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"# Ordinary Differential Equations (ODE)\n",
"\n",
"Ordinary differential equations (ODEs) arise in many fields of physics, but also in social and other natural sciences. \n",
"Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time $\\dot{x}(t)$, $\\dot{y}(t)$ are related to $x(t)$, $y(t)$ and $t$). This results in ODE. \n",
"\n",
"## Definition \n",
"\n",
"If differential equation contains only one independent variable (such as time $t$) and hence only derivatives with respect to this single independent variable are present (like $\\dot{x}$, $\\ddot{x}$,...), we classify it as an ordinary differential equation (ODE). If derivatives with respect to more than one independent variables appear, we call it a `partial differential equation`. The latter is more challenging to solve (for example using `Finite element method`) and we will not discuss it here.\n",
"\n",
"In ODE only total derivatives (and no partial derivatives) appear. In general, it might be written in a form\n",
"$$F(t, y(t), \\frac{d y(t)}{dt}, \\frac{d^2 y(t)}{dt^2}, ... \\frac{d^n y(t)}{dt^n})=0$$\n",
"where $F$ is an arbitrary function, and it could be non-linear in its arguments.\n",
"\n",
"One of the simplest examples is the Newton's law:\n",
"\n",
"$$m \\frac{d^2 x_i(t)}{dt^2} = F_i(x_1,x_2,x_3,t)$$\n",
"\n",
"Here $(x_1,x_2,x_3)=(x,y,z)$ and $F_i$ is the force."
]
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"## Classification\n",
"\n",
"ODE's are usually classified into:\n",
"- Linear ODE : in which F is a linear function of its arguments, for example\n",
" $$ \\sum_{n=0}^N a_n \\frac{d^n y(t)}{dt^n} -r (t)= 0 $$\n",
" Here $r(t)$ is an arbitrary function, which we usually call source term.\n",
"\n",
"- Homogeneous ODE : In this case source term $r(t)=0$ and hence $y(t)=0$ is also a trivial solution. But note that homogeneous ODE can be non-linear.\n",
"\n",
"- Autonomous ODE : If it does not explicitely depent on $t$.\n",
"- Non-linear ODE : at least one derivative appears at higher power than 1, i.e., $\\left(\\frac{d^n y(t)}{dt^n}\\right)^2$.\n",
"- inhomogeneous : r(t) is nonzero.\n",
"\n",
"\n",
"What can we say about the Newton's equation and this classification?"
]
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"## Numerical solvers\n",
"\n",
"Many general purpose numerical solvers have been developed, which are easy to use, and can solve an arbitrary ODE. \n",
"\n",
"We will discuss a few below: `Runge Kutta method`, `Numerov`, `Verlet`, etc.\n",
"\n",
"While very generic solvers exist in `scipy.integrate.ode`, the precision of the solution can be a problem. For example, it is hard to follow Newton's eq. of motion for a very long time as the precision might deteriorate (molecular dynamics is challenging). If ODE is non-linear, it tends to be even more challenging to solve numerically. For example, the numerical solution might exhibit instability in some regimes, which is called `stiffness`. This is often caused by the presence of different time scales in the underlying problem. For example, a non-elastic collision in a mechanical system typically occurs at much smaller time scale than the time for the motion of objects, and this discrepancy causes a very \"sharp turns\" in the curves of the state parameters. These are difficult to capture numerically.\n"
]
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"source": [
"## Reduction to a first-order system\n",
"\n",
"\n",
"Most ODE integration algorithms (integrators) solve first order ODE's only, but with any number of components. It is simple to see that any high order ODE can be reduced to a larger system of first order ODE. \n",
"\n",
"For a generic form\n",
"$$F(t, y(t), \\frac{d y(t)}{dt}, \\frac{d^2 y(t)}{dt^2}, ... \\frac{d^n y(t)}{dt^n})=0$$\n",
"we could, always rewrite into\n",
"$$\\frac{d^n y(t)}{dt^n} = \\widetilde{F}(t, y(t), \\frac{d y(t)}{dt}, \\frac{d^2 y(t)}{dt^2}, ...\\frac{d^{n-1} y(t)}{dt^{n-1}})$$\n",
"\n",
"Than we can choose\n",
"\\begin{eqnarray}\n",
"&&y(t) \\equiv y_0(t) \\\\\n",
"&&\\frac{d y(t)}{dt}=\\frac{d y_0(t)}{dt}\\equiv y_1(t)\\\\\n",
"&&\\frac{d^2 y(t)}{dt^2}=\\frac{d y_1(t)}{dt}\\equiv y_2(t)\\\\\n",
"&&\\frac{d^3 y(t)}{dt^3}=\\frac{d y_2(t)}{dt}\\equiv y_3(t)\\\\\n",
"&&...\\\\\n",
"&&\\frac{d^n y(t)}{dt^n}=\\frac{d y_{n-1}(t)}{dt}=\\widetilde{F}(t, y_0(t), y_1(t), y_2(t), ...y_{n-1}(t))\n",
"\\end{eqnarray}\n",
"This proves that $n$-th order ODE is equivalent to $n$ component first order ODE. Here $y(t)$ could itself be multi-component function, for example $(x,y,z)$, and we would than have $3 n$ component first order ODE.\n",
"\n",
"\n",
"A good example of such transformation in physics is transformation of Lagrangian $L$ equations, which involve the second order derivatives $\\ddot{x}(t)$, to Hamiltonian $H$ equations, which involve only $\\dot{p}(t)$ and $\\dot{x}(t)$.\n",
"\n",
"\n",
"Since it is always possible to transform n-other ODE into n-component first order ODE, we are going to discuss numeric treatment of the first order ODE of the form:\n",
"\n",
"$$\\frac{d y(t)}{dt}=\\overline{F}(t, y(t))$$\n",
"\n",
"where $y=[y_0,y_1,...y_{n-1}]$ and $\\overline{F}=[\\dot{y}_0,\\dot{y}_1,...,\\widetilde{F}(t,y_0,....y_{n-1})]$"
]
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"source": [
"## Boundary conditions\n",
"\n",
"To solve ODE, the boundary conditions need to be specified. For $n$-th component first order ODE (or n-th order ODE) we need exactly $n$ boundary condistions.\n",
"\n",
"\n",
"\n",
"Boundary conditions can be classified into:\n",
"- **Initial value problems** : all necessary conditions are specified at the starting point ($t_0$): \n",
"\\begin{eqnarray}\n",
"&&y_0(t_0)=x_0\\\\ \n",
"&&y_1(t_0)=x_1\\\\ \n",
"&&...\\\\\n",
"&&y_{n-1}(t_0)=x_{n-1}\n",
"\\end{eqnarray}\n",
"\n",
" For example, in projectile motion, we give the initial position $x_0=y(t_0)$ and the initial velocity $v_0=dy(t_0)/dt$.\n",
"\n",
"- **Two point boundary problems** : part of the conditions are specified at the starting point ($t_0$), and the rest at the end point ($t_f$)\n",
"\n",
" For example, projectile motion, in which we are given the initial position $x_0=y(t_0)$ and the end position $x_f=y(t_f)$. The initial velocity needs to be guessed by so-called shooting method.\n",
" \n",
"- **More complicated boundary conditions** : an arbitrary set of nonlinear equations relating values of $y_i(t)$ and their derivatives $d y_i(t)/dt$ at any points $t$. \n",
"\n",
"Standard numeric solvers can only solve **Initial value problem**. All other boundary conditions have to be solved by iterations or **shooting**, in which we attempt to solve ODE many times, and try to satisfy the boundary conditions better and better with iterations."
]
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"source": [
"## Euler's method\n",
"\n"
]
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"From any point on a curve, you can find an approximation of a nearby point on the curve by moving a short distance along a line tangent to the curve.\n",
"\n",
"We replace the derivative $\\frac{dy(t)}{dt}$ by the finite difference approximation:\n",
"$$\\frac{dy(t)}{dt}\\approx \\frac{y(t+h)-y(t)}{h}$$\n",
"When inserting this approximation into ODE, we get\n",
"$$y(t+h) \\approx y(t) + h \\overline{F}(t, y(t))$$\n",
"\n",
"If we choose a constant step $h$, so that $t_1 = t_0+h$, $t_2=t_0+2 h$,..., $t_n=t_0+n h=t_f$, and we define $y_i \\equiv y(t_i)=y(t_0+i h)$\n",
"we have simple recurrence relation:\n",
"\n",
"$$y_{i+1}=y_i + h \\overline{F}(t, y_i) + O(h^2)$$\n",
"\n",
"which shows that each step give an error of the order $h^2$. The error grows very quickly, and Euler's method is not being used in practice."
]
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"## Runge-Kutta methods\n",
"\n",
"The second order Runge-Kutta is only slightly better than Euler's, but demonstrates the idea of this method. \n",
"\n",
"In Euler's method the derivative is taken at the beginning of the interval.\n",
"The precision would increase if one could estimate derivative in the middle of the interval $$y_{i+1}=y_i + h \\overline{F}(t_i+h/2,y(t_i + h/2))$$.\n",
"\n",
"The second order Runge-Kutta (**RK2**) method implements precisely this idea, namely,\n",
"\\begin{eqnarray}\n",
" && k_1 = h \\overline{F}(t_i,y_i)\\\\\n",
" && y_{i+1} = y_i + h \\overline{F}(t_i+\\frac{1}{2}h,y_i + \\frac{1}{2}k_1) + O(h^3)\n",
"\\end{eqnarray}\n",
"It is called the second order, because error is of the order of $h^3$. In\n",
"general, the error of the $n$-th order routine is $O(h^{n+1})$."
]
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"Most popular is the **forth-order Runge Kutta (RK4)** method, which builds on the above idea of evaluating derivative somewhere inside the interval:\n",
"\\begin{eqnarray}\n",
" && k_1 = h \\overline{F}(t_i,y_i)\\\\\n",
" && k_2 = h \\overline{F}(t_i+\\frac{1}{2}h,y_i+\\frac{1}{2}k_1)\\\\\n",
" && k_3 = h \\overline{F}(t_i+\\frac{1}{2}h,y_i+\\frac{1}{2}k_2)\\\\\n",
" && k_4 = h \\overline{F}(t_i+h, y_i+k_3)\\\\\n",
" && y_{i+1} = y_i + \\frac{1}{6}k_1+\\frac{1}{3}k_2+\\frac{1}{3}k_3+\\frac{1}{6}k_4+O(h^5)\n",
"\\end{eqnarray}\n",
"\n",
"How do we understand the method? Looking at the above figure, we see:\n",
"- $k_1$ is the slope at the beginning of the interval;\n",
"- $k_2$ is the slope at the midpoint of the interval, using slope $k_1$ to determine the value of $y$ at the point $t_i + h/2$ using Euler's method;\n",
"- $k_3$ is again the slope at the midpoint, but now using the slope $k_2$ to determine the $y$-value;\n",
"- $k_4$ is the slope at the end of the interval, with its $y$-value determined using $k_3$;\n",
"- in averaging the four slopes, greater weight is given to the slopes at the midpoint.\n",
"\n",
"The RK4 method is a fourth-order method, meaning that the error per\n",
"step is on the order of $h^5$, while the total accumulated error has\n",
"order $h^4$. With only four function evaluations, for fourth order\n",
"accuracy is extremely good.\n"
]
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"source": [
" "
]
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"## Example: Bouncing Ball\n",
"\n",
"The bouncing ball has Newton's Eq:\n",
"$$ \\frac{d^2 y(t)}{dt^2}=-g$$\n",
"which can be reduce to two first order ODE's:\n",
"$$\\frac{dy}{dt} = v$$\n",
"$$\\frac{dv}{dt} = -g$$\n",
"\n",
"The initial condition is $v(0)=0$ and $y(0)=y_0$.\n",
"\n",
"We will first solve this with direct Euler's method. Next we will use RK4 and other more advanced method to get more precise solution.\n",
"\n",
"Euler's method requires:\n",
"\\begin{eqnarray}\n",
"&&y(t+h) = y(t) + h\\; v(t)\\\\\n",
"&&v(t+h) = v(t) - h\\; g\n",
"\\end{eqnarray}"
]
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"source": [
"### Free fall first"
]
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"import numpy as np\n",
"\n",
"g = 9.81\n",
"\n",
"# intital conditions\n",
"y = 10.\n",
"v = 0.0\n",
"\n",
"ti = 0\n",
"tf = 2.\n",
"Nt=201\n",
"\n",
"# fixed time point\n",
"t = np.linspace(ti,tf,Nt)\n",
"dt=t[1]-t[0]\n",
"\n",
"data = np.zeros((len(t),2))\n",
"data[0,:]=[y,v]\n",
"for i in range(Nt-1):\n",
" y = y + v*dt\n",
" v = v - g*dt\n",
" data[i+1,:] = [y, v] "
]
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"cell_type": "code",
"execution_count": 2,
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"plt.plot(t, data[:,0],'.-')"
]
},
{
"cell_type": "markdown",
"id": "9f899a01",
"metadata": {},
"source": [
"### Bouncing\n",
"\n",
"Add a floor at $y=0$.\n",
"\n",
"What happens at the floor? – \n",
"The ball bounces back elastically, hence velocity is reversed on collision $v\\rightarrow -v$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a329d199",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"g = 9.81\n",
"\n",
"# intital conditions\n",
"y = 10.\n",
"v = 0.0\n",
"y_floor = 0\n",
"\n",
"\n",
"ti = 0\n",
"tf = 20.\n",
"Nt=2001\n",
"\n",
"# fixed time point\n",
"t = np.linspace(ti,tf,Nt)\n",
"dt=t[1]-t[0]\n",
"\n",
"data = np.zeros((len(t),2))\n",
"data[0,:]=[y,v]\n",
"for i in range(Nt-1):\n",
" y = y + v*dt\n",
" if y > y_floor:\n",
" v = v - g*dt\n",
" else:\n",
" v = -v # bounce off\n",
" data[i+1,:] = [y, v] \n",
" "
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "6c9d5e4f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, data[:,0])\n",
"plt.xlabel(\"time (s)\")\n",
"plt.ylabel(\"position (m)\");"
]
},
{
"cell_type": "markdown",
"id": "1c1a440e",
"metadata": {},
"source": [
"## Example: Oscilators\n",
"\n",
"Harmonic oscilator : $V=\\frac{1}{2} k x^2$ and $F=-\\frac{dV(x)}{dx}=-k x$\n",
"\n",
"Anharmonic oscilator : $V=\\frac{1}{2} k x^2 (1-\\frac{2}{3}\\alpha x)$ and $F=-kx (1-\\alpha x)$\n",
"\n",
"$$m \\ddot{x} = F$$\n",
"\n",
"Harmonic oscilator : $$\\ddot{x}+ \\omega^2 x=0$$\n",
"Anharmonic oscilator: $$\\ddot{x}+\\omega^2 x(1-\\alpha x)=0$$\n",
"where we used $\\omega=\\sqrt{\\frac{k}{m}}$ and we can just set $\\alpha=0$ to recover harmonic oscilator from anharmonic.\n",
"\n",
"Corresponding First order Eq:\n",
"\\begin{eqnarray}\n",
"&&\\frac{d x(t)}{dt} = v\\\\\n",
"&&\\frac{d v(t)}{dt}= -\\omega^2 x (1-\\alpha x)\n",
"\\end{eqnarray}\n",
"\n",
"Total energy should be conserved. The expression for total energy is\n",
"$$E=T+V = \\frac{1}{2} m \\dot{x}^2+k(\\frac{1}{2} x^2-\\frac{1}{3}\\alpha x^3),$$ which can also be written as\n",
"$$\\frac{E}{m} = \\frac{1}{2}\\dot{x}^2+\\omega^2(\\frac{1}{2} x^2-\\frac{1}{3}\\alpha x^3)$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "54312c7a",
"metadata": {},
"source": [
"### Recall the integration methods:\n",
"- Euler: \n",
"\\begin{eqnarray}\n",
"y_{i+1}=y_i + h \\overline{F}(t, y_i) + O(h^2)\n",
"\\end{eqnarray}\n",
"- RK2:\n",
"\\begin{eqnarray}\n",
" && k_1 = h \\overline{F}(t_i,y_i)\\\\\n",
" && k_2 = h \\overline{F}(t_i+\\frac{1}{2}h,y_i+\\frac{1}{2}k_1)\\\\\n",
" && y_{i+1} = y_i + h k_2+O(h^3)\n",
"\\end{eqnarray}\n",
"\n",
"- RK4: \n",
"\\begin{eqnarray}\n",
" && k_1 = h \\overline{F}(t_i,y_i)\\\\\n",
" && k_2 = h \\overline{F}(t_i+\\frac{1}{2}h,y_i+\\frac{1}{2}k_1)\\\\\n",
" && k_3 = h \\overline{F}(t_i+\\frac{1}{2}h,y_i+\\frac{1}{2}k_2)\\\\\n",
" && k_4 = h \\overline{F}(t_i+h, y_i+k_3)\\\\\n",
" && y_{i+1} = y_i + \\frac{1}{6}k_1+\\frac{1}{3}k_2+\\frac{1}{3}k_3+\\frac{1}{6}k_4+O(h^5)\n",
"\\end{eqnarray}\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5d43ca2e",
"metadata": {},
"outputs": [],
"source": [
"## Three simple integrators implementations\n",
"\n",
"def euler(y, f, t, h):\n",
" \"\"\"Euler integrator.\n",
" Returns new y(t+h), where y=y(t).\n",
" \"\"\"\n",
" return y + h * f(t, y)\n",
"\n",
"def rk2(y, f, t, h):\n",
" \"\"\"Runge-Kutta RK2 midpoint\"\"\"\n",
" k1 = f(t, y)\n",
" k2 = f(t + 0.5*h, y + 0.5*h*k1)\n",
" return y + h*k2\n",
"\n",
"def rk4(y, f, t, h):\n",
" \"\"\"Runge-Kutta RK4\"\"\"\n",
" k1 = f(t, y)\n",
" k2 = f(t + 0.5*h, y + 0.5*h*k1)\n",
" k3 = f(t + 0.5*h, y + 0.5*h*k2)\n",
" k4 = f(t + h, y + h*k3)\n",
" return y + h/6 * (k1 + 2*k2 + 2*k3 + k4)"
]
},
{
"cell_type": "markdown",
"id": "58dbc016",
"metadata": {},
"source": [
"Recall First order Eq:\n",
"\\begin{eqnarray}\n",
"\\begin{bmatrix}\\frac{d x(t)}{dt}\\\\ \\frac{d v(t)}{dt}\\end{bmatrix}=\n",
"\\begin{bmatrix}v \\\\ -\\omega^2 x (1-\\alpha x)\\end{bmatrix}\n",
"\\end{eqnarray}\n",
"\n",
"Total energy :\n",
"$$\\frac{E}{m} = \\frac{1}{2}v^2+\\frac{1}{2} x^2 \\omega^2(1-\\frac{2}{3}\\alpha\\; x)$$\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "36c146ba",
"metadata": {},
"outputs": [],
"source": [
"def Harmonic(t, y, w2=1):\n",
" \"\"\"Harmonic EOM\"\"\"\n",
" return np.array([y[1],-w2*y[0]])\n",
"\n",
"def anHarmonic(t, y, alpha=0.5, w2=1):\n",
" \"\"\"anharmonic EOM\"\"\"\n",
" return np.array([y[1],-w2*y[0]*(1-alpha*y[0])])\n",
"\n",
"def E_harmonic(y, w2=1):\n",
" \"\"\"Harmonic total energy E(v,x)/m = 1/2*(v^2+ w^2 x^2) \"\"\"\n",
" T = 0.5*y[1]**2\n",
" V = 0.5*w2*y[0]**2\n",
" return np.array([T+V,T,V])\n",
"\n",
"def E_anharmonic(y, alpha=0.5, w2=1):\n",
" \"\"\"Anharmonic total energy E(v,x)/m = 1/2*(v^2 + w^2 x^2 (1 - 2/3 alpha x)\"\"\"\n",
" T = 0.5*y[1]**2\n",
" V = 0.5*w2*y[0]**2*(1 - 2./3.*alpha*y[0])\n",
" return np.array([T+V,T,V])"
]
},
{
"cell_type": "markdown",
"id": "4d7ffb70",
"metadata": {},
"source": [
"Next we code a generic `Solve` for fixed step integrators, which we just implemented. \n",
"It will take arguments `solver`, which can be `euler` or `rk4` and `derivs`, which can be `Harmonic` or `anHarmonic`."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "07439a62",
"metadata": {},
"outputs": [],
"source": [
"def Solve(t, y0, solver=euler, derivs=Harmonic):\n",
" \"\"\" t is independent variable, which needs to be a predefined mesh of points (could be non-equidistant).\n",
" y0 is the initial value for [x,v]\n",
" solver can be euler/rk2/rk4/verlet, etc\n",
" derivs needs to provide derivatives, for example Harmonic or anHarmonic\n",
" \"\"\"\n",
" data = np.zeros((len(t),2)) # storage for solution\n",
" y = np.array(y0)\n",
" data[0,:]=y\n",
" for i in range(len(t)-1):\n",
" y = solver(y,derivs,t[i],t[i+1]-t[i])\n",
" data[i+1,:] = y \n",
" return data\n",
"\n",
"# Next we evaluate for Harmonic oscilator using Euler and RK4\n",
"# intital conditions\n",
"x = 0 # initial position\n",
"v = 1.0 # initial velocity\n",
"# time mesh\n",
"ti = 0 # initial time\n",
"tf = 100. # end time\n",
"Nt=2001 # number of points, gives step of 0.05\n",
"t = np.linspace(ti,tf,Nt)\n",
"\n",
"dataE = Solve(t, [x,v], euler, Harmonic)\n",
"dataR = Solve(t, [x,v], rk4, Harmonic)\n",
"\n",
"Ene = E_harmonic(dataE.T)\n",
"Enr = E_harmonic(dataR.T)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e0db7595",
"metadata": {},
"outputs": [
{
"data": {
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7K8fd1GVVVeEL+476unnmvEFqNxnf//738eyzz+Lhhx/GhAkTsHLlSnzxi19EeXk5/vKXv2D69On4zW9+g5tvvhnXX389KisrcddddwEAFEVBbW0tnnnmGZSVlWH16tX46le/iurqanzuc58DADz88MO49dZb8dOf/hTnnnsu3G43Vq1aBQBYt24dKioq8Pjjj+Occ86ByTT4zU8QBDGS8YcicS/sIunpY+5JiTPqqBTkmeELRdAr2FnhYiXPOtiDiPZZIbEyYvCFfZj393lHfd21l6+Fw+JI69i+vj788pe/xFtvvYVTTz0VADB27Fi89957+MMf/oC///3v+MMf/oArrrgCra2teOGFF7Bx40ZYLOwXwmKx4Ec/+pH+/RoaGrB69Wo888wzulj5yU9+gm9961u4+eab9eNOOukkAEB5eTkAoKioCFVVVcZ/eIIgiGHE/a/uwMPv7MG3l03CDYvG52wdLkgK8mLEit2C1t4Aen1ixYpfEyJ5cZ2VkR8GOu7Eykhg27Zt8Pv9OPvsswc8HgwGMXv2bADAZz/7WTz33HO477778PDDD2PixIkDjn3kkUfw5z//Gfv374fP50MwGMSsWbMAAG1tbTh06BDOOuuso/LzEARBDBe6+4J4aMUeAMAvXvsE15w+FlZzbjIieJM2lz16qeXCJWfOShyxciwk2B53YiXPnIe1l68dknXTRVHYZMyXXnoJo0aNGvCczcbq9Pv7+7F+/XqYTCbs2rVrwDHPPPMMbrnlFjzwwAM49dRT4XK58POf/xxr17KfOy8v/ddCEARxLLFmb6f+b0UFNh/owdz6kpys1evnTdqizkohFyuCc1b8IXbdsMURK85joIPtcSdWJElKOxwzVEyZMgU2mw1NTU1YuHBh3GO+9a1vQZZlvPLKK/jUpz6F8847D2eeeSYA4N1338X8+fNxww036Mfv2bNH/7fL5UJ9fT3efPNNLF68OO73t1gsiERG7hubIAgiHlsOuQd8vbEpd2LFq7knA5wV7d9uwWGgdJyVkTwb6LgTKyMBl8uF2267DbfccgsURcHpp5+O3t5erF69Gvn5+SgrK8Njjz2G999/H3PmzMF3v/tdXHnlldi8eTOKi4sxfvx4/PWvf8Vrr72GhoYG/O1vf8O6devQ0NCgr3HXXXfh+uuvR0VFBc4991x4PB6sWrUK3/jGNwBAFzOnnXYabDYbiouLh2o7CIIghLHjsAcA633S3R/C3g5vztby+Ae3vx+KMJCes6K5LyMRKl0eptx99934wQ9+gPvuuw+TJ0/GsmXL8MILL6C+vh5XX3017rrrLsyZMwcA8MMf/hA1NTW4/vrrAQDXX389LrnkElx22WWYN28eOjs7B7gsAHDllVfiwQcfxEMPPYSpU6fi05/+9IBw0gMPPIDly5ejrq5Oz5MhCIIY6TR39wMAFk+qAADsae/L2Vpxc1bsPAyUowRb62Cxwque/KGR65aTszJMkSQJN910E2666aZBz7W0tAz42mw26/koAMtrefzxx/H4448POO6+++4b8PV1112H6667Lu76559/Ps4///xsXz5BEMSwQ1VVHOxmrStOn1CGZzceRFNnf07WiiiqntAa2wyOCxeezyKKZH1WeEfbwAgWK+SsEARBEMcFbl9I7zVy4hgW2m73BoS3vgcAb4wYcdpMMf9mYoW3xxeFXxcrgy/rNjN3VigMRBAEQRDDmgOaq1KWb8OoojzIEnNAOvsCwtfyBFiYx2qWdbEARPNXRCe7JstZ4QLGHyZnhSAIgiCGNVysjCrOg9kkoyyftYJodYsXKzxfpcB+xARkXpkTECsc/EnEStRZIbFCEARBEMOado8fAFBVwERKZYEdANDa6xe+VrxKoNivRYeBfGkl2FIYiCAIgiCGNR1eNliQOyq6WPGIFys8ZyX/CGeF56yI7iabrCmcHgYiZ2V4w6cTE2KhfSUIYiTBc1NKdbHCw0A5cFZ42XJM91ogmmzrFe2sJM1ZYY8FwsqI/dw+psUKH+zX35+b0rTjnWCQ3aXQVGaCIEYCnbqzYtX+ZmKlsy8ofC2P1vQtkbPSFwgLFQ7piBWACZaRyDHdZ8VkMqGoqAhtbW0AAIfDAUmShvhVHRsoioL29nY4HA6Yzcf024ggiGMELlZKnUykFDvYDW13v3ixwsNALtuRCbbs67CiIhhRBlQKGUFPsLUO9iDsMYMa/aFI3F4sw51j/ipTVVUFALpgIcQhyzJGjx5NApAgiBFBhxYGKnEyZ6VY+7u7T2w3WSCaYOs60lmJSYDtC0SEiRWeYBtPiJhNMsyyhLCijtgk22NerEiShOrqalRUVCAUEv+GPJ6xWq2Q5WM6kkgQxDHEkWGgIocmVnLhrGg5KY4jnBWzSYbNLCMQVtAXCOvCySi8h0oi18RuMcEbCI/YJNtjXqxwTCYT5VYQBEEMM3zBCK756zp0eoP44xVzMbrUkZN1QhFFn3TME2x5GKinX/yNLHc6nHFKifNtZgTCQaGN4XxB5pjEy1kBWEWQNzByG8PRbTFBEAQxZPx7wwGs2t2JHS0ePLRid87WcccMDizUJh8X59BZ6ddzSAZ7AtEkW3HCIVlTOGDkt9wnsUIQBEEMGW9tb9X/vXxbK5QczOkBomLFZTfDJLM8O56zEggruhMiin4tDBTPWYl2sRXjrKiqGq0GirMeMPJ7rZBYIQiCIIYEVVXx4f5u/evOvqDeEl80vZpYKYiZgOy0mmAxMeEi2l3pT9JRVnQX21BE1YcxJstZAUisEARBEERGHHL74fGHYZYlTKp0AQC2He7NyVrcWeEhIIAVYPAk2y7BvVZ4GMgRJwzk0IcZihEOsXko8aYuA4DNzJ0VCgMRBEEQRNrsbPEAAMaWOzG9tpA91urJyVq9WilxQd5A8cDFS69fbJJtsjBQvk1sGMiviR5ZAqym+Jf1aBdbclYIgiAIIm2aulh38YYyJ0aXsCqggzkKA8VzVoBoHxTeF0UUycJA3G0RVQ0U2702Ud8rXayQs0IQBEEQ6XOwhwmTUUUOjCrKAwAc6MnNeJTehGKFfS1arPiShIFE56ykSq4FYhJsyVkhCIIgiPThLsqo4jzUFucNeEw08RJsgVhnRWwYiAsRRxwBwUUF741iFH3icpJuuHYzJdgSBEEQRMYc0J2VPNTyMFCPLyfly4nCQAU5CANFFFUfGBhXrGghGZ8g4RBttZ/4km6zUJ8VgiAIgsgY7qLUFueh0mWDWZYQiqho8wSEr8UTaAsShoHEOSuxIiRuNZDurAhKsA1nEAYiZ4UgCIIg0iMYVtDhZaKkpigPZpOMMq0NfpvHL3y9hAm2Wv6IV1D+CBCtBJKk+G6HXbCzEgynEQYiZ4UgCIIgMoM3YTPLEoo0AVHmYj1PuIgRSa8vfukyz1npFRgG4pVAjgTVOdEwkBjhwENOicqWgZicFUqwJQiCIIj0aNdCPSVOK2St/T13Vjo84mf1JHJW8nNQDRQtW44/K5iHa/yCmsIFNIfGliRnhcJABEEQxDGDqqrYfKAH3YI7uh5Jp/b9+QRkICpW2nPhrPiPXjWQL6Q1hLPFD8uITrAN6GGgZGKF+qwQBEEQxwgPv7MHF/xuFc7+1Ttw94st542lUxMkZflW/bHS/NyEgVRV1Z0TV0KxIs5Z4dOUE01AHpqcFXJWCIIgiGOAUETBn1buBQB0eIN4duOBnK3V6dWcFWdUrJTzMJBXrKsTCCv6oL8j3Y6CHFQD6TkrCapzotVAYp0VaxrOCuWsEARBECOa7Yd70R3jpqz4pD1na3X08ZyVwWGgDsGly7GVPk5r/ARbkc5KNAyUImdFWBhIy1lJIlZokCFBEARxTLCxqQdANDSzoak7Jw3agBhnJU4YqLNPrFiJ7SbLk3k5PCzUH4wgHBFzIU8VBuKP9wt2VpKFgaJN4chZIQiCIEYwm5p7AABfOHk0rCYZHn9Yn98jmng5K8UO9m9euSMK7qzkx3E6uLMSe5xRfCnCQLE5K6pqXAzypNmk1UDUbp8gCII4FvikxQMAmFFbhDGlrP39vo6+nKylVwPFhIF4WXGP4MRe7nTEEysWk6wnn4oKBek5KynCQEDUFTFCMMLWS9ZnhQuZoCD36GhDYoUgCIKAqqpo6mITj+tLHWgocwLIoVjRwkAlMc5KoYOJlUBYEeoA8DBQohwSnsciKizTr7XRd6QIAwFikmzTcVZ4zgqVLhMEQRAjlq6+ILyBMCQJqCtxoKGciZW97d6crNejdbAtcUTFistmhknLKREZCvIEkvc9cWiP9wma1ZPKWTHJkl65I6J8Oa2cFTM5KwRBEMQIZ7/mqlQV2GG3mDCWOyud/cLXCkUU9GkX9NiOspIk5SQU1JckZwWIcVYCopyV5DkrgNjGcOlVA1FTOEPcddddkCRpwJ+qqqqhflkEQRDHFU2aKBldwnJVaoryAAAtbvEJtr0xrklsgisQFS8inZVUYSAuKkQ5K7x0OS2xIiAMFEyjg611hDsr8f/njjJTp07FG2+8oX9tMiX+DyYIgiDEc0gTJaOKmUipLrQDAA67xU9A5kMD821mmI9ICo06K+Iaw3lT5azYeM6K2Goge5KwjMheK+k0heNCJqKoCEeUQfs+3BkWYsVsNpObQhAEMYS09bJS4soC+4C/Pf4w+oNhOBIM5cuGREMFAaBIS7LtyYGzkigMpDsrgsJA/nRKiQX2WkkvZyX6XHAEipVh8Wp37dqFmpoaNDQ04POf/zz27t2b8NhAIIDe3t4BfwiCII5VnlnXjC899gHW7O3M6TptHuagVLhYKbHLboFTu4i3CHZXeBjoyBAQABRpAqZXoFjxaiLkyO61nGg1kBhnhbe0tyeoBgKAPIvIBNvUU5djXZeRmLcy5GJl3rx5+Otf/4rXXnsNf/rTn9DS0oL58+ejszP+L+Z9992HwsJC/U9dXd1RfsUEQRBHh30dfbj92c1YubMd3/znppw29OLOSoXLrj9WpYWCRIuVZM5KLhNsU1YDCXZWEnWwBaA7VSL+T9PJWTHJEsxapZWI3i5HmyEXK+eeey4uvfRSTJ8+HUuWLMFLL70EAPjLX/4S9/g77rgDbrdb/9Pc3Hw0Xy5BEMRR49/rm8EbnLb0+rFqd0fO1mrT5vFUFESbtFXlKG+Fi5WCeGJFK2Xu8YnLWeFiJZ6TA4h3VgKh1M6KXWCCbSANsQLEJNmSWDGO0+nE9OnTsWvXrrjP22w2FBQUDPhDEARxLPLebuYw8w6rK3fmZrCgqqpo7WWCpDLGWYlOQRY7q6fXnyRnRa8GEjdY0JOyGog93ieoKZxfFyuJL7E8wVZIGCiUOmeFPa81hhuBk5eHnVgJBALYvn07qqurh/qlEARBDBnBsIKtB90AgJvOmgAA+Fj7WjS9/rB+dx7rrJRqYqWrT5zLAaQbBhLvrCSuBtKSXQXNBvJre3nUc1bSdFYoDJQFt912G9555x3s27cPa9euxWc+8xn09vbiyiuvHOqXRhAEMWTsafcirKhw2c1YMrkSAJvdk4spyO1acq3Lbh5wgS1x8inIYsUKT54tsA8WKzxUI2qoIJBONVCOnJVkpct8CrLQPiupnBWtMdwIFCtDXrp84MABfOELX0BHRwfKy8txyimnYM2aNRgzZsxQvzSCIIghgw8VPKHKhbFlTlhNMvqCERzo9mG0NmRQFK16cq1twOOlmlgR7az0aiGewrzBl6B8LlYEDRUE0qgG4s6KgJwVVVV1tyRZGMguMgyURp+V2OdHYs7KkIuVf/7zn0P9EgiCIIYd21tYW4YTqgpgNsmYUJmPrYd6saOlV7hY4TkpZfkDxUqunJVkCbYuG3tsSJwVAdVAwYiiJ0XbklUDWcQMTwxHFIQ1ty1VGIhyVgiCIAih8Pb3Y7WBgvXarB4+GVkkvEyYixNOaT53Vo5egq1oZyWiRJ2ORKXLvJ+MCGfFH9PDJHmCrZicldj2+cn6rAAj21khsUIQBDEMOdDN2t/XFjMXpU77mz8ukm4tmbXIMVCslDi1BFvv0Uuw5e6HNxgWkp8TO+8nYTWQTZyzwsuWJQmwJukSy3ODjPZZiRUeydYDYp0VEisEQRDHNKGIgvBRGAZ3sEeb1aMNFKzVZvY058BZ6dbCPCXOgeKBOy19wYjQhnRJw0Cas6KqQL+ANfkkZZMsJQyT5MJZsZtNkCQp4XF2QVOQufAwyVLKFvo8wZacFYIgiGOYfR19OONnb2PO3cuxJUdlxAC7aPKkVj5YsE6bhtzcnQOxooWBio9wVgrsZlhM7IIrKslWVVW9Giies2Izy3qnVY/feBdbHmZxWBKLB91ZEVCZE221n0I4aM/7DeaPRHuspL6cU+kyQRDEccB9L29HS68fvf4wfvTC1pytc1AL9bjsZv2CHnVWfFBVseXLicJAkiTpAkaUWOkLRsCjO/E6ykqSFC1fFpC3wt0SXn0TD+6sBMMKQgZdM38a3WuBqMvhN+yspNdjJfYYSrAlCII4RnH3h/DWjjb963WN3TkJyQDRvBQeAgKAmkL2b18ogl6BZb1AbILtYKdDdEUQb7wmS4ln5/AkW4+AiiAuHhxJxErsRGmj1Tl6GCiFWOHOi1HhkM7EZQ4l2BIEQRzjrG/qQlhR0VDmxNwxxQCA9/fkZhLygR6eXBsVK3lWE1xauII3cRMFd02OdFaAaGhIVEdZXpLstJoThmXyefmyEGeFiYFkQwWtZlkPdxnNW+HiKHUZsShnJb0eK7FrUhiIIAjiGOXDxm4AwEn1xTi5oQQAsK6xKydrtbiZWKmJcVYAoFxrhc8nJIuCC5Ejc1aAaF4JzzMxChcPjgRlxAB0USai14ouVpI4K4C4XitcrKRaT5yzknkYiJwVgiCIY5QNTUyszB1Tgpl1RQCijdtE065NQC4/okkb7zDLJySLIBhW9MTSYsfgMFCB1mXWLUiseFPM6QHE9lpJJwwEiKsI0ucCpQjLREuXxTgrqXqsACM7Z2XIO9gSBEGMBHa2egEAU2oK9AvtrlYvIooKk5y4RDUbOrS+JuWuI8UKm4jcLlCscFdFluLP6tGdFUF5MlwMJGp9D0R7rfQKqAZKJwwERJ0QUc5KymogTTgYLQlPd+IyQDkrBEEQxzSd3gC6+oKQJGBceT5GlzhgM8sIhJWcJNlyMXJk+/uosyIuZ4WXLRc5rJDjiC4uVtz9opyV5N1kgRhnRUAYyKeHgZLfm/MwkHHxkF41EH/eaP4I72CbWTUQiRWCIIhjjt1tzFUZVZSHPKsJJlnC+Ip8AMDOVo/w9fRZPUc6KwXiw0DR5NrBrgoQI1ZE5awEUjsres6KADeH91nJS+F0cOfFaPv79KuBouXSRjr1cnGUToItOSsEQRBDwMsfH8ap972Jb//ro5x2ld3dzsQKFygAMLac/Xt/p1hnRVVVXawkCgOJTLBNllwLRLvMigjJAOnlrLgEOis87ORI4azoU5ANli6nM3EZGOiEGHE6oqXLVA1EEAQx7Oj0BnDrM5tw2O3Hv9YfwNMfNudsLT48sL7UqT9Wx5u0Ce4o6/aFEIqwO+3SIwYL5jIMlEqsiHJW+vQwUOqcFRF9VnxBdmFOVZ3DnRfjzgqvzknVFC5WrGS/ZiZ9VigMRBAEcZR5buPBAZUUT61pytlaB+M0adPb3wvOWeGuistuHhRK4E5Lh8DBgsmGCsY+LiwMpCfYJstZEddnxRdi3yNlgq2gwYLphoHMpuhYASMVQcEMnBXrCK4GIrFCEMSI5J2d7QCAb5w5HpIEbDvcixa32GZpnINxmrTxKcjNgqcgt3viVwIBQLHmtPT6Q8LCXnz+TrzW90C0QkhUn5W0Spe5syJiNlAwvdLlPEFhoHRnA7FjjAskLjyoKRxBEMQwIxCO6A3ZPj2jBjNGFQIA1u7LTUdZ3VmJFSsl0SnIImf1tHvjVwIBQJHmcqiqOKfDo7kXBQnECndWPIGwoURQDi8lTlYNJDZnJb3qnDwLW9PopOd0ZwOxY4yHZajdPkEQxDBl66Fe+EMKSp1WTKzMxyytSdvHB8RPQg6EI3r1TWwYqFqb1RMIK8Lm5gBAhyd+ci3AQgdcPHQLbn/vitNjBYg2hVPVqLARsV4yZ4U/Z7TnCRAzdTmls6LlrBh0VnjfE3sGTochZyWUTVM4EisEQRA5Z9sh1jl26qhCSJKE6bVFAIDNB8WLlcM9LLRkt8j6UD+A3aWW5bOvRVbn6JVAcZwVINpltltQ3xMeaslP4KzYzCbdARDTpC116bKobrJABmEgYTkr6TsrXGAYWTMYSb/dftRZoZwVgiCOYxRFFXKBScX2w0ysTKkuAADMqGVhoK0H3UJDMkA0X2VUUd6gwXu8lLi1V1yujN5jJT9+dQ7PW+kS5ObwzrSJclYAsUm23jSqgRzcWTHocgDph4HsovqshDMIAwnIIeHOSno5K+SsEARxnOP2hXDRQ6sw/a7X8bNXd+R0LS5WJle7AAANZU6YZQl9wQhaBAoHADjUE3+oIABUak3aRIqVnpiOsvEo0R7vFiRWeMVNfhLxIFKsRJvCJb6Y8+eCYQUhg4nE0dlAyfusCEuw1auB0hAPApwVylkhCILIgIdW7MbmA25EFBUPr9iDTc09OVtrT3sfAGBiJRMrFpOM0Vop8Z62PqFr8XyVygL7oOeqCrmzIrBJW4pSYt1ZEZSz4gnwaqD46wFiK4L60shZie2J0m9QPKQ9G0hYB9uj7KxkNHWZqoEIgjiOCYQjeGYda8rG74r/+UFu+p709Af1O/wxpQ798bHlrGHb3g6v0PXakyS86mEggU3aelOJFS1npUfUrJ4U1UCxr0WEs9KXRjWQNaYHidGwot5u/1jNWcmogy05KwRBHMd82NiN7v4Qyl02PHLFiQCA5dtaheePAECj1t6+ssA2wNrn7e/3tot2VpgQqYgjVrjb0iYwDMQFQaJZPSJzVlRV1St8EiXYAuJa7quqmpazIkmSnhBrtCIoOsgwvT4rRp2cdJvCAVFnxS+gdDmznBVKsCUI4jhk1e4OAMAZ48swr6EUdouMzr6gPgBQJPs7mRgZE9P6Hoi2wm8S3FGWOyvcRYmF56yIzJNJ1VFWZM6KP6QgrPVOSRYG0vueGCxdDoSj6yUTK7HPG3FWwhFFn0rsOEphoEBGTeE08XCUclb4MYqKnM7SygUkVgiCMMyavawZ26njSmE1y5gzuhgAsHZfl/C1Gjv4nB7HgMd5w7aDgjvKtiUJA3FnpcUtJmclGFb0O/ujkbPC81UkKUX7e0GzemJdi1TiwSHA6YgVHuk6K35RzkoG4kFIzkoa4sgqaHjiUEBihSCOURRFxetbW/DOzvachGM4EUXFNq06Z84YJlLm1pcAQE6SbBM5K7xh28Een7CfV1VVvYdKvDAQf6yrLyCku2tsTkgip4MPHBSRs+KJqQQ6siw7lnxBzgoPAdktMsym5JcfEc4KDwFJUuqcDlHOii+LDrZHK2dlJIuV5D4cQRAjlh+/uA1PrG4EwObnfGvppJyss6+jD/6QgjyLSQ/F8P4nvMRYJDzMM+ZIZ0UTK95AGL2+MAoT5HxkgjcQ1i8+yWb1KCqr4ilxxi83ThcuVgrsZpjk+OKhxMl+LhE5K9FW+8n3ymUT0/6+L42GcBwROSt691qLKakYA8T0WQlFFEQ00ZrJbCAx7fZTr2eSJZhlCWFFHXFJtuSsEMQxyJ52L/7yfqP+9cMr9uRsyB93VU6odukXWC5WdrV6hcfGD2s/x5F9T/KsJpRqYuFAj5i8FZ6v4rSa4uZYWGLa33f1GQ8F6fkqSYQWd1bcPuPDDL1pNIQDYpwVo2IljeRaDhc0RpyV/jSTa2OP8YeUrF2yWIckrWogs4A+K6H0c1Zi1xxpSbYkVgjiGOTZDQegqsBZJ1Tg5PoShBUV/9lwICdr8db3kzWBArDpxE6rCcGIgr0d4qpzIoqqJ7PWFA5u0sbzVg4Iylvh+SoVcXqscLhA6vAadzrcPvY9EuWrANHKHMD4rB691X4K8ZBvswhZj7skqVrfAzFdbA04KxmJlRhxka3TwfNVgDRLiQVOXU5nPWDkNoYjsUIQxxiqquKlzYcBABfOHoULZ9cAAN7a0ZaT9Xa0DBYrsixhvNawbW+7uIqgdk8AEUWFSZbihmX0vBXBYiXeWpxSrS1+pxCxkrwSCGBuDk+GNdr3xJOus8ITbA2WLnNnJZU4AsTMB9K711pSrxfrhGQbCuLr2cxyyrATPw44elOXY48baTkrJFYI4hjjYI8PjZ39MMkSzjyhAosnVQAANjR1C2vRHkuj5pyMKx+Y8Nqg5ZTs6xBXSnzYzURIpcsWN6eDixXeIt8oyRrCcUqd0SRbo7h5q/285Lkvopq0eVJMXOa4RIWB+FDBNMQK76FjZD6QPhcoDWfFJEu6eMhWIAUymAsUe5yIBNt0+qzEHkdihSCIuLy9ow1fe3I9Hn1vX06rc9bv7wYATK0pQL7NjJqiPIwrd0JVmWARSSii6CGXhrIj+p5oXzcKDAPxfJXqOHN6gJgmbR4xpcSdfKhgksTZknyRYSAt4TWJsxL7vNEmbakmLnNE9VmJOiupL+a8w22/AYEUm2CbDtG8lWydlfTnArHjonky2RCORPvWHOthIKoGIoijwKbmHlzz1w8RUVS8sqUFsgR8+bSGnKy1rpH1Npk7pkR/bPboYuxp78Om5h6cNblS2FqHenwIKypsZhmVRzRN4+JlX6c4scIdEz6T50gqtCZtbYLa33drvUxKnImdlTKBHWV70shZAaJi5WiHgfqCET0Mlw2ZVANx4WDEWfFp66WTswKwvJUehOALZpuzkpmzYjTZNRiTYJ1OnxWAjTIwsuZQQc4KQRwFHnj9E0QUVU/i+/WbuwzPIEnEh43MPZlbX6w/Nnt0EQDxzgpvfT+m1AH5iAsYL2MW6azwiqaaRGLFxdvfi3FWuADh5cLx4OXKnSKrgVKJFX2woDGnQ68GSpVgGyNm+gzkkAznaiDAeK+VTBrCAcadlUDMedYUfWs4XNSMNGeFxApB5Jjmrn68p7Wjf+XmMzCqKA89/SG8sb1V+FqBcERvcT+zrkh/fMYo9u9th3qFhqASNWgDomGgNk9Av0gZhYeBquJUAgHR9veiwkDdfUw8FCcJA5XmszVFhIF6U8wF4ojLWUk9cRlgSZn8YmgkFMQre5INMeSI7rOSDkZ7rUSdlXTDQMZKl7mzYpallE32OPz/MUjt9gmCiOWVLYehqsCpY0tRX+bEhbNYdc4LHx0Svta+jj6EFRUum3mA+zC+Ih+SBHT3h4RcVDmJWt8D7ILKL7rN3WKSbA9pCbYJnRUtZ8UbCAsRSLylPZ/HE49SgWGgdJ0VYWIlzTAQIKbXCv8/caQRBuLui89QGChDZ0U7Lts1/Rkm2PLKnGxdDu6spJtcG3ssOSsEMQJw94fwzX9uxAW/ew//3XQwp2u9t5vNzVkyheWKLJtaBQBYvbtTeMO0T1o8AICJVa4BpZN5VhPGlDBBsavVI2y9xiTOChCtzjncIyaHpFV3VuKLlXybWS95FeGu9GhiJR1nhSfjGlsvzTBQHruQG0+wTb+UWET5Mg8hpbOe7qwIaLefaRjIeIJtuk6OMWcl0x4rsceSWCGIEcAtz2zC85sOYfMBN27+5yZ9EJ9oAuEIPtjHvvfp48sAANNGFaLAboYnEMaWQ2Lb0e/UhMhErcdJLPyxTwSKlWgYaLCzAkS7zB4QUEqsqiravambtPHnWg1OQlYUFd2aeEjWRp/3WekR0FH26Dsr6YWBgFixYjwMlE5TuOhsIAOly5oIyMuwGijbNTMNAxnteZJpjxWASpcJYsSwencH3trRBrMs4URt8N4vXvskJ2ttbOqBP6SgLN+GiZX5AFg/h3ljSwFAFzKi2NnK8lUmaWvFMqnKpR0jRqyoqqrnkIxKUEossu+J2xdCKMLybUqTiAc+XNCos+Lxh/U5L8lySHj7e1WFLm6yJfME25EZBsrIWTGwHp+gnI44AkQk2GbaZ8Wos6KJlTTFEWA89DRUkFghjjueWtsEAPj8yXV4+P/NgVmW8OH+bmw95Ba+1kfa1OGT6osHhGVmacmvmw+IXVN3VqoGOyvjK5iA4Qm4RvEEwvodaKKwTE0Re1yEWOnQXBWX3Zz0YsCdlTaDzgrPV8m3mZPeuZpkCQXahZy3y88GfyiiX3xSDWHkYsaoWPEG0hcrBQJ6rWTSFC5aDSSi3X56XTqMhoH4/1/G1UBZOyvsdaZbCRR7LCXYEkQW7Ovow3f/sxl3v7hNSKJiIjz+EJZvY1U4Xzh5NCoK7Fg6leWS8Bb1Ivn4IBMj00YVDnh8Ri37estBcWLFH4roE4njhYF4KfH+TjHJrjx/xGU3J0yYrBHorLR72PuiPD9xzxOAdbcFjDsr/H2YqjIHiOa0GHFWuKsiS0B+iosrFzNGwkDhiKJfzDMJA4lxVtKZDRTNWcm2gi3bMFC2Cbb8vPTDQOy4iKJmFULMxlmhMBBBZMnBHh8++8hq/HNdMx59bx8u/9OanPUgWbW7E8GIgoYyJ6bWMMHAE15f3ya+lJiLkelHiBX+dWNnv95i3SgHe3xQVXZRiRcm4WKlzRMw1LuCwwcKVidwVYBYsWI8wZY7K2VJWt8D0cZwRnNWuvUeK8lb3wNAkRYK6hEgVgrzLIN61hyJHgYSkD8CpJlgazees8Lfd2lVA2nHqGr2fUgyDQOJK13ObD0gO3cl04nLQKxYoaZwBJERP31lBzq8QYwpdaDUacWOFg/+9v7+nKz1zs52AMDCieX6Y4smVUCWWHiEz54RQa8/pDdNO1KsFDmsqCthF/ItgsJPzZqrUlucF3eIWqHDoocPuANjBJ6vUpkk2ZXnrLT0+g0nn+pzelI4K2V6dY4xh46HgYqTlC1zirR95R1vsyHdfJXYY9y+UNauA68kspnltEpfRUxe9maQsxLrhmRbEdQfCg/6XumsmbVY4dU5GXawBbILPfFQDlUDEcctqqqi3ROAouRuhg0AHOjux4ubWb+R318+B7efcwIA4A8r9yCUg5jqSi5WJkXFSmGeBVNq2MTgD/Z1CVuLuyqjivLilr5O0aYU83Jjo/AZPbXF8StzgGg/lEYBwwV5GCiZs1Keb4PFJCGiqIbDMrqzkp9cPESbtBlbLxNnpVgLy/QYECvpli0D0dLliKJmndMRTa5NvR47joeBsnOPwhFFd0jS6WAry5IuHvqzbAyXeZ8VLeE162qgzGYDSZJkKCwT0AQO9VkhjksO9fhw/u/ew0n3vIEzH1ghrHokHv9ZfxCqCswfV4ppowpx8ZxRKMu3osMbxDuftAtd67Dbh4M9PsgScHJ9yYDnTq5n1Tl8ro4ItmllydNGFcR9fkIFyyvZJSjhNSpW4lfmAMBoLRTU1GW8Bf5hLcxSlcRZkWVJd14OGsxbiYqV5M5Kqd7+/ig6KwLDQKmGGALMAbCYpAHnZUomybWA8ZyV/hjnIN2wjDMmbyUbdLFytJwVHgbKICxjN2dfERQtXSaxQhxnhCMKbnhqA7YcZBfaxs5+XPOXD3OSQ6KqKp7beAAA8Lm5dQAAi0nGhbNGAQBe2Cy2w+umph4AwAlVBYPu7E5uYOJl3T5xs3P2aTNxeBXOkUzQyov3CBIrvEtsMrGiOysCkmxbU7S+53DnxWgOCe+8W54iZ4WLma6+oCFnsKeP91hJLR54Eq6IBNuiNMSRJEmGe61Ee6xkJlayDQPx5FqzLKV9cXUYnA/EBVLapcsGK5AybQoHRENGxsRKBjkrJkqwJXJIOKIYajudLi9sPoRNzT0osJvxwo2no7rQjqaufjz63j7hazV29qOxsx8Wk4Szp0QnAfOE15U72/U+FyLYqJUR86F+scwZwx7b2eYRknwKRMVKQ1l8sTKuPF9fU8S8Hu6s1JUkDgON1p5rEiBWonN6UiW8crEiKgyUfD0etokoqqEOr11pdK/lcPfFSOlyNGclPfFgtNdKJj1WAOMJtrEN4eLlVMXDYbBJW7YdbLN1VgLhzKqBYo/NRjwEs3BWuDgiZ4UQzoubD2HuPW9gyg9fxa1Pb8pZpYyiqHjo7T0AgOsWjsP02kJ8e9kkAMATqxuFZ4+/80kbAOCk+pIBTsec0UVw2c3o7g/ppb8i2KhNHJ49unjQcxUuOypcNqgqsP2wmLBXVKzEb0U/rpzN6+npDxkOWQDAga7Uzgpvi79fQBioVQ8DJXdWok3ajDkrPME2VTWQ1SzrPUGMzEHSc1bSCgNpzkqfAWdFE0fp5KwA0XBR1s5KBsmuQHQyc7ZN2jJpCMdx6mtm/tkTUVRdAKRfumysSVum1UBANGSUnbOSec6KjfqsELlg9e4OfOMfG9HTH4KqAs9uPIg7nv04J2ttbO7GrjYvnFYTrjh1DADg0zNqUFlgQ7snIDyHZOUuNol4QUxlDgCYTTLOmMBa0/OEWKOEIoregC2eswIAU7Uk220CqnN8wYjuPIxNIFbyrCbUFfN5PcZCQf3BsC54kiXYjtKETIvbbyhEEghH9PUSNYTjVOpN2rJ3VlRV1at7UiXYsmOMz+vJxFnhoZujVQ0ECBArGbTaB4x3sOV5J+k0hONEnZXM1/QPyJFJb00uMoyHgTJxOgwk2Bpot0/OynFAa68ff1ndiP9uOpjTWvVwRMEdz30MVQUumT0Kj101F7IEPLfxIFbv7hC+3gsfsaZoy6ZW6Raz1Szj/BlsSvCLApumhSIK3t/DWs0vmFA+6PlTtXb0H+4Xk0Oyr6MPgbACp9WEhgRD93jfFZ6vYwQ+4K/IYUl6sZugd5U15uYc1EJABXZz0otdpcsGkywhFInO2ckGLjysZlmvhEm4poC+J72+sH4nmCoMBETn9RhxrLizkk6CbbGAJm16zkpe6vWAqKjJNiyTaRjIaTDBlrsj6VQC6Wtas3dzYgVHumES44MMM3dW9PlAWfSS0fusZNEUbqSJlfTfNQQA4N0djXjs1WvQ4myBK2TBf1d+Fr+4+ra0yhsz5bmNB7G/sx9nlP0Prf0f4JH3VVw+YTae3HkJfr9iN+Zrg/FEEFFUvPQxEyMLahpxy99uxJ5QL0521uKsmb/An98D3tjeCn8oktEvYiJ2tnrgC0XgspvRUKzgwf98BivcO1FlysM35t2OOWPOAgBs3N+NiKLClKJJVipipxHLsoTX3/0J/rL7PwhBxedqz8SlZ/1Cd1a2HjburPAQEG/Etq9xBX797p3YG/JgnrMWN537J7gKRukhIqMJr9HkWuaqBPxuPPTSV/COexeqTHm4ad4dmHLCRTCbZFQV2HGwh1VGJeuRkgw9X6XArucfvPbu3fjr7mcRgorLas/CJWf9HJIso8KlOSsGSpfb47Tab2x8B79693vYp+3pN875AwoKWaJ2qdOYsxJRVPRo4qFYS7AN+N34/Utfxjvu3ag25eGbp9yJEyZdACAqMEQ4K7HVQHxPw1BxWd0SXHzm/ZBkdrHhoa5s83J423xXjHjY17gCD757J/aFPDjFWYebz3sUzvyqAcf1BVhH2XTzTjjcHXHG5I/4+rvw8MtXY2XvHlSbHLj5lO/pewoYy1mJrQSKbbL36sof4a97nkcEKj5fdzYuOvNn+p7y3JasxUp4sFjZ17gCv1p5JxrDHpyaPxo3ferP+p6yY7Nv0haMDJ66zPf0nd49qDE58M1Tv49JEz+tPx9NsB1ZTeFIrGRAS48Xv3/7EmwtDgGQAGsYduXv+PGTEn711e9m/MubisdWNWJ+8d+wqXyr/th2fIiFlQfxzu6bse1Qr94fxCibmrvR7glgUv5O/HL3o+iWJcAE7PM3Y/P7l2N0wV1o6mWlvWfEcUIy5WMtJDNjlAO3PLMMq9APmIA96MeG93+AP8wNwmktgicQxq42D06oMvZz8vLrSZUu/Hv5rfjRoeW6r/ijQ8vR9t//h/MXPsqObfEiFFFgyWDexpFwsTK2zIn9+9/FlW/fOHBP/3Me/vL5t/VpxXx6cbZEk2vzEAkHcdPTZ2M1fDF7+n08Gglh+tTPoqaIiZVDPT7MiZO/kw68ey0PAT3z+jdx9+E39T2969DraPtfC7520VNCnBWeXMsbwjU3r8IX3/463DF7uuXZC/DYZW8iz1GCEs1ZyTZnhTVbY/8udlgRCQdx89NL9ffpXvRjw+rv4XElhKmTL0WRJmj8ISVrQd9zRBjo6dduwk9a3tb39IcHX0PbCy24/sInAURFTa8vW2dlYBhoX+MKfPHtG9Gr72kTPv7XuXj882/BnlesOyKKyhJQ0w2tcLgjw79PKNSPm/51Dtbo79M+rF/9PTyhKphywkUAoi33sxIrcSqB/vnqN3BP6wp9T39w8FW0vdCC6y78G4DY/JEsO+byMJD2ffbuewtXrLgpuqe+/WxPv7ACNjtzckU4K9wtCYX68Y1/LcNa+LX3aR/Wr/ou/qJGMHnShWw9A2GnoYTCQBnwwDPXYKsjBLui4vtVS3CSYodflrDF9CRe3yx2au/WQ270db2PnRVbAACX2etwfcE0AMCGksOY5nhbL/sVwdp9XZAQRkHlX9AtS5ismHDv6AtQoqjYLkcws+y3AID3dokJP23WEmcbzA9hFfqRp6i4q2Yp5sEOnyzhe+vuwdxa9kv8YaPxUBAXK/X2rfjpgdcBAJ+P2dNH3B+jtekZOK0mBCOKYfGgOyslFtz51s0D9rRYUbFNjuDXL3wpmvBq0FmJbQj3t1dvwGr4Bu3p7Wt/DL+vW8i8nhat029VgR17972J+w++AQD4gn00riuYCgB4uOcjbPjor3o1kMcfzrqiTU+uzbchEg7i9jduhFuWMEXb0yJFxRY5jN++9GV2nN5rJTtnhc8FctnNsJhkPPHKdfr79EejluFk1QafLOG77/8IwYAHLptZd/+y7bXSGyNW9jWuwE8PvwUA+H959fhqwRQAwO97PsLHW/8FILblvvFqICUSxvfevgW9soRpihn31J2PQm1Pf//SVwDwKh52bjbDDHljN55g+7dXb8Qa7X3641Hn4CRtT7+9+v8QCvRpa2ZfuszP4cJx77638LOWtwGwPb3WNRkA8Pvujdiyje2pPhsoFMmqQi8aBpIRCQfxvRW3DtrTj+Uwfq+9T/mxQNSVyYQjc1b++urXsRZ+OBQVP649F3P5nq76vr6nNMjwGGfT7q1YaWGJrV8tWYTLlv0Kv770eVSEVbRaZDy/8g4h5aec/6w/iFEVTyMgSzgVefjeZ/6Hr1/8D1xqrQYAyJWv4fmNB4SV9q7b14WTi/6NHdYIHIqKXy97FOcvvgf3TrseAPCutRV11m14V5BY+fiAG4WmVizHZgDAd2qX4tKzH8CvLn4elREVB0zAaCtzOjY0iRArLIF1U9uvEZAlzEce7tD29BJrFVRJwi83/hrjysUkvHKxIvf+CR/JIThj93TqdQCAf/bvQ17wIwDA/q5+QwmvvNV+tb0dD7WvAQDcXrsMl579AH550bOoiKhoNgFPv3W7LlZ4nks2tLiZCKgutONX7/4fArKE0+DAHZ99ATde/E9cZKmEKkl4YMOvkG+R9VyAbCuConOBrHj53R/jYzkMl6LiQX1PvwoA+HvfHjQ3v693sc225T7vRFvitKKrazf+2LEOAHBH3bm4ZMkv8KuLn0NpREWjScVTy78JSZIMtdxXVTWmz4oFP1/5XYQlCWdITtz+mf/iGxc/jfPNzNG874N7oSqK3sU269JlXp1jN+N/K+7EFjnM3qef+hsuOPNe3DOZiZQnvbvQ1PQeJEnSByxmk7fCz3FYTejo2IFHOj4AAHxv9Hm4eMnP8auLn0VZREWTCfjHm7foxwJinJX7V96BsCRhgZSP2z/zX9x0yTM4z1wGVZJw31q2p1zYRBQVoUjmv4+BmD4r/1txJ7bKEeQrKn5z3pO44Mx7cfcJVwEA/ubZiebmVQAMOivhaBioo307HtHep98b82lcfNb9ePDiZ1EaUbHfBPzzzVsBjNycFRIrafK3t29HvyxjbFDCNef/BgDgKhiF6+o+BQDY7NyJ1Z/sFbKWqqr4aNt/sSU/CElV8d0F90E2sQ+Jb5z9O+QpKvbZgTrpOSEX8oii4sP97XCXbgQAXFM6B9U1JwIATjvpRpwhORGRJIwp/w+2He413MY8EI5gR0svZpb9A/2yjMmKCZee9QsAbE+/Pobt6dvKx7BLHr0TbLb4QxE0dvZhgv1DrJL7IKsqbl/w05g9/S3ytDue6c6XAbA5QUbY19EHGWG86n4TAHBN2Vx9T08/+Rs4DQ6EJQnPb74PZllCMKyg1UBpL3dWDrb8Ej7NxbnkrJ8DAAoK63Dj6HMBAI+2rUaVk11MDxoYLtjSy9YrDK3ECtXD9nRhNPZ/89m/hV1RsVkOY9X638cMF8zuvaOHgRwyHtn3XwDAV2L29IyTb8JpcCAiSfjTe/8XTbDNUqx0xSTXPvH2d9Cv7emFi+8DwPb0Zu19+pe2tQj43Xr5cjbOii8U0S+O7Ydex7tqH0yqitsX/lzf01uX/l5/n76/4RFhzorTKuGx/a8AAK4rn4eKSuY2LjzlVv19+tiqHwMwVhEUW7r8j3d/CJ8sYbpi1ve0sHA0bqxbBgB4tHU1ggGPnmBrKGfFasL2T/6LVeiHWVVx+6Lonn5L+zzdLIexduOfBpQ4Z9prJaKoulthNal4rOlVAMD1FaeivIK5jYvm3Yr5yBuwpzYDgwVjO9j+/d0fwi9LmKGYccGiewHwPV0KAPhz6yoEAx6aunws0+11Y62JNUW7tOZC/Y0OAJee+RPUhFX0mmS88N69Qtbb2eqFI+8FAMBScwnGNpylP1daNhGXuSYAAMzFa/DWjjbD633S4sF4y8s4aJXgUlR8ftF9A56//kR2l7M934siUws+NNiS/pMWDySlH3sKWYfar064bMCenr/gxxgVAdwmGbOL/otdbV5DvWV2t3mhqkBNGQv/LDOXYmzDmfrzZWUn4HP54wEAhxQmLoy0wHf3h9DVF8RM12vYb0LcPf2atqevBlsxsZiFxIyEgpq7+2GT+rA8tBsAcN2kLwzc04V3Y1QE6JYl9Lczx8pYGIgJnT3d/wQAnGMpQ0P9Iv35svLJ+Gz+OADAP3b8HZUuY11sOzxMPOQHnkeTtqeXL75/wDHXz7kJAPBioAVOtLDzsgwDcXekLC+E53p3su8/6XJd4ALApxfchaqIik6ThJff+4leNZTNfCAucMyyhH9vYiHXs80lGDPmDP2YsvLJuNhZDwD469a/CMtZad3/F+wzqchXVHxu0T0Djrl21g0AgBf9h9DVtdtQRVAfFw+SB0/3sDy8r0z43ID36QWL7kZlREWXLOGVVffoYZlsqoG42MizmPDkenaDeba5FKNHn64fU14xFRc5WJuGv2x5HBaTpIfzMv3MiT1+4+aH0Ki9Tz+7MLqnkizj2plsT1/wHUR31x7dzckmT4a7I2bVjafd2wAAX5k48PP0wkU/QYW2p6+uuk93cshZOQb526v3wm2SURZW8IWl3xvwnMlsxbkFswEA2yPrDJUuclZs+QQ7XewC9vlpXxn0/Ofm3QYA2OEIYcP2dwyvt66xC/aitQCAC50NcBWMGvD89MmfxWTFhKAsYXrxc1hvsJx48wE3ZhW8iF6TjMqIisWnfGvA82aLHZ8pZ3fMvqKtiCiqoflEn7R44JR7sN3ZAwC4bHriPV1v9qHGutuQWNmn5bs4ipnNfWH+WOS7qgccM2PK59ieShIm5P8HQPZJth5/CD39IcwqeBFuWUZVRMWik28ZcIzZYsdnyuYAAFb2rAQAHDIwYbq1N4B8uRsrVdYH57I479PLTmZ7+p7iRV3eXu08Y2GgnX3sbvXC/LFw5FcMOGbm1C9gsmJCSJKwY89DAIw4K+z3uFx5Gj2yhKqIioUnf3PAMRaLA5dXzAMA/Kf5TUMt9/nnRo2jBy8FmdD6oiYUYvniqXcCAFarfVD72AU/62ogTQCsOPw8AODS/PEDqlQAYM70KzBFMSEgS3jh/fuj84GyyFnhgiPY8xTcsoRREQz63bdYHPhC+UkAgGf2v6bPBsqmoyx3Y4pMbXgl2AoAuGL2jYOOu2I++0xfpXrR2rIp61k9scc/v4f9Tn/GNWHQ+/TEGV/CZG1PX1xzvxBn5VDTo+iVJdRFmHsTi8XiwBfK2OfpM/tfpanLxzJrOlny4CnyWFgsg7t1XnHmD2BWVey1q/jvyr8bXm/7rt+iX5ZRG2Zv7COpqzsNp6h5UCUJNvwbB7qNJWdu3LUJO5zsInLxnMEfkJIs47Ja5u60FzZiXWOnofU+PuCGUrSJrVc8HSbz4LLvi0/9Hsyqij12FWPtG7HVQChoZ5sHMwpfgE+WUR+RMGf6FYOOGT36dMyDHaokYXzRi9jT7s06H2hfhxelpkPY5mB7esns+Hv6uVrm7uy2fAJAydpZ4QMClWKW/5NoTy+afwfMqootpjAabJvQ0x/K6o5VUVS09voxo+gF+GUJDREJs6d/cdBxY8acoe+pKfw0gGiibKa0ewMoMx3AByYm6D479+ZBx0iyjEtrFgAAXu3+AIACty+U1Ycyd1aaVCbiP1M6O+6efvrkW2FSVXwkh1Ahs5y2nixa7nOxMsn1OkKShPGKjJnTPj/ouLq6U3GyaoMqSdi0548AsstZUVUVHn8Y+XI3PgAT5hcl+N2/RNvTF9rWxkxezj7hdXc/29PziqfE3dMLT/kOZJWFZiKeDQCydFY0sVKo/A8hScIERcb0qZ8ddFxd3WmYq+3pC+t+NSDJNhP82vus2NKD1Qq7ubroxMHiSJJlXFzN3J0XWtfq7e+zawrHXuPHve8DAD5VPDXpnn4kh9DdzvJaKMH2GGPLng+xxcY+YD9/yq1xjyktnYATw6yq48N9/zS0ni8YQbO0CQDwqaLZA+y8WC5pYPHyFtdhvLcz+1CQqqrwdD6FsCRhcsSEiePPjXvcslNug1VVcdAqwdexwlBYZu+BzdiZxz58LjrCAeCUlk3EGTIr7astXIGtBrrK7mzxIFC4HQBwScVJCff04jHsZ28pOIxgOJy1CNzX3ofJRa8gLLGY/ITx58Q9btm8b8GiqmiyAOPsm7IWK81dPpSbm7Ajj/2fXDTvW3GPKys7AafLrAS8vpg5coezcFc6+gIIKyr8BXxPT064pxeNYT/7VuwDoBgIAwUwqfANKBKrrIgNjcbyqVNvh1VVsdekYnzeJgDZJbx29QVRZGrBFgs797wTvx73uPKKqThNZtOzQ0F2N51NzgoXK34bc0vOLpqS8NgLRi8BACzv/RiAAk8gnHFyti8UQURRMVUTR/URCeMalsQ99px5t8KsqvhEVlChibdsxIM3EIZDcmODzMTR2VP+X9zjyson41SJfZ7uOshKio0k2LZqSfxnF09NeOwFdezG4X8dG2EzszBQppVr/DNxWsHrCEsSxkakhO/Tc+d9C2aVVVqavO8NOD8TAiEFTrkH6yRtT6cNvhED2Pt0nsSKB1Zu/QMAlmMTHkGChcRKCl5Y83uokoSJARkzJy9OeNziUewXfbu5CV4Dw8ze2fwBdtnZm/Yz87+Z8LiFJ94Au6LisEXCR9ufz3q9/Z39cOftAgCco4Ve4pHvqsYZpiIAQGXBCmzJcmaPPxSBLfQ8VEnC1IgZo0adnPDYc8awPW1xtWDLwZ6s1gOAlrYd2K3t6blzv5HwuEVzb4BN29MJ9g1ZVwTt7eiDP5+FPZZVnJTwOFfBKJxhYoJsVOE7Wc/rOdDdj4kFzP2boVhQUzM34bHnaBe6Q/mHACh6Ym4mtLj9KDM3Y7edfdCde9JNCY9ddOINsKoqmsxMkGWTYKuqKjq8QQRdLB9nSdmshMe6CkbhNE3kjiliF4FsEsK7+4KYXLAcisQSa2trT0l47Pn1TJBtwX4Ait75NhPc/SE45R5ss7H/jyXTBzuqnLNPvhV2hVXNjLdvgKoC3gxLe3kYRy5geQ5nF01KKDgLi+qxSPvdjygsEdeTZUfZaQVvIKCFKyZN+HTCY8/T3qfv+nYAULISK/3BCPLlbnxs1fZ0WuI9XTrvVtgUFY0moMHG3JyMnRXteMXJBOeS4skJjy0qbsAC7Xe/1f0cgCwHGUYUTHW9gaAkYXQEmDgu/s0mAHy6ju3pqz1M5PLzRwokVlLwkXcTAGCmPbEqB4CLFnwTdkVFi0XGf9/9W9brrf74T0wcBWVUV89JeJwjvwLzJPZmb+t9Meuy6VXbN2G35nKcPeuapMeeM4ZllR9ytWDdvuxCQdsO98Kfzy46S8sT/3wAsOjEr+uCLNT9ZlZhGY8/hGLpRajaHXlV1ayExzrzq7DAXAQAqC5cmXXeSlvHLuzS9vSsmYNzOWI5V9vTw67D2N/hzer/8UC3D34XG0B5dqo91QTZIYuECfYP9RBSJrS4/ZhU8CZUiVUeVFbOSHhsvqtaFw+jClZmVfHU6w/DrrZidx5zH86aflXS45eOZnfJh5wHAShZ5a109QehuFhi7ZLS6UmPPWPOdbCqKg6YJYy1f6Q3d8sEty/ELjqyhDERYMLYZQmPdeRX4DQzdx1Z+WumoaBefxh5Ui92aaHKs6cODuPFslQTDztNBwAoWTsrZhcLlS0pnJBQHAHAWSfdDLvCyu3H2zdkJVb8oQimupZrzhEwfuzShMc686v0PXVZV+jnZ7aeAofkxid52p4mcI44S+uY67I50pjVegBzVswFfE8nJt/Tk2+CTWFlzOPsmwCMrLwVEitJaDy0Ezts7EPgvLlfTXqs01mO2WFmB3/Q+EzWa+4KbAIAzHUmVuWccxvYB9p+x2HszXK2zJZPHkdEkjAuJKGu7tSkxy6ceyPyFNZXZvee57Nab+Ouj9IWR478CpxhZh1WS50rsbc9c/Gws9WLcD5zjs4qm5ny+KW6eGjBzpbM3SNVVWEL/BeKJGFSRE56Rw4AC+Z+XRe5VdL7WSVntrbv1Pd0SYo9HSjI3sXhLMqXW3r9ustxZhKXg7NsNPtQbnUdRntvFmEnbwBTCpYjrOVy1NcvTHo8d3MOWJh46MrC6fD3HcYuBztvSQpx5MyvwnwtvFbrehfuLMNAZhdrALmkMLHLwTmrlrm87fmsoi7TiiBvIIyprjcR0BJdT5hwftLjz5hzHSyqimYzUG/bklWCbdjvxm4nC3UunfyFpMc68itwquY81LhWZ90UTi7QXI409nRJ7SIAQLO1GUDm1TmBUARTXcw5qk3hHAHAgjnXwayq2G8Gxtg+zq6UONyjC86lUy5Peqgzvwqnmtj7dFQBE7kkVjLkoYceQkNDA+x2O0488US8++67Q/2SAADPvvsbRCQJ9UHgxCmLUh5/Rg37UN4mH0QwlPkv1+4De7DDzj4gz5+T/KIDAItPYnfJrRYZb334dMbrAcD+MOutMs8xKeWxeY4S3c3p6X8tKxdg976/IiJJGJ+GOAKApWPOBgC0uNqwNYtQ0Pb9O7HLwS4eS6Z/OcXRwIK5N+jiobf9zYzXa/cEEHTuAACcVZL8jhwAHI4yXZBVF65CU1fmeSsR77+ZOAqnFkdAzJ7mt+Jgd+ahp5b2fWm7HABzc6yqikNWCRXShxnnArR7ApBcbE+XJMnl4OS7qqPioWBlVsMMy/CSfkeeKO8gliW1LAm1y3UoqwTbXm+XfiE/e0ryCzkALNQudE1WCaNtWzOuCPL4Q7AVaLkcBeNTXsjzXdU4RWZDN+sK3oU3kLkLUGt+BT6tWm3qCZemPP7MUSwJtdt1CL5QJOO8HL+vC7u1C/mSqckv5ECMeLACo63bMs9ZCUdg0VyOs1M4RwALWc7TcnNGF6zMqilcve11+GUJ1REVUyZdnPJ4fU/zDwIYWb1WhlysPP300/jmN7+JO++8Exs3bsQZZ5yBc889F01NTUP90rDJzZLJZpjHp3X8xQtvhk1R0WKR8MqazMXDi6t/h7AkoS6kYtoJ8ZPdYnE4yjA7wj5Athx4NuP19rc04RMtefjcWVeldc6yeuY8NOcdxqEsElAbw5sAACc7Ul90AGDBnOv1PJJPdr2c8Xq79/4VYUlCfQgp78gBtqenaBc6JbI8Y0G2o2mvfke+dPqVaZ1zNnce8lvR2J65Q9ZlZnePZxSmFkdANGxx2CrD15156Xt32z8RliQ0hKW09jTWeRhV8G7GXWxbuw5jl4O9T5dMTW6tc5bWMeehI/9QxsMMwxEFYQe76CxypRbxALBozvUwqSr22wBL4KOM1gOAYPe/2IU8nN5Fp6CwTr/QjXG9k3EYqMfTjd1OJlSXnHBZWucsqWEXuh5XM7yBzNZTVRWyg90YLXY0pLyQA8DC2V+FrKpotAHVlt0Zt6OXvc+yC3lYxZSJF6U8vrBwNE7WklDHFKzIOGelr787KjhPSC04AWBJzWkAAHd+c1bt9k3OTQCARc6xme+peQ+JlUz45S9/iauvvhrXXHMNJk+ejAcffBB1dXV4+OGHh/R1tXYexFYLs6zPTpLsFkt+fjmmh9ibfdXOzKuCNvesBgBMlxvSPueUCnZH94ncDCWS2Zv95dW/R1CWMCqkYuYJiROzYjlz7teYeLDKeGf9cxmt19bZpDtHy9IUR478CsxW2Ifyga7/ZrQeAOwLsDK9OdZxaZ/DxcNh56GMS203bnsMIUlCbUhN644cABaceL3uPOzfvzyj9Q60NWKn5nIsm5U8P4bjzK/CXJWJ3Ej49YzWA4BDEXbRyWRPufPQkX8o4+nLe/f8DQHtojNx/KfSOoffJTfbJHg6389ovZauVv2OfGma4qiwqB4ngrU1KLNkLnI7wmxEwlxzXVoXHQA4q3o+AMDtakJvhmGZpsan0C/LKA8rmD75M2mds2jO9fqFTu3fmvqEGHq9buzOZ2HcMyd9Lq1zikvGYQ5YM8GxrrczzlvpjLA+R3PNozPe015XU8Y5JAcan4JPllERVjBtcmrnCAAWz74ekso6kttDOzJar7/fjd1OtqcLx6e3XknJeMzW9nRc4dsUBkqXYDCI9evXY+nSgYlPS5cuxerVq+OeEwgE0NvbO+BPLnj2nd8gKEuoCalYMPuC1CdozC1ldx9blH0ZfWD19XXhYwu701kwMb1fZgC4aMFNsGglxe9t+l/a5wHAhk7WHGwq0v9lduRXYHqYCbJNTZm5Ry+v/j1zjoIq5kyJX84bj1MrWBfPPebM3DZffxe2Wdmdzqnj07t7BIAz596g7+kHH7+U0Zpb3SwWPCWDPXXmV2GWtqdNHZkJwLfWPazv6Qnjz0x9gsaCKranh+zNGdnr/f0d2Krt6Zz6wT0rErFozvW6eNi3LzM35xMPq+qZqoxKe08LC0djZkQboOh5IaP11mz6M/yyhMqQgmknXJj2eWdWshCcO39/RnfloUAfttpYftS06uS5I7EsnnOdfqHrat+U9nkAsKOHDfSbEq4a0JU3GSUl4zFDYT08LKEXM1rv/U2Pok+WURpWMHf64P4xiTizQmsOmd+oD0JMh2DAg602dm04oTJ57siA9WazPd1rB/p6MhNk23vY+/qEUFXa79PSson6nhZIr2S03qqNf0K/tqczp2bw+VbBkvD9+fuoGihdOjo6EIlEUFlZOeDxyspKtLS0xD3nvvvuQ2Fhof6nrq4uJ6+tL+hGUUTBdKkOsin9ce+XLriJfShbJby3Kf0L3f/e/R38soSKsIKl89KzEAGgtKgWUwPsQ/nNrelXIQX8bmw2s1/m2XUXpX0eAMwqYncfW5XGjM5b08ZykcZFMvs/+9SpN8Kk7enGba+lfd6b6x5hexpScMac9O48ABaf53v64Z5/pH1ewO/GR9qeTqhM/6IDADMLWf7OJ1JjRufxPR0TrM3ovHPm3ajnPHz8Sfq5Oas2/BEBfiGflP7PWFhUjylB9qG8vTl91zEY8GCTqQcAUFeUnvvHmV3ALnT75d0Znbf6ECsDr/dXpn3RAYAlc1gS/h67ir1NG9M+b81Hj8KrXXTGjUvP5QBY35zJIdY191Br+jcOoUAf1kusmq8sLz33jzPXNQsA0GbZldF5K/azz8IxfaUwmy1pn7d4Bssz250XRnvXnrTPW7Ppz7o4qq5LX3CWlU/G5BATb12d/0r7vFCgD+u0PXVZ0r9pAIB5hSzxv8uW2fv07UYWFq/zlsBuGdwILhGLp0f3tLd7X0ZrDiVDHgYCAInPHddQVXXQY5w77rgDbrdb/9Pc3JyT13Tb5x/Bm1/cgG9f9OeMzqsqr8fUABva9vrmJ9I+770DzP4/IVwFiyW9Ox3OCU7Wy2NDMP0PkBUf/hH9MhshsOSU1MlnsZw192vahQ74ZHd6YYtgwIONMrt7bChLz8rnVJXV4wQ/+2V8ffPjaZ/3ViMTNg3+Cjjt6f8yA8A4O7vQbQzuTPuc9zf9Wd/TyRMuyWi9udOuZcl9FmBf44q0zgn43fgQTBy58hKXZcajtGQMJvrZRePNLenv6RuNLGxU4y1HdZEjozUbzOxDeXMwfbt77UeP6xedytr0HU4AmDnpK5BUFbttKg4fWp/WOaFAH95X2GRxk7ogo/UqK6djvJ99bq3a8mja572xhzk/dd4SFDsHd8hOxkQzqxrcGUzfBfhg8+PwyDKKwwqspem7DgAwZwILiX9iC6OzI73fjVCoH++FWLv7gD91Un0stbWnoD4IKJKEjdvS/yxevoeJozpvCZx2W0Zr8j3dFdqS9jlrP3oMXllGSVhBJD9x2Xk8TtT2dKctjK6u9ARLKNSPd4KsGajbMw9mU/qX8rq6U1EfBCKShG17nsjotQ4lQypWysrKYDKZBrkobW1tg9wWjs1mQ0FBwYA/ucJqtaGydFTqA49gZgFrdLY5+Elax4dC/dgos+GAM6rPy3i9M2Yzi73RAjTuX5nWOcv3MFU+1leGqsL8jNabWj8Rk3zs4v/ihvQ+lNdseizGskzf5eDUyayXx1rvtrSODwX6sEa76BRYM7vTAYCJDVfCpKrYa1HR1PReWucs36vd6XhKMbbCldl6dRMwoZ+Jh9c/eiytc9Z+9Bh8soSysILiyvTDapzyMOsdtLo3vQ/lUKAPK0NsT72+0/S25OlSVfV5SKqKnRYlbfHw5h4WbqjzlqCi0JnRenXVUzHez17jWx+ld6H7YPPj0YuOK7OLDgBUBsYCAN7v+jCt48MhP97yHwYA9Hjm6vOF0l6vnIXitlqCaV/olu9m4eIxfUUodGQmOGtrT0J9AFAlCSs2/iGtcz7c/Fe4ZRlFEQWtyMzJAYBRATZo8IPONWkdHwr14+0Au6b09J4EhzWzm7+yUvb5tNUSRHeabs7yPWxPR3uLYbfZM1qvuuZk1AeYIHtnQ3p7um7T4+iVJRSHFewNLspoPQCoDY4GAKzvTm9PhwNDKlasVitOPPFELF8+8O58+fLlmD9//hC9KuNcMP/rkFUVe63AxztTi4d3P3wMHhP7ZT5nfnpJkrHMmzQNE3zsQ+5/6/6Y8vhwyI81EabKq/Mzv5BLkoRqMPHwnic98fCGfqdTjJl1pRmvWVd7BWRVxS6LigMHUv+Crdv8hH73WFl7UcbrTRpzAib42Ifc8o9SC7JwyI93Auzu0d03DzVFmd0hlzqtsPexypPlnelVk7y1l8W4a70lqCvN7EIOAGbXZyCrKj4xKzh48IOUx7O7RwklYQX99swvOpUVU3Tx8OZHf0p5fCjUjzf9rI+I23MiyvIzc8fKnDY4PCxZ/Y3WdWmd8/pulsQ92luMYmdmF3IACJmYa7hJ9sPd05jy+PUf/xU9soTCiIJt3gUozMtMrBSVzdEvdCs2PJLy+Eg4iLe1Pe3tnasPJkwXp82EIg8L4755aFVa5yzf9TwAoN5bBIc9s98LAAiCicZ1ch88vQdTHs/EkbanfWcgz5KZqHYUxexpGoIsVnC6PXNht2R2WbWZZRR72E3xG4fSvDHaExWcljizgFIR1vZ0fZp7OhwY8jDQrbfeij//+c947LHHsH37dtxyyy1oamrC9ddfP9QvLWsmjZmGEwLsQ+eFD1K/2V/d+TwAYIKvGGPKijJez2Y2oUZld8kr3R+nPH7DlifhNskojCiYPjm9aocjGT36CphUFbvNKpqbk39oRcJBvKN9QEqheSjLz8yWBYCpDdMwXhMPb6YhHri1PqavCCfUlGS83rjyfFg9EwAAyztS5x+s/5h9QBZFFPjzlulj5tNFkiT0mS9k4sGkoLk5eQVL7EXH7ZmD2uLMLwLlZRNjxENq54Hv6WhvMSozdOMAoLLArouH5WmIh3UfPaFfyLd6F2b8vinIM2Ofh4nxDfCnDFswccRdjpNQ4sz8IiC75mB0QEVEkvDOhtQ3Dq/tZC0H6r2FMJntsGd4YS3Is6DIw/KV0hEPH25+Al2yhAJtT/lgwnRx2Sxo7mXJ2WtUL7yew0mPD4f8eNN3AADQ23sinBm6HAAQtJ+M2qCKsCRhxfrUVaJ8T8f2FSECKxwZOoB2q0kXD28eTN3za93mge/TTP8P7RYTmnpZyPF9xYM+b/x8TU4o1I83fUxg9PbOhc2c2XoA0Gedi1FBFSFJwjtpiNzhwJCLlcsuuwwPPvggfvzjH2PWrFlYuXIlXn75ZYwZM2aoX5ohpthZfH6DL7nFHgkHsTbCfuHHFWbucnDGjvmSfpd86FByC/r1T1jFSb23EPPGVWe13pwJM3TxsHxTcvGwccvf0WWS4FQUOMtT95CIx5SaAti9zGJf3pY8hBAJB/FWf/QDclJVZiEZAChyWNEaOheSqmKrHEkZtnhDv3ssRH15UcbrAUBZ2QTdzUklyDZseRJdsoT8iIJt3oWoK8ncBaguzEOeh+3pG2ns6dsxLkd1YWZWNwBUFNiw280cmY0IoKMjee7K69qeNnjZRafclZlYkSQJIdsUNPjTu0te99ETuuDc5l2AIkfmYqUoz4JSbw0A4I0DyauewiE/3tAu5J7ekzJ2VQCgwG5Gc8yFLpV4eOWTfwMAJgdKEIYNLntma9otMpqC01CjXejeTRG2+OCjx9Cl7ekW72I4bZlfWB1WE8o9bE+XN7+d9NhQqB9vaO/THvdJ2mvOUDyYZV2QrU5DPHBxNDNchgisGa9nM8toDEyP2dPkIveDTY+hW5ZQHFGxxbsItgydHLamGRUe9tn/RvNbGZ8/FAy5WAGAG264AY2NjQgEAli/fj0WLMgssW04snTudQCAT6wK9h/YkPC4DR8/hS6TjPyIggUnXp31evOnztXvkl9P8gESDvnxRv9+AIAcPBFjSjO/yAHArNoi2DysWV4q5+GlHayiZry3ANNGV2W1XlWBHS0BlpfxkRxCa+vmhMdu2PIkOk3sQr6zfxHGlmXuAgBASdlkTND29I1NiT9AwiE/3uhjZdVezyzUl2UekgGA0SWO6J62JxcPL21nFTXjvIUIw4ZRGYadAKCmKA873az54CYE0N6WOElz/cd/1e/It3kXorIgC7HisqMlPBYNfpbz8HaS9+mAEFDvSXDZzBlfBACgxGlFoZeFLd5I4TxwcTQlyC46pVk4K0UOCw71skZfqyNu9HsTT0T/YNOj6JYlFGkXnaJsxEqeBY2BaagNpRYPoUCffiEP+1mYPdMwkCRJyLdZUellOYXLm95Ievyru9iF/CRUIQIrnBmuBzCxclATD6sUd1Lx8MGmx+CWJRQrKrZ6F+rnZ0Ke1YR9gRkYleaeLtf21GVmN5s2c+ZhIEBGpbcCALC8KXnRwqva+/R0Sw0isMKaQXJtdM3onr4XTv4+Xbvhj7js8Vn4zxu3ZbyOSIaFWDkWOWXKKZjgZ9v77OrfJTzuPx8/CQCY0F+AeROyL8OeUVsEp5c16UrmPKzZ+Cd0mphlWT7q8oRVV6kodFjgNV0ASVWxRQ4ndB6CAQ9e0yxLt/sUzK4rymo9SZJQUTED47Rqi7c2JhYP/9v2dwDsQj66vAzWDD88OOPK82Och8Ru1eoNf0CHid09fuxZgoYs8kcAYHSpE5/0LoGkqtgsh9HSsinucQG/G6/zC7n7FJS7bFldyGuK7GgL12N8QIIqSXgziR38P00cTQuyO/JsnJVihwUWk4RCD0vue+NwYvGwduOj6NEu5Fu9CzN2VThl+TbdYl+jetHrjl89GAx49Au5FGL9UoqzEitW7PbPwaiwioAs4bW1v0h47Cu7mMN5qoldyLNzViwAZFT1sbvkl/YnLu1/f9Of4ZYllEZUbO9bBAAZh4EAJnAOudmeroj0oCdB+SvbUyYsavPZiIdswkAOmxl7/LNQGwaCkoS31iX+PH1Fu5CfaatFBOz/L9OcFXa8jPoAc3Neaky2p39EryyhPKKiy8Qq8jL9XTSbZJhlCYfdTDy8He5OmO8UDHjwppY8PL2SFWNk46xYzTL2+GejVnufvv1h4j39346nsU2OYEtH6hSDXEJiJUdIkoRJWgncGnd8Z6W/vwMrIuyNV2E7N+uLKsDefHku1qNhsymx8/C/ncwGbvCUYt74zHpzHMn4upm6m7N8U/y7j3c//D08WsXKtr5FmF5bmPV6U2oK4PKw8OCrLfFzOvr7O/C69svc1XN6ViEgzrhyp+48bEQAba3xQ3r/2/UfAMDE/nKEYcO4iuycnNElDnSE6zAxoLk5G+OLh5XanlZEVGzpW5hVvgoAPQk4v5eJh9cS7am3Td/TUIDtR2UWYkWSJJTn27C/dxEAYK3an3BPn/2E9Q05zcTuHsuyFCslTiv2B6ajISwhLEl46f2fxT3uzTUPwK3t6bb+M7VzMxcPrJpHxuTwRADAc83xe9h4eg/iNW1PxxezpNysxEoeu/jv7WJi4F3Fk3BPn9d+95fl16M3wER/QYZhIADIt5ux2z8XE8MyQpKEl9bcH/e4N9c8oL9PA052Yc3KWdHEw0ywm7Fn978a9zhP70H9fXr6WPZZaDPLkDPMH+PipjfIyrrfVXoTuo7P7WS/+8vyG+CPsPOyuXGwmWXs8s/FxAjf05/HPe6NNb/Q97Sw6mLt3MzXs2puzhwTc3KfbYw/yqTX3YzXtcKBC6ZckfE6IiGxkkPOmH4dTKqKbdYIduwc3CDutdX3o0+WURVSMH9OenNkkjFj4smY4GP/pf9afe+g5zs7duLNMGtc1NK9CKeOy7wqJ5ZZo4vg8LAPkP+0rIESGdzy+5ndzAau663EuIqijGPksUyuLsDOnmUwqSo2SEF8sivenv4M/bKEmrCKbf1nGBIr4yvy0RauxyS/DFWS8K/V9ww6pqNjB94Os7Lzpg5mO48rz06sjNHyTrhD9p/Dq6EqgztM/kubeH2SNAYqzBidRb4KwCqQrGYZu3qWQVZVfCgFsGv34AvBK+//DD5ZwpgIsKFnHgAWlsuG8gI7moJTMD1sRkSS8O9EexrpAQDUl7AE8PIskrIB6Emys2SWQ/bMoZVx9/Q/jey9dHHxNPBZkiXOzNcsymPrdUc+A5OqYqMUxN59gwXLS6t/Cp8sYWxEQsTFmutl76wA+wNTMVuxQpEk/HftYPHQ2roZb0W6AQAXzvya3mE3P0tnBQBOy58LAHi2Jf779Jl9rOz8kuLp8IWZYMgqZ0Vbz57/Jf192tg4OB/oxdX3wSdLGBeRMHoMK+nONAQEsARbAGgOTcMs1YKIJOG/cQRZS8sm/X166Ynf0NvzZ1oNBAA2TZAtLWG/X88dfi/unj6t7elnSmYgrLJ9yTTsBEC/MS4v/jJkVcUHUgD79w9OJn5h9X3wyxLGRyTMmpZZPy7RkFjJIWfNWYBpfexC8viaBwY8pyoKnmhiF4aa3gYsm5Z5P5cjOW18GUxdrJnZMz1bEPC7Bzz/zHt3IShJGOuX0GdbkFVSZiyz64rwUffFcCgK9ppUrFr/0IDnd+95Havhg6yq2N19AWZlGQLiTK52oTXcgKn9zBH4x4e/HvC8EgnjL01aI7j+CQBkTK424qww0WHu5nv68aA9ffrdHyEoSZgaMWOXfy6KHZasqkgA5nTIErCh8yI4FBW7TSpWffj7Acfs2v0q3tf21GZndzrZihVJklBTyPJITgfrV/TUul8OOEaJhPHXZhZDv6T8ZPT42AdyTWF2bk6F5pCc5GLuxb+6P0YwMHB449Pv/ghhScJMxYJeC/vwzj4MxP4vQnlXIk/b0w82Dax8+mTni1gLPyRVxadPvBXeABPdJdkk2Gp9Ug4FRuEMbXjjU2sH3iVHwkH84xC72H62ej56tTbyhRn2WAHYXTy/8JxTzfb0Hx0bBv/ur74HEUnCHNWKmrqz9cezCQNxd6Rm1LWwqip2ygrWHdEb6JNdL+FDKQCTquLSU2/X9zTbnBUA6JXG4gyZ/T4/ueanA45he8raRHy2+nT4wmyERKYhIACwa06FP6TgUm2v/tGxftD79JnV9yIiSZir2jB+3FIEuFjJwumwa/+HMyd9HVZVxQ5ZwYcfDWzW+MnOF7FBCsKkqrjk1O/q62UlVrQ8l6BtEk7Tpmk/uea+AcdEwkH88zArpf5szRkZdXPOBSRWcojNbEKNnVl1ryttA5Tr8lX3Yq9JhUNRUFR6Y1a/xEcyY1QhmpTPoCKkoFuW8PRb39af6+nehye7WWjI1jUHi06I33QvE06ociFkKsMkdzkA4A9bnxjgrvx+9Y8BALMCDhwKTsCsumJD602ocMFiktDdwT6U/xc4NKBs+vVV92KPSYVTUfF+K2vsNKkq+6aBo4ryYDPLWNdzPqoiKrpkCc+89R39+e6uPXiqh8VxFxQtBSBjbJauCsDudqoL8+BRSnGOhYVm/rjtiQF3WL9//24AwFmmIuztZ2XARkQnDwWdWM5mi7A9jYaDXl91D/aaVOQrKk6Z+T0A7OLBww+ZwsWK4roCFREVHSYJT78ZTdxz9zTiSW1PvzT+En2QZLZihbsj7YFCXOBge/r7zX8YsKePrGUXvnPMpbAXsv5BJlnK6kLOxUpPfwhXzmDt95/1HxiQ0/Xqez/BXpMKl6Ligvl3wq1NTM7GWQGi7sr0KbeiMqKi3SThPyu+pz/f1bUbT2lzbi4fdxE82tBDu0WGJYvkTL4vAbkKF+exPX3oo0eOeJ8yZ/csczGqqmbpc32cWTgd/BxfMIIrp18DAHjW3zxgT195727sM6koUFRccNqdunOUaePC2HP8wQg+dfr3URFR0WaS8J+379CP6erajafcrMfU5eNZt2p/SMl6TZsmqkx5dTF7+vCAPf3dGranZ5tLUFk5Q5+YnE36AM9zCYYVXKXt6X98TWg5HC2WePndH6NR39PvZ7yGaEis5JhzTv0yJveZEZYk3LviNiiRMNzuJty/iyUsTuoehQvnzRaylixLWDy5FpWd0wEAD7eu1n+hf/nqteiVJYwJAuvdF+LsycbFitkkY8aoIuzo+CzyFBUfySE899btAID3Pvgt3lDckFUVbe1MsM0eXWRoPatZxrjyfGzrPx1zI3aEJAn3vHWrvqe/2P0MAOAzjilwh4vhsptRk0VuBUeWJYwtz0cEVlxQwJLfHmpdpf9CP/DqdfDIEiYpMgL5rGX2uPLskms5vDprUu3NyFNYGOE5TSCtXPtrvKn0wqSquGH+D3Cgm00Fz9ZZAVj5MgD028/FqchDSJJw71u3sD3tacTPd7P5KF8qnomeIMs3qiq0Z52YXeFi/x/t/TK+VscSEh/R9lRVFNz/8tXwyhImKjKWzP8uOrxMrGTaEI5Tqp3X4Q3i2kU/hW3Qnv4KbyhuSKqKa0+5A119bCp4scOSca4DAL3cuac/hBNnXomTVRvCkoQfLb8BqqLA3dOIX+5lodErS2ajoLDOuFjRhGN/2IprahYDAH57+B09QfuXr16PPlnCZMWEs+ffgV4/Wy/flt16PEnWGwjj6jPuhlVVsV4K4Pm3vwuA7enbai9kVcXXT7sLANAXzN5ZydPW6wtGcNLsq3GSakNIkvDj5V/X9/RXe1my8lWlc+AqGAWfNqE50+61QNSN8YUisNpcuLqGhXd/e3gFWls3Q1UUPPDqV9EvS5iqmHDWqey95A8bCANpgsMfiuDqM+6GRQt3/VcTSCvWPIAVqof97p/ObgK5WMkmZ8XGnZWIgpNmfgUn6nv6NaiKgp7ufXhw3/MAgC+Xnoh8V3YtLkRCYiXHLDqhEpLvSlgVFavRjxufOh3XPHs+Wk1sGFxL5CYsmlghbL0lkyvxfvcXMC4gwStLuPrVq3DbkwvwXLAVkqoCh5fBaskznK/CmT26CG3heiyOsGTiew6+hrv+sRTf3soSbi8012G7dwaKHRZMqsw+JMOZUl0AQMbM4hthVVWs0vb0am1PayNA7egfAAAmVxVkfVHljNeSZa1lN2GaYmZ7+sqXcNuTC/DfENvTO+bcir2d7CKXbb4KhwuP1lADritjfSJ+cuBV3PWPpfjONtb19fOOBjQ0nI0D3Sy5woizMqqIiYfDvQF85/SfwKKqeA99bE+fuxBtJgl1EeAr5zyEw24/gOxDQADrtQIAbZ4ALlp0L6YoJvRqe/qtpxbif6E2SKqKO+d8C7LJjHavMWeFlx939QVRWTkDX9P29B5tT7+9jfWz+X+OBkwYfw66+7lYyU4c8fLjYESBLxTBnQt/BpvC3qdff3I+vqzt6ZgIcMXZvwIAuPvFOCu9/jA+u+QBTOfv05evwK1/Ox3/DbVCVlV8d86tkE1meDVnpSAL5wiI5rl4A2FU15yIr5ey8SJ3N7+Mu/6xFLfxPXWOw9gG1lenTwsDZSMeos4K+x53nnEfrPx9+uRpuErb0/oI8MUlDwIA+jWxkk0YiJ8TVlSEIgo+d9YDmKaY4ZElXP3S/8O3nlqA/4XaIasqbj/xNn1qtV8Py2TvrARCCqprTsQNpSwf6O7ml9jv/nYWEvp/znFoqF/Ejg0bCAOZo86KJMv4/hn3wqqqeFftwzeePE1/n9ZHJHzx7Acz/v65gMRKjpFlCZct/gzGt8yBSXsz7JAVuCIK1AOX4SsLZ2R1B5eI0yeUId9uR0vTtaiMqGg2Aa9piXUXKNOxpX8xFkwsyypjPR7zxrLusKvar8EyUzFCkoT/BA/DK0s4SbWhrILFQU8dVyrk55xSw8I6O7zT8OP6S/Q9/URWUKCo+PWC+7GllcWrZ9ZlX3nE4U7J3o4QHlj2J1RGVDTF7OltFfNx4swrsbfdCwCGwkAAMFpzVpq6+nHVuX/AUlORvqd9soSTVRtuvfDvaOn1IxRRYTFJWSe7AkC1FgY61OPD+HFL8eP6iwfsaaGi4sEF98NmL8RhN3Nysilb5lTqYsUPs8WOB85+BFXani5XegAA3644DXNmMqdKDwPlZ7dmqZaY26mJni9/6k84Wy5CUNvTflnCPNhxy4Ws3J07K9nmHTmsJlhM7H3e0x/C2Iaz8MP6iyBre7pLVlCkqPjlgvvhcJQBgO6sZDoXiFOgiZxeXwgmsxU/W/KQ/j5drrDcle9UnqHvKQ8DZZNcC0QTbLkA+dI5D2GJXKi/T33ant58/l/1c/q0MFCmfV2AaFiFf49x487GXWNYt+eVqhe7tT19YMH9yHOwzyMjYSC7NXpZ9IUiMFvsuH/JQ6iIqNgfs6e3Vy3E7Blf1I/lYaBsq4GAqFty1TmP4Cy5QH+f+mQJpyIPN1/wpH5OkDsrWZYux643ftxS/HD0BZBVFe+oXuw2qShWVPxq4S9gzzMWvheF8UQJIiUXzRqFv6+9HhX7X0VtyUrIqg2b2y6Ao3ImPjs3+94q8bBbTLhgZg2eWhvGpdafYaLrn+jwd2LxuIvxjVfqAQRx6RxjJcuxnDqW9TE54A7j2qv+i4U7foGNretxQvEkXLzoXnzpLyz/4NRxZULWY84K8PFBNx654scYs206XtryV+SZ8/C5+d9DVdUsfPQKSwqbaTChF4g6JbvbvaipmY9/X/wC/rny/9Dp78LSiZfipNlXQ1FU7G3v0443FgbizkpTVz9MZit+/oW3sWjlD6N7euZ9sFgcaD7Iqrpqix0Zt/aPheescNfk04vuRv22GfqeXnba91FZyfI4DmnHVGfRgI7Dw0BtvUw81Naegqcveh7PvHsX29NJn8FJs9h8LEVR0eFl4iH7nBUmOvqCEfhDEdgtZvzi8rfx4js/wKa2DTih5ARcvPheWCxs37mzkq1YkSQJRQ4r2j0B9PSHUFOUh/MX/wQN22bixS1/heOIPQUgIGeFfYzz8E5d3an410X/xT9X/gBdge4BewpAT3bNJicHiAoO7tCYLXb84gtv4aWVd2FT2wZMLpmMixb+BBZb9HchGgbKImdFW48LEAA4f/E9aNg2S9/Tz5/2A1RUTtOf5y5MNs6K1SRDkgBVZW5Jgd2i7enzeHrlD9AV6MGySZ/D3FlXDTjPSDUQFzj8e5gtdjzwhbfx4sof4KO2TWxPF9+jv0+BqNCwmrIRR+wcLngA4IIz70X91pl4aevfkG9x4rL5/zdgT4caEitHAVmW8LvL5+BzfwjgrYOsumFUUR4e/uIcQxeaRHz+pNF4am0Tnt8m4c1bH0F9mRP/Xn8AnX0focJlw5kniAs75VlNOGVsKVbubMfKXd24dvE9OF97ri8Qxvom5kCcOlZM2GlmXRFMsoSDPT4c6vFh2pTPYtqUz+rP+0MRbD/cy46tLTK8ni5W2rxQVRVFxQ24/sInBxxzsMcHXygCi0kyXGE1poR9wO/vZCEe2WTG+TF7ymnqMh4CAqDn9Bzs8emPHbmnnBYuVgw4KzzBtsMbQERRYZIllJSMH7SnANDjCyGiMJesNMuclQK7GRaThFBERWdfEKOK8iCbzLjgzHtxQZzjOzVxlE1DOE5RnkUTK0H9sUR7CggQK7qzEk1uLy4Zh69d9FTc4z2aqHFlmbPCHRlPILqeyWxNuKdA1IUxUg3UF7MekHxP+/Wclcwv5JIkIc9iQn8wAn8wejEvKRmPr13097jnKIqqiwcRzgrA9vTCM3+KCxOcEwiJc1Y4M6ZehhlTL8v4+x0NKAx0lKgqtOPVb56Bn14yHfdcPA2vfvMM1BYbu9AkYnptIRZPKkdEUfGTl7ahqy+IB17/BADw5dMaYM6iAiAZiyayaqDl21sHPP7WjjYEwwrGlDoMOw4cp82MqVooaF1j16Dntx/uRVhRUeq0Zt0sLZax5U6YZAluXwitmhtwJNs0ccSqlYztLXdWOrwB9AcH963hNHOxYvBn5C6Jxx/WL2KJONRjPAxUmm+DLAGKGg3NJIKHgFjn2+z2VZIk3SXp8gZTHB3jrGSZswLEVAT5ku8nAEQUVXdEsplFBMTmrKRejx0nNgyUDn2aeMhOrGjOSjCS4sgoes5KFmIFGJhkmw6xF/1sxAo/h+ehpLemgNLlyOBeLsMVEitHEYfVjM+fPBr/b94YQ83R0uHby06A1STjje1tOOXeN3HY7cfoEgeuml8vfK1l06ogScAH+7r0iygAvPwxG6p23vRqw4muscwdw+LSHzZ2D3pu/X722My6IiFr2i0mTNCSbLccdMc9hjs5k6uzL5PmFDos+h12U8xeHokoZyXfZtbDCDwUlAg9wdZAGMgkS3oeSZsnPbGSbQiIU6qVL3f0JV8PiOasGHJWYiqCUuHxh6Ay88hwNVBvGuKIrSkoDJSmWAlFFD3cYKR0uS8Yhso3KwVcZGTjrABR8ZCuWPHHHGfPppRYrwZKXzwEDVQD6c5Kmj/fcIDEyjHKlJoC/PyzM2AzywhGFJS7bPjjl07M+k4jGaOK8jBfqy7693o2RbbdE8Cb29lwrE9NF1v2dlI9S/iK56ys2t0BADhFS/wVwdQalqi75VAqsWK82gmIyVvpTCxWeI7M2CyHJsZSE5Nkm4j+YFgPV1QZcFaAaCiozZNcHLV72fNlWXav5fAQUkbOShat9jm8IqjHl3o9Lmjybeas3aNMnRXuoGXTah+IuiPpipVYByarUmLtM0tRB4ctEuHTnZXsBFleTG+XdOBlyxaTlJVzHQ0DZeKsGOizYiZnhRhGXDhrFFZ+ZzGeumYeVty2CCcYaJCWistOYo2MnljdCHd/CH96dy+CEQWzRxdh2ijjVTmxnNxQAkkCdrR49DwKgN3BfbCPCZj5ghJ6AWDaKLZvWw72xn2eh4F4pZJReK+VfR19cZ9XVRV7tOqjbOcQxTJKFyuJxQN3VZgTY8wV1MVKgrAap8NjLLmWw8uXO9NyVtiFPJtW+5zYxnCp6DGYrwLEz1lJhjBnxZ/eelzUWE1yVhfWWIHTn6Z4MJKzAkSTZP1pige9EigLl4OtF+2amy6iSpdHCiRWjnEqC+w4bXyZkA65yThvejUmVOTD7QvhM4+sxqPvsUmsNy4eL3yt0nyb3rr/zR3RPJmNTT3oC0ZQ7LDoVUMi4GJraxxnxeMPobmLORKi1pxQwRyana3euM+39PrRH4zALEuGGsJxqrVeK8mcFRH5Khy9IihVGIj3WDHorHDh0dmX2uno0gSNsZwVHgZKx1kJaucYECtHVAOlotegs5JpzgovOc6mEghgoUN+QU6WxxWLL8T7uhjLWfGnKY64A2PLsiWEEWeFxApBZIBJlvDA52bCbpGxq82LiKLikjmjcJaATrnxWKJ93+XbomKF58gsnFgutHfN5OoCSBJzF9qPuMByt6Wm0J51guSRTKxkbsmuNk/c5/e0McdlTKnDcEIvEBMGcicWK1yQGc2RAWIbwyUPA7X1amEgo86KFgbqTBEGUlUV3ZqzUmwkDJSBs2K0xwoQ46ykHQbSmsJlOTKBJ+b2BSN6tVYyjMwF4vBzM3VWsildBrLIWQnzsFN2v4887yTdMBcQWw2UffURhYGI45IZtUV47obTcN2Csbj34um4/9IZqU/KkmVTqwAA7+7qQIvbj2BYwUuaWPn0jBqha+XbzHr33SPzZPjXc8aIa5w0QVtrV6sXSpyLwW5NxBjtlsvhHWmTOSs8oVeEk1NRMLDXSiJaeo2XSgMDu9gmoy8Y0T+8s+2zAkQnL6dTDcQFDT8nG/SclbTDQFrpskFnBYj2T0kGd2CyaQjH4aIjY7FylKqB/AaGGAIxYacMEl6NVQNFO+aOFKjPCiGUydUFQqpiUjG+Ih8n15fgg8Yu/OndvZhQkY92TwAVLhsWaKXUIjm5oQQ7WjxYu7dzQMIwFysnN4hL6K0vdcBqkuELRXCwxzfIzdjDk2sFiRVe4s3dk3g0C6o+AmITbFOIFS1PxkiHXiCmi20KsdKtPW8zy1nfkQOxzkr6CbbZTFzmcIfE4w9BUdSUriIXNdnmrNjMMsyyhLCioi8QThlOMtJjhcNDSP1php58BnNWMk6w1RvCGQ0DZZKzkn0YSB9kSM4KQeSeGxaPAwA8+t4+fP/5LQCAa88Ym1USXyrmNbBqp7X7os5KOKJgg1YqzcupRWA2yRir9aXZ2To4FLS7TUuuFdS7Zkwp+z6H3L6Ed3ZCnRVNrBwZUotFVVXdWTFafcRdklR9XTpjWu0bKXvnybLpJdhqOStGEmw1saCo6TkdRquBJEmKzgdKI8lWRBiIV/Wk76zwDrbZrWnPMCyjT1w2GHbKpJTYyCBDvc8K5awQRO5ZNKkCn5vLRgeEFRVzxxTjyhz0kQGizsmOFo+eS7FBS+gtsJsxqUpM2TKHh4KOTLJVVRXbW1iejKg1y/KtcNnMUFUM6JMTS07CQB5/3DAXwHI5+AWg0qCzwic2pwoDdXj4hGdjOTK8R0uPL5SyL4geBjLgrNgtJl2g96YQD+GIojdoy9ZZAQZOXk5FNAyUvVsV22slHYbKWcmmm2zseZk5K9mvSQm2BHGU+eklM/CnL83Frz8/C09eMy8nrgrAymd5BdJrW1sAAMu3sb/PmlwpfGwC79lyZCO6A90+9PSHYDFJwsSKJEmo1/q1xCuXdveH9ETQuhLjXYErXKyLbSiioiOB28FLpUucVsNDN7mz0h+MJL34dBic8MzRJy+HlZSlqHo1kIGcFSA2byW5mxMrLow0pnTZMxArvHttlj1PgKjoSNtZOcpN4XyGw0CZ55DoCbZGqoEiSsIbhuEGiRViRCPLEs6eUokLZ40SNkk6EZ+azpJ6/73+AIJhBf/ddAgAsHSK+IqnWdpco03NPQMe5+XTEytdWdm/iUgmVpq7matSlm/NqqnXkVhMsp6HcjBBUi8PARl1VQCW2Mk/nJP1WmnXnRVjwiF28nJ3irwVvc+KAWcFSL+LLa8Esluy63nCcWZQviwiDOTIOAx0tBNsjYaBMuvrAhgLA8UKnJGSt0JihSDS5JI5tbCZZXx0wI0vP/EB2jwBVBbYclKePb22EJLELuaxJb4fa07LdMGN9hq0RnSNnYPFiqjW/rHwcumEYkXA0ESOJEnRxnBJype5s2I0DMQnLwOp81bcejWQQbGid7FNLh56DVYCcXhljyeNnBUR1UC6s5KGOIooqh7eyFZc8xLkdPusGJm4DGTprAhoCgeQWCGIY46yfBuuOGUMAGDV7k4AwPULx+Uk9OSyW/SZRB81R0NB3GkR3RU4mbOyR0vobSgVk9ALAKO0CqSD3fHFCg8DGU2u5ZSmkbfSLigMBKTfcr9H77NiMAyUl14YyGglECeTxnBCnZU0nI7YxnFGw0Dpd7A1FgbK1FlR1eiU56xyVmL6M42UvBUSKwSRAbctm4RL5oxCucuGa05vwJWn1udsrTmjWe+W9/cwYeQPRfThjSJnHwHJxcouTazwpF8RjErhrLQKKlvm8C627Ukqgnh7f6POChBNmHUncVYURRXSwRZIv4ut0UogTibDDIUk2GZQuszzkiQpO9cBiMlZydBZyTYMlKmzEoqo+gDMbMJAkiTpgiWTpN6hhPqsEEQG2C0m/PJzs47KWgsmluOf65qxYmcbfoAp2LC/G4GwggqXTVhDOM54zcVp7Q2gpz844E6fl09PEDCHiJNqeOLhXrFihbfsT1YuLSrBFgAKtYTZ7iRixRsMQzE4cZnjSrMxnNG5QBzuknjSEiu83b6R0uX0E2z1uUAWU9Yl6NnmrBytdvuxoZtsBRkfckvOCkEQhjh9QhlMsoS97X3Y1erBi1qH3gUTyw31AYlHgd2iN4fbfjja2yUcUfQJzxNFOivaWgcShIEOaEm9/DUZpaqQCZDW3sQt/tsFlS4DQLEjdRiIuy52i2w4OVxPsE3hrOhzgQyKI73l/lEKAzkzSLCNJtca75jrS9Pp8BnMWcl0kGFsP5ZsxcpIK18msUIQw5QCuwVnnVABAPj927vx4kes+uiS2aNysh4fxLj9cHS6dFNXP4IRBXkWkzDhAAC1ScJAiqLigMBZREDUoUkkVvyhiO4SCMlZSSMMJKLVPifd0mV9LpBBZ8WVweRlIe32dWcljTCQwSGGsetlmmCbfRgo6qyk6s3DjmMCw2qWs75xIbFCEIQwrtKa3D2/6RB6/WGMLXfilLGlOVmLj0nYFiNWuMsyviJf6HBIHgby+MOD3IBWjx/BiAKzLAmpBgKijehaEswj4q6K1SQbvpAD0cZwyVr887JmoyEgIP1hhkbnAnGces5K6ou5kHb71ujwxFT0G2wIB2Se8Gq83T47T1FZg8tUGGm1z4n2Wkm/XHooIbFCEMOY+ePL9Aokp9WE+y+dIVQ0xDKlhomVrYeiYmVTM0vonVkntvrIaTPr5cRNnQO75vKvRxXnwSxgqjQQdVbaEjgrsfkqIkJsZVpCb7LqI/5cqcG+LkBMgm2aOStGBZnebj+QeqSAV0CCrSODjrJGe6wA2STYGuuzElvRk84ww2jZcvY/o55gO0KGGVKCLUEMc+6+aBquPr0BxQ6r4eZhyZitdejd0dILty+EwjwLNjb1aM+JmyrNaShzorMviL0dfQNKsZu1PJa6YnF9XSr1Fv8BRBR1UMdhUQ3hOFyAJJtHFDuLyCjpOivi+qxo7e9TOCuqqkY72Aros5JOu32jrfYBA1OXs+6zEj0vEFaQKjvMSPdafU3e4p/6rBAEIYr6MmdOhQrAQiVjy5xQVWDdvi70B8PYrDWhmz26SPh6fFjj3vaB849y0YSuLN8KWWINw+J1sW31cGdFVF8X5qx0JGlC1ymoCR0Q2xQuvZwV431W2HqpSpcDYQURLaxhrCkcOzcjZyXLIYZATM5Khu32s60GkiRJFx7pOSvZ91jhjLRhhiRWCILQmaflw7z9SRve29WBYFhBbXEeGsrENYTjNJSxUugje7s0aV10RQxN5JhNsp442+oeLFYOa4m+NUWCxIqesxJImDDZJdBZKcxLLwzUq4eBjOassItyKrES+7yh2UC6k5PaWeFJuCKclVBERTgN58Fogi0Qm2Sbej0hYSBKsCUIYqTC5x+9uPkwnt1wEACwZHKl8FJpINZZGShWeBO6ceViBVJlkoqgaHt/MRVPPAzkDykJy2256yImZ4WJD48/lHQwncfHw0BGq4E0ZyVFNRAXFw6ryVCulZ6zkobrICIMFJso60/jYs5zVoyUoHNXJp0cEhFhICtvREdihSCIkcb8cWWoLrTD7QvhVW269CVzclMqPbYsGgbi7kNEUbFbEysi+7oAUbHSEkesHHKLdVYcVrN+sUw0j6hLC0eVCsxZUdTkeR1uQe39ubPiC0WSOg8ieqwA0TBQKKKmdAJ4S34jCbaxIiCd0JPRnJXYc9OpQIotXc4WGzkrBEGMVEyyhDvPm6x/fcnsUZihTYAWzZhSJywmCX3BiN4crrmrH4GwAptZFpqzAgCVBSwMxF2UWA4Lbu8PRB2TjgSTnjv1aiDjOSs2s6znICQaZqiqaswsIjFN4YDk5cQ8AddIvgow0CVJJR5EOCuSJOkhnXRySMSEgTJwVgwMMeREw0Ajo3SZqoEIghjAp2fUoKHMiRa3H4smVeRsHatZxsRKF7Ye6sXWQ27UlTiwo4X1dRlXnj+oYscotVp10ZGN6FRV1cUK7/8iglKnDc1dvsTOildczookSSjIM6PDG0SvL6TPXorFEwjrya5Ge7vYzCZYTaxduzcQTvj9oj1WjHXotZhkfb2+YDhpsnk0Z8XY5S3PaoIvFEkZelJVVQ8VGQkDZeOsGMlZsfEEW6oGIghipDK1phBnTa4ULhiOZLpWsvyxVnXEp0pPFzxVGoiWQvNqI05XX1C3wisFOitlScqXA+Fox1zek8UoqbrYimzvD0QFSLKkVz0MZFA4ANEk21Qt96PVQMZ+xrw0e62EIqouAu1GxEMmzopefWTcWRkpfVZIrBAEMWTw/iob9vewv5tYE7o5Y4qEr8Wri5qPECvcVSnLtxnKATiSUk2ExOtiyyuBzLKkz/UxikvvtRJfPIhs7w9EQ0GeJEm2IlrtcxyW9FruiwgDAVEhkCoMFOuE2K3Gc0jSGWYoooOtnrNCzgpBEERy5o9jpdLr93ejuy+IzQd6AABzRotvQldXwkIjbZ7AgAsQH5o4SuDsIyAmZyWOs9IZEwISVWkV7WIb31nhQxWN5qtw9Bb46TgrIsSKja+XprNiUKyk2xiOv5ckKdq7JBvsmVQDCQgDUekyQRBEmjSUOVFbnIdgRMH9r+2AP6SgqsCOceX5wtcqzLPoJbtcoABAo9bev75UbEIvT5yNl7Misnsth1cEeRI0htOdFUFixaW33E8sVkQ1oQNiy5eTOyu8GshwzkqaCbb+oJavYjYZEp6ZOSviEmypdJkgCCIFkiThnKmst8s/PmgGAJw7vSon848kSYqbt7Jfa0I3plRsXxees9LmGVx9pJctC2rvD8R2sU0QBvKJDQM505i8LKq9PxDTcj+Fs+IT0BQOiDozKZ2VsBgnJ6OmcCERHWzZ66UwEEEQRBpcOb9ev7DYLTK+clpDztbieSuNHTHOSkdunJUqvQldnPb+2mMVgtr7A9BzXxIn2IoNA+Xb0ndWROTlpNtyX1QYKDrMMPnFXO+xYjDfyZ5BqbTIMNBISbCl0mWCIIaUuhIH/nb1yfjPhoP4zIm1wvurxDK+Ih/YGu2SCwCNOXJWqgq1JnRuP1RVHRAi4L1eRFYfpZoP1K2FgUTNmEpPrOTAWTlKCbbpige+ntEKq+za7R8/CbYkVgiCGHJOHFOCE8eU5HydiVWsK+7OVtbPxd0f0quBxgvOk+FCxBeKoNc3sDcIb/lfVSCmbBmI9k7houRIhFcD2VIn2PJZRQUCc1bSLV12GBhkCAB5WogldRjIeI+V2PMzc1aOn6ZwFAYiCOK4YZLWwn9niweqqmJ7Sy8AYFRRnvCp1naLSQ+5HNnin3/N3RcR8Lb9XXFKpQHArVUDFYtyVnjpcjJnJcAEktHBiUA0DJSsdFlRVF1ciKoGSplgK6DVPpBtzgpVAxEEQRxzNJSxFv+eQBhNXf3YdoiJlSk1BTlZj+etHHYP7JrLw0BVggYnAtHqo0RiRXQ1UDrOSi6qgZI5K7E9TwyHgXiCbQonJypWjPZ1Obrt9jMRR8MBEisEQRw3WM2y3h33g31deufcKdU5EiuFgyc9RxQVbR6WYCtyFhEvg47X1wWIVgMVCg4DJa0G8onLWeHVR/1JqoF4/owkCagGyrDPitGOuVw8pNNun+eZCMlZIbFCEAQx/Jg3ljWiW7O3C+/v6WSPNeQmX4aLkRZ3VEB0egOIKCpkKVreLAL+vTz+cNxeHaKdFWeKBFtVVYVWA3Ex0J9EPPCyZqfVbLjZXjSHJPnFXFiCbSbOSkhgU7gRkmBLYoUgiOOK08aVAQD+s+EAWnr9yLOYMGeM+I65QDTJNjYMxPNVyl02mA10PD2SArsFZq0/zZGhIFVV9ZwVYWGgFE3h/CEFYW1mjhhnRRMrScJOogYnAhnkrISN9zwBoqXPGQ0yFNFnhZwVgiCI4cep40pRE5PY+ukZ1UIG+8WD93XZ3xnt63JIm/osMl8FAGRZ0kNBR3bNdftCCEWYcBDVNddlSz4biJdQyxLgNBiSAWITbFOHgUS09z/qYaCjnLNCHWwJgiCGMSZZwr2XTEeexYTRJQ7ctmxSztaqL2O9W3gvFyAqXEQ3oQOiQuTI4Yk8j6XAbjYUOoiFOzTuBE3oYnusiJh/FE2wPTqDE9NNsPWJSrDNapChkSnPIytnhfqsEARx3LFoUgU2/fBsmGUZphy09udwQXLY7Yc/FIHdYtJnEYluQgewydGAB51HJNm2e5h4KXOJ7OvChFGvP4SIog7ax16BlUBAhs6KwblAQPrOCndCjJYup5sjE7smOSsEQRDHODazKadCBWBOB79Yc0dFn0WUg069fNbQkWEg7qyU5YtvQqeq8Ycn8kogET1WgPRKl/UEWxHOiiY+0u2zIqoaKJNBhkYEEjWFIwiCIACw4YkNR4SC9DBQWQ7EilOb9JwgDFQuUKxYzbIuIHridM0V2WMFiEmwTSsMdPQSbMWHgdLJWRFQDWSiaiCCIAhCo14L9+zr6IPHH8JBLcG2oUxse38g1lkZGAbiYkXklGcAKNLclZ44eSvRsmUxzkqeFtrpO0oJtvY0w0CiByemFQYS0G4/Vhypqpr19zlakFghCILIIZO0eURbDrqx9VC0vb+oqpxYShMl2PKcFYHOCgAUOth68ZJse/UEW0HOijVaahtO4AaITLDNSzfBVtDgxHTDQOGIgohWEm41JFbY61VV6CXmwxkSKwRBEDlkVl0RAGBjUw+2aB1zp+aovT9vuX9kF9tc5KwAMc5K/+AW/zyPRVTOSqxb0pegiy2fyCyydDmV08HDUnkGByfa0yxdjg0TiWgKB4yMiiASKwRBEDlkRm0hJAk42OPDq1taAEBv+S+a6CyigYMTo2JFcBgoSfmyW0+wFeOsWEyynlDaGyehFwC8QhNsNScnxsmIR79gZyUYUaAkWS9WrBhxVkisEARBEDouu0UXJx/u7wYAnD6hLCdr1RQxsdLhDQy4AHV4xZcuA1GxEi/Btltv7y9OIOXb2HqJGtHlIsEWSJ5ky3NaDIuVmPWSJb3yMJHFJBmqZjPJ0fNHQvkyiRWCIIgcc9GsUfq/x5Q6MLO2KCfrlDitsJllqGp0eGJEUfUW/9WF4gYnAtFeK/HECg8NFTvFhIGAqEsTr1QaEJtgG5u8mizJVliCbcx6ycSRiLlAnJHUGI7ECkEQRI754iljsHRKJaoK7PjpJTMg56i/iyRJuiDhVUdtHr/etK3CJVqs8GqgwTkr3X1MUBQLdFZc9uQt/vsEihVZlvSwU7Ik22iCrbE1zSY5LadDRCUQJzrMcPj3WhlSsVJfXw9Jkgb8+e53vzuUL4kgCEI4VrOMP35pLtZ87yycOq40p2vVFLGZQ3x4oj6LqMAuvAmenrOSzFkRKlbYeomGJ3Kx4hIgVoDUvVZUVdUTbI2GgYCYYYbJnBUBc4E4vNfKSAgDDXm7/R//+Me49tpr9a/z88X3HiAIgjheqNYGJB7qYaGfg9rfo4rEDk4EotVA8RJsu3IgVvJtqcJA4hJsAZ5kG0oYBgqEFfBcWKNhIIDlrfQFI0nFA69OsgkYvjmSWu4PuVhxuVyoqqoa6pdBEARxTMCTbLmjwv/mj4uk0BG/KZw/FNEvqkUCc1Z4GKg3ZYKtqHlEyVv8x4aHHALEg95rJUn5sl9Qx9zY9ShnJQ1+9rOfobS0FLNmzcI999yDYHBw7DOWQCCA3t7eAX8IgiAIBndQDnQzkdLcxdr71+TEWYmfYNutuSpmWRIWkgGiYaB4OSsRRdUdEFHOCv8+iVr892vrWU0yzCbjl1O9i22SxnBRsSIiZyXaaG+4M6TOys0334w5c+aguLgYH3zwAe644w7s27cPf/7znxOec9999+FHP/rRUXyVBEEQI4dxFSyUvrvNO+Dv8RXiQ+zR0uUgVFWFJLGcmC6tg26Rw6o/JoJ8zVnxBgaHgfpiBIVTQOkyEHVWEjWh8/GGcAJCQEB6zoo+i0hANZD1eHZW7rrrrkFJs0f++fDDDwEAt9xyCxYuXIgZM2bgmmuuwSOPPIJHH30UnZ2dCb//HXfcAbfbrf9pbm4W/SMQBEGMWCZoouRgjw/eQFgXKxMqXMLX4rOGwoo6IG+FOy3FDnEhICC2dHmw08FDQBaTJKSsFwCcfB5RgoReUQ3hOOm03OdCRkiOzAgaZijcWbnxxhvx+c9/Pukx9fX1cR8/5ZRTAAC7d+9GaWn8jHmbzQabTWxjI4IgiGOFIocV5S4b2j0BfLCvU58TNK7CKXwtm9mEArsZvf4w2j0BvQFcdw6Sa4Hkpcsiy5Y5/HslGp4oqscKx5ZGi38eIhITBkpvHtFwQLhYKSsrQ1lZdt0ZN27cCACorq4W+ZIIgiCOKyZVutDuCeDf6w8AAGqL8wz3AUlEucvGxIo3gAmVzL3p7hPfEA6I7WAbr72/NuVZ0CwiIBpO6k/grIgaYshJx1nha4oIA42kBNshy1l5//33sWbNGixevBiFhYVYt24dbrnlFlxwwQUYPXr0UL0sgiCIEc+JY4rx3u4OvPwxm0V0Un1JztYqd9mwp70P7Z7o8MSuHDSEA5I7K3xeUEGeuMsaF3ipnBWHwSGGHHs6zor2nF2AQDquc1bSxWaz4emnn8aiRYswZcoU/OAHP8C1116Lf/zjH0P1kgiCII4Jjpw9ND+HjejK9EnP0UrONg/r7VIheBZRUrHiEzvlGQCceulyopyVHCXYJnNWcpBgS31WkjBnzhysWbNmqJYnCII4Zpk7phhTqguw7XAvSp1WfHpGTc7WKtcESayz0qb9u7xAbG8XV5LZQLkQKw6es5KoGkjQEEMOTwxO3hSO58lQB1uCIAhiBCNJEv505Vw8t+EAlkypFHbnHw/urMQTK+KdlWi7/dhSaSDaKI7PKxKBnmCbohpI1P7ypNl02u0LyVmxjJwwEIkVgiCIY5BRRXm48cwJOV+HOysd3qhYae/NbRhIUZlQiK380Z0VgTkrPAzUlzAMdPSdFT3BVkS7fZPWFG4ElC4PeQdbgiAIYuRyZBhIVVW0a8KlQnAYKM9i0ocxHpm34s5FGMjKO9gmbwonqtIqHWeFEmwJgiAIIkO4e9KquSnd/SGEImy6X3m+WGdFkqSY+UAD81ai1UDiS5dThoEEuBxAmjkrehjo+OqzQmKFIAiCyJraYgcAoLMviL5AGIfdbCZRqdOqXwxFwic9814unF6f+JyVVM6K6DCQ7qwkWA8QGwYaSX1WSKwQBEEQWVOYZ9Hb4B/o9qGpkw1OrCtx5GS9aJfcRM6KuJyV/FSDDPUwkBixwhN1fcnCQJqwEOHmkFghCIIgjhu4MGnu6sd+bcrzmNLciJXimOGJseQmZ4UJAm/KaiAxAokLkGRiJRASmGBrHjmzgUisEARBEIao00JBzd392K85K2Ny5KwUOxM4K75c5KwwEeIPKYgo6qDneUjGKdhZSRR2AmKawomYDWQiZ4UgCII4ThituSj7O/vR1NUHIHdhIN7CP9ZZUVVV77OSC2cFiB8K4o5Lvl2Ms8LXS14NJN5ZGQlN4UisEARBEIaYqA0w3H64F7tavQCAseXipzwD0TBQd4xY6QtGdOdDZM6KzSzrpdLx3A6v4EnPXIAkdVaEJtimrj4aLlBTOIIgCMIQU6oLAABr93UBAGQJmKw9Jpp4Cba8MshqloWVEQOsVNppNaHXH45bvszFikuQWOHVR74kYoUn2AoJA1GCLUEQBHG8MKEyf8AFe1JVgbBGaUcSLwzUpYmVUqd1QAt+ETht8cuXVVXVBYyoMFCqBFtFUXVhIUKUkVghCIIgjhssJhkLJpXrXy+bWpmztaJhoKizwsVKiZZ8K5JEFUGBsKI3vxMVBuJrJXJW/DHN28S026emcARBEMRxxC1LJqLYYUFdSR4uP3l0ztYpiuOsdOZQrDgT9FqJFS9OYe32o86KEqf6iLfajz3WCPogwxFQukw5KwRBEIRhxlfkY833zoIsSbCYcncfXOzkfVZC+uTlrj42i6g0p87KQPeBh4Cc1ui8IlFrAcy5OXKaM68EsppkIWtS6TJBEARx3GEzm3IqVIBozkpYiZYrR50VsbOIAMCllUJ7jphFxAcpigoBAQPzUOKVSvNcFpuA5FqAOtgSBEEQRE6wW0z6MEM+6bnLqyXY5ot3Vgp0sRI/DCQquRYAZFnSBUS8JFvurIiqeKI+KwRBEASRIyoL7ACANm3Scy4TbPUpz76BzorXL7ZsmZMsyZbnrIjIVwGifVbIWSEIgiAIwVQWsHBPq4eJlTbNYSnPFx8G4u37j3RW+oLiw0BA1DWJ1xjOL7DVPhB1VsKKGjehdzhBYoUgCIIYUVS6mLPS2stEymE3Ey3VRXbha/GJ0r0JclbyRYuVJJOXcxUGAoZ/RRCJFYIgCGJEUVHAxYofgXAEHV4mWqoL84SvdTRzVoAYsZIkDGQTJVZikqGHe94KiRWCIAhiRMHDQG2eAFrdTKjYzLLeME4kiXJW9O61onNWLFrL/TjOCq8QEuWsWEzR8udEjeG6+4Jo6uyH+4gp10cbEisEQRDEiKK6kDkrB7p9OOT2AQBqivKEt9oHYkuXBzoruQoD2a2Jc1a4gHHaxIgVSZJSli///YMmLPj527j35e1C1swWEisEQRDEiKK+jE103tvuxWFNrHABIxo+xfnIPiu5CgM5kswH6tMa04mcu5RqPpDopN5sIbFCEARBjCjqS52QJOZufNjYDQCoLRafrwJEnZXeQc4KEy+iS5ejOSuDm8LxMJDDKm6ytO6sJEiw9euN6MStmQ0kVgiCIIgRhd1iwqgiJk5e29oCAJhY6crJWrwayBsIIxJT3uvWclgKHWJ7u0TFymDxwENDQp0VPswwFF+s8MRbu5mcFYIgCILIiHHl+QCADq17ba7ECndWgGgjOIDNJgKAwjyxSb16n5XQUXJWtPXIWSEIgiAIwZw4plj/tywBM2uLcrKO1SzroZLYXiu8OqhIsFjhQsQfJ8E26qyIDwOlclZs5KwQBEEQRGYsnFiu/3vO6GIU5qBsmcO72MaKlR4uVgSva0/SwTYXCbbcMfHHSeiNfVxUi/9sIbFCEARBjDhm1BbiylPHYHSJA3d86oScrsXzVnieSjCs6GJCdBjIkaSDrS/EW/yLEw55lsSDE4Hh46yITWMmCIIgiKOAJEn40YXT8KOjsFaJ04o97X16ngoXLZI0MKdFBDxnJV4HW+6siGoKB0Qdk0RihZwVgiAIghgBFGsVP53adGe3j/3tsplhksU2ostL1hQuyJvCifMZuPAJJBQrw8NZIbFCEARBEEkozWdipVsXKzxfRWzZMhDtiNsXp88KfyxPYIJtKmdFL10mZ4UgCIIghi/cWenSxAoPB4lOrgWirgnvkBsLd1ucAhNs7XqCbYJqIAoDEQRBEMTwp8Q5UKzwv3PqrMQVK+L7rNhHSIItiRWCIAiCSMKRYqXdyyY9l+fbhK/FxYr3iPb+EUXV3Q+RYiWPSpcJgiAIYuQzSKx4NLHiEi9WnHrOSgRKTHv/WOdDZIKtPYVYIWeFIAiCIEYAR1OsuGKmOPfHCIh+LSwkSWKFQ16KnBVyVgiCIAhiBFDhsgNg4Z+IouZUrNjMsl4OHRsKik2ulSRx5dJ6zkqcUulwREFYc3fIWSEIgiCIYUy5ywazLCGiqGjz+HOasyJJEpxaTkpsRVAuypaBmDBQeLBY4SGg2OOGChIrBEEQBJEEkyyhsoC5K4d6/Dl1VoBoV9zYiiC9IVyOxEo8ZyU2j4WcFYIgCIIY5tQUMbGyp90LjxaeqSjIjVjhs39inRVPgJcti52So+eshAfnrHBnxWqSIQvu1JspJFYIgiAIIgXVhXkAgDV7OwGwhnAFgucCcfLjNIbj+SuxCbgi4GElfxJnxWYZeqkw9K+AIAiCIIY51Zqz8v4eJlbGlDhytpYzTmM4jy5WxAoknmAbL2clOhdoaPNVABIrBEEQBJGS8eX5AIDDbj8AYHSpM2drxXNWPH7W4r9AsLOSLGeF93YR2YQuW0isEARBEEQKptQUDPh62hFfiyS+WGH/zs+RWInXFI4LGBIrBEEQBDECmFDhGnDRnj26OGdrxQsDceEiPGclSVM43zBpCAeQWCEIgiCIlFjNMi6dUwsAGFWUh9mji3K2Vrz5QL1aGEh8zgoTIsGIgkhMe38gKlbyhoFYESvRCIIgCOIY5c7zJuOEahfOGF8Oiyl39/o81OOJFwYSOBcIGChE/KHIgLlDvhxMec4WEisEQRAEkQZ2iwn/b96YnK/DS6I9/sEJtqLDQLHN3gaLFS0MNAzECoWBCIIgCGIYUeRgYsXdH9If4zkronu7yLKkCxbfEUm2Pi2PZTiEgUisEARBEMQwoiiPCZIeX1B/LFfVQEBsRdDAJNvhFAYisUIQBEEQw4hCzVnpiXFWPDnqYAvEVgQd6axQgi1BEARBEHEo1J2VEFRVhaoCbh8TLkV5VuHr6V1sE4iV4VC6TGKFIAiCIIYRRQ4mSIJhBf6QgmA4WlbM81lEonexPUKs9A+jpnAkVgiCIAhiGOG0mmCWJYQVFT2+oJ5L4rSacuJyJMpZ4U5L3jAQK5SzQhAEQRDDCEmSohVBvhC6+liibbFTfAgIiOakDKoGCg6fMBCJFYIgCIIYZuh5K/0hdGtipSRXYsXKhxmGBzw+nMJAJFYIgiAIYpjB81a6+4Lo7tecFUduxAoXI/1HTF72UzUQQRAEQRCJKM+3AQDavQFdNOTKWXFaBw9OBKh0mSAIgiCIJFQWMLHS2utHRMt7zZWzok95DsavBhoOCbYkVgiCIAhimFFRYAcAtPYGIGmPlTjFly0DgNPGxMiRzspwqgYisUIQBEEQw4xKXaz49ceqCvNyspburATiVwMNhzBQThNs77nnHsyfPx8OhwNFRUVxj2lqasL5558Pp9OJsrIy3HTTTQgGg3GPJQiCIIjjgdgw0KEeH/D/27v32CirdY/jv+ltOi3tcKl0WtpCe3RbsV6g6A5CBNFAYtUYc4igQNkmJqjFIlFBMYLGWhIvMRrFIyFgggZjQINoDEWxytGAFqoFEtGItCDdRIF22IXe5jl/0I4MLZxCZzpv6feTTNJZ72Lm4Umhv6x3ramkDG9iRN4rOaHryoqZqWmgrKy0tLRo+vTpGj9+vFatWtXlent7u4qKinTZZZdp27Zt+uuvv1RcXCwz0xtvvBHJ0gAAcKzOlZX6hlNq6/j02oiFleCelb/DSnNbQHb6bR2xshLRsPLcc89JktasWdPt9c2bN2vv3r2qq6tTZmamJOmVV17R3LlzVVZWptTU1EiWBwCAI3UGk8ZTbWeMReY2UFI3p4FOnrHZ1glhJaqfs/Ldd9+poKAgGFQkadq0aWpublZVVVW3f6a5uVmNjY0hDwAALiUpifEhKynZQz0Rux0zqGNl5czPWTnREVwS42MUFxv9j2SLagX19fVKT08PGRsyZIgSEhJUX1/f7Z8pLy+X1+sNPrKzs/uiVAAA+tQ/0lOCX1+ZHrk7DUmdp4HOuA3UGVY6g0y0XXBYWbZsmVwu13kfP/zwQ49fz+VydRkzs27HJempp55SQ0ND8FFXV3ehfwUAABzvn3lDg19fn+2N2PsM6uY00H8cFlYuuIqSkhLNmDHjvHNGjRrVo9fy+Xzavn17yNixY8fU2traZcWlk9vtltvt7tHrAwDQX/332Cz9T+VvinFJ94zNitj7JHVzGsjf8XVyfw0raWlpSktLC8ubjx8/XmVlZTp8+LAyMjIknd5063a7VVhYGJb3AACgPxqemqhvF0+RFNnQ0Ll60twWUFt7QHGxMf1/ZeVC1NbW6ujRo6qtrVV7e7uqq6slSZdffrkGDRqkqVOnavTo0Zo9e7ZeeuklHT16VI8//rgefPBBTgIBAAa8vljZ6DwNJJ3+yH2vJ0YnTg2gsPLss8/q3XffDT4fM2aMJGnr1q2aPHmyYmNj9emnn+rhhx/WhAkT5PF4dN999+nll1+OZFkAAKBDQlyMEmJj1NIe0H+a2+T1xP+9wTZxAISVNWvWnPMzVjrl5ORo06ZNkSwDAACcR5I7Vi1NATV1nAg64bA9K9E/PA0AAKIqueNW0ImOE0Gde1ZSCCsAAMAJzv7Ny6ysAAAAR0lJjJck+U+1Svp7hcUpG2wJKwAADHCDPafDSsPJ02HFaUeXCSsAAAxw3o6wcrzpdFjpXGFxymkgwgoAAAOcNyl0ZeVYR2gZ3DEebYQVAAAGuODKSkdYOd7UIkka7EmIWk1nIqwAADDAnblnxcyCt4OGJLOyAgAAHCB4G6ipVf7mNrUFTJI0JImVFQAA4ACdt3saTraqoWNVxR0Xo8T42GiWFURYAQBggEsN7llp0bGO/SpOWVWRCCsAAAx4nad+jje1Ou4kkERYAQBgwEtLdkuS/Kfa9O/GU5JYWQEAAA6S6olTQtzpSLCv3i+JlRUAAOAgLpdLw1NOr678dLBBkpSemhjNkkIQVgAAQDCs/HjwuCQpczBhBQAAOIjPezqcNLcFJEkZXk80ywlBWAEAAMpNSw55zsoKAABwlP+6bFDI8yvSU6JUSVeEFQAAoH+cEU5GDPYoNZHTQAAAwEGuykhVZse+lSn5w6NcTai4aBcAAACiLzbGpdX/ulH/++ufuu+fOdEuJwRhBQAASJKu9KXoSp9z9qp04jYQAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwNMIKAABwtH7/W5fNTJLU2NgY5UoAAEBPdf7c7vw5fj79Pqz4/X5JUnZ2dpQrAQAAF8rv98vr9Z53jst6EmkcLBAI6I8//lBKSopcLldYX7uxsVHZ2dmqq6tTampqWF8bf6PPfYM+9w363Dfoc9+JVK/NTH6/X5mZmYqJOf+ulH6/shITE6OsrKyIvkdqair/GPoAfe4b9Llv0Oe+QZ/7TiR6/f+tqHRigy0AAHA0wgoAAHA0wsp5uN1uLV26VG63O9qlXNLoc9+gz32DPvcN+tx3nNDrfr/BFgAAXNpYWQEAAI5GWAEAAI5GWAEAAI5GWAEAAI5GWDmHt956S7m5uUpMTFRhYaG++eabaJfUr5WXl+uGG25QSkqKhg8frrvvvls///xzyBwz07Jly5SZmSmPx6PJkydrz549Uar40lBeXi6Xy6UFCxYEx+hzeBw6dEizZs3SsGHDlJSUpOuvv15VVVXB6/S599ra2vTMM88oNzdXHo9HeXl5ev755xUIBIJz6PPF+frrr3XnnXcqMzNTLpdLH3/8ccj1nvS1ublZ8+fPV1pampKTk3XXXXfp4MGDkSnY0MW6dessPj7eVq5caXv37rXS0lJLTk62AwcORLu0fmvatGm2evVq2717t1VXV1tRUZHl5OTYiRMngnOWL19uKSkptn79equpqbF7773XMjIyrLGxMYqV9187duywUaNG2bXXXmulpaXBcfrce0ePHrWRI0fa3Llzbfv27bZ//37bsmWL/frrr8E59Ln3XnjhBRs2bJht2rTJ9u/fbx9++KENGjTIXnvtteAc+nxxPvvsM1uyZImtX7/eJNlHH30Ucr0nfZ03b56NGDHCKioqbOfOnXbLLbfYddddZ21tbWGvl7DSjRtvvNHmzZsXMpafn2+LFy+OUkWXniNHjpgkq6ysNDOzQCBgPp/Pli9fHpxz6tQp83q99vbbb0erzH7L7/fbFVdcYRUVFTZp0qRgWKHP4bFo0SKbOHHiOa/T5/AoKiqyBx54IGTsnnvusVmzZpkZfQ6Xs8NKT/p6/Phxi4+Pt3Xr1gXnHDp0yGJiYuzzzz8Pe43cBjpLS0uLqqqqNHXq1JDxqVOn6ttvv41SVZeehoYGSdLQoUMlSfv371d9fX1I391utyZNmkTfL8IjjzyioqIi3XbbbSHj9Dk8Nm7cqHHjxmn69OkaPny4xowZo5UrVwav0+fwmDhxor744gvt27dPkvTjjz9q27Ztuv322yXR50jpSV+rqqrU2toaMiczM1MFBQUR6X2//0WG4fbnn3+qvb1d6enpIePp6emqr6+PUlWXFjPTwoULNXHiRBUUFEhSsLfd9f3AgQN9XmN/tm7dOu3cuVPff/99l2v0OTx+++03rVixQgsXLtTTTz+tHTt26NFHH5Xb7dacOXPoc5gsWrRIDQ0Nys/PV2xsrNrb21VWVqaZM2dK4vs5UnrS1/r6eiUkJGjIkCFd5kTiZyVh5RxcLlfIczPrMoaLU1JSop9++knbtm3rco2+905dXZ1KS0u1efNmJSYmnnMefe6dQCCgcePG6cUXX5QkjRkzRnv27NGKFSs0Z86c4Dz63DsffPCB1q5dq/fff19XX321qqurtWDBAmVmZqq4uDg4jz5HxsX0NVK95zbQWdLS0hQbG9slGR45cqRLysSFmz9/vjZu3KitW7cqKysrOO7z+SSJvvdSVVWVjhw5osLCQsXFxSkuLk6VlZV6/fXXFRcXF+wlfe6djIwMjR49OmTsqquuUm1trSS+n8PliSee0OLFizVjxgxdc801mj17th577DGVl5dLos+R0pO++nw+tbS06NixY+ecE06ElbMkJCSosLBQFRUVIeMVFRW66aabolRV/2dmKikp0YYNG/Tll18qNzc35Hpubq58Pl9I31taWlRZWUnfL8Ctt96qmpoaVVdXBx/jxo3T/fffr+rqauXl5dHnMJgwYUKXo/f79u3TyJEjJfH9HC5NTU2KiQn9MRUbGxs8ukyfI6MnfS0sLFR8fHzInMOHD2v37t2R6X3Yt+xeAjqPLq9atcr27t1rCxYssOTkZPv999+jXVq/9dBDD5nX67WvvvrKDh8+HHw0NTUF5yxfvty8Xq9t2LDBampqbObMmRxBDIMzTwOZ0edw2LFjh8XFxVlZWZn98ssv9t5771lSUpKtXbs2OIc+915xcbGNGDEieHR5w4YNlpaWZk8++WRwDn2+OH6/33bt2mW7du0ySfbqq6/arl27gh/R0ZO+zps3z7KysmzLli22c+dOmzJlCkeX+9qbb75pI0eOtISEBBs7dmzwiC0ujqRuH6tXrw7OCQQCtnTpUvP5fOZ2u+3mm2+2mpqa6BV9iTg7rNDn8Pjkk0+soKDA3G635efn2zvvvBNynT73XmNjo5WWllpOTo4lJiZaXl6eLVmyxJqbm4Nz6PPF2bp1a7f/JxcXF5tZz/p68uRJKykpsaFDh5rH47E77rjDamtrI1Kvy8ws/Os1AAAA4cGeFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4GiEFQAA4Gj/B8qNxSBTcg+HAAAAAElFTkSuQmCC",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, dataE[:,0], label='Euler')\n",
"plt.plot(t, dataR[:,0], label='RK4')\n",
"plt.plot(t, np.sin(t), label='exact')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "markdown",
"id": "1973ef1a",
"metadata": {},
"source": [
"We notice that $RK4$ is orders of magnitude better than Euler in solving the harmonic oscillator (HO). Euler's method increases the amplitude of oscillations, which means that energy is erroneously increasing.\n",
"\n",
"Next we plot the energy change with time"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "d9f41e56",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"E0=Ene[0,0]\n",
"plt.plot(t,Ene[0]-E0)\n",
"plt.plot(t,Enr[0]-E0);"
]
},
{
"cell_type": "markdown",
"id": "cc4d8c2f",
"metadata": {},
"source": [
"Indeed, the energy shows huge increase in Euler's method, but mostly constant in RK4.\n",
"Using Euler's method we are clearly not solving the equations of motions in a physically meaningful way.\n",
"\n",
"Next we plot RK4 energy alone to see the error better:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "9964c4c8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-2.1694602519994888e-07\n"
]
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t,Enr[0]-E0)\n",
"print(Enr[0,-1]-E0)"
]
},
{
"cell_type": "markdown",
"id": "106e6433",
"metadata": {},
"source": [
"The error of RK4 method is small, and is excellent for small times. Of course the error depends on timestep, but for 2000 function evaluations, this is small error. \n",
"\n",
"But we do see a problem: The energy is monotonically decreasing. If we simulate Newton's motion long enough we will loose all energy, and system will halt. This is very unphysical, therefore RK4 is not acceptable for molecular dynamics simulation."
]
},
{
"cell_type": "markdown",
"id": "3d8702fa",
"metadata": {},
"source": [
"Next we check the anharmonic oscilator."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "f18f75c5",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/j8/d9m3r0zx7j37l3ktfl_n1xw00000gn/T/ipykernel_56755/1125370763.py:7: RuntimeWarning: overflow encountered in scalar multiply\n",
" return np.array([y[1],-w2*y[0]*(1-alpha*y[0])])\n"
]
}
],
"source": [
"data2E = Solve(t, [x,v], euler, anHarmonic)\n",
"data2R = Solve(t, [x,v], rk4, anHarmonic)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "5caad5a6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-1.2, 1.7)"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t, data2E[:,0], label='x:Euler')\n",
"plt.plot(t, data2R[:,0], label='x:RK4')\n",
"plt.plot(t, data2R[:,1], label='v:RK4')\n",
"plt.legend(loc='best')\n",
"plt.ylim([-1.2,1.7])"
]
},
{
"cell_type": "markdown",
"id": "fae5021d",
"metadata": {},
"source": [
"The Euler solution becomes unstable after just one period, while RK4 remains reasonable many periods.\n",
"\n",
"Next we plot Phase-space portrait $(x,p)$ for HO and anharmonic oscilator."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "a33bea33",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(dataR[:,0], dataR[:,1], label='Harmonic')\n",
"plt.plot(data2R[:,0],data2R[:,1], label='anHarmonic')\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "markdown",
"id": "9ce14a44",
"metadata": {},
"source": [
"How good is the energy of the ahharmonic oscilator?"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "1dd87716",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Energy for the anharmonic oscilator\n",
"En2 = E_anharmonic(data2R.T)\n",
"plt.plot(t, En2[1], 'r-', label='$E_{kin}$')\n",
"plt.plot(t, En2[2], 'b-', label='$E_{pot}$')\n",
"plt.plot(t, En2[0], 'k-', label='$E_{tot}$')\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "markdown",
"id": "3c0806c9",
"metadata": {},
"source": [
"But zoom-in shows that the algorithm is loosing energy with time. The error is small with small time-step, but long time unstable."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "122695a9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-3.023807507718246e-07\n"
]
},
{
"data": {
"image/png": 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S4y8rz9ACFwAoyLTi+WtPh0mvwwf7avBfb58U//fItAW/9DIYW6VtA2Ve1H43Ydwy3puGbpmdYhbtEhERGLyEbEJKLABohbgOlxu/23gQAHDbuRORNya2xznTs2y4/qxcAMD/e+cbdLk9AIAjx5X3GD8mpsc5ffEfDxDuZZRgal4AMf1uupNlWSsInpwWBwAoqWfwQkREDF5CNjFV+UFaXNcGp8uD17aVo6KpAylxZlw3L6fP81YvmoDkWBNK69vxunfnjBoAqQFRMNQlHbdHRqvDdYLfRe+0mpcBlo0SBYxJ6K650wW3t5eOOpKguK69nzOIiGi0YPASogxrFGzRRrg8MrYVN+CPHx0GoGRdLCZ9n+fFmA249ZyJAIDf//cQSuraUGXvhE4C8r0BUTCijHqYDMr/tnDvONJqXgZYNhI9HBLwLUnFmPTa51PKzAsREYHBS8gkScK8vCQAwNUvfIm6VgdykqJx5RnZA577vdljkZVgwfEWB2786w4AwNSMeMRF9R8sdCdqx1Gwy0aDEry0+wZW5npriFjzQkREAIOXE7J0WnrAr+++YBKM+oE/SpNBh58szgcAHPIuGZ0zKSXk64vYcdTl9qDFuww1UOZFZNGwqtFvYKVaAF1a387t0kRExODlRCyblo4lp6RBJwE3npWLZd2Cmf5cMiMTs3MTAShByNVzx4V8fbXuJZzBg38gFB/kspGI7doqdaeRLdqErAQL9DoJHV1u1DSf/FgGIiKKbOzzcgL0OgnPXjMLDpcbZkPfdS690ekk/O362fj8cB2mpMefUN8SEcs2aiAUH2UYsNuvFjwJ7PPSqE3bNsKo1yErwYLS+naU1LehrtWBl7aU4Lr5OSjItAq7ByIiGp4YvJyEUAMX//POmZx6wte1eoczhrPmJZiJ0iqbX/Dk8cjQBTnaIBT+NS8AkJMUg9L6dhTXteHpTYdR3tCB3eVN2Hjn2VrTPyIiGh24bBSBhGRevMHCQN11Ad+ykkcGWp3h3a6t0mpeotXgJRoA8O/CCpQ3KDOhDte2alO5iYho9GDwEoFs2nDG8C3bqD1bgsm8RBn1iDJ6t2sLmLEUcD9q5sVbtPvF0YaA4/ZXNYOIiEYXBi8RyCZgsnS9N1hIjh04eAHEb5dWhz5qmZfk3rsQF1W39Po8ERGNXAxeIpBVQJ+XOu/yS3KsOajjbQLqbvz5al6U73W6X2GuJAEr5+cAACqbOoRcn4iIhi8GLxFISPDSqgYvQWZetO3aYnYc+fd5AYCkWDOum6dsK//J+fkY7x2p4D/dm4iIRgfuNopAIpZs1GWjpJjgMi8il408HhmN3sAswa8GZ83Fp+Cu8yfBGm3Eh9/UAACqmxm8EBGNNsy8RCC1qDacgcNxddkoLthlIzEjCgCgxW8oo//uJ0mStIxPmlXpj1PZxOCFiGi0YfASgRK8P8BbHS44XO6wvKcv8xJawa6ILrvqklGs2dBnL50x3iCrsd0Jj0f8yIDiujbsKmsUfh0iIhoYg5cIZLUYYfZOlq4OQ82HxyNrW5ODLtiNFpd5aehWrNvf9d0eGS2dYnrNqI63OHDxHz/D5U9vwaeHjgu9FhERDYw1LxFIkiRk2CwormtDZVMnxiX13Ebc2ObE6zvK8fWxJugkCbPGJeCK07MRa+75v7y2xQG3R4ZeJ4VQsBv+pSuVOhogoZ+eM2aDHrFmA1odLjS0O7XlJBE+OXhcG1r5wb5qnDVxjLBrERHRwBi8RKgMWxSK69pQZe+5VfizQ3X48au7AgKL/3xdhac+PoI/XTMLs8YlBBx/rLEdAJBujYIhiOnYgN+OJwG7jRqCCF4AJTPT6nChoc2J3D76wISDfyO87cVcOiIiGmpcNopQ6VYLgJ5bhXeWNuKHL26HvaMLk9PicP+Fk3HPkknISYpGXasDV//5yx5daY81KgFQVoIl6OuLLNjtvk26L2pwo2ZqRCmq8TXCO1rXqhUTExHR0GDwEqEytN02vsxLq8OF2/6+G063B+dNScG/V38LPzp7PG5ZOAHv3HYW5o9PQkeXG7e8sgudXb5C3wrve2TaooO+vtiC3Z7bpHujBS8Cp1sDQI3fduwut8zGeEREQ4zBS4TK9GZJyhrateee/+QoKpo6kJ1owe+uPDVgp06M2YCnrjoNqfFmFNe14c+fHtVeU5eNQsq8aE3qRNa89F/HomZmRAcvjd2yS6X17X0cSUREg4HBS4SakBIHADhU0woAqG91aAHJz5ZMQVxUzx/8CTEm3Ld0CgDg6U1HtN4uxXVtAICxicFnXtTxAO1ON5wuzwl+F73Tal6CXDZqaBMzogAAZFnWgqmp6fEAgJL6NmHXIyKigTF4iVATU5X2+NXNnWhqd+LpTUfQ5nSjIDMeSwvS+jzvklMzMD3LinanG09+dAiyLOObSqUGZor3h3Mw4qIMkCTl63DvOAq+5kUJ0ETWvLQ4XHB5a1xmjrUBAEoZvBARDSkGLxEqPsqo7bD51+4K/G1rKQDgpxdMhk4n9XmeJEm4d8lkAMCr28rw6aE6NHe6YNRLmOCdFxQMnU5CfJQ6IiC8wUOwNS82b3Ajar4S4AuMok16TPR+PuUNrHkhIhpKDF4i2LcmJAEA1rz9DZxuD+bmJeLsiclBnJeMsyYmo8st49q/bAMAzBqXAJMhtN8OouYbaTUv/TSpE3l9f/7btscmKctq/nVGREQ0+Bi8RLArZmVrXxt0Eh64cCokqe+siz81+6JaWpAe8vVFdNlVhjJ6l40GyrwI3K6tavTr9qvWBJU3tEOWuV2aiGioCA1eGhsbcc0118BqtcJqteKaa65BU1NTv+esXLkSkiQFPObOnSvyNiPWjGwbHr58GublJeHp75+GaVnWoM8tyLTizvPyoddJOCMnAd+bPTbk64vIfDR3dkFto2IbKHiJHozMi28JKytBCV5aHC6hARMREfVPaIfdq666CseOHcP7778PAPjRj36Ea665Bm+//Xa/5y1ZsgTr1q3Tfm0yBdeyfjRaMXssVpxA4AEAt583ETctyIPZoAs6Y+PPKiDzoda7xJkNAy5jDcayUZNf8XCUUY/UeDNqmh0ob2zHfw/U4tEPinDHeRNP+P8BERGFTljwsn//frz//vv44osvMGfOHADA888/j3nz5qGoqAiTJk3q81yz2Yy0tL53zFD4RBl7n9ocDBG9XtQaE9sA9S5A4HZth8vd5wTqcNyPWjycnRCNmmYHjhxvxf1v7oHT7cGv/vMNvj0rC8YgRysQEdHJEfa37datW2G1WrXABQDmzp0Lq9WKLVu29Hvupk2bkJKSgvz8fNx4442ora3t81iHw4Hm5uaABw0OEV121WLdgepdALHbtbX76bZtW617efXLMjjdSn+bdqdb65VDRETiCQteqqurkZKS0uP5lJQUVFdX93ne0qVL8corr+Cjjz7CY489hu3bt+Occ86Bw+Ho9fi1a9dqNTVWqxXZ2dm9Hkfhp2Y+msLY4ba+Tfn/nBRrHvBY/+3aIsYUAD0b5qm9cLaXBA5oPFDdAiIiGhwhBy9r1qzpUVDb/bFjxw4A6LWOQpblfusrrrzySixbtgwFBQVYvnw53nvvPRw8eBDvvPNOr8ffd999sNvt2qO8vDzUb4lOkIiak7pWJVhIGqBBnUrEjid/jVrBrnKd7kXR6kiFQzUMXoiIBkvINS+rV6/GihUr+j0mJycHX3/9NWpqanq8dvz4caSmpgZ9vfT0dIwbNw6HDh3q9XWz2QyzeeB/pVP4WQXUvNS1KpmX5Ljg/p/aLEaUQlzw0tBt2/ap2TbYoo1oau9CfJQB3z09G49vPIjKps7+3oaIiMIo5OAlOTkZyckDN0KbN28e7HY7tm3bhtmzZwMAvvzyS9jtdsyfPz/o69XX16O8vBzp6aH3ISGxbAIyL/UhZl7iBe84auy2bBRl1OPXlxbgr1tKsfqcCdp8KP/J00REJJawmpcpU6ZgyZIluPHGG/HFF1/giy++wI033oiLLrooYKfR5MmTsX79egBAa2sr7r77bmzduhUlJSXYtGkTli9fjuTkZFx22WWibpVOkJp5sYcx66FlXoKoeQF8vWBETLf2eGTtff3nLF00PQP/WDUPZ+ePQZo1CgBQZefIACKiwSJ0b+crr7yCadOmYfHixVi8eDGmT5+Ov/3tbwHHFBUVwW63AwD0ej327NmDSy65BPn5+bjuuuuQn5+PrVu3Ii4uTuSt0gnQCnY7usLWcVbLvMQGWfOiZl7CWDSsaul0we3tmKfW1nSXGq8ELzXNvReUExFR+AltUpeYmIiXX36532P8f+hZLBZ88MEHIm+Jwkj9ge72yGjudGkFvCdD220UE1zmRWSjOrXeJdZs6LOHzBhvbU6rw4XOLvdJ9c0Jxj93lONYYwd+vGhCyLOoiIhGCqHBC41sUUY9EqKNaGzvQpW946SDF6fLg3pvjcmYYAt2BRQNqxqCGBAZH2WAXifB7ZHR1N6FNKu44KWiqQM//b+vAQAp8WZ8f844YdciIhrOGLzQSUm3WpTgpakTk9Pie7z+2aE6/OmTIygsa4IkKdOrVy0Yjzl5ST2OrbZ3QpYBs0GH5CCXjURmXhq7ddftjSRJSIg2oq7ViYY2p1YDI8JH+32797YcrmfwQkSjFvPOdFIybEqfk4qmwIJVWZbxu40HcfULX+LTQ3VocbjQ3OnCx0XHceVzX+DZzUd6vNexpnYAQKbNEvSsJRHzlVTqslF/wQvgVzQsoO7G3zdVvl4yu8oa+zmSiGhkY+aFTkqmTck0VHYLXl7bXo7f/1fpzXPN3HG4as5YeGQZL35egn/uPIaH3zuAMbFmfHtWlnZORaPyHpnexm/BUAMHkZmXxAG2bas9YBoEBy9lDb4RBFX2TrQ7XYg28Y8wEY0+zLzQSVEzL/7By7HGdvzy7X0AgJ+cn4//d2kBpqTH45QMK/73ihm49ZwJAICf/2tvwHlq9ibTFkrwInDZqF3trtt/8KLWxDQKapSnKq1v7/fXRESjBYMXOilZCcqgwhK/H6S/23gInV0ezM5NxI8XTehxzp3n5eOMnAR0dLnx8HsHtOe1zEsIwYtv2cgJjyc827VVvsxL/4XIanCjHi+CLMuotiuN8FK8xcwMXohotGLwQiclPzUWgDLbx+ORUVTdgjd3HwMAPHDhFOh0PWtXdDoJDy4/BZIEvPVVJb4+1gQAOOidD5Q3Jjbo66vBi0cGWp2uk/lWetBqXgZYNlJfbxS4bNTicMHlDc5OzbYBCFxGIiIaTRi80EnJSY6BSa9Dm9ON8sZ2PLqhCLIMLC1IwwzvD9neFGRacdmpmQCAh987ALdHRpE3eJmSHnxDwiijHlFG5bdxODv9An6Zl4GWjbxLVyIzL03eAZEWox6T0pTPp4SZFyIapRi80Ekx6nUoyFS2SD/18WFs/KYGOgn4yeJJA5wJ3Hl+Pkx6HbYcqcezm4+gs8uDWLMB45JiQroHUdul1cyLbaDdRhZxRcOqRm3nkxFjE5WluvIGBi9ENDoxeKGTtnBSCgDgHzuU5aLvzMrChJSBl36yE6NxzTylV8n/flAEADhzQjL0vSw19UcbUyAq8zLAspE6HFJEozyVfyClBi9lDF6IaJRi8EInbcXsbMSalS27ybFm3B1E1kX140UTEGf2bff13zodLBGZF7ffUMb+OuwCYnc8qdQeMokxJoxNUoKXisYOuNweYdckIhqu2CSCTlpKXBRe+9FcfHqoDstnpCMlPvgus4kxJjx37en440eHMDs3EedNSQn5+lZtRED4ak7sHV1Qx24NtFVaDZ6aRS4beWtebNFGpMZFwaTXwen2oMreiawEC4rr2jA2MRoGPf89QkQjH4MXCouCTCsKMq0ndO688UmYN77nuIBg2QR02VVrTOKiDDAOEBD4d/mVZTno7sChaPLr9qvTSchKtODo8TaUN7Tj+U+P4q9bS/Ht07Lw2HdnhP3aRETDDf+ZRhFPROYjmLlGKnXZyOWR0e50h+0e/DX4FewC0Ope9lU2469bSwEAb+w6huZOsY3yiIiGAwYvFPG0ydJhzLzUtSrBQlIQAyItRj2MeiXbIqruRev26y0eHucNXv782dGA44qqW0BENNIxeKGIZ1UHI4ax5qW+zQEASIoxD3isJElCp1sDgctGAHBKhrJEV9PsCDjuUE2rkOsTEQ0nDF4o4okIHOq9mZfkIDIv/vcgYro1EFiwC6BHA8D53pqhw7UMXoho5GPwQhFPRMFufas38xJi8CJu2Sgw8zIxJRZ5yUozv4LMeJw/NRUAUN3c0fsbEBGNINxtRBFPRJ+VOm/BbjDLRoD47dKN7YEN83Q6Cc9dOwtvFVZixeyx+Kq8CQC04Y1ERCMZgxeKeGKWjULLvNgE1N2oOrvc6OzyeK/ja5g3ISUOd3kbAlY3K0FL9xoYIqKRiMtGFPHU8QDtTjccrvBsVfbVvISWeRGxbKRmXQw6Setk3F2atzFgTXMnPN7p00REIxWDF4p4cVEGqOOQ1MLWk1UXYuYlXmDw0tDmm2vUVwM8NchyeWThvV5kWcadrxfikqc+R00zl6mIaPAxeKGIp9NJWuahyt53wWqbw4XC8iZ8Vd6Ejn6ayXU43VpflfR4S1D3IHK3kfqeCdF9z1gyGXSIMekB+HrCiLK9pBHrd1fgq/ImvPxFqdBrERH1hjUvNCJk2CyotHeioqkDM8cmBLzmcLnxu42H8NetJVoH3FizASvn5+C2cyfCZAiM4Su9AVCs2YB4S3B/RGyDsGyUMMB064QYE9qcHWhsdyIXMWG/D9WO0gbt652ljcKuQ0TUF2ZeaETIsCkZksqmwMyLw+XGD9Ztx7Obj6Dd6caYODOSY01odbjw5MeHcf1L23vUyVQ0dnjfMyroOUUidxv5RhX0P91a3UatNrQTpfh4m/b1V+VNkGXW2BDR4GLwQiNCZoIavATWYDz0zn5sOVKPWLMBz149C9vuPxfb7j8PT111GqJNenx6qA6/fPubgHPUACjTFtySEeCbbC0m86IuG/WfeVF3IoWr7qcvJfW+4KXN6cbxFu5wIqLBxeCFRgQ181Lhl3k5XNuCl78sAwD88XszsaQgDZIkQaeTsGx6Op7+/mkAgFe/LMOWI3XaeWrwkhFC8KI1yhO4bGQbIHhRg5tGwZmXsob2fn9NRCQagxcaEbK9mZfiOl9W4JH3i+D2yDhvSioWTU7pcc7CSSn4/pyxAICH3zugLX+U1Cs/jLMSooO+vv+yUbi3KqsFu4kxAy0beTMvAoMXWZa1beRqh9/SegYvRDS4GLzQiDA5LR6AErx0drmxrbgBG7+pgU4CfrZ0Up/n3Xl+PqJNenx9zI4N39QA8E1mnpQWG/T11a3SHhlodbpO9Nvolf9W6f6oBb0idxu1OlxweYMzdb5SKTMvRDTIGLzQiJAab0ZCtBFuj4wD1S1Y+95+AMCVZ4zFhJS4Ps9LjjXjB9/KAQD8buNBdDjdOHJcGW6oBkTBiDLqEWVU/jjZwxw8dJ8o3Rdt2ahNXOZFraeJMuqQn6p8rmV+NTBERIOBwQuNCJIk4YycRADAT/5RiN1lTbAY9bjzvIkDnvujs8YjLsqAA9UtWPPWPrg8MlLjzUi3RoV0D6K67DYG0ecFEDPjqee9+AKpcUnKshprXohosDF4oRHjPO9k5SPerby3LByPlPiBAxBrtBE3npUHAHh9RzkAYEH+mKC3SWvvIyx4Ca7Pi8hGed3vxRZtwthENXjhJGsiGlwMXmjEuPTUTExJV5Z65uQmYtXC8UGfe/2ZucgboxSg6nUSfvCt3JCvr85YCmfw0uX2oKVTqaEZaNlI5HwllW+6tRHZ3uClrtWBNkd463yIiPrDDrs0YpgMOqy/ZT4O17ZiclocDPrgY/MYswH/vGke/rnzGKZnWbUgKBTxAjIf6ntJki846YvIRnkqtebFFm2C1WKELdqIpvYulDe2IynGjLe+qsRlMzOROECWiIjoZDB4oRElyqhHQab1hM5NijVj1YLgszXdich8qMW68VFG6HX9L2Opu5FaHC643J6QgrdQ7yfRe62xidFoarejtL4dv3r7G2w5Uo9/F1bgrdVnhv3aREQqLhsRhYmI4EXdJh1MJiM+yvdvkeZOMcs4De2BowrUpaPtxQ3YcqQeAPD1MTuONbKIl4jEYfBCFCa+3T7h26pc7w1ekoIIXgx6HWLNSgAjar6RuvNJzfLkJil1Qn/+rDjgOLVXDhGRCAxeiMJEROalvlWZG5QUG1wNieii3cZumaBpWb0v0am9coiIRBAavPzmN7/B/PnzER0dDZvNFtQ5sixjzZo1yMjIgMViwcKFC7Fv3z6Rt0kUFiIChzpvK/6kWPOQ3YM/X+ZFuc7MsbaA11eckQ0AOHqcjeuISByhwYvT6cQVV1yBm2++Oehzfvvb3+Lxxx/Hk08+ie3btyMtLQ3nn38+WlqYhqbhTZ0sHc7dRvVtSuYlOcjdO6KDl+7dflPionC+t7/O8hkZOG1sAgCgurmz9zcgIgoDobuNfvnLXwIAXnzxxaCOl2UZTzzxBB544AFcfvnlAICXXnoJqampePXVV3HTTTeJulWikyayYDfYzIvoLru9FRA/edVM7C5rwunjEvDZYWU6d02zQ8j1iYiAYVbzUlxcjOrqaixevFh7zmw2Y8GCBdiyZUuv5zgcDjQ3Nwc8iIaCun24vtWpTag+WeqyUbB9U7QASkCX3Q6nGw6XB4AvSAIAs0GPuXlJMOh1SPOOVKhh5oWIBBpWwUt1dTUAIDU1NeD51NRU7bXu1q5dC6vVqj2ys7OF3ydRb9Qf3B1d7rBtVQ65YFdduhKQeVG76xp0krarqbvUOOUzaGhzwuFyh/0eumtzuLRsEBGNHiEHL2vWrIEkSf0+duzYcVI31X2mjCzLfc6Zue+++2C327VHeXn5SV2b6ERFGfVa5iNcmYda7/JLStzQF+yqQUJCjKnPP4+2aCMM3mZ6ajdeUTq73Fj2h08x/+H/4qvyJqHXIqLhJeSal9WrV2PFihX9HpOTk3NCN5OWlgZAycCkp6drz9fW1vbIxqjMZjPM5uD+YicSLS0+CvaOLlTbO5GfGtfjdY9HxpYj9dhd1ghJAmaOTcC8vCToeume29zZhRbvzKAMmyWo64sMXpqCmG4tSRJs0UbUtTrR2O7UslEifHaoDiX1SjO817aXYUa2Tdi1iGh4CTl4SU5ORnJysoh7QW5uLtLS0rBx40bMnDkTgLJjafPmzXjkkUeEXJMonFLizSiqael1t01pfRtu/ftufH3MHvD89Cwrfr9iJnKTYwKer2xSpjXboo2INgX3R1UbDimg5sV/onS/9xBt0oIXkfZV+urbCsvt/RxJRCON0JqXsrIyFBYWoqysDG63G4WFhSgsLERrq6+B1eTJk7F+/XoAyr/a7rjjDjz00ENYv3499u7di5UrVyI6OhpXXXWVyFslCou0eG/Bqj0weKmyd+DKP32Br4/ZEWc24LKZmbhsZibizAZ8fcyOK/+0FeUNgS31q5qU98iwBpd1AcRmXhq7zTXqS4KALeO9Ka7z/T1ysKZlUGpsiGh4ELpV+he/+AVeeukl7ddqNuXjjz/GwoULAQBFRUWw233/arrnnnvQ0dGBW265BY2NjZgzZw42bNiAuLieKXii4Sbdu0xSae8IeP6e//sa1c2dmJASi79dPxvp3oCk2t6Ja//yJQ7WtOLWv+/GGzfP1wYwVngzL8EuGQGCgxdvDUtCTP/TrdXMjOhC2qN1vkZ4bo+MisYO5I2JFXpNIhoehGZeXnzxRciy3OOhBi6AUoy7cuVK7deSJGHNmjWoqqpCZ2cnNm/ejIKCApG3SRQ26g/Pw7W+rMAnB4/j00N1MOol/Pna07XABVB2KK37wWzEmQ0oLG/Cy1+Uaq+pwUumLfi6EZu22yj8gUNjtwZ1ffFlXsQGL1XdslulDRwGSTRaDKut0kSRbmKqErwcrGmFLMvweGSsfe8AAOCauTnI6VbXAgCZNgvuWToZAPDHjw6h3akU6R7xBkDjknqe05d4b+als8sT9mWU4IMXk/d4cctGsixrc5YKMuMBoMeyGxGNXAxeiMJo/JhY6CRl2eZ4iwPrd1dgf1Uz4qIMuPWcCX2et+KMbGQnWlDX6tSyL0U1ykiMyWnBL5nGmQ1QdzGHe+mo+1yjvti04EVc5qXV4YLLozQCnJFlAwCU1jN4IRotGLwQhVGUUY8cb6ZkR2kjHttQBAD48aIJSOinS65Rr8Ot50wEADy7+SiONbajzJtJmBRC8KLTScK67KrLQAN1+x2Mgl31vc0Gnfb5MHghGj0YvBCF2dzxSQCAW17ZhUp7JzKsUVg5P2fA8y6fmYm85Bg0tDmxct12yDIwMSU26LlGKlFFu2oBbjBbpQGxmRf/GUtjE6MBcNmIaDRh8EIUZsunZwT8+n8umoooo37A8wx6HX6yeBIAX8HvuVN6b87YH5ug4CWYJnWA+MnWQGDPGbUmqKyhPWwzpYhoeGPwQhRm88Yn4YffyoUt2ojbzp2IpdPSBz7J68JpabhsZiYAIDnWhOvPzA35+mrRbjiXbZwuD1q93X4HWjZSa2KaByF4SYwxItNmgU5SZkodb+E0a6LRQGifF6LR6hfLp+IXy6eGfJ4kSXj8uzNw04I8pMdbtEGLoRCR+VDrXXQSEB8VfOalv7lkJ0PtOWOLNsFk0CHdakFFUwfKGpRaoT9+dBg3nJWLsyaOCfu1iWjoMfNCNMxIkoTJafEnFLgAvsxHOIOXBm/wYrUYe53D1Nv1u9wy2p1iut527/Y7Lkmpeymtb8e9b3yNzQeP447XCuHxcBmJaCRi8EI0wojIvDS0KsFCMMXDFqMeRr0U9nvw5+s5o3yvavDy0YFaHDmudN6tb3PiqN8IASIaORi8EI0wIoKXeu/unqQB6l0AJXNkFVB34883qkC5H3Wo5Tt7qgKO48BGopGJwQvRCKNOlg5ne/76VqUQNil24OAFEL/jqHu335ljEwJejzIqf7WV+M0/IqKRg8EL0QgTL2LZSMu8BNdzRnzwEtjtd1qmVXvNqJewcr6yS0udD0VEIwuDF6IRRkTgUNcWXHddldqozi5gQCQAba6Rej9RRj3uWzoZZoMO9184BVPSla67DF6IRiZulSYaYYTsNvIW7CYPg2UjWZZ7HRJ504Lx+NHZeZAkCTtLGwAAlQxeiEYkZl6IRhg1G9HY3gV3mLYK17c5vO899MtGHV1uOFweAOgxL0rtKZPs3RVV3ypuRAERDR0GL0QjTHKsGXqdBLdH1gptT1a9tlU6tMyLiN1Gar2LUS8hxtT72AU1gOvocqNDUK8Zf3sr7HhvTxXHExANEgYvRCOMXidhjDfzUGXvPOn3k2UZlXZl+SXdGhXUOSIzL2q9S0K0qc/uvbFmA0x65a83NWskSmObE995dgtufmUX1u+uEHotIlKw5oVoBEq1RqG6uRPVzZ2Y0cvrVfYOvLilBLtLmwAAp4614dp545CVEN3j2Mb2LnR2Kcs0aUEGLyLqbnz307PepTtJkpAYY0J1cyca2py9fl/hsq2kQft8PthXjctPyxJ2LSJSMHghGoHS46PwFYDqXjIvG7+pwe2v7Q5o3b+tpAF/3VqCR6+YgYu6TcVWi16TY80wGwaejg0Izryo061j+h+fkOAXvIi0q6xR+3pvRbPQaxGRgsEL0QikZkiqmwODly+P1uPml3fC5ZExa1wCvj9nLCQJ+PuX5dhW0oDb/r4b8VFGnJ3vG2ioBi8ZtuCyLsDgLRv1R+0GLDp48W+EV9HUgaZ2p7ZVnIjEYM0L0QikBi/HGn1bhVs6u3DXP76CyyPjwmlpeP1Hc3H5aVm4bGYW/v6jubj8tEx4ZOD213YHdOdV62YyrJagr68uG4kp2PUGLwP0nEkcpOCley+ZsoZ2odcjIgYvRCPShDGxAIBDNS3ac89/WoyKpg5kJ1rw2+/MgEHv++Ov10lYe/k0TEqNQ2N7F/73gyLtNfWHcYYt+OBF7fLb3NkV9snOvsxL/8tGavBSLzp48QaI6s6n8gb2liESjcEL0Qg0KU3pMHv0eBu63B40tDnxwqdHAQD3L52CWHPPFWOzQY9fXXIKAODv28q0wOeg978TU2ODvr66bCTLQIvDdeLfSC+0mpcBlmbU4CWcM56663C6tfuZk5cEAChvZOaFSDQGL0QjUKbNgmiTHk63B6X1bXhm02G0Od0oyIzHkoK0Ps+bk5eEJaekwSMDj7x/AIAveMlPjQv6+maDHhajkomwh3npKJjdRoDYpStVg/deTHodpqbHAwDKuWxEJByDF6IRSKeTtOzL219V4aWtpQCAnyye1GdvFNU9SyZBr5Pw4f5avLHzGGqaHdD7vV+wRBXt+mpe+l82Ej0cEvAtYdmijRibqGzHZs0LkXgMXohGqAXeHUO//+8hOF0ezMtLwkK/XUR9yRsTi6tmjwUA/OSfXwEAZmRZe11q6o+W+QjzcMbGtuCWjUR2+VU1+S1hZSUqNUH+RdJEJAaDF6IR6rKZmTAZlD/iRr2EB5ZNGTDrorrt3IkBrfcvnpHRz9G9ixedeRlw2UidbC0w8+K9F6tf5uVYY3vYZkoRUe8YvBCNUOOSYvD0VafhO7Oy8OIPZqMg0xr0uWPizHjo8mlIjTdjQf4YrPBmYkJhExC8dHa5teZ6A22VtmmZF3EFu03tvp1P6VYLTHodutyy1huHQQyRGGxSRzSCnTc1FedNTT2hcy85NROXnJp5wtcWsWyjvpdeJyE+qv+/vtRlqzanG06XR8tChZP/zie9TsLYpGgcrm1FSX0bNh88jl+9/Q1WLcjDXYsnhf3aRKMZMy9EJIQavDSHMfOiDlnsbyijKi7KCPUQUUtH6rKRukSVk6QsHR093obfbTwIp9uDP3x0eFAmWxONJgxeiEgIEVuV1W65SQMsGQFqdkZduhKzdOQr2FWuk5MUAwB4c9exgOZ4+yrtQq5PNFoxeCEiIURsVVaDl8QgghdAfK+X7sXDE1KURn5fHQsMVvZUMHghCicGL0QkhIjdRnWt3uAlNsjgRfB2abXmRQ2STs9JCHhdDWbY+4UovBi8EJEQah1IU1gzL0rNS3KQmRergHvw19RtSOT4MbFI9w7FTIuPwve8u7Qqm9j7hSicuNuIiIQQUbDrWzYyB3W86O3S3YdESpKE3115Kv78aTGuPzMXbd65TpVNnUKuTzRaMXghIiFE9HmpD3XZKFrciACX24PmTpf3Or77mZuXhLneIY3fVDYDAKrszLwQhROXjYhICLWItdXhQmdXeLYKh7LbCBATQKn831O9TnfJccp9NrQ54WHDOqKwYfBCRELEWwzaZOma5vAsm1R73yclLrhlI63mRUDBrlqsGxdlgEHf+1+lagDnkcXV3fj729YS3Pt/X6O5U/y1iIYSgxciEkKSJK14tcref/DS2eUesJGbxyNrQVC6zRLUPWhdfgUEDk1BzFgy6nVaJ+CGNnFjCgCgoqkD//PvfXh9Rzn+8lmx0GsRDTWhwctvfvMbzJ8/H9HR0bDZbEGds3LlSkiSFPCYO3euyNskIkHSvMFLdS/BiyzLeHdPFZb94VNM/p/3MeUX72PJE5/gzV3HIMs9l1jqWh3ocsvQSUBqkJkXbdlIQMFuY7cGdX1Re9KIDl6+PFqvfb31SH0/RxJFPqHBi9PpxBVXXIGbb745pPOWLFmCqqoq7fHuu+8KukMiEimtj8yLLMtY+94B3PLKLuzzFrUCwIHqFtz1j6/wszf29KgRqbSrS0ZRfS7TdKc1qROYebENMN16sIKXr/0a431T2cwaGxrRhO42+uUvfwkAePHFF0M6z2w2Iy0tTcAdEdFgStcyL4G7bf72RSme++QoAODHi8bjuvk50EkSXv2yDE98eBCv7yhHui0Kd5yXr51T5e2Vkm6LCvr6IjvsNnVrUNeXwQpejjX6GuG1OFyoaOpAdmK00GsSDZVhWfOyadMmpKSkID8/HzfeeCNqa2v7PNbhcKC5uTngQUTDQ7pVqU0pb/QFL+UN7fjNO/sBAPdfOBk/vWAyUuKikBxrxm3nTsTD354OAPjDfw9pW40BX+YlwxpcvQsAWC1K4NDc2QV3mDMR3UcD9EUNXhoF9ZpRHWsMDBDLG9nVl0auYRe8LF26FK+88go++ugjPPbYY9i+fTvOOeccOByOXo9fu3YtrFar9sjOzh7kOyaivqjt8YuqW7TnfvfhQThcHszLS8INZ+b1OOe7p2dj2fR0eGRgzVv7tPqX4rpWAMDYpOCzCWrBriwDLWHegdN9NEBf1O67ao8aEWRZ1oKXTG8x87EG9pahkSvk4GXNmjU9Cmq7P3bs2HHCN3TllVdi2bJlKCgowPLly/Hee+/h4MGDeOedd3o9/r777oPdbtce5eXlJ3xtIgqvyWlxAJSdMC2dXThY04L1uysAAPdfOAU6ndTreT9fNgVRRh22lTTg4yIl83qwRgle8lNjg76+yaBDjEnZrh3upaNgdhsBQGK0+MxLR5cbrd5uvmd45ysx80IjWcg1L6tXr8aKFSv6PSYnJ+dE76eH9PR0jBs3DocOHer1dbPZDLM5uJ0HRDS4bNEmpMabUdPswMGaFjz3yVHIMrDklDRMy7L2eV661YLr5ufgT5uP4rfvF+HsiWO07M3ElLiQ76HN2RH2ot1GrWC3/8yLyC6/KjWrYzboMCktHkAlh0HSiBZy8JKcnIzk5GQR99Kr+vp6lJeXIz09fdCuSUThU5BhRU1zLZ7++Aj+e6AWOgn4yeL8Ac+7ecF4vPplGQ5Ut+DRDQdh7+hCtEmPSWmhBS9WixEVTR1hn2/UpG2V7j/zotbdiJqvBAR2Hh7rLdItZ/BCI5jQmpeysjIUFhairKwMbrcbhYWFKCwsRGtrq3bM5MmTsX79egBAa2sr7r77bmzduhUlJSXYtGkTli9fjuTkZFx22WUib5WIBDlvaioA4L8HlOWfK2ZlY2LqwAGILdqEm85WamKe3XwEAHBGTiKMQW6T9r2PmMxHQ1twy0Yit2v3uJcYE7ITexZJE400QoOXX/ziF5g5cyYefPBBtLa2YubMmZg5c2ZATUxRURHsdqU/gV6vx549e3DJJZcgPz8f1113HfLz87F161bExYX2ry0iGh6Wz8jQikjT4qNw9wWTgj73B9/KDRgFcPXccSFfX0TwIsuytmw00JBI7foCtmurfNO2fZmX4y0OtDtdwq5JNJSE9nl58cUXB+zx4t9J02Kx4IMPPhB5S0Q0yGLNBrxx83xsPVqHsyaOQXJs8DVqMWYDXrlhDp78+DAKMqw4b0pKyNf3LduEL3hodbjQ5Vb+7kocKPOiXr+jC7IsQ5J6L1I+Gf7LRrZoE6wWI+wdXSitb8eElFhsL27AjGwbYsxC/8onGjT8nUxEwqVZo3DZzKwTOndiahx+v2LmCV9bm28UxuBFDRYsRj0s3t1MfVEzL26PjFaHC3FR/Rf4noh6v2UjAMhJjsFX5U0oqWvDi5+X4PUd5fjWhCS8cgNHrdDIMOz6vBARhZOv5iR8BbP+yzQDiTLqYTYof9WK6PSr3I/SByvJez+53l44X1fY8Y+dSvuIzw/Xh226N9FQY/BCRCOabzhj+AIHrd4liOAFEL9duqGty3s/ypJcbrLSC+fFz0vgP+Nyb4W9x7lEkYjBCxGNaCJ2+6h9VRKCDV4E1N34UzMviTHK9zopTQleOrrcAcf5D8EkimQMXohoRBPRZ0XNvCQFGbxYBSxd+fMtYymZl9NzEgNeP3eyUujM3i80UjB4IaIRTcSSjbpMM1CPF+0eBBQN+2vUGuYp10mONWNunhLAzMiyYuk0pclnlZ01LzQycLcREY1o2rJRe/i2Kndfpgn2HkTUvLg9Mpo71SGRvmDqqatOw3++rsKSgjQcqVUag1ba2biORgYGL0Q0oqn1Ji6PjDanG7Fh6HXSvUB2wHuIFjcioKWzSyvKVbeFA0BSrBnXzc8BALQ7ldqXamZeaITgshERjWhRRh1M2lbl8AQPda1q5iXImheBy0bqe8aY9Nr32V2ytwtwu9ONDqe712PCzb8BKVG4MXghohFNkqSw15yoGYx0a1RQx4ucb6S+p62f+ptYswFGvbJc1iBwQCSgBC23vLIT8x/+CAdrWoRei0YvBi9ENOKpwUNjPz+461od2PhNDTbsq+53ecXl9qC2JcTgxbt0JaLmRf2e1O+xN5IkaVmixjaxwctXx+x4d081quydWPd5sdBr0ejFmhciGvHSrRYcrGlFZVPPgtV2pwu/fmc/XttWBo93pUOSgItnZOBXlxQE1JEAQG2LAx4ZMOikoOc0iRzOqL5nf8ELoOyMqml2aNuqRdlzrEn7endZU5/HEZ0MZl6IaMTLTlSmWpc3BAYvHU43rvvLNrz6pRK4TE6Lw9T0eMgy8O/CSnz7mS096mSqvDt2UuOjoNMFt3NJq3kR0OdFvT81u9MXLfMieNnoYE2r9vXh2lY4XINTY0OjCzMvRDTiZSUos37KGwObtP3qP99ge0kj4qMMePbqWZg/IRkAUFjehFV/24nDta244/VCrFt5hrbFWu2VkmELbskICNyuHW5qzYt1oMyLN3gRnXkprmvTvnZ5ZBw93oYp6fFCr0mjDzMvRDTiZavBi1+H2W3FDfj7tjJIEvCMX+ACAKdm2/DCytNhNuiwqeg43vqqUnvtWKOSeUm3WoK+vlpM63B50NkV3kyEGhDZLP0HL4nRg1Pzou7EUpX4BTNE4cLghYhGPG3ZyBt4yLKM//3gAABgxRnZ+JZf4KI6JcOK1YsmAADWvntACzoOexu+jR8TG/T1Y0x6GLxLTOHOvtg7gqx5UTMvgpeN1O9v/JgYAEBxPYMXCj8GL0Q04uWNiYUkAcdbHKhrdWDTwePYXtIIs0GH28/N7/O8G8/OQ6bNgurmTry0pQSAL3iZmBp88CJJkt926fAGD0HXvKg7rtrEjCgAlKBQDY5OG5sAACit4zwlCj8GL0Q04sWaDchLVjIBX5U34X/fLwIAXDc/B2n9bHeOMupxx3kTAQBPbzqCulYH9lcpk5knpcWFdA+iGtUFW/NiFTiiQNXudMPp8gAAZnqDF2ZeSAQGL0Q0Kswap/wwveP1QnxT1Yw4swGrFowf8LzLT8vCxJRY2Du6cMsru+BweZAUY9KCoWD5RgSEedkoyJoXNTMjarI14CsGNhl0mJqhFOmWMnghARi8ENGooE5Wbul0AQBWLRwfVHt/vU7CTy+YBEAp8gWABfljQh7wqAYX9nAvGwXRYRfwZV5ETbb2f+/EaBNyk5TgrqbZgXanS9g1aXRi8EJEo8KCiWNwwSmpAICFk8bgxrPygj73/KmpONNb1GvQSfjhmbkhX19E8ODxyL6al4GWjSzil43UepeEGBOs0UbtnkpY90Jhxj4vRDQq6HQSnvn+LNS3OZEcawopcyJJEv583el4d08VJqTEoiDTGvL1fcs24QseWp0urStw907APa+vvN7S6YLbI0MfZIO9UKjbsBO8QUtOUgwK25tQWt+GhBgjXtpSiuUz0nFKRuifH5E/Zl6IaNTQ6SSMiTOHvOQDKMW7l5+WhelZthO6tohGdWq9S5RRhyijvt9j4/2Cm2ZB2ZdGv8wLAOQkKf11iuvbcOfrhXh28xH86K874fZw4jSdHAYvRESDQJtvFMaaF1+DuoFrd4x6HWLNSrJdxHRrwJd5URvi5XiLmrcVN+CLo0q9UEVTB6dN00lj8EJENAhEbJUOZqJ07/cgZseRVvPit2wEAJuKjgccp243JzpRDF6IiAaBiK3Saiv+YKdbiy7aVRvgactGfWwnP1DNzAudHAYvRESDQETgUN+qZDqSYgdeNgL8l67E1ryoW9DzU2NhMvh+zKycnwNAWToiOhkMXoiIBoFNwJLNcMu8NGi7jZTgJdpkwKqzlS3pl56agdm5iQCAau9kbqITxa3SRESDQM16tHlb6PtnJE7U8RCDFxE7nvxpu438GubdeX4+Lp2ZiZykGHx1rAkAUMXMC50kZl6IiAZBXJQR6g7tcGU+Ql02slrEjCgAlKGMje1qzYuvgFiSJOSNiYVOJyHdqkz3rmlxcLs0nRQGL0REg0CvkxAfFd7t0uqy0ZhhsGzkP5Sxr7ELapDl9sjCes34a2p3clv2CMXghYhokIR72UbNvIS6bBTu+UpA4FBGSx8N84x6HeKilGqFBkHbtVUOlxsXP/k5Fv/uE3ywr1rotWjwseaFiGiQ2KJNKK1vR31b7z+4u9wevL+3GjtKGuCRgelZViyfkdFr91yX26PVvKTED33mRdtpFN3/6IXEGBNaOl1KQ7sxYb8NzY6SRpQ1KDOV3v6qEheckibuYjToGLwQEQ2SDGsUvioHKhp7Fqwerm3FTX/bgSPH2wKef2zDQTx99Wk4bWxCwPNV9k64PTJMBl3Qy0Y2AY3yVL56l/7rbxK8AVxDHwFcuPg3wlOngdPIwWUjIqJBMjZRmfVT3hg4ZflYYzuu/NNWHDnehuRYE244Mxc3LchDps2C6uZOfO+5L7DnmL3bOUoAlGWzQBfkkEWrwD4v2miAmP67/ar1MI2Cl42K/Brh1bY4tDlQNDIweCEiGiRZavDS4Mu8uD0y7nitEPVtTkxNj8cHd5yNn180FfctnYINd56NsyYmw+HyYNXLO9HudGnnHfMGQJkJlqCvr40H6OiCLId3t4+aSbFFD5x5AXyZGlEq7YHZrdKGtj6OpEjE4IWIaJBomZcGX+bl34UV2FHaiFizAX+6ZhaS/JaAYswGPHnVachKsKCiqQNPfXxYe03LvCREB319NbBwujzo7PKc1PfSnX/NS3/UzEyj4GWjhrbA4Ki4jsHLSMLghYhokGR7syRlDe3weGQ4XR787sODAIBbFo1HdmLPQMRqMeIXF00FADz/SbHWWr+0XvlhnBVC5iXGpIfeu8QU7qUjrUHdQDUv3tdF17yowdHktDgAQGl9e3+HU4QRFryUlJTg+uuvR25uLiwWC8aPH48HH3wQTmf/v2FlWcaaNWuQkZEBi8WChQsXYt++faJuk4ho0IxNjEaUUYeOLjeK69vw2vYylDd0YEycGT+Yn9vneedPTcXcvEQ43R48sVEJdr7xFqROSY8L+vqSJPmKdsO8XVobyjjAhGvfspG44EVpmKe8/8yxNgBAST0zLyOJsODlwIED8Hg8+NOf/oR9+/bhd7/7HZ599lncf//9/Z7329/+Fo8//jiefPJJbN++HWlpaTj//PPR0sJGQ0QU2Qx6HU7JsAIAthypxx/+qywD3XbOBFhMvfdGAZSg494lkwEAb+w6hq/Km7RdSVPTrSHdg1a0G+aakwatYLf/zItN8HwlAOjocsPhbZg3I8sGIHCpjiKfsOBlyZIlWLduHRYvXoy8vDxcfPHFuPvuu/Hmm2/2eY4sy3jiiSfwwAMP4PLLL0dBQQFeeukltLe349VXXxV1q0REg2aOdzjh//xrL+paHRiXFI0Vs8cOeN7MsQm44JRUeGTgkqc+h9sjIzvRgtQge7yo/It2w6m3uUa9Xl/wfCUgsGHeJO+ykX+RNEW+Qa15sdvtSExM7PP14uJiVFdXY/HixdpzZrMZCxYswJYtW3o9x+FwoLm5OeBBRDRcXTYzM+DX9y6ZDKM+uL+Kf3rBJPjvil5ySlq/DeF6o2U+whw8aAW7A2ZevPOVBGZe/Jew1CLp6uZOdHa5hV2TBtegBS9HjhzBH//4R6xatarPY6qrlRbOqampAc+npqZqr3W3du1aWK1W7ZGdnR2+myYiCrOJqXH4zWUFmJwWhwcunIILp6UHfe6ElDjceV4+ACDTZsGqBeNDvr6ILruyLGsBg22Amhf/XjPh3q6t8s8CJcaYEONdkqvgNOsRI+TgZc2aNZAkqd/Hjh07As6prKzEkiVLcMUVV+CGG24Y8Brd/yUhy3Kf/7q47777YLfbtUd5eXmo3xIR0aD6/pxxeP+Os3Hj2Xkhn3vruROx7YFz8d+fLAjYVh0sdbt0OAt225xuON39D2XUru8NnkRs11b5Z4EkSdJ2cZU1tOOLo/VY9odP8cqXpUKuTYMj5PEAq1evxooVK/o9JicnR/u6srISixYtwrx58/Dcc8/1e15amjJ7orq6Gunpvn+N1NbW9sjGqMxmM8zm0P8AExFFqpS4qBM+V0TmRd2WbO5nKKMq2qSHUS+hyy2jqcMJiyn4rd7BUmte1G3Z2YnROFDdgvKGdvzls2KU1LdjzVv7cMmpmYg1c0pOJAr5/1pycjKSk5ODOraiogKLFi3CrFmzsG7dOuh0/Sd6cnNzkZaWho0bN2LmzJkAAKfTic2bN+ORRx4J9VaJiKgbq4D5Rv7LNAPV4EiSBKvFiLpWJ+wdXUi3hj940UYVeLNMat3Lxm9qUOLt99LllrG3wo65eUlhvz6JJ6zmpbKyEgsXLkR2djYeffRRHD9+HNXV1T1qVyZPnoz169cDUH5T33HHHXjooYewfv167N27FytXrkR0dDSuuuoqUbdKRDRq2ATMN6pvVYKFpNj+l4xUIgIofw3dGuapjeo+PVQXcJz//COKLMLyZRs2bMDhw4dx+PBhZGVlBbzmX6RVVFQEu903cOyee+5BR0cHbrnlFjQ2NmLOnDnYsGED4uKCb8RERES9E7FsVNfqAICga3BEBy/ahGtvoDYtK7AXTlKMCfVtThysYfASqYRlXlauXAlZlnt9+JNlGStXrtR+LUkS1qxZg6qqKnR2dmLz5s0oKCgQdZtERKOKTUCflTpv5iU5yMyLWjTcLGi7dGO3hnkTU+KQbvXVCd20QCmUruTuo4jF2UZERKOI1dtnJbzLRkrmJTnIzIuoEQUqrWDXGyTpdRJ+vmwqshIsWLN8KvJTlUx+dbNDyPVJPJZZExGNIuqSTXNnF9weWRvUeDLq20LLvMQLXzbq2TBv2fR0LJuu7GI9UK00M622M/MSqZh5ISIaRdTgRZaBls7wBA9azUtMkJkXAUXDKv+GeX1NuE6PV3Y4NbZ3setuhGLwQkQ0ipgMOq23iZoxOVl1Ie42sgmarwQA7X4N8/qacB1vMcCoVzJODWH6DPqz5Ugd/vzpUThcDJTChcELEdEok+YtXq22d4bl/Y63hFbzImqyNeALRvprmCdJklYPIzp46XC6ccNLO/Drd/bjL5+VCL3WaMKaFyKiUSbdGoXDta197rY5crwVf9p8BDtKGuGWZUzPsuH6M3Nxaratx7GdXW5t2SjTFlzDOZuAomFV99EAfUmINqG2xSF0ujWgZF3anUrG5ZODx3HzwtDnUVFPDF6IiEaZDG9X28qmnpmXt7+qxF3/KESX29fWorS+HW9/VYl7l0zu8cNXDYCiTfoBhzKq1MyLiN1G3Xca9SUhRrkHtaGdKHsrmrWvC8ubwlYkPdoxeCEiGmXSbcqyUVW33TZbjtTh9td2wyMDZ+ePwQ+/lQOTXod/7jyG9bsr8Mj7B5AQbcSK2WO1c441Ku+RabMMOBpAJbJJnfqeAw2IVF9vFLxsVNrQpn3d0eVGdXNn0Bkq6huDFyKiUSbD+8Oz0q/mpdXhwp2vF8IjA5ecmoHHv3uqliGYPyEZOUkx+N2HB/GLt/Zhbl4ScpJjAAAV3sxLVkLwP5DVgt2WTlfYMxFq5mWgLJBtkGpeyryzlFSldW0MXsKABbtERKOMGmiU1vuyAi98WoyaZgfGJkZj7eXTegQUt54zAWdOSIbT5cGv39mvPV+hZl5CCF7UPi9A+Lvs9tbjpTfq0MYmwctGanCn3k9Jt2CGTgyDFyKiUUbtMFvW0I4OpxsNbU48/+lRAMBPL5iEaFPPpLxOJ2HNxVNh0En4cH8NvjhaDwA4VKvMB8pJign6+ka9b7t2uLdLB1/z4s28CC7YVe/ntLE2AIHLSHTiGLwQEY0yybFmJMWYIMtAUU0Lnv74MFodLpySEY9l09L7PG9CShxWzM4GADz83gHIsoxvqpSC1Knp8SHdg4gBkUDwmRe1B4zImpcOpxsOl9JzZkaWDQBQWsfMSzgweCEiGoXUbc/rdx3DX78oBaBkXXQD1J/cdu5EWIx6FJY34eUvy1DeoCyLTDnB4CXcyzYDdddViezyq92L93sz6CTt8ylrYPASDgxeiIhGobPzxwAAXtpaCqfLgzm5iVjgfa4/KXFRuOGsXADA//xrLwBgepZ1wGChO1HBg5Z5GWDZyCp4OKT/vSTEmDAuKRoAUN7QDlmW+zuNgsDghYhoFLr01EztB7hJr8Mvlk8Neqvzj87OC2i9f/GMjJCvLyp4CXa3kbZsJbDmRcsCRRuRlaAELy0Ol9Bsz2jB4IWIaBSyRhvx1x/Oxg1n5uK1m+bilAxr0OfGRRnx1PdPw9T0eFxyagaunZcT+vUF9HqRZTnomhert8tvi8MFj0dMJkS9F1u0CRaTHilxyvgEdemoqd0p7NojHfu8EBGNUjOybZjRS8v/YMwfn4x3bz/rhK9tFTAioNXh0joDD7TbKHC6tkvr+htOaj2PmqUamxiN2hYHyhrasbusCWve3oeLpmfgj9+bGfZrj3TMvBAR0aATkXlR38ti1MNi6n0oo8rkN7hRVN1LY7u6bKQEUmMTlaWjkro2/P6/hyDLyjiGvmZMUd8YvBAR0aDz1byEL3CobwtuyUglaru2yr9gFwDGeot239hVEdDZd0+FXcj1RzIGL0RENOhsAgKHuhZlunVybHDBi+jt0o1tgctGai+c4rrARnWHalqEXH8kY/BCRESDTsSyUX2bErwkxZqDOj5eeOZFeV91jtKp3eqL1K67h2pbhVx/JGPwQkREg04tkA3neIC6ViXTkRTispGI6dbK+waOKkiJj8Ls3ETvc0ZcPXccAKDKb0AmBYe7jYiIaNCp2Qh7RxdkWQ66x0x/6tXgJcjMi/iaF+V9E2N8O5nWXj4NL35egu+eno2OLjcAoKaZwUuoGLwQEdGgUwMHp8uDzi7PgLuDgqEuGwVd8+K9h3BPtlb593lRjR8Ti/93aQEA31Tvantn2AK40YLLRkRENOhiTHoYvHOUwrVV2Zd5GfrdRl1uD1o6XQD67jmTGh8FAHC4POy6GyIGL0RENOgkSdIyEg1hmuxc1+ot2I0JctkoWlzNi/qekuQLkrqLMuoRZ1YWQOoFTrdWPbPpCK7+85eoGAF9ZRi8EBHRkEi3KpmHqqa+az48HhmVTR0oq2+Hy+3p9/3Uwtc07/sORGTmRS3WtVqM0PczqVvtARPu6drd1bc68Mj7B/DZ4To8/fFhodcaDKx5ISKiIZFhi8KeCjsq7T0zAbIs4/Xt5fjjR4e1TEFijAkr5+fg5oXjYdQH/tu71W/gYYbNEtT1RQYv3bvr9iUh2oiyBqChTeyy0aeH6rSvd5U1Cb3WYGDwQkREQ0INMrovY8iyjP/59168/EUZAMColyBJEhranHh840F8WVyPF647A1FGX5FvRaPyHlaLEbHm4H60iQ1egpturWZeGgVnXo4c9/WSKapuRrvThWhT5IYAXDYiIqIhkekNXiq7LRu9tKUEL39RBp0E/GzpZOxZcwG++eUFeOLKUxFj0uPzw/V4YP3egHPU+UCZQWZdAMHBS1tgj5e+qK83Cq55Kalv1772yL7J1pGKwQsREQ2JDC148WVeGtuceGzjQQDAA8umYtWC8Ygy6mHQ63DpzEw8f+3p0EnAG7uO4eMDtdp5x7zvEeySEeALXlodrgHraUIV/LKRmnkRu2ykbsv2/ZrBCxERUciyE3xTllVPfXwYLZ0uTE6Lw8r5OT3OmT8hGdefmQsA+M27++H2yACAcm8mISsh9OAFAJq925rDxdddd4BlI23Hk9jMizr3aZx3OGQZgxciIqLQTUiJhSQp24SPtzhQ3tCOv24tBQDcd+GUPnfp3HruRFgtRhyubcW/CysAAAeqleGGE1Njg76+Qa/T6mPCHTx0nyjdF1tMeLeL930/SmZnRpYNAFDa0NbP0cMfgxciIhoSFpMeuUkxAIC9lXY8tqEITrcHZ05IxtkTk/s8Lz7KiJsW5AEAfv/fQ+hye7C/qhkAMMU7uTlYoupefEMZ+8+8JEaLL9jt7HJrowhmeIdDctmIiIjoBM0alwAAePKjw/hXYSUApUh3oFb5183LQVKMCaX17fjfD4pwvMUBk16HyWlxIV1fWPDizaQkDlDzogY3IjvsqoGRQSdhqje4K2fBLhER0Yk5d0oKAGBnaSMA4PLTMlGQaR3wvBizATcvHA8AeO6TowCA2bmJIW//FZd56TnXaDCvH3AvbWoWyKTVvBxr7NDqhSIRgxciIhoy509NwzRvsJKdaMEvLpoa9LlXzx2HfL8al+t6KfAdiKjgQR0PkBDT/7KRen0RIwpUaiCVGGNEanwUTHodXB4ZVb00B4wUkduhhoiIIp5eJ+HvP5qLHSUNmDUuAXFR/f+w9xdl1OOVG+biL58XIzc5BudPTQ35+lrwEsbgweOR0dQR3FZpdb6Sw+VBZ5c7oPFeuPhngfQ6CVkJFhyta0NZfTuSY834YF81ZucmIt0a/E6toSYs81JSUoLrr78eubm5sFgsGD9+PB588EE4nf0XJa1cuRKSJAU85s6dK+o2iYhoiMWaDVg4KSWkwEU1Js6Me5dMxndPzz6ha4uoOWnpdGlLMgMV7MaaDFA3VTULWjry9ZxR7mWsul26oR1r3tqH218rxNV//hKeCFpGEpZ5OXDgADweD/70pz9hwoQJ2Lt3L2688Ua0tbXh0Ucf7ffcJUuWYN26ddqvTabgxpsTERGFIl7AspGa6Ygx6WE29J9J0ekkxFuMaGrvQlNHF1LigxsqGdL9qMXD3m3ZYxOV4OVQbSv+5d1qfuR4G76pag6q3mg4EBa8LFmyBEuWLNF+nZeXh6KiIjzzzDMDBi9msxlpaWmibo2IiAiAX81JGIOX+jalIVxSrDmo423e4EVU0W734uEc7/b0F7eUBBTtHqhuiZjgZVALdu12OxITEwc8btOmTUhJSUF+fj5uvPFG1NbW9nmsw+FAc3NzwIOIiCgYIgp261qVYCEpNrhVAxF1N/6aui0bTctSApTuu40O1bYIub4Igxa8HDlyBH/84x+xatWqfo9bunQpXnnlFXz00Ud47LHHsH37dpxzzjlwOBy9Hr927VpYrVbtkZ19YuueREQ0+qg1KeGsN6lXg5cBuuuq4gVkf/w1dBsSWZBhhX/z4ktPzQAAHKmNnK67IQcva9as6VFQ2/2xY8eOgHMqKyuxZMkSXHHFFbjhhhv6ff8rr7wSy5YtQ0FBAZYvX4733nsPBw8exDvvvNPr8ffddx/sdrv2KC8vD/VbIiKiUUrEVuX6Vu+yUUyQy0beoELUspFvzpJyHYtJj4umKwHLKRnxWOb9uqa5s/c3GIZCrnlZvXo1VqxY0e8xOTk52teVlZVYtGgR5s2bh+eeey7kG0xPT8e4ceNw6NChXl83m80wm4P7DUJERORPxLJRfVuoy0aGsN+Dv8Zees789jvTsaQgDWdOTNaGNFaP5OAlOTkZycl9z5zwV1FRgUWLFmHWrFlYt24ddLrQV6nq6+tRXl6O9PT0kM8lIiLqj7oDp6PLjXanK+QOvb3xBS/B/cPaV/MiZr5RY7dlI0DpkXPhNOXnakq8cp91rQ643B4Y9MO/f62wO6ysrMTChQuRnZ2NRx99FMePH0d1dTWqq6sDjps8eTLWr18PAGhtbcXdd9+NrVu3oqSkBJs2bcLy5cuRnJyMyy67TNStEhHRKBUXZUSMSdnOXG0PT+ZBXTZKDjLzYrOIWzbqcnvQ4nAB6LthXlKMGXqdBFkGjrf2Xl863AjbKr1hwwYcPnwYhw8fRlZWVsBrsuyrcC4qKoLdbgcA6PV67NmzB3/961/R1NSE9PR0LFq0CK+//jri4kIbtkVERBSM1PgoHK1rQ02zA3ljYgc+YQC1LaHVvIicb6TW8kiSrzC4O71OQmKMCcdbHKhvdUZEp11hwcvKlSuxcuXKAY/zD2QsFgs++OADUbdERETUgy946TvzcuR4K3aUNKDLLWNaphXTs6y9Tr6WZRmVTcrMoAxbcA3nRO420nq8WIzQ6/qe1J0QbcTxFofQGUvhxNlGREQ0qqVZlSCjt+DF3tGFB9bvwX++rgp4fta4BDz+3RkY52345n98u9MNAMiwBZfBEDGiQNVbvUvv96C83iio7ibchn9VDhERkUCp3pb83XfbtDtduPaFL/Gfr6ugk4B5eUk4Z3IKoow67CxtxLef2art1FFVeLMuybGmoIcsqstGImYbqTuNBpqxpDawi5TghZkXIiIa1dK9mRd1uUe19t0D+OqYHQnRRqz7wWycmm0DoAQo17+4HQeqW3DTyzvx1upvwejdoVPRqC4ZBV834t9rRpblXpejTpQajCQO0DBPfb2xLTKWjZh5ISKiUS1vjLL0c7i2VXvuyPFWvLqtDADw5FWnaYELAGTaLHjph7NhizZif1Uznv/0qPaaVu8SQtGrGry4PLK25BQu3eca9YXLRkRERBFkYoqym7Wkvh0OlxI8/Pb9A3B7ZJw3JQXfmtCzt1lqfBT+Z9lUAMAzm45oc4mO1ikt9sclRQd9/WiTHka9km0Jd91L97lGfVFfb2LwQkRENPylxpsRZzbA7ZFRXNeG7SUN+GBfDXQS8LOlk/s877KZmZiUGoeWTpeWfTlQrQw3nJQWfHsPSZKEjCkA/OYaDbBs5Mu8cNmIiIho2JMkCRNTlf4ueyua8dC7+wEAV54xFhNS+g5CdDoJd56fDwBY93kxals6sb+qGUBowQvg2y4d/sxLcLuN1NeZeSEiIooQc/OSAAB3//Mr7C5rgsWox53nTRzwvAtOScW0TCvanG7c8vIutHS6EB9lwKTU0IIXm6DgpTHUZSNB85XCjcELERGNeksLAufn3XruBKTED9xkTpIk/GSxkn3ZUdoIADg7f0zI84F8XXbDm/loDDLzIrLLrwgMXoiIaNSblmXFD7+VC50EXDQ9HT86Ky/ocxfkj8G3T1PG4Jj0Ovx40YSQry8qeGgMsubF6tcoz+OR+z12OGCfFyIiIgC/WD4VP1s6GSZDaP+ulyQJj14xHd89PQsp8VHITY4Z+KRu1ILZcAYvHo+svd9ATerU4EmWgRaHS/v1cMXghYiIyCvUwEUlSRLmeOtmTkS8gN1GzZ1dUJMo6uTqvpgNekQZdejs8sDe3jXsgxcuGxEREQ0xEctGda3KklF8lCGooEwNcCKh7oXBCxER0RATsdtI7fGSFGsO6vhIKtpl8EJERDTERAQO9a0OAEDSAMW63e+hKcw7nkRg8EJERDTE/Hf7hEtdW3BDGUXegygMXoiIiIaYkGWj1hNbNgr3iAIRGLwQERENMf9lo3D1WalvC23ZSA2gmpl5ISIiooGofV5k2dcV92TVa5mX0GpeuGxEREREAzIZdFqGpLq5MyzvWect2A215oXLRkRERBSUNKsyS6kmTMGLGgSlWy1BHR9JmRd22CUiIhoG0uKjsK+yGdV2R6+vtztd+L+dx/Dl0QZ0uT0oyLRixRnZvQ6Q9HhkVDWpwcvAAyYBBi9EREQUolRvkNHbstH+qmZc/+J2VNp9r234pgbPbj6C//3ODCybHjgVu77NCafbA0nyZXQGwuCFiIiIQpLmzaDU2AODl/KGdqx47gvYO7qQlWDB9+eMQ5RRh38XVqKwvAmr/74LJsPpOH9qqnZOZVMHACA1LgpGfXAVIiKGQ4rCmhciIqJhQF3eqfAGHoCy/HPba7th7+jC9Cwr3rntLNy8cDx+8K1cvHHzfHz39CzIMvCTfxQG1MqowUu6LbisC+DLvLQ6XOhye8LxLQnD4IWIiGgYGJ8SCwA4VNuiPffOnirsLmtCrNmAZ66eFTDtWa+T8OtLp2F6lhXNnS789v0i7bVjjUrwkmELrlgXUAY4qoZ7rxcGL0RERMPARG/wUtPsgL29C11uDx7feBAAcONZecjsJRAxGXT41SUFAIA3dh3Dvko7AF8ANGFMbNDXN+h1iDMrAcxwXzpi8EJERDQMxEUZtQDlYG0L/m/nMRTXtSEpxoTrz8rt87xTs224eEYGAODRD5TsS1FNKwAgPzUupHuI14YzMnghIiKiIExKU4KNrUfq8cSHStbllkUTEGvuf3/NnefnQ6+T8HHRcXx66Dj2VzYDAKakhxa82CJkOCODFyIiomHirInJAIDHNx5ETbMDmTYLvj9n7IDn5SbH4LunZwMArnlhG5xuD9KtUchNjgnp+tp26WHeZZfBCxER0TBx4bR0WIx67df/c9FURPn9uj+3nTsBJoPvx/qF09IhSVJI14+UXi8MXoiIiIaJ1Pgo/H7FqVg0aQzWXj4NSwrSgj433WrB2sumwWTQIW9MDG5eOD7k60fKshGb1BEREQ0ji09Jw+JTgg9a/H17VhaWz8iAQSdBpwst6wL4FewO82UjBi9EREQjiP/SUai4bEREREQRxWZRRwQ4h/hO+sfghYiIiAAw80JEREQRJlIKdhm8EBEREQBf5mW4F+wKDV4uvvhijB07FlFRUUhPT8c111yDysrKfs+RZRlr1qxBRkYGLBYLFi5ciH379om8TSIiIgKXjQAAixYtwj/+8Q8UFRXhjTfewJEjR/Cd73yn33N++9vf4vHHH8eTTz6J7du3Iy0tDeeffz5aWlr6PY+IiIhOjtW7bORwedDZ5R7iu+mbJMuyPFgXe+utt3DppZfC4XDAaDT2eF2WZWRkZOCOO+7AvffeCwBwOBxITU3FI488gptuumnAazQ3N8NqtcJutyM+Pj7s3wMREdFIJcsy8n/+HrrcMj67dxGyEqIH7dqh/PwetJqXhoYGvPLKK5g/f36vgQsAFBcXo7q6GosXL9aeM5vNWLBgAbZs2dLrOQ6HA83NzQEPIiIiCp0kSUiJiwIA1DR3DvHd9E148HLvvfciJiYGSUlJKCsrw7///e8+j62urgYApKamBjyfmpqqvdbd2rVrYbVatUd2dnb4bp6IiGiUSbcqwUu13THEd9K3kIOXNWvWQJKkfh87duzQjv/pT3+K3bt3Y8OGDdDr9bj22msx0EpV90FSsiz3OVzqvvvug91u1x7l5eWhfktERETkleYNXqrsHb2+vvVIPTYV1Q7mLfUQ8niA1atXY8WKFf0ek5OTo32dnJyM5ORk5OfnY8qUKcjOzsYXX3yBefPm9TgvLU2Z5VBdXY309HTt+dra2h7ZGJXZbIbZbA712yAiIqJepMWrmZeey0b/3FGOe9/4GnFRRrx3+1nIsFkG+/YAnEDwogYjJ0LNuDgcvaeicnNzkZaWho0bN2LmzJkAAKfTic2bN+ORRx45oWsSERFR8NTMS3W3mpdPDx3HPW98DVkGzp2cojW0GwrCal62bduGJ598EoWFhSgtLcXHH3+Mq666CuPHjw/IukyePBnr168HoCwX3XHHHXjooYewfv167N27FytXrkR0dDSuuuoqUbdKREREXmo2pbzRt2zU0tmFu//5FWQZ+O7pWXjsuzMQbRq62c7CrmyxWPDmm2/iwQcfRFtbG9LT07FkyRK89tprAcs8RUVFsNvt2q/vuecedHR04JZbbkFjYyPmzJmDDRs2IC4uTtStEhERkdfElFgAwOGaFng8MnQ6CS98VoyaZgdykqLxy4sL+qxDHSyD2udlMLDPCxER0Ynrcntwyi8+gNPtwaf3LEKs2YCzfvsxWh0uPHXVaVg2PX3gNzkBofz8HrqcDxEREQ07Rr0OeWNicKC6BUXVLdhW0oBWhwtT0+OxtCBtqG8PAAczEhERUTenZFgBAP8qrMCLW0oAAD+9YBJ0uqFdLlIxeCEiIqIA50xOAQD85+sqOF0ezM1LxMJJY4b4rnwYvBAREVGAc6ekICdJmWsUZdThweWnDHmRrj/WvBAREVGAKKMer9w4F+/tqcLZ+WOQnzq8dvwyeCEiIqIeMm0W3HBW3lDfRq+4bEREREQRhcELERERRRQGL0RERBRRGLwQERFRRGHwQkRERBGFwQsRERFFFAYvREREFFEYvBAREVFEYfBCREREEYXBCxEREUUUBi9EREQUURi8EBERUURh8EJEREQRZcRNlZZlGQDQ3Nw8xHdCREREwVJ/bqs/x/sz4oKXlpYWAEB2dvYQ3wkRERGFqqWlBVartd9jJDmYECeCeDweVFZWIi4uDpIkhfW9m5ubkZ2djfLycsTHx4f1vcmHn/Pg4Oc8ePhZDw5+zoND1OcsyzJaWlqQkZEBna7/qpYRl3nR6XTIysoSeo34+Hj+wRgE/JwHBz/nwcPPenDwcx4cIj7ngTIuKhbsEhERUURh8EJEREQRhcFLCMxmMx588EGYzeahvpURjZ/z4ODnPHj4WQ8Ofs6DYzh8ziOuYJeIiIhGNmZeiIiIKKIweCEiIqKIwuCFiIiIIgqDFyIiIoooDF6C9PTTTyM3NxdRUVGYNWsWPv3006G+pYi2du1anHHGGYiLi0NKSgouvfRSFBUVBRwjyzLWrFmDjIwMWCwWLFy4EPv27RuiOx4Z1q5dC0mScMcdd2jP8XMOn4qKClx99dVISkpCdHQ0Tj31VOzcuVN7nZ/1yXO5XPj5z3+O3NxcWCwW5OXl4Ve/+hU8Ho92DD/n0H3yySdYvnw5MjIyIEkS/vWvfwW8Hsxn6nA4cOuttyI5ORkxMTG4+OKLcezYMTE3LNOAXnvtNdloNMrPP/+8/M0338i33367HBMTI5eWlg71rUWsCy64QF63bp28d+9eubCwUF62bJk8duxYubW1VTvm4YcfluPi4uQ33nhD3rNnj3zllVfK6enpcnNz8xDeeeTatm2bnJOTI0+fPl2+/fbbtef5OYdHQ0ODPG7cOHnlypXyl19+KRcXF8sffvihfPjwYe0YftYn79e//rWclJQk/+c//5GLi4vlf/7zn3JsbKz8xBNPaMfwcw7du+++Kz/wwAPyG2+8IQOQ169fH/B6MJ/pqlWr5MzMTHnjxo3yrl275EWLFskzZsyQXS5X2O+XwUsQZs+eLa9atSrgucmTJ8s/+9nPhuiORp7a2loZgLx582ZZlmXZ4/HIaWlp8sMPP6wd09nZKVutVvnZZ58dqtuMWC0tLfLEiRPljRs3ygsWLNCCF37O4XPvvffKZ555Zp+v87MOj2XLlsk//OEPA567/PLL5auvvlqWZX7O4dA9eAnmM21qapKNRqP82muvacdUVFTIOp1Ofv/998N+j1w2GoDT6cTOnTuxePHigOcXL16MLVu2DNFdjTx2ux0AkJiYCAAoLi5GdXV1wOduNpuxYMECfu4n4Mc//jGWLVuG8847L+B5fs7h89Zbb+H000/HFVdcgZSUFMycORPPP/+89jo/6/A488wz8d///hcHDx4EAHz11Vf47LPPcOGFFwLg5yxCMJ/pzp070dXVFXBMRkYGCgoKhHzuI24wY7jV1dXB7XYjNTU14PnU1FRUV1cP0V2NLLIs46677sKZZ56JgoICANA+294+99LS0kG/x0j22muvYdeuXdi+fXuP1/g5h8/Ro0fxzDPP4K677sL999+Pbdu24bbbboPZbMa1117LzzpM7r33XtjtdkyePBl6vR5utxu/+c1v8L3vfQ8Af0+LEMxnWl1dDZPJhISEhB7HiPhZyeAlSJIkBfxaluUez9GJWb16Nb7++mt89tlnPV7j535yysvLcfvtt2PDhg2Iiorq8zh+zifP4/Hg9NNPx0MPPQQAmDlzJvbt24dnnnkG1157rXYcP+uT8/rrr+Pll1/Gq6++ilNOOQWFhYW44447kJGRgeuuu047jp9z+J3IZyrqc+ey0QCSk5Oh1+t7RI61tbU9olAK3a233oq33noLH3/8MbKysrTn09LSAICf+0nauXMnamtrMWvWLBgMBhgMBmzevBl/+MMfYDAYtM+Sn/PJS09Px9SpUwOemzJlCsrKygDw93S4/PSnP8XPfvYzrFixAtOmTcM111yDO++8E2vXrgXAz1mEYD7TtLQ0OJ1ONDY29nlMODF4GYDJZMKsWbOwcePGgOc3btyI+fPnD9FdRT5ZlrF69Wq8+eab+Oijj5Cbmxvwem5uLtLS0gI+d6fTic2bN/NzD8G5556LPXv2oLCwUHucfvrp+P73v4/CwkLk5eXxcw6Tb33rWz22+x88eBDjxo0DwN/T4dLe3g6dLvBHl16v17ZK83MOv2A+01mzZsFoNAYcU1VVhb1794r53MNeAjwCqVulX3jhBfmbb76R77jjDjkmJkYuKSkZ6luLWDfffLNstVrlTZs2yVVVVdqjvb1dO+bhhx+WrVar/Oabb8p79uyRv/e973G7Yxj47zaSZX7O4bJt2zbZYDDIv/nNb+RDhw7Jr7zyihwdHS2//PLL2jH8rE/eddddJ2dmZmpbpd988005OTlZvueee7Rj+DmHrqWlRd69e7e8e/duGYD8+OOPy7t379ZaggTzma5atUrOysqSP/zwQ3nXrl3yOeecw63SQ+2pp56Sx40bJ5tMJvm0007TtvTSiQHQ62PdunXaMR6PR37wwQfltLQ02Ww2y2effba8Z8+eobvpEaJ78MLPOXzefvttuaCgQDabzfLkyZPl5557LuB1ftYnr7m5Wb799tvlsWPHylFRUXJeXp78wAMPyA6HQzuGn3PoPv74417/Tr7uuutkWQ7uM+3o6JBXr14tJyYmyhaLRb7ooovksrIyIfcrybIshz+fQ0RERCQGa16IiIgoojB4ISIioojC4IWIiIgiCoMXIiIiiigMXoiIiCiiMHghIiKiiMLghYiIiCIKgxciIiKKKAxeiIiIKKIweCEiIqKIwuCFiIiIIgqDFyIiIooo/x/rI/oxzpCWngAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"E0=En2[0,0]\n",
"plt.plot(t,En2[0]-E0)\n",
"print(En2[0,-1]-E0)"
]
},
{
"cell_type": "markdown",
"id": "cae7892b",
"metadata": {},
"source": [
"Let's try `scipy` recomended solver `scipy.solve_ivp`, which is also RK4, but with variable step and more powerful algorithm RK45, oe even eith order RK (`DOP853`)."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "12ed90ea",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Help on function solve_ivp in module scipy.integrate._ivp.ivp:\n",
"\n",
"solve_ivp(fun, t_span, y0, method='RK45', t_eval=None, dense_output=False, events=None, vectorized=False, args=None, **options)\n",
" Solve an initial value problem for a system of ODEs.\n",
" \n",
" This function numerically integrates a system of ordinary differential\n",
" equations given an initial value::\n",
" \n",
" dy / dt = f(t, y)\n",
" y(t0) = y0\n",
" \n",
" Here t is a 1-D independent variable (time), y(t) is an\n",
" N-D vector-valued function (state), and an N-D\n",
" vector-valued function f(t, y) determines the differential equations.\n",
" The goal is to find y(t) approximately satisfying the differential\n",
" equations, given an initial value y(t0)=y0.\n",
" \n",
" Some of the solvers support integration in the complex domain, but note\n",
" that for stiff ODE solvers, the right-hand side must be\n",
" complex-differentiable (satisfy Cauchy-Riemann equations [11]_).\n",
" To solve a problem in the complex domain, pass y0 with a complex data type.\n",
" Another option always available is to rewrite your problem for real and\n",
" imaginary parts separately.\n",
" \n",
" Parameters\n",
" ----------\n",
" fun : callable\n",
" Right-hand side of the system. The calling signature is ``fun(t, y)``.\n",
" Here `t` is a scalar, and there are two options for the ndarray `y`:\n",
" It can either have shape (n,); then `fun` must return array_like with\n",
" shape (n,). Alternatively, it can have shape (n, k); then `fun`\n",
" must return an array_like with shape (n, k), i.e., each column\n",
" corresponds to a single column in `y`. The choice between the two\n",
" options is determined by `vectorized` argument (see below). The\n",
" vectorized implementation allows a faster approximation of the Jacobian\n",
" by finite differences (required for stiff solvers).\n",
" t_span : 2-tuple of floats\n",
" Interval of integration (t0, tf). The solver starts with t=t0 and\n",
" integrates until it reaches t=tf.\n",
" y0 : array_like, shape (n,)\n",
" Initial state. For problems in the complex domain, pass `y0` with a\n",
" complex data type (even if the initial value is purely real).\n",
" method : string or `OdeSolver`, optional\n",
" Integration method to use:\n",
" \n",
" * 'RK45' (default): Explicit Runge-Kutta method of order 5(4) [1]_.\n",
" The error is controlled assuming accuracy of the fourth-order\n",
" method, but steps are taken using the fifth-order accurate\n",
" formula (local extrapolation is done). A quartic interpolation\n",
" polynomial is used for the dense output [2]_. Can be applied in\n",
" the complex domain.\n",
" * 'RK23': Explicit Runge-Kutta method of order 3(2) [3]_. The error\n",
" is controlled assuming accuracy of the second-order method, but\n",
" steps are taken using the third-order accurate formula (local\n",
" extrapolation is done). A cubic Hermite polynomial is used for the\n",
" dense output. Can be applied in the complex domain.\n",
" * 'DOP853': Explicit Runge-Kutta method of order 8 [13]_.\n",
" Python implementation of the \"DOP853\" algorithm originally\n",
" written in Fortran [14]_. A 7-th order interpolation polynomial\n",
" accurate to 7-th order is used for the dense output.\n",
" Can be applied in the complex domain.\n",
" * 'Radau': Implicit Runge-Kutta method of the Radau IIA family of\n",
" order 5 [4]_. The error is controlled with a third-order accurate\n",
" embedded formula. A cubic polynomial which satisfies the\n",
" collocation conditions is used for the dense output.\n",
" * 'BDF': Implicit multi-step variable-order (1 to 5) method based\n",
" on a backward differentiation formula for the derivative\n",
" approximation [5]_. The implementation follows the one described\n",
" in [6]_. A quasi-constant step scheme is used and accuracy is\n",
" enhanced using the NDF modification. Can be applied in the\n",
" complex domain.\n",
" * 'LSODA': Adams/BDF method with automatic stiffness detection and\n",
" switching [7]_, [8]_. This is a wrapper of the Fortran solver\n",
" from ODEPACK.\n",
" \n",
" Explicit Runge-Kutta methods ('RK23', 'RK45', 'DOP853') should be used\n",
" for non-stiff problems and implicit methods ('Radau', 'BDF') for\n",
" stiff problems [9]_. Among Runge-Kutta methods, 'DOP853' is recommended\n",
" for solving with high precision (low values of `rtol` and `atol`).\n",
" \n",
" If not sure, first try to run 'RK45'. If it makes unusually many\n",
" iterations, diverges, or fails, your problem is likely to be stiff and\n",
" you should use 'Radau' or 'BDF'. 'LSODA' can also be a good universal\n",
" choice, but it might be somewhat less convenient to work with as it\n",
" wraps old Fortran code.\n",
" \n",
" You can also pass an arbitrary class derived from `OdeSolver` which\n",
" implements the solver.\n",
" t_eval : array_like or None, optional\n",
" Times at which to store the computed solution, must be sorted and lie\n",
" within `t_span`. If None (default), use points selected by the solver.\n",
" dense_output : bool, optional\n",
" Whether to compute a continuous solution. Default is False.\n",
" events : callable, or list of callables, optional\n",
" Events to track. If None (default), no events will be tracked.\n",
" Each event occurs at the zeros of a continuous function of time and\n",
" state. Each function must have the signature ``event(t, y)`` and return\n",
" a float. The solver will find an accurate value of `t` at which\n",
" ``event(t, y(t)) = 0`` using a root-finding algorithm. By default, all\n",
" zeros will be found. The solver looks for a sign change over each step,\n",
" so if multiple zero crossings occur within one step, events may be\n",
" missed. Additionally each `event` function might have the following\n",
" attributes:\n",
" \n",
" terminal: bool, optional\n",
" Whether to terminate integration if this event occurs.\n",
" Implicitly False if not assigned.\n",
" direction: float, optional\n",
" Direction of a zero crossing. If `direction` is positive,\n",
" `event` will only trigger when going from negative to positive,\n",
" and vice versa if `direction` is negative. If 0, then either\n",
" direction will trigger event. Implicitly 0 if not assigned.\n",
" \n",
" You can assign attributes like ``event.terminal = True`` to any\n",
" function in Python.\n",
" vectorized : bool, optional\n",
" Whether `fun` is implemented in a vectorized fashion. Default is False.\n",
" args : tuple, optional\n",
" Additional arguments to pass to the user-defined functions. If given,\n",
" the additional arguments are passed to all user-defined functions.\n",
" So if, for example, `fun` has the signature ``fun(t, y, a, b, c)``,\n",
" then `jac` (if given) and any event functions must have the same\n",
" signature, and `args` must be a tuple of length 3.\n",
" **options\n",
" Options passed to a chosen solver. All options available for already\n",
" implemented solvers are listed below.\n",
" first_step : float or None, optional\n",
" Initial step size. Default is `None` which means that the algorithm\n",
" should choose.\n",
" max_step : float, optional\n",
" Maximum allowed step size. Default is np.inf, i.e., the step size is not\n",
" bounded and determined solely by the solver.\n",
" rtol, atol : float or array_like, optional\n",
" Relative and absolute tolerances. The solver keeps the local error\n",
" estimates less than ``atol + rtol * abs(y)``. Here `rtol` controls a\n",
" relative accuracy (number of correct digits), while `atol` controls\n",
" absolute accuracy (number of correct decimal places). To achieve the\n",
" desired `rtol`, set `atol` to be smaller than the smallest value that\n",
" can be expected from ``rtol * abs(y)`` so that `rtol` dominates the\n",
" allowable error. If `atol` is larger than ``rtol * abs(y)`` the\n",
" number of correct digits is not guaranteed. Conversely, to achieve the\n",
" desired `atol` set `rtol` such that ``rtol * abs(y)`` is always smaller\n",
" than `atol`. If components of y have different scales, it might be\n",
" beneficial to set different `atol` values for different components by\n",
" passing array_like with shape (n,) for `atol`. Default values are\n",
" 1e-3 for `rtol` and 1e-6 for `atol`.\n",
" jac : array_like, sparse_matrix, callable or None, optional\n",
" Jacobian matrix of the right-hand side of the system with respect\n",
" to y, required by the 'Radau', 'BDF' and 'LSODA' method. The\n",
" Jacobian matrix has shape (n, n) and its element (i, j) is equal to\n",
" ``d f_i / d y_j``. There are three ways to define the Jacobian:\n",
" \n",
" * If array_like or sparse_matrix, the Jacobian is assumed to\n",
" be constant. Not supported by 'LSODA'.\n",
" * If callable, the Jacobian is assumed to depend on both\n",
" t and y; it will be called as ``jac(t, y)``, as necessary.\n",
" For 'Radau' and 'BDF' methods, the return value might be a\n",
" sparse matrix.\n",
" * If None (default), the Jacobian will be approximated by\n",
" finite differences.\n",
" \n",
" It is generally recommended to provide the Jacobian rather than\n",
" relying on a finite-difference approximation.\n",
" jac_sparsity : array_like, sparse matrix or None, optional\n",
" Defines a sparsity structure of the Jacobian matrix for a finite-\n",
" difference approximation. Its shape must be (n, n). This argument\n",
" is ignored if `jac` is not `None`. If the Jacobian has only few\n",
" non-zero elements in *each* row, providing the sparsity structure\n",
" will greatly speed up the computations [10]_. A zero entry means that\n",
" a corresponding element in the Jacobian is always zero. If None\n",
" (default), the Jacobian is assumed to be dense.\n",
" Not supported by 'LSODA', see `lband` and `uband` instead.\n",
" lband, uband : int or None, optional\n",
" Parameters defining the bandwidth of the Jacobian for the 'LSODA'\n",
" method, i.e., ``jac[i, j] != 0 only for i - lband <= j <= i + uband``.\n",
" Default is None. Setting these requires your jac routine to return the\n",
" Jacobian in the packed format: the returned array must have ``n``\n",
" columns and ``uband + lband + 1`` rows in which Jacobian diagonals are\n",
" written. Specifically ``jac_packed[uband + i - j , j] = jac[i, j]``.\n",
" The same format is used in `scipy.linalg.solve_banded` (check for an\n",
" illustration). These parameters can be also used with ``jac=None`` to\n",
" reduce the number of Jacobian elements estimated by finite differences.\n",
" min_step : float, optional\n",
" The minimum allowed step size for 'LSODA' method.\n",
" By default `min_step` is zero.\n",
" \n",
" Returns\n",
" -------\n",
" Bunch object with the following fields defined:\n",
" t : ndarray, shape (n_points,)\n",
" Time points.\n",
" y : ndarray, shape (n, n_points)\n",
" Values of the solution at `t`.\n",
" sol : `OdeSolution` or None\n",
" Found solution as `OdeSolution` instance; None if `dense_output` was\n",
" set to False.\n",
" t_events : list of ndarray or None\n",
" Contains for each event type a list of arrays at which an event of\n",
" that type event was detected. None if `events` was None.\n",
" y_events : list of ndarray or None\n",
" For each value of `t_events`, the corresponding value of the solution.\n",
" None if `events` was None.\n",
" nfev : int\n",
" Number of evaluations of the right-hand side.\n",
" njev : int\n",
" Number of evaluations of the Jacobian.\n",
" nlu : int\n",
" Number of LU decompositions.\n",
" status : int\n",
" Reason for algorithm termination:\n",
" \n",
" * -1: Integration step failed.\n",
" * 0: The solver successfully reached the end of `tspan`.\n",
" * 1: A termination event occurred.\n",
" \n",
" message : string\n",
" Human-readable description of the termination reason.\n",
" success : bool\n",
" True if the solver reached the interval end or a termination event\n",
" occurred (``status >= 0``).\n",
" \n",
" References\n",
" ----------\n",
" .. [1] J. R. Dormand, P. J. Prince, \"A family of embedded Runge-Kutta\n",
" formulae\", Journal of Computational and Applied Mathematics, Vol. 6,\n",
" No. 1, pp. 19-26, 1980.\n",
" .. [2] L. W. Shampine, \"Some Practical Runge-Kutta Formulas\", Mathematics\n",
" of Computation,, Vol. 46, No. 173, pp. 135-150, 1986.\n",
" .. [3] P. Bogacki, L.F. Shampine, \"A 3(2) Pair of Runge-Kutta Formulas\",\n",
" Appl. Math. Lett. Vol. 2, No. 4. pp. 321-325, 1989.\n",
" .. [4] E. Hairer, G. Wanner, \"Solving Ordinary Differential Equations II:\n",
" Stiff and Differential-Algebraic Problems\", Sec. IV.8.\n",
" .. [5] `Backward Differentiation Formula\n",
" `_\n",
" on Wikipedia.\n",
" .. [6] L. F. Shampine, M. W. Reichelt, \"THE MATLAB ODE SUITE\", SIAM J. SCI.\n",
" COMPUTE., Vol. 18, No. 1, pp. 1-22, January 1997.\n",
" .. [7] A. C. Hindmarsh, \"ODEPACK, A Systematized Collection of ODE\n",
" Solvers,\" IMACS Transactions on Scientific Computation, Vol 1.,\n",
" pp. 55-64, 1983.\n",
" .. [8] L. Petzold, \"Automatic selection of methods for solving stiff and\n",
" nonstiff systems of ordinary differential equations\", SIAM Journal\n",
" on Scientific and Statistical Computing, Vol. 4, No. 1, pp. 136-148,\n",
" 1983.\n",
" .. [9] `Stiff equation `_ on\n",
" Wikipedia.\n",
" .. [10] A. Curtis, M. J. D. Powell, and J. Reid, \"On the estimation of\n",
" sparse Jacobian matrices\", Journal of the Institute of Mathematics\n",
" and its Applications, 13, pp. 117-120, 1974.\n",
" .. [11] `Cauchy-Riemann equations\n",
" `_ on\n",
" Wikipedia.\n",
" .. [12] `Lotka-Volterra equations\n",
" `_\n",
" on Wikipedia.\n",
" .. [13] E. Hairer, S. P. Norsett G. Wanner, \"Solving Ordinary Differential\n",
" Equations I: Nonstiff Problems\", Sec. II.\n",
" .. [14] `Page with original Fortran code of DOP853\n",
" `_.\n",
" \n",
" Examples\n",
" --------\n",
" Basic exponential decay showing automatically chosen time points.\n",
" \n",
" >>> from scipy.integrate import solve_ivp\n",
" >>> def exponential_decay(t, y): return -0.5 * y\n",
" >>> sol = solve_ivp(exponential_decay, [0, 10], [2, 4, 8])\n",
" >>> print(sol.t)\n",
" [ 0. 0.11487653 1.26364188 3.06061781 4.81611105 6.57445806\n",
" 8.33328988 10. ]\n",
" >>> print(sol.y)\n",
" [[2. 1.88836035 1.06327177 0.43319312 0.18017253 0.07483045\n",
" 0.03107158 0.01350781]\n",
" [4. 3.7767207 2.12654355 0.86638624 0.36034507 0.14966091\n",
" 0.06214316 0.02701561]\n",
" [8. 7.5534414 4.25308709 1.73277247 0.72069014 0.29932181\n",
" 0.12428631 0.05403123]]\n",
" \n",
" Specifying points where the solution is desired.\n",
" \n",
" >>> sol = solve_ivp(exponential_decay, [0, 10], [2, 4, 8],\n",
" ... t_eval=[0, 1, 2, 4, 10])\n",
" >>> print(sol.t)\n",
" [ 0 1 2 4 10]\n",
" >>> print(sol.y)\n",
" [[2. 1.21305369 0.73534021 0.27066736 0.01350938]\n",
" [4. 2.42610739 1.47068043 0.54133472 0.02701876]\n",
" [8. 4.85221478 2.94136085 1.08266944 0.05403753]]\n",
" \n",
" Cannon fired upward with terminal event upon impact. The ``terminal`` and\n",
" ``direction`` fields of an event are applied by monkey patching a function.\n",
" Here ``y[0]`` is position and ``y[1]`` is velocity. The projectile starts\n",
" at position 0 with velocity +10. Note that the integration never reaches\n",
" t=100 because the event is terminal.\n",
" \n",
" >>> def upward_cannon(t, y): return [y[1], -0.5]\n",
" >>> def hit_ground(t, y): return y[0]\n",
" >>> hit_ground.terminal = True\n",
" >>> hit_ground.direction = -1\n",
" >>> sol = solve_ivp(upward_cannon, [0, 100], [0, 10], events=hit_ground)\n",
" >>> print(sol.t_events)\n",
" [array([40.])]\n",
" >>> print(sol.t)\n",
" [0.00000000e+00 9.99900010e-05 1.09989001e-03 1.10988901e-02\n",
" 1.11088891e-01 1.11098890e+00 1.11099890e+01 4.00000000e+01]\n",
" \n",
" Use `dense_output` and `events` to find position, which is 100, at the apex\n",
" of the cannonball's trajectory. Apex is not defined as terminal, so both\n",
" apex and hit_ground are found. There is no information at t=20, so the sol\n",
" attribute is used to evaluate the solution. The sol attribute is returned\n",
" by setting ``dense_output=True``. Alternatively, the `y_events` attribute\n",
" can be used to access the solution at the time of the event.\n",
" \n",
" >>> def apex(t, y): return y[1]\n",
" >>> sol = solve_ivp(upward_cannon, [0, 100], [0, 10],\n",
" ... events=(hit_ground, apex), dense_output=True)\n",
" >>> print(sol.t_events)\n",
" [array([40.]), array([20.])]\n",
" >>> print(sol.t)\n",
" [0.00000000e+00 9.99900010e-05 1.09989001e-03 1.10988901e-02\n",
" 1.11088891e-01 1.11098890e+00 1.11099890e+01 4.00000000e+01]\n",
" >>> print(sol.sol(sol.t_events[1][0]))\n",
" [100. 0.]\n",
" >>> print(sol.y_events)\n",
" [array([[-5.68434189e-14, -1.00000000e+01]]), array([[1.00000000e+02, 1.77635684e-15]])]\n",
" \n",
" As an example of a system with additional parameters, we'll implement\n",
" the Lotka-Volterra equations [12]_.\n",
" \n",
" >>> def lotkavolterra(t, z, a, b, c, d):\n",
" ... x, y = z\n",
" ... return [a*x - b*x*y, -c*y + d*x*y]\n",
" ...\n",
" \n",
" We pass in the parameter values a=1.5, b=1, c=3 and d=1 with the `args`\n",
" argument.\n",
" \n",
" >>> sol = solve_ivp(lotkavolterra, [0, 15], [10, 5], args=(1.5, 1, 3, 1),\n",
" ... dense_output=True)\n",
" \n",
" Compute a dense solution and plot it.\n",
" \n",
" >>> t = np.linspace(0, 15, 300)\n",
" >>> z = sol.sol(t)\n",
" >>> import matplotlib.pyplot as plt\n",
" >>> plt.plot(t, z.T)\n",
" >>> plt.xlabel('t')\n",
" >>> plt.legend(['x', 'y'], shadow=True)\n",
" >>> plt.title('Lotka-Volterra System')\n",
" >>> plt.show()\n",
"\n"
]
}
],
"source": [
"from scipy.integrate import solve_ivp\n",
"help(solve_ivp)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "b8b5b049",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" message: 'The solver successfully reached the end of the integration interval.'\n",
" nfev: 2630\n",
" njev: 0\n",
" nlu: 0\n",
" sol: None\n",
" status: 0\n",
" success: True\n",
" t: array([0.00000000e+00, 2.34367291e-02, 2.32365158e-01, 4.47372590e-01,\n",
" 6.87883729e-01, 9.61928130e-01, 1.26831360e+00, 1.59744802e+00,\n",
" 1.96014689e+00, 2.35100741e+00, 2.73837360e+00, 3.12707393e+00,\n",
" 3.51178920e+00, 3.87096546e+00, 4.20505645e+00, 4.54962871e+00,\n",
" 4.78908650e+00, 5.00018945e+00, 5.21129240e+00, 5.40503334e+00,\n",
" 5.58675814e+00, 5.76098202e+00, 5.93054034e+00, 6.09727981e+00,\n",
" 6.26240404e+00, 6.42670351e+00, 6.59080280e+00, 6.75541163e+00,\n",
" 6.92150115e+00, 7.09038495e+00, 7.26376557e+00, 7.44382418e+00,\n",
" 7.63341909e+00, 7.83647041e+00, 8.05863759e+00, 8.30811077e+00,\n",
" 8.59284643e+00, 8.90607918e+00, 9.24346658e+00, 9.61767274e+00,\n",
" 1.00087745e+01, 1.03957536e+01, 1.07849143e+01, 1.11642218e+01,\n",
" 1.15142969e+01, 1.18459430e+01, 1.21422326e+01, 1.23752485e+01,\n",
" 1.25822851e+01, 1.27893218e+01, 1.29805028e+01, 1.31606602e+01,\n",
" 1.33339061e+01, 1.35028646e+01, 1.36692523e+01, 1.38341849e+01,\n",
" 1.39984056e+01, 1.41625367e+01, 1.43273237e+01, 1.44937933e+01,\n",
" 1.46633229e+01, 1.48376894e+01, 1.50191730e+01, 1.52107819e+01,\n",
" 1.54166794e+01, 1.56429183e+01, 1.58981004e+01, 1.61888364e+01,\n",
" 1.65057985e+01, 1.68487205e+01, 1.72290004e+01, 1.76192308e+01,\n",
" 1.80064171e+01, 1.83953852e+01, 1.87704807e+01, 1.91156414e+01,\n",
" 1.94475159e+01, 1.97249054e+01, 1.99528431e+01, 2.01568430e+01,\n",
" 2.03608430e+01, 2.05500833e+01, 2.07290416e+01, 2.09015393e+01,\n",
" 2.10700415e+01, 2.12361639e+01, 2.14009549e+01, 2.15651242e+01,\n",
" 2.17292981e+01, 2.18942551e+01, 2.20610693e+01, 2.22311717e+01,\n",
" 2.24064026e+01, 2.25891289e+01, 2.27824918e+01, 2.29908719e+01,\n",
" 2.32206672e+01, 2.34807557e+01, 2.37761563e+01, 2.40961914e+01,\n",
" 2.44440623e+01, 2.48285572e+01, 2.52178865e+01, 2.56054149e+01,\n",
" 2.59938479e+01, 2.63649919e+01, 2.67064977e+01, 2.70397294e+01,\n",
" 2.73041712e+01, 2.75277137e+01, 2.77512561e+01, 2.79526153e+01,\n",
" 2.81388903e+01, 2.83159402e+01, 2.84872467e+01, 2.86550280e+01,\n",
" 2.88207364e+01, 2.89853130e+01, 2.91494223e+01, 2.93137092e+01,\n",
" 2.94790169e+01, 2.96465047e+01, 2.98176998e+01, 2.99945592e+01,\n",
" 3.01796138e+01, 3.03762599e+01, 3.05892980e+01, 3.08257683e+01,\n",
" 3.10947763e+01, 3.13975395e+01, 3.17232454e+01, 3.20804902e+01,\n",
" 3.24699831e+01, 3.28578891e+01, 3.32461855e+01, 3.36326475e+01,\n",
" 3.39961956e+01, 3.43324483e+01, 3.46713857e+01, 3.49188239e+01,\n",
" 3.51343365e+01, 3.53498491e+01, 3.55463294e+01, 3.57297119e+01,\n",
" 3.59049684e+01, 3.60751634e+01, 3.62422798e+01, 3.64076130e+01,\n",
" 3.65720067e+01, 3.67360952e+01, 3.69005586e+01, 3.70663161e+01,\n",
" 3.72346202e+01, 3.74071036e+01, 3.75858566e+01, 3.77736025e+01,\n",
" 3.79740439e+01, 3.81924849e+01, 3.84366742e+01, 3.87153342e+01,\n",
" 3.90247652e+01, 3.93572576e+01, 3.97249564e+01, 4.01162944e+01,\n",
" 4.05033707e+01, 4.08923596e+01, 4.12750462e+01, 4.16302593e+01,\n",
" 4.19629170e+01, 4.23147985e+01, 4.25473133e+01, 4.27544459e+01,\n",
" 4.29615784e+01, 4.31528127e+01, 4.33330025e+01, 4.35062686e+01,\n",
" 4.36752396e+01, 4.38416345e+01, 4.40065712e+01, 4.41707934e+01,\n",
" 4.43349237e+01, 4.44997067e+01, 4.46661679e+01, 4.48356832e+01,\n",
" 4.50100280e+01, 4.51914802e+01, 4.53830448e+01, 4.55888796e+01,\n",
" 4.58150287e+01, 4.60700858e+01, 4.63606971e+01, 4.66775802e+01,\n",
" 4.70203784e+01, 4.74005383e+01, 4.77907922e+01, 4.81779728e+01,\n",
" 4.85669509e+01, 4.89421434e+01, 4.92874035e+01, 4.96192583e+01,\n",
" 4.98970113e+01, 5.01250597e+01, 5.03291260e+01, 5.05331923e+01,\n",
" 5.07224752e+01, 5.09014600e+01, 5.10739743e+01, 5.12424866e+01,\n",
" 5.14086149e+01, 5.15734091e+01, 5.17375795e+01, 5.19017523e+01,\n",
" 5.20667054e+01, 5.22335116e+01, 5.24036006e+01, 5.25788114e+01,\n",
" 5.27615090e+01, 5.29548312e+01, 5.31631537e+01, 5.33928663e+01,\n",
" 5.36528417e+01, 5.39481401e+01, 5.42681050e+01, 5.46158600e+01,\n",
" 5.50002696e+01, 5.53896209e+01, 5.57771417e+01, 5.61655921e+01,\n",
" 5.65368292e+01, 5.68784126e+01, 5.72116009e+01, 5.74763049e+01,\n",
" 5.76999479e+01, 5.79235909e+01, 5.81250108e+01, 5.83113212e+01,\n",
" 5.84883931e+01, 5.86597133e+01, 5.88275029e+01, 5.89932160e+01,\n",
" 5.91577951e+01, 5.93219049e+01, 5.94861903e+01, 5.96514935e+01,\n",
" 5.98189727e+01, 5.99901539e+01, 6.01669928e+01, 6.03520181e+01,\n",
" 6.05486230e+01, 6.07616024e+01, 6.09979886e+01, 6.12668870e+01,\n",
" 6.15695680e+01, 6.18952020e+01, 6.22523294e+01, 6.26417821e+01,\n",
" 6.30297036e+01, 6.34179920e+01, 6.38044872e+01, 6.41681294e+01,\n",
" 6.45044353e+01, 6.48432742e+01, 6.50908899e+01, 6.53064983e+01,\n",
" 6.55221067e+01, 6.57186460e+01, 6.59020639e+01, 6.60773426e+01,\n",
" 6.62475513e+01, 6.64146759e+01, 6.65800137e+01, 6.67444097e+01,\n",
" 6.69084983e+01, 6.70729590e+01, 6.72387102e+01, 6.74070030e+01,\n",
" 6.75794688e+01, 6.77581960e+01, 6.79459053e+01, 6.81462950e+01,\n",
" 6.83646623e+01, 6.86087465e+01, 6.88872812e+01, 6.91966318e+01,\n",
" 6.95290292e+01, 6.98965919e+01, 7.02879263e+01, 7.06750094e+01,\n",
" 7.10639933e+01, 7.14467412e+01, 7.18020610e+01, 7.21347505e+01,\n",
" 7.24864018e+01, 7.27191012e+01, 7.29263408e+01, 7.31335805e+01,\n",
" 7.33248830e+01, 7.35051147e+01, 7.36784071e+01, 7.38473941e+01,\n",
" 7.40137985e+01, 7.41787403e+01, 7.43429646e+01, 7.45070939e+01,\n",
" 7.46718716e+01, 7.48383218e+01, 7.50078187e+01, 7.51821353e+01,\n",
" 7.53635470e+01, 7.55550543e+01, 7.57608080e+01, 7.59868409e+01,\n",
" 7.62417362e+01, 7.65321857e+01, 7.68489663e+01, 7.71916045e+01,\n",
" 7.75716081e+01, 7.79618920e+01, 7.83490649e+01, 7.87380553e+01,\n",
" 7.91133731e+01, 7.94587626e+01, 7.97905929e+01, 8.00688202e+01,\n",
" 8.02970121e+01, 8.05011644e+01, 8.07053166e+01, 8.08946549e+01,\n",
" 8.10736739e+01, 8.12462096e+01, 8.14147350e+01, 8.15808709e+01,\n",
" 8.17456692e+01, 8.19098410e+01, 8.20740125e+01, 8.22389604e+01,\n",
" 8.24057561e+01, 8.25758280e+01, 8.27510128e+01, 8.29336731e+01,\n",
" 8.31269427e+01, 8.33351906e+01, 8.35647963e+01, 8.38246255e+01,\n",
" 8.41197912e+01, 8.44396652e+01, 8.47872704e+01, 8.51715687e+01,\n",
" 8.55609481e+01, 8.59484587e+01, 8.63369311e+01, 8.67082887e+01,\n",
" 8.70499730e+01, 8.73831059e+01, 8.76481522e+01, 8.78719257e+01,\n",
" 8.80956992e+01, 8.82971977e+01, 8.84835541e+01, 8.86606543e+01,\n",
" 8.88319923e+01, 8.89997926e+01, 8.91655118e+01, 8.93300941e+01,\n",
" 8.94942047e+01, 8.96584880e+01, 8.98237852e+01, 8.99912533e+01,\n",
" 9.01624166e+01, 9.03392291e+01, 9.05242165e+01, 9.07207679e+01,\n",
" 9.09336713e+01, 9.11699488e+01, 9.14387055e+01, 9.17412796e+01,\n",
" 9.20668206e+01, 9.24237960e+01, 9.28131960e+01, 9.32011373e+01,\n",
" 9.35894148e+01, 9.39759524e+01, 9.43397167e+01, 9.46760918e+01,\n",
" 9.50148041e+01, 9.52626508e+01, 9.54783836e+01, 9.56941164e+01,\n",
" 9.58907323e+01, 9.60741963e+01, 9.62495037e+01, 9.64197302e+01,\n",
" 9.65868654e+01, 9.67522091e+01, 9.69166079e+01, 9.70806966e+01,\n",
" 9.72451540e+01, 9.74108970e+01, 9.75791752e+01, 9.77516182e+01,\n",
" 9.79303120e+01, 9.81179738e+01, 9.83182966e+01, 9.85365684e+01,\n",
" 9.87805167e+01, 9.90588886e+01, 9.93681347e+01, 9.97004092e+01,\n",
" 1.00000000e+02])\n",
" t_events: None\n",
" y: array([[ 0. , 0.0234346 , 0.23040018, 0.43421579, 0.64358859,\n",
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" 0.97317907, 0.99913497, 0.98903859, 0.94331978, 0.86251376,\n",
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" -0.75726773, -0.60195743, -0.42103162, -0.22233739, -0.01473609,\n",
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" 0.9300893 , 0.98307046, 0.99997862, 0.98091083, 0.92635933,\n",
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" -0.28759657, -0.47362669, -0.65484179, -0.81438621, -0.94194828,\n",
" -0.9933982 , -0.99498935, -0.94599223, -0.85163628, -0.71979348,\n",
" -0.55713352, -0.37079687, -0.1689007 , 0.03946425, 0.24466651,\n",
" 0.43735868, 0.6093942 , 0.75441891, 0.86797801, 0.94729433,\n",
" 0.99093393, 0.99846688, 0.97012949, 0.90645203, 0.80793853,\n",
" 0.67630161, 0.52224349, 0.35958202, 0.21952698]])\n",
" y_events: None\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/haule/opt/anaconda3/lib/python3.8/site-packages/scipy/integrate/_ivp/common.py:47: UserWarning: At least one element of `rtol` is too small. Setting `rtol = np.maximum(rtol, 2.220446049250313e-14)`.\n",
" warn(\"At least one element of `rtol` is too small. \"\n"
]
}
],
"source": [
"tf=100.\n",
"sol=solve_ivp(anHarmonic, [0,tf], [x,v], rtol=1e-14, atol=5e-7)\n",
"print(sol)"
]
},
{
"cell_type": "markdown",
"id": "0c411712",
"metadata": {},
"source": [
"We choose absolute tolerance `atol=5e-7` so that it uses approximately the same function evaluations, namely, around 2000."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "8dd4b62a",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(sol.t, sol.y[0], label='x:scipy.solve_ivp')\n",
"plt.plot(t, data2R[:,0], label='x:RK4')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "markdown",
"id": "a8fa4b82",
"metadata": {},
"source": [
"Solution is very similar to our `RK4`. What about total energy and stability?"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "e367be81",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-5.527636871005548e-06\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Enr = E_anharmonic(sol.y)\n",
"\n",
"plt.plot(sol.t, Enr[0]-E0)\n",
"print(Enr[0,-1]-E0)"
]
},
{
"cell_type": "markdown",
"id": "39a7eb0a",
"metadata": {},
"source": [
"Dissapointingly, the error is even a bit larger, and definitely not stable."
]
},
{
"cell_type": "markdown",
"id": "50060a13",
"metadata": {},
"source": [
"## Verlet algorithm\n",
"\n",
"Verlet algorithm is used in molecular dynamics simulations (when there is no energy loss), because it is stable and does not lead to energy loss with time. The precision of Verlet algorithm is only $O(h^3)$, which is worse than RK4, but stability is here more important than precision.\n",
"Below we derive Verlet's algorithm.\n",
"\n",
"\n",
"If there is no friction, we can explore the time-symmetry of Newton's Eq: they are time invariant when there is no friction.\n",
"\n",
"First we recall the Taylor expansion of the soltuion, which should exist:\n",
"\n",
"$$r(t+h)=r(t)+\\dot{r}(t) h + \\frac{1}{2}\\ddot{r}(t) h^2 + O(h^3)$$\n",
"\n",
"and because of the symmetry of Newton's Eq, we also have:\n",
"\n",
"$$r(t-h)=r(t)-\\dot{r}(t) h + \\frac{1}{2}\\ddot{r}(t) h^2 - O(h^3)$$\n",
"\n",
"Next we assume that the explicit form for the acceleration $\\ddot{r}(t)=a(t)$ exists in the form of the Newton's Eq. We will also replace $\\dot{r}(t)$ with symbol for velocity $v$. \n",
"\n",
"We will now rewrite the last equation, but shift the time variable from $t\\rightarrow t+h$:\n",
"$$r(t)=r(t+h)-v(t+h) h + \\frac{1}{2}a(t+h) h^2 + O(h^3)$$\n",
"The very first Eq. above can be simply rewritten with $v$ and $a$ as:\n",
"$$r(t+h)=r(t)+ v(t) h + \\frac{1}{2}a(t) h^2 + O(h^3)$$\n",
"\n",
"If we sum these two Eq. together we get:\n",
"$$ v(t+h) = v(t) + \\frac{1}{2}(a(t)+a(t+h)) h + O(h^3)$$\n",
"\n",
"The velocity Verlet algorithm uses the last two Eq. (for $r(t+h)$ and $v(t+h)$).\n",
"\n",
"We notice that both Equations contain a common term, which we will call $v(t+h/2)$, namely,\n",
"$$v(t+\\frac{1}{2}h) \\equiv v(t) + \\frac{h}{2} a(t)$$\n",
"In terms of this quantity, we can rewrite the above two Equations as\n",
"\\begin{eqnarray}\n",
"&& v(t+h) = v(t+\\frac{1}{2}h) + \\frac{h}{2}a(t+h) \\\\\n",
"&& r(t+h) = r(t) + h\\; v(t+\\frac{1}{2}h)\n",
"\\end{eqnarray}\n",
"\n",
"\n",
"Below we implement velocity Verlet algorithm:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "82e18a34",
"metadata": {},
"outputs": [],
"source": [
"def velocity_verlet(y, f, t, h):\n",
" \"\"\"Velocity Verlet\n",
"\n",
" Low-performance implementation because the force is calculated\n",
" twice; should remember the second force calculation and use as\n",
" input for the next step.\n",
"\n",
" For comparing different algorithms it is ok to use this\n",
" implementation for convenience. For production level code you\n",
" should use a better implementation that saves the second force\n",
" evaluation.\n",
"\n",
" \"\"\"\n",
" F = f(t, y) # [dy/dt, a]\n",
" # a = F[1] # this is a(t)\n",
" # half step velocity\n",
" y[1] += 0.5*h*F[1] # y[1] <- v[t+h/2] = v[t] + h/2 * a\n",
" # full step position\n",
" y[0] += h*y[1] # r[t+h] = r[t] + h * v[t+h/2]\n",
" # full step velocity (updated positions!)\n",
" F = f(t+h, y) # this is a(t+h), which should be reused in state of the art implementation\n",
" y[1] += 0.5*h*F[1] # v[t+h] = v[t+h/2] + h/2 * a\n",
" return y"
]
},
{
"cell_type": "markdown",
"id": "21a57625",
"metadata": {},
"source": [
"Now we can just use it with previously developed fixed step `Solve` routine:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "68317c11",
"metadata": {},
"outputs": [],
"source": [
"data3R = Solve(t, [x,v], velocity_verlet, anHarmonic)\n",
"Env = E_anharmonic(data3R.T)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "f87c04c2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t,data3R[:,0], label='verlet')\n",
"plt.plot(t,data2R[:,0], label='RK4')\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "markdown",
"id": "17237b5e",
"metadata": {},
"source": [
"The verlet algorithm gives similar result as RK4 (but slightly less precise).\n",
"\n",
"What about total energy?"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "25ea4435",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
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}
],
"source": [
"plt.plot(t,Env[0]-E0)"
]
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"The total energy is substantially less precise, however, it is stable, in the sense that no matter how long we evolve the system, the error of the total energy is bounded. It can be shown that the cummulative error of Verlet algorithm is $O((\\Delta t)^2)$, where $\\Delta t$ is time-step. While RK4 is locally $O(h^5)$ for each step, but cummulative error is unbounded, hence diverging. Only Verlet has finite cummulative error."
]
},
{
"cell_type": "markdown",
"id": "a6bdc163",
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"source": [
"## Homework: The Keppler problem\n",
"\n",
"1) Simulate the motion of Earth in the solar system as a two body problem (taking into account only the Sun and the Earth). Derive the Newton's equation for the relative coordinate:\n",
"$$m \\ddot{\\vec{r}}=-G m M \\frac{\\vec{r}}{r}.$$ \n",
"\n",
"Turn the above equation into atronomical units (AU).\n",
"The astronomical units are:\n",
" - length is meassured in units of distance between Earth and Sun $R\\approx 1.5\\;10^{11}$m\n",
" - time is meassured in years.\n",
"\n",
"Plot the Earth's orbit $(x,y)$ for 5000 years, and verify it is stable (the orbit is a circle with no time dependence). Also plot $x(t)$ and $y(t)$ for the last 5 out of 5000 years to see that period is what is expected.\n",
"\n",
"2) Simulate the three body problem, which consists of Sun, Earth and Jupiter. The latter has mass $m_J/m_S\\approx 9.55\\; 10^{-4}$, and distance $5.2\\; AU$. Note that the mass of Earth is $m_E/m_S\\approx 3 10^{-6}$ and distance $1\\; AU$. \n",
"\n",
" - Simulate 5000 Earth years and plot the orbits of Sun, Eart, and Jupiter ($x(t)$ versus $y(t)$ for all three objects). Are the orbits stable?\n",
"\n",
" - Check how strong is the influence of the Jupiter on motion of the Earth. Plot $x(t)$ for the last 5 years of 5000 years for the case with and withouth Jupiter. \n",
"\n",
"\n",
"\n",
"4) It turns out that our solar system has uneven distribution of asteroids, as demonstrated by the picture below. We are plotting the number of asteroids as a function of the distance from the Sun. There are many gaps in the distribution plot, which are now named Kirkwood gaps, after Daniel Kirkwood, who discovered them. He showed that gaps are associated with Jupiter, because the orbits are in resonance with Jupiter's motion. For example, the 2/1 gap is such that an asteroid placed there would complete two orbits every time Jupiter completes one. Similarly there are 3/1, 5/2, and 7/3 resonance, all related to Jupiter. \n",
" \n",
"\n",
"\n",
"We would like to simulate Kirkwood gaps. To simulate 2/1 gap, we need to find the distance from the Sun that such asteroid would be placed at, and his initial velocity. Than we need to check the long term stability of such orbit. \n",
"\n",
"We first recall that all orbits in the solar system satisfy $R_i^3/T_i^2=const$. This is because centrifugal force ($m_i\\omega_i^2 R_i$) and gravitational force ($G M m_i/R_i^2$) have to be balanced, hence $m_i (2\\pi/T_i)^2 R_i = G M m_i/R_i^2$, where $M$ is the Solar's mass. We hence see that $R_i^3/T_i^2=G M/(4\\pi^2)$. In AU units this equation is $R_i^3/T_i^2=1$\n",
"\n",
"For Asteroid that completes the orbit in half the Saturn's year, it must satisfy $T_{asteroid}=R_{Saturn}^{3/2}/2$, and hence $R_{asteroid}=R_{Saturn}/2^{2/3}$, which is $R_{asteroid}=5.2/2^{2/3}\\approx 3.2758$. It's starting velocity should be $v_{asteroid}=2\\pi/\\sqrt{R_{asteroid}}\\approx 3.4715$.\n",
"\n",
"For 3/1 gap, we should similarly have $R_{asteroid}=5.2/3^{2/3}\\approx 2.5$ and $v_{asteroid}=2\\pi/\\sqrt{R_{asteroid}}\\approx 3.974$.\n",
"\n",
"For homework, simulate the three body problem: Sun, Jupiter and Asteroid. You can assume that the mass of Asteroid is vanishingly small. Here it is also safe to ignore Earth and its influence on Asteroid. Simulate 5000 Earth years of motion, and plot the orbits of the three objects $x(t)$ versus $y(t)$. Make sure you subtract the center of motion movement $\\vec{R}_{cm}=m_1\\vec{r}_1+m_2\\vec{r}_2+m_3\\vec{r_3}$ when plotting the orbits.\n",
"\n",
"Do you see any change of the orbit of Asteroid over 5000 years?\n"
]
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"source": [
"### Sketch of the solution\n",
"\n",
"1) For Keppler problem we use $\\vec{r}_1$ and $\\vec{r}_2$ for vector positions of the two bodies, like the Earth and the Sun. The Newton's Eq require:\n",
"\n",
"\\begin{eqnarray}\n",
"m_1 \\ddot{\\vec{r}_1} = -G m_1 m_2 \\frac{\\vec{r}_1-\\vec{r}_2}{|\\vec{r}_1-\\vec{r}_2|^3}\\\\\n",
"m_2 \\ddot{\\vec{r}_2} = -G m_1 m_2 \\frac{\\vec{r}_2-\\vec{r}_1}{|\\vec{r}_2-\\vec{r}_1|^3}\n",
"\\end{eqnarray}\n",
"\n",
"The center of mass can be fixed at the origin $m_1 \\vec{r}_1+m_2 \\vec{r}_2=0$.\n",
"\n",
"The relative vector $$\\vec{r}=\\vec{r}_1-\\vec{r}_2$$ then satisfies the equation\n",
"\\begin{equation}\n",
"\\ddot{\\vec{r}}=G(m_1+m_2)\\frac{\\vec{r}}{|\\vec{r}|^3}\n",
"\\end{equation}\n",
"The gravitational constant $G$ can be obtained from information about the Earth's orbit. We know that Earth's orbit is almost circular. For circular orbits we know that centrifugal force and gravitational force have to be balanced, which means $m_E \\omega^2 R= G m_S m_E/R^2$, where $R$ is Sun-Earth distance $m_S$ and $m_E$ are Sun and Earth mass, and $\\omega$ frequency of the Earth's rotation, which is $\\omega=2\\pi/T$, with $T$ being one year. We thus have $$G=\\frac{R^3}{m_S} \\left(\\frac{2\\pi}{T}\\right)^2 .$$\n",
"\n",
"We want to meassure time in years $T$, and distance in Sun-Earth distance $R$. We thus define \n",
"$$\\vec{r}=R \\vec{r_d}$$\n",
"$$t = T t_d $$\n",
"and in this AU units the above equation for relative vector is\n",
"$$\\ddot{\\vec{r}_d} = -4\\pi^2 (1+\\frac{m_E}{m_S})\\frac{\\vec{r}_d}{r_d^3}$$\n",
"The ratio of the mass $m_E/m_S= 3\\, 10^{-6}$ is safe to neglect.\n",
"\n",
"The initial conditions will be choosen so that we have a circular orbit. For example $\\vec{r}_d=[1,0]$ and $\\dot{\\vec{r}_d}=[0,2\\pi]$. The velocity for a circular motion is $v=\\omega R$, which is $v=2\\pi R/T$, and hence in AU units is just $\\dot{y}_0=2\\pi$.\n",
"\n",
"We can choose the following set of variables $[x,y,\\dot{x},\\dot{y}]$, where $\\vec{r}_d=[x,y]$. With these we can solve the Kepler equations by:\n",
"\\begin{eqnarray}\n",
"\\begin{bmatrix}\\frac{d x}{dt}\\\\\\frac{d y}{dt}\\\\ \\frac{d \\dot{x}}{dt}\\\\ \\frac{d \\dot{y}}{dt}\\\\ \\end{bmatrix}\n",
"=\\begin{bmatrix}\n",
"\\dot{x}\\\\\\dot{y}\\\\ -4\\pi^2 \\frac{x}{(x^2+y^2)^{3/2}}\\\\ -4\\pi^2 \\frac{x}{(x^2+y^2)^{3/2}}\n",
"\\end{bmatrix}\n",
"\\end{eqnarray}\n",
"with initial conditions $y_0=[1,0,0,2\\pi]$"
]
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"2) In the Keppler's three body problem, we have Sun, Earth and Jupiter with $$\\frac{m_2}{m_1}=3\\; 10^{-6}$$ and $$\\frac{m_3}{m_1}=9.55\\; 10^{-4}.$$ \n",
"\n",
"The Newton's equations are\n",
"\\begin{eqnarray}\n",
"&& \\ddot{\\vec{r}}_1 = -G m_1\\left( \\frac{m_2}{m_1}\\frac{\\vec{r}_1-\\vec{r}_2}{|\\vec{r}_1-\\vec{r}_2|^3} +\\frac{m_3}{m_1}\\frac{\\vec{r}_1-\\vec{r}_3}{|\\vec{r}_1-\\vec{r}_3|^3}\\right) \\\\\n",
"&& \\ddot{\\vec{r}}_2 = -G m_1\\left(\\frac{\\vec{r}_2-\\vec{r}_1}{|\\vec{r}_2-\\vec{r}_1|^3} +\\frac{m_3}{m_1}\\frac{\\vec{r}_2-\\vec{r}_3}{|\\vec{r}_2-\\vec{r}_3|^3}\\right) \\\\\n",
"&& \\ddot{\\vec{r}}_3 = -G m_1\\left(\\frac{\\vec{r}_3-\\vec{r}_1}{|\\vec{r}_3-\\vec{r}_1|^3} +\\frac{m_2}{m_1}\\frac{\\vec{r}_3-\\vec{r}_2}{|\\vec{r}_3-\\vec{r}_2|^3}\\right) \\\\\n",
"\\end{eqnarray}\n",
"and in AU units become\n",
"\\begin{eqnarray}\n",
"&& \\ddot{\\vec{r}}_1 = -4\\pi^2\\left( \\frac{m_2}{m_1}\\frac{\\vec{r}_1-\\vec{r}_2}{|\\vec{r}_1-\\vec{r}_2|^3} +\\frac{m_3}{m_1}\\frac{\\vec{r}_1-\\vec{r}_3}{|\\vec{r}_1-\\vec{r}_3|^3}\\right) \\\\\n",
"&& \\ddot{\\vec{r}}_2 = -4\\pi^2\\left(\\frac{\\vec{r}_2-\\vec{r}_1}{|\\vec{r}_2-\\vec{r}_1|^3} +\\frac{m_3}{m_1}\\frac{\\vec{r}_2-\\vec{r}_3}{|\\vec{r}_2-\\vec{r}_3|^3}\\right) \\\\\n",
"&& \\ddot{\\vec{r}}_3 = -4\\pi^2\\left(\\frac{\\vec{r}_3-\\vec{r}_1}{|\\vec{r}_3-\\vec{r}_1|^3} +\\frac{m_2}{m_1}\\frac{\\vec{r}_3-\\vec{r}_2}{|\\vec{r}_3-\\vec{r}_2|^3}\\right) \\\\\n",
"\\end{eqnarray}\n",
"\n",
"The initial condistions for Sun can be $\\vec{r}_1=0$ and $\\dot{\\vec{r}}_1=0$, for Earth as before $\\vec{r}_2=[1,0]$ and $\\dot{\\vec{r}}_2=[0,2\\pi]$, and for Jupiter $\\vec{r}_3=[R_J/R,0]$ and $\\dot{\\vec{r}}_3=[0,\\frac{2\\pi}{\\sqrt{R_J/R}}]$, where $R_J/R\\approx 5.2$. The velocity folows from circular motion of planets, for which we know that gravitational force and centrigunal force are balanced $\\omega^2 R_i = G m_S/R_i^2$ or $v_i^2/R_i=G m_S/R_i^2$ and hence $v_i^2 R_i=G m_S = R^3 (2\\pi/T)^2$. In AU units each planet with circular orbit should satisfy $v_i=\\frac{2\\pi}{\\sqrt{R_i}}$\n",
"\n",
"3) Because asteroids are very light, we can neglect their mass compared to mass of Sun and Jupiter. In this case we can treat each Asteroid as an independent problem. We need to simulate the three bodies: Sun, Jupiter, and Asteroid. The masses are $m_2/m_1=9.55\\; 10^{-4}$ and $m_3/m_1=0$.\n",
"The equations are identical to previous equations simulating Sun, Eart and Jupiter. \n",
"\n",
"The initial condistions for circular orbits are also $R_{asteroid\\;(2/1)}=R_{Saturn}/2^{2/3}$, $R_{asteroid\\;(3/1)}=R_{Saturn}/3^{2/3}$ and $v_{asteroid}=2\\pi/\\sqrt{R_{asteroid}}$.\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "4054173f",
"metadata": {},
"outputs": [
{
"data": {
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zCz3mKNqVGA4EhX9ZMXa0pFhNgi1YwTHRPVhKamhReptm451hMRkwsCBgC6rrSgzsb3pYD3unGoLnw3GccC+RqLbyIKdLQrafDCzSnaltd8Q4qutKKAfLAimUQQWxN+llKUaq60oMB8ric7qAUDH9rmDBMdE9WDorltQiY3gwxbjnbH0ih6Rb9gSdrpExFNEzhhQxp4scYKVBTpdE8DyPQ8FaiaExRlcAkDJ9gjlUEVjoBxbEvtCzYvodQY0vonsIka6i2G0xUjjBWJ/AEemXfcEi+s5aYnUEFdMnlj1nYq/nYrA15gBFuhQHOV0SUdnggqPFA6OBQ9/clJhfzwpVT1Q3odXjS/TwdEVDa6jupDuRrr1nHHB5yRbdodXjw9Gg/lxcTlewmH7PGQeJB3cTt9ePQ0H9uVjT7kDI6dp7horpu4vL6xNqHWM5ucgYGryXDpQ5yRYKg5wuiWCTWe/s5E57mXVEbpoV9iQz/DxwvKop0cPTFYeDEceCdBsyU6Ivomf0zk5GVooFbp9fiAwQ8XGkohE+P4/MZDMK0qMv3GYMyE9FktmIRpcXx6upaLg7HK5ogNvnR7rNhOKsrgVqz4cV0ztbvThdS8r03eFgWQM8vsB90TMzdlv0y0uFxWhAQ6uXDjYoDHK6JIIt9APzY4+sAIHiyAH5gRMsRypJDb07MDX5gXFEuYCALVidBatHIuLjQFkghTIkxsJthsloECIsOynd2y1Y/c+wHva4bGExGTCokIrpEwGr5xrRMyMuW5iNBgwoCKwXVNelLMjpkgjmdA2I0+kCgH55aRHvRcTH96yIvjB+W/QP2vEYHcnuFvGeXAyHiaTSCcbusbcbRfQMUqZPDEx7Lp4iesbQQtoYKhFyuiTiUEVgcY43ugIgFOmqoIW+OzC5iMFxFNEz+gV1c0gHp3sIJxfjqOdisELjvWdooe8O++JQoj+fEWF1XUT8sA1EPEX0jKE9SDZCiZDTJQF+P4+jQqQrepG78+kfjHQdoYU+bnieF9KL3Yl0XZBHTld38ft5QbpjSGH8Cz1L2R+tbKSi4Tjx+vxC4fawbjjAw8JOMJIt4qPF7cOx4OGS4d2JdJFshCIhp0sCzta3oMntg8VoQO/s2E8uMpjDdqqGTjDGyzlHKxpavTAZOPTNid8B7hd0usqdrWho9SRqeLqitK4ZjS4vLCZDXCd6Gb2yk2E0cGhy+1DZ4ErgCPXD0apGuLx+pFpN6NOtOYqK6bvLieom8DxgTzIjN9Ua9/sMKkgHxwEVTheqG+m+UArkdEkAq8Hqm5sCszH+f3I6wdh9vg/u5vvlpcJiit8W9iQzctMCE+IxskVcsHquAfmp3bovrCYjioMnvFiEgIgNllocUpQOQwzq5+djMYUKuFkUk4gNdgq3b25KXEX0jBSrCSVBB5pSjMqBnC4JOByswepOET0QODXXP49OMHYHIbXYjdo6BtV1dY/uKNGfD+tNRw5wfLCNYSJtcbKGbBEPbEPdnUg8g9VKkkiqciCnSwIEuYgELPTs1BydYIwPVrcyKAGLSz+q6+oWiTi5yGDpyeMU6YqLE9XBhb4baV5GSU7gPU6QAxwX7G84EbZgyvRU16UcyOmSACaM2t1IV+A96ARjdzjUTY2ucMjp6h4HhZOL8RcLM/pSpKtbMKerO/VcDMHpqiZbxMPx4L/bBQlwuth6QfeFciCnS2R8fl5ocxKvMGo4dIIxflo9PmFC645cBIM5XVRHFDvNbi/OOVoBQEiZdweW0qJIV+z4/DxO1wSK3pnD1B1YWuw4OV0xw/N8KL2Y2/37ok/Qnqdqmug0qUIgp0tkTtU0we31I8lsjKudw/nQCcb4OVoZaDmTkWxGfnr8p4IYzOk6VdNEPRhjhJ1ssyeZ42rFdD4sFXO2voXuixg5V98Ct88Pi8mAoozuz1F9cpIBANWNLjjpZG9MVDW40OjywsAF2o11l+LMZBg4oNntQxWd7FUE5HSJDKu96p+f2q1TQQw6wRg/4a2YunMqiJGXZkWa1QQ/D5yspuPxsXBSSGd1f2EBgOwUC+xJZvA8pbVihUWkemcFpDe6S5otdLL3JNkiJlgasGdmMqym2Hv0no/FZEDPzMA9RveFMiCnS2QOlSfm5CKDTjDGz8nqxIXtgYAtSCQ1Pk4G01l9EpDOAgK2CBXT0+ISC+y+SERqkUF1XfERLheRKFjEjE6TKgNyukTmcGX3lejPh51gpGL62BAW+gRFVwAqpo+XU8EFoDtiwecTko0gW8TCCRGcrr455ADHQyLlIhghB5ii8UqAnC6ROSKkFxMT6QJChcckGxEbp4J1RImolWAIThct9DFxIsHpRYBkI+JFDKeLvRcV08dGIuUiGOxE6imKdCkC1TldL730EkpKSmCz2TBmzBhs2LChw2vvvPNOcBzX5mfo0KHCNUuXLm33mtbW1m6Pled5nApGVy5I4M6FpSrpBGNsnA5OOr2yEjehkUBqfJxKcHoRCEUH6Hh8bIjpdJ2opvsiFo4nUC+NQaleZaEqp2v58uVYsGABfvvb32Lnzp2YNGkSrr76apw+fbrd65977jmUlZUJP6WlpcjKysItt9wScV16enrEdWVlZbDZbN0eb2WDCy6vH0YDh8KM7r8fo3/YCUa315+w99UyjhYP6poDJ6l6iRDpOl4VOBlJdE2rx4eyoFxEInShGP3yQpEuOh4fHW6vH2fqEicXwWBOw4kqkiqIFpfXh9JgNP6CBNWdAqHI/qmaZrKFAlCV0/XMM89gzpw5uOuuuzB48GAsWbIExcXF+Nvf/tbu9Xa7HQUFBcLPtm3bUFdXh5/+9KcR13EcF3FdQUFBQsbLjsUXZdi61VvufPLSrLCZDfDzgePeRNcwHaKcVCtSraaEvW9xVjIsJgNcXj/O1pEtooFFudJtJmQmmxP2vr2yUqjxdYycrm2GnwdSLEbhxGEiKM4KSBU0kVRB1JSG2SIvwbYwGji0eHyocJIt5EY1Tpfb7cb27dsxbdq0iMenTZuGb7/9Nqr3eP311zFlyhT07t074vHGxkb07t0bPXv2xIwZM7Bz585O38flcsHpdEb8tAdb6HtlJS6yAgScxOLgMWDm2BGdc6qWFW4n1hZGAycUDR+tohq7aGCnqPrkdK+h7/lYTAbhXjtG6d6oEFKL3WyufD5Wk1GQKqC6rug4FiaKmkhbmI0GQSOSUozyoxqnq7q6Gj6fD/n5+RGP5+fno7y8vMvXl5WV4dNPP8Vdd90V8figQYOwdOlSfPTRR3j//fdhs9lwySWX4MiRIx2+1+LFi2G324Wf4uLidq9jDlGina7w9yytI6crGlh0pbcItmCyEccqaUKLBjFOLjKYA3yMFpeoOJnA9j/nQ7VEsRFSok+8LaiYXjmoxulinL8D4Hk+ql3B0qVLkZGRgR/96EcRj48fPx533HEHRo4ciUmTJuGDDz7AgAED8MILL3T4XosWLYLD4RB+SktL270u5HQl/iYqzqJIVyywySaR9VwMcoBjgx1dLxHBFiEHmCJd0SAUbiewnotBTldsCCcXE3joisFOCZ8gp0t2ElfcIjI5OTkwGo1tolqVlZVtol/nw/M83njjDcyePRsWS+ctRwwGAy666KJOI11WqxVWa9c5dzEjXczpKiWnKyqE03Ii7OhZqpdsER1SRLoopRUd7HRhiQjRFRKrjQ0xTi4y2Clh6hAgP6qJdFksFowZMwZr1qyJeHzNmjWYOHFip6/9+uuvcfToUcyZM6fLz+F5Hrt27UJhYWG3xgtIlF6speLtaBBsIUJ0pTgrUC9RSoX0USGGXASjLzW+jgnWvkrc9CLZIhrE0OhihJwu2hjKjWoiXQCwcOFCzJ49G2PHjsWECRPw6quv4vTp07j77rsBBNJ+Z8+exdtvvx3xutdffx3jxo3DsGHD2rznY489hvHjx6N///5wOp14/vnnsWvXLvz1r3/t1lhbwk7tiBPpCiz0lF7smnCJAjFqulik60xdc9Tpbr3S6vHhnCPgnCZSGJXB3rPM0Qqvzw9TAk8Na41mtxflzsB9kUi5CAZ7z9O1zWSLLqhrcguSNqLYgtV01TbB7+cT0geYiA9VOV2zZs1CTU0NHn/8cZSVlWHYsGFYtWqVcBqxrKysjWaXw+HAihUr8Nxzz7X7nvX19Zg3bx7Ky8tht9sxevRorF+/HhdffHG3xsqcIXuSGfYEHotnsIXe0eKBo8UDe1LiP0MrsLRfmtWErJTO08vxUJSRBI4DWj1+VDe6E3r0XmuU1jaD58WzRU6qFRaTAW6vH2WOViENT7SFRT0yk83ISBbhvrAnCbY4W98iSjpZK7B60Lw0K5ItiV+We2QmwWjg0Orxo6KhFYX2pIR/BhEdqnK6AGD+/PmYP39+u88tXbq0zWN2ux3NzR1Hg5599lk8++yziRqegJipRQBIsZqQk2pBdaMbpbXNsPewi/I5WoCls3plJ4sShbKYDChIt6HM0YrSumZyujohvNG1GLYwGDj0zEjC8eomnKlrIaerE8RQog/HYOBQkp2CQxUNOF7VRE5XJ5wJliaI9fdqNhpQnJmEkzXNOFHdRE6XjFC8VyTEdroACDo4VMDdOWL0XDwfKqaPDlbIK6YtegQ1ic7QadJOYXppJSKclmMwO1MZROewv9UeGeI5Q1TXpQzI6RIJtviKudMmqYLoEKPn4vn0zGILPRXTd0ZooRfRFkKNHdmiM06K0HT8fJgDfJY6Z3QK62bBREzFgLS6lAE5XSIROhYvvtNFu8jOEVJaEkS6KLrSOYJIrYippp6Z5ABHA3OEeoi40DMHmFpkdc4ZwekSb44StLpINkJWyOkSCSnSi6ETjDShdYaYchEMttCThEfnnJAgutKT0otRIThdIqa02HufoUhXpzCnS0wHmKUX2caHkAdyukTA7+cFzSZxna5gdIUiXR3i8/PC4itmdKWYUr1d4vKG5CLEjXRRerEr/H4eZfUBuQhxI13B9CLZokN4nhccYDHTi0LUsb4FPM+L9jlE55DTJQKVDS64vX4YDRwK7TbRPoc5dGfqWuDz003UHufqW+Dx8bAYAycMxYI5XefqyRYdUe5oBc8DNrMBOamJlyhgFAcXrnJnQKuLaEtVowtuX2COEvO+YJGu6kYXWj0+0T5HzThaPGh0eQGIG3UsygjYudHlhbPVK9rnEJ1DTpcIsHquHhlJogoCFtqTYDJwcPv8qAiKHBKRsFB6cVZAp0YsCtJtMBk4eHw82aIDwtNZYgrIMq0un58XRHGJSFgUsCDdJuoclZFsRrLFCICK6TuC2SIn1Qqb2Sja5yRbQtp4FHmUD3K6ROC0BBIFAGA0cEJqgKQK2udUrXh9/sIxGjgUZZAtOuNcMJ1VJOJuHgjoQwm1RLS4tMs5Ceq5AIDjOEoxdsEZCU4uMli06xw5wLJBTpcISCEXwaATjJ3DCtvFrK1jUA/GzmGLrtgLPUDF9F0hxclFBrM3RbraR9DoIlvoAnK6RECKk4sMQSCVFvp2YTs6tsMTExJI7ZyQLaR0uui+aA8pHeAeFOnqFGkjXYHPoEiXfJDTJQJSOl2CQCot9O1S5pBuoS/OolNzncFOLkoT6SJbdIa0ka7QqTmiLaGTi+KvFyThIT/kdImAHE4XpRfbR6o6IiBMq4tSWu1yVpZIF9miPeSIdJEt2keIdElhC4p0yQ45XQmm1eNDdaMbgDThYqGOiJyuNvj8PMqDJwmLJGjwKkRXyBZt4HlesuJtgNKLnRGuCyVpHRHZol2YMyrFekGpXvkhpyvBsCPqSWYj7Elm0T+PRboqG1xocZMOTjiVDa3w+XmYDBxy06yifx5zgMucrXB7SR8qnNomN1o9fnAcUCCidh2DOcCk1dUWZ4tXEl0oRrhumodsEYGjxYOGoGaWFA4wizJXNrjg8tJ6IQfkdCWYsuAOsjDDJqoWEcOeZEaq1QQgVDNDBGCRlQK7TVSNLkZuqhU2swE8T+H782Fp3ry0gIaW2OSmWmExklZXe5ypD0RWclItoupCMXKCtvDzAYFcIgSLOGWlWJBsMYn+edkpFliD91+FwyX65xFtIacrwZxzSJfOAgI6OEz1nrX1IAII9VwS2oIKuNvnbHChl6KeCwhqdVGKsV2krOcCArZgp4epmD4SKVOLQGCOChXTUxmEHJDTlWCESJcEKRRGISuOpEhXBFLKRTComL59zkp4oIFBxfTtI+WBBgbVErWPFE3Hz4fZ4hxt0mWBnK4EwyJdhRLeRIXB3mkUuo/knJDqlc4WpNXVPlIW0TOomL59pI50hX8W2SISKTW6GCzyTw6wPJDTlWAEXShJI122iM8mAgipXhl2kVRHFIk8ThelettDypOLjJBWF21GwgmlF8WXF2KEIl10X8gBOV0JhtVVSRldYTsXChdHElroJXSA7eQAt4ccKS2h5x8t9BHIGXWkmq5I5EgvsnuQbCEP5HQlmHMyRLoKaKFvFxZtKpSokB4ACijV2y5y1tdRpCsSWSJdVNPVLkJ6MUv6VC9FuuSBnK4E0ujyCporkka6hPQiLfSMFrcPtU0BkVopoyvMwStztILneck+V8mECwZLW0cUSNmUOUirixEh3pwhYUorIxSN9/vpvgAC60V9sweAPPV1Z+tbaI6SAXK6EkhFMNKUZjMJ2llSwBb6htaQ6KHeYRHHFIsR6TbpbJFvD4iwurx+1AUnVL3DdtQpFmkEgxm5aVaYDBx8fh5VjaRJBISiXKlWE9KTpLsvCuw2GDjA7fOjmmwBIBT1syeZkWaT7r4osNvAcYE5qia4MSWkg5yuBFLmDEwmUu5aACDFahIcizIKGQMI1dYVZSRJIlLLsJqMyEm1BMZA6V4Akf0vpbSF0cAhL9iJgNK9AcJPLkppC7PRIKTeSynFCCA85S7temExGYT7gtK90kNOVwIpl0GjixGe1iLkm9CAUI0dLfQByBbKQY56LgY7oUcF3AFYX1g51osiquuSDXK6Ekh5MNIlZT0Xg2QjIhEONEhYuM0oSCcHOBw5Ti4yaDMSiRwaXQwqpo+E/U1K0Yv0fHrQCUbZIKcrgZTLcHKRUUiyEREI0RUJTy4ySDYiEjaxSykAyRAiXU66LwB5I13MFhVkCwBABXO60snp0hPkdCWQChbpknGhpzRKgHMytJ1hFNJp0gjkkItgkIRHJGwjIEdKi9mCNiMBypwyRrpIIFU2yOlKIGVO1nZGjkhX4DOp/2IA9u8gpy1ooQ8gZ9SRaroiKZcxuhKKOtLpRSAU6ZKlpstOkS65IKcrgbAJTY7FhUV0KLoC8Dwvi+o2g9V00UIP+P28LO2YGEKq10mLC8/zYcXbctwXwfQi3RcAQhE/WdKLVF8nG+R0JZBWT0CAUY5wsbC4kOAd6po9yrAFCaSiuskFt9cPAyePLfKFhd6le1s4W7zCfZGXbpX885n9qxpduherbXZ74QwKactxXzBHLzBX+iT/fD2jOqfrpZdeQklJCWw2G8aMGYMNGzZ0eO26devAcVybn++//z7iuhUrVmDIkCGwWq0YMmQIVq5cGff4slMssJmNcb8+XtjOtcntQ4POBVJZlCsn1QqrSXpbsEm0xeODo0XfAqks2pebZoXZKP10w5wut88vdCjQKyzKlZlslmWOykm1whgUq2Wq+HqF3RcpFqOkwqiMjGQzLKbA/VhJ6V5JUZXTtXz5cixYsAC//e1vsXPnTkyaNAlXX301Tp8+3enrDh06hLKyMuGnf//+wnObNm3CrFmzMHv2bOzevRuzZ8/GzJkzsWXLlrjGKEcNEQAkWYzISA7cvGU6P8EoR6PrcGxmI7JSmECqvm0hZw0REBCCzEkNRHV0b4ug05Uvky0ixGp1foKxXEa5CADgOC50yETntpAaVTldzzzzDObMmYO77roLgwcPxpIlS1BcXIy//e1vnb4uLy8PBQUFwo/RGNrlLVmyBFOnTsWiRYswaNAgLFq0CFdeeSWWLFkS1xjlqJU4/7P1XkwvR6Pr86FTcwEqZF7oATrYwKiQeaEHQn8HereFnLV1DKHGjpwuSVGN0+V2u7F9+3ZMmzYt4vFp06bh22+/7fS1o0ePRmFhIa688kqsXbs24rlNmza1ec/p06d3+p4ulwtOpzPihyGHRheDFpcAciqgM8LruvRMuYzH4hn5tKMHECbGKaMDHNqM0MYQkHczkk+6abKgGqeruroaPp8P+fn5EY/n5+ejvLy83dcUFhbi1VdfxYoVK/Cvf/0LAwcOxJVXXon169cL15SXl8f0ngCwePFi2O124ae4uDj0mUpY6HV+DLhMxqPYjAISSAUQ0q6jSJf8KMEBJtmIAOVKmKPSqS+pHEjXZj5BnN+klef5Dhu3Dhw4EAMHDhR+nzBhAkpLS/HnP/8Zl112WVzvCQCLFi3CwoULhd+dTqfgeMl5Ewn9tHR+Ewm1KwqIOuo90qWE9GIB2QJAyBayRroougJAGXMURYDlQTWRrpycHBiNxjYRqMrKyjaRqs4YP348jhw5IvxeUFAQ83tarVakp6dH/DCUkdLSd3SlUgGLC6vV0PsuUu5CeiAs0qVzrS5mCzkXelKlDyBEusgB1h2qcbosFgvGjBmDNWvWRDy+Zs0aTJw4Mer32blzJwoLC4XfJ0yY0OY9P//885jeMxxlpLT0exPxPB+W0pJei4hBDnCAUEpLPlvQoYYAyop06Ty9qIRUL0W6ZEFV6cWFCxdi9uzZGDt2LCZMmIBXX30Vp0+fxt133w0gkPY7e/Ys3n77bQCBk4l9+vTB0KFD4Xa78e6772LFihVYsWKF8J733XcfLrvsMjz11FP44Q9/iP/85z/44osvsHHjxpjHx3HyplGYEn5ZfWuXKVKt4mz1oiUo9qeUlJZebdHs9qIhKACZR7aQFZfXh5qgTpkyCun1awu314/qxoDTqYQDJhVOl25t0ez24rcr90r6mapyumbNmoWamho8/vjjKCsrw7Bhw7Bq1Sr07t0bAFBWVhah2eV2u/Hggw/i7NmzSEpKwtChQ/HJJ5/gmmuuEa6ZOHEili1bhocffhiPPPIILrjgAixfvhzjxo2LeXxZyRZZBCAZ54tyZiRbZBuLXLDUoj1JHgFIBrNFs9sHZ6sX9iTpBRDlhkUzki1GpFnlm2rCbdHg8iJdBjFKuWECmBaTQdDzk4PwOcrZ4oVdxrHIRWVDK3gesBgNyJJxjhaEg71+1DV7BG1BPVHuaMV/dp2T9DNV5XQBwPz58zF//vx2n1u6dGnE7w899BAeeuihLt/z5ptvxs0339ztseXKmM4CQqKctU1unKtv1aXTFRKAlNcWyRYT7ElmOFo8KHe06tLpCq/nknMXnWwxId1mgrPVi3JHqy6drnKnMmxhMxtD94WzVZdOF0vz5qVbYTDIZwuLyYDsFAtqmtwod7Tq0umSI82tmpouNZCfJu9CD4QJ3jXoM0+vBIkCht7rupRwcpGh94MNciughxM62KBPWyhB0oaRr3OB1EoZ1klyuhJIbpoSbqKA41ep05tIWQu9vgu4lVAszCjQuS2UUETPCDUh16ctQg6wfCfdGXo/wShH30lyuhJIngIiXWxC02sT0wqFpBeB0KSq19Ok4WkUudG7bpqSIl0h2Qid20IB94XetbrkcDbJ6UoguQpwuvJ0n15Uzo6e0ovKsUVocdGnLeRudh1Ogc7Ti6EIsPyRLrY51Wukq6JB+uBETIX0PM/j66+/xoYNG3Dy5Ek0NzcjNzcXo0ePxpQpUyLa4egRJezoQzeRPiNdrL2InBIFDL23PFGCMCpD96leBdlC7yktJbQAYuhdw06xka6WlhY8+eSTKC4uxtVXX41PPvkE9fX1MBqNOHr0KH7/+9+jpKQE11xzDTZv3iz2mBVLbqoCnK40ll7U502kBDV6Bks369UWwqEGJSwuek8vKkCklqH39KISml0z8nW+MZRjbo4q0jVgwACMGzcOL7/8MqZPnw6zue0x31OnTuEf//gHZs2ahYcffhhz585N+GCVTp4iCun1q/js8/OobFDO6UWhvk6GELbc+P28wg41BE8v6tAB5nleqPFUQkpLz5Euv58XTswpKdKlR1vwPC/L3ByV0/Xpp59i2LBhnV7Tu3dvLFq0CA888ABOnTqVkMGpDSXonLAUZ1WjCz4/D6OMOjBSU9MU+M4GDshJld8WzNmobXLD7fXDYtJPCWVtsxtePw+OU8YBE7a41Dd70OrxySqcKzW1TW64fX7F2aK2ya07W9Q0ueHxBe4LJdQAh9vC5fXBatKPLRpdXjS7fZJ/blSrQFcOVzgWiwX9+/ePe0BqRk6hO0Z2igUGLhD1qWnSV4SlwhH4vjmpVphk7AzAyEw2w2wM/E1UNerLFqxGJDvFKmuXBkZ6kglJwcVdb/UrLLqnFFtkJJuFDYjeTlmziFJuKtlCblg2KNUmraMZl9U3bNiAO+64AxMmTMDZs2cBAO+8805c/QqJxGIyGpCTymqJ9HYTKSedBQAcxwkpZ72F7ysUVEMEBG3BNOx0lu5Voi302my5TEHSHYC+bcHquaQuC4rZ6VqxYgWmT5+OpKQk7Ny5Ey5XYAJraGjAk08+mfABErGjV5VhJpOhFKcLCKUQ9OYACxIFCqhzZOTr1AEuU9DJRYZeZSOUtjEE9HuCka0XUqfcY3a6/vCHP+Dll1/Ga6+9FlFQP3HiROzYsSOhgyPiQ6+yERXCqSBl7OiBsA4BOtNNU9LJRUauXiNdCjotxwgt9PrSTWN/e0qorWPk6/RgA9sI50isOhCz03Xo0CFcdtllbR5PT09HfX19IsZEdJM8vUa6FNR3kaHXDgEVCoyu6FVOhUWTlHBajhFqy6Sv+0KulFZnFOhUIJWtF7kSb9JjdroKCwtx9OjRNo9v3LgRffv2TcigiO4hLC46i66UK0iji8F2tHqb0BRpC51GusoVuBkRNOx0NkeFJG0UFOkSarr0dV8I6UWlR7p+/vOf47777sOWLVvAcRzOnTuH9957Dw8++CDmz58vxhiJGNFtelFBvf4YobZM+rSFktKLul3oFVhHlKfTCDD721PSHCXopumspkuuqGNMbYAA4KGHHoLD4cAVV1yB1tZWXHbZZbBarXjwwQdxzz33iDFGIkZCopw6u4kamACkchaXUHpRX7YI9fpTzuKiV+FgoY5ISbbQqQPM/vaUlV7U66GGYHoxTVpNx5idLgB44okn8Nvf/hYHDhyA3+/HkCFDkJqamuixEXGSp8NIl8vrQ22TG4CyTsyFoiv6sUWrx4f6Zg8AhaUXddiWyePzC/eFkhZ6IdKlo/vC5+dR06hABzjM6eJ5Hhwnv96k2ATU6IOaaUqPdDkcDvh8PmRlZWHs2LHC47W1tTCZTEhPT0/oAInYYTdRdaMLXp9fEUKhYsPSFBaTARnJbdtUyYUeVemZLawmA+xJyrEFW+idrV7dKKFXBxd5k4FDhpJsEXSAm90+NLq8SLXGtf9XFTWNLvh5wMAFhGqVAnMA3V4/HC0eZCTL381DbAJzgB+A9J0BYl4Bbr31VixbtqzN4x988AFuvfXWhAyK6B5ZyRaYDBx4HqhudMs9HEmoCEtnKWmnpkdV+vKwGiIl2SLdZoJVZ+rbVQ0shWJVRMcMRorVhBRLwOnVS+SxIkyiQEnt2awmo7BRrdJJ5JH9zdmTzJJvvmJ2urZs2YIrrriizeOXX345tmzZkpBBEd3DYOB0d2pOkItQUAoF0KcqfWWD8uq5gPNV6XViC2fI6VIaeksxVipQvJmRm6qvMoiQvJD090XMTpfL5YLX623zuMfjQUuLvoTulIzetLrKFXhajiEs9DqMriiNkCq9TmzBaogUaItcnW0MlSiMytDbZkTOzgAxO10XXXQRXn311TaPv/zyyxgzZkxCBkV0H0E2Qic7l0oFtp1h6E03rapBeSe0GHpbXJQc6WILnn5SWsoromewSJdebFEhFNFLb4uYqxefeOIJTJkyBbt378aVV14JAPjyyy+xdetWfP755wkfIBEfepMqUFpT33DydKb4XKngSFdemr5SWlWN8pzQiga9neytkOm0XDToTTetUkbB4JgjXZdccgk2bdqE4uJifPDBB/j444/Rr18/7NmzB5MmTRJjjEQc6LWmS4nRFb21AlJyelF3DrCCI116k/ColLGOqCuESJdODvsI9XVqiHQBwKhRo/Dee+8leixEAsnTmRBkpUwd46NBcIB1sqNXQ6RLL2kUJdd06a0tU5UwRylvY6i3ulM5+/TG5XT5/X4cPXoUlZWV8Pv9Ec+11wybkJ58nRXSVylQdZuRp7NUb5WCC4bzKdKlGPSW6g1F45VnC/b3oZdIV6hlnAqcrs2bN+O2227DqVOnwPN8xHMcx8Hn8yVscET85OtoF9nq8cHZGjhRm5uqvF2knmzh9flR00QLvRLgeV7ZkS4dlUD4/bwgVKtEyQg9pXp5ng8dakizAmirxiAmMdd03X333Rg7diz27duH2tpa1NXVCT+1tbVijJGIA3ZirrbJDZdX244wi6xYTAakJylP2TrcFm6vv4ur1U1tkxu8AlW3GcwBrm/2aP6+cLZ4hb+3nFTl2YJFGRqCHQK0TG2zG14/D44DclKVp/jOivudOrCFo8UDty9wX8iRGYl5hTpy5Aj++c9/ol+/fmKMh0gQGclmWIwGuH1+VDW40DMzWe4hiQbbzeemKkuNnhFhi0YXemQkyT0k0WARpGyFqW4z7ElmWEwGuL1+VDpdKM7S8n0hn+p2NLAOAa6gLXpla9cWLJqXnWJRZFu2dJtJuC+qGrR9X7A0b2ayGVaTEVLHvGO2/rhx43D06FExxkIkkEj1bW2nUpRctwIEbKEXIUjh5KICIytA0BY6Ud9Ww32hF9200OES5aUWAdY5Qx91XXIKowJxRLp++ctf4oEHHkB5eTmGDx8OszmyieqIESMSNjiie+Sn23CmrgUVDm1PaEquW2Hkp1txtr5F86eDlHyggRGyBd0XcpOXZkNpbYvmHeAqBctFMHLTrDhTp/05ijldcm1GYo503XTTTTh48CB+9rOf4aKLLsKoUaMwevRo4b9i89JLL6GkpAQ2mw1jxozBhg0bOrz2X//6F6ZOnYrc3Fykp6djwoQJ+OyzzyKuWbp0KTiOa/PT2qr+CVkv2itK1oVi5OlElZ59P6VGugD9FNMrPdIF6KeAWzgtpwJbVGl+jpL3QEPMka4TJ06IMY6oWL58ORYsWICXXnoJl1xyCV555RVcffXVOHDgAHr16tXm+vXr12Pq1Kl48sknkZGRgTfffBPXXXcdtmzZEuEgpqen49ChQxGvtdmUGQaOBRZt0LomUZWMLR2iRS9SBWqJdAHad4DVEOkSpG00PkeF+i4qd10RZCO0bgshvSjPfRGz09W7d28xxhEVzzzzDObMmYO77roLALBkyRJ89tln+Nvf/obFixe3uX7JkiURvz/55JP4z3/+g48//jjC6eI4DgUFBaKOXQ6E2hWNh4uV3OuPoZc2G5UKr+kC9CMcXClzGiUactP0MUcJCugK3ozoJQIspzAqEKc4KgAcOHAAp0+fhtvtjnj8+uuv7/ag2sPtdmP79u349a9/HfH4tGnT8O2330b1Hn6/Hw0NDcjKyop4vLGxEb1794bP58OoUaPw//7f/+s0VepyueByhf4wnU5nDN9EOoRIl8bTi0pWQGfoRZU+FOlSrgMsLPRat0WjCjYjafqIOiq9kB7QT6SrQubOADE7XcePH8cNN9yAvXv3guM4QSCVHdUXSxy1uroaPp8P+fn5EY/n5+ejvLw8qvf4y1/+gqamJsycOVN4bNCgQVi6dCmGDx8Op9OJ5557Dpdccgl2796N/v37t/s+ixcvxmOPPRb/l5EIvdxESlZAZ+hFlV4NDrBemsGroqYrXR9tmQQxTkVHuvSxGZHbFjEX0t93330oKSlBRUUFkpOTsX//fqxfvx5jx47FunXrRBhiJOfrMPE8H5U20/vvv49HH30Uy5cvR15envD4+PHjcccdd2DkyJGYNGkSPvjgAwwYMAAvvPBCh++1aNEiOBwO4ae0tDT+LyQiTJ1dy7vIcKVnRS8uwbFVazjqyPO84iUjAP0sLmqo6dKDLcLvCyXbQg+bdJ7nZe/TG3Oka9OmTfjqq6+Qm5sLg8EAg8GASy+9FIsXL8a9996LnTt3ijFO5OTkwGg0tolqVVZWtol+nc/y5csxZ84cfPjhh5gyZUqn1xoMBlx00UU4cuRIh9dYrVZYrcq9eRjMk69udMPv52FQoFhld6lv8cDjC0Rblai6zWATWk2TG16fX5ECid2lye1DS1DNWskOMIt0sQ4BFpP2bOHy+lDf7AGgbFuwhU/LtqhvDimgK9sWgfuiutGl3fWiObReqEYywufzITU1FUDAETp37hyAQIH9+ScAE4nFYsGYMWOwZs2aiMfXrFmDiRMndvi6999/H3feeSf+8Y9/4Nprr+3yc3iex65du1BYWNjtMctNdooFHAf4/Dxqm91dv0CFsF1ZZrJZ0RN2VrIFRgMHng84XlqEpetSLEakWJXXjomRmWyG2RhYULRa71jdGPgbsxgNsCeZu7haPjKTLZq3BashYgroSiU7NbBeeP086jS6XrCIaoaMtoh5lRo2bBj27NkDIKBO//TTT+Obb77B448/jr59+yZ8gOEsXLgQf//73/HGG2/g4MGDuP/++3H69GncfffdAAJpv5/85CfC9e+//z5+8pOf4C9/+QvGjx+P8vJylJeXw+FwCNc89thj+Oyzz3D8+HHs2rULc+bMwa5du4T3VDMmowHZKYE+X1oNGVeqQC4CAAwGTui5ptWTWmooogfOU6XXaF1X+MlFJbbGYhgMerCF8g80AIDZaEBWcnCO0uh6oYQ0b8xO18MPPwy/PxAq/cMf/oBTp05h0qRJWLVqFZ577rmEDzCcWbNmYcmSJXj88ccxatQorF+/HqtWrRJkLMrKynD69Gnh+ldeeQVerxe/+MUvUFhYKPzcd999wjX19fWYN28eBg8ejGnTpuHs2bNYv349Lr74YlG/i1SwlJtWnS41yEUw2BhZTzytoQa5CEYuK6bX+H2Ro/DNCKB9WwgaXQouomdova6Lzb1ybtJjzgFMnz5d+P++ffviwIEDqK2tRWZmpiQ7qvnz52P+/PntPrd06dKI36Mp7H/22Wfx7LPPJmBkyiQ3zYrvyxs0P6EpPdIF6GBCY7ZQweKSp3FbVCpgRx8tWi+mV0s0HtDBeuGUf2MYc6TrZz/7GRoaGiIey8rKQnNzM372s58lbGBEYhCiKxq9idTQAoihdbFaVUW6NL7Qq+m+EBxgjaYX1RiN1+qJdyWUQMTsdL311ltoaWlp83hLSwvefvvthAyKSByhxUXjN5EaFheNi9WqoQUQgyJdykHrSuhqsoXmo/GN8m8Mo04vOp1O8DwPnufR0NAQ0ZvQ5/Nh1apVEfpXhDLQ/uKirtA9oN1IlxImtGgJLS7a3oyo4b7Qel9SNdlC86leBQgGR+10ZWRkgOM4cByHAQMGtHme4zhVqLTrDc3vXFQ4oWk10qWGXn8M7afd5W11Egvs74XJXGiNahXNUZpfLxQgGBy107V27VrwPI8f/OAHWLFiRUT/QovFgt69e6OoqEiUQRLxo/WbSI2he62meqtV0OuPofX7Qk2bEbKFctB6ZkQJtoja6Zo8eTIA4MSJE+jVq5eitV+IEFq+iVo9PjS0egEou5EsIzy6Em37KrXg9fkF0Vc1LC65YVFHrdmC53lF7OijRctK6C1uHxpcbI5Svi207AC3enxwtMjfpSHmQvqDBw/im2++EX7/61//ilGjRuG2225DXV1dQgdHdB/2x9Xg8qLFLU4zcrlgE4PFZEC6TbkK6Aymmdbq8aMxOBFrhZomN3geMBo4ZAUFeZUME6r1+HihXY5WCG91ouTWWIzsoC20qITO5iib2YA0BXdpYLBTfY0uL5rd2pqjWCRe7i4NMTtd//d//wen0wkA2Lt3LxYuXIhrrrkGx48fx8KFCxM+QKJ7pFpNSDIH2h1obfcSLlGghkhFksUoTLxaK1RlBarZKYF2R0rHajIiIzkw8WrOFippjcUwGw2Co661esdwMU41zFEpFqNm14vw1KKctoj5jjxx4gSGDBkCAFixYgWuu+46PPnkk3jppZfw6aefJnyARPfgOC4slaKtWiI1SRQwmHCo5ia04N+Wmmyh1dS7EupWYiVXo50zqsI2hmqA4zjhHtbqZkTuLg0xO10WiwXNzc0AgC+++ALTpk0DEBBIZREwQlloVaqAndBSy4QGhAmkam1CU4DSc6xo9WBDpYpOLjK0WktEDrByUIqmY8xJ5ksvvRQLFy7EJZdcgu+++w7Lly8HABw+fBg9e/ZM+ACJ7qNVqQI1RrpYzYR2JzT1LPRalY1Q5UKvUX0oNdpCiHRpTDdNKbaIOdL14osvwmQy4Z///Cf+9re/oUePHgCATz/9FFdddVXCB0h0H81GugQxTvUs9KFIl8YmtEZlTGixoNWFXk0yKgzNpnpVJKPC0GqHAKW0KYs50tWrVy/897//bfO4lptGqx2tTmhKUBeOlTyN1nSp0hYavS+UsqOPBa2mF9V4X2jVFkrJjETldDmdTqSnpwv/3xnsOkI55Go1vagiLSKGZusl1GgLjdd00UIvP2pqjcXQagRYKbaIyunKzMxEWVkZ8vLyhHZA58MEBn0+bWlBaQHNLi60i1QMtNArB1VGulI1ujFUoy20el8opE1ZVE7XV199JbT9Wbt2ragDIhKPFguG/X4+1HZGVYX02pvQeJ5XaSG9Nnf0lSq0RajuVDsbQ9XOURq8LyK6NKTLe19E5XSxFkDn/z+hDsIbyvr8vCrEK7uivsUDrz+gup2dop4Jje3oa5rc8Pj8MBuVL17ZFQ0uL1o9fgDy7yJjgbWOamj1otXjgy0oCqlmIltjqccWzEF0asgWjpZQZwBVzVHBv5vaJpdm1otwW7BuFHIRldO1Z8+eqN9wxIgRcQ+GEIfsFAs4DvAF22yooTVIV7B0llpUtxmZyRaYDBy8fh41jW4U2NUTjegIFuVKs5qQZFHPYpluM8FiMsDt9aOqwYXirGS5h9RtmC2sKmmNxUhPMsFiNMDt86O60YWemeq3hdo6AzCyU6wwcICfB2oaXbJHhhIBs4U9yQyrSd45Kqq7ctSoUeA4LqrGsFTTpTxMRgOyUyyobnSjqsGlCadLjeksADAYOOSkWlHubEVVg0tTTpeaIitAsFtDqhVn61tQqRGnqzLMFmpoO8NgnTPO1regqkEbTpda7wujgUN2qhVVDS5UNmjD6VKKMCoQpU7XiRMncPz4cZw4cQIrVqxASUkJXnrpJezcuRM7d+7ESy+9hAsuuAArVqwQe7xEnORoTAldjUX0DK0dbFBKe4140FqNXZWgRq8+W+RorIA7vO+i2tCanIqSHOCoIl29e/cW/v+WW27B888/j2uuuUZ4bMSIESguLsYjjzyCH/3oRwkfJNF98tJt+L68QTs3kQolChhandDUaIuQhIc2HGAlLS6xorUWWWqNxgPaO8GopNPVMSea9+7di5KSkjaPl5SU4MCBAwkZFJF4tKaErurFRWOng5Q0ocWK1iJdajy5yNCaLdQ8R+VpLBqvpI1hzE7X4MGD8Yc//AGtrSFjuFwu/OEPf8DgwYMTOjgicWhtQqvUwISmFVuoekefqq2WJ2pe6LWm1aWUtjPxoLWNoZLui5iPt7z88su47rrrUFxcjJEjRwIAdu/eDY7j2m0PRCgDrSmhV6k4uqK1mi4lTWixotXNiBJ29LGitZSWqu8LjWk7KikCHLPTdfHFF+PEiRN499138f3334PnecyaNQu33XYbUlJSxBgjkQC0tnNRc6QrV2MTmpJC97Gi1Toidd4X5HQpBa0JpCrJFnEJuSQnJ2PevHmJHgshIuwmqtbYTaSEnUusaK0XppodYO1FutjpRRXfFxqxhZoP+2jVFkqYo9Sj2EZ0Cy1FutSqus0QdpFOF3iel3k03cPj86O2yQ1A3YtLdaMLfr+6bRFoOxOwhZrvi6oG9d8XLq8P9c0eAGq1Bat1bNWULZQwR5HTpROYwF2jy4tmt1fm0XQPtvuyqEx1m8EmYZfXjwaXum1RE1zkjQYOmcnytteIB6Zf5w12a1Aztc2BNl8cB2TL3OokHpgt3D4/nC3qvi+Y82s2crAnmWUeTeywOarV40ejyucopdmCnC6dkGIxIinYz6y6Qd2LS3ixsJpUtxk2sxFpQWeRibyqFZbOykm1wKDCHm1mowFZKQEHRe1RYLYZyUq2qLKnp81sFDZRTFhUrQg1RKnqnKOSLEakWYNzlMrvC9ZEXSm2UN+dScQFa7MBqP/UnJpPLjK0Ihuh5to6hlZsoebaOoZWyiCUVLgdL1qp6xJsoZB2RnE7XW63G2fOnMHp06cjfgjlopXFRc2n5RhacYC1tNBr5b4gW8hPyBbKWOjjQSsOsNL00mJ2uo4cOYJJkyYhKSkJvXv3RklJCUpKStCnT592leoTzUsvvYSSkhLYbDaMGTMGGzZs6PT6r7/+GmPGjIHNZkPfvn3x8ssvt7lmxYoVGDJkCKxWK4YMGYKVK1eKNXxZ0dxNpOLFRSs6OJpwgDUiG6Hmk4sMrd0Xap6jhPXCqe6NoTBHpSvDFjE7XXfeeScMBgP++9//Yvv27dixYwd27NiBnTt3YseOHWKMUWD58uVYsGABfvvb32Lnzp2YNGkSrr766g4jbCdOnMA111yDSZMmYefOnfjNb36De++9N6Ix96ZNmzBr1izMnj0bu3fvxuzZszFz5kxs2bJF1O8iB9qLdKl3cdGKbISaWwAxcjUiG6GlhV7tttDCfSE4wKqfo5QV6Yr56NeuXbuwfft2DBo0SIzxdMozzzyDOXPm4K677gIALFmyBJ999hn+9re/YfHixW2uf/nll9GrVy8sWbIEQKCF0bZt2/DnP/8ZN910k/AeU6dOxaJFiwAAixYtwtdff40lS5bg/fffl+aLSYRWJjRNLS4qL6TXVqRL3Tt6NavRM2iOUg6am6PUGukaMmQIqqurxRhLp7jdbmzfvh3Tpk2LeHzatGn49ttv233Npk2b2lw/ffp0bNu2DR6Pp9NrOnpPINBr0ul0RvyoAc3VESlk5xIPeRqJdGlhcWFyKrTQy49W+i+qWRiVoZ05KnR6UQnE7HQ99dRTeOihh7Bu3TrU1NRI5nxUV1fD5/MhPz8/4vH8/HyUl5e3+5ry8vJ2r/d6vYLj2NE1Hb0nACxevBh2u134KS4ujucrSY5WwsVK27nEQ6heQt220EJ9nVb6kmoi6kiRLsWglTkqtF4ooxwl5vTilClTAABXXnllxOM8z4PjOPh8vsSMrAPO19lgnxvL9ec/Hut7Llq0CAsXLhR+dzqdqnC8tHATBVS31T+hacEB5nleE/V1WmkFpIWFntlCzYcawu8LpURX4kG4L9Q+RylsvYjZ6Vq7dq0Y4+iSnJwcGI3GNhGoysrKNpEqRkFBQbvXm0wmZGdnd3pNR+8JAFarFVarMgwYC2wHXNMUUK42qlDMsq7ZDW+wXUuOiic0NgHUNrnh8flVKWbpbPXC5fUDUM6EFg9s7A0uL1rcPiRZjDKPKHaa3V5BOVwpO/p4YE4K3RfyE24Lt9cPi0l9tqhv9sDjY+uFMro0xOx0TZ48WYxxdInFYsGYMWOwZs0a3HDDDcLja9aswQ9/+MN2XzNhwgR8/PHHEY99/vnnGDt2LMxms3DNmjVrcP/990dcM3HiRBG+hbxkpVjAcYAv2PJEjU4L27VkpahTdZuRkWSGycDBG4zcFdqT5B5SzLDdfJrNBJtZfY4KI81qgs1sQKvHj6oGF3plJ8s9pJhhtkgyG5GiQqeRkZlsgdHAwefnUdPoRoFdfQ6kVu6LzGSLMEfVNKl0jgquFxnJZlhNyrBFzE7X+vXrO33+sssui3swXbFw4ULMnj0bY8eOxYQJE/Dqq6/i9OnTuPvuuwEE0n5nz57F22+/DQC4++678eKLL2LhwoWYO3cuNm3ahNdffz3iVOJ9992Hyy67DE899RR++MMf4j//+Q+++OILbNy4UbTvIRcmowHZKRZUN7pR6XSp0uliqVE1h+0BwGAIdAgoc7SiqkGdE5oWjsUDoW4NpbUtqGxoVaXTVRlW56iEVifxYjBwyEm1oMLpQlWDS9VOl5pr64DIOarSqdI5yqk8W8TsdF1++eVtHgu/ycWs6Zo1axZqamrw+OOPo6ysDMOGDcOqVavQu3dvAEBZWVmEZldJSQlWrVqF+++/H3/9619RVFSE559/XpCLAICJEydi2bJlePjhh/HII4/gggsuwPLlyzFu3DjRvoec5KbZUN3oVm2eXgtF9IzwCU2NaGVxAQI1aaW1Laqt69JCDREjN80acLoaWwHY5R5OzCithqg7hG8M1Qjr4akkW8TsdNXV1UX87vF4sHPnTjzyyCN44oknEjawjpg/fz7mz5/f7nNLly5t89jkyZO7FG29+eabcfPNNydieIonN82Kg2XqVRnWglwEQ+1HsrXQ6oShdlV6dj9rYTMSOJThVP1mREv3hVrnKCVmRmJ2uuz2tjuPqVOnwmq14v7778f27dsTMjBCHDSz0GtgcVH7aVItRbrULlUgRFcUtLjEi9olPCoVpgvVHYTTpGqfoxR0uCRhlci5ubk4dOhQot6OEAlaXJRDriAboc6ooxYkChhqb5El1K4oaHGJF7W3yNLSfRGKdKlzjlJiZiTmSNeePXsifud5HmVlZfjjH/+IkSNHJmxghDhoJY2iiQlN7Qu9Aie0eFF7twZtbUbUfV9QBFg5KLEGOGana9SoUeA4ThAZZYwfPx5vvPFGwgZGiIPahSBD7TU0sKNXuQOsxAktXtQuBCnUrmjAFlpZ6GljKD9KTPXG7HSdOHEi4neDwYDc3FzYbOpfBPWA2uslWPNVLUxoaneAtSIZAQC5qYH5S7W1KxqKdOWlqXszooWOGQxWAqFWWyhxYxiz08XkGQh1oubmvi1uHxoE1W3l3ETxEh7p6qr1lNJwe/2oaw40jddC1JH9PamxW0NASFSbKS213Rdenx81TW4A2nC68lRsi1aPD87WwHrBNlVKIOpC+i1btuDTTz+NeOztt99GSUkJ8vLyMG/ePLhc6lvI9QabCBpdXjS7vTKPJjbYDtJqMiDNGvN+QXEwW7i9fmFyUAvMFiYDh4wks8yj6T7ZYd0aaoOLplqoaXLBzwMGDsjWQKSLiTa3eHxocovbyzfR1DS5wfOA0cAhK1kZbWe6A5ujXF6/sOFVCyywYDEZkJ6knPUiaqfr0UcfjSii37t3L+bMmYMpU6bg17/+NT7++GMsXrxYlEESiSPFYkRSsDWF2qJd4eksNe24OsJmNiLdFpgMqlRWwB1et2JQUVSoI1i3BkCF94WTtcayqipC1xEpVpPQykhttmDjzUm1aOK+sJmNSAvOUWpLvYcf9FHSehG107Vr1y5ceeWVwu/Lli3DuHHj8Nprr2HhwoV4/vnn8cEHH4gySCJxcByn2loiLZ0KYrB0r9pqJio1VCzMyBHSvSpzgDWUWmSotYBbS0X0DLXbQmmlKFE7XXV1dcjPzxd+//rrr3HVVVcJv1900UUoLS1N7OgIUVDrqTktLvRqPdigZQdYdbbQ0OEShlolPLTUjomhVlX6KgWeXARicLry8/OFk4tutxs7duzAhAkThOcbGhpgNqu/tkMPqD/SpZyiyO6i9l2kphZ6lW5GtBjpYve42u4LLZ3oZah9jlJtpOuqq67Cr3/9a2zYsAGLFi1CcnIyJk2aJDy/Z88eXHDBBaIMkkgsao+uaGlCU6sSuhL1b7qLWjcjWhIMZqh+odfQxjBPkI1QV9QxVNOlLFtEXdL/hz/8ATfeeCMmT56M1NRUvPXWW7BYQqcz3njjDUybNk2UQRKJRa2he02mF1WqSRTqgamsCa07qHYzosFIl2qdLg1pdDFUawuFRrqidrpyc3OxYcMGOBwOpKamwmg0Rjz/4YcfIjU1NeEDJBKPWkP32qwjUueEpqUWQAy1Li6CGr2GoivqrSMip0spKHWOirnhtd1uFxyu999/H01NTQCArKysiMgXoVzUGl3RZL1EqsodYIXtIruDkOpV20LfqD1bqHWhJ6dLOSh1jorZ6Qrn5z//OSoqKhI1FkIi1HgT+f08qhsDopVaqpdQY6qX53ltntJitnCqyxZCpEuLtlDRHAUoN7rSHdRYdxpYL5TpAHfL6Tq/6TWhDthNxFqeqIHa5sBYOQ7ITtVORJXZoq7ZA7fXL/NoosPZ4oXbFxir0ia07sAkI5rcPjSpRH27ye1Diyeg2q4pW7A5qtGlmjmqyeVFs1t7tmDfpbbZDY9PHXNUXbMb3uDfTY7CHOBuOV2EOslSYcsTtsvKSrbAbNTOn21GshlmY0AtuVolaa2qxkAkKN1mgs1s7OJq9aDGbg0sKpdiMSJFA62xGGyO8vNQ3RylNVtkJltgNHDg1WSLRtalQXnrRbdG8+mnn6KoqChRYyEkItDyRF0hYy3WSgCBDgFqOzVXqUExTuC8bg1qcYCFuhXtpNwBdbZl0uLJRSDQR1JttmBzlBIPXXXL6br00kths2nrZtcLaqsl0qJcBENt9SshiQLt3fuCQKpK+sxpsYaIkaOyE4xa3RgCoWJ0tawXSrZFzE5XRUUFZs+ejaKiIphMJhiNxogfQh2orThSyTdRd8lVmYSHViNdQLiEh8oWF4Wd0EoEQl9SlRxsYOPU8mZENXOUgjcjMSee77zzTpw+fRqPPPIICgsLFdW9m4ieXJUdj9eiXARDbadJtSjGyVBbKyAlLy7dRW1aXVpNLwIqnKMUvBmJ2enauHEjNmzYgFGjRokwHEIqQsfj1XUTaXIXqbZUrwbbzjDU1vRaqVpEiUC1C70G7wu1lUAouU1ZzOnF4uJikorQAGoTgtTyhKa6VK8GxTgZ6ot0KXdx6S5qc7q0HHVUWxcTJR8widnpWrJkCX7961/j5MmTIgyHkAphQlNZpEuLE5rqdpGCGKfyJrTukquytkxKXly6i+qcLqdyU1rdRW22UPJ6EVV6MTMzM6J2q6mpCRdccAGSk5NhNpsjrq2trU3sCAlREHYuKot0aTG6QpEu5aC2SJeSF5fuorb7olIogdCeLdRWA6zk9SIqp2vJkiUiD4OQGjXtXFrcPjQEFcK1mF4MtwXP84o+nOLy+lDf7AGg7YW+timghG40KNcWHp8ftc3B1lgKXFy6i5oiwF6fHzVN2q07zQurAVb6HKX09SIqp+t//ud/xB4HITHsj7HR5UWz24tki3IVlJljaDMbkKYhpWcG0yNy+/xwtnhhTzZ38Qr5YP0vzUYOGQoeZ7xkp1phCCqh1zS5FL2A1jS6wfMB8crMZO20xmLkqWiOqmkK2YIJiWoJNke1eHxocvuQquB5WOnrRcw1XUajEZWVlW0er6mpIZ0uFZFqNSHZoo6WJ6ztTG6aVdE7rHixmY2wJwUcGPZdlUp4OkuLtjAaOGSlqONkLyuiz0m1KDoiFy+pVpPQlknxtgiOLyfVAoMGbZFiNSFFJetFuLyQEueomJ2ujk4uulwuWCza8/C1jFrC96HCbeWFihOFWiQ8tCwXwVDLyd5QqxPlRuO6Q3hbJsXPUQ3aFUZlqKUkRenyQlHH3p5//nkAgRvh73//O1JTU4XnfD4f1q9fj0GDBiV+hIRo5KVZcaqmWfk3kYbbzjDy0qw4Wtmo+IU+JACpXVvkplmBMuWf7GWOSL4G67kY+Wk2nKppVryGnZaL6Bl5aTacVJEtlLpJj9rpevbZZwEEIl0vv/xyRCrRYrGgT58+ePnllxM/wiB1dXW499578dFHHwEArr/+erzwwgvIyMho93qPx4OHH34Yq1atwvHjx2G32zFlyhT88Y9/jGjSffnll+Prr7+OeO2sWbOwbNky0b6LUlDLzkXLbWcY6ol0ad8Waol0VQhRRw07wEGHskLh9wWzhRYPNDDUMkcp+eQiEIPTdeLECQDAFVdcgZUrV3bo7IjFbbfdhjNnzmD16tUAgHnz5mH27Nn4+OOP272+ubkZO3bswCOPPIKRI0eirq4OCxYswPXXX49t27ZFXDt37lw8/vjjwu9JSUnifREFEToer+ydS5UudpHqWOi13OqEEVpclH1f6CO6oo45SoiuaNgBVluqV/WRLiAQPTp16hTOnTsnqdN18OBBrF69Gps3b8a4ceMAAK+99homTJiAQ4cOYeDAgW1eY7fbsWbNmojHXnjhBVx88cU4ffo0evXqJTyenJyMgoICcb+EAlFLyxM9LfRKtwVzRLSc0lKNA9yg/eiKoCeo8OhKqL5O+7ZQ+mZE6ZGumArpzWYzXC6X5CcCNm3aBLvdLjhcADB+/HjY7XZ8++23Ub+Pw+EAx3FtHMb33nsPOTk5GDp0KB588EE0NDR0+j4ulwtOpzPiR42oRQhSy82uGWrpvyjUEWl4R58rLC5Kvy+0b4s8lRz2ERxgDc9R+aqJdCl7kx7z6cVf/vKXeOqpp+D1esUYT7uUl5cjLy+vzeN5eXkoLy+P6j1aW1vx61//GrfddhvS09OFx2+//Xa8//77WLduHR555BGsWLECN954Y6fvtXjxYtjtduGnuLg4ti+kENTS8kTpp1ESgVp6m+mhdoV9N6VHuvRkC7VsRrTYjonB5qgKtUS6FLpexKwctmXLFnz55Zf4/PPPMXz4cKSkpEQ8/69//Svq93r00Ufx2GOPdXrN1q1bAaDd6Fq0yrgejwe33nor/H4/XnrppYjn5s6dK/z/sGHD0L9/f4wdOxY7duzAhRde2O77LVq0CAsXLhR+dzqdqnS8WKRLyQu9388LgpxK3bkkAjXId/jCbJGv4cVFiAArWH073BZKXVwSAfs7U3Ihvd/P66PuVAWRrsB9oexIV8xOV0ZGBm666aaEfPg999yDW2+9tdNr+vTpgz179qCioqLNc1VVVcjPz+/09R6PBzNnzsSJEyfw1VdfRUS52uPCCy+E2WzGkSNHOnS6rFYrrFZlGjQW2ARR3ajclic1TW74/Dw4DshO1a4OHLNFfbMHLq8PVpPyhIZrgq1xOA6aVN1msMlayerbtWH3RY4O7gtHiwetHh9sZuXdF3XNbnj9Af3KHIUWbycClsZWsi1qm9zw81D0HBXzbPLmm28m7MNzcnKQk5PT5XUTJkyAw+HAd999h4svvhhAIOLmcDgwceLEDl/HHK4jR45g7dq1yM7O7vKz9u/fD4/Hg8LCwui/iEoJb3lS2+RW5M6ApRWyU6wwG2POhqsGe5IZFqMBbp8f1Y1u9MhQ3gnakOq2FSYN24Kpbze5fah0tiI1N7XrF0lM+H2hZVvYk8ywmAxwe/2oanChOCtZ7iG1gUV+slIssJi0a4v0JJMKbMHuC4ti7wtljuo8Bg8ejKuuugpz587F5s2bsXnzZsydOxczZsyIOLk4aNAgrFy5EgDg9Xpx8803Y9u2bXjvvffg8/lQXl6O8vJyuN2BsPyxY8fw+OOPY9u2bTh58iRWrVqFW265BaNHj8Yll1wiy3eVkoiWJwqtmWALvZZPywGB9LnSTzBW6qBYmKF4W+jgtBwQvC8UfuBHD9IdQMAW+YJumjLXiyoVSHfEFTf/5z//iQ8++ACnT58WHBjGjh07EjKw83nvvfdw7733Ytq0aQAC4qgvvvhixDWHDh2Cw+EAAJw5c0YQUh01alTEdWvXrsXll18Oi8WCL7/8Es899xwaGxtRXFyMa6+9Fr///e9100cyL82K6kaXYheXCkGiQLk3UaLISbPibH2LYm0RcoC1b4uQ+rZCbaEDuQhGXjq7L5S50OuhNRYjL82G0toWBd8Xyq7nAuJwup5//nn89re/xf/8z//gP//5D37605/i2LFj2Lp1K37xi1+IMUYAQFZWFt59991OrwnvC9mnT58O+0QyiouL26jR6w2h5YlCb6IKnezoAeWL1erKFiqJdGlZLoKRn6bsYvpQOyYd2IIV0ys90qXg2rqY04svvfQSXn31Vbz44ouwWCx46KGHsGbNGtx7771ClIlQD0o/NVch7Oi1P6HlKVzCo1JHtshVuEBqSKJAuYtLolC6bIQeTi4yBNkIhc5RShdGBeJwuk6fPi0UryclJQlCorNnz8b777+f2NERopOnlh29gm+iRKH02hU9RrqUKpAqaHTpwBZ5CreFHmsdlWoLTUa6CgoKUFNTAwDo3bs3Nm/eDCDQm7GrdB6hPJTe24yNSw9pFKVHulhNjR7SKEpvBaSHXn8Mof2MQu8L4VCDDu4Ldu8rdb3QZKTrBz/4gdBkes6cObj//vsxdepUzJo1CzfccEPCB0iIi3ATKXTnoqdCeop0KQelN72uatBRBFjhJ+b0cnoRUE/UUcmRrpgL6V999VX4/X4AwN13342srCxs3LgR1113He6+++6ED5AQF7Y7K1fghOYLV3rWw+LCxGoV6HT5/bwQ9dGDA8yiK9UKjHTxPK+r+rp8BbfI4nk+LNWrA1uwDgGKj3Qp1xYxO10GgwEGQyhANnPmTMycOTOhgyKkI3QaRXktT2qaXPDzgEHB6sKJhE0UVQ1KtIU+FNAZzAGuaXLD6/MrSmixrtkDjy9QyqHkHX2iYBuumiY3PD6/okSSna1euLyBIIQeNoZK7pzR5PKiye0DoGzJiKj/ep9++mm0tLQIv69fvx4uV2jn0dDQgPnz5yd2dITosN2Z2+dHfbNH5tFEohcFdAZzZtw+PxwtCrOFThTQGVkpFhgNHHg+sNgrCWYLrSugM7KSLTAFW5QpLfLI6hzTbCZFtsVJNBnJgc4ZgPIij2w8yRajIlt3MaK+YxctWiScVASAGTNm4OzZs8Lvzc3NeOWVVxI7OkJ0LCaDEEVSWshYT/VcAGA1GZGZbAagPE0ivSigM4wGTrgvlFa/ojdbGAyc0NOQbCEv4Z0zFDdHqUAYFYjB6Tr/ZCKdVNQOQl2XQ2lOl74mNCDkYCqtxk44RaqDFApDOE3aqDRbqGNxSSR5Ci2mDxXR62NjCITmAKV1CFBDET2gkt6LhLiE13UpCT0VCzOEQlWFLS4hB1g/tshVaHRFT4XbDKXKRuipHRMjT6EdAljQIN+u7PuCnC4irM2GMhd6PUVXCpjTpbCoox4jXUptBaQnuQhGSJVeWbbQW3oRUG6HAPa3UaDwTXpM1WZ///vfkZqaCgDwer1YunQpcnJyACCi3otQF2zyVlxKS2c1XUDIFsqrrwumtHRki1DLE2XZQk8K6IxQ5wyl2UJ/EeBQNF5ZDjCLdGnG6erVqxdee+014feCggK88847ba4h1AcLxyrtJqrQYXSF2aLcoSxbCE19dbTQK/W+0JMCOkNILyrNFjpMLyq1Xy8LGig9vRi103Xy5EkRh0HISb5QL6GwXaQO64iUmuplUUc9LfQFSq2v03GkS2lRRz3WOoa6mCjLFkJmROH3BdV0EYos3vb6/IImj552kQV25dnCH9YZQE9RxwIFnurleT6sCbweF3rlRFd4ng+ltBQeXUkkeQqMdPE8L0S6lG6LqJyuZcuWRf2GpaWl+Oabb+IeECE9+WGNlr0+v8yjCVDT5IafZ3pJ+lno2eJS3agcW9Q2u+EV1Oh1ZAt7sC2TgmwRroCuR8mI6kYXfH5lyBU5W71o8QQU0JVeR5RI2BxV2+SG26uQ+6LFi1ZPYCxK34xE5XT97W9/w6BBg/DUU0/h4MGDbZ53OBxYtWoVbrvtNowZMwa1tbUJHyghHtmpVhgNHPwKUt9mkZ7c4Nj0QnZKQH3bz0PodSg3LLqQnWJRVAsWsclJsSrOFqyQPF0nCuiMnLA5Simq9GyOSreZkGTRjy0yk80wGwNzslLuCxblsieZFX9fRDWDfv311/jzn/+Mr776CsOGDUN6ejr69++P4cOHo2fPnsjOzsacOXPQp08f7Nu3D9ddd53Y4yYSiNHACZpESklrCbUSOkpnAQH17TyFKT6HaoiUvYNMNOG2UEqKsUKHqUUgco5Sii30mFoEgqr0goadMmzB1i01RByjLqSfMWMGZsyYgZqaGmzcuBEnT55ES0sLcnJyMHr0aIwePTqiETahLvLTrSh3tipmoa/U6UIPBIrVzzlaA5N6sdyjAap06gADgZNQ5xytitmMlOl0oQcCtih3tqLM0YqRCrgvQjVESTKPRHrYHKWU9UItJxeBGHW6ACA7Oxs//OEPxRgLISOBU2kOxWh16VEYlcF2a0o5TSr0wNShA6y0Yno17egTTWG6DbuhoGi8oAulvzlKabpparJFzKGpL774osPnqOG1eilQ2DFgPQqjMgrsylroBQFIFUxoiSbUC1MZO/oyRwsAoFAFO/pEI9wXCpmjynXsACutR2xI01H5tojZ6br22mvxwAMPwO0OFVxXVVXhuuuuw6JFixI6OEI68hXWUFaIruhwoc9TWIeAUK8//dlCaXIqTDRXDWmURJOv0KijHm1RoDARZ+G+0KLTtX79enz88ce46KKLsH//fnzyyScYNmwYGhsbsXv3bjHGSEhAnsJ29Hpsr8EoUJgmUYWOa1cK7Aor3nbqN9JVqLAIsJ4jXYItgn+PcqOmtHvMTte4ceOwc+dOjBgxAmPGjMENN9yABx54AF999RWKixVQ3UjEhdJUhvV6ehFQXuieFW/rcaFXbKRLBYtLolHafcGcPz3agkW6yhTmAKvBFnEdNzx06BC2bt2Knj17wmQy4fvvv0dzc3Oix0ZIiJLSix6fHzVNtLgoxRZMi0ePJ+YKwhZ6npdXlNPtDXVpKNRh1DE80qUMWwRKbPR4X7C/PyXYIrx7CRM0VjIxO11//OMfMWHCBEydOhX79u3D1q1bhcjXpk2bxBgjIQFscalr9sDl9ck6lupGF3geMBk4ZCVbZB2LHLBJvKHVi2a3V9axVDYEbGExGnRti2a3Dw0uuW0RcMItJgMyk82yjkUOmC1aPD44W5VhC7NRp3NUeui+kNsWVWHrRY4KupfE7HQ999xz+Pe//40XXngBNpsNQ4cOxXfffYcbb7wRl19+uQhDJKTAnmSGxRT4c5C7loiF7fPSrDDoSI2ekWo1ISWocC13/Up58LRcvl2ftki2mJBmCyjrVMhui1DdCsfpzxY2sxH2pICzKfd9ETpcYtPlfZFkCdlC7oi82taLmJ2uvXv34uqrr454zGw2409/+hM+//zzhA2MkBaO4xSTYhRqiDL0l0Jh5AuNr+V1gAVbpOvXFgUKqSXSc+E2o1AhshGstk6PdY6MQoXUdYXqf9Vhi5idrpycnA6fmzx5crcGQ8gLE79UzEKv4wktZAu5Fxf9KqAzlKKbRrYIq3eU2xY6lotghO4LeU8wqunkIhBnIT2hTfIVsossq9fvsXiGUoQgyQFWzsEGcrpCC6v80RV1LfRioJRIV6gdkzpsQU4XIcCiK3LLRpTpWBeKQQu9clBKerGMFnrFbEbC6+v0SkF66ASjnFSoSC4CUJHTVVdXh9mzZ8Nut8Nut2P27Nmor6/v9DV33nknOI6L+Bk/fnzENS6XC7/85S+Rk5ODlJQUXH/99Thz5oyI30S5KKamKxjpKtLxQq8YW+i47QxDiADLrL5NDnDou8t9X1B6MUw4WGZbqK17iWqcrttuuw27du3C6tWrsXr1auzatQuzZ8/u8nVXXXUVysrKhJ9Vq1ZFPL9gwQKsXLkSy5Ytw8aNG9HY2IgZM2bA55NXNkEOlCI+SItLaActd31dyBb6jToWUNRRMShFlJPSi6E5Qe5Il9qijia5BxANBw8exOrVq7F582aMGzcOAPDaa69hwoQJOHToEAYOHNjha61WKwoKCtp9zuFw4PXXX8c777yDKVOmAADeffddFBcX44svvsD06dMT/2UUjBJy9D4/j4pgC6AiHZ9eFNoyKcQWeo50KcHp8vt5WuihDFvwPK+6hV4MlLBeAKGNqVqijqqIdG3atAl2u11wuABg/PjxsNvt+Pbbbzt97bp165CXl4cBAwZg7ty5qKysFJ7bvn07PB4Ppk2bJjxWVFSEYcOGdfq+LpcLTqcz4kcLMCenTEaV4aoGF3x+PiB0l6qOcLEYsB19ZUMr/H55bFHdGLCFUee2YCrX1Y0ueH1+WcZQ0+SG18/DwAG5Omw8zmBOTm2TG60eebIR9c0euLyBvwM9tiljsDnK0eKRTcS50eVFY1C0mGq6Ekh5eTny8vLaPJ6Xl4fy8vIOX3f11Vfjvffew1dffYW//OUv2Lp1K37wgx/A5XIJ72uxWJCZmRnxuvz8/E7fd/HixUJtmd1u10zPyfx0Gzgu0OKipsktyxjOMTHOdBuMKhC6E4u84MLq8fGoa5bHFmwHm59m1bUtclKsMBk4+HkILZGkhkVWclKtMBtVMW2LQkayGVaZRZxZ+UVmshk2s1GWMSiBNAWIOLOIZ6rVhFSrKhJ38jpdjz76aJtC9/N/tm3bBgDtKjDzPN+pMvOsWbNw7bXXYtiwYbjuuuvw6aef4vDhw/jkk086HVdX77to0SI4HA7hp7S0NMpvrGwsJgNygxGNc/XyaK9Q3UoAs9GAnNRAexG5auyY/o7ebWEwcIITLNfiwv4G9JzmBQLrgNwnGNXUXFlMOI6TXWaI6bWppYgekLmm65577sGtt97a6TV9+vTBnj17UFFR0ea5qqoq5OfnR/15hYWF6N27N44cOQIAKCgogNvtRl1dXUS0q7KyEhMnTuzwfaxWK6xW9Rg5FgozklDZ4MK5+laM6Cn9558jjS6BQnsSqhvdKKtvxdAiu+SfH9Lo0m9tHSPfbsM5R6tstUTlYRFgvZOfbsOpmmbhZK3UVJB2nUCh3YbjVU3yRboa1LdJl9XpysnJ6VThnjFhwgQ4HA589913uPjiiwEAW7ZsgcPh6NQ5Op+amhqUlpaisLAQADBmzBiYzWasWbMGM2fOBACUlZVh3759ePrpp+P4RuqnyG7D7lLINqGV04QmUJRhw96zDiHlKjUUdQxRIPPBBop0hSiUWTZCbWKcYsK0uuQqphdKIFS0GVFFccDgwYNx1VVXYe7cudi8eTM2b96MuXPnYsaMGREnFwcNGoSVK1cCABobG/Hggw9i06ZNOHnyJNatW4frrrsOOTk5uOGGGwAAdrsdc+bMwQMPPIAvv/wSO3fuxB133IHhw4cLpxn1Biumlyu9SNGVEMwWZ2W3hXomNLEIyanIU0ckLC5kizAHWB5bqE2MU0yEXpgyOV1n6wJzY08VnXRXR+UZgPfeew/33nuvcNLw+uuvx4svvhhxzaFDh+BwOAAARqMRe/fuxdtvv436+noUFhbiiiuuwPLly5GWlia85tlnn4XJZMLMmTPR0tKCK6+8EkuXLoXRqM8CSXYTnZNt50LpRUYPwQGWK6VFO3qG3KKcFRTpEgg5wDJHgMnpkl03jQUH1CQvpBqnKysrC++++26n14TLHCQlJeGzzz7r8n1tNhteeOEFvPDCC90eoxYQZCNkjq7QQi9/1JFSWiHYv4HcUUeKrsgfXSlXmS6UmMitm8Y2pGpyulSRXiSko0jG6IrX50clCaMKyOl0RQhAUqoXPTOVYQtKu4ecHbm6NVA0PgRFumKHnC4iAtbvsLKhVXIhyKpGEkYNpygjtIuU2ha1TW64fX5wXEgzTM+wSb3c0QqfxGK1DS4vmt0BIVBKaUUW0kstHNzk8qK+2QMglP7XM8wW1Y0uuL3SzlHOVg8agsKobK5UA+R0EREExBcDQpCsBYxUhKdQ9CzGychJscJiNMhqC72LcTLy0mwwGTh4w9rxSAWTKLAnmZFk0WetaTi5qVYYOMDr51EtsVgti6yk2UxIs5kl/WwlkpVigSU4P0h9XzBbZCabkWxRTaUUOV1EJAZDSHxQ6lRKWT3Vc4VjMHAozJDHFiTdEYlRzvuCbBGByWhAXpo8NXZngp9HUa4AcorVqjG1CJDTRbQDqxuRfnGhWonzKZRroafmym3oIZOERxl1BmgDq7GT2haCREGmuhZ6MZFLw47ZgpwuQvX0CGt8LSW0o2+LXFpd5eQAt0Eup4stLhRdCdGDOV11EtuCIl1tKJDpNOnZYGZEbbYgp4tog1zRFTqh1ZYeMp1gLKOTi22Qa6E/I0RXkiX9XCUjuwNMkS6BkLajtLY4p1IHmJwuog2FMslGnKPoShvkkvCgmq62yOUAn6GUVhuYA3pGtkgXOcCMHjLJqVBNF6EZemQw7RWZIl0qu4nERC6tLra4kNMVQq5Ur7DQk9MlIFfUMbTQ033BYJuB0lqyRTSQ00W0QY5Ceq/PT61O2oE5wFIu9D4/L9i+OIt29IzwhT68+4WYeHx+YfNDka4Q4elFKW3B5ihygEOEoo7Nkn2m1+cXTktSepFQPUVBp6uu2YOWoCij2FQ1uuDnQcKo58Ec4IZWL5ytHkk+s7KhFR5fQKSW2s6EYPdFk9sHZ4tXks8sd7TCzwMWkwE5KXRfMNhC2+jywtEizX1BtmgfZgtnq3S2qGgIrBdmo/rWC3K6iDakJ5mQEhRhlCrFyGqWSBg1khSrCRnJARHGMonquliaoCgjiWwRRpLFiOwUCwDgTL00u3qhnisjCQayhUCSxYic1KAtJEoxngk7RUq2CJFiNSEreF9Ile5ln1NoV58tyOki2sBxnFBXJZVsBAtNqy0/LwVFEqd7mS2Ks9QVtpeCUNGwNPcF1XN1jNQnGEkuomNY6luqFKNaTy4C5HQRHcDqqqSa0NgukmqI2iJ1AXcoukK2OB/mAJ+VaHFhixjVc7VF6mJ6NS/0YhNyuqR1gNV2chEgp4voAEEgVbKUVjC6QlpEbeghcSsgZgta6NvSQ2IldBJG7RipZSNIo6tjpLZFyAFWX2aEnC6iXVgBt1Q1XaVCSoucrvORWjaCoo4dI7VuGgmjdkwovShN1FHN0RWxkSu9qEZbkNNFtEuhxFIFrHi7mHaRbRDEaqWqr6unSFdHsIX+jNR1RGSLNlBNl3KQOr3INj3kdBGaQUr1ba/PL0xovbJpR38+UqYXvT6/MKFRdKUtUt4X4Xpp5AC3pYeEC73fzwtzFNmiLVJrdVGki9Ac4TsXv19c8cEyRyt8fh4WowH5aerL0YsNm1jKg/9OYlLuDNkiL01d+jdSwBb6qgYXWj3iathVOFvh9Qf00vLovmgDs0V9swdNLnF106qbXHB7/TBwoQbPRAi2Xkih1eVo8aAhaG81nnYnp4toF6bR5PL6UdngEvWzWD1Xj0z1aa5IQV5aQLvM6+dRJbItzoQVC5Mt2pKZbEaSOaBhVy5yuje8hoj00tqSbjMj3WYCIH6KMVxH0GykZfN8ki0mQcNO7NOkLMqVmWxGssUk6meJAf31EO1iNhqEVMrpWnFDxmdqKWzfGUYDh4J0aWrs6ORi53AcJ+yuxbYFS9VQDVHH9JAorUWnSLtGqmL6cyqvcySni+iQ3sH6qlM1TaJ+Dot09aLTch3SQ6IJjU7LdQ1b6MXe0Z+to81IVwjF9GLbop6JN5MtOkIq2QihnsuuTluQ00V0CJMMEDvSJWh0kdPVIb2zmAMssi1IjLNLpGpCfoZ0obpEiK6IbAvS6OoaqU4wnlFxET1AThfRCVIt9KdJGLVL+uSkABDfFmcoutIlUkkVhE7L0X3RET0lUqUnuYiuYbYoFTkaf6o68P69VXrSnZwuokPYH7XokS5BjJMmtI6QKtV7loRRu6RIopQWOcBdI+imie50BQrpKdLVMVKlF08G58A+2Smifo5YkNNFdIgU6cVWj084kUeRro7pnRWYYE6KGOny+PxCBwJa6DumlwT3RbguFEVXOoYt9KJHHVnanWzRIVIU0vM8L0T7KdJFaI7ewZ1EbZMbDa3iaK+wGzTNakJGslmUz9ACTDS2utGFRpE0icrqW+HnAavJgNxU0ujqCJbqPedoEU2rq7oxoAtlNHBC83miLVLoptU3u+Fs9UZ8HtEW9m/TIKJWV2WDCy0eH4wGTrVpd3K6iA5JtYa0V8Ta1bP2Pz2zksFxpEXUEfYkM7KYLUSKdp0JK6InW3RMdooFaVYTeF7E+yKYoilIt8FEulAdEq6bJlaXgBPVgXRWQbpNlbpQUhGu1SVWtOtk0BY9MpJgManzvlDnqAnJEFKMIi30QqNr2kF2idh1XaGTi+rcQUoFx3FCtIstyImGei5GB8dxQi2oWA4ws3FJjjpriKRE7BOMak8tAuR0EV0gLPQiTWjMmaPC7a5hhaNi1XVR4Xb0MKfrpEhOlyBSSzVEXVIisgPMbNyHnK4u6ZklbjG92ovoAXK6iC7oLXLRMAmjRk+vLHEjXWfo5GLUlAQ3IydFssXxKoquREtJTioA8Zyu48H37Uu26BKxi+kp0iUhdXV1mD17Nux2O+x2O2bPno36+vpOX8NxXLs/f/rTn4RrLr/88jbP33rrrSJ/G/UgenqxluQioqVPjrgLPbUAih6x04vHqxsBAH1zU0V5fy3RV+xIVw1FuqKFlSaUipzqVXOkSzVVgbfddhvOnDmD1atXAwDmzZuH2bNn4+OPP+7wNWVlZRG/f/rpp5gzZw5uuummiMfnzp2Lxx9/XPg9KYkWHQY7wXiqVtw6IpKL6BpmC7Hr66imq2tC6cXE24LneSHS1TdXvYuLVLB/I/Zvlkh4nscJIepI90VXMAf4uAgOcEAuQv0OsCqcroMHD2L16tXYvHkzxo0bBwB47bXXMGHCBBw6dAgDBw5s93UFBQURv//nP//BFVdcgb59+0Y8npyc3OZaIgAL456rb4XH54c5gSepHM0eNASPYtNC3zVsd3fO0YpWjw+24KmtRNDo8qLCGdBLK1HxLlIq2L9RubMVLW4fkiyJs0Vds0c4ck/pxa4pOU/CI5H3RVWjC01uHwwcpd2jgTnAp2uaE75eVDe60eT2gePUnRlRRXpx06ZNsNvtgsMFAOPHj4fdbse3334b1XtUVFTgk08+wZw5c9o899577yEnJwdDhw7Fgw8+iIaGhk7fy+Vywel0RvxoldxUK6wmA3x+PuFHsllkJSfVmtBFS6tkJpuRZgvskxIdvj9eFUhn5aRaYSe9tC7JTLHAnhT4d0p0upfZokdGUkIdCK2SlWJBui0g4ZFoW7BIZo/MJFhNZIuuCMhqGOH18wlvWcaiXEV2ddtCFU5XeXk58vLy2jyel5eH8vLyqN7jrbfeQlpaGm688caIx2+//Xa8//77WLduHR555BGsWLGizTXns3jxYqG2zG63o7i4OPovozIMBi6sgDuxN5HQc1HFuxYp4ThOiDwm+gTjseBCfwGls6JGrBOMlFqMDY7jUBKsfTuR4BTjiWBtHSvWJzqH4zhcELQF2zwkCjbn9VF5mldWp+vRRx/tsNid/Wzbtg0A2hVr5Hk+ahHHN954A7fffjtstkh157lz52LKlCkYNmwYbr31Vvzzn//EF198gR07dnT4XosWLYLD4RB+SktLY/jW6kMs2Qh2U1IKJXqEGrsE7+iPVQber18eLS7Rwk4wnki0LVgRPd0XUXOBSLVEJ4KRrhIVn5aTGrZZOJZgB5htbnqrvPxB1pque+65p8uTgn369MGePXtQUVHR5rmqqirk5+d3+TkbNmzAoUOHsHz58i6vvfDCC2E2m3HkyBFceOGF7V5jtVphteqnTUqvYN+/RKe0jlQGFpf+eWkJfV8t0ydbnKjj0UoW6SKnK1rEinSdILmImGH/VokupmeRLjUXbksNm0OOJTzSFbwvyOmKn5ycHOTk5HR53YQJE+BwOPDdd9/h4osvBgBs2bIFDocDEydO7PL1r7/+OsaMGYORI0d2ee3+/fvh8XhQWFjY9RfQCb2C6b9ER1eOVDCnixb6aOktCKQmOLrC0otki6hhC32iU72CLhQ5wFFTkstkIxK80LNIFzldUSNWelELGl2ASmq6Bg8ejKuuugpz587F5s2bsXnzZsydOxczZsyIOLk4aNAgrFy5MuK1TqcTH374Ie66664273vs2DE8/vjj2LZtG06ePIlVq1bhlltuwejRo3HJJZeI/r3UQiillbjFxefnhYW+fz4tLtHSRwRbeH1+wYmjmq7oEToEJDDS5fX5hc0N1XRFT18RBFL9fj4UXSGnK2rC04s8zyfkPXme14xemiqcLiBwwnD48OGYNm0apk2bhhEjRuCdd96JuObQoUNwOBwRjy1btgw8z+PHP/5xm/e0WCz48ssvMX36dAwcOBD33nsvpk2bhi+++AJGo3pPRySaXtkhVfpE3URn6prh8vphMRlILiIG2C7vbH0LPD5/Qt6ztK4FHh+PJLMRRXY61BAtbPKvbHChyeVNyHsG7MrDajKQLWKAFVfXNXtQ1+ROyHuWOVvh8vphMnDoQe2YoqYkJwUcBzhaPKhJkC3qwuSF1N69RBU6XQCQlZWFd999t9Nr2nMI5s2bh3nz5rV7fXFxMb7++uuEjE/L9MpKhtnIodntw5m6loTo1YTXEBkN0R2GIIC8NCtsZgNaPX6crWtJyK7vWCVTP0+BgWwRNfYkM7JSLKhtcuNkTROGFtm7/Z7h7X/IFtGTbDGh0G5DmaMVx6ubMCbF0u33ZBHMXtnJMCVQb0rr2MxG9MhIwpm6FhyvakJOavfrn1kEs9BuU72MCv0lEV1iNhqEPP2h8s41zKIlVERPqcVY4DgurPF1YlIpR6uoiD5e2MGGRCnTs5Q7pRZjJ9GNr1ltndoLt+Ug0cX0pzTQ6JpBThcRFQMLAicMD1UkyOmiIvq4YSnGRC0ux+jkYtwIJxgT5ACHmiuTLWKlb4KL6Vmki+q5YkdwuioTZAuNaHQB5HQRUSI4XQmKdB2tDLwP6ULFzsD8gC2+L0uMLUInF2lxiRW2806UA0xyEfFTkuBieqG5MtkiZoR+mImKOgbnKLVrdAHkdBFRMiiBThfP80JNF51cjJ1BhekAgIPl3W8/xfO8IGJIka7YSbRW1/FqSi/GS98Ea3VRpCt+Ep1e/D647rDNv5ohp4uIioEFgYX+WFUj3N7unZorc7Siye2DycBpYuciNYODTteh8gZ4u3mCsabJDUeLBxxHi0s8sIX+aFVjt0/2hjcdJ42u2AmlF5vg93fPFl6fX2hTRvdF7LCoeWltM1xeX7feq9XjEyJdQ4Nzn5ohp4uIiiK7DWlWE7x+vtvhe1ZEX5KTktAu9Hqhd1Yyki1GuLz+bgtzspqL4sxk1Z8KkoP++akwGTjUN3twztHarfdikZWc1FAzbSJ6emQkwWzk4PL6Uebspi1qmuD1B2RUCtJtXb+AiCA31Yo0qwl+vvuagofKG+DngewUC3LT1N8JhlY8Iio4jsOAYGj3+26mtY5UUD1XdzAYOCHMfrCse7Y4So2uu4XVZBT+jvefdXRxdecco16k3cJkNAgaTt1VQ99/LnBfDSlKJ+mOOOA4Dn3zElNMf6AsZItoey0rGXK6iKhhC/3hbp5gPEpyEd1mUDDd212nizW6pnqu+GH6XGyhjhdWi0QnF+OH9XHt7iGTfUEHeliR+tNZcnGBoEzfTacreF8N1kBqESCni4iBRBXTs/Riv3z1F0XKxZDCxES6qOdi9xnWI7AYdNfpYq8foIFiYbkY3jPgAO/pZtRx39mALYb26L7grV4J9WDsXjkKm+OGkNNF6I0BTKqgG05XxMlFWujjhu36DnZzR8+cLkr1xg+LdB04172Ffs+ZegDAyJ600MfLiOC/3d7gv2U88DyPfedYpItsES8s0nW4Mv45yu/nBaeLIl2E7mCRrjN1LWiMs9dcVaMLjhYPDHRarluwVG+5szXuXnMNrR6crW8BQOnF7jA4GHU852hFbZy2KHe0orLBBQMXqF0h4oM5SSdrmuFo8cT1HqW1LWho9cJiNJCkTTdgm5FD5Q1o9cR3grG0rhlNbh8sJoNmZFTI6SKiJiPZgvz0wOmReOu6jgaV6Htl0Wm57pBmM6M4K9CEN169rj1nHOB5oGdmErIS0KtOr6TZzEI7oP1xRrtYlGtAfhqSLappias4MlMswn0R78EGFuUaVJhGp6u7Qc/MJOSkWuDx8XGn3lk918B87dhCG9+CkAyWYoy3ruuwcHKR6la6y+CC7qUYd56uAwCM7pWZsDHple4W0+85E1joR1BqsduM6JEBIP66LlZEn4gG5nqG4ziM7JkBANhVWh/Xe4RSi9pZL8jpImKiu8X07OajFEr3CdV1xbfQM1uMLs5I0Ij0C/t7jtfp2h2MdI0ILlJE/AwX6rrijXQFbMgOSBDxMyo4t+yO0+k6oLEieoCcLiJGmDJ9vE7X1pOB6MpFfSi60l2643TxPI+dp+sBAKN7ZSRwVPpkqOB0xb7Q8zyPvWcp0pUoRgRPHO6NI9LF87yQlqQi+u4zKji3xB/pCqwzWimiB8jpImJEiHRVNMTc9qTc0Yqz9S0wcJTSSgQs5H6kohGeGNsBlda2oKbJDYvRQFHHBMBSUSeqm9AU4yGT0toW1Dd7YDEaBP01In6YzMPp2mbUN8d2sKHc2YqaJjeMYQLERPywyO3p2mbUNLpiem19s1s46DNYQ3MUOV1ETPTLS4XRwKG2yR1z25Ntp2oBBHYtqVYqFu4uxZnJSLEY4fb5Y27NtLM0EHEcUpQOq4kONHSX3DQr8tOt4PnYI48stTi4MA0WE03J3cWeFDrYEGu0i+lz9c9LpYM+CcCeZBZOHe6OUcaDRbl6ZiYh3aadtlh0hxMxYTMbhRTIpmM1Mb12m5BazEr4uPSIwcBhUJwpRkotJp54i+n3UD1Xwhke/LfcE2Ndl6BET6KoCYPVde0qjc0WWqznAsjpIuJg4gXZAIBvj1XH9DoW6RrTm1KLiYKlGHfHOKHRycXEE29d1+6gYzCc6rkShlDXFaPTtf8ctf9JNKMFp6s+ptcdDOu5qCXI6SJiZuIFOQCAb4/WRF3X1ejyCporY6mIPmGM7xtwgDcerYr6Na0enxCNoZOLiWNoHCcYfX5eiK6MpEhXwhgWZzE9Sy9SpCtxjAw7wRhLHfC2k4FNutYONJDTRcTMmN6ZsJgMKHe2Rl1LtOt0Pfw80CMjCYX2JJFHqB8u7ZcDAwccrmjEuWDRaVfsP+eA188jJ9WKnplki0TB0ouHKxqi7thwvKoRzW4fki1GasWUQJjcw9n6lqgLuKsbXSh3toLjtHVaTm4GFaTDYjLA0eKJer04Ud2EkzXNMBs5jA9mVrQCOV1EzNjMRowJpqW+jbKua2tw10JRrsSSkWwRdpIbjkQX7Qqv5+I4TqSR6Y+emUnonZ0Mj4/HxihtwVKLw4rsMBrIFokizRYq4I422sXmsgF5aUihgz4Jw2IyCOnaaIvp1x2qBBCo/9XaoStyuoi4iLWua/upQA3RWCqiTziX9c8FAHx9OHani0gcHMdhyuB8AMCaA5VRvYaJRlI9V+Jh6drNx2ujuv6z/eUAgCsH54k1JN0yqjiw2d4VnHu6Yu2hwFx2xUDt2YKcLiIuJvYLOF2bjtXA7+88T+/1+YXC7bFURJ9wJg8MOF0bj1TDG4VeFytoHUX1XAmHOV1rD1XC18V94ffz+PJgBQDg4hLajCQa5jyt2lvWZS2Ry+vDuu8DjvK0oQWij01vjCwObCp2RlFM3+L2YfPxQNTx8uDcpiXI6SLiYkTPDKRYjKhr9uD7LtTpvy9vQJPbhzSbSejdSCSOkT0zYE8yw9nq7TJ8X1rbLAjUkkRB4hnbJxP2JDNqm9zCRqMjdpyuwzlHK1KtJkweoL3FRW5+MCgPNrMBp2ubuzzc8O2xGjS5fchPtwonH4nEwWSC9p51dFl7uul4NdxeP3pkJGmyzpGcLiIuzEaDsDvvKsXITqFc2CuT6lZEwGjgcGn/wInSrw93bosVO84ACJx61FqthBIwGw3C7nxNMIrVER/vPgcAmDY0n4Q4RSDZYsIPBgWiXZ/sLev02s/3B2w1dUg+DDRHJZyijCSMK8kCzwP/3nW202vXBVOLlw/M1WTNKTldRNwI0hFdFNN/vCcw4Y3rSykUsWCRks7quvx+Hh9uCzhdsy4qlmRceoSlGL840LHT5fX5BUfgupFFkoxLj1wzvBAA8MmejlOMfj+PNUFbTRtCqUWxuOnCngCAFdvPdGgLnuexNlhEr8V6LoCcLqIbTAgW0285XtNh7789Z+qx/VQdzEYON4/pKeXwdAUrpt9zph51Te33m9t0vAZn61uQZjNhOtWtiMbkgbkwGTgcq2rq8Ij8lhO1qG50IyPZjEv75Ug8Qv0QTYpxZ2kdqhtdSLOaBN07IvFcPbwANrMBx6qaOuwUcLy6CaW1LbAYDULdsNYgp4uImyGF6chMNqPJ7cPqfeXtXrP0m5MAgBkjipCXZpNwdPqiwG7DoII08Dyw8Wj7KcYPtpUCAH44qojSWSKSbjMLUd0vO0gxstTi1cMKYTbSNCwWyRaTEDHpKMXIUotXDMqj3pcikmYzC5u9fwXLHM5nbfAww7i+WUi2aLP8gf7CiLgxGDjcObEEAPDnzw+1iXZVNrTi4z2BxeXOiX2kHp7uuCyYYvywnfC9o9mDT4OO8cyxlFoUm5B0RFuny+31C7a4nlKLonPtiI5TjDzPC1IR04bmSz42vXFjMMX40e5zcHsj1wue5/F58H65XKOpRYCcLqKb3DWpBDmpVpyqacb7352OeO79LaXw+Hhc2CtDEPAkxGPWRcWwGA1Yf7gKHwUjKYyP9gQmuUEFaRhOp7NEhzldW0/WCm1+GBuOVMHR4kFempWkIiSgsxTjnjMOnKxphsVooBOkEnBpvxzkpVlR1+wRarcYK3eexXcnamEycJg2RLsOsGqcrieeeAITJ05EcnIyMjIyonoNz/N49NFHUVRUhKSkJFx++eXYv39/xDUulwu//OUvkZOTg5SUFFx//fU4c6b90CfRlhSrCfdN6Q8AeO6LI0L7E7fXj3e3nAIA3HlJiWzj0xMX5Kbilz/oBwB47OMDqA2r7fowmFq8ZWyxJk8EKY3irGRMGZwPPw/8/J3tgi1aPT68vvEEgEAEhk7zik94inHxpwfR4vYBACqdrZj/3g4AwJQheUizmWUbo14wGjjcMLoHAAiHeoBAu6bf/yewNi+Y0h/FWcmyjE8KVON0ud1u3HLLLfjf//3fqF/z9NNP45lnnsGLL76IrVu3oqCgAFOnTkVDQ0hXasGCBVi5ciWWLVuGjRs3orGxETNmzIDP5xPja2iSWy8qRklOCmqa3Hh1/XEcq2rEs18cRlWDC/npVlw9jIq2peLnky/AoII01Da58fjH+1Fa24wFy3ZizxkHzEYOPxpF6Syp+MvMkeiTnYyz9S245x87UOZowaxXN+PbYzUwGzk6QSohd0++AElmI745WoOfvLEFFc5W/OytrThb34KSnBQ88aPhcg9RN9wUPFD1xcEK/O+721HhbMWDH+xGg8uL0b0ycPfkC2QeobhwfCxtvxXA0qVLsWDBAtTX13d6Hc/zKCoqwoIFC/CrX/0KQCCqlZ+fj6eeego///nP4XA4kJubi3feeQezZs0CAJw7dw7FxcVYtWoVpk+fHtWYnE4n7HY7HA4H0tP12Sh11d4yYdcYzv9NH4hfXNFPhhHpl92l9bjhpW/g5wGzkYPHF7jFF0zpjwVTBsg8On1xuKIBN/z1GzS5fbCaDHB5/chINuPlO8bQSTmJ2X6qFne+uRUNrV7BFtkpFvxr/kT0zk6Re3i64q9rj+LZNYfh9fOwGA1w+/xIMhvx6X2T0CdHWltIvX6rJtIVKydOnEB5eTmmTZsmPGa1WjF58mR8++23AIDt27fD4/FEXFNUVIRhw4YJ17SHy+WC0+mM+NE7Vw8rEFr8WEwB4dRfXTUIP7+sr8wj0x8jizMw59JAStfj43Fpvxz895eXksMlAwPy0/CXmSMBAC6vH31zUrBy/iXkcMnAmN5ZeH/ueGSlWODy+mE1GfDa/4wlh0sGfnFFP3x0z6UY3sMOd/AA1m+vHSy5wyUH2jyTCaC8PHAiJT8/siAvPz8fp06dEq6xWCzIzMxscw17fXssXrwYjz32WIJHrG44jsPSn12Mk9VN6J+fCquJJAnk5MHpA1FgT8LA/DRBrZ6Qh6uGFeLPt4zEvrMO3D9lAOzJVDskF8N62PHBzyfgpbVHceOFPXFhL+oFKxdDitKxcv5ELN9WCpfHj9vH9ZJ7SJIga6Tr0UcfBcdxnf5s27atW59xftEwz/NdFhJ3dc2iRYvgcDiEn9LS0m6NUSukWk0Y1sNODpcCsJqMmHNpCTlcCuHmMT3x6PVDyeFSAP3yUvHMrFF0bygAk9GA28f1xs8uLdHNAR9ZI1333HMPbr311k6v6dOnT1zvXVAQKN4uLy9HYWGh8HhlZaUQ/SooKIDb7UZdXV1EtKuyshITJ07s8L2tViusVmtc4yIIgiAIQp/I6nTl5OQgJ0ec3UZJSQkKCgqwZs0ajB49GkDgBOTXX3+Np556CgAwZswYmM1mrFmzBjNnzgQAlJWVYd++fXj66adFGRdBEARBEPpENTVdp0+fRm1tLU6fPg2fz4ddu3YBAPr164fU1FQAwKBBg7B48WLccMMN4DgOCxYswJNPPon+/fujf//+ePLJJ5GcnIzbbrsNAGC32zFnzhw88MADyM7ORlZWFh588EEMHz4cU6ZMkeurEgRBEAShQVTjdP3ud7/DW2+9JfzOoldr167F5ZdfDgA4dOgQHI6Q+vNDDz2ElpYWzJ8/H3V1dRg3bhw+//xzpKWlCdc8++yzMJlMmDlzJlpaWnDllVdi6dKlMBqpLokgCIIgiMShOp0uJUI6XQRBEAShPkiniyAIgiAIQoOQ00UQBEEQBCEB5HQRBEEQBEFIADldBEEQBEEQEkBOF0EQBEEQhASQ00UQBEEQBCEB5HQRBEEQBEFIADldBEEQBEEQEkBOF0EQBEEQhASopg2QkmGi/k6nU+aREARBEAQRLWzdlqo5DzldCaCmpgYAUFxcLPNICIIgCIKIlZqaGtjtdtE/h5yuBJCVlQUAOH36tCRGIzrG6XSiuLgYpaWl1AdTZsgWyoLsoRzIFsrB4XCgV69ewjouNuR0JQCDIVAaZ7fb6QZSCOnp6WQLhUC2UBZkD+VAtlAObB0X/XMk+RSCIAiCIAidQ04XQRAEQRCEBJDTlQCsVit+//vfw2q1yj0U3UO2UA5kC2VB9lAOZAvlILUtOF6qc5IEQRAEQRA6hiJdBEEQBEEQEkBOF0EQBEEQhASQ00UQBEEQBCEB5HQRBEEQBEFIADld7bB48WJwHIcFCxYIj1VUVODOO+9EUVERkpOTcdVVV+HIkSMRrzt27BhuuOEG5ObmIj09HTNnzkRFRUXENX369AHHcRE/v/71r6X4WqpETFsAwCeffIJx48YhKSkJOTk5uPHGG8X+SqpFLFusW7euzT3BfrZu3SrV11MVYt4Xhw8fxg9/+EPk5OQgPT0dl1xyCdauXSvF11ItYtpjx44dmDp1KjIyMpCdnY158+ahsbFRiq+lCh599NE280ZBQYHwPM/zePTRR1FUVISkpCRcfvnl2L9/f8R7uFwu/PKXv0ROTg5SUlJw/fXX48yZMxHX1NXVYfbs2bDb7bDb7Zg9ezbq6+tjHi85XeexdetWvPrqqxgxYoTwGM/z+NGPfoTjx4/jP//5D3bu3InevXtjypQpaGpqAgA0NTVh2rRp4DgOX331Fb755hu43W5cd9118Pv9EZ/x+OOPo6ysTPh5+OGHJf2OakFsW6xYsQKzZ8/GT3/6U+zevRvffPMNbrvtNsm/pxoQ0xYTJ06MuB/Kyspw1113oU+fPhg7dqws31fJiH1fXHvttfB6vfjqq6+wfft2jBo1CjNmzEB5ebnk31UNiGmPc+fOYcqUKejXrx+2bNmC1atXY//+/bjzzjvl+KqKZejQoRHzx969e4Xnnn76aTzzzDN48cUXsXXrVhQUFGDq1KloaGgQrlmwYAFWrlyJZcuWYePGjWhsbMSMGTPg8/mEa2677Tbs2rULq1evxurVq7Fr1y7Mnj079sHyhEBDQwPfv39/fs2aNfzkyZP5++67j+d5nj906BAPgN+3b59wrdfr5bOysvjXXnuN53me/+yzz3iDwcA7HA7hmtraWh4Av2bNGuGx3r17888++6wk30fNiG0Lj8fD9+jRg//73/8u3ZdSKVLcF+G43W4+Ly+Pf/zxx8X7UipFbFtUVVXxAPj169cL1zidTh4A/8UXX0jwDdWF2PZ45ZVX+Ly8PN7n8wnX7Ny5kwfAHzlyRIJvqHx+//vf8yNHjmz3Ob/fzxcUFPB//OMfhcdaW1t5u93Ov/zyyzzP83x9fT1vNpv5ZcuWCdecPXuWNxgM/OrVq3me5/kDBw7wAPjNmzcL12zatIkHwH///fcxjZciXWH84he/wLXXXospU6ZEPO5yuQAANptNeMxoNMJisWDjxo3CNRzHRQis2Ww2GAwG4RrGU089hezsbIwaNQpPPPEE3G63WF9JtYhtix07duDs2bMwGAwYPXo0CgsLcfXVV7cJOxPS3ReMjz76CNXV1bSbbwexbZGdnY3Bgwfj7bffRlNTE7xeL1555RXk5+djzJgxYn891SG2PVwuFywWS0RfwKSkJADo8P7RI0eOHEFRURFKSkpw66234vjx4wCAEydOoLy8HNOmTROutVqtmDx5Mr799lsAwPbt2+HxeCKuKSoqwrBhw4RrNm3aBLvdjnHjxgnXjB8/Hna7XbgmWsjpCrJs2TLs2LEDixcvbvPcoEGD0Lt3byxatAh1dXVwu9344x//iPLycpSVlQEIGCAlJQW/+tWv0NzcjKamJvzf//0f/H6/cA0A3HfffVi2bBnWrl2Le+65B0uWLMH8+fMl+55qQApbsJvy0UcfxcMPP4z//ve/yMzMxOTJk1FbWyvdl1U4Ut0X4bz++uuYPn06iouLRf1uakMKW3AchzVr1mDnzp1IS0uDzWbDs88+i9WrVyMjI0PKr6t4pLDHD37wA5SXl+NPf/oT3G436urq8Jvf/AYAOrx/9Ma4cePw9ttv47PPPsNrr72G8vJyTJw4ETU1NUJKPD8/P+I1+fn5wnPl5eWwWCzIzMzs9Jq8vLw2n52Xlxdz2p2cLgClpaW477778O6770bsTBhmsxkrVqzA4cOHkZWVheTkZKxbtw5XX301jEYjACA3NxcffvghPv74Y6SmpsJut8PhcODCCy8UrgGA+++/H5MnT8aIESNw11134eWXX8brr7+Ompoayb6vkpHKFqxm4re//S1uuukmjBkzBm+++SY4jsOHH34o3RdWMFLeF4wzZ87gs88+w5w5c0T/fmpCKlvwPI/58+cjLy8PGzZswHfffYcf/vCHmDFjBi3yYUhlj6FDh+Ktt97CX/7yFyQnJ6OgoAB9+/ZFfn5+u/ePHrn66qtx0003Yfjw4ZgyZQo++eQTAMBbb70lXMNxXMRreJ5v89j5nH9Ne9dH8z7tvUj3rFy5kgfAG41G4QcAz3EcbzQaea/XK1xbX1/PV1ZW8jzP8xdffDE/f/78Nu9XVVXF19XV8TzP8/n5+fzTTz/d4WefOXOmTa5Yz0hli6+++ooHwG/YsCHi+osvvpj/zW9+I9K3Uxdy3BePP/44n5uby7vdbnG+lEqRyhZffPFFmzojnuf5fv368YsXLxbp26kPOe6N8vJyvqGhgW9sbOQNBgP/wQcfiPPlNMCUKVP4u+++mz927BgPgN+xY0fE89dffz3/k5/8hOd5nv/yyy95AHxtbW3ENSNGjOB/97vf8TzP86+//jpvt9vbfI7dbuffeOONmMZGThcfKBTdu3dvxM/YsWP5O+64g9+7d2+7rzl8+DBvMBj4zz77rMP3/fLLL3mO4zottPv44495APypU6e6/T20gFS2cDgcvNVqjSikZwXcr7zySmK/lEqR+r7w+/18SUkJ/8ADDyT0e2gBqWzx0Ucf8QaDgW9oaIi4bsCAAfwTTzyRuC+kcuRcM15//XU+OTlZcNKISFpbW/kePXrwjz32mFBI/9RTTwnPu1yudgvply9fLlxz7ty5dgvpt2zZIlyzefPmuArpyenqgPCTKDzP8x988AG/du1a/tixY/y///1vvnfv3vyNN94Y8Zo33niD37RpE3/06FH+nXfe4bOysviFCxcKz3/77bf8M888w+/cuZM/fvw4v3z5cr6oqIi//vrrpfpaqkQMW/A8z9933318jx49+M8++4z//vvv+Tlz5vB5eXltdjxECLFswfOBKAsA/sCBA2J/DU0ghi2qqqr47Oxs/sYbb+R37drFHzp0iH/wwQd5s9nM79q1S6qvpkrEujdeeOEFfvv27fyhQ4f4F198kU9KSuKfe+45Kb6SKnjggQf4devW8cePH+c3b97Mz5gxg09LS+NPnjzJ8zzP//GPf+Ttdjv/r3/9i9+7dy//4x//mC8sLOSdTqfwHnfffTffs2dP/osvvuB37NjB/+AHP+BHjhwZEbG86qqr+BEjRvCbNm3iN23axA8fPpyfMWNGzOMlp6sDzr+BnnvuOb5nz5682Wzme/XqxT/88MO8y+WKeM2vfvUrPj8/nzebzXz//v35v/zlL7zf7xee3759Oz9u3DjebrfzNpuNHzhwIP/73/+eb2pqkuprqRIxbMHzgcjWAw88wOfl5fFpaWn8lClTIo54E20RyxY8z/M//vGP+YkTJ4r9FTSDWLbYunUrP23aND4rK4tPS0vjx48fz69atUqKr6RqxLLH7Nmz+aysLN5isfAjRozg3377bSm+jmqYNWsWX1hYyJvNZr6oqIi/8cYb+f379wvP+/1+/ve//z1fUFDAW61W/rLLLmsTjWxpaeHvuecePisri09KSuJnzJjBnz59OuKampoa/vbbb+fT0tL4tLQ0/vbbb48r2sjxPM/HVgVGEARBEARBxAqdXiQIgiAIgpAAcroIgiAIgiAkgJwugiAIgiAICSCniyAIgiAIQgLI6SIIgiAIgpAAcroIgiAIgiAkgJwugiAIgiAICSCniyAIgiAIQgLI6SIIQnM88sgjmDdvntzD6JIXX3wR119/vdzDIAhCIkiRniAI1XL55Zdj1KhRWLJkifBYRUUF+vfvjz179qBPnz6yjS0aXC4X+vTpgw8//BCXXnqp3MMhCEJkKNJFEISmeP311zFhwgTZHS6fzwe/39/pNVarFbfddhteeOEFiUZFEISckNNFEIQqufPOO/H111/jueeeA8dx4DgOJ0+exLJlyyJSdm+//Tays7PhcrkiXn/TTTfhJz/5ifD7xx9/jDFjxsBms6Fv37547LHH4PV6heefeeYZDB8+HCkpKSguLsb8+fPR2NgoPL906VJkZGTgv//9L4YMGQKr1YpTp05h3bp1uPjii5GSkoKMjAxccsklOHXqlPC666+/Hv/+97/R0tIixj8TQRAKgpwugiBUyXPPPYcJEyZg7ty5KCsrQ1lZGdLS0rBv3z6MHTtWuO6WW26Bz+fDRx99JDxWXV2N//73v/jpT38KAPjss89wxx134N5778WBAwfwyiuvYOnSpXjiiSeE1xgMBjz//PPYt28f3nrrLXz11Vd46KGHIsbU3NyMxYsX4+9//zv279+PrKws/OhHP8LkyZOxZ88ebNq0CfPmzQPHccJrxo4dC4/Hg++++06sfyqCIJQCTxAEoVImT57M33fffcLvO3fu5AHwp0+fjrjuf//3f/mrr75a+H3JkiV83759eb/fz/M8z0+aNIl/8sknI17zzjvv8IWFhR1+9gcffMBnZ2cLv7/55ps8AH7Xrl3CYzU1NTwAft26dZ1+j8zMTH7p0qWdXkMQhPoxyezzEQRBJAyWorPZbBGPz507FxdddBHOnj2LHj164M0338Sdd94pRJy2b9+OrVu3RkS2fD4fWltb0dzcjOTkZKxduxZPPvkkDhw4AKfTCa/Xi9bWVjQ1NSElJQUAYLFYMGLECOE9srKycOedd2L69OmYOnUqpkyZgpkzZ6KwsDBifElJSWhubhbl34QgCOVA6UWCIDRDTk4OAKCuri7i8dGjR2PkyJF4++23sWPHDuzduxd33nmn8Lzf78djjz2GXbt2CT979+7FkSNHYLPZcOrUKVxzzTUYNmwYVqxYge3bt+Ovf/0rAMDj8Qjvk5SUFJE6BIA333wTmzZtwsSJE7F8+XIMGDAAmzdvjrimtrYWubm5ifynIAhCgVCkiyAI1WKxWODz+YTfL7jgAqSnp+PAgQMYMGBAxLV33XUXnn32WZw9exZTpkxBcXGx8NyFF16IQ4cOoV+/fu1+zrZt2+D1evGXv/wFBkNgr/rBBx9EPc7Ro0dj9OjRWLRoESZMmIB//OMfGD9+PADg2LFjaG1txejRo6N+P4Ig1AlFugiCUC19+vTBli1bcPLkSVRXVwMApkyZgo0bN7a59vbbb8fZs2fx2muv4Wc/+1nEc7/73e/w9ttv49FHH8X+/ftx8OBBLF++HA8//DCAgDPn9Xrxwgsv4Pjx43jnnXfw8ssvdzm+EydOYNGiRdi0aRNOnTqFzz//HIcPH8bgwYOFazZs2IC+ffviggsu6M4/BUEQKoCcLoIgVMuDDz4Io9GIIUOGIDc3F6dPn8a8efOwbNmyNhpZ6enpuOmmm5Camoof/ehHEc9Nnz4d//3vf7FmzRpcdNFFGD9+PJ555hn07t0bADBq1Cg888wzeOqppzBs2DC89957WLx4cZfjS05Oxvfff4+bbroJAwYMwLx583DPPffg5z//uXDN+++/j7lz53b/H4MgCMVDivQEQWgKnucxfvx4LFiwAD/+8Y8jnps6dSoGDx6M559/XqbRRbJv3z5ceeWVOHz4MOx2u9zDIQhCZCjSRRCEpuA4Dq+++mqEsGltbS2WLVuGr776Cr/4xS9kHF0k586dw9tvv00OF0HoBIp0EQShefr06YO6ujo88sgjePDBB+UeDkEQOoWcLoIgCIIgCAmg9CJBEARBEIQEkNNFEARBEAQhAeR0EQRBEARBSAA5XQRBEARBEBJAThdBEARBEIQEkNNFEARBEAQhAeR0EQRBEARBSAA5XQRBEARBEBLw/wEiuYJSkU105wAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# last 5 of 5000 years\n",
"plt.plot(sol.t, sol.y[0])\n",
"plt.xlim([4995,5000]);\n",
"plt.xlabel('t(years)')\n",
"plt.ylabel('x(Earth-Sun distance)');"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "bee0c4fa",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Eart's orbit for 5000 years\n",
"fig, ax = plt.subplots(1,1)\n",
"ax.set_title('Earts orbit over 5000 years')\n",
"ax.plot(sol.y[0],sol.y[1],lw=0.1)\n",
"ax.set_aspect('equal', adjustable='box')"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "2f81e4f4",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": []
},
{
"cell_type": "code",
"execution_count": 32,
"id": "5edbc1a0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": []
},
{
"cell_type": "code",
"execution_count": 34,
"id": "26c12b88",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": []
},
{
"cell_type": "code",
"execution_count": 36,
"id": "68a6e8f8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "62db569b",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.18"
}
},
"nbformat": 4,
"nbformat_minor": 5
}