06_Hyperbolic_PDEs.ipynb

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    "from IPython.display import HTML\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
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    "![title](figs/title.png)\n",
    "\n",
    "<h1><center>Module 10: Numerical Solutions to Hyperbolic PDEs</center></h1>\n",
    "\n",
    "This module focuses on generating numerical solutions of **hyperbolic** partial differential equations (PDEs).  Recall that these types of second-order PDEs\n",
    "\n",
    "$$Au_{xx}+2Bu_{xy}+Cu_{yy}+Du_{x}+Eu_{y}+Fu+G=0 \\tag{1}$$\n",
    "\n",
    "are defined by the condition $B^2-AC > 0$ (where $y$ is considered the $t$ variable and thus $A=1$, $C=-\\frac{1}{c}$ and all others are equal 0).\n",
    "\n",
    "Three interesting examples (with increasing complexity) are the following:\n",
    "\n",
    "   * **Acoustic wave equation (Homogeneous medium)**: The acoustic wave equation (AWE) is normally used to model the pressure disturbance $\\phi=\\phi(x,y,z,t)$ generated by an acoustic wave propagation through a fluid medium defined by constant velocity $v=\\sqrt{\\frac{K}{\\rho}}$ where $K$ is the bulk compressibility and $\\rho$ is the density.\n",
    "   \n",
    "$$\\frac{\\partial^2 \\phi}{\\partial t^2} - v^2\\nabla^2 \\phi = F(x,y,z,t) \\tag{2}$$ \n",
    "\n",
    "where $F(x,y,z,t)$ is an external force term.  Note that the acoustic wave equation is commonly used in exploration seismology to approximate compressional (i.e., P-wave) propagation through complex heterogeneous media.\n",
    "   \n",
    "   * **Acoustic wave equation (variable density)**: This is like the example above, except now that the density, $\\rho$, is assumed to spatially vary:\n",
    "\n",
    "$$\\frac{\\partial^2 \\phi}{\\partial t^2}  -  K \\nabla \\cdot \\left(\\frac{1}{\\rho} \\nabla \\phi  \\right) = F(x,y,z,t), \\tag{3}$$ \n",
    "   \n",
    "where $K$ is the bulk compressability.  This equation is commonly used in computational ocean acoustics because it allows one to introduce variations in density caused by temperature and salinity concentration among others.  This wave equation requires the same type of initial and boundary conditions as the homogenous equation above.\n",
    "\n",
    "\n",
    "   * **One-way wave equations**:  We have actually looked at this hyperbolic equation in Module 7 of the course. One can recognize this to be the case if we **factorize** the 1D AWE given above in the following way\n",
    "   \n",
    "$$\\left[\\frac{\\partial^2 }{\\partial t^2} - v^2\\frac{\\partial}{\\partial x^2} \\right] \\phi = \n",
    "\\left(\\frac{\\partial }{\\partial t}-v \\frac{\\partial}{\\partial x} \\right)\\left( \\frac{\\partial }{\\partial t}+v \\frac{\\partial}{\\partial x}\\right) \\phi = F(x,t). \\tag{4}$$ \n",
    "Here we see that we have the produce of the left- and right-going advection equations. This was recognized in 1747 by French scientist [d'Alembert](https://en.wikipedia.org/wiki/D%27Alembert%27s_formula).  Note that one sometimes see the **d'Alembert operator** $\\Box^2$ in various problems in mathematical physics, which is given by the following in Cartesian coordinates:\n",
    "\n",
    "$$\\Box^2 \\phi = \\left[\\frac{\\partial^2 }{\\partial t^2} - v^2\\frac{\\partial}{\\partial x^2} \\right] \\phi\\tag{5}$$\n",
    "\n",
    "### Initial and Boundary Conditions\n",
    "\n",
    "Because this is a **second-order** temporal partial derivative, uniquely defining a wavefield solution requires implementing **two initial conditions** that define the wavefield at, say, time zero: \n",
    "\n",
    "$$\\phi(x,y,z,t=0)=f(x,y,z) \\tag{6}$$ \n",
    "\n",
    "as well as its derivative. \n",
    "\n",
    "$$\\frac{\\partial \\phi}{\\partial t}(x,y,z,t=0) = g(x,y,z).\\tag{7}$$\n",
    "\n",
    "One also has to prescribe the behavior of the wavefield solution on the domain boundary $D$ (e.g., $\\left. \\phi\\right|_{\\partial D}=B(x,y,z)$). In some circumstances, one may want to apply a Dirchelet BC\n",
    "\n",
    "$$ \\phi(\\mathbf {x}) = f(\\mathbf {x}), \\quad \\forall \\mathbf {x}\\in \\delta \\Omega \\tag{8}$$\n",
    "\n",
    "where one sets $f(x)=0$ to obtain an inward moving reflected wave with the oppositing polarity. This is commonly used for waves approaching the free surface of a fluid acoustic medium.  However, in most other circumstances one wants to have perfectly absorbing boundary conditions such that no energy is reflected back into the finite-sized computational domain. These are the so-called (Sommerville) radiation boundary conditions which require the wave disturbance to vanish at infinity in an unbounded medium.  This topic, though, remains an active area of research and goes well beyond the scope of this course."
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    "# 1D Acoustic wave equation\n",
    "\n",
    "Let's first look at the problem of an acoustic wave propagating on a 1D medium.  Because of the easy connection with everyday experience, let's assume examine the propagation of a wave on a homogeneous taut string of length $L$ where both of the string ends and fixed. In this case, we can assume that there is no external forcing function (i.e., $F(x,t)=0$) and the string starts from some combination of an initial displacement disturbance $\\phi(x,t=0) = f(x)$ and an initial velocity $\\frac{\\partial \\phi}{\\partial t}(x,t=0) = g(x)$. Thus, the PDE we are solving is\n",
    "\n",
    "$$\\frac{\\partial^2 \\phi}{\\partial t^2} = v^2\\frac{\\partial^2 \\phi}{\\partial x^2}. \\tag{9}$$ \n",
    "\n",
    "Let's now look at an **explicit** discretization method to solve equation 9 (as opposed to the **implicit** ones like Crank-Nicolson approach we studied in Module 9).  Let's start by using a standard **centered in time centered in space** (CTCS) $\\mathcal{O}(\\Delta x^2,\\Delta t^2)$ discretization:\n",
    "\n",
    "$$\\frac{\\phi^{n+1}_i - 2\\phi^{n}_i +\\phi^{n-1}_i}{\\Delta t^2} = \n",
    "v^2 \\left( \\frac{\\phi^{n}_{i+i} - 2\\phi^{n}_i +\\phi^{n}_{i-1}}{\\Delta x^2} \\right). \\tag{10}$$\n",
    "\n",
    "Let's now multiply through by $\\Delta t^2$ and use the square of the Courant number $C^2 = \\frac{v^2\\Delta t^2}{\\Delta x^2}$ from the previous modules to write:\n",
    "\n",
    "$$\\phi^{n+1}_i - 2\\phi^{n}_i +\\phi^{n-1}_i = C^2 \\left( \\phi^{n}_{i+i} - 2\\phi^{n}_i +\\phi^{n}_{i-1}\\right). \\tag{11}$$\n",
    "\n",
    "Rearranging terms to isolate the unknown quantity at time step $n+1$ on the left-hand side and keeping the known quantities on the right-hand side leads to:\n",
    "\n",
    "$$\\phi^{n+1}_i = 2\\phi^{n}_i -\\phi^{n-1}_i +C^2 \\left(\\phi^{n}_{i+i} -2 \\phi^{n}_i + \\phi^{n}_{i-1}\\right). \\tag{12}$$\n",
    "\n",
    "You may note that one could combine the $\\phi^n_i$ terms into a more compact stencil. However, I am avoiding doing this because we will look at higher-order  finite-difference expansions of the spatial second partial derivative in sections below \n",
    "\n",
    "### Initial Conditions\n",
    "\n",
    "Above we noted that two initial conditions are required for this PDE because of the second temporal derivative. However, based on the above discretization it may not be apparent how the derivative initial condition can be introduced.  One thing to note is that the discretization now contains term $\\phi^{n-1}_i$, which represents the wavefield at the previous time step. Thus, this can be used to set the second condition by:\n",
    "\n",
    "$$\\frac{\\partial \\phi}{\\partial t} \\approx \\frac{\\phi^n_i - \\phi^{n-1}_i}{\\Delta t} = g(x).  \\tag{13}$$\n",
    "\n",
    "The common assumption is that the wavefield is **quiescent** (i.e., no energy) at time steps $n=0$ and $n=-1$. This means that $g(x)=0$ in equation 13 and thus $\\phi^0_i=\\phi^{-1}_i=0$.  However, in cases where we have $g(x)\\neq 0$ then we can use a  finite-difference approximation to specify the wavefield at the previous time step as\n",
    "\n",
    "$$\\phi^{n-1}_i = \\phi^n_i-\\Delta t g(x).\\tag{14}$$\n",
    "\n",
    "Alternatively, it may also be possible that $\\phi^{n-1}_i$ is known analytically and can just be stated (e.g., it is a translation of the waveform at $\\phi^n_i$.\n",
    "\n",
    "### Handling Boundaries with Ghost Points\n",
    "\n",
    "We can also explore what happens at the left and right boundaries from equation 12.  At the left hand boundary (i.e., $i=0$) we can write\n",
    "\n",
    "$$\\phi^{n+1}_1 = 2\\phi^{n}_1 -\\phi^{n-1}_1 +C^2 \\left(\\phi^{n}_{2} -2 \\phi^{n}_1 + \\phi^{n}_{0}\\right). \\tag{14}$$\n",
    "\n",
    "Note that there is a $ \\phi^{n}_{0}$ term in this equation.  Currently, we are able to handle this because we can use the Dirchelet boundary condition to set this point equal to zero.  However, if we were to use higher-order finite-difference stencils for our second derivative, these would require using additional points such as $\\phi^n_{-1}$ which represent a point falling out of the grid! Let's assume that we can set $ \\phi^{n}_{-1}=0$ (as well those with an increasing negative index).  This is termed using **ghost points** which are not formally defined, but are conjured up for numerical expediency.  Similarly, on the right-hand side we will have to do the same at ghost point $ \\phi^{n}_{N+1}=0$ as well as those with greater indices.\n",
    "\n",
    "## 1D AWE Solver\n",
    "\n",
    "Given this machinary, we can now adapt the types of solvers we constructed in the previous modules to the current scenario. Let's first build a 1D AWE solver of $\\mathcal{O}(\\Delta x^2,\\Delta t^2)$ that is appropriate for homogeneous medium where $v$=const."
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    "def awe_explicit_solver_homogeneous_2nd_order(Wo,Wm,dx,dt,v):\n",
    "    '''Set up second-order solver of the acoustic wave equation\n",
    "    usage: U = awe_explicit_solver_homogeneous(Wo,Wm,dx,dt,v)\n",
    "    input: \n",
    "        Wo: Acoustic pressure vector (nx) at time step n\n",
    "        Wm: Acoustic pressure vector (nx) at time step n-1\n",
    "        dx: Spatial sampling (float)\n",
    "        dt: Temporal sampling (float)\n",
    "        v : Homogeneous propagation velocity (float)\n",
    "    output:\n",
    "        Wm: Acoustic pressure vector (nx) at time n+1\n",
    "    dependencies:\n",
    "        None\n",
    "    written by Jeff Shragge, jshragge@mines.edu, 10/2019\n",
    "    '''        \n",
    "    ## . . Get dimensions of wavefield\n",
    "    nx = len(Wo)\n",
    "    \n",
    "    ## . . Define Courant number (squared)\n",
    "    C2 = (v*dt/dx)**2\n",
    "        \n",
    "    ## . . Update solution. Note that I am overwriting Wm because this wavefield\n",
    "    ## . . isn't needed after this calculation!\n",
    "    Wm[1:nx-1] = 2*Wo[1:nx-1]-Wm[1:nx-1]+C2*(Wo[2:nx]-2*Wo[1:nx-1]+Wo[0:nx-2])\n",
    "\n",
    "    return Wm ## . . Return updated wavefield at time step n+1"
   ]
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   "source": [
    "Let's now build up a scenario that we are trying to model.  I will assume that the length of the region to be modeled is $L=1000$ mm, that is discretized into $nx=201$ (and thus $\\Delta x = 5$ mm segments), and the velocity is $v=1000$ mm/s. "
   ]
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    "## . . Define spatial grid\n",
    "L  = 1000               # . . String length (mm)\n",
    "nx = 201                # . . Number of points in discretization \n",
    "dx = L/(nx-1)           # . . Discretization interval\n",
    "x = np.linspace(0,L,nx) # . . Xline\n",
    "v  = 1000               # . . Velocity (mm/s)"
   ]
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    "Let's now define the time stepping conditions.  Because we have define our $\\Delta x$ and $v$, we know that we need to obey the following Courant condition for stability (usually called the CFL condition):\n",
    "\n",
    "$$C \\equiv \\frac{v \\Delta t}{\\Delta x} \\le 1. \\tag{15}$$\n",
    "\n",
    "Thus, let's be a bit conservative and choose $C=0.5$.  Thus, we can set our $\\Delta t$ time step parameter to satisfy the CFL condition:\n",
    "\n",
    "$$ \\Delta t = \\frac{0.8\\Delta x}{v} = \\frac{0.8 \\times 5 {\\rm mm}}{1000 {\\rm mm/s}} = 0.004 {\\rm ms}. \\tag{16}$$\n",
    "\n",
    "We also want to define our two initial conditions, which we we assume to have the shape of a stationary Ricker wavelet with no prior velocity:\n",
    "\n",
    "$$\\phi(x,t=0) = f(x) = \\frac{2}{\\sqrt{3\\sqrt{\\pi}}} \\left(1 - ((x-3L/4)/\\sigma)^2\\right)e^{-\\frac{(x-3L/4)^2}{2\\sigma^2}}\\tag{17}$$\n",
    "\n",
    "and \n",
    "\n",
    "$$\\left.\\frac{\\partial \\phi}{\\partial t}\\right|_{t=0} = g(x) = 0  \\rightarrow \\phi^{n-1}_i=0 \\tag{18}$$\n",
    "\n",
    "where the right arrow shows the impliction that the $n-1$ time step is zero.  For this simulation we will use $\\sigma=40$, though this will be varied in the section below. Let's now compute the solution"
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       "\n",
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    "## . . Time stepping parameters\n",
    "CC = 0.5     # . . Courant #\n",
    "nt = 800     # . . Number of time steps\n",
    "dt = CC*dx/v # . . Define dt based on Courant\n",
    "\n",
    "## . . Define Initial waveform\n",
    "ss=40        # . . sigma for Ricker wavelet\n",
    "\n",
    "## . . Init wavefields on spatial grid\n",
    "Up = np.zeros((nx))\n",
    "Uo = np.zeros((nx))\n",
    "Um = np.zeros((nx))\n",
    "\n",
    "## . . Define initial disturbance\n",
    "Uo = 2/np.sqrt(3*ss*np.sqrt(np.pi))*(1-((x-3*L/4)/ss)**2)*np.exp(-(x-3*L/4)**2/(2*ss**2))\n",
    "\n",
    "## . . Total Solution space\n",
    "c = np.zeros((nx,nt)) \n",
    "\n",
    "## . . Iterate over solution time steps\n",
    "for it in range(nt):\n",
    "    tmp = awe_explicit_solver_homogeneous_2nd_order(Uo,Um,dx,dt,v) #calc solution at n+1\n",
    "    c[:,it]=tmp  ## save solution vector\n",
    "    Um=Uo        ## move solution at n to n-1 to prepare for next iteration\n",
    "    Uo=tmp       ## move solution at n+1 to n to prepare for next iteration\n",
    "\n",
    "amax = np.max(np.abs(c))\n",
    "\n",
    "## . . 1D animation fucntion\n",
    "def AWE_1D_animate(i):\n",
    "    global k\n",
    "    ax1.clear()\n",
    "    ax1.plot(x,c[:,k],color='cyan',linewidth=3)\n",
    "    ax1.grid(True)\n",
    "    ax1.set_xlim([0,L])\n",
    "    ax1.set_ylim([-1.1*amax,1.1*amax])\n",
    "    ax1.set(xlabel='Distance (m)',ylabel='Amplitude')\n",
    "    k += kskip\n",
    "    \n",
    "k = 0\n",
    "kskip = 4\n",
    "\n",
    "## . . Set up movie\n",
    "fig1,ax1 = plt.subplots(1)\n",
    "fig1.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig1.set_dpi(100)\n",
    "\n",
    "## . . Call the animator.  \n",
    "anim1 = animation.FuncAnimation(fig1,AWE_1D_animate,frames=int((nt-2*kskip)/kskip),interval=100)\n",
    "anim1.save('./movies/Ex8_1.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_1.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
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    "**Figure 1. Illustration of wave equation solution when one only defines the wavefield $\\phi(x,t=0)$ and $\\phi(x,t=-\\Delta t)=0$. Note that there is a two-way solution because  we have not specified a constraint forcing the solution to propagate one way or the other (see below).**\n",
    "\n",
    "Let's now look at what happens when we specify the previous wavefield state at $\\phi(x,t=-\\Delta t)$, which requires establishing what the wave looks like at the previous time step. Given the initial Ricker wavelet above, it is reasonable to expect that the wavefield solution at $\\phi(x,t=-\\Delta t)$ will be given by some wavefield shift $t_0$:\n",
    "\n",
    "$$\\phi(x,t=-\\Delta t) = \\frac{2}{\\sqrt{3\\sqrt{\\pi}}} \\left(1 - ((x-3L/4-v\\Delta t )/\\sigma)^2\\right)e^{-\\frac{(x-3L/4-v\\Delta t)^2}{2\\sigma^2}}, \\tag{19}$$\n",
    "\n",
    "where $t_0=v\\Delta t$ has been introduced to account for a spatial shift.  Let's rerun the solution from above, but now where we set the value of $\\phi^{n-1}_i$ as non-zero: "
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       "  <source src=\"./movies/Ex8_2.mp4\" type=\"video/mp4\">\n",
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   "source": [
    "## Time stepping parameters\n",
    "CC = 0.5     # . . Courant #\n",
    "nt = 800     # . . Number of time steps\n",
    "dt = CC*dx/v # . . Define dt based on Courant\n",
    "\n",
    "## . . Define Initial waveform\n",
    "ss=40        # . . sigma for Ricker wavelet\n",
    "\n",
    "## . . reinit wavefields on spatial grid\n",
    "Up = np.zeros((nx))\n",
    "Uo = np.zeros((nx))\n",
    "Um = np.zeros((nx))\n",
    "\n",
    "## . . Define initial time solution at t=0\n",
    "Uo = 2/np.sqrt(3*ss*np.sqrt(np.pi))*(1-((x-3*L/4     )/ss)**2)*np.exp(-(x-3*L/4     )**2/(2*ss**2))\n",
    "\n",
    "## . . Define previous time step at t=-∆t\n",
    "Um = 2/np.sqrt(3*ss*np.sqrt(np.pi))*(1-((x-3*L/4-dt*v)/ss)**2)*np.exp(-(x-3*L/4-dt*v)**2/(2*ss**2))\n",
    "\n",
    "## . . Total Solution space\n",
    "c = np.zeros((nx,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "for it in range(nt):\n",
    "    tmp = awe_explicit_solver_homogeneous_2nd_order(Uo,Um,dx,dt,v) #calc solution at n+1\n",
    "    c[:,it]=tmp  ## save solution vector\n",
    "    Um=Uo        ## move solution at n to n-1 to prepare for next iteration\n",
    "    Uo=tmp       ## move solution at n+1 to n to prepare for next iteration\n",
    "    \n",
    "amax = np.max(np.abs(c))\n",
    "\n",
    "## . . 1D animation fucntion\n",
    "def AWE_1D_animate(i):\n",
    "    global k\n",
    "    ax1.clear()\n",
    "    ax1.plot(x,c[:,k],color='cyan',linewidth=3)\n",
    "    ax1.grid(True)\n",
    "    ax1.set_xlim([0,L])\n",
    "    ax1.set_ylim([-1.1*amax,1.1*amax])\n",
    "    ax1.set(xlabel='Distance (m)',ylabel='Amplitude')\n",
    "    k += kskip\n",
    "    \n",
    "k = 0\n",
    "kskip = 4\n",
    "\n",
    "## . . Set up movie\n",
    "fig2,ax1 = plt.subplots(1)\n",
    "fig2.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig2.set_dpi(100)\n",
    "\n",
    "## . . Call the animator.  \n",
    "anim2 = animation.FuncAnimation(fig2,AWE_1D_animate,frames=int((nt-2*kskip)/kskip),interval=100)\n",
    "anim2.save('./movies/Ex8_2.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_2.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 2. Illustration of wave-equation solution when defining the wavefield at $t=0$ and $t=-\\Delta t$.  Note that the wave initially travels to the left instead of both directions like in Figure 10.1 above.**\n",
    "\n",
    "Parameter $\\sigma$ is of course related to the **frequency** content of the Ricker wavelet. Let's now investigate what happens when we set $\\sigma=15$ instead of using $\\sigma=40$ as we did in the simulations above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_3.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Time stepping parameters\n",
    "CC = 0.5     # . . Courant #\n",
    "nt = 500     # . . Number of time steps\n",
    "dt = CC*dx/v # . . Define dt based on Courant\n",
    "\n",
    "## . . Define Initial waveform\n",
    "ss = 15      # . . sigma for Ricker wavelet\n",
    "\n",
    "## . . Init wavefields on spatial grid\n",
    "Up = np.zeros((nx))\n",
    "Uo = np.zeros((nx))\n",
    "Um = np.zeros((nx))\n",
    "\n",
    "## . . Define wavefield at t=0\n",
    "Uo = 2/np.sqrt(3*ss*np.sqrt(np.pi))*(1-((x-3*L/4     )/ss)**2)*np.exp(-(x-3*L/4     )**2/(2*ss**2))\n",
    "\n",
    "## . . Define wavefield at t=-∆t\n",
    "Um = 2/np.sqrt(3*ss*np.sqrt(np.pi))*(1-((x-3*L/4-dt*v)/ss)**2)*np.exp(-(x-3*L/4-dt*v)**2/(2*ss**2))\n",
    "\n",
    "## . . Total Solution space\n",
    "c = np.zeros((nx,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "for it in range(nt):\n",
    "    tmp = awe_explicit_solver_homogeneous_2nd_order(Uo,Um,dx,dt,v) #calc solution at n+1\n",
    "    c[:,it]=tmp  ## save solution vector\n",
    "    Um=Uo        ## move solution at n to n-1 to prepare for next iteration\n",
    "    Uo=tmp       ## move solution at n+1 to n to prepare for next iteration\n",
    "    \n",
    "amax = np.max(np.abs(c))\n",
    "\n",
    "## . . 1D animation fucntion\n",
    "def AWE_1D_animate(i):\n",
    "    global k\n",
    "    ax1.clear()\n",
    "    ax1.plot(x,c[:,k],color='cyan',linewidth=3)\n",
    "    ax1.grid(True)\n",
    "    ax1.set_xlim([0,L])\n",
    "    ax1.set_ylim([-1.1*amax,1.1*amax])\n",
    "    ax1.set(xlabel='Distance (m)',ylabel='Amplitude')\n",
    "    k += kskip\n",
    "    \n",
    "k = 0\n",
    "kskip = 4\n",
    "\n",
    "## . . Set up movie\n",
    "fig3,ax1 = plt.subplots(1)\n",
    "fig3.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig3.set_dpi(100)\n",
    "\n",
    "## . . Call the animator.  \n",
    "anim3 = animation.FuncAnimation(fig3,AWE_1D_animate,frames=int((nt-2*kskip)/kskip),interval=100)\n",
    "anim3.save('./movies/Ex8_3.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_3.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 3. Illustration of how numerical dispersion can degrade the solution over time.  The initial wave packet starts to develop a long \"tail\" that represents non-physical dispersive behaviour.**\n",
    "\n",
    "## Higher-order derivatives\n",
    "\n",
    "It's clear that the numerical solution behavior noted in Figure 3 is less than idea.  Thus, we need to look at different methods for trying to eliminate these artifacts. One strategy would be to use a smaller $\\Delta x$, which is easy to do in a 1D solution because the computational cost scales according to $\\mathcal{O}(N)$ where $N$ is the number of points. However, in 3D this approach would scale according to $\\mathcal{O}(N^3)$ since we would have to apply it in each dimension!  This would significantly affect our computational efficiency. \n",
    "\n",
    "Another strategy would be to use higher-order spatial derivatives, which we we know lead to a more accurate representation of numerical derivatives. To do this, let's rewrite the 1D solver for homogeneous media from above to incorporate an $\\mathcal{O}(\\Delta x^8)$ centered approximation of the second-order spatial partial derivative.  This requires using a nine-point stencil that incorporates four points to the left and right of the  center point:\n",
    "\n",
    "$$\\phi^{n+1}_i = 2\\phi^{n}_i -\\phi^{n-1}_i +C^2 \\left(-\\frac{1}{560}\\phi^{n}_{i+4}+\\frac{8}{315}\\phi^{n}_{i+3}-\\frac{1}{5}\\phi^{n}_{i+2}+\\frac{8}{5}\\phi^{n}_{i+1} -\\frac{205}{72} \\phi^{n}_i +\\frac{8}{5} \\phi^{n}_{i-1}-\\frac{1}{5}\\phi^{n}_{i-2}+\\frac{8}{315}\\phi^{n}_{i-3}-\\frac{1}{560} \\phi^{n}_{i-4}\\right), \\tag{20}$$\n",
    "\n",
    "where these [finite-difference coefficients](https://en.wikipedia.org/wiki/Finite_difference_coefficient#Central_finite_difference) are for a **centered second derivative of $O(\\Delta x^8)$**. \n",
    "\n",
    "Note that we will again have issues at the boundaries where we will need **ghost points**. However, because we have longer stencil, we will now need to have four ghost points instead of just one.  Let's see how this work in our solver:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def awe_explicit_solver_homogeneous_8th_order(Wo,Wm,dx,dt,v):\n",
    "    '''Set up eight-order solver of the acoustic wave equation\n",
    "    usage: U = awe_explicit_solver_homogeneous(Wo,Wm,dx,dt,v)\n",
    "    input: \n",
    "        Wo: Acoustic pressure vector (nx) at time step n\n",
    "        Wm: Acoustic pressure vector (nx) at time step n-1\n",
    "        dx: Spatial sampling\n",
    "        dt: Temporal sampling\n",
    "        v : Homogeneous propagation velocity \n",
    "    output:\n",
    "        Wm: Acoustic pressure vector (nx) at time n+1\n",
    "    dependencies:\n",
    "        None\n",
    "    written by Jeff Shragge, jshragge@mines.edu, 10/2019\n",
    "    '''        \n",
    "    ## . . Get dimensions of wavefield\n",
    "    nx = len(Wo)\n",
    "    \n",
    "    ## . . Define Courant number (squared)\n",
    "    C2 = (v*dt/dx)**2\n",
    "        \n",
    "    ## . . Update solution. Note that I am overwriting Wm because this wavefield\n",
    "    ## . . isn't needed after this calculation! I am also starting at index 4 (and ending)\n",
    "    ## . . at index nx-4 because of the ghost points discussed above.\n",
    "    Wm[4:nx-4] = 2*Wo[4:nx-4]-Wm[4:nx-4]+C2*( \n",
    "                    -1/560 *Wo[0:nx-8] \n",
    "                    +8/315 *Wo[1:nx-7]  \n",
    "                    -1/5   *Wo[2:nx-6]  \n",
    "                    +8/5   *Wo[3:nx-5]  \n",
    "                    -205/72*Wo[4:nx-4]  \n",
    "                    +8/5   *Wo[5:nx-3]  \n",
    "                    -1/5   *Wo[6:nx-2]  \n",
    "                    +8/315 *Wo[7:nx-1]  \n",
    "                    -1/560 *Wo[8:nx  ])    \n",
    "    \n",
    "    return Wm ## . . Return updated wavefield at time step n+1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now rerun our numerically dispersive example where we set $\\sigma=15$ from above but using our $\\mathcal{O}(\\Delta x^8)$ solver for homogeneous media."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_4.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Time stepping parameters\n",
    "CC = 0.5     # . . Courant #\n",
    "nt = 500     # . . Number of time steps\n",
    "dt = CC*dx/v # . . Define dt based on Courant\n",
    "\n",
    "## . . Define Initial waveform\n",
    "ss=15        # . . sigma for Ricker wavelet\n",
    "\n",
    "## . . Init wavefields on spatial grid\n",
    "Up = np.zeros((nx))\n",
    "Uo = np.zeros((nx))\n",
    "Um = np.zeros((nx))\n",
    "\n",
    "## . . Define wavefield at t=0\n",
    "Uo = 2./np.sqrt(3.*ss*np.sqrt(np.pi))*(1-((x-3.*L/4.     )/ss)**2)*np.exp(-(x-3.*L/4.     )**2/(2*ss**2))\n",
    "\n",
    "## . . Define wavefield at t=-∆t\n",
    "Um = 2./np.sqrt(3.*ss*np.sqrt(np.pi))*(1-((x-3.*L/4.-dt*v)/ss)**2)*np.exp(-(x-3.*L/4.-dt*v)**2/(2*ss**2))\n",
    "\n",
    "## . . Total Solution space\n",
    "d = np.zeros((nx,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "for it in range(nt):\n",
    "    tmp = awe_explicit_solver_homogeneous_8th_order(Uo,Um,dx,dt,v) #calc solution at n+1\n",
    "    d[:,it]=tmp  ## save solution vector\n",
    "    Um=Uo        ## move solution at n to n-1 to prepare for next iteration\n",
    "    Uo=tmp       ## move solution at n+1 to n to prepare for next iteration\n",
    "    \n",
    "amax = np.max(np.abs(d))\n",
    "\n",
    "## . . 1D animation fucntion\n",
    "def AWE_1D_animate(i):\n",
    "    global k\n",
    "    ax1.clear()\n",
    "    ax1.plot(x,d[:,k],color='cyan',linewidth=3)\n",
    "    ax1.grid(True)\n",
    "    ax1.set_xlim([0,L])\n",
    "    ax1.set_ylim([-1.1*amax,1.1*amax])\n",
    "    ax1.set(xlabel='Distance (m)',ylabel='Amplitude')\n",
    "    k += kskip\n",
    "    \n",
    "k = 0\n",
    "kskip = 4\n",
    "\n",
    "## . . Set up movie\n",
    "fig4,ax1 = plt.subplots(1)\n",
    "fig4.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig4.set_dpi(100)\n",
    "\n",
    "## . . Call the animator.  \n",
    "anim4 = animation.FuncAnimation(fig4,AWE_1D_animate,frames=int((nt-2*kskip)/kskip),interval=100)\n",
    "anim4.save('./movies/Ex8_4.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_4.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4. As in Figure 3, but using the 8th-order solver for homogeneous media. Note that the previously noted \"tail\" has largely - but not completely - disappeared.  This indicates that the higher-order finite-difference approximation has helped to reduce numerical dispersion, but is not a panacea for this issue.**\n",
    "\n",
    "It is also illustrative to plot the two previous solutions over top of each other. Note that because of the different number of ghost points used, the location of the boundary reflection will be at slightly different locations; thus, I'll only plot it up to the point where the waves reach the boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_5.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 0\n",
    "kskip = 4\n",
    "amax = np.max(np.abs(d))\n",
    "def AWE_1D_animate2(i):\n",
    "    global k\n",
    "    ax1.clear()\n",
    "    ax1.plot(x,c[:,k],color='cyan',linewidth=3)\n",
    "    ax1.plot(x,d[:,k],color='magenta',linewidth=3)\n",
    "    ax1.legend(['2nd','8th'])\n",
    "    ax1.grid(True)\n",
    "    ax1.set_xlim([0,L])\n",
    "    ax1.set_ylim([-1.1*amax,1.1*amax])\n",
    "    ax1.set(xlabel='Distance (m)',ylabel='Amplitude')\n",
    "    k += kskip\n",
    "\n",
    "## . . Set up movie\n",
    "fig5,ax1 = plt.subplots(1)\n",
    "fig5.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig5.set_dpi(100)\n",
    "\n",
    "## . . Call the animator.  \n",
    "anim5 = animation.FuncAnimation(fig5,AWE_1D_animate2,frames=int((nt-2*kskip)/kskip),interval=100)\n",
    "anim5.save('./movies/Ex8_5.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"500\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_5.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 5. Comparison of the solutions generated by the eighth- and second-order solvers. The higher-order method clearly produces a more accurate result - though it is itself not perfect.**\n",
    "\n",
    "\n",
    "# 2D Acoustic wave equation\n",
    "\n",
    "Let's now look at the problem of an acoustic wave propagating through a homogeneous 2D domain. In this case, we can assume that there is an external forcing function $F(x,y,t)\\neq0$ and the wave disturbance is initially zero in a **quiescent** state. Thus, the 2D PDE we are solving is\n",
    "\n",
    "$$\\frac{\\partial^2 \\phi}{\\partial t^2} = v^2\\left(\\frac{\\partial^2 \\phi}{\\partial x^2}+\\frac{\\partial^2 \\phi}{\\partial y^2} \\right) + F(x,y,t). \\tag{21}$$ \n",
    "\n",
    "One commmon thing that people use is to model the acoustic wavefield eminating from a spatially localized point source.  In these scenarios, one can write the following for the force source\n",
    "\n",
    "$$F(x,y,t) = W(t)\\delta(x-s_x)\\delta(y-s_y), \\tag{22}$$\n",
    "\n",
    "where point ${\\bf s}=[s_x,s_y]$ represents the coordinates of point source and $W(t)$ represents the wavelet to be **injected** into the domain. \n",
    "\n",
    "### Discretizing the 2D AWE\n",
    "\n",
    "Let's now look at an **explicit** discretization method.  Let's use a $\\mathcal{O}(\\Delta x^8,\\Delta t^2)$ discretization:\n",
    "\n",
    "$$\\frac{\\phi^{n+1}_{i,j} - 2\\phi^{n}_{i,j} +\\phi^{n-1}_{i,j}}{\\Delta t^2} = \n",
    "\\frac{v^2}{\\Delta x^2} \\sum_{k=-4}^4 c_k \\phi^{n}_{i+k,j}+ \\frac{v^2}{\\Delta y^2} \\sum_{k=-4}^4 c_k \\phi^{n}_{i,j+k} + F_{i,j}, \\tag{23}$$\n",
    "\n",
    "where $c_k$ are the finite-difference coefficients discussed above.  Let's now multiply through by $\\Delta t^2$ and use the square of the Courant number $C_x^2 = \\frac{v^2\\Delta t^2}{\\Delta x^2}$ and $C_y^2 = \\frac{v^2\\Delta t^2}{\\Delta y^2}$ from the previous modules to write\n",
    "\n",
    "$$\\phi^{n+1}_{i,j} = 2\\phi^{n}_{i,j} - \\phi^{n-1}_{i,j} +\n",
    "C_x^2 \\sum_{k=-4}^4 c_k \\phi^{n}_{i+k,j}+ C_y^2\\sum_{k=-4}^4 c_k \\phi^{n}_{i,j+k} +\\Delta t^2 F_{i,j}. \\tag{24}$$\n",
    "\n",
    "This is pretty much the same as in 1D, so let's just move right to the 2D solver!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def awe_2d_explicit_solver_homogeneous_8th_order(UUo,UUm,dx,dy,dt,v,F,it,sx,sy):\n",
    "    '''Set up eight-order solver of the acoustic wave equation\n",
    "    usage: U= awe_2d_explicit_solver_homogeneous_8th_order(UUo,UUm,dx,dy,dt,v,F)\n",
    "    input: \n",
    "        UUo: Acoustic pressure vector (nx,ny) at time step n\n",
    "        UUm: Acoustic pressure vector (nx,ny) at time step n-1\n",
    "        dx : Spatial sampling in x\n",
    "        dy : Spatial sampling in y        \n",
    "        dt : Temporal sampling\n",
    "        v  : Homogeneous propagation velocity \n",
    "        F  : Forcing function (nt)\n",
    "        it : Time index\n",
    "        sx : Location of source in x (meters)\n",
    "        sy : Location of source in y (meters)\n",
    "    output:\n",
    "        UUm: Acoustic pressure vector (nx,ny) at time n+1\n",
    "    dependencies:\n",
    "        None\n",
    "    written by Jeff Shragge, jshragge@mines.edu, 11/2019\n",
    "    '''        \n",
    "    ## . . Get dimensions of wavefield\n",
    "    nx,ny = np.size(UUo,0),np.size(UUo,1)\n",
    "    \n",
    "    ## . . Define Courant numbers (squared)\n",
    "    Cx2,Cy2 = (v*dt/dx)**2,(v*dt/dy)**2\n",
    "        \n",
    "    ## Source location\n",
    "    isx,isy = int(sx/dx),int(sy/dy) ## . . Force to be integer (note assumes model origin at [0,0])\n",
    " \n",
    "    ## . . Inject wavelet\n",
    "    UUo[isx,isy] += dt*dt*F[it]\n",
    "    \n",
    "    ## . . Update solution. Again, I am starting the array at index 4 and ending \n",
    "    ## . . at index nx-4 and ny-4 because of the ghost points\n",
    "    UUm[4:nx-4,4:ny-4] =  2*UUo[4:nx-4,4:ny-4]-UUm[4:nx-4,4:ny-4]+Cx2*( \n",
    "                    -1/560 *UUo[0:nx-8,4:ny-4] \n",
    "                    +8/315 *UUo[1:nx-7,4:ny-4]  \n",
    "                    -1/5   *UUo[2:nx-6,4:ny-4]  \n",
    "                    +8/5   *UUo[3:nx-5,4:ny-4]  \n",
    "                    -205/72*UUo[4:nx-4,4:ny-4]  \n",
    "                    +8/5   *UUo[5:nx-3,4:ny-4]  \n",
    "                    -1/5   *UUo[6:nx-2,4:ny-4]  \n",
    "                    +8/315 *UUo[7:nx-1,4:ny-4]  \n",
    "                    -1/560 *UUo[8:nx  ,4:ny-4])+Cy2*( \n",
    "                    -1/560 *UUo[4:nx-4,0:ny-8] \n",
    "                    +8/315 *UUo[4:nx-4,1:ny-7]  \n",
    "                    -1/5   *UUo[4:nx-4,2:ny-6]  \n",
    "                    +8/5   *UUo[4:nx-4,3:ny-5]  \n",
    "                    -205/72*UUo[4:nx-4,4:ny-4]  \n",
    "                    +8/5   *UUo[4:nx-4,5:ny-3]  \n",
    "                    -1/5   *UUo[4:nx-4,6:ny-2]  \n",
    "                    +8/315 *UUo[4:nx-4,7:ny-1]  \n",
    "                    -1/560 *UUo[4:nx-4,8:ny  ])\n",
    "\n",
    "    return UUm ## . . Return updated wavefield at time step n+1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll note that I've changed things a bit here since I am now **injecting the wavelet** into the 2D domain at the current time step $it$.  Here, I've calculated the location of the incidies $[isx,isy]$ at which to inject the wavelet.  I could have also created a force source term $F^n_{i,j}$ as a 3D array; however, this would be wasteful of memory since I'm only injecting at one location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## . . Define spatial grid\n",
    "Lx,Ly = 2000,2000           # . . length (m)\n",
    "nx,ny = 401,401             # . . Number of points in discretization \n",
    "dx,dy = Lx/(nx-1),Ly/(ny-1) # . . Discretization interval\n",
    "x ,y  = np.linspace(0,Lx,nx),np.linspace(0,Ly,ny) # . . Xline\n",
    "v  = 1000        # . . Velocity (m/s)\n",
    "\n",
    "## . . Meshgrid\n",
    "yyy,xxx = np.meshgrid(x,y)\n",
    "\n",
    "## . . Init wavefields on spatial grid\n",
    "UUo,UUm = np.zeros((nx,ny)),np.zeros((nx,ny))\n",
    "\n",
    "## Time stepping parameters\n",
    "CC = 0.5     # . . Courant #\n",
    "nt,dt,t0 = 800,CC*dx/v,0.1       # . . Number of time steps, dt and wavelet shift\n",
    "t  = np.linspace(0,nt*dt,nt)\n",
    "\n",
    "## . . Define Initial waveform\n",
    "ss=0.02 ## sigma for Ricker wavelet\n",
    "F = (1-((t-t0)/ss)**2)*np.exp(-(t-t0)**2/(2*ss**2))\n",
    "sx,sy=Lx/2,Ly/2\n",
    "\n",
    "## . . Total Solution space\n",
    "eee = np.zeros((nx,ny,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "for it in range(nt):\n",
    "    tmp = awe_2d_explicit_solver_homogeneous_8th_order(UUo,UUm,dx,dy,dt,v,F,it,sx,sy) #calc solution at n+1\n",
    "    eee[:,:,it]=tmp  ## save solution vector\n",
    "    UUm=UUo          ## move solution at n to n-1 to prepare for next iteration\n",
    "    UUo=tmp          ## move solution at n+1 to n to prepare for next iteration\n",
    "    \n",
    "amax = np.max(np.abs(eee))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_6.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## . . Animate Solution and compute error\n",
    "k,kskip = 0,20\n",
    "\n",
    "## . . Set up movie\n",
    "fig6,ax1 = plt.subplots(1)\n",
    "fig6.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig6.set_dpi(100)\n",
    "\n",
    "def AWE_2D_animate(i):\n",
    "    global k\n",
    "    x = eee[:,:,k]\n",
    "    ax1.imshow(x,cmap='gray',extent=[0,Lx,0,Ly],vmin=-0.1*amax,vmax=0.1*amax)\n",
    "    ax1.set(xlabel='X(m)', ylabel='Y(m)')\n",
    "    ax1.set_title('NUMERICAL Step %s'%k,fontsize=14)\n",
    "    k += kskip\n",
    "\n",
    "## . . Call the animator\n",
    "anim6 = animation.FuncAnimation(fig6,AWE_2D_animate,frames=int((nt-2*kskip)/kskip),interval=100)\n",
    "anim6.save('./movies/Ex8_6.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_6.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 6. Propagating 2D acoustic wavefield generated by the 8th-order finite-difference AWE solver.  Note that the reflections from the boundary are with the opposite sign.**\n",
    "\n",
    "## Wavefields, surface seismic and VSP data\n",
    "\n",
    "Since we have the full 3D volume of $[nx,ny,nt]$ it is possible to slice it in different ways. Figure 7 shows the 2D slice at a constant depth (a) representing a surface seismic data set  as well as a 2D slice taken a constant x-location (b) which would represent a vertical seismic profile (VSP) data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.imshow(eee[5,:,:].T,cmap='gray',extent=[0,Lx,nt*dt*1000,0])\n",
    "plt.xlabel('Distance (m)',fontsize=12)\n",
    "plt.ylabel('Time (ms)',fontsize=12)\n",
    "plt.title('(a) Surface Seismic data from buried source',fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.imshow(eee[:,int(nx/4),:],cmap='gray',extent=[0,Lx,nt*dt*1000,0])\n",
    "plt.ylabel('Depth (m)',fontsize=12)\n",
    "plt.xlabel('Time (ms)',fontsize=12)\n",
    "plt.title('(b) VSP data from buried source',fontsize=14)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 8. (a) Constant depth slice extracted 5m down from the first ghost point representing surface seismic data. (b) Constant X-location slice extracted at 500m distance representing a vertical seismic profile (VSP).**\n",
    "\n",
    "## 2D Acoustic Wave Equation for Heterogeneous Media\n",
    "\n",
    "While solutions of the 2D acoustic wave equation for homogeneous media are important for evaluating our finite-difference scheme, they have quite limited use in practice. This is because velocity models usually are heterogeneous: $v=v(x,y)$. Thus, we need to account for this spatial heterogeneity in our numerical solvers.  To do so, let's adapt our eight-order solver above to include heterogeneity. The most common practice in this situation would be to introduce a spatially varying velocity function into equation 24 above:\n",
    "\n",
    "$$\\phi^{n+1}_{i,j} = 2\\phi^{n}_{i,j} - \\phi^{n-1}_{i,j} +\n",
    "\\left(\\frac{v_{i,j}\\Delta t}{\\Delta x}\\right)^2 \\sum_{k=-4}^4 c_k \\phi^{n}_{i+k,j}+ \\left(\\frac{v_{i,j}\\Delta t}{\\Delta y}\\right)^2\\sum_{k=-4}^4 c_k \\phi^{n}_{i,j+k} +\\Delta t^2 F_{i,j}, \\tag{25}$$\n",
    "\n",
    "which leads to only a modest change in the *awe_2d_explicit_solver_heterogeneous_8th_order* solver below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def awe_2d_explicit_solver_heterogeneous_8th_order(UUo,UUm,dx,dy,dt,v,F,it,sx,sy):\n",
    "    '''Set up eight-order solver of the acoustic wave equation\n",
    "    usage: U=awe_2d_explicit_solver_heterogeneous_8th_order(UUo,UUm,dx,dy,dt,v,F,it,sx,sy):\n",
    "    input: \n",
    "        UUo: Acoustic pressure vector (nx,ny) at time step n\n",
    "        UUm: Acoustic pressure vector (nx,ny) at time step n-1\n",
    "        dx : Spatial sampling in x\n",
    "        dy : Spatial sampling in y        \n",
    "        dt : Temporal sampling\n",
    "        v  : Heterogeneous propagation velocity (nx,ny)\n",
    "        F  : Forcing function (nt)\n",
    "        it : Time index\n",
    "        sx : Location of source in x (meters)\n",
    "        sy : Location of source in y (meters)\n",
    "    output:\n",
    "        UUm: Acoustic pressure vector (nx,ny) at time n+1\n",
    "    dependencies:\n",
    "        None\n",
    "    written by Jeff Shragge, jshragge@mines.edu, 10/2019\n",
    "    '''        \n",
    "    ## . . Get dimensions of wavefield\n",
    "    nx,ny = np.size(UUo,0),np.size(UUo,1)\n",
    "    \n",
    "    ## . . Define Courant numbers (squared)\n",
    "    dtdx2,dtdy2 = (dt/dx)**2,(dt/dy)**2\n",
    "        \n",
    "    ## Source location\n",
    "    isx,isy = int(sx/dx),int(sy/dy) ## . . Force to be integer\n",
    " \n",
    "    ## . . Inject wavelet\n",
    "    UUo[isx,isy] += dt*dt*F[it]\n",
    "\n",
    "    ## . . Update solution \n",
    "    UUm[4:nx-4,4:ny-4] =  2*UUo[4:nx-4,4:ny-4]-UUm[4:nx-4,4:ny-4]+dtdx2*v[4:nx-4,4:ny-4]**2*( \n",
    "                    -1/560 *UUo[0:nx-8,4:ny-4] \n",
    "                    +8/315 *UUo[1:nx-7,4:ny-4]  \n",
    "                    -1/5   *UUo[2:nx-6,4:ny-4]  \n",
    "                    +8/5   *UUo[3:nx-5,4:ny-4]  \n",
    "                    -205/72*UUo[4:nx-4,4:ny-4]  \n",
    "                    +8/5   *UUo[5:nx-3,4:ny-4]  \n",
    "                    -1/5   *UUo[6:nx-2,4:ny-4]  \n",
    "                    +8/315 *UUo[7:nx-1,4:ny-4]  \n",
    "                    -1/560 *UUo[8:nx  ,4:ny-4])+dtdy2*v[4:nx-4,4:ny-4]**2*( \n",
    "                    -1/560 *UUo[4:nx-4,0:ny-8] \n",
    "                    +8/315 *UUo[4:nx-4,1:ny-7]  \n",
    "                    -1/5   *UUo[4:nx-4,2:ny-6]  \n",
    "                    +8/5   *UUo[4:nx-4,3:ny-5]  \n",
    "                    -205/72*UUo[4:nx-4,4:ny-4]  \n",
    "                    +8/5   *UUo[4:nx-4,5:ny-3]  \n",
    "                    -1/5   *UUo[4:nx-4,6:ny-2]  \n",
    "                    +8/315 *UUo[4:nx-4,7:ny-1]  \n",
    "                    -1/560 *UUo[4:nx-4,8:ny  ])\n",
    "\n",
    "    return UUm ## . . Return updated wavefield at time step n+1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now generate a simple 1D velocity model that has a single reflector located at 250m depth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## . . Define spatial grid\n",
    "Lx,Ly = 2000,1200           # . . lengths (m)\n",
    "nx,ny = 401,241             # . . Number of points in discretization \n",
    "dx,dy = Lx/(nx-1),Ly/(ny-1) # . . Discretization intervals\n",
    "\n",
    "## . . Create velocity function\n",
    "v = np.zeros((nx,ny))+1500\n",
    "v[:,50:]=2000\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(v.T,cmap='jet',extent=[0,Lx,Ly,0])\n",
    "cbar=plt.colorbar()\n",
    "cbar.set_label('Velocity (m/s)',fontsize=12)\n",
    "plt.xlabel('Distance (m)',fontsize=12)\n",
    "plt.ylabel('Depth (m)',fontsize=12)\n",
    "plt.title('Heterogeneous Velocity Model',fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 9. Heterogeneous velocity model with a single discontinuity located at 250 m depth.**\n",
    "\n",
    "Let's now call our solver for heterogeneous media:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## . . Init wavefields on spatial grid\n",
    "UUo = np.zeros((nx,ny))\n",
    "UUm = np.zeros((nx,ny))\n",
    "\n",
    "## Time stepping parameters\n",
    "CC = 0.5                     # . . Courant #\n",
    "nt = 800                     # . . Number of time steps\n",
    "dt = CC*dx/np.max(v)         # . . Define dt based on Courant\n",
    "t  = np.linspace(0,nt*dt,nt) # . . Time lin\n",
    "t0 = 0.05                    # . . Wavelet shift \n",
    "\n",
    "## . . Define forcing function\n",
    "ss=0.01                      # . . sigma for Ricker wavelet\n",
    "F = (1-((t-t0)/ss)**2)*np.exp(-(t-t0)**2/(2*ss**2))\n",
    "\n",
    "## . . Define source location\n",
    "sx,sy=Lx/2,25                # . . source x,y location (in physical m units)\n",
    "\n",
    "## . . Total Solution space\n",
    "fff = np.zeros((nx,ny,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "for it in range(nt):\n",
    "    tmp = awe_2d_explicit_solver_heterogeneous_8th_order(UUo,UUm,dx,dy,dt,v,F,it,sx,sy) #calc solution at n+1\n",
    "    fff[:,:,it]=tmp  ## save solution vector\n",
    "    UUm=UUo          ## move solution at n to n-1 to prepare for next iteration\n",
    "    UUo=tmp          ## move solution at n+1 to n to prepare for next iteration\n",
    "\n",
    "## . . compute maximum for scaling\n",
    "amax = np.max(np.abs(fff))\n",
    "\n",
    "## . . Add (demeaned) velocity model to wavefield to illustrate interactions\n",
    "vscale = (v.T-np.mean(v))\n",
    "vscale = -vscale/np.max(vscale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_7.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def AWE_2D_animate(i):\n",
    "    global k\n",
    "    wfld = fff[:,:,k].T/np.max(np.abs(fff))\n",
    "    data = wfld+0.0025*vscale[:,::-1]\n",
    "    ax1.clear()\n",
    "    ax1.imshow(data,cmap='gray',extent=[0,Lx,0,Ly],vmin=-0.08,vmax=0.08)\n",
    "    ax1.set(xlabel='X(m)', ylabel='Y(m)')\n",
    "    ax1.set_title('2D AWE Step %s'%k,fontsize=14)\n",
    "    k += kskip\n",
    "\n",
    "## . . Animate Solution and compute error\n",
    "k,kskip = 0,5\n",
    "\n",
    "## . . Set up movie\n",
    "fig7,ax1 = plt.subplots(1)\n",
    "fig7.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig7.set_dpi(100)\n",
    "\n",
    "## . . Call the animator\n",
    "anim7 = animation.FuncAnimation(fig7,AWE_2D_animate,frames=int((nt-2*kskip)/kskip),interval=100)\n",
    "anim7.save('./movies/Ex8_7.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_7.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 10. Animation of wavefield propagation in layered half space. For illustration purposes, I have added in a scaled version of the velocity model to the (scaled) wavefield solution so that it is easy to see where all of the wavefield scattering occurs.**\n",
    "\n",
    "We can also look at what the surface seismic data look like by taking a slice through the second coordinate of the 3D wavefield solution volume."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "amax = np.max(np.abs(fff[:,5,:].T))\n",
    "plt.figure()\n",
    "plt.imshow(fff[:,5,:].T,cmap='gray',extent=[0,Lx,dt*nt*1000,0],vmin=-0.1*amax,vmax=0.1*amax)\n",
    "plt.xlabel('Distance (m)',fontsize=12)\n",
    "plt.ylabel('Time (ms)',fontsize=12)\n",
    "plt.title('Seismic data',fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Figure 11.  Surface seismic data from the wavefield animation shown in Figure 10.  We observe the direct and reflected arrivals.**\n",
    "\n",
    "Let's now create a velocity model with a lot more spatial variations. For this example, I'm going to import an image from the **skimage** package, convert it to float, scale it by $1000\\times$, and add it to a background velocity of $1500$ m/s. **(Note: you may need to install the scikit-image package to run this example, the command for which is given below.)** The result is shown in Figure 12 below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1No/6r0UwMAFTcxQdqk0EUiTV4mEvpjxmAbhgrAmyYE5QK6g0qva0iKiPY/kN025MIAVpSbSU2QdAd6/871His0+YnLiVs9WLlOZutS7MKkJrpb7mAK2go7lhzZHFW9qzW/a1/rZ7r370s7Peay22Oy39aNDUYO9T/cYMh+5vPyWt3ioHigzDWIVUoGAYRitw8tecdy/S4rr38XLkm/+90o9SRP2vKRaptdNiYRamaKVBRwOTlRuwrsIjMS2n8UgA0WKg5mK0wX0sEpzewdTr2ZH6tqAq17oyq1VNc1x61c9QbegJ5IQ+IkwQU7thVfhrUNbja8HUTWkuxQo6+JHgtpu+327pUsd0Z0lmXavxQHPFYcOFMKuErZC9hK201slNEiaY7s13BCGoOTvtgiX6GgasoqgGLw1qGmCsyn2rbKbb0XX0+Q3IRUWLoLpdzS261Zau2tHAaTWm6LZakAuY5jatQG8FwyDK8eL/Kx3cj54ODYADCTQgX6IgErC0HklbzvQkKUeKfR4kUOnz9MpeiwmAWtzRSmUfEpS07iwD6fGjFe7aMqcVzuuQgFeg2tK/FfRVaIeV8QYSKAzlrqE4Lisn1aLq25ETdSwmeOu+G4CgdgdVHBK9mECnN5BSxS5kxiHF5Wkwj1Hta/2lJs3RpKgyexTYY4EoxZHpvrVCS4+hSW1+td+sytYT5i61SLgW06qsN70YuFXzDZjcnu5TP2utA23BBCnN1Wku143puqNdbvSz1EYKTdqVyIMJqlMxVSMaRLWKxLrINCITYB0A46K2ou7PdrDToSGigikmlAMTe6EhytTLWMVNNyYY6Jf8HdXGOEwxcJU6V4uPIMFsHOZEmKnaWKXK1iIBTLetASBoaadW1dc6G81Bdu+C7gGYIJOMfEWjTKBNx7TigSlOabcYPem0kSLYHznpNTvlxxRR9euv3f13YSqYusAXZXJKGvStk12TBvQwx6aNCJp/2IUZKqE5NQ14veo6ldh6c5T0ytIWZ82hWkVmzW1ptYLWm2UgnYqnqntway/8To0hHfmMGzAXHjCfUzx9uTyrxVovcI2Yi9BY4DQYesFnTOEtsqgjmVa8DOKWrL9KXSz0dT7WOuEDQN+DDu5HQ4cGwOmrbEByExVRZpRBDKYDrubQWjBdQOKRHNhpcPVZD5BNNXlUUkE+z3ERn947VhoiNiPBRYOHBwmmYBoxUpCcVS6msjofk6OKV8c0GLVAWOeGXXKfM5NhXbJyQ6lR1zfcBOsKdS356n8GfZXZWsEdBOlGmKQGsANIg5g0uASi7tlF78gB0LIeKbYmy7EQBPxSF6cndC2mYl6T7s9qcAFpUY0HWjRwDkACWyuQTIwvSEJigCI+IIs6/nLc7VC+TdZdkGz6EcK+HZez1K/H0m8DMBHGvLean/EYPpxkU83iZ6bjw4mfBFbdPpGOqwbCgl3gHGBydppTr8UEas3B6UVLA71P9vPX5+dwbc3fYRtsHzIQBz2kN7dDMxx9ciW/OfkePvnLuL7jD4PbgQnRPDQm9jfTjy6byP9CIqvA4K5yCW56ldYrvebsNBdkRwKWB3jJ4LZhdzKKDcxjDhNZRQot5FFJXqASvyMBGyFaSeZJ5vKQuBVShPRf05PeiZwkGUjQ1KCXhWld1ECbguQkrK4Ds2H2809zHY8QTQAXXzKwuQPWwfbpA7mMf7BC5IMzA3ytUJAs69ViTjyreKr7C4NeDVwynEnPvMmNPEgdWSTgx08CTaRxX83v2TU0itNtb7H2wlNgwWJgOlKMTAN6pcMumJZFqyuHvq9766fiAd8ueaPHHs2ED9/hCa4iu207/sQoWmzJeBhCCBsbyOeWX/4V7m+ClLS+AAOmL5q+Js3R6fPuh7dvmshKTsKFl5kspJwC6hhGKUVkUs941hBNgBe5gH/eeJnksoKYelOtQ9McqbVfrb5ww57fCkQlMByMGPgg6VjSaKaL/vg4jCxqSQj5sQVDXOV4ggV3XWH68k0ERroxDM+3QrkRQhiP7ee5p8D6r3P0PRjo0NDBxRnyBd2E6TulAUVzOJrz0uLh7XDxsCcYxQbqyeQBfkEWtfRnN7VkcZXjCRZxJquYSDQBHmj7NT8xFplK6gxMTqwWU7+nXT+gr9VOj8sqbuXDsc+vJYta6slkN7GUMYbOxH5wJAxevZPFgTMgN0MZSpJNsVqLWvGWdsHUNdEqzzlzODEPtTGThWRSTzKt9KeLANGk0cSC4WexwTaK63iEF58/k6lGQDWYZjrtah2hBmzNZXnoa+0EC7j1yh330Zz14QLe6fwJVeRQlTSUgM1BBaPw4KaWYVzE89T9eRD8Lg1adsl2NLjs7e6iRUm9XwCzb3qaMgrxk0A0AfrTRXHnuxRRSjx+vsJJE6kk0MH5vMDsB582dXoeTF2b1jtqsjoYA7kPfkzAAVsnpLPDlYQ3KQkPQ7ARxIkPJ19RSxYbbKPwONw8EbiKgXd+YRptGjggdKD84A4GOjQ4uOEFRr+1q9njizPB5E2kPsaDyWGsRXJ54+D3J9xMGk0sYgZOfOSzgTWcSCb1VJKHjRD/YgaTWEkCft5gOvZQCFswRPzskBQhz0RybKepgWhDufa9cmP6bWlgVRxmRm8N9fUj4FF45/8m8BKzeL7pIvZ0R3Ps4DJ+w31EE8BBDwn4Of6KCpi3S7pVaNFMW1LTkaKi1uf5DMgSnFPzLMWU4MNJF7H4SSABP13EkkILXlx0EUsP0ZzPi3hx4WUQ9/NLXHj5VKQBQ0xrptZ7aRcU1O9ITCNP2JgwAGjCWJ4OqfBG7qnUMYxfND/Os6nnUEA57zOeIXgYQxmHtXWzOOlUruJxGsVQ00ik9WsaZLVVtKEXyqO4b/SN+EnARpBWUshjIwl0MLPzNWI2wa6CKDba8ljDibSSjBsP+Wwgmy2kZvpNA0E6pg8d9HUL6Yabnr+HQsoI4MCnANOFlwQ6cPIVraRgI4SfeBLoIJN6PLg5v/0VoucbYQ6QmfkYRsW34uCOFMKYv5/njo1wcAcH7WmMM62LI3vlN5fSMfUqmuvYDENP+Aw/CWRSTwJ+CijndJbiZhtZ1DKeNfiUv4WNIH/ml/hw8qDtRkJ2G4+9eompT8vHtNLpyajFx27MWFerWHo7fMxxEhCHQy1Z1JGFK80LHVH4SaCWYTSTxjImM7r9U856egHQK/sYS99wLu2eoPVECHgdCimjhGLKKKSKHEopYiUT8TIIJz58OKkiBxshmkillCKuCj2Jr9VJHpWQMgToMvsBMwpAK+F1v9o9BbscJw0wMQ26YXPuYLwMYjTroRx6iMaLixB2qsghabFESz8JrGSSbEbr9qx+dppr9QEpUdw0+h5i6aKVZOrIwkaQEHaaSSWmHdoKYwjYHGRSTxGl3BW4kyxqSaMZL4OkqkKT9lWzcqmb1bOcKe9lF7FUkgdACDutpJBNNQl00Epy+J1x4SWLWnqIpi5xMMdev9aSreXA+MFF3EQkHRoApy2S2n2gJUqGNNUCBdBvaqc8ngKcCaPYgJtt/I1ruJn7yaeCo+q3soYT8ZPADBZRRCl3chd2QjzBXLy42EA+82xzyKJOhnJpMUobALQezIMZ+6r9qgqQQJECY+5cTfql7Wydkc7WOenkUckUluLrdDLhqHcoopQQdhYzDSc+nk88j7k8CTcky/bXqWuxGhbCiv5eyILfHXULC5mJnwT8JODBTRf9CWHHwxAqyWMbbtY0jSefDYTUxJtnm8MTyVfxeueZ8jvx+E0rajcmh6OdYbWYp30Fw0r0/vxk5b/YOiWdZUxmN7Gk0cT2KQM5kipeUPkTvLhYO/1YxOfQTCobyDd1ivqatJsOmGD+O8iknjIKiaULLy7qyaSCfGrJYq3rWAB8ODks5KMgUE7c/D1hcbWeTE4tfMMUUXXkg74OywIy9YxXGYSX8byPCy95VJJDFSFsZFKPm2248ZBGEz04FEcZYgxl1DKMB7jJtAgfABtDREQ16VC4RukJUYEZqwhhf6mY/Da6VyWFj117xp84iVUsYgY2ghxXswk64dX8qbyjZM2Rgc1McyzhYa5jEivZQjarOIlb+T+eYC61ZPHhCfkcP65CTvDJyMkwGSmKTlb9T0bGm0LY1eBa40/89Z+38NkzQ1nGZK4vewpXbiMTPvgI56lfMZ0ldBHL8KUNvDplKjlUsQ03p9yyFmOAQHR3An6ITzMjIlYZEC+ABngog9nXP81ippFCKzZCuPCSTwWxdPEys0jAz0MltxE/bifj09ZwddmztBXGKBCMxUaIf8Rdxt/mXsPqqRPldWi/Mg06FZjOsSnsFXPpYagRw9L6s/hT5rU0k8b95b+FZHh6yGyuqFjAY/mSs/JrF5EgpNKMgx6+rHQySNRBSrLp1DySPkaGq695AC8uogkQxMZcniCEHRdeeojmIwqpYBTn8wJ+WwIBWzRVc3P4EheZ1OOgh3u4neCHNlb8cqps+01MnaKyrMav2sm/2s9hfeIxeHHhxkMleTjxUUwJ6fXt0A2lw6NJo5mza95k3fBjiA11kdNRQ0Kin6EVjRx/xgo+fGGSmezzW1DETcSkQ4ODE5gWRe2DlAsEofuhJDN5ZS048dFKMs2k8iUueW47rOQkQIpJv3bcy+udZ5Lk7SaZFlx4KWc0hW2fcgKluPBSTyY8qvrRzsIZmBkrKjAtZ2H/sV381XsLO85LopYsyimAVIiZDyyGq1c/S4Boht/XAEfICX/Uq1uZWr9C5lydBqyKhaw004cuBshQ3v9kEDV7FyFs2AmRQxWxdGEjRDElVJHDpg+O48O/TWJw8WaiY3qwEYROSKropoJ81jCeFpI5mWWs7xzNu4efApvX942Q0I7UGZgWyHDURC/EjKauORdaIYVW8qmAeGgcksiRVEEy5FAlxURgVKACyiVnHcIm7+2yZDN7iDakbCbsRJtGE60kE8tucqjivA/eCLv4nOZdzRSW0kM0FYzChxMbISo5mmRa6cER1kkuL5vW19I9EgnY6YAb5sY9SVQb5AUqeZ0ZnFHxLlnUYiMox9kENEMWdXhxQb3kGptsaQDYCIEdfsZj8h5++1DUCAdnoUMD4AwkkJxmmFEF2o1jtooIKIfXHyxmMstZxmQlWnhYN/wYnp4wm0LKuJO7whPswrjnYRfEshsnPmbxMuISeI6LCBBNKUU8dc2FEsjOxLRk1mK+WT5Mw8ZkYL4MR/LioodoFlRfAe3wr2t+AhNg+4SBDJ3XKMXZdTDh4Y+k328NTHO9wgMFV2NsFn1zoGkdGL2wCWYkLyKEjTwq+QqpS5vOYib88yOyqeasExYQf8lOCijnj7ZbuYs7MfKB1VBPJqk0U8EoZvMCAKeuXsNAY6Cpy7R67GtQ8CEjLtwAUTy2+xJYLbniejLx4Oa9keOIJkAlefwp81ou5DmWMJ1YuljsmMabN03iQW7kEa7Dg5ueAiHD77qRBh1rJEM5lFBMKs0k4KeEYt48YRKxdOHDya60KFJp4hf1j+PDiTvgYXDzTkop4hkuZQ3jAWglmX8WniGNRJobLccMzs+AO0J3QxDiavYwi5fZlRfFadtW04ODFpIhHnaeEI8bD8WUwBAYQTWugJdVieM4om0nH+fmMiOwqG+uum9BER2cSYcGwPUiRcMW0deFo1sdy4B+j3YChCfBeNYQwkYJxSxmOoWUMYxa7uYO6sgii1o+HplLLF0k4KeKHHYujqeL/sxjDvH4GYRXZg5ZgPyS6O+QQGvtX3M5DXDlxQ/zsSsXgGh6oAXa8mOoJputZ6czuHmn9Lf1AkNVvXYgFYopIYcqycVpfaPWU6UAziiLHk5yqh0k4MQnOYs2GM8akmmlY9NAprGEIDZ8OFmWNA5SoYk0MqlnCm9RTyZ3xd0JmyW3RXdr37jPfMzwrQ6AqHAc8HSWsPPseLqIJYCDIkpJwE9SeTd1ZGEnxODFO/k192IjhA8nX+JiGHXkUMUIqilLPJaH/jq3r5+fchv5yeh/yfsHRBNgOkuoIwsnPqrIYZFtBlvIhm7Io5J6RyY0g5tt5LGRFpIJYSMBPx0k8NrpU0xLewxmMoUzYcDqXqgBtkJ++yYG1PTS6epHNtWEsLN95EAcoQA2gnhwwxcw1NtIkyODOBEZAAAgAElEQVSVcgoQFRAgGr8jgZj8tgMGcJFQLUmHBsDFIzmlVZjhVTqWsQEoB2eKFE1fZhY2QlSRE3abKGc0TaThYQhLOqfxdvVPeZAbuYx/sLBpJvVk0kwa1/MwQ/DQuF36rFWRww0X/EGC2h+RAOdBcgDrkECkrawN8AduJZN6QtgoZzS0wG5iuW3bQwxd2sjO1HhTBGxFfrCmUP7XYvEOV5KZH07rxLR4HJQTWlvz+rMbLy6qyWbtNcfyS/6EnwRiRrbxMrOo5Gi+VMp5CmAai9lNf5z4GM8aAjggC1a/dRrEJJvcm1YFaL2cFulagFvlhF7Gycr3zM+kig/Zhhti4P4Vv8WJD0bIR6fHGk0PRZQyh3kcs6gGOyGur3/KDEPTVuoUmMEieojGRhAHPVSRQwnFHP5BGwWUU08m/emCGEimhVSaaMxNNPV9SO5Ng+9PF71tcqP6ejyQPmGr9HYZDuSBJzEDHBDXvIcRVNNFf3YTS0J7L7Gd3dQyDALQGwdLOV0uDE1gJ4QHNycmrjkgbJUAouz7tx3sdEgAXHRst+Sg0jFdNLTBQYXJzLQtpIk01jCeaSzmZWbhxsOD3Mg1PMZf+TleBjE37kluz/41F/I841lDbHwX1WRTTTYuvExjCRcPnocHN+spoIhSCaTaJ24sZobZFGRspRJdkxZ148HNMOpYxUkMPOMLDve2wQdAKnTRn7bzYmACcIQcN9vg6QmzceJjIqtI7mzrG6OpHHvHVb7H8NGf4sHNRvKoJ5NM6vEyiKVMYVzzJ6x/dzx/5pfcnHg/k1lGNtUsYzKXV7/IsOGbKKEYJz4+ohAXXppJJX7sTnmTNxmmtbgDM8MJqHjNJuiG2y//NUObG0mjmWbSyGMja/OPpZQifpt7G5snDaaIUtpGxtCDgxyqyGYL2VRTECgnv30TOCCVJj7LHMp5xj/kgjWZcPYPreDfop5LMq08wC8gGQ7f3MZv2v5CJvVgg6Rt3VzPI5zLS5zEKoopwU8CARw0k8pCZsIQ5KKkARv5ew2PyWCOTth1RBSZnQ1MGfIaBOGwtm5C2AkQTVXSULriYihgPbTDZYlP4SDAGSvehQII4GAx0/ktdx8YgBNgt+/fdrDTIQFwPa0x4bTkMVPbzC9dZaltEyTgx4ObG3iQCkbxM/7GdTxCU2saOVRRRClf4qKFZFx4KaQMN9t4O+40XHjJoYoE/FSQTzEl/Ilf0kUspRTJoHutv/Fg+ohpkOtA6pOaoT9dNJNKAeXs/OAIWAJMAmpgcNlOkuq7pYj6hXl9ARyEsBFNAE/cYAmaHsxsGMACLsBBD7VkcaISvz24iWU3mz44jgWpZ0El/I1r+BJX2Ml3WWgylMMsXuZS5vNI6DoyqcdGiEXMYHPcSNlBUJhuKdoxVruoxCOtuvFwAqV0x0mxNp8KUmhlHnMYgocQdhYxg+e4iKRN3VSSRzQBuuhPAn5swT1EfQndEyAl1EoXsbxYf7ns/3XCfnFdxJJMK3lU8jDXkYCf7Lbt4IXeQSBqJADVuDLYOSSeBW9dwXjeZ1bnK5zetoLJLA+DXAJ+SERy4GCGfxVIN5TeAbAu/xgW26azMO4siiilZkgGYimk0IKPw0imFZA6zGfPPgcHAU6lBGzQeUQ/dtOfWLo4DN8BA7go2/5tBzsdEgBnTw6oTCG90iXEienZvwxIh1qGSasZk6knkwt4kV/wALck/5GzPlvKTTseIJ8KXm6fxf9xK0uYxm5ieY2ZJNOKnwS24caJTzrldjbSRX/KKeC2398hJ6DOZJGCTABdQDjYOup3u2A4eBjCVzhJpRmcsG7uMVCGTNrZifld1yOQE+9IlDgWIoQNd+d2fjXhLtP3zwNcAmewmAT8ZFLP+4znHm7HiY/Htt3EfSfcyIV3LcR90+fct/j3PN7+c/KpCIuHFReMIJMvOImVPGq7hmHUUUUOmdSzjMnQDZdnP2oG2+sEBtrJGKDDgI5dnLZoNSF7P1pJpodo3mc8Cfh5grnYCHISK7mj8/eQKIHKiY9Ydod1arSCLQi2oBTrKEHqxLKQHO0NKKuo1HkltHfjZhsbk4bTOxqi1kN3LixMmkoJxcxjDref/mvO5WViVoNYCrPffY1CysIxue8MmcCWuZlmZmYVVlVEKVFlMLb+UxwEeIyfcfuiv5DZ2UDn2f2YxhK58AX8xHZ2M4xamkhlXsXPGbxgJ3SC1+HCiY8A0Wxg1IFxE4lwcGE6JAAuGHBANySmt5ppdrQuazJgl+4K9WQSVM6Zp/MW01jCYfj41VF3cczhFdSTyaWJ83HiYxtuqslmDvMAcBCgglG48FJEKQ/G3UAxJRRRSh4bzXxiWoTLwkxLHgRnsg9GysiINJo5iZUMPOoLRrd/Kr9N6gVGQk1qhvxcgkVU+gon0QRoJo26uKFkUWtGSQCnPvMGbrbhJ4FRbMBOCBshmkll3ZBjKKGY2+68g0t5ht9Ov43liRNYxUTm8gT32H5DLLtJoZWxT37KedvewE8CzaRyF3dyK3+Abgii2AHt8R92C0G5wQhIGQDD5aR2Bzyk0kQIO/VkMouXaSWFVJqoixsK3VDHML7EFQZvRwBIBHtI6rnceNgxJ6lvFpOxhB1sU2kmqg22kM0SpnN34m3ggpg2eJ/xZFFLCcWcyBo5/jjkx5g/l7o5HbfqJ4Hh8xv6iv4d4Ap4wx/M6yKWEVTLRQiIa9+Ds7OdakYQstuI+VyOYwavszU/XS5U7dKoBVIP52XQv31v538hISDKsX/bwU4/KMAJITKFECuFEJ8LIT4TQlyvjv9OCLFDCFGhtimWOrcJIWqFENVCiOL96qgLSIH28vS+Ob9qCXuku/FQoFJ93MiDgAy/eYK53N90MwWU48bDGsbz6Qtjw+4hGxhFl7JH5VCFGw85VJFGE1vIpoBypgeWmGl3ytW2DtPTP4gEJaR7w4ucTwvJ7PzLEdQlDpZWupNlvbRQk7SktiJ9plqhgwS2kE1QubB4cfX5KPJcnmQ6S8L6pRyqeJlZ1JPJI1zH6urTuJk/c3fTHRxNJdVk00Usl/EMTnwML2vg7Fff5LO5Q1kw5CzqySSaHsoZzaXMJ/eCj1mPDmc0zEwpbkwnXwUOH+fmkhZq4mXHLFpJoZ5MnPgoYD0uvAytb6SMQkiEn/MIARyk0UQqTYitso2uuH50J8EwamVolM5x1yifZVBZvwE+GzIUJz6KKCWFVi4Z+RirM8eQQivLFLfuw8kxzTXSIp0IBKCOLELYpdgIUg+qUxvFA2Mh7oM9EAAjToqrxZSw67woYmqAxdAaJx3IAzYHfACn1KwlhI3dOmtyJyR3tuHDSQJ+enBI7vzbUsQRLkw/NAcXBG4yDONIpPr9GiFEjip70DCMfLUtBVBl5wJHIb2THhNCfKMmoV9isG/GEJ0GJ5dwhpHbvX8JK7Qf5EbeD53IL3iAms+OISetCi8ulnEyfhI49oK15FBFGWOoJ5MTWcNoyjmfFzilbC2Dtu/kTBbRRSz3czMbHCrZl0f1q/Ok6aD7LOlATDmcyBopCnMunNuNnwR6ZyNX/DSI7u5llytKToR2IBnyqaCYEjpIoItYGeakJ3wG/PS+t8mhihaSKaaETOpZyhSc+HCpr7dtIZudaSn4SWBu51PUMYy7uFOGaLXCO2dPoIxCFnIWPUTjJ4EQdkopopgSNlUfJ4HNLUzxv0FtWt+4UF7ngK29BIimlWQ8uJm/+WfksVFyw60wM7SQh1Ov5JilNbjZRoBoDmszWcI7HXdhC0LSP7ulxXWcKmiU/TaTxnSWMIoNLGY60fSwiDMpoxAfTp5kLo+EruM5LuIJruLsijflIjICOk/uB2fDBvLpIZojqZJ9fIEZYqdilntHA5/DtqR0yhmNiy8J2By8lz8OXLKNVlKkqJ8IlMtjTnzyvUuEmM+l36OOL44A3IGlHxTgDMP40jCMT9R/P/I7p//pi9dnAC8ZhhEwDGMbkgcb80397Nlth5FG2C8rKmtXn3TgUaftgk54iVmczwu82Hk+j9iuYxYvc9NR92AjhBcXNeuP4VGuIYfPKaaEh7me1zmTAA5SaCWbLVAJNEZxMc+RRhNTWMq4ik/M2NBG+vqHKcfjTdvzIQZmtr1JvoqFvfLwJ0nAT9Tf5J15vPBiQvZ+eG0u+cXKI4FkuPj0V3C1tTFIGT/qmrJMP7hueV4AB62kEMQm/fOQQfwtJHN59qOMffhTrucRuohlQtwqVndO5FoeZWbnazROSeQqnmAZk8mijiA2XHhZz2icfMVipnFM9jr5NDyt5jcndCojdc39sjrJoYreVJjCUvwk0Eoy3ZkwtKaRWoaxIv94qm3ZnMkiKJCqgx4c+BOjJOeaJLml1sREOFIahzhN9ZcFVEhDjU4UoJNb9uBgGotV+qIQ423v8zDXSfBR7h9tI1VISSu0ksIw6sLifDgh5Wb1Gw/rE4+BfMl1F/IRBYFyBjZ30EIyC6acxdRNK1jCNOlm44Kt56WTQxWHL22TomyBfA/8JFBIGcuZLMXkA0ERgAN+eA4uTEIINzAKqVIHuFYIsVEI8Q8hxGHq2OFAvaVaA18DiEKIK4UQ5UKIcnw7pUPvMqAbelcNkP/LgXwoSi7lveHj+A338RozeTzuary4KKOQPCqZzDJaSeam0fdQRiG76c8yJnMnd9GiMkY48eEKeNl1aRR/LZzDq53nsJE88qjkzfxJcHOvnCTaEfYSJBDoPHFzoiARViYdTwcJXMCL/Jp7Gbl6O2/+ehLu8z6nlBOodOQxsn675Py+AD6HFW8dT0nSBHpwUEoRe8bGmQHoGbBgxlmUUkQRpcznUnYTy3jWUEQpBaynkDJOvn4Jz6++kvG8zxzmURp3PCuYxBlxr1NFDp4PjuQinlP6MDvVjGAbbrLZokKblNtofrI0qNiRgKNz4vlgz8I40traCdnhPn5DEBt/4leE7P0gIIFLpxFyte+kM7EfG8gnhI0B5b3sGJIE7VJ1kL65HeMIOGrpVulMrUXiZXA0lWwkL2yYOO7hTdzM/ZzEKj4InEAdw3i94nzOq3+Ds+e/Ce1QMyGDVlKIq9kDwM38WaU78kuAG0vfr4R1wCmd7/Fe/jjmtD8rg/W/2MNnqUOZzHLmMQfa4dHOn/MIP2fYqZsIYeeYeTWwDemQ7YDeTOmMfNq21TS8MPyA6OAQSF3i/mwHOf1/AXBCiHjgNeAGwzB2AY8Dw5CQ8CXwF33qPqrvM6GdYRhPGYZRYBhGAckDzVxh65ATYSThdEkVgXx8OPHiooUUUmghli56iGYZkymjMKzofp0ZvLZjJrN4iRU7JuNmG4uZRi3D2ODIp96WybXz/s71cQ9hJ0QZhZwUWMWpg5eaHxtpwPx2wjK1XwushXw28BVORpZtZ3DZTvDC68zAF3DiV6ksHs68UhodOoFuKKOQQXjxqkBxPLvMBI1B2E1/HARYwjRshOhSmTu2MIJra/7OFd4FpEhvYerI4or6BTzHhQzc1MG7n53BpA8+hICMxy2liEry6MFBMe9SzQhu4Y/UlB1jJu9UTrSA+RGXdOBNaEpKpDpuODZC7CaWCc0fSRE+VSraFzITgDWJx+N3JISzb4DkzEByowSRXN02THH4HXl/q8lmMssJYZPOtM0w/N0Gktvbme54g/N5UYqC5cj7WAnVjGB4cwO0QveRMHSTtILH45eGgOHqenTeu3joeGkgHtxErYCVjolgh2RaWcoUsqmGZIh5F27mfnKo4gqeZsecJBqvSWTXuCjaXDH4EuOlGiBOXceByFgeEVHD9IMDnBAiCgluLxiG8S8AwzCaDMMIGYaxB3gaUwxtADIt1TNAyVv/iXYjnW3zCVtNiQGyDEiBfEcFI6jGh5OTWMlXOBlGLRNZyRTeYhi1FFLGSk4iAT83HP4grzODYw8vp5CPiGU32WyRHEioHlIJW2R7iGalYyKzeFmOdqTq/3Y1eh32kwKMknnEtpDNq4VTpYVuAlzCM+Q5KmkmjXIKWMZk/jHnPFl3uGmJAxj76qfAAFNE9cjjGxhFgGgKKCeNJurJZARbaByeSJsrhtGU89vht+HCS+8AuIonWZt7LFcf9YBUsMdJq2YTqbjZho0QFeQzigpWcRK5hR9LINsMxMfKJ+XBzAUXBFaBBzcptDKLl7mQ58KJMP+Reh61ZHE+L5BJPc9xIWUUkk215KBckNTcDSFlkImDhPZe821oIGxsiCZAFrW0kkw0ARgCn506lGsTHyKFVoopYUdhktRruuCdORMYRYVcMDohppPw5N9NLCFsdA/BzDW3Drk4KZ1i2wzplEwrJLe348ZDNtXsGJkEuTCu/BOWbDqHYkpYyUmEsGELhthCNh7c+Eng2dRzZJ8HQkQVyGvbn+0gpx/aiiqAvwOfG4bxgOX4IMtpM5AqWYDFwLlCCIcQYghyXf3oGzsyMK2K6zAzeVQIWCetn+spwIUXGyF6cPAY1wCwhOkk4MeHk99wLy68nMVClfW2lWY14esYRp1KR919sgxH0inATwqs4vIdyuNeB587gZcwPza9CUSlZEZHU04TaZw/5O+sdo3hTu5iDvPIoYoXOZ/fcK8Uv+xAvLQAH91WIw0Gr2ICuOrnuvaHiaWLB7gJJz5aSCaaHp5fcSXRBFjK6ZzIGg5TcakliZNIppWbeIDJLKPmVxnQJCME3uMURlGBm21MYzGZ1HMhz0mw0gYcvemAfzuSQw0S5pTryeSYihpwyUwbCfjxMojB3p1sw8293M543mfspk+Z5P2QtkzFEgbh8Po2AKqTBsN9mB/Vzpf9FFFKGYW48bCcyWydk84fuZWbuZ+nQ1cwvKxBcoNx8PglFzMIL4eXtUlu8AjgCVgx8njshGghWT7/uETz61n5qj833PTCY1zNExQHSiBZ6uWk03UPh9/SBomwtSCd3ky4LvAIsz94DRshljkmkxeoJCdQRQ5VXFL2srxfB2JGRji4MP3QHNwJwIXApL1cQv4khKgUQmwETgJuBDAM4zPgFaAKKZBcYxjGNyeYicNMa+3GzAmn0l7bCNJCMmsYzzD1/QOZ1+toFXTdgVf5Yy2suZAnuYo6hlFy6Zm8z3heZwYLmUkTqZRQzNi4D1nunRZ2g1jqmAItMX2zz65F6nX05E8B7ocK8nHxJQWUU0gZL3I+lzKfi5tfAeAO7qZWfTpq3ZBj4C0poi5K+gnHbdsEd2OmDwrK6+6+NYkSismmmhyqOJpKqTNbC0lLu0mjiWqyyaGKUorYTSzLOJmJ8kPmPMiNYJfpmdZTQClFxLKbBDqwqbRLy5ksP9Icj5nJV4lyYdeKDJke6Lj6TTj5ClxAJ6Q/3M5oypnR+QZsklbQLmKlO4XyAbSHQnTHqWe5Wj2+Tdsll1sgnyPrZN+V5BHCRoBo+tPFciaTTTXJtDCgRHJ9SRXdNE5IJIfPyQrUyY+LDUFaO+2EP7qTQivJtBIb6jK/zeBT/bUAy6QP3IuO85k25BWC2JhU/yH5bJBvd1C25UnMILp7D3SiXHkG4XckELLbaCXZ9Inc841v8zdTBODC9ENbUdcahiEMwzja6hJiGMaFhmHkqePTDcP40lLnXsMwhhmGkW0Yxtv71dEezIBzzd2sRQbfT4UvcbGE6bzPeEopIo0mEvBTTyYPcz038iDTWIIPJzXDM9hNf7qIhVzJfQCMoYw1nMgqJvLp+rGc7FqCgwBdxHJ2/ZsyN9xIlAiH+UUoN6ZFNShjLAd6O3Di43xeZBqLKaaEp1NnM40lnHbf6rCOsJI8sGPmHnsVxHLD/GKYcmdgE/gCTirIJ5VmvsIpXRWS5f3w4aSabEBOxipy2E0sFeTjwS0dlY+Uw02mlUJlB/IyiFaS+RV/ZjxrAGFybiP595Tinl4e4To+yxxKcfsKtqamS7v5yVDBKGJWw79O/QmjKaeKHBmA3wrUw4DWXmLakQqJOKAddubGSxcRnUwzV97X5UwOP781nEgelUxkJT6crJ4yBjrh8fyLuZs72MII4ir3SNNVABozE+ESGWyvyUaIAct75TU5kYDqJpwDb01gPGMo41KekbnramBc/ScQD22uGHariAx7CHacmkSAaIbgYSUTKbMVSrceLf4eCB2cHHTEyMAPz8F9f1SAmUN/E5J72gy8Ca+Nnx3OCHIiayingHw2kEclCQE/ZYyhlWRKKOZ6HpZc2d1nMeKmCiaykg+XT+KO9j9QQjH96eK80f/gXF6miFL8xLM9cyDMw/yAtI7ZXKf+u5GTsxGu5glYDSM3b6eVZBLooIJ8JrJKAktAKtnrySQeP29eP4mZLGQai3ngV1fDtRshuKvvNzfXVrGDw5nHHEopYgge+aGca06FbpmpI5MvKKOQYkp4jot4hOvYSB6/qHicq+9+lu5UmM5ivAxiIqsYRi1LmE4QG9twc/sCZQdSQBbO2KITb8YD9ijejDqbxUynNTERLy42XzKYnbnx/HT122ydkk4leYzb/Al+Eijo/MQEtEWw0xUv9UZJMo3UwAUdJN/UYKZ+7wbWGrw2fDYgU0h9+uRYxv7tU8Zt/oShSxtZyFkUD38dPwncwh+5wrsANsEDk64GIL25nV1pMiBUL3QDmztoPDXRBGy1aOhkDe1T08nfsZHiQAldjlhwwaOZl9M4KZGkzd2Mbv+Ugc0dPJd0Dq62NunaAqzhRFpIZsVdU81PVx6IJG0RDi5MhwbAdWEGfWvxKQvJRaUAuXAXdzKacmrJIpN6JYL5KXUUMZ9Lw24jNkLygyv50IMDOyFOPfkNemL6sXXHMA7Dxz38hnIKeITrcNAjfa3chDmMcIofrXzXgBcDH144SYpJG2Bk8/YwF2gjSAX5YJMizs/an2INJ1JPJn/lOob+qZGbhj8GKUdD+gAz+aMdcObwsmMWmdSTRhNuPPhJkCmZ2qCActZTQCpNzGh7myJKuYO72cgxPJ5/MSooACc+EvBTx7BwJEcKrUxnCRfOfsoyYaLMCaRBIZzSfBslFLOSiYzf8QG1DGNgWQc7J0hrYiFl9A6CIj6QkQCjCCvEB87rkJxWshRZ6Ya2qYebzzQeyBVQ20ULKVQwiuPnrgCH9HFrmxLDl7hIpZliSnDQA5th14VRNCE/gEMnbLTlhS23Xlx8nJorRVSlRwyDqQcJ4mOBJ2JY6piCl0E8O/Ic3Gwj/dV2to8ciD8xhrbUGBnvnBhFPZl8hZNM6qVon2F5Fw4ERQAuTIcGwA0w5MtoJ/xhF17HjAcdSzgrb4XyNM+ilqVM4UFu5GSWUU8mr3I2Cfg5mWXcOP0+QtgYRh2X8Axx/9rDpMOXcRd3ch+/oYlULuQ5maSxvcb8ypZWiNuRIo8W4XQap4Ug/mlQc14GLIWx5Z9yxrZ3qWAUy5hM4x2JXDv/78xPnM1kllFGIUWUIiYYZtZgHZu5jnDs5OX9X2Sj/GQ1Xlw46KEHBysuOZ4SipnDPApYz8ak4Ty/4krKKWDg5g6uXvwsswrn0xMTFdZHBnAQSxdZ1IazAy8QV5jfJAWTewzHzPZKLpohrBbFnL/8dYzf9ZfWx3Kpe6xmBP3ZzZrE49lCNqUU0Znaj+0TBsp2VAhUTW4GA5b3MnfOQ/BOlynub0Z9fEZ+PzafDdzC/5E/50POYDG3cy9jKCONJuyEcHa2s2tCFH5bAhfxHCvyj2fzkMF4GEIelXhx4cFNgGgesV1n5rTTiUrtmJzXWjgnbwkLkfkBe3Dw+NkXs54C6shiFSfx+01/YLFtOh6G8BGFzGMOf3/4WjNsMANp8f+2FLGihunQALhuYX6cxI5pzRzbLSfdOIM8NoatZiFsBLExkZVEE8DHYeSzgTHVlVzEcyTgl5lwm1ysYTxFlNJ4XiIX8CJHNW+lihzSaMZOiEy+oDRxjPnNgrGYEQ3a019n4NXRDgvWcnT7p1Lv1QY4oDhQwp/bfkt6c/v/Y+/cw6Oqrv7/2WRChlxITEISYoIBEokxSKzRUIGCiKBUwWsVXyxesGrFa6lUKypqtVisN6pVsWpF8YIvghaFIoKCNRokSIxgAokkxCQmMXdymXB+f6yzZp9QrdjSX+2L+3nmyeTMmXObvb/7u9b6rrXpOEfU81sZzg7SuXjxEhiZDx2O3CfuseOxoNNRTB7vU0MiIQRcqNsazCtVhlpPPPRHwGVwH+iBmSziyZCLqCGRLvrSQwgtRHHftpukwm/b68Amz6LS2GIGyq4ItcEUPiHlxBIYKxFPIgiWgm8hkvG1fyOSFk5veo2lYWdLRDsDYba1bpJ7NDx2xTXgC7emsBZR8MPCq24gl000EsNMFjGOt6gnjkKODkZZ10WM5d2Q44OloWpI4B23uolGzqtIZnT+h8x9c4ErLcKWuPL3Pie5cOezd/EC53If17GSH1NBKp30JY562jL68C7H8yqn8WTnReyce6QVfivjPhDtewYXbAcHwOldlmNZRQrwil9+5AWGYrJIcEGpgFwaOYQTWMcwPuU5zieVCsYPe40p9SuoJZEAIaxNHM+D9VfTRRjFZHHxoiU8kjCDLIpJoIaVTGZm09NcwwPis1GxiwJBAAtIWmWksR4YRUdMLH/KmybarLUQ3rYXcy98kJDNoxE/oy9drGISG9afhMl3kNK+5bLgsZriCqCRwOgsPuVwVjKZTxnGGN5mOB+xleHB9V9FsJDFe7kjOINlnBf2PJ+dMYC8nnyu2fgYidQw1NWXVZDKA5lyHT+OeBX4gX3ebvXg4H1B76q7HMHjXMrO6UnENTXBWMmnTWeHCJXbBGBDOwUAE6nhkbEzJMqZDBHv7eX3eVfAH+ttxDgFCTgoK/4jQbBKpoo9hHM2S6kglTVMIItiBlLFg1zNVobzFuMIo4tUKoLMtJR0KQe1HmH8+pupya33pBNUEfAUFF16LBuWn8S6tnH0EEIhR1PMEcwIe5qVTGb1X6bSdKf7w+sE53OP/70P7oC2g2Nl+yNzHSg7HNEAACAASURBVP63QDpTEZANfZLa2FsQYReB8UHTzL78JWQyewjnBc4li2Ims5IFzGYgVRztJrWfx/OkUyq1whpO59nYs6glgetXPsLcyTdyFFsZwzssYDYTWMMpA9fZNJ8U7Ar2OlDAJuA3ggj3WsDXn/Hdr/E4lwYlJ/OZEyxwWUcc1ZcOgUXe/J5QYRnKMOKBgnZgN6RkMKTiY85gGVG00I92dpDOdobJ4iuUBUEmmSpe4FyWFl4At0D3M3BX9A0kU0Uc9SRQwyE0cuSKnZip7k344npr4eKx/ioFvFYQp2gLjEtk4lvLmc0C+tJFMUfQg4/hbOX4pve5PfpGctnE1EtX0/C4n7v4NafxKu8whrnmSiARksLt+ZQl6/NtdUhyynicS2nkEFqIJJ0dwWrNyVSxmRyiaOVoN6jUSV/C2UMFqbzFOO4ouhtzyB4Y55d6fgoMaqr6PPcWwFarcTWKVHt+dwX7dM/vrtFuFWZfn4uzo+BfiqXmxhqnYML+7Wte+n5l+//+5uYOBjvia7B3cYRVpOcCPqgLiWMdJwQDCTVu5kAOhZzAOlYxiXfcOmLn8xw3cRcXxT7M9G0vk0Mh/zv5lKBspJShLFg/l5MXrbcrvfuwy9upnqrSvQYNNgAyBfeHwF9Zm3oqQx/9nFks5M9cwC5SqSeOok3HUv2bIbBIsxhCwR8qA0mDJ+qPyw0HfwZU1lNRn8oyziDgLh1YQWpQ9pHorkJVRxyTelbx8o7/YXnORDgCQrdJDqias6OLPuQ8nueDKdnAbqB5Hye5Y5mNd8EWAMKBWNgmzK2UoYTTHmRrxRxBeXSKlPgG2hb2ITa/gwms4fim95l77wIkauOWHVK9XSu9yrTDRqrHDOFVppBIDensIIQeTmcZidSQTJWbS9tXVsBCkvvriXOLnX9KdXY0pPgFlBSo1QzP8dxfNbZkuwJ7DBbsGvl7IbSapeqv1D7yr7bvGVywHRQAZ6J6LLh0YBdi1ujVe0ARDJ33OVfzII9yWdAnVE4a6ZSSRjnn8xyRtDCPW9lMDjdyN6N4l/WZxzF+/d84c/HrtNOPUtIZs2kTx499E/OAy5DrkAHRiAW3bUglDK2AqwMiBmRBzQlQWQaXV/K+OYTlZiDVppVKEwu5r8PNZfRaAE71ZhqwUBYV477i4+iO78/ZLOUTsjic7cRRT186uZI/UEMCdcSRzg76v9nNWUOfZSWT6bgF+KNEFGfUvkguBdyTPYvTWcZxZg2yMMFgew0BwOeSkNJmGfwK8sEWCtX13HPSrfx8x5P8hpvYRC7nlLzG0RSSUVLJ1IrV5FJAeNteduYl0Y899H3Kgdme47fSmyF2eJ4xo+E9eMxcQw2JlDLUrb3WyvG8SwyNQZZ+PO+SQA0AxWTxNmOoYiADj3XLMVUjLg63vBY+rNhXBeTewpt6bdrH1FenvmD1jyrDUxP1AKyLeiCDDMYYvzHmfWPMFrdm4zx3+7eu2WiMOcYV8JcaYx50M5n+re2gADhnT4g12TTqVYcbcUMiqW8Aa+BK/sDZLOV43mUSqyh3K/fWksBk/sK02uV8xHDiqWc2Cygglxi+5PGx02EVRNFKOqVMPGY5d3OjreIboLcmLM29HnW8p3j26wABjT3uhn7uF45z3wcQmbyG8lwTVQcKWCmKLnATLKfWzD0f30oNidzMb5jHLTQSQwtRwVWrTmMFDBbpTAtRZEZ8wktPnir+sYAEOFqI4s5+d7kHr//7h67mGD4LbCrIpQYJiQZgTRmMNCx/YhpvcQJrM35IJ2F8nDGEbamH0Y92CmKzJZjCn+Ba5HwB956VBelv2uF56fOkmQueWMowPnWjowPpRzsjK7aQRhlx7toJFaRSRhrFZBFGF3MufcgeU9e38P5O6disGM1yiKc3gOlzaHV/D2V6ytaU3ep+B8JjdGAZXCcw3nGcEcgUfbIxZqT72bet2fgI8DMkZJThfv5vbQcFwNEXa8LUITNxB7Z44XnAr+T/9ReczPW1j/AWJwQTvfvRTgK1vE8eHRFwRttyEqjhrI9XUk8cz/E/9KWL9c9ITYAYGvk5DzPu2Xyg25oxlYhERAeNDkxtaq7o4KQfsi5dLNCMBbtm97UH6c3NgJvBoPmSagapAzvo7+sPoyV7IZEabuB3nMEr1BEf1LbF1nbwccYQviSG33M9b3Ayh7Odk9Zv4K/Jo+lHO5+QJWuhEgu+LPcaPC04eFwzUt0EACmJSP9OBHZDXTPM7GbxtEuD1Uqe5X9I7azgffK4lXlMXPUOO43WVQgFX2hvEy8eC0AqG/GD+Pv6w8yPOPGUd7mdWziaQj5lGCWpKQypqiYZSZSpJTG4yv05NS9JrrD+HnpMNUMDiMC42j13Oh72jTVL9TvKpL3mqh8rPdHn9R0DOEea/nJqLvyjq/zKmo1ufnl/x3H+5ojj/89INcR/azs4ggzDch2uLpCOuQ5ZQtCPzWzIRNbxjEHY3LXw8ozJPMjV/Irfcgyb2MQxweUBZ/M7hhRWi2I94RJmbXyC5aMmEk47m8kJlsNeMuBim7KkLEAHRA42MpeJDBYFPzW7tFvRjgBbKQJ4Cnz18jcy1MpClKWCBdWRSGoa2MWZRwL3w4y8RxjGp1zd+SDvhI1hGWeQSgXXdd5HVVgyBRzDeQ3LMbUwM/MhFm27CvOoA/eXIIiyB2GQsfxdnpFOKnQjo8nssy2UYMABn3tfNVg1bX/3QHvcfXWf8N4sSAFDxbLqJ2uldxCAGiR5tQFOjoOFDiOG5rPls2NIOqyC6s9S4behAmwqDM9EwK2O3jnMldjFi5SteYFK16VQFqfrcKgpqpFuPY/+Xlfl4uz8F4MMCcYpOHf/9jUL+Qwb8gB4zHGcx3rtIwxsk3sHf3AcZ44x5jakqmEzMmp+4TjOl8aYhcB7juMsdr/7BPA6Qit+6zjOBHf7GGCO4zin/pO3uV/t4GBwYM21swn63IKrope62wvcfW6DGhJoIZKlnM2AilbSKGcopQznIx7lcpxBQANc2fAEC0ddQhbFJFMVLCy55LqLbXpYJdYHlYN0k3UQXMbAh81s0IEaBAGwozYNa5K2Exy5an4qy9BtaoKrRkxBMBN47yMYCU/nX0EPIWwNG85x5DObBZzBMqrCksmoqmRa1XK2xx7G+ZlPsLTzbMx8B+53WREN7vXEQrz5e0YQBBbPB0HQVj2EKluVoSpLbXG3hWLXYe9PkBEqO1Im5MnnDZqo+lnw9D6CZv8b9ZAeYIsZCWmhVPcbAumh8Mdi+zxVw6dAqcfVSUirCMdj8361n9W51+idqHSbMvf3sIERPeeByA/9dgUv67Ruovt6bN/DuaXLcpBedJwxJptvX7Nxv2s5Hsh2EMRREBO1EbuyFYjjeBF2YZRSbKntSvj5mKdgJmzqHsPimWexiklczYPE0MiPeIc/x/4kWOFjK8MBqUi7laM4whTLcb1+IM1hTELmsnEIoCooaaYD7rWAmGEBjZLq4OwPhLqsoB/BBPdIhAUmud9Pw5pA1di1YMvd/92KJIzcxFwWMBcHFhrGXvkG67ecLIwvG1iMFOUsL0YALeBeQ2LvZ+zlAN5ooQ9ZMxWw/Xk3thBzHJah9vccALlPurEAZ+QYfmOd/Goy7tuTlRl569F1xLnRynDo8EprypCCbwBZ9hJU6wZW86aTRB02l1j7lk6WXjNVWxo2XU1dp/sKe1s5sCbqAW6O4zQaY9YBJzuOsyB4OmMeR2wg+PqajZX0noJ1+7+1HRwAtxfrh1J/yJ0IwV6EdEyVVejAfkXemwIHp8qQl5zPGk4M5l8mU8WSzKlMu305v59zPVPClrN21alwOXZGr8NKBrzygWwEaLzmi3fwgMe0CvfcSMD9vwZaE2Wg68zv1VbFYxd+LvccyxNokFYGHIX0vUSY9RHrZw1DqlH1R0brEe4B0hCQKQei5N9yd2JWxhlwzU6f+z7gVa067kWEYvu5g4BbAxbcohD2loiAmzI6FyR9xjrmwb4PeLbtC3h67wE9pxGzHt0+2IKSRj69Zq42r+7NK+tQ5l1Or0rRQYD3e94HsL91OXYiggM3GjWKeiAOZcwAoNsFt36IBmG+MWagp8rPvjUbnzPG/B4piJUBvO84To8xpsUNUOQDPwUeOjBX+fXt4AE49XdomH42wk40+lXqfjYO8cGcioz7cRBS2kpzZ38ub3sa8yRwIuTn5DGUUl66RVwIb649DXO6Y4FMBb3qw/HqoDIR9ubDAlowsIA1uRrbISbcNcfa7WcdkggeZIlgq1uUI0xUswZUopGEFRe37sEysBKEtXyEZCPsdi+4GQE3ZVAgtY3SAOOyTR21Lov0ylX0vRYS8Irk1MHdYRDAbgA3uV32a/b8H4oFN88pddKIxPoVlU0FgdxzyODpXfbX2i7n9pqT3uY9vt6D+jd1X6/A12uGeoNF+j31z3nFwDGe/fR8B7Lg5YFpA4GnXT9cH+BFx3FeM8Y8Y4zJQWaMcuAykJqNxhit2Rigd83GK4CnkA71uvv6t7aDB+BAxuYGrNA2gMxHAazMQP0q5QgQZcLe3AgiU3psNVc/cKP7+UIgUIxMXFgzJQ07IEqxgyEHq1OD3uu0qk5KB1V8uP1eY7g70LoRUOiGbaFW45brHjcby0JVGuPHMkYfWHCrRybYSoTJOQiT6kbM4UPdv/2EOQX6iXkXD1TWg9ZMa3RZUQpQqe4W1wTs0KDbHoLI5DcWEHzIcdmDMLd+WIkM9MpdUlPcm++qrFy3J2FBRCcb9aEl4UmNCrfPQzVqXsbbSO+IbPk+zzTGPU46dpnEOnoHlQL7vJTB68TW4flfPz8Q7QACnOM4HyE1XfbdfsE/+M5vgN98xfYCgsuR//9pB0eQIQTrC6vE5izqo45EOqoyOdWp5SCgpp14HKKXu9n9+7z7nfQsSDEWZE7GDoA1WClIKbCU3o7lFPfYOpgK3X3183J6M4Y0HfChlhk2Iv6gANZ/F4+Nqvo930/C7fzNBMW5QcDzgkoiUEvQPAx0Q/xgVzDtEAS3ePfAqrcL+pI9AuQgSrtsrLWboLMpoNcS7rmOULkWXzhBf6NXngEWmLzAUYl16nuBThlWKb19cmouKtNSKYeXramZ6g0wKLPTyUu/Nw67sFCke+5Wz7mqsSCr1oROUMo+D5TQd185yNe9/o+3gwPgdObXzq5mWxpWm+b1t6S577dhB5B2TI2mqaminVU7aiZ2oWMvcGoAQP0vQTPU/U4pAmYahWttt+fRjhholn30u8pgWhGzVM1vb1Mw1etXsPWrz0v1dA7W0a+SDG8gIdRT9cTYAdIIvYTGMZ6vBD3mKhNp9rxaELO7HUEqDaZEYRmf515VPKvnUWmGgrxGjL337TVVvdFWBfokLENLwU5uCliNyO/WgUxeuq2S3uJpvY59Bb7KEGM8n2kf0n6gfQH3swNVZff7ir7AQYHhyHhRuYb6p8qxHXQNttP5sdExryO5DokTKUtTn1oa1gRqxJrBYAMNCnQd7vnVHRugt09HWyXCXnpp4YC0/va69XyR7jGV+aVj1STKJtT/5sc1J4GA6/CPjOud6hQJtCrAhNMruq/PwbtvAAiE946iBlvAjQTr/yr58GH9ei0ETW4fENgDkeEQSLHXpb+T3/Ne2ZeCug8JGj2FZV6Rns+87/W5x2Mnu2r3OVZjn3saopnUiW4bvSfK4P1jGaTX9wa9QUylO95AElhtpEZs/9X2b4qi/je2/ziDM8aUu/lphcaYAndbrDHmr8aYEvfvIZ79vzLP7R+2PvTWhGnnVsBLQ4BhAlbc6VWd12H9Y2oWRWLNPa+oUxmYvvcyGtVP6fY0z2d6PvXJgQU3ZR76mZqeAUf0ezoAW7F15sqxrNLLskD8adQA7Tb66QUB1PlPbwYCNlvA6zeM5OtbAAQsG9xraPB8EPBcV3hvEQEQZIBeVuo1r9R3pqZjEX8fPfW+lM2CfVbeYIKye2VjKUgwSAMHyuz0eWg/UubqiaMEc4K9oKrsWf9vpffEEODAyUS+L3gJfAcAzm0nuPlsKn39FfCm4zgZwJvu/9+U5/b1TR3MmfQ2MVROoSJN7cwaFHjP3U8FwDEI22vEmp7V2I6djgVS9c9sc//3auJ0JtfBqc5tZSTxCHhp6+iWYpYBx7KoViDJiB9QWaI3auoDiuqhzk3h8oW6AYo9YuqSgmVRoV894KC3vynSvafKdvuZjkgFuSQQ0NL8VP2biPXJqfRFMyDc45S7kc0OoKOZr8yM8Drwvb5M1QEqm8LxvKc301NJkPorNeikfUIZ1QasrKcREWerXy2S3mt8KJipFaC/iQ/5bXVixfN9/VzZXTXfLxt4gNt3BeD2bVOBp933T2Nz1r4yz+0bj9aJBYV4pOPn0jun0IcAmR9bdTcbcRwnYVmedkplSipTUBblw2qh0pGARhFuhBHLgLSzd2BNVr22Uh3cym4051R1b93W9+SNRqZgBcMBkECACS6OYqmD+t9223Ps2+G9zE39jOq3jAnvXdrJp9fR7QKk+vX0gP3dbfUIqKr2rcHdbx8wi3S/o4Nfm7Il3dbo+duBMNFILEirXCMSa643Yp39mdjfyxsY0MBBAOuCKEJ+Sy8LzMayWa8MRG9b5StqMiub9k4iaiXo8z4Q9TW+B7hg+y4AnAOsNsZsMsb8zN2WqCJC92+Cu/1QZNkRbZVYSXyvZoz5mTGmwBhTQNMXcLZbzns0duDorJrpvp+JNZOUpVViI6LqW9OBoIM+gERcNyAD4TUsG6zD+t0UDHXQKYNLx7K4unpZNAYHy3j628FKN/hDLVPLxGZj6PUos1S2Ug5ikqp52G2Pyyfyv5px2hRE1Dz3spNIbGBGn1UMCDvUYEUKEoXdI+yRWITFRbnXgvu/Zil47ndfca0yND2/9/Ne5mGoR0torOmqPjNvAEBZoE5W+j2dxLKxcqFKbCTdGyzYRm9/XDnWf6fn0j6g7Bd6a+C0v+nE6f0N/tn27VK1/k+37wKGj3Icp8oYkwD81Riz7R/su9/5bG5O3WMA5vBch3L3qwpGbyBGrpqmOUj2Qg525t6AFYIGsD4ZECGw+rrU/FHQTKP3Ijca5SwnuDhxL8FqKa756P4cjYifLKCMJwAdCnrdrrYM6/jO9JxPWaUCWx32e7QT1LUxGKs5w/3M43fzzvAKauoj1Iij3kPAgUZNIwMB0hokgBDl6gQBXxYEKt399rj7uBkLvlAk86FbAg3K4DTyDNaHpb+Jgp1eq9fPpalYvq/Q0el1e/2kXlN3NCICV02bV06iQK+uCWXSCkxe9liO9CcFWpWzaHQ2yT1OGtYiOJALP3/f/vMMznGcKvdvLbAMMTlr3PIquH9r3d0r+eo8t3/cDESO/EI68lNYbZuaFpnYRHiv+aOzr5dFJCGzexE24pZEb/lGHTaa6Y2O+ZHBo4Oh2nPsoAYt1sNISrGSjXp3o8vCvKJRr+xBQU7ZDnps1bZlIaZrMcLeEjyfe8xVr99N/ypY++gtZMVgyzhVuseLw/rX+gO17r5e01RPtsczIEPd/T06OXXoe4Mv+0ZUA15JioetBpBrCuyzv96jCoH1PAqaafT+7XUfjcCrDMXrqgiez23aT3SC1PN6zW59r/fmTZH9Z5vx3Ms3vf6Pt/8owBljIowxUfoemIh0iRXADHe3GcBy9/0K4DxjTJgxZjBunts3nqgDWt8bYEFMO/cbWEmFH6sVK0c68kjPMdQs9QGF3bbzK4sbiRXupmCrhrjnD5Ym90oB6vDUg1OHf8DdVo8sJNOA+MpAen+K/a4yTWU5aioqy+gAAQr1tbUgg/8TbNZAAzYQsCd4Cb0CIAGszESvX31PQQJtsFkQev0KcFqmqBjJmND77edeWz/3Wmvc77trUuC5r0osiOm19VL+K7lvdi+sxn1fA5EpFng0OqrH8ZqN6mtUJqjmq1f2oRNHByKn0c+3Ib/Fr5BofDXWLQHST7wBCg2S6CSl/tQDEdn83kQNtv80kU0ElrmVi33Ac47jvGGM+QB40RhzCbALOAe+Mc/t65v6bxRQlHGlILPsNqz/pA4bVS3HRlW1I54K5Ib21rKpk9gLMoXYLAVlhtsQExV6DxSvsDWYJtUPAYlm930sUCupUjrY9JzxnmMFHf7aDDLyaoAoSA+H3ER4XoW1uiKWnhNryqkPSVlcAXbQq2mqZigAWz3XGnDPGYeAaAuC+CXulxUItTSS+ukgWDVFJ4xGXG2eC2J6r3XNWLNYzV03nawjTk5X2t1bTOt18GtkPIA1ub0SH69MBywAAlAPaXHyaCcAmeCf0MCPot+hjjg+3J1LZEwLrWcPsOasN6DglY8ogPo5cOWS/tMj+zvS/qOPwXGcncCIr9heD5z4Nd/5yjy3b2w6M2tnqkTArRLL2kZigwcqO1BgS0MqhWTDtSfezYM1V7N3XQT81t2vADszR2Jnap9nm0ZO9Zxp+l57ZChjnXe5jvuY+uhqgfY8mDPlNu4Zcyts6Nfbd6RaLj22gl2QvWlrgJgUKOymK8YQugwYDR9fOYTse3fA7BJ6J7hjo87aQ/TZaXDBDzQa1zeo+rZYyEkR3+ZIIAWOO2Y97388ViaGRqBxt3sepVSa7wo2qNJtn5uCd6mxubjqgwya7rHuy4GR4bC0A8r9DBi1iy/mDhJ/WrnnXvQ3VXZV7d6XAp2CnoKOBpL0euoA+jGxbDktRNFOOMlUkUMh4bRTTxyph1YQTz2bX8/hw3tHyzV4AySZ2IiwN3hzoCqkfQ9wwMFS0Tc71+FpNzrQis1JVBMsHmFkOlOrJuo9IBJef30ci5hJDoUMpZRw9pBPHmF0ctuq+Vw76W7uN9cIc1D5CdhBkeI5r4LdaKRwZIokfTvDDR1PwvaIDB7iak5nGS1E8SPeIbmhAXMBMBlMtSN+RPUJ6mD1SmCKQEohtYDvKN7sPp4T4v5Gcf0Q8skjmSpOLlwvlupI4CkwjznWXI7BAqSaovsGRZQVB7qDO2Q7hWxddBx/nTmaEHrI7ZFnvjnkaMpJY8aiFzEndUG2W4GYj7C14dIQoEsgKD3ZN6IY3FZJkPFFhsJiuHHqLQymjEsXL2bu9BsZau7mwgQgA8ZteJ315kSID7Vyjhz3mHofOon5Ea2j+h0jkWBTEJyaIbc/P/vgAbYynHN5gXDaaSGKMtJI5nPa6ccgKviSGOqJJ446tnIUR7OZXwx/2AqUJ2DlIzHus776ACwbeLhxChbu375m0vfLBv7faDpDtmIT7dUxD3bwvgH8EZF6FMHLr0/mah5gOFsZxnYAqhjIXRvvoI44Rkx6jxB64PlwkSB7wUblACo1UTYSD9wP+MKhEpwfG5gO/nthxLEl3MnNvMsoHuZKfssczC6EIa4HZ4yRxZ3rHLsWgDcQoOdmMPiPAj+Mn/Q3zJmyVsThbOfkovViKXYCG4EEcG52GRJl0FhvfZX7shk1r4Lg0wzsBn8oW/OP408zpwXXFA2EhND/gm7GrnifGbUvcs/MWbxy2KmwQJ/7bjk56dgimt7gwFdNvg74UhDGVgIBiD65mlwK2M4wSIBbmu7mJxGQXwskwyRWwZ2hUNduI7NeM1EDGMrgwJqj6ltr1QBMf374wVr60kka5XTSly+JIYZGEqklj3wGUUEkLYSzh1QqSKSWLIr5khixAtLcWy7Fgqtez3dsTYb/9nZQAFyfvgGI6ehdLlrZVTkyQ2e6O8cgsuI7of7LfiRQw9m8zPG8yzkFr5HLJvYQDslwC3eQw2bu3X4z/pMbZObfgDV31AxV6YkypDfcXpwCzm8MHANvTBnLZ7cMgAhIWtLEXSV38M7iiTy0bQ4AO2uSJNcyAe5ybhAZSSkCyGrmlGMjwwAdxTg/N3CNfC+uzQWPMKDNvaY/IqZwNDhnGyY6HwFbhQUqi1NQ1oBKij4/B2iAdSk4pxiW503k4rVLuLh2Cb/qnE/srA7YCQwC3oTrmhYydchqqi83OBcbWHMKAlR7EFOzG/xulZK/G3zd7vnc2nPXhlLonI7zmWGXbxCnNb3OnW1zYSbUR0cTHgt5qTDvxRu46YL74HQ4zvnAHlsBRU1GnRzSsBF27SN1iPawAKZ2L+FslvJwzZUs+ewCPieZo9hKAjVMYA1VJBNHPfHUB9ldBamEEKAHH7ddOYfVj4wRSVIaFuBUr3egZCLfp2oBBwnAGeNAIMTKPjTqqBEw9SulIcnVuVB5liwCHUULqewii2LwQxx11JDInMG3MaCslct5FH9SA0dHFxJdWi3MbJ3n5F4Hd1DcaWwdugAsnnYWdcTTQ4iYjVIBnS+mR1KdGS3+G5D6qPlw4+H3S7pVAMvgdLB6JQtPZcFLCFhFgL8ARpd9yJaMDJwpCPBmAA3Qdk4fmAWrEk+HpHFyjBysLy6AFUVrNJAGiM/gk7FpOIvk2dwzfhbsgoiFe2l/CokxtEHJtBR8PcDtkJgH//ubU3CeN8BnWFmJBh7clLS/kz26VU+SYOJ9y0nmc/IS1vF2yBjOiX6O2yPmwkJIym+C4TBz10Pcdt18yIRZR95D/tpxtgCpN5CiEcxGz6mU3amusaOGGcc8wtEUspmjiYppYfxhqzif50ijnFNr11JALsPYTg8h9KWLHkLII5+hlOKjh0RqqCOOGBqlkvQarBZOz3cg2vcMLtgOCoDrCfjEMa0gUEBvIa5Xp+YGArYzjBoSeIirubzhaRKaGvh99hUs4JdMYhVjeBs+gTjqGRb9KVUkc1rYqzCr2UpPNEVHO7CafY1yDc7vDUyC6bNeZg0nMmRkNUwGauGDjGximlpJWtsEGyCMLhpy/JKZmwHjnbd757X6PceOBKjn1RknSqgmFtH1tgGdMKKihKrYWLEu24DpUBWWjJMB7W2w7vM8uWavH0dNfDXvAOLjGP/Fa2Su/AyzCkYv/lAmgleBIgjPcPerhXriMCXwwfRsWARnrn8dZz5Q427TdgAAIABJREFUOharwWtwWeM+FUyCLRRo4eHPL+QyHiVhuUhJEqll+Y7zCCEgJncT/O9fTuGJVbPg2m4e+vVMHhoyRwKt27ARcD2+Tggq91D/ZgB3xbNmuDmRWhKpIZGj2cyfwi7mIp7i2PVFZFZ8xpaEDMLo5NiiImJopIVIismiL13yTJCFs+OpZxEzeWzqBb0DT3qfBzKK+j3AHRwAhwORKV/I4MxFGNtoeuuRwOqtkiCZKs7lBc7nOapiYwldC2exlFoSGF/0N3aQDp1QThrP8j8s5Ep+xW/htv5WNKraOD1PtT3fjC8fgTjYmZcEyfBUxc/FXPQBO+HYbUWEloGTA0yWwQHQ/TgQC/eZ02w1knL32tWvWAfkxjE+cq1I6UYDQxAwewbYAIcWNAjQZwMboYu+mJ3wXusP8RtXWjgba7KBjTZHArTDOnhz5GlsmZwB0UAy7CGc6nnRPP3kT6jeHC0g2QQj/7CF5txQlnEGM7MfgotgTexonBl9ICYRQVs36y6oFfQ6pFTwXMkVi55mJZPhdDif5zi2oIgBQyu4Y/XdkAAbJv6AYWzHCTU4D/dl1vonaK6CmvOhtTXECrv39cMpq1OTX/tGen8m3rGcLIo5gbcYSBVn5r/O9NqXaRvZhzdSx/IzHufSFYupzo6mkRgaOYStDGcNJ7KVo7h+2yOM4W3qiCOLYnaRivOwsQwxhu+T7f8N7aAAOBPSQ2vhAGsuqmmq0VLt5K5JcsmohbK6eafMvp30hTw4rPYLsijmpuy5xNDIvDNuYBWT+ANXcjzv0kIUV9z6+95ZBDpLb8P6dTLhqeE/h4WQ2FkrZuInCEPbhTj/Q+TvR7EZdPwCnuN83uFHbIoeAT446gbEJ5eC+AzV7PIBAYfpHzxOeAQQAdRDW04fGIX49H2IP78JOXcuEigZBInUkDcZ63PzylDARlB94TiOgXthRFVJ8H7riOM33MR2hvEj1vPS4FMhA/505TTeDhnDr3p+y6Kiq+BEOKlqA91/gbFfvkGwMIAPj7DWLYPOR0hUJACRWZRdCm9xAoyDBGogGRrrY2A9UAb1xIsZ2IRUyI2A/oMgMRci7torv4WapBpMUBdFPHat3HFIQGdNNzUk0o920ihnWtFyCIFjEt7h0rDHCaGHB7gGDhfmP5yttBBJOWn0uCiyOPMsJjWtJYtiiTCzifWDj5Pz6P0mcWAq+sL3Ql+3HRQA5/SEWBGsCm21U5ViO3klwehgOO1sDRtODyHsIZzPkgdAFZzOMnYwlEZiKCaL4WzlbJbSRRibyeHhl35hczXXYH1WKh5OQZjdIKAEIp7aK761KllZnQjEpKyC6rxonuGnLIq4hBoS+SX3ENBe2QPz51y1T1ABF4gMz9z1MzF3N8H6UccR3raX3cmxMugHI76+HLkWJxcyqz6jOiGaSFrofg4revZ5nkuje/1usKQ+B7qzoTsCdo+PpW1UH1qIIoti7v7N7UzhVXIopHqUsJpTC9fSr7Wbhmw/Tz/+E3gUro+ez7r1pxBMwPcyaoDyGvAdBdkZkBvK9JbHGTwRMfvek7/LkyeSFVcMg6BjPqxkMglNDTKAIxDFzE3u+zAsQ1TGpvdWh7Ba/c0WO0AzNx52B2N4O+hP25KdwYbcH/DhltHUE8eYtg2MLNvCzswkakkgs+Sz4OV30Zc99KOKgVREJ5HM54QQoJ1+rOFE7rryOsuk/HxfstxtxphQY0y2MWa0+zf0m7/19+2gADiMY9mTV98Ujzj7wTKgDli08ir6sYc64tjOMPppOe1kCGcPyVSxnWFcxYOkUc74or+RVNZEIUeLRk3NRI2QgWUFpZDx5BaYAkxDGFQJMBYKyJXtZXKupIomftcwl4s6n+S5wkv4dFEOo+d8KMxtINwwbqEV99Z5zgM49wJXAjnwo4b3MTuhH+1sucU1J2Oh+cxQqAVTAFwKSduaSG76gtAGoKjbsttMbAqYMtHTIe4ZCF0NoQ1w6K0NRBTuJYoWftr5DM5iw4IL5pIxq5Kk2U38vO0R7s65lhuj7yC2VsKzj8ybwSZy5ZnlJLomt0ZL3fckQgB+sfVOuFl8eQyHs1kKI8X/FkYnD3ANd192LQ9GzKLGLT6ze0osHAOsgC0XZghoZ2CrgajUJQlbOikbm5GC4WbnXu5eJWCdx/usYhKLmMkd3ILTbbiQJ/GXwBuDx3If13F602tQABN4kyyK6UsXXxLDMD5lFZPIYTM7SKeCVBqJIY0yu1RhMG3vX2z/xVFUY8yPjTGvIlPxRqTi4UagyRjzmjHm1G9zvIMD4BxjWZr6WnTG1hxTZXgAhRDDl2RRTDjthLOHMLqgUxZ5Pp1XCKedz0lmbNn7NGSLaZlLgbAjH+L3GodNb9IARxp8WpEDf4G1N/1QiEsEbBj8A57jfOsj7AQ2g9kF4W17xX82EikWVYHIxXYCRY7NkdXzjAYTjaw+mQylsSkszL2E2BUdZDWV0DaoD6/ljqd/SbecP4CwvQ4IXQbbBh9G7WFuZoAyXX0+mkExAbEqI+CzwQP4YF42j+dNpwcfEXP28qdPppH2zCc8vnC6RHBvl0d7OstojgtlRsWL1BNPAjV0LESiio2IHMO7cI0PyIEFVXNZPXUMK0vOgkzoSydUQyd9uY/rGFv2Pi9wLhWkEk89Xf4+IotxU1PfZAIdb2IrsOgE50OApZreVUGSABzuqL2bqZOW0EIUA2pbaSWKRGoZwzs0Hx3K5yRDFaRRTiOHEPo5MAhCCDCQKlKpIIwuqhjIMD7lU4YxiVU0cgi5bJJJUYXgAf4+cPzPtP9SBmeM2YgsLbgESHccJ9pxnBTHcaKBocCzwOXufvvVDh6AU9YG9of1YXMPPQLP7ithxKIShhRUM7JoC+30o5gsKIEoWsjnOBKoYSBVbBt8GLGFHWwY+wMuXbGY5gdC5VgpWP1YNrZkZyXkDwJ6YHzt38APMVM+51WmEEIPTjJ0aJLa4UACmCYE8JrgtefG0zwtVEzcy+Es51nLtOqAcTDgnV0CiJ8AIZDeUMm5vMAjU2bwafQQIhbu5dSCtbyROVaCDyXQcSGwGpwpkNpZwYDzW2VxGTUZlV24vrmJly2H22HL5Az2EE4NCZzFUmY9+gRcLj69PPJpIUokbj64seR+Rt/7If03d7MkdSoxNLKqaRK/jJjP3sEGGrstSKeAsrnQNc1ckPwYh7NdgH0KnD/tFVgEV/BH3m4aw4mDX+WvnMRDt85h0eqr2Bo2HH8RQb/k9WWP4L8UOBGcpcYKr/H0C2XeuN/jE0KcVs7mZVqIYnnCRGpIpJShVJDK9SG/5/ptj8AgeIFzSaSGkswUvhgVySomsYlc6onjfJ4jkVreYhw1JJJMFcPYTjlp5FLAU/9zrq06ciDafynAAZc7jnOq4zjPaZUhbY7jfO44zhLHcU7FXYN1f9rBAXDGsRqnbVgBZxLWaT6BYKpTl7+PMKlmIAKGlFSziJnMHP8QIfRww/qFhNFFOjvILPmMnTlJvMvxEA39t7rVdouwi5AUYDV4KbbsZEcEfHzGEBpXDeQ0VlBOGifEvo6/CYIrLPkQsNoMDaP8nLpxLcUhWfL5EbB0yQW2Hl2HnPdxLpVgwlhYOPYSTC0MeKCVK0qkSPLiX5wFZTCUHcICo8FfIucztdC3Y68UofJKT5T1um0ut8M1MKKshGWcQTo7iF3RIcWsNkMxWTzANVy/8RExiQPw14zRMATeyB1LFC20EEVqdAU9+DCzkCURvdKXmFCINHS1R/Pnhp9xWMUX8nmTe22lEl2+JfoOKkhlPnN4Y95Y3ps4gr8wWUz/CMTHWQLcIt+tHOfeRCGelcKwEW9ldClZ9PV3UsVAJrCGKFrIYTPh7GEet5JGOVRBt1vAK41yCjiGVUyiBx/thJNHPgMWt7px1Ua66MvbjOHctheJooUQephR9KJMIjkc1FFUx3G27ud+Rd+8l7SDA+B6PDN2OnaRZ++Mqfmpp0JLWBTrc46DVPhgcDbdCRJdfGLTLImoRsBlbY+xhgnQBvE99ZzAOkEuLaRe6TlXEvb8PjjlQiAW/A3wa+6ExfA+eXTSlzv5NcuTJ9I2vI8AWxsCQskQW9LB+lHHkdO2RQAogDilI7FZE40wtWC1AMBGWMc46A/dF8ptHjlnJ4uYCdGQUVIpLDEg+zIJqIHQZmxE1sve0ux9jF78IeyC6sHRpFEmx4wDikTUG0cd85kjPq8wYBCMa9rAx2cMIYQeJrStZQormMkiYmjEWUXvlc7AjW42QxiYVe62we4zng3HzVjPMLbzCqfzLNOJoZGf8md+ye9oJUqYcxvByPEbmWPhHiG2QVeFBjTUJ6e5w9WQUbGF3OhNDONTDq1qII469hDOPG4laUmT9IUwCF0vgB5CgDC6qCeOdvqRSA1Hlu2EXcL8+9FOCD1E0Up7hJ++dMkxAljJT9+v6cPfsjkh+/f6rjZjzPXGmBz3/UhjzC5jzE5jzPHf5jgHB8D5HGuGVmMlD16GUg60wk/GPk3SvU2MLXqf7gQY3lZEj0+ida3ZIXQRxvrc47g84mG2czizc+6g/+ZucpqKZDCvRwZWGpJG5cMuTKI+HxATczNk8QnLX5zI9Yc/wqf5OYwu+ZAWooh4Zi8dGQgDiUMG9SLYxDHkRxyHMwcxWxXo9Li5COhlAxmwtPYCtiRn8Gn0EIiA3fNj+RMXsWVihuzX6u5/BMJoihC/XAZ2lleZiEprznPPOVp0gEdTSBrlPD5qOiRDxrZKWojivvNvojohmuZfh0IJhJZBO+GctHYDUyNeAeCXDQsZTBkmF1tWSs3UeKR8ewHwB6AEqpOjMXMcPjkyjfyScaRRzlxup4cQHuUyvnhhECH0MIZ3cAZhS919Aic/tR4ug5MS3OvPRiahHPf38gp+k6CRQ8gjnyha+GvyaI5qKGEgVazhRBgJd5Tdze5RsdwzZRYJ1BBPPfXEUU4aYXRxImukguFE2xUbiSGcdroII4tiisnikZwZHHflennGXf+wJ+9Xc/pAl3//Xt/hdh3S6wHuBn6PVBG679sc5OAAuL3GMgN1kqtTt4NeGqgoWqACGrL9hBaBvxb8bTCQKiLK9tKXTj7lcH7LjYTRxYLaufCoRBOdZKRynTJDTa4Hq8GLRLIRkoHDoZAcYT/TYXdeLJTA8WyESeAvQ1ihDwG6yWJWJlJDp0bAPsGaVpFyHyV5KdI1VkF1QjQjCkp4ixM4N/kpDn2qgSEV1YxYViLX9CowCrqPQYBE81TPoXfgBawkpRo6zgEnQ8yy7QzjBN7i0sLFNEz3w3tw56a7oB6S1jZxe8gttM3vA3NgKKU0jPczmZUsYiY/jn2ZIygWkCnEMimVqVSXiXn5G9n2LscTuqZZpBh+yCOfSU1rWcEUKjdl8PC5F7Ku8BTOXPS6RIfPRI4d6z5zH5TUYjM+MuV+elXpLZfvfLFpEH3pYiiltLvl3HeQzjv8iMWDz2LL4Ax+ye94nzx+xDukUU5fugihh3bCSaVCJjKfFDoIZw996aQvnRRwDFG00EUYLURxFQ/JuQ9Asr1jIBDSZ79e3+EW7ThOk1sQdwTwkOM4TwDDvs1BvtN3eMBaH8eWFlIWkuK+T8fNNQQa3YyBCDE5KEKEt0tgE7k4CZDXJAwrrqlJfDBtQLJILsw1sHbUD+VcRdiKEaOxCfh+KKsAauG1zPG8vvxMXl37E5gpIlmq4C5+DTWwIfsHlGSmCLgNkvNMfWm1pAJFREqwoQ3rG3Mrl9zMnbI9GpKqmqANZhU+wWRW0nEOwjLfRKKxo4ASKI9OEdbWI+cxexy5/njsGq6al5oEyyKm0h7Rhye5iHc5nhVMgWh4lSmceOGrck1HAGGwhgmUh6UxZ9VtHNLQQexdHeSTx7yeW7mbX0kkUtlbL1bRDcTBOXDd2LvYMjmDa3iA2XELYBksTL2EzeQQ2iYRbCfCiLA2GvHT+SQ6TROwFrm/eyA9Fgug6k5w/aOku6/XYOoxS4iihTC6aKcfz8dOJZUKcimgglS2chRns5RJrGIzR7OA2eSTx/G8y3A+4pCGDuiAkpwUMioqSaTGNWHjKeRochuKCKGHo9jK9Ltelmd2AKQbjjH0+Hz79foOtwrXHD0PeNtxnB5jTH++pVLw4AC4gLHMQMsJaZ5oKTbzIFuU6ETA0Z2FMusPAUbBONbxx9gZhG4TFf386F+wleHMG3wDpEJLSBRMQvxOddjlAtOxjLFS/gYAtsIwPuW2qXO4bPz9OH4YUVgC0bBo9lVQBKPXf0jGikoWZ5/FTWfMFaBbCeE97QwoaKUmJNGW7nYDDNTBizt+KsA8GZoTQ/ls7ADwwWRWSgAjB6oXRgszGgTsgoy7KmVwDUZM31lY6YRODEnyXeIhmc9pCYtiK8O5mgeZ3XQ/7IIWojiERpJO3AnT4eNRQ4iiJajw3xU7ADLgd/ySn4Y8zYi7SljFJHiA3qXBAZGJ9Mf8zWENE6gglcqPM0inFLLlXJNYxYbkH5BPHnwqpZGaB4VKpkYNDKZc7jFM7qN9BRjVRPoQ1qgaP7AykXHwU57haDbTTj+6CCOZzxnGdhKoIdldCqSYLABqSWASq0h0P+vBhwkAcZDaVgk7JW85yi3F3kgMplZ8u8Vk2cDJgViTAegJCdmv13e4/RJYCvwauMPddir7s0SBpx0cABfiSEcGGyUDu0JWOkHw2zn/SEiGZWFniO9rM5APY8vep4swCJNO+Q5j2MFQtjKcq2bO549cBoNh9byp1pejLNE7aKvh0AigU1TuUbTw6OxrMfORpXWGQ8MCvwCJGyif/sDLlJMm6qBb4L6Q68TXlV8JdyHAo87xSuByI2DYBv13dnPY6i+gFgZsbOXw5ELWZv+QpMVNYt7uQsxg91l8MTFSGJ5euw78InqV9+khhKSKJs5mKb/mTo6MLqRfTj0xNFJHPGfwCvjgL0xmKKUMpZQpPSvkGZbBoRc18GzndGiAw9mOU+KeZ1+/UAA4D4oePZZzml6CIniW86EWfsqfGf2HD7mf6ziNFfx1ymja6Uf/Xd0SWNgGh9Y2CLhlADMhPA+pyZaCmKI6OcS796bxuUw4nnc5nO304COXApKp4tCCBroIYyilrOFEjuddN3DQ4mY67HCDCQHaovtAGCJXOUK0ewOpop1+jOMt+Y1w3SIj2afU/D/fHAw9hOzX67vWjDHpAI7jrHQcJ9lxnDTHcTa5H7+ESOH3u30jR3VTJEYidnAM0g22AO85jnOA5pt/c+syMM6BQmPBrRFhWWA1cI0EF3GJ4UsYDB3uiqzvRvxQ8h4LYGbOIhYxk3bCOY0VTFu93ILYGgScvFFU9fO5wY27W2/kjo13c3jTTo5c+wgd86SU0Z/GTmM4Wzn2pSLIhW3TDiNzyWcQB889dQkMgjsH/4Kf8zD8BDgCTLZjV2LXxG2Qsk3LgGSonhxN0uomyIDtDTl8GesXf9QFCIvLRIDOJwJV5iPmq6Y0KXvTShvrYNivt1OdGu3KJtqJp547fXOpIIXpy15myxmSMXHDRQvFH3g9UAb9p1SK/CUBloadTcWCVGpIoKY+WvLp/fRegSrQDYFQnPWGey6bxfyzf0UjMbAEDh3VALvg6c4ZbA0bzklLNvDFtEicaDARSMbHMmAgIufIh3VN8Oibz8AYbCBDRd9+bBn5CVBBKsdWFPFBajYAqT0VUAvD2E4ZafyYlRSSQx3x9GMPR67cyVuTT6CYLFqJoiYsgSH+agiDNxLGcnLher7IiaQHH3vchXaGsZ1OwmQ5iyM5IPXgHIxN6fvva38xskjLSqTs7NuO43QB/DN487UMzhgTb4xZgPCIRcBJyFA4CXgCqDLGLDDGxH/dMb6pGWOGGWMKPa9mY8y1xpjbjDG7Pdsne75zozGm1Biz3RgzaX/v0h//pVXip7vb1fRSmHcHcfPoUFqI4rLB93NNxP1URKRwK/Pw0YNzJows2MKibVfxdNMlTPvDcqiF6inRfDEl0rKoeKzmTitFuBHVO2+8S5zfQPd4WBUxkY/HDuHikUs49q4i8YstgsxFn0lUtA35uXeJk/4FzoWboGSR7Ec51hR2U9FiJn0eLI9UT5wAWJOcM6qpg4bxfmE5rQhrCQCfQGxFhyyAjWPLlWsU1WPaHbqsgRaiCKOLGhLZynD8nyCmYgiMuKdEzp8NTAZnNJRckyJpWbVyXdsZxs1r76WeeM7jeetCUDPRh5QZZxPME6bTUHAoG9vGwBHwccYQts0/jPC2vWwmB46GAWWtlMamUD0qWoC1BvnrMsSTBsPLp0z/++UPvRH1GOkL4bTDTjlvDI2EBHqgTVLeWoiikRj60kU6pTIhNhE0TzsJE7YaIvd7ctF6iIYWIqklQar7VkEkLWLuRnPAhL4Ohi73/N/0+q41x3GGIat67AB+Aew2xix3F3JP+bbH+0cm6jvIsMxxHGeY4zhTHceZ7v49HGF0NcDb3/42pDmOs91xnBzHcXKQrMF2ZM4FuE8/cxxnJYAxJgtxOh6JPISHjTHfPFV1Q0fdIdKByrHRwFyseaqVRTIh+v4uBlPOYx9fEwzr/4mLOWfla5gOuCl3LsRC6EpwpoHjwm/CRnepO2U+mVgTKB1bE64c6ush9AEIbRMAOnLxTvF7AbOT7xCzqsp9RQBnAGNh2sblzNr2BDsnJ5Ex0z32SNx8Tvf+1kFTfBJtz/SBe8X345wpkWEzC/Kjf8AqJvG/2afQcTkSDBgOTIayQTDmltVSlLMOy6RUXhOJAPcRkNxZxZNcxIyKF1m17HRm5j7ElJ4V0ACzb7hDCht0wiM3zMCsgFuZJ/dyJjBe/FAvjT+Vi3iS9WNOtpklXjO1rhI4CtPgMIlVnJW3mH6lDk/f/xOOXL2Tdzke0wFXbHua1zLHw1bIKKsUoI1FgONNuY49HcAcLKsGu3JaEraOXySsy8ujhkTwiWkZQyONYTHQJkURZK2FelKpoIUoydjIEIDroi8xbtEkXYsHgHqpdNLXhRdnOJQzWD6LcM9/AIjXf7OJCrIYleM4DzmOcwriQX0c6d3vGGM+Msb81hizX9HUfwRwIxzHWeA4zu6v+tBxnCrHcX6HXb7jX20nAjscx/nsH+wzFXjecZxOx3FUUnvcNx45DFm5SiOpldiE6gACdCB3UgQUiF7r2iPv5gGuoY44lnI2WyZn0B0B5/K8+KkGgSkBo/rrC+m9FJ0yAvX7ad7raxA3DdgIjt8NbOQhzC0C7myby+JbzhL9WA/iK4uAD3KzaRjlhzAY8uNqHnl8hpU1pGHXXnWvITK3h5qNkLS4ibLYJMLbOqAJuggjl02cue11KiJSgiXLWQ+Dt8KG+Sf1ngzAZjK0AifDA5k/Y03YBOKoY1vqYXx2xgCeWD6LK0P+QNQ5tSxYPJerZs7n7puuJZFa3rtwhAz4TKQm3Sx4uOgXVJHMmLYNsKFdkuy9SfB+ID4FyIfFMKSimmu5D+4U045CuHjREp5O/gnzMm/ghM51PD3lJ7BR5CPNw0PF9xYJ3Ruhnx/M8x5/rLJ3zQLR/7fJpFPhrjEe5lbnbXR9DI3E0EMIxWRRTxwtREklmGiRzaRSISDX1iTA5ZfJBT9B5ldPHCYg/txGYmyu8gFaA+q/GeC8zXGcPY7jvOY4zs8dxxmMlKioJ1j3+h+3rwU4tXv34wIOgDQREGa2xPP/LBet/2SMOcTddijiHdJWSbBKYu/mUtoCY0wBdV+IE119SWBBpxIpMe52bHxAGizjdDoJI6mqiaMaSrjxpfs5h5cIzYcR95bIftHIYGmCqM4W8en5seXQtdxQIdbXMxKYDmaWQ/FqMJ9I5G92xh28N3gEj18znYKIHzC96GXyQ/IoGZ8ic1gZ3Md1xK7vgE4oWwk/H/OUDWiok3ocVtaxDc5w3oQaifb5lwGPixQm49pKugdCxsZKtt10GGRC9+/BXOHI4sXx9F7dXa/fB2yAa7c8Sjv9mMCbxNDIm0zAecXwQv25tG4YwJjpq3mVKaRTSgG5BAghhkaafxwqUdpc2J0dSx75+P8ARIbb3Fc1i9PcczMaFn4ES2B07Ye88tIkLuVxLrvhfqpnRhNHHbeW3UPE+r0kUsPu6bEkPdVE/5pueXaZEJoJnzQhU+I4ei+kk441VyOBbIJ5ojSJSdpJX2F09ZJnG0MjaZQTQg+d9BVzFkgqaeJwttNOOP4GgpKV2NoO8Akwp1JBX7roDiMINUDvkun/QlMf3P68vsvNGBP+/9g79/Aoi7P/f4YkZEkCiUkIEYImSDRi0KhRULAgKCr1rGjxxXqop7a02taK53q2WGm14qtVKrZYabVqRYoVC8orKGhqoyCiQQgSMQSSJpCEDdkwvz/uuXdmo2Ko6Vt4+5vreq7dfXZ3Zp55nvnO9z6OMeZgY8zReiD+cT+z1v6xK3V0yYpqjNnHGPNrY8zbxpgPw+MrXYGvvydiHXnanXoIyR5QBnwKTNOffs7fP3fNs9Y+Yq0tt9aWk95XWJq6OTgQI0biDvQaUpUM0y+9BoDv9Z/Kn7PHwAh4r6kMW464jgxzMYglUHVqARlXdSTGbRbgw7M08F7941YB34AhTwFLYMySNxjNK6xmMMfwGk/yXzxUeoHLUJEF4+HRKydxNK+LLul6ONu+JhvcKMNagU+5jevHYHij7xi+96OpnNxvIZTAY/0ncnbLM9ibRTxmCZRUruPpUSfTs836tE6Frt/lxA0vcXZVAEwSp9ckYvEEl+ZCy6M5l3LyCU/z2vpxrGo5kAlL5tKbrYyc8jZ3Vd1On4ntkArfe3Yqv+Wb/IFzab8cb4gheL8at+FzK3Cw6BAb4LQl8zmd53iOM7iNmznlzwtYV9QX9hGH7AEbGlh84WESSzwH0QWuh0MusX7RUZ2ihqKpCJ4FbIafcTUHLVkDyZC9NspHDKaVXjBU2NEG+rOegQxkPWlsE3baAdH+4ozcSi8iEFs1AAAgAElEQVSi2Y65xaAqrwA2SjaaHDZTTw4pL4iP4OscLTG8q+k2I0MHyV06vqwYYyLGmDeNMe8YY94zxtzqzmcbY142xlS5172C/3yuntwYc7gxZrn77pfOmPBF7X4TuSsLgT8Ex+93ZSy66ibyNPI43IykMwmP7ignAW9bazcCWGs3Wms7rLU7EPlbxdAacHKDlALizhQ7KapLrUX0QqrI1vTU4Wquk6sZHrr1hxzMclYyhC39UqjPzJR6osRDj8iB/X+1XjaGWYXf46HE1bPZnVcjQ677vgDMfEv99XL+5BULmbTwGUrWr+Ob/JYD+JDebKWQahYOPCq+beE7lxRDC7zde6QHzVCsU30irt1cmF58DUs3HgI3wMVPzCZSB2YBAop5wGw4p+gFMQhs7lRfflCfuqM0A9Uy0Qc21dJBMoNZzVOjTuGCe56SyX4JtKZHeGtEKZfzsOjdHnTtVcG1TGU7PbmQmfRs3ubHXu8Lrt0CI/vNZkHtnZnQJEkHbp9yN5ve24c/dJwLZVFJZ5UuIuCWfim8yrFy31dA/TREDzaDxNx5YfwpCMC4ax3MR2LYaQKbKRvqNLIXJIthIIkY6xnIdnpSTw4b6M/ckjG0pkd4hrMZwkq2pmeQvSoKHVBcVwMVPqJhIOtpmBShnAphnaOypR/dBHDb6dmlowulDRhjrT0EoQMnGmOGIzx/gbW2GNFyXgtfqid/CLgMURwUu++/qNwDnGWtzbXWDgyOfXZlLLoKcCXARU4WXhAeu9LYTspEAvHUGLN38N0ZeO+kOcA3jDGpxpgiZJC+3PHPuhrKkStRkUTF0sbgyHK/SwbmwmXnz2LK7x7ggKRVfI1FpCXVUzbxDapGFXB42Wsi0j2O3KoS114EH3uagTcw1BCEIAF/hOmxa2gd664sBmsG5tObrbTSi3pyqCeHMVVvUEg1x89fzCFHVGHWWL//QphUUxmj6stKiDPKo0wlZv4OzFE7WFOUz5YzUzh63ALM9yzmbWcxVW/+4fgsvprGR0GggHgmlltuncrKzGK+zy/ZSm9JqHlNMbPmX8bTL53MdlL5WtMipnIt+w1bAcnw2PSJcCH0b2hgNK9ySFUVFKxPsAAzOLg2DZ9q3MLeZgFUQvYTUTgT7L2GrY29KR2wnK+xiOkDv0U9ucxMuohLmMHcojG0PwQ5J4CJOKKvzssalZEbtFODxA9vhsVnHA8fwzsTijFLZa+JlQyBdOIJK4ewkgy2chx/5Wz+yHIO5gVOJYvG+EYzfOzqflqeq/34iBw28y5DyV4S5RVGc37LExT8rl6eu24xMtBtIqqVotw6xR0W0Yf/xp3/DT4h2Ofqyd2c7mOtfcPKbvO/Df7zeWU7ifvT/VOlqwD3AjDqqzb2ecUYk4a4njwbnL7HUdl3gWORwFuste8BTwErkUfxu9baLw/d6IFPQ60rtjI1ZTzK5vRhL0Qm2grgYah9ZxC51HNR5uOMZx6HtbzN2xNG+s1rdHIq4OgE1ckE3kWlEtEDTYJbiqaSdh+ieE+XzCQHrVoTd5g9oGEdWwal8AEHsPYEuPqt272OT0FH41zVMhiw0HgiAWVh5Yb9zKdkJm/nDTNGfvNX16dY8H9VvutCoH594PcumCuhWY1kESOJrzcs5JBFVdSOy2TCc3PJr2zi65nz+C3ns+aZg2ifARdfPVvcJTJT2MDemI8tRNz2W8oOFXz0PgFE+gDFnH/5I/KkpANlsH11JiumHUHVskOoppB7uZokOpjJRaSxTWKEZwEV7V43GY6HMsbGsC33+QSxetImurJt9IKNsJE8l/woi2qKyGCrC7bfzAF8wH58xKscKwwpk/i+ENSJgWIrvSnnbywecRjHsUBSVb3q7mm3qMV2SUTNVV21Oy77TG3GJBljKuUKeNlauwzoZ639FCRXG7g0yl+sJx/g3nc+/0XlJuDnX8UNDbqeEer7wOvGmI+IJ8+XYq29+Kt0wFrbisQMhOfO38nv70RCr7teQj8ndRHRhzoWnM/A736l7Ge0+3wLvHHtGJYVDmPH6nTZAasAeTA1G8UqhFmBBx0FBRAQqUV2q3rc9SMXTC+L7W/gTOgzs12U6We+LZy2FPqsamdU0ps8a09imvmh369U9WKhIy7uWgYjE3qx61M1UGpgRQ1kFEgaIvo437ZWiKXJBitZKdJPFU1XkRgnquNYKNdz0zv3cvQhR3NFx694LvskzmIePTa28LMzfswPlz3EEo6m9vlBFJ/1Dqed9QyXMIMzp7xIn/7tfK3sNTiuCvKLE0PCdEHIcONIDUQLgN48YS5lVvFlMn7pwFKo+ZFYuTfSj8V/OJ7qcwvZ3JTD0szh2Cvg2vpbgBTPovV+6wKgagptMwq82g53iN8h6d4XjjoRg0HEzd5sZQgrSe7o4M2kYQxkPYWsJdkF3JPeIFO/BWgQR+rtpHLaqvm8VyJhbHG2v5nuySbi3ES6WDZba8t39gNHIsqMMVnAc8aY0p38/Iv05F3Wn7vyIXAb8J1AVWekO11P9NRVgJuJd1jY1tXKd5uSgmdmKgJpDOJmfPokFdFWI4CQj8+Wmwv8FHZE033ao9CYoJbGGvymyauJB6dTiVdu/xUBiEJXxy1gki2ZH9fSuGBvae9hoD9cfvN9PDLxSvHp7oUHTAWafLwvlzr7qjVOIw9CAMxyvpLJfcQtI2bEgpmMpAsP/dAaSXQgVhB41V13AXA2jJ30Opf95H6GshybaXinXzGHzBcm9+mA/Zj7yRgO4EOKF9bA32Hh1KN4hdHcse5WSE6BWgvJJjFNkgJeFlBb4Nr+BGjHpFvsNUYUG20woKqBKz9+hDVz8rlr8+2wFu4pmsybDOP2+pt5xvQBWqE2zccga/0RvO4t1M3mp9BS3oN9F26CdPGFO4GXoE6s3vP4Ov3YyHFtf6U6tZDVSYPZj49oJIuJVc/zUPEFvMQJ9C+eSfqSHQJyddCbZj5gfwYOrGEthZSjUUiuD90UPPmvcAGx1jYaY15FFDIbjTF7W2s/deJnnfvZF+nJa9z7zue/qMxCxNg/8BUwp6sANwbob63d+s829G8tuk4k49Pi6EodWtNUfFUmB4mGCNU/qQizGgEydTlRHVgWfictrVOjGZqDOqP4vUk3Q1NBPqbcZT5JQ4BkL7z4q/UR9CU3aEPrLsO7pjRvETBTsADvxZ9lgvfuO/Xb06JsR/V6uggoqEeApfDI367E5hlYAH8qO4NDptxD/vImGCd+d8Uja2AGLB5zGANZzyy+CWUpwh5z0zzADMaH02m7saA/5EDly5gHLPULetFuovRrAibAoBm1ovO6Dc6d+Qeu5H6eN99AgLGXr0Lvr2qWtG1l9bnAqi1UpJYzqvlNqBe92/GrFsOpkojh1VQJyRqaupyN9COLRj5kfzbQn4MeXAP3SVTH1tTeXDRmJvkrmqAJspqamZp5LdPTv8sQVtJKL6ZPOhtuddfbDQC3iwxup8UY0xdod+DWC8l9PRXRGl8A/NS9Pu/+Mgd40hjzcyQgsBh402UD2eoMFMuAbwIP7KTpHOBmp6/7p0tXh/NdOomRe1zJbydj9CYY3u5ZnK7gseBQURUSdTKh82kWXvxUPVEBXqSqxuedq3aH/lf1fQpyhXjFdz4irizFW12zXN0KnNpnBb3Qt0/ZmrZzBZDbJ9GJVS2HatHVfqkTdFZQNyQaYNSJuCBoE9ffyXDrwGtgrBPh6oAT4JOZ2eRQD3lgnZbmCh5i3YQSB6Zpfsy1P+qPlgBuFgGpZKAf3LGYHLOSq+0jrFyBZCSeh4iCE6Hw1jqeN8ORUIJ+gPHMNIJ3CQoXMGXFAPThF1wlkQ/94fjZi2EBvFw6kvQlO+hwfn2vMJr1DGQDe/N3DpUccE2SueU4/grAK4zmk9JsouPhycxz+A3fjKds304q31sww19vNwFcG6ldOrpQ9gZecfrwtxAd3FwE2I43xlQhOvSfwpfqyb+N2LJXI6FYL+6k3ZlItPRXKqYrAGmMuR041zXaWQf32FftxL+6JJcfYjv+UAmbjdeNqf4N/ORXhpeM3AIVZ/S7UIxxzCW+pZ6CnOrFFLRCEFlNYrylMhTVOVWTyCi1ryX4bQjVzUTZ21K8n53WWevaOg7RwWXhRfTk4FUBPATIENwUPHWcNJhfdZQ1JFol3fWf9NqzzNtwFtP7f4tyKhi+6B2qRhXwHKcz5cEH5BGvbAXSvJgdMkU12tQE4xAFAbmtiDNgL0SHWACxjYjT22BEizIE+BsSg9YAkYLEjC66QOkCQTAeWQSbdLdSb3PI/lUUyuDCYf/NndzIgGUN0ATrxvVl3xWbWFp6CHuzgV9xBXetv13GPBPscIl0scXQlgqR9fBeySD2b1rDvMxxnFY1Hx4E02G9yP+Tcuzqiq+0t1ZxeR97X8WXB/gAnGwW/O3LdHD/jmKMWYy4h2lEcbxYa7/W1Xq6KqKORHj+uE7nLbDbA9yODiO6piygIAqxJGhMSRTFQoudKnz1XGdwU+BT8VTFV/AuIAoancGks7/aarxIFkFATkVADe1SkCrHA4C2q64p1e41/K/634XXqSxGASWXRDFVrYlaR2h1LsQ7Aus1KfNrBla3QkYaLxadiTndMvIXL/NXxjJw1HqmT71G/n8VXiwNF5Bo0J8Yfn+GBBa3FejjOtIAbINYPUT6QfRtV8EQRAIqdJUMgeha0JhPfeKVBcfwyRFUd6kW8Fgv7uIG7p15E7OXnkYzvRkwo4Epl9zC1HtuYd8DN8HHkFXaSCNZfJ9fSlaQOiRpaAtsKU8hKdZBWssO1pTkc9Bza2CEGCja8yAlHdmHQResbtj4uTtF1H9jedQdX6l0icHt6SWl/GAb+827kBWF1RGvH1PACplNFiImKitT8Sl0WyjAW2PBA4gyrs0ICKhhQZlVqNDWz+q6sio4X4O3lKrFNxex6CqjAe9OocyqGs9+ChF2pwwx9JlThlmAZ4U6JgXBdSnYEFy76hn/0un/ugA452JqWxHdsGo22qXxXOPrPxHvGxiKiZ3dXeI6xnpXXxXiuRtDohz6QX4a1LYj2pSD8QG62xBQdEVBO2Tlna+xwL3WSPjVI/ZyLp3xBCyE/Z+s5MNFZRw+6jV+ynUikrrSRk/6UUdP2sieH4UYPDH+LCZVPQMbYOkoicft5fZkKP5VDSZq/X2PAtPKsWu+GoMbXJ5p76kY0aXfnmVe3C0ZXHeVnaVL6pKbszFm98u50qns2NEDIhaqIx4wVGmugACJurGQ0YTMopDEFDsKMrXBeRWv1OVB21QxDuIuInFwUGaRi08VrmCmn6vxmUlAQLCARNtUoWvr93iA0O/1mhVk1XBR6+pUUVjFYAWaMhL1dqvxoVzgHZvVThZFGFpJjr8mUiASGDVw/wmdeQvx+eyUTYV6uThY9kOASw0HW6F2JcLqChEwHUwcVLWoaKpisZ7TEvoTNuqAbeV3/BeUQftD8DOuYeGoo/gvnuR/OIYPOIA2erJf07p4VpHtpIp6Hdlfw+ZIl4dXvBNPjlm8vsZt3I33DsuiG7OJdE+o1v9mMcZ0KZllV38HO1dpvmuMucYY0/8LGtnbGHMNkvN2ty5xkqqTOlSkKxsKgU3dQBTkmvF7myrgKUiouFaIZzOh538GHgxCS2cE79ypop6yxlrkwde+1JLIbBQElTVBIiDXIJZZFcFCI0O+O/Ta1a0lZEvKqBR8Xw2uOx+JdIi5MVD2NzioR3Vy1a5ven2hQ7SOgd4T3P+WuvE6Hc9qoiSK2fTGg1ua+2EOAmgCSgKAgflVRfOQHUbxC5EuTuEr7UBvFp1/Ii1De7Ahsy+nzZ/PvVzND6c8xDzGU8HhpLKdxswMRjS8zUbyWM1+4haSI47Cph4hnB3ivpG9IQr3wz1TJyeORTeVPThd0jeMMStcLOvRxpgcY0xP93qUMeZaY8wKJN1rl8rOIHwkEl/2jjHmH8AHyJPTG9lNMwtxt+yywu/fVeyOHqKDU3FTJ2EoGukErw7OhW4YylZ00g3Hi4dqtBiMiKUlyOTX+vV9KBbn4lMchUYFZRn6+1eRO6H/URCM4pXhyQggliJgqPUqO1GmCYlgGral1zv4c64r6touQQCo0bVVgwe+ahLdZKrxC4W2rU61ZSQ6WTcHv1OmquOSH/wX55wcB64aBNi24NmdPtIp4HbCAhKBXllhZxE8vO+AoNI2eGItGZs7sMcYOBDmVZ3F9KnfoqLhGP4n+0h+zM8kXXn2aoaxjEF1tdACa4blc8T6FVJVC7wzrJhDVlXBS3D9vTdx9163wdmd2uymWNS27tpg9X+xWGvPM8YMRXaun4UoTpWefITYyc91ltoulZ2lS9psrb0aCaf4FmLSXeEauRgosNZOsdZu/qI6dqsSPuDK1HT1hER9W2jRG239Kh+ypWo8CCnbAa+IzyWRsejkDS23OslDvVouAh7D3X/LEN1bIR5sFBjU+hieD1mIunaopTNkqNoHHQ8dI/1tRlC/irEr8IyrGe9qURiMZcgEQ2u1jkdycA53riD4rfZTx0o/x8Dr0pSd9UGYXBoJfm6kkFhsosGITmOm46BjsBmI2aCdHPhLK49dP1HcUJCIhIuy/5tRa9/khbpz6MdGiqhmYJNYjDYVZTBoRS21A2Vzn9qiTD5isBiM9oG7r7vNs/AQ4LrND27PE1FBdre31k621u6HPB0Dgd7W2v2ttVftCrjBf4iRwRxymOW3byfGaOqkVRFUmYgCjU7ySrxIpqwmioCO6pBUVCx05wrwTFCfoSgCXKpzUr1TNR4Y9FVZRmhdVYW4ip3KehqD7wj6H4rJ+fgwLr12FU1DBqOAHAKUAoCKoDX46A+10OpnvTYVPUMwDt0xlKlmkchq1cCi1xwL2tBrVJGeLe6H2xBRUo0JyQjAtbvXXu59WqLKQYE6NDjlkxgHC+DyvMmq1Qv+WEz1WXnsW7kJ3oc1E/P5I2dzKi/wEidwOs+xV0cjfaraqS3JJL+qib8Uj+LojtfpM6OdTy7PpmBgvTfoFJKYUuvGcmzVVzMyFJbn2Bsqvt6l315mZv1nGhn+z5XOVrOMTudU96XAoV7tKorNDepSESyCd/YtxIuHm0n0IVNDwGq8b1d1p/bBT95qvM/cavyEq8WLe9rnjOB8dfBdKF5CIusrxbOwcEJnBP/Rfg3GM8mQYTXiU0KFIKdth0aKEMAySGTOupCEOs+QVRfyWdYFCGgpg1P2prq5kJkEomp4r6PBT5o7HQklDdHMOKPF2e9S2vKeBNEPhUEVtaSynV/wA/LYyL6rNvGPpCzWlOST1tHK4uLDSKKDPhXtUAEF36737Dy8dr3ebssHt0fq4Lq97H4c9V9QjLHYzi4IjSSyIRWjIFE0wr2ejo9L1QmiE15BIpfE8C9lXMoS1FigD3U1HnTUwqpMQvtYimdRKhIuxbPB0N0kGWFq5UEb5fiUUKq/qwzqC/WQ2j81lGQgAFuOB1plmVkkxtfqZFWgVPap46fgSfD7LHfNlXhxWMGzAJ8xJawLELWMGhW2IbqyPgirS3Hn8hCrajtEUjxoa11qpQ4V/No/3PlmFVN74V1ettCckYv5k8WmSHTElfMfYc24fJLo4OWSkezHalLZTiwpicF8RP68JqiDex6dLIFL1YjuTV1ylFXmQ3eozv6P+MF1S/mPADjbkZTo2qETOvRjyw8+4z6vdq+hZTTukxX8R5mailO1eDFQxTadzDqhFQwL8Nnu1Kqn+qqM4HOoFywkUYGvdYe6M7VsVgTXqKCivwv1P9pHFRMLEGBrDP7bWcen7FUBTK3MCo4FQV2ddV56fWqNVkaooKkiXCxoOy46xvAhWP3wEQ64P6uPnDM8RJ242uxeVaWgAKcivC5C2hZbg4EHAbrecv70tzG8ApWjeeOQMoa2LacttSf92UBvmum7qln87xuiHHPGfBYfczxc6tr7Bl7dEVpPV9MtqSw0VOv/l/8UEbWHTQx9Cl0P9GHXiaqTXL9XMU6L6maSO73PJ9GJFLzBQEU3Vfrr51q8Hk1BTY0WCgban1AZrvXr+QxcphB3XgEmNIpAos+fss+4SwRedAYvhkddfSpa6xipKK0ApLo5HWcFCWW6Kp5q3TqWet2FeMurAmo13i8urhNDGBn9EMYWbpUZausbgvOdjA7R4Gfh9evYxpd91eeF77XewXKurIqjTCUZd3RwBBXcxs28ztFsKU7hN6POwXxsWWyOF+PCaOR5qCTxvmr1yXRrsP2eLKIaY77/VXPBQRcZnHP6vRAfnBQv1tpvftVO/OuL9Z78qlwHz7Z0JQ31XeAfOmVSoRgXukLoxAaZJCX4SaPuGmo4UNCKIe4f1XixT0E21OEp81G2MzhoTxXTzfjkAZXIps9/ce2rGNSIZ5qq22rGB9Bre5AIQAqUahBQRqoiZWedVSheh31UsTbUxYXuK6vwTtS6UGThdZ9qCKjFMbIGhE2lIEC3Bb8/XzJeL6fRDxBnbzrWem2r8amz9NmIgejfLN6/rpe7IBWNi5Goiga4YwBr7shnDefxVOEFwTPhUqHl4p8FVS/oohjqSUMg/wpldwavLpbjgLtceqZZwJ+stW27WklXRdTfIPugvkCnwNc9pmwmMexKJ2dnB0sFGf0+VLgrW4FEINTJqHo7/a22owBH8P/koA4VdcM6tE0V01RnlB/UoWJOMyLmDkZYwlI8KGm7Ci6NwWvIWPTIDeoejDdgKACGLFVF8BCoYsH3ylp1EsfdPYK2lck04vV9yg43k7iBti4sjSmQ3A9iIXtLCSrfioCQegioRZVEhb6Ot37W1wSQUYOmglyDq6TdHYchQLiSuLNkDc7NJAYlKYljNhzJB1gatBkJvu8Gp4Y9fGd7AKy1pxpjchCB/irgYWPMM8BvrbVd3ou5qwB3IlBkrW380l/ujqWjh2dPq0kEOtVX6YquDEInvFo2lf0oKOpI6IQudHXruQiJllIFMvAsohpvZdUJVxP8XtlR6COnei3wALEKOBkBNoI6onjgy8WzKmWdCqAqQiogh8wsFIdrXV1hHwrwjC8EDwXsEMC17sbg+5GInnCwGz/VyYFPH6X6RhXvcYk64w6+ytjUZUQBbZt71Y5ZiBriKJJsfL9DlUS8dE5EK5ENUq8qyzRqohfiUpLmwMpAVorcmxJcRmW8G5Ey6VAkzqBb/eD29GKtrUe2KnrQGHMwwuQuMsasRwLx7w/2i/jc0tXh/Bj2YK2lPqOqZFeleCmJ+jN1UVC9m4oRylZWIBNQAUH1RKpPU8CIIGCjE7yzE6uu3INJnFQKkGpsWB30Q/tWjQdjZWLfcH0LrwM8uISsTd1JQh+90C9M9XyOjCT44pUG/dSFQsVGnbC1QLVzrNWFQ0V/8ItLoTu3OGi3JBhXBfhCEheeGPgbqmKoglgyYk1NI1F35nLBRXTzbyNHKBqG9yqODdpOGp7WxfDicDsi0KTgA/ttomVWLdWD8UXvkT4LoW64m8qeroPTYowZa4yZicT0bEQSZZ4PHMrO88kBO2FwxpgxwcffAs8bY+7ns7mZFnahk48hHKPOWlvqzmUj6YgLkSl3jrX2H+6765DoiQ7g+9bal9z5w5HwsF5IRMWVXcr42WOHZzuqb9ErVyulTioFo8181q9NAWwVoo3UFVgnYw3eglpIIjApkKkIqOKvKtTVCqmAUY53SwmtmJ1Fys0ISIS+b8quQvcHZUIRfFB9NV6PqCA0nER/MG1zM4np3TuPSyj+ZphE8V8ZsE52BQAdi8agXoL69AjX6Lj4aIMPNYjRoQEf7dDLfb8NSPPOwdEgs0ioD+zswhJvAwTotuBdT/pJ/Rk5gZ4tyBqsQKVSg15reB16/xIAlW4TUbu4JeBuW4wx9yJLdxOCPzdaaz8Jvl8K/OPL6tkZj/3155y7q9Nni2yD/GXlcWA60lEt1yL7Kv7UGHOt+zyl076K/YG/GmP2d1lBdV/FpQjAnUgXUNz02CHPTWf9WKgzU1+kUAcTCc6BBzRlKgkK6aDeZASgKvAGilDXpw92KIIqOI1EDARRfKxpYfDfEFRDHRYkBrAru9L+KyArEKteTxXrCjahniz0E9OJCl7c1LbUhUavXUFP+5kRHLp45OOjIXThqAjqDEE2vOYoJOrWNNIAvJgYRjC0ypGcBrFeif0+GXi8HTJSEl1gCNvQ933wPnd1wPvQnIKIrBoq5gAuNFIpUwtdjZSR6uIX3s9uKP8XdHDIqJ1hrX3r87601rYbY8q/rJKdxaIWdeHoCrjhlIINnU7/q/dV9O3Hkon7vRWSyKogMaNEKAqpeAX+/6pfqsZPwmp8HjSdxGrx1Ac8PGLBe51Q+vD/Ce+MqyK0srJY8DsFKAXmUMRWHY+KwKr70f5uDo7mdi9yajvKLvKD/wwO3offxYJXcMp1IGoTw8Y2B2NZ5l7V902NJArW4WKg4PsZ8U31Xhvd+7fx4mIvvCyfI59jG4F2MUzoGLyK/L4G76IDnYAmBmUG746iTO1gvINxmMUkqEMXQV3kSvC63FBETQDWr1725FjUoOz4PHAzxtyn7621q76ski7p4Iwxz3/B+Wc/73wXy796X0VfdgCRYEVWgAB50FQJX0hicLyKjIVQMLOK0ufeonTmW+KFPpxE51VlIVqXshC1BIZMSJmU9iMUXxW4chHRU5mVinehT5mCXVlQr+r6VHfXjPDd0EgS6t4KUzygaB0hc1VGVkNiqiVlfsqCG11fC1Rv1SmcMmROupCE49PZVeLzWHO8hHUrezqYRBcODdlS8OlHom4Ov3cGfBbc422kOD1kaLQAAdTQv04ZYyfDhYJ8qONUxhbB63j1P18pCtWX/wM6uAu/4Pwu7dPQVSPDsV9wfvSuNNbF0i37KhpjLtPNbGmqg0b3d33gFAhUd1SL188FOqwbX7weO9owy+zPA+ZIHjBHMv9aQ9PdhpNmPwuDIWX6FhGWFVhCkSS6SM4AACAASURBVLQQH7mgRdlQNZ61NcMtz03BPmfY/idD5Wv7s2Lrftj7jBjJlaWp1VfFn3z8ps2bSQz0Xyq/tcaweb3Bphhakgz2MIP9u8E+b5hfbZjVaERcU8tvM/JZQVlZrQJarWu/Aq/PWwH2SIMdYrA3G+yPDKy2iYtAgft9Ld4iHF5HQTAuytzUPy0XiG5xynplamkwvB/MLcJ+kslV9jH2tW1EGtMQZqV+cUvcayviF+eKsixtJ9QTxsnN2iBUrA+QB6v6UG1PwY7Kx07KxS4eyDR7Ld75uEbGrRBvhdfnQY0ZMfddJd64spn/+FhUY8zFxpiLgWR9Hxx3kOh2/6VlpxzVGHObe9szeK9lELBuVxrrVP6l+ypaax8BHgEwBx9uyXIuAtUk7jegD5/qQgImZe8xtDfBqyOFKhZmQkqp9PRvVTBvn7MAePFGOGk5kn5awUH1Z8kI21PjQzUCaGe7jq4ASsH+WIDM3gyzMifSi1bS2MY/hmVh6w0mZn04URme9amFTv3eFOTAg89qyEkmnuqndRn0GgGfNAjv2QjYMoN5wsqm1EtdHwvwIKesowQPhGVABRy1bSGv7zMWxrp2o1AzDV6b1oNjCq0H5D/hmXJ+UI/q9NS4ErJQZbTVQGEfWK37K1i4D8ZcOZcFPzkFDoVfzL+e7437JRuyajmG+cimMxshebTzmWsg4RHS62oMPhM8GzFlfishdwhsfpFr7JtM/cktgnVFSND9g/DDix6il23lO3s/DqV9cBtq+ecqFL9V/5aFz+irTL6b3ET2YB2cMrSeJLI1izyqF+xKZV8mhCvQ9CARdCwiRt6yK411Kv/qfRWD3gZiQyiahkYFPQrwurbbIKUORt+HV4BXAsPg8BL42wtQnAojUmFdaV8BkBWI930BiaKf+oLlIz7acxGDQiVMevlRbA78oz5C9j1RLp43WzY1niP9sJXQvCGJjMEdXlfVjF/5FezUjUQn6GoY+eLLsA8yEQ+ElCWQkgqMhYIKIAny6mDj1fCaPZxjDvybF58UNNWyuBoB783Aqo1wXD+4Al4fMJa1G6CoDvb78wqeMqUcPhEKPgZ7m8GcZeU/w0m0HirA6Fipb2AyXsxXcIy57yiQ67vPsP1sQ8qZCEGrh5enj+T4JYvJT4cfNS9jP37Hd8wvIfY48oiF6yNe7A1FYB3XRqA2BXUBmb/pGH7HeUw95xYB9kPd/UtFluY8+PbQ3/Cd2sc9ww3vjbYTWpZ1wSAYj25icNv3UK8ua+2xAMaYO6y1N37V+nYKcNbai1xjr1tr/+kdbowxsxFxNtcYUwP8BAG2p4wx30L87Ca4Nt8zxui+ijE+u6/i44jC40W6YEEFJBZ1tfFiUGe9GXir6mI5d/sNV7PWQEEmpHwNSZLchDCMOfJ6+DnufR30WbLJi7nK2HRiKkDk4/3HjgP+Cic/9zSz7rkMZkGTiZI9yrWzyPVrKFQsKOWIsSuwvzKMHf8CC4tPFgaok3I1ia4Oq921TYbXThgHQ4HxMsopU5Fte/sBZwDLIPYp9HsK+g14m/c/KeTA86uljyUIoKuVVxlHNXBFPyY/dA8PTJ4Cz8Pq8pHs3bKYj04olW3Cm4ARwEtgCwym2fpkmmUkZlJRETAEHNWB1gb3qgwYnYLdz0ARvJc5iNXPDmY9A3mNY7iEGZAMaVfAvRU3QQ58u/w3mIp3EA3HRuJiZCRwFyFoF3zcLaDGhZUM4fHZ34FRyGI33F1jf3eMBy4Ee77BrNgMyTkeqKP43chURCcYV71vUbpFB7enZhMxxpjA7etmY8zn8llrbZeXgS4RYmvto8aYYmPMDcaYB91rcVcbsdZOtNbuba1NsdYWWGt/ba2tt9aOtdYWu9eG4Pd3Wmv3s9YeYK19MThfYa0tdd9N7vKu15bEIHrwIKeKeDXTlwL5cGO/aRSVQspNwNcRICtDhOIKhK05cCMdNo5ExJJyvOsDrt58mxhqlUXc/+yFkecIvP8EiorALpf6KEaAYgMc8asV0AZcCi9knCKTS11Q1McsVFw70dv2MrJs3Of6nglVpQXCPC6RzwApxQgTSYJUs84bJUJfNhW1lFE9XMUD50yB62Fo+ZvcyQ1EJrt6b3Dj0+DamAg3rr1errscL5IqE1WLouqnwLtWqOHF6R4H3f0ef7lkFJwPB01ew+mLXuIj9uMUXuC4hsXS7gZgC7xXNIiNFcDvDwbqIVkzj/RJjLrQa1QDTEwfGrdL1+g0rpzziABZDBFNF7t7r/VkIluyjoXr7P2JwfQxEu+Piv2FeH2tqke6Kf/sHqqDawrex/BhKXrouS6XLtmJjTHnIfqsPyN6t6HAtcaYy621T+5Kg/+WYqyfPMqmQnYFHuR09S4G7kQmzIHwyeXZ9KKV7GlROX8qwrLWApXQ77vw3oOGg4ZbrzfSybrKJD7QurLnIhLQWFfXeDDLEJbwXeAeZDL9GegP7SsgLRPsgY4RqYNs3PJHPJeanWzgR4imdDhsGZ5CH9opfrpGJvXHrs2ByN18AbgZiuaAjbj6a/D7LOjCMBhYAX+yk2E2MAOW9zuSVZfvy7qZfdl3/SaYJtde9WgBxVU1VBUXcHvd3fT++1amHPWAV+TX4C3XuuDo+Kii310P5WDrjChDb4U/bIC50x9hW4shsgoB8jqw74NJBWbCQXlr4H2wfzeYSgtlGsLl9nZQNyFl8Y3u+xgIlUqB0Ydjv2ZE/zlQ7kd0LEQeBjaAdbZ/s4b4wnTX5Nu5+9XbRGZRJqxGBXUdUWPKSHzYnDb7FcserIM7KHhf1B0VdlWleQcw3lp7rrX2GmvtNxBS3tnxd/cs1ngXCvhs7KHq4txDFrmwgfY/u9+WQ3s2/JQpZP8kKhPpQOSBnY2wuHSgSfb8zfxGbaLiWEUdfcCbSYyHrQLuh6oVYGcjrA3gNuBDBKD2kf+nFANXIgxlNMLKFKBD/7tC4Dn53aYnM9hUmkGfqnZZH9PdsQS5g+NdfRtcX9bDsqfxvmEK1KGOrBxOmz1fxFfgvcsHsZ6BpLKdhoGRuNtKEjGohOK1NbAExprpiSFrufg0SxESdy6L4i2tGfDirNHS7xFAfzi3P8w68zIq0w+RezARGAubszNgHMyedRqnlD7FwpKjYAvYSQ6weJV4tIPqWmvcKymJLhvAI6+cL4tBHsLY+kF1+r5wJjABZmRPYnj2q7AW7EhkYUTbI9H6HC56Cny1eKNXLt0oou55fnDW2tA9rBbYYK1dpwfylNZ+/r8/v3QV4HoDb3Q6txR55PaMoiJQqH+DRANDDCiFbXU5tA8AHoTZeaeRshYemDFFxLg25OF8GgGbcsRjJxnOLYPGCXv7/UrL271Iqof6PkXhvrMuF3NJPRSPAzMZmSAHIv6pdyET60CEZTUhKDoCVly5n9wBFXmq8dlElHENhZlcKGE79fJ/OxwJgCtDRMiFxB3zaQBGwbBy4qwpPk4R4mFcRz66SMS1Fnj55pEctHYNQ1hJv4Ym6uhHy8QeMAeS6BDwuV+u4/CpeHBT9hyyuQx3DaX49FCA/bNhdMsiGAXtj+KBugGGr39HxuhM+d8G9mbLOSl8Sn/u5/uMmfEGvA/LVgC0QsZof9/hs0aAmOtDIXAtXDr2CTmXLWPD+7Ca/fhe0VRogdP5E0NZDmvBVMBb40oFbMcgqgHwlnl1aFZ2GqpGtHRjqFZXjt24vAwc3unc4cBLu1JJVwHu50hupgiAMaYXIqj9fFca+7cVA2REISMQ37OsOP/qCqsiI/DM/pC2BiiDiTc8D5ORCZ2DTKxMhG1Mc69V7vtToXUhFFxe5UJzUnwmDPBRBs5iduXoR2TSNABtsOXmFJm8eciEWuqOKkRUzkZY0xI46LY1YqioRibKaOKOszZDtrdjDFwzdjrrGSjAvB5MFQIg+lqCtOlYIjHXfgyfaVgZbjVwIiwbOlr6UQ7Hr10Ms2AzOfwx+2SWMYznUs+gJbMH+z69SWzto1w9YxBXEdW/aXvKQkfjWW61ez8aHsubSORpaLgyQsoqBJDvg/deHcTQgW9ijt8m9YyAQ6ZU8W7SUM5nFoMW1QqTbYECm83mpHTxV2TxZ0FGAQ/ixqJv3/1zXl5IPGHJmrJ8ohOgkb34Pg9wfelN9L2tmXv4sSxM9ZDDZj4ZkQ0LYc03jBeDdaHTBUnZnFq8QzXDVywqonbl2I3LUGT5D8ubSNq2LpeuAtx3EHfTLcaYjciU+AHwbWPMx3rsSsP/m8UYZ3RpThFgSwaS3RMdGhkA8ts5ayDU5mUKaC1HgKw/ctVD4ZOSbGFB+yAJXPYhbk1LK4L18/aHWuhR4BzPOhs4ql2bZQhQXCKne+e1ywRQRflQPKtIJa5PYyKwBIrPfSdxQ+kshHnMRtjfDLhjwY8YPvQd2ADPXnOS9CEd0SelIwCUhLA1t1lxPNJAS+i7VYGwpXnAHFhX1BeWwHoGciTLWM5QCllLetUOAcg8dy37yGGLjHdpCd1R1JqogBdBRMjj4OKK2VABjWRJXXdB+wgY0rCG5U8cySMDLpXzlTKm69Wjqc3dszEwoKqBnKug9Om3IGtkon8fJBoDHKP7WduPOX6E+74BUtnOS+nj4vCQRiuf3JxN9oqoaIzSoV9bHb1ohVOgSJm8+ieCT4+ueuBIp7a7LZJhzxNRO5UmxOQdln7EvTm7VroKcJMQvnA84jBxvPt8fqdj9yzGEslohSw3a7OAqAuzUeaWAWRYPtx3EIyE/Cea5IE7ASHFMWi5sgebSjIYMKNB2NRYsJnI6p2HgMCFsPHrkH3yJ+xYlU7G4E30yGoRYI0hD3o5wp4qEFeNacCTYGYj7KTCtbvA/W6oq78eYY/zwVbAyxwv1zAcH0KVi1h1NwBXwbn8gcXLD4N6OPP+F7FDXXstyOQqcq95+ID8feCkmc96h2LVl2XBCy+P5b1bBxF9FjgTPmIw1790E6lsZ9+7NpFDPSPr3uaT0mwZlxEIOC9FAGgiXqRWHVgG3qI6Er+r2GRxtn6nvBgmwKCqWmrPyITpkPIpmMVS92oGwz7w1pWlnD7xSQaynr5LmmG+jM2Wc9y9/i68mnykb0utpsqytDjgSz9zhxh70oFxMGBVA6ctmc9eNNK/pZYpTdMYsKRB7pdj9ukf7yB7TlRmQxQfA6xRKKqPU32jLk7dCHB7ciRDUJ5B/GFLjTFpbkPo3wJP7UolXXUTWdSV45+4iP+1khrZTkbWVmg2kGwTlb3g4gYNxffUCBtLhbmTxsg6Mgp4Af6YejZ9n26Wh3kfoALMNCRPSh4i9v1eAoL6J22AZmhe1ZcdtemuXSAGGWWbpE11wH0Y4cdLkbbrXH/GISwEBJDyEMNDDMw+sO/aTX5bQ2VdGdKvfiWIbq+ihg6Sab8QKHPWvmKEqb3v6nXuInHxuxx+wC8Sk3o6FjeMN8mikUgVnDvpcV5hNDe03cnxyxZTe30muWxmS06KTPwYYswowxs3piCiaBZeXA+tppX4DCpZwDQ4uKEq3seN5EEeNJREIALvTRjEr9ou54mSs3iNY8ilnlS2y48HAknQ5+/CjKuKCsgZjt93Ije4PoL3Tk/bughhhuXQkBfhsZKJrBmRz4l1i4hUidM0bfKssMiNXYM76hB/Q9UvKktTf0jVBSd3av//A5yWG5An9E1kCVgGfABctyuVdDXYPtUYc6cxZo0xpsmdG2eMmbxrff73lKSkHSQlO1/hrHYJ2YoRvOKtdw8Dw4AqOPmJhfKg5gBnwAUrnpIHeRQCLKnILRiPuB8nA0XiHHwHNxIZ2ZAofmVZiELzq33FZ64JESeXINbZFuT3GxBQWIhMoGz3m+GuL8vx2wmqRVatcZuhvQ3x3dsHWAaj5rzJDzOniitIG+Il0eT6rhMUBBxbpO0JbU8ninDO4bbvr5rJaWng+bJxtNGTr/Earamy72j+2ib250NeSTpWJrsbD1YhTOZjIBMqf7K/Z4s1+Hx4WUFbGXDk7bJm/iM7IvWtgEM2VNEwKkL2+ihXj7ud0pM+oiy1kqG8y4XMFPEQxLgBAjbLoL0PpNEqi5CKhgn6N5uY8SUL0g5E1AIbROztIEkMJy14H7j+CHA7oGovAYqhYVhErvt0fNLOMJIhP7hWtaI2023bQO3pOjhrbdRaq/y5H5DufF93aV+Grg7nL5Ap9V94O897SGTBbl8MlqykRjLSt4ICXTI+w4haWPNh5VrkgR8O6yb1lYlVB+vK+opYkYM8uO8jbGMsosdKRhhDKaTsDRvMfKKV2V4EKWyHzUYedmet5WHEny4Vqft9ZMJMwzOfPERELUaAVK2rEWRN00mqYlaui5d9ydV/hvTvgSemSJuzEcPCBtcWiMicCfwdMU4sgvGp86TuSvwikAzcJ24S47Pm86f55zG6aTF9FzXDQGgoitBBEqetmk9DaUSAuNjVv4G4TizFVEm9oQVzNd4v7Djp4yNcykNlF/AhB1BVVCCP+g2QvSTK9IHf4rd8k+2/NzzMFQxu+4iPGMwDN0zhXq6WRagOAdg6SLka/k6Z3K9CEnVfAFlBhl91Kcp2YzQMTmMOx/Aa+1Ztiv/vnXHFct/2d7/rgMbMDFgkOjCG4VNDdQ4JzMJHu+i96yaV2A56sJ3ULh27c3HBBDchbmo37UpwgZauAtwZwHnW2jdw0XIuu2bX0hXtBmU7Pdne4W5oxFlQI24x0Ic85rIHNAB54g1ur5T37zNEHsBsJOLHxXYyDHGr6o+wFGfx7AVQYL14l9zhLWgFSF0b3f9K3W9uQ1jbcgTsit13fZAJ+6D0hYcRxpeHFyPV/SIMd2qC9/oPkn4mIe4b/fEW01A8ag7+nwMvdZwg5wvcUejayIET+QvVTfL/7ZEebBmZAi9A9g1RDuADzi95hOwNUelfOcwtGSPidrGM25BheHG6EO/4DN6KWgOH3FbFhxzAcoaynZ40jIsIe1orBodLmEHK7VBBORWp5RyxcAVkQh4b5f60ufsUBYrg5KqFMo43kggmWSSqKrKC79ymWXdzLSsZQnueqzcdDllbJdeV6u5Zf0jtaINR0LulWf6rqoMwQiMEtNDpvBvLni6iGmNOAf6GLMcNwAFAhTHm1F2pp6sAt51O64sxpi8JuWd232KwtHak0RFLIiWy3VtQwYOdM9P3ApmYeTCoshbTAqTCVnr7TZRXIKJLJnF/sPiry4kyCgRAI66NaCpkBIaGZOD3CMOYjHj4rEBYYDKijH8cATznhPvOvcUyWZyOx5bjGUApPq1Qf/efPDho3hoRDfvD1tTevs/KYJLxxotsxDqcBw3TB/gNbVSERyIFfsaPKR4DvxlzDltTe9NnTTvRSbDoziMZUNHAsbzCX/qPElG4Eio51HtMRt3gqDFBrYz6dKmVEbnm8cyjjEoOWr+G7PVRuEL6exx/5Wv8D9Pv/RandsxhWMubsmAUQy71Mq7DENZ7hVTXUByBEph8wT2JOlg1OOTi2XwEWQjS4ehxC5i46Hme5DzmZY4TQOuQftTmZUo0S6b0t09VO1UjCmhNj3jRXEXTcAapc3Nore5GN5HuAjhjzEBjzCvGmPeNMe8ZY650528xxnxijKl0x/jgP9cZY1YbYz4wxpwQnD/cGLPcffdLY8zONI53AadZa8+z1l5nrf0vJBnuLgUXdBXgngZ+Y4wpch3dG1Gt/35XGvt3lo5YEm3RnnTEksSC2mxgc0Rem018pR2Vjc8Q8TFwP0T7w9kNc8WdYx/irg+LrzkMZsOqifvKhHGuJLbF5XaNJZFSukUANWrkNYbfs+FDhI1dgkyEYkTc/RgB0/H49ESZcMhFVfK7dGAplGe/5hmiKucXw9FPLWBtHQKE9yNi2XxnGQYBNGUVLa5NBew81/ZqV6/G1jrfNTMTjmQZdy+4iq305hf8gEXFR/LH9LMYwkq2HJrCxSfMpoJyEc+S4cbzpkE6rBvRV/o0HA67YXFirjkV25a6z8Nh8azD+IADOGLZCmw6rBq4r4jRE2D4me/QShrn8Tv6LGjno/RBAupN8JPb7oHnYNGEI2EpLCw6ijXX5/M6R/PEqLN4YNkUvzAo+KhbSrTdG20myL14fdlYaIPv8N8A/KD4LmwZsEqC8Ml247cGogOFXWavjxJPO6/thC4pYfxw6HyuaSW+QpHdKrpNBxcDfmStPRDRAn/XbSsA8AtrbZk75gF02nLgROC/jTHakG45UOyOE3fSbgHwWqdzi/lMSpidl64C3PXIersceQyrkMfp1l1p7N9VdtCDjlgS26Op7GjsFHyhD3gGkNWOuRJ4DlaV7svcU8fA+xBpADMd0SsVISt2EYy86G0ASirXCTAkAy1gkmWwMvPraV/RB2LJ7mFO9gaHGoThrEV8ytTqNszVox5ADcAGaLg8Im1cjwBUG7y9bKSPjBhMPMvuG7eOoagUtryPAOhsaL8GcbQdKPXFs++5CAecyEnM9Uk978EzrCxgKOzV0cgLnMLkhb/mWF5h1Dlvcm7TMzSSxd+TDoVyKKeCh864QHSB6bCpPIN+LZvYcmoKpMMJzPeOyqGriF7PX2AIK2mlFw3DIrSm9xDG0Q8BjfVwZsWLvMbXoAgOmrMGexECNjnAKChkLWyB3mzlIwZTTy4b2JtoKZ+N342XFCTt+loZi0xgIzw97mTSaOVoXqeVNDZmZ8IoF63R4MYvAlvTMziicoWoGybggVT9LUOdWzM+07I+i90SbN99oVrW2k+ttW+791sR5cnOVFPdteVAJRJNHZYfEg8Q7FrpqpvIdmvtVdbaDOQR622t/YG1dvuuNLZblIwoRNr9qh0/ZyGagvm6hTboH1nHybctFAifBXYyZM+Lsq6sL+23IuLj+chD+SAyqWJAOmxpglPHQ9PifHqUtJCStVXajDkXlcFRqIaslz4V/ZhaHG9zfSoGFoAtdnVWQfaUqJyfhjCyGLI5TQF+o2fVlUVh3fK+JCdD+6HyfcpkRNztQO5gJgJkOcR1dNQjBo0FJIZQJRNPNXV30VV8kHQAQ1gJ/eHEhYtomdWDWZkTqSeHLP7BojuP5MRfLWI9+4j4jehAI2uhz83tsAjuvvQ2sSRrRIO2VUY8KenrHM3BLKeSQ7k39WoGdqzn/EmPCKu9D6iE056bz5ZBKTScGuHB7G8JxwCuL72JfW/YBAvgiKdXMISVdJBEI3sR+TpeTaDgGlpxMUAh3xk/jegEaDmhB3M4lUaySCLGr+quopVeMAdG1b0pY18HpEJaW6u8n4i4/lTjrcTK5AjGVCNEQn3cVyy7KKLmauZrd1z2RfUaYwqRTHgaYTDZGPOuMeYxY8xe7lx3bTnwbeASY8wGY8wyY8wG4FJ20bDZVTeRIcaYy912fmciU2KPKRZDa3MaO6Iu9k43oQEnHgRUPRn4GPrMgrk3jxFAGA43Z1/HmvH57HvEJlLOQ8REZQsxYA3Cb5ugdzqs+XM+RCArt5F2bTdZluceyR1wnKVper64nagz7CXEFeKUgplK3LWCTOA5aH0O4c8aJ6qMMB+fcj0fCj/aSFoZtCsjA59jbjF+B4yN+N3w2qQ9+z4SUlWBd06tkbauP/8XHDFvBa9wrGTSKIK21J5cPGc2r3AsCziOUUveZNPlGdx1w+0CliXQi1a2HJgi17kWn823gMR9CxRQC2Biy+9ZxjCqKeQnG+6hz/J2Hm67gkX9j+QvI0ZBOdx/xmUsSxrGXg1RH1vZAnfdfzsNd0bi/oofcAA51LOdntQsQoD0ZPz+rMqwgq0CH3r+h7yefhTplTt44nuXspF+bCONuXljxNeuFAGzT919qoP0ph3e8bsJv82kWtPD2N5QelB2102xqG307NIBbLbWlgfHI59XpzEmA3G+vcpauwURN/dzI/kpsvTKwH1el3ZxywG3ocyBwLmu7nOAIdba97syBlp2CnBGymPI1L0ecWq4AXjXGDPzS5SEu00xOo7RFGh2T1gQbN0jsl3YlepCJsjrySsWQhVsGZXCDS13M2heLcxEREm1fI5BgKGY+AO7qAEu4LdQ0M72aE+ocW1G2kTfB+IykoswkWXw2J0TRYfngKxhYkR0cBrZUAdMgrRbgWFw3nd/nZjySY0BzYi4ep/hL4tH8XaL+80q4oYH1iMAXef6/r5rNx22nAo9ZlmpQ9mUjotaBA+Ej2aUYt6HaB68yTBuOvU6UmnjBw0PQSX0PdNZEdOBUZC9NkqfDe2iq6oKbk6of1Lx1Hn+359+JX+njJ5shwdhadkhpE/dQRIxsmjksbKJAPRnAxuyszmd59iUlyHXE4HlHCwivzMO5bCZDpIoUD3jX/FOv3FLZ/BIXwtj6t6A/nDSA89y4boneJDvUk0ROS0NvDxqpFxLDO9P2CDuMlQhC1dGcITXrNeb0elct+3J0H2hWsaYFATcfmetfRbAWrvRWtvhkk8+Chzpfl5DN2w54NqIWWtfs9Y+Za1dbK3dpVxw8OUM7jLE73y4tXZfa+1R1tp9gKOAY4DLd7XBf0ex1tAz0iYhUyoq6kqabMUJOCMKWe1klGzCDLbUTswUIHsJ+vy5nchtwDwkBGkREsQ9HiHNLtKBGPyhEvayxSx+/niIptBc05dISYOAaHMEkmFHpdMDFkDDeNHrXXzqbOwMsGOBWeJyQT+kn9fD3fddxeyJp1H7o0zWngezb73YhzqV40POooiWYjicdOmrfNu+Sf37UFUBdincMeJH8vv7iYMPI6TvzIPMIuu3EIzigTwZAYRvgHlTnGKfGHEWr6WPZG82cFvD3VzITC7NfoDohRCd5canAhG9m2QsGQGnv/WkPO6D3T3Q0CkNbRopbc7gEnKpp5pCHrtzIpvJ4a2bSxk5420ayeKnTOEDDuAVjuVhLieNbfSta+aTmdlQBaOuelNA/FSxgm8nlaN5XVw7cvEp5NXIAf65AFi1DPOGhXqx5j657wTSaOUAPmBregZZNDL3jDFynYcjKZPyMkyYiQAAIABJREFUoJ5cqANzo/XbR4YsVUVT9S0kaH83S3jpSMyvgfettT8Pzu8d/OwMfGqGOcA3XHBAEX7LgU+BrcaY4a7Ob+K3KdA614ex7V907Mo4fBnAnY/sLJ+wP6H7fBW7c/xpWAx0xORJSsnY5k3zLpqhPdozLqYmJXdALuQ/3kTtrExhMTcgrgYTYMBVDWz6bobYkDXqYSrwFGxZAueWQtlLH8JgBFDdg7sjliQiasSSUr4lzohyrtsGbVA/D8zTLh7VJdkkhoDCfDiVORxKJflLmnjQ3u43z1FmpfGOqjCfK9+vmHgEfeqhOA+2tsCNp07zzj2p7vibXItxkRZx0VRDjFQZXgbcC7wKCycdxS+4ig30ZyVD2JqZwlSuZcbC73Fd+l1sTc8QcFyFgKiyU+D5CRMTM/WGzq/5xFOVv/GMJMdroyen8AKVHCoK/LGwmVy+zjzmMZ5lDGMEr/MCp8A0GHBOA4/eO8kH+leIwQIgh3p+M+ucxCzCIZGJgd9MureowfNg8pJf80N+ThIdLGMYHSS56IZkL2qOlaiL4lU1orKYhIjAuhCpzk/bSeazxo5u2nSmG/3gRiDzfEwnl5B7nMvHu8iuez8A2XIAiRddiWiJO285MAOB/Y/47JYDk/hsfPvnHV0uXzacQ/Cam85lkft+ty+GHaRG2hjYb724iWRYyIjSI7eFlPwtgABfRm4jWamNEIGzL5xF/plNkAOPLZ/ImqJ8yIH2W5F41NvgvXGDvIPuINjWBuZeSU/eI7eFpOQOeuS2kJzcIX5wUSOAurqPD2AvgJ4/bSJnBiJazXHHItnI5pOl2RCFg76+hpIl6+BjmPbjG+Op1eNhWiXuYnXSliHAVAo977CY/7ZURI8S8JyHKOPLgToYf+szmB1WjBXH4dOKazhVlnstRPh8Poy97nX+dsMxXLD+KdYzkNakNAaynrljxohlEeD30PCWUKKGPGGq5pdWGGYj3ps/F68LU0EmA5gLx/AaaWzjj5zFjRumcVPZdZAOQ3mXw/kbG5tEmXjSB69yacUTkAmLnjqSS+c8waPXT5Jrmgit9OJ1jmbMsje48Lo/+OwetfjkmuAALs196AdsxAxYz19GjKL2e4O4/qOf05M29n6pkRlcwnZ6Es12YxZDHJzfB5NtfQZfZcOh06/q/DQLjBoZuisWdUdSl44vrUtEQ2OtPTh0CbHWnm+tHerOn6p7HLv//FNbDvwrYt6/TAhPcqbhz7vwrV+0KcTuWlpxhobkGERT2QHsaDZECuPbQZBEBykFW3jmpUlQcT78CC5eO1uYwNNQd182A4Y2wFo4aMUaWd/mQNUiKKltju/HkJTcQUcsSZgbSJsRN9zNxiucy6F9bh96nVHPtqYcAaCbgUzY99BNwuQ0ZCgVBk78UPqiE1LzzamlLoKPbywIvpsBY3//OvctuJwrpz0Cg+DlM0by9fo/035sH/ntalensqnm4LM6KKuObBVEn4DIIvhx+nQmZM8ijzqWM5RhLm3SwHvXUzy/hk9+lM2AIxokM8df8SLv/2Pv3MPjKsu1/1uZY+aQDEmahDShSZvQUlIIEGihLS0F2lK1bBBBsAh8oG4BP9C6RTyAyucBtigoiCgKbJDKWRALlFNry6EQILUBUhLatElDThMmnclkTivr++NZ71prAgpIVNzlva51zWQys04z617389z387xq6cMuvG/C7n7bKszrGY4iQoQXqho5iK08Ur6Io/RnOHhXB2N1hfyIr8MQ3Dr/VI5rfhyAvpXFvEVEbKHFMEaA43hcbsu/xM6BqdyXYr4RJthGosBsTvjyepnnYryAGl6H5+BPh38SbQMipNRhcYv7TjoBtKxMqg35Ya9icE5vnLNd1yQMY1wjnfpwl2G929A0zYdcCacDpYZhFGuathTY3zCM697ret4NoDyaph2jadqSd1p4j6K2KSMPaJrW5njtvzVNazdl5vs1TYuYr9dqmjbmoMO/dHzm/TihHQdp4PVn0HWXXYuqDrB6D4HQGKlEgMLgGL0j+5JNFIIf5ux6XsK1++C6+efCSpj6uWEGZ4XgbBhsDPHA/KXceRVUpQoY7wxCG1TP7CAQSuJy61I5AWapVlqATjEisJhM6vcllF7YI6rmfthJ6pMQkFsFK5rvpefMBsnpKGVOjYTjubI7hLCZilnpcPG9N+I9ewRtncHSczaSbSyyy6XmkR8uqrBXfcumkirHA8uDcnN+q8TPQjZSyhDbmMlm5rLkq8/SsLaHPcd6mHr1MHwXtpzdkG+XUKHdLMdjNTarisHhHW1EiBEgyTZm0k0NR+nPUHRdFkZhMevZfumBPDx/MZfzXe7hFHykeZzj+NrV1/GTuV+EKKTxsYNa6d9n7r91Q1A3B/V9WImwQgiZQco1ezByGlwL3U/vz22Xn8JTJUcKYDab524XsAY+qa2FSk/eubIWlVJwhqZOgJsMkcHQ0HOu97R8iMek1L9rf2tiKk3TuniXtKdhGO86OYSmaUcjX+P/GIbRaL62FHjSMIycpmlXmuu6xPTaPKTeN2E9zyONwp9DAq2fOSnwXxu+5gONkpY/4kYnng4zMhSBnIsCf0aMv/4s/kicVFcJlKUoqYwy3DbV6nTx88+cx4XX/wZWiGroX4v8mN8EjgaKQXvEkB+6+cP1LxgmFQuDW6fArTOec8ljLMiUmbsYfHE/O2R5HPkq1YVWD2fNv4GZvM7l0e+SvabIToSrUHRi00gFZCnzPYqNKTaXQqYjaDbP3jxskFTrLENSxSovpkqXFNtUeTMFQAngP+HimT9kIRs5ue1haYc0F7Zc1kAN3ZRcnqLvu8Xse0hMPrec/DkZlEWiyTyGeiR/2CT7NXKcl3tcp9BPBRX0A6KaLkxvJBgVNFhW9QceGP0P/B3wUNMSmnmRKKXkcBEhxvPMBYTBn/W9u9CeMuxKDbfjWBTQlJnHSBTxAUn+jh/NxnBrDK4O4fMnKDoZ8Q+eLKytmxou1m4E+sFfITcOpRuWYU/gg/07sb5DJbL8rhljV8sHClQLmg4xPE++t0guU1r8omEYzR9ke/+IoWnam0C9YRijmqYNG4ZRYr4eMwwj8i4ft8bfZHCGYdQahlH3t5b3shHDMP6MOK2cr60zDEPdt57jXUow/g4ntL0tCqxC+3TKa9aj6oynvEyf+QoAqURAcnOdfuKxsP1DL4MvPXGTeLeeBt1dIIVrK4G5kDwDmbFpuXkEZVCyfDdut44nNIbHn7HC1PGcC1IQi0YcU8cZklptQy7qHnl+65Vf5Bvf/SnZPxTlh5195kEpv5hiQWDn31RplQK/Tmxj6RACbl3Yua9a7HZRToalwEdd+Cp/pN5zD3ATXDPlUj6n/5rtjZVs+NMRMB0Ovr6DktYUi7/7MPsuNGO+TyOgqvZXscVK7DkrnjO3/RDwIyi+JUMLzWxlDv/DZ+mlins4hWB0nNHSAtZUnciZ3EbhcwYdTdW8SDNe0jzDUUQpo4s6IsTYl14q6KfmstfzJ5N2Lmqf1M2CImAPRGYDDfD1V9EqDV7kMIqasDo8E4XrOZ+LD78RSAq4zXKsz3nu1LBM5uQzvMnwwRkauazrPS0f4jEp9e+T4JuelPF/gDsdf9dpmvYyUsz0LcMwNvI+ndCmI/vzAO79RNF2oQuQ5exQdfuLB1JQLYJANuci1Bwj0TVFercNaXLR14L30hGuLf2/nMadBL+fYrAhxNSS3WTvLLJZgMl2hjuniohhgmiBP2Pn5FKQbS2C+qzMnJ7QhFk1Yifyc+ZjG/mtkBTolCFMR4kMXeTP3KQ+q5hJmWPdCvAqsVuEt2KbbFUZkyrVqsXOvSlWCMIEFyBgehwMf3oqM2JvCoCppPkfsJVeJ7iC3c1WJdyd+b967F53t8DGcxdyGncyg04eZRmzeZVvV11KGVEuavsVDzUuwZiuMYyfuWym5OoUM1a/IdUGSL3oJXf+XI7l0+RP/t034VzkXREeCHkg1o/MuwSs6uCEVT9D8gZjsLYHKITPFZkMLWDfLJxGbCeIqRBViQ9KaIkwSS3LNcb1D8ul/XcPVf/+ZbAIzjW8z/r3f7lIoGnaN5Gf1u/Ml94E9jMM4xCk9uwOTdOKeP9O6F8pd7Y2pRSAWDoirctTHqZMHQC3TknTbgB8/jS4dRKtU6RsK2Z24K2Vvcu2F3H+tlso3TKGtt2g/MY42UeKbBe8mTOSO7Ls1njORUn1AF5/mmyikPGhIJ76PcLa3Hp+DqrS8Xl14SsWUG/uhwqd1IUzhM02lO0hhF3R4ARBZx4N8sPOSvO1Rmz2l8L2azktHSpP9wg2GKr96cMGp3rs8iuwxRAVQqtwFMf21f6o4zBzc22PHk4VvczkdcLEqaGbet5gBp080riIuTzPA3VLeZMqlvduAD8s6X2WCgaIEJNOML8H5u2R7TorFxSrUoCXA3IOP2kCpMdMAGF0FebSA4yZz00xIWbY30eX4ztSbC2FXSKmbkbquNWNajKGgdzE38vy4R2TUv/+LwU4TdPOQgpmPqMkY7NIN2o+fxHxy+zP3+GEtraDQcAlSX+3aerNpL0UuHXisTDjKS85M0dGpSFCQGUq/66rfqSRrPwwZ5HvQ3O+153D48/g8WfIpLy43Tr+SBz8hnjuTBVXwsZsvtFUecGqsU2oihHkEIDpIz9UVKFkGfmTQXdhiw8q36feW4l9galw2RkuKoVR5YeUnUGFvRFsZqeU1WoE9JrJb8SpgDJi/t1uvq8LG/jU9tTftdjm5Xvgp3yZKKWcxP2UMkQtXaznGJIEmNKa4MTN66jRu6VKYyVwt/jntjJH2ic9AuC4ITnFE5WLtEiPh/yh/lGIgNrESdY95jImf6rzo24MOcdqlBUm4Vjcjv9PgsjAuAYp93tbPmRDOTMmq/79X3aEmqYtR1LSiwzDSDpenwIMG4aha5o2HXFCbzcMY1jTtLimafOQYt/PAj9/b1sz8JJhKFGK262LiNBXSnGZmRsKJYnHwmZFQ1KEh5Bunx11hw2Z0qfbY4cg6uJWrMMPuHV8/rQVlib6ysjrQadGCJnpS4GnctcrsEk5niu204XNktTFoS4ixaJUWKTep0SBIWz7iDOf5mRX1dgG3xA2eKvnapvqIlZMqBZbZS1zrF+tO0d+/zcVtqnPKNEE8gFoFtAKbccczsXfOpzosYW0cgi97MtcNhMnzOKmh2mmRYSIuf2UEiVy0Vucxp28xmy+ePmvuDh0I6QM6dyrzpfKS+I4NhU6AwJgWSzgsj5UiA122K+5Pfa61flS7FatUx1XxPE/9f9qJm1Wrcm0nfyTx25N024DbjMMYyuAYRiDf+/K/ikMTtO0NcjE0TM1TevRNO1cpBYgDDw2wQ5yNFLrugVJY/+nYRhKoHg3J/Q7b9/x3OXWcblE2XQ5lrzhNqSsypl4ViPls5mO+68sQM6U4b3+DKHKIamgcOckRAaxjPiN/OnjVO5LMR11Iaj8lbooIL/FkHr/ELb3TSmniQnrzzmeO20KzhAtgj3pC47PQf7sUCpXqEKuCPmAq/ZLfc5py1D7qbajQE+FcCrUUyAXA86Dw2mhgn7Wcwy1dBEgyWxepYtajubPMgkzEGCMWziH67kAbaVhHsuYDdhOcFGVBuomZbE7DwJkRebOhB07VehYJvjd1DlQx6IsQWrb6gagzrs6934mB+AM3i6g/LXlwzf+E3EVPq9p2kuapl1kkp6/a/xTGJxhGKe/w8u/+SvvvRcp7H2n/7Ugwc37Ghrj6LiIFAtji41EKK2Ikkl78foyxEdCRMpiJBOF+PxpElZ+wpP/Y0j5sOpYVQjmvCjM/FuBWyeT8uGLiEfaAtCUR0QOpKPIeEIzQcuAPs2+8zvXq4ACJJQqQ8LalCcfBJwXprpolaKqmIkTYFTYqFiWenTm3BTQ5bBZndvxWIstWDhBCfKVXcVQFFBVI8LGYkQMUSwSdZ6xGSfm+hfLZ7eHD6Txmjco+Pgo4Yo4c9jKIbzMX5hDKVG2MZNWmljLCjY+uJTVT/1CbqXVwHEBm212OrZR7XjuFAcSaodATACF5vM4Nth57MdEEgjYoOZk1c5owBke43jfZAGOArh/w2EYxgPAA6Yv9jTEPn2lpmnrgFuBB99P0f2/XGT4ZwyDApJW+Q1kUj6ZYQmooJ9AaAyXS0fPucUBPmRenW4jn+mo15wMxY/dYtst+TsFaF5fBj3nIpkI4POn8VcOW2GxsoxYE984wc15d63EVtnmpaDPrKft4e05wmrDBjSliqqLSTEUJSo4L8Cc4+9Z2IyslnyW4WSWoQnrUyqo2hcFeupGUO/4TJfjuNQ6+7Bzem5shqfU4T7z+SnANTB+T5A7OY21rOBlDmEjR/Mqs3GZJ27TA8ej+czys2Zzm+1YVRgWqCpQ78FmoQrgADu/5mRrbvNR5eEUyI3Z36WzGkIdg/oO1Huc4axiv5NxRRrY0fW7LR/SYRhGzDCMGw3DWIBI1i2I+ffNv/3J/PHhyzL+A4abHBX0mw0Ldbz+NP0j5fj8GbpGa60qB58/TSIWhrIUxPwQygLut5+lkNneSuWQajFBQYNKnWzKS0llVJpCu12Ulg7Rt7sqbxUef4ZsNcIKwd5GmSHWEQVwKh+VQMLmash2FVHQOMp4j9mVRIWrKc1+rwpRFSOZhQ2KtQhzasbOgTVi58lUGKXyawkEoBSrUeCkPHlOYFBhmDNEVeGYlct07FuTuS8KbJxAWelYX8p8n7LT3AI99Q08tczH4Bs1cLvGltw8m1G2IQZqdbxKkVY3ERU+qvOlcorqfKYgv42ZAjcPNjKUY4sOCgTNUe/Yb7UPTjFHnSt1ThTjniyAe1+T6314h1mydTjS1qICeOb9fH6vALgCxgmQJEmAOGHCxSIt6roLry9DgCRpvCRzhVZuLhtySOiqE68aQ2aY6jeT1uosVqYEuFJekolCCMlcEGO5AB6/sDllAM6mRMUdd+fEMlLpk7yc2VJJ5m/15AsNDk/beFfQzm+p8C414XktdujlzOmphLbzbwWKkJ/Tq8UGA6caGEIuYqXuKgtLGQKStdhtl5qwbRPOkFUBkQqpnUqmAlIFjopltju2+3UYPHs/O8el1gM2iChgdobMatQjobLzvCmF2g2ENEcTzAD5tEcJDArUokCJfWzKBqJuFgrI1L6qbajzWm0+ToZz4984RFVD07QFiJB4KtL06jbgfMMwdr6f9ewVISqAFwEyFzl03SXL3/IBuXXp4eZPIy3OzTrSnAPQcpp94YUEAHWHv8jlskUMpaq63LrV4dfl1lGlXJbK6s+aP3q3vW4V7rjJD5vVbGAp8JTtsfdLgY6zCkEtzlDJKTgoVhNDcnydSMjrVBXVZ5X1xCnCOC/YBNI1uBZhTgrEnOH+RCCox1Z4lck4NmHdIcf/ahHgVOGwEmuUKurMNzovduc+P+c8r47nzhRBBGwW148tOhRig50b6Yig2etWQAZ2DjTleLtzf5zndDLGv7HIoMlsXW8gHRYBPmYYxv6GYVzxfsEN9hIGJxPhenGZfUzHHMA2NlqIL/h2Pl/gUFfHzb+tziARUxRwqnGqQ4k/LZ43hCGqoSwjaupClwlo2Vyhtd68baihQk0FRtbratLqLOQ8ZGPht08So0BuYkjk/GFPBJxaYEhsMKHKIRKdpoClcnHuCZ9V6qcKkxVYHIedD6yfsA9qeyr87sGuS3XuE+RfjGrdiu0oNteObddRVhe1z3/tQlb7q0JWBcwR8kHQec7JIiCmdrAICU3foSP3RPVUfSfOG4p6TyV2Lm6yQtQPIXi9xzEP6cD4B8MwUu/25ncbewXA6RTQTwVe0qip0lxunYArSSwXseZM1XNuvP40brf+zu1mcm4TUNwU1I8CZqjYA9S7KTA7iARCY2RSXuKxsFRImGM85yISjJELCtRm0l4C1QMM90mlRSCUFAXX7TYZowuGPBRUjzJuqq+4c+D2oCat9vgzEBrD5c6Rcoel/AveXoyvxsScGOTnzJQ4cVyKxENTbHBSuTwFuM6wUgGfEicUi1LVCmXYKizYqqzaHxWKqgvdydycYoYbYZbOvGGLuY0W7FK0VuzQVL2mGB7mupZjt3lXx6aASAGlOgZr1CHoMUaePUSBm5MVK8BV+Ul183HagtS5SPD2G88HGf/GAGcYxvLJXN9eEaIWYOBCx0cGNzaTEsFBjNEqXHU7mJvLVEQ9Zi2phKc6pDQTyJIiClRCQShJIJREz7mIx8J4HSxNhab+UFImPtF9jI0W4nLrVLl6KS6LUeDWyeVchCJxC7xIeaAsK6wuZ15Ebl3C1JTPyuupkFe8dggoVGft55Xke+icwOZMtOMIdXv89mTSCmgU2DgXtZ6I4z3V2ExK5dkqsWf9qsQGH5W7U0CpQjnl/6s3t9GDnS9TLKsd2ccEdjcWpf4qZbTHsX7n+D22qVoxUCfjfRvzsyejsR/7ecehAEwBmzNkVRUOE8NVxfAmq3rq3zREneyxVwBcBg86LnMeIQErry9DLB0RoHMJ0EVKY6RTPgsAUwlhdi53jnAkblcyhLJkE4UkhsysfFnKYljhSFyADwiExsjlXNT4uk2rSIZuvYZkotAC1uN4nJG+UsYTAcLFCXIqRLUmx3FLTs9tEKocgoSfglASf9lb6DmX7FfMT6qvhOxQEZRlpVW68t45Q1XID+OcF7OZx8q2mq2Zygw7p6VsDJVIaFydzQc5lT9TF6tSBHMI41K+OmXkVaClwK2e/Nblah+d+6cS9c7HHPn1m0q5VGKMAl51HE4QVvk7p4FaAX2tuT6nMJMXgirLkZs8r4Xb8f4u7PyiYriK0fXx9s84wfWDjnFsJfjdlv/lY68AOJdZ4FfBgOV/EwuHAJ2uC8iBFN2HgnG8/vy8nMulowqUZQIZj6lyamL1cIgIukNkAOhO11BaOkRaqatgMb3fcxrFlVGmzdjG4M59RWX1Z7D8dmo//GkBv1DKytNFVKmZukD8WatzCUN+u0RLsRNLnMD+HOTno9Tr7pzJ3Iy3K4DqPZXYQAP5IKeUwWrHZ9Q2lN+tz7EvzrpMBU5Om4Vij05BoBa7/lWxwjJsgKomX8xwevrc5IOLWiLIbCMwwQ83cag4cALAKWBWirRar9Pu4tyu8ztIMCkz2/87iwyTPfaKHJyPNGHi6LiIIzWnbnR0l06YODEi6LrLrGQQZuU2Q0o1MmmvsKKEn3Fl37CUN7sES7HBTMpLKBgnXJwgFo0Q8cVwu3WSiQCBUJJkIkA25aVvd5UU/ROGlMcq8RL11lx/zk1xZdTqZafnXPj8GckhpiIUREYZjwUFeEE6EkO+I98JburiAgfwmeVMKdMC49btXJ/Vdt1t/+0ULBT7UOzKaaLFsS21L50IKD2OXd2g8mrKaOy0jai81sTkfA82y1LsCPJbNClW5ryYnWCj8l/O/BnvsO/WUIKC2hFHYb7avgI4/4Tnzpyo8ztQ+6RW/0HHv3EObrLHXgFw4yZR7acCHZutZdJe4r7w2/JvidGwlYfLmeJDOmWqnG5D8mEhTEuHLnkzIB4LU1oh/fgKg2PouHGRo6a0mwxeyoMDxPwRYkN2qdhIZyWlB8pMaDG3VFNYgoIFJjJxteQEc1YIHBuNkEwECEfiJN064Uic2FBEmGXIAL9mA48CACUCKNBT4V+fZl+E/qwAqVuXffGnLeU3EBoT9umXLiyEPNKBpVOzgeKdEvTqYldiQhdiNFag0GjuT5fjM05Pn/OGolhjrbm0YjM35cVzhsZqv5wsUA3FKp2m5VXmvnU6tusHUk61VBl7nZ1H9kDIrFtVwFlP/s1AgbG1TvOjij1ORjeRjwDOGntFiDpOgTlJWg4XumXfcLl1y+xr/W2C3USPnJ5zS2joT0suThl/Uz4SsbAJQAKKyUQhPtJk0l503JQxRISYBa5ef9oqKfJXDxOLRhjcXY7Pn7bZW06TMDPlAb9BdqgIPecmZW5Hz7lIp3wWG8zrsR9KCRNTP3IVoqq/nSqh84KzwiWPmXuUeSQKTB+f22xUUOhL4lV2mJBhb8vJlFIIWHVNeA3sNknKYKtYmLrInUl4p8LoDOeUOKDUWfVciQp5lhrHPqjtpBzvcbLEHHaFB47X/hpg5FGEwvzQ2hnSq32cGJ46/W9/NRz+O8ZHISqwlwCcYd51M/hIEqDK1UshScKuOC6Xjo90HrAlhiKmCqoTKY6RTRSKUtmnEv8uKcvq8UBOE6Muorpm0l4qigesdflIs4M6CYNxUcMuq+gfoKw4SjYWJhSJk+iZQjgSl3pVt4Gneo8IBp0a1TM70E2VtdQ1RDrlo7Z0B+XBAVzuHONDQQp9SREdci7bBFyZslVQyPeLqeFMgpsgFQglKS0doqQySmlFlEQsTCQYI8JbhInjduukekrkPKSAxqzdgFMxIrVNZ1JdKauqOsJp0YhhszqVU5t4ETpDOxXyKZaaww5xVemZsmzUYnv2nIl/le+rxbaUKOOw2gbm6xZ7U6mLMcipwk8AT76R2o+dB3Xm5CC/yaeTPU4mg/sI4PYOgNMYx0eaJAECJIkTJsY+FqtTw7JzROJEXPIL73ujjuLKqLApN6Jutot9g0oD2mB8KGj55/Sci7geJo2P2mCXtY0cLuLpMANU4DYzyemUl6QewF/2FsmEdLqIx8KMtFWCO0f2kSLpTVcLPbtrGI8FSSYCjCHhalQvs0rPph/4Cj4ypFNeYX1gNlc0QbkLCbkUsKiw1WmhcLCbdMrHWDog1RjkJE+YDhMmTle0jsLgmNTqWjkwT766qYBCMRbly3M7tgU2s1H5uzbsAn4FxMpyod6v1q8sJc58nGKjTobqFCcU8Kh9iznWq8SWPvJZ1kQ2iAfppj+x0bQJdhMFHSdLdo6JIDNZgDOOWPXey/K/fOwVAAcaaXwkKbTm9AZRUt3o5JhYceCmd2RfcxLotMzC5Qw7yhAQadMFQgvwAAAgAElEQVSsSZ5TsTA5M2xMJgpFmUVHx2UBmp5zkcZnbS9cnCA2FCHVV2Lms2C8LQg5RDCYZ1gMIBSJQ07MwkldLCd6zkUm7cVH2qq19fkz4mWD/OS58qKpY1D5pWYjv6RrgnLoIoePjITVbp1eqgiEkmTSXrNLcfadw1xl7m0n/9z12Ou23qvAyrkeBTIqdxZyfE4dUxm2t06xQBWOK9UUbPByAkjEsU0cn4k4HoG3CRQxZ2H9HoS9qZWYhfdqe2ooljlR3FHrd/49WQxOf4/L//KxV4gMYOAix350kzMBJ4wIAzH2wUeawuAYsWjESuT7/Bniehja/NCYkpbXi7FZj6PQ3etPkzJ9bIoR6rjp1mvwutL4yIjROBi1MoFKyIiUxRjuCUKXxwYX9a3ENKvLb6JHSqZCkTgBV5K0S1o+xXXpS9adriHsi4NPQHo45YWUXy405TVToaqzEDznyJ85xIdsopB4zoWrTAeXCDAAGd0nbBMzT9nnSLIrRqXyY63YnVaGzHVX83YFV9lGFANrxM6j9ZA/74QKLZ3Kq9p2yLE+VQbW53jdaUmpxc61qRBRgZJios6qgyGQ0DSAGHzD5NejjmH3iMMGLsU+lbgy8f8px//9TA7AwV4Rfr6XsZcAnACOG7Fj+MgwRCkVDFiAZAFTzk025ZXGlG1+uRDW+5m++hWq6MWFzlZ9DvFYWEyxfZApk7KuTNoL2IX0Va5e4oTxkpbSLLzE02FL1Ij4Yuy8cxbMk3pS/FhdN8Z7gjYTiGCVJCUTAUqD0opJgZuXDIU+yQvpuouwK85wYqr9+WqEsYUQ0HGGpIqthLBbDeWAnBvIWF1RADIpL15/RtpKtU+xc2BqXYoBKvbU6Nh3VVaVcGxDgYdTWFBgokDYyaAU61KAWDlhHUqFzWH779Q6QxMWp5LptIikHI+K1Vm2jgACckmkVdJuhM2VI+A2jFWf6mSzzueo80t+6KvOx2R29P1o7B0hqocsNXRbTS/TePGRIU6YMqKk8aHjlgQ9SC+4IT+e5j28MXNfej5TytPMZ+NVS1m/5gSiN1eTuaIYI6RhTNc4p+JmyGmW8hj2xQm74myLzgRE3NBxUUpU/kecdMpHLB2BJglHb5t7CusPnouhaRidGsY9GsZLGsYNGsbzGiOf9uKp38N4ykuSANFoGbWuHVS5eonpERKjYZK6CCg7t8wiVD0ofe0ciforT/wSxjqN8as0jKc1jA0axh0axu80pi96xQaWBJDSGDeBXgFbYihCJuUl0TaFzx92rQkk2XwzrZnTW/DNxzD8GsYvNca/r2GkNIx5ml1upbajwEnl2xQznmU+lmFbSJwhtALjmPk8gV0l8XFsW4xijl3kMzK1HVVaBvmCgirjUuBrAZTqCaeZHyw3nw8gk0R73h56K+aqtqEYs3oPjmP7qGX5pI69AuAAetmXiJlRFn+abhl/AySt9kmBUJIpB+6CSJbMYDEV6QGmdg9T+fQIW77WILM2FSMz258JbIWbbv8Si2Y+QmIoQjwWJkKMNF5qS3dYOb80Xmu2dRc5SkuHGOmpgCHQfxNiWLuXMoYYXVbADy+4WHJX9wEnAUuhaHWWzHAx9HgIE6eqtJcBKujVq/C60hwVfEaMv0SYcvAuaoNdou62A52w7jMLWa5dB62gLUImLK4AlgCHwRvfa+Q7F1wiANSOFa4VuHUSsTDxWJiS6gGSiQCe+j08znEQSWG1dVIsMAHGIo2NZyyFlfDAC0u5rORSvrT6Sh75wiKMQvMKNkNvKxRVF3wEu7uuAge1fjUU+HVhh6LXwee3XssvHjubdTcs5PStv4WvY1dbKJBRDK2P/LkgFDtUXkE/MJS1Q/pEFNgB93i42viB3Biu0Vhl3CRlX5Q7upMk7RxkI3bHFMi3jyjQ7sFmnpMBOh+ValnjnzXpzG81TRvQNK3N8dp3NE3bbU4406pp2grH/y7VNK1T07RtmqYtc7x+mKZpW83//UzTtPd0v9NxEyZBBi9h4gRIEiaO12x7qjs6jOg5F4Mb9qNnWiUEIfj0OIwCI3BwbwesgPZPTZOp6ZoQwNsO6285gcpp3dSUdtOdrjFDUh8ucuY2x0jqAcbS0nRzJq/jicQxSjWGv+HnSyXwgradlb4H6KYGvg1UIfOHdSBE4RL4zfwz6B3Zl7TZ/snrSuNGFxFFD9CzuYHBp/eja7SW8U1BWGBw11mfoFbbxEGzgPOAk5HGGKuQ5jQHwPBlfi7vvopfXX6mZbANlcUIhJL4HU0ExnMusrEw23fPgC4/9JjzSnQCXWB8VmOwOcR9d5zAfTUnMIe/MJ9neJXZ/JIvcOt9p2J0a3zrom/kF9nPwp5wR4WbiumocFJZR1rNL9ZkSAueeoyReV7O4A7c6GxjJne0n4tRqfGHx5ZJm/MI0qNOAcrEigmVd1PLELDcY+cty0pJpOoxDtX4yoU3yHeyAm478/O83qrxprEPXAgk9kBlwG70mcCed0LtcyX5DLIJu6X7R8X2kzr+WQzuFqRBzcTxU8MwmsxlLYCmabOR+ccPND/zC03T1Nd+AzJbfYO5vNM63zY0DMoYsjqKgJRvqeS/C2mdpMqsoosKKR8ZhlG4b8kJUATZ+dBXVcyyxj/QQrMkqM9GfpzzgAH4CV9h++8OBFQ+TsA1SSER3sLl0in1RSkjyobdi3m59BB2zyqh5Ha5lZ59MzxR8Ql+MW81e05FOtHPBdYhAHcyLNXWoOfcVj5QgDpDNzVEXDFKmndDBGkEkINrZvwnTdpDNHwKYW0lQAoGzwvB/ZBqAqZDyZoU2SL4XMvtGHG5byRap5DonEIqEcBrmpD9oaQYkVM+uwV6F1ALxhEaGxqOYCtziBBjBp10UccM3uC/+DHncAutNHHddedyEFsxLtM4dPUmO7xVj8rGUokwIKfZVoFRCPg4/GDrlzmNO+l3VbCRhXRSz3oWc/asX8AOOHHDOowCjQWPPZYfcq7HVmJrsaczrMQGm03Q2PECxuWSMkj7vKTKkXmflsFzDQfzym3TaXgZKltGaPvhDEZ8xTz85mL54bWSb052KrtKKXaajYfIz8v9veOjENUa/xSAMwzjz0gG9r2ME4HfmxNA70C4wRGapu0LFBmG8aw5SfT/AP/xXlboISs1qKbIAJihou4ovheVcLhzKv5QCs8OuH3WJzl5zcOMlhbg2QxPsZir+C9Wtd0rIWoOSbs0yHZOn/MAnuV7CPviVjumOGF081eu7BwAtPt5QdvO1PZhuA20lQiQXQkEoagOkrcgoBQF7gaKoPo6yPYU8dLOuei4LMBW661y9XLogZsg5qHklN1cdMCvaFiKXECLYHB1iC3nNTClIwH3gf81YDtwCHg6YEtzgxxTJyaQSGumlDlvbCoWlhwl2O2O2mHRwY/QftI0FnU/z0y2MTe9mYOGO1jyg2dpaOlhecsGVg6v46d3f4NShmiiFUbgxZaF0AmeeXtsw65SFfuww0WlhKZke8yCT557O5defQ31dEqVCDrb2J8mWvkst0EjfHvRpTAfNn5uqQ1iKunvrFNVAKtYYww4BbZuPgIaYfeiEkruTuG/H2FvUZjXsYUD794OI9DRXE2IOEX3wbGRDayLL5Sb33PZfPBUobbfsSjWmmPybCL/5pPOTNb4V+fgLtQ07S9mCLuP+dpUJPBTo8d8bSr5Lir1+jsOTdM+r2lai6ZpLelBKagHiBHBa7I3H2m8pPO8cdNmthN4GeiFVb33QjO4cuP8dunpHM1GDh7oYGfjlPxEdRBYBFwL55XeRM/OWiLBmMzYRdIGNSBOmF69ispjtzPLOBhGgIuQi+b7QA76niiGCyFwNrABmI9ckGlgBC49+DJKqqVaQkLVHJ0jM9j+6IF0p2t4aedcaIHoL6vlMyeb++eGKd0JDhrugAeB6cCosFMAWqGKN8kuge+cdomEVgDuHAX+jC3C5JDyLCUqLID1F5/ARhbCVph6yDBJX4D+kmI4G7Y3V7Km+US0EaBB5iyNEeGxpgWsaT6RX11+Jtn2ony/2kSjrjNczcGSix7iEq7kutXnsvxzG7iJ83iRwxiggvv5D44ZfhbOhGNYL63JZ8GzNzeJkhvBnuC6EWHjCnh6kOOuhudvnsNP5n4RWmFq+zCpFQiTHoWOFaIa9H2qmNsXfZKG7h6mtQ8yvMKP59tw/E2bOOLlDXCexz4OJ0inHM9jjr8/8sFN6vhXAtwNwAzkPvcmcLX5+jvl1d6hJ7T1+jsOwzB+ZRhGs2EYza4p+xAyc27l9KPjppCkyeDGLItIJu2l65wDwA+bVhwKTwPD0B2sZiEbmbpumE3lh1I1MigXTQ3yw9wAg3NDPLJkEb84djVLp60lNhphCOnUKwKDJLZiaSm2f4TlbGMmnI7A+ZUIKxyAygdHBNhWQN/3iyXUWYIwq5NhhXaFKJtmDjHAGHOLn6fkuN1y8H0ejCs1eA0BxyiSc6qDbBE8WrKIPRd74AuwZ4GHaHExqRr5JqZcniBWHOLyzVdx6FmbIKdR4M8wnnMx3FUFKQ8FlaP2/KYJMFIaHddU87mnb6dvRTGPvLyI9SzmZs6BH4CPDKc//QC8Bo81LaCKXvN7cPE6M4kTZsr8XbbSqABOgYIfuy1SNUx7rJ0n1n0CgBq6YQOcwj0s41Fm8AbH8QTaduCbsOTyZ+EQ0P5jnHltWyQH2e5Yt/KnDTm21QbRrYUcfn8bX1lzA7ihfdY0fGmgF7mhAbwGa1lBhLfkBnURlDyY4snVR8Ii2HzVYtnOcdiiiQKzBPmTXatc32SEjR+FqNb4lwGcYRj9hmHohmGMA78GjjD/1YNAhxrVyM+qh/zuYur1dx0aBj4yZBC/mgK0CDEL5ACpWFgNT9YcKUbgIFAODTf20LC2B9xwkC4zp/MaGKWIO6AO4oTYn23sfqKENXyao4LPEGMfwsTxkaHUzAGGfXHGU14O/kEHZ111F8kB8yjWIcxhP+BFYCvgh4CelBDYLdsxyuHQIESCMdN+4iZGhM0jRxBwJan1dUmzypXyfvxIeFslS1dxNQfwKkX9WeiGba6ZMqNY0C8X2EnC8iiHF5ctBH+W8SG5ogtCSfyVw1J1UWlAD5Qs3w1pKGWI3fNLqGwfYXnvBj7V+hDNtEAQeqmCWyC6EmbzKod3t5HBxw5qyeHiLSIMtE6zlcQQcvHXY7M3BUY98Hs+DW7wkpaUQwMUkmRfeqllB98d/Q5cC+2rpsGj8FDNEvCnubbx8xj7awKUtdjhbgv5ZWW/hJL2lEwYvQ5GP1XAoyxDa5Lfg7EIakZ7uGHlWZyWvpMyohLmfwoohSW9z9LRID9V40FNxI0IcnxDju04C/4xn09Wu6RJKtXSNK1G07SnNE17TdO0VzRNu8h8vUTTtMc0TeswH/dxfGZSRcIPMv5lAGfm1NQ4CTsgehD4tKZpPk3T6pDL+3nDMN4E4pqmzTNPzGeBB97LtlwOLi5VDAky+IgRIYMXHRcBktwx9dM80riIUoYE4EaArbD7CyUSxrVAUW+WZ4qPgAbQdsGTS49kTfOJTF/bx1YOopN6dmgp1u1cYYWmXkTpVFUMS6etZXR1AayEwKeQC3gudqi7CPglbFnSQNETWWFufmAXaN+DwNfgVs6yjslLmrLiKLHRCHHCGN8ugC8goLYU4chp2HOAh5rRHqZ1DJINAqdDOf2UpaOULE6R3RdGDyiADfBAndg8SHnwVw/j8WdMocGN9MXToAeiz1Wzc8kUvsZ/M7V9mD0NHgw/7Jnj4TBaYAMc3toGS6D0dJjaMky2CBp6eziFe/GR4SC2yjEqU7Mz8W6qpwXVo/L6hVm2MgdukiqUVW338sKfGqlPv8HHu59kNq/i74A9t3i4nvOJtsh3/vGpf5Q0xTcxa3TtdSsFmBb5Lt48N8KmWYfCanjh5kaCu8Zlm6dD+4ppvFXiZ1uwgRq6ud93EvO+uYXRMwvYcN4RwvoHoOH2Hk752m3wBTBWmddxNcKkndUqKiRXpuvJmnRm8kLUHLDaMIwDEDntAlMI/DrwhGEYDcAT5t//EJHwg4x/lk1kDfAsMFPTtB5N084FrjLR/C/AMcCXAQzDeAW4C3gVKZC6wDAM9VV8EbgJ+Um+ATz8nrZvzsmgRsAMT5U/zYWOlzSn73iAOWzFbaqtw6f7YboIEp4ngWIYrAlRRS/sgcGmELN5ldv4LE+uOBKACG9x2Hw4YdofqaDfqmJQooYbnS/xM4JXjwugNQA+5Ae+C5n9cTvQBgdf2yE/rwbEPqAEjQZY0vIsXtJk8LIPMaroZd9gr1heeoEOSK2UR5qBEoi7wnQFpzHc4Ke3eAqpEqgYHcSbGocRwa1gxzgiErfwwAVL+dbMb5AxJ+BR5VqipJrr9cG0jkHO5mboh7TLR29JCUXPZXHrum112WGe/D3gGQVaYRv7cx43sZm53FpzKg1f2GKHTurCN03A44kA5KB6Whdnj9wOu6AG6aN3+Jlt3OE7A26C0298AFrhTtdp/PzUSyidB8u/t4HTuJOzuRnjl3Dk6idlvadk8ys9muA3j51B5fUjLPjmSzAHmofboBe54Q0IG40RoYs63qCeG/kC3ALelMy9y1zk3NTAYbwo39f9CIvrI3+OBnWMqhFBiA9dNxHDMN40DOMl83kcSXxMRcTAW8233Yot+E26SPhBxj9LRT3dMIx9DcPwGIZRbRjGbwzDONMwjDmGYRxkGMZKk6Gp93/fMIwZhmHMNAzjYcfrLYZhNJr/u9A8Ue95TCy0VzksnwlCPAdTO4aJEGNqxzAlO1JkawQE8AE56KKWKKUM/jjERhai4+Ik7udxjuMonsGNTvZPcC0XkcaHG50khZa5uJAkH299Un5c2xHT8DAS6qaRsDKIAN4AcoGMIPfOUeBY8//nwD7EmM2reMmQw0WYuFRrLAUOAP8G+dzwBX4eq1rADmrpp4IXaaaLOglLgbGQB5aCloPRhgIYgbAep5sarrj9h4zHgug5l91tGMCf5YqDvwr3w7UNn6ebGtoXTSODlyFK2TT/UIp+mZVjeM08hjnALNhdVcIrK6bzBvU8xWJiRIgR4Tnm2azNWQQPUpc7BGl8eO4HymH63X1iexmFeziFJ797JN5TRjjj7N9wPyfBc5BshZ7LYYxCps0b5HslX2Mx64UttXnsetVGYJMw2jUXnEj0SiAK2oNyvh9kJX+5RTyTXWb7q5lsYy6bMVKwtngpEWKMziuQ7ycIn+V/YAHwCaS6Yh62MKWYqmJvqgTN2T/z7x3vD+DKlBhnLp//a6vVNK0WOAS5ZVWoa9Z8LDffNiki4WSNf7WK+k8Z0vAyZ6qmGatkCyR8EX9cGp4EemHq/cPyFQXB0wr+NUADGKfD4evaqKGbsuEEJ3c/zNTuYT63+HbGKCRJIZ3Uc0vxKhoqeuinnLccFnzVmYOrgArINgHXIhfXCOJ724MAmQK5NUjI6kOC9ygCigfIOl9lNr1UWXW2mbQXToaOumo5hhEo6U3JPhMlQJIZdFLDLjL4iAZLKIpmSV0GfeXFstIgFL2cpZ5OuExm2lJdhC2rSM7Nt66/mqu+fyGncSdHs5EhSvkzCykjSpg4D12wRJThleYJqBFwKx0dZv+R7TTxMgexlTO4g23MlJtMD/kT5KhyrhRQD5/hd+w+u4Qn7zuS0ZUFDFaF4FNwNjez5PBnyXy9mJ9q5/ITvsLOXVMILIGSIJw5ejs7n5vC4xzH+doVdhMAhy/t4pd/SB1dnL7/AyRy5nywZv4vwlsctAKOX7eJGrrpp5wTFq7nx2d8G+0AOLFlHTEiDPlEWHqleTpTNwxTW/MaD61egrFVk9hDVUooEUVVWii1eLLmZHjvNpEhJcaZy6/eaZWapoWAe4GLDcPY8ze2Piki4WSNvQTg5Nw62ZuaQjBtwl45A8I0QMCjBgGaYuBYyJZDMlgAbpg6MEzahzSV6AWWwGLWE2CMhfxZGMJ+om6WETUNxXK7TOOV7TSBZy1iEbkf+cEvQcBMDZOdkEaU1DrYOX+KsKKUsJkZvEGEt9hFDRl8lPv64XXJcal76itV0+mmBh0XabxM7+hjem8fkdERSkeHSQXBPwKVO0YIDoxbDGoHtbBSZgqLBGMEQmMCdDmTXjXBx1hLJzN4kE+wYMNLNPMiccL8gZN4HanF5ZfmeVokjQG6g9X8ofjjHLyhg25qqKGbY3iKR1lmG3HLDPvR7CZSfXAHndSTxksvVQS3jhMeTUCpiBfsCx2/rqaiSoD/Tk4DNwSq4M7gqfyYr5KkkPVgdylRSf9W+Om13+DA9u1QB9N2DEp4vQAYgZeeWCCK9JXC4ioQmw6m+vxA81JJXQC7a0ropYq+RcV8ggc5Wt8o3+MsZB4KZ5smBXbrkTB2ssYk2kQ0TfMg4PY7wzDuM1/uV3l089E8IZMvEn6QsVcAnItx6WlmGm3dZu4NJLcSIcaAiQbti6bx2KwFAjp3Q0dTNS/UNeIZgOAT4/AysA4yfg/GdOBBKXOqp5MpOxLsM5wSe4Q5b7QyFmfwWaZcrkGY2B7gJNjwpyPgVOAHiD1ER5hDEMm77cISGgKMCXB1ODqg4EbHTQX9LONRjAXClPpOKmb4JD81ejfH924iQoz5wy+xoeEIskGIBYtx5RD7QzeSIL8MHpq1hOEmP8t4FFZJFxHVwy6ZCMj0hcCW+Q3ECbOVOaJQPwlJCpnVsZPLb7+KM7kN/ojcJJqBVgGeCDGaaOXXi1ZRQzcN3T3UqskYrMJ984af0Kxw7sv8lJls4xnmU0M3X22+An8bcJswcfaHhoEentx9JP2Ucwzrab9vGte9fi5n3XIXh9BKBQOcVowwOFXHaqqq9110gtT/3gZb6hrYVH4oHbOqoQV6ji1l4TfWQbscw82cA37YcmUDL1zXKL+jdExK8ghwfPcmAnqSn/dewtGuP5PdBNyOhKqQPxerH7GSzGNyQtRJrEU1Bb3fAK8ZhvETx78eBEvpOgtb8Jt0kfCDjL0C4ArMzK2yieTMdH/OnCtVxy2h5CjMGtgpd+IosAq2MoenWCzgk0PuUznodtWgtcrfUcrE0zYKb5X4yeCFeXaeT4kYqlQs24T8qJsANyx6+nm5sBYhoKZEBx0RF1IIm5srAEIp8DEFbAI8dexgiDKqeBOtQ4C1mxpKWlN4U1l2V5WQJICWgkUXPo9bl3V52kAblW0+tGoJXCDespKBFDpu+pqLScTCjKUD5mxeadLmNImqp94K1nIcj8PNcPBNHbADXljVSCtN8GkwrkTyb5thIwuZsjnBZuZyAK9y4MB2RssL6GQGz3AUVJoNNCtT+TmqBCQJ0E8FtezAR5pP8Ecx4p4JB351O3wNdlTAkpXP8sULb6WKXrqoZStzSF4Ix/I4Oi76R7DBzY3VjeQ4/XEJI0fFQjST1+X8rhTmvelPx8N9whabaYGvw4/5L2anX6WWHQR7x61651QJtLiaoR3q6aSruJo/zFxmt4FSuUWVb1R/f/gqGeYjbSWWTKgb/xFwvKZpHcDx5t//EJHwg4y9AuDUUKxNWTYUq7LalruBXqhNd8F+sKnqUFpoZi7PwyXAn4ELYfhsv4S7LuAiqB/u4eTuh6FFQLSJVijBrJaQigm3aRLxkuZrxT+AWZBqRJjiLcgPfBcCrFGsAn+rnGcUUlXCOI0qGPxxiBgRkhRa7dgBVvAnKBa1r4pe6IVtwQZc6DS09fBCVSOcLOH268wUNvgaUC7729dcLJUOacyc4gwwC+0BvGYn4QK3zhgBuqlh2sAgB161HU6G3553Oj9cejFxwnRRy63Np6KlkDZpm2AhG3lo7hLm8Bfq6OKB8qUEW8apo4sv81Pru7KmbHQU3afxMpfNvMZsauniDWbwlVtu4PylV0si/zV4zjhRrCBPwI+4hAdZySncg8cN0wYG+Tbfo7rO8aNQnUVyUHRllj29cq7HCDClNyEAl5ObGOvlO9pmmpOLF/RxW/fn6feVUzfcJ37A0WECepJtwQZ0XIzOL+DbfI8MXk68fp0Eas4+d+r7VTm4yWqXNEkhqmEYmwzD0Ewx0KobNwwjahjGsYZhNJiPw47P/ENEwr9n7BUApzlymapmMUDSmulKx80+xEitB/wQXDsOx8KCM17iBydfwaI1z2OUw84fT4F+CIymmDGyk92LShhsDPHnkiPABd8++1I6mcFK/UFYAaVEKTS9cIo1AqLwnYGomLch4Vsx+Z1n90VyNk2AD0abC/CfI055bQ7MZxOlDKHaoUeIkaSQg3d0gA9m0Mlm5pKdD2VEqbx7BIKiElIHQ75SlrdtYHS/AmGM3XD8hk10UctQSYjBmhA1dLPgxpeYNu0Nqip6cbl1MimvNXfFPZxCIUkeK18ADXDVNRdyxugaLv3cNSxpe5bPtdzOWe13Yfgh2wCfeOIuFrU9Tw3dvEgzUz82zIkd6+iYX20qwIWQ8FB9YAepREBar4fMyXMi8DozeYajWMx6tjGTw2hh99klXD+8Whj23VBHF4/MXQRXw0r+yC/aVlOhbcLzMlxXfi6vMZvNO7BVzGpZLl1zGXsu8VD0IOxsnMKsgZ3cWnUq+49sp6+umDmjbXT9dznadAMdFzc+eDF9ObFyZvChvQaY4f6jrmXMHO2QuXjd0pLrKY7hLxea36kqF1NmXyV0wOR29P2okmHvADgDzdHsUkQF5zwMPtLkcPGt4BWQgD0rPZL+VD+8QyBe7GEfPcbO5inEgsV4/giRdIxfcD7N6RbYA1X0kiDMo65l4JfqBh03XlPQUB1MdFwwCiX3pyTvUoOtFLoRBjeA5MVMH1za5xXx4wAwUtA9UmOF2Tlc9FIljvpW6Ksrxo3OyZsfxtMq+0mDKKtjBGAApn1zEKIQGB2XvnA52Z4LnSilbGUOJWtT8CcpL8uZUx6mUz5resM4YcYIECZOx0nVHMRW/B2I+OIDhmFPgwctCi8WH8wp3Ab2gWEAACAASURBVMOTjUea5XE6XAOPNCyilSYeZZm0iYqkmMtmCtw6FaX90rnEb0AO/sxCi7nVsIuDWzvYxky057CsGfNu3MLyDRtgrcyDy5VQH4Q1dSfiIsfP+L8cWozNnMyi/h9svoKi1VkoMQWGEQnVo8XFVA6M4B+FN6iHR+BlmuDP4MrJcc5at9Pa/o6SSqk+DvpJ4+MtV4QEYeKEOaDYPM+15u9K+eGGsIHuQ+aD+3cfewXAgeTDAoyZM9y7CTBm5a8ixAiTkBzQKPS6qsgehjCrZimPKmrJUvRElmn3D1LZNsLgqhDBDeNc3nsVAJtmHcp5I7dSQ7coeiWy3TKG8JImjY9Cxqz61GNf+KOkY0cQH5zP3N4mhLWNAovAmAPtVdMouT4lQLgDLohezeziVwFhD26TkSqgqVw7Qif1bJnbAL3Q6ZsBflFWZ7XvlDKwk4AO0FIwPMsvoHqXMD8dF3PTm6VsbLPM9DWWDjA2WojPL97BcETaNCmRpnbEYXG6VsLp7Fy42XUO7Q3TcKFzVvdddFFLw0APK1gLaVjesYFl+qPsSy8ff/pJSPj508gKxlNeenbXyGQ7/jSexj30bZnOMxxFiDgv0gzl0Ky3SNOAzcjjUmS/T4ZVFfdy/m1X81ziSNbyMR5lGeX04zkJuzQrhNxkWuSzHc3VPFS3hJ0NU+iilm5qGC7382T5kTTxMhd+8yqOZiMsgTuKT4WLYffSErJ18l12UcdsXuVFmnGR4w3qKWSMGrrx/BgJhzuxm3yq6g1lap6MoO2jhpfW2GsADoSpKT9cgCRe0xeXNw4QM69nGKlTLBfhgFZ4Zel0mCslTzEiclG0Q7+vHDc6YyEPXjKUM8C15Z+nji56qRLWBFZ7o/5oBa36IWTvh46bEOV0P9kWlyHMrRkISq5s1vd2gg82nXcoHUuruWH3+QxQAdhVGRFi9FLFq8yGHFTQTwUD7DnVw218lu2zKumrKmZwVgiWwc7mKWw671DYACU3pcguAkIiTsQJ87jvOGGxp8ukOmqiGcCcPcxLFb3M4A1u4jxuKV4lQs0wcDL4d4CnW7q33MMplghTRS8Mw5S1CelkUg5F27OcMvKAlW9LxcIU+DOEInFcbp0Cty7z0uYgSinPM5dtzOTWqlO5yXUeL8xqhEbYc56H3XUlHFX3BAuXrGNN/4lsY3/u4AyW8ShjBPgt/4cbbj7LVjFVN48S4JtSU6ssNRFiRCmlmxpcSM6xlUOsOuWT9PuhTlTVjL8AiuV5Gi9z2EoFA6YxuJY5/IXRMwsE1JrkOK0W62aDUSUkf+DxEYOzxl4BcOMUmDYRSfoXkrSAzWe1S8qh4+K88p9Lh4rXkB99qeTciMJbRNheVcl/u74qPrOlgE9Cl3m9W+h1VdFLFV3UcjPnEDJVRlXrCiISLCt9FIAfxy6m4Up45dfT2dPsEWBbC30XFEsHi7ppEkJOB4pFBGi4ugd/KEk8HUbHZR2HEhVu40xeWCm2ha3M4R7XKcygk+kX91F5/whTnk5ATsqrdNzCXu6G7uJKOEnCs3ltW6S9+wB0XFNNpFg6+6rJsFXJVoQYDQM9lNPPEGU8wXHcsOQsqcZ4VI4lQoxvbbiaVZfcC1fD8h0bJIQdBS4Cz++BNHyr+Dv8v7mrTZBz4/Wnre15/WkRHUKS15zNq1TQz2eH7+IrN90gFSnfh6Kbs+ygltm8ysbbl/JHVvJg+kRq6WIrcwgTZ9olg5y/+Zb8uRn8kF0ByQ4o6U4RpYxWDsFLmsWjG3iRZnrZFy8ZNr14PHHCZJug6LospCWvGXxtnFQ5LONRfGQI6Em6qSFJwAJLwK59VS3Ue7CBJsHkXZEfARywlwAcYFk1VD4sY048k8ZnzbTlJWN5nFKLkM6tOWEjxn/CgtaX2MxcjmYjV1VdyP9rXs3d8z/O8W2bYA/MatlJDbuoohcfafMiyRAiLsl9BOC6qSHsiosRtRhq9G76XRUCDKdLd1jqYNbmnWh3y/4bx8Lh17ehHWdQUTxAqS9qdporRDfLtHRcDFFGJzOY2j5MGi/7s40vfuxWmAuppUiuaA3QAYt6n2ewLsTuR0uk7KkOnqs7WJRkdsBrME9/jgBjRHwxMikvaVNkALhIv5bflp/OH1lJ9P+3d+7xcdVl/n9/cyZzMpMZMs2kTQgNDb1YhCK3aisCRagirKDiFX8qu8qCq+7i/mBdr4u4XlaFXXXFC1Z/i6CIq4uii6AFwXIrFixQCqUXCilpkmbaiTOZW2Zyfn883+eck9gq0Grb5DyvV16ZnDlzzvmeyXzmuXyez0OW1SyRosfhwBA89qG5XHLzNWxcNpv/+fxZPP2tmT6p9u43n8Bv718EW+CxRXP5/D2f5BPXXgmpCqmuYWp2vmwhn6ZRj0k/bMyjQIrVLKGfbt7Vfg3fufB8KawMiYebo0O869vg+x98D1e772MJq+2dKkta4InQP4btlCinmkkeAQM9bRzH75jFIK/tu4OVrafzI97EkyzkQU6ETQJo69sW6D8WLjXuOu5lvKR1LQvO3cZqlnCvc5JVcs7Ty1ZuZzlXupcFKr6z5T6QQWQmbCFln1gkeOnbtAG4RqiKqQUH0YSTr7EwAN7IW2kZRXJVO4F2pHOhDX86l8x5KJAlx28XLWLLkV1sXDybzuoQ/8QXOZR+uumnTMKeX85dxfXDyr5GD7+9eBGJ4piEPXVElyGF0EduARzwzhblEu98YfPPYxMdDPukZQ1RHRrkyfASHuXnR55OBzlWcaoQi+dCyy3gHY6wmoaAdRJCHrZxJ7gStmqVtXtkB7nPQ344Q74hn7xEaxm3RUYUJlNldt59GAlKvJ3vsZVeHhp5Gb/hVOHzjcLRK7bAB+EzfJTfcRxzbtnBr3pOhiOgSJrjRkRAJktOaDiLgWKgHxSLNUimSn7eD+Chu04mQ544NRayQV47BP9+9t/xJAt9IjFnyvu2nqN4lGO4mXO4buNFfOHxDwTT7EP9rvGK9M320UOMBk+ykI09s+1cjQaX3/EF/obvwHx8GSz65BhpCvTyFBs3vwSWiohAlhx99Ph9toN0spolUmDQQTaqXGwFBciz71q1IsFLYJoAnMGzMOD4NJE4NRrEfB6cL3pJnCw5vBjSaeBApQ0KrSm2HNHFyTc8xEI28AZuIkuO0zfex0vXrWPuEwM8yjH0uT2s4hTKJCfk+BqWVOxQp59uepGRf3/F/9K8AtZwIlyN0EW+iuT3tgBnCxH3sePm4nojbHu2h/UcRYoCVeLEqVElTtl6C32NHo7auYUcHSx94mEc6ty94AQpZmwE0w9berp8TypDXlrB7D/73I0DDCxoo3kUsjfINsdp2FGLVeJuzaemkBF+2N+tk+LKq9p+QY4sZ7/hx6KN1gdjv4PbWc7xrIUYXM37+Pdz/47jWEutpYmxjwrIPn33TD/pXa24PhVFPcZ4S5XmTAFahN92J6cBIjh55pKfUMUlS47lrKSOw9nv+DGcDYt5kA0slHV+E/75I/8pOS8NTzPyO9/aBovxpe3zZLiXkyiQFjB7HAY+MpeLTvwyy9Y8IBp3AG8QXlxHNQdPGFgK263iyEncC0j6oESC0/h1IK45TDDlS7XuFHD31qIcnG/TAuDUNBeWZdhSOBzyZGyjU5BXSlJiafudfP3iC3jiwjnkW9uYOSTs+/vPP5aeah9H9j/NO77wY6neVWD0iCYaOLyb79BDHzKWMOZz1TQH41JjHpsok0SHxhx66WbOH/0B53zph9x/9rFs/Opsnv1WOwPXtXF99xt5Uc9aXjL4CI26Q3uXDK3po8fvh1S6yHqOotvpZ377OpazkruPPIH3Nr7J4tGHGFsCGz86G/qho5GDHhi7GGbeUYQ22PmGFjpHd3D/gmNF++xvwbzII269J70/2r3gOPL33/90Bd9a9A7+o/+juFS55fI3soTV3LpsGU9cMYehtnZ+y0uFMHwEvJUbOZEHqRKnEXN4sm0uPdU+eq8eghZoyoxK72s2T6mYJN1WnFDgoMNjYPVcjmMt89jEclZyEvfiUGctx/EV/oHjWUsvW7li8Ye4idezkuXcfsY5mFd6olSm5F5V0E1B11Uj8Ax+eHoMj1KyAgrd9MNGWPW5E7nm2ksYWwCPcxQMgjcX7uUk7nVPkiLB49LZkaDEKk5lM/P8dMWprAoa7MOKvjp3Yil+i99e2Tj7TPDyYLdpAXAGj4TlXtVxKJP0+0I13AHp89RuhyouK7iQ1SzBocFoWxPdbKeOI5ppILSNHtixOEWf28PVvN9PKIunWPePJR0H6s0FX9U14tQaLtWKy8qRM3jlyB0sbdzPK7iHV/ErPs6n2fjsQpKpkng1FliUT6fnUQoMQL6R4bCrdrKdbg55fIzvt57PUFs7vSPb2PHqFIc8PoZ3DFIpXgTcL3STlqfEG/HVVjJjfkFB9ey0t1afpwirWcIT3XOYx2aeuGIOeTKcNnoXR978NIddvpMbeSs99PHVBe+hkyFcqsxZt4MNzkJSFCi4aZrfJgIV47ZrojxqQ/uGgxOrk0yVJVQtCtX/Fs5mFacSp8Y8NhOjwSwGWc5KCqSZzyZ62cqprOJdfJe7bn+Z5Lq2EoztU2pGEckbnivvzXqOIk2BAmmWc7v8f7wCTl73EN++4O3Er/So4sIyMPdLJftVG+8WgGqVNMZCnqSbfs5gJZuYz6McIxXuTQRKvsNMHJUI+05fIwpRATB/gW6J/W4zFx/uvW7NhyzNVsK6JCWfB1ci6W/PWZ6atEElqRKnhz7+ilv4x51fZ7BdiJ87ZqXIkWUT87iRt7GZeSRCOTHNi6licNwC0iCdZNhFg5jIG1lljLQNOWu4lBDOmRMTiXMQkNSKb4a8yDuFbJBOSiRxqJPLdZDOFMj9v9mS17oLBi5po3PnCI+0L+DYvo2MzmrCqY9Tam0hT4YMeW7jTFxqnMavyf64DEsrtHXkJUR0qiQp2xCuTq3hsnPbLMg3Q2aMs+b8jJ+OvJGPt32SJCXOYCUn3/MQ9MOtb17GKdVV/M49DpcaeTI2b7WVrhUjmCM8+BE0fXKUTId4ulLQcHFidR9kS8WkCF/qwJsUrD32ReTo4CjW0/XUiPD5WuDriy5gM/N5H1fzGm5l4xXHijJIB/AjxJPTvtCWMS6Ys4Krqx9g2M2ylSPopp81nEiaApfwFTY/tYi7jziBBjFOe2w1y46+lTs/exacCzsXtbCKU/ka7+O2q17Ppy+9lPdxNQ+y2B8s/jE+zYNnnoKZ6wUCl3mEJqITvWLAjYvxhtbsVcOWMYs9yXE8p70f9Dxv8d6c70C2aeHBqUkvaABudRz5Jgbfw9NhNEpidakxRCff5V18pv1SVnEKT8yaw22cyY28lds4kyd50QTPTz0pNe2aUN05maUQ5AOzVg/IpUYng/TwDJnWPAm35HudSRswxUPApvJPKnYp/L4y6UyBnVu7ufbCtzD64iYeu2QuXb8cwTwuPZY39LyOFe6FfL/1fDYzn7l3DABw/j0/5TR+Tft5FZpOHqW9K+efK/B4d/ke6Mw525l57DOwrpk38SM2t80hQ55hsmynm9++YhGsEdml9a54Res5yn5xuHQNjfD2C78tH/APwPg2mf2g82lBOHEgPbCZjjxNqRKkxvzJ8ac3fs0pI/cxyCyoSqHk54tOZ4hO+ulm3j3b2fj0UQIkW5HQ9DTkGBmgZQwqzVy7+b0AzPnyDkD4dkraLpDm/iOO9fuK+Sq8gZukIv2MFCbms0luVApWspwcHcSp0U0/K1nud5n4E7wU5Cbn3v7sUwqml00bgFMOnHo+WgnV5L9rfzTXpCCngJInwze5GIcGn+Jf+BFvZCXLeYAlFtSKxGjQwbAf4tVsmUE9NcAOag4URgA6GSJLzvaTJv3za+5Ow880hQlTwBTgYgRqJWH76w030nrpOEf3bxGScjcsvelhzl/7Uy654xreffMNvPSedTx8+gLSIxXueMXLaT+jAufie21KCdFjh3NwSUrsWH04VOA9D3+fD/M5TuE3nMoq0hTYSi/eCgn71nAi2+mmhz428CKWXf8Ad816GTdc+26YD6neHbBOuiYaDWkLc1uqtHXlSLSWaVg1YSfWoDlVhpgHR3rsvPUwFrQ9zna6oSj8vuNZyze4mBuefqeA593NEhL2AgOw7IxboWh1ifLNErrebYTcfIsQvfvpppMh5vYPsOPGw1nJctZyHEufeBg64O18Xwoplp/4FL0islAXbqUA5DPkyfAox1DFZexJgpYs1YQrEgBcjAjg9rHtq7rNAW0GkbHRhndtawIpPOiU1HDV0/F9vDp5MmQt+P2a07iXk3Bo+MWEHqvQrDw0nTovRQ0J6+LUqBEnRYGiHQYtgDVEnowfLmfJUSZhnytNOJ6AZFCVDVeEhYgqHlzJSdA17ylyuQ7iV4xQa7SRoMRjR8ylt3srN7pv5TR+TZoibqPK/Opm7mw7mVNG7+bnt5/OOffczpzsE+SrGTJu3p+92iDGEJ0BzSXXI/JGLc0wDLeNnMlRbY+znJWc3n+fUGxukfkO3+BijmctWXKs4hR+/o7TuY53Sd4q5lEc6KDtbQMk3BLlatJv6gfJwwGkXels2Lm1m+ZMgbHhQ2A2PP3gkZy16U7xiDYDCiThToFh/Ab3u54+ww6Z9qBuBPg2Cb2D1l/6xODz+n7hHydDnhezHnO7xxv/9XqZPGYHcl/+iiv4HB8Wz/Z/4LbY63n24nYu5wqquGxiPl/kn4hf5sm5uggqqFpF1aJDBHD71P5SQ2e+Y4wZMsasC227MaQvtdUYs9Zu7zXGlEPPfSP0mhc0dqyZOofSTwc5HOpSwZvUbA/CzarZITSATyNRLypBmQdZzDw2+eqtSrAFO92KYUSKKe6DkhsCTZ2Pql6Y5vy0equglabALpurKhB0LQyTJWGVUEC4fNrUDyJxlKRMcTSNE5NzvHPWNUIhoYfWjeOcwUqG6CRHlpKTpOCmmccm+lu7eN3gzZAJuIJyfwJQ1XUmKZHNDtOcKtM8+/fQAZWV7XzusU9xE6/n7u4TuHvRCVy/5I300cOFrGDpPQ+zmXlCPuYb/PD2C0QxpKVKU6rEyHCGocFOMm6eTKvk/rJujqRTIuGWqONQKiZomy2kaVrGoKMi+av5TJx1mkJAxFZJfQ22DOK1tSCimqkKZDwh+5LEWwHLbnqAJCW+3HMRjy2Y69+HMkkWvf+3/OjydwZUHhcu40rmXjbAf/CPXHv7W+AQOKx/J2dyG9etvYjj+R3n3fULURKpENBUdKq9at1ufS7/zc/FojKq2l+kyGCMORX5jvqu53mLdvP8VcCI53mfsoMtfr6H/R5ARL7vR2iwXwnrTe3JuhZ3e+etuYwcWbrp94sNDg1KJP3kvX6oGziUSPjhqnp+KvmdpIxrG+iVeiI8rGEaxHzRwwJpEpSoWXJvlhyDSN9qHcfPxRVIW55ZzQcz9QABHygD/p6cs45DjAbDZP2qahUZh5ivZoIBMUBx00zajhzgi+4/cQ4/YwUX0skgZ7CSJ1nI3/AdBu6aS9ORo4xX4rRkCtKiRdn3eEskbc/rof790PMUBzqkwrkOAZJtwGJoX/4spWKCytr2YFzfIgLmfgWaZ/+edEY86rhTte+BeLj5RkbCVetd56pZqpU4tYor81ljDchbcrCGf2GhTI1RigQ9n0Vo6h1lvO4ExOIizD3xMR6pvoTWT43z2Gfm0lvdylL3fj7Hh7mTV3LlXZ/ghmWv49zqz2jEHB5xjqFMkletvhtvAWxqn80aTqSb7SQp8dL+dZzd/WMu40pKJDjnntvl2lSaXOkhqibSBXxjMV7f3hYZjvekwfm5WNuULjL8RUJUz/N+Y4HrD8x6YW9BJhLs0cJjx+zfOnbsOaiCGt8DquJa70lyYo6FLyXLBgBS9vNmypOTLoSy/2GrW4pGgvKEvlMFGgEm1/cIk5R8b6hu91OaSsGOW3Js72LYw9QKrxYp9HgCyFV/cHXY0m6BquvKEBqgfdGz7Nw2i4uGr4MYvOXYa9lKLzdzLlvpZeAxATcFGgjl2yzYqrimkKPL5MkQdyX0Fi+swXilNfCk1sHO4cOCSVLaaK5/1yE1fwfxlpovqJnJNsiwi1yjg4bjEHdULDQA/FisQSPWwEnJusdaXAk1w/NUBxDAyIzBcHNAC7E9qE6swXi+ldTsHRSHM8xeuJUtDx7NihMv5JL3X8PRH9vCtz7zDh4dehlcCN+8+b3csezlvH3zTQzNO4QGDiff9RBblnXx2JK5ft/pZuazhNV0Vod4truds7mF0//rPsyIJ8UNvS7tXAABXlUY3id6cMr0jexAyMGdAgx6nrcxtO0IY8zvkF6Cj3uet4q9GDtm8ChZ3TIIJmlNHggdhKaOX70Mm4ayk1+njfR5S2b6A4US8HXb9PggCrXajK0AmmEXZVtldKj7MutxW30tkaSTQXaRsYooNZ96oZw4lWEHcFwZsNM32MOCOevJz5mBQ52bcm9gbOCQoIqX8qSw4AYKx+qFar9rkrJf0RWPNyG/3QR0wMimLlmsVgiPtMcOD1m2wMeRCPiEzInVybCLoWonWTcX6heWMlCtGqdRd0i0lqnXHZKpMrVKnLGWuHhiCqyqlKv/3bpN5YFaYGz4EJoyoxQ3zaSpa5RtVy2AI2EJq2EItn0Wej7ThymMs/3mGfyg+jZah8bpmvcUK7iQ9zeuhqcguaxMmqJfGV7MGnJ0sNU9ggaOHG8FcBbwA8R7XerBWkt1CU/22ld6cH4zamQHAsCdj7R/q20HDvc8L2eMORH4iTHmaJ7n2DE73/EigNThM1jIBl8GR4ixpQkAlrA0jAYx8Uxsnim8TxhsyiQngKKGlilb7dRtYd25HB0TPZHQY/UCizasVfqKct7Ue3Sok6KAkm41bA43okHBl1PqIMcgnWQ7c3QyRAc5hskSyzYoZQrUKnESrWUKIym627aTq2ZJuHV73TG62W7XHvepMEGVWK5RwbRltqhWV4ZniEelqhmnSTK/KTPK+EArTaeNAjBeiZNtzZGvZujMDhKnxvbRbua1biZHFuX8ifeYpObGwYVSIylenJ3VmsoUBCMqLsTqUI/RvKhAo+4wXndo7hBPT6uwjbpDOlNgZG0XXUu2MDTYSdelWxj48lxe/r21/Pj/nM15t/2C2XfdRe24Jv6Ld/C3/3I93j/DF/kQN/JWPvL5L8FO6PryCA9fsoCX9q0Ddx0Ds9qoEvd5hR+4/NuYv/cEXE8bk5D6iRYJz2cjQLwVAeAONLDYS4sATm2/0kSMMTHgPOBG3WYnYufs4weRutiLeJ5jxzzPu0ZnPSZnJlnOSrLk/B5UBSYNGcs22xRO8gsB2KVMkmKYwQ8hQNFqackvRsRsaJqmEMqdVX1w1fOGm+SlhJG0PL2yTwnRD7cWIGI0fE9Rr2MGeZ8mEoxGlN9CVH6GTgbZwEL66CHX6KDUSBJ3qqRaC9SqcTJteamKWlOvtEzCBzfJixVRyfc4VZ9/l3BLuC01OzPVeie99idWh1RFZI96dzJeicvjTIFCI03CLVFqCNk625qjn27bop73Cde6pgyiagL4uTiApljDBzdidcaKCeItVVKZAmP5NGPDhzBedxgrJhgfbmVkOEPz/N8zNNiJE2sw8Gw3vEau93KuYMerU3jnQfNG+Nt7rueYzz/APe0nkKYgcy9ejVRrs3DsDRvxWuHhWQvoGhqhTJIruYyFbMC8uwZLx6QIMtAMm1qCPCUEsk3qxe2TlLhHVGQQ298e3HLgCc/z/NDTGDMT2Ol5XsMYMxcZO7bF87ydxpiCMWYp0gH6LuA/n8tJPOB7vB0IqpdV4ja3VvKLBSDhowCTO6FCGva81KvTSqY/Ud6+Xhu2Y7YoAPjHK9keVG2UDxcV4panp10LCcoUSPk5NgWxhP27l63UiPudARraitcTVFU1D6iV34yT94saAFXbLUFWBCnzzPDD0H66yTLsy4y7FtQaOMyw65e1C+g0p8riO3TYf61UXbYNH0Kl4tKcKTBzznYBVTdvizw1cIIvjQy7/OtzEG6hhuRV4mRa8wLQQDJVplRMkM4UqFbiNOoxOrODbHu6l0oxSSpToKVjF416TEQzi82QGqMlVaJSTELFZbylKiGuDWHX3fNSZsUKFPsdWj82Dg7c9YpTATiax/grbuH3x3+fQ64eg41APwy2t9FHD1+b9X6OYj3fHPogP531arjV8u0WETT4n0wwMlBDdwW5feJyRDk4tb8UTeQG4D5goTFmmzHmPfaptzExPAU4FXjEGPMw0lTz3tDEnr0aO6bFAp0jqv2VWjQID4ZWi1uBTNmuIFTzPRz147QlS1+jH9YkJd8D0nxb3E/U1/2cmUo31flDikmY0Bu2HFlbgXV97y+YlSrX4k5al6oZp22Yq17YDPJ0kLNgKIUT9aLS1r1IU/C7KRRoNScXpyb0jmyeVEdeZinE6lBppjM7SFvvADPn9UlfKSUybn7Cl4dWgcOFmN2to0HMD98dp2EJwTXibs0X5gRo68rR1pEn0VommSqTyeZpbqlBpkJLpuB7fqmuYdneMjZxwtU2+Lj7afkPvVDC8PZ1Fbrp50TW8CnnX6RQeSRwCHRtHOG16+6gSpxLNl4D18Hr77lNOhdmh47b4gXnUcCDIH84Me37Ai0ShFP7S1VRz9/D9r/ezbYfI1O0d7f/GuS78AXZ5CS/PJ4IamHduIn7OX6vaR3HT37XbF1R95ncTaBAp8AVCG4GFqaj1CzcxhDaSpacf5wM+Qn0knCVs48eC0YFNjMPJSrr2mrWKwTJ92lVVL1DPZ7m2RS4u+knScmKglYt8AaiAeoFg3jFaQqUWpM4sQalYpJGi1Sb426NwkiKzrYhn2ojEu5Vf6JWY9K/o6YK6jbPONnKowm/pUvAu0Yt5lLHIesGbWY1R0jeyVSJRot0Z1QG2kUHcCJzYwAAFRRJREFUrisXqJXEPIjZ3OFijy/d9REuW3Ylh122k5mnF2EI/nHRl1jFKSLBfj8iuNApMyhua301H+OzcB589NFPwFXIJ+xNFRiwRZBYHVpiQdVXqSxKbdknRN/Ig1ObFs32hy7u9t615mL/Q6tAp2ClvyU3V/eLAxouAv7jcA4tHObBxLmr4eZ4CLhsYX04BcjwNQV5uMBD1NfrflrcUI9QNcs0VM2T8ddTJkFi0lo01IvR8L3T7XSTJTdhDSraqIWOXWR8TwuYUJnOk6GPHrLk/LBb7elne5l9mHR7ZMhTIO2POZx8H8P8vpRdi4b6qtNWIhGIToIPvoDfMRLOjwa0HXnvdIh1caBDOiKKCT93p+IBDDRLp8Odhpe/5w7+mzdz2Oqdghufkp+HlyxgLcdzQd8PxZtzYcebU8z6ckG+hovQctpOKj9p9zs2fKuYgLOH7EsR+MBivI17y4N7sSfDdp+LLZ3SPLhp04uq//DqQQXcKvEa1IsS2kfZDxe1R1U5b7FQOBX29Bq+ZxWbcE59Pvw4XEUN95AG9JW6DzRxPzSbGLtobiprf/SV2hamYwo1bFUggyB3qNJRDWKkbI+sVkYTNozVDosCaf96pUdXQFiBWLsrHOp+Dk3X22YVQqq2HS4sRqC5SwVdTQGoufwh5canwNhqeIZdfgFJ16XniVMlS45OBm0ZqUzCLZFoLfsdEU0tNQmp1QaaaeodhU3SxnXf/57OK7mDLUu6qBwHrIDR45oYopMLngrA7fo3v5FZ5xeCjoUuqGxtlzA1VQnC9lg9CFVTXpCL07m4e22R4qXa/i4y/EVMe1HDHQHqQWkyv59D/aS5fqA1TwWSQi9Z+XENm+ohsApXRGuWJqDmULcUkbqvttHNdoaY5dMxXGo2JB2mbENTvQYN38IT7IWDVqdMkiRlnmQhsxj0j6MFDa3ulkjSTT814uTIiroF4nnptLEari/GGbfcuvCwHAhkm8L3ST2wLDlyZKkSt21xQmVZ6G5gQ3UhaVdGNuq1aaVY75+uLfByYzZsFn5gnhmAKJo41H3KS5IyWYb9+5SkzAzyVHHpZIg+eohT9UPyJGW5fzEHt6VKteJKV0M9RlPXKONbWxnf2iog1QvUYePqY5lX3B7otu3EtnshYWUS+ClCPQ/3l3Z4trrriEgAMFaJk+rIU8ynoe5AV4Pmlpr01u4THpy2akU2TQBOrGYT/QpEjgW5Mgk67BT6PJkJ3h7gFxHCHQOaf5pMywjvr16TelMqzyQglPCvSUE3wy5carY5KkGOLDp3AfCrvZro19CtgcOJrPH9Ur0eDXvD6iaODT31/AqkAsjhEetiCjBlEv7xVGVFZdn1fBl2+dQYbR8rkOYZevycWIE0WYZ92onqy6Up+iAEoEOAFOTLJP2+XX1eQbKGy2bmo73Au/vy0f1UNEDzoHWrUtIUa0g1Vd6woJVMvauMB7OrMNwS7KN9rloFrYReqx4ZQKWZlq6dxGIN6nUHJ1WnWpko3duoO3K8iOi7T21aAJyHwbH5pnDLkwxjLlG0tA5V+WjQ8L0amNhkrtVXbf3S3+H9AD/cEu6ajikMwEy9pLgFPq3sNkJ5wbCyiRw/hlYcw9tL1i9RtV3Nr4GAq55LAUE5eVoUCN8PPYdUd7XwIUl6EfAUkNV7ptcSo+HPKdDcoHpgel+UOyeiBkJdSVJCBUcnf2GIx1vy9wkXQWQf8YiLpH1uoIKwkqqz5OhgGK0YCzDKGuNO1QehWsWlyc5+qMRaJXSMmQDg6ka8rbC0kQ6OUa8uzGfTokFLlaaYVHobdQfXjkLMD2dottv8ntrUGDQ/9//rP25TP/x8LjYtAK6ZMTuHQVU5gl7SHB32AyReXJiXph/CuG0WCufXVJpIQUU/yIHXUJ/geWm+yqc4WFDRkYUJ8j4QyfFrNhRr+N6SKgQrcAJ+V4PkzCT/1k+3XYOsYxZDDDHL9ygbxHwSrVYy1VPSa9WcY4OYvZa8v1Y1AcjA61NaiSqXaFO+hrcKVEkbPiqJOUPeL4aUSZCigIoILORJvyWshz4G6aRsQ9EYos7iUmUem+05RR25045prFlYS9qvAf3SUkBMOwXibVUpZlh5Jjoq4tHF4oFuXMsYLZkCFdICRnUHMs2+YKZ4bGMQs/tbSkhLqkSjHqNUTOK2VGnYodlha+vKMbK1S/pU9wkuRR6c2rQAOC9Uew8n+7WPVD7YWf95BTjNPyk1Q8NCtUYIBMLH19xYuBoapotAUFAI960GzVYqLln09w3vpzmwKq5/HG3NmhyaKf1DOyTkuAWfjKxqJ/paVT2u+6Fi1ZZZ4v76NeQNn0stT8Y2qwVtaurRhe9p+F4BPqjlydiCR400RX8MYI04W+mdlNsMjlcm4RcctDKr9ybsRcp9s0oyjSTlulBakqkyjtNgx+Yemuz8i3GgqcOqjgCNegxiDQE/oLmjjBOrU6m0Q8sYTS01xluarecmFVMFzZidEqZWQ3Jx1B2hqeiy9hlNJAI4mCZV1HG7TJfahAoeyBBf5beph6JVuMmcNiWbhvl0SthtTPqwax7OH7dHUKULq2NI+CQJ/nCOC6DDSpmrtxcmJIfBQQmy6qXMY9MEINdQNFz11AqknK86IV8YJjpriKqDesLheBjstVNCCw9heaesDRG1EBMAed2/f+GQVa8h7UNlwVZJAx6fSrgreOvxw4RgvS7tygivK01BiMJWuTju2JRE3diRhXWINUhnCkIEBj9XF/fDzirJVJmmzCgtGRHjJObZCmnVP5aGpY26Q8bNc1Tren9aGfUYY1ZJZd8JXkZVVLVp4cGBhGVaoVTACOu8pSj4HwptdaoiIpjyd4Nwvi1hP8gO0guapsAwHX6SPBPaFuTM6nQyNCFXpvSLmM1PaY4LQLXqNCGftN0OObK+x5Ow4WSNQOOuSNrvXdXQMswL08qs5iCDXFnMD1dnkGfYCqiFq8lSbAmuVUFSJoclbQeEzG3Q8FAmadX89Ya7KDQfp+FyN/0M0olq9ul9zrBrQrtYmQRFAqVkpcNo5VYpLv0c6gNbmiL9HGqPXKWHZ6g5AbD2001br8yncGINMm22Fc22fFUrLm5LlWI+7Q/jSTsFGhmZBNbT2Uc+laFUTMqwnEyBuGvBsSGhqd7HjrYc24pJP0c3nm+VEHVoX/y3R1VUtWnhwYUtnANTT0EfKyjohzPclD+506EWCg8BH7S0UV6H1wTS6DH/uGFvK2h/qvkfvHDjfLj5Xj0UBdm0BTl9rACmA3SGyaLim0EXQ8kvBkjVs+hfH4jHlgh5POoh6dqd0JrDXq6CsnilOR9IFZAVpGcxyDBZH9wSlIlTZR6byJC308FEdy4bah1TgA+H39qRkbIhaJpi6N6WyJH1CyN6LSozr3SRcO7UoeHLojuOvGPF0TQ92T6qFVcUT1pqzDxsiLRbEM8PGYadTEl+0bGeXaZNALDRcORHCwzU0X7kllSJ5paaDNvRGQ27/pD39/wtatVSmxYeXBPjPo9Kv+2Vi1UiM4FUq3km/SCph6TdDhDkwDTZH3QXBC6/5pOy9sMuPK/EBE8qAM2Y732Fe0fVy1QQU16bvCZo6tfXxKn5op0uVY7hUUAa/XNk/bBSm+5rxBlilp/X0usqkaRgPS8tuuj5MuQttSbpHyf8pVG1XleSEikKfuFAeW41XI5nLU/Ry6H0M0QnWQrkmWE93EE/x6fnU/6fEoxViFQpIS41BlHFZdcPgyVs3u6vPUeH71nr9YIIDITzhGknSGMc2trP9tFuerNPCVA6BfLVDLjQySBV/cJqFaJy2imQb8kIgLrCt4vRoOoEhQ6lIklltcFYVwU6NL0xMYXywixq1VKbFh5cE+O+pxJOUge5KyGGZtjlg0mQ9wrY8WGhzLilkYRzUfpbK48KNOoNhXNv6gkGlIya74U5u/nnnJwPDCqnAe1D8lJlH8S3002ODj+01jybcu+0oT4sNKDHCcs7xUPen1ItwgIErs3hqdemVVr1ClMUGCbre4RawQzoKwnfGw084WAwkHo8Cmy69hLJCa/R66wiPDypnKeI20KJFismvgfOhBye5vzCOdOjWteHuIL4npm+12EKSpISSaeECimECx3Be21l2W3xokmLDz9pZt8IwkUenNq0ADiXKt30+56XhgnqfSnATC4iaKgW5p0F0BR4Tn9YHa3bD1Ld927C/Lmwh6ahm+wTHCO49toEAJq4rkDLLvzhVJUUVSgBBYyiL7UU9romm+avtBKquS/l1IUtXFhRUFOvUO+DtrDpuvrppoMcJZL08hQzrMcVFFmCLwX9W+knNVvN1WvSe6Nrdy2dR1MIBcttBPHUJubsAqK0XP8u38NTkJPcoesfO06Vbqd/gpcX1u7T+6AdKnqPkxPeC6GrOLEGidayFBzqMfg32DdM36jIoDYtQtQ8Ge7lJN8zqRL3k9qBHoh8qDoZtIUBCQ9LJJgRasFSPlyBND30+Ry1id6ZfJg7GSJnp2Dph1uPG0eAVpn8IKCjYAsTpc+VvweB16ShtfLXwufXyqRWSFVNREEvZT+U2o6l7VY6qlA9De08kC4Bab4PqDV69+S3toIdakO+DnLE2c5Wev2KcAOR8d7AQrrpp48ev81LM5Bpiv46VIppiFk+8AIM20KCgOWwP4FMPctjeJR+O4dVr1kHwuj7oOCuVdbwPdbeWv0S66OHOo4ftitoKfhOvuc6V1UrxeEvCy2CJF0RQRhu66DQVmTHwG3sm+JAVGRQmxZqIsaYArBhf1/Hn9F08udUtumyxlbP82buzUGMMbcSzBD7Uzbsed5r9uZ8B7JNF4BbM5UlYab6+iBaY2QvzKZFDi6yyCKbnhYBXGSRRTZlbboA3DX7+wL+zDbV1wfRGiN7ATYtcnCRRRbZ9LTp4sFFFllk09AigIssssimrE1pgDPGvMYYs8EYs8kY8+H9fT17Y8aYrcaYR40xa40xa+y2dmPMr4wxG+3vGaH9P2LXvcEYc+b+u/LdmzHmO8aYIWPMutC2570eY8yJ9r5sMsZ8xRizTwSH9oXtYY2fNMY8a9/HtcaYs0PPHXRrPODN87wp+YOM0N0MzEUa/B4Gjtrf17UX69kKdEza9gXgw/bxh4HP28dH2fW6wBH2Pjj7ew2Trv1U4ARg3d6sB3gAeDmipPYL4Kz9vbY/scZPApftZt+Dco0H+s9U9uBeBmzyPG+L53k14AfA6/bzNe1rex1wrX18LTLTSbf/wPO8qud5TyGjjF+2H65vj+Z53m+Q2VRhe17rMcYcChzied59niDBd0Ov2e+2hzXuyQ7KNR7oNpUB7jCgL/T3NrvtYDUP+KUx5kFjzEV2W6fnedsB7O9ZdvvBuvbnu57D7OPJ2w90+4Ax5hEbwmoYPtXWeEDYVAa43eUpDmZOzCs8zzsBOAt4vzHm1D+y71Rb+57WczCu8+vAPOA4YDtwld0+ldZ4wNhUBrhtQE/o79lgFRoPQvM8r9/+HgJuQkLOQRvCYH+r4PXBuvbnu55t9vHk7QeseZ436Hlew/O8ceBbBKmDKbPGA8mmMsD9FlhgjDnCGBMH3gbcvJ+v6QWZMabVGJPWx8CrgXXIei6wu12AzFbHbn+bMcY1xhwBLEAS1Qe6Pa/12DC2YIxZaiuL7wq95oA0BXBrb0DeR5hCazygbH9XOf6cP8DZwJNIRepj+/t69mIdc5EK28PAY7oWIAvcDmy0v9tDr/mYXfcGDsCqG3ADEqKNIV7Ke17IeoDFCEhsBr6K7c45EH72sMbrgEeBRxBQO/RgXuOB/hO1akUWWWRT1qZyiBpZZJFNc4sALrLIIpuyFgFcZJFFNmUtArjIIotsyloEcJFFFtmUtQjgpogZY75hjPnE/r6OF2qW/7XeGNP1Al//gDHm6H19XZEd3BYB3EFgViqpbIwpGGPyxph7jTHvNcb475/nee/1PO9fn+Oxlv95r/gF2UXAbzzPG3iBr78S+NQ+vJ7IpoBFAHfw2Dme56WBOcgM9H8Gvr1/L2mf2sUICfaF2s3AKyd1CkQ2zS0CuIPMPM8b8TzvZuCtwAXGmEUAxpj/MsZ82j7uMMb83Hp7O40xq4wxTcaY64DDgZ8ZY4rGmA/Z/f/bGDNgjBkxxvwmHOrZ415tjPlf60GuNsbMCz1/tBWn3GmMGTTGfNRubzLGfNgYs9kYkzPG/NAY0767NRljDkca0FdPOu/XjDG/sNd6jzGmyxjzJWPMLmPME8aY40P3pQI8iLSxRRYZEAHcQWue5z2AtP+cspunL7XPzQQ6gY/KS7x3As8g3mDK87wv2P1/gfQ+zgIeAr436XjnA1cAMxCdss8A2P7YlcCtQDcwH2mxAvgHRLdsmX1uF3D1HpZzDLDF87z6pO1vAT6OTGmvAvfZ6+sAfgT8+6T9HweO3cM5IpuGFgHcwW39wO68ojHgUGCO53ljnuet8v5IT57ned/xPK/geV4VUZw91hjTFtrlfzzPe8AC0PcQqR+A1wIDnudd5XlexR5DvbCLkZ7ZbaHjvskYE9vNJWSAwm623+R53oPWO7sJqHie913P8xrAjcDxk/Yv2GNFFhkQAdzBboexe8XYLyKe1i+NMVvMH5lHYYxxjDH/ZkPJ3yPS6CBeklo48V8CUvZxD9IAvjubA9xkw+Q84l01EI9ysu0C0rvZPhh6XN7N36mJu5MG8nu4nsimoUUAd5CaMealCMDdPfk560ld6nneXOAc4P8aY87Qpyft/nZELns50Ab06imew2X0IbmzPT13lud5mdBPi+d5z+5m30eAuXvw7p6PvRhRXIksMiACuIPOjDGHGGNei8yYuN7zvEd3s89rjTHzrX7Y7xHPqWGfHkTkl9TSSH4rBySBzz6Py/k50GWM+aDlsaWNMUvsc98APmOMmWOvaaYxZrczMTzP24ZIJL3guRHGGBc4EfjVCz1GZFPPIoA7eOxnxpgC4hl9DEmw/80e9l2AJP+LSGL+a57n3Wmf+xzwcRs6XoYMMXkaeBZYD9z/XC/I87wC8CrESxxAQOqV9ukvI9SNX9rrvh9YsrvjWPsm8M7neu7d2LnAnZ5VPo4sMiDSg4vswDDrgf0OOMOzg2ee5+tXA+/xPG/dn9w5smljEcBFFllkU9aiEDWyyCKbshYBXGSRRTZlLQK4yCKLbMpaBHCRRRbZlLUI4CKLLLIpaxHARRZZZFPWIoCLLLLIpqz9f3jE4y2P9ztXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from imageio import imread\n",
    "testin = imread('https://raw.githubusercontent.com/scikit-image/scikit-image/v0.10.1/skimage/data/coins.png')\n",
    "test = testin.astype(float)\n",
    "\n",
    "## . . Define model dimensions\n",
    "nx,ny = np.size(test,0),np.size(test,1)\n",
    "dx,dy=5,5\n",
    "Lx = (nx-1)*dx\n",
    "Ly = (ny-1)*dy\n",
    "\n",
    "## . . Define velocity model\n",
    "newvel = np.zeros((nx,ny))\n",
    "newvel = 1500+10*test[::-1,:]\n",
    "\n",
    "plt.figure()\n",
    "plt.title('Velocity Model',fontsize=14)\n",
    "plt.imshow(newvel, cmap=plt.cm.jet,extent=[0,nx*dx,ny*dy,0])\n",
    "plt.xlabel('Distance (m)',fontsize=12)\n",
    "plt.ylabel('Depth (m)',fontsize=12)\n",
    "cbar=plt.colorbar()\n",
    "cbar.set_label('Velocity (m/s)',fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 12. A whimsical velocity model made from the *coins* image in the skimage tool kit.**\n",
    "\n",
    "Let's now rerun the wave propagation simulation for heterogeneous media from above, but using this new velocity model!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "## . . Init wavefields on spatial grid\n",
    "UUo,UUm  = np.zeros((nx,ny)),np.zeros((nx,ny))\n",
    "\n",
    "## Time stepping parameters\n",
    "CC = 0.5                     # . . Courant #\n",
    "nt = 500                     # . . Number of time steps\n",
    "dt = CC*dx/np.max(newvel)    # . . Define dt based on Courant\n",
    "t  = np.linspace(0,nt*dt,nt) # . . Time lin\n",
    "t0 = 0.05                    # . . Wavelet shift \n",
    "\n",
    "## . . Define forcing function\n",
    "ss=0.01                      # . . sigma for Ricker wavelet\n",
    "F = (1-((t-t0)/ss)**2)*np.exp(-(t-t0)**2/(2*ss**2))\n",
    "\n",
    "## . . Define source location\n",
    "sx,sy=Lx/2,Ly/2                # . . source x,y location (in physical m units)\n",
    "\n",
    "## . . Total Solution space\n",
    "ggg = np.zeros((nx,ny,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "for it in range(nt):\n",
    "    tmp = awe_2d_explicit_solver_heterogeneous_8th_order(UUo,UUm,dx,dy,dt,newvel,F,it,sx,sy) #calc solution at n+1\n",
    "    ggg[:,:,it]=tmp  ## save solution vector\n",
    "    UUm=UUo          ## move solution at n to n-1 to prepare for next iteration\n",
    "    UUo=tmp          ## move solution at n+1 to n to prepare for next iteration\n",
    "\n",
    "## . . compute maximum for scaling\n",
    "amax = np.max(np.abs(ggg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_8.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vscale = (newvel.T-np.mean(newvel))\n",
    "vscale = -vscale/np.max(vscale)\n",
    "\n",
    "def AWE_2D_animate(i):\n",
    "    global k\n",
    "    wfld = ggg[:,:,k].T/np.max(np.abs(ggg))\n",
    "    data = wfld+0.02*vscale[:,::-1]\n",
    "    ax1.clear()\n",
    "    ax1.imshow(data,cmap='gray',extent=[0,Lx,0,Ly],vmin=-0.08,vmax=0.08)\n",
    "    ax1.set(xlabel='X(m)', ylabel='Y(m)')\n",
    "    ax1.set_title('2D AWE Step %s'%k,fontsize=14)\n",
    "    k += kskip\n",
    "\n",
    "## . . Animate Solution and compute error\n",
    "k,kskip = 0,5\n",
    "\n",
    "## . . Set up movie\n",
    "fig8,ax1 = plt.subplots(1)\n",
    "fig8.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig8.set_dpi(100)\n",
    "\n",
    "## . . Call the animator\n",
    "anim8 = animation.FuncAnimation(fig8,AWE_2D_animate,frames=int((nt-2*kskip)/kskip),interval=75)\n",
    "anim8.save('./movies/Ex8_8.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_8.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 13. 2D Acoustic wave propagation through velocity model shown in Figure 12.**\n",
    "\n",
    "# Time-reversal acoustics\n",
    "\n",
    "One of the most important features of the acoustic wave equation (and hyperbolic PDEs in general) is that one can time reverse the wave propagation (but it gets complicated at the boundary) from maximum time back to zero time.  This is due to the analytical PDE operator being [self-adjoint](https://en.wikipedia.org/wiki/Self-adjoint_operator). (In principle, this does not mean that the numerical implementation is necessarily self-adjoint; one needs to ensure that this is so by applying a [dot-product test](http://sepwww.stanford.edu/sep/prof/bei/conj/paper_html/node11.html)).\n",
    "\n",
    "To illustrate this principle, we can use the last two time-steps of the wavefield generated from the previous example which we'll call $\\psi^n_i$. Let's initialize the present time-reverse wavefield simulation using:\n",
    "\n",
    "$$\\phi^0_i = \\psi^{nt-2}_i \\tag{26}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\phi^{-1}_i = \\psi^{nt-1}_i \\tag{27}$$\n",
    "\n",
    "where you should note reverse ordering of $[-1,0]$ for $\\phi$ and $[nt-1,nt-2]$ for $\\psi$. Let's rerun the simulation from above **but this time not inject any source term $F(x) = F_{i,j}=0$**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "## . . Init wavefields on spatial grid\n",
    "UUp,UUo,UUm  = np.zeros((nx,ny)),np.zeros((nx,ny)),np.zeros((nx,ny))\n",
    "\n",
    "## Time stepping parameters\n",
    "CC = 0.5                     # . . Courant #\n",
    "nt = 450                     # . . Number of time steps\n",
    "dt = CC*dx/np.max(newvel)    # . . Define dt based on Courant\n",
    "t  = np.linspace(0,nt*dt,nt) # . . Time line\n",
    "t0 = 0.05                    # . . Wavelet shift \n",
    "\n",
    "## . . Define forcing function\n",
    "ss=0.01                      # . . sigma for Ricker wavelet\n",
    "F = np.zeros((nt))\n",
    "\n",
    "## . . Define source location\n",
    "sx,sy=Lx/2,Ly/2                # . . source x,y location (in physical m units)\n",
    "\n",
    "## . . Define initial wavefields for time reversal\n",
    "UUo = ggg[:,:,nt-2]\n",
    "UUm = ggg[:,:,nt-1]\n",
    "\n",
    "## . . Total Solution space\n",
    "hhh = np.zeros((nx,ny,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "for it in range(nt):\n",
    "    tmp = awe_2d_explicit_solver_heterogeneous_8th_order(UUo,UUm,dx,dy,dt,newvel,F,it,sx,sy) #calc solution at n+1\n",
    "    hhh[:,:,it]=tmp  ## save solution vector\n",
    "    UUm=UUo          ## move solution at n to n-1 to prepare for next iteration\n",
    "    UUo=tmp          ## move solution at n+1 to n to prepare for next iteration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now compute the animation of the time-reversing acoustic wavefield through the same velocity model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_9.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## . . compute maximum for scaling\n",
    "amax = np.max(np.abs(hhh))\n",
    "vscale = (newvel.T-np.mean(newvel))\n",
    "vscale = -vscale/np.max(vscale)\n",
    "\n",
    "def AWE_2D_animate2(i):\n",
    "    global k\n",
    "    wfld = hhh[:,:,k].T/amax\n",
    "    data = wfld+0.02*vscale[:,::-1]\n",
    "    ax1.clear()\n",
    "    ax1.imshow(data,cmap='gray',extent=[0,Lx,0,Ly],vmin=-0.08,vmax=0.08)\n",
    "    ax1.set(xlabel='X(m)', ylabel='Y(m)')\n",
    "    ax1.set_title('2D AWE Step %s'%k,fontsize=14)\n",
    "    k += kskip\n",
    "\n",
    "## . . Animate Solution and compute error\n",
    "k,kskip = 0,5\n",
    "\n",
    "## . . Set up movie\n",
    "fig9,ax1 = plt.subplots(1)\n",
    "fig9.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig9.set_dpi(100)\n",
    "\n",
    "## . . Call the animator\n",
    "anim9 = animation.FuncAnimation(fig9,AWE_2D_animate2,frames=int((nt-2*kskip)/kskip),interval=75)\n",
    "anim9.save('./movies/Ex8_9.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_9.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 14. Movie showing time-reverse propagation of that shown in Figure 12 above.**\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def awe_2d_heterogeneous_8th_order_data_time_reverse(UUo,UUm,dx,dy,dt,v,D,it,ry):\n",
    "    '''Set up eight-order solver of the acoustic wave equation\n",
    "    usage: U=awe_2d_heterogeneous_8th_order_data_time_reverse(UUo,UUm,dx,dy,dt,v,D,it,ry):\n",
    "    input: \n",
    "        Uo: Acoustic pressure vector (nx,ny) at time step n\n",
    "        Um: Acoustic pressure vector (nx,ny) at time step n-1\n",
    "        dx: Spatial sampling in x\n",
    "        dy: Spatial sampling in y        \n",
    "        dt: Temporal sampling\n",
    "        v : Heterogeneous propagation velocity (nx,ny)\n",
    "        D : Data to be time reversed\n",
    "        it: Time index\n",
    "        ry: Injection depth (meters)\n",
    "    output:\n",
    "        Um: Acoustic pressure vector (nx,ny) at time n+1\n",
    "    dependencies:\n",
    "        None\n",
    "    written by Jeff Shragge, jshragge@mines.edu, 10/2019\n",
    "    '''        \n",
    "    ## . . Get dimensions of wavefield\n",
    "    nx,ny = np.size(UUo,0),np.size(UUo,1)\n",
    "    \n",
    "    ## . . Define Courant numbers (squared)\n",
    "    dtdx2 = (dt/dx)**2\n",
    "    dtdy2 = (dt/dy)**2\n",
    "        \n",
    "    ## Source location\n",
    "    iry = int(ry/dy) ## . . Force to be integer\n",
    " \n",
    "    ## . . Inject wavelet\n",
    "    UUo[:,iry] += dt*dt*D[:,it]\n",
    "\n",
    "    ## . . Update solution \n",
    "    UUm[4:nx-4,4:ny-4] =  2*UUo[4:nx-4,4:ny-4]-UUm[4:nx-4,4:ny-4]+dtdx2*v[4:nx-4,4:ny-4]**2*( \n",
    "                    -1/560 *UUo[0:nx-8,4:ny-4] \n",
    "                    +8/315 *UUo[1:nx-7,4:ny-4]  \n",
    "                    -1/5   *UUo[2:nx-6,4:ny-4]  \n",
    "                    +8/5   *UUo[3:nx-5,4:ny-4]  \n",
    "                    -205/72*UUo[4:nx-4,4:ny-4]  \n",
    "                    +8/5   *UUo[5:nx-3,4:ny-4]  \n",
    "                    -1/5   *UUo[6:nx-2,4:ny-4]  \n",
    "                    +8/315 *UUo[7:nx-1,4:ny-4]  \n",
    "                    -1/560 *UUo[8:nx  ,4:ny-4])+dtdy2*v[4:nx-4,4:ny-4]**2*( \n",
    "                    -1/560 *UUo[4:nx-4,0:ny-8] \n",
    "                    +8/315 *UUo[4:nx-4,1:ny-7]  \n",
    "                    -1/5   *UUo[4:nx-4,2:ny-6]  \n",
    "                    +8/5   *UUo[4:nx-4,3:ny-5]  \n",
    "                    -205/72*UUo[4:nx-4,4:ny-4]  \n",
    "                    +8/5   *UUo[4:nx-4,5:ny-3]  \n",
    "                    -1/5   *UUo[4:nx-4,6:ny-2]  \n",
    "                    +8/315 *UUo[4:nx-4,7:ny-1]  \n",
    "                    -1/560 *UUo[4:nx-4,8:ny  ])\n",
    "\n",
    "    return UUm ## . . Return updated wavefield at time step n+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "## . . Define spatial grid\n",
    "Lx,Ly = 2000,1200        # . . length (m)\n",
    "nx,ny = 401,241      # . . Number of points in discretization \n",
    "dx = Lx/(nx-1) # . . Discretization interval\n",
    "dy = Ly/(ny-1) # . . Discretization interval\n",
    "\n",
    "## . . Create velocity function\n",
    "v = np.zeros((nx,ny))+1500\n",
    "v[:,50:]=2000\n",
    "\n",
    "## . . Init wavefields on spatial grid\n",
    "UUp = np.zeros((nx,ny))\n",
    "UUo = np.zeros((nx,ny))\n",
    "UUm = np.zeros((nx,ny))\n",
    "\n",
    "## Time stepping parameters\n",
    "CC = 0.5                     # . . Courant #\n",
    "nt = 800                     # . . Number of time steps\n",
    "dt = CC*dx/np.max(v)         # . . Define dt based on Courant\n",
    "t  = np.linspace(0,nt*dt,nt) # . . Time lin\n",
    "t0 = 0.05                    # . . Wavelet shift \n",
    "\n",
    "## . . Define forcing function\n",
    "ss=0.01                      # . . sigma for Ricker wavelet\n",
    "\n",
    "## . . Get the data from fff above\n",
    "data = fff[:,5,:]\n",
    "\n",
    "## . . Define source location\n",
    "ry=25                        # . . receiver injection location in y (in physical m units)\n",
    "\n",
    "## . . Total Solution space\n",
    "mmm = np.zeros((nx,ny,nt)) \n",
    "\n",
    "## . . Iterate over solution\n",
    "## . . Note time reversal\n",
    "for it in range(nt-1,0,-1):\n",
    "    tmp = awe_2d_heterogeneous_8th_order_data_time_reverse(UUo,UUm,dx,dy,dt,v,data,it,ry) #calc solution at n+1\n",
    "    mmm[:,:,nt-1-it]=tmp  ## save solution vector\n",
    "    UUm=UUo          ## move solution at n to n-1 to prepare for next iteration\n",
    "    UUo=tmp          ## move solution at n+1 to n to prepare for next iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
       "  <source src=\"./movies/Ex8_10.mp4\" type=\"video/mp4\">\n",
       "</video>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## . . compute maximum for scaling\n",
    "amax = np.max(np.abs(mmm))\n",
    "vscale = (v.T-np.mean(v))\n",
    "vscale = -vscale/np.max(vscale)\n",
    "\n",
    "def AWE_2D_animate3(i):\n",
    "    global k\n",
    "    wfld = mmm[:,:,k].T/amax\n",
    "    data = wfld+0.0025*vscale[:,::-1]\n",
    "    ax1.clear()\n",
    "    ax1.imshow(data,cmap='gray',extent=[0,Lx,0,Ly],vmin=-0.08,vmax=0.08)\n",
    "    ax1.set(xlabel='X(m)', ylabel='Y(m)')\n",
    "    ax1.set_title('2D AWE Step %s'%k,fontsize=14)\n",
    "    k += kskip\n",
    "\n",
    "## . . Animate Solution and compute error\n",
    "k,kskip = 0,5\n",
    "\n",
    "## . . Set up movie\n",
    "fig10,ax1 = plt.subplots(1)\n",
    "fig10.subplots_adjust(0.1,0.1,0.9,0.9)\n",
    "fig10.set_dpi(100)\n",
    "\n",
    "## . . Call the animator\n",
    "anim10 = animation.FuncAnimation(fig10,AWE_2D_animate3,frames=int((nt-2*kskip)/kskip),interval=75)\n",
    "anim10.save('./movies/Ex8_10.mp4')\n",
    "plt.close()\n",
    "\n",
    "HTML(\"\"\"\n",
    "<video width=\"800\" controls style=\"display:block; margin:0 auto;\">\n",
    "  <source src=\"./movies/Ex8_10.mp4\" type=\"video/mp4\">\n",
    "</video>\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Figure 15.  Movie showing the time-reverse behavior in the layered half-space model.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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