{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Random numbers\n", "\n", "Random numbers play important role, both in modeling physics processes (some of which are regarded as truly random, such as radioactive decay) and as a tool to tackle otherwise intractable problems.\n", "\n", "Numbers generated on a computer are not truly random, but a good generator produces numbers that reflect the desired properties of a random variable, hence they are called truly random.\n", "\n", "The most basic routine typically produces a random integer number $x$ between 0 and some maximum value $m$. By dividing over $m$ one can get a real pseudo-random number $\\eta = x/m$ which is uniformly distributed in an interval $\\eta \\in [0,1)$. By applying various tranformations and techniques to the sequence of $\\eta$ one can obtain various other distributions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Linear congruential generator\n", "\n", "Historically, one of the simplest generators is linear congruential generator (LCG).\n", "Although it should not be used in practice, it illustrates some of the key concepts and issues.\n", "\n", "It generates a sequence of pseudo-random numbers in accordance with an iterative procedure\n", "$$\n", "x_{n+1} = (a x_n + c) ~ \\text{mod} ~ m,\n", "$$\n", "for some parameters $a,x,m$.\n", "\n", "It is clear that the next number only depends on the present value, and that the sequence of numbers will be periodic, with a period of at most $m$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "# Linear congruential generator\n", "\n", "# Parameters (based on Numerical Recipes)\n", "lcg_a = 1664525\n", "lcg_c = 1013904223\n", "lcg_m = 4294967296\n", "# Current value (initial seed)\n", "lcg_x = 1\n", "\n", "def lcg():\n", " global lcg_x\n", " lcg_x = (lcg_a * lcg_x + lcg_c)%lcg_m\n", " return lcg_x" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot\n", "import matplotlib.pyplot as plt\n", "\n", "results = []\n", "\n", "N = 1000\n", "for i in range(N):\n", " results.append(lcg()/lcg_m)\n", " \n", "plt.xlabel(\"N\")\n", "plt.ylabel(\"${\\eta}$\")\n", "plt.plot(results,\"o\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apart from rather short period, LCG also typically generates numbers across a hyperplane (rather than the full space), if random numbers are to be regarded as components $(x,y,z,...)$ of a vector.\n", "\n", "For a good choice parameters and small dimension this issue maybe less visible:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 2D plot\n", "\n", "resultsx = []\n", "resultsy = []\n", "\n", "N = 1000\n", "for i in range(N):\n", " resultsx.append(lcg()/lcg_m)\n", " resultsy.append(lcg()/lcg_m)\n", " \n", "plt.plot(resultsx,resultsy,\"o\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "but for other parameters the artefacts are clearly visible already in 2D:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Slightly different choice of m\n", "lcg_m = 3000000000\n", "\n", "resultsx = []\n", "resultsy = []\n", "\n", "N = 1000\n", "for i in range(N):\n", " resultsx.append(lcg()/lcg_m)\n", " resultsy.append(lcg()/lcg_m)\n", " \n", "plt.plot(resultsx,resultsy,\"o\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this reason LCG is not and should not be used in any serious calculations.\n", "\n", "Other methods have been developed over the years and the general method of choice is **Mersenne Twister** random number generator which is implemented by default in many programming environments. It has a long period of $2^{19937} - 1$, passes most statistical randomness tests, fast, and suitable for most physical applications.\n", "\n", "We will not reimplement it but take it for granted." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Use Mersenne Twister\n", "import numpy as np\n", "\n", "np.random.rand() # Random number \\eta uniformly distributed over (0,1)\n", "\n", "resultsx = []\n", "resultsy = []\n", "\n", "N = 1000\n", "for i in range(N):\n", " resultsx.append(np.random.rand())\n", " resultsy.append(np.random.rand())\n", " \n", "plt.plot(resultsx,resultsy,\"o\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pseudo-random number generators are iterative constructs that generate a pre-determined sequence of numbers from an initial state. The initial state can be changes by modifying the seed value." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "resultsx = []\n", "resultsy = []\n", "\n", "N = 1000\n", "np.random.seed(1)\n", "for i in range(N):\n", " resultsx.append(np.random.rand())\n", " resultsy.append(np.random.rand())\n", " \n", "plt.plot(resultsx,resultsy,\"o\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()\n", "\n", "np.random.seed(1)\n", "for i in range(N):\n", " resultsx.append(np.random.rand())\n", " resultsy.append(np.random.rand())\n", " \n", "plt.plot(resultsx,resultsy,\"o\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deterministic nature for a specified seed is useful for debugging the code, since the sequence of pseudo-random numbers can be guaranteed to be the same, and the error will thus be reproduced each time.\n", "\n", "In production runs (e.g. on a cluster) one has to make sure that different seed (or better yet, different entire state) is used for each run" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulation example: Radioactive decay\n", "*Example 10.1*\n", "\n", "Some physical processes are truly random (recall quantum mechanics), for instance radiactive decay.\n", "\n", "The number of radioactive isotopes with a half-life of $\\tau$ evolves as\n", "\n", "$$\n", "N(t) = N(0) 2^{-t/\\tau},\n", "$$\n", "\n", "therefore, the probability for a single atom to decay over the time interval $t$ is \n", "\n", "$$\n", "p(t) = 1 - 2^{-t/\\tau}.\n", "$$\n", "\n", "Let us simulate the time evolution for a sample of thallium atoms decaying (half-life of $\\tau = 3.053$ minutes) into lead atoms." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Decay constants\n", "NTl = 100 # Number of thallium atoms\n", "NPb = 0 # Number of lead atoms\n", "tau = 3.053*60 # Half life of thallium in seconds\n", "h = 1.0 # Size of time-step in seconds\n", "p = 1 - 2**(-h/tau) # Probability of decay in one step\n", "tmax = 1000 # Total time\n", "ctime = 0 # Current time\n", "\n", "# Lists of plot points\n", "tpoints = np.arange(0.0,tmax,h)\n", "Tlpoints = []\n", "Pbpoints = []\n", "TlpointsTh = [] # Expected number\n", "\n", "# Main loop\n", "for t in tpoints:\n", " Tlpoints.append(NTl)\n", " Pbpoints.append(NPb)\n", "\n", " # Calculate the number of atoms that decay\n", " decay = 0\n", " for i in range(NTl):\n", " if np.random.rand()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Decay constants\n", "NTl = 10000 # Number of thallium atoms\n", "NPb = 0 # Number of lead atoms\n", "tau = 3.053*60 # Half life of thallium in seconds\n", "h = 1.0 # Size of time-step in seconds\n", "p = 1 - 2**(-h/tau) # Probability of decay in one step\n", "tmax = 1000 # Total time\n", "ctime = 0 # Current time\n", "\n", "# Lists of plot points\n", "tpoints = np.arange(0.0,tmax,h)\n", "Tlpoints = []\n", "Pbpoints = []\n", "TlpointsTh = [] # Expected number\n", "\n", "# Main loop\n", "for t in tpoints:\n", " Tlpoints.append(NTl)\n", " Pbpoints.append(NPb)\n", "\n", " # Calculate the number of atoms that decay\n", " decay = 0\n", " for i in range(NTl):\n", " if np.random.rand()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 100000\n", "x = 0\n", "y = 0\n", "\n", "dirs = [ [1,0], [-1,0], [0,1], [0,-1] ]\n", "\n", "points_x = [x]\n", "points_y = [y]\n", "for i in range(N):\n", " direction = np.random.randint(4)\n", " x += dirs[direction][0]\n", " y += dirs[direction][1]\n", " points_x.append(x)\n", " points_y.append(y)\n", " \n", "plt.title(\"Brownian motion\")\n", "plt.plot(points_x,points_y)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing an integral as area under the curve\n", "\n", "Recall the interpratation of a definite integral as the area under the curve.\n", "We can use this interpretation to apply random numbers for approximating integrals.\n", "Consider\n", "\n", "$$\n", "I = \\int_0^\\pi \\sin(x) dx\n", "$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return np.sin(x)\n", "\n", "xplot = np.linspace(0,np.pi, 100)\n", "yplot = f(xplot)\n", "\n", "plt.xlim(0,np.pi)\n", "plt.ylim(0,1.1)\n", "plt.plot(xplot, yplot,color='r',label=\"sin(x)\")\n", "plt.fill_between(xplot, yplot, step=\"pre\", alpha = 0.4, color='orange',label=\"I = area\")\n", "plt.axhline(1.0,linestyle='--', color='r')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can estimate the area by sampling the points uniformly from an enveloping rectangle and counting the fraction of points under the curve given by the integrand $f(x)$.\n", "\n", "Assuming an integral\n", "\n", "$$\n", "I = \\int_a^b f(x) dx\n", "$$\n", "\n", "where $f(x) \\geq 0$ and $f(x) \\leq y_{\\rm max}$, the integrand can be evaluated as\n", "\n", "$$\n", "I = (b-a) y_{\\rm max} \\frac{C}{N},\n", "$$\n", "\n", "where $C$ is the number of the sampled points that fall under $f(x)$.\n", "\n", "The statistical error of the integrand can be estimated using the properties of the binomial distribution with $p = C/N$:\n", "\n", "$$\n", "\\delta I = (b-a) y_{\\rm max} \\sqrt{\\frac{p(1-p)}{N}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "I = 2.0451768174869556 +- 0.04735360863042119\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# For visualization\n", "points_in = []\n", "points_out = []\n", "\n", "# Compute integral \\int_a^b f(x) dx as an area below the curve\n", "# Assumes that f(x) is non-negative and bounded from above by ymax\n", "# Returns the value of the integral and the error estimate\n", "def areaMC(f, N, a, b, ymax):\n", " global points_in, points_out\n", " points_in = []\n", " points_out = []\n", " count = 0\n", " for i in range(N):\n", " x = a + (b-a)*np.random.rand()\n", " y = ymax * np.random.rand()\n", " if y" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute the value of \\pi through the fraction of random points inside a square\n", "# that are also inside a circle around the origin\n", "# Returns the value of the integral and the error estimate\n", "def piMC(N): \n", " global points_in, points_out\n", " points_in = []\n", " points_out = []\n", " count = 0\n", " for i in range(N):\n", " x = -1 + 2 * np.random.rand()\n", " y = -1 + 2 * np.random.rand()\n", " r2 = x**2 + y**2\n", " if (r2 < 1.):\n", " count += 1\n", " points_in.append([x,y])\n", " else:\n", " points_out.append([x,y])\n", " p = count/N\n", " return 4. * p, 4. * np.sqrt(p*(1-p)/N)\n", " \n", "\n", "N = 100000\n", "piMC, piMCerr = piMC(N)\n", "print(\"pi = \",piMC,\" +- \",piMCerr)\n", "\n", "xpoints = np.arange(0,np.pi,0.01)\n", "plt.xlim(-1.2,1.2)\n", "plt.ylim(-1.2,1.2)\n", "\n", "xcircle= [np.cos(phi) for phi in np.arange(0.,2*np.pi,0.1)]\n", "ycircle= [np.sin(phi) for phi in np.arange(0.,2*np.pi,0.1)]\n", "plt.plot(xcircle,ycircle,color='r')\n", "\n", "x2 = [x[0] for x in points_out]\n", "y2 = [x[1] for x in points_out]\n", "plt.plot(x2,y2,'o',color='b')\n", "x1 = [x[0] for x in points_in]\n", "y1 = [x[1] for x in points_in]\n", "plt.plot(x1,y1,'o',color='r')\n", "plt.gca().set_aspect('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Computing integral as the average\n", "\n", "An integral\n", "\n", "$$\n", "I = \\int_a^b f(x) dx\n", "$$\n", "\n", "corresponds to the mean value $\\langle f \\rangle$ over $(a,b)$\n", "\n", "$$\n", "\\langle f \\rangle = \\frac{\\int_a^b f(x) dx}{b - a} = \\frac{I}{b-a},\n", "$$\n", "\n", "so that\n", "\n", "$$\n", "I = (b-a) \\langle f \\rangle\n", "$$\n", "\n", "The integral can therefore be estimated by evaluating $\\langle f \\rangle$ as the average value of $f(x)$ obtained through random sampling of the variable $x$ uniformly over the interval $(a,b)$:\n", "\n", "$$\n", "\\langle f \\rangle = \\frac{1}{N} \\sum_{i=1}^N f(x_i).\n", "$$\n", "\n", "The error estimate comes from the law of averages and involves the estimate of $\\langle f^2 \\rangle$\n", "\n", "$$\n", "\\delta I = (b-a) \\sqrt{\\frac{\\langle f^2 \\rangle - \\langle f \\rangle^2}{N}}\n", "$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "I = 2.0238547377310927 +- 0.029430579356107937\n" ] } ], "source": [ "# Compute integral \\int_a^b f(x) dx as an average of f(x) over the interval (a,b)\n", "# Returns the value of the integral and the error estimate\n", "def intMC(f, N, a, b):\n", " total = 0\n", " total_sq = 0\n", " for i in range(N):\n", " x = a + (b-a)*np.random.rand()\n", " fval = f(x)\n", " total += fval\n", " total_sq += fval * fval\n", " f_av = total / N\n", " fsq_av = total_sq / N \n", " return (b-a) * f_av, (b-a) * np.sqrt((fsq_av - f_av*f_av)/N)\n", " \n", "\n", "def f(x):\n", " return np.sin(x)\n", "\n", "N = 1000\n", "I, err = intMC(f, N, 0, np.pi)\n", "print(\"I = \",I,\" +- \",err)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Another way to compute $\\pi$\n", "\n", "Consider an integral\n", "$$\n", "4 \\int_0^1 \\frac{1}{1+x^2} dx = \\left. 4 \\arctan(x) \\right|^1_0 = \\pi\n", "$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pi = 3.120397125394039 +- 0.02038793077097405\n" ] } ], "source": [ "def fpi(x):\n", " return 4 / (1 + x**2)\n", "\n", "N = 1000\n", "I, err = intMC(fpi, N, 0, 1)\n", "print(\"pi = \",I,\" +- \",err)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integrals in multiple dimensions\n", "\n", "Monte Carlo methods really shine when it comes to numerical evaluation of integrals in multiple dimensions.\n", "Consider the following $D$-dimensional integral\n", "\n", "$$\n", "I = \\int_{a_1}^{b_1} d x_1 \\ldots \\int_{a_D}^{b_D} d x_D f(x_1,\\ldots,x_D).\n", "$$\n", "\n", "Computing it numerically using, for instance, the rectangle rule would involves the evaluation of multi-dimensional sum\n", "\n", "$$\n", "I \\approx \\sum_{k_1 = 1}^{N_1} \\ldots \\sum_{k_D = 1}^{N_D} f(x_{k_1},\\ldots,x_{k_D}) \\prod_{d=1}^D h_d,\n", "$$\n", "\n", "where $h_d = (b_d - a_d)/N_d$ and $x_{k_d} = a_d + h_d (k_d - 1/2)$.\n", "\n", "The total number of integrand evalutions is $N_{\\rm tot} = \\prod_{d=1}^D N_D$, e.g. if we use the same number $N$ of points in each dimension, it scales exponentially with $D$,\n", "\n", "$$\n", "N_{\\rm tot} = N^D,\n", "$$\n", "\n", "making the method impractical for large number of dimensions." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# Composite rectangle rule for evaluating a multi-dimensional integral\n", "def rectangle_rule_multi(f, Nrect, a, b):\n", " xks = []\n", " hs = []\n", " toth = 1\n", " dim = len(Nrect)\n", " \n", " multi_index_max = 1\n", " for idim in range(dim):\n", " multi_index_max *= Nrect[idim]\n", " h = (b[idim] - a[idim]) / Nrect[idim]\n", " hs.append(h)\n", " toth *= h\n", " xk = []\n", " for k in range(Nrect[idim]):\n", " xk.append(a[idim] + h * (k - 1./2.))\n", " xks.append(xk)\n", " \n", " ret = 0.\n", " for multiindex in range(multi_index_max):\n", " cindex = multiindex\n", " x = []\n", " for idim in range(dim):\n", " index = cindex % Nrect[idim]\n", " x.append(xks[idim][index])\n", " cindex = cindex // Nrect[idim]\n", " \n", " ret += f(x)\n", " \n", " ret *= toth\n", " \n", " return ret" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us consider the following integral as an example\n", "$$\n", "I = \\int_0^{\\pi/2} d x_1 \\ldots \\int_{0}^{\\pi/2} d x_D \\, \\sin(x_1 + x_2 + \\ldots + x_D).\n", "$$\n", "\n", "We can evaluate this integral analytically through an iterative procedure for any finite $D$.\n", "The first few results are\n", "\n", "| D | I = |\n", "| -------- | -------- |\n", "| 1 | 1 |\n", "| 2 | 2 |\n", "| 3 | 2 |\n", "| 4 | 0 |\n", "| 5 | -4 |\n", "| 6 | -8 |\n", "\n", "#### Rectangle rule\n", "\n", "Applying the rectangle rule we get" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "D = 1 I = 0.9681356137777438\n", "D = 2 I = 1.9962176337747817\n", "D = 3 I = 2.1796094400043926\n", "D = 4 I = 0.5014154076818487\n", "CPU times: user 7.11 s, sys: 49.4 ms, total: 7.16 s\n", "Wall time: 7.18 s\n" ] } ], "source": [ "%%time\n", "\n", "def f(x):\n", " xsum = 0\n", " for i in range(len(x)):\n", " xsum += x[i]\n", " return np.sin(xsum)\n", "\n", "Ndimmax = 4\n", "\n", "for Ndim in range(1,Ndimmax + 1):\n", " Nrect = [50 for i in range(Ndim)]\n", " a = [0. for i in range(Ndim)]\n", " b = [np.pi/2 for i in range(Ndim)]\n", " I = rectangle_rule_multi(f,Nrect,a,b)\n", " print(\"D =\",Ndim, \" I =\",I)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can only make $N$ so large when we go to higher dimensions without calculation becoming unfeasible.\n", "As a result, calculating the integral for $D \\gtrsim 4$ even with moderate accuracy becomes challenging." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Monte Carlo way \n", "\n", "Monte Carlo techniques, on the other hand, are not plagued by the curse of dimensionality.\n", "The integral can be approximated by computing the mean value of the integrand in $D$-dimensional space\n", "$$\n", "I = \\langle f(x_1,\\ldots,x_D) \\rangle \\prod_{k=1}^D (b_k-a_k).\n", "$$\n", "Here $x_1,\\ldots,x_D$ are independent random variables distributed uniformly in intervals $x_k \\in [a_k,b_k]$.\n", "Adding one more dimension thus only entails sampling one more number for each sample.\n", "Thus the complexity of the method is linear in $D$ as opposed to the exponential complexity of other methods.\n", "\n", "Error estimate\n", "$$\n", "\\delta I = \\sqrt{\\frac{\\langle f^2 \\rangle - \\langle f \\rangle^2}{N}} \\, \\prod_{k=1}^D (b_k-a_k),\n", "$$\n", "scales with $1/\\sqrt{N}$ as before." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "# Evaluating a multi-dimensional integral\n", "# by sampling uniformly distributed numbers\n", "# and calculating the average of the integrand\n", "def intMC_multi(f, nMC, a, b):\n", " dim = len(a)\n", " \n", " total = 0\n", " total_sq = 0\n", " for iMC in range(nMC):\n", " x = [a[idim] + (b[idim] - a[idim]) * np.random.rand() for idim in range(dim)]\n", " fval = f(x)\n", " total += fval\n", " total_sq += fval * fval\n", " \n", " f_av = total / nMC\n", " fsq_av = total_sq / nMC \n", " \n", " vol = 1.\n", " for idim in range(dim):\n", " vol *= (b[idim] - a[idim])\n", " \n", " return vol * f_av, vol * np.sqrt((fsq_av - f_av*f_av)/nMC)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "D = 1 I = 0.9993739322835572 +- 0.00048374555149185663\n", "D = 2 I = 1.999673583869861 +- 0.0005271898298378077\n", "D = 3 I = 2.000281719209202 +- 0.001873864337864639\n", "D = 4 I = -0.005527473307926931 +- 0.0039355870900790605\n", "D = 5 I = -4.00658532586375 +- 0.00544752767681332\n", "D = 6 I = -7.993067705005959 +- 0.007511157283780776\n", "D = 7 I = -8.002001902682919 +- 0.014639212383786052\n", "D = 8 I = -0.010555898125154409 +- 0.025874692253323058\n", "D = 9 I = 16.018663094391286 +- 0.03791332298430485\n", "D = 10 I = 31.982668453813293 +- 0.05662481958581747\n", "CPU times: user 22.8 s, sys: 533 ms, total: 23.3 s\n", "Wall time: 23.3 s\n" ] } ], "source": [ "%%time\n", "\n", "def f(x):\n", " xsum = 0\n", " for i in range(len(x)):\n", " xsum += x[i]\n", " return np.sin(xsum)\n", "\n", "Ndimmax = 10\n", "NMC = 1000000\n", "for Ndim in range(1,Ndimmax + 1):\n", " a = [0. for i in range(Ndim)]\n", " b = [np.pi/2 for i in range(Ndim)]\n", " I, Ierr = intMC_multi(f,NMC,a,b)\n", " print(\"D =\",Ndim, \" I =\",I,\"+-\",Ierr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Volume of a D-dimensional ball\n", "\n", "Let us consider an $D$-dimensional ball of radius $R$.\n", "Its volume is given by an $D$-dimensional integral\n", "\n", "$$\n", "V_D(R) = \\int_{\\sqrt{x_1^2+\\ldots x_{D}^2} < R} d x_1 \\ldots d x_D.\n", "$$\n", "\n", "This can be written with the recursion formula\n", "\n", "$$\n", "V_D(R) = R^D \\int_{-1}^1 V_{D-1} \\left(\\sqrt{1-t^2} \\right) dt,\n", "$$\n", "\n", "with $V_0(R) = 1$.\n", "\n", "Let us use the rectangle method to evalute this integral for $R = 1$.\n", "We will have to use rectangle method recursively since the integral is multi-dimensional." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "# Computes volume of a D-dimensional ball\n", "# using a recursion relation and rectangle rule\n", "# with nrect slices for each dimension\n", "def VD(D, R, nrect):\n", " if (D == 0):\n", " return 1.\n", " \n", " ret = 0.\n", " h = 2. / nrect;\n", " for k in range(nrect):\n", " xk = -1. + h * (k+1/2.)\n", " ret += VD(D-1,np.sqrt(1-xk**2), nrect)\n", " ret *= h * R**D\n", " return ret" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "V 0 (1) = 1.0\n", "V 1 (1) = 2.0\n", "V 2 (1) = 3.144340711294003\n", "V 3 (1) = 4.193292772581682\n", "V 4 (1) = 4.940233310235603\n", "V 5 (1) = 5.2695829353261505\n", "CPU times: user 2min 39s, sys: 3.58 s, total: 2min 42s\n", "Wall time: 2min 42s\n" ] } ], "source": [ "%%time\n", "\n", "nrect = 50\n", "for n in range(6):\n", " print(\"V\",n,\"(1) = \",VD(n,1,nrect))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The calculation, again, quickly becomes untenable in larger dimensions\n", "\n", "This can be overcome with Monte Carlo techniques.\n", "\n", "Here we observe that the ball $\\sqrt{x_1^2+\\ldots x_{n}^2} < R$ is a subvolume of a hypercube $-R < x_1,\\ldots,x_D < R$.\n", "If we will now randomly sample points that are uniformly distributed inside a hypercube,\n", "the fraction $C/N$ of those that are also inside the ball will reflect\n", "the ratio of the ball and hypercube volumes $V_D(R)$ and $V_{\\rm cube} (R) = (2R)^D$.\n", "Therefore,\n", "\n", "$$\n", "V_D(R) = (2R)^D \\frac{C}{N},\n", "$$\n", "\n", "in the limit of large $N$." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "def VD_MC(D, R, N = 100):\n", " if (D == 0):\n", " return 1., 0., 1.\n", " count = 0\n", " for iMC in range(N):\n", " xs = [-R + 2 * R * np.random.rand() for i in range(n)]\n", " r2 = 0.\n", " for i in range (D):\n", " r2 += xs[i]**2\n", " if (r2 < R**2):\n", " count += 1\n", " \n", " p = count/N\n", " return (2*R)**D * p, (2*R)**D * np.sqrt(p*(1-p)/N), p" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "V 0 (1) = 1.0 +- 0.0\n", "V 1 (1) = 2.0 +- 0.0\n", "V 2 (1) = 3.142232 +- 0.0023217691780950144\n", "V 3 (1) = 4.195456 +- 0.005650096804845737\n", "V 4 (1) = 4.948736 +- 0.010458469104252686\n", "V 5 (1) = 5.276672 +- 0.016793465193605278\n", "V 6 (1) = 5.12192 +- 0.024558860540082068\n", "V 7 (1) = 4.740864 +- 0.034186394970324205\n", "V 8 (1) = 4.066816 +- 0.045267337090271705\n", "V 9 (1) = 3.279872 +- 0.057767411291551156\n", "V 10 (1) = 2.52928 +- 0.07188303642281119\n", "V 11 (1) = 1.8432 +- 0.08685017229412961\n", "V 12 (1) = 1.236992 +- 0.10064977975924176\n", "V 13 (1) = 0.884736 +- 0.12039081820645878\n", "V 14 (1) = 0.688128 +- 0.15015868694055376\n", "V 15 (1) = 0.32768 +- 0.14654221825683955\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 21.2 s, sys: 511 ms, total: 21.7 s\n", "Wall time: 21.5 s\n" ] } ], "source": [ "%%time\n", "\n", "nMC = 500000\n", "ds = []\n", "ps = []\n", "for n in range(16):\n", " Vnval, Vnerr, p = VD_MC(n, 1, nMC)\n", " print(\"V\",n,\"(1) = \",Vnval, \"+-\", Vnerr)\n", " ds.append(n)\n", " ps.append(p)\n", " \n", "plt.plot(ds,ps,\"o\")\n", "plt.yscale(\"log\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Nonuniformly distributed random numbers\n", "\n", "In many cases we deal with random numbers $\\xi$ that are distributed non-uniformly.\n", "Common examples are:\n", "- Exponential distribution $\\rho(x) = e^{-x}$.\n", "- Gaussian distribution $\\rho(x) \\propto e^{-\\frac{x^2}{2\\sigma^2}}$.\n", "- Power-law distribution $\\rho(x) \\propto x^{\\alpha}$.\n", "- Arbitrary peaked distributions.\n", "\n", "There are two common methods for generating nonunifrom random variates.\n", "They both make use of uniformly distributed variates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Inverse transform sampling\n", "\n", "The basic idea is that if $\\eta$ is a uniformly distibuted random variable, some function of it, $\\xi = f(\\eta)$, is not. The idea is to sample $\\eta$ and calculate $\\xi$ via this function such that $\\xi$ corresponds to a desired probability density $\\rho(\\xi)$. How to find the function $f(\\eta)$?\n", "\n", "Without the loss of generality assume that $\\xi \\in (-\\infty, \\infty)$ and that $f(\\eta)$ maps $\\eta$ to $\\xi$ such that $f(0) \\to -\\infty$. Consider now the cumulative distribution function \n", "\n", "$$G(x) = Pr(\\xi < x) = \\int_{-\\infty}^x \\rho(\\xi) d\\xi.$$ \n", "\n", "It corresponds to the probability that $\\eta < y$ where $y$ is such that $x = f(y)$. Since $\\eta$ is uniformly distributed, this probablity equals to $y$. Therefore,\n", "\n", "$$\n", "G[x = f(y)] = y,\n", "$$\n", "\n", "thus\n", "\n", "$$\n", "f(y) = G^{-1}(y).\n", "$$\n", "\n", "If we can calculate the inverse of $G^{-1}(y)$ of the cumulative distribution function for $\\xi$, we are good.\n", "\n", "The algorithm is the following:\n", "1. Calculate the cumulative distribution\n", "\n", "$$\n", "G(x) = \\int_{-\\infty}^x \\rho(\\xi) d\\xi\n", "$$\n", "\n", "2. Find the inverse function $G^{-1}(y)$ as the solution to the equation\n", "\n", "$$\n", "G(x) = y\n", "$$\n", "\n", "with respect to $x$.\n", "3. Sample uniformly distributed randon variables $\\eta$ and calculate $\\xi = G^{-1}(\\eta)$\n", "\n", "Sometimes, evaluating $G(x)$ and/or $G^{-1}(y)$ explicitly is challenging.\n", "In such cases one would resort to numerical integration and/or non-linear equation solvers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Exponential distribution\n", "\n", "Recall the radioactive decay process. The time of decay is distributed in accordance with\n", "$$\n", "\\rho(t) = \\frac{1}{\\tau} e^{-\\frac{t}{\\tau}}.\n", "$$\n", "\n", "The cumulative distibution function reads\n", "$$\n", "F(x) = \\int_0^{x} \\frac{1}{\\tau} e^{-\\frac{t}{\\tau}} dt = 1 - e^{-\\frac{x}{\\tau}}.\n", "$$\n", "To apply inverse transform sampling we have to invert $F(x)$ by solving the equation\n", "$$\n", "1 - e^{-\\frac{t}{\\tau}} = \\eta.\n", "$$\n", "This can be done straightforwardly to give\n", "$$\n", "t(\\eta) = -\\tau \\ln(1-\\eta).\n", "$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Radioactive decay sampler\n", "def sample_tdecay(tau):\n", " eta = np.random.rand()\n", " return -tau * np.log(1-eta)\n", " \n", "\n", "tau = 3.053 # Half-time in minutes\n", "N = 10000 # Number of samples\n", "tdecays = [sample_tdecay(tau) for i in range(N)]\n", "\n", "# Show a histogram\n", "plt.xlabel(\"t [minutes]\")\n", "plt.ylabel(\"Counts\")\n", "plt.hist(tdecays, bins = 40, range=(0,20), density=True, label = 'Sample')\n", "# Show true distribution\n", "plt.plot([x for x in np.arange(0,20)], [1/tau * np.exp(-t/tau) for t in np.arange(0,20)], color='r', label='${\\\\rho(t)}$')\n", "plt.legend()\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Points inside a circle\n", "\n", "Let us sample points on a plane inside a unit circle.\n", "One way to do that is to switch to polar coordinates\n", "\n", "$$\n", "x = r \\cos(\\phi), \\qquad y = r \\sin(\\phi),\n", "$$\n", "\n", "and sample $r$ and $\\phi$.\n", "\n", "Since $r \\in [0,1)$ and $\\phi \\in [0,2\\pi)$,\n", "naively one could sample $r$ and $\\phi$ independently from two uniform distributions.\n", "Let us see what happens" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def sample_xy_naive():\n", " r = np.random.rand()\n", " phi = 2 * np.pi * np.random.rand()\n", " return r*np.cos(phi), r*np.sin(phi)\n", "\n", "xplot = []\n", "yplot = []\n", "N = 1000\n", "for i in range(N):\n", " x, y = sample_xy_naive()\n", " xplot.append(x)\n", " yplot.append(y)\n", " \n", "plt.plot(xplot,yplot,'o',color='r')\n", "plt.gca().set_aspect('equal')\n", "plt.show()\n", "\n", "# density plot\n", "import seaborn as sns\n", "sns.kdeplot(x=xplot, y=yplot, cmap=\"Blues\", fill=True, thresh=0)\n", "plt.xlabel(\"X-axis\")\n", "plt.ylabel(\"Y-axis\")\n", "plt.title(\"Density Plot from Discrete (x, y) Samples\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The points clump more in the centre! Why? Because $r$ is not uniformly distributed.\n", "Recall\n", "\n", "$$\n", "dx dy = r dr d\\phi,\n", "$$\n", "\n", "therefore\n", "\n", "$$\n", "\\rho_r(r) = 2r, \\qquad \\rho_\\phi(\\phi) = \\frac{1}{2\\pi}.\n", "$$\n", "\n", "Cumulative distribution function\n", "\n", "$$\n", "F_r(r) = \\int_0^r \\rho_r(r') dr' = r^2.\n", "$$\n", "\n", "Solving $F_r(r) = \\eta$ we get\n", "\n", "$$\n", "r = \\sqrt{\\eta}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def sample_xy_correct():\n", " eta = np.random.rand()\n", " r = np.sqrt(eta)\n", " phi = 2 * np.pi * np.random.rand()\n", " return r*np.cos(phi), r*np.sin(phi)\n", "\n", "xplot = []\n", "yplot = []\n", "rs = []\n", "N = 1000\n", "for i in range(N):\n", " x, y = sample_xy_correct()\n", " xplot.append(x)\n", " yplot.append(y)\n", " rs.append(np.sqrt(x*x+y*y))\n", " \n", "plt.plot(xplot,yplot,'o',color='r')\n", "plt.gca().set_aspect('equal')\n", "plt.show()\n", "\n", "# Show a density plot\n", "import seaborn as sns\n", "sns.kdeplot(x=xplot, y=yplot, cmap=\"Blues\", fill=True, thresh=0)\n", "plt.xlabel(\"X-axis\")\n", "plt.ylabel(\"Y-axis\")\n", "plt.title(\"Density Plot from Discrete (x, y) Samples\")\n", "plt.show()\n", "\n", "# Show a histogram\n", "plt.xlabel(\"r\")\n", "plt.ylabel(\"Counts\")\n", "plt.hist(rs, bins = 40, range=(0,1), density=True)\n", "# Show true distribution\n", "plt.plot([r for r in np.arange(0,1,0.01)], [2*r for r in np.arange(0,1,0.01)], color='r')\n", "plt.show() \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling on a unit sphere (isotropic direction)\n", "\n", "One common problem that occurs in Monte Carlo simulations is random sampling of an isotropic direction in 3D space.\n", "For instance, this issue occurs when sampling a random orientation of some axially symmetric object (such as a rod) or the momentum of a particle.\n", "\n", "This problem is equivalent to choosing a random point on a unit sphere. The coordinates $x,y,z$ on a unit sphere can be parametrized by azimuthal and polar angles, $\\phi \\in [0,2\\pi)$ and $\\theta \\in [0,\\pi]$:\n", "\n", "\\begin{align*}\n", "x & = \\sin(\\theta) \\cos(\\phi),\\\\\n", "y & = \\sin(\\theta) \\sin(\\phi),\\\\\n", "z & = \\cos(\\theta).\n", "\\end{align*}\n", "\n", "Recall that\n", "\n", "$$\n", "d\\Omega = \\sin(\\theta) d \\theta d\\phi,\n", "$$\n", "\n", "thus the random variable $\\phi$ and $\\theta$ are independent.\n", "$\\phi$ is uniformly distributed in $[0,2\\pi)$, thus, its sampling is straightforward.\n", "However, the polar angle $\\theta$ has a weighted probability density\n", "\n", "$$\n", "\\rho_{\\theta} (\\theta) = \\frac{1}{2} \\sin(\\theta),\n", "$$\n", "\n", "thus, its, distribution is non-uniform.\n", "The cumulative distribution function reads\n", "\n", "$$\n", "F_{\\theta}(\\theta) = \\int_0^\\theta \\frac{1}{2} \\sin(\\theta') d \\theta' = \\frac{1-\\cos(\\theta)}{2},\n", "$$\n", "thus\n", "$$\n", "\\theta = \\arccos(2\\eta - 1).\n", "$$\n", "\n", "In practice, it can make sense to work directly with $\\cos(\\theta)$ and $\\sin(\\theta)$. Indeed, we have\n", "\n", "$$\n", "\\cos(\\theta) = 2 \\eta - 1,\n", "$$\n", "and\n", "$$\n", "\\sin(\\theta) = \\sqrt{1 - [\\cos(\\theta)]^2}\n", "$$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def sample_xyz_isotropic():\n", " phi = 2 * np.pi * np.random.rand()\n", " costh = 2 * np.random.rand() - 1\n", " sinth = np.sqrt(1-costh*costh)\n", " return sinth * np.cos(phi), sinth * np.sin(phi), costh\n", "\n", "xplot = []\n", "yplot = []\n", "zplot = []\n", "N = 500\n", "for i in range(N):\n", " x, y, z = sample_xyz_isotropic()\n", " xplot.append(x)\n", " yplot.append(y)\n", " zplot.append(z)\n", " \n", "fig = plt.figure()\n", "ax = fig.add_subplot(projection='3d')\n", "\n", "ax.scatter(xplot,yplot,zplot)\n", "\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('y')\n", "ax.set_zlabel('z')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sampling normally distributed variables\n", "\n", "One of the most common distribution is the normal (or Gaussian) distribution\n", "$$\n", "\\rho(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}.\n", "$$\n", "\n", "There are a lot of standard implementations of sampling this distribution. Let us go through one such method.\n", "First, we can make a change of variable $x \\to \\mu + \\sigma x$. The new variable then has a normal distribution with zero mean and standard deviation of unity\n", "$$\n", "\\rho(x) = \\frac{1}{\\sqrt{2\\pi}} e^{-\\frac{x^2}{2}}.\n", "$$\n", "\n", "Calculating the cumulative distribution function $F(x) = \\int_{-\\infty}^x \\rho(x)$ is not entirely trivial.\n", "\n", "Instead of one variable, we can consider a pair of independent normally distributed variables $x,y$:\n", "$$\n", "\\rho(x,y) = \\frac{1}{2\\pi} e^{-\\frac{x^2}{2}} e^{-\\frac{y^2}{2}},\n", "$$\n", "Making a change of variables to polar coordinates\n", "$$\n", "x = r \\cos(\\phi), \\qquad y = r \\sin(\\phi),\n", "$$\n", "and taking into account\n", "$$\n", "dx dy = r dr d\\phi\n", "$$\n", "we get\n", "$$\n", "\\rho(r,\\phi) = \\frac{1}{2\\pi} r e^{-r^2/2}.\n", "$$\n", "\n", "Therefore, we can sample $x$ and $y$ by sampling two independent random variables $r$ and $\\phi$.\n", "$\\phi$ is uniformly distributed in $[0,2\\pi)$.\n", "For $r$ we have the following probability density\n", "$$\n", "\\rho_r(r) = r e^{-r^2/2},\n", "$$\n", "and the cumulative distribution function\n", "$$\n", "F_r(r) = \\int_0^r r' e^{-r'^2/2} dr' = 1 - e^{-r^2/2},\n", "$$\n", "therefore\n", "$$\n", "r = \\sqrt{-2 \\ln(1-\\eta)}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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fH5+j9yUi+eTaNat19Gir1WKxWsFqLVfOap03z2pNSbm98546ZbUOGmQ7J1itAQFW65YtuZNZRPJMdr6/jY4BCgkJYfLkyYwfP5769euzdu1alixZgr+/PwCxsbH/OifQjVq0aMHcuXOZOXMmdevWJSwsjPDw8LQWIhEpIM6cgU6d4PXXbWXKE0/A7t3QuzfcYsxflpQqBZ98AmvXQkCAbQxRixbw2We5k11EjDM6D5C90jxAInYuJgY6d7YVPHfcYStWHn44b17r7FlbF9nixbb7Y8bYbrdbZIlIrnOIeYBERHJk1y5ba8zu3VChAmzcmHfFD0CJEvDddzB6tO3+uHEwZIhtALWIOCwVQCLiOPbuhfbtbYOVa9a0Xb5ep07ev67FYhtg/dFHtoHTn3yiIkjEwRm7DF5EJFv+/NNW/Bw/DvXqwcqVtrE611V+5ccsn+rQxPtylmHIENvVZA8/DJ9+Cu7u8L//qTtMxAGpBUhE7N+JExAcDMeOQe3asGJFuuInX4WEwBdf2IqeadNs44FExOGoBUhE7Nvly9C9u+1KrCpVbMWPj4/ZTP362eYbGjLEdhXanXfaBkqTTy1RInLb1AIkIvYrJQVCQ22zM5csCUuWwC1mdc9XgwfDiBG27SeegNWrzeYRkWxRC5CI2K9Jk2D+fNtYm+++s83abMDNWnUs1uZ8ENia7rvXcvq+nnR99APwKp3P6UQkJ9QCJCL2KSICRo2ybU+daluWws5YLS682OV5fvetQqnLCUz/bgLu166ajiUiWaACSETsz5Ej8NBDti6wgQNh0CDTiW4qsZAHT/YcwTnPotSP/YPRqz4xHUlEskBdYCJiX1JSYMAAOH2aHb5VeLD4fSRmY2BxVmRnoHJWHClelmFd/0PYt2MJjVrCmjuDWHmXlt8RsWdqARIR+/L++7YBxXfcwbPdXyLRzd10oixZU6URnzTuCcCkpVPwuXjWbCARuSUVQCJiP7Zvh1dftW2//z6HSlYwmyeb3mndn92lK+NzKZ5JS6fYFmkVEbukAkhE7MOVK/DII5CUBN262S4tdzCJbu4M6/YfEl3d6LB/M49ELzUdSURuQgWQiNiHN9+E33+HMmVsy0w46PISe0tX5u02jwLw6urPKZ9wwmwgEcmUCiARMe/332HiRNv2tGm2IsiBfd6oO5sr1KTI1SuMXz5dXWEidkgFkIiYlZJim1X52jXo0QPuv990ottmtbgwovMzJLm4cc/+zdy791fTkUTkBiqARMSsjz6CDRugaNECtbL6nz6VmN6sNwDjVnyE15ULhhOJyD+pABIRc44dg1desW1PmAAVK5rNk8umNu/D/pIVKX3xHK+sCTMdR0T+QQWQiJjzyitw/jw0aQJPPmk6Ta5LcivEiM7PANB32zJqxf1pOJGIpFIBJCJmbNwIX31l2546FVxdzebJI7/51WZhzba4YGXMyhkaEC1iJ1QAiUj+S0mB55+3bT/2GDRqZDZPHpvU5lEuFfKgyV+76Lpnnek4IoIKIBExYdYs+O0328Dnt94ynSbPxXn5MO36gOgRq2fiefWK4UQiogJIRPLX+fN/D3wePRrKljWbJ5980rgXf3mVocL5kwzdNN90HBGnpwJIRPLXO+9AbCxUqfJ3N5gTSCzkwZvtHgdgyKYFlL5wxnAiEefmZjqAiDiREyfg3Xdt2xMngoeH2Tz5bGn1lkSWr0HQsT08t34ulV8pmeXnHpp4Xx4mE3E+agESkfzzxhtw8SI0bgwPPGA6Tf6zWJjU9lHAdlm8/9ljZvOIODEVQCKSPw4csM36DLbWnwIy43N2/eZXm1V3NqJQSjL/WfuV6TgiTksFkIjkj9deg6tXITgY2rc3ncaot9sMIAUL3faso7YmRxQxQgWQiOS97dth9mzbduqq705sT5kAvqvVFoCXfv7CbBgRJ6UCSETy3rhxthmQ+/SBBg1Mp7EL7939CFddXGl9KIqGf+02HUfE6agAEpG8tWMHLFhgG/MzZozpNHbjr+Jl+bZ2BwCG/TrbcBoR56PL4EUkb73+uu1n795U/vIgcNBoHHsytXkfeu9YQetDUTQ4uoeoCjVMRxJxGmoBEpG8s3MnfPutbXvUKLNZ7NBfxcuyoLZtQPjzv84xnEbEuRgvgKZNm0ZAQACenp4EBQWxbt3NFwr85ZdfaNmyJaVKlaJw4cLUqFGD999/P90xYWFhWCyWDLcrV7T2jki+e/1129ifBx6AOnVMp7FL/2sewjWLC20PRlLv2F7TcUSchtECKDw8nGHDhjFy5EiioqJo1aoVXbp0ISYmJtPjixQpwjPPPMPatWvZvXs3o0aNYtSoUcyYMSPdcV5eXsTGxqa7eXp65sdbEpFUu3fDvHm27ddeM5vFjsWUKMd3tdoB8Nz6uYbTiDgPowXQe++9x8CBAxk0aBCBgYFMnjwZPz8/pk+fnunxDRo04KGHHqJWrVpUrlyZfv360alTpwytRhaLhbJly6a7iUg+e+MNW+tPr15Qt67pNHbtf837kGxxocP+zdSJ3Wc6johTMFYAJSUlERkZSXBwcLr9wcHBrF+/PkvniIqKYv369bRp0ybd/gsXLuDv70/FihXp2rUrUVFRtzxPYmIiCQkJ6W4ichv+/BPmXm/NGD3abBYHcKhkBRbVtP0ee3ZDuOE0Is7BWAF06tQpkpOT8fX1Tbff19eXuLi4Wz63YsWKeHh40KhRI55++mkGDRqU9liNGjUICwtj8eLFzJkzB09PT1q2bMm+fTf/q2rChAl4e3un3fz8/G7vzYk4u3ffhZQUuPdezfuTRVOb9QHgnn2bqHL6iOE0IgWf8UHQlhvWA7JarRn23WjdunVs2bKFjz76iMmTJzNnzt9XTzRr1ox+/fpRr149WrVqxbx586hWrRoffvjhTc83YsQI4uPj025HjuiXj0iOHT8OM2fatl9+2WwWB7Lfx4+Iu5rigpVBvy00HUekwDM2D5CPjw+urq4ZWntOnDiRoVXoRgEBAQDUqVOH48ePM3bsWB566KFMj3VxcaFx48a3bAHy8PDAw8Mjm+9ARDL1v/9BYiI0bQqtWplO41A+avoAHf/cxP07V/Feq1BOFi1hOpJIgWWsBcjd3Z2goCAiIiLS7Y+IiKBFixZZPo/VaiUxMfGWj0dHR1OuXLkcZxWRLLpwAaZOtW2/9JLTrvieU5EVa7KlQiAeydd4NHKx6TgiBZrRmaCHDx9OaGgojRo1onnz5syYMYOYmBiGDh0K2Lqmjh49ypdffgnA1KlTqVSpEjVq2GZL/eWXX3jnnXd49tln0845btw4mjVrRtWqVUlISGDKlClER0czNfWXsojkqsqv/Ji2/diWRYw5e5YDJcpzz0Y3Un778RbPlMx83PQBGi14g9CoJUxr1puLHneYjiRSIBktgEJCQjh9+jTjx48nNjaW2rVrs2TJEvz9/QGIjY1NNydQSkoKI0aM4ODBg7i5uVGlShUmTpzIkCFD0o45d+4cgwcPJi4uDm9vbxo0aMDatWtp0qRJvr8/EWfilnyNgZu/A+DTJr1IcXE1G8hBrbirCftLVqTKmb/ou20ZnzXpZTqSSIFksVqtVtMh7E1CQgLe3t7Ex8fj5eVlOo6IXUttAeq+aw1Tvn+Hk3cU5+6hn5FYSOPqcipk2zIm/fQhx4r50HrIp1xzdePQxPtMxxKxe9n5/jZ+FZiIFABWK0M2LQAgLKibip/b9F2tdpwoUoLy50/Rbfda03FECiQVQCJy25r8tZNaJw5w2c2DWQ3uNR3H4SW6uRMW1A2AxyIX22bUFpFcpQJIRG7bo1tsVywtrNWO+MLFDKcpGObU68QVN3fqxv1J0NHdpuOIFDgqgETktlSIP0GnfRsBmHm91UJu39k7vPmuZlsAHtuiS+JFcpsKIBG5LaFRP+JqTeEX/3rsK+1vOk6BMrNRdwA6/7EeNEO9SK5SASQiOXfpEn23LQMgLKi74TAFz97SlVlfqS5u1pS/J5gUkVyhAkhEcu7rryl+5QKHi5dlVZVGptMUSKmDoZkxAy5dMhtGpABRASQiOWO1wgcfAPBlw66a+DCPrLirCTHevnD2LMyaZTqOSIGhAkhEcmb1ati5k4uFPPmmzj2m0xRYKS6ufNGwq+3OlCm6JF4kl6gAEpGcmTIFgPm1O5DgWdRwmIJtXr1gKFIEdu60FZ4ictuMrgUmIg7q4EFYbLs0+4ugrobDFHznPYrwddVWPBL9Ez88NYZnel7+1+do6QyRW1MLkIhk30cf2bpigoPZX8rPdBqnkDrDdqd9Gyh94YzhNCKOTwWQiGRPYiJ8/rlt+6mnzGZxIrvL3Elk+RoUSkkmZPty03FEHJ4KIBHJngUL4NQpqFAB7lM3S35KbQV6KHoZLinJhtOIODYVQCKSPR99ZPv5xBPgpmGE+WlJjbs5U9iLCudP0u7AFtNxRByaCiARybrdu2HtWnB1hUGDTKdxOolu7mlTDvSLWmI4jYhjUwEkIln38ce2n9262brAJN/NqdcJgDYHtlLxXJzhNCKOSwWQiGTNpUvwxRe27SFDzGZxYodKVmBt5Qa4YOWR6J9MxxFxWCqARCRr5s2Dc+egcmUIDjadxql93aALAH22L8f92lXDaUQckwogEcma1MHPQ4aAi351mLTirqbEFi1FqcsJdP5jvek4Ig5Jv8VE5N9FRcGmTVCoEDz2mOk0Ti/ZxZW518cCPRy91HAaEcekAkhE/l3q4Of77wdfX7NZBIB5dTuSgoVmR36n8pmjpuOIOBwVQCJyaxcvwuzZtm0NfrYbsV6l+fnOhgD02RFhOI2I41EBJCK39s03cP483HUXtG1rOo38Q3hd22D0B3esxFUzQ4tkiwogEbm1zz6z/XzsMbBYzGaRdFbe1YRTd3hT5uJZ2u3XzNAi2aECSERu7o8/4JdfbFd9DRhgOo3c4KprIRbUag+gBVJFskkFkIjcXOqq7126aOZnO5XaDdZu/2ZKXzhjOI2I49BKhiKSQeVXfsQ1JZkN02ZQBhjiXo9lr/xoOpZkYr+PH1sqBNLo6G4e/H0l05v1Nh1JxCGoBUhEMtVu/xbKXDzLqTu8WVWlsek4cguprUB9ti8Hq9VwGhHHoAJIRDKVemn1glrtuepayHAauZUfa9zNBffCBJyNpemR303HEXEIKoBEJIPSF87S/s/fgL9bF8R+XXIvzOLA1oAGQ4tklQogEcng/p0rcbOmEFm+Bvt9/EzHkSyYd71QvXfvr3hduWA4jYj9UwEkIulZrfTZbuv+mle3o+EwklXR5aqxx8cfz2tJdN+91nQcEbtnvACaNm0aAQEBeHp6EhQUxLp162567C+//ELLli0pVaoUhQsXpkaNGrz//vsZjps/fz41a9bEw8ODmjVrsnDhwrx8CyIFy/r1VDlzlIuFPPmhRivTaSSrLJa0VqCQbcsMhxGxf0YLoPDwcIYNG8bIkSOJioqiVatWdOnShZiYmEyPL1KkCM888wxr165l9+7djBo1ilGjRjFjxoy0YzZs2EBISAihoaFs27aN0NBQ+vTpw6ZNm/LrbYk4tuszP/9Y424uetxhOIxkx8JabUlycaPO8f2wY4fpOCJ2zWK1mrtmsmnTpjRs2JDp06en7QsMDKRnz55MmDAhS+e4//77KVKkCF999RUAISEhJCQksHTp0rRjOnfuTIkSJZgzZ06WzpmQkIC3tzfx8fF4eXll4x2JOLjz56FcObh4kQceeZvIijVNJ5Js+mjhm3T+YwP83//BO++YjiOSr7Lz/W2sBSgpKYnIyEiCg9NfYRIcHMz69euzdI6oqCjWr19PmzZt0vZt2LAhwzk7dep0y3MmJiaSkJCQ7ibilObPh4sX2V+yApEVAk2nkRyYX7uDbWPWLLh2zWwYETtmrAA6deoUycnJ+Pr6ptvv6+tLXFzcLZ9bsWJFPDw8aNSoEU8//TSDBg1KeywuLi7b55wwYQLe3t5pNz8/XfUiTuqLL4DrX6Ja+NQhrbkziNOFveD4cViuS+JFbsb4IGjLDb9krVZrhn03WrduHVu2bOGjjz5i8uTJGbq2snvOESNGEB8fn3Y7cuRINt+FSAFw+DCsWQMWC9/Vams6jeTQVddCLK55vVX8ekErIhkZWwvMx8cHV1fXDC0zJ06cyNCCc6OAgAAA6tSpw/Hjxxk7diwPPfQQAGXLls32OT08PPDw8MjJ2xApOK6Po6NdO455lTGbRW7Lt7U78Fjk97BoEZw9CyVKmI4kYneMtQC5u7sTFBREREREuv0RERG0aNEiy+exWq0kJiam3W/evHmGcy5fvjxb5xRxOlYrfPmlbbt/f7NZ5Lbt9K0CtWtDYiLMm2c6johdMtoFNnz4cD799FM+//xzdu/ezQsvvEBMTAxDhw4FbF1T/f/xy3jq1Kl8//337Nu3j3379jFz5kzeeecd+vXrl3bM888/z/Lly5k0aRJ79uxh0qRJrFixgmHDhuX32xNxHBs3wr59UKQIPPCA6TRyuywWGDDAtq1uMJFMGesCA9sl66dPn2b8+PHExsZSu3ZtlixZgr+/PwCxsbHp5gRKSUlhxIgRHDx4EDc3N6pUqcLEiRMZMmRI2jEtWrRg7ty5jBo1itGjR1OlShXCw8Np2rRpvr8/EYeR+iX5wANQtKjZLJI7HnkEXn4ZNmyAP/6AatVMJxKxK0bnAbJXmgdInMqVK7a5f86dgxUroEMHKr/yo+lUcpsOTbwP7r0Xli6FkSPhjTdMRxLJcw4xD5CI2Invv7cVP35+0K6d6TSSm1K7wb76ClJSzGYRsTMqgEScXWr3V79+4KJfCQVKjx7g7Q0xMbYpDkQkjX7biTiz48fhp59s26mtBVJweHpCSIhtW4OhRdJRASTizGbPhuRkaNoUqlc3nUbyQmphO38+XLhgNouIHVEBJOLMUlsFNPdPwdW8OVStChcv2oogEQFUAIk4r23bbLdChaBvX9NpJK9YLH8XuOoGE0mjAkjEWaXO/NytG5QsaTaL5K3QUNvP1attA6JFRAWQiFO6dg2+/tq2rcHPBZ+/P7S5vkDqDYtHizgrFUAizmjFCtsVYD4+0KWL6TSSH1KXDEotfEWcnAogEWeU+iUYEmIbAyQF34MPgrs77NgB27ebTiNinNG1wEQk/6Qub1E46Qpbwr+lCHB/fGW2atkL51C8OHTtCgsWwKxZ8PbbphOJGKUWIBEn0/HPTRS5eoUYb1+2lq9hOo7kp9RusNT5n0ScmAogESfTY9caABbVbGu7RFqcx7332lqCjh6Fn382nUbEKBVAIk6kxKV4Wh/cCsB3NduaDSP5z8MD+vSxbWswtDg5FUAiTuS+vb9SKCWZ332rsN/Hz3QcMSG1G+zbb+HyZbNZRAxSASTiRHrsXAPAdzXbmA0i5rRsCZUqQUIC/PCD6TQixqgAEnESFeOP0/joLlKw8H1ga9NxxBQXF3jkEdv2rFlms4gYpAJIxEl032Ub9LrBvw7Hi/kYTiNGpXaDLVkCp06ZzSJiiAogEWdgtdIzrfurrdEoYgdq1oQGDWxLonzzjek0IkaoABJxBtu2Ue10DImubiyr1sJ0GrEHWhpDnJwKIBFnMHs2AKuqNCHBs6jhMGIX+va1jQf69Vc4cMB0GpF8pwJIpKBLSUlbAVzdX5KmfHno0MG2fb1AFnEmWgtMpKBbuxb++osEjyKsqdLIdBrJJ5WzsMbbA4Vq8y4RtqvBRo7UzODiVNQCJFLQXR/jsaR6SxLd3A2HEXuyrFpzLrt5wN69EBlpOo5IvlIBJFKQJSbaZvzl+tpfIv9wweMOIqo2td3RYGhxMiqARAqyJUvg3DmoUIFNfrVMpxE7tLBWO9vGnDm2y+JFnIQKIJGCLPWv+r59SXFxNZtF7NK6yg3AxweOH4cVK0zHEck3KoBECqr4+L/Xekpd+kDkBtdc3SAkxHZH3WDiRFQAiRRUCxbYxgAFBkL9+qbTiD1LLZAXLoSLF81mEcknKoBECqrUv+YfeUSXN8utNWsGd95pK34WLzadRiRfqAASKYiOHYNVq2zbDz9sNovYP4vl7/9O1A0mTkIFkEhBNHcuWK3QogUEBJhOI44gtRts2TKtEC9OQTNBizioW830+33YNOoAo4rUY1YWZgQWoUYNCAqyTYg4bx489ZTpRCJ5yngL0LRp0wgICMDT05OgoCDWrVt302MXLFhAx44dKV26NF5eXjRv3pxly5alOyYsLAyLxZLhduXKlbx+KyJ2ocrpI9Q5vp9rFheW1LjbdBxxJKmtQOoGEydgtAAKDw9n2LBhjBw5kqioKFq1akWXLl2IiYnJ9Pi1a9fSsWNHlixZQmRkJO3ataNbt25ERUWlO87Ly4vY2Nh0N09Pz/x4SyLG9di5BoC1AQ05c4e32TDiWFJXiF+/Hg4eNJ1GJE8ZLYDee+89Bg4cyKBBgwgMDGTy5Mn4+fkxffr0TI+fPHkyL730Eo0bN6Zq1aq89dZbVK1ale+//z7dcRaLhbJly6a7iTgFq5Ueu38G4Ltabc1mEcdTrhy0b2/b1grxUsAZK4CSkpKIjIwkODg43f7g4GDWr1+fpXOkpKRw/vx5SpYsmW7/hQsX8Pf3p2LFinTt2jVDC9GNEhMTSUhISHcTcUQNju3F/1wcFwt5EnFXM9NxxBGldoPNmmUbSC9SQBkrgE6dOkVycjK+vr7p9vv6+hIXF5elc7z77rtcvHiRPn36pO2rUaMGYWFhLF68mDlz5uDp6UnLli3Zt2/fTc8zYcIEvL29025+fn45e1MihvXYtQaA5VWbcdld3b6SA/ffD56esGcP/MsfjyKOzPggaMsNE7RZrdYM+zIzZ84cxo4dS3h4OGXKlEnb36xZM/r160e9evVo1aoV8+bNo1q1anz44Yc3PdeIESOIj49Pux05ciTnb0jEELfka3TdY7uIQCu/S455eUG3brZtDYaWAsxYAeTj44Orq2uG1p4TJ05kaBW6UXh4OAMHDmTevHncc889tzzWxcWFxo0b37IFyMPDAy8vr3Q3EUdz96FofC7Fc+oOb36pXN90HHFkqd1gc+ZAcrLZLCJ5xFgB5O7uTlBQEBEREen2R0RE0KJFi5s+b86cOTz66KPMnj2b++67719fx2q1Eh0dTbly5W47s4g9S+3++rHG3bYFLkVyqksXKFECYmNhzRrTaUTyhNEusOHDh/Ppp5/y+eefs3v3bl544QViYmIYOnQoYOua6t+/f9rxc+bMoX///rz77rs0a9aMuLg44uLiiI+PTztm3LhxLFu2jAMHDhAdHc3AgQOJjo5OO6dIQVQ46QrB+zYC6v6SXODuDr1727bVDSYFlNECKCQkhMmTJzN+/Hjq16/P2rVrWbJkCf7+/gDExsammxPo448/5tq1azz99NOUK1cu7fb888+nHXPu3DkGDx5MYGAgwcHBHD16lLVr19KkSZN8f38i+aXjn5socvUKh4uXZWv5GqbjSEGQ2g02fz5oIlkpgCxWq65zvFFCQgLe3t7Ex8drPJDYrX8uhfHZt+PosH8zU5qH8F7rUIOpxBEdmpjJcIKUFNs6cjEx8M038OCD+R9MJJuy8/1t/CowEbk9JS7F0/rgVgAWafJDyS0uLlohXgo0jZQUcXD37fmFQinJ7PCtwv5SmsNKsu9mC+tWO1mR5UDi9z/QeFg4CZ5FM28tEnFAagEScXA9r1/99Z0GP0su+6N0ZXaXroxH8jXu3fOL6TgiuUoFkIgDq3gujkZHd5OChR8CW5mOIwVQ6ppyva4X2iIFhQogEQfWY5dt4dMN/nU4XszHcBopiBYHtiEFC02P/E75hBOm44jkGhVAIo7KalX3l+S5WK/S/OZXC4Duu9YaTiOSe1QAiTiomicOUvX0ERJdC/FT9Zam40gBllpg91A3mBQgOSqAtm7dyo4dO9LuL1q0iJ49e/Lqq6+SlJSUa+FE5OZSv4xWVmnMeY8iZsNIgbakxt0kuroRePIQ/ON3v4gjy9Fl8EOGDOGVV16hTp06HDhwgL59+9KrVy+++eYbLl26xOTJk3M5pohzuNnlyDdySUnm1+vjfzT3j+S1BM+irLmzEZ32bbTNCTRxoulIIrctRy1Af/zxB/Xr1wfgm2++oXXr1syePZuwsDDmz5+fm/lEJBNNj+yk3IXTxHsUYfWdjU3HESeQNs5s9mzbLNEiDi5HBZDVaiXl+v8AK1as4N577wXAz8+PU6dO5V46EclUavfXkuotSXIrZDaMOIVVdzUhwf0OOHIEftGcQOL4clQANWrUiDfeeIOvvvqKn3/+mfvus80MevDgQXx9fXM1oIik53EtiXv3/gqo+0vyT6KbO0tTB9traQwpAHJUAL3//vts3bqVZ555hpEjR3LXXXcB8O2339KiRYtcDSgi6bXdvwWvxIscK+bDJr/apuOIE0mdFJFvvgFd8CIOLkeDoOvVq5fuKrBU//3vf3Fz0/JiInmp167VACwObI3VopksJP9s8qsN5cvDsWOwdCn06GE6kkiO5ei355133snp06cz7L9y5QrVqlW77VAikjmvKxdot38zoO4vyX8pLq7w0EO2O+oGEweXowLo0KFDJCcnZ9ifmJjIX3/9dduhRCRzXfb+ikfyNfb6VGJ36QDTccQZPfKI7efixRAfbzaLyG3IVn/V4sWL07aXLVuGt7d32v3k5GRWrlxJQIB+KYvkldSlLxbVbAsWi9Es4qTq14fAQNi9GxYsgMceM51IJEeyVQD17NkTAIvFwoABA9I9VqhQISpXrsy7776ba+FE5G9lE07RNOZ34HoBJGKCxWJrBRo1ytYNpgJIHFS2usBSUlJISUmhUqVKnDhxIu1+SkoKiYmJ7N27l65du+ZVVhGn1n33z7hg5beKNTnqXcZ0HHFmDz9s+7lqlW1AtIgDytEYoIMHD+Lj45PbWUTkFtJWfq/VzmwQkYAAaNECrFaYO9d0GpEcyfE16ytXrmTlypVpLUH/9Pnnn992MBH5W9WTh6l54iBJLm78WP1u03FEbN1g69fbusGGDzedRiTbctQCNG7cOIKDg1m5ciWnTp3i7Nmz6W4ikrtSW39+vjOI+MLFzIYRAejTB9zcYOtW2LPHdBqRbMtRC9BHH31EWFgYoaGhuZ1HRG5gsabQ4/rK799p8LPYCx8f6NQJfvzR1gr0+uumE4lkS45agJKSkrTkhUg+CTq6m4oJJzjvXpgVdzUxHUfkb/362X7Onm0bDyTiQHJUAA0aNIjZs2fndhYRyUTPnWsAWFatBYmFPMyGEfmn7t2haFE4cAA2bjSdRiRbctQFduXKFWbMmMGKFSuoW7cuhQoVSvf4e++9lyvhRJxdoeSr3LfnF0DdX2KH7rgDevWCr76ydYM1b246kUiW5agA2r59O/Xr1wfg999/T/eYRbPTiuSaNge2UuLKeU4UKcF6/7qm44hk9MgjtgIoPBzefx9u+INYxF7lqABavXp1bucQkUykXv31fWBr20KUIvamQwcoUwZOnIDly+G++0wnEsmSHI0BEpG8VzTxEvf8uQlQ95fYMTc36NvXtq0V4sWB5KgFqF27drfs6lq1alWOA4mITac/NuB5LYn9JSuwo+xdpuOI3Nwjj8CUKbBoEVy4YBsYLWLnclQApY7/SXX16lWio6P5/fffMyySKiI50yN16Qut/C72rnFjuOsu+PNP+O67vy+PF7FjOSqA3n///Uz3jx07lgsXLtxWIBGB0hfO0vLwNkArv4sDSF0hftw4WzeYCiBxALk6Bqhfv35aB0wkF3TbvRZXawpby1cnpkQ503FE/t0jj9h+RkTYBkSL2LlcLYA2bNiAp6dntp4zbdo0AgIC8PT0JCgoiHXr1t302AULFtCxY0dKly6Nl5cXzZs3Z9myZRmOmz9/PjVr1sTDw4OaNWuycOHCbL8XEZPSdX+JOIKqVW1dYcnJtkviRexcjgqg+++/P92tV69eNGvWjMcee4whQ4Zk+Tzh4eEMGzaMkSNHEhUVRatWrejSpQsxMTGZHr927Vo6duzIkiVLiIyMpF27dnTr1o2oqKi0YzZs2EBISAihoaFs27aN0NBQ+vTpw6ZNm3LyVkXyXZVTR6gXt49rFhd+rNHKdByRrEvt+tLVYOIALFZr9hdweeyxx9Ldd3FxoXTp0rRv357g4OAsn6dp06Y0bNiQ6dOnp+0LDAykZ8+eTJgwIUvnqFWrFiEhIbz22msAhISEkJCQwNKlS9OO6dy5MyVKlGDOnDlZOmdCQgLe3t7Ex8fj5eWV5fcjcrsqv/IjL/78BU9v/IYVVRoz6MExpiOJpHNo4i3m+Tl+HCpUsLUC7dtnGxgtko+y8/2do0HQM2fOzFGwf0pKSiIyMpJXXnkl3f7g4GDWr1+fpXOkpKRw/vx5SpYsmbZvw4YNvPDCC+mO69SpE5MnT77peRITE0lMTEy7n5CQkKXXF8ltFmtK2tpfC2p3MBtGJBOVX/nxlo9/UakebQ5u5b3HxjJ83ax8SiWSfbc1BigyMpJZs2bx9ddfp+uGyopTp06RnJyMr69vuv2+vr7ExcVl6RzvvvsuFy9epE+fPmn74uLisn3OCRMm4O3tnXbz8/PLxjsRyT3NYn6nwvmTJHgUYaVWfhcHlDpurceuNVohXuxajlqATpw4Qd++fVmzZg3FixfHarUSHx9Pu3btmDt3LqVLl87yuW6cUNFqtWZpPbE5c+YwduxYFi1aRJkyZW7rnCNGjGD48OFp9xMSElQEiRH3/26bRPSHGq1IdHM3nEYk+5ZXbcZlNw+qnDkKW7bYBkaL2KEctQA9++yzJCQksHPnTs6cOcPZs2f5/fffSUhI4LnnnsvSOXx8fHB1dc3QMnPixIkMLTg3Cg8PZ+DAgcybN4977rkn3WNly5bN9jk9PDzw8vJKdxPJdxcv0uWPXwGYX7u94TAiOXPR4w4iqja13dFgaLFjOSqAfvrpJ6ZPn05gYGDavpo1azJ16tR0g49vxd3dnaCgICIiItLtj4iIoEWLFjd93pw5c3j00UeZPXs292Wy6F7z5s0znHP58uW3PKeIXfjuO4omXeZw8bJEVgj89+NF7FTa9A1z58K1a0aziNxMjrrAUlJSKFSoUIb9hQoVIiUlJcvnGT58OKGhoTRq1IjmzZszY8YMYmJiGDp0KGDrmjp69ChffvklYCt++vfvzwcffECzZs3SWnoKFy6Mt7c3AM8//zytW7dm0qRJ9OjRg0WLFrFixQp++eWXnLxVkfzz1VcALKzVTktfiENbG9CQM4W9KHn8OKxaBdm4Olgkv+SoBah9+/Y8//zzHDt2LG3f0aNHeeGFF+jQIetXroSEhDB58mTGjx9P/fr1Wbt2LUuWLMHf3x+A2NjYdHMCffzxx1y7do2nn36acuXKpd2ef/75tGNatGjB3LlzmTlzJnXr1iUsLIzw8HCaNm2ak7cqkj+OHbPNoAssqKXuL3Fs11zd+LHG3bY76gYTO5WjeYCOHDlCjx49+P333/Hz88NisRATE0OdOnVYtGgRFStWzIus+UbzAEm+e+cdePFFNleoSe9+b5tOI3Lbgv7axfyvX7KtDH/8ONxxh+lI4gTyfB4gPz8/tm7dSkREBHv27MFqtVKzZs0MA5JFJIuud/Mu0OBnKSAiKwRC5cpw6BAsWgQPPWQ6kkg62eoCW7VqFTVr1kybKLBjx448++yzPPfcczRu3JhatWrdci0vEcnEtm2wYwe4u//dbSDi6CwW6N/ftv3FF2aziGQiWwXQ5MmTeeKJJzJtVvL29mbIkCG89957uRZOxClcb/2he3cSPIuazSKSm1ILoIgIOHrUbBaRG2SrANq2bRudO3e+6ePBwcFERkbedigRp3Ht2t+DRFO/LEQKiipVoFUrSElJu8pRxF5kqwA6fvx4ppe/p3Jzc+PkyZO3HUrEaURE2AaI+vjALf64EHFYjz5q+xkWpqUxxK5kqwCqUKECO3bsuOnj27dvp1y5crcdSsRppHZ/Pfww3OKPCxGH1bu37QqwvXth0ybTaUTSZKsAuvfee3nttde4cuVKhscuX77MmDFj6Nq1a66FEynQEhLgu+9s26GhRqOI5JlixeCBB2zbGgwtdiRbBdCoUaM4c+YM1apV4+2332bRokUsXryYSZMmUb16dc6cOcPIkSPzKqtIwfLtt3DlCgQGQlCQ6TQieWfAANvPOXNs/82L2IFszQPk6+vL+vXrefLJJxkxYgSpcyhaLBY6derEtGnT/nUhUxG5LvWv4dBQLX0hBVLlV34EwGJN4ZdipakQf5JnQsbwQ2DrTI8/NDHj+o4ieSXbEyH6+/uzZMkSzp49y59//onVaqVq1aqUKFEiL/KJFEx//glr14KLi7q/pMCzWlyYX7s9z20I58EdK29aAInkpxytBQZQokQJGjduTJMmTVT8iGRXWJjtZ3AwOPjSMSJZkTrLeatDUZQ5f9pwGpHbKIBEJIeSk//u/nrsMbNZRPLJoZIV2FyhJq7WFHrtWm06jogKIJF8t2IF/PUXlCwJPXqYTiOSb76t0wGAB3es1JxAYpwKIJH8NnOm7efDD4OHh9ksIvloSY27ueLmTtXTR6gX+4fpOOLkcrQavIhkXeqVMADel8/z27fz8QDuu1CVnf94TKSgO+9RhJ+qNafnrp958PeVbCtf3XQkcWJqARLJR913/4xH8jV2lQlgp28V03FE8t23te8BoNvutXhcSzKcRpyZCiCRfNR7xwoAvqlzj+EkImas96/LsWI+FL9ygQ5//mY6jjgxFUAi+aTGiYPUjfuTJBc3vqvZ1nQcESNSXFxZWKsdAA9e/4NAxAQVQCL5JLX1Z8VdTTh7h7fhNCLmzK9tuxqszcGt+J4/ZTiNOCsVQCL5oFDyVXrutM198k3djobTiJh1oFTFtDmBHvh9lek44qRUAInkg/Z/bqbU5QSOFy3J2oCGpuOIGBdeLxiAkO3LsVhTDKcRZ6QCSCQf9N4RAcCCWu1JdnE1nEbEvB+r381598L4n4ujWczvpuOIE1IBJJLHSl84Q7sDkYCu/hJJddndk8U12wAQsn2Z4TTijFQAieSx+3euwtWawpYKgRwopYVPRVLNrdsJgC571+N9+bzhNOJsVACJ5CWrlT7bbd1fav0RSW9H2bvYVSYAj+Sr9Ny1xnQccTIqgETy0tq1VDlzlAvuhfmhRivTaUTsi8XC3Lq2wdB9ty3TAqmSr1QAieSlGTMAWBzYhosedxgOI2J/vqvVjkTXQgSePASRkabjiBNRASSSV06fhm+/BWBOvU6Gw4jYpwTPoiyt3sJ259NPzYYRp6ICSCSvfPUVJCXxu28VdpS9y3QaEbsVfn0wNLNnw8WLZsOI01ABJJIXrNa07q859TqBxWI4kIj92lipNoeKl4Pz5+Gbb0zHESehAkgkL/z6K+zeDXfcwSItfCpyS1aLC/NSl4hRN5jkExVAInnhk09sP/v25YIGP4v8q29rdwBX17//eBDJYyqARHLb2bMwb55te/Bgs1lEHMSJYqWga1fbnevdxyJ5yXgBNG3aNAICAvD09CQoKIh169bd9NjY2FgefvhhqlevjouLC8OGDctwTFhYGBaLJcPtypUrefguRP5h1iy4cgXq1IEmTUynEXEcQ4fafoaFwaVLRqNIwWe0AAoPD2fYsGGMHDmSqKgoWrVqRZcuXYiJicn0+MTEREqXLs3IkSOpV6/eTc/r5eVFbGxsupunp2devQ2Rv1mtf3d/DR6swc8i2REcDJUrw7lzf7eiiuQRowXQe++9x8CBAxk0aBCBgYFMnjwZPz8/pk+fnunxlStX5oMPPqB///54e3vf9LwWi4WyZcumu4nki02bYMcO8PSEfv1MpxFxLC4uMGSIbfsm3wMiucVYAZSUlERkZCTBwcHp9gcHB7N+/frbOveFCxfw9/enYsWKdO3alaioqFsen5iYSEJCQrqbSI6kjl3o0weKFzcaRcQhPf44FCoEv/0GW7eaTiMFmLEC6NSpUyQnJ+Pr65tuv6+vL3FxcTk+b40aNQgLC2Px4sXMmTMHT09PWrZsyb59+276nAkTJuDt7Z128/Pzy/HrixM7dw7Cw23bGvwskjNlysADD9i2P/7YbBYp0IwPgrbcMEbCarVm2JcdzZo1o1+/ftSrV49WrVoxb948qlWrxocffnjT54wYMYL4+Pi025EjR3L8+uLEvvjCNnCzdm1o0cJ0GhHH9eSTtp9ffw1qkZc84mbqhX18fHB1dc3Q2nPixIkMrUK3w8XFhcaNG9+yBcjDwwMPD49ce01xQikpMG2abfvppzX4WSQHKr/yo23DaiWilB9VTx9h1IOvMKvhfRmOPTQx4z6R7DDWAuTu7k5QUBARERHp9kdERNAiF/96tlqtREdHU65cuVw7p0gGK1fCH39AsWLwyCOm04g4NouFr+t3AaBf1BLb1ZUiucxoF9jw4cP59NNP+fzzz9m9ezcvvPACMTExDL0+F8SIESPo379/uudER0cTHR3NhQsXOHnyJNHR0ezatSvt8XHjxrFs2TIOHDhAdHQ0AwcOJDo6Ou2cInkitfVnwABbESQit2VB7fZcdvOgxqnDBB3VzNCS+4x1gQGEhIRw+vRpxo8fT2xsLLVr12bJkiX4+/sDtokPb5wTqEGDBmnbkZGRzJ49G39/fw4dOgTAuXPnGDx4MHFxcXh7e9OgQQPWrl1LE01IJ3klJgYWL7ZtP/WU2SwiBUSCZ1EWB7YmZEcEj0QvJbJiTdORpICxWK1qW7xRQkIC3t7exMfH4+XlZTqO2LuRI+Gtt6B9e1tX2A3SxjWISLbUid3H91++QKKrG82e+oKzd/w9/5vGAElmsvP9bfwqMBGHlpj49+rVav0RyVU7ylVle9m78Ei+Rp8dEf/+BJFsMNoFJuKoUlt1uu9aw5QTJ4gtWoq7NxUiebNae0Ry06z69/L2T1PoF7WUTxr3IsXF1XQkKSDUAiRyG/pvtRU8s+t3Jlm/mEVy3aKabTjrWQy/+ON02L/ZdBwpQFQAieRQzeMHaHR0N1ddXJlbr5PpOCIFUmIhj7T/vx6NXGw4jRQkKoBEcqhflK3156dqLThZtKThNCIF11cN7yXZ4kLLw9upevKw6ThSQKgAEskBrysX6LlrDQBfZjJLrYjknmNeZVhetRkAj2793nAaKShUAInkQJ/ty7njaiJ7fPzZXLGW6TgiBV5YUDcAeu1cjdeVC4bTSEGgAkgku65d49HIHwD4vFEPrfslkg82+dVmd+nK3HE1kT7bl5uOIwWACiCR7Fq0iIoJJzhd2ItFNduYTiPiHCyWtFag/lt/hORkw4HE0WkeIBGyN1vzN7NeozHwdf0uJBbyyLtQIpLOopptGLFmJpXij8OPP0L37qYjiQNTC5BINtSN/YPGR3eR5OLGVxr8LJKvrhTy/HvKiQ8/NBtGHJ4KIJFseGyLbR6S7wNb6dJ3EQO+anAfyRYXWLECduwwHUccmAogkSwqc/40XfesA2Bmox6G04g4p6PeZfipWnPbnffeMxtGHJoKIJEs6h/1I4VSktlUsRa/l73LdBwRp/VJk/ttG19/DbGxZsOIw1IBJJIFnlev8HD0TwB83litPyImRZevDi1bwtWr8L//mY4jDkpXgYlkQc+dayh5OYEj3r5E3NXUdBwRpzekTBs+5lfOvTeF5pcbctnd86bHHpqoCxYkI7UAifwLizWFgVsWARDWsCspWvVdxLiIu5pyqHg5il+5QO8dEabjiANSASTyLzr8uZmqp4+Q4FGEcK36LmIXUlxc+ex6d/TALYtwSdHEiJI9KoBE/sWQTfMBmNWgCxc87jCcRkRSfVv7Hs56FsP/XBwd920yHUccjAogkVsI+msXjY/uItHVjZlBmnVWxJ5cdvdkVoN7AXhi80LDacTRqAASuYWh11t/5tfuoIkPRezQlw27kujqRqOju2l4dLfpOOJAVACJ3ESVU0fo+OcmUrDwaeNepuOISCZOFi3Bopptgb+7q0WyQgWQyE0M/m0BAMurNeNAqYqG04jIzXzc5AFSsNBp30buOhVjOo44CBVAIpnwPX+KXjtXA/BR0wcNpxGRW9nv48ey68tjPLnxG8NpxFGoABLJxGNbFuOeco1NfrVts86KiF2b1qw3AD12/UzFc3GG04gjUAEkcoNiiRd5JHopAB81fcBwGhHJih3lqrK2cgPcrCkM/k1XhMm/UwEkcoMBkd9TLOkye30qsfrORqbjiEgWTWtuawUK2b6c0hfOGk4j9k4FkMg/FEm8xMDNtmUvpjYPAYvFcCIRyaqNfnXYWr46HslXefz68jUiN6MCSOQf+kUvocSV8+wvWYEfatxtOo6IZIfFwtTmfQDoF/UjXlcuGA4k9kwFkMh1hZOu8MT1sQNTm/fRoqciDmhVlcbsLl2ZYkmX6b/1B9NxxI6pABK57uFtP+FzKZ7DxcumTawmIo7FanFhejPb1BWPbVnMHUmXDScSe6UCSATwuJqYNovstGa9SVbrj4jD+rFGKw4VL0epywn03/qj6Thip1QAiWC7aqTMxbP85VWaBbXbm44jIrch2cWVKS37AtdndD9/3nAisUfGC6Bp06YREBCAp6cnQUFBrFu37qbHxsbG8vDDD1O9enVcXFwYNmxYpsfNnz+fmjVr4uHhQc2aNVm4UHNCyC0kJqYtevpRs95cdS1kOJCI3K5FNdtyoER5Sl5OgP/9z3QcsUNGC6Dw8HCGDRvGyJEjiYqKolWrVnTp0oWYmMzXcklMTKR06dKMHDmSevXqZXrMhg0bCAkJITQ0lG3bthEaGkqfPn3YtGlTXr4VcWRhYZQ/f4q4oiX5ps49ptOISC6wtQI9ZLvz3/9CQoLZQGJ3LFar1WrqxZs2bUrDhg2ZPn162r7AwEB69uzJhAkTbvnctm3bUr9+fSZPnpxuf0hICAkJCSxdujRtX+fOnSlRogRz5szJUq6EhAS8vb2Jj4/Hy8sr629IHE9iIlSrBjExjOvwBDMb9TCdSERyiUtKMhGfPU2VM3/B66/DqFGmI0key873t7EWoKSkJCIjIwkODk63Pzg4mPXr1+f4vBs2bMhwzk6dOt3ynImJiSQkJKS7iZOYMQNiYogrWpLZ9TqbTiMiuSjFxZUPUluB3n0X4uPNBhK7YqwAOnXqFMnJyfj6+qbb7+vrS1xczheyi4uLy/Y5J0yYgLe3d9rNz88vx68vDuTiRXjjDQA+bNGXxEIehgOJSG77ocbdEBgI587BBx+YjiN2xPggaMsNSw1YrdYM+/L6nCNGjCA+Pj7tduTIkdt6fXEQH34IJ07AnXcyr25H02lEJA+kuLjC2LG2O++9ZyuERDBYAPn4+ODq6pqhZebEiRMZWnCyo2zZstk+p4eHB15eXuluUsCdOwdvv23bHjtWV36JFGQPPgi1a9u6wN5913QasRPGCiB3d3eCgoKIiIhItz8iIoIWLVrk+LzNmzfPcM7ly5ff1jmlAHr3XTh7FmrWhIcfNp1GRPKSiwuMG2fbfv99uI1hFlJwuJl88eHDhxMaGkqjRo1o3rw5M2bMICYmhqFDhwK2rqmjR4/y5Zdfpj0nOjoagAsXLnDy5Emio6Nxd3enZs2aADz//PO0bt2aSZMm0aNHDxYtWsSKFSv45Zdf8v39iZ06ccL2SxBsV4a4atZnkQKvVy9o2hQ2bbL9fz91qulEYpjRAigkJITTp08zfvx4YmNjqV27NkuWLMHf3x+wTXx445xADRo0SNuOjIxk9uzZ+Pv7c+jQIQBatGjB3LlzGTVqFKNHj6ZKlSqEh4fTtGnTfHtfYucmTrQNgA4Ksv1SFJECrfIrtuUwmt7Zk/BNm7j60cd0vFqPQyUrZHr8oYn35Wc8McToPED2SvMAFQypv/T+qWzCKX6e8QQeyVfp33sca+8MMpBMREz57NtxdNi/mR9qtOKZHi9neowKIMflEPMAiZjwf+tm4ZF8lU0Va7E2oKHpOCKSz95uM4AULHTds466sX+YjiMGqQASp1Hz+AEe+H0lABPaPQ63Od2CiDievaUrpy14/MqaMFAniNNSASTOwWrl1dWf4YKVxYGtiS5f3XQiETHk/bsfIdHVjRYx22l9cKvpOGKICiBxCm0PRHL34W0kurrxduv+puOIiEFHvcvwZcOuALzycxguKcmGE4kJKoCkwHNNSebV1Z8DEBbUnb+KlzWcSERMm9q8DwkeRah54mBa17g4FxVAUuD13h5BtdMxnPUsxtTmfUzHERE7cK6wF1NahADw0tovKZp4yXAiyW8qgKRAK5p4if/7ZRYAU1r2JcGzqOFEImIvvgjqxoES5Sl98RxPb5hnOo7kMxVAUqA9u34upS+e40CJ8sxqcK/pOCJiR666FuLN9gMBeHzLd1Q6G2s4keQnFUBSYFU5fYTHtywCYHyHJ7TgqYhksLJKE9ZWboBH8jVeXfO56TiSj1QAScFktfLayk8olJLMiiqNWVOlselEImKPLBZebz+IaxYXOv+xgeaHt5tOJPlEBZAUTIsX0+bgVhJd3Xi9wxOm04iIHdtX2p+vG3QBYMyKj+HqVcOJJD+oAJKC58oVeOEFAD5t3IvDJcobDiQi9u79ux/hTGEvapw6DB9+aDqO5AMVQFLwvPMOHDxIbNFSuuxdRLLkXGEvJrZ51HZnzBj46y+jeSTvqQCSgmX/fnjzTcC23tcl98KGA4mIo/im7j1Elq8BFy6ktSJLwaUCSAoOqxWefNLWBdahA4sDW5tOJCIOxGpxYWSnp8HVFb79Fn76yXQkyUMqgKTgmDMHIiLAwwOmT9dq7yKSbXvKBMBzz9nuPPOM7Q8qKZBUAEnBcOYMDBtm2x49GqpWNRpHRBzYuHFQvrytS/2tt0ynkTyiAkgKhpdfhpMnITAQXnzRdBoRcWTFisEHH9i2J0yA7ZobqCBSASSOb906+PRT2/aMGeDubjaPiDi+Bx6AXr3g2jV4/HHbTylQVACJY7t0yfbLCWDQILj7brN5RKRgsFhg6lQoXhwiI+G990wnklymAkgc26uvwp9/QoUK8N//mk4jIgVJuXJ/Fz5jxsAff5jNI7lKBZA4rnXrYMoU2/Ynn9j+UhMRyU2PPgrBwbarwQYOhJQU04kkl6gAEsd08SI89pht7p+BA6FLF9OJRKQgsljg44+hSBH45Rctk1GAqAASx/Tqq7ZLVCtWhHffNZ1GRAqyypXh7bdt2y+/DLt2GY0juUMFkDie1av/7vr67DPw9jabR0QKviefhM6dITERHnkEkpJMJ5LbpAJIHMvp0xAaatsePNjWNy8iktcsFvj8cyhZEqKjYexY04nkNrmZDiCSZVYrP7XoRuejR9lfsiJdiwRz+ZUfTacSEWdRrpxtrrEHH4RJk+DeezX1hgNTC5A4jk8+ofMfG0hyceO57i9y2d3TdCIRcTYPPAADBtiuBgsNhfh404kkh1QAiWPYsydtra+32/Rnp28Vs3lExHl98IFtYPShQ7YJWK1W04kkB1QAif27cgUeegguX2Zt5QZ81rin6UQi4sy8vWHuXHBzg2+/hWnTTCeSHFABJPbvuedsgw59fPjPvcOwWvSfrYgY1rTp35fGDx8OW7eazSPZpm8SsW9hYbZZni0WmD2bE8VKmU4kImIzbBh07267JL5PH40HcjC6Ckzs17Zttrk3AMaNg44dYaWu+hKRvFU5G1eXHpo5Exo2tE3MOnAgfPON7Q82sXvGW4CmTZtGQEAAnp6eBAUFsW7dulse//PPPxMUFISnpyd33nknH330UbrHw8LCsFgsGW5XrlzJy7chue3cOdvVFleu2Ja5GDnSdCIRkYxKloTwcChUCObPh4kTTSeSLDLaAhQeHs6wYcOYNm0aLVu25OOPP6ZLly7s2rWLSpUqZTj+4MGD3HvvvTzxxBPMmjWLX3/9laeeeorSpUvzwAMPpB3n5eXF3r170z3X01OXTNujzP7SslhTmLHgTTru389fXmW4r2p/4l9daiCdiMitpf4Oe7j9YN5aNpWUV0fy+NZE1lRpnOHYQxPvy+94cgtGW4Dee+89Bg4cyKBBgwgMDGTy5Mn4+fkxffr0TI//6KOPqFSpEpMnTyYwMJBBgwbx+OOP884776Q7zmKxULZs2XQ3cRz/WfsVHf/cRKJrIZ7sOYL4wsVMRxIRuaXZ9bswu15nXLAy5ft3CDhz1HQk+RfGCqCkpCQiIyMJvmEpg+DgYNavX5/pczZs2JDh+E6dOrFlyxauXr2atu/ChQv4+/tTsWJFunbtSlRUVO6/AckTPXeu5umN3wDwUpfn2FGuquFEIiJZM6bjEDZXqIlX4kU+mf86RRMvmY4kt2CsADp16hTJycn4+vqm2+/r60tcXFymz4mLi8v0+GvXrnHq1CkAatSoQVhYGIsXL2bOnDl4enrSsmVL9u3bd9MsiYmJJCQkpLtJ/mtwdA+TltoWOZ3arDeLarUznEhEJOuuuhbiqZ4jiC1airvO/MWHiyfhmpJsOpbchPFB0JYbRstbrdYM+/7t+H/ub9asGf369aNevXq0atWKefPmUa1aNT788MObnnPChAl4e3un3fz8/HL6diSHyiWcZMbCN/BIvsqyqs14p3Wo6UgiItl2smgJhtw/kstuHrQ7EMnry6drpmg7ZawA8vHxwdXVNUNrz4kTJzK08qQqW7Zspse7ublRqlTm88O4uLjQuHHjW7YAjRgxgvj4+LTbkSNHsvlu5HZ4XblA2DdjKH3xHLtLV+aFrv+nyQ5FxGFtL1eN57q/SAoWHt72E09u+tZ0JMmEsW8Zd3d3goKCiIiISLc/IiKCFi1aZPqc5s2bZzh++fLlNGrUiEKFCmX6HKvVSnR0NOXKlbtpFg8PD7y8vNLdJH94XE3k0/njqX4qhriiJRn44Gtcci9sOpaIyG2JqNqM8R2eAODln7+g+66fDSeSGxn9M3v48OF8+umnfP755+zevZsXXniBmJgYhg4dCthaZvr37592/NChQzl8+DDDhw9n9+7dfP7553z22Wf85z//STtm3LhxLFu2jAMHDhAdHc3AgQOJjo5OO6fYkeRkpnz/X5r8tYsEjyIM6DOeY15lTKcSEckVYY2681mjHgD8d8n7sGqV4UTyT0bnAQoJCeH06dOMHz+e2NhYateuzZIlS/D39wcgNjaWmJiYtOMDAgJYsmQJL7zwAlOnTqV8+fJMmTIl3RxA586dY/DgwcTFxeHt7U2DBg1Yu3YtTZo0yff3J7dgtcLTT9Np30YSXQsx6IHR7C1d2XQqEZFc9Wa7xymfcJIuf6y3LZuxcqVtHTExzmK1anTWjRISEvD29iY+Pl7dYXnBaoURI2DSJJItLjzV4xWWVc+821NExNF5XEvis2/HcffhbVCiBKxZA3Xrmo5VIGXn+1sjTSX/jRkDkyYBMDr4SRU/IlKgJbq5M/j+UdC8OZw9C8HBcIsLcyR/qACS/PXGG/D667btDz5gdv0uZvOIiOSDS+6FYckSqF8fjh+HDh3gwAHTsZyaCiDJP2+/DaNH27bfeQeee85sHhGR/FS8OCxbBjVqwJEj0Lo1/PGH6VROy+ggaHESViuMHw9jx9ruv/UW/N//GY0kImJEmTKwerWtBWjXLmjTxjYwumbNdIdltlD0rWih1exTC5DkLasVhg//u/h5803bAGgREWdVtuzfA6Hj4qBtW9i+3XQqp6MWIMk7yckweDB8/rnt/pQp8OyzZjOJiBhyY6tO8bav8NXx0dQ5vp/4Ji0Y9MBoNvvVNpTO+agFSPLG5csQEmIrflxcICxMxY+IyD+cK+zFI33fZEuFQLwTLzIrfDSd9/5qOpbTUAEkue/ECWjXDubPB3d3+OYbGDDAdCoREbuT4FmUR0LeYHnVZngkX2XadxPpH/m96VhOQQWQ5K7du6FZM9i0CUqWhIgIuP9+06lEROxWYiEPhvYcwaz6XXDByvgVH/Pqqs9wSUk2Ha1AUwEkuWfFCmjRAg4ehCpVYMMG22WeIiJySykurowKfor/tgoFYPDmhXz+7Xi8rlwwnKzg0lIYmdBSGNlktdrm+Hn1VUhJYXOFmgy+fyRn7/A2nUxExOHct3sd7yyZTOFriewvWYHB949ifym/Wz5Hl8HbaCkMyT8JCfDgg/DKK5CSAo89Rr++b6j4ERHJoR8DW/Fgv7c5Wqw0Vc4cZeGX/0enP9abjlXgqACSnNuxw7aq8YIFUKgQfPQRfPYZiW7uppOJiDi0nb5V6D7gfTZVrIVX0iU+XvgWY1Z8jPu1q6ajFRjqAsuEusAySjd/hdXKo5HfM2LNTDySrxJbtBRP9RxBVIUa5gKKiBRAbsnX+M/aLxn62wIAdvhW4ZkeL3O4RPl0x6kLzEZdYJJnSl08x+ffjmPsyhl4JF9l1Z2N6ProByp+RETywDVXNya2e5xHHxzDmcJe1Dm+nx/Cnidk2zLb+EvJMRVAkjVWK/fu+YWfPn+G9ge2kOhaiNfuGcLjD47hdJHiptOJiBRoa6o05t5Hp7DJrzbFki4z6acPmfntWHzPnzIdzWGpCywT6gK7QWwsy9rcT6d9GwHY4+PP891fZG/pymZziYg4GZeUZB7fsogX136FR/JV4j2KML7DYN794V2wWEzHMy47398qgDKhAui6lBT47DN48UWIj+eqiyvTmvVhavM+JLkVMp1ORMRpVTl1hHeXvEf92H22HW3awLRpGVaVdzYqgG6TCiBg40bb2l1btgCwrWxVXu7yHHvKBBgOJiIiAK4pyTzx20Ke/3UOha8lctXFlU+a9OLD5n257O550+cV5AHTKoBuk1MXQLGxMGIEfPGF7b6XF4wbR5Vjd5Ls4mo2m4iIZFAx/jhjVnxMxz9/AyCuaEnebRXK/NrtScnk97YKIBsVQJlwlgLon5e2F7+cwNBN8xkQ+QOFryUCMK/OPbzdZgCnipQwFVFERLKo476NvLbyE/zijwOwu3RlJrR9jLUBDdOND1IBZOOWT5nETt2RdJnHtyxi8KYFeCVdAmBLhUDeaD+I6PLVDacTEZGsiqjajJ8Dgui/9XueXR9O4MlDfPnNGDZVrMWUlg/xq389DZT+B7UAZcIpWoBOn+a9ns8zIPJ7Sl1OAGx/LbzdZgCr72yk/0lERBxY8csJPLM+nNCoH/FIvgbY/rid0qIvX4aPLrC/49UFdpsKdAF0+DC89x58+ilcsrX4HCxRjvfv7sf3ga2wWjQ1lIhIQeF7/hRDN83noW3L8LyWZNsZFATDhkGfPuBesJYuUgF0mwpcAZSSAqtX29bqWrgQkpMB+N23Ch83uZ8lNe7WAGcRkQKs9IUzDNk0n0eif0ob50nZsvDkkzB0KJQpYzZgLlEBdJsKTAF0+jSEhcHHH8O+fX/vv+ceeOklKq9ILLDNoCIiklHJS/E8FP0ToVE/UvbCGQASXd2IuKsZ39a5h7UBDdJdOeZoA6ZVAN0mhy6ALl+G77+Hr7+GpUvh6vWVg4sVg9BQGDIE6tYFbljgVEREnIZb8jXu3fsrj21ZTIPYvWn744qWZEHt9syv1YH9Pn4qgJyNwxVAly7BypUwfz4sWADnz//9WFCQrXmzb18oWjTd01QAiYhIreP7eXDHCnruXEOJK39/f+z1qUT1Zx6H3r0dZoZpFUC3ySEKoOPH4YcfYPFiiIiwtfxcd8Tbl0U127AosA37SvsbDCkiIo7C/dpVOvy5iQd/X0nrg1splJL894OBgdC1K3TpAi1b2u3gaRVAt8kuC6CLF+GXX2DVKtstMhL++U9XqRJhPnX5PrA1kRUCNbZHRERyzOvKBTru28S7lj9g+fK/h1OArTehQwdbMdS+Pdx1l91856gAuk12UQCdPAmbNvHhW7NoemQH9Y/9gXvKtXSHbCtblRV3NWFF1absLh1gN/8BiohIwXBo4n0QH28bU7p0Kfz0E5w4kf6gsmXh7ruhVSvbrW5dcDVzZbEKoNuU7wXQuXPw+++weTNs2mS7HTqU4bC/vEqz3r+e7VapLieKlcr7bCIi4rQyDIJOSYHoaFsxtGyZ7fsqKSn9MUWKQP36tjGoDRvaftaoAW55v/iECqDblGcFUGIi7NrFC6NnUf3kIaqfOkz1k4cpf/5UhkNTsLC/VEWiy1VnS8VA1vvX44i3r1p5RETEbnhcS6Ju7B80/msXL91xAn79Nf2FOKkKF4Y6daBWLdutdm1o0wY8b75qfU44VAE0bdo0/vvf/xIbG0utWrWYPHkyrVq1uunxP//8M8OHD2fnzp2UL1+el156iaFDh6Y7Zv78+YwePZr9+/dTpUoV3nzzTXr16pXlTHlWAP34o20QWSaOFivNLt87iSpfnehy1dhRrirnPYrk3muLiIjkoUMT77NNtPvHH7Zxqqm3qCi4cCHjE06fhpIlczWDwyyGGh4ezrBhw5g2bRotW7bk448/pkuXLuzatYtKlSplOP7gwYPce++9PPHEE8yaNYtff/2Vp556itKlS/PAAw8AsGHDBkJCQnj99dfp1asXCxcupE+fPvzyyy80bdo0v99ienXqQMmSbCxSnj2lK/NHaX/2+FRmX+lKKnZERMShpZ9apQR43AMt7sHSPIU7zxyl+snDVDt1mKqnYvC5FE/TXC5+sstoC1DTpk1p2LAh06dPT9sXGBhIz549mTBhQobjX375ZRYvXszu3bvT9g0dOpRt27axYcMGAEJCQkhISGDp0qVpx3Tu3JkSJUowZ86cLOXKsxag6x915RFLcu+cIiIiDigvJlnMzve3sZUvk5KSiIyMJDg4ON3+4OBg1q9fn+lzNmzYkOH4Tp06sWXLFq5ev0TvZsfc7Jz5ymLRGB4RERE7YKwL7NSpUyQnJ+Pr65tuv6+vL3FxcZk+Jy4uLtPjr127xqlTpyhXrtxNj7nZOQESExNJTExMux8fHw/YKsm8kJJ4KU/OKyIi4ijy4js29ZxZ6dwyOgYIwHJDi4jVas2w79+Ov3F/ds85YcIExo0bl2G/n5/fzYOLiIhIjnlPzrtznz9/Hm9v71seY6wA8vHxwdXVNUPLzIkTJzK04KQqW7Zspse7ublRqlSpWx5zs3MCjBgxguHDh6fdT0lJ4cyZM5QqVeqWhVNOJCQk4Ofnx5EjR+xnlmk7pc8q6/RZZZ0+q6zTZ5U9+ryyLq8+K6vVyvnz5ylfvvy/HmusAHJ3dycoKIiIiIh0l6hHRETQo0ePTJ/TvHlzvv/++3T7li9fTqNGjShUqFDaMREREbzwwgvpjmnRosVNs3h4eODh4ZFuX/HixbP7lrLFy8tL/4NkkT6rrNNnlXX6rLJOn1X26PPKurz4rP6t5SeV0S6w4cOHExoaSqNGjWjevDkzZswgJiYmbV6fESNGcPToUb788kvAdsXX//73P4YPH84TTzzBhg0b+Oyzz9Jd3fX888/TunVrJk2aRI8ePVi0aBErVqzgl19+MfIeRURExP4YLYBCQkI4ffo048ePJzY2ltq1a7NkyRL8/W0rmMfGxhITE5N2fEBAAEuWLOGFF15g6tSplC9fnilTpqTNAQTQokUL5s6dy6hRoxg9ejRVqlQhPDzc/BxAIiIiYjeMD4J+6qmneOqppzJ9LCwsLMO+Nm3asHXr1lue88EHH+TBBx/MjXi5zsPDgzFjxmTocpOM9FllnT6rrNNnlXX6rLJHn1fW2cNnZXwpDBEREZH8ZmwiRBERERFTVACJiIiI01EBJCIiIk5HBZCIiIg4HRVABnXv3p1KlSrh6elJuXLlCA0N5dixY6Zj2Z1Dhw4xcOBAAgICKFy4MFWqVGHMmDEkJSWZjmaX3nzzTVq0aMEdd9yR5xN6OqJp06YREBCAp6cnQUFBrFu3znQku7R27Vq6detG+fLlsVgsfPfdd6Yj2aUJEybQuHFjihUrRpkyZejZsyd79+41HcsuTZ8+nbp166ZNfti8eXOWLl1qLI8KIIPatWvHvHnz2Lt3L/Pnz2f//v12e/m+SXv27CElJYWPP/6YnTt38v777/PRRx/x6quvmo5ml5KSkujduzdPPvmk6Sh2Jzw8nGHDhjFy5EiioqJo1aoVXbp0STffmNhcvHiRevXq8b///c90FLv2888/8/TTT7Nx40YiIiK4du0awcHBXLx40XQ0u1OxYkUmTpzIli1b2LJlC+3bt6dHjx7s3LnTSB5dBm9HFi9eTM+ePUlMTExb2kMy99///pfp06dz4MAB01HsVlhYGMOGDePcuXOmo9iNpk2b0rBhQ6ZPn562LzAwkJ49ezJhwgSDyeybxWJh4cKF9OzZ03QUu3fy5EnKlCnDzz//TOvWrU3HsXslS5bkv//9LwMHDsz311YLkJ04c+YMX3/9NS1atFDxkwXx8fGULFnSdAxxIElJSURGRhIcHJxuf3BwMOvXrzeUSgqa+Ph4AP1++hfJycnMnTuXixcv0rx5cyMZVAAZ9vLLL1OkSBFKlSpFTEwMixYtMh3J7u3fv58PP/wwbc04kaw4deoUycnJ+Pr6ptvv6+tLXFycoVRSkFitVoYPH87dd99N7dq1TcexSzt27KBo0aJ4eHgwdOhQFi5cSM2aNY1kUQGUy8aOHYvFYrnlbcuWLWnHv/jii0RFRbF8+XJcXV3p378/ztIrmd3PCuDYsWN07tyZ3r17M2jQIEPJ819OPivJnMViSXffarVm2CeSE8888wzbt29Pt0C3pFe9enWio6PZuHEjTz75JAMGDGDXrl1GshhfC6ygeeaZZ+jbt+8tj6lcuXLato+PDz4+PlSrVo3AwED8/PzYuHGjsSbB/JTdz+rYsWO0a9eO5s2bM2PGjDxOZ1+y+1lJRj4+Pri6umZo7Tlx4kSGViGR7Hr22WdZvHgxa9eupWLFiqbj2C13d3fuuusuABo1asTmzZv54IMP+Pjjj/M9iwqgXJZa0OREastPYmJibkayW9n5rI4ePUq7du0ICgpi5syZuLg4V+Pl7fx3JTbu7u4EBQURERFBr1690vZHRETQo0cPg8nEkVmtVp599lkWLlzImjVrCAgIMB3JoVitVmPfeSqADPntt9/47bffuPvuuylRogQHDhzgtddeo0qVKk7R+pMdx44do23btlSqVIl33nmHkydPpj1WtmxZg8nsU0xMDGfOnCEmJobk5GSio6MBuOuuuyhatKjZcIYNHz6c0NBQGjVqlNaSGBMTo/Fkmbhw4QJ//vln2v2DBw8SHR1NyZIlqVSpksFk9uXpp59m9uzZLFq0iGLFiqW1MHp7e1O4cGHD6ezLq6++SpcuXfDz8+P8+fPMnTuXNWvW8NNPP5kJZBUjtm/fbm3Xrp21ZMmSVg8PD2vlypWtQ4cOtf7111+mo9mdmTNnWoFMb5LRgAEDMv2sVq9ebTqaXZg6darV39/f6u7ubm3YsKH1559/Nh3JLq1evTrT/44GDBhgOppdudnvppkzZ5qOZncef/zxtP/3Spcube3QoYN1+fLlxvJoHiARERFxOs41kEJEREQEFUAiIiLihFQAiYiIiNNRASQiIiJORwWQiIiIOB0VQCIiIuJ0VACJiIiI01EBJCIiIk5HBZCIiIg4HRVAIiIi4nRUAImIUzh58iRly5blrbfeStu3adMm3N3dWb58ucFkImKC1gITEaexZMkSevbsyfr166lRowYNGjTgvvvuY/LkyaajiUg+UwEkIk7l6aefZsWKFTRu3Jht27axefNmPD09TccSkXymAkhEnMrly5epXbs2R44cYcuWLdStW9d0JBExQGOARMSpHDhwgGPHjpGSksLhw4dNxxERQ9QCJCJOIykpiSZNmlC/fn1q1KjBe++9x44dO/D19TUdTUTymQogEXEaL774It9++y3btm2jaNGitGvXjmLFivHDDz+YjiYi+UxdYCLiFNasWcPkyZP56quv8PLywsXFha+++opffvmF6dOnm44nIvlMLUAiIiLidNQCJCIiIk5HBZCIiIg4HRVAIiIi4nRUAImIiIjTUQEkIiIiTkcFkIiIiDgdFUAiIiLidFQAiYiIiNNRASQiIiJORwWQiIiIOB0VQCIiIuJ0VACJiIiI0/l/nrTT5ZGNrzIAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def sample_xy_normal():\n", " phi = 2 * np.pi * np.random.rand()\n", " eta = np.random.rand()\n", " r = np.sqrt(-2*np.log(1-eta))\n", " return r * np.cos(phi), r * np.sin(phi)\n", "\n", "N = 10000\n", "samples = []\n", "for i in np.arange(0,N,2):\n", " x, y = sample_xy_normal()\n", " samples.append(x)\n", " samples.append(y)\n", " \n", "# Show a histogram\n", "plt.title(\"Normal distribution\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"Counts\")\n", "plt.hist(samples, bins = 40, range=(-3,3), density=True)\n", "# Show true distribution\n", "plt.plot([x for x in np.arange(-3,3,0.01)], [1/np.sqrt(2*np.pi)*np.exp(-x**2/2) for x in np.arange(-3,3,0.01)], color='r')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rejection sampling\n", "\n", "In the rejection sampling method one samples a variable $\\xi$ from an envelope distribution and accepts this value with a certain probability. \n", "\n", "Consider the distribution function for the polar angle again:\n", "$$\n", "\\rho_\\theta(\\theta) = \\frac{\\sin(\\theta)}{2}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def rho_th(x):\n", " return np.sin(x) / 2\n", "\n", "xplot = np.linspace(0,np.pi, 100)\n", "yplot = rho_th(xplot)\n", "\n", "plt.xlim(0,np.pi)\n", "plt.ylim(0,0.6)\n", "plt.plot(xplot, yplot,color='r')\n", "plt.fill_between(xplot, yplot, step=\"pre\", alpha = 0.4, color='orange')\n", "plt.axhline(0.5,linestyle='--', color='r')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that $\\rho_\\theta$ is bounded from above $\\rho_\\theta < \\rho_\\theta^{\\rm max} = 1/2$.\n", "The rejection sampling method proceeds by\n", "1. Sampling a candidate value $\\theta_{\\rm cand}$ from a uniform distribution over $(0,\\pi)$.\n", "2. Accepting the value $\\theta_{\\rm cand}$ with a probability $p = \\rho_\\theta(\\theta_{\\rm cand}) / \\rho_\\theta^{\\rm max}$.\n", "\n", "The second step can be performed by sampling $y$ as a uniform distribution over $(0,\\rho_\\theta^{\\rm max})$ and accepting $\\theta_{\\rm cand}$ is $y < \\rho_\\theta(\\theta_{\\rm cand})$.\n", "\n", "The procedure has simple geometrical interpretation. Considering $\\theta_{\\rm cand} \\equiv x$ and $y$ to be the coordinates of a point on a plane, we accept $\\theta_{\\rm cand}$ for all points that lie below the curve given by the probability density $\\rho_{\\theta}(x)$. This ensures that the $\\theta_{\\rm cand}$ are accepted with a rate proprotional to $\\rho_\\theta(\\theta)$, as desired.\n", "\n", "One advantage of rejection sampling is that $\\rho_\\theta(\\theta)$ need not be a normalized distribution for the method to work." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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//hGtMyiJiJhivOVm7NixFCtWDD8/P0JDQ1m5cuUN9122bBkOh+O6286dOzMxsYiIiGRlRoub2bNn07dvXwYNGkRERAT169enZcuWHDx48Kav27VrF5GRkUm3UqVKZVJiERERyeoclmVZpj68Vq1aVK9enXHjxiVtK1euHO3atWP48OHX7b9s2TIaN27M6dOnyZUrV5o+MyYmhsDAQKKjowkICEhrdBHJRKm91JRRdAlLxJzUfH8b63MTFxfHhg0bGDBgQLLtYWFhrF69+qavrVatGpcuXaJ8+fIMHjyYxo0b33Df2NhYYmNjkx7HxMTcWXARMcL3ciyFo49T5Ewkd585RuHofwi8dJ6A2HMExJ4n4NJ5PBPisRwO4j08SXA4uOTlw6nsgZzKFkhU9kBO5sjF/tyF2Ju3MEcC8mE5jF+ZF5EMYKy4OXnyJPHx8QQHByfbHhwczLFjx1J8TcGCBRk/fjyhoaHExsYydepUmjZtyrJly2jQoEGKrxk+fDhDhw5N9/wikoEuXoSNG2HdOli3jiU/L6P46aPp+hGXvHzYl7sQ24JLsuGusmy4qxx7gkJU8Ii4AOOjpRwOR7LHlmVdty1RmTJlKFOmTNLjOnXqcOjQIUaOHHnD4mbgwIH0798/6XFMTAwhISHpkFxE0o1lwfbt8Msv8OuvsHIl/KfFtfjVn2d9snEwV0EO5CrA4cBgTmUPJMYvBzG+OTjrm4PLHp54Wgl4JiTgwCLb5VjyXIgm74Vo8lyMJvjcKYqdOkLR00fxuxJHuRP7KXdiP49uWwRAjG8O/ihcnqUlarK4xD0cCwgycDBE5E4ZK26CgoLw9PS8rpXm+PHj17Xm3Ezt2rWZNm3aDZ/39fXF19c3zTlFJINYFqxfDzNnwjffwOHDyZ8vWBBq1oSaNemyJYHtwSWIyh4IN/jjJzU8EuIpHH2cUlEHqXJ0N6FHd1D16G4CYs/TbO86mu1dxzuMZXv+4iwqWYsfyjfk77yF7/hzRSRzGCtufHx8CA0NJTw8nAcffDBpe3h4OG3btr3t94mIiKBgwYIZEVFEMsK+fTB5MsyYAXv2/Ls9WzZo1Ajuuw9atIDSpZMKmRXp3KE4wcOTg7kLcjB3QRaXrAWAZ0I8ZY/vo+G+jTTZu47qR3ZS4fjfVDj+Ny+unsmmgqXh7gPw2GOQJ0+65hGR9GX0slT//v3p3LkzNWrUoE6dOowfP56DBw/Ss2dPwL6kdOTIEaZMmQLA6NGjKVq0KBUqVCAuLo5p06YxZ84c5syZY/LXEJFbSUiA8HD49FOYP99utQG7oGnbFh5/HMLCwM/PWMR4D0+2FyjJ9gIlGVunPXkuRNN473pa7VpFw783UDVyN/TuDf36waOP2j9DQ43lFZEbM1rcdOjQgaioKIYNG0ZkZCQVK1ZkwYIFFClSBIDIyMhkc97ExcXx8ssvc+TIEbJly0aFChWYP38+rVq1MvUriMjNXLwIEyfCJ5/A7t3/bm/eHLp2tQubnDnN5buJU9kDmVOpKXMqNSXfudM88Ocy3ohaB1u2wPTp9q1+fejfH9q0AU9P05FF5Cqj89yYoHluRDLBhQvwxRfw/vuQ2K8uIACefBJ69bIvOaVClprnZv16GD0aZs+GK1fsJ0qVgiFD7EtWKnJEMkRqvr815lFE0s/FizByJBQrZrdoHDsGd99tX446csQuClJZ2GQ5NWrAtGmwfz8MGAC5c8Nff0GnTlC5MsyZY1+GExFjVNyIyJ2zLHvUU9my8MorcPy4XeB8+aX9xd+7d5a9/JRmd90Fw4fDgQPwzjuQKxf8+Sc88ojdF2fpUtMJRdyWihsRuTNr1kDdutCxIxw8CIUL2/1sdu2C7t3Bx8d0wozl7w+vv26PAnvzTfvxpk3QpInd8fjAAdMJRdyO+tyISNqcPAkvvQRXRzOSIwcjqz/IVzXbccn71qOeUrNOU5bqc3MrJ0/CW2/BuHH25Sk/P3jtNfuWLVuGZxRxVepzIyIZx7LsPiflytmFjcMBTz0Ff/3Fp3Ufu63CxqUFBdl9jCIi7Hl7Ll2CoUPt/jgrVphOJ+IW1HIjIrfv77+hZ097zhqAihXtfjW1awNZp4UlK9g/orVdCM6ZA3372h2qAZ57Dt57z758JSK3TS03IpK+LAsmTLBbH8LDwdfX7kS7YUNSYSMpcDjsDsbbt8Mzz9jbxo2DChVg4UKz2URcmIobEbm5kyfhoYfszsHnz0ODBrB1q92J1tU7C6eXwEAYPx4WLbJHkR06ZC8z0b9/sgVCRSR9qLgRkRv79VeoVAm+/x68ve3LKUuW2JPWSeo1bWoXhr162Y8/+gjq1LFHlolIujG6/IKIZFFXrtjDmocPtx+XK2cvN1CtmtlcTuSm/Y/8W9Hsoby8//PH5ImI4EKlKrzVtAf/q9z8tlY9T81IMxF3pJYbEUnu+HH7kkliYdO7t923RoVNulpUqhYtn/yE34pUJvvlWN7/5RPe//ljfK/EmY4m4vRU3IjIv1avtouYJUsgRw6YNcse1qz5WTLEP/5BdG7/f7zfoAvxDg/ab13EN9NfpVDMcdPRRJyaihsRsX3+OTRsCEeP2ssorFsHHTqYTuXyEjw8GVunPV0fHcppP38qH9vDvMl9qXNgs+loIk5L89yIuLsrV+xRO2PG2I/bt4evvgJ/f81bk8kKR//D53PfpeI/e4l3eDCs6TN8Hdrmuv3U50bcUWq+v1XciLiZ/xYs/rHnGfPD+zTatwGA9xt0YWztR2+rU6tkDN/Lsbz766c8vN1eeHNSaBv+r0l3Ejw8k/ZRcSPuSJP4icgtFT5zjDlTX6HRvg1c9PKlZ7uBjK3TXoWNYbHevrzUuj8jGnYD4MkN8/hi7jtkj7toNpiIE1FxI+KGKhzbw9ypL1M66iDHcubhkSfe45cy9UzHkkQOB5/XfoRebQcQ6+lN8z1/MHvGAPKfjTKdTMQpqLgRcTN1Dmxm1syB5Ltwhu35i9O2yyi2FyhpOpakYEHZe3n88Xc5mT2QSv/s5btpL1Ps1BHTsUSyPBU3Iu7k22+Z/M0Q/OMusvruynToOIJ//INMp5Kb2HhXOR7s/CF789xF4ZgTfDP9Vdi40XQskSxNxY2Iuxg3Dtq3xzf+CvPL1OPJR9/inG9206nkNhzKVYD2Hd9ja3AJgi5EQ+PGsGKF6VgiWZaKGxF38P779npGlsXUaq14/oFXifXSopfOJCpHLh5/fDhrQypCTIw9i/RPP5mOJZIlqbgRcXVvvw2vvWbff+MN3mj+XLJhxeI8zvlmp+ujQ6FNG7h0Cdq1g2+/NR1LJMvRwpkiLiDFyfYsi36rpvPi6lnA1Tls4mqBRno7tVhvX5gzB5580l7M9LHHYOZMePRR09FEsgwVNyKuyLIYsHwyPX+fA8A7jZ7iy1oPGQ4l6cbbG77+Gjw9YcoUePxxSEjQchkiV6m4EXE11xQ2bzV9lsk1HjAcStKdpydMnAgeHjB5MjzxBFiW3ZIj4uZU3Ii4mBd/m5lU2AwO68W0aq0MJ5IM4+kJEybYs0pPmmQXOB4e9vpgIm5MHYpFXMizv8+h328zABjW5BkVNu7Aw8Ne6PTpp+1LU088AQsWmE4lYpRabkRcROeNP/H6skmA3Xl4Ys22hhNJpvHwgC++gIsXYcYMePhh+OUXaNgwVSu7a0FOcRVquRFxAY9uCef/wj8H4JM6HewFMMW9eHrafW8Sh4nffz/88YfpVCJGqOVGxNn9+CMjfhkDwJc12zGqfifDgSSj3aw1xrf0k0wscoB6B7ZwpmFTynQcwa58RTMvnEgWoJYbEWf222/QoQOeVgKzKzXnncZP251LxW3FevnwzENvsLFQGXJdOseU/73JXdHHTccSyVQqbkSc1fbt9qWHS5dYVKImr7foo8JGALjgk41ujw5lZ1ARgs+dYvI3Qwi8eNZ0LJFMo+JGxBkdPGivLXTmDNSpQ5+2rxGvJRXkP2L8ctLt0aEc9Q+iVNQhvvzu//C9Emc6lkimUHEj4mxOn4YWLeDIEShXDn76iUvefqZTSRZ0LCCIbo++RYxvDu45/CcfzRuJR0K86VgiGU7FjYgziYuzh/nu2AF33QW//gp58phOJVnY7nxFeeahwcR6etFq92reWPKVPZOxiAtTcSPiLCwLnnsOli6FnDlh/nwICTGdSpzA73dXon/rlwB4csM8um78yXAikYyl4kbEWbz33r9rCc2eDVWqmE4kTmR+ufq80+gpAN5c/CWN9q43nEgk46i4EXEG33wDAwfa9z/+GFppWQVJvS/veZDZlZrjaSUw5sf3KH1iv+lIIhlCxY1IVrduHXTpYt9/4QXo08dsHnFeDgeD7+vF2pCK+MddZMKc/yPv+TOmU4mkOxU3IlnZsWPw4IP2dPqtW8OoUaYTiZO77OlNzwdfZ1/ugoRE/8MXc9/REHFxOVp+QSQLKjpgPt7xl5kxcxA1jxxhT57CtCvVlXODfjEdTVzAmWwBdH/4Tb6b+jI1juzg/xaO5dWWL5qOJZJu1HIjkkUNWTSemkf+JMYnO888/AbnfLObjiQuZG/eEHq3HUC8w4P2WxfROeL2Vw8XyepU3IhkQY9v+oVOm34mAQcvPvAK+/LcZTqSuKBVxaoxomE3wB5BxcqVZgOJpBMVNyJZzerVDA3/HICRDTqztERNw4HElX15z4P8WK4B3gnx8MgjcPiw6Ugid0zFjUhWcuQIPPwwPglXmF+mHmNrP2o6kbg6h4PXWrzAjnxF4fhxeOghuwO7iBNTcSOSVcTG2ksrHDvGzqAivNKqr1b5lkxx0cePZx4abC/lsW6dphsQp6fiRiSreOUV+P13yJ2bZx8azAWfbKYTiRs5nKuAPfO1hwdMmABTppiOJJJmKm5EsoJvv4UxY+z7U6dyMHdBs3nEPTVrBkOG2Pefew62bzebRySNVNyImLZnDzz9tH3/1VftyfpETBk0CJo3hwsX4NFH4dw504lEUk3FjYhJly7ZXyAxMXDvvfD226YTibvz9IRp06BQIdixw27BsSzTqURSRcWNiEn9+sGmTRAUBLNmgbe36UQikD+/fT4mFjoTJphOJJIqWn5BJJMUHZB8BtgH/lzOJ/M+JwEH3Ro/z4oxm4BNJqKJXK9+fXjnHRgwwB49VaMGVK1qOpXIbVHLjYgBxaMO8+6vnwLwWZ32rCgeajiRSApeecXuAxYb++/lUxEnoJYbkUzmc+Uyn/74HjnjLrI2pCKj7+1oOpIIcH3rIkCuEk/wU8AfFN6zh7l12tKvzctJz+0foc7vkjWp5UYkk726fDLlj+/jZPZAnn/gVeI9PE1HErmhM9kCeOGBV7ni8ODBP5fRdvtS05FEbknFjUgmqr9vI93X/wDAqy1f5ETOPIYTidzaxrvKMabuYwD838JxFD5zzHAikZtTcSOSSXJfiObD+R8BMKVaa5aUvMdwIpHb92ndDqy7qzwBcRcY/dOHeCbEm44kckMqbkQyg2Xx/s+fkP/8af7KG8I7jZ8ynUgkVeI9POnX5iVifLJT48gOeq/5n+lIIjdkvLgZO3YsxYoVw8/Pj9DQUFauXHlbr/vtt9/w8vKiqoYmijMYP57me34n1tOLFx54hVhvX9OJRFLtcGAwg+/rBcALv82ENWsMJxJJmdHiZvbs2fTt25dBgwYRERFB/fr1admyJQcPHrzp66Kjo+nSpQtNmzbNpKQid2DnTnuyPuD9ht3Ykb+44UAiafdj+UbMLd8ILysBnnhCw8MlSzJa3IwaNYqnn36a7t27U65cOUaPHk1ISAjjxo276et69OhBx44dqVOnTiYlFUmj2Fjo2BEuXmRF0WpMrPGA6UQid+zNsOc4FBgM+/ZB796m44hcx1hxExcXx4YNGwgLC0u2PSwsjNWrV9/wdZMmTWLv3r0MSVy59hZiY2OJiYlJdhPJNEOGQEQE5M3Ly636YjmMXwkWuWNnfXPw4v0vg4eHvTzDN9+YjiSSjLF/aU+ePEl8fDzBwcHJtgcHB3PsWMrDDP/66y8GDBjA9OnT8fK6vfkHhw8fTmBgYNItJCTkjrOL3JY1a+CDD+z7X33Fcf+8ZvOIpKONhcvB66/bD557Dv75x2wgkf8w/mekw+FI9tiyrOu2AcTHx9OxY0eGDh1K6dKlb/v9Bw4cSHR0dNLt0KFDd5xZ5JYuXICuXSEhATp3hnbtTCcSSX9vvAFVqkBUFPTsqdXDJcswtvxCUFAQnp6e17XSHD9+/LrWHICzZ8+yfv16IiIi6NOnDwAJCQlYloWXlxcLFy6kSZMm173O19cXX1+NTJFMNmgQ/PUXFCoEH39sOo1IxvDxgSlT7EU1v/8epk+HTp1MpxIx13Lj4+NDaGgo4eHhybaHh4dTt27d6/YPCAhg69atbNq0KenWs2dPypQpw6ZNm6hVq1ZmRRe5uRUr/i1oJkyA3LnN5hHJSJUr233LAJ5/Ho4cMZtHBMMLZ/bv35/OnTtTo0YN6tSpw/jx4zl48CA9e/YE7EtKR44cYcqUKXh4eFCxYsVkr8+fPz9+fn7XbRcx5tw56NbNbp7v3h1atDCdSCTjvfYa/PADrFsHzzwD8+dDCt0LRDKL0eKmQ4cOREVFMWzYMCIjI6lYsSILFiygSJEiAERGRt5yzhsRk65dRXnYwnF02bePwwH5aJEzjHMprLIs4nK8vODrr6FaNfj5Z7vFsnt306nEjTksy716gMXExBAYGEh0dDQBAQGm44iT+29xU3f/JmbMHgxAxw5vs7poVUOpRDLH/hGtk28YORJeeQX8/WHrVrj6h6pIekjN97fRlhsRV5Ez9gLv/2z3s5lSrbUKG3EL17ZceiSUZvZd5al55E9+a/gAT3R4J+ny1HWFkEgGMj4UXMQVvLZ8MoVjTnAgVwFGNOpmOo6IEQkenrzcui8XvXypd2AL7beE3/pFIhlAxY3IHap5aBudIxYAMKDFC1zwyWY4kYg5B3IX4sP6TwAwaOkE8p07ZTiRuCMVNyJ3wPdKHCN++RSAmZXDWFOksuFEIuZNqtGWLQVKEhh7nqHhn5uOI25IxY3IHeizejYlTh3meI7cDG/8lOk4IllCvIcnr7V8gcsenrTavZr7dt94vUCRjKDiRiSttmyh5+/fAvBG8+eI8ctpOJBI1rEjf3G+qPUwAMPCP4czZ8wGErei4kYkLeLjoXt3vBPi+aV0HX4tc/2s2iLubkzdx9ib5y6Cz52CV181HUfciIobkbT45BNYt44Y3xy82ayn6TQiWVKslw8DWzxvP/jyS1i2zGgecR8qbkRSa98+GGxP1vduoyc57p/XcCCRrOuPkIpMq9rSfvDMM3DxotlA4hZU3IikhmVBz55w4QI0asSsKveZTiSS5b3XqBsUKgR79sDQoabjiBtQcSOSGjNnwsKF4OsL48drcUCR23DWNweMG2c/+PBD2LbNbCBxeVp+QeR2nTkD/fvb9wcPhlKlgN0mE4k4jaKrPRlfqjZhf63l95aP0aHjiBv+caClGuROqeVG5HYNHgz//ANlytiLA4pIqrzV7FkuePtS6/B2Htm22HQccWEqbkRux/r1MHasfX/sWPuylIikytGA/Iyu1xGA15dOJNfFGMOJxFWpuBG5lfh4uxOxZcETT0CTJqYTiTitiTXasjOoCHkuxvDassmm44iLUnEjciuffw4bNkBgoN0ZUkTS7IqnF4Pv6wXA41sWUv3wDsOJxBWpuBG5mchIeP11+/6770JwsNk8Ii5gfeEKzK7UHIB3Fn6GV/wVw4nE1ai4EbmZl16CmBioUQN69DCdRsRljGjUjdN+/pQ7sZ9uG340HUdcjIaCi1yj6ID5ANTbv4nps2cS7/CgbYVObBv0i+FkIq7jdPZA3m38JB/8/An9Vs1gftn6RAbkMx1LXIRabkRS4B1/2V7JGJhSvTXbCpQ0nEjE9XxbqRl/FC5PjsuXGLRkguk44kJU3Iik4Mn1P1Li1GFOZM/FqPqdTMcRcUmWw4MhzXsS7/Dg/l2rqHNgi+lI4iJU3IhcI9+5U7ywehZgr4lz1jeH4UQirmtH/uJMv7qw5pBFX+CZEG84kbgCFTci1xiwbBI54y4SUbAMcypqThuRjPZh/U6cyhZA2ZMH6Lxxvuk44gJU3Ij81+rVPLx9KQk4GNK8B5ZD/4uIZLTobP6MbNAZgP6rpsPx44YTibPTv9wiieLj4fnnAfhf5eZsKVjacCAR9zGrchhbg0sQEHv+37mlRNJIxY1IogkTYONGYnxz8EGDLqbTiLiVBA9PhjTraT+YOBHWrTMbSJyaihsRgNOnk/5a/OjejkTlyGU2j4gb2li4HHMqNLbXcevTBxISTEcSJ6XiRgTgzTchKgoqVGBqtdam04i4rRGNngR/f/jjD/j6a9NxxEmpuBHZsgXGjrXvf/IJVzw1cbeIKSdy5rH/2AAYMACio80GEqek4kbcm2VBv3528/cjj0ATDf0WMe6FF6BMGXvU1Lvvmk4jTkjFjbi3efNgyRLw9YUPPjCdRkQAfHzgww/t+6NHw99/G40jzkft7+LyEhfCvJZ3/GV+ndCb4sBn1R7gg8+3A9szNZuI3ECrVtC8OYSHw6uvwrffmk4kTkQtN+K2Om9cQPHTRzmRPRdjaz9qOo6I/JfDAaNGgYcHzJkDK1aYTiRORMWNuKVcF2N48bcZgD31+3nf7IYTich1KlaEZ5+17/fvr6HhcttU3IhbevG3mQTGnmdHvqL8r3Jz03FE5EaGDYOAANiwAaZONZ1GnISKG3E7JaIOJS3O939NupPg4Wk4kYjcUL58MHiwff/11+H8ebN5xCmouBG38/rSiXhZCYSXvIfVRauajiMit/LCC1C8OBw9Cu+/bzqNOAEVN+JW7t0XQdO967js4cm7jZ82HUdEboev779FzQcfwKFDZvNIlqeh4OI2PBPiGbzkKwCmVmvNvjx3GU4kIilJcfoGy5fZIRWpdWgbc1t0oV+blwHYP0LLpcj11HIjbuORrYsoe/IAZ/xy8nG9x03HEZHUcDj4vybdAXjwz2VUOLbHcCDJylTciFvIFneJ/qumAzCm7mNEZ/M3nEhEUmtbgZLMLd8IgIHLJtnLp4ikQMWNuIWn1v9A8LlTHAoM1qrfIk7swwadifX04t4Dm2mwb6PpOJJFqbgRl5fnQjQ9f7enbv+gQWfivLwNJxKRtDocGMyU6vcDV1tv4uMNJ5KsSMWNuLznV8/CP+4iW4NLMK9cA9NxROQOfVanPTG+OSh3Yj9Mn246jmRBKm7Ete3dyxMRPwMwvNGTWA6d8iLO7ky2AD6rc3U9uMGD4dIls4Eky9G/9OLaBg3CJ+EKy4tV14R9Ii5kcvU2HPUPsue8GTPGdBzJYlTciOtatw5mzyYBByMadTOdRkTSUay3L6Pqd7IfvPsunDplNpBkKSpuxDVZFrz6KgBzKzRiR/7ihgOJSHr7rkJjqFQJzpyxCxyRq1TciGv6+WdYtgx8fRlVv7PpNCKSARI8POG99+wHY8bA/v1G80jWoeJGXE98PLz2mn3/+ec5EpjfbB4RyTgtWkCTJhAXB2+8YTqNZBEqbsT1TJ0K27ZBrlwwcKDpNCKSkRyOfxfVnD4dIiLM5pEsQcWNuJaLF//96+311yFPHrN5RCTjhYbCY4/Zfe0SW23Fram4Edfy6adw+DCEhMDzz5tOIyKZ5Z13wNsbwsNhyRLTacQwFTfiOqKjYcQI+/6wYeDnZzaPiGSe4sWhRw/7/qBBWlTTzam4EdcxapQ910W5ctBZI6RE3M6gQZAtG6xdCz/9ZDqNGKTiRlzDiRN2cQN2q42np9k8IpL5ChSAF1+07w8aBAkJZvOIMV6mA4ikRdEB85M9fn3JBJ49d46twSV4YJ0v1vr5N3iliLi0V16BceNg61aYPRsef9x0IjFALTfi9ArEnKTrRrsJemSDLlocU8Sd5cljFzgAb74Jly+bzSNG6FtAnN7za2bhG3+Z3wtXYHmx6qbjiIhpL74I+fLBnj0webLpNGKA8eJm7NixFCtWDD8/P0JDQ1m5cuUN9121ahX16tUjb968ZMuWjbJly/LRRx9lYlrJau4+HUn7LeEAjGzQ2Z7QS0TcW86c9jxXAEOHwqVLZvNIpjNa3MyePZu+ffsyaNAgIiIiqF+/Pi1btuTgwYMp7p8jRw769OnDihUr2LFjB4MHD2bw4MGMHz8+k5NLVtH3txl4J8SzrFgo60Iqmo4jIllFz55QuDAcOWL3wRG34rAsc5MB1KpVi+rVqzPuPydeuXLlaNeuHcOHD7+t93jooYfIkSMHU6dOva39Y2JiCAwMJDo6moCAgDTlFvOKDphP6RP7+WXi83hgcX/X0WwrUNJ0LBHJZPtHtL7xk199Bc88A0FB8Pff4O+fecEk3aXm+9vYaKm4uDg2bNjAgAEDkm0PCwtj9erVt/UeERERrF69mrfffvuG+8TGxhIbG5v0OCYmJm2BJct5aeU0PLCYX6aeChsRN3XtyMn/8orPx8LchSh+8igftnqOMfUev3kxJC7D2GWpkydPEh8fT3BwcLLtwcHBHDt27KavLVy4ML6+vtSoUYPevXvTvXv3G+47fPhwAgMDk24hISHpkl/Mqhy5m/v+Wku8w4NR93YyHUdEsqArnl58dO8TADzzx1wCL541nEgyS5qKm40bN7J169akxz/88APt2rXj9ddfJy4uLlXv5bimA6hlWddtu9bKlStZv349n3/+OaNHj2bmzJk33HfgwIFER0cn3Q4dOpSqfJI1vbzCvgw5t0Jj9gapYBWRlP1Urj478hUlIO4CPX+fYzqOZJI0FTc9evRg9+7dAPz999889thjZM+enW+++YZXX331tt4jKCgIT0/P61ppjh8/fl1rzrWKFStGpUqVeOaZZ+jXrx9vvfXWDff19fUlICAg2U2c3LJlNNgfQZyHF6PraYIuEbkxy+Fhj6QEum2YB5GRhhNJZkhTcbN7926qVq0KwDfffEODBg2YMWMGkydPZs6c26uMfXx8CA0NJTw8PNn28PBw6tate9tZLMtK1qdGXJxlweDBAMyseh+HcxUwHEhEsrrFJe5hY6EyZLsSC++9ZzqOZII0FTeWZZFwdc2ORYsW0apVKwBCQkI4efLkbb9P//79+eqrr5g4cSI7duygX79+HDx4kJ49ewL2JaUuXbok7f/ZZ58xb948/vrrL/766y8mTZrEyJEj6dRJfS7cxqJF8NtvxHp681nt9qbTiIgzcDj+7Zv3+edw9KjZPJLh0jRaqkaNGrz99ts0a9aM5cuXJw3l3rdv3y0vKf1Xhw4diIqKYtiwYURGRlKxYkUWLFhAkSJFAIiMjEw2501CQgIDBw5k3759eHl5UaJECUaMGEGPxGXuxbVZFgwZAsD0qi057p/XcCARcRarilZl3V3lqXnkTxg+HMaMMR1JMlCa5rnZvHkznTp14uDBg/Tv358hV79wnn/+eaKiopgxY0a6B00vmufGif36K7RoAX5+1Hx6PCdy5jGdSEScSN39m5gxezD4+MDevfYkf+I0UvP9na6T+F26dAkvLy+8vLLuYuMqbpyUZUHdurB2LfTrR1GfpqYTiYizsSz2r3kfVq6EXr3gs89MJ5JUSM33d5r63BQvXpyoqKjrtl+6dInSpUun5S1Fbu7XX+3CJls2eO0102lExBk5HPZaU2DPXqypQVxWmoqb/fv3Ex8ff9322NhYDh8+fMehRJL5T18bevWCVPTrEhFJpnFjaNgQ4uLg3XdNp5EMkqrrRz/++GPS/V9//ZXAwMCkx/Hx8SxevJhixYqlXzoRgJ9/hj/+sFttXnnFdBoRcXZDh0KjRjBhAgwYAFcHsYjrSFVx065dO8CeVbhr167JnvP29qZo0aJ8+OGH6RZOJFmrTe/earURkTvXsKHdgrN0qd1688UXphNJOkvVZamEhAQSEhK4++67OX78eNLjhIQEYmNj2bVrF/fff39GZRV3NH8+rF8P2bOr1UZE0k9i35uJE2H/fqNRJP2lqc/Nvn37CAoKSu8sIslZFiQurdGnD+TPbzSOiLiQ+vWhWTO4cgXeecd0GklnaR6zvXjxYhYvXpzUgvNfEydOvONgIsybBxs2QI4carURkfQ3dKg96/nkyfD666A+oy4jTS03Q4cOJSwsjMWLF3Py5ElOnz6d7CZyx/7bavP886CWQhFJb3XrQliY3Xrz9tum00g6SlPLzeeff87kyZPp3LlzeucRsf3wA0REQM6c8PLLptOIiKsaOhQWLoSvv4aBA6FkSdOJJB2kqbiJi4tL1crdIrej6ID59h3LYv7kl6gAfFqpFSM/WGs0l4i4sNq17WVdfvnFXnNqwgTTiSQdpOmyVPfu3bP0+lHi3Jru/YMKx//mnE82vqrZznQcEXF1b75p/5wyRSOnXESaWm4uXbrE+PHjWbRoEZUrV8bb2zvZ86NGjUqXcOKGLIvnV88CYGq11pzJpvW/RCT9JLUQX2NakSrce2Az0x7sxeD7egOwf0TrzIwm6ShNxc2WLVuoWrUqANu2bUv2nMPhuONQ4r7q74+gauRfXPTyVauNiGSaMXUf494Dm3l0azhj6nbgH38NYnBmaSpuli5dmt45RJK12syo2oKoHLnM5hERt/H73ZX4vXAFah3eTo/fv2NYs2dNR5I7kKY+NyIZofahrdxz+E9iPb354p6HTMcRETczpu5jAHTc/AtB5zWtiTNLU8tN48aNb3r5acmSJWkOJO4rsdVmduUwjvvnNZxGRNzNqqJViShYhmqRu+j+x1ygk+lIkkZparmpWrUqVapUSbqVL1+euLg4Nm7cSKVKldI7o7iD1aupd2ALlz08+bz2w6bTiIg7cjj4pJ7detM5YgGcPGk4kKRVmlpuPvrooxS3v/XWW5w7d+6OAombujo76JyKTTkaoDWkRMSMpcVrsDW4BJX+2QujR2vmYieVrn1uOnXqpHWlJPXWr4eff+aKw4OxtR81nUZE3JnDwad1O9j3x4yBM2eMxpG0SdfiZs2aNfj5+aXnW4o7uPqX0Q/lG3Iwd0HDYUTE3S0sVZudQUUgJsYucMTppOmy1EMPJR/JYlkWkZGRrF+/njfeeCNdgomb2LLFXkfK4WBsnfam04iIYDk8+KxOe8bM+8C+NNW3L/j7m44lqZCmlpvAwMBktzx58tCoUSMWLFjAkCFD0jujuLLE69mPPsrevCFms4iIXDW/7L1QpgycOgVjx5qOI6nksCzLMh0iM8XExBAYGEh0dDQBAZra36gdO6BCBbAs2LKFotMPmk4kIpJkf/ko6NoV8uWDffsgRw7Tkdxaar6/76jPzYYNG5g2bRrTp08nIiLiTt5K3NG779qFTbt2oCkERCSr6dgRiheHEydg/HjTaSQV0lTcHD9+nCZNmlCzZk1eeOEF+vTpQ2hoKE2bNuXEiRPpnVFc0d9/Q+LK8oMHm80iIpISLy8YONC+/+GHEBtrNo/ctjQVN88//zwxMTFs376dU6dOcfr0abZt20ZMTAwvvPBCemcUV/TBB5CQAPfdB6GhptOIiKSsc2coVAiOHIFp00ynkduUpj43gYGBLFq0iJo1aybb/scffxAWFsaZLDwvgPrcZAHHjkHRovZfQcuWQcOGABQdMN9oLBGRlDz9x1zeWDqBv3MXoln3cSR4eF63z/4RrQ0kcy8Z3ucmISEBb2/v67Z7e3uTkJCQlrcUd/LRR3ZhU6cONGhgOo2IyE3NrNqC037+FD99lBa715iOI7chTcVNkyZNePHFFzl69GjStiNHjtCvXz+aNm2abuHEBZ05A+PG2fcHDoSbLMAqIpIVXPDJxteh9wPQa+039kAIydLSVNx8+umnnD17lqJFi1KiRAlKlixJsWLFOHv2LGM0m6PczGefwdmzULEitFYzrog4h8mhbTjv7UfFf/bSYN9G03HkFtI0Q3FISAgbN24kPDycnTt3YlkW5cuXp1mzZumdT1zJhQv2bJ8AAwaAR7qu/iEikmHOZAtgZpX76L7+B3qt/YYVxTUQIitL1bfLkiVLKF++PDExMQA0b96c559/nhdeeIGaNWtSoUIFVq5cmSFBxQVMnAgnT9qdiTt0MJ1GRCRVvqr5IHEeXtQ+tI3qR3aYjiM3kariZvTo0TzzzDMp9lIODAykR48ejBo1Kt3CiQu5fNke/g3wyiv2/BEiIk7kWEAQ31VsAsBza78xnEZuJlXfMJs3b+a999674fNhYWGMHDnyjkOJ60gc3v3QtsWMOniQE9lzce/eAsRq2LeIOKEvaj1M+y3hNN/zB6VP7Gd3vqKmI0kKUtVy888//6Q4BDyRl5eXZiiW6zisBJ5b+y0AE2u2Jdbb13AiEZG02ZfnLhaUqQeQ9O+aZD2pKm7uuusutm7desPnt2zZQsGCBe84lLiW5n/9TqmoQ8T4ZGdatVam44iI3JFxtR8BoM2OFRQ+c8xwGklJqoqbVq1a8eabb3Lp0qXrnrt48SJDhgzh/vvvT7dw4gIsy54XAphavTVnfbWqrog4t+0FSrKiaDW8rAR6/PGd6TiSglQVN4MHD+bUqVOULl2a999/nx9++IEff/yR9957jzJlynDq1CkGDRqUUVnFCdU5uIWqkbu55OXDpBoPmI4jIpIuxtZ5FID2W8LJd+604TRyrVR1KA4ODmb16tU899xzDBw4kMRlqRwOB/fddx9jx44lODg4Q4KKc0q8Jv2/Ss05mSO34TQiIuljbUglNhYqQ/Wju3hq/Q9AJ9OR5D/StHAmwOnTp9mzZw+WZVGqVCly53aOLy4tnJmJNmyAGjW44vCgUY8vORyowldEXEezv37nq+/+j7M+2fD/5yjkymU6kkvL8IUzAXLnzk3NmjW55557nKawkUw2fDgAP5ZvqMJGRFzO4pI12RV0N/5xF/9dM0+yBM1/Lxlj5074zu5oN67WI4bDiIikP8vhwbjadt8bPvrIXmJGsgQVN5IxPvgALIvwkrX4K18R02lERDLEvHINOBQYDCdOwNdfm44jV6m4kfR39ChMmwao1UZEXFu8hydf1WxnP/jwQ4iPN5pHbCpuJP198gnExUG9emwsXM50GhGRDPW/Ss0hTx7YuxfmzjUdR1BxI+nt7Fn4/HP7/iuvmM0iIpIJLvr4Qe/e9oOrl+TFLBU3kr6+/BKio6FMGWjTxnQaEZHM0acP+PnBH3/AypWm07g9FTeSfi5fhtGj7fsvvQQeOr1ExE3kzw9du9r3P/jAbBZRcSPpaPZsOHQIgoOhc2fTaUREMtdLL4HDAT/9BH/+aTqNW1NxI+nDsuD99+37L7xgN8+KiLiTUqXgwQft+yNHms3i5lTcSPpYuBC2boUcOeC550ynERExI3EgxbRp9rQYYoSKG0kfideYu3cHLcchIu6qdm2oX9/ug/jxx6bTuC0VN3LnNm6ExYvB0xP69TOdRkTErMTWm88/h5gYs1nclIobuXOJrTbt20MRLbUgIm6udWsoW9YubL780nQat+RlOoA4uf374Ztv7PuatE9E3FTRAfOTPW5fNIz3d+4k8q3hNDhWgsue3knP7R/ROrPjuR0VN5Iq1/4PPGTRFzwZH8/KIlXpPPsozFYHOhGR7ys05uWVUyl4Loo2O1bwXcWmpiO5FV2WkjQLvHiWDlsWAjC+1kOG04iIZB1xXt5MqvEAAM/+/p2WZMhkxoubsWPHUqxYMfz8/AgNDWXlTaat/u6772jevDn58uUjICCAOnXq8Ouvv2ZiWvmvThELyH45lj/zF2Nl0Wqm44iIZCnTq7bknE82yp48QKO/N5iO41aMFjezZ8+mb9++DBo0iIiICOrXr0/Lli05ePBgivuvWLGC5s2bs2DBAjZs2EDjxo1p06YNERERmZxcfK/E0W3DPADG3/OQPSuniIgkifHLyazKYQA8+8d3htO4F6PFzahRo3j66afp3r075cqVY/To0YSEhDBu3LgU9x89ejSvvvoqNWvWpFSpUrz77ruUKlWKefPmZXJyeWjbEvJdOMMR/3z8VLa+6TgiIlnSxJptuezhSd2DW6gU+ZfpOG7DWHETFxfHhg0bCAsLS7Y9LCyM1atX39Z7JCQkcPbsWfLkyXPDfWJjY4mJiUl2kzvjsBLovm4uYP+Pe8VT/dJFRFJyNCA/88o1AKCHWm8yjbHi5uTJk8THxxMcHJxse3BwMMeOHbut9/jwww85f/487du3v+E+w4cPJzAwMOkWEhJyR7kFmu35gxKnjhDjmyOpyVVERFI2/h57wEXLXb9ROPofw2ncg/EOxY5r+mpYlnXdtpTMnDmTt956i9mzZ5M/f/4b7jdw4ECio6OTbocOHbrjzO6u+7rvAZhRtQXnfbObDSMiksXtzF+MlUWq4mkl0HWDulFkBmPFTVBQEJ6ente10hw/fvy61pxrzZ49m6effpr//e9/NGvW7Kb7+vr6EhAQkOwmaVcp8i9qHdrGZQ9PJldvYzqOiIhTmFCzHQCPbf4VoqPNhnEDxoobHx8fQkNDCQ8PT7Y9PDycunXr3vB1M2fOpFu3bsyYMYPWrTXLY2Z7ev33APxUtj7HAoLMhhERcRLLi1fnr7wh+MddhAkTTMdxeUYvS/Xv35+vvvqKiRMnsmPHDvr168fBgwfp2bMnYF9S6tKlS9L+M2fOpEuXLnz44YfUrl2bY8eOcezYMaJVBWeOQ4dovXMV8O9fISIicmuWw4OvEv/d/PhjuHLFaB5XZ7S46dChA6NHj2bYsGFUrVqVFStWsGDBAopcXXwxMjIy2Zw3X3zxBVeuXKF3794ULFgw6fbiiy+a+hXcy6ef4p0Qz9qQimwrUNJ0GhERp/J9+UaczB4IBw/Cdxo5lZEcluVec0LHxMQQGBhIdHS0+t+kxrlzULgwREfT/aE3WFSqlulEIiJOp++q6fT9bSbccw+sXasJUFMhNd/fxkdLiZOYNAmio9mXuyCLS9Y0nUZExClNrdYafH3hjz/gNud0k9RTcSO3Fh9vXyMGJtRoh+XQaSMikhZROXJB5872g1GjjGZxZfqWklubNw/27oXcuZlTsanpNCIizq1vX/vn3Ln2v62S7lTcyK0l/nXRsycXffzMZhERcXYVKkCLFmBZSa3ikr5U3MjNrVsHK1eCtzf06WM6jYiIa3jpJfvnxIlw+rTZLC5IxY3c3Ecf2T8fewwKFTKbRUTEVTRtCpUqwfnz8OWXptO4HBU3cmOHDsH//mff79fPbBYREVficED//vb9Tz6BuDizeVyMihu5sTFj7JFSjRtDtWqm04iIuJbHH4cCBeDIEfjmG9NpXIqKG0nZ2bMwfrx9P/GvCxERST++vv/2ZRw1yu5gLOlCxY2k7OqkfZQuDa1amU4jIuKaevSAbNlg40ZYscJ0Gpeh4kauFx8Po0fb9/v1Aw+dJiIiGSIoCLp2te9/+KHZLC5E31pyvR9+gH37IE8e+M+q7CIikgESB2zMmwe7dpnN4iK8TAcQ84oOmJ/s8TfT3qAmMKZMcz4cttRMKBERF3Xtv7kAX5a8h+Z7/mDK4y/xZthzyZ7bP6J1ZkVzGWq5kWSqHt1FzSN/EufhxZTq+h9KRCQzTKzRFoBHti0i4NI5w2mcn4obSebpdd8D8GP5hpzImcdsGBERN7Hm7srsyFeU7Jdj6bB5oek4Tk/FjSQpFHOclrt+A2BCzbaG04iIuBGHg4k1HgCg68Z5eCbEGw7k3FTcSJIuG37Cy0rgtyKV2ZG/uOk4IiJu5cfyjYjKFkDhmBM0/2ut6ThOTcWNAJAt7hKPb/4VgEmharUREclssV4+TK/aEoCn1v9gOI1zU3EjADy0fQmBsec5kKsAS0rUMB1HRMQtTavWissentxz+E8qHttjOo7TUnEjYFl02zAPgK+rtyHBw9NwIBER93TcPy8/la0PwJNqvUkzFTdC/f0RlIo6xDmfbHxTuZnpOCIibm3S1Y7FbXasJN+5U4bTOCcVN8KT638E4JtKzTjrm8NwGhER97alYGnW31UOn4QrdIr42XQcp6Tixt3t3k2Tv9eTgIPJoW1MpxEREf6d1O+JTQvg0iXDaZyPiht3N2YMAEtK1OBA7kKGw4iICMCvpetwxD8fQReiYeZM03GcjoobdxYdDZMnAzCphoZ/i4hkFfEenkwJvboEzscfg2WZDeRkVNy4s4kT4dw5dgXdzW9FqphOIyIi/zGr8n1c9PKFzZth+XLTcZyKiht3FR+fdElqcugD4HAYDiQiIv8Vnc2fORWb2A8+/thsGCej4sZd/fQT7NsHefIwt0Ij02lERCQFk0LtYeH88AP8/bfZME5ExY27Svwr4JlnuOTtZzaLiIikaG9QCNx3n93n5mpru9yaiht3tGULLF0Knp7Qu7fpNCIicjN9+9o/J0yAmBijUZyFl+kAkjGKDph/w+dG/PwJjwE/laxDn8+2ZF4oERFJvbAwKFMGdu2yR7i+8ILpRFmeWm7cTO4L0bT7cxnw7xTfIiKShXl4wIsv2vc/+QQSEszmcQIqbtzM45t/xe9KHFsKlGTDXeVMxxERkdvRpQvkygV798L8G7fMi03FjRvxir9C5432/xSTNPxbRMR55MgBzzxj3x892mgUZ6Dixo203PUbBc9FcSJHLuaXrW86joiIpEafPvZAkCVLYOtW02myNBU3buTJDfbq39OqtiLOy9twGhERSZW774YHH7Tvf/KJ2SxZnIobN1Hl6C6qH91FrKcX06u1NB1HRETSInGk1PTpcOqU2SxZmIobN5HYavNTuQaczJHbcBoREUmTe++FKlXg4kV73htJkYobN5D/bBStd64CYGKohn+LiDgth+Pf1pvPPrPXCZTraBI/N9ApYgHeCfH8Ubg82wuUNB1HRERS4dpJWX0v52JNtgDyHDjAs48OYWHpOknP7R/ROrPjZUlquXFxvlfi6Lj5F+A/C7CJiIjTivX2ZXblMAC6bpxnOE3WpOLGxT3w53KCLkRzOCBfsupeRESc17RqrYh3eFDvwBZKnThgOk6Wo+LGlVkW3TbYVf3U6q2J9/A0HEhERNLDkcD8LCxVG4CuG38ynCbrUXHjwmoc+ZMKx//mopcvsyrfZzqOiIiko69D7wfgoe1LCLh0znCarEXFjQvrtsGu5r8v35DobP6G04iISHpaG1KJnUFFyH45lke3hJuOk6WouHFRwWdPct/u1QBMuVrdi4iIC3E4+Dq0DQBdIubjkaBh4YlU3Liojpt+wTshnt8LV2BH/uKm44iISAb4vnwjzvjlpMiZYzT6e4PpOFmGihtXFBtLx0328O/Eql5ERFzPRR+/pGHhiQNIRMWNa/r2W/JdOENkzrxJvelFRMQ1Ta3WigQcNNgfATt3mo6TJai4cUVjxgAwvVpLrnhqEmoREVd2OFcBFpe8x37w6admw2QRKm5czbp18PvvxHp6MauKhn+LiLiDSYldEL7+GqKjzYbJAlTcuJqrVfv8svW1+reIiJtYXaQKu/PeDefOweTJpuMYp+LGlZw4AbNmATCluoZ/i4i4DYfj32k/Pv0UEhLM5jFMxY0r+fJLiIuDmjXZVKiM6TQiIpKJvqvQGAIDYc8e+PVX03GMUnHjKq5cgXHj7PvPP282i4iIZLoLPtngqafsB1cHlrgrFTeu4ocf4PBhyJcP2rc3nUZEREzo3RscDvj5Z9i923QaY1TcuIrEKv3ZZ8HX12wWERExo0QJaNXKvv/ZZ2azGKTixhVs3QrLl4OnJ/TsaTqNiIiYlNg1YdIkOHvWbBZDjBc3Y8eOpVixYvj5+REaGsrKlStvuG9kZCQdO3akTJkyeHh40Ldv38wLmpUlTtr04INQuLDZLCIiYlbz5lCmjF3YTJliOo0RRoub2bNn07dvXwYNGkRERAT169enZcuWHDx4MMX9Y2NjyZcvH4MGDaJKlSqZnDaLOn0apk2z7/fpYzaLiIiY5+Hx7/eBmw4LN1rcjBo1iqeffpru3btTrlw5Ro8eTUhICOMSR/1co2jRonz88cd06dKFwMDATE6bRU2aBBcuQKVK0KCB6TQiIpIVdO0K/v72WlOLFplOk+mMFTdxcXFs2LCBsLCwZNvDwsJYvXp1un1ObGwsMTExyW4uIz7+3w5jffrYPeRFRET8/aFbN/u+Gw4LN1bcnDx5kvj4eIKDg5NtDw4O5tixY+n2OcOHDycwMDDpFhISkm7vbdwvv8Dff0OuXPDEE6bTiIhIVpJ4aWr+fNi3z2yWTGZ8yWjHNa0NlmVdt+1ODBw4kP79+yc9jomJccoCp+iA+ddt+/p/b9IQGF+qMe/+37LMjiQiIllZ6dIQFgYLF9qTvL7/vulEmcZYcRMUFISnp+d1rTTHjx+/rjXnTvj6+uLrgvO+FDt1hIb7NpKAg6nVW5uOIyIiWcC1fwg39a/FBBZyeszn1I6vTaz3v9+H+0e47neHsctSPj4+hIaGEh4enmx7eHg4devWNZTKeXTZ+BMAS0rU4FCuAobTiIhIVrS0eA0OB+Qn96WzPLBjhek4mcboaKn+/fvz1VdfMXHiRHbs2EG/fv04ePAgPa9ORDdw4EC6dOmS7DWbNm1i06ZNnDt3jhMnTrBp0yb+/PNPE/GNyRF7gUe22r3ftfq3iIjcSIKHJ9Oq2TMWd9n4E1iW4USZw2ifmw4dOhAVFcWwYcOIjIykYsWKLFiwgCJFigD2pH3XznlTrVq1pPsbNmxgxowZFClShP3792dmdKMe3L4U/7iL7M1zFyuLVbv1C0RExG3NrtycfqumU+mfvVQ7uouIu8qajpThjHco7tWrF7169UrxucmTJ1+3zXKTqvOGLIuuVy9JTa3WGsthfJJpERHJwk5nD2ReuQY8sm0xnSPmu0Vxo29GJ1P3wGZKRR3inE82vq3UzHQcERFxAlOuDjxpvXMlec+fMRsmE6i4cTLdrrbazKnYhHO+2Q2nERERZ7ClYGk2FSyFb/wVOmxZaDpOhlNx40QKR/9D0z1/ADClmjoSi4jI7UscgPJExM94JsQbTpOxVNw4kU4RC/C0ElhZpCp7g5xvIkIRETFnftn6RGUL4K6zJ5L+UHZVKm6chO+VONpvsecEmhKqVhsREUmdWC8f/lfZXs+x88brZ713JSpunETrnSvJczGGwwH5WFyipuk4IiLihKZXa0kCDuof2GSvGO6iVNw4iS5Xq+wZVVuS4OFpOI2IiDijw4HBLC55j/1g7FizYTKQihtnsH49VSN3E+fhxeyrTYoiIiJpkTgsnK+/hrNnzYbJICpunMHV6npB2XpE5chlNouIiDi1VUWr8nfuQhATA9OmmY6TIVTcZHVRUTBzJqDh3yIicucshwdTE1tvPvvMJdebUnGT1U2eDJcusT1/cTa6wZTZIiKS8eZUbArZs8P27bDC9VYLV3GTlSUkwLhxAEyt1gocDsOBRETEFcT45YROnewHn35qNkwGUHGTlS1cCHv3QmAgP5RvZDqNiIi4kt697Z9z58KRI2azpDMVN1nZZ5/ZP7t146KPn9ksIiLiWipXhvr1IT4exo83nSZdqbjJqvbvh/lXZ5B87jmjUURExEUltt588QXExZnNko5U3GRVn39u92Bv1gzKlDGdRkREXNGDD0KBAvDPP/Ddd6bTpBsVN1nRpUswYYJ9P7GqFhERSW8+PtCjh30/sSuEC1BxkxV98w2cPAkhIXC/5rYREZEM9Oyz4OUFq1bB5s2m06QLFTdZUWL13KOHfcKJiIhklEKF7MtT4DKtNypuspoNG+D338HbG7p3N51GRETcQWIXiOnT4cwZo1HSg4qbrCZxldZHHoHgYLNZRETEPTRoABUrwoUL9sz4Tk7XPLKS06dhxgz7vjoSi4hIBio6YH6yx08UasA727axb9j7NIksgeVI3v6xf0TrzIx3R9Ryk5VMmmSPlKpcGerWNZ1GRETcyNwKjYnxyU6x05HU3xdhOs4dUXGTVfxnHSl699Y6UiIikqku+GRjTqWmAHSOmH+LvbM2FTdZRXg47NkDAQHQsaPpNCIi4oamVWsFQNM96yh85pjhNGmnPjcG/fd655dz/o/mwKRSDRn69nJzoURExG3tzRvCyiJVqX9gE502/cyIRk+ajpQmarnJAu6KPk6TveuAf6tmERERE6ZWtzsOt98Sju/lWMNp0kbFTRbQcdPPeFoJrCpShb15Q0zHERERN7a45D0cDshHnosxtNm50nScNFFxY5jPlct02LIQgKnVnGeYnYiIuKZ4D09mVG0JQKeIBYbTpI2KG8Na7VpF0IVoInPmZVGpWqbjiIiIMLtyGHEeXlSN3E2lyL9Mx0k1FTeGdd5odyqeUbUF8R6ehtOIiIhAVI5cLChbD3DOYeEqbgyq8M9eQo/uJM7Di1lVWpiOIyIikiSxq8QDO1YQePGs4TSpo+LGoE5XW21+KVOXEzlzG04jIiLyrw13lWNHvqL4XYnjka2LTMdJFRU3ppw+Tbs/7flspmr4t4iIZDUOB1Oq3w9Ap00L7Jn0nYSKG1O+/ppsV2LZka8o6wpXMJ1GRETkOj+Ub5i03hSLnKf1RsWNCQkJMHYscHXSPq0jJSIiWdB/15vis8/MhkkFFTcmLF4Mf/3FWZ9szK3Q2HQaERGRG5pW9WrXiZ9+ggMHzIa5TSpuTLha/c6p2JQLPtkMhxEREbmxvUEh/Faksn3VYfx403Fui4qbzHbwIMybB2hGYhERcQ5J31dffQWxWX+9KRU3me2LL+zqt3Fj9gZpHSkREcn6FpWsBYUKwfHj8N13puPckoqbzBQbC19+ad/v3dtsFhERkdt0xdMLnn3WfuAEHYtV3GSmOXPgxAm7+n3gAdNpREREbt8zz4CXF/z2G2zebDrNTam4yUyJ1W6PHuDtbTaLiIhIahQqBA8+aN8fN85slltQcZNZNm2C1avtqveZZ0ynERERSb1eveyf06ZBdLTZLDeh4iazXJ20j4cegoIFzWYRERFJi4YNoVw5OH8epk41neaGVNxkhjNnYPp0+746EouIiLNyOP5tvRk7FizLbJ4bUHGTGb7+Gi5cgAoVoH5902lERETSrksXyJEDduyAZctMp0mRipuMZln/XpLq3VvrSImIiHMLCIDOne37id9vWYyKm4y2eDHs3g3+/tCpk+k0IiIid+655+yfc+fC0aNms6TAy3QAV1N0wPxkjz+f+w4tgK9LNWDIOyvMhBIREUlPlSvDvffCqlX25LRDhphOlIyKmwxUMOYEzf/6HfjPqqoiIiJO6No/3tvkrsMYVnFs5Cfce66qPYvxVftHmF07UZelMlDHTb/gaSWw5u5K/JWviOk4IiIi6eaXMnU5kT0XBc6dovlfa03HSUbFTQbxjr/MY5t/BbT6t4iIuJ7Lnt7MqnIfAJ0jFhhOk5yKmwzSctdq8l04w7GceVhYqrbpOCIiIuluZtX7iHd4UPfgFkqcPGQ6ThIVNxmkU4R9bXJmlRbJrkOKiIi4iqMB+Vlc8h4AOm3KOq03Km4yQNnj+7jn8J9c9vBk5tUmOxEREVc05WrXi4e3LiZ73EXDaWwqbjJA56utNr+WqsNx/7yG04iIiGSc34pW4e/chQiIu0C7P5eZjgOouEl3/rHnabd9GQDTqmv4t4iIuDbL4cH0avb3XeeN87PEelPGi5uxY8dSrFgx/Pz8CA0NZeXKlTfdf/ny5YSGhuLn50fx4sX5/PPPMynp7Xlo2xJyXL7E7rx3szakkuk4IiIiGe6bSs246OVLuRP7CT2yw3Qcs8XN7Nmz6du3L4MGDSIiIoL69evTsmVLDh48mOL++/bto1WrVtSvX5+IiAhef/11XnjhBebMmZPJyW/AsuyqFZhavZXWkRIREbcQ45eTH8o3BP7tmmGSw7LMtR/VqlWL6tWrM27cuKRt5cqVo127dgwfPvy6/V977TV+/PFHduz4tyrs2bMnmzdvZs2aNbf1mTExMQQGBhIdHU1AQMCd/xL/tWQJNG3KOZ9s1O71Ned8s6fv+4uIiGRRFY7tYf7XfYnz8MIn8gjkz5+u75+a729jLTdxcXFs2LCBsLCwZNvDwsJYvXp1iq9Zs2bNdfvfd999rF+/nsuXL2dY1tv22WcAzK3QWIWNiIi4le0FShJRsAw+CVfgq6+MZjE2AcvJkyeJj48nODg42fbg4GCOHTuW4muOHTuW4v5Xrlzh5MmTFCxY8LrXxMbGEhsbm/Q4OjoasCvAdHXkCHz/PQCTKjQmIfZC+r6/iIhIFvdVpaYMj9wF334Lffqk63snfm/fzgUn47PLOa7pl2JZ1nXbbrV/StsTDR8+nKFDh163PSQkJLVRb9+0VzLuvUVERLKosVdvRERAYGCGfMbZs2cJvMV7GytugoKC8PT0vK6V5vjx49e1ziQqUKBAivt7eXmRN2/K88kMHDiQ/v37Jz1OSEjg1KlT5M2b96ZFVFrExMQQEhLCoUOH0r8/jwvQ8bkxHZub0/G5OR2fm9PxuTlnOT6WZXH27FkKFSp0y32NFTc+Pj6EhoYSHh7Ogw8+mLQ9PDyctm3bpviaOnXqMG/evGTbFi5cSI0aNfD29k7xNb6+vvj6+ibblitXrjsLfwsBAQFZ+gQxTcfnxnRsbk7H5+Z0fG5Ox+fmnOH43KrFJpHRoeD9+/fnq6++YuLEiezYsYN+/fpx8OBBevbsCditLl26dEnav2fPnhw4cID+/fuzY8cOJk6cyIQJE3j55ZdN/QoiIiKSxRjtc9OhQweioqIYNmwYkZGRVKxYkQULFlCkSBEAIiMjk815U6xYMRYsWEC/fv347LPPKFSoEJ988gkPP/ywqV9BREREshjjHYp79epFr169Unxu8uTJ121r2LAhGzduzOBUaePr68uQIUOuuwwmNh2fG9OxuTkdn5vT8bk5HZ+bc8XjY3QSPxEREZH0ZnxtKREREZH0pOJGREREXIqKGxEREXEpKm5ERETEpai4SaWxY8dSrFgx/Pz8CA0NZeXKlTfdf/ny5YSGhuLn50fx4sX5/PPPMympGak5PsuWLcPhcFx327lzZyYmzhwrVqygTZs2FCpUCIfDwfdX1yG7GXc6d1J7fNzp3Bk+fDg1a9bE39+f/Pnz065dO3bt2nXL17nL+ZOW4+NO58+4ceOoXLly0gR9derU4eeff77pa1zh3FFxkwqzZ8+mb9++DBo0iIiICOrXr0/Lli2TzcXzX/v27aNVq1bUr1+fiIgIXn/9dV544QXmzJmTyckzR2qPT6Jdu3YRGRmZdCtVqlQmJc4858+fp0qVKnz66ae3tb+7nTupPT6J3OHcWb58Ob1792bt2rWEh4dz5coVwsLCOH/+/A1f407nT1qOTyJ3OH8KFy7MiBEjWL9+PevXr6dJkya0bduW7du3p7i/y5w7lty2e+65x+rZs2eybWXLlrUGDBiQ4v6vvvqqVbZs2WTbevToYdWuXTvDMpqU2uOzdOlSC7BOnz6dCemyDsCaO3fuTfdxt3Pnv27n+LjruWNZlnX8+HELsJYvX37Dfdz5/Lmd4+PO549lWVbu3Lmtr776KsXnXOXcUcvNbYqLi2PDhg2EhYUl2x4WFsbq1atTfM2aNWuu2/++++5j/fr1XL58OcOympCW45OoWrVqFCxYkKZNm7J06dKMjOk03OncuRPueO5ER0cDkCdPnhvu487nz+0cn0Tudv7Ex8cza9Yszp8/T506dVLcx1XOHRU3t+nkyZPEx8dft2J5cHDwdSuVJzp27FiK+1+5coWTJ09mWFYT0nJ8ChYsyPjx45kzZw7fffcdZcqUoWnTpqxYsSIzImdp7nTupIW7njuWZdG/f3/uvfdeKlaseMP93PX8ud3j427nz9atW8mZMye+vr707NmTuXPnUr58+RT3dZVzx/jyC87G4XAke2xZ1nXbbrV/SttdRWqOT5kyZShTpkzS4zp16nDo0CFGjhxJgwYNMjSnM3C3cyc13PXc6dOnD1u2bGHVqlW33Ncdz5/bPT7udv6UKVOGTZs2cebMGebMmUPXrl1Zvnz5DQscVzh31HJzm4KCgvD09LyuFeL48ePXVbmJChQokOL+Xl5e5M2bN8OympCW45OS2rVr89dff6V3PKfjTudOenH1c+f555/nxx9/ZOnSpRQuXPim+7rj+ZOa45MSVz5/fHx8KFmyJDVq1GD48OFUqVKFjz/+OMV9XeXcUXFzm3x8fAgNDSU8PDzZ9vDwcOrWrZvia+rUqXPd/gsXLqRGjRp4e3tnWFYT0nJ8UhIREUHBggXTO57TcadzJ7246rljWRZ9+vThu+++Y8mSJRQrVuyWr3Gn8yctxyclrnr+pMSyLGJjY1N8zmXOHUMdmZ3SrFmzLG9vb2vChAnWn3/+afXt29fKkSOHtX//fsuyLGvAgAFW586dk/b/+++/rezZs1v9+vWz/vzzT2vChAmWt7e39e2335r6FTJUao/PRx99ZM2dO9favXu3tW3bNmvAgAEWYM2ZM8fUr5Bhzp49a0VERFgREREWYI0aNcqKiIiwDhw4YFmWzp3UHh93Oneee+45KzAw0Fq2bJkVGRmZdLtw4ULSPu58/qTl+LjT+TNw4EBrxYoV1r59+6wtW7ZYr7/+uuXh4WEtXLjQsizXPXdU3KTSZ599ZhUpUsTy8fGxqlevnmy4YdeuXa2GDRsm23/ZsmVWtWrVLB8fH6to0aLWuHHjMjlx5krN8XnvvfesEiVKWH5+flbu3Lmte++915o/f76B1BkvcejptbeuXbtalqVzJ7XHx53OnZSOC2BNmjQpaR93Pn/Scnzc6fx56qmnkv5Nzpcvn9W0adOkwsayXPfccVjW1Z5CIiIiIi5AfW5ERETEpai4EREREZei4kZERERcioobERERcSkqbkRERMSlqLgRERERl6LiRkRERFyKihsRERFxKSpuRMRlfPzxxxQrVozs2bPTrl07oqOjTUcSEQNU3IiIS3j99df59NNP+frrr1m1ahUREREMHTrUdCwRMUDLL4iI01u3bh21a9dm3bp1VK9eHYB3332XyZMns3v3bsPpRCSzqeVGRJzeyJEjadKkSVJhA5AvXz5OnjxpMJWImKLiRkScWmxsLPPmzePBBx9Mtv3ixYsEBgYaSiUiJumylIg4tTVr1lC3bl38/Pzw9PRM2n758mUaN27ML7/8YjCdiJjgZTqAiMid2L17N35+fmzdujXZ9gceeIB69eoZSiUiJqm4ERGnFhMTQ/78+SlZsmTStoMHD7Jz504efvhhg8lExBT1uRERpxYUFERMTAz/vcL+zjvv0KpVK8qXL28wmYiYopYbEXFqTZo04dKlS4wYMYLHH3+cGTNm8OOPP/LHH3+YjiYihqjlRkScWnBwMJMnT2bcuHGUL1+e1atXs2rVKkJCQkxHExFDNFpKREREXIpabkRERMSlqLgRERERl6LiRkRERFyKihsRERFxKSpuRERExKWouBERERGXouJGREREXIqKGxEREXEpKm5ERETEpai4EREREZei4kZERERcioobERERcSn/D2RiAYksv3YEAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def sample_rejection(rho, a, b, rhomax):\n", " while True:\n", " x_cand = a + (b-a)*np.random.rand()\n", " y = rhomax * np.random.rand()\n", " if (y < rho(x_cand)):\n", " return x_cand\n", " return 0.\n", "\n", "def rho_theta(theta):\n", " return np.sin(theta) / 2\n", "\n", "N = 100000\n", "samples = []\n", "for i in np.arange(0,N,1):\n", " theta = sample_rejection(rho_theta, 0., np.pi, 1.5)\n", " samples.append(theta)\n", " \n", "# Show a histogram\n", "plt.title(\"Polar angle distribution\")\n", "plt.xlabel(\"${\\\\theta}$\")\n", "plt.ylabel(\"Counts\")\n", "plt.hist(samples, bins = 40, range=(0,np.pi), density=True)\n", "# Show true distribution\n", "plt.plot([x for x in np.arange(0,np.pi,0.01)], [rho_theta(x) for x in np.arange(0,np.pi,0.01)], color='r')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rejection sampling has the following pros and cons\n", "\n", "Pros:\n", "- Does not need the distribution to be normalized\n", "- Will also work if $y_{\\rm max}$ is larger than the true maximum of $\\rho(x)$\n", "- Works for generic distributions and does not require the evaluation of cumulative distribution function\n", "\n", "Cons:\n", "- Can be inefficient if the rejection rate is very high (highly peaked distribution)\n", "- Not directly applicable to distributions over infinite ranges\n", "\n", "Generalization of rejection sampling can take care of some of the deficiencies. These include:\n", "- Adaptive rejection sampling by considering several enveloping rectangles\n", "- Variable transformation to map infinite interval into a finite one\n", "- Sampling from a non-uniform enveloping distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Importance sampling\n", "\n", "Recall the calculation of integral as statistical average\n", "$$\n", "I = \\int_a^b f(x) dx = (b - a) \\langle f \\rangle,\n", "$$\n", "where \n", "$$\n", "\\langle f \\rangle = \\frac{1}{N} \\sum_{i=1}^N f(x_i),\n", "$$\n", "and $x_i$ are sampled from a uniform distribution over $(a,b)$, i.e.\n", "$$\n", "x_i \\in U(a,b)\n", "$$\n", "\n", "In some cases, in particular, when $f(x)$ is highly peaked, only small part of the interval $(a,b)$ contributes to the total value of the integral. In this case sampling $x$ from $(a,b)$ with equal probability everywhere may be wasteful. Another issue may arise when $f(x)$ has integrable singularities. The method will still work, but the convergence rate for the statistical uncertainty can be slow.\n", "\n", "An improvement can be obtained by applying the so-called *importance sampling* technique.\n", "It is based on the following observation: Let $w(x)$ be the probability density for some random variable $x$.\n", "We will assume $w(x)$ is normalized, i.e. \n", "$$\\int_a^b w(x) dx = 1.$$\n", "Then the mean value of an arbitrary random variable function $g(x)$ reads\n", "$$\n", "\\langle g(x) \\rangle_w = \\int_a^b g(x) w(x) dx,\n", "$$\n", "where the subscript $w$ indicates that $x$ is distributed in accordance with probability density $w(x)$.\n", "\n", "Let us return to our integral. Divinding and multiplying the integrand by $w(x)$ we can rewrite $I$ as\n", "$$\n", "I = \\int_a^b \\frac{f(x)}{w(x)} w(x) dx = \\left\\langle \\frac{f(x)}{w(x)} \\right\\rangle_w~.\n", "$$\n", "The mean value $\\frac{f(x)}{w(x)}$ is well-defined as long as $w(x) > 0$.\n", "For $w(x) = \\frac{1}{b-a}$ we reproduce the original method.\n", "\n", "By choosing $w(x)$ to sample regions where the integrand $f(x)$ is most relevant, or to cancel away the integrable singularities one can significantly improve the statistical convergence of the method.\n", "\n", "\n", "The error estimate reads in essentially the same way as for the standard case\n", "$$\n", "\\delta I = \\frac{\\sqrt{\\left\\langle \\left[\\frac{f(x)}{w(x)} \\right]^2 \\right\\rangle_w - \\left\\langle \\frac{f(x)}{w(x)} \\right\\rangle_w^2}}{\\sqrt{N}}.\n", "$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# Calculate integral \\int_a^b f(x) dx using importance sampling\n", "# f = f(x) is the integrand\n", "# N is the number of random samples\n", "# wx = w(x) is the normalized probability density from which\n", "# the sampling takes place\n", "# sampler is a function which samples a random number from w(x)\n", "def intMC_weighted(f, N, wx, sampler):\n", " total = 0\n", " total_sq = 0\n", " for i in range(N):\n", " x = sampler()\n", " fval = f(x)\n", " total += fval / wx(x)\n", " total_sq += (fval / wx(x))**2\n", " fw_av = total / N\n", " fwsq_av = total_sq / N \n", " return fw_av, np.sqrt((fwsq_av - fw_av*fw_av)/N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example\n", "Let us consider integral\n", "$$\n", "\\int_0^1 \\frac{x^{-1/2}}{e^x + 1} dx\n", "$$\n", "which has an integrable singularity at $x = 0$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def f(x):\n", " return 1. / np.sqrt(x) / (np.exp(x) + 1)\n", "\n", "xplot = np.linspace(0.01,1, 400)\n", "yplot = f(xplot)\n", "\n", "plt.xlim(0,1)\n", "plt.ylim(0,3)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"f(x)\")\n", "plt.plot(xplot, yplot,color='r')\n", "plt.fill_between(xplot, yplot, step=\"pre\", alpha = 0.4, color='orange')\n", "# plt.axhline(0.5,linestyle='--', color='r')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can apply the standard mean value technique to estimate the integrand.\n", "Let us take $N = 10^6$ samples" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "I = 0.8374063441946126 +- 0.0017772180714415427\n", "CPU times: user 1.1 s, sys: 19.3 ms, total: 1.12 s\n", "Wall time: 1.11 s\n" ] } ], "source": [ "%%time\n", "\n", "np.random.seed(1)\n", "N = 1000000\n", "I, err = intMC(f, N, 0, 1)\n", "print(\"I = \",I,\" +- \",err)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that using importance sampling routine with the weight $w(x) = \\frac{1}{b-a}$ will reproduce the same result." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "I = 0.8374063441946126 +- 0.0017772180714415427\n", "CPU times: user 1.24 s, sys: 22.2 ms, total: 1.27 s\n", "Wall time: 1.26 s\n" ] } ], "source": [ "%%time\n", "\n", "def uniform_sample():\n", " eta = np.random.rand()\n", " return eta\n", "\n", "def uniform_w(x):\n", " return 1.\n", "\n", "np.random.seed(1)\n", "N = 1000000\n", "I, err = intMC_weighted(f, N, uniform_w, uniform_sample)\n", "print(\"I = \",I,\" +- \",err)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the method works, the convergence is rather slow. Can we improve upon it?\n", "\n", "Let us choose the weight function such that it cancels out the singularity in the ratio $f(x)/w(x)$.\n", "A natural choice here is\n", "$$\n", "w(x) = \\frac{1}{2\\sqrt{x}},\n", "$$\n", "such that $f(x)/w(x) = 2 / (e^x + 1)$ and thus\n", "$$\n", "I = \\left\\langle \\frac{2}{e^x + 1} \\right\\rangle_w~.\n", "$$\n", "\n", "We can sample from $w(x)$ through the inverse transform method.\n", "The cumulative distribution function reads\n", "$$\n", "G_w(x) = \\int_0^x w(x) = \\sqrt{x} = \\eta,\n", "$$\n", "thus,\n", "$$\n", "x = \\eta^2.\n", "$$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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Sk5Mv+/PHjh2r3Nzc4ldZh9AA16lXT3rkEbNzdVaW9PLLUqtWZin+7NlSUpKZX/Tb30pr1piwBABVnGNzhM6dO6caNWpo9uzZuuuuu4rbH3vsMW3evFmrV68u9Z7hw4fr7Nmzmj17dnHb2rVrlZCQoP379yuqDAdRMkcIKAfLkjIypJQUaeZM6cABz7VrrzW9SffdJ/36187VCMAV/G6OUEhIiGJjY5WWllaiPS0tTfHx8Zd8z+nTpxUYWLLkoKAgSaYnCYDNAgLMBOrXXpNycjzDZeHhUna29Mor0o03mtcrr5h7AKAKcXRobMyYMXr33Xc1depUbd++XY8//riys7OLh7rGjh2rESNGFN/fr18/zZs3TxMnTlRWVpbWrVunUaNGqWPHjmrIChfAu4KCzKn3U6dKBw96hsuqVTPL8595xvQS3XqrNHmydPy40xUDwC9yfGfpCRMm6NVXX9WBAwcUExOjN954Q127dpUkjRw5Urt379aqVauK73/zzTc1adIk7dq1S1dffbVuv/12vfLKK2rUqFGZPo+hMcBmx49Lc+aY4bOLh7RDQqTevc3QWd++UliYczUCqPI4YsMmBCHAi3JyzFyiDz80vURFwsPNWWf33Wd6jP7/kDYAlBVByCYEIaCSbN1qeolmzCg5d6hhQ7Nh4333Se3amXlIAPALCEI2IQgBlaywUFq71oSi2bNLzh1q1coEomHDpGbNnKsRgM8jCNmEIAQ4KD9fWr7chKLFi80eRUXi400oGjxYqlvXuRoB+CSCkE0IQoCPyMuT5s0zoejTTz0bNAYHSz17mlDUv7/Z/RqA6xGEbEIQAnzQ/v3SrFkmFH31lae9Rg1pwAAzdJaYaFaiAXAlgpBNCEKAj9uxwzPJOivL0167tjRokNnNumtXKdDxE4IAVCKCkE0IQkAVYVnSxo0mEKWmmk0cixStPLv3Xik2lpVngAsQhGxCEAKqoIICadUqs0fR3LnSjz96rl1/vQlE995rVqEB8EsEIZsQhIAqrmjl2cyZ0qJF0pkznmvt2pn5REOGSE2aOFcjANsRhGxCEAL8yIkTJgzNmCGtXClduOC5lpBgQtGgQSzHB/wAQcgmBCHATx05Ys48mzlTWrPG0x4cbFac3XuvWYFWq5ZzNQKoMIKQTQhCgAvk5JgJ1jNnllyOX7261K+fCUW9ekmhoc7VCKBcCEI2IQgBLvPttyYQzZghff+9pz0iwhwEO2wYB8ECVQBByCYEIcClLMv0DhUtx9+3z3OtQQMzwfree6WOHVmOD/gggpBNCEIAVFgopaebUDRnjnTsmOdas2ae5fht2jhXI4ASCEI2IQgBKOHcObPibOZMacEC6fRpz7UbbzSBaOhQ6Ve/cqpCACII2YYgBOCyTp2SFi82PUXLl0vnz3uuxcebUHTPPVJkpHM1Ai5FELIJQQhAmRw7Js2bZ0LRqlVmjpFkzji77TbTSzRwoDkDDYDXEYRsQhACUG779kkffSTNmiV98YWnPThY6tnTTLQeMEDivymA1xCEbEIQAnBFsrLMqrPUVGnLFk97aKjUp4/pKerTR6pRw7kaAT9EELIJQQiAbbZvN4Fo1iyzX1GRmjWl/v1NKOrZk40bARsQhGxCEAJgO8uSvv7aBKJZs6Tduz3XIiLMXKIhQ6Tbb5eqVXOsTKAqIwjZhCAEwKssy8wjmjXLzCvav99zrW5dcwjs0KHSLbewmzVQDgQhmxCEAFSawkJp7VoTiubMkX74wXMtKkoaPNiEok6d2M0a+AUEIZsQhAA44sIF6bPPTCiaN0/68UfPtaZNTSAaMkRq25ZQBFwCQcgmBCEAjsvPN7tZp6aa3axPnfJca9HCE4puuMGxEgFfQxCyCUEIgE85fVpautT0FC1ZIp0967n26197QtF11zlXI+ADCEI2IQgB8FknTkiLFplQtGJFySM+OnQwgWjwYKlJE+dqBBxCELIJQQhAlXDsmDR/vhk+++QTM/G6yC23mFB0991m0jXgAgQhmxCEAFQ5hw5Jc+eanqL0dE97QIDUtavpJbr7bg6DhV8jCNmEIASgStu7V5o92+xR9H//52kPDJS6dTOhaOBAqX5952oEvIAgZBOCEAC/sWeP2Z/oo49KHgYbGCjddpsJRXfdJdWr51yNgE0IQjYhCAHwS7t3e3qKvvzS0x4UZI72KApFdeo4ViJwJQhCNiEIAfB7WVmeUPTVV572oCCpe3cTipKSpNq1HSsRKC+CkE0IQgBc5d//9oSizZs97cHBUo8eJhQNGCBdc41jJQJlQRCyCUEIgGt9950nFH39tae9WjUpMdETiiIinKsRuAyCkE0IQgAgaccOTyj65htPe0iI1LOnCUX9+0v8dxI+giBkE4IQAPxEZqYJRamp0vbtnvbQUOnOO00o6tdPqlXLuRrhegQhmxCEAOBnbNtmeok++sj0GhUJDZV69zahqG9f6aqrnKsRrkQQsglBCADKwLLMkFlRKPruO8+1sDCpTx/pnnvM/yQUoRIQhGxCEAKAcrIsM7m6KBT9+9+ea2FhUq9e0qBBpqeI/67CSwhCNiEIAcAVsCyzDP+jj8y8op07PdeKJloPGmQmWl99tVNVwg8RhGxCEAIAmxT1FM2ZY0LRt996rlWrZvYpGjTILMln80ZcIYKQTQhCAOAFlmUmWs+ZY17btnmuBQebYz4GDTI7WnP2GSqAIGQTghAAVILt26W5c01P0cWbNwYGSrfeaiZa33WXFBnpWImoWghCNiEIAUAl++47E4rmzCl59llAgNS1q+kpGjhQatjQuRrh8whCNiEIAYCDsrI8PUUbN3raAwKkLl08oahJE+dqhE8iCNmEIAQAPmLPHk9P0YYNJa/dfLMJRXffLf3qV46UB99CELIJQQgAfNDevZ5QtG6dmXxdJC7OhKJBg6TrrnOuRjiKIGQTghAA+Lj9+6X5800oWrNGKiz0XGvXzhOKWrRwrkZUOoKQTQhCAFCFHDrkCUWffVYyFMXEmKGzgQOlX//azDOC3yII2YQgBABV1A8/SAsXmlD0ySfShQuea82bm0A0cKDUoYNZpg+/QhCyCUEIAPzAsWPS4sXSvHnSihVSfr7nWqNGnlB0yy1mQ0dUeQQhmxCEAMDPnDghLVtmQtGSJdLJk55rdeua3awHDjS7W4eGOlYmrgxByCYEIQDwY2fPSmlpJhQtXCgdP+65Fh4u9etnQlHPnlLNms7ViXIjCNmEIAQALnH+vFl1NneumXB98KDnWvXqUq9eJhT17StFRDhXJ8qEIGQTghAAuFBhofR//2dC0bx50u7dnmvVqkndu5tQNGAAh8L6KIKQTQhCAOByliVt3mwC0dy55oDYIoGBUkKCWZZ/111S48aOlYmSCEI2IQgBAErYvt0Mnc2dW/JQWEnq2NGzV1Hz5s7UB0kEIdsQhAAAl7V7twlF8+aVPurj17/2hKKYGDZwrGQEIZsQhAAAZXLggFl5Nm+e9OmnUkGB59p115ll+XfdZQ6IDQpyrEy3IAjZhCAEACi3n9vAsX59qX9/E4puv10KC3OuTj9GELIJQQgAcEVOnjRhaP586eOPpdxcz7WrrpJ69za9Rb17syzfRt76/nb8MJYJEyYoOjpaYWFhio2NVXp6+s/en5+fr3Hjxqlp06YKDQ3Vddddp6lTp1ZStQAA17vqKjNX6MMPzflnaWnSI49IDRuakPTRR9KwYWYZ/p13SpMmSfv3O101LsPRHqHU1FQNHz5cEyZMUJcuXfT222/r3XffVWZmpq699tpLvmfAgAE6dOiQXn75ZTVv3lyHDx/WhQsXFB8fX6bPpEcIAOAVhYXSpk2mp2jBgpLL8iWpUyczfJaUJLVs6USFVZpfDo116tRJ7du318SJE4vbWrduraSkJI0fP77U/cuXL9fQoUOVlZWl2rVrV+gzCUIAgErx7bcmEC1YYDZzvFirVp5QFBdn9i/Cz/K7obFz585p06ZNSkxMLNGemJio9evXX/I9ixYtUlxcnF599VU1atRILVq00JNPPqkzZ85c9nPy8/OVl5dX4gUAgNe1bCk9/bS0YYO0b580caI546xaNWnHDmn8eNNLdO210qOPmiG28+edrtp1HAtCR44cUUFBgSIjI0u0R0ZG6uDF58FcJCsrS2vXrtU333yj+fPn6+9//7vmzJmjRx999LKfM378eEVERBS/mjRpYuvvAQDAL2rYUEpOlpYvlw4flmbMkAYPNvON9u2TJkyQEhPNvKL775fmzDHzjeB1jvfFBfxkQyrLskq1FSksLFRAQIBSUlLUsWNH9e7dW6+//rref//9y/YKjR07Vrm5ucWvnJwc238HAADK7OqrpXvvlVJTzWTrJUukhx4yy/Bzc6WUFOmee6S6daV+/aQpU0x4glc4FoTq1q2roKCgUr0/hw8fLtVLVCQqKkqNGjVSxEXLEVu3bi3LsrR3795Lvic0NFTh4eElXgAA+ISwMLPMfvJks7Js7VrpiSekZs3MXkUff2xCUlSU1LWr9Prr0s6dTlftVxwLQiEhIYqNjVVaWlqJ9rS0tMuuAOvSpYv279+vkxd1F3733XcKDAxUYw7GAwBUZUFBUpcu0t/+Jv3739LWrdJLL0nt25sVaenpJiQ1by61aSM9+6yZhF1Y6HTlVZpPLJ+fNGmSOnfurHfeeUeTJ0/Wtm3b1LRpU40dO1b79u3TtGnTJEknT55U69atdfPNN+vFF1/UkSNH9NBDD6lbt26aPHlymT6TVWMAgCpnzx5z3MeCBdKaNSWP+4iMNENo/ftL3btL1as7VqY3+eXyeclsqPjqq6/qwIEDiomJ0RtvvKGuXbtKkkaOHKndu3dr1apVxffv2LFDf/jDH7Ru3TrVqVNHgwcP1ssvv6zqZXzwBCEAQJV2/Li0bJm0aJH5nxevhq5e3Uy6HjBA6tPHzDvyE34bhCobQQgA4DfOnZNWrza9RYsWSRcvCAoIkDp3NqGof3+zd1EVRhCyCUEIAOCXLEvassUTir76quT1Fi1MIOrfX4qPN3OSqhCCkE0IQgAAV8jJkRYvNqHo009LbtZYp47Ut68JRYmJZj8jH0cQsglBCADgOnl50ooVJhQtWWLmGRUJDZXuuMMMofXtazZ/9EE+G4Ty8/MVGhpqVz1eRxACALja+fPSunUmFC1cKGVllbzeoYNnXlFMjJlr5AN8JgitWLFCM2fOVHp6urKzs1VYWKgaNWqoffv2SkxM1IMPPqiGPpomJYIQAADFLEvKzPSEos8/L3k9OtozryghwZyT5hDHg9CCBQv09NNPKzc3V71791bHjh3VqFEjVa9eXceOHdM333yj9PR0bdiwQSNHjtR///d/q169erYVaheCEAAAl3HwoNnNeuFC6V//ks6e9VwLD5fuvNMMn/XqZY4AqUSOB6GOHTvqT3/6k/r06aPAwMtvSL1v3z794x//UGRkpJ544gnbCrULQQgAgDI4dcqEoYULzbyii887Cww0S/P79jWvNm28PoTmeBDyFwQhAADKqbBQ2rjR9BYtXmyW6V/sV7/yhKJbbzUTsG3mU0HozJkzl93J+cCBA4qKirriwryFIAQAwBXKyTG9RIsXS598Yg6ILVKzplmS36+fOVD2Mgepl5e3vr8rdOhqu3bt9NVPN2qSNGfOHN14441XXBQAAPBhTZpIyckmDB09aiZbP/ywFBVlhtTmz5f+4z+kBg2kTp2kl1+WNm82k7N9TIWCUI8ePRQfH6+//OUvsixLJ0+e1MiRI/XAAw/oueees7tGAADgq2rWNL0/77wj7dsnbdokvfCCFBdnrn/xhfSnP0nt2knXXiv97ncmQJ0542jZRSo8R2j58uV68MEH1bx5c+3fv1/h4eFKSUnRDTfcYHeNtmJoDACASrJ/v7R0qZlblJYmnT7tuVa9utS9u2du0S9sveNTc4QkqbCwUH/4wx80ceJEBQcHa/HixerZs6dthXkLQQgAAAecOSOtWuWZcH3xAbGS1L69CUT9+pn//Scr1H0qCO3cuVPDhg3TwYMH9e6772r16tX629/+plGjRul//ud/VM3BDZd+CUEIAACHWZa0dasnFH3+ecn5Qw0aSH36mFf37lKtWr4VhGrVqqU+ffpo0qRJuvrqqyVJ69ev14gRI1SrVi1lZGTYVqDdCEIAAPiYw4elZctMKFqxQjp50nMtJETq1k15d9yhiGee8Y0gNH36dA0fPrxU+4kTJzR69GhNmTLFluK8gSAEAIAPy8+X0tNNKFqyRNq5U5KUJylC8o0gVJURhAAAqCIsS/ruO2nJEuUtXKiINWuc20dow4YNZf6hp06d0rZt2ypUEAAAgCRzbEfLltKYMaaHyAvKHIRGjBihHj166KOPPtLJi8fuLpKZmalnn31WzZs3v+SGiwAAAL4kuKw3ZmZm6u2339Zzzz2n++67Ty1atFDDhg0VFham48ePa8eOHTp16pQGDhyotLQ0xcTEeLNuAACAK1ahOUJfffWV0tPTtXv3bp05c0Z169ZVu3btdNttt6l27dreqNM2zBECAKDq8db3d5l7hC7Wvn17tW/f3rYiAAAAnFChs8YmT56s77//3u5aAAAAKlWFgtBrr72mli1bqmHDhrr33nv19ttva8eOHXbXBgAA4FUVCkI7duzQ/v379dprrykiIkJvvPGG2rRpowYNGmjo0KF21wgAAOAVV7yh4qlTp7R27VrNmjVLH374oSzL0oULF+yqz3ZMlgYAoOrxqcnSy5Yt0+rVq7Vq1Spt2bJFbdq0UdeuXTV37lwlJCTYVhwAAIA3VSgI9enTR/Xq1dMTTzyhFStWKCIiwu66AAAAvK5Cc4Ref/11denSRX/961/VsmVLDRkyRBMnTtT27dvtrg8AAMBrrniO0NatW7V69Wp99tlnWrx4serUqaMDBw7YVZ/tmCMEAEDV41NzhIpkZGRo1apV+uyzz5Senq7CwkI1btzYrtoAAAC8qkJDY/3791ft2rXVoUMHpaSkqEWLFpo+fbqOHTumjRs32l0jAACAV1SoR6hFixb6z//8T3Xt2pXhJQAAUGWVKwgNGzZMSUlJeu655whAAACgyivX0FjLli31yiuvqH79+kpMTNRbb72lnJwcb9UGAADgVRVaNZaTk6PFixdr4cKFWr16tW644Qb1799fAwYMULt27bxRp21YNQYAQNXjre/vK14+f+LECS1btkwLFy7UsmXLVKtWLfXr10+/+93v1KZNG7vqtA1BCACAqsdb398VWjV2sVq1amnw4MFKSUnRDz/8oKlTpyooKEgbNmywoz4AAACvueIeoaqGHiEAAKoen9lQ8dtvv9XMmTOVnp6u3bt36/Tp06pXr57atWunxMREDRo0SKGhobYVCAAA4C1l7hHKyMjQH//4R6Wnpys+Pl4dO3ZUo0aNVL16dR07dkzffPON0tPTlZeXpz/+8Y8aPXq0TwYieoQAAKh6HO8RSkpK0lNPPaXU1FTVrl37svdt2LBBb7zxhl577TU9++yzthQJAADgDWXuETp37pxCQkLK/IPLe39loUcIAICqx/FVY2UNNadPny7X/QAAAE6p0PL5W2+9VXv37i3V/vnnn6tt27ZXWhMAAEClqFAQCg8P14033qhZs2ZJkgoLC/XCCy+oa9eu6t+/v60FAgAAeEuFTp9ftGiRJk2apIceekiLFi3S7t27lZ2drSVLlqh79+521wgAAOAVFQpCkpScnKw9e/bolVdeUXBwsFatWqX4+Hg7awMAAPCqCg2NHT9+XHfffbcmTpyot99+W4MHD1ZiYqImTJhgd30AAABeU6EeoZiYGEVHRysjI0PR0dF6+OGHlZqaqkceeURLlizRkiVL7K4TAADAdhXqEUpOTtaaNWsUHR1d3DZkyBBt2bJF586ds604AAAAb+LQVQAA4PMc31AxOzu7XD9437595S4GAACgMpU5CHXo0EEPP/ywvvjii8vek5ubq8mTJysmJkbz5s2zpUAAAABvKfNk6e3bt+vPf/6z7rzzTlWrVk1xcXFq2LChwsLCdPz4cWVmZmrbtm2Ki4vTX//6V/Xq1cubdQMAAFyxMs8R+vrrr9WmTRudP39ey5Yt05o1a7R7926dOXNGdevWVbt27dSzZ0/FxMR4u+YrwhwhAACqHm99f5c5CAUFBengwYOqV6+emjVrpo0bN6pOnTq2FVJZCEIAAFQ9jk+Wvvrqq5WVlSVJ2r17twoLC20rAgAAwAllniN09913q1u3boqKilJAQIDi4uIUFBR0yXuLAhMAAIAvK3MQeueddzRw4ED9+9//1qhRo/Twww+rVq1a3qwNAADAq8p1xMadd94pSdq0aZMee+wxghAAAKjSKnTW2HvvvWd3HQAAAJWuQmeNAQAA+APHg9CECRMUHR2tsLAwxcbGKj09vUzvW7dunYKDg9W2bVvvFggAAPyWo0EoNTVVo0eP1rhx45SRkaGEhAT16tXrF881y83N1YgRI3THHXdUUqUAAMAfOXr6fKdOndS+fXtNnDixuK1169ZKSkrS+PHjL/u+oUOH6vrrr1dQUJAWLFigzZs3l/kz2VARAICqx/ENFe127tw5bdq0SYmJiSXaExMTtX79+su+77333tPOnTv1/PPPl+lz8vPzlZeXV+IFAAAgORiEjhw5ooKCAkVGRpZoj4yM1MGDBy/5nu+//17PPPOMUlJSFBxctgVv48ePV0RERPGrSZMmV1w7AADwD45Plg4ICCjxZ8uySrVJUkFBgYYNG6YXX3xRLVq0KPPPHzt2rHJzc4tfOTk5V1wzAADwDxXaR8gOdevWLT7I9WKHDx8u1UskSSdOnNCXX36pjIwM/f73v5ckFRYWyrIsBQcHa+XKlbr99ttLvS80NFShoaHe+SUAAECV5liPUEhIiGJjY5WWllaiPS0tTfHx8aXuDw8P19atW7V58+biV3Jyslq2bKnNmzerU6dOlVU6AADwE471CEnSmDFjNHz4cMXFxalz58565513lJ2dreTkZElmWGvfvn2aNm2aAgMDFRMTU+L99evXV1hYWKl2AACAsnA0CA0ZMkRHjx7VSy+9pAMHDigmJkZLly5V06ZNJUkHDhz4xT2FAAAAKsrRfYScwD5CAABUPX63jxAAAIDTCEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1CEIAAMC1HA9CEyZMUHR0tMLCwhQbG6v09PTL3jtv3jz16NFD9erVU3h4uDp37qwVK1ZUYrUAAMCfOBqEUlNTNXr0aI0bN04ZGRlKSEhQr169lJ2dfcn716xZox49emjp0qXatGmTbrvtNvXr108ZGRmVXDkAAPAHAZZlWU59eKdOndS+fXtNnDixuK1169ZKSkrS+PHjy/Qz2rRpoyFDhui5554r0/15eXmKiIhQbm6uwsPDK1Q3AACoXN76/nasR+jcuXPatGmTEhMTS7QnJiZq/fr1ZfoZhYWFOnHihGrXrn3Ze/Lz85WXl1fiBQAAIDkYhI4cOaKCggJFRkaWaI+MjNTBgwfL9DNee+01nTp1SoMHD77sPePHj1dERETxq0mTJldUNwAA8B+OT5YOCAgo8WfLskq1XcrMmTP1wgsvKDU1VfXr17/sfWPHjlVubm7xKycn54prBgAA/iHYqQ+uW7eugoKCSvX+HD58uFQv0U+lpqbqN7/5jWbPnq3u3bv/7L2hoaEKDQ294noBAID/caxHKCQkRLGxsUpLSyvRnpaWpvj4+Mu+b+bMmRo5cqRmzJihPn36eLtMAADgxxzrEZKkMWPGaPjw4YqLi1Pnzp31zjvvKDs7W8nJyZLMsNa+ffs0bdo0SSYEjRgxQv/4xz908803F/cmVa9eXREREY79HgAAoGpyNAgNGTJER48e1UsvvaQDBw4oJiZGS5cuVdOmTSVJBw4cKLGn0Ntvv60LFy7o0Ucf1aOPPlrc/sADD+j999+v7PIBAEAV5+g+Qk5gHyEAAKoev9tHCAAAwGkEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FqOB6EJEyYoOjpaYWFhio2NVXp6+s/ev3r1asXGxiosLEzNmjXTpEmTKqlSAADgbxwNQqmpqRo9erTGjRunjIwMJSQkqFevXsrOzr7k/bt27VLv3r2VkJCgjIwMPfvssxo1apTmzp1byZUDAAB/EGBZluXUh3fq1Ent27fXxIkTi9tat26tpKQkjR8/vtT9Tz/9tBYtWqTt27cXtyUnJ2vLli3asGFDmT4zLy9PERERys3NVXh4+JX/EgAAwOu89f0dbNtPKqdz585p06ZNeuaZZ0q0JyYmav369Zd8z4YNG5SYmFiirWfPnpoyZYrOnz+vatWqlXpPfn6+8vPzi/+cm5sryfyFAgCAqqHoe9vu/hvHgtCRI0dUUFCgyMjIEu2RkZE6ePDgJd9z8ODBS95/4cIFHTlyRFFRUaXeM378eL344oul2ps0aXIF1QMAACccPXpUERERtv08x4JQkYCAgBJ/tiyrVNsv3X+p9iJjx47VmDFjiv/8448/qmnTpsrOzrb1LxIVk5eXpyZNmignJ4ehSofxLHwHz8J38Cx8R25urq699lrVrl3b1p/rWBCqW7eugoKCSvX+HD58uFSvT5EGDRpc8v7g4GDVqVPnku8JDQ1VaGhoqfaIiAj+j9qHhIeH8zx8BM/Cd/AsfAfPwncEBtq7zsuxVWMhISGKjY1VWlpaifa0tDTFx8df8j2dO3cudf/KlSsVFxd3yflBAAAAP8fR5fNjxozRu+++q6lTp2r79u16/PHHlZ2dreTkZElmWGvEiBHF9ycnJ2vPnj0aM2aMtm/frqlTp2rKlCl68sknnfoVAABAFeboHKEhQ4bo6NGjeumll3TgwAHFxMRo6dKlatq0qSTpwIEDJfYUio6O1tKlS/X444/rrbfeUsOGDfXPf/5Td999d5k/MzQ0VM8///wlh8tQ+XgevoNn4Tt4Fr6DZ+E7vPUsHN1HCAAAwEmOH7EBAADgFIIQAABwLYIQAABwLYIQAABwLb8MQhMmTFB0dLTCwsIUGxur9PT0n71/9erVio2NVVhYmJo1a6ZJkyZVUqX+rzzPYt68eerRo4fq1aun8PBwde7cWStWrKjEav1fef9tFFm3bp2Cg4PVtm1b7xboIuV9Fvn5+Ro3bpyaNm2q0NBQXXfddZo6dWolVevfyvssUlJSdNNNN6lGjRqKiorSgw8+qKNHj1ZStf5rzZo16tevnxo2bKiAgAAtWLDgF99jy/e35WdmzZplVatWzZo8ebKVmZlpPfbYY1bNmjWtPXv2XPL+rKwsq0aNGtZjjz1mZWZmWpMnT7aqVatmzZkzp5Ir9z/lfRaPPfaY9corr1hffPGF9d1331ljx461qlWrZn311VeVXLl/Ku/zKPLjjz9azZo1sxITE62bbrqpcor1cxV5Fv3797c6depkpaWlWbt27bI+//xza926dZVYtX8q77NIT0+3AgMDrX/84x9WVlaWlZ6ebrVp08ZKSkqq5Mr9z9KlS61x48ZZc+fOtSRZ8+fP/9n77fr+9rsg1LFjRys5OblEW6tWraxnnnnmkvf/8Y9/tFq1alWi7be//a118803e61Gtyjvs7iUG264wXrxxRftLs2VKvo8hgwZYv3Xf/2X9fzzzxOEbFLeZ7Fs2TIrIiLCOnr0aGWU5yrlfRZ//etfrWbNmpVo++c//2k1btzYazW6UVmCkF3f3341NHbu3Dlt2rRJiYmJJdoTExO1fv36S75nw4YNpe7v2bOnvvzyS50/f95rtfq7ijyLnyosLNSJEydsP2DPjSr6PN577z3t3LlTzz//vLdLdI2KPItFixYpLi5Or776qho1aqQWLVroySef1JkzZyqjZL9VkWcRHx+vvXv3aunSpbIsS4cOHdKcOXPUp0+fyigZF7Hr+9vx0+ftdOTIERUUFJQ6tDUyMrLUYa1FDh48eMn7L1y4oCNHjigqKspr9fqzijyLn3rttdd06tQpDR482BslukpFnsf333+vZ555Runp6QoO9qv/VDiqIs8iKytLa9euVVhYmObPn68jR47okUce0bFjx5gndAUq8izi4+OVkpKiIUOG6OzZs7pw4YL69++vN998szJKxkXs+v72qx6hIgEBASX+bFlWqbZfuv9S7Si/8j6LIjNnztQLL7yg1NRU1a9f31vluU5Zn0dBQYGGDRumF198US1atKis8lylPP82CgsLFRAQoJSUFHXs2FG9e/fW66+/rvfff59eIRuU51lkZmZq1KhReu6557Rp0yYtX75cu3btKj4jE5XLju9vv/p/8+rWraugoKBSSf7w4cOlUmORBg0aXPL+4OBg1alTx2u1+ruKPIsiqamp+s1vfqPZs2ere/fu3izTNcr7PE6cOKEvv/xSGRkZ+v3vfy/JfBlblqXg4GCtXLlSt99+e6XU7m8q8m8jKipKjRo1UkRERHFb69atZVmW9u7dq+uvv96rNfurijyL8ePHq0uXLnrqqackSTfeeKNq1qyphIQEvfzyy4wiVCK7vr/9qkcoJCREsbGxSktLK9Gelpam+Pj4S76nc+fOpe5fuXKl4uLiVK1aNa/V6u8q8iwk0xM0cuRIzZgxgzF3G5X3eYSHh2vr1q3avHlz8Ss5OVktW7bU5s2b1alTp8oq3e9U5N9Gly5dtH//fp08ebK47bvvvlNgYKAaN27s1Xr9WUWexenTpxUYWPKrMygoSJKnNwKVw7bv73JNra4CipZCTpkyxcrMzLRGjx5t1axZ09q9e7dlWZb1zDPPWMOHDy++v2j53eOPP25lZmZaU6ZMYfm8Tcr7LGbMmGEFBwdbb731lnXgwIHi148//ujUr+BXyvs8fopVY/Yp77M4ceKE1bhxY2vQoEHWtm3brNWrV1vXX3+99dBDDzn1K/iN8j6L9957zwoODrYmTJhg7dy501q7dq0VFxdndezY0alfwW+cOHHCysjIsDIyMixJ1uuvv25lZGQUb2Xgre9vvwtClmVZb731ltW0aVMrJCTEat++vbV69eriaw888IDVrVu3EvevWrXKateunRUSEmL96le/siZOnFjJFfuv8jyLbt26WZJKvR544IHKL9xPlfffxsUIQvYq77PYvn271b17d6t69epW48aNrTFjxlinT5+u5Kr9U3mfxT//+U/rhhtusKpXr25FRUVZ9913n7V3795Krtr/fPbZZz/7HeCt7+8Ay6IvDwAAuJNfzRECAAAoD4IQAABwLYIQAABwLYIQAABwLYIQAABwLYIQAABwLYIQAABwLYIQAABwLYIQAABwLYIQAABwLYIQgCrvhx9+UIMGDfTnP/+5uO3zzz9XSEiIVq5c6WBlAHwdZ40B8AtLly5VUlKS1q9fr1atWqldu3bq06eP/v73vztdGgAfRhAC4DceffRR/etf/1KHDh20ZcsWbdy4UWFhYU6XBcCHEYQA+I0zZ84oJiZGOTk5+vLLL3XjjTc6XRIAH8ccIQB+IysrS/v371dhYaH27NnjdDkAqgB6hAD4hXPnzqljx45q27atWrVqpddff11bt25VZGSk06UB8GEEIQB+4amnntKcOXO0ZcsWXXXVVbrttttUq1Ytffzxx06XBsCHMTQGoMpbtWqV/v73v2v69OkKDw9XYGCgpk+frrVr12rixIlOlwfAh9EjBAAAXIseIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4FoEIQAA4Fr/D20yNDsgkzlpAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def rsqrt_sample():\n", " eta = np.random.rand()\n", " return eta * eta\n", "\n", "def rsqrt_w(x):\n", " return 1. / (2. * np.sqrt(x))\n", "\n", "xplot = np.linspace(0.01,1, 400)\n", "yplot = [f(x) / rsqrt_w(x) for x in xplot]\n", "\n", "plt.xlim(0,1)\n", "plt.ylim(0,1)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"f(x)/w(x)\")\n", "plt.plot(xplot, yplot,color='r')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that $f(x)/w(x)$ has much smaller variation than $f(x)$ over $(0,1)$.\n", "In general, the smoother one can make $f(x)/w(x)$, the smaller statistical error of the calculation would be.\n", "\n", "Let us calculate the integral with using importance sampling with the same number of samples." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "I = 0.838925024000155 +- 0.00014086883299036244\n", "CPU times: user 2 s, sys: 26.2 ms, total: 2.02 s\n", "Wall time: 2.03 s\n" ] } ], "source": [ "%%time\n", "\n", "N = 1000000\n", "I, err = intMC_weighted(f, N, rsqrt_w, rsqrt_sample)\n", "print(\"I = \",I,\" +- \",err)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the statistical error is more than x10 smaller than the direct method.\n", "We would need more than x100 samples in the direct method to reach the same accuracy as importance sampling in this case." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }