{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numpy and Matplotlib" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numpy numerical library\n", "\n", "NumPy is a linear algebra library in Python, with computationally expensive methods written in FORTRAN for speed. \n", "\n", "* The reference manual is at . \n", "* A nice tutorial can be found at \n", "* or: \n", "* If you already know Matlab, a comparison is at " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Importing libraries\n", "\n", "To import a library in Python, you only need to use the keyword `import` at the beginning of your script / notebook (or more exactly, before you use it).\n", "\n", "```python\n", "import numpy\n", "```\n", "\n", "Think of it as the equivalent of `#include ` in C/C++ (if you know Java, you will not be shocked). You can then use the functions and objects provided by the library using the namespace of the library:\n", "\n", "```python\n", "x = numpy.array([1, 2, 3])\n", "```\n", "\n", "If you do not want to type `numpy.` everytime, and if you are not afraid that numpy redefines any important function, you can also simply import every definition declared by the library in your current namespace with:\n", "\n", "```python\n", "from numpy import *\n", "```\n", "\n", "and use the objects directly:\n", "\n", "```python\n", "x = array([1, 2, 3])\n", "```\n", "\n", "However, it is good practice to give an alias to the library when its name is too long (numpy is still okay, but think of matplotlib...):\n", "\n", "```python\n", "import numpy as np \n", "```\n", "\n", "You can then use the objects like this:\n", "\n", "```python\n", "x = np.array([1, 2, 3])\n", "```\n", "\n", "Remember that you can get help on any NumPy function:\n", "\n", "```python\n", "help(np.array)\n", "help(np.ndarray.transpose)\n", "```" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Vectors and matrices\n", "\n", "The basic object in NumPy is an **array** with d-dimensions (1D = vector, 2D = matrix, 3D or more = tensor). They can store either integers or floats, using various precisions.\n", "\n", "In order to create a vector of three floats, you simply have to build an `array()` object by providing a list of floats as input:\n", "\n", "```python\n", "A = np.array( [ 1., 2., 3.] )\n", "```\n", "\n", "Matrices should be initialized with a list of lists. For a 3x4 matrix of 8 bits unsigned integers, it is:\n", "\n", "```python\n", "B = np.array( [ \n", " [ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 4, 3, 2, 1] \n", " ] , dtype=np.uint8)\n", "```\n", "\n", "Most of the time, you won't care about the type (the default floating-point precision is what you want for machine learning), but if you need it, you can always specify it with the parameter `dtype={int32, uint16, float64, ...}`. Note that even if you pass integers to the array (`np.array( [ 1, 2, 3] )`), they will be converted to floats by default." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following attributes of an array can be accessed:\n", "\n", "- `A.shape` : returns the shape of the vector `(n,)` or matrix `(m, n)`.\n", "\n", "- `A.size` : returns the total number of elements in the array.\n", "\n", "- `A.ndim` : returns the number of dimensions of the array (vector: 1, matrix:2).\n", "\n", "- `A.dtype.name` : returns the type of data stored in the array (int32, uint16, float64...)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Q:** Define the two arrays $A$ and $B$ from above and print those attributes. Modify the arrays (number of elements, type) and observe how they change. \n", "\n", "*Hint:* you can print an array just like any other Python object." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1. 2. 3.]\n", "Shape of A is : (3,)\n", "Size of A is : 3\n", "Number of dimensions of A is : 1\n", "Type of elements in A is : float64\n", "[[1 2 3 4]\n", " [5 6 7 8]\n", " [4 3 2 1]]\n", "Shape of B is : (3, 4)\n", "Size of B is : 12\n", "Number of dimensions of B is : 2\n", "Type of elements in B is : uint8\n" ] } ], "source": [ "A = np.array( [ 1., 2., 3.] )\n", "\n", "print(A)\n", "print('Shape of A is :', A.shape)\n", "print('Size of A is :', A.size)\n", "print('Number of dimensions of A is :', A.ndim)\n", "print('Type of elements in A is :', A.dtype.name)\n", "\n", "B = np.array( [ \n", " [ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 4, 3, 2, 1] \n", "] , dtype=np.uint8)\n", "\n", "print(B)\n", "print('Shape of B is :', B.shape)\n", "print('Size of B is :', B.size)\n", "print('Number of dimensions of B is :', B.ndim)\n", "print('Type of elements in B is :', B.dtype.name)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Internally, the values are stored sequentially as a vector, even if your array has more than one dimension. The apparent shape is just used for mathematical operations. You can **reshape** a matrix very easily with the `reshape()` method:\n", "\n", "```python\n", "B = np.array( [ \n", " [ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 4, 3, 2, 1] \n", "]) # B has 3 rows, 4 columns\n", "\n", "C = B.reshape((6, 2)) # C has 6 rows, 2 columns\n", "```\n", "\n", "The only thing to respect is that the total number of elements must be the same. Beware also of the order in which the elements will be put.\n", "\n", "**Q:** Create a vector with 8 elements and reshape it into a 2x4 matrix." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3 4]\n", " [5 6 7 8]]\n" ] } ], "source": [ "B = np.array( [1, 2, 3, 4, 5, 6, 7, 8])\n", "\n", "C = B.reshape((2, 4))\n", "print(C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Initialization of an array\n", "\n", "Providing a list of values to `array()` would be tedious for large arrays. Numpy offers constructors that allow to construct simply most vectors or matrices.\n", "\n", "`np.zeros(shape)` creates an array of shape `shape` filled with zeros. Note: if you give a single integer for the shape, it will be interpreted as a vector of shape `(d,)`. \n", "\n", "`np.ones(shape)` creates an array of shape `shape` filled with ones. \n", "\n", "`np.full(shape, val)` creates an array of shape `shape` filled with `val`. \n", "\n", "`np.eye(n)` creates a diagonal matrix of shape `(n, n)`.\n", "\n", "`np.arange(a, b)` creates a vector of integers whose value linearly increase from `a` to `b` (excluded).\n", "\n", "`np.linspace(a, b, n)` creates a vector of `n` values evenly distributed between `a` and `b` (included).\n", "\n", "\n", "**Q:** Create and print:\n", "\n", "* a 2x3 matrix filled with zeros.\n", "* a vector of 12 elements initialized to 3.14.\n", "* a vector of 11 elements whose value linearly increases from 0.0 to 10.0.\n", "* a vector of 11 elements whose value linearly increases from 10 to 20." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "A = np.zeros((2,3)) \n", "B = np.full(12, 3.14) # 3.14 * np.ones(12) would also work\n", "C = np.linspace(0.0, 10.0, 11) \n", "D = np.arange(10, 21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Random distributions\n", "\n", "In many cases, it is useful to initialize a vector or matrix with random values. **Random number generators** (rng) allows to draw numbers from any probability distribution (uniform, normal, etc.) using pseudo-random methods. \n", "\n", "In numpy versions before 1.16, the `numpy.random` module had direct methods allowing to initialize arrays:\n", "\n", "```python\n", "A = np.random.uniform(-1.0, 1.0, (10, 10)) # a 10x10 matrix with values uniformly taken between -1 and 1\n", "```\n", "\n", "Since numpy 1.16, this method has been deprecated in favor of a more explicit initialization of the underlying rng:\n", "\n", "```python\n", "rng = np.random.default_rng()\n", "A = rng.uniform(-1.0, 1.0, (10, 10))\n", "```\n", "\n", "The advantages of this new method (reproducibility, parallel seeds) will not matter for these exercises, but let's take good habits already.\n", "\n", "The generator has many built-in methods, covering virtually any useful probability distribution. Read the documentation of the random generator:\n", "\n", "\n", "\n", "**Q:** Create:\n", "\n", "* A vector of 20 elements following a normal distribution with mean 2.0 and standard devation 3.0.\n", "* A 10x10 matrix whose elements come from the exponential distribution with $\\beta = 2$.\n", "* A vector of 10 integers randomly chosen between 1 and 100 (hint: involves `arange` and `rng.choice`)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "rng = np.random.default_rng()\n", "A = rng.normal(2.0, 3.0, 20)\n", "B = rng.exponential(2.0, (10, 10))\n", "C = rng.choice(np.arange(1, 101), 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Manipulation of matrices: indices, slices\n", "\n", "To access a particular element of a matrix, you can use the usual Python list style (the first element has a rank of 0), once per dimension:\n", "\n", "```python\n", "A = np.array(\n", " [ \n", " [ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 9, 10, 11, 12]\n", " ]\n", ")\n", "\n", "x = A[0, 2] # The element on the first row and third column\n", "```\n", "\n", "For matrices, the first index represents the rows, the second the columns. [0, 2] represents the element at the first row, third column.\n", "\n", "**Q:** Define this matrix and replace the element `12` by a zero using indices:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 3 4]\n", " [ 5 6 7 8]\n", " [ 9 10 11 0]]\n" ] } ], "source": [ "A = np.array(\n", " [ \n", " [ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 9, 10, 11, 12]\n", " ]\n", ")\n", "\n", "A[2, 3] = 0.\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is possible to access complete row or columns of a matrix using **slices**. The `:` symbol is a shortcut for \"everything\":\n", "\n", "```python\n", "b = A[:, 2] # third column\n", "c = A[0, :] # first row\n", "```\n", "\n", "**Q:** Set the fourth column of A to 1." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 3 1]\n", " [ 5 6 7 1]\n", " [ 9 10 11 1]]\n" ] } ], "source": [ "A[:, 3] = 1.\n", "\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As for python lists, you can specify a range `start:stop` to get only a subset of a row/column (beware, stop is excluded):\n", "\n", "```python\n", "d = A[0, 1:3] # second and third elements of the first row\n", "e = A[1, :2] # first and second elements of the second row\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can use boolean arrays to retrieve indices:\n", "\n", "```python\n", "A = np.array( \n", " [ [ -2, 2, 1, -4],\n", " [ 3, -1, -5, -3] ])\n", "\n", "negatives = A < 0 # Boolean array where each element is True when the condition is met.\n", "A[negatives] = 0 # All negative elements of A (where the boolean matrix is True) will be set to 0\n", "```\n", "\n", "A simpler way to write it is:\n", "\n", "```python\n", "A[A < 0] = 0\n", "```\n", "\n", "**Q:** print A, negatives and A again after the assignment:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ True False False True]\n", " [False True True True]]\n", "[[0 2 1 0]\n", " [3 0 0 0]]\n" ] } ], "source": [ "A = np.array( \n", " [ [ -2, 2, 1, -4],\n", " [ 3, -1, -5, -3] ])\n", "negatives = A < 0\n", "A[negatives] = 0\n", "\n", "print(negatives)\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basic linear algebra \n", "\n", "Let's first define some matrices:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "A = np.array( [ [ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8] ])\n", "\n", "B = np.array( [ [ 1, 2],\n", " [ 3, 4],\n", " [ 5, 6],\n", " [ 7, 8] ])\n", "\n", "C = np.array( [ [ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 9, 0, 1, 1],\n", " [ 13, 7, 2, 6] ])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Transpose a matrix \n", "\n", "A matrix can be transposed with the `transpose()` method or the `.T` shortcut:\n", "\n", "```python\n", "D = A.transpose() \n", "E = A.T # equivalent\n", "```\n", "\n", "**Q:** Try it:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3 4]\n", " [5 6 7 8]]\n", "[[1 5]\n", " [2 6]\n", " [3 7]\n", " [4 8]]\n" ] } ], "source": [ "D = A.transpose() \n", "E = A.T\n", "\n", "print(A)\n", "print(D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`transpose()` does not change `A`, it only returns a transposed copy. To transpose `A` definitely, you have to use the assigment `A = A.T`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multiply two matrices \n", "\n", "There are two manners to multiply matrices:\n", "\n", "- element-wise: Two arrays of **exactly** the same shape can be multiplied *element-wise* by using the `*` operator:\n", "\n", "```python\n", "D = A * B\n", "```\n", "\n", "- algebrically: To perform a **matrix multiplication**, you have to use the `dot()` method. Beware: the dimensions must match! `(m, n) * (n, p) = (m, p)`\n", "\n", "```python\n", "E = np.dot(A, B)\n", "```\n", "\n", "**Q:** Use the matrices `A` and `B` previously defined and multiply them element-wise and algebrically. You may have to transpose one of them." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 6 15 28]\n", " [10 24 42 64]]\n", "[[ 1 10]\n", " [ 6 24]\n", " [15 42]\n", " [28 64]]\n", "[[ 50 60]\n", " [114 140]]\n", "[[11 14 17 20]\n", " [23 30 37 44]\n", " [35 46 57 68]\n", " [47 62 77 92]]\n" ] } ], "source": [ "D = A * B.T\n", "E = A.T * B\n", "\n", "print(D)\n", "print(E)\n", "\n", "F = np.dot(A, B)\n", "G = np.dot(B, A)\n", "\n", "print(F)\n", "print(G)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multiplying a matrix with a vector\n", "\n", "`*` and `np.dot` also apply on matrix-vector multiplications $\\mathbf{y} = A \\times \\mathbf{x}$ or vector-vector multiplications.\n", "\n", "**Q:** Define a vector $\\mathbf{x}$ with four elements and multiply it with the matrix $A$ using `*` and `np.dot`. What do you obtain? Try the same by multiplying the vector $\\mathbf{x}$ and itself." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[30 70]\n", "[[ 1 4 9 16]\n", " [ 5 12 21 32]]\n", "[ 1 4 9 16]\n", "30\n" ] } ], "source": [ "x = np.array([1, 2, 3, 4])\n", "\n", "y = np.dot(A, x)\n", "z = A*x\n", "\n", "p = x*x\n", "q = np.dot(x, x)\n", "\n", "print(y)\n", "print(z)\n", "print(p)\n", "print(q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**A:** the element-wise multiplies each column of the matrix by the corresponding element of the vector. `np.dot` works as expected. The same happens for vector-vector multiplications: element-wise for `*`, dot-product for `np.dot` (hence the name of the method)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Inverting a matrix\n", "\n", "Inverting a Matrix (when possible) can be done using the `inv()` method whitch is defined in the `linalg` submodule of NumPy.\n", "\n", "```python\n", "inv_C = np.linalg.inv(C)\n", "```\n", "\n", "**Q:**\n", "\n", "1. Invert `C` and print the result.\n", "2. Multiply `C` with its inverse and print the result. What do observe? Why is Numpy called a *numerical computation* library?" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.0467033 0.00274725 0.0989011 0.01098901]\n", " [-0.62362637 0.27197802 -0.20879121 0.08791209]\n", " [-0.61263736 0.4478022 0.12087912 -0.20879121]\n", " [ 1.03296703 -0.47252747 -0.01098901 0.10989011]]\n", "[[ 1.00000000e+00 -2.22044605e-16 -5.55111512e-17 1.11022302e-16]\n", " [ 0.00000000e+00 1.00000000e+00 -2.22044605e-16 -2.22044605e-16]\n", " [ 0.00000000e+00 -5.55111512e-17 1.00000000e+00 -6.93889390e-17]\n", " [-2.22044605e-16 -2.22044605e-16 -2.22044605e-16 1.00000000e+00]]\n" ] } ], "source": [ "inv_C = np.linalg.inv(C)\n", "\n", "print(inv_C)\n", "print(np.dot(C,inv_C))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**A:** Some elements which should be 0 have a very small value. This is due to numerical precision issues. Numpy does not make symbolic computations like Mathematica or sympy, it deals with numbers up to a certain precision." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Summing elements \n", "\n", "One can sum the elements of a matrix globally, row-wise or column-wise:\n", "\n", "```python\n", "# Globally\n", "S1 = np.sum(A)\n", "\n", "# Per column\n", "S2 = np.sum(A, axis=0) \n", "\n", "# Per row\n", "S3 = np.sum(A, axis=1) \n", "```\n", "\n", "**Q:** Try them:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3 4]\n", " [5 6 7 8]]\n", "36\n", "[ 6 8 10 12]\n", "[10 26]\n" ] } ], "source": [ "# Globally\n", "S1 = np.sum(A)\n", "\n", "# Per column\n", "S2 = np.sum(A, axis=0) \n", "\n", "# Per row\n", "S3 = np.sum(A, axis=1) \n", "\n", "print(A)\n", "print(S1)\n", "print(S2)\n", "print(S3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You also have access to the minimum (`np.min()`), maximum (`np.max()`), mean (`np.mean()`) of an array, also per row/column. \n", "\n", "**Q:** Try them out:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1\n", "8\n", "4.5\n", "[1 2 3 4]\n", "[5 6 7 8]\n", "[3. 4. 5. 6.]\n", "[1 5]\n", "[4 8]\n", "[2.5 6.5]\n" ] } ], "source": [ "print(np.min(A))\n", "print(np.max(A))\n", "print(np.mean(A))\n", "\n", "print(np.min(A, axis=0))\n", "print(np.max(A, axis=0))\n", "print(np.mean(A, axis=0))\n", "\n", "print(np.min(A, axis=1))\n", "print(np.max(A, axis=1))\n", "print(np.mean(A, axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mathematical operations \n", "\n", "You can apply any usual mathematical operations (cos, sin, exp, etc...) on each element of a matrix (element-wise):\n", "\n", "```python\n", "D = np.exp(A)\n", "E = np.cos(A)\n", "F = np.log(A)\n", "G = (A+3) * np.cos(A-2)\n", "```\n", "\n", "**Q:** Try it." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2.71828183e+00 7.38905610e+00 2.00855369e+01 5.45981500e+01]\n", " [1.48413159e+02 4.03428793e+02 1.09663316e+03 2.98095799e+03]]\n", "[[ 0.54030231 -0.41614684 -0.9899925 -0.65364362]\n", " [ 0.28366219 0.96017029 0.75390225 -0.14550003]]\n", "[[0. 0.69314718 1.09861229 1.38629436]\n", " [1.60943791 1.79175947 1.94591015 2.07944154]]\n", "[[ 2.16120922 5. 3.24181384 -2.91302786]\n", " [-7.91993997 -5.88279259 2.83662185 10.56187315]]\n" ] } ], "source": [ "D = np.exp(A)\n", "E = np.cos(A)\n", "F = np.log(A)\n", "G = (A+3) * np.cos(A-2)\n", "\n", "print(D)\n", "print(E)\n", "print(F)\n", "print(G)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matplotlib\n", "\n", "Matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.\n", "\n", "* Reference: \n", "* Tutorial by N. Rougier: \n", "\n", "This is the default historical visualization library in Python, which anybody should know, but not the nicest. If you are interested in having better visualizations, have a look at:\n", "\n", "* `seaborn` \n", "* `ggplot2` \n", "* `bokeh` \n", "* `plotly` \n", "\n", "We will nevertheless stick to matplotlib in these exercises.\n", "\n", "The `pyplot` module is the most famous, as it has a similar interface to Matlab. It is customary to use the `plt` namescape for it:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `plt.plot()`\n", "\n", "The `plt.plot()` command allows to make simple line drawings:\n", "\n", "```python\n", "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "\n", "plt.figure()\n", "plt.plot(x, y)\n", "plt.show()\n", "```" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "\n", "plt.figure()\n", "plt.plot(x, y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`plot()` takes two vectors `x` and `y` as inputs (they must have the same size) and plots them against each other. It is standard to define the x-axis with `np.linspace()` if you just want to plot a function. 100 points is usually a good choice, but you can experiments with less points.\n", "\n", "The call to `plt.show()` is obligatory at the end to display the window when using a script (very common mistake to forget it!). It is not needed in Jupyter notebooks as it is implicitly called, but let's take the habit anyway. \n", "\n", "The call to `plt.figure()` is also optional, as a new figure is created when you call `plt.plot()` for the first time.\n", "\n", "**Q:** Create a third vector `z` (e.g. `z = -x**2 + 2`) and plot it against `x` right after `y` (i.e. between `plt.plot(x, y)` and `plt.show()`). What happens?" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "z = -x**2 + 2.\n", "\n", "plt.figure()\n", "plt.plot(x, y)\n", "plt.plot(x, z)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Q:** Now call `plt.figure()` again between the two plots. What happens?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "z = -x**2 + 2.\n", "\n", "plt.figure()\n", "plt.plot(x, y)\n", "plt.figure()\n", "plt.plot(x, z)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, the plot is quite empty. This is fine when experimenting in a notebook, but not when incorporating the figures in your thesis. You can make a plot look better by adding a title, labels on the axes, etc. \n", "\n", "```python\n", "plt.title('My title')\n", "plt.xlabel('x-axis')\n", "plt.ylabel('y-axis')\n", "```\n", "\n", "**Q:** Make the previous plots nicer by adding legends and axes.\n", "\n", "*Hint:* if you know LateX equations, you can insert simple formulas in the title or axes by using two dollar signs `$$`." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "z = -x**2 + 2.\n", "\n", "plt.figure()\n", "plt.plot(x, y)\n", "plt.title(\"Function $x^2 + 1$\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "\n", "plt.figure()\n", "plt.plot(x, z)\n", "plt.title(\"Function $-x^2 + 2$\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you make multiple plots on the same figure by calling `plt.plot()` multiple times, you can add a label to each plot to create a legend with `plt.legend()`:\n", "\n", "```python\n", "plt.plot(x, y, label='y')\n", "plt.plot(x, z, label='z')\n", "plt.legend()\n", "```" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "z = -x**2 + 2.\n", "\n", "plt.figure()\n", "plt.plot(x, y, label=\"$x^2 + 1$\")\n", "plt.plot(x, z, label=\"$-x^2 + 2$\")\n", "plt.title(\"Functions $x^2 + 1$ and $-x^2 + 2$\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another advantage of declaring a figure is that you can modify its size (which is very small in a notebook by default) with the `figsize` argument in inches:\n", "\n", "```python\n", "plt.figure(figsize=(16, 10))\n", "```\n", "\n", "**Q:** Experiment with figure sizes." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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vCwAAAABPR+sBAAAAAMBDUPIBAAAAAPAQlHwAAAAAADwEJR8AAAAAAA9ByccJ27Nnj4YPH64uXbqoR48e+vjjj62OBAAAAAD4BW6hhxPm5eWl559/Xr169VJubq769u2rUaNGKTAw0OpoAAAAAABR8nES4uLiFBcXJ0mKjY1VZGSkCgsLKfkAAAAA0Exwuj5OyYoVK+R0OpWUlNRor/njjz9q9OjRio+Pl81m04wZMxrttQEAAACgNaDk46QVFhbq+uuv12uvvXZCxw8fPlxvvfXWcY8rLy9Xz5499dJLL51mQgAAAABonSj5qPfhhx/K399fOTk59WM33nijevTooeLiYklSdXW1xowZo3vvvVdnnHFGo379kSNH6vHHH9ell17aqK8LAAAAAK0F1+S7mWEYqqx1WvK1/b0dstlsJ3z8uHHj9Le//U1PPvmkpk2bpocfflhz5szR4sWLFRoaKsMwNGHCBJ1zzjm67rrr3JgcAAAAAHAqKPluVlnrVJeHvrXka2987AIF+Jz4W2yz2fTEE09o7Nixio2N1bRp0zR//nwlJCRIkn766Sd99NFH6tGjR/318u+++666d+/ujvgAAAAAgJNEyUcDF198sbp06aLHHntMs2fPVteuXev3DR06VC6X67iv8eSTT+rJJ5+sf15ZWanFixdr8uTJ9WMbN25UcnJy44YHAAAAgFaOku9m/t4ObXzsAsu+9smaNWuWMjIy5HQ6FRMTc0pf97bbbtOVV15Z//zaa6/V5Zdfrssuu6x+LD4+/pReGwAAAABwdJR8N7PZbCd1yryVVq5cqSuvvFJvvvmm3nrrLT344IP6+OOPT/p1wsPDFR4eXv/c399f0dHRSktLa8y4AAAAAIBfaRntE263c+dOXXTRRbr//vt19dVXq127dho8eLBWrlypPn36NEmGsrIybdu2rf55ZmamVq9erfDwcE7tBwAAAIATwC30oMLCQl144YW65JJLdO+990qSBg4cqJEjR+r+++9vshzLly9X79691bt3b0nSlClT1Lt3bz300ENNlgEAAAAAWjJm8qHw8HBlZGQcNv7VV181yuvPnTv3hI4bPny4DMNolK8JAAAAAK0RM/kAAAAAAHgISj4AAAAAAB6Ckg8AAAAAgIeg5AMAAAAA4CEo+QAAAACAVmnJjv36am2O1TEaVYsq+T/++KNGjx6t+Ph42Ww2zZgxo8F+wzD00EMPKS4uTv7+/hoxYoS2bt3a4JjCwkJde+21CgkJUVhYmG6++WaVlZU14XcBAAAAALDaR8t2a/ybS3T3f1ZrfVax1XEaTYsq+eXl5erZs6deeumlI+5/+umn9cILL+iVV17RkiVLFBgYqAsuuEBVVVX1x1x77bXasGGDvvvuO3355Zf68ccfdeuttzbVtwAAAAAAsFCd06XHvtioe/67TrVOQ+d1iVH7qCCrYzUaL6sDnIyRI0dq5MiRR9xnGIaef/55PfDAA7rkkkskSe+8845iYmI0Y8YMjRs3Tps2bdKsWbO0bNky9evXT5I0bdo0jRo1Sn//+98VHx/fZN8LAAAAAKBpFVfW6o4PV+nHLQWSpCnnddQd56TJZrNZnKzxtKiZ/GPJzMxUbm6uRowYUT8WGhqqgQMHatGiRZKkRYsWKSwsrL7gS9KIESNkt9u1ZMmSI75udXW1SkpKGmwAAAAAgJZlR0GZLv3XT/pxS4H8vO3617V9dOe5HTyq4EseVPJzc3MlSTExMQ3GY2Ji6vfl5uYqOjq6wX4vLy+Fh4fXH/NrU6dOVWhoaP2WlJTkhvQAAAAAAHdZsHWfxrz0k3YUlCsu1E+f3HaGRnWPszqWW3hMyXeX++67T8XFxfXbnj17rI4EAAAAADgBhmHonUU7dcP0pSqpqlPv5DB9PnmIuiWEWh3NbTym5MfGxkqS8vLyGozn5eXV74uNjVV+fn6D/XV1dSosLKw/5td8fX0VEhLSYMPx7dmzR8OHD1eXLl3Uo0cPffzxx1ZHAgAAANCK1DpdemDGej30+QY5XYYu65OgD28ZpOhgP6ujuZXHlPzU1FTFxsbq+++/rx8rKSnRkiVLNHjwYEnS4MGDVVRUpBUrVtQf88MPP8jlcmngwIFNntmTeXl56fnnn9fGjRs1e/Zs3XXXXSovL7c6FgAAAIBWoLC8Rte9uUTvL9ktm026b2S6nr2ip/y8HVZHc7sWtbp+WVmZtm3bVv88MzNTq1evVnh4uJKTk3XXXXfp8ccfV4cOHZSamqoHH3xQ8fHxGjNmjCSpc+fOuvDCC3XLLbfolVdeUW1trSZPnqxx48axsn4ji4uLU1yceY1LbGysIiMjVVhYqMDAQIuTAQAAAPBkm3JKdMs7y7X3QKUCfRz657jeGtEl5vif6CFa1Ez+8uXL1bt3b/Xu3VuSNGXKFPXu3VsPPfSQJOnPf/6z7rjjDt16663q37+/ysrKNGvWLPn5HTod4/3331d6errOPfdcjRo1SkOHDtVrr71myffTWqxYsUJOp7PRFy2cOnWq+vfvr+DgYEVHR2vMmDHavHlzo34NAAAAAC3HrPW5uvzlhdp7oFIpEQH6bNKQVlXwJclmGIZhdYiWpKSkRKGhoSouLj7s+vyqqiplZmYqNTW1wS8WWrPCwkINGzZMr7/+us4444zjHj98+HBNmDBBEyZMOO6xF154ocaNG6f+/furrq5O999/v9avX6+NGzce8YwB3h8AAADAMxmGoWk/bNM/vtsiSRqSFqGXrumjsAAfi5M1jmP10F9rUTP5aD4+/PBD+fv7Kycnp37sxhtvVI8ePVRcXCxJqq6u1pgxY3TvvfeeUME/WbNmzdKECRPUtWtX9ezZU2+99ZZ2797dYM0FAAAAAJ6toqZOkz9YVV/wJ5zRVm/fOMBjCv7JouTjlIwbN04dO3bUk08+KUl6+OGHNWfOHH3zzTcKDQ2VYRiaMGGCzjnnHF133XVNkunnXy6Eh4c3ydcDAAAAYK29Byo09uVF+mpdjrwdNj11eXc98puu8nK03qrbohbea5EMQ6qtsOZrewdINptbXtpms+mJJ57Q2LFjFRsbq2nTpmn+/PlKSEiQJP3000/66KOP1KNHD82YMUOS9O6776p79+5uyeNyuXTXXXdpyJAh6tatm1u+BgAAAIDmY9nOQt327grtL69RZJCPXhnfV/3aMuHHNfkn6aSvya8pl560aOX++7MlnxNfzf7ee+/VU089dcxjNm3apPT09Prnffr00YYNGzR79mydddZZJx3xySefrD8bQJIqKyvl7e0tL69Dv3/auHGjkpOTj/k6t99+u7755hstWLBAiYmJRzyGa/IBAAAAz/DBkt16eOZ61ToNdY0P0WvX91NCmL/VsdzmZK7JZyYf9f7whz8cd8G7du3a1X88a9YsZWRkyOl0Kibm1FasvO2223TllVfWP7/22mt1+eWX67LLLqsfO97tDSdPnqwvv/xSP/7441ELPgAAAICWr6bOpUe/2KD3l+yWJF3UI05/H9tT/j4Oi5M1H5R8d/MOMGfUrfraJyEqKkpRUVEndOzKlSt15ZVX6s0339Rbb72lBx98UB9//PFJRwwPD29wDb2/v7+io6OVlpZ23M81DEN33HGHPvvsM82dO1epqakn/fUBAAAAtAz7yqo18b2VWrqzUDab9MfzO2ni8PayuekS5ZaKku9uNttJnTLfEuzcuVMXXXSR7r//fl199dVq166dBg8erJUrV6pPnz5NlmPSpEn64IMP9Pnnnys4OFi5ubmSpNDQUPn7e+6pOgAAAEBrsz6rWLe+s1zZxVUK9vXSP6/upXPST+1sYk/XepccxCkpLCzUhRdeqEsuuUT33nuvJGngwIEaOXKk7r///ibN8vLLL6u4uFjDhw9XXFxc/fbRRx81aQ4AAAAA7vP56iyNfWWhsour1C4yUJ9NGkLBPwZm8nFSwsPDlZGRcdj4V1991SivP3fu3BM+ljUjAQAAAM/ldBl65tvNemXedknS8E5R+ue43gr197Y4WfNGyQcAAAAANCvFlbX6/b9Xae7mAknS7cPb64/nd5LDzvX3x0PJBwAAAAA0G1vzSnXruyuUua9cft52PXV5D13SK8HqWC0GJR8AAAAA0Cx8uyFXUz5arfIapxLC/PXqdX3VLSHU6lgtCiUfAAAAAGApl8vQ899v1Qvfb5UkDWoXrpeu6aOIIF+Lk7U8lHwAAAAAgGVKqmo15aPVmrMpX5J045C2un9UZ3k7uBncqaDkuwGrvjdPvC8AAABA87Itv0y3vrtcOwrK5eNl19RLu+vyvolWx2rRKPmNyNvbvJVDRUWF/P39LU6DX6uoqJB06H0CAAAAYJ05G/N010erVVZdp7hQP716XV/1SAyzOlaLR8lvRA6HQ2FhYcrPN08zCQgIkM3GLR6sZhiGKioqlJ+fr7CwMDkcDqsjAQAAAK2Wy2Xoxf9t0z++2yJJGtA2XC9d20dRwVx/3xgo+Y0sNjZWkuqLPpqPsLCw+vcHAAAAQNMzr79fozmb8iRJ1w9O0QMXdZGPF9ffNxZKfiOz2WyKi4tTdHS0amtrrY6Dg7y9vZnBBwAAACy0Lb9Ut767wrz+3mHX42O66cr+SVbH8jiUfDdxOByUSgAAAACQNGt9rv7wn9Uqr3EqLtRPr4zvq55JYVbH8kiUfAAAAACAWzhdhp77bote/N82SdLAVPP6+8ggrr93F0o+AAAAAKDRFVfU6s5/r9K8LQWSpJuGpOq+UenydnD9vTtR8gEAAAAAjWpTTol+9+4K7S6skJ+3XU9d3kOX9EqwOlarQMkHAAAAADSaL9Zk68+frFVlrVNJ4f56ZXxfdY0PtTpWq0HJBwAAAACctlqnS3/7JkNvLsiUJA3rEKlpV/dWWICPxclaF0o+AAAAAOC0FJRWa/IHK7Uks1CSNHF4e/3h/E5y2G0WJ2t9KPkAAAAAgFO2cvcB3f7eCuWVVCvI10t/v6KnLuwWa3WsVouSDwAAAAA4aYZh6L0lu/XYFxtU6zTUITpIr1zXV+2jgqyO1qpR8gEAAAAAJ6Wq1qm/fLZe/125V5I0qnusnh7bU0G+VEyr8Q4AAAAAAE7YnsIK3fbeCm3ILpHdJt07Ml23DGsnm43r75sDSj4AAAAA4ITM3Zyvuz5araKKWkUE+mjaNb11RvtIq2PhFyj5AAAAAIBjcrkMvfDDVv3z+60yDKlnYqheHt9X8WH+VkfDr1DyAQAAAABHVVRRo7s+Wq25mwskSdcOTNZDo7vI18thcTIcCSUfAAAAAHBE67OKddt7K7T3QKV8vex68tLuurxvotWxcAyUfAAAAADAYT5atlsPfr5BNXUuJYcH6JXxfdUlPsTqWDgOSj4AAAAAoF5VrVMPf75BHy3fI0k6Nz1a/7iyl0IDvC1OhhNByQcAAAAASDJvjzfx/ZVal1Usm036w3kdNXF4mux2bo/XUlDyAQAAAAD6X4Z5e7ziylq1CfDWC1f31rAOUVbHwkmi5AMAAABAK+Z0GXruuy168X/bJEk9k8L0r2v7KIHb47VIlHwAAAAAaKX2lVXr9/9epZ+27ZckXT84RX+5qDO3x2vBKPkAAAAA0Aqt2FWoSe+vUm5JlQJ8HJp6WXdd0ivB6lg4TZR8AAAAAGhFDMPQ//20U1O/3qQ6l6G06CC9fG0fdYgJtjoaGgElHwAAAABaidKqWt3z37X6el2uJGl0z3j97bLuCvSlGnoK3kkAAAAAaAUycks08b2V2rGvXN4Omx64qIuuH5wim43b43kSSj4AAAAAeLiPl+/Rg5+vV1WtS/Ghfnrp2j7qndzG6lhwA0o+AAAAAHioyhqnHp65Xv9ZvleSdFbHKD13VS+FB/pYnAzuQskHAAAAAA+0o6BME99fqYzcUtlt0pTzOmri8DTZ7Zye78ko+QAAAADgYb5cm617Plmr8hqnIoN89cK4XjojLdLqWGgClHwAAAAA8BDVdU49+dUmvb1olyRpQGq4Xry6t6JD/CxOhqZCyQcAAAAAD7D3QIUmvb9Sa/YWS5ImDm+vKed1lJfDbnEyNCVKPgAAAAC0cHM25ukPH69RcWWtQv299dxVPXVOeozVsWABSj4AAAAAtFC1TpeenpWh1+dnSpJ6JoXppWt6K7FNgMXJYBVKPgAAAAC0QFlFlZr8wUqt2l0kSbppSKruHZkuHy9Oz2/NKPkAAAAA0ML8kJGnKf9Zo6KKWgX7eemZsT11YbdYq2OhGaDkAwAAAEALUet06e+zN+vVeTskST0SQ/XSNX2UFM7p+TBR8gEAAACgBcguqtQdH67Sil0HJEkTzmir+0aly9fLYXEyNCeUfAAAAABo5v6Xka8p/1mtAxW1Cvb10tNje2hk9zirY6EZouQDAAAAQDNV63Tp799u1qs/mqfnd0sI0UvX9FFKRKDFydBcUfIBAAAAoBnae6BCd3y4qn71fE7Px4mg5AMAAABAM/Pthlz96eM1KqmqO7h6fg9d2I3T83F8lHwAAAAAaCaq65z62zcZmv7TTklSz6QwvXh1b1bPxwmj5AMAAABAM7Brf7kmf7BK67KKJUm3DEvVny5Il4+X3eJkaEko+QAAAABgsS/XZuu+/65TaXWdwgK89ewVPXVu5xirY6EFouQDAAAAgEUqa5x67MuN+nDpbklSv5Q2euHq3ooP87c4GVoqSj4AAAAAWGBLXqkmf7BSW/LKZLNJt5/VXlPO6ygvB6fn49RR8gEAAACgCRmGoY+W7dEjX2xQVa1LkUG+ev6qXhraIdLqaPAAlHwAAAAAaCIlVbW6/9N1+nJtjiRpWIdI/ePKXooK9rU4GTwFJR8AAAAAmsCaPUW648NV2l1YIS+7TX+8oJNuHdZOdrvN6mjwIJR8AAAAAHAjl8vQmwsy9dSsDNW5DCW28dcLV/dWn+Q2VkeDB6LkAwAAAICbFJRW648fr9G8LQWSpFHdYzX1sh4K9fe2OBk8FSUfAAAAANxg/tYC3f3RGu0rq5avl10Pje6iawYky2bj9Hy4DyUfAAAAABpRTZ1Lz363Wa/O2yFJ6hgTpGlX91Gn2GCLk6E1oOQDAAAAQCPZtb9cd364Smv2FkuSxg9K1gMXdZGft8PiZGgtKPkAAAAA0AhmrMrSAzPWq6y6TqH+3nrq8h66sFus1bHQylDyAQAAAOA0lFXX6aHP1+vTlVmSpAFtw/XcuF5KCPO3OBlaI0o+AAAAAJyitXuL9Pt/r1bmvnLZbdKd53bQ5LPT5OWwWx0NrRQlHwAAAABOkstl6LX5O/T3bzerzmUoLtRP/xzXWwNSw62OhlbOo3691LZtW9lstsO2SZMmSZKGDx9+2L7bbrvN4tQAAAAAWpLc4ipd939L9LdvMlTnMjSqe6y++f0wCj6aBY+ayV+2bJmcTmf98/Xr1+u8887TFVdcUT92yy236LHHHqt/HhAQ0KQZAQAAALRcszfk6p7/rtWBilr5ezv0yG+66Mp+SbLZbFZHAyR5WMmPiopq8Pxvf/ub2rdvr7POOqt+LCAgQLGxrHAJAAAA4MRV1jj1xNcb9d7i3ZKkrvEheuHq3mofFWRxMqAhjzpd/5dqamr03nvv6aabbmrwW7X3339fkZGR6tatm+677z5VVFQc83Wqq6tVUlLSYAMAAADQemzKKdFvXlxQX/BvPbOdPp14BgUfzZJHzeT/0owZM1RUVKQJEybUj11zzTVKSUlRfHy81q5dq3vuuUebN2/Wp59+etTXmTp1qh599NEmSAwAAACgOXG5DL21cKf+9k2GapwuRQX76h9X9tSwDlHH/2TAIjbDMAyrQ7jDBRdcIB8fH33xxRdHPeaHH37Queeeq23btql9+/ZHPKa6ulrV1dX1z0tKSpSUlKTi4mKFhIQ0em4AAAAA1ssvqdIfP1mrH7cUSJLOTY/W02N7KCLI1+JkaI1KSkoUGhp6Qj3UI2fyd+3apTlz5hxzhl6SBg4cKEnHLPm+vr7y9eV/ZAAAAKC1+G5jnu7571oVltfI18uuBy7qrPGDUlhcDy2CR5b86dOnKzo6WhdddNExj1u9erUkKS4urglSAQAAAGjOKmrq9PhXm/TBEvPa+y5xIXrh6l5Kiw62OBlw4jyu5LtcLk2fPl033HCDvLwOfXvbt2/XBx98oFGjRikiIkJr167V3XffrTPPPFM9evSwMDEAAAAAq63PKtad/16lHQXlkszF9f5wfkf5ejksTgacHI8r+XPmzNHu3bt10003NRj38fHRnDlz9Pzzz6u8vFxJSUm6/PLL9cADD1iUFAAAAIDVnC5Dr8/foWdnb1at01BMiK/+cWUvDUmLtDoacEo8duE9dzmZBQ8AAAAANF/ZRZX6w3/WaNGO/ZKkkd1i9eSl3dUm0MfiZEBDrX7hPQAAAAA4ls9XZ+mBGetVWlWnAB+HHhndVVf0S2RxPbR4lHwAAAAArUZxZa0enLFeM9dkS5J6JYXpuat6KTUy0OJkQOOg5AMAAABoFRZt368//Ge1sour5LDbdMc5aZp8dpq8HHarowGNhpIPAAAAwKNV1zn1j9lb9Nr8HTIMqW1EgJ67qpd6J7exOhrQ6Cj5AAAAADzW5txS3fXRam3KKZEkXT0gSQ9c1EWBvlQheCb+ywYAAADgcVwuQ9MX7tRTszJUU+dSeKCP/nZZd53fNdbqaIBbUfIBAAAAeJSsokr96eM1WrjdvDXe2Z2i9NTYHooO9rM4GeB+lHwAAAAAHsEwDM1YnaWHPt+g0qo6+Xs7dP9FnTV+YDK3xkOrQckHAAAA0OIdKK/RAzPW66t1OZKknklheu7KnmoXFWRxMqBpUfIBAAAAtGhzN+frz5+sVX5ptbzsNt15bgdNHN6eW+OhVaLkAwAAAGiRKmrq9OTXm/Te4t2SpPZRgXruql7qkRhmbTDAQpR8AAAAAC3Oyt0H9If/rFHmvnJJ0oQz2urekeny83ZYnAywFiUfAAAAQItRU+fSP7/fopfnbpfLkGJD/PTMFT00rEOU1dGAZoGSDwAAAKBF2JRToin/WaNNOSWSpDG94vXob7opNMDb4mRA80HJBwAAANCsOV2GXvtxh577botqnC61CfDWE5d216jucVZHA5odSj4AAACAZmvnvnL98eM1Wr7rgCTp3PRoTb28u6KD/SxOBjRPlHwAAAAAzY5hGHp/yW498dUmVdY6FeTrpYcu7qIr+iXKZrNZHQ9otij5AAAAAJqV7KJK3fPftZq/dZ8kaVC7cD0ztqeSwgMsTgY0f5R8AAAAAM2CYRj678osPfrFBpVW1cnXy657LkzXhDPaym5n9h44EZR8AAAAAJbLL63S/Z+u05xN+ZKkXklhevbKnmofFWRxMqBloeQDAAAAsNQXa7L14OfrVVRRK2+HTXef11G3DmsnL4fd6mhAi0PJBwAAAGCJwvIaPThjvb5alyNJ6hofomev7Kn02BCLkwEtFyUfAAAAQJObvSFX93+2TvvKauRlt2nS2WmafE6avJm9B04LJR8AAABAkymqqNGjX2zUZ6uyJEkdY4L07BW91D0x1OJkgGeg5AMAAABoEt9tzNP9n61TQWm17Dbp1jPb6+7zOsjXy2F1NMBjUPIBAAAAuNWvZ+/bRwXq71f0VO/kNhYnAzwPJR8AAACA28w5OHuff3D2/pZh7XT3eR3l583sPeAOlHwAAAAAja64olaPfrlBn640Z+/bHZy978PsPeBWlHwAAAAAjeqHjDzd9+k65ZUwew80NUo+AAAAgEbx62vv20UG6pkreqpvCrP3QFOh5AMAAAA4bbPW5+qBGeu1r8ycvb95aKr+cH4nZu+BJkbJBwAAAHDK9pdV6+GZG/Tl2hxJUlp0kJ4Z24OV8wGLUPIBAAAAnDTDMPTl2hw9PHODCstr5LDb9Lsz2+nOczswew9YiJIPAAAA4KTkl1bpwRnr9e2GPElSemywnhnbU90TQy1OBoCSDwAAAOCEGIahz1Zl6bEvN6qoolZedpsmnp2myWenycfLbnU8AKLkAwAAADgBWUWV+stn6zR3c4EkqUtciJ65ooe6xjN7DzQnlHwAAAAAR+VyGXp/6W797etNKq9xysdh1+9HdNCtZ7aTt4PZe6C5oeQDAAAAOKLMfeW6579rtTSzUJLUN6WNnrq8h9KigyxOBuBoKPkAAAAAGqhzuvTmgkz947stqq5zyd/boT9f2EnXD24rh91mdTwAx0DJBwAAAFAvI7dEf/5krdbuLZYkDU2L1NTLuispPMDiZABOBCUfAAAAgKrrnHrxh216ee521bkMBft56cGLuuiKfomy2Zi9B1oKSj4AAADQyi3fWah7/rtW2wvKJUnndYnR42O6KSbEz+JkAE4WJR8AAABopUqravX0rM16d/EuSVJkkK/+eklXXdgtltl7oIWi5AMAAACt0A8ZefrLZ+uVU1wlSbqyX6L+MqqLQgO8LU4G4HRQ8gEAAIBWZF9ZtR79YqO+WJMtSUoOD9DUy7prSFqkxckANAZKPgAAANAKGIahT1dm6fGvNupARa3sNum3w9rp7hEd5e/jsDoegEZCyQcAAAA83K795frLZ+u1YNs+SVJ6bLCeHttDPRLDrA0GoNFR8gEAAAAPVet06Y35mXp+zhZV17nk62XX70d00C3D2snbYbc6HgA3oOQDAAAAHmjNniLd++k6bcopkSQNSYvQE2O6q21koMXJALgTJR8AAADwIOXVdXp29ha9tTBTLkMKC/DWAxd10eV9ErgtHtAKUPIBAAAAD/G/jHw9MGO9sooqJUljesXrwYu7KCLI1+JkAJoKJR8AAABo4fJLqvToFxv11bocSVJiG389cWl3ndUxyuJkAJoaJR8AAABooVwuQ+8v3a2nv8lQaXWdHHabbh6aqrtGdFCADz/qA60R/+cDAAAALdCmnBLd/9k6rdpdJEnqmRSmJy/tpq7xodYGA2ApSj4AAADQglTWOPXP77fqjfk7VOcyFOTrpT9f2EnXDkyRw87CekBrR8kHAAAAWoi5m82F9fYeMBfWG9ktVg+P7qrYUD+LkwFoLij5AAAAQDOXV1Klv365UV+uNRfWiw/102OXdNOILjEWJwPQ3FDyAQAAgGbK6TL03uJd+vu3m1VaXSe7TbpxSKqmnNdRgb78KA/gcPzNAAAAADRD6/YW6/7P1mldVrEkc2G9J8Z0U7cEFtYDcHSUfAAAAKAZKamq1T9mb9E7i3bKZUjBfl6658J0XT0gmYX1ABwXJR8AAABoBgzD0NfrcvXoFxuUX1otSbqkV7z+clFnRQezsB6AE0PJBwAAACy2c1+5Hp65QfO2FEiSUiMD9ddLumloh0iLkwFoaSj5AAAAgEWqap16Zd52/WvudtXUueTjsGvi2e1121nt5eftsDoegBaIkg8AAABYYO7mfD08c4N27a+QJA3rEKlHf9NV7aKCLE4GoCWj5AMAAABNKKe4Un/9cqO+XpcrSYoJ8dVDF3fVqO6xstlYWA/A6aHkAwAAAE2g1unS9J8y9fycraqoccpht+nGM9rqrvM6Koh73gNoJPxtAgAAALjZ0sxCPThjvTbnlUqS+qa00eNjuqlzXIjFyQB4Gko+AAAA4Cb5pVWa+nWGPluVJUkKD/TRvSPTNbZPouzc8x6AG1DyAQAAgEZW53TpnUW79Nx3W1RaXSebTRrXP1l/vqCT2gT6WB0PgAej5AMAAACNaGlmoR76fL0ycs1T83skhuqvl3RTz6Qwa4MBaBUo+QAAAEAjyC+t0t++ztCnB0/NDwvw1p8vSNdV/ZPk4NR8AE2Ekg8AAACchjqnS+8u3qV/zObUfADWo+QDAAAAp2jxjv16ZOaGBqfmP3ZJN/Xi1HwAFqHkAwAAACcpt7hKT369STPXZEsyT83/4/mddPWAZE7NB2ApSj4AAABwgmrqXHpzQaam/bBVFTVO2WzSNQOS9cfzOTUfQPNAyQcAAABOwLwtBXp05gbt2FcuSeqTHKbHLummbgmhFicDgEMo+QAAAMAx7Cms0F+/3KjZG/MkSZFBvrpvZLou7Z0gO6fmA2hm7FYHaEyPPPKIbDZbgy09Pb1+f1VVlSZNmqSIiAgFBQXp8ssvV15enoWJAQAA0FxV1NTpH7M369x/zNPsjXnystv026Gp+uGPZ+nyvokUfADNksfN5Hft2lVz5sypf+7ldehbvPvuu/XVV1/p448/VmhoqCZPnqzLLrtMP/30kxVRAQAA0AwZhqEv1uZo6teblFNcJUkakhahR0Z3VYeYYIvTAcCxeVzJ9/LyUmxs7GHjxcXFevPNN/XBBx/onHPOkSRNnz5dnTt31uLFizVo0KCmjgoAAIBmZkN2sR6duVFLdxZKkhLb+OuBi7rogq4xstmYuQfQ/Hlcyd+6davi4+Pl5+enwYMHa+rUqUpOTtaKFStUW1urESNG1B+bnp6u5ORkLVq06Kglv7q6WtXV1fXPS0pK3P49AAAAoGkVltfo2dmb9eHS3XIZkp+3XZOGp+mWM9vJz9thdTwAOGEeVfIHDhyot956S506dVJOTo4effRRDRs2TOvXr1dubq58fHwUFhbW4HNiYmKUm5t71NecOnWqHn30UTcnBwAAgBXqnC69v2S3np29WSVVdZKk0T3jdd/IdMWH+VucDgBOnkeV/JEjR9Z/3KNHDw0cOFApKSn6z3/+I3//U/tL+r777tOUKVPqn5eUlCgpKem0swIAAMBa87cW6K9fbtSWvDJJUue4ED0yuosGtouwOBkAnDqPKvm/FhYWpo4dO2rbtm0677zzVFNTo6Kiogaz+Xl5eUe8hv9nvr6+8vX1bYK0AAAAaAqZ+8r1xFebNGeTeZelNgHe+sP5nXT1gGQ5WDEfQAvnUbfQ+7WysjJt375dcXFx6tu3r7y9vfX999/X79+8ebN2796twYMHW5gSAAAATaGkqlZPfr1J5z83T3M2mbfEu2lIqub+8WyNH5RCwQfgETxqJv+Pf/yjRo8erZSUFGVnZ+vhhx+Ww+HQ1VdfrdDQUN18882aMmWKwsPDFRISojvuuEODBw9mZX0AAAAP5nQZ+nj5Hv199mbtK6uRJA3vFKUHLuqitOggi9MBQOPyqJK/d+9eXX311dq/f7+ioqI0dOhQLV68WFFRUZKk5557Tna7XZdffrmqq6t1wQUX6F//+pfFqQEAAOAuS3bs12NfbtSGbPMOSe2iAvXgRV10dnq0xckAwD1shmEYVodoSUpKShQaGqri4mKFhIRYHQcAAABHsGt/uaZ+naFZG8y7KAX7een353bQ9YPbysfLo69YBeCBTqaHetRMPgAAAFq3kqpavfTDNk3/aadqnC7ZbdLVA5I15byOighiMWUAno+SDwAAgBavzunSv5ft0XPfbdH+cvO6+2EdIvXARV3UKTbY4nQA0HQo+QAAAGjRftxSoMe/OnS/+3ZRgXrgos46u1O0bDZWzAfQulDyAQAA0CJtyy/Vk19n6IeMfElSWIC37jq3g64dlCJvB9fdA2idKPkAAABoUfaVVev5OVv04dI9croMedltun5wW915bprCAnysjgcAlqLkAwAAoEWoqnVq+k879dL/tqmsuk6SNKJzjO4bla72UdzvHgAkSj4AAACaOcMwNHNNtp6etVlZRZWSpG4JIfrLqC4a3D7C4nQA0LxQ8gEAANBsLd9ZqL9+tUlr9hRJkmJD/PSnCzrp0t4JsttZVA8Afo2SDwAAgGYnc1+5np6VoW/W50qSAnwcuv2s9vrtsHby93FYnA4Ami9KPgAAAJqNwvIavfD9Vr23eJfqXIbsNumq/km6+7yOig72szoeADR7lHwAAABYrqrWqf/7KVMv/2+7Sg8uqje8U5TuG9lZnWKDLU4HAC0HJR8AAACWcbkMfboqS8/O3qyc4ipJUtf4EN0/qrOGpEVanA4AWh5KPgAAACwxf2uBnvw6Q5tySiRJCWH++uMFHXVJTxbVA4BTRckHAABAk9qQXay/fZOh+Vv3SZKC/bw06ew0TTijrfy8WVQPAE4HJR8AAABNYk9hhZ6dvVkzVmdLkrwdNo0flKI7z+mgNoE+FqcDAM9AyQcAAIBbHSiv0Yv/26Z3F+1SjdMlSfpNz3j98fxOSo4IsDgdAHgWSj4AAADcon7F/LnbVVplrpg/JC1C917YWd0TQy1OBwCeiZIPAACARlXndOnTlVn6x3dblFtirpjfOS5E941M17AOkbLZWFQPANyFkg8AAIBGYRiGvt2Qp7/P3qxt+WWSWDEfAJoaJR8AAACnbdH2/XpqVoZW7ymSJLUJ8Naks9M0flAKK+YDQBOi5AMAAOCUrc8q1tPfbtaPWwokSf7eDv12WKpuObOdQvy8LU4HAK0PJR8AAAAnbdf+cj07e4tmrjFvh+dlt+magcmafE6aooP9LE4HAK0XJR8AAAAnLL+kSi/8sFX/XrpHdS5Dknk7vD+c31EpEYEWpwMAUPIBAABwXEUVNXp53na9vXCnqmrNe92f1TFKf76wk7rGczs8AGguKPkAAAA4qvLqOv3fgky99uMOlVab97rvm9JGf7qgkwa1i7A4HQDg1yj5AAAAOEx1nVPvL96tl/63TfvLaySZ97r/0wUddXanaO51DwDNFCUfAAAA9eqcLn26Mkv//H6rsooqJUltIwI05fxOurh7HPe6B4BmjpIPAAAAuVyGvlibrefnbFXmvnJJUmyIn34/ooPG9k2Ut8NucUIAwImg5AMAALRihmHo2w15eu67LdqcVypJCg/00cTh7TV+UIr8vB0WJwQAnAxKPgAAQCtkGIbmbSnQs7O3aF1WsSQpxM9LvzurvSac0VaBvvyYCAAtEX97AwAAtDKLtu/Xs7M3a/muA5KkQB+Hbhqaqt8Oa6dQf2+L0wEATgclHwAAoJVYsatQ//hui37atl+S5Otl1w1ntNXvzmyniCBfi9MBABoDJR8AAMDDrdp9QM/N2aoftxRIkrwdNl09IFmTzk5TTIifxekAAI2Jkg8AAOCh1u0t1nNztuiHjHxJkpfdpiv6JWrS2WlKbBNgcToAgDtQ8gEAADzMxuwSPT9ni2ZvzJMkOew2XdY7QXec00HJEZR7APBklHwAAAAPsTm3VP/8fou+XpcrSbLZpDG9EnTnuR2UGhlocToAQFOg5AMAALRwm3NL9cL3W/XVuhxJZrm/qHuc7hrRQWnRwRanAwA0JUo+AABAC/Xrci+Z5f7OczuoUyzlHgBaI0o+AABAC3O0cn/HuWlKjw2xMBkAwGqUfAAAgBYiI7dE077fRrkHABwVJR8AAKCZW59VrGk/bNW3G/Lqxyj3AIAjoeQDAAA0U2v2FGnaD1s1Z5N5n3ubTRrVjXIPADg6Sj4AAEAzs2LXAb3w/VbN21IgSbLbpNE94zX57DR1iGFBPQDA0VHyAQAAmomlmYV64futWrBtnyTJYbfpkl5muW8XFWRxOgBAS0DJBwAAsJBhGFqwbZ+m/bBNSzMLJUledpsu75OoiWe3V0pEoMUJAQAtCSUfAADAAoZhaM6mfL34w1at2VssSfJ22DS2b5ImDm+vpPAAixMCAFoiSj4AAEATcroMfbM+Ry/+sE0ZuaWSJD9vu64ekKxbz2ynuFB/ixMCAFoySj4AAEATqHW6NHN1tl6au007CsolSYE+Dl1/RlvdPDRVkUG+FicEAHgCSj4AAIAbVdU69fHyPXpl3g5lFVVKkkL9vXXjkLaacEZbhQX4WJwQAOBJKPkAAABuUFpVq/cW79abCzK1r6xakhQZ5KPfDmun8YNSFOTLj2EAgMbHvy4AAACNaH9Ztab/tFNvL9qp0qo6SVJCmL9+d1Y7XdkvSX7eDosTAgA8GSUfAACgEWQXVer1+Tv04dLdqqp1SZLSooN0+1nt9Zte8fJ22C1OCABoDSj5AAAAp2FbfqlembdDM1Zlqc5lSJJ6JIZq4vA0nd8lRna7zeKEAIDWhJIPAABwClbsOqCX527XnE159WOD20Vo0tlpGpIWIZuNcg8AaHqUfAAAgBNkGIbmbi7Qy3O3a+nOQkmSzSZd0CVWtw1vr15JYdYGBAC0epR8AACA46h1uvTV2hy9Mm+7MnJLJUneDpsu652oW89qp/ZRQRYnBADARMkHAAA4ivLqOn20bI/eXJBZf4/7QB+Hrh2UopuGpCo21M/ihAAANETJBwAA+JX80iq9vXCn3lu8W8WVtZKkiEAf3TQ0VeMHpig0wNvihAAAHBklHwAA4KDtBWV6Y/4O/XdllmrqzNvgpUYG6pZh7XRZnwTucQ8AaPYo+QAAoNVbsatQr87boe825ckw74KnPslhuvXM9jqvS4wc3AYPANBCUPIBAECr5HQZ+nZDrl6fv0OrdhfVj4/oHKPbzmqnfm3DrQsHAMApouQDAIBWpby6Tv9Zvkf/91Om9hSai+n5OOy6rE+CfjusndKiWSkfANByUfIBAECrkFdSpbcW7tT7i3eppKpOktQmwFvXDUrRdYPbKirY1+KEAACcPko+AADwaBuzS/TGgh36Yk22ap3mBfepkYG6eWiqLu+TKH8fFtMDAHgOSj4AAPA4LpehHzLy9eaCTC3asb9+fEDbcP12WKpGdI6RncX0AAAeiJIPAAA8RkVNnT5ZsVfTf9qpzH3lkiSH3aaR3WJ1y7B26pkUZm1AAADcjJIPAABavOyiSr29aKc+XLK7/nr7YD8vXTMgWdef0VYJYf4WJwQAoGlQ8gEAQIu1avcB/d9PO/X1uhw5Xeb19m0jAnTjkFSN7ZuoQF9+1AEAtC78ywcAAFqUmjqXvlmfo//7aafW7CmqHx/ULlw3D22nc9Kj5eB6ewBAK0XJBwAALcK+smp9sGS33lu8S/ml1ZLM+9uP7hmvG4e0VbeEUIsTAgBgPUo+AABo1jZkF2v6Tzs1c022aupckqSoYF+NH5iiawYmc397AAB+gZIPAACanVqnS7M35OnthTu1dGdh/XjPxFDdOCRVo7rHycfLbmFCAACaJ0o+AABoNvaVVevDJbv1/pLdyi2pknToFng3DklVn+Qw2Wxcbw8AwNFQ8gEAgOXW7CnS2wt36su1OapxmqfkRwb56OoBybpmYLLiQrkFHgAAJ4KSDwAALFFd59TX63L09sJdWv2LVfJ7JoVpwhkpGtU9Tr5eDusCAgDQAlHyAQBAk8oqqtT7i3fpo2V7tL+8RpK5Sv7FPeJ0/Rlt1SspzNqAAAC0YJR8AADgdi6XoQXb9umdRbv0Q0aeXIY5Hhvip/GDkjVuQLIig1glHwCA0+VRy9JOnTpV/fv3V3BwsKKjozVmzBht3ry5wTHDhw+XzWZrsN12220WJQYAwLMVV9Tqjfk7dO4/5un6/1uqOZvMgj8kLUKvjO+rBfecrcnndKDgAwDQSDxqJn/evHmaNGmS+vfvr7q6Ot1///06//zztXHjRgUGBtYfd8stt+ixxx6rfx4QEGBFXAAAPNbavUV6b/EuzVyTrapacyG9YF8vXd43UeMHpSgtOsjihAAAeCaPKvmzZs1q8Pytt95SdHS0VqxYoTPPPLN+PCAgQLGxsU0dDwAAj1ZRU6cv1mTrvcW7tS6ruH48PTZY1w9uq0t6xSvQ16N+9AAAoNnx6H9pi4vNHzDCw8MbjL///vt67733FBsbq9GjR+vBBx886mx+dXW1qqur65+XlJS4LzAAAC3QlrxSvb94lz5dmaXS6jpJ5kJ6o7rH6tpBKeqX0oZ72wMA0EQ8tuS7XC7dddddGjJkiLp161Y/fs011yglJUXx8fFau3at7rnnHm3evFmffvrpEV9n6tSpevTRR5sqNgAALUJ1nVOz1ufq/cW7tXRnYf14SkSArhmQrCv6JSk80MfChAAAtE42wzAMq0O4w+23365vvvlGCxYsUGJi4lGP++GHH3Tuuedq27Ztat++/WH7jzSTn5SUpOLiYoWEhLglOwAAzdX2gjL9e+lufbJirw5U1EqSHHabRnSO1vhBKRrSPlJ2O7P2AAA0ppKSEoWGhp5QD/XImfzJkyfryy+/1I8//njMgi9JAwcOlKSjlnxfX1/5+rLiLwCg9aqqderbDbn6YMluLck8NGsfG+KncQOSNK5/smJD/SxMCAAAfuZRJd8wDN1xxx367LPPNHfuXKWmph73c1avXi1JiouLc3M6AABalm35Zfpw6W79d+VeFR2ctbfbpHPSo3X1gGSd1TFKXg6PuhsvAAAtnkeV/EmTJumDDz7Q559/ruDgYOXm5kqSQkND5e/vr+3bt+uDDz7QqFGjFBERobVr1+ruu+/WmWeeqR49elicHgAA61XWOPXN+hz9e9keLf3FrH1cqJ+u6p+kq/onKS7U38KEAADgWDzqmvyjrdw7ffp0TZgwQXv27NH48eO1fv16lZeXKykpSZdeeqkeeOCBE76+/mSuhQAAoKVYn1Wsj5bt0YzVWSqtMlfIN2ftY3TNwCSd1TFaDq61BwDAEq32mvzj/b4iKSlJ8+bNa6I0AAA0byVVtfp8dbY+WrZb67MO3SI2sY2/ruqXpLH9Epm1BwCghfGokg8AAI7NMAwtzSzUR8v36Ot1OaqqdUky72t/ftcYjeufrDPaR7BCPgAALRQlHwCAViC3uEr/XblXHy/fo537K+rHO8YE6ar+ybq0dwL3tQcAwANQ8gEA8FDVdU59vylf/1m+Rz9uKZDr4FVtgT4OXdwjXlcNSFLvpLCjrmkDAABaHko+AAAeZmN2iT5esUczVmXpwMFb30nSgNRwXdkvSaO6xyrAhx8BAADwRPwLDwCAB9hfVq3PV2frkxV7tTHn0CJ6MSG+Gts3UWP7Jik1MtDChAAAoClQ8gEAaKFq6lz63+Z8fbJir/6Xka+6g+fj+zjsGtElWlf0S9KZHaK49R0AAK0IJR8AgBbEMAxtyC7RJyv2auaabBWW19Tv65kYqsv7Jmp0j3i1YRE9AABaJUo+AAAtQF5JlWasytJnq7KUkVtaPx4V7KvLeifo8r6J6hgTbGFCAADQHFDyAQBopipq6jR7Q57+u3Kvftq2r351fB+HXed1idHYvoka1iFSXg67tUEBAECzQckHAKAZcboMLd6xX5+uzNKs9Tkqr3HW7+uX0kaX9knQxd3jFRrgbWFKAADQXFHyAQBoBjbllGjG6izNXJ2tnOKq+vHk8ABd2jtBl/ZOUFtWxwcAAMdByQcAwCLZRZX6fHW2Pl/d8Dr7ED8vXdQjXpf3SVDflDay2VgdHwAAnBhKPgAATai4olZfr8/RjFVZWpJZWD/u47Dr7PQojemVoLPTo+Xn7bAwJQAAaKko+QAAuFlljVPfZ+Rp5upszd1coBqnq37fwNRwXdo7QSO7xXGdPQAAOG2UfAAA3KDW6dKCrfs0c022Zm/IbbCAXnpssC7plaDf9IpXQpi/hSkBAICnoeQDANBIXC5Dy3YWauaabH29LkcHKmrr9yW28dfonvH6Tc94dY4LsTAlAADwZJR8AABOg2EYWrO3WF+uydZX63IarIwfGeSji3vEa3TPePVJDmMBPQAA4HaUfAAATpJhGNqYU6Iv1uToq3XZ2lNYWb8v2M9LF3aN1W96xWtwuwh5OewWJgUAAK0NJR8AgBO0Ja9UX67J1pdrc7RjX3n9uL+3QyO6xOjiHnE6q2MUK+MDAADLUPIBADiGrXml+mpdjr5el6MteWX1475edp3dKVqje8brnPRo+ftQ7AEAgPUo+QAA/MqWvFJ9tdYs9lvzDxV7b4dNZ3WM0sU94jWiS4yCfPlnFAAANC/8dAIAaPUMw9CWvLL6Gfttvyj2Pg67hnWI1KjucRrRJUah/tzLHgAANF+UfABAq2QYhtZnleib9TmatT63wTX2Pg67zux4qNiH+FHsAQBAy0DJBwC0Gi6XoZW7D+ib9bmatT5XWUWHVsWn2AMAAE9AyQcAeLRap0tLMws1a32uvt2Qq/zS6vp9/t4OnZ0epQu6xuqc9GgFU+wBAEALR8kHAHicyhqn5m0p0OyNufp+U76KK2vr9wX7euncztG6sJt5uztWxQcAAJ6Ekg8A8AgHymv0fUa+vt2Qq/lbC1RV66rfFx7ooxGdozWyW5zOSIuQrxfFHgAAeCZKPgCgxdpTWKE5m/I0e0Oelu4slNNl1O9LCPPXBV1jdUHXGPVrGy6H3WZhUgAAgKZByQcAtBgul6H12cX6bmOevtuYp4zc0gb702ODdf7BYt8lLkQ2G8UeAAC0LpR8AECzVl3n1MLt+zVnY57mbMpTXsmhhfPsNqlf23Cd1zlG53eNUUpEoIVJAQAArEfJBwA0OwWl1fpfRr6+z8jT/K37VFHjrN8X4OPQWR2jNKJzjM5Jj1abQB8LkwIAADQvlHwAgOUMw9DGnBL9sClfczLytWZPUYP90cG+GtElRud1idHgdhHy82bhPAAAgCOh5AMALFFRU6dF2/frh4x8/ZCRr5ziqgb7uyeE6tzO0To3PUZd40NkZ+E8AACA46LkAwCazK795fpfRr5+2FygxTv2q6bu0G3u/LztGpoWpXM7R+uc9GjFhPhZmBQAAKBlouQDANymus6pZZkH9L/N+fpfRr527CtvsD8hzF9np0fp3PQYDW7PafgAAACni5IPAGhUu/dXaN6WfM3bUqCF2/c3WDTPy25T/7bhOjs9Smd3ilZadBC3uQMAAGhElHwAwGmprHFqceZ+zdtcoHlbCpT5q9n6qGBfnd3JLPVDO0Qq2M/boqQAAACej5IPADgphmFoc16pFmzdp3lbCrQks7DBtfVedpv6prTRWZ2idFbHKHWJC2G2HgAAoIlQ8gEAx1VQWq2ftu3Tj1sLtGDrPuWXVjfYnxDmrzM7mqV+SFoEs/UAAAAWoeQDAA5TVevU8p0HNH9bgeZv2aeNOSUN9vt52zUwNULDOkRqeKcotY/i2noAAIDmgJIPAJDTZWhDdrEWbNunn7bt07KdBxqcgi9JXeNDNKxDlM7sEKk+KW1YCR8AAKAZouQDQCtkGIZ27q/Qgm37tHDbPi3cvl/FlbUNjokN8dOQtEid2TFSQ9IiFRnka1FaAAAAnChKPgC0EllFlVq0fb8Wbt+nxdv3K7u4qsH+YF8vDWofoaFpZqlvHxXIKfgAAAAtDCUfADxUfmmVFm3fb2479mvX/ooG+70d5ir4P5f67gmh8nLYLUoLAACAxkDJBwAPkV9apSU7CrV4x34tySzUtvyyBvsddpu6J4TqjPYRGtw+Qv1SwuXvw3X1AAAAnoSSDwAtVF5JlRbv2K/FOwq1JHO/dhSUN9hvs0ld4kI0uF2EzkiLUP+24dzaDgAAwMNR8gGgBTAMQ3sPVGppZqG57SxU5r7DS316bIgGtQvXwNQIDUwNV5tAH4sSAwAAwAqUfABohlwuQ1vzy7R0p1nql2UWKrek4UJ5dpvUJT5EA1MjNKhdhAa0DVdoADP1AAAArRklHwCageo6p9btLdbyXQe0fOcBLd9VqKKKhre087Lb1D0xVANSwzWgbbj6tQ1XqD+lHgAAAIdQ8gHAAoXlNVqxyyzzK3Ye0Nq9xapxuhoc4+/tUJ+UMPVvG64BqeHqndSGhfIAAABwTJR8AHAzl8vQtoIyrdx1QCt3H9DyXQcOWyRPkiKDfNQ3pY36pYSrf2q4usaHyJtb2gEAAOAkUPIBoJEVV9Zq9Z6i+lK/ek+RSqvqDjsuLTpI/VLaqG9KG/VvG66UiADZbDYLEgMAAMBTUPIB4DTUOV3anFeqNXuKtXrPAa3aXaRtBWUyjIbH+Xs71DMpVH2S26hPslnsWfkeAAAAjY2SDwAnyDAM5RRXafWeInPbXaR1WcWqrHUedmxyeID6prRRn+Qw9U5uo/TYYHlx6j0AAADcjJIPAEdRWF6jNXuLtHZPsdZlFWnN3mIVlFYfdlywr5d6JIWqV1KYeiW1Ue/kMEUG+VqQGAAAAK0dJR8AJJVU1Wp9VrHW7i3W2r1FWru3WHsPVB52nMNuU3ps8MFCH6beyWFqFxkku51r6QEAAGA9Sj6AVqeookbrs0q0LqtY67OLtT6rWLv2Vxzx2HZRgeqZGKbuCaHqmRSqLnGh3MYOAAAAzRYlH4DHMgxD+aXV2phdog3ZxdqQbRb7I83QS1JiG3+z0CeGqkdiqLolhCrEz7uJUwMAAACnjpIPwCM4XYYy95VrY45Z6Ddml2hTTon2ldUc8fiUiAB1SwhVt/hQdU8IVbeEEIUFsNo9AAAAWjZKPoAWp7iyVhk5JcrILVVGbok25ZRqc27pEVe5t9uk9lFB6hIfoq7xIeqWEKqu8aEK9WeGHgAAAJ6Hkg+g2ap1urRzX7kycs0Sv+lgsc8qOvLp9v7eDqXHBatrfIi6xIWqS3yIOsUEcw09AAAAWg1KPgDLuVyG9h6o1Oa8Um3JMwv9lrxSbS8oU63TOOLnJIT5q3NcsNJjQ9Q5LkSdYoOVGhkoB6vcAwAAoBWj5ANoMk6Xob0HKrQ1r0xb88u0Nb9U2/LLtC2/TBU1h59qL0mBPg51jA1WemywOseFKD3WLPScbg8AAAAcjpIPoNFV1Tq1a3+FtheUaXt+mbYVlGlrXpm2F5Spus51xM/x8bIrLSpInWKD1TEmWJ1ig9QxJlgJYf6y2ZidBwAAAE4EJR/AKTEMQ/vKapS5r7y+zG8vKNOOfeXaU1gh15HPspevl13to4LUISZIHaKDlBYdrLToILWNCJCXw9603wQAAADgYSj5AI6puLJWO/eVK/MX28795cosKFdpdd1RPy/Yz0vto4LULipQHaKD1SHaLPaJbQK4bh4AAABwE0o+0MoZhqHC8hrtKqzQrv3l2rW/4uBmfry//Mj3mZckm81cAK99VJC5RQfWF/uoIF9OswcAAACaGCUfaAWq65zKOlCp3YUV2nOgUnsLK7T7521/xTFn5CUpOthXbSMD1S4yUKmRgfUfJ4UHyM+b29MBAAAAzQUlH/AA1XVOZRdVKetApbKKKpR1oFJ7iyq1p7BCeworlVdaJeMo18j/LD7UT8kRAWobEajkiAClhAcqJSJAbSMDFeTLXxUAAABAS8BP7kAzZxiG9pfXKKeoStnFlcopqlROcZWyiirN7UCl8kurj/s6AT4OJYcHKLFNgJLC/ZUcHqCkNgFqG2mOMSMPAAAAtHyUfMBCTpehfWXVyi2uUm5JlfJKquo/zimqUk6xWeiPdtu5X/LztiuxTYASwvyV0MZfCWH+SgoPOFjm/RUe6MM18gAAAICHo+QDblDndGlfWY3yS6tUUFqt/NJq5ZdU1z/PK61WXnGVCsqq5TzaveZ+JSrYV/GhfooL9VdcmJ/iQ/2V2OZQoafEAwAAAKDke6qacqm2UpLNXAJdOvhoa/hos0t2L8nmkOyOQ8fiMJU1ThVW1Gh/WbX2lVVrX1mN+Vhao/3l1Q0+3l9ec9xr4H/msNsUHeyr6BA/xYb4KjbETzGhZomPC/VTfJi/YkL85OPFPeQBAAAAHBsl31MtnCbNnXryn2ez/6LwO8xfADi8JLu35PA58sdevuZzL9+DH/se+tjLV/LyMzdv/4NbgPno9avnPoGST5DkE2Ae76ZfOBiGofIap4oqalRUUWtulT9/XKP95TU6UF6jwopaFZZX60B5rfaXV6uq9vinzP+Sw25TZJCPooP9DpZ4X0UF+ykq2Fcxwb6KDfVTbIifIoJ8uW88AAAAgEZx0iX/hhtu0M0336wzzzzTHXlgNcNlbq5aa3PY7AcLf6C5eQdIviGSb7BcvsGq8wpUtSNQ1fZAVdgCVGELUJn8VWwEqNDpr/1OfxXU+WlftY+Kq50qrqxVSWWtiivrVFxZo1rnCU6z/4qPw67wQB9FBvsoMshXEYG+igz2UVSQryKCDo1Fh/gqPMBHdso7AAAAgCZ00iW/uLhYI0aMUEpKim688UbdcMMNSkhIcEc2nI7h90pn3SPznHHj6I8up2Q4Dz66zEdX3aExl9Ms/M7aQ4/OWslZYx7nrJWc1VJdzcHHajlrq+SsqZSrtlrOmiq5aqvkqqmQq7ZSRk2lVFsh1VbKVlclu7NS9rpKeTnNzdt1cJV4wyVVl5jbr9gl+Rzcgo/zx+AybCqVv0qMQJUoQEVGkIrsgSq2BanUHqxq71DV+oTJ5Rcm+bWRPTBc3iFR8g+JVJvgQIUHeis80Czs4UE+CvRxcN07AAAAgGbLZhgneuXwIQUFBXr33Xf19ttva+PGjRoxYoRuvvlmXXLJJfL29nZHzmajpKREoaGhKi4uVkhIiNVxjmrelgLN3Zxff124yzBkGJKhnx/Nnm8Yhpyug9vBj131Y5LT5VKdy1Ct06U6p/lYe/Dx5/Fap0vVdS7V1JmPJ7qQ3JHY5VKAquSvagXaqhSoagWoSoG2SgWqWkG2SgWpQsG2SoXYqtTGq1qhdvPjEFuFglWhQKNM/s4yeRs1p/eH6BcmBURIgZHm489bYJS5BR18DIw2xx1c/QIAAACg8Z1MDz2lkv9LK1eu1PTp0/XGG28oKChI48eP18SJE9WhQ4fTeVm3e+mll/TMM88oNzdXPXv21LRp0zRgwIDjfl5LKfnPz9mi5+dstTqG7DbJ18shfx+H/Lzs8vNxyN/b3PwObj/vC/T1UoCP49Cjj5cCfM1Hfx+Hgny9FOznpSBfLwX5ecnX6zj3da+tMs8EqCqWKoukqiLz44pCqfLAwe2XHx+QKvabx+pk/7ewSQHhZuEPjJSCY6WgGHMLjpWCoqWgWCk4xvzlAWcDAAAAADhBJ9NDT2vqMScnR999952+++47ORwOjRo1SuvWrVOXLl309NNP6+677z6dl3ebjz76SFOmTNErr7yigQMH6vnnn9cFF1ygzZs3Kzo62up4jWJA23BNHN7eXEBftoOPkmw22aT6cbtNcjhscthsctgPbfafn9ts8vayyctul7fDLm+HTV4HH70ddnnZzUc/b7t8HA75etvl47DXP3o5LFwR3tvP3IJO8j11OQ8V/vJ95mPFwcfygx+X5Zv7yvPNccN18Lj9UsFxXt/ha5b94HgpJO4Xjwe3n8e8/U75WwcAAADQOp30TH5tba1mzpyp6dOna/bs2erRo4d++9vf6pprrqn/jcJnn32mm266SQcOHHBL6NM1cOBA9e/fXy+++KIkyeVyKSkpSXfccYfuvffeY35uS5nJRxNyOc2zA8rzD5b/AqksTyrNNR/L8qTSPKks1zyT4EQFREghCVJo4sHHBCk06dDHwXGSw7MvjwEAAADg5pn8uLg4uVwuXX311Vq6dKl69ep12DFnn322wsLCTvalm0RNTY1WrFih++67r37MbrdrxIgRWrRo0WHHV1dXq7q6uv55ScnhC8GhlbM7zOvzg6KkmK7HPra28lDpL82WSnJ+8XhwK8mR6ioPnRmQu/bIr2WzmzP+YUlm+W/wmGw+evs3/vcLAAAAoNk66ZL/3HPP6YorrpCf39FPJQ4LC1NmZuZpBXOXffv2yel0KiYmpsF4TEyMMjIyDjt+6tSpevTRR5sqHjydt7/Upq25HY1hmJcLlGRLJVlS8V5zK8mSirOkkr3mPmfNwY/3Sjr8F1SSzDUC2rSV2qRIYSkNPw5JYLFAAAAAwMOc9E/41113nTtyNFv33XefpkyZUv+8pKRESUlJFiaCx7MdXMQvIFyK7XbkY1wu87KA4j1S0e5Dj0V7Dn68R6opNS8hKM+X9i49/DXsXualAOHtzK1N6sGPU81fBnAWAAAAANDitLppvMjISDkcDuXl5TUYz8vLU2xs7GHH+/r6ytfXt6niASfGbj+4eF+MlNjv8P0/nw1QtEs6sOvg407z4wM7zV8EOGsOju2Utv9w+GsEx5ulP6KdFJEmhbc/+JgqefH/BAAAANActbqS7+Pjo759++r777/XmDFjJJkL733//feaPHmyteGAxvLLswHiex++3+Uyr/8/kCkVZkqFOw5+vMN8Xl1irhVQmi3tWvDrFzev9/9l8Y/sIEV2NC8BsFt4RwUAAACglWt1JV+SpkyZohtuuEH9+vXTgAED9Pzzz6u8vFw33nij1dGApmG3H1ytP0FqO7ThPsMw7xZwIFPav90s/vu3SYXbzefVJQcvDdh9+BkA3gENS//PjxFpnP4PAAAANIFWWfKvuuoqFRQU6KGHHlJubq569eqlWbNmHbYYH9Aq2WxSYIS5/fpSAMMw1wLYv90s/j9v+7aavwyorTDvBnDYHQFs5nX+UelSVKdDj5EdJd+gpvrOAAAAAI9nMwzDsDpES3Iy9ycEWhVnrXnN//6t0r4tB7etUsFmqaro6J8XmmwW/ujOUnQX8zGqEzP/AAAAwEEn00Mp+SeJkg+cJMOQyvdJBRkHt82HHsvzj/w5Nru52v8vi39MV3MNAG77BwAAgFaGku9GlHygEVUUmmU/f6NZ/PM3SXkbpMrCIx/v5Wee6h/TzSz9MV3NjwMjmjY3AAAA0IROpocyJQbAOgHhUspgc/vZz9f95280S3/+Rinv4Me15VLOanP7peA4s/DHdpdie5hbeDtW+gcAAECrQ8kH0LzYbFJQtLm1G35o3OUyV/zP23BwW29uB3aatwMszZG2zTl0vHegFNvtF8W/u3nqv7dfU39HAAAAQJPhdP2TxOn6QDNTXWrO8ueulXLXmVveBqmu6vBj7V5SVGcprqcU38t8jOkm+QQ0eWwAAADgRHFNvhtR8oEWwFln3tovd52Uu8Z8zFl75Gv9bXYpstOh0h/fx5z1p/gDAACgmaDkuxElH2ihDEMq3ivlrDl4Xf8aKXv1kVf4tznMFf3je0sJfczH6K6Sl09TpwYAAAAo+e5EyQc8iGFIpbm/KP2rzK0s7/BjHb7mNf7xfaTEflJCPymivbmGAAAAAOBGlHw3ouQDHs4wpJLsg4V/pZS10vy4qujwY/3CpIS+B0t/X7P4czs/AAAANDJKvhtR8oFWyDDMlf2zDpb+rOXmzP+RFvdr01ZK7C8lDpCSBpgL+zm4kQkAAABOHSXfjSj5ACRJzlrzFn57l0tZK8zH/VsPP847wDzFP+kXxT8wsunzAgAAoMWi5LsRJR/AUVUWHSz8y6Q9S83iX118+HHh7aSkgVLyIClpkBTZUbLbmzwuAAAAWgZKvhtR8gGcMJdL2rdF2rv0YOlfJhVkHH6cX9jB0j/QLP0JfSRv/yaPCwAAgOaJku9GlHwAp6XygDnDv3uxtGeJ+XFdZcNj7N7mbftSBkspQ8xfAPiHWRIXAAAA1qPkuxElH0CjctZKuWul3UukPYvNx7LcXx1kk2K6SilnSMmDzcfgWEviAgAAoOlR8t2Ikg/ArQxDOrBT2r1I2rXQfNy/7fDjwtuZs/xth0lth0ihiU0eFQAAAE2Dku9GlHwATa407xelf6GUu17Sr/7qbtNWShkqtR1qlv6wZCuSAgAAwA0o+W5EyQdgucoi83r+nQvMLWeNZDgbHhOaLKUOk1LPNGf7QxMsiQoAAIDTR8l3I0o+gGanquRQ6d/1k5S18vDSH97eLPypw6S2Z0pBUdZkBQAAwEmj5LsRJR9As1ddZi7ilzlf2jlfyl4lGa6Gx0R1Nkt/u+Hm6f1+oZZEBQAAwPFR8t2Ikg+gxakqNq/nz5wvZf4o5a1ruN/mkBL6mIW/3XApsb/k5WtFUgAAABwBJd+NKPkAWrzy/dKuBdKOudKOeVLh9ob7vfzN2/S1Gy61P1uK7irZ7VYkBQAAgCj5bkXJB+BxivZImfMOlv65UnlBw/2B0WbZb3+OWfyDYy0ICQAA0HpR8t2Ikg/AoxmGlL/RLPvb/2cu5Fdb0fCY6K6HSn/KGZK3vyVRAQAAWgtKvhtR8gG0KnXV0p6l0vYfzC1njaRf/LPh5SelDJHSRphbZAfJZrMsLgAAgCei5LsRJR9Aq1a+79As//YfpNLshvtDk6W0c83Cn3qm5MffkwAAAKeLku9GlHwAOMgwpIIMadv30rbvzBX8nTWH9tu9pKRBUocRUofzpeguzPIDAACcAkq+G1HyAeAoasqlnQukbXPMrXBHw/0hiVKH88zC3+4sySfQmpwAAAAtDCXfjSj5AHCC9m8/NMuf+aNUV3Von8NHajvULPwdzpci2luXEwAAoJmj5LsRJR8ATkFtpZQ5X9o6W9r6rVS0u+H+iDSp44XmljxIcnhbkxMAAKAZouS7ESUfAE6TYUj7tpplf+ts81p+V92h/X6h5sJ9HS80HwPCrcsKAADQDFDy3YiSDwCNrKrYXK1/yyyz9FfsP7TPZjcX7+t0odRplHmLPgAAgFaGku9GlHwAcCOXU8paYRb+zbOk/A0N90d0kNJHmYU/sb9kd1iTEwAAoAlR8t2Ikg8ATahot7TlW2nz1+Y1/a7aQ/sCIs1T+juNlNqfzWr9AADAY1Hy3YiSDwAWqSoxb823+Rvzev6q4kP7vPyk9udI6RebxT8wwrqcAAAAjYyS70aUfABoBpy10u5FUsbX0uavGq7Wb7NLKUPMwp9+kRSWZF1OAACARkDJdyNKPgA0M4Yh5W2QMr6SMr6Qctc13B/XU0ofLXW+WIpKl2w2a3ICAACcIkq+G1HyAaCZO7DzYOH/ypztN1yH9kV0kDqPlrr8RorrReEHAAAtAiXfjSj5ANCClBVIW76RNn0p7fif5Kw5tC8sWer8G3NL7C/Z7dblBAAAOAZKvhtR8gGghaoqkbbOljZ+bi7gV1txaF9QrHk6f5dLzOv5uTUfAABoRij5bkTJBwAPUFMhbf9e2jhT2jJLqi45tC8w6uAp/WPMwu/wsiwmAACARMl3K0o+AHiYumppxzxzhj/jS6mq6NC+gEiz8HcdI6UMpfADAABLUPLdiJIPAB7MWStlzpM2zDALf+WBQ/sCIs1T+rteJrUdyin9AACgyVDy3YiSDwCthLNWyvxR2jjDXLivsvDQvsBo8/r9bpdLSQNZtA8AALgVJd+NKPkA0Ao5a6Wd86X1n0qbvmh4Sn9wvNT1UqnbZVJCX27LBwAAGh0l340o+QDQytXVSDvmShs+lTK+arhoX1iyObvfbawU05XCDwAAGgUl340o+QCAerVV5u34Nnwqbf6m4W35otKl7mPNwh+eal1GAADQ4lHy3YiSDwA4opoK83Z86/8rbZ0tOWsO7UvoK3W/wjytPzjWuowAAKBFouS7ESUfAHBclUXm6vzrPjFX6zdc5rjNLrUdJvW40rw1n1+opTEBAEDLQMl3I0o+AOCklOVLGz4zC//epYfGHb5Sp5Fm4U87T/LysS4jAABo1ij5bkTJBwCcsgO7pPWfSGv/IxVkHBr3CzNP5e9xpZQ0iFvyAQCABij5bkTJBwCcNsOQctdJaz8yZ/jLcg/tC02Welwh9RgnRXW0LiMAAGg2KPluRMkHADQql1PaOd+c3d84U6opPbQvvo/U82rztnyBEdZlBAAAlqLkuxElHwDgNrWV5q341n4kbf1OMpzmuN1L6nC+1HOc1PFCycvX2pwAAKBJUfLdiJIPAGgSZQXm9ftr/i3lrD407hcqdb1M6nWNlNhfstksiwgAAJoGJd+NKPkAgCaXnyGt/bd5Sn9J1qHxiDSz7PcYJ4UmWJcPAAC4FSXfjSj5AADL/Hz9/pp/Sxs/l2orDu6wSe3PlnpeI6VfJPkEWBoTAAA0Lkq+G1HyAQDNQnWpuVDf6g+kXQsOjfuGmLfj63WtlDSA0/kBAPAAlHw3ouQDAJqdwkxzsb7VH0hFuw6NR3SQeo83F+wLjrUuHwAAOC2UfDei5AMAmi2XS9q9UFr1vrRxxqHT+W0Oc3X+3uOljhdIDm9LYwIAgJNDyXcjSj4AoEWoLpU2fCatek/as+TQeECkObPfe7wU3dm6fAAA4IRR8t2Ikg8AaHEKtkir3zMX7CvLOzSe2F/qc715Sz7fIOvyAQCAY6LkuxElHwDQYjnrpG1zpFXvSltmSa46c9wnSOp2mdTnBimhL4v1AQDQzFDy3YiSDwDwCKV50poPpZXvSIXbD41HdzFn93tcJQWEW5cPAADUo+S7ESUfAOBRDEPatdAs+xtnSHVV5rjDR+r8G6nvBKntUGb3AQCwECXfjSj5AACPVVkkrftYWvm2lLvu0HhEmnkqf69rpMBIy+IBANBaUfLdiJIPAGgVsldJK942S39NmTlm95Y6j5b63Si1HcbsPgAATYSS70aUfABAq1JdJq3/RFrxlln8fxbeXup7g9TrWmb3AQBwM0q+G1HyAQCtVvZq81T+tR9LNaXmmMNH6nKJ1O8mKXkws/sAALgBJd+NKPkAgFavukxa/19pxfSGs/tRnc2y3/MqyS/UunwAAHgYSr4bUfIBAPiFrJVm2V/3iVRbYY55B0jdLpf63yzF97Y2HwAAHoCS70aUfAAAjqCySFr7H2n5m1JBxqHx+N5S/1ukbpdJ3v6WxQMAoCWj5LsRJR8AgGMwDGn3Imn5/0kbP5ecNea4fxup93jzdP7wdtZmBACghaHkuxElHwCAE1S+T1r5jrR8ulS8++CgTUobIfX/rdThPMnusDQiAAAtASXfjSj5AACcJJdT2jpbWvaGtG3OofGwZHNmv/f1UmCEdfkAAGjmKPluRMkHAOA07N9unsq/6j2pqsgcc/hK3a+QBtwixfeyMh0AAM0SJd+NKPkAADSCmgppw6fS0teknDWHxpMGSgNulTr/RvLysS4fAADNyMn0UHsTZXK7nTt36uabb1Zqaqr8/f3Vvn17Pfzww6qpqWlwjM1mO2xbvHixhckBAGiFfALMhfhunSfd/J3Ubaxk95L2LJH+e7P0fHdp7t+k0jyrkwIA0KJ4WR2gsWRkZMjlcunVV19VWlqa1q9fr1tuuUXl5eX6+9//3uDYOXPmqGvXrvXPIyK4DhAAAEvYbFLSAHMrfUJa8ZZ5On9ZrjR3qvTj36WuY6SBt0mJ/axOCwBAs+fRp+s/88wzevnll7Vjxw5J5kx+amqqVq1apV69ep3Sa3K6PgAAblZXI22aaZ7Kv2fJofGEftKg26Uul0gOb+vyAQDQxFrl6fpHUlxcrPDw8MPGf/Ob3yg6OlpDhw7VzJkzj/ka1dXVKikpabABAAA38vKRuo+Vbp4t3TpX6nm15PCRspYfOpV/3jPmLfoAAEADHlvyt23bpmnTpul3v/td/VhQUJCeffZZffzxx/rqq680dOhQjRkz5phFf+rUqQoNDa3fkpKSmiI+AACQpPje0qWvSHdvkIbfLwXFSKU50v8el/7RRZoxScpdZ3VKAACajWZ/uv69996rp5566pjHbNq0Senp6fXPs7KydNZZZ2n48OF64403jvm5119/vTIzMzV//vwj7q+urlZ1dXX985KSEiUlJXG6PgAAVqirkTZ8Ji15WcpedWi87TBp0ESp44WS3WPnMAAArZRH3UKvoKBA+/fvP+Yx7dq1k4+PeZud7OxsDR8+XIMGDdJbb70l+3H+oX/ppZf0+OOPKycn54TycE0+AADNgGFIe5dJi1+WNn4uGU5zPLydNPB2qdc1km+QtRkBAGgkJ9NDm/3q+lFRUYqKijqhY7OysnT22Werb9++mj59+nELviStXr1acXFxpxsTAAA0pV+uyl+811ykb8VbUuEO6Zs/mafz97lBGvg7KTTR6rQAADSZZj+Tf6KysrI0fPhwpaSk6O2335bD4ajfFxsbK0l6++235ePjo969e0uSPv30Uz344IN64403dOONN57Q12EmHwCAZqq6TFrzoTm7X7jdHLM5zNX4B0/iFnwAgBbLo2byT9R3332nbdu2adu2bUpMbPgb+1/+HuOvf/2rdu3aJS8vL6Wnp+ujjz7S2LFjmzouAABobL5B0oBbpH43S1u/lRa9JO2cL2341NySBklnTJY6jZLsjuO/HgAALZDHzOQ3FWbyAQBoQXLWmjP76z6WXLXmWHg7c5G+XtdIPoHW5gMA4AR41MJ7zQ0lHwCAFqg017xuf9mbUlWROebfxpz1H3CrFBxjaTwAAI6Fku9GlHwAAFqwmnJp9QfSohelAzvNMYeP1P1K81T+6M6WxgMA4Ego+W5EyQcAwAO4nFLGV2bZ37Pk0HiH86Uz7pTaDjVX8AcAoBmg5LsRJR8AAA+zZ5m0aJq06QvJcJlj8X2kIXdKnX/DIn0AAMtR8t2Ikg8AgIfav91ckX/1+1JdlTnWpq00eLLU61rJJ8DSeACA1ouS70aUfAAAPFz5PnORvqWvS5WF5ph/uLlA34BbpcAIa/MBAFodSr4bUfIBAGglairMWf2F06SiXeaYl7/U53pzkb6wZGvzAQBaDUq+G1HyAQBoZZx10qaZ0k//lHJWm2M2h9R9rDTk91JMV0vjAQA8HyXfjSj5AAC0UoYh7Zgr/fS8+fizDhdIQ++WUgZbFAwA4Oko+W5EyQcAAMpeJS14Xtr4uaSDP0olDTTLfscLuf0eAKBRUfLdiJIPAADq7d8uLXxBWv2B5Kwxx6K7mmW/66WSw8vafAAAj0DJdyNKPgAAOExpnrT4X9KyN6WaUnOsTVtpyF1Sr2skL18r0wEAWjhKvhtR8gEAwFFVFknLXpcWvyxV7DfHgmLN1fj73ij5BlkaDwDQMlHy3YiSDwAAjqumQlr5jnn7vZK95phfmDTwNmng76SAcEvjAQBaFkq+G1HyAQDACaurkdb9x1ykb/9Wc8wnSOp/szR4shQUbWk8AEDLQMl3I0o+AAA4aS6ntOkLaf7fpdx15piXn9TnBmnInVJoorX5AADNGiXfjSj5AADglBmGtHW29OMz0t5l5pjdW+p1tbkif3g7a/MBAJolSr4bUfIBAMBpMwwp80ez7O+cb47Z7FK3sdKwP0jR6dbmAwA0KyfTQ+1NlAkAAAA/s9mkdmdJE76UbvpWSjtPMlzm9fv/GiR9PEHK22B1SgBAC0TJBwAAsFLyIGn8J9Ktc6X0iyUZ0obPpJfPkP59rZSzxuqEAIAWhJIPAADQHMT3lsa9L92+UOp6qSSblPGl9OqZ0gfjpKwVVicEALQAlHwAAIDmJKardMVb0qQlUvcrzWv1t3wjvX6O9N5Yac9SqxMCAJoxSj4AAEBzFNVJuvx1adIyqec1ks0hbftOevM86d1LKfsAgCOi5AMAADRnkWnSpS9LdyyXel8n2b2k7T9Q9gEAR0TJBwAAaAnC20mXvCjdsULqcz1lHwBwRJR8AACAlqRNW+k30yj7AIAjouQDAAC0RD+X/clHOY1/73KrEwIALEDJBwAAaMnCU83T+H9d9t84V3r/Sil7ldUJAQBNiJIPAADgCX5Z9nuNN1fj3/qt9Npw6cNrpJy1VicEADQBSj4AAIAnCU+VxrwkTV4m9bhKstmlzV9Jrw6TPrpOyttodUIAgBtR8gEAADxRRHvpstekiYulbpdLskmbZkovnyF9cpNUsMXqhAAAN6DkAwAAeLKoTtLY/5NuXyh1uUSSIa3/r/SvgdJnt0sHdlqdEADQiCj5AAAArUFMF+nKd6TbFkidRkmGS1rzgTStr/Tl3VJxltUJAQCNgJIPAADQmsR2l67+UPrtD1L7cyRXnbT8/6QXekuz7pfKCqxOCAA4DZR8AACA1iixr3TdZ9KEr6XkMyRntbT4JemfPaU5j0oVhVYnBACcAko+AABAa9Z2iHTj19L4T6X4PlJtubTgH9I/e0k/PiNVl1mdEABwEij5AAAArZ3NJqWdK93ygzTuQym6q1RdLP3wuPRCL2nxK1JdtdUpAQAngJIPAAAAk80mpY8yF+e7/E2pTapUXiDNusdcoG/Ve5KzzuqUAIBjoOQDAACgIbtd6j5WmrxMuvh5KThOKt4jfT5JenmwtGGGZBhWpwQAHAElHwAAAEfm8Jb63SjduUo6/3HJP1zat0X6+AbpteHStu8p+wDQzFDyAQAAcGze/tIZd0i/XyOddY/kEyTlrJbeu0x65zdS1gqrEwIADqLkAwAA4MT4hUhn32+W/UETJYePlPmj9Po50kfXSfu2Wp0QAFo9Sj4AAABOTmCkdOFU6Y4VUs9rJNmkTTOllwZKM++QirOsTggArRYlHwAAAKcmLFm69GXp9oVSp1GS4ZRWviNN6yPNflCqKLQ6IQC0OpR8AAAAnJ6YLtLVH0o3fSslD5bqqqSFL0j/7CUteE6qrbQ6IQC0GpR8AAAANI7kQdKN30jX/EeK7ipVF0tzHpGm9ZVWvSe5nFYnBACPR8kHAABA47HZpI4XSLfNl8a8IoUkSiVZ0ueTpJeHSJtncds9AHAjSj4AAAAan90h9braXJzvvL9KfmFSwSbpw6ukty6S9i63OiEAeCRKPgAAANzH208acqf0+9XSkN9LDl9p10/SG+dK/7le2r/d6oQA4FEo+QAAAHA//zbSeY9Jd66Ueo2XZJM2fi69NED6+k9S+T6rEwKAR6DkAwAAoOmEJkpjXjJvu9fhfMlVJy19TXqhtzT/H6zEDwCniZIPAACAphfTRbr2Y+n6mVJsD6m6RPr+UXMl/tUfSC6X1QkBoEWi5AMAAMA67c6Sbp0nXfqaFJpkrsQ/43bp1TOl7T9YnQ4AWhxKPgAAAKxlt0s9r5ImL5dGPCr5hkp566R3L5XevUzK22h1QgBoMSj5AAAAaB68/aShd5kr8Q+8XbJ7S9u/l14ZIs28UyrNszohADR7lHwAAAA0LwHh0si/SZOXSl0ukQyXtPJtaVofad4zUk2F1QkBoNmi5AMAAKB5Cm8nXfmOdOMsKaGvVFMm/e9x6cV+0uoPWZwPAI6Akg8AAIDmLWWwdPMc6fI3pdDkg4vz3Sa9PlzKnG91OgBoVij5AAAAaP7sdqn7WGnyMmnEI5JviJSzRnr7YunDa6T9261OCADNAiUfAAAALYe3nzT0bunOVVL/30o2h7T5K+mlgdK3f5Eqi6xOCACWouQDAACg5QmMlC56Vrp9oZR2nuSqlRa9KL3QW1r6uuSsszohAFiCkg8AAICWKzpdGv+JNP6/UlS6VFkoff1H6eUzpK1zrE4HAE2Okg8AAICWL22EdNtP5uy+f7i0b7P0/uXSe5dL+RlWpwOAJkPJBwAAgGdweJnX6d+5Sho8WbJ7S9vmmLP6X/9Jqii0OiEAuB0lHwAAAJ7FP0y64Alp0hIp/WLJcEpLXzOv11/yGtfrA/BolHwAAAB4poj20rj3petnStFdpaoi6Zs/Sa8MkbZ9b3U6AHALSj4AAAA8W7uzpN/9eOh6/YIM6b3LpA/GSfu3W50OABoVJR8AAACer/56/ZXSoImS3Uva8o300kDp279IVcVWJwSARkHJBwAAQOvh30a6cKp0+yIp7TzJVSstelGa1lda+a7kclmdEABOCyUfAAAArU9UR2n8J9I1H0sRHaTyAmnmZOmNc6Q9S61OBwCnjJIPAACA1qvj+dLtC6XzH5d8/r+9Ow/Tcl78OP5+ZqaZ1hnti1KTLUuUSlqVUueITk52aZO0iBZLnGM5SNZOBy1K1EnIUkoolUobEhMiS0o52iw1bWZqZn5/PMf8zJEUNfcz97xf13Vf3Mvz9Hmu68b18b3v77cUfPM+jDsbpvaC7RuDTidJB82SL0mSpMItIREa94u+r1+3U/TYimeij/Av+ifszQg2nyQdBEu+JEmSBFCyAvxlBPR4A46sD5k7YM4dMPIM+HRm0Okk6YBY8iVJkqSfq1oPrpwNHUZDyYrw/ZfwzMUw6SKX3JMU8yz5kiRJ0v+Ki4M6l0K/5dDkOogrAp/Pio7qz70TMncGnVCS9smSL0mSJP2apFJw9p3QZykcfRZkZcLCh+DRBrByKuTkBJ1QkvKw5EuSJEm/pdyx0GkKXDwJjjgK0v8Dz3eFCefB5k+CTidJuUJV8mvUqEEkEsmz3XvvvXmu+eCDD2jWrBlFixalWrVq3H///QGllSRJUoESicAJ50Lfd6DFzZBQFNYuhFFNYOYt8OO2oBNKUrhKPsCdd97Jhg0bcrd+/frlnktPT6dNmzZUr16d5cuX88ADD3DHHXcwZsyYABNLkiSpQClSDFoMhr5vQ61zIScL3hoBj9SHFc/6CL+kQCUEHeBQK1WqFJUqVdrnuUmTJpGZmckTTzxBYmIiJ510EmlpaQwbNoyePXvmc1JJkiQVaKVrwCWT4Is58NpN8N0XMPVqWD4B2j0IFU8KOqGkQih0I/n33nsvZcuWpW7dujzwwAPs3bs399zSpUtp3rw5iYmJucfatm3Lp59+yg8//LDP78vIyCA9PT3PJkmSJOU6pjX0XgKtbocixWHdEhjdDGbe7CP8kvJdqEr+tddey7PPPsu8efO4+uqrueeee7jxxhtzz2/cuJGKFSvm+cxP+xs3btzndw4dOpSUlJTcrVq1aofvB0iSJKlgSkiCZgOj7+uf0P6/j/CPjM7C/8FzPsIvKd/EfMkfPHjwLybT+99t1apVAAwcOJAWLVpwyimn0KtXLx566CEeeeQRMjIyfveff/PNN7Nt27bcbf369Yfqp0mSJClsjqgGF0+ETi9CmaNhxyaYchWMbwebPg46naRCIObfyR80aBBdu3bd7zU1a9bc5/GGDRuyd+9e1q5dy/HHH0+lSpXYtGlTnmt+2v+19/iTkpJISko6+OCSJEkqvI5pDX2WwpJH4M0H4avFMLopnNE7OmlfUqmgE0oKqZgv+eXLl6d8+fK/67NpaWnExcVRoUIFABo1asTf/vY39uzZQ5EiRQCYPXs2xx9/PKVLlz5kmSVJkiQSkqD59XDKRdH381fNgKWPwkcvwp+GwokdosvySdIhFPOP6x+opUuXMnz4cFasWMGXX37JpEmTGDBgAJ06dcot8JdddhmJiYlceeWVrFy5ksmTJ/Ovf/2LgQMHBpxekiRJoXXEUdFZ+C9/IToj//YN8HxXeOqv8N3qoNNJCplITk44ZgF577336NOnD6tWrSIjI4PU1FSuuOIKBg4cmOdx+w8++IC+ffuybNkyypUrR79+/bjpppsO+M9JT08nJSWFbdu2kZycfDh+iiRJksJqz25YNBwWDYOsTIhPhKYDoluRYkGnkxSjDqaHhqbk5xdLviRJkv6w71bDq9fD6jei+6VrwDkPwrFnBxpLUmw6mB4amsf1JUmSpAKj7NHQaQpcOAFKVYEf1sKkC2ByJ9j2n6DTSSrALPmSJElSECIROKkDXPMONLoGIvHwycsw4nRYOgKy9gadUFIBZMmXJEmSgpRUCtoOgavfhGoNIXMHzLoFxraAr5cHnU5SAWPJlyRJkmJBpZOh20w472EoegRs/BAebwUzBsLurUGnk1RAWPIlSZKkWBEXB/W6wDXvwqmXAjnw7jh4tAF8+AI4Z7ak32DJlyRJkmJNyfJw/mjo8jKUPRZ2boYXr4SJHaIz80vSr7DkS5IkSbEqtTn0Xgxn/R0SisKX82FkI1jwAOzNDDqdpBhkyZckSZJiWUISNL8B+iyFo8+CrAyYdzeMbgpfLQ06naQYY8mXJEmSCoIyNaHTFOg4DkqUh28/hSf/BNP7wa7vg04nKUZY8iVJkqSCIhKB2hfANcvgtC7RY+/9G0acDh8878R8kiz5kiRJUoFTrDS0fzi65F75WrBzC0zpARPPh++/DDqdpABZ8iVJkqSCqnojuHphdGK++CT4cl50Yr6FwyBrT9DpJAXAki9JkiQVZAmJ/z8xX+qZsPdHmPsPGNMCvl4edDpJ+cySL0mSJIVB2aOh8zToMBqKlYFNH8HjreC1wZCxPeh0kvKJJV+SJEkKi0gE6lwanZjvlEuAHHh7FIw4Az6bFXQ6SfnAki9JkiSFTYly8NfHokvuHVEd0r+Gpy+C57vC9k1Bp5N0GFnyJUmSpLA6phX0eQsaXwuReFg5FUY0gOUTXG5PCilLviRJkhRmicWhzV3Qcx5UrgM/boOXr4UJ58F3q4NOJ+kQs+RLkiRJhUHlU6HHXGgzBBKKwdqFMKoxLP4XZO0NOp2kQ8SSL0mSJBUW8QnQ+Jrocns1W0SX25t9Gzx+Fmz4IOh0kg4BS74kSZJU2JRJhStegr+MhKJHwIYVMKYFzLkD9uwONpukP8SSL0mSJBVGkQjUvRz6vgMndoCcLFj0TxjVBNYuCjqdpN/Jki9JkiQVZqUqwkUT4JKnoVRl+H41jG8HL/eHH9ODTifpIFnyJUmSJEGtdtD3bajXLbq//EkYeQZ89nqwuSQdFEu+JEmSpKiiKXDecOgyA0qnQvp/4OkL4cWrYOd3QaeTdAAs+ZIkSZLySm0GvZdAo2sgEgcfPgcjToePpkBOTtDpJO2HJV+SJEnSLyUWh7ZD4Mo5UP4E2PUtvNANJneC9A1Bp5P0Kyz5kiRJkn5d1Xpw9Ztw5mCIS4BVM2BEQ3j/KUf1pRhkyZckSZK0fwmJ0PLmaNmvUhcytsG0vvBUR9i6Puh0kn7Gki9JkiTpwFQ8Kfr4fut/QHwSrJ4LIxvBu084qi/FCEu+JEmSpAMXnwBN+0OvRVD1dMjcDjMGwL/bww9rg04nFXqWfEmSJEkHr/xx0H0mtB0KCcVgzZswsjG8PQays4NOJxValnxJkiRJv09cPDTqA70XQ/UmsGcnvHYDTDgXvlsddDqpULLkS5IkSfpjyh4NXWbAOQ9CkRLw1WIY1QSWjnRUX8pnlnxJkiRJf1xcHJx+FfRZAqlnwt7dMOtmGH+Oo/pSPrLkS5IkSTp0SteAztOg3TBILAnrlkZH9d8a5ai+lA8s+ZIkSZIOrUgEGlwJvZdAavPoqP7MwdF39b//Muh0UqhZ8iVJkiQdHqWrQ+fp0VH9n7+r//ZjjupLh4klX5IkSdLh89Oofp+l0VH9PbvgtRthwnnw/Zqg00mhY8mXJEmSdPiVrg5XTPvZDPyLoqP674x1VF86hCz5kiRJkvLHz2fgr9EM9uyEV6+Hp86HreuDTieFgiVfkiRJUv4qXSP6rv6f7oOEYvDlfBjVGN6bCDk5QaeTCjRLviRJkqT8FxcHZ/SCXoug6umQkQ7Tr4GnL4b0DUGnkwosS74kSZKk4JQ7BrrPhNb/gPhE+HwWjDwDPnjeUX3pd7DkS5IkSQpWXDw07Q9XvwmV68CPW2FKD3juCtj5bcDhpILFki9JkiQpNlQ4AXrMgZZ/g7gE+OTl6Kj+qleCTiYVGJZ8SZIkSbEjvgiceSNc9QZUOBF2boFnL4OpveHHbUGnk2KeJV+SJElS7Kl8KvScD02uAyKw4mkY2Ri+XBB0MimmWfIlSZIkxaaEJDj7zujEfKVTIf1r+Hd7ePVGyNwVdDopJlnyJUmSJMW2o86ILrVX/8ro/juPwWPN4Ot3g80lxSBLviRJkqTYl1QSzh0GnV6EUpXhuy9g3Nkw9y7Ymxl0OilmWPIlSZIkFRzHtIY+S6H2RZCTDQsfhHGtYfOqoJNJMcGSL0mSJKlgKVYaOo6FC8dH/37DCnisObw1CrKzg04nBcqSL0mSJKlgOul86L0Ujm4FWRkwczBM7ADbvg46mRQYS74kSZKkgiu5cvQ9/XYPQUIxWLMgutTeB89DTk7Q6aR8Z8mXJEmSVLBFItCgR3QG/iPrQcY2mNIDXugGu74POp2Uryz5kiRJksKh3DHQ/XVocQtE4mHlVBjVGL6YG3QyKd9Y8iVJkiSFR3wCtLgJesyGssfC9g3w1F/htZtgz+6g00mHnSVfkiRJUvgcWQ+ufhMaXBXdf3s0jGkRnYlfCjFLviRJkqRwSiwO7R6Ey56HEhVgyyoY2woWDYfsrKDTSYeFJV+SJElSuB3XBvoshVrnQvYemHM7TGgPW9cFnUw65Cz5kiRJksKvRDm4+Clo/wgUKQFfLYJRTeCD51xqT6FiyZckSZJUOEQicFpn6L0IqjaAjHSYchW80B12/xB0OumQsORLkiRJKlzK1IRuM6Hl3/671N4UGNUU1i4KOpn0h1nyJUmSJBU+8Qlw5o1w5etQOhXSv4bx58Kcf8DezKDTSb+bJV+SJElS4VW1PvRaCHU7ATmwaBg80Qa+/SLoZNLvYsmXJEmSVLgllYK/jIALJ0DRI+Cb9+GxZrB8gpPyqcCx5EuSJEkSwEkdoPcSqNEM9uyCl6+FyZ1g1/dBJ5MOmCVfkiRJkn6SciR0ng5n3wlxRWDVDBjZCFbPCzqZdEAs+ZIkSZL0c3Fx0OQ6uGoulDsOdmyEiefD67c6KZ9iniVfkiRJkval8qnQcwHU7w7kwJKHYdzZTsqnmGbJlyRJkqRfk1gczv0nXDwJipWGDWnRSfnem+ikfIpJlnxJkiRJ+i0nnJt3Ur7p18DzXWH3D0Enk/Kw5EuSJEnSgUiuAp2nQes7IC4BPn4JRjWFr5YEnUzKZcmXJEmSpAMVFw9NB8CVr0OZmpD+NYxvB28Mgay9QaeTLPmSJEmSdNCOrAdXvwl1LoecbHjzfhh/DmxdF3QyFXKWfEmSJEn6PZJKQYeR0HEcJCXD+rejj++vnBp0MhVioSn58+fPJxKJ7HNbtmwZAGvXrt3n+bfeeivg9JIkSZIKrNoXQK+FULUBZGyLTsg3/VrI3BV0MhVCoSn5jRs3ZsOGDXm2Hj16kJqaSv369fNcO2fOnDzX1atXL6DUkiRJkkKhdA3o9ho0GwRE4L0JMKYFbPwo4GAqbBKCDnCoJCYmUqlSpdz9PXv2MG3aNPr160ckEslzbdmyZfNcK0mSJEl/WHwRaHUbpDaHKVfDt5/C2LOg7RBo0AP+p5dIh0NoRvL/1/Tp0/nuu+/o1q3bL861b9+eChUq0LRpU6ZPn77f78nIyCA9PT3PJkmSJEm/qmYL6L0Yjm0LWRnw6vXw7GWw6/ugk6kQCG3JHzduHG3btqVq1aq5x0qWLMlDDz3E888/zyuvvELTpk3p0KHDfov+0KFDSUlJyd2qVauWH/ElSZIkFWQlysFlk+FP90F8Inz6KoxqAmsXB51MIRfJycnJCTrE/gwePJj77rtvv9d88skn1KpVK3f/66+/pnr16jz33HN07Nhxv5/t3Lkza9asYeHChfs8n5GRQUZGRu5+eno61apVY9u2bSQnJx/EL5EkSZJUKG1YAS90h+++gEgcnDkYml8PcfFBJ1MBkZ6eTkpKygH10Jh/J3/QoEF07dp1v9fUrFkzz/6TTz5J2bJlad++/W9+f8OGDZk9e/avnk9KSiIpKemAskqSJEnSL1Q+FXougFdvgBVPw/x7YO1C+OtYSK4cdDqFTMyX/PLly1O+fPkDvj4nJ4cnn3ySzp07U6RIkd+8Pi0tjcqV/QdLkiRJ0mGUVBLOHwU1z4QZA6Mlf3QT6DAajmsTdDqFSMyX/IP1xhtvsGbNGnr06PGLcxMmTCAxMZG6desCMGXKFJ544gkef/zx/I4pSZIkqTA69RI4sj680BU2fghPXwiNroFWt0NCYtDpFAKhK/njxo2jcePGed7R/7m77rqLr776ioSEBGrVqsXkyZO54IIL8jmlJEmSpEKr3DHQYy7Mvg3eHg1LH4WvFsMFT0CZmr/9eWk/Yn7ivVhzMBMeSJIkSdJ+rXoFXuoDP26FxFLQ/mE4+a9Bp1KMOZgeGtol9CRJkiQp5tVqB70Xw1GNIHM7vNANXu4Pe3YHnUwFlCVfkiRJkoKUUhW6zIBmg4AILH8SHm8N334edDIVQJZ8SZIkSQpafAK0ug06vQjFy8Gmj+CxM2HF5KCTqYCx5EuSJElSrDimVfTx/RrNYM9OmNoTXuoLmTuDTqYCwpIvSZIkSbGkVCXoPA1a3AKROEh7CsaeBZs/CTqZCgBLviRJkiTFmrh4aHETdJ4OJSvBllUwpiW8929wgTTthyVfkiRJkmJVajPotQiOPgv27obp/WBqLx/f16+y5EuSJElSLCtZHi5/MToxXyQOPng2Oqrv4/vaB0u+JEmSJMW6uLjoEntdZkQf3//202jRf39S0MkUYyz5kiRJklRQ1GgSfXy/Zsvo4/vT+sBLfSBzV9DJFCMs+ZIkSZJUkJQsD52mwFl//+/s+5P+O/v+qqCTKQZY8iVJkiSpoImLg+Y3/Hf2/Yqw5RMY2xLSngk6mQJmyZckSZKkguqn2fdTz4Q9u+ClXtEZ+PfsDjqZAmLJlyRJkqSCrGQFuGIqtLgZiMB7/4bHz4bvVgedTAGw5EuSJElSQRcXDy0GR8t+8XKw6UN47Ez4eFrQyZTPLPmSJEmSFBZHt4ReC+GoRpC5HZ7rDK8Nhr2ZQSdTPrHkS5IkSVKYJFeBLjOgyXXR/bdHwfhzYOv6YHMpX1jyJUmSJCls4hPg7DvhkmegaAp8vQweawafzw46mQ4zS74kSZIkhVWtc+DqN6FKXdj9A0y6AObeCdlZQSfTYWLJlyRJkqQwK10Dus+CBldF9xc+BBM7wI4tQabSYWLJlyRJkqSwS0iCdg9Cx3FQpASseTP6+P66t4JOpkPMki9JkiRJhUXtC6DnPCh3PGzfAOPbwdIRkJMTdDIdIpZ8SZIkSSpMyh8PV70BJ18A2Xth1i3RpfZ+TA86mQ4BS74kSZIkFTZJJaHj43DOgxBXBD6ZDmNawKaVQSfTH2TJlyRJkqTCKBKB06+C7jMhuSp8vxrGtoK0Z4JOpj/Aki9JkiRJhVnV+tFl9o5uBXt3w0u94OX+sDcj6GT6HSz5kiRJklTYlSgLlz8PLW4GIrD8SXjiT7B1fdDJdJAs+ZIkSZIkiIuHFoPh8hegWGn45j14rDl8MTfoZDoIlnxJkiRJ0v87tjX0XACV68Du7+GpjrDgAcjODjqZDoAlX5IkSZKUV+nq0H0WnNYZyIF5d8Ozl8LuH4JOpt9gyZckSZIk/VKRotD+EWj/KMQnwWczo8vsbfgg6GTaD0u+JEmSJOnXnXYFXPk6HHEU/LAWxp0N708KOpV+hSVfkiRJkrR/VepE39M/tg3s/RGm9YEZA2FvZtDJ9D8s+ZIkSZKk31a8DFw6+f+X2Xt3HIw/B9K/CTqZfsaSL0mSJEk6MHFx0WX2LnsOiqbA18uiy+ytXRR0Mv2XJV+SJEmSdHCOawM950PFk2HnFpjQHpaOgJycoJMVepZ8SZIkSdLBK1MTrpwNp1wMOVkw6xZ4oTtk7Ag6WaFmyZckSZIk/T6JxeH8x+DPD0BcAqycAo+3hu9WB52s0LLkS5IkSZJ+v0gEGvaELjOgZEXY8gmMaQGfvhZ0skLJki9JkiRJ+uOqN4Kr34SjGkFGOjxzCcwbCtnZQScrVCz5kiRJkqRDo1Ql6DwdTu8Z3V9wLzx7Kfy4LdhchYglX5IkSZJ06CQkwjkPQIdRkFAUPpsJY1rC5k+CTlYoWPIlSZIkSYdencug+0xIqQbfr4axrWDlS0GnCj1LviRJkiTp8KhSF3rOh9TmsGcnPN8F5twB2VlBJwstS74kSZIk6fApUQ46TYXG/aL7i/4Jky6AXd8HmyukLPmSJEmSpMMrPgHa3A0dx0GR4rD6jegyexs/DDpZ6FjyJUmSJEn5o/YFcOVsKF0Dtn4F49rAR1OCThUqlnxJkiRJUv6pdDJcNQ+OPgv27IIXusHs231P/xCx5EuSJEmS8lfxMnD5C9Dkuuj+4uEw6ULf0z8ELPmSJEmSpPwXFw9n3xl9Tz+hGKyeC2NbwqaVQScr0Cz5kiRJkqTg1L4AesyGI46CH9bC42fDypeCTlVgWfIlSZIkScGqVBuumg+pzWHPTni+C8z5h+/p/w6WfEmSJElS8EqUhU5TodE10f1Fw+CZS+DHbcHmKmAs+ZIkSZKk2BCfAG2HwPljIKEofP46jG0F334edLICw5IvSZIkSYotp14M3WdC8pHw3ecw9iz47PWgUxUIlnxJkiRJUuypUhd6zodqZ0BGOjx9ESz6J+TkBJ0splnyJUmSJEmxqWQF6PIy1OsK5MCcO+DFKyFzV8DBYpclX5IkSZIUuxIS4bx/QbthEJcAH70IT7SFreuDThaTLPmSJEmSpNjX4EroPB2Kl4ONH8CYFrB2cdCpYo4lX5IkSZJUMNRoEn1Pv9IpsOtb+Hd7ePeJoFPFFEu+JEmSJKngOKIadJ8FJ3eE7L0wYwC8Mgiy9gSdLCZY8iVJkiRJBUticeg4DlrdBkRg2eMw8XzY+V3QyQJnyZckSZIkFTyRCDQbBJc+A4klYe1CGNsCNq0MOlmgLPmSJEmSpILr+D9DjzlQugZsXQePnw2fzAg6VWAs+ZIkSZKkgq3CCXDVPEhtDnt2wuTLYcH9kJMTdLJ8Z8mXJEmSJBV8xctApylw+tXR/XlD4PkukLkz2Fz5zJIvSZIkSQqH+CJwzv1w3sMQVwQ+ngZPtIVtXwedLN9Y8iVJkiRJ4VKvC3R5GYqXg40fwpiWsP6doFPlC0u+JEmSJCl8qjeCnvOg4smwczOMbwcrng061WFnyZckSZIkhdMRR0H3WVDrXMjKhKlXw+zbITsr6GSHjSVfkiRJkhReSSXhoonQ7Pro/uLh8OzlkLE90FiHiyVfkiRJkhRucXHQ6lb46+OQUBQ+ew3GtYEf1gad7JCz5EuSJEmSCodTLoRur0LJSrD54+iEfGsXB53qkLLkS5IkSZIKjyPrRSfkq1IXdn8P/24P65cFneqQSQg6gCRJkiRJ+Sq5CnR7Dab1hYwdcORpQSc6ZCz5kiRJkqTCp0gx6DgO9v4IcfFBpzlkfFxfkiRJklQ4RSLRsh8iBabkDxkyhMaNG1O8eHGOOOKIfV6zbt062rVrR/HixalQoQI33HADe/fuzXPN/PnzOe2000hKSuKYY45h/Pjxhz+8JEmSJEn5oMCU/MzMTC688EJ69+69z/NZWVm0a9eOzMxMlixZwoQJExg/fjy33XZb7jVr1qyhXbt2tGzZkrS0NPr370+PHj2YNWtWfv0MSZIkSZIOm0hOTk5O0CEOxvjx4+nfvz9bt27Nc/y1117j3HPP5ZtvvqFixYoAjB49mptuuoktW7aQmJjITTfdxCuvvMJHH32U+7lLLrmErVu3MnPmzAP689PT00lJSWHbtm0kJycfst8lSZIkSdK+HEwPLTAj+b9l6dKl1K5dO7fgA7Rt25b09HRWrlyZe03r1q3zfK5t27YsXbr0V783IyOD9PT0PJskSZIkSbEoNCV/48aNeQo+kLu/cePG/V6Tnp7O7t279/m9Q4cOJSUlJXerVq3aYUgvSZIkSdIfF2jJHzx4MJFIZL/bqlWrgozIzTffzLZt23K39evXB5pHkiRJkqRfkxDkHz5o0CC6du2632tq1qx5QN9VqVIl3nnnnTzHNm3alHvup7/+dOzn1yQnJ1Os2L6XTUhKSiIpKemAMkiSJEmSFKRAS3758uUpX778IfmuRo0aMWTIEDZv3kyFChUAmD17NsnJyZx44om517z66qt5Pjd79mwaNWp0SDJIkiRJkhSkAvNO/rp160hLS2PdunVkZWWRlpZGWloaO3bsAKBNmzaceOKJXHHFFaxYsYJZs2bx97//nb59++aOxPfq1Ysvv/ySG2+8kVWrVjFy5Eiee+45BgwYEORPkyRJkiTpkCgwS+h17dqVCRMm/OL4vHnzaNGiBQBfffUVvXv3Zv78+ZQoUYIuXbpw7733kpDw/w8szJ8/nwEDBvDxxx9TtWpVbr311t98ZeDnXEJPkiRJkpSfDqaHFpiSHyss+ZIkSZKk/HQwPbTAPK4vSZIkSZL2z5IvSZIkSVJIWPIlSZIkSQoJS74kSZIkSSFhyZckSZIkKSQs+ZIkSZIkhYQlX5IkSZKkkLDkS5IkSZIUEpZ8SZIkSZJCwpIvSZIkSVJIWPIlSZIkSQoJS74kSZIkSSFhyZckSZIkKSQs+ZIkSZIkhYQlX5IkSZKkkLDkS5IkSZIUEpZ8SZIkSZJCwpIvSZIkSVJIWPIlSZIkSQoJS74kSZIkSSGREHSAgiYnJweA9PT0gJNIkiRJkgqDn/rnT310fyz5B2n79u0AVKtWLeAkkiRJkqTCZPv27aSkpOz3mkjOgfyvAOXKzs7mm2++oVSpUkQikaDj7Fd6ejrVqlVj/fr1JCcnBx1H+gXvUcU671HFOu9RxTrvUcW6gnKP5uTksH37dqpUqUJc3P7funck/yDFxcVRtWrVoGMclOTk5Ji+YSXvUcU671HFOu9RxTrvUcW6gnCP/tYI/k+ceE+SJEmSpJCw5EuSJEmSFBKW/BBLSkri9ttvJykpKego0j55jyrWeY8q1nmPKtZ5jyrWhfEedeI9SZIkSZJCwpF8SZIkSZJCwpIvSZIkSVJIWPIlSZIkSQoJS74kSZIkSSFhyQ+pESNGUKNGDYoWLUrDhg155513go4kATB06FAaNGhAqVKlqFChAh06dODTTz8NOpb0q+69914ikQj9+/cPOoqU6z//+Q+dOnWibNmyFCtWjNq1a/Puu+8GHUsCICsri1tvvZXU1FSKFSvG0UcfzV133YXzfStIb775Jueddx5VqlQhEonw0ksv5Tmfk5PDbbfdRuXKlSlWrBitW7fm888/DybsH2TJD6HJkyczcOBAbr/9dt577z1OPfVU2rZty+bNm4OOJrFgwQL69u3LW2+9xezZs9mzZw9t2rRh586dQUeTfmHZsmU89thjnHLKKUFHkXL98MMPNGnShCJFivDaa6/x8ccf89BDD1G6dOmgo0kA3HfffYwaNYpHH32UTz75hPvuu4/777+fRx55JOhoKsR27tzJqaeeyogRI/Z5/v777+fhhx9m9OjRvP3225QoUYK2bdvy448/5nPSP84l9EKoYcOGNGjQgEcffRSA7OxsqlWrRr9+/Rg8eHDA6aS8tmzZQoUKFViwYAHNmzcPOo6Ua8eOHZx22mmMHDmSu+++mzp16jB8+PCgY0kMHjyYxYsXs3DhwqCjSPt07rnnUrFiRcaNG5d7rGPHjhQrVoynnnoqwGRSVCQSYerUqXTo0AGIjuJXqVKFQYMGcf311wOwbds2KlasyPjx47nkkksCTHvwHMkPmczMTJYvX07r1q1zj8XFxdG6dWuWLl0aYDJp37Zt2wZAmTJlAk4i5dW3b1/atWuX59+nUiyYPn069evX58ILL6RChQrUrVuXsWPHBh1LytW4cWPmzp3LZ599BsCKFStYtGgRf/7znwNOJu3bmjVr2LhxY57/5qekpNCwYcMC2aESgg6gQ+vbb78lKyuLihUr5jlesWJFVq1aFVAqad+ys7Pp378/TZo04eSTTw46jpTr2Wef5b333mPZsmVBR5F+4csvv2TUqFEMHDiQW265hWXLlnHttdeSmJhIly5dgo4nMXjwYNLT06lVqxbx8fFkZWUxZMgQLr/88qCjSfu0ceNGgH12qJ/OFSSWfEmB6du3Lx999BGLFi0KOoqUa/369Vx33XXMnj2bokWLBh1H+oXs7Gzq16/PPffcA0DdunX56KOPGD16tCVfMeG5555j0qRJPP3005x00kmkpaXRv39/qlSp4j0q5QMf1w+ZcuXKER8fz6ZNm/Ic37RpE5UqVQoolfRL11xzDTNmzGDevHlUrVo16DhSruXLl7N582ZOO+00EhISSEhIYMGCBTz88MMkJCSQlZUVdEQVcpUrV+bEE0/Mc+yEE05g3bp1ASWS8rrhhhsYPHgwl1xyCbVr1+aKK65gwIABDB06NOho0j791JPC0qEs+SGTmJhIvXr1mDt3bu6x7Oxs5s6dS6NGjQJMJkXl5ORwzTXXMHXqVN544w1SU1ODjiTl0apVKz788EPS0tJyt/r163P55ZeTlpZGfHx80BFVyDVp0uQXS49+9tlnVK9ePaBEUl67du0iLi5vzYiPjyc7OzugRNL+paamUqlSpTwdKj09nbfffrtAdigf1w+hgQMH0qVLF+rXr8/pp5/O8OHD2blzJ926dQs6mkTfvn15+umnmTZtGqVKlcp9zyklJYVixYoFnE6CUqVK/WKOiBIlSlC2bFnnjlBMGDBgAI0bN+aee+7hoosu4p133mHMmDGMGTMm6GgSAOeddx5DhgzhqKOO4qSTTuL9999n2LBhdO/ePehoKsR27NjBF198kbu/Zs0a0tLSKFOmDEcddRT9+/fn7rvv5thjjyU1NZVbb72VKlWq5M7AX5C4hF5IPfroozzwwANs3LiROnXq8PDDD9OwYcOgY0lEIpF9Hn/yySfp2rVr/oaRDlCLFi1cQk8xZcaMGdx88818/vnnpKamMnDgQK666qqgY0kAbN++nVtvvZWpU6eyefNmqlSpwqWXXsptt91GYmJi0PFUSM2fP5+WLVv+4niXLl0YP348OTk53H777YwZM4atW7fStGlTRo4cyXHHHRdA2j/Gki9JkiRJUkj4Tr4kSZIkSSFhyZckSZIkKSQs+ZIkSZIkhYQlX5IkSZKkkLDkS5IkSZIUEpZ8SZIkSZJCwpIvSZIkSVJIWPIlSZIkSQoJS74kSZIkSSFhyZckSZIkKSQs+ZIkSZIkhYQlX5IkHVZbtmyhUqVK3HPPPbnHlixZQmJiInPnzg0wmSRJ4RPJycnJCTqEJEkKt1dffZUOHTqwZMkSjj/+eOrUqcNf/vIXhg0bFnQ0SZJCxZIvSZLyRd++fZkzZw7169fnww8/ZNmyZSQlJQUdS5KkULHkS5KkfLF7925OPvlk1q9fz/Lly6ldu3bQkSRJCh3fyZckSfli9erVfPPNN2RnZ7N27dqg40iSFEqO5EuSpMMuMzOT008/nTp16nD88cczfPhwPvzwQypUqBB0NEmSQsWSL0mSDrsbbriBF154gRUrVlCyZEnOPPNMUlJSmDFjRtDRJEkKFR/XlyRJh9X8+fMZPnw4EydOJDk5mbi4OCZOnMjChQsZNWpU0PEkSQoVR/IlSZIkSQoJR/IlSZIkSQoJS74kSZIkSSFhyZckSZIkKSQs+ZIkSZIkhYQlX5IkSZKkkLDkS5IkSZIUEpZ8SZIkSZJCwpIvSZIkSVJIWPIlSZIkSQoJS74kSZIkSSFhyZckSZIkKST+D2vAfqtrr3YyAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "z = -x**2 + 2.\n", "\n", "plt.figure(figsize=(12, 10))\n", "plt.plot(x, y, label=\"$x^2 + 1$\")\n", "plt.plot(x, z, label=\"$-x^2 + 2$\")\n", "plt.title(\"Functions $x^2 + 1$ and $-x^2 + 2$\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Side-by-side plots\n", "\n", "To make separate plots in the same figure, you can use `plt.subplot(abc)`.\n", "\n", "The function takes three digits a, b, c as input (e.g. 221 or 122) where:\n", "\n", "- a is the number of rows.\n", "- b is the number of columns.\n", "- c is the index (starting at 1) of the current subplot.\n", "\n", "Here is a dummy example of a 2x2 grid of plots:\n", "\n", "```python\n", "plt.subplot(221)\n", "plt.plot(x, y)\n", "\n", "plt.subplot(222)\n", "plt.plot(x, z)\n", "\n", "plt.subplot(223)\n", "plt.plot(y, x)\n", "\n", "plt.subplot(224)\n", "plt.plot(z, x)\n", "```\n", "\n", "**Q:** Try it." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0., 10., 100)\n", "y = x**2 + 1.\n", "z = -x**2 + 2.\n", "\n", "plt.figure(figsize=(12, 10))\n", "plt.subplot(221)\n", "plt.plot(x, y)\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "\n", "plt.subplot(222)\n", "plt.plot(x, z)\n", "plt.xlabel('x')\n", "plt.ylabel('z')\n", "\n", "plt.subplot(223)\n", "plt.plot(y, x)\n", "plt.xlabel('y')\n", "plt.ylabel('x')\n", "\n", "plt.subplot(224)\n", "plt.plot(z, x)\n", "plt.xlabel('z')\n", "plt.ylabel('x')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `plt.imshow`\n", "\n", "Matrices can be displayed using `plt.imshow()`. You can choose the color code with the `cmap` argument (e.g. `gray` or `hot`).\n", "\n", "```python\n", "plt.imshow(A, cmap=plt.cm.hot, interpolation='nearest')\n", "plt.colorbar()\n", "```\n", "\n", "`plt.colorbar()` allows to show a vertical bar indicating the color code. \n", "\n", "The interpolation method can also be selected for small matrices (`'nearest` by default, but you can choose `interpolation=\"bicubic\"` for a smoother display).\n", "\n", "(0, 0) is at the top-left of the image, the first axis is vertical. Change it with the `origin` parameter.\n", "\n", "**Q:** Create a 10x10 matrix (e.g. randomly) and plot it. Try different color maps ( and interpolation methods." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = rng.uniform(0., 1., (10, 10))\n", "\n", "plt.figure()\n", "plt.imshow(A, cmap=plt.cm.hot, interpolation='nearest')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `plt.scatter`\n", "\n", "If you want to display dots instead of of lines or pixels, `plt.scatter` takes two vectors of same size and plots them against each other:\n", "\n", "```python\n", "plt.scatter(x, y)\n", "```\n", "\n", "**Q:** Create two vectors with 100 elements and make a scatter plot." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = rng.uniform(0., 1., 100)\n", "y = rng.uniform(0., 1., 100)\n", "\n", "plt.figure()\n", "plt.scatter(x, y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `plt.hist()`\n", "\n", "Histograms can be useful to visualize the distribution of some data. If `z` is a vector of values, the histogram is simply:\n", "\n", "```python\n", "plt.hist(z, bins=20)\n", "```\n", "\n", "The number of bins is 10 by default, but you can of course change it.\n", "\n", "**Q:** Draw 1000 values from a normal distribution of your choice and make an histogram." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "z = rng.normal(10., 2.0, 1000)\n", "\n", "plt.figure()\n", "plt.hist(z, bins=20)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "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": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 4 }