{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "82c6da03",
   "metadata": {},
   "source": [
    "## Gradient descent in presence of extreme flatness and steepness"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "183a3042",
   "metadata": {},
   "source": [
    "Typical theoretical analysis of convergence of gradient descent requires assumptions like convexity and smoothness that do not hold in practice. In particular, the theoretical studies for designing good learning rates rarely discuss realistic settings that are highly non-convex. For example, for $L$-Lipschitz and convex functions, the theory suggests the use of a learning rate smaller than $2/L$ as a sufficient condition for convergence. Here we will construct minimalist non-convex and non-smooth examples where this theory fails and setting the learning rate adaptively is necessary.\n",
    "\n",
    "### Basin sigmoid, a simple class of challenging functions\n",
    "\n",
    "Towards understanding the challenges and potential solutions for learning in the presence of non-convex non-smooth functions, we will study the convergence of gradient descent for a simple sigmoid-based function family. The functions in this family simultaneously exhibit extreme flatness and extreme sharpness. This makes it particularly challenging to choose a step size.\n",
    "\n",
    "The function $f(x)$ is constructed using the sigmoid function with temperature, i.e. $\\frac{1}{1+e^{\\beta x}}$. Here $\\beta$ is the temperature parameter that controls the steepness of the function, larger $\\beta$ corresponds to higher steepness. Our functions will have two sigmoids added together, and have a second width parameter that controls the width of the basin corresponding to the minimum.\n",
    " \n",
    "$$f(x)=\\frac{1}{1+e^{\\beta x}}+\\frac{1}{1+e^{\\beta (w-x)}}$$\n",
    "\n",
    "We illustrate this function family via the following code snippet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3a55f82c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "import math \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Sigmoidal-basin function family, its gradients and second derivatives\n",
    "\n",
    "# The family consists of a sum of two sigmoidal functions that form a basin.\n",
    "# Steepness: beta, corresponds to temperature of the sigmoid\n",
    "# Basin width: w, corresponds to gap between the inflection points of the two sigmoids.\n",
    "\n",
    "def basin_sigmoid(beta, w, x):\n",
    "    z1 = 1/(1 + np.exp(beta * x)) \n",
    "    z2 = 1/(1 + np.exp(beta * (w-x)))\n",
    "    return z1+z2\n",
    "\n",
    "def basin_sigmoid_derivative(beta, w, x):\n",
    "    z1 = np.exp(beta * x)\n",
    "    z2 = np.exp(beta * w) / math.pow(z1 + np.exp(beta * w), 2)\n",
    "    z3 = 1 / math.pow(z1 + 1, 2)\n",
    "    return beta * z1 * (z2 - z3)\n",
    "\n",
    "def basin_sigmoid_second_derivative(beta, w, x):\n",
    "    z0 = np.exp(beta * w)\n",
    "    z1 = np.exp(beta * x)\n",
    "    z2 = z0 * (z0-z1) / math.pow(z1 + z0, 3)\n",
    "    z3 = (1-z1) / math.pow(z1 + 1, 3)\n",
    "    return beta * beta * z1  * (z2 - z3)\n",
    "\n",
    "\n",
    "# E.g. plot(20, 1)\n",
    "def plot(beta, w):\n",
    "    # test function plots\n",
    "    x = np.linspace(-1, 2, 400) # Generates 400 points between -1 and 2\n",
    "    y = basin_sigmoid(beta, w, x)\n",
    "    y1 = [basin_sigmoid_derivative(beta, w, x1) for x1 in x]\n",
    "    y2 = [basin_sigmoid_second_derivative(beta, w, x1) for x1 in x]\n",
    "    \n",
    "    # Plot the function\n",
    "    plt.plot(x, y)\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"f(x)\")\n",
    "    plt.title(\"Plot of basin_sigmoid with width=%.2f and steepness=%.2f\" % (w, beta))\n",
    "    plt.show()\n",
    "    \n",
    "    # Plot the function along with first and second derivatives\n",
    "    plt.plot(x, y, label=r\"$f(x)$\")\n",
    "    plt.plot(x, y1, label=r\"$f'(x)$\")\n",
    "    plt.plot(x, y2, label=r\"$f''(x)$\")\n",
    "    plt.legend(loc=\"upper left\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.title(\"Plot of basin_sigmoid and derivatives\")\n",
    "    \n",
    "    # Add grid lines\n",
    "    plt.grid(True)\n",
    "    \n",
    "    # Show the plot\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "beta = 20.0\n",
    "w = 1.0\n",
    "\n",
    "plot(beta, w)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2335e6b9",
   "metadata": {},
   "source": [
    "As the above plots show, the second derivative can take large negative values outside of the basin given by $(0,w)$. The functions are always convex within the basin, and non-convex outside of it. Moreover, there is no absolute smoothness (Lipschitzness) bound, as by making the steepness $\\beta$ large, we can arbitrarily increase the slope of the function $f(x)$ close the basin end points $x=0,x=w$.\n",
    "\n",
    "\n",
    "### Both small and large learning rates fail\n",
    "\n",
    "\n",
    "Now if the initial point is $x_0=-0.5$, gradient descent would be really slow initially due to the flatness (depending on the learning rate) but will move towards the \"cliff\" near $x=0$. Higher learning rates are generally better in this flat non-convex region.\n",
    "\n",
    "Once we are at $x=-\\epsilon$ for some small $\\epsilon$, the situation reverses. Gradient descent steps with a fixed learning rate $\\eta$ can easily overshoot (we can make $\\beta$ large enough for any fixed $\\eta$ so that this happens). So we really want to step very carefully in this region. The following piece of code illustrates this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "16421060",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# gradient descent with initial point x0 and fixed step size eta\n",
    "def grad_descent(x0, eta, iterations):\n",
    "    points = [x0]\n",
    "    # Gradient Descent optimization\n",
    "    for i in range(iterations):\n",
    "        x = points[i]\n",
    "        \n",
    "        # Compute the gradient at the current point\n",
    "        grad = basin_sigmoid_derivative(beta, w, x)\n",
    "        \n",
    "        # Update x using the Gradient Descent formula\n",
    "        x = x - eta * grad\n",
    "        \n",
    "        points.append(x)\n",
    "    return points\n",
    "\n",
    "# pts  = grad_descent(-1, 10, 10000)\n",
    "\n",
    "def plot_gd(beta, w, x0, eta, iterations):\n",
    "    # test function plots\n",
    "    x = np.linspace(-1, 2, 400) # Generates 400 points between -1 and 2\n",
    "    y = basin_sigmoid(beta, w, x)\n",
    "    y1 = [basin_sigmoid_derivative(beta, w, x1) for x1 in x]\n",
    "    y2 = [basin_sigmoid_second_derivative(beta, w, x1) for x1 in x]\n",
    "    \n",
    "    iterates = grad_descent(x0, eta, iterations)\n",
    "    pts = [basin_sigmoid(beta, w, xi) for xi in iterates]\n",
    "    \n",
    "    # Plot the function\n",
    "    plt.plot(x, y)\n",
    "    plt.plot(iterates, pts, '.r', alpha=.8)\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"f(x)\")\n",
    "    plt.title(\"Gradient descent on basin_sigmoid with lr=%.2f, %i iterations\" % (eta, iterations))\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "x0 = -0.6\n",
    "\n",
    "eta = 0.3\n",
    "itrns = 1000\n",
    "\n",
    "plot_gd(beta, w, x0, eta, itrns)\n",
    "\n",
    "eta = 0.4\n",
    "itrns = 1000\n",
    "\n",
    "plot_gd(beta, w, x0, eta, itrns)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "726ca3ff",
   "metadata": {},
   "source": [
    "If the learning rate is too small, gradient descent gets stuck in the flat part. On the other hand, if it is large enough to make progress, it can get vastly overshoot once it gets to the steep portions near the edge of the basin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "32b6b112",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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II4+Ijh07irlz5wohhLh+/XqZOux1mVfWPffyyy/bbF+4cKEAIJKTkyus0V73XFhYmFCpVOLcuXNl9pf+Biu73VnrX//613JriYmJEW3atKmwRiGEGDt2rFi9erXYs2ePWL9+vRg8eLAAIN577z2b/TQajZg8eXKZ++/bt89uF1d1lPe7kH6Xd75PS9asWWPTbViVY9K6dWub9zdJUlKSACA++uijCuu19zsur1usqp9VBoNBZGZmVvj8JpNJlJSUiHnz5gk/Pz+bz6Dy6rDXBd6zZ08RGBgocnJyrNuMRqN1DJv0uI7+TTjyGeaIet89V57IyEhoNBrr7dNPPy2zz6hRo8psS0tLw5QpU9C0aVOo1WpoNBpr0+qZM2cAAHl5eTh06BBGjhwJvV5vva+XlxeGDRtWaW2bN29GREQEOnfuDKPRaL0NGjTIbrda37594eXlZf05KCgIgYGBuHr1qkPH4m7nzp1DUlISxo4da/MtISwsrMw3lM2bN8PHxwfDhg2zqbVz584IDg621tq5c2dotVq8+OKL+Pe//12mKw0A/t//+3/Q6/X405/+VG5tmzdvhkKhwLPPPmvzfMHBwejUqVOZYxMcHIzu3bvbbOvYsWO1jw1gaaLt378/mjZtarN9woQJyM/PR3x8vM32xx57rMzzA3C4hmeeecbm59GjR0OtVmPnzp3WbZcuXcLYsWMRHBwMlUoFjUaDPn36ALh9Xvr6+qJly5b4+OOPsWjRIhw9etTaTemIIUOG2LSMVfV1AED37t1x7NgxvPzyy/jpp5+QnZ1d6X3279+PoqIijB492mZ7z549y53JOXToUJuf27dvb30Nd2/PzMy0dtFJ3yrv7i5/8skn4eHhUeGsqp07d8LLy6vM73vs2LHl3udO/fv3R0FBgbUretu2bRg4cCAGDBiAuLg46zYAGDBggEOPWZ57PSfv1rFjR7stfl988QUOHTpU6c1ed3h5LWmOzN5bvXo1xo4di969e2PUqFHYunUrhg4divnz55fp2q7o8epipmBVnt/RY1JXr6mqn1X9+vVDo0aNyjzOjh07MGDAABgMBuv71wcffICMjAykpaVVua68vDwcOHAATzzxBDw9Pa3bVSoVnnvuOVy7dq3MEInK/iYc+QxzRL0OTf7+/nBzc7P7RrBmzRocOnQI33//vd37uru7l2nSNpvNiImJwcaNG/HWW29h+/btOHjwoHVcR0FBAQDg5s2bMJvNCA4OLvO49rbdLTU1FcePH7cJdRqNBl5eXhBClBk/5efnV+YxdDqdtZ6qysjIKLfWu7elpqbi1q1b0Gq1ZepNSUmx1tqyZUts27YNgYGBeOWVV9CyZUu0bNnSZizLjRs3EBoaWuF4gNTUVAghEBQUVOb59u/fX+vHBrAcH3vdvdK4OOn4lVeD1KTsaA13H3O1Wg0/Pz/r8+Tm5qJ37944cOAAPvzwQ+zatQuHDh3Cxo0bbZ5HoVBg+/btGDRoEBYuXIiuXbsiICAAU6dORU5OTqV13OvrAIBZs2bhk08+wf79+zF48GD4+fmhf//+FU6Bl17nnd2uEnvbAEtAvJM0nrG87YWFhdbnUqvVCAgIsNlPoVAgODi4zO/27jrt1ePI3zwAREdHw93dHdu2bcOFCxdw5coVa2g6cOAAcnNzsW3bNrRo0QLh4eEOPWZ5auJ3eafyhj+0atUKnTt3rvQmdcvcWZu9Y52ZmVnmd+go6YvWnefanX9Hdz8PUPZ8qUmNGjWCQqFw6Pmrckzq8jVV9bPK3nly8OBBxMTEAAD+9a9/4ddff8WhQ4fw7rvvAqjeOXnz5k0IIWr0fdqRzzBH1OsxTSqVCv369cPPP/+M5ORkmwMojecpby0Ye2n85MmTOHbsGFauXInx48dbt1+4cMFmP+mPwd4AUEcGhUphb8WKFeX+e22STh5H6pcGzf344492H+vOFrDevXujd+/eMJlMOHz4MP7xj39g2rRpCAoKwlNPPYWAgAD88ssvMJvN5QYnf39/KBQK7N27125/dkV93DXFz88PycnJZbZLgwZr+veTkpJiM67CaDQiIyPD+nvasWMHkpKSsGvXLmvrEgC744TCwsKwfPlyAMAff/yB7777DnPmzEFxcTGWLVtWo3Xbo1arMWPGDMyYMQO3bt3Ctm3b8M4772DQoEFITEy0Oy5Aep32xgOmpKTU6Lphfn5+MBqNuHHjhk1wEkIgJSXFOmmgvPsePHjQbo2O0Gq1ePDBB7Ft2zY0adIEwcHB6NChA1q0aAHAMsh9+/btZVrR6oPyWi/69++P3bt3V3r/8ePHWwfxdujQAQBw4sQJm3GXRqMRZ8+exdNPP12tGkXp2Ko731s6dOiAEydOlNlX2hYREVGt53KEm5sbWrVqVe7zu7m5WX/3VTkmHTp0wNq1a2E0Gm3GNdXGa6rqZ5W98+Tbb7+FRqPB5s2bbXpm7K0z5qhGjRpBqVTW+Pt0ZZ9hjqjXLU2A5ZutyWTClClTUFJSck+PJf3C7/5g/uKLL2x+9vDwQPfu3bFx40brN1jAMmPlhx9+qPR5hg4diosXL8LPzw/dunUrc6vOh0RVvkm2bdsWISEhWLt2rc0gzqtXr9rMYpNqzcjIgMlksltr27Ztyzy+SqVCjx498PnnnwOAdSG3wYMHo7CwsMIFyoYOHQohBK5fv273+aQ3l6qo6rfs/v37W4PKnb7++mu4u7ujZ8+eVa6hIqtXr7b5+bvvvoPRaLTOiHL0vLxbmzZt8N5776FDhw7lLqZXm3x8fPDEE0/glVdeQWZmZrlfYHr06AGdTod169bZbN+/f/89dbPaI82SXbVqlc32DRs2IC8vz/rv9vTt2xc5OTllWq/XrFnj8PMPGDAAR44cwYYNG6xdcB4eHujZsyf+8Y9/ICkpyaGuuXttTa0p1eme69GjB0JCQsq8D6xfvx65ubkYOXJktWr55ptvoNFoEBkZad02YsQInD171mZGmdFoxKpVq9CjRw+bWdW1YcSIEdixYwcSExOt23JycrBx40Y89thj1tBTlWMyYsQI5ObmYsOGDTb7/vvf/0ZoaCh69OhR5TrLO59q4rNKoVBArVbbdP0XFBTgm2++cbiOu3l4eKBHjx7YuHGjzf5msxmrVq1CkyZN7HYnO6q8zzBH1OuWJgDo1asXPv/8c7z22mvo2rUrXnzxRdx///3WFCqdWHd3xdnTrl07tGzZEjNnzoQQAr6+vvjhhx+s4w3u9Je//AWPPPIIBg4ciNdffx0mkwkLFiyAh4eHtZm0PNOmTcOGDRvw0EMPYfr06ejYsSPMZjMSEhLw888/4/XXX6/yiS+Fif/7v//D+PHjodFo0LZtW5uWIIlSqcRf/vIXTJo0CSNGjMALL7yAW7duYc6cOWW6Gp566imsXr0ajz76KP785z+je/fu0Gg0uHbtGnbu3Inhw4djxIgRWLZsGXbs2IEhQ4agWbNmKCwstH47kT4Enn76aXz11VeYMmUKzp07h759+8JsNuPAgQNo3749nnrqKfTq1QsvvvgiJk6ciMOHD+Ohhx6Ch4cHkpOT8csvv6BDhw546aWXqnRspFXiV69ejfbt28PT0xOhoaHlvmHOnj0bmzdvRt++ffHBBx/A19cXq1evxpYtW7Bw4UKHZ5I5auPGjVCr1Rg4cKB19lynTp2sY3yio6PRqFEjTJkyBbNnz4ZGo8Hq1atx7Ngxm8c5fvw4Xn31VTz55JNo3bo1tFotduzYgePHj2PmzJk1WnN5hg0bhoiICHTr1g0BAQG4evUqFi9ejLCwMLRu3drufXx9fTFjxgzExsaiUaNGGDFiBK5du4a5c+ciJCTE4endjhg4cCAGDRqEt99+G9nZ2ejVq5d19lyXLl3w3HPPlXvfcePG4W9/+xvGjRuHv/71r2jdujW2bt2Kn376yeHn79+/P0wmE7Zv326zhMWAAQMwe/ZsKBQK9OvXr9LH6dChA3bt2oUffvgBISEh8PLysvsFprZV5zlVKhUWLlyI5557DpMnT8bTTz+N8+fP46233sLAgQPxyCOPWPfdvXs3+vfvjw8++MA6y+rjjz/G6dOn0b9/fzRp0gRpaWlYvnw5fv75Z8yZM8emheFPf/oTPv/8czz55JOYP38+AgMDsWTJEpw7d846fkwyZ84czJ07Fzt37qx0Jfjdu3dbx06ZTCZcvXoV69evBwD06dPH2or5xhtv4JtvvsGQIUMwb9486HQ6zJ8/H4WFhTZBsirHZPDgwRg4cCBeeuklZGdno1WrVli7di1+/PFHrFq1yqEZu3fr0KEDvv32W6xbtw4tWrSAXq9Hhw4dauSzasiQIVi0aBHGjh2LF198ERkZGfjkk0/s9hqUV4c9sbGxGDhwIPr27Ys33ngDWq0WS5YswcmTJ7F27doqj+1y5DPMIfc0jLwO/f7772LixIkiPDxc6HQ6odfrRatWrcS4cePE9u3bbfYdP3688PDwsPs4p0+fFgMHDhReXl6iUaNG4sknnxQJCQkCgJg9e7bNvt9//73o2LGj0Gq1olmzZmL+/Pnlzj65e3ZFbm6ueO+990Tbtm2FVqsVBoNBdOjQQUyfPl2kpKRY90M5i7jZe8xZs2aJ0NBQoVQqBQCxc+fOCo/Zl19+KVq3bi20Wq1o06aNWLFihd2ZOiUlJeKTTz4RnTp1Enq9Xnh6eop27dqJyZMni/PnzwshLDOdRowYIcLCwoROpxN+fn6iT58+4vvvv7d5rIKCAvHBBx9Yn9fPz0/069fPZvE5IYRYsWKF6NGjh/Dw8BBubm6iZcuWYty4ceLw4cPWffr06SPuv//+Mq/L3mtYu3ataNeundBoNHZ/l3c7ceKEGDZsmDAYDEKr1YpOnTqVmR0lzeT6z3/+Y7Pd0cUOpXPlyJEjYtiwYcLT01N4eXmJp59+WqSmptrsu2/fPhEVFSXc3d1FQECAmDRpkvjtt99snic1NVVMmDBBtGvXTnh4eAhPT0/RsWNH8be//c1mVlx5s+c+/vjjMjU6cqzu9Omnn4ro6Gjh7+9v/bt4/vnnbRb3u3v2nBCWGYEffvihaNKkidBqtaJjx45i8+bNolOnTmLEiBHW/co75uUt6mhvAdGCggLx9ttvi7CwMKHRaERISIh46aWXxM2bN23ue/dxEkKIa9euiVGjRll/V6NGjbLOxHJkdqbZbBb+/v4CgM2Cu7/++qsAILp27VrmPvbO599//1306tVLuLu728wwLO84SMetsveE8t6/hgwZUulrq6o1a9ZY3z+Dg4PF1KlTbWZCCXG77jvPwe+//148+OCDIiAgQKjVauHl5SV69+5d7izPlJQUMW7cOOHr6yv0er3o2bOniIuLK7Pf66+/LhQKhThz5kyltVc0a/DuY3zhwgXx+OOPC29vb+Hu7i769+8vjhw5Uu1jIoQQOTk5YurUqSI4ONj69+LoLFd7v+MrV66ImJgY4eXlJQDYnG/3+lklhOX9vG3btkKn04kWLVqI2NhYsXz58jLvA+XVUd576t69e0W/fv2snxM9e/YUP/zwg80+jv5NOPoZVhlF6cEgIqpTly9fRrt27TB79my88847cpdDTq579+4ICwvDf/7zH7lLoQaMoYmIat2xY8ewdu1aREdHw9vbG+fOncPChQuRnZ2NkydPljuLjqgmZGdnIyAgAL///rt1+Qqi6qj3Y5qIqPYJIWAymSrcR6VSVXuNGA8PDxw+fBjLly/HrVu3YDAY8PDDD+Ovf/0rAxPVOm9vbxQVFcldBjkBtjQREXbt2oW+fftWuM9XX31VZtFIIiJXwtBERMjJyan0IsTh4eF2FxslInIVDE1EREREDqj3i1sSERER1QcuNxDcbDYjKSkJXl5edXIxRyIiIrp3Qgjk5ORUeo3T2uRyoSkpKanM1e2JiIioYUhMTESTJk1keW6XC03SZUcSExMduvQKERERyS87OxtNmza1e/mwuuJyoUnqkvP29mZoIiIiamDkHFrDgeBEREREDmBoIiIiInIAQxMRERGRAxiaiIiIiBzA0ERERETkAIYmIiIiIgcwNBERERE5gKGJiIiIyAEMTUREREQOYGgiIiIicoCsoWnPnj0YNmwYQkNDoVAo8N///rfS++zevRuRkZHQ6/Vo0aIFli1bVvuFEhERkcuT9dpzeXl56NSpEyZOnIhRo0ZVuv/ly5fx6KOP4oUXXsCqVavw66+/4uWXX0ZAQIBD9691d14PRwj56nBWQ4cCW7bUzGMpFIBGY7lptZabwQC4uVm2eXsDXl5AQADg7g54eADNm1vul54O+PlZfm7cGLh+3fKYnTsDgYE1Ux8REdU7soamwYMHY/DgwQ7vv2zZMjRr1gyLFy8GALRv3x6HDx/GJ598In9ouvsCggpFnQen3CIjbuUX31GCbU13/nTnPynu+Bfb7Xepxn3urMGR57/7AaT9PNy0NdssKgRQXGy55eVZtqWm2t213EtDKhS3C1QqAX9/4I03gOees2xLSACaNWOQImogzGYBo1nALCz/NZkETKXv40L6b+m+d769C2mr7X+s+1j/3Wab9LNzfsFWKRUIMbjJXUaNkzU0VVV8fDxiYmJstg0aNAjLly9HSUkJNBpNmfsUFRWhqKjI+nN2dnbNF1beFZfrODht+u0a3v/fqTp7vrqy5Ls5cDxa17xyf4NCAMLydiiEgDIlBeLtt1E0fyGUahVUKiVUXl5QzJ8PREUxRBHVovxiI66k5yMhMx/puUVIzy1CRm4xMvOKkVtkREGxCfklRuQXm1BYbEJ+iQklRrMlHJkt4chJ84ssAr10OPjuALnLqHENKjSlpKQgKCjIZltQUBCMRiPS09MREhJS5j6xsbGYO3duXZUoK5VSCb3G0h5z9x+/KOcHe9+AyuwP229DwmZ7tUqtkt4JJ2r/Se6RojQ8mUxmaDLSIQBcbhQK76w0KMe/AIW7G9xNJdD6eEO9cAEwfLjcJRM1WEVGE45fy8KhK5k4cuUmTiVlIyW7ULZ6pO/NCuvPirt+lv7ddsdyW7GdgE7jnPPMGlRoAsp2OUkf5ndvl8yaNQszZsyw/pydnY2mTZvWXoEyGtujGcb2aCZ3GVY2QaucQFZeGLO5z4n+wNatNV5fTbHpdlSprIUrFApk6dwRnpmMrGJPXPX0QaOkGyie/GfsFCF4tH8nBBRksQWKyAFms8Ce8zfwv9+TEHc6FblFxjL7NHLXoJmfBwK9dPD31MHfUws/Dy08dGq4a9Vw16rgplXBvfSmVamgVAJqpdL6X5VSAZVSAbVSAaXC8v9lwk95vQvk9BpUaAoODkZKSorNtrS0NKjVavj5+dm9j06ng06nq93ChLDfRefibb0245nKHxhU+QNt2VLRA8hHGtNU2k0HpRLq4CAgJQVQKNAywAOmGzegVCog/PygUWhwE4AhPw//+W884lf9gHn7V8MXxVB7eQHz57MFiuguJrPAhiPX8MWei7h4I8+63d9Ti25hvujWvBE6N/VBywBPNPLQylgpuYIGFZqioqLwww8/2Gz7+eef0a1bN7vjmerU3cHJxQNTjROiZmfPKZWWWXJqtf3ZcwaDZQbdnbPnwsIs983IuD17LjQUSEoC9u0DVq8GCgqA0m5iRW4u1L6+gF6PAHMhAnzdYTJmI9fPB82b+GHa0k9gLs7HBTcvNL6RCc+ZM6GIimKLE1Gpowk38f7/TuLkdctYVC+dGqMim2BYpxB0adoISmU9/DJFTk3W0JSbm4sLFy5Yf758+TJ+//13+Pr6olmzZpg1axauX7+Or7/+GgAwZcoUfPbZZ5gxYwZeeOEFxMfHY/ny5Vi7dq1cL8EWg1Lt2rxZ7grsu/9+YOBA4KWXgMREQOr+lf4/Ph6YNQu4dQsqHx8YYmPxWePGKF5hRoq+EYrNClwD4J+SicLj59B0AEMTuTYhBL7YcwkLfzwLswC89Gq81q8Vnu7eDF56mb8gk0uTNTQdPnwYffv2tf4sjT0aP348Vq5cieTkZCQkJFj/PTw8HFu3bsX06dPx+eefIzQ0FH//+9/lX26ACLC0EN3ZSiT9//DhltlzUogKDATS0qA1eKNZdjYMnt4oTLmJWzp3vPhzMha1uYkuzRrJ8xqIZFZYYsKb64/jh2NJAIDhnUPx3pD7EOBVy8MsiBygEM66SEQ5srOzYTAYkJWVBW9vb7nLIVf2v/9ZWqByclDi7omFD4/Hvxp1gLtWhS/HdUN0K3+5KySqU0aTGS+t/g1xp1OhViow+7H78WyPZhx4TQDqx+c3QxORnNLSrC1QeQZfvPjNYfx6IQNuGhW+mxyFDk0McldIVCfMZoE31x/Hht+uQatWYsX4B/Bga35xoNvqw+e3cy6kQNRQBAYCkZFAYCA8dGqsmPAAerf2R0GJCZO+PoSM3KLKH4PICXy28wI2/HYNKqUCn4/tysBE9RJDE1E9olOr8PkzXdEywAOp2UWY8d0xp73MApFk/6UMLN72BwAgdkQHDLwvqJJ7EMmDoYmonvHWa7DkmUjo1Ers/uMG/nP4mtwlEdWa/GIj3lp/HGYBPBnZBKMfcM7Fh8k5MDQR1UNtg70wY2AbAMBftpxmNx05rb9vv4CEzHyEGvT4YNh9cpdDVCGGJqJ66vkHw3FfiDdyCo1YvO283OUQ1biEjHys+OUyAGDu8AiuwUT1HkMTUT2lVinx/lDLN+81BxNwJT2vknsQNSyfxp1DscmM3q39MaA9F3Wl+o+hiagei2rph75tA2AyC3y+80LldyBqIC7eyLUuYPn2I+24FhM1CAxNRPXc1P6tAQAbj17H9VsFMldDVDOW7boIswAGtA9CRGOuR0YNA0MTUT3XpVkjRLf0g8ks8E38VbnLIbpn6blF+N/vllaml/u2lLkaIscxNBE1ABN7hQMA1h5MQEGxSeZqiO7NtwcTUGwyo1NTH3TldRapAWFoImoA+rULRJNGbsgqKMFPp1LkLoeo2sxmgW8PJQIAxkeFyVwNUdUwNBE1ACqlAk9GWhb9+8+RRJmrIaq+/ZczcO1mAbx0ajzaIUTucoiqhKGJqIEY2bUxAGDfxQwOCKcGa/0Rywr3QzuFQq9RyVwNUdUwNBE1EE193dEj3BdCAFuPJ8tdDlGVFRlNiDuVCuD2lwCihoShiagBGdLR0p2x5QRDEzU8v5xPR06REcHeekRyADg1QAxNRA3II/cHQ6EAfk+8xS46anCksP9IRDCUSi5mSQ0PQxNRAxLorUe3MMs39B1nUmWuhshxJrPAzrNpACyhiaghYmgiamD6trNco2vnuRsyV0LkuN8Tb+Fmfgm89Wpr8CdqaBiaiBqYfqWhad/FdBSWcKFLahikVqaH2gRAreJHDzVMPHOJGpi2QV4INehRWGLG/ksZcpdD5JBdf1hCU9+2gTJXQlR9DE1EDYxCoUDv1gEAgPiLDE1U/93KL8appGwAQO82/jJXQ1R9DE1EDVBUSz8AloUuieq7/ZcyIQTQKtATgV56ucshqjaGJqIGSApNJ5OykJVfInM1RBWLv5gOAIguPW+JGiqGJqIGKMhbj5YBHhDCci0vovosvnTsHUMTNXQMTUQNVPdwywfQkas3Za6EqHxZ+SX4IzUXAPBAc1+ZqyG6NwxNRA1UZOlaNwxNVJ/9lmg5P8P9PeDnqZO5GqJ7w9BE1EBJoenEtSwUGbleE9VPv5WG+q681hw5AYYmogaquZ87/Dy0KDaZcfJ6ttzlENkltYR2a87QRA0fQxNRA6VQKNCl9Nv70QR20VH9YzILHEu8BYAtTeQcGJqIGrBOTQwAgBPXs2SuhKisy+m5yCs2wV2rQqtAT7nLIbpnDE1EDViHJgb45d1CUfxBIC1N7nKIbBy/Zgnz94d6Q6VUyFwN0b1Ty10AEVVf16N7sG7NTLiXFML009+gWrAAGD5c7rKIANwOTR0a+8hbCFENYUsTUUOVlgbvue/DYCxAlt4DxptZwKxZbHGiekPqNu5Y2o1M1NAxNBE1VAkJQG4uirwboUSlQa6nN5CTAyQmyl0ZEcxmgdOlF+mNaMzQRM6BoYmooWrWDPD0hE9BNjSmEqhu3gS8vICmTeWujAiJN/NRUGKCTq1EuL+H3OUQ1QiGJqKGKjAQmD8fMBhgKMxDttYdiI21bCeS2bmUHABAq0BPDgInp8GB4EQN2fDhyGrXCZNj/4cbPgH4ZegwaOSuiQjAH6mW0NQ2yEvmSohqDluaiBq40DZhuBLWDql6Ay7dyJO7HCIAwLnSi/S2CWZoIufB0ETUwCkUCrQr/WA6k8zLqVD9cL60palNEBe1JOfB0ETkBNqWhqazpeNIiORUYjLj4o3SliZ2z5ETYWgicgLSJSoulX5QEcnpSnoeSkwCHloVGvu4yV0OUY1haCJyAi0CSkNTOsc0kfzOlXbNtQ7ygkLBmXPkPBiaiJxAi9J1cK5m5MFoMstcDbm6P0oHgXPmHDkbhiYiJ9DYxw06tRIlJoHEmwVyl0Mu7o/SsXWcOUfOhqGJyAkolQrrqssc10Ry+4Mz58hJMTQROYmW1sHgHNdE8iksMeFKhuUcZPccORuGJiIn0bK0pekiW5pIRomZ+TALwEunRoCXTu5yiGoUQxORk7DOoGNLE8noSkY+ACDM350z58jpMDQROYmW1mUH2NJE8rla2jUX5ushcyVENY+hichJhAdYPqTSc4uRlV8iczXkqq5KLU1+7jJXQlTzGJqInISnTo1gbz0A4CJbm0gm0iDw5n5saSLnw9BE5ERaBEjLDnBcE8kjIZMtTeS8GJqInIgUmjiDjuRQYjLjWuniqmFsaSInxNBE5ESkLpGE0nElRHXp+s0CmMwCeo0SgVxugJwQQxORE2nqa+kSuXaToYnq3lWpa87XA0ollxsg5yN7aFqyZAnCw8Oh1+sRGRmJvXv3Vrj/6tWr0alTJ7i7uyMkJAQTJ05ERkZGHVVLVL81bWQJTbz+HMlBWm6gGcczkZOSNTStW7cO06ZNw7vvvoujR4+id+/eGDx4MBISEuzu/8svv2DcuHF4/vnncerUKfznP//BoUOHMGnSpDqunKh+auLrBgDIzCtGXpFR5mrI1VxJt7Q0NWdoIicla2hatGgRnn/+eUyaNAnt27fH4sWL0bRpUyxdutTu/vv370fz5s0xdepUhIeH48EHH8TkyZNx+PDhOq6cqH7y1mtgcNMAgHVALlFdsS5syUHg5KRkC03FxcU4cuQIYmJibLbHxMRg3759du8THR2Na9euYevWrRBCIDU1FevXr8eQIUPKfZ6ioiJkZ2fb3IicWZNGltamxEyOa6K6dZXLDZCTky00paenw2QyISgoyGZ7UFAQUlJS7N4nOjoaq1evxpgxY6DVahEcHAwfHx/84x//KPd5YmNjYTAYrLemTZvW6Osgqm+kcU0cDE51yWQW1lmbXNiSnJXsA8HvvqCjEKLcizyePn0aU6dOxQcffIAjR47gxx9/xOXLlzFlypRyH3/WrFnIysqy3hITE2u0fqL6xtrSxO45qkMp2YUoNpmhUSkQYtDLXQ5RrVDL9cT+/v5QqVRlWpXS0tLKtD5JYmNj0atXL7z55psAgI4dO8LDwwO9e/fGhx9+iJCQkDL30el00Om4Xgi5Di47QHK4XhrSQwxuUKtk/z5OVCtkO7O1Wi0iIyMRFxdnsz0uLg7R0dF275Ofnw+l0rZklUoFwNJCRURAU19pTBNbmqjuJN2ynG+NfdxkroSo9sj6dWDGjBn48ssvsWLFCpw5cwbTp09HQkKCtbtt1qxZGDdunHX/YcOGYePGjVi6dCkuXbqEX3/9FVOnTkX37t0RGhoq18sgqleacEwTyeB6aWgKZWgiJyZb9xwAjBkzBhkZGZg3bx6Sk5MRERGBrVu3IiwsDACQnJxss2bThAkTkJOTg88++wyvv/46fHx80K9fPyxYsECul0BU70hjmrILjcgqKLEuQUBUm263NHE8EzkvhXCxfq3s7GwYDAZkZWXB29tb7nKIakXkX+KQkVeMza89iIjGBrnLIRcw8auD2HnuBuaP7ICnujeTuxxyQvXh85uj9YicUBPrYHCOa6K6kZxVCIDdc+TcGJqInJDURcdxTVRXbo9pYvccOS+GJiIndHuBS7Y0Ue3LLixBTqHlWochBrY0kfNiaCJyQmxporqUfMvSNefjroGHTtb5RUS1iqGJyAlJXSTSOBOi2iTNnAtlKxM5OYYmIicU7G358EphaKI6wDWayFUwNBE5oeDSa39l5BWjyGiSuRpydlyjiVwFQxORE2rkroFWbfnzTssukrkacnZJbGkiF8HQROSEFIrbV5rnuCaqbUm3uEYTuQaGJiInFeQthSYuO0C1i2OayFUwNBE5KamlKTWbLU1Ue0xmYT3HGjM0kZNjaCJyUsHsnqM6cCOnCEazgFqpQICXTu5yiGoVQxORkwop7Z7jsgNUm6SuuSBvPVRKhczVENUuhiYiJyW1NKWwe45qkdQ1J3UHEzkzhiYiJxVs4AKXVPuk0CRNPCByZgxNRE5K+uafllMEk1nIXA05q9TSdcACvTmeiZwfQxORk/L31EGlVMBkFkjP5QKXVDvS2NJELoShichJqZQKBJbOZuIMOqotqTlSaGJLEzk/hiYiJ2YdDM4FLqmWSJfpCfRiSxM5P4YmIicW7M21mqh23R4IzpYmcn4MTUROjMsOUG0qKDYhu9AIAAjkmCZyAQxNRE4sxMAFLqn2pJWOZ3LTqOClU8tcDVHtY2gicmLSWk3snqPaIC03EOStg0LB1cDJ+TE0ETmxoNLZczdyuOQA1TxpPBO75shVMDQRObEAhiaqRVwNnFwNQxORE5NCU26REfnFRpmrIWeTVhrGpRZNImfH0ETkxDx1arhpVADY2kQ173b3HEMTuQaGJiInplAorK1NaQxNVMPSrAPB2T1HroGhicjJBXJcE9US6RIqXA2cXAVDE5GTs7Y0cYFLqmFpdyw5QOQKGJqInJy1pSmXLU1Uc3KLjMgt4mrg5FoYmoicHJcdoNogtVx66tTw5Grg5CIYmoicHAeCU22QVgPnzDlyJQxNRE5OGqTLliaqSWnWQeAMTeQ6GJqInBxbmqg2SCE8gDPnyIUwNBE5OaklICO3CCazkLkachbSxAJ/T63MlRDVHYYmIifn66GFQgGYBZCZVyx3OeQk0nMs51IAu+fIhTA0ETk5tUoJPw+pi45rNVHNSLe2NDE0ketgaCJyAVx2gGqaFJoCGJrIhTA0EbmAQA4GpxomBXC2NJErYWgicgFsaaKaZDYLZORxTBO5HoYmIhfA0EQ16VZBiXUmph9nz5ELYWgicgGBDE1Ug6TxTD7uGmhU/Bgh18GzncgFsKWJahLHM5GrYmgicgHSpVS45ADVBM6cI1fF0ETkAqRVmzNyubgl3TtrSxMHgZOLYWgicgF+pS0COUVGFJaYZK6GGrr00vDNS6iQq2FoInIB3no1NCoFAFinihNV1+2L9bKliVwLQxORC1AoFNZLqWTkcjA43RteQoVcFUMTkYvw47gmqiEcCE6uiqGJyEVIrQLpbGmie8SWJnJVDE1ELsLa0sQxTXQPzGZhHQjOMU3kahiaiFyE1CrAMU10L3gJFXJlDE1ELsLPg2Oa6N7xEirkynjGE7kIaa2mdHbP0T3gJVTIlTE0EbmI27Pn2D1H1ceZc+TKZA9NS5YsQXh4OPR6PSIjI7F3794K9y8qKsK7776LsLAw6HQ6tGzZEitWrKijaokaLn/rOk1saaLq4yVUyJWp5XzydevWYdq0aViyZAl69eqFL774AoMHD8bp06fRrFkzu/cZPXo0UlNTsXz5crRq1QppaWkwGo11XDlRw3N79lwRhBBQKBQyV0QNkTT7UhojR+RKZA1NixYtwvPPP49JkyYBABYvXoyffvoJS5cuRWxsbJn9f/zxR+zevRuXLl2Cr68vAKB58+Z1WTJRg+Vb+iFXYhLILjTC4KaRuSJqiDJ53TlyYbJ1zxUXF+PIkSOIiYmx2R4TE4N9+/bZvc/333+Pbt26YeHChWjcuDHatGmDN954AwUFBeU+T1FREbKzs21uRK5Ir1HBS2f5nsQFLqm6MvIs546vB7vnyPXI1tKUnp4Ok8mEoKAgm+1BQUFISUmxe59Lly7hl19+gV6vx6ZNm5Ceno6XX34ZmZmZ5Y5rio2Nxdy5c2u8fqKGyM9Ti5wiIzJyi9EyQO5qqCGyds+xpYlckOwDwe8eV1HRWAuz2QyFQoHVq1eje/fuePTRR7Fo0SKsXLmy3NamWbNmISsry3pLTEys8ddA1FBwgUu6V9JEAo5pIlckW0uTv78/VCpVmValtLS0Mq1PkpCQEDRu3BgGg8G6rX379hBC4Nq1a2jdunWZ++h0Ouh0bEYmAm63DnCtJqquTGtLE99XyfXI1tKk1WoRGRmJuLg4m+1xcXGIjo62e59evXohKSkJubm51m1//PEHlEolmjRpUqv1EjkDP7Y00T0oLDEht8gyW9mXLU3kgmTtnpsxYwa+/PJLrFixAmfOnMH06dORkJCAKVOmALB0rY0bN866/9ixY+Hn54eJEyfi9OnT2LNnD95880386U9/gpubm1wvg6jB8OelVOgeSK1MGpUC3npZJ18TyULWs37MmDHIyMjAvHnzkJycjIiICGzduhVhYWEAgOTkZCQkJFj39/T0RFxcHF577TV069YNfn5+GD16ND788EO5XgJRg2JtacpjSxNVnRS2fT20XOeLXJLsXxVefvllvPzyy3b/beXKlWW2tWvXrkyXHhE5xjqmiS1NVA1S2PbjcgPkomSfPUdEdcfPg2OaqPqsM+e43AC5KIYmIhfib72UCluaqOoyeQkVcnEMTUQuRBrTdCu/BCUms8zVUEOTztXAycUxNBG5EB83DZSl43dvsrWJqojdc+TqGJqIXIhSqbC2EtzguCaqInbPkatjaCJyMdZxTZxBR1UkTSDgauDkqhiaiFyMP9dqomqSJhBwNXByVQxNRC7Gjy1NVE3SOePPMU3kohiaiFyMtFYTF7ikqsgvNqKgxASALU3kuhiaiFzM7ZYmds+R46RWJq1aCU+d7BeTIJIFQxORi+ECl1Qdd86c43XnyFUxNBG5GF5KharDet05jmciF8bQRORieNFeqg6pe46rgZMrY2gicjF3LjkghJC5GmoopO5cfw4CJxfG0ETkYqSWpsISM/KKTTJXQw1FJtdoImJoInI17lo13DQqAEAmu+jIQelcDZyIoYnIFUmtBVwVnBzF684RMTQRuSRef46qSjpXOHuOXFmVVyg7d+4c1q5di7179+LKlSvIz89HQEAAunTpgkGDBmHUqFHQ6dh8S1SfSS1NmVyriRxkbWli9xy5MIdbmo4ePYqBAweiU6dO2LNnDx544AFMmzYNf/nLX/Dss89CCIF3330XoaGhWLBgAYqK2OxPVF9JH3zp7J4jBwghbo9pYvccuTCHW5oef/xxvPnmm1i3bh18fX3L3S8+Ph5/+9vf8Omnn+Kdd96pkSKJqGZJH3wcCE6OyCs2ochoBsDuOXJtDoem8+fPQ6ut/I8lKioKUVFRKC7mmzFRfeXHS6lQFUjhWq9Rwl3L686R63K4e86RwAQA+fn5VdqfiOqetKozQxM5QurG9eNq4OTiqjV77uGHH8a1a9fKbD9w4AA6d+58rzURUS2ztjTx+nPkgEzOnCMCUM3Q5O3tjY4dO+Lbb78FAJjNZsyZMwcPPfQQHnvssRotkIhqnjSmiUsOkCOsF+vlIHBycdXqnP7++++xbNkyTJo0Cd9//z2uXLmChIQEbNmyBQMGDKjpGomohkmz5zLziiGEgEKhkLkiqs8y8nixXiKgmqEJAKZMmYKrV69iwYIFUKvV2LVrF6Kjo2uyNiKqJVKLQbHJjJwiI7z1GpkrovpMapH0Z/ccubhqdc/dvHkTo0aNwtKlS/HFF19g9OjRiImJwZIlS2q6PiKqBXqNCh5aXn+OHMOL9RJZVCs0RUREIDU1FUePHsULL7yAVatWYfny5Xj//fcxZMiQmq6RiGqBryevP0eO4cV6iSyqFZqmTJmCPXv2IDw83LptzJgxOHbsGNdnImogpOnjHAxOleHFeoksqjWm6f3337e7vUmTJoiLi7ungoioblhn0HGtJqoEL9ZLZOFwS1NCQkKVHvj69etVLoaI6o70AciL9lJFhBAc00RUyuHQ9MADD+CFF17AwYMHy90nKysL//rXvxAREYGNGzfWSIFEVDuk6ePpXOCSKpBTZESxqfS6c1xygFycw91zZ86cwUcffYRHHnkEGo0G3bp1Q2hoKPR6PW7evInTp0/j1KlT6NatGz7++GMMHjy4Nusmonvkz5YmcoA0u9Jdq4Jb6YxLIlflcEvTtWvXsGDBAiQlJWHZsmVo06YN0tPTcf78eQDAM888gyNHjuDXX39lYCJqAHy5Kjg5wLoaOMczETne0tSlSxekpKQgICAAr7/+Og4dOgQ/P7/arI2IapE0fZwDwaki6blcDZxI4nBLk4+PDy5dugQAuHLlCsxmc60VRUS17/b15zimicondd/6cxA4keMtTaNGjUKfPn0QEhIChUKBbt26QaWy378thSsiqr/unD3H689ReaRQzZlzRFUITf/85z8xcuRIXLhwAVOnTsULL7wALy+v2qyNiGqR9CFoNAtkFxhhcOf156gsqfuWq4ETVXFxy0ceeQQAcOTIEfz5z39maCJqwHRqFbx0auQUGZGRV8TQRHZZF7ZkSxNR9S6j8tVXXzEwETmB29ef42Bwsk+aPefvxdBEVK3QRETOwY/LDlAlbrc0sXuOiKGJyIVJ08il1gSiu6XzunNEVgxNRC7Muio4W5rIDrNZIFPqnuNAcCKGJiJXZl0VnGOayI5bBSUwC8v/N3JnSxMRQxORC+Oq4FQRaY0mg5sGWjU/Loj4V0DkwrgqOFWE45mIbDE0EbmwO1cFJ7qbdbkBzpwjAsDQROTSpDFN6RwITnZksKWJyAZDE5ELk2ZE3cwvhlka8UtUSuq2ZWgismBoInJh0owok1kgq6BE5mqovknP48KWRHdiaCJyYVq1Et56yyUoOYOO7ia1NPmzpYkIAEMTkcuzLjvAGXR0l9tjmtjSRAQwNBG5PGnZAc6go7tJrY9cDZzIgqGJyMVJg3zTGZroLukcCE5kg6GJyMVJF+3l9efoTkVGE3IKjQC4ThORRPbQtGTJEoSHh0Ov1yMyMhJ79+516H6//vor1Go1OnfuXLsFEjk5aZCvtJAhEXB7PJNaqYC3m1rmaojqB1lD07p16zBt2jS8++67OHr0KHr37o3BgwcjISGhwvtlZWVh3Lhx6N+/fx1VSuS8eNFesufOhS0VCoXM1RDVD7KGpkWLFuH555/HpEmT0L59eyxevBhNmzbF0qVLK7zf5MmTMXbsWERFRdVRpUTOi7PnyJ700pZHrtFEdJtsoam4uBhHjhxBTEyMzfaYmBjs27ev3Pt99dVXuHjxImbPnl3bJRK5BM6eI3t4CRWismTrqE5PT4fJZEJQUJDN9qCgIKSkpNi9z/nz5zFz5kzs3bsXarVjpRcVFaGo6PY36Ozs7OoXTeSEpA/FDA4EpzvcXtiSLU1EEtkHgt/dVy6EsNt/bjKZMHbsWMydOxdt2rRx+PFjY2NhMBist6ZNm95zzUTORBrTlJlfDBOvP0elMqyXUGFLE5FEttDk7+8PlUpVplUpLS2tTOsTAOTk5ODw4cN49dVXoVaroVarMW/ePBw7dgxqtRo7duyw+zyzZs1CVlaW9ZaYmFgrr4eoofItvf6cEMCtfLY2kcXtNZrY0kQkka17TqvVIjIyEnFxcRgxYoR1e1xcHIYPH15mf29vb5w4ccJm25IlS7Bjxw6sX78e4eHhdp9Hp9NBp+MfPVF51ColfNw1uJVfgoy8Yn5IEgCOaSKyR9bFN2bMmIHnnnsO3bp1Q1RUFP75z38iISEBU6ZMAWBpJbp+/Tq+/vprKJVKRERE2Nw/MDAQer2+zHYiqho/Dy1u5ZcgPbcIbYK85C6H6gFp3S5erJfoNllD05gxY5CRkYF58+YhOTkZERER2Lp1K8LCwgAAycnJla7ZRET3zt9Th4s38pDOweBUSmpp4kBwotsUQgiXGvmZnZ0Ng8GArKwseHt7y10OUb3wyprfsOV4Mj4Yeh/+9KD9rm5yHUIItH3vRxSbzPh1Zj809nGTuySievH5LfvsOSKSX0Bpa8INLnBJAHKKjCg2mQFw9hzRnRiaiAgBXpbQlJ7D0ES3u+Y8dWroNSqZqyGqPxiaiMg62DedLU2E2wtbcuYckS2GJiKyDvZl9xwBsE4IYNcckS2GJiK6o3uOs+fo9nIDXLOLyBZDExFZW5oy8orgYhNqyY7byw2wpYnoTgxNRGQdu1JiEsgqKJG5GpKb9RIqHmxpIroTQxMRQadWwVtvWev2BmfQuTxeQoXIPoYmIgJwe1wTB4MTL9ZLZB9DExEBuD2uiZdSISk0cUwTkS2GJiICAPhzgUsqlVZ6DgR66WWuhKh+YWgiIgC8lApZFJaYkFNoBHC7y5aILBiaiAgAL6VCFtJEAK1aaZ0cQEQWDE1EBICXUiGL211zOigUCpmrIapfGJqICAAvpUIWN3IKAbBrjsgehiYiAsBLqZBFztXr6JB8Hi1FntylENU77LAmIgBlL6XCrhkX9L//od9rM9DrVjbU272AJn8Dhg+XuyqieoMtTUQEgJdScXlpacDMmVDn5iBL7wH3wjxg1izLdiICwNBERKV4KRUXl5AA5OYi28MbJSoNSnwaATk5QGKi3JUR1RsMTURkxUupuLBmzQBPT7jlZEFjKoFbzi3Aywto2lTuyojqDYYmIrKyzqBjS5PrCQwE5s9HjtYdhsI8wNsAxMZathMRAA4EJ6I7BHlbLpuRls3Q5IrMwx7DmKfzEJh1A8vfexz6VmFyl0RUrzA0EZFVkLelpSmtdK0eci0384uR5mZAmpsBvuHsliO6G7vniMhKamlKZUuTS5LGsvl6aKFR8eOB6G78qyAiq0BraGJLkyuSumWlizcTkS2GJiKyCvKSuufY0uSKpAkAgd4MTUT2MDQRkVXQHS1NQgiZq6G6JoVltjQR2cfQRERWUgtDfrEJuUVGmauhuia1NAWwpYnILoYmIrJy16rhVboqOAeDux5p1iRbmojsY2giIhuB0rgmDgZ3ObfHNOllroSofmJoIiIb1gUuORjc5dzgmCaiCjE0EZGNIC474JKEEEgp/Z1z9hyRfQxNRGRD+sDkmCbXklNkRH6xCQAQYmD3HJE9DE1EZCPIq7SliZdScSmpWZbft7deDXctr7BFZA9DExHZuH3RXoYmV5JcGppCDG4yV0JUfzE0EZGNIHbPuaSU0tAUzK45onIxNBGRDa4K7pqkQeDBXG6AqFwMTURkI6B0naYioxnZBVwV3FUks6WJqFIMTURkQ69RweCmAXB7hWhyfilZBQA4c46oIgxNRFQGxzW5HqmlKYihiahcDE1EVIY0rimFM+hchrSYKVuaiMrH0EREZQRzVXCXUlhiws38EgBAiDeXHCAqD0MTEZUR4mP54Lx+q0DmSqguSMsNuGlU8HbjwpZE5WFoIqIyGvtYWpqSGJpcgnW5AYMeCoVC5mqI6i+GJiIqI7S0pYmhyTVYF7bkGk1EFWJoIqIypNB0/WYBF7h0AbcvocLQRFQRhiYiKiO09PpjecUmZBdygUtnJw3453IDRBVjaCKiMty0Kvh6aAGwi84VJHNhSyKHMDQRkV2hHAzuMjimicgxDE1EZJfURcfQ5Px43TkixzA0EZFd1sHgt7jApTMrNppxI9dyuRyGJqKKMTQRkV1S95w03oWcU3JWAYQAdGolAjx1cpdDVK8xNBGRXVyryTUkZlp+v00auXFhS6JKMDQRkV23QxO755zZtZv5AICmvu4yV0JU/zE0EZFdjUtDU0p2IYwms8zVUG1JLA1NTRrxQr1ElWFoIiK7Ajx10KgUMJkF0nKK5C6Hasm1m5buuaaN2NJEVBnZQ9OSJUsQHh4OvV6PyMhI7N27t9x9N27ciIEDByIgIADe3t6IiorCTz/9VIfVErkOpVJhnU3FcU3OKzGT3XNEjpI1NK1btw7Tpk3Du+++i6NHj6J3794YPHgwEhIS7O6/Z88eDBw4EFu3bsWRI0fQt29fDBs2DEePHq3jyolcg7RW03WGJqcltTSxe46ocrKGpkWLFuH555/HpEmT0L59eyxevBhNmzbF0qVL7e6/ePFivPXWW3jggQfQunVrfPTRR2jdujV++OGHOq6cyDU09mFocmaFJSZr1yu754gqJ1toKi4uxpEjRxATE2OzPSYmBvv27XPoMcxmM3JycuDr61sbJRK5PKn1QZqWTs5FamXy0Krg466RuRqi+k8t1xOnp6fDZDIhKCjIZntQUBBSUlIceoxPP/0UeXl5GD16dLn7FBUVoajo9iDW7Ozs6hVM5ILC/DwAAAmZeTJXQrXhzuUGuEYTUeVkHwh+9x+qEMKhP961a9dizpw5WLduHQIDA8vdLzY2FgaDwXpr2rTpPddM5CrC/CxdNlfS82WuhGpDonU8E7vmiBwhW2jy9/eHSqUq06qUlpZWpvXpbuvWrcPzzz+P7777DgMGDKhw31mzZiErK8t6S0xMvOfaiVyF1NKUlFWAIqNJ5mqopl3jGk1EVSJbaNJqtYiMjERcXJzN9ri4OERHR5d7v7Vr12LChAlYs2YNhgwZUunz6HQ6eHt729yIyDH+nlp4aFUQ4vb4F3Ie10rHqnG5ASLHyNo9N2PGDHz55ZdYsWIFzpw5g+nTpyMhIQFTpkwBYGklGjdunHX/tWvXYty4cfj000/Rs2dPpKSkICUlBVlZWXK9BCKnplAo0Ky0telqBsc1ORu2NBFVjayhacyYMVi8eDHmzZuHzp07Y8+ePdi6dSvCwsIAAMnJyTZrNn3xxRcwGo145ZVXEBISYr39+c9/luslEDm95hzX5LQSuRo4UZXINntO8vLLL+Pll1+2+28rV660+XnXrl21XxAR2QhjS5NTyisyIjOvGADQxJctTUSOkH32HBHVb9IMuquZbGlyJpfTLSHY10MLbz3XaCJyBEMTEVXIGpoyGJqcycUbuQCAlgEeMldC1HAwNBFRhZqXds8lZubDaDLLXA3VlEs3LC1NLfw9Za6EqOFgaCKiCgV766FVK2E0CyRnFcpdDtUQqaWpBVuaiBzG0EREFVIqFWhWuo7PFQ4GdxpSS1PLALY0ETmKoYmIKmVddoDjmpyC2SysA8HZ0kTkOIYmIqqUddmBdLY0OYPk7EIUlJigViq4GjhRFTA0EVGlwv0toUkaB0MN26XS32OYnzs0Kn4MEDmKfy1EVKm2wV4AgD9SGZqcwcU0aRA4xzMRVQVDExFVqk2gJTRdv1WAnMISmauhe3WJ45mIqoWhiYgqZXDXIMhbBwA4n8bWpoaOM+eIqoehiYgc0iaotIsuJUfmSuhecTVwouphaCIih7QtDU3nUhmaGrK8IqN1kVKuBk5UNQxNROQQa0sTQ1ODJnXN+Xpo0chDK3M1RA0LQxMROaQNZ9A5hTMp2QButxwSkeMYmojIIa0DLV05N3KKkJlXLHM1VF1nky0the1CGJqIqoqhiYgc4qFTo6mvGwB20TVkZ0tbmtqHeMtcCVHDw9BERA6T1ms6z9DUIAkhcCa5NDQFMzQRVRVDExE5TBrXxBl0DVNaThFu5pdAqQBaB3HmHFFVMTQRkcPalYam00nZMldC1SH93loEeEKvUclcDVHDw9BERA6LaGwAAJxOzobRZJa5Gqqq49eyAAAdSn+PRFQ1DE1E5LBwPw946tQoLDHjwg0uPdDQnLh+CwBDE1F1MTQRkcOUSgXuD7UMID5R2mpBDceJ65bfWccmDE1E1cHQRERVIn3gSh/A1DCkZhciNbsISgVwXyhnzhFVB0MTEVVJhyY+AIBjibdkrYOqRvp9tQr0hLtWLW8xRA0UQxMRVUnXZj4AgFNJ2SgoNslbDDnsSMJNAEDXZo1kroSo4WJoIqIqaezjhiBvHYxmgePXbsldDjnot6uloSmMoYmouhiaiKhKFAoFIks/eKXWC6rfio1mHCsduB/J0ERUbQxNRFRlUhfPkSsMTQ3ByaQsFBvNaOSuQQt/D7nLIWqwGJqIqMq6NfcFABy8kgmTWchcDVXmwKVMAEBkmC8UCoXM1RA1XAxNRFRlEaHe8NKpkVNo5CVVGoD4SxkAgOiWfjJXQtSwMTQRUZWpVUr0aGFpbdp3MV3maqgixUYzDl22tDRFt2JoIroXDE1EVC1RLf0BAPsuZshcCVXk2LVbKCgxwc9DizaBXnKXQ9SgMTQRUbX0Km21OHA5A4UlXK+pvtrzxw0AQFRLPyiVHM9EdC8YmoioWtoGeSHEoEdhiRn7L7G1qb7aeS4NANC3baDMlRA1fAxNRFQtCoUCD5d+EO88myZzNWRPWnYhTl7PhkIB9GkbIHc5RA0eQxMRVVu/dpbQtP1sGoTg0gP1zY7SMNuxiQ/8PXUyV0PU8DE0EVG1PdjKH24aFa7dLMDJ61x6oL7ZejIFADCwPbvmiGoCQxMRVZubVoW+7SzdPltOJMtcDd3pVn4x9l2wLAfxaIcQmashcg4MTUR0T6QP5K0nktlFV4/8fCoVRrNAu2AvtAjwlLscIqfA0ERE96Rfu0C4a1VIyMzH4au8Fl19sf63awCAYZ1CZa6EyHkwNBHRPXHXqjGktLVp/eFrMldDAHA1Iw8HL2dCqQBGdm0sdzlEToOhiYju2ZPdmgIANh9PQk5hiczV0HeHEwEAD7YOQIjBTeZqiJwHQxMR3bMHmjdCq0BP5BWbsP4IW5vkVFhiwpoDCQCAsd2bylwNkXNhaCKie6ZQKDAhujkA4N/7rsBk5oBwuXz/exJu5pegsY8bBrQPkrscIqfC0ERENWJk18YwuGlwJSOfyw/IxGgyY+nuiwCA8dFhUKv4Fk9Uk/gXRUQ1wl2rxvMPhgMA/rH9PFubZPDD8SRcTs9DI3cNnukRJnc5RE6HoYmIasyEXs3hrVfjfFou1h9JlLscl1JYYsInP/0BAJjUuwU8dGqZKyJyPgxNRFRjvPUaTO3fGgDw8U/nkFXAmXR15Z97LuH6rQKEGPT4U69wucshckoMTURUo8ZFNUcLfw+k5xbjoy1n5C7HJVxIy8FnOy4AAGYObgc3rUrmioicE0MTEdUorVqJ+aM6AgDWHU5E3OlUmStybkVGE2Z8dwzFJjMebhuAx7gCOFGtYWgiohrXPdwXk0oHhb/xn2O4dCNX5oqckxACf9l8GsevZcHHXYOPRnSAQqGQuywip8XQRES14q1H2qFLMx9kFZTg2S8PIOlWgdwlOZ1/7b2EVfsToFAAi0Z3QqgPV/8mqk0MTURUK7RqJb4c1w0tAjyQlFWIZ5cfQHIWg1NNEELgi90X8dHWswCAdwa3R792XMiSqLYxNBFRrfHz1GHV8z0QatDj0o08DPvHrzh8JVPushq0whIT3vjPccT+P0tgerVvK0zqzdlyRHWBoYmIalWojxvWTY5Cu2AvpOcW4el/7cein8+hsMQkd2kNzpGrNzFiyT5s+O0aVEoF3h96H16PacNxTER1RCGEcKlle7Ozs2EwGJCVlQVvb2+5yyFyGfnFRry5/ji2HLdcYqVJIze81q8VhnduDL2GU+Qrci4lB1/svoiNR68DABq5a/DZ2K7o1cpf5sqI6k59+PyWvaVpyZIlCA8Ph16vR2RkJPbu3Vvh/rt370ZkZCT0ej1atGiBZcuW1VGlRHQv3LVqfPZ0Fyx9pitCDHpcu1mAtzecwIMLduDDzafxW8JNmHnpFavMvGJ8ezABY/+1H4MW77EGptHdmmDbjD4MTEQykLWlad26dXjuueewZMkS9OrVC1988QW+/PJLnD59Gs2aNSuz/+XLlxEREYEXXngBkydPxq+//oqXX34Za9euxahRoxx6zvqQVIlcXV6REasPXMVXv15Bclahdbu3Xo2uYY3wQHNf3BfqjRb+Hmjs4+b0F57NKSzB+bRc/JGSg7MpOTh4ORNnUrIhvTsrFcAjEcGY/FBLdGrqI2utRHKpD5/fsoamHj16oGvXrli6dKl1W/v27fH4448jNja2zP5vv/02vv/+e5w5c3uV4SlTpuDYsWOIj4936Dnrw0EnIosSkxk7zqZhy/FkbD+TirzisuOcNCoFgrz18PfUwd9ThwAvLXzctXDXqOCmtdzctSq4adTQa5TQqJRQKRW3bwrLf9Wq2/9f2Rigyt4WBQCTWcBoEjCazSgxidKfzTCaLdss/yZQZDQht9CI3CITcotKkFdkQlZBCdJyCpGaXYTU7ELkFBrtPs99Id4Y0jEEj3UKRVNfd4ePK5Ezqg+f37Jd0bG4uBhHjhzBzJkzbbbHxMRg3759du8THx+PmJgYm22DBg3C8uXLUVJSAo1GU+Y+RUVFKCoqsv6cnZ1dA9UTUU3QqJQYdH8wBt0fjBKTGWeSs3H4yk0cSbiJC6m5uJKRhyKjGdduFuDaTederiDQS4e2wV5oE+SFLs180D3cF4FeernLIqI7yBaa0tPTYTKZEBRku7ZIUFAQUlJS7N4nJSXF7v5GoxHp6ekICQkpc5/Y2FjMnTu35gonolqhUSnRsYkPOjbxwZ9gmUJvNgskZxciJasA6bnFSM8tQkZuMW7ll6CgxIj8YhPyi00oKDYhv9iIghIzTGYzTGZLy49JCJjNgNFshskMmMyWliBHVDYfTa1SQq1UWG7S/6sUUCmV0KhKtyuV0KqV8NSp4aFTw0uvhodOBS+9BkHeOgR56RHorUeQtw5e+rJf+oiofpEtNEnubiYXQlTYdG5vf3vbJbNmzcKMGTOsP2dnZ6Np06bVLZeI6pBSqUBjHzc05krXRFQPyBaa/P39oVKpyrQqpaWllWlNkgQHB9vdX61Ww8/Pz+59dDoddDpdzRRNRERELku2KSlarRaRkZGIi4uz2R4XF4fo6Gi794mKiiqz/88//4xu3brZHc9EREREVFNkncc7Y8YMfPnll1ixYgXOnDmD6dOnIyEhAVOmTAFg6VobN26cdf8pU6bg6tWrmDFjBs6cOYMVK1Zg+fLleOONN+R6CUREROQiZB3TNGbMGGRkZGDevHlITk5GREQEtm7dirCwMABAcnIyEhISrPuHh4dj69atmD59Oj7//HOEhobi73//u8NrNBERERFVFy+jQkRERPVeffj8du5ldomIiIhqCEMTERERkQMYmoiIiIgcwNBERERE5ACGJiIiIiIHMDQREREROYChiYiIiMgBDE1EREREDmBoIiIiInKArJdRkYO0AHp2drbMlRAREZGjpM9tOS9k4nKhKScnBwDQtGlTmSshIiKiqsrJyYHBYJDluV3u2nNmsxlJSUnw8vKCQqGQu5wal52djaZNmyIxMZHX1ivFY2Ifj4t9PC5l8ZjYx+NiX20dFyEEcnJyEBoaCqVSntFFLtfSpFQq0aRJE7nLqHXe3t78I74Lj4l9PC728biUxWNiH4+LfbVxXORqYZJwIDgRERGRAxiaiIiIiBzA0ORkdDodZs+eDZ1OJ3cp9QaPiX08LvbxuJTFY2Ifj4t9znxcXG4gOBEREVF1sKWJiIiIyAEMTUREREQOYGgiIiIicgBDExEREZEDGJoauL/+9a+Ijo6Gu7s7fHx8HLqPEAJz5sxBaGgo3Nzc8PDDD+PUqVO1W2gdu3nzJp577jkYDAYYDAY899xzuHXrVoX3mTBhAhQKhc2tZ8+edVNwLVmyZAnCw8Oh1+sRGRmJvXv3Vrj/7t27ERkZCb1ejxYtWmDZsmV1VGndqspx2bVrV5nzQqFQ4OzZs3VYce3as2cPhg0bhtDQUCgUCvz3v/+t9D6ucK5U9bi4wrkSGxuLBx54AF5eXggMDMTjjz+Oc+fOVXo/ZzlfGJoauOLiYjz55JN46aWXHL7PwoULsWjRInz22Wc4dOgQgoODMXDgQOt1+ZzB2LFj8fvvv+PHH3/Ejz/+iN9//x3PPfdcpfd75JFHkJycbL1t3bq1DqqtHevWrcO0adPw7rvv4ujRo+jduzcGDx6MhIQEu/tfvnwZjz76KHr37o2jR4/inXfewdSpU7Fhw4Y6rrx2VfW4SM6dO2dzbrRu3bqOKq59eXl56NSpEz777DOH9neVc6Wqx0XizOfK7t278corr2D//v2Ii4uD0WhETEwM8vLyyr2PU50vgpzCV199JQwGQ6X7mc1mERwcLObPn2/dVlhYKAwGg1i2bFktVlh3Tp8+LQCI/fv3W7fFx8cLAOLs2bPl3m/8+PFi+PDhdVBh3ejevbuYMmWKzbZ27dqJmTNn2t3/rbfeEu3atbPZNnnyZNGzZ89aq1EOVT0uO3fuFADEzZs366A6+QEQmzZtqnAfVzlX7uTIcXG1c0UIIdLS0gQAsXv37nL3cabzhS1NLuby5ctISUlBTEyMdZtOp0OfPn2wb98+GSurOfHx8TAYDOjRo4d1W8+ePWEwGCp9jbt27UJgYCDatGmDF154AWlpabVdbq0oLi7GkSNHbH7PABATE1PuMYiPjy+z/6BBg3D48GGUlJTUWq11qTrHRdKlSxeEhISgf//+2LlzZ22WWe+5wrlyL1zpXMnKygIA+Pr6lruPM50vDE0uJiUlBQAQFBRksz0oKMj6bw1dSkoKAgMDy2wPDAys8DUOHjwYq1evxo4dO/Dpp5/i0KFD6NevH4qKimqz3FqRnp4Ok8lUpd9zSkqK3f2NRiPS09Nrrda6VJ3jEhISgn/+85/YsGEDNm7ciLZt26J///7Ys2dPXZRcL7nCuVIdrnauCCEwY8YMPPjgg4iIiCh3P2c6X9RyF0BlzZkzB3Pnzq1wn0OHDqFbt27Vfg6FQmHzsxCizLb6xtHjApR9fUDlr3HMmDHW/4+IiEC3bt0QFhaGLVu2YOTIkdWsWl5V/T3b29/e9oauKselbdu2aNu2rfXnqKgoJCYm4pNPPsFDDz1Uq3XWZ65yrlSFq50rr776Ko4fP45ffvml0n2d5XxhaKqHXn31VTz11FMV7tO8efNqPXZwcDAAS/IPCQmxbk9LSyvzTaC+cfS4HD9+HKmpqWX+7caNG1V6jSEhIQgLC8P58+erXKvc/P39oVKpyrSeVPR7Dg4Otru/Wq2Gn59frdVal6pzXOzp2bMnVq1aVdPlNRiucK7UFGc9V1577TV8//332LNnD5o0aVLhvs50vjA01UP+/v7w9/evlccODw9HcHAw4uLi0KVLFwCWcR67d+/GggULauU5a4qjxyUqKgpZWVk4ePAgunfvDgA4cOAAsrKyEB0d7fDzZWRkIDEx0SZcNhRarRaRkZGIi4vDiBEjrNvj4uIwfPhwu/eJiorCDz/8YLPt559/Rrdu3aDRaGq13rpSneNiz9GjRxvkeVFTXOFcqSnOdq4IIfDaa69h06ZN2LVrF8LDwyu9j1OdL7INQacacfXqVXH06FExd+5c4enpKY4ePSqOHj0qcnJyrPu0bdtWbNy40frz/PnzhcFgEBs3bhQnTpwQTz/9tAgJCRHZ2dlyvIRa8cgjj4iOHTuK+Ph4ER8fLzp06CCGDh1qs8+dxyUnJ0e8/vrrYt++feLy5cti586dIioqSjRu3LjBHpdvv/1WaDQasXz5cnH69Gkxbdo04eHhIa5cuSKEEGLmzJniueees+5/6dIl4e7uLqZPny5Onz4tli9fLjQajVi/fr1cL6FWVPW4/O1vfxObNm0Sf/zxhzh58qSYOXOmACA2bNgg10uocTk5Odb3DgBi0aJF4ujRo+Lq1atCCNc9V6p6XFzhXHnppZeEwWAQu3btEsnJydZbfn6+dR9nPl8Ymhq48ePHCwBlbjt37rTuA0B89dVX1p/NZrOYPXu2CA4OFjqdTjz00EPixIkTdV98LcrIyBDPPPOM8PLyEl5eXuKZZ54pMw34zuOSn58vYmJiREBAgNBoNKJZs2Zi/PjxIiEhoe6Lr0Gff/65CAsLE1qtVnTt2tVmWvD48eNFnz59bPbftWuX6NKli9BqtaJ58+Zi6dKldVxx3ajKcVmwYIFo2bKl0Ov1olGjRuLBBx8UW7ZskaHq2iNNlb/7Nn78eCGE654rVT0urnCu2Dsed3/GOPP5ohCidDQWEREREZWLSw4QEREROYChiYiIiMgBDE1EREREDmBoIiIiInIAQxMRERGRAxiaiIiIiBzA0ERERETkAIYmIiIiIgcwNBERERE5gKGJiIiIyAEMTUTU4N24cQPBwcH46KOPrNsOHDgArVaLn3/+WcbKiMiZ8NpzROQUtm7discffxz79u1Du3bt0KVLFwwZMgSLFy+WuzQichIMTUTkNF555RVs27YNDzzwAI4dO4ZDhw5Br9fLXRYROQmGJiJyGgUFBYiIiEBiYiIOHz6Mjh07yl0SETkRjmkiIqdx6dIlJCUlwWw24+rVq3KXQ0ROhi1NROQUiouL0b17d3Tu3Bnt2rXDokWLcOLECQQFBcldGhE5CYYmInIKb775JtavX49jx47B09MTffv2hZeXFzZv3ix3aUTkJNg9R0QN3q5du7B48WJ888038Pb2hlKpxDfffINffvkFS5culbs8InISbGkiIiIicgBbmoiIiIgcwNBERERE5ACGJiIiIiIHMDQREREROYChiYiIiMgBDE1EREREDmBoIiIiInIAQxMRERGRAxiaiIiIiBzA0ERERETkAIYmIiIiIgcwNBERERE54P8DsziQqhyN5Q8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta = 0.5\n",
    "itrns = 1000\n",
    "\n",
    "plot_gd(beta, w, x0, eta, itrns)\n",
    "\n",
    "eta = 1.0\n",
    "itrns = 1000\n",
    "\n",
    "plot_gd(beta, w, x0, eta, itrns)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75f01015",
   "metadata": {},
   "source": [
    "Unlike the nice regimes of convergence for small learning rates for smooth and convex functions, here convergence happens very irregularly---for example, if we luckily wander into the basin. However, we will see that it is very hard to predict which learning rate will work."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "87116b1c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "etas = np.linspace(0.01, 1.0, 200)\n",
    "itrns = 1000\n",
    "converged = []\n",
    "for eta in etas:\n",
    "    iterates = grad_descent(x0, eta, itrns)\n",
    "    converged.append(basin_sigmoid(beta, w, iterates[-1]))\n",
    "\n",
    "plt.plot(etas, converged)\n",
    "plt.xlabel(\"learning rate\")\n",
    "plt.ylabel(r\"$f(x_T)$, function value after $T$ steps\")\n",
    "plt.title(\"Gradient descent performance (smaller is better)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c130b958",
   "metadata": {},
   "source": [
    "### Newton's step fails too\n",
    "\n",
    "Thus small learning rates just fail to make enough progress given a bounded number of total iterations. And large step sizes can converge or diverge depending upon where they land on the steep portion of the function. As an alternative, we study a regularized version of Newton's step next. In principle, Newton's step should at least work well once we are inside the basin i.e. within $x\\in[0,w]$, but there is still a danger of overshooting in the non-convex parts of the \"cliff\" which are too steep and the second derivative points in the wrong direction. Formally, a regularized Newton's step is given by\n",
    "\n",
    "$$x_{t+1}=x_t-(H+\\alpha I)^{-1}\\nabla f (x_t).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "bfe1068b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Regularized Newton's step with initial point x0\n",
    "def reg_newton_step(x0, alpha, iterations):\n",
    "    points = [x0]\n",
    "    for i in range(iterations):\n",
    "        x = points[i]\n",
    "        \n",
    "        # Compute the gradient at the current point\n",
    "        grad = basin_sigmoid_derivative(beta, w, x)\n",
    "        \n",
    "        # Compute the second derivative at the current point\n",
    "        grad2 = basin_sigmoid_second_derivative(beta, w, x)\n",
    "        \n",
    "        # Update x using regularized Newton's step\n",
    "        x = x - (1/(grad2 + alpha)) * grad\n",
    "        \n",
    "        points.append(x)\n",
    "    return points\n",
    "\n",
    "alphas = np.linspace(0.01, 1.0, 100)\n",
    "itrns = 1000\n",
    "converged = []\n",
    "for alpha in alphas:\n",
    "    iterates = reg_newton_step(x0, alpha, itrns)\n",
    "    converged.append(basin_sigmoid(beta, w, iterates[-1]))\n",
    "\n",
    "plt.plot(alphas, converged)\n",
    "plt.xlabel(\"regularization\")\n",
    "plt.ylabel(r\"$f(x_T)$, function value after $T$ steps\")\n",
    "plt.title(\"Newton step performance (smaller is better)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77d525e5",
   "metadata": {},
   "source": [
    "### Newton-damped gradient descent---a novel, more effective approach\n",
    "\n",
    "Clearly, regularized Newton's step has a similar behavior as gradient descent with sufficiently large learning rate. It is not clear which values of $\\alpha$ one should set to achieve convergence, which seems highly sensitive to small changes in $\\alpha$ and the initial point $x_0$.\n",
    "\n",
    "We propose a novel version of Newton's method that overcomes the limitation of both gradient descent and regularized Newton's method above. In one dimension, our update step is given as\n",
    "\n",
    "$$x_{t+1}=x_t-(f''(x_t)^2+\\alpha)^{-1/2}f'(x_t).$$\n",
    "\n",
    "A straightforward generalization to higher dimensions is stated below:\n",
    "\n",
    "$$x_{t+1}=x_t-(H^TH+\\alpha I)^{-1/2}\\nabla f (x_t).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "22632fe1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Gradient descent + newton \"damping\" with initial point x0\n",
    "def grad_newton_descent_l2(x0, alpha, iterations):\n",
    "    points = [x0]\n",
    "    # Gradient Descent optimization\n",
    "    for i in range(iterations):\n",
    "        x = points[i]\n",
    "        \n",
    "        # Compute the gradient at the current point\n",
    "        grad = basin_sigmoid_derivative(beta, w, x)\n",
    "        \n",
    "        # Compute the second derivative at the current point\n",
    "        grad2 = basin_sigmoid_second_derivative(beta, w, x)\n",
    "        \n",
    "        # Update x using the Gradient Descent formula\n",
    "        x = x - math.sqrt(1/(grad2*grad2 + alpha)) * grad\n",
    "        \n",
    "        points.append(x)\n",
    "    return points\n",
    "\n",
    "    \n",
    "\n",
    "alphas = np.linspace(0.01, 1.0, 100)\n",
    "itrns = 1000\n",
    "converged = []\n",
    "for alpha in alphas:\n",
    "    iterates = grad_newton_descent_l2(x0, alpha, itrns)\n",
    "    converged.append(basin_sigmoid(beta, w, iterates[-1]))\n",
    "\n",
    "plt.plot(alphas, converged)\n",
    "plt.xlabel(\"regularization\")\n",
    "plt.ylabel(r\"$f(x_T)$, function value after $T$ steps\")\n",
    "plt.title(\"Newton damped GD performance (smaller is better)\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18a87468",
   "metadata": {},
   "source": [
    "Remarkably, our proposed method leads to a dramatic decrease in non-convergence. The intuition for this comes from the observation that Newton method only fails in the non-convex regions. Thus, by taking the squared second derivative, we avoid this issue and successfully damp the steep gradient steps by exploiting the observation that the magnitude of the second derivative is also large in these steep regions, which effectively counters the overshooting tendencies of vanilla gradient descent. In practice, the Hessian is often computationally expensive to compute and one use some approximation (e.g., Shampoo in deep learning or L-BFGS in constrained optimization)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac5823bd",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "\n",
    "We expect these observations to prompt significant future research for the research on non-convex non-smooth optimization using gradient-based methods. Our initial experiments indicate the following:\n",
    "\n",
    "* A combination of gradient descent carefully damped with Newton's step can lead to much better empirical convergence for the basin sigmoid function studied above. Our functional form of sigmoidal basins is naturally inspired from typical neural network activations.\n",
    "* We only investigate one-dimensional functions that take a specific sigmoidal form for simplicity, but expect this phenomenon of steepness-induced overshooting and flatness-induced stagnation to happen in higher dimensions and for other functional forms. This is a basis for further empirical examination.\n",
    "* The theory of convergence for non-smooth and non-convex functions should perhaps look at probability of convergence for random initializations instead of worst-case guarantees for arbitrary initializations. We suspect a smoothed analysis of this kind would potentially capture our empirical observations above well. Note that some prior work (e.g., Paquette et al., COLT 2021) has performed average case analysis for convergence of SGD with random initialization, but again only in convex and strongly-convex settings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "061276b2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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   "file_extension": ".py",
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