es/scipy/io/__init__.py'>\n",
"t ndarray 100000: 100000 elems, type `float64`, 800000 bytes (781.25 kb)\n"
]
}
],
"source": [
"whos"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 9. Determine the dimensions of an array\n",
"\n",
"To examine the dimensions of an array, we can ask for the `shape`,"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1, 4)\n",
"(1, 4)\n"
]
}
],
"source": [
"a = array([[1,2,3,4]])\n",
"print(a.shape)\n",
"print(shape(a))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We find that the shape of `a` is `(1,4)` or 1 row and 4 columns. Notice we have two options to execute the `shape` function:\n",
"\n",
"- In `a.shape` we return the attribute `shape` of the variable `a`. \n",
"\n",
"- In `shape(a)` we apply the function `shape` to the variable `a`.\n",
"\n",
"The result is equivalent."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 10. Sometimes we need to reset the workspace\n",
"\n",
"By doing so, we get rid of all the variables. To do so, type `%reset` and enter `y`"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"%reset"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** What command could we use to confirm there are no variables in the workspace?\n",
"\n",
"**A.** Consider `who`.\n",
"\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Interactive namespace is empty.\n"
]
}
],
"source": [
"who"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"The `%reset` command is an example of a *magic*. Magics are commands that start with the `%` symbol and use a language other than Python. They are only available in the notebook environment. In fact, the set of magics that is available is specific to the notebook kernel. This means that if you have a Jupyter notebook running a Ruby kernel the magics will be different.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 11. We can define matrices in Python.\n",
"A matrix is an array with more than one dimensio. Consider the following:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"from pylab import * # Have to reimport as we cleared the workspace above!\n",
"\n",
"p = array( [[1,2,3],[4,5,6]] )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This creates a matrix with two rows and three columns. Consider,"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[1 2 3]\n",
" [4 5 6]]\n"
]
}
],
"source": [
"print( p )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q:** Can you see the two rows and three columns?\n",
"\n",
"
\n",
"\n",
"We can manipulate matrices like we manipulate vectors."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[3 4 5]\n",
" [6 7 8]]\n",
"[[ 2 4 6]\n",
" [ 8 10 12]]\n",
"[[ 1 4 9]\n",
" [16 25 36]]\n"
]
}
],
"source": [
"print( p + 2 )\n",
"print( 2 * p )\n",
"print( p * p )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 12. Indexing matrices and vectors.\n",
"Matrices and vectors are arrays of numbers, and sometimes we want to\n",
"access individual elements or small subsets of these lists. That's\n",
"easy to do in Python. Consider,"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"a = array( [1, 2, 3, 4, 5] )\n",
"b = array( [6, 7, 8, 9, 10] )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Python indexes from 0 (like C, C++, Java, and unlike MATLAB and Fortran which start at 1). \n",
" To access the 2nd element of `a` or `b`, type `a[1] / b[1]`.\n",
" We'll be a bit fancier with our printing now to distinguish variables. \n",
" Calling `str(a)` converts the variable `a` to a string that can be printed easily.\n",
" Adding two strings just concatenates them: `\"hi\" + \" bye\" = \"hi bye\". `"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a[1] = 2\n",
"b[1] = 7\n"
]
}
],
"source": [
"print( \"a[1] = \" + str(a[1]) )\n",
"print( \"b[1] = \" + str(b[1]) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"**Q.** Do the results make sense? How would you access the 4th element of each vector?\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" We can combine `a` and `b` to form a matrix with `a` as the first row and `b` as the second.\n",
" Note that we apply the function `array()` to the *list* `[a,b]`, which it converts to a matrix."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c = \n",
"[[ 1 2 3 4 5]\n",
" [ 6 7 8 9 10]]\n"
]
}
],
"source": [
"c = array([a,b])\n",
"print( \"c = \\n\" + str(c) ) # \\n is a newline, or carriage return, which makes the printed matrix lineup better "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" To learn the size (or shape)\n",
" of `c` we use `shape()`:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"shape of c = (2, 5)\n"
]
}
],
"source": [
"print( \"shape of c = \" + str( shape(c) ) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" The shape of `c` is `[2 5]`. It has two rows and five columns. To access\n",
" the individual element in the 1st row and 4th column of `c`, type `c[0,3]`"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c[0,3] = 4\n"
]
}
],
"source": [
"print( \"c[0,3] = \" + str( c[0,3] ) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"We access matrices using 'row, column' notation. So `c[0,3]` means\n",
"print the element in row 0, column 3 of `c`.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** How would you print all rows in the 2nd column of `c`?\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 13: We can find subsets of elements in matrices and vectors.\n",
"Often we are interested in only some of the elements of a matrix or vector. For example, we might want to look at the data from a single experimental trial which is stored in a particular row of a matrix. Alternatively, we might want to find out when the values in a time series cross a given boundary. Doing this is simple in Python."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Slicing\n",
"*Slicing* means that we want to look at a specific portion of a vector or matrix, for example, the first row of a matrix. We will continue with the matrix `c` from the previous example. The notation '`:`' means '*all indices*'. To access all columns in the entire first row of `c`, type `c[0,:]`. To access the 2nd thru 4th columns of the first row of `c`, type `c[0,1:4]`."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c[0,:] = [1 2 3 4 5]\n",
"2nd through 4th columns of the first row are c[0,1:4] = [2 3 4]\n"
]
}
],
"source": [
"print( \"c[0,:] = \" + str( c[0,:] ) )\n",
"print( \"2nd through 4th columns of the first row are c[0,1:4] = \" + str(c[0,1:4]) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
" \n",
" The notation `1:4` means *all integers from 1 up to, but not including 4*, \n",
" which in this case gives columns 1, 2, and 3. \n",
" \n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Leaving out the number before the colon tells Python to start at index 0. Leaving out the number after the colon tells Python to continue all the way to the end."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c[0, :4] = [1 2 3 4]\n",
"c[0, 1:] = [2 3 4 5]\n"
]
}
],
"source": [
"print(\"c[0, :4] = \" + str( c[0,:4]))\n",
"print(\"c[0, 1:] = \" + str( c[0,1:]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also tell Python how to step through the indices. To access only the even columns of `c`, we can use the following:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 3, 5])"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c[0,::2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This code tells Python to start at 0, continue to the end, and step by 2. The result should be the values in row 0, columns 0, 2, and 4 of `c`. We could write this explicitly as `c[0,0:5:2]`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" #### Selecting elements that satisfy a condition\n",
" Sometimes we're interested in locating particular values within a\n",
" matrix or vector. As an example, let's first define a vector."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = [ 2 4 6 8 10 12 14 16 18]\n"
]
}
],
"source": [
"a = arange(1,10) # this creates a vector of increasing values from 1 to 9\n",
"a = 2*a \n",
"\n",
"print( \"a = \" + str(a) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Calculate the shape of `a`. What is the maximum value of `a`? \n",
"*Hint:* Use the `max()` function.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Now let's find all values in `a` that exceed 10."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([12, 14, 16, 18])"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[a > 10]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is called logical indexing, let's look at what `a>10` returns:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([False, False, False, False, False, True, True, True, True])"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lgIdx = a > 10\n",
"lgIdx"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"When we index `a` using this array `lgIdx` we get back only the entries \n",
"in `a` corresponding to `True`, as above:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([12, 14, 16, 18])"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[lgIdx]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sometimes we want to know the actual indices in a where `a > 10`.\n",
"We can get them using the `nonzero()` array method, which returns the\n",
"index of all entries that were `True`, or non-zero."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([5, 6, 7, 8]),)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lgIdx.nonzero()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"The command `nonzero()` can be used as both a *function* and a *method*. A method is called by adding it after the object it is meant to operate on with a period in between ( `lgIdx.nonzero()` ). A function is called with the *argument* explicitly provided inside the parentheses ( `nonzero(lgIdx)` ). Basically, a function and a method do the same thing, but a function needs to be given an argument, while a method assumes that the argument is the object that the method is attached to. Note that if we use `nonzero()` as a function, we need to tell it to look in NumPy for the definition (i.e. add `` at the beginning of the function call). \n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we have another way to select the desired elements of `a`:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([12, 14, 16, 18])"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a[ (a > 10).nonzero() ]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use these two types of indexing to change subsets of the values of `a`."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a = [ 2 4 6 8 10 12 14 16 18]\n",
"a = [ 2 4 6 8 10 100 100 100 100]\n"
]
}
],
"source": [
"print(\"a = \" + str(a))\n",
"a[a > 10] = 100\n",
"print(\"a = \" + str(a))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q:** How does `a` change in the first and second print statements?\n",
"\n",
"We can perform these same logical operations for a matrix,"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"b = \n",
"[[1 2 3]\n",
" [4 5 6]\n",
" [7 8 9]]\n",
" b > 5 is \n",
"[[False False False]\n",
" [False False True]\n",
" [ True True True]]\n",
" b[b>5] is an array: [6 7 8 9]\n"
]
}
],
"source": [
"b = array([[1,2,3],[4,5,6],[7,8,9]])\n",
"print( \"b = \\n\" + str(b) )\n",
"print( \" b > 5 is \\n\" + str(b > 5) )\n",
"print(\" b[b>5] is an array: \" + str(b[b>5]) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"Notice that the last line collapses the `True` entries to an array, \n",
"ordered by row and then by column. If you've used MATLAB, this is \n",
"the opposite of what it does!\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 14: Plotting data in Python.\n",
"It's not easy to look at lists of numbers and gain an intuitive\n",
"feeling for their behavior, especially when the lists are long. In\n",
"these cases, it's better to visualize the lists of numbers by\n",
"plotting them. Consider"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x = [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.]\n",
"y = [ 0. 0.84147098 0.90929743 0.14112001 -0.7568025 -0.95892427\n",
" -0.2794155 0.6569866 0.98935825 0.41211849 -0.54402111]\n"
]
}
],
"source": [
"x = linspace(0,10,11) \n",
"print( \"x = \" + str(x) )\n",
"\n",
"# The above line constructs a vector that starts at 0, ends at 10, and\n",
"# has 11 entries (takes steps of size 1 from 0 to 10). Let\n",
"\n",
"y = sin(x)\n",
"print( \"y = \" + str(y) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Looking at the values in 'y' printed above, can you tell what's happending?\n",
"\n",
"**A.** Not really ... let's visualize `y` vs `x` instead.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### matplotlib\n",
"To visualize `y` versus `x` let's plot it. To do so, let's first import some basic plotting routines from `matplotlib`, which provides a nice 2D plotting library . We'll also tell Python to show `matplotlib` graphics inline, in this notebook.\n",
"\n",
"Let's start by plotting a simple example for `x` and `y`,"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"from pylab import *\n",
"\n",
"x = ([1, 2, 3, 4])\n",
"y = x\n",
"plot(x,y) \n",
"show() # this is the plotting equivalent of print()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Does the plot above make sense for the variables `x` and `y`?\n",
"\n",
"
\n",
"\n",
"Now, let's go back to the definitions of `x` and `y` that we started this example with and plot `y` versus `x`."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = linspace(0,10,11) \n",
"y = sin(x)\n",
"\n",
"plot(x, y)\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" The plot of `x` versus `y` should look a bit jagged, and not \n",
" smooth like a sinusoid. To make the curve smoother,\n",
" let's redefine `x` as,"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 1.1 1.2 1.3\n",
" 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 2.3 2.4 2.5 2.6 2.7\n",
" 2.8 2.9 3. 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4. 4.1\n",
" 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5. 5.1 5.2 5.3 5.4 5.5\n",
" 5.6 5.7 5.8 5.9 6. 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9\n",
" 7. 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8. 8.1 8.2 8.3\n",
" 8.4 8.5 8.6 8.7 8.8 8.9 9. 9.1 9.2 9.3 9.4 9.5 9.6 9.7\n",
" 9.8 9.9 10. ]\n"
]
}
],
"source": [
"x = linspace(0,10, 101)\n",
"print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Compare this definition of `x` to the definition above. How do these\n",
"two definitions differ?\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"**Q.** What is the size of `x`? Does this make sense?\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's replot the sine function."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"y = sin(x)\n",
"plot(x,y,'k') # the 'k' we've added makes the curve black instead of blue\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Does this plot make sense, given your knowledge of `x`, `y`, and trigonometry?\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 15: What if we want to compare several functions?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Continuing the example in the previous section, let’s define a second vector"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"z = cos(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and plot it:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot(x,z)\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We’d now like to compare the two variables `y` and `z`. To do this, let’s plot both vectors on\n",
"the same figure, label the axes, and provide a legend,"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot(x,z) # plot z vs x.\n",
"plot(x,y,'r') # plot y vs x in red\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice that we’ve included a third input to the function `plot`. Here the third input tells Python to draw the curve in a particular color: `'r'` for red. There are many options we can use to plot; to see more, check out the documentation for plot .\n",
"\n",
"We can also label the axes, give the figure a title, and provide a legend,"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot(x,z) # plot z vs x\n",
"plot(x,y,'r') # plot y vs x in red\n",
"xlabel('x') # x-axis label\n",
"ylabel('y or z') # y-axis label\n",
"title('y vs x and z vs x') # title\n",
"legend(('y','z')) # make a legend labeling each line\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To futher edit this plot, you might decide - for example - that the font size for the labels is too small. We can change the default with:"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rcParams.update({'font.size': 12}) \n",
"rcParams['axes.labelsize']=14 # make the xlabel/ylabel sizes a bit bigger to match up better\n",
"rcParams['lines.linewidth']=2 # we can change the default linewidth with\n",
"\n",
" # let's make a new plot to check \n",
"plot(x,y, label='y') # sometimes it is easier to name a trace within the plot() call\n",
"plot(x,z, label='z') # notice without a color matplotlib will assign one\n",
"xlabel('x')\n",
"ylabel('y')\n",
"title('y vs x')\n",
"legend()\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 16: We can make random numbers in Python.\n",
"To generate a single Gaussian random number in Python, use the function in the NumPy `random` module."
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a Gaussian random number (mean=0, variance=1): -2.472931934943898\n",
"a uniform random number from [0,1): 0.6818555754880623\n"
]
}
],
"source": [
"print(\"a Gaussian random number (mean=0, variance=1): \" + str( randn() ))\n",
"\n",
"# a uniform random number on [0,1)\n",
"print(\"a uniform random number from [0,1): \" + str(rand()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's generate a vector of 1000 Gaussian random numbers:"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"r = randn(1000)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"... and look at a histogram of the vector:"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"hist(r)\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Does this histogram make sense? Is it what you expect for a distribution of Gaussian random variables?\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"See Python Help (`hist?`) to learn about the function `hist()`.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 17: Repeating commands over and over and over . . . \n",
" Sometimes we'll want to repeat the same command over and over again.\n",
" For example, what if we want to plot `sin(x + k*pi/4)` where `k` varies from 1 to 5 in\n",
" steps of 1; how do we do it? Consider the following:"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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B5Wd/i6fX6iF8X323k46AcQMQQLg9KJ/9QxAC+cpPkFfOGyr/fYnUyOn6CYqMEfEsI5Kz1vCP2LNnD0NDQxQVFVG24mNEvKtQZIzcjh+ATEwtYAquXIzS25XA4RRsu28B69atA+D11183xA2yq36QN68OYrcIfndbOSvWuAE4czzM4MDsn1F5+Rzy5WdBCDyf/T3+YGsVioAXz/dxttNYN46w2lCe/q/g9sCZo8h92VqdAN6eX2CN95CwlxAs/IDpn5dVENNA9nUjn/0aAOJTv4Uor+L+2lw2VfkIJzT+aX8bSaPN7LqliAc/ClJD++b/RkYmKBvxK4Jr8CD28DU0i5dAyaNgkM87zbVr1zh79iwWi4UdO3ZgtdkIlHyEhK0Ia6wTd/+uWckf6Etw8bReOmPVejcOp8KGDRsoLy8nFAqxa9fs5PeFE3ztcCcAT68tpSbPwZwaG3OqbSQT8M4bnWizeEZlPI723S+DlIiHnkAsXc2iIhdPLC1EAv/nQDvD8eSs7mEsIq8Q8cln9M9Xv4HsvSWBjLcN9tAF3EOHkFgYKv04KLMPbJiKrIKYBtqPvgHRCKzeiNh8H6Cbwf9lQxmFbisXeyK8enniujwzRTz6JFTOhe4O5HPfMlz++wVLrBtv76sADBV/BGkxduE+Eonw1ltvAbB58+aRiCWpOAiUfBQAT98uLLGZvaCkJjl1JIyUMK/OMZKjoCgKO3bswGazceXKFRobG2d8D/95rIvhuMbaCg8P1OpJmkIIlq9x4XILerqi1F+OTiFlknt47Tm96F7pHMSHPj6y/ePLi6gtcNAVivPNo8a44kYjNmyHVRsgPIz2nf//V9bVJJIRfF3PAxAqfGAkYslssgpiCuTpo3BsPzicKJ94+oZoDZ/DwjMpV9P3T3UzEJm9G2I0wmZD+c0/0mPDd7+KbLxqqPz3BVLi634RIeOEfauJecet2TgrDh06RDgcpqKiglWrVt2wL+6aT9i3BkESX/dLNxVgnA6N12IM9idxugWLl99Y/DEnJ4f169cDsGvXLhKJzJ+hkx0h3mkYwm4RPLOu9IZn1GZXWL5WdzVdOhMhEtYyli87WpE//zEAylO/c0Oug1UR/MHmCqyK4I2rg1zsMdbSFUKg/NrvgMcH504g979lqPz3C57+nViSAeKOKobzZhf6mwlZBTEJMhZFS7uWHvkkouDmEt0bKr2sLvcQiml894TxJrConIu450MgJdoP//1XbgZlD53TXUuKi2DRhwyX39vby6lTpxBCsH379nHDNYNFD6EpbuzhqzhT9Z6mSzSqcSHlWlq6avyCeqtWraKgoIDBwUGOHj2akfx4UhtxLfmXFVLqvTlRrbTcRtVcD4kEnD+Z2QtcSon2vX+DRByx+T7EopuLGlbnOnh0cT4A/3GkE83gZ1Tk5iM+/jn9el74LjLyyxe2OhmWWBeugX1IBIHiR2dVpj5TsgpiEuSrz0F3B1RUI+57ZNxjhBA8vbYUqwJvmjCDAhCPfBx8uXDlHPLwHsPl37bIBN5evTJoqOABpMVtrHgp2b17N1JKli9fPmGJZGnxECzSkyG9Pb+YuIz4OFw4FSEekxSVWimvHN9nbLFY2L59OwBHjhyZtIz4WF4430frUIw5OXY+smTiisAb7ipCUaClMU5v9/StFPnuO3qFYm8O4mO/MeFxTywrJN9l5VJvhF31N9drmi1iwzaYVweD/chXnjdc/m2LlHi7f4ZAI5KzdsbVAmZKVkFMgOztRr7yHADKk59HWCcubDYnx86ji/XB+bXDncYvWLu9iI8+pV/XT76FjN7cJ+CXEffAfqzxPhL2EsK56w2Xf/XqVVpaWnA6nWzcOHlPgojvTmLOuShaCPfAO9OS39+boOlaDKHAsjtdkyaTVVZWsnjxYpLJJHv2TG8S0BdO8OMzeo7Ab68rxTZJSXpfro3axXpC3pljw8hpPKMyEUe++D0AxGOfRnjHFlm+jttm4dOrdAv7Oye6jV+wVhSUtBXxxovIXuPXO25H7MPncYQvoylOgoUPvuefn1UQEyB/9kPdrF63FVE3td/7Y8uKKHRbudoXYU+jCTOoLfdBda3ene7V5wyXf7shEgHcfTsBCBZ+EETmda4mI5FIjLyIN27ciNM5RWMoIQgW6UUU3QP7UBKT/8ZSSs6l3Dnz6xz4cqa+/i1btmCz2aivr6e9vX3K49XTPcSSko1V3pECkpOxYIkTl1swNKDR3DB12Kvc/Rr0dEJ51UhwxmRsn5fDwkIn/eEEPzljfHKbqF2MWLcV4rGROmi/1MjESEJcqOB+w4MzpkNWQYyD7GjRF8MURY8kmgYum8KnVuguih+e7jE+u1SxoHzyaf36Xn8ROWR81NTthKfvLRQZJepeRMxTZ7j8M2fOEAgEKCwsZNmyZdM6J+GsJuJZipDxEeU1ET2dCfq6k9jsgoVLpteV0OPxsHKlXgU/XV58IjoCMV6/MoAi4MmV02tfa7UKFq/Q+zlcOhtBS078jMrIMPLnepKm8thTCMvUCk5JuVsBXr7QT++w8VUAxOOfAZsdeXgP8uoFw+XfTjiHjuoWtK2YcK55XfcmI6sgxkG+9APQNMSW+zPqcnXPvFwqfDbaA3HevmZshjWAWHAHrFgHsSjytRcMl3+7oMT7cQ0dRiJGfP9GEo/HOXLkCKBbD5P1dRhLqPBBJALX0OEJa/BLKUcWpmsXO7DZp5+zceedd+JwOGhpaZk0w/rZ0z0kpT5rr86dfi2nOVU2vDkK4WFJ0yQZ1vL1F/UeJ7WLYeX0S8osKnKxqcpHXJM8f65v2udNF1FYgnjgUQC0l75vuPzbBpnA0/82oIe1Gm1BT5esghiDbLqKPLJXbxk6Kt57OlgUwSdX6LO5H53uIZ7MPKRwKpQPf0q/zl0/Rw71Gy7/dsDTvwuBRtS7kqS9xHD5hw8fZnh4mOLiYubPz6xcR9JeQsS3BoGGp++NcY/pak8w0JfE7hDMW5hZIT6n08mdd94JwP79+8eNWmsciLK7fgirAp9YnlktKqEIFi3TLZrL5yIkEzfLl0MDyNf1lvHKY5/JuBDfJ5breSSvXR4wx4p48KPgcsP5k8gr5wyXfzvgGjyMJTFIwl5G1GN8aPd0ySqIMWgv6rMSsf3hccNap+KuGh/VuXa6hxO8cdUEK6KmVk8cisV+KaM5lPgAzqGjSAShgnsMlx+Px29Ye5hJFdJQwX1IYcUZPIU1euNawWjrYeESx6R9oidi1apVuFwuOjs7uXbt2k37v3+yGwnsWJA3bljrVJRX2sjJsxAJSxqv3pw8J197AaJhWLFuWutvY5mb72RLtW5FPHfWhLUIjxdxrx7yrP0y1irT4iOZ+8GC+9/TsNaxGNqT2u/3FwDfAB4EeoA/VVX1B+Mc9wowOtvDDlxUVXV5an8DUAqkQyH2q6pq+hK+rL8Ep4+Aw4V4+IkZyVCE4FMrivnbPa2oZ3q5b34uDquxP7DyyCfRThzSe1rv+Cgib+Lwxvcb7v5dCJJETLIeTp8+TSgUorS0lLlz585IhmbLI5yzHvfgftz9uxkq+8TIvvaWOEMDSZwuQc2CmZXxttlsrF+/nt27d3Po0CHmz58/osjq+yMcaglitwg+tmxmlWyF0K2Iw3tDXD4fpbr2uiKToQBy9yvAdWt1Jnx8eRH7mwK8dmWQx5YWUuQ2tiyEuP/DyDd/CueOI69eQNQuNlT+rcQ19C6W5BBxezkxzx239FqMVk1fBmLoL/cnga/4/f6bpiCqqj6kqqo3/R+wH/jxmMMeGXXMexLfpb2qz8jF9g9M2lN6KjZWeaktcNAfToy0aTQSUT0fVm/Uozl+iSKalPgArqEjKevhXsPlx+PxkUS0DRs2zKqHwXDeViQKjuApLHF9liyl5PI5fUa+8A4nFsvM5S9duhSPx0NPTw9NTU0j29N+/R0L8sh3zXx+V1phJa/AQix6oxUhd/5cLytzx2rdWp0hNXkONlf7SJhlRXhzEPd+EADt56rh8m8Zo6yHUOH9htccyxTDFITf7/cAjwP/XVXVoKqqe4GXgaemOG8uujXxXaOuZSYkWpvg+AGwWhH3z64JkBCCJ5bqftiXL/QZnhcBoHz4kwDId15DBowPq70VuAd2I0gS9S43xXo4e/Ys4XCYyspKampqZiVLs+UR8a1GIHH16y6rns4EQwNJHE5B1bzMXT+jsVqtI2U/0kqtMxhjb+MQFgGPTpIUNx2EECy8Q1+LuHYpiqZJZDSC3PlTAJQZWtCj+cSKIgTw+pVB+sPGlqEBEA98BBxOOH0EWX/ZcPm3AmfgGJZkkLijgph7ya2+HENdTHVAUlXVS6O2nQS2TXHep4E9qqrWj9n+fb/frwDHgT9WVfXkeCf7/f5ngGcAVFWdMBt2KgJf/XuQEuf2h8hdsGhGMkbzwYJCvneqj9bBCGcHBfcuNLaxDUVF9K/ZROzoAVyHd+P1T5zlOhFWq3XG35fhxAOIq/qL0D7/MYrcxl5XMpnk9OnTAGzbto3i4szXl27C8yicPIorcBTngo9xdL8+E1+6Mp/S0tm7/bZt28aRI0doaWkhGo3yan0ETcIHFhezpKY8I1nj/daFhZJLZ5sY7I8T6HdSdmknwWAAW91S8jePX3YkE4qKYGvtEO9c7eXtlijPbDKmM9/oDwg8/DjDL3wf286fkvcnf33TIbfVMz4VUkO07AfAUvUhiopm9owaec9GKggvMNafMghM1Un708Bfjdn2JHAMvU/q7wOv+f3+xaqq3hT8r6rq14Gvp/6UM+k/Kwf70d76OQhBbNtDhvWw/VBdLl87HOE7hxpYnicNa8uYRm57GI4eIPQzlfDWHRk3jL+d+vW6+3bilXGi7kUMDjtg2Njrunz5Mv39/eTm5rJw4UKD7ttGrucOHKFz9J97ibbmzVisUFyRMOx7XbZsGUePHuXV19/kZ6EFADxc681Y/kS/dU2tlVNH4pw43M2Wnd9HAMkHPkJvrzFuoYfne3jnai/Pn2zjg/Nchq/Hyc0PwMs/InroHbrPn0EU36iEbqdnfCrswXPkRbpIWvPoldUww+ueYU/qcTHy1woCY3Pxc4AJm0T7/f67gDLgJ6O3q6q6T1XVsKqqw6qq/g0wwI2L2oYi33oZLanByg2IskrD5N43P5cch4XLvRHOdZnQz2HxCqiaB4FBvZnR+xWZwDWoJ4YN591lvHgpOXbsGACrV6/OKO9hKkL5uoGcM3wIuyVC9Tw7drtx8leuXImiKDTWX8USC7G2wkNNnjE9rAEq59pxOAVDgxq9ohQqqvVcG4NYXOyirtBJIJpkpxm5QXkFena11JA7f2a4/PcS94DuqhzO23LL8h7GYqSCuARY/X7/6AapK4Gzk5zzGeB5VVWDU8iW6NaE4fS1Bdnfu4xzdb+G8oHHDJXtsCo8XJcHwAvnTVioEwLx4EcAkG+89L6t9OoMnNT9rvYy4q6ZL4xORHt7O52dnTidTpYsMdavm3BWE7bPx6rEqCs6xfxF08uani5er5eFdbrLszrcwGOptS2jsFgEcxfolue1mocROx5DGKhAhRAj6yUvX+gzvNIrgHhAXzOUe99ADocMl/9eYI00Y480oClOIjnGKejZYpiLSVXVkN/vfx74S7/f/zlgFfAosHm84/1+vwv4GPDYmO3VQBVwGF2B/S5QBOwz6lpHY224SH9OLUPeKu6oKsboHk0P1+Xz/Lk+DreGaBqMZpT1Oh3E2q3I576jN3M5cwyWm9uj1nCkxDWwF4Bw3l2mRG2krYfly5djsxnfhevywDpWuK+xvPw4Qff9hsuPFtfBhfNUxNqY7zP++6kR9VxJFNBTuJzAQiczj98bn01VPko8VtoCcQ63BtlQOZXXOTNEdS0sWg4XTyP3vjEyaXo/kbYewjnrkYqx74jZYHSY6+8ALqALeBb4vKqqZ/1+/1a/3z/WSvgI+hrF22O2+4CvAP1AK/AB4CFVVY2fggM5m9dQmJsgqdhpmUYBs0zJdVq5d74+5H5x0fjMZ2G1Iu5LJQ298aLh8s3GFr6GLdZB0uIl4ltpuPyBgQGuXbuGoiisWLHCcPmJhOTElWoC0VzclgHsw5emPikDpJS82abRaytEkRrnzxvfn5DsHpAAACAASURBVNz2zk+patsNQH298dn/FkXwSKra8UvnjS+/AaCkIg/lzp8hk8ZWkjUbJd6PI3gGiUI4b9z59C3D0EQ5VVX70F/8Y7fvQV/EHr3tWXQlMvbYs4DxI3kS5i7NoXf/MPVXosxdaDd8MfmDdfm8enmAt+uH+PTqYtw2Y/2L4u4dyJ/9SC890NaEqKg2VL6ZjMyccjeBMPRxBODUqVMALF68GI9n6oqnmdLaGCMeV2gIrWG5Yyeuwf3EPMYlbZ3rDtM4EEX6aijs05sbrV692rBnVPb1II8foNpdT0P1DlqbYtyxymnoOgrA/bW5/PBUD2e7wlzrizC/wFhXHCvWQUk5dLXDiYOwZoux8k3ENXgIgSTiXYFmNdp+mx3ZUhtA2Rwbbo+FUECjp9P4eO3qPAfLSlxEEhq7zWim4vbqDVXQ8yLeLyjxPuzDl5DCSjh3+gXhpksikRiZcS9ffnMntNkipaThim51asXrkMKKY/jyjHtXj8fPU1bnhmUL8fl8DA0Nzap39Vjk7ldB0/Atnk9RqRUtCS2TFPGbKW6bhXtSlvRrV0zo364oI029tPfTYrVM4ArohSOHczfd4ou5mayCABRFsGip/vCmB7zRPFSnt2R85dKAKYvJYpveq0Du3/m+aSjkGjqcmjktR1qMn91funSJaDRKSUkJpaWlhsvv700yNKAX5SupziXi0xPbXIMHDZHfOxznYHMARcAH6gpGlFzaKpotMh5D7tEnFOLeD40sVjdciZnyjO5YqAds7KofMryhEIDYdK+eOHfpLLJ94kq4txOO4BmUZIi4vYyE8/az/LMKIkXdHTkIBTra4gyHjPfDbqj0ke+00DgY5Vy3CW1Jq+fD/EUQDultIm93ZALXkD5ziuQY3y0OGEmMM8N6AGi4oifGVc+zY7EIwrm6/9g5dBSh3VwEL1NevzJAUurPTpHbxtKlS7FYLDQ0NDA4OPuQUXl4r17Su2oeLFhCaYUNp0sQCppkSeeabEm73Ij1dwPvH0vaNXgIQO/3cIvLaoxHVkGkcHusVFTaQDJuhcvZYrMIHligz6BeuWROme4RK2L3q6bINxJH6DxKMkjCXkrcObuyF+PR1dVFZ2cndrudujrjGw5FIxrtzXop65pafeadcJTrbUllFEfgxKzkJzTJa1d0JZAOlXa5XCP3klZ+s0G+oz8n4p4PIoRAUQQ1tXoEjVmW9I6FuiX96mWzLOkPACD3v4WMGT+OjcQS7dBDW4WdaMr6vN3IKohRzE3V7m+6Fpu029ZM2bEwD0XAgeaAObVp1m4BtxcaryAbbu/aNCMzp5z1psyc0i/QJUuWmBLa2lQfQ9P0ondu7/Wgg/Raimvo8Kzkv9uiPyNVuXaWl7pHtqcjsc6ePUsiMfNnSLY2wdUL4HSNzLoBqufbEUK3pMPDxlvSm6p85DosNAxEudhjvCtU1CyAmgUwHEIeMSUy3jBcQ/oYiPhW31ahraPJKohR5Bda8OUoxKKSznbjG50UuW2sr/SS0ODNqyYs1Nkdeu9qQO56xXD5RmGJdWMPX0UKGxHfnYbLj0ajXLx4ETBvcbrpqj7DTs+4Rz7bsxRNcWGLtmKNts34M9JVgB9ckHdDxFJpaSnFxcVEo9Fxe0VMF7lXb3Yk1m9DOK5HFDldCuUpS7rpmjmW9P21+nrfK5fNsqRTVsQ7t68lLbQozqHjALesneh0yCqIUQghqJqvuwuarplkYqfcTG9eHTR3sfrwO7dtVml6dh3xrkRaDA53BC5evEgikWDOnDkUFBjfK6O3K8FwSMPpFpSUjQnNVWwji9XO1BpLpvQMxzneHsKqwPa5Y6vXwB136D0Czp6drEjBxMh4HHlQ76kttj5w0/60y6y53rzFagHsawwwFDVhsXrdVr3j3NULJBqvGi7fCBzBUygySsxZQ9JhcBFDA8kqiDFUzrUjFOjqSJhiYq8s81DostIRjJtSn0mUVuhZpbEY8sgew+XPGpnAOaRXbQ3nmrM4fe6c3oZy2bJlpshP93KummtHKDe7x8KpUgnOwHHQMrdEd14dREstTuc4b84NWbRoERaLhebmZoaGMl/slScOQjAAlfN0d8wYCkusuDx632ozFqtLvXZWlXuIa5I9DSYsVjtdiA3bARhOtU693UiPgduprMZ4ZBXEGBwOhbIK3cRuNiGz2qKIkczqN68Z72YCEFv0cg9y31umyJ8NjtAFFG1YD+tzGFcYMU1vby9dXV3Y7XZqa42v6xSPSdpb9Jf+RD0fko5y4o5KFC2CI3QmI/malLyZKmqXdsWMxel0smCB/mJPK8NMkHteB0Dc/eC4CXdCCKrnXbcizOC+1Bh4y6wxcPcOACLvvIaMm3MPM8US68YeadQXp73mTGKMIqsgxiHtZmq+Zo6JfV9q4O9rDJgTD37nZnC64NrF2y4e/PrMaY0pi9PpF2ZdXR1Wq/GZ2a1NMbSkPsv2eCfOiE9bEa4M3UxnOofpDMYpdltZWTZxbkjazXT+/Hk0bfqWruzugPMnwWZHrJ+4VUvlXH0MtLfEicVMCPuu8uKxK1zti9LQb8JiddU8qJ6PDAbg5LuGy58N6TEQ9S6/bRen02QVxDiUlFpxugTDIY3eLuNN7HKfnaUlLqJJyd7GCauhzxjhcOh+WG4vK0JJBPTMaRQiXuPD+pLJJBcuXACuv0CNJj2jrp6iY1zUtwIpbNjD17DEpl+b/43U4vR9tblYxnFfpamsrCQnJ4dAIEBz8/QnAXLfmwCINZsRHu+Ex7k9ip5ZrUFbo/EBG3aLwt01+vrKWyaUAQcQm/WADW3/TlPkzwip6a5HIJKz9hZfzNRkFcQ4COV6y8gmk0zs+2uvL1abgdis93SWB9++bYqXOQInEGjEPIuR1olfTjOloaGBcDhMfn6+KZnTQwNJBvqSWG1QVjl56KxUnES8ekiqM3B0WvKD0SQHmgII4L75eZMeK4QYUYLTdTNJTUMe0GtjirtuXpweS7XJYyBtSe+uHyJhQltesX4bWK1w9hhywJwigZliH76MJTlEwlZoSv6P0WQVxASkB0d7S5x43PiHd3O1D6dV4WJPmOZBExJ6apdA6RwY7Iezx4yXnylS4kq9KMMmhLYCI3WXli5danjBRbhuPcyptmO1Ti0/kqPfpzNwAuTUbpo9jUPENcmKMjcl3qlzN9K9La5evUokMg03zeWz0NcNhSWwcOmUh5fNsWGzCQb79ZIiRrOgwElNroPBaJIjrVO1hMkc4cvBsWYLaBry0G7D5c+E9GQh4jPHxWo0WQUxAW6vhYJiC1oS2puNn0E5rQpba/S6+KZ02hJixIrQbgM3kzXaijXWiaZ4iHlm3/N7LMPDwzQ0NCCEYNEi4+VrmqSlMRW9NIV7KU3cOZekNQ9LYgBbpGHK43elyk+kgximwufzUVVVhaZpXLlyZcrj5YFUaOuG7dNqCmSxCubU6IrKDCtCCMG9tea6mZz3PgykMqtvcUMtkQzhCJ5DIkYmD7c7WQUxCZU1+oug1QQfLFx/EeyuHzKn09ame0EocPJdZND4cMJMuD5zWmVKWe+LFy+iaRpz5841pax3d2eCWFTi9SnkFUyzXLtQRuVEHJ/00PZAjAs9YZxWwcaq6TfUWbxYLy2eXnuZCBmNII/u1y9r0/Zpy69KLVa3NcXQTHADbZ+biyLgSGuQAROqCzju3AS+XGhrgsaplaiZOAOnECSJuRfcdmW9J8LQker3+wuAbwAPAj3An6qq+oNxjvsS8GfAaN/KClVVr6X2r0rJWQKcB35TVdXZFbeZARVVNs4cC9PTpedEuNzG6tPFxS5KPDa6QnHOdA6zYpKolZkg8gthyUo4dxx5ZB9i+0OGyp82MoEzcBJIRS+ZQPoFmX5hGk1rKuR5ztzM+oVEfKvx9O/CETpNQPswKOO7jnan8gE2Vuqux+lSW1vL22+/TVtbG4ODg+Tmjv/iibz7DkTCMK8uo77ruQUWPF5FL+DXlaCkzNiyJXkuK2sqvBxuDbKncWiksZBRCKsVsWEb8s2XkfveQsxdOOU5ZuEM6q8wM6oHmIXRFsSXgRhQCjwJfMXv90/k7PyRqqreUf+llYMdeAn4HpAPfBt4KbX9PcVmVyit0AdEa6PxJrYiBNtSmbK7TUgYAq73ibiFPlh76BKKFk7lPpQbLr+vr4/u7m7sdjvz5s0zXH4iLmlv1a3IyurMXpBJe0kqJyKKIzR+NzgpJbvqdRfL9mm6l9KMzvdIlxcZj8jbqcJ8m+7JSL4QYiTktdWEvCDA/DGwKRWwcXgPMmGON2AqlHgftkiTnvvgMSfCzgwMUxB+v98DPA78d1VVg6qq7gVeBp7KUNR2dMvm/6iqGlVV9V8AAdxr1LVmQnpwtDSYkxOxbZ4+OPY3BYgljY83F3duBLsdrpxD9nYZLn86pGdOZlWsTL8YFyxYYEruQ3trHC0JBUWWGwrzTZeIbzUAzsD4wQKXeiO0B+LkOy2sGFWYb7qk11wuXrw47jMqB/uJnXwXLBbE2q0Zy0+vQ7S3xkkkjB8D6yu9OK0Kl3sjtA2ZoISq5kFFNYQCcO49d0QAjIS2xrx3gPKez3VnjJGjqQ5Iqqo6uinvSWCibJxH/H5/H9AO/Kuqql9JbV8KnFJVdfSTeCq1/abqW36//xngGQBVVSkqKprRxVut1nHPzc+XnDpST2BIQyGHwiJjE1uKimBRSRcXu0JcHFK4Z+HMrn8yBtbfTXTvm7jPHMHz+KdHtk90z4aSCCOu6u4fd/V23I5CQ8VLKUcWaNevXz+t+8n0vo/ubwVg0dICiopm4DvOvQfZ+wvsw5cpyrGD/cb6St8+rdcL2rGklNKS4ozF5+fns3PnTvr7+4nFYsyZM+eG/aF9bxDUNBzrt5I3b37G8ouKoLg0RndnlOEhJ/Prpr9GMl22Lxzg1fNdHOlK8Nn5FYbJtVqtFBcXE7rnIYLf/xr2k4fIvfc9drVKiWjRM+rtc7ZRlGfumDNyXBupILzA2FCEQWC8p0kFvg50AhuA5/x+/0CqT3UmclBV9espWQCyp2f6SUmjKSoqYqJzyyutNFyJceZEF0tXu2YkfzK2VHq42BXip6daWJ5vuHjkqk2w902Cb/2c4bsfGvGhT3bPRuEcOkqOjBNzzmMgICFg7Oe1t7fT39+Px+PB6/VO634yue9IWKOtJYxQICc/OuPvK9dVh2P4PMGmtwnnXe+XHE9K3rioW3Ybyuwzlr9gwQJOnDjBwYMH2bbtxjlZcufP9c+6c8uM5ZfOUejuhPNneskpMD4se2O5g1fPwyvn2nmk1mVYmHL6t5ZL9bWvyMHdxFpbbqhgazbWSCsFkQ40i5eeeDGYPOYyHdcVFRMrZCPXIILA2NKTOcBNqcKqqp5TVbVNVdWkqqr7gX8GnshUznvFSDRTUwxpQiTH1rk5KAKOtgUJmFDdkqWrweuD9mZorjde/iQ40ovTvpWmyE8vTtfV1aFMI3QzU1qbYiChtNyG3TFz+SPRTKnvI83xdv03r8l1MC9/5tZpenH+0qVLJEclRsqOFmi6hnB7YMXMM3crqmwIAd0dCaIR412hK0rd5DkttAXiXOkzofRGcRnULoZYFHnikOHyJ2Mkc9q7HETmLsqp6O7uJhQyp3KzkSPqEmD1+/2jwwRWAtOpSSzR1xlIHb/C7/ePnkKsmKYcU8grtOD2KkQjkt5u40PxClxWVpR5SGiwt9GE6pZWK2LtXcB7u1itJALYw1eQWEwpSpZMJrl8WW+MZFr0UirEOe2HnylRz2I0YccWbUaJX8/q3ZMqtXL33JxZzZqLi4vJz88nHA7T0tIysl2+q1f0dWzYhrDN3PftcCoUl1mREtqajV/otSiCranSG2a0I4VbFLAhkziCeg/x9FqU0bz99tt885vfzKjkynQxTEGoqhoCngf+0u/3e/x+/xbgUeC7Y4/1+/2P+v3+fL/fL/x+/3rg99AjlwB2AUng9/x+v8Pv938htf2WFVQRQjAnFb3S2mROFEQ6ksMMBQGjBse77yC196b0hiN4CoEk5q5DWozPTWhqaiISiVBQUGDKWkowkGSwXy+tkY5mmzGKnZhHz3x2pl4Y0YTGuy26gtg6d3Z+fSHESDvSS5f0ZUApJfKwriCcW++flXy4HrBhRkQfXA/Y2NM4RNKM0htrtoCi6GHfgfcmL8gevoolGSBhKzSlevHQ0BAdHR1YLBbKyozvK2G0Tf47gAvoAp4FPq+q6lm/37/V7/ePzqX/BHAF3W30HeDvVFX9NoCqqjHgI8CngQHgs8BHUttvGRVV10tvmJEwtLHKi00RnO0K0ztsghKqXaKXWBjohcuZl4ieCc5AOu7bnOil9Itw0aJFppTWaEtNBsrm2LBYZi8/7WZLu92OtAaJJCR1hU5KvbOPbEkriKtXr+rtSJvroaMFvDnYl8++MFxphQ2LBfp7kwyHjHczLShwUuGzMRBJcqpz2HD5IicP7lgFySTy6HvTjtQRSE0GvCtNKa2RtqDnz59vSmtdQ2MCVVXtQ3+5j92+B33xOf33J6eQcxwwJ6NqhuTk6e1IA0Ma3Z0JSsuN/THcNgtr5ng42Bxkf1PA+IQhIRDrtyJfeQ55ZC9ikfGtOEdjifdii7ak4r6Nd/8kEomRlpsLF5qT/NTWpM9JKqqNCUuMuReiKU5ssQ4ssU72pNxXW8fpGjcT8vPzRxYom5qamHtctx7E2i0IA8J/rVZBaYWNtuY4bc0xFiw2dqFXCMHWuTn86HQvexuHWF1uvNUp1m9Dnjmmu5nMThyVCRwh3TNu1hpcepJk1hjIltrIgPSLIv3iMJq7qtMmtjnr8SPrEEf3m17h1RE8DUDMY07cd2NjI/F4nJKSEvLyJq98OhOGBpIEhjRsdkFxqUHzKGEdWYuxDJ7kSGsIAWypNi5sdLSbKe1eEuvuNkx+RcrV2maSqzU9Bg42B4gnTXAzrd4AtlReUH+v4fJHYx++jKJFSNjLSNpLDJff398/kiBaU2NOZdisgsiA9ODoaImTNOHhXVfpxWERXOwJ0xU0YQBWzYeSCggMwsXTxssfRdq0jvjMsVTMnjm1pQo0llfaUCbpy5ApEa8+k7QMniCuaSwtcVHoNs4aTSuIa1evEO/rgfwiWLDEMPkl5TasVhjsTxIKGD/JqM5zUJ1rJxjTONVhfGSOcLphue6cMNvNlF5rSpd9N5rR7iUzEkQhqyAywuuzkJtvIZGArnbjX+BOq8LaObonbm+TCdFMQiDWpayII3sNl5/GEuvGFmtHUxzE3HWGy4/H49TX6+G6ZigIKeXIDLmiylhXYtw1D83ixUc/de4+7qoxxr2UJicnh9LSUhJJjYacIsS6u6ZVuXW6WCyC0jmpgA0TopmAke/EjDEAoyxpE8cAWhx7UC+tEvWaO0lKTwrMIKsgMsRsE3vrSDSTSW6mdKe5YweQCeNDdgEcQT1rNOq5w5TKrfX19SQSCcrKysjJMfYFC7p7KRTUsDsEhSUGX7+wMOTS3Uw7iurZbKB7KU1dSmleyS0b+b2NZI7JrtYtqTL4h5qDxM0oP7N8rV5+5uoFZG+34fIB7MOXUGSUuKOCpN34CLve3l76+vpwOp1UVVUZLj9NVkFkSDqaqaPNnLo0ayo8uKwKV/sitAdMGIAV1VBeBaEAsVOZ9UueLiNhnCab1ma5l1pHWQ9GupfSHArqxfV2FDeR6zA+cWqBVYKUNOYUESuvNlx+cakVm00QGNQIDBrvZqrM0ZMGQ3GN4+1muJlckIrqMsvNZPYYSFsPtbW1WCzGP0NpsgoiQ9wehfxCvZGQGW4mu0VhQ6XuZtpjRtKcECMmdiTVn9hILLEurLEONMVJzL3AcPmxWIyGhgZALy9hNFLKkUSw9GTAaF5qyqE75qLQGsAabTVcvufMESpCAySFMuKKMxLFIkZarraZ0EwLri9Wm2VJK2a6mbQY9pCe4R8xwb0kpXxP3EuQVRAzojzll2432Qe7v8lcN1P04DuGlz9ORy9FPUtNcy8lk0kqKirw+Yx3zwz2JQmHNBxOQUGx8TOzoWiSkx3D7O7Xo07S35dRSE1DHjtA7VAnwLQ6zc0Es12tI26mliDRhPFuJpavBbsD6i8hezoNFe0YvogiY8QdlWg2Y8PVAXp6ehgcHMTlct1UmNFosgpiBpRX6jPLTpPcTKvK3bhtCvX9UVPcTKK8EirnIoeDcNbY8sfOtIIwaWHObPdSW4v+wiuvtJmSfPduSwBNQiN6bogzeBqMLCN/5TwM9lGr6C/VxsZGYjHjn6GiEis2uyAYMMfNVO6zU1vgJJLQOGaGm8nhRKxcDxjvZkorfbOil9JKv7a21pT6Y6PJKogZ4PbobSeTSejuMH4GZbMorE9FM5lmRazRK4rKY/sNk2mJdab6TrtMcy81NjYCjDTJMRIp5YhVWG6Seyn9e5aVLiRp8WJJ9GONthkmP/2y867eQHl5OclkcsQlZySKIihLRTO1t5iVE6FbEaaNgbWpMXDYQDeTFsMe0vuTmFF/bHR5ezNcrGPJKogZYrababPZg2PNZgDkiUOGRTNdj15aakrVyoaGBpLJJOXl5Xi93qlPyJChAb2EhMMpKCwy/vqD0SQnO0IoAtZX5oy8QIxyM+nupVTf6bVbRqystNVlNOkxYNY6xKbUGDjcYk40E8vWgMMJjVeQ3R2GiLQPXx7lXjK+dn9fXx/9/f04nU7T3UuQVRAzpiK1SNfRFidpipvJg9OqcKUvQmfQDDdTFZaqeTAcNCxpbkRBeCfqMjs7zJ45pReny+bYECZEL73bGiShwbJSN7lOK1GP7oZzhAxyM127AAN9es2tuQtHrCyz3EzFJVasNggMagRNSJor99mZl+8gnNA40W5CbSa7Qw95BeTxA4bIvO5iNd56gOtjYP78+aZGL6XJKogZ4vbqSXPJBHR3Gp9P4LAqrJuj16I50GyOFeHcuB0wxgdrifVgi3WkkuOMf4HH43HTo5fam81JjkuzLxWVtrlKnxnHXXPRLF6s8T6ssfZZy5dH9N9RrNmMEAKfz0dZWRmJRMIUK0KxCMoqTLakU9/VfpPGAHemLOljBigImRiJXjJbQbwX7iXIKohZYbaJbbabybFZb2AvTxyadW0mR0i3HmLuJaZELzU2NpJIJCgtLTUleikwqI0kxxUUG3/9oViSEyn30qbUSw+hEPHo1tZs3Uzp6CUAkXrpwfUXydmz5rRTKR9V5dgM0mPg3ZYACTNKgC9fo9dmunph1rWZdPdSlLi9nKTN2Na6oLuXent7cTgcpibHjSarIGZB2s3U2WZObaY1FenaTBG6Q8YPQGtNLZSU67WZLs/uBZJ2L0VMmjldvar3bTZr5tTeoiv5sjnmJMcdTrmX7ihxk+e6roDS0V6O4JnZuZkaLkN/qvbSvOux8env69KlS8Tjxj9DxWVWLOnaTEETkuZyHVSlajOdNqMEuNOld1xk9m6m6y5WcyL40mPgvXIvgcHlvv1+fwHwDeBBoAf4U1VVfzDOcX8MfAaoSR33b6qq/sOo/Q1AKXrjIID9qqo+aOS1GoHHZyEnT2FoQKOnMzH7pjJjcFgV1szxsr8pwMFmk0qAr9mslwA/th+xeGZheUq8H1u0FU3YTam9NLq0t9nrD+UmuZfSVmDaZZIm7pqLpriwxnuwxLtI2ktnJP+69bDphtpL6dpMnZ2dNDU1GR79ZUm5mVqb4rS3xFmw2PgX1+ZqHz863cv+JpNKgN+5Wbeijx2Aez80MyEygSOk91kxy72UdhO+V+4lMN6C+DIQQ3+5Pwl8xe/3j7diKdAbAuUDHwC+4Pf7PzHmmEdUVfWm/rvtlEOadE6EWSZ22h2xz6xophEf7EGkNrNIkfTMKeZZBIrxL9jm5mbi8TjFxcXk5uYaLj8wlCSYKu1dZHTtJSCSuF4yYmPVmOgrYdFrVgGO4MysOCnlyOxXrN500/60UkjPQI3G9Ii+quu1mUzpNLdyHViscOksMjA4Ixn24Wup0t6lJO3FBl8hDA4O0tPTg81me8/cS2CggvD7/R7gceC/q6oaVFV1L/Ay8NTYY1VV/XtVVY+pqppQVfUiervRLUZdy3tJ+Sg3kxmd5tbO8WBVBBe6wwyETSiuV7NAj3oZ7IOrF2YkIt0UJep5fy7MdaSUe2mF1RT30rG2ILGkZFGRc9zS3umor/T3mDGtDdDVDr5cWHhzae+0gkhnoRtNcZkNxQIDfUnCw8aHo9bkOajw2RiMJjnbZYKbye2FJStBasjjB2ckI70GF/WYE8GXVu7z5s0zrbT3eBj5SXVAUlXVS6O2nQS2TXaS3+8XwFbga2N2fd/v9yvAceCPVVU9OcH5zwDPAKiqOuPexFardUbnFhZKcvIiDA3EScY9lMxxz+jzJ2NDTQ/76vs5OwCPVhlXGdJqtVJcXExgy70Mv/xDnBdO4NuUYXOZ2ABKpBEprPiqN+OzGNtlbHSi19q1aw3pPT32t97foTd7X3RHEUVFxrswjh3RFz/vW1w2/vUXbER2qdiibRR5JTgzm4EG33yREODauI2ckptdVEVFRSNupkAgYIqiraxJ0HQtRGDATlW18Q2c7l0U4ntHWjjRk+DeZdN/BqY7rsPbHmTozFFsZ46Q/9iTmV2c1BAN+uTKVbkVl8f46q3pBNFVq1ZNeT8zfZeNK8sQKTpeYKx9NghMFXLyJXRL5j9HbXsSOIbuivp94DW/379YVdWBsSerqvp14OupP2VPT0/mVw4jrRpnQkmZwtAAXDzbg81hvIK4s9TBvnp443w7W8qN+8nS9ywXr4KXf8jwvp1EPvTJjEpMuAYP4ENvpznYHwSCU52SEc3NzYTDYfLz8xFCzPg3Gs3o33o4pNHbHcViBYdrmJ6e8Kzljyae1Nh3TVcQKwqUCa8/x1WHM3iKUPNewvmZlehO7n0LgOgdqyeUv3jxYjo7Ozl2O6BzFAAAIABJREFU7JgpHfgKiyVN1+DKxQFKKoy3dFcVWfgesOtSN7+2NAdlms/odMe1rF0KikLs1BG6GxsQnuknYtrC9eQnAiRsBfQNOyA8+2d0NKFQiObmZiwWCwUFBVPeT6bvsoqKign3GbkGEQTGFufPASZ0nvv9/i+gr0V8UFXVaHq7qqr7VFUNq6o6rKrq3wAD6FbGbUm6smV7SxxpZF2dFOvneFEEnOoIEYyZ0Cq0dhHk5EFvl97oPgMcwdTCnEmm9ei6M2bQ0aq7l0rKbFisxruXTnUMMxzXmJvnoNw3cfmOkazqDN1MsrMNWhvB5YFJggzuuENf57h27RraDNeaJqO0wooQ0NedIBo1Xv6CAieFbiu94QRXeiOGyxe+HFi4FJJJ5OnDGZ2bXjvSKwgY/wylAzSqq6ux280pATMRRiqIS4DV7/ePrqK2Ehj3iff7/Z8Fvgjcp6pqyxSyJbo1cVuSV2DB6RJEwpKBPuNf4DlOK0tL3CQlHGk1doYOIBQLYtUGgIx8sCIZxha+hkQh6jGurWUaKeXI4DBNQbRcby1qBukkx01VkxvSMXcdUlixRxpREtMv8z4SvbRyHcI68T2kmysNDw/T0WFMWYnR2OwKRaVWpITOVuMXq4UQbEyVwT9oUtJceoE/o3UIKUetwb0/KwhMhmEKQlXVEPA88Jd+v9/j9/u3AI8C3x17rN/vfxL4a+ABVVWvjdlX7ff7t/j9frvf73emQmKLAHMbyM4CIcTIC6bD5Ggm8wfH9GPBHaHzCDTirnlIi/GutY6ODkKhEF6vl5IS45u+RyMavT1JhKL3WjaapCY51KIr9Juil8YgFQcxtz63SodLTofJopdGI4QYUbJmlQBPF+/rMEFBAGxMj4EW4ydJAGK1PknizDFkLDr5wSmssXYsiQGSFh8Jp/HRRZFIhNbWVoQQzJs3z3D5U2F0mOvvAC6gC3gW+Lyq/l/23jxGjizP7/u8yDuz7sq6T1aRxfsmm93N7pnunmOvmZ3RjhBeY/YwJGGMXawkQLZsLYwFBEGwLNsyZAHrlQdY2KtZ7Uph7UozO6vZ2ZmePtjdbJJNskk2r2Ld933mfcTzH5GRlUXWkZn1gt1t1xcodDMz8mVkZrx47/f7fX/fr3Ff1/VXdV0v/FX/KVAP3NB1PZL7+9e55yqBPwCWgUksGuwvGIaxtzZHh+F0mulS7gZzcyrqjD7+kZNWmmJyFDlXnLqo0zunwujBCentmck0yJxDmlf9+A/n46wls7RUeuiq8e16fDLfVV1cmkkuLcBwv2WfefzcrsfbO9DBwUFHrlF7gZifyZBJqx//eGOQSp+LybUU46vF3cBLgahrsFh9qSQ8uF3Uazbb66rvOx4eHsY0Tdrb2/H71RJAioFSvpRhGEvAN7d4/ApWEdv+97ZLoWEY9wFnhNQdRF3YjdcniEZM1ldNqmrUNgyFgx4O1ft5spjg9nQ0v5tSBeH2IE5eQF5/B3n7Q8TP/crOLzBTeGNW406y4pjSc4HNssZO1x/sG5tq2OmlF9sri1rgkqGjSDQ88SFENo50BXY8Xt65Zv3P8XMI3+4LUHNzM8FgkPX1debn55VHZf6ARm3YxfJClrnpNK2davPlLk1wsa2Cnw2tcnV8nY7q3T9zqRBnX0SODiBvfYg48+Kux280xzlLb3VqDuyGfakNRdA0ke+kdirEttNMVx1rmsulmYoQLvPGniBk2pI1dqtvXltaWmJ1dRW/378jy6JcpNOShdkMCGcWCCkl1+z6Q2dxi7l0BUkHDiAw8cZ270mxc+XF3Mhgc5rJsaa5gkjaCdipug/HHUoz2XPg7o1dZfBdqfmc/4mfdKBH+bmk0+k8vbWnR/34xWB/gVCI55WDvTEVcUS4jBPnLOGyocfIlZ0zevn0ksM7p56eHkdcs+am05gm1IVd+Pzqxx9aTjIfy1AbcHOovvjUQLFd1TKak2nXNKsTuEjYNxo7facaLbk5MDvtjD7ZmeYQfrdgcMkZfTLR0gHNbRBd31WfzI4eUqEjjvifjI6Oks1maWpqcsT/pBjsLxAK0dC0IVwWi6qvE7RVeemo9hJNmc50lPr8G8JlH1/b/kCZxRd9CDjfOeoce8nZ9JJNJrjUXlE0Zx8KFohYP5jb3wDl3RtgmtB3AhEqPt3Y3t6O1+tlcXGRlZVn2or2jGCFpU+WzcDCnDMy+OdanxebaedIehO91QE4zeArBvsLhEK43ILGZmejiEvtti6NU5PDSlfI29svEJ74cE53ptER3Zm1tTXm5+cd053JZiVz0zlxPocWiGvjNnuptFqR6akh7WtDyDTe+PYeDhvspeLSSzZcLleeDeNUFNHcZtUenGL05emujrGZ7AXi2rb6ZFpmDU9yHCncJB0QqMxmswwPWz1J+wvE/4fgfJppY3I4wUQRpy5abIzHd5GxrSfgBntJfXEaNm5cXV1djujOTE/EyGSgqkYjWKE+NTC9nmJ0NUnIo3GisXT67wabaWu6q0wm4f4tgHz/Simw00xO1SHsOTA75Qyj73xbBS4BD+ZirCUdaBztPmjJpq8swujWlGBvLoJOBQ+Bpr55bWpqimQySW1tLbW16q1Li8X+AqEYjQUdpSkHOkp76/zUB9wsxjIMLDnQUVpRBX12R+nNZw+Q0vHu6cL6gxMYHbKUVZ1KL12bsKK7820VeFyl02dtVpgv+hDkFjfAh7chlYKugxY1s0R0dXXhcrmYnp4mFlOfqqyq0QiENJIJyfKi+ht4hdfFyeYQplONo0IgzrwAbJ9qdZri/Wmzl2zsLxCK4fVq1DfmOkqn1OdgNSF4IRdiX3OKyWHvSreYHO7kJK7sGllXFRmfetP0eDzO1NQUmqY50hgkpWR82NkFwmbY2KmQUpH1NJLx1KOZMTzx0Weet9N/paaXbHi93nzqzok0kxDC+Uja6a7qM3aq9dmuapFN4I0NIREkQ0eUv3ehgsCnxV6ysb9AOICW58RmsneqqpGX3bh3E/mUC9kG7/uYI7ozIyMjSClpa2vDVwS3v1QsL2aJx7MEgkJ5rwrASjzDo/k4Hk1wtrVMZVghNtJMT2kzyWwWefe6dViZCwQ8PzbTjFP6ZLkF4va0Q42jfSesxtHpceTM5KanvLFHCLKk/d1Il3r13/n5eSKRCKFQiKam8gykVGF/gXAATbnJMTeTJpNRPzlONAUJeTTGVlNMran3wxbhJug4AMk4PLq76bn8AvE5Da3zzXHtXke6s69PRpDA6eYgQU/5C1CezRR9sNmKdOAhRNahsRVayi/g2wvE2NgYqZT6a6g27Mo3jkbW1N/A63ONo6mszJsxqYRwuxGnLgAFDYk5bNokOYDCFKsT12gp2F8gHEAgqFFT58LMwvyMA17SmuBCm12sdjrE3qD6uVILBY1B6tM/6XSasbExAMfSS8+N3rrHTveMv4OsqxJXZgV3ajr/uPw41xx39tKebh7BYJCWlhZM08z7bajE82gcfbHd4Uj67BZpJpnBG30MfH43SaVgf4FwCE7nYC853lGamxwfX0OaVqHRazcGBZ1pDBobGyOTydDU1ERlpVopEYDImkk0YuLza9SF1Z9/LJ3l7kwMgSXRvicIjVROIdcmBVjWoqV1T++EQqc5J2DPAae6qu05cGPCGStSjp8Ft8dqHF1dBsAbG0STKdLeFkyPenbRysoKS0tLeL1e2trU1/hKxf4C4RCa81akGUesSM+1VODRBP0LDlmRtnVDuAnWV2HIMgl0OrR2ujBnL9Yd3SFHrEVvT0dJm5IjDQFqAnun59ppJnthZmLE8uyoqoGevXPv7e/ZMSvSJjcul9U46oQVaXuVl9ZKL+spkwfzDjSO+oM5K1KJvGPVfZ7XHDhw4AAul/pNTKnYXyAcQkWlRqhCI52SLC2on3wBj8bp5iASK++tGhbVz44iPkRk1vEkxpDCTcqBxiDTNPM7WacXiM4D6guLsMEqu1Qme+lppIK9mMKLJzWNll7KUy7F6RcQ2t5vHjU1NdTV1ZFKpZicnNz9BSXC5RY05BpHHfOIcDqSPrsRSSPNjSja4R6gT5u9ZGN/gXAIQoh8FOFcmsnprmrbROhazvtBkgr0IjX17KKpqSkSiUT+pqUa8ZjJylIWzQVtHeq9KzKm5KMpe4FQlB4TblKhw4DVE5GvP5TRHLcdnBbvy6eZHFYWuD6x7kzj6OmLFlvv4ce41wZwZSNk3TVkvC3K3ysWi+Up3l1dXcrHLwf7C4SDKKxDOHHxXmyrQAB3ZmLE0w5Q/XqPQkUlzE3hW7I6d53unnaKuTE7Zd2gGprduD3qL/v7czGiKZOOai+tVeo6a/NsppWPYWwIfH4r7aEIhXRXJ65R24p0cS5DOqX+Gu0L+6nxu5iLZhhedsAjoqoWeo9AJoNv/B3A9n5Qf43aEfSnYS26HZTqGOi6Xgf8IfBVYAH4XcMw/mSL4wTwPwF/J/fQHwL/vWEYMvf8mdxjR4GHwN82DONjlef6PFBb58LnF8SjznhE1AbcHA4HeLQQ5/Z0hJc7n7YE3xuEy4U49QLceAtvegypCcetRZ1OLzmnvWSL86ktrqeChy2PiPQEwu9CHj+H8Ki7eTQ2NhIKhYhGo8zNzSnn3Xt9GnUNbhbnMsxNZ2jrUnvjsxtH/3pglesTEXrq1JvqiDMvIgce4staTYtOi/N9VtJLoD6C+H0gBTQB3wb+QNf1rb7N72AZC53GMgf6GvBfA+i67gW+D/wxUAv8EfD93OOOQEpJMunA7uM5UP0uOd1VffYSvgMhhCZJ+zuRbvXsosXFRdbW1ggEAjQ3NysfP52SlrKogMZWh7wfirQWLXlsV4B0oAchwN9boYS9VAghhONNc44z+tptK1LnGkdddV7coSymFiAdUJ/+SaVSjlK8y4WyBULX9RDwLeD3DMOIGIbxHvAD4Ne3OPw3gX9hGMaEYRiTwL8A/qvcc69hRTb/0jCMpGEY/woQwBuqzrUQExMT/NEf/RHf//73nRj+OVD9HPaIOHoW3+EaAJKaM3nRwp2TI94PM2mk7f3gc8b7YSGWoS7gpteBHWzCY9UJ/H1ViJMXlI9v1yGcWyCsRIVTHhGnmoP43RrDy0lmIw40jja14j9vNSUm002OUbyz2SzNzc2EQs6QKMqByhRTH5A1DKO/4LE7wBe3OPZ47rnC444XPHfXTjflcDf3+F89PZCu69/BikgwDINwOFzSSWuaxtraGk+ePOFXfuVXlKuH1tSY3Lo6zNpKFr+vmopKtTvYcBi666YZWYozkfBwobOm6Ne63e7dvy8zA4eqAYk2A+FTpX2/xcB2zTpz5kzJv18x+OTmDAAH+2oJh2uK+9wl4D8+sc7/iwfDNDaolz9PfCLAD77eKhraW8BVOklgp89cU1PDj370IxYXFxFCUF9fv9dT3oww1NUnWVpMkU4EaepSfwN8qXuRtwYWebACx7s3Pqeq39o8Vg9EMSfShC+rv0bfffddAE6ePLnn81V5fau8G1YAq089tgpslZN4+thVoCJXmyhlHAzD+C7w3dw/5cLCQomnDeFwmIWFBe7cueMIe6Ch2c30RJoH9+bo6VPPADrfHGBkKc5fP5ikO1h8T4T9uXeCJzZIrUeSXkiwdu0a0XO/sNfT3YT19XWmp6fxeDxUV1fvej6lIpuVjI9Y6Z+KmiQLCwtFfe5S8Fb/HACnwm7l5w+QvfIB7hNxvC0BVieulUWx3O0zd3V10d/fz82bNzl37txeTnfr928WLC1C/8NF/KG48vHPNHp5awDefDTD6+0b2WgVv7WWWSPsjyLTJutv3iLyxrxSIoVpmjx8aMmHNzc37/l8S/3MO1n6qoy3I8DTVdIqYKvE4NPHVgGRXNRQyjhK8LxysE5wwWEz3VU1EyXfGPQkAg/vIuNqG5Ls77yzs9MR74fFuQyZDFRWa4Qc8H6YWU8xupIk6NE42aR+ZyxTSbh/m+STNQB8kYfK3wOe3xxwitF3odXyiLg/F2NdsUeE7f2QnEwh5xdgTC0leHJy8jPh/bAVVC4Q/YBb1/VDBY+dBrYydr2fe26r4+4Dp3LRhI1T24yjBE5T/WyPiEWHPCIO1fupDbhZiGUYUkn1kzK/QCSSYchmkJ9s4RGxBzwv9pJz3g9WdHKhtTzvh13x8C4kEyTWrdSh5RGh/hrq6upC0zQHPSJcBIKCZEKysuSAR4TPxfGmoCMeEflNkmnttHe04y0DTjeI7gXKFgjDMKLAnwP/RNf1kK7rl4FvAN/b4vB/A/wDXdfbdF1vBf4b4P/OPfc2kAX+nq7rPl3Xfyf3+M9UnevTaGhooLq6mmg0yuzsrPLxN3lETDvjEXHJAX18d2oaV2aFrKuSTFeuOWsLffxykUgkmJiYQAjhnDif4wuE9X2/oKh7+mnYzXHZ3otkPHVoZhRP4lmPiL3C5/PR0dGBlNIRbabn4xGhns0kzATe2KDl/dB6GdjaI6JcSCk/U+J8T0M1peO3gQAwB/wp8FuGYdzXdf1VXdcLl/X/E/gL4B7wCfCXuccwDCOFRYH9DWAF+FvAN3OPOwIhBEeOWMYfn9s0k013VejTa4vEpUJHN2Q3PrmJzKj5DIXeD36/evbPylKWZELiDwqqa9Wnl1YTGR7Ox3FrcL7NgfSSmc1rAIkzL5HKe0RsbUW6Vzy3NJNDjL68R8SUOo8Ib7Q/5/3QhTxyEQJBmBxFzk3v/uIisLCwwPr6+mfC+2ErKE36GoaxhHVzf/rxK1jFZ/vfEvjvcn9bjXMbOK/y3HbD0aNHuXbtGoODg7z88svKx29q9fDJrThzM2myGYnLrTYdcbIpRNCjMbqSZGY9RXPl3ttGvAW2iiLUDO3dlmDc408spcs94nl5P7S0eRzpzr4xGcGUcKY5tCfvh20x9NgSS2xohrYukgkIrlzBF3lApP4XlXfz9vT08NZbb+U9IlR389Y1uPF4BZF1k/W1LJVVar+zhpCH3jo/g0sJ7sxEeUFB0+KG/8kxhNuDOHEeeeMK8uNriK8+c6srGfYcOHDgwKfu/bAV9qU2cujq6sLn87G8vMzy8rLy8YMhjepaF9kMVtOWYnhcgvM5BzMVUYSWXsKTmsHUfKSC1s6yULxvr8hkMvnGIMfqDw57P1zPfc+XFDfH2chbi562vB/S/k5MVwhXZglXSn0qNBQK0dzcTDabzf82KmF5ROR6Ihy2IlUSScsM3tgjgLz0OmfVzQH4bHZPF2J/gcjB5XLl8+Cf1xD7kkIDFV/e++EwCGtS58X7Pr6GNPcWwo+Pj5NOp2loaHDI+yFLZN3E4xXUNahnRyUzZt7JTMVO9WlY3g+WWZP9vSM0ksGcR8TnPc3kMKPvugKPCG98CM1MkvE2kfVafQXixHlwuWHgEXJtZU/jr66usrCwgMfjob29fU9jOYX9BaIA9uRwWtlyZiqNdKDr+XxbCLcGD+fjrCb2FqXY9YdNujMdPVDXACtLMDqwp/GfV3qpqcXtmPdDKivpq/dTp8D74RlMjcP8DFRUWaKJOdg+BE97VatCoUeEucdNwFZoaPaguSxv8ERc/fid1V6aKzysJbM8Wthbv4U3spFesiECQTh6CqSJvHtjT+Pbi3B3d7cjFG8V2F8gCtDZ2YnL5WJmZoZoVL3PbWW1RjCkkUpKlhbVU/2CHhenmkKY0sqPlwuRjeBJjCBxkQpteD8IIba2YSwRz9P7wZZcVw07Sturteh2yEt7n7qIKDCOSQUOIoUHT3IKLb23HexWqKuro7a2lmQy6YhHhNstaGiyboZORBGWR4QCGXxpWpRinhXn2+QRsQfYC8Rnkb1kY3+BKIDX66WzsxNwJsR+HlQ/Ox++lxysL/rI8n4I9iK1zewicfoFYG+TY2Zmhng8TlVVlXpZByARN1lezKJp0NCkfoHImpIbdv3BKXqrbS169ilxPs1DMmfYtJ9m2hqFjL5y+5rcyUlc2TWy7moyvs2dxuL0JYsgcP82MlFelBKPxz9z3g9bYX+BeAqOT472jTqEE015dj784+koiTKpfoXMjWdw6DgEK2B6HDkzUdb4heklJ5gb9o0n3OTG7VE//v25GOspk7YqLx3V6qVT5OK8lcLz+eHYmWeeT1Y8H7rr4OCgQx4RHrA9ItLqxz8cDlDtczETSTO0WF7T36Y58NQ1KqproecwZNJw/3ZZ4w8PDyOlpL29HZ9P/TWkCvsLxFOw6Wbj4+OOSIDX1bvw+gSxnEeE8vEDbg6H/aSykttTZaTJzBTe2BOggLlRAOF2I05dBMpLMxV6PzhOb3UovfShLe3tWHNcLjo7fg7hffbmkQoesTwi4sOIrPpUqK0oGolEmJ+fVz6+z69RF3ZhmjA3rT6KcGmCi7nf5t3BxbLG8EVsivfWule2q1+5bKbPcnNcIfYXiKcQDAZpaWnBNM28yqhKCE3Q7LBHRL6jtIwcrC/Wj5AZ0r4OTPfWBkQbVqSlT47FxUVWV1efi/dDk1PeD7nv9UWn6g9Ps5eeft72iMDEF32s/P0LPSIcJ2w4xOiz50A5C4QrNYc7PY+p+UkHtu7wz1O+795AZkojhKTTaccp3qqwv0BsAcd9etud9Yh4cQ8eETY7xk5jbInj58DjheF+5HJpE7CwMcgR74fpAu8Hv/rxB5YSee+Hg/Xqu79lZA2e3AeXC3Hy4rbHOc1mcnoO2NGdUx4Rp1ssj4j++WjJHhEbDL6j23o/iOY2aOmAWBT6Pylp/NHR0c+k98NW2F8gtoA9OUZGRsiUuDsoBuEmNy43rK1kiUXVs5laq7x0VHuJpkw+mS0hByuzeKNWY9BO3tPC5893UpdarLZvOAcPHizpdcVi2nFr0Y3itOZA/UTevQGmCX0nEKHtU1j27+ONPQFTvQpNW1sbXq+XpaUlhxpHXVTV5BpHZ9XPMa9LK7tx1FegILATymX0fV7SS7C/QGyJqqoqwuEw6XSaiYnyCrE7weUSNLU8nxC7lDSTJz6EZiZyjUE7G99sTI6rRY/vdGNQNivzOW2n6K22EJxz6SWbvfTSjseZ7mrSvnaETOdrRipR2DjqdBTh2BzoKH0OaJlVPMkJpPCQCh7a8VhR0FVdbONoNpvNU7z3F4jPMZ5bmsmpOoQ9OSYimEUyUXYrzBVCnH4BNA36P0FGi5uA9nfpVGPQwmyGbMaSlg6G1GsjTa6lGF9NEfJqnGgKKh9fJpPwwGLF2EXQnZDMi/c5m2ZynO7qUOPohbYQHpfgwVyclSIbR/NzINgH2i5aVF0HoS5sNY6OFLdIT0xMkEqlqKuro6amePfHTwv7C8Q2KJwcTnSUNrZ4EBosLWRJJtSP31vnoyHoZjme4cliYvcXSLOA2rdzaA0gQpVw+CRks8g7xXWUOs1esms6jrGXcjvRi60VuB3ozub+LUil4EAfonb3/pCNOsQjkOpTlV1dXfnG0UhErccC5BpHK3KNowvONI6eb69BsqGbtRvyEjPFbJKEyEd68lZxkfTnoTmuEPsLxDaor6+nurqaeDzO9LQaad9CeDyCcKMbJMxOOdNReqmEENudGMeVXSfrrnmmMWjb9yghBxuLxRxtDDJNmf8enRLn+/C5sZd2Ti/ZyHobyXga0Mw4nrh6DwePx+N446hdK3Iqkv7iQWuhLWYOiGwUT3wYiWYVqItAfoG4fXXXnpHnQfFWjf0FYhsIIZ4bk8M5NtOGidBuF++mwlyRxVeb6seDW1Z6ZAcUWos60Ri0tJAllZSEKjQqq9Vf1ouxNP2LCbwuwdlWB7wfMul8JPZM9/QO2Gia+3yymTYaR1OONOW9cqAOAdyZiRFL7xylWAoCJulAD9IVKO4NDh219LLmpmFqZwVcW8KnsrKShoada3yfFShJBOu6Xgf8IfBVYAH4XcMw/mSbY/8h8JtAV+7Y/8MwjP+l4PkRoAnLVQ7gA8MwvqriPEtFb28vt27dYmBggFdffVV5129zm4e7H8VZmLU6Sj2Ku36PNQSp9LmYWk8ztpqiq2abG7OU+CNF0FufgqithwN9MNxvpUfObb/ztW8wzkl7W0ye5nZnvB8+zLGXzrWG8Lsd2Fc9ugfxKLR1WRTKIpEMnSC0/Da+yH0i4a+DUHtuduPo5OQkiURCubFTbb0Ln18Qj0lWl7PU1KmtTdWFvBxtCPBgPs7NySivdm/d2wMF3dOlzAHNhTj9AvL9nyJvX0W0bR8dF86Bz6L3w1ZQdTX9PpDCurF/G/gDXde3+5YFlltcLfDzwO/ouv6rTx3zdcMwKnJ/n8riAJs7Sufm5pSP7/Nr1DXkOkodSDO5tA0r0qs7hNiu1AyuzBKmK0TaX1r6pxg2UzKZZHx8fFMDlkpIKTforQ7VH+zv7yWn00s7LLJbIeNrJeuuwZVdx50YV35egUCA9vZ2TNP83OqT2SnBneaAMJN4Y/1AcSSNTa89t3sdQkrJwIClgOwUxdsJ7HmB0HU9BHwL+D3DMCKGYbwH/AD49a2ONwzjfzYM45ZhGBnDMB4D3wcu7/U8nEBhmsn+cVWjpd1iSjiVZrJvaFfHtp8cG+mlYyXvQPM52Ds3trUitaWjW1paCAbVs39WlrIkYhJ/QFBT54y16P25GG4NLrSpl9eQZnaD3lriAoEQeVKB/3OaZsqnWsedTbXenIqSym5NCPHaCgL+zm0VBLbF0dPgC8D4MHJ+ZstDFhYWWFtbIxAI0NLSUtr4nyJUxHN9QNYwjP6Cx+4AX9zthbquC+BVcn7UBfi3uq5rwG3gHxqGcWeHMb4DfAfAMAzC4XCJp2/B7XZv+dpz585x9+5dRkZG+OVf/mXloaHfl+b+7VHmZzLUVNfh9qhNEbxRU8f/9sE0IytJEu4Q7TUbuVX7M4spqznO1/ISvtoSv79wmMXOHjJjQ1RNjuA7/+wNbnzc2tmeOXOm7N9nJwz3LwBw4GBVUbnd7X7r7XD1kxlMCS901tLdqt43OPXgY5bXV3G7eK0UAAAgAElEQVQ1t1F/+kLp15j3Mqy+TyD+AH/9r29ZQyr1Mxfi4sWLvPPOO4yPj1NZWam8hlRXK7n94TCRdRO3VkVNnTqrU7fbzfHuVg43zvJ4Lspg1MWrPc8yxMSyRVN1NV4q63taufgyyffeJNh/l9DRE888f+eOdQs7fvw4jY2NJY9fCvbyWz8zloIxKoDVpx5bBYqJxf8xVhTzfxU89m3gFlYq6u8DP9Z1/YhhGFuK3xuG8V3gu7l/yoWFheLPvADhcJitXltRUYHf72dxcZH+/n5H5Klr6lysLGV5eH8mH1GoxIXWEO+MrPGXd8b41vGN8w+HwyxPPaQ+Nomp+VnINEAZ3595+gUYG2L17b9C69rcXJRKpejvt/YOzc3NW37He4GUkqEnVnRUE84WNf52v/V2+MlDi8V2vtmn/PwBzJ/9yPrv6RdYXCxDXE5WU++qxJVcZHnq3pYstFI/89NoaWlhamqKmzdv0tfXt/sLSkRji5vxkRQP7s3Rd1xdncP+3BdbAjyei/LjTyY5WvVUMdxME166gwCWRDdmGd+TPH4e3nuTyJWfEr/8bFb87t27ALS3tztyDRWi1N+6tXV71uKuC4Su62+zfTTwPvB3gadjsipgR16Zruu/g1WLeNUwjDwFxjCM9wsO+2e6rv8mVpTxF7udqxPQNI2enh4ePHjAwMCAIwtES7uHlaUs0xNpRxaIlzoreWdkjavj65sWCChsjjuatxYtFeL8ZeRf/Duro/TXfnuTwU2h7kxFhfr0zNqKSSxi4vUJ6sPq00vRVJY7M1E04Yz3w2Zr0RLTSzaERjJ0jODaNXyRT4qmKZeC3t5epqamGBgYcGSBaOnwMD6SYnoipXSBsPFyZxV/fGeB6xMR0lmJx7URZXnjT9BkirSvFdNTV94bnDhv6ZMNPkIuL27qY7HlSnw+H21txRMQPgvY9Y5gGMZrOz2fq0G4dV0/ZBiG3U54Gtg2Iarr+t8C/hHwBcMwdtOykFjRxKeG3t5eHjx4wODgIJcu7d7hWiqa2z08vJtgdiqNmZVoLrUf91xLCJ9L8GQxwXw0TUNoo5Dri94DLDZM2WjthKY2mJ20hMuOns4/5XRhbtpmL7V5EA40r92YjJAx4URTkGq/A7aQowOwtAA1dRYjrEwkK45bC0T0PtF69byO3t5erly5wujoKJlMRnknfLjJjdttLfjRSJZQhdrFvq3KS1e1j9HVJPdmo5xr3VjsfRFLbG8vc0D4A3DiHNz+EHnrKuJLX8s/V8hecrnUb2KklI6xovac8DYMIwr8OfBPdF0P6bp+GfgG8L2tjtd1/dvA/wh8xTCMoaee69R1/bKu615d1/05SmwYK1L51NDR0YHH42FhYYGVFfU2jxWVLiqrNTJpmJ9TL1zmc2ucb9voicgjMY8nOYUpvLvqzuwEIcSWTI5MJsPIyAjw+e+efqnDIe+Hmx8AFhtM7EHdNh3owdQCuFNzuFLqGXdVVVU0NjaSTqcdkcF3uURent0xwkan9Rt+UEjYkJkNa9GKPWySsCJpAHlr8+3K3iQ5NQfu3Ihz/b0I66vqu9FVVUR/GwgAc8CfAr9lGMZ9AF3XX9V1vbDP/Z8C9cANXdcjub9/nXuuEvgDYBmYxKLB/oJhGOW5fiiC2+3O0zOdZjPNOMTksNlMmybH0i0AUqEjoO3tBivOvwzkOkpz0iRjY2Ok02kaGhqorq7e0/hbYX0tS2TN3OhKV4xExuRmznTJie5pKSXypnUzEedf2dtgwpWnZ/oi9/Z6alviuemTOTwHrk1EyOa0n7yxwaIFKneDOHUR3G548gC5aingrq6uMj8/v6krXSWyGcnUeIrZyQwOBCdqGuUMw1gCvrnNc1ewCtn2v7d24LCeuw+cUnFOqnHw4EEeP37MkydPuHDhgvLxW9o99N9PMD2Z5qQp0RSnSy60hXBrgofzcZbjGWoDbkRugdjrzgmAzl6ob4TFORh8BIeOOZ5eslVAm9rcytNyAB9NRkhlJYfDAcJBByKUsSGYn4GqGqsjd49IVpwgsH4Tf+QesbovKTjBzTh06BBXr15laGjIkTRTY4sHzWXRluMxk0BQLaOvq8ZHa6WXqfUU9+dinGoOFS3tXQxEIAjHzsLdG8jbHyJe+4VN/idOCFTOzaTJZqC61kVQcVoO9qU2ikZXVxcej4f5+XlWV58mbe0dldUaFVXahiOaYgQ9Ls62hJBYDUNaZhURGUIKD8ng4T2PL4TYiCJufbBJ1tipBWJq3Ko/OFHYB3g/F21d7nSoOc6OHs69hND2PrlTwYOYmh93ataRNFNNTQ3hcJhUKpWnLquE270hg+9EmkkIwcudBZG0zObNgRIqNkmwaQ4APHlilWUdq8Hloq3WDmdSrPsLRJFwu915fXz7R1cJIUT+R54ecybEfqXLmhzvj65tFOaKkTUuEuJcbnLc/ICxsTGSySR1dXXU1tYqGb8QkfUsaysmbg80NDuTXvpo0sqMvuzAArE5vaSoT1S4C9JMpbmcFYtDh6xalRNzACw2E8DUmHoTJNhIM304vo4rOoRmRsl46sl61djfitOXwOWCx/dYnZpkdnYWj8fjiEBlNiOZySkwtOwvEJ8+7MnheFf1ZBrTAX38F9or8GiC+3NxXGs59pKinRNgsXDqwrC8wMCtmwCOUCIBpnI7p+ZWDy6H00uFrC9lGB+2BN4qq6Fv7+kNG8mKk4BzdQh7J2ynmVSjKZdmWl600kyq0Vvno7nCw3IiS2LR8t5IVpwqWqByN4hQBRw5BabJkw/eBaz0ksej/hoqTC+pZn3Z2F8gSoCdZpqbm3MuzVTpcJqpNUTYEyWYGrVcs4qUNS4GQtMQ5y+TFYLBqSnAwdA6t8Ns7fy8ppds9pKa9JINO83kSc3gSs0rG9dGbW2ts2kmz0aayU4hqoQQgsudlbiESW3SYi8lKtSWPe2IcGDS4TngcHoJ9heIklCYZnIiihBC0NrpLJPjcmclb9TnaIq1J5GaWtkEcfFVxivqSEnLU6OurszGox0QWcuytmqll8JNn/P00gXFMmTCnfcy+LymmZyeA690VXG+apqgliDjaSDrVSufIs69xJo/xJzw4HG76e7uVjo+WPa6sw6nl2B/gSgZ9m7geYj3OZVm+nL9CABroTPKx6f7EAONVr71UJ0zlor59FKb0+klvzPppckRq6mwogr6FKb4cvi8p5kaC9JMsaj6NNOBWh9fb7K8G8Y4oiy9ZEOEKhk4aDWLdof8jrCX5mcyZBxOL8H+AlEy7DTT7Ozs5zLNVMEaJyrmiWfd/HRevapkNptlOGRFDQcXdjZQKRd26qG1w+n0UomqnkVC3shFD2df3CRLogqp4CFMzYcnNf35TDO5C5vmHEgzYfJKjRVF/2heffEYYDA/B3YTiigPG3PAuegB9heIkuHxeJxnM3U6x2ayd5Xvr7TzkydryscfGxsjJSEcX6P6zodIU2135/palvVceqnBgfRSPP0c0ks3rOKluPiq8vGtgQvZTHcdeQvH00x5NpP6OeCNDeAXSYZi1fxgxJtvmlOF1dVV5mIJPNkMnf23kStLSsfPZiSzk86nl2B/gSgLNjPHVilVDXtnPD1paTOphD93w3hnuZu7U2ssxtROwDzvOxOD1WV48lDp+NMF6SUnmuOuT6w7y14aGbCa46pr4bD69JKNZIWV4vCv3wUHrDztBWJwcNCxNJMr1zSnOs1kb5JuRA+ylsxybzamdHx7DnS7JG4zmyckqMLsdPq5pJdgf4EoC7av8sLCAktLancHAJXVljZTOiWZm1E3+VzpRTzJSUzhJRk8jGQjnaICmUwm7zp26JCVp5YfvadsfCklk2POppeujFpR1Re6HWIv2dHDhVeUspeehsVmCuJOz+FKbW1isxfU1NTktZlsvS2VKEwzKe2JkJl897TdHPfeqNpI2t442ouo/OiK0vHtqKqty9noAfYXiLLgdrvzujRORRFtOfqmyslh75xSoaO81GXlSN8dUTc5RkZGSKfTNDY2UvOipRAvb76PzKpJM62tmJb2klc40hy3nsxye9qS9n7FgfqDNE3kDWvBdCy9ZEO48j0u/vVt/bb2BDuSfvz4sSPj26nWSYVpJm/sSU57qZnjHVaq+MPxddKKIvXFxUUWFhbw+Xx0f+F1SwJ84CFySY0HRDq9wV5yapNUiP0FokwUppmkAyF8W+eGT28mo2Z837qVXkpUnOJCWwUBj4sniwmm1tQsQvaNoq+vDzp6oLkN1lfhoZob1Eb04FGuVQWWBEnGhJNNQWoCDkh7DzyAlUVLs6pn7/ImuyFRmUszRZxNM42MjJBMJnc5unQ0tnhwe2BtJatMqdS//jFgfTedNT66anysp0xuT0d2eWVxsDeMvb29uEOVcPI8oC6SnplIY5pQ3+BSrlW1FfYXiDLR3t5OIBBgZWWF+Xn1TJFghYvaehfZLPmC1F7gSs7iSU1jan5SoT58bo0vHrRMTa4oCLGTyWQ+1dDX12dpM72QiyKuvbPn8QvTS21dDqWXRuz0kkPspeu59NILrzqm31+ItL+brKsKV2YZIkO7v6BEVFZW0traSjabzacWVcLlErTmaN+TCiJpYSbz0t6JXI3G/q1VRNJSyvwCcfiwtQHQcpGi/dvvFZMON4g+jf0FokxompbfQTmdZlIxOfwRa+eUrDiZd477Sp8lb/zOyNqeo6DBwUGy2Szt7e155zhx6QsAyNsfIve4w1xayJKISfxBQZ0DznFL8Qz3ZmO4NeGMtHcms9E9ffELysffEkLL90SIxRuOvIV9I3QqzWTn2SdH03u+Rr3RBwiZJuXvxvRY+mBf6LIWiGsTEWLpvUUpNvU9FAptOMedugj+AIwOIGf2RnlNJkwWZjMI4Ty91YayOFrX9TrgD4GvAgvA7xqG8SfbHPuPgf8BKLxrnLINhHRdP5Mb6yjwEPjbhmF8rOpcVaGvr4+7d+/y5MkTLl++rHxX2Nrp4ZOP48zNZEglTby+MtdzaRaE1hvNcRc6qqn2uZhcSzG8nKSnrnyrR/sGYd8wAERjq6XPNNyPvHt9T3n3ydFc9NDpdWT3/f7oGhI43xqiwutA8fjRXYisQUsHtHerH38bJCpPE1x9HxY/gtAbINTuCQ8ePMg777zD+Pg4sViMYDCodPz6Bjc+vyAWNVlZylJbX/4ty54DycoNx8PGCg/HGgI8mI9zbTzC6z3l+5YUFqe1nPmT8PoQ519Gvv8m8to7iG98u+zxpyfSSGn5d5d9LygRKt/l94EU0AR8G/gDXdd3UiH794ZhVBT82YuDF/g+8MdALfBHwPdzj3+m0NLSQkVFBevr60zltIdUwufXCDe6kebe5I89iVFcmRWy7mrS/u78426XxuWcwus7ewixo9Eo4+PjaJr2jGuWuLT3NJNpyvznb3MotLZTDK92OZReuvY2YBWnn0d6yUbG107GU4dIr+KJq08DBQIBOjs7kVI6Iz+jiY1IerT8SFpkI3hjA0g0ErmoyoaKNJNpmvkF4mmBSnHpNcCaA3uJgvIp1ueUXgJFC0TOl/pbwO8ZhhExDOM94AfAr5cx3GtYkc2/NAwjaRjGv8LypH5DxbmqhBAiv2N+9OiRI+/RpoDJkY8eKk4/s4O0J8eVkTXMMi9ee2J0d3fj92+OQsTFV6z3/OQmMlLeBJyfzZBKSiqqNKpq1O+cptdT9C8m8LsFL7SrtxaViXjeilW8+Jry8XeEECQrrKjRv37bkbdwms1kz4Gp8fLlZ/yRewhMUsFDSFdo03OXu6pwCfh4JspKojxa+eTkJLFYjOrqapqantJ2OnzC8hyfn4Gh8r6jWNRkaT6L5rJ6gJ4XVM22PiBrGEZhMv4OsFME8XVd15d0Xb+v6/pvFTx+HLhrGEbhlXB3l7E+NRw5cgSwmmOcaBhqafeiuWBxLlNew5DM5OmtheklG0fCARpDbhbjGe7PldcwtFV6yYaoqoWjpyFbfsOQ0+mlt4ctyZSXOirxudUvQPL2h5BKwsGjiAY1vgOlIFF5FsiJ95nqpSt6enpwu91MT0874tleXeciVKGRTJQvP+PLUX23mgNVPhfnWkOYEt4fLa8vqJDB9/Q1KjQX4oVcPS4XSZaKidwcaGnz4PY8vwhUVQ2iAnhamGgVy2N6KxjAd4FZ4BLwZ7qurxiG8aeljqXr+neA7wAYhkE4HC7rA7jd7rJeGw6HaW1tZWpqioWFBU6cUN8d23Ugy/BAhOV5N51dJaqjLn2MZsaRgTZq2zaH1m63m4aGBn7uaJTvfTTBh1MpXj9emjbNwsICc3Nz+Hw+Lly4sKXuffzLX2PtwW3ct96n7lu/VtL46ZTJ7KR1OZw800Rl9d53T4W/tZSSd0ct57tvnukkHFYvMLh88z1SQOWXv06wzOtzbwjDci/a+iBhbQzCLyp/h+PHj3Pnzh3Gx8cdkbc+dFTj4xvLLExrHDtR/HfodrsJV0i0xChS81LZ+QqVrmdrbV87Kbkx+Zj3J2L85uVDJZ1bKpXKp9deeumlLe8j6Z/7Bkt//Z/g5gfU//Y/QpQg4CelZHrc0jU7dipMOBza8fhy72VbjlXMQbquvw18cZun3wf+LvB08rYK2HI5NgzjQcE/P9B1/X8H/ibwp0CkxLG+i7XYAMiFhfIaUsLhMOW+9uDBg0xNTXH9+nWam9XvEBtaJMMD8PjBCq1d2ZJ20VUz7+IHosGTxJ76fPZnfrHFw/eAN/vn+fWT1fhL2EVfvWqlTnp6erYVL5QHj4PXS/rBHeYfflLSLnpsKEkmI6lrcJFMr5JU0G9U+Fvfn4sxtZakPuimw58u+xrYDnJ5EfPuR+B2Ez1y5pnf4HkhXP8i2vog6cl3WUX9DfzAgQPcuXOHmzdvcuLECeWRXl2jxTAaGVyn74RW9C46HA4TG3uTCiAZPMracgTrFrMZR6olfrfg/sw6d4emaK0qPs//6NEjUqlUfu5vdQ3Jyjpo6UBOj7Nw5aeIk8X72i8vZlhbSePzC7yBGAsL8R2PL/Ve1trauu1zRd0JDMN4zTAMsc3fK0A/4NZ1vXDpPQ3cL/IcJVadgdxrTum6XngFnCphrOcOO6wcGxsjFlOr6wKWpabPL4iuW0yOYiGycXzRh0hEnve9FdqrfPTV+4lnTD4cLz7ENk2Thw8tXvnRo9sbD4lAEHH2JQDk1beKHh9gYsQKrTu6nSnMvTVkLWqvdVfhcqD5Tl5/x2pSO/WC5Tb2aaH+AhIX3vgAWka9SGN7ezuhUIi1tTWmp6eVjx+qcFEXtvqCSjISkiaBtVsAxKu2vyn73Rov57rnfzZUmkpzUXNAiA3CRplzoK3L60iD6E5QknA1DCMK/DnwT3RdD+m6fhn4BvC9rY7Xdf0buq7X6roudF1/Afh7WMwlgLeBLPD3dF336br+O7nHf6biXJ1AMBikq6trE5NBJbQCJod9sRQDX+QuQmZIB3owPTunTt7I0ftKmRwTExNEIhGqqqo2eN/bQLz8JQDk1Z8hzeJqKbFIlsVcYa7FAVmBZMbMa1Hthd64E+ybgfbSa46MXzQ8FSRDRxBIfOvqGeOapuXrcfYNUzU6DpQ+B1gfwJVZthh8gZ4dD/2SPQeGV4tWeF1fX88z+Oy+qO0gXnwdhLD6gqLFdW5nszJPUHFqk7QTVFbkfhsIAHNYqaLfMgzjPoCu66/qul74jfwqMICVNvo3wD83DOOPAAzDSAHfBH4DWAH+FvDN3OOfWdiTwyk2U3u33TSXJlukbkxg7SMA4lXndz321a4q3Jrg7kyM+WhxjKnCndOuKYUjJy2/6oVZePJg52NzmBjNSRq3e/A4UJi7PhEhljY5VO+no1qtsx6AHB+GyVGoqIQTu/8GTsMuVjvFZnKcsNGRI2zMZ4lFioukxbxFjEhUnt21B+RYY4DmCg+LsUzRCq92cbqnp+cZBt8z51LfYPlVZ9J50cbdMDedJp2SVNVoVNU4q9y6FZQ1yhmGsYR1Y9/quStYxWf73//lLmPdBj79GVUCenp68Hq9zM3Nsbi4SH19vdLxq2tdVFVrrK2azE2n885z28GVmsWTnMDUfCRDuxPAKnwuLrVX8P7YOu8Mr/E3T+x8/slkksHBQWDjxrAThOZCvPgG8j8byA/eROwidS2lZNzp9FKOvfT6AYeihw+soFdceBXhfn7UxO2QCh3G1AJ4UjO4k1NkfNvnnstBfX09jY2NzM3NMTQ09Ew/wF7h8Qha2j1MjqYZH0lz+MTON0xhJq0GQSBReW7X8TUheL2nmj+9u8CbQ6ucadm5GCylLCq9tOmcLn8Z+fAO8v034bVf3PX4iRFrk9T+KUQPsC+1oQxutzs/IR48KG6HXCrsi2S8iBDbv3YTyPkCaMVdXG8UhNi7NfTYu8S2tjaqq4u7wYrLViuLvPk+MrFzoW1pIUssYuIPCMKN6oXzluMZbk9HcQl4tcsBaY10GvmhlV6y02ufOoR7Q8AvF12qhn2jdCzN1L2RZtrtGvVF7iPMJCl/F1lvQ1Hjv37AqkN8OL5ONLVzlDI7O8vy8nK+WbAYiLMvQiAEI0+Qk6M7HptMmMxOp0E83+a4QuwvEApx/Li1U3/48CFZRRLXhWjr8iIEzE1lSMR3yOPLbD6NUEx6ycbZlhA1fkt6o38xseOx9g3g2LFjRY8vGlvh4DFIJnbtibDzzO3dXoQDhbk3h1YxJVxsr6DK74By651rlrRG+wHoVs8aKheJqotALs1kqndr6+vrQ9M0xsbGWF9X5zViI9zoxh8Q+caxneBft4rTxUQPNpoqvJxsCpLKyl29Uuw5cPjwYVxFWscKrw/xQk7A7/2f7njsxEgKaUJjsxt/4NO5Ve8vEArR2NhIOBwmkUg4om7pD2g0tXqQEsaHt48ivLF+XNkIGU8DGV9H0eO7NMFruXTLTwa2b3haWVlhenoaj8fzjLTGbhAv56KID97c9phMekO51YnQ2pQy//m+2qu+7wHAvPITAMSrX3mu0hq7IeNrJe1rQzMTeeMclQgEAvT29iKldCSSFprIXxNjw9sLQGrpZbzxQaTwkKw4VdJ72MXqnw5uT9hIp9P5+kMpmySw0kwA8sO3kdvUaqSUjA5Zc6CrV319rFjsLxAKIYTIRxH37zvDyu3syU2Ooe1DbDu9lKg6DyXenL7Sa02OK6Nr26pb2p/t4MGDeL2l3cDFhVfA64X+T5CzW+tXTY6lyGagrsFFZZX6wtztiVVmImkagu5d88zlQC7MwsOPwe3J6/B8lhDPRRGBNWcUXu058ODBA8wiGWuloDPHZpoaT5NKbT1+/rPVnUVu0Ri3E17qrMTv1ni8EGd8detF6MmTJ/neh5Kb0roPWaKN66twb+tU39JClui6ic8vaGxxIMItEvsLhGLY4ebY2Bhra+r55o3NbvxBK8TeSnZAy6xv9D7kWCuloL3ax4nGAImM3FK8LJvN5neG5XSNi0Awr+oq3/3xlseMDuZ2Tj3O7Jy+/4llwfnl3hpneh/efxOkRJx/+dPtfdgGycrTSOHBGx/ClVLfuNfR0UFVVRXr6+uMjY0pHz9U6SLc5MbMwuTIFmkymc3XWGTTdv2928Pv1vhiTqPsx0+2jqQ/+eQToMw5IATiFSuKMN/7yZbHjA1aC1PHgeff+1CI/QVCMfx+f15qwKkQu/OAdeMcG3w2zeRf+8gSJQsdxXSXp0z61YNW2uXHT1aeiVIGBweJx+OEw+Gyu8bFF38BAPnBT5HpzRN8ZSnD6nIWj1fQ4oDm/Voiw7uDi2gCvtSrnr0kzWw+tyxe/ary8VVAan4SubSLE8Xq5xFJd/VaUcToUPKZa9QXfYgru07G0wiVpclm2Pj5Q9Yc+NnwKsnM5ihlYWGBmZkZvF7vrr0P20G8+Dq43HDvJnJxs+FYKmUylVMvtjMGnxb2FwgHYOckHQuxe7wgLDvSZLJgfGkSWLsOQLz6Utnjv9RZSaXPxdBykoGlzcXqe/cs4b89ySl0H4KOAxBZR97aXKy2o4f2bi8ul/qd01vDa6SzkrMtIRpCDlBP738MywvQ2AJ96nW5VCGR6yr2r98CqZ5QcezYMYQQDA0NEY1GlY/f3OrB6xOsr5osL24+f/+qPQculpxitdFT5+dQvZ9oynymWG1HD4cPH95Se6wYiKoaxPmXQZrPRNKTo2nMLISb3IQqnn/vQyH2FwgH0N7eTnV1NZFIhNHRnals5SAQ1GhsdmOam7tKvbHHuDIrZDx1pALlM2e8Lo03cnS/vy4oVi8tLTE5OYnH49lSubVYCCE2ooh3/yr/eGFx2t4hqoSUMv957ChJNczc5xGXv/yZKk4/jbS/i4ynEVd2HW9UfXNnKBTiwIEDjhWrNZfI1yJGBzfqBK70Ir74E6Rwl8Re2gp2FPFXT5bzj6XT6Xwz7F6FOfNz4L2/RmasiEFKmU8vfdrRA+wvEI5ACJG/eO7evevIe9gXz+jgRrE6sHoNgETVpT07h9k30HdHNorV9s6pr68Pn29v9QFx6QvgC0D/feSUlad2ujj9YC7OxFqK+qCHC20O+D4szMKdG+By53PMn1kIYe2wgeDqVUfewp4D9+/f37Nd6Fbo7H22WO1ftYrTiYqTSNfe3O1e7aoi5NF4vJBgKBdJDwwMkEqlaGpqoqGhuN6KbXHoGLR2wtoK8rY1d5cXs6ytmni84rn6PmyH/QXCIRw7dgyXy8Xo6CjLy8u7v6BENLV68AcsAb/52QxaeglvrB8p3CX1PmyHwmL1O8NrZDIZZTsnAOEPboiXvftjpJSMDDhbnP5hv/U7fO1EM24nitNv/wikibhw2fLB+IwjUXk+V6wexJWcVT5+Z2cnlZWVrK2tMTIyonz8UMVGsXpiJA0yQ2DdlpcpP8Vqw+fWeC1Hef1xLvK0N3xK5oAQiNdyUcQ7PwJg5IkVPXT1OpNiLRX7C4RDCAQC+TSMnbdXCZXFOi0AACAASURBVE0TdB+0bqTD/UkCq9cRSJIVJ55xzCoXP3fIusn98PEy/f39JBIJGhsbn3XMKhPiiz8HWAJ+i1Nx1layeH2WnIJqzEfTfDi+jkvA3zipXpJdppLIHCNFvPE15eM7AekKEM+lYQIORBGapnHqlFUM//hjZyzl7VTkyJMkvvVP0LJRMt4mMv7iOpt3w8/nIum3h9cYGZ9kdnYWn8+nTEZEvPg6+Pzw+B7xkQmmxtMI8en2PhRif4FwEKdPW7IGDx48IJVSrzXY2etF02BxJoF/Vd3OycbLnZXUB9xMrCa5+pHVlXry5MldXlU8RGcv9ByGWJThG5ZEdFevF5db/c7pR/3LmNKyl2yocECY7/q7EF2H7kOInvLrM88b8WpLhj2wfguR3Vn+pBwcP34ct9vN+Pg4i4uLysdvbvMQCAqikSyehfcAiFW/VHZx+ml01vg43hggkTF586o1x06cOFF2cfppiMBGJD3y4ShSWp8pGPps3Jo/G2fxKUOYCUguKR+3oaGB1tZWUqmUIyqvPp9GW5eX3rr7uGSUtLeFtL80R7id4NYEv3i4lprMMtGVpU1RkSqIL3+DmD/MTKIWIchHRSqRzJj54vTXDqtP/UgpkT/7IQDi9V9SPr6TyPqaSAV6ETKNf/2m8vH9fn9en8mJepymCQ4c8tEYmiRoTmJqgbL6f3bC14/U4csmiMyMIYTIR0WqIF77RbLCzVjaUj040PfZiB5gf4HAG31M/cg/R4z+e0fGty+mO3fuOFKoO3DQy4kmqzC3XvmKsp2Tja8erKE7YTGxuvuO4S7BKrEYiHMvMXrol0FotFauOaI5887IGuspS9b7cDigfHwGHsL4MFRWIy6+on58hxGzo4jVqyDV07LtOfDw4UMSiZ01vspBZ4+Xk83WHFjxvVC0OGWxeKGtgsPmJAJJTWsXlZVqxR1FxwGmz/5NUt4qqrR16sKfLrW1EP+/XyAyvhaEmYal27hS87u/oET09vYSCoVYXl5mfHxc+fgNvkFqA4tEUxU8mVef2jDj69Sn5smiMeDe2RSoHGRNjfHmywB0Pfn+LkeXDiklP3ycK047ED0AyDf/ArAa44Tn06cmlopU6ChZdw3u9BLe2GPl49fX19PR0UEmk3Gkcc4nVuiqfkLW1Lg3pTZ6AKv5sSk+AcATV/HaZkWPLyWjrZZGWdfgDyGr3kujXCjZDuq6Xgf8IfBVYAH4XcMw/mSbY38EvFrwkBd4bBjGydzzI0ATlqscwAeGYTjWkmq6q0hUnSOwdoPgyhXWG39F6fgul4tTp05x9epVbt68WbQscLEIrlh51wdz5xmKZuk+KJWqn9rFxVlfC0PjSX4tmaXSp26HMz6SIiM91K4OUHPvJ8ixX0J07uz8VQruzcYYXUlS63dxubO8zvKdIGenkLeuWtTWHK/9cwehEat+icrFHxFcvkIqVJy3QSk4c+YM4+Pj3L17l7Nnz6Jp6vamwZUPEEIyvHSMoTEfPSdNfH514z969AgznSTiqeZOxE//Qpw+hZHo0kKW1YQfTyZK6/BPkR8dsYrXnwGo+hZ/H0hh3di/DfyBrutbutQYhvELhmFU2H/AB8D/89RhXy84xnG9gljNq0gE/rVbjvj1njp1Co/Hw/j4OLOz6uiE7uQ03vgApvAyGjtLLLLRoq8CiUQi3+QU6jhCMivzdD8VkKZkuN+i9R2otqI3+VO1UcR/uG8VRn+xrxaPA7RB+eM/t6itL76GqCtRtO0zhET1C5iaH29iGHdcfXNnd3c3NTU1rK+vK7XlFWYiLxcyZV7CNDe68VVASsnt25Z0fkPPURCCHzxSW68ceGil3bpqV3CZaeSP/5Mj6ehysOcFQtf1EPAt4PcMw4gYhvEe8APg14t4bTdWNLGld/XzQtbbALVnEGQJrOzsU1AOfD5fPg/70UfqtG8CK1cASzahs8+i4w08SCi7uO7du0cmk6Gjo4Ovne0G4AePlp7RpikXU+NpohGTYEij+TXLElJev4JcVsN26V+Ic2cmRsCt8Yt9DhSnVxaRV38GQiB+Xm3k+bwhNX+e0RRaflv5+EIIzp+3+nM++ugjZdeof/U6mkyS8h8g3NMNwFB/kkxazfiDg4MsLy9TWVnJL798CpeA98fWmYuo2YitLGWYm87gckPPFw5BVQ1MDMPDO0rG3ytUpJj6gKxhGIXbgjtAMTKKvwFcMQxj+KnH/62u6xpwG/iHhmFs+23puv4d4DsAhmGULr2bgxb6JeTybYLr1wkc/Ba41RYz33jjDe7cucPQ0BBSyr13YSYXEYN3rcjnwNc46wkz8HCEtdUsiWiQju7deyHcbve231cymeTOHetrf/311+nt7eTf31/m4WyE96bT/Bdn91aPkFJy5SdWTebMxXqajvew8tJrJD/4Gb53/pKqv/MP9jQ+wP961Yp+vnWmle62jd6NnT53KVj/4b8jlsnge+k1ak6c2fN4TqKoz1z9deTt9/HFHhEOJiDYrvQcLl++zEcffcTS0hLz8/Ml+yg8g2wSMWqlWN1dX+dwTTODjyaZm0kwP+3m5LnaPf3WUkoMwwDgi1/8IscPtPOlvih//Xie/zwU5b99Y+9GUPc+sujdR47X0NYdJvI1neiffBf3Wz+k9gvldeOrur5BzQJRATztrLEKFFPq/w3gnz712LeBW4AA/j7wY13XjxiGsWVuwzCM7wLfzf1TLiyUJ18cDneR8R/AmxgmOvwjYrVfKGucnXDkyBE++eQT3nzzTb785b1JMVTO/UcCMkui4jRrEQEscqDPw4OPs9z8cA5/qGJXLaBwOMx239fNmzeJxWI0NzdTXV3N4uIif+NINQ9nI3zvxjivtnrwusoPQKcnUqwspfAHBLXhFAsLC8ivfBM++BnxH3+f5Gu/hKgp39d7ZDnBlaElvC7BVzr9mz7nTp+7WMhoBPOv/iMA6Te+vufxnEaxn7mi8jzB1aukhv4Ta82/qvw8zpw5wzvvvMObb75JQ0PDnvSqAivvUZleJ+1rYznTDIuLHOhzMTcDd28t0dCaobm5oezfZnh4mJmZGUKhEJ2dnSwsLPDLhyr4yeN5/uL+DL/UuzfBx/W1LCODUTQNWrtMaw5c/AL82fdIfXyd+WvvIXp393t/GqVe362t23uT7zrDdV1/W9d1uc3fe0AEeLr6VwXs6Nen6/orQDPwHwofNwzjfcMw4oZhxAzD+GfACpuL2o7BXhQCK1fAVN/Ydu7cOYQQPHr0aE92jFp6Gf/aTSSCaN0b+ce7en14vILlxSyLW3hFFIt0Os2tW1Zj3KVLl/KT+IW2Cg7U+liOZ3hzB7et3SClpP++VXs4eNSPlqsNiPZuOPcSZNLIv/rzsscH+LMHVp74K73V1ATUG67It/4SknE4ehrRXZ7k82cRsZovINHwRe6ipdX3Bh0/fpxgMMj8/PzehCzNNMHldwGI1n0pT+9uaHZTXesildwQvSsHUkquX7dUYc+dO5end3dU+3ilq5KMCX92f2+p0MGHG54PNr1bVFQhvmR14ps/2JLn81yx6wJhGMZrhmGIbf5eAfoBt67rhbPkNLAbn+03gT83DCOyy3ESK5pwHKngYdK+NlzZiCMCZjU1NRw6dAjTNPdUiwgtv4UgS7LiNNn/t70zj47iOhP971bvrW6tLQkJJEAYkMUmDAYMxjYG4iRO7MTLjTNZ7JnMm0zyMu8kJ5k9eeMkzuxLcrJOZjxOMnE8U57YxM+OHcfYYMCYHQuJVQjtEtrVanWrt6r3R0kyS0vqllrIoPqd0+eou7pv36uuqm+932cvGH3dahWUDW+yOXdy8hfHiRMnCIVCFBYWXpZ1JYTg4eWGVv/Lmm6i8cn5eTvaYvj74jic71bkHEH5kKG16m/+Br1vcjeotoEIexv8RlmNislbIWOhBwPovzWC6coHHkr7+DOJZstmyFuJQCej9420j2+1Wlm92khFnco14PIfwhIfIOooJuJ+V8sWQrBkmdFBrvZ0mNgk42UjCSVOp/OquktyhQ8B/PZ8P52Dk4tFBAfjNDdEQMCi8ss3xon3fQScLjh5HP3s9PTTSJYpB6lVVR0EngO+IaXMkFJuAu5nnMCzlNIFPAz85IrXS6WUm6SUdimlU0r5x4AP2DfVeSaFEAzmGUlT7t7d01J6YN26dQghqK6upq8v9YwgJdqT0HoYYeFiO1YbdHXE6LqY+skbjUY5csTYUXup9TDCbSVeSrLsdAZjvHEhdSvCsB6MrI1F5Y6rymqIkoWwegNEI+i/eT7l8QF+8U4Xmg53Lcyalp4P+ivPQTBg9HsoT++u2vcCwZwt6Cg4/UewRDrSPv6KFStwOBy0trZOzorQorh7dwMwmHP3VZtDC4utZGZbCA/pnDuVuqV+qfWwevXqq8pqlGY52DTfS0zTJ21FnDkxhK7D3FLbVT0fRIYXse1+YOatiHSluX4ecAEdwDPA51RVrQGQUm6WUl5pJXwEI05xpYriBX4I9AItwPuBD6iqmv4iLmMQcS0m4ipD0UK4h7OE0klubi4333wzuq6zf3/qVophPWgMeSuN7KsrsNkVFi01NKiT76Se0TRiPRQUFDB//tVlOxQhkMuNANh/VXWlnNHU3hKlr8coyjdWQbJ3rYiXU7YiaruHeLPBj00RPLIi/Wmnel8P+s4XjHk+8On3dM+HyRK3+whl3opAx9OduC3sVLDb7aMZTfv27Uv5HDWsBz9RexGRjKsD3YYVYZxb7xzuSTmj6cKFC7S2tuJ0Oscsq/Gx5ZO3Ivp74zQ3RBEKlC9P3C9bbL8PXBlw5gT6mfQX+0yWtDhnVVXtwbjpJzq2ByOQfelrz2AIkivfWwPMrEomBIHc95Hb8iNcffsIZm1Et6a3d8D69es5c+YM586dY82aNRQUFEz8IcAS6cTpP4qOQjDnauthhLKlDuprw/T3xmltijK3NLndvaFQiEOHjJIFGzZsGPPmd/t8L8+fdFDXG+ZXp3qQSd6ItbjOqXcM62HpcifWMYryidIyqNwAx99G/9XTiEf/KKnxdV3np8cMjffepTkUeKbBenjxvyASgdUbJhVAvF4I5t6Na+AojsGTWEMNxFzpq/EFRrC6qqqKrq4uTp8+PVqvaSJEPERGj9HSdTB325ilZebMtZGda6GvJ875M0MsXZ5cVmI8HmffPsNhsW7dujH7npRmG1bE3oYBnn6nky9uHDvQeyWnqgzPxIJFdtxjdIwTbg9i+/3oL/wCbcfTKH/yNzOijMz6UhuJiLnmE3aXo+iRafHDer3e0UqvIydjMni6XjKsh8w1xO1j35StVsHSYc3kdNUQ8SRjBQcOHCAcDlNSUpLQehhBEYLfvcUQar882U1vKLmAeP35CIMBDY9XmbBblvLgo2CxoO97Db3xfFLjH2sbpOpiEI9d4eFl0xB7uNiKvudVEArKRyfc5nNdo1kzCWYbJVA83a9AmjduWa1WbrvN2Hexf/9+YrHkzqGMnp0oWoiIq2zcHd9CCJZVGkKh9nSYUDA5S7empobe3l6ysrImrFz8qVX5WBXBGxf8nO1Kzh3ddTFKZ3sMqw0WL0tsPYyuYeuHweOF2pNw5Np42a/EFBBjMJj3PnQErv4D0+KHXbt2LQ6Hg6amJhobGyd8v33wNI7gGTTFQSB34s3lJQvteDIVgoNaUjtLu7u7OXHiBEII7rjjjgm1lZVzMrh1roehmM4zVROn1EUi2mjsoaLShTJBORAxZy5iy4dA19H++8kJ3RBxTecnx4zd2A8ty8OTxnIgI+g7fg6ahth4N6Io/TV53msEs+9EU1zYh+qxB9NfjXjp0qX4fD4CgcDonpvxsEQ6cfXvR0cQ8N07YWHK3HwrCxZloMUNn/9EhMNhDhwwOrtt2rQJi2X8c2iO18595cYGzH8/0jHhOarrOieHLeibyp04HOPffoU7A/ERQxHRnv0P9PDkE08miykgxiDmKGIocy2CON7OF9KuQTmdzlE/7O7du8fXoPQYni6jnPRgztakXF6KIrh5paFBna0ZIhIeX4Pau3cvuq6zfPly8vKS074fW52PIuC35/to6Bv/5D13Mkw0opNXYKWgKDnPpvjQxwwN6mw1HBs/XrOzrp+GvjD5biv3TkdJ75PH0A/vBZsd8eGPp3389yK6xclgjlETyNP1EmjpK+MCRkOhTZsMK+XQoUMEg8Fx3+/pfnk4/raGmCM5l86a23wIxaj51d87vpVy5MgRQqEQRUVFLFq0KKnxH16eR7bTwpmuEHsaxg+IN9dH6e81sveSLektNm+HkoXQ04X+yi+T+kw6MQXEOATy7kFT3NhD53EE0r/1vbKykpycHHp7e0f3HSTC3fcW1mg3MVs+oezbkh6/sNhKXoGVaETn5PGxNaj6+noaGhqw2+2sX598w6F5WQ7evzgbTYd/P3xxTA1qoD/OheFWihWrnEn7UkWGB3H/JwDQnn0KPZrYEuoNxUZjD59eXTClDXyJ0CNhtKd/ZMzpw48g8qa4C/46IpR9GzF7IdZo97S4W+fPn09paSmRSIQ9e8ZOCrEFa3EMnkITdgbztic9fmaWjYXDPUaqj4XGPEd7e3tHay5t3rw56XPUbbPwyVXG+fDTYx1jJm2EhzRqjhtuqJtXusaMv12JUCwoH/8sYNT90rvS3xp2PEwBMQ66JYOAz6jQ6el6CRFPby17q9XKli2Ghnbo0KGEvauVmB93z+sAw2Z18nkFQghWrnWhDGtQne1Xa4CRSIRdu3YBRlDO7U6t0fvHV/jIdFiouhjk1dqr0151Tef4wSC6ZtTtz85NLS9CbL7HaOzedRH9xcQ9O/7t8EUCEY1bijLYPD+9tfoB9F8/Cx1tUFyK2J4wF+PGRVgZyDfW7O59E0sk/Teou+66C6vVypkzZxL3rtYieDuNlOdgzl1o1tSq8i5e5sDhFPR0xmmovVrJ0DSN1157jXg8TkVFBXPmpNaS9u6yLMpyHHQFY2O6W2uOh4hGdHyFVuYtSC15QiyuQKy7E6IRNPXJlD47VUwBMQFD3luIOOdjiQfI6Hk17ePPmzePiooK4vE4b7zxxuUajq7j7fgfFD1M2H0zkYzU+z14vJbRjUNVh0PEYpdrUHv37sXv95Ofnz8aOE+FTKeV/7XWqHP01NGOq1L+6s6G6euJ43QJKlalXt9KWCwon/o8CIH+8i/R6y7vV3CweYB9jQM4LII/XFeY9kwPva1pdFe38qnPI9LcMOl6IOpaQChzneFu7Xg+7U2FsrOz2bBhAwCvv/76Ve15Pd2vYI32ELXPIZiTelEFu11hxRrj3DtZFSIYiF92vKqqira2NtxuN7ffnnrDJ4si+MN1c1AE7DjVw6nOy11lHW1RWhqiKBZYucY1qXNUPPSY0bv62NtoB9+87FjfUIzuYHrdfyOYAmIihMJA/v3oKLj638YWrE37V2zatAmn00lzczOnTp0afd3lfxtH8Bya4mKgYPKa66JyB5lZRsD6TPW7VlBtbS3V1dUoisL27dsnDMqNxeb5XtbP8xCKaXz/QPuokAsMxDk9/H0r17qx2Sd38xY3VRiau66hPfVt9IjhrgpG4/zokKHRfrIyn0JPepv16Foc7Wffh3jMaAZ00xSLy13HBPLeT9ziwT7UgNN/KO3jV1ZWUlBQQCAQ4K233q2obAvW4e7fj47CQOHDKVnQl1I0z05xiY14DN459K6rqb+/f/T7tmzZgtM5fmbRWCz1uXigIg8d+PZbbQwNu5piMZ2qI4ZraekyJxneyV1jIicP8fDvAaA//UP0HiMhI67p/NO+Vr746/qrBFM6MAVEEsQdRQRztiDQybyoImKTr6OUCJfLxebNhma0a9cuuru7sUQ68XS9DMBAwUdTNqsvRVEEq251gzA0+q6OGOFwmB07dgDGvoypVH8UwtCgPHaFY22D7KzrR9d03jkURIvDvAU2CountidBfOQTUFQC7S3oO36Oruv866GLdAdjLM5zcu90lPN+4RkjxTArB/Hgo2kf/3pCt7gI+D4MgLfrJSzh9rSOrygKW7duRVEUqqqqaGxsRGhhMjuMUm2DuVuSDkyPxfJbXNgdgq6OGA3nI2iaxs6dO4nFYixevDjpwPRYPLIij/nZDtoDUX56zMhqqj4aIjSokZmtULZ0ar2mxR33wMpbITiI9tR30DWNZ6u7qWoPIoCCaagaYHn88cfTPugM8vhki+C53e5xsyiirgXYQhewRS9iDbcT9q5Ka/9nn89Hf38/nZ2dtLY0cXveUazxPkLe1QQTlNRIFadbQYvr9HTGudga4XzDHtrb2ygsLGTbtm1Tds24bAo5LisHmgO80zZISdBBd6uRsbHu9oyrSmqkirBYEAuWoO97DerO8ErWcn7ZGMNhEXztrhJyUijIN9FvDaBXH0H/zx8Yex7+918iitPbCfBak8yaJyLuKESJ9mELN2MP1TKUecukNfpEZGRkoGkaLS0t1NdfYNOcWlyRRqL2IgYKJYjU9dlL1221CtxuhbbmKF0dMVovHqG29gxOp5P77rvvqpIaqWJRBEt9Ll4738fZ7iHmRh101MVQLLBusweXe2r6uBACcfNK9P1vQGsjVdZ8vtdoQwB/fuc8ynKdV605GYZ7bH890THTgkgWoeCf8zE0JQNH6Fzay3AIIdiyZQs5OdncXlyPPdJC3JpFwHdf2r5j6XInvkIrnT1VnD9/DpvNzvbt29PW/nHLwky2LMxknuagqz4OAm65zY19gnzvZBELFyPulZzxlvBkozHmFzYUUZo9Nc3sSvSeTrQn/9n4zvt/B3ED1luaLAP59xG1z8Ea7cbb8Vza07/XrVtHaWkpa4u7yRyqRhM2/IUSRHr2tRSV2ChZaGdgsJ4T1UcRQvD+978/5eSMsSjLdfLxlT58WOmpNWIdK9e4ycpJz/xFZg7Kp79Aj93LP3fkoANyRR6VRRP3f5kMpoBIAc2ahb/QqN6Z0f0q9kB6Ky3a7XY+tcXHraUhonE4MnArumVyPtFEKIogq6CV3kGjz/SK8u3k5uambXwhBJ9Yks8dliwALrhDZPvSG9Tt3/oQ/1D5GWKKhXu7j7I5zeWW9PAQ2r/+PQQGYNlqxA1WrXXKKHb8cz6BJhw4AydwDfdET9vwisJH71zIPUsNT8De9qXE7IUTfCp5hBAUzR+ky2/EHYoLbmXu3PRuevzwTTl80JGLBUG9MoS3KL232cjyW/mnjf+HfruHFf11yNz0xx5GMAVEikQyyhnM2YpAI6v9GezB9PXXdQwcp2BoD7oOzx7P5oU3aqipSZ8QunjxIrt2GXVs8rxr6O3IG93dnA6Cg3GO7w9iQXBBDLGzv58fHWxHS5OW6R+K8fXdLfQoLm4OtfFotYr2w79Bj6Ung0MPh9G+9wTUnYFcH8pnvoxIk3V1IxG3+xgYVpS83b/G2X8gbWNbw23k9TyHELDzXBavHunmwIEDaWtROjAwwMsvv4Smx8jMKMOmL6XqcDBt40fCGgd2B7HHFfyWGK9H+vjr3S1E4unJ/IrENf56dzOnyCJXC/HFmp8jvvt19L7pqWdqnv2TYDB3K8GsjQjiZLX9HFuofspj2gMnybxoBOQC+feSu9jYDLRz505Onjw55fFbWlrYsWMHsViMiooK7tyyFiHgTPUQp6rG3kCULAP9cfbtDDAU1MnJs7D9rkxsiuC35/v5zlttxLSpjd8XivGXrzVyoTdMsdfOn9y7DGtWNpytQfvuE+ihqWlRejSC9oNvwekqyMpB+dI3Ed7JJwbc6IQ9yxnwGY1tMjt34Ow/OOUxraEGslv+DUWPMOSpxHnTAwghOHjw4KSqvl5Jb28vzz77LH6/n8LCQj704W1YrILm+ihH9wfRJtnfZITwkMb+XQH8fXEyPApb784kz23lTFeIJ3Y1MxiJTzzIOETjGn/7ZgvH24NkOS184wM3kVMyD3q60L7zjSlfA4kwg9TDpBTYEYKIezFKrB9buBlHoJq43XdZ856k0XXcfW/i7XwegUYwayPB3G0UFRdjtVppamqirq4Ot9tNQUHBpILJ586d48UXXyQWi1FWVsb27dvJzrUxpziLxrpBejrjxKJGN67JjN/bHWP/rkEiYZ3cfAvrN3sozLSzNN/F/qYAtT1D1PUMsaHEi3WCGkyJ6A5G+drOJpr8EUqy7HxrWym5OV5E+Ur0Y/uhpR79xBFE5TqEc2Jf8pW/tT44gPajv4OTx8GbhfKVbyGK0tuPeaZJR5D6SmLOUjTFiSN4DkfwNJriJuaYN6nkDXughuz2n6HoEcLum/EXSvJ8BeTm5lJXV0drayuhUIgFCxakdI6OrLujo4Pnn3+eYDBIUVER999/P5lZTnLzLLQ3R+nv0+jriTNnrm20w2EqDIU03t4dYKBfI8OrsPFuD9mZVlYVZbC/aYCGvgiHWwdZO9dDhj31eEQgHOcf97ZypHUQr8PCE9tKKc11I1atRz9+ADpaEUuXIfKL0hqkNgXEMClfQEIQySjHEu3GFmnBGTiBiAeJuBcln22hRfF2Pk9G3x4EEMi9x2hYNHwBFBcXoygKzc3N1NfX093dTUlJSdLZFvF4nMOHD7Nr1y50XWfFihWX7XeYW5KDxTZEW0uU3q44PZ1xcvMt2O3JzV/XdOprIxw7ECQWhYIiK+tu92C1GfOf47FTWeRmf1OA+r4wx9oGWZznTDrjSNd19jQM8K1dzXQFY8zPdvDNbaWjnxdZOYjVt6FXH4W2JvQj+xALlyByxy+FcelvrZ+uQvv249BYB55MQzhc5xlLiZgOAQHDQkI4cITO4QiexRppI+JaBEqSe1L0GO7eN/F27kCgEcq8FX/hw6AYv3FeXh75+fmcP3+e9vZ2WlpaKC4uTnq/gtPp5ODBg/zmN78hHA5TWlrKfffdh91uzM/tsZA/x0p7S5SBfo2Othg5eZbRFqDJ0NoU4eCeQUKDSwhwXwAADQFJREFUOp5MhY1bPKOfz3Za2Vjq5VjbIE39EfY2DLAkz5lSI6uajiB/9XoTtT1hPHaFb24tZWGOsX7hcCBWrEWsXIuoqDTWlEYBIdLhe5NSfgF4DFgBPKOq6mMTvP9LwJ9iNBn6JUaDofDwsQXAU8B6oBH4gqqqryU5Fb21tXUSK5hCI3tdx9X/Fp6ulxHEidqLGMzdapQiHktQ6HGc/sNk9LyOJe5HH87UCHuWJ3z7qVOn2LVrF9FolIyMDDZv3syiRYvG3Nim6zp1dXXs3buX/n6j/MXGjRtZs2bNZdrXyJo72qIcOxAkEtaxWKB8pYv5i+xYxtGk+ntjVB0O0ddjmM3z5ttYtc6dsEprc3+Yx19vojMYQxFGr4bfWenDbRtbk7oYiPDkkQ4ONBu9piqLMvjypmIyE1Rp1Qf8aN9/As4bFUfFrZsRDz6KyEts0fl8PjrPnkb/7a+M5j+6DmVLUX7/y4j81MosXC9M+vxOEsfAMbydv0LRwmgWDwO+DxL2rBg3DdY+eBpP10tYo8a8ArnbjD4nCSyEpqYmXnnlFUKhEBaLhdtuu42VK1eO9opORFdXF2+++SbNzc0ALFmyZMwNoYGBOAd2DxIc1EAYvRrKVzixjaMsBQc1Tr0TorXJiIH5Cq3cssGNw3n1ZwLhOH/9ZjM1HcamuY2lXh6tzGeOd2xB2h2M8v9O9/Kr0z1oOizOc/LlTcUUjfMZSP23Li4uhjHaOqdLQDwAaMA9gGs8ASGlvAf4GXA30Ao8D7ytquqfDR/fD+wH/hL4IPAksFhV1c4kpnLtBcQw1qEmstqfwRIz6inFrTmEMtcRsxegWbPQFTvWcJuRQz5Yg3W4IXzUUcxA/gPEnHPHHb+/v59XX32VtrY2wNCMysvLKS0txeFw4HA48Pv9tLS00NjYSGen8e/KycnhjjvuSNjf4dI1h4c0qo+FaG00TnarDeYU2ygqseNwCoQATYOuizHaW4yqlABOl2D5LS7mzLWNa/oPRuL8oqqLX5/tRdPBZVWoLHKzdq6HRblOYppOLK5T1xtmT4OfU53GheSyKvzemgK2L8oad3w9Ekb/9bPor+6AaMRYwPI1htm9eDlYLDA4gN7bhe34ASJH3zZKRggF8aGPIe6ViEnuJL8emG4BAaBE+8jseBZ7qA4ATXEx5F1NxL0EzeJCV5wosX7swfPYQ+ewhY1rNWbzEfB9aMJSMqFQiD179nD6tKEI2Gw2ysrKuOmmm/B4PAghiMfjo27Zjg6jgGNGRgZ33nknixYtGvccikZ1zlYPceFcGF0HqxV8hTYKiqzk5FnRNJ143Ii3tTRG6Ok0rgGLFSpWGUrVuOPHNdTqbnac6iES17EqsKbYw7ICNxUFLhwWhf5wjJ5gjL2NAxxuCaDpxp37oWV5PLLSl5SL9j0nIEaQUj4BzJtAQPwCqFdV9S+Gn28FnlZVdY6UcglwAvCpqjowfHzP8PEfJTGFGRMQAEIL4/Qfwt23H0ts/FaZMZuPwdzthtWQpEtK0zSqq6s5ceIE3d3jZy04HA7Wr1/PihUrxrQ0Eq25rTnC2Zow/r7xA2qKBeYvclC+3DnqUkqGup4hfnz44qgAGAu7RbChxMunK/NTMsf17k70536GfnD3+G+0WBGrNyDe9xHEwiVJj3+9ci0EBAC6htN/yChLExl/t7WmOBjM2WpUKE5hw119fT379+8fVYLGwmq1smbNGiorK8fsDJcIf1+c6qNBujsnvgaK5tooX+EcszNcIrqCUX5+vJM3LvjHfZ9FwIYSL/ffnMtSX/J1zNIpIGai8tgy4FeXPH8HKJRS5g0fqxsRDpccXzbWYFLKPwD+AEBV1UmXjLBarVMqNzFKwVzQ70PrrUL0VUOkx3jEQuCeCxkL0D0LUbIr8AoLqdYevfvuu9myZQutra0cP36c7u5uQqEQoVAIt9vNggULKCsro7S0dNTPOhaJ1uzzwYpK6O+LcOFcgLbmILGYjqbp6DrkFzopXZhB0TwXVmvqSXA+H6xbMo82/xD7L/TyVn0Pbf4wdovAZlHIy7Bz1015bC7Lwz2JYB4+H/z53xDvaCNy4giRmuNEz1SDxYLizUTxZuFYthrHHe9DyUp/eY73Kmk7v5Mh/17QP4gWbER07odQm3H+x0NgcUBmOXpWOXgXk2FxkOoWL5/Px9q1a+nu7qampoba2loikQi6rqPrOsXFxZSXl1NWVobb7U66W92740PZTRDwR2luDNLcMIi/P4rFIrBYFVwuC/PLMphf5hnXBTXm+MATpUW0+Yc42txPVYufE21+dCDbZSPbZWP5HC8fuLmA3IzU64ul87eeCQHhAS6tCz3ytzfBsZHjY/pfVFX9MfDj4af6ZLWk9GtY8yBzjEyYONB9dWnvVBixEMbC7x9fO4GJ1zxvIcxbmCgYGKKvL7kWi2NhA+6Ya+OOuYk3QQX9vUwppKrYYNUG4zGMNvzIHln3tdCo3yNcMwviMjLAs+2KjvTDxIDeAWBqdc0qKiqoqEhcRNHv92O326e0bt8c8M2xA1feqCP0+8f3EkyEDVhfYGF9QQ6svlpZ0UJ+kuxkehmTtCASMqGAkFLuAu4c4/A+VVVTrY8bAC5NMB/5eyDBsZHj6a2OZ2JiYmIyIRMKCFVV70rzd9YAqwB1+Pkq4KKqqt1SyhqgTErpvcTNtAr4RZrnYGJiYmIyAWlxMUkprcNjWQCLlNIJxFRVTeT8+xnwEynl00Ab8FXgJwCqqp6VUh4H/kpK+VXgA8BK4MF0zNPExMTEJHnSVWrjq0AI+DPgk8N/fxVASlkqpQxIKUsBVFV9Bfh74A2gYfjxV5eM9QiwFugF/hZ4KMkUVxMTExOTNJLWNNf3ADOa5nq9MRvXDLNz3bNxzTA7153ONFezWJ+JiYmJSUJMAWFiYmJikhBTQJiYmJiYJOSGi0HM9ARMTExMrkNmRQxCTPYhpTwylc9fj4/ZuObZuu7ZuObZuu5JrjkhN5qAMDExMTFJE6aAMDExMTFJiCkg3uXHE7/lhmM2rhlm57pn45phdq47bWu+0YLUJiYmJiZpwrQgTExMTEwSYgoIExMTE5OEmALCxMTExCQhM9FR7j2FlDIXeBJ4H9AF/Lmqqjds/wkppQP4AbANyAVqgb9QVfXlGZ3YNURKuRij9/n/qKr6yZmez3QjpXwEo2JyKdAOPKaq6p6ZndX0IqVcgHGe3waEgf8BvjhGC4LrEinlF4DHgBXAM6qqPnbJsa3A9zF+8wMYv3lDqt9hWhDGPzECFAKfAH4opRyzB/YNgBVowugSmAV8DVCHL6jZwveBQzM9iWuBlHI78HfA72K09b0DqJvRSV0bfgB0AEVAJcb5/vkZnVH6aQWeAP7j0hellD7gOYxrOxc4DPz3ZL5gVlsQUsoMjGZEy1VVDQB7pZQvAJ/C6G1xw6Gq6iDw+CUvvSilvACsAepnYk7XkmFtug94C7hphqdzLfg68A1VVd8eft4yk5O5hiwEvqeq6hDQLqV8BbihFD9VVZ8DkFKuBeZdcugBoEZV1WeHjz8OdEkpy1VVPZ3Kd8xqAQEsAeKqqp695LV3GLsH9w2HlLIQ4/9QM9NzmW6klJnAN4CtwGdmeDrTjpTSgtF86wUpZS3gBHYAf6yqamhGJzf9fAd4REq5C8jB6E75tRmd0bVjGcZ9DDCUQinl+eHXUxIQs93F5AH6r3itH8MUv+GRUtqAp4GfpqpZXKd8E3hSVdWmmZ7INaIQsAEPAZsxXC2rGe72eIOzG+OG6AeaMdwsO2Z0RteOtN3XZruACACZV7yWCQzMwFyuKVJKBfhPjPjLF2Z4OtOOlLISIzD/LzM9l2vIiJXwXVVV21RV7QL+GfjgDM5p2hk+t3+D4YfPAHwYVsTfzeS8riFpu6/NdgFxFrAOZ7WMsIob3N0ipRQYmVuFwIOqqkZneErXgruABUCjlLId+ArwoJTy6ExOajpRVbUXQ3uebeUScoESjBhEWFXVbuApbnDBeAk1GPcxYDTWuohJ3NdmdQxi2Df3HPANKeXvY5jg9wMbZ3Zm084PgZuBbbPAFz3Cj4H/uuT5VzAExudmZDbXjqeAPxoO0kaBLwIvzuyUphdVVbuGEy8+J6X8RwyXy6Nc4pe/EZBSWjHu4RbAIqV0AjHgeeAfpJQPAi8B/xeomowbeVYLiGE+j5Em1gF0A59TVfWGtSCklPOBz2LkhrdLKUcOfVZV1adnbGLTjKqqQSA48lxKGQCGVFXtnLlZXRO+ieFiOQsMASrwrRmd0bXhAeDbwJ8CceAN4EszOqP081WM/S0jfBL4uqqqjw8Lh+8BP8fYB/HIZL7ALNZnYmJiYpKQ2R6DMDExMTEZA1NAmJiYmJgkxBQQJiYmJiYJMQWEiYmJiUlCTAFhYmJiYpIQU0CYmJiYmCTEFBAmJiYmJgkxBYSJiYmJSUL+P4Yt+UW6gKFiAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = arange(0,10,0.1) # Define a vector x that ranges from 0 to 9.9 with step 0.1.\n",
"k = 1 # Fix k=1,\n",
"y = sin(x + k*pi/4) # ... and define y at this k.\n",
"\n",
"figure() # Make a new figure,\n",
"plot(x,y) # ... and plot y versus x.\n",
"\n",
"k = 2 # Let's repeat this, for k=2,\n",
"y = sin(x + k*pi/4) # ... and redefine y at this k,\n",
"plot(x,y) # ... and plot it.\n",
"\n",
"k = 3 # Let's repeat this, for k=3,\n",
"y = sin(x + k*pi/4) # ... and redefine y at this k,\n",
"plot(x,y) # ... and plot it.\n",
"\n",
"k = 4 # Let's repeat this, for k=4,\n",
"y = sin(x + k*pi/4) # ... and redefine y at this k,\n",
"plot(x,y) # ... and plot it.\n",
"\n",
"k = 5 # Let's repeat this, for k=5,\n",
"y = sin(x + k*pi/4) # ... and redefine y at this k,\n",
"plot(x,y) # ... and plot it.\n",
"\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's horrible code! All I did was cut and paste the same thing four times. As a general rule, if you're repeatedly cutting and pasting in code, what you're doing is inefficient and typically error prone. There's a much more elegant way to do this, and it involves making a `for` loop. Consider:"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [],
"source": [
"x = arange(0,10,0.1) #First, define the vector x."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's declare a `for` loop where `k` successively takes the values 1, then 2, then 3, ..., up to 5. Note, any code we want to execute as part of the loop must be indented one level. The first line of code that is not indented, in this case `show()` below, executes after the for loop completes"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"for k in range(1,6): \n",
" y = sin(x + k*pi/4) #Define y (note the variable 'k' in sin), also note we have indented here!\n",
" plot(x,y) #Plot y versus x\n",
" \n",
"# no indentation now, so this code follows the loop\n",
"show() "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The small section of code above replaces all the cutting-and-pasting.\n",
" Instead of cutting and pasting, we update the definition of `y` with different values of `k` and plot it within this for-loop.\n",
" \n",
"\n",
"\n",
"**Q.** Spend some time studying this for-loop. Does it make sense?\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"**Important note:** Python uses **indentation** to define `for` loops.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 18: Defining a new function.\n",
"We've spent some time in this notebook writing and executing code. Sometimes we'll need to write our own Python functions. Let's do that now.\n",
"\n",
"Our function will do something very simple: it will take as input a\n",
"vector and return as output the vector elements squared plus an additive\n",
"constant.\n",
"\n",
"If have a vector, `v`, and a constant, `b`, we would like to call:\n",
"\n",
" vsq = my_square_function(v, b)\n",
" \n",
"This won't work! We first need to define `my_square_function`. Let's do so now,"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [],
"source": [
"def my_square_function(x, c):\n",
" \"\"\"Square a vector and add a constant.\n",
"\n",
" Arguments:\n",
" x -- vector to square\n",
" c -- constant to add to the square of x\n",
" \n",
" Returns:\n",
" x*x + c\n",
" \"\"\"\n",
" \n",
" return x * x + c "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function begins with the keyword `def` followed by the function name and the inputs in parentheses. Notice that this first line ends with a colon `:`. All of the function components that follow this first line should be **indented one level**. This is just like the `for` loop we applied earlier; the operations performed by the for loop were indented one leve."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"When defining the function, the code the function executes should be indented one level.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The text inside triple quotes provides an optional documentation string that describes our function. While optional, including a '*doc string*' is an important part of making your code understandable and reuseable.\n",
"\n",
"The keyword `return` exits the function, and in this case returns the expression `x * x + c`. Note that a return statement with no arguments returns `None`, indicating the absence of a value.\n",
"\n",
"With the function defined, let's now call it. To do so we first define the inputs, and then run the function, as follows:"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"v = [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.]\n",
"v*v+2.5 = [ 2.5 3.5 6.5 11.5 18.5 27.5 38.5 51.5 66.5 83.5 102.5]\n"
]
}
],
"source": [
"v = linspace(0.,10.,11)\n",
"b = 2.5\n",
"\n",
"# Now let's run the code,\n",
"v2 = my_square_function(v, b)\n",
"print(\"v = \" + str(v))\n",
"print(\"v*v+2.5 = \" + str(v2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To see the doc string that describes our function, type `my_square_function?`"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [],
"source": [
"# Let's check that our docstring works\n",
"my_square_function?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Try to make a function, my_power, so that \n",
"`y = power(x,n)` evaluates $y = x^n$, \n",
"(in Python you can use `x**n` to take the power)\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"**Q.** Try to make a function, my_power, so that \n",
"`y = power(x,n)` evaluates $y = x^n$, \n",
"(in Python you can use `x**n` to take the power)\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 19: Animating figures \n",
"Finally, let's make an animation in Python. To do this we need two additional functions from external modules: `HTML()` and `FuncAnimation()`. `FuncAnimation` is what creates the animated figure, while `HTML` tells the notebook that to interpret the argument as HTML and show the results."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import HTML\n",
"from matplotlib.animation import FuncAnimation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In English, we set up (or initialize) the figure and then make a function that does all of the updates for each frame of the animation. Finally, we pass the figure, the function, and the frame numbers to `FuncAnimation()` and we have our animation.\n",
"\n",
"Here's an example in which we plot a sinusoid of different heights, and allow the user to adjust the heights with a slider."
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
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},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
},
{
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = linspace(0.,2.,1001) # Define x from 0 to 2 with 1001 steps.\n",
"lines = plot(x, 0. * sin(x*pi)) # Make the first plot, save the curve in \"lines\"\n",
"axis([0, 2, -1, 1]) # Set the x and y limits in the plot\n",
"title(\"plot number = 0\") # ... and label the plot.\n",
"\n",
"def animate(frame): # Define the function to perform the animation.\n",
" lines[0].set_ydata(float(frame) / 100. * sin(x * pi)) # Change the y values at each x location\n",
" title('plot number = ' + str(frame))# Update the title with the new plot number\n",
" \n",
"fig = FuncAnimation(gcf(), animate, frames=range(100))\n",
"HTML(fig.to_jshtml())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 20: Load MATLAB data into Python\n",
"For our last example let's load a MATLAB file in the `.mat` format into Python. Before doing so, let's clear all of the variables and functions we have defined. This command is not necessary, but we perform it here so that any new variables we subsequently load are obvious."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [],
"source": [
"%reset"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then, let's import the `scipy.io` module, which we'll use to import the `.mat` data,"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"import scipy.io as sio"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let's load a data file using the function `loadmat`,"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"dict"
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mat = sio.loadmat('matfiles/sample_data.mat')\n",
"type(mat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The variable that holds the loaded data is a dictionary. In Python, a dictionary is like a list, with the elements of the dictionary accessed via “keys”. Let's print these keys:"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"dict_keys(['__header__', '__version__', '__globals__', 't', 'LFP'])\n"
]
}
],
"source": [
"print(mat.keys())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"Use the `keys()` method to see what variables are contained in `mat`. In other words, run the command `mat.keys()`.\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The two keys of interest to us are `t` and `LFP`. Our collaborator who provided the data tells us that these correspond to a time axis (`t`) and voltage recording (`LFP`), respectively, for her data. Let's define variables to hold the data corresponding to each key,"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [],
"source": [
"t = mat['t'][0] # Get the values associated with the key 't' from the dictorary.\n",
"LFP = mat['LFP'][0] # Get the values associated with the key 'LFP' from the dictorary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let's plot the LFP data versus the time axis,"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from pylab import *\n",
"%matplotlib inline\n",
"\n",
"# Choose a subset to plot\n",
"t = t[0:500]\n",
"LFP = LFP[0:500]\n",
"\n",
"plot(t, LFP)\n",
"title('My plot')\n",
"xlabel('Time [s]')\n",
"ylabel('Voltage [$\\mu$ V]') # Wrap latex characters in $..$\n",
"show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
"## Donate\n",
"If you enjoy Case-Studies-Python, and would like to share your enjoyment with us, sponsor our coffee consuption here ."
]
}
],
"metadata": {
"jupytext": {
"formats": "ipynb,md:myst"
},
"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": "3.7.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}