ODEs.ipynb

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                "# Lab 5: Ordinary Differential Equations\n",
                "\n",
                "Today we will begin our study of ordinary differential equations (ODEs). ODEs are by far the most common kind of equations in physics, from classical mechanics to particle physics. \n",
                "\n",
                "Let's start with a simple, very familiar example:\n",
                "\n",
                "$$ F = ma.$$\n",
                "\n",
                "This looks like a simple, algebraic equation, but in fact it is a second order differential equation for the position $x$ of the particle in question:\n",
                "\n",
                "$$ \\frac{d^2 x}{dt^2} = \\frac{F}{m}.  $$\n",
                "\n",
                "Before we get into the study of numerical methods for solving ODEs, this example allows us to illustrate an important point. Any ODE can be brought into a *first order form*, in which we can convert higher order derivatives into a set of coupled first order equations. Remember that the \"order\" of an ODE refers to the highest derivative found in it. Newton's second law can be recast into *two* first order eqautions by creating what we call an **auxiliary variable**,\n",
                "\n",
                "$$ \n",
                "\\begin{align}\n",
                "\\frac{d x}{d t} \u0026= v\\\\\n",
                "\\frac{d v}{d t} \u0026= \\frac{F}{m}\n",
                "\\end{align}\n",
                "$$\n",
                "where we have added $v$. In this case, $v$ is the particle's velocity, which is itself a quantity we might care about in our solution. However, there's no requirement that auxiliary variables be things we care about. They may not even have a concrete physical meaning. They are there to make the solution possible in terms of a first order formulation. The auxiliary variables may also be used to eliminate otherwise singular behavior in your ODE that can lead to overflow or other numerical errors. \n",
                "\n",
                "This leads us to our standard form for ODEs:\n",
                "\n",
                "$$\n",
                "\\frac{d \\mathbf{f}}{dt} = \\mathbf{g}(t,\\mathbf{f}),\n",
                "$$\n",
                "where $\\mathbf{f}$ is a vector ($\\mathbf{f} = [x , v]$ in the above case of Newton's 2nd law), and $\\mathbf{g}$ is a vector representing the derivatives of $\\mathbf{f}$. In our example $\\mathbf{g} = [v , F/m]$.\n",
                "## Boundary Conditions\n",
                "\n",
                "As you already know from other physics classes, ODEs are not completely specified by their equations alone. In order to get a solution, you also need to specify one or more **boundary conditions**. These are algebraic conditions on the variables at one or more points. Sometimes they are simple conditions, like $x = 0$ at $t = 0$; other times they can be complex algebraic equations between the variables. Boundary conditions can be used to divide ODEs into two broad classes:\n",
                "\n",
                "* initial value problems (IVP)\n",
                "* boundary value problems (BVP)\n",
                "\n",
                "In today's lab, we will deal only with IVPs, which are generally easier to solve.\n",
                "\n",
                "## Methods for Solving ODEs\n",
                "\n",
                "There are many, many methods for solving ODEs, but we are only going to focus on one type in this class, the so-called Runga-Kutta family of integrators. Note that algorithms are often called \"integrators\", because solving a differential equation\n",
                "\n",
                "$$\n",
                "\\frac{d f}{d t} = g(t),\n",
                "$$\n",
                "\n",
                "with initial condition $f(0) = a$ to find $f(b)$ is formally identical to integrating\n",
                "\n",
                "$$\n",
                "f(b) = \\int_a^b g(t) dt.\n",
                "$$\n",
                "\n",
                "Why then are we developing new methods, rather than simply casting the ODE in that form and then using the integration methods we derived last week? The answer lies in the fact that $g(t)$ in physical ODEs are often charactersized by multiple timescales and have complex behavior. We then want to tailor the stepsize $h$ as time goes on (you can substitute space for time, if your problem is spatial rather than temporal). This is what ODE integrators excel at.\n",
                "\n",
                "\n",
                "### Euler's method\n",
                "\n",
                "First, we will start with the simplest method, Euler's method. Here we use the definition of the derivative, with a finite stepsize $h = t_{i+1} - t_i$:\n",
                "\n",
                "$$\n",
                "\\frac{d f}{d t} \\simeq \\frac{f_{i+1} - f_i}{h} = g(t_i,f_i)\n",
                "$$\n",
                "\n",
                "then we rearrange this to solve for the future $f_{i+1} = f(t_{i+1})$ in terms of the past $f_i = f(t_i)$:\n",
                "\n",
                "$$\n",
                "f_{i+1} \\simeq f_i + h g(t_i, f_i).\n",
                "$$\n",
                "\n",
                "This is called an *explicit* method, because the future solution $f_{i+1}$ is definied entirely by quantities known in the past. It may sound like some kind of strange magic, but there are indeed other kinds of methods called *implicit* methods, in which the future solution depends on other future quantities. We will not cover such methods today.\n",
                "\n",
                "To solve our ODE (or system of ODEs), we simply start at $t= t_0$ and step forwards $h$ at a time until we reach $t = t_{end}$.\n",
                "\n",
                "Euler's method is $O(h^2)$, and it is asymmetric: it wants to solve the differential equation from $t_i$ to $t_{i+1}$, but uses information only at $t_i$. It's a pretty terrible method to use, because it requires very small $h$ to get an accurate solution, which over a long integration will lead to a lot of round-off error. Furthermore, it is **unstable** for many applications, in which it will give you non-sense solutions.\n",
                "\n",
                "However, Euler's method is conceptually very important, in the same way that the Trapezoidal rule was very important for integration. It is the building block of more useful methods.\n",
                "\n",
                "### Second Order Runga-Kutta\n",
                "We can improve Euler's method by using it to take a \"trial\" step to the middle of the interval, $t_{i+1/2} = t_i + h/2$, and then evaluate the derivative function $g(t,f)$ at that point. Then, we just combine all the information:\n",
                "\n",
                "$$\n",
                "\\begin{align}\n",
                "k_1 \u0026= h g(t_i, f_i)\\\\\n",
                "k_2 \u0026= h g(t_i + h/2, f_i + k_1/2)\\\\\n",
                "f_{i+1} \u0026= f_i + k_2 + O(h^3)\n",
                "\\end{align}\n",
                "$$\n",
                "where we've explicitly included the error term ($O(h^3)$). You should note a very important difference between this and Euler's method: it takes twice as many evaluations of the derivative function, $g(t,f)$. This is called the second order Runga-Kutta method (aka rk2). \n",
                "\n",
                "Now it's time to code up rk2. Write a function below that takes a stepsize $h$, an initial $t$, and a function $g(t,f)$ and returns an update value for $f_{i+1}$. "
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            "source": [
                "import numpy as np\n",
                "\n",
                "def rk2_step(f, h, t, g):\n",
                "    k1 = h*g(t,f)\n",
                "    k2 = h*g(t+h/2,f+k1/2)\n",
                "    return f + k2"
            ]
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            "source": [
                "Now, let's use this to solve a very simple ODE:\n",
                "\n",
                "$$\n",
                "\\frac{d N}{dt} = -\\gamma N\n",
                "$$\n",
                "\n",
                "with $\\gamma = 1$, starting with $N(0) = 10^6$ at $t=0$,  and integrating it until $t=5$. \n",
                "\n",
                "I'll give you code for $g(t, N) = -\\gamma N$, which as you can see does not depend on $t$. However, we still formally include it, because ODEs in our standard form can depend on the independent variable."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "def g(t,N,gamma=1):\n",
                "    return -gamma*N"
            ]
        },
        {
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            "source": [
                "Now, in the space below, make a list of times, starting with $t=0$, and a list of $N$, starting with $N_0 = 10^6$ and using a timestep $h=0.01$. Using a while loop, that continues as long as $t \u003c t_{stop} = 5$, take an rk2 step to update $N$ and update the value of time $t = t+h$."
            ]
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            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [],
            "source": [
                "N0 = 1e6\n",
                "t_stop = 5\n",
                "h = 0.01\n",
                "t = [0,]\n",
                "N = [N0,]\n",
                "\n",
                "while t[-1] \u003c t_stop:\n",
                "    N_new = rk2_step(N[-1],h,t[-1],g)\n",
                "    N.append(N_new)\n",
                "    t.append(round(t[-1]+h,3))\n",
                "\n",
                "N = np.array(N)\n",
                "t = np.array(t)\n",
                ""
            ]
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            "source": [
                "Now that that's done, plot a graph of $N(t)$. Of course, you know the analytic solution for this problem too. So solve the ODE by hand, and then plot on the same plot the value for $N_{exact}$ at each of the $t$ points your ODE integrator used to find its approximate values. Looking at the plot by eye, was your solution accurate?"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [],
            "source": [
                "import matplotlib.pyplot as plt\n",
                "%matplotlib inline\n",
                "plt.style.use('ggplot')"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": "\u003cmatplotlib.legend.Legend at 0x7f7d8e9fd0c0\u003e"
                    },
                    "execution_count": 5,
                    "metadata": {},
                    "output_type": "execute_result"
                },
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\n",
                        "text/plain": "\u003cFigure size 640x480 with 1 Axes\u003e"
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plt.semilogy(t,N,'+', label='RK2 simulation')\n",
                "plt.semilogy(t,N[0]*np.exp(-t), label='analytic')\n",
                "plt.xlabel(r'$t$')\n",
                "plt.ylabel(r'$N$')\n",
                "plt.legend(loc='upper right')"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We have developed the rk2 solver and used it to solve a simple ODE. However, as we will see, it is not terribly accurate and requires very small stepsize $h$ to get a good solution. We're also going to focus on writing good **production code**, because starting next week, we will be using our rk solvers as workhorses to run many simulations. Doing so will allow us to focus on the *physics* we can learn from solving complex, non-linear differential equations via computer. \n",
                "\n",
                "Now, we will\n",
                "\n",
                "* generalize rk2 to more useful, higher order schemes\n",
                "* see how our rk methods can be used on *systems* of ODEs\n",
                "* learn about what constitutes \"good\" code \n",
                "* compare rk2 to our more powerful rk4 scheme"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Generalizing rk2\n",
                "\n",
                "Recall from last time that the rk2 algorithm can be written as \n",
                "\n",
                "$$\n",
                "\\begin{align}\n",
                "k_1 \u0026= h g(t_i, f_i)\\\\\n",
                "k_2 \u0026= h g(t_i + h/2, f_i + k_1/2)\\\\\n",
                "f_{i+1} \u0026= f_i + k_2 + O(h^3)\n",
                "\\end{align}\n",
                "$$\n",
                "\n",
                "Hopefully, you coded up something like this:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [],
            "source": [
                "def rk2(f,t,h,g):\n",
                "    k1 = h*g(t,f)\n",
                "    k2 = h*g(t+h/2,f+k1/2)\n",
                "    return f + k2"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "It has probably occurred to you that you need not stop with just two function calls. Of course, the more function calls your method has, the slower it will be for a single timestep. So, in order to make it worthwhile, your new method had better allow you to take a  much larger timestep.\n",
                "\n",
                "By far the most popular ODE integrator for general-purpose scientific work is 4th order Runga-Kutta (aka rk4). This method has an error that is $O(h^5)$. Why is this method so popular? It's because rk4 requires exactly four function evaluations; higher order methods require more than their order: 5th order requires 6 function calls, 6th order requires 7, 7th order requires 9, 8th order requires 11 (Numerical Recipes, Ch. 17, p 912). \n",
                "\n",
                "So let's code it up:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [],
            "source": [
                "def rk4(f,t,h,g):\n",
                "    k1 = h*g(t,f)\n",
                "    k2 = h*g(t+0.5*h, f+0.5*k1)\n",
                "    k3 = h*g(t+0.5*h, f+0.5*k2)\n",
                "    k4 = h*g(t+h, f+k3)\n",
                "    \n",
                "    return f+ k1/6. + k2/3. + k3/3. + k4/6."
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Solving systems of ODEs\n",
                "\n",
                "\n",
                "Now we'll test it, but not on the simple decay problem from last time, but a more complex problem: a damped harmonic oscillator. First, remember from last time that we can solve arbitrarily high order ODEs by reformulating them as a *system* of first order ODEs. \n",
                "\n",
                "$$\n",
                "\\frac{d \\mathbf{f}}{dt} = \\mathbf{g}(t,\\mathbf{f}),\n",
                "$$\n",
                "where $\\mathbf{f}$ is a vector ($\\mathbf{f} = [x , v]$ in the above case of Newton's 2nd law), and $\\mathbf{g}$ is a vector representing the derivatives of $\\mathbf{f}$. In our example $\\mathbf{g} = [v , F/m]$.\n",
                "\n",
                "Look closely: the `dho` function expects `f` to be a numpy array of length 2, and it returns a numpy array of length two representing the right hand side (here I rename $\\mathbf{g}$ to `RHS`): "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {},
            "outputs": [],
            "source": [
                "def dho(t,f):\n",
                "    \"\"\"the damped harmonic oscillator has\n",
                "    \n",
                "    F = -k*x - gamma*v\n",
                "    \n",
                "    recall that for a Newton's second law system, we have\n",
                "    \n",
                "    df_vec/dt = RHS:\n",
                "    \n",
                "    df_vec[0]/dt = v\n",
                "    df_vec[1]/dt = F/m\n",
                "    \n",
                "    where f[0] is the position x\n",
                "          f[1] is the velocity v\n",
                "    \"\"\"\n",
                "    \n",
                "    gamma = 0.1\n",
                "    m = 1.\n",
                "    k = 1.\n",
                "    \n",
                "    x = f[0]\n",
                "    v = f[1]\n",
                "    RHS = np.array([v,(-k*x - gamma*v)/m])\n",
                "    return RHS "
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Feel free to play around with values of `gamma` and `k`. You may need to adjust the stop time `t_stop` below. Make sure you understand what is going on. In particular, now would be a **great** time to think about units. How do the units work here? \n",
                "\n",
                "Other things you should consider in the following code:\n",
                "\n",
                "* How does the loop work?\n",
                "* Why are we storing the new solution in a variable called `xold`?\n",
                "* Why are we appending the values of `x = f[0]` and `v = f[1]` to lists separately? Do we have to do this?\n",
                "* Could we wrap the code in the following cell in a function, and call it with different $h$? What parameters should this function take? You might call this function something like `rk_driver`, since it will *drive* the rk."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [],
            "source": [
                "# initial conditions:\n",
                "x0 = np.array([1., 0.]) # spring is at x = 1, with no initial velocity.\n",
                "t0 = 0. # start at t= 0\n",
                "\n",
                "t_stop = 32*np.pi\n",
                "x = [x0[0],]\n",
                "v = [x0[1],]\n",
                "t = [t0,]\n",
                "xold = x0\n",
                "h=0.001 # modify this!\n",
                "while t[-1] \u003c t_stop:\n",
                "    xold = rk4(xold,t[-1],h,dho)\n",
                "    x.append(xold[0])\n",
                "    v.append(xold[1])\n",
                "    t.append(t[-1]+h)"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "In the cell below, make a plot of $x$ and $v$ as a function of time. Make sure to label all axes!"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": "Text(0, 0.5, 'Position/Velocity')"
                    },
                    "execution_count": 10,
                    "metadata": {},
                    "output_type": "execute_result"
                },
                {
                    "data": {
                        "image/png": 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f55GH3+MTw6lwn0dVGEGv16O+vh47d+5MeH7nzp2YNGmS5rF79+5FR0cHFixYkHEcSimamppOvcJv09B8mJyyYLIwwZhvYj8HAlFlH/GtV4FQCPTjdaAdLUOYLIfD4XA4XxxGlWACgMWLF+Pdd9/F+vXr0dLSghdeeAE9PT247LLLAACvvPIKnn766ZTj1q9fj4kTJ6K2tjZl2/Lly7F9+3Z0dnaisbERf/rTn9DY2IjLL798xK8nJ4ZoXNkvrZCT028FZhZV6g+y56m7H2g+quxP9+0Eh8PhcDicUZaSA4B58+bB7Xbj9ddfh9PpxJgxY3Dfffcp+Uen04menp6EY3w+HzZv3oylS5eqntPr9eIvf/kLXC4XrFYr6urq8NBDD2HChAkjfTm5YRiaYPKGRQAsFQdAScMpEaa25sQDWhoHNQ6Hw+FwOF80Rp1gAoBFixZh0aJFqtvuvPPOlOesVitefvnltOdbunRpWjF1SiFHmKJR0EgEJMfOy54QE0Z5RiaUYhEm9jxtO56wP21tHMJkORwOh8P54jDqUnKnNbJgAgYVZfKEWITJJgmmWA2TtKqvXRJMk2eynz2dg5snh8PhcDhfMLhgGk3o9QCRXrJBCCavEmFKTMm5JSFFnSyVSRqmsQP6naBh7gTO4XA4HA4XTKMIQsiQCr9lwSRHmGyScPJJz8PVx8apGRsbx9k9hBlzOBwOh/PFgAum0YYx5sWUK3JKTq5hshnYT7kYXBZMcBQDxWXscS8XTBwOh8PhcME02hhkhCkqUvjCcg2TkPDTG4qCilFgwMl2dhSxfwBof98wTJrD4XA4nNENF0yjjUEKJiWKhFiEySpHmEIiMNAPiCKrkbI7QOwOtvOAa6gz5nA4HA5n1MMF02hjsIJJqlMy6wn0UqNdJcIUjgJyJCnfAaLTAflSq5mB/qHPmcPhcDicUQ4XTKMNqT0KDeYmmDxJBd/xjwMRimi/JIxkoZTvYD/dXDBxOBwOh8MF02hDbsAbyW25v1cu+DbECSZD7OX3uD3sQV4++2lnwonylByHw+FwOFwwjTpkwRQeXEpOTsMBgE4gMOultJzHDwAg1jz2U65h4hEmDofD4XC4YBptEEUw5RZh8kdYhMliSHzJFS8mX0B6ws5+yik5HmHicDgcDocLplGH3sB+hkM5HeaXVsnJESUZOUXnDUgCzJYnbZCEk3dgcPPkcDgcDucLBBdMow3FuDI3wRRIE2GyyivlFMEkCSVZOIVCvD0Kh8PhcE57uGAabShF34OLMFmSIkxWQ8y8EkAssmS2AoTZD8DnGdxcORwOh8P5gsAF02jDIKfkcov6yBGm5JScHHEKhCIAACJFloggABYb24kLJg6Hw+Gc5nDBNNowyMaVOUaY0qTk5IiTP0LZE1Z7bKOclvNywcThcDic0xsumEYbhsEWfTNBlBxhMssRpqgkmGxxgkmyGOARJg6Hw+Gc7nDBNNoYpHFluqJvJcIkSvVKclQJAKwsJUe5YOJwOBzOaQ4XTKMNSTDRHHvJpSv6VgSTThJiKoIJXu8gJsrhcDgczhcHLphGG4M0rkwbYZJTcjoToNPHjDERc/3mKTkOh8PhnO5wwTTKIHINU662AmlWyZmVCJMJsFgSD1IEE48wcTgcDuf0hgum0Ya8Si7XCJPi9E0Sno9FmIyAKUkw2YYnwtQfiGD57h40uXJLI3I4HA6Hc6rABdNoQ44w5VrDlCElxyJM1sSDpAjTUIu+n/qkHS/v6MG/vduMoDQPDofD4XBGE1wwjTYGUcMUFSlCkm1ActG3nJIL6EyAOSnCJAsov29wcwXQ54/g8zaW0nMFotjeztN7HA6Hwxl9cME02hhEDVMgLqqTNsKkN7F2KHEQWUAF/IOYKGN/d6LY2tM1ePHF4XA4HM7Jggum0cYgnL7ldJyOAHohqYYpruibJEeYhkEwHewJAAAM0rhHnbyOicPhcDijDy6YRhuD6CUnF3xbDAIIURdMEUGPsNw7TkaOOA1BMLUMMGF3SX0+AOCYMzDoc3E4HA6Hc7Lggmm0oTh95x5hSrYUAGKtUQAgYMxL2ihHmAafRuvwsHmeWcnO7QmJ8ASjgz4fh8PhcDgnAy6YRhtGSTBFo6DR7ISHP6y+Qg5gKToD2HkCSTVMStF3MAAq5i5yKKXo9LBI2LhCExxmHQCg05ubJQKHw+FwOCcbLphGG/qYE3e2DXgDGhEmADBTJob8xiTBFF/TFMg9ldbnjyAUpRAIUGozoDyPzV2OOgEADQYgLnsO4to3QCnNeQwOh8PhcE4EXDCNNuQaJiDrOqZghAkRUxrBZBHZefyGJMGkNwA6PXs8iDqmLim6VGI1QC8QVOSxuctRJwCgq/4Buu5N0OX/DezYkvMYHA6Hw+GcCLhgGmUQQQD0kojJMsIUjLIIk0lHVLebRXaegMGcOBYhsShTMHfB1BeIAACKrfqEn31+9jylFPSTDcr+dPP7OY/B4XA4HM6JQH+yJzAY1qxZgzfffBMulws1NTVYunQpJk+erLrvnj178NBDD6U8/8QTT6C6ulr5fdOmTVi2bBk6OztRXl6Om266CXPmzBmxaxgSBiMQiWQtmGTTSqMuTUouGgIMQEBnVtloAbzuQZlXuvws1SfXLhVZJMHkY4IJzh7A1avsTw/vBaU0ZSUfh8PhcDgnm1EnmDZu3IgXXngBt99+OyZNmoR169bh0UcfxRNPPIGSkpK0xz355JOwWmMpp/z8fOXxwYMH8eSTT+LGG2/EnDlzsGXLFjzxxBN4+OGHMXHixBG9nkGhl60FsowwSTVMJn2aCFOEeSMF9SaVjYP3YnJJESaHmb3NCiXB5JQiTDh2iP2sqAa6OwBXH+DsBYrSv44cDofD4ZwMRl1KbuXKlViwYAEWLlyoRJdKSkqwdu1azeMKCgrgcDiUf4IQu/RVq1ZhxowZWLJkCaqrq7FkyRJMmzYNq1atGunLGRzG3BrwBqUIkylNhMkYlQSTYEjdKK+UG4S1gCyMZKGkCCZJSNHWRgAAGT8ZKK1gB3W05DwOh8PhcDgjzaiKMEUiERw9ehTXXnttwvMzZszAgQMHNI/96U9/inA4jJqaGlx33XWYNm2asu3gwYO46qqrEvafOXMmVq9enfZ84XAY4TjBQgiBxWJRHg8X8rkSzikVfpNIKKux5JScWZ9qXAkA5hCLHoX0xpTtxGwBBYBAIOfrcgVYSq7QogchBEVWNm+nP8LO1dPJxiivArxu0I5WoLMVZOrsnMYZDlTvM2fY4ff5xMDv88jD7/GJ4VS6z6NKMA0MDEAURRQUFCQ8X1BQAJfLpXpMYWEhvv3tb6O+vh6RSAQffPABfvWrX+HBBx/ElClTAAAulwsOhyPhOIfDkfacALBixQq89tpryu91dXV4/PHHUVpaOqhry0RFRYXyuMNiQxhAkd0Oc2VlxmP1e90AgGKHHZVJ+9NoFKaI1L7E7kjZ3lNYDD+AfKMe9izGiscTZdGiuqpSVFaWwlEcBXAEgQhFfnEpPP19CAEobJiMEAHc2zfDOtCHwhzHGU7i7zNn5OD3+cTA7/PIw+/xieFUuM+jSjDJqCnNdOqzqqoKVVVVyu8NDQ3o6enBW2+9pQgmNTIVHy9ZsgSLFy9OGb+7uxuRSCTjNWQLIQQVFRXo6OhQfIoi0li9nR0Q2tsznsM54AEAhPw+tCftT/0+GKMsUtbj8adsl4JTGOjqhCeLseLpHpDqnvxutLeze2IxCPCHRew71oLy1uMAAJfeBGq1AwC8zccQyHGc4UDtPnOGH36fTwz8Po88/B6fGE7Efdbr9VkFO0aVYMrPz4cgCCmRn/7+/pSokxYNDQ348MMPld/VokmZzmkwGGAwqNT8ACPyolJKY+eV2qPQUDCrsWTjSqOOpOxPgwHFViAopm6X+8lRvy+n66KUxhV965Rj8006+MMi+t1+lPf3sX1LyoGBfva4r+ek/vFJuM+cEYPf5xMDv88jD7/HJ4ZT4T6PqqJvvV6P+vp67Ny5M+H5nTt3YtKkSVmf59ixYwkpuIaGBuzatSvlnA0NDUOa74hhGMZVcsEATFKESS4OT2CQq+T8ERHSsMg36ZTn5ccDvc7Y+a15sZVxfT05jcPhcDgczolgVAkmAFi8eDHeffddrF+/Hi0tLXjhhRfQ09ODyy67DADwyiuv4Omnn1b2X7VqFbZs2YL29nYcP34cr7zyCjZv3owrrrhC2efKK6/Ejh078MYbb6C1tRVvvPEGdu3alVIIfsogt0cZjlVyoSBMUSnCJCuceCyDa8DrlhrsGgSS4DBuNzLB5B7wsicKilg6s1ASTD4PaDD3NiwcDofD4YwkoyolBwDz5s2D2+3G66+/DqfTiTFjxuC+++5T8o9OpxM9PbEoRSQSwUsvvYS+vj4YjUaMGTMGP/vZz3DmmWcq+0yaNAl33303Xn31VSxbtgwVFRW4++67T00PJgDEaGQr17I1rswUYZKdvqMqgsnIzCxzFTHeEDtXXlx0CYiLMHmkiFWBAwBArDYWbQr4maFlRU1O43E4HA6HM5KMOsEEAIsWLcKiRYtUt915550Jv19zzTW45pprMp5z7ty5mDt37rDMb8TJNSWn5fSdEGFSScmZJPfvYDCnKbpDLMJkNyaOaZcEk9vHxiT5hbGNhSVA+3GWluOCicPhcDinEKMuJceBUvSN0DDUMIWCMEnNd9VScsQkmWSGcosweSTBlGdME2EKSisJC+IEk6MIAEAHXDmNxeFwOBzOSMMF02hErmGKZFfDFFKa76a+3DQYYL3kEGvSm4BRjjDlKJiC6ik5JcIUlqJZ+Q5lG7FLqxLd/TmNxeFwOBzOSMMF02jEIGVSsxRMcqotvvhaIRSMrZJTS8mZBymYlAhT4phyhMkdlaJd8REmRTC5chqLw+FwOJyRhgum0YjcfDdbwaREmNSKvoOxom+1VXLGwdUwpUvJyRGmAcpEX0INkyyYBniEicPhcDinFlwwjUbkGqYsir4ppUovOWPaCJOcktMo+h7mGiY3kWqj4lJy8mPKU3IcDofDOcXggmk0IkeYwplbsEREClHSQaoRplBAs+gbctF3MJCTy6pbrmFKE2Fy683MGsGer2wbrhomSimO9AXQ7c0uAsfhcDgcTiZGpa3AaY8kmGgWKbn4uiTVGqZgQIkwhaIUIqUQ4nvoySk5UWQpQDm6lQFvmhommySgRKJDUDDAaosJplhKzpXVGOlYecCJ5z7vgllP8MSX6lCVn92cORwOh8NJB48wjUZy8GGS65d0BNALaWwForHzpBR+yyk5IKfCb8WHKWmVnElHIE/Da84HjHFiRk7PDSHCFBUp/rG7FwAQiFC8daBv0OficDgcDkeGC6bRSA5F35or5AAgGIRRjKX2kq0FiE4XGy+Hwm85wmRLSskRQmCTnvLai1lbFBk5whQKDro9yuG+AAaktiwA8FmrZ1Dn4XA4HA4nHi6YRiHEkL1gkj2YjGr1SwBoKAgBFEbC9lOvY8q98DtdDRMA2HRMxPmsBanjyCm/QUaZdnWynnezK20QCNDljaDLw2uZOBwOhzM0Bi2YHnvsMWzfvn0Yp8LJGqXoO4sIUzRDhEkSQWbC9lNvjyIVfgeyE0wipfBLwstmTB3XRlgEyGtzJDxPCAGseewX3+AiQ01OFgWbVm5FXSGb95E+3syXw+FwOENj0IKptbUVv/71r3HXXXdh9erV8Ply62bPGQI5RJiUtihpIkwIMYFhkt4Jmm7fWUaY4v2crIbUt5iVsnl7zfkp22CTBJN3cIKp0cXmOM5hwlgHE0xN/bFUIqUU4qb3IP7zddAse/FxOBwOhzPoVXJ/+MMfsHXrVqxZswYvvvgiXn31VcyfPx9XXHEFamtrh3OOnGSGuYYJkARVJI15pSk3t29fmJ1DLwAGlUJzmxgCYIHPbE892Db4CFM4StE6wETQWIcJzf1MMDW74gTTlg9A//o79ourD+T//UvO43A4HA7n9GNItgJnnnkmzjzzTHR0dGDNmjV477338O6772Ly5Mm44oorMGfOHAgCL5MadnJKyWWIMEkiSF7Mpp6SY4KJBoNIc5YE/JJgsuiFxKJuCVuUCRiv0ZZ6sJSSo153VmPF0+kNIUoBs56gxKpHbQETTMfjI0zrV8Yef/QO6Fe+BZKlVQKHw+FwTl+GxYepoqIC3/rWt/CVr3wFv/vd77Bnzx7s27cPRUVFuPrqq3HFFVeofnByBokh++a7isu3SuNdtoMUYZIiUJpF30F/VtOTI0wWQ2rBNwDYIn5AAHx6S8o2YrMzQ0uvN6ux4un2stV+ZTYDCCGotLP71OkJM9NNvxc4dih2QDAAHNgNTDsz57E4HA6Hc3oxLIKpt7cX77zzDt59910MDAxg1qxZmDdvHj799FO88MILaGtrw2233TYcQ3GA3CJMcg2TPl0Nk1T0rRcAiKrtUYjRxERMlrYCcoRJrX4JAKwhL2AGvHpz6kalhsmd1VjxyKvhSm3s/pTZ2Ns7GKUYCEaRf2gfQEWgrApk/CTQTzaAHtkPwgUTh8PhcDIwJMG0e/du/POf/8Tnn38Oo9GIiy66CF/60pdQWVkJALjooouwevVqLF++nAum4UQvvWzZ1DApKTntCJNRrwMgqtcwmXMr+vaF2So4SxrBZAtKgklQSYUNYZVcl9QKpUwSTAadgCKLHn3+CLq8YdibDgMAyPgzgHETgE82gErPcTgcDoejxaAF049+9CO0tbWhrKwMX//613HJJZfAarWm7DdhwgS+gm64UZrvDq3om4oiEGJF0majDkBYPSVnzK3oO2OEKTAAFABeYkjdaGOF4HQwEaYkwSQ/7vNH0OkJY3z7cfZk9ViQsRNY1IwLJg6Hw+FkwaAFU1FREb72ta/hrLPO0qxPqq+vx9NPPz3YYThqyLYCVASNRpkbdxpiNUzqbVFkTMZY+ioFpYYpu5RcrIYpTYTJx0wpvVRl3kOwFZCb7ZblxQmmPAP29/jR5QmDSoKJVNYAVdJKzgEXqM8DYlNZscfhcDgcjsSgl7B973vfw6xZs1TFUjQaRU9PDwBAr9ejtLR08DPkpKKPi8xkSMtpOn3HCSajgQmmkGrRt2RcmWXRd6YIk83nAgD4xNTtxDp4wSRHmEqTIkwA0O0NAZ2t7MnKMSAWK1BQyH7vbM95LA6Hw+GcXgxaMN15551obGxU3dbU1IQ777xzsKfmZCJeMGUwXwxrrZKTU2xGI0x6Fu1RjTAZBxlhSpMGtMoRpmjKZiUlB19uKTlKKfoDbJVckSUWOJUf9/V7gUiEpTOLy9jG8mp2bGdLTmNxOBwO5/RjREySRFHkNgIjCNHpANnfKmOEiQkgg2qESRJbRrMSgQqpOX1LRd80y6JvuS2KVc1WIBRgtgIAPGGVsZSUXG62Ap6QCDk4VmCOjVtoYY+dXulai8tApHtHyqvYcx2tOY3F4XA4nNOPYRdM4XAY27Ztg93Oa0JGlCytBcKaNUxyhMkUE0xqxpU5Fn1r1jAFArBKxpUREQgnCzRZMAX9oFmsApRxSdElm1FIiKYVWdh96gtI4xTFpYfL2GpO9HRmPQ6Hw+FwTk9yKvpevnw5XnvtNeX3n//852n3Xbhw4eBnxcmM3sBqkDKICtlWQD3CJKXYjKaYcaWaD5PJLPkwZbtKTsNWIBiAJRqM21eEIT5daIlbaenzAPmFWY3p9DPB5DAnvqWVCFNUAAUgFMcJJkk8UWdPVmNwOBwO5/QlJ8E0YcIELFq0CJRSrF27Fueeey4cDkfiCfV61NbWYv78+cM5T04yWVoLaNYwKSk5k3ZKTin6zi3CpFr0HfBDR0UYxTBCggH+iIj4FrxE0AFmCxDwA35/1oLJFWAirdCcmAYslGqYIhDg0VuQX1gSG6uohAnBPi6YOBwOh6NNToJp9uzZmD17NgAgGAziq1/9KsrKykZkYpwMZGleGRKlGiaVJrgIyxEmoyKoNIu+Q8Pg9C2ttLNIgsmnVsdksUmCKfs6JrnguyApwmTUCbAbBbhDIpzGfOTHp+QKpcfOXuZJNUgopfi8zYuwSDG3Jo/X73E4HM4XkEH7MN1xxx3DOQ9OrsheTBkEU1jDVoDKESaDUWnOq2orYJQiTCHtFXkymjVMUpTKSsPoR0xcJWCxAk4A/uwNT+UIk8OS+pYutOjhDoXQZ8rHuKJYhAmOIoAIQDQCDLiA6uqsx4tnzWEX/rSF1UHdPKMEN04vyXAEh8PhcEYbOQmmvXv3or6+HmazGXv37s24/5QpUwY9MU4G9Nml5DRXyYVjgsko1TCFVCNMsmDKLcKkaisQYBEmM40k7JuAXMeUQ4RJrmFKTskBTDA194fgNNqBuBomotMx0eTsGXRaLipSvLa7V/n9jX19uPqMorSmnRwOh8MZneQkmB566CE88sgjmDBhAh566KGM+y9btmzQE+NkIOsIk0YNkySYSHyESa2GKUfBFKthUrEVkASTlUQT9k3AYgMAUL8P2Sa35FVyyUXfAOCQblW/MQ8oKE7cWFQCOHtA+7qzHCmR/T1+dPsisBkEGPUCnP4Itnd4cd4YvkqUw+FwvkjkJJgefPBB1NTUKI85J5Fsa5iyjTBp1TDJRd/RCGgkAqJP/7YJRynCUt2Ueg0TS8lZCBNKfpUUILFYWTF2DhEmJSWnIpgKCBNTA2YHiHwt8liFUuG3qzfluGzY08nShrMqbXBY9Fh1wIltbYmCiQZ8zOupdrziAcXhcDic0UVOgik+xcbTbScZyYeJhkOaURitGiZFMBmNMOqzqGGSj9EQTPECSLOGSWCiSj0lxyJMyKFpc6zoOzWqZRcDAAQMWB2pB0rtUeiAK+ux4tndxeY4tcyKEisTTPu7Yy1kqLMX4iP/CvT3gcy5CORf/nVQ43A4HA7n5DLor7uRSASBgPoy80AggEgkMuhJcbIgS1sBZZWcltN3XEpONcKkNwDyyq8MaTnZg8moI9CprcyTa5h08v5aNUzZCyZPiI2bb0oVTAWSs/iAOT9lG/Id7Ge/M+uxZCilONzH/g9MLrVgQjFbTXh8IIiAJBzp6uVAfx97vOV90CP7cx6Hw+FwOCefQQumZ599Fs8++6zqtr/85S947rnnBj0pThbITt8ZhKlSw6SWClJJyYWiFJQmiiZCSNZ1TFoF3wAUWwGrFNHyhVUayuVY9B2OighIDuV5KoLJHmJ96QYMttSDhyCY+vwReEMiBAKMKTCi2GpAoUUPkQLH+gKg0Sjolg/Yzg5WO0U/XpfzOBwOh8M5+QzaVmDv3r24+eabVbedddZZeOWVVwY9qUysWbMGb775JlwuF2pqarB06VJMnjxZdd/Nmzdj7dq1aGxsRCQSQU1NDa6//nrMmjVL2ee9997DM888k3Lsyy+/DKPROFKXMSSI3sBqbzSa71JKlRom9dYocREmfWx7WKSp+xtNLJ2WwVpAFi7mdKvEpKikRS8AYfUaJlilou9AdhEmd4idQyDqdVP5/gEAFRjQWVK2kYJCUAB0IHfB1NzP7kWl3ai4ldcXmvC5P4JGVxBnDDQyt3JrHoRv3AHxD78C3bMNlFLu1cThcDijjEELpv7+fhQWqrswOxwOuFyuwZ5ak40bN+KFF17A7bffjkmTJmHdunV49NFH8cQTT6CkJNX/Zt++fZgxYwZuuukm2Gw2bNiwAY8//jgeffRR1NXVKftZLBY89dRTCceeqmIJQFar5CJiLFKkWfQdZ1wJsH5yxuRATZYRJjkVZVZblQeAysaVBgHwD09KzhNkUao8ow6CihAp8LOU2ABReT1lJ/FB1DA1u9i9qC2InXdMgQmft3nROhAC7dgFACBTZgGTZrDar75uoKsdkBv/cjgcDmdUMOiUnNVqRUdHh+q2jo4OWCyp3+aHg5UrV2LBggVYuHChEl0qKSnB2rVrVfdfunQprrnmGkyYMAGVlZW4+eabUVlZic8//zxhP0IIHA5Hwr9TmiwEU7ynkmbRt8EEvUAglxwF1awF5JqpDIIpKAsmQ5oIihxhkhSZmq0AMecmmNxxgkkNu5utgPNBr6QoFQoc7OeAK2e37+Z+di/GFMSK4qvz2X1qHQiBNh1hT9Y1sNV5YycAAOixgzmNw+FwOJyTz6AjTFOnTsUbb7yBc889F3l5ecrzHo8Hb7zxBqZNmzYsE4wnEong6NGjuPbaaxOenzFjBg4cOJDVOURRhN/vT5gzwArV77jjDoiiiHHjxuHGG29MiEAlEw6HEY4ruCaEKCJxONMt8rlSzhlXw5RuvHgtYtAJqfvJPkxGIwghMOkE+CMiQqLKeHKEKRzUvL6AJEjMepXxgNgqORObvz8ipu4npeTg92Z1Lz3ShdpNOtX9bf1dEPKiEIkO7lAUxVZDbKPdwQraRRGiuz+n167Tw17/mgKTclyNJJ5aBkJA82EAgDBuAgghIGMnsKLv5qMg512S9ThfJNK+nznDCr/PIw+/xyeGU+k+D1ow3XDDDbjvvvvwwx/+EPPmzUNRURF6e3uxadMmRCIR3HDDDcM5TwDAwMAARFFEQUFBwvMFBQVZpwBXrlyJYDCI8847T3muqqoKd9xxB2pra+H3+7F69Wo88MAD+M1vfoPKykrV86xYsQKvvfaa8ntdXR0ef/xxlJaWqu4/VCoqKhJ+dxUWwQ3AZjSgMM0c0e8HcAgmvYCqqtQUUJdAEATgKC2DrbISZuNh+CMiCgqLUVmaKCg77XaEABTarLCmGw+AqYuJl4I8q+q96xAjCAMoLysGWoMIU13KfiHfADoBCMFA2vsfj66HibSSfPUx231e2MM+9BvtMNmLUFmWeG2t9gKIAy5Enb2oGDch43gyvYFjAIApYytRWcnek6b8ELC2Cd3eMIIuF0wAKubMg2DNg3fGWehbvxLGjuMoy+K6vsgkv585IwO/zyMPv8cnhlPhPg9aMFVVVeGhhx7C3/72N7z77rsQRRGCIGDKlCn45je/qfoBPVyoKc1s1OdHH32E5cuX45577kkQXQ0NDWhoaFB+nzRpEu699168/fbbuPXWW1XPtWTJEixevDhl/O7u7mG1VCCEoKKiAh0dHQmr16IBlg7y9rsQaG9XPbZFShnpBaBdZZ+Ih60ec/l8GGhvh5xFa+3ogi3iTtg3Krk9OTs70J9mPADo6mXF0yQSUh/TPcB+So1/3f5gyn7Uy1Jxoteteo5kjneyGiUjjaiP6exBfrUX/UY7jrR0IC+auFpOtBcAAy6Izh50mPNSVgmqERUpOgZYtEwX6Ed7O5szpRQ2gwBvWESnuRi1NoLOfjfQ7waVXMaDRw6gra3tlPjGdKJJ937mDC/8Po88/B6fGE7Efdbr9VkFOwYtmABg3Lhx+Ld/+zeEQiF4PB7k5eWNaKF0fn4+BEFIiSb19/enRJ2S2bhxI5599ln8+Mc/xowZMzT3FQQB48ePT1ujBQAGgwEGg0F120i8qJQmLfeXzSPD4bTjyW1OjAJR30de8aY3gNLYyrhgREzZnxpYqokGg5rXJxdxm/RpxpSdvs1GACH4wipjyUXfoRDEcFjTWRwA3EEmUPOMQuq5wiHA70N+mFkUuAKR1HnlO4DWJkSdvaAVY7N6/Xq8YYgU0AsEDrMu4ZiyPAOOOYPoNheittyqbKNllSz95/OAuvsBu/Z79otMyvuZMyLw+zzy8Ht8YjgV7vOw9Wk4Ed+W9Xo96uvrsXPnzoTnd+7ciUmTJqU97qOPPsIf//hH/PCHP8SZZ56ZcRxKKZqamk7twu8sjCtjbVHSvMxxPkwAEgRTMiTHVXKmDD5MFiszeVRdJScXfQNZFX67JdNKNQ8mSFE0e5idRy4Qj4fYHQAAMQcvpi4vu+9lNn3KyrxSGxPS3WYHSFks0kqMJqBI+hbT3pL1WMl4Q1E8vOE4bl1xGBuO9g/6PBwOh8PJniFFmA4cOIC///3vOHTokJKSa2howNe+9rWEFNdwsnjxYvzhD39AfX09GhoasG7dOvT09OCyyy4DALzyyivo6+vD97//fQAxsbR06VI0NDQo0Smj0QirlX0wL1++HBMnTkRlZaVSw9TY2IjbbrttRK5hWJBbo2iskgtreTABcbYCJmm/mHllCqbsBJMsttSMK2k0qkS12L0fQFikCEdpgu0B0ekAk5lFo/xewK7i0B2HOygVfautkvOxyFIBZfPuD6qkS6XzRweyFx8xwZQaZZSf6zIXAmVJqemKaqC3C7SzFaRhatbjxfPCti583sau6+nN7WgosSir8zgcDoczMgxaMB08eBAPP/wwrFYrFi5ciKKiIvT19WHz5s146KGH8Mtf/hITJ04czrkCAObNmwe3243XX38dTqcTY8aMwX333afkH51OJ3p6epT9161bh2g0ir/+9a/461//qjx/0UUX4c477wQAeL1e/OUvf4HL5YLVakVdXR0eeughTJiQfQHwCSeL5rtySk7VgwmIM65kH/ByPzlVW4Fsnb4l40rVCFMw1krHkheznfBHRBh0SWLHYpUEU+YIk9wWxa4WYfJ5AAB5JCrtq3JteUwwif2ujGPJdEkr5Mry0gumbnMhSHlicTepqAHds4014x0EA4EINhxldWBGHUEoSrHqoBPfPrt8UOfjcDgcTnYMWjD94x//QG1tLR588EGYzWbl+a9//et46KGH8I9//AM///nPh2WSySxatAiLFi1S3SaLIJlf/vKXGc+3dOlSLF26dBhmdgKR66c0nL4zR5gk8SPVJ5m0IkzGHH2Y9CpjyoJJEKAzGpUPfH84mtoDzmIDXH1ZtUeJ+TCpiDRZMAlsXh6VlJwimHIwr+yUIkylKhGmUiu7lm6TSoSpvBoAQDsHJ5g+Oe5BWKSoLzThm7PL8Mv1x/FB4wBuO7MMOqlWja5eDrpxPcjsc0Gu+xaIWlscDofD4eTEoP+SHjp0CNdcc02CWAIAs9mMq6++GgcPcnO+kYTINUxZGFemr2GSjjUm1jCFhhBhUpy+VSNMrH4JZgvzrZLamGi6fWfRHsWtEWGiUkouT1oCKEej4iFKSi77GqY+P0vtlVhVBJPI5txlKQSKyxLHKpWWxvZ0Zj1WPNs72PWcO8aOGeVW2AwC3MEojkhNgLH1E9A3Xga62kDXrAD9YM2gxuFwOBxOIoMWTKIoQp9m9ZLBYICYo2syJ0eyaL4bFuXGu6nRHkppStG33E8uGFGLMA2DYApIgsnE0nFynZOWYKK+LASTFDVSr2FiESa7JM7Uir4Hk5JzSoKp0JL6f6AswM7jMuYjjKR7XyIJqJ6unFd8REWKnZJgmlVhg04gmFHBLBK2tbPnxdXL2c42OwCAvr0cVFS5Zg6Hw+HkxKAF09ixY/HOO++oblu3bh3Gjh076ElxskAWTJqr5DRqmOJTecoqOTkllz7CRDMKppjTdwpySs7EopJyo1zN9igZIkzBiKhE0lRXyUkRJjn6pBZhGkxKTo4wFZpTx8xz98AYZfe3z5ckaOVVckE/4HUjF1rdIXhCIsx6gonF7B5OK2fi80CPH7S1GWg+Auj0EB78PWDNA/p6gEN7cxqHw+FwOKkMWjBde+212L59O37605/irbfewkcffYS33noL9957L7Zt25bSvoQzzCi95AZZwxQvtAzJKbnBR5iCkZgPUwpSHzmYpQiThmCKtUfRFkyyABJITIAlIEWYbGaDtL9G0bdnIKtoTDhKlUhVkUqEiTh7UBRihdm9/kTBRIwmoEBq+NvbnXGseI5Kabe6QjN0UtSwoZjdy4O9AYg7trAdp84GKSwGmT0XAEA//zincTgcDoeTyqCLvs8++2z84Ac/wMsvv4yXX35Zeb6oqAg/+MEPcPbZZw/LBDlpyCrCpFHDJBd8C4JiDCkXfQdVBBMxmkCBLFbJpU/JUTlaJEWYlJSciu+TLKoyCSavJLasBiHFD4ntIKXkrEYgxASWSGnivlL6CqLIIlLy72lwBZgI0gtpVuY5e1AUNKHDUpIaYQJYXVO/E+jtBMaO1xwrHlkw1RfF6gbrClnjZHcwiva2Y6gEQKbMAgCQGWeDfrwOdP+urMfgcDgcjjpD8mGaP38+zj//fLS1tcHtdsNut6Oqquq0bPlwwsmmhkkrwhRKrF8CYrYCITUBI0eYgtmuktNIySVFmDTNKzOk5HwhWTCpCBcAVFplZ7NZABcgUjaeLa7eiej1bFWe3wt4BjIKJjkd5zDrVd/r1NmDoqA9Yd94SHEZ6NEDoD1dyRVOmhxxsntfX2hSnjPoBNQVmnCoN4AjvX4mmCZJja8bpJ/tx0EHXCD5jhxG43A4HE48Q15vTAhBdXU1zjjjDFRXV3OxdKJQnL7Tp+S0a5jCieeBdoRJEUwa4wHZ1TAROcJk0IgwSaaimSJMvjBLjdnULAUAJSVnstkU4ahVxwSp150WcsG3WjoOANDXg0IpJacmmJSVc71dGceSoZTimFOKMBUmrkwd62CvzXFjEatbqmL1gyQvH6iWagmHWMfU549gY/OAEl3jcDic042cIkx79+b2R3fKlCk57c/JgWyMKzVWySkpubjef0O1FYiIFBFRSzDFbAWADKvkpAgTzZSSC8VScqpIRd/EaoPdqEOvPwJ3UER5XtJ+9nygux3U058x6qO1Qo7t0ItiO3MNT5uSA0BzEEz9gSi8IRECAcYUJLp6y4Kp2VYOjB2f4LtE6ieBtjaBNh0GOWte1uPF0+gM4L53muELi7CbdHjs8lrU5JsyH8jhcDhfIHISTA899FBOJ1+2bFlO+3NyQCn6zqY1ioqYUFJysQ8+RTCp2gpkNq4MxEWKVI0rFVuBpAiT2io5i5XVTGVKyYW1U3JyhAnWPORJgknViynPzsbLIsLUpxFhopEwMOBEkUku+k59fUhxGRsrh6LvVjd7vcpshpSatNoCKcJkqwApSJp/LauRos1Hsh4rHkop/ri5Q7nP7mAUz27pxL9fWpu4n3uA+WulaUjN4XA4o52cBNODDz44UvPg5IpcwySKoNEo67+WRKzoW8NWIO4DTm5nMtgIk1y/JBBArxbVUmwFkmqY1FJyluxScl45JZcuwuSVnMKtNuSZmHhRT8kVsJ+e7AWTaoTJ1QdQisKIN2HfBAqLpH17M44l0zbAXq9Ke2rPuFopwtRhKUaouh7xCTsydgITZ01HQCnNOWW+p8uPg70BGHUEj1xai/veacauTh8O9vjRUGIBFaOgf3sa9ON3AXsBhDvuB5kwOacxOBwOZzSQk2DiKbZTiLjaI0TCgIpgCkvCR91WQKXoWyf3ktO2FUj3wSvXL1n0gvoHc7KtgJ7NWbPoO1MNk5ySU6lhotFoLA1ozUOekYkhVfNKye2begaGlpJzMhFULPkz9fkiqffLUcx+egZAw+GsojJtUoSpSqXJrsMkIC/sg8dgRWtxLRLW3dWMZe8NzwDg7In5QGXJ+40stXjRuHw0lFhwfq0d7zcOYP3RfiaYNrzNxBIAuPshPvsYhH9/FkRe5cjhcDhfEIalyVRbWxv279+PQCCQeWfO8KCP+5BNk5bTijBRWTAZ41NyUoRJy+lbFIGoeuFvQPFgUn9b0XQpOa0Ik3xMGpSib7WUnC+uD53VpmleSeSi7ywiTJpF3/19AIBCqcdcMEoV6wMFmz32+mUZZWqVIkzVKhEm0teNah+rh2ozFiVuMxiBihr2S0tjVmPJREWKzS0spTl/LLs/C+pZJG5jsxvRUBB0FUu7k+u+BZRWAP1O0A2rcxqHw+FwRgNDEkzvv/8+vvvd7+JHP/oRHnzwQbS1tQEAfve732HdunXDMkGOOkSnA4j08qXxYsquhikuJadEmDRSckDatFxAq/EuEFf0neTDpNVLzu/VbCHi1YgwwS/VL5ksIDod8oyyYEpvXpmNYHIFmOBymFVqmNwsImOy25WVe8lpOUIIUChFmVx9GccDtCNM6GhFlb8HANDuUxGDVazeiLa3ZDWWzOG+APoDUdgMAqaVs9djapkVFr2A/mAURz/dDrj7gcISkMuuAbnqRjbOh2tybvvC4XA4pzqDFkyffPIJnnnmGdTV1eG2225L2FZfX49PPvlkyJPjZEAWO2mW+sur5Ayqq+TUfJjkGiaVDzudHpBXX6URTJoeTECcrUAOPkyiGBN3KsjRG9UIk1y/ZGOu4XZj5vYoNEPRN6UUA0EmgApU2qJAaq9C8h0oliJQqivlHCwSRLOIMEVFinY3E8VV9tT0He1qQ4UsmNwq4lmOMLU3Zxwrnj1dLB06rdyq1KQZdAQzKthr8/k+JsDIuReB6PUgZ5/P6tO6O4DD+3Iai8PhcE51Bi2Y3njjDVx88cW49957cemllyZsq66uRktLbt9mOYMgg3llNjVMJG6VnEnDVoAQkrHwW8vlG0B640q1lJzJDMh1Pxor5eSUnFZbFFiZh4Ac8VGrYSJ5klmlR7u/my8sQp5uvprL9wCLMMFeoNQ4OdXMK+U6JmdmwdTnjyAiUugFoMSqUu/U2YZKPztPh1tFXFaOAZB7hGlfN4sITilLrEeaXckE6J4gixSSc+aznyYzyOxz2Vhym5ZBsqfLh2c2d+DN/X2KVQWHw+GcTAYtmFpaWnD++eerbsvLy4PH4xn0pDhZksFaQHOVnCx64lJysea7aT6gMgimoFT7lK6GKdlWwKplK0BIXOG3N2W7jLzcXc24kvpiK+SADA14bVJKzqsdYRqQxJZZT1Svk7pd7IHdoaTsnGpmj4XZC6YeH3t9iywGpYdcwphdbaiQBFObimAilXKEqSXrVJlIaUwwlVoTtk0ulfrX5dUgancANXWxjdPOYnPa/XlW46jxaYsHP3+nGWsOu/DXz7vwnx+18hQfh8M56QxaMJlMJvh86t/8+/r6YJPSIJwRRK+dktOsYZJFllGlNUqUQlT7gMrQHiWQMcIkC6ZE48pARFQfT6ljSl/47dVqjZIUYVJqmIIqES1plRx8Xra6Lg2yYMo3pVlgGpeSkyNM/QGV88kRpixScr1SSq/EmmbMzjZUSik5VyCqRN0UyqtZvZvfy3rYZUHbQAjuYBRGHUnoXQcAYwpMsCCKgN6E41POTzTKnDKbRQZbm0CzEIPJBCIint7cDgpgSqkFBoHgk+MevN8YE7LihtWI/ujriP7rNyHKK/Q4HA5nhBm0YJo0aRL++c9/qn7ze++997gFwYlgSBGm9MaVQExsJZAhwhQIZyj6TrYViEujBTRXymWRklMr+pZdvi2JESa3WoTJGmf97U2flusPaNQvAawIGgDsBco+aik5WTBlU8MkR5jU0nE0EgZ6umCLBJBvZPe9I6mOiRgMbAUbALQfzzgeABzpi7VhSfbU0gkEDYEOAMD+qumJY9nzY2aZB3dnNVY8qw864QpEUZFnwMMLa3HjdHaflu3qQVSkELd8APrKs6w4f8AF+sJToNs35TwOh8Ph5MqgBdNXv/pVHDp0CPfffz9Wr2bLiLds2YLHHnsM+/btw3XXXTdsk+SkQa8tmLRrmFJbo5jiIlHaXkzqEa1ANH2EiUYisXlKq+SMOgL5s1i98FuqnUmTkqOUxlJyWjVMNjnCxPZRtRXQ6SDIK+U0BFMswpRGMEkRJuQ7UCil5NT6rxHZvDKblJyXHV+sFmHq6QSoCJjMqLSz16ddtY6JpeVoR2vG8QDgmNTot64wtQUKjUYxqfsgAOCAsSxlu2JceSS3wm9KKd457AIAfHVqMQw6gsWTimA3Cmhzh7G12QX66n+xMRZ+GeSiKwAA4it/Ac3QFJrD4XCGyqAF0/jx43HfffchEAjgpZdeAgCsWLEC7e3tuO+++1BbW5vhDJwho6Tk0kSYxCwiTHF+TjqBQNY6Wm7fNEMNk1bjXQBKDRMhJGYtoBphYpEhmiYlF4hQyPXANmP2KblQlCor+uIR8iW3b42VcnJ6TU0w0VAwVqeVXwCHRRZMGim5/r6M9Tk9ckrOpiKYOpmVB8oqFRdwtZVypLSSPehu1xxL5phLFkzm1I3txzHe1cj2C6S+1rJgojmulDvQE0CbOwyTjuD8sawI32IQcHEde13Wf3aYRfBKykG+egvIDbcxI05nD+gn63Mai8PhcHIlJ6fve+65BwsXLsT8+fORl5eHadOm4YknnkBHRwf6+/tht9tRVVU1UnPlJJMhJafUMAkqAkYWWcbECIJRJyAiitrmlelWyYU1apjk+iWdHiROpJkNArxhcVD95OR0nEBiK/wSd0gs+rYaBAgEECmLMiUXbQv5DqDteFYRpgIVDyZFaOn1gMUGhxT1cKmm5KQIUyTC0kv2grRjyim5YrWUXE8ne1BaibI8tr3Lq/J+KGOCiXZ3pB0nnkYnE7jj1CJMjYdQ52FCrWUghGBETLyXcoSppQk04AMxW1POocbHzez+nTfGnlCTtqC+AG8dcGKL3wq/zgTroutA9HoAepDLrwV99b9A168EveiKnFu/AMy24ZWdPfjnISdMegE3TCvGFRMLcz4Ph8P5YpNThMnj8eD555/Hd77zHTz55JPYuXMnAKCiogKTJk3iYulEIwkPqhJhopQqNUxqKTkqp+QMiUaIxmzMKzP4MJnUapiSLAVkNM0rM6Tk5IJvm0G9FQtNijARQjTNKwVJtFAN80rZg0ndUsDFftodIIQoKbmBYBTRpKXxRG+IiaQMaTnNou9e5vBNiktRLgmmThXBRCTBhK7MESaXPwJXIAoCYKwjVTCh6TCKg/2wIwyRAs39ie8H4igGistYqvDowYzjyWxtY6/znJq8hOfrCk2oNAMRQYcdJWeAzLkwNta8hSxi2X4caDyU9Vjx/NdnnXhtTy88IRG9vgj+tKUTqw7EiuNp02FE//RrRH9zH8QNq0FFlfcqh8P5wpOTYHrmmWdw//3345xzzsFnn32GRx55BHfeeSeWL1+O7u7sO69zhgmNVXLx3jXazXeTBVN6awGSqehbo4Yp2VJARrs9irTSMk1KzqsUfKepJ5KLvq2xFZtadUxKSk7Di0krJQfFUoCdx27SQSAABdCv1r9OjjL1p3f7johUKRovVYsw9Un/74rLUCa1Y+nypI8wobsj4we+nI6rtBvV69GOHQIBUG9l7xG53ikeUtfA9m0+ojmWTJcnjJaBEAQCzKxIXGFLCMHZYSb0Phs/P+H1JBYryIxz2FhbPsxqrHh2dnjx9iEXCIDvn1uB66eyVOnzW7vQ7g6BHtgF8fGfAVs/AQ7uAX3lWdCXn+E2BxzOaUhOgokQgpkzZ+Luu+/GX/7yF9x6662w2+147bXX8IMf/ACPPPIINm7ciEgaI0XOMCOLHZX7HS941Iu+U20F4vdVq/FRIkzhTKvkBiGYVNujSBGmdCk5xVIgzds4KcIExFsLqAkmB3ugGWGSBJPKKjkaV/ANsJowWVipp+XklXLpBZPTHwEFoBfUx0QvE0ykKBZh6vaGU20aikpZE95wKGM7Fjkdp1rwHYkArY1seymrMzrap9JDUloph6bsBNO2diZuJ5VYkKciRs9uZCvhPreMSbk2MucCNrfPPsop+kMpxQvb2P37UoMDl01w4GszSzCr0oawSPHiZ+0Qn/sdu2dTZ4Nc+3WACKAfruU1UxzOaUhONUzxWK1WLFq0CIsWLUJzczM2bNiAjz76CE899RRsNhvmz5+PW2+9dTjnykmC6A2sxkelhkmuXyJAyrJwAEqUiCRFmExa7VEyRZiyKfrOKSUn+zCpCyav1go5QFUwaZlX6uQUmYZ5pRxhKlDzYZIsBUhcPZLDrIcrEFVfKecoYq+fRkquxxurXxLU6nOklByKS6V9gLBI4QpEE5oDE52Opcm62lnhd1FJ2jHlRr81BSp967rbmUA3WVBXXQQ0teOoWoRpbD0oso8w7ZbasMxKii4BLIo2+ehmmCuvRD9MaHQGE72hpp7FvL1cvcDxY8DY8VmNuafLjyN9ARh1BDdNZ/eDEILbzizDD1Ydw6Y2H1pCAmrKqiB8734QkwkiAPrGy6DL/xt01tyEaFe2UErx3rEBvH3IiUCE4tyaPHx1anF6w1cOh3NKMCz/Q2tra/Gtb30Lzz77LK6++mp4vV6sWbNmOE7N0UKjl1y8B5NqIWyalJxWexQlGpXGVkCue1KrYaJyhClZMGWRkqNpBJNPIyVHKU0p+gZiq+lUa5ikyBDVSMnFir41apjkSBWQYaVc5pScvEKu2JIq0GgoGPN9KiqFXiDKflppOZqhjkkWTNV2FcHU2sR+Vo1RREujM5Aa0ZIjTF3tMcd1DQ71svfHpFJLyja6dzv0VMSUMBOHsriSIQYDMHkG2zcHh/GVB9h9X1BfgPy4Iv5ahwlzKsygIFhVPR/CDbeCmNiXBbLoOtabz+MG3bAq67HieWFbN578pB0HegJocgXxj929eODdZuX9LG5+H9EH7kD0u9ch+ut7BuVnxeFwhp9hEUwDAwNYuXIlfvrTn+LNN9+ETqfDOeecMxyn5mihsUouJGp4MAGxlFy6ou8hrJKzaEWYklNyGhEmMpSUXNDPGvcCiREmjX5ysRom9QhTKCoqBpt2rT5y+fERpixScloRJtm00qbSQ66PuXvDZAZsLD2mFH57VFqkZGkt0Cr5OFXlpwom2sYa+JKqWlTbjTAIBMEoRWeSQCN5+SyiBQDHj2qO5w5GFSuECUUqNgZ7tgEAphWw125XZ+r7geTYksUTiuLTVibkrpjoSNl+lZdZInxYeSaCU86KjaPXg1x1Axtr3f/l7P/03rF+vLGPCbUbpxfjrvMqkWcUcKAngD9u7kB01XLQ534LdLQA0Qhw9ADE3z0A8dOPchqHw+EMP4NOyYmiiK1bt2LDhg3Ytm0botEoqqur8fWvfx0XXXQR8vPzh3OeHDX00geayiq5sBJhSqOJVYwrAcCYTUouzYdEbJVcelsBkkvR91BScnJUQ6dPuMZYhEmjhimNrYCcjtML6mMqfeTiI0wa/eSUlFwWESbVFXJywXdRqRJFLMszAF1+bWsBjQiTJxRVrrNaQzChqhY6gaDWYcKRvgCOOQOKD5TC2PFAbxdo0xGQSdNTziVzWKqBqrQbUoQopRR0P1uNO31iJbAH2NPpQ1SkCX31yLSz2L08cgDU6wGxJa60S2bTcTciIkVtgRHjklYCUkoxdfP/obzuG+i0FGNTi0fxggIAcs4FoG+8zK7t849B5i3QHEvGE4ziuc9ZlOz/TS/GTTNKAQBVdiPuf6cJHzW5ce6eHTgfAPnSV0HOuwR05TLQLR+APv8kaFklSJbpxuTr+bDJjXcOu9Dnj6C+0IwlU4oS0prU52HpWkdRrDE0h8NJIGfB1Nraig0bNuCDDz5Af38/zGYzLrzwQixYsAANDQ0jMUdOOgzSy6cWYdKwFGA7pLZGATKl5LSNKzVrmAJpapg0i77lVXLaKTlt00pbQkpSq4ZJthVIF2GS03F2k149zSn3kbM7lKcKLVKESSslp1GE3avVFiWufklGWSmnZi1QWslEhYZgapPScYUWvXp/vtZYhAkAximCKYh5SV61pHY86NZPMhZ+H+phYnpicWo6Dp1t7PUwGFE/ZQIsBxrhDYtodAUxPu4DnxSXApVjmL3Avu3A2fM1x5R70104Lj/1tTy8D0JXGy7J245Xaxdiw9H+RMGk04FccDmrZfpwDZClYFq2uwfuYBS1BUbcMC1WQ3ZGqQVfPaMAy/b142/jr8ScqbUwX/dNtvG2H7N09s5PIb7wFISf/07yoMqOqEjx5Mb2hF58LQMhfNQ8gO+eU4HLx5hAX38B9KN3YotHpsyCcPN3Qcq5TQyHE09OKblf/OIX+PGPf4y33noL5eXl+M53voM///nP+O53v8vF0slAiTClpl+UCJNawXf8MYbED2LZViDXlBylVKlhMqdLkQFK410ZzaLvDCk5r1ZKzitFmJIiDVo+TDolwuQFFVMFjtJHLl1blLg+cjIOjfYoitu3u5+tPlNBO8LEUnKkKNaeJCtrga6OtMvilfoltehSOAx0Sc7ikmCSV9I1uVQKv+WechkKvw/2MjE9sTg1HUeP7GcPxk2A3mjE1DL2ntjVmVoXRabMYscc2KU5nicUxW4prTd/bGokXF4Bd2Elu5c7O30YSHr9yPmXAoIAHN4HKolILQIREe8cZu+PpbPLEqJjALCk+T0UB1zoNhfh7ZnXxsYRBAhLfwjk2YGWRtB338o4Vjx/2tKB9xsHoBdYCvDBS2owd0weRAo8s6UD6599AfS9t5lYshewJs17t0N85Megh/fmNFY8Ta4gXtrejd9+3Ibnt3bhQE+iNQgNBUFbm0C72rmvFWfUkFOEqbOzE4sXL8aCBQtQXV09UnPiZItWDZNWHzkgJpiSUnJywbaacSUxmliEQkUwhaKxNiWqzXcDaWqYJLGj2nxXScn5QSlNiQRoRpj8UoTJkriKSdOHSRY6VGQpvbzED1OtPnJUjMacvlVScqo1THn5LGUYjQADTrb0Pwml6FslwqSskItb8abp9l1SDhDCxKu7P2GeMpoF352trC7MYgMKmdiTncDVvJgwtl45jgYDKelYgAltueBbTTDJ/ejIeOYePrXcis/avNjd6ce1kxN3JZOmg777Fuh+bcG0o8MLkQI1+caUNCIVRdAdWwAAVXPOQX2jCUedQWxq8eDyCY7YWI4iYMY5wPbNoJs3gFz3Lc0xP2oagD8iotJuwOyqxPck9XlhXPcG/l/hVPzxjBvwfwcHcNXkEuXLC7EXgFz3LdC/PQ26ejnoBZdntTpv7b5OrD3sgkCAn86vxrljWJ3b7Eob/vvzTrx5wIVnii/A2LLDGP/1b4JMngna3QHxr78DjuyH+PtfQbj3MZDqsRnHkomIFM9v7cKqA07ES/I39vXhvDF5+N5UG+yrXwHdtCEW5S4qAbnsGpCLr8opepaMbNbLWjzl7vjO4WQipwjT3Llzcc4553CxdKqgrJLLrYaJRiKxguiklJyWcaVWhCm+Wa9JrW4qmGGVnFZKjoqJvegktCJMNE2EyS6JK7Wib2IwxOanslJOy4MJXg+bJ5AgtJSib5WUHBEEoEBqwaFS+B2OUkVoqfWRizetlCm3MQHQ5Y2k+hUZDDFRliYtJxd8a9cvjVHE6ziHWRovDG+SCCX5hUBBEUAp0NKoOl6Pj7mKCwSoV+lbJ/ejI+PPAABMK2Miem+3L8U9HQ3TmCDsaAF1pS+klx3Fz6xSER3HDrLUqsUKNEzDvFomMj5uTn0/CHMvZnPc8mHGKMk/D7kAAJePd6TYQ9CN7wJBPy4UelBs1cPpj2D90f6Efcj5C1nK0ecBfecNzbEAFtF87J0DAIAbphUrYglg1gnfal2Ps3v2IiLo8eTZ30ZoIqsxI6UVEH70K2DiFMDvhfjsY6BpIrzJhKMifvVeC1ZKYuncmjwsnV2Ki+vyoSPAJ8c9uPeNvejavJmJJauNLTrp6wFd9leI/3m/5uuWjk5PCM9u6cAt/3sYNyw7iBtePYCf/LMRbx90IhyloK1NEN94GdE/PoroHx+B+NoLoIf3cfNRTs7kJOcPHjyItWvXoqCgAHPmzMHcuXMxZcoUCGq9yjgjj9waJdcapvgUXlJKTokwaRlXhlLFi7y/XiAp6QYg3lYgzSo51fGMLO0hiiwtlyS2fGGNlJwUYSLJESYpOpT84R7bIZ+ZbKoUfsc8mDRWyOXZE74ly7YCA8EoIiJN/ebrKGLF2yqF3zHTSqLuLC4JJhInmIqteggk5hCeEpkqrWDFyl3tSpPceNo0UnLJ9UsAqwkrturR64ugyRXElLKkvnG19cCuPtDmI4roiUeOLo1zmFIWC1Cvh9UkAYB07PgiM8x6Ad6QiOb+YEJzYGLLA8bUA81HQA/sBjn3opTxKKVxgim1MJzu2MzONe0sEL0B59fm4+UdPdjZ4cVAIJJgP4DpZ7P3ZG8XcHQ/MGFK6j0DM/Y81BuAXgAWjE/sGUhFUbEnMF7yJSypKMJzn3dhxd4+XDbeofxfIoIOwrVfg/inx0Df+T/QBV8GsadfWLN8Vw/cwQjqC024Pq5eCgBo81GQVf/AnXoLflz+Cxz36bB8dy++PouJaWIyQfje/RAfvgvoaAV95c8gt/4o7Vgyz2/twvZ2L8x6gn89vwpzamIi7WpbP379uQvt5mI8cNadePwcGwqnTgUiYdBPNoC+/gKLaj12L4R7Hk14T6eDUopVB514fmt3QmeDKAUO9bJ7/ubmI/jhtufR4D4eOw4AXfO/wITJEG76Dkhtfcax4unzR/BBYz+2tfvQ7TsGUYyiIs+I6eVWXFyXjyJ3N+iuz1hENhgE8gtA6icBU2aDmFXq9HKAUoooBXQEg+qbyBkaOQmmxx9/HF1dXdi0aRM2b96Md955B3l5eTj77LMxd+5cTJ8+HfohhFSzZc2aNXjzzTfhcrlQU1ODpUuXYvLk1D/+Mnv37sWLL76IlpYWFBYW4uqrr8bll1+esM+mTZuwbNkydHZ2ory8HDfddBPmzJkz0pcyNPQaESYxW8GUfWuUmGBKrZmSU2qq6TggzlYg+wgTIYSl5Xwe1h7FkbhdMyWXRQ2TSGmqGWSeHejpVC38VvrIqTXeHZB6j8UVfAMsoiU3/O0PqAgYqfCbuvqQfOcUSwGrPjUqIYoxW4G4VJ5OICixGtDlDaPLE04Zj5RVslVnKtYCIqVoyybClJSiGecwodcXQaOKYCK19ezDo1ndWuCQUr+k8kFylEVIUF6tmIHqBILJpRZsa/did6cvQTABADljOquZOrALUBFMTa4g+vwRGHVEqYdKuMbtLB2Hmez/flW+EXWFJhxTS8sZTSCzzwP9ZD3olg9A0gimtYddAIBza+xKilZhzzYW7bPYQOZejMv0Jizb3YsOTxibjrtxfnyN1ezzmL9V8xHQtStAvqKeBuz0hPD2IfZ+vOXM8gSRTimF+D9/AagIx8zZ+M75tXjsg1as2NeLi+vzUZMv+U3Z8yF85x6I/3E/EzRnz1da0KjxcdMAVh1k13nP/GqcXR37f0f7ujHuxUfxSAh48JwfoN1YgH8/bsIjkygsBiPIhYtAz5gO8amHgK52iL+5H8I9v2aF/GmIihRPb+5QInHTy624bkoRJpVY4AuL+GR3M17b50KbIQ+/mP093BLYhSvr7YBOAI7sB/3sY+DwPoiP/ivIl29iqxIzfPH3haNYvrsXKw84U/4+trvD2NbuxcvbOnFp+xbc0PgOikKxL10UAEwWkPMuAbnyepDC7FYihqMiPmv1YmOzGwd7/eiQahNtRgG1BSbMKiQ433UA1ce2s8baAR8bp7wKqGsAmXUuSEl5VmPF4wlGccwVQLc3gohIYdQRlNsMGFNgQp5Jx7oadHewbIOgAwocQHE5i2J/gclZ3ZSVleHqq6/G1Vdfjb6+PkU8Pf744zCbzTjzzDMxd+5czJo1C0ajyrfUIbJx40a88MILuP322zFp0iSsW7cOjz76KJ544gmUlKS6F3d1deHXv/41Fi5ciB/84Ac4cOAAnnvuOeTn52Pu3LkAWOTsySefxI033og5c+Zgy5YteOKJJ/Dwww9j4sSJw34Nw4bSGiV9DVOmPnLJ31JMWTXfVYswsT8gad2KJcGUYiugVfQNsNSIz6PagNerFWFScfkGYjVMFCxClZcktkhePvsG6nGnCBitPnJULvhOqgvSCQQFJh2cAbZcP0XAOIrZH1OVVESsfimNQItGWAROXm0nUZbHBFOnN4yUrxFxhd8p43kjCEUp9EKseDwB2YOpckzC03WFZnze5kWjmuN3rez4nUkwZU7HyUwrs2Jbuxd7unz48hmJ104mTQdd+4ZiRZCMHF2aXm5Vvhwo43W2sYiWTgcyPea9NK/WjmPOIDY2uxMEEwCQORcywfTZx6A33J5SgxOIiHjvGBPfi1T8nsT1K9l5zr8UxGyBGcCVDQ4s29WL/93bh3m1duX/KCEEwtU3QXz630HXrwS97BoQlTq0v+/oQUQEzh1biJmVtoTUE938PnB4L2A0gVx/K+YW5uHsKhs+a/Piz1s68fDCWLqVTJgCctk1oGtXQHzpjxAeehrEmhqVa3eH8IdN7P30lSlFiWIpHIL4zK8Bdz9Kaurwb4un4N4N7TjSF8RvPmrFzy+qgU4gIGVVEH7yKMT/vJ+Jpt/9gommpPc2wMTS7ze1471jAxAIcNtZZbiqoVCZt7VxH6565RFcHIziTzO/gY35E/Ff1tnocBTi1jPLIFx8JehXvgXxf/4L2LqRrXZsPATh1h+BWKwp4wHAwR4/fvtxmyJYJhabcUldAc6aUIXetlYc2/A+PvSYsb+gDmur5uKDirPwVVMnvpzXD2NfJ+i+HczE9b3VoB+vA1n4ZSbS0tSiRUSKd4/0Y9nuHqX5djzekIh93X7s6wb+B2MwLRTElR4nzuk5DB0oaNNhYMsHoMueA8afAXLxl0DOmq8paAIREVtaPFL0zAu1oD+hFOP8nZjZsw9n9e7HGQNN0MmlCHo9MKYepGEayKw5QP0kECHNAhmwL2hNriC2t3txqDeAdncIvX4m0AgAh4GgmPpRF+jGpGAX6tv2oNTdCeEr3wLJsAp2pBhSOKioqAhXXnklrrzySrhcLmzZsgWbN2/GE088AYPBgFmzZuHHP/7xcM0VALBy5UosWLAACxcuBAAsXboUO3bswNq1a3HzzTen7L927VqUlJRg6dKlAICamhocOXIEb731liKYVq1ahRkzZmDJkiUAgCVLlmDv3r1YtWoV7r77btV5hMNhhOMiO4QQWKRVXcMZKn1zfx92ftiBC2qsuKguMQRPDLHWKMljyvrDqBNS5xO3Qi5FMMX5MKUcJ6fTQsGUbXINk1ltPCBWw2SxJmyXXbr9EVH9OPkPWMCfsJ1Sqogsm1GXeqxfbrybl7DNqNfBpGNmi96QCLvU4kTZR6o/It6BlHO6FZfvVFsB4u4HhVSgm7TNYdHDGYjCFYimHid7MbmcKdt6lRVyqa+TEl0qLIGQ9CFdbjNgN1gdU8p4ZVVMwHS3p2yTo0uVdiP0yWIiHAZ62Iciqa5NOFaO8hxzBVLnOXYC+9naBEQjSiseQgiiIlU8mBpKLKnHHmUr5MiEyQnbplVYgR2stYl8LoWGaUxEdncAzh6QpEL6rVLPurOq8lLGk4u9ScM0CLZYOmn+2Hz8XUrLeUJiolfUlFlsdZm7H9i/A2T62Qnn/KjJrRR7z6hItLignW3A7s8BQiAsuErZtnhSEVbs7cPhvgD2dPkxPb5dzMw5wLgJQONh0LUrIFyf2H7qmDOADyQLge9fNAGExr5o0IAP9LUXAADC4hshSBGcb59TgZ0rj2Jnpw8fNLkTLBSEa7+G6I7NQGcb6PLn2Yq9OEJREY9/2Ap/RMSUUgu+PqtMuQ5KKejfnwWaDgM2O3R33o/qEjseuESPn7/ThM/bvHju8y5855xyEEJAikpAfvIoov9xLxNNT/wbdPc8mtBqKCpSPPUJs0kQCItmxUfhxM8+gvjcb4FIBLbxk/HTb1yMFc1hvLitC2/td6LXF8GP5lXBVFgC4Y77IH70DsSXnwG2b4b46L9C9737EorcoyLFir29+PuObkQpUGrT47vnVODs6jwIgoCC5t3o+f2vcIarD18iBPsuuAEvFp6Lg/3Ay+EarAvX4daLyzHnazbgwC6Ib74CHNoL+s/XQT96B8LVN4FceIUitKMixQeNA/ifnd2KOCuy6HHRuHycWZ2HamczdBtWou/gIRy0j8GWkqnYVjQJuwsnYHfhBJQZKa4sCuJS/xHYDmwDPbCbRdSO7Add/jzIhYsgzL9MiTpFRIptbR580DiATcfdCbWo5TY9KkgARlcPAh4v2s1F6DEX4pi1AsdqK/BG7SWwRQOY5WnCWd27cWbnLuQfOwh67CBLeeblg0w/C2T62SBTZoPk2dHtDWNHhxc72r3Y3uFVvoSq4QkBLTBiB6oBQzUwdjbK/b24sTOKS09SOnLY8mcOhwOXX345Lr/8cng8HkU8DSeRSARHjx7Ftddem/D8jBkzcODAAdVjDh06hBkzZiQ8N2vWLGzYsAGRSAR6vR4HDx7EVVddlbDPzJkzsXr16rRzWbFiBV577TXl97q6Ojz++OMoLU0fRh4Mfbv6saXJiVnVDlRWViZs85dVoAeAAUBF0jZzcwhAJwrybCnHhXz96AQgmC0p28r6CIAOQGdI2Ra1mNAGAKEQKsrLE0LYR/29AJqQZzGmHAcAbeEQogBKqmtgittu8YcBHEEoSlFaXg59Uli8s8CBUAtQaDHBGnecNxSBSNkH6oTaapiTPIO6oxEEABRUVSMvaT4F1qPocgdhyi9EZUWiCLWVV8IDwAYKR9Jx3ihrC1JfVYbKysKEbS4xAjcAW0UVCpOOKy/oxDFnENScl3JvvHXj0QfA6POgLPn13ctC+mPLUl9736Fd6AVgqqhOOW58ZQDvHu2HR9SnvvZTprPXvqczZduH7S3s+NL8lG3hpiPoEEUQqw2VZ0xN+OA/x5gPfNSK5v4QyisqEtKHtKICbXn5ED0DKAn5YRzD6p8qKipwtMcLf1iE2SDgnDPGJrz2NBpBa+MhAEDZ3AtgiJtPSZkI07vHMRCMwm/Mx/iSxKhH58QpCB3YjYKOZtimxv7ve0MR7O1m75krZtWhsjAxmtC1dxuCAAouvAz2uPEqK4GJpV041O3BfreAq8cl3hvnxVfA89YymHdsRvHlX07Ytv7dVgDAV2fXoroq0dfI+dYr8AAwn30+SmeeGRsPwNXTfXhteytWHfHi8tkTEo7zf+v76HnobuC91Sj7xnehi0vvPPbxDlAAl51RhjPK7QBiwq//pT9hoL8P+soaVHzzu4p4rawEbp9H8cyHR/H8tm5cOXs8CiyxSETwXx9G173/AvrRO3AsvBIWqdkxADy29gCOOYNwWAz4zVfORJk9tojEs+o1OD9eBwgCSu/7NcwzZivj/cqUh5/9326sPujEpOpi3Hx2rXKzI4/9BV33/guibc0Qnv53lP36WQi2PEREEb9cvQ/vNw5AJxA8+uWpWNAQq3Vyv/kqXH/5LUApLOddjKJ7/h2CyYzvNwAN1Z345dt7sbHZDXe4HY9dM53N9fpvIjjzLPQ+8lNEO1ohPvoTFP7wF7BdfAV6PEE8vGovPmtm6c1LJ5Xh/ssnwW42QPS44fzLb9HzLosQ6qtqUXT3v2HM1Fm4jFK8vbcTf3j/MDo8ITz6fgvOHVuIHy+4AHWXLEJgy4dw/ffvEWlphPjKn6F//23kL/0BNhZNwX9tbMSxXiZyC60GLD13HK6bXgG69WO4X30Gwd1bAelVPWNaA7721QvgrG7A/+5oxf/uaEOXP4wXOsx41TAdV11xORZ/24Lqre/A//briPZ2ga5cBt/bK3Bw9hXYMuYcfOSzoD8YCyVV2w1YWBDG/M5tKPvonxD7nco2fc04+OZcij01s/Bp0IZPml3o9wMfF0zCxwWTQCZ8BVNsIs70NqL4yA6Yff0IHelDT8tmHP+gCfuLG9BuSPx7ayYipkd7MbX3ICo7DqIk4IJRjCBKBPSb8tBdMwVNFQ04qCvC4YABnZZilMweq/oZcyIYkYKjvLw8LFiwAAsWZGfoli0DAwMQRREFBYmFkwUFBXC5XKrHuFwu1f2j0SjcbjcKCwvhcrngcDgS9nE4HGnPCbAo1OLFi5Xf5Q+Q7u5uRNJ46gyGsJTKcg4MoL09se5EdLMP1LDPl7Kt18VSRJGQP2UblX4XdfqUbX6pdsftC6QeJxduA2hvbkpIr3V0s+N0NJpyHABEpZqiXrcXJG57OO4bzbHmtpRO9VGd5JTd1or+uOPkprQ6AvR1d6ZECyLSqrP+UATupPlYpSEa2zpRKH0DJ4SgoqICPiLZDnS0wZ90XJ+HpZwi3n60tyemJaNtTGz49EYEko6zCOxbVGN7D9qTShdEsMkEu9pT7ltTN3sNLTSY+tofPggACNkLUrbZKJvn0a7+1NeQsPspuvvRdvhQgiP23hZWRF5kpKnj7WTtSWh5NTo6EtN5BqnGIRAWse1gc0pLFVozDti/E91bN0NnK0BFRQU6Ojqw8TD7Y1xfaEJ3Z2fiMc1H2fvNYkW33pzwngGASSVm7Ozw4b3dTbBOSkzbROvPAA7shnPTBxiIa2uy6bgbUZGiIs8AfaAf7e2xlWjU3Y/o3h0AAHf9ZHiSxptTZcGhbg9W7TyOc0qSIlMz5gBvLYNv43oEjx0BkewwjvYFsKedeSCdUyYk3FMa8CG69v8AAKHzL0u535eNNeN/dwAbj/Vi495jCbVatKYeqGsAPXYQ7S/+CbobbwMA7O70YuOxXugI8NVJ7IOpo4N5btG+bkRffwkAIC75Jjp6ElPAC2uMWFlgQnN/EI+/vRM/OC9O3BWVg1x6Neg7/4eeJx6C7qGnQewFeP9YP17f0QYC4O7zKhD19KFdyoTTQ3sQ/fNvAADCdd+Cs2IsEHeNk+3A0jPL8PzWLjy54TDMUT/Oq5U/THXA3Q8B/3Efwkf2o/W+74He9Uv87rM+fNzsho4A915Qjcl29reGilGIy19QVg+SS65E6KZvo7Mv9mE/3QE8tGAMHnm/BbvaB3DzC5vwr+dXY1alDbAXAT//Lchf/hN033b0/uYXWLlxD/7Ldhb6QyJMOoLvzKnAwvoCuHu7MLD5fYj/+yJb2UoIhMuuBb32a+gzmpRrnF0E/HFxHZbv7sEb+/qwucmJm17YjEUTHZhfW4Xan/4W5JP1aF+/Djt0ldjwTidarexvoU0QcW2FiMWWLpg/3IDupz6Jufrr9CBzL4aw6DqEq8agDwC8TiyZYMWV4+rxfuMA3trfhyZXEK9vb8Xr2wGLYTzKL7gfpoAXAx4/OnV5EIkAOAFAhCPkxvl9e3BB53ZMdB5VShFEALA7QM69EMJ5l4DWjoeVEJwD4BwA3zmrGAd7/fis1YPPWj045gxij1fAHtQD49UL6QUqYrz7OGb2HcJM5yE0DDTDQOOiTGPqQabMBDljBsj4ySCS8XBFRQWOHm/Fvi4f6ouNqp8xQ0Gv12cV7BiSYNq/fz8++ugjdHd3I5RUCEwIwb/9278N5fRpUUvdaKXBUkLvUk5f6xg13594DAYDDGnywcO5XFUuCQpFaep5laLvUMq2kJSANggkZRuVC7ANxpRtRiG2Si7luLgCcRoMxGqaEKtBMuoF9euXxqQmM1tmHnd9eoEgIlL4wlHYjEn1SNKHD/V7E84r+yjJKb2UMb0xp+/kbXIdkzsQTT3Oxv5oU89AwraoSOGWxrQbU69RrmGi9vyUbYWStYDTH0kdT7YVcPWlbJNFYbFVnzqe4sFUmrKtXLIg6PSEU8czmthS//4+0K42YFysRq+1nwmt6nxD6njSajVSUZOyTSDAmALZ8duPSnvS/4vaemD/TtCmI6Dz2bGUUhyUzAwbii0p5xRlw8q6BoCkvoenllmxs8OH3V0+fKkhMdpHJk0Hffs10P07IYqxVO/nrew9cVZV6ntC3Pkps4WoqVO9p/PG5OHvO7qxo90LdyCSIOzp2AlARTXQ0Qrxs40QzmflAmukwutza+woMOkSziluXM8c7MurgckzU8aryDPgvDF2fNzsxoq9vfjRvMTolHD1TRCfegj0/dUQFy0B8h14YSt7T1w+waG8BpSyvxvi//6NpeIbpgKzzk0ZTy8Ad8wpx8/eacY7R5iz+bTyWASOLPkG6O6tQPtxRF/6I9pu+hH+uJkJ569OLcbsuFop2tfN6paiUVZrcvm1qn8TrjmjEO3uEP55yIXfftyGXxgEzJTTjxU1EH70MMT/vB/+xiN48pWP8Kl5DPQC8NMLqnFuTR67Nq8b4vNPAXI69dqvg1x5fdr3zG+vGIfHPmhFoyuIf3u3GXPH5OFLEwsxvsiG8Hd+jj2r12F1F8FeQz0QEjFOHMBPKj2o7u6AuOM46Gcfxiw5SitRds+v0FdUrtzneMx6gm/MKsWl4wvw/NYubG7x4O2DLrwtFccDY4HJtyn7WyN+LG75CF9u+RC2iPT3UtmYB3LhIpBLrgKRfNdS/nbrCC4bX4BL6/Oxq9OH1Qed2NHhgy8sotEVAmBQPjOKSQhne45i7tGPMa3vUKwOSRDYIosps1h6+YwZILq493rcmAIBziix4IwSC74+sxQ9vjA+b/Vid5cPrkCERY/1AvJNOowxRlDv78SU/qOwRbqAYj9QWgPYJgMlZSA1dUDt+JSVn/HjWfQCZlfaVK/9RDFowbRhwwY8++yzyMtjaYZk8TASF5Sfnw9BEFIiP/39/SlRJBm1SNHAwAB0Oh3y8vLS7qN1zhOJ7NQdVlu1Jgsm1ea78io5lYLouKLvZEwaveSIILBjwqEUL6agxio5Gg6zAmUgxVYAYCvl3MGoYhOQQJx5ZTw+Sbyo9pED0hZ9AzFrATXzSuRJKYwkWwF33L7qjXddAKBahFtoSd9PTnH79ntTzB0126IoHkyp34pk88oeX1jdyqC0QhJM7SBxgkmuYapSM62U0nVIKviWqStM3yIFY9i3TZrUhFer4FteIUfqJ6mOJ/sx7en0pX65mTCF/d/o6wE6WoFKJvK2SeGP2ZUqdgLbJTuBWeeqjldTYMLYAhOa+oPY3OLGwvEOZRshBGTuJax4eNMG4PyFmsXelFLQ9cxKgFxyVdrVWUumFOHjZjc+bBzA12eWojS+EH/qmUD9JODoAdB/vo5PzrsBB3sDMOsJbpyeZCNw7CDopvcAAMINt6X9Iji5zIpFExxYc9iFpz5pw2+/VKcscCAGI4Tbfwzx0Z/At2Mrfu3Yj4BoxrRyK26aERuPej0Q//DvrKZrTB3I0h+mHY8Qgm+fXY5ubxift3nx0Prj+MasUnz5jCLoBQIypg6Hbn0QT2/pxHFzOQxiBPeW9OJsazFotxd052egby8H+p2A3gByy10Q5lyoOpZMpd2I/1g0Fi9u68Lbh1zYdNyDTcc9cXuMBxyAgUawpGkDrmveAKMYSTDhhMUKcsVXIFx6NUzj6hIiZ+nGvP+iGuzo8GL90X7s7PChT/JXsxkFTCq24LwKI+b1tsEaiYDSGvY31poHUlULMu1MZklgMmmOE39fZ1TYMKPChqhI0TIQQp8/glBEhMUgoKbAhCKLHsAMUPHL7G+X38f+zxQWg+jVAwGZKLEasGiiQ3VxA2MsgFN85XkGBi2Y3nzzTZx33nm4884700Zahhu9Xo/6+nrs3LkzYcn/zp07cc456kteJ06ciM8/T+xgvmPHDtTX1ysWCA0NDdi1a1dCim3nzp2nRLsX2XgykmzSB8QZV2q0RlFdJScJLBXBZNTqJQewCIWaYJLbomiZVgKAUUUw6ZlgUjevlAVT4io5zRVyQKz5rsoqlDyNBryK6aTs2i2h9JEzCqo+U7JgSrYVAOIa8Kq5fZstzP08GGA95aT+XeEoVcwuVduiSBGm+LYoMoUWPYw6glCUoscbRkWSACJllaztRZx5ZTAiotvL5qdqKdAhRZgq1U1r5Qa2qi1Sxo5nHzjHjyktZ8JREY0ujRVyx7QFU0OJGQaBwBmIos0dTpgzMZmY8eK+HaB7toJU1qBlIIQubwR6gWB6RWLtEg0F2fJ+pBdMADBvrB1NO4P4uDlRMAEAOfci1pD3wC7Qvm585DQoxd7TyxPHw55tQEcLYLZoNu6dWGzBtHIrdnf68Nb+Ptx6Vmx5OFsxdzPEJx9E6P21eMnILBSunVykCHSAmdSKf/sjO+a8S0DGJtZDJfOt2aXY2elFuzuM337Uil9cXKP8DSK14xG+8dv4ze4wWkUzioUw7jm/Svn/QJ29EP/4CNByDLAXQLjz56ru7vHoBIKfXViNP3zSgQ+aBvDCtm78334nJhab0esL40gfAGs5CsMe3LPrRZwx0ATxtaSTVI6BcMvdIHXZrWg26QV8+5wKLJpYiNUHnfi0xYNe6f9mTb4Rc8fYsWhCAUo7BNCtVtb6JhoBKSkDGqaBnDkPxKyySCEDMytsSgQtrKxijv/7VQ5cMLxlLDqBYKzDhLEOdbFFBB370sYbLmfFoAVTd3c3brnllhMmlmQWL16MP/zhD6ivr0dDQwPWrVuHnp4eXHbZZQCAV155BX19ffj+978PALj88suxZs0avPjii1i4cCEOHjyI9evX46677lLOeeWVV+LBBx/EG2+8gXPOOQeffvopdu3ahYcffviEXpsa2UWYUj+IFeNKNRPJsPShpmL7IEeYVHvJAUwwed0pztsBLVsBeV+9QbX1geLFpLaONW6VXDyKaaWKBxONhGOCTi3CpNFPjsiCKTnCFIg13lUlja0AAOnbnLpgIoSwP1adrQmCqc8fBgV7/dVNK6VVcioRJoEQlNkMaBkIocOTKphi1gIxwdThYePZjELKeFQUWaQGACrUI0yaLVLKq9j7JhhgY1bX4JgziIjILBqSLQyo1x0br079S4tRJ6ChxIw9XX7s6fKliDwy9UzQfTtA924HLr1asROYVmZJbQ69fyd7vxSWsPRhGs6vteN/dvZgR4cXnlA0wZKClJSzdNfBPRA3bsBqHftCp+bsLb77Jjtm/mVpl7HLXDe5CLs7fVhz2IWrJxclRhunzALGn4GVoXK0+6IoMOtwzeTEei76z9eZgMmzgyStqFPDZtThZxdU4541Tdje4cO/v9eCH82rgsOiR7c3jCciU7CnyA9zNIiffv4X2LvLIZ59PtDbDbr+LeaQn2eH8K//npX5JMBeyx+fX4npFVa8vL0bTn8EW1pY1EcgwCV1BfjGlFoUVF/KXNFbm5ij+5h6kPmXMksGlS9/mRjrMOF7cyrwvTnsC0NKS5UJU9J6aw0VtQ4MnFOfQQum6upq9Pf3Z95xmJk3bx7cbjdef/11OJ1OjBkzBvfdd59SsOV0OtHT06PsX1ZWhvvuuw8vvvgi1qxZg8LCQtxyyy2KpQAATJo0CXfffTdeffVVLFu2DBUVFbj77rtPCQ8mOUIUVmu9IP+RUI0wafgwhdKn5IyKD1MawSSHhdOk5ExafeTSuNzGvJhUIj5KSi6xPYNXKyXni4tGWVLHtGtFmGyxlFx8qkezj1zAH7sf9tQ0rpKS86dZQusoYv3WXL1KwWW8B1NKDZ7PG4u4qfSfA4DyPIMUVUnfhJd2x4q3ZYfvKnuqNxecPez69HqWzlMhuUVKvJkoEXRAzTiWPmo+Csw+Bwfj+seljHfsoDTPqpiAVWFqmRV7uvzY3elL9UeaOgv0NbCITzis2AmounvL6biZczSjBmPi0nIfNg6k1k6dfxnowT04+Ok2HGmYAYNAcGmys3f7cWD3VoAQkAWLkYkzq2yYVGLBgR4/nvusEz+7sCY2HiHoWLwUy7ay99XX8/tgNcT+ZgW2bYL4f6+wfW+4PWF5vhbjCs34xcU1eOS9Fmzv8OH2N46gOt+IlgEmcs16gp/nt2Oirw3YdZwZk8rU1EH43r0gZVXpB1CBEILLJzhwSV0Bdnf50OEOIc+ow7Ryayxidtk1wGXXSFFKktFoMhfS+sdxOHEMWjDddNNNeOmllzB16lQUFaWai40kixYtwqJFi1S33XnnnSnPTZkyBY8//rjmOefOnZsgok4V5AiTekpOevki4ZQ6jlhrFLUaJvYhqvatLD4lp1r4nqafXKyGSWU8uRdVmvC8dj+5WNF3PJptUeT6JYtN1ThNLixX6yen1DBFo0ykSSk9zT5ycnTJaFS9xkJLzGsqEBFT7hEpkL2YYu1R5IJv1XScXL+UZ0+b8qiQ6pg63KlimpRWsPHi3L6VHnKq9UtSW4myqoQC0HgytUghteNBjx4AbToCADjUo5GOy1C/JDO1zAqgF7u7VOqYqscpxe3Bg3uxp5ONk9w/jooi6M5P2XgzM9dXXDqhAH/9vAv/POTCFRMdCWOSOReA/u/f8Hb+NADA/LH2FFd4uvIf7MGsc0HSiM94CCG4Y045fvR2Iz457sGaQy6lRsQXjuLxRgtCuiBm9B3Egg9fgGi7E+Tci0G3fYKeF54CqAhy/kIQqe9dtsyssOGxy8fimS0dONQbQKOUap1WZsH3zq1ATf4k0HOmgb7/T9DWJvZ/beYckHMvSvseyQaDjrDC3sr0zYW1zBA5nJFk0IJpzZo18Pl8uOuuuzBu3DilgFqGEIKf/vSnQ57g6Y4SYdJKyQGsqDrud+0aJknsaBR9ixSIiIAh+W+TLJiCiYJJScmp1jBliDBppOSIxco+3HNIycWvkFPDrlH0TYwmdo2hIGuPIp2jX26LolHwDbtDNUJh0QuKWabTH0FlsigplL5wxLl9x5tWpiALpjTRJQAoz2NjdKpFmEqllFy/EzTgBzFbYhEm1folqeC7oiZlWzx1UouUY840PeUApUWKvEJOrSWKLJiQQTCdUWqBjrB71eUNK9cMSIXYU2aBfrIeu3YfQVicglKrHjXJ13f0ACsaNluASdM1xwOABXUFeGl7NxpdQezr9idcJ9Eb0HvRNfjYxaI8X5qQFF1qOQb66QcAAGHx/8s4lsy4QjNunlGCl3f04NlPO+D0RzC+yIy/7+xGU38QhWYdfmhuAolGQJ9/CvT5p2JzmnYWyNe+Nygz3foiM36zaCya+0Po8YZRaTcmvD9IRQ3IjbfnfF4OZ7Qy6Dhkc3MzBEFAfn4++vr60NzcnPKPM3TknHpYNcIU98c/qZ9cSKuXnJySU6thittfvT0K+6ZO0xR9q6bkMgkmrfYo8jFJKTmlj5xq4930Bd+Adg0T2yG1jkkrJQe3i/1UqV8C2Ie3nFboUyv8lts/xEeY5BVyKi1KaK8smNLXiJRLEaZOT6pgIra8WCRNSstls0KOVGoLpnGSV5Bq4bckmGjzEfT7Q0pEqyEpwkRFUUnJZYowmfUCJkiCa3enL2U7mckWgmzpZGOdqebuveV9ad85WfXByjPpcOE49v54fU9qO5vXi89GRNBjmvMwJu7eEHddUYgv/wmgFOSs83Nu+PrVqcVYNMEBkQL/s6sH//5+C445gygw6/DAJWNQcusdINd+HZCbTVusyP9/t0H4/s8HVd8jQwgrGj6rOk9VTHM4pxODjjD98Y9/HM55cNKgGWHSxb18SdYCmjVMGrYCeoEozWK1G/Bmn5JTDC+HkJJLEUyS2LGoCCaqRJhS61WAOMGklpIDmJjo62YFrBJurT5yA+kLvmWKLHp0eMLqhd9SPzmaIJg0+shJESat5qSyYOpQEUwAWJTJ42ZpuTF1SoRJdYWcnJJLYykgI6+UO+ZM7TWIqrGATgd43di1n32ZqrQbUhsZtzWxGjSjKaXJrxrTylh9z/YOX8rKNUw7G1GTBZvt4wGwnnAJ1xWJgH76EQDklLL6ypRirD/aj8/aWANg2a+o0RnAO41MrN/YuA50Xwto/SRg7ATQFS8DR/azxqhZFF8nQwjB9+aUY3KpBf885IInFMXUMitunF6s9CckV90Auug6YMAFUuBAwZha+NrbT5pnDYfzRWNEnL45w4fWKjkiCKwQNxJJKfzWrmFKL5gIIcy1OUIV88uE7UYTS5GF0qTkVFfJZRBM+vQpOeUbcyCp6FvuI5eSM0QswmRTF0x2k+TmrVb0DSiF39QzoBRha0aYZA8mjaLaQo2VcrEIUyxi0aOk5DRqmIpSm03LyIKJ+VtFYU26T6S0kvnzdLXDG4yiX7q+lHQhoKxYyxRhqiuMWQtERZpgv0AMBqCyFmg5hp0HmQBrUEvHHdjDHkyYrLqiMplzavLw+t4+fNriQTgqJqw+IiYT9s9ehH6jHXkIJxgxAgD2bGVpV3sBMHlWxrFkqvKNuHyCA/885MLvN7XjPxeNhU4g+N3GdkQpMLfGhqndBcCeoxD/4z5WZN/K2uqQr31XU+hqQQjBJfUFuKQ+/fuM6PVAUcmw9rPkcDiMIQmmSCSCDz74ALt27YLH44Hdbsf06dNxwQUXKB5HnKEhfwCopuQAVrcUiahEmNLbCiiCSSUlB7A6pEAkqr5STl4ll2QroLlKTtqXmDLUMKlGmKRjAn5QUVRWxsgr6lSLvqUIE7Gop+TkFVzBKEUoKqaISpKXz0ShN+bFFBNMKu9rDUsBGU3BVBBLycnFy5qmlYoHU/oPXqtBB7tJB3cwik5PGHWFSUIvzlpATscVWfQpETvqGYhdX7m6B5NMpd0Io1Sr1ekJp6RwyNjxoC3HsLt9AIAdk0pUBNPB3WzfhmmaY8lMKrGg2KJHrz+C7e0+nFOTKJI/rjwLcAJzevZAF2lIcKcX17M+YOS8S3IuVP7GrFJsa/ei0xPGD1cdgyAQ9PoiKDTr8O1zKiCccw/EP/8HsHc7E0s6PciNt0M475KcxuFwOKcOg1Y1Pp8PDz/8MI4dOwaTyQSHw4EDBw7g448/xtq1a/HAAw/AatX2GOFkRk6pRdIt8zcYWUF0cg2TVtG3hq0AkMG8Mm1Kjo2nvkpu8EXfiq0ApUx4SSk6JcKU3EoFiNkKpIkwWQ2Cknb0hEQUWZLOIdf3uFVqmNRWySlF3xoRJtm8UsvtOxIGvG6ELXnappWKB5O2z01FniFOMCVF92RrgTjBpFqj0tqsjJWNCWFtgQmH+wI45gqknq9hGujH63AgaAAEZj4ZD6UUkAXTpOwEk0AIzqu1Y+UBJz5sGkgQTIGIiA88FgAiLmjdArrJAXLhFWys48eYmCECyCVXqZ9cgzyjDg9cXIOHN7Qo1g3FVj1+cVGNlCIzQLj7IeDwPtC+bpCJU5WWFhwOZ3QyaMH0P//zP2hra8Pdd9+N8847T3l+06ZN+NOf/oRXX30Vt96ae66ek4hBq+gbSNseRa5hUi361kjJAawfHJDGvDKNYArIRd9qKcBMNUxaRd8GI6vVikZYHZMkmGK2AhopuTQRJoEQ2Iws+uIJRRVjSQWl6FstwqRSwyRHYDRTcuy4PhUvJmIwMJHmcQOuPvRSdp8MAklpw0IjkVhxuEaECQDKbAYc6g2oF36XVbIoWlc7WgfSWwrQlkb2oGac5lgy4wqZYGp0BnF+UosUMmka2i0lGBDMMAgx7yaFtuMsRWY0JvS4y8RF4/Kx8oATHze7ceuZETik1/ODxgH4wiIqhBCmO4+ArvwH6JyLAJMZ4vL/ZnM6+3xmOjkIxhSY8PTiOmxtZ30OZ1fmJUToCCHAxCngyTEO54vBoFfJffrpp7jhhhsSxBLA/Iyuv/56bNmyZciT48QXfadZ0ZWmPYq8Sk7NUZZmEEymQUWY0veSU2qYVPrIAdopOUJIXFouVsck95JTS8kpRd9pIkxArAGvauF3XANegN2HgHR9ufaRk5FTci61lBwQizK5+pT6pVJbqmklXL2sSaxerynQgDgvJk+qFxPkeiRnD1qd7L6mNM0FgNZGAADJVjBJhd+Naivlisuwq2Y2AKDBEk2JftI9UgujCVNy6mfVUGJBQ7EZEZFi5QHW8DYiUrwmrWK7YmoFhJIywNkD8b/+E/SVZ4F9O5jz/JJvZD2OGia9gPPG2DGvNl91AQKHw/niMOj/4QMDAxg7Vn0Vy9ixY+GOS2dwBk/WEaZwmhqmwUSYdBoRJjlKlM6HSas1ymBSckCK2zelNM6HSctWQEswZdGAV1olJ0eXdCSNjYGckssvTN0modUeBYBS+E1dvTFLAS0PpsKSjE7HckqsZUDFvNKax1qBADjex+7rmILUflNyhClbwTShiL0/DnT7IaqsztpTyVJt0wNtqWPtkAwkZ+TeoHPJFHb/3tjXhyZXEK/u7EGnJwyHWYcvTSmBsPQuJjJ3fgr63ttsnJu+nZV5JIfD4QBDEExFRUXYv3+/6rYDBw6gsDD9hwcne/RatgJATPTEpeQopdo1TJJgIumKvvVye5T0EaZ4HyZKaVzRt5atwCB8mIAUa4FQlEK+HZpF32l8mID49iiZ+8kNxFkKpPj4RCIxv6b89BEfOU3UH4yquraTuMLvbtnl25aaMadZmFbKyAKotV8lwgQA1bWIEAFt0stTmySYqCgqq7tQPS7jeAAwodgCk46gPxhFc1KUiVKKXQaW/pp2ZFPCcnfq9QCH9wIAyIyzsxornvPG2DGr0oawSPHDVcewXIou3XZWOcx6AWTSNAg/+hUwZTYwcQqE7/wUwoXq3QI4HA5HjUELpnnz5mHFihVYuXKlEk1yu91YvXo1VqxYgXnz5g3bJE9nMkeYpA/VuAhT/AeypnFlhghTtj5MYZFC3lM9JSdFmDL5MKWLMCkNeJlgkgu+CWJiKwG5NUoWESb19iiSYJJScpor5DxS/ZIgxPrQqZBv0kF+KVxqhd+FckquN85SQCXC1Ct7MGVubCp7KvX6I4rRZzykaizaLSWIgMCsF1CaLNB6OtjrbDDGVtVlwKAjUssSYEdHohVEkyuI/qgAYzSEiU1bgbaYuS3duhEQRaCqdlBRH0II/vX8KmXlnUCAb8wsVUwmAYA0TIXuRw9B99PHQM6en/MYHA7n9GbQRd/XX389jh07hpdeegkvvfQSdDodolH2R3nmzJm44YYbhm2SpzNyhEikSPG2YTuwD0UaDinFpfFCx6CWtslUwyRHmNR8mEyyD1PMViAQl7rTKvrOxlZAtX+dWe4n5wNBYv2Sqt+MvEpOI8KUp+XFFJeSo5QqgsmeYYWcVopMIAQOM1v+7vRHUsVQgZySi0WYSlVcvrNpi6JchlGHQrMOzkAULf0hNCQv468ei2Yb6+02pkCl6a5c8F05Jqdl9zMqrNja7sWODi+umRzrM7lJ6kA/G30w0Cjo5vdArvsWAIB+vA4AW+I/WPJNOjx+eS2O94eQb9IpUT0Oh8MZDgb9F8VgMODnP/85tm/fjj179sDtdis+TDNmzBjOOZ7WxAueiJpgUlbJxaIWcvqOAFBtwp1lDVO2ESZZWOkFkjo/IOvWKLK7eLKXk9JPTkrJaTXepaI49BomOVIUCQPBgBKFytRHLhOFlphgSoY4Yg14tUwrZQ8mLdPKeGoKTHAGfGgZSBVMpHosjttYiiw5HQcAtPEw229MXVZjyZxZlYcXtnVjR4cPnlBUudebjrNI9CWTKoAPAfr+GtArb2DC7Mh+QKcDmTs0nyJCCGodqdfC4XA4Q2XIX8FmzZqFWbNmDcNUOGrE1yCFoxQpWSEVW4H4+iXVCIxiXKn+wSKvktOqYVITTKrpOCBmK5BmlVy8d5M/IqbWQSWl5DQb7wb8zLMJ0I4wafWTM5klQ1DmizQQZNel3hbFxR5orJCTiZlXqoi0wvhVcun7yKG7EwCyTlvV5Buxq9OHlv7UVWuorEGzjZ2n1pQq4mjjIfagviGrsWTGOkwYW2BCU38Qm467cel4B472BXDMGYSOAAsumwfPm5VAVzvo355WmvuSeQtBHEUZzs7hcDgnB74O9hRHR6Ck2tTqmIiKrUBI1PBgit83TbNRWbCEtHyY4lbJKSvk1NJxQMYaJp1AFLGl3oA3sejbq9V4V65fMhg1m47K9gBqtgKEkLi03EB2bVGyEExyX7hev0p/Nykl5/f64JVEXHKEiYpRQI4wZSuYCjRWyhlNOF7A7AVqPR1JY4mAJJhInXYTXDXk2qGVB5yglOItabn/vNp8FOaZIdz8HTbOpx8Cx48BeXaQq2/KeRwOh8M5UeQUYfr+97+Pn/zkJxg3bhzuvPNOzX5FhBD84Q9/GPIET3cIITDqBQQjovpKOZUIU1iJMKURMErRt3qEyagVYZJFj0qESXWFHKVxPkzqKTmApeUCkWhWDXjlfVR9b7Io+AZiDuHudP3k8vKZQaTHjYEgm7dmSk5jhZxMqVS31O1VKfrOLwB0OvQY85X5pZhy9vUwA0+dPhaRyoC8Uq5JxRfJF46izeAAAIzr3A/gnNjGzlZ2v40moKo25dhMXD7RgeV7enHMGcTvPm7Hh02sgP7LZzBhKEw7C/SWu0FXLwdseRBu/i6II7tr4nA4nJNBToJpypQpSruTKVOm8AaPJwiDThJMaivl5ChKODUlpxZhoqIYE1fpIky51jBFNVJy4RBb/QSktRUAmPhxBqJpGvBKRd/yKrmQRuPdLAq+gZitgDeLBrwDAfZBriqYsugjJyPbBPR4VZy3BR1QVIruKBNMqivkuqUoUEk52z8L6qWWKB2eMDzBKPLiruFIXwCUEJQEnCho3ZNwHD28jz0YOz7nPmsAu1c3zyjBf2/twgeSWFpQX4AzSmPvAWHeAmDegpzPzeFwOCeDnATTHXfcoTy+8847h30yHHWMWm7fBo0Ik1oBdnwLlTQ+TEZJ+Gim5MIhUDEKIugUF2xN00og1rhXBc0GvEkpOXmJvKpppRJh0hZMsnBwq9UwIa4Br8cd10dOpQg7h6JvJcLkU0nJAUBpBXqdRmlflbFkwZTDsnu7SYeKPAM6PGEccQYwsyJ2Xw73stdmgrsFaDoMGgnHHLb37QAAkEmDX8Bx9RmFECnFx81uTC614BuzMq/s43A4nFOVQdcwvf/++2ndvD0eD95///1BT4qTiF6K+KhGmPQqNUzZ9JED0qbk5AiTetF3XB2SlNrTdPmWC76NRs2oiJZ5JbEk1zBprJLzZV4hB8SKvr2hqKojtVLD5B2+GqZYhCmiOiYpqUC3ySHtmz7CREpz6302XnLflgWSzOE+9vv4UA97LQ8x40gqiqCyYJo8M6ex4iGEYMmUYvznFeNw21nlyupLDofDGY0M+i/YM888g87OTtVtXV1deOaZZwY9KU4i8gdNRC1FphVhUvuAkgWTIKRNtcRqmDTGA5S0nHYfObngO306DshgXqmskmPiy68hmOQIk5bLNxDrJSfSNFEtybySurMTTNmk5IqtBhAw4Su7hydQVoEuC6vxKVcRTLS7nT0ozc5EUmZCMRNMh+IEE6UU+7rZ/WwoY+KS7vyMbTx2kJl2mi1Afe4F3xwOh/NFZES+8oVCIQgZ+lxxsseQVYRJ3VYghQwF30B8Sk4l2iMIsVSeLJikSJSWaaVWwTcAWPRMjGin5Fj0SK5hSimKBpS2KJkiTEadoAhDLfNKn9evOKcnCyYqRgE3q8/JpuhbLxClp5xaWo6UVqDDzOqlytUa4eZoKSAzqZjd+73dPiWy1eYOo9cXgV4gOGPqeHY92z4BFZmhJACQWXNB9Nz8kcPhcIAca5h6enrQ1dWl/H7s2DGEQonLlUOhENatW4eSkuyM9TiZMWr1k1OLMEkf8Ea1GqYMlgJAfEouTTsWo5kJL8laQE7JmbVqmNJYCshkFWHyM/El1zDZtGqYNNqUyNiNOvT6I+peTDYWYXL5w4CNpQxTUo4eN0ClY/MyCyaApdp6/RF0e8OYWJwkIksq0Glhr0tlXmJ9GaWUrVwDsm5TItNQYoFZT9AfiKLRGUR9kRk7O5j4PKPUAtOMsyDa7EBvF+gHa0A3bgAAkLkX5zQOh8PhfJHJSTBt2LABr732mvL7c889l3bfpUuXDnpSnESMWhGmuNYoMnINk1bj3XQF32y89K1R2A6JK+VitgJqKbksI0xaRd+yYAr6QcWoptO3EmGyaafkAFb43euPqPaTk4u++4NsrAKttih59qwjMaU2PQ70qFsL+AvL0G9kr0+ZPml7Xw8TnzodUFaV1VgyBh3B9HIrPm31Ymu7F/VFZqVNyawKK4jJBHLxl0BX/QP078+yg2rrgSmzchqHw+FwvsjkJJjOO+88jBkzBgDwxBNP4KabbkJFRWJ6wGAwYMyYMSgry9wclJMdBimyoe3DlNoaRbvxbvqUnGJcmTbClEYwqaTkaCDLCJNG0beSkgOAgF8RTGq2AjRLHyYglmIbUG3AyyJUrjC7hw6VFXKKpUAWK+RktFbKdUXYGPawFzZnJ5Afdw3tUqPasqpBpcnOrs7Dp61ebDjajwX1BUqEaf5YFkkjV17PCr2PHgCseRCW3sVtQzgcDieOnP7y1tTUoKaGOQN/73vfw1lnnQW7PXPqgzM0NCNMmjVMWo13tVJyGsaVQJxgYmJIOyUnRZiGUPRNDIZYqxK/X2m+q25cyYQAyUIwyVGj/oCKkaRU9O0S2RgOi4o4c/VJJyrMOJaM3FC305MqmNql58r9vaBtAyBjx8fGajvOHlSNyXqseC4Ym4///rwLLQMh3LumESIFziixoNLOIo3EaILw08eA5iNAeVVW94/D4XBOJwZdmX3xxRdzsXSCkIVPRKs1SiSWktOMMGVovAtkaI0CxPyUkou+1VJyUoSJDCUlByT0k5NtBVRrmLyS1UVWgol9X3CprViTaqD6BRYZU40wSYIpF4fq6nx239tUWpV0ethzFf4+oLUxcWM7E0ykMnfXbQCwGXWKy3aXlA68aUZinSHR6UDqGrhY4nA4HBVyijC99tprWLBgAYqKihJqmdLx1a9+ddAT48TQLPpWjTClr2GiWQgmebxQhggTDQZBoN0aJRZh0k7JydEp1aJvgNVAufsR8XoRirJ9VVfJ5VD07TBpRJgsVkCng8vIzuNQq2Fy9bKfhdk3jK2SIjodnhCiIoUurjC/bYC9hhWBXtDW7oTjaGuTdILBRZgA4P9NL4Y3FMXeLj++1ODArMrMdV4cDofDYeQkmJYvX45Zs2ahqKgIy5cvz7g/F0zDQ8xWQM3pW6U1Sjar5DSLvtl4UcqiWvrk8+SSklNsBbQFkzVjhIl9uPu8fgC2hGNkKKWx1ihZFH3LEab+dA147Q64DCzaohZhorJgyiHCVGLTw6gjCEUpurxhJSUGAMf7WcSu2tsFOJtj40QirEEtAFI7HoPFoBPw3Tm5WRJwOBwOh5GTYFq2bJnqY87IYsyq6DvVuFLVWTmUTUouJpBCURH6JIduYjKztiFZrZLL0rhSq+gbUFJyXl8AgA0mHUmIzgBg4kwWlUOtYQIARxH6jekFUywll32ESSAElXYjmlxBtA6EFMFEKUWzJJhqfR2ApxfUMwCSlw+0NrHX12rL2VKAw+FwOMMDd5ccBWgaVxpSW6OEtYwrpf2IhmAyCATykUGtfnKKYJJao6gJNFkwZVvDpJWSA+DzszGtRo10nN4AYky/ClAmJpjSNOB1FCspOVVbgUFEmIBYWq7NHXvNXIEoPCERAgGq8qTX9MgBAABtPMR+HzuBr1zjcDick8SgBVMoFILP50t4buPGjfj73/+OnTt3DnlinBiarVFytRXIooaJEKJdx5QkmAJRuTWKmq1AdjVMmYq+5X5yPj+LpNlUPZikgm9bdkXLDqXoWz3CRDQiTFQUgX6ndKLcBJNc+N3SHxNMcnSpPM8A88Qz2BgHd7ONB3ax+fA2JRwOh3PSGLRgevrpp/H8888rv69evRpPPfUU3nzzTTzyyCPYunXrsEyQE4sUaRlXJjTfFYdmXAnE0oCaEaZgNr3ksrQVkMYLRET1ZrhySi7EBJOmaWWWq7zkqFEgQhFQiWwFCooR0LFrTbEV8PQD0ShASFZ95OKpK2TnPOqM9XZrdErpuAITMHEqAIAe2MValezbDgAgU2bnNA6Hw+Fwho9BN4o6fPgwvva1rym/v/3227jgggtw66234tlnn8Vbb72FM888c1gmKePxePD888/js89Yk9Czzz4bt956K2xpCnwjkQheffVVbNu2DV1dXbBarZg+fTpuvvlmFBXF6k5++ctfYu/evQnHzps3D3ffffewzn+wKD5MqhEm6SXMtoYpiwgTwLyY3EjjxZQcYZJTcqpF37nZCrDziakr4CTzSq9UoJ2nmpKTC76zE0wWvaAUYKvVMfXbS4F+wEgjiqBTcEoeTPmOnI0kJxSxaNsxZxDhKIVBR3CghwnLicVmkJqZoEQAmg6DfrSOtWCx2HgjXA6HwzmJDFowDQwMKKKjq6sLXV1duOuuu2C1WrFgwQI8/fTTwzZJmd///vfo7e3Fz3/+cwDAn//8Z/zhD3/Az372M9X9Q6EQjh07hq985SsYN24cPB4PXnzxRfzHf/wHHnvssYR9Fy5ciBtvvFH53ZghAnMiUYq+NSNMKsaVaqvksij6BmJiS9XtO86HiVKawVYgO6dvo45AIIBIWVouRTDJEaYwBfTqgikXl2+ApR4LTDp0+yKqdUwuKzOkLIj4UmuHBlm/BLC0W55RgCckork/iPFFZhzqZYJpUokFxGEDJs8E9m4DfemPbK7nXsgb4XI4HM5JZNApOZPJpNQw7du3D2azGePHsyXPBoMBgUBA6/CcaWlpwfbt2/Hd734XDQ0NaGhowHe+8x1s3boVbW1tqsdYrVY88MADmDdvHqqqqtDQ0IBbbrkFR48eRU9PT8r1OBwO5Z/ValU958nAoFXDJBd9UxE0yj70Q0OsYQJiK95U+8kpPkwBhEUKeVaqKbksbQUIIdor5STB5JGuTavxbi7Gi4q1gEqEqc/ACr6LAq6UbbRPev/ksEJOhhCiRJn2dfvQ4wujyxsBATChmD0vXHl97ACDEeSya3Ieh8PhcDjDx6C/stbW1mLNmjUoLS3F2rVrMXXqVOVbeE9PDxwOx3DNEQBw8OBBWK1WTJw4UXmuoaEBVqsVBw4cQFVVdg1JfT4WLUgWRB9++CE+/PBDFBQUYNasWbj++uthsaRPI4XDYYTjojqEEGX/4VzJxAqwYxGmlHPHCR8SjYDo9QjLxpV6IXV/ac7EaNKcp0kZM/V6iMkCCoCEQgjGiTizXpd6TkkwEbM1432xGAR4wyICkdTrJBYbKACvZFqZZ1IZKy4ll+1rIBtSyl5M8cf16awAQij2O4FQECQ+StbbxfYvrRjU6z2rMg/bO3z4rNULg8CuaVKJBTYj+y9JzpgOfPde0B1bIMy/DKS8OucxTkXke8VX+40s/D6PPPwenxhOpfs8aMH0la98BY899hjuuece6PV6PPDAA8q2rVu3oq6ublgmKONyuVBQUJDyfEFBAVwuV1bnCIVCeOWVV3D++ecnCKb58+ejrKwMDocDx48fxyuvvIKmpqaEa0pmxYoVCW7ndXV1ePzxx1FaWpr9RWWJobMVAKAzmlBZmejDQ6MRtEiPy4sKoct3gArMFbqytASVlYl9znp0BH4ABSWlyKtM7+mTZ+0A4IclLx+VlYlmh77yCvQCMEBEQVEpgEMw6AhqqhNFKxVFtEhF3+Vjx0FXqJ2+slua0OOLwJLvQGVlYuTGX1WNHgA+6S1bWVyYci/6aBReAPbyChRoXFs8FUVOoM2LiJ6J3fhm0oH9HgAuFAUHUGrUwxB3zh5PP7uPdRNgz3KseK405uOFbV3Y3eWDM8hE54LJlYnX9OXr2b8vIMlNuzkjA7/PIw+/xyeGU+E+D1owTZs2DU888QSOHj2KcePGoby8PGHbuHHjsjrPP/7xj4xtVn7961+n3UapStRFhUgkgieffBKUUtx+++0J2y699FLlcW1tLSorK/Gzn/0MR48eRX19ver5lixZgsWLFyu/y3Po7u5GJJLGCHEQxEeY3F4/2tvbU3cSBEAU0dnaAuL1wxdkUaQBlxPthsTUaNTNlt73+/xwq51LHjfKztHZ60R7e2IqUPSyVGzI40FHWwcAViSePDfFUgBAZ/8ASCC1f1o8BrDIWEtnD2qMwaRzsd8HpGa4YtCbMl60m0V9PCLg07i2eKxg19nY6QQwDh0dHcwxHEBzTz8AoDjYj679eyCQ2H+XSAsTpQNGCzxZjhWPiVI0FJtxsDeAxj4fBAKcXSKov75fIAghqKioSLjPnOGH3+eRh9/jE8OJuM96vT6rYMeQqkhLS0tVB7nsssuyPscVV1yB888/P+M4TU1N6O/vT9k2MDCgGnmKJxKJ4Ikn/n979x4cVZ3mDfx7+pp0upPOlQRCIAHCTSOgAwhYIqM7FlLr4I6ZWcfS2cDqCisy+84irsN4eWURa1/dGmpqlnm9sMZ3Ri5lFksp19uWCtYMo44LIy4RuQQNIRfoJJ1O38/7x7l0d/qkb0l3csL3U2Ulfc7pPie/oDw+v+f3/J5DV1cXfvGLXyStT6qtrYXRaERHR8ewAZPZbIZZqR8aYrR/qeaoom/NzzZbAJ8Xot8PiGJU0Xf8s4jyyjbRbE74nEr9ky8Yir9ObSvgVeuNrEZD/L0G5T5dggGi2QIkGZc8tRdT/D1FuS3BgPxHtsAsxF8j1zCJNnvKv4OSfOnzuj1S4CSKkTHukY+V+nshdrZDnNMQeWPPRelrWUXGv++mRRX4xfvn4Q+J+OHVZSi1ma6Y//BGjzNlD8c5+zjGuTEexnlEAVMwGMSHH36I48ePw+12w+Fw4Oqrr8YNN9wAU4oregoLC1FYWJj0uvr6eng8Hpw6dQozZ84EAHz11VfweDyYPXv45dZKsNTR0YHHHnsMDkfyTVnPnz+PUCg06nVYmUrYVgCQmlf6vGprAaWGKVHRd6JO30Ck6NufpNN3whVyUQXfqWQBUyn6HjBI99ZsKzCQftF3mU0Kens88VlB5Viprxfo7FCPi16PtNQfAEonxb0vVXMrbNh9+wy4fSHUOJN3JiciorGTccDk8Xjw5JNP4syZM+oKs5MnT+LIkSN4++23sW3btlFdaVZdXY0FCxZg9+7d+Nu//VsAwG9+8xssWrQopuB78+bNuOuuu7B48WKEQiE8++yzOHPmDB5++GGEw2G13slut8NkMqGjowOHDx/GwoUL4XA48M0336C5uRm1tbWYM2fOqD3/SKir5LQ23wXitkfxp7A1yojaCkQHTKFE+8il1rRSkbDbt7JKzigVXmsGTO4+6asjeQCuKCuQM0wDgZjjoiiqAVOJrxdiVyRgQrecXSpwqB3IM1WSb1KzXERENH5l/F/q3/3ud2hvb8fmzZtx/fXXq8d///vf49e//jVeffVVNDU1jcpDKjZt2oQXX3wR27dvBwBce+21WLduXcw17e3taruDnp4etcnlli1bYq577LHHMH/+fJhMJhw/fhyHDh2C1+tFaWkpFi1ahDvvvBMGw/jYak/JFCXMMAFAIABRFFNrXJmkz5RVmZLTalxpjZqSkzNMcY0dgZRbCiiU7t0erYBJbnw5IBdna7YVUAIme+oBU6mcYer1heALRnox9ftCat+rEl8f0BVVW9QhFeFzI1wioitHxgHTH//4RzQ2NsYESwCwdOlSdHd344033hj1gMlut2PTpk0Jr9m3b5/6fUVFRcxrLWVlZXjiiSdG5fmyxZJo810gki0KBhAMQ+2LpJ1hCsS+J8k9fZqNK+WMUSiIQbnAPF9rqxKlF1eKGaYCuVnlQCC+iaRgMsNvscFvlAKcgiEZJtHvizTJTCNgclgi3b673H4on9olZ5eKzIBZDAFdHeoCA7H9vPRMk6emfB8iItK3jFMofX19mDZtmua5adOmoV9ejUUjpxZ9D5thkuPeQACBqGk7zRomueg7acCUqHFlVD8ir7zyTauGSfTKRd9JtkVROKxSuOL2a089DjiktgQCNPaSU7JLRpM6fZcKQRBQZpPG72J/ZEVhh1v6uSoLrdJ+cd7ByGa7F6SACVU1Kd+HiIj0LeOAqaSkBP/zP/+jee7kyZMoLi7WPEfpSz3D5I8JqjS3Rkl5Lzm5hkmj6FswmdRpQK9XyjDlaW6LokzJpZhhkqfZ3L74DBMADBSWSdcZRRiGFpFHTcel2+BMmZbr7I+0Mujol36uSocVUJpGnj8DABAvMMNERHSlyThgWrZsGVpaWvDGG2+o2aT+/n4cOnQILS0tWLZs2ag95JUu4dYogBq8iIFgzD5ymoFDilNy6tYoWjVMgFqXpGSY8hNsi5Js412FUsjt9msHTG67FIQXCBrn1YAp+SrIocoLpPH71hXVN8otjdMkuxlCjdRaQjx/GqLPB3TIrUIna2dYiYho4sm4hunOO+/EmTNn0NzcjObmZhiNRoTkvcyuueYaNDY2jtpDXunUou/hMkxK0XcwEFXwHR/AiOEQEJKXzycp+lYyRl6tKTlAqkty92PQH4y5PoY3vVVyDkuSKbkCOWBCfAsAsT/9gm/FFIc0Fm2XPUCtFAhekKfkqhwWoKYOOPoh0HYaOPcVEApJe8iVlKV9LyIi0qe0Aya/34+jR4+iu7sb119/PW666SacOXMG/f39ah+mhoaG5B9EKTNH9WHS7Gwe1VbAr+wjl6jgG0iaYUoaMMlZI18gCMCkNp2MoRRhpzslN0yGaSBPyh7Zwxodw+UMk5BBwDS5UBq/c5c8AKQtWdQpObsZwvRZEAGIrX8GqqdLb6qbPS72NiIiotxIK2C6dOkSHnvsMXR2dqrHbDYbHnnkEdTX14/6w5FECZhEACERGDr7JZjM0sq4YEDNQmkXfEcFGsN0KVdEAqZhslpyEOQNpNJWIN2i75BmYDhgdQA+oCDkjX9zBj2YFFMKpTYJbZcHIYoiBgNhdMp9maYUWoCSOdLP0N8L8eD/AwAIcxekfR8iItKvtGqYXn31VVy6dAl/9Vd/ha1bt+Lee++FyWTC888/n63nI8T2U9JcKadkiwKBqKaVWj2Y5KJmowmCQaPxY5TkU3LS1JXShynhlFyaNUxhMfK50fotBdJ1AU/8m9UapsTb5GipcpghAHD7gnB5Q2jrlcapOM+IojwTBJMZQsN3Im8wGiEsXJr2fYiISL/SCpiOHz+OtWvXorGxEQsXLsTq1avxwAMP4Ny5c2oHbRp95qiUkmYdkzm+hkl7hZw8JZekfgkA8uR7JpuSUzJQWgGTmGbAZDEK6nO7fRoBk9zl2+GLb1kh9sv7DGYwJWcxGjDJLo3hWZcX51xSwDStONI+QbitUR03YdUaCEVcBUpEdCVJa0rO5XJh3rx5MceU1729veNm77WJxmQwwCBImRdpn7gh2SFTqjVMqfVgAqIyTFpdtwEI1jyIALzyae3GlUrRd2qdvgVBgN1iwGVvCG5/CBWInTbsE6Sps6JBV/yblb3dMlglBwD1ZfnocAfQ2u1Vt0mZHrW/mzC5Bob//Wug6yJQPz+jexARkX6llWEKh8OwDMlOKK+VFXKUHSY58xJMMcOkvfFuai0FgEjA5AuJCGvtEC1njQZDsdfHkIu+U20rAEQ6eGsVfvfJ8b1j4FL8G/tc0r0c6U/JAcDsMukZT3Z58OdOacpvXkXscwsl5RBmX8VibyKiK1Daq+Ta29tj9lgLy52l29vb466tq6sbwaNRNLO8fYdmDZMpxRomf2pNKwHErHrzBUXkm4cECXKrAK8oXTcaNUxAbOH3UP0hI4AgCt09EMNhCNF7/fXKQZSzJOV7RZtfIXUH/6R9AABgEID55aO3eTQREelb2gHTr371K83ju3btiju2d+/e9J+INCm1Pdo1TPKvMdkqOXVKLvEKuaHv9wXD8VNueVEBkwDkDQ2ogIwCJrvaWiB+KrBPbr/k8LuBwQGgQJp+E/0+wCMFOijKLGCqLbZieokNZy9J2aUFlQWwWxMXxhMR0ZUjrYDpgQceyNZzUBJKTVLiVXJRNUwJi76t8eeGMAgC8kwCvEFRu/BbqWGS66lGo60AENXtW2N7lD75WGFgAOjvVQMmdY83kxmwFaR8r2iCIGDDDTOw9fXjMBkE/HUDm1ISEVFEWgHTypUrs/QYlIzZkGA/ObXTd2RrFM1O3yluvKuwmgzwBkPDBkxBwYiQoD0lJ4bDkb3kUuz0DUQCpv4hU3LeYFj92QoDA4DrElBZLZ1UAqai4hHVF91UX47/+/2ZsBiAwryMm+ATEdEExL8VdCJhhkndS84fVfStkfEJpl70DUhZo16EtJtX5tngNUYyVXE1TEpwBqSXYRqmhqnPK702iyHkhfwQXT1QQyMlYMqwfilaeYEZolaROxERXdEy3nyXcsucyiq5gD+q6DtBp+80MkyAdi8mIS8Pg0bpcyxGAcahU4DKdJxgSGkKUFEkB0y93iEBkzIdh4AUKF2OrJQTlYLvDOuXiIiIkmHApBOmhDVMckASCKgBVaKibyGFom8gSbdva76aYUq8Qi4vrWkypzwV5vLGbrDb55NeOwxyIOXqiZx0SQETm0kSEVG2MGDSiUSr5ASLRtF3oj5MKWZ8Enb7zsuDV84waQZMg/L2JXnpLc135kkZJtdwGSZ5NZ6oETCNxpQcERGRFgZMOqEEQNpTcnLA5PdFir4NI+vDBCTJMOVFMkyaK+QG5WX++WkGTPlyhmkwNsOkTNEVKcXYlyMBk9hzUfqmtCKtexEREaWKAZNOqBkmrSm5qAxTIFENUxp9mIBUpuSUDJPGvZQMU5rL/IvkDJMvFNvO4JIcQBUXyD+rK6rbd7cUMAllk9K6FxERUaoYMOmEukourBG8KDVM0RkmzYBJzjClPCWnBEzaW6MMKjVMGv0dRTXDlF7AlG8yqM8enWVSAqYSp/x5vZcghkIQg4FIATgDJiIiyhIGTDqh9mFKlGHy++XNeYfJMPnkDFO6NUxaG/BarPCa5IDJoPFMcudtIc0pOUEQNOuY1AyT0yH9vOGwlFm61A2IYWmasdCZ1r2IiIhSxYBJJyIZpiSdvuXz2p2+lRqm1AKmhG0FBAFeq5TtyRM0AiplSi7NgAmI1ClFr5S7LAdMpQVmoGKKdLDjW6C7Q/q+tIKb4hIRUdYwYNIJU5o1TFqNK9VO35bUG1cCgC+kERAB8FqkYChPjN/GRC36zmCrEq3WAkrAVJxvgjBpMgBAvPgNxPY26YKq6rTvQ0RElCp2+tYJq5xh8ifqwwTAH5Q7Yms2rkxvSk7JMA0GtDtfqxkmMRB/Us0wpR8wFedLU3JKkOQNhuGRpwVL8k1AZVSGSe7KLUyZlvZ9iIiIUsWASSciW6NoFX1HMkYBefpMs+hbDpgEa2oBU75ZzjBprZID4JEzTLawP+6cmGFbAQAot0mr+LoGpIDpkkf6ajUKyDcZIE6uke7RdjrypskMmIiIKHsYMOmEMsWmlWESTCbAYADC4UjjSq0aprQzTAkaVwLwmKU94vJDPo2Tma2SA4AKuxQwdQ5ImauL8tcKu1mqU5o5FyIAnDulvkeom532fYiIiFLFGiadsCSakgPUaTnlvFWrmaQ/vaLv/ER9mAAMGvMAALagV+OkNCUnZFDDVF6gZJjkgMktPXelHEgJJeWxTSrLKyGUlqd9HyIiolQxYNKJpAGTXMidsA9ThjVMw2aY5D5MNr8n/uQIpuQqogKmUFjERbcUOE2yR6YehetXRb5fujLtexAREaWDU3I6YTEpU3LawYtSx+SXT2utkks3YFIyTINajSsBeAwWQARs/oH4kyMo+i7JN8EoACERuOwNRgVMkQ7lwq13AD2dgNEI4Xt3pH0PIiKidDBg0omEW6MAgMUCEVEBk9Z2JekGTGZllZxG2wAAg4IJEIF8X2zAJIpiVIYp/YDJaBBQXmBGhzuA9j4/vu2LnZIDAMGaB6Fpc9qfTURElAlOyemEVe2JNFzAZIXfEIl/h07JieEQEAyo16aiwBzZGiWk0TDTI0rL/22DfbEn/H4gJAdZtvSn5ABgerH0jF/1ePFNnxToTXOm9txERESjjQGTTiRsKwAAZgv8hkiNj3XolJw/aul/yhmmyCZxg0O2RxFFEYOidI/8oQGTkl0SDIA1P6V7DVVbLBWUf3SuD8GwFLwptU1ERES5pqspObfbjZdeegmffPIJAOC6665DU1MTCgqGn/b51a9+hQ8++CDm2KxZs7B9+3b1dSAQQHNzM44cOQK/34+rrroK69evR2lpaXZ+kAxYDMmKvq3wGaWAwihI01oxAlEBkzm1wMNsFGAxCvCHRAwEQrBbIwGUNygiDOkeNo8r9o0et/Q135bxdiV1cobpzGUpuzSjNI9bnxAR0ZjRVcD0y1/+Ej09PXj00UcBALt378auXbuwdevWhO9bsGABNmzYoL42mWJ/7D179uDTTz/FQw89BIfDgZdffhlPP/00du7cCYNhfCThIkXfw7UVsMBvkAKhhAXfZguENH6mfLMB/lAoLsPkkeuaDGII1oHe2De5+6WvdkfK9xnqqkk2mA2Cunfewsr0a6GIiIhGy/iIBlLwzTff4PPPP8ff/d3fob6+HvX19bj//vvx2Wefob29PeF7TSYTnE6n+o/dblfPeTwevP/++7jnnnvQ0NCA2tpaPPjgg2hra8OxY8ey/WOlzJJkSk4wW9QaptEo+FYodUwDQwImJYCyBX0QPENWyQ3IAVNB5gGTzWzEDdOl91uNAm6sLcz4s4iIiEZKNxmm1tZW2Gw2zJo1Sz1WX18Pm82GkydPYvLkycO+98SJE1i/fj0KCgowd+5c/PVf/zWKiooAAKdPn0YoFEJDQ4N6fUlJCWpqatDa2ooFCxZofmYgEEAgENlDTRAE5Ofnq9+PFuWzrFEZJs3Pt1jVDJPVaIi/RqlhsljTej6b2QgggMFAOOZ9HrnVQH7IK7UQEEU1cyXKAZNgLxzRWGxYUoV5FQWYXZaHsoLUNgzOlPKcnPbLLo5zbnCcs49jnBvjaZx1EzC5XC41yIlWVFQEl8s17PsWLlyI66+/HmVlZejs7MTevXvx5JNP4umnn4bZbIbL5YLJZIrJOqXyuS0tLThw4ID6ura2Fjt37kR5eXY6Tk+pnATgawTCQFVVVdz5S04n/HINU0GeOe4aX08HOgGYbDbN9w/Hae8ALnlhKShEVVWlerzNdwmAlGGCGEZlcREMNmkM+wxAL4D88gqUpnEvLfdWTxnR+9NVWVmZ/CIaMY5zbnCcs49jnBvjYZzHPGDat29fTOChZceOHcOeE8VhMi6yZcuWqd/X1NRgxowZ2LBhAz777DMsWbIk4ecmsnbtWqxZs0Z9rTxDV1cXgsFgwvemQxAEVFZWovdSNwCpceW37e0wDPmZQ4GgmmEyiGFcuHAh5ny4Q5q2DBqMcecSMYlSFq296xIuXIiMyTcXpZVxNnkfuY7TX0OQtysJXZDuNWgwpXWvsaSMc0dHR9LfPWWO45wbHOfs4xjnRi7G2WQypZTsGPOA6dZbb8Xy5csTXlNeXo5z586ht7c37lxfX59m5mk4xcXFKC8vV/8idzqdCAaDcLvdMVmmvr4+zJ49/IauZrMZ5mFWm2Xjlxq9NZw/GI7fKy6m6FuIfwZfpIYpneezKTVM/lDM+wb8UtF3PqTgUHT3AyXyHzi33GagwKG7/5CIoqi7Z9YjjnNucJyzj2OcG+NhnMc8YCosLERhYfKC3vr6eng8Hpw6dQozZ84EAHz11VfweDwJA5uh+vv70dPTg+LiYgBAXV0djEYjjh07pmajLl++jLa2Nvz4xz/O4CfKjuiVb4GQCOvQ35zFAl9UwDSUmGHRt9KLyRO3Sk4u+jbIx92RYFYchVVyRERE44luVslVV1djwYIF2L17N1pbW9Ha2ordu3dj0aJFMQXfmzdvxtGjRwEAXq8XL7/8MlpbW9HZ2YkvvvgCO3fuhMPhwOLFiwEANpsNq1atQnNzM44fP44zZ85g165dqKmpiSkEH2smgwCltZJPa6Wc2arWMI3GPnIKZZWcZ8j2KB55Dxab3JpJ7IvK/g0oGSaubCMioolhzDNM6di0aRNefPFFtenktddei3Xr1sVc097eDo9H2vjVYDDg/Pnz+PDDDzEwMIDi4mLMnz8fmzdvVle0AcC9994Lo9GI5557Tm1c+fDDD4+bHkwKi1GANyhq7ydniZ2SiyMHTELaGSY5YPLHBmlueUrOobQwiMowKX2YBGaYiIhogtBVwGS327Fp06aE1+zbt0/93mKxqE0uE7FYLGhqakJTU9OInzGbLEYDvMGQdvNKc2RKzpqwD1N6y/MLlCm5YGzA1C8HTAVK9+/+qO1RRqEPExER0XgyvlIolJCyn9xwAVPiKTm5D5M50wxT7JSc2ydnmPLkmLtfyjCJ4VAkeCpMvRifiIhoPGPApCNWNWCKr2ESLNZIp+8EU3KZ1zANzTBJr+350ueJcsCE/j5ADAOCADicad2LiIhovGLApCNmY4L95FLdSy7NgMlm0d4aRWkr4LDLtWBKwNQrNbSEowiC0QgiIqKJgAGTjkT2k0tc9J24him9gMlhkYIeZQpOodQw2R3yprjKNFyvS/paVJzWfYiIiMYzBkw6YkkwJRfdVsA6ihmmQrmoeyAQRjAsBWqiKEZqmJxyYbdSw6RkmBgwERHRBMKASUcSTslFbb6r2bgyoGy+m+YqOYsRyqcpQdJgMAzlEezlpdI3gwMQvR6g9zIAQGDAREREEwgDJh2xJloll6wPk88rX5dehsloEGCX65j65IDJ7Qur98krKIi0D+jpAlw90vdFJWndh4iIaDxjwKQj5kRTclYrfEpbAcPwAZOQlx9/LgmHvA9LvxIwKfVLcn0TSsqkrz2dELsvSt+XTUr7PkREROMVAyYdsSTKMFnzIxkmhOLPewfl6/LSvq9DrmNSMkxqwbeceUJpBQBA7OkCuqSASWDAREREEwgDJh1R2gVorpKLbisQ9sefV6bkrOlnmJTCbyVQcg0GAQBOuWmlIAdM6L4I9MgZpvLKtO9DREQ0XjFg0pFEU3KCwQC/USrotoSC8W9WAqa8EWSYvHLAJH9VAiaUVwEAxC8+A4JBwGgCisvSvg8REdF4xYBJR6yJVskBkRqmkE/jZOZTcnEZJq8UkBXlS8eFmjrpwm/PSV+nTGPTSiIimlAYMOlIwr3kgEjjymAg5rgYDEiZHyCjKblIDZP0GZflKbliJcM0dbq0FYpMmDYj7XsQERGNZwyYdCRh40ogspdc0Bt7wheVcbKm11YAAIrzpIDp0uDQKTk5w5RnA2rrI2+YuyDtexAREY1nDJh0JNEqOVEUozJMQ6bklOk4owmCyZz2fUtt0nt6PFLmSpmSU2uYABhWNwJGIzC1FsKCJWnfg4iIaDwzJb+ExgtLghqm6GPmwGDsSSXDlEH9EgCU2aQ/Jj0eKVC6pEzJ5Uf++AjXfAeG//MyYM2HYOIfKyIimlj4N5uOJJqS8wUjx6z+oVNycgCVwQo5IJJh8gTCuDwYRK88JVdeEJutEpSO30RERBMMp+R0xGqSfl2+YHyGySsfM4cDMPqHZpgy78EEAPlmAwrkJpVfdnkAADazIdK4koiIaILj33g6ouwl59PIMHnlY9aQP7bIGwC8SsCUWYYJAMrypWzSiU4pGKsoMEMQNLZgISIimoAYMOlInpxh8gaHn5LLC/kjU3AycQQ9mBSVDilg+qTdDQCYZE+/eJyIiEivGDDpSCRg0pqSS5Bh8o08wzTNKbUjuNAvrZSrKUq/PQEREZFeMWDSEaWGya+ZYZKCqLxwIC7DpLwWRhAwTXfGBki1xQyYiIjoysGASUesJqlmSGtKLjrDJA5Xw5SXWdE3AMwpj33v3Apbxp9FRESkNwyYdCRP7sMUEoHAkF5M3gQ1TPCPfEqu1GbGkmo7AGBJtR0l+exIQUREVw7+racjypQcIBV5m6M2uFWm5KwhP+Af/VVyAPC/lk/GF50ezGd2iYiIrjDMMOmI2ShA7iwQ11pAzTCFNTJM3pGvkgOkgG3RZHtM4EZERHQl4N98OmMdZqVcolVy4qDUbBL5zAwRERFlggGTzkS6fcdmmGL7MA3ZGmVwQPqaX5D15yMiIpqIGDDpTN4wK+W80TVMXk/sm+QMk8AMExERUUYYMOmM0rzSN2SVnJJhsoalDJMYCkVOMsNEREQ0IgyYdMZi1N4eRdlLLi/klw9EZZlYw0RERDQiDJh0RpmSG1rD5A3IGSZBPu6RskqiKEYFTMwwERERZUJXfZjcbjdeeuklfPLJJwCA6667Dk1NTSgoGD4QaGxs1Dx+99134y//8i8BAI8//jhOnDgRc37ZsmXYvHnz6Dz4KBpuA16lhilP6c2kTMMF/EAoKH3PDBMREVFGdBUw/fKXv0RPTw8effRRAMDu3buxa9cubN26ddj3/OY3v4l5/ac//Qn/9m//hiVLlsQc/+53v4sf/vCH6muLxTKKTz56IqvkhtQwyVNyVrOcNJQzTGp2SRBGtDUKERHRlUw3AdM333yDzz//HNu3b8esWbMAAPfffz9+/vOfo729HZMnT9Z8n9PpjHn9xz/+EfPnz8ekSZNijlut1rhrxyOrcZgpOaWtgEXJMMmBkpJpyrNBMHAGloiIKBO6CZhaW1ths9nUYAkA6uvrYbPZcPLkyWEDpmgulwt/+tOfsHHjxrhzH330ET766CMUFRVhwYIFuPPOO5GfP3xGJhAIIBAIqK8FQVCvFwQhnR8tIeWzlK95cgbJGxJj7qNknPIsZunAoEc6Pyh3+c63jepzTTRDx5myg+OcGxzn7OMY58Z4GmfdBEwulwtFRUVxx4uKiuByuVL6jA8++AB5eXlYvHhxzPEVK1agoqICTqcT58+fx29/+1ucO3cO27ZtG/azWlpacODAAfV1bW0tdu7cifLy8tR+oDRVVlYCAMqcHgCXYbLmo6qqSj3vC7UCAIqKpA1yC81GOKqq4O04hy4A5sIiVEZdT9qUcabs4jjnBsc5+zjGuTEexnnMA6Z9+/bFBB5aduzYMew5URRTjjz/67/+CzfccENcfdLNN9+sfl9TU4Oqqips3boVp0+fRl1dneZnrV27FmvWrFFfK8/Q1dWFYDCY0vOkQhAEVFZWoqOjA6IoIiC3C7jU248LFy4AAMKiiAG/1HfJBGlqru/iBbgvXED4m28AAAGzRb2e4g0dZ8oOjnNucJyzj2OcG7kYZ5PJlFKyY8wDpltvvRXLly9PeE15eTnOnTuH3t7euHN9fX2amaehvvzyS7S3t6e08q22thZGoxEdHR3DBkxmsxlms1nzXDZ+qaIoQhRFtYbJGwyr9xkMRJpU5udJwaA4MCC9Z6BfPlHAf6lToIwzZRfHOTc4ztnHMc6N8TDOYx4wFRYWorCwMOl19fX18Hg8OHXqFGbOnAkA+Oqrr+DxeDB79uyk73///fdRV1eH6dOnJ732/PnzCIVC47IIXKutwKDcg8koABal7kop9pYDJsGefIyJiIhIm26WTVVXV2PBggXYvXs3Wltb0drait27d2PRokUxBd+bN2/G0aNHY97r8Xjw+9//HqtWrYr73I6ODhw4cABff/01Ojs78dlnn+G5555DbW0t5syZk/WfK102uejbE4gETMr3NrMBQoFUwyQqAZO7T/rKgImIiChjY55hSsemTZvw4osvYvv27QCAa6+9FuvWrYu5pr29HR5P7OazH3/8MURRxIoVK+I+02Qy4fjx4zh06BC8Xi9KS0uxaNEi3HnnnTCMw2X4iQKmfLMRsMlNPAfc0td+BkxEREQjpauAyW63Y9OmTQmv2bdvX9yxm2++OaawO1pZWRmeeOKJUXm+XLCZpT5L0QHTYHSGqdAJEQD6XAAAUc0wOXL4lERERBPL+EuhUEI2i1aGSSr6tpkNgEMugO+XC+TlgElwMMNERESUKQZMOqNOyflD6oqByJScASh0ShcO9EMMhdSibxQwYCIiIsoUAyadUQKmkAj4Q0pbgciUHOwOQDAAoihll1j0TURENGIMmHQmz2SA0qZTySxFVskZIRiMkXqlns7IJrxK5omIiIjSxoBJZwyCIE29IT5gUo4rwZHY9rX02poXWT1HREREaWPApEOR1gJSsXfMlBwQKfw+e0r6Wlw6LjYuJCIi0isGTDo0tBeTEjgpGSahVNoTRzz1pfSG4rIcPyEREdHEwoBJh4b2Yur3S1/tFuk4yqukrxe/BQAIztLcPiAREdEEw4BJh6JbCwCA2yd9LbTKAVPF5Ng3VE3N2bMRERFNRAyYdGho88p+OXBSMkzCpKqY64Wq6hw+HRER0cTDgEmHCuQpuQF5Kk7JMNmt8q9z8jTAZI68YfqsnD4fERHRRMOASYeUqbdeXxChsIgBOdNUqGSYTCYI198kXTxvIQRnyZg8JxER0UShq813SVKUJwdM3hDc8nQcABQoRd8AhLvuh7BwKTBrXs6fj4iIaKJhwKRDSoapzxdS65cKLAYYDZFeS4LJDFx93Zg8HxER0UTDKTkdKsqT4tw+bwj9cv2SIyq7RERERKOLAZMOqVNyviBc3iEtBYiIiGjUMWDSoegpuUueIACg1MbZVSIiomxhwKRDhVYpOAqLwPleHwCgJJ8BExERUbYwYNIhs1GAQ25e2drjBQCU5JsTvYWIiIhGgAGTTk2yWwAAX1+SAqbifNYwERERZQsDJp2aZI/NKFXKARQRERGNPgZMOlU5JGCaUsiAiYiIKFsYMOnU1CKr+r3DYlBbDRAREdHoY8CkU1dX2tTv51XYIAhCgquJiIhoJBgw6VSZzYzvzy1Bpd2MH11dNtaPQ0RENKGxeY+O/c2iCvzNooqxfgwiIqIJjxkmIiIioiQYMBERERElwYCJiIiIKAkGTERERERJMGAiIiIiSoIBExEREVESDJiIiIiIktBVH6bXXnsNn332Gc6ePQuTyYQ9e/YkfY8oiti/fz/ee+89uN1uzJo1C+vWrcPUqVPVawKBAJqbm3HkyBH4/X5cddVVWL9+PUpLS7P40xAREZFe6CrDFAwGsXTpUvzFX/xFyu85ePAg3nzzTTQ1NWHHjh1wOp146qmnMDg4qF6zZ88eHD16FA899BCefPJJeL1ePP300wiHw9n4MYiIiEhndBUwNTY2Ys2aNaipqUnpelEUcejQIaxduxZLlixBTU0NNm7cCJ/Ph8OHDwMAPB4P3n//fdxzzz1oaGhAbW0tHnzwQbS1teHYsWPZ/HGIiIhIJ3Q1JZeuzs5OuFwuXHPNNeoxs9mMefPm4eTJk7jllltw+vRphEIhNDQ0qNeUlJSgpqYGra2tWLBggeZnBwIBBAIB9bUgCMjPz1e/Hy3KZ3Fz3eziOOcGxzk3OM7ZxzHOjfE0zhM6YHK5XACAoqKimONFRUXo7u5WrzGZTLDb7XHXKO/X0tLSggMHDqiva2trsXPnTpSXl4/Oww9RWVmZlc+lWBzn3OA45wbHOfs4xrkxHsZ5zAOmffv2xQQeWnbs2IEZM2ZkfI+hkakoiknfk+yatWvXYs2aNXH36OrqQjAYzOAptQmCgMrKSnR0dKT03JQZjnNucJxzg+OcfRzj3MjFOJtMppSSHWMeMN16661Yvnx5wmsyzdo4nU4AUhapuLhYPd7X16dmnZxOJ4LBINxud0yWqa+vD7Nnzx72s81mM8xms+a5bPxSRVHkv5Q5wHHODY5zbnCcs49jnBvjYZzHPGAqLCxEYWFhVj67oqICTqcTx44dQ21tLQBppd2JEyfw4x//GABQV1cHo9GIY8eOYdmyZQCAy5cvo62tTb0mHSZTdoY0W59LsTjOucFxzg2Oc/ZxjHMjm+Oc6mfr6jfd3d0Nt9uN7u5uhMNhnD17FoA0t5mXlwcA2Lx5M+666y4sXrwYgiBg9erVaGlpQVVVFSorK9HS0gKr1YoVK1YAAGw2G1atWoXm5mY4HA7Y7XY0NzejpqYmphA8VdGZrNGUrdooisVxzg2Oc25wnLOPY5wb42GcddVWYO/evdiyZQv27dsHr9eLLVu2YMuWLfj666/Va9rb2+HxeNTXt99+O1avXo3nn38ejzzyCC5duoRHH31UXdEGAPfeey++853v4LnnnsO2bdtgsVjw8MMPw2AY++EZHBzEww8/HNM3ikYfxzk3OM65wXHOPo5xboyncdZVhmnjxo3YuHFjwmv27dsX81oQBDQ2NqKxsXHY91gsFjQ1NaGpqWlUnnM0iaKIM2fOjPnc7UTHcc4NjnNucJyzj2OcG+NpnMc+hUJEREQ0zjFgIiIiIkqCAdM4Zzab8YMf/GDYFgY0OjjOucFxzg2Oc/ZxjHNjPI2zII6HiUEiIiKicYwZJiIiIqIkGDARERERJcGAiYiIiCgJBkxERERESeiqceWV6D//8z/x+uuvw+Vyobq6Gj/5yU8wd+7csX4sXWppacHRo0fx7bffwmKxoL6+HnfffTcmT56sXiOKIvbv34/33nsPbrcbs2bNwrp16zB16tQxfHJ9a2lpwe9+9zusXr0aP/nJTwBwnEfLpUuX8Morr+Dzzz+H3+9HVVUVHnjgAdTV1QHgOI9UKBTC/v378dFHH6mbuK9cuRJ33HGHuhMExzh9J06cwOuvv44zZ87g8uXL+NnPfobFixer51MZ00AggObmZhw5cgR+vx9XXXUV1q9fj9LS0qw9NzNM49jHH3+MPXv24I477sDOnTsxd+5c/PM//zO6u7vH+tF06cSJE/je976H7du34+c//znC4TCeeuopeL1e9ZqDBw/izTffRFNTE3bs2AGn04mnnnpqXLTl16NTp07h3XffxbRp02KOc5xHzu12Y9u2bTCZTPinf/onPPvss7jnnntgs9nUazjOI3Pw4EG88847WLduHZ577jncfffdeP311/HWW2/FXMMxTo/P58P06dOH3V0jlTHds2cPjh49ioceeghPPvkkvF4vnn76aYTD4aw9NwOmceyNN97AqlWr8N3vflfNLpWVleHtt98e60fTpUcffRQrV67E1KlTMX36dGzYsAHd3d04ffo0AOn/ag4dOoS1a9diyZIlqKmpwcaNG+Hz+XD48OExfnr98Xq92LVrF+6//34UFBSoxznOo+PgwYMoLS3Fhg0bMHPmTFRUVODqq69GZWUlAI7zaGhtbcV1112HRYsWoaKiAkuXLkVDQ4O6fynHODMLFy7Ej370IyxZsiTuXCpj6vF48P777+Oee+5BQ0MDamtr8eCDD6KtrQ3Hjh3L2nMzYBqngsEgTp8+jWuuuSbmeENDA06ePDlGTzWxKJs02+12AEBnZydcLlfMmJvNZsybN49jnoHnn38eCxcuRENDQ8xxjvPo+OSTT1BXV4dnn30W69evx5YtW/Duu++q5znOIzdnzhz8+c9/Rnt7OwDg7NmzOHnyJBYuXAiAY5wNqYzp6dOnEQqFYv7bUlJSgpqaGrS2tmbt2VjDNE719fUhHA6jqKgo5nhRURFcLtfYPNQEIooi/v3f/x1z5sxBTU0NAKjjqjXmnAZNz5EjR3DmzBns2LEj7hzHeXR0dnbinXfewW233Ya1a9fi1KlTeOmll2A2m3HjjTdynEfB7bffDo/Hg5/+9KcwGAwIh8P40Y9+hBUrVgDgn+VsSGVMXS4XTCaT+j+70ddk8+9HBkzjnCAIKR2j9Lzwwgtoa2vDk08+GXdu6PiyGX56uru7sWfPHjz66KOwWCzDXsdxHplwOIwZM2bgrrvuAgDU1tbi/PnzePvtt3HjjTeq13GcM/fxxx/jo48+wqZNmzB16lScPXsWe/bsUYu/FRzj0ZfJmGZ73BkwjVOFhYUwGAxx0XJvb29c5E3pefHFF/Hpp5/iiSeeiFlR4XQ6AUBdDaPo6+vjmKfh9OnT6O3txdatW9Vj4XAYX375Jd566y3867/+KwCO80gVFxejuro65lh1dTX+8Ic/AOCf59Hwyiuv4Pbbb8fy5csBADU1Nejq6sJ//Md/YOXKlRzjLEhlTJ1OJ4LBINxud0yWqa+vD7Nnz87as7GGaZwymUyoq6uLK2A7duxYVv9ATGSiKOKFF17AH/7wB/ziF79ARUVFzPmKigo4nc6YMQ8Ggzhx4gTHPA1XX301/uVf/gXPPPOM+s+MGTOwYsUKPPPMM5g0aRLHeRTMnj1bra1RtLe3o7y8HAD/PI8Gn8+ntg9QGAwGNZPBMR59qYxpXV0djEZjzDWXL19GW1sb6uvrs/ZszDCNY2vWrMGuXbtQV1eH+vp6vPvuu+ju7sYtt9wy1o+mSy+88AIOHz6MLVu2ID8/X83e2Ww2WCwWCIKA1atXo6WlBVVVVaisrERLSwusVqtas0DJ5efnq3VhCqvVCofDoR7nOI/cbbfdhm3btuG1117DsmXLcOrUKbz33nu47777AIB/nkfBtddei9deew1lZWWorq7G2bNn8cYbb+Cmm24CwDHOlNfrRUdHh/q6s7MTZ8+ehd1uR1lZWdIxtdlsWLVqFZqbm+FwOGC329Hc3Iyampq4RSajSRA52TquKY0rL1++jKlTp+Lee+/FvHnzxvqxdKmxsVHz+IYNG9R6BKVh2rvvvouBgQHMnDkT69atiwsAKD2PP/44pk+fHte4kuM8Mp9++il++9vfoqOjAxUVFbjttttw8803q+c5ziMzODiIvXv34ujRo+jt7UVJSQmWL1+OH/zgBzCZpHwDxzh9X3zxBZ544om44zfeeCM2btyY0pj6/X688sorOHz4cEzjyrKysqw9NwMmIiIioiRYw0RERESUBAMmIiIioiQYMBERERElwYCJiIiIKAkGTERERERJMGAiIiIiSoIBExEREVESDJiIiIiIkmDAREQT2smTJ7Fv3z4MDAzEHH/88cfx+OOPj81DEZHucC85IprQTp48iQMHDmDlypUoKChQj69fv34Mn4qI9IYBExFdkaqrq8f6EYhIR7iXHBFNWPv27cOBAwfijj/22GPYv38/AKjTcp2dnfj7v/973H333QiHw3jnnXfgcrkwa9Ys3HfffaioqMDevXvx4Ycfwuv14qqrrsJ9992HoqKimM/++OOP8eabb6KtrQ0AMGfOHNx1112ora3N7g9LRFnFgImIJqyenh4cPHgQb731Fn72s5/B6XQCkLJLzzzzDID4gKm8vBw1NTW45ZZbMDAwgJdffhk2mw2zZs2C0WjE9ddfj66uLjQ3N2P+/Pl4+OGH1fu99tpr2Lt3L1auXIklS5YgGAzi9ddfx7lz57Bjxw5mtYh0jFNyRDRhlZaWoqysDAAwffp0VFRUJH2PzWbDP/7jP8JgkNbE9Pf3Y8+ePZgyZQq2bNmiXvftt9/i0KFD8Hg8sNls6O7uxv79+/G9730PTU1N6nUNDQ3YtGkT9u/fj5/+9Kej/BMSUa5wlRwRUZSFCxeqwRIATJkyBQCwaNGimOuUbFF3dzcA4L//+78RCoVw4403IhQKqf+YzWbMmzcPJ06cyNFPQETZwAwTEVEUu90e89pkMiU8HggEAAC9vb0AgEceeUTzcwVBGNXnJKLcYsBERDQKHA4HAOAf/uEfUF5ePsZPQ0SjjQETEU1oZrMZAOD3+7N6n2uuuQZGoxEXL17E0qVLs3ovIso9BkxENKHV1NQAAA4dOoSVK1fCaDRi8uTJo36fiooKNDY24tVXX8XFixexYMEC2O12uFwunDp1Cnl5eWhsbBz1+xJRbjBgIqIJbf78+fj+97+PDz74AO+99x5EUcRjjz2WlXutXbsW1dXVOHToEI4cOYJgMAin04kZM2bglltuyco9iSg32IeJiIiIKAm2FSAiIiJKggETERERURIMmIiIiIiSYMBERERElAQDJiIiIqIkGDARERERJcGAiYiIiCgJBkxERERESTBgIiIiIkqCARMRERFREgyYiIiIiJL4/+NaDLrLJoGnAAAAAElFTkSuQmCC\n",
                        "text/plain": "\u003cFigure size 640x480 with 1 Axes\u003e"
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plt.figure()\n",
                "plt.plot(t,x,label='x')\n",
                "plt.plot(t,v, label='v')\n",
                "plt.legend()\n",
                "plt.xlabel(\"time\")\n",
                "plt.ylabel('Position/Velocity')"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Comparing rk2 and rk4\n",
                "\n",
                "Given that rk4 costs more to run, we would hope that rk4 can be run with a much larger stepsize $h$ to compensate, otherwise we would simply use rk2. \n",
                "\n",
                "Let's consider a new model problem: the non-linear oscillator. We've considered a damped harmonic oscillator so far, which is still a linear problem. A simple harmonic oscillator arises when we have something like a spring that has a force $F_k = -k x$ which is proportional to the distance $x$ from equilibrium. Given this force alone,\n",
                "\n",
                "$$\n",
                "m \\frac{d^2 x}{dt^2} = -k x.\n",
                "$$\n",
                "\n",
                "However, real springs (and the many, many other things we model as springs like waves and molecules and a host of other things) are *non-linear*. One way to model the nonlinearity is to consider the potential function that creates the force in the first place. One particularly simple model is to consider potentials of the form\n",
                "\n",
                "$$\n",
                "V_p(x) = \\frac{1}{p} k x^p\n",
                "$$\n",
                "where $p$ is *even*. Remember that every conservative force is the negative gradient of a potential, so\n",
                "\n",
                "$$\n",
                "F_p = - \\frac{d V}{dx} = -k x^{p-1}\n",
                "$$\n",
                "\n",
                "Think for a bit about why $p$ must be even for this to work. As a hint, set the equilibrium point to be $x = 0$. What happens to the force for an odd $p$ as you go to the left ($x \u003c 0$) and right ($x \u003e0$).\n",
                "\n",
                ""
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "To test our integrators, let's use $p=2$. This is, of course, gives a linear force and thus a simple harmonic oscillator. The question we want to ask is: for what value of $h$ do we get a good solution?\n",
                "\n",
                "First, code up a force function for $F_k = -k x$. Make sure the function takes both $t$ and $\\mathbf{f} = [x,v]$! The rk2 and rk4 routines always expect the right hand side functions to take both, even if we don't use one. This allows us to use the *same* ODE integrator for many problems. **Good code is reusable code!** Don't reinvent the wheel. Of course, in a sense we are reinventing the wheel here, since all these ODE integrators have been written by others in a much more efficient manner. But you *must* write your own code to understand how others' works. \n",
                "\n",
                "For this test, we don't need to save a list of all `x` and `v` as functions of time. All we're going to care about is the final point. What you need to do is write a simple \"driver\" function that runs either `rk2` or `rk4` from a start time to a stop time with a given stepsize `h`. Then, run this function for both `rk2` and `rk4` on a set of decreasing $h$. Save the final values of $x$ and $v$ for each $h$ for both rk2 and rk4. Finally, make a plot of the fractional error $\\epsilon_x = |x - x_{analytic}|/x_{analytic}$ and $\\epsilon_v = |v - v_{analytic}|/v_{analytic}$.\n",
                "\n",
                "For the analytic solution, remember that the frequency $\\omega = \\sqrt{k/m}$, and the oscillation will occur over a time period $T = 2 \\pi/\\omega$. Choose $k$ and $m$ such that $T$ is a convenient number to work with, and make sure `t_stop` is at least 5 periods. "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 11,
            "metadata": {},
            "outputs": [],
            "source": [
                "def rk_driver(f0, tstart, tstop, h, rhs, method='rk2'):\n",
                "    if method == 'rk2':\n",
                "        stepper = rk2\n",
                "    elif method == 'rk4':\n",
                "        stepper = rk4\n",
                "    else:\n",
                "        raise ValueError(\"{} is not a supported integrator. Valid choices are rk2 or rk4\".format(stepper))\n",
                "    \n",
                "    t = tstart\n",
                "    xold = f0\n",
                "    while t \u003c t_stop:\n",
                "        xold = stepper(xold,t,h,rhs)\n",
                "        t = round(t+h, 8) # will work as long as step size \u003e10^-8 and will avoid rounding errors which caue end point errors\n",
                "    return xold, t"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 12,
            "metadata": {},
            "outputs": [],
            "source": [
                "def sho(t,f):\n",
                "    \"\"\"simple harmonic oscillator has\n",
                "    \n",
                "    F = -k*x\n",
                "    \n",
                "    recall that for a Newton's second law system, we have\n",
                "    \n",
                "    df_vec/dt = RHS:\n",
                "    \n",
                "    df_vec[0]/dt = v\n",
                "    df_vec[1]/dt = F/m\n",
                "    \n",
                "    where f[0] is the position x\n",
                "          f[1] is the velocity v\n",
                "    \"\"\"\n",
                "\n",
                "    m = 1.\n",
                "    k = np.pi**2\n",
                "    \n",
                "    x = f[0]\n",
                "    v = f[1]\n",
                "    RHS = np.array([v,(-k*x)/m])\n",
                "    return RHS "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 19,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": "\u003cfunction matplotlib.pyplot.show(close=None, block=None)\u003e"
                    },
                    "execution_count": 19,
                    "metadata": {},
                    "output_type": "execute_result"
                },
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": "\u003cFigure size 640x480 with 1 Axes\u003e"
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# initial conditions:\n",
                "t_start = 0\n",
                "t_stop = 6 # BY DEFINITION OF M AND K THIS IS 3 FULL CYCLES\n",
                "ha = np.array([0.1,0.05,0.01,0.005,0.001,0.0005,0.0001])\n",
                "curr_pos_v = ([3., 2.])\n",
                "\n",
                "rk_options = ['rk2', 'rk4']\n",
                "\n",
                "rk2_xout = []\n",
                "rk2_vout = []\n",
                "rk4_xout = []\n",
                "rk4_vout = []\n",
                "\n",
                "for i in range(len(rk_options)):\n",
                "    for h in ha:\n",
                "        rk_func_str = rk_options[i]\n",
                "        x0,t_final = rk_driver(curr_pos_v,t_start, t_stop ,h,sho, method = rk_func_str)\n",
                "        if t_final != 6: # with out round in rk_driver it is ok to compare floats\n",
                "            raise Error(\"t_final is not exactly 6 seconds or three periods so out fracitonal errors will be wrong!\")\n",
                "        x_out = x0[0]\n",
                "        v_out = x0[1]\n",
                "        if i == 0: #rk2\n",
                "            rk2_xout.append(x_out)\n",
                "            rk2_vout.append(v_out)\n",
                "        if i == 1: #RK4\n",
                "            rk4_xout.append(x_out)\n",
                "            rk4_vout.append(v_out)\n",
                "\n",
                "x_analytical = 3 # because we went exactly 3 periods (6s)(T = 2 \\pi/(k/m)^(.5) = 2s)\n",
                "v_analytical = 2\n",
                "\n",
                "# converting to numpy arrays so we can do algebra with them\n",
                "rk2_xout = np.array(rk2_xout)\n",
                "rk2_vout = np.array(rk2_vout)\n",
                "rk4_xout = np.array(rk4_xout)\n",
                "rk4_vout = np.array(rk4_vout)\n",
                "\n",
                "rk2_x_err = abs(rk2_xout - x_analytical)/ x_analytical\n",
                "rk2_v_err = abs(rk2_vout - v_analytical)/ v_analytical\n",
                "rk4_x_err = abs(rk4_xout - x_analytical)/ x_analytical\n",
                "rk4_v_err = abs(rk4_vout - v_analytical)/ v_analytical\n",
                "\n",
                "\n",
                "\n",
                "plt.plot(ha, rk2_x_err, label = 'rk2 x error')\n",
                "plt.plot(ha, rk2_v_err, label = 'rk2 v error')\n",
                "plt.plot(ha, rk4_x_err, label = 'rk4 x error')\n",
                "plt.plot(ha, rk4_v_err, label = 'rk4 v error')\n",
                "plt.xscale('log')\n",
                "plt.legend()\n",
                "plt.xlabel(\"Step Size (s)\")\n",
                "plt.ylabel(\"Fractional Error\")\n",
                "plt.title(\"The Fractional Error in Position and Velocity after 3 Periods of Simple Harmonic Motion\")\n",
                "plt.show()"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "It is clear that rk2 is worse in both cases though for this simple case they all appear to work for small enough step sizes. Lets look more closely at smaller step sizes. "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 20,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": "\u003cFigure size 640x480 with 1 Axes\u003e"
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plt.plot(ha[2:], rk2_x_err[2:], label = 'rk2 x error')\n",
                "plt.plot(ha[2:], rk2_v_err[2:], label = 'rk2 v error')\n",
                "plt.plot(ha[2:], rk4_x_err[2:], label = 'rk4 x error')\n",
                "plt.plot(ha[2:], rk4_v_err[2:], label = 'rk4 v error')\n",
                "plt.xscale('log')\n",
                "plt.legend()\n",
                "plt.xlabel(\"Step Size (s)\")\n",
                "plt.ylabel(\"Fractional Error\")\n",
                "plt.title(\"The Fractional Error in Position and Velocity after 3 Periods of Simple Harmonic Motion\")\n",
                "plt.show()"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We see this same shape. Lets look at the errors without the error in the velocity in rk2 as it is so large and messes the scale. "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 22,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": "\u003cFigure size 640x480 with 1 Axes\u003e"
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plt.plot(ha[2:], rk2_x_err[2:], label = 'rk2 x error')\n",
                "plt.plot(ha[2:], rk4_x_err[2:], label = 'rk4 x error')\n",
                "plt.plot(ha[2:], rk4_v_err[2:], label = 'rk4 v error')\n",
                "plt.xscale('log')\n",
                "plt.legend()\n",
                "plt.xlabel(\"Step Size (s)\")\n",
                "plt.ylabel(\"Fractional Error\")\n",
                "plt.title(\"The Fractional Error in Position and Velocity after 3 Periods of Simple Harmonic Motion\")\n",
                "plt.show()"
            ]
        },
        {
            "attachments": {},
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We see that even though the error in rk2 for position looked comparable to rk4, when we adjust the scale it is not. This was for a simple ODE, too. I see why it is worth the computational expences to use rk4 for general purpose scientific work. "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 0,
            "metadata": {},
            "outputs": [],
            "source": [
                ""
            ]
        }
    ]
}