Solutions to Chapter 2 Training versus Testing.ipynb

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    "# Chapter 2 Training and Testing\n",
    "## Exercises\n",
    "\n",
    "#### Exercise 2.1\n",
    "1. Positive rays: break point $k = 2$ and $m_{\\mathcal{H}}(k) = k+1 = 3 \\lt 2^k = 4$.\n",
    "1. Positive intervals: break point $k = 3$ and $m_{\\mathcal{H}}(k) = {k+1 \\choose 2} +1 = 7 \\lt 2^k = 8$.\n",
    "1. Convex sets: no break point exists. For any $k$, we can find a set of $k$ points on a circle that can be shattered. \n",
    "\n",
    "#### Exercise 2.2\n",
    "1. (a) \n",
    "  * (i) $k=2$, $RHS = \\sum^{1}_{i=0}{N \\choose i} = N+1$, while $m_{\\mathcal{H}}(N) = N+1$, so $m_{\\mathcal{H}}(N) \\le \\sum^{k}_{i=0}{N \\choose i}$\n",
    "  * (ii) $k=3$, $RHS = \\sum^{2}_{i=0}{N \\choose i} = \\frac{N(N-1)}{2} + N+1 = \\frac{N(N+1)}{2} + 1$, while $m_{\\mathcal{H}}(N) = {N+1 \\choose 2}+1 = \\frac{N(N+1)}{2} + 1$, so $m_{\\mathcal{H}}(N) \\le \\sum^{k}_{i=0}{N \\choose i}$\n",
    "  * (iii) There's no such $k$ exists. Maximum $k = N+1$, since $\\sum^{N}_{i=0}{N \\choose i} = 2^N$, we still have $m_{\\mathcal{H}}(N) \\le \\sum^{k}_{i=0}{N \\choose i}$\n",
    "  \n",
    "1. (b) If $m_{\\mathcal{H}}(N) = N+2^{\\frac{N}{2}}$, then the break point $k=3$. According to bound theorem 2.4, we have for all $N$, $m_{\\mathcal{H}}(N) = N+2^{\\frac{N}{2}} \\le \\sum^{2}_{i=0}{N \\choose i} = \\frac{N(N+1)}{2} + 1$. But this won't hold for all $N$ since left hand side is exponentially increasing while the RHS is polynomical increasing. For example, when $N=20$, the inequality breaks. So such hypothesis set doesn't exist. \n",
    "\n",
    "#### Exercise 2.3\n",
    "1. (i) $d_{VC} = 1$\n",
    "1. (ii) $d_{VC} = 2$\n",
    "1. (iii) $d_{VC} = \\infty$\n",
    "\n",
    "#### Exercise 2.4 TODO\n",
    "1. (a) \n",
    "\n",
    "#### Exercise 2.5\n",
    "Through equation (2.12), we find that $\\delta = 709.527509678$, so the probability is just greater or equal to zero. "
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       "(709.5275096780147, 1.1331484530668263)"
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   "source": [
    "# Exercise 2.5\n",
    "import numpy as np\n",
    "N = 100\n",
    "d = 0.1\n",
    "mh = 2*N + 1\n",
    "delta = 4*mh / np.exp(N * d**2 /8)\n",
    "delta, np.exp(N * d**2 /8)"
   ]
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   "metadata": {},
   "source": [
    "#### Exercise 2.6\n",
    "* (a) Apply the error bar in $(2.1)$, i.e. $E_{out}(g) \\le E_{in}(g) + \\sqrt{\\frac{1}{2N}\\ln{\\frac{2M}{\\delta}}}$. \n",
    "\n",
    "The following calculation shows that error on $E_{in}(g) = 0.1151$ and error on $E_{test}(g) = 0.096$. So the error bar on in-sample error is higher than the error bar from test error. \n",
    "\n",
    "* (b) If we reserve more examples for testing, then we'll have less samples for training. We may end up with a hypothesis that is not as good as we could have arrived if using more training samples. So $E_{test}(g)$ might be way too off even the error bar on it is small."
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     "text": [
      "test bound:  0.09603227913199208\n",
      "train bound:  0.11509037065006825\n"
     ]
    }
   ],
   "source": [
    "# Exercise 2.6\n",
    "import numpy as np\n",
    "epsilon = 0.05\n",
    "\n",
    "N = 200\n",
    "# test bound\n",
    "print('test bound: ', np.sqrt(np.log(2/epsilon)/2/N))\n",
    "\n",
    "# train bound\n",
    "M = 1000\n",
    "N = 400\n",
    "print('train bound: ', np.sqrt(np.log(2*M/epsilon)/2/N))"
   ]
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   "source": [
    "#### Exercise 2.7 \n",
    "1. (a) \n",
    "\n",
    "\\begin{align*}\n",
    "P[h(x)\\ne f(x)] &= P[h(x)\\ne f(x)]\\cdot 1 + P[h(x) = f(x)]\\cdot0 \\\\\n",
    "&= P[h(x)\\ne f(x)] (h(x)-f(x))^2 + P[h(x) = f(x)] (h(x)-f(x))^2 \\\\\n",
    "&= E[(h(x)-f(x))^2]\n",
    "\\end{align*}\n",
    "\n",
    "1. (b) \n",
    "\n",
    "\\begin{align*}\n",
    "P[h(x)\\ne f(x)] &= \\frac{1}{4}P[h(x)\\ne f(x)]\\cdot 4 + \\frac{1}{4}P[h(x) = f(x)]\\cdot0 \\\\\n",
    "&= \\frac{1}{4}P[h(x)\\ne f(x)] (h(x)-f(x))^2 + \\frac{1}{4}P[h(x) = f(x)] (h(x)-f(x))^2 \\\\\n",
    "&= \\frac{1}{4}E[(h(x)-f(x))^2]\n",
    "\\end{align*}\n",
    "\n",
    "#### Exercise 2.8\n",
    "\n",
    "1. (a) If $\\mathcal{H}$ is closed under linear combination, for any $x$, $\\bar{g}(x)$ is weighted (by probability of data) average of hypotheses in $\\mathcal{H}$, so $\\bar{g}(x) \\in \\mathcal{H}$.\n",
    "\n",
    "1. (b) If $\\mathcal{H}$ is a set of functions defined on intervals, e.g. $f(x) = c$ when $x \\in [a,b]$, otherwise $f(x) = 0$. Then $\\bar{g}(x)$ probably won't have constant value in an interval and not in the original hypothesis set.\n",
    "\n",
    "1. (c) For binary classification, each $g(x)$ will have value $+1$ or $-1$, when weighted by probabilities, the average is not binary any more. "
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   "source": [
    "#### Problem 2.1\n",
    "\n",
    "For $\\epsilon \\le k$, we have $N \\ge \\frac{1}{2k^2}ln\\frac{2M}{\\delta}$"
   ]
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   "execution_count": 10,
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     "text": [
      "Samples needed for M = 1:\tN = 839.9410155759854\n",
      "Samples needed for M = 100:\tN = 1760.9750527736032\n",
      "Samples needed for M = 10000:\tN = 2682.0090899712213\n"
     ]
    }
   ],
   "source": [
    "def calc_N(M, delta, k):\n",
    "    return np.log(2*M/delta)/2/k/k\n",
    "delta = 0.03\n",
    "k = 0.05\n",
    "for M in [1,100, 10000]:\n",
    "    N = calc_N(M, delta, k)\n",
    "    print(\"Samples needed for M = {}:\\tN = {}\".format(M, N))\n"
   ]
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   "source": [
    "#### Problem 2.2\n",
    "For $N=4$, we can pick points: $(1,3),(2,4),(3,1),(4,2)$. It's easy to see that these points are shattered by positive rectangles. So $m_{\\mathcal{H}}(4) = 2^4$.\n",
    "\n",
    "The idea is that for any two points, if we draw a rectangle using them as diagnoal points, the rectangle should NOT contain any other point. Otherwise, whenever the two diagnoal points have values 1, the middle point will have value 1 as well, which excludes the possibility of having -1. \n",
    "\n",
    "For $N=5$, if we draw horizontal and vertical lines through each of the four points above, the plane is divided into grids. The four points enclusing a 9-grid area. It's clear that the fifth point can't lie within the 9-grid area. Otherwise, there'll always a rectangle (constructed by two points) contains the fifth point. \n",
    "\n",
    "In the same way, if we place the fifth point outside the 9-grid area, it's easy to see that the point will always lie below or above at least two points (in either x or y direction). These three points construct a rectangle which contains a point in it. \n",
    "This shows that $m_{\\mathcal{H}}(5) \\lt 2^5$.\n",
    "\n",
    "We have the VC dimension $d_{VC}(\\mathcal{H}) = 4$, and $m_{\\mathcal{H}}(N) \\le \\sum^{4}_{i=0} {N \\choose i}$.\n",
    "\n",
    "#### Problem 2.3\n",
    "1. (a) $d_{VC}(\\mathcal{H}) = 2$, $m_{\\mathcal{H}}(N) = {N+1 \\choose 1} + {N-1 \\choose 1} = 2N$\n",
    "\n",
    "1. (b) $d_{VC}(\\mathcal{H}) = 3$, $m_{\\mathcal{H}}(N) = {N+1 \\choose 2}+1 +{N-1 \\choose 2} = N^2 - N + 2$\n",
    "\n",
    "1. (c) $d_{VC}(\\mathcal{H}) = 2$, $m_{\\mathcal{H}}(N) = {N+1 \\choose 2}+1 = \\frac{(N+1)N}{2} + 1$"
   ]
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   "source": [
    "#### Problem 2.4 TODO\n",
    "\n",
    "#### Problem 2.5\n",
    "\n",
    "* For $N=1$, \n",
    "  * if $D=0$, $\\sum^{D}_{i=0}{N \\choose i} = {1 \\choose 0 }\\le N^D + 1 = 2$.\n",
    "  * if $D=1$, $\\sum^{D}_{i=0}{N \\choose i} = {1 \\choose 0 } + {1 \\choose 1} \\le N^D + 1 = 2$.\n",
    "* Suppose the inequality is valid at $N$ or less. let's see what happens at $N+1$.\n",
    "\n",
    "\\begin{align*}\n",
    "\\sum^{D}_{i=0}{N+1 \\choose i} &= \\sum^{D}_{i=0}{N \\choose i} + {N \\choose i-1}\\\\\n",
    "&= \\sum^{D}_{i=0}{N \\choose i} + \\sum^{D-1}_{k=0}{N \\choose k}\\\\\n",
    "&\\le N^D + 1 + N^{D-1} + 1\\\\\n",
    "&= (N^D + N^{D-1} + 1) + 1\\\\\n",
    "&\\le (N+1)^D + 1\n",
    "\\end{align*}\n",
    "\n",
    "The last inequality is obvious when $D \\gt 1$ and we expand $(N+1)^D$ into terms of $N$, i.e. $(N+1)^D = \\sum_{k=0}^{D} {D \\choose k}N^k$\n",
    "\n",
    "* When $D=0$, we have $\\sum^{D}_{i=0}{N \\choose i} = {N \\choose 0 }\\le N^0 + 1 = 1$.\n",
    "* When $D=1$, we have $\\sum^{D}_{i=0}{N \\choose i} = {N \\choose 0 } + {N \\choose 1 } = 1 + N \\le N^1 + 1$.\n",
    "\n",
    "So we proved $\\sum^{D}_{i=0}{N \\choose i} \\le N^D + 1$. Hence $m_{\\mathcal{H}}(N) \\le  \\sum^{d_{VC}}_{i=0}{N \\choose i} \\le N^{d_{VC}}+1$.\n",
    "\n",
    "#### Problem 2.6\n",
    "1. (a) $\\sum^{d}_{i=0}{N \\choose i} \\le \\sum^{d}_{i=0}{N \\choose i} (\\frac{N}{d})^{d-i} = (\\frac{N}{d})^d \\sum^{d}_{i=0}{N \\choose i} (\\frac{d}{N})^{i} \\le (\\frac{N}{d})^d \\sum^{N}_{i=0}{N \\choose i} (\\frac{d}{N})^{i}$\n",
    "\n",
    "The first inequality is valid because $\\frac{N}{d} \\ge 1$ for $N\\ge d$, and $d-i\\ge 0$, so $(\\frac{N}{d})^{d-i} \\ge 1$.\n",
    "\n",
    "1. (b) $\\sum^{N}_{i=0}{N \\choose i} (\\frac{d}{N})^{i} = (\\frac{d}{N} + 1)^N = (1 + \\frac{1}{N/d})^{(N/d)d} \\le e^d$ from Binomial theorem $(1+\\frac{1}{x})^x \\le e$ for $x\\gt 0$.\n",
    "We thus have $\\sum^{d}_{i=0}{N \\choose i} \\le (\\frac{N}{d})^d \\sum^{N}_{i=0}{N \\choose i} (\\frac{d}{N})^{i} \\le (\\frac{N}{d})^d e^d \\le (\\frac{eN}{d})^d$.\n",
    "\n",
    "By theorem 2.4, we have $m_{\\mathcal{H}}(N) \\le \\sum^{d_{VC}}_{i=0}{N \\choose i} \\le (\\frac{eN}{d_{VC}})^{d_{VC}}$."
   ]
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   "source": [
    "#### Problem 2.7\n",
    "When $d_{VC}$ is small, I would like to use bound in problem 2.5, and when $d_{VC}$ is large, I would like to use bound in problem 2.6. The point is to choose a smaller bound so we get a tigher bound on error estimate."
   ]
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   "execution_count": 62,
   "metadata": {
    "scrolled": true
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'dvc = 5')"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Problem 2.7\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def bound1(N, d):\n",
    "    return N**d + 1\n",
    "def bound2(N, d):\n",
    "    return np.power((np.exp(1)*N/d),d)\n",
    "\n",
    "fig, axs = plt.subplots(1,2)\n",
    "dvc = 2\n",
    "x = np.arange(1,1000)*1.0 #need to float the avoid overflow\n",
    "y1 = bound1(x, dvc)\n",
    "y2 = bound2(x, dvc)\n",
    "axs[0].plot(x, y1, color='red', label='Problem 2.5: Bound N^d + 1')\n",
    "axs[0].plot(x, y2, color='blue', label='Problem 2.6: Bound (eN/d)^d')\n",
    "axs[0].legend()\n",
    "axs[0].set_yscale('log')\n",
    "axs[0].set_title(\"dvc = 2\")\n",
    "\n",
    "dvc = 5\n",
    "y21 = bound1(x, dvc)\n",
    "y22 = bound2(x, dvc)\n",
    "axs[1].plot(x, y21, color='red', label='Problem 2.5: Bound N^d + 1')\n",
    "axs[1].plot(x, y22, color='blue', label='Problem 2.6: Bound (eN/d)^d')\n",
    "axs[1].set_yscale('log')\n",
    "axs[1].legend()\n",
    "axs[1].set_title(\"dvc = 5\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.8\n",
    "\n",
    "They are all possible since they $\\le 2^N$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.9 TODO\n",
    "\n",
    "#### Problem 2.10 TODO\n",
    "\n",
    "Suppose the VC dimension is $d_{VC}$\n",
    "* When $2N \\le d_{VC}$, $m_{\\mathcal{H}}(2N) = 2^{2N} = (2^{N})^2 = m_{\\mathcal{H}}(N)^2 $.\n",
    "* When $N \\le d_{VC}$ and $2N \\gt d_{VC}$, we have $m_{\\mathcal{H}}(N) = 2^N$ and $m_{\\mathcal{H}}(2N) < 2^{2N}$, so $m_{\\mathcal{H}}(2N) \\le m_{\\mathcal{H}}(N)^2$.\n",
    "* When $N \\gt d_{VC}$, we look at the upper bounds here. $ m_{\\mathcal{H}}(N) \\le N^{d_{VC}} + 1$ and $ m_{\\mathcal{H}}(2N) \\le (2N)^{d_{VC}} + 1$. So we have $m_{\\mathcal{H}}(N)^2 \\le \\left(N^{d_{VC}} + 1\\right)^2$, clearly $ (2N)^{d_{VC}} + 1 \\le \\left(N^{d_{VC}} + 1\\right)^2$, so $m_{\\mathcal{H}}(2N) \\le m_{\\mathcal{H}}(N)^2$.\n",
    "\n",
    "#### Problem 2.11\n",
    "\n",
    "The larger number of training samples, the smaller generalization bound."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N=100: VC bound = 0.8481596247015304\n",
      "N=10000: VC bound = 0.10427815497178729\n"
     ]
    }
   ],
   "source": [
    "#### Problem 2.11\n",
    "\n",
    "import numpy as np\n",
    "def vc_bound(N, growth, delta):\n",
    "    return np.sqrt(8*np.log(4*growth(2*N)/delta)/N)\n",
    "\n",
    "def growth(N):\n",
    "    return N+1\n",
    "\n",
    "delta = 0.1\n",
    "for N in [100, 10000]:\n",
    "    print('N={}: VC bound = {}'.format(N, vc_bound(N, growth, delta)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.12\n",
    "\n",
    "For an $\\mathcal{H}$ with $d_{VC}=10$, we need a sample size of about 452950."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample size: 452950\n"
     ]
    }
   ],
   "source": [
    "#### Problem 2.12\n",
    "\n",
    "dvc = 10\n",
    "delta = 0.05\n",
    "epsilon = 0.05\n",
    "\n",
    "def sample_size(N0, d, delta, epsilon, maxit=1000, tol = 10):\n",
    "    N = N0\n",
    "    for it in range(maxit):\n",
    "        rhs = 8 * np.log(4*((2*N)**d+1)/delta)/epsilon/epsilon\n",
    "        res = N - rhs\n",
    "        #print('rhs: ', rhs, 'N: ', N)\n",
    "        if np.abs(res) <= tol:\n",
    "            break\n",
    "        N = int(rhs)\n",
    "    return N\n",
    "\n",
    "N0 = 1000\n",
    "print('Sample size: {}'.format(sample_size(N0, dvc, delta, epsilon)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.13\n",
    "\n",
    "1. (a) if $d_{VC}(\\mathcal{H}) \\gt log_2M$, we know that the growth function for $d_{VC}$ points is $m_{\\mathcal{H}}(d_{VC}) = 2^{d_{VC}} \\gt M$, meaning the number of hypotheses that shatters $d_{VC}$ points are larger than $M$. This contradicts with the fact that $\\mathcal{H}$ only has finite $M$ hypotheses. \n",
    "\n",
    "1. (b) $d_{VC}\\left(\\cap^{K}_{k=1}\\mathcal{H}_k\\right) \\le min_{k} d_{VC}(\\mathcal{H}_k)$ and $d_{VC}\\left(\\cap^{K}_{k=1}\\mathcal{H}_k\\right) \\ge 0$\n",
    "\n",
    "The lower bound of the intersection set can be zero because the intersection of the hypothesis sets can be empty. \n",
    "If $d_{VC}\\left(\\cap^{K}_{k=1}\\mathcal{H}_k\\right) \\gt min_{k} d_{VC}(\\mathcal{H}_k)$, it means that there exists $\\hat{d} = d_{VC}\\left(\\cap^{K}_{k=1}\\mathcal{H}_k\\right)$ points such that the intersection hypothesis set can shatter.  Since it comes from the intersection, it means the hypotheses belong to one of the hypothesis sets as well, including the set with minimum VC dimension. That says this set is capable of shatter points more than its VC dimension. This contradicts. \n",
    "\n",
    "1. (c)  $d_{VC}\\left(\\cup^{K}_{k=1}\\mathcal{H}_k\\right) \\le \\sum_{k=1}^{K} d_{VC}(\\mathcal{H}_k)$, otherwise, if the union set's VC dimension is larger than the sum, it requires at least one of the sets to shatter more than its VC dimension, this contradicts.\n",
    "\n",
    "$d_{VC}\\left(\\cup^{K}_{k=1}\\mathcal{H}_k\\right) \\ge max_{k} d_{VC}(\\mathcal{H}_k)$ because we can always pick the set with the largest VC dimension from the union set, and it'll always be able so shatter the number of VC dimension points.\n",
    "\n",
    "#### Problem 2.14 TODO\n",
    "1. (a) \n",
    "1. (b) Take the log on both sides of $2^l \\gt 2Kl^{d_{VC}}$, we have $l \\gt 1 + logK + d_{VC} log l$, i.e. $d_{VC} log l\\lt l - 1 - logK $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.15 TODO\n",
    "#### Problem 2.16 \n",
    "\n",
    "1. (a) The polynomial $\\sum_{i=0}^D c_ix^i$ has $D$ roots, for a set of $D+1$ points, assume we can find a solution for the $c_i$s given these point and the coefficients $c_i$ are such that the $D$ roots will fall on the $D$ intervals (between the minimum and maximum of the $D+1$ points) of the $D+1$ points. Then we know that the polynomial will change sign when we move from the left of a root to its right. So for any dichotomy of the $D+1$ points, one can choose a polynomial that matches the signs on each point. Thus there are $D+1$ points that can be shattered by $\\mathcal{H}$.\n",
    "\n",
    "1. (b) For any given $D+2$ points, since there are only $D$ roots, there are at least two points that are either on the left most or right most side of all roots, or are between two neighboring roots. Either case, these two points have the same sign, thus the $D+2$ points can't be shattered by $\\mathcal{H}$. \n",
    "\n",
    "From above two, we see that the VC dimension of $\\mathcal{H}$ is exactly $D+1$. \n",
    "\n",
    "\n",
    "#### Problem 2.17\n",
    "\n",
    "* Proof\n",
    "\n",
    "If the VC dimension $d_1$ of $\\mathcal{H}$ w.r.t. $\\mathcal{X}_1$ is larger than the VC dimension $d_2$ of $\\mathcal{H}$ w.r.t. $\\mathcal{X}_2$, i.e. $d_1 \\gt d_2$.  Then it means for any given $d_1$ points in $\\mathcal{X}_1$, they can be shattered by $\\mathcal{H}$, since $\\mathcal{X}_1 \\subseteq \\mathcal{X}_2$, it means these $d_1$ points also belong to $\\mathcal{X}_2$, so $\\mathcal{H}$ can shatter $d_1$ points in  $\\mathcal{X}_2$ as well. However, this contraditcs with the fact that the VC dimension of $\\mathcal{H}$ w.r.t. $\\mathcal{X}_2$ is $d_2 \\lt d1$.\n",
    "\n",
    "* Apply this to the 2.16 (b) problem: \n",
    "\n",
    "From above proof, we can apply this to problem 2.16 (b). For any given $D+2$ points, consider its subsets of $D+1$ points. As proved in 2.16 (a) the maximum VC dimension of any $D+1$ points is $D+1$. From proof in 2.17, we see the maximum VC dimension the $D+1$ points can have is the VC dimension of the $D+2$ points. $D+1$ is the maximum VC dimension of the $D+1$ points, so this is also the VC dimension of $D+2$ points. This shows that $D+2$ points can't be shattered by $\\mathcal{H}$.\n",
    "\n",
    "* Relationship of problem 2.16 with a perceptron in $D$ dimensions\n",
    "\n",
    "If we treat each $x^i$ as a coordinate in the $i$th dimension, then the hypothesis $\\mathcal{H}$ in problem 2.16 is just the perceptron hypothesis with a special input space $\\mathcal{X}$, where the coordinates are in ratio. Thus problem 2.16 proves that the VC dimension for such perceptron in $D$ dimension is just $D+1$. \n",
    "\n",
    "#### Problem 2.18\n",
    "\n",
    "Consider $N$ points of $x_1, \\dots, x_N$, where $x_n = 10^n$. For an arbitrary dichotomy $y_1, \\dots, y_N$, for example, $(-1,1,1,\\dots,-1,1)$, lets replace $-1$ with $1$ and $1$ with $0$ so we actually get a number like $K=100\\dots10$ for the $N$ points. \n",
    "\n",
    "Now if we pick $\\alpha$ to be $\\frac{K}{10^N}$, e.g. $\\alpha=0.100\\dots10$ such that the $\\alpha x_n$ is odd if $x_n=-1$, and $\\alpha x_n$ is even if $x_n = 1$. So $h_{\\alpha}(x) = 1$ if $x_n=1$, else $h_{\\alpha}(x) = -1$ if $x_n = -1$.\n",
    "\n",
    "Thus there always exists $\\alpha$, and $h_{\\alpha}(x)$ that can shatter the $N$ points. \n",
    "The VC dimension is infinite for such hypothesis set and input space $x\\in \\mathcal{R}$.\n",
    "\n",
    "#### Problem 2.19 TODO\n",
    "\n",
    "#### Problem 2.20\n",
    "\n",
    "For (c) and (d) we need solve for the $\\epsilon$. Square both sides of the inequations, and move terms related to $\\epsilon$ to left side, make a square of $\\epsilon$, we can obtain following bounds:\n",
    "\n",
    "* (c) Parrondo and Van den Broek\n",
    "\n",
    "\\begin{align*}\n",
    "\\epsilon &\\le \\frac{1}{N} + \\sqrt{\\frac{1}{N^2} + \\frac{1}{N}\\ln\\frac{6m_{\\mathcal{H}}(2N)}{\\delta}}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "If we solve for $\\epsilon$ using this formula and compare with the solution when solving with iterative methods using the original formula, we get the same bounds. \n",
    "\n",
    "* (d) Devroye bound:\n",
    "\n",
    "\\begin{align*}\n",
    "\\epsilon &\\le \\frac{1}{N-2} + \\sqrt{\\frac{1}{(N-2)^2} + \\frac{1}{2(N-2)}\\ln\\frac{4m_{\\mathcal{H}}(N^2)}{\\delta}}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Solve Devroye bound iteratively using the original formula doesn't work, the soltuion won't converge, so we use this one instead.\n",
    "\n",
    "Compare the plots of bounds versus $N$, we see that Parrondo and Van den Broek bound decreases fastest and lowest among the bounds. It looks like the best bound we can have here. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x118de0490>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Problem 2.20\n",
    "import numpy as np\n",
    "from functools import partial\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def vc_bound(N, growth, delta):\n",
    "    return np.sqrt(8*np.log(4*growth(2*N)/delta)/N)\n",
    "\n",
    "def rade_penalty_bound(N, growth, delta):\n",
    "    a = np.sqrt(2*np.log(2*N*growth(N))/N)\n",
    "    b = np.sqrt(-2*np.log(delta)/N)\n",
    "    return a + b + 1.0/N\n",
    "\n",
    "# solve Parrondo and Van den Broek bound using iterative methods\n",
    "def pv_bound_iterative(N, growth, delta, epsilon0 = 0, maxit=1000, tol = 1.0e-6):\n",
    "    epsilon = epsilon0\n",
    "    for it in range(maxit):\n",
    "        rhs = np.sqrt((2*epsilon + np.log(6*growth(2*N)/delta))/N)\n",
    "        if np.abs(rhs - epsilon) <= tol:\n",
    "            break\n",
    "        epsilon = rhs\n",
    "    return epsilon\n",
    "\n",
    "# solve Parrondo and Van den Broek bound using direct method\n",
    "def pv_bound(N, growth, delta):\n",
    "    return 1.0/N + np.sqrt(1/N/N + np.log(6*growth(2*N)/delta)/N)\n",
    "\n",
    "# This doesn't converge\n",
    "def devroye_bound_iterative(N, growth, delta, d, epsilon0 = 0, maxit=1000, tol = 1.0e-6):\n",
    "    epsilon = epsilon0\n",
    "    for it in range(maxit):\n",
    "        #If we use m = N^d + 1, when d is larger, the calculation will overflow\n",
    "        #rhs = np.sqrt((4*epsilon*(1+epsilon) + np.log(4*growth(N**2)/delta))/2.0/N)\n",
    "        a = 4*epsilon*(1.0+epsilon)\n",
    "        b = np.log(4/delta)+2*d*np.log(N)\n",
    "        rhs = np.sqrt((a + b)/2.0/N)\n",
    "        print('rhs: ', rhs, 'epsilon: ', epsilon, \"a: \", a, \"b: \", b, \"N: \", N)\n",
    "        if rhs - epsilon <= tol:\n",
    "            break\n",
    "        epsilon = rhs\n",
    "    return epsilon\n",
    "\n",
    "def devroye_bound(N, growth, delta, d):\n",
    "    a = 1/(N-2)\n",
    "    b = a**2\n",
    "    #c = a*np.log(4*growth(N**2)/delta)/2 #this overflows easily with N^d\n",
    "    c = a*(np.log(4/delta)+2*d*np.log(N))\n",
    "    return a + np.sqrt(b + c)\n",
    "\n",
    "dvc = 50.0\n",
    "delta = 0.05\n",
    "def growth(N, d):\n",
    "    return N**d + 1\n",
    "\n",
    "g = partial(growth, d = dvc)\n",
    "\n",
    "x = np.arange(3, 5000)*1.0\n",
    "y1,y2,y3,y4, y31 = [],[],[],[], []\n",
    "for N in x:\n",
    "    y1.append(vc_bound(N, g, delta))\n",
    "    y2.append(rade_penalty_bound(N, g, delta))\n",
    "    y31.append(pv_bound1(N, g, delta))\n",
    "    y3.append(pv_bound(N, g, delta))\n",
    "    y4.append(devroye_bound(N, g, delta, dvc))\n",
    "\n",
    "plt.plot(x, y1, color='red', label='Problem 2.20: VC Bound')\n",
    "plt.plot(x, y2, color='green', label='Problem 2.20: Rademacher Penalty Bound')\n",
    "plt.plot(x, y31, color='red', label='Problem 2.20: Parrondo and Van den Broek Bound (Iterative)')\n",
    "plt.plot(x, y3, color='blue', label='Problem 2.20: Parrondo and Van den Broek Bound')\n",
    "plt.plot(x, y4, color='black', label='Problem 2.20: Devroye Bound')\n",
    "plt.yscale('log')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.21\n",
    "\n",
    "Consider\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{E_{out}(g) - E_{in}(g)}{\\sqrt{E_{out}(g)}} &\\le \\epsilon\\\\\n",
    "E_{out}(g) - E_{in}(g) &\\le \\epsilon\\sqrt{E_{out}(g)} \\\\\n",
    "(\\sqrt{E_{out}(g)} - \\frac{\\epsilon}{2})^2 - \\frac{\\epsilon^2}{4} - E_{in}(g) \\le 0\\\\\n",
    "(\\sqrt{E_{out}(g)} - \\frac{\\epsilon}{2})^2 &\\le \\frac{\\epsilon^2}{4} + E_{in}(g)\\\\\n",
    "\\sqrt{E_{out}(g)} - \\frac{\\epsilon}{2} &\\le \\sqrt{\\frac{\\epsilon^2}{4} + E_{in}(g)}\\\\\n",
    "\\sqrt{E_{out}(g)} &\\le \\frac{\\epsilon}{2} + \\sqrt{\\frac{\\epsilon^2}{4} + E_{in}(g)}\\\\\n",
    "E_{out}(g) &\\le \\left(\\frac{\\epsilon}{2} + \\sqrt{\\frac{\\epsilon^2}{4} + E_{in}(g)}\\right)^2\\\\\n",
    "E_{out}(g) &\\le \\frac{\\epsilon^2}{4} + \\frac{\\epsilon^2}{4} + E_{in}(g) + \\epsilon \\sqrt{\\frac{\\epsilon^2}{4} + E_{in}(g)}\\\\\n",
    "E_{out}(g) &\\le E_{in}(g) + \\frac{\\epsilon^2}{2} + \\epsilon \\sqrt{\\frac{\\epsilon^2}{4} + E_{in}(g)}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Now let $\\delta = cm_{\\mathcal{H}}(2N)\\exp(-\\frac{\\epsilon^2N}{4})$, we have $\\epsilon^2 = \\frac{4}{N}\\log\\frac{cm_{\\mathcal{H}}(2N)}{\\delta} = \\xi$, replace this into above inequation, we have\n",
    "\n",
    "\\begin{align*}\n",
    "E_{out}(g) &\\le E_{in}(g) + \\frac{\\epsilon^2}{2} + \\epsilon \\sqrt{\\frac{\\epsilon^2}{4} + E_{in}(g)}\\\\\n",
    "E_{out}(g) &\\le E_{in}(g) + \\frac{\\xi}{2} + \\sqrt{\\xi}\\sqrt{\\frac{\\xi}{4} + E_{in}(g)}\\\\\n",
    "E_{out}(g) &\\le E_{in}(g) + \\frac{\\xi}{2}\\left[1 + \\sqrt{1 + \\frac{4E_{in}(g)}{\\xi}}\\right]\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Now use the probability inequation given in the theorem, \n",
    "\n",
    "\\begin{align*}\n",
    "P\\left[E_{out}(g) \\le E_{in}(g) + \\frac{\\xi}{2}\\left[1 + \\sqrt{1 + \\frac{4E_{in}(g)}{\\xi}}\\right]\\right] &= P\\left[\\frac{E_{out}(g) - E_{in}(g)}{\\sqrt{E_{out}(g)}} \\le \\epsilon\\right] \\\\\n",
    "&= 1 - P\\left[\\frac{E_{out}(g) - E_{in}(g)}{\\sqrt{E_{out}(g)}} \\gt \\epsilon\\right]\\\\\n",
    "&\\ge 1 - cm_{\\mathcal{H}}(2N)\\exp(-\\frac{\\epsilon^2N}{4})\\\\\n",
    "&\\ge 1-\\delta\\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.22 \n",
    "\n",
    "\\begin{align*}\n",
    "E_\\mathcal{D}\\left[E_{out}(g^\\mathcal{D})\\right] &= E_\\mathcal{D}\\left[E_{x,y}\\left[\\left(g^\\mathcal{D}(x) - y(x)\\right)^2\\right]\\right]\\\\\n",
    "&= E_\\mathcal{D}\\left[E_{x,y}\\left[\\left(g^\\mathcal{D}(x) - (f(x) + \\epsilon)\\right)^2\\right]\\right]\\\\\n",
    "&= E_{x,y}\\left[E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x) - (f(x) + \\epsilon)\\right)^2\\right]\\right]\\\\\n",
    "&= E_{x,y}\\left[E_\\mathcal{D}\\left[g^\\mathcal{D}(x)^2 - 2g^\\mathcal{D}(x)(f(x) + \\epsilon) + (f(x) + \\epsilon)^2\\right]\\right]\\\\\n",
    "&= E_{x,y}\\left[E_\\mathcal{D}[g^\\mathcal{D}(x)^2] - 2E_\\mathcal{D}[g^\\mathcal{D}(x)](f(x) + \\epsilon) + (f(x) + \\epsilon)^2\\right]\\\\\n",
    "&= E_{x,y}\\left[E_\\mathcal{D}[g^\\mathcal{D}(x)^2] - \\bar{g}(x)^2 + \\bar{g}(x)^2 - 2\\bar{g}(x)(f(x) + \\epsilon) + (f(x) + \\epsilon)^2\\right]\\\\\n",
    "&= E_{x,y}\\left[E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x)-\\bar{g}(x)\\right)^2\\right] + \\left(\\bar{g}(x) -f(x)\\right)^2 - 2\\bar{g}(x)\\epsilon + 2f(x)\\epsilon + \\epsilon^2\\right]\\\\\n",
    "&= E_{x,y}\\left[E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x)-\\bar{g}(x)\\right)^2\\right]\\right] + E_{x,y}\\left[\\left(\\bar{g}(x) -f(x)\\right)^2\\right]  + E_{x,y}\\left[\\epsilon^2\\right]\\\\\n",
    "&= variance + bias + \\sigma^2\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Where the 'average function' $\\bar{g}(x) = E_\\mathcal{D}[g^\\mathcal{D}(x)]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.23\n",
    "\n",
    "* (i) Find the best hypothesis that appriximates $f$ in the mean-squared-error sense\n",
    "\n",
    "To find the best hypothesis that approximates $f$ in the mean-squared-error sense, we find the hypothesis that minimizes the mean-squared-error, assume we have $h(x)=ax+b$, then\n",
    "\n",
    "\\begin{align*}\n",
    "E_x\\left[\\left(f(x)-h(x)\\right)^2\\right] &= E_x\\left[\\left(\\sin(\\pi x)-(ax+b)\\right)^2\\right]\\\\\n",
    "&= \\int^1_{-1}\\left[\\sin(\\pi x)-(ax+b)\\right]^2p(x)dx\\\\\n",
    "&= \\int^1_{-1}\\frac{1}{2}\\left[\\sin(\\pi x)-(ax+b)\\right]^2dx\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Take derivative w.r.t. $a$ and $b$ respectively, and let them equal to $0$, we have\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial E}{\\partial a} &= -\\int^1_{-1} x\\left[\\sin(\\pi x) - (ax+b)\\right]dx = 0\\\\\n",
    "\\frac{\\partial E}{\\partial b} &= -\\int^1_{-1} \\left[\\sin(\\pi x) - (ax+b)\\right]dx = 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Solve them we have\n",
    "\\begin{align*}\n",
    "\\frac{2}{\\pi}-\\frac{2}{3}a&=0 \\\\\n",
    "b &= 0\\\\\n",
    "\\end{align*}\n",
    "We have $a=\\frac{3}{\\pi}$\n",
    "\n",
    " \n",
    "So the best hypothesis that approximates $f$ in the mean-squared-error sense are:\n",
    "  * (a) $h(x) = \\frac{3}{\\pi} x$.\n",
    "  * (b) $h(x) = \\frac{3}{\\pi} x$.\n",
    "  * (c) $h(x) = 0$.\n",
    "\n",
    "\n",
    "* (ii) Find the expected value w.r.t. $\\mathcal{D}$ of the hypothesis that the learning algorithm produces\n",
    "\n",
    "Given two points $x_1$ and $x_2$, we have \n",
    "\n",
    "\\begin{align*}\n",
    "E_{in}(g) &= \\sum^{N}_{i=1} (f(x_i) - h(x_i))^2\\\\\n",
    "&= \\sum^{N}_{i=1} (\\sin(\\pi x_i) - (ax_i+b))^2\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Take derivative w.r.t. $a$ and $b$ respectively and set to zero, we have\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial E_{in}(g)}{\\partial a} &= -2\\sum^{N}_{i=1} x_i(\\sin(\\pi x_i) - (ax_i+b)) = 0\\\\\n",
    "\\frac{\\partial E_{in}(g)}{\\partial b} &= -2\\sum^{N}_{i=1} (\\sin(\\pi x_i) - (ax_i+b)) = 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "To sovle for $a$ and $b$ we multiple second equation by $x_1$ and $x_2$ respectively, and subtract from the first equation, we obtain two equations\n",
    "\n",
    "\\begin{align*}\n",
    "(x_2 - x_1)(\\sin\\pi x_2 - ax_2 -b) &= 0\\\\\n",
    "(x_1 - x_2)(\\sin\\pi x_1 - ax_1 -b) &= 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "If we assume $x_1 \\ne x_2$, we can solve for $a$ and $b$ and get\n",
    "\n",
    "\\begin{align*}\n",
    "a &= \\frac{\\sin\\pi x_2 - \\sin\\pi x_1}{x_2-x_1}\\\\\n",
    "b &= \\frac{x_2\\sin\\pi x_1 - x_1\\sin\\pi x_2}{x_2-x_1}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "If $x_1 = x_2$, let $x_2 = x_1 + h$, take this into above equations and let $h \\to \\infty$, we can obtain a hypothesis tangential to $f$.\n",
    "\n",
    "So the final hypothesis generated by learning algorithm is: \n",
    "\n",
    "$g^{\\mathcal{D}}(x) = \\frac{\\sin\\pi x_2 - \\sin\\pi x_1}{x_2-x_1} x + \\frac{x_2\\sin\\pi x_1 - x_1\\sin\\pi x_2}{x_2-x_1}$\n",
    "\n",
    "Similarly for hypothesis set $h(x) = ax$, we can obtain\n",
    "\n",
    "$g^{\\mathcal{D}}(x) =\\frac{x_1\\sin\\pi x_1 + x_2\\sin\\pi x_2}{x_1^2+x_2^2} x$\n",
    "\n",
    "for hypothesis set $h(x) = b$, we can obtain\n",
    "\n",
    "$g^{\\mathcal{D}}(x) =\\frac{1}{2}(\\sin\\pi x_1 + \\sin\\pi x_2)$\n",
    "\n",
    "It looks like we can only calculate the bias, variance with the hypothesis $h(x)=b$. \n",
    "\n",
    "\\begin{align*}\n",
    "E_{\\mathcal{D}}\\left[g^{\\mathcal{D}}(x)\\right] &= E_{\\mathcal{D}}\\left[\\frac{1}{2}(\\sin\\pi x_1 + \\sin\\pi x_2)\\right]\\\\\n",
    "&= 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "That's because $x$ is uniformly distributed between $[-1,1]$. \n",
    "\n",
    "* Let's compute the bias component\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{bias} &= E_x\\left[(\\bar{g}(x) - f(x))^2\\right]\\\\\n",
    "&= E_x\\left[(0 - \\sin(\\pi x))^2\\right]\\\\\n",
    "&= E_x\\left[\\sin(\\pi x)^2\\right]\\\\\n",
    "&= \\frac{1}{2}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "* Let's compute the variance component\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{variance} &= E_x\\left[E_{\\mathcal{D}}\\left[(g^{\\mathcal{D}}(x) - \\bar{g}(x))^2\\right]\\right]\\\\\n",
    "&= E_x\\left[E_{\\mathcal{D}}\\left(\\frac{1}{2}(\\sin\\pi x_1 + \\sin\\pi x_2) -0\\right)^2\\right]\\\\\n",
    "&= E_x\\left[\\frac{1}{4}E_{\\mathcal{D}}\\left(\\sin\\pi x_1 + \\sin\\pi x_2\\right)^2\\right]\\\\\n",
    "&= E_x\\left[E_{\\mathcal{D}}\\left(\\sin^2\\pi x_1 +\\sin^2\\pi x_2 + 2\\sin\\pi x_1 \\sin\\pi x_2  \\right)\\right]\\\\\n",
    "&= E_x\\left[\\frac{1}{4}(\\frac{1}{2}+\\frac{1}{2}+0)\\right]\\\\\n",
    "&= 0.25\\\\\n",
    "\\end{align*}\n",
    "\n",
    "* Let's compute the out-of-sample error\n",
    "\n",
    "\\begin{align*}\n",
    "E_{\\mathcal{D}}\\left[E_{out}(g^{\\mathcal{D}})\\right] &= \\text{variance}+\\text{bias}\\\\\n",
    "&= \\frac{1}{2} + \\frac{1}{4}\\\\\n",
    "&= 0.75\\\\\n",
    "\\end{align*}\n",
    "\n",
    "* The following code calculates the bias, variance and out-of-sample error\n",
    "  * The bias and variance for hypothesis: $h(x)=b$ and $h(x)  = ax+b$ are close to the values in example 2.8. \n",
    "  * The graphs for the average function are similar to the example 2.8\n",
    "  * For $h(x)=b$, the bias, variance, out-of-sample error are consistent with the analytical results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------ Hypothesis set: h(x) = ax + b ------\n",
      "The variance is:  1.6688032109708237\n",
      "The bias is:  0.21592376683987358\n",
      "The expected out-of-sample error is:  1.8848023782261147\n",
      "The variance+bias is:  1.8847269778106974\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Problem 2.23\n",
    "import numpy as np\n",
    "from functools import partial\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "from matplotlib.font_manager import FontProperties\n",
    "\n",
    "def sample(lb, ub, sz):\n",
    "    # sample randomly from a uniform distribution \n",
    "    return lb + np.random.random_sample((sz,))*(ub-lb)\n",
    "\n",
    "def gd_funca(x, x1, x2):\n",
    "    #hypothesis found by learning algorithm\n",
    "    a = (np.sin(math.pi*x2)-np.sin(math.pi*x1))/(x2-x1)\n",
    "    b = (x2*np.sin(math.pi*x1)-x1*np.sin(math.pi*x2))/(x2-x1)\n",
    "    return a*x + b\n",
    "\n",
    "def gd_funcb(x, x1, x2):\n",
    "    #hypothesis found by learning algorithm\n",
    "    a = (x1*np.sin(math.pi*x1)+x2*np.sin(math.pi*x2))/(x1**2+x2**2)\n",
    "    return a*x\n",
    "\n",
    "def gd_funcc(x, x1, x2):\n",
    "    #hypothesis found by learning algorithm\n",
    "    return 0.5*(np.sin(math.pi*x1)+np.sin(math.pi*x2))\n",
    "\n",
    "def avg_g(x, gdfunc, num_samples, targetfunc):\n",
    "    #compute the average hypothesis \\bar{g} at given point x\n",
    "    bias_at_x = 0\n",
    "    gd_funcs = []\n",
    "    for i in range(num_samples):\n",
    "        #generate 2 sample data each time\n",
    "        x1, x2 = sample(-1, 1, 2)\n",
    "        v = gdfunc(x, x1, x2)\n",
    "        gd_funcs.append(v)\n",
    "        \n",
    "    average_gfunc_at_x = np.mean(gd_funcs)\n",
    "    #print('x: ', x, 'average_gfunc_at_x: ', average_gfunc_at_x)\n",
    "    variance_gfunc_at_x = np.var(gd_funcs)\n",
    "    bias_at_x = (average_gfunc_at_x - targetfunc(x))**2\n",
    "    return average_gfunc_at_x, variance_gfunc_at_x, bias_at_x\n",
    "\n",
    "# Compute the expected value of variance, bias and out-of-sample error\n",
    "def calc_bias_var_eout(gd_func, target_func, num_data_samples, num_x_samples):\n",
    "    variances, biases, eouts = [], [], []\n",
    "    for i in range(num_x_samples):\n",
    "        x = sample(-1, 1, 1)\n",
    "        _, variance, bias = avg_g(x, gd_func, num_data_samples, target_func)\n",
    "        variances.append(variance)\n",
    "        biases.append(bias)\n",
    "\n",
    "        # Compute the expected value of out-of-sample error w.r.t. data\n",
    "        eout_on_data = []\n",
    "        for i in range(num_data_samples):\n",
    "            x1, x2 = sample(-1, 1, 2)\n",
    "            v= gd_func(x, x1, x2)\n",
    "            eout_on_data.append((v-target_func(x))**2) # (g^{D}(x) - f(x))**2\n",
    "\n",
    "        eout_data_avg = np.mean(eout_on_data)\n",
    "        eouts.append(eout_data_avg)\n",
    "\n",
    "\n",
    "\n",
    "    variance = np.mean(variances)    \n",
    "    bias = np.mean(biases)\n",
    "    eout = np.mean(eouts)\n",
    "    print('The variance is: ', variance)\n",
    "    print('The bias is: ', bias)\n",
    "    print('The expected out-of-sample error is: ', eout)\n",
    "    print('The variance+bias is: ', variance+bias)\n",
    "\n",
    "\n",
    "    xs = np.arange(-1, 1, 0.01)\n",
    "    true_f, avg_gf, var_gf, ubs, lbs = [],[], [], [], []\n",
    "    for x in xs:\n",
    "        true_f.append(target_func(x))\n",
    "        mean_g, var_g, bias_g = avg_g(x, gd_func, num_data_samples, target_func)\n",
    "        avg_gf.append(mean_g)\n",
    "        var_gf.append(var_g)\n",
    "        ubs.append(mean_g + np.sqrt(var_g))\n",
    "        lbs.append(mean_g - np.sqrt(var_g))\n",
    "        \n",
    "    plt.plot(xs, true_f, color='red', label='Problem 2.23: True Function')\n",
    "    plt.plot(xs, avg_gf, color='green', label='Problem 2.23: Average Hypothesis g_bar')\n",
    "    plt.plot(xs, ubs, color='blue', label='Problem 2.23: Upper bound of the average hypothesis')\n",
    "    plt.plot(xs, lbs, color='blue', label='Problem 2.23: Lower bound of the average hypothesis')\n",
    "    legend_x = 2.0\n",
    "    legend_y = 0.5\n",
    "    plt.legend(['Problem 2.23: True Function', \n",
    "                'Problem 2.23: Average Hypothesis g_bar',\n",
    "                'Problem 2.23: Upper bound of the average hypothesis',\n",
    "                'Problem 2.23: Lower bound of the average hypothesis'], \n",
    "               loc='center right', bbox_to_anchor=(legend_x, legend_y))\n",
    "    \n",
    "num_data_samples = 1000\n",
    "num_x_samples = 1000    \n",
    "print('------ Hypothesis set: h(x) = ax + b ------')\n",
    "calc_bias_var_eout(gd_funca, lambda x: np.sin(math.pi*x), num_data_samples, num_x_samples)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1d6cfd44e48>"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Check if the average function is good\n",
    "xs = np.arange(-1, 1, 0.01)\n",
    "ss = []\n",
    "for x in xs:    \n",
    "    ss.append(avg_g(x, gd_funca, 1000, lambda x: np.sin(math.pi*x))[0])\n",
    "plt.plot(xs, ss, color='blue', label='Problem 2.23: True Function')\n",
    "legend_x = 1.5\n",
    "legend_y = 0.5\n",
    "plt.legend([\"average function\"], loc='center right', bbox_to_anchor=(legend_x, legend_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------ Hypothesis set: h(x) = ax ------\n",
      "The variance is:  0.23692599271382705\n",
      "The bias is:  0.2787220177271571\n",
      "The expected out-of-sample error is:  0.5165234716291182\n",
      "The variance+bias is:  0.5156480104409842\n"
     ]
    },
    {
     "data": {
      "image/png": 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JNDyekMaiuhrYvBlwdwf8/YHMTODHH9mNY7/8ArRujXnzgDVrgI8/ZveQlZWxEoZ3EexuS9wGz5WeyHiQgTvFdzBkxxDYGdkhOiQa6z5ch7gxcTgXeo4FuwBgawvMm8fqjDdsYKnnjz4CHByApUtZLTAhhBDyEpR209qroBpeQpSI54GDB4HPPwfi4wGxmGVCg4MBDY3azc6eBXx9gaFDgbVr3+0SH1Y8hGipCPfK7sFc3xxV1VUoqSrB6VGn4d7C/eV2wvOs7mL+fCAmhnWNmDOHBcFC4ds9gXqCangJIeT1UIaXkIbs/Hmga1egd2+gtBTYtImlbkeOfCzYPX6clcJaWAA//fTulne7+DaWxS7DuP3jkF+Wjz8++AMV8gpYGlgiLizu5YNdgGV4e/cGoqOBEycAc3Ng1CjA1RXYu5cFxIQQQkgdKMNLSEOUkwNMmwZs2waYmrKRaGPGPBbkFhYCt28Dv//OglyxmCWCLS3fzRLLZGXwXOmJxHuJAICxbcfitz6/oUxWBi01LQi4N3y/zfPAzp3AF18AaWmsj+/Spay3byNFGV5CCHk9dNMaIQ1JVRWry50zB1AogK++YoGvvv5jm+3dCwwYwDbnOCA0FFi4EDA0fDvLOnfzHCIzIqGjroOo61G4W3IX2uraSLqXhF2DdkHcTIxWRq0AADrqOso5KMcBQUFA377A6tXAl18CbdsCEyey62NAU9cIIYQwFPAS0lAcP86CueRk4IMPgCVLABubxzaRy1nS86OPADc34NNP2TRf5xeOg3l1yfeSce3hNdwpvoPxB8ZDppABAOyM7GCub46zN89idpfZ+FD8ofIP/ih1dWDsWBbhf/kly/Ju2QJ8/z0rWP6PDqkghBDyLyppIKS+KyhgkevataxzwdKlrJb1EQoFe/rLL1kZg7MzcPIk0LSpcpfC8zyOXTuGxWcXIzIjsvZxHysf7B60GwJOAEMtQ3AcB1m1DOpCFbQPu3ABmDAB+PtvoHt3VtPxxBuDhopKGggh5PVQhpeQ+mzfPpa9zMtjtapffvlUD7GqKvbJ/v79gJcXmzPRu/dj5bxKwfM8huwYgi2JW9Bctznmdp2LLjZdUFBegPfs3oO2+uPrUkmwC7CyhrNngRUrgBkzWPS/aBG7jm9lVnLjcOHCBVM1NbXfATiDbmgmhDQ8CgAJcrk8tG3btnlPPkkBLyH10YMHwCefAOvXs5qEfftYIPcPhYLFbnI5q8/dv59VOEyapNyYTq6QI+ZGDMz0zJCYl4gtiVvwmfdn+KrLV9BS01LegZRNIGBzkv392c18EyYAW7eyQRZ2dqpeXb2kpqb2u5mZmZOJiUmBQCCglheEkAZFoVBw9+7dk+Tm5v4OoO+Tz1PAS0h9c+QIMGIEcO8euyntiy8eS9f+/jsbHOHjA2RlsbkM8+YBU6YodxmHMg5h+K7huFd2DwJOAD0NPbQ2a4253eZCTdBAfnVYW7Opc6tXA1OnsjcPERGsnRnV9j7JmYJdQkhDJRAIeBMTk8Lc3Nw671qhj60IqS8qK4Hp0wE/P8DIiNWgzp79WLB79ChLXLq4AHfvAlZWwO7dLCZWhqNZRxGyJwTzY+YjcEsgWui3wLYB2/Bxu4+hIdTA8j7LG06wW4Pj2GjlhASgQweWEh84kNVGk0cJKNglhDRk//wOqzO2pYCXkPogNZUV4C5eDIwfD8TGshHB/6iqAubOZbW5Tk6sYUNCAhAVxRo2vEmykud5xN2Ow5SDU+C33g+bEzbj82Ofw8rACkeGH0F/SX9E+Efg3ox78DT3VMLJqoilJcueL1jA3iW4urIL+JZUVrK+x7NnAw8fssdoNsbzCYXCtmKxWOLg4CD19/e3Ky4ufqV/o3R0dOqcZBIUFGTzxx9/GClnlUxxcbGgS5cu9ra2tlJ7e3vphAkTzOvabteuXU2kUqmTSCSSSKVSp71799b2EPT19XVwdHSU2NvbS4ODg63kcvkzj7djx44mYrFYIhaLJTo6Ou42NjbOYrFYEhgYaKPM8wKAyZMntzQ1NXWtOd6kSZPqPLfXtXbtWsNLly7V1kRNmjTJfN++ffrP+x5C3hQFvISo2po1QJs2wI0bwJ49wLJlgM6/vWovXADatWOzJfr1Y8Fukyavfzie55HxIAN7UvZgQ/wGtP+9PdqtbIefY39GaJtQ5M/Ix9XxV3Fm9BmY6pq++fnVJwIBMHMmu6lNW5tNqQsPB6qrlbL7/Hx2n5yJCaClBfTqBXz9NRAQwNrFtWkDZGYq5VCNkqampiIlJSUpPT09UV1dnV+8eLHJo88rFApUK+m1UoZp06bdvXbtWmJCQkLS+fPn9bZu3frU/5mmpqayAwcOZKSlpSWtWbPmWmhoqG3Nc3v27MlMTU1NSktLS7x//7766tWrnxmUBwUFFaWkpCSlpKQkOTs7l61bty4rJSUladeuXdmPbieTyZRybhMnTsytOd7SpUtvKWWn/9i5c6dRQkJCbcC7dOnSWwEBAcXKPAYhT6KAlxBVKS9nH6+HhLCP2uPj2RCFR+zdC3TsyAKpPXvY5GATk2fs7yXE342Hy68ucFjqgA+3fIjhu4YjrzQPv/b+FXen38WKgBXQ1dCFs6kzjLWN3/AE6zEPD+DiRVYrPXcum7t8795Lf3tGBpvgXFr672NZWaz38eLFLI6eM4fda7hhA3D6NOukUVbGGm6QF/Px8SnJyMjQTE1N1bCzs5MOGzbMSiqVSjIzMzWWL19uLBKJJA4ODtLx48c/ln0cM2aMhUQicfLy8hLdvn37qfqb6OhonXbt2jlKpVInHx8fh+vXr6sDgKenp+Po0aMtPTw8HO3s7KRRUVE6fn5+raytrZ0nT57c8sn96OvrK2qCNC0tLd7V1bUsJyfnqd4o3t7e5TY2NjIAaNu2bUVVVZWgvLycAwBjY2MFAMhkMk4mk3Hca35U88MPPzTr06ePXdeuXe07d+7ssHv3bv333nuvVc3zwcHBVsuWLTMGgKioqNrz79Spk0NOTs5L1yg1b97cNT8/XwgAx44d0+3YsaMIYBnhgQMHWrdr187RwsLC5bvvvqv9LfXTTz81FYlEEkdHR0n//v1tIiMj9U6ePGnw2WefWYrFYklqaqrGBx98YLt+/XpDgGXExWKxRCQSSQYPHmxdUVHB1Rx76tSpLZ2cnCQikUgSHx+v+VoXi/xnUcBLiCpkZQHe3qxrwP/9H3D4MNDy339TT54EwsJYRtfNrc5Y+JXtSNoBr1VeKKgowM/+P+Pv0L9xZdwVpE1KwziPcWim0+zNDtDQ6OkBf/zBXoOYGJZ+PXsWAGt1PGAAcOwYex26dmVvNo4fZ/e7OTiwbmfNmrFBd6tWAe+/D1RUsGqUrVuB//0P6NOHzb7YuZNtk5DAKlfI88lkMhw6dKiJi4tLOQBkZ2drhYSE3E9OTk7S0NDgZ8+ebX7y5Mm0pKSkxEuXLunWBEvl5eWCNm3alCUlJSV7e3sXf/bZZ48FqpWVldzkyZOt9uzZk5mYmJg8YsSI/OnTp9cGzBoaGoq4uLjUkJCQewMGDLBfuXLljZSUlMQtW7Y0y83NFT5rvfn5+cIjR44Y+vv7Fz3vvNauXWskkUjKtLW1a4tbfHx8HExMTNx0dXWrQ0JCCgBg4cKFJgsXLnylt7YXL17U3bp167UzZ86kP2ub8vJy7pNPPrHau3dvZmJiYvKQIUPuz5w5s85yhZ9//tmspqRh9+7dLyw3yMzM1IqOjk47f/588oIFC8zlcjnOnj2rvWTJErPo6OjU1NTUpF9++SWnZ8+eJV26dCmcP39+TkpKSpKjo2NVzT6Ki4sF48ePt9mxY0dmWlpaUllZmeCHH36o/cXUvHlzWXJyctJHH32UP3/+/Oavcn0IaWB3nxDSCOzbx0ahcRzrJ/bIEAmFgtV8zp3L4rHgYOCXX56aHPzSKuWVSLyXiK2JW7Hg9AJ0sOiAnQN3ooV+C+WcSwPy4AFrzduuHYtvt20D/vwTcB01CnB3x9W+X+COzxyUjJyIyat7QygEtm9ng9wsLNhrAQBqaqxsoU0bVqO7ZAl73YyN2dePdI+r9eFbHjandKNGWSIhQUkzoP/h7FyG1atznrdJZWWlQCwWSwCgffv2xVOmTMm/fv26eosWLaq6d+9eCgAxMTG6HTp0KG7ZsqUcAAYNGvQgKipKb/jw4Q8FAgFCQ0MfsFMYdb9fv372j+4/Pj5eMz09Xbtbt24igJVImJiY1NYABAYGPgQANze3cnt7+3Jra2sZAFhaWlZmZWVpmJmZlT+5ZplMhn79+tmFhYXdlUgkVU8+XyMuLk4rPDzcPDIy8rGANCYmJr2srIwLDAy027dvX5PAwMCimTNnvvzHDf/o1KlTkYmJyXPrPS5duqSVkZGh1bVr19rzNzMzq7MGYuLEibnh4eEv/XlEz549C7W0tHhzc3O5gYGB/Pbt22qHDx/W//DDDwuaN29eDQA1/32Wy5cva9nY2FRIpdJKABgxYsT9VatWNQNwDwCCg4MLAMDT07P00KFDNDucvBIKeAl5V+RyVi/63XcsWtq+nU1OA7uZaccOdj9VXByrcli2jNWBvipZtQybEjbh579/xuXcy7Ujf0e2Holfe/9av/vnvkUzZ7Isaw1tbWD4cPae47uV7vjt1l/geQ5YDbQxysKB2OaIjNaFtzdr3XvyJCsBFouBFv+8Xxg8GPj2W3ZToYUFC47J66up4X3ycR0dHUXN319lOuiTJQI8z3P29vblly9fTqlrey0tLR4ABAIBNDU1aw8kEAggl8vrrDcIDg62sbOzq3hecJiZmanev39/+1WrVl2rCeYepaOjw/fp0+fhrl27DAMDA5+bJX6WR6+RmpoaFApF7XorKysFALt2IpGo/MKFC6mvcww1NTW+poa6vLz8sU+INTU1a48vEAh4mUzG8Tz/SmUaL3ptazLjQqEQ1dXV1FeQvBIKeAl5Fx48AAYNYn3FwsKAn36qjWZLStgQsD//BEQiFpSFhLx654WC8gJsSdyChacX4trDa3AxdcFUr6lo06IN2rRoA3tj+xfvpIG6cQM4d451dLtwAUhOZuW5NZnx+HjWinfCBDaLomVL4M4dVnJgbc0C2cmTOXTvqsCpH2IxOXogzPrqYeSePYA9u27du9d9bHOl3r9eT7wgE6tKnTp1Kp01a5blnTt31ExMTOTbtm0znjBhQh7AMpZ//PGHUVhYWMGaNWuaenp6PnYjlKura8WDBw/Ujh49qvvee++VVlZWclevXtX08PCoeJ21TJ48uWVRUZFw8+bN2c/aJj8/X9irVy+H2bNn3/Tz86ut+i4sLBQ8fPhQaG1tLZPJZIiMjDTw9vZWyo1b9vb2lenp6VoVFRVccXGx4MyZM/rdu3cvatOmTcXdu3c1Tpw4odO1a9eyiooKLiEh4aXP39zcvOrMmTO6gYGBRdu2bTN80fb+/v5FgwcPtps1a9bd5s2bV9+9e1fYvHnzaj09veqioqKnSird3d0rsrOztZKSkjQkEknV+vXrm/r6+tLNbEQpKOAl5G1LTmYFuDdusGh21KjapxITgf79gbQ0VsbwxRevPintZtFNTD00FTuTd6Kar4anuSd+6vkT+oj6PJXhaozOnWNdEPLz2bVT/JNnmj8f+PFHVn87bhxgaMiusfEj9+J9/TUb3PH556wuFxAg4IP2wPE/WBGvpyerfXhWtEveOWtra1l4ePitzp07i3ie57p37144bNiwhwCgra2tSExM1JZKpWb6+vrVO3fuzHr0e7W0tPjNmzdnTp482aq4uFhYXV3NjR8//u7rBLyZmZnqS5cubWFra1shlUolABAWFpY3derU/I0bNxrExsbqLlmy5PbChQtNb9y4oTl//vyW8+fPbwkAx44dS1MoFOjdu7d9VVUVp1AoOG9v76IZM2bcA1gNLwC8TmkDAIjF4qqePXs+FIvFUjs7uwqpVFr2z/XhN2/enDllyhTLkpISYXV1NTdx4sTclz3/8PDw2x9//LH1vHnzZG3atCl90fbt27cvnzJlSq6Pj49YKBTyrq6upVu3br0+bNiwBx9//LH10qVLzfbs2ZNRs72+vr5i2bJl2f369bNXKBRwd3cv/fTTT/M72UuiAAAgAElEQVRf5xoQ8iTuVT4eUhYPDw8+Li7unR+XkHfur7+AIUPY5+c7d7KWCwDS09lH4Zs2AQYG7L/dur3cLn869xMWnVkEHysfCDgB9qXtQ7WiGhM9JyLIKQie5p6NMtCVy1liPDMTmDyZVYP88gt7k2BhwWppY2JYyYGdHZvMfOkSu/RyObB2LXspXlpWFnujkpLCdv7xxyqfzsZx3AWe5z3exr6vXLmS7ebmRsEFIaRBu3LlSjM3NzebJx+nDC8hbwPPA99/D8yaBbRuzXqKWVoCAC5fBt57j93RHxLCynpbvMQ9ZHeK7+DrqK+x/MJyeJp74mjWUQgFQgyQDMD/Ov0Ptka2L95JPVJYyIZmaGmxy9SxI0uG79jBuhkUF7OSBD09lrmNj2fXTl0d+PXXf/fTty8bt2xiwkoUasTGsjro/ftZtte9zpEEz2FnB5w5AwwbBkyaBFy9yto3aDzVeYoQQkg9RwEvIcpWUcHqdNevZx+L//EHoKuLwkIWqM2fz7K6588DrVq9eHfp99Ox6MwirL2yFnKFHJ92+BSL3l8EAcdqHxpKNreoiJVweHmxFsQBAawLmJERy27XlCMIhayW2ciItcYtLmZzIYyNWU9bPz+Wra2qAqRSFvDWdQmEQhanTpr0Botu0oRNZfvyS3azYUoKu9nwTZohE0IIeeco4CVEmfLzWQR29iybPPDllwDHISqKJQpv3mQB2/LlgI3Ns3dzs+gmYm7EYEfyDuxI2gENoQZGtR6FaR2nNaibz+7fB5KSWH2svz/L0G7YwGLImBhWyhEQwLKwV68CZmas7MD4BTMvpk9/N+sHwCLxb79ljXdHj2Z1vQcOABLJO1wEIYSQN0EBLyHKkpXFJnbl5LAsYFAQ5HIW986bx272P3uWDVV7lpzCHCw6swjLYpehmq+GgaYBPvP5DFPaT0FzvfrTZ/3hQ3aKMhnQpQu76Ss+npVqVFayjKyzM/DDDyxLy3GsEsDFhbUC43lg0SLWuAIABg5kf+q14GAWuQcEsPqLnTtfvvCaEEKISlHAS4gyxMayAlK5nI3n6tgRJ06wTOTFi6xWNyKC1aM+ied5HEg/gG+jv8XZm2ch4AQIaxOGsLZhcDZ1hrqw/jR3Xb8e+O031iu46pEW+9raQOfOrLWakRG7DBs3srrZH34AoqNZQOvszLbr1o1NKGtw2rVjbSF69wZ69GDFwyNGqHpVhBBCXoACXkLe1IEDLJozNQUiI1Fl64ipE1kHAUtLNmZ2wICnv62qugpHs45iTtQcnL91HnZGdpjffT76S/qjlfFLFPe+BTzPAllNTeD6dZaZTkwEXF2B9u1ZRzUXF9YlYeBANnXs4EEgKAhwdHx8P9evs+4JamqsnKNGcrLKmx28GRsb4PRp1k9u5EiW2Z89u4GfFCGENG4U8BLyJlauBMaPZ50Y9u9H4n0zhPiwhO/UqcA33zw9LS39fjq+if4G25K2oUxWBisDK6wMWIkRbiPeejaX51k5wrVr7Gawli1Z665z54DcXJaJvXuXjc7duJGVJLu7s0Tm8uXshrPjxx8/p7q6H3Dcs2uUG0VcaGjIWs6NG8dqVq5dYz8LmpqqXhkhhJA6vGKLe0IIABY5hoezbgx+fijedxKfLTGDuzuLfbZvBxYv/jcwfFD+AHOi5sDlVxeIfhZha+JWDHMZht2DdiNtYhpC24S+1WBXJmMlBEZG7Iawtm1Z7a1IxOpoly9n9cWenqwy49tvWduwU6dYEBwby7K6u3e/3rjjRklDgw0SmTeP1Xr06AEUFKh6VQ2aUChsKxaLJQ4ODlJ/f3+74uLiV/o3SkdHp87mc0FBQTZ//PGHkXJWyRQXFwu6dOlib2trK7W3t5dOmDChzpl7u3btaiKVSp1EIpFEKpU67d27V7/mOV9fXwdHR0eJvb29NDg42Eoul7/UsUNCQixNTU1da8b81mdTp05tGR4e/tgNCObm5i537txRasLts88+M6v5e2pqqoaDg4P0Tfd56tQpnZEjR1q+6X7q4unp6Xjq1Cmdt7FvUjfK8BLyqmQyFuiuWQPFqFCs9foVn7ur4e5dVs65aNG/XatuF9/GknNL8GvcryipKkFXm66Y330+RrQeATM9s+cf5zWUlbG2Z/HxrOPBxYssS6uuzqa5DRkCeHiw7Ku+Pusa4ejIyhWEwn/3c/gwYGXFhjgALIv7yn1s/ws4Dvi//2NTMEJCWAr8r79YD1/yyjQ1NRUpKSlJANC3b1/bxYsXm8yePftuzfMKhQI8z0P46A+rCk2bNu1uQEBAcUVFBeft7S3aunVrk4EDBxY9uo2pqanswIEDGTY2NrLY2Fit3r17i/Ly8uIBYM+ePZnGxsYKhUIBf3//VqtXrzYKCwt77rum6upqREZGGrZo0aLq4MGD+n369Hnj0bsymQzq6vXnXoHXERER0WL+/Pm5ytxnp06dyjp16lSmzH0qQ2N4vVSBMryEvIriYpYCXbMGGZMj0CV9BUaNUYOtLeuru2YN0KwZj0MZh9B9XXdY/GCBxWcXI0AUgPhx8Tg+4jhm+cx67WC3tJTFVyIR6y/7008s89qrF4u1HBzY+NzkZGDLFvYJu6cnC343bWI3lU2dCvTrB7z/PovROnZ8PNgFWOu0mmCXvITgYODIESAvj70QFy6oekUNno+PT0lGRoZmamqqhp2dnXTYsGFWUqlUkpmZqbF8+XJjkUgkcXBwkI4fP/6xzOqYMWMsJBKJk5eXl+j27dtPJXWio6N12rVr5yiVSp18fHwcrl+/rg6wjNvo0aMtPTw8HO3s7KRRUVE6fn5+raytrZ0nT57c8sn96OvrKwICAooBNrLY1dW1LCcn56mpJN7e3uU2NjYyAGjbtm1FVVWVoLy8nAMAY2NjBQDIZDJOJpNxL9NTe//+/foikag8NDT03p9//mkMsCDY3NzcJT8/v/b/ZCsrK+ecnBy127dvq/Xo0aOVs7Ozk7Ozs9Phw4d1AZZ5HTJkiLW3t7dDv379bFNTUzXatm3rKJFInCQSidORI0d0a/Y9bNgwK3t7e2nXrl3tO3fubF+TLX/WtXxZU6ZMaTl37lzTmq8nTZpkPm/ePNP9+/fre3h4OL7//vutWrVqJQ0ODraqyWbX9dpPmDDBvLKyUiAWiyV9+/a1rVn34MGDre3t7aXe3t4OJSUlHAAkJiZq+vr6OkilUqe2bds6Xrp0SQsAVq9ebeTg4CB1dHSUeHh4ONZc665du9oDwIEDB/TEYrFELBZLnJycJAUFBU/FTzNmzGhha2sr7dixo0NAQIDtk5ntJ61Zs6apu7u72MHBQXrixAkdADhx4oSOu7u72MnJSeLu7i6+cuWKJgBEREQ09ff3t+vWrZu9r6+v6FWuM2Eow0vIy7pzB+jVC9Xxifhp0Hl8udKz9lPtkBCguKoIqy5uw8qLK3H+1nlYGVjhf53+h4/cPnrlm9AUClZLe/cua/OVlcVKC7ZtYxlbb29gxQp2g5m+Pmt51rQpayLw6aesEwJ5xzp1YpPZevZkL8D27ezvDdCoPaMsE/ISlPpxq7Opc9nqD1bnvMy2MpkMhw4dauLn51cEANnZ2VorV67M3rBhw43s7Gz12bNnm1+4cCHZxMRE7uvrK1q/fr3h8OHDH5aXlwvatGlTtnLlypvTp09v8dlnn7Vct27djZr9VlZWcpMnT7Y6cOBARsuWLeUrV640mj59uvm2bduyAUBDQ0MRFxeXOnfuXNMBAwbYx8bGJpuamsptbGxcvvjii7tmZmZ11hDk5+cLjxw5Yjhjxoy7dT1fY+3atUYSiaRMW1ubr3nMx8fHIT4+Xrdz586FISEhBQCwcOFCEwCYOXPmvSf38eeffxoPHDjwwZAhQx7OnTvXvLKyktPU1OT9/Pwebty40XDKlCn3jx8/rmthYVFlaWkpDwgIsJ06derdHj16lKSnp2v06NHDISsrKxEA4uPjdc6fP5+ip6fHFxcXC6Kjo9N0dHT4q1evag4ZMsQuISEhed26dUY5OTkaqampibdu3VJzdnZ2Hjly5P0XXctH/fbbb823bt3atObrvLw8dQCYMGFCfmBgYKv//e9/edXV1di9e7dRbGxsclxcnM7Vq1d1L126lCASiao6derksG7dOqOuXbuW1PXaL1u27NaaNWtMaz4dSE1N1bhx44bWhg0bsjp27Hi9V69eduvWrTOaMGHCg9DQUOsVK1Zcd3FxqTx+/Lju+PHjrc6dO5c2f/78FocPH06ztbWVPfrGocbixYvNIiIirvv5+ZUWFhYKdHR0FI8+f+rUKZ19+/YZXb16NUkmk3GtW7eWuLu7Pzc7XFZWJrh06VLKwYMH9cLCwmzT09MT3dzcKv7+++8UdXV17N69W3/mzJkWhw4dygSAixcv6sXHxyc2b968/tey1EMU8BLyMpKTAX9/JOaZYJRDHv7eYog+fYCfl8lxtTwSg3esx97UvaiQV0DcTIxfev2C0e6joan2cjcxKRSsG0J0NLsp7MgRNpnsUdrabKbFpEks4C0sZMGwiUkjuRGsMRCLWTF0r16sXy+1LXslNVk6AGjfvn3xlClT8q9fv67eokWLqu7du5cCQExMjG6HDh2KW7ZsKQeAQYMGPYiKitIbPnz4Q4FAgNDQ0AcAMGrUqPv9+vV7bEpLfHy8Znp6una3bt1EACuRMDExkdU8HxgY+BAA3Nzcyu3t7cutra1lAGBpaVmZlZWlYWZmVv7kmmUyGfr162cXFhZ2VyKRVD35fI24uDit8PBw88jIyPRHH4+JiUkvKyvjAgMD7fbt29ckMDCwqK5AFwAqKiq4EydOGPz22285RkZGitatW5fu2rWryeDBgwuDg4MfzJkzp+WUKVPub9y40TgoKOgBAJw+fbpJenq6ds0+SkpKhDXZyZ49ez7U09PjAaCqqoobPXq0dVJSkrZAIMD169c1ASA6OlqvX79+BUKhEFZWVvIOHToUv8y1fNS4cePuzpkzp/bNgLm5uQsAODo6VhkaGspPnz6tfefOHXWpVFpW86bCxcWltOZ6Dhw48EF0dLSeuro6/6zX/sljmpubV3bs2LEcANzd3cuys7M1CwsLBZcuXdIbMGBAbQaiqqqKAwAPD4+SoUOH2gQFBRUMHTr0qbKSDh06lEyfPt3ynzcbBa1atXos4D158qSev79/zfXk33///afW9KTg4OAHAODv719SUlIiyM/PFz58+FAwaNAg2+zsbC2O43iZTFb7293X17eIgt3XRwEvIS8SHQ1Z3yDMl03DXNkMGNwXYOFvN1EqWgWf7b/jZtFNNNVuitHuozHMdRjam7evc9xvfj6Qmcm6JDx8yO5vunePlUKcPs0eAwBzc9byy92dlSJoarL2ZmIxu0+qhoHBOzp/8mpatACiolivtpEjgVu32GSOBvSu5GUzscr2aA3vox7NpvE8/+TTz/Tk/4c8z3P29vblly9fTqlrey0tLR4ABAIBNDU1aw8kEAggl8vrfAGDg4Nt7OzsKsLDw/OetY7MzEz1/v37269ateqaVCqtfPJ5HR0dvk+fPg937dplGBgYWFTXPgBgx44dTYqLi4XOzs5SACgvLxdoa2srBg8eXNi9e/fS0aNHa96+fVstMjLS8Jtvvrn9zzkjLi4uuSawfZSurm7tdf3mm2+am5qaynbs2HFNoVBAW1u7bc331+VF1/JlhYSE5P/+++/N8vLy1ENCQu7XPP7ka8dx3Cu99hoaGrUbC4VCvry8XFBdXQ19fX15XT9jf/75543jx4/r7t2716B169bSy5cvJz76/Lfffpv74YcfFu7Zs8egY8eOTpGRkWnu7u4VNc+/ytoePacnv541a5Z5586di48cOZKZmpqq0a1bt9qGj09mlcmroRpeQp5n+3Zc7D4D7cqjEF46C1497sDuyz6YmWuJr0/NhriZGLsG7cKdaXfwc6+f0cGiAziOQ1kZi3lWrGD3t0kkLBPboQP7lHvwYNbNLDwcyMhgsdGaNSwgzslhHa4mTGC1tr17sz64Gk9VB5J6q0kT1p956FBWdP3xx2z8HHljnTp1Kj1//rz+nTt31ORyObZt22bcpUuXEoBlGWvqS9esWdPU09PzsRu6XF1dKx48eKB29OhRXYCVOMTFxb1235HJkye3LCoqEq5ateqZbxDy8/OFvXr1cpg9e/ZNPz+/0prHCwsLBTU1rzKZDJGRkQZisfipDPKjNm/ebLxkyZLrt27dunrr1q2r2dnZV6Ojo5sUFxcLBAIB/P39H06YMMHS3t6+vCZT6uPjU7RgwYLaOtkzZ85o17XvwsJCYYsWLWRCoRDLli1rWlMz6+vrW7J7926j6upq5OTkqJ0/f14fUN61HD58+MMTJ04YXLlyRTcoKKiw5vGrV6/qpqSkaFRXV2P79u3Gvr6+xc977dXU1PjKysrnvqs0NjZWWFhYVK1evdoIYD8vZ8+e1QZYbW+3bt1KlyxZctvIyEielZX12G/cxMRETU9Pz/Jvvvkm18XFpTQhIeGxc+3SpUvJoUOHDMrKyrjCwkLB0aNHDV907ps2bTICgEOHDunp6+tXN23atLqoqEhoYWFRBQDLly9v9nJXkbwMpWR4OY7rCeAnAEIAv/M8P18Z+yVElSoWLcXcmcVYgBjoGJfDdOhYnLJaASveCj/4/YBBzoOgq2iJlBTgzw1ASgrrhHD9OnD16r+TyAwMWAnCRx+xSWPGxqyNq5ER+692nf/8kAZPQwNYt46l7BcuZDXgf/5JL/gbsra2loWHh9/q3LmziOd5rnv37oXDhg17CADa2tqKxMREbalUaqavr1+9c+fOrEe/V0tLi9+8eXPm5MmTrYqLi4XV1dXc+PHj73p4eFTUfbRny8zMVF+6dGkLW1vbCqlUKgGAsLCwvKlTp+Zv3LjRIDY2VnfJkiW3Fy5caHrjxg3N+fPnt5w/f35LADh27FiaQqFA79697auqqjiFQsF5e3sXzZgx4x5Qdw1vcXGx4NSpUwZr1669XvNYkyZNFB4eHiWbN282GDNmTMHQoUMfdO7c2SkiIiK7ZpsVK1bkhIaGWolEIkl1dTXXvn374o4dO9bWNdf45JNP8oKCglrt3r3byMfHp1hbW1sBACNGjCg4evSovkgkktra2la4ubmVGhoaVivrWmppafEdO3YsMjQ0rFZT+zckad26dcm0adMsUlJStNu3b188fPjwh0KhEM967YcOHXrPyclJ4uzsXLZo0aJbzzrepk2bssaMGWO9YMGCFnK5nAsMDHzg5eVV/umnn1pkZ2dr8jzP+fj4FHXo0KH8r7/+qm0ht3DhQtMzZ840EQgEvEgkKu/fv3/ho/vt3LlzWc+ePQslEonU3Ny80tXVtdTAwOC573KNjIyq3d3dxSUlJcIVK1ZcA4BZs2blhoaG2kZERJj5+vo+M9tPXh33Omn4x3bAcUIAaQDeB3ATQCyAITzPP/WRQQ0PDw8+Li7ujY5LyFujUODs0AgEb/dDtlwCQZu1UPjMhrNgIETlI/AwXYyUFAFKS1kdbQ11daBVK8Damk0j69oVkEpZOYKAPkv5b1u6FJgyhXVw2LuX3WH4GjiOu8DzvIeSVwcAuHLlSrabm1v+29g3adgKCwsFBgYGitzcXGG7du2cTp8+nWJlZfVyTYNfoLq6GlKpVLJt27ZMFxeXSoB1R1i8eHHzEydOZCjjGO9KzXUqLi4WeHl5Of7222/XfXx86l1bs8buypUrzdzc3GyefFwZGV5PABk8z2cBAMdxmwF8AOCZAe9rKypi9XBOTkrfNSEAkJVegME9zyM2azKgUQKB5d/Qz/VHYcQIJABIFrLygh49AD09NjpXLGZ/7OzYGF1CnjJpEqvtHTGCTfFooN0byH/T+++/71BUVCSUyWTcjBkz7igr2L1w4YLWBx984ODv719QE+w2ZMOGDbNOT0/Xrqys5AYPHnyfgt36RRkZ3v4AevI8H/rP18MBtOd5fuKzvue1M7wffcSyI7t3szFRhLyme/dY2UFKCmvAcCG+BJcu86goqv0EC0L1aogcACexEB4eLDnXrh2gq6vChZOGLS8PMDV98XbPQBleQhqW4cOHW8XGxuo9+tj48ePvTpky5f6zvoe8mbeZ4a2rSPypKJrjuDAAYQBgZWX1ekeaNw+Ii2PptXXr2ExUQp6joIDV1F67Bhw7BiQlsRvDbjxSwSbQLIVCWAaUmUJDIx8j+lzBjPndYGsrpIwtUa43CHYJIQ3P+vXrn6qXJqqhjH/ObwJ4dNa0BYDbT27E8/wKACsAluF9rSNZWQExMcCHH7Lb3G/dYmOjyH/e/fvsvVBqKqt8uXYNuHQJuHwZqPkQQ1cXcHMDnNs+hNX7UbiMNSi5rwfuxAJwhc0xTncpvt/RGjo9uqv2ZAghhBCiVMoIeGMBOHAcZwvgFoDBAIKVsN+6GRsDhw8Dw4cD06axHk6LF9NdQf8Rt2+zbk/nzgHZ2WzUbl4eC3AfZWrKbhibPZt1RjBroUCW1nb8dikCf+WchnqRCM1j1qPkb0+IBUlYZToO7Y9/x76JEEIIIY3KGwe8PM/LOY6bCOAQWFuy1TzPJ77g296MlhaweTPL7i5ZwqKgtWvZ46RR4Hk2fSwmBti5k7XwSk5m01oVChbQtmrFWn5ZWQFjx7L6WhcX9lhNz9rCikLsTN6JeX8vxaXcS3AwdEKf/BM4tqozChRyfCP4EtOkh6AZuQdo2VK1J00IIYSQt0IpaVGe5//ieV7E83wrnue/UcY+X0goZMHu998DW7eyut6Cp6YBknqsvBw4eRJIT2fvX0JDgWXLgIkTWfmBmhq7N3HFCmDOHCAyEpg+HUhIAHJzgTNngEOH2Ms/axbQrRsb7qCuzuNk9kkEbQ1C8++bY9TeUSipKsF3zvthsCER+3/ugves0pFSaYsvup2HZswxCnYJqQeEQmFbsVgscXBwkPr7+9sVFxe/0r9ROjo67nU9HhQUZFMzkEJZiouLBV26dLG3tbWV2tvbSydMmGBe13a7du1qIpVKnUQikUQqlTrt3bu39s5YX19fB0dHR4m9vb00ODjYSi5/fvODiIiIph999NFjN8F4eno6njp1SkcpJ/USUlNTNRwcHN7pR2FTp05tGR4e3vxlt799+7aaq6ur2MnJSRIZGfnYDWNz5swxffTn6lk/M41RXT8/yvY2rm92drZ6z5497d50Pw37lhyOY2UNLVuydj++vsDBg6zxKVE5ngfi41nf/WbN2Nd79gDbtrHe+/v3A3fv/ru9nh6wahXrZxscDNjasixuv37s/Q3Axuw+y43CG9gYvxG7UnYh9nYsTHRMMM5jHIJdgpER1Q6jh3Fo0oTHlu4rMODYWHDDhwO//04jzAipJx4dLdy3b1/bxYsXm8yePbv2t4RCoQDP8xDW/EJQsWnTpt0NCAgorqio4Ly9vUVbt25tMnDgwMeGBZiamsoOHDiQYWNjI4uNjdXq3bu3KC8vLx4A9uzZk2lsbKxQKBTw9/dvtXr1aqOwsLB6lbmRyWRQV1dX9TJeyf79+/Xt7e0rdu7cmf3kc8uXL28+ZsyYB/r6+vVyTK9cLodaA75b+m1cXxsbG1lkZGTWi7d8vsZR+DpkCEv15eSw2a3x8ape0X9WTSnCiRPA++8DrVuzwHXYMMDDAwgMBI4eZd3l3NyAHTuA1auBI0fYEIeMDNZVYc0a4Kuv2Pfp6LBA91nB7qU7lzB051DY/WSHL45/AQWvwFL/pbj+yXXMdF2CpZ95YuhQDu3aVOOqy1AMPDYW3BdfsDIYCnYJqZd8fHxKMjIyNFNTUzXs7Oykw4YNs5JKpZLMzEyN5cuXG4tEIomDg4N0/Pjxj2VWx4wZYyGRSJy8vLxEt2/ffipyiI6O1mnXrp2jVCp18vHxcagZ7+vp6ek4evRoSw8PD0c7OztpVFSUjp+fXytra2vnyZMnP/URkL6+viIgIKAYYNPCXF1dy3Jycp76heLt7V1uY2MjA4C2bdtWVFVVCcrLyzmAjboFAJlMxslkMo7jnjsZ94V0dHTc6zp/T09Px1GjRlm6u7uLHRwcpCdOnNABgKKiIsGAAQNsnJ2dnZycnCQbNmwwBFgm0N/f365bt272vr6+oiePI5fL0a9fPxuRSCTp2bNnbSZ+z549+k5OThKRSCQZMGCATc15mpubu9y5c0cNAE6dOqXj6enpCLDM7YABA2w8PT0dLSwsXObNm1fbxmTWrFlmNjY2zh07dhSlp6fX+ds/LS1Nw8vLSyQSiSReXl6i9PR0jTNnzmh/9dVXFidOnDAQi8WSkpKS2os6b94807y8PPXOnTuL2rdvX3tekyZNMnd0dJS4ubmJc3Jy1ACWJe7Ro0crZ2dnJ2dnZ6fDhw8/1ZAyNTVVo23bto4SicRJIpE4HTlyRBcAevfubbdlyxaDmu2CgoJs1qxZYyiXyzF27FgLZ2dnJ5FIJFm0aFEzgAXo7du3FwUEBNg6OjpKAeC9995rJZVKnezt7aXff/997YjhH3/8sZmNjY2zp6en4+DBg61rMrYvs14AyM3NVff19XWwtrZ2HjdunEXNPkePHl2bKVy8eHGz0NBQi9TUVA1bW1vpy77Wyri+Bw4c0BOLxRKxWCxxcnKSFBQUCB79VCEuLk7LxcXFSSwWS0QikeTq1avPSYM9rnEEvAAbaxUTw7K+vr4s4iJvhVzObha7cQMIC2ODGNq1qyknYONyu3VjHRIWLAB69WLvR7S1gV9+Yc018vLYY/36ASEhwHvvsfsOW7Vi/flf5MLtCxi7bywcf3ZEmxVtsDd1L6a0n4LsKdmIC4vDkFYTMXOqNlq1YiUPX04pxtFSL5ie3AosXw588w37WSGE1DsymQyHDh1q4uLiUg4A2dnZWiEhIfeTk5OTNDQ0+NmzZ5ufPHkyLSkpKfHSpUu669evNwSA8vJyQZs2bdvLiVYAACAASURBVMqSkpKSvb29iz/77LPHAtXKykpu8uTJVnv27MlMTExMHjFiRP706dNrA2YNDQ1FXFxcakhIyL0BAwbYr1y58kZKSkrili1bmuXm5j4zrZyfny88cuSIob+//3NHwa5du9ZIIpGUaWtr13Yq8vHxcTAxMXHT1dWtDgkJKQDYaOGa8cKv4nnnX1ZWJrh06VJKRETE9bCwMFsA+OKLL1p07dq1KCEhITk6Ojr1yy+/tCgqKhIAwMWLF/U2bdp07dy5c2lPHic7O1tr3Lhx99LS0pL09fUVixYtMikrK+PGjh1ru2XLlsy0tLQkuVyORYsWvfAcMjIytKKiotJiY2OTv//++5aVlZVcdHS0zq5du4yvXr2atH///owrV67UGbyNGzfOKjg4+H5aWlrSoEGD7o8fP96yY8eO5Z9//vntgICAgpSUlCQ9Pb3aa/3ll1/mmZqayqKiotLOnz+fVnPNvLy8SlJTU5O8vLxKli5dagIAY8eOtZw6derdhISE5F27dmWOGzfO5snjt2zZUh4dHZ2WlJSUvGXLlqxPP/3UCgAGDRr0YMuWLUYAUFFRwZ0+fbpJ//79C5csWdLMwMCgOiEhIfnKlSvJa9euNUlJSdEAgPj4eN1FixbdyszMTASAjRs3ZicmJiZfvnw5afny5c1zc3OF2dnZ6t9//32L8+fPJ0dHR6elp6fX3rj0MusFgKSkJJ3du3dnJScnJ+7du9coIyNDffTo0Q8OHz5sUFlZyQHAhg0bmoWFhd1/1ddaGdd38eLFZhEREddTUlKSzp07l6Knp/dYpnjp0qUmEyZMuJuSkpIUHx+fbGtrW/Win7EaDTdvXhcXF+DsWcDf/99evYMHq3pVDQLPAzdvsslhj8aBGRksMP3gAzYgato0loFV/PMjqKHBgtXqapbNNTVlpdQdOwJBQSzIVaa/b/2Nz499juPXjkNXXRfdbLthgscEjGg9AoZahgDYQIm+fdn5fPQR8EX/NLQa+x7w4AGwbx/7+SCEPNOoUbBMSIBS60KdnVG2ejVynrdNZWWlQCwWSwCgffv2xVOmTMm/fv26eosWLaq6d+9eCgAxMTG6HTp0KG7ZsqUcYMFFVFSU3vDhwx8KBAKEhoY+YOcw6n6/fv3sH91/fHy8Znp6una3bt1EACuRMDExkdU8HxgY+BAA3Nzcyu3t7cutra1lAGBpaVmZlZWlYWZmVv7kmmUyGfr162cXFhZ2VyKRPPMf37i4OK3w8HDzyMjI9Ecfj4mJSS8rK+MCAwPt9u3b1yQwMLBo5syZ9+rax7MywDWPP+/8g4ODHwCAv79/SUlJiSA/P1948uTJJocOHTKMiIgw++f6cxkZGRoA4OvrW9S8efPquo5nZmZW5efnVwoAw4cPvx8REWF65cqVIgsLi0pXV9dKABg5cuT9X375xRRA3rOuCQD4+fk91NbW5rW1teXGxsaymzdvqp04cUKvV69eD2s+Fvfz83tY1/deunRJ9+DBg5kAMH78+Adff/21xfOOVRd1dXV+8ODBhQDQtm3b0qNHjzYBgNOnTzdJT0+v/RespKREWFBQIDAyMqoNwKqqqrjRo0dbJyUlaQsEAly/fl0TAPr37184c+ZMq/Lycm7Hjh0Gnp6exXp6evzRo0ebpKSk6Ozdu9cIAIqLi4VJSUlaGhoavKura6lYLK79+VmwYEHzAwcO/H979x0W1fH1Afw7LFJFFAQRAaVKUVFBsKAo9i6Iid3EFjVGY/2lmsREoyQmlsSoUeJr1FhiL8GosfdVsWCwoFhBQdrSt8z7x+yaFalSFvB8nmcf4O7du+fOrnKYPfdMbUDMykZFRRk9efKkhr+/v0zzugQHByffunXLqLjxAkBAQECapaWlEgBcXFyyY2JiDF1cXNLbtWsn27x5s3nTpk2z5XI58/Pzy7p586ZBaV/rko5v69at02fOnGn/1ltvJQ0ZMiTZ2dn5pfjbtGmT8f3339d/9OiRweDBg0u0Ql/1SngBUb+r6dU7ZIjIembMoNm8PGJjxUyqoaGYsX3nHWDDBrFq86hRYob2p5/ENqUSmDYNkMuBli1FmUFN9WUAb70FNGpU/vE+kT3BV0e/wqpLq2BlYoVF3RZhTIsxMDd68akRkpKAr78WF75ZWgKnTgF+ssNiGtnUFDhxAmjxxlyfQEiVo13Dq83ExOTFL72SrA6aN0HknDMXF5esyMjI6Pz2NzIy4oBIHA0NDV88kZ6eHhQKRb6/RIYOHdrIyckpe86cOQUmdjExMTVCQ0Nd1qxZc8/Ly+uVX9AmJia8T58+KTt27KgdHBxc4Cxx3bp1FSkpKS/NNKekpEjq1auX79Vu2uefdywYY+Cc488//7zj7e39UkwnT5401R7zwo6rfayCSCQSrlLPkmRlZb30ybL2OEskkhfjXNryjuLS19fneuq2pvr6+i+en3MOqVT6r/YMcV7z5s2rZ21tLd+2bds9lUoFY2NjH0C8nq1bt5Zt37691ubNm+sMGTIkSX1MtmjRogcDBw586TXeu3evmfZ479271+zYsWNmUqk02szMTOXn59c4KytLr7AxLk68AGBgYKA93lwulzMAGD9+fOK8efNs3NzcsocPH/5ixcWSvtZ5lXR858+fHz9gwIDUXbt2mbdt29YjIiLilvbYTJgwIal9+/YZO3bsMO/Zs6fb8uXLY/v16ycrTizVp6RBW+3aYlryrbeAWbOASZNEtkYAAOvXAy4uQI8eYondIUNEYjtmjChL+OgjwM9PXFw2daqY2R07Fpg9W3RGmDtXfD97dvkmu7IcGZadW4bGPzVGgx8aYPXl1ZjRZgZipsRgepvpLyW727cDnp7A0qViVvfSJcDv3/8TJ2lvLxr3UrJLSLGEh+Ph+fO4WZa3omZ3i6tDhw4Z586dM4uLi9NXKBTYunWrRceOHdMBMWOr6cawdu1aSz8/v5d+ETZr1iw7KSlJ/9ChQ6aAmNGUSqWv3c9yypQptmlpaZI1a9YUeG6JiYmSXr16uX755ZePNDNlAJCamqqnqR+Wy+WIiIgwd3d3f2UGWVtAQEDGxYsXaz548OBFPWxubq6es7NzblHn/8cff9QBgAMHDtQ0MzNTWlpaKjt16pS2aNGieppk9NSpU8X6TC4uLs5AM4YbN260aNu2bXrz5s2zHz9+bHD9+nVDAFi3bp1l+/btZQBgZ2eXe+rUKRMA2LJlS5HdMoKCgtL37dtXOz09nSUnJ+sdPHiwdn77tWjRImP16tV1AGDlypUWvr6+6UUd29TUVJmamlpk7hMQEJC2cOHCFzXFp0+ffmVsUlNTJfXr15dLJBIsX77cUqn8b0J88ODBSWvXrq174cIFs5CQkDQA6Nq1a+ovv/xipSkduHr1qqGmhERbSkqKxNzcXGlmZqa6fPmykaako3379hnnzp0zS0hIkMjlcuzatevFWBYn3sIEBQVlxMXFGezYscNyzJgxSZrtJX2tSzu+UVFRhn5+flnz5s2Lb9q0acb169df+vd548YNAw8Pj5zPPvvsWbdu3VIiIyOLfZ7Vb4ZXw9AQ+OMPwMkJWLBArCe7ZYtIht8QOTmiCcH9+6LeNipKzOZGR4vFGI4eFbmgXC7W7tAsWnftmpgkHzjwv5VQfX0rLu5TD05h1sFZOP/4PJRciXb27TC+5Xj0cu0FDyuPl/bNyhJxr1ghZp8jIoDm3lxk5V9+Kaaqt217o153Qqqzhg0byufMmfM4MDDQjXPOOnfunDp8+PAUADA2NlZFRUUZe3l52ZiZmSm3b9/+0pXdRkZGfNOmTTFTpkxxkMlkEqVSySZOnPjU19c3u6RxxMTE1Fi2bFl9R0fHbC8vL08AGD9+/LPp06cnbtiwwfzChQumixcvfhIWFmb94MEDwwULFtguWLDAFgAOHz58S6VSoXfv3i65ublMpVKxdu3apc2aNSsBEDW8AJC3tMHe3l6xcOHChz169HBVqVTM1NRUuX79+ruarhWFnX+dOnWULVq0cE9PT5esWrXqHgAsWLDgyfjx4x3c3d09OefMzs4u58iRI3eKOncnJ6fs8PBwy0mTJjV0dHTMmTlzZoKJiQlfsWJF7KBBg5yVSiW8vb0zZ86cmQAAc+bMeTJhwoRGCxculPv4+GQUdfyAgIDM4ODgpCZNmng1aNAgx8/PL99E9pdffnkwatSoRkuWLLGxtLRUrFu3LraoY48aNSqxZ8+ertbW1nJNnWl+Vq1a9XDs2LEObm5unkqlkvn7+8vatm370jLBH3744bOBAwc679y5s05AQIDM2Nj4xUxkcHBw2oQJExy7dOmSovnkYNq0aYmxsbGGTZs29eCcMwsLC/n+/ftj8j73wIEDU1etWmXl5ubm6ezsnO3t7Z0BAI6OjvJp06bFtWrVysPa2lru5uaWZW5urixuvEUZMGBA8tWrV02srKxeZO4lfa1LO75hYWHWp0+frqWnp8fd3NyyQkNDUx88ePCiTcjvv/9usXXrVkt9fX1uZWUl//bbb19Z2bcgrCRT02XF19eXS6XSinvC334TV1e5uopeWE6lbudWKf39N7BsmUhWO3USie6lS6KO1sZGJLnGxiLJ/eYb0Qlh5UoxK9q+vW5jP3LvCH6L/A3J2cnYf3s/HMwdMLTJUPRx64M29m1e2T8nBwgLE+ebkCBmm7/5BqihygEmTBAnN3Ik8Ouv1ImBVBuMsYuc83L58/PKlSux3t7eiUXvSSorExOTFpmZmZfzbvfz82v8/fffP+zQoUOmLuIiZSc1NVXP3NxcJZfL0b17d5d33nknceTIkfnWOJdUp06dXD788MOn/fv3lwGiC0WfPn1cb9++Xb6LiZWxK1eu1PX29m6Ud3v1neHV9u67ojdWSAjg7w/s3Am0a6frqIqUliZyNSMjUVbQoAFQr54oL0hKEqdjZCS6G1y9KhoP2NkBffqIdsQqlTjV/v3zP/6ECeKmK3eS7uCHMz/gzKMziIyPhKWxJeqb1ce4luMQ1jUMtQxr5fu46GhRhhEZKc519mx1wp6QIKalT5wA5swRM7xUu00IIaSamDVrlu3x48dr5eTksMDAwDTNpxulkZiYKPH19fXw8PDI1CS71dGbMcOrceuWyJDu3xfNX4cNq/gYCpCZCUilQMOG4iKxTZvEp/JGRmJC+vJlUV8bFARs3iwWckjMMxczdKgoYTA2FjOgenqiTVhlwjnHpbhLOBBzAPNOzAMDg7+dP/o37o/xPuNhpF94Od22beICO0NDMXHft6/6juvXxQ9xceKOIUPK/VwIqWg0w0sIIYV7s2d4NdzcxMVLISGi1cDt22J1gwqaBUxPF80CGBNtwOLjxVdLS6BbN9FVQNvAgWL/q1dFGfKvv4pkd8oU4IcfgBs3xApkKpU4TpMm/51KYSuS6YqKqzBh7wT8eulXAEA3525Y028N7GoV3UlGoQA++0z09fXzE4mvneZh+/aJBNfUFDh+XOxACCGEEKL2ZiW8AGBhIYpd33sP+Oor8fn4mjUiWSoDDx6Itlj9+4vkc/t2MTN78qRYXaxzZ1FNER4uOqbp6QFeXuJCsUWLRLsvAwPA3V0sGqdt7FhRqjB4sEh0mzYtk5DLDeccZx6dQVJWErLkWdhyYwv+vPEnZrSZgan+U2FvXrwloCMjRaONM2fEy7ZkiTqh5xz48Udg5kzRBHj3bq0smBBCCCFEePMSXkBklOHhounsRx+JpHfHDlHnWwpnz4r2v0+fiplIQCSmSiVgbi6Stc2bgcOHRbesWbOAe/dEh4HPP/+vS0JBLC3FxHRVcOHxBcw+NBtHY4++2GYoMcQXgV/gi8AvitVj8dYtUdaxcaMo4fj9d63zz8kB3n9f/LEycKBYJriM/mghhBBCSPXyZia8gJh+nT1brIs7ZIjou7VpE9C1a4EPUanE9VD//CNmajt0ENufPxcLM6xfL2pwz50DrlwR9w0eLD6ONzQETExEaYJMJjolaISFVb5a25LinOPso7M4EHMAF+MuYu+tvbAyscKynsvg38AfekwPTes1hYGk6I4JKSliPNetEzXMM2cCH38M1NF0HHz4EAgNBc6fF3UOX30lpsoJIYQQQvLxRmYJnAMXL4qZV/ToIa4Ws7UV34eFiR0gEtxvvxX1tT/9JEoMOnYUs45BQeLT9KtXgcBAMXM7a5Z6wQM/YNw4cTMzE4maiXqRztq1X052gaqd7D5Oe4x5x+eh5aqWaBveFnOPzcW1p9fweYfPcWfKHUz2m4xWDVrBx9anWMnu06eipdqGDcCHHwJ374qX5EWy+88/gI8P8O+/ol7k668p2SWkmpBIJD7u7u6erq6uXj179nSSyWQl+sdtYmKS7+oyAwcObKRZkKGsyGQyvY4dO7o4Ojp6ubi4eE2aNKlBfvvt2LGjlpeXl4ebm5unl5eXx+7du80097Vv3961cePGni4uLl5Dhw51UCjyXTDthb1795p16tTJpdCdytnSpUstR44c6VCRz+nn59f4+PHjxV7qOiIioqaLi4uXu7u7Z3p6+ouPExMTEyULFiyw0vxcGcazIpXHvwNt5TW+GzZsMP/kk09sSnucNzJT2LhRTOgOH65egM3ZWRSIDhyI7P/NweFO32DeF7kIDAQ++UQ0APjgg/+aOzx+LHLj6dMBb2+xTG9EhChjqFNub6XKhXOO3Td3o+kvTfHZkc9gIDHAit4rkPZxGmI/jMXcTnMLbCuWn8hIUQ7SqBFw8yawZ4+oaa5X78UTAt99J2bg69YVs7vBweVyboQQ3dAsLXz79u2oGjVq8EWLFllp369SqaC9mpWuzZgx4+m9e/eirl+/fuPcuXM1t2zZ8sp/etbW1vJ9+/bduXXr1o21a9feGzt27IvauV27dsXcvHnzxq1bt6KeP39eIzw8vNL9BpFXwVVK161bZ/HBBx/ER0dH39Beuvb58+eSNWvWWBf2WF2riuOtUV7jO2zYsNT58+fHl/Y41TrhzcoCDh0SuRLnYrZQoRCfgFtaigqGTp3E7GzM05pY2m4zrA1T0eXY5/hsrgEex+Zi5UqR4F66JBKxd98Vk8G7d4sL0X75RZQwdOqk67OtGFHPojDlrymw/9Ee/Tf1R6PajXBz8k2cG3sO7/m+h5oGNUt0vJQUMTPu6yuWLR43TtRCd++utZNMJpaJnj1bdNg4d05c1UcIqbYCAgLS79y5Y3jz5k0DJycnr+HDhzt4eXl5xsTEGKxcudLCzc3N09XV1WvixIkvzayOGzfOztPT06NNmzZuT548eaVs78SJEyatWrVq7OXl5REQEOCqWd7Xz8+v8ZgxY+x9fX0bOzk5eR07dsykW7duzg0bNmwyZcoU27zHMTMzU/Xt21cGiBXcmjVrlvnw4cNXPsZq165dVqNGjeQA4OPjk52bm6uXlZXFAMDCwkIFAHK5nMnlclacaxvys2vXLjMPDw9PNzc3z0GDBjXKyspiR44cMenWrZszAKxfv762kZFRy+zsbJaZmcns7OyaAmIZ1/bt27t6eXl5+Pj4NL58+bIRIGYCx44da+fv7+82adKkV64Efvz4cY327du7NmrUqMmMGTPqa7Z/+eWX9VxdXb1cXV295s6daw2IxQtcXV29NPvMmTOn3vTp0201Yz5x4sQGTZs29WjUqFGTiIiImgCQnp7O+vTp4+Tm5ubZu3dvp+zs7HwHJr/z/uGHH+ru27fPIiwszLZfv34vXZgzY8YMu4cPHxq6u7t7vvfee3YAkJGRIenRo4eTo6OjV79+/Rw1yywX9D7RtnHjRvNmzZq5e3h4eLZt29bt4cOH+kqlEg0aNGiamJgo0ezn4ODQ5OHDh/pPnjzR7969u3OTJk08mjRp4vH333+bAsD06dNthwwZ0rBdu3auISEhjjdv3jTw8fFp7Onp6eHp6elx8OBBUwBQKpUYPny4g4uLi1enTp1cAgMDXTQztsWJFwCOHTtWs0WLFu52dnZNNY8dMGCA4/r1618sR9qvXz/HDRs2mC9dutSyc+fOzsV9rctifL/55htrZ2dnLzc3N88+ffo4AS9/qhAeHl7H1dXVq3Hjxp6+vr6N8zvHAnHOK/zm4+PDy9Iff3Bua8v54MGcjx7N+dixnMfHcz5okEh1Fy/mfP588b2np/i6Ywfnq1dzbm+vSYfFrXt3zvd8dZGnWDhybmrK+fr1ZRprVaRQKrhKpeJhJ8M4vgQ3+NqAh2wO4asvruZZ8qzXPu6+fZxbWHDOGOdjxnCelJTPTtevc+7hwbmeHufffce5SvX6J0JIFQdAysvp/+XIyMhYzrlUlzdjY2Ml51yam5srDQoKSl6wYMH96Ojoq4wxfujQoX8559J79+5dsbGxyXn8+HFkbm6u1N/fP23dunV3OOdSAHz58uV3OefSGTNmPB4xYsQzzrk0JCQkMTw8PCY7O/ti8+bN0x8/fhzJOZeuWrUqJjQ0NJFzLm3VqpVswoQJcZxz6dy5cx9YWVnlxsbGXsnMzLxobW2dGxcXd7mguBMSEi43aNAgJyoq6mph5xceHh7Tpk2bNO1t7dq1SzUzM1P06dPnuVwul3LOpQsXLry/cOHC+3kfv2fPnpsdO3ZM0d6WkZFxsV69erlXrly5xjmXDhgwIPGrr756kJubK7W1tc3hnEvHjRsX7+XllXHgwIF/9+7dG92nT5/nnHNp69at065evXqNcy49fPjwv/7+/mma8erYsWOKJh7t25IlS+7VrVs3Ny4u7rJMJrvo4uKSdezYsRvHjx+/4erqmpmamnopJSXlkrOzc9bJkyejoqOjr7q4uGRpHv/5558/nDZt2hPNmI8dOzaecy7dtGnTbc3YfPHFFw81r8vZs2ejJBIJP3bs2I3inLf265039ryx7Nmz52bNmjUVd+7cuaJQKKTe3t7pERER0YW9T7Rvz549u6xUKqWcc+miRYtiNefyzjvvPF28ePE9zbhqzqtPnz7PIyIiojnn0lu3bl11dHTM4pxLp02b9sTT0zNDJpNd5JxL09LSLmVkZFzknEuvXr16zcvLK0Pz/unQoUOKQqGQ3r9/P9LMzExR1Pta+xYSEpLYo0ePJIVCIZVKpdft7e2zOefSvXv3Rnfu3DmZcy5NTEy8bGtrm5Obm1vq1/p1xtfKyio3MzPzoubfleY9p/m37Orqmnn37t0r2vfnvan/L3vl/7hqcdHa99+L0oRjx0TampwMbNkiViqzsxMziAoF0KYNEBUlZhM1bcPeeUfMKN66JT4+79kTYKwlMOaEuJht+HDg6FGx/q6xsa5PtULJcmT4+PDHWCFdAZuaNngse4y3vN7Cz71+Rl2Tuq99XJVKNFeYOFG0Vjt0CGiRt/KOc9F4eOpUoFYt4OBBUThNCCl3o0fD/vp1FLtmsjiaNEFmeDgeFrZPTk6Onru7uycA+Pv7y6ZOnZp4//79GvXr18/t3LlzBgCcPHnStHXr1jJbW1sFALz99ttJx44dqzlixIgUPT09jB07Nkmcw+jnISEhL9UPXr161fD27dvGQUFBboAokbCysnrxGXJwcHAKAHh7e2e5uLhkNWzYUA4A9vb2OXfv3jWwsbHJyhuzXC5HSEiI0/jx4596enrmFnRuUqnUaM6cOQ0iIiJua28/efLk7czMTBYcHOy0Z8+eWsHBwWmzZ89OKGyctF25csXIzs4up1mzZjkA8M477zz/+eefrWvUqPGsYcOG2ZcuXTK6dOmS6QcffPD0yJEjZkqlkrVr1y49NTVV7/LlyzUHDRrkrDlWbm7ui5nUkJCQZH39/FOEgICANBsbGyUA9O7dO/no0aM1GWPo1atXSq1atVSa7UeOHDEbNGhQoSuBDRo0KBkA2rZtmzFr1iwD9ZjUnDJlyjMA8Pf3z3Jzc3tlSeSCzhvAs+KOHQA0bdo0w9nZWQ4AXl5emTExMQYWFhaKwt4nGvfu3TMYMGCAXUJCQo3c3Fw9e3v7HAAYOnRo0ty5c22nTp36fMOGDRYDBw5MAoBTp07Vun379otEIj09XZKcnKwHAD169EjRlF/k5uayMWPGNLxx44axnp4e7t+/bwgAJ06cqBkSEpIskUjg4OCgaN26tQwo+n2trV+/fikSiQQ+Pj7Zz58/rwEAvXv3Tv/www8bPn78WH/Dhg11evfunVxDfXFRaV/rko5v48aNs4KDgx379euXMmzYsFeO5+vrmz5s2LBGAwcOTB42bFhyES/vS6pcwpubK/Kg3FyRuNaqJS5AW7pU1NkCovwgJATo1Uv0bG3RQrTfPXhQJL6M/bdAg0Qi+uK+stJwgwbiAqkvvgDmzxdZ8ZYtopVZNaRUKbHt3234LfI3NDBrgM6OnfHR4Y/wMPUhRniPQKY8E971vPFJ+0+gx16/Eub2bfF3xMWLIn/dsUO8hi9JSQHGjwe2bhU1u+vWATalrlcnhFRymhrevNtNTExUmu95CVYHzVsiwDlnLi4uWZGRkdH57W9kZMQBQE9PD4aGhi+eSE9PDwqFIt+P1YcOHdrIyckpe86cOQUmWjExMTVCQ0Nd1qxZc8/Lyysn7/0mJia8T58+KTt27KgdHBycVszT05xTgfe1bds2fffu3eY1atTgffv2TRs6dGgjpVLJfvjhh4dKpRJmZmaK/MYbAGrWrKnKbzvw6rgyxgqMQ19fn2s+xgaA7Ozsl36BaMZcX18fSqXyxYGLKu8oyfugMNqvs0QigUKhYEW9TzQmT57sMHXq1Phhw4al7t2712zu3Lm2ANC5c+eMMWPGGD558kQ/IiKi9rx5855oYpZKpf9q1xVrmJqavhikefPm1bO2tpZv27btnkqlgrGxsU9h51zceIH/xjvv8d56663nq1evtti2bZtFeHh4rGZ7SV7r/JR0fI8cOXL7r7/+Mtu5c2ftsLAw29u3b1/Xvn/jxo0P/vnnH9Pdu3ebN2/e3CsyMjJKk5AXpUrV8MbGAu3bA5MnOzeuXAAAHtFJREFUiwvGOnQQy+kaGIivGi1bAjEx4uI0a2tx0dm5c6JNq7l5PglWQfT1gXnzxGoP8fHiwMuWvejiUF3EyeLQ5fcuePvPt3Ej4QbWX12PoduHwljfGCdHn8T/Dfg/bB20FZ91+KxUya5cLtq03bsn2ub+/Xc+r8XZs+IvlB07xFWAERGU7BJSwcLD8fD8edwsy1tRs7vF1aFDh4xz586ZxcXF6SsUCmzdutWiY8eO6YCYKdLUJa5du9bSz89Ppv3YZs2aZSclJekfOnTIFABycnKYVCotfD3zQkyZMsU2LS1NsmbNmgLPLTExUdKrVy/XL7/88lG3bt0yNNtTU1P1NHWLcrkcERER5u7u7q/MIBelefPm2Y8fPza4fv26IQCsW7fOsn379jIA6NixY/rKlSutW7VqlW5ra6tITk7Wv3v3rpGPj0+2hYWFys7OLldzoZxKpcKZM2eK9THmyZMnaz19+lSSnp7O9u/fXzswMDA9KCgoff/+/bVlMpleWlqa3v79++t06tRJZmdnp0hKStKPj4+XZGVlsQMHDpgXdfyAgID09evXWwDAhQsXjG7duvXKpw2FnXdBzM3NlRkZGUX+Eivu+0Qmk0kcHBzkgHi/abbr6emhZ8+eKZMmTbJ3cXHJ0iRkAQEBaQsXLnxxUdfp06fzHe/U1FRJ/fr15RKJBMuXL7fUXKjZvn379J07d9ZRKpV4+PCh/rlz58xKEm9hJkyYkLhy5cp6AODr65ut2V6S17q046tUKhETE2PQt29f2fLlyx/JZDJJamqqRPuxUVFRhkFBQRmLFy9+UqdOHcXdu3eLbv+kVqVmeL/4QqwR8eefoj3YlCkiqX3rLXERmjaJ1hCVunNCjx6i/9iYMeJJ9+4FfvtNXL1WRSlVSkj0JEjISID/an8kZiZiTb81GOU9CvHp8Tj76Cx6u/WGkf5r/y54SWIi8M03YvZ9+/Z8Gizk5oqrCRcsABwcRMPjvEvNEULeeA0bNpTPmTPncWBgoBvnnHXu3Dl1+PDhKQBgbGysioqKMvby8rIxMzNTbt++/a72Y42MjPimTZtipkyZ4iCTySRKpZJNnDjxqfYv+OKKiYmpsWzZsvqOjo7ZXl5engAwfvz4Z9OnT0/csGGD+YULF0wXL178JCwszPrBgweGCxYssF2wYIEtABw+fPiWSqVC7969XXJzc5lKpWLt2rVLmzVrVgIAhIWFWQFAfqUNZ86cqVWvXr1mmp83bNgQs2LFithBgwY5K5VKeHt7Z86cOTMBEAnv8+fPa2j+IPD09Mx6+vSpQk/dyvGPP/64O27cuIYLFy6sr1AoWHBwcFKbNm2KTLp9fX3T3377bcfY2FijgQMHPu/QoUMmAAwdOvR5y5YtPQBgxIgRCe3atcsCgBkzZsT5+fl52NnZ5bi4uBQ51jNnznw2ePBgR3Urt8ymTZtm5N3HxMSEF3TeBbGxsVH6+Piku7q6egUFBaX27ds3Nb/9ivs++fTTT58MGTLEuV69erm+vr4ZDx48MNTcN2zYsKTAwECPpUuXxmq2rVq16uHYsWMd3NzcPJVKJfP395e1bdv2Qd7n//DDD58NHDjQeefOnXUCAgJkxsbGKgAYNWpU8qFDh8zc3Ny8HB0ds729vTNq166tLIv3tb29vcLZ2Tm7b9++L5URlPS1Ls34Nm3aNGfo0KGOMplMwjln77333tO6deu+NHs7bdo0u9jYWEPOOQsICEhr3bp1sf9IZGX1sUBJ+Pr6cqlUWuLHJScDSUmiixggakHXrxcdEvL2ti0XnIu2DDNninrelSvFAghVzKkHpxC8ORitGrRCjiIHJx+cxIl3T6BVg1Zl+jyciwnaJUvEbC7nwOjRon73JVevAiNHitU63n1XNDg2L3ISgJA3DmPsIufctzyOfeXKlVhvb+/E8jg2IaRspKam6pmbm6vi4+MlrVq18jh16lS0g4ND4Q2ci0Emk+l5enp6RkZG/mtpaakERHcEqVRqum7duleS8srsypUrdb29vRvl3V6lShrq1Pkv2QXEegMjR1ZQsguIwt9Jk4DLlwEnJ2DQIHGLL3V7uApxP+U+vjn+Dbr83gUmNUxwNPYoDt87jGU9l5V5snvjBtCli6ijvnZNLIh29qyov35BoRAre/j6ijHcvVs0OqZklxBCCHlF165dXd3d3T3btWvnPmvWrLiySHZ37txp5ubm5jVu3LhnmmS3OqpSM7yVilwulgCbO1cUB//wAzBq1H9Xw1UCnHNs+3cbrj29huMPjuNo7FEAQA+XHlg3YB3SctJwMe4iBnkOKvICgeJKSgJWrBDVCTVriuEZPz6f1eQuXBB3REaKmpTly1+tSyGEvIRmeAkhpHAFzfBWqRreSqVGDeDTT4GBA8VqCe++K9bDXblSzP5WAl8c/QJfH/8aDAyN6zbG3I5zMbzZcDjWEb24rUyt4GzhXMRRiicjA/j4Y3H6ubmiRnfFCnHR4EvS0sR0708/iYvRtm6tkmUhhBBCCKk6KOEtLXd30QB45Urgf/8DPD1Fje/HH4uZ3wrEOcfJBycRHhmOJ7In+Dvmb4xuPhor+qxADUm+i66UiRMnRD/je/dE7j9hQgF9dbdvF311nzwB3n9fXMVG5QuEVBYqlUrF9PT0qlcbGkLIG0OlUjEA+bbUq1I1vJWWnp5YReHff8Vs5bx5QOPGooVEBZWMRD2LQpffu6DD2g7YGb0TzzKeYZLvJKzsu7Lckl3Oga+/BgIDxfdHj4q8/5VkVyoVbTVCQ4G6dUUx77JllOwSUrlcT0hIMFf/wiCEkCpFpVKxhIQEcwDX87ufZnjLUoMGom3EpEmifdmwYaI2NSwMaNu2zJ+Oc44tUVvw66VfcST2CMwNzbG4+2KM8xkHkxplukjSK1QqMYkdFiYWo/vlF1Gz+5KHD4FPPhFjYmUldho7VvQ3JoRUKgqFYmx8fPzq+Pj4JqDJEEJI1aMCcF2hUIzN7066aK28KJWiV++nnwLPnok1i7/+GvDxKdVhcxQ56LWxF+4l34O5kTki4yPhYuGCwV6DMbX11FIt+Vtc58+LigSpVJQv/PyzmOR+4elTYNGi/xbpmD4d+OijEqz4QQjJT3letEYIIdUZ/RVfXiQSMZt5965YTOHsWdF+KyRE9J19TdMOTMM/9/5B47qNAQC/9v0VNyffxNdBX5d7sqtSia4LbduKMtzffxcT2C+S3bg4kdw6OoqENzQUuHlTLM1MyS4hhBBCdIRmeCtKaiqweLFIBGUyoFs3kRx265ZvK7MseRbG7hkLMwMz+DXww6qLq3D92XVkyDMwu+1sLOy6sELD5xx47z3RR3f4cNFk4UUJ7u3bwNKl4k6FQuzwySeAm1uFxkhIdUczvIQQ8noo4a1omka1P/0kZkQ9PYFp04ChQwETE8TJ4iDLleGjQx9hZ/ROGOobIluRDTdLN/R27Q1XC1eM8xkHfb2KqYONjRUT1FFRwMmTokLjm28gSjb27xf1DAcOiLrckSNFoutcNq3OCCEvo4SXEEJeDyW8upKbC2zeLBasiIxEVm1TfPmuIxaZ34BS3VFjSY8lGNFsBKITo+HXwA8SPUm5h8X5fxPOR4+KqoSsLNF9LSQE+GRoLNgfG8VsbmwsYGsrpn7HjQPq1y/3+Ah5k1HCSwghr4cul9cVAwNgxAhg+HDwEycwbN9I7DC5jtGXgE7pdWHVtgu6S9oChuZoY9+mQkJKShLdw2rVArp2FdfYuboCu5Y/htv17SJB/+yU2DkwULRoGDAgn2XUCCGEEEIqj1IlvIyxQQC+BOABwI9z/oZP2xZPbEospkZMhY2pDTo7dcYddgc7TO7ju8B5mOnSEFi3Dpi/Bfhmk5hB7d0bCAoSSWY5zaLm5IgZ3Js3AfNaKpw6pYc+Lv9ig/5Y1Ao6LXby8hIXoA0ZAjRqVC5xEEIIIYSUtVKVNDDGPCD6nq0EMLO4Ce+bWNKg4iocjDmI51nP8dGhj5CSnQIAkOXKAAA9XHpg39B90GPqlgeJiaJGds8eUSMrE/vB1RVo1Qpo2VLc3NxEEqz3mg03kpOxa3UCpn9ng7sJtbDB6XP0vr8cJ5Wt0VNyEHptWwP9+wN9+9JFaIToGJU0EELI6ymTGl7G2FFQwpuv5KxkPM96jukHpmPPrT0AgLomdXFwxEF4Wnni+rPriEmKQTfnbjA3KmDlMYUCiIwURbUnTgCXLgGPHv13v7GxaAVWv75Y4MHKCjAxAQwNRemEQiGmcLOyRN1CQoLolRsbi5ik2nBHNNwRje9NvkB3/xTA3x/o1En0H3tlNQlCiK5QwksIIa+nwhJexth4AOMBwMHBwef+/fulft7K6MzDMxi1cxTsatkhITMB15+JFe709fQR1iUM3V26w66WHWoZlrIv7bNnop/vnTuiLdjduyKJTUgQt6wscWGchr6+SIAtLf9Lihs1wojzH2DbdTfcPfYINv4N822RRgipHCjhJYSQ11NkwssYOwTAJp+7PuWc71LvcxQ0w4uU7BR4r/CGXCmHvbk9ahrURFenrrA2tYavrS+a1WtWsQFxDsjlItnVKnm4exeYOFHktn//DcyaBSys2La+hJDXQAkvIYS8niIvWuOcd6mIQKq6LHkWRuwYgSeyJzj57kn42/nrOiSR0RoYvLRJ02pMqQTq1RPXxM2erZvwCCGEEEIqAi0tXAbiZHEIXBuIfbf2YUmPJZUj2c1DpRJrRHTtKqoZzp8HoqNFKbClpa6jI4QQQggpP6VtSxYMYBkAKwD7GGORnPPuZRJZJcQ5x4GYA5h/Yj5SslNgb26PoEZB+PHsj0jJTsGOt3egv3t/XYf5khMngFOngI0bgWvXgB49gE2btJYFJoQQQgip5kqV8HLOdwDYUUaxVFpKlRK7bu7CwlMLcf7xeTSq3Qje9bwRlRCF/bf3w76WPU6OPonmNs11HepLdu4EgoPF956ewIYNwNtvA5LyX7CNEEIIIaTSoJXWivDX7b8wNWIqbifdhnMdZ/zS+xeMbjEaBhIDcM5x6/kt1DerX/quC2UsIUGs+NuiBfDPP0Dt2rqOiBBCCCFENyjhLQDnHIvOLMLsg7PhaeWJLaFbEOIRAonef9OjjDE0rttYh1G+SqUSM7lffw2kpACHD1OySwghhJA3GyW8WjjnOP1QLKO75vIa/Bb5G0I9Q7G2/1qYGpjqOLrCcQ6cPg3MnAmcPQt4e4tF2po00XVkhBBCCCG69UYmvBm5Gfj8yOc48eAEHGs7YkWfFbAwtsAPZ37AzIMzX+z3ZeCX+Dzw8/+W+62kjh0DJk0CbtwQHRjWrQOGD6c1JAghhBBCgDc04f35ws/48eyPCGwYiJ3ROyF9IoVfAz9sjtqMUM9QjG4+GnWM66C1XWtdh1qk774DPvoIcHICVq8G3noLMDPTdVSEEEIIIZXHG5fw5ipzseTcEnR27IxDIw/h9MPTmLx/Ms4+OotQz1D8Hvw7jPSNdB1moZRKIDNTtBebPVskuWvWADVr6joyQgghhJDKp1onvEfuHcHUiKlYH7IenHN8fPhj1DaqjSeyJwjvFw4AaGvfFpfeu6TjSIsvPR1o1w64elX83KMHsH49UKOGbuMihBBCCKmsqm3Cq+IqTI2YimvPrqH/pv7IVmQjLScNmfJMNLdpjm7O3XQd4mv54AOxgMQnn4jShfffp2SXEEIIIaQw1SLhfZD6AHOOzMGluEtoWq8pJreajMj4SFx7dg2z2s7C0nNLYVLDBBfGXYBJDROY1jAFq4JXdP30E7B2LfD558DcubqOhhBCCCGkamCc8wp/Ul9fXy6VSsvseMGbg3HgzgG0b9gepx+eRnpuOgCghU0LSMdLcSnuEswMzCpdz9yiHDwolgBu3hxYuhSYNQvo1w/Ytg3QrxZ/qhBCSoIxdpFz7qvrOAghpKqp8mlTdGI0dkXvwucdPsdXnb5CUlYSDt89jLScNHRy7AQ9pgdf26r3++HCBaB7d9Ff18wMkMlEsrt1KyW7hBBCCCElUaVTp2xFNuafmA9DfUNM9psMALAwtsAgr0E6juz1RUYCenpiWWAbGzGre/Gi6KvbvTv11iWEEEIIKakql/ByznE5/jK+PfktdkbvhEKlwORWk2FlaqXr0ErtwgWgTRvRdgwAtmwBBlXd3J0QQgghpFKoUgnv/BPzsfjsYiRkJsDMwAwf+H2AAIcA9HXrq+vQSi0rCxg5EqhfH5g3D1AogNBQXUdFCCGEEFL1VamE18rECj1de6K9Q3uEeITAwthC1yGVmU8/BaKjxYVqXbroOhpCCCGEkOqjWnRpqGoyMoCZM8UKaZ06AceOia8TJwI//6zr6AghlRV1aSCEkNejp+sA3kQffwysWCFmckNDReLr7AyEhek6MkIIIYSQ6qdKlTRUBwcPAsuWAePGATk5wN9/A97eItk1NdV1dIQQQggh1Q8lvBUkOxv48ENg1SrA1RX48UdKcAkhhBBCKgKVNFQAuVyULaxcCUydCpw/T8kuIYQQQkhFoRnecnD1KvDvv0BsLHDnDnDiBHDzJrB8ubgwjRBCCCGEVBxKeMvYpk3AkCH//Vy3LtCypWg7NmKE7uIihBBCCHlTUcJbhuRykdg2bw78/jvQsCFgZqbrqAghhBBC3myU8Jah8HDg7l1g/36gSRNdR0MIIYQQQgC6aK3MXLoE/O9/QEAA0KOHrqMhhBBCCCEalPC+JpUKSE4W31+8CHTrBtSuDWzcCDCm29gIIYQQQsh/KOF9DY8eAZ07AxYWQFCQmNU1NQUOHQLs7XUdHSGEEEII0UYJbwlt2wY0awZcuABMmiRakPn7i59dXHQdHSGEEEIIyYsS3mL6808gMBAIDQWcnYHLl4Gffwbi44EjRwBra11HSAghhBBC8kMJbzFs3QoMGgTExQFhYcCpU2J5YADQ16eaXUIIIYSQyozakhXh+nXg3XeBNm2Ao0cBAwNdR0QIIYQQQkqCZngLceqUKGMwMxOzvJTsEkIIIYRUPZTwFiA6GujaFbC0BE6eBBo00HVEhBBCCCHkdVBJg5asLGD2bKBjR+D77wFjY+DYMaB+fV1HRgghhBBCXlepEl7G2HcA+gLIBRAD4F3OeUpZBFbeOAcmTwaePgX++AOoUQOYPx/46SdxA8QiEpTsEkIIIYRUbaWd4T0I4GPOuYIxthDAxwD+V/qwyl94OLB8ufh+xgxg6FDRgWHIELGYRGIiMHiwbmMkhBBCCCGlxzjnZXMgxoIBhHLOhxW1r6+vL5dKpWXyvK8jNhbw8hKdF5o0AZYsEdvNzUXtro2NzkIjhJACMcYucs59dR0HIYRUNWVZwzsawOYyPF65+eknIDcX+O03UbLQsiWgVAIdOlCySwghhBBS3RSZ8DLGDgHILw38lHO+S73PpwAUADYUcpzxAMYDgIODw2sFWxayskQ5Q3AwYG8vto0cqbNwCCGEEEJIOSsy4eWcdynsfsbYKAB9AHTmhdRHcM5XAVgFiJKGEsb5WmQy0T932DBATw/45x/g9GkgORl4//2KiIAQQgghhOhaabs09IC4SC2Qc55ZNiGVnbAw4JtvgP37RQnDnj1ie5MmonyBEEIIIYRUf6Wt4f0JgCGAg4wxADjLOZ9Q6qjKgFwOrF4tanS3bRPbvv8e8PYGGjcGRLiEEEIIIaS6K1XCyzl3KatAykJsLGBtDZiYALt3A/HxwN69oteuhQUwYICuIySEEEIIIRWtWqy0plSKRSO++gpo0QLYvl2UMzg4AD16ABKJriMkhBBCCCG6Ui0S3jlzRMLbvTtw+DDg6Ci2r11LyS4hhBBCyJtOT9cBlFZMjKjNHT4c+OsvsUxwmzbAyZNiGyGEEEIIebNV+RnemTOBGjWAhQvFhWihoeJGCCGEEEIIUMUT3tWrgZ07gW+/BWxtdR0NIYQQQgipjKpsSYNUCkyeDHTrBsyapetoCCGEEEJIZVWlZnhv3BBLA5ubA336ADY2wIYNdGEaIYQQQggpWJWa4f3+e8DXF3BzEwtLREQAdevqOipCCCGEEFKZVakZ3gULgKAg4PhxYNw4wN1d1xERQgghhJDKrkolvNbWotUYtRsjhBBCCCHFVaVKGgghhBBCCCkpSngJIYQQQki1RgkvIYQQQgip1ijhJYQQQggh1RolvIQQQgghpFqjhJcQQgghhFRrlPASQgghhJBqjRJeQgghhBBSrTHOecU/KWMJAO6/5sPrAkgsw3DKSmWNC6i8sVFcJVNZ4wIqb2zVLa6GnHOrsg6GEEKqO50kvKXBGJNyzn11HUdelTUuoPLGRnGVTGWNC6i8sVFchBBCACppIIQQQggh1RwlvIQQQgghpFqrignvKl0HUIDKGhdQeWOjuEqmssYFVN7YKC5CCCFVr4aXEEIIIYSQkqiKM7yEEEIIIYQUW6VMeBljgxhjUYwxFWOswCuZGWM9GGM3GWN3GGMfaW13ZIydY4zdZoxtZowZlFFcFoyxg+rjHmSM1clnn06MsUitWzZjbID6vrWMsXta9zUvi7iKG5t6P6XW8+/W2q7LMWvOGDujfs2vMsbe1rqvTMesoPeM1v2G6vO/ox6PRlr3fazefpMx1r00cbxGXNMZYzfU43OYMdZQ6758X9MKiusdxliC1vOP1bpvlPp1v80YG1XBcf2oFdMtxliK1n3lOV7hjLFnjLHrBdzPGGNL1XFfZYy11Lqv3MaLEELeeJzzSncD4AGgMYCjAHwL2EcCIAaAEwADAFcAeKrv2wJgsPr7FQAmllFcYQA+Un//EYCFRexvASAJgIn657UAQstpzIoVG4D0ArbrbMwAuAFwVX9vCyAOQO2yHrPC3jNa+0wCsEL9/WAAm9Xfe6r3NwTgqD6OpALj6qT1Ppqoiauw17SC4noHwE/5PNYCwF311zrq7+tUVFx59v8AQHh5j5f62B0AtARwvYD7ewH4CwAD0BrAufIeL7rRjW50oxuvnDO8nPN/Oec3i9jND8AdzvldznkugE0A+jPGGIAgAH+q9/s/AAPKKLT+6uMV97ihAP7inGeW0fMXpqSxvaDrMeOc3+Kc31Z//wTAMwDl0Vw/3/dMIfH+CaCzenz6A9jEOc/hnN8DcEd9vAqJi3N+ROt9dBaAXRk9d6niKkR3AAc550mc82QABwH00FFcQwD8UUbPXSjO+XGIP3IL0h/AOi6cBVCbMVYf5TtehBDyxquUCW8xNQDwUOvnR+ptlgBSOOeKPNvLQj3OeRwAqL9aF7H/YLz6i3ae+qPMHxljhmUUV0liM2KMSRljZzWlFqhEY8YY84OYtYvR2lxWY1bQeybffdTjkQoxPsV5bHnGpW0MxCyhRn6vaUXGNVD9+vzJGLMv4WPLMy6oSz8cAfyjtbm8xqs4Coq9PMeLEELeePq6emLG2CEANvnc9SnnfFdxDpHPNl7I9lLHVdxjqI9TH0BTAAe0Nn8MIB4ioVsF4H8A5lZwbA6c8yeMMScA/zDGrgFIy2c/XY3Z7wBGcc5V6s2lGrO8T5HPtrznWS7vqyIU+9iMseEAfAEEam1+5TXlnMfk9/hyiGsPgD845zmMsQkQs+NBxXxsecalMRjAn5xzpda28hqv4tDF+4sQQt54Okt4OeddSnmIRwDstX62A/AEYn362owxffUMnWZ7qeNijD1ljNXnnMepk7NnhRzqLQA7OOdyrWPHqb/NYYz9BmBmceMqq9jUJQPgnN9ljB0F0ALANuh4zBhjtQDsA/CZ+qNezbFLNWZ5FPSeyW+fR4wxfQDmEB9RF+ex5RkXGGNdIP6ICOSc52i2F/CalkUCV2RcnPPnWj/+CmCh1mM75nns0TKIqVhxaRkM4H3tDeU4XsVRUOzlOV6EEPLGq8olDRcAuDLRXcAA4hfbbs45B3AEon4WAEYBKM6McXHsVh+vOMd9pW5QnfBpamYHAMj3Su7yio0xVkdTEsAYqwugHYAbuh4z9eu3A6K2cWue+8pyzPJ9zxQSbyiAf9TjsxvAYCa6ODgCcAVwvhSxlCguxlgLACsB9OOcP9Panu9rWoFx1df6sR+Af9XfHwDQTR1fHQDd8PKnHeUalzq2xhAXgJ3R2lae41UcuwGMVHdraA0gVf1HXXmOFyGEEF1fNZffDUAwxIxHDoCnAA6ot9sC2K+1Xy8AtyBmZz7V2u4EkYzcAbAVgGEZxWUJ4DCA2+qvFurtvgBWa+3XCMBjAHp5Hv8PgGsQSdt6ADXLcMyKjA1AW/XzX1F/HVMZxgzAcAByAJFat+blMWb5vWcgSiT6qb83Up//HfV4OGk99lP1424C6FnG7/mi4jqk/regGZ/dRb2mFRTXtwCi1M9/BIC71mNHq8fxDoB3KzIu9c9fAliQ53HlPV5/QHQZkUP8HzYGwAQAE9T3MwA/q+O+Bq0uNOU5XnSjG93o9qbfaKU1QgghhBBSrVXlkgZCCCGEEEKKRAkvIYQQQgip1ijhJYQQQggh1RolvIQQQgghpFqjhJcQQgghhFRrlPASQgghhJBqjRJeQgghhBBSrVHCSwghhBBCqrX/B3fKRm9fPNcoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('------ Hypothesis set: h(x) = ax ------')\n",
    "calc_bias_var_eout(gd_funcb, lambda x: np.sin(math.pi*x), num_data_samples, num_x_samples)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------ Hypothesis set: h(x) = b ------\n",
      "The variance is:  0.2493902010400458\n",
      "The bias is:  0.4840971440072216\n",
      "The expected out-of-sample error is:  0.7338247229043513\n",
      "The variance+bias is:  0.7334873450472674\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('------ Hypothesis set: h(x) = b ------')\n",
    "calc_bias_var_eout(gd_funcc, lambda x: np.sin(math.pi*x), num_data_samples, num_x_samples) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 2.24\n",
    "\n",
    "* To find the average function $\\bar{g}(x)$, let's find the final hypothesis that learing algorithm will arrive. We have our target function $E_{in}(g) = \\sum^2_{i=1} \\left[f(x_i) - h(x_i)\\right]^2 = \\sum^2_{i=1} \\left[x_i^2 - (ax_i+b)\\right]^2$. Take derivative w.r.t. $a$ and $b$ and set the derivatives to zero. We have\n",
    "\n",
    "\\begin{align*}\n",
    "\\frac{\\partial E_{in}(g)}{\\partial a} &= -2\\sum^{2}_{i=1} x_i(x_i^2 - ax_i-b) = 0\\\\\n",
    "\\frac{\\partial E_{in}(g)}{\\partial b} &= -2\\sum^{2}_{i=1} (x_i^2 - ax_i-b) = 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Multiply the second equation by $x_1$ and $x_2$ respectively, and subtract from the first equation, we have:\n",
    "\n",
    "\\begin{align*}\n",
    "x^2_1 - ax_1 - b &= 0\\\\\n",
    "x^2_2 - ax_2 - b &= 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Solve the equations we have:\n",
    "\n",
    "\\begin{align*}\n",
    "a &= x_1 + x_2\\\\\n",
    "b &= -x_1x_2\\\\\n",
    "\\end{align*}\n",
    "\n",
    "So the final hypothesis learning algorithm find is: $g^{\\mathcal{D}}(x) = (x_1 + x_2)x -x_1x_2$.\n",
    "\n",
    "* Now let's compute the average function $\\bar{g}(x)$.\n",
    "\n",
    "\\begin{align*}\n",
    "\\bar{g}(x) &= E_{\\mathcal{D}}\\left[g^{\\mathcal{D}}(x)\\right]\\\\\n",
    "&= E_{\\mathcal{D}}\\left[(x_1 + x_2)x -x_1x_2\\right]\\\\\n",
    "&= E_{\\mathcal{D}}[x_1x] + E_{\\mathcal{D}}[x_2x] -E_{\\mathcal{D}}[x_1x_2]\\\\\n",
    "&= E_{\\mathcal{D}}[x_1]x + E_{\\mathcal{D}}[x_2]x -E_{\\mathcal{D}}[x_1]E_{\\mathcal{D}}[x_2]\\\\\n",
    "\\end{align*}\n",
    "\n",
    "The last step is due to the independence of points $x_1$ and $x_2$. \n",
    "\n",
    "Since the data follows a uniform distribution in the interval $[-1,1]$, we have following moments for $x_1$ and $x_2$: \n",
    "\n",
    "\\begin{align*}\n",
    "E_{\\mathcal{D}}[x] &= 0\\\\\n",
    "E_{\\mathcal{D}}[x^2] &= \\frac{1}{3}\\\\\n",
    "E_{\\mathcal{D}}[x^3] &= 0\\\\\n",
    "E_{\\mathcal{D}}[x^4] &= \\frac{1}{5}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "Take this results into the above equation, we have\n",
    "\n",
    "\\begin{align*}\n",
    "\\bar{g}(x) &= 0\\\\\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "* Let's compute the variance component\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{variance} &= E_x\\left[E_{\\mathcal{D}}\\left[(g^{\\mathcal{D}}(x) - \\bar{g}(x))^2\\right]\\right]\\\\\n",
    "&= E_x\\left[E_{\\mathcal{D}}\\left((x_1 + x_2)x -x_1x_2 -0\\right)^2\\right]\\\\\n",
    "&= E_x\\left[E_{\\mathcal{D}}\\left((x_1 + x_2)x -x_1x_2 \\right)^2\\right]\\\\\n",
    "&= E_x\\left[E_{\\mathcal{D}}\\left((x_1 + x_2)^2x^2 + x_1^2x_2^2 -2x_1x_2(x_1+x_2)x\\right)\\right]\\\\\n",
    "&= E_x\\left[x^2E_{\\mathcal{D}}(x_1^2 + x_2^2+2x_1x_2) + E_{\\mathcal{D}}(x_1^2x_2^2) - 2xE_{\\mathcal{D}}(x_1^2x_2+x_1x_2^2)\\right]\\\\\n",
    "\\end{align*}\n",
    "\n",
    "We know $x_1$, $x_2$ are independent, take their moments into above equation, we get\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{variance} &= E_x\\left[x^2(\\frac{1}{3} + \\frac{1}{3}) + (\\frac{1}{3}\\frac{1}{3})\\right]\\\\\n",
    "&=E_x\\left[\\frac{2}{3}x^2 + \\frac{1}{9}\\right]\\\\\n",
    "&= \\frac{2}{3}\\frac{1}{3} + \\frac{1}{9}\\\\\n",
    "&=\\frac{1}{3}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "* Let's compute the bias component\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{bias} &= E_x\\left[(\\bar{g}(x) - f(x))^2\\right]\\\\\n",
    "&= E_x\\left[(0 - x^2)^2\\right]\\\\\n",
    "&= E_x\\left[x^4\\right]\\\\\n",
    "&= \\frac{1}{5}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "* Let's compute the out-of-sample error\n",
    "\n",
    "\\begin{align*}\n",
    "E_{\\mathcal{D}}\\left[E_{out}(g^{\\mathcal{D}})\\right] &= \\text{variance}+\\text{bias}\\\\\n",
    "&= \\frac{1}{3} + \\frac{1}{5}\\\\\n",
    "&= \\frac{8}{15}\\\\\n",
    "\\end{align*}\n",
    "\n",
    "* Procedure to run the experiment\n",
    "\n",
    "1. To calculate $\\bar{g}(x)$\n",
    "  * Fix a $x$\n",
    "  * Do following for a number of times, e.g. 1000\n",
    "    * Sample two data points from a uniform distribution on $[-1,1]$.\n",
    "    * Compute the value of $g^{\\mathcal{D}}(x)$ at $x$ using the coefficients $a$ and $b$ derived above (or you can find the best fit through some linear regression library, and then compute the value of the best fit at point $x$)\n",
    "   * Take the average value of function $g^{\\mathcal{D}}(x)$. This is the value of $\\bar{g}(x)$ at $x$. \n",
    "   \n",
    "1. To compute bias, variance and out-of-sample error\n",
    "  * Do following for a number of times, e.g. 5000\n",
    "    * Sample a $x$ from uniform distribution on $[-1,1]$.\n",
    "    * Follow the procedure to calculate $\\bar{g}(x)$ to generate an array of values of function $g^{\\mathcal{D}}(x)$ evaluated at the given $x$.\n",
    "    * Compute the variance of the values, we get $E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x)-\\bar{g}(x)\\right)^2\\right]$\n",
    "    * Use the $\\bar{g}(x)$ to compute $\\left[\\left(\\bar{g}(x) -f(x)\\right)^2\\right]$ at each $x$\n",
    "    * Use the array of values to compute an array of $\\left(g^\\mathcal{D}(x) - f(x)\\right)^2$. Take the average of the resulting array, we have $E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x) - f(x)\\right)^2\\right]$\n",
    "  * Now take the average of above calculated $E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x)-\\bar{g}(x)\\right)^2\\right]$,     $\\left[\\left(\\bar{g}(x) -f(x)\\right)^2\\right]$, $E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x) - f(x)\\right)^2\\right]$ we obtain the expected values of variance, bias and out-of-sample error: \n",
    "  \n",
    "  $E_x\\left[E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x)-\\bar{g}(x)\\right)^2\\right]\\right]$,     $E_x\\left[\\left[\\left(\\bar{g}(x) -f(x)\\right)^2\\right]\\right]$, $E_x\\left[E_\\mathcal{D}\\left[\\left(g^\\mathcal{D}(x) - f(x)\\right)^2\\right]\\right]$\n",
    "  \n",
    "\n",
    "* The following code shows how to compute the bias, variance, out-of-sample error respectively. \n",
    "  * You can see that the calculated values are close to analytical results.\n",
    "  * The bias+variance is close to the value calculated directly for out-of-sample error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variance is:  0.32930656143125864\n",
      "The bias is:  0.19668934099203592\n",
      "The expected out-of-sample error is:  0.525192493981031\n",
      "The variance+bias is:  0.5259959024232945\n"
     ]
    },
    {
     "data": {
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EX0LCW+1uyBBASwv4+2+6n5VFuZczZgA7dqihvYyVYD4+1OkbE0P3t26lYPm332jA7Jw5QKVKwMcfv8VB4uJo5pI7d6ibuoQEy4wxxgqPe5jflT17gB49aASflxdgYlLoXXXuTIORTpwApkyhQYIAlaCLjn6NQUqMvac6dQL27QN69wa2bKHz1bQ0GuCnUgGenlTvvHnzQh4gMZFKR169SsFymzZqbX9R4x5mxhgrHHVMjc1eR+fO9A3euzd1bx048Nxcuq9v1CigXTvKZ9bSovkRatUCWrQAtm8HMjMpx3n5csDcPP99SEnTcReyCYwVO9HR9G9lZUU9yzo6NHBv3jxar6sL9Ov3FgdISaHi6Zcv0+WcEhYsM8YYKzzuYX7Xtm6lb+3mzakrzMioULvx9QX8/ChobtyYAmBHRyr/evMm9arZ2QETJ1JQffo01XjO7VlbtYoGO9269fKgmrHiLCuLTgyPHaNMJ0NDYMkSGms7aRJNOlK+PP3tW1i85cFSUqj7+vhxyoHq3Vstz+Fd4x5mxhgrHA6YNWHDBuDTTykPcvfuZ+fPfgs//wz88ANle6xeDYweTTVnAaqyUbo0BdrVqgEuLsC1a/Td36ePWg7PWJHIzKSrKJ0700kgAJw9C3z2GRAcTIGytjZVwmjShCYCUqu8wfKaNfS/W0JxwMwYY4XDg/40YcAAYOVKmtKvRw+1Td83cCAFD7Nn027v3AEiImi8YXAwbdO1K122vnaN7h89qpZDM1Zk9u0DJkygqyM3b1IVtz596N9m2zaaH+jWLZp0ZP58NR88OfnpHPZr15boYJkxxljhcQ+zJi1fDnz5JdChAyUfq6GnOSXl5VkeR47Qd79KRYF1w4ZUni4s7K0Py1iR6dABuHSJepoBKnfs40M9yY0bF+GBc4NlHx8KlgcMKMKDvRvcw8wYY4XDPcyaNGwYsGwZJWJ27kzR7lsqKCW6TRvqrdPXp8vZXbpQz9ytW299WMbUZvx4KnF8/z5NCe/lReeVPj5A3bo0R8ioUe8wWF637r0IlhljjBUe9zAXB2vWAJ9/Ttec9+4FjI2L9HBxcZTnHBICKJV0GXvcOBocyJgmJSbSAL20NJqRr0wZSh8KDweqVqVtbt2iShja2kXUiORkqmRz8iTNnf1WpTWKF+5hZoyxwuEQqTj47DMaCHjyJNWLe8vJTV6lbFkqseXsTIHHhAkUo9vYADNnFumhGXuGSkVXPVQqur9jBwXLv/9Of6f6+nRClxssAzRotciC5YQEmmDoPQyWGWOMFR7XYS4u+vWj6KBPH6qecfDgW0+j/SpCUMmto0dpHgY/P2DaNCAjgw7v4EBxPGNFZdEiKn04diywcCH9vVWvThVexox5x42JiaFg+do1qpneq9c7bgBjjLHiSi09zEIIDyFEkBDiphBiaj7rPxNCxAghruTchuZZN0gIEZJzG6SO9pRYPXpQF9vVq0CrVkBsbJEfskoVYNAgYMECyhX96CMqT3flCrBxI038wNjbOH6cqrU8LyODpqw2NKQe5T59qKbygAF0MvdO3b1LKVEBAVTqkYNlxhhjebx1wCyE0AbwJ4D2ABQA+gohFPlsulVKWTvn9nfOY8sC+BFAAwD1AfwohCjabtXirlMn+sIODKSRT5GR7+zQOjo0dfDixVS+q3x56nFOTQVu36Ye6BKY8s40KCaGTsJatXox02jzZopTt22jAaiHDgGtWwNfffWOGxkWBri7Ux1GLy+gfft33ADGGGPFnTp6mOsDuCmlDJNSZgDYAqDLaz62HYDDUso4KeUjAIcBeKihTSWbhwd9cd+9SzMxBAa+s0ObmlIFAisrYMoUCmKMjGgAlosL5TsnJgJz5tCkhUeP0rI//uDydOxFW7fSjHzh4UD//vT3Eh9PWQ/ffktTun/8MbBrFw1GPXwYqFjxHTYwIICC5YQEalzuVJiMMcZYHurIYbYEkLcb9A6ox/h5PYQQzQAEAxgvpYx8yWMt8zuIEGIYgGEAYGVlpYZmF3PNmwMnTlDw3LQpzTZSr947bcLo0XRpXKWiAVjnz9Ml9E2bqORXLh0dqpE7ejRNz718OXWOM7ZhA51oDR5MlVj276dqLHp69De1fr0G0i9yXbpEg2x1dKhWXY0aGmoIY4yx4k4dPcz5fd09f+F+LwAbKWUtAEcArH2Dx9JCKZdLKetKKeuam5sXurEliqsrjcorXRpo2ZJmHnmH9PWp93jq1Kclozt3pmDH25tK1O7cSZ1zwcGUh5qaCgwfTr2K7MMWEkInWQMG0KC+e/foT/j772mM67lz1MOsEYcP00lpqVJUEYODZcYYYwVQRw/zHQB5ij6hCoCovBtIKR/mubsCwJw8j23x3GNPqKFN7w87Owqa27WjKc82btTYgCQdHbp0np39Ylkve3u6VawI9O5Neanu7tSLWNBkKuz9kZFBPcgPH1KQPHky9Sb37UvrK1akW+vWmm0n1q+nuucKBV25qVxZww1ijDFW3Kmjh/kCAHshRDUhhB6APgD25N1ACFEpz93OAG7k/H4QQFshhFnOYL+2OctYXpUqUZdu/foUjS5ZorGmCFFwDdyePamzbtAgqp1buTKVDUtOpokMz57lgYMl0Z07T9+3+PgX18fEUBnC7t2BL76g937XLqq+YplvkpUGSEnJ959+SmdzPj4cLDPGGHstbx0wSykzAYwCBbo3AGyTUvoLIWYIITrnbDZGCOEvhLgKYAyAz3IeGwdgJijovgBgRs4y9jwzMxqB17EjMHIkdd9lZ2u6VS/Q0qIqG+3aAb/+SgUHFiyg9GuFgqYzXrny2cfExtIAw5gYzbSZFWzrVgqABwyg9BwzM2DSJPrzu3GDepYnTaIxqjt3Atu3UzrP1KmUilEsZGVRYeepU6nL+8ABGuHKGGOMvQaeGrukycykKGTJEurOXbeOCtkWY0ePUs6quTmlY1+5QvNCODrSbcgQYNUq4MsvgaVLNd1alldcHM0IqasLREVRJ62rK3D5MqVXREdTD/LduxSL/vILPU5KDQ7me15aGkX727dTUv7cuR/sPPA8NTZjjBUOB8wlkZRUrmLiRKBBA2DPHopGi7H0dAq6HjwAatd+WmWjUydg716gQgXKfb1xg3KhmebEx1MZuOhoii19fABfXxrcmZhIFzm+/ZYG7XXuTPnqiYnAhQvFMF89Jgbo1o3GASxYAIwfr+kWaRQHzIwxVjgcMJdkO3ZQcdvKlYF//6Xu2hIgJoYmMzx+HJg9m3oqfXyo/JibG43J+hAqBxYHiYn0p1OrFqVdHDtGJeAePaL1ZcoAM2dSbe4Sx9+fovvoaGDtWuCTTzTdIo3jgJkxxgqHA+aS7vx56qbNzKRRViWsALKfH+W7OjpSWsbIkXQpf98+mh3ueVJS6bpi15NZgiQlUQlid3fqId6//9n1deoA33wDGBtT5bVinvGTvwMHaIBsqVI0c2b9+ppuUbHAATNjjBUOB8zvg7AwKjkXFgb8+SeVKSihbt+mAYOJiZRpsmkTDS5r1Ig6CL/6is4LAgOp95O9nhs3qAbyyJFUyWL3bhqEGRAA/PQTzeT48CEFyYMG0UlMiSQlsGgR8PXX1G2+Zw91nTMAHDAzxlhhccD8voiPp9H/Xl4UFf32GyUNl0CXL1NqtkpFk6To6lJZun79KIAGgJ9/Br77juKjdetoeycnzba7OMj9d8474E5KOuE4f56qlJw5QxcljhyhjIWtW4vRAL23oVLRdJPLlgFdu1Juj7GxpltVrHDAzBhjhfNhDhV/H5UpQ3kMkyZRL/NHH5XYOm2ursDff9OMgaGhdC7QowcFyzVr0lNbuJDybEeMAD77jAqGZGZquuXvXkoK/YyPp8kgTU3pNbp58+k2R45QsNyoEQXL9epR+nt0NLB583sSLMfG0jTyy5ZRuY7t2zlYZowxpjbcw/w+2rgRGDoUsLCg/IXatTXdoreWkQHMm0eTHN6/T/m3uTw8nnasHzpEAeAXX1BqwblzwOrVlH5gakpx1VdfAdWqae65vI3UVErP7dSJCj+0bUuzPIeE0HMePJiyEISg+TksLakH/uFDCqL37qXAudhMJqIOvr50RnX/PgXMgwZpukXFFvcwM8ZY4XDA/L7y9aVyWnFxFDG+ZxUCFi2iXlVXV0oraN2aqm7Y2ABVqgCnTtGMhFlZT0vWZWVR+V1jYxpg2KOHpp/Fm5GSsm62bqVBeYcOARcv0lv76BGlsIeE0G3IEPoTSEujKc3XrKGCKu+dVavoMoOFBXWbu7lpukXFGgfMjDFWSFLKEndzc3OT7DXcuydl48ZSAlKOHStlerqmW1RkQkOl/PZbKePi6L6/v5RTpkj5++/0tJOSaN2tW1I2bCilEFKuWfPifjIzpZwzR8qQkKJra2amlCkpzy4LD5dy2DB6ux4+lPLCBSlHjZIyNVXK7GwpDx+m9YCUDg70E5DSyUlKXV0ptbWl/OabF4/z6NF7+ranpT19Qdq0kTImRtMtKhEA+Mpi8BnON77xjW8l7abxBhTmxgHzG0hPl3LMGHqrGzSQMiJC0y3SuORkirGEkHLECCnv33+6bt48eqnq1aOAMzRUyu++k/KTT6Q8eJCCVymlzMqi3x89krJLFylHj6Zl+cnKknLkSNouK0vKL7+U0sqKgmEpKUA2M5NST09KHR0pPTykrFSJ2rFkiZRz58onAfKQIVImJkppby+lm5uUfn5P112+XLSvW7Fx+7aU9evTk/7mG3qj2GvhgJlvfOMb3wp303gDCnPjgLkQPD2lNDGRsmxZKffv13RrNC4lhYJlbW0pLS2ljIyUMjBQSgMDKW1t6T+jY0fqvdXSopcNkLJ/f9rWzk7KqlWlrF6d1gNSDh8uZUbGs8fJzqae4tyg9ttvn26/YgVt87//0f0LF54G7EZGUioU1DYTEyk7dKDgPFdyspSPH9PvTZtST3NuMP9eO3BASnNzKY2Npdy+XdOtKXE4YOYb3/jGt8LdOIf5QxISQuUk/PwoCXbGDEpw/YBdugS0aEGzDcbE0GC569eBgQNp1rtevWhGZXNzYNYsmvXOxITC3+bNKW/4jz+AgwdpGmkrK6rioaUFtGkD/PMP4OkJTJgAeHtTXrGJCW2XmQlcuQLY2gI1alBOcnY28MMPNKhRSiqvratLk9a9bMrwmBgaFPleDeR7XkYG1RGcN4/KgGzbxnUEC6GocpgvXrxYQUdH528ANcDVlxhjJU82gOuZmZlD3dzcHuS3AQfMH5rUVGDMGKrb1rw5sGEDjZL7gHl5UdWJpk2BpUtp1sGHD+m8okWLp2XXpKTzjD/+oGoTLVs+3YeUNGPe/PlAUBC9zPHxFDjPmUMB86lT9JL/9BPg4AD06UM/g4OpDe3aPdsuKSlgr1uXKqV9sMLC6MW6cIFqDc6fX0KnH9S8ogqYr169uqdixYrO5ubmiVpaWiXvS4Ux9kHLzs4WMTExptHR0QEuLi6d89uGA+YP1dq1VF1AX59KcfXqpekWaVR8PJWde52axBkZNKFKQbKyAB8fKo/t6vp0+e3bNPFcVha9/GFhVOJu+fL3pB6yum3dCgwbRmcef/9d8kqbFDNFGDCH1axZ8xEHy4yxkio7O1tcu3bNzMXFxTa/9R/29fgP2aBBNO1b//5Ul+yzz6hWm4mJplumEW8yzfargmWAStrl7YHOZWVFP3V0KEhmL/H4MTB+PAXJjRrRDCvW1ppuFXs5LQ6WGWMlWc5n2EtTyjjX7ENmb0+zX3z/Pc1uUbs2cPasplvFPnSnTgEuLsDKlZQD4+3NwTJ7JW1tbTcnJyeFvb29sn379rZJSUlv9P1mZGTkmt/yHj162KxevdpMPa0kSUlJWi1atLCrVq2a0s7OTjlixIh8RyDs3LmztFKpdHZwcFAolUrnPXv2POnRcHd3t3d0dFTY2dkp+/XrZ5VZwFSn27dvL+3k5KRwcnJSGBkZudrY2NRwcnJSdOvWzUadzwsAxowZU7lChQq1co83evRotY6uWLt2bZnLly8b5N4fPXq05d69ez/Mnh72TqklYBZCeAghgoQQN4UQL2RbCiG+FkIECCH8hBBHhRDWedZlCSGu5Nz2qKM97A3o6tJINm9vyhNwdwcpSrE3AAAgAElEQVSmTwdUKk23jH1o0tJoavdmzSiB+8QJ4H//o79Rxl5BX18/OzAwMCAkJMRfV1dXzp8/3zzv+uzsbGRlZWmqeS+YMGHC/Vu3bvlfv3494Pz588bbtm0r/fw2FSpUUO3fv/9mcHBwwJo1a24NHTr0yRylu3fvDg0KCgoIDg72f/jwoe6qVateGtT36NEjMTAwMCAwMDCgRo0aKevWrQsLDAwM2LlzZ3je7VRq+twfNWpUdO7xFi9efFctO82xY8cOs+vXrz8JmBcvXny3U6dOSeo8BmP5eeuAWQihDeBPAO0BKAD0FUIontvsMoC6UspaAP4BMDfPulQpZe2cW76J1uwdaNoUuHqVppL76SegQQMq4cDYu3DxIs3SN28e8OWXNOKyWTNNt4qVUE2bNn188+ZN/aCgID1bW1vlgAEDrJRKpSI0NFRv2bJlZR0cHBT29vbK4cOHP9P7+cUXX1RRKBTOjRo1coiKinohZfHkyZNG9erVc1Qqlc5Nmza1j4iI0AWA+vXrOw4ZMqRq3bp1HW1tbZXe3t5Gbdu2rW5tbV1jzJgxlZ/fj4mJSXZukGdgYCBr1aqVEhkZ+UKyV5MmTVJtbGxUAODm5paWkZGhlZqaKgCgbNmy2QCgUqmESqUSopCDIBYsWFC+Y8eOti1btrRr3ry5/a5du0zatGlTPXd9v379rJYsWVIWALy9vZ88/2bNmtlHRka+dlqnhYVFrdjYWG0AOHr0aKnGjRs7ANQj/cknn1jXq1fPsUqVKjV/+eWXJyc6v//+ezkHBweFo6OjomfPnjZeXl7GJ06cMJ06dWpVJycnRVBQkF6XLl2qrV+/vgxAPfJOTk4KBwcHRZ8+fazT0tJE7rG//vrrys7OzgoHBweFn5+ffqFeLPZBU0cPc30AN6WUYVLKDABbAHTJu4GU8riUMiXn7jkAH3ZZhuLK1BRYvx7Yvh2IigLq1QOmTQPS0zXdMva+UqnoBK1hQxp56eUF/PUXzV/OWCGoVCocPHiwdM2aNVMBIDw83GDw4MEPb9y4EaCnpyenT59ueeLEieCAgAD/y5cvl8oNtlJTU7Xq1KmTEhAQcKNJkyZJU6dOfSbQTU9PF2PGjLHavXt3qL+//41BgwbFTpw48UnAraenl+3r6xs0ePDgmF69etmtWLHidmBgoP/WrVvLR0dHa7+svbGxsdqHDx8u0759+8SCntfatWvNFApFiqGh4ZNc8aZNm9qbm5u7lCpVKmvw4MGPAGDu3Lnmc+fONX/5nl506dKlUtu2bbt15syZkJdtk5qaKsaNG2e1Z8+eUH9//xt9+/Z9OHny5HzTLf7444+KuSkZu3btemW6RGhoqMHJkyeDz58/f2POnDmWmZmZOHv2rOHChQsrnjx5MigoKCjgzz//jPTw8HjcokWLhNmzZ0cGBgYGODo6ZuTuIykpSWv48OE227dvDw0ODg5ISUnRWrBgQfnc9RYWFqobN24EfPrpp7GzZ8+2eJPXhzFAPYP+LAFE5rl/B0CDArYfAuBAnvsGQghfAJkAZkspd+X3ICHEMADDAMAqd+QUKxrdu1M9tfHjKV1j+3Zg1SrqdWZMXc6epQoY168DAwbQoFMztaaKMk34/POquH7dSK37rFEjBatWRRa0SXp6upaTk5MCABo0aJA0duzY2IiICN1KlSpltG7dOhkATp06Vaphw4ZJlStXzgSA3r17x3l7exsPHDgwXktLC0OHDo2jp/D5w+7du9vl3b+fn59+SEiIYatWrRwASvEwNzd/ksPQrVu3eABwcXFJtbOzS7W2tlYBQNWqVdPDwsL0KlasmPp8m1UqFbp37247bNiw+wqFIuP59bl8fX0Npk2bZunl5fVMQHvq1KmQlJQU0a1bN9u9e/eW7tatW+LkyZNjCnqd8tOsWbNEc3PzAvNVLl++bHDz5k2Dli1bPnn+FStWzDeHY9SoUdHTpk3Lt5Ztfjw8PBIMDAykpaVlpqmpaWZUVJTOoUOHTLp27frIwsIiCwByf77MlStXDGxsbNKUSmU6AAwaNOjhypUrywOIAYB+/fo9AoD69esnHzx40PR128ZYLnUEzPldB8p3tLQQYgCAugCa51lsJaWMEkLYAjgmhLgmpQx9YYdSLgewHKCycm/fbFagsmWp9FyfPhTUNG5MAfSMGYCRer8L2QcmIYEG8y1dSjXA9+yhQtiMvYXcHObnlxsZGWXn/v4mZVSfT3GQUgo7O7vUK1euBOa3vYGBgQQALS0t6OvrPzmQlpYWMjMz882X6Nevn42trW1aQcFlaGiobs+ePe1Wrlx5KzcYzMvIyEh27NgxfufOnWW6detWYC/1y+R9jXR0dJCdnf2kvenp6VoAvXYODg6pFy9eDCrMMXR0dGRuDnlqauozV7f19fWfHF9LS0uqVCohpXyjNJNXvbe5PfPa2trIysriIp7sjakjYL4DoGqe+1UARD2/kRCiDYDvADSXUj75p5dSRuX8DBNCnADgCuCFgJlpSPv2NM3c5Mk0YYSnJ/D770CXLlw4mL0ZKelqxZgxwP37wNixdAWD0y/eL6/oCdakZs2aJU+ZMqXqvXv3dMzNzTM9PT3Ljhgx4gFAPaarV682GzZs2KM1a9aUq1+//jMDyWrVqpUWFxenc+TIkVJt2rRJTk9PF9euXdOvW7duWmHaMmbMmMqJiYnaW7ZsCX/ZNrGxsdodOnSwnz59+p22bdsm5y5PSEjQio+P17a2tlapVCp4eXmZNmnSRC0D3+zs7NJDQkIM0tLSRFJSktaZM2dMWrdunVinTp20+/fv6x0/ftyoZcuWKWlpaeL69euv/fwtLS0zzpw5U6pbt26Jnp6eryzk2b59+8Q+ffrYTpky5b6FhUXW/fv3tS0sLLKMjY2zEhMTX0gndXV1TQsPDzcICAjQUygUGevXry/n7u7OgwGZ2qgjh/kCAHshRDUhhB6APgCeqXYhhHAFsAxAZynlgzzLzYQQ+jm/lwfQBMALPQRMw0qXpt5AHx/6vVs3oGNHIJTPa9hrCg+nk6xevWge8v/+A377jYNl9k5ZW1urpk2bdrd58+YOzs7Oylq1aqUMGDAgHgAMDQ2z/f39DZVKpbOPj4/JL7/8ci/vYw0MDOSWLVtCp06dWsXR0VGhVCoV3t7ehfoDDg0N1V28eHGlkJAQA6VSqXByclLk5ttu3LjRdNy4cZUBYO7cuRVu376tP3v27Mq5OcF3797VSUxM1Pr444/tHBwcFM7Ozsry5curJk2aFJPzmDfOYc7Lyckpw8PDI97JyUnZu3fvakqlMiXn9ZFbtmwJnThxYlVHR0dFjRo1FKdOnSr1uvudNm1a1Lhx46zc3Nwc9fT0XtnV36BBg9SxY8dGN23a1CmnPF0VABgwYEDc/PnzK+UO+svd3sTEJHvJkiXh3bt3t3NwcFDo6+tnjx8/PrYwrwFj+VHLTH9CiA4AFgLQBrBKSjlLCDEDgK+Uco8Q4giAmgByP4BuSyk7CyEagwLpbFDwvlBKufJVx+OZ/jRIpaK5oX/8kaa8mzKF5m3mqYpZfh4/BmbPpuoX2trUozxmDM3cwt65IpzpL9zFxYWDE8ZYiXb16tXyLi4uNvmtU8u3lpTyXwD/PrdsWp7f27zkcWdAgTQrKXR1KZe5d2+qmTtjBlXWmDePep45TYMBQHY2sGkTnVBFRdGgvtmzAUu1zmHAGGOMvRM80x8rnMqVgY0bgePHaRBgjx406QnPFMjOn6dBogMHUoB85gydVHGwzBhjrITigJm9nRYtaIKT5cspp7lxY8pTvXlT0y1j71pICE1807AhEBEBrFkDnDsHNGqk6ZYxxhhjb4UDZvb2dHSAL76ggGn6dODAAcDZmXJVY964JCgraSIjqfSgszOViPv2WyA4GBg0CNDijxjGGGMlH3+bMfUxNqbBgDdvAp9/Dvz5J2BjQ3msHDi/f2JigK+/BuztqTd5xAi6yjBrFmDyysm9GGOMsRKDA2amfhUrAsuWUf3mbt1oQKCNDdVyfvDakz+x4urBA+C77wBbW6rJ3bcv9SgvWkTvPWOMMfae4YCZFR0nJ2DDhqeB8/z5QLVqVF3j/n1Nt469qYgIYPRowNoa+OUXmtTm+nVg9Wo6IWKMMcbeUxwws6KXGzgHBADduwMLFgBWVsCQIRRwseLN3x/49FOgenW6ctCvH72X27ZR3jJjxYC2trabk5OTwt7eXtm+fXvbpKSkN/p+MzIycs1veY8ePWxWr15tpp5WkqSkJK0WLVrYVatWTWlnZ6ccMWJEviVkdu7cWVqpVDo7ODgolEql8549e57kOrm7u9s7Ojoq7OzslP369bPKzMx8rWMPHjy4aoUKFWrlTlNdnH399deVp02bZpF3maWlZc179+6ptZD71KlTn1waCwoK0rO3t1e+7T59fHyMPvvss6qv3vLN1a9f39HHx8eoKPbNXo4DZvbuODpSebHAQGDoUGDzZqBmTcDDAzh0iKZOZsWDlMDhw0DnzkCNGjSl9ejRlKO8ciWdBDFWjOjr62cHBgYGhISE+Ovq6sr58+c/M9tddnY2ilOQOGHChPu3bt3yv379esD58+eNt23bVvr5bSpUqKDav3//zeDg4IA1a9bcGjp0aLXcdbt37w4NCgoKCA4O9n/48KHuqlWrXhnUZ2VlwcvLq0ylSpUyDhw4oJaBBiqVSh270ahFixZVUvc+mzVrlrJmzZpiN038+/B+aQoHzOzds7enAYGRkTRA7OpVoF07Cp5XrKDZ4ZhmJCXRe6NQAG3bUk3lH3+kdIzffgOqFkmHCWNq1bRp08c3b97UDwoK0rO1tVUOGDDASqlUKkJDQ/WWLVtW1sHBQWFvb68cPnz4Mz27X3zxRRWFQuHcqFEjh6ioqBd6MU+ePGlUr149R6VS6dy0aVP7iIgIXYB6/IYMGVK1bt26jra2tkpvb2+jtm3bVre2tq4xZsyYys/vx8TEJLtTp05JAE25XatWrZTIyEi957dr0qRJqo2NjQoA3Nzc0jIyMrRSU1MFAJQtWzYbAFQqlVCpVEK8xqRR+/btM3FwcEgdOnRozKZNm8oCFERbWlrWjI2N1c7dzsrKqkZkZKROVFSUTrt27arXqFHDuUaNGs6HDh0qBVDPb9++fa2bNGli371792pBQUF6bm5ujgqFwlmhUDgfPny4VO6+BwwYYGVnZ6ds2bKlXfPmze1ye+tf9lq+rrFjx1aeOXNmhdz7o0ePtvz5558r7Nu3z6Ru3bqOH330UfXq1asr+/XrZ5V7opTfez9ixAjL9PR0LScnJ0Xnzp2r5ba7T58+1nZ2dsomTZrYP378WACAv7+/vru7u71SqXR2c3NzvHz5sgEArFq1ysze3l7p6OioqFu3rmPua92yZUs7ANi/f79x7tTmzs7OikePHr0Qe02aNKlStWrVlI0bN7bv1KlTted71p+3Zs2acq6urk729vbK48ePGwHA8ePHjVxdXZ2cnZ0Vrq6uTlevXtUHgEWLFpVr3769batWrezc3d0d3uR1Zk/x/LRMc8qVoxJkEyYAW7dSjvOwYXS/f3/63TXfq6RMnaQELl6knuNNm4DERKBePWDdOuCTTwB9fU23kJUgn+/+vOr1B9fVerm4RoUaKau6rHqt3jqVSoWDBw+Wbtu2bSIAhIeHG6xYsSJ8w4YNt8PDw3WnT59uefHixRvm5uaZ7u7uDuvXry8zcODA+NTUVK06deqkrFix4s7EiRMrTZ06tfK6detu5+43PT1djBkzxmr//v03K1eunLlixQqziRMnWnp6eoYDgJ6eXravr2/QzJkzK/Tq1cvuwoULNypUqJBpY2NT89tvv71fsWLFfLu3Y2NjtQ8fPlxm0qRJBQ7sWLt2rZlCoUgxNDR8cimuadOm9n5+fqWaN2+eMHjw4EcAMHfuXHMAmDx58guliTZt2lT2k08+ievbt2/8zJkzLdPT04W+vr5s27Zt/MaNG8uMHTv24bFjx0pVqVIlo2rVqpmdOnWq9vXXX99v167d45CQEL127drZh4WF+QOAn5+f0fnz5wONjY1lUlKS1smTJ4ONjIzktWvX9Pv27Wt7/fr1G+vWrTOLjIzUCwoK8r97965OjRo1anz22WcPX/Va5rV06VKLbdu2lcu9/+DBA10AGDFiRGy3bt2q//DDDw+ysrKwa9cuswsXLtzw9fU1unbtWqnLly9fd3BwyGjWrJn9unXrzFq2bPk4v/d+yZIld9esWVMhMDAwAKCUjNu3bxts2LAhrHHjxhEdOnSwXbdundmIESPihg4dar18+fKImjVrph87dqzU8OHDrc6dOxc8e/bsSocOHQquVq2aKu+JR6758+dXXLRoUUTbtm2TExIStIyMjLLzrvfx8THau3ev2bVr1wJUKpWoXbu2wtXVNaWgv4eUlBSty5cvBx44cMB42LBh1UJCQvxdXFzS/vvvv0BdXV3s2rXLZPLkyVUOHjwYCgCXLl0y9vPz87ewsCg+l1lKGA6Ymebp61OO7MCBNFPgsmVUpmzpUqBuXWDwYArcypfXdEvfL3FxlFu+ciXg5wcYGgI9ewIjRwINGmi6dYy9kdxeQgBo0KBB0tixY2MjIiJ0K1WqlNG6detkADh16lSphg0bJlWuXDkTAHr37h3n7e1tPHDgwHgtLS0MHTo0DgA+//zzh927d7fLu38/Pz/9kJAQw1atWjkAlOJhbm7+5Pp2t27d4gHAxcUl1c7OLtXa2loFAFWrVk0PCwvTq1ixYurzbVapVOjevbvtsGHD7isUioyXPTdfX1+DadOmWXp5eYXkXX7q1KmQlJQU0a1bN9u9e/eW7tatW2J+gTIApKWliePHj5suXbo00szMLLt27drJO3fuLN2nT5+Efv36xc2YMaPy2LFjH27cuLFsjx494gDg9OnTpUNCQgxz9/H48WPt3N5RDw+PeGNjYwkAGRkZYsiQIdYBAQGGWlpaiIiI0AeAkydPGnfv3v2RtrY2rKysMhs2bJj0Oq9lXl999dX9GTNmPDmZsLS0rAkAjo6OGWXKlMk8ffq04b1793SVSmVK7klJzZo1k3Nfz08++STu5MmTxrq6uvJl7/3zx7S0tExv3LhxKgC4urqmhIeH6yckJGhdvnzZuFevXtVzt8vIyBAAULdu3cf9+/e36dGjx6P+/fs/en5/DRs2fDxx4sSqOScrj6pXr/5MwHzixAnj9u3b576e8qOPPnqhTc/r169fHAC0b9/+8ePHj7ViY2O14+PjtXr37l0tPDzcQAghVSrVk8sO7u7uiRwsvx0OmFnxIQTNFNi4MbBwIQVzK1ZQADd2LFVlGDgQ6NiRgjv25h4/pslFNm8GDh4EVCo6KfnrLyoPZ2qq6RayEu51e4LVLTeH+fnleXvz5BuMk3g+xUFKKezs7FKvXLkSmN/2BgYGEgC0tLSgr6//5EBaWlrIzMzMN1+iX79+Nra2tmnTpk17ab3N0NBQ3Z49e9qtXLnyllKpTH9+vZGRkezYsWP8zp07y3Tr1i3xZfvZvn176aSkJO0aNWooASA1NVXL0NAwu0+fPgmtW7dOHjJkiH5UVJSOl5dXmVmzZkXlPGf4+vreyA2M8ypVqtST13XWrFkWFSpUUG3fvv1WdnY2DA0N3XIfn59XvZava/DgwbF///13+QcPHugOHjz4Ye7y5987IcQbvfd6enpPNtbW1papqalaWVlZMDExyczvb2zTpk23jx07VmrPnj2mtWvXVl65csU/7/r//e9/0V27dk3YvXu3aePGjZ29vLyCXV1d03LXv0nb8j6n5+9PmTLFsnnz5kmHDx8ODQoK0mvVqpVj7vrne7XZm+McZlY8mZnRIDM/P5p6e9w4Shv45BPAwoKCO09Pznd+HUlJwD//AH360GvXvz+9pmPG0M8LF4CvvuJgmb33mjVrlnz+/HmTe/fu6WRmZsLT07NsixYtHgPUy5mbX7tmzZpy9evXT8r72Fq1aqXFxcXpHDlypBRAKRq+vr4GhW3LmDFjKicmJmqvXLnypScYsbGx2h06dLCfPn36nbZt2ybnLk9ISNDKzflVqVTw8vIydXJyeqEHO68tW7aUXbhwYcTdu3ev3b1791p4ePi1kydPlk5KStLS0tJC+/bt40eMGFHVzs4uNbentmnTpolz5sx5kid85syZfHsqEhIStCtVqqTS1tbGkiVLyuXmDLu7uz/etWuXWVZWFiIjI3XOnz9vAqjvtRw4cGD88ePHTa9evVqqR48eCbnLr127ViowMFAvKysL//zzT1l3d/ekgt57HR0dmZ6eXmASeNmyZbOrVKmSkTu4Mjs7G2fPnjUEKLe5VatWyQsXLowyMzPLDAsLeyYf3d/fX79+/fqps2bNiq5Zs2by9evXn3muLVq0eHzw4EHTlJQUkZCQoHXkyJEyr3rumzdvNgOAgwcPGpuYmGSVK1cuKzExUbtKlSoZALBs2TK+JKtmHDC/pjORZ+CxwQOpqgI/k1hRcHEBfv0VuH2bKjf06QMcPfo0TaNLF0oruHNH0y0tPqKiKLWlQwd6jXr1otfs008Bb28axDdvHr22jH0grK2tVdOmTbvbvHlzB2dnZ2WtWrVSBgwYEA8AhoaG2f7+/oZKpdLZx8fH5JdffrmX97EGBgZyy5YtoVOnTq3i6OioUCqVCm9vb+PCtCM0NFR38eLFlUJCQgyUSqXCyclJsWDBgvIAsHHjRtNx48ZVBoC5c+dWuH37tv7s2bMr5w4au3v3rk5iYqLWxx9/bOfg4KBwdnZWli9fXjVp0qSYnMeY5+Yx50pKStLy8fEx7dWr15NL/aVLl86uW7fu4y1btpgCQP/+/eN2795dtmfPnk9SCpYvXx556dKlUg4ODorq1asr//jjj2f2m2vcuHEPNm/eXM7FxcUpODjYwNDQMBsABg0a9KhSpUoZDg4OysGDB1u7uLgklylTJktdr6WBgYFs3LhxYufOneN0dJ5eMK9du/bjCRMmVHFwcFBaWVmlDxw4ML6g975///4xzs7OTwb9vczmzZvDVq9eXd7R0VFhb2+v3L59exkAGD9+fJXcwYQNGzZMatiw4TOBwty5cyvkDgo0NDTM7tmzZ0Le9c2bN0/x8PBIUCgUyg4dOlSvVatWsqmpaYHpE2ZmZlmurq5Oo0aNsl62bFk4AEyZMiV6+vTpVerUqeNUnCrCvC9EYS4FaFrdunWlr6/vOz1mj209sOPGDhzofwAedh5v9FgpJXYF7kLb6m1RSq/US7fbF7wPSnMlqpm9/H92hvcMlNYvjXENx71RG/Jr08PUhyhvVEJPQrOygFOngB07gJ07qeIGQCXQ2renqhuNGgFGH0ipyuRkwMeHTigOH35a39rWlk4ounQBmjQBdDgLqyQJexSGZb7LMKv1LOhovf17J4S4KKWsq4amPePq1avhLi4usereLyv5EhIStExNTbOjo6O169Wr53z69OlAKyur1ysa/QpZWVlQKpUKT0/P0Jo1a6YDVJ1i/vz5FsePH7+pjmO8K7mvU1JSklajRo0cly5dGtG0adMCB/4x9bt69Wp5FxcXm/zWfXA9zKosFeadmYfE9Jemer3gUeoj7AveBwA4FHrojY/pG+WL7tu647dzv710m2O3jqHT5k6YcGhCgfv58cSPWHhu4Ru34XlLfZei6m9Vcf/x04HZN2Ju4HbC7QIeVYxoawPNm9PUzBERwLVr1AttYUH5z23aAGXKUJD4zTfAgQNA/CvHUZQcsbGUizxlCuDuTiksHToAS5bQazB7NgXNN2/SRDHNm5eYYDktMw0pKvV9T0w9MlUt/zNSSsSnxUOV9e7qmP529jfMPTMX5+6ce2fHZEydPvroI3snJydFkyZNnCZNmnRPXcHyxYsXDaytrWu6u7sn5gbLJdmAAQOsnZycFLVq1XLu1KnTIw6Wix+1fIMKITwA/A5AG8DfUsrZz63XB7AOgBuAhwB6SynDc9Z9A2AIgCwAY6SUB9XRppfZE7QHkw5PQhmDMhhaZygAYP3V9dgfsh8bu2+EttYLFWGw/cZ2ZGRloGrpqgUGzDHJMRjx7wj87vE7Kps8Lb25N3gvAMAzwBPfN/seALDp2iasvrIaBwccRHJGMj7f/TkA4N+Qf5GYnojS+k9r2Ic8DMGt+Fv42ednAEBEQgTuJd3DvuB9eJT2CJObTH6j10BKib98/0JaZhqO3TqGvjX7IiMrAy3XtoRDOQf4DPbBLJ9ZMNAxwITGLw/giw0hqGe5Rg1g4kTKa/bxeXqbNw+YPRsqLeBWbWs4ODamgW5ubvSYcuWe2V1GVgb0tF8oiao5sbGUa3z5Mv28eBEICqJ1urpAnTrAuHHIatMKkbVsYFy6/CuvHGRlZ2GG9ww0rtoY7ezaFbpp6Znp0Nd5u7JzcalxKGtYFgD9bX686WMkpSfh/NDzLwxseZXrD65je8B2VDapjM6OnRGXGoc5p+dAT1sPnR07w9bMttDt/OO/PzDGawwEBH796NfX/t/44dgPSEhPwKL2i54s87rpBXcr9wKvOEkpsStoFwDgaNhRNLVqWui2M6Yp//33X1BR7NfNzS3tzp07155f3rFjx6SOHTsm5feY4mzv3r23nl82cOBAqwsXLjyTqjJ8+PD7Y8eOffj8tqzovXUPsxBCG8CfANoDUADoK4RQPLfZEACPpJR2AH4DMCfnsQoAfQAoAXgAWJKzvyLzz41/AADX7j/9P1t9ZTW2+m/FqsurcDvhNnYF7kJSOv2/qbJUWHl5JRzLOWJ0/dHwj/HHncT8c2W3+W/DPwH/YMXFFc8s3xu8F1pCC373/RD8MBgAsPbqWhwJO4L/7v6HBWcX4HbCbcxtMxfpWenYE7TnyWPP3zkPl6UuaLehHU7ePolBLoMAAKcjT2PaiWmYdnzaa/WWR8RHPOm1u3TvEq49oOd/7NYxAMDuwG9USdEAACAASURBVN24n3wfJ2+fxNXoq5jhMwPzzs576ejd2wm3n1l3MuIkfjrxE7LliwNxs7KzsPDcQmzw24Cs7HeQV2VsTL2ts2cDZ84A8fGYsWoQzKcZwLFzBBbHHaBazy1aUH6vhQXQsiUwciTuLJwBy9nmmL9jIpCUBClloUYw5xURH/HM63In8Q6Ohh19dqOEBHifWINJS3sgecFsGoTXsiVQuTJgbg589BEweTJw8iTNmPjLLzi0cx6q/1oF1/f8jcjvRqPcpT6otswZbsvdkJ758g4XKSVG/jsSM3xmoMuWLjgZcfKZ9ZnZmVh1eRU6be5U4BWHu4l3UXZuWay6vKrAY0XER2DemXn4at9XL7Rrqe9SVPi1Ak6EnwAA7LixA8duHcOFqAu4HH35yT68w73h6e+Jm3Evv8r6s8/PqL20NqZ7T8ewfcPgvtod072nw0DHADpaOvj26Lf5Pi45Ixmj/h2Frlu64kFy/sUKpJRY/N9i1KhQA82sm+HHEz/mu216ZjpWX1795PPjavRVzDo5C0suLEFsCmUs3Ii5gfYb27/0atL1B9cx9/RcnL97HncS70BLaOHoraP5bssYe3+tX7/+dmBgYEDeGwfLmqOOHub6AG5KKcMAQAixBUAXAHlLr3QBMD3n938A/JEzLVEXAFuklOkAbgkhbubs76wa2vWCVFXqk9SK3IAxKzsL/939DwAw5cgUTDw8EYnpiTDUMUQb2zaIfhyNC1EXsKTDEjSxaoLJRybjcOhhDHYdDIAuH1+6dwmNqjTCgZsHAAAbrm3AtObTIITAncQ7uBJ9BaPrj8bi/xbD098Tk5tMxqnbpwBQgOAZ4Ik2tm0wofEELP5vMdZcWQNVlgo3Ym9g9ZXVqGRSCX92+BMJaQno5NgJm69vxu/nf0f042gAwK7AXfjU5dMnz3PL9S3YFbgL3zT9Bi4VXXA74Tac/nSCRSkLzGkzB/tD9kNfWx8NqjTA8fDjAIBlF5ehnGE5PEx9iD7b+yAjKwPRj6MREhcCh3JPJwbyf+CP8QfH43DYYSzyWITRDUYjKDYIHTd3RGJ6IsxLmWNEvRFPto9JjkHvf3o/Oc63R7+Foa4hmlZtinlt58HM0Azh8eHw9PfEMLdhMDV4/UoNsSmxWHtlLfwe+KGzQ2f0UPTId7uNobvw4+216OTQCcmqZEzQOgmLH5bBKCIK7lE6ML1xCwgIADZswC9NExFbH/jh0nwopszH8M5aiCidjYrpepj5sBYG6dVDTHlDLNO7hkoG5hhs/hH0TcwAPT1AS4t6u7VyzkPT03Eo5hzaRfyMHgZ1sF73Exg+eowB2avgrReFX2/ZY+J/OsCdO1hfLQlDugAqbeBcxA7s9DJFeWtnoG1b+DmXxWSDk2in7IJ+Db+AhbEFLt+7jJ5rmiMpIwnrr65HJZNKSEhPwNcNv8aCcwuw3m/9kysoPhE+WHhuIW4n3MbIeiNx4OYBeAZ4YnT90Tgcdhidt3TGpWGXUM2sGrJlNjw2eDwJ0FJUKTg88DAeZzzG+qvrYaxnjE9dPoUQAp4BnkhRpeC7Y9+ht7I3SumVwuxTs7HNfxuOfHoE3uHeGPnvSNx7/HTsVI0KNTCq/igAlJ874dAEZMks/HrmVzSs0hCTj0yGYzlHhMeHY82VNahTqQ6239iOXp69AACGOoa48tUVpGWmwSfCB1+6fQldbV3cjLuJH47/gO7O3fHXx3/havRVfLzpY4TEheArt69gXsocM31mYnzD8WhQ5WmNad8oX/Tf0R8hD0Ogp62HusvrYm/fvXCpSIMh49PiERQbhNTMVITEhWBt17VoYNkAiiUKzD09F/Paznvmb22p71KMOzgOv575FQvaLcDc03NhoGOA1MxU7LyxE1+4ffHkf3/FpRUYUW8EalnUwsGbB7Hh2gb0dO6JL/Z+gZiUGFQyrgRtoY3PXT/H6iur8TjjMYz1CjXGjDHG2Ft660F/QoieADyklENz7g8E0EBKOSrPNtdztrmTcz8UQANQEH1OSrkhZ/lKAAeklP8UdMzCDvrbHbgbXbd2RXWz6khIT8CDiQ9w7cE1uCx1weTGk7Hg3ALUqVQH05pNw78h/+LAzQNITE/EXx//hV7KXpBSwmqhFcoalsW5Iedw9NZRjDkwBrfib2FNlzUYvn84yhiUwb3H93B+6HnUt6yPpb5LMXz/cPiP8McXe79AYnoilndcjsarGsNI1wgCAsmqZKzvth4Dag3AxEMTMf/sfACAnrYenMs7Y1uvbc8ErY1WNsK5O+ego6UDi1IWqGlRE0Ndh+Le43voX7M/qi+qjkdpjyAgsKj9ItyIuYEVl1bA1swWQQ/p6ljfGn1R37I+xh8cD6/+XvDY6IGZLWf+n73zDovqaNv4fXbpVUBQel/K0pRiASxYYo+IXWMXy5tobIlpxhh9FY0x0VcTezeW2LAEW7DnM66CSEcEQYrSWfruMt8fw9KkiChGM7/rOtfunjNnzsycA3vvM888D07EnEBYZhiMNY2RJk7DtiHbMNN9JgDgWdEzdNraCRWyCuio6qBMWoawWWHw2eWDnNIcOLR3wL2Me7g25Ro8jDyQW5oLv71+iMuJw5ZBW6ChpIHfIn8DAcHZ+LPQVtaGfXt73E2/iwpZBT60+xALui7AvJB5WNJ9CSa6TKxz/8qkZXha+BRl0jIQQuB/xB+JeYnQUtZCYXkhZnSagdicWJRLy2GiZQIFngKKJcUITQqFp7Enrky6gsLyQrj96obUQrpIUE1RDfO7zMcqv1VILUiBzSZbDGzfFZey7qCUVMBQpoaZWWb4UzkdN3UKwRGARwBZlSZuV7UWWsoDdEuB3acBvySgkqOb62wgUwPIUwV8UoDvrnHwm0RgKVZAkqYUG9Kc0VlTgF5aJ9BbzRETLIZhVuw6AMBAm4HYO3wvhh8ZjtuptyGtlILP8eFk4ISIZxEw0jSCkaYR8svyYahpiLzSPDyY/QCe2z2RX5aP2I9jEXQzCF+Hfg09VT3oq+sjNjsWKgoq+Mr3K3zl+xWS85PhttUNQn0hrk+9jgMRBzD19FSs778emkqaCDwbCA8jD8RkxaBYQqNajXQcib3D96Lf/n5IyElAVkkWvvD5Ah5GHgg4Sn+09LXqi79S/4Ktni2muU3DBzYfIPBMIOJy4pA4LxEKPAX47fXDw+cPMVY4Ftvub4OfpR/+TPoTFydexM6wnbj0+BLCZoXBa7sXjLWMsXnQZgw6OAjGWsZILUhFQXkBupl0w9FRR7HxzkZs+L8NSPk0BYaahgCAXWG7sCx0Ga5NuQYDdQPYbrKFrZ4tjo48itU3VyNNnIbguGB01OiI/f77oaWshQ8Pf4iiiiKcH38ebh3d0HNPT9xNvwtDDUOUSEqQvigdaopqmHxqMo5GHcXjeY+rr0cIgeuvriiRlKCgvKDaovzzgJ+x6e9NsGhngUsfXcLU01NxOvY0OI6DfXt77Bq2C912dkNeGQ1OoK+mj8GCwdgTvgd+ln5Y6r0U/Q/0x/nx5zHQdmCL/+/Vhi36YzAYjMZpatHf6xDMowB8UE8wexFCPqlVJqqqTG3B7AVgBYC/6gnm84SQ4w1cJxBAIACYmZm5P3nypMVtnXhiIkIeheALny+w+NJiZCzKQHBcMGadnYXEeYlQ5ivDQN0AivyalPaEkDp+lOcTzmPwocFw1HdEdFY0nAycUC4tR5o4DSWSEhwacQjTgqdheqfp+HnAz/DY7oGiiiLEfxyPPeF7MC14GnpZ9MLV5KtY3nM5ll9bDg0lDWQuyoS6kjqyirNw6OEh9LLoBZcOLg36cC68sBAb/m8D+ln1g7uhO4JuBYGA3kdHfUfEZMUgdHIo1v+1HucSzoHP8THFbQo2DdyEv9P+RlZJFnzNfJEuTofbVjco8BSgrqiOmP/EYH/Efnx++XP8OvhXfHv1W/S16ouVfitx+fFl7A7fjbCMMPzfjP/D08KnGHxoMMy1zZEmTsPljy7DSscKblvdkFuaCzs9O+SX5SOvLA9nx51FP+t+dfpwP+M+1t1eh3RxOuz17NFRoyNWXF8BDhwU+YqokFVgSfclWNx9MfTV9LEnfA/mh8yHuKLGNU1PVQ9nxp1BZ8POmHJ6Cg5HHoZbRzfoq+kjXZwOGZFBXVEdFu0ssGngpmph87z4Oe5n3IcyXxnb72/Hb5G/YWbnmQjLDMODzAd4NO8RTsWewvb723FyzEnY6NqAEILguGCEZYZBIinHdLuxeJQZjSNxx6FayYcS4SEk+/+QVJoOb21nhOaFwVbdFHHFT3DC538o4xNMuDYPygrKUFVQRdL8JEwLnoaTMSfRXq09tJS1ED47HBpKGnj47CEORBzAhv/bAPN25niU+whbBm1BL4te2B+xHzdSbqCvZV/M6DwDwXHBmHueWvS/6fENVvRegRMxJxBwNAAqCiook5ZhgvMEbB+6HUp8JYQmh0KgJ4CZtln1OB6OPIxxx8fBz9IPD589hI2uDW5OuwkOHCafmoz7GffRw7wHprpNxbUn1/DZpc/Qz7ofLiZexMreKyHKEOFULPW1de3gig/tPsSK6yvQXq09wmeFw1jLGAB12+mxpwemuE0BAOwJ34PDAYfhZ+kH0w2mKJeV44d+P2BR90W48OgCBhyk0Wj4HB+iQBHcOrpVt9VaxxoLuy3E0stLYaBugPyyfPS06Injo+v+66j997tVtBWzz82GjooOSiQlsGhnga4mXfHjBz9W+1An5yej776+SMpPgp2eHWKyYzBaOBpHo45ifpf5+GkAXTyYmJsIu//Z4T+e/0Ffq75YemUpZnaeiQUXFuCXwb9gtHA0HmQ+QKm0FANsBuCbP79B0K0gZCzKgM9uH9i3t8cY4RhMOklnhpT4Srg65SquP7mOATYD4KjviNU3VqOvVV84d3CGTpAObWv/H+Fu5N7Mf7rGYYKZwWAwGudNC+ZuAJYTQj6o+vwFABBCVtcqc6GqzF8cxykAyASgD2Bp7bK1yzV1zVe1MG+7tw35ZfnwNPKE3z4/XJh4AYcjD+Ns/Fk8W/zspRcYffPnN1h5YyU+7fIpgvoF4Y+EPzD8yHAo85WR+3ku5p6biwMRBzDGaQwOPTyEIyOPYLRwNCQyCez+Z4ek/CQ46jvi4sSLMNlggiluU7D7w90v3Y+jUUcx5vcx2DxoM3pZ9ELnrZ0x1W0qSqWl2Ptgb3V9xRXF8Nntg8jnkYj/OP6FcHWVpBLGPxqDx/EQMiEEzh2ckVeah5/v/IzPvD/D1NNTq32cs0uyochTxO4Pd2OCywQQQuDyqwsin0di86DN1W4YcjeJGyk3oKygjJmdZ6KvVd9m+0QIwayzs5AmTsPOYTvx5ZUvsTt8N/gcH0p8JZRKS9HLohemuE6BsoIyMosyMVQwFNa61VlKX1gs+TIQQjDvj3n4393/QVdVFzuG7oC/g3+L6pCTXZKNgQcHIrMoE8MEw3Aj5Qasda1xYvQJcByH9bfXY/GlxdXCtkRSgp57eiIsIww3p91EV5Oudeo7GHEQE09OhEBPgMg5kXV+yMlJK0yDyQYTAMC9wHvobNgZlaQSG+9sRFphGmx0bRDoHtjss73m5hpsvbcVGeIM3J5+G50NOzdadu2ttfj88ucAgLiP42CqZYrzCeeRWpiK0cLR6KDeAd9e/RaDbAehu2n3Oud+cv4TbBFtQSWpxFLvpVjdl/6b2CrailJpaXW4REIIjkQdwZP8J+hs2LnOD66z8WfhaeSJDhod8FfqX+i3vx+KJcW4MPEC+lv3b7Td0kopOm3thOySbJwdd7ZR4Zldko2gm0HYdn8blnovxRe+XyAhJwFm2mZ1FjjOCJ6B/RH7ocxXrv4hp6KggoxFGWinUjfvwMNnD+Hyqwv+4/kfbL67GWv6rMHnPp/javJVBJ4JxFKfpZjWaVqjbf/p/37CstBlEFeIq2evXoX3WTDz+Xx3W1vbUplMxtnY2JQePXo0WVNT86Wzm6mpqXUqKSkJq78/ICDAYsiQIQVTp059IeXxqyIWi3lDhw61evLkiTKfz0f//v3zt2zZkla/3MmTJ7W+/vprY4lEwikqKpLVq1c/HTZsmBgAfH19bZ8/f64ok8k4Ly8v8b59+1IUmoiEs3HjRj2RSKS+b9++6oUJXl5edj/88ENqjx492iQiQ1xcnNKQIUNsExISopov/XpYuHChkYaGhqx2eu2mSE9PVxgwYICNRCLhbdiwIWXAgAHV2bFWrFhhsGDBgmz5c9XYM/M+0tDz87p5E+ObnJysOHv2bNOQkJDHL1P+TQtmBQDxAPoASANwF8B4QkhUrTL/AeBMCJnNcdxYACMIIaM5jhMCOARqbTYCcAWALSGkyZVhrY3DnF2SDf11+vih3w/YGbYTNro2CB4X3PyJVRBCkFGUUR0JgxCCXnt7ob1aexwffRzicjF67e2F+xn30deqLy5OvFgtWHbc34GZZ2ZirsdcbB68GRceXUAnw04wUDdo6pJ1KJGUIOhmEBZ3XwxNZU2USkqhqqgKaaUUhx4ewjC7YdVf2Pll+UgpSIFLB5cG60rKS4KWshb01PReOPbL3V8w9/xc6Knq4cLEC3DQd4CaYk1c47CMMNxNv4uZnWe2OJrByxCbHYuDEQdRJi2DfXt7TO00FTzu9UdCrCSVOBp1FD3Ne1ZboVtTFweuwfEghOBu+l10NuxcHVO3sLwQKQUpcDJwarC+8wnnYaVjBfv29o1es8uOLsgsykTy/ORW3QdCCMqkZVBVbDrtOCEEs8/ORnpROs6MO9Pi6yTlJeGvp39hjHBMg1FpWsqtlFv449EfWNF7RbPPR0FZAXgcD5rKms3WW392qT5P8p/AdpMt2qm0Q8jEECy+uBgeRh5Y229tg+XH/D4GR6OOAgBuTL3R4qgXBWUF+D36d0zrNO2V7/P7LJhrf7kOGzbMsnPnziXLly+vFkmVlZUghIDPb/iZa2vBfPXqVfWhQ4eKy8rKOG9vb8Hnn3+eMXr06DoruG/duqVqbGwstbCwkNy9e1dl8ODBgufPn0cAQG5uLk9XV7eysrISAwcOtA4ICMgNDAxstI1vQzBLJBIoKtb80H8XBPO2bdt0QkJCtE+cOJFc/5ixsbGzSCSKMTQ0lAL/PMEslUrR1I+m1tAWgvmfML5vNA4zIUQK4GMAFwDEADhKCIniOG4Fx3HDqortBKBXtahvIWosy1EAjoIuEAwB8J/mxPLroL1ae3TU6IjDUYcRkx3zgmWvOTiOqxM2juM4XP7oMo6OpF+GmsqaOD/+PGa7z8a2IdvqfLlNcp2EWe6zqv2CP7D5oEViGaB+t9/1/q76S18ucBR4CpjkOqmOdaudSrtGxTIAWOpYNiiWAWCo3VB0NemKs+OpNa62WAaAToadXsp6+arYt7fH937fY13/dZjeefobEcsAwON4GOs0ttViWV5XY+PBcRy8jL3qJKDQUtZqVCwDwCDbQU2KZQA4OOIgzo472+r7wHFcs2JZXm7r0K2vJJYB+syNdx7/WsQyAHibeWOl38qXej60VbRfSiwDaHY8zduZ49z4c7g65So6G3bGn5P/bFQsA8DavnQBoCJPEe6GLXer0FbRxvTO09/Y39v7hI+PT9GjR4+U4+LilKysrIQTJ040EwqFjomJiUpbt27VlWdlmzNnjnHt82bOnGni6Ojo0K1bN0F6evoLyuPGjRtqnp6edkKh0MHHx8dWnp7ay8vLbvr06aYeHh52VlZWwmvXrqn179/f2tzc3GnevHlG9evR1NSsHDp0qBig2epcXFxKUlNTX4hl6e3tXWphYSEBaBi1iooKXmlpKQfQVM0AIJFIOIlEwrX2uVBTU+vUUP+9vLzspk2bZtqpUyd7W1tbYWhoqBoAFBYW8kaNGmXh5OTk4ODg4HjgwIF2ABVWAwcOtPLz87Px9fUV1L+OVCrFiBEjLAQCgeOAAQOsxGIxDwBOnz6t6eDg4CgQCBxHjRplIe+nsbGxc0ZGhgIAXL9+Xc3Ly8sOoEJ41KhRFl5eXnYmJibOK1eurP4i/fzzzztaWFg4de/eXZCQkNBg3Mv4+Hilbt26CQQCgWO3bt0ECQkJSrdv31b99ttvTUJDQ7Xt7e0di4qKqgd15cqVBs+fP1fs2bOnoEuXLtX9+uSTT4zt7OwcXV1d7VNTUxUAaqX+4IMPrJ2cnBycnJwcLl68+EL8yLi4OCV3d3c7R0dHB0dHR4dLly6pA8DgwYOtjhw5Ur36PSAgwGLPnj3tpFIpZs2aZeLk5OQgEAgc161b1x6giVq6dOkiGDp0qKWdnZ0QAPr27WstFAodbGxshD/88EN1jNENGza0t7CwcPLy8rIbO3as+aRJk8xetr0AkJmZqejr62trbm7uNHv2bBN5ndOnTzeVl1m/fn37GTNmmMTFxSlZWloKX/Zev47xPXfunIY8I6aDg4NjXl4eLy4uTsnW1lYIACKRSMXZ2dnB3t7eUSAQOD58+LBlMVHlYbPepc3d3Z20ln77+hEsBxFuFpLUgtRW18dgMBjNsU20jXx28bO3dn0AIvIG/ieHh4cnE0JEb3NTVVWVEUJEFRUVIj8/v7w1a9Y8iY2NjeA4jly+fDmGECJKSkp60LFjx/K0tLTwiooKUZcuXQr37dv3iBAiAkC2bNnymBAiWrRoUdpHH330nBAiGjFiRPauXbsSy8rK7rm5uRWlpaWFE0JE27ZtSxw5cmQ2IUTk6ekpnj17dgYhRLRixYoUfX39iuTk5AclJSX3DAwMKjIyMsIaa3dWVlaYsbFxeVRUVERT/du1a1dit27dCmvv8/b2LtDU1JQOGTIkRyKRiAghoqCgoCdBQUFP6p//888/J8n7JN88PT3F165di26q/56enuIxY8ZkEUJE58+fj7WxsSklhIj+85//ZGzevPmxvA/m5uZlBQUF93/++eckAwODiszMzBf6HBsbGwGAXLhwIYYQIho5cmT2N998k1pcXHyvQ4cOFQ8ePHhICBENHz48+7vvvkshhIiMjIzK09PTwwkhomvXrkV7enqKCSGiBQsWpLu5uRWVlJTcS09PD9fW1paWlZXdu379erStrW1JYWHh/ZycnPumpqZl33zzTWr9tvTu3Tt/48aNSYQQ0YYNG5L69OmT19g4ybfabZGP2cGDBxMIIaJZs2ZlLlmyJI0QIhoyZEhOSEhILCFEFB8fH2FpaVlav67CwsL7xcXF9wghooiIiIdCobCYECLau3fvI39//2xCiKi0tPRehw4dKsRi8b1169Yly+svKSm5JxQKi2NiYiLOnDkTp6KiIouJial+fuRjLxaL79nY2JRmZGSEJSUlPTAyMirPzMwMKysru9e5c2exvJ8v096ff/45ydjYuDw7OzusuLj4nqGhYXlCQsKDgoKC+yYmJmVlZWX3CCEiNze3ojt37kS19l6/yvj27t07X369/Pz8+xUVFaLY2NgI+TM7adKkZ/JnvLS09J5YLL5Xv59V/8sa/D/3bqT+egN81+s7DLMbhkD3wH9WkgoGg/HeIp9Zep+ZNg2mkZF4rTnpnZxQsmsXUpsqU15ezrO3t3cEgC5duojnz5+f/eTJE0VDQ8OKPn36FAPAzZs31bt27So2MjKSAsCYMWNyr127pvHRRx/l83g8zJgxI5f2YVrOiBEjbGrXHxERoZyQkKDq5+cnAKiLh76+fnXaR39//3wAcHV1LbWxsSk1NzeXAICpqWn548ePlTp27Fhav80SiQQjRoywCgwMfObo6FjRWN9EIpHKsmXLjENCQhJq779582ZCSUkJ5+/vb3XmzBktf3//ws8++yyroTqamvkCgKb6P378+FwAGDhwYFFRUREvOzubf/XqVa0LFy6027hxY8eq8ecePXqkBAC+vr6FHTp0aHC2uGPHjhX9+/cvBoCPPvooZ+PGjQYPHjwoNDExKXdxcSkHgClTpuRs3rzZAEDDgdGr6N+/f76qqipRVVWV6urqSp4+faoQGhqqMWjQoHy5H2z//v0bTPEaFham/scffyQCwJw5c3K/++47k6au1RCKiopk7NixBQDg7u5efPnyZS0AuHXrllZCQkL1dF1RURE/Ly+Pp6OjU+1TX1FRwU2fPt08Ojpalcfj4cmTJ8oAMHLkyILPPvvMrLS0lDt+/Li2l5eXWENDg1y+fFkrNjZWLTg4WAcAxGIxPzo6WkVJSYm4uLgU29vbVz8/QUFBHc6dO9cOoFbhqKgolfT0dMUuXbqI5ffF398/Lz4+XuVl2wsAPj4+hXp6ejIAsLGxKUtMTFS2sbEp8vb2Fh85ckTb2dm5TCKRcF5eXqVxcXFKrb3XLR3frl27Fi1evNh09OjRuePGjcuztrau0/5u3boV//DDD4ZPnz5VGjt2bF5LM0T+awVzN9Nu6Gba7W03g8FgMBivAWVl5crY2Njo+vvV1NSqvzRJC9bs1BeYhBDOxsamNDw8PLah8ioqKgSgwlNZWbn6QjweD1KptEG1On78eAsrK6uyZcuWNSoMExMTFUeOHGmzc+fOJKFQ+MIXvJqaGhkyZEj+yZMn2/n7+zeaxap9+/bS/Pz8On5Q+fn5/A4dOjSYqrp2/+uPBcdxIITg999/f+Tq6lqnTTdv3lSvPeZN1Vu7rsbg8/mkspJWV1paWsfvqvY48/n86nFuK7clBQUFwquKu6+goFB9fUIIRCJRjIaGRqMdW7VqVQcDAwPJ8ePHkyorK6GqquoO0PvZtWtX8YkTJ7SOHDmiM27cuNyqOrn169enBAQE1LnHZ8+e1aw93mfPntW8du2apkgkitXU1Kz08vKyKy0t5TU1xi/TXgBQUlKqPd5EIpFwABAYGJi9atWqjgKBoGzixInVaxlaeq/r09Lx/e9//5s5fPjwgtOnT2t3797dISQkJL722MyePTvX19e3+OTJk9oDBw4UbNmyJVm+iPZleDNOoQwGg8H4lO2vrQAAIABJREFUV7JrF1L//htxr3Nrzrr8svTo0aP4zp07mhkZGQpSqRTHjh3T7dWrVxFALca7d+/WAYA9e/boeXl51fkidXFxKcvNzVW4fPmyOkAtqiKRSOVV2zJv3jyjwsJC/s6dOxvtW3Z2Nn/QoEG2y5cvfyq31AFAQUEBT+4/LZFIEBISom1vb/+CBbs2Pj4+xffu3dNISUmp9geuqKjgWVtbVzTX/99++00HAC5cuKChqakp09PTk/Xu3btw/fr1HeRi9tatW80vgACQkZGhJB/DQ4cO6Xbv3r3Izc2tLC0tTSkyMlIZAPbt26fn6+srBgATE5OKW7duqQHA0aNHdZqr38/Pr+jcuXPtioqKuLy8PN6lS5faNVSuU6dOxTt27NABgK1bt+p6eHgUNVSuNurq6rKCgoJmdZOPj09hUFBQtU/17du3XxibgoICvqGhoYTP52PLli16MlmNQX7s2LG5e/bsaX/37l3NESNGFAJAv379Cn755Rf98vJyDqAzHoWFhS+0JT8/n6+trS3T1NSsDAsLU3nw4IE6APj6+hbfuXNHMysriy+RSHD69OnqsXyZ9jaFn59fcUZGhtLJkyf1pk+fnivf39J73drxjYqKUvby8ipdtWpVprOzc3FkZGSdv8/o6GglBweH8q+//vp5//7988PDw1vUz3+thZnBYDAY/y7Mzc0ly5YtS+vZs6eAEML16dOnYOLEifkAoKqqWhkVFaUqFAo7ampqyk6cOFEnDJWKigo5fPhw4rx588zEYjFfJpNxc+bMeebh4VHW0nYkJiYqbtq0ydDS0rJMKBQ6AkBgYODzhQsXZh88eFD77t276j/99FP62rVrDVJSUpTXrFljtGbNGiMAuHLlSnxlZSUGDx5sU1FRwVVWVnLe3t6FS5YsyQKAtWvX6gNAfdcMU1NTaVBQUOqAAQNsKysrOXV1ddmBAwcey6OGNNV/HR0dWadOneyLior427ZtSwKANWvWpAcGBprZ29s7EkI4ExOT8tDQ0MZz11dhZWVVtmvXLr25c+eaW1pali9evDhLTU2N/Prrr8mjRo2ylslkcHV1LVm8eHEWACxbtix99uzZFkFBQRJ3d/fi5ur38fEp8ff3z3VychIaGxuXe3l5NSiEf/nll5TJkydb/Pzzzx319PSk+/btS26u7smTJ2cPHDjQ1sDAQHLnzp34xspt27YtdcaMGWYCgcBRJpNxXbp0EXfv3r1OdIlPP/30eUBAgPWpU6d0fHx8xKqqqtWWUH9//8LZs2db9u3bN18+c7FgwYLs5ORkZWdnZwdCCKerqys5f/58Yv1rBwQEFGzbtk1fIBA4Wltbl7m6uhYDgKWlpWTBggUZnp6eDgYGBhKBQFCqra0te9n2Nsfw4cPzIiIi1PT19auVf0vvdWvHd+3atQa3b9/W4vF4RCAQlI4cObIgJSWlOkzL/v37dY8dO6anoKBA9PX1JatXr05vSR9bHVbubdDasHIMBoPxb+R9DivHaB2NhfBq61jNjDdHQUEBT1tbu1IikeCDDz6wmTJlSvakSZMa9PFuKb1797b59NNPn3344Ydi4O2EEHwdvNGwcgwGg8FgMBiMfzZLliwxqgqpJjQzMyuXz660huzsbL6FhYWTiopKpVwsv68wCzODwWD8S2AWZgaDwWgcZmFmMBgMBoPBYDBeESaYGQwGg8FgMBiMJmCCmcFgMBgMBoPBaAImmBkMBoPBYDAYjCZggpnBYDAY7zx8Pt/d3t7e0dbWVjhw4EArsVjcou83NTW1Tg3tDwgIsJAn9HhdiMViXq9evWwsLS2FNjY2wrlz5xo3VO7kyZNaQqHQQSAQOAqFQofg4GBN+TFfX19bOzs7RxsbG+H48ePNpNIGE/ZVc/bsWc3evXvbNFnoDbNx40a9SZMmmbXlNb28vOyuX7/+0qnaQ0JCNGxsbIT29vaORUVF1anqsrOz+WvWrNGXf/4njGdb8ib+Dmrzpsb34MGD2l9++WXH1tYDMMHMYDAYjPcAeWrshISEKEVFRbJ+/Xr92scrKytRO5va22bRokXPkpKSoiIjI6Pv3LmjcfToUa36ZQwMDCTnzp17FB8fH71nz56kGTNmWMqPnT59OjEuLi46Pj4+KicnR3HXrl1vTMy8KhKJ5G03ocXs27dP95NPPsmMjY2Nrp16OScnh79z506Dps5927yL4y3nTY3vhAkTCv773/9mvo66mGBmMBgMxnuFj49P0aNHj5Tj4uKUrKyshBMnTjQTCoWOiYmJSlu3btUVCASOtra2wjlz5tSx7M6cOdPE0dHRoVu3boL09PQXMuHeuHFDzdPT004oFDr4+PjYytNTe3l52U2fPt3Uw8PDzsrKSnjt2jW1/v37W5ubmzvNmzfPqH49mpqalUOHDhUDNIOgi4tLSWpqqlL9ct7e3qUWFhYSAHB3dy+rqKjglZaWcgCgq6tbCQASiYSTSCQcx3H1T38pTp8+reng4OAoEAgcR40aZVFaWsqFhoaq9e/f3xoADhw40E5FRaVzWVkZV1JSwpmYmDgDNA2xr6+vrVAodHB3d7cLCwtTAaglcsaMGSZdunQRzJ0716T+9dLS0hR9fX1tLSwsnBYtWmQo3798+fIOtra2QltbW+GKFSsMAJr8wtbWVigvs2zZsg4LFy40ko/5nDlzjJ2dnR0sLCycQkJCNACgqKiIGzJkiJVAIHAcPHiwVVlZWYMD01C/f/zxx/bnzp3TXbt2rdGwYcMsa5dftGiRSWpqqrK9vb3jrFmzTACguLiYP2DAACtLS0vhsGHDLOVpwht7Tmpz6NAhbRcXF3sHBwfH7t27C1JTUxVkMhmMjY2ds7Oz+fJyZmZmTqmpqQrp6ekKH3zwgbWTk5ODk5OTw8WLF9UBYOHChUbjxo0z9/b2th0xYoRlXFyckru7u52jo6ODo6Ojw6VLl9QBQCaTYeLEiWY2NjbC3r172/Ts2dNGbjF+mfYCwLVr1zQ6depkb2Ji4iw/d/jw4ZYHDhyoTj8+bNgwy4MHD2pv3LhRr0+fPtYve69fx/iuXLnSwNraWigQCByHDBliBdSd1di1a5eOra2t0M7OztHDw8OuoT42BRPMDAaDwXhvkEgkuHDhgpazs3MpACQnJ6tMnTo1JyYmJlpJSYksX77c+OrVq/HR0dFRYWFh6vv3728HAKWlpbzOnTuXREdHx3h7e4uXLl1aR+iWl5dz8+bNMzt9+nRiVFRUzOTJk7MXL15cLbiVlJQqRSJR3NSpU7NGjRpls3379pTY2NioI0eOtM/MzOSjEbKzs/mXLl1qN3DgwMKm+rV3714dR0fHElVV1Wqrp4+Pj62+vr6rurq6bOrUqXkATY0tT4/dHCUlJdysWbMsjxw5khgfHx8tlUqxbt06fR8fn5KoqCg1ALh+/bqGjY1N6fXr19VCQ0PVO3XqVAQAM2bMMN+yZUtKVFRUzLp1657OmTOn2tUiMTFR5datW/Hbt29/Wv+aERER6seOHXscGRkZFRwcrHv9+nW1GzduqB06dEjv3r17MSKRKGbfvn36t27dUm2u/VKplHv48GFMUFBQ6ooVK4wA4IcffjBQVVWtjI+Pj162bFlGdHS0+sv2e+HChdl9+/bNX7ly5dPg4OCk2uesX7/+qampaXlsbGz01q1bnwJATEyM6ubNm1MfPXoUlZKSonzp0iWN5p4TOf369SsKDw+PjYmJiR45cmTuihUrOvL5fPTv3z//4MGD7QDgzz//VDcxMakwNTWVzpo1y3ThwoXPIiMjY06ePJk4e/Zsi1pjqnbhwoVHZ86cSTIyMpLeuHEjPjo6OubIkSOPFyxYYAYA+/bt00lNTVWKi4uL2rt3b3JYWJgG0PxzXZtnz54pikSi2NOnTyd8++23xgAwc+bMrD179ugB1Ep87949jdGjRxe09F6/jvHduHFjx8jIyOiqGZkn9du/Zs0aw4sXL8bHxcVFh4SENJvGvT4v/IJmMBgMBuNVmTYNppGReGmf0ZfByQklu3Yhtaky5eXlPHt7e0cA6NKli3j+/PnZT548UTQ0NKzo06dPMQDcvHlTvWvXrmIjIyMpAIwZMyb32rVrGh999FE+j8fDjBkzcmkfpuWMGDGijv9kRESEckJCgqqfn58AoC4e+vr61XPg/v7++QDg6upaamNjU2pubi4BAFNT0/LHjx8rdezYsbR+myUSCUaMGGEVGBj4zNHRsaKxvolEIpVly5YZh4SEJNTef/PmzYSSkhLO39/f6syZM1r+/v6Fn332WVZT41SbBw8eqJiYmJS7uLiUA8CUKVNyNm/ebKCoqPjc3Ny87P79+yr3799X/+STT56FhoZqymQyztvbu6igoIAXFhamMWrUKGt5XRUVFdWW3BEjRuQpKDQsL3x8fAo7duwoA4DBgwfnXb16VYPjOAwaNChfS0urUr4/NDRUc9SoUU1mohs1alQeAHTv3r14yZIlSlVjojFv3rznANClS5dSgUDwQkrvxvoN4PnLjh0AODs7F1tbW0sAQCgUliQmJirp6upKm3pO5CQlJSkNHz7cJCsrS7GiooJnampaDgDjx4/PXbFihdH8+fNzDh48qBsQEJALALdu3dJKSEio/hFRVFTEz8vL4wHAgAED8uXuIxUVFdz06dPNo6OjVXk8Hp48eaIMADdu3NAYMWJEHp/Ph5mZmbRr165ioPnnujbDhg3L5/P5cHd3L8vJyVEEgMGDBxd9+umn5mlpaQoHDx7UGTx4cJ6iIjVQt/Zet3R87ezsSv39/S2HDRuWP2HChBfq8/DwKJowYYJFQEBA3oQJE/Kaub0v0CrBzHGcLoAjACwAJAMYTQjJq1fGDcAvALQAyACsIoQcqTq2B0BPAAVVxacQQsJb0yYGg8Fg/PuQ+zDX36+mplYpf9+SzLb1XRwIIZyNjU1peHh4bEPlVVRUCADweDwoKytXX4jH40EqlTboFjB+/HgLKyursmXLljUq1BITExVHjhxps3PnziShUFhe/7iamhoZMmRI/smTJ9v5+/s3aaWuT1Pj0b1796Lg4GBtRUVFMnTo0MLx48dbyGQy7scff0yVyWTQ1NSUNjTeAKChoVHZ0H7gxXHlOK7RdigoKBD5NDwAlJWV1ZkVl4+5goICZDJZdcXNuae8rgzHte8zn8+HVCrlmntO5Hz88cdm8+fPz5wwYULB2bNnNeUW8j59+hRPnz5dOT09XSEkJKTdqlWr0uVtFolEMbX9quWoq6tXD9KqVas6GBgYSI4fP55UWVkJVVVV96b6/LLtBWrGu359o0ePztmxY4fu8ePHdXft2pUs39+Se90QLR3f0NDQhD/++EPz1KlT7dauXWuUkJAQWfv4oUOHUv7880/14OBgbTc3N2F4eHiUXNC/DK11yVgK4AohxBbAlarP9SkBMIkQIgQwAMBPHMe1q3V8CSHErWpjYpnBYDDeYXbtQurffyPudW7NWZdflh49ehTfuXNHMyMjQ0EqleLYsWO6vXr1KgKopUrul7lnzx49Ly8vce1zXVxcynJzcxUuX76sDtCpbJFIpPKqbZk3b55RYWEhf+fOnY32LTs7mz9o0CDb5cuXP+3fv3+xfH9BQQFP7rcpkUgQEhKibW9v/4IFuznc3NzK0tLSlCIjI5UBYN++fXq+vr5iAOjVq1fR1q1bDTw9PYuMjIykeXl5Co8fP1Zxd3cv09XVrTQxMamQLzSsrKzEX3/91awLBQDcvHlT69mzZ/yioiLu/Pnz7Xr27Fnk5+dXdP78+XZisZhXWFjIO3/+vE7v3r3FJiYm0tzcXIXMzEx+aWkpd+HCBe3m6vfx8Sk6cOCALgDcvXtXJT4+/oXZjqb63Rja2tqy4uLiZjXTyz4nYrGYb2ZmJgHo8ybfz+PxMHDgwPy5c+ea2tjYlMoFnY+PT2FQUFD1orjbt283ON4FBQV8Q0NDCZ/Px5YtW/TkC119fX2LTp06pSOTyZCamqpw584dzZa0tylmz56dvXXr1g4A4OHhUSbf35J73drxlclkSExMVBo6dKh4y5YtT8ViMb+goKCOK1RUVJSyn59f8U8//ZSuo6Mjffz48QvrBpqitS4ZHwLoVfV+L4CrAD6vXYAQEl/rfTrHcc8B6ANocqqFwWAwGIzXibm5uWTZsmVpPXv2FBBCuD59+hRMnDgxHwBUVVUro6KiVIVCYUdNTU3ZiRMnHtc+V0VFhRw+fDhx3rx5ZmKxmC+Tybg5c+Y8qy0QXpbExETFTZs2GVpaWpYJhUJHAAgMDHy+cOHC7IMHD2rfvXtX/aeffkpfu3atQUpKivKaNWuM1qxZYwQAV65cia+srMTgwYNtKioquMrKSs7b27twyZIlWQD1YQaAhlwz/vrrL60OHTq4yD8fPHgw8ddff00eNWqUtUwmg6ura8nixYuzACqYc3JyFOU/KBwdHUufPXsm5fGopvntt98ez5w50zwoKMhQKpVy/v7+ud26dWtWtHt4eBSNGTPGMjk5WSUgICCnR48eJQAwfvz4nM6dOzsAwEcffZTl7e1dCgCLFi3K8PLycjAxMSm3sbFpdqwXL178fOzYsZZVofhKnJ2di+uXUVNTI431uzE6duwoc3d3L7K1tRX6+fkVDB06tKChci/7nHz11Vfp48aNs+7QoUOFh4dHcUpKirL82IQJE3J79uzpsHHjxmT5vm3btqXOmDHDTCAQOMpkMq5Lly7i7t27p9S//qeffvo8ICDA+tSpUzo+Pj5iVVXVSgCYPHly3uXLlzUFAoHQ0tKyzNXVtbhdu3ay1/Fcm5qaSq2trcuGDh1aR9e19F63ZnydnZ3Lx48fbykWi/mEEG7WrFnP2rdvX8d6vGDBApPk5GRlQgjn4+NT2LVr1xb9yORaMzXBcVw+IaRdrc95hJBGQ9twHOcFKqyFhJDKKpeMbgDKUWWhJoS8MOVUHw8PDyISiV653QwGg/FvhOO4e4QQj9dd74MHD5JdXV2zX3e9DAbj9VFQUMDT1tauzMzM5Ht6ejrcunUr1szMrOkA3i+BWCzmOTo6OoaHh8fo6enJABqdQiQSqe/bt+8FUf9P5sGDB+1dXV0tGjrWrIWZ47jLABoK+vxVSxrBcZwhgP0AJhNC5P42XwDIBKAEYBuodXpFI+cHAggEADOzNo17zmAwGAwGg/FO069fP9vCwkK+RCLhlixZkvE6xPKpU6c058yZYzFnzpxncrH8vtJaC3McgF6EkIwqQXyVEPJCbDuO47RA3TVWE0KONVJXLwCLCSFDmrsuszAzGAxGy2EWZgaDwWicpizMrV30FwxgctX7yQBO1y/AcZwSgJMA9tUXy1UiG1UR14cDiKx/PoPBYDAYDAaD8TZprWBeA6Afx3EJAPpVfQbHcR4cx+2oKjMaQA8AUziOC6/a3KqOHeQ47iGAhwDaA1jZyvYwGAwGo+2prKysfLVUcwwGg/EPoOp/WKMhEVsVJYMQkgOgTwP7RQBmVL0/AOBAI+f7teb6DMa7QF4eoNPoUlgG470gMisry1FfX7+Ax+O9niC3DAaD0UZUVlZyWVlZ2mjC04Fl+mMwalFZCQQFASNHAra2ra/v4UOgUyfg99+B4cPrHsvOBnR1AR5LUM94x5FKpTMyMzN3ZGZmOqH1M5cMBoPR1lQCiJRKpTMaK8AEM4NRiz//BL78Ejh/nm4TJgCGhsDcuYCrK5CTA5w5A7RvD/j4AO3aNV3f7t2ATAbs3FkjmM+eBebNA5KSgB9/BBYsoPufPaPXHzECUFZuvE4G45+Gu7v7cwDD3nY7GAwG403RqigZbwsWJYPRUvLzge3bqQjevh2wsWm4XEAAcPIkQAjg6AjExlLxWlYGfPopcPo08LgqnYGREXDwINCrF/D8ObBvHzBnDqCuTo9LpYCJCZCVRa3IGRnUomxXFUdGVZW26/FjoKKCCvCwMMDUFNi/H+jZs6aev/8GunUDmsn4ymA0yZuKksFgMBjvO2zqjPGvwN8f+Owz4MYN4OuvqaV45kxg3Tpq6QWAtDQqiBcsAFxcgOhoejw9HZg6FdiwARCLgUuX6KahAfj5AUuX0tclS+hWUABs2wZs2kStxsuWUdF77Bhw+TLw6BHw3XfA998DqanAb7/R+sPDgdWrAUVFYMYMQCKh7frvfwFvb9peaVXUzLw8YMUKwNOzRsDHxdH2P3jQ9uPLYDAYDMZ7DSHkndvc3d0Jg/GyJCYSAhDy/feEfPklfd+pEyE8Hn2voUHI5cuETJhAPz96REhMDCG//kpIZWVNPVeuEJKSUvNZLCZkyhR6jooKIUOG0PempvQVIERXl5DyckKEQkJsbAjp1o0QAwNCysoIkUoJsbSsKRsUROs9c4Z+3rqVkOxsQjQ1a+qcPZu2ycur5ry1awl5+LDms74+rbspZDJCPDwI2bDh9Y83458LABH5B/wPZxvb2Ma2d2176w14lY0JZkZLWLmSPulPnhCSk0OIlhb9vH8/FccCAakWm1991fL6z5wh5O+/CSkpIcTRkRBDQ0L++IOQXbsIuXiRlrlwge4HCPnii5pzDx4kpHt3QkJDa/ZVVlJhra9PiJ8fIRxHSGQkIR9/TAifT8jmzbSeX34hxMGBkAED6I8BgJBvvqGvN2/W1NeQeL56lZbr3Lnl/WW8uzDBzDa2sY1tr7YxH2bGO8v9+3RR3ccf1/gFyyktpb7ImprUZUJXl7pjAHTRXnY2dYMAqG/xokXAuHHA0KGta1NREfVXVlN78VhJCV3wN3hwjZ9zY4SHA9OnU/eKKVOAHTuAzEzA0pL6UxsZUVeMxYuBXbsABwfq33zpEqCvT/evXk1dPry8gMBA6gYiZ9Ys6jYC0Ho7dGhdvxnvBsyHmcFgMF4NJpgZ7yQSCQ3XFhUF8PmAvT2NWKGtDRQXAxER1M9XzpYtdEHeu0Z5OfVploeeW7iQ+lKvW0dF8cmTNKoGACxfDnz7LfWnfv4ciIykPwIOH6bHN2ygCwltbAALC8DYmIa927cP+Oijt9E7RlvDBDODwWC8GiysHOOdZMsWKpa3bwcSE4H4eBpxIiODWm+HDQMmTaKW5MuXgfHj33aLX4364eW+/hrQ0qoR/z17UssyIdRyDVAr+cKFVDwfPgx88QVw505N+DpVVWqB372bLiQMCXlRMJeXA7dv0wggLDIHg8FgMP7tMAsz450hK4vGP87JoVbSrl2BP/5ggs7DA3j6lEbz4PGoq4ZAQOM/OzgAIhG1wt+8WRNH+tkz6h4yYwYdw2fPaqzYEglN3BIcTMPwDRz4dvvHeH0wCzODwWC8GszCzHgnSEmhbhdjx1K3C7GYJv34t4tlgFrbi4trBK+VFbW483jU7UJRke7vU5XEfvTomnOHDKExn0NDa45/8gkVywoKNExdY4JZLAa6dwc2bgR6934zfWMwGAwG458Ai8PMaBMWLgT27KHvr1+nPsYNkZZGYyCPG1ezSA+gi97kbgQ//0wX7Dk6vvFmvxN4eb0oWK2sqJ+yXCw3xrBhgI4OHV+ALgDcsYNmNvzwQ2qNbmwS6t496ictP5fBYDAYjPcVZmFmvHHCwuiCMzU1wMCAJhFRV6f7CaGWUDMzWnbzZuqbnJFBF7SJRDQCxo4dwIAB1KJ8/XrdiA+MV0dFBZg4Edi6lbprHDhAXTk++YT6PR8/TqORuLtTi7JUSgU2QBcMAtRtQyJpXpwzGAwGg/GuwizMjDfOTz9RgSxfmKatTUVZ9+6AtTXdPvsMyM2li/iGDaOiWVsbmDCBZsTLyKBWz+BgusjP2Pht9+r9YcYMmpp77Voaoq5bN+r+MmgQ/TETHEzvV58+gK8vUFlJz5PPEuTn0x8xDAaDwWC8rzALM+ONkpFBUz/Pnk1F7tKlVBQDwOTJ1JIpFtMwaTt20FBwn3xCLdG7d1OBHREBuLpSX1oFBRYz+HXj4gIMH04FM1Bzf/T1aRSOjRvpPbp7l+6/dAn44AN6X7p0obGiT5+mgjozk/7YkftDMxgMBoPxPsCiZDBeCzIZ9THW0Ki7/7vvaHzg+Hga2SItDTAxoccIqVm0d+UKDQPXoQP1jZXvT0ykbgCWloCSUpt1518HIcCxY8DFi9RHXJ5YJTmZzgRkZAA9etD72Lkz9W3W1KRh6ZKS6D17/Jj6np88CcTGUteNu3eppZrxz4BFyWAwGIxXo1UuGRzH6XIcd4njuISqV51Gysk4jguv2oJr7bfkOO5O1flHOI5jkugd5fvvqWtFSUnNPpmMWo379wdsbakIlotloG6Eiz59qDi+fr3ufmtr6sPMxPKbheNo9IwdO+pmIbSwoHGaBwygmQFnz6Y+y3/8Qe+1iwvdl5YGfPMNFcuEUGv1yJF0huD+fWqBFgiAgoK31kUGg8FgMF6Z1vowLwVwhRBiC+BK1eeGKCWEuFVtw2rtDwKwoer8PADTW9keRiuYNw/44Qf6/sQJakWsz5MnwPz51M/13j26Ty6Mnz+n58kJCaHxgQMDX+76KiovWqgZbx8XFyqQ7eyoONbUpLMBAODsTMV0165UJCso0EWdO3fW/PjZtIm64iQkAH/++Xb7wmAwGAzGq9AqlwyO4+IA9CKEZHAcZwjgKiHEroFyRYQQjXr7OABZADoSQqQcx3UDsJwQ8kFz12UuGa8fmYxmkDM3B6KjqWVRR4dGsqjNwIFU9MhkVGD/+CN1p+jblybH6NWL+ib/+CNQVER9X1NTWQSF94kdO6grBsfRe6ymRrMp9utH7/0331Bx3acPfY62bas5d84cGjea8XZgLhkMBoPxarTWwtyBEJIBAFWvBo2UU+E4TsRx3P9xHDe8ap8egHxCiLTq81MALPbBWyIujk6xx8bS7ckT+iqT1ZQpLweuXaNWxh49gKtX6f79+6nYXrKEiudp0+jUe3Y2TcfMxPL7xfTp1C+5UycqlgEqjg8dAoKCqBvN/fs0JN3HH9Pj9vawRhWpAAAaPklEQVT0x9alSzX1EELDCAoE1A9aTkYGnZlgMBgMBuOfQrOCmeO4yxzHRTawfdiC65hVWTXGA/iJ4zhrAA3laGvU3M1xXGCV6BZlZWW14NKMl0HuXkEInUIHgLIyuuhLzl9/0YV9fftSS3J4OLUeHz9O/VVnzaJWRzs7apnOywM+/7yte8J403AccOpU3cQyHEcX/MkjmLi4UPcaZ2cqordto5E1Hj2qeaYWLKCCOiEBOHyY7jt2jD4/Q4a0aZcYDAaDwWiSZsPKEUL6NnaM47hnHMcZ1nLJeN5IHelVr485jrsKoBOA4wDacRynUGVlNgGQ3kQ7tgHYBlCXjObazWiaykpqxZMnDLl/H1BWplZkeUY+AIiJoRZDgE678/k01JiWFhXXkybRaflZs+j0+/XrVPBoa7d1jxhtiaLiy88cfPYZfdXVpa+XLwOmpjQax8cf0x9ip0/TEHWjR1Oh/eAB/cGl0+AyYgaDwWAw2pbWumQEA5hc9X4ygNP1C3Acp8NxnHLV+/YAvAFEE+o8HQpgZFPnM94M//sfDfOWXvUT5d49Gi7M3p66ZsjTTkdH15xz+TIVNVpa9FVZmbpl9O1L0zMDgI8Pjd/LYNTH0ZH+qFqyhKY2t7Oji0yHD6dZBRcsoLG6jx2j5f/66602l8FgMBiMalormNcA6MdxXAKAflWfwXGcB8dxO6rKOAAQcRz3AFQgryGEyGXY5wAWchz3CNSneWcr28N4SXbupOmMr16l1uawMJr+uEsXenzAAMDQkArmw4epy8XduzUJKVRUaKQMAPjyy7fSBcY7BscBFy5Q3+fnz2k6bmVl4MMq566ICOrC4+tLZzJu33677WUwGAwGQ06rMv0RQnIAvJDTixAiAjCj6v1tAM6NnP8YgFdr2sBoORERNWmNr16lQrmoiFqYy8qAvXupGH7wABCJaGpkPp9m2xs7tqaeTz4BhELqz8xgvAwCAV0YmpsL6OnRfU5OgJUVUFxM03SrqlJRXV8w//03XRw4Zkzbt5vBYDAY/25Yaux3jGvXaKxbb28qaEtLaQzclnDgAK3D05MKZjc3ut/DA+jYkYrpAQOoP/KVK/TYzZv0mrUZMYJuDEZL4LgasSz//Ntv9L2qKn3t3p2Gr5NIqK/02bN0lqOigj7v5uYv1hsRQRPj6OrS8/h8gNfaOTQGg8FgMNB6lwxGGzNnDvX1BIBPP6Uh3FqCSATs2kUFcUAAjVCwYgX1QXZyov7Hv/xCF17J/Zi7dKEChsF4U3h51fjBA/THWUkJXRi4YAF127Czo+K6dlxnOTIZDXU4cCBdzCoQ0BkQBoPBYDBeB61KXPK2+LcmLikuplnWNDWB/HzqY5ybS4WFQhNzBYTQaezERCAqilqRz5+n1mmPqhQG587R2Lq1uXuXipjjx5klmdG25OZSt6D4eCqSZ82imQQnTKALBH//nSbFkT+zCQlUJANAu3b070NZmabsXrqUpmaXR+v4N8MSlzAYDMarwSzM7xAPHlDxW1hIE408e0annmvHSm6IyEgaeYDPp4JDJKLWYzc3Ki48Pallrj6enlSIMLHMaGt0dWninIgIuvD0l1/oD8U5c+iCwR49gMGDa3zxHzygr926UbH81Vc0ROK4cdS1Y906QCpt/HoMBoPBYDQF82F+h7h/v+Z9cHDN+/h4GiJOzpkz1E+5c2dg7twaP+Tjx2n8Wzl8PvDHH9TizDWURgZ162Uw2hKOo4lPavPBBzQqi5ERFcXffgucPEmFM48HXLwIpKTQH4R//kkzC2po0KyT167VRHlhMBgMBqMlMMH8DnH/PqCkRBc+1RbMcXE1U9Pl5VQk5+QAR49S67Pcp7O2WJbT0gWDDMbbhMcDVq2i73NyqGAWiaiF2c6uru/9vHk0ssaJEzTW8++/M8HMYDAYjFeDuWS8A6SmUnEQFkaz7Kmq0pBbCgrUpSIurqbs7t1UIAcH0wWBe/YAoaFMKDDePz79lD7/a9dSC7OLS93jY8ZQt6V+/Wiq7RMn6OJABoPBYDBaChPM/3AqK2kiB1dX6ovs4UEXMBFCU1Y7OFCXDAB48gRYvZr6cfbpAyxcSOMqFxczwcx4/9DSAmbOpEI4OZn+jdSmdvi6kSOp7/ONGw3XtWkTWxTIYDAYjMZhgvkfQm4uXcQkj0cr5/p1KoQzMuiipc6d6dQzQF8FAmph3r+fiuesLGDNGioWhEIaPo7jgN69275PDMabZu5c+uMReNHCXJtBg+jMjDztdm0OHaLuG+vW1SwiZDAYDAajNkwwvyUePaJf1ADNsjdoEA31tmFD3XKHDgHq6sDly0D//jSrXm3BbGcHpKfTsFseHjSyQI8eNef/8gtd7Ker2ybdYjDaFAuLmtTaTQlmdXX6N1bfLSMpiboude8OqKnRuM8MBoPBYNSHCea3xI8/AhMnUneJzZtpbNl+/Wjs4/R0Wqa8nFrE/P2phfjCBaB9+xctzADNhvbbb4CZWd3rWFjQ8xmM95V16+gPTROTpsuNHAlkZtZNub15MxXQR44AkyYBBw9S142GePCAJlFh4ekYDAbj3wcTzG1EaWndz7GxdCo5Ohq4d4/6I//4Iz127hw99v33NKbs+PF1z/X1peHeevYEOnWi4eHWrweMjdumLwzGPwlra7oAsLHQiHIGD6bJTPbsoX9fJSXAzp00zriJCTB/Po1A8+WXDZ+/cyfw00/A//732rvAYDAYjH84LKxcG/D8OWBpSa1Xw4fTffLIFpGR1G/S2Zn6HFtaUn/k8+eBU6eAjz6irhi1MTenCUXkZGfTaAEMBqNxNDWBKVOArVupMNbRoT9IP/6YHre3p1kBV6+m7hv1E/bIk4suWwaMHk1jQTMYDAbj3wGzMLcB9+5Ra1ZICP1cWFjjdvH331T8urhQC9nQoXQlf0gI8MMPwN691ILcFEwsMxgvx+bNwDff0B+vmzYB7u6Aj0/N8eXL6VqA2bPrzgpJpUB4ODBsGBXbq1e3edMZDAaD8RZhgrkNkK+8l/tOysPAAXRBXmVlzYKlhQuplSs2Fli0qPlpZgaD8fLw+cCKFTSazOPHNPtf7b8xJSX6QzUri2bLlBMTQwX06NH0R+2xYyymM4PBYPybYIK5DXj4kL5GRlLrstwdw9OTfjEDNYLZ3Jxar8zN276dDMa/BT096v6krv7isR496NqADRtqQtbJ3TE8POjiwWfPgFu32q69DAaDwXi7tEowcxyny3HcJY7jEqpedRoo05vjuPBaWxnHccOrju3hOC6p1jG31rTnbfP8OV1Y9PRp3f0PH9IkC4RQF4zYWGrpkvszq6kBVlZt314Gg/EiHEdnemJiaBKgyZOpJVpTkyYNGjwYUFGhqbZfhnXraGx0BoPBYLy7tNbCvBTAFUKILYArVZ/rQAgJJYS4EULcAPgBKAFwsVaRJfLjhJDwVrbnrXLpEl2sd+RIzT6JhH7xjh9Pv4hv36YWZktLmoQEoIv9mvNTZjAYbcfo0UBAAHXROHCAriVwdwd4PEBDAxg4sMadqil++olmENy4sW3azWAwGIw3Q2sF84cA9la93wtgeDPlRwL4gxBS0srrtjkREcDUqVQAN0Z4ldy/cKFmX1wcPcfHB3B0pNO4sbF0Rb6TEy3TVMIFBoPR9igpUQvy9evAtm10n5dXzfGAALpwV+6qIaeoiFqUS0ro4t0FC2g0jowMIC+v7drPYDAYjNdLawVzB0JIBgBUvRo0U34sgHrJn7GK47gIjuM2cByn3Mr2vDF++IHGbw1vwgb+4AF9vX69ZoW93H/Z2Rno2xe4eJHus7OjcZNnzKAJTBgMxj+T6dOp+P3885p9AwdSa/PZs3XLHjhALcpffEHLGxnRMHYAjbnOYDAYjHeTZgUzx3GXOY6LbGD7sCUX4jjOEIAzgFr2V3wBwB6AJwBdAJ83cKr8/ECO40Qcx4my5Cvl2ojSUhoTGaCZ+BqCECqmzcxohr7r1+n+hw8BBQVqUf7vf+kUbdeudKU9xwHbt9N01wwG45+Lj0/d9PK6uoC394uC+fx5+rpxI/DXXzRMnacn3VdbMD9+3Lw7B4PBYDD+OTQrmAkhfQkhTg1spwE8qxLCckHcSFJZAMBoACcJIdVODYSQDEIpB7AbgFdjJxNCthFCPAghHvr6+i/bv9fCH38AYjF9X38KVk5mJo14MWcOzSZ28SJNirBvH11Zr6REF/fNn0+/SHv2bLv2MxiM18+QIUBYGJCWRj+XlQFXrtBFghYWgIMDdeMyM6N/+1FRtFxaGp1h2rmz+WukpNBEKUxcMxgMxtultS4ZwQAmV72fDOB0E2XHoZ47Ri2xzYH6P0e2sj1vhMOHAX19oF+/FwVzWRld5Ce3PHfrBvTpA2zZAgwYQIX0pk1t32YGg/FmGTKEvk6ZAowdSzN0lpQAY8YA9+8DN2/S2SUej65fkFuY79+niVBOnGj+Gnv2AN9/TxcOMxgMBuPt0VrBvAZAP47jEgD0q/oMjuM8OI7bIS/EcZwFAFMA1+qdf5DjuIcAHgJoD2BlK9vTav7+G1i1qubzo0fA6dN01XzXrtRKVFxcc3ztWvplGRhIP7u6Art2AX5+wJ071JfRw6Nt+8BgMN48Dg504e6tW8CZM/R/gIoKdbHS0anrwuHoWGNhlq9rCA2t+7+kIeTrIuSx2xkMBoPxdmiVYCaE5BBC+hBCbKtec6v2iwghM2qVS/7/9u49RqryjOP49xEE2rRVUIqLKKJSWxqvbKi1Ki1eUGMEKVqa2mLRGIX6h02NWk20jU0LGo0NJpa23mrEC40R4oWAiMak2NKkVixFFo1ZBO9SvEG1PP3jeadzus7MzjJzZmZ3fp/kZM685z3nPPvO2Z133/Occ9x9f3ff1WP9Ke5+eErxOM/d368lnt315pvFL7MbboBrroHu7shLnjcvUix++tPIRdy1q3jh3/bt8XCD4cPjQQZjx8ZjqkeNitzGtWvhZz9rxk8kInkzi9/xbdviosARI+CMM+Azn/l03a9+Ne6qsW1bdJjN4lqHJ56ovI9Chzn7dFAREWm8tnzS36pVcUq04NprI5Xiww9h9eooW7ECHnoocpGvvz6udp84MZYV0jIWLowvwMcfj9Ow555b3KZZ8b6tIjIwDR0a1yccc0xcyHfXXaXrTZgQr+vXR4f5lFPiYUaFiwbdI72rMP/OO3HdxKZNUaYRZhGR5mq77tyaNZFjvGxZsWzTpvhyuvFGeOutKFuxIu5occghMHdulI0eHaPIixfHhTsLFkQe46RJkee8YEHjfx4RaQ177RUPNSll4sT4J3rZsuj8TpwIU6fCAw9ELvPUqfH35bnn4iFHY8fG3yCIPGh1mEVEmmtwswNotKdSFvUrrxTLCo+yLjy+dvLk+GL74AOYPz++sAquvx6+//0Ykd6xA266qTFxi0j/1dER92G/5ZY4u3X44TBnDqxbFw9BGTo0Otxf+1qkakDxvs+nnhrXQ4iISPO03QjzM8/E69atxbLu7nj96KMYUZ4zJzrLe+4ZV8Bnfe978dCC7u7IdR4/viFhi0g/N2dOpH1BdJgPPTQuMr7uuvi7tGpVdJrnzo1/2ru64vqIk06Ct9+OSUREmqOtRph37Yor2qHYYd6+PdIxpkyJL6wpU2IkCGDGDPhij2cXmsEdd8C99xZTNUREejN9elwU/MEHcR9miBSOa68t1nn11Tijde+9cTbsyCOLdTdsgOOOa3zcIiLSZh3m9evh3XdjfsuWeC2MLp9/fpw2vfDCyCV88MG4jVwpo0bBZZflHq6IDCDDhsVjs9eti7NXpRTSv2bMiL9DJ5ygDrOISCtoqw5zIR3jiCOKI8yF/OVx4+Cee4p1Z85sbGwiMvBddVV19YYNg3/+s3iLuj331MNLRESaqa1ymJ95JkaHjz++2GEujDAfcEDz4hIR6enzn48R58GD4cQT44mhT/V89JOIiDREW3WYjzgiUi46OiI1Y8eOGGE2i9OfIiKtaPHiOAt25pnFh5mIiEjjtFVKxuWXx+vtt8fra6/FCPN++5XPKRQRabaRI2Hlyrijhu7MIyLSeG3VYS7o6IjXrVtjhHnMmObGIyLSm9GjYdGiZkchItKe2ioloyDbYe7uVodZRERERMpr6w7zli0xwqwL/kRERESknLbsMI8cCYMGxW2b3ntPI8wiIiIiUl5bdpj32CNuL3f33fF+0qTmxiMiIiIirastO8wQF9C89148Bnvy5GZHIyIiIiKtqqYOs5mdY2YvmNkuM+usUO80M9tgZl1mdmWmfJyZPWtmG83sfjMbUks8fVHIY16woFF7FBEREZH+qNYR5nXADODpchXMbBBwK3A6MAH4rplNSIvnAze7+3jgXeCCGuOp2qWXwsKFcPTRjdqjiIiIiPRHNXWY3X29u2/opdokoMvdX3L3fwP3AdPMzIApwJJU7y5gei3x9MUpp8C8eY3am4iIiIj0V43IYd4f6M6835zK9gG2ufsnPcpFRERERFpGr0/6M7OVwH4lFl3t7g9XsQ8rUeYVysvFcRFwEcCBBx5YxW5FRERERGrXa4fZ3U+ucR+bgeyjQcYAW4C3gL3NbHAaZS6Ul4tjEbAIoLOzs2zHWkRERESknhqRkvEXYHy6I8YQYBaw1N0deBKYmerNBqoZsRYRERERaZhabyt3tpltBr4OPGJmy1P5aDN7FCCNHv8IWA6sBx5w9xfSJq4AfmxmXURO8+9riUdEREREpN4sBnr7l87OTl+7dm2zwxAR6VfM7K/uXvae+SIiUlrbPulPRERERKQa6jCLiIiIiFTQL1MyzOxN4JXdXH1f4g4draZV44LWjU1x9Y3i6rtWjW134xrr7iPrHYyIyEDXLzvMtTCzta2Yw9eqcUHrxqa4+kZx9V2rxtaqcYmIDFRKyRARERERqUAdZhERERGRCtqxw7yo2QGU0apxQevGprj6RnH1XavG1qpxiYgMSG2XwywiIiIi0hftOMIsIiIiIlK1AdlhNrNzzOwFM9tlZmWvJDez08xsg5l1mdmVmfJxZvasmW00s/vNbEid4hphZivSdleY2fASdb5lZn/LTDvMbHpadqeZvZxZdlSj4kr1/pPZ99JMeS7tVW1sZnaUmf0pfeZ/N7PvZJbVtc3KHTOZ5UNTG3SlNjkos+yqVL7BzKbWEsduxPVjM/tHap8nzGxsZlnJz7VBcZ1vZm9m9n9hZtns9LlvNLPZDY7r5kxML5rZtsyyPNvrdjN7w8zWlVluZvbrFPffzeyYzLLc2ktEpO25+4CbgK8AhwGrgc4ydQYBm4CDgSHAc8CEtOwBYFaavw24pE5xLQCuTPNXAvN7qT8CeAf4bHp/JzAzh/aqKi7g/TLlubRXtbEBXwLGp/nRwFZg73q3WaVjJlNnLnBbmp8F3J/mJ6T6Q4FxaTuDGhjXtzLH0SWFuCp9rg2K63xgYYl1RwAvpdfhaX54o+LqUf9S4Pa82ytt+0TgGGBdmeVnAI8BBhwLPJt3e2nSpEmTJh+YI8zuvt7dN/RSbRLQ5e4vufu/gfuAaWZmwBRgSap3FzC9TqFNS9urdrszgcfc/cM67b+cvsb1Pzm3V1WxufuL7r4xzW8B3gDyeDhDyWOmQrxLgJNSG00D7nP3ne7+MtCVtteQuNz9ycxxtAYYU6d91xRXBVOBFe7+jru/C6wATmtSXN8FFtdp3xW5+9PEP8nlTAPu9rAG2NvMOsi3vURE2t6A7DBXaX+gO/N+cyrbB9jm7p/0KK+HUe6+FSC9frGX+rP49Bf1L9Kp2JvNbGiD4xpmZmvNbE0hTYR826svsQFgZpOIUcNNmeJ6tVm5Y6ZkndQm/yLaqJp184wr6wJilLKg1OfayLi+nT6fJWZ2QB/XzTMuUurKOGBVpjiv9qpGudjzbC8RkbY3uNkB7C4zWwnsV2LR1e7+cDWbKFHmFcprjqvabaTtdACHA8szxVcBrxEdwkXAFcDPGxjXge6+xcwOBlaZ2fPA9hL1+nTrlTq32R+A2e6+KxXvdpuV2kWJsp4/ay7HVS+q3raZnQd0ApMzxZ/6XN19U6n1c4hrGbDY3Xea2cXE6PyUKtfNM66CWcASd/9Ppiyv9qpGM44vEZG21287zO5+co2b2AwckHk/BtgCvEWc5hycRggL5TXHZWavm1mHu29Nnbs3KmzqXOAhd/84s+2taXanmd0B/KSRcaV0B9z9JTNbDRwN/JEa2qtesZnZF4BHgGvSqerCtne7zUood8yUqrPZzAYDexGn2KtZN8+4MLOTiX9CJrv7zkJ5mc+1Hh3AXuNy97czb38LzM+s+80e666uQ0xVxZUxC5iXLcixvapRLvY820tEpO21c0rGX4DxFnd4GEJ8MS51dweeJPKHAWYD1YxYV2Np2l412/1U3mTqMBbyhqcDJa+kzyMuMxteSGcws32BbwD/yLm9qo1tCPAQkdv5YI9l9WyzksdMhXhnAqtSGy0FZlncRWMcMB74cw2x9CkuMzsa+A1wlru/kSkv+bk2MK6OzNuzgPVpfjlwaopvOHAq/3+2Jde4UmyHERfQ/SlTlmd7VWMp8IN0t4xjgX+lfwrzbC8REWn2VYd5TMDZxIjLTuB1YHkqHw08mql3BvAiMTp0dab8YKIz0wU8CAytU1z7AE8AG9PriFTeCfwuU+8g4FVgjx7rrwKeJzp99wCfa1RcwHFp38+l1wvybq8+xHYe8DHwt8x0VB5tVuqYIVI8zkrzw1IbdKU2OTiz7tVpvQ3A6XU+5nuLa2X6XSi0z9LePtcGxfVL4IW0/yeBL2fWnZPasQv4YSPjSu+vA37VY72822sxcZeXj4m/YRcAFwMXp+UG3Jrifp7MXYDybC9NmjRpavdJT/oTEREREamgnVMyRERERER6pQ6ziIiIiEgF6jCLiIiIiFSgDrOIiIiISAXqMIuIiIiIVKAOs4iIiIhIBeowi4iIiIhUoA6ziIiIiEgF/wV4KrSk5KfViQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_data_samples = 1000\n",
    "num_x_samples = 1000   \n",
    "def gd_func(x, x1, x2):\n",
    "    #hypothesis found by learning algorithm\n",
    "    a = x1 + x2\n",
    "    b = -x1 * x2\n",
    "    return a*x + b\n",
    "\n",
    "calc_bias_var_eout(gd_func, lambda x: x**2, num_data_samples, num_x_samples)    "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}