{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Applications of Linear Systems and Matrix Algebra\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The need to solve linear systems arises in a wide variety of fields. We show in this section an example of the linear system that arises in fitting a curve to a data set. We also discuss the application of matrix algebra to cryptography and graph theory." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interpolation\n", "\n", "Interpolation is the process of estimating unknown data values that fall between known values. This process commonly involves fitting a curve through the known set of data points in order to make predictions about the unknown values. The curve is described by a set of parameters, and \"fitting the curve\" means choosing the parameters such that the curve best represents the data. A simple way to fit a curve is to require that it passes through all the data provided. \n", "\n", "Let's look at the the data points $(2,8)$, $(5,12)$, $(6,14)$, and $(15,15)$ as an example." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import laguide as lag\n", "\n", "x = np.array([2,5,6,15])\n", "y = np.array([8,12,14,15])\n", "\n", "fig,ax = plt.subplots()\n", "ax.scatter(x,y,color='red');\n", "\n", "ax.set_xlim(0,20);\n", "ax.set_ylim(0,20);\n", "ax.set_xlabel('x');\n", "ax.set_ylabel('y');\n", "ax.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Polynomials are a common curve used for interpolation. In this case, since we have four data points there will be four equations that must be satisfied for the graph to pass through each point. We will choose a third degree polynomial, $P_3$, since that will give us four parameters with which to satisfy the equations.\n", "\n", "$$\n", "\\begin{equation}\n", "P_3(x) = a_0 + a_1x + a_2x^2 + a_3x^3\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data gives us the four equations $P_3(2) = 8$, $P_3(5) = 12$, $P_3(6) = 14$, and $P_3(15) = 15$. This set of equations is a linear system for the unknown coefficients.\n", "\n", "\n", "$$\n", "\\begin{eqnarray*}\n", "a_0 + 2a_1 + 2^2a_2 + 2^3a_3 & = & 8\\\\\n", "a_0 + 5a_1 + 5^2a_2 + 5^3a_3 & = & 12\\\\\n", "a_0 + 6a_1 + 6^2a_2 + 6^3a_3 & = & 14\\\\\n", "a_0 + 15a_1 + 15^2a_2 + 15^3a_3 & = & 15\n", "\\end{eqnarray*}\n", "$$\n", "\n", "We assemble the matrix $A$ and right-hand side vector $B$ as NumPy arrays." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1.000e+00 2.000e+00 4.000e+00 8.000e+00]\n", " [1.000e+00 5.000e+00 2.500e+01 1.250e+02]\n", " [1.000e+00 6.000e+00 3.600e+01 2.160e+02]\n", " [1.000e+00 1.500e+01 2.250e+02 3.375e+03]] \n", "\n", "[[ 8.]\n", " [12.]\n", " [14.]\n", " [15.]]\n" ] } ], "source": [ "A = np.zeros((4,4))\n", "B = np.zeros((4,1))\n", "\n", "for i in range(4):\n", " B[i,0] = y[i]\n", " for j in range(4):\n", " A[i,j] = x[i]**(j)\n", " \n", "print(A,'\\n')\n", "print(B)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can solve the system $AX=B$ with elimination. To avoid confusion with the $x$ variable, we will label our solution $\\texttt{coeffs}$ since they represent the coefficients of the polynomial." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 8.64102564]\n", " [-1.25555556]\n", " [ 0.52222222]\n", " [-0.02735043]]\n" ] } ], "source": [ "coeffs = lag.SolveSystem(A,B)\n", "print(coeffs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we plot the graph of the polynomial over the data to see the fit. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_fit = np.linspace(x[0],x[3],50)\n", "y_fit = coeffs[0] + coeffs[1]*x_fit + coeffs[2]*x_fit**2 + coeffs[3]*x_fit**3\n", "\n", "fig,ax = plt.subplots()\n", "\n", "ax.scatter(x,y,color='red');\n", "ax.plot(x_fit,y_fit,'b');\n", "ax.set_xlim(0,20);\n", "ax.set_ylim(0,30);\n", "ax.set_xlabel('x');\n", "ax.set_ylabel('y');\n", "ax.grid(True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the curve that we produce does indeed pass through each of the data points, this polynomial may not be the best model of the underlying process. One potential concern is that the curve does not seem to connect the third and fourth data point in a direct way, but rather exhibits an oscillation. When constructing a curve to fit a set of data points, there are other factors that may be more important than simply requiring that the curve passes through each point. In a later chapter we will revisit the problem and consider the idea of finding a curve that \"fits\" the data without actually passing through each point. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise 1:** In 2017, researchers from the Universities of British Columbia, Alberta, and Toronto published their findings regarding the population of snowshoe hares around Kluane Lake, Yukon. They measured the density of hares per hectare, taking a reading once every two years. Here are some of their measurements:\n", "\n", "| Measurement # | Density per ha. |\n", "| ---------------- | --------------- |\n", "| 1 | 0.26 |\n", "| 2 | 0.20 |\n", "| 3 | 1.17 |\n", "| 4 | 2.65 |\n", "| 5 | 0.14 |\n", "| 6 | 0.42 |\n", "| 7 | 1.65 |\n", "| 8 | 2.73 |\n", "| 9 | 0.09 |\n", "| 10 | 0.21 |\n", "\n", "$(a)$ Find the unique ninth degree polynomial whose graph passes through each of these points. Plot the data points together with the graph of the polynomial to observe the fit.\n", " \n", "$(b)$ Using the polynomial that we found, what should we expect the density of hares to be if we measured their population in the year between the third and fourth measurement? What about between the fourth and the fifth?\n", " \n", "$(c)$ Why might this method of interpolation not be an appropriate model of our data over time?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "## Code solution here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise 2:** The further you travel out into the solar system and away from the Sun, the slower an object must be travelling to remain in its orbit. Here are the average radii of the orbits of the planets in our solar system, and their average orbital velocity around the Sun.\n", "\n", "|Planet | Distance from Sun (million km) | Orbital Velocity (km/s) |\n", "| ------------------------------- | ------------------------------- | ------------------------------- |\n", "|Mercury | 57.9 | 47.4 |\n", "|Venus | 108.2 | 35.0 | \n", "|Earth | 149.6 | 29.8 |\n", "|Mars | 228.0 | 24.1 |\n", "|Jupiter | 778.5 | 13.1 |\n", "|Saturn | 1432.0 | 9.7 |\n", "|Uranus | 2867.0 | 6.8 |\n", "|Neptune | 4515.0 | 5.4 |\n", "\n", "$(a)$ Find the unique first degree polynomial whose graph passes through points defined by Mercury and Jupiter. Plot the data points together with the graph of the polynomial to observe the fit. Amend your polynomial and graph by adding Saturn, and then Earth. What do you notice as you add more points? What if you had started with different planets?\n", " \n", "$(b)$ Expand your work in part $(a)$ to a seventh degree poynomial that passes through all eight planets. The first object in the Kuiper Belt, Ceres, was discovered by Giuseppe Piazzi in 1801. Ceres has an average distance from the sun of 413.5 million km. Based on the points on the graph, estimate the orbital velocity of Ceres. What does the polynomial suggest the value would be?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "## Code solution here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cryptography\n", "\n", "One of the primary goals of cryptography is to secure communications by encoding messages. The encoded message is difficult to read by anyone except for the intended recipient, who possesses some secret knowledge that allows them to reverse the process and decode the message. The original message is known as _plaintext_, and the encoded message is known as _ciphertext_. We demonstrate here the well-known Hill Cipher, which is a method of transforming plaintext to ciphertext using familiar matrix multiplication.\n", "\n", "#### Encryption\n", "\n", "Let's assume that the plaintext and ciphertext will be made up of characters from the same predefined _alphabet_. This alphabet can contain letters, numbers, punctuation, and any number of other symbols that might be appropriate. We also need a square invertible matrix $B$, called the encryption matrix. Given these parameters, we take the following steps to get from plaintext to ciphertext.\n", "\n", "1. Translate the plaintext from alphabet characters into a list of numbers.\n", "2. Divide the list of numbers into a collection of $N\\times 1$ vectors. Use these numbers as columns in a plaintext array $P$.\n", "3. Apply the cipher by multiplying each vector by the matrix $B$. This produces a ciphertext array $C=BP$.\n", "4. Translate the columns of $C$ back into a string of alphabet characters.\n", "\n", "In order to get started, we first need a way to transform a message that includes letters, numbers, and possibly other characters, into to a message that consists of only numbers. The easiest thing to do is to substitute each possible character in the message for a number. For example we might let A=1, B=2, C=3, and so on. In order to make this process less obvious, we might scramble the order of the numbers (A=23, B=5, C=12, ...), or substitute single numbers for common groups of letters (TH=32, EE=20, ING=17, ...). However we choose to convert our message from text to numbers, there will still be patterns that remain among the numbers due to the natural patterns of the underlying language. \n", "\n", "For the purpose of this demonstration, we will make use of a list named $\\texttt{alphabet}$ to convert between letters and numbers. This list is included in the $\\texttt{hillcipher}$ module, which contains some other functions that we will need. If we print the list, we can see that it contains a space, a period, a question mark, and all uppercase letters. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[' ', '.', '?', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z']\n" ] } ], "source": [ "import hillcipher as hc\n", "print(hc.alphabet)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To find which character goes with which number, we can use the number as an index to the list as usual." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The character ? is associated with the number 2 .\n" ] } ], "source": [ "num = 2\n", "char = hc.alphabet[num]\n", "print(\"The character\",char,\"is associated with the number\",num,\".\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To find which number is associated with each letter, we need to look up the index for that letter. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The number 20 is associated with the character R .\n" ] } ], "source": [ "char = 'R'\n", "num = hc.alphabet.index(char)\n", "print(\"The number\",num,\"is associated with the character\",char,\".\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the code in the first cell will produce an error if we choose an index that is larger than 28, and the code in the second cell will produce an error if we choose a letter that is not in $\\texttt{alphabet}$. \n", "\n", "To complete this step of the encryption, we write a loop that builds a list of numbers corresponding to each letter in a message and define a NumPy array based on that list." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[25 7 0 6 17 16 22 0 10 3 24 7 0 16 23 15 4 7 20 21 0 11 16 0\n", " 17 23 20 0 3 14 18 10 3 4 7 22 1 0 0 25 7 0 10 3 24 7 0 22\n", " 17 0 21 18 7 14 14 0 22 25 17 1]\n" ] } ], "source": [ "plaintext = \"WE DONT HAVE NUMBERS IN OUR ALPHABET. WE HAVE TO SPELL TWO.\"\n", "number_message = []\n", " \n", "for char in plaintext:\n", " number_message.append(hc.alphabet.index(char))\n", " \n", "array_message = np.array(number_message)\n", "print(array_message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next step is to arrange our numerical message into the plaintext array $P$ which must have dimensions compatible with our encryption matrix $B$. We will choose $B$ to be a $4\\times 4$ matrix for this example.\n", "\n", "$$\n", "B = \\left[ \\begin{array}{rrrr} 1 & 0 & -2 & -1 \\\\ 3 & -1 & -3 & 2 \\\\ 2 & 0 & -4 & 4 \\\\ 2 & 1 & -1 & -1 \\end{array}\\right]\n", "$$\n", "\n", "We now take the plaintext message and break it into chunks which contain 4 numbers each. (*Note that if the number of characters in our message is not divisible by 4, we can add extra characters at the end.*) Each chunk will form a column of $P$, and we will have as many columns as needed to accommodate the entire message. We make use of the $\\texttt{reshape}$ and $\\texttt{transpose}$ methods to manipulate the entries in the array." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[25 17 10 0 4 0 17 3 3 1 7 24 17 7 22]\n", " [ 7 16 3 16 7 11 23 14 4 0 0 7 0 14 25]\n", " [ 0 22 24 23 20 16 20 18 7 0 10 0 21 14 17]\n", " [ 6 0 7 15 21 0 0 10 22 25 3 22 18 0 1]]\n" ] } ], "source": [ "# Find the number of chucks needed.\n", "chunks = int(len(number_message)/4)\n", "P = array_message.reshape((chunks,4))\n", "P = P.transpose()\n", "print(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next step is one multiplication multiplication. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 19 -27 -45 -61 -57 -32 -23 -43 -33 -24 -16 2 -43 -21 -13]\n", " [ 80 -31 -31 -55 -13 -59 -32 -39 28 53 -3 109 24 -35 -8]\n", " [ 74 -54 -48 -32 12 -64 -46 -26 66 102 -14 136 22 -42 -20]\n", " [ 51 28 -8 -22 -26 -5 37 -8 -19 -23 1 33 -5 14 51]]\n" ] } ], "source": [ "B = np.array([[1,0,-2,-1],[3,-1,-3,2],[2,0,-4,4],[2,1,-1,-1]])\n", "C = B@P\n", "print(C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final task is to translate the numbers in $C$ back to characters of the alphabet. This step requires a bit more thought since most of the numbers in $C$ are outside the index range of the alphabet (0-28). We can let these numbers be associated with letters by letting the count wrap around at 29. That is, 29 is associated with the same character as 0, 30 is associated with the same character as 1, and so forth. We can also let -1 be associated with the same character as 28, -2 be associated with the same character as 27, and so forth to address negative numbers. This concept is known as *congruence* in *modular arithmetic* and is performed using the $\\texttt{%}$ operator in Python. Try it out! " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "22\n" ] } ], "source": [ "print(80%29)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With that detail in place, we can step through the elements of $C$ and generate the final encrypted message from the characters in our alphabet. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "QTNT?YBZKYHSXAXE.NJAXZUVDXJFMQASWZFHCVMDKXM.?TRBMVTVFUNLNSGT\n" ] } ], "source": [ "# We begin with an empty string and add one character for each entry in C\n", "encrypted_message = ''\n", "\n", "for j in range(C.shape[1]): # For each column j ...\n", " for i in range(C.shape[0]): # ... we step through each row i and add a letter for that entry\n", " encrypted_message = encrypted_message + hc.alphabet[C[i,j]%29]\n", " \n", "print(encrypted_message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that this last step of the process cannot be reversed. It is not possible to start with the encrypted message and determine the ciphertext array $C$. Indeed, there are an infinite number of matrices that could have generated this same encrypted message since any of the entries can be have a multiple of 29 added to it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Decryption" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the encryption matrix $B$ is known, we might hope to multiply by the inverse matrix to determine the plaintext array $P = B^{-1}C$. As we just noted however, we cannot reconstruct $C$ from the encrypted message. To overcome this difficulty, we need to find the *modular inverse* of the matrix $B$. That is, we need a matrix $B^{-1}$ such that the entries of $B^{-1}B$ are congruent to the entries of $I$ in the modular arithmetic. (*Note that we use the same symbol for the modular inverse as we do for the usual inverse matrix.*)\n", "\n", "The method for finding the modular inverse is beyond our scope, but we will make use of the $\\texttt{ModularInverseMatrix}$ function in the $\\texttt{hillcipher}$ module to calculate $B^{-1}$ for the purpose of demonstration." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-300 300 -150 300]\n", " [-150 -450 300 450]\n", " [-450 150 -150 150]\n", " [-300 0 150 0]] \n", "\n", "[[900 0 0 0]\n", " [ 0 900 0 0]\n", " [ 0 0 900 0]\n", " [ 0 0 0 900]] \n", "\n", "[[1 0 0 0]\n", " [0 1 0 0]\n", " [0 0 1 0]\n", " [0 0 0 1]]\n" ] } ], "source": [ "B_inv = hc.ModularInverseMatrix(B)\n", "print(B_inv,'\\n')\n", "print(B_inv@B,'\\n')\n", "print((B_inv@B)%29)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is important to observe here is that $B^{-1}B$ is not exactly $I$, but is congruent to $I$ if we work out the equivalent number between 0 and 28 for each entry. To proceed with the decryption, we assemble the encrypted message into an array (we call it $\\texttt{decryptionC}$ to avoid confusion) and multiply by $B^{-1}$. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[19 2 13 26 1 26 6 15 25 5 13 2 15 8 16]\n", " [22 27 27 3 16 28 26 19 28 24 26 22 24 23 21]\n", " [16 4 10 26 12 23 12 3 8 15 15 20 22 16 9]\n", " [22 28 21 7 3 24 8 21 10 6 1 4 24 14 22]]\n", "\n", "\n", "[[ 5100 15300 9000 -8700 3600 4350 6600 7050 2700 5250\n", " 1950 4200 6600 6300 6750]\n", " [ 1950 1350 -1650 5700 -2400 1200 -5400 -450 -9450 -4350\n", " -8700 -2400 4350 -450 750]\n", " [ -4350 6750 -150 -14100 600 -7350 600 -1200 -6750 0\n", " -4050 0 -2850 -450 -2100]\n", " [ -3300 0 -2400 -3900 1500 -4350 0 -4050 -6300 750\n", " -1650 2400 -1200 0 -3450]]\n" ] } ], "source": [ "number_of_columns = int(len(encrypted_message)/4)\n", "decryptionC = np.zeros((4,number_of_columns),dtype='int')\n", "\n", "# For each column, we step down the column and fill in with the characters of the encrypted messsage.\n", "\n", "k = 0\n", "for j in range(number_of_columns): \n", " for i in range(4):\n", " decryptionC[i,j] = hc.alphabet.index(encrypted_message[k])\n", " k += 1\n", "\n", "decryptionP = B_inv@decryptionC\n", " \n", "print(decryptionC)\n", "print('\\n')\n", "print(decryptionP)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, multiplication by $B^{-1}$ produces numbers that are outside of the range 0-28, so again we apply modular congruence before translating the numbers back into characters in the alphabet." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WE DONT HAVE NUMBERS IN OUR ALPHABET. WE HAVE TO SPELL TWO.\n" ] } ], "source": [ "decrypted_message = ''\n", "for j in range(number_of_columns):\n", " for i in range(4):\n", " decrypted_message = decrypted_message + hc.alphabet[decryptionP[i,j]%29]\n", "\n", "print(decrypted_message)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercises\n", "\n", "The $\\texttt{hillcipher}$ module contains two functions that carry out the same steps we have demonstrated here to encrypt/decrypt a message using the included alphabet. The following cell shows how they are called." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "! is not included in the current alphabet.\n", "ARQVI.?KSJZUZTFJ?W.AYTWXJR?Y.XZPOWRYLUIB\n", "WATER IN SHORT SUPPLY. SEND HELP SOONM?\n" ] } ], "source": [ "msg = \"Water in short supply. Send help soon!\"\n", "en_msg = hc.HillCipherEncryption(msg,B)\n", "print(en_msg)\n", "\n", "de_msg = hc.HillCipherDecryption(en_msg,B)\n", "print(de_msg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that these functions do some error checking of the original message to be sure that all letters are in uppercase, and no characters outside the alphabet are included in the message that gets encrypted.\n", "\n", "**Exercise 1:** Create your own encryption matrix and apply the steps above to encrypt a message of your choosing. Check the results with those produced by $\\texttt{HillCipherEncryption}$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "## Code solution here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise 2:** Create your own alphabet list to translate messages into numbers." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "## Code solution here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Graph Theory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A **directed graph** is defined as a set of nodes together with ordered pairs of nodes which define directed edges. For example, a graph might consist of nodes labeled 0, 1, 2, and 3, and edges (0,1), (1,3), (2,0), (2,1), and (3,1). The graph can be visualized using points for the nodes and arrows for the edges.\n", "\n", "![title](img/Graph_example.png)\n", "\n", "Graphs may be used to represent many types of information. The nodes might represent hubs in a transportation network (such as airports), and the edges the possible routes (flights) available in the network. The nodes could also represent players in a tournament, with the edges representing results of individual competitions between the players. The nodes might also represent units of interconnected computer code, with the edges indicating how each unit depends on the others.\n", "\n", "A graph can be described using an **adjacency matrix** $A$. The entries $a_{ij}$ of the matrix are 1 if there is an edge from node $i$ to node $j$ and 0 otherwise. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 0 0]\n", " [0 0 0 1]\n", " [1 1 0 0]\n", " [0 1 0 0]]\n" ] } ], "source": [ "A = np.array([[0,1,0,0],[0,0,0,1],[1,1,0,0],[0,1,0,0]])\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the visualizations we use functions included in the $\\texttt{laguide}$ module. These functions make use of $\\texttt{matplotlib}$ and a module called $\\texttt{networkx}$. The first function we will use is called $\\texttt{DrawGraph}$, which requires an adjacency matrix in the form of a NumPy array. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "node_positions = lag.DrawGraph(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function produces a visualization with $\\texttt{matplotlib}$, and then returns a Python object containing the positions of the nodes used in making the picture. Notice that the nodes in this picture are in a different arrangement than in the first picture. Both pictures represent the same graph so long as edges connect the nodes in the same way. When we call the function $\\texttt{DrawGraph}$, it will generate suitable positions for the nodes *unless we supply it with pre-defined positions.* We only need to use supply node positions if we want to replicate previous node positions, or if we draw additional features on a graph under consideration.\n", "\n", "We demonstrate here with two examples. If we use $\\texttt{DrawGraph}$ this way\n", "```\n", "old_node_positions = lag.DrawGraph(A,node_positions)\n", "```\n", "we will get an exact copy of the previous picture, and $\\texttt{old_node_positions}$ will be a copy of $\\texttt{node_positions}$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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sbt26hcmTJ6NTp0546qmnEB8fL4vbdomiiNOnT2PYsGFo06YNcnNzcfz4cYSFhSEwMJClZ2V4jY+ITO7evXtYsGABfvjhB4waNQpXrlxBvXr1pI4FrVaLrVu3YtGiRcjOzsbkyZOxbNkyuLq6Sh2NTIjFR0Qmo9PpsGzZMsyZMwcvv/wyzp8/jyeffFLqWEhPT8fSpUuxbNkytG3bFv/+978RGBgIlUoldTQyAxYfERmdIAjYsmULZs2aBT8/P4SHh+PZZ5+VPNPRo0exatUqhIWFYdiwYThy5Ahat24taS4yPxYfERnViRMnMHXqVNjZ2WHlypV46aWXJM2TkJCAtWvX4qeffkKdOnUwZswYLF68GG5ubpLmIumw+IjIKNLS0vDxxx8jMjIS8+fPx+uvvy7Z1oTCwkJs27YNq1evxm+//YYRI0Zgx44d3GxOAFh8RPSY9Ho9Fi5ciHnz5mH8+PG4cuUKatWqZfYc91dmrlmzBqGhoejSpQsmTJiA/v378/w7KoPFR0Slrl+/jmXLluHbb7+t0mgtIiICkydPho+PD06dOgU/Pz8zpCwrLS0NP//8M9auXQtBEDB27FhcvnwZjRo1MnsWsgwsPiIC8OeIaezYsTh16hTatGmD0aNHV/rc5ORkTJ8+HefOncP333+P/v37m3VaU6vVYs+ePVizZg1OnTqFIUOGYNWqVXjhhRdkc+cXki/uyiQiAMDevXtx8eJFCIKAyZMnIz09vdxztFotvvrqK7Rr1w6tW7dGXFwcBgwYYJayEUURFy9exJQpU+Dl5YXFixcjODgYKSkpWLlyJbp27crSoyrhiI+IoNVq8e6776KgoADAn/epHD16NMLDw0vLJDw8HFOmTEGrVq0QHR2Npk2bmjyXKIq4fPkyQkJCEBISgsLCQowePRpnz541y+eTdWLxEREWLFiAu3fvlv57SUkJTp48iZCQEHTs2BHTpk1DbGwsFi5ciN69e5s0iyiK+PXXXxESEoLQ0FAUFRVh6NChWLNmDZ5//nnePoweG29STWTj0tPT4evri8LCwnKPaTQaODk54aOPPsL06dNNtjpSFEVcunSptOx0Oh2CgoIQFBSEjh07cgqTjIojPiIb98EHH0Cv11f4mE6nw4svvoiZM2ca/XNFUURMTAxCQ0MREhICQRAQFBSEDRs2oEOHDiw7MhmO+IisQIlBQEpOEbQlAjR2Sni5OcJO9egpwejoaPTo0QNFRUWVPsfJyQmbNm1C//79HzunKIq4cOFC6chOoVAgKCgIQ4cOxXPPPceyI7Ng8RFZqJwCHbacT0ZoTAqSsgqgVimhVCggiCL0BgGNPZwx9DkvDOvojTpO9uVeLwgC2rZti9jY2Ed+lpubG27evIk6depUO6cgCDh37hxCQ0MRGhoKtVpdWnbPPvssy47MjsVHZGF0JQIWRsRj5ckEKBRAsV6o9LkOaiVEERjn/ySm9vSDvd3/jwLXrl2LSZMmla7kfBiNRoMhQ4Zgw4YNVcqYmZmJgwcPIiwsDAcOHEDdunUxePBgBAUFoW3btiw7khSLj8iCpOYWYeTKM7iVV4yihxTe3zmqlWhQ2wEbxnVGozqOuHfvHnx8fJCbm1ul1yuVSgiCgOjoaHTs2LHc4waDAefPn0dYWBjCwsJw9epV9OjRA4GBgXjttdfQpEmTKmclMjUWH5GFSM0tQr//ncTdQj0Mf/22Lbh6Eto/LkN3+yZ0txMg6org/FQP1O33UbnXqxQKuDqpsWeSPz56fyw2b95c+pijoyPs7e0hCAKKi4uhUqnQoEEDeHt7w9fXF35+fvDx8cGAAQNK78N5+/ZtHDhwAGFhYTh48CA8PT0RGBiIwMBAdO3alffHJNniqk4iC6ArETBy5ZkypQcAd09tgf52AhT2jlC5eKAkK6XS9zCIIu4W6vHGyjOIOxoJb29vtGvXDi1atEDTpk3h4+MDHx8feHt7V3gCucFgwNmzZxEeHo6wsDDEx8cjICAAgYGBmDdvHnx8fEzyvRMZG4uPyAIsjIjHrbziMqUHAO4934HKxQN2bg2h/eM33Nr08G0HBlFERp4W//j5KD56pcUjPzcjI6N0VHfo0CE0atQIgYGB+Pbbb/HCCy/A3r78ohkiuWPxEclcToEOK08mQFtS/pqeQ+O21X6/Ir0BK07cxDj/J8ut9rxz5w4iIyNx7NgxHDt2DCkpKejVqxcCAwMxf/58eHl51fj7IJILFh+RzG05nwxjL4JUKP5838GtauP48eM4evRoadH5+/ujR48eWLt2LZ599lnY2fGPCbIu/BVNJHOhMSkP3bJQE8V6AV9vjcQn6z9k0ZHN4a9wIhkrMQhIynr0PruaULo2QMat23DQ8Dod2Rbe5pxIxlJyiqCuwq3HasLeToWMexXfo5PImrH4iGRMWyJAaaK7nCgVigoXzBBZOxYfkYxp7JQQTHSPCUEUobHjHwFke/irnkjGvNwcoTeYZlSmNwjwcnM0yXsTyRmLj0jG7FRKNPZwNsl7N/FwrtLRRUTWhqs6iWRu6HNe+D4ivsItDYXxp1EYfwYAYCjIAQBoU68ic+93AACVU224Bbxd7nUOaiWC2nMzOtkmFh+RzA3r6I3vDsdX+Jju1k0UXI4o87WS3AyU5GYAAFS161dYfKIIvN7B2/hhiSwAT2cgsgDfHriK1VEJ1TqKqDKOahXe9n+ySvfqJLJGnOAnsgBTe/qhQW0HqB5za4NKoYBnbQ2m9mxupGRElofFR2QB7O2U2DCuM1yd1DUuv/vn8a0f19lkm+KJLAGnOoksSM1PYFfBs7YG6/86gZ3IlrH4iCxMYbEOI79ajzjhCSgUeOgNrB3VSggi8E63ppjaszlHekTgqk4ii/L777/jlVdewc2bN5FyJwd747IQeiEFiVkFUKuUUCoUEEQReoOAJh7OCGrvhdc7eJc7d4/IlnHER2QBRFHEqlWrMHXqVBQWFgIA9Hp96RFCJQYBI8ZPRvyNBOzcFgIvN0duTieqBIuPSOYyMzPxxhtv4MSJE6Wlp1QqYTAYSp+Tk5MDT09PGAwG/P7772jcuLFUcYlkjz8SEslYWFgYmjdvjiNHjpSWHoByh8V+/vnnEAQBoihi7ty55o5JZFE44iOSoaKiIkyZMgUbNmxAUVFRucednZ2Rn58PAEhNTUXz5s1Ln+fo6Ig//vgDdevWNWtmIkvBER+RzMTExKBly5aVlh4AqNXq0n+eMWMGSkpKSv9dFEV89913Js9JZKk44iOSCYPBgK+++gpz586ttPDuq1+/Pm7duoVr167h2WefRXFxcZnHa9WqhYyMDDg7m+ZkByJLxhEfkUz069cPX3zxxSNLDwA0Gg0AYNq0adDpdOUeFwQBy5YtM3pGImvA4iOSiYkTJ6JBgwZVGqVpNBqcO3cOkZGREIQKjisqLMTcuXMrLEUiW8fiI5KJPn36ICEhAQsWLECdOnXg5ORU6XM1Gg0mT55cZqXn32m1WmzcuNEUUYksGq/xEclQYWEh5s+fj88//xwqlQp6vb7M482bN0daWhoKCgoe+j7e3t5ITEyEUsmfcYnu4+8GIhlycnJCixYt0KZNG4wbNw4ODg5l9u6lpKQ8svSAPze2792715RRiSwOR3xEMqTVatGyZUusXr0aL730EhITE/HRRx9h//79KCoqglKprPDaXkWeeuop/Pbbb1A85ll+RNaCxUckQwsWLEBkZCR2795d5uu//PIL+vbtizt37kCj0aCkpAR6vR4GgwGCIEClUkGlUkGpVJb+lZ+fj9jYWLRu3Vqi74ZIXlh8RDKTlZWFli1b4vjx42jVqlWVX+fp6YmoqCh4eHhAq9VCq9VCp9PBYDDAz8+PIz6iv7D4iGRm2rRp0Gq1WLJkSbVe5+rqiqSkJNSpU8c0wYisBIuPSEauXr0Kf39/xMbGokGDBtV6rb29PfLz82Fvz7P3iB6GqzqJZEIURUyePBmzZs2qdundv8734D08iahiLD4imQgNDUVGRgYmTZpU7dcWFRXB0dGR1/GIqsDu0U8hIlPLz8/Hhx9+iA0bNpQ7a68qcnNz4ebmZoJkRNaHIz4iGZg9ezZ69OiB7t271+j1WVlZcHd3N3IqIuvEER+RxK5evYpVq1bh119/rfF7ZGdnw8PDw4ipiKwXR3xEErq/oOWzzz7DE088UeP3yc7O5oiPqIpYfEQSepwFLQ/iVCdR1XGqk0gij7ug5UGc6iSqOo74iCTyuAtaHsQRH1HVccRHJAFjLGh5UHZ2Np566imjvBeRteOIj8jMjLWg5UFc3EJUdSw+IjMz1oKWB3Gqk6jqONVJZEbGXNDyIC5uIao6jviIzMiYC1oexKlOoqrjsUREZnL16lV069YNv/76q9Gu7QF/XjPUaDS4d+8eNBqN0d6XyFpxxEdkBqZY0HLf/TP4WHpEVcPiIzKDbdu2GX1By31c2EJUPVzcQmRi+fn5mDZtmtEXtNzHhS1E1cMRH5GJmWpBy31c2EJUPRzxEZmQse/QUpGsrCyO+IiqgSM+IhMx5YKWB3HER1Q9LD4iEzHlgpYHcXELUfVwqpPIBEy9oOVB2dnZaNSokUk/g8iacMRHZAKmXtDyIE51ElUPR3xERmaOBS0P4lQnUfVwxEdkROZa0PIg7uMjqh4WH5ERmWtBy4M41UlUPZzqJDIScy5oeRD38RFVD09nIDKSGTNmIDU1FevWrTPbZ4qiCHt7exQUFMDe3t5sn0tkyTjiIzICcy9ouS8vLw8ODg4sPaJq4DU+osckxYKW+7iwhaj6WHxEj2n9+vW4ffu2WRe03MeFLUTVx6lOoseQnp6O6dOn48CBA2Zd0HIfF7YQVR9HfEQ1JIoi3n33Xbz33nto166dJBk44iOqPo74iGpow4YNSExMRGhoqGQZWHxE1cfiI6qB9PR0fPjhhwgLC5N0RSVvV0ZUfZzqJKomURTx3nvvYfz48Wjfvr2kWdLS0sy+kpTI0rH4iKpp06ZNuHnzJv75z39KHQV//PEHGjduLHUMIovCqU6iasjIyMC0adOwb98+aDQaqePgjz/+gI+Pj9QxiCwKb1lGVEWiKGLw4MFo3bo15syZI3UcAICrqysSExPh5uYmdRQii8ERH1EVbdmyBfHx8di8ebPUUQAAubm5EEURderUkToKkUVh8RFVwa1btzB16lTs3btXFlOcwP9PcyoUCqmjEFkULm4hegRRFPH+++9j7Nix6Nixo9RxSvH6HlHNcMRH9Ahbt27F1atXsXHjRqmjlMHiI6oZFh/RQ9y+fRtTp07Frl274ODgIHWcMpKSkriVgagGONVJ9BATJ07EW2+9hU6dOkkdpRyO+IhqhiM+okqEhITg8uXLZj1RvTpYfEQ1w+IjqsCdO3cwefJk7Ny5U3ZTnPex+IhqhhvYiSoQHByMxo0b45tvvpE6SoX0ej2cnZ1RWFgoyTmARJaMv2OI/iY0NBS//PIL1q5dK3WUSqWmpsLT05OlR1QD/F1D9ID7U5zbt2+Ho6Oj1HEqxWlOoprjqk6iB0yePBkjR45Ely5dpI7yUDyVgajmOOIj+su2bdtw8eJFrFmzRuooj5SUlMQRH1ENccRHBCAzMxOTJk3C6tWrZT3FeR+nOolqjsVHBGDKlCkYPnw4unbtKnWUKmHxEdUcpzrJ5u3YsQPnz5/HpUuXpI5SZbzGR1Rz3MdHNi0rKwtPP/00tm7dCn9/f6njVIkoinBxcUFaWhpq164tdRwii8OpTrJpU6ZMQXBwsMWUHgDk5OTAzs6OpUdUQ5zqJJu1c+dOREdH45dffpE6SrVwmpPo8bD4yCZlZ2djwoQJ2LJlC5ycnKSOUy1c2EL0eDjVSTZp6tSpCAoKQrdu3aSOUm3cw0f0eDjiI5uze/dunDp1Cr/++qvUUWqEIz6ix8MRH9mU1NRUjB8/Hj/99BOcnZ2ljlMjvMZH9HhYfGQzDAYD3njjDUycONGiVnH+HUd8RI+HxUc2Y+7cuQCAmTNnSpzk8fAaH9Hj4QZ2sgknTpxAUFAQYmJi0LBhQ6nj1JhWq0Xt2rVRWFgIlUoldRwii8QRH1m9rKwsjBw5EqtWrbLo0gP+vEbZsGFDlh7RY2DxkVUTRRFvv/02hg4dij59+kgd57Hx+h7R4+N2BrJqixcvRkpKCrZs2SJ1FKPg9T2ix8fiI6t16dIlfP755zh9+jQ0Go3UcYyCxUf0+DjVSVYpPz8fwcHBWLhwIXx9faWOYzTx8fHw8/OTOgaRRWPxkVWaNGkSunbtihEjRkgdxahiY2PRunVrqWMQWTROdZLVWb9+Pc6cOYMLFy5IHcWoDAYDrl27hlatWkkdhciisfjIqly/fh3Tpk3D4cOHLfaWZJVJTExE/fr1UatWLamjEFk0TnWS1dBqtRg2bBj+85//4JlnnpE6jtHFxcVxmpPICFh8ZDVmzJgBHx8fTJgwQeooJhEbG4unnnpK6hhEFo9TnWQV9uzZg+3bt+PixYtQKBRSxzGJuLg4vPTSS1LHILJ4HPGRxUtJScE777yDjRs3wt3dXeo4JsOpTiLj4E2qyaIZDAb07NkTL7/8Mj777DOp45iMIAioXbs20tPT4eLiInUcIovGER9ZtDlz5kClUmHGjBlSRzGppKQkuLu7s/SIjIDX+MhiHT9+HD/++CMuXLhg9acVcJqTyHg44iOLdP+oodWrV1v8UUNVwRWdRMbD4iOLI4oixowZg+DgYAQGBkodxyw44iMyHhYfWZwffvgB6enpmDt3rtRRzIbFR2Q8XNVJFuXixYt45ZVXcObMGTRr1kzqOGYhCAJcXV2RkpICV1dXqeMQWTyO+Mhi3Lt3D8HBwfjhhx9spvQAIDk5Ga6uriw9IiNh8ZHFmDRpErp3745hw4ZJHcWsOM1JZFzczkAW4eeff0Z0dDTOnz8vdRSz4xl8RMbF4iPZi4+Px/Tp0xEREWF1Rw1VRVxcHLp06SJ1DCKrwalOkjWtVovg4GB88cUXaNu2rdRxJMGpTiLj4qpOkrWpU6ciJSUFoaGhVnvqwsOIoghXV1ckJSXBzc1N6jhEVoFTnSRbO3bswK5du6z6qKFHSUlJQa1atVh6REbE4iNZio2Nxfjx47F//36b/kOf05xExsdrfCQ7OTk5GDhwIBYsWICOHTtKHUdSLD4i42PxkawYDAYMGzYMffv2xZtvvil1HMnx5tRExsfiI1n59NNPYTAY8O2330odRRY44iMyPl7jI9nYuHEjQkNDce7cOdjZ8ZemKIosPiIT4J8uJAsxMTGYOnUqIiIi4OHhIXUcWUhLS4ODgwP/exAZGac6SXK3b9/G4MGDsWTJEpvdpF4RjvaITIPFR5LS6/UICgrCyJEjERQUJHUcWWHxEZkGi48kNW3aNLi4uODLL7+UOorscEUnkWmw+Egyq1atwuHDh7FhwwYolfyl+Hcc8RGZBu/VSZI4ffo0BgwYgBMnTqBFixZSx5EdURTh4eGBa9euoV69elLHIbIq/DGbzC4tLQ1Dhw7F6tWrWXqVSEtLg1qtZukRmQCLj8yquLgYgwcPxoQJE9C3b1+p48hWdHS0zd+ujchUWHxkNqIoYsKECfD29sbMmTOljiNrZ8+exfPPPy91DCKrxOIjs/nf//6H8+fPY82aNTZ7zFBVnT17Fp06dZI6BpFV4uIWMoujR49i+PDhOH36NJ588kmp48iawWCAm5sbEhMT4e7uLnUcIqvDER+ZXGJiIoYPH44NGzaw9KrgypUr8PT0ZOkRmQiLj0yqsLAQAwcOxCeffIKePXtKHcciREdHc5qTyIRYfGQyoihi7NixaNu2LT744AOp41gMLmwhMi0WH5nMN998g99//x3Lli3jYpZq4MIWItPi4hYyibCwMIwbNw5nz56Fl5eX1HEsRkFBAerXr4/s7GxoNBqp4xBZJZ7HR0YXHx+Pt956Czt27GDpVVNMTAzatGnD0iMyIU51klHl5eVh4MCBmD17Nrp27Sp1HIvDaU4i02PxkdEIgoBRo0ahe/fuGD9+vNRxLFJ0dDQXthCZGIuPjObzzz9HdnY2Fi1aJHUUi8URH5Hp8RofGcX27duxZs0anDt3Dvb29lLHsUgZGRm4d+8efH19pY5CZNVYfPTYLl++jHfffRdhYWFo0KCB1HEs1v1pTm79IDItTnXSY8nOzsbAgQPx3//+Fx06dJA6jkXjNCeRebD4qMa0Wi2GDBmCAQMGYNSoUVLHsXhc2EJkHtzATjUiCAJGjBgBvV6PrVu3QqVSSR3JogmCAHd3d1y/fp2nrhOZGK/xUY18/PHHSE1NxcGDB1l6RnDt2jW4u7uz9IjMgMVH1fb9999j//79OHnyJBwdHaWOYxV4IgOR+bD4qFpCQkIwf/58REVF8bw4I+LCFiLz4eIWqrLjx49j4sSJ2Lt3Lxo3bix1HKvChS1E5sPFLVQlsbGxCAgIwIYNG9CrVy+p41iVoqIi1K1bF5mZmZw6JjIDjvjokVJTU9G7d28sWLCApWcCFy9eRMuWLVl6RGbC4qOHunv3LgIDA/H+++/jjTfekDqOVeLCFiLzYvFRpXQ6HQYPHozu3bvjk08+kTqO1eLCFiLzYvFRhQRBwJgxY+Dq6oqFCxfy/pEmxIUtRObF7QxUoU8//RSJiYk4fPgwN6ib0J07d5CVlYUWLVpIHYXIZrD4qJwffvgBu3btQlRUFBdcmFh0dDQ6dOgApZKTL0TmwuKjMrZt24Z58+YhKioKHh4eUsexelzYQmR+/DGTSp08eRLvv/8+9u7diyZNmkgdxyZwYQuR+XEDOwEArly5gh49emDdunV45ZVXpI5jE0RRhIeHB+Li4uDp6Sl1HCKbwREfIS0tDYGBgfj2229ZemZ0/fp1uLi4sPSIzIzFZ+Py8vLQu3dvjB8/Hm+++abUcWzK0aNH0b17d6ljENkcFp8N0+l0GDJkCLp06YJPP/1U6jg2JyIiAj179pQ6BpHN4TU+GyWKIt58803k5eVh+/bt3KtnZoIgoEGDBoiJiYG3t7fUcYhsCrcz2KiZM2fixo0biIiIYOlJ4Ndff4W7uztLj0gCLD4btGTJEmzfvh1RUVFwcnKSOo5N4jQnkXR4jc/G7NixA7Nnz0ZYWBjq1q0rdRybxeIjkg6v8dmQU6dOYeDAgQgLC0P79u2ljmOzdDod6tati8TERLi7u0sdh8jmcMRnI65du4bBgwfj559/ZulJ7OzZs2jevDlLj0giLD4bkJ6ejtdeew3z5s3Da6+9JnUcm8dpTiJpsfis3L1799CnTx+MHTsWo0ePljoOgcVHJDVe47NiOp0O/fr1Q5MmTbB06VIeJisD+fn58PT0xK1bt+Ds7Cx1HCKbxBGfldLr9QgODoazszMWL17M0pOJEydOoH379iw9IglxH58VKikpwciRI6HX67F9+3bY2fF/s1xERESgV69eUscgsmkc8VkZg8GA0aNH4+7duwgNDYW9vb3UkegBvL5HJD1e47MigiBg3LhxSExMxL59++Do6Ch1JHpAZmYmmjVrhszMTKjVaqnjENkszoFZCVEUMWHCBNy4cQNhYWEsPRk6evQounXrxtIjkhiLzwqIooipU6fil19+wcGDB7lwQqYOHz7MaU4iGeA1PgsniiI+/vhjnDp1CmFhYXBxcZE6ElWC1/eI5IEjPgsmiiJmzZqFQ4cO4ciRI6hTp47UkagSSUlJyMvLQ5s2baSOQmTzWHwW7Msvv8SuXbtw7Ngx3vdR5iIiIhAQEAClkpMsRFJj8Vmor7/+Ghs3bkRkZCSPF7IAnOYkkg9uZ7BA3333HZYsWYLIyEg0bNhQ6jj0CKIoomHDhoiKikLTpk2ljkNk8zjiszCLFy/GDz/8wNKzIHFxcXB0dGTpEckEi8+CrFixAt988w2OHTsGb29vqeNQFXGak0heeKXdQvz000/44osvEBERgSeffFLqOFQNLD4ieeE1PguwadMmfPTRR4iIiEDLli2ljkPVUFJSgrp16yI+Ph7169eXOg4RgVOdsrdt2zZ8+OGHOHToEEvPAl24cAE+Pj4sPSIZYfHJ2O7duzFx4kSEh4dz47OF4m3KiOSH1/hkKiwsDO+88w727t2LZ599Vuo4VEO8vkckP7zGJ0OHDx/GiBEjsHv3bnTu3FnqOFRDRUVFqFevHtLS0lC7dm2p4xDRXzjik5nIyEiMGDEC27ZtY+lZuKioKLRt25alRyQzLD4ZiYqKQlBQEDZv3oxu3bpJHYceE6c5ieSJxScT0dHRGDRoENatW4eAgACp45ARcGELkTzxGp8MxMTEIDAwEKtWrULfvn2ljkNGkJaWhjZt2uDWrVs8cZ1IZjjik9hvv/2G3r17Y+nSpSw9K7J792707t2bpUckQyw+CcXFxeHVV1/FokWLMGjQIKnjkBHt3LkTAwYMkDoGEVWAU50SiY+PR0BAAObNm4c33nhD6jhkRHfv3oW3tzdSU1Ph4uIidRwi+huO+CRw5coV9OzZE1988QVLzwqFh4ejW7duLD0imWLxmVlMTAwCAgIwd+5cjB07Vuo4ZAI7d+7EwIEDpY5BRJXgVKcZnThxAkOGDMHy5cv5B6OV0mq18PT0xJUrV+Dp6Sl1HCKqAG9SbSZhYWF46623sGnTJu7tsmLHjh1Dq1atWHpEMsapTjPYsmULRo8ejd27d7P0rBynOYnkj1OdJrZixQr85z//QVhYGNq2bSt1HDIhQRDg7e2No0ePws/PT+o4RFQJTnWa0Pz587F48WJERkbC19dX6jhkYufPn4erqytLj0jmWHwmIIoi/vnPf2Lbtm04ceIEvLy8pI5EZsBpTiLLwOIzMkEQMGXKFJw+fRrHjx9HvXr1pI5EZrJz506sWbNG6hhE9AgsPiPS6/UYO3YskpKScOTIEbi6ukodiczk2rVryM3NRceOHaWOQkSPwOIzkuLiYgQHB0Ov1yM8PBxOTk5SRyIz2rVrFwYMGAClkgulieSOv0uN4N69e+jTpw8cHR2xc+dOlp4N2rVrF6/vEVkIbmd4TNnZ2ejduzfatm2LH3/8ESqVSupIZGYZGRlo1aoVbt26BXt7e6njENEjcMT3GNLT0/Hiiy+iW7duWLZsGUvPRu3ZswevvvoqS4/IQrD4aighIQHdunXD8OHD8c0330ChUEgdiSTCbQxEloVTnTVw/wDZTz/9FBMmTJA6Dkno3r17aNSoEZKTk7mKl8hCcFVnNZ0/fx59+/bF/PnzeZYe4cCBA3jhhRdYekQWhMVXDZGRkQgKCsKKFSswYMAAqeOQDHCak8jycKqzivbt24cxY8bwWCEqpdfr0aBBA1y+fBkNGzaUOg4RVREXt1TBpk2bMHbsWOzZs4elR6UiIyPRvHlzlh6RheFU5yMsW7YMX375JQ4fPoynn35a6jgkI5zmJLJMnOp8iG+++QZLly7FoUOH0KxZM6njkIyIoggfHx8cPHgQrVq1kjoOEVUDR3wVEEURn332GXbu3IkTJ06gUaNGUkcimYmJiYGTkxNatmwpdRQiqiYW398IgoBJkyYhOjoax48fR926daWORDK0c+dODBgwgDcuILJAXNzyAL1ej1GjRiE2NhZHjhxh6VGleH2PyHJxxPeXoqIiBAcHw2AwIDw8HI6OjlJHIpm6ceMG7ty5g06dOkkdhYhqgCM+AHfu3EHPnj3h4uKCHTt2sPTooXbt2oX+/fvzpuREFsrmi+/GjRt44YUX0KNHD6xbt4532KdH4tl7RJbNprcznD59GoMHD8Z//vMfvPvuu1LHIQuQkZGBli1bIiMjAw4ODlLHIaIasNlrfDt27MD48eOxdu1a9OnTR+o4ZCE2btyIgQMHsvSILJhNTnUuXLgQkyZNQnh4OEuPqmX9+vUYNWqU1DGI6DHY1IhPEARMnz4dBw4cQFRUFJo0aSJ1JLIgsbGxuH37Nnr06CF1FCJ6DDZTfEVFRRg1ahQyMzMRFRUFNzc3qSORhVm3bh1GjhzJ1ZxEFs4mpjozMzPRs2dP2Nvb48CBAyw9qjZBELBhwwYePkxkBSyq+EoMAhIzC3At4x4SMwtQYhAe+Zr72xVefPFFrF+/HhqNxgxJydocO3YMHh4ePKGDyArIfqozp0CHLeeTERqTgqSsAqhVSigVCgiiCL1BQGMPZwx9zgvDOnqjjlPZPXhnzpzBoEGDuF2BHhsXtRBZD9nu49OVCFgYEY+VJxOgUADF+spHdw5qJUQRGOf/JKb29IO9nZLbFchoCgsL0ahRI8TFxeGJJ56QOg4RPSZZjvhSc4swcuUZ3Morhrbk0dOZ90txdVQC9v2Wjl6qK/hx/hyEhYWhQ4cOpo5LVm737t14/vnnWXpEVkJ2xZeaW4R+/zuJu4V6GB4YjJbkZSL3xHoUJ8TAUJQHlbM7nPw6w9V/BFQOtQAARXoBf2QXYpXWA9vDj6LD035SfRtkRdatW8dFLURWRFZTnboSAa98H4nk7KIypafPSUfGun9AKMyFY/POUHt4QZsWD+0fv8LO3Queo76ByrF26fNVCgV83B1xcNqLUKssav0Oyczt27fh5+eHlJQU1KpVS+o4RGQEsmqFhRHxuJVXXKb0ACD74BIIhblw6/Uu6g+ZBbceo+E5Yi5cOg5ASXYKciN/LvN8gygiI0+LhRHXzRmfrNDmzZvRr18/lh6RFZFN8eUU6LDyZAKK/raIRZ+bgeKEi1C5NoBL+7KLVOr4j4RC7YCC2KMQdMVlHivSG7DixE3kFupMnp2s17p167iak8jKyKb4tpxPhkJR/uvFSb8AAByfbAeFomxcpcYJGq9WEPVaaNOulnutQvHn+1aFKIo4c+YM3n33XbRq1QolJSXV/ybIqly9ehUpKSkICAiQOgoRGZFsFreExqRUuGWhJCsVAKB2a1jh69RuDVGccBEl2WlAk2fLPFasFxB6IQXvdm9W6edeuXIFP/30E9auXYv8/HwUFRVBrVbztlSEdevWYcSIEbCzk81vEyIyAln8ji4xCEjKKqjwMUH759cVDs4VPq7QOP/1vPwKH0/M+vMOL3YPLHJJSUnBxo0bsWLFCqSmpqKkpAR6vb70cU9PTygqGn6Szbh/i7KdO3dKHYWIjEwWxZeSUwS1Sgm9wVCDV99fCFNxUalVSqTkFKG2UovQ0FAsW7YMsbGxUCgUKC4urvA1jRs3rkEOsiYnT56Ei4sLnnnmGamjEJGRyaL4tCUClJWMsJR/jejE4opHhKK2sMzz/s5QUoLX+vTFzYtRUKvVKCwsfGSeli1bViU2WbH7i1o48ieyPrIoPo2dEkIl2wntPBoBAPQ5aRU+fv/rdu4VXwM0CCKSb1yHXq8vM51ZGXt7e/j5ceO7LSsuLsa2bdvw66+/Sh2FiExAFqs6vdwcoa/kpAUHn7YAgKKEixDFss8RtIXQplyBwk4DTcOKR2kKlQpXY07B398fzs4VjwofZDAYcOjQISxZsgSRkZHIzMys5ndDlm7Pnj1o164dvLy8pI5CRCYgi+KzUynR2KPiUlK7PQGHJ9vBcPcW7l3YV+ax3JMbIOqL4dzmJSjtHSp8fRMPZzzZ2AfHjx/Hd999B2dn54eu0tNoNGjTpg0uXbqEmTNnwtfXFw0aNEBAQACmTJmCZcuW4eTJk8jJyan5N0yyxpMYiKybbG5ZtjTyd3wfEV/hloaH37KsETxHfVvmlmX3OaiV+LCXH8Y/sJ0hOTkZI0aMwMWLF1FQUP66oUajQVpaGtzd3QH8ub8vLS0NsbGxuHz5MmJjYxEbG4u4uDi4uLigY8eO6NSpE55//nl06NABrq6uRvyvQuaWmZkJX19fJCcnw8XFReo4RGQCsim+3EIdOn0VUelpDCV5d5B7YgOKb16AoegeVLXc4NT8r5tUO1b8B5TGTomzn/Ysd06fKIpYuXIlpk2bBq1WW2azukajQVFR0SMXNYiiiMTERJw7dw7R0dE4e/YsLl68CB8fHzz//POlf7Vt2xb29vYPfS+Sj8WLFyMqKgobN26UOgoRmYhsig8Avj1wFaujyt+2rCYc1Sq87f8kPnqlRaXPqWj017hxYyQmJtboM0tKShAbG4uzZ8+WluHNmzfRtm1bPP/886Ujw2bNmnG1oEx17twZ//rXv9C7d2+poxCRiciq+Co7naG6qnM6w4Ojv6KiIvj7+yMyMrLGn/139+7dQ0xMTGkZRkdHo6CgAJ07d8ZLL72EgIAAPPPMM7xTjAxcv34d/v7+SE1N5d1aiKyYrIoPqPw8vqpSKRRwdVJjzyR/NKrjWOXXJScnY9SoUejSpQu++uqran9udaSnpyMqKgpHjx7FkSNHcOvWLfTo0aO0CFu3bs0RoQT+/e9/4+7du/j++++ljkJEJiS74gPKnsBenWlPR7UKnrU1WD+uc7VKT2ppaWk4evRoaREWFhaWluBLL73EqVEzEEURvr6+2Lp1K9q3by91HCIyIVkWH/DntOfCiHisPJkAhQIVrva8z1GthCAC73Rriqk9m1v84bMJCQmlJXjkyBHY2dkhICCgtAi9vb2ljmh1oqKi8M4775Tezo6IrJdsi+++3EIdtpxPRuiFFCRmFUCtUkKpUEAQRegNApp4OCOovRde7+BdbvWmNRBFEfHx8aUleOzYMdSvXx/9+/dHv3790KlTJ14fNIL33nsPPj4+mDlzptRRiMjEZF98DyoxCEjJKYK2RIDGTgkvN8cypy7YAkEQcO7cOezevRt79uxBRkYG+vTpg/79++Pll1/mSeE1oNVq0bBhQ8TExPAG5UQ2wKKKj8pLTEzEnj17sHv3bpw9exb+/v7o378/+vbty1tuVdGOHTuwcOFCHDt2TOooRGQGLD4rcvfuXRw4cAB79uzB/v370aRJE/Tr1w/9+/dHu3bteO2qEoMHD0afPn3w9ttvSx2FiMyAxWelSkpKcOrUKezevRu7d+9GYWEh+vfvj2HDhsHf3x9KpW1NEVcmIyMDLVu2RFJSEm83R2QjWHw24tq1a9ixYwc2bdqE7OxsDBs2DMOHD7f5keBXX32F33//HStXrpQ6ChGZCYvPBsXGxmLTpk3YuHEj7O3tMXz4cAwfPtzmziEUBAG+vr7YsmULOnbsKHUcIjITFp8NE0UR0dHR2LhxI7Zu3YpGjRphxIgRCA4ORqNGjaSOZ3IHDx7EjBkzcOHCBZse9RLZGhYfAfjzmuCxY8ewadMm7NixA8888wyGDx+OoUOHlh7RZG2GDBmCl19+Ge+9957UUYjIjFh8VE5xcTHCwsKwadMmHDhwAN27d8eYMWPQr18/qNVqqeMZRXp6Olq3bo2kpCTUrl3+LEcisl4sPnqovLw87NixA6tWrcL169cxevRojBs3Ds2aNXv0i2Vs7ty5SEhIwIoVK6SOQkRmxuKjKrty5QpWrlyJn3/+Gc8++yzeeecdDBw40OIO2hUEAc2aNUNISAg6dOggdRwiMjNu5qIqa9WqFRYsWIDk5GSMHTsWS5cuhbe3Nz7++GPEx8dLHa/KDh06BHd3d5YekY1i8VG1OTg4YPjw4Thy5AhOnDgBAOjWrRteeuklbNq0CVqtVuKED7ds2TKMHz9e6hhEJBFOdZJR6HQ67Nq1C8uXL8elS5fw5ptv4p133kHLli2ljlbG/UUtf/zxB1xcXKSOQ0QS4IiPjMLe3h5BQUE4dOgQzpw5A3t7e/To0QM9e/bEvn37IAhVP1DYlFavXo2goCCWHpEN44iPTEan0yEkJAQLFixAYWEhpk2bhlGjRsHJyUmSPAaDAc2aNcO2bdt4yjqRDeOIj0zG3t4eI0eOxIULF7B06VLs27cPTZo0wb/+9S9kZGSYPc+hQ4dQt25dlh6RjWPxkckpFAr06NEDu3fvxokTJ3Dnzh20atUKY8eOxW+//Wb0zysxCEjMLMC1jHtIzCxAieHPaVYuaiEigFOdJJHMzEwsW7YM//vf//D0009j+vTpeOWVV2p8z8ycAh22nE9GaEwKkrIKoFYpoVQoIIgi9AYBjVw1uLJvNS5s/QFe9a3zFmxEVDUsPpKUVqvF5s2bsWDBAhgMBnz44YcYOXIkHBwcqvR6XYmAhRHxWHkyAQoFUKyvfBGNWgkolUqM838SU3v6wd6OEx5EtojFR7IgiiIiIiLw3//+FzExMZg0aRImTZqEOnXqVPqa1NwijFx5BrfyilH0kML7O0e1Eg1qO2DDuM5oVMfRCOmJyJKw+Eh24uLi8PXXX2Pv3r14//338cEHH6Bu3bplnpOaW4R+/zuJu4V6GEQRhqI8FMafRtGNc9DfSYIhPwtQ2cG+XhM4P90Ltdr2gkLx/yM8lUIBVyc19kzyZ/kR2RjO9ZDstG7dGj/99BPOnTuHO3fuwM/PDx999BHS09MB/Dm9OXLlmdLSA4DCqyeRHfYDdOnxsG/oB5cO/eHk9wJ0d5KQHbYImTvn4cGf8QyiiLuFeryx8gz0BnnsMSQi8+CIj2QvJSUF8+fPx88//4zhw4ej/svjsDkmo8z0ZlHiLxD1xXD07VhmZGfIz0H6zx/CkHcHdQd+CueWXcu8t6Nahbf9n8RHr7Qw2/dDRNLiiI9kz8vLC99//z2uXr0KZ7f6WH8urdw1Pccmz8CpeacypQcAqlpucHk2EACg/aP81okivQErTtxEbqHOdN8AEckKi48sRv369dH05TegUlXzl61K9efflaoKH1YogC3nkx8zHRFZChYfWZTQmJSHbln4O1EwoODyEQCAY9PnKnxOsV5A6IUUo+QjIvlj8ZHFKDEISMoqqNZrco+thf5OEhybdYBj08pvVZaY9f93eCEi68biI4uRklMEdTWmOfPO70Ze9A7YeXjBo+/0hz5XrVIiJafocSMSkQVg8ZHF0JYIUFbxlmb3LuxFzuHlUNf1gefwr6ByfPgxREqFAtoSjviIbIGd1AGIqkpjp4RQhd03eed2ISdiBdT1GqPBsDlQOdd55GsEUYSGtzAjsgksPrIYXm6Oj9xsfvdMKHKPrYW6flM0GPYlVE6uVXpvvUGAlxvv4EJkC/gjLlkMO5USjT2cK308N2oTco+thb2nLxoMn1Pl0gOAJh7OsKvuNgkiskgc8ZFFGfqcF76PiC+3pSH/twjcPbEBUCih8XoK987vLvdaO9cGqNW2V7mvO6iVCGrvZbLMRCQvLD6yKMM6euO7w/Hlvl6S+9eJ7qKAe+d3VfhajXebCotPFIHXO3gbNScRyRfv1UkW59sDV7E6KqFaRxFVhvfqJLI9vKhBFmdqTz80qO0AVQ1Pa79PpVDAs7YGU3s2N1IyIrIELD6yOPZ2SmwY1xmuTuoal9/98/jWj+tcrU3xRGT5ONVJFqvmJ7Cr4Flbg/U8gZ3IJrH4yKLpSgQsjIjHypMJUCjw0BtYO6qVEETgnW5NMbVnc470iGwUi4+sQm6hDlvOJyP0QgoSswqgVimhVCggiCL0BgFNPJwR1N4Lr3fwRh0ne6njEpGEWHxkdUoMAlJyiqAtEaCxU8LLzZGb04moFIuPiIhsCn8MJiIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim8LiIyIim/J/dqnsDFPkcSYAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "old_node_positions = lag.DrawGraph(A,node_positions)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we use $\\texttt{DrawGraph}$ this way\n", "```\n", "new_node_positions = lag.DrawGraph(A)\n", "```\n", "the function generates a new set of positions and draws a different, but equivalent, picture." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "new_node_positions = lag.DrawGraph(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the discussion in this section we will place two restrictions on the edges.\n", "\n", "1. No edges will be allowed from a node to itself.\n", "2. No edges will be repeated.\n", "\n", "The first restriction means that the adjacency matrix will have zeros along the main diagonal. \n", "\n", "Here is another example of a graph, this one with six nodes." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 1 0 0 0]\n", " [1 0 1 0 0 0]\n", " [0 0 0 0 1 1]\n", " [1 1 0 0 1 0]\n", " [0 1 0 1 0 0]\n", " [0 0 0 0 1 0]]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "B = np.array([[0,1,1,0,0,0],[1,0,1,0,0,0],[0,0,0,0,1,1],[1,1,0,0,1,0],[0,1,0,1,0,0,],[0,0,0,0,1,0]])\n", "print(B)\n", "node_positions = lag.DrawGraph(B)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Counting paths\n", "\n", "One use of the adjacency matrix is in computation of paths from one node to another. The $(i,j)$ entries in *powers* of the adjacency matrix will tell us the number of paths between nodes $i$ and $j$ that have length equal to the power. For example, if $B$ is the adjacency matrix, then $B^3$ contains information about paths of length 3. \n", "\n", "Let's try it out for the previous example. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 2 1 1 2 1]\n", " [1 1 1 1 2 1]\n", " [2 2 1 1 1 0]\n", " [3 2 3 0 3 2]\n", " [1 3 3 1 1 1]\n", " [2 1 1 0 1 0]]\n" ] } ], "source": [ "print(B@B@B)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see for example that $B^3_{50} = 2$. This means that there are 2 paths of length 3 from node 5 to node 0. Similarly we see that $B^3_{22} = 1$, which means that there is only 1 path of length 3 from node 2 back to itself. Check the graph for yourself to verify these counts. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Finding cliques\n", "\n", "A **clique** is a set of three or more nodes within a graph such that there is an edge between each node in the clique *in both directions*. In the example shown below, nodes 2, 3, and 4 form a clique.\n", "\n", "![title](img/Clique_example.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that node 1 in this graph is not part of the clique because it is not connected in both directions to nodes 2 and 4. In order for a node to be included in the clique, it must be connected in both directions to *every other node in the clique.*\n", "\n", "Identifying cliques in large graphs is a difficult problem. A graph may contain many cliques, and it may be that some nodes belong to multiple different cliques. If in the previous example there were an edge from node 2 to node 1, then the graph would have a clique made up of nodes 1, 2 and 3, as well as the clique made up of nodes 2, 3 and 4.\n", "\n", "![title](img/Clique_example2.png)\n", "\n", "Counting paths using adjacency matrices can be used as a way to identify which nodes are in cliques. Since these nodes must be connected to other clique nodes in both directions, we will only allow steps in the paths between nodes that are connected by edges in both directions. If a node is in a clique, there is at least one such path of length 3 that starts and ends at that node.\n", "\n", "Starting with an adjacency matrix $A$, we have a two step process:\n", "\n", "1. Build an adjacency matrix $C$ that includes only the edges between nodes that are connected in both directions. That is, $c_{ij} = 1$ only if $a_{ij} = 1$ and $a_{ji}=1$.\n", "2. Use $C^3$ to identify which nodes have paths to themselves of length 3. That is, check which entries on the main diagonal of $C^3$ are nonzero." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 1 1 0 0]\n", " [1 0 1 1 0 0]\n", " [0 0 0 0 1 1]\n", " [1 1 0 0 1 0]\n", " [0 1 0 1 0 0]\n", " [0 0 0 0 1 0]]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = np.array([[0,1,1,1,0,0],[1,0,1,1,0,0],[0,0,0,0,1,1],[1,1,0,0,1,0],[0,1,0,1,0,0,],[0,0,0,0,1,0]])\n", "print(A)\n", "node_positions = lag.DrawGraph(A)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0. 1. 0. 1. 0.]\n", " [1. 0. 0. 1. 0.]\n", " [0. 0. 0. 0. 0.]\n", " [1. 1. 0. 0. 1.]\n", " [0. 0. 0. 1. 0.]]\n", "\n", "\n", "[[2. 3. 0. 4. 1.]\n", " [3. 2. 0. 4. 1.]\n", " [0. 0. 0. 0. 0.]\n", " [4. 4. 0. 2. 3.]\n", " [1. 1. 0. 3. 0.]]\n" ] } ], "source": [ "C = np.zeros((5,5))\n", "for i in range(5):\n", " for j in range(5):\n", " if (A[i,j] == 1 and A[j,i] == 1):\n", " C[i,j] = 1\n", "print(C)\n", "print('\\n')\n", "print(C@C@C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see from the result that nodes 0, 1, and 3 are clique nodes. Since there are only three such nodes, they all must be in the same clique. We can highlight the clique nodes using the function $\\texttt{HighlightSubgraph}$, which works similarly to $\\texttt{DrawGraph}$ but also accepts a list of nodes to highlight." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lag.HighlightSubgraph(A,node_positions,[0,1,3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try one more example with a larger graph that we build at random." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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wcDDs7e0B5Ie4kpKSirSNKd5b7cePH/j16xcMDAzECmONGjVgZGQEbW1tqKmpUeFVGRAIBEhNTRXZSb60bvOmpqZiRc3S0lJpPfvv37+DwWCIrNFJCMGSJUvg4+ODXr164fjx4+Dz+SX2rQ4ePBhHTp7F0dD32HHlAVT0zcGg0aDCYiI3j4c8Ph9aNC6m926G4Y7lb/NVWVDCR1HhCAQChIeH48aNG8KtAr169UK/fv3Qs2fPIrUERZGSlYuWG6VvnFkaqkw6VPxXI+LZY6mu09LSws+fP6X+EuTxeEhISCi16WhiYiLS0tLA4/GgpaUFbW1tqR6Fr9HQ0KjS4snj8ZCTkyN8ZGRklBAqcf8mJydDXV29zG7yhY8ZGxv/dR55Xl4eRo8ejbCwMKSmpgLIj7CIYtmyZVi7di2uXLmC3bt349HjJzC0tsXNoNtw6tsLn14+BhHw8fDhQ7Rq1aoiX4Zc+Lv+shRKS1paGoKCgoSenYGBAfr16wcPDw+0bt1aqi8ZHTUVTGxnjaP3Y6RahxBHQfr1pAWBaNCgAWJjYyW7jsPBokWLynXnz2QyheuDZcHlcpGWlobU1FSxj58/f+LDhw9iz+NyudDU1CwijGw2G0wmE0wmEwwGQ6J/JT2XwWAgNzdXKFRcLreIcBV/lPU8nU4Hm80Gm82GqqqqWCGrXbt2iWN6enologbVjWfPnsHJyQkJCQmg0+mlVhtis9kwMTEBAISFhSE9PR052VmIe/8StLR4fHnzFESQv12ib9++ePv2LYyNjSvkdcgLyuOjUBjR0dFCr+7Ro0do27Yt+vXrh759+8La2lqmsUV1ZygPxbszREZGokWLFhKVLFNXV0d8fLzCkhTkSV5eXglR5HK5JcK5kvwr6bmqqqpCoSoQrdIe4s5TVVX967yviuLNmzeYOXMm7t69CwAiu4wUR1NTE0eOHMGwYcNgZ2eHmJgYcLlcsNlsDBw4EJcvXxa26KLT6XBwcMCDBw+q1N+IEj4KuUEIwbNnz3D+/Hlcv34dKSkp6Nu3L/r164du3bpJtA9JGor345MWOg1g0wUIdO8Kc93/JcKcOnUKkydPLlX82Gw23N3dsW7dunLZTkFREbi5ucHT01Oqa7S1tXHlyhXUr18fJiYmRcSSzWaXCI9yOBxMmDABu3fvlovNFUHVSMGhUFoIIXjz5g2WLl2KOnXqYNSoUVBRUcGpU6cQFxcHT09PDBw4UO6iBwBmOhxcn9EOFnoccFjSvZU5LAY0aVxE7Z6Advb1cebMGWH4Z8yYMRg9enSZIcx58+aV23YKCkXz6tUr+Pv7w8nJCWw2W+LrBAIBjIyM4ObmVmJdWNSaYHZ2No4ePYpz587JbHNFQXl8FOUiKioK586dg7e3NzIyMjBixAiMHDkS9vb2FZ5EkcsTwCM4Cp73YspMv6YLeGCpqMCtvQ0G1GKhgZ0t8vLyoKGhAQ6HgyVLlsDNzQ0sFgsODg549+5difJPDAYDLBYLo0aNwurVq2Fhobw1CSmqJyEhIRgxYgT27t2LYcOGYciQIbh06ZJE16qqquLSpUsYMGCAVJ1H1NTU8OTJEzRo0KC8ZlcYlPBRSMyXL1/g7e0Nb29vxMfHY/jw4Rg5ciRatmwJOr3ygwcpWbnwDv+OPb7hyKSrAQI+WEwG6AwmsnJyYcgmiLp5Aq4dbeGxeQMIIdDS0hI27ATyP7x0Oh2zZs3CsGHD0LFjxxKFqdlsNl69eoXjx4/jwIEDcHV1xb///gt9ff2KfskUFCW4cOECpk+fjvPnz6NTp04AgMzMTMyZMwdHjhwpc52PRqPBzMxM4iSvwpiZmSEyMhLa2hJWS6osCAVFKcTFxZGdO3eSVq1aEQMDAzJ58mQSEhJCeDxeZZsmli5dupAbfn6k/+gJZKfXeXL0/HUCGp00aNCAACBMJpMsWrSICAQC0q5dOwKgxIPNZhMOh0N69uxJ2Gy28DiLxSJubm7CuX78+EGmTJlC9PX1ybp160hGRkYlvnKK6s7u3buJmZkZefnyZYnnkpKSiKWlJVFTUxP5ni/8HudwOKWeI+6hqqpKunXrRvh8fiW8esmhhI+iBElJSWT//v2kY8eORFdXl7i4uBB/f3+Sm5tb2aZJhKGhIYmNjSWDBg0iPj4+5J9//hEKHo1GIwCImpoamT17NlmxYgVhMpliP8hMJpMwGAzCYDCEgvjt27cSc0ZFRZHhw4eTGjVqkP3791eZ3xXF38PGjRtJ7dq1SUxMTInncnJySIcOHYi7uzvh8/lkxIgRYt/zBZ+R8j7U1NTIqlWrKv4XIAWU8FEQQgjh8/kkODiYjBo1imhra5MRI0aQq1evkpycnMo2TSoSEhKIrq4uEQgExMnJiVy5coXo6OiI/YD26dOHaGpqSvyhtrW1LXX+p0+fkm7dupE6deoQb29vpb/zpaj6CAQCsnr1amJra0vi4uJEPu/s7EwGDx4sfD+6ubmRXr16ERUVFZlETtyDw+GQgICAiv5VSAwlfNWcuLg4sn79emJjY0MaN25Mdu/eTZKSkirbrHJz69Yt0qFDB0IIIb169SI7d+4kGhoapd6dSnKHy2QyCZPJJFeuXJHIjqCgIOLg4EAcHBxIUFCQIl8yRTVGIBCQpUuXkgYNGpCfP3+KPGf58uWkZcuWJDMzkxBCyM2bN0nNmjVJamoqiY+PJ/Xq1SNqamqlRj6keRR8VoYPH16RvwqpoISvGpKbm0uuXLlCnJyciK6uLpk8eTJ5+vQpEQgElW2azOzYsYNMmzaNEEJIt27dyKhRowiLxZI5dNOiRQuSmJgolS18Pp94e3uT2rVrk379+pFPnz4p4iVTVFMEAgFZsGABadKkidj3ppeXF7G2tiYJCQmEEEJSUlKIhYVFkZuxvLw8kpKSQtq0aUMAEDqdTgAQDQ0NqaIhdDqd6OnpkZ49eyr9zTMlfNWIjx8/ksWLFxMTExPSpk0b4uXl9dclY4wfP57s37+fEEJIp06diJmZmcyiN23aNJKXl1dum3JycsimTZuIvr4+Wbp06V/3O6eoeAQCAZk9ezZxcHAQKzK3bt0iRkZG5N27d8JjEyZMIFOmTBE77q9fv0hoaCixsrIiz549I7t27RIKoaiHu7s7UVdXJ6mpqXJ/jYqEEr6/nKysLHLq1CnSqVMnYmhoSNzd3cnbt28r2yyF0bx5c3Lv3j1CCCGOjo4yeXs0Go0cOnRIbrbFxsaSUaNGEUtLS3L+/Pm/wsOmqHj4fD6ZOnUqadmyJUlOThZ5TmRkJDE0NCR37twRHvPz8yNWVlYkLS2t1PH37t1LXFxcCCGE3Lhxg3Tp0oVkZGSQFy9ekK9fvxKBQEBSU1MJh8MhqampRF9fn8THx8vt9VUElPD9pURERJAZM2YIQw8XLlwgXC63ss1SKHw+n6irq5OUlBRCCCFWVlZFtiJII3iGhoakX79+xNXVVe523rlzhzRs2JB06dKFREZGyn18ir8XPp9PJk6cSNq0aSPWy4qPjydWVlbk5MmTwmPJycnEwsKCBAcHlznHyJEjydGjRwkhhHh4eAiXDopTr149EhERQdq1a0du375djldTeVT+rmMKuSEQCODv748ePXqgW7du0NXVxbNnzxAQEIChQ4dCRaVq9cySlpiYGOjp6Qk3z/7+/Vts25XSIIRg0aJFOHv2LO7fv48zZ87I1c6OHTvixYsXGDhwIDp27Ih58+YJ28RQUIiDz+dj/PjxiIqKws2bN6GlpVXinMzMTDg5OcHV1RVjxowBkP9+njRpEgYOHIguXbqUOgchBGFhYWjfvj0A4PPnz7CxsRF5roWFBb5//w47Ozu8e/dOxldXsVDC9xeQlZWFAwcOoEGDBvj333/h7OyML1++YM2aNbCysqps8yqMN2/eoFGjRgDyfyeZmZlSj1G/fn2EhYVh3rx50NDQgLe3N2bPno1Pnz7J1VYmk4mZM2ciMjISaWlpsLW1xfHjxyEQyK/HIMXfA4/Hw9ixYxEbGws/Pz+RtW/5fD6cnZ3RoEEDLF++XHjc09MTUVFR2Lx5c5nzfPnyBXw+H7Vq1QKQL3wF/y+OhYUFYmNjKeGjqFji4uKwZMkS1KxZE/7+/ti/fz9evHiBcePGQVVVtbLNq3AiIyPRsGFDAMCtW7ckrhlKp9NhaGiIEydOIDIyEu3atRNe27RpU6xYsQKjRo1Cbm6u3G02MjKCp6cnrl69ir1796Jdu3Z4/vy53OehqLrw+XyMHTsWSUlJuH79OtTV1UWe5+7ujrS0NBw6dEj4/o2MjMSSJUvg7e0tUaHqAm+v4HpJPD5bW1tK+CgUT3h4OJydndGwYUOkp6fjwYMHuHr1Kjp16lSlu2zLSlRUFOrVqwcAOH/+fBHvicFgFDlXX18fgwcPBpPJhKurK378+IF//vlH5LgzZsxAjRo1sGTJEoXZ3qJFCzx69AgTJkxAnz59MGXKFCQlJSlsPoqqASEEU6dOxc+fP3H58mWxHUN2796NwMBAXLx4UbikkZ2djREjRmDz5s3Cz0VZPHnyRNhRnRCCmJgYsb0zq3Kok0puqSLweDxy8eJF0q5dO2JpaUm2bNkiNqOrutKmTRsSGhpKCCGkcePGhE6nk2bNmpE5c+YQe3t70rBhQ8JgMIR7mgghxMnJiejp6ZVZYeX379/EwsKC+Pr6KvQ1EELInz9/yMyZM4mhoSE5ePAgVf2lmiIQCIi7uztp2bJlqZmYV69eJaampiVKlU2ZMoWMGjVKquzhli1bCj9DP378IIaGhmLP9ff3J927dyd8Pp+oqakJk8qqApTwKTmpqalk+/btxMrKirRu3ZqcP39epj1lfzNGRkbCkk0CgYBYWFiQr1+/FjnHxsaGfPjwQfizv78/UVdXJ/7+/mWOf/fuXWJiYiKyLJQiePXqFWnRogXp1KkT+fjxY4XMSaE8rFmzhjRq1KjUzeDh4eHEwMCAPH78uMhxHx8fUqtWLan21+Xm5hI1NTWhyN67d4+0bNmy1Lnt7e0JIYTY29uTR48eSTxXZUOFOpWUX79+YfHixbC2tsaTJ09w7tw5PHjwAMOGDQOTyaxs85SOtLQ0ZGRkwNTUFEB+a5W8vLwSvysrKyvExMQIf+7atStoNBp27txZ5hzt27fH1KlTMW7cuDJbu8iDxo0b48GDB+jXrx9atWqFbdu2legNSPF34uHhgZMnTyIwMBB6enoiz/ny5Qv69++Pw4cPo0WLFsLjX79+xdSpU3H27FmRmZ/iePv2LWrWrAlNTU0AwKdPn8QmtgCAgYEBfv/+DQBVLtxJCZ+SkZCQgAULFqBevXpIS0vD8+fPcfbsWbRs2bKyTVNqPn36hNq1axdZ4+Tz+SXW9qytrfHlyxfhzywWC/3798fdu3fx48ePMudZsmQJUlNTcejQIbnZXhoMBgPu7u549OgRbty4gTZt2iAyMrJC5qaoHI4ePYrt27cjKCgIJiYmIs+Jj49H9+7dsXjxYgwcOFB4nMfjYfTo0Vi4cCGaN28u1bzh4eFwdHQU/vz27VvUr19f7PmU8FHIzI8fPzB37lzY2dmBy+Xi9evX2LdvH2rWrFnZplUJCoSvMEwms4SHZG1tXcTjA4DBgwdDX18fR48eLXMeJpOJY8eOYdmyZUUEVNHUrl0bwcHBGD9+PDp16oQ1a9YoJMuUonK5cOECli1bhqCgILGf/aSkJPTo0QPjxo3DzJkzizy3atUqaGpqYt68eVLPXVz4IiIiSu2mrqamBkIIsrKyKOGjkI7Y2FjMnDkTDRs2BI1GQ2RkJHbt2gVzc/PKNq1KIU748vLyihwrHuoEgO7duyMpKQmHDx+WKJRYv359zJ8/HxMmTKjQfXd0Oh2TJ0/G8+fP8fjxYzg6OiI8PLzC5qdQLP7+/pgxYwb8/f1Rt25dkeekpaWhd+/e6N27N5YuXVrkudu3b8PLywvHjx8HnS79V3tx4Su8PUgUNBpN6PVRwkchEd++fcO0adPQuHFjsNlsvHv3Dtu3bxeuUVFIhyjhY7FY4PF4RY4VD3UCgJaWFtq1awcWi4WbN29KNJ+7uzsyMzNx8OBBmewuDxYWFrhx4wYWLVqEvn37YuHChcjOzq5wOyjkR2hoKMaNG4erV6+iSZMmIs/JysqCk5MTHBwc8N9//xUJ6//8+RNjx47F8ePHYWxsLPX8XC4XkZGRaNq0KQAgIyMDv379EruVoYAC4atduza+f/9erkpJlQElfBVMTEwMJk2aBHt7e2hra+PDhw/YsmVLud6sFP/j06dPqFOnTpFjTCZTpPAV9/gAwMnJCaamptixY4dE8xWEPJcvXy5yPEVDo9Hg7OyMN2/e4OvXr2jSpAnu3r1b4XZQyE54eDiGDRuGs2fPCvfQFSc3NxdDhw6FhYUF9u7dW0T0cnNzMWzYMEycOBHdunUrlw0RERGoXbs21NTUAOSv79WrV6/EGnlxCoRPRUUFVlZW+PjxY7nmr2go4asgoqOjMWHCBDg6OsLIyAhRUVHYuHEjDA0NK9u0v4KPHz+KDHUWFz4TExOkp6cjIyOjyHEnJye8f/8eb9++xatXrySa09bWFosXL8b48eMrrdSYkZERvL29sXnzZowaNQrTp09Henp6pdhCIT3R0dFwcnKCp6cnunbtKvIcHo8HZ2dnqKiowMvLq0QYc968edDV1cWKFSvKbYeo9b3SwpwFVNUEF0r4FMy3b9/g6uqKli1bwsLCAp8+fcK6deugr69f2ab9NWRkZCA1NRU1atQoclzUGh+NRkPNmjVLhDutrKxgYmKC/v37Y/v27RLPPXfuXHC5XOzbt6/c9suDgQMHIiIiAjk5OWjYsCGCgoIq1R6Ksvnz5w/69OmD5cuXo3///iLPEQgEcHNzQ0pKCs6dOwcWi1XkeS8vLwQFBeHkyZPlWtcrQNT6XmmJLQVQwkdRhJSUFCxatAj29vYwMzPDp0+fsGrVKujq6la2aX8d0dHRsLGxKfHBF7XGB4he5wPyvT42m43r169LtLUByN9u4OXlhVWrViE6Orpc9ssLXV1dHDlyBJ6enhg/fjzmzZsHLpdbqTZRiIbL5WLgwIHo378/pk2bJvIcQgjmzp2LqKgoXLlypUStzadPn2LRokW4cuWKsCNJeaGEj0ImuFwudu7cibp16+LPnz948+YN1q1bBx0dnco27a9F1PoeIDrUCYhf5+vXrx9u3boFZ2dn7N69W+L569WrhyVLlsDV1VUpuit0794dL1++xJcvX9CyZUu8ffu2sk2iKIRAIICrqyuMjY3x33//iT1vxYoVuHv3Lnx9fUsUpk5MTMSQIUNw8OBB2NnZyWRPdnY2Pnz4gMaNGwuPlbWVoQBK+Ko5AoEA586dg52dHYKDgxESEoLDhw+XCL9RyB9RGZ2AeOETtaUBAFq2bImEhAQMHToUhw8fLrEOWBqzZ8+GQCCQSjAVib6+Pi5evIjp06ejY8eO2L9/f4VUm6Eom+XLl+PLly84ceKE2PDk5s2b4ePjg8DAwBI3zXl5eRg+fDjGjRuHQYMGyWzP69evYWtrK/QoU1JSkJKSItEe4sLCZ2tri48fP1aJ6kKU8MmBO3fuoGXLlti2bRuOHDmC69evS3S3RCEfRCW2AKV7fKJCnQwGA3369MGbN2/QqVMneHl5SWxDQchz7dq1SpPZRqPR4Obmhnv37sHT0xMDBw7Er1+/Ktusao2npye8vb1x9epVsZ0WDhw4gAMHDiAoKEhk8tv8+fOhrq6O1atXy8UmcRVbJFkzLCx8Ghoa0NPTQ2xsrFzsUiSU8MlAZGQk+vXrh/Hjx8Pd3R2PHz9G586dK9usakdpHl/x5BZAfKgTyF/nu379Otzd3bFz506p7l7r1KmD5cuXY8KECUrlXdWrVw8PHz5EvXr10LRpUyrxpZIIDAzEsmXL4OfnJzab+9SpU1i3bh2CgoJEFrE4ceIE/Pz8cPr0aZmSWQpT3vU9IF/4Ct9MWVpa4vv373KxS6FUaonsKkpsbCyZMGECMTQ0JDt27CA5OTmVbVK1xszMjHz58qXE8V69ehE/P78Sx3/9+kW0tbVFjpWWlkY0NTVJWloaad26NfHx8ZHKFh6PRxwdHcmxY8ekuq6iuHXrFjEzMyPz5s2j3rcVyKtXr4ihoSEJCwsTe87ly5eJsbExiYiIEPl8QScGcc+Xl4YNG5Jnz54Jf541axbZsmWLRNfGxsYSExMT4c/Dhw8np0+flqt9ioDy+KQgLS0Ny5YtQ+PGjWFgYICoqCjMmTOnWnY7VxaysrKQlJQECwuLEs+JC3Xq6+uDz+cjJSWlxHOamppo3bo1AgMD4e7ujm3btkllD4PBwP79+7Fo0SL8+fNHqmsrgq5du+LVq1eIiYlBq1atqkwyQlUmLi4O/fr1w65du9CuXTuR5wQFBWHSpEnw9fUV6W39+vULQ4YMwYEDB+S6jJKZmYno6Ogie/bKKlVWGAMDAyQlJQkjHFXF46OETwIEAgGOHTuGevXqITY2Fi9evMCmTZuoTE0lIDo6GtbW1iLDPuKEj0ajlRru7NevH65fv46BAwciISEBDx8+lMomR0dHDBkypEQtRWWhIPFl6tSp6NChAw4cOKBUodm/ifT0dPTr1w/Tpk3DyJEjRZ5z//59jB49GhcvXoSDg0OJ57OzszFgwACMGTMGQ4YMkat9L1++RMOGDYVd2wHpQp2qqqpgs9lIS0sDkF9O79u3b3K1URFUO+HLzs7GhAkTRN7ti+LVq1fo0KED9u3bh+vXr+PYsWOwtLRUrJEUEiNufQ8Qv8YHlL3O5+fnBwCYM2eO1F4fAKxbtw5XrlzBkydPpL62IqDRaJg0aRLCwsJw6NAhDBo0SJikQCEfBAIBxo4dCwcHByxatEjkOQ8fPsSgQYNw8uRJtG/fXuQY//zzD6ytrbF27Vq521h8fS8pKQlZWVlSFckvnOBCeXxKyn///Ydjx45h6tSppZ6XmpqKOXPmoHv37hg7diwePnxY5A1CoRyUJnziNrAD+VsaxLUVsrKygrGxMZ48eQJXV1fcuXNH6s3purq62Lx5M6ZMmaLU6d22trZ4+PAh6tSpg6ZNm1L1PuXIhg0bkJCQUKK2ZgGhoaHo378/jh8/jl69eokcY9GiRUhMTMTRo0dFjiErohJb6tevL9VchYWP8viUkB8/fmDLli0QCAS4du2a8K6+MIQQnD59GnZ2dsjIyMDbt28xadKkMou1UlQO4javA+JDnUDpHh/wv+xODQ0NTJkyBZs3b5batjFjxkBLSwv79++X+tqKRFVVFVu2bMGRI0cwbNgw7Nixgwp9yoivry/2798PHx8fkTkAt27dwtChQ3Hu3Dn07t1b5BgFUaYrV64oLI9A2lZEoigufFXB46tWWZ1Dhw4lLBaLACAAiJ6eHklJSRE+HxERQTp27Ejs7e3Jw4cPK9FSCknp0qULCQwMFPmcq6srOXLkiMjnrly5Qvr27St23AcPHpCGDRsSQgj5/fs30dfXF5k5WhaRkZHEwMCAxMfHS31tZRATE0OaNWtGRowYQdLT0yvbnCpJVFQUMTQ0JPfu3RP5/I0bN4ihoSG5e/eu2DFu3LhBTE1NSXR0tKLMJKmpqURdXZ3k5eUJj02fPp3s2LFDqnH++ecfYRazQCAgbDabZGRkyNNUuVNtPL4nT57A19e3yJpPZmYmpk2bhvT0dCxYsACdOnXCsGHD8PTpU7HtQSiUi0+fPqFWrVoinyttjU9c9ZYCWrRogcTERHz58gX6+vqYMmUK1q9fL7V99evXx4QJE+Du7i71tZWBlZUV7t+/D3V1dbRs2RIfPnyobJOqFOnp6Rg4cCDWrFmDtm3blnj+8uXLGD9+PK5duyZyTQ8Anj17BldXV1y+fBk2NjYKs/XFixdo3LgxmEym8JikpcoKU9jjo9FoMDc3V3qvr1oIHyEEEydOLNGsk8vlwsfHB9bW1vj16xciIiIwffp0KqxZRRAIBIiPj4eZmZnI58ta4/v69avYsQuquFy/fh1AfheGixcvil0XLI3ly5fj/v37uH37ttTXVgZsNhtHjhzB3Llz0b59e1y+fLmyTaoSEELg4uKCNm3aYPLkySWeP3fuHKZOnQp/f3+xN9bfvn3DgAEDcODAAbRs2VKh9hYPcwLSZXQWUFj4gKqR4FIthO/MmTP4/PmzyOdyc3ORl5cHDw8PqhlsFePPnz/Q0NAQu/5R2hqflpYWeDwesrKyxI5fsK0ByN8CMHXqVGzYsEFqO9XV1eHh4YFp06YhNzdX6usri4kTJ8LX1xdz587F4sWLxf4uKfLZtGkT4uLisGfPnhLJIcePH8e8efMQFBSEZs2aibw+NTUVffr0gbu7OwYPHqxwe4sLX2JiIvh8PkxNTaUap7jwVYUElyolfDy+AF9+Z+LDz3R8+Z0JHr/sSviZmZmYPXs2MjMzxZ7D5XIxY8YMeZpKUQHEx8eX+iEtTfhoNBoMDQ1LrV3Zo0cPPHz4UNjYVRavr3///qhTpw62bt0q9bWVSfPmzREeHo7nz5+jZ8+eSExMrGyTlJKAgADs3r0bFy9eLHEjdujQISxduhTBwcFo1KiRyOtzc3MxZMgQdO7cGXPmzKkAi0U3n23QoIHU2aOihI/y+GQkOTMXB0Kj0W1HKOxWBqDP7jAMOfAAfXaHwW5lALrtCMWB0GikZIm+k96wYUOpd/VAvvBdunQJgYGBingJFApCEuETt8YHoEzh09TURJs2bYTvC1m8PhqNhl27dmH79u3lEs7KxMDAAP7+/mjdujUcHR3x+PHjyjZJqYiOjsa4cePg7e1dIuy+e/durF+/Hnfu3BHbPogQgsmTJ0NNTQ07d+5UyLaF4iQnJ+Pnz5+oV6+e8Fh5wpwAFeqUK7k8AbbcfI9Wm4KxMzgKnxIzkMcnyMrlI4PLQ1YuH3l8gk+JGdgZHIWWG4Ox5eZ75PL+5wV+//4dO3bsKLG2J4qsrCw4OzsLKxBQKD+yeHxA2cIH/G9bQwEFXl9piTHisLa2xsyZM7FkyRKpr61sGAwG1q1bhz179sDJyYmq9vL/ZGRkYODAgVixYkWJZJUtW7Zg586dCA0NFbvXlBCCBQsW4O3btzh79myF5Rc8f/4c9vb2ReYrz1YGgAp1yo24lGz02BmKo/djwOUJkJNXekgzJ08ALk+Ao/dj0GNnKOJS8oVu5syZEq+pMJlMpKSkYOPGjTLbT1Ex/Pz5s1ThKy25BZBc+Pz8/ISb0GXx+oD8ljKhoaFKW9GlLPr374/79+9j7969cHV1leim8m+FEIJJkybB0dGxSBd1QgjWrl0LT09PhIaGwsrKSuwY69atw82bN+Hv71+i2awikVdiC1A1PT5m2adULHEp2XDacw+pWXngF7qjzPr0FOnh15CX9A2C7HQw1HWhYlIbWi0GQtUsP4SQnSfA9z/517s3yMO1a9eEd6UqKirCRotcLheEEBgbG8PS0hJ169ZFvXr1YGVlJTbFmEL5iI+PL7V8HJPJRE5OjtjnJRG+mjVrwsTEBI8fP0abNm0A5Ht9devWxZIlS2BtbS2Vzerq6lizZo1QACsirCVv6tSpg0ePHmHSpElo06YNLl++XOqX+9+Kl5cXXr9+jadPnwr/joQQLFu2DFevXkVoaChMTEzEXu/h4YETJ04gLCwMenp6FWU2gHzhK9zElhBSrq0MAKCnp4fk5GTw+XwwGAyhx0cIUdr3t1IJXy5PAGfPRyVELznEC2mPL4LO0YJanVagq2mBl/wDWR8fI+vDA+j3mweNhvl98PiEIDUrD6vDkqGprYPGDRugQYMGqFu3LqysrFCzZk1YWVlBT09Paf8oFJIRHx9fasp3WWt8RkZGEiVrFGR3FghfYa/v8OHDUtvt4uKCnTt34tq1axgwYIDU1ysD6urqOHXqFHbt2oU2bdrg0qVL1Wrv67t377Bo0SLcuXNH2FCWEIL58+fj9u3buHPnDgwMDMRe7+Xlhe3bt+Pu3buliqOiCA8PL7IvNT4+HkwmE0ZGRlKPxWQyoaWlhZSUFOjr60NTUxOqqqr48+cP9PX15Wm23FAq4fMIjkJCWk4R0eNnJCPtyWXQ1XVQY/weMNR1hM/lfH2NhLNLkBp2Sih8QL74qWjoY7n3Q8zvUQ8UfyfyWOOTpFu6k5MT3NzcioTBZfH6GAwGtm7dilmzZqFPnz5gsVhSXa8s0Gg0zJ49G7Vr10b//v2xe/dujBgxorLNUjg5OTkYOXIk1q9fL/SQBAIBZs6ciadPn+L27dvQ1dUVe/2FCxewdOlShISEoGbNmhVltpDfv3/jz58/RdYdy7u+V0BBuLNA6AoyO5VV+JRmjS85Mxee92KQXWw9j5eWCBABVE3rFRE9AGDXbAyaCgf87JIJKdl5fBwO+yw225Oi6lOW8MljjQ/4XxWXwgktBV5feaq5AEDPnj1hZWWFQ4cOlet6ZaJv374ICgrCggULsH79+r8+6WX+/PmoV68e3NzcAAB8Ph+TJk3Cq1evcOvWrVJFz9/fHzNmzICfn1+RjMqK5NmzZ3BwcCjSyqu863sFVLUEF6URPu/w7xAVeWTq1gAYTOTGR4GflVrkuZxvESC52WDXbCJyTBotf1xJ+fPnD/bs2YMxY8ZIZTtF5VBWcos8sjqBfA+tb9++uHHjRpHj8+bNw9WrV8vdzHXLli1Yu3YtUlNTyz5ZyWnSpAkeP36My5cvw9XVtUpt1JeGK1euwNfXF4cOHQKNRkN2djaGDx+OmJgYBAQEQEtLS+y1d+/exdixY3HlyhU0bdq04owuhqjElvKu7xVQ1RJclEb4fJ7HiszeZHA0odvJFfzMFPzwnIYk/91IvnMMv65sQoL3crCt7KHfS/Tm85w8AXyexZY6L4/Hg5+fH/r27YsaNWpgwYIFuHbtmlxeE4XiyMjIAJ/Ph6ampthz5CV8QL5X4+/vX+SYnp4eFi1aJLbXWlk0btwYffv2xaZNm8p1vbJhamqK0NBQpKamokePHkhKSqpsk+TK9+/fMXnyZJw5cwY6OjpISkpC9+7doaKiAj8/P2hoaIi9Njw8HEOHDsXZs2fRunXrCrRatC3yyugsgPL4ygGPL8DXJPGVVbSaD4Dh4CWAgI+MVzeR9sgHWe/vgallAI1GXUuEQAvzJUl0hZd3795h7ty5MDQ0xMiRI+Hn5wcul4ucnJxSF6UplIOCMGdpCUqybmAvTMeOHXH//v0SQjpjxgy8efMGd+7ckWic4qxZswaHDh1S6i8JaVBXV8fFixfRokULtG7dWqI11KoAj8fD6NGjMWfOHLRu3RpfvnxB27Zt0aZNG5w+fbrUtkGRkZHo168fDh8+jG7dulWg1aIpLnyEELkLn6mpqVJX+VEK4YtNzgaLId6U1Ec++HV5I9QbdUWNKZ6wcPeBictOMHVM8Pv6ViSHHBV7LYtBR2xy/l6jlJQU7N+/H/Xr14eDgwP27t2LlJQUYUmqAsQVPaZQHspa3wPyt7BwuVyxz2trayMnJ6fULQ8FGBoawtLSEi9evChynM1mY+PGjZg/fz4EgrJL6BXHzMwM06dPx9KlS6W+Vlmh0+nYvHkzFixYgPbt2/8VzW3Xrl0LVVVVLFq0CC9evEDbtm0xffp0bN68uchaWXGioqLQs2dPbN26VSkyeH/+/InMzMwiCVnfv3+Hurq6TIkoxYVPT08Pf/78kclWRaIUwsflCUAXc+ee8/U1Uu4cA6dOS+h1dQNLxwR0FhuqJrVhOHgpGJr6SHtyBXkpP0VeT6cBt0PDMGDAAJiammLBggV49+4dsrOzxXoDlZFpRSEdkgiftrZ2qZV4JKnXWZhOnTohJCSkxPERI0aATqfj7NmzEo1TnAULFiA4OBjPnz8v1/XKipubG06dOoWhQ4fixIkTlW1OuQkNDcWhQ4dw8uRJBAUFoUePHti1axdmzpxZ6nXv3r1D586dsXr1aqXJG3j9+jWaNm1aJFIiq7cHUMJXLlSZdAjEZIJlRz8FALAtG5d4js5iQ8W0LkAEyP0ZLfL6rOwcTJ6Y3/8qJyen1GLVQP6Xobj+bhTKQ1mJLQCgo6ODlJSUUs+RRvg6d+4sMqRJo9GwdetWLFmypFyVTDQ1NbFq1Sq4u7v/dRmR3bp1w507d7Bq1SosX768XF5xZfL792+MGTMGXl5euHnzJsaNG4crV65gyJAhpV735s0bdO3aFZs2bcKECRMqyNqyef/+fYmaoZTwVRLmuhzkiem0QHj5XpkgS3TmW8FxGkP0lkQGSwUr588Am80uNSRRAJ1Ox71797B3714EBQXh69evVe7DWh2QxOPT0dEpM2NSGuHr0KGDyHW+gueaNWuGXbt2STRWccaPH4/ExMQSCTR/A/Xr18ejR49w69YtjB49WqLQsrIwdepUDBs2DOHh4Vi9ejXu3LkjssFsYV6+fInu3btj27Zt+OeffyrIUsl4//49bG1tixyTdQ8fUFLoKOGTACaDjpr6ouvUqVrk34mkvwoAL/13keeyo8PBjX0HGlMFquaiK59b6atj2dIleP/+Pdq3bw81NbVSbVFVVYWNjQ3evHmDDRs2oE2bNtDQ0EDjxo0xdOhQLFmyBMeOHcODBw/w+/fvv+4OvaoQHx9fZsULbW1tuXp8BgYGqFmzptiQ5H///YctW7ZIPF5hmEwm1qxZg1WrVv2V7ykjIyNhI97OnTsX8Q6UlfPnzyMiIgIpKSm4dOkSHjx4UEI0ihMeHo6ePXtiz549GDVqVAVZKjmihE/WrQwAwOFwitzQ6Orq4s+fP0r7XlYK4QOAoc3MwWaVNEfNti3YVk0hyEzBj8NT8fvGdiSHeCHRZw0SL6wGQKDTcRwYnJL7Z9gsOoY5mAPIX7cLCQnBoUOHoKWlBRUVFZF2MJlMzJgxAwcOHEBISAji4uKQmJiI48ePY9iwYeBwOAgODsbcuXNRu3Zt6Ovro1WrVhg7dizWrVuH8+fP4+XLl2WGVClkQ1KPT57CB+Sv84nL4Kxbty5GjRqFNWvWSDxeYQYNGoScnBz4+fmV63plh8Ph4MyZM+jUqRPat2+v1Pu8EhISMHPmTOjp6SEuLg6hoaFlvt8ePXqEPn364NChQxg6dGgFWSodxYVPIBDg3bt3qF+/vkzjstnsIsLHZrPBZDLLbAlXWShNybKRzS2w41ZUieM0Gh1Gw1Yh/bkvMt/dRVbUQ5A8LugcTXBqOULT0Qkca9EdjQkBhjtaFBqLBmdnZ/Tq1QvTpk3D9evXS6zJcLlc1KhRo8gxDQ0N2Nvbw97evtj4BL9//0ZUVJTw4e3tjQ8fPiA6Ohr6+vqoW7duiYeNjQ2YTKX51VdJJBE+TU1NZGZmgsfjif19l0f4Dh8+jIULF4p8fsWKFbCzs8PMmTNRt25diccF8sPsK1euxKpVq9CnT5+/spYsnU7Hxo0boa+vj/bt2yMwMFDq35M8+PLlCwYMGIAtW7agR48eRZ4jhGDChAmg0+moU6cODh8+XGZZuXv37mHw4ME4duwY+vTpo0jTy01qairS0tKKZK1//foVOjo60NHRkWlsNptd4ru0INxZkV0nJEVpvn111FQwsZ01jt4vWbaMxmBCq/kAaDWXPB2Yw2JgQjtr6KiV9Oz09fXh7e2N4OBgjBkzBqmpqcI/Go/Hk3gfX0FWoKGhYYm4P5/Px/fv34uIYmBgID58+IDExEQ0atQIzZo1Ez4aNGhQ6l4giqJIktxCp9OhpaWFtLQ0sdXvjYyMpGoR1LFjR7i4uCAvL0/kl6GhoSEWLFiAxYsX49KlSxKPW8CgQYOwevVqYVGFv5X58+dDV1cXHTt2hK+vL5o1E33zqigKPpODBg1Cly5dcPDgQeENr4eHBwIDA+Hu7o4NGzaUeQNy584dDBs2DKdPny4hosrEhw8fUK9evSK5DhERETKv7wElPT7gf8JnYWEh5qrKQ2mEDwBmd60L3zfx+P4nu0ihamlh0GjI/hOPl6fO4szvnmjWrBnq1q1bIrmla9eu+Pz5M5YsWYKDBw8iOzsburq6crnTZjAYsLKygpWVVYkPQ1paGl6+fInnz5/j7t278PDwQHR0NGxtbdGsWTPY29ujWbNmaNKkSZlrktWR3NxcpKamSnSDUhDuFCd80np8+vr6sLa2xvPnz8V2hpg1axZsbW0RFhYmdZur6uD1FTBhwgTo6uqiV69e8PHxQYcOHSps7sTERDCZTGRkZCAgIAB16tTBmjVrULduXbi7u2PhwoUS9eYMCgrC6NGj4e3tjS5dulSA5eXn/fv3JeqDyiOjEyhd+JQRpRI+FSYdpye2EtmPT1IYNBq01VhIub4XpyOe4ZLPBdDpdPB4PNSrVw9t2rRBmzZt4ODggHr16oHD4WDHjh0YN24cRo0aVWrZIXmhpaWFDh06FPmgZ2Vl4c2bN3j+/DmeP3+Oo0eP4t27d7C2ti7iGTZt2hTa2toKt1GZSUhIgKGhoURZutra2qVmdkorfMD/1vnECR+Hw8H69evh7u6OR48eSWRnYaqL1wcAgwcPhpaWFoYMGQIvLy/069evQuZNTEwU1hPl8Xjg8XhYunQpuFwuOnfuLJHo+fv7Y+zYsbh06VKV6OP54cOHEoktz58/h5OTk8xjVzXhU5rklgLMdDi4PqMdLPQ44IhIdikNDosBS73864/v2yGMO2dmZoLL5eL169c4cOAApk2bhpYtW0JNTQ0NGzbE5MmT8fLlS/j4+CAwMFBBr6x01NTU0LJlS0ydOhWHDx/Gs2fPkJKSgtOnT6Nz586Ijo7Gv//+CzMzM9SuXRvDhw/Hpk2bEBgYWK4swqrMz58/Je5hVlaCS3mFT9RG9sKMHj0aDAYDR44ckWpsoKjXp6xZcfKkW7duuHHjBiZOnIjTp09XyJw/fvwoUUi7oMrPo0ePMGbMmFJrjZ46dQouLi64du1alRA9QHRG55MnT0rtaSkpBcJX+P1akNmpjCid8AH54hc4pyPGt7WGKpMuMtuzMGwmHYSXi0H1tRE4tyPMdDho37692NTjjIwMZGRkIDc3F5GRkTh06BCmTp2KZs2aic32rAxUVFTQtGlTjB8/Hnv27MGDBw+QmpqK69evY8CAAfj16xc2btyIOnXqwNLSEgMHDsSaNWsQHBz8V2eVpqamSrwYX5bw6evrS11MuUOHDnjw4EGpdUDpdDr279+PpUuXluvGZNCgQeByufD19ZX62qpIy5YtERwcjMWLF2P37t0Kn6+0jNLs7GxcuHAB1tbW8PT0LLGPt6BYwe3btyu94LQ0FBe+hIQEpKamFunLV14YDEaJ2riUx1cOVJh0LOhpi8f/dsXcbnVRx0gDLAYNaioMaKgyoabCAItBQx0jDczrXhcT9D/j9an1RWp+btq0SeKMIjqdDg8PD6XMQCoMg8GAnZ0dnJ2dsW3bNoSEhODPnz8ICQmBs7MzMjMzsWLFChgZGaF169ZYtGgRfH19y0zrr0qkp6eX2v6lMGUJn7q6utQp1/r6+rCxscGzZ89KPa9p06ZwdnYuV/eG6ub1AUCDBg0QFhaGXbt2YfXq1Qp93T9+/Cj1+dzcXKSnp2PWrFlo06YNCCEQCARwd3eHl5cX7t+/L5e1sYqCx+Ph8+fPqFOnjvDY06dP0bx5c6lD8eIoHu5UZuFTqjU+UeioqWByh1qY3KEWeHwBYpOzweUJoMqkw1yXA+b/C11uq5lo5HUIvr6+wnWRHj16wMzMDFFRJbdJFIbNZsPJyQmTJ09W+OtRBHQ6HbVq1UKtWrUwbNgwAPlrho8fP0ZYWBh27NiBkSNHonbt2sK1xfbt28PIyKiSLS8faWlppbYjKkxZwsdms5GbmwuBQCDVF0DBOl+rVq1KPW/16tWoX78+7t27h3bt2kk8PvC/tT5fX98KW/uqbKysrHDv3j307NkTf/78wY4dO+T2xVwYSfYQMhgMAPl/h7y8PLi4uODbt28ICwsTmyylrMTExMDU1BQcDkd47MmTJ2jRooXc5igQvoKbUj09PURHiy4lWdkorccnCiaDDisDddQz0YSVgbpQ9ID8sODOnTsxZ84cYayeRqNh48aNpSas0Ol0mJub4+jRo39VBp2amho6d+6MFStW4NatW0hKSsL+/fthZmYGLy8v1K1bF7a2tpg0aRJOnTpVpdriyNPjo9FoIvcglUVpG9kLo6Wlhe3bt2Pq1KmlhkZFUR29PgAwNjbGnTt38OzZM4wbN07q31tZXLp0qcz3u7q6Otq0aYPIyEhMmzYNffv2RVZWFoKCgqqc6AGiMzoVIXyFP0fK7PFVKeEri969e8POzg47duwQHhs4cGCp7TY4HA4CAgL++m0DKioqaNWqFRYuXIgbN24gKSkJ586dQ6NGjXD16lU0b94cVlZWGDt2LDw9PfHhwwel/bJNT0+X2OMrK6sTyL9JkDbcKck6XwHDhg2DqalpudauBg0ahNzc3Gqz1leAjo4OAgMDkZSUhCFDhpSr+HdxBAIBVqxYgTlz5gi9ueKoqqpCR0cHR44cQWhoKNTU1NCpUyfY2NjAx8eniMdUlSi+vkcIwZMnT9C8eXO5zVGVQp1/lfABwI4dO7BlyxbExcUByL9rXrdunUivj8lkVtutAQwGA02bNsXMmTNx4cIF/Pz5Ezdv3kT79u0RGhqKHj16wMTEBMOGDcPu3bvx6tUrpSnWLc9QJ5AvfNJ+serp6cHGxgbh4eFlnkuj0bBnzx5s2LABsbGxUs1T4PUpes1LGVFTU8OVK1egoaGBvn37ypSwlZaWhkGDBuH27dtiPXUOh4PRo0cjJiYGI0aMQHR0NNq2bQsnJyccOHCgSldbKr6VITo6GhoaGmUWgZAGSvgqkVq1amHKlClYsGCB8NjIkSNLJK2oqalhzpw5WL58Odq2bYuwsLCKNlWpoNFoqFevHtzc3HDy5El8/foVT548wYABA/DmzRuMGDEC+vr6GDx4MDw9PYU3FpWBPEOdQP4XXnlqCoprUySKunXrYvr06Zg7d67U8wwaNAipqal/RUNXaVFRUcHJkydRs2ZN9O3bFxkZGVKP8fHjR7Rq1QomJia4ffs2aDRakSpJampqsLGxQXBwMI4ePQodHR08e/YMHTp0wIIFC7Bq1aoqvwxS3OOTd5gTKFmoWpmFD+QvJCMjg1hYWJC7d+8Kjx04cICoq6sTAITFYpFWrVoRHo9HCCHk5s2bxNDQkBw/fryyTK4SxMfHk5MnT5KRI0cSPT090rRpU7JkyRJy7949kpeXV2F2jB07lhw7dkyic2/fvk06duxY6jlNmzYlz549k9qOK1eukB49ekh8flZWFrGxsSH+/v5Sz7Vv3z7i5OQk9XV/C3w+n4wfP560b9+epKWlSXxdQEAAMTQ0JPv37xcee/ToEVFRUSE0Go1wOByyfv16kpubK3w+MDCQGBoaksuXL8vzJVQq+vr65OfPn8KfZ8+eTf777z+5ztGhQwdy584d4c/p6elETU1NrnPIi79S+Agh5Ny5c6RJkyZCccvJySF6enoEANHX1yeJiYlFzo+MjCTW1tZk6dKlhM/nV4bJVYq8vDxy7949smTJEtK0aVOip6dHRo4cSU6cOFHidytvBg4cSC5evCjRuc+fPydNmjQp9Zw2bdqQe/fuSW1HUlIS0dDQIFwuV+Jr/Pz8SK1atUh2drZUc2VmZhJDQ0Py/v17ac38a+Dz+cTNzY20adOGpKamlnpubh6PLNm4g5jaNiPn/UJIHu9/n+lDhw4RAKRFixbk8+fPRa47ePAgMTY2LnLTXNX59esX0dHRIQKBQHisdevWJCQkRK7z9OjRgwQEBAh/FggEhMViSf1erwj+ulBnAcOHD4eOjg72798PIH/ReunSpWAwGLhx4wYMDQ2LnF+/fn08fvwYISEhGDlypFwW0/9mmEwm2rZti/Xr1+PFixd4/fo1unbtisuXL6NOnTpo1aoV1qxZg/DwcLmvDUoT6pSkJ195Q516enqoXbu2ROt8BfTu3RtNmzbFf//9J9VcampqmDx5cpHEreoGnU7HgQMH0LhxY/Ts2bNE0lJyZi4OhEaj67YQ1F3mi9NJltAZtg4rH+XAbmUAuu0IxYHQaNi3aoetW7fi0aNHsLa2BpBfVN7d3R3btm0rV41VZaYgzFkQrs3Ly8OrV6/g6Ogo13mKr/HRaDTo6ekhOTlZrvPIg79W+Gg0Gvbu3YvVq1fj58+fAIAZM2YgPDxc7N4rQ0NDBAcHg8VioVOnTsLrKMrGzMwMEydOxKVLl5CYmIgNGzYgNTUV//zzD2rUqAFXV1dcuHBBLhvppcnqlDS5pbx9w6RZ5ytgx44d2L17Nz59+iTVdTNmzIC3t3e1K1FXGDqdjn379qFZs2bo0aMHUlJSkMsTYMvN92i1KRg7bn1A9O8sEBoDYKoiK0+ArFw+8vgEnxIzsDM4Cs7nv0DQsC/y+PnJQhkZGRg8eDCeP3+Ohw8fFtnk/TdQfCvDmzdvYGNjI/e6xKK2Bcny2VIkf63wAfmVIMaPH4/58+cD+F8JsNJgs9k4deoU+vbti1atWuH169cVYOnfhYqKCrp06YJt27bh3bt3ePDgARwdHXHs2DFYWlqiY8eO+O+//xAREVGuTEVpsjq1tLSQnp5eqtdZnqzOAiTdz1cYCwsLLFmyBBMnTpTKGzY2NsaQIUOEUYzqSkGWbNu2bbFh53702BmKo/djwOUJkJMnQMarQMSfcMe37cPwbesQ/Dg6C2nh10AEfOTkCcDlCXD0fgx67AxF+LvPaN++PQwMDHDz5s0quUevLCoisQUQXahaRUWlRE1UZeCvFj4AWL58OcLCwnD79m2Jr6HRaFixYgU2bdqEbt26/bUdsSsKGxsbTJ8+Hb6+vkhISMCiRYvw/ft3ODk5oWbNmpgyZQquXbsmcbq6NKFOJpMJdXV1pKeniz2nvKFOAGjfvj0ePnwo9Yd79uzZyMvLw759+6S6bt68edi3b1+JL5jqBo1Gg/uK9bjFdMT3P9nCHp5JN7YjyX8XeCkJULdtD40mPQABD8m3DuH31f+EN1rZeQJ8/5ONEUefod+I/L2rylSnV54U38qgKOErntUJ5C8xFRQUUSb+euHT0NCAh4cHpk2bJvWX08iRI3H16lVMnDgRu3btqnb7qBQBh8NBnz59sGfPHnz+/FnYgdvDwwM1atTA8OHDcfHixVI9MGlCnUDZ4U5ZwjG6urqoU6cOnj59KtV1DAYDXl5eWLVqlVQhz/r166NZs2Y4deqUtKb+VeTyBHD2fISUrFxh+7KsqIfIjAwBU9sYNSbuhX6fWdDrPhmmrrvAqdMKWR8eIPNNsHAMPiEASx33mE3BE/y9n+3iHt/jx48rzONTVVWlPL7KYsCAAahTpw62bt0q9bWtW7fGgwcPcOjQIcyYMQM8Hk8BFlZPaDQabG1tMW/ePAQHB+Pz58/o3r079u/fD1NTUzg7O+Pq1atF7hgJIcjIyJBqfUIS4ZMlmak84U4gf2/f0qVLMX78eKlCnu7u7ti+fbvSFBSoDDyCoxCfko3CepX14QEAQKvFIDDU/leYgsZgQqfDGABA+rPrRcbhE4KfaVx4BH9UvNGVAJfLxffv31GrVi0A+csEX758kUvX9eKIC3VSHl8lQaPRsGvXLmzfvh0xMTFSX29lZYX79+/j06dP6NevX5klsCjKh76+Ptzc3HDr1i18+PABbdu2xY4dO2Bqaopx48bBz88PycnJ4HA4YktOiaKszE5ZQp1A+RJcCpg1axYIIVKVM+vSpQtUVFQQEBBQrjmrOn8yuTgY+glcflEvjZ+ZAgBg6pTs1VhwLDchGoKcopvgs/P4OBz2GSlZyueZyMqnT59gZWUFFosFAHj27BmaNm0q/FmeUB6fEmJtbY158+Zh5syZ5QpZamtrw9fXF7Vq1UKbNm3KJaAUkmNsbIxp06bhzp07iIiIgIODA9avX49atWpBIBAgMDBQYu9bkaFOIH+d79GjR+X6gBeEPNeuXYuPHyXzOmg0mjD1vrqRnp6OwfO3gieiRipdLX/dl5eaUOI5Xsr/MrTzkkqWjaPRAO/wsjs2VDUqKrEFoDw+pWX+/PmIjo7G1atXy3U9k8nEnj17MHnyZLRp0wYPHz6Us4UUoqhRowZmzZqF+/fv49KlS9DQ0MCyZctQo0YNTJkyBSEhIeDz+WKv19HRKdVLlzXUqaOjg7p16+LJkyflur527dpYsWIFXF1dS30dhRkxYgQ+fPiAFy9elGvOqsjLly/h6OiIRA0bgFkyEUWtVn7B5bQnV8DP/l8yExHwkRp2RvhzcY8PAHLyBPB5Jl0d1apA8a0Miha+4p8jKrlFCVBRUcG+ffswe/bsche8pdFomDVrFjw9PdG/f3+cPXtWzlZSlIampiYsLS3x5MkTPH78GNbW1nB3d4eZmRlmzJiBsLCwEmtfZXl8soY6gfKv8xUwY8YMMBgMeHh4SHS+iooKZs6cWS28PkII9u7di+7du2PZipXIUxVdWF6tfgewbRzAS4nHD8+pSPLfjT+3DiH+6Exkfw4HU7dG/oli+vt9ScoEj/93rZtWVEYnQG1nUGo6d+6M9u3bY82aNTKN07dvXwQHB2Px4sVYv349lfFZQRTO6LS2tsaiRYvw/Plz3L17FyYmJpg+fTosLS0xd+5cPHz4EIQQhYc6AaBt27Z49OhRua+n0+k4evQoNmzYgA8fPkh0zaRJk3Djxg38/v273PMqO8nJyRgyZAiOHDmCBw8eoH3PAWAxRH9t0Wh0GA1dAd3O48FQ10VmZAgyXgeBoWkA4zGbQefkv28Yajoir2cx6IhN/rsqNhUOdf748QNZWVmwsbFRyFzUdgYlZ9u2bTh69CgiIiJkGqdx48Z49OgRvL29MW/evGqdZVdRpKWlidzDV7duXSxbtgyvX79GYGAgtLW1MX78eFhZWSEsLKzU9TNZQ50A4OjoiPDwcJlugGrVqoVVq1bBxcVFopCnrq4uBgwYgGPHjpV7TmXm0aNHsLe3h7m5ubCiCpcnAL2UTgk0OgNaLQejxvjdsJx/CZbzLsB4xBqw9C2QlxgDGlMVLANLkdfSaTRweX/PZ5gQUiTU+fTpU7Ro0UJhnSYoj0/JMTY2xurVqzFt2jSZPTVTU1OEhobiyZMncHV1pbY7KBhJ9vDVr18fq1atwtu3b3H9+nWoq6vj0qVLaN68OQ4ePFhivU8eoU4LCwsIBAKZ2zVNmzYNbDYb27dvl+j8SZMm4dChQ39VxEEgEGDz5s0YMGAAdu7ciV27dgnbCKky6RCU47VmRoaA8HKhZtsONIbovnoCQqDK/Hu+EuPj48HhcITVaJ48eYKWLVsqbD5xWZ2Ux6dETJ48GdnZ2Thx4oTMY+nq6iIwMBCJiYkYMmRIta+qoUik2bxOo9HQuHFjTJw4EV26dMHatWsRFBSEmjVrwsXFBffu3QMhRC4eH41GE3p9slAQ8vzvv//w7t27Ms9v06YNVFRUZFpfVCYSExPRt29fXL16FU+ePMHAgQOLPG+uy0FeKetwAm7JGxhufBRS7hwDTYUD7XajxF6bxxfAXLdqdlgXRUVmdALUdoYqAYPBwP79+7Fo0SK5NEtUV1fH1atXweFw0Lt3b6SlpcnBSoripKenS11c18zMDD9+/ECvXr3g4+ODqKgoNGrUCG5ubrCzs4OPj49c9mY6Ojri2bNnMo9jbW2N9evXY/To0WXeLdNoNEyePBmHDh2Sed7KJiQkBM2aNYO9vT3u3LmDmjVrljiHyaCjpr66iKvzSTi3DD9PL8afwP1IvnMMiT5r8PPEfBB+HgwHLgZLxB6/Aqz01cEUs35YFSkc5hQIBHj69CmaN2+usPmo7QxVBEdHRwwdOhRLliyRy3gqKio4ffo0bG1t0aVLl2pdRV9R8Pl8qTffmpubIzb2f6nqRkZGcHd3x9u3b3HkyBF8/foVERERGDJkCPz9/SXeUlAceXh8BUyaNAk2NjZYuHBhmeeOGTMG/v7+Vfb9xufzsXLlSjg7OwsTfEr7Gw9tZg42S/RXl5ptW5DcbGRE3kHa0yvI/fUVGk16oMaEfeDYOIgdk82iY5iDucyvRZko7PF9/PgRenp6JdqxyRNx2xkoj08JWbduHa5du4bHjx/LZTwGg4F9+/ahV69eaN++Pb5///s2xVYmAoEAdDHp6OIwNjZGcnJyiQ8gjUZD27ZtsWbNGtSvXx89e/bEypUrYWVlhRUrVuDLly9SzePg4CBzgkth2zw9PXH16lVcu3at1HN1dXUxcODAKpnkEhcXh65du+LevXt49uwZevToUeY1Vvw4cLmiv0y1Ww6BqasHLOd6o+aCKzCfegT6vWaAqWNc6piEAMMdLcr1GpSVwlsZFB3mBCiPr0qho6ODLVu2YOrUqXJLTKHRaFi3bh0mTZqEdu3aSZyeTlE25RE+BoMBY2Nj/PjxQ+yYTCYTkyZNwpMnT+Dr64vU1FQ4OjqiR48e8Pb2lujDW6NGDTCZTHz79k0q+8Shq6uL06dPw83NrYjHKoqCcGdVSnK5cOECHBwc0K1bNwQGBsLU1FTkeVlZWXjz5g3OnTuHjh07on+vbrDK+QyOGK9PWpgQoLOpAAy+8n1By0Jhj68ihE/cdgbK41NSRo8eDR0dHalbxJTFvHnzsHr1anTq1Ekuaz8U5RM+oGS4s/iYhVO8GzduDA8PD8TGxmL8+PE4fPgwzM3NMXfu3FK3wMgrwaUwbdu2xaxZs+Ds7FwiBCsQCPDvv/8Ke0ey2WyEhITIbW5F8fv3b4wcORLLly/HlStXsGzZMnC5XLx+/RqXLl3Cpk2b4OzsDHt7e+jp6UFbWxutWrWCs7Mz7t69i7y8PMzsXAvGWmwwZEzNZ9BoyEv7hYMzB0BPTw+WlpYYOXIkDh48iBcvXiBPRGm0qkBmZiYSExOF66SUx1cUSviQ/4W1b98+rF27Vu6hSRcXF+zfvx+9e/f+azLvKpPiIiUp5ubmYrcaEEJEiimbzcbIkSNx69YtPH78GOrq6ujVqxdatWoFT09PkT3+5C18ALB48WIwmUysW7dOeCw1NRXdunXDrl27cOvWLfB4vCqR5HL16lU0btwYZmZmePHiBa5cuQJdXV1oa2ujXbt2cHV1xfLly3HmzBm8fPkSycnJ4PF4yMrKEu6T7dOnDwYP7I/TE1tBW41VbvFj0GjQVmNhSx9LqDAZ4PF4+P79O7y9vTF37lx07NgRGhoaaNSoEWbOnAlvb298+fKlSnjVUVFRqF27NhgMBrhcLiIiImBvb6/QOantDFUQW1tbzJo1C1OnTpX7G3vgwIE4d+4chg8fXuZ6DUXplNfjMzMzK9XjK2tMGxsbrFu3Dl++fMHy5cvh6+sLS0tLTJw4Ea9evRKeJ6/MzsIwGAycPHkSBw4cQGhoKN69e4cGDRrgwYMHyMrKgqqqKiIiIjBmzBgEBAQgMTFRrvPLg+TkZIwdOxbu7u44f/48tm3bBg6Hg0aNGiEnJwc8Hg/p6elIS0srdcmBw+Fg165dAAAzHQ6uz2gHCz2O1GFPDosBS73864f16Qpra+siz2dnZyM9PR25ubmIiIjAnj174Obmhvr160NbWxtdunRRyt9zAd++fYOVlRWA/BqnderUgbq6+GxYeUBtYK+iLFq0CF+/foW3t7fcx+7SpQt8fX0xadIkuewdrK7IEuoU5/FJMyaTyUTfvn1x+fJlvHv3DjY2Nujbty+6dOmC69evw97eXm4JLoWpUaMGjh49isGDB8PR0RE/fvwQ3knzeDw8evQIOjo6GDRokNIlufj5+aFRo0bQ1tbGq1ev0K5dO+Fzzs7O6N69u0Tdz1VVVfHPP/8Ie8sB+eIXOKcjxre1hiqTDsIr3btQZdBAeLnoV0cNgXM7wkyHAxqNhrVr15a5TSY9PR3Z2dnIyMjAx48foaamVqbNlUVsbCzMzfOzVO/evYsOHToofE7K46uiqKiowNPTE3PnzkVSUpLcx2/evDlCQkKwbNkyiYsRUxRFXFiyLMpa4yvPmCYmJliyZAliYmIwceJErFmzBp06dQIhROZyeKJsDA0NRVpaGrKysooIa3Z2tnBtb/LkyTh8+LBSlM9LTU3FhAkTMH36dJw8eRK7d+8W6XUcO3ZMIm+EwWBg/fr1JY6rMOlY0NMWXgNMkfnQG4yMRLAYNKipMMAED0wIwGLQUMdIAyMaaCB2z1jsduuBc2dOC8cYPHiwxIUR1NTUEBQUJPV+0ookLi6uwoWPyWSWWBNVVo8PhKIEc+bMIf/884/Cxv/69SupW7cuWb58OREIBAqb529k0aJFZNOmTVJfd/fuXdK6dWuRz4WFhZG2bdvKahoRCAQkLCyMmJqaEg0NDbJw4ULy7ds3mcdNSUkhnTt3JmpqagSAyIe5ubnQhsaNG5Pg4GCZ55WFoKAgYmlpSSZNmkTS0tLKPN/f35+wWCyxr09NTY2sXbu21DEGDx5MABAdHR2Sx+OT6MQ0omVhS9SMapLff5IJIYQ8efJE+HtUU1MjEyZMIFwulxBCyL59+4i6urpYGwAQDodDLl++LOuvR+H8888/xMvLi/B4PKKjo0N+/vyp8Dm5XC5hsVhFjp09e5YMHz5c4XNLC+XxiWDdunUICwtTWIdrS0tLhIWF4caNG5g5c6ZS3J1XFSo71FkaNBoN7dq1w7Rp0zBq1Cjk5uaiSZMmGDVqVLl79RVfzxNHQkICUlNTQaPR4OLiUmnh9IyMDEydOhWurq44dOgQDh48WKYnlZiYiGXLliEvLw8MBkPkORwOB+7u7mLHCAkJwZUrVwDkZzSmJP/BpxcPwU2MATcpFkv/XQwAyMvLE26Oz8rKwpkzZ+Dg4IDv37/DxcVF7PxAvqc3e/bsEmXUlJGCUGdERASMjY1hbFz6PkZ5wOPxSvz+Cv++lQlK+ESgrq6OgwcPYsqUKcjIKNm0Uh4YGRkhJCQEb968wZgxY6ps2nRFU96szho1aiA+Pl5kVRZ5CV8Bjo6OiI6Oxo4dOxATE4MWLVpgxIgRaNu2LXx8fCTeL3r79m04ODgUWc8TB4fDEWaTjho1ClevXi13z8nyEhoaisaNGyMnJwdv3rxBz549Sz2fz+dj06ZNMDc3R0JCAp4+fSryC1pdXR1btmwBhyO6jmZUVBT69+8vvIHkcDh49OgRtm7dCi6XCz6fjxMnTuDVq1clfvfZ2dl49+4dGjZsiPv378Pd3V3sPDY2NiJDrcpIgfBVVJgTyP97MplFC4BTwlfF6NGjBzp27Ihly5YpbA5tbW0EBAQgPT0dI0aMoMRPAsorUqqqqtDR0RGZiVdeMRWHg4MDnj17BoFAAG1tbcydOxcfP37EvHnzsHPnTtSuXRvbt28vsz6oQCCArq6uROtfWVlZePjwIYD8tcfWrVsLPSBFk5WVhdmzZ2P06NHYtWsXvLy8oKOjI/Z8gUCACxcuwNraGitWrMDkyZPx9etXODo64tKlSyWEx8TEBGPHjhU5VlJSEjp37lzkBjU9PR3Xr1/H3bt3hcdycnIwbtw4kZ8xPp+PtLQ09O/fv8T6aQFGRkZISkrCjh07lH47AyEEsbGxMDMzq1Dh4/F4lPD9DWzfvh3e3t4yNRgtCw6Hg4sXLyIvLw+jR4+m2hqVgSzembhwp7w9PkNDQ+jo6CA6Olp4jMlkYsiQIbh37x4uXLiA8PBwWFtbY86cOfj8+bPIcbp164Zv377h+PHjsLOzK1UAeTwegoODhT+PHTu2QsKdDx48QNOmTfH792+8efMG/fr1E3uuQCDApUuX0LhxY0yfPh1cLhchISHYvXu38PffsmVLzJ49W5gxqa6ujn379okMQebm5qJXr14lapQSQkqIPiEEnz59gr+/v1j7srOzsXv3bujr6xf5slZTU0NISAgeP36MY8eOYcaMGUr9OU1JSYGKigo0NDQo4RMDJXyloK+vj507d2LixIkKzUxSUVGBj48PMjMzMWbMGKX+UFU2soiUuL18pJyZoqVRULdTFM2bN8eZM2fw+vVrsNlstGzZEoMGDcLdu3dLeBMMBgODBw9GZGQk/Pz80KFDB3A4HJH2Pn/+XHj9gAED8PTpU7Fl2mQlJycHCxYswJAhQ7Bp0yacPn1a2PetOIQQXL16FQ4ODli2bBmysrLQoUMHvH//Hm3bti1x/po1a1CzZk3QaDQ0adJEZP1OQgjGjh2LyMhIkV5cYmJiifBwZmYm9u/fX6rHlpWVhV+/fgnHVFNTw4kTJ1C/fn1YWFjg3r17+PjxIwYOHKiwZRBZKQhzRkVFgc1mw9JSdONdeUMJ31/E8OHDYW1tjY0bNyp0HlVVVVy6dAnJyckYN25cuTsE/O3I6vGJEj55e3yAZBVczM3NsWnTJnz58gU9evSAm5sbHB0dcerUKZEFtTt06IDQ0FA8fvwYgwcPBpvNLvKlkpubK6wTyuFwMGjQIJw5cwYAwOML8OV3Jj78TMeX35ngldLTrizCwsJgb2+PL1++4PXr1xg8eLDI8wghuHHjBhwdHbFy5Up06NABv379wsKFC3HhwgXo6uqKvI7FYuHSpUvQ0NDA3r17RZ6zbt06XL9+Xeo+inl5eWVeU/h3P3DgQAwZMkT4s7a2Nnx9fWFsbIwOHToo7MZCFgrCnGFhYRXm7QGik1tEiaEyQAlfGdBoNOzfvx979uxBZGSkQudis9m4cuUKEhMT4erqSomfCGTxzioq1AlIV7pMXV0dU6dOxbt377BmzRocO3YM1tbW2LJli8iyaI0aNcKFCxfw4cMHuLm5gcPhgMlkgsvl4t69e8Lzhv/jiotv09BtRyjsVgagz+4wDDnwAH12h8FuZQC67QjFgdBopGRJFs1ITk6Gm5sbRo0ahXXr1uH8+fMi29wQQuDv74+WLVvi33//xdy5c9GoUSMEBQXh9u3bmDJlSplrqra2tkhKSkLTpk1LPHfhwgVs3Lix1CxXceTl5ZW5lq6qqgpVVVXUr19f5H5bFosFT09PDBkyBK1bt5b7nk1ZqYzEFoBKbvnrMDc3x5o1azBx4kSFixGHw8HVq1cRGxuLiRMnUlsdiiFLIoq4UKcihM/BwQEvXryQ6u9Hp9PRt29f3Lp1C35+fnj+/DlsbGywevVqkc2SLS0tsXfvXsTFxWH58uXC0ma5PAG23HyPWcHpSDZvjU+JGcjjE2Tl8pHB5SErl488PsGnxAzsDI5Cy43B2HLzPXJ5om0lhODs2bOoX78+VFVVERkZiSFDhpT4O2RlZeHw4cNo0qQJ5s+fj/nz58PLywtr1qyBqqoqnj59ikaNGkn8+xD1hRkeHg4XFxepPT1JYLPZUFNTw/Tp0/Ht2zdERkbCwMBA5Lk0Gg1Lly7Fhg0b0KVLF4SFhcndnvJSWcJHhTr/QiZPngwWiyX3Dg6iUFNTw/Xr1xETE4NJkyZR4leIqpDcAkDY9DMqKqpc1zdp0gRnz57FgwcP8O3bN9SpUweLFi1CQkJCiXN1dXWxYsUKpKamYueh4+ixMxRH78eAyxMgJ6/0905OngBcngBH78egx85QxKUUFZSYmBj07t0bGzduxOXLl7Fnzx5oa2uXOGf+/PmwtLTE9evXsW3bNrx+/Rrx8fHo06cP1qxZA09PT5lrRQoEAvTu3Vvuosdms0Gj0TBnzhzExsZi27ZtMDIykuhaZ2dnnD59GoMHD8bNmzflald5iY2NBYfDQXZ2NurWrVth81LC9xdCp9Nx+PBhrF69Gl+/flX4fOrq6rhx4wY+fPiAqVOnUuL3/1SVNT5APp0a6tSpgyNHjuDFixfIysqCnZ0dZs6cKbLnX3IuDaNPvMb3P9nI/n/By3x/D38CD+DnqYX4tn0Yvm7qh9/Xt5a4NjtPgO9/suG05x7iUrKRl5eHzZs3o3nz5ujcuTOePXuGVq1aCc8nhCAoKAj9+/dH8+bNAeS3vrl27RocHR0xaNAgnD59Gg8fPsTIkSNl+h0UQKfTcf78ecybNw8NGjQAi8WSuV6mlpYWVq1ahX79+sHU1FTsumNpdO/eHVeuXME///yDS5cuyWSPPIiLi0NSUhI6dOgg1206ZUEJ319KvXr1MHfuXEyZMqVC9vJoaGjAz88PERERmDFjhtLvH6oI5JHVWfz3qCjhKy2zU1osLS2xe/duvH37FhwOB/b29pgwYQI+fvwIAMjlCeDs+QipWXngF3p9qQ+8kf78BnITY8DQ1C91Dj4hSM3Kw5A9oXBo3gLBwcF48uQJFi1aJPzySk9Px549e2BnZwd3d3c4OTnh69ev2Lp1K2xsbBAZGYkWLVrA2toa9+7dK1JQWh507twZW7duRUREBFJSUuDk5AQLCwsYGRmJ3PKgqqoKBoMBdXV1aGhoCM+h0WjQ09NDQEAAFi1ahCVLlmDnzp3lXspo27Ytbt68ienTp1d6EfrY2FjExMRUaJgToCq3/NUsXLgQP378wOnTp8s+WQ5oamrC398fL168wKxZs6q9+MkiUpqammCxWEhJSSkxpiLujBXRm8/ExASbN2/Gx48fYWFhgTZt2mDUqFHYcO0FEtJyiogeAOh1dUONSQdhMfc89HtMK3N8PiFISMtBs7HLEBAQABsbGxBC8OTJE0yfPh01a9bEnTt3cPDgQbx69Qpubm7CEOalS5fQqVMnrFixAh4eHhJ1XJAFNTU1fPz4ERwOB97e3vDy8kKzZs3QqFEjmJiYgMFgoFu3brC3t8fKlSvx8uVLvHjxAqdPnwaXy0VSUhJat24NIH//oL6+Pvz8/Mptj729PW7fvo2lS5eKzUatCGJjY/Hq1asKFz5RyS08Hk8phU/58kyVHBaLhSNHjqBfv37o2bOnyKw2eaOlpYWAgAB0794dc+fOxY4dOyo0hKFMyOqdFYQ7C4e0FLGPDwCaNWuGV69egc/nl1oDsjzo6elh1apVcHd3x57DXvB6noBcfsmbInbNxlKPTRgsPExWxdtPX3DN5xxOnDgBHo+HsWPH4tWrV7CwsChyvkAgwIoVK3Dy5En4+/vD0dGx3K9LGlJTU/H+/XuwWCy0bdsWLBYL//zzj/D5vLw80Ol0uLi4wMjISOh9ikqwodFomDVrFnbv3g0nJ6dy22RnZ4e7d++ie/fuSEtLw7///lvuscpDeno6uFwufv/+jYYNG1bo3OJCndR2hr8ER0dHjBkzBrNmzaqwObW1tREYGIh79+5hwYIF1dbzk1X4RGV2KirUqaOjA1NTU7x//17uYxegqakJXYe+oNPleyOUl5uLrpOW4+vXrzhy5AiioqKwfPnyEqKXkpKC/v37IywsDE+fPq0w0QOA+/fvw9LSEj169BDpVbBYLDAYDGhpaSEtLa3M8YYPH47Xr1/L/PeytrbG3bt3cerUKSxevLhCP6txcXHQ0dFBu3bt5H6zVRbUGl81YM2aNXj+/DkuXrxYYXPq6OggMDAQt2/frvAP1N+CqMxORQkfoJhwZ3F8nseWmb0pLQI6Ew2dJuLAgQNo06aNyAjDu3fvhOt5t27dkjgTUl7cvXsXNBoNffr0KfU8DodTokGqKFRVVeHm5oY9e/bIbFuNGjUQGhqKW7duYfr06RWWnBYXFwcGg1HhYU6AWuOrFqipqeHYsWOYPn26yMLHikJPTw9BQUG4efMmli1bVu3ET1VVVaIvMXGIyuzMzc1VWDhG0cLH4wvwNUkxXRi+/skSW+Hl6tWr6NixI/7991/s3r27Ur7c7ty5g2/fvqF3796lnieqM7g4pkyZgjNnzkjkIZaFgYEBbt++jYiICLi4uFRIKcLY2FhhSbiKhvL4qgmtW7fGuHHjKizLswB9fX3cunUL169fx6pVqypsXmVATU2tXBU7CjAzMyvh8aWnp0NLS0tW00Qiz8xOUcQmZ4PFUMzHmMWgIza56J45gUCAVatWYcaMGbhx4wZcXV0VMndZZGZm4tWrV6hbt26ZveYK9rRJgpmZGbp3745jx47Jwcr/rc//+vULw4cPL7O9lKx8/PgRmZmZaNasmULnEQVVuaUasXr1akRFRQlrIlYUBgYGuHXrFnx8fLBmzZoKnbsyUVNTk2kDsyiPLz09vcxmqeXF3t4er1+/VljLKS5PALqCEp3oNBq4haq5pKWlYdCgQQgODsbTp0/RokUL/Pz5E9evX8eyZcvQrl076OjowMfHRyH2FObhw4fQ19dH//79yzxXGo8PAGbOnIndu3fLLTyppqaGq1evAoDC248VdP2oDLGhPL5qBJvNxvHjxzF37twKL1hrZGSE27dv49y5c9iyZUuFzl1ZcDgcmTw+ccKnKI9PS0sLpqamYlsPyYoqkw6BgqINAkKgysz/ivjw4QMcHR0hEAjQpUsXjB49Gnp6erCyssKYMWOwceNG3L9/H1wuFzY2NgqxpzChoaHIyckpc30PkHyNr4C2bdtCQ0NDrpVYVFRUcO7cOfD5fDg7Oyss7Pnhwwe0bNlSIWOXhSjho4pU/8U4ODhg6tSpcHNzq/A1N2NjYwQFBWHv3r2VvnG2IpDV4xMV6kxLS1OYxwfkFz5QVGanuS4HeTJ0WigNbh4fe7esgYODA+zs7PD582fcvXsXGzZsQEhICJKTk8HlcpGWlib0jphMpsjC0vImMDAQPB5PoixSNpst1Xum8NYGeaKiooILFy4gLS1NYR1Y4uPjRbZxqgio5JZqyNKlS/Hjxw8cPXq0wuc2MzNDQEAAFi5cWGqjzb8BWT0+fX19ZGVlITPzfwkhigx1AvmdBj58+KCQsZkMOmrqy1YDU+zY2X+wdfNmYZ+/gk7lpXkrHTt2VFiGbAE5OTl4+fIl+vbtK9Fc0oY6AWDkyJEIDw8XVsaRF2w2G5cvX8bPnz/lXoQ+NjYWubm56NKli9zGlAZR3l1ubq7CCxmUB0r45ISKigpOnDiBxYsXV0gtz+LY2triypUrGDduHB4/flzh81cUsia30Gi0EuHOtLQ0hYU6gfy/jSL38g1tZg42S/RHOSvqIX7f2IHfN3Yg9VH+2hs37r3wWPLtIyKvU2XSYZD2Eebm5lBVVZXIDjU1NQwYMKB8L0IKnjx5Ag6HI/Fc0oY6C66ZMGGCQiqwcDgcXLt2DdHR0Zg6darcokT+/v6g0WhlJvsoClHJLampqSWKmisDlPDJkUaNGmHevHmYMGFCpRSVbtWqFY4ePYoBAwYozMOobGQNdQJArVq18OnTJ+HPivb46tWrp9C/x8jmFhD33Zmb8BmZEcHIjAhGTsxzAAAv5afwWOb7+yKv43K5qMP4jejoaOzZswccDqdMOwQCQYWE2W7duoWsrCyJ55I21FnA1KlTcfLkSYV0WldXV4evry9ev34tt1KEvr6+0NHRUbjHLQ5RHl9KSkq5Cn8rGkr45MyCBQuQnp6OAwcOVMr8/fr1w8aNG9GrVy+l7A4tK7KGOoGSHlhFhDrfvXunsPVfHTUVTGxnDY4Ir0+nvTNqLr4h9mE+rWRonuTloBErAV4H90JFRQUTJ07ExYsXy2wrxOVysWzZMly6dKlIKFneXL9+HXXr1oWOjo5E55cn1AnkFwbv1KmTwtbOC+rwPnr0CPPnz5fp/UEIQVhYGKytreVooXSIEz5J/04VCSV8cobJZOL48eNYsWJFEa+iInF1dYWbmxt69+6N1NTUSrFBUcga6gRKrrkpOtRZUM/19+/fCptjekcbMPMyIWvlMiLgQ4WfjZcnNxTJauzduzdCQ0NL9SiGDRuG1q1bY//+/TA1NcWAAQNw7Ngxub7uvLw8REZGYujQoRJfU55QZwEzZ87Enj17FHfToqODmzdvCotbl3eeiIgIsFgs1K5dW84WSk7x5BaBQKDwz1Z5oYRPAdja2mLp0qVwdXVVeMd2cfz777/o0KEDBgwYIFOlE2VDms3I4iieZaloj49Goyk03Mnn8zFxvAsM35yFDocFRjn39REBH1qqDNxZOQTHvI5iypQpcHNzE1YxcXBwwPPnz1GjRo0SmXpaWloYOXIkpk2bhqCgIHz9+hXDhg3DjRs3UKtWLXTu3BkeHh4yr38XFAOQRvjKG+oE8pN1GAwGgoODy3W9JBRUY7p27Vq59+TeunULVlZWMDc3l7N1klPc40tPT4eamhq1naE6MXv2bNBoNHh4eFTK/DQaDTt37oSRkRHGjBlTaQIsbxTh8SlyH1/hORWR4MLn8+Hi4oJfv37B98IpXJ/ZHhZ6HJFhz1LJ48JMWxUB87rATIeDrl274vXr1wDyu8Hfvn0bQH4B5hcvXsDOzg5sNlt4eU5ODjp37iz8WVdXF2PGjIGPjw9+/vyJefPm4dWrV3B0dISDgwPWrl2LiIgIqT2cCxcuQFVVFQ0aNJD4mvKGOoH8z1HBhnZFYmBggODgYJw9exabNm2S+vqgoCDo6enBzMxMAdZJRvHkFmUNcwKU8CkMOp0OLy8vbNiwAe/evasUGxgMBk6ePIk/f/5g9uzZf0VdT3kkt5iamiI7Oxt//vwBIQTp6enQ0NCQk4WiUcRePoFAgAkTJuDHjx+4evUqOBwOzHQ4CJzTEePbWkOVSReb7VkAjZ8H8PPg0toSoYu6w0znf0ksWlpaOHz4MPbt24exY8di5syZyMzMhIGBAR4+fIgOHToIO6Db2NiI/ZLjcDhwcnLC0aNHER8fj+3bt+PPnz/o168f6tSpg4ULF+LVq1cSvWZ/f3+xRbPFIUuoEwCcnZ1x//59xMTElHsMSTA2Nsbt27dx6NAheHp6Snxdbm4u7t27BwaDoVQeHyV81ZRatWphzZo1GDduXIUUqBWFqqoqLl++jHv37mHDhg2VYoM8kUdyS+HQY1ZWFlRVVRUejpH3Xj6BQAA3Nzd8+fIF165dEwoQAKgw6VjQ0xaP/+2Kud3qoo6RBlgMGkheDjRUmVBTYYDFoIGengBu+EXcm98Bq4Y4iq352bt3b7x58wYpKSlC709NTQ1+fn4YOXIkaDSaxFsLmEwmOnbsiB07diAmJgY+Pj5gsVjo378/GjdujC1btpQoMFAAn8/Hx48fi/TckwRZQp1Afgamq6sr9u3bV+4xJKVGjRoICAjAsmXLcOPGDYmuefToEerVq4fExERK+CSFUCgUPp9PunXrRtavX1+pdvz48YNYW1sTT0/PSrVDVhITE4m+vr7M44wZM4Z4eXmR+Ph4YmxsLAfLSufdu3ekdu3achmLz+cTNzc30r59e5Keni7RNTncXMLSrUHex6eRx28/E3sHR+Li4kJ0dHTIt2/fJJ772rVrxMLCgri4uJDfv38TgUBADh48SKKjo8v7cggh+a8pNDSUTJw4kejq6pKuXbuSY8eOkbS0NOE5d+7cITQajWRmZko1dmpqKtHU1JTJvs+fPxN9fX2SkZEh0ziS8ujRI2JgYEAePnxY5rnLli0jixcvJmZmZlL9LeXNxo0bycKFC4U/X7lyhTg5OVWaPaVBeXwKhk6n48iRI9ixY4dwzaQyMDU1Fd5JXr9+vdLskBV5JLcA/ws9KrpcWQE2Njb4/v27zNX5CSGYMWMGIiMj4evrK3GIlgYCZPwC/893jOjTBUMGDcTRo0cxevRoqaoNOTk5ITIyEtra2mjQoAFOnz4NNzc3metz0ul0dOjQAYcPH8aPHz8wefJkXLx4ERYWFnB2dkZAQACOHDkCc3PzIt6tJMjq8QH5a5tt27bF6dOnZRpHUlq2bIljx45h4MCBZUYKbt26hS5duiAxMREmJiYVYp8oKI+PogRHjhwhTZo0ITk5OZVqx+PHj4mBgQG5f/9+pdpRXng8HqHRaEQgEMg0zoULF8iAAQNIeHg4sbe3l5N1pVO3bl0SGRlZ7usFAgGZPn06adWqFUlNTZXq2szMTKKiokKMjIzIiRMnhMdfvnxJzM3NCY/Hk9qeJ0+ekCZNmpDu3bvL7PGJIzExkezevZu0aNGC0Ol0YmdnR549eybV318gEBAajUby8vJksiUoKIg0bNhQ5veeNBw5coRYW1uTHz9+iHw+JSWFaGhokI8fPxJTU9MKs0sUq1atIitWrBD+vHPnTjJr1qxKtEg8lMdXQbi6usLKygrLly+vVDtatGiBkydPYtCgQXj79m2l2lIeGAwGVFRUZN6iUbDmVpH7jGTJ7CSEYO7cuXjy5AkCAgKktvns2bPIzc3FmTNniqyRNWnSRLiuJC3NmzfH06dP0b17d7Ro0QKbN2+We8sdQ0NDzJgxA3fv3gUhBC1btsSQIUPQsGFDbNq0Cd+/fy9zDBqNBg6HI7O33bVrV/D5fISGhso0jjSMHz8erq6u6NOnj8jmuCEhIWjdujV+//5dqet7QNXy+CjhqyBoNBo8PT1x+vRphe4JkoRevXph69at6N27d4kWPVUBeYQ7a9eujZiYGCQnJ1dIqBOQrXTZhg0bEBoaisDAQKlqHxJCsGnTJqxcuRIaGhro2rVriXMmTZqEQ4cOlcsuFouFBQsW4MmTJwgODhaKobw5evQoVFRU4OXlhejoaBw4cACfP39G06ZN0aVLF5w4caLUmyF5hDtpNBpmzJih8K0NxVm2bBlatWqFwYMHIzc3t8hzt27dQvfu3REbG0sJnxRQwleBGBgYwMvLCy4uLkhKSqpUW/755x/MmDEDvXr1QnJycqXaIi3y2MvHZrNhZmaGz58/K73Hd/LkSRw+fBh+fn5SfZHw+XxMmzYNZ8+ehb+/v9gq+SNGjEBYWJjYbEpJsLGxEXYI6d+/P2bPno309PRyj1ec48ePC9sd0el0tG/fHocOHUJcXBymT5+OM2fOwMLCAgsXLkR0dHSJ62XZy1eYsWPH4s6dO/j27ZvMY0kKjUbDnj17oKmpCVdX1yJ1gG/duoVu3brh58+fMDU1rTCbRFG8cgslfBRCevTogWHDhmHy5MmVvq9u/vz56NGjBwYMGFDiTlKZkWeCS3R0dIV5fOURvuDgYMyfPx9+fn5SfbHl5eVhzJgx+PDhA8LCwmBkZFSiV1oBGhoaGDFihMwttWg0GkaPHo2IiAikp6ejQYMGckmk4nK5eP78OUaOHFniOTabjSFDhiAgIAAPHz4EIQStWrVC7969cf36dWHhBln38hWgoaGBsWPH4uDBgzKPJQ0MBgNnzpzB169fsWjRIgDA9+/fkZSUhCZNmihFMejiHl9ycjIlfBT/Y8OGDfj48SO8vLwq1Q4ajYatW7dCT08P06dPr3QhlhR5eHxAvhB9/fq1wkOdkv6e37x5g1GjRuH8+fOoX7++xPNwuVwMGzYM6enp8PX1hZaWVpmdsCdNmgRPT0+5VPjR19fH0aNHcfz4cbi7u2Po0KEyFUwvWH8cOHBgqefVrl0bW7Zswbdv3zBy5EisX78eNjY22LBhA5hMplxulgBgwoQJOHHiRIVXQypoZ+Tr64udO3fi1q1b6Nq1K+h0OlJSUiq9/Q+fz6c8PgrxsNlsnDlzBosWLZJ7o0tpodPpOHnyJB49elThaxflRZ7C9+PHjwoLderr64PFYiEhIaHMc+Pi4tC3b194eHigY8eOEs+RlZWF/v37g8Vi4dKlS8J2QsW/lIpjb28PIyMjBAYGSjxXWXTu3BmvX7+GnZ0dmjRpggMHDpSrXZenpyc0NDRQs2ZNic7ncDgYN24cHj16hMuXLyMmJgafPn3C/PnzERYWJvMNXsOGDYVVVioaPT09BAQEYNu2bfDy8kK3bt0AKIfIZGRkFNleoww2iYMSvkqiQYMGWLlyJZydneWeCSctmpqauHbtGjZu3IigoKBKtUUS1NXV5dL2pqDaRUV5fIBkFVzS0tLQp08fTJ8+HaNGjZJ47PT0dPTu3RvGxsY4e/ZskTU9UU1CiyNLkos42Gw21q5dizt37uDUqVNo3rw57t27J/H12dnZCA4ORteuXaUqU1ZAs2bNcPjwYTRv3hz16tWDm5sbGjdujP3798u0Buni4oJjx46V+3pZsLS0hI+PD+7duwcLCwsAyiEyxW1QBpvEQQlfJTJ9+nQYGhpi9erVlW0KrK2tce7cOYwZMwZRUVGVbU6p6Ovry6XVja2tLZKSkir0w1lWzc68vDwMHToUbdq0wcKFCyUeNzk5Gd26dYOdnR2OHTtWQuSKJx6IYuTIkbhz545C+jg2aNAAYWFhcHd3x+jRozFixAiJOjUUJPQUeDblRUNDA/369cO7d+/g4eGB4OBg1KxZE9OmTcObN2+kHm/UqFHw9fWttLZffD4f5ubmmDJlCn79+oXU1NRKFxlK+Cgkgkaj4ejRozh69Cju3r1b2eagY8eOWLNmDfr374+UlJTKNkcshoaG+PXrl8zjGBkZQSAQSF0JRBZKS3AhhGDSpElQVVXF7t27JfZwEhMT0blzZ7Rt2xb79+8X2S+vrFAnkO/5Dx8+HIcPH5ZoXmkpSH55//496tevj2bNmmH58uWleu/e3t6g0Who3ry5THMXJLfQaDR06dIFPj4+ePPmDYyNjdGrVy906NAB165dkzgUq6+vj65du+LChQsy2VVefH194ezsjNGjR2Po0KFKkUiSmpoqXGcUCATIyMio9HVHcVDCV8kYGxvD09MTY8eOVQqxmTx5Mrp164ZRo0YpbSsjIyMjJCYmyjwOjUYDi8WSy3qhpJS2l2/NmjV48+YNzp07J3HR7Li4OHTs2BH9+/fHtm3byhUOLMysWbNw4MABmTd7l4aamhpWrlyJly9f4vPnz6hXrx5OnjxZQnQyMjIQEBCA5ORkqdoQiULUPj4zMzOsXLkSX758wYwZM7B69Wo0atQIx44dkyjLuTLDnX5+fujbty/Wrl0LHR0dfPz4sdIbvhb28NLS0qChoSG2aXFlo5xWVTP69OkDJycnTJ06VSkyK3fs2IHc3FypQm0Vibw8PiD/zrQibzjEeXxeXl44fvw4bty4AXV1dYnG+vLlCzp06AAXFxesWbOmVNFjsVgSrSU3aNAADRs2hLe3t0Q2yIKFhQVOnz6NCxcuYPfu3WjTpg0ePXokfP769eto0KABbG1toaqqKtNcNBpN7GeLxWJh+PDhCA8Ph4eHB06fPo1atWph+/btpa4D9urVC58+farwBLW4uDh8+/YNrVq1Ap1Ox6lTp5CZmYnLly9XqB3FKSx8f/78qfTtFaVBCZ+SsHnzZrx+/brCiuCWBovFwoULF3D16tVKu6MtDXkJX25uLng8XoVWr7G2tkZ8fHwR7yMwMBCLFy+Gn5+fxEWGo6Ki0KFDB8yZM0e4r6s0JBU+AJgzZw527txZYTdhrVu3xqNHjzBt2jQMHToUY8aMQWxsLLy9vVGnTh04ODjIPIckoV4ajYZu3bohKCgIV65cwePHj2FjY4Nly5aJjDCwWCyMHj0aJ06ckNk+afDz80OPHj2EUYECz2rHjh2VVhWKEFIk1BkXF4caNWpUii2SQAmfksDhcHDmzBnMmzdP4Q0vJUFPTw/Xrl3DggUL8ODBg8o2pwjyEr6fP39CW1u7QpN5mEwmrK2t8enTJwDAq1evhJ3KbW1tJRojIiICnTt3xqpVqzBz5kyJrpFG+Hr37o2MjAypsi9lhU6nY+zYsXj//j2sra3RuHFjBAQEIC8vD82aNZN5fEmyWgvj4OAAb29vPHz4EElJSbC1tcW0adPw+fPnIue5uLjg+PHj5dqmUV58fX3Rt29f4c/Z2dlgMpnw9vbG6NGjhe+tiiQzMxOqqqpgsVgA8oWvMrvBlwUlfEpEkyZN8O+//2LMmDGV1ri2MPXr18fx48cxdOjQCi3RVBbyEr74+HjUqFFD7p3Ry6Ig3Pn9+3f069cPe/bsQfv27SW69tmzZ+jWrRu2bt2K8ePHSzynNMJHp9Mxe/Zs7Ny5U+Lx5YWGhgbWrl2LZcuWQV9fHxcvXkRSUpLM3qckWa2iqF27Nvbv3493795BV1cXLVq0wMiRI/HixQsAQOPGjWFgYICQkBCZ7JMULpeLkJAQ9OrVS3isYPN6p06dsHr1avTv319kQWtFUjyDUxlqh5YGJXxKxuzZs6Gurq403dL79OmDuXPnYsCAAXLZOycP5Onx1axZE9++favQkm22trZ49eoV+vTpg9mzZ2P48OESXXf//n307t0bBw8elGp/HyCd8AHAuHHjcOfOnUqLPgQHB2P9+vWg0+m4ePEi2rdvL1Pxa0lCnaVhbGyM9evXIyYmBs2bN4eTkxN69OiB4OBgjBs3DsePHy/32NIQGhqKBg0awMDAQHissOhMmTIFnTp1wujRoys0Oa248FEeH4VU0Ol0HDt2DPv27cPDhw8r2xwA+TU9GzVqBBcXlwoN6YhDX18fKSkpMnvF8fHxMDMzg6WlpcjCxoqiVq1aOHLkCDp27Ah3d3eJrgkODsbAgQNx8uRJDBgwQOo5pRU+DQ0NjB8/Hnv27JF6Lln58+cP7t27B2tra9SrVw/h4eEYP348Bg0ahMGDByMiIkLqMWUVvgI0NTXh7u6Oz58/Y9SoUZgxYwaOHj2KixcvVkiSVEE2Z2GKi46HhweysrKwZMkShdsjzgZK+CikpkaNGjh48CDGjBlT4SELUdBoNBw6dAixsbFYu3ZtZZsDBoMBXV1dmTtcxMfHw8TERKY+edJCCIGPjw+ys7Ph4eEh0faD4OBgjBo1Cj4+PujZs2e55pVW+ABgxowZOHbsmFy7LEjC5cuX0b17d7x//x7NmjUDg8HA+PHj8fHjR7Rr1w5du3aFs7OzVGtZ0q7xlYWKigpcXV0RGRmJtWvXQlVVFQ0bNsSVK1cUmhTk6+uLPn36FDlWfPN6QXLa+fPncenSJYXZUpjitUKpUCdFuRgwYAC6d++OadOmKcUWBzabjUuXLuHIkSO4ePFiZZsjl3BnfHw8TE1Ny6ymIk9WrFiBxMRE8Pl8ifY43b9/Xyh60tTsLA6TyQSfz5fqvVSzZk106dKlwsJ4BXh7e2PkyJF4/vx5kYxODoeDefPm4dOnT7Czs0Pr1q3h5uYm0fpzedf4yoJOp6N///44evQodHR0sGrVKrRo0QI3b96U++c2KioKWVlZwvZMBYgqUK2vr4/z589jypQpFRLNKC6+lMdHUW62b9+OV69eVXoXhwJMTU1x+fJlTJkyBS9fvqxUW+QpfJLUz5QHx44dw5kzZ+Dv7w82m13mJvzw8HAMGjQIp06dQocOHWSam0ajgclkSu31zZ49Gx4eHhUW4k5MTMSTJ0/Qp08fPHv2TGRGp6amJpYtW4aoqCgYGRnB3t4es2bNws+fP8WOK69Qpzj69OmDxMREXLhwAQsWLMDs2bPRsWNHhIWFyW2OAm+veJRAXGmw5s2bY8WKFRg+fLhcWjKVRmEbBAKBMHFMWaGET4lRU1PD+fPnsWjRonKtaygCBwcH7NmzBwMGDJCoy4CikIfwFTTvrAiPLyIiAvPnz8f169dhZGQEc3PzUvcPvnnzBv369cPhw4fRo0cPudhQnnBn27Ztoa2tDT8/P7nYUBYXL15Enz59wGQy8fbtWzRp0kTsubq6uli/fj3evXsHJpOJBg0aYNGiRSJD4IoWPhUVFYwePRqnTp3C8OHDERERgQkTJmDs2LHo2bOnXLrSF9/GUEBpNTGnT5+OWrVqYd68eTLPXxqFbUhMTISOjo7MRQcUCSV8So6dnR22bduG4cOHK01W5YgRIzB27FgMHjxYoaWtSkMRHp+iQsqZmZkYPnw4tm7dKuyrZ25uLrbj+YcPH9CzZ094eHiUK5FFHOURPhqNJtzQXhF4e3tjxIgRiIyMhLW1tURVbIyMjITRkdTUVNSrVw+rVq0qsj4u7zU+Ubi4uODEiRMQCARgMpkYN24cPnz4gIEDB2LQoEEYNGhQuQpiA/mdNx4/fiyyWHdpBappNBoOHz6MoKAgnD17tlxzS0LhcKuyhzkBSviqBGPHjkXLli0xffr0yjZFyOrVq2FoaKjwO0lxyCp8AoEAiYmJMDY2hoGBARgMhsI82BkzZqB58+ZwcXERHhPn8cXExKB79+7YsGEDRowYIVc7yiN8ADB8+HC8ffu23F/akvLjxw+8fv0avXr1KrG+Jwnm5uY4cOAAnjx5gpiYGNSuXRubN29GZmamwtb4CtO0aVNoaWkVKTivoqKCqVOn4uPHj2jfvj26deuG0aNHS13m7NatW2jdunWRfncFlNUFQVtbGxcuXMCsWbMUFtIvLL6U8FHIjT179uDp06cVnmggjoJtFwEBATh//nyFzy9roerfv39DS0tL2LOuYcOGeP36tbzME3LixAk8evQIe/fuLXLczMyshMcXGxuLrl27YvHixUVEUl6UV/hUVFQwbdo07Nq1S+42FebEiRMYPHgwVFVVxa7vSYKNjQ2OHz+O0NBQhIeHo06dOkhISKiQfW3iClcXTsypX78+WrdujQkTJkjUmgkQnc1ZgCTd15s2bYr169dj2LBhCinKXlh8lT2jE6CEr8qgrq6O8+fPY/78+Xj79m1lmwMA0NHRwfnz5zF9+vQKL9Qrq8dXEOYswNHREc+ePZOHaULev38Pd3d3eHt7l7hTL+7xJSQkoFu3bpg6dSqmTZsmVzsKKK/wAfldO3x8fORWHLw4hBB4enrCzc0NAMrl8RXHzs4O58+fh6+vL9LS0uDk5IQtW7YodIuQs7Mzrl69ioyMDJHPFyTmfPz4ESYmJmjWrBlmzpyJ+Ph4sWMSQkTu3ytA0r53bm5uaNSoEWbNmiXRa5GGwjZQHh+FXGnQoAH+++8/DB8+vEJb6ZSGg4MDVq5cWSGZY4WRVfgKElsKcHR0RHh4uDxMA5BfP3H48OFYv349GjduXOL5wsL3588fdO/eHSNHjsSCBQvkZkNxZBE+Q0NDDBkyRO4d2gsIDQ0Fh8NBixYtwOPx8ObNmxJp++XF3t4e5ubm2L9/P168eAEbGxv8+++/pWaBlhcjIyO0b9++zC0/hRNzWCwWGjZsiLVr15ZonQQAL168gIaGBurUqSNyLEmFj0aj4eDBg7h//77cC2tTa3wUCsXV1VV4l6gsTJ8+HXXq1MHcuXMrbE5FeHzyFL65c+eiQYMGQg+mOAWhztTUVPTs2RM9e/bEypUr5Ta/KGQRPiB/a8O+ffsUUt6twNuj0Wh49+4dLCwsoKmpKbfxeTweGjZsiDNnzuDp06dIT09H/fr1MXnyZLlHK6Tp01eQmBMeHo5Xr17B1tYW3t7eRRKtxGVzFiBN93UNDQ1cuHAB7u7uiIyMlOgaSShsQ1UIdYJQVDnS09OJra0tOXnyZGWbIiQlJYXUqlWLnDlzpkLmi4+PJ4aGhuW+fsOGDWThwoXCnwUCAdHR0SEJCQky23bu3DlSq1YtkpqaKvactLQ0oqamRtq2bUumTZtGBAKBzPOWRcOGDcmrV69kGqNLly7k1KlTcrIonz9//hBtbW2SlJRECCHk2LFjZNSoUXKdw8bGhnz8+LHIscTERLJ8+XJiYGBAhg4dSp4+fSqXubhcLjEwMCCfP3+W+to7d+6Qpk2bkrZt2wrtadGiBQkKChJ7jYmJCYmLi5NqHi8vL2JnZ0fS09OltlEURkZGJD4+nhBCiK2tLYmIiJDLuIqCEr4qyuvXr4mBgQF59+5dZZsi5NmzZ8TAwIB8+PBB4XPl5uYSBoNBeDxeua6fOXMm2bFjR5FjXbp0IX5+fjLZ9fHjR2JgYECePXtW6nnZ2dmEwWCQ0aNHEz6fL9OckmJvb0/Cw8NlGuPatWvE0dFRrkK9e/fuIkI3c+ZMsnXrVrmNTwghNWvWFCtE6enpZOfOncTS0pJ06dKF3Lx5U+bXN2PGDLJ69epyXcvj8cjhw4eJiYkJGTZsGNHV1SW5ubliz2ez2SQzM1PqeVxcXMj48ePLZWNhBAIBUVFRIdnZ2YQQQjQ1NUlycrLM4yoSSviqMIcOHSKNGjUiWVlZlW2KkH379pHGjRtXiE16enokMTGxXNcOHfp/7J11XJPr+8c/Y8RGNyIN0oiEYCuIIip2t8fu7u7uLmzF7i5EbAUUGxUDMGlptl2/P/ixr5MNtjFQz3nerxevc3ieux6Q57P7uq9oTwcOHBC5NmHCBJozZ47c68nNzSUvLy9au3Ztie3y8vIoODiYtLS0yrwDkwVfX1+6c+dOmcbg8/lkZ2dHt27dUsiaBAIBubu709WrV4XX6tSpQ9euXVPI+EWYm5vTx48fS2yTn59Pu3fvJldXV/L09KTQ0FAqKCiQa76HDx+SjY1NmT7UpKenU0BAAKmqqtKCBQuEwvIzubm5pKKiIpdQZ2RkkK2tLZ04cULuNRIRZWdnk6qqqnDNGhoaFWLBKAvMGd9fTL9+/eDm5oaRI0f+7qUIGTRoEJydnTFq1Khyn6ss53y/nvEBZffsHD9+PKytrUuMt+TxeOjevTtYLBZ8fX1L9OZTNGU94wMUX6svMjISmZmZ8PPzA1AYaP748WN4enoqZPwipInjU1FRQY8ePRATE4M5c+Zg/fr1cHBwwIYNG8Q6nZSEl5cX1NXVy1RhRVtbG0SEVatW4d69e3BxccHRo0dFzv+KztakSXb+K1paWti9ezcGDRpUptAgcR6d8qynImGE7y+myEvr+vXr5ZqVQRaKKjmEhYVh//795TqXiYmJ3J55v3p1AmVzcDl+/DhOnz6NkJAQiX/0RITBgwcjLS0Nhw4dgoWFRYlpyxSNIoQPKHTeuHr1qtQxaCWxbds29O3bV5iwOzY2FiYmJlI7a0iLLCnLlJSUEBwcjIiICOzduxcXL16EtbU1Zs2ahU+fPkk1BovFQvv27ctUHSE5ORkPHz5Er169cOLECWzduhWzZs2Cv7+/MFeuNDF8JVGnTh307t0b/fv3lztz0d8WvA4wwvfXo6WlhUOHDmHEiBGIjY393csBUPhJ9dChQxg5cmS55sC0trbG+/fvZe4nEAiQmJhYLImutbU1cnJyZN6FvX//HgMHDsSBAwdKfGHPmzcPUVFROHbsGDgcTolpy8oDRQmflpYWevfuXSwoX1aysrJw6NAhkWD9yMjIMsfviUPeXJ21a9fGyZMncf36dXz79g1ubm7o0KEDwsLCShWKdu3aFduhycLp06fRqFEjqKurAwACAgIQHR2Nzp07IygoCAMGDEBcXFyZPyTMnj0bHz58kDsZ/t8WvA4wwvevwMPDA3Pnzq3wWLqS8PDwwLx588otUwQgv/AlJiZCT0+vWB5IFosFb29vmcyd+fn56NSpEyZNmoQaNWpIbLdr1y5s374dZ8+eFQazl5aoWtEoSvgACAuwliV/7OHDh1G3bl2RDyBRUVFyZ2wpibLm6nR2dsaGDRvw/v17+Pv7Y/jw4XBxccGaNWskFqB1c3ODqqoqoqKi5Jrz+PHjaNOmjcg1ZWVlDBo0CC9fvoSmpiY6duyI9PT0MoWYqKqqYu/evZg4cSLi4uJk7v/zrpMRPoYKZeDAgXB0dPxtuTPFMWDAgHLLFAEANjY2ePfuncz93rx5IzEYWFZz55QpU2BsbFxiDOOVK1cwYcIEnDt3DpUqVRJeNzMz+2uFz8bGBg0aNEBISIjcY2zbtg39+vUTuVZeOz5F5erU1tbGkCFD8OTJE2zZsgV37tyBjY0N+vfvj+joaJG2LBYLbdu2lcvcmZmZibCwMAQHB4u9r6urixUrVmDOnDn48eMHPDw8cPPmTbmeCSgU6cmTJ6NXr14yp3b7ecf39u1b2NnZyb2OioIRvn8JRVnYL126hIMHD/7u5QD43xlkREQE9uzZo/DxyyJ8VapUEXtPFuE7c+YMDh06hJ07d0o814uJiUHXrl1x+PBhODs7i9yraFMnl8uV2UmjJKZMmYIlS5bIZWV48eIF4uLiRPJPCgQCPHr0SOGOLYDiyxKxWCzUq1cPoaGhePnyJWxsbNCqVSvUqlULu3fvFv5M5DV3XrhwAbVq1SrVjKmhoYHmzZtjzpw56NSpEwYNGiRxB1oao0aNgrKyMpYtWyZTv5/P+N68ecMIH0PFoq2tjcOHD2P48OF/TD5PLS0tHD58GGPGjMGLFy8UOra8wvf69esShS8yMrLUF1VCQgL69euH/fv3w8DAQGKb4OBgrFmzRmwh2Yo2derq6sr9UhSHt7c3PDw85Dob2rZtG3r37i1ifoyLi4Oenp7En2dZKM96fCYmJpgyZQrevXuHyZMnIzQ0FJaWlpgwYQL09PSQnZ0t89/jsWPHipk5xVG022rfvj2ePXsGFosFV1dXHD58WGaxLUo8v3z5cjx+/Fjqfj/v+Er6UPknwQjfvwxPT08sXboUbdu2LddkvLLg7u6OhQsXokOHDgqtKWhmZoakpCSZawKW9MdpYWEBPp9fovcej8dDly5dMHLkSNStW1dsm/T0dDRr1gzDhg1D586dxbYxMDBAVlaWQndhJaFo4QOA6dOnY9GiRTKdMeXl5WHPnj3o06ePyPWXL18W2xUrioqox8dms9GyZUucP38et2/fBhGhVq1aUFJSwoIFC6Q2Iebn5+P8+fNS1WL8WXR0dXWxceNGHDp0CLNmzULLli3x8eNHmZ7BysoKy5YtQ/fu3aXeyRed8WVlZSE9Pf2PrrxeBCN8/0J69eoFf39/9O7du9yKq8pK37594enpqdAco2w2G+bm5jK71ZckfCwWq1Rz55IlS8DlcjFx4kSx9wsKCtC+fXvUq1evxKTTLBZLbHmi8qI8hK9GjRpwcnKSKenxqVOn4ObmVux38OrVKzg6Oip0fUBhGIlAIBCGTFQEVapUwdKlS/Hx40d069YNJ06cgK2tLaZNm1ZqTbxr167BxcWlWLiNOMQlqK5Tpw6io6NRo0YNeHl5YdWqVTKd2/Xo0QOOjo6YNm2aVO2L1vD27VvY2tpW6M9ZXv78FTLIxapVq/Dp0ycsWbLkdy8FQOFLfuPGjbhz545CawrKau4kIrx9+7ZEc4y3t7dE4Xvz5g1WrFiBLVu2iP0DJyL0798fXC4Xq1evLjWQtyIdXPT09BQufAAwY8YMLFiwQGrHGXFOLUBhDJ+Dg4Oilyd0bPkdQdVcLhdz5syBlpYW1q1bh5ycHPj5+cHHxwdr1qwRGzh+7NgxtG3bVqrxJSWoVlVVxbRp03D79m2cPHkSNWvWLOZ8IwkWi4VNmzYhNDQU4eHhUq/hbznfAxjh+9eipqaGI0eOYPXq1bh69ervXg4A0czwiorvkzWk4dOnT9DS0iox87+kHR8RYciQIZg0aRKsra3F9p09ezaeP3+O0NBQqUxrFXnOp6uri9TUVIWPW6dOHdjY2GDfvn2ltn3//j0iIyPFvtjLa8eXkZEBbW1thY8rLWw2G61bt8bLly+xfPlyxMfHY968eXjw4AEcHBwQHByMgwcPIicnB3w+HydPnpTqfA8oPYDdwcEB165dw5AhQxAUFIQJEyZIddxgaGiIzZs3o0+fPqWGI/284/sbzvcARvj+1Zibm2Pfvn3o3r27zLb+8qKo7liPHj0U4lov645PmsP3IuH71UwcGhqKb9++SUwRt337duzZswenT58uFiMoiYr07CwPU2cR06dPx4IFC8Dj8Upst2PHDnTt2hUcDqfYvfLa8aWnp5cpu4kiKPLuBApj8Zo0aYI9e/YgISEBnTp1QkhICMzMzNCyZUtoampK/GD1K9JkbmGxWPjnn3/w5MkTJCYmomrVqrh48WKpYwcHB6NmzZqYMWOGVGv4WxxbAEb4/vX4+/tj7NixaN++/R8T3D5o0CAYGBhg4cKFZR6rPISvcuXKUFZWRnx8vPBaSkoKxo4di82bN0NFRaVYn4sXL2LKlCk4d+4cTExMpF7Pv8HUCQANGjRApUqVSgyl4fP52L59u1gzZ0ZGBtLT08sl3VV6evpv3fEBgJ+fH16/fl3sd62pqYkePXrg0qVLePr0KX78+IGsrCzY2NhgypQppXqD5uTkCDO7lIaxsTH27duHjRs3YvDgwejWrVupOTpXrVqFvXv34v79+xLbFO34GFMnwx/F2LFjYWVlVW6B5LLCYrEQEhKCdevWlSkpNFAofLKYOksKXv95fb+aOydNmoR27dqJzc7y6NEj9OjRA0ePHpXZVPdvMHUChT+zGTNmYN68eRIdKS5dugRTU1OxFeljY2Nhb29fLo4Rf8KOT0VFBS1atMDx48cltjE1NUV8fDwuXbqE06dPg8fjoXHjxvD29saqVavw9evXYn14PJ7U3qodOnTAkiVL0KRJEzx58gRmZmaoWrUqdu3aJdEJzsjICKtWrUKfPn0keu7+jaZOpizRf4SMjAxydnambdu2/e6lCNm3bx85OzuXqYTRp0+fZCpIK64ckThmzpxJkydPJiKiiIgIMjMzo7S0tGLtPnz4QGZmZnT48GHpF/0Td+/eJR8fH7n6ysq3b9/IwMCg3MYXCARUs2ZNOnjwoNj7LVq0oC1btoi9t2/fPurYsWO5rOvEiRMUHBxcLmPLwsmTJ6lBgwYS70dFRZGdnZ1ISR8ej0eXL1+mnj17kq6uLjVp0oQ2bdokLPrq6upKT548KXXurKwsUlVVJXV1dRo8eLCwXFJUVBRVq1aNgoOD6dOnT2L7CgQCatGiBc2aNavYvfwCHmmYWFPU2y/kWT+QcnLzSl3LnwAjfP8hXrx4QUZGRgqrNF1WBAIBtW/fnsaMGVOmMbhcrtSVpKtVqyZVMdbTp09T48aNKS8vj1xdXenQoUPF2qSlpZGrqystX75c5nUXER8fT6ampnL3l4X8/HxSVlYu11pp586dIzc3t2J16F69ekVGRkYSC6bOmDGDpk2bVi5r2rVrF3Xr1q1cxpaFnJwc0tHRoa9fv4q9P336dBo3bpzE/pmZmXTo0CHq0qUL6erqUq1atcjIyIguXLhQ6twXLlwgbW1tAkDq6urUvHlzYX2/vLw8mj59OhkbG9P+/fvF/vtISEgQFplOycyjjdffUMCK61RlylmyHHOEXGdeIOcZ56nK1LMUsOI6bbz+hlKz/lwRZEyd/yGcnJywadMmtG/fHklJSb97OcIQB2ndpiWNYWVlJZW5k4ikPocoCmlYtmwZrKys0L59e5H7fD4fXbp0gZ+fX4l5OkujUqVKSEpKUlgOzZJQUVGBmpoaMjMzy22OoKAgcDgcnDhxQuT66tWrMWDAAInnUbGxseXi0Qn8GaZOAOBwOAgKCsLJkyfF3heXlPpnNDQ00KFDB+zfvx9fv37FzJkzkZeXhx49esDNzQ3Tp0+XmHXo7Nmzwt97dnY2rl27hrp16yI1NRWqqqqYM2cOzp49K0x2/2udSzMzMxw+egz7nmSg5qKrWHU1Fm++ZaJAQGCpcpCZx0N2Ph8FfMKbb5lYdTUWNRZexdKLL5HPE5Thp1Y+MML3H6Nt27bo3LkzunTpInMy2vLA0NAQW7ZsQe/evfHjxw+5xpD2nO/r16/gcrlSlXExNTWFqqoqli5divXr1xeLAZsxYways7OxcuXKMsWHKSsrw8jISO66grJSnp6dwP/O+ubOnSt8AaekpCA0NLTEAr3lFcoA/DnCBxT+/RV5d/5MbGwskpKSULNmTanGUVVVRZMmTaCnp4c7d+5g27ZtyM/PR5cuXYTn+WFhYUIv29OnT0Mg+J8A5eTk4MmTJ/D09BR6fFevXh1RUVGwsbGBu7u7yHlkYloOZt3n4dDj78jjCZBbIAAvIwlJZ1chYV1PfFjaGgkb+iDlyhbwczORWyBAHk+A7bfeIXBVOBLTKiY7kbQwwvcfZN68eRAIBKW6KVcUwcHBCAgIkLuyhLW1tVSendI4thRB/5/tIzg4uJhr+dGjR7Fv3z4cPnxYrIenrFSkg0t5enYWUVRR4MyZMwCALVu2oGXLlhIzkRBRuYUyAIUeo3+K8DVr1gy3b98u5mR06NAhtG/fXmbnHj6fD1VVVdSsWROLFy/Gq1evcOHCBZiYmGD8+PGoVKkSOnXqJDZkJj8/H/Hx8fD09BTm5uRwOFiyZAmOHj2KiRMnolevXohPyUKLdTcRn5KDnIJC8SxI/YzPO0ch68kVqJo6QNunNZR1K+HHw1P4snsc+DmF6RJzCgSIT8lBi3U3/yjxY4TvP4iysjIOHDiAvXv3SjS7VDQrVqzAlStXhC9LWZA2pKGk5NS/cuDAASgpKRULTXj69CkGDRqEY8eOwcjISOa1iqOiY/nKy7OzCBaLhenTp2POnDnIy8vD2rVrSzQHf/r0CZqamuUmTn/Sjk9TUxP+/v7F/p0fOHBAYk7XkvjVq5PFYsHFxQVTp07Fw4cPER0dDQ6HI7Lb+xmBQICUlBTUqVMHV65cEV6vXbs2Hj16hBq1aqPH9vtIzy4A/ycTasqlDRBkp0Gv0UAYt5sGPb/eqNR1AbR8WoGXkoC08P+lsOMTIT27AN233UUB/88wezLC9x/FyMgIhw8fRv/+/f+Iyu3a2trYuXMnBgwYIPP5o7SmTmkDbFNTUzF27FhMnDhRJM1TamoqWrdujZUrVyq0WGpFxvKVt6mziNatWyM3NxfTp0+Hk5MTqlWrJrFtee72gD9L+ADRYHYAwvi9WrVqyTxWaeEMFhYWyM3NLfVYIysrCy1bthQpH6auro4smwb4mpErInoFaV+Q+y4abB0TaHk3FxlHt243sFQ4yHoWBkH+/+KG+UT4kpGH1Vdfy/qI5QIjfP9hfH19MW/ePLRt27ZcHR6kpUGDBujSpQsGDx4sU3JtaXd80grf5MmT0aZNG3Tr1g2RkZEQCARCZ5aWLVuie/fuUq9NGv5tpk6gsMTN1KlTsWHDBowaNarEtuV5vgf8ecLXokULXLt2Tfg3d+DAAXTq1EmuGMbSCuwSES5fvizVWDk5Oejbty/GjBkDIkJqVj623XwnNG8Wkfuh0CzKtfEEiyW6ZiU1daiZO4MK8pD3STQtYU4BH1sj4pCWLX+1eEXBCN9/nP79+6NGjRro16/fH1HJYf78+cJcl9IiyxlfacJ3+/ZtnD59GgsWLICxsTF0dHTw9u1bTJs2DQUFBeWS9NvAwAApKSkKH1ccFWHqLMLExAQFBQVQU1Mrsd1/bcenp6eHWrVq4fz58yAiuc2cQOnlll69eiV12S5lZWUIBAKsXLkSly9fxsGH8RDnt8VLLjTLq+iJLz9UdJ2XUry0F4sFHHwYX+x6RcMI338cFouF9evXIy4uDosWLfrdywGHw8Hu3bsxatQoqc+99PX1IRAIir3Qc3NzhSWLiAivX78u0bmloKAAAwcOxMqVK4UvyurVq2PdunU4cOAADh48WC413SrK/FjRc61evRpdu3bFvHnzSmz3X9vxAf8zd0ZGRkJJSUnuqvOlmTovXbok9nxPWVkZ2traUFFRQaVKlRAcHIxFixbh2rVr+PHjBwIDA3EkKgG5BcX7CvIKk1yzOOLz0bLUNP6/XXErUm6BAEciK674siTKtzIjw18Bh8PB8ePHUaNGDbi6uqJly5a/dT3e3t4YNmwY+vTpgwsXLpQaLiAQCGBqaoqQkBBkZGTg3r17ePr0Kb58+QIlJSXk5uYiOTkZKioqWLRoEYKCguDv719snOXLl8PCwgIdOnQQXjM3N8eWLVtw+/ZtGBoaKvxZgYoVIz09vQpJWP7mzRvcunULb968QfXq1REeHo4GDRqIbfvq1av/1I4PKDwDnTBhAipVqoTOnTvLHRJTmvAdO3YMeXl50NbWRl5eHrS0tODp6Qk/Pz9hvT49Pb3i4/IF+JAsb9HoIsuR+Gd6n5wFHl8AZfbv23cxwscAoNDB4tixYwgODsa1a9fg5ub2W9czefJk1KlTB5s2bcLgwYOF11NSUnDv3j3ExMTg3r17ePz4MeLj44XhGXl5eSKfcD09PcFms4VmzpUrV2Lt2rVwd3fH4sWL8e3bN7Rr1w7v37/HsmXL8ODBA+FLKCUlBYcPH4a5ubncn8iloaJ3fEWu6+XJ6tWr0b9/f+jo6GDq1KmYM2eO2PJY+fn5SEhIgK2tbbmt5U8UPmNjY7i7u2Pfvn1yJ28ASj/jCwwMRIMGDVCzZk14e3vD2NhYqnETUnOgwlZCgRinGKX/39FRrnhhpLxskXa/osJWQkJqDqwNpatgUh4wwscgxNfXFytXrkSrVq1w7969ctvhSIOKigp2796NunXronHjxsKzuVGjRuHAgQMAUCzbSU6OaJwQh8NBt27dABTuKuzt7REVFYWcnBzcu3cPTZo0QV5eHtzd3aGvr48JEybAxsYGQOELpXPnzujQoQNCQkLw48ePEmv4lQVdXV2kp6eXy9ji5ipvkU1NTcXevXvx7NkzAEC3bt0wZ84c3Lx5E3Xr1hVp+/btW1hYWEBVVbVc1sLn85GdnQ1NTc1yGb8seHp64unTp3BxcZGrv0AgABGV6BSTlZWFx48fQ01NDQKBAO7u7jA3Ny91h5nHE0BJQhtlg8IKGgWpxc/wfr6urC/+DFCJxULeb87mwpzxMYjQrVs3dOjQAR06dKiQNFol4eTkhOnTp6Nnz55Cd+yFCxeCy+VKtTYWiyU02z558gRVq1YV2Q0WHfrHxMTg+vXrIsI2ZcoUEBGWL1+O6tWr49atW4p8NBEq2tRZ3nNt3boVwcHBqFy58MWnoqKCyZMnY+7cucXalmeqMqAweF1TU7Ncqj6UleTkZPB4PLmdyoocW0oSsdTUVJw7dw4zZ85E165d4ejoCA0NDXh4eKB///7YunUr7t27V8yrW01ZCQIJ6+JYFlbXyHkXDSJRARPkZSMv4QVYympQq+wktr+ACGrKv/f38ef9a2D47cyfPx8aGhoSC65WJMOHDweHw8HSpUsBFJpk9+3bJ1UNMgMDA2FezidPnsDNzU1iIC8ADBkyBFWqVMHy5ctx5MgRHDhwAMrKyvDz88P169cV8jzi0NHRQXp6eoV41Za3V2dBQYHYgPVevXrh5cuXuHPnjsj1/+L5HlBoUbh8+TK0tbVLrblX0hilOVu1a9cOWlpa4PF4yMjIQE5ODnJycvD48WNs27YNo0aNQmBgIPT09FCpUiXUr18fderUwaAeHZBXID72T0XPFBwbT/DTv+JH5FmRe2k394EKcqHh5g8l1eLFhgGggC+AuR5XrmdWFIzwMRSDzWZj//79uH79OjZu3Phb16KkpIQdO3Zg+fLliImJAVCYEuuff/4Blyv5j0dJSUkksfTTp0/h6upa6nxv377FuHHjYG1tLTSd+vn5ISwsrIxPIhllZWVwOJwKiaUs793lkSNHUKVKlWIB/qqqqpg5cyYmTpwoIvDlveP7U4UvLCwMVlZWaN68OS5duiTXGNIIX7169STW0QMKE1ZnZGSAx+Ph69eviIiIwO3bt2FW2RRW+pL/vvQDh0BJXRepVzbj29F5SL2+E1/2T8GPByehrG8G3QY9Jfa1NtD4rY4tACN8DBLQ1tbGqVOnMHv27HLd7UiDlZUVFi5ciH79+glNnitWrIC1tbVEE5aGhgbatWsHAEhKSkJOTg5MTU2lNnmFhYVhwIABAICaNWvi2bNnyMjIUMDTiKeizJ0GBgZISkoql90lEWHFihUS05P16tULqampOH36tPBaee/4/qQ8nT9TFLsXGBhYJuErybEFKPzAUa9ePanH1NDQwK1btxASEoKOPlbgqIj/e1HRM4Vp75XQqNoI+Z9eIeP+CfDSPkPLuwUq9VgGNld8xXuOihI6eJtLvZ7yghE+BolUqVIF+/btQ+fOnREXF/db19K3b1+oq6tj7dq1AAr/oE+fPi1x10dEwhRQP5s5ZTnrCQ8PR48ePSAQCODj4/OvOOfT0tKCsrJyuTjT3Lp1C2lpacIk1b/CZrOxZMkSTJw4UVg14L+448vLy8OJEyfQsWNHNGzYEDdv3kRubm7pHX+htOD1Ijp16lSidQQoPA/X1dXF7du3Ubt2bQBAZx8LlPT5SFnbCIbNR8F8+B5YTTgB8yE7oN94INhcyU5gREDH6halrrm8YYSPoUQCAgIwbdo0tGrVSu6yQYqAxWJhy5YtmDdvnjAvp52dHbZu3Sr2vC8wMFD4abjIsYXH48kUL5WdnY0jR47AxcUF7u7u5brzrUjPzvLKDbpixQqMGjWqxA8XQUFBqFy5MkJCQpCWlobs7GyJVRsUwZ8ofJcuXYKrqyvMzc2hp6cHNzc33L59W+ZxJJk6+Xw+oqKisHLlSrRo0QIjRowo5vH8M2w2G0ZGRrh//z7c3d0hEAjw5s0b7Ni8Ho0tlMCVsOuTFa4KG/3r2UJXvXw8eGWBET6GUhk6dChq1aqF7t27l+gcUt44ODhg7NixGDRokNBU16VLF7Rp0wYczv8O0rW0tERSQBUJH5/PlzlQmMViISUlBTY2NuUufBXl2VkeuUHfvn2LGzduoHfv3iW2Y7FYWLJkCWbPno1Hjx7BwcGhTPUMS+NPFL5fU5TJa+4sEj4ej4cHDx5g2bJlaNGiBQwNDdG6dWts2rQJV69ehY+PDypVqiR2DBUVFRgbG2PSpElYvnw5qlWrBg0NDbi6umLMmDHQib8NE20O2GX8HbFZLFTSVsPIAOnKgpU3jPAxlAqLxcK6deuQmpqK6dOn/9a1jBs3Dp8/f8b+/fuF17Zs2SLyh52Xl4cmTZoIv3/69KnMwsflcqGpqYmpU6fi8+fPGDRoULme8/3twrdmzRr069cPGhqlByV7e3ujYcOGWL16dbme7wF/nvBlZ2fj7NmzIo5XsgpfQUEB7t69i7Vr1yI5ORkGBgb4559/cP/+fRARVFVVYWJigsGDByMuLg7Xr19Hv379xO4OCwoKkJGRgenTp2Pz5s2IiYlBbm4u8vPzYWBggFkzpmFfv5rQUVeRW/zYLBZ01FWwt19NqPxmp5Yi/oxVMPzxqKqq4ujRo9i/f79MCaQVjYqKCrZu3YqxY8cKyxepq6vjzJkzwnMMDw8PaGsXHq4LBAI8e/YMbm5uUpk61dTUoK6ujjFjxiAhIQFTp06FhoYGOBwOfH19cfPmzXJ5Lh0dnb9W+JKSkrBnzx4MGzZM6j7z5s3DxYsXFVbTUBJ/mvCdPXsWvr6+IhlUfH19ERcXh2/fvontk5eXh5s3b2L+/PkIDAyEgYEBBg0ahK9fv0JTUxPDhg0DEeHBgwfw9PREeHg4Hjx4gFGjRgk/ECYlJQnPVX8lKysLWVmiWVg0NDQwf/58qKiowEyXi9PD6sJCnyuz2ZOrwoalfmF/M93fG8LwM4zwMUiNkZERTp48iREjRuDhw4e/bR2+vr7o2rWrSMV2V1dXrFixAkBhlesiPnz4AG1tbejp6YHP50v0ZlRVVQWXy8WwYcMQHx+PefPmFXthlmc8X0Xv+BRZ+HbFihXo0KEDzM2l99aztraGg4MDoqKiFLYOcfxpwieuEoOKigr8/f2FhWBzc3MRHh6OOXPmoGHDhjAwMMDIkSORnJyMoUOH4tGjRxgyZAiePn2KlJQUpKSkYMuWLYiLi8PcuXPh5FQ8cHz48OEyrZPD4eCff/4Rfm+my8WlUQ3Q2dMExMuHMqvkIw+uihLUlJXQt64NLo1u8EeJHsAIH4OMuLu7Y8uWLWjTpg0+f/7829YxZ84cRERE4OLFi8JrAwcORKtWrdChYye8T8rCqy8/cO3+E7hVLcw0wePxkJeXB1VVVaioqAAofOlwOBz0799fmK9TX19f7Jz/JuFT1I4vOTkZmzdvxpQpU2TuW7lyZTx58gQvXrxQyFrE8ScJX0ZGBq5cuYI2bdqIXM/KyoKlpSUWL16MBg0awNDQEBMmTEBmZibGjh2LxMRE3L59G3Xr1sWuXbvg6emJK1euoFevXnB0dMTGjRtRp06dEq0ZLi4uUhe61dDQwIwZM4qlkVNVVoLhpzuo8eUUfDnfoCXIhAqbBRY/H+oqSlBXZUOFzYK9sSZGN3LAvckBGBfo+MeYN0UgBgY5mDNnDtWoUYNycnJ+2xrOnz9P1tbWlJmZSSmZebTx+hsKWHGdqkw9S84zzpPrzAvkMPUM2Uw6TQErrtPyczHk5O5FK1euJACkqqpKffv2pcTERKnmy83NJU1NTUpLS1P4s2zZsoX69u2r8HHF8ejRI3Jzc1PIWFOmTKH+/fvL1dfb25tGjBhBLVu2VMhaxNGoUSO6cOFCuY0vCyEhIdS8eXO6efMmrV69mnr06EEuLi7E5XLJ09OTNDQ06Ny5c5SRkUFERHw+n8LDw6l///6kr69P/v7+FBISIvz39+jRI3J3d5d6/rt375KHhwdxOBxCYQkFsV+6urqUnZ0tdoxatWrR2bNnacSIEbRixQo6evwEKeuaUs8Rk+jd90wq4PHL/oOqAJgk1QxyMW3aNDx58gT9+/fH7t27y9UzTxJBQUGoXbc+eiw7jGc8E7BYENYPE80qz8Kbb5nYkpoNajkP93PT4VuzFg4dCIWVlZXU86mpqQnP+Zo3b67QZ6nIcAZF7fiSk5OxadMmREZGytX/06dPGD58OBo3bowbN26gfv36ZV7TryQmJsLMzEzh40pDZmYmHj16hMjISERGRuLo0aPCDCne3t6oX78+Ro8eDVdXV6iqqsLOzg4WFhbIzc3Fxo0bsXnzZqirq6NHjx549OgRLCxE49+kCWD/mRo1auDu3bvw8vLCixcvxJr91dXVMWXKFLFxf2/fvsXbt2/RuHFjbN++HbVq1cLY0aPAS/uMI9vWYN28Kb89I4u0MMLHIBcsFgs7d+6En58fZs+ejVmzZlX4GhLTcpDg3htfM3KlyvZeJIrR2TowaTcfyjrSlWj5mSJzZ3kIX0WZOvX19ZGbm4vMzMwyVS1YuXIl2rZtC2tra5n78ng8JCUlwdraGvPnz8f48eNx9+5dhX+A+vTpU4UI368iFxkZiXfv3sHNzQ3e3t5wcXHB6dOnhQ4pv0JEcHNzQ8+ePREXF4c2bdogNDQUPj4+En8m0gaw/8yXL1+gra0NJSUlYRakn2Gz2RgyZIjYvvv27UOnTp2goqKChIQEPH/+HN+/fxeuf8OGDZg4caJM6/lt/OYdJ8NfzpcvX8ja2pp27dpVofMmpGaT59xLZDv5LFlNOkMGzUaVaL4BQGApkdWkM2Q16QzZTj5LnnMvUUKqeJOOJG7cuEHVq1dX+PPcu3evXMaVRJUqVejly5dy909OTiZ9fX2Ki4uTq398fDyZmpoSUaFJz8vLiw4ePCj3esSRmZlJXC6XBAKBQsf98eMHRURE0KpVq6h79+7k7OxM6urq5OPjQ4MGDaKtW7dSdHQ05efnC/vMmjWLhg0bVmys9PR0WrduHbm5uVHlypXJycmJUlJSpFrHrVu3qFatWlK1FQgEtGfPHjI0NKSFCxfS6dOnicvlivx9cLlcmjt3rsT+Dg4OdPfuXSIiMjMzIwMDg2Im0t959CELzI6PoUyYmJjg7Nmz8PPzg6WlJfz8/Mp9znyeAN223UV6dgH4/2+uUTWxhU6dLmLb5yU8Q+6HGHBtvYXX+ERIzy5A9213cWl0A6kP4H19ffHy5UuFO01U5I4P+J9np7zpwlauXIk2bdoI6xfKys8mSCUlJSxduhT9+/dHq1atoKamJteY4uaoXLmy3LtIIsLXr1/x6tUrREdHC3dyHz58EO7k/Pz8MHbsWLi6ugodpsSNs3v3bhw8eFB4LTo6Ghs3bsThw4fRuHFjrFmzBh4eHrC0tCw1vVgR0iSpBgoLKhfFoV66dElYVHnYsGFYv349srMLC8ey2WyJFVkiIyMhEAjg6+sLHo+HL1++FPs9FRQUYMeOHSKFo/9UGOFjKDMuLi4IDQ1Fp06dEB4eLtadWpGsvhqLrxm5QtEDCoVP1UR8Fe/Pu8cCADQ9gkSu84nwJSMPq6++xrhA6QRATU0NNWrUQEREhMSclPLwO4RP3nO+lJQUbNy4Effv35d7/k+fPgnr9QFAw4YN4eTkhE2bNimsHJa0Zs7c3Fy8efMGL1++xKtXr0S+lJWV4ejoiGrVqkklcuK4desWOBwOXFxcsHPnTmzcuBFfvnzBgAED8OLFC5HkC1WrVsXNmzfRqFGjUseV5ozv8uXL6NOnD9q1a4ddu3aJiOrChQtx48YNREZGQllZGaNGjZJYbPnw4cPo2LEjWCwW4uLiIBAIhIJZRFZWFmbPno3+/fvLbIKtaP7s1TH8NQQEBGDx4sVo3rw57ty5IxKgq0hSs/Kx7eY7qSs4539/j/xPr8DWMgDXrnqx+zkFfGyNiEO/ujZS5xAsOudTpPAVBbATUYU4CpUlX+eqVavQqlUr2NqK/6AhDeKcThYvXoyAgAD06tULurq6co/98xxF4kpE+Pz5s4ioFQndp0+fYGNjA0dHRzg6OsLPzw+DBg2Co6MjDAwMyryONWvWQF9fH5aWlqhRowamT5+Opk2bihWtoiwu0ghfSWd8OTk5mDRpEo4dO4bt27ejcePGxdqw2WycPHkSzs7OyMvLw9ixY8WORUQ4evQoDh06BKAwbpPFYol1jsnKysKhQ4fQtWvXUtf/O2GEj0Fh9O7dG2/fvkWrVq1w7do1qU02snDwYTxk0YXM6AsAAE33QLCUxH86ZrEKxx1Y306qMf38/DBq1CjpFyEFampqUFFRQXZ2tlRpv8qKubm5XAVQU1NTsWHDhjLt9gDxwufm5obg4GAsWrQIixYtkmvcnJwcvH79Gq9evcKuXbuQkJAAHx8fvHr1ChwORyhuTk5OaNiwIRwdHWFjYyPTDk4aCgoKcOLECaxbtw4REREYOnQodu/eXappODAwEEOGDMGSJUtKnUOSqTMqKgrdu3eHu7s7Hj9+LDEuFSg8qrh48SJiY2MlftiIiYkBn8+Hp6cn0tLSsHPnTok5ezMzMzFt2jR06dLlt3h6SwsjfAwKZc6cOYiLi0OPHj1w6NAhmcoAScORqAShd2ZpCArykPUsDGApQbNaoMR2uQUCHIlMkFr4fH198erVK6SlpSlkZ1JEUUhDRQmfPImRV61ahZYtW5ZptwcUmiHFnQfPmTMH7u7uGDJkCCwtLYvdz8vLQ2JiIhITE5GQkIDExER8/PgRsbGxePnyJb58+QJbW1s4OTkhJSUF1apVw4gRI+Do6FiiACiKjx8/YsuWLQgJCYGjoyPc3d2hqqoqLKdVGr6+vvjw4QO+fv0KExOTEtv+Knx8Ph9LlizBypUrsWrVKqnFx8fHBz4+PhLvHz16FO3atQOLxcL8+fPFeoP+zPfv33H27FmFWkQUDSN8DAqFxWJh+/btaNSoESZPnozFixcrbGweX4APyVmlN/x/sl/ehCAvC1w7Hyhrl5wT8n1yFnh8gVRxSKqqqqhZsyZu3rxZLubOn8++ygt5zvjS0tKwfv163Lt3r8zz/7rjIyJkZGQgPT0dTZo0QZcuXRAUFCQicAkJCUhPT0flypVhZmYGc3NzmJmZwdraGk2aNIGjoyOsra2FYtChQwe0bt1a6owlZeH27dtYunQpbty4ge7du+Pq1atwcXFBUFCQSOqv0lBWVhamL+vWrVuJbX8+43v37h169OgBVVVVPHz4UOyHBnk5evQotm3bhi9fvmD9+vUSc34WkZmZiSlTpqB58+Z/7K6PET4GhaOmpoYTJ06gVq1asLOzE1YyLysJqTlQYSv9EpwumcxH/2/m/MWpRRwqbCUkpObA2lC63Zafnx/CwsL+WgcXefJ1rlq1Ci1atICdnXQ74yIEAgG+f/8uImCPHj3C+vXrsWTJEuF1IoK5uTlMTEwQFRUFJycneHt7o2nTpkKRMzY2ltqKUN7B6wKBAGfOnMGSJUvw+fNnjB07Fnv37hXu2D99+oT79+/j2LFjMo1bdM5XmvDx+Xyw2Wzs2LEDEyZMwOTJk0uthygrL1++RFpaGmrUqIGBAweWutsrIi4uDjdu3ECDBg0UthZFwggfQ7lgYGCAc+fOoW7durC0tERQUOniUxp5PAGUpPwEmZ/0EXmJL8DWMhTr1PIrfB4PYTduwtVcDzo6OsIvDocj9lOrn58fRowYIfMzlERFCp+xsTFSU1ORl5cnVfjAt2/fsGbNGhw6dAgPHjxAWlqa1F9JSUnQ0tISipe5uTkyMzPRuHFj2Nvbw9zcHObm5tDW1hb+rNevX49Tp04hJCRE7mcsL+HLy8vDvn37sHTpUmhoaGDChAlo27ZtsfO2vXv3om3btmILJZdEYGAgZs+eXaqjU0pKCu7du4c3b97g2rVrqFq1qlzPUxJHjx5F27ZtkZubi507d0JNTQ18Ph8cDgfKysrIy8sTfk9EICIIBALk5eVh9uzZuHbtmsLXpAgY4WMoN6pUqYKjR4+iTZs2uHLlCtzd3cs0npqyEgQSqiv8Smb0eQCApntjiU4tP1PA42Hn9p3I+fYRaWlpSE9PR3p6OgQCAXR0dKCrqysiiFpaWnjy5AkGDx4MbW1tqKqqQk1NTeTr12ultVFXV8e3b98gEAiKfWonIvB4PBQUFCjsv1paWli+fDlUVFRKFa+cnByoqqpi0KBB0NXVFftlamoq/Dn9fN3Q0FDE0SkzMxN79uzB0KFDJb7YBwwYgNWrV+PSpUsIDJR8PisJgUCAL1++KNRsnJ6ejs2bN2P16tWoWrUq1q9fD39/f7HPQETYtWsXNm3aJPM8tra20NDQENaRFMe5c+cwceJEmJqa4v79+wqLffyVo0ePYsWKFVBXV8fTp0+RkZGB1q1bY8mSJTA2NsaBAweQlJSE7t27Iz8/HwUFBcL/ypIOsKJhhI+hXKlTpw7Wrl2L4OBg3L17t0wvInM9Lgr4pTu2EC9fKqeWn2GrqOLqyUPFzvhyc3OFIlj0lZaWhoyMDNy/fx8FBQXQ09NDfn4+cnJykJaWhry8POTl5SE/P1/4/9J8n56ejlOnTuGff/6BsrIyVFVVwefzUVBQAIFAAGVlZSgrK0NFRUUh/2Wz2bhz5w6cnJygq6uLypUrC8XqZ/ECgGrVquHu3buwty97Be2inVhJuxkVFRUsXLgQEyZMQEBAgEw5KQEId5mKEITExESsXr0aISEhaNq0Kc6dO4dq1aqV2CcqKgo5OTmoW7euXHMWmTt/Fb6MjAxMnDgR58+fx4gRI/DixYtyE724uDgkJCSgXr16AABHR0cIBAIkJSWhbdu24HK5CA8Ph42NDTp06FAuaygvGOFjKHc6deqEuLg4BAcH48aNG3Lnh1RmK8HKQANvvmWW2C7r5U0IcjOlcmopwtpAQ6xjC4fDAYfDEeth9+XLFyQnJ2PSpEnSPUApTJ48Gdra2pg0aZLwk3OR2LHZbIU7CnTq1AmtW7dGly7iM94UMWfOHAQHBytE9ADpTZBt27bFihUrsHPnTvTt27dc5iiJ58+fY9myZThx4gR69uyJqKgoqXcxu3btQs+ePeX+nQUGBmLDhg0isXWnTp3C0KFDERgYiMePHyM8PLxc6xkeO3YMrVu3FvnQUfSBomgHn5aWVu4JK8qDvyOVNsNfz6RJk+Dl5YXOnTtLfUAujvZe5uCUUgVaFqcWAOCoKKGDt/RFVIsocnBRFEVnfCwWC6qqqtDU1BSepZSHd5w0np3p6elYu3Ytpk2bprB5f83aIgkWi4W1a9diypQpSE5OlmkOeYWPiHDz5k20bNkSDRs2hK2tLd68eYNVq1ZJLXr5+fkIDQ1Fz549ZZ6/CD8/P9y5cwcFBQX4/Pkz2rdvj3HjxmH37t0ICQmBjo4OuFwucnNz5Z6jNIrCGH7m3bt3Ij8HRYf0VBSM8DFUCCwWCxs3bkReXh5GjRolsRJ6aXT2sUBJXQuS4pGX8FxqpxYAIAI6VrcoveEv+Pj44M2bN0hNTZW5rzi0tbUrrDQRIJ1n55o1a9C0aVOF7fYA2UTJy8sLnTp1wuTJk2WaQ1pxLUIgEODEiROoU6cO/vnnHzRr1gzv3r3DtGnTZI7/O3fuHJydncsU66irqwtLS0vMnDkT7u7ucHZ2RkxMDPz9/YVtOBxOuQlfQkICYmNjReYDCr08nZ2dhd//rcLHmDoZKgwVFRUcOXIEderUwapVqzB69GiZx9BVV0W/ujbYfusdcsQEsqsYWsBq0hmpx+OqsNFXhnRlInOpqKBWrVqIiIhAy5YtZe7/K6qqqsjPzy/zONJiZWVVotddRkYG1qxZg1u3bil03sTERJlEYe7cuXB2dsbdu3dRs2ZNqeeQNk/n3r17sXTpUujo6GDixInFzHuysmvXLvTq1Uvu/gDw4sULJCcnIzQ0FGFhYXBzcyvWpjyF7/jx4wgODi5Whf3ly5cips2/VfiYHR9DhaKjo4OzZ89i+fLlItnqZWFkgANMtDlgl9X8J+BDhZeFgXVk3+0V4efnpzCXbRUVlVKDgxWJk5MTXr16JfH+kiVL0KxZMzg4OCh0Xll3Yzo6Oli6dCmGDBki9c+nNOHLycnBypUrYWtri+PHj2Pz5s24d+8e2rVrVybRS0pKQlhYmNzOHnl5eZg1axbq16+PRo0aoUaNGmJFDyhf4Ttx4gTatm1b7PqvwpeamsoIHwODNFhZWeHcuXMYPnw4rly5InN/VWUl7OtXEzrqKnKLH5vFgrIgH8/XD4aOliaqV6+OOXPmCM9VpCUoKAjnzp2Taw2/oqysXKHCZ2dnh48fP4rdZSYkJGDjxo2YN2+ewueV5/yta9eu0NHRwcaNG6VqL0lc8/PzsXHjRtjb2+PGjRs4f/68sKyWIs5RQ0ND0bx5c2hra8vcNyIiAh4eHnj06BGio6Mxffr0ErPklJfwZWZm4v79+wgICCh27+XLlyKlrJgdHwODDLi7u+PIkSPo2rWrXJ5pZrpcnB5WFxb6XHBLcXb5Fa4KGxb6XHzYMhT8jO8gIkRGRmLu3LkICgqClpYW6tati6VLlyIqKqpEZxwPDw/k5OSUuHOSlooWPjU1NVhYWODt27fF7k2bNg2DBg2ChYX8u2FJyCN8LBYLGzZswJw5c/D582eZ5+DxeNixYwccHR1x6tQpnDhxAsePHy81LEEWiAghISHo3bu3TP3S0tIwcOBAdOnSBQsWLMCJEydgbm4OBwcH/PjxA58+fRLbr7yELywsDL6+vsW8rwsKCvDu3TuR815G+BgYZKR+/frYtGkTgoODxb58S8NMl4tLoxqgTx0bqCkrlertCV4+iJePdm56uDy6AXzdqoje5vGQkZGBvLw83Lp1C9OnT0eDBg2gra2Nxo0bY+3atXj27JmIYw6LxUJwcDBOnz4t8/p/paKFDxBv7oyOjsaFCxcwceJEhc9XFFhuamoqc19nZ2f069cP48aNK7VtkfAJBAKEhobCxcUFu3btwp49e3D+/HlUry6d45MsPHz4EBkZGWJ3SuIgIhw5cgSurq5gs9l49uwZ2rRpI7zPYrFQs2ZN3LlzR2z/8hK+ixcvokmTJsWux8XFwczMDBwOBwCQnZ0NPp9fIUnVFQ0jfAy/lbZt22LmzJlo0qQJvn79KnN/VWUljG/ihHuTAzC6kQPsjTWhwmZBXZUNTTVlqKuyocJmwd5YEzU0kqB9bRFeHloKFbYSevToUWLwb15eHjIzM5GdnY0rV65gwoQJ8PT0LFZrTJHCJ4uZVRE4Ojri5cuXwu+JCOPGjcPMmTPlMteVxvfv36GjoyN30PW0adNw69atEs9V8/LykJGRgYiICFSrVg1r1qzBxo0bERYWJndAuTRs2bIF/fv3lypXZnx8PFq1aoUZM2bg0KFD2LBhA3R0dIq1q127tkTh43K5yMnJKfO6f+XChQtiUwy+evVK5HyvrBXufyvEwPAHMGvWLPL09KT09PQyj1XA49O775n08nMGvfueSQU8PhER/fjxg4yNjcnU1JTCwsLow4cPxOFwCIDUXxoaGvT48WOR+bKzs0lbW5uSk5PLtO5z585RUFBQmcaQla1bt1Lv3r2F3589e5acnJwoPz+/XOaLjIykatWqlWmMEydOkJOTE+Xl5RW7JxAIaMeOHaSqqkoeHh505swZEggEZZpPGjIyMkhXV5c+f/5cYjsej0dr1qwhQ0NDmjNnDuXm5pbY/tq1a1SrVi2x9woKCojNZsu9ZnG8fv2aTE1Nxf7MFi9eTGPGjBF+HxYWRnXr1lXo/BUFs+Nj+COYMWMGatSogbZt2yIvL69MYymzlWBtqAHHSlqwNvxfRhZNTU2MHz8elpaWGDVqFMzMzGBkJF1mF6DQ9LRw4cJiOUe5XC78/Pxw4cKFsq37N5g6f97x8Xg8jB8/HkuWLFF4YdYiFJFRpWXLlrCzs8OKFStErl+/fh316tXD7NmzYW1tjcjIyAorjRMaGgp/f39UqlRJYpuYmBjUrl0bhw8fRkREBKZPn17qztfHxwePHz8W+zdRlBRbkf9misyc4n5mv3p0lnf1i/KEET6GPwIWi4V169ZBR0cHvXr1kljhuawMGTIEHz9+BJvNRkhICNq0aSN1GRcOhyOxykSLFi3KbO78nWd8RIQdO3bAyMioXAuISlNgtTRYLBbWrFmDZcuW4cOHD7h79y4aNWqEfv36YfDgwViwYAHc3d0VXgS5JLZs2SKx/FZqaipGjx4tXOP169elTvOlqakJJycniQ5gij7nk3S+BzDCx8BQLrDZbOzbtw+fP38uU3aXklBXV8fEiROhpaWFGTNmICAgQKrDeXV1dTx//lxiBpPmzZvj4sWLZTqj+x1nfIaGhgCA9+/fY+bMmVi2bFm57pDS09MV4gVoa2uLTp06oUaNGujYsSM6d+6MFy9eoFu3bgqvylAaUVFRSEpKQuPGjUWu83g8bNiwAU5OTsjJycHTp0+lPgP8mVq1auH27dti7ylS+PLz8xEeHl7sOYDCs99fQxkY4WNgUBAcDgcnT55EeHg4Fi1aVC5zDBw4EG/evEHNmjVx7do1qcRGRUUFT548kXjf1NQUdnZ2uHnzptzr+h07PhaLBScnJ8yePRsNGzYsF2/Hn0lPTxfrxCELz58/R4cOHXDs2DEIBAKsXr0a/fr1E5pnK/qFvHXrVvTr108k8P3KlSvw9PTEkSNHcPnyZWzatAnGxsZyjV+Sg4sihe/WrVtwcnKCgYFBsXvfv38HAJGjAUb4GBgUiK6uLs6fP48tW7Zgx44dCh+fw+Fg1qxZ+Pz5M/bs2VNiLJe6ujoOHz4MFouFPn36YPLkyRLFqazmzorO3FKEhYUFjhw5gvnz55f7XGURvs+fP6NPnz7w9/dHjRo18PbtW+zbtw9jx45Fdna2sF18fDzMzWVPOi4PmZmZOHjwIP755x8AwOvXr9GqVSsMHDgQc+bMwdWrV8tch7J27dq4deuWWAuIIoVPkjcn8D8z58/WAEb4GBgUTOXKlXHx4kVMmTIFZ85In3tTWv755x8UFBQgODgYqampIoVSf+bOnTto3749zp49C6AwAXFgYKDY0Isi4ZPXRPs7dnxAYXyWi4tLhRQOlUf4cnNzsWDBAlStWhXGxsZ4/fo1xo0bB3V1dTRu3Bi+vr5YuHChsH1sbKzC06xJ4tChQ6hXrx40NTUxbtw41KpVC3Xq1MHz58/Rpk0bhZiNi34vHz58KHZPkcJX0vner6EMACN8DAzlgoODA06ePIk+ffpIPOOQFzabjdWrV+P69etiBUdFRQVDhw7F8OHDUVBQgNq1a+PixYv4+vUrtLS04O3tjYiICJE+Hh4eyM3NlTuLy+8QvpiYGLx+/Rp6enoVMp8swkf/H+Dt7OyMyMhI3Lt3D4sWLSoWX7h8+XJs3LhR6KTz+vXrChO+zZs3w9LSEo6OjkhLS8PTp08xYcIEhRaHZbFYEs2diorl+/z5Mz5+/AhfX1+x9391bCmPCvcVCSN8DH80vr6+2L17N9q2bYvnz58rdOx69eqhZs2aqFOnjjAtGYfDgYqKCiIiIrBmzRpoampiwoQJAApL5Fy7dg1RUVFo3bo12rdvj2XLlgl3eEVZXOTdof4O55bx48dj+PDhcmXOkQdphS86Ohp+fn6YO3cutm/fjqNHj8LOzk5sWzMzM0ydOhXDhg1DQkICtLS0yiX4/le2bduG6OhoPH78GOfPn8e2bdtKDGcoC5IcXBS147t06RICAgKEIRK/8qvwffv2rUyJCH47vy+EkIFBevbs2UOWlpb08eNHhY77/v170tfXJycnJwJAy5YtEwmMTklJITs7O9q3b5/w2tu3b8nGxoYmT55MPj4+1Lp1a0pLSyOiwgDw+vXry7WW169fk62tbdkeSAYuXLhA9vb2lJWVRWpqaqUGUysCLy8vevDggcT7X758oX79+pGJiQlt3ryZeDyeVOMWFBSQu7s7TZ8+Xe6fv7S8ffuW2rRpQ1paWtShQ4cKCZC/desWeXl5FbveqFEjunTpUpnH79atG23evFnifVtbW3r16pXw+4cPH5Y5EcHvhNnxMfwVdO/eHSNGjEBQUBBSUlIUNq6VlRWGDh0Ka2trGBgYoGbNmiI1yPT09HDs2DGMHDkSMTExAApd6SMiInD8+HEEBATA1NQU3t7eePz4Mfz9/fHo0SO51liRzi18Ph/jxo3DkiVLoK6uDisrK7x586bc55W048vLy8OSJUvg6uoKHR0dvHr1CgMGDJC6RJCysjI2bNiANWvWwMbGRtHLBlBYn3DSpEnw9fWFu7s7VFRUyj38owgvLy+8fPkSWVlZItcVteO7efMm6tevL/Zebm4uEhMTRX6uf/P5HsCYOhn+IsaOHYvmzZujadOm+PHjh8LGnThxIp4+fYoRI0Zg0KBBxcyN7u7uWL16Ndq2bSustm5mZobw8HBcuHABqqqqmD17Nho1aoQDBw7Az88P58+fl3kdFXnGt3PnTujp6aFVq1YASq/Npyh+FT4iwokTJ+Dq6oqbN2/izp07WLZsmVyen3Xq1IGZmRni4uIUuWTw+XyEhITAyckJX758QUxMDGxsbFCzZk1YWloqdC5JcDgcuLu748GDB8Wul1X44uPjkZWVJRKj9zOvX7+GjY2NSDYfRvgYGCqQxYsXw8vLCy1atFBYgl4NDQ0sXrwYJ0+eROXKlbFy5cpibbp27YoWLVqgW7duwqwyxsbGCAsLw/379xEWFoZr165hyZIlSElJwfHjx2VeR0UJX1ZWFmbMmCGyW/k1WXV5QEQiwhcTE4NGjRph2rRp2LhxI06dOiUxQYC0mJqaIiYmBo8fP1bEknHjxg34+Phgx44dOHXqFHbu3InKlStj69atEjO1lBe1a9cuds6nCOG7desW6tatK3Hn+uv5HgB8/PixXEpWVRSM8DH8VbBYLKxfvx7m5uZo166d2CKq8tClSxeoqanB398fS5Yswfv374u1WbJkCbKysrB48WLhNV1dXVy6dAnv37/H/PnzcevWLejr6+PEiRMyC0lFObcsX74cDRo0EPHgq4gdX25uLpSUlJCRkYFBgwahcePGaNeuHR49eiQ2W4g8vHv3DmPGjMGQIUPKlPbu4cOHaNq0KXr27IkJEyYgIiJCGNz/7NkzvHv3Ds2bN1fImqWlVq1axTw7FSF8N2/eLLFqhbhQhooMGSkXfvchIwODPBQUFFDr1q2pffv2VFBQoJAx79+/T5UqVaJp06ZRcHCwWKeFDx8+kKGhIcXExIhcz8nJoWbNmlHHjh0pPz+fLC0tSVdXl44fPy71/GlpaaSlpVXWxyiRT58+kYGBAb17907k+s2bN8nX17dc5/7w4QNpamqSoaEhjRw5klJSUhQ6fm5urtBJp0aNGrRp0yaZx4iJiaHWrVuTmZkZbdiwQWwFiJEjR9K0adMUsWSZSExMJAMDA5F/l8OHD6c1a9aUaVx3d3e6e/euxPvdunWjnTt3ilxzc3OjqKioMs37O2GEj+GvJTc3lwIDA6lXr17E5/MVMmbv3r1p7Nix5OzsTMeOHRPbZtu2beTp6VmsdE9OTg41atSIevToQTNnzqTOnTuTpaUljR8/XipxzsrKIi6Xq5DnkETv3r1p/Pjxxa4nJSWRjo5OuXgoCgQCOn36NFlbW5O6ujq9ePFC4XMQET179ozs7e2F/29oaFhM4CXx8uVL6ty5M5mYmNCKFSsoOztbbLucnByxHxwqCisrKxHvyvHjx9PixYvlHi81NZU0NTXFCnwR3t7eIsLI5/OJw+HQjx8/5J73d8OYOhn+WtTU1HDs2DG8ffsWI0aMUEhS6wULFmDHjh2YOnUqRowYIdaJpk+fPjA1NS2W4qsoz+iHDx8QExODBw8e4OHDh4iJiUFAQAA+f/5c4tzlfcYXERGBK1euYPr06cXuGRgYQEVFRa5iwCWRkJCA1q1bY9y4cRg5ciScnZ2lrkwgK7GxsUIHDRcXF4wfPx59+/Yt0eT57t07/PPPP6hbty7c3d3x5s0bjB49WmImn6NHj6J69eqwtrYuj0colV/j+cpq6rxz5w58fHxEPJl/hojw6tUrEceXhIQE6OvrQ1NTU+55fzeM8DH81WhoaODMmTO4e/cupk6dWubxTE1NMWHCBOzcuRMBAQGYOXNmsTYsFgtbt27Fhg0bEBkZKXJPXV0dZ86cwZcvX/D161ckJSXh7NmzwgTQ4eHhEucuT+ErKCjA4MGDsXLlSmhpaYlt4+joqLBzPj6fj3Xr1sHT0xNeXl54/PixMFShvHj16pXIuVNRDs+NGzcWa5uQkIDBgwejevXqsLS0xOvXrzF58uRSX+br1q3DoEGDFL52afnVwaWswlfa+V5iYiI0NDREKmr89ed7YISP4V+Ajo4OLly4gJMnT4rkbJSXsWPHIi0tDW5ubti3bx+io6OLtSny/uzVq1exIqFaWlo4f/48uFwuBg0aBCUlJcycORPbt29Hp06dsGjRImGmmJ8pKlcj7l5ZWblyJSwsLNCuXTuJbZycnPDixYsyz/XkyRPUrVsXBw8exI0bNzBz5kyoqakhIyOjXIXv5x0fUJiWbufOnZg5c6YwM823b98wZswYVKtWDdra2nj16hVmz54tVamk+/fv48uXL2jRokV5PUKpKHrHFxERUaLwifPoZISPgeEPwdDQEFeuXMH27duxdu3aMo2lrKyMXbt2YdGiRRgzZgwGDhwoVoy6du0KBwcHsbtCHR0drF27FpGRkcL7TZo0wYMHD3Du3DkEBASITTpcHkHsHz58wJIlS7Bu3boSg609PDzEiry05OTkYOrUqWjYsCH++ecfhIeHw9nZWXhfESWJSuJXkxxQuIudOnUqunfvjsmTJ8PZ2Rk8Hg9Pnz7F4sWLhfUIpWHt2rUYNmyY1EH15UG1atXw9u1bYShPWYQvLy8PkZGRqFmzpsQ2/0qPTjDCx/AvwtTUFJcvX8bSpUvLXM7IxcUFkyZNwvnz56GqqopNmzYVa8NisbBp0ybs3LlTbALhli1bAijM4F90HmhhYYGwsDA0bdoU1atXx969e0XOJsvD3Dly5EiMHDlSYq7LIry9vfHw4UO55rh27Rrc3d0RGxuLmJgYDBgwoFjB1fIWPnEv5IyMDKSnp+Phw4cIDw9HdHQ01qxZA1NTU5nG/vz5M86ePYu+ffsqcskyo6KiAgcHB2He2rIIX2RkJBwdHUvMa8rs+BgY/gKsra1x+fJlTJ06FYcPHy7TWKNHjwaPx0P9+vUxa9YssRlBjI2NsX79evTq1UukJhxQmDk/ICAAw4YNw65du7B8+XIAhSa4iRMn4tKlS1iwYAG6dOkizAijaOE7ffo0Xrx4IUy0XRLVqlXDixcvipluSyI5ORl9+vRB7969sXz5chw+fFiiqJSn8KWmpiI3N1eYJDorKwtLlixBlSpVEBcXhwsXLiA2NlZukdi8eTM6d+6skOrxZaVq1arC9HlcLlfuZ7p58ybq1atXYhtG+BgY/hIcHR1x/vx5DBs2TFhHTx7YbDZ27NiBLVu2CF/u4jwE27Vrh+rVq2PKlCnF7rVo0QI3b97E1atXsX79eqxfv154z9PTE5GRkTAxMYG7uzuuXr2qUOHLysrC8OHDsWHDBqmy6Kurq6NKlSolVpovgoiwf/9+uLq6QlNTE8+ePRPucCVRnsJX9DLOycnBmjVrUKVKFTx8+BDXr1/H7t27hY5KvXv3lvkMNS8vD5s3b8bw4cPLZe2y4u7uLhS+suz4SjvfA4oLX35+PhISEsotH2qF8XujKRgYyo+7d++SkZERXbt2rUzjrF27lmrUqEF16tShFStWiG2TnJxMlStXprCwMJHrnz59Il1dXcrPz6e4uDiysLCgrVu3Fut/8eJFMjMzIy6Xq7AYsUmTJlGXLl1k6vPPP/+UGvj97t07CgoKoqpVq5YY+Cxu7G3btsm0HmlZv349Va1alYyNjal169YUHR1drA2fzyc/Pz9aunSpTGPv3r2bAgMDFbTSsnP+/HkKCAggIqJz585RUFCQzGMIBAIyNDSk+Ph4iW0yMjKIy+WKxMi+fPmSqlSpIvui/zAY4WP4VxMWFkZGRkYyvaB/hc/nk7+/P40fP54MDAwkBmCfOXOGrK2tKSMjQ+S6j48PXb16lYiIYmNjyczMjHbv3l2sf1JSEnE4HHJwcKBHjx7JvV6i/wVwf/78WaZ+69ato379+om9V1BQQMuWLSMDAwNasGBBsQD+0mjbti0dPnxYpj6l8e7dOxo+fDhxOBzy8vIqNTg+Li6ODA0N6fnz51KNLxAIyNvbm86cOaOI5SqEhIQEMjIyIiKia9eukZ+fn8xjxMfHk5GRUYkJCx4+fEju7u4i106dOkXNmjWTeb4/DcbUyfCvxs/PDzt27EDLli3lTlyspKSE7du3Y8eOHRg8eDB69eol1hzZvHlz1K9fH3PmzBG5HhwcjNOnTwMA7O3tcenSJUyYMAGHDh0SaWdgYABjY2MMGDAAjRo1wtKlS+UKbSAiDBkyBDNnzpS5MGr16tWLxSYCQFRUFGrUqIFz587hzp07mDx5ski2fmlQpKkzOjoaXbt2hbe3N9TV1REQEIDx48eXGhxvY2ODuXPnSvwd/sqdO3eQnp6Opk2bKmTdiqBy5crg8/n4+vWr3KbO6OhoeHp6lujl+2893wOYMz6G/wDNmzfHunXr0LRpU7nj1KytrbFw4UKcPXsWWlpaWLJkidh2ixcvxo4dO/D69WvhtRYtWuD06dNC700XFxdcvHgRI0aMKHYGqaysjFatWuHBgwc4deoUAgIC8PHjR5nWumfPHmRmZmLw4MEyPmXh+dHLly+FL9OsrCyMGzcOQUFBGD58OK5cuSJ3BYX09PQyVUYnIly5cgWBgYFo0aIFvLy88O7dOyxatAgfP36U+oU8cOBA6OjoYOnSpaW2XbNmDYYPH17MQ/V3wmKxhA4uZRW+khAXyvDixQuJ5Yv+Kn7zjpOBocLYvXs3Va5cWe5ckQKBgJo2bUqjR48mIyMjiebIxYsXU4sWLUT6WVpaFktsfffuXTI0NKR79+4Jr1lZWVFcXBwREfF4PFq4cCEZGRnR3r17pcqjmZycTJUqVSqxynlpVKtWje7fv09Xrlwha2tr6tatG339+lXu8Yqwt7eX62dfUFBAoaGh5OnpSS4uLrRjxw6R3JJ8Pp+4XK5MuSPfv38vNtn4z8THx5O+vj6lp6fLvObyZvjw4bRs2TJ6/vw5OTk5ydy/devWdODAgRLbdOjQgfbv3y9yzcvLi+7cuSPzfH8ajPAx/KfYuXMnmZmZ0cuXL+XqX3S+MnPmTHJ3dxeb3Dc3N5fs7OzowoULwmtjx44Vm9H/1KlTVKlSJXr9+jUREZmZmRVzOIiKiiJnZ2fq1KlTqRUNBg4cSEOGDJHn0YT07NmT/P39yczMjM6dO1emsX7G2NiYPn36JHX7rKwsWrt2LVlbW1O9evXo9OnTYpORv3//nipXrizzerZu3UpeXl4SzyqnTJlCI0aMkHncimDLli3Uq1cvev/+PVlYWMjc/9dk1+KoWrWqSAWGvLw84nK5lJWVJfN8fxqM8DH859ixYweZmZmV+ocvidDQULKzs6OgoCCaOnWq2DYnT54kZ2dn4Uv1/v37ZG9vL9y15ebm0vHjx6lZs2akq6tLdnZ29PXrVzIxMRHrkJKdnU3Dhw8nc3NzunLlitg57969S6amppSamirXcxERRUdHU6VKlcjGxoaSkpLkHkccampqUr00v3//TrNmzSIjIyNq06YN3b59u8T2ly5dIn9/f5nXIxAIKCgoiGbPnl3sXnZ2NhkZGVFsbKzM41YEd+/eJU9PT/rx4wdpaGjI1Dc5OZk0NTVLrGjC4/GIw+FQZmam8Fp0dDQ5OzvLveY/CUb4GP6ThISEkLm5udwvthEjRlCjRo0keowKBAJq3LixsFaaQCAga2tr2rRpE3Xu3JnU1dVJS0uLAJCOjg5NmzaNfHx8SE9Pj75//y5x3gsXLpCZmRmNHj2acnJyhNcLCgrIw8OD9u7dK9fz8Hg8WrRoERkaGtLMmTOpWrVqco0jiby8PFJWVi7RXBsXF0fDhg0jPT096tevn9S78rVr19KgQYPkWld8fDwZGhoWC38ICQmh5s2byzVmRfDjxw/icrmUn59PampqEssoiePq1atUp06dEtu8fv2aLC0tRa5t376dunbtKtd6/zQY4WP4z7Jt2zYyNzcXmhllIT8/n+rVq0ft27cnR0dHsS+ep0+fkqGhIV28eJEGDRpEampqpKqqSiwWiwAIv1xcXEggEFDv3r1JWVm51J1WUlIStWvXjtzc3ITnjKtWraKGDRvKVU/v3bt3VK9ePapfvz69f/+ecnJyiMvlyvQyLY2MjAyJO5MHDx5Q586dycDAgCZNmiSTOZSo8LxLUnylNOzcuVPEbC0QCMjd3Z0uXrwo95gVgZ2dHT1//lysebwkli1bRsOGDSuxzcGDB6l169Yi14YPHy5zDOSfCiN8DP9ptmzZQhYWFnKJ3+fPn8nMzIzq1atHY8aMEbl3+/ZtsrW1JQ6HQyoqKqSkpCQidj9/tWzZkogKxVRJSYl69+5dqoAJBALauXMnGRoa0vTp00uML5RmjCVLlhCPxxPe8/DwKFPs46+kpqaSjo6O8PusrCwKCQkhHx8fsrKyoqVLl8rtRBIYGEhnz56Ve20CgYCCg4Np+vTpRER0/fp1cnJyKpeivIqkTZs2dODAAapWrZrYgH1JdOvWjUJCQkpsM378eJo3b57Itbp160o0s/9tMMLH8J9n8+bNZGFhQW/evJG57+3bt8nQ0JCMjY0pPDyciApNSZJETtzXpEmThOMpKyuTp6cnzZkzR6r5iwKyzc3N6enTp1Kv+/v378V2jT/Tt29fWr9+vdTjSTOfvr4+PX/+nEaOHEkGBgYUHBxMZ86cERFcebCyspLrg8vPJCYmkpGRET148IDatm1LGzZsKNN4FcGMGTNo6tSpFBAQQJcvX5a6n4uLi4jTijj8/f1FnLP4fD5paWlRcnKy3Ov9k2CEj4GBiDZu3EiWlpb09u1bmftu2LCBrKysyMrKiqKiosjY2LiYOVPSl7q6ukgaLxaLRYmJiWRjY1Pqp3KiwlRn1tbWtGzZMuJwODR27FjKzc0tsc/58+epcuXKNGbMGJFzwp/ZuHEj/fPPP7L9ICSQl5dHmzZtIhUVFTIxMaEpU6bQ+/fvFTJ2SkpKqY4a0rJ3716qUqUKGRgYyBQa8bs4cuQItWjRgjp16kShoaFS9cnKyiIulyvWG7kIPp9P2traImfNsbGxxc78/mYY4WNg+H+KBKwojk5ais7nKleuLPYMr6QvHR0dYTozPp9PLBaLiApzIpqYmJQYTpCZmUm2trZ09uxZCgkJIRaLRfr6+uTo6Eg3btwo1j4rK4uGDh1KlpaWwjklcf/+/WLpqmTl3bt3NGXKFKpUqRLVrl2bdHV1S3zhysOVK1eobt26ChlLIBCQvb09+fr6KmS88ubVq1dkbW1NQ4cOpbVr10rV5+7du+Th4SHVuD9z8OBBatWqlbxL/eP4c9IRMDD8ZgYPHozx48ejYcOGeP/+vdT9WCwWOnTogC9fviA/P1+kvp6qqmqJqb14PB6sra0BAAUFBVBWVgZQWGHi+PHj6Nmzp8QaeVOnTkXt2rXRpEkTTJ8+HUSE3NxcVK1aFV26dMHAgQORlpYGAHj48CG8vLyQmpqKx48fo2HDhiU+k7u7O16/fi0seCotfD4fZ86cQXBwMLy9vZGVlYWwsDAcOHAAmpqaUFVVlWm80oiKioK3t7dCxsrOzkZycjLi4uLE1lf807Czs8O3b9+gqamJpKQkqfpIk7Hl4cOHqF69usz9/iYY4WNg+ImhQ4di7Nix8Pf3F1shXRyHDx9G+/btxZYsys/Ph4ODA7hcrti+ubm5sLCwAFAogj+LZK1atbB161a0bNmyWC3AW7du4dChQ1i9ejUOHDiAjIwMAIUv77Nnz2LdunVQUlKCq6srOnfujKZNm2LWrFnYt2+fVDXl1NTU4OTkJHV+0y9fvmDBggWws7PDnDlz0K5dO8THx2PVqlVwcnICj8crl8rlkZGR8PLyUshYe/fuRb169bB161Z07dpVWCPxT4XNZsPFxQX5+flSC9/Tp0/h7u5eYpv/gvAxpk4GBjGsXr2abGxs6MOHDyW227hxI3G53FLP8bZu3UpqamrF7hkYGAjHSktLI21t7WJzrF+/nuzt7YVnLtnZ2eTg4EBHjx4lPp9PlpaWYk2oERER5OrqSurq6tS4cWOZXN6JiPr371+iCU0gEFBYWBh17NiRdHV1qV+/fvTw4UOxbV+/fk22trYyzS8N9vb2Mjn1SEIgEJCLi4uwhNWwYcOobdu2f7xnZ58+fahPnz7UqVMnqdo3bty41Gw89erVE/HeFAgEZGxsTB8/fizTWv8kmB0fA4MYRowYgZEjR8Lf319skmgiwuzZszFmzJhSzYFsNhvOzs7Yvn17sV1P0W4PEDV1/syQIUPQrl07tGjRArm5uZg5cyY8PDzQtm1bHD16FCkpKcX6/PjxA35+fujTpw+SkpJQp04deHh4YN26dVJXfPD29hZbqSE1NRWrV6+Gi4sLhg4dinr16uH9+/fYunWrRLMjn89X+I4vPT0dnz59UkjS5KtXr0JJSQl+fn4AgKVLl+Ldu3fYsGFDmccuT9zd3fH9+3epd3ylVVfg8/mIjo4W2UV//vwZfD4f5ubmZV7vH8PvVl4Ghj+ZFStWkK2tbbFPuxs2bJDaiYXNZtP48eOJqDDLyM/3OnToIBzz8+fPZGxsLHYdAoGAOnToQM2aNSNjY2P69u0bCQQCsrOzkzgvh8OhoUOHCsd4/vw51alTh2rWrElPnjwp9dkfPnxIbm5uRFTomXnixAlq3749aWtrU5cuXSg8PFzqHdGzZ88Unu7q+vXrVKtWLYWM1aJFi2IFgmNjY8VmdfmTuHr1Knl6ekqVaScnJ4fU1NSooKBAYptnz54VKzR74sSJP6oQryJghI+BoRSWL19OdnZ2IqbCz58/06RJk8jAwECYeqykLzs7O2HfgIAAUlZWJgA0Y8YM4fX4+HgyMzOTuI7k5GRSU1OjHj16EFFhgmtNTc0S5+VyuXTkyBHhGHw+nzZt2kSGhoY0depUieEMRIUvSlVVVerXrx8ZGBhQ/fr1acuWLaUmyhbH48ePhSKqKJYvXy4i7PLy5s0bMjQ0FJtHdN++fWRvb1+suPCfwrdv30hLS0uqJN1Pnz4ttZLDrl27qHPnziLXxo0bJ3Vc6d8CY+pkYCiFMWPGYPDgwWjQoAHevXsHAKhUqRIWLlyIr1+/4siRIwgODoaamhrU1dXFjpGQkIAvX74AALZu3QoOhwMAwkKgPL4A75OyoGxggfdJWeDxizvKrFixAvXr18fly5dx+fJlTJw4EZmZmSWuPScnB7169RLWB1RSUsLAgQPx+PFjvHjxAtWqVUN4eLhIn5cvX2LatGlwdnaGkpIS2Gw2IiMjER4ejv79+0NPT0+Gn14h5WHqVJRH57p169C3b1+xv7uuXbuifv36GDx4sIi37p+CkZER1NXVkZSUVOr6pCkiK86x5ebNm6hbt26Z1/pH8buVl4Hhb2HdunVkYWEhsapDcnIyrVmzhqpUqULq6urEZrNFzJ07duwQth0wYAC169qTVpyPoYAV16nK1LPkNP0cVZl0gpxnnKcqU89SwIrrtPH6G0rNyqPIyEgyMjKiT58+0fXr10lXV7dUp5qiLxaLRXZ2dmJzbx4/fpzMzMyoa9euNH/+fPL29iZTU1MaO3YsRUdH0+DBg2nZsmVl/tk9ePCAvLy8yjzOzzg7O0usiSgtGRkZpK+vX6ITU1ZWFrm4uND27dvLNFd5ERgYSGpqaqUG3S9atIjGjRtXYptatWrR9evXhd9nZWWRurr6v6IU0c8wOz4GBikZOnQoZs2aBX9/fzx9+rTYfX19fQwfPhyvX7/GrVu30LdvX2hqaoLL5YLP52PRokUAgHyeAMaN+iHasj02307Am2+ZKOATcgoEKIAysvP5KOAT3nzLxKqrsaix8Co6L9yPRUuXwdTUFPXr14e6unqpTjWqqqrQ1taGiooKMjIyioVEZGZmIjMzE46Ojjhy5AjmzZuHpk2b4uPHj1i2bBk8PDzg7++P69evl/lnx+fzxTruyEtmZiY+fPgAFxeXMo2za9cuNGzYEJaWlhLbqKur49ChQxg/fjyeP39epvnKg6pVq4LL5Zbq4FLajo/H4+Hx48ciYQsPHjxA1apVJVoy/lYY4WNgkIE+ffpg2bJlaNSoEaKioiS28/DwwObNm5GUlIRdu3bB2toar169woNnbxC4KhxHniSBDyXkFhQ3af5MboEAeTwB+FXqY/d3CySm5SAsLAzfv38XacflcqGtrQ1lZWWYmZmhZcuWmDdvHo4dO4ZPnz7h27dvcHV1BY/Hw/nz59GtWzeYm5vj4MGD6N+/P1JTU3HlyhUcO3YMbdq0EXqy1q9fHxEREVJ7gkpC0XF8jx8/hqura4nJAUpDIBBgzZo1GDlyZKltXV1dsXjxYnTq1AnZ2dlyz1keuLu7g8VilVn4nj9/DktLS2hrawuv/SvNnAAU9xGMgeE/QpcuXcDhcNC0aVOcOHECtWrVkthWTU0NHTp0QIcOHTB1wXJ02h4FqGlA8MtxTG78U/x4cAp5iS/Az/0BNkcLKkbW0PZpCa6dD/hgIz4lBy3W3cT3PWNRUFAANpsNFRUV2NvbY/DgwfD09IS7u3uxT+dEhAcPHmDv3r04cOAAbG1t0b17d6xatQpGRkbCdrVr10Z0dDQWL14MLy8vTJkyBcOGDUPlypXx+PHjMgWKK/qMLzIysszne+fPn4empibq1KkjVfs+ffrg2rVrGDVqFLZs2VKmuRWJq6srCgoKyix84s73IiIiMGjQIIWs80+C2fExMMhBmzZtsGvXLrRq1UoqU2A+T4Bbql4QKHOLiV7arQP4um8ScuOfgmPrDW3fNuBW8YUgNxO5H58I2/GJkJ5dAJMu83H3/gPk5OTg/fv3SEtLg4mJCWrWrCkUPSLCo0ePMGPGDDg5OaFr167Q19fHrVu3cOfOHQwdOlRE9IpQVVXF9OnTcevWLVy5cgVVq1aFtbU1wsLCyvTzUrTwRUVFlUmIiQgLFizAhAkThA5GpcFisbBp0yZhCrY/BTs7O+Tm5hazAvxMWloasrOzUalSJYltfhU+Pp+PO3fuSP3B4G+C2fExMMhJUFAQDh48iI4dO2LPnj1o0qSJxLarr8bia0YuoCT6WTPr5U2kR+wFx9oDRm2mQEntl90anyfyPZ8IWQIVRKRqoYaKCkxMTHD8+HEEBQUJX4BHjx7F0aNHQURo164ddu/eDV9fX6lf8EBhrtBz587h/Pnz6NevHx4+fIimTZvKfaam6DO+yMhIjBgxQu7+4eHh+P79Ozp06CBTPy0tLRw8eBBNmjRB9erVUaVKFbnXoCh0dXXBZrNLTLH3+vVrODg4lPhv4OHDh+jWrZvw+ydPnqBy5cpiPyD97TA7PgaGMuDv748TJ06gZ8+eOHnypNg2qVn52HbzHXJ+Oc8jEiAtbAdYKmowbDm+mOgBAItdXCxyCvjYGhGHtOx88Pl8ZGZmwsvLC97e3ujRowfU1NRw5MgRvH37FkuXLkWNGjVkEr2fadq0Ke7evYvMzEw0aNAAw4cPF5sppjQUecaXnZ2Nt2/fwtXVVe4x5s+fj0mTJsm1Ji8vL8yYMQOdOnVCXl6e3GtQJAYGBnjz5o3E+7GxsbC3t5d4Pz8/H0+fPoWHh4fw2r/1fA9ghI+BoczUrl0b586dw8CBA3Hw4MFi9w8+jIc43clLeAFe+ldwbatDiaOJ7DcPkH73CDIenERe4osS5ySBAB0mrUTlypUxevRo1K9fH71794a5uTlmzJgBT09PsWIXFxcn88vawsIClpaWOHjwIPh8PpycnLBu3TrweLzSO/8/ijR1xsTEwNnZGWpqanL1v3//PmJjY9G9e3e51zBs2DBYWlpi4sSJco+hSCpVqoT4+HiJ90s733v69ClsbW2hoaEhvMYIHwMDQ4l4e3vj8uXLGDNmDHbu3Cly70hUgljvzfzPhUHlbA1dfN4xEt+PzEba9Z1IvboVX/aMx5d9k8DPThc7X74ASNa2x507dxAVFYWpU6di8+bNUFNTw7hx40TaJiYmYsmSJahSpQrs7OzkOq/z8/NDTEwMNmzYgKtXr+LEiROoVq0aLl26JFV/RQpfWc/35s+fj/Hjx5epRBKLxcL27dtx4sQJiTv9isTCwkKYIEEcb9++hZ2dncT7v57vEREiIiL+tcLHnPExMCiIqlWr4tq1a2jcuDGys7MxZMgQ8PgCfEjOEtuen50GAPgRfR7KuiYw7jwPapUdwUv/htRrIch9F4XvxxeiUrdFYvv/AAeWVtbC79lsNkJDQ1GjRg2sW7cOHA4HmzZtwtOnT8FisZCbmwstLS1UrlxZ5mdr0KABDh48iFGjRqFq1aq4fPkyTp06hSFDhsDZ2RnLly8vNfmxos74IiMj4ePjI1ffJ0+e4P79+wpxTtHT00NoaChat24NT0/PEmMByxtbW1vcvXtX4v3ExMQSk0z/Knzv378HEcHW1lah6/xTYHZ8DAwKxNHREeHh4Vi2bBmWL1+OhNQcqLAl/JnR/3aBRq0ng2vtASVVLlSNrGDUdirYWobIi38q0eypwlZCQur/gthzc3Nx7do1GBkZYfjw4Rg+fDgiIyORl5eH3NxcYRsrKyuZn6tBgwaIiIgQ1hxksVho1aoVnj17hgYNGqB27doYM2aMsPDtryjyjK8sO76FCxdi9OjREusjykqtWrUwduxYdOnSBQUFBQoZUx6cnJzw48cPifcTExNL/MDzq/AVmTnlPRv+02GEj4FBwdjY2ODGjRvYsmULVq/fACUJLw8ljiYAQFnXBKomop+slVTUwLUpfLnnfYoV35/FQnZ+Aa5du4Zu3brBwMAAvXv3xq1btwBAKHY/o6ysDB0dHZmfqXLlyjAwMMCTJ09ErheZVp89e4bMzEw4OTlh06ZNxQLeFWXqzM3NxatXr0otpiqON2/e4PLlyxg8eHCZ1/Ez48aNg7a2NmbMmKHQcWXB3d1d7O8bKDRbJiYmwszMTOz93NxcvHz5EtWqVRNeCwsLQ/369ctlrX8CjPAxMJQD5ubmuHHjBi6dO4tcCc4kKvqFpiclNU2x94uEkXj5Yu8XFPDg7eGOJk2aYP/+/cjOzi7xUz8AmJiYSPsIxfDz85MYs2hiYoItW7bg/PnzCA0NhaenJ65duya8ryjhe/r0Kezt7YVJvmVh0aJFGDJkCLS0tMq8jp9RUlLC7t27sWfPHly8eFGhY0uLu7s7BAKBWPFLT0+HkpKSSEaWn4mJiYGDg4NwF0xEuHjxIoKCgsp1zb8TRvgYGMoJExMTXDtzBLxfI9b/HzULV0CJjYLUTyB+cTNZflJhXJayjrHY/gIWCw19q8lkjpLHzFmEn59fsUoOv+Lp6Ynr169jxowZ6Nu3L9q2bYu4uDiFnfFFRkbKZeaMj4/HsWPHyhT7VxJGRkbYu3cvevfujc+fP5fLHCWhrq4OFouFZ8+eFbtX0m4PKG7mfPr0KTgczh8Ro1heMMLHwFCOmBgZwtZI/A6Dra4DDed6oLwspN0SdbbIeReN3LgosNQ0wLUVn5rL2kADZ8+cxvXr12FmZibVudXNmzdRrVo1dOnSRZjL89WrV1KFJjRo0AA3btwQnvNJgsVioX379njx4gWqV68OX19fHDhwoMz5PgH5SxEtXboUffv2hYGBQZnXIAk/Pz8MGjQI3bt3V8izygqHw0FMTEyx67IK34ULF/7Vuz2AET4GhnKno48VOMri/9T0GvaDsp4pMm4fxJe9E5F6LQTfjy/Et0MzASUlGDQdLjR5/gxHRQkdvAtNpbVr18br16/Rr1+/EsVPRUUF8+bNw/bt29GsWTNkZmZi586daNasGbS0tODu7o7OnTtj7ty5OHbsGF6+fCkiiGZmZtDT0xO7qxAHh8PBlClTEBMTg7S0NJw4cQIhISFlEgV5dnxfv37F3r17MWbMGLnnlZZp06ZBIBBg9uzZ5T7Xr2hqauLFi+KOUJ8+fZJJ+C5evFhiFqJ/AyyiP7C6IgPDv4i07HzUWHgVeTzxOyV+zg+k3z6A7Ni74P9IhpIqF2rmLtCp1QFqZk5i+7AEPKzy10DLJgEips47d+6gY8eOSE5OLla2SEVFBQcOHEDbtm2LjZednY2XL1/i2bNneP78OZ49e4Znz57h06dPqFq1Knx9feHr64tTp06hXr16UlU0+JktW7bg3LlzSE5ORnJyMubMmYO2bdtCSUn6z975+fnQ1dXF9+/fRQKtS2PSpEn48eMH1q9fL9Oa5eXr16/w9fXFihUr0K5duwqZEyj07HRxccGxY8dErs+fPx+ZmZlYuHBhsT7Z2dkwNDREamoq1NTUkJWVhUqVKuHTp08KPwv9k2Di+BgYyhlddVX0q2uD7beKpy0DADZXC/oB/aEf0F+q8bgqSvDRzseEkROwSF8f06ZNQ7NmzcBisVCrVi3ExsZi8uTJ2LJli4j48fl8PHnyRKzwqaurw8vLq9huKisrC9HR0bh//z7OnTuHGzdu4NSpUzh9+rRQDH19fUuNDVRTU4O2tjaOHz+OixcvYtq0aZg/fz7mzp2L5s2bS3VO+ezZM9jY2Mgkeqmpqdi6dWuJJaQUTVH+1CZNmsDe3l4uD1R55y0qJ/UziYmJEnOsPnr0CC4uLsIsONevX0f16tX/1aIHMKZOBoYKYWSAA0y0OWCXMS6KzWKhkjYHIaPb4fnz5xg1ahQmTZoEb29vHDt2DAKBAFwuF6tWrUJYWBgsLS2FFRvYbDbWrl0r1hwmCQ0NDdStWxdjxozBgQMHEBkZCS0tLYwaNQqqqqrYunUrqlWrBnNzc7Rt2xaLFi3CtWvXkJ4umnGGy+UiNzcXLBYLQUFBePDgAWbOnInJkyejVq1auHLlCkozPslzvrd27Vq0bNmyTE498uDl5YU1a9agdevWpZYLUhTm5uZiHWtKOuP7L57vAYzwMTBUCKrKStjXryZ01FXkFj82iwUddRXs7VcTKmwlsNlsdOrUCY8fP8bMmTOxYMECuLu7Y//+/eDxeKhRowZevXqFwYMHg8PhgMViYeHChejYsWOp1dslYWFhAV1dXVhbW2PWrFk4e/Ysvn37hoiICHTq1Anfv3/HzJkzYWZmBhcXF/Tu3Rvbtm1DWlqayJwsFgutW7fG48ePMWrUKAwdOhT+/v6IiIiQOPetW7dQo0YNqdeamZmJdevWYdKkSXI9a1np0qULOnbsiI4dO1ZIcLutrS2Sk5OLXZdF+P4L53sAc8bHwFChJKbloNu2u/iakSvW7CkRfj6sjXWxr19NmOmKd2Apir9asGABPnz4gBEjRqBfv37Q0dHBgwcPcOnSJUyZMgXdunWDpqam3MVU+/btCy8vLwwdOlRiGx6Ph2fPnuHevXsIDw/HhQsXkJ2djc6dO6Nhw4bw9/cXSaHF4/Gwd+9ezJ49G46Ojpg7d26xtGRVqlTBiRMn4ObmJtU6ly9fjvv374tNHF5R8Pl8tGjRAlWqVMGaNWvKda6tW7di6NCh+Pr1K/T09ITXTU1N8fDhQ7Hi5+Ligv3798PDwwNxcXGoU6cOPn369K/N2FIEs+NjYKhAzHS5uDSqAfrUsYGashI4KiX/CXJVlKDKZuHHg5MwidwqUfQACM2IN27cwJEjR/Dw4UPY2NhgzJgxMDY2xtSpU8FisbB582Zcv34doaGhcj1DgwYNSi2+q6ysjGrVqmHAgAHYt28fjh8/DldXV/j4+ODUqVPw8PCAg4ODsKJFcnIyevfujVevXqF169Zo06YNWrduLXTPT0xMRFpamtT1AHNzc7F8+XJMmTJFrmdUFGw2G/v378fFixcREhJSrnMZGRmBy+UiLi5OeK2goADJycliExdkZmbiw4cPwvJOFy9eRGBg4L9e9ABG+BgYKhxVZSWMb+KEe5MDMLqRA+yNNaGsBFBBLlRZAqirsqHCZsHeWBOjGzng/pRGODClGw4fPIC1a9dKNYePjw9CQ0Px6NEjKCkpwcvLC506dcL9+/eFxVRHjBiB169fy7z+Bg0aIDw8vNQzuZ8pCrMYMmQIDh8+jG/fvuHIkSNwdnbG/v374ejoCDc3N4wdOxYmJia4d+8e/Pz8EBgYiM6dOyM0NBT16tWT2gt0x44d8PLyEknD9bvQ1dXFqVOnMHnyZNy+fbvc5jE0NISysrKI8H3//h0GBgZikwdER0ejatWqUFFRAfDfOd8DABADA8Nvp4DHp7CHT8mqWi2aOG8Z5RfwirWZN28eKSkpUUREhMzjp6en04oVK8jKyorq1q1Lx44do7Vr15Knpyfl5OTIPJ6NjQ09e/ZM6vYxMTHk6uoq8T6Px6MHnwYTXwAAJYxJREFUDx7Q4sWLqUmTJqSlpUWenp40bNgw6tu3L3E4HPLx8aG3b9+WOld+fj5ZWVnR7du3pV5fRXD27FmqXLkyxcfHl8v4L168ID09PVq0aJHw2tOnT8nZ2Vls+xUrVtDQoUOJiCgvL4+0tbXp+/fv5bK2Pw1G+BgY/iASExPJzc2NRo8eTXw+v9j9oKAg4nK59P79e7nGLygooIMHD5Kvry/Z2tqSh4eH8OUnC3379qVVq1ZJ3f7169dkZ2cndfu8vDy6efMmzZ49m3x9fYnFYpGtrS1pampS7969SxSPnTt3kr+/v9RzVSSLFi2i6tWrU3Z2tsLHTk5OJg6HQwMGDBBeu3nzJtWqVUts+65du9KOHTuIiCgsLIx8fHwUvqY/FUb4GBj+MFJSUqhOnTrUo0cPys/PF7mXm5tLZmZmVKlSJUpJSZF7DoFAQDdv3qTmzZsTi8Wirl27UmJiotT9jx49So0bN5a6fXx8PFWuXFmepdLXr19JW1ubNm/eTEFBQaSqqkrKyspUr149unXrlkhbHo9Hjo6OdOXKFbnmKm8EAgF17tyZunfvTgKBQOFjq6qqioj+mTNnqFmzZmLb29vb05MnT4iIaNSoUTRr1iyFrudPhhE+BoY/kKysLGrevDk1b96csrKyRO7FxsYSl8slLy8vucyUv7JlyxbS1tYmXV1d6tGjB929e7fUl3JGRgZpampSRkaGVHMkJSWRvr6+XOs7cuSIyMs7Ozubdu/eTW5ubsRisUhfX5+GDh1K4eHhFBoaSjVq1FC4qCiSrKws8vT0pGXLlil8bGtra7KwsBB+v3fvXuratWuxdt++fSNtbW3i8XgkEAjI0tJSKIL/BRjnFgaGPxB1dXUcP34c+vr6aNy4MVJTU4X37O3tsXv3brx48QKdOnUqNWl0afTv3x/t2rVD69at4ebmhm7dusHDwwPr16+XWFhWS0tLGHguDRwOR2K9uNIIDw9HgwYNhN9zuVz06NEDT548wbt37+Dn54ft27ejQ4cO6NatG7hcLo4cOYKMjAy55itv1NXVceLECSxbtkzhZYxsbGzw5csXYY7V1NRU6OrqFmt38+ZN1K5dG2w2Gw8fPgSHwxF6d/4XYISPgeEPRUVFBTt37kSNGjVQv359JCQkCO+1b98eY8eORVhYGEaNGlXmuVauXIlr166hWrVqiI2NxYoVK3Djxg1YW1vjn3/+wZ07d4p5cQYHB+PMmTNSjc/hcJCTkyOTJ2gRN27ckFgU1crKCkePHsWzZ8/g6+sLoDCn55o1a2BmZobAwEBs375dooD/LiwtLXHo0CH07NlTLs/aksbV0tJCfHw8ACAtLU2s8EVERKBevXoAgKNHj6Jdu3b/iTCGIhjhY2D4g1FSUsLy5cvRs2dP1K5dW6TszJw5c9CwYUPs3r0by5cvL9M8Ojo6CAkJQb9+/ZCRkYGAgAAcPHgQsbGxcHFxQc+ePVG1alWsWbNGuPts3rw5zp49K9WOk81mQ1lZWeYMJqmpqXj79m2pqcqsra2RnJyMTZs2ITAwEK9evUKDBg1Qv359nDlzBlZWVmjTpg0OHTqE7OxsmdZQXtSrVw9z585Fy5YtFbY7tbCwgJaWljCkoTThIyKh8P2n+M2mVgYGBikJDQ0lIyMjunTpkvBaVlYWubm5kY6ODh04cKDMcwwdOpR69uxZ7LpAIKCwsDDq0qUL6ejoUI8ePSgiIoKcnJzo/v37Uo2tpaVFaWlpMq3n5MmT1KhRo1LbhYWFkYODA/F4hWEgWVlZtH79erK1taU6derQvn37aNu2bdS4cWPS0dGh7t2707lz54o5D/0OBg8eTMHBwWK9eGVl8+bNZG9vT1u2bCEiop49e9KsWbPozJkzwlCQHz9+kIaGBuXk5NDjx4/J2tr6jz4TLQ8Y4WNg+IsIDw8nY2NjoRs6EdHHjx/JyMiIdHR0KCwsrEzjZ2Zmkp2dHR0/flxim+/fv9Py5cvJ0dGRDAwMKDAwkJKSkkod28jIiL58+SLTesaOHUtz584ttV2jRo1o+/btxa4XhW94e3uTk5MTbdu2jd6/f09r1qyhmjVrkqGhIQ0ePJhu3LihEOGRh7y8PKpfvz5NnTpV5r4ZGRkUExND1tbWpKKiQmw2mwAQi8UiFosl/H8AVKlSJfL29iZnZ2cyNDQkIqIZM2bQmDFjFP1IfzyM8DEw/GW8ePGCbGxsaNasWcJP6nfu3CEdHR3S19cvs3deREQEVapUib59+1ZiO4FAQKtXryY9PT3S0dGhbt260dWrV4W7rl+xtLSUOf6wevXqFB4eXmKbe/fukaWlJeXl5ZW41mvXrlFQUBCZmprSokWLKDU1ld6+fUvz588nV1dXsrCwoPHjx1N0dHSF74C+fv1KVlZWdPDgQanax8TEkJaWFikrK5OWlhapqqoSAKm/TE1NiYjI1dW1WEjIfwFG+BgY/kK+fPlC1atXp969ewtf+Lt37yZjY2MyNTWl169fl2n8cePGUfv27UsVgPz8fNLT06MnT57QypUrycPDgypXrkyjR4+mBw8eiPR3cHCgFy9eSL2GjIwMoUmuJFq2bElr166VetzHjx9Tjx49SF9fn8aOHSsMho+JiaHJkyeTlZUVOTk50Zw5c6TKFKMooqKiyNDQkKKjo8XeT05OppUrVxJR4S7R1tZWJrEr+lJSUqIVK1bQy5cvqXLlyr9tp/s7YYSPgeEvJTMzk4KDg6lRo0bCs7Px48eTg4MDWVpa0rt37+QeOycnh5ydnSk0NLTUtp07dxaeKRERPX/+nKZPn05VqlShKlWq0IwZM+jFixfk7u4u8aUujvPnz1P9+vVLbBMTE0OVKlWSKxPKhw8faPTo0aSnp0e9evUS7pQFAgHdvn2bhg0bRoaGhtS4cWM6fPhwiTtKRXHgwAGysrIqttt+//49WVhYkJKSklCMHz58SFwuV2bhY7PZlJ6eTvPnz5cra8+/AUb4GBj+YgoKCmjw4MFUtWpVio+PJx6PR82bN6c6deqQra1tmfJCPnjwgIyNjenTp08lttu7dy+1bNmy2HWBQED379+n0aNHk6mpKamrq9PQoUPp48ePUs0/efJkmj59eoltOnfuTIsXL5ZqPEmkpKTQggULqFKlStSsWTO6fv26cKeak5ND+/btowYNGpCJiQlNnDixzLvp0pg8eTLVr19f6HgTHR1Nenp6pKSkROrq6rRx40Zh2wkTJpC6urrUoqeqqirM3enl5UXXrl0r12f5U2GEj4HhL0cgENCSJUvI3NycHj16ROnp6eTi4kJt2rQhBwcH+vz5s9xjT58+nZo3b16iyTMpKYm0tLRKNEnyeDyqVq0aNWvWjPT19al+/fq0cePGEpMi165dmy5fvizxfmxsLBkaGkqdPaY0cnJyaMuWLeTg4EC+vr505MgRkfPKly9f0tixY8nIyIgCAgLowIEDlJubq5C5f4bP51NwcDANGDCALl26RBoaGiLiFRgYKGybm5tLNjY2Uu/03NzcaMSIERQXF0dGRkZUUFCg8PX/DTDCx8DwL+HAgQNkZGREFy9epDdv3pCJiQn17t2bXFxcSnVUkUReXh55eHhQSEhIie3q1q1L58+fL7FNkyZN6Ny5c5Sbm0snT56kzp07k46ODjVr1oz27t1LP378ELbNysoidXV1yszMlDhenz59aObMmTI9jzTweDw6duwY1axZk6pUqUIbNmwQWVtubi4dOHCAGjZsSEZGRjRu3Dh69eqVQteQkZFBFhYWpKKiUkzA1NXVRQRZWpMnh8Mhf39/Onz4MC1fvpz69eun0DX/TTDCx8DwL+LGjRtkYmJC27dvp2vXrpGxsTENGDCAPDw8KDk5Wa4xY2JiyNDQsESPzEWLFpV6XtS6dWs6duyYyLUfP37Qvn37qHnz5qSjo0OtWrWibdu20ZEjR6hmzZoSx/rw4QPp6+vL/UzSIBAIKCIiglq3bk16eno0ZMgQiomJEWkTGxtLEyZMIGNjY/Lz86P9+/eXOX+qQCCgefPmEYfDEStgWlpadO/ePZE+48ePL9HkqaKiQr179yZdXV368uUL1apVq9QPKv9mGOFjYPiX8fLlS7KxsaEZM2bQ7t27qXLlytS3b1/y8fGROYC8iHnz5pVo8nzy5AlZWVmVaBLt3Lkz7du3T+L95ORk2rt3L3Xs2JHU1NTI1NSU5s+fTzExMcXGHT58OI0fP16uZ5GH+Ph4mjlzJpmZmVGdOnVoz549IgKXl5dHhw4dokaNGpGhoSGNHj1aJg/WIng8HvXv379UEZs9e7ZIv9JMnlwul65cuUL29vb09u1bMjIy+iOC938XLCI5kucxMDD80Xz9+hUtWrSAi4sLfH19sXjxYvj5+eHNmze4ePEiNDU1ZRovPz8fHh4emDdvHtq2bVvsPhHBxsYGZ86cgZubm9gx/vnnH9SrVw99+vQpdT4/Pz80btwY3759w6lTpwAALVq0QIsWLeDk5IRq1arh+fPnqFSpkkzPUVZ4PB7OnDmDTZs2ITIyEr169cKAAQPg4OAgbPP27VuEhIRg+/bt8PT0xNixYxEQEFBqLszc3Fy0bdsW4eHhpaZV8/DwQHR0tMi1yMhI1KtXDzk5OSLXORwOhgwZAltbW0RFRQkTWa9bt07Gp/8X8ZuFl4GBoZzIzMykFi1aUEBAAC1YsIDs7OyoS5cu5OfnV6zUkTSEh4eTubm5RGeSoUOH0sKFCyX2Hzx4MK1bt67UeXJzc0lDQ0O4OxUIBPTkyROaP38+1axZk9TU1MjOzo52794tVcaY8uLNmzc0ceJEMjY2poCAADp8+LDILionJ4dCQkLI1dWV3N3daefOnRKdYQQCAXl5eYk90xP3paqqKnLuWMT48eOLmUg1NDQoJSWFOnbsSDt27CBHR0e6c+dOuf1c/gYY4WNg+BfD4/Fo6NCh5ObmRuPGjSNnZ2dq3749BQYGynUW1bt3bxo1apTYe+fPn6c6depI7Dt69GipatBFRESQl5eX2HtJSUmkp6dHixcvptatW5O2tjbVq1ePlixZQi9evPgtOSdzc3MpNDSU6tevT5UqVaKpU6eKnIcKBAK6cOECNW7cWGi+/fVs8ujRo6SsrEwmJiakoaEhTDMm6UtbW5vOnj0rdi1WVlZCL04ANGfOHBIIBGRqakrHjx8nOzu7/1xuzl9hqjMwMPyLYbPZWLt2LXr37o3Q0FD4+vrizZs3UFdXR8eOHZGfny/TeEuXLsX+/fuLmdmAQvNkTEwMkpKSxPblcrlS1eS7ceOGSP29n1myZAk6deqECRMm4Pjx4/jy5QsmTZqEt2/fonHjxrCwsECPHj2wY8cOfPjwQaZnkxc1NTV07twZ4eHhuHr1Kn78+AEvLy8EBwcLq1c0adIEly5dwoULF/D69WvY2dlh6NChwpJEGzduBI/HQ2ZmJlatWoV27dqBw+FAXV1d7Jw/fvwQWxJKTU0NR44cAQBUrlwZysrKGDNmDOLi4sBisXD9+nV07979P1WCSCy/W3kZGBgqhpMnT5KhoSEFBQWRr68vNW/enNq1aydzLFdISAj5+PiIzcnZqlUr2rNnj9h+c+bMkSoRc2BgoNgk2YmJiaSvr08JCQli+wkEAoqNjaXNmzdTp06dyNjYmGxsbKhv3760d+9eSkxMLHVuRZGVlUXbt28nX19fsrS0pHnz5okkAvj06RNNnTqVDA0NqWnTpiImTi0tLXr8+DGlpKTQqlWryMrKSuwu8OdK67+yes1aqu7flK5FvaR33zNp2/Yd1LFjRzIxMaHY2NiK+BH80TDOLQwM/yFiYmLQsmVL6OvrQ1NTExwOB4aGhti9ezeUlZWlGkMgEMDPzw+dO3fGkCFDRO5t27YNV65cwYEDB4r1W7FiBT5+/IhVq1ZJHJvH40FfXx/v3r2DgYGByL2hQ4eCy+Vi2bJlUq2TiPD8+XOEhYXh2rVrCA8Ph5GRERo2bAh/f3/4+fnByMhIqrHKQlRUFDZv3oxDhw6hUaNGGDRoEPz9/aGkpISsrCwMGDAAoaGhIkV6dXR0cPfuXTg5OYGIcOfOHaxatQqnT58Gi8VCTk4OlJWV8f79e5iZmQEAUrPycfBhPI5EJeBDchbYLECZzYaACHkFfOir8MCLvYmwkPnQVVct9+f+k2GEj4HhP8bXr1/Rpk0bJCQkwN7eHsrKytDQ0EBoaCjU1NSkGuPZs2dC06apqanw+qdPn+Dm5oavX79CRUUFAMDn8xEREYFFixZBT08PGzZsQFJSkshX3bp1YW9vj/v376Nv37548uSJyHxxcXHw8fHBq1evYGhoKNdzCwQCPH78WCiEN2/ehKWlpVAIGzRoILZoq6JIT0/Hvn37sHHjRuTl5WHgwIFo3LgxevbsicePHxdrr6enhwcPHsDOzk54LTU1FXv27MHSpUuRkJCA6dOnY9qMWVh9NRbbbr4DiwXkFkguDMxRUQIR0K+uDUYGOEBV+b952sUIHwPDf5Dc3Fz069cPZ8+ehY+PD7S0tJCZmYnjx49LPFf6lSlTpuDdu3cIDQ0Vue7m5oaqVasiNTUVT58+xefPn0GFjnQAAFVVVaiqqoLNZoOIkJ2djXXr1mHgwIFYsGABvn79itWrV4uM2atXL9jY2GDWrFkKeX6gcHcZGRkpFMI7d+7A3Nwcvr6+wi93d3epPwxIS9EObtOmTdi3b1+JFew1NDRw584dVK1atdgYJ0+ehLapNeZEpOJrRi5yShC8X+GqKMFEm4N9/WrCTJcr97P8rTDCx8DwH4WIsGDBAsydOxf169eHqakp4uLicObMGejo6JTaPzs7G66urti8eTMCAwNBRHjy5Al69OiBmJgYqdfB4XDw9etXaGtro0GDBpg0aRKaNm0qvP/8+XNhDKK2trZczyoNPB4Pz549w/3793H//n08ePAAr1+/hpubm4gY2tvbQ0lJMTsldXX1YnF3P1PkhDJs2DBMnz5dxDSbmJaDFutuIj27APz/f40nbOgDfsY3sWMpaejCYvhe4fdsFgs66io4Pazuf078GOFjYPiPc/DgQfTo0QM1a9aEm5sb7t+/jwsXLkhlUjx37hwGDx6Mbt26Yc+ePUhJSUF+fj54PJ5UcyspKaFr167Ys2cPMjIyYGZmhq9fv4rsOtu3b4+aNWti3Lhxcj+jvGRlZSE6Oloohvfv30dKSgp8fHyEQujj44PKlSvLPDafz5fqXJXNZoPL5YLNZqNPnz4YP348DIxMELgqHPEpOULRAwqFT5CXBe3qLYuNw1LlQqeGaPIBNosFS30uLo1uABX2f8fsyQgfAwMD7t69C39/f5ibm6Nly5a4cOECrly5InJ+9yupqamoV68eXrx4AQAlmuwkoa6ujhs3bsDb2xsnTpzAhg0bcOnSJeH9hw8folWrVnjz5g243D9jV/L9+3c8ePBARAw5HA58fHxQtWpVuLi4wNXVFQ4ODiWaSS9fvozAwECp5mSz2bCwsEBQUBAOHjyIhqNX4VmBUTHzZsKGwqw45kO2S/08XBU2+ta1wbhAR6n7/O0wwsfAwAAAiI+Ph7e3N/h8Pvr164ejR4/iypUrsLa2LtZ25syZWL58OWrVqoWbN29KFZ8nDicnJ6FwDho0CPb29hg7dqzwflBQEFq1aoXBgwfLNX5FQER4//49Hjx4gGfPnuHZs2d4/vw53r17BysrK7i6ugrF0MXFBY6OjlBTU0OnTp1w6NAhmeYyMDBAxL0otNr+BPliPmfII3wAoKashHuTA/4z3p7S+S8zMDD867GwsMCHDx/g4+ODNWvWYPDgwahfvz4uX74MR8f/7QbatWuHY8eOAQBcXV2hq6uLkydPoqCgQKb5NDQ0MH78eACF4nHhwgUMHz5ceD88PByxsbHo27evAp6u/GCxWLCxsYGNjY3I9fz8fMTGxuL58+d49uwZjh49ijlz5uDdu3ewsLBAXFycVONzuVy4urrC0tIS6urquP4xD0psJUDSDptfgMynYeBnfAdLRQ2qxjZQs3AFS4ldwjMABx/GY2B9O4lt/k0wOz4GBgYRiAgtW7bE+fPn0bdvX5w+fRrnz59HtWrVsHnzZgwaNEjYVkNDA9++fUOfPn1w6NAhyPI6UVdXx/fv36Guro5Xr16hUaNG+PjxI1gsFogI9erVw8CBA9GjR4/yeMzfRn5+Pq5cuYLmzZtL1V5VVRWamprYu3cvmjZtikYrw/HmW6bYtpKcW5R1TGDQfBQ4llXF9CrE3lgTl0eLz5jzb+O/c5rJwMAgFSwWC6dPn8bIkSOxdetW1KlTB4GBgdi3b5+I6AFAQUEBjh07hv3796NZs2ZSz8Fms9G9e3ehE8uFCxfQpEkToRfj+fPnkZqaiq5duyruwf4QVFVV0axZM3Ts2FGq9vn5+UhJSUGzZs0wbfoMfEjOkthW070RjDvPh/nwPbAYewSmfddB0yMIvPRv+HZoFvK/St5lvk/OAo8v+znt3wgjfAwMDGJZvnw5Nm7ciGPHjqFKlSro3r17sTb5+flYtGgRlJSUcPr0aTg4OEjlqaiqqoqRI0cKv7948SKCgoIAFDrJTJ06FXPnzgWbLdk897fz7t27UtuoqalBWVkZ9vb2aNu2LdJ4bJT0E9Gt2xVc62pga+hBSYUDVSNrGAQNg7ZvaxAvD2k390vsq8JWQkKq5NCKfxPMGR8DA4NEBg4cCDs7OzRu3Fhim9jYWDx69AgeHh64fv06bG1toaysLOLwUvQCz8oq3K04OTnBxcUFQGEwfUREBPbt2wcAOHLkCNhsNtq0aVOOT1YxZGZm4vPnz/jy5YvIfz9//iw2WwtQuONmsVjQ1NSEvb09nJycoKenB3V1deSrcaEkAMCXbR2ank2Rcf848uKfSWyjxGIhj/ff2PExwsfAwFAiixcvLvF+QUEBli9fjj179sDU1BQzZ87E1q1b8eXLF2FBVRsbGxARXr16BQ6HIxKTFxERAXd3d+jp6YHH42HGjBlYs2aNTBUEPn78iOzsbDg5Ocn3kHLy7ds3PH36FE+fPsXbt2+LiRyfz4epqSlMTU1RqVIl4X/r1KmD3bt3C8dRVlaGqqoqjI2N0b9/f3Tv3h2WlpbF5nuflIWLayMgq/Kx1XUBAIICyd63AiKo/UdSmDHCx8DAIJG5c+fiypUrpbY7dOgQ1q1bBx0dHYwePRrbtm1DcHAwTp06hdzcXFSpUgXTp09H7dq1QURo166dsO+FCxeEZs49e/agUqVKJe4wf+X169eoUaMG7Ozs8ODBA9kfUgoyMjLw7NkzPH36FE+ePBGKHY/Hg5ubG9zc3GBvb49atWoJBc7U1BRaWlpiBfz58+cijkBaWlpwd3dH3bp1YWFhgcTERHC5XBgaGor0N9fjokCOc7i8xMKQERVdyRXrC/gCmOv9GbGS5Q0jfAz/197dBzV5H3AA/+YJ4SFJpRLkRaFYoOqgiE6QRKs1aO22Hue8bX25zW3urPafVTd3u3W1V7vbXbsetVevd+3+cKveaXf1uN11p1Pc2chLjxerFIgoLEQYLwUhEBQDCcnz7A+XrJgEAkRq+3w/dzmOJDw84Ti+/H55fr8vUUjnzp3Dq6++GtFzJyYmcOzYMezduxeiKOKtt97CgQMHsH//frz++utISEhAUVERCgsLkZCQMGlh99mzZ/HBBx/A7Xbjtddew4cffhjxaM9ms8FkMsHpdKK5uRn9/f1ISUmZ1esF7ky7Xrt2LSjgHA4HcnNzAyFXUlKCvLw8LF68eFbddhkZGUhMTITD4QBwZzOAiooKVFZWQq/XQxAEuN1uqFQqpKWlBaY8tVotli56EraB4AtcPAOdUD9ggFq7YNL93pEbGPrXnwEA+keLw57Tw4l6xChk9xYuZyCiIJIkQavVzqioNjk5GX19fYHlCFu3bsX27dvR2NiITZs2YceOHfD6JHQNu+Dx/m9azTWEwjXfRn9/P9577z2Ul5eHLFgNxR96Q0NDkGUZOp0OpaWlQVVJ4fh8Pnz++ee4cOECampqYLVa0dnZiUceeSQQcP5bZmZm1Pbn9Dt06BBeeeWVGS3+F0URb/7jMt6v7gxqYXBWncBIbRniluYj5sEUCLFaeJ1fYKz9M8heD7TZhUj6wQGo1Jqg48ZpBOx/Yjn2cB0fESnV3ev1IqFSqWCxWALt6VarFZs3b8ZlaytOXR0K9MRp1AIElQqSLMPjlZAY68PPN67AH3/xFM58XIbVq1dP+73a29thNBoDoee3Zs0aXLp0KeTXSJKEpqYmWCwWWCwWVFVVYcmSJTCbzdiwYQPy8/OxbNkyxMbOz+4lXV1dWL58eUTBp1KpkJSUhIsXLyJ+USqMb5wPuhBl/D/NuNVwBp5+O3y3hyFPjEMQ9YhNyYL+0WLo8zaHHZ0qbecWBh8RBeno6MDRo0dRXl4Oq9UKl8s1qVoonKKiItTV1QEAPF4J+46U45MeRNQT5/NJ2PN49rQ9ce3t7TCZTHA4HEHnI4oiOjo6kJqaCkmSYLVaceHCBVgsFlRWViIpKSlQQms2m+c0LRoNK1euhNVqnfI5giAgKSkJdXV1WLp0KQCgtPwa/vrp9RlVEYXDvTqJiEIYGBhAQ0MDampqcObMmUlheLeenh7IugT85Eht1Hvi7HY7jEZjyNAD7lQclZSUQJZlVFRUICEhAWazOVA0O5sWhWhzOp2orKyExWLByZMn0dvbG/a5giBg0aJFqK+vD4QecOefilDtDDPFdgYiohkYGhpCQ0MDqqqqcPr0aVy+fBk6nQ4tHV/g++/XTOqJC2XU+gkcp94GABi+9yIWrPoOgPA9cdevX4fRaMTg4OCUI0+DwYDDhw/DbDYjPT09Sq929kZGRlBdXR2YYm1ra4PJZILZbEZeXh6effZZuN3uoK/zh15dXV3IjcJD9fHNBPv4iIiiINKRiPfmAHr/8ktAliB7xiYFHxA8EvGHnsPhmLb+SBRF2O32r2x0d+vWLVRXVwemWFtaWlBUVITi4mIUFxdj7dq1k65qXbVqVVBxryAISExMRH19fcjQ8+txjs1yZK1GaryI4wptYOdyBiKKmsPn29B/c3zK0JNlGY7T70CtXQDd8vW4Wf/3oOf4ZBl9N904fP7f+OGyWBQUFMDpdEa0CbYgCCgrK8PevXvn9FoiMTo6GljfZ7VaUVtbi+bmZhQWFsJsNqO0tBRGoxFxcXFhj7Fr1y689NJLgSZ2f+iFG+l9WdpCLc79ahMOn2/Dkerr076XqtUIkGRg14ZM7NuyTFHTm1/GER8RRcXwbQ9Mfwq+2vBuNy9+jOHzR5Dy4zcw3tmIkU//FjTi8xNjBAwc2YPhvm5oNJqIq4/y8/PDbgk2G263G62trYGA89/6+vqQk5MTWPZQUFCAdevWzag0t7e3F1lZWYF1e/7Qy8rKmtE5Ol0efPRZF8oudaPjrqtnJ3wSHk7U4+mCdDxT+JBirt4MhyM+IoqKjz7rwnRruScGu+CsOIYFhdsQl5GH8c6pw0mlAg4cOQXTwlHYbDa0traiqakJbW1t6O7uhiRJEEURsixjdHQ0MCJsaWlBT08P0tLSZvQafD4f7HZ7UMDZ7XZkZmYGAm7nzp3Iy8tDdnb2nDfSXrJkCXJyctDY2Djr0AOAhbpYvPB4Nl54PBten4Tu4TG4vRLEGAHpCVrFLE6PBIOPiKKi7HL3lNNssuTD4KlDUMcnYeGmn0V0zPEJCWfbnPjNrzfhsccem3w8WcbQ0BBsNhtsNhva2trQ1NSE1tZW9PT04MqVK5OCz+fz4caNG0EbRvs/dnR04OrVq0hOTg4E3LZt2/Dyyy9jxYoVU05XztXu3btx8OBB1NbWzir07hajFvDwIn0UzuybiVOdRDRnXp+EnINnMeEL/+fEWXkcIzUnkbrjTYhpOXfuqzox5VQnAGjUKlz9w3dDjlg8Hg9cLhccDkfIMPtyG4LD4YDBYAjaMNr/MSMjA7m5uYiPj4/OD2UGJEnC2NgY9HqG1XzgiI+I5qx7eAwatYAJX+jWAHdvK0ZqTiK+aHsg9CLl9bixbmsJ3IPdcLlcuH37NlwuF1wuF1QqFXQ6HQwGQ1CYrV+/ftLnycnJEXUFfhUEQWDozaP787eAiL5W3F4JQpg3+O5Mcb4NjSENCzf+dMbHFmNj8dvf/R7fWvwgdDod9Ho9dDoddDodNJrgfSeJpsOpTiKas47B23jq3Sq4PMEjPml8FF3vPBfRcRYUboPhiT2T7tPFqvHPFzfyPSuKGo74iGjOpuyJU2vwQP6TIR/y9LfD098OMT0XGkM6xLTgIlkl9cTR/GDwEdGcxagFLE3Uw3ZjNOgxQSMi8anQi8mdVSfg6W+HfuWWsBe3KKknjuYHf5uIKCp+tCYdcZro/kmJ0wh4uuCr32+TvlkYfEQUFc+tfQjRvmJAloFnCh+K7kFJ8XhxCxFFDXvi6OuAIz4iipp9W5YjJT4O6un2LpuGWqVCaryIfVuWRenMiP6PwUdEURMbI+DE8yY8qNPMOvz8PXHHnzcptj2A7i1OdRJR1LEnju5nDD4iuic8XmnGPXG7N2YpuieO5geDj4juKfbE0f2GwUdE84Y9cXQ/YPAREZGi8F8tIiJSFAYfEREpCoOPiIgUhcFHRESKwuAjIiJFYfAREZGiMPiIiEhRGHxERKQoDD4iIlIUBh8RESkKg4+IiBSFwUdERIrC4CMiIkVh8BERkaIw+IiISFEYfEREpCgMPiIiUhQGHxERKQqDj4iIFIXBR0REisLgIyIiRWHwERGRojD4iIhIURh8RESkKAw+IiJSFAYfEREpCoOPiIgUhcFHRESKwuAjIiJFYfAREZGi/Bf1gCzPKXQNHAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random\n", "\n", "N = 10\n", "R = np.zeros((N,N))\n", "for i in range(N):\n", " for j in range(N):\n", " if(random.random() > 0.5 and i != j):\n", " R[i,j] = 1\n", " \n", "big_graph_positions = lag.DrawGraph(R)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2. 5. 3. 3. 2. 6. 7. 4. 0. 2.]\n", " [5. 0. 6. 1. 2. 3. 2. 2. 0. 1.]\n", " [3. 6. 2. 7. 4. 4. 9. 6. 0. 1.]\n", " [3. 1. 7. 0. 1. 8. 2. 4. 0. 5.]\n", " [2. 2. 4. 1. 0. 8. 2. 6. 0. 5.]\n", " [6. 3. 4. 8. 8. 2. 9. 3. 0. 0.]\n", " [7. 2. 9. 2. 2. 9. 4. 7. 0. 4.]\n", " [4. 2. 6. 4. 6. 3. 7. 2. 0. 1.]\n", " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", " [2. 1. 1. 5. 5. 0. 4. 1. 0. 0.]]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C = np.zeros((N,N))\n", "for i in range(N):\n", " for j in range(N):\n", " if (R[i,j] == 1 and R[j,i] == 1):\n", " C[i,j] = 1\n", "\n", "C_3 = C@C@C \n", "clique_nodes = []\n", "for i in range(N):\n", " if (C_3[i,i] != 0):\n", " clique_nodes.append(i)\n", "print(C_3)\n", "lag.HighlightSubgraph(R,big_graph_positions,clique_nodes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the exact picture will change with each new random matrix, we will likely see that there are more than three nodes in the list $\\texttt{clique_nodes}$, and that this set of nodes defines more than one clique. For a graph with 10 nodes, we can still see fairly easily how to sort the nodes into different cliques. For large graphs we would want to make use of a sorting algorithm." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Tournament analysis\n", "\n", "In a **dominance directed graph** every node is connected to each other node, but only in one direction. This means the in the adjacency matrix $D$, either $d_{ij} = 1$, or $d_{ji}=1$, but not both. A dominance directed graph could be used to represent the results of a tournament where every player faced each other player exactly once, and either won or lost the competition. An edge from player 2 to player 4 means that player 2 won. Let's look at an example. " ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 1 0 0]\n", " [0 0 0 0 1]\n", " [0 1 0 1 1]\n", " [1 1 0 0 1]\n", " [1 0 0 0 0]]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "D = np.array([[0,1,1,0,0],[0,0,0,0,1],[0,1,0,1,1],[1,1,0,0,1],[1,0,0,0,0]])\n", "print(D)\n", "positions = lag.DrawGraph(D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this scenario the sum of the rows of $D$ indicate how many wins were earned by each player. In the example, players 2 and 3 both earned 3 wins, player 0 earned 2 wins, and players 1 and 4 earned a single win each. In order to distinguish the tournament standings between players 2 and 3, we might also look at all the two-step paths between players using the matrix $D^2$." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 1 0 1 2]\n", " [1 0 0 0 0]\n", " [2 1 0 0 2]\n", " [1 1 1 0 1]\n", " [0 1 1 0 0]]\n" ] } ], "source": [ "print(D@D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The number of two-step paths from player 2 represents the number of wins among the players that were defeated by player 2. Thus if we want to determine a player's tournament standing based not only on their number of wins, but also on the relative standings of the players they defeated, we can add the number of one-step paths (direct wins) to the number of two-step paths (indirect wins). " ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[0 2 1 1 2]\n", " [1 0 0 0 1]\n", " [2 2 0 1 3]\n", " [2 2 1 0 2]\n", " [1 1 1 0 0]]\n" ] } ], "source": [ "print(D + D@D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the sum of the rows of $D + D^2$ we see that player 2 has the highest rating in this particular tournament." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercises\n", "\n", "**Exercise 1:** Create your own adjacency matrix and use $\\texttt{DrawGraph}$ to make a visualization of the associated graph." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise 2:** Edit your matrix and redraw the graph to see the changes. Reuse the positions if you want the nodes to remain in the same locations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise 3:** Rerun the code in the two cells below until it produces a graph that has at least 5 nodes in the list $\\texttt{clique_nodes}$. Sort the nodes if they belong to different cliques." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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UHGzEV0YJCAhA+/btERQUVGx74nIiKioKTk5OiI6OhoqKSrbjwcHBaNSoEW7dugUnJ6dC9fHw4UMMHDgQdevWxaZNm1CpUqWiul0gUlNTsX37dqxatQoNGzbEvHnzUL169RL1gcFgFB9sxFcGEQgEGD58OFatWlWiogcApqamcHFxwaVLl3I8Xq1aNaxZswZdunRBYmJiofqoV68enj17Bl1dXdSoUSPXvooLNTU1TJ48Ge/fv4e7uztatmyJHj16sChQBqOcwISvDLJ27VoYGhqiX79+Mum/V69eOHLkSK7HBwwYgGbNmmHIkCGFLh+krq6OjRs3Yu/evRg5ciRGjRqVa9Ls4kJdXR1Tp07Fhw8fUKdOHbRo0QI9e/bEmzdvStQPBoMhXZjwlTE+fPiAVatWYfv27QUOIJEWXbt2hZ+fX56JrDds2ICIiAisW7euSH21aNECL1++REZGBmrWrFki2x7+RF1dHf/88w8+fPgANzc3NGvWDL1798bbt29L3BcGg1F0mPCVIeh/aclmzJgBa2trmfmhr6+P+vXr4/z587m2UVZWxokTJ7By5coii5W2tjZ8fHywfv169OrVC1OmTJEoU4y00dDQwPTp0/HhwwfUrFkTTZo0QZ8+fRAcHFzivjAYjMLDhK8MsW/fPvz8+TPfhNAlQX7TncCv0kT//fcfevfujejo6CL32b59e7x8+RKfP3+Gm5sbnjx5UmSbhUFDQwMzZszAhw8f4OzsjMaNG6Nfv354//69TPxhMBgFRJabCBmS8+3bNzI0NKQnT57I2hUiIoqPjyctLS2Ki4vLt+3ChQupUaNGlJGRIZW+OY6jw4cPk6GhIc2bN09qdgtLQkICLV68mPT09GjSpEn048cPmfrDYDDyho34ygiTJk1C//79UatWLVm7AuDX9GPz5s1x5syZfNvOmTMHGhoamDlzplT65vF46NWrF549e4aAgAC4u7vLNOJSS0sLc+bMwevXr5Gamopq1aph/fr1yMjIkJlPDAYjD2StvIz88fPzIysrK0pOTpa1K1k4cuQItW7dWqK2P378IEtLSzp+/LhUfeA4jry9vUlfX59WrFhBQqFQqvYLw6tXr6hNmzZkY2NDp06dIo7jZO0Sg8H4DbaBvZSTkpICZ2dn7NixA61atZK1O1lISUmBqakp3r9/DwMDg3zbP336FG3btsXdu3dhb28vVV8+fvyIQYMGQSgUYu/evbCxsZGq/cJw5coVTJkyBbq6ulizZg1q164ta5cYDAZYcEupZ+nSpahfv36pEz3gV5i/l5cXTp48KVH7WrVqYenSpejSpYvU9+RZWlrixo0b6N69Ozw8PLB169ZC7yGUFq1atcLz58/Rr18/dOjQAf3798fnz59l6hODwWApy0o1YWFhqFOnDl6+fInKlSvL2p0cOXv2LNatW4dbt25J1J6IMHToUPD5fBw8eLBY9iIGBwdj0KBBUFJSwrZt2wqdOk2aJCUlYeXKldi6dStGjx6N6dOnQ1NTU9ZuMRgVEjbiK8X8888/mDx5cqkVPQBo06YNXr58icjISIna83g8bNmyBW/fvsX69euLxadq1arh/v376NWrF5o2bYpZs2YhNTW1WPqSFE1NTSxevBjPnz/Hp0+fYGdnh507d0IoFMrULwajIsKEr5Ry48YNBAYGYvLkybJ2JU+UlZXRsWPHbAVq80JVVRVnzpzBqlWr4OvrWyx+ycvLY8yYMXj58iXCwsLg7OwMPz+/YumrIJibm2Pfvn24cOECDh06BBcXF1y+fFnWbjEYFQtZRtYwckYgEFD16tWlHgFZXFy6dInc3d0LfN7Dhw/JwMCAXrx4UQxeZeXSpUtkbW1N3bt3p8jIyGLvTxI4jqPTp0+Tra0ttW7dml69eiVrlxiMCgEb8ZVCdu3aBV1dXXTt2lXWrkhE8+bNERYWhvDw8AKd5+HhgY0bN6JDhw74+vVrMXn3i9atWyMoKAj29vaoWbMmNm3aBJFIVKx95gePx0OnTp0QFBQELy8vNG/eHCNGjCj2z4LBqOgw4StlxMXFYf78+Vi/fr3MklAXFEVFRXTt2jXXArV50atXLwwePBidOnVCWlpaMXj3/6iqqmLx4sW4c+cOTp48CXd3dzx9+rRY+5QEJSUljB8/Hu/evYOmpiacnZ2xfv16tv7HYBQTLKqzlDFp0iSkpqZix44dsnalQNy+fRsTJkzA8+fPC3wuEaFv377gOA6HDx8uEcEnIuzbtw/Tp09Hjx49sGTJEmhpaRV7v5IQHByM0aNHIzExEdu3b0edOnVk7RKDUa5gI75SRHBwMPbv34/FixfL2pUC07BhQ8TExBSqVA+Px4OPjw8iIiKwcOHCYvAu5z4HDhwoTjPm6OiI48ePy3zvH/ArKvXGjRuYOHEi2rdvj3HjxiEhIUHWbjEY5QYmfKWIyZMnY9asWTA0NJS1KwVGXl4ePXr0KNR0JwCoqKjgzJkz2Lt3Lw4dOiRl73JHT08Pu3btwuHDh7FgwQK0a9cOYWFhJdZ/bvB4PPTv3x9v3rxBeno6HB0dcezYsVIhzAxGmUeWkTWM/8fX15fs7OwoPT1d1q4UmkePHpG9vX2RclO+fPmSDAwM6MGDB1L0TDLS09Np2bJlpKenR//++2+p+l3cu3ePnJ2dqU2bNvT+/XtZu8NglGnYiK8UkJGRgcmTJ2Pt2rVQUlKStTuFpm7dusjIyMCLFy8KbaN69erYu3cvunbtio8fP0rPOQlQUlLCjBkzEBAQgLt378LV1RV3794tUR9yo0GDBggMDESzZs3g7u6OpUuXsuoPDEYhYcJXCtiyZQusrKzg5eUla1eKRGa5oPwK1OaHl5cXZsyYgfbt2yMxMVFK3kmOlZUVfH19sXDhQvTu3RsDBgzAly9fStyPP1FUVMS0adPw5MkTPHz4EC4uLrh9+7as3WIwyhwsqlPGxMTEwNHREXfu3IGDg4Os3SkyL1++RIcOHRAeHl6k6EwiwtixY/Hx40ecO3cOCgoKUvRScpKSkrB8+XJs374dY8aMwbRp00pFjk0iwunTpzFhwgR4enpi1apV0NfXl7VbDEaZgI34ZMzcuXPRt2/fciF6wK+pSjU1Nfj7+xfJDo/Hw4YNG8BxHEaOHCmzoA5NTU0sXboUz549w8ePH2Fvbw9vb+9Ssfm9S5cuePPmDXR0dODk5AQfHx9wHCdTvxiMsgAb8cmQFy9eoFWrVggODkalSpVk7Y7UWLRoEX7+/CmVJNQpKSlo0aIFmjRpghUrVhTduSISEBCAKVOmID4+HqtXry415aICAwMxcuRIqKqqlpqKFAxGqUWGgTUVGo7jqGnTprR161ZZuyJ1goODycTERGrV0GNjY8nBwYFWrlwpFXtFheM4OnXqFNnY2FDbtm0pKChI1i4REZFQKKTNmzeTvr4+zZw5k1JSUmTtEoNRKmFTnTLi9OnTiI2NxfDhw2XtitSxt7eHsbGx1CIi9fT0cOXKFWzZsgU+Pj5SsVkUeDweOnfujNevX6NVq1Zo1qwZRo0ahW/fvsnUL3l5eYwdOxYvXrwQV6S4ceOGTH1iMEojTPhkAJ/Px5QpU7B+/XqZBW0UN506dcK5c+ekZs/MzAxXrlzB7NmzcebMGanZLQpKSkqYOHEigoODoaamBicnJyxbtqzYc47mh6mpKY4cOYLNmzdjwIABGD9+vMzrETIYpQkmfDJg7dq1cHFxQYsWLWTtSrHx119/Sb3Wnp2dHS5cuIARI0ZIXPG9JNDV1cXatWvx6NEjPHnyBNWqVcOhQ4dkHmji5eWFly9f4sePH3BxccHDhw9l6g+DUWqQ9VxrRSM2NpZ0dXUpNDRU1q4UKxzHkYmJCYWEhEjd9vXr18nAwIACAwOlblsa3Llzh2rXrk116tShu3fvytodIiI6fvw4GRkZ0YwZM4jP58vaHQZDprARXwmzcuVKdO/eHTY2NrJ2pVjh8Xjw8vIqlgrrzZs3x/bt29GuXTuEhoZK3X5RadSoEfz9/TFhwgT07dsXXbt2xfv372XqU7du3fDixQu8efMGdevWLVJ2HQajzCNr5a1IREVFUaVKlejz58+ydqVEOHXqFHl6ehab/Z07d5KlpSV9+fKl2PooKqmpqfTvv/+Snp4eTZo0iWJiYmTqD8dxtHfvXtLX16clS5aQQCCQqT8MhixgI74S5N9//8XAgQNhZmYma1dKBE9PTzx69AhJSUnFYn/48OEYOXIkWrdujZ8/fxZLH0VFVVUVM2fOxOvXr5Geng57e3vMnDkTsbGxMvEnsxzT06dPcfPmTTRo0ADv3r2TiS8MhqxgwldCRERE4NChQ5g5c6asXSkxNDU14eHhgWvXrhVbH9OnT0fr1q3x119/ISUlpdj6KSpGRkbYsmULnj17hri4ONjb22PWrFn48eOHTPypUqUKrly5ggEDBqBBgwbiLDkMRkWACV8JsXjxYowaNapM1torCsUR3fk7PB4Pq1atgr29Pdq3b1+qxQ/4JTjbt29HYGAgfvz4ATs7O8yePVsmI1Y5OTmMHTsWDx8+xNGjR9GiRYsSr4jBYMgCJnwlQGhoKM6cOYOpU6fK2pUSp127dvD19S3W0YScnBx27doFc3PzMiF+AGBhYYEdO3bg6dOn+P79O2xtbTF37lzExcWVuC+2tra4e/cu2rRpgzp16mD37t2s4C2jXMOErwSYP38+Jk6cWK7ycUqKjY0NtLS08OzZs2LtR15eHj4+PmVK/ADA0tIS3t7eePLkCaKjo2Fra4t58+aVuADKy8tj+vTpuHHjBjZv3oz27dsjOjq6RH1gMEoKJnzFzKtXr3D9+nVMmDBB1q7IjMxRX3FTVsUP+FUDcNeuXXj8+DEiIyNha2uLBQsWID4+vkT9qF69Ovz9/eHm5gYXF5ci11ZkMEojTPiKmXnz5mH69OmlooabrCgp4QPKtvgBgLW1NXbv3g1/f39ERETAxsYGCxcuREJCQon5oKSkhEWLFuH8+fNYuHAhevbsWeICzGAUJ0z4ipGAgAAEBARg9OjRsnZFpjRq1Ajv3r3D9+/fS6S/TPGrUqVKmRQ/AKhatSr27NmDR48eITw8HDY2Nli8eHGJVqSvW7cuAgMDYWhoCDc3Nzx+/LjE+mYwihMmfMXInDlzMGfOHKiqqsraFZmipKQET09P+Pn5lVif8vLy2L17d5kWP+DXGunevXvx4MEDhIaGomrVqliyZEmJCaCqqio2bdqEVatW4a+//sL69etZ4AujzMOEr5i4c+cOQkNDMWTIEFm7Uipo164dLly4UKJ9lhfxA35FXu7btw/37t3Du3fvYGNjg7lz55ZYKaSuXbvi0aNHOHjwIDp37iyT6FMGQ1ow4SsGiAizZ8/G/PnzoaSkJGt3SgVt27bFtWvXIBAISrTf8iR+wK9ah/v378e9e/fw48cPODg4YOjQoXj9+nWx921tbY179+7B0tISrq6u8Pf3L/Y+GYzigAlfMXDlyhXExsaiX79+snal1GBsbAwbGxvcu3evxPsub+IH/CrRtHXrVoSEhMDKygqenp5o27Ytrl69WqxTkcrKyli/fj3WrVuH9u3bY+3atWzqk1Hm4BH71koVIkLdunUxbdo0dO/eXdbulCoWLlyIpKQkrF69Wib9i0QiDB06FBERETh37ly5irTl8/k4dOgQ1q5dC3l5eUyePBm9e/cu1hmHjx8/omfPnjAyMsLevXuhq6tbbH0xGNKEjfikzJkzZyAUCtG1a1dZu1LqKMltDTmROfKzs7NDs2bNEBMTIzNfpI2KigqGDBmCV69eYcWKFTh48CCsrKywbNmyYkuHZmlpibt378LGxgaurq6s0C2j7CC7whDlD6FQSE5OTnT+/HlZu1IqEYlEZGRkRO/fv5epHxzH0ezZs8nOzo4iIiJk6ktx8uLFCxo4cCBVqlSJxo4dW6zFj8+ePUuGhoa0cuVKEolExdYPgyEN2IhPihw5cgSamppo166drF0plcjJyRVbcdqCwOPxsGTJEowZMwYNGzbEmzdvZOpPcVGjRg3s3bsXQUFB0NbWRr169dClSxfcu3dP6utyHTp0wOPHj3Hq1Cm0b99eZmWXGAxJYMInJQQCARYsWIClS5eCx+PJ2p1Si6ynO39nwoQJ+Pfff9G8eXM8evRI1u4UG6ampli6dCk+fvyIFi1aYNCgQfDw8MCxY8cgFAql1o+FhQXu3LkDR0dHuLm5ySSQicGQCFkPOcsLe/fupaZNm8rajVJPQkICaWpqUlJSkqxdEePr60v6+vp06dIlWbtSIgiFQjp16hQ1aNCALC0tad26dZSYmCjVPs6fP0+Ghoa0bNkyNvXJKHWwEZ8U4DgOq1atqlBFZguLlpYW6tati+vXr8vaFTFeXl44c+YMBgwYUCGSMsvLy6Nz5864d+8ejhw5gocPH6JKlSoYOXIknjx5IpVp0L/++gsBAQE4f/482rVrV64CiRhlHyZ8UuDixYtQUlJCy5YtZe1KmaA0TXdm0qBBA1y7dg1Tp07Fli1bZO1OieHu7o6jR4/i9evXqFKlCrp3745atWph27ZtRUqMnZ6eDjMzM9y6dQs1atSAm5sb7t+/L0XPGYwiIOshZ3mgYcOGdPjwYVm7UWZ49+4dmZqaEsdxsnYlG2FhYWRjY0Pz588vlf4VNyKRiC5fvkzdunUjbW1tGjx4MD148KDAn0XHjh2pUaNGxOfziYjowoULZGBgQNu2bauQnyujdME2sBeRBw8eoF+/fggJCYGCgoKs3Skz2Nra4tixY3B1dZW1K9n49u0b2rZti3r16mHjxo2Ql5eXtUsy4du3b/jvv//g7e0NFRUVjBgxAv369cu3oHJSUhIMDAzA4/HQoEED8YxIaGgoOnXqhHr16mHLli1QVlYuoSthMLLCpjqLyMqVKzFlyhQmegXkr7/+KnXTnZkYGRnh5s2beP36Nfr06QM+ny9rl2SCkZERpk2bhnfv3mHjxo148OABrKysMGDAANy9ezfXtcBz585BUVERfD4fDx48QIcOHSAQCGBra4tHjx4hPj4eTZo0QWRkpMS+CEUcPsam4N3XJHyMTYFQxEnrMhkVEDbiKwLBwcFo0qQJwsPDoaamJmt3yhTXrl3D3LlzS3W2Dz6fj/79+yMqKgqnT5+GoaGhrF2SObGxsdi3bx+8vb0BAMOHD8eAAQOgr68vbtOkSRPcuXNH/H9VVVW0bNkSJ0+ehIKCAogIy5Ytw5YtW3D06FE0bNgwx77iUjJw9MlnnAj8gogfKVCUl4McjweOCAIRBws9dXRzM0OvOubQUWPJ4BmSw4SvCAwdOhQWFhaYN2+erF0pc2RkZMDAwAAfPnzIctMsbXAch3nz5uHQoUM4f/48nJyccm1LRODz+RWi/iIR4d69e/D29sa5c+fQtm1bDB8+HDVq1ICZmRnS09OztFdTU4OXlxeOHDkinjr28/PDwIEDsWDBAowePVq8/zVDyGHD9RDsuhcOHg/gC3If3akoyoEIGNbQChNa2EFJgU1iMfKHCV8hiYyMRPXq1REaGgo9PT1Zu1Mmadu2LUaMGIHOnTvL2pV82b9/P6ZMmYJ9+/ahTZs2ObYZNWoU7t+/j5cvX1aoJAZxcXE4cOAAdu7ciW/fviE+Pj7H8lNqamro2LEjDhw4ADm5XwL1/v17dOrUCe7u7tiyZQt+8Al9dz3Ct0Q+0vIQvD9RVZSDkZYKDg7zQGWd8v/gwSgaTPgKybRp05Ceno4NGzbI2pUyy7Jly/D9+3esW7dO1q5IxP3799GtWzfMmjULf//9d5Zjhw8fxrBhw8Dj8XDy5Em0bt1aRl7KDiKCo6MjgoODc22jpqaG7t27Y8+ePeKHg+TkZAwePBh8eTVEOvdDQqoAojxuS8lBN/DjwloAgG7bv6FZ89dnLc/jQVtNEefHNWTix8gTJnyFID4+HlWrVkVgYCAsLCxk7U6Z5cGDBxg3bhwCAwNl7YrEhIWFoX379mjatCk2bNgABQUFvH37FrVr10ZqaioAwMXFBc+ePZOxpyVPdHQ0rKyssk1z/omamhr69u2LHTt2iMUvXSCC59qbiErIyFP0hIkxiNo9DiAOlJGWRfiAX+JXRVcVVyY1gaI8m/Zk5Az7ZhSC7du3w8vLi4leEalduzZCQ0OLtFG6pLG2tsaDBw/w4cMHtGvXDp8/f0br1q2RlpYmbhMaGpoluKOicOTIEfEUZl6kpqZi//79+Pvvv8WRoRtvhCI2Je+RHhHhh+96yKtqQtOlbY5tRET4mpiODddDC3cRjAoBE74CwufzsXHjRvzzzz+ydqXMo6SkhLp165a5ZMba2tq4cOEC7Ozs4OjoiG/fvmUJ7U9JSamQ6eu8vb2zPADkBZ/Px5YtW9ClSxfEpWRg173wfNf0kp6cAz/iJfS8JoKnmPsewDSBCN53wxCfmlEg/xkVByZ8BWT//v1wcXFBjRo1ZO1KuaBx48ZlcnSkoKAAKysrZGRkICMj+w322bNnCAgIkIFnsiEsLAzh4eHZ3ufxeNDQ0IC2tjZUVVWhoKAAU1NT1KtXD+3bt4erqyuOPvmM/GKBBLGfEX/7P2jW7gCVKs75+sPjAUeffC7s5TDKOWzXdQEQiURYvXo1du7cKWtXyg1NmjTBjBkzZO1GgXnw4AHmzJmTo+gBv0Y0M2fOxLVr10rYs6wEBQXh0qVLmDp1arH24+vri4yMDMjLy0NLSwvm5uawtbWFs7MzqlatCisrK1hbW8PY2DjbdKjnutt5blkgToTYC2sgr2UAnSYDJPKHL+Bw4ukXjGxctUjXxSifMOErAGfPnoWOjg4aN24sa1fKDe7u7ggKCkJycjI0NDRk7Y5EfP/+He3bt89zWo+I8ODBA7x69QrVq1cvQe/+n8ePH8PT0xN8Ph8jRoyAlpZWsfU1ZMgQtG7dGhYWFgVKRSYUcYj4kZJnm4R7h5HxLQzG/VZALo8pzj/5+ONXhhcFFuTC+AMmfBJCRFixYgWmT59eofZoFTeqqqpwdXXFw4cPy0R1C5FIhA4dOiAxMTHftunp6ZgzZw7Onj2bb1uhiMOXuDSkCzkoK8jBrJJqkW7YN2/eRPv27ZGSkgJNTU1cvXoVXbt2LbS9/FBWVoa2tjbev3+P2NhYxMTEIDY2Vvz6+fMn+Hw+0tPTxf+mp6cjXUkL8o0nIPuuv1+kR71DwsNj0KrbCcqVHQrkk6K8HL7EpcFSX73oF8goVzDhk5A7d+4gLi4OHTt2lLUr5Y4mTZrg9u3bZUL4VqxYgYCAAHBc/purOY7DlStXEBoaCltb22zHiysl19mzZ9G7d2/xiDQpKQnHjh0rtPBlZGQgPDwcISEh4ld0dLRY1GJiYpCUlIRKlSrBwMAA+vr64peBgQEsLCzg4uICVVVVKCsrQ1lZGSoqKlBWVkZMhiJm3/oJ5FAJ/tcU51oo6laGTqP+BfZbjsdDupDl9GRkh+3jkxAvLy907twZw4cPl7Ur5Y4rV65gyZIlZSLI5fXr1zh69Cju3LmDly9fIjU1FSoqKkhJSYEwh5s3j8dDr169cOjQIfF7xZmSa//+/Rg5cmS2aVhNTU3Ex8fnut2A4zhERkZmEbfM1+fPn2FmZgY7OzvY2dnB1tYWlStXziJy58+fx+DBg6Gvrw9HR0d4eHjA1dUV1atXh52dHRQVFXPs92NsCrw23UVqhii7T/xkfF7fK8/rFV9f7Q7Q9RyR5T01JXlc/LsRG/ExssGETwJevnyJNm3aICwsDCoqKrJ2p9yRnJwMY2NjxMTElLk8l9++fUNgYCCePHmC27dv48WLF0hMTISqqqpYDHk8HkJCQmBjY4PI+LRiS8m1adMmTJ8+Pce1x8zpTnd3d3Ach5CQEDx8+BAPHz5EQEAAQkJCoK2tLRa331/W1tZQUsp7xBkaGooaNWqIK1lkRnNm5i81NzdHzZo14eHhgRo1aqB69eqoXLkyRBzBYf4lCETZb0OcIB1xV3fk2F/Gtw/I+PYBymaOUNQ1g4qVC9Qdsq69K8rz8HZhG7bGx8gGEz4J6N+/P5ycnMpk9GFZwd3dHStXrkSTJk1k7UqRiY2NxbNnz/DkyRPcuHED9+7dw8iRI/HPgmVov/letpRcwsRYxN89AH54IERpiZBX14WanQe0G/aBvMr/B/zklZJr0aJFWLFihTh7zJ/Iy8vDw8MDmpqa8Pf3h46ODjw8PFCvXj24u7ujWrVqRQ5+MTU1RXR0dJ5tFBUVoaqqCj6fD5FIhIYNG0Kh40K8/55coL7i7x5Ewv3D2TK3/I6toQauTir73yeG9GHClw/fv3+HnZ0dwsPD8y3AySg806ZNg4aGRrmtdJEh5NBq/W18/pmWRfQEcdH4uv8fcKnxULX1gKKeGdKjQpD+6SUUdM1g3H8l5FX/X5D+TMlFRJg8eTJ27tyZq+hloq2tjb1798LDwwPGxsZSv8a///4bW7dulWj9E/gVEHP06FFE6zhj/fWQPKd8/yQ/4VNRlMNkTzuMYNsZGDnA5gDywcfHB126dGGiV8yU1Y3skrLhegi+JfKzpeT6eWUruNR4VPIcCcOuc1Cp6SAY9/kXmnU6QvjzC+Jv78vS/veUXCKRCIMHD5ZI9IBfUaa1atUqFtEDgC5duki0JYXH46FSpUp4/PgxOnbsiF51zCHtx28ioEdtc+kaZZQbmPDlgUgkwo4dOzB69GhZu1LuadiwIfz9/XPdEF6WyS0llyD+K/jhzyCvbQTNWu2yHNNp2Bc8RRWkvL4JLiNrBfjMlFyuHg3x33//SSR6ACAnJ4cLFy4U7WL+QCAQ4OnTp9i8eTO8vb2RlJSUZ3t5eXkYGBjg8ePH4uxHOmpKGNbQCqqKkt+OdBr1hcWMCzmO9lQV5TG8kTUrTsvIFSZ8eXD58mXo6+ujTp06snal3KOjowMbGxs8ffpU1q5IndxScvEjXgAAVK1cweNl/VOUU1aDspkDSJCO9KjsZX54PECrZivUqFED+vr6UFRUhJaWFtTU1HL1IzU1FYcPHy70dcTFxcHf3x/79+/H9OnT0bhxY1SqVAkDBw7Eixcv4OnpiUaNGuV6vqKiIipXroynT5/CxsYmy7EJLeygxhMU+YYkz+PBWEsZE1pk3z7CYGTC9vHlwbZt29horwTJ3M9Xr149WbsiVU4Efslx/Ur4IxIAoFjJNMfzFCuZgh/+DMKfUYClS5ZjfAEHVafmuLdrIQAgMTERr1+/xqtXrxAQEIAnT54gJCQEHMdBSUkJaWlpEAgEePjwIVJTU3MVyLS0NHz48CHLdoZ3794hJCQE6enp4khPBwcHzJ07F3Xr1oW2trb4fCUlJQQGBiI5OWuwipKSEqysrHD37l0YGBiI309JSYGfnx/++ecfRCfwYTfeB0npIhAKniRCjgdoqsjhwDAPVpKIkSdM+HIhIiICDx8+xNGjR2XtSoWhSZMm2LlzZ7mKns0rJReX/ut9nkrO+8x4yur/a5dzxOPvKbm0tLRQr1491KtXDyNG/NrPRkSIjo7Gy5cv8eTJE9y7dw8fPnzAsWPHwOPxsmRWiYiIQEhICL5+/Qpra2uxwNWvXx+DBg2CnZ0djIyM8s1a1KZNm2zT1SoqKnB0dMSNGzegra2NhIQEXLhwAf/99x/u3LkDjuMgEAjQoUMHqH46h1cGzcApaxZwu4c8hEmxeL1lCmaEtsKsWbPg4FCwTC+MigMTvlzYuXMn+vXrl+fUEUO6NGrUCIMGDYJQKISCQvn4an6JS4OivBwEouwbtPMnM+IjZ7EhkRBT5v8L5YzELGnAUlNT8ePHjyxpw5SVlcWZVI4dO5Ylu4q1tTU6d+4Me3t7WFhYFOmz19fXh52dHYKCggD8SklXt25d7N+/HydPnsTevXvh7+8PJSWlLKNCZWVlNG3aFFu2bEHA0xXY9ShKog3+yvI8gMfD0IZWsEhMRa+NsTh48CBOnjwJV1dXzJ07F61atZKoTiCj4lA+7i5SJiMjA7t378atW7dk7UqFQl9fH+bm5nj+/Dlq164ta3ekQrqQg1wuoyS5/43oiJ/ziJDSU7O0y6EF5BSUoKepJ04BpqysDFVV1Swpw/T09Eo08ULv3r2xYMECKCgowMbGBikpKbCxsYGioiJSUn5d65+jQl1dXaxYsQInT55EJW0t/NNaCwPqmqHp0Fkwr9MOX1NE2VK6KWckoZp8HHbNHAIdNSXExOhCQUEBGRkZSEtLw4MHD9C9e3fo6Ohg5syZGDhwINTVWRYXBhO+HDl9+jQcHR1RrVo1WbtS4cjc1lBehI+fmgQul1h9Bb3KAABBXFSOxzPfV9DNeQ1QSUkZE8aNLXUpuTp06IDZs2dDJBLhw4cP4qjT3CJ2lZSUoKmpiS5duqBBgwYAfkVUD+jVFcFXrmD3Xy4YMHBQtiTez58FomfPntBePBIAYGBgAAMDA0RGRoptJycnIzk5GdOmTcP06dMxfPhwTJo0CebmbKtDRYaN/3OABbXIjswAl7LKz58/cebMGUyYMAE1a9ZEYzcnpAtynuZUqfIrnD8t/BmIsk7ncempSP/yFjwFZSib5vwAJhBxMKtU+lK8OTk5YdSoUVBRUZFoq0VmDo0FCxaI/z906FDxjMurV6+gIC8HS3112BtrwlJfHQrycqhVqxaUlZXx4MEDsa3cMv+kpKQgOTkZW7ZsgZ2dHdq3b49Hjx4V7UIZZRYmfH/w5s0bhISEoFOnTrJ2pULSuHFj3L17V+LsH7ImPj4e586dw6RJk+Dq6gpLS0ts374dJiYm2LlzJ37ExsDKIOdN3YqVTKBi5QpRwjckPfXNavfeQZCAD3XnZpBTynma0lJPvVTmoeTxeNi2bRtmz54t0Rq5SCTC8ePHxXX8pk2bhuPHj4tHiA8fPsy1nwEDBmDfvv/f5N+qVas8N9FnZGSAz+fD19cXDRs2xPTp0wtyaYxyAktZ9gfjx4+HtrY2Fi9eLGtXKix2dnY4ceKEeINzaSItLQ23b9/GtWvXcPPmTYSEhKBevXpo2rQpmjVrhtq1a2erRLD99odcU3LlnbKsMoz7r8qSsiyTspKSK78conJycmjWrJm4Uv2qVauwYMGCLO01NTVzrX/45csX1KxZE5GRkVBRUUFYWBiqV6+e70hTWVkZpqamuHHjBiwtLQt3cYwyCxO+30hOTkaVKlXw4sULtgYgQ4YNGwYXFxeMGzdO1q4AAD58+AA/Pz9cvHgR9+7dg4uLC1q1aoVmzZqhTp06+VYuiE/NgPuy67nWhhMmxiD+7kHww55ClJYEeY1KULP9X5JqVc0cz1FWkIP/zBZlIjvJtGnTsGbNmhxH8TweD2/fvoW9vT327t2LMWPGZKsuoaysjI8fP+aaaq1ly5YYMWIEunfvDiJCpUqVkJCQkKs/ampqqFevHk6fPg1NzZw/X0b5hgW3/Mbhw4fRqFEjJnoypkmTJjh37pzMhI/P5+P27dtisUtKSkLbtm0xePBgHDp0CDo6OgWyl5mSy+d+9rRlAKCgZQD9dhMltqeqKI+hDa3KhOhFR0fDz88PioqK4v16v2NhYQF7e3ucO3cuR9EDfgnfixcvchW+zOnO7t27g8fjoV69erh06VKObdXU1DB8+HCsWbMG8vLyRb9ARpmk9C0QyAgiYkEtpYQmTZrgzp07KMnJiPDwcGzZsgV//fUXDA0NsXjxYhgaGuLo0aOIjIyEj4+PODS+MExoYQctRapQKblCQ0NRv359JCQkYNy4cRg/fnyWNT8FBQWMGzcOd+7cQa9evXIUPeDX9PKzZ89y7adz5864d+8evn//DuDXJvrctm/Mnz8f69evZ6JXwWHC9z8eP36MhIQEtGrVStauVHiqVKkCVVVVvHv3rtj6SE9Px9WrVzF58mRUq1YN9erVQ0BAAAYMGICIiAjcu3cPs2bNgqurq1Q2P798HoiPPpOhocSDfD7ZT3Ijsx5fWUjJFRAQgMaNG0NLSwtNmjTBypUrsWrVKgwbNkwcxCIvL4/q1avDy8srV9EDfiXCvn//fq7HNTQ00KFDB3Ee0saNG2dZZ5WTk4O2tjbGjh2L48ePIz09XUpXySirsDW+/zFo0CA4Ojpi2rRpsnaFAWDgwIFo0KCBOP2WNPj48SP8/Pzg5+eHW7duoXr16mjbti3atm0rNYHLibCwMDRs2BDbt29HrcYtC1WBnQR8GGgo4exEz1wrsJcWLl++jH79+ok/0/Pnz4uFKDExEZUrV0ZaWhrs7OwQHR2N+Pj4fG2amZnh8+fPuR6/fv06pk2bhqdPn0IoFEJTUxN8Pj9LEIuFhQW6du0KU1NTbN68WVqXyyiDlO7HxhIic+/V4MGDZe0K43/UrVsXT548KZINoVCI69evY8qUKXB0dIS7uzsePXqEPn364OPHj7h//z7mzJmDWrVqFZvoxcTEoE2bNpg3bx46dOiAyjqquDKxCZwVY6Ekz4NKPqV4VBXloKwgh8QnZxG4pAsunTxUolPABeXgwYMYMGAA2rVrh7i4OJw4cSLL6Gv27Nno2rUrJk2aBJFIJM7kkh9fv37Nc1TYtGlTxMTE4MWLF1BQUEDNmjWhqKiIhg0b4sWLF7C0tASPx4OPjw8uXbrEcvBWdIhBa9asob59+8raDcZvPHjwgGrVqlXg8wQCAV25coWGDx9O+vr6VKdOHVq4cCEFBASQSCQqBk9zJyUlhdzd3WnWrFni99LT06lfv34EgLbs2kvbb78nz7W3qOrMC2T5zylymn+JHOb5keX0s2Q6bCtN87lMcSnpVKVKFQJAcnJy1KhRIwoNDS3Ra5GENWvWkLm5Oc2ZM4dsbGzo27dvWY7fv3+fTExM6MePH0REFB0dTbt27aJWrVqRiooKaWlpEY/HI/xKUprlpampSQEBAXn2v3DhQho9ejQREe3Zs4emTZtGQqEwW7unT5+Svr4+BQcHS+nKGWWNCi98IpGIbG1t6d69e7J2hfEbKSkppKqqSunp6fm2FQgEdPXqVRoxYgQZGBhQ3bp1afXq1fTx48cS8DR3nzp06EADBgwgjuOIiOjz589UvXp1UlBQIAUFBTpz5oy4/c1bt8m9xV8UHJ1I4THJpKunTwBISUmJXr9+TU2bNhWLAI/HI1VVVfrnn38oJSVFVpcoRiQS0dSpU8nBwYG2b99Opqam9OHDhyxt+Hw+OTg40LFjx3K0kZ6eTjdv3qTatWuTlpYWqaiokJqamvia1dTUaNeuXXn68eXLF6pUqRIlJSXl6/P27dvJ2dm5VHx+jJKnwgvftWvXqHr16uKbE6P04OTkRIGBgTkeEwgEdO3aNRo5ciQZGBhQnTp1aOXKlRQeHl6yTuYAx3E0cuRIatmypVi4b9y4Qdra2iQvL08ASF1dnY4fPy4+5+bNm9S4cWMiIkpLSyM5OTnxTV9bW5u6d++ebRSkqqpK+vr6dPz4cZl9f9PS0qhPnz7k4eFB586dIwMDgxx/Z/PmzaOOHTvm6SfHcVS1alV68uQJffz4kbZu3UpNmjQhZWVlUlBQoFGjRuXrT6dOnWjnzp35tuM4jvr27UuDBg3Kty2j/FHhha9///60fv16WbvByIH+/ftnecoXCAR0/fp1GjVqFBkaGlLt2rVpxYoVFBYWJkMvs7Nx40aqUaMGJSYmEsdxtGTJElJVVc02dXfo0CHxOdeuXaNmzZoREdG9e/dISUkpS3t1dXWxaP75UldXp/r165f41F1UVBTVrVuXevToQf7+/mRoaEhXr17N1u7Vq1ekr69PX758ydNeYGAgWVtbZxPHtLQ0unz5Mj19+jRfn/z8/MjNzU0i/5OSksjBwYF2794tUXtG+aFCC19ycjJpa2vT169fZe0KIwfWrVtHo0ePphs3bojFrlatWrR8+fJsU2mlhTt37pChoSF9+PCBEhISqE2bNlmm7H4Xq//++0983pUrV8jT05OIiFauXJnrWlduLzk5OVJRUaFJkyZJNNVXVJ48eULm5ua0aNEi+vjxI5mZmdHhw4eztROJRFSvXj3avn17vjZnzJhBM2bMKJJfIpGILC0t810PzOT169ekr69Pz58/L1K/jLJFhRa+gwcPUps2bWTtBuMPhEIh3bx5kzp27EiKiork5uZGy5Yto/fv38vatTz5/PkzmZiY0KVLlygoKIgqV65MysrKOQrVn2tWfn5+1KpVKyIi8vT0LJDo/Tn9qaurS7dv3y626zx27Bjp6+vTiRMnKDY2lqpVq0br1q3Lse3evXupbt26+QYWcRxH1tbWEo3q8uPff/+loUOHStz+wIEDZGtrSwkJCUXum1E2qNApyw4cOIB+/frJ2g0GAI7jcPfuXRw/fhwnT56EiYkJOnTogCtXrsDf37/UV2RPT09Ht27dMH78ePz48QNdunTJM1EyEWVJ3yUSiSAvLw8iQkBAQKH94Diu2CpbcByHxYsXw8fHB1euXIG9vT1atGiBDh06YOLEidnaJyYmYubMmThz5ky+20WePXsGHo8HV1fXIvs5ZMgQVKtWDWvWrIG2tna+7fv27Yu7d+9i6NChOHbsGHiFTDDAKDtU2H18379/x4MHD1j5IRnz6dMnLFq0CFWrVsXff/8NU1NT3LlzB4GBgViwYAHMzc0RHBwsazfzJdP3iIgIDB8+PN/qAH/mrcwUvs+fP+e5Xy0vVFVV0a1bN4SFhaFx48aFspEbqamp6NWrFy5dugR/f39Ur14dPXv2hK2tLZYtW5bjOYsWLUKbNm1Qt27dfO0fO3ZMnGuzqBgZGaFVq1Y4cOCAxOesX78eYWFh2LRpU5H7Z5R+SvdjdDFy9OhRtG/fHurqpat6dUWAz+fj7Nmz2L17N54+fYrevXvj5MmTcHV1zXbjc3NzQ2BgIJydnWXkbf7s3LkT9+/fx8GDB1G/fn2JRlx/Ch/HcZCXl8fDhw8LvJleXl4eioqKuHDhApo3b15g//Pjy5cv6NixI5ycnHDz5k0oKytj2LBhEAgE2L17d47+BgcH47///kNQUFC+9okIx48fx4kTJ6Tm88iRIzFhwgSMGTNGIjFVUVHB8ePH4eHhAXd3d7i7u0vNF0bpo8KO+Ng0Z8nz/PlzjB8/HmZmZvD29sbgwYPx5csXbN68GW5ubjneoGrVqoWnT5/KwFvJePToEebMmYPTp0/DxcUFUVFRmDlzJjQ1NfMswkpEEAqF4v+LRCLIycnh1q1b4PP5EvfP4/Hg4uICOzs7iUSmoPj7+8Pd3R09e/bEf//9BxUVFcybNw+vXr3KlpUlEyLChAkTMGvWLBgZGeXbx5MnTyAnJwcXFxep+d2sWTNkZGTkWsQ2J6ytrbFz50706NEDP378kJovjFKITFcYZcS7d+/IyMiIBAKBrF0p9/z8+ZM2b95Mrq6uVKVKFZo/f36B9tpdv36dGjZsWHwOFoHo6GgyMzOj8+fPZzuWnJxMa9asIU1NzRwjNHk8Hi1ZskTc/ujRo9StWzeyt7cvUDCLiooK6erq0vXr18nQ0JDu3Lkjtes7cOAAGRgY0Llz58TvbdmyhWxtben79++5nnfmzBlycHCgjIwMifoZPXo0LV68uMj+/snq1aupf//+BT5vypQp1LZt2xLP9MMoOSqk8M2bN48mTpwoazfKLSKRiK5evUq9e/cmbW1t6tmzJ125ciXH9FH58fPnT9LQ0Ch1N6H09HRq2LAhzZ8/P9c2QqGQatSoQSNGjCBTU1PS0NDIIlrz5s0Ttz1+/Lg4ilUSwdPQ0KBhw4ZRWloaLVu2jDp27Eh+fn5kampKkZGRRbo2kUhEM2fOJCsrK3r16pX4/bNnz+aYleV30tLSyMrKKsf9fDmRmppKurq69OnTpyL5nBMxMTGkra0tTpEmKRkZGdSgQQNaunSp1H1ilA4qnPBlhk0/efJE1q6UOz5+/Ejz588nCwsLcnFxoU2bNhX4ppMTVlZWpS6v4rhx4+ivv/7KU5C9vb2pYcOGxHEcCYVCOnLkCFWtWlUsgNOnTxe39fPzozp16mQTx99HiFWqVKFq1apl+yz4fD5VrVqVrly5QkuWLKF69epJlOotJ37+/Ent27enxo0bZxnVvXz5kvT19cnf3z/P8xcvXkxdunSRuL+DBw+Kt3EUB3379qW1a9cW+LzPnz+TsbEx3bhxoxi8YsiaCid8Dx48oGrVqrEUZVIiLS2NDh8+TJ6enqSrq0tjx47NNc1YYenatWuWLCeyZu/evWRra0vx8fG5tklISCBjY+NsD1gcx5Gvry/VrFmT1qxZI37/7t27ZGlpKU5VJicnR9WrV6dly5bRkCFDqF69ernulSP6Nb3o6OhIfD6fOnbsSGPGjCnwdQUEBJCVlRVNnDgxi3B+//6drKys6ODBg3me/+nTJ9LT0yvQVLanpycdOXKkwL5Kyt27d8ne3r5Qf++XL18mU1NTio6OLgbPGLKkwgnfmDFjsqytMArHs2fPaNy4caSnp0eenp50+PBhSktLK5a+/v33X5oyZUqx2C4oT548IX19fQoKCsqz3T///EODBw+W2O7z58/JwcGBbty4QU+ePMkykjx8+DC5urpSnz59cj2f4zhq2bIlbdiwgeLj48nOzo727NkjUd8cx9GWLVvIwMCATpw4keVYeno6NW7cWKKMKj169Mhz6vdPwsPDSU9Pr9i+N0S/rs3JyYlu3rxZqPPnzZtHnp6epW6qnVE0KpTwpaenk76+fqnL7VhWEAqFdPLkSWrUqBGZmZkVOFClsFy6dEmcx1KWfP/+nSwsLLKJw5+EhoaSnp5egUYK79+/J2tr6xyPhYeHk6GhIdnY2ORp4/Xr12RgYEAxMTHiVFz5ZUJJTEykXr16kYuLS7ZSRxzH0YgRI6h9+/b53vhv3rxJFhYWBap2sGDBAho3bpzE7QvLxo0bqVevXoU6VyAQkLu7O23cuFHKXjFkSYUSvnPnzlGDBg1k7UaZIy4ujlavXk2WlpZUr149Onr0qMQRe9Lg27dvpK2tLdPpaY7j6K+//qJp06bl27Zjx460bNmyAtn/+vUrGRgY5Nq3np4eaWho5LtmOn78eHEVg+PHj5OFhQXFxMTk2Pbly5dkZ2dHI0aMoNTU1GzHN23aRE5OTpSYmJhnn5lBPL9Xm8gPkUhEFhYWUklRlh9xcXGko6OTrT6gpLx794709PTo7du3UvaMISsqlPD16NGDtm3bJms3ygwhISE0btw4qlSpEvXp0yffwIbixMzMTKaJqX18fMjFxSXfoJFr166RlZVVgafvkpOTSVVVNdfjrVu3JmdnZ7p06VKedn7+/EmGhobipMvTpk0jT0/PbBG1Pj4+pK+vT/v378/1OoyMjCT6zPft20f169cv0IPJ9evXqWbNmiX2MDN48GBavnx5oc/funUr1apVq0Qf+BjFR4URvoSEBNLS0qLY2FhZu1Kq4TiOrl69Su3atSMDAwOaPXt2vuVkSoKOHTvmWsS0uPn48SPp6+vTy5cv82wnEAjI2dk536nQnOA4juTk5HLd8jF79myqX78+LVq0KF9b27ZtoyZNmhDHcSQQCKhFixbiNbqUlBQaNGgQOTg40OvXr3M8PyQkhAwNDSVaF+Pz+WRpaVng/YN9+/alDRs2FOicouDv70/W1taFXqvjOI7atGmTZQsKo+xSYYRvz5491LFjR1m7UWpJTU2lnTt3kpOTEzk7O5O3t3eO01+yYuHChUUuWVMYRCIRNW/eXKKpy8zCqYUdxWhqauZaIeD06dPk5uZGf/31V752/px6zFyb3LBhAzk7O1Pfvn1zLV0UHx9P1apVk3hmZMOGDdSuXTuJ2mYSFxdH2traJfoQynEcubi40OXLlwttIyoqigwNDenRo0dS9IwhCyqM8LVo0aJAaxAVhS9fvtCsWbPIwMCA/vrrL7p27Vqp3Opx/vz5Yt3vlRubN28mDw+PfLP8xMXFkaGhIT179qzQfZmYmOQ6uv78+TPp6+uTgYGBRL+fzGCTzIeXpUuXEo/HowULFuR6vlAopLZt20q8FSIxMZGMjIzoxYsXErXPZNu2bdStW7cCnSMNtm/fTp06dSqSjePHj5OtrS0lJydLySuGLKgQwvflyxeqVKlSsYZNlzX8/f2pd+/eVKlSJfr7778pJCRE1i7lSWRkJOnr65eoKIeEhJC+vj69e/cu37Z///03DR8+vEj92dra5rpRn+M4MjIyIgMDA/r48aNE9rp160bz5s2jMWPGUNWqVWnevHlkb2+f66hy6tSp1KxZM4nXsRYsWED9+vWTqO3v1K1bly5evFjg84pKUlIS6evrZ4teLSj9+vWj0aNHS8krhiyoEMK3atWqAhWmLK9kZGTQkSNHyMPDgywtLWnNmjUUFxcna7ckxtjYmCIiIkqkL6FQSPXr15doHerWrVtkYmJS5Kk7V1fXPDMKeXl5UZ06dSRe6/T19SV5eXny8vISb7YfOXIkderUKdta1969e6lq1aoSX8O3b99IV1e3wFuDnj9/TpUrVy5U+jppMHv27CKLVlxcHFWpUkUm4s2QDhVC+GrWrFnoDazlgfj4eFq+fDmZmZlRkyZN6NSpUzK78RQFLy8vOn36dIn0tXLlSmratGm+wRCJiYlkZWWVJZFzYWnUqBHdunUr1+Pz5s2jJk2a0NSpU/O0IxQKadmyZaSvr0+dOnXKsoeNz+eTu7s7/fvvv+L3Hjx4QAYGBrkGu+TE+PHj6e+//5a4fSZDhw6VaQKJr1+/ko6OTp5JtiXh+vXrZGpqyoLlyijlXviCg4PJ1NS0QmZe+PHjB82bN4/09PSoX79+Uk8lVtLMmTOH5s6dW+z9BAUFkb6+vkSb80eOHFmgDC154eXllWOlh0zOnTtHtWvXpsaNG+fa5sOHD9SgQQNq2rQpffz4kZKTk8nU1DTLSPLz589kYmJCly9fpk+fPpGpqSlduHBBYj/Dw8NJV1eXvn79KvE5RL+SRktDdIrKsGHDaMGCBUW2M2nSJOrWrVupXBNn5E25F74VK1ZUuPn4mJgYmjlzJunq6tLQoUPp/fv3snZJKpw6darAEYQFJSMjg2rVqkU7d+7Mt+2lS5eoSpUqeebsLAg9evSgw4cP53o8MjKSdHV1SV1dPVuwDcdxtGvXLtLX16c1a9ZkedDbunUrtWnTJkv7W7dukYGBATk7O9OKFSsK5Gf//v0LFdb/77//Su0hoSi8ffuWDA0NC5RlJifS0tLI0dEx172QjNJLuRe+evXq5bvpt7zw9etXmjp1Kunq6tKoUaNKJJ1YSRIREUEmJibF2sfChQupTZs2+T7F//z5k8zMzCQuvyMJQ4YMIW9v7zzbmJqakpWVVZY9hd++faMOHTpQzZo1s5QRyiQ9PZ2srKzo9u3b4vcyw/srVapUoAjFFy9ekKGhYa4BMrmRkZFBZmZmpWbWoUOHDrR169Yi2wkMDCR9ff0SW3tmSIdyXYH927dvePPmDZo2bSprV4qVqKgoTJw4EQ4ODkhPT8eLFy+wbds2WFpayto1qWJubo6MjAxER0cXi/3AwEBs3rwZu3btyrEa/O9MmDABHTt2hKenp9T619DQQHJycp5tateuDTMzMzx+/BgAcO7cOdSsWROOjo7w9/eHs7NztnOUlJSwYMECzJ49G0QEAFiyZAmUlZXRsmVLjB49Wvx+fsyePRszZ86ElpZWga7tzJkzsLKygqura4HOKy7++ecfrFmzBiKRqEh2XF1dMWnSJAwaNAgcx0nJO0axI2vlLU68vb2pR48esnaj2IiIiKAxY8ZQpUqVaPLkyRQVFSVrl4qdli1bFmg9SlL4fD45OTnRgQMH8m17+vRpqlq1qtT3cs2aNSvfzCyLFi2iFi1a0KBBg2jo0KFkZWVFd+/ezde2UCgkBwcHunjxIp08eZLMzMwoKiqKkpOTqXr16rR58+Z8bdy7d4+qVKlSqG1BDRs2LFX7aDmOIw8Pj0Jl2fkTgUBA9evXL1TdP4ZsKNfC165du1JVx01ahIWF0fDhw0lXV5emTZtW6OS7ZZEpU6ZkiUiUFtOnT6cuXbrkO8X5/ft3MjY2pnv37kndh2XLluWbBPvixYtUrVo1UlJSoqFDh+abQPp3Tp48SQ4ODqSnp0cBAQHi99+/f08GBgb5XlOrVq0kWvv8k6dPn5K5uXm+SQBKmhMnTpC7u7tUglPev39Penp6+ZarYpQOyq3wJSUlkaamZpnap5YfISEhNGjQINLT06PZs2fnmnW/PLNz506pB0i8efOG9PX1832A4DiOunbtmu92gsKyadOmPLOmpKWl0d9//008Ho8UFRULnFIuKSmJVFRUxNUbfsfX15dMTU1zzRzz+PFjMjMzK1Rl94EDBxYpQXRxIRQKycbGRqIRsyTs3LlTokTmDNlTbtf4rly5And3d+jo6MjalSLz9u1b9OvXD/Xr14elpSVCQ0OxZMkS6Ovry9q1EsfOzg4hISFStTl58mTMnj0bhoaGebY7cuQI3rx5g8WLF0u1/0zyWuO7c+cOXFxc8OXLF1SuXBl2dnZ49uxZgeyPHz8eDRo0wM2bNyEUCrMc8/Lywt9//42//voLSUlJ2c5dunQp/vnnHygpKRWoz+/fv+Ps2bMYNmxYgc4rCeTl5TF58mSsWrVKKvaGDRsGMzMzLFy4UCr2GMWIrJW3uBgwYABt2rRJ1m4UiVevXlHPnj3JwMCAli5dWuBIuvJIVFRUrnXrCoOvry/Z2dnl+5QeGRlJBgYGWaYIpc3x48epc+fOWd77+fMnDRs2jCpXrkynTp0iIqIuXbpQixYtClQcde/evVStWjVKTEykJk2akI+PT7Y2HMfR0KFDycvLK8u05MuXL8nIyKhQ4f+LFy+mYcOGFfi8kiI1NZUMDQ2lVmsvOjqajIyMimUqnCE9yqXwCQQC0tPTo0+fPsnalULx9u1b6tq1KxkbG9PKlStzzaRfEeE4jjQ1Nennz59FtpWRkUH29vb5BstwHEdeXl7FXpLm2rVr1KRJE3GfR48eJRMTExozZkyWvYJLly6lxo0b08SJEyWym7khP3OrQ2aQCp/Pz9Y2IyODWrZsSWPGjBGvffXu3bvAhXUzbZmamuZbzknWLFiwQKrifOLECbK3t8/x82WUDsql8N28eZPc3Nxk7UaBiY6OplGjRpG+vj6tXLmyyBtsyyu1atWSSlHc9evXU+vWrfMNbti1axe5uroW+9rN+/fvycLCgj5+/Ejt2rUjJycnevDgQbZ2ly9fJkdHR4nKbCUnJ5ODgwPt2bMny/vt2rXLdcQYHx9Pzs7OtGbNGgoNDSU9Pb1CzTYcOnSImjVrVuDzSprMjDLR0dFSscdxHHXo0EEq2WEYxUO5FL6JEyfSwoULZe2GxCQlJdH8+fNJV1eXpkyZQj9+/JC1S6Wa3r170759+4pkIyYmRqL8lJmBLyUxaklNTSU5OTnS09OjJUuW5Cq0sbGxpK6uTjVq1MjTHsdxNGDAABo4cGC2Y8+ePSNjY+Nct2RERERQ5cqVqUWLFoUa6XIcR66urnT27NkCnysLRo8eTbNmzZKavU+fPpGenp7UplAZ0qXcCR/HcWRpaVngGmGyICMjg7Zt20bGxsbUt2/fcpdppbiYP38+zZkzp0g2xowZk2+S5YSEBLK3t6fdu3cXqS9JePbsGdWuXZuUlZXp2rVr+ba3sLAgdXX1PEerPj4+5OjomKu49ezZM8+tIRcuXCAej0dXrlzJ/wL+4OLFi1S9evUykyM3NDSU9PX1pbqssH79+iIVJmYUH+VO+F68eEGWlpal+svGcRydPn2a7O3tqXnz5vT06VNZu1SmOHjwYL6JCfLaXP7q1SsyMDDIM7O+SCSijh07Fnue15SUFPrnn3/I0NCQfHx8qFGjRnT9+vV8z+vevTupqqrmOjvw6tUr0tfXz3NE++7dO9LX1891vfTvv/+mzp07k4mJSYHKD3EcR/Xr188z72hppGvXrhKVoZIUoVBItWvXLpEHJ0bBKHfCt2jRIpowYYKs3ciVBw8eUIMGDah69erk5+dXqgW6tBIQEEAuLi55tlFXV6cGDRpkyU9J9Oum7OnpmW9E5OLFi6l+/frFuq53+fJlsrKyoj59+oj3EA4cOJB27dqV77krVqwgfX39HOv3JSUlUbVq1ei///7L187QoUNznOL7+vUrVapUiaKiomjjxo3k4OAgcUDRzZs3ydbWtsyVvnr06BFZWlpKdaP9s2fPyNDQsEIlmSgLlDvhq1WrFt24cUPWbmQjJCSEunbtSubm5rRnz54yd1MoTSQkJOQ7zaegoEAAxGthvr6+xHEcnT17lhwcHPKsMp65mTsyMrI43KeIiAjq2bMnWVpakp+fX5Zj8+fPp9mzZ+dr4/r166Srq5st5RbHcdSvXz+JN/lHRETkWGJo2rRpWTbTT5gwgZo1aybRg4Cnp2eZHeU0atRI6iPVqVOnUt++faVqk1E0ypXwffr0iXR1dUtVaqRv377R2LFjSV9fn5YvX17gbBuMnDE2Ns41ywgRkbKyMgEQv9TV1cna2pqMjIzI19c31/NCQ0MlSt9VGJKTk2nu3Lmkq6tL8+fPzzFqd+/evRLdJOPi4khRUTFbSSFvb29ycnIqUETwhAkTaPz48eL///jxgypVqkQfP34UvycUCqljx440YMCAPB84/P39qUqVKmU2e8nZs2fJzc1NqjMxycnJZGlpWWGqxJQFypXwbd68mfr37y9rN4jo15d98eLFpKenRxMnTqyQ6cWKk8aNG+c5sldTU8sifJkveXl5MjU1JW9v72w356SkJHJ2dpZKuZrf4TiODhw4QGZmZtS7d+8895fevn2b6tevL5FdAwODLNXVX7x4Qfr6+vTmzZsC+Zc5rZk56lu6dGmOkaDJyclUu3btPCOmO3ToIFHC69KKSCSiatWqSbXcFNGvYB8rKyu2RamUUK6Er2XLllLJtl4UBAIBeXt7k6mpKfXq1Ys+fPggU3/KK8OGDaNt27blelxTUzNH4ft9BKinp0dr1qyh5ORk4jiOevToQYMHD5bq076/vz95eHhQrVq1JBpFfvr0SeKag40bNxZvaUhMTCQ7O7tCF0UdO3YszZw5kzIyMqhy5cr07NmzHNtFR0eThYVFjv28fPmSTExMyvysxv79+6l+/fpSX3/v2bMnTZ8+Xao2GYWjzAnfzZs3afny5fT06dMsodJxcXGkqakpsywnHMfR+fPnydHRkZo0aUKPHz+WiR8VhZUrV9KkSZNyPa6jo5On8GW+FBQUqGXLlrRy5UqqXbt2oUru5ERkZCQNGDCATExMyMfHR+KwfqFQSEpKShL5MXHiRNLV1SWO46h37940dOjQQvsbFhZGenp65OPjQ40bN86zbVBQEBkYGNCtW7eyvN+rVy9auXJloX0oLWSWcPpz/bWoREdHk76+fpnYalXeKXPCt3z5cpKXlycNDQ1SV1enVq1a0ZYtW2jNmjXk5eUlE5/evXtHrVq1IkdHRzp//jyL1CwBzpw5Q+3atcv1uL6+fr6ip6qqStWqVaP9+/eTsbGxVFLcpaam0pIlS0hXV5dmzJhRoLJBmVStWpWCg4PzbXf48GGSk5Oj7du3U/Xq1Ys80urbty9ZWFjQyZMn82177do1MjQ0FPuZuTWiMNdbGjl69CjVqVNH6n/LO3fuJHd3dxbcJmPKnPDdvHmTtLS0st3A5OXlSV1dnXr06EH79+8vkaKsKSkpNHv2bNLT06O1a9fmGSnIkC5v3rwhW1vbXI8bGxvnKXpqamrUt29fCg4OJiMjI7p582aR/OE4jo4fP06WlpbUuXPnIk1xe3p6SjTaePv2LcnJyZGurq5UMoQcPnyY5OXlJZ418fHxIWtra/r+/TsNHjy4XKXoEolEVKNGDTp37pzU7TZs2LBMr4OWB8qc8CUmJpKiomKeNzUNDQ1SVlYmMzMzmjBhQrGMwM6ePUuWlpbUs2fPPKMLGcUDn88nZWXlXB82zMzM8hzpbd++nVJTU8nV1bXIlbOfPXsmXm+Txlaa4cOH57l+mUlsbCwBKHIWm0z69+9P1apVox07dkh8zpw5c8jV1ZV0dXXLXaq906dPk4uLi9Szz2SmwWP3DdlR5oSPiMjc3Fyi9RtFRUWpJ8kNCwujv/76i+zt7SVKLcUoPqpWrUrv3r3L8ZilpWWO3wdDQ0N68uSJeL9bnz59Cv1g9OHDB+rfvz8ZGhrS9u3bpTZ9tXTp0nwrsXMcR7169SJFRUWprKtFR0eTjo4O+fr6UtWqVSW+Fo7jyNbWluzs7MpMejJJ4TiO3NzciiVgbu7cudSlSxep22VIRpksRFuvXr182ygoKMDa2hrnzp2TSp/p6elYvHgx6tSpg/r16+PFixdo0aKFVGwzCkdeRWkVFRWz/F9NTQ3u7u548+YNatWqhTVr1uDly5fw9vYGj8crUL+RkZEYPXo06tatC2tra4SGhmLkyJGQl5cv9LX8jpWVFcLDw/Nsc+jQIbx8+RJVqlQpcEHanNi5cyd69OgBLy8vGBsb4+TJkxKd9+HDB/z8+RO6urqYMWNGkf0oTfB4PCxatAjz588Hx3FStT1r1iwEBQVJ7f7EKCCyVt7CsHXrVlJVVc1ztGdgYJDrOl9BN9deunSJbG1tqVOnTlk29TJky4QJE2j16tU5HnNwcMgytTljxgzxKObw4cNkZmZW4GCWmJgYmjJlCunq6tI///xTbHszHz58SHXq1Mn1+JcvX8jAwICePHlCrVq1otq1axepv/T0dDIxMRHX6zt//jy5urpKNBLu3bs3LV68mGJjY8nOzo62b99eJF9KGxzHkbu7e7HkHb1x4waZm5uXm4CgskSZFL4nT57kuU9LQ0Mj1+S8b968ITU1NQoMDMy3n0+fPlHXrl3Jysoq32KljJJny5YtNGLEiByP2dvbi/fr/R6gcOPGDTIwMChQmaH4+HiaN28e6erq0pgxY4otlVkmX79+JX19/RyPcRxHrVq1Em8inzx5MhkbGxepvwMHDlDz5s3F/xeJROTs7EyXL1/O87zAwEAyNjYWB8OEhoaSsbGx1LcByJorV66Qvb19sWSEGjRoUKnOLVxeKZPCl56enmuAi6qqarb9Rb/TqFEj4vF4VLVq1VxHfhkZGbRy5UrS09OjefPmlfkNueWVq1evUpOmzSg8JpmCoxMpPCaZBMJf60xGRkakp6dH79+/F7d/+fIlGRgYSByAkpKSQsuXLycDAwMaOHBggSoUFAWO40hVVTXH6MqtW7dS7dq1xUE9R44cIWVl5SL1V7duXTpz5kyW9/bv35/v+njr1q2zRSfev39fPBotL3AcR40aNZIo6XdBiY2NJSMjIwoICJC6bUbulEnhI8o6lfW76B04cCDXcy5evEjq6uricPacsijcvHmTHB0dqU2bNhQaGlqcl8AoJD+T02nbrffUeMVVqvLPGXKY50dO8y+Rwzw/spntSy3W3qKZ/12nT1//v+zQp0+fyNzcnA4dOpSvfT6fT5s2bSITExPq1q1bgVOASQMHBwfx1GMmmdXQf/cnKiqKABR6NPLo0SOysrLKFsySkZFBFhYW9OjRoxzPu3HjBllbW+f48HjmzBkyMjKioKCgQvlUGrl58yZZW1sXy5alffv2Ua1atcpdcFBppswK38iRI7Pty1q8eHGu7TMyMrJFg6qqqopr4UVHR1Pfvn3J3NycTp48yTahl0LSBSJaeekt2c25SPZzL5LFjAu5vuznXiS7ORdp5aW39D32Bzk5OdGqVavytC8QCMjHx4csLCyobdu2Mq2T6OXllWWKVigUUv369WndunXZ2srJyRU6U1CfPn1ozZo1OR7buHEjde7cOdv7HMdR3bp16eDBg7naPXDgAFWuXDnLiLus07x5c4lKRhUUjuPIw8OjWEaUjJwpk1GdANCoUSOoqakB+BWx17NnT8yePTvX9lu2bMHPnz+zvJeWloZu3bph7dq1qF69OszMzPD27Vt06dKlwJF+jOIlMj4Nrdbfhs/9cKQLOfAFeUfZ8QUc0oUcfO6Ho/6Si6jn2Q5TpkzJsa1QKMShQ4fg7OyMvXv34sCBA7h48SLc3NyK41Ik4s/IztWrV0NJSQnjx4/P1lZdXR3+/v4F7iM2NhYXLlzA4MGDczw+dOhQ3L9/H2/fvs3y/unTp5Geno5evXrlartv376YO3cuWrZsiS9fvhTYt9LI4sWLsXjxYmRkZEjVLo/Hw7p16zBr1iwkJydL1TYjF2StvIUlJCSElJSUSE5Ojpo3b57nVM+PHz9IQ0MjxzVBHo9H5ubmeVaqZsiWL3Gp5Lr4ClnP9BWP6OS1DHMNbpJT18ky+rOccZ5cF1+hL3FZ12rT09Np165dZGNjQw0bNqTLly+XmpH+5s2bafjw4UT0a21SX1+fwsPDc2xrampKf//9d4H72LBhA/Xp0yfPNosWLcpS208gEFC1atXo4sWLEvWxatUqqlatWrkpxNqmTRupV+/IpE+fPjR37txisc3IioKM9LbI2NjYQCQSwdjYGOfOnYOCQu6XMnPmTAgEghyPERFiY2ORlpZWXK4yikCGkEPfXY+QkCqAiCjLMZ6yOrRqd8h2Dk9JNcv/CTwkpArQb9cjXJnUBMKMdPj4+GDlypWwt7fH7t270bhx42K9joJSt25deHt7IyMjA/3798eKFStgaWmZY9tKlSohLCyswH34+PhgzZo1ebYZO3YsbGxssHDhQpibm+O///6DkZER2rRpI1EfU6dORWJiIlq3bo2bN29CR0enwH6WJhYtWoTOnTtj8ODBUFFRkart5cuXw8XFBcOGDUOVKlWkapuRFR7RH3eTUoxQxOFLXBrShRyUFeSwYdl8jBszGlWrVs31nLdv36JWrVr5CpuVlRXevn0LZWVlabvNKAKrLgfD53440v6Y2vyydQgAwGyMj8S2VBXl4KTwDfe3zUTdunUxe/Zs1K1bV6r+Sov09HTo6upi7NixePv2Lc6dO5fr9HuzZs0QGxuLV69eSWz/2bNn6Ny5M8LCwiAnl/eKx5QpU0BEWLp0Kezs7HD8+HF4eHhI3BcRYdKkSXj8+DGuXLkCDQ0Nic8tjXTs2BEtWrTIcdq5qMybNw8fPnzAwYMHpW6b8f+UeuGLS8nA0SefcSLwCyJ+pEBRXg5yPB44IghEHCz01NHNzQy96phDR00p2/lNmzbF3bt38828oKamhrFjx2LlypXFdSmMAhKXkgGP5deRLsz+uyuM8AEAjxPiQLcqaFDHVSo+FidOTk6Ijo7GmzdvYGxsnGu73r174/Lly9nWsPPi77//hp6eHhYsWJBv2y9fvqBGjRqYNGkSAgMDcfr0aYn7yYTjOAwfPhwRERG4cOGC1EdLJcnz58/h5eWF9+/fi+MMpEVycjKqVauGEydOFOjhglEwSm1wS4aQw6rLwfBYfh3rr4fg/fdkCESE1AwRktOFSM0QQSAivP+ejPXXQ+C+7DpWXQ5Gxm83yUuXLiEgIECidEOpqanYvHkznj59WpyXxSgAR598Rp4xRiIBkoNuIuHBMSQGnAU/4iWIE+VpU1lZCUFpWtJ1tBhITU1FVFQU2rdvn6foAYCxsTGSk5MlDozg8/k4fPgwBg0aJFF7MzMzNGvWDCtWrMDSpUslOudP5OTksHPnTujp6aFXr165Lj2UBVxcXFC/fn1s3bpV6rY1NDSwdOlSTJo0CaV8TFKmKZXCV5QIvlbrbyMyPg0CgQDDhg1DampqrucpKChAU1MTWlpaUFZWhlAoxKVLl6R9OYxCciLwS56/e1FKHH5cWIP4O/sQd90b3w7PQtSOEeB/yn3Kjy/gcOJp6Y8ynDFjBhwcHJCenp5vW21tbejq6uaat/RPzp07BxcXl1zXDHNCTk4OCgoKcHBwkPicP5GXl8f+/fshFAoxaNAgiER5P6SUZhYuXIhVq1YhKSlJ6rb79+8PgUCAI0eOSN024xelLrglMj4N7TffyzGYgf85CEkB55Ae+RYifhLkVTShaGAJrTodoFq1DtIEHD7//HW+W8xVREZGQlFREaqqqsjIyIBIJIKhoSEsLCxgZ2cHBwcHWFlZwdLSEpaWltDX10dwcDD4fH6ZnoopTaSlpUFJSanACZyFIg4RP1JyPa5RwxPKZk5QMqgCnpIqhPFfkfT0ApKfX8b3Ywtg3H8VlIysczz3448UCEUcFORL5XMfrl+/jlOnTuHUqVN5bhnIRENDA9ra2ggODpZoC4aPj0+uWxhyIigoCDdv3kTlypVx/fp1eHp6SnzunygpKeH48ePw8vLCmDFjsH379jK5dcjJyQktWrTApk2bMGvWLKnalpOTw/r169GnTx907NhR6tOpjFK2xpch5NBq/W18/pmWTfTi7x9Bwt0DkFPVgqpNXchrVAKXmoiMb2FQsaiOSs2GiNvK83jQ4PFRL+46mjVpLBY3AwODXP/I3r17h4kTJ+LSpUs4ffo0OnXqVJyXWmHw8vLCrVu34OHhgY4dO8LT0xOOjo753uw+xqbAa9NdpGYUbFQQd2M3Eh+fhqqtBwy7zsmxjZqSPC7+3QiW+uoFsl0SJCQkoEaNGtixYwdatWoFXV1dhIaGwsDAINdztm/fDm9vb7Rr1w6LFi3K0/7nz59Rs2ZNREZGQlVVNc+2wK/AlBYtWqBLly5QVFQU/30UlaSkJHh6eqJRo0ZYtWpVmRS/0NBQ1K9fH69fv4ahoaHU7ffo0QPVq1fH3LlzpW67olOqRnwbrofgWyI/m+ilBN9Dwt0DULF0gUHnWZBTzvoERCJhlv+LiJChoAabTuPRs5V9nn1GRkZixowZOHHiBDIyMqCurs62NkgRJycnXLp0CTdv3sTDhw8hLy8POTk5NGnSBO3bt4enpyesrKyy3fjShRzkCnEz1HBti8THp5H++XWubeR4vBwDZkoDEyZMgJeXl3i7QJ06dRAQEAAvL69cz9HQ0ICKigqCg4Pztb9v3z707NlTItEDgBMnTiA2NhajRo0Cn8/HrFmz8PnzZ5ibm0t2QbmgqakJPz8/NG3aFNra2mXy5m5ra4v+/ftj3rx52L59u9Ttr1ixAnXq1MHQoUNhamoqdfsVmVIz1xOXkoFd97KHrRNxiL+5BzxFZeh3+Ceb6AEATz67fqcJRPC+G4b41JyzLMTFxWHixImwtbXF0aNHwefzxUEwkqyrMCSjYcOG0NTUBPArqCIlJQVJSUm4cOECJk+eDGdnZxgaGqJXr144ePAgoqKiAADKCnLgCjEZIa+mAwDgBPxc23BEUFYoNV99MWfOnMG9e/ewatUq8Xt169bF48eP8zxPQ0MDCgoK+Qofx3Hw8fHBkCFD8myXSWpqKqZOnYqNGzdCQUEBGhoa6Nu3L3bs2CHR+fmhq6uLK1euYP/+/Vi/fr1UbJY0c+fOxenTpwu0lURSrKysMHz4cKlPpTJK0Ygvtwi+9C9vIUz4BjX7BpBT0UDq+wAIYiPAk1eEsqkdlCvnvtjO4/2yO7Lx/+/zS01Nxdq1a7F8+XIIhcJsIsdxHBM+KVK3bt1cP8+UlF9reGlpaTh69CjOnj0LgUAAZWVl3L13HwJRwUdl6ZG/0msp6uQeCSkQcTCrlH3EIxQK8e3bN0RHR+Pr16+Ijo5GVFQUwsLCkJCQgP/++w/a2toF9kkSvn//jtGjR+P48eNZ9rnVrVs3X6HJfLAIDQ2FSCTKdT317t27UFVVRe3atSXyafny5fDw8EDTpk3F740ZMwZNmzbFvHnzoKSUfftQQTE2Nsa1a9fQuHFjaGpqYujQoUW2WZJUqlQJ8+bNw6RJk3D16lWpT9nOnDkT1apVw9OnT1GrVi2p2q7IlBrhyy2CLyM6FAAgr66D6D0TIIj5mOW4srkzDDrPhLxa9htSZgTfyMZVIRAIsHv3bsyaNQvp6em5Rnsy4ZMuJiYmUFdXl+gz5fP5UFRURKNGjVDd2QkWtxLw/nv2EP2MmAjIa+hCXlUzy/vChO/4efXXlJO6U7Nc+1HOSMSM6dPw+fNnfP78GdHR0fjx4wdSUlKgrKwsrt4uFAqRlpYGIoKGhobE04MFhYgwevRo9O/fHw0bNsxyLHOqi4hyvalqaGiAz+fDwMAAnz59gpWVVY7t9uzZgyFDhkh0cw4PD8eWLVvw/PnzLO9Xq1YNTk5OOHnyJHr37i3ZBeZDlSpVcPXqVTRt2hQaGhro2bOnVOyWFCNHjsSWLVtw4cIFtG/fXqq2tbS0sGjRIkycOBF37twpk2uhpZFSIXx5RfCJUuMBAEnP/KCgYwTDXkugbGoPYcJ3xN3YDX54IGJOL4Nx3+U5nv/xRwoOHz2GqZMnISEhQTzKyA2RSITIyEhERERAQUEBioqKUFBQyPYz+wLmDcdxiIiIwOvXr6GnpyfR5mpVVVVs2bJFHHHYzc0M66+HZHsgSg2+h4RHJ6BiUQMK2kaQU1KFMD4aaR+egIQZUK1aG1runXPsQ1mBh6jbJ7Hm4Ykcj6elpWVb45WXl8eAAQOkMsLJiTNnzuD169c5ZuswNTWFiooKwsPDYW2dc5SqhoaGeONzcHBwjsKXlpaGM2fOYPnynP9O/mTy5MmYNGlSjmt5Y8eOxbp166QmfMCv9TI/Pz+0bNkSGhoaaNeundRsFzcKCgpYu3YtJkyYgNatW0v9ezJ48GBs3rwZJ06cQPfu3aVqu6JSKoTvS1waFOXlIMhpXw/9/03PoNNMcYi6koEFDLrMRtTOkUj/HIT0yLc5TntyQgEGjJoIYXy0RL4IhUJ4e3vjyJEjEAgEEAqFEAqF4p8FAoF4OikvYcz8OfNfZWVl6OjoQFtbGzo6OuLX7///81hZ2FJBRIiKisLr168RFBSEoKAgvH79Gm/evIG2tjacnZ1hbGyMsLCwXPdtKSgoQEdHB35+flmm4XrVMce6a9n3pqlY1IDgZyQyvoUhPTIYJOBDTlkdymaOUHdqBnXn5rk+mKSnZyDhWcH2anIcV2w5JpOSkjB+/Hjs378/19935jpfXsKXlJQkFr62bdtma3P58mW4urrmuxkeAK5cuYIXL17g8OHDOR7v0KEDxo8fj5cvX6JGjRr52pOUGjVq4Ny5c2jfvj2OHj2KZs1yH7WXNtq0aQNra2ts3boVEydOlKpteXl5rFu3DkOGDEH79u3LxH2htFMqhC+vCD45lV/rHQo6Rtn2ZckpKkPVyg3JL68gPSokR+FTVVHGuk2bsfXfOfj06VO+Iz4AGD16dJ4ZKogIIpEoV2H8873MKbOEhAQkJCQgPj4e8fHxiI2Nxfv378X///1YfHw8AOQrkrq6uqhcubL4ZWhomG/uxYJARPjx4wc+fvyI8PBwhIeHZ/k5IiIC2tracHR0hLOzMzw8PDB06FA4OTmJxeLOnTto3749EhMTs9lXU1ODo6MjfH19s4WE66gpYVhDq2y5OlWqVIdKleoFvhYVRTm0tFbDdiEfBV09bNCgQYH7k4R58+ahRYsWWdbR/iRT+HLb0/f7iO/Fixc5tjl+/Dh69OiRrz8ZGRmYMGEC1q1bl+sNVkFBQTy9J61Al0zc3d1x7Ngx9OjRA+fPn4e7u7tU7Rcna9asQdOmTdG/f3/o6elJ1XazZs3g4uKC9evXY8aMGVK1XREpFcKXVwSfoq4ZAEBOOefEtpnCSMKcozeTklOwbdMmWFpawtraGq9evUJ0dDSEQmGuKYHy287A4/HEI7vihM/n5yiKv//86dMn+Pr6IjIyEpGRkYiPj4exsTHMzMyyCGLlypWzvKeiogIiQkJCAr5//y5+ffr0KZu4KSgowMrKSrwf0tHREe3atRNv/FdXz3s/XK1atXJcU1VTU0O/fv2wefNm8bran0xoYQffV9E57u0sEMQh/WcMBnaqCbMlS7Bw4UKJt62YmprmOIoqKoGBgTh06BBev8596wXwS/jmzZuX63FNTU2x8B09ejTb8bS0NPj6+mLt2rX5+rR582ZYWFigQ4fsVS9+Z/jw4XBwcMDKlSulHvDTtGlT7NmzBx06dMDVq1elOqosThwdHdGjRw8sWLAAmzZtkrr9VatWwcPDA4MGDZJo5M7InVKxgV0o4uAw/xIEouyuiFIT8GXzAPAUVWA+/gB48llvkN+OzQc/7Cn0O/wDdccm2c5XlOPhSFcTREdF4vPnz/jy5QtevHgBf39//PjxI0fxs7S0RPPmzWFgYAB9fX0YGBiIf9bX14empibU1dWhoqIi1dFVUcjIyEBKSgp+/vyJjx8/4sOHD3j//j0iIiIQFRWF79+/Iy4uDklJSVkCTeTl5aGmpiZOe1WlShXY2dnBxcUFzs7OsLS0lMo0n5WVFT5+/Cj+v6qqKrZu3SpRvsi8svlIAnEiaCnLY5RVAhZMm4DZs2fj5MmT8Pf3lyhnpLe3N4YNG1bgfvNCJBLBw8MDo0ePznd7QUJCAipXroy4uLhcHxCUlJTw9u1bNGrUSLwlJJPTp09j06ZNuHHjRp79fP36Fc7Ozrh37x6qVauW7zX06tUL9evXL5YqBQBw7NgxTJw4EZcvX0b16gUf4cuC2NhYODg44M6dO0VK75YbU6dORUJCAry9vaVuuyJRKoQPADzX3c4xgg8AYs+vRsrrW9Cq3xOVGvcXv58W/gzfj84DT1kNZqN3i0d/v1NJjo/jg2vCxsYm27GwsDAsWbIEhw4dAhGJKys3bdoUffr0QUxMDGJjYxETE5Pl55SUFKSmpopTm6mpqUFNTQ3q6urin/98T1VVFTweL4vQZv7857+//ywSiZCSkpLvC/hViTvzpa2tDUNDw2yvTAFXVFQEn89HTEyMeLQYGRmJL1++iIN7VFVVYW9vD3t7e9jZ2Yl/tra2LvACfv/+/XHgwAEoKipCW1sbly5dKlB4dmR8GvrueoRvifxsez3zQlVRHlqKHD76TMaZQ3tgaGiI3r17Q1tbG48fP85x+vV3VFRUoK6ujtatW2P69OlSG31s3rwZx44dw+3btyUKlHJ0dMShQ4fg4uKS43FdXV0EBwfDzMwMKSkpWQSyT58+aNy4MUaNGpVnH927d4eNjQ2WLVsm0TXcvXsXw4cPx9u3b4st2OvIkSOYOHEiLl68KFE6ttLAunXrcPXqVVy8eFHqtuPj42FnZ4fbt28Xi7BWFEqN8G2//SHHCD4AEKXE4+uBfyCMi4aymROUTe0gTPiO1JCHAI/3a7RXrWG285TkAKuU13h+eA1MTEzQtWtXdO3aFY6Ojlnaff/+HatXr8bWrVuRnp6Ozp0749ixY/n6zHEc0tLSkJqamu2VKY6/vzL5/SaR+fOf/2b+LCcnl0XQcntJO5KMiBAdHY13794hJCQE7969E7++fPkCc3NzsRD+Lo7GxsY53gR3796NESNGoFatWvD19c0zBVduZAg5bLgegl33wsHjIc8E1qqKcuAIGN7IGhNa2OL61SsYMGAA/Pz8xGmgdu3ahZSUlDy3WmzevBn9+vXDjh07sH79eri6umLGjBlo1KhRgf3PJCoqCjVr1sTt27ezfRdzY9CgQahfvz5GjBgBAAgJCcG5c+fg5+eH//77D87OzqhcuTIiIyNx/PhxeHp6gsfjIS0tDSYmJggJCckzrdaZM2cwbdo0vHjxQuJtG0SEGjVqYP369WjRooVE5xSG06dPY+TIkTh37lyZKNWTkZEBZ2dnbNy4UeKCvQVh+fLleP78OUtiXQRKjfDFp2bAfVnOtdcAQJSWhIQHR5Aa8giipB+QU1KFspkjtOt1h3LlnKdllBXk4D+zBTSV5XH//n2cPHkSJ0+ehJaWFrp27Ypu3bqhRo0a4ht1UlIStm3bBhMTE/Tv3z9Hm4xff9gfPnwQC+HvwpiRkZFldJj5s46ODo4dO4bJkycXeW00PvV/NRqffsHH/9VoFGSkI0MggqKSMqwMNNC9lhl61M5ao/HMmTMYNWoUrl27BmdnZ9y4cQOdO3dGSkpKrhGnQ4cOxdKlS2FkZAQ+n499+/Zh5cqVMDExwYoVK1C/fv0C+9+jRw/Y2toWqMTPxo0bcfnyZVhZWeHUqVOIj48Xz1J8/vwZLi4u+PnzJziOg7KyMtTU1PDXX3/B1NQUDx48wO3bt3O1HR8fD2dnZxw8eBBNmmRfLsiL7du348qVKzh16lSBzisoFy9exKBBg3DixAk0bty4WPuSBufOncOMGTPw8uVLqccCJCcnw8bGBlevXi0zU8CljVIjfEDu1bYLg6qiPIY2tMLUP3J1chyHx48f4+TJkzhx4gTk5eXRtWtXdOrUCXXr1i1wFQFGVn7+/JlthPju3Tt8+PABBgYGcHJygpubG2rVqgU3NzdYWFgUaZpMKOLwJS4N+w4exuGD+zC8dxdMnjQx1/ZHjhzBlClTcOPGDdjb2yMuLg42NjY57jMcNGgQ9PT0sHfvXkybNg0TJkyAsrIyRCIRDhw4gDlz5qBevXpYtmwZqlatmkNv2fHz88O4ceMQFBSU78jq+/fv8PPzw5EjR3Dz5k3xeuTv9SXV1dWRlJQEBwcHfPnyJVvUsoKCAogItWrVQs+ePdGuXTvY2dll+cxHjhwJAIWK0ExKSoKFhQVevnwJMzOzAp9fEK5fv47evXvj0KFDRaoQURIQEVq2bInOnTtj7NixUre/du1a3Lt3r9gfOMorpUr48qrOUBCIE8FQTQ4P5nhBMY/SM0SEZ8+e4eTJkzh//jyioqLQpk0beHl5oXXr1lIPSa7IiEQifPr0Ca9evUJgYCCePn2Kp0+fIj09PYsQ1qpVC9bW1gUWw7Nnz2LevHmoWbMm9u3bl2fbPXv2YP78+bh16xasra3x4cMHODs7g8/Pmt/z06dPMDc3R2hoKKZOnYrXr19j9erV6NixI3g8njj93bp16zBo0CDMmTMHlSpVyrXf1NRUODs7Y9u2bWjdunWubVavXo2jR4/iw4cPUFRUzLPArKurKwIDA1GvXj08ffo0z2CdzGAsDQ0NDB8+HEuWLMHt27fRt29fvH79utDRmePGjYOBgQHmz59fqPMLwt27d9G1a1fs2bOn1G9yf/nyJVq2bIng4OA8vxeFITU1FTY2Nrhw4UKZWfssTZQq4QOKHsEnz+NBXRH4eXg6Rg/shVmzZkl8E/38+TMuXryIixcv4tatW3B2doaXlxe8vLzg4uLCsrUUA9HR0Xj27BmePn0qFsTExES4ubllEURbW9s8I2gDAgIwYMAAyMvLIygoKN9+d+zYgaVLl+L69euwtbXF/v37MWrUKPFabK9evXDo0KEsv/OrV69i0qRJMDQ0xPr168WBLl+/fsX8+fNx+vRpzJ49G6NHj85xzXXWrFkICwvLc20mKioKtra2eRZQ/p2RI0di+/btaNSoEZ49eybRPlVlZWUMHToUq1evRo0aNcRiXlgCAgLQu3dvhIaGlsjfiL+/Pzp06IDt27ejc+ecM/SUFkaOHAl1dXWJtpIUlE2bNuHy5cu4cOGC1G2Xd0qd8AFFi+Az1lLGgWEe4KXGoVOnTrC2toaPj0+Bizmmp6fjzp078PX1xcWLF5GcnCwWQU9PT2hpaRX0shgSEhMTg8DAQLEQBgYGIjY2Fi4uLllGhvb29uKp6cjISNSqVQuJiYmIjY2V6Pe9e/duzJ8/H9euXUO1atXQs2dPnDx5Es2bN0dMTAyMjIywY8cOWFhYiM8RCoXYuXMnFi5ciE6dOmHx4sXioJGgoCD8888/eP/+PVasWIHOnTuLheD169do2rQpXr58CRMTkzz9evToETw9PfMVMXV1daxfvx7Dhg1D/fr1kZSUlK/oq6qqok2bNjhx4oRYiCUJ5MoLIoKjoyN2795dqDXPwvDs2TN4eXlh7dq1Uk2dJm2+f/8OR0dHPHjwAHZ2dlK1zefzYWdnh+PHj5epjf6lAiqlpAtEtPLSW7Kbc5Hs514kixkXcn1Vm3uR7OZcpFWXgylDKBLbSE1NpX79+pGbmxt9+vSpSP6EhITQ+vXrqVWrVqShoUHNmzen1atX05s3b4jjuKJeLiMffvz4QdeuXaMVK1ZQz549ycbGhtTV1al+/fo0btw42r9/PykoKJCrqys9fPhQYrt79+4lExMTCgoKoqSkJGrVqhWFhYVRRkYG/fvvv6Snp0ebN28mkUiU5byfP3/SxIkTSV9fn9asWUMCgUB87PLly1S9enVq1KgRPX78mEQiETVs2JC2bNkisV9XrlwhNTU1ApDrS0tLi/z9/YmIyN3dnfr06ZNnexUVFWrSpAllZGTQ06dPycDAgL5+/SqxT3nx77//0siRI6ViS1JevXpFpqam5OPjU6L9FpQVK1ZQhw4disX29u3bqVWrVsViuzxTaoUvk7iUdNp++z15rr1FNrN9yWGeHznNv0QO8/zIZrYvea69RTtuv6e4lPQcz+c4jlauXEkmJiZ0//59qfiUnJxM586do5EjR5K5uTlZWVnR2LFjydfXl1JTU6XSByN/4uPj6ebNm7R69Wrq1KkT8Xg8UldXJw8PD9q7dy+FhYVJ9FBy8OBBMjY2pufPn2c79vbtW6pfvz41aNCAnjx5ku14cHAweXp6kqurKwUEBIjfFwqF5O3tTSYmJuTu7k6urq4kFAoLdH3Hjx8nVVXVXIVMQUGBkpOTiYiodu3atHjxYlJXV8+xrZKSErm4uFBKSgoJBAJydXWlPXv2FMifvIiIiCBdXV3i8/lSsykJwcHBZG5uTlu3bi3RfgsCn88na2trunbtmtRtp6enk6WlJd29e1fqtsszpV74fkcgFFF4TDIFRydSeEwyCYSi/E/6H76+vmRgYEA7d+6U6giN4zh69eoVrVixgho3bkyamprk5eVFmzdvpg8fPrDRYAlSq1YtGjx4MNWvX5969uxJxsbGZGZmRn379qUdO3ZQcHBwrr+PY8eOkZGRET19+jTbMaFQSDt37iQTExPq169fttkDjuNo3759ZGRkRBMnTqSkpCTxsbCwMFJTU6NKlSrR/v37C/x92LVrV67iZ2RkJG7n6upKx48fz1H4FBQUyNramn7+/ElEv0YgLVu2lPp3s1mzZnTixAmp2pSEDx8+kKWlJa1du7bE+5aUEydOUPXq1bPMDEgLHx8fatq0qdTtlmfKlPAVleDgYHJycqKBAwdSSkpKsfQRFxdHx44do0GDBpGxsTGZm5tTv379aOfOnXneeBlFp0OHDrR8+XJydXUlol+CFBISQrt27aL+/fuThYUFGRoaUrdu3WjTpk304sWLLFOYp06dIkNDQ3r8+HGO9hMTE2nOnDmkq6tLs2bNosTExCzHY2JiaODAgVSlShU6d+4cERENGDCAJk+eTI8fP6bq1atTu3btCjztvnr16hynPVu0aCFuU7NmTQoICCBFRcUsbXg8HhkbG1NUVBQR/Zqy19PTo7CwsAL5IAl79uwptim9/Pj06RPZ2NjQ0qVLZdJ/fnAcR56enrRq1Sqp2xYIBGRjY0M3btyQuu3ySoUSPqJf05R9+/alGjVqUEhISLH2xXEcvXv3jry9valfv35kbm5ORkZG1L179xxvvIyiMWrUKFq7di2pqqrmOuX28eNH2rdvHw0bNozs7OxIV1eXOnToQKtXr6bHjx/T6dOnycDAgB48eJBrP58/f6YBAwaQsbExbdu2LdtT/LVr18jGxoYaN25MlStXFo8A09PTacGCBaSvr0/bt28v0O9+5syZWcRPTk6OZs+eLT7u7OxML168IFtb2yzCp6OjQ+/fvyciIpFIRE2aNCm2kVFiYiJpa2tTTExMsdjPj6ioKHJwcKC5c+eWygfM0NBQ0tPTo/DwcKnb3r9/PzVo0KBUXndppMIJH9EvQdq2bRsZGBiU+NTMx48f6b///qOhQ4eSra0tVapUSXzjDQgIKJapkIrCokWLaNasWVSjRo1cR21/EhUVRUePHqUxY8aQs7MzaWlpkZubG6mrq9PWrVvzXJd7+vQpNW3alBwdHcnX1zfLTScuLo50dXVJS0uLtm3bJha5Hz9+kLu7O9WsWZOaNm0qFqX84DiORowYIRY/NTW1LN9dBwcHCgoKyhLgoqGhkWXdcv369VS/fv0CrzUWhD59+tCmTZuKzX5+fPv2jWrUqEFTp04tlSKwdOlSatu2rdR9EwqF5ODgQJcuXZKq3fJKhRS+TB4/fkyWlpY0adIkysjIkIkPkZGRdOTIERozZgw5OTmRlpYWtW7dmpYuXUr37t0r8WCBssyuXbto4MCBNHLkSFq/fn2hbMTGxtLp06epS5cuJC8vT5qamtS7d2/av38/ff/+PVt7juPo3LlzZG9vT56enmKhWbhwIXXs2JFevXpF9erVo/r161NQUBBt2LCBFBQUyMLCghYuXEh6enq0du1aicRIJBJRjx49SEFBgRQVFendu3fiY3Z2dvT27VvauHEjASB5efksAQ9v3rwhfX19iYW2sPj5+VGdOnWKtY/8+PHjB9WuXZvGjRtX6mZU0tPTycnJiY4cOSJ120ePHqU6deqUSsEvbVRo4SP69Ufi5eVFDRo0oC9fvsjaHYqJiaFTp07RxIkTxSOPpk2b0vz58+n69evFtjZZHvDz86OWLVvSvn37qHv37kW2d/PmTdLV1aVJkyZRp06dSEtLizw8PGjRokX05MmTLDfVjIwM2rx5MxkaGlLXrl1JR0eHIiIiiOiXYG3bto309fVJR0eHAJCioiLVqFGDnj9/To0bNyYPDw96/fp1vj4JBAKqU6cO8Xi8LGJpY2NDISEhdOHCBQJAnTp1yuJb7dq1afv27UX+TCTxz9jYmN6+fVvsfeVFfHw81a9fn4YNG1asI9zC8ODBAzIxMREHG0kLkUhE1atXF68vM3Knwgsf0a8vzJIlS8jExISuX78ua3eyEB8fT76+vjR9+nTy8PAgNTU1qlOnDo0aNYp27txJT58+ZaPC//HixQtycnKi9+/fk6mpqVSefO/evUsGBgbk6+tLfD6frl27RpMmTSJ7e3syNjamwYMH0/Hjxyk+Pp6Ifv2+HB0dSU1Njbp3755lC8Tly5dJXl5ePBWprKxMjRs3Jj6fT1u3biU9PT36999/871Rp6Sk0Lp164jo/yOdm3ToRU/eRRA/PYNmzpxJvXr1ErdfsGABtWnTpsRGAlOmTKFZs2aVSF95kZSURM2aNaO+ffuWuiWE0aNH04gRI6Ru99SpU+Ti4sJGffnAhO83rl27RsbGxrR06dJSN0WSSXJyMt29e5fWr19PAwYMICcnJ1JVVSU3NzcaNmwYbdu2jfz9/SktLU3WrpY4MTExpKOjQxzHkZGREX38+FEqdh8+fEiGhoa0b9++LO+/f/+eNm3aRG3atCENDQ1q0qQJjRkzhoyNjenr16+0du1aqly5MrVs2ZKuX79Ow4YNIzk5uWybyrt06UIikYgiIiKocePG1KxZszxnH34mp9O2W++pRS57W+st9qUaPSdTXEo6BQQEkKGhIUVGRkrls5CE58+fU5UqVUrF31Bqaiq1bt2aunXrRunpOe/1lQXx8fFUuXJlqe+/4ziO3Nzc6OTJk1K1W94olSnLZElkZCR69OiBSpUqYd++fdDV1ZW1S/mSmpqKFy9eZEnxFRISAltb2ywpvmrWrFng1G1lCSKCiooK4uLi0L9/f3Tt2hV9+vSRiu03b96gbdu2GDduHKZOnZotJ2Vqaipu3LiBYcOGQSgUQkNDA15eXmjZsiW+ffuGtWvX4sOHD1kqK2SirKyMIUOGYMuWLeA4Dv/++y+2bNkCb29vtG/fXtyuIPUIIUyHsooqNKMCMMnTHn1795TK5yApNWvWxIYNG9C0adMS7Tcn0tPT0aNHDxARjh07BhUVFVm7BAA4ceIE5s+fj2fPnkm1nqavry9mzJiBFy9e5JnftiLDhC8HBAIBpk+fjtOnT+P48eOoXbu2rF0qMHw+H69evcqS/Pnt27ewtrbOIoYuLi7Q0Mheub6sYmVlhatXr+LcuXP48OEDtmzZIjXbX758QZs2bdCqVSusXr06203lyJEjWL16Nfz9/fHu3TtcvHgRvr6+ePLkCaysrPD27VsIhcIcbSsoKGD27NlYsGABAOD+/fvo27cvOnTogJUrV+IHnwqZv1YORloqODjMA5V1JCswKw3WrFmD169fw8fHp8T6zAuBQIC+ffvix48fOHXqVKErUUgTIkKHDh3g7u6OOXPmSNVuvXr1MHHiRPTq1UtqdssTTPjy4MSJExg9ejSWLFmCESNGlPnqDBkZGQgKCsoyMgwKCkKVKlXg5uYGJycnceFYW1vbUvNkXBBq166NrVu3guM4jB49Gs+ePZOq/bi4OHTs2BGVK1fG3r17oaysDABIS0uDg4MD9u3bl61QakJCAurUqYPQ0NA8bcvJyWHevHni8j5xcXEYPnw40uXVEFm9f5aKJSnB95D+KQgZ38OQ8T0clJEGdaem0G8/NZtdeR4P2mqKOD+uYYmJX3R0NBwdHREZGVlqZhlEIhEmTJiAO3fu4OLFi8VeP1ASPn36BDc3N6knsb569Sr+/vtvvH79mtUYzQEmfPkQEhKCbt26wd7eHtu3by93NfoEAgHevn2LwMBAvH37Vlw4Njw8HCYmJlmqqGe+KleuXGqnUFq0aIEZM2agSZMm0NXVRXR0NDQ1NaXaR1paGvr27YvExEScOnUKWlpaWL58OR4/fpxjYdDw8HA4Ojpmq/eXG0OHDsXOnTshJyeHdIEILdfdQmR8epYyXVE+f0PwPRw8JVXIa+pB+ONLrsIH/BK/KrqquDKpSZ41KqVJmzZtMHDgwFJVPYGIsHr1amzatAm+vr6looL5unXrcP78eVy/fl1qD9dEhCZNmmDkyJHo27evVGyWJ5jwSQCfz8esWbNw7Ngx7NmzBy1btpS1S8WOUCjEx48fs1RRz6ysnpCQAFtbW7EQ/i6Msi7X1KVLF/Tp0wfdunVD48aNMXfu3GL5fYlEIowbNw7+/v7Yt28fmjZtiocPH8LW1jZbW319ffz8+RMF+VNzdXXF+fPncSgoCT73w7NNb/IjXkJeUw8KlUyR/ukVvh2elafwAb/Kdg1taIWprewlv9AicPDgQRw4cAB+fn4l0l9BOHz4MCZMmIAjR46gefPmMvVFKBTC3d0d48ePx8CBA6Vm18/PDzNmzMDz58/L/GyVtGHCVwCuXbuGwYMHo1u3bli2bFmZnAqUBomJiQgJCREL4e/CqKWllUUI7ezsYG5ujsqVK0NfX7/Y/wAHDRqExo0bY8iQIZg5cyaUlZXF62bShoiwZMkSrF69Gp07d8bevXuzteE4DoqKijkGtfyOkpISFBUVkZGRIa6irq5rCOORuyGkvD8zfsRLiYQPAJQV5OA/swV01KQXTJEbKSkpqFy5MkJCQsQ1C0sTt27dQs+ePbF27VqZj4oCAwPRtm1bBAX9X3tnHRdV9v7xzwQxdIeUIiYgCAYqxtqirmKvimvv2mutueqquCprd6/d3d2KzSIqJqBgEdJM3uf3hz/mK0vNwFBy3q/XfTHce+K5wzCfe855nueEwdLSUiNtEhFq1aqFRYsWoXXr1hpp83tBWNIGlCVatmyJf//9F7/88gvq1KmDnTt3wsPDo6TNKnaMjIxQp06dbE4/HMfh/fv3WcTwwoULiI6ORkxMDNLT01GhQgXY2dnBzs4O9vb2yteZR4UKFQrl4WZsbIykpCQAQMOGDbFixYpC3Wte8Hg8dOnSBQsXLsSZM2dw79491K1bN0uZW7du5Sh6fD4fDg4OqFWrFlxcXODo6AgbGxvY2trC1tYWKSkpmH/kPu6JZYBQcyLF4wF777/DL00qa6zN3NDX10fr1q1x7NgxDB48uMj7U5dmzZrh0qVL8PPzw7t37zBp0qQSGxl5eXmhT58+GD9+PLZt26aRNnk8HiZMmIC///6bCd9/YCO+AkBE2L59O8aPH4/Jkydj7NixpXbNqzSRnp6O9+/fIyYmRimG/z0+fvwIU1PTLGKYk0AaGxvn+CU1Y8YM8Pl8zJo1C/Hx8XB2dkZCQkKRLfD7+fmhdevWcHZ2xuDBg7F9+3a0adNGeT0pKQmurq6IiYnJVldfXx9aWlr4/fffMWLEiGzTxC2XXMWrz6n52qDOiA8AqlgZ4PzYpircXeHZs2cPtm/fjpMnTxZLfwXh/fv38PPzQ8OGDbF8+XIIhSUzHkhNTYWrqys2bdqEli1baqRNqVQKZ2dnnDhxAp6enhpp83uACV8hiIiIQEBAAHR0dLB169ZS4SVW1lEoFPj8+XMWMfyvSEZHR4PjOJiamsLY2BgmJibKIyIiAnK5HN26dYOxsTFmz56NadOmwdvbO0tZTUxTnzt3DiNGjMCTJ0+gra2NW7duoUuXLggKCkJAQICynIeHB0JDQ3NtRyQSgcfjYdiwYZg4cSKsra0hV3CoMfMMZIr8/z3VFT4tAQ/P/mwLYTE4uSQnJ8Pe3h7R0dElvv6bF8nJyejWrRt0dXWxe/du6Ovrl4gdJ0+exJgxY/D48WOIRJrxwA0KCsK///6LHTt2aKS97wEmfIVELpdjwYIFWLZsGVauXIkePXqUtEnlgtTUVCQmJmY5kpKScPLkSTx//hwtWrRAYmIizp8/D11dXRgZGWUpCyCLYGaKopGRkXK9TSgUQigUKl9/e04gECAoKAg//vgj6tWrpzz/6dMnBAYGom3btujTpw+0tLQwcuRIhIeH53tPQqEQPB4PdevWxdJNO/Hz7nCkSxX51lNX+PS0BTg1qjEqWhTPl7ufnx/69etX6mPKZDIZhgwZgmfPnuH48eMlti7Zo0cPVKlSBYGBgRppLykpCc7Oznj06BEcHR010mZZhwmfhrh37x769u2L+vXrY8WKFaUiQLY8sm/fPuzbtw8HDhwAAGzevBkXL17Ezp07s5QTi8VZBPPb1zKZDHK5XPkzp9f//vsvnj17Bj8/PygUiixlUlNTERwcDJFIhOrVq+Phw4dITk5WyX6BQAA9PT1sO3YB0698Qaok54D3LPeipvAZ6Ahx8NeGqGaj2TCP3NiwYQMuXLiAvXv3Fkt/hYGIMHPmTOzatQunT5/O0Uu3qPnw4QNq1aqFy5cvw83NTSNtTpgwARzHYfHixRppr6zDnFs0RN26dfHw4UNMmDABnp6e2LZtGxo3blzSZpU7jI2Ns4hMo0aNMHv27GzldHV1YWNjAxsbG7X7SElJQbVq1XDs2LFcs/pkZGRg8ODBePHiBTw8PHD9+vU829TX14eenh4WLVqEPn364G1CBrjLedcpKBwRdITFtybdqVMnTJw4EWKxuNR7QvN4PMyePRuOjo5o0qQJDh8+DB8fn2K1wdbWFnPmzMHQoUNx48YNjfgPjBkzBh4eHpgxYwZMTEwKb2QZh3lkaBB9fX2sWbMGy5cvR48ePTB16lRIpdKSNqtcYWRkpPTqBICqVasiNTU1R+eSgrJgwQK0bNkyz1R2IpEIO3bsQNeuXXHv3r08yxkZGWHu3Ll49+4dAgICwOfzYW8qgkyhemoydZApONibFl/6MisrK9SqVQsXLlwotj4Ly+DBg7Fp0yZ07NgRR48eLfb+hw4dCoFAgKVLl2qkPQcHB3To0AFr167VSHtlHSZ8RUDHjh0REhKCsLAweHl5ITg4uKRNKjd8G84AfH2Cb9iwIW7evKmR9t+9e4c1a9aotP7C4/EwefJkeHt7Z7umra0NPT09jBs3DtHR0fjtt9+U6c8AQCjgw8m8aNbgKprrF4tjy7f4+/vj8OHDxdpnYfHz88Pp06cxbNgwjeZ8VQU+n4+tW7fir7/+QlhYmEbanDBhAlasWAGJRKKR9soyTPiKCGtraxw9ehTTp0+Hv78/xowZg9TU/F3TGYXjv1OdwNfpzlu3bmmk/alTp2L48OFwcHBQuU7lyv+LmePxeNDV1cWAAQMQERGBuXPn5ppSrZuXPXRzmZJMf3EbcSeWIO7EEiQFf13PlMSEK899ubQpx3q6Wnx09y5+72N/f38cO3Ys1yTdpZU6derg5s2bWLFiBSZNmpRvIgJN4uzsjPnz56Nv374aEatatWrB3d0du3bt0oB1ZRsmfEUIj8dDr169EBYWpoznKo3pm74n/jvVCXwVPk2M+O7fv4+LFy9i0qRJatXLTNKsq6sLMzMzNG7cGEFBQXl6DaakpOD+vuUQ5/KFJ/30BmlhF5EWdhHiiIcAAHniR+W5tPCc71cslsAmI1It+zVBxYoV4eDgoLGRd3FSqVIl3Lx5U7ljRnGOmAYOHAhHR0eNZR/KDGgvTgEvjTCvzmLk/Pnz+OWXX9CgQQMsXbpUY6mJGP+DiCAUCiEWi6GlpQXg635slpaWiIqKgqmpaYHbbdq0Kfr166d2FpKVK1fi8OHDWLJkCapXr44RI0bgzp07OHbsGCpWrJit/Llz5zB06FC0aNECFX8chV0PPqi1FVFuiLT4aGguxuVl4+Hq6oqgoCBUr1690O2qypw5cxAXF4dly5YVW5+aJCMjAwEBAYiLi8ORI0eKzUnk06dP8PT0xP79++Hr61uotogIXl5emDt3Ltq3b68hC8sebMRXjLRq1QqPHz+Gra0t3NzcsGPHDrUSFzPyh8fjwcjICCkpKcpzOjo68PX1xcWLFwvc7rFjx5CYmIgBAwaoXXfkyJG4ePEiatWqBW1tbaxfvx6DBw9GgwYNsnh7JiYmYtCgQRg6dCjWr1+PTZs2YVL7WrA20oWgkKm0BDwebIx0sXZkJzx79gzNmjVD48aNMWLECMTGxhaqbVXx9/fHkSNHyuxnXiQSYe/evahduzYaNWqEt2/fFku/1tbWWLt2Lfr165flc10QeDweJk6ciKCgIA1ZVzZhwlfM6Ovr4++//8bJkycRFBSEdu3aITIysqTN+q7IabqzTZs2OHv2bIHa4zgOM2bMQGBgoEZSn/F4PIwePRpbt25Ft27dsGnTJpw4cQJubm7Q1dXF48ePlbkVtYV87BzsA2M9rYKLH3EwFgmxY7APtAR86OjoYPz48QgPD4dQKESNGjWwYMEClbdNKiiurq7Q1tbGw4cPi7SfokQgEGDJkiUYPHgwGjZsiJCQkGLpt1OnTvjhhx8wbty4QrfVvXt3RERE5Olt/L3DhK+EqFOnDu7fv4+mTZuiTp06WLp0KRSK/LN0MPLnv56dANC6dWucO3euQKONw4cPQ1tbGx06dNCUiUqbzp8/jwkTJqB3797YvHkzVq1alc3Zxc5EhOMjfeFgJoJIS81/WYUUiqRP0L+xErqK9CyXzM3NsWzZMty6dQvBwcGoXr06tm3bVmSfw8yk3mXNuzMnxo4diyVLliiTcBcHS5YswcWLFwvdn5aWFsaOHVuuR31sja8U8OLFCwwZMgRisRgbN24sFZtjlmUaN26MwMDALDuhExGcnJxw7tw5tda1OI6Dh4cH5s+fr/E1kfDwcPTs2ROVKlWCQqHAx48fsW/fPlSqVCnH8lI5h2UXX2DjjQjweIA4j3U/kRYfMrkCdinhMIy8jvcx75CcnIxjx46hZs2aOda5du0apkyZgi9fvmD27Nno0qWLxpOvBwcHY+DAgXj69KlG2y0p7ty5g27dumHw4MH4448/ijxZ/fXr19GjRw/8+++/hUqplpKSgkqVKuHu3btwdnbWoIVlAzbiKwVUrVoVly9fxqBBg9C8eXP88ccfRT7t9D2T01Qnj8dTjvrU4eDBg9DT04Ofn5/G7CMi/PPPP8o1tsOHD+PYsWPo06cPfHx8cn2i1xbyMbFNddyZ0gJjW1aFuVAKHnHQ0xbAQEcIPW0BtAQ8VLEywNiWVTGjlhgW729jx/atSE5ORosWLdCsWTOcOnUqx/abNGmCGzduYNGiRfjrr79Qp04dnDx5UqNrcvXq1UNiYiKeP3+usTZLkvr16+PevXs4d+4cunTponJquoLSuHFj9OvXD0OHDi3U38XQ0BBDhgzBkiVLNGhdGYIYpYqYmBjq3LkzValShU6cOFHS5pRJfvrpJ9q+fXu28/v27SM/Pz+V21EoFOTq6kqnTp3SmG3JycnUp08fcnV1pcePH2e7fvv2bXJ0dKQJEyaQVCrNs60xY8bQwqC/KSI2lcI/JFNEbCrJ5Arl9fPnz1Pz5s2JiOjff/8lCwsL2rZtG9na2lJQUBBxHJdr2xzH0cGDB6lmzZrUoEEDunjxYgHvODvDhg2jv/76S2PtlQYkEgn98ssvVKNGDXr+/HmR9iUWi6lWrVq0efPmQrXz/v17MjU1pbi4OA1ZVnZgwldKOXnyJFWpUoXatWtH4eHhJW1OmeLXX3+lVatWZTsfHx9PhoaGJBaLVWpnz549VL9+/TwFQh3u379PLi4uNHToUEpLS8u1XFxcHPn5+VHDhg3p3bt3uZbz8/Ojo0eP5tmfl5eX8vcdO3aQi4sLhYaGkqenJ/Xr148yMjLytFkul9OOHTuocuXK1Lx5c7p161ae5VXh/PnzVLdu3UK3UxpZu3YtWVpa0smTJ4u0n9DQULKwsKA3b94Uqp2BAwfS7NmzNWRV2YEJXylGIpFQUFAQmZub04QJEygpKamkTSoT/P777zRv3rwcr9WvX1+l0YtcLqcaNWrQ6dOnC20Px3G0ZMkSsrS0pL1796pUR6FQ0Pz588na2jpXG6pUqUJPnz7NtY1Xr15RpUqVspz77bffqHnz5pSQkEBdu3alBg0a0IcPH/K1RyqV0oYNG8jBwYH8/Pzo4cOHKt1Hbm0ZGRnR58+fC9xGaebGjRtUoUIFCgwM1NhDU04EBQWRr68vyeXyArfx9OlTsra2JolEokHLSj9M+MoAHz58oAEDBpCtrS1t3ryZFApF/pXKMYGBgTRp0qQcr/3xxx+5XvuWXbt2kY+PT6G/uGJjY6lDhw5Ur169Aj2dX716lezs7GjatGkkk8mU56VSKWlra+c5eo2LiyNTU9Ms5+RyOXXq1In69etHcrmcZs6cSY6OjioLmVgspuXLl5ONjQ117dqVnjx5ovY9ERF17NiRdu3aVaC6ZYHo6GiqV68edevWjVJSUoqkD7lcTk2aNKEFCxYUqp3mzZvTnj17NGRV2YAJXxnizp07VL9+fapbty7dvn27pM0ptaxcuZKGDRuW47UbN26Qp6dnnvXlcjlVr16dzp49Wyg7Ll++TPb29vT777/nu16XF58+faIWLVpQs2bN6P3790RE9OLFC6pYsWKe9WQyGQkEgmwPSqmpqVS3bl2aNWsWEX1d+7SwsKD9+/erbFNaWhotWLCALC0tqW/fvvTq1Su17mnFihU0YMAAteqUNTIyMmjgwIHk5uam9vujKhEREWRhYUEhISEFbmPv3r30ww8/aNCq0g8TvjKGQqGgrVu3UoUKFSggIIBiYmJK2qRSx7Zt26h37945XpNKpWRiYkIfP37Mtf7OnTupYcOGBR7tcRxHy5YtIxsbGzpz5kyB2vgvmaMzW1tbunjxIp08eZJatWqVbz1DQ8Mcp8g/fvxIFStWpH/++YeIiB48eEAODg40d+5cte47KSmJ/vzzTzI3N6chQ4bQ27dvVaoXHh5O9vb2RToVWBrgOI5WrlxJVlZWhX6Qyo0tW7aQu7t7vuu1uSGRSMja2pqePXumYctKL0z4yijJyck0adIkMjc3p/nz56vssFEeOHr0KLVv3z7X6/7+/rRjx44cr8nlcqpWrRqdP3++QH3LZDIaPnw41axZs9COBzlx7tw5srGxofbt29OQIUPyLe/g4ECRkZE5Xnv69ClZWVkp1zxjYmLIw8ODRowYofa6UVxcHE2ePJlMTU1p4MCB+X6JchxHDg4Oea5Rfk9cvXqVbGxsaOHChRoXe47jyN/fnyZMmFDgNiZPnkxjx47VoFWlGyZ8ZZyXL19Sx44dycXFhY4dO/bdP0GrwpUrV6hx48a5Xl+zZg0FBATkeG379u3k6+tboPcxKSmJ2rZtS61bt6bExES166tKTEwMOTg4kJOTE71+/TrPsu7u7nlOg126dIksLS0pLCyMiIgSExOpWbNm1LVr1wKNIOLi4mjWrFlkaWlJnTt3znNKftCgQbRs2TK1+yirvH37lry9valXr155evUWhM+fP5OtrS1duXKlQPVfv35NFhYWlJ6erlG7SitM+L4Tzpw5Q9WqVaM2bdoU2OHge+HRo0dUq1atXK+/efOGrK2ts4mbTCajKlWq0IULF9TuMyIiglxdXWnYsGFZnFCKil69elHv3r3JwsKC1q9fn6tQN27cON8vw23btpGTk5PSu1MsFlP37t2padOm9OXLlwLZl5qaSsuXLycnJydq2rQpnTp1KpuNe/bsoQ4dOhSo/bJKeno6BQQEkKenJ0VERGi07ePHj5OTk1OB/2Zt2rShbdu2adSm0goTvu8IqVRKixcvJktLS+rXr5/G/7HKCq9fvyYnJ6c8y7i4uGQbCW3dupUaN26s9mjv9u3bZGtrS0uXLi22Ebevry9dvnyZwsLCyNPTkzp06JDjuuWPP/5Ihw8fzre92bNnk7e3N6WmphLR17XkUaNGkbu7O0VHRxfYTqlUSjt27CB3d3eqVasW7dixQ/lgEBsbS4aGhuXOlZ7jOFq6dClZW1trNDEAEdGIESOoc+fOBfocHj58mBo1aqRRe0orTPi+QxITE+mPP/4gMzMzGjlypEpxWt8TObnx/5cRI0bQwoULlb/LZDJycXGhS5cuqdXXnj17yMLCgo4fP14gWwuKk5OT0lNQIpHQ1KlTydramg4dOpSlXL9+/WjLli35tsdxHPXv3586duyoXN/jOI7mzZtHTk5OhXZ84DiOTp06RU2bNiUnJydavnw5paamkre3N129erVQbZdVLl68SNbW1rRkyRKNPTCJxWKqU6cOLVq0SO26MpmMKlSokGNGoe8NJnzfMZ8+faLffvuNzMzMaMqUKZSQkFDSJhULYrGYhEJhnmWOHj1KLVq0UP6+ZcsWatq0qcp9cBxHc+bMIUdHx0K5khcEuVxOWlpa2Ryabt68SZUrV6b+/fsrPTlHjx5NS5YsUaldiURCLVq0oBEjRmT5It6yZQtZW1trJGsLEVFwcDD5+/uTpaUl+fr60vjx4zXSblkkIiKCPD09KSAgQGPra2/evCFLS0u6efOm2nVnzJhBI0eO1IgdpRkmfOWAqKgoGjRoEFlYWNC8efOU01nfKxzHEYA8n6KTk5PJwMCA0tLSSCqVkrOzs8qOAWKxmAICAqhOnTrKuLriJCYmhqysrHK8lpKSQkOHDqWKFSvSlStXaMaMGTRz5kyV205MTKRatWrR1KlTs7x/J0+e1PjINjw8nNq1a0cCgYBGjx6dq/fp905aWhr99NNP5O3tTVFRURpp89ixY+Tg4ECxsbFq1Xv79i2ZmZl9998RTPjKEeHh4dS9e3eytbWllStXftdrK1paWlnuL3Pdb968ecrF/yZNmtCpU6do06ZNKgfwxsbGkq+vL3Xp0kXjnnmqEhwcTN7e3nmWOXHiBFWoUIF++OEHGj58uFrtf/78mdzd3bOJX3BwMFlbW9OmTZsKZHdOiMViMjAwoFGjRpGZmRn17du32EfQpQGO4ygoKIhsbGw0NvX7+++/U5s2bdTO9NSxY0fauHGjRmworTDhK4c8ePCA2rZtSxUrVqStW7cWKtdfaUVfXz9LqqjQ0FDS1dUlkUhEIpGIfv31V5o0aRL98ssvVKlSJbp27Vq+bX78+JFcXV1pwoQJJZo2bv/+/dS5c+d8y8XGxpK3tzeZmJioLSa5iV94eDhVrFhR7UD3vGjbti0dOHCAvnz5Qn/99RfZ2dlRo0aNaOfOneUuPvXs2bNkZWVFixYtKvRnTCqVkq+vr9pJqE+ePPndJhHPhAlfOebq1avUqFEjqlmzJh06dOi7igH873Yrr1+/JgMDAwJAAEhLS4u0tbVJKBSSq6srTZ06Nc8whPfv31P16tXpzz//LA7z82Tx4sU0atQolcoeOnSIateuTZaWljRv3jy1UqflJn6Zge7Dhw/XyEPT4sWLaejQocrfZTIZHTp0iFq2bElWVlY0ZcqUcjUN+ubNG6pfvz75+fkVOpF3dHQ02djYqBWiI5fLydHRkR48eFCovkszTPjKORzH0cmTJ8nDw4Pq1q1LZ86c+S4E0NraOsv624cPH0gkEimF79uDz+cTAHJ1dc0x8Dw6OpqqVq1Kc+fOLc5byJWxY8dSUFCQSmWvXLlCTZo0oaioKGrdujV5eHjQ3bt3Ve4rN/FLTEykpk2bUt++fQsdt/j48eNsu0hkEh4ernTQ6tixI506dapcJGmXSqU0adIksrOzK3TIw/nz58nGxkat9IZz587N8jDyvcGEj0FEX+O2du/eTa6uruTl5UX79u0r01Og/03VlZycTFpaWjkK37eHQCCguXPnKhf33759S5UrVy50BnxN0q1bN5Wz6T948IA8PDyI6OtDzo4dO8jGxoZGjx5NycnJKrWRm/ilpaVRy5YtqVevXoUSP47jyNbWNs9EzmlpabRp0yby8vIiZ2dnWrhwodqOG2WRc+fOka2tbbbdOdTlzz//pMaNG6vcxvv378nExOS73QqNCR8jCwqFgo4ePUo+Pj5UtWpV2rhxY5l0gqlcuTK9ePFC+btcLicej5ev8GUe3bp1o4iICKpUqRItXry4BO8kO/Xr11fZVT00NJRcXV2znIuLi6OBAweSg4NDnhvZfktu4peenk5t27alrl27FmoHin79+tHq1avzLcdxHN25c4d+/vlnMjExoX79+tHt27e/i1mK3Pj48SO1bt2aGjZsWOApX4VCQa1bt6bff/9d5Tpdu3alNWvWFKi/0g4TPkaOcBxHly9fptatW5O9vT0tXry4yPYVKwpq1qypzD+ZiVAoVFn49PT0yNrampYvX15Cd5A7FSpUUHkXhGfPnlHVqlVzvHb58mWqWrUqdenSRaVpsNzETywWU8eOHalTp04FdkbZvn07+fv7q1UnLi6OgoKCyNnZmWrXrk0bNmz4bt3wFQqFchuogwcPFqiNz58/k4ODAx07dkyl8ufOnSMPD4/v8qGCCR8jX+7fv0/du3cnS0tLmjlzZhankdKKp6dnts1V9fT0VBa+TAeY3bt3l9Ad5IxUKiUtLS2Vp6xevXpFzs7OuV7PyMigP/74gywsLGj16tX5rp/lJn4SiYT8/f3Jz8+vQMmtP3z4QCYmJgWazlMoFHT69Gn68ccfyczMjMaMGfPd7voQHBxMlSpVomHDhhUo4P3mzZtkZWWlUjpDhUJBlStX/i73/mTCx1CZ58+f06BBg8jU1JTGjh1L7969K2mTcqVevXoUHByc5ZypqalawgeARCIR/fXXX6XmqTfTS09VIiMjycHBId9yT548oUaNGlGDBg3yTVmVKX5jx47NIpRSqZS6d+9OrVu3pvT0dJJIJCqvIxJ9HaUX1pMwMjKSpkyZQra2tuTt7U1Lly6lT58+FarN0kZiYiL17NmT3N3dC5SQftGiRVSnTh2VRucLFiyg/v37F8TMUg0TPobavHv3jsaOHUumpqY0aNAgev78eUmblA1fX99ssXm2trZqC1/mtOeQIUNKhbNPTmt2eRETE0O2trYqlVUoFLR27VqysLCgqVOn5jmiiI+Pp8aNG1PXrl2zlJPJZNS7d29q3rw5NWnShHx8fFS2dejQobR06VKVy+eFXC6ns2fPUt++fcnY2Jj8/Pxo9+7d3822OxzH0caNG8nCwoI2bNig1oNZ5v59I0aMyPG6QqGg7du3U1paGn3+/JmMjY2/u3SHTPgYBSYuLo5mzpxJFhYW1K1btwI/rctkMo176DVv3jxb7JKzs3MWQdPW1laGMuR38Pl8GjdunEZtLAj57TX4Xz59+kQWFhZq9fH+/Xvq0aMHubi45Bn/JRaLqXfv3uTj45NlVCWXy8nLy4v4fD6JRCK6fv26Sv1u376dunbtqpatqpCSkkLbtm2jVq1akYmJCQ0YMIAuXbr0XYRFPHnyhNzd3alHjx5q7QH55csXqly5cjbv4NTUVGrXrh0BoCNHjhAR0U8//fTd7ZvIhI9RaFJSUmjx4sVkb29Pvr6+tGfPHrU8QRcuXEjGxsZZvDALS9u2benUqVNZzrm6umYZxVWsWDFfwTMwMCA9PT369ddf8930tTg4ePCgSllbMklISCBjY+MC9XXixAlycnKi7t2757omxHEcTZ8+nZydnSk8PJwSEhJo6dKlpKurq3wP80uvlklERESO+yRqkpiYGAoKCqJatWqRg4MDTZ48uczvX5menk7Dhw+nSpUqZZvez4uHDx+ShYUFhYeHE9HXmZyqVauSrq4u8Xg8Gj16NBF93UXC09OzSGwvKZjwMTSGTCajAwcOULNmzcjW1pZmzpyZr7cgx3Hk6OhIAMjS0lJlb8X8+PHHH5VPrJl4eXkRANLV1aUlS5aQhYVFrrF8enp6VLNmTdq8eXOJ5eTMiQ0bNtDAgQNVLp+cnEz6+voF7i89PZ1mz55N5ubmNHXq1Fw9ezdt2kRWVlbUtm3bHEfLJ06cyLcvjuPI3t5eow9AefHvv//ShAkTqEKFCuTl5VXm1wMPHTpEVlZWNH/+fJVHs+vWrSM3Nze6cuUKmZqakkAgUP7datSoQURfpz4dHBzo33//LUrzixUmfIwiISwsjIYNG0YmJibUo0cPunr1ao5P8vfv3yd9fX2l4Njb2xc6TZNMrqAOPw2g5Vv3U0RsKsnkX78EnJ2dSSgU0sWLF+n169dZRiUASCgUklAopJ9//pkePXpUKBuKivnz59PEiRNVLp+RkUHa2tqF7jc6OpoCAgKoQoUKtGXLlhy/WHfs2JHnOml8fHy+/fTq1UujSbBVQS6X07lz5yggICDLemBpeuBRlaioKGrUqBG1atVKpX04L126RPXr188ieN96NWe+B1OmTKEJEyYUtfnFBhM+RpGSmJhIy5cvp2rVqpG7uzutW7cuS6zV0KFDs6yzCYVCqlq1qlrrFURECakSWnPlFbVYfIVcpp2kqtNOUI0/TlGNGafJZdpJarH4Cg1etJcu3bxDRESrV69W9quvr0/Ozs40atQolaflSorff/+d/vrrL5XLy+Vy4vP5Gus/ODiYfHx8yNvbO9vaXeaIOqcj8++auTNGbqxatYoGDBigMXvVJSUlhbZv306tW7cmY2Nj6t69O+3cuVPtz2NJIpPJaPr06WRra0tnz57NtVxISIjygTOnv5mRkRFdvnyZiIiePn1Ktra2hU5PV1pgwscoFjiOo/Pnz1OnTp3IzMyMfvvtNwoLC8uSOPpbpxMvLy+VnrglMgUtPPOMqk4/RdX+OEVOk0/kelT74xRVnX6KFp55RtVruhGPx6Nu3bpRcHAwcRxHUqmUzM3N851uPXXqFO3atUtTb41aDBo0iNatW6dy+cy9CTXpyMFxHO3cuZMcHByoZ8+eFBkZSQcPHsx3vdTKyop8fHzyDHEIDQ0lFxcXjdlaGD59+kQbN26k9u3bk6GhIbVp04bWrFlTInswFoRLly6RnZ0d/f7779my6nz58kU505JXHOusWbOUdTJz+X4P8IiIwGAUI1FRUVi7di1Wr16NtLQ0KBSKbGV0dXVRv359nDt3Dtra2jm2E5OYgT4bg/EpWYwMGady/yItPoy1gTU9aqJ2Vacs1wYMGABPT0+MGTMmW73k5GQMHz4ce/fuRY0aNRAaGqpyn5qiS5cu6NOnD7p27apyHW1tbaSmpub6PhaUtLQ0BAUFYfny5UhOTs7x7/gtenp6+OGHH5CWloaTJ09CT08vWxmO42Bubo7HT55Crm0EiZyDjpAPe1MRhAK+Ru1Xh5SUFJw5cwaHDx/G6dOnUb16dfj7+8Pf3x9VqlQpMbvyIzY2FgMGDEBsbCx2794NZ2dnREdHw9PTE/Hx8fnW9/Hxwe3btwEAK1euxO3bt7Fz586iNrvIYcLHKDGaN2+Oy5cv53pdJBKhZcuWOHz4MAQCQZZrMYkZ6LjyBpLSZVAQITX0AuJPLc27Qx4fTpOOAQAEPB6M9bRwfKQv7ExEyiLHjx/H33//jatXr2apeunSJfTq1QvJycmQSCQwMTHBly9f1LthDdCsWTPMnDkTP/zwg8p19PT0EBsbC319fY3bQ0SoV68e7t+/r1L52rVrw9XVFbGxsTh69Ch0dHSU176kSbH3/jusOHEXEm0jaAsF4PN44IggU3BwMtdHNy979KrrABM9zYq4OkilUly+fBmHDx/G0aNHYWZmBn9/f3Tu3Bne3t7g8XglZltOEBGWLVuGwMBALF26FOPGjcPnz59Vqqurq4vU1FQIBALExcXBxcUFb9++hZGRURFbXbQw4WOUCHFxcbC3t4dEIsmznJ6eHrp27YqtW7cqv1Ckcg6tl17Fu4QMKP7/4yv99AbpL27n2IYk+gnEUaEQVa4Lq+4zlecFPB4czUQ4N7YptP5/NCEWi2FjY4Pnz5/D2toaaWlp+O2337Br1y6kp6f/r65AgNTUVOjq6hbqfVAXd3d37Ny5E7Vq1VK5jrGxMaKiomBiYqJxezZv3oxBgwapXF5fXx+HDx/GunXrIJfLsX//fhBPgGUXX2DjjQjweIA4j9G7rhYfRMBg30oY06IqtIUFHwV++fIFpqamBa4PfB2h3rlzB0eOHMHhw4chFovRuXNndO7cGU2aNIFQKCxU+5rk4cOH6Nu3LyIjI5GRkaFSHUNDQ1y9ehW1a9cGAHTu3BmdOnXCgAEDitLUIqfk5g4Y5Zpdu3ZlG8XlRHp6Og4cOIBx48Ypzy27+AKfksVK0QMAbWtnmDTuk+PByb6Kq4Fn2yxtK4jwMVmCZRdfKs/p6uqiXbt2OHLkCG7evIkqVapgx44dWUQP+DoajYyMLMitF4qEhASYmZmpVUcoFEIulxeJPfr6+mp9uaelpWHixInYuXMnZDIZeg74Fa2XXsXmmxGQyLk8RQ/4KooSOYfNNyPQeulVxCSq9gX+LcnJyejXrx+srKyQkpKidv1v4fP5aNCgARYsWIDnz5/j9OnTsLa2xu+//w4bGxv0798f+/btU2lasajx8vJCt27dIJPJVK4jk8lw/fp15e/9+vXDtm3bisK8YoWN+BglQrVq1fDixQu16gQEBGDZmo3wmX8RErlqa3rS2Eh82DQSAkNz2A3bDB4/u9jqCPm4M6WFcvps586dmDJlCuLi4nJ9MjYyMsLu3bvh5+enkh1EhPT0dKSkpOR5ZE4r6ejoQFdXF7q6usrXOjo66N69O44fPw4TE5Ms1/5bjs//3zOtjY0NHj16BFtbW5VsVYemTZvi+vXrUPdrZPfu3aj3Q1v4Lb0CGU8LCgIUGclIf3EbGa/uQRYbBUVqPCAQQtuyIvTdW8KgVkvweP+7r9ymq/Pi9OnTCAgIQGpqKoRCIe7cuQNXV1e1bFeVt2/f4ujRozh79iyuXbuGKlWqoFWrVmjZsiV8fX2LfbYgLCwM9erVU3m0l0m7du1w6tQpAIBEIoGdnR0ePHgAJycnyBUcor9klJq1WFVhwscodp48eYI6depALBZnOa+jowMdHR3weDxIpVJIpVIYGRnB2toaIpEIbm5uaDhoJpZefJHvyCCThHNrkfLwBIwb/QSTxn1yLKOrxcfYllXxS5PKuHfvHrp27Yp3797l2a5QKESnTp3g6emZr5hlCpqOjg4MDQ3zPAwMDMBxHCQSCcRisfKQSCRIS0vDmTNn4Ovrm+X8f19LJBJoaWkphTAhIQH29vYwMzODvb097O3t4eDgoHydeYhEqolHJrdu3UKrVq2yjYZzg8fjwdLSEgYGBmjRqjVeuPTIMl2d8ugUEs6uhsDADDqO7hAaWUKRloj0F7dBkjToVWsIi85Tsqyh5TRdnRNfvnzBsGHDcPz4caW96j68FAapVIo7d+7gwoULOH/+PB4/fgwfHx+0bNkSrVq1gqenZ5aHlaLo38PDA8+fP8/zIUUoFMLY2BgZGRkQi8XgOA6GhoZISkpSvu+DR4xBmnUtxBq6ICo+DVoCfqlci80LJnyMYmfdunUYMWIEzMzMYGNjAycnJ7i4uKBSpUrKL2E7OztYW1tnm0ZrueQqXn1OVakfTiZBzMp+4KQZsBu2CUIjy1zLuljqw+nJduzYsQNSqVSl9t3d3dGxY8d8xSxT0Aq73vPu3Tv4+PggJiYmz3JEBKlUqhRCb29v/PPPPzA2NkZMTAzevXuH6Oho5fHu3TvExMTAwMAgR1H89vdvPTE7d+6M06dP5yqY3361ZIq5TCZDQEAA3PtMxeabEVm8cTMi/wXJxBC51M0yslOkfsGHbeOgSI6FRecp0K/eKEs/Ii0BBvlWwoTW1XK04+jRoxgwYADS09OzrCmLRCIsXrwYv/76a57vZ1GQlJSEK1euKIUwLi4OLVq0UAphxYoVNdqfi4sLIiIiwHH5PzDq6upi+/btOHDgAA4dOgSZTIaQkBDUcHXHsosvsOH6G/B4gESeu3Roci22KGDCxyh26Gv8qNpPuHIFhxozz0CmUO0jm/r4IuJPLsnm1JITfHCIWNAZPJDK03bNmjXL0ytV0zx9+hRdunRBeHi4WvWqVq2KEydOoGrVqrmWISLExcUphfC/wpj5WiQSKcXQ3Nwc+vr6sLCwgJ2dHRwdHSESiSCXy6FQKCCXy7O9/vjxIxxcquOP+3yVp6sBIOnWPiRe2wZDrw4wa51dqP47XQ0A8fHxGDx4MM6dO5frqHTChAkICgpS2Y6i4t27d7hw4YLyMDQ0VE6LNm/evFBOOC9evEC1ajk/FOQEj8dDvXr1cPv2bXz+/Bnjxo3DqMkzMflsTIFCh6yNdLFzsI/K09HFQelxOWKUG3g8XoFcvqO/ZEBLwIcsn3ixTFJDzgDI7tSSE7raWrgfHoHg88exYcMGhIeH5+txGhERoZIdmkIikRRoXUgoFObr0JA5DWlpaan04PsvRISEhIRswvj27VucP38eT548gbGxMVxdXeHm5gY3Nze4urqiZs2aMDAwULaz9upr8Hjqre8i0xEqhzXar/YDe++/wy9NKgMA9u/fjyFDhiAjIyPPEfy3DxEcxyEjIwPp6ekFOjiOg56envLQ19fP8jOv1/b29hgwYAAGDBgAjuMQFhaGCxcuYOPGjejfvz+qV68OX19f+Pj4oEGDBnBwcFD5fyg5ORl8Pj/LaE8gEEBfX1+59vxtDCYR4eHDhzhw4AC6d++Ohas2ZgkdAoAvl7dA+vElZAnvwWUkgyfUhsDICnpVfWDo3QEC0ddwhwwZh3cJX0OP1FmLLWqY8DHKDBI5B76K/+zSuLeQxDyDwNACosp18i3P5/FgYGSKESNGYMSIEXj37h0GDRqEe/fuQSwWg4iyCeGHDx9ARMUWtyUWiwskfFpaWhrx6uTxeDA3N4e5uTkcHR0xY8YMdOrUCT/88AOEQiE4jsO7d+8QFhaGsLAwXL58GStWrMDz589hZWWlFMLrRs1UXqMFAOIUSAu7BAAQOXvlWEYs43DgQTQ6VzPAwIEDceXKFZXWHs+cOQMLCwukp6dDLBZDJBJlES9VDhMTE+jp6YHH4ymFMy0tDbGxsUhLS1MKY16vpVJpjsJoa2uLgIAAAMCnT5+watUqDB8+HDo6OmjYsKFSCL29vXP9bKSkpMDAwADJycnKc9ra2nBxccGvv/6KuLg4PH/+HC9evEBUVBQ+f/4MmUyGgQMHopN/V/TZGJxF9AAg+d5RaNtUhm5FTwj0TUBSMSTvnyPpxi6khpyBTb9FyqUFBRGS0mXouzE437XY4oIJH6PMoCPkg1NxGjL10WkAgEGtVjl6cv4Xjgg636xDODg4YN26dahXrx4ePHiAAwcOYPPmzYiNjYVUKoVcLgePx0NsbCysrKwKdkNqUlDhU2XEpy5JSUlYs2aN0rW9e/fu6N+/Pxo1agQnJye0b99eWVahUODNmzcICwvD47An+JgqB6D6w0LilX8gi42CqHIdiJy9cy0XEZcGO3sHKOSq36u+vj6eP38OPT096OrqlljwuUKhQEZGRhZBTE1Nxfv37/H27VtERUVBIpEgIyMDAoEA8fHxuH79OoKDgzF//nwkJSXBwcEBnp6eaNKkCfz8/FClShXweDyEhoZme2jLyMjA48ePMWXKFBw5cgRTpkxRXiMifP78GZ8+fcoxdAgAHMftA0+Y3XHly9VtSL69D0m398O8zfD/3d83oUO5rcUWJ2yNj1FmUHWNj+RSRK/sB06Snq9Ti7KOQgbBoYmo5eaKJk2aoHHjxqhZsyb8/PwwZswYdOnSBcBXl/Dt27dj69at+PTpEx48eAAvr5xHIZrmzJkzWLp0Kc6cOaNWPR8fHyxZsgQNGjTQmC1yuRy6urrKKTI+nw89PT1oa2ujd+/e+Pnnn3PMYhIZlwa/FdeRLlVtujr5/jF8ubAeQnN72PQNgkBkmGtZPW0B+pq/w8Wje3Dz5k0IhUKkpaXl2T6fz4dYLIaWlpZK9pQWMjIylIL49u1bvHr1CiEhIXj58iU+fvyI9PR08Pl8GBsbg4iQmJiYa1sikQiTJ0/G9OnTs6y7f0mTqhU6BHxNJPFhy2joVvSEda+52a7ntBZbErARH6PMIBTw4WSun69XZ1r4DXDiVIgq11VJ9ADAUhdwqeONR48e4cyZM1AoFOA4Drq6uhg0aBCuXLmC+vXrw9XVFbNmzcL8+fMRHh5erHkaxWJxlhRfqqKpqc5vEQqFMDc3V6a+4jgOqalf/y5r1qzBli1bYGhoiJ9//hkBAQHKWDl1pqtTHpzAlwvroWXhCOtegXmKHvB1urprj16YOnoIkpKScODAAaxduxZhYWEAkC18BvjqwRgTE6NxL8qiRiQSoVq1ark6rcjlcty7dw/nzp3DwoUL82wrIyMD8+bNw8mTJ3Hs2DFYW1sD+Lpmqu4AOP3VXQCAlmXFHK//dy22pGDCxyhTdPOyzzeOTx2nFuCr6/XQlu4YOrszgK9TPW/fvsXdu3dx+vRpbN26FevXr8emTZsgEAiQnp4OfX192Nvbo1KlSnBwcMgxLi6nJMyFoTRNdQKAo6NjjjkfFQoF0tLSkJaWhsWLF2PFihUwNTVFmzZtMGD07ypNVyffO4ovFzdAy9Lpq+jpm+Rb59vpamNjYwwaNAiDBg1CdHQ0duzYgfXr1+PTp0/KqWrg60PB27dvy5zw5YdQKESDBg2we/duldY6JRIJ7t69C1tbW9SuXRtt27bFbdMW+a7FJt05BJJmgJOkQ/rxJSTRT6FlWRHGDbrnWD5zLZYJH4OhBr3qOmDJhdw9AmVx7yCJfqqyUwsAEAE96jgof+fxeHBycoKTkxO6d+8OuVyO2rVr48cff8T9+/dx9+5dPHjwAE+ePEFERASsra1hZGSkTA2WnJyMDx8+KMUxr9g4dRJHl7Rzy3+pXr16vsmpZTIZZDIZ0tPTsXnzZtR0dYNMkfcaT1LwASRe+QdaVs6w7jUHAj1jlezJkEixc/1yeHrUQq1atWBvbw8ejwd7e3tMnjwZkydPRmhoKLZs2YKtW7dCLpcjPT0dUVFRKt9zWeP06dNqlScihISEoFNnf7z7kn2E/F+S7x4Cl5ao/F3X2RsW7X/L828WGZ8GuYIr0QwvbI2PUeYIOhueLfi5oOQX/AwAFy9exIQJE/Do0aNs1xISEvD06VOEhYXhyZMnePLkCcLCwiCTyVC1alU4ODjAzMxMGeT95cuXLEHkOjo6WQTR2Ng4WwqyzOPatWt4+/Ytxo8fn2OqstzSlvn5+WHEiBFo3749OI5DWlpavplmkpOT8y3z5cuXfLciAr4mGndwcMCBAwfg5uaWZxKCxJu7kXR9J7RtXGDVc06+05vfYqktR9O063j8+DFCQ0MhFovh7u6OWrVqKX+6ubnB0NAQCoUC165dw5YtWzBo0CA0bdpU5X7KEvXr18fdu3dzvS4UCqGlpQVDQ0N06dIFXbt2RZMmTfA+WabWWqwi7Qsk0c/w5epWkDQDlt1mQMfGJceyetoCnBrVGBUtNL9biKow4WOUOXLanaEgqJruiuM4VKxYEcePH4eHh4dKbcfGxmYRwsyffD4frq6uysPR0RFGRkZITU1FdHQ0UlJSckxHJhaLERYWhqSkJLi4uOSYquzb379NWyaRSKCnp6cc4YhEIpWyzRgZGeV5/fz58xg2bFieiZ5FIhHGjx+PGTNmKB1I1l59neN0dWbCAfD4MPTuCL5O9qliobE1DGq1zHZeV4uPcS2rYug3U2ixsbFKEcz8+fTpU1haWqJSpUpwdHSEk5NTlp+ZQfjfC02aNMmSZDondHR00KNHD0ydOhXVq1cHADz/mIKua28hVaLeTIE86TNi1g+FlmkFVBi8OscyBjpCHPy1IarZqP5Qo2mY8DHKJP/dj09dBDwehCTF3gFe8KzqmG/56dOnIz09HYsXLy6IuQC+TiN9/PgxmyA+efIEurq6yji3zMPZ2Rk2NjbKkduCBQsQHx+fr7NCZl+Zacu6d++OXr16oWvXrjAwMNBYTsgHDx6gefPmWeLDMhGJRLCxscGBAweyeb0mpktR/6/s3oKJ13ci6ebuPPvUcXCDTZ/52c+r6C2oUCgQERGh9IaMiorK8jo6OhpGRkZZBPG/4mhubl7q9tzLjdq1ayMkJETl8np6emjSpAnWbD+g1ojvW95vHg3Z5zewH70zxylPNuJjMApBwXdgF8DaSAe35vaCPDkWTZo0wahRo9ChQ4dcvSZfvHiBJk2a4N27dxp3fScixMTEZBHCp0+fIjIyEomJiXBwcEDFihWRkJAAIyMjDBo0CBUrVkTFihVha2ub7/ZObdq0wdixY9G2rWrOPqqSkJAAW1vbbJlRRCIRhg0bhnnz5uX6fhb3dLWqcByHT58+5SiKmT+lUmm20aK1tTX09fXzzdKipaWlcdHMfMjJKZvMokWLcPDgQbXbzBBL4D7ngsrpAb/l3fK+4NITYf/bHgh0DbJd1xLw8OzPtmyNj8EoKFI5p/ImppBLoKMrwpDGzhjTogratm6FS5e+ZgQxNDQEx3Ho1asXfv311xxj0Bo1aoQpU6agQ4cORXlLWUhPT8fbt28RGRmJZcuWIT09HRUqVEBkZCSioqIQHx8PBwcHODk5KcUw83BycoKdnR1atGih9q7tqkBE0NfXV25zIxKJYGZmhgMHDsDHxyfPusU9Xa1JkpOTs4nh58+fs2VkySlDS+Z7ll8Ks2+nplU5hEKhMghfW1sbQqEQfD4fRITXr1+rfG9ubm6YN28ezp07h3uWbfExhx2MZPHvwNcxgMAga/5QIg6J13Yg+fY+6NjVgE1AzjlQq1gZ4PzYkl1TZcLH+C5ITJdi7/13OPAgGpE5bJVS0Vwf4mdX0LaKEaZNHAsA2LZtG4YNG5ZtZ3VdXV2Ym5tj+PDh6Nevn3Ifu/Xr1+PcuXM4cOBAidzjuHHjYGdnh/HjxyvPicVipTBGRUUhMjIyy+vY2FjweDy4urqiVq1aWYSxQoUKsLCwgLGxcYGnPytXrow3b95AJBLh559/xqJFi1QO44hJzECroPMQkwBcAb6FCrIfX0mT6eGqSiozLS0tpQjy+XxlNpfk5GQkJiYiISEBcXFx+Pz5Mz5+/Ij379+D4zjY2dmhQoUKymPp0qX5OiHx+Xz4+vri5cuXsLS0RM+ePaHj2QEbgmOyPUwm3zuKL5c3Q9fBFUITW/BFhlCkJULyLgzyxI8Q6JvC6qdAaFtkX0LIaS22JGDCx/juyG1zzNDQULRt2xavX7+GSCRCbGwsHBwcck1GraurCyJCvXr1MGrUKDRu3BjVq1fHmzdv1N4FXRMMHz4cNWvWxMiRI1WuI5FIULt2bYwaNQra2tpKYYyMjMTHjx+V+STNzc1hYWGhPCwtLbP8/t9zmeLWvn17PHjwAPv27UOTJk3Uup+DBw9i3PQ5cOy/CHFpUrWnq22MdLCjlGX9V4fMBNGfP3/G+/fvcz0+fPgAiUSSRcy+PWxtbZWvDQ0Ns81U2Nra4uPHj7naIRAIUKlSJQQEBKBHjx5KB5fc1mKlsZFIeXQakuinUKTEgxOngqetCy1TO4gq14FhnR9z9cYtLZlbmPAxyhWdOnVCq1atlOJRs2ZNPHv2LN96mS7wderUQc+ePTF8+PB862iaYcOGwc3NDSNGjFCrXs2aNbFv3z64ubnleF0mkyE+Ph5xcXGIjY1FXFyc8sjp99jYWPD5fFhYWMDU1BSWlpawtrbOJpBmZmbQ09ODSCSCSCSCrq6u8vXr16/RsmVLnD59GrU8vVSerhZp8cERlNPVJZHwmIggFouRnJyMpKQkJCcnq/06KSkJKSkp0NbWhpWVVb6iZmJiUuC1wUaNGuHWrVs5XvP19cXq1avh7u6e4/XSuhZbWFgAO6NcMX36dHTt2hVDhw6FtrY2evTogXnz5uWb2UQsFsPGxgZDhgzB8uXLS0T4BAKBSnFz/0UikeSZ6kxLSws2NjawsbFRqb3MkUpuwvjo0SPExcUhPj4eGRkZykMsFitfp6enQyAQoHnz5kpR1DUyA1x8IXTwhlxkBh5x4IEAHg/E40Ofy4Az9wk1dRIhf/gvVj8TgcfjgeM4KBSKLEdO59Q9z3EcpFKpMq7xWwHj8/kwMjKCsbFxlp/fvjY3N4ezs3Ou1w0NDYslR6izs3M24TMzM8PFixfh6emZY52PHz/i1KlTqG5tA2sjkUbWYm2MdDCmRfGl+MsLJnyMckXdunVRs2ZNbNu2DYMHD8aPP/6IRYsW5Sl82tracHZ2xvXr12FqaqrMAFKrVq1itLzohE9deDye0oPRyclJrbocx6FTp05wcnLC4sWLcxRFsViM1LR0xCSKkSqWQCEVQ1eeBok4sxyHL1++4P379yAiCAQC8Pl8CASCLAefz4eOjk6O51U5JxAIIBQKswmXkZGRRt/PokAmk+Hs2bP4559/cPLkSeV5Pp+PgQMHYuXKlcp7+Pz5Mx48eIC7d+/i6tWrCAkJQWpqKmQyGQYMGICdi1cVOnTIWE8LOwb7lIotiQA21ckoh9y4cQM///wznj9/DoFAADMzs1yz12fG1128eBFGRl8315wzZw6io6Oxbt26YrT6q3NLhQoVMGHCBLXqWVpaIiwsTJl8uCSZNWsWLl68iEuXLpW5HRHKAo8fP8Y///yDnTt3wtnZGf3794e7uzsaNmwIIyMjbN26Fbq6urh37x6uXLmCkJAQpKWlQUdHB+np6VlS2+nq6uLTp08wMjIqVOhQaVyLZSM+RrnD19cXDg4O2LNnD/r27Qs/Pz/s2rUrWzmhUIhGjRrh+PHjWbJ5DBkyBDVq1MD8+fNhamqarV5RUZgRX0FyfGqaY8eOYdOmTbh37x4TPQ0SFxeHXbt2YevWrfj8+TP69euHq1evZtm5Ydy4cdi6dSt69uwJkUiEtLS0LCL3XwcvHR0d/Pbbb8qHPTsTEc791lTttdhBvpVKbC02L0qXNQxGMTF9+nQEBgaC4zh0795d+Q+eiUgkgo6ODnr37p0thZWNjQ3at2+PLVu2FKfJpWaqsyA8f/4cgwcPxv79+1VeS2Tkjkwmw9GjR+Hv7w8XFxfcvXsXCxYsQGRkJAIDA7NtVzR06FCkp6dDKpUiKSkp36TlfD4/S9gMAGgL+ZjYpjruTGmBsS2rooqVAbQEPOhpC2CgI4SetgBaAh6qWBlgbMuquDOlBSa0rlbqRA8AQAxGOYTjOKpfvz7t27ePUlJSSFtbmwAQANLT06MhQ4ZQaGgoWVhY0IMHD7LVv337Njk7O5NCoSg2m6dNm0azZ89Wqw7HcQSgWO38L2lpaVSjRg3asGFDidnwvfDo0SMaM2YMWVlZka+vL23cuJGSkpJUqrt//34SiUTKz3luh7a2Ng0fPlylNmVyBUXEplL4h2SKiE0lmbzkPmfqUAqlmMEoeng8Hv744w/MmjULurq6qF27NoCvuQp/++03rFu3Du7u7li9ejW6du2KuLi4LPXr168PMzMztbd9KQwFGfFJpVJoaWlpLD9nQRg/fjy8vb0xePDgErOhLJOSkoLVq1fD09MTnTp1gpGREW7evInr169j0KBB2WYrcqNbt24YPHhwvgkG+Hw+pk6dqlKbQgEfFS30Uc3GEBUt9Es0DZk6lA0rGYwiwM/PD1ZWVti0aRN++uknAMDs2bMRGBiojJnq3r07unfvjp9++imL6PB4PIwcORIrV64sNnsLInwlPc15/PhxnDlzpljfp++F58+fY/To0XBycsKlS5ewaNEiREREYPbs2XBxyXnLn/xYvHgxXF1dc83vKhAI0K1bN9jZ2RXG9FIPEz5GuYXH42HRokWYNWsWunbtiosXL2Zb1wCAefPmgYgwbdq0LOd79uyJBw8e4MWL3DfG1SRlTfg+ffqEoUOHYvv27TA2Vm0z2fKOQqHA8ePH0aZNGzRp0gSGhob4999/ceDAAbRo0aLQI3eZTAZ3d3dQLs78WlpamDlzZqH6KAsw4WOUa7y8vNC6dWusWbMGzZs3z7GMUCjEnj17sGfPniyZ7nV1dTF48GCsXp3zvmOapiwJHxFh4MCBGDRoEHx9fYu9/7JGQkIC/v77b1SpUgWzZ89Gnz59EBUVhcDAQDg4OGikj9DQUNStWxepqak4efJkNqctPp+P1q1bF3g0WaYo4TVGBqPEeffuHZmZmdHbt2/zLHf//n2ysLCgJ0+eKM9FRUWRmZkZpaSkFLWZtHDhQho/frxadV69ekWVKlUqIotyZ+XKlVSnTh2SSqXF3ndZIiQkhAYPHkwmJibUt29funPnjsb7UCgUtHTpUrKwsKCtW7cSx3FERLRkyRLS09NTOrWIRCL6999/Nd5/aYSN+BjlHnt7ewwfPjzfBX1vb28EBQXB398fSUlJAABHR0c0a9YM27dvL3I7y8qI79mzZ5g5cyZ27tzJ4vVyQCaTKZN6t2/fHk5OTggPD8f27dtRr149jfb14cMH+Pn5Yc+ePQgODka/fv2U69djxoxBmzZtlDGePj4+xZ6NqKRgwsdgAPj9999x8eJF3L9/P89y/fv3R8uWLdGvXz9w3NcA3kwnFyriJEhlQfikUin69OmDefPmoWrVqsXWb1ng48ePmDNnDipWrIhVq1Zh9OjRiIiIwPTp04skq87x48fh5eWF+vXr49q1a6hcOetWQDweD9u3b1duZjxv3jyN21BaYcLHYODr7gt//vknxo8fn6+ALVmyBHFxccovimbNmoHH4+Hy5ctFaqNQKMw38Pi/FLfw/fHHH3B0dMSQIUOKrc/SDBEhODgYffv2RY0aNRAdHY3Tp0/j6tWr6NatW5GMiNPT0zF8+HCMHj0aBw4cwJ9//plrP/r6+jh79iwmTpyY7+bB3xNM+BiM/2fgwIFISEjA0aNH8yynra2N/fv3Y82aNTh9+nSxhTbo6+sjLS1NrTrFKXxXrlzB9u3bsWHDhgJvofO9QEQ4ceIEfH190adPH3h5eeHNmzdYt25dkU4nhoSEoE6dOkhKSkJISAgaNWqUb50qVargr7/+KjKbSiUlu8TIYJQuzpw5Q1WqVCGJRJJv2evXr5OVlRW9evWKUlJSyMzMjCIjI4vMtoMHD1Lnzp3VqnP27Flq2bJlEVn0PxISEsjBwYFOnTpV5H2VZmQyGe3atYtq1apFHh4etHfvXpLL5UXer0KhoL///pssLCxox44dRd5fWYeN+BiMb2jTpg2cnZ2xdu3afMv6+vpixowZ8Pf3B4/HQ79+/VSqV1CMjIyQnJysVp3iGPEREYYNG4ZOnTqhXbt2RdpXaUUikWDDhg2oXr06Vq1ahb/++guPHj1Cjx49cg0W1xTv379HmzZtcOjQIdy9exd9+vQp0v6+B5jwMRj/4e+//0ZgYCC+fPmSb9nhw4ejdu3aGDJkCIYPH45NmzYhIyOjSOwqrcK3c+dOPH78GAsXLizSfkojqampWLJkCSpXroxDhw5hy5YtuHHjBvz8/IpluvfIkSPw8vJC48aNcfXqVVSqVKnI+/weYMLHYPwHNzc3dOrUCYGBgfmW5fF4WLt2LcLDw3HixAnUqVMHe/fuLRK7SqPwRUZGYuzYsdi5c2e2gOjvmYSEBMyePRvOzs64ffs2jh07htOnT6Nx48bF0n9cXBz69u2L8ePH4/Dhw5gxYwaEQrbLnKow4WMwcmD27Nn4559/8ObNm3zLikQiHDp0CAsWLECzZs2wYsWKIgltKG3Cp1AoEBAQgEmTJsHT07NI+ihtfPjwARMnTkSVKlUQGRmJ69evY9++ffDy8iqW/okIe/fuhbu7O6ytrREaGooGDRoUS9/fE0z4GIwcsLGxwW+//YbJkyerVL5ixYrYsmULVq9ejcTERNy8eVPjNpU24Zs/fz60tLQwbty4Imm/NPHmzRsMGzYMrq6ukEqlePToETZv3pxt37uiJCYmBp07d8acOXNw5MgRLFq0CPr6+sXW//cEEz4GIxfGjRuH27dv49atWyqVb9euHVq2bAk7O7sicQ/X19eHWCxWK5avqITv/v37WLZsGbZu3VqiWx4VNWFhYejbty/q1q0LMzMzhIeHY9myZXB0dCw2G4gIGzZsgKenJ7y8vPDw4UPUr1+/2Pr/HmGTwgxGLujp6SEwMBDjx4/HrVu3VHJWWLRoEdzc3JCeno6QkBCNTgHyeDwYGhoiNTUVJiYmKtUpCuFTKBQYOnQoFi9erLEEyqWN0NBQzJgxA8HBwfjtt9+watWqEtlh4tWrVxg6dCjS0tJw+fJluLm5FbsN3yPf76Mag6EB+vbtC6lUin379qlU3tjYGBs3bgQRYfbs2Rq3x9DQUK3pzqSkJI1/Ya9fvx6Ghobfpdv8mzdvEBAQgNatW6Np06Z48+YNJk+eXOyiJ5fLsWjRIvj4+KBjx464desWEz0NwoSPwcgDPp+PRYsWYfLkyRCLxSrVadOmDX788UecPn0az58/16g96q7zxcfHw8zMTGP9x8XFYebMmVi5cuV3lZ3l48ePGDlyJOrWrQsXFxe8fPkSY8eOzXe38qLg8ePHaNiwIU6dOoU7d+5g7NixRR4LWN5gwsdg5EOzZs3g4eGhVpza8uXLoaOjg9GjR2vUFnWFLyEhAebm5hrrf+rUqejduzfc3d011mZJkpiYiGnTpsHV1RXa2toIDw/HzJkzYWhoWOy2SCQSzJw5Ey1atMAvv/yCCxcuZEsszdAMbI2PwVCBlStXwsvLC507d1Yp16KRkRE2bdqEHj16ICwsTGPTVCU54rt37x6OHz+OZ8+eaaS9kiQjIwMrV65EUFAQOnTogEePHhWrw8p/CQ4OxqBBg1ClShWEhISgQoUKJWZLeYCN+BgMFbC3t8eCBQvQv39/yGQylep07doVbm5u6Nmzp8bsKKkRH8dxGDFiBObPn6+yY01pRC6XY8OGDahSpQpu376NK1euYPPmzSUmemlpaRg7diz8/f0xc+ZMHD58mIleMcCEj8FQkf79+8PW1latUIUDBw4gPDxcY9lcjI2NVUqllommRnybN2+GUChEQEBAodsqCTiOw759+1CzZk3s3r0bBw8exKFDh1CzZs0Ss+nMmTNwd3dHfHw8wsLC0KNHj+9q3bRUU6IpshmMMkZ0dDRZWlpSSEiIynU6duxIRkZGlJiYWOj+p06dSn/++afK5fX09CglJaVQfcbHx5OVlRU9fPiwUO2UBBzH0ZkzZ8jLy4u8vb3p3LlzxHFcidr08uVL6tixI7m4uNDp06dL1JbyChvxMRhqYGdnh4ULF6o15bl8+XJIJBKMGjWq0P3b2triw4cPKpUVi8WQyWSFzu7xxx9/oGvXrqhdu3ah2ilugoOD0bx5c4wePRpTpkzBvXv30KpVqxIbVaWlpWHatGnw8fFBo0aNEBYWhrZt25aILeUdJnwMhpr8/PPPqFChgnIH9vyoWLEi/P39cfz4cZw5c6ZQfasjfJnre4X5on/06BEOHjyIuXPnFriN4ubly5fw9/dH9+7d0adPHzx58gTdunUrMcEjIuzZswfVq1dHVFQUQkNDMWnSpGLbIJiRAyU95GQwyiKZU56PHj1SqfzTp0/JxMSE7O3tCzXlefPmTapfv75KZUNDQ6lmzZoF7kuhUFCDBg1ow4YNBW6jOElOTqZJkyaRubk5zZ8/n9LT00vaJAoJCaEmTZqQp6cnXb9+vaTNYfw/bMTHYBSAb6c8pVJpvuVr1KiB5s2bw9HREePHjy9wvwUZ8RWU7du3Qy6XY+DAgQVuozggIuzcuRM1atTA+/fv8fjxY0yaNKlEt0lKSEjAiBEj0Lp1a/z000+4f/8+fH19S8weRlaY8DEYBeTnn3+Gvb29ylOeU6ZMQWRkJC5cuFDgKU9bW1t8/PhRpW2PCuPRmZSUhMmTJ2PVqlWlOgn1o0eP0LhxYyxevBj79u3Dtm3bYGtrW2L2KBQKrF27FjVq1AAAPHv2DL/++ivLvFLKYAHsDEYB4fF4WLduHWrXro3OnTvnm5C6Tp06cHNzg7u7O4YOHYrHjx+rnQNSV1cXenp6Ko3mCjPimzlzJjp06IC6desWqH5REx8fj+nTp+Pw4cOYM2cOBg4cWOLicuPGDYwaNQqGhoY4d+4cPDw8StQeRu6U3kc5BqMMYGdnh6CgIPz8888qTXlOnToVR48ehZ+fX4H3sbOxsVFpurOgI77Hjx9j165dRbK1UmGRy+VYvXo1atSoAS0tLTx79gxDhgwpUdGLiYlB37598dNPP2HSpEm4evUqE71SDhM+BqOQ9OvXDw4ODggMDMy3bJMmTWBlZQUfHx9cunSpQFOemdOd+VGQER8RYeTIkZg1axYsLCzUtq0ouXbtGry9vbF//35cvHgRy5cvh6mpaYnZI5FIsGDBAnh4eMDJyQnPnj1Dr169WBB6GYAJH4NRSHg8HtavX481a9bg0aNH+ZadNm0alixZgtWrV2P06NEqjRS/RVUHl4KM+Pbs2YOUlBT88ssvatUrSqKjo/HTTz+hb9++mDZtGi5dulSiSbKJCAcPHoS7uztu3LiB4OBgBAYGwsDAoMRsYqgHEz4GQwNUqFABf//9t0penu3atYNAIEBGRgacnZ2xdu1atfpSVfjUHfHJ5XJMnz4dS5YsKfH1MuBrAP68efPg6ekJFxcXPHv2rMTTel24cAH16tVDYGAgVqxYgePHj8PFxaXE7GEUDCZ8DIaGCAgIgKOjY77B3jweD4GBgZg2bRrmz5+PwMBAtfJvqjPiU0f4du3aBUdHRzRt2lTlOkUBEeH48eNwc3PD3bt3cffuXcyZM6fQGWgKw71799CyZUsMHz4cEyZMwP3799GmTZsSs4dROJjwMRgaItPLc+3atXj48GGeZdu2bQtra2s8fPgQnTt3Vml9MBN1RnyqTnXK5XLMnTsXM2bMUNmOoiAqKgodOnTAxIkTsWrVKhw5cgTOzs4lZk94eDi6desGf39/9OjRA0+ePEHPnj1LdYgHI3/YX4/B0CAVKlTAokWLMGDAgDynPHk8Hv766y/MmjULU6dOxT///IPXr1+r1Ieqzi3qjPj27t0La2trNGvWTKXymobjOKxcuRLe3t5o1KgRQkNDS3RE9e7dOwwaNAiNGzdGvXr18OLFCwwdOhRaWlolZhNDc/BIlUhYBoOhMkSEzp07w8XFBYsWLcqzbOfOndG4cWOIxWKEhIRg//79+bb/8uVLtG3bNk+hJCKIRCJ8+fIl3wwmCoUCbm5uWLFiBVq2bJlv/5omPDwcgwcPBgBs3LgR1atXL3YbMomLi8Nff/2Ff/75B7/++ismTpxYpvcfZORCiSVLYzC+Y+Lj46lSpUq0e/fuPMuFhYWRpaUlvX//nhwcHOjGjRv5ti2RSEhHR4ekUmmuZVJTU0kkEqlk6+7du6lBgwbFvl2PVCqlwMBAMjc3p5UrV5JCoSjW/r8lOTmZ/vzzTzI3N6fhw4fT+/fvS8wWRtHDhI/BKCJCQkLIwsKCQkND8yzXv39/mj59Om3bto3q16+vkgBVqlSJXr58mev1t2/fkp2dXb7tKBQKqlmzZrHvC/fgwQPy8PCgtm3bUmRkZLH2/S1isZiWLVtG1tbW1KdPH3r16lWJ2cIoPtgaH4NRRHh4eGDp0qXw9/dHYmJiruVmzZqF1atXo0WLFpDL5Srt1u7i4oJXr17lel3V9b1Dhw7BwMCg2NbTMjIyMHnyZLRr1w7jx4/HqVOn4OTkVCx9f4tCocC2bdtQrVo1nDt3DmfPnsWOHTtQuXLlYreFUfww4WMwipA+ffqgQ4cO6NOnDziOy7GMk5MT+vXrh3nz5mHRokWYMmUKxGJxnu3mJ3yqeHRyHIfZs2djxowZxRIbd+3aNXh4eCAiIgKhoaEICAgo9pg8hUKB/fv3w8PDA+vXr8eOHTtw4sQJlmKsnMGEj8EoYoKCgpCamorZs2fnWmbq1KnYs2cPHBwc4OHhgeXLl+fZZuXKlQs94jt69Ci0tbXh5+eX9w0UkuTkZAwfPhy9e/fGwoULlR6kxYlUKsXmzZtRs2ZNLFmyBAsXLsT169fZVkHlFCZ8DEYRo6WlhX379mHTpk04fvx4jmUsLS0xevRozJgxAwsXLsTChQsRGxuba5uFHfERUbGM9k6dOgU3NzfIZDKEhYWhc+fORdZXTqSlpWHZsmVwcXHB3r17sX79ety8eRN+fn4sp2Y5hgkfg1EMWFtbY//+/Rg0aBBevnyZY5mxY8fiwoULyMjIQO/evfHnn3/m2l5h1/iOHz8OIkLHjh1Vvwk1iIuLQ9++fTFq1Chs2bIFGzZsKNawgMTERAQGBsLZ2RnXrl3DoUOHcPbsWTRt2pQJHoMJH4NRXPj4+GDOnDno3LkzUlNTs103NDTE1KlTMXXqVMyYMQN79+5FeHh4jm05OzsjKioKCoUiy3mZTIbk5GTEx8fnunNBUY72iAh79uyBm5sbrK2tERoaihYtWmi0j7z49OkTJk+ejMqVK+Ply5e4cuUKDh48iDp16hSbDYzSDwtgZzCKESLCkCFDkJycjL1792YTHolEgurVq2Pr1q24e/curl27hmPHjimvS6VSaGtrA/hflpgPHz4gODgYDx48QFRUFKpXrw47OztcvnwZvXr1wpgxY+Dt7a1s49SpU5g8eTJCQkI0mnrry5cv+OWXX/DkyRNs3rwZ9evX11jb+REVFYWgoCDs2rULvXv3xoQJE1CxYsVi659RxijBUAoGo1ySkZFBdevWpYULF+Z4fdu2bdSwYUPKyMigSpUq0fnz5ykkJIR69uxJQqGQatWqRaampsTj8UhfX590dHQIAAEgHo9HQ4cOJS8vL9LR0SE+n096enpUpUoVWr16NSUmJlK9evVo3759Gr2nK1eukIODA40ePZrS09M12nZePH36lPr160dmZmY0efJk+vjxY7H1zSi7MOFjMEqAt2/fko2NDV24cCHbNblcTm5ubnT06FHau3cvaWtrK4Utv8PIyIjOnDlDTk5OWQQRAOnr65O2tjYZGRlRcHCwRjK1SKVSmjJlCtna2tKpU6cK3Z6q3Lt3j7p06UJWVlYUGBhIX758Kba+GWUfJnwMRglx6dIlsrGxyTFzyZYtW0hHR4fq1atHPB5PZeHT0dGh9PR00tXVzbVe5kixcuXKtHLlSkpMTCyQ/S9evKA6deqQn58fffr0qbBvR75wHEeXLl2iVq1akYODAy1btozS0tKKvF/G9wcTPgajBFm0aBF5eXllmR4MCQkhPT09lcXu26Np06YUHx9PxsbGpKurm295fX190tXVpYkTJ6psM8dxtHHjRrKwsKCVK1cWeY7P1NRUWrduHbm7u1P16tVp8+bNJJFIirRPxvcN8+pkMEqQsWPHomrVqhg+fDg4jsOCBQtQu3ZtpKenq92Wnp4eevbsiejoaNjZ2akUPpCWlgYejwdtbW3UqFED79+/z7N8QkICunfvjuXLl+PKlSsYMWJEkYUHvH79GuPHj4eTkxNOnTqFxYsX4+nTpxgwYIDSwYfBKAhM+BiMEoTH42Hjxo24ceMGKlSogMmTJ4MK6GjNcRzat2+PmJgY2NnZqZSrUyQSYfPmzXj16hVevHgBPz+/XPcRvHTpEjw8PODo6Ig7d+7A1dW1QHbmBcdxOHPmDDp06AAfHx8IhULcv38fR44cQcuWLVkMHkMjCEvaAAajvKOtrY2oqCjIZDKVyvP5/BzzflpbW8PR0RHnzp2DnZ0d5HI5njx5kms7BgYGOH78OJydnTFgwABwHIcXL15g1KhRWLdunbKcVCrFH3/8gR07dmDz5s1FktA6KSkJW7ZswapVq2BoaIhRo0Zh//79+e4lyGAUBCZ8DEYJc+DAAbXi6czMzJCWloaMjAzlOT6fD39/fwBQjvjkcnmO9QUCAUxMTHDlyhW4ublh6NChykD4jIwM7NixA02aNEGfPn3w/Plz9O7dG3Z2dggJCYGlpWUh7jQ7YWFhWLVqFfbs2YN27dph69ataNCgARvZMYoUNtXJYJQgq1evxqBBgyCRSFSuw+Px4OzsnEUsDQwMlHkwM4XP3t4+W11tbW04ODjg0aNHcHNzw+fPn7Fjx44so8309HQMHToUs2bNgq+vLwYPHoyjR49qTPTkcjkOHTqE5s2bo3Xr1rCxscHTp0+xa9cuNGzYkIkeo8hhIz4GowQgIsyZMwfz58/PMnJThYSEBNy6dQu1a9dWpj6TyWRo2LAhgK/C16FDB8hkMujo6ChFVSQSoWbNmrhw4YLS8WXhwoU5Tpump6dj3rx5uHHjBurVq1eIO/0fsbGx2LhxI9asWQNHR0eMHDkSXbp0YY4qjGKHjfgYjBJgw4YNmDlzptqiB3wVzTt37mD79u3Q1dUFADRr1gxaWloA/jfis7KygkAgAPDV47N58+a4ceOGUvSSkpKwZs2aXEebfD4f06dPz3UfQVXgOA5Xr15Fv379ULVqVbx69QpHjhzBjRs30KtXLyZ6jBKBCR+DUQJ07NgRv//+O8zNzWFoaKhWXY7jEBgYiB9//BH9+/cHAOX6HvA/4bO0tIREIoGWlhYCAgJw7NgxpVACwPLly/P0IJVIJLh16xYCAwPVuzkAb968waxZs1C5cmWMHDkSHh4eePXqFTZt2gQvLy+122MwNErJhhEyGOUbhUJBFy5cIH9/f9LV1SV9ff0cA821tbXJ0NCQ+Hw+8Xg8ql27Nh04cIAkEgl5eHjQ64hIiohNpdCoONK1dCCJVEZ3794lADRjxoxsQeZpaWlkZGSkUlC8SCSi8+fP53svycnJtHnzZmrSpAlZWFjQqFGj6MGDB0Ue4M5gqAvbnYHBKCUkJydj//79WLFiBZ4/fw6O45QxdVpaWvjzzz9x69YtnDhxAsuWLcPmnXvx68JtOPAwGlHxadAS8MHnAWKJFDyBEE5menA3SMPMvq1gopd1SnHp0qWYNm2ayoHyBgYGeP36NaysrLKc5zgOV65cwT///INjx46hadOm6N+/P9q3b8+mMRmlFiZ8DEYpJHNacOPGjcjIyEBaWhqqVauG8PBwnDl3Hv8q7LDh2hsItQQQy3Jfg9PV4oMIGOxbCWNaVIW2kA+pVIoKFSogPj4+13oGBgYAvjrNVK1aFb6+vggMDFTu8ffq1Sts3boV27Ztg6mpKfr374/evXtnE0YGozTChI/BKMVkOofMnTsXd+7cwfPoWPTZGIxPyWJk5CF4/0WkxYe1kS52DvbBkZ2bMWbMGGXsnr6+Png8HqRSKapUqQJfX180bNgQderUQbVq1ZQOMsnJydi3bx+2bt2K58+fo0+fPvj555/h6elZFLfOYBQZTPgYjDJCTGIGOq68gaR0GRT//29LREgLPY+Uf89CFvcW4DgIzexgUKslDL3ag8cXKOsLeDwY62khYu2vSHofgapVq6Jx48Zo1KgR6tSpg+rVq0MozBrhpFAocOnSJWzduhUnTpxA8+bN0b9/f7Rr107pRcpglDWY8DEYZQCpnEPrpVfxLiFDKXoAEHd8EdKeXAZfzwR6LvXA09KBOOpfyOLeQq9aQ1h0npIlIFzA46GCsTbOjmkMPV2dHPsiIjx8+BD79u3Drl27YGVlhf79++Onn36ChYVFkd8rg1HUsAB2BqMMsOziC3xKFmcRvfQXt5H25DKExtaw+XkxBHrGAABSyBF7ZD7Sn99C2uOLMKjVUllHQYS4NDlWX4vEhNbVlOeJCKGhodi7dy/27dsHAOjRowdOnToFd3f3YrpLBqN4YMLHYJRyvqRJsfFGBCTyrGt66c9vAQCM6vkrRQ8AeAIhTJr0RcbLYKQ8OJ5F+AAgQ6bAhutvMNi3EqLfvMC+ffuwd+9eSKVS9OjRA3v37oWXlxdLHcb4bmHCx2CUcvbef4ecNEiRlggAEJrYZLuWeU766TU4cSr4ugZZ6yrkqNtrDMSPTqBHjx7Yvn076taty8SOUS5gwsdglHIOPIzOMWSBr2cEAJAnfcp2TZ74UflaFh8NHbvqWa8TH3b1f8T1I6vU2hmCwfgeYJ94BqMUI1dwiIpPy/GaXuW6AIDku0egyEhRnidOgaTru5S/c+LUHOt/ziBwzLWNUQ5hIz4GoxQT/SUDWgI+ZP8fc/ctejWbQPfJZYjfPMD7jcOg51L/q1dnZAjkiR8hNK0A+Zf3QC4jOi0BH9FfMlDRQr+ob4PBKFWwER+DUYqRyDnwc1l34/H4sOo2A6Y/DIRA3xRpTy4jNfQ8BIYWsO67EHzR1+TXAj2THOvzebxsDjMMRnmAjfgYjFKMjpAPLo9QWx5fAKP6XWBUv0uW85xMAtnnCPCEOtCycMyxLkcEHSF79mWUP9innsEoxdibiiBTqD8qS3tyGSSXQq+6L3iCnJ9vZQoO9qaiwprIYJQ5mPAxGKUYoYAPJ/Pc1+A4SfbdFSQfXiDxyj/gaYtg7PtTrnUrmutDKGBfAYzyB5vqZDBKOd287LH04oscQxo+7ZkOnlAb2pZO4GmLIIt7i4zX98ETasHSfyq0cojxA77u2tDd276oTWcwSiUsVyeDUcpJTJei/l8Xc3RESbpzEOlPr0GW+BEkl0BgYA5Rpdow9ukOoYl1rm3qCPm4M6VFtn36GIzyABM+BqMMEHQ2HJtvRqi1FVFuiLQEGORbKUuuTgajPMEm+BmMMsCYFlVhbaQLQSFTigl4PNgY6WBMiyoasozBKHsw4WMwygDaQj52DvaBsZ5WgcUvcz++HYN9oMWcWhjlGDbVyWCUIWISMwq4A7sANkY62DHYB3YmLISBUb5hwsdglDGkcg7LLr7AxhsR4PGQo7dnJiItPjgChjR2xpgWVdhIj8EAEz4Go8ySmC7F3vvvcOBBNCLj06Al4IPP44EjgkzBoaK5Prp726NHHQfmvclgfAMTPgbjO0Cu4BD9JQMSOQcdIR/2piIWnM5g5AITPgaDwWCUK9gjIYPBYDDKFUz4GAwGg1GuYMLHYDAYjHIFEz4Gg8FglCuY8DEYDAajXMGEj8FgMBjlCiZ8DAaDwShXMOFjMBgMRrmCCR+DwWAwyhVM+BgMBoNRrmDCx2AwGIxyBRM+BoPBYJQrmPAxGAwGo1zBhI/BYDAY5QomfAwGg8EoVzDhYzAYDEa5ggkfg8FgMMoVTPgYDAaDUa5gwsdgMBiMcgUTPgaDwWCUK5jwMRgMBqNcwYSPwWAwGOUKJnwMBoPBKFcw4WMwGAxGuYIJH4PBYDDKFUz4GAwGg1GuYMLHYDAYjHIFEz4Gg8FglCuY8DEYDAajXMGEj8FgMBjlCiZ8DAaDwShX/B87ibS5fIcQggAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10\n", "R = np.zeros((N,N))\n", "for i in range(N):\n", " for j in range(N):\n", " if(random.random() > 0.5 and i != j):\n", " R[i,j] = 1\n", " \n", "big_graph_positions = lag.DrawGraph(R)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[4. 6. 2. 2. 7. 6. 2. 1. 1. 1.]\n", " [6. 4. 2. 2. 8. 7. 4. 1. 1. 1.]\n", " [2. 2. 0. 6. 2. 5. 1. 5. 1. 0.]\n", " [2. 2. 6. 0. 6. 2. 1. 0. 0. 5.]\n", " [7. 8. 2. 6. 2. 3. 1. 2. 4. 0.]\n", " [6. 7. 5. 2. 3. 2. 1. 0. 2. 2.]\n", " [2. 4. 1. 1. 1. 1. 0. 0. 1. 0.]\n", " [1. 1. 5. 0. 2. 0. 0. 0. 0. 4.]\n", " [1. 1. 1. 0. 4. 2. 1. 0. 0. 1.]\n", " [1. 1. 0. 5. 0. 2. 0. 4. 1. 0.]]\n" ] }, { "data": { "image/png": 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nz9KtWzdCQ0MN2g7sRWR6R1FRUZiYmOR4/tq1a7Rs2ZI9e/bg6en5Stc4d+4cgwcPxt3dnQULFhTq/YHoSf/555/8/PPPtG7dmmnTplG3bt1CtUFCQqLgkDy+YohSqWT48OH88ssvhS4KNWrUwMXFJc9Eltq1a/PHH3/Qv39/nj59+krX8PT0JDg4mGrVqtGgQQO2b9/+Oia/NNbW1kyaNImwsDDeeust2rZty8CBA7l8+XKh2iEhIVEwSMJXDPnll1+oUKECb7/9tlGu7+/vz9q1a/N8fsCAAXTr1o2hQ4e+cosyCwsLfv75Z/7991/Gjx/PBx98QEJCwqua/ErY2NhoBdDLy4u2bdvi7+/PlStXCtUOCQkJwyIJXzHj5s2b/PLLLyxcuPClppwbkoEDB7Jt2zZSU1PzPOenn34iJiaG2bNnv9a1fH19uXjxIgqFgvr167/2nL9XwcbGhs8//5ywsDAaNWpEmzZtGDRokCSAEhLFFEn4ihEajYYRI0YwZcqUXOfgFRbOzs40bNiQ3bt353mOmZkZ69evZ+7cuRw6dOi1rmdra8vixYv5448/eOedd/j0009JSUl5rTVfBRsbG7744gvCwsJo2LChVgCvXr1a6LZISEi8OpLwFSOWLVtGSkoKH330kbFNYdCgQc8Nd4LYn3PFihW88847REVFvfY1u3btSkhICFFRUXh6ehptAkOmAN66dYsGDRrQqlUr3n77bcLDw41ij4SExEti3DJCifwSFRUllClTpsgUWcfExAh2dnZCQkLCC8/95ptvhBYtWgjp6ekGu/7atWuFMmXKCNOnTzfouq9CQkKC8O233wqlS5cWJkyY8EpF/BISEoWH5PEVE8aNG8eoUaPw8PAwtikAlC5dmpYtW7Jt27YXnjt58mRsbW356quvDHZ9f39/Lly4wKlTp/D29jbqfputrS1Tpkzh0qVLJCQkULt2bX7//XeUSqXRbJKQkMgbSfiKAVu3buXSpUtMnjzZ2Kbo4e/vn2cxuy5yuZyVK1eyceNGNm/ebLDrOzs7899//zFixAh8fX2ZM2eOwQfdvgzly5dn8eLF7N+/n127dlGvXj22bdtWaIX4EhIS+UMqYC/ipKSk4O7uzj///EPr1q2NbY4ez549o1KlSoSHh+drusKZM2fo2rUrx44do1atWga1JSwsjKFDh2JiYsI///xDtWrVDLr+qxAQEMDEiRMpU6YMv/zyyysX9EtISBgWyeMr4vz88880adKkyIkeiCG+Tp06sWnTpnyd37hxY2bOnEm/fv1ITk42qC01atTg8OHDdO3alcaNG7Nw4UKjen8AnTt35sKFCwwaNIiuXbsydOjQQutDKiEhkTeSx1eEiYiIoGHDhtouJkWRLVu2MG/evHyXLAiCwODBg1EoFPzzzz8FUot46dIlRo4ciSAILFq0qEjM3Hv27Bk//PADCxcuZOzYsXz++eeF0lhcQkIiJ5LHV4T54osvGDt2bJEVPQA/Pz8uXLjA/fv383V+5vy+kJCQlxpc+zLUq1ePoKAghg0bRvv27Zk0aRJJSUkFcq38Ymtry6xZszh//jy3b9/G1dWVpUuXolarjWqXhERJRBK+IkpQUBBBQUF88cUXxjbluVhYWNCzZ082bNiQ79dYW1uzY8cO5s6dy9atWwvELrlczsiRIwkNDeXBgwfUrVuXHTt2FMi1XoYqVaqwcuVKtm3bxooVK2jUqBH79u0ztlkSEiULI5ZSSOSBSqUSPD09hTVr1hjblHwREBAgNGnS5KVfd/r0acHJyUk4f/684Y3Kxr59+4SaNWsKvXv3FiIiIgr8evlBo9EImzdvFmrWrCn4+fkJly9fNrZJEhIlAsnjK4L8888/WFpa4u/vb2xT8kW7du24c+cOYWFhL/W6xo0b8+eff9KjRw8ePHhQQNaJtG/fntDQUDw8PGjYsCG//fYbKpWqQK/5ImQyGb179+by5ct07NiR1q1b8+GHH/Lo0SOj2iUh8aYjCV8RIz4+nilTpjB37lyjNaF+WUxMTOjXr1++avqy079/f0aOHEnPnj0LvP+mhYUFM2fOJCgoiG3bttG0aVOjtT3TxczMjPHjx3Pt2jUsLS2pU6cOv/76q9GFWULiTUXK6ixiTJw4kbi4OJYuXWpsU16KoKAgRo8e/UpTy4WMTE+lUsnatWuRywv+85ggCKxcuZLPP/+cAQMG8N1332FnZ1fg180PN27c4MMPP+Tp06csXLiQJk2aGNskCYk3CsnjK0Jcv36d5cuXM2vWLGOb8tL4+PgQHx//SsInk8lYunQpERERzJw5swCsy/2aQ4YM4fLlyyQnJ1OnTh02bNhQJLqsuLq6sn//fj777DN69uzJRx99RHx8vLHNkpB4Y5CErwjx2Wef8eWXX1KuXDljm/LSyOXyFw6ofR4WFhZs2bKFFStWsGbNGgNblzelS5dm6dKlrF27lhkzZtC1a1du375daNfPC5lMxrvvvsvly5dJT0+nTp06rF+/vkgIs4REsceYmTUSWezatUuoVauWkJaWZmxTXpng4GChevXqgkajeeU1QkJChDJlygjHjx83oGX5Iy0tTfj++++F0qVLC//73/+MPvVBl6CgIKFevXpC586dhbCwMGObIyFRrJE8viJAeno6n332Gb/++itmZmbGNueVadSoESYmJpw+ffqV1/Dw8ODvv/+mb9++3L1714DWvRgzMzO++uorTp8+zeHDh2nUqBHHjh0rVBvyonnz5pw7d47WrVvTpEkT/ve//5Genm5ssyQkiiWS8BUB5s+fT/Xq1enatauxTXktZDJZvgbUvoiuXbvy+eef0717d549e2Yg6/JP9erV+e+//5g2bRoDBgxg8ODBREREFLod2TE1NeWLL77gzJkzBAUF4enpSVBQkLHNkpAodkhZnUbm0aNH1K1bl6NHj1K7dm1jm/PaXLt2jbZt2xIREYFCoXjldQRBYPTo0dy/f5+tW7diYmJiQCvzz7Nnz5g9ezZ//vknH374IV988QW2trZGsUUXQRDYtGkT48ePp3Pnzvz444/5mpAhISEheXxGZ8qUKQwePPiNED2A2rVrU65cOY4cOfJa68hkMubPn49arWbEiBFGS+qwtbXl22+/5cKFC9y7dw9XV1cWL15s9Bo7mUxGv379uHLlClZWVtStW5cVK1ZIyS8SEvlA8viMyLlz5+jSpQvXrl3DwcHB2OYYjNmzZ3Pr1i0WL1782mslJSXRvn17WrRowU8//WQA616P4OBgJkyYQExMDL/88gudOnUytkkAnD17llGjRmFvb8+CBQtwc3MztkkSEkUX4+XVlGw0Go3QokULYfHixcY2xeDcuXNHKF26tKBSqQyyXmxsrFC3bl3hxx9/NMh6r4tGoxG2bNki1KpVS+jUqZMQGhpqbJMEQRAEpVIp/Pbbb0Lp0qWFadOmCSkpKcY2SUKiSCKFOo3EunXrSExM5P333ze2KQanatWqVKxYkVOnThlkvVKlSrFnzx4WLFjAX3/9ZZA1XweZTEavXr24dOkSfn5+tG3blpEjRxIdHW1Uu0xMTPjkk0+4cOECly5dwsPDg/379xvVJgmJoogkfEYgOTmZzz//nHnz5r1WAkhRpmvXruzcudNg61WsWJE9e/YwdepUtmzZYrB1XwczMzM++eQTrl+/jq2tLfXq1WPWrFkF3nP0RVSqVIlNmzbx66+/8sEHHzB69GgSExONapOERFFCEj4j8Ntvv9GsWTNatmxpbFMKjG7durFr1y6Drunq6srOnTsZNWoUgYGBBl37dXB0dOSXX37h1KlTnD9/Hjc3N1auXIlGozGqXd26dSMkJITU1FQaNmwolT5ISGQgJbcUMnFxcdSqVYugoKA3OgFBrVZTvnx5goODqVKlikHXDgwMZMCAAQQEBODp6WnQtQ1BUFAQEyZMQK1WM2fOHHx9fY1tElu3buXDDz9kyJAhfPPNN5ibmxvbJAkJoyF5fIXMzz//TI8ePd5o0QNQKBR07tzZ4F4fQOvWrVm8eDHdunXjxo0bBl//dWnRogUnTpxgwoQJDB48mD59+nDz5k2j2tSrVy8uXrzIzZs3eeutt7hw4YJR7ZGQMCaS8BUijx49YsGCBUybNs3YphQKBRHuzKRXr158++23dOrUifv37xfINV4HuVzOoEGDuHbtGk2aNMHb25vx48cTExNjNJvKli3Lpk2bmDRpEh07dmTWrFlGr0eUkDAGUqizEPn0009RqVT8/vvvxjalUIiLi6NKlSpER0djZWVVINeYPXs2K1as4MiRI5QqVapArmEIHj16xIwZM1i3bh2jRo1iwoQJRu20EhERwbBhw0hMTGTFihW4uroazRYJicJG8vgKicjISJYvX87kyZONbUqh4eDggKenJwcPHiywa3z++ef4+fnRtWtXkpKSCuw6r0vZsmX5888/CQ4OJjY2FldXVyZPnkxsbKxR7KlcuTJ79+7l3XffpXnz5syfP9/oyTgSEoWFJHyFxLfffsuIESMoX768sU0pVAoy3JnJ7NmzcXd3p2fPniQnJxfotV6XatWqsWjRIoKDg3n8+LFWAJ88eVLotsjlcj766COOHTvGqlWr6NSpU5Foxi0hUdBIwlcIhIWFsWnTJj7//HNjm1LodOvWjZ07dxZoD0mZTMaSJUtwdnamR48eRV78QBTAxYsXExwczKNHj6hVqxZTpkwxigC6uroSFBRE69at8fLyYuXKlVLPT4k3Gkn4CoEZM2bw8ccfl8ju+W5ubpiZmRESElKg11EoFPz9999UrFiR7t27FwvxA1EAlyxZwtmzZ3n48CG1atVi6tSphS6AJiYmTJ48mT179jB79mz69u3L48ePC9UGCYnCQhK+AubSpUvs3buX8ePHG9sUoyCTyQol3Ami+C1btozKlSvTrVu3Ir3nlx0XFxeWLFnCmTNnePDggVYAnz59Wqh2NGrUiLNnz1KrVi3q16/Ptm3bCvX6EhKFgSR8Bcy0adOYNGkSdnZ2xjbFaGSGOwsDhULBX3/9RdWqVYud+IE4BHfp0qV6Ajht2rRCFUBzc3N+/PFHNmzYwGeffcawYcOIj48vtOtLSBQ0kvAVIGfPnuXUqVOMHTvW2KYYFV9fXy5fvlxooTOFQsHSpUtxcXEpluIHWQJ4+vRp7t+/T61atZg+fXqhCmCLFi24ePEiFhYW1K9fn6NHjxbatSUkChJJ+AqQKVOmMGXKFCwtLY1tilExNzenXbt2BAQEFNo1dcWvqJc6PI/q1avz119/cfr0aSIiIrQCGBcXVyjXt7GxYcGCBSxYsID+/fvzww8/SGUPEsUeSfgKiKNHj3Ljxg0++OADY5tSJCjMcGcmcrmcpUuXUqNGDbp06VKsJxRUr16dZcuWcerUKSIiIqhZsybTp08vtE4wXbp04cyZM+zYsYPu3bsbtQONhMTrIglfASAIApMnT2b69OmYmZkZ25wiQZcuXdi7dy9KpbJQryuXy1myZAm1atUq9uIHUKNGDZYtW8bJkye1IdDRo0dz7dq1Ar925cqVCQwMpG7dunh6enL8+PECv6aEREEgCV8BsHfvXh4/fsy7775rbFOKDOXLl6dmzZocO3as0K8tl8tZvHgxbm5ub4T4AdSsWZOlS5dy7do1ypcvT6tWrejWrRsHDx4s0Bo8U1NTZs+ezR9//EHv3r35+eefpZo/iWKH1KvTwAiCQOPGjfniiy/o37+/sc0pUsycOZNnz57x888/G+X6Go2G0aNHc/XqVf777z9sbW2NYkdBkJKSwurVq5kzZw5mZmZ89tln+Pv7F2jE4e7duwwcOJCyZcvyzz//FOleqRISukgen4HZsmULGo2Gvn37GtuUIoehp7K/LHK5nIULF1K3bl06duxolC4pBYWlpSXDhw/n0qVL/PDDD6xatYpq1arx/fffF1g/0KpVq3LkyBFq1qyJp6cnJ0+eLJDrSEgYGkn4DIharWbq1Kl89913yOXSrzY7np6exMfHc+vWLaPZIJfLWbBgAb6+vrRs2ZLIyEij2VIQyOVyOnfuzN69ewkICODWrVvUrFmTMWPGFMjsQjMzM+bMmcNvv/1Gjx49+PXXX6XQp0SRR3p3NiBr167FwcEBPz8/Y5tSJJHL5XTt2rVQurg8D5lMxo8//sj7779P8+bNuXr1qlHtKSjq16/PsmXLuHr1Kk5OTrRo0YIePXoQGBhocHHq1asXp06dYs2aNfTu3bvQO85ISLwMkvAZCKVSyYwZM5g1axYymczY5hRZjFHWkBcTJkzg22+/pU2bNpw6dcrY5hQY5cuX55tvvuHOnTt069aN0aNH4+XlxapVq0hPTzfYdVxcXAgKCqJq1ap4eXlx5swZg60tIWFQBAmDsGLFCqF169bGNqPI8+zZM8HGxkZISEgwtiladu3aJZQpU0bYvXu3sU0pFNRqtbBr1y6hXbt2QsWKFYX//e9/QmxsrEGvsXHjRqFMmTLCvHnzBI1GY9C1JSReF8njMwCCIDB79my+/PJLY5tS5LGxscHHx4d9+/YZ2xQtXbp0Ydu2bQwdOpTVq1cb25wCRy6X06VLF/bv38+uXbu4evUqNWrU4KOPPuLy5csGuUbfvn05ceIE//zzD/3795d6fUoUKSThMwC7d+9GoVDQsWNHY5tSLChK4c5MvL29OXjwIF9++SVz5841tjmFRoMGDVi+fDmXL1/G0dGRjh074uPjw7Jly1673rFGjRocO3aMcuXK4enpyblz5wxktYTEa2Jsl/NNoFWrVsLq1auNbUaxISwsTChXrpygVquNbUoO7t69K7i5uQlfffVViQzRKZVKYfv27UKPHj0ER0dHYeTIkcLp06df+XehUqmEe/fuCf/++6/g5OQk/PHHHyXy9ypRtJA8vtfk1KlT3LlzhwEDBhjblGJD9erVKVWqFMHBwcY2JQdVqlQhKCiIAwcOMGLECFQqlbFNKlRMTEzo3r0727Zt49KlS1StWpWBAwfSqFEj5s+f/9LZmitXrqRmzZqUL1+e48ePs2jRIoYNG0ZqamoB3YGExIuRhO81+fHHH5kwYQImJibGNqVYUVjDaV8FJycnDhw4QEREBP369SMlJcXYJhkFZ2dnvv76a27dusUvv/zCsWPHcHFxYfDgwRw+fDhfJRFLly4lPT2dLl26EB0dzfHjx0lJScHX1/eNq6GUKD5IwvcaXL9+naCgIN5//31jm1LsMHYXlxdhY2PDjh07sLKyolOnTiW6Lk0ul9OuXTvWrl1LWFgYXl5ejBkzBjc3N2bPns3Dhw9zfV1sbCxnz54FIDk5GT8/Py5evMi///5L3759adKkiVF6t0pISML3Gvz888+MHTsWa2trY5tS7PD29ub69etFOtvPzMyMVatW0bhxY5o1a1YgnU+KG6VLl2b8+PFcunSJ5cuXc/36dWrXrk2fPn3YvXs3arVae+6mTZtQKBTan5OSkujYsSOnTp3iiy++4K+//qJ3794sWrQo7wuGhsKYMeDuDubmIJOJX93dxeOhoQV5uxJvKsbeZCyuREVFCY6OjsLjx4+NbUqxpW3btsLOnTuNbUa+WLJkiVC2bFlh3759xjalyBEfHy8sWrRIaNy4sVC5cmVh+vTpwp07d4TGjRsLQI6HjY2NcPr0aUEQBOHGjRuCu7u7MHLkSCEtLS1r0bAwQfDxEQQrK0GjUAgC5HhoFApBsLISzwsLM9LdSxRHJI/vFZk7dy7vvvsuTk5Oxjal2NKqVSsOHz5sbDPyxfDhw1m3bh3vvvsuCxYseO65Fy9e5MCBA4VkmfGxs7Nj5MiRnD59mh07dhAbG0vDhg21Yc7sJCYm0rZtW4KDg6lVqxYnT54kOjqatm3bEh0dDevXg4cHmlOnIDkZmY4XCbASkAFytZqlycnieR4e4uskJPKDsZW3OBIXFyeUKlVKuH37trFNKdYEBgYKTZo0MbYZL8WtW7cEd3d3YezYsYJSqczx/KNHj4RSpUoJpUqVElJTU41gYdHgl19+EczMzHL1+DIftra2wrlz5wRBELvJTJ8+XRhVqpSgMjfP1cMTQLgHgj0INhlrLNF93tJSENatM/KdSxQHJI/vFVi0aBGdO3emWrVqxjalWNO0aVMuX77Ms2fPjG1KvqlRowYnTpwgLCyMLl266CW9qNVqevXqxbNnz0hLS+Ovv/4yoqXGZcWKFS/sA/rs2TNat27NxYsXkcvlzBgyhPlJSSjS0nI9XwCGAaWB0bmdkJICw4bB7duvab3Em44kfC9JWloac+fO5fPPPze2KcUeCwsLPD09OX78uLFNeSns7e3ZsWMHdevWpVmzZty8eROAadOmceHCBZRKJUlJSUyfPt2gTaCLC5GRkVy7dg0AE8AaKAVUAKoCLkB1oCZQLiGB9318uLFtG/Tvj1yZd93kPOAg8HfGmrmhSUuDd9811K1IvKFIxWcvyapVq6hfvz4NGjQwtilvBK1ateLIkSN06tTJ2Ka8FCYmJvz666/UqVOHFi1aMGHCBH799Ve9mr+UlBSWL1/OiBEjjGipgRAESE6GuDiIjxe/JiZCWlqOx82AACaq1cjJ5yfr5GQO9upFLRMT5Bp1rqdcBb4EPgF8EQUwN+RqNZw/L2Z7eni89G1KlAwk4XsJNBoNP/300wuTGyTyT6tWrZgxY4axzXhlRowYgYODAwMHDsxR0J2UlMTUqVMZNmxYoTc40Gg0LzcMWRBEIYuL0xc33e+VynwtdeX4cUyydbwxNTFBoVCg0WhQqVRYWlpib29PmTJlcHJyotaNG3D/fq7rqYDBQBXg+/zcSno6soUL4Y8/8mWvRMlDEr6XYPv27djZ2dG6dWtjm/LG4O3tzYULF0hOTsbKysrY5rw0SqWS77//HrlcrlfDlkliYiKrV69m6NChhWbTjcuX+cTXl+/GjMGreXNwcwMXF/2Tnj0ThSYqKuuRnPza105PTycmJgaFXI6trS2Ojo6ULVsWJycnSpUqhaOjI/b29nr1fQCEhIjimwvfAOeBIMAyHzbI1Go4dOg170TiTUYmZP+YKpErgiDg4+PDxIkT6du3r7HNeaPw8fHhu+++o23btsY25aX5+OOP+euvv0h+jmhUrFiRu3fv5nyzLwCuHj7Mcj8/LFNSqFOnDv379xc9tZo1oUYNUeDu3xeFz4BoNBpSUlJISUkhISEBpVJJamoqycnJ2uMpKSmkpqai0WhyPD548IDcfjunAR/gM2C2zvEZwExgCTA8N4PMzMTQq4RELkgeXz4JCgoiNjaWXr16GduUN47Mer7iJnxbtmx5oegBxMfHs27dOt5+++0CtSd071429OiBdVoaDoBw/TqaEyeQp6XBsWNQvz6UKvXS62o0GuLj44mNjSUmJobY2FiePn2qJ2rp6emYm5tjZWWFkJKCo6kp1tbWmDs4YO3kRJkyZbC0tMTc3ByFQoFcLtc+FAoFiiVLclw3M8TpCnz7skbnMywrUTKRPL580q1bN3r06MHIkSONbcobR0BAAD/88AOBgYHGNiXfhIeH06BBg3zPrKtSpQq3b9/Oue8WGgoLFoihufBwSE8XvZXq1aFNG/jww3wlaZzfsoUzAwZQRqXCHjGpRCGX4+HhgYODg3iSoyPkkZQlCAJJSUnExsbmeDx9+hRra2tKly6tfZQqVQorKyusrKywtLTEwsICGSDcuMGxjRtRqVQo5HIUgKlGg6mJCSZWVmjKl0fm5oZThQqULl0aMzMz0YDvvoNsoeI4wDFfv10x6eU33QOSxyfxHCThyweXLl2iQ4cO3L59GwsLC2Ob88aRkJCAs7MzMTExxeb3++mnnzJ//nysrKxITExEo9E893xra2v+/vtvMfQIosgNHgwXLiCkpeXoTgIgKBTIzM2hYUNYuVIUw1w4u2wZMSNHYpFtDWvAvkIFXF1dxQMyGfj4IJiY8PjxYyIiIoiIiODRo0fExsaiUCj0xE1X5ExNTV/8SwkLg7t3Cbt2jWePH2MJmCF2WdElRSZjj4kJCSoVFhYW2NraMujpUxyyeWkpwLg8LnUOcd+vBeAGdAAG6p7g7g5XrrzYZokSiSR8+WDo0KHUrl2br776ytimvLE0btyYOXPm0LJlS2Obki8EQeDu3bucP3+e4OBggoKCCA0NJTExEUtLS234Txet17dxIwwbhiYtDblaTSQwDQgAYhHr3XoB0xE9Ho1CgdzcHP7+G7LNfTywaxdPe/TAKZvw2iHWzj0yMcGrWTOePXtGfHw8l9RqLj1+jKWlJZUrV6Zy5cqUL1+e0qVLY2mZn9QRHTQaSEoS9wsTEuDCBUhNJSUlhUePHmlbtGgyHpnfA0QAK3SOjzAxobVGg+wFHyAymUHee3yCQoFs1Cgpq1MiTyThewEPHz6kdu3a3L59OytkJGFwJk6ciIODA1OmTDG2Ka9FTEwMFy5c4Pz58wQFBXHu3Dmio6NRKBSkpaWx67336LJundhlBAhDTN54BPQEaiMmdBxC9GSOIXYqAcDSEv75Ryt+O3bsYE6/fkzPJrAOGQ+Ap8AzmQwbGxvs7e0xr1wZBx8fbGxsXu7GNBoxDCsIYkgyNVW8B7kcTEzEPbVLl0AmQwOcPHkSBaBE3KvLjhroDaSZmeHu7s7RP/7Atn17cd18MIPnJLdYWkJm/04JiVyQkltewF9//UW/fv0k0StgWrVqxbx584q98Dk5OdG+fXvat2/PpEmTAHEWXWhoKIHLltFx+XK9vacxiKI3D/2w3mfAr8BkYGHmwcyWXI0bs/7MGd577z26ZxM9BWJoMQUwBawA+0qVqJ4ZJrW0hNxET60W7TI3B1NTUdAyRU6tBpUqaywQ5FxDpYJbtwBQpqVhbmODQ2IiCkSvLgWIQfTuMu2sYGaGQ8OGHDhwAJv0dChbFk1EBPLX+CyuUSiQN2okiZ7Ec5E8vuegVqupUaMGmzdvxtPT09jmvNHExcVRpUoVYmNj87efVBxp3hzNqVNidxEgHKgBVEP0/HTTXp4hhjwFRGHMbNGlUSh47OJC1YgI0tLSqAP8QdY+Wma3FFnGVwVgYWaGR926otcml0Pt2qJQWViIQqhQiMkgNjai9/YSaDQaHj58SEREBCYXL5IWE4NGo8HCwgKLxESsEb2+h+h7fmq5nG+8vQnYtw9Lc3NYtoynR45gs2oVpq/zlmRlJXqe2esWJSR0kDy+5xAQEEC5cuUk0SsEHBwcqFGjBmfPnsXb29vY5hiekBC4cEErepDVdqsjOVt72QLNgb3ASaBdxnG5Wo3jrVv8DDxGFLjM/by8kKWno4yJwdTaGsqXBycnsLUVPbt8IggCycnJetmeUVFR3L9/Hzs7OypXrox7tWrUrlgRS0tLNBoN54KCMAOiEUObmchlMs67ubH3wAFu377NiR9+IH7rVhISEqgtCPSRyTB5BfFLlcm4Pn489atVy5FQIyGhiyR8z2HBggWMHp1rH3iJAsDX15fDhw+/mcK3cKGYvalz6HrGV9c8XlILUfhukCV8IP6n7VOxIkdtbXn06BEHnjyhvUxGaUCTIRgCkIoYYkwDFKamVKpYERo1Auu8WjyLnVdyK2mIjY0FxFBuZrZns2bNqFSpUlbHncREyJjBp1AoMLWz40FCAnrpKnI5D5ydqeriwm/lyhGXlEQptZqkDLuvyWQEmJvTRakEjSZfYU+NQkGKWs17gsDuuXMptXIlX3zxBe+99x7Wz7lXiZKLFOrMg7t37+Ll5cW9e/eKZSut4sjmzZtZunQp//33n7FNMTzu7pAxsSCTkYjJGXl1H5mM2JvyeyBHPrGTE4wdC4jeWEJCAnE3bpAaEUFibCwJCQkIyclaz0ltZ0eD3r1Jksv1OqkkJyfr1e+lpqZSqlSpXMsaLC0tkcme40sJApw+rU3cefDgAbdu3SJNoyEZ0atNl8uxEwRtONM54/ghIBKwsrSkdu3a9GjZErZsQX3/Pmg0uXZ1UQEmlpbQqBEDlUrWnzmjfS5T8IYNG8aECROkEWISekgeXx4sXryYd999VxK9QsTX15dhw4ahUqkKvalzgRMe/tIvyfxEmpvUaGJjOXzokF7bL5VKRaogkGJpSQqQrFCQlpxMqlKJaUoKodu2aQvOdR/ly5enbt26lC5dGjs7u+eL2/OQyaBaNbhxA2xtsXdy4vKNG5RBzEx9BjhoNMgz7q00YgIOQGtgc8Z1O3XqBObmhLz1FsciI7EE3q5RA7OICDF71NQUoUYNVt65Q+t//8WlRw88f/yRrRcvaktIkpKSAHF25tKlS2nZsiVff/01rVq1evX7k3hjeMPeXQxDeno6f/31V7HqJPIm4OTkROXKlblw4QJvvfWWsc0xLLnM5bPP+Bqfx0sSsp2ni0wQkMlkmJqa6rUAyy5qVlZWmJubv9ykhpfBxAQqVABnZ6hYUfz++nU4eBCzlBSqymSYCwKxiDWJmVZYIO5japcBXASBhr17Y25uzq1bt9ixYwcBgkCwpSXW//tfVvE/4oeB0M8+I/zMGb7t0YNWrVphYWGRo3ZSqVSiVCrZt28fJ06coEyZMnz99de88847L1+3KPHGIAlfLmzdupU6depQu3ZtY5tS4sjs2/mmCF9cXBxBQUF0lssxyVac7Zbx9UYer72Z8TW3PUCZQlH4U0KsrcHBQUyQqVhRFLsyZcSsUF3KlIGGDTHZuZPKvr4EHz9OVZ2uLHLEjFU5+kkvjmZm1KpVi/v377N+3TqiVSqOAaSmcvr0aT3hAxg8eDB9+vRh5syZeHp6kvqCGsDExEQSExMZN24cX375JVFRUVkt0yRKFJLw5cKCBQv48MMPjW1GiaRVq1asWrWKCRMmGNuUV+LJkyccPXqUwMBADh8+zM2bN2natClNS5WiTEyM3rltMr7uRax1y17OcAxxDE+z3C7kmN8uli+Bra0obPb24lfd7+3txZKH/GJjA2Zm1Ktdm1rp6ZwLDob0dGwAJ8T7Ssj2kioeHjy5f5+IZcvor9HwEHHo7CZB4NixYzku0bBhQ6ytrTl27BgtW7bEw8OD4ODgF5omk8n4/vvvJdErwUjCl42rV69y7do1aQqDkfD19WXUqFGo1epCGePzusTExHDkyBEOHz5MYGAg4eHheHt707p1a37//XcaN24svsEOGoSwbh0ynVyyGoilDHsRa/F0C9inA0nAKLJq+DIRZDJkuskaMplYnyeXi+Jkbv5yD3t7sLN76Rq+FxIVBdeuYW5mhqenJxeDg7FVKrFE9PR0/d80oFSdOjxetozyGg0xiMkrZYDRwPpz5xAywrtZty1j8ODBrFy5kpYtW9KlSxcuXryISpVbrxjxfBsbG7Zv3y7N1CzhSFmd2Rg/fjw2NjZ89913xjalxOLm5sb69etpkMckAWOiVCo5ceIEAQEBBAQEEBYWho+PD61ataJ169Z4eXnlLMAPD4dffoElS3KMy8nesswdOIWY5egKHEenZVkmlpZw/Lg4Zkgmy+qmUlQQBDh6FDZvFvt3IjaDCLl4Ebtnz3AE0hHLLUAUwYe2tpilp+OUlkYy4u9Dl1S5nPo3b+KcrVF3REQEDRs25P79+xw/fpzevXuTkJDdlwQzMzPKli3LwYMHqVWrlmHvV6LYIXl8OiQnJ7Nq1ap8hUskCo7Mfb6iInwRERFaoTtw4AA1atSgc+fOzJs3j6ZNmz6/00xUFPz7r7jvVa4cmvv39WrTagBnyWpS/R/i/tfHiF5f9sJ0bUuuhg0Neo8GQ6OB3bvhzBkxRFqxIso7dwgJCcEsKYnS9vYkPXuGOmO/UwXEyGTI0tKwS09Hg9ioOzvWwO0NG3D+4gu945UrV6ZBgwbs2rULPz8/UjJKKXSRy+WULVuWkJAQHAsiRCxR7CigVK/iyb///ou3tzdVq1Y1tiklmkzhMxZpaWkcOHCASZMmUa9ePRo1asShQ4fo2bMn169fJzg4mFmzZtGiRYvni15sLKxenZXR2aePGI7MRmXgb+ABoid0F5hL7t1Y5ObmsGrV695iwaBSwcaNouhl8KxcOfZfuoQmJYVKdnY4ODhQrkIFZHI5KsSuLjaCgJCejinwBNEDtAJ0u4FqNBruXbyY62Uzw51WVlY5vDkrKyt69+6NUqnkQob3KSEhCZ8OCxculDq1FAFatWrFkSNHKMwo/O3bt/nzzz/p0aMHZcuWZfLkydjY2PDXX3/x8OFD1qxZw5AhQyhXrlz+Fnz2TJyhl1FPBnA7Lo4dCgWaV927tLQURxMVxT6UqamiIOvMwIuNjeWvZcu4JZNRzsEBB3uxMMPExAQTS0seyWSYIu71mSJ2mUkEzBH39sx1llcBt0NCcr103759OXToELGxsXTq1ElbumFpacnMmTPZsGEDK1eu5J133iEqKsrgty5R/JCEL4Pg4GAePXpE586djW1KiadSpUrY2dlxpQAHiaakpBAQEMD48eNxc3OjWbNmnDp1ikGDBhEeHs7JkyeZPn06TZs2ffkkm5QUUfTi4rSHoqOj2bhxI/X9/ZH37o1gYkL+Js+Jb/rJwNUvv8wxj69I8OyZKMh37mgPRUVF8ffff2NlZYWHnR2V69RBZmcHQFJ6OpFKJQ28vNAgTlq3lMmIRRTAcoh1ero5l0+AJJ31dbGzs6Nr166sWbOGdu3aYWJigrW1NevXr2fixInIZDI6dOjA6NGj8ff3zzP5RaLkIAlfBgsWLGDUqFHFIpOwJNCyZUuCgoIMtp4gCNy4cYO5c+fi5+dH2bJlmTVrFmXLlmXt2rU8ePCA5cuXM2jQIEqXzpFOkn+USli7Fh5lpWc8ffqU1atX06VLF1xcXEisWpXV9vbEIE4pEPJITlEBGgsLTstk1AUazppFnz59ipbXEhsLf/0FDx9qD4WHh7N69WoqVKiAg0JBy2rVkMnlULo0yqpV2RMXR8UWLbBu2pRmffvStFkzylWtikOpUihkMp4hZnlmFz6LlBTiHj/O1YwRI0awePFimjdvTtOmTTlx4gTdunXTO2fKlClYWVnx9ddfG/zXIFG8kJJbEIuMN23axLVsvRQljMdbb73FuXPnXmsNjUbDsWPH2LhxIzt27CA9PZ3OnTszfPhw1q5da/gZi4IAW7bAvXvaQ0lJSaxatQpfX1/q1q3L/fv3Wb16NXGpqQQBH/n4UC81FVVYGLKnT8X5dTIZMYLAPmBTpUpsCw8Xm0+np7Njxw727NnD5MmTmThxonFr0e7fF/cwk5O1hy5fvsx///2Hq6sr0VFRvN+gAYrMPU57e/ZHRqJwc8O5ZUsAZGlpmD97RhkzM8rIZAiCwIkTJ7AoXZrY+HjkKSnI5HJiNRrkcjkXL1ygVYcOOUxp3bo1aWlpXLlyhSNHjuRqrlwuZ9WqVXh5eeHj4yOVLJVgJI8PWLlyJZ06dcr//o1EgePp6flKwqdWqzly5Ajjxo2jUqVKjB07FicnJ7Zt20ZERARLly6lb9++BTNY+PBhvT2u9PR0Vq9eTd26dWncuDHBZ86wYtkynqWksFoQSJLLeWZlBV278rh/f5aUKwfTp7PM2Zk/gW+ArWFhepdQqVQkJycza9YsqlevTkBAgOHvIz/cuiVOg9cRvTNnzhAQEICXlxd37txhcKtWmGaKnpMTdx0cuHLjBh07dsxap3JlqFRJW5KRmJiIQqHA1dWVt5o0wdvHh+oNGlCrTh0Szcx49PRprubIZDJGjhzJ4sWLn2u2k5MT69evZ+TIkYRl+91KlBxKvMcnCAILFixgwYIFxjZFQocGDRpw+fJl0tPTX+jVqNVqgoKC2LBhA5s2baJs2bL079+fQ4cO4ebm9tzXGozLl0Gnt6tGo2H9+vWUL18e3+bNufDXX9jev4+/IBCJWMMWl9FYOvN8uVyOIAhER0cD4j6XjyCAIHAVMdyXSXJyMsnJyfTt2xdvb28WL16cNWW9oLl4EbZtE0sXEP8PHTx4kMuXL+Pr68uRI0d4398fq4yJ7Dg7o6xWje2LFtG1a1f9HpkdO8K+fZCQAI8f8/jxY8qUKaMtVDc1NaVizZr0d3Ghf69ezy3jeO+996hZsyZPnz59btlC06ZNmTZtGv369eP48eNSz84SSIn3+I4ePQqIHUMkig7W1ta4uLjkmeCiVqs5dOgQY8aMoWLFiowfPx5nZ2cOHz7MxYsXmTJlSuGJ3oMHsHWr3qH9+/cjCAKtfXwInTcPx8hIzDKaNauBrkA/QJmWpr0fhULB06dPEQSB6sBC4LuMxzpgRC6XTk5OJjAwkHr16vHFF19opxIUCIIAR46I4dwM0UtPT2f9+vXcvXuXjh07EhgYyKBBg3B8/Fg8v1o1qFWLwMOHKV++vH7/26pVxb6fajXUrYvQrBmn4uJwdHXV7yJTpQp07/7C2kUnJyf8/PxYlY9yj7Fjx1K7dm0+/vjjV/hFSBR3SrzwLVy4kFGjRkmjSoog2cOdKpWKgwcP8uGHH+Ls7MyECROoXLkyR48e5fz583z99de4uuY11rWASEwUk1l0OrKEhoZy9epVWjRoQOjChTgmJyMATxHT9TOpClg/Ef24TI8vMjKS8hoNLdFP5zcB3gY+ysUEtVpNSkoK8+bNw8XFhfv37xv4JhHvb9MmOHhQeyg+Pp5ly5Zhbm5O586d2bFjB3379sXZxETMaHV1hWrVePjoERcuXKBLly5Z65maQs+eeqHhh3FxPFIocGjeHJo3h6ZNoX17mDEDvLzyZeaoUaNYtGjRC0thZDIZixcvJigoiH/++eclfhESbwIlOtSZkJDArl27+P33341tikQueHp6cvbsWapWrcqGDRvYsmULlSpVon///hw7doyaNWsa10CVSuzKotMi68GDB+zevZtW7u7c27aNMhmeUQI5xw/JAKuM12YK3507d6hL7jP4ALohTm7fl8tzMpmMbt264eTk9Fq3lYP4ePE+HzzQHoqMjGTdunU0a9aMOnXq8Pfff+Pn50f1KlUgOBjq1QMnJwRBYPfu3bRu3Vp/GnrbtmJnFx3hu3LlCnXq1Mn6EGppCd7eOac/PIdWrVpp28r5+Pg891xbW1s2btxI69atadSoUZHpFCRR8JRo4duyZQutWrV6vfR1CYOjUqkIDAzk0KFD7N69WzuS5vjx49SoUcPY5okIAuzYAZGR2kNJSUn8+++/VCtVitQLFzDVaLBCLMx+gjiDzgKxbg0yxC1jjy8z1Hnn9m0ye49k+ixysho6mwOdEdP9M3MXLS0tKVWqFGvWrDF8yD4iQhQ9nRBqaGgou3fvpmfPnlSqVIlly5bRvHlz6tWrJ2a0urmJooaY5ZmamoqXrsfm7Cx6c/fuiR4z4j7hlStX6N27t/7169Z9KXMzk1wWLVr0QuETl6/Lb7/9Rr9+/Th79iz29rlNP5R40yjRwrd69Wo++OADY5shgfjGFxQUxMqVK9m6dSvVqlWje/fu7N+/n5MnTxa9iezHj4tJHhmo1Wo2btxI3bp1kV+7hkwQcACUwGPEYbIOiBMXdEnJ6DKi0WiQyWQkx8VpvT0BURzLI7b2yhQ/R8SRRo+Aa0CfPn1YsmSJ4ZM0zp+HnTvFPTjEf6PAwEAuXrzI0KFDcXR0ZPny5dSpU4emTZuKr3FyAisrQNz/27t3L/369csahCuTQdeuYuu2y5e1l3r8+DFKpRJnZ+es65cqBa+QaT106NB8Jblk8s4773Ds2DHef/99Nm7cKG17lABK7B5fdHQ0Z86coXv37sY2pURz//59/ve//+Hq6sro0aOpVasWp0+f5vTp00ydOpVKlSpx/fp1Y5upz40bsH+/3qF9+/ahUCho37497Zs0oVHdujhaWBAjk2GPKFYy9EOYqUBqxl6URqMhPT0dW4WCtIznBcQibjNE8cv8z5rZw7Mz0KJ5c06ePElaWhoGQ6OBgAAxczND9NLT09mwYQPh4eEMHz4cJycn1q1bR7ly5Wjbti2ULi024s4QPYAjR45QrVo1qlSpkrW2l5c4xFajeX6YE0Rv7xVEyMnJiS5durBy5cp8v+bXX3/l3r17/Pbbby99PYniR4kVvn///ZeePXtipfMfVaJwSE9PZ9OmTXTt2hUPDw/u3r3L6tWruXTpEpMmTaKazqy5V63nKzAePRKTPHSSJy5evMiNGzfo27ev6NmYm2OrVlPBw4MGb72FzNGRR4gNqHXfxp8Cgk6oMzU1FUu1Gt35ApktsM2Ashnf2yGGamqVKUN0eDjt27dnyJAhaDT5bYL2HFJSxKL0kye1hxISEvj7778xNTVl6NChWFtbs3XrVkxMTOjWrRsyFxdo3Bh0uqrExsZy7tw5OugWm1tZQbt24vd372rDp4IgEBISQt3sYc2XDHPqkhnuzG+/V3NzczZs2MAPP/yQ69BbiTeLEit8q1ev5p133jG2GSWK0NBQPv30UypVqsT8+fPx9/cnMjKShQsX0qRJk1xDTEVK+JKTxQxOHe8qKiqKPXv24O/vnxVqtLUVB7xaWWFpaYkgCJSrVg25szNxMhlymYw4xL0/lY5YJSUlYYa4f5d51ASxT2cMYshULpNRuWJFPhk8mDFjx9LM25ty5coRExPD999//3r39/ixODNQp7D7/v37LF26lLp169KrVy8UCgV79uwhPj5eDGE2aQL9+4vz9zLITGhp0aIFtra2Wet36CAmrICetxcREYFCoaBixYpZ55Yu/UphzkxatWqFSqXi+PHj+X5NtWrVWLZsGf7+/jx6lH0ioMSbRBHbOCkcrl+/TmRkpBiikShQ4uLiWLt2LcuWLSM6Opr33nuPEydO5DtJxcvLi5kzZxawlflArYb160Gnc0hiYiLr1q2je/fulC2b4Y8JgjjR3NUVHj7kyZMnpKWlUblyZeRyOdUyyg2uREVRTakkMcMjMTU1JSUlBQExxJmK6B0+k8uRyWTIZDKqV6uGs7Oz+AFBqYSKFZk1bBienp7s2rWL3r1707hxYzp16vTy93fzpjhSSEfUL126xH///UePHj209XenTp0iLCyM94cPx7RXL9HT++8/veSX69evEx8fn7XvB2KHlsw6vGxhzgsXLtCwYUODhDkz0U1yad68eb5f17VrV4YMGcLbb7/Nnj17pN69bygl0uNbvXo1/v7+0h91AaHRaDhw4ADvvPMO1apVIzAwkO+++447d+7w7bffvlRmZqNGjbhw4YJhwnivQ0CA3vQBtVrNhg0baNCgAe7u7lnnyWSit1K7NuratQm5fZsaNWpokztMTEyoWr8+wydNwq1BA8o1aqQ9LpfLSTU3x8baGqdKlWjWpAne3t5oNBo0Gk2W6IFYQtGjB1WqVOGTTz7hl19+Ye3atQwZMoQ7eUwxyBVBgKAgWLNGK3qZSSz79u1jyJAhWtELCwvj6NGjDPrgAyxHjhRF78EDvfl7SqWSPXv24Ofnl/X/KzOhJdP2O3e0Qpmens6VK1eoX7++vl2vEebMZOjQoWzfvp0nT568+GQdvvnmGwRBYMaMGa9tg0TRpMR5fIIgsHr1atavX29sU9447t69yz///MPff/+Ng4MDH3zwAfPmzXutcpFSpUpRunRpbt26VfjF6ZkEB+u9uQPs2bMHc3Nz2rRpk3XQ2locOptRzB587x6RZcvSunVrsewh01usWhWTChVwefttXDIEwNzcnLJlyzJi+HAIDRWnHWg0kDFiJy0tjeTkZKzt7KBsWbHrSYaQTJw4kTp16qDRaPjyyy/p06cPx44de3GWZ3Ky2IXl5k2dQ8ls3ryZ9PR0RowYgY2NOA42JiaGzZs302vkSEp98QU4OoqiuWuX3n7n8ePHqVChgn77tCZNxA4tmegMhL169SpVqlTRD4k6OYn3+JroJrl88skn+X6dQqFgzZo1eHl54e3trV94L/FGUOI8vlOnTmFqaoqnp6exTXkjSE1NZe3atXTo0AEvLy9iYmLYsmULFy5cYNy4cQapkTTqPl9MjOjt6XD+/HnCw8Pp06dPlgdmaiqG8zJELyUlhcOHD9Opc2dkpUtDgwbg4wN+fvDVVzB6tJgFSebLTVEqlaKY1asH1auLe4VyORaOjsTZ2HDH3l7saOLmBhYWYqNoxDq+X375hY8//piPPvoIV1dXxowZ8/zEjrt3YeFCPdGLjIxk0aJFlC1blqFDh2pFLyUlhbVr1/LWu+9S64cfRNEDCAnRq2OMi4vj5MmT+k2obWxA98NBamquYU49XjPMqcuoUaNYvHjxSw81LleuHGvXruWDDz7goc7IJYk3gxInfKtWreKdd96RanVek4sXLzJ27FgqVqzIP//8w/Dhw4mMjOT333+nUUb4zlB4eXkZR/jUajGDU6cdWWRkJPv378ff3x8LC4usc9u0EcscMjhy5Aju7u5Ze38gitWwYVChgtiNRKc20czMjPTMSQZyOdSoAX37QsuWKD09iTA3J/zpU/G5THRCmr1796ZcuXIsWrSIpUuXcubMmdwnFQiCmIiyfLm244wgCJw8eZK1a9fi5+dHx44dtWFKjUbDhg0bkLdpQ5uFC8WkHRB/Jzrty0D0gr29vfUnX3TsKN53JqGh2qL9p0+f8vDhw5yevAHCnJn4+vqiUqleKVOzZcuWDBs2jBEjRry0cEoUbUqU8CmVStavX8/bb79tbFOKJWq1mq1bt9K6dWu6du1K2bJlOXfuHHv27GHgwIH6QmBAPD09CQ4OLpC1n8uhQ3ptupKSkli/fj09evTQbwvWurWYCZmxDxkbG8vFixf1w6Aghvx0hTAv4cskY1yPs7MzSUlJOXtw6tgmk8mYO3cu33zzDampqWzevJmpU6dy6tSprPOTkmDVKjhwQGtrWloaGzZs4OLFiwwfPly/iTTw3759HHN2ZtS//+p7YadOia3MMggPDyc6Olq/W0q1auDhoW+zzgeYixcv4uHhod+coFIlg4Q5M8nvuKK8mDFjBpGRkSxdutRgNkkYnxK1x7dv3z5q1KhRdNpeFRMymxH//vvvlC1blvHjx9O3b19MTU1f/GID0KhRI86dO4cgCIXnqd+5AzpegiAI7Ny5Ew8PD/2pD/XqiftXOiOJ9u3bR/PmzfV7U1pbiwKpi84bvjbUqUtGKNTJyYnU1FSSk5P1xzQlJIgtvzJCknXr1uXtt99mypQpLFy4kCVLltC/f3/Onj1L2eRk0Xt99ky7fHR0NOvXr6d69er06dMnR3ec45cv8+Pjx+w4e1b/uaSkHOUL+/bto0OHDlnnyeXQpYu+WD54oBVrQRC4cOECAwcO1L/nAtiCyOzk8uTJE0qVKvXiF+hgZmamHSTcpk0b4/eHlTAIJcrjW716Ne+++66xzSg23Lp1i08++QQXFxdOnz7NmjVrOHnyJP7+/oUmeiDut1hbW79ctuLrkJICmzfrJW2EhoYSGxur78WVLStmK+7Zoz10+/ZtHj58qJ/KD2LhdnaPOJvwqVQq/ZCaqSk4OiKXy6lQoQIODg480PHyAIiK0vtxxowZbN26lfPnz9OzZ08Gv/MO/+vUCfXff+uJ3vnz51mxYgVt2rShW7duOUTvWnIy7wQGsmz37pxDe48cyVH2IJfL9bNbGzfO6bnpeHt37tzB3Nyc8rpJL2ZmBg1zZvIqnVx0qVOnDlOnTmXIkCHa+YkSxZsSI3yJiYns2rWLAQMGGNuUIo0gCBw4cIAePXrg7e2NtbU1ISEhrF27lmbNmhnNrkJLcBEEsT+lzsSFZ8+esWfPHnr16pUlEAqFuAd35ow2W1Oj0bBnzx59zwfEpsy57XvqnCOTyTAxMdH3+lQq8bWAs7MzlpaWROokkwA5hM/BwYHvvvuOcePGITx7xreurngmJHAwo8WaUqlk69atHD9+nGHDhuGRPRQJPHBxoe3y5SxZu5ZatWrpPxkbq5fhqlarOXjwIO3bt8/yxs3NoVUr/dcpleL+XgYXLlygUaNGOWv3zM0pCPI7rigvxo0bh5WVFT/88IOBLZMwBiVG+LZu3Urz5s0po5NJJ5FFSkoKf/31F/Xr1+fjjz+mW7du3L17l++//55KlSoZ2zy8vLwKZ58vJESvebIgCGzfvp3GjRvrN1Du0EH04HRCfhcuXMDMzEzf84GcIb9MsnlZOfb5dISvYsWKaDSanPt82YQPYNiwYZSOj+fCqFHI796lb9++XL58mVOnTrF06VI0Gg0jRozI+X/B0pLEHj1oP3s2k6dNo3379jlt1tkfBAgODqZ06dK4uLhkndOypV7PTgCuXhUzOhH3Fa9fv55TdAsw09rX1xdBEDh06NArvV4ul/PPP/8wb948zp49a2DrJAqbEiN8Uouy3ImKimLKlClUrVqVLVu2MGfOHC5dusTIkSOLVB/TQvH4nj4V69J0OH/+PImJibRs2TLrYI0a4lidffu0GZ9paWkcOnSITp066XsxDRuKCRu5kU34cuzzZfP4EhIScvf4dL0YtRpFYCC/N23KoZ07SU9Px8rKCi8vLwICAnB3d6d3795Z+4SZVKmCesQI/KdNw9fXlzFjxuS0NyJCrxQhPT2dI0eO6Aukvb34u8mOzr/d5cuXqVatmv4eaJkyef+eDIBMJuOzzz7jl19+eeU1KlWqxLx583j33XdJTk42oHUShU2JEL5Hjx5x4sQJevbsaWxTigxnzpzhnXfeoV69esTFxREUFMTOnTvp0KFDkSz1yBS+Aksr12jEfT0djysuLo79+/fTu3fvrC4kVlbQq5dYB3fpkvbcAwcOULNmTf1+k+bm4gTxvMi2T5qrx1ehAgCOjo6oVCqUSiXPdPbqSEzM2rt7+FDstXn0KFUqVcLFxYXAwED+++8/zp07h6+vL5cuXcqZPdqyJbz3Hl/98ANJSUnMmzcv59+AIMDevXqHTpw4gYuLi/4+Xdu2Oe6L2Fi90ovz58/nLHlp1MhgtXt5MXjwYIKDg7ms49G/LP7+/nh5efHFF18Y0DKJwqZECF9mP0W9T5glEJVKxfr162nevDn9+/fH09OT8PBw5s+fb7yuKPkks11XjlCfoThyRPRoMhAEQRse16vF69FDTMLYtk17KDw8nOvXr+fskdmqlTbjMlde5PEplWI4tVQpZBllDY6Ojjm9vshI0f7FiyE6Wnu4fv36nDx5kqdPnzJq1CjatGlD1apV2bZtm/gBwtoa3n0X2rVj+cqVbN68mY0bN+aeuHT1qt7vJykpiVOnTun3u61QAbK3HgNxrl8GUVFRJCQk6O8dKhRigX8BY2FhwdixY5kzZ85rrTN//ny2bdvGHp2kJoniRYkQvsyi9ZJKXFwcs2fPpnr16syfP58JEyZw69YtJkyYkDNjr4gik8kKrpA9Uzh0OH36NGq1Gm9v76yDnp5Quzbs3q1NaElNTWXbtm306NFDv47RySn3kJ8u+dnjA71wp5mZmb7wJSXBX3+JxeQZs/M0Gg1Hjx5l8+bNuLm5YWlpqbXNz8+P+Ph4dl+7JnaPqVmT48ePM2nSJLZv3557px21Osf8waNHj1KvXj39Qa8dOuT02tRqvRZlp0+fpnHjxlmDaUHsRFNIH0o//PBDNm/enDM79iVwdHTkn3/+4YMPPiA2NtaA1kkUFm+88N28eZM7d+7kvlH/hhMbG8vUqVOpWbMmoaGhbN26lSNHjuRas1UcKJBC9rQ0sb5NJ2EjJiaGw4cP06tXr6w36NKloXNnMfFF5418z5491KpVK2dtqJ+f6Mk8j/zs8YGe8CmVStHrFQTRAwsOhtu3tS958uQJf//9N+Hh4YwcOZJevXoRHh6uHbNjYmpKj19+4YPAQA6eOcO9e/fo168f//zzD3Xq1MndzrNnQafR89OnTwkJCaGVbuZmrVpim7XsXLkihmMRvcRr167lbBdYiO0DnZycePvtt5k/f/5rrdO2bVsGDBjA6NGjpa4uxZA3XvjWrl3LwIEDi+Ub/avy+PFjvvrqK1xdXYmOjub06dOsXLmy2PcnLZAEl4AAvVFDGo1G251G6/3I5dCnj1jft2OH9tzr169z584d/d6UIHqF+WmS8JIeX8WKFYmLi+PJ/ftozp/P6hbz7BmCIBAcHKydnTdkyBDs7e0xNzenefPmHDx4UAy7Dh5MOX9/Vq1Zw6BBg/Dz82PChAl5N2JOT4fDh/UOHTp0iCZNmmRtHchkoreXHUGAEye0PwYHB1OnTh39pCl7+9wFswD59NNPWbRoEYkZgvyqfP/991y9epXVq1cbyDKJwuKNF76tW7fSr18/Y5tRKDx8+JBJkybh5uZGfHw8586dY8mSJfqd8osxBhe+e/f09p9AnC5gampK48aNsw62aSPuX23Zok3JT05OZufOnfTq1Us/Q9LCQvT28kN+Pb4KFUAmw9bGhgoaDc1MTEjWKWNIT0pi4+rVnDlzhvfee49mzZrpJac0btyYU48fc9rTUysybdq0oUyZMjx69IixY8fmbeOZM+IUhwwePnxIeHi4fgi4UaPc24zdu6ctt1Cr1Zw9ezZnYX/Dhvr9RwuBmjVr0qpVK/7+++/XWsfCwoJVq1bx2WefcffuXQNZJ1EYvNHCFxERwb179/T7B76BREVF8emnn+Lu7k5aWhohISH8+eefVK1a1dimGZSqVauSmppKtE4Cxyuj0YgDVHV4+PAhx48fp2fPnlnCUbWqOBHhxAm9zMT//vuPevXq5fwdd+0qejH5Ib8eX8Y0d1loKA2srLA0MyMho8A+JiaGs2fPUsnenhEjRugn4mRcw6RrV+r98ANffvedNiw3Y8YM7O3t8fHx4dNPP83dvvR0vbZtAPv376dly5aYZxaam5rqT1/Q5eRJ7bdXr16lVKlSlNOdqq5QwFtv5f7aAmbSpEn8+uuvr92JpWHDhkyYMIGhQ4caf2akRL55o4Vv+/btdO3a9Y0Nc0ZGRjJu3Djq1auHTCbj8uXLzJs3r0gUnBcEMpkMT09Pzmfz0l6Jc+f0MiDVajVbtmyhQ4cOWQk/5ubQu7dYJqAzieDy5ctER0frZzSCmNGYSyeUPMmPxycIold68SI8fYqtrS1yuZz4+HiuXbvGrVu3qFu3Lt516+YcrFyxIowaBd7eDB02jPv377N//342bNjAihUr2Lx5MytXruTQoUP8888/Oe3L5u3du3ePx48f4+XllXWOj484Pik7T57AtWvaH0+fPp3T26tXL/fXFgLNmjXD2dmZLVu2vPZaEydORKPRvHa2qETh8cYLX48ePYxthsG5e/cuH374IfXr18fS0pKrV68yZ84cKmTUfL3JNGzY8PWFLyVF7ECiw5EjR7Czs9OfDdetm5htuGmTNmMyMTGR3bt307t3b/20fwcHsUPLy/CiOr6nT8VpCtu2aft82trakpaWxqNHj5DJZLz11lvY29vr9eFEoRB7g37wgbbRtYmJCd9++y2fffaZNrOxXLly2NnZsXnzZiZNmsTp06ez1khPh+PHc/yOWrZsmfVB0tJSFL7cOHVKW1gfFRVFfHy8fnNvAN1wqRGYOHEiP/3002snpygUClasWMGPP/5ISEiIgayTKEjeWOFLSEjgxIkTORMPijHh4eGMGDECT09PHB0duX79OrNnz9YPH73h1K5dmxs6c+9eiYMHRfHLIDo6mrNnz9K9e/esEKerq+i97d0rDqNFrO3bsWMHnp6e+oXqMpmY/PKyY5lyCXUqlUoxDHvnjmhnWJj4pK0tGo2GJ0+ekJxhe40aNbJE6NkzUWjKl4cRI8Si9Gx7Z127duXWrVv06dNHL9GpTp06LFu2jF69emU1Aj97ViyVyCAqKopHjx7RQLferlmz3Htrpqbq7Z3mWsLg4qI/ld0IdO/eXdu84XWpVq0aP//8M++++y5pOg28JYomb6zw7dmzh+bNm2NrpFCKIbl58ybvvfceTZo0oUKFCty8eZPvv/++RPYddXV1fT3hi44W39QzEASBPXv20KpVq6y/FYVCLF24fl2vIfPFixeJi4vTT+MHUWSqVHl5W3IJdZo8eyZe884dvS4y95484ezZs6SlpWFuZoa1tbV+Bxe1WiwLGDEiT0H59NNPadKkCUePHs2xt9W9e3e+/PJLunbtStzjxzn29o4ePUrz5s2zhNbCIu86xXPntLbnWcJgxIbnmSgUCj777DN++ukng6w3ZMgQatWqxZQpUwyynkTB8cYK37Zt24p9i7KrV6/y7rvv4uPjQ/Xq1bl16xbffPPNS88Ue5N4LeETBLH4XCe0dePGDRITE3lLN8nCx0fszrJ9u/ZQfHw8+/bt029fBuI+WnYhzC+6af3p6Tg9fkyFR4+yvNG0NFJSUtixYwcbt2yhcu3a1K1bFzs7O0xMTEjJPM/KSsysrFkzz9rB1atXExgYyPbt2ylbtmyuI3o+/vhj2rVrx9QuXVDrTKd49OgRERER+uLl7Z27h6vRiGHODHItYShdWvSoiwBDhgzh5MmTXNPZj3xVZDIZixYtYvXq1ZzQKeOQKHq8kcKnVCrZvXs33bp1M7Ypr8Tly5fx9/enVatW1KlTh7CwMKZNm1ZsuqwUJGXLlkWpVPJEp6A631y+LPbYzECtVrN37146duyYFYazs4MWLWDrVm2oTxAEtm3bRrNmzXLOj+vb98WF6nlhbS2GSe/fh9OnsU9N1YbJBEHgUXQ0i//4A7lczpgxY6hQqxYymQzbjLBnSmoqVK4sZkba2eU6qQHg2rVrjB8/ng0bNmBvb8///vc/ZsyYkWtI7tfZs2mUlMSuXbu0e19Hjx6lWbNmWXuaz/P2rl7VTmZXq9WcOXMmZ1JLs2YF3pczv1hZWTFmzBiDJaY4OTnx66+/MnLkyJyDhSWKDG+k8B07dgwXF5dil914//59PvjgA9q2bYunpydhYWF8/fXX2NnZGdu0IoNMJsPV1ZWbN2++3AvT03M0WT5z5gyOjo76fSM7dBD3p27d0h7KDDE2b95cf83OneF1vO/oaFEobt4ElQoLCwtSU1NJTU0lNDSUu3fv0q97d7p27Sq2HMsIxdra2pKoVnPVwkIslM8U7YzuLLokJyfTv39/vv/+e+3+nI+PD/Xr12fRokU5zldcuMC7vXrx4MEDjh07xpMnTwgLC9Ova2zWLO/9TB1P5+rVq5QuXVp/D9rSslD6cr4MY8aMYcOGDTx8+NAg6w0YMIAqVarw888/G2Q9CcPzRgpfccvmTEhIYMqUKdSvX58yZcpw/fp1Pv/88zdif7IgeKVw59GjesNlk5OTOXLkiH7yU9WqYthQRyBjY2M5dOgQvXv31k/OcHfPfbhsfkhLEzvGLF6sl2STmdwSHByMvb09Xl5eVHRyynpdRsNra1dXjqWlEZW984jO/WXy0Ucf0aBBA4YPH653fNasWXz//ff63UuUSggKwszMjLfffpszZ86wY8cOGjdunFW3Z26et7cXESH2PUX0WIOCgvQL3QG8vERPuQhRtmxZBg4cyB9//GGQ9WQyGX/88Qe//PILt3Q+QEkUHd444csMSxWH/T2lUsmff/6Jm5sbERERnD9/nh9++EEKab6Alxa+J09ypOYfPnyYunXrZhV8y2TiG/rGjdq+nenp6axbt442bdrgpCtAtrbQvfvLh+sEQexdOX++WNwtCNqsyGfPnnHu3DlkMhnu7u5UrVpVFNqMTjGAGNZs1AizunWxtrPLGe7NCDFmsnz5ck6cOMHChQtzjBmqX78+bdu25bfffss6eO6ctq+mra0t3bt3586dO/qRk2bNRK8tN3Ram928eRNBEPSnfsjl0KTJ839HRuLTTz9l4cKFBpuzV61aNb7++mupl2cR5Y0TvitXrqBSqaif23iUIkLmyJt69eqxZcsWdu/ezfLly6nyKpmBJZBatWq9nPDt2aOtwwOx20loaCitW7fOOqd+fb0yh8x/o0qVKuknvoBY1P6yQ3ofPRJr8tav16u5UyoU3Lp1i5CQECpVqiTW5OmSliZ6SJ06wccfi/WCiENRlUqlft1faqo2m/Ly5ctMnDiRDRs2YJPHaKRvvvmG3377TZwwoFJBtrT+mzdv4u7uzrZt20SRNTfPOxvz/n1teFgQBI4ePUrLli31BbduXXEvsgji5uaGj49P7oX8r8jHH3/M06dPc00kkjAub5zwZYY5i+IwVYCTJ0/i6+vLtGnTmDdvHnv37tUvmpZ4Ifn2+CIiYMMGCAzUCynu3buXFi1aZDVZNjcXvcKMej2AoKAgEhIS6NKli/7fkrf3yzVVTkwUG1svWJBVk5fBjRs32LhjB0qlksaNG1O+fHntPp+WMmVg7Fjxuqam2nCns7MzpqamPNVpsA1AQgKJiYn079+f2bNnU69evTxNq1mzJv369ePHH38Uh+rqCHJiYiIhISH4+fnRqlUr1qxZQ4K7e97eXmCg9ts7d+6QnJycc9qDkQvWX8SkSZOYM2cOap0PSa+DiYkJixcv5vPPPydG529Lwvi8scJX1AgLC2PAgAH069eP999/n/Pnz9OpU6ciK9BFmVq1amlDabmiVIqCt3QpLF8u1uOdOgWhodwNCSEmJoYmuiE3a2u9Ias3btzgzJkzOad6ODuLHVHyg1IpzvibN08cHaRja0JCAhs2bCAgIIAW7drh7u6ubXRtYWEhlilYWIgF9B4e+r0/Mzwm54yJDXFxcXqXFeLiGDNmDE2bNmXYsGEvNHPq1Kn8tXQpcbt36x0/efIk9erVw9bWlsaNG1Pd3Z1+v/ySe3H2/ftigk4GmR1e9PZEq1fXTpkoqvj4+FCmTBm26QwZfl28vLx45513mDBhgsHWlHh93ijhi46O5tq1azkLjI1ITEwMn3zyCU2bNqVhw4bcuHGDYcOG5eyrKJFv7O3tsbGxISqX9P2IiAg+adCA0H//RRMTo92zAhBiYni0Zw/9atTAJLMriVIJOsNEY2Nj2bZtG/3799dPLrK1BX//HEXnORAECAmB338XQ6c6oUilUsnhw4dZsGABpUqV4sMPP6RyzZp6L7ewtCRSLofGjcV6t+wJKxkiWKFCBdLT03Ps821dsYJz587lO1GjYsWKTOzblxNbt2qPpaSkEBwcrJfF2nnaNGzKlGHEiBE5P3Do7O1FRkby9OlTPLL3LNUNKxdRZDIZEydOZPbs2Qbdl5s5cyaHDx/mQLY2eRLG440Svp07d9KpUyf9MTFGIiUlhR9//BF3d3fUajVXrlzh66+/1i/klXhl8gp3xsbE4HDjBjt27GDf0qVERkZqQ1cPHjzA1NSUClZW4jDZmzfFfbEMrzstLY1///2Xtm3bUrly5axFTUxE0XvR/tTdu7BkCWzerCdYgiAQGhrK/PnzefjwISNHjqRdu3ZiXZxuyy97e9SNGnFDpcqqDUxI0PMWM20wNTXFyspKT/wfPnzIP/PmsWHDhpf6OxvdsCEhISEkZXwYOHPmDG5ubllJViYmyH18WLVqFdeuXePbb7/NenFUFOj8Oxw5coTmzZvrf7BzcXm1zjZGoFevXsTHx7M3W+nL62BjY8Off/7JqFGjspoOSBiVN0r4ikKYU6PRsHLlSmrXrs3p06c5duwY8+fPzzkuRuK1yEv4LNPTsVAosFEqMU9P5054OGePHycsLIzbt29To0YNMbysVIoZlhnCIwgCW7ZsoWrVqvrTBwB69hQ7tOTFkyewbh38/XeOIvL79++zbNkyjh8/Tp8+fRgwYACOjo5ZJ2SKX+3a0LAhdhUq6O/bqVR6ExJ0xdfR0VG7d5SWlsb69ev59P33cXd3f8FvT4eYGBwfP6ZOnTqcPn1aW3SuV4ZQvz5YW2NlZcX27dtZtmwZq1atEp/T8faio6N58OABjbKXeRQDby8ThULBjBkzmDZtmkG9vi5duuDl5cV3331nsDUlXp03Zl5PcnIygYGBLF++3Gg27N+/n0mTJmFpacmaNWtyFjxLGIy8itgtzM0RBIFqmQcEgXKCQGpkJKaIzZarVq6MRVwcODlBXByULcvhw4e1xd56tGyZ96ihlBTxjf/MGb2sURD38Q4cOEB4eDht27alYcOGue/nenmJYdSMkKy1tbU2W1MbuUhIEPchQW+/r2zZsly7dk3bPLtq1aq0zt4T80VkzMxr3rw5S5cuxcHBAScnJ/2ic51MzvLly7Nr1y7atGlDTWtrml2/rn3u6NGjeHt76++LuriI9ZHFiP79+/Pdd9+xa9cug3Z/mjt3LvXr18ff3z9nKFiiUHljPL59+/bRuHFj/U/ThcSlS5fw8/Nj9OjRTJ48mWPHjkmiV8Dk5fGZW1tjr9GQ6Rdlfma3AEoBMdHR3D5zhnsPHpCYng5KJdevX+fcuXMMGDBAP0Tn5gbZZ+6BKHInT4qJKydP6ome7j6enZ0dH330EY0aNcopepUrw/Dh0KOHKMAZyGQyHBwc9L0+3X0+HY+vYsWKpKSkcPbsWR4/foyfn1+uRex5kpwszvkDSpUqRfXq1Tl8+LB+4k+NGjmmq9etW5c1a9bw93vvaT3OmJgY7ty5k7P0owjtt+cXuVzOzJkzDe71lS9fnu+++46RI0dKQ2uNTLESPkEQtJOns2OMMOezZ8+YMGECbdu2xc/PjytXrtCvXz8pU7MQyEv4zKysqKDzppL5tpUCRAHWgCUQmZhIcHAwB4KD2b59OwMHDtSvdytbVhw1pPtvqVaL7cx+/13svKKzX6O7j/fo0SNGjRpFu3btsjqeZOLoCP37w/vvQ2ZheLbaPQcHB/1sTd3CdB3hc3Z2RhAEDh06xIABA8Q9w2xF7M8lOFgM+Wbg6upKQkICNWrUyDonjxKE9nXrMiqjzCE5OZmgoCCaNGmiv79erZr4KIb07t0bgK06ST+GYPjw4ZiYmLBw4UKDrivxchSrUOf58+fx8vKiSpUq+Pn50blzZ1q1aoWdnR07d+5k8uTJhWKHIAhs2rSJTz/9lPbt23P58uUSOSLImNSoUYM7d+6gUqn0QmsW1tbY6XxKF4B44ClgBTgASYBKJiPBwoLw8HDat2+vP1/PygoGDcpKPNFoIDRUDGvm0hw7MjKSgIAANBoNffr0oWpuoT0LC/D1FTuXZM8MzZY04+joqC98uh/2bG1FMRYEbGxsEICmTZtSunRp8fm0NPGR25w8XdRq0B08i1hyU6pUKS5duiROYihTRvT4cuPwYTw9PXny5AkrV64kLi6Ojz/+WP+cYujtZSKTyZg5cyaTJ0+mZ8+e+qUZr4FcLmfx4sX4+vrSs2dP/b87iUKjWHl8tWrVwsTEhHv37rF48WKGDh1K+fLlqVatGiqViuvXr+v3HiwAbt26hZ+fHzNmzBDDPX//LYmeETA3N6dChQpZg1Mzj1tbo5s3JyCKnhmQGVB8JpMhK1eOhAoVqOXqqp+MIZfDwIGiZ5YpeH/+CVu25BC9+Ph4Nm/ezLp163jrrbcYMWJETtHLbNP18cfiuKPcyiGyCd9zQ51yOdjaIggCAQEByGUyLLMXlecn3Hn5co6C9evXr9OhQweOHTsmhuLymqLw4AFkjPFp164daWlp2NjYiI20M6latdh6e5l069YNCwsLNm7caNB13d3dGTNmTM4PChKFRrESPltbW23hbmbYMz09XVs75O/vT6lSpahXrx5ffvklBw8eNFgsPTU1lZkzZ9KsWTPat2/P+fPnadmypUHWlng1cgt3KkxNuZbtzdoUKIf4x54MWDRqhLJmTdJVKjp16qS/aNeuYur9lSuwcCFs2qTX0QVEkQgICGDhwoXY29szbty43JNX3NxgzBjo0uX5Lc5eJtQJYGfHpUuXePjwIXZ2djx48ED/+ReFOwVBb4oCiHPz6tati6urK1ZWVlwKDxezOXN77b592h/j4uJITU3F1NSUQ4cOZZ3XqlWRGT30qshkMr755htmzJhhsG4umXz11VdcunTJoMXyEvmnWAkfkGfSSKYQKpVKLl++zE8//US7du04qzNt+1XZu3cvHh4ehISEcP78eSZOnJg1m0zCaOS1zzffxITMt34FougpAKVMhk3XrpjVqMHFkJCcySxNmojZk4sWiT01s435SU5OZv/+/dri8LFjx9KuXbucdaPly8PQoWK4VLe5dV68TKgTiFWrCQgIoHfv3jg4OORsh/Uij+/uXdFry0CtVnP27FmaNGmCTCajRYsW/HH6NEJu3mlYGISHa388ePAgTZs25Z133iE0NJTz58+LHxxcXJ5vQzGhU6dOODg48O+//xp0XQsLCxYvXsy4ceN4puN5SxQOxU742rRpk6/iXAsLCyZNmqSfofaS3L9/nwEDBjB69Gjmzp3Lpk2b9AubJYxKXsL3xNycscARxGQWJRBlYYHTsGEIZcqwa9cu/P39s3p1CoLokd27B//+K87J0yE1NZXAwEDmz59Pamoqo0ePpnPnzjmbP9vaQq9eMHLky73x5xHq1GYU6hSxC4LAnCVLaNy4Mc7OzpQtW5b47B7ei4Qv24fB7HPzarm7c06hYJ+OZweIoV+dwu4HDx5w+/ZtvL29sba25p133mH//v0cMzUt9t5eJjKZjG+//ZaZM2eiUqkMunarVq3o0KEDU6ZMMei6Ei+m2Alf06ZNX7jRbGlpSadOncTmuxlEREQwZsyYfIUsVCoVv/76Kw0aNKB27dpcvnyZLl26vLbtEoYlL+EzNTXlIXAX2G1iwgVXV9769FOU5uasX7+ePn36UKFCBVFMnjwRO4/Ex+cQvPT0dI4ePcrvv/9OXFwcI0aMoFu3bjknKJiaikXa48ZBw4ZZg2Hzi6WluEYGmXtl2mbVarV2GvyiRYuISkzUhtmdnZ1zdgN5nvAlJ4vDb3U4deqU3pR0ef36fPz11/zwww/6r714Uc8LPnDgAL6+vlqP18nJiR7jxtHr0085mVEf+CbQtm1bKlSowOrVqw2+9k8//cT69es5nS3RSKJgKVZZnSDWECl1UrCzY2ZmRp06dVi7dq3ensu4cePYsWMHVapU4csvv8zz9cePH+fDDz+kTJkyHDt2DDc3N4PaL2E48hI+E5mM/oCLQoGvry8tWrQgPj6eVatW0blzZ2pUry7257x3TxQUT0894VEqlZw9e5Zjx45RrVo1hg0bpj+PT3shE3jrLWjRQjs14ZWQyUSvL6NnqEwm04Y7tYkrsbGEPXzIlClTOLlsGYpz5wBx7ptSpUIQhKy/9+ft8YWG6tUdRkVFkZCQoP933qwZ/qVLM3Xq1CxRTE8Xe49mcPv2bWJjY3N0uXEbN47lGRmL+/btK9LjwfJL5l7f+++/z9tvv23QbY5SpUrx008/8dFHH3Hy5EmDZY9KPJ9i91tWKBQ5x51kIJfLKVeuHHv37tWrnzp58iT79u1Do9HwzTffcDXbJ14QC3CHDx9O//79+eqrr9i3b58kekWZ0FCqzp7N3shIBHNzUTzMzcHdnVXx8bSSyRg0aBAtW7YkJSWFVatW4ePtjUe5cmL9WmiomNVYr5428SSzXdfvv//O3bt3GTx4MP369cspegpFVqZm586vJ3qZZGu8kD2zUx0RwdChQ5k8eTI1dbqzODg4IAMe6e5H5uXxCYI4bFaHU6dO0aRJk6w33CpVoHx5TE1NmThxYpbXd/KkNgtUEAT2799P27Zt9fdI69WDihXp0qULv//+O507d365uYlFmFatWuHi4lIgnaHefvtt5HJ5gXiUErlT7IQPxH2+3IrEbW1tCQwMpFSpUtpjgiAwcuRI7WTl1NRU+vXrp43XazQali5dSt26dbG2tubKlSv4+/tLRehFlfBwaN4cmjVDtmQJtQUBWeYEhPR0uHaN9mo1IxUKahw+TPrDh6xdvZrGlSrRTC4XszUTE0WhrFMHHBzQaDScP3+e33//nRs3buDv74+/v79+2y4QQ5heXqLgdeli2KGqFSro/Zg9wWXn4sWYmJjwySef5Liuqakpd+/ezTqQl/BFRcHDh9ofk5KSuH79un45h87377//PsePH+fa2bN6Q2qvXr2KRqPRn/WnUOiNbBowYADfffcdHTp04N69e8+782LDN998w7fffpv7aKbXQC6X8+uvv/L1119rG4VLFCzFLtQJ0KJFC5YuXarXxcXKyoq9e/dSPduQ0HXr1hGuk4UmCAJ37txh1qxZ9OrViw8//BCNRkNAQEDO5roSRYv162HYMDRpaVRXq7mbx2nlgGiVCk1kJIpFi+hgb09le3u9Tiu4uqJ2dOTSxYscOXIEW1tb+vTpQ5XcpgjI5dCggViAXlAt8bLNqnNwcODx48eAOHXhxKZN/H3pkuiZ2diINmWU6lhYWOhnduZVxH7+vN6PFy9epHbt2lnJYubm4pT0DKysrPj444/Z/eWX1G7RAhA/KB44cAA/Pz/9D4dNmuT43bz//vskJCTQvn17jhw5Qvny5V/611KU8PHxoU6dOixbtowPP/zQoGt7e3vTsmVLfvrpJ2bMmGHQtSVyUiyFr2nTpqTrzDmztLRk1apVOTI4U1NT+fjjj3N8ikpOTua7775j7ty5/PDDDwwfPlyKrRd11q+H996DlBRtmMIeGJ/LqZmBR3lGJmTlhARkjx9re06qqlThXEQEx9etw9HRkW7duuGSWxamTCbWsvn6irPxCpJswlehQgUuXryIWq1my5YtDGjXDpdMr1AuF8OzGc0aLC0tc05iT0/XF770dDG8m4EgCFy4cEE/aatePchWmjF24EAWfPcd8R4e2Nvbc/78eezs7PTbmmV2pcmF8ePHk5CQQMeOHXNEY4ojM2fOpE+fPgwbNky/YN8A/PDDD3h6ejJ8+HAqZbazkygQiqXwOTs7Y2lpSWpqKpaWlnz77bfa3nq6/PTTT3mGDlQqFY6OjgwbNkwSvaJOeDgMG6bvsSG2H5uRj5fLNBq4fh2VlRXX1GoCNm2iUuXK9OvXL/c3GJlM9Hxat85fHZ4hsLMTawgz/l4rVKjA48ePOXToEHZ2dmI04sGDrDIJnRo7KyurnCUN2VPvr1wRvcAMHjx4gFKp1O80k8tkB4ezZ/Fq1Ijjx4/Tvn17AgMDc24F+PqKmal5MHXqVBISEvDz82P//v36A36LGU2aNMHT05PFixcbvPNKlSpV+PDDD/nqq69YuXKlQdeW0KfYvuO7uroCMHjwYCZMmJDj+YcPH/LDDz9o9/ZyIzo6munTpxeYjRIGYvBgNK+5r6LRaIg/d44bKhVDhg7F398/d9GrUwc+/BD69Ss80QNRbHW8PlNTU+zt7QkODqZ79+6i0Oh2aNERPhsbm5xF0NmFL1tSy/nz5/W7zZQtm8Pr5O5duHYNb29vLl68SFBQEJUrV9bvL+ngIIY5n3trMn766ScaNGhAz549i/0w1pkzZ77wveVV+eKLLzh48KBU3lDAFFvha9SoEa6urvz555+5Pj9p0qQXFpwmJyfz22+/cS7bm4JEESIkBC5cQJ5L/WUasAr4HpgLHALyqtKUA6UUCvq0aJFzKLBMBu7uMHo0DBiQYwxPoaEjPEqlksTERFxdXbM8JN0ht9mELz09XS/8ryd8MTFi6Yb2KRWXLl2iQYMGWed4euoXnQuCtljd1tYWFxcXTpw4QTudBBZATGjJrcNLNmQyGQsWLKBcuXL079//uSVJRZ1GjRrh7e3NggULDL62jY0Ns2bNYvz48QYdiSShT7ERvpjENBYeDmP8uvO8v/wM5q1H8uni/4hLySluoaGhbNiwQf+NIA9SUlLo16+fwTO1JAzEwoUIefzbRAODgcmIe31tgVrA4VzPRqxf0+1aIpeLBedjx4qNqY2dfKEjfPv378fJyUm/4UIewmdmZoalpaV+gouu8GVLarl+/Trly5fHwcFBPKBQ5OzLee4c3L+v/VGhUCCXy/X36JydxX3BfKJQKFixYgVyuZzBgwcbvP9lYTJjxgxmz55dIE3xhwwZQlpaGuvWrTP42hIiRV74LkbEMXLlWZr/eJBZyzazZNpHrBjbibnvNOGjbo2pUt8bv4lzuRgRB4ib9qNGjcq3kFlaWnLnzh2+//77ArwLiejoaP73v/9x+PDhl/uQcegQslzeIIcBBxDFLwkIBUYBdwA/4GIuS8kEAe7cEYvVmzaFTz4RW4wVZkjzeWQI3+3bt7l69SqdO3fmvo748ORJ1j5nNuHLkdmZ6VGp1XDhgt5lzp8/r5/B7O6u30Q7ORn279f+GBMTQ3h4ODY2Nty+fTvrvI4dX7o1mampKevXr+fx48eMHj262Ho1Hh4etGnThnnz5hl87czyhi+//LLYh4WLKkVa+FadvIP/kpPsu/qQh4fXELnic1IjLmFR3Qu7Jr2xrNEEVUoix4OO4L/kJKtO3uHff//l5MmT2v9Qpqam2NnZYWdnp/1kXKNGDTp06MBHH31Ejx49sLS0ZMuWLUa+2zebqKgopk6dSo8ePbCzs8PLy4vp06dz9OjR5wuhTimKLtMRPbxyiHP26gELgc8Qh87OyGu9uDgYPx78/HJMRTA6trakmJiwdetWunfvrp2wrpeglbnPp9M9xNTUFDMzs9w9vrAwbcIMQEJCApGRkbi7u2edm72MZ/9+rcAKgsDu3bvx9fWlWbNmnDlzRjzHze2Vxw5ZWFiwbds2QkNDmThxYrEVv2+//ZY5c+bwUKc20lD4+vry1ltvMWfOHIOvLVGEszpXnbzDrP+ukqLUkHQtiPijq7Co1pAyvb9Gbq7fpFpQq0hRqpn131W4cAgrKyvq1q1LnTp1cHd3p0aNGri4uODi4oKjoyOCILBx40bGjx9PfHw8ycnJBbJRLZGFh4cHCoVCW3t57tw5QkJC+O2330hNTcXDw4Nu3brRvn17GjdunNV5Jx/hal1GA78gNqjOFbVazJ4soizft4+aNWtSq1YtACpWrEhkZGRWF6GoKKhePYfHZ2JikrvwXb6st35ISAh16tTJarvl4CCul0lkpF4izLVr13j27BmNGzdGpVJx4MAB4hMTsW/f/rXu08bGhv/++482bdrw7bffMm3atNdazxjUqlWLoUOHMnXqVBYvXmzw9WfPnk2TJk14//33xd6yEgajSArfxYg4Zv13jRSlBkHQEHfob2Sm5jj1mJRD9ABkCvE2UpQaLBv24fifs6lfySHXtQMDAxk7dix3797V+yQt7fEVLKampri7u3PxYlYQUqVSaYUwODiYkJAQfv31V1JTU6lfvz7NmjVjrokJ8pfoip+ZlpJn/4tc+iymJCTw4PJlHt6+Tezt2zy9e5eHd+8S/vAhpVq04Lv58/N9/ddh27ZtHLl5k3/ee097rFKlSty/f19f+CCH8CkUipzCp1JpB8aC6L2dP3+eXr16ZZ3XqFFWuFKjgV27tE8plUr27NlDz549USgUKBQKPDw82PLgAe8ZYPhyqVKl2Lt3Ly1btsTW1pZPP/30tdcsbKZOnYqbmxtjx47VTxYyANWrV+eDDz5g8uTJLFu2zKBrl3SKpPD9EXiLVJW4r5MWeRVV/EOs3Jojt7Ah+dYZlDF3kSlMMXd2xbyiu95rU1Vq/gy8xcJ339I7HhISwrhx4zh79myu3p0kfAVP27ZtCQkJyTO0pVQqtdl+Z8+e5ezZs0yytqbKSwhf5njV6nk8/9jenknvvUd4eDhP7t3j7fv3aaRSYS2XkyaTkQA8UKtJRgyjellYiAkxb72Vx4qGIXPPa8cvv2Cm09+yYsWK+pMOchE+U1NTZDIZT548QaPRiHWpKpUYJtb5u46MjATQL+Pw8Mj6/uxZvZKJoKAgKlasqFfc79m6NU1WrODt9PSccwhfgXLlyrF//358fX2xs7Pjgw8+eO01CxMHBwemT5/Op59+yoEDBwze6nDy5Mm4ublx7tw5PHOps5R4NYrcHl9MYhqHbzzOHD9G+oObACisHXjw9yc83jiTuMB/eHpgCdErJxG9+kvUyVnFu4IAh64/JjZR/A9/7949BgwYQLNmzTh69GieIc38ZIBKvB6+vr75Ll62sLBgzpw5VB4yBEG3ETJwGXiSy2vuAh9lfP9uLs+rgWOPH7Ni+XJOHj3KhLt38VGpsESs8zNVq3FWq2kC1AfKKxQ0btgQ/vtPDAEWEIIgMHr0aN59913e6tFD77mKFSsSFRWV9WEhLk5MPsnm8alUKmxtbbM6uKhUOcKcFy5c0K/dq1ABMrM0ExP1pi88ffqU06dP07FjR701yr/3HjXr1GHz5s2vf+MZVKlShX379jFt2rRimck4cuRIHj58yPbt2w2+tp2dHTNnzuTTTz8ttnuhRZEi5/FtDNZ/g1EnxwHw7PxuTBzKUdb/O8yd3VDFP+Lpwb9IvX2Ox1v+R/l3smaHyYAVQTcI37WYv/76C6VS+cKavrS0NG7fvo1CocDExEQb2sn8XveYXC6Xmli/AEEQuHfvHqGhodrHuXPn9Pqr5oZcLsfGxoYtW7bQtm1bsY5v+XLxzT6DDcAPQBvABbAFwoBdQCrQBZiYy9pqIAoYknHe80bFlgJKqdUoTp8Ww4Hnz0MBtZHatGkTV69eFbvzW1iIXVwyfk/W1tbaUoUymeHFqKgcHl96ejpOTk7ExMRQunRpSE3VC3MqlUquXLmi32NSpy8n+/aJr8kgICAAHx8f/dmDNWqAuztjx47lt99+w9/f32C/g1q1arF79246dOiAjY0NXbt2NdjaBY2JiQlz5szho48+ws/PzyCesC4ffPABf/zxB1u2bKFPnz4GXbukUuSE71p0AmkqTdYBIev7Mr2+wqycGMQyK1OVMn0mE7V4FGkRl0i7f1Ub9kxVafjfn8t5vCP/ezOpqam0bdsWlUqFWq3WftX9XqVSaQU0L1HMfszExAQbGxvs7e31Hg4ODjmOZX/e0L0ACwKVSkVkZCTh4eFcvXpVK3KXLl3C2toaDw8PPDw86NSpExMnTqRTp076e1E6mJubU6lSJfbt25cVXqtfHxo2RHPqlLaIvQ1wHTiPGNpMQmxf1gKxrm8w4ocfXTQyGdGCwCOgGtASsEAUQAAF4n8Gk4zv1UCKTEYpGxsxM3LtWjERpHFjUZwMREJCAuPHj2ft2rVZ/97OznoTFjL3+fISPjMzM5RKpVb43NzcxK4rOmHO69ev4+zsjJ3uZIfM8V5374pDZjO4efMmjx8/pn///lnnKhTiRAqZjB49evDJJ58QEhJi0Hl79evXZ/v27XTr1o0NGzbQunVrg61d0HTq1AlXV1fmz5/PZ599ZtC1FQoFc+bMYeTIkXTt2lVv5JrEq1HkhC8hVd8zk1uILYdNHMppRU/7nKk5li6eJIbsJS3qht5+n2ezFpgK19m3bx+CILwwlCmTyQgPD8+XJ6fRaHIVxbyEMjExkfj4eOLi4oiPj9c+IiIiuHTpkt4x3fOA54pjqVKlqFChAhUrVtQ+SpcubVBvVBAEnjx5Qnh4OOHh4dy+fVvva2RkJOXKlcPFxQU3Nzc8PDzw9/fHw8ND9Dyy4e3tzY4dO3Ict7KyonXr1qxfvx7r7FmXK1ci9/DQen2tMh4vgwa4UacOpjduoFSpkCHu4cUDcYhiV46s2P9joGrVqll9XBUKOHAAjh0TawCbNXtuf8r8MnXqVDp16qSdqA6IwqfjrWVmdjZs2FA88OCB3hgjXY8vIiJCPBgWpnedK1eu6I8RcnYWw5xqtV5Ci0qlIiAgAD8/P0x0O7I0b65t1G1qasrIkSP5888/Wbhw4ev9ArLRtGlT1q9fz4ABA9i5c2eOxvNFmZ9//hlfX1+GDBmS++Di16Bdu3bUq1ePuXPn8vnnnxt07ZJIkRM+Owt9k0xLieEluXnuwz4zhVFQ6QvbrSshPAwMxNTUFHNzc54+fYpMJsuzW4RMJkOpVOYrTCGXy5HL5QadxJwbqampOURR9xEbG8vJkye5f/++9pGcnIyzszMVK1bUfs3+cHZ2xsLCAo1Gw5MnT3j06BGPHj3i4cOHPHz4kLt372qFLTw8HLlcTvXq1bWPRo0a0bdvX1xcXKhatepLfQJt164d+/btI1UnrGZpacmkSZOYPn167qJdvTr8/bd2OsPLolEouFilClcePMDa2lr80IGYAOMAWAIxwEOgPCAAyaA/RidTxFNT4fBhOHFC9P58fF65PCI4OJh///2Xy9n24rL3zKxUqZJeNixRUVC5svbHTI+vdOnSXLhwQczOjIiAjAbU6enphIWF0a1bt6w1Mr2906dBZ4jtyZMncXJy0pZTAKKnqyvMwIgRI6hTpw4//vijfjjUALRp04Zly5bRvXt39u/fj4duAk4Rxt3dnUGDBjF9+nT++OMPg6//008/4ePjw9ChQ3POipR4KYqc8NUub4e5SbQ23GleuS7IFSifRiGolcgU+mKTHiNOZTOxz+qvqEDDsD6d+HrlVOLj47l37x5XrlxhzZo17N27V+uN6aLRaHB1daVChQqULVs210epUqWwtrbWexSk+FlYWGBhYfHCP/JMjzYpKYmYmBhu377NnTt3CAsL4+7du5w+fZpHjx7x9OlTEhMTtRmsgiBgamqKlZUV9vb2ODk5Ub58eWrWrEnPnj2pV68e1atXx9GAM+h8fHwwMzPTCp+1tTVr1qyhR7akjhwMGCB+zZjHl1vvzuxoZDJQKNghl+PRogVtk5PZtWsXcrmc2xoNtQBnwDzj61PgEWJBvIWFBWfOnKF8+fJUrFEDy+xv7unpovd3+rQ4nNbH56UG06rVakaPHs2PP/6Y0zvIVrNVvnx5YmJiUCqV4t9bfLxeGDPT47O3txf3UJ880Xv+5s2bVKpUKWvuHoj7e/HxcOiQ9lBCQgLHjx9n+PDh+vb4+eUoA6lQoQIdO3ZkxYoVjBs3Lt/3nV+6devGvHnz6NixIwEBAQYvFSgopk+fjru7O2PGjKGu7h6qAXB1dWXIkCFMmzaNRYsWGXTtkoZMKGKpQjGJaTT/8aDePl/Mjp9JuhyInc9AHH0Ha4+n3D7Po3XTkJlbUenDv7Ten1xQk7z2M8o72tC/f3/69++vneaQlpbGypUrmTlzJnFxcdpee+bm5hw+fBiNRqP1gHQ9oUePHvHkyROSkpL0HgqFIocY6j5sbGywsrJCkS0zMb8olcoc10xMTMxxTC6X613TxsZGT7TLlSun/d7JyUkrPo8ePdLzGDMft2/fxsrKCjc3N9zc3HB1ddV+X7169VcW/PT0dG1mZ5kyZdi3b59+F5EXER4OgwfD+fMI6em5tjMTFApkZmZiMoqfH3cTEli3bh2DBg3CysqKlStXkpCQgEwQ8AUqkvUJMBXR+2vWvDlqtZrIyEhOP3yIee3a+Pj45D1M1cQEWrQQQ4L5+N3Mnz+fDRs2EBgYmLuX+9tvYgZnBkuWLKFjx45ZY4Rq19aGQwVB4Ntvv+XLL7/kxx9/ZHKfPsgVCvEcYMOGDVSvXh0vLy/xtc7OMGIErF4Nt25pr7Fx40ZKly5NmzZtsuxwdYW33871Hg4fPszo0aO5cuVKgSV7rV+/nnHjxrFr1y7eKuCSEkMxd+5cdu/eTUBAgMHXfvr0KbVr1+bQoUPUyfTaJV6aIid8ACNXnmXf1YfakgZ1UhzRqyahevoA80p1MXd2RRX/iOQbJ0Amw6nHJKxrixOiZTLoVKccfwxqRFBQEBs3bmTTpk04OTlpRbB27dpoNBp27tzJ1KlTCQsLIzU1lbCwMP35ZC9A19PKTYwyjycnJ6PRaF68YC6YmJjkKqYF7XkKgkBUVBTXr1/nxo0bXL9+Xfu4f/8+VatW1RPDzEfZsmVf+CbYpEkTLCws2L59e1aj5JclNBQWLhQ9lrAwhPR00gGFqysm7duLkxbq1oWjRyEwkFs3b7JlyxbeffddypQpw6JFi3gcE4MJ0BAog5gdmrlrp7SxoaKbG9a2tqTWr0/wlSucPHmScuXK0bx5c6pVq5b7fTo4QOfOYkuvPH4PUVFRNGjQgCNHjuQt+hs26JUj7N69m1JWVjR1dRW9udKlxSSbjH/3//3vf4wfN46Nf/yBf9WqmDo5Qe3aKG1t+fmPP/j4k0+y9k47dBDDs1u3ate/desWO3fuZOzYsVl/SyYmYgPvPDx+QRDw8PBg3rx5YgZuAbFt2zZGjBjB1q1b8fHxKbDrGAqlUkm9evX47bff8PPzM/j6s2fP5uzZs6xfv97ga5cUiqTwXYyIw3/JSVKUWZ/m1SnPiD/+L8k3TqJ+FovczBLzSnWw9+6PecXa2vMsTOSsH+Wt17lFo9Fw/PhxNmzYwKZNm3BwcKB///7069ePunXrcvz4cZYuXcq8efOwscl9L1Eii7S0NG7dupVDEK9fv45ardYTxMzva9WqpQ21JSYmYmVlZdABwFOmTGHlypX8/fffOd+Eb9+GTZu4euYMu3btYujQoTg4ODB37lwSk5IwBRohhjgVQMPq1dHExREdF0e8iwt1e/fG2toalUpFaGgox44dw9ramo4dO+rPptOlZk1RAHNJchg4cCA1a9Zk1qxZed/QuXOwfbvYZ/PxYyIvXiQ+MjIrfJaWJoqXhwfY2zP3558Z6e1N2PHj1LKzw9zREcqW5fHjx9yOjqZJp05QsaL4mvffhzVrtOULaWlp/Pnnn/To0UN/snqbNtDq+WlEf/75JwcPHmTjxo3PPe91CQgIYMiQIaxfv75YZHvu3LmTSZMmERISYvAPpUlJSdSoUYO9e/caNKu2JFEkhQ/0e3XmFwVqVKfXs+2XiVkZcNnQaDScPHmSjRs3snHjRszNzenatSvdunXD19fX4DU4JY3Y2NgcYnj9+nXCw8MpV64c7u7uNGrUCC8vL7y8vPL2nF6SP//8kwULFvDee+/lOpiYxETYvJmQrVvZt28fQ4cORaPRsGTJEpQqFSZATcBZoaBl8+bIFArSTUy4deMGJ6Kjqd2yJU2bNsXExASNRsOFCxc4dOgQ1apVo127drl7rgqFmP3p6wsZCUABAQGMHTuWS5cuYfm8rNDYWNHbio4GxPFZFy5cwNvbW3w+ORlBoSAJuF+pEpd27OD/7Z13VFNJG8afEDoISJEuKIIIiqiggl0RECv23l377ura26pr11XX3nsXe1dsrF1BBVQEUUBAEOklhJT3+4OPrEgLEJrM75x7SO6dOzM3Cfe5M/OWTtbWSP74EbpKSlDT1QX09fH27Vtoamr+J9AtWmSnYnr/XtLUlStXIBQK0bNnz//a19YGJk0qMtdeamoqzMzM4O/vn39iXxly9+5dDBgwAEeOHMnjWF/ZICK4ubmhR48emDJlStEnFJMNGzbAx8eHBdcvIZVW+IAc8QtCplCEwnrJ4QDK8lzM97CGQvhTTJkyBTt37izS2ZOI8Pr1a1y+fBlXrlzBu3fv0LFjR3Tr1g0eHh4Fr+cwio1QKER4eDjevHkDPz8/+Pn5wdfXFzweD02bNpUIYbNmzVC3bt1ii+G5c+ewdOlS2Nra4siRI/kXIgKePMHLdetw5+ZNDB8+HOHh4bhx4wYEQiHkOBwYGxmhf8+eqKGrm/3DEomQ/O4dfJ8+xbvUVHRwdUWDBg3A4XCQlZWFhw8f4tmzZ2jWrBnatGmTv4VrjRqAqyt4FhZo2KgRtm7dCnd398Iv6MoVYOtWiQsHEeHRo0do1qwZMjMzkfjlC9Li45EgEiFKVRUGGRngAjDlcKCqqIgaenpQMjPDkydP0Lx58/8e6GrWzLb2/L9Qh4eHw8vLC5MnT87tNzpqlMQqtCgmT54MPT09LF68WKrypeHhw4fw9PTE3r170b179zJvrzQEBgaiY8eOeP/+vUwNxIDsB6F69erh4sWL/63dMqSmUgsfAPhHJmHbvQ+4+z4OHGQ7p+egLC8HAtChvh4mta8nmd588eIFPD09MWHCBMybN0/qm2hcXByuXbuGK1eu4ObNm7CwsEC3bt3QtWtXNGvWTKZTc4xsYmJi4OvrC19fX4kYpqWloWnTprkE0cLCotDP/+nTpxgzZgyIKK97wI98/Yqnc+bgwenTGDp0KO7cuYPg4GB4enoiISEBz58/h4uLS+7wXiIRPgcE4N6DBxCqqsLN3R1G/3c7SElJwd27dxESEoJ27doV+Fs58+IFbnC52HXhQuH94/OB1auB4GAgMhJCoRCJiYkICQ4GVygER04OIrEYNZGdj1BoYgL5yEgoIts6FQAUAEQByJKTQ526daGtrQ0VRcXs5LvGxoCVFQQCAXbs2IHOnTvD2vq/5QI0b57trC4lvr6+6NevH0JDQ8slotHz58/RrVs3bN26FX379i3z9krDxIkToaysjA0bNsi87i1btuDGjRv5+sUyCqfSC18O8Wl8ePlFIuhLKlIyBdBQVoC1YQ30bWoCHfW8T9nR0dHo1asXLCwssG/fvsKnlfJBIBDg4cOHuHLlCq5cuYKEhAR4eHiga9eu6Ny5c+4IGAyZ8vXr1zximJycjCZNmuQSQ0tLS4nAfP78GU5OTkhISMC3b99ym+7nh0gE70WL4LdpEwb+/6bdvn17cDgcxMTE4MKFC1BTU0P37t1z+amJRSK89vXF7X//hUXdunBxcZFYqcbExODmzZtISUmBq6srLC0tJUIQFxeH/fv3Y8KkSdBwdQU6dix4GjEyEinr1+OTnx9Efn5IT02FDocDJSJwkW11mgXAEEAkAC1HR8Q+fw4dADnjClVk+yKKASRxOEgDoM3lQkFXF1r16kH///6USUlJuSO0aGllT3EWY8qfiGBra4tdu3ahdevWUp9XGl6/fg13d3esW7cOQ4YMKZc2S0JcXBxsbGzw4MGD/zJsyIjMzExYWVnh9OnTaNGihUzr/tmpMsJXEng8HsaOHYuQkBCcP39e8oReEj5+/CgRwYcPH6JFixbo2rUrunbtKnGVYJQdcXFxEhHM+RsfHy8RQ3t7e4lT9c6dO6W+EVzcvh1PZ8/G1MGDc01ti0QiPHz4EE+ePEGnTp3QtGnTXKMZfmYm7j55Av9nz9C+fXs4ODhATk4ORISQkBDcunUL6urqcHNzg76+Pg4cOABbW9v/IpHUqgV4eubx2QOA9UuWIG3JEihwuWghFEIO2RanOXFwopEdks0QQLycHPR69MDrS5dgJRIh5xFQEdnimIHvfBORHdw7Wk4OzsOGwcvLCxMnTswdKWf48Nz5+aRk5cqVCAsLK1f/srdv38LV1RVLliyp1Fkd1q1bBx8fnzIJYr1z506cO3euTFwnfmZ+auEDsp9GV61aha1bt+L48eO5Q0OVkLS0NNy+fVsihGpqahIRZAYy5Ud8fLxkvfD58+c4e/YslJWVYWdnh3HjxqFdu3awsLAocvrtzIkTODNxIv7u3z9Pws+vX7/iwoULkJOTg5ubWx4Djq9fv+Ls1auQz8pCtx49JOIpFovh5+eHe/fuQVtbG1lZWfjll19yT4HKyQHt22f7/323PyI8HCsbNYJBaioaITtgNgBoIntEF45sp3sDAGkAzKdMwc3du9H0O6d1DrJ9EmP+/9oY2WHYeHJyMOvXDzfu3kWrVq1yWwU2awaUcN0sIiICTZo0QVRUVLnGmA0JCYGLiwtmzZqFyZMnl1u7xYHP58PW1hY7duyASykT+P5IVlYWrKyscPToUbRq1Uqmdf/M/PTCl8P169cxcuRIzJ49G7///rvM1iKICK9evcKVK1dw+fJlBAUFoVOnTujcuTPatWsHa2trlsmhnMgZ/eVEKrl//z4AoF27dpKtfv36+X4f586dw8px43Bm2DCY/hClRSwWw9/fH3fu3EHt2rXRqVOnXMYKRATf169x89YtONrbo127dpKHn8TERGzbtg1cLhfu7u5o3Lhx3vZNTLJHf9/FNg319cXBNm1Qm8dDve+K1gCQiuzRmwGAdA4HNgsX4vS6dWiRkYGcf2YBgC/InurURfaIL5LDgZGrK6L4fERFRWHQoEH/9UVDI9uKtBQBkDt27IjJkyejT58+Ja6jJHz69AmdOnXC5MmT87forQScO3cOixYtwsuXL3PHQJUBe/fuxbFjx3D79m2Z1vszU22EDwDCwsLQt29f1K1bF3v37pU6N1xx+Pr1K65fv47bt2/j/v374PF4aNu2reTGa2try4xkyggPDw906NABJ06cgK+vL4gIoaGhuH//vmTj8/m5vg8bGxvJ93HhwgVMHTcOt2fMgGU+eRuzsrLw+PFjPHnyBE2aNEHbtm1zjW7SUlNx+fZtxIaFwaNrV1haWuLChQtQVFREkyZNcP78edSoUQPdu3fPu0asoJDtWO7oKHF8f3f/Pi66uqJFPgHWVZAdVDtdWRm2s2dj/4YN6JiSIhG+nCnOnHI8AGJnZ+g1bowDBw5gwoQJufswdGi272Ep2L9/P86fP48LRRnvlAGRkZHo2LEjhg8fjgULFpR7+0VBROjcuTO6du0q80zzAoEADRo0wJ49e6qEj2NloFoJH5C9IPzbb7/Bx8cHZ86cKfOwP+Hh4bluvElJSWjTpo3kxmtnZ1ficGaM3IwdOxZNmzbFzJkz8fXr17xZHpD98PP995GSkpLr+wgPD8e4ceNwa9MmNI6OzpUeKIfU1FTcvXsX79+/R9u2beHg4JDrO/wYEoLrV69Cu0YNRCUmYsqUKVBSUoJIJMKDBw/w7NkzdOrUCU2aNMk7+rOwAHr2lMT99L9+HR+6dYP2D6HZVAHUAhBrZoYWI0diy5YtaBkfjxx3+QxkG8EYIdvCM8XaGrb9+mHv3r0SAyEJ9vZAr17F+7DzISUlBaampggNDZV5dgJpiImJgYuLC3r27Illy5ZVupmWkJAQODk5wdfXt1gRoqTh0KFD2LNnD+7fv1/prrsyUu2EL4cDBw5g5syZ2LJlCwYMGFBu7UZFReW68cbGxqJ169aSG2+TJk1kPhVSXVi0aBG4XC6uX7+OlStXSvX0GxkZmev7iIuLg5WVFd68eYMt69djqJkZuE+fZqfv+YHY2FjcvHkTSUlJ6Ny5c65p1MzMTOz95x+oiERo2qYNGrduLTkWGxuL8+fPQ1VVFT169Mib3UBZOdudoFEjgMPBy717EfPLL1D5LuydKpA9MuzcGc2dnLB582aoCoVokZICdWTnKAQANQ4HKUZGaDR6NB4/eYKQkBAMHz78v5tjjRrZVpwySLEEAIMHD0arVq0qbL3t27dv6Ny5Mzp06IC///670onA8uXL8fjxY1y6dEmmfRMKhWjYsCG2bNki83XEn5FqK3wA8OrVK/Tp0wfdu3fHmjVrKsQoJSYmBj4+Prh//z58fHwQEREBZ2dniRA6ODiUefqjn4UdO3bg5cuXUFNTg56eHubOnVvsOr58+QIfHx8cPnwY169fh7KyMjzbtcNoIyM4aGjkOz3+4cMH3Lx5E6qqqnB1dYWRkRH+/fdfREREwMXFBU/OnoW6UAg7Dw/omZkBiYkQpaXh1OXL+JyWhk6urnmsRgFkpw7q1g1QVcXdU6fgM2QIjIVCCJDtxqChqIj+AweiTp062LhxIwwNDfExKAj1kJ1uiTgciExM4DZyJBISErBv3z6MHTsW2tra/7UxaFB2XFEZce3aNSxZsgRPnjyRWZ3FJTExEe7u7mjWrBm2bNlSqZYWsrKy0LRpU/z555+53UhkwPHjx7Fp0yY8evSo0gl+ZaNaCx+Q/U8yfPhwJCQk4NSpUwXHXiwnvn37hn///Rf379/HvXv3EBoaipYtW0qE0NHRsUpkZq8ILl68iN27d2PEiBE4ePBgqR17b968icGDB2P8+PH4+PEjPly9iv4aGnCoWxdWVlYwMjKS3GDEYjFevnyJe/fuwdjYGGFhYRg/fjxq1qyZHSHoyRMk3rmDBlpa0DM3RyYRXvj6gicnh2gtLchraqJHjx55Q59paAD9+gGmpjh//jwGDx4MHo8HewB9uFz8/vvvUFdXx/r16+Ho6AgfHx9whUKYcDjINDLCyJEjweFwsG/fPtjb28PR0fG/uhs1AmRsiCIUCiWGRbL2WysOKSkp6Pr/ddbdu3dXquWER48eoV+/fnjz5k3Jg7Tng0gkgp2dHdatW1cmwbF/JirPo1AFUbNmTVy4cAFdu3aFo6Mj7n6Xn6wi0NXVhaenJzZu3IhXr14hIiICv/76K5KSkjB9+nRoa2ujSZMmGDt2LLZv345nz57lSupanTE0NER0dDScnZ3x+PFjlPaZztXVFSdPnsTu3bsxYMAAPI6PR4uDB/HO2BheFy5g3bp1OH/+PN68eYOsrCw0a9YMU6ZMQVxcHEQiEe7cuYOYmBhwOBzYOzrCuVUrZAoEiH75EklBQVADoCIWwzw5GSba2ti1axeeP3+eu98pKdlJeB89Qq+ePbF7926oqKhADtnJk3PWMcViMQwMDEBiMRoAUOJyMWzYMMjLy8PHxwcqKiq50/qoqWXn2ZMx8vLyGDx4cMFh48oJDQ0NXL9+HeHh4Rg+fHie/JsVibOzM3r27Ik5c+bItF4ul4slS5Zg0aJFpf7t/+xU+xHf93h7e2PYsGGYNm0aZs6cWSmnC3g8Hvz9/SWRTXx9fREcHAxLS8tc8S4bN25c7Gg1VZ2oqCg4OjoiOjoaZmZmuHXrlkyCC/j6+qJ79+5YsmQJxo0bl70zORmxR44g/MoVBAcH4/PnzzAyMoKOjg6Cg4Pxyy+/4PXr13j69Cn09PTQ0dISRjweOBwOEmJi8O39eygi290gDUAylwvTvn3h/eAB5OXl4enpmXftz8oK8PTEzkOHsG/CBAyoUQPTp08HAKxevRoTJ06E14YNsJSTQ4aWFtymTkVkZCROnDiB8ePH556mlfEU5/e8fPkSvXv3RmhoaIVPM/J4PPTp0wcqKio4fvx4pfGxTU5Ohq2tLU6cOCHTaDdisRhNmjTBX3/9VXRy52oME74f+Pz5M/r27QsjIyMcOHAg782nEpKZmYmAgIBcYhgUFIR69erlCvFlb29fdCivKoxQKISqqioyMjIwbNgwuLm5YeTIkTKpOyQkBO7u7hg5ciQWLFjw30PRp0/AjRvIiojAx48fcfHiRRARVFRUYGlpCQsLC6SmpCDt3j2oAahduza4XC4+vHkDZSJoINvBHABS5eVhNmYM/D98wOPHj9GjR4+804WamkC/ftg3fDjavnyJevLyQGIiIBKB5OSQ+f8yj3g8tJk2TRKLM1fev1I4qktDTp6+7du3yyRgRGnh8/kYMGAAhEIhvLy8Ks1SwZkzZ7Bw4UK8fPky/+DmJeTChQv4888/4efnV+EPHpUVJnz5wOfzMX36dNy6dQtnzpxBo0aNKrpLxYbP5+cSQz8/P7x9+xZ169bNI4Y/Uw5CQ0ND+Pr64syZMwgICMCuXbtkVndMTAzc3d3RunVr/PPPP/+tGxEBISF4vGoV3ty8iTFjxiA2NhbBwcEICQlBemwsOmpoQElJCampqUhPS4MREZKQHVZMF9kuBwCQrKgIq99+w7f4eHh5ecHGxgYuLi7/tZWYCJw7B3z9mp2BPp9/XwIgApCipoYXpqZw/d5qWVs7O0lvGY98Vq9ejdDQUJl+/qVBIBBg2LBh+PbtG86ePVspYu0SEXr27AlHR0csXLhQpvU6Ojpi7ty55R5MoKrAhK8Qjhw5gmnTpmHp0qWYMGFCpZz6LA5ZWVkIDAzMNTJ88+YNzM3N0aRJE1hbW0sSyH6fOLYq0axZM0m8yFGjRiEgIECm9ScnJ6NXr17Q1dXFkSNHJE/qPB4P9a2scO7vv9EsPR0ID5eckxkYiKTAQCQkJCAhIQEKIhH0kS1Q35Dtc6eN7KgsAOCnqYmuEydCLBbj/PnzSEtLQ9++fVEzOhq4cAFioRBniXAfwCsAr5EdzWUIgO9X1kQA5OTlwenVKzsbvZxcdhLaMs6bB2S7idjZ2SE6OrrSjLBEIhGmTp2KR48e4cqVKxVuyAZkzzA1adIEDx8+lKkx0NWrVzFr1iz4+/uzUV8+MOErguDgYAwePBiGhobYu3cvatWqVdFdkilZWVl4+/YtXr58KUkaGxwcjI8fP6JWrVq5sqnnbKamppX2n6lr166YMGEC3N3dUbNmTURGRsrUcg7InloeNmwY4uPjcf78eWhoaGDFihXw8/P7LxN5eDhw/z7w8SPg6wukpoKIEB0djeQPH6CKbOETIjvCigDZUVZ0AfgD+GZkhFGjRoHL5eLp06eIvXsX3UUiyP3fn9Ae2YKnDsAEQBDyCp8EeflsB/XJk7Njg5YTLi4uGD9+vMzN9ksDEWH16tXYvn07rl69+l9G+wrkn3/+wblz53D37l2ZhlJ0cnLC77//joEDB8qkzp8JJnxSkJWVhcWLF+PAgQPYs2cPPIqRq6yqkpM49nsxzHmdmJiIevXqSYTwe3GUtcgUlyFDhsDDwwNDhgxB+/btMXfuXLi5ucm8nZzRw+PHj3Ho0CF06NABT548Qb0fw35FRgJz5wKfPyMuLg5v3r6FArJHY+J86pUHEAggFoCpqSlGjBgBbkoKxNu2Qe47y8S7yBa8egDuA+iAQoQPyJ7afPOm1GHJisPBgwdx5syZMslKUFqOHTuGadOm4cSJE+jQoUOF9kUkEqFly5aYOHEiRo8eLbN6b9y4gWnTpiEwMLDSPqhWFEz4ioGPjw+GDx+Obt26Ye3atdXOajKH1NRUhISE5BHF4OBgqKqq5hFDc3NzGBsbQ1tbu8yniydOnAg7OztMnDgRc+fOhZKSUpllBiciLFu2DOvWrUPv3r2xf//+/At6eQGPHyPkzh18fvWqUB8iAYB+AFoAcAKgpamJ32rUAEVFQa6Af9V7KFr4xHJcyLVsATx8KNW1yYLU1FSYmpoiJCQEenp65dautNy9excDBw7Ehg0bMHjw4Arty6tXr+Dm5oaAgACZzSoREZo2bYply5aha9euMqnzZ4EJXzFJSkrCpEmT8OrVKxw7dgz29vYV3aVKQ85U3vejw/fv3yMiIgJRUVHg8XgwMjKCsbFxgZuRkVGpLNxmzZoFHR0dzJ49G5cuXcLmzZtx8+ZNGV5lbt6+fYsWLVpATU0NV65cyR0DM4fYWGDPHpw+dgzBb9/CANm59H5cQRUC2CQvj/uqqhCJRDBNT8d4AJOQnV+vIO5BihEfkB2W7OnTbMf1cmLw4MFo06YNJk6cWG5tFofAwEDJ9PicOXMqdB1/1qxZiIqKwtGjR2VW59GjR7Fnz54K90+ubDDhKyFHjx7FtGnTMGvWLEyfPp1NJUhBRkYGoqKiEBUVhejoaMnr77cvX75AQ0OjUHE0NjaGjo5OvjepZcuWgcfjYfny5fj27RssLCyQkJBQZpE7unbtChcXF5ibm2P8+PE4duxY/rESP33CrEaNoJqeLtmlgex1PQ6AjwAea2vDpm9fdO7cGaampjA1NYXunDmQP3y40FHiPUgnfMTlgjN+PLB1a7Gvs6ScOXMGO3fuLNOHj9ISFRUFDw8PODs7Y/PmzRUWKzc9PV3iBiKr6XmBQAALCwucPXs2dwCDag4TvlIQFhaGYcOGQVFREQcPHsyTpJRRfMRiMeLi4goVx6ioKGRkZMDAwABaWlrQ1NSUbGFhYeDxeBgwYAA0NTXx559/YtGiRbC3t89VTk1NrdRP997e3pgwYQLevn0LRUVF+Pj4oG/fvvjnn38waNCgPOWXLl6M7WvWgHg8pCM7kPSP/3zq6uqoVasWlixZggEDBkDBzg4ICiq0H/cg5YgPABo0AN6+lfIKS096ejoMDQ0RERFR4eu/hZGSkoK+fftCSUkJJ06cyDezR3lw/fp1TJo0CYGBgTKzql6/fj2eP3+O48ePy6S+nwEmfKVEJBJh1apV2LRpE7Zs2VKpLNh+ZjIyMhATE4Pk5ORc282bN/HmzRu4uLggKSkJt27dgpqaGmrUqJGrHJ/Ph4aGBjQ1NfOIZ44wcrlccLlcyMvL53ktJyeHNWvWoFu3bmjevLnkeHR0NNauXYuOHTti0KBBUFBQkJwTEhKCWbNmIf27UV9BKCkpgcvlIjkzE/Li/Mxg/uMeiiF8iorAd5nay4MePXpg4MCBFb6OVhQCgQDjxo3D27dvcenSJejr61dIPwYPHgxTU1OsXr1aJvWlpKSgTp068PX1hbm5uUzqrOow4ZMRz549w5AhQ9C6dWts2rSpTJLcMorm7NmzOHz4MM6dOwcA2LVrFx4+fIiDBw/mKicQCJCSkpJHOHO29PR0iEQiiEQiCIXCPH8DAwPx5s0bdOvWDWKxONex9PR0PHz4EMrKypLgB0KhEMnJyXj16hVE+aQ4+hE5OTlwOBwIpSh7D8UQPg4HKEJIZc3+/ftx9epVnD59ulzbLQlEhMWLF+PIkSO4du2aTELeFZfY2Fg0atQIN2/elJkNwaxZsyAQCLBhwwaZ1FflIYbMSE1NpbFjx1LdunXp0aNHFd2dasmtW7eoY8eOkvf+/v5kaWkp0zbS0tLI2NiYnjx5UmAZHo9Hw4cPpyZNmtDnz5+JiCg4OJjU1dUJ2TOc+W5cLpeUlZVp9OjRFBMTQ6SoSJQdG6bA7e7/zx1SRDkCsusrZ75+/UoaGhrE4/HKve2SsmfPHtLX16eHDx9WWPuOjo4kFAplUt/nz5+pZs2alJCQIJP6qjrMIkOGqKurY/fu3Vi3bh08PT2xYMECljmhnNHQ0EDKd1nTbWxsEBsbi7i4OJm18ffff6NNmzZo0aJFgWWUlZVx4MABDBo0CC1atMDTp0+hrKxcaNR8VVVVuLu7w9/fH3v37s2eaqtbV2b9BpCd4b2c0dPTg729Pby9vcu97ZIyZswY7N+/Hz179sTZs2fLvf3Ro0dDVVUVW7ZskUl9JiYm6NatW6UJIVfhVLTy/qxER0eTp6cnWVtb07///lvR3ak2vHv3jqysrHLtc3V1pQsXLsik/ujoaNLW1qaPHz9Kfc6lS5dIT0+Ptm7dSsrKynlGeWpqauTo6EjPnj3Le/LEiSTmcmUy4hNzuUSTJsnkcyguGzZsoDFjxlRI26XB19eXjIyMaOPGjeXe9vv370lHR4fevXsnk/pevXpFRkZGxOfzZVJfVYYJXxnj5eVFhoaGNGnSJEpOTq7o7vz0REVFkYGBQa59S5YsoRkzZsik/jFjxtDMmTOLfV5AQACZmZmRnJxcLsGrW7cuXbt2jcRicb7n+R85QhkcTh4ROwfQiP9vbv+vr+53+/7IR/iyFBRI4OdX2o+gRHz69In09PRkNnVXnnz69IkaNGhA06ZNI5FIVK5tb9u2jRwcHCgrK0sm9XXu3JkOHDggk7qqMkz4yoGEhAQaM2YMmZqa0qVLlyq6Oz81qamppKqqmmvfgwcPyN7evtR1v379mmrVqkWJiYklOj8qKkqyjqejo0MHDx4sUAhSU1Pp999/JwMDA/pqaUmiH0Z9fxayTgiAzH4QPZGcHPlraFDDhg3p5s2bpfgUSo69vT35+PhUSNulJSEhgdq2bUt9+/Yt17VKsVhMXbp0oYULF8qkvhs3blDDhg0LfNCqLjDhK0du375NdevWpYEDB1JsbGxFd+enRCwWk5ycHAkEAsm+rKws0tTUzDYWKQWurq60adOmUvXN3t6emjdvTra2tvTp06d8y12/fp3Mzc1p+PDh9O3bN6LQUCJV1aINVwrbVFVJHBpKZ8+eJQsLC/Lw8KC3b9+W+FpKwuLFi2natGnl2qYs4fF41L9/f2rVqlX291JOREdHk76+vkwM5sRiMdnZ2dG1a9dk0LOqCxO+ciY9PZ1mzJhBtWrVokOHDlX7J6+yQFNTM4/1Wq9evejIkSMlrvPatWtkZWUlkyknsVhMGzduJAMDg1zrv/Hx8TRs2DAyNzenGzdu5D7p5EkiFZUSiZ5YRSX7/P+TmZlJ69atI11dXZoyZQrFxcWV+pqk4fXr11SnTp0q/ZsXiUQ0Y8YMql+/frHWeUvLmTNnyMLCglJTU0td16FDh6hTp04y6FXVhQlfBfHixQtq3Lgxubm5FfjkzygZpqamFBYWlmvftm3baPjw4SWqTygUkq2tLZ0/f14W3ZNw/fp10tPTo3379tG9e/fI1NSUfv3114JvbidPEqmq5pn2LGgTcDiUBtCm1q3zFey4uDiaPHky6erq0po1ayg9PV2m1/cjYrGY6tSpQ69fvy7TdsqDzZs3k6GhIT1//rzc2hw5ciSNGzeu1PXw+XwyNjYmvwpa760MMOGrQLKysmjFihWko6NDGzdurJIL/5URW1tb8vf3z7Xvw4cPZGhoWKLRxpEjR6hVq1ZlMlIJCAggbW1tUlVVlc7yNDSUyNmZSEWlQGtPMZdLpKJCn83MqG+zZqSpqUnt2rUrcHru7du31Lt3bzIyMqJt27aVqdXf9OnTafHixWVWf3ly9uxZ0tXVLbd1++TkZDI3N6eLFy+Wuq41a9bQkCFDZNCrqgkTvkpAUFAQtWnThlq0aEGBgYEV3Z0qj5OTEz148CDP/jp16lBAQECx6hIKhWRlZUXe3t6y6p6ET58+kZOTE3Xs2JG6du1KzZo1k376zN+fPvfsSZ9UVLKd0jmc7L8NGmS7LPj7086dO2nMmDHUo0cPatq0KVlYWBS6rvfs2TNydXWlOnXq0KFDh8rkQczHx0cmhkaVhcePH5OhoSGtWLGiXKZwfXx8yMDAoNQ2AklJSaStrU0REREy6lnVgglfJUEkEtGOHTtIV1eXFi1aRJmZmRXdpSqLm5sbXb16Nc/+8ePH099//12suo4cOUKtW7eW+U3txIkTpKenR+vWrSORSCRZ99PT05N6SnX79u00duzYAo+fOnWK+vbtS4mJiVS3bl2aNGkS6enp5fvZfM/du3fJ2dmZbGxs6OzZszK9dqFQSHp6euW6PlbWREREkKOjI/Xt21cma3BFMXv2bOrRo0epv5fp06fTH3/8IaNeVS2Y8FUyIiMjqWfPnlSvXj26dOlSlTYEqCj69etHJ06cyLP/zJkz5ObmJnU9ZTHaS0tLo9GjR5OlpSW9ePEiz/HHjx+TmZkZTZ8+vUhDmt9//53WrFlT4PGbN29KjBh8fX1JV1eXDh8+TIaGhvT3338X+tsSi8V0+fJlaty4MTk4ONDNmzdl9lscM2YMbdiwQSZ1VRZ4PB6NHDmSGjZsSB8+fCjTtvh8PjVu3Jj27NlTqnrCw8NJW1ubkpKSZNSzqgMTvkrK1atXycrKitzd3SkoKKiiu1OlGDNmDO3atSvP/sTERFJXV5faD0vWoz0/Pz+ysrKikSNHFjoy+PbtG3Xt2pWcnJwKnYry8PAodF3w2bNn1KxZM8n7o0ePkpmZGT179owaN25Mo0ePLnJmQSQS0cmTJ8nKyorat28vk9iVly9fprZt25a6nsqGWCymLVu2UK1atcrcXSAwMJB0dXVLLbKDBw+mtWvXyqhXVQcmfJUYPp9P69atIx0dHZo+fXq1fDIrCdOmTaN169ble6xly5Z069atIusQCoVUv359qcoWhUgkovXr15Oenh4dO3ZM6nNWr15N+vr6BU5NWlhYFPpQFBwcTBYWFrn2LVmyhBwdHSk2NpY8PT2pdevWUq0XCQQC2rt3L5mamlK3bt3o1atXUl1HfvB4PNLU1KSvX7+WuI7KzP3798nQ0JBWrlxZpjM2GzZsICcnp1w+q8XFz8+PTExMql0YMyZ8VYCYmBgaPXo0GRgY0N69e8s9bFJV488//6RFixble2zRokU0a9asIus4evSoTCw5Y2NjqUuXLtSyZcsSrWv5+PiQsbExzZs3L9cNjs/nk5KSUqHToXFxcaSjo5Nrn1gspmHDhpGnpycJBAKaP38+mZub57GCLQgej0f//PMP6evr04ABA+j9+/fFviYior59+9L+/ftLdG5VIGfdr1+/fmW27icSiahjx460fPnyUtXTqVMnOnTokIx6VTVgwleFeP78OTk5OZGDgwNLe1QIf//9N/3+++/5HpMmfJmsRnve3t5kZGRE8+fPL5Xje2xsLLm4uFC7du0oOjqaiIhCQkKoTp06hZ6XlZVFXC43j3hnZmZS27ZtJfFLjx49Srq6usUK5J2amkrLly8nHR0dGjt2bLGtA3fv3v3Tm9OXx7pfREQE6enp5bteLC0XLlygli1byrBXlR8mfFUMkUhEhw8fJmNjYxo6dChFRUVVdJcqHbt376bRo0fne0ya8GWyGO3t2LGD9PX16fbt2yWu43uEQiEtWbKEDA0N6fbt2+Tt7U3t27cv8jw1NTVKSUnJsz8+Pp6srKxox44dRET09OlTMjY2Lvb0XEJCAs2dO5dq1qxJkydPljoYw6dPn0hfX/+nN976ft3v+vXrZdLGsWPHyNramjIyMkp0vkAgIBMTk58isIC0MOGroqSkpNCcOXNIW1ubVq5cydwfvuPkyZPUt2/fAo8XFr6stKM9oVBI06ZNo/r161NISEiJ6igMb29vMjQ0pF69etGwYcOKLG9sbFzgaCwkJIT09fUlN+TIyEhq2rQp/fLLL8VeN/ry5QvNnj2btLW1aciQIVJNnVpYWEg9xVrVyVn3W7VqVZmI/cCBA2nq1KklPv/PP/+kyZMny7BHlRsmfFWckJAQ6tGjB1lYWNCFCxd++idoabh27Rq5uroWeHzr1q0Fhi87evQoOTs7l+hzTE1Npe7du1OHDh3KNNN1VFQUmZubU+3atYtcN8wvis33/Pvvv6Snpydx7E9JSSEXFxfq1atXibIQJCYm0sqVK8nAwIC6du1aaC7KCRMm0Pr164vdRlWlLNf9EhISyNTUNG+M12L0TVtbu8zD1lUWmPD9JNy4cYOsra3J1dWV3rx5U9HdqVAePnxY6JpFSEhIvuHLhEIhWVtblyhtz+fPn8ne3p7GjBlTLhZyI0aMoL59+5Kuri7t3bu3QKFu3bo13b9/v9C6ctwcvnz5QkTZhjMDBw6kNm3alDgFE4/Hox07dlDdunWpVatWdOnSpTxGWV5eXuTh4VGi+qsqOet+jRo1kvm6n7e3NxkbG1N8fHyJzu/WrRvt27dPpn2qrDDh+4nIysqiDRs2kK6uLo0aNSpPoObqQkBAANnY2BR4PCdY8o/hy44dO1ai0d6LFy/I2NiY1qxZU24j7o4dO9LNmzcpICCAGjduTD169Mh33bJbt25SGa3kuDnkPPGLRCL69ddfqVGjRqVaRxYIBHTixAmyt7enhg0b0uHDhyWGPvHx8aShoVHtTOnLct3v999/p379+pXod3jx4sVqY+TChO8nJDExkRYsWEDa2to0derUUuehq2qEh4eTiYlJoWV+DF9W0tHeuXPnSFdXl86ePVuivpaUevXqSXz4+Hw+zZs3j/T19fP0Y+jQoXTw4MEi6/vezSFnZCYWi2nlypVkbm5e6iAKYrGYrl+/Tu3btyczMzPatGkTpaenk4ODQ5VNTltaymLdLyMjgxo1akQ7d+4s9rnVyciFCd9PTGxsLP3++++kra1N8+bNK9N1p8pEYmIiaWhoFFrmx/BlxR3ticViWrNmDRkbG5drahqi7NGYkpJSHiu+hw8fkoWFBY0YMUIS7GDKlCn0zz//SFVvjpvDb7/9lutz2LdvHxkYGNDTp09l0v8nT56Qp6cn1apVi9q0aSNxq6iOREREkIODA/Xv35/S0tJkUuf79+9JV1e3RC4O1cXIhQlfNSA8PJzGjBlDurq6tGLFCpn9g1VWhEIhycnJFero/334suKO9rKysmjs2LHUuHFj+vz5s6y6LTVfvnwhPT29fI+lpqbShAkTyMzMjO7cuUMLFy6kJUuWSF13QkICNWnShGbMmJFL/C5dukS6uroyDcX19u1bcnNzIy6XS9OnT6+Qz7Iy8P26X2hoqEzqPHXqFNWpU6fYD7s5Ri4/+z2CCV81IigoiAYMGEAGBga0adOmn9oFQkVFpUjLOWdnZ7p69SodP36cnJycpBrtJSQkUMeOHalbt27lEok/P548eUIODg6Flrl69SoZGRlR27ZtacqUKcWqPz4+Pl/xe/jwIdWqVYsOHz5con7nB4/HIzU1NZo0aRLVrFmTRo4cWSpn7KqKWCymzZs3U61atUpsmfkjv/32G3Xr1q3YkZ6qg5ELE75qyMuXL6lr165kZmZG+/btK1Wsv8qKlpZWkU+769atozFjxlCDBg2kutlERUWRtbU1TZs2rUKTBp86dYp69+5dZLlv376Rg4MDaWpqFltMChK/N2/ekKmpaYGxUEtC586d6cKFCxQfH08rVqwgMzMzat68OR08eLBELhVVmZx1v9WrV5d63Y/P55OTkxOtXLmyWOddunSJWrRoUaq2KztM+KoxDx48oLZt25K1tTWdPn36p4oBqqenJzHq+fjxI82cOTPPNNLHjx9JQ0ODWrZsWeRNJjIykiwtLYt9EykL1q5dW2BIth/x8vIiBwcH0tPTo6VLlxbrIacg8YuIiKAGDRrQjBkzZPKbWb16dS7na6FQSBcvXiR3d3fS1dXN97v7mclZ9+vTp0+p1+UjIiJIX1+f7t69K/U5OUYupQlEXtlhwlfNEYvFdOPGDWrWrBk1bdqUrl279lM4wRsZGUnWjK5du0YKCgqkrKxMrq6u9O+//5JYLCahUEhKSkpFpmX5/Pkz1atXj1avXl0eXS+SqVOnSp3P7s6dO9S+fXuKjIwkV1dXcnBwID8/P6nbKkj84uPjycnJiYYNG1aqOKRE2bkCra2t8z0WEhJCM2bMIF1dXfLw8KDLly9X6Gi7vODxeDR16lQyMzMrdSqomzdvkqGhoSTOqzQsXryYJk2aVKp2KzNM+BhElC2AXl5e1KBBA2rRogWdO3euSo8AzczMJFFN/v33X9LU1CQABIDU1NTI2tqaxowZQ0pKSgVGcSH6T/QKS/ha3vTs2ZPOnDkjVVlfX19JUG6xWEz79u2jWrVq0fTp06VeoyxI/NLT06lr167Us2fPUvniiUQi0tHRKdS4JSMjg/bv308ODg5Up04dWr16NcXFxZW4zarCxYsXSV9fn/76669SCf6SJUuoTZs2Uo/4P3/+TDVr1vxpjVyY8DFyIRQKycvLi5o1a0bW1ta0f//+KulgXK9ePUnKHD8/P9LQ0JAIX87G4XAkr/OzVoyIiCALC4tKl6jT3t5e6jW7wMDAPM78X79+peHDh1Pt2rXp0qVLUtVTkPjx+Xzq2bMnde/evVTGUv3796cDBw5IVfbZs2c0cuRI0tLSomHDhtGTJ09+ilmKgoiMjKT27dtTu3btSmz5KhKJyM3NTaqUXDl07979pzVyYcLHyBexWEze3t7k4uJCJiYmtGHDhgqzYiwJNjY2ksgswcHBpK6unkf4ftw6duwoCSMVHh5OdevWzeXkXlnQ0dGRKnksUbYlr6WlZb7Hbt++TZaWltSnTx+KjIwssq6CxC8rK4t69+5NXbt2LbExyq5du2jo0KHFOufbt2+0bt06srCwoKZNm9KePXt+2liTQqGQli1bRrVq1aLz58+XqI64uDiqXbu21Of/zEYuTPgYRfLixQvq168f6enp0Z9//lklppgaN24sWcuKjo4mFRWVIoUPAMnJydG8efOobt26lTKAslAoJC6XK/W0V2hoaKF5+3g8Hi1cuJB0dXVp8+bNRdZbmPj169eP3N3dSyR+Hz9+JAMDgxKN3EQiEV27do26d+9OOjo6NG3atJ82Xu3Dhw/J3NycpkyZUqLP+fHjx6SnpydVnFChUPjTGrkw4WNIzfv372ncuHFUs2ZN+vXXXyk8PLyiu1QgDg4OkkgjKSkppKCgIJXwASAVFZVKN72ZQ1xcHGlra0tdPjw8nExNTYss9/btW2rTpg01b96cXr58WWjZHPH7448/cgmVQCCgAQMGkKura4lyw9WtWzdP/NTi8unTJ5o7dy4ZGxtT06ZNacOGDT9dyL7ExETq168fNWrUqEQCv2nTJrK3t5fqO/pZjVyY8DGKTVRUFM2cOZO0tbVp+PDhFBgYWNFdyoOTkxM9ePCAiLKfXL9fzytqU1BQoBYtWlTKEG+FTV3mR1RUFBkYGEhVViQS0Z49e0hPT49mzJhRqGFDfHw8tWjRggYNGpRr5CEQCGjw4MHk4uJS7GnHX375RWajbKFQSLdu3aLhw4eTlpYWdenShY4dO/bTTIWKxWLas2cP6erq0q5du4o1UhaLxTRgwAAaO3ZskWV/ViMXOTAYxcTIyAhr1qzBhw8fUL9+fXTq1Ak9evTAo0ePKrprEhQUFCAQCAAAXC4X8vLyUp8rEAjw8uVL2Nvb4+PHj2XVxRLx7ds36OjoSF1eQUEBQqFQqrJycnIYM2YMAgMDERMTA1tbW1y9ejXfstra2rh79y6EQiFcXFwQFxcHAJCXl8ehQ4dgYGCAbt26IT09HRcvXsTTp0+LbL9Dhw7w8fGR+toKg8vlwsXFBQcPHkRkZCSGDBmCgwcPwtjYGKNGjcKdO3cgFotl0lZFwOFwMGbMGPj4+GDLli3o378/EhMTpT539+7d+Pfff3HgwIFCy5qYmKB169Y4efKkDHpdiaho5WVUfTIyMmjbtm1Up04datOmDZ0/f77EptelzQKQg4uLS65oLNIYt/y4ycnJkaamJj169EgmfZIFFy5coK5du0pdPiEhgbS0tErU1s2bN8nCwoL69etXoPGLSCSSrIm+e/dOsl8oFNKIESPI0dGRFBQUqG7dukW6x0RERJCenl6ZWmhGR0fT33//Tfb29mRiYkKzZ8+ulDMWxaGkPn+BgYGkq6tbYDaGoKAgOnfuHF2+fPmnM3JhwseQGQKBgI4dO0ZOTk5Uu3ZtWr58ebHWV16/fk0AZGJJ2aVLF7p8+bLkvZ6eXrGFD/+f9jQ3Ny91f2TFvn37aMSIEVKXT0lJITU1tRK3l5GRQfPnzydtbW1asmRJgVOFOf6Bt2/fJqLs6bQ3b95IHjhUVVXp+PHjRbZXu3ZtiRtKWRMQEECzZs0iY2NjatKkCa1fv16SjLcqUhKfvyNHjpClpaUkm0cON27cIDU1NdLV1f0pjVyY8DHKBF9fXxo7dixpaWnRoEGDJNFSCmPq1KnE5XJJVVWVdu/eXar2e/ToQefOnZO8r127di4xK2rNT11dnYyMjGjjxo15bgoVyZo1a2j69OlSl+fxeKSkpFTqdj9+/Ej9+/cnU1NTOnz4cL6jtzt37lCtWrVo3759dP36dclnnfOZGhoaFulAPWjQoHL3HRMKheTt7U0jRowgLS0tcnd3p6NHj1bJ9cCS+PxNmDCB+vTpI/n/3Lx5s8QKWkVFhcLDw2nhwoVSh8mrCjDhY5QpiYmJtHHjRrKysiI7OzvasWNHvv6AQqEwV3QVFRUVOnHiRInb7dOnD506dUryvn79+gSAlJWVycjIKF+x43K5xOFwqFOnTnTz5s1KGblm9uzZtHz5cqnLCwQC4nK5Mmv/wYMH5OjoSI6OjhLjoe8JCgqiunXrUo0aNfKdOt60aVOh9W/ZsoXGjBkjs/4Wl7S0NDpy5Ai5ubmRlpYWDRgwgI4fP16pHn6Korg+fzwej5o1a0Zr166lcePGkaqqaq4HwCNHjlBwcDDp6+v/NAHtmfAxygWxWEy3bt0iT09PqlmzJk2ZMoXevn0rOX7jxo08N0sVFZVc05XFYdCgQXT06FHJezMzMwJAc+fOJQMDgzyjO3V1dfr1119JS0uLIiIi8tQnEokqhRiOHTu2WNm1xWIxAZDpuplIJKLDhw+TiYkJ9e/fnz59+pTr+ObNmwscScvLyxfqfP/y5UuqX7++zPpaGmJiYmjXrl3k4eFBNWrUIDc3N9qxY0exYl5WJA8fPiQzM7Miff4EAgE1aNCAuFwuKSkp5fnOckL6tWjRQqb5GCsSJnyMciciIoIWLlxIBgYG1KFDBzp9+jT16tWrQJ+64kSWj0vNpO33PpDzjF3UZdUF+u2EH22/94F69h9Cq1atoqioKJKTk5OsO1lZWdH+/fslN4YRI0bkyVgeHh5OLVq0IACl9jMrLZ6enuTl5VWsc+Tl5UsdSDo/0tPTacmSJaStrU1z5syh5ORkEggE+d48vxc+CwuLAqcRhUIhaWhoVLogCSkpKXTq1CkaPHgwaWlpUcuWLWnVqlUyM8YqK6Tx+Zs+fXqh0/4mJiZElP1AM3jw4PLsfpnBhI9RYfD5fDpx4gS1atWq0H88NTU1iTN6QSz5e2uRhiocjhzNWJk9GunatWu+MR4vXrxI7dq1I6Ls0dKBAwdITU2NuFwu1ahRo8ThomRFmzZtivUgQESkrKxcIodyaYmMjKQRI0aQgYEBNWvWTCqDoU6dOhUY29PV1ZUuXLhQZv0tLXw+n27cuEETJ04kQ0NDatCgAc2dO5eePn1a4TMC+SEWi2n37t2ko6OTx+fvyJEjRX5fioqK9PXrV4qLiyNNTU1KSUmpwKuRDUz4GBXOwYMHc60r5LfVqFGD/P398z3/8ONPZD5uC2m2HkSarfJuymZ22aNHC0eqv/AqbbpWsHUaj8cjTU1Nevv2Lbm7u5OamlquG3ZFZ2mwsbEp8HMoCHV1dUpOTi6jHv3H7t27pbKUVVFRIVtbW/L09Mx3zWjJkiXFCqZckYhEInr69CnNnTuXrK2tycjIiCZOnEg3b96sdMHd3759S3Z2dtS3b19KSEigffv2SRXYQUNDg86ePUtE2YGrpQ0mXplhDuyMCmfbtm3IyMgotExqairatm2L4ODgXPuPPAnD8qvvQDrm0Go9BFpt8m5iAR8AoG7vjkyBGNseRePIk7B821FWVkajRo3QrFkz3L59G+np6ZJjAoEAgYGBpbvYUhIfHw9dXd1inVMcJ/aSkpSUhOnTp0tVlsfjISwsDKmpqRg1alQeR3K75q1wPVyE30++xOiDz/H7yZfYcT8U8Wn8UvXxw4cPaN68Ofbt21eqer5HTk4OzZs3x4oVK/Du3Tvcvn0bZmZmWLRoEQwMDDBkyBCcPn0aSUlJMmuzpDRo0ABPnz6FkZERLC0tMXr0aBBRkeelpqbC29sbADBs2DAcPny4rLta5nBImitnMMqIqKgoWFhYgM+X7qamo6MDPz8/1K5dG68/J2Hg7ifgCUQFls+KC8OXvVPAraED44n7wJHjAgBUFLg4+UtL2JloScqmpqZi4sSJOH36NLKysvKtz8HBAc+fP5eqr2KxGGlpaUhJSZFsycnJSElJQUZGBkQiEUQiEYRCoeR1Qfvk5OSgpKSEBQsWYOPGjVBXV4eSkhKUlZUlf79/raGhAW1tbaipqUFfXx+BgYGoVauWVP0uCYsXL8aSJUukLq+srIzffvsNjx8/ho2NDbZt2wafgE9Y+M8++D28g6yvYRCmxgNceSjqmUOrcWdo2HdGB2t9TGpXD41NtaRuSywWY+PGjViwYAEyMzMxcuRImYpfQURHR+PSpUs4f/48Hjx4ABsbG7i4uMDFxQVOTk5QVlYu8z4UxJ49ezBu3Dipy1taWiI4OBg8Hg/GxsYICAiAsbFxGfawbJE+jhODUQYcOXIEHA5H6vLx8fGwtrZGeHg4tt4LR6awYNEDgLSX1wEA6nauEtEDgEyhCNvufcCOoQ4AgAcPHqBv375ITk4uUPQAIDQ0FPfv38eXL19ybV+/fs0jcOnp6VBTU4OGhkaeTVVVVRJKjcvl5try2ycWi/H161dwuVy8ffsWmZmZyMzMBJ/Pz/Oax+MhNTUV8fHxEhFt06YNDAwMoK2tDR0dHejo6OR6bWxsDHNzc+jp6RXr+8jBzMwMKioq4PF4UpXPzMzExo0b8f79e/Tv3x+DF23DXb8gxF7dAq66NpRqN4JKfT2I0pOQEfwYsVf+QeqH57jhORc+wd8w38MaQ1uaF9nOx48f0b9/fwQFBUn69v79+2JfX0kwMjLC+PHjMX78ePD5fDx+/Bje3t6YO3cu3rx5AycnJ7i4uKBTp06wt7cHl8stulIZIBaLsW3bNsjJyUkdti0sLAwpKSnQ0NBA7969cezYMcycObOMe1p2sBEfo0KpU6cOwsLCcu1TVVWFgoICxGIxeDweFBQUUKtWLZiYmMDExAQcDgcrN2yB29Zn4AsL/scVC/iI2jIc4iwejCfuhbyGXq7jSvJyuDetNVYvXYhdu3ZJfdN2cnKCiYkJDA0NJVutWrWgpaWVS9zU1dVlejP7/PkznJycEBkZKfU5PB4PlpaW2Lt3L5SUlJCQkID4+Phcf799+4aoqCiEhYUhIyMDZmZmMDc3h7m5OerUqSN5bW5uDl1d3TzCKBQKYWZmhujo6GJfU8+ePdHl1xX4+/YnJH98DRJkQqWeIzic/1ZhRGmJ+HJoOkQpcdDtNRdq1q2goiCH+R4NChQ/sViMrVu3Ys6cOcjMzMx1gzcyMkJUVFSx+ypLkpKScP/+fXh7e+P27duIjY1Fx44d0alTJ7i4uMDCwqJEDyBFERcXh4kTJ+LatWtFLi98T40aNXD69Gm4ubnh/v37mDp1Kvz9/WXev/KCjfgYFUZKSgoSEhKgr68PY2Nj1KlTB1ZWVqhTpw5MTU1Ru3ZtmJqaokaNGnnO3XE/tMj6M4IeQMxPh4qFYx7RAwAOAId+kxF9R/o1ixo1amDfvn2wtraW+hxZkZmZCRUVlWKdo6KiAiUlJdSrVw8WFhZFlk9NTUV4eDjCwsIk29OnTyWveTxeLiE0NzfH58+f8eXLF8jLy4OIwOFwQNmGc5ItPxo0aICBk2Zjyb0IZIkBFfPG+ZbjqtdEDfsuSPI5BH5EANSsW4EnEGP51SDYmWjlmq4GskcnAwcORGBgYL43969fv0r6WVFoaWmhZ8+e6NmzJ4DsKf/bt2/D29sbf/31FxQUFCQi2LFjR+jr68uk3UOHDuHMmTNSl1dTU0N6ejpSU1Nx69YtuLm5oU2bNkhOTsb9p354l6mJoJgUpGQKoaEsD2sDDfRrZgIddSWZ9LesYMLHqDA0NDSQnJxconODYlIKHe0BQNqr/09z2rvnezxTKIZz1/5QMQYuX74MgUCAjIyMQqd/OBwOPnz4UGHCV5J1IXl5eUmmiqKoUaMGGjZsiIYNG+Z7PDU1NZcohoWFISgoCMbGxoiPj4ecnBwMDAygr68PfX191KpVC7q6upLp2pw1y5xsDndiFYqcrgYA5IycC5muJiLs2LEDM2fORGZmJkSi/OuVl5dHTEwMDA0N8xwTi8XIyMhAeno60tLSkJ6eLtl+fP/9vpzvRlVVFaqqqlBTUyvWa2NjYwwfPhzDhw8HESEoKAje3t44efIkJk6ciNq1a8PFxQXt27dHixYtSiSEYrEYa9eulbq8goICmjdvjrS0NDx//hwHDx7EunXrEBCVAq5ZU3QZMAqChGiIeCngyCuCq1ELGtZOWOfQHZ2aWBR7LbY8YcLHqJKkZBZupZj1LQL8qHfg1tCFioVDgeU0dPSx99AhiMViPH78GIcOHcKpU6cgEomQlpaWZ7SSmZmJkJAQmVxDcSmp8MnSqrNGjRpo1KgRGjVqJNk3adIkKCgoYNSoUWjSpAk+fPiAgIAA+Pv74+nTp3j//j1MTExgZ2eHRo0aSf5q1DJGm7X3UNRiC4lFSA+8AwBQqdv0v/0E3H0fh/g0PjISv2LgwIF4/fp1Lkvc/BAKhejWrRvk5eXzFTAVFRWoq6tDTU1Nsv34PmefpqYmjIyMoKysDD6fLxHNmJgYyeuMjIxCX2dkZEBBQSFfQdTU1ET//v0hLy+PyMhIifVozZo14eTkhBYtWqBly5Zo0qQJlJQKH2W9ffsWsbGxRXzD/yEQCPDo0SM8efIEAoEA586d+78VdRA+PbwMRQMLKJnbg6umBcrKBD/6PeJ9jiLJ7xqujvi7WGux5Q0TPkaVREO58J9u2strAAB1u865jFp+JDYyDJ8/G8DExAStWrVCq1atsH37djx8+BBbt27FqVOnoK6ujvT0dIjFYmRlZeHNmzcyvRZp4fF4JR7xlaU7Q2xsLK5evYp///0XAoEALi4uGDVqFCZPngwVFRUIBAKEhITA398f/v7+2LdvH/z9/ZFl0RYarQYVWX/SvQMQxIVDxcIBKnWb5TrGATB+9X6cXzmlwBHej8jLy8PNzQ09evTII2oqKiqQkytfLy8ikojmj6KYmJiIiIgIhIeHIz4+HkQEZWVlxMTE4O7du3jw4AF4PB5SUlJgamqKpk2bol27dnB3d8+zTtiwYUPo6OggPj4+V/tycnKQl5eHqqoqUlNToaSkBAUFBYmxVNeuXREVFYX3Ij0sv/oOPIEYtaefAkdeMc+1JN4/hJTHp5D06DS4bpOw/Oo7AKh04seEj1ElsTbQgJJ8TL7TnSTMQvqbuwBHDuqNXQuuRJiFx1e9YLZwALhcLgwNDdGwYUO0a9cO7dq1w549exATE4NOnTohPDwcp0+fRmZmZoUJX3lMdZYEOzs7nD9/HqmpqQCyp43v378PgUAAV1dXjBo1Cu7u7rCxscHAgQMl5/163BcX/WMKrTvlxUWkPDsHeR0T6HT7I8/xTKEYyfLq0NXVRUJCAgAUea1ZWVlQUVFBy5Yti3upZQKHw5G4o2hra0t1TkZGBiIiIiTTzSEhIXj16hWePXuGS5cuYerUqeByuahZsybMzMzQqFEj2Nvb5+tPKBaLIRAIkJWVhZ07d6Jz584IDw9HeHg4AgMD8fz5c7z6nIjlV4PAE2T/v+UnegCgZt0aKY9PQZiYbehU2FpsRcKEj1El6dvMBBu8g/M9lh70AOLMtAKNWnJQUlaG741DEGVsxs2bN3Hjxg34+vpKMouLxWKoqKjA398fY8aMwc6dO5GcnAwtLa0KMY6oDFOd+WFlZQU1NTWJ8AGQvL548aLk83Rzc8OoUaPg6uoKZWVlpGUVvkab6nsZid67oKBbG/oDl4OrktfICQBq16uPWzEx+PTpE44ePYo9e/YgLi4OAoEgXxEUi8UV9vAiK1RVVWFtbV3gWjOPx8OzZ8/g7e2Np0+f4vbt2zh48GCBhkZEhIyMDPz666/o0qUL9u/fjzZt2kiO/3L4hVRrsRkfngEAFPTMJft+XIutDDDhY1RJdNWV0M5KD7fexeZZIyrKqAUAOBygQ329bOsz9VoYOnQohg4dCiD7JhAREYEnT57g6tWrOHLkCDZt2gR5eXnJFNCIESNgamoKS0tL1K1bN4/5v7a2tsyFsSRWnUDZT3XWq1ev0GvNEcHz58/j+vXrEAqFsLOzQ5tZewo8J+X5BSTe3g0FPbNs0VPTKrCsMjf7B1CnTh0sWLAACxYsQEBAAA4dOoSDBw+Cx+PlMVqqqHXa8kJFRUUycwEAwcHBqF+/fpHnZWRk4Ny5c7h58yaWLl2Kvn37QklTF/eD4/Jdi01+ehaUxYOYn4GsmBDwI99CQc8cmk79JGW+X4utLNaeTPgYVZbJ7evh35BvuSK3CL59Bj/ybZFGLcryXExqXy/fYxwOB2ZmZjAzM8OAAQMAZE/neXh4wN/fH4GBgXj58iUCAgJw+/Zt+Pv7o0aNGpCTk0NmZia+ffsGkUiUxwcuZzM1NYW2tjbk5Yv371fZpjqJCCkpKRCJRFL7hGVmZkJeXh62trYFTlcnP/FC0r0DUKhVF/oD/wJXVbPA+uTEQpzauR5XFz6Fvb09GjduDHt7e9jb22PNmjVYs2YNnj59iv379+PEiRMgIqSmpuLz58+luvaqhoKCgtRlxWIxUlNTMW3aNCxcuBDOYxYBNfK38k15dhbi9CTJe+W6zaDb9fc83xkHgJdfJMa3LdqlpjxgwseosjQ21cJ8D2vJgjsAKOiawmzO5ULPU5QDfm1rIvWaw4gRIzB9+nT88ccfaNCggUQMASA9PR3v3r1DYGCgZOPz+UhJSYGcnBz4fD6ioqIQHR0Nb29vxMTEIDIyEomJiVBTU8sVQaWgv5qamlBWVkZoaCj4fD4iIyNzhSmTl5cvdMSV31QnEUmiuuQYR+SEUytoS05ORnJyMr5+/SqJWJOzNipNBBAVFRUYGBjg7NmzsLe3x7c0fp7p6qSHx5H871EoGtRDrQF/FTi9Kbk2RUW8ubIfSTGf8fr1a7x69Qq7d+/Gq1evkJ6eLhHDli1bYsyYMfjy5QuOHz+Od+/eFdnfnwkzMzOpyikoKEgsTFu2bImZM2fiTHQNvH+df3AC06lHAACi9ETwI98h8f5BfNn/G/T6LoKSwX8PlplCMYK+pOZbR0XAIrcwqjw5JtaZQlGhpvEcTvZIL/3BYUTeOw53d3dMnDgR7u7uhT4Ri8Vi1KlTBxcuXIC9vb1UfUpMTMwlhoGBgQgICIC8vDwaNmwIW1tbWFhYwNjYGLq6uuDz+ZJoKj9GVklOTgafz0d0dDQyMjJQo0aNXCHKRCJRrlidXC43V6zP1NRUSQSZnH1EJAmHpqqqmiekmqamZr6h1jQ0NFCrVi1JxBp1dXUA2c7oQUFBBX4eKioqGDduHNasWZPL7P6Xwy8k09VpAbcRf2UDwJFDjWbdIaekmqceeU19qNu5SL5PNxv9AteO4uLiJGL46tUr+Pv74+PHj1BQUJCMvr+PUpPzXktLq0Kd28sKaa/J1tYWixcvhqenJ7hcLkYffI47QV+lOleY/BVRu36BQk0jGI3dlutYJ+ta2DvCsdj9LguY8DF+Cvwjk7Dt3gfcfR8HDrKfMHNQks+eguxQvxamu9vijtcBTJ8+HUQkiQozcOBAjBs3Dg4ODvneIBYuXIi0tDRs2LChxH0kIsTExEhEMEcQ3759C21tbTRq1AgNGzaURK/JmRbNEeU1a9bg27dvWLNmTa56RSJRrpidIpEoV7zPoUOHYsSIEejZs6dkn5ycnExv7r169cKFCxfy7FdSUoKWlhZOnz6dy1gih+8DjSf9exTJD48X2o6SaUMYDFkFIP9A40VBREhISMjlgP9jpBoOh1OoMJbF+m1ZU5KsHkD292o2cBHOv5I+HF30vl8h+PoRJr8ezTXl6WlvjA0D7Ivdh7KACR/jpyI+jQ8vv0gEfUlFSqYAGsoKsDasgRent0JHTRGrVq3C58+fYWlpmSsjBJfLhbKyMrS0tPDLL79gxIgRuaaHQkJC0Lp1a0RGRhZrvUQaxGIxwsLCJIIYEhIiuQl/+fIFBgYGMDc3R3JyMjQ1NTFq1CiJIY2xsXGRa4XdunXD+PHj0b17d5n2+3sWLVqEZcuW5bIaVFVVRa9evbBjx458w87lsNcnGCuvv4ewGFnSiorVWVKICElJSXmi0+SI46dPnyAWi3OJoqmpKTQ0NKSK0KKqqipzP0GRSJRvdJnvXwcGBuZ5YJKGCRMmQGTVEfcT1IuMlJTD501DIc5IgsnvJ8BVzp4RUJaXw7TOVpVmjY8JH6NaEB4ejqZNmyI0NBRaWlqwsLDAx48f8y2rpKQEDocDa2trTJ48Gf369YOmpiZat26NWbNmoUePHuXWb4FAgMjISISFhWHt2rXIzMyEiYkJPn36hLCwMHz9+hVGRka5DGm+f21kZAR3d3fMmjULnTt3LrN+HjlyBBMnTkRaWppkjejgwYOSWJQFQUQYOHAgkvQaIULbQerp6oqMCJKUlJRrlPj582eJyBQVpYXH40FJSUkqkVRUVJScX1DYtLS0NAgEglzCqqCgAC6XCw6HIwkTx+fzERsbW2jmke/R1taGkpISatasiaFjJuJAooVE+ATxnyGnpA6ues1c5xCJkeRzBCmPT0HJuAEMhv0XHk1JXg6PZnesNFadTPgY1YaRI0fC0tIS8+fPx/z587F27doirR3V1NQgEokwefJk1K9fH9evXy9WkF9ZMm3aNNSuXRvTpk2T7MvKypI4MueI4fevc+Jn2tjYoGnTphJBNDY2hp6eHvT09EpkYfojT58+RYcOHcDhcNC6dWscOXIEenoF+1DmsHLlSpw7dw4+Pj4I/pZZ4HS1srwcCNkuKJPa16tUztDFQSwWIzMzs0iBTE9PR1ZWlkQM5eXlkZmZifT0dKSkpCAxMVGSWSMmJgZRUVH48uWLJO6nsbExjIyMJK+NjY3x/Plz/PXXX0X2sVatWpg0aRL69esHGxsbALnXYlOeX0Di3X1QNrWFvJYh5FRqQJSeBP7nQAiTYsBVq4lag5ZDUbc2gKLXYisCJnyMasO7d+/Qvn17fPr0SfI6LS2tyPNUVFSwd+9eeHh4wMzMDKGhodDR0SmHHudm0qRJsLW1xeTJk6U+JzMzE46Ojhg3bhyUlJTw6dMnfPr0CV++fEFcXBy+ffuGxMREaGpqQldXF3p6epK/37/+8a+qqmquda6kpCTY2Nhg+fLlGDlypFRrYFeuXMEvv/yCZ8+e5UpqWtB0dd+mlT/qf3EQCoUSS9nExERER0cjKipKsn3/Pj09PY+Q/fje0NAQqqp5DYJyeP/+faHB1b9PPfQj36/FZsWFIfXlNfAj30KUGg9xZho4ispQqGkMFQsH1HDokcsatyRrsWUNEz5GtaJPnz5o164dpk6dCm1t7XxDOH2PiooKjh07hl69egEABg8eDGdnZ0yZMqXsO/sDkydPRoMGDYrdtp2dHQ4fPozGjfNP+yMSiSSjhxwxLOxvTmaFosRRS0sLKioqUFFRgbKycq7XERER6NixI86fPw9nZ+dSfzblDZ/Pl4jW964e0m4pKSng8/kSC1otLa1ChU1HR6fUBjVElO/6IofDwdSpU7F+/XpwuVzweDxJ+DNvb2/cuXMHHh4e6PnH2lyuQ9JQVmuxpYX58TGqFXPnzoWnpycmTJiAHj164NChQwWWVVVVxfnz53OtjY0YMQILFiyoEOHjcrlSB2L+nqIc37lcrkTEGjRoUGR9OeGtChLHsLAwyUgyJyN8zt+c12lpaZCTk4Orq6tEEPMTyPxef/9eQUFB4qLx4/a9S0dpymRlZeURLpFIBE1NzUI3Q0NDWFtbS1xDfjyupqZWLtahycnJ8PLywsGDB/Mc09DQwNatW8Hj8TBixAg8evQInz9/hqqqKjIzM5GVlQUOh4Np06bB+f/iVRzXocqanYGN+BjVDjc3NwwYMAAGBgYYNGgQUlJS8pRRU1PDzZs384xGRCIRzMzMcO3atVypecqDadOmwdTUFNOnTy/WeWZmZrh//z7Mzc3LpmPFQCQSoWfPnjA3N8eGDRtyCWJ+AlnUa4FAIHHR+H773p2joE2aMlwuF4qKihKxyhEwFRWVSu3SIBQK4e3tjUOHDuHKlSvo2LEjRowYgdGjRyMxMRFA9tQmn8+HkpJSodF3nJ2d8fDhQ8n7wlyHqspaLBvxMaodc+fOxfjx4+Hn55fLpSEHRUVFNGvWLN/o/VwuF2PHjsW2bduwffv28uhurrbLYsRXnixatEjiD5kTJaQwVwdG8ciJUXr06FGYmJhgxIgR2LRpk8SHb8mSJRLhy4mhWpilp5qaGpYvX55rn52JFnYMdajaa7HEYFQzxGIxOTk50alTp6hTp04EgACQnJwcaWtr06tXr6hVq1a0ePHifM+Pjo4mLS0tSkxMLNd+z5o1i1auXFns8zQ1NSkhIaEMelQ8Tp48SWZmZvT169eK7spPRWxsLG3YsIGaNGlCxsbGNGfOHHr79m2+ZTMyMqhVq1akqKgo+d0XttnY2JBYLC7nKyp7yjfjIoNRCeBwOJg3bx6WL1+OQYMGQU1NTbLO9fz5czRu3BheXl7Ys2cPLl68mOd8Q0NDSeqW8qQqj/g+fPiAyZMn49y5c1K5OTAKJzMzE15eXujevTusrKzg5+eHNWvWIDw8HCtXrixwrVZFRQUXL16UKu+furo6VqxYUamndEsKEz5GtaRr165QUVGRrBcZGxvD19cXdevWBQAYGBjg9OnTGDt2LN6/f5/n/KlTp2Lr1q1SBWeWFSURPvp/du/v42OWNwKBAIMHD8bChQvRpEmTCutHVYeI8OTJE0yYMAHGxsbYtm0b+vbti8+fP+PQoUNwcXGRxGQtDG1tbVy/fr1Q1wcAqFmzZplG+6lImPAxqiUcDgfr1q3D6tWrsWXLFrx48SKXLxkAtGzZEitWrECvXr3yGMC0bNkSWlpauHbtWrn1uSTCl5WVBQUFBZmHySoOS5Ysga6uLqZOnVphfajKZGRkYO/evWjWrBmGDBkCU1NT+Pn54c6dOxgxYkSJ1kgbN26MFStWFPi7UFdXx9KlSyv0d1OW/JxXxWBIQatWreDo6Ijk5OQCp9/Gjh2Ldu3aYcSIEblGdxwOB1OmTMGWLVvKq7slEr6KHu35+Phg79692L9//085ZVaWhIaGYsaMGahduzbOnTuH5cuXIyQkBPPnz5c6zVBBeHl5YcWKFXBwcMh35KesrIwhQ4aUqo3KDBM+RrVm1apVWLduncQpOz82bdqEr1+/YsWKFbn2Dxw4EL6+vggODi7gTNlSEuGryPW9xMREDBs2DHv27IG+vn6F9KGqIRaLce3aNXTt2hUtWrQAh8PBs2fPcPnyZXTp0qXUI7D09HSMGzcOc+bMwaVLl/DgwQNYW1vnClmnqqqKefPmyTwYe2WCCR+jWmNpaYnBgwdj6dKlBZZRVFSEl5cXduzYgStXrkj2KysrY+zYsdi6dWt5dLVKjfiISBIkoGvXruXeflUjMTER69evh5WVFebPn48+ffogIiICa9eulaw7lxY/Pz80bdoUAoEAL1++RPPmzaGgoIArV65AQ0NDUo7L5eKXX36RSZuVlgq2KmUwKpy4uDjS1dWl9+/fF1ru4cOHpKenl6tcREQE1axZk1JSUsq6m7R27VqaPn16sc4JDg4mCwuLMupRwRw4cIBsbW0pIyOj3NuuSrx8+ZLGjh1LWlpaNHjwYHr06JHM3QdEIhGtXbuWdHV16dixY/mWefToEamoqJCioiItWrRIpu1XRtiIj1Ht0dXVxYwZMzBnzpxCyzk7O+Ovv/6Cp6enxPnX1NQUHTt2LDT0mawo6YivvKc6P3z4gBkzZuDYsWNQUVEp17arAllZWThx4gRat26Nbt26wczMDEFBQTh69CicnJxkuhb65csXuLu749y5c3j+/DkGDRqUbzknJyesXbsWXC4Xv/32m8zar6ww4WMwAPz666/w9fXFgwcPCi03fvx4tGrVCiNHjpQkXZ06dSq2bNmSKwlrWVDSNb7ynOoUCAQYMmQIFixYADs7u3JrtyoQHR2NP//8E2ZmZti5cyemTZuGsLAwLFiwoEzWQC9fvoymTZvC2dlZqpB1kyZNQlRUlFQ+flUdJnwMBrIde5cvX44ZM2YUKWCbN29GVFQUVq5cCQBo27YtFBQU4O3tXaZ9rAojvqVLl0JbWxu//vprubVZ2Xn06BH69+8PW1tbxMXFwdvbG3fv3kWfPn1KnQcxP3g8HqZMmYIpU6bg9OnTWLx4sVTtcDgc1KxZs8hyPwNM+BiM/zN48GAIBAKcPn260HJKSko4c+YMtm7dimvXrknSupS1a4OKigp4PF6xzinPEd+///6LPXv2MNcFZBv3XL9+He3atcOQIUPQunVrhIWFYdu2bbC1tS2zdgMCAuDo6Ii4uDi8evUKrVu3LrO2qjQVu8TIYFQu7ty5Q3Xq1KHMzMwiyz548ID09PQoJCSE0tPTSUdHhz5+/FhmfTt9+jT17t27WOdcuXKFunTpUkY9+o/ExESqXbs2Xbp0qczbqswIhUI6deoUNWnShGxtbenIkSMkEAjKvF2xWEybN28mXV1d2r9//08ZX1OWsBEfg/EdHTp0gK2trVQuCq1atcKSJUvQq1cviMVijBw5Etu2bSuzvmlqaiI5OblY55THiI/+77rQvXt3dOvWrUzbqqxkZWVh3759sLGxwfr167F48WL4+/tjyJAhZTKd+T1xcXHo0aMHDh48iEePHmHkyJHVfsRdFEz4GIwfWLNmDVatWoWEhIQiy06YMAEtWrTAqFGjMHHiROzfv7/AvGalRUNDI9/cgYVRHmt8hw8fRkBAANauXVum7VRG0tPTsXHjRlhYWODEiRPYuXMnHj16hB49epRLuC8vLy80btwYtra2ePjwISwtLcu8zZ8BJnwMxg80aNAAvXv3zpOHLD84HA62bt2KiIgIeHl5wdnZGUePHi2TfmlqahZb+Mp6xBcaGoo//vgDx48fr1auC4mJifjrr79Qp04dPHjwAOfOncPNmzfRvn37chltxcTEoE+fPliwYAG8vLywatUqKCoqlnm7PwtM+BiMfFi8eDEOHjyIjx8/FllWWVkZZ86cwT///IN27dph8+bNZeLaoKGhUeypzrIc8eW4LsyfP7/auC58+fIFM2fORL169fDx40f4+PjAy8sLDg4O5dI+EeHgwYOws7ODtbU1Xr16BWdn53Jp+2eCCR+DkQ8GBgb47bffMG/ePKnKm5iYYMeOHdi+fTv4fD58fHxk3qeSTHWW5Yjvr7/+gpaWVrVwXfj48SMmTJgAW1tb8Pl8vHz5Evv374e1tXW59SEiIgIeHh7YuHEjbty4geXLl1d4nsWqChM+BqMApk+fjgcPHuDp06dSle/RowecnJxgaGiIDRs2yLw/ampq4PP5EAqFUp9TViO+Fy9eYNeuXdi/f/9Pm7oGyHYPGDJkCJo3bw5dXV28f/8emzZtQu3atcutD2KxGNu2bUOzZs3QunVrPHv2jOU1LCVla27EYFRh1NTUsHTpUsyYMQM+Pj5Srd38888/aNiwIfh8PgICAtCoUSOZ9YfD4aBGjRpISUmROrpGWYz4xGIxJk+ejFWrVsHQ0FCmdVcWAgMDsWDBAjx9+hS///47tm/fniuQc3kREhKCsWPHIisrC/fv34eNjU259+Fn5Od9VGMwZMCIESOQnJyM8+fPS1VeW1sbO3fuBJA9FShrimvgUhYjvpxR3vDhw2Vab2Xg06dPGD58ODp16oR27drh48ePmD17drmLnlAoxLp16+Dk5ARPT088ePCAiZ4MYcLHYBQCl8vF2rVrMXv2bPD5fKnO6d69O1xdXXHp0iV8+PBBpv0proFLRkaGTK0tExISMH/+fGzduvWnmuKMjY3Fr7/+CgcHB9StWxchISGYNm1ahViqBgQEwNnZGdeuXcOzZ8/w+++/g8vllns/fmZ+nl8ug1FGuLm5wcbGplgjuG3btkFBQUHmke6La+ASHx8PHR0dmbW/aNEieHp6omnTpjKrsyJJTk7GwoULYWNjAzk5Obx79w6LFy+ukGnNrKwsLF68GB07dsS4cePg7e0ts1x8jNywNT4GQwq2b98Oe3t79OrVSyrT9Zo1a2LHjh0YNmwY3r9/j/r168ukH8Wd6vz27ZvMhO/Vq1c4ffo03r17J5P6KhIej4dt27Zh9erV6Nq1K/z8/GBmZlZh/Xn+/DnGjBmD2rVr4+XLlzAxMamwvlQH2IiPwZACQ0NDrF+/HiNHjpR6ynPw4MGwtrZG//79ZdaP4k51ymrER0SYPHkyli1bVqXT1giFQuzZswdWVlZ48OAB7t69i/3791eY6PF4PMyaNQvdu3fHnDlzcOnSJSZ65QATPgZDSgYPHox69eph6dKlUp/j5eWFgIAAnDt3TiZ9KO6IT1bCd/jwYWRlZWH06NGlrqsiICJ4eXmhYcOGOHr0KE6fPo1z586VaaaEovpz4cIF2NraIjw8HP7+/hg8eDCLsVlOsKlOBkNKOBwOduzYgcaNG8PT01OqKc8GDRqgS5cuGD16NDp37gx1dfVS9UFTUxOJiYlSl4+Pj4eurm6p2kxOTsacOXNw/vz5Kmlk4e3tjTlz5oCIsGnTJnTu3LlCBeb9+/f47bffEB4ejp07d6Jz584V1pfqChvxMRjFwMDAABs2bCjWlOe2bduQkZGBadOmlbp9Q0NDfPnyRaqyAoEA6enp0NTULFWbixcvhoeHB5o3b16qesqbZ8+eoVOnTpg0aRJmz56N58+fw9XVtcJELzU1FbNmzUKrVq3QuXNnvH79moleBcGEj8EoJoMGDYKlpSWWLFkiVXkzMzP06dMHp06dwt27d0vVtpGRkdTCl5CQAC0trVK5HQQGBuLo0aOSbPNVgeDgYPTp0we9e/fGwIED8ebNG/Tr16/C3C+ICEeOHIG1tTW+fv2KgIAA/PHHHyyodEVScakAGYyqy5cvX6hWrVr07NkzqcoHBQWRhoYGmZubU2pqaonb/ffff8nZ2Vmqsm/evKH69euXuC2xWEzt2rWjLVu2lLiO8iQlJYVmzpxJurq6tHr1asrIyKjoLpGfnx+1atWKmjVrRo8eParo7jD+DxvxMRglwMDAABs3bsTIkSORmZlZZPn69evD3d0durq6mD17donbNTIyQnR0tFRlS7u+d/LkSSQnJ2PChAklrqM8oHxGVLNmzarQNEnx8fGYOHEi3N3dMWLECDx9+hROTk4V1h9GbpjwMRglZODAgahfv77UU57z5s1DZGQkLly4gDt37pSozZw1PpIi7VFpLDpTU1MxY8YMbNmypVIbtLx8+RJt2rTBxo0b4eXlhQMHDsDAwKDC+iMSibB9+3bY2NhAXl4eQUFBGDduXKX+DKsjzKqTwSghHA4H27dvh52dHTw9PYs0/mjcuDEcHBxgZmaGMWPGICAgoNhWnioqKlBRUUFiYmKR/nSlcV5ftmwZOnXqhFatWpXo/LImPj4eCxYswLlz5/DXX39h9OjRFS4uDx48wNSpU6GhoYFbt25VmxyFVRE24mMwSoG+vj7++ecfqac8582bh8uXL6Ndu3aYNWtWidqUdrqzpFOdQUFB2LdvH1avXl2S7pUpOSOqBg0aQF5eHu/evavwEVV0dDSGDh2KQYMGYfbs2bh37x4TvUoOEz4Go5QMGDAADRo0wOLFi4ss6+TkhLp166J58+a4fPlyiaY8iyN8xR3xERGmTp2K+fPnV+iUYX48ePAADg4OOHHiBLy9vbF582bUrFmzwvqTlZWFNWvWwM7ODrVr18a7d+8wcOBA5oReBWDCx2CUEg6Hg23btuHAgQNSJa2dP38+Nm3ahO3bt2Ps2LFSjRS/x9DQsMyE7+zZs4iJicGUKVOKdV5ZUtlGVGKxGKdPn0bDhg3h4+ODx48fY8WKFaUOTsAoP5jwMRgyoDhTnh07doSWlhYyMjJgZ2eHLVu2FKstaX35irvGl5WVhT/++AObN2+GvHzFL/9XthEVEeHWrVto3rw5Vq1ahS1btuDy5cuwtLSskP4wSg4TPgZDRvTv3x+2trb4888/Cy3H4XAwf/58LFu2DCtXrsTq1asRHx8vdTtltcZ38OBBWFtbo3379lKfU1Zcv34djRo1qjQjqmfPnsHFxQVTpkzJFQWGUTVhwsdgyIicKc+DBw/iyZMnhZbt1q0blJWV8fLlS/Tv3x/Lli2Tup2yWOMTCARYuXIlFixYIHU/yoKPHz+iZ8+emDJlCv7+++8KH1G9ffsWvXv3Rp8+fTBo0KAKjwLDkA3s22MwZEitWrWwadMmjBo1qtApTw6Hg9WrV2PBggWYO3cuDh8+jNDQUKnaKIs1vuPHj8PMzAytW7eWqrysEYlE+Pvvv9G8eXO0aNECgYGB6NatW4X0BQAiIiIwevRotG/fHs7OzggODsbYsWMrxRQwo/RwSBpPWAaDUSz69esHMzMzrFu3rtByHh4e6NKlC1JTU/Hq1SucOnWqyLo/ffqEDh06ICwsrMAyYrEYSkpKyMjIgIKCQqH1iUQi2NjYYPv27ejYsWOR7cuaN2/eYMyYMVBWVsaePXtQr169cu9DDnFxcVixYgUOHTqESZMmYcaMGaUO8s2ohFRkvDQG42fl69evVLt2bTpz5kyh5V69ekX6+voUExNDJiYmUsVz5PF4pKioSCKRqMAyCQkJpKmpKVVfjx8/Ts7OziQWi6UqLyv4fD4tXbqUdHV1afv27YVeT1mTkpJCixcvJm1tbZoyZQp9+fKlwvrCKHvYVCeDUQbo6enhzJkzGD9+PN6+fVtgucaNG6Nz587Yvn07li1bhhkzZhQZjkxZWRk6OjqIiooqsIy005xisRjLli3DwoULy9Va0tfXF46Ojnj8+DH8/PwwYcKEClk34/P52LhxIywtLREaGooXL15g8+bNlc6HkSFbmPAxGGWEg4MD1q5dC09PTyQnJxdYbunSpdi8eTM6d+6M9PR0nD17tsi6LS0tERISUuBxaYXv/PnzUFFRgZubW5FlZQGPx8OcOXPg4eGBGTNm4MqVKzA1NS2Xtr9HJBLhwIEDsLKywp07d3Dr1i0cOnQIderUKfe+MMofJnwMRhkycuRIuLq6YujQoRCLxfmWqVOnDoYNG4aVK1di3bp1mDNnDrKysgqt19LSEsHBwQUe//btW5GuDESEZcuWYcGCBeUy2nvw4AHs7e0RGhoKf39/DBs2rNx98sRiMby8vGBnZ4d9+/bh+PHjuHjxIho1alSu/WBULEz4GIwyZv369UhOTi40i8P8+fNx/Phx1KlTB/Xq1cOOHTsKrVMWI76rV69CJBKhR48ehV9AKUlLS8PUqVPRv39/rFy5EqdPn4a+vn6ZtvkjWVlZ2L9/P2xsbLBu3TqsXbsW9+/fh7Ozc7n2g1E5YMLHYJQxCgoKOH36NPbv348LFy7kW0ZPTw+//fYbFi5ciLVr12L58uVISkoqsE4rK6tSCR8R4a+//irz0d6tW7fQqFEjpKamIjAwEL179y6ztvIjIyMDmzZtQr169XD8+HFs374djx8/hoeHB4upWY1hwsdglAP6+vrw8vLCuHHjEBQUlG+ZadOm4e7duxAIBOjevTtWrlxZYH3SjPgKm+r09vZGSkoK+vTpI/1FFIPExESMHj0aY8eOxfbt23HgwIEi0yjJuv1ly5ahTp06uH//Ps6ePYubN2+iQ4cOTPAYTPgYjPIiJ8Zjr1698jV2UVdXx8KFCzFnzhwsXboUe/bsQXh4eL51WVhYICwsDCKRKN/jRY34li1bhnnz5pWJJeWFCxfQqFEjqKioIDAwEO7u7jJvoyBiYmIwe/Zs1KtXDx8+fMC9e/dw5swZODg4lFsfGJUfJnwMRjkyevRodOrUCcOGDcvX2GXcuHH4+PEj3r17hylTpmD+/Pn51qOiogI9PT1ERETke7ywANU+Pj6IiorCwIEDS34h+RAXF4eBAwdi5syZOHbsGLZu3YoaNWrItI2C+PTpEyZNmgQbGxvweDz4+fnhwIEDaNCgQbm0z6haMOFjMMqZDRs2ICEhAX/99VeeYwoKCli2bBnmzJmDGTNm4M6dO3jx4kW+9RQ23VnYiO+vv/7CvHnzZBp+68aNG7C3t4epqSlev36Ntm3byqzuwggMDMTQoUPh6OiImjVrIigoCJs2bYKZmVm5tM+omjDhYzDKGUVFRXh5eWHPnj24ePFinuP9+vUDEeH69etYvHgxZs6cma9Tu5WVlcSlIS4uDrdu3cLq1avh4eEBX19ffPnyJc95T548QUhICIYNGyaTa+Hz+fjjjz8wduxYHDlyBGvXroWKiopM6i6MJ0+eoGfPnujcuTMaNWqE0NBQLF++HLVq1Srzthk/ARUZNobBqM48fvyY9PT0KCgoKM+xW7duUb169SgjI4NsbGzo4sWLREQUEBBADg4ONG3aNOrYsSMZGRlRzZo1SVFRkTQ0NEhBQYEAEABSU1MjExMTWrVqFcXGxhIRkYeHB23fvl0m/X/37h3Z29tTr1696Nu3bzKpszDEYjHdvHmTOnToQObm5rR161bKyMgo83YZPx8sSDWDUYHs2bMHf//9N54+fQoNDY1cx1xdXdG7d2+IxWLMmzcPXC4XCQkJALJHjQKBIN+RYO3atXOt/SkrK4OIYG9vjw8fPiAsLKxUue2ICHv27MG8efOwfPlyjBs3rkwtJXk8Hk6ePInNmzcjMzMTc+bMwcCBA4sMvs1gFAQTPgajgpkwYQJiY2Nx5syZXFaWfn5+aNeuHRQVFSWCVxTy8vIYOHAgjh49mq8oKikpQVVVFePGjcP48eNRt27dYvU1ISEB48aNQ2hoKI4fP16mxiOfPn3C9u3bsX//fjRv3hyTJ0+Gu7s7y4XHKDXsF8RgVDCbNm3C169fsXz5csk+IsI///yDtLQ0qUUPyLb2bNKkSYGBrvl8PhITE7Fx40bY2tqiWbNmWLp0qVR137t3D/b29qhduzaePHlSJqInFotx48YNdO/eHY6OjhCLxXjy5AmuXLkCDw8PJnoMmcCyKjIYFUyOsYujoyOaNGkCZ2dnODs74/3798WuSyQSoUaNGlBUVCw03mfOsVevXsHPzw/16tXD4MGD8y0rEAiwePFi7N+/H3v37kWXLl2K3a+iSEpKwoEDB7Bt2zaoqalhypQpOHnyJFRVVWXeFoPBhI/BqAQYGhrixIkT6NKlC3g8XoGO6UXRoUMHREdHQ01NrchA16qqqhCJRODz+Rg3bhzs7OzQsGHDXGVCQ0MxePBgaGtr4+XLlzKPsenv74+tW7fi1KlT6NKlCw4cOAAnJycWXYVRprB5AwajkrB+/XqkpaWVWPTU1dXRr18/REZGFhkeTFVVFa6urhJfvoyMDLi5uUnigxIRDh8+jJYtW2Lw4MG4cuWKzERPIBDg1KlTaNu2LTw8PGBiYoJ3797h2LFjcHZ2ZqLHKHPYiI/BqARkZGTg06dPpapDIBDAzc0NJ06cgJGREUJDQ/Mtp6KignXr1mHNmjVIT0+X7P/27Rt69+6NM2fOYMqUKXj58iW8vb3RuHHjUvUrhy9fvmDXrl3YtWsXrKys8Ouvv6Jnz57MOpNR7rARH4NRwaSkpKBt27YFBq8uCC6Xm+u9iYkJDAwMEBkZiXr16uV7jqqqKo4cOYLatWvj27dvuY5lZWXh8ePHqFOnDjQ0NPDixYtSix4R4cGDBxg4cCBsbGwQExODGzdu4O7du+jbty8TPUaFwEZ8DEYFkpCQgDZt2iA0NBR8Pl/q8zgcDlRVVZGamgogWwQ9PT0BAJGRkRgyZAiUlJRy1amuro4rV66gbdu2aNy4MdLS0vLUm5mZCbFYjK5du5bKsCQyMhJHjhzBoUOHIBKJMHnyZOzcuROampolrpPBkBVsxMdgVCDdu3dHUFBQsUQPyBa+kSNHSsKDKSsro3v37khLSwOfz0fdunWhqKgIAJCTk0PNmjXx8OFDtG3bFg8ePChwGhTIHvkNGjQIHz58KFaf0tPTcfjwYXTu3Bl2dnb49OkTdu/ejaCgIPz6669M9BiVBiZ8DEYFsm3bNowaNQrq6urFymSgqKiI27dvY/bs2eByucjKyoKTkxOioqJgYmICQ0NDCAQCcDgcGBoawtfXF3Z2dgCABQsW5Frby4/09HS4ubkVWU4sFuPOnTsYOXIkTExMcPLkSYwbNw5RUVHYuXMnWrVqxYxVGJUOJnwMRgXSuHFj7NmzB/Hx8Thy5Ajc3d2hpKQENTW1fMtzOBzIyckhKysLCQkJaNu2LczNzWFqagoFBQVERkbCxMQE+vr6yMzMRO3atfHy5UvUqVMHQLb7wLNnz4rsFxEhOjoaQ4YMydcZ/v3795g/fz7Mzc0xffp0NG7cGO/evcPly5fRv3//cglUzWCUFBayjMGoZCQlJeHUqVPYunUrgoODIRaLJT55SkpKaN26NW7fvo3OnTtDTk4O2/Ydxsln4Yjlc/H+YwQSYqMwrHsnnFo1DZfPnMgVA7RXr164dOlSvrkAv0dRURFKSkpIS0tDUFAQrKyskJCQgBMnTuDQoUMICwvDkCFDMHz4cJlZfTIY5QUTPgajEvPp0yccOHAAu3fvRmJiIjIzMzFhwgS0aNEC4pqmWH/9Db5FfkLyy2vgx0UAYjHktY1R074zNB26oUMDA0xqVw+NTbXw8eNH2NjY5FlP5HK5UFNTQ2ZmJjQ0NODg4IAOHTqgefPmaNiwIR4+fIhDhw7B29sbXbp0wYgRI9C5c2eZ5vNjMMoTJnwMRhWAiPDs2TMsXLgQSkpKGDB/M5ZfDcLnc2uQHngXcqpaUK3XHBwFJWSGv4bgWwRU6ztDz3MuVBTkMd/DGvvnj8GdO3egrKwMIHtUZ29vj/bt26Nly5ZwcHCAnp4eiAh+fn44ePAgTpw4gfr162P48OHo168ftLS0KvaDYDBkABM+BqOKceRJGJZffYf4Nw8Rd3Y55DX1YTBiPbiq2VaTJBIi7vwq8EKeQMfjd6jbuUBFQQ7qITdhLf8Nnp6ecHR0hImJicTwhIgQEBCA06dP4/Tp08jKysLw4cMxbNgwWFhYVOTlMhgyh81VMBhViNefk7D8ahB4AjEy3j8CAGg095SIHgBwuPLQajsUvJAnSPW9BHU7F/AEYsDSDTN/aQk7Ey0A2WL3+vVridhlZmaiX79+OHjwIJo3b86sMRk/LUz4GIwqxNZ7H5ApzI7lKUpPAgDIaxnkKZezLys2FOLMNMgpqyNTKMLWex8wsaF8rpFdv379cPjwYTg6OjKxY1QLmPAxGFWEb2l83A+OQ87ihJxqtrWmMDk2T1lhUozktSA+EkrG1iACbvhH4sayhejfowuOHj0KBwcHJnaMagcTPgajiuDlG5nrvaqFIzLe3kfKs/NQbdAWXJVsB3gSi5D87zFJOXHmf6HJFBUVMX3neUxox9btGNUXJnwMRhUhKCYFfOF//neqNm2h/OYuMj/6InrPRKjWa5Ft1Rn2CsKkGMjXNIIwMRr4Lmt5lojwPia1IrrPYFQaWOQWBqOKkJIpzPWew5FDrb6LULPDaHDVaiL9zV2k+d8Ct4Yu9Ieugdz/R4BcVa0f6hGUV5cZjEoJG/ExGFUEDeW8/64cOS40WvSGRoveufaLBXwIvn4CR14JCrq1f6iHpQJiVG/YiI/BqCJYG2hASV66f9n0N3dBwiyoWrcGh/ufYCrLy8HaUPpg2AzGzwgTPgajitC3mUmefWJ+Rp59/C/BSLp3ABxFFWi2HpTrGAHo2zRvPQxGdYJNdTIYVQRddSW0s9LDrXexEpeG2BMLwJFXhKKeGTiKKhB8iwAv9AU48grQ85wHhe98/DgcoEN9Peio9SYwUwAAAftJREFUK1XQFTAYlQMmfAxGFWJy+3r4N+QbeIJsJ3ZV61bIeOuDtDf3QEI+uOo6UG/sCs2W/SCvpZ/rXGV5Lia1r1cR3WYwKhUsVieDUcXIidXJExSeWuh7VBTkMN+jAYa2NC+7jjEYVQQ24mMwqhg54rX8ahAyhSIU9ujK4WSP9OZ7WDPRYzD+DxvxMRhVFP/IJGy79wF338eBAyDzO+d2ZXk5ELLX9Ca1rycJTM1gMJjwMRhVnvg0Prz8IhH0JRUpmQJoKCvA2rAG+jY1YYYsDEY+MOFjMBgMRrWC+fExGAwGo1rBhI/BYDAY1QomfAwGg8GoVjDhYzAYDEa1ggkfg8FgMKoVTPgYDAaDUa1gwsdgMBiMagUTPgaDwWBUK5jwMRgMBqNawYSPwWAwGNUKJnwMBoPBqFYw4WMwGAxGtYIJH4PBYDCqFUz4GAwGg1GtYMLHYDAYjGoFEz4Gg8FgVCuY8DEYDAajWsGEj8FgMBjVCiZ8DAaDwahWMOFjMBgMRrWCCR+DwWAwqhVM+BgMBoNRrWDCx2AwGIxqBRM+BoPBYFQrmPAxGAwGo1rBhI/BYDAY1QomfAwGg8GoVjDhYzAYDEa1ggkfg8FgMKoVTPgYDAaDUa1gwsdgMBiMagUTPgaDwWBUK5jwMRgMBqNawYSPwWAwGNWK/wEhMs7WrkpYaQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C = np.zeros((N,N))\n", "for i in range(N):\n", " for j in range(N):\n", " if (R[i,j] == 1 and R[j,i] == 1):\n", " C[i,j] = 1\n", "\n", "C_3 = C@C@C \n", "clique_nodes = []\n", "for i in range(N):\n", " if (C_3[i,i] != 0):\n", " clique_nodes.append(i)\n", "print(C_3)\n", "lag.HighlightSubgraph(R,big_graph_positions,clique_nodes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise 4:** Write a code cell to sort the $\\texttt{clique_nodes}$ list into different cliques. Print the result or store it in a list of lists. " ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "## Code solution here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References\n", "\n", "- Anton, Howard and Chris Rorres. *Elementary Linear Algebra Applications Version*. 8th ed., John Wiley & Sons Inc., 2000. \n", "\n", "- Krebs, Charles J.; Boonstra, Rudy; Boutin, Stan (2017), Using experimentation to understand the 10‐year snowshoe hare cycle in the boreal forest of North America, Journal of Animal Ecology, Article-journal, https://doi.org/10.1111/1365-2656.12720\n", "\n", "- Kwak, Jin Ho and Sungpyo Hong. *Linear Algebra*. 2nd ed., Birkhauser., 2004.\n", "\n", "- Williams, David, *Planetary Fact Sheet*, https://nssdc.gsfc.nasa.gov/planetary/factsheet/, NASA Goddard Space Flight Center, 2021" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }