXlfbDmsmXLsGjRIkRFRaF9+/YvPc7t27eRkZEBJycnbcrTCnvqiMjQcfiViIrTevZrUFAQ1q9fj82bN+PSpUuYNGmSxoM1x44di+DgYHX7pUuXYu7cudi4cSMaNGiA9PR0pKenIycnBwCQk5ODWbNm4dSpU7h58yaio6MxcOBANG7cGD4+Pjo6zZLYU0dEho6hjoiK0/qeupEjR+LBgwcICQlBeno63N3dNR6smZKSAhOT/8uKa9euRV5eHoYNG6axn3nz5mH+/PkwNTXF33//jc2bNyMrKwvOzs7o06cPFi1a9MrvQ3wR9tQRkbFgqCMioJwTJaZMmYIpU6aUui0mJkbj882bN1+4L0tLSxw4cKA8ZbwSS0tLAP8+YoWIyBDxnjoiKq5crwkzBkWTKxQKBS+MRGSQOPxKRMVJPtTl5+dzCJaIDBpDHREBEg51VlZW6p/L80YKIiKxcZSBiIqTbKgzMTFRB7vs7GyRqyEi0h6HX4moOMmGOkDzvjoiIkPDUEdExUk61NnY2ABgqCMiw8ZQR0SAxENdUU8dh1+JyBDxnjoiKk7Soc7Ozg4AcP/+fZErISLSHodfiag4SYe6onfLpqWliVwJEZH2GOqIqDiGOjDUEZFhY6gjIoChDgBDHREZJt5TR0TFMdQBuHPnjsiVEBFpj8OvRFScpEOdq6srAOCff/7hb7xEZHAY6oioOEmHuiZNmkAmkyErKwsPHjwQuxwionJhqCMiQOKhztLSEvXr1wcAXL58WeRqiIi0wxEGIipO0qEOANzc3AAAly5dErkSIiLtcPiViIqTfKh7/fXXAQCnT58WuRIiovJhqCMigKEOb7zxBgDg1KlTIldCRKQdDr8SUXGSD3UeHh4AgIsXLyIrK0vcYoiItMDhVyIqTvKhzsHBAc2aNYMgCDh48KDY5RARlRlDHREVJ/lQBwD9+/cHAPz6668iV0JEpD2GOiICGOoAAH5+fgCAffv24dmzZyJXQ0RUNrynjoiKY6gD4OXlhbp16yIzMxN79uwRuxwiojLh8CsRFcdQB8DU1BTjx48HAKxZs4a//RKRQWCoI6LiGOr+v/Hjx8Pc3BwnTpzAoUOHxC6HiKjMGOqICGCoU6tTpw7ef/99AMCsWbOQn58vckVERC/GUQUiKo6hrpiPP/4YNWvWxNmzZ/H555+LXQ4R0Qtx+JWIimOoK6Z27dpYs2YNAGDhwoXYu3evyBURkSH5/PPP0alTJ1StWhU1atTQ+/EY6oioOIa6/xg5ciT+97//QRAE+Pv7IyoqSuySiMhA5OXlYfjw4Zg0aVKFHpehjogAwEzsAiobmUyGb775Bnfu3MG+ffvg5+eH1atX43//+x8vnET0QgsWLAAAhIeHV8jx2rdvj6ioKFhZWVXI8YiocmNPXSnMzMywe/duvPXWWygoKMCkSZMwdOhQ3LlzR+zSiMjIKJVKKBQKjaWs7Ozs4OPjg06dOumxQiIyFAx1z2Fubo4ffvgBy5cvR5UqVbBnzx40bdoUixYtQnZ2ttjlEZGRCA0NhY2NjXpxcXERuyQiMlAMdS9gYmKCoKAgxMfHo1OnTnjy5AlCQkJQr149zJkzBzdv3hS7RCLSszlz5kAmk71wuXz5crn3HxwcjOzsbPWSmpqqw+qJSEpkghE86EihUMDGxgbZ2dmwtrbWyzEEQcDOnTvx2Wef4cKFC+r1vXr1QkBAAAYMGKC3YxNR+eji2vDgwQNkZGS8sE3Dhg1hbm6u/hweHo7p06cjKytL6+NVxPWMiAxLWa8LnChRRjKZDKNGjcKIESPw22+/YeXKlTh8+DCio6MRHR2NKlWqoFevXhg8eDD69+8PZ2dnsUsmIh2oXbs2ateuLXYZREQvxVCnJRMTE/j5+cHPzw83b97E5s2bsWPHDly5cgVRUVHqR6A0a9YMPXv2RK9evdC9e3fUrFlT5MqJSN9SUlLw6NEjpKSkoLCwEElJSQCAxo0bo3r16uIWR0RGj8OvOnL58mXs2bMHkZGROH36dInX9zRr1gweHh7w8PDAG2+8gVatWsHMjJmaSJ8q+toQEBCAzZs3l1h/5MgRdO/evUz7qAzXMyKqXMp6XWCo04PMzEwcPXoU0dHROHz4MC5evFiijaWlJVq3bq2xtGrVCra2tiJUTGScKtu1oSwMsWYi0i+GukrkwYMHiI+PR1xcHE6dOoX4+PjnPhalbt26aNmyJZo2bapemjRpAhcXF5iamlZw5USGrbJfG0pjiDUTkX4x1FViKpUK165dw9mzZ/H333+rl1u3bj33O3K5HI0bN0aTJk3QoEED1KtXD/Xr11cvtWrV4hsviP7D0K4NgGHWTET6xVBngLKzs3Hu3DlcunQJV69exbVr13D16lVcv34d+fn5L/xu1apV1UGvbt26cHJygqOjI5ycnNSLo6MjLCwsKuhsiMRniNcGQ6yZiPSLjzQxQDY2NujcuTM6d+6ssb6goAApKSnqgHfr1i2N5d69e3jy5AkuX7780oeg2traqgNe7dq1UatWLdjZ2Wn8t/jP1atXZw8gERGRAShXqFuzZg2++OILpKeno02bNli9ejU6duz43PY//vgj5s6di5s3b6JJkyZYunQp3nzzTfV2QRAwb948rF+/HllZWfDy8sLatWvRpEmT8pRndMzMzNCwYUM0bNiw1O3Pnj1DamqqOuTdvXsXaWlpSE9PR1pamnrJy8tDZmYmMjMzS528URpzc3PUqlULtra2Gq8yKstiZWWFatWqwcLCgsGQiIhIz7QOdTt37kRQUBDCwsLg4eGBFStWwMfHB1euXIG9vX2J9idPnoS/vz9CQ0PRv39/bN++HYMGDcKZM2fQsmVLAMCyZcuwatUqbN68Ga6urpg7dy58fHxw8eJFDheWgYWFBZo0afLCECwIArKystQBLz09HQ8fPkRGRobGf4v/rFQqkZeXp/5OeZmYmKBatWqoVq0aqlevrv75ZZ8tLCxKLJaWlqWuL1pMTPjmOyIikiat76nz8PBAhw4d8M033wD496Z/FxcXfPDBB5gzZ06J9iNHjkRubi727dunXvfGG2/A3d0dYWFhEAQBzs7O+PDDDzFz5kwA/95b5uDggPDwcIwaNeqlNfEeFN0TBAFPnjxRB72srCyN91OWZXn27FmF112lSpUSwc/c3Bzm5uaoUqVKiZ/L+t/nbTMzM4OZmRlMTU319l/2cpafIV4bDLFmItIvvdxTl5eXh8TERAQHB6vXmZiYwNvbG7GxsaV+JzY2FkFBQRrrfHx8EBkZCQBITk5Geno6vL291dttbGzg4eGB2NjYMoU60j2ZTKbuMatfv3659lFQUIAnT54gJycHubm56uVln4uWZ8+evXB5+vQpnj59CpVKpT5mfn4+8vPzoVAodPVHIToTExONkGdqagoTExOtF5lMVq7vabOPohfcF//5v8urbmvUqBEmTpwo9v8sRESVjlah7uHDhygsLISDg4PGegcHh+feoJ+enl5q+/T0dPX2onXPa/NfSqUSSqVS/bnomW/G9H/kxqR69ep6fUVSQUEBnj17BqVSqQ58xX/Oy8tTh73iPxd9LigoKLVNadv+u76goAAFBQUoLCxUL0WfCwoKoFKpND4/r92LOsxVKhVUKtVLZ0BLhZeXV5l/2Su6JhjSJP+iWnk9I6IiZb2WGeTs19DQUCxYsKDEehcXFxGqIaKKdOLECdjY2Gj1ncePH2v9HbE8fvwYAK9nRFTSy65lWoU6Ozs7mJqa4t69exrr7927B0dHx1K/4+jo+ML2Rf+9d+8enJycNNq4u7uXus/g4GCNIV2VSoVHjx6V+QG8CoUCLi4uSE1NNdp7VniOxsHYz1Hf5ycIAh4/fgxnZ2ed71tfnJ2dkZqaCisrK17P/j9jP0djPz+A5/iqynot0yrUmZubo127doiOjsagQYMA/BuooqOjMWXKlFK/4+npiejoaEyfPl297uDBg/D09AQAuLq6wtHREdHR0eoQp1AoEBcXh0mTJpW6T7lcDrlcrrGuRo0a2pwKAMDa2tpo/3IV4TkaB2M/R32en6H00BUxMTFB3bp1tf6esf8dAYz/HI39/ACe46soy7VM6+HXoKAgjBs3Du3bt0fHjh2xYsUK5ObmIjAwEAAwduxY1KlTB6GhoQCAadOmoVu3bli+fDn69euHiIgIJCQkYN26dQD+vSF/+vTp+Oyzz9CkSRP1I02cnZ3VwZGIiIiIXkzrUDdy5Eg8ePAAISEhSE9Ph7u7O6KiotQTHVJSUjSeFdapUyds374dn376KT7++GM0adIEkZGR6mfUAcDs2bORm5uLiRMnIisrC507d0ZUVBSfUUdERERURuWaKDFlypTnDrfGxMSUWDd8+HAMHz78ufuTyWRYuHAhFi5cWJ5ytCaXyzFv3rwSQ7jGhOdoHIz9HI39/CqCFP4Mjf0cjf38AJ5jRdH64cNEREREVPnwnUpERERERoChjoiIiMgIMNQRERERGQFJhro1a9agQYMGsLCwgIeHB+Lj48UuqVShoaHo0KEDrKysYG9vj0GDBuHKlSsabZ49e4bJkyejVq1aqF69OoYOHVriYc8pKSno168fqlatCnt7e8yaNQsFBQUabWJiYvD6669DLpejcePGCA8P1/fplbBkyRL1I26KGMP53blzB2+//TZq1aoFS0tLtGrVCgkJCertgiAgJCQETk5OsLS0hLe3N65du6axj0ePHmH06NGwtrZGjRo18O677yInJ0ejzd9//40uXbrAwsICLi4uWLZsWYWcX2FhIebOnQtXV1dYWlqiUaNGWLRokcbrbAz9HCsrXssq17/1IsZ6LQOM+3pmFNcyQWIiIiIEc3NzYePGjcKFCxeECRMmCDVq1BDu3bsndmkl+Pj4CJs2bRLOnz8vJCUlCW+++aZQr149IScnR93mvffeE1xcXITo6GghISFBeOONN4ROnTqptxcUFAgtW7YUvL29hb/++kvYv3+/YGdnJwQHB6vb3LhxQ6hataoQFBQkXLx4UVi9erVgamoqREVFVdi5xsfHCw0aNBBat24tTJs2zWjO79GjR0L9+vWFgIAAIS4uTrhx44Zw4MAB4fr16+o2S5YsEWxsbITIyEjh7NmzwoABAwRXV1fh6dOn6jZ9+/YV2rRpI5w6dUr4888/hcaNGwv+/v7q7dnZ2YKDg4MwevRo4fz588KOHTsES0tL4bvvvtP7OX7++edCrVq1hH379gnJycnCjz/+KFSvXl1YuXKl0ZxjZcRrWeX6t17EWK9lgmD81zNjuJZJLtR17NhRmDx5svpzYWGh4OzsLISGhopYVdncv39fACAcPXpUEARByMrKEqpUqSL8+OOP6jaXLl0SAAixsbGCIAjC/v37BRMTEyE9PV3dZu3atYK1tbWgVCoFQRCE2bNnCy1atNA41siRIwUfHx99n5IgCILw+PFjoUmTJsLBgweFbt26qS+ExnB+H330kdC5c+fnblepVIKjo6PwxRdfqNdlZWUJcrlc2LFjhyAIgnDx4kUBgHD69Gl1m99//12QyWTCnTt3BEEQhG+//VawtbVVn3PRsd3c3HR9SiX069dPeOeddzTWDRkyRBg9erQgCMZxjpURr2WV69+6IBj3tUwQjP96ZgzXMkkNv+bl5SExMRHe3t7qdSYmJvD29kZsbKyIlZVNdnY2AKBmzZoAgMTEROTn52ucT7NmzVCvXj31+cTGxqJVq1bqh0MDgI+PDxQKBS5cuKBuU3wfRW0q6s9k8uTJ6NevX4kajOH8fvnlF7Rv3x7Dhw+Hvb092rZti/Xr16u3JycnIz09XaM+GxsbeHh4aJxjjRo10L59e3Ubb29vmJiYIC4uTt2ma9euMDc3V7fx8fHBlStXkJmZqddz7NSpE6Kjo3H16lUAwNmzZ3H8+HH4+voazTlWNryW/asy/VsHjPtaBhj/9cwYrmXleviwoXr48CEKCws1/tEAgIODAy5fvixSVWWjUqkwffp0eHl5qd/GkZ6eDnNz8xLvvXVwcEB6erq6TWnnW7TtRW0UCgWePn0KS0tLfZwSACAiIgJnzpzB6dOnS2wzhvO7ceMG1q5di6CgIHz88cc4ffo0pk6dCnNzc4wbN05dY2n1Fa/f3t5eY7uZmRlq1qyp0cbV1bXEPoq22dra6uX8AGDOnDlQKBRo1qwZTE1NUVhYiM8//xyjR49WH794PcXrM5RzrGx4Lfu/7UXbXtSG1zLdMPbrmTFcyyQV6gzZ5MmTcf78eRw/flzsUnQmNTUV06ZNw8GDB432lXAqlQrt27fH4sWLAQBt27bF+fPnERYWhnHjxolcnW7s2rUL27Ztw/bt29GiRQskJSVh+vTpcHZ2NppzJN3htcxwGfv1zBiuZZIafrWzs4OpqWmJGUf37t2Do6OjSFW93JQpU7Bv3z4cOXIEdevWVa93dHREXl4esrKyNNoXPx9HR8dSz7do24vaWFtb6/U3v8TERNy/fx+vv/46zMzMYGZmhqNHj2LVqlUwMzODg4ODQZ8fADg5OaF58+Ya61577TWkpKRo1Piiv5OOjo64f/++xvaCggI8evRIqz8HfZk1axbmzJmDUaNGoVWrVhgzZgxmzJiB0NBQjeMb8jlWNryW/d/2om0vasNrmW4Y+/XMGK5lkgp15ubmaNeuHaKjo9XrVCoVoqOj4enpKWJlpRMEAVOmTMGePXtw+PDhEt217dq1Q5UqVTTO58qVK0hJSVGfj6enJ86dO6fxl+zgwYOwtrZW/+P09PTU2EdRG33/mfTq1Qvnzp1DUlKSemnfvj1Gjx6t/tmQzw8AvLy8Sjy64erVq6hfvz4AwNXVFY6Ojhr1KRQKxMXFaZxjVlYWEhMT1W0OHz4MlUoFDw8PdZtjx44hPz9f3ebgwYNwc3PT+7DkkydPYGKieSkxNTWFSqUCYBznWNnwWvavyvJvXQrXMsD4r2dGcS175akWBiYiIkKQy+VCeHi4cPHiRWHixIlCjRo1NGYcVRaTJk0SbGxshJiYGCEtLU29PHnyRN3mvffeE+rVqyccPnxYSEhIEDw9PQVPT0/19qJp8n369BGSkpKEqKgooXbt2qVOk581a5Zw6dIlYc2aNRX+GIAixWeMCYLhn198fLxgZmYmfP7558K1a9eEbdu2CVWrVhW2bt2qbrNkyRKhRo0awt69e4W///5bGDhwYKlT5Nu2bSvExcUJx48fF5o0aaIxRT4rK0twcHAQxowZI5w/f16IiIgQqlatWiGP+xg3bpxQp04d9WMAfv75Z8HOzk6YPXu20ZxjZcRrWeX6t/5fxnYtEwTjv54Zw7VMcqFOEARh9erVQr169QRzc3OhY8eOwqlTp8QuqVQASl02bdqkbvP06VPh/fffF2xtbYWqVasKgwcPFtLS0jT2c/PmTcHX11ewtLQU7OzshA8//FDIz8/XaHPkyBHB3d1dMDc3Fxo2bKhxjIr03wuhMZzfr7/+KrRs2VKQy+VCs2bNhHXr1mlsV6lUwty5cwUHBwdBLpcLvXr1Eq5cuaLRJiMjQ/D39xeqV68uWFtbC4GBgcLjx4812pw9e1bo3LmzIJfLhTp16ghLlizR+7kJgiAoFAph2rRpQr169QQLCwuhYcOGwieffKIxXd/Qz7Gy4rWscv1bL84Yr2WCYNzXM2O4lskEodijkomIiIjIIEnqnjoiIiIiY8VQR0RERGQEGOqIiIiIjABDHREREZERYKgjIiIiMgIMdURERERGgKGOiIiIyAgw1BEREREZAYY6qvS6d++O6dOni10GEdELBQQEYNCgQS9so4/r2fz58+Hu7v7c7TExMZDJZMjKytLpcanyMRO7ACIiImOwcuVK8CVNJCaGOiIikry8vDyYm5u/0j5sbGx0VA1R+XD4lQxKZmYmxo4dC1tbW1StWhW+vr64du2aevutW7fg5+cHW1tbVKtWDS1atMD+/fvV3x09ejRq164NS0tLNGnSBJs2bRLrVIhIRN27d8eUKVMwffp02NnZwcfHBwBw/vx5+Pr6onr16nBwcMCYMWPw8OFD9fd++ukntGrVCpaWlqhVqxa8vb2Rm5sLoOTwa25uLsaOHYvq1avDyckJy5cvL1GHTCZDZGSkxroaNWogPDxc/fmjjz5C06ZNUbVqVTRs2BBz585Ffn7+K53/7t270aJFC8jlcjRo0KBEbd9++y2aNGkCCwsLODg4YNiwYWX6MyBxMdSRQQkICEBCQgJ++eUXxMbGQhAEvPnmm+oL3OTJk6FUKnHs2DGcO3cOS5cuRfXq1QEAc+fOxcWLF/H777/j0qVLWLt2Lezs7MQ8HSIS0ebNm2Fubo4TJ04gLCwMWVlZ6NmzJ9q2bYuEhARERUXh3r17GDFiBAAgLS0N/v7+eOedd3Dp0iXExMRgyJAhzx1ynTVrFo4ePYq9e/fijz/+QExMDM6cOaN1nVZWVggPD8fFixexcuVKrF+/Hl9//XW5zzsxMREjRozAqFGjcO7cOcyfPx9z585VB8mEhARMnToVCxcuxJUrVxAVFYWuXbuW68+AKphAVMl169ZNmDZtmnD16lUBgHDixAn1tocPHwqWlpbCrl27BEEQhFatWgnz588vdT9+fn5CYGBghdRMRJVbt27dhLZt22qsW7RokdCnTx+NdampqQIA4cqVK0JiYqIAQLh582ap+xw3bpwwcOBAQRAE4fHjx4K5ubn62iQIgpCRkSFYWloK06ZNU68DIOzZs0djPzY2NsKmTZueW/sXX3whtGvXTv153rx5Qps2bZ7b/siRIwIAITMzUxAEQXjrrbeE3r17a7SZNWuW0Lx5c0EQBGH37t2CtbW1oFAoSuzrZX8GJC721JHBuHTpEszMzODh4aFeV6tWLbi5ueHSpUsAgKlTp+Kzzz6Dl5cX5s2bh7///lvddtKkSYiIiIC7uztmz56NkydPVvg5EFHl0a5dO43PZ8+exZEjR1C9enX10qxZMwDAP//8gzZt2qBXr15o1aoVhg8fjvXr1yMzM7PUff/zzz/Iy8vTuF7VrFkTbm5uWte5c+dOeHl5wdHREdWrV8enn36KlJQUrfdT5NKlS/Dy8tJY5+XlhWvXrqGwsBC9e/dG/fr10bBhQ4wZMwbbtm3DkydPAECrPwOqeAx1ZFTGjx+PGzduYMyYMTh37hzat2+P1atXAwB8fX1x69YtzJgxA3fv3kWvXr0wc+ZMkSsmIrFUq1ZN43NOTg78/PyQlJSksVy7dg1du3aFqakpDh48iN9//x3NmzfH6tWr4ebmhuTk5HLXIJPJSgxdFr9fLjY2FqNHj8abb76Jffv24a+//sInn3yCvLy8ch/zZaysrHDmzBns2LEDTk5OCAkJQZs2bZCVlaWXPwPSHYY6MhivvfYaCgoKEBcXp16XkZGBK1euoHnz5up1Li4ueO+99/Dzzz/jww8/xPr169XbateujXHjxmHr1q1YsWIF1q1bV6HnQESV1+uvv44LFy6gQYMGaNy4scZSFABlMhm8vLywYMEC/PXXXzA3N8eePXtK7KtRo0aoUqWKxvUqMzMTV69e1WhXu3ZtpKWlqT9fu3ZN3SsGACdPnkT9+vXxySefoH379mjSpAlu3br1Suf52muv4cSJExrrTpw4gaZNm8LU1BQAYGZmBm9vbyxbtgx///03bt68icOHD2v1Z0AVj480IYPRpEkTDBw4EBMmTMB3330HKysrzJkzB3Xq1MHAgQMBANOnT4evry+aNm2KzMxMHDlyBK+99hoAICQkBO3atUOLFi2gVCqxb98+9TYiosmTJ2P9+vXw9/fH7NmzUbNmTVy/fh0RERH4/vvvkZCQgOjoaPTp0wf29vaIi4vDgwcPSr2OVK9eHe+++y5mzZqFWrVqwd7eHp988glMTDT7Unr27IlvvvkGnp6eKCwsxEcffYQqVaqotzdp0gQpKSmIiIhAhw4d8Ntvv71ygPrwww/RoUMHLFq0CCNHjkRsbCy++eYbfPvttwCAffv24caNG+jatStsbW2xf/9+qFQquLm5IS4ursx/BlTxGOrIoGzatAnTpk1D//79kZeXh65du2L//v3qi2BhYSEmT56M27dvw9raGn379lXPEjM3N0dwcDBu3rwJS0tLdOnSBREREWKeDhFVIs7Ozjhx4gQ++ugj9OnTB0qlEvXr10ffvn1hYmICa2trHDt2DCtWrIBCoUD9+vWxfPly+Pr6lrq/L774Qj2ka2VlhQ8//BDZ2dkabZYvX47AwEB06dIFzs7OWLlyJRITE9XbBwwYgBkzZmDKlClQKpXo168f5s6di/nz55f7PF9//XXs2rULISEhWLRoEZycnLBw4UIEBAQA+PeRKj///DPmz5+PZ8+eoUmTJtixYwdatGiBS5cuafVnQBVLJvx3MJ+IiIiIDA7vqSMiIiIyAgx1REREREaAoY6IiIjICDDUERERERkBhjoiIiIiI8BQR0RERGQEGOqIiIiIjABDHREREZERYKgjIiIiMgIMdURERERGgKGOiIiIyAgw1BEREREZgf8H76SwvBrN3VoAAAAASUVORK5CYII=",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "loss = []\n",
+    "res_loss = []\n",
+    "psi_dag = network_2d(x, p_dag)\n",
+    "for psi in psi_k_s:\n",
+    "    l = np.linalg.norm(psi - psi_dag)\n",
+    "    loss.append(l)\n",
+    "\n",
+    "\n",
+    "for i in range(1, len(loss)):\n",
+    "    res_loss.append(np.log(loss[i] / np.linalg.norm(psi_k_s[i-1] - psi_dag)**2))\n",
+    "    \n",
+    "fig, ax = plt.subplots(1, 2)\n",
+    "ax[0].plot(range(1, len(loss)+1), loss, c= 'black')\n",
+    "ax[0].set_xlabel(r\"loss\")\n",
+    "ax[0].set_ylim(0)\n",
+    "\n",
+    "ax[1].plot(range(1, len(loss)), res_loss, c= 'black')\n",
+    "ax[1].set_xlabel(r\"residual loss\")\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('./lw_loss.png', dpi=300)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "venv",
+   "language": "python",
+   "name": "venv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/ricam_sem/code/lw_coeff.png b/ricam_sem/code/lw_coeff.png
Binary files differ.
diff --git a/ricam_sem/code/lw_loss.png b/ricam_sem/code/lw_loss.png
Binary files differ.
diff --git a/ricam_sem/summary_talk/cite.bib b/ricam_sem/summary_talk/cite.bib
@@ -27,3 +27,16 @@
       archivePrefix={arXiv},
       primaryClass={math.NA}
 }
+
+@article{scherzer2023newton,
+  title={Newton's methods for solving linear inverse problems with neural network coders},
+  author={Scherzer, Otmar and Hofmann, Bernd and Nashed, Zuhair},
+  journal={arXiv preprint arXiv:2303.14058},
+  year={2023}
+}
+
+@url{code,
+    title={Result Code},
+    author={Milutin Popovic},
+    url={https://github.com/miksa234/gauss_newton_inverse_problems},
+}
diff --git a/ricam_sem/summary_talk/main.tex b/ricam_sem/summary_talk/main.tex
@@ -8,12 +8,19 @@
 \tableofcontents
 
 \section{Intro}
-The following questions are answered:
-\begin{itemize}
-    \item iterative regularization with NN functions
-    \item application of NNs on inverse problems
-    \item What generalized NNs are best suited for IPs?
-\end{itemize}
+The talk is about the paper \cite{scherzer2023newton}, in which the authors
+consider using a modified version of the Newton algorithm to reconstruct the
+coefficients of neural network coders in inverse problems. Instead of using
+the inverse of the Jacobian in the iteration, the authors use a more general
+Moore-Penrose inverse. It can be proven that under conditions this modified
+form of the Newton iteration, calling it the Gauss-Newton iteration converges
+locally, quadratically. The aim is to use these results on specifically
+shallow neural networks, because they satisfy an immersion property, i.e. are
+Lipschitz-differentiable immersions, which is the requisite of the
+convergence of the Gauss-Newton method. Additionally, presented results clearly show a
+quicker and reliable solution with its comparison, the Landweber method.
+These results were also checked by me, in terms of writing the code and using
+the same initial setup to come to the same conclusions \cite{code}.
 
 \subsection{Posing the problem}
 Consider linear operator equation between Hilbert spaces $\mathbf{X}$ and
@@ -21,18 +28,16 @@ $\mathbf{Y}$
 \begin{align}
     F\mathbf{x} = \mathbf{y}.
 \end{align}
-For the problem modeling we introduce a function, called \textbf{Coding}
+For the problem modeling a function is introduced, called \textbf{Coding}
 $\Psi: \vec{P} \to \mathbf{X}$ which maps NN parameters to images functions,
-a nonlinear operator. Our problem can be written as follows
+a nonlinear operator. The problem equation can be written as follows
 \begin{align}
     N(\vec{p}) = F\Psi(\vec{p}) = \mathbf{y}, \label{eq: main}
 \end{align}
 where $\mathbf{X}$ is the image space, $\mathbf{Y}$ the data space and $\vec{P}$ the parameter
-space. In the case the operator in question $F$ is nonlinear then we would of
-course have a nonlinear equation, which we are not considering right now. The
-talk aims to explain the link between the general regularization of the
-degree of ill-posedness and nonlinearity and investigates generalized
-Gauss-Newton solvers, by the outer inverse or by approximations.
+space. In the case the operator in question, $F$ is nonlinear, then we would of
+course have a nonlinear equation, which we are not considering right now.
+
 \subsection{Decomposition cases (review)}
 An operator $N$ satisfies the \textit{1st decomposition case} in an open empty
 neighborhood $\mathcal{B}\left(\vec{p}\;^{\dagger}; \rho \right) \subseteq
@@ -48,21 +53,24 @@ and a nonlinear operator $\Psi: \vec{P} \to \mathbf{X}$ such that
 \begin{align}
     N(\vec{p}) = F\Psi(\vec{p}).
 \end{align}
+
 \subsection{Gauss-Newton type method for 2nd decomposition case}
-We are dealing with the operator $\Psi:\mathcal{D} \subseteq \vec{P} :=
-\mathbb{R}^{n_*} \to \mathbf{X}$. The derivative of $\Psi$ \textbf{cannot be
-invertible}!. So how do we decompose the 2nd case
+The main object is the operator $\Psi:\mathcal{D} \subseteq \vec{P} :=
+\mathbb{R}^{n_*} \to \mathbf{X}$. The derivative of $\Psi$ is generally not
+invertible.
 \begin{align}
     N(\vec{p}) = F\Psi(\vec{p}).
 \end{align}
-To prove convergence we need introduce the Lipschitz-differentiable immersion.
+The aim is to use the modified version of the Newton method to reconstruct
+the parameters $\vec{p}$. The prerequisite for this is some background on the
+general local convergence of the Newton Method, conditions called
+Newton-Mysovskii and the definition of the Moore-Penrose inverse.
 \section{Background}
 \subsection{Newton-Mysovskii}
 The local convergence of the Newton method is guaranteed under the so called Newton-Mysovskii
- conditions. In this section the results are shown for the simple case in the
+ conditions. In this section the results are summarized for the simple case in the
  finite dimensional space, when the nonlinear operator has derivative which
  are invertible. This result is going to be extended as aim of the summary.
-
  \begin{theorem}
      Let $N: \mathcal{D}(N) \subseteq \mathbb{R}^{n}\to \mathbb{R}^{n}$ be
      continuously Fr\'echet differentiable on a non-empty, open and convex
@@ -105,12 +113,12 @@ The local convergence of the Newton method is guaranteed under the so called New
  \end{theorem}
 
 \subsection{Moore-Penrose Inverse}
-We study the case where $\mathbf{Y}$ is an infinite dimensional Hilbert
-space. In this regard it is necessary to replace the inverse in the classical
-Newton method because the liberalizations of the operator $N$ cannot be be
-invertible. This is done by introducing the so called Moore-Penrose inverse
-or more general the outer inverse and we refer to the Gauss-Newton method to
-distinguish between the classical version.
+Now, the case where $\mathbf{Y}$  is an infinite dimensional Hilbert
+space, is introduced. It is necessary to replace the inverse in the classical
+Newton method because the liberalizations of the operator $N$, which
+generally cannot be invertible. This is done by introducing the so called
+Moore-Penrose inverse or more general the outer inverse and we refer to the
+Gauss-Newton method to distinguish between the classical version.
 \begin{mydef}{Inner, outer and Moore Penrose inverse
         \label{def: moore-penrose}}
     $L: \vec{P} \to \mathbf{Y}$ be a linear and bounded operator between
@@ -184,9 +192,9 @@ distinguish between the classical version.
     which replaces the standard $\Psi^{-1}$ in the standard Newton's method.
     TODO: more in detail definition.
 \end{mydef}
-We link the inverse of the Lipschitz Lipschitz-differentiable immersion with
-the Moore-Penrose inverse together with the necessary boundary constraints
-for the Gauss-Newton method
+Linking the inverse of the Lipschitz Lipschitz-differentiable immersion with
+the Moore-Penrose inverse together with the following results delivers the
+Gauss-Newton method
 \begin{theorem}
     \label{thm: moore-penrose}
     \begin{enumerate}
@@ -213,7 +221,7 @@ for the Gauss-Newton method
 \end{proof}
 
 We can now wrap the results back to the original problem of the Gauss-Newton
-iteration of \ref{eq: main}
+method \ref{eq: main}
 \begin{lemma}
     \label{lem: moore-penrose}
     Let $F$ be as in \ref{eq: main} linear, bounded with trivial nullspace
@@ -290,6 +298,7 @@ and a Lipschitz-differentiable immersion.
 \subsection{Neural networks}
 Shallow neural network coders are of the following form
 \begin{align}
+    \label{eq: shallow-nn}
     \Psi:
     \mathcal{D}(\Psi) := \mathbb{R}^{n_*} =
     \mathbb{R}^{N}\times \mathbb{R}^{n \times N}
@@ -298,7 +307,7 @@ Shallow neural network coders are of the following form
     L^{2}\left([0, 1]^{n}\right),\\
     \vec{p} = (\vec{\alpha}, \mathbf{w}, \vec{\theta}) &\mapsto
     \left(\vec{x} \to \sum_{j=1}^{N} \alpha_j\sigma\left(
-    \vec{\mathbf{w}}_j^{T}\vec{x} + \omega_j \right)  \right),
+    \vec{\mathbf{w}}_j^{T}\vec{x} + \theta_j \right)  \right),
 \end{align}q
 where $\sigma$ is an activation function, such as tanh or sigmoid.
 
@@ -308,45 +317,39 @@ A standard deep neural network (DNN) with $L$ layers is a function depending on 
 \begin{align}
     \vec{x}\to\Psi(\vec{x}) := \sum_{j_L=1}^{N_L} \alpha_{j_L,L}\sigma_L\
     \left( p_{j_L, L} \left( \sum_{j_{L-1}=1}^{N_{L-1}}\cdots
-    \left( \sum_{j_1=1}^{N_1}\alpha_{j_1,1}\sigma_1\left(p_{j_1,1}(\vec{x})
+    \left( \sum_{j_1=1}^{N_1}\alpha_{j_1,1}\sigma_1\left(\rho_{j_1,1}(\vec{x})
     \right)  \right)  \right)  \right),
 \end{align}
 where
 \begin{align}
-    p_{j_l}(\vec{x}) = \mathbf{w}_{j, l}^{T}\vec{x} + \theta_{j,l},
+    \rho_{j_l}(\vec{x}) = \mathbf{w}_{j, l}^{T}\vec{x} + \theta_{j,l},
 \end{align}
 with $\alpha_{j,l}, \theta_{j,l} \in \mathbb{R}$ and $\vec{x},
 \mathbf{w}_{j,l} \in \mathbb{R}^{n} \;\; \forall l=1,\ldots,L$. And is
 probably not a Lipschitz-continuous immersion!
 
-
-The solution involves either reconstructing the function or the coefficient use
-Tikhonov regularization or use newton type methods, the talk explains the
-solution for decomposable operators wrt. the 2nd decomposition case for
-Gauss-Newton type methods.
-
-Using variational methods, Tikhonov regularization (some background on this
-here)
+Then the inverse problem
+\begin{align}
+    N(\vec{p}\;) = F\Psi(\vec{p}\;) = \mathbf{y},
+\end{align}
+can be solved using variational methods, e.g. Tikhonov regularization
 \begin{align}
     \|N(\vec{p}) - \mathbf{y}\|^{2} + \alpha \|\vec{p}\|^{2} \to \min,
 \end{align}
-or alternatively state space regularization (some background on this)
+or alternatively state space regularization
 \begin{align}
     \|N(\vec{p}) - \mathbf{y}\|^{2}
     + \alpha \|\mathbf{x} - \mathbf{x}_0\|^{2}
     \to \min \quad \text{s.t} \quad \Psi(\vec{p}) = \mathbf{x}.
 \end{align}
-Alternatively use iterative methods, Newton's iteration would look like the
-following
+Here the analysis the iterative method, the Gauss-Newton method is
+considered.
 \begin{align}
-    \vec{p}\;^{k+1} = \vec{p} - N'\left(p^{-k}\right)^{-1}\left(N(\vec{p}) -
-    \mathbf{y}  \right),
+    \vec{p}\;^{k+1} = \vec{p}\;^{k} -
+    N'( \vec{p}\;^{k})^{-1} (N(\vec{p}\;^{k}) -
+    \mathbf{y}  ),
 \end{align}
-where $N'$ is the Jacobian.
-
-Usually it is assumed that the nonlinear operator $\Psi$ is well-posed.
-Here we need to see B. Hofmann On the degree of ill-posedness of nonlinear
-problems. Where we assume that the nonlinear operator $\Psi$ is well-posed.
+where $N'$ is the Jacobian. And we assume that the nonlinear operator $\Psi$ is well-posed.
 
 
 \section{Newton's method with the neural network operator}
@@ -355,20 +358,20 @@ the universal approximation properties of neural networks, the fact that they
 can approximate continuous functions arbitrarily well, to the inverse problem
 in \ref{eq: main} using the Gauss-Newton method. To ensure convergence it is
 necessary to show that the considered neural network structure is a
-Lipschitz-differentiable immersion. As it will be shown, a direct implication
-of this is to show that the among other the activation function, its
+Lipschitz-differentiable immersion. As it will be summarized, a direct implication
+of this is to show that the activation function, its
 derivative and its first moment of the derivative are linearly independent.
 For this, results from \cite{lamperski_2022} are used and it is conjectured
 that the statement from \ref{eq: lpdi-property} is fulfilled, meaning that
-the function from $\mathbf{X}_{\vec{p}}$ are linearly independent.
+the functions forming $\mathbf{X}_{\vec{p}}$ are linearly independent.
 \newline
 Convergence is based on the immersion property of the network functions
 \begin{align}
     \text{span}\{\partial_{p_i}\Psi(\vec{p})\;:\;i=1,\ldots,n_*\}, \qquad
     \text{has rank}(n_*).
 \end{align}
-To show the Newton-Mysovskii conditions for neural network functions the
-notation.
+To show the Newton-Mysovskii conditions for neural network functions
+following notation is adapted
 \begin{align}
     \vec{p} := (\vec{\alpha}, \mathbf{w}, \vec{\theta}) \in
     \mathbb{R}^{N}\times \mathbb{R}^{n\cdot N} \times \mathbb{R}^{N} =
@@ -430,7 +433,7 @@ linearly independent and the results are build from here on out.
     Assume that the functions from \ref{eq: linear_indep} are locally
     linearly independent.
 \end{conjecture}
-From this it follows that the shallow network coders are a
+From the above Conjecture it follows that the shallow network coders are a
 Lipschitz-differentiable immersion (for a suitable choice of an activation
 function), so Gauss-Newton method converges locally.
 \subsection{Gauss-Newton iteration with coding networks}
@@ -469,6 +472,9 @@ for shallow network coders.
     \mathcal{D}(\Psi)$ the solution of equation \ref{eq: main}. Then the
     Gauss-Newton method converges quadratically if
     $\vec{p}\;^{0}$ is sufficiently close to $\vec{p}\;^{\dagger}$.
+    \begin{align}
+        \vec{p}\;^{k+1} = \vec{p}
+    \end{align}
 \end{theorem}
 \begin{proof}
 
@@ -480,6 +486,8 @@ for shallow network coders.
 
 
 \section{Results}
+In the following section the results presented in the paper
+\cite{scherzer2023newton} are rerun.
 \subsection{Numerical results(simplified)}
 The simplification is
 \begin{align}
@@ -487,32 +495,77 @@ The simplification is
     &\mathbf{y}^{\dagger} = F\Psi(\vec{p}\;^{\dagger}) \qquad \text{is
     attainable}
 \end{align}
-Then the Gauss-Newton method is
+The aim is to recostruct the coefficients of a 2d neural network function
+\ref{eq: shallow-nn} with
 \begin{align}
-    \vec{p}\;^{k+1} = \vec{p}\;^{k} - \Psi'\left(\vec{p})\;^{k}  \right)^{\dagger}
-    \left( \Psi(\vec{p}\;^{k} - \Psi^{\dagger} \right) \qquad k \in
-    \mathbb{N}_0.
+    \vec{p}\;^{\dagger} = \left(
+        \begin{pmatrix} 1.0\\1.0\\0.1\\0.1 \end{pmatrix};
+        \begin{pmatrix} 0.3\\0.1\\1.0\\0.8 \end{pmatrix} \right).
 \end{align}
-Do some numerical  results or explain the ones in the talk.
-\subsection{Landweber iteration}
-Instead of the Gauss-Newton iteration we consider the Landweber iteration
+Meaning that it is aimed to reconstruct the following function
 \begin{align}
-    \vec{p}\;^{k+1} = \vec{p}\;^{k} - \lambda \Psi'\left(\vec{p}\;^{k})  \right)^{\dagger}
-    \left( \Psi(\vec{p}\;^{k} - \Psi^{\dagger} \right) \qquad k \in
+    \Psi^{\dagger}(\vec{x})
+    &= \Psi(\vec{p}\;^{\dagger})(\vec{x})\\
+    &=1.0\sigma\left( (1.0,0.1)^{T}\vec{x} + 0.1 \right)
+    +0.3 \sigma\left( (0.1, 1.0)^{T}\vec{x} + 0.8 \right).
+\end{align}
+The stopping criterion is $\|\Psi(\vec{p}\;^{k_s+1}) - \Psi^{\dagger})\| \le
+\delta = 0.001$
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.8\textwidth]{./pics/gn_coeff.png}
+    \caption{Coefficients, left truth, middle starting point, right
+    iteration stop}
+    \label{fig: gn_coeff}
+\end{figure}
+The below figure shows the standard loss used for the breaking criterion and
+the residual loss
+\begin{align}
+    \log \left( \frac{\|\Psi(\vec{p}\;^{k+1}) -
+    \Psi^{\dagger}\|}{\|\Psi(\vec{p}\;^{k}) - \Psi^{\dagger}\|} \right)
+\end{align}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.8\textwidth]{./pics/gn_loss.png}
+    \caption{Gauss-Newton loss, left standard norm loss, right residual loss}
+    \label{fig: gn_loss}
+\end{figure}
+
+
+For comparison with the Gauss-Newton iteration, consider the Landweber iteration
+\begin{align}
+    \vec{p}\;^{k+1} = \vec{p}\;^{k} - \lambda \Psi'\left(\vec{p}\;^{k}  \right)^{\dagger}
+    \left( \Psi(\vec{p}\;^{k}) - \Psi^{\dagger} \right) \qquad k \in
     \mathbb{N}_0.
 \end{align}
-Needs about 500 iterations
-\subsection{The catch}
-If the observed convergence rate of the Gauss-New ton change completely if the
+Around $8000$ iteration are needed to reach the same accuracy that the
+Gauss-Newton method reaches in $5$, with $\lambda = 0.02$ (e.g. $\lambda=0.2$
+diverges).
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.8\textwidth]{./pics/lw_coeff.png}
+    \caption{Coefficients, left truth, middle starting point, right
+    iteration stop}
+    \label{fig: lw_coeff}
+\end{figure}
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.8\textwidth]{./pics/lw_loss.png}
+    \caption{Landweber loss, left standard norm loss, right residual loss}
+    \label{fig: lw_loss}
+\end{figure}
+
+If the observed convergence rate of the Gauss-Newton can change completely if the
 solution is not attainable. Then the conjecture is that the non-convergence
-because of multiple solutions.
+because of multiple solutions, which can be observed when not using enough
+reconstruction data.
 Also the implementation of the simplified Gauss-Newton requires inversion of
-$F$ , which is not done in practice, this is for Landweber.
-
+$F$ , which is not done in practice, this is not true for Landweber.
 \subsection{Alternative to DNNs}
-Instead of using Deep Neural Networks where we do not know the result if the
-the immersion is invertible, we consider Quadratic neural network functions
-defined as follows
+Instead of using Deep Neural Networks where it is unknown if
+the immersion is invertible, another considerable option is to use
+Quadratic neural network functions defined as follows
 \begin{align}
     \Psi(\vec{x}) := \sum_{j=1}^{N} \alpha_j\sigma\left(\vec{x}^{T}A_j\vec{x}
         + \mathbf{w}_j^{T}\vec{x} + \theta_j \right),
@@ -550,8 +603,7 @@ are \textbf{linearly independent}.
 
 Results of these types of networks is that the Shepp-Logan can be represented
 with \textbf{10 nodes} with elliptic neurons and \textbf{one layer}. Where as
-for affine networks, both shallow and deep we need infinity neurons. Here
-figure tensorflow approximations of a circle 15 neurons linear.
+for affine networks, both shallow and deep we need infinity neurons.
 
 \appendix
 \section{Proofs}
diff --git a/ricam_sem/summary_talk/pics/gn_coeff.png b/ricam_sem/summary_talk/pics/gn_coeff.png
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diff --git a/ricam_sem/summary_talk/pics/gn_loss.png b/ricam_sem/summary_talk/pics/gn_loss.png
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diff --git a/ricam_sem/summary_talk/pics/lw_coeff.png b/ricam_sem/summary_talk/pics/lw_coeff.png
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diff --git a/ricam_sem/summary_talk/pics/lw_loss.png b/ricam_sem/summary_talk/pics/lw_loss.png
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diff --git a/ricam_sem/summary_talk/preamble.tex b/ricam_sem/summary_talk/preamble.tex
@@ -277,6 +277,9 @@
 \title{University of Vienna\\
 \vspace{1cm}Seminar:\\Joint RICAM Seminar\\
 \vspace{0.5cm}
-Summary of talk by Otmar Scherzer
+Summary of talk by Otmar Scherzer\\
+\vspace{0.5cm}
+Gauss-Newton method for solving linear inverse problems with neural network
+coders
 }
 \author{Milutin Popovic}