smc_cranfield.ipynb

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    "%%capture\n",
    "# Load the quadrotor simulator from a previous notebook\n",
    "%run quadsim.ipynb"
   ]
  },
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   "execution_count": 2,
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    "from IPython.core.display import HTML\n",
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   "source": [
    "# Sliding Mode Control\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook discusses and implements a sliding mode controller for the attitude control of a quadrotor. The discussion follows the 2016 work of Shaik and Whidborne from Cranfield, UK [1]. An error representation is used to enable tracking of trajectories in $\\phi$, $\\theta$, $\\psi$, or $r_z$. Note that there is currently no outer loop control of the quadrotor.\n",
    "\n",
    "Compared to the [SMC implementation based on L'Afflitto](sliding_mode_control.ipynb), this implementation is more introductory and follows the motivating example of [2, Ch 14.1.1]."
   ]
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   "source": [
    "## Quadrotor Model\n",
    "\n",
    "The derivation of the standard quadrotor model used herein can be found in the [Quadrotor Model](quadrotor_model.ipynb) notebook. We use the form with inertial translational kinematics and dynamics, and it is restated below, with the state defined as\n",
    "\\begin{align}\n",
    "x &\\triangleq\n",
    "\\begin{bmatrix} r_x & r_y & r_z & \\dot{r}_x & \\dot{r}_y & \\dot{r}_z & \\phi & \\theta & \\psi & p & q & r \\end{bmatrix}^\\top,\n",
    "\\end{align}\n",
    "\n",
    "which evolves with the following simplified dynamics (i.e., $\\Gamma\\approx I_{3\\times 3}$ so that we can easily perform control)\n",
    "\n",
    "\\begin{equation}\n",
    "x =\n",
    "\\begin{bmatrix} \\dot{r}_x \\\\ \\dot{r}_y \\\\ \\dot{r}_z \\\\ \\ddot{r}_x \\\\ \\ddot{r}_y \\\\ \\ddot{r}_z \\\\ \\dot{\\phi} \\\\ \\dot{\\theta} \\\\ \\dot{\\psi} \\\\ \\dot{p} \\\\ \\dot{q} \\\\ \\dot{r} \\end{bmatrix} =\n",
    "\\begin{bmatrix}\n",
    "\\dot{r}_x \\\\ \\dot{r}_y \\\\ \\dot{r}_z \\\\\n",
    "-\\frac{u_1}{m}(\\cos\\phi\\sin\\theta\\cos\\psi+\\sin\\phi\\sin\\psi) \\\\\n",
    "-\\frac{u_1}{m}(\\cos\\phi\\sin\\theta\\sin\\psi-\\sin\\phi\\sin\\psi) \\\\\n",
    "g-\\frac{u_1}{m}(\\cos\\phi\\cos\\theta) \\\\\n",
    "p \\\\ q \\\\ r \\\\\n",
    "\\frac{J_y - J_z}{J_x} qr + \\frac{1}{J_x} u_2 \\\\\n",
    "\\frac{J_z - J_x}{J_y} pr + \\frac{1}{J_y} u_3 \\\\\n",
    "\\frac{J_x - J_y}{J_z} pq + \\frac{1}{J_z} u_4\n",
    "\\end{bmatrix}.\n",
    "\\end{equation}\n",
    "\n",
    "<!--\n",
    "\\begin{equation}\n",
    "x =\n",
    "\\begin{bmatrix} \\dot{r_x} \\\\ \\dot{r_y} \\\\ \\dot{r_z} \\\\ \\ddot{r_x} \\\\ \\ddot{r_y} \\\\ \\ddot{r_z} \\\\ \\dot{\\phi} \\\\ \\dot{\\theta} \\\\ \\dot{\\psi} \\\\ \\dot{p} \\\\ \\dot{q} \\\\ \\dot{r} \\end{bmatrix} =\n",
    "\\begin{bmatrix}\n",
    "x_4 \\\\ x_5 \\\\ x_6 \\\\\n",
    "-\\frac{u_1}{m}(\\cos x_7\\sin x_8\\cos x_9+\\sin x_7\\sin x_9) \\\\\n",
    "-\\frac{u_1}{m}(\\cos x_7\\sin x_8\\sin x_9-\\sin x_7\\sin x_9) \\\\\n",
    "g-\\frac{u_1}{m}(\\cos x_7\\cos x_8) \\\\\n",
    "x_{10} \\\\ x_{11} \\\\ x_{12} \\\\\n",
    "\\frac{J_y - J_z}{J_x} x_{11} x_{12} + \\frac{1}{J_x} u_2 \\\\\n",
    "\\frac{J_z - J_x}{J_y} x_{10} x_{12} + \\frac{1}{J_y} u_3 \\\\\n",
    "\\frac{J_x - J_y}{J_z} x_{10} x_{11} + \\frac{1}{J_z} u_4\n",
    "\\end{bmatrix}.\n",
    "\\end{equation}\n",
    "-->\n",
    "\n",
    "The input to this system is defined as\n",
    "\\begin{align}\n",
    "u &\\triangleq\n",
    "\\begin{bmatrix} T & \\tau_\\phi & \\tau_\\theta & \\tau_\\psi \\end{bmatrix}^\\top.\n",
    "\\end{align}"
   ]
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   "source": [
    "## Shaik's Implementation\n",
    "\n",
    "In Shaik [1], four scalar sliding surfaces are defined as\n",
    "$$\n",
    "\\begin{equation}\n",
    "s_\\alpha = \\dot{e}_\\alpha + \\lambda_\\alpha e_\\alpha = 0,\n",
    "\\end{equation}\n",
    "$$\n",
    "where $\\lambda_\\alpha$ is a tuning gain and the relevant tracking error is defined as $e_\\alpha = \\alpha^d - \\alpha$. The variable $\\alpha$ is used as a placeholder for one of the relevant states: $\\phi$, $\\theta$, $\\psi$, or $r_z$. The time derivative of the sliding manifold is\n",
    "$$\n",
    "\\begin{equation}\n",
    "\\dot{s}_\\alpha = -f -u + \\ddot\\alpha^d + \\lambda_\\alpha \\dot{e}_\\alpha.\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "The objective of the sliding mode controller is to choose an input $u$ for each choice of $\\alpha$ s.t. system trajectories are driven to the sliding manifold ($s_\\alpha=0$) in finite time, which is then asymptotically driven to zero. This is done by choosing the following control inputs, with $k_\\alpha$ a scalar tuning gain:\n",
    "$$\n",
    "\\begin{align}\n",
    "u_1 &= - \\frac{m}{\\cos\\phi\\cos\\theta}\\left[ -g +\\ddot{r}_z^d +\\lambda_{r_z}\\dot{e}_{r_z} + k_{r_z}\\text{sgn}(s_{r_z})\\right] \\label{eq:shaik-u1} \\\\\n",
    "u_2 &= J_x\\left[ -\\frac{J_y - J_z}{J_x} qr + \\ddot\\phi^d + \\lambda_\\phi \\dot{e}_\\phi + k_\\phi \\text{sgn}(s_\\phi)\\right] \\\\\n",
    "u_3 &= J_y\\left[ -\\frac{J_z - J_x}{J_y} pr + \\ddot\\theta^d + \\lambda_\\theta \\dot{e}_\\theta + k_\\theta \\text{sgn}(s_\\theta)\\right] \\\\\n",
    "u_4 &= J_z\\left[ -\\frac{J_x - J_y}{J_z} pq + \\ddot\\psi^d + \\lambda_\\psi \\dot{e}_\\psi + k_\\psi \\text{sgn}(s_\\psi)\\right]. \\label{eq:shaik-u4}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
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   "source": [
    "## Discussion of Shaik's Implementation\n",
    "\n",
    "Note that in [1], a right-handed coordinate frame with $z$ up is used (as opposed to NED, which is used in this series of notebooks). Therefore, the body coordinate frame is a front-left-up (FLU). As a result, the sign of equation \\eqref{eq:shaik-u1} is different than $U_4$ in the paper. Also notice that in this notebook we have used $u_1$ for the force equation corresponding to thrust.\n",
    "\n",
    "The sign issue can be more easily seen if fill in some of the gaps in Shaik's paper. Consider equation (15) of Shaik, which is a common sliding surface definition. Note how the sliding surface is $s_\\alpha = \\dot{e}_\\alpha - \\phi(e_\\alpha) = 0$, where $\\phi(e_\\alpha) = -\\lambda_\\alpha e_\\alpha$ is a linear control law, resulting in $s_\\alpha = \\dot{e}_\\alpha + \\lambda_\\alpha e_\\alpha$.\n",
    "\n",
    "Now that we have identified a sliding surface such that $e_\\alpha \\to 0$ when the system is steered to the surface, we need to choose an input $u_\\alpha$ to drive all system trajectories to the surface $s_\\alpha=0$. Choosing the Lyapunov function $V = \\frac{1}{2}s_\\alpha^2$, we desire that $\\dot{V} = s_\\alpha\\dot{s}_\\alpha < 0$. The time-derivative of $s_\\alpha$ is\n",
    "\\begin{align}\n",
    "\\dot{s}_\\alpha &= \\ddot{e}_\\alpha + \\lambda_\\alpha \\dot{e}_\\alpha \\\\\n",
    "&= \\ddot{\\alpha}^d - \\ddot{\\alpha} + \\lambda_\\alpha \\dot{e}_\\alpha \\\\\n",
    "&= \\ddot{\\alpha}^d - f(\\alpha, u_\\alpha) + \\lambda_\\alpha \\dot{e}_\\alpha \\\\\n",
    "&= \\ddot{\\alpha}^d - f_1(\\alpha) - bu_\\alpha + \\lambda_\\alpha \\dot{e}_\\alpha.  \\quad \\text{*} \\label{eq:sdot}\n",
    "\\end{align}\n",
    "\n",
    "Note that in step $\\text{*}$ we have assumed that the dynamics $f(\\alpha, u_\\alpha)$ are linear in the control input $u_\\alpha$. That is, $\\;f(\\alpha, u_\\alpha) = f_1(\\alpha) + bu_\\alpha$. Here, we have a choice (see [2, p565]) on whether we design a control $u_\\alpha$ that has only a switching component, or we may also add a continuous component that cancels any of the known quantities in \\eqref{eq:sdot}. Given that we know the dynamics (albeit, with some uncertainty), we design a control that has the switching component $\\beta(e_\\alpha) sgn(s_\\alpha)$ and a continuous component to cancel out what we know. Therefore, our designed control input is\n",
    "$$\n",
    "\\begin{equation}\n",
    "u_\\alpha = \\frac{1}{b}\\left[\\underbrace{\\ddot{\\alpha}^d - f_1(\\alpha) + \\lambda_\\alpha \\dot{e}_\\alpha}_{continuous} + \\underbrace{k_\\alpha \\text{sgn}(s_\\alpha)}_{switching}\\right].\n",
    "\\end{equation}\n",
    "$$\n",
    "\n",
    "The switching component is a fundamental aspect of sliding mode control. Its purpose is ensure that $\\dot{V} = s_\\alpha\\dot{s}_\\alpha < -\\eta \\left|s_\\alpha\\right| < 0$ for some value of $\\eta$. See Khalil p552 [2] for more information."
   ]
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    "def sat(v):\n",
    "    return v if np.abs(v) <= 1 else np.sign(v)\n",
    "\n",
    "class ShaikSMC(Controller):\n",
    "    \"\"\"Sliding Mode Controller\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        self.name = \"Shaik SMC\"\n",
    "        \n",
    "        # dirty derivative filters\n",
    "        self.dZdt = DirtyDerivative(order=1, tau=0.05)\n",
    "        self.dZdt2 = DirtyDerivative(order=2, tau=0.05)\n",
    "        self.dphdt = DirtyDerivative(order=1, tau=0.05)\n",
    "        self.dphdt2 = DirtyDerivative(order=2, tau=0.05)\n",
    "        self.dthdt = DirtyDerivative(order=1, tau=0.05)\n",
    "        self.dthdt2 = DirtyDerivative(order=2, tau=0.05)\n",
    "        self.dpsdt = DirtyDerivative(order=1, tau=0.05)\n",
    "        self.dpsdt2 = DirtyDerivative(order=2, tau=0.05)\n",
    "        \n",
    "        # estimates of the physical properties of the quadrotor\n",
    "        self.g = 9.8\n",
    "        self.mass = 4\n",
    "#         Jxx = 0.060224; Jyy = 0.122198; Jzz = 0.132166\n",
    "        Jxx = 0.1; Jyy = 0.1; Jzz = 0.1\n",
    "        self.I = np.array([[Jxx,0,0],\n",
    "                           [0,Jyy,0],\n",
    "                           [0,0,Jzz]])\n",
    "        \n",
    "    def inner(self, commanded, state, Ts):\n",
    "        # Transform the system into the form of HK (14.4) and (14.5)\n",
    "        eta = np.array([state.flatten()[[2, 6, 7, 8]]]).T # r_z, ph, th, ps\n",
    "        xi = np.array([state.flatten()[[5, 9, 10, 11]]]).T # \\dot{r_z}, p, q, r\n",
    "        \n",
    "        ph = eta.flatten()[1]\n",
    "        th = eta.flatten()[2]\n",
    "        ps = eta.flatten()[3]\n",
    "        \n",
    "        Jx = self.I[0,0]\n",
    "        Jy = self.I[1,1]\n",
    "        Jz = self.I[2,2]\n",
    "        \n",
    "        #\n",
    "        # r_z\n",
    "        #\n",
    "        \n",
    "        # Desired\n",
    "        des_Z = commanded[0]\n",
    "        des_Zdot = self.dZdt.update(des_Z, Ts)\n",
    "        des_Zddot = self.dZdt2.update(des_Zdot, Ts)\n",
    "        \n",
    "        # Gains\n",
    "        lam_Z = 3\n",
    "        kZ = 6\n",
    "        \n",
    "        # error\n",
    "        e_Z = des_Z - eta[0]\n",
    "        e_Zdot = des_Zdot - xi[0]\n",
    "        \n",
    "        \n",
    "        sZ = e_Zdot + lam_Z*e_Z\n",
    "#         u1 = -self.mass/(np.cos(ph)*np.cos(th))*(-self.g + des_Zddot + lam_Z*e_Zdot + kZ*np.sign(sZ))\n",
    "        u1 = -self.mass/(np.cos(ph)*np.cos(th))*(-self.g + des_Zddot + lam_Z*e_Zdot + kZ*sat(sZ/0.5))\n",
    "    \n",
    "        # sign difference -- it seems that because of the way the tracking error was defined, it\n",
    "        # it doesn't look quite the same as in Khalil [2] (Should be all positive -- see other nb).\n",
    "        u1 = self.mass/(np.cos(ph)*np.cos(th))*(self.g + des_Zddot - lam_Z*e_Zdot) + kZ*sat(-sZ/0.5)\n",
    "        \n",
    "        #\n",
    "        # \\phi\n",
    "        #\n",
    "        \n",
    "        # Desired\n",
    "        des_ph = commanded[1]\n",
    "        des_phdot = self.dphdt.update(des_ph, Ts)\n",
    "        des_phddot = self.dphdt2.update(des_phdot, Ts)\n",
    "\n",
    "        # Gains\n",
    "        lam_ph = 3\n",
    "        kph = 1\n",
    "        \n",
    "        # error\n",
    "        e_ph = des_ph - eta[1]\n",
    "        e_phdot = des_phdot - xi[1]\n",
    "        \n",
    "        sph = e_phdot + lam_ph*e_ph       \n",
    "        u2 = Jx*(-(Jy-Jz)/Jx*xi[2]*xi[3] + des_phddot + lam_ph*e_phdot + kph*np.sign(sph))\n",
    "        \n",
    "        #\n",
    "        # \\theta\n",
    "        #\n",
    "        \n",
    "        # Desired\n",
    "        des_th = commanded[2]\n",
    "        des_thdot = self.dthdt.update(des_th, Ts)\n",
    "        des_thddot = self.dthdt2.update(des_thdot, Ts)\n",
    "\n",
    "        # Gains\n",
    "        lam_th = 3\n",
    "        kth = 1\n",
    "        \n",
    "        # error\n",
    "        e_th = des_th - eta[2]\n",
    "        e_thdot = des_thdot - xi[2]\n",
    "        \n",
    "        sth = e_thdot + lam_th*e_th       \n",
    "        u3 = Jy*(-(Jz-Jx)/Jy*xi[1]*xi[3] + des_thddot + lam_th*e_thdot + kth*np.sign(sth))\n",
    "        \n",
    "        #\n",
    "        # \\psi\n",
    "        #\n",
    "        \n",
    "        # Desired\n",
    "        des_ps = commanded[3]\n",
    "        des_psdot = self.dpsdt.update(des_ps, Ts)\n",
    "        des_psddot = self.dpsdt2.update(des_psdot, Ts)\n",
    "\n",
    "        # Gains\n",
    "        lam_ps = 3\n",
    "        kps = 1\n",
    "        \n",
    "        # error\n",
    "        e_ps = des_ps - eta[3]\n",
    "        e_psdot = des_psdot - xi[3]\n",
    "        \n",
    "        sps = e_psdot + lam_ps*e_ps       \n",
    "        u4 = Jz*((Jx-Jy)/Jz*xi[1]*xi[2] + des_psddot + lam_ps*e_psdot + kps*np.sign(sps))\n",
    "              \n",
    "        u = np.hstack(np.array([u1,u2,u3,u4]))\n",
    "        \n",
    "        return u\n",
    "    \n",
    "    def outer(self):\n",
    "        pass\n",
    "    \n",
    "    def update(self, commanded, state, pkt, Ts):\n",
    "        \n",
    "        #\n",
    "        # Outer Loop\n",
    "        #\n",
    "        \n",
    "        #\n",
    "        # Inner Loop\n",
    "        #\n",
    "        \n",
    "        cmd = commanded[[2,6,7,8]]\n",
    "        \n",
    "        u = self.inner(cmd, state, Ts)\n",
    "        \n",
    "        # actuator commands\n",
    "        return u, commanded"
   ]
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UR3GLI9IxKNmWQmnvXlvFbdo0mDrVLlessPtKlLBEuls3aNvW+t62apX/iU8icmS89wOBgQChke27MyfaQZg6FRYtgjffjMzzO2ddTuLj4aab4Kyz4LPPbAEpESk+lGxLobBjB0yeDElJ1tN25sy0FRLr1rUR65tussu2bQt29EhECqehQ+1Y0atXZF9nwABrBdi7t/Xi/vprm2gtIsWDkm2JSjt3lmDsWEuuk5Isud6/3/pUt2+fllh36mTJtogUDt77JCAp4DDYvx8++gjOO886kURar142AbNnT1sIZ9w462QkIkWfkm2JCvv2wY8/2ojP11/DjBknc+CAJdcnnGDLKCcmwoknasVEETlykyfbnI5LLy241zzzTJgwwRa+6dzZjnUtWxbc64tIMAJPtp1z9YB3gRqABwZ7719wzlUBRgAJwEqgl/d+a1BxSvj98Udacj1uHGzbZu2xTjgBrrzyN669NoFOnZRci0j4jRoFcXG2imtB6tjRSuHOOgtOPRU+/xxOPrlgYxCRghUNnT/3AXd575sBnYCbnHPNgPuB8d77RsD40NdSiB04AD/9ZMshH3881K8Pffva5MZLLrE/fps22bLHffqspGtXJdoiEn4HDlgJybnnFkwJSWbHHWcj6zVr2mj3qFEFH4OIFJzAR7a992uBtaHrO5xzC4E6QA8gMbTbO1iN330BhChHYO9eq7kePdoWelizxrqFdOkCffrA2WdDs2ZqvyciBWfmTOvB37NncDHUr28j3D16WD33Qw/BY49p8RuRoijwZDs951wC0Ab4EagRSsQB1mFlJlII/PWXlYaMGGGnSLdvt1XVunWDCy+0CUnhWKlNRCQ/xo61f/C7dQs2jvh4q+G+6SZ4/HH45Rd47z2tUitS1ERNsu2cKwd8BNzuvd/u0g11eu+9cy7LpbeCWHEsUqIhjvzGsH8/zJ5dmQkTqjNxYjzJybFUqJDCKadspHPnTbRr9yelSh0ArD92pOIIN8WhOKI5BsmfsWOhQwdLdoN21FHwv//ZWgB33GEL7Hz6qTqViBQlUZFsO+disUR7qPf+49DN651ztbz3a51ztYANWT22oFcci6RoiCOvq6/NnAnvvgsjR9rM/nLl7NTs5ZfDGWfEEhtbG6gd0TgiSXEojmiOQfJu82brfPTww0FHksY5uOUWq+Xu1cvam777Lpx/ftCRiUg4BF4d5mwI+01goff+2XR3jQGuCV2/Bvi0oGOTrG3aBC+8AK1b2+jQ4MHWxmrUKNiwwf5InHOOte0TEYkm33xjAwXnnBN0JIc64wyYPh0SEuCCC+D++60tqogUbtEwst0ZuAr4xTk3O3TbA8CTwEjn3PXAb0CE1/iSnOzfb+35hgyxU5x791qi/eqrcNllWn5YRAqHsWNtNcf27YOOJGvHHGMdmW6/HZ56yq4PGwZ16gQdmYjkV+DJtvf+ByC7XhSnF2QscqjNm+HNN+G//4XffrM/UjfeaJ1EWrQIOjoRkdzzHr791trtlSgRdDTZi4uD116DU06BG26ANm3g/fetN7eIFD6Bl5FIdPr5Z7j+elsK/b77bLLOyJGwejU895wSbREpfJYssZZ/p50WdCS5c+WVVlZSvbq1Sb3tNti9O+ioRCSvlGzLQfv3w/ffV+Pkk6FtWxg+HK691tpRTZhgyxofdVTQUYqI5E9q85jCNK/1uOMs4b71VnjxRSt/mT378I8TkeihZFvYs8cmOTZtCo8+2px16+DZZ20U+9VXbbVHEZHCLikJatWCRo2CjiRvSpe2Selffw1bt9qS708/bQMkIhL9lGwXY9u2wZNP2sz3G26wSY6PPjqPxYut36smPYpIUeG9JduJiYV3xdqzzrIzjd27W3nfKafAwoVBRyUih6NkuxjautV6zNavDwMH2mIK48fDTz9Bly6bonrikIhIfqTWaxemEpKsVK1qbVbfew8WL7YWrI8/bh2iRCQ6KdkuRrZvh3/8Axo0gH/+00ZJZs2yU5Nduxbe0R4RkcP5/nu77NIl2DjCwTno3dtGtXv2hL//3Wq5p08POjIRyYqS7WIgORmeeMKS7EcesZn4s2fb6EibNkFHJyKFiXOueha3NQkilrxISoKaNaFx46AjCZ/q1W0i+6efWpvWTp2sY8mffwYdmYikp2S7CNu3z3q1HnMMPPAAnHgizJgBn3xipSMiIvkwyTl3cJEx59xdwCcBxpMrU6bAyScXzTN43bvDggU29+all6BJE3j7bThwIOjIRATCnGw755plcVtiOF9DDs97+OILaNkSBgywA+/UqfD559CuXdDRiUghlwhc5Zwb5ZybCDQGOgYbUs7WrYOVK23AoaiqWNEWH5sxwwZYrrsObrmlDTNnBh2ZiIR7ZHukc+4+Z0o7514Cngjza0gOZs+GM86A88+3ke1PPrFaxU6dgo5MRIoC7/1a4CvgRCABeMd7nxxoUIcxbZpdFuVkO1XbtvDDDzayvXZtaTp0gL59Yc2aoCMTKb7CnWyfANQDpgDTgTVA5zC/hmRhyxbo398OtHPm2KnE+fPhwguL5mlTEQmGc+5b7Fh/PHAe8Lxz7plgo8rZ1KkQG1t85qjExMA118C77/7I7bfDO+/AscfaRMrt24OOTqT4KRnm50sBdgOlgThghfdeVWMRdOCAjWDcd5+19LvtNpsEqR7ZkhcpKSmsWrWKPXv25LhfxYoVWRgFjX2jIY7DxRAXF0fdunWJjY0twKgKxFfAMO/9n8CfzrmTgIGHe5Bzrh7wLlAD8MBg7/0LEY00ZNo0S7Tj4gri1aJHuXL7efZZuPlmePBBaxH4+uv2N6JfP/sHREQiL9zJ9nTgU6ADEA+85py72Ht/aZhfR7CSkZtusok/nTtbvV7LlkFHJYXRqlWrKF++PAkJCbgcToXs2LGD8uXLF2Bk0RtHTjF479m8eTOrVq2iQYMGBRxZxJUFvnHObQFGAKO89//MxeP2AXd572c558oDM51z47z3CyIZbEqKtcTr1y+SrxLdGjaEYcPgzjvh3nst+X7uORvpvvJKKBnuTEBEMgh3Gcn13vuHvfcp3vu13vsewJgwv0axt3u3HTDbtbOFGt56CyZOVKIt+bdnzx6qVq2aY6Itueeco2rVqoc9U1AYee8f8943B24CagHfh0pLDve4td77WaHrO4CFQJ2IBoutuLh7t+atAHToABMm2GT5ChXg2muhaVMrM9m3L+joRIqusCbb3vsZWdz2Xjhfo7ibPNlWDBs0CPr0gUWL7IAZoyaOcoSUaIdXMXg/NwDrgM3AIb23c+KcSwDaAD+GPapMitPkyNxwDs47D2bOtP7c6ZPut9+2MwEiEl46eVRI7NxpvbJfegmOPhrGjbOuIyISrKSkJJ555hk+//zzoEMpEM65G4FeQDVgFNA3L6UgzrlywEfA7d777Znu6wf0A6hRowZJSUl5ji85OTnD40aPbkqVKpVZvnwqK1bk+enyLXMcQThcDBUqwH/+A1OmVOWddxK47rry3H//Hi6+eBXnnbeWMmX2F0gcBUVxKI6gYlCyXQhMmmQzy1essFq7J56AcuWCjkpEiql6WKI8O68PdM7FYon2UO/9x5nv994PBgYDtG/f3icmJuY5uKSkJNI/rn9/W8zmtNPy/lxHInMcQchtDKedZoM5X3wBgwbF8d//HsvQocfSvz/ceivUrl0wcUSa4lAcQcWg4oMolpICDz0EiYlWJjJxoo1sK9GWourdd9+lZcuWtGrViquuuoqVK1fStWtXWrZsyemnn87vv/8OQP/+/RkwYACdOnWiYcOGJCUl0adPH4477jiuvfbag89Xrlw57rnnHpo3b84ZZ5zBTz/9RGJiIg0bNmTMGJtOsnLlSk455RTatm1L27ZtmTJlCpB28L3kkkto2rQpV155Jd57AL766ivatWtH27Zt+fjjQ3LGIs17PzCfibYD3gQWeu+fDX9kh9qxA379VYt55YZztj7D999b6c1ZZ1m5YkKClZlocRyR/NPIdpRautRmif/0k9VmP/88REETCCkObr/dWt1kofT+/VCiRN6fs3Vr+yXOwfz583n88ceZMmUK8fHxbNmyhWuuuebgNmTIEG699VZGjx4NwNatW5k6dSpjxoyhe/fuTJ48mTfeeIMOHTowe/ZsWrduzc6dO+natSuDBg2iZ8+ePPTQQ4wbN44FCxZwzTXX0L17d6pXr864ceOIi4tjyZIlXH755cyYYdNPfv75Z+bPn0/t2rXp3LkzkydPpn379vTt25cxY8bQunVr/va3v+X9/SieOgNXAb8451J/wR7w3n8ZqRecM8dW1FWynTcnnAAjR8KyZfaxHTLEJlF27Ag33gi9ekHp0kFHKVJ4aGQ7ynhv3UVat7YRmZEj4c03lWhL0TdhwgQuvfRS4uPjAahSpQpTp07liiuuAOCqq67ihx9+OLj/BRdcgHOOFi1aUKNGDVq0aEFMTAzNmzdn5cqVAJQqVYpu3boB0KJFC7p06UJsbCwtWrQ4uE9KSgp9+/alRYsWXHrppSxYkFZ+3LFjR+rWrUtMTAytW7dm5cqVLFq0iAYNGnDsscfinKN3794F8O4Uft77H7z3znvf0nvfOrRFLNEGmDXLLtu2jeSrFF3HHGNnU9esgRdftAVxrr0W6taFe+6xZFxEDk8j21Fk9+4YrrkG3nvPSkfefRfq1Qs6Kil2chiB3h0F/a1THXXUUQDExMQcvJ769b5QH7PY2NiDXUHS75d+n+eee44aNWowZ84cDhw4QFy6lU/SP2+JEiUOPkYKh5kzoWZNqFUr6EgKt4oV4ZZbbM5QUpKt6fDcc/DMM3DqqZaAX3KJBoVEsqOR7SixeDHcdFNb3n8fHnsMvv1WibYUL127dmXUqFFs3rwZgC1btnDSSScxfPhwAIYOHcopp5wS9tfdtm0btWrVIiYmhvfee4/9+3PuwNC0aVNWrlzJ8uXLARg2bFjYY5LwmDVLJSTh5JxNphw1Cn77Df79b1i3zkoda9a0ifzffWcrG4tIGiXbUeDDD22xgc2bj+Krr+Dhh/NXFitSmDVv3pwHH3yQLl260KpVK+68805eeukl3nrrLVq2bMl7773HCy+Ef3XvG2+8kXfeeYdWrVqxaNEiypYtm+P+cXFxDB48mEsvvZS2bdtSvXqeWkxLAdm1CxYsUAlJpNSpAwMH2loPU6ZA794wejR07WorVt53n51ZCM0pFinWVEYSoJQUWwny+edtdbM77pjBWWdp5QUpvlInQ6Y3YcKEQ/Z77bXXDpazJCQkMG/evIP3vf322wevJycnH7z+6KOPZniO1PsaNWrE3LlzD97+1FNPAZCYmJihFdTLL7988Hq3bt2YOXNm1JTUyKHmzrURViXbkeWcLRh04on2t2z0aCuBfPZZePppq/s+4YQGVKoErVrZ/iLFjUa2A7JlC5xzjh2cbrnF2i1Vr/5X0GGJiBQJmhxZ8EqXhssvh7FjrbzkjTdslHv48Pq0aWOrVD7wgLUWVKmJFCdKtgOwcKG1Vpo0yTqPvPgilCoVdFQiIkXHrFkQH6+5L0GpWhWuvx6++QY++mgKr79uXUyeftpGwWvVsvtHj7YVkkWKMiXbBWzsWCsZ2b7dJpKkW39DRETCZNYsG9VW2ULwKlVKoV8/GD8eNm6EoUOttvujj6BnT0vMzzsPXn7ZmgWozluKGiXbBcR7q2E7/3xo0ACmT4eTTgo6KhGRouevv2DePJWQRKPKleGKK2DYMEu8x4+HAQMsyb7lFis1OfpoG/UePtz2ESnsNEGyAKSk2Kpbb7wBF19sK3EdpuGBiIjk06JFdtxt3TroSCQnsbE2wt21q/XtXr4cxo2z7eOPbeVKgDZtbJ9TToGTT7aRcJHCRCPbEbZ9u50ee+MNePBBWxFSibaISOT88otdtmgRbBySNw0bwg03WDvcTZvgxx/h8cdtsZyXX4YLL7Q6/ObNoX9/+OAD+OOPoKMWOTyNbEfQH39Yor1woS253qdP0BGJFA2TJk2iUqVKnHQEtVjlypXPjCjeAAAgAElEQVTL0BpQio65c23SeePGQUci+VWiBHTsaNuDD8KePTBjBkycaM0FPvgAXn/d9q1f35oOpO7fti2UKxds/CLpKdmOkJ9/tkR7506bFHnGGUFHJFJ0TJo0iapVqx5Rsi1F19y50KwZlNRfuCIjLs5KSE4+2b7ev99+zhMnwuTJNg9q1Ci7LybGfv6pyXeHDjYaLhIUlZFEwJdfWm1ZyZJ2EFCiLZI7F154Ie3ataN58+YMHjwYgK+++oq2bdvSqlUrTj/9dFauXMmQIUN47rnnaN26NZMmTeLaa6/lww8/PPg85ULDWsnJyZx++um0bduWFi1a8OmnnwbyfUnB+uUXaNky6CgkkkqUsFru226z8swVK2DDBvjiC/j7363l46efWrlJu3Y20t2nT3t694ZBg6wl4fr1QX8XUlzo//4we/VVuPlmm5jz2WdQu3bQEYnkze23w+zZWd+3f39pSpTI+3O2bm0LOB3OkCFDqFKlCrt376ZDhw706NGDvn37MnHiRBo0aMCWLVuoUqUKffr0oWrVqtx9990AvPnmm1k+X1xcHJ988gkVKlRg06ZNdOrUie7du+PUD67I2ratJGvWqF67OKpWDc491zawLmArVlj5yZw5MGHCX3z/fTmGDk17TI0atrJlixZw3HHWDaVpU03ClPBSsh0mBw7AfffBM89Y+cjw4aoZE8mrF198kU8++QSAP/74g8GDB3PqqafSoEEDAKpUqZKn5/Pe88ADDzBx4kRiYmJYvXo169evp2bNmmGPXaLDihV24NXItjhnky4bNoRevSAp6RcSExPZvNlKUObMSdteecXqwlNVq5aWeKdPwuvVU3mS5J1+ZcIgORmuvho++QRuuslG8PRhlMIqpxHoHTt2U758+Yi8blJSEt9++y1Tp06lTJkyJCYm0rp1axYtWnTYx5YsWZIDofWfDxw4wN69ewEYOnQoGzduZObMmcTGxpKQkMCe9H9RpchZtszaPWlkW7JTtSqcdpptqfbvh99/t4YGixbZtnCh/V3/3//S9itZEhISLIE/5phDLzXIJllRSniEli+HHj1gwQLrE3rbbVqxTCQ/tm3bRuXKlSlTpgyLFi1i2rRp7Nmzh4kTJ7JixYoMZSTly5dnx44dBx+bkJDAzJkz6dWrF2PGjCElJeXgc1avXp3Y2Fi+++47fvvtt6C+PSkgK1aUJT4edPJC8qJECVtwrkGDtDKUVJs2WfK9eDEsW2bb8uU2KXPr1oz7Vq9uz1GvnnVJqVcv41ajRsF9TxI9lGwfgQkT4NJLrS7s6681EVLkSHTr1o3XXnuN4447jiZNmtCpUyeqVavG4MGDueiiizhw4ADVq1dn3LhxdOvWjWuvvZZPP/2Ul156ib59+9KjRw9atWpFt27dKBtqZn/llVdywQUX0KJFC9q3b0/Tpk0D/i4l0pYtK0eLFhr0kPCJj8/YCSW9rVst8V6+PC0RX7HCylS++AJ27864f2wsVK16Ao0aWfJdt679Y5i61apllxUr6ne4KFGynQ/798OTT8Ijj0CTJjbj+dhjg45KpHA76qijGDt2bJb3nXPOORm+btSoEXPnzs1w27Rp0w5ef+qppwCIj49n6tSpWT6nemwXPQcOwMqVZTn77KAjkeKicmXrdtKu3aH3eQ9bttiaG+m3GTO2s3dvaaZOhdWrIVT1lsFRR2VMwlO3GjWsDCY+3raqVW2Li4v89yr5p2Q7j9asgauuslHtyy6zpvoVKgQdlYiILF8Oe/aUUL22RAXn0pLh1q3Tbk9KWkhiotWTeA9//gnr1tm2dm3a9dRt+XKYMgU2bsz+tcqWzZiAZ07GK1Wy0fL0lzt3lsB7jaAXBCXbueQ9vP8+3HGHnRZ680247jr9koqIRIvUZdrViUQKC+dsdLxyZet6kpOUFKsf37w542VWty1bZpfbtuX0jKcQE2MDhpUqZZ2QV6gA5cvbxM/DbaVLKyfKTtQn2865bsALQAngDe/9kwUdw+LFcOut1gS/UycYMuTwHwoREcko0sfzuXPBOU/z5vqLL0VPbKzVdNeqlfvHpKRYKcu2bbb9+adt27bBzJnLiI8/5uDXqfetWJG2z/btNtiYG85lnYSXKWOJePotLi7t+urVdVm0KOd90t9WqpSV2eRnzYegRHWy7ZwrAbwCnAmsAqY758Z47xcUxOv//jv86182il26NLz0EgwYULh+wCK55b3XYi9h5HP7F6qYKIjj+S+/QJ06uylTpky4nlKkUIuNtTrvrLqgHHvsHyQmHpPj4723s/nJyXnfdu60y61brTxm9+5DNztM5m/SW0yMJd2pyfeRXK5dm0DnzvZ+RUJUJ9tAR2Cp9345gHNuONADiFiyvXs3fPstvPWWTXwsUQJuvBEeesha+ogURXFxcWzevJmqVasq4Q4D7z2bN28mTrOW0ov48XzuXGjYcCegZFskHJyzkekyZcKfA3lvk0PHjfuBdu1OzjIZ37Mn49d//WXb3r2Hv0y9vmePjdLn/JgEslmIOCyiPdmuA/yR7utVwAnhevK9u/fzxjWTWLoqmY9LzWHu6nim/16dXXtjqVp2N/eevoABJ/9C/SrJMDJcr5q9OkuWwLx5kX+hKI9BcRR8HHVLlmRVkyZsLFMmx6K7lJQUYiP1r38eREMcKSkpxFaunO37FRcXR926dQs4qqgW0eP5rh37Wbo0hm5VZsDLy8L1tPkWDceOaIhBcSiO7DjgKKDJkiXUWjk7dw8qGdrKhjeWX39dQgmexSrcwi/ak+3Dcs71A/oB1KhRg6SkpFw/dv/ufdw0yppjl2MHxzOP6/mI8/mcxJ1JlBqXAuMiEXXWGhXcS2UrGmIAxZFZpOOIBRpE+DWKou+/+QafQ9KvRXTy5kiO5/t27eNb/2/q//g7/Bh8sh0Nx45oiAEUR2aKI6NoiKMx8P0F5+d4PD8S0Z5srwbqpfu6bui2g7z3g4HBAO3bt/eJiYm5f3bvWTd/MwsWTOG0xBOxH3kj4IojizqfJk+eTOfOnQN57WiKQXEojsIQx+TJk+lyxhmafp97ET+es7E1kydP5lj9jkZNDIpDcRSGOCJ9PI/2ZHs60Mg51wA7KF9GODNh56jRrCoLN5S3hpQBS6lYMfA4oiEGxaE4CkMcKVriLa8ifjwnPj4qfjcgin5H9V4oDsWRuxgieDyP6mTbe7/POXcz8DVWSDPEez8/4LBERCSPdDwXkeLKFaX2VM65jUB+iiTjgU1hDic/oiGOaIgBFEdmiiOjaIgjvzEc7b2vFu5gihodz4tMDKA4MlMcGUVDHBE9nhepZDu/nHMzvPftFUd0xKA4FEdhiCMaYpBDRcvPJRriiIYYFIfiKAxxRDqGmEg9sYiIiIhIcadkW0REREQkQpRsm8FBBxASDXFEQwygODJTHBlFQxzREIMcKlp+LtEQRzTEAIojM8WRUTTEEdEYVLMtIiIiIhIhGtkWEREREYmQYpNsO+e6OecWO+eWOufuz+L+o5xzI0L3/+icS4hADPWcc9855xY45+Y7527LYp9E59w259zs0PZwuOMIvc5K59wvodeYkcX9zjn3Yuj9mOucaxuBGJqk+z5nO+e2O+duz7RPRN4P59wQ59wG59y8dLdVcc6Nc84tCV1Wzuax14T2WeKcuyYCcQxyzi0Kve+fOOcqZfPYHH+GYYjjUefc6nTv/bnZPDbHz1YY4hiRLoaVzrnZ2Tw2LO9Hdp/TIH4/JGs6nh/yOjqe63h+uDh0PA/yeO69L/IbtoDCMqAhUAqYAzTLtM+NwGuh65cBIyIQRy2gbeh6eeDXLOJIBD4vgPdkJRCfw/3nAmMBB3QCfiyAn9E6rGdlxN8P4FSgLTAv3W1PA/eHrt8PPJXF46oAy0OXlUPXK4c5jrOAkqHrT2UVR25+hmGI41Hg7lz83HL8bB1pHJnu/w/wcCTfj+w+p0H8fmjL3++cjueH3K/juY7nOp4HeDwvLiPbHYGl3vvl3vu9wHCgR6Z9egDvhK5/CJzuXHjX7vTer/Xezwpd3wEsBOqE8zXCqAfwrjfTgErOuVoRfL3TgWXe+/wsYpFn3vuJwJZMN6f/HXgHuDCLh54NjPPeb/HebwXGAd3CGYf3/hvv/b7Ql9OAuvl9/iOJI5dy89kKSxyhz2MvYFh+nz+XMWT3OS3w3w/Jko7neafjuY7nuaHjeUZh+/0oLsl2HeCPdF+v4tCD4sF9Qh+MbUDVSAUUOq3ZBvgxi7tPdM7Ncc6Ndc41j1AIHvjGOTfTOdcvi/tz856F02Vk/6EriPcDoIb3fm3o+jqgRhb7FPT70gcbkcrK4X6G4XBz6PTnkGxOsxXk+3EKsN57vySb+8P+fmT6nEbj70dxpOP5oXQ8P1Q0fl51PE9TrI7nxSXZjirOuXLAR8Dt3vvtme6ehZ16awW8BIyOUBgne+/bAucANznnTo3Q6xyWc64U0B0YlcXdBfV+ZODtHFKgrXqccw8C+4Ch2ewS6Z/hq8AxQGtgLXbKL0iXk/MoSFjfj5w+p9Hw+yHRQcfzjHQ8z5qO54coVsfz4pJsrwbqpfu6bui2LPdxzpUEKgKbwx2Icy4W+4EP9d5/nPl+7/12731y6PqXQKxzLj7ccXjvV4cuNwCfYKeP0svNexYu5wCzvPfrs4izQN6PkPWpp1ZDlxuy2KdA3hfn3LXA+cCVoQPBIXLxMzwi3vv13vv93vsDwP+yef6Cej9KAhcBI7LbJ5zvRzaf06j5/SjmdDw/9HV0PD9U1HxedTzPqDgez4tLsj0daOScaxD6r/syYEymfcYAqTNNLwEmZPehyK9QjdKbwELv/bPZ7FMztbbQOdcR+xmF9Y+Ec66sc6586nVsAse8TLuNAa52phOwLd0pl3DL9j/cgng/0kn/O3AN8GkW+3wNnOWcqxw6DXdW6Lawcc51A+4Funvvd2WzT25+hkcaR/qazp7ZPH9uPlvhcAawyHu/Kqs7w/l+5PA5jYrfD9HxPNNr6Hietaj4vOp4nqXidzz3YZj5Whg2bDb2r9hM2wdDt/0D+wAAxGGnvZYCPwENIxDDydipirnA7NB2LtAf6B/a52ZgPjYLeBpwUgTiaBh6/jmh10p9P9LH4YBXQu/XL0D7CP1cymIH24rpbov4+4H9MVgLpGB1WNdjNZ3jgSXAt0CV0L7tgTfSPbZP6PdkKXBdBOJYitWJpf6OpHZVqA18mdPPMMxxvBf62c/FDky1MseR3WcrnHGEbn879Xci3b4ReT9y+JwW+O+Htmx/Rjqep8Wh47mO57mJQ8fzAI/nRWoFyfj4eJ+QkJDnx+3cuZOyZcuGP6BCGEc0xKA4FEdhiCO/McycOXOT975aBEIqUnQ8LxoxKA7FURjiiPjxPBz/VUbL1q5dO58f3333Xb4eF27REEc0xOC94shMcWQUDXHkNwZgho+C42W0bzqeF40YvFccmSmOjKIhjkgfz4tLzbaIiIiISIErGXQAUnzs2AGrVsGGDbBpE2zcaNumTZCcDDt3wq5dtq1d24ajjkp7rE9X7RQbC6VLZ9zKlIEKFaBKFduqVk27Hh8PtWpBqVIF/z2LSPBWr4Ybb4R9++D556FRo6AjEpHiRMm2hNW2bTB/vm2LFsHKlfDbb3a5OZs55xUq2FamDJQta5dlyuynZk1Iv+abc5Z0p6TA7t2wdSusWWPXd++G7dstoc9OtWpQp45ttWvbZf36cMwxttWqBTE61yNS5Fx3HUyaBEcdBV27wpw59o+4iEhBULIt+bZxI/z4o20zZsC8eTZynap0aUhIgKOPhg4d7Hq9elC9uiW+1arZqHNWI85JSXNJTEzMc0x791oSvmWLJfdbtlicq1dbYr56tW3Tp9sIe3pxcdCwoSXexx5ro19//VWR5s0tVhEpfObNg3HjYNAgSEyEE0+Ee+6BN98MOjIRKS6UbEuu/f47jB9v25QpsGKF3V6iBBx/vP0hO/54aN7ctqOPLviR4lKloEYN2w5n71744w9Ytsy2pUvTrn/7rY2WQxvuuMOS7dTvq1kzu2zZEipnteCtiESNkSPtOHTNNfY5vvVWeO45uO02+wyLiESakm3J1p49lnR++aUl2L/+arfXqAEnnwwDBsAJJ0C7dlb+UdiUKpVWQpKZ9zYC/sEHcyhZshULFlhpzLvvZixVadAA2ra1rV07aNPGRu5FJDr88IN9LlPPTj34ILz1ll1+9lmwsYlI8aBkWzJITi7BsGHwySeWZO/caYl0YqIl12ecYaO66WupiyLnoG5d6NhxK+mrWby3Upn582H2bJg1y7aPPkrbp25dS77bt7dT1h07Wk26iBSslBSYNg369Uu7rUoVuOMOePhhq91u1Sq4+ESkeFCyLaSkwNdf26jt6NGdSUmBmjWhd2/o2RNOO02dPFI5Z3Xn9epBt25pt//5Z8bke+ZMGDMm7THHH2+Jd+rWuHHR/4dFJGjz51s52IknZrz95puthvvf/4YRI4KJTUSKDyXbxdiiRTB4MAwdapMF4+PhggvWcNdddenUSZ058qJSJRv9Tz8K/uefNnl06lTbRoyw9xtsdK1TJzjlFOjSxUbBY2ODiFyk6FqwwC6bN894e+XKcNNN8NRT8I9/QJMmBR+biBQfSraLmf37YexYePFFm6EfGwvnn2+Th845B6ZMWcpJJ9UNOswioVIlOPts2wAOHLB/cFKT7ylTrFQHrN1h586WeHfpYt1b0vcZF5G8W7TIBg2y6qt9xx3wwgvwxBPw9tsFHpqIFCNKtouJ3but1dVzz8Hy5dZn+vHHoW9fTegrKDEx1smkWTO4/nq7bcMGmDgRvv/etocestvj4uzUd5cu1hd43z7VnIjk1cKF1s4zq39cq1e3498rr8Ajj9hkZxGRSFChQBGXnAzPPGN/SG65xWqxR4ywRWYefFCJdtCqV4dLLoGXXoK5c60n+Mcfww03WL/wxx6DU0+F7t07c8EFdkZi4cKMK2qKSNYWLoTjjsv+/nvvhZIl4Z//LLiYRKT4UbJdRO3aBU8+ab2u77nH+sl+/z1Mngy9eqk+OFrFx9uk1Oefh59/toV5Pv4YzjxzPQsXWm/gZs1sguZ118EHHxy6OI+IWNnWkiU512PXqWPLuL/zTlprUxGRcFOyXcTs3289ZBs3hoEDrRRh2jT45hsbIZXCpXJlS77vuGMJS5daCdDrr9vP9dNP4corre95q1Y2SpeUZN1lRIq79ett4arDlYfcf7+VbT36aIGEJSLFkJLtIuSbb6B1a+jTx0Zsvv8ePv/cFp6RoqFBA+sZPGqUlZxMn27ty6pWtdHw006z0fFLL7V/utatCzpikWD8/rtd1q+f837Vq9sZo+HDYcaMyMclIsWPku0iYNUqS67OPtsmQo4caaPZGsku2kqUsJaBAwfChAlpJSe9elmnkz59oFYt2+eRR6wN4YEDQUctUjBym2wD3HefJd0336zPiIiEn5LtQiwlBZ591iYAff65dReZP98Sby2YUvyUL28lJ//7n/0D9vPP8K9/WSeGxx+3vt41a8LVV9sk2e3bg45YJHLykmxXrGiL3Pz4o50REhEJJyXbhdQvv1h5yF132Qj2/PnWXUS9mQXsn63WreGBB2xS7IYNtnjRWWdZb+/LLrNyk27d4NVXYfXqoCMWCa/ff7d/QCtWzN3+vXvDySdbDfemTZGNTUSKFyXbhcz+/bbqWfv2Nnr54Yc2qt2wYdCRSTSrWhWuuALef98mjv3wg9WpLl9u3Rjq1oWOHW0kfN48tRaUwu/3321UO7dn+ZyD//7Xzvj07avPgIiEj5LtQmTJkrSRlwsusNHsiy9WyYjkTYkStlrloEGweLEtaf3vf9uiOw89BC1a2Ip7d90FkybZP3gihU1qsp0XLVrYP5yjR8Nrr0UmLhEpfpRsFxLDhkHbtpYcffCBdaOoVi3oqKSwc85q/gcOtEm1q1dbktG4Mbz8spUo1axpky2/+AL27tV/dlI4/PGH9aPPqzvvhHPOgVtvhfHjwx+XiBQ/Sraj3O7dtprgFVfYwjRz5sDll2s0WyKjdm37ffvyS6tbHTnSutx8/DGcfz5cdFFneve2kb/du4OOVqKFc66bc26xc26pc+7+LO6/0zm3wDk31zk33jl3dCTjSUmx399atfL+2JgYawPYpImt7vrzz+GPT0SKFyXbUWzZMlu8ZPBga02VlJS/kRqR/Chf3jrbvP++TbAcOxa6dNnI2LHW9aRaNZto+eGHsHNn0NFKUJxzJYBXgHOAZsDlzrlmmXb7GWjvvW8JfAg8HcmYNm60muuaNfP3+AoV7ExOhQpwxhk2yCEikl9KtqPU+PHQoYOdCv3iC1t6XUusS1BKlbLOJffcs5h162DcOOveMGGCJeTVqtn8gWHD1FKwGOoILPXeL/fe7wWGAz3S7+C9/857vyv05TSgbiQDWr/eLmvUyP9zHH00fPcdlCkDXbtamZWISH4o2Y4y3lut7Nln2yn96dPh3HODjkokTWysjfa99hqsXWtnXK6/HqZOtXKnatWge3d4913488+go5UCUAf4I93Xq0K3Zed6YGwkA0pdOfVIkm2wLk/ffw9VqljCPWbMkccmIsVPyaADkDT79jn697eykQsusNP3FSoEHZVI9kqUgC5dbHvhBUu4P/wQPvoIPvssbUT8ssvsd7pcuaAjliA553oD7YEu2dzfD+gHUKNGDZKSkvL8GsnJyfzwwyKgKStXTmPv3j35Dzhk0KBYBg5sQc+e5RkwYBkXX7zqsPNmkpOT8xV/OEVDDIpDcRSGOCIdg5LtKLFzJzz00PH8+KO19vvXv2yijkhhERNjLQU7d7aVTX/6ySZYjhxpI4KlS9sky8sus24PpUsHHbGEyWog/WySuqHbMnDOnQE8CHTx3v+V1RN57wcDgwHat2/vExMT8xxMUlISlSs3BaBHj06ULZvnp8jSmWda6dQrrxzL9u3H8vrrOf8OJyUlkZ/4wykaYlAciqMwxBHpGJTORYFNm+D002H69Cq8/jo88YQSbSncnLMVTv/zH/jtN+vX3aePnZK/+GI7vX/11db1ZO/eoKOVIzQdaOSca+CcKwVcBmQouHDOtQFeB7p77zdEOqB166BsWcKWaIM910cfwWOPwXvvwSmnpC0JLyKSE6V0AfvtN1uoZs4ceOyx+fTrF3REIuEVE2O/4y+/bH28x42DXr1s5dPzzrOOEX372qRgLaBT+Hjv9wE3A18DC4GR3vv5zrl/OOe6h3YbBJQDRjnnZjvnIlr9vH59/juR5CQmBh5+GD79FH79FVq3tjaYIiI5CSzZzkVf1mudcxtDB+bZzrn/CyLOSPr1Vzvlvn69JSAnn7wp6JBEIqpkSZtc+cYbNvqYmnAPH26316kDt9xiy8kfOBB0tJJb3vsvvfeNvffHeO//FbrtYe/9mND1M7z3Nbz3rUNb95yf8cisW3fkkyNz0r07zJxpEyh79rTf2T1HXhouIkVUIMl2LvuyAoxId3B+o0CDjLBFiyAx0U6hT5xoI38ixUmpUpZov/ee9fH+8ENbsfKNN+wUfUKC9ZefOzfoSKWwidTIdnqNGsGUKbbi5MsvQ6dOtsKviEhmQY1sH7Yva1G2YIEl2gcOWNu0Fi2CjkgkWKVLWy33yJGWeA8daiumPvsstGpl1596yvrOixzO+vWRHdlOVaqUzUv4/HMrkWrbFl55RWdlRCSjoJLt3PZlvTi0vO+HzrkisXbivHmWaDtniXazrMbzRYqx8uWtX/fnn1sf71desdvuvx/q17fPz+ef12Lr1qAjlWi0b59j8+aCSbZTnXcezJ5tZ2RuvtkmvK9ZE1dwAYhIVIvm1n+fAcO89385524A3gG6Zt4pXH1ZC6LH4+rVcdx6axucg2eemc26dbsPLr5QkHHkJBpiUByKI71mzawV5po1cYwfX4Nvv63O99834cUXD9Cp02ZOP309J564hVKlCnY4MVp+JuHknLsA+MJ7X2jHZrdutaV2CzLZBptvMHYsDBlipSXXX9+BrVthwAB1lxIp7oJKtg/bl9V7vzndl28AT2f1ROHqyxrpHo9r1ljrM7Aa7WbNTggkjsOJhhgUh+LIzhVX2Cqr//vfDBYtas+wYdWYNKkaFStaGUrv3rbATkEkN0G/FxHyN+B559xHwBDv/aKgA8qrbdtKAbaSaUFzzlZTPessuPjibdx8cxVGjYLXX4cmTQo+HhGJDkf8J8k5d4tzrnIeH5abvqy10n3ZHWspVSht2WIH340bbeRDpSMi+eccNG6czLPPwqpV8M03cOGFMGqULaldvz7cc4+d1vc+6GgLF+99b6ANsAx42zk31TnXzzlXPuDQcm3bNhtDqlo1uBjq1YOnnprLG2/Y72HLlvD3v8Pu3cHFJCLBCcf4Tw1gunNuZKid32EWsc11X9ZbnXPznXNzgFuBa8MQa4HbuRPOPReWLLHerB07Bh2RSNFRooSt7Pf229bubfhwm6T2/PPQpo1NPn7ySU2szAvv/XbgQ2ziei2gJzDLOXdLoIHl0vbtVkYSHx9sHKmj3IsXW1/5xx+H5s1tIScRKV6OONn23j8ENALexBLiJc65fzvnjjnM4w7Xl3Wg9765976V9/60wng6c/9+O+09fbolAV0PqTgXkXApUwb+9jdbGn7tWvjvf6FSJRg4EI4+2vp4v/suJCcHHWn0cs51d859AiQBsUBH7/05QCvgriBjy63UZDvIke30atSw9pbffQdxcTaZskcPtQkUKU7CUtnovffAutC2D6gMfOicy7LOuri49177w//CC7bwgYgUjPh4m5j2ww+wdCk88gisXAnXXGPJz1VX2UJSWrHyEMOAZ733Lbz3g1KXVvfe7wKuDza03Im2ZDtVYqKVlDz5pCXexx8Pt90Gmzcf9qEiUsiFo2b7NufcTGwC42Sghfd+ANAOuPhIn7+weuK1+F0AACAASURBVO016xF8yy3WCkpEgnHMMZZsL1kCkydbov355zaPon59+6d43rygo4wag4DXnHOTnHM3O+cO9vTw3o8PMK5c2769JOXKWQ/saFOqlC3UtHQp/N//2WI4xx5rvbr/+ivo6EQkUsIxsl0FuMh7f7b3fpT3PgUg1Drq/DA8f6Hz9deWYJ93Hjz3XNDRiAhYDe1JJ9k/wmvX2oTKdu3sM9qiRVqt9/r1QUcaHO/9o9775sBNWL329865bwMOK0+2bYuNulHtzKpXh1dftdVRTzwR7r7bJs4PG6YFcUSKonDUbD/ivf8tm/sKbQeR/Fq61OpGjz/eDpwlSgQdkYhkFhcHl1xiZV5r1sCLL9pn9Y47rF/y+efDiBHFunvEBqwscDNQPeBY8mT79uhPtlOlTpj8+msoW9bm+LRqBZ98ok46IkWJWu2H0a5d1uu3RAkYPdpWvROR6FatmpV7TZ8OCxZYWcmcOXDZZVCzJvTtC5MmFY8RR+fcjc65JGA8UBXo671vGWxUeVMYRrYzO+ssq+cePhxSUuCii6B9e/jiCyXdIkWBku0w8R769YNffoGhQyEhIeiIRCSvjjsO/v1v+O03GD/eJjYPHw6nnmq13w8/bLXfRVg94PZQJ6hHvfcLgg4orwrTyHZ6MTF2VnTePHjnHfjzTzvD0ratnWXZty/oCEUkv5Rsh8krr1iS/dhj0K1b0NGIyJGIibFWnan9u99/Hxo3tmXjGze22u8xY2qza1fQkYZXqOXq7KDjOBLbt5cMvMf2kShZEq6+GhYtsqXf9+yxsyxNm9p8gz17go5QRPJKyXYYzJoFd95poxAPPhh0NCISTmXLwpVXWl3t77/D00/Djh3w6qvHFIvSksJk3z5ITi6cI9uZxcbCddfB/PlWw121qrWzTEiw9oF//hl0hCKSW0q2j9DOnTappVo1GwWL0TsqUmTVqWNLwc+dC++88xPlygUdkaS3datdFoVkO1VMDFx4IUybBhMm2ATKgQPtd3HAAJtnICLRTanhEbrzTvj1V1uZrigd4EUke85B9epqjBxtUheIKYrHYufgtNPsDMusWVbf/dZb1tHk9NNtUr4WaRKJTkq2j8Do0TB4sPVIPf30oKMRESneinKynV6bNlbPvWoVPPGETdrt2dNKTB55xCb4ikj0ULKdT1u2QP/+0Lo1PP540NGIiEhxSbZTxcfD/ffD8uXw0Ue2vsM//wkNGsDZZ0NSUjX27g06ShFRsp1Pd90FmzbZabxoXBZYRKS42bTJLotLsp2qZEnrzT12LKxcaaPbCxfCY481p3Ztq+3+4Yfi0SteJBop2c6HceNsMuR999nItoiIBC91ZLswt/47UvXrW7K9YgU89dRczjzT+nafcoqNeN9/v60HISIFR8l2Hu3caYvXNGkCf/970NGIiEiqzZuhZMkD6hKDrWTcseMWhg2DDRvgvfdsMuUzz0DLltCihdV7//pr0JGKFH1KtvPo2WftNN3gwRAXF3Q0IiKSavNmqFAhBeeCjiS6lCsHvXvDl1/C2rXw8stQoQI88IANHDVrZu0Ef/xRpSYikaBkOw/Wr7cFLXr2tOWbRUQkeliyrXXNc1KtGtx0E0yebF1LXnwRateGQYOgUyeoW9dqvL/+Gk2uFAkTJdt58NhjtlTuk08GHYmIiGSWOrItuVO/PtxyC3z7bVqpSefOdtmtm0007dHDRsJ//RW8DzpikcKpZNABFBaLF1vpSP/+0Lhx0NGIiEhmmzdDlSpKtvOjShUrNend2waVxo+Hzz+3hgBjxtg+Rx8NZ54JZ51la0tUqRJszCKFhUa2c+n++6FMGXj44aAjERGJLs65bs65xc65pc65+7O4/yjn3IjQ/T865xIiEYdGtsMjLg7OOw9effX/2bvzMCmqe//j7+8wbI7INjiyKSCi4o4jLjE4iUrQGDHeaNDcSBITYoy5MctVc801XpdE440mLr8oUeO+xB0TRYnaGi/BCIoCbiyigCwCyiIgA3x/f5wa6ZnpnrW7q2b683qeerq6q7r6Q3XXmUPVqXNg3rww/fGPMGIEPPAAnHpq6PFl5MjQK9fjj4exJ0QkM53ZboJ//COMFnnZZbDzznGnERFJDjPrANwAHAssBl42s0nu/kbaamcCH7n7UDMbB1wJfD2XOdzVZjtfdt89TGedBVu2wMsvw9NPh7Pe11wT7mWC0NvJkUeGbgaPPDKcCRcRVbYb5Q7/+Z/hBpKf/CTuNCIiiTMSmOfuCwDM7D5gLJBe2R4LXBzNPwhcb2bmnrtWwBs2QLdu0KOH7urLp9JSOPzwMP3qV7BxY6h8v/hiODF1771w001h3YEDQ6W7vLw/nTqFcSl22CHe/CJxUGW7EQ8+GLpDuuUWFRIiIhn0BxalPV8MHJptHXffYmZrgN7AylyFKOu8hVVf/g7L5i2DM3bJ1WZbbK9ly+DWW9t9hq7AqGiiD2z9ijHr44G8uGIYL64YxvOPDuODjXtw3XVQYtvYp/tiDu69kMre73Jwr4Uc0PN9upYWpulPEr4T5Uhmjr2WLQv/MyzNT7VYle0GbN4c+h7dd18YPz7uNCIi7ZuZTQAmAFRUVJBKpZr+3upqRv7973Tbto2Ns2fnKWHTJSFHXBn2jKYzAe8OS8p2ZubWA3ml+gBe3bgfT7x7ALfND/3ndmALw0vf5qCOr3NAxznsXfo2w0vfYucOq3KeKwnfiXIkM0e3bdt4/rnn8I4d87J9VbYbcOONMH9+GAigQ4e404iIJNISYGDa8wHRa5nWWWxmpUB3oF5tyt0nAhMBKisrvaqqqnlJPviAVCpFs9+XB0nIkYQMAEtSKU6pquKU6Lk7LFkC06fDjBmlTJ++D0/O2Ic7Ptz+nvLy0AZ8n33CCa+a+d69W54jKftDOZKXI98ZVNnO4uOP4ZJLQvdGY8bEnUZEJLFeBvYws8GESvU44PQ660wCxgP/BL4GPJvL9trStpiFwXMGDICTTgqvucOyZTBnTphmzw6Pd90Fa9duf29FRah07703DB26fRo8GDp3juffI9IYVbazuPLKcGf7b3+Lhv4VEckiaoN9DvAU0AG41d3nmNklwHR3nwTcAtxpZvOA1YQKuchnzKBv3zAdc8z2191h8eL6lfA776xdCTcLN2TWVL533732fFlZ4f9NIjVU2c5g0SL4/e9D5/4jRsSdRkQk2dz9CeCJOq9dlDa/CT5rRSDSZDWV6IEDa19ldoeVK0NTz5q+wGvmH344LEtXUQE9e45g+PCwrQEDaj/265e3e+NEVNnO5IILwoF82WVxJxEREZG6zKBPnzAddlj95WvWbK981zy+/voW3nwz9BG+fn3t9UtKYJddalfAa+b79QvLKipgxx11tVuaT5XtOqZOhXvugV/+Uh3yi4iItEXdu4cr0+lXp1Op16mqqsI9NEFZtCg0UVm0qPb8nDkweTJ88kn97e6wQ6h410wVFWEqLw83b9adyspUORdVtmuproYf/Sj8L/b88+NOIyIiIrlmFirj3buHnk4ycQ8dJSxaFG7cXL48PKbPv/02PP98uL8rm06d6lfAP/10GE89lbly3qMH7LQTdO2qSnp7Eltl28zGAH8g3FBzs7tfUWd5Z+AO4GBCF1Ffd/eF+cx02WXwyivw0EPhUpGIiIgUHzPo2TNM++/f8LrV1bB6dah0Nza99RYsXVrOU0/Bli3Zt9mhQxgRtVu3UPneaaft89kesy3r0kUV97jFUtk2sw7ADcCxhNHGXjazSe6ePrzvmcBH7j7UzMYBVwJfz1emhx6CSy+FM86Ak0/O16eIiIhIe9Kx4/bmJE2RSk3lqKOqWLeufmV8zRpYty40c1m7dvv8unVh2eLFtV9vSgeapaWh0r3DDuGMedeuoQL+6acH0rfv9uc1y9LXac7zmtdUua8vrjPbI4F57r4AwMzuA8YC6ZXtscDF0fyDwPVmZrnsm3XL5m28ctvr3PVQGbc94xy2zzpuPGM2vLgtVx/RLN1nzYr9dugkZFAO5WgLObrPmgWjRoU7q0REmsFs+9nowYNbtg132LChduW7bgU9/XHjxtrT0qWhqczSpbVf37QpPG5rRVWopiJeU/nu3Dk0qck0rV27D/3713+9Q4fMU0lJ9mVNnepuY9as7nktzuP6a9UfWJT2fDFwaLZ1on5c1wC9gTod+rTcxnVbOOz7++OUcBr3cNPs79P1mPWNvzFPDortk7dLQgZQjrqUo7Yk5DgI4PvfD38VREQKzCzcgFlWFvonb65UambWURPdQ/OYuhXwTJXyprxWXQ2bN2+fPv00nKnfvBk++mgHli6tv3zr1tpTfh2U1+I8/lNUrWRmE4AJABUVFaRSqaa/eds2rjvzI/r1+IAhfTez4LMT6fHYuHEjXbt2LfoMyqEcbSHHxo0b2fTiizqzLSLtjtn2M8zdu+f3s1Kpl5s0VPq2bdsr3unzLZnqvv/VV1+jtPSAvP0b46psLwEGpj0fEL2WaZ3FZlYKdCfcKFmLu08EJgJUVlZ6c8e2r/oipFIpDmjm+/IhlUpxWMw5kpBBOZSjLeRIpVJN+gMhIiKtV1ISpo4d87Htj/J63iSuUzIvA3uY2WAz60QYundSnXUmAeOj+a8Bz+ayvbaIiIiISL5ZXPVXMzse+D2h679b3f1yM7sEmO7uk8ysC3AnoWnkamBczQ2VDWzzQ+C9FsQpJ4dtwVshCTmSkAGUoy7lqC0JOVqaYTd375PrMO2NyvN2kwGUoy7lqC0JOfJansdW2U4SM5vu7pXKkYwMyqEcbSFHEjJIfUn5XpKQIwkZlEM52kKOfGfQnT0iIiIiInmiyraIiIiISJ6osh1MjDtAJAk5kpABlKMu5agtCTmSkEHqS8r3koQcScgAylGXctSWhBx5zaA22yIiIiIieaIz2yIiIiIieVI0lW0zG2Nmb5vZPDO7IMPyzmZ2f7T8JTMblIcMA83sOTN7w8zmmNmPM6xTZWZrzGxmNF2U6xzR5yw0s1nRZ0zPsNzM7Npof7xuZiPykGHPtH/nTDNba2bn1lknL/vDzG41sxVmNjvttV5mNsXM5kaPPbO8d3y0zlwzG59pnVbmuMrM3or2+yNm1iPLexv8DnOQ42IzW5K274/P8t4Gj60c5Lg/LcNCM5uZ5b052R/ZjtM4fh+Smcrzep+j8lzleWM5VJ7HWZ67e7ufCH15zweGAJ2A14DhddY5G7gxmh8H3J+HHH2BEdF8N+CdDDmqgL8WYJ8sBMobWH488CRgwGHASwX4jpYR+qzM+/4ARgEjgNlpr/0WuCCavwC4MsP7egELosee0XzPHOcYDZRG81dmytGU7zAHOS4Gft6E763BY6u1Oeos/x1wUT73R7bjNI7fh6aW/eZUntdbrvJc5bnK8xjL82I5sz0SmOfuC9x9M3AfMLbOOmOB26P5B4GjzcxyGcLdl7r7K9H8OuBNoH8uPyOHxgJ3eDAN6GFmffP4eUcD8929JYNYNJu7v0AYLCld+m/gduCkDG/9EjDF3Ve7+0fAFGBMLnO4+9PuviV6Og0Y0NLttyZHEzXl2MpJjuh4PBW4t6Xbb2KGbMdpwX8fkpHK8+ZTea7yvClUnteWs99HsVS2+wOL0p4vpn6h+Nk60YGxBuidr0DRZc2DgJcyLD7czF4zsyfNbJ88RXDgaTObYWYTMixvyj7LpXFkP+gKsT8AKtx9aTS/DKjIsE6h98t3CGekMmnsO8yFc6LLn7dmucxWyP3xeWC5u8/Nsjzn+6POcZrE30cxUnlen8rz+pJ4vKo8366oyvNiqWwnipntCDwEnOvua+ssfoVw6e0A4Drg0TzFONLdRwDHAT80s1F5+pxGmVkn4ETggQyLC7U/avFwDSnWrnrM7EJgC3B3llXy/R3+EdgdOBBYSrjkF6fTaPgsSE73R0PHaRJ+H5IMKs9rU3memcrzeoqqPC+WyvYSYGDa8wHRaxnXMbNSoDuwKtdBzKwj4Qu/290frrvc3de6+/po/gmgo5mV5zqHuy+JHlcAjxAuH6Vryj7LleOAV9x9eYacBdkfkeU1l1ajxxUZ1inIfjGzbwEnAN+ICoJ6mvAdtoq7L3f3re6+DfhTlu0Xan+UAicD92dbJ5f7I8txmpjfR5FTeV7/c1Se15eY41XleW3FWJ4XS2X7ZWAPMxsc/a97HDCpzjqTgJo7Tb8GPJvtoGipqI3SLcCb7n51lnV2qWlbaGYjCd9RTv9ImFmZmXWrmSfcwDG7zmqTgDMsOAxYk3bJJdey/g+3EPsjTfpvYDzwWIZ1ngJGm1nP6DLc6Oi1nDGzMcB5wInuviHLOk35DlubI71N51ezbL8px1YuHAO85e6LMy3M5f5o4DhNxO9DVJ7X+QyV55kl4nhVeZ5R8ZXnnoM7X9vCRLgb+x3CnbYXRq9dQjgAALoQLnvNA/4FDMlDhiMJlypeB2ZG0/HAWcBZ0TrnAHMIdwFPA47IQ44h0fZfiz6rZn+k5zDghmh/zQIq8/S9lBEK2+5pr+V9fxD+GCwFqgntsM4ktOl8BpgL/B3oFa1bCdyc9t7vRL+TecC385BjHqGdWM1vpKZXhX7AEw19hznOcWf03b9OKJj61s2R7djKZY7o9dtqfhNp6+ZlfzRwnBb896Ep63ek8nx7DpXnKs+bkkPleYzluUaQFBERERHJk9K4A+RSeXm5Dxo0qNnv++STTygrK8t9oDaYIwkZlEM52kKOlmaYMWPGSnfvk4dI7YrK8/aRQTmUoy3kyHt5notLODm4BHQroXF6egfsvQh9Gs6NHhvtSPzggw/2lnjuueda9L5cS0KOJGRwV466lKO2JORoaQZguieg3E36pPK8fWRwV466lKO2JOTId3melDPbtwHXA3ekvXYB8Iy7X2FhyNALgPNjyJbV5s3w/vuwYAG8+26YPv4YtmwJU0kJ7LQTdO8OvXrBoEEweDAMGQI77hh3ehGR4rJpE9x5J0ybFsrhCROgj64xiEieJaKy7e4vRJ2NpxtLGNoVwug+KQpc2XaHZcu2V6bTK9ULFsCSJbBt2/b1O3aEnj3DY2kpbN0Ka9eGqa5hw6CyMkyjRsGBBxbu3yUiUmxWrIDjj4cZM0IFe+VKuPpqeOwxOPLIuNOJSHuWiMp2Fk0Z3adVqqvhjjvgtdf6M20arFsHH3wAixbB4sXw3nvhTEi6fv3C2emqqu1nqQcPDlO/ftChQ/3P2bYNVq2ChQtDRf3tt+GVV+CFF+Cee8I6vXrBvvvuw2mnwejRYbsiItJ61dXwb/8Gb7wBDz0EX/0qvPkmnHxyqIC/9BLsvXfcKUWkvUpyZfsz7u5mlrHblGgYzwkAFRUVpFKpJm+3utr47nePAvYAoKTE6dVrMzvvvIlddvmUAw74lL59N9K37yb69t3ELrtsolOnbfW2s20bzJ8fpsbsvHOYPv/58Hzlyk68+moPXnmlJ9On9+AHPwiv77bbJxx22CoOP3wV++67lg4dCtNrzPr165u1D5VDOYo1RxIySNNccw28+CLcfXeoYAMMHw5TpoSri6eeGk6AdOwYb04RaZ+SXNlebmZ93X1pA6P74O4TgYkAlZWVXlVV1awPee89ePXVFxk9+ki6dDHMOgOdWxm9eb72tfD43HMp+vWrYvJk+Otfy3j44TLuv39XevaEMWPghBPCY69e+cuSSqVo7j5UDuUoxhxJyCCNW74cLr0UTjwRTj+99rKBA+FPf4KxY0OTkvMTdVeQiLQXSR5Bsimj+7TarrtC9+5b6NoVwrhW8TGDPfeEH/84nHFZuRIefDD8Ifj73+Eb3whtDUeNgv/9X3jnnXjziogk3fXXwyefwG9/m3n5iSeG6fLLYfXqwmYTkeKQiMq2md0L/BPY08wWm9mZwBXAsWY2lzC05xVxZozDTjuFdoZ//nO4UXPaNPiv/wo3XP7nf4aK+d57h7MxU6eGGzJFRCTYsAH++MdQmd5zz+zrXX55uGfnmmsKl01EikciKtvufpq793X3ju4+wN1vcfdV7n60u+/h7se4e1GfcygpgUMPDZdDZ84MN1teey0MGBAuf37uc9C3L5x5Zri7fsOGuBOLiMTrwQfDzek/+UnD6+27L5xyCvzhD5l7jxIRaY1EVLal+XbbDX70o9Dc5MMP4d574eijwx+Xk06C3r3D2Zybbw5tFkVEis0994TxDUaNanzd884LZ7fvvDPvsUSkyKiy3Q706AHjxoUK94cfhvbd3/sevP56eOzbFw4/HK64InR95YXp2EREJDY1ZeFppzXtfpzKSjjkELjhBpWRIpJbqmy3M506hTPc114b+vSeORP+53/CiJa/+AXssw/ssQf87Gfw/PPhdRGR9ubBB8N9LKed1vT3nH126H/7+efzl0tEio8q2+2YGRxwAPz3f8PLL4fBev74x1DZvv76MDBPRQWccUb4w7RuXdyJRURy4/HHQ1m3335Nf8/Xvx5uTL/99vzlEpHio8p2ERkwAM46C558MnQr+MAD8OUvw9/+Fm4OKi+H88/fjxtvDEPRi4i0RRs3wnPPwXHHNe99XbuGHqAeeihsQ0QkF1TZLlLduoXBdO64I9xAmUrBOefA4sU78IMfhIr5IYeE3k9ef11tGEWk7Xj+edi0qfmVbYB///dwle/xx3OfS0SKkyrbQmkpHHUU/O53cNddLzFnDvz61+H1X/0qNEUZPBj+4z/gmWegujruxCIi2T35JHTpEsq15jrqKOjXLwztLiKSC6psSy1mMHx4uJnyn/+EDz4Iwxnvv394POaYMIrl6afDfffBmjVxJxYRqe2pp+ALXwjNQpqrQ4dwU+UTT8BHH+U+m4gUH1W2pUG77ALf/S5MmhTaeT/6aGjTWNOlVnk5HHtsuOHyvffiTisixW716k68/TZ88Yst38bXvhZ6anriidzlEpHipcq2NFlZGYwdC7fcAkuXwv/9H/z0p7B4cRhgZ9AgOPDA0PRkxgy18xaRwps1qzsAn/98y7cxcmQYn+CRR3IUSkSKmirb0iIdOsARR8CVV4Z+ad9+G666KnSbddllYYCIgQNDv7WTJ8Onn8adWESKwWuvdWeHHWDEiJZvo6QknFh48kn1SiIirafKtuTEsGHw85/DCy/AsmVw223h7NDtt4ceAcrLQ/eCd90Fq1fHnVZE2qtZs7pz+OHQsWPrtvPVr8KGDaHJnIhIa6iyLTnXpw+MHw8PPwyrVsFf/xpuqHzxRfjmN2HnncOAOtdcA/Pnx51WRNqLjz+G+fN3ZNSo1m+rqgq6d1dTEhFpPVW2Ja+6dAkD59x0Uxgo56WX4Pzzw9ntn/4Uhg4NQ8j/13/BtGmwbVvciUWkucxsjJm9bWbzzOyCDMs7m9n90fKXzGxQPnJMnQru1qr22jU6dQpl1+OPh2HfRURaSpVtKZiSktC05PLLw0A58+fD738fejz57W/h8MND/7bf+x5MndqbDRviTiwijTGzDsANwHHAcOA0MxteZ7UzgY/cfShwDXBlPrK88AKUlm7j0ENzs70TTgi9ME2fnpvtiUhxUmVbYjNkCPz4x2GgnA8/DINIVFXBX/4CF164H+Xl4SalW28No1yKSCKNBOa5+wJ33wzcB4yts85Y4PZo/kHgaDOzXAf5xz9gzz3XscMOudne6NHhJMGTT+ZmeyJSnErjDiAC0LNnaNd9+umweTNce+1rvPfeAUyaFPr4NoPDDguV7xNPhL32Cq+JSOz6A4vSni8G6p5b/mwdd99iZmuA3sDKXIXYuG4LL0+D7+z9D7joXznZZm/g0H7f5Yk/lXDxtonNeu+ghQvh2WdzkqOlkpBBOZSjLeQYtHAhHHlkGDo7D1TZlsTp1AkqKz/i5z+Ha6+F117js0r3BReEaejQ7RXvI47I2/EhIgVkZhOACQAVFRWkUqkmv3fz+q3cvO129p/zOv7G6znLNMbhYi5m+aU3sbN92OT37QbEPdRAEjKActSlHLUlIcduwPPf/Cbe2m6MslAVRRLNLAyUc+CBcNFFYQCdxx8PFe/rroPf/Q569Qo3Mo0dGy77dusWd2qRorIEGJj2fED0WqZ1FptZKdAdWFV3Q+4+EZgIUFlZ6VVVVc1L4keTSqWw5r6vAV+eAb+qhKfvWM43v9n096VSKZqdP8eSkEE5lKMt5Mh3BrXZljZlwAD4wQ9CG8qVK+GBB0JF+29/C0Msl5eHfr1vvDH0fiIiefcysIeZDTazTsA4YFKddSYB46P5rwHPureNMWYPOih0V6p22yLt05Yt8MYb+T1Lp8q2tFnduoUK9h13hBsoUyk45xyYOzdUyAcMCCNZXnppaIrSNv60i7Qt7r4FOAd4CngT+Iu7zzGzS8zsxGi1W4DeZjYP+ClQr3vApCopCf+Bf+opdQEo0t5MmwYHHADnnnsQH3yQv89RZVvahdJSOOqo0Kxk7lyYMwd+85vQ/vtXvwrNUAYNgh/9KIwIt3lz3IlF2g93f8Ldh7n77u5+efTaRe4+KZrf5O6nuPtQdx/p7gviTdw8xx0Xxgb4V27uuxSRmG3bBv/93/C5z8H69XDRRW/Qt2/+Pk+VbWl3zGD48HAj5dSpsHQp3HxzqHDfcgsce2wY5XLcOLj33jDqnIhINjVdAD7xRNxJRKS1Nm2CU0+Fyy6DM86AWbPgyCNX5rWHM1W2pd2rqIAzz4THHgvtvB97DE45BZ57LnQ12KcPHH106Pnk3XfjTisiSdOzZxh0a/LkuJOISGtUV4eK9kMPhSvht94KO+2U/89VZVuKyg47hO4Cb745nPGeOhV+/nNYtiwMsDNkCOy/P/zyl/Dyyxo+XkSCMWPCSJIrVsSdRERawh2+//3Qo9n118NPf1q48ToSX9k2s4VmNsvMZpqZBs2VnCkpCWerfvOb0MZ77tztXQn+5jdhaPlTTz2c738/XD7etCnuxCItZ2a3mNmBdV67OKY4bc5xdKFD3gAAIABJREFUx4XHp5+ON4eItMwtt8Cf/xxOpv3wh4X97MRXtiNfcPcD3b0y7iDSfg0dGv6nm0qFs1d33AH77ruGe+4J3QuWl8PJJ8Ptt4fmKCJtzJeA283sjLTXTsy2stRW0wWgmpKItD1vvx06SDj2WLj44sJ/fk4r22b2jJkdX+e15o1xK5IAvXvDN78JF1/8BitXhj52zzgj9EbwrW+FduCf/zxcdRW8807caUWaZAUwCjjFzG6IBpcp0EXUtq+kBL70pdAFoJqXibQd7nDWWdClSziJ1qFD4TPk+sz2YOB8M/tV2mutPRvtwNNmNiMaylekoDp3Du01/9//g0WLYMaMcBlq/Xo47zzYc0/Ya68w/3//p754JbncfY27fwX4EEgRRnKUJhozJlzVmq4GjSJtxj33hCvWV1wBu+wST4ZcD9f+MXA0cK2ZPQ78ew62eaS7LzGznYEpZvaWu79QszCqgE8AqKioIJVKNfsD1q9f36L35VoSciQhQ1vI8YUvhGn58s5MnVrO1Km9ueaaHlx1VQndu2/m8MNX8bnPreLgg1fTtWvrT4MlfX8UY44kZGimPc2sn7t/4O4Xm9kM4Cdxh2pLRo8ON1RNnhzu6RCRZNu8OfSnPWIEfO978eXIdWXbotHEzjazbwEvAj1bs0F3XxI9rjCzR4CRwAtpyycCEwEqKyu9JWPbp1IpWvK+XEtCjiRkaGs5vv718LhmTfgjPGlSJ554oi+TJ/elc2c45pjQA8pXvkKLO81vS/ujWHIkIUMzXUU4YbEauB94wN2/GHOmNqW8HA45JDQru+iiuNOISGNuvTV06XvDDaEpWFxy/dE31sy4+23At4AW37ttZmVm1q1mHhgNzG5dRJH86N49VLzvvjvcYPnss6Gd2Jw5obuhfv3g0EPh8sth9mwNHy+F5e4Xu/s+wA+BvsDzZvb3mGO1OccdF+7dWLUq7iQi0pAtW0LPYkccEZqAxSmnlW13v6nO8xnu/p1WbLICeNHMXgP+BfzN3XUvuCRex46hmcnvfw8LFoQRqi67LCz75S9hv/1g993h3HPD4DrV1fHmlaKyAlgGrAJ2jjlLmzNmTLhBcsqUuJOISEMefRTefz/cT1Wo/rSzSXTXf+6+wN0PiKZ93P3yuDOJNJcZ7LsvXHghvPQSfPABTJwYhpS/8Ub44hdDl2Lf+Abcf39ojiKSa2Z2tpmlgGeA3sD33H3/eFO1PYccEvriVxeAIsn2hz/A4MFwwglxJ8l9m20RaUTfvuFGje99Dz75JJwhe+wx+Otfw13THTtCVVVo533iibDrrnEnlnZiIHCuu8+MO0hb1qFDuFFy8uRwhjvOdqAiktnMmfDii2Gguji6+qtLxYRIjMrK4KSTwqhWy5aFwuHcc8Olrx/9CHbbLQym8ec/D+KVV9TOW1rO3X+hinZuHHccLF8Or70WdxIRyeTPf4ZOncK4GEmgyrZIQnToAJ/7HPz2t/DWW2G66irYcUe4667dOPjgcJb77LPDwBqffhp3YpHi9KUvhccnn4w3h4jUV10N994bmo/06hV3mkCVbZGE2nNP+PnP4R//gIcemsptt4X2orffHm7SKi+HU06Bu+6C1avjTitSPCoqQr+9arctkjxTpsCHH4ZRoJNClW2RNqBHj2rGj4eHHw5djv3tb3D66WHEym9+M9xgWVUFV18N8+fHnVak/RszBqZOhY8/jjuJiKS7665wRvv44+NOsp0q2yJtTJcuoRC56SZYvDj0+fuLX4Sz2z/7GQwdCvvsE16bNi3cxCUiuXXccbB1KzzzTNxJRKRGdXU4GfXVr4Y220mhyrZIG1ZSEpqWXHopvP566NP7D3+AXXYJ7b0PPzwMpvPd78Ljj8OGDXEnFmkfDjssDGSldtsiyTFtGqxdG/4znCSqbIu0I4MHw3/8Rzjb9uGHoSvBqip44IHQjWB5OYwdC7fcEnpTEJGWKS2FY48N7bbVS5BIMkyeHDobOOaYuJPUpsq2SDvVsyecdhrcd1+oeE+ZEs5wz5wZHvv2DcPYXnEFvPmmKgwizTVmDCxZArNnx51ERCBUto84Ilx1ShJVtkWKQKdO4X/6114LCxeGCvf//A9s3hzadg8fDsOGhTbfL7wAW7bEnVgk+caMCY9qSiISv2XL4JVXth+XSaLKtkiRMYMDDoD//m+YPh0WLYI//jHcWHn99XDUUaFrszPOgAcfhHXr4k4skkz9+8N++6kLQJEkePrp8Ji09tqgyrZI0RswAM46K5ydW7kyVLBPOCHc0X3KKaGd93HHhQr5hx8m6PZukQQ47rgw8qv+UyoSr8mTw4miAw6IO0l9qmyLyGe6dYN/+7cwcM7y5fD882HY+HnzwsiVp556BJWVcMklYahqtfOWYjdmTOhuTF0AisRn69ZwZvtLXwq9dCVNAiOJSBKUlsKoUfC//wvvvANvvAETJsynUye4+GI48EAYNChUxqdMCe2/RYrNkUeGm7EmTYo7iUjxmj49DPiWxCYkoMq2iDSBGey9N5x22iKmToWlS0P3gQcdFB5Hj4Y+fWDcuNDdoEbVk2LRsSN8+cuhH/utW+NOI1KcJk8Of6eOPTbuJJmpsi0izVZRAd/5Djz6aGjnPWkSnHoqpFLwjW+EivfRR4cBdt59N+60Ivl10knhOJg6Ne4kIsVp8mQYORJ69447SWaqbItIq+ywA3zlK/CnP8EHH8A//wn/+Z+hG6Zzz4UhQ2D//eGXvwxDy2v4eGlvxowJ3Ws++mjcSUSKz6pV8NJLyezyr4Yq2yKSMyUlYRjrX/8a5syBuXPh6qvD2YYrroBDDw29n3z/+6G3k02b4k4srWFmvcxsipnNjR57Zllvq5nNjKZ217q5W7dwJeexx3TTsEihTZkSjrukttcGVbZFJI+GDoWf/ASeey70bnLnneGGsnvuCd0L9u4NJ58Mt90WRrmUNucC4Bl33wN4JnqeyUZ3PzCaTixcvMI56SSYPx9mzYo7iUhxmTwZevWCysq4k2SnyraIFETv3vDv/w5/+Uto3zp5MnzrW/Dyy/Dtb8Muu8DnPw9XXQVvvx13WmmiscDt0fztwEkxZonVV78abpa85Za4k4gUj23bwt+S0aOhQ4e402SnyraIFFznzqE/1BtugPffhxkzwoiWn3wC550He+0VpvPOCwOGqJeHxKpw96XR/DKgIst6XcxsuplNM7N2WSHv0ycMAnXbbbB+fdxpRIrDa6+Fq6ZJbkICUBp3ABEpbmYwYkSYLr44VL4ffzz0cPL734cz3eXlodnJiSeGMxhSOGb2d2CXDIsuTH/i7m5m2Vos7+buS8xsCPCsmc1y9/kZPmsCMAGgoqKCVCrV7Lzr169v0fty4YgjduKee0bws5/N5ytfiS9HjTj3hXIoRyFy3H33rsAQdtxxKqlUywd7yPe+UGVbRBJl113hhz8M05o18NRToeL96KPhrGHnznDQQfvx7W+HXlD69o07cfvm7sdkW2Zmy82sr7svNbO+wIos21gSPS4wsxRwEFCvsu3uE4GJAJWVlV5VVdXsvKlUipa8LxeqquCJJ+Avf9mdE05YSlXVkbHkqBHnvlAO5ShEjosuCuM9nHzyEbFlaAo1IxGRxOrePfTffdddsGIFPPss/OAH8N57O/D970O/fqGHk8svDzemqSeIgpsEjI/mxwOP1V3BzHqaWedovhz4HPBGwRIW2G9+A+vWwXXXDY07iki7tnp16Nv+y1+OO0njVNkWkTahY0f4whfgmmvg7rtfYtasUMk2C314778/7L576Nv72WehujruxEXhCuBYM5sLHBM9x8wqzezmaJ29gelm9hrwHHCFu7fbyvb++4f7D6ZM2UU3S4rk0ZNPhvt5Tjgh7iSNS3xl28zGmNnbZjbPzLJ1KyUiRcQM9t0X/uu/YNq0MJjOxImwzz5w442hz+Oddw6jWd5/f2iOIrnn7qvc/Wh338Pdj3H31dHr0939u9H8VHffz90PiB7bfRX0wguhsnI1EyaEqzIiknuPPx5GMz7kkLiTNC7RlW0z6wDcABwHDAdOM7Ph8aYSkaTp2xe+971Q+K5aBY88Erpie/ppGDcu9BQxejRcfz28917caaW9Ky2FSy6Zw6hR8M1vwtlnw0cfxZ1KpP345JNwf8QJJ4TB1JIu6RFHAvPcfYG7bwbuI/TrKiKSUVlZGGDk1lvDkPEvvhgG1nn/ffjRj2DQoHBDzXnnhbPe8+aprbfkXteuW3n66fDbu+kmGDIEfvpT+Ne/1JWlSGs99FC4N+KMM+JO0jRJ742kP7Ao7fli4NCcbX3bNnj+eXrMnJmIv7ZJyJGEDMqhHLnK0YFwN97nxsCVY+Dt97vy+D/LeWxqOb+/Zieqt4TzDTt02crgXTYyeJdNDNplE316VNN7p+1Ttx220rXzVrp22kbXzmHq/NYs/POjsA5JP2chcenYEa6+GsaPh1//Gq67Ltxz0KNHaNs9fHjofadPnzB17w5du0KXLtunDh1Cs6mSktqP2V5Lt2FDB9ati+ffrhytz5FexGWbb+p6meY//rgjK1Y0ff18zS9d2oV33236ez79NNyvs9deYSC0tiDple1GtaZfVquu5qjRozkwT9maKwk5kpABlKMu5aitpTn2jKafA5vpyGz25RVGMGfTPry7cDDvLhzMP9iNNfRowtaO5On9/k7HsjZfjEqeHXBAuIqyciVMmQKpFMyZE17Lb/OSpNRElKO2pOT4XNwBIoe16F2TJtX/D2ZSJf2vxBJgYNrzAdFrn2lVv6zbtkEqxauvvspBBx3U6rCtlYQcScigHMpRiBydgBHRtN3HwMdUbzFWry1l1dqOrFrbkfUbO7Dx05Lt0+YS5i1YxjFjvqgz29Jk5eVw2mlhqrFxI3z4Yejact062LRp+7RxY2hy4h7+XLlnn9+2rf7nzZ8/j913j78LQuVoeg732hXIpsw3db268++88w7Dhg1r0XtzOf/WW2+x9957NevfM2QIHNG6rrULKumV7ZeBPcxsMKGSPQ44PWdbLymBo45ijTscdVTONttSSciRhAzKoRxx5+hIGHc829jjAKnUElW0pdW6dg1NSXbdNffbTqUWU1UVf+VSOZKa4wOqqobFHYNUahlVVXs1vmIblujKtrtvMbNzgKcIzS9vdfc5MccSEREREWkS8wTc7JQrZvYh0JKOvcqBlTmO0xJJyJGEDKAcdSlHbUnI0dIMu7l7n1yHaW9UnrebDKAcdSlHbUnIkdfyvF1VtlvKzKa7e6VyJCODcihHW8iRhAxSX1K+lyTkSEIG5VCOtpAj3xnU4FBEREREJE9U2RYRERERyRNVtoOJcQeIJCFHEjKActSlHLUlIUcSMkh9SflekpAjCRlAOepSjtqSkCOvGdRmW0REREQkT3RmW0REREQkT4qmsm1mY8zsbTObZ2YXZFje2czuj5a/ZGaD8pBhoJk9Z2ZvmNkcM/txhnWqzGyNmc2MpotynSP6nIVmNiv6jOkZlpuZXRvtj9fNbESm7bQyw55p/86ZZrbWzM6ts05e9oeZ3WpmK8xsdtprvcxsipnNjR57Znnv+GiduWY2Pg85rjKzt6L9/oiZZRw7vLHvMAc5LjazJWn7/vgs723w2MpBjvvTMiw0s5lZ3puT/ZHtOI3j9yGZqTyv9zkqz1WeN5ZD5Xmc5bm7t/uJMCDOfGAIYZTm14DhddY5G7gxmh8H3J+HHH2BEdF8N+CdDDmqgL8WYJ8sBMobWH488CRgwGHASwX4jpYR+qzM+/4ARhFG6p6d9tpvgQui+QuAKzO8rxewIHrsGc33zHGO0UBpNH9lphxN+Q5zkONi4OdN+N4aPLZam6PO8t8BF+Vzf2Q7TuP4fWhq2W9O5Xm95SrPVZ6rPI+xPC+WM9sjgXnuvsDdNwP3AWPrrDMWuD2afxA42swslyHcfam7vxLNrwPeBPrn8jNyaCxwhwfTgB5m1jePn3c0MN/dWzKIRbO5+wvA6jovp/8GbgdOyvDWLwFT3H21u38ETAHG5DKHuz/t7luip9OAAS3dfmtyNFFTjq2c5IiOx1OBe1u6/SZmyHacFvz3IRmpPG8+lecqz5tC5XltOft9FEtluz+wKO35YuoXip+tEx0Ya4De+QoUXdY8CHgpw+LDzew1M3vSzPbJUwQHnjazGWY2IcPypuyzXBpH9oOuEPsDoMLdl0bzy4CKDOsUer98h3BGKpPGvsNcOCe6/HlrlstshdwfnweWu/vcLMtzvj/qHKdJ/H0UI5Xn9ak8ry+Jx6vK8+2Kqjwvlsp2opjZjsBDwLnuvrbO4lcIl94OAK4DHs1TjCPdfQRwHPBDMxuVp89plJl1Ak4EHsiwuFD7oxYP15Bi7arHzC4EtgB3Z1kl39/hH4HdgQOBpYRLfnE6jYbPguR0fzR0nCbh9yHJoPK8NpXnmak8r6eoyvNiqWwvAQamPR8QvZZxHTMrBboDq3IdxMw6Er7wu9394brL3X2tu6+P5p8AOppZea5zuPuS6HEF8Ajh8lG6puyzXDkOeMXdl2fIWZD9EVlec2k1elyRYZ2C7Bcz+xZwAvCNqCCopwnfYau4+3J33+ru24A/Zdl+ofZHKXAycH+2dXK5P7Icp4n5fRQ5lef1P0fleX2JOV5VntdWjOV5sVS2Xwb2MLPB0f+6xwGT6qwzCai50/RrwLPZDoqWitoo3QK86e5XZ1lnl5q2hWY2kvAd5fSPhJmVmVm3mnnCDRyz66w2CTjDgsOANWmXXHIt6/9wC7E/0qT/BsYDj2VY5ylgtJn1jC7DjY5eyxkzGwOcB5zo7huyrNOU77C1OdLbdH41y/abcmzlwjHAW+6+ONPCXO6PBo7TRPw+ROV5nc9QeZ5ZIo5XlecZFV957jm487UtTIS7sd8h3Gl7YfTaJYQDAKAL4bLXPOBfwJA8ZDiScKnidWBmNB0PnAWcFa1zDjCHcBfwNOCIPOQYEm3/teizavZHeg4Dboj21yygMk/fSxmhsO2e9lre9wfhj8FSoJrQDutMQpvOZ4C5wN+BXtG6lcDNae/9TvQ7mQd8Ow855hHaidX8Rmp6VegHPNHQd5jjHHdG3/3rhIKpb90c2Y6tXOaIXr+t5jeRtm5e9kcDx2nBfx+asn5HKs+351B5rvK8KTlUnsdYnmsESRERERGRPCmNO0AulZeX+6BBg5r9vk8++YSysrLcB2qDOZKQQTmUoy3kaGmGGTNmrHT3PnmI1K6oPG8fGZRDOdpCjryX57m4hJOU6eCDD/aWeO6551r0vlxLQo4kZHBXjrqUo7Yk5GhpBmC6J6C8TPqk8rx9ZHBXjrqUo7Yk5Mh3eV4sN0hmdeWVsGxZl7hjiIhIzDZsgMcy3SYlItIK7aoZSXMtWgS/+Q307r0vp54KJUX/Xw8RkeJ1+unbK9uu25lEJEeKuno5cCBccw0sWLAjL2Ua90tERNq1Bx6Ad98N8088sf31LrrgKSI5UtSVbYCxY6GkxHlKPeGKiLSImY0xs7fNbJ6ZXZBheWczuz9a/lI0bHLs1q+HU0+FIUPADKqrty/79NPw2vjxsHlzfBlFpO0r6mYkAL16wbBh60ildoo7iohIm2NmHQh9OB9L6Ev3ZTOb5O5vpK12JvCRuw81s3HAlcDXC5+2tk2bGl/njjvC1HxVLXlTjlXFHSBSFXeASFXcASJVcQeIVMUdIFIVdwAOO2w/XngBOnbMz/aL/sw2hMr2zJlqoyci0gIjgXnuvsDdNwP3AWPrrDMWuD2afxA4umYkwTht3Bh3AhFJgmnTeud1+4k4s21mtwInACvcfd/otV7A/cAgYCFwqrt/lI/PHzp0PZMmhXZ7Q4bk4xNERNqt/oQR8mosBg7Nto67bzGzNYQR3FbmLMWWLXDuueyxZAk8+GCT3nLNiycDX8xZBBFpuzraFvJVLU5EZZswdOf1QPrFuguAZ9z9iqgN4AXA+fn48D32WA/Aq6+qsi0iEhczmwBMAKioqCCVSjX9vdXVHHHnnfRxp7oJJ837r5vHhxpbSEQizz/3HJ6ndiSJqGy7+wsZbpgZy/aGPLcDKfJU2d5tt08AeOutfGxdRKRdWwIMTHs+IHot0zqLzawU6A6sqrshd58ITASorKz0qqqq5iVZs4ZUKkVj73vkEfjw5OzL3eFvf4MTTmjex4tI23XUscfmbdtJbrNd4e5Lo/llQEW+Pqhr12307w9z5+brE0RE2q2XgT3MbLCZdQLGAZPqrDMJGB/Nfw14Nhp9LRa//nXt5xMnwrZtMHkyzJ4dXvvyl0Ole9Mm+OUvC59RRNqPRJzZboy7u5llLJhbc9mxxvr16+nT5yOmTy8hlXq1VVlbY/369S3K394yKIdytIUcSciQBFEb7HOAp4AOwK3uPsfMLiEMZTwJuAW408zmAasJFfKc2rgxNAP8t3/rT2MnxOtW83faKXTz96Uv1V+3c2e49NIwNUdTzrDnWxIyKIdytIUcoSzPX4YkV7aXm1lfd19qZn2BFZlWavVlR8JOHjmyJw8/TKxfeFJ+cHFnUA7laAs5kpAhKdz9CeCJOq9dlDa/CTglnxk6d4bly2Ht2sbbXH76ae3np+Q1mYgUuyQ3I0m/7DgeeCyfHzZsGKxcCR/lpb8TERHJp5IS2GEH2LSpQ6Pr9u+/fd49vFdEJF8SUcSY2b3AP4E9zWyxmZ0JXAEca2ZzgWOi53kzdGh4nDcvn58iIiL5UlYGGzc2XtmuGTF4y5Y8BxIRISHNSNz9tCyLji5UhkGDwuN778EhhxTqU0VEJFfKyho/s50+kE2HxuvlIiKtlogz20mw667h8f33480hIiIts+OOsGlTw3/WfvCDAoUREYmosh3p0QO6dQtntkVEpO1pypnt229vcLGISM6psh0xg912U2VbRKStamqbbRGRQlJlO82uu6qyLSLSVjVW2U7vbWr06AIEEhFBle1adGZbRKTtaqwZyeLF2+dvuy3/eUREQJXtWnbbLZz5WLcu7iQiItJcjd0gmd77SN++BQgkIoIq27Xstlt4VI8kIiJtT2NntrduLWAYEZGIKttp1P2fiEjbVdNm2z3z8k2bwuMf/lC4TCIiqmynqRnC94MP4s0hIiLNV1YG7vZZpbquTz8Nj8OHFy6TiIgq22lq2vAtWRJvDhERab4ddwyPn3ySefnzz4fHzp0Lk0dEBFTZrqVTJ+jTR2e2RUTaorKy8Jitsv3LXxYui4hIDVW26+jXT2e2RUTaoprK9vr1Da+3ZUv+s4iI1FBlu45+/XRmW0SkLWrszHaNTp3yn0VEpIYq23X0768z2yIibVFjbbZrHHFE/rOIiNRQZbuOfv1gxQqoro47iYiINEdNZTvTwGTpTUvMCpNHRARU2a6nf39wh2XL4k4iIiLN0b17eFyzpv6ymm7/REQKTZXtOvr1C49qty0i0rY0VNmePbuwWUREaqiyXYcGthERaZsaqmxfdllhs4iI1FBlu46aM9u6SVJEpG3p3Bk6ddqasbJd00778MMLm0lEJGeVbTPrZGZdc7W9uPTpA6WlOrMtItIWlZVt5eOP678+ZUp4HDeusHlERHJS2TazHwNLgXlm9qaZnZOL7cahpCQM264z2yLS3phZFzP7qZk9bGYPmdlPzKxL3Llyaccdt2Q8s13j1FMLl0VEBFpZ2TazP5jZeODHwN7u3h8YBQw3s0tzEdDMFprZLDObaWbTc7HNxqivbRFpp+4A9gGuA64HhgN3xpoox8rKGq5si4gUWmkr3/8cMAIoB6aa2VrgdWAWcJaZXe3uH7XyMwC+4O4rc7CdJunfH954o1CfJiJSMPu6+/C058+ZWbsq7Ro7s73zzoXLIiICrTyz7e6PuvtFwDRgLHAMcBuwBegFPGtm81sbstD694fFi+NOISKSc6+Y2WE1T8zsUKAgVwwLpbEz2yXqFkBECqy1Z7Zr/BD4CzCTcFZ7b2CWu1eZWadWbtuBp83MgZvcfWIrt9eoAQPCCGRr18JOO+X700RECuZgwlXI96PnuwJvm9kswN19//ii5Ua2GyRFROKSk8q2u8+NzpAcCxxAaEpyXrRscys3f6S7LzGznYEpZvaWu79Qs9DMJgATACoqKkilUs3+gPXr19d635o1OwPDeeSRf7HbbhtaGb/lOeKQhAzKoRxtIUcSMrTAmLgD5JvabItI0uTqzHZNpfpv0ZQz7r4kelxhZo8AI4EX0pZPBCYCVFZWelVVVbM/I5VKkf4+M7j8cujffyQt2FyL1c0RhyRkUA7laAs5kpChudz9vbgz5NuOO25hwwaoroaOHcNrs2bFm0lEiluiW6+ZWZmZdauZB0YDeR90d8CA8Kh22yIibUtZ2Rag9iiS1dUxhRERIYdntvOkAnjEwtBfpcA97j453x+qUSRFRNqmnXYKle3Vq6G8PLxWGv2lGzkyplAiUtQSXdl29wWENuAF1bUr9O6tyraISFvTvXu4TejDD2HYsPDae1HjmQsvjCmUiBS1RDcjiZO6/xMRaXt69AhtRj78cPtr48eHx1deiSGQiBQ9VbazGDBAlW0RkbYmU2VbRCROqmxnMWgQLFwYdwoRkeQys15mNsXM5kaPPTOsc6CZ/dPM5pjZ62b29Xxm6t49VLZXpo05/JOfhMezz87nJ4uIZKbKdhZDh8JHH4WbbEREJKMLgGfcfQ/gmeh5XRuAM9x9H0I/3783sx75CtS58zbKymqf2a65/6Z793x9qohIdqpsZ7H77uFx3rx4c4iIJNhY4PZo/nbgpLoruPs77j43mv8AWAH0yWeoPn1qV7Zvuik81vS7LSJSSKpsZzF0aHhUZVtEJKsKd18azS8jdNealZmNBDoB8/MZqm5lu0aJ/uKJSAwS3fVfnIYMCSNJqrItIsXMzP4O7JJhUa2O9Nzdzcwb2E5f4E5gvLtvy7LOBGACQEVFBalUqtl5169fT0ntPKPEAAAgAElEQVTJKhYs6EQqNQOAXr0OZ/Xqzi3aXkutX7++oJ+X1AzKoRxtIUe+M6iynUWXLqFHkvl5Pf8iIpJs7n5MtmVmttzM+rr70qgyvSLLejsBfwMudPdpDXzWRGAiQGVlpVdVVTU7byqVYq+9evPss1Dz/oMOgk2btj8vhFQqVdDPS2oG5VCOtpAj3xl0Ua0BQ4fqzLaISAMmAVEv1owHHqu7gpl1Ah4B7nD3BwsRapddYPly2BadP3/mGfjXvwrxySIi9amy3YDdd1dlW0SkAVcAx5rZXOCY6DlmVmlmN0frnAqMAr5lZjOj6cB8hhowADZvrt1uu7o6n58oIpKdmpE0YOhQWLEC1qxRl1EiInW5+yrg6AyvTwe+G83fBdxVyFwDBoTHxYuhosFbNkVE8k9nthuwzz7h8Y034s0hIiJNl17ZrnH++fFkERFRZbsB++4bHmfNijeHiIg03cCB4XHxYti6NczvsEN8eUSkuKmy3YBdd4Udd4TZs+NOIiIiTdWnTxjAZvHi0HYbwLN2Sigikl+qbDegpCSc3VZlW0Sk7Sgpgf79Q2X7kUfCa5dcEm8mESleqmw3Yt99QzMSnRUREWk7Bg6EhQthp53C8698JdY4IlLEVNluxIgRsHIlvPtu3ElERKSphg2DuXOhrCw8P/fcePOISPFSZbsRo0aFxxdeiDeHiIg03bBhYWCblSvD844d480jIsVLle1G7L039O4N//hH3ElERKSphg0Lj3PmhMdOneLLIiLFTZXtRpSUhLPbU6ao3baISFtRU9m+++7wWKoh3EQkJqpsN8GJJ8KiRTBjRtxJRESkKXbfPZwsmTcvPF+3Lt48IlK8VNlugq98JZwVuaugAw6LiEhLde4Me+65/fmRR8aXRUSKW+Ir22Y2xszeNrN5ZnZBHBl694avfx1uuQU+/jiOBCIi0lwHHxweO3YMZ7lFROKQ6OLHzDoANwDHAcOB08xseBxZfvYzWL9eAyOIiLQVlZXhsbo63hwiUtySfsvISGCeuy8AMLP7gLHAGznZujssXEiXpUsb7Uj7oB5w9r/35pprduLIPZZz8pgNOYmQrik58i0JGZRDOdpCji5Ll4YyxCzWHJJdTWVbRCROSa9s9wcWpT1fDByas61XV8OQIRzWxNWvphMv8w9OPXsE53AvX+NBDuFlOlLNQgaxgCF8QD/WshNr6M5GuvIpnammI1soZVt0IcGxz+ZrOOEP9q1MwfDPnudS3e1m+5xbmdLs9zTnc5v6nvQcTdluLrJl2kbdHIXaJ3XXaWx/tDRbc9+TKUchfxfpx0pLPscI3QrVvFb3eVPf04GtVI6tpnQH9SmXVCNGxJ1ARCT5le1GmdkEYAJARUUFqVSq6W/eupWK88/n008/pXPnzk16y/Wf/o1Ln+7IDW/9iD9sO5fSkq10Kt3Chs31319i2+jYYSulJVvpULKNEvPodQ9/vA2o6U7QwNxxa/of/Kas0+z3RGfqGquAZaooteQ9dX22TpYcDb6nJZ/T2PO0M5fN/ffl9PtyauVoynZbkqXR/VjnTG4hKvcZ31PnWGnwPQ61Np92zGV8XvNaI8+3uvHVF16kY5dEt8Yral27xp1ARCT5le0lwMC05wOi1z7j7hOBiQCVlZVeVVXVvE84+mhSqRTNed/jwJo18MwzMH16Bz7+uAMHHQR77AH9+0P37mHq1KkEsxKgaUOXNTdHPiQhg3IoR1vIETJ8MdYM0rgXX4S33447hYgUs6RXtl8G9jCzwYRK9jjg9HgjBd27w8knh0lERJLpc58Lk4hIXBJd2Xb3LWZ2DvAU0AG41d3nxBxLRERERKRJzNvRGORm9iHwXgveWg6szHGclkhCjiRkAOWoSzlqS0KOlmbYzd375DpMe6PyvN1kAOWoSzlqS0KOvJbn7aqy3VJmNt3dY+8kKgk5kpBBOZSjLeRIQgapLynfSxJyJCGDcihHW8iR7wy6jV5EREREJE9U2RYRERERyRNVtoOJcQeIJCFHEjKActSlHLUlIUcSMkh9SflekpAjCRlAOepSjtqSkCOvGdRmW0REREQkT3RmW0REREQkT4qmsm1mY8zsbTObZ2YXZFje2czuj5a/ZGaD8pBhoJk9Z2ZvmNkcM/txhnWqzGyNmc2MpotynSP6nIVmNiv6jOkZlpuZXRvtj9fNbEQeMuyZ9u+caWZrzezcOuvkZX+Y2a1mtsLMZqe91svMppjZ3OixZ5b3jo/WmWtm4/OQ4yozeyva74+YWY8s723wO8xBjovNbEnavj8+y3sbPLZykOP+tAwLzWxmlvfmZH9kO07j+H1IZirP632OynOV543lUHkeZ3nu7u1+IgyIMx8YAnQCXgOG11nnbODGaH4ccH8ecvQFRkTz3YB3MuSoAv5agH2yEChvYPnxwJOAAYcBLxXgO1pG6LMy7/sDGAWMAGanvfZb4IJo/gLgygzv6wUsiB57RvM9c5xjNFAazV+ZKUdTvsMc5LgY+HkTvrcGj63W5qiz/HfARfncH9mO0zh+H5pa9ptTeV5vucpzlecqz2Msz4vlzPZIYJ67L3D3zcB9wNg664wFbo/mHwSONjPLZQh3X+rur0Tz64A3gf65/IwcGgvc4cE0oIeZ9c3j5x0NzHf3lgxi0Wzu/gKwus7L6b+B24GTMrz1S8AUd1/t7h8BU4Axuczh7k+7+5bo6TRgQEu335ocTdSUYysnOaLj8VTg3pZuv4kZsh2nBf99SEYqz5tP5bnK86ZQeV5bzn4fxVLZ7g8sSnu+mPqF4mfrRAfGGqB3vgJFlzUPAl7KsPhwM3vNzJ40s33yFMGBp81shplNyLC8Kfssl8aR/aArxP4AqHD3pdH8MqAiwzqF3i/fIZyRyqSx7zAXzokuf96a5TJbIffH54Hl7j43y/Kc7486x2kSfx/FSOV5fSrP60vi8aryfLuiKs+LpbKdKGa2I/AQcK67r62z+BXCpbcDgOuAR/MU40h3HwEcB/zQzEbl6XMaZWadgBOBBzIsLtT+qMXDNaRYu+oxswuBLcDdWVbJ93f4R2B34EBgKeGSX5xOo+GzIDndHw0dp0n4fUgyqDyvTeV5ZirP6ymq8rxYKttLgIFpzwdEr2Vcx8xKge7AqlwHMbOOhC/8bnd/uO5yd1/r7uuj+SeAjmZWnusc7r4kelwBPEK4fJSuKfssV44DXnH35RlyFmR/RJbXXFqNHldkWKcg+8XMvgWcAHwjKgjqacJ32Cruvtzdt7r7NuBPWbZfqP1RCpwM3J9tnVzujyzHaWJ+H0VO5Xn9z1F5Xl9ijleV57UVY3leLJXtl4E9zGxw9L/uccCkOutMAmruNP0a8Gy2g6KlojZKtwBvuvvVWdbZpaZtoZmNJHxHOf0jYWZlZtatZp5wA8fsOqtNAs6w4DBgTdoll1zL+j/cQuyPNOm/gfHAYxnWeQoYbWY9o8two6PXcsbMxgDnASe6+4Ys6zTlO2xtjvQ2nV/Nsv2mHFu5cAzwlrsvzrQwl/ujgeM0Eb8PUXle5zNUnmeWiONV5XlGxVeeew7ufG0LE+Fu7HcId9peGL12CeEAAOhCuOw1D/gXMCQPGY4kXKp4HZgZTccDZwFnReucA8wh3AU8DTgiDzmGRNt/Lfqsmv2RnsOAG6L9NQuozNP3UkYobLunvZb3/UH4Y7AUqCa0wzqT0KbzGWAu8HegV7RuJXBz2nu/E/1O5gHfzkOOeYR2YjW/kZpeFfoBTzT0HeY4x53Rd/86oWDqWzdHtmMrlzmi12+r+U2krZuX/dHAcVrw34emrN+RyvPtOVSeqzxvSg6V5zGW54kfQTL6X+EfCF3S3OzuV8QcSURERESkSRJd2TazDoT/YR1L+F/Ry8Bp7v5GpvXLy8t90KBBzf6cTz75hLKyslYkzY0k5EhCBuVQjraQo6UZZsyYsdLd++QhUrui8rx9ZFAO5WgLOfJenufiEk6+JuBw4Km0578AfpFt/f/f3p3HyVHX+R9/fWaSCeSABAJDSEI4BCQsKDACuhwjICSsmyiIG0QXVtYsLNnVH+6yuOyPBX66LmYFXYlHRFZQ5JArUcMVSYsuhiNckoQwIQSSCAk5DORkjs/vj6rO9PR0z/T0VHVVT7+fj0c/qrvO91R3f/NJVfW3jjvuOC/HggULylouamnIkYYM7sqRTzm6SkOOcjMAz3gK2te0P9SeD4wM7sqRTzm6SkOOuNvzQX0u4yurUB+HJ0S29o4OeOwxRr3wArS19T5/zPJztLdDe4fR3mF0dECHB8/dCR50Ps/Kji8kd77s7R0878RG++KlvLUu+d/Nti9eytq3gxyl5Dbr37hi22l/qXN/9DRf3Hk6lgT7o9C2K6kj531JUik5LOzJKff7UGhcdnyp47LLdyxeip98Claf/P6Q+LS2wpIlMHEiDB6cdBoRqUZpL7Z7FXZ2Ph2gsbGRTCZT+rKtrZx65pl8IKZspdrBEBZxHC9yNN9nKC9yNK9wGOtJ4kxzYt2z5lGOrpSjqzTkOIX5J8ynfveqb0Yljzv87//C7NkwZw688w789KdwwQVJJxORapT2fyV67ePQ3WcDswGampq8ubm59LV3dMBvf8tzzz3HMccc0++wfdHRAfN+P4ofP9jIQ0+NYuv2egBGDm/j6EO2cs6EbTSOeoMhDR3U10GdOfX1wbAuPJBmFhx3M+t6lDM7Psth1+vskdT8cVlvvLGKAw7I3eXB/PlHUeMe98Ybqxg/fvyunLlHgHPHZZeNYlx2X+SOW7Uq2B+Ftl3JPG+sWs0B48d1GZe77S77MsZxq1Z1fV/yVSrP6jBHsfmyJwDcbdf3odC47Lx9HUeYofmM06gfrCPbA8lTT8GXvwy/+x3ssQdMmRIU2usK9cIrIlKCtBfbu/p8JCiypwGfiWztdXVw0klsbmuDk06KbLW9efJJ+MIX4A9/gH33hc9dCJMmwc6dv+e88z6M2Z4E92CovExmNc3N70tk28qhHNWUI5NZrUJ7AGlthauvhuuvD9rlWbPgwguhoSEotrcV7CFZRKR3qS623b3NzGYQdCJeD9zi7osTjlU2d/iP/4B//3cYOxZ+9jP41Kc6rwPMZHYmch2uiEgt27oVPvlJePRR+Nu/hRtugBEjOqcPGqRiW0TKl+piG3bd0nVe0jn6yx0uuwy+9z2YNi0YjhyZdCoRkdq2YwecfXZw2cjNN8PFF3efZ+hQFdsiUj6dA62Qb3wjKLD/+Z+DI9oqtEVEkuUOf/d38Pjj8JOfFC60ISi2t26tbDYRGThUbFfA738P//qv8Fd/FVwPqEtFRESSd+utcNttcO218Jkefg301lvwox9VLpeIDCwqtmPW2gqf/zyMHx90I6VCW0QkeWvWwJe+BCefDP/2b73P39ERfyYRGZhSf812tZs9G15+GebODbqREhGR5F11VXC99i23sKs71WIuuACeeKIyuURk4NGR7Rjt3Alf/Sqceip8/ONJpxEREQi6Xb3tNvjHf4T3ldCD5Ntvw2uvdb/bq4hIKXRkO0Z33hlc63frrbp8REQkLa69NjjTeOWVpc3/6qvBcO1a2G+/+HKJyMCkI9sx+v73YeJE+NjHkk4iIiIQHKG+/3649FLYa6/Slsle060eSUSkHCq2Y/LWW7BwIZx/vo5qi4ikxXe+E1yjPWNG6ctkb3CjYltEyqFiOya/+EUwnDIl2RwiIhLYuRN+/OPgzr1jx5a+3LBhwVDFtoiUQ8V2TObOhQMPhKOOSjqJiIgA/OpXsGkTXHRR35ZTsS0i/aFiOwZbt8L8+cFRbV1CIiKSDrfdFvzA8fTT+7ZcttheuDD6TCIy8KnYjsGjjwb9t+oSEhGRdNiwAebNC+4UOaiP/XCNGhUMf/jD6HOJyMCnYjsGc+fCnnvCKacknURERAB++cvgjr7TpvV92YMOCobnnhttJhGpDSq2I9beHjTqZ58NgwcnnUZERCD40fr++8Nxx5W/jhtvjC6PiNQOFdsRW7gwuNvY1KlJJxEREQh6IXn44eBOvr3dml1EJGpqdiI2Z05wPeCkSUknERERgN/8BrZsgb/8y/LXcd558P73R5dJRGqHiu2IzZ0Lzc3BNdsiIpK8+fOhoQFOO638dQwfHhTsIiJ9pWI7QsuWBQ9dQiIikh6ZDJxwAgwdWv46hg9XP9siUh4V2xGaOzcY9udUpYiIRGfzZli0CD760f6tZ9264IY427dHk0tEaoeK7QjNmQMf/CBMmJB0EhGRyjGzSWa2zMyWm9mVBaZfbmZLzOxFM/u1mVWslfzd76CjI7i8rz8eeigYPv10vyOJSI1RsR2Rt9+GJ57QjWxEpLaYWT0wC5gMTATON7OJebM9BzS5+9HAPcA3KpUvkwmu1z7xxP6t53/+Jxi+9Va/I4lIjVGxHZFf/QrcVWyLSM05Hlju7ivc/T3gTqDLL1fcfYG7bwtfLgTGVSrck08GfWvvvnv/1rNzZzCcMaP/mUSktqjYjsicOTB2LBx7bNJJREQqaiywKuf16nBcMRcDD8aaKNTeDs8+Cx/6UP/X9clPBsNjjun/ukSktgxKOsBAsH07PPIIXHghmCWdRkQknczss0ATcGqR6dOB6QCNjY1kMpk+b2PLli27lnvttWFs3fohhg1bSiaztszUuZp55BFKypWbIylpyKAcylENOeLOoGI7Ar/+NWzbpktIRKQmrQHG57weF47rwszOAK4CTnX3nYVW5O6zgdkATU1N3lzGrxozmQzZ5V57LRj31399BO9//xF9XlcxpeTKzZGUNGRQDuWohhxxZ1CxHYG5c2HEiP53LSUiUoWeBg41s4MIiuxpwGdyZzCzY4AfAJPcfV2lgj3zTNA2H3ZYNOubMgVefz2adYlI7dA12/3U0QG/+EVwe/YhQ5JOIyJSWe7eBswAHgaWAne7+2Izu87Msuf7ZgLDgZ+b2fNmNrcS2V54IeiOtS6if+lGjIB3341mXSJSO3Rku5+efjroCkqXkIhIrXL3ecC8vHFX5zw/o/KZYMkS+Ku/im6dS5fCihVBzyQ6uCIipdKR7X6aMwfq6+Hss5NOIiIiWW+9FdzxcWJ+j9/98OyzwbClJbp1isjA1+uRbTM7ELgMOATYCDwP/MLddeUaQbF98smw115JJxER6R8zu7yn6e5+Q6Wy9NeSJcEwymL7X/4Frr8ebr0VZs6Mbr0iMrCVcmR7DvAywR3CPgZ8AHjczGaZWU2fSFu+PGjQp07tfV4RkSrQBFxK0E/2WOAS4FhgRPioGnEU2+97XzC8667o1ikiA18pxXa9u//I3X8NbHT3LxAc5V5J2EVTrZob/sRH12uLyAAxDjjW3b/s7l8GjgMOcPdr3f3ahLP1yZIlMGoU7LdfdOv87GeD4apVPc8nIpKrlGJ7vpllb1DrEPz63N1nAh+OLVkVmDsX/uzP4OCDk04iIhKJRuC9nNfvheOqzpIlcMQR0d5oTD+KFJFylNIbyeXAV8zsGWD/8A5f2wgK7Q1xhkuzDRvgt7+Fr3wl6SQiIpG5DXjKzO4PX38C+HFyccr36qtwRsR9oOgOwSJSjl6PbLt7h7t/DTiF4Da6+xGcWnwJmBxvvPSaNy/oY1uXkIjIQBG29X8DbAoff+PuX082Vd/t2AFr1sRz1rGpKRi2t0e/bhEZmEruZ9vdtwFzw0fNmzMHxozpbHhFRAYCd38WeDbpHP2xcmUwjKPYPv/84M6UW7bAnntGv34RGXjUz3YZduyAhx6Cv/zL6O5MJiIi0VixIhjGUWy3tgbDp56Kft0iMjCpVCzDggWwdau6/BMRSaM4i+0nngiG06ZFv24RGZhUbJfh3nth+HA47bSkk4iISL4VK2D33aExhn5Uvh5ewb5xY/TrFpGBScV2H7W1wQMPBJeQ7LZb0mlERCTfihXBUe04eg/J3thGRKRUKrb76De/Cbr9O/fcpJOIiEghK1bAQQfFs+6Ghs7nf/xjPNsQkYEl0WLbzGaa2ctm9qKZ3W9mI3OmfcXMlpvZMjM7K8mcue69F4YOhck12+mhiEi6rVoFEybEv50f/CD+bYhI9Uv6yPajwJ+5+9HAK8BXAMxsIjANOBKYBHzXzOoTSxlqb4f77gsK7aFDk04jIiL5tm+v409/gnHj4tvG3/5tMLzuuvi2ISIDR6LFtrs/4u5t4cuFQLZ5nArc6e473f01YDlwfBIZcz3xBKxdC5/6VNJJRESkkPXrg3uqjx0b3zZmzoxv3SIy8CR9ZDvX54EHw+djgVU501aH4xJ1zz0wZAj8xV8knURERArJFttxHtkeObL3eUREskq+g2S5zGw+wS3e813l7nPCea4C2oDby1j/dILbyNPY2Egmk+lzxi1btvS6XEcH3HHHiRx33BYWLXqpz9uIKkfc0pBBOZSjGnKkIYN09/bb8R/ZBvjIR4Kzne7x9HoiIgNH7MW2u5/R03Qzuwj4OHC6u3s4eg0wPme2ceG4QuufDcwGaGpq8ubm5j5nzGQy9Lbc738Pb78N//Vfu/U6b7lKyRG3NGRQDuWohhxpyCDdVeIyEui8uc2CBbrngoj0LOneSCYBVwBT3H1bzqS5wDQzG2JmBwGHAoneHPf224N+tT/xiSRTiIhIT9avb2DkSBg2rDLbO/30ymxHRKpX0tds3wSMAB41s+fN7PsA7r4YuBtYAjwEXObu7UmFbG2Fu+8ObmSzxx5JpRARkd68/faQ2I9qQ9AzlYhIKWK/jKQn7l70Xlzu/jXgaxWMU9T8+cElJBdckHQSERHpyfr1QyrSx3buWc6f/xzOOy/+bYpIdUr6yHZVuP324NfnkyYlnURERHpSqSPbuT+K/PSn49+eiFQvFdu92LoVHnggOGoxZEjSaUREpJiODti0qYExYyqzvTvu6Hy+bVvx+USktqnY7sU99wQF92c/m3QSERHpycaN0NFhNDZWZnvTpnU+r9QPMkWk+qjY7sXs2XDYYXDyyUknERGRnqxbFwz33TfZHCIiuVRs9+Cll4K+VKdP100LRETSLolie9Omym1LRKqTiu0ezJ4NDQ1w4YVJJxERkd6sXRsMK1ls5966/fvfr9x2RaR6qNguYssWuO02OPdcGD066TQiItKbpC8jufRSePfdZLYtIumlYruIH/4QNm+GL34x6SQiIlKKdeugrs7Za6/KbvfMMzuf77FH0CuKiEiWiu0CWlvhhhvg1FPhhBOSTiMiIqVYtw723LOV+vrKbvfhh7u+rq+H9sTueSwiaaNiu4Dbb4fVq+GKK5JOIiIipVq7FkaNei+Rba9e3fX1GWc0s2ZNIlFEJGVUbOfZsQOuvhqOOw4mT046jYiIlGrdOhg5sjWRbY8dC3ff3XXcuHHB9eO6rESktqnYzvPtb8OqVTBzprr7ExEphZlNMrNlZrbczK4sMH2Imd0VTn/SzA6MI0dQbCdzZBuCOw1/85tdx739dnBZic6UitQuFds5XnkFrr0Wpk6Fj3406TQiIulnZvXALGAyMBE438wm5s12MbDJ3d8H3AhcH0eWdetg1KhkjmxnXX45zJ/fffzMmZXPIiLpMCjpAGmxbRtccAHstht897tJpxERqRrHA8vdfQWAmd0JTAWW5MwzFbgmfH4PcJOZmbt7VCG2bw+63UvyyHbW6afDww8/zllnndJlfOXPljZXeoNFNCcdINScdIBQc9IBQs1JBwg1Jx2Aq67al+YYY6jYBrZurefcc2HRInjgAdh//6QTiYhUjbHAqpzXq4H8fpx2zePubWa2GdgbWB9ViIa6Np7/3Ld4b20LfHl4VKst2xGrVuGXz+H1d0Zx4M3/lnQcEenB1742ka9e0waD4imLa7rY3rwZLrsMfvWrE3j33eCOkVOmJJ1KRKQ2mdl0YDpAY2MjmUym9GVbW/nze64GoO3XcaTrmzFAG8H/MkDFtkjaZR5bAA2DY1l3TRfbI0YER7OPPnozM2fuw/HHJ51IRKTqrAHG57weF44rNM9qMxsE7AlsyF+Ru88GZgM0NTV5c1/P627bRiaToc/LxSA3x9p10NiYbB4R6dnxJ32MoUPjWXdN/0Cyrg6WLoVrr12sQltEpDxPA4ea2UFm1gBMA+bmzTMXuDB8/ingsSiv1067ffcF98o/FizIJLJd5VCOasuxYEEmtkIbavzItoiI9E94DfYM4GGgHrjF3Reb2XXAM+4+F/gR8BMzWw5sJCjIRURqgoptERHpF3efB8zLG3d1zvMdwHmVziUikgY2kM7kmdnbwOtlLDqaCH8V3w9pyJGGDKAc+ZSjqzTkKDfDBHffJ+owA43a8wGTAZQjn3J0lYYcsbbnA6rYLpeZPePuTcqRjgzKoRzVkCMNGaS7tLwvaciRhgzKoRzVkCPuDDX9A0kRERERkTip2BYRERERiYmK7cDspAOE0pAjDRlAOfIpR1dpyJGGDNJdWt6XNORIQwZQjnzK0VUacsSaQddsi4iIiIjEREe2RURERERiUjPFtplNMrNlZrbczK4sMH2Imd0VTn/SzA6MIcN4M1tgZkvMbLGZfbHAPM1mttnMng8fVxdaVwRZVprZH8JtPFNgupnZf4f740UzOzaGDIfn/J3Pm9k7ZvalvHli2R9mdouZrTOzl3LG7WVmj5pZSzgcVWTZC8N5WszswhhyzDSzl8P9fr+ZjSyybI/vYQQ5rjGzNTn7/uwiy/b43Yogx105GVaa2fNFlo1kfxT7nibx+ZDC1J53247ac7XnveVQe55ke+7uA/5BcFezV4GDgQbgBWBi3jx/D3w/fD4NuCuGHGOAY8PnI4BXCuRoBn5ZgX2yEhjdw/SzgQcBA04EnqzAe/QWQZ+Vse8P4BTgWOClnHHfAK4Mn18JXF9gub2AFeFwVPh8VMQ5zgQGhc+vL5SjlPcwghzXAP9UwvvW43ervznypn8TuDrO/VHse5rE50OP8j5zas+7TVd7rvZc7fD/mIAAABxlSURBVHmC7XmtHNk+Hlju7ivc/T3gTmBq3jxTgVvD5/cAp5uZRRnC3d9092fD5+8CS4GxUW4jQlOB2zywEBhpZmNi3N7pwKvuXs5NLPrM3R8nuG10rtzPwK3AJwosehbwqLtvdPdNwKPApChzuPsj7t4WvlwIjCt3/f3JUaJSvluR5Ai/j58G7ih3/SVmKPY9rfjnQwpSe953as/VnpdC7XlXkX0+aqXYHgusynm9mu6N4q55wi/GZmDvuAKFpzWPAZ4sMPnDZvaCmT1oZkfGFMGBR8xskZlNLzC9lH0WpWkU/9JVYn8ANLr7m+Hzt4DGAvNUer98nuCIVCG9vYdRmBGe/rylyGm2Su6Pk4G17t5SZHrk+yPve5rGz0ctUnvendrz7tL4fVV73qmm2vNaKbZTxcyGA/cCX3L3d/ImP0tw6u0DwHeAB2KKcZK7HwtMBi4zs1Ni2k6vzKwBmAL8vMDkSu2PLjw4h5RoVz1mdhXQBtxeZJa438PvAYcAHwTeJDjll6Tz6fkoSKT7o6fvaRo+H5IOas+7UntemNrzbmqqPa+VYnsNMD7n9bhwXMF5zGwQsCewIeogZjaY4A2/3d3vy5/u7u+4+5bw+TxgsJmNjjqHu68Jh+uA+wlOH+UqZZ9FZTLwrLuvLZCzIvsjtDZ7ajUcriswT0X2i5ldBHwcuCBsCLop4T3sF3df6+7t7t4B/LDI+iu1PwYB5wB3FZsnyv1R5Huams9HjVN73n07as+7S833Ve15V7XYntdKsf00cKiZHRT+r3saMDdvnrlA9pemnwIeK/alKFd4jdKPgKXufkORefbLXltoZscTvEeR/iNhZsPMbET2OcEPOF7Km20u8NcWOBHYnHPKJWpF/4dbif2RI/czcCEwp8A8DwNnmtmo8DTcmeG4yJjZJOAKYIq7bysyTynvYX9z5F7T+cki6y/luxWFM4CX3X11oYlR7o8evqep+HyI2vO8bag9LywV31e15wXVXnvuEfzytRoeBL/GfoXgl7ZXheOuI/gCAOxGcNprOfAUcHAMGU4iOFXxIvB8+DgbuAS4JJxnBrCY4FfAC4GPxJDj4HD9L4Tbyu6P3BwGzAr31x+Appjel2EEje2eOeNi3x8E/xi8CbQSXId1McE1nb8GWoD5wF7hvE3AzTnLfj78nCwH/iaGHMsJrhPLfkayvSrsD8zr6T2MOMdPwvf+RYKGaUx+jmLfrShzhON/nP1M5Mwby/7o4Xta8c+HHkXfI7XnnTnUnqs9LyWH2vME2/PU30Ey/F/htwm6pLnZ3f+z2LyjR4/2Aw88sM/b2Lp1K8OGDSs7Y1TSkCMNGZRDOaohR7kZFi1atN7d94kh0oCi9nxgZFAO5aiGHLG351H8rzKuB33s8/G4447zcixYsKCs5aKWhhxpyOCuHPmUo6s05Cg3A/CMp6B9TftD7fnAyOCuHPmUo6s05Ii7PR/U5zK+snb1+QhgZtk+H5dEsnZ32LCBwZs3w/r1kayyP9KQIw0ZlEM5qiHH4M2bgzYk2u6bJUZ6u0QkCWkvtgv1cXhCZGtvbYV99uHPI1thV1sYxkoO5E3G8Bb7sZG9+BMjeYc92MowtjKM92hgO7vTymBaGcZ7LMExWhlMB3W0U09H+DvWduoxnA7q6KBu1/M6OnbNA3QZZ2FvNh3UUU/7rnUAOLZrvs75DwfWd1tHdlvZddTREY61buOALtkKjcvNlpujc9wR1PWQo7R1dP37snkLraP43zeRetb36e/L3c+l5C1tH02kjg19/psLTcvPVug9LZ7tSOrYWNLnotC+7y1b6eO65uht/tL/vtI/9/BnLH23lYbhDX1uG6Ty3KGuDi67DG66Kek0IlJL0l5s9yrs7Hw6QGNjI5lMpvSF29sZ+4//yM6dOxkyZEi/s7R3GI+8+gHmvtzEC2snsH7bHgXnGzp4J7sNeo+hg3fSUN/GkPo2Bte3UUc7QwZ1YOYMrmvHzKk3p846AKgzD4pb68BoD4oGa6XD66izVozgVwBmjrthFl6PHz7PjnMge3DH86Z1dLRjNmjXfHXhtOzzDrddQwu3lT+OMEdP4+rCbPnb35WjvQPq6rvNn7ut3tZRbP7sc88Ow3V0+/ty9kfuOPLmLzSu2Hpz931P2br8fUBHRzt1dfWd73HeOnpbb3Z6f99T72jHwvelL+so9/0r9p7m5sidr5T1Wl6Ovrx/HbvWEXw2fvvE69Q31EqnTtVt5cpgOGuWim0Rqay0F9u99nHo7rOB2QBNTU3e3Nzcty2cfjqZTIY+L5fn2Wfhkkvg6adhwgT4i/Pg8MPh4INhzBjYbz8YPRr22AMGDRoCDAFGdFlHFDn6Kw0ZlEM5qiFHkOG0RDNI6R5/PBgefniyOUSk9qS92N7V5yNBkT0N+EyykbpqbYUrroD//m/YZx/4yU/g/POhvj7pZCIikpUttpctSzaHiNSeVBfb7t5mZjMIOhGvB25x98UJx9plxw6YOhUeeQQuvRT+4z9g5MikU4mISL7f/S7pBCJSq1JdbMOuW7rOSzpHvo6O4Aj2o4/CzTfDxRcnnUhERArZvBleeSV4vueeyWYRkdqjX/aU6bvfhQcegBtuUKEtIpJmzz0XDD/4QdhW8IbZIiLxUbFdhrfegiuvhLPOgi9+Mek0IiLSk2eeCYYnnxz8zqatLdk8IlJbVGyX4ZprYOfOoPso3SBBRCTdFi2C8eODnqIAtm9PNo+I1BYV2330xhvBNdqXXALve1/SaUREpDeLFsFxx3VeQvLaa8nmEZHaomK7j2bPDn4c+eUvJ51ERER6s307LF8OH/gA/P73wbg77kg2k4jUFhXbfdDWFhzV/vjH4cADk04jIiK9WbYsuFX7xInw1a8G4445JtlMIlJbVGz3weOPw9q1cNFFSScREUkPM5tkZsvMbLmZXVlg+uVmtsTMXjSzX5vZhEplW7o0GB5xBOy1V/BcPZKISCWp2O6De++FoUNh0qSkk4iIpIOZ1QOzgMnAROB8M5uYN9tzQJO7Hw3cA3yjUvmWLoW6OjjssKD9Bti6tVJbFxFRsV0y96Bf7cmTOxtsERHheGC5u69w9/eAO4GpuTO4+wJ3zx5PXgiMq1S4pUvh4INhyJDOtltHtkWkklRsl+jll+GPf9RRbRGRPGOBVTmvV4fjirkYeDDWRDmWLg0uIYHOYvuKKyq1dRGRKrhde1o89lgwPO20ZHOIiFQrM/ss0AScWmT6dGA6QGNjI5lMps/b2LJly67l2tuNZctO5qijVpPJrAjnaAYoa93l5khKGjIoh3JUQ464M6jYLtGCBXDAAXDQQUknERFJlTXA+JzX48JxXZjZGcBVwKnuvrPQitx9NjAboKmpyZubm/scJpPJkF2upSXoRerMMw+gufkAILic5JBDoJx1l5sjKWnIoBzKUQ054s6gy0hKtHAh/Pmf646RIiJ5ngYONbODzKwBmAbMzZ3BzI4BfgBMcfd1lQq2IjyYnXsDstNO0+9uRKSyVGyX4M03Yc0a+NCHkk4iIpIu7t4GzAAeBpYCd7v7YjO7zsymhLPNBIYDPzez581sbpHVRSp7p8iDD+4cN2yYeiMRkcrSZSQlWLQoGKrYFhHpzt3nAfPyxl2d8/yMiociOLI9ZAiMGdM5rqOjs+9tEZFK0JHtEjz9dNBPq+46JiJSPVasCO72W5fzL9199wXDNd2uKhcRiYeK7RI89xy8//3B6UcREakOr73W9RISCG5uA7B9e+XziEhtUrFdgldeCYptERGpHitWdO9B6utfD4a6bltEKkXFdi/a24MG+9BDk04iIiKl2rQJ/vSn7ke2s2coVWyLSKWo2O7FG29Aa6uKbRGRalKoJxLoLLbXrq1sHhGpXSq2e9HSEgxVbIuIVI9sH9v5l5HU1wfDc86pbB4RqV2pLbbN7BozWxP2yfq8mZ2dRI5ssZ17UwQREUm3VauC4YQJXcfvvXfls4hIbUt7P9s3uvt/JRmgpSU47ZjbT6uIiKTb6tXBnSJHjuw6PtsbiYhIpaT2yHZaLF8eHNXWbdpFRKrH6tUwdqzabhFJXtqL7Rlm9qKZ3WJmo5II0NKi67VFRKrNmjUwblzhaVOnBoW4iEglJHoZiZnNB/YrMOkq4HvA/wM8HH4T+HyBdUwHpgM0NjaSyWT6nGPLli0Fl2tvN1599WSamlaRybzW5/VGlaOS0pBBOZSjGnKkIYMUt3o1nHJK4Wn77QdtbZXNIyK1K9Fi293PKGU+M/sh8Msi65gNzAZoamry5ubmPufIZDIUWu7VV4N+tk8/fQLNzRO6LxixYjkqKQ0ZlEM5qiFHGjJIYR0dPR/Z3rQp6Ppv+3bYfffKZhOR2tPrZSRmdoeZ/YuZTTaz0ZUIFW439yeJnwReqtS2s9Ttn4hI9Vm3LjhyXexSkbvvDoaPPFK5TCJSu0q5Zvt7wDbgXGC+md1vZiPijQXAN8zsD2b2IvBR4P9UYJtdLF8eDFVsi8hAZ4HxSeeIwurVwbDYke1sH9vf+lZl8ohIbSul2D4Q+A1wibt/ELgHuDbOUADu/jl3P8rdj3b3Ke7+ZtzbzNfSAsOHQ2NjpbcsIlJZ7u7AvKRzRGHNmmBYrNg+99xgqEvuRaQSSim2DwW+CrxsZs8BZwLnmNnpZrZPrOkS1tKibv9EpKY8a2YfSjpEf/V2ZPvTnw6Gf//3lckjIrWtlB9Ifsfd1wGE3e81AZOBC4D/BKq+YS6mpQWOOSbpFCIiFXMCcIGZvQ5sBYzgoPfRycbqm9WrYfBg2KfI4aBBg4I7SepAiohUQinF9kNhkf0ysAx4P3CHu38x1mQJa22FlSs7j4CIiNSAs5IOEIU//jHo3q+uh3O3GzbArFlw002VyyUitanXYtvdjzWzeoIi+3BgPvBQ3MGStnJl8Gt2/ThSRGqFu79eznJmNgn4NlAP3Ozu/5k3/RTgW8DRwDR3v6e/WXuydm3pv7Vx1xFuEYlXSXeQdPd2d1/s7ve5+y/dfcDfDkDd/omI9C48GDOL4PLCicD5ZjYxb7Y3gIuAn1UiU1+K7eefjzeLiEjab9eemGyxfdhhyeYQEUm544Hl7r7C3d8D7gSm5s7g7ivd/UWgoxKB+lJsf+1r8WYREVGxXcQrr8Cee8Loit3GR0SkKo0FVuW8Xh2OS0RHR3BTm/3263m+yy4LhvPnx59JRGpbordrT7OWluASEl3LJyJSGWY2HZgO0NjYSKaMjrDffHMn7e3wzjstZDJris43adIgZs06icmT3yCTWVFu5KK2bNlSVv6BlkE5lKMacsSdQcV2ES0t8JGPJJ1CRCT11gC5d54cF47rM3efDcwGaGpq8ubm5j6v43/+5ykATjrpUJqbe//RzebNB9DcfECft9ObTCZDOfkHWgblUI5qyBF3Bl1GUsDOnfD66/pxpIhICZ4GDjWzg8ysAZgGzE0qzKZNDUDp12w/+GCMYUREULFd0KuvBt1BqdgWEelZ2DvVDOBhYClwt7svNrPrzGwKgJl9yMxWA+cBPzCzxXHl6WuxDcE13iIicdFlJAWo2z8RkdK5+zxgXt64q3OeP01weUnsyim2L70U7r03pkAiUvN0ZLsAFdsiItVp06bBDB4Mo0b1Pu/++wfD++6LN5OI1DYV2wW0tARd/pXSWIuISHps2tTAvvuW1pPUb34Tfx4RERXbBbzyio5qi4hUo02bGkq+hOSQQ4LhmDHx5RERUbFdwJIlMDH/ZsMiIpJ6mzYNZt99S5s3e/T7zTeDm+GIiMRBxXae9euDX6ar2BYRqT6bNw9mn336vtzMmdFnEREBFdvdLA47pDryyGRziIhI373zzmD22qvvy115ZfRZRERAxXY3S5YEQxXbIiLVpbUVtm0bxN57l77MjTd2Pld/2yISBxXbeRYvhj32gLFjk04iIiJ9sXFjMOxLsf0P/9D5vC99c4uIlErFdp7Fi4PrtUvpNkpERNJjw4Zg2Jdiu74+niwiIlkqtvOoJxIRkepUTrENsGxZ9FlERLISLbbN7DwzW2xmHWbWlDftK2a23MyWmdlZlcijnkhERKpXucX2YYd1Pt+xI7o8IiKQ/JHtl4BzgMdzR5rZRGAacCQwCfiumcV+su/ZZ4PhMcfEvSUREYlattgupzeSrN13jyaLiEhWosW2uy9190In8KYCd7r7Tnd/DVgOHB93nmeeCYbHHhv3lkREJGrlHtnO99Of9j+LiEhW0ke2ixkLrMp5vTocF6tFi4Lb944cGfeWREQkahs2wODBHQwb1vdlf/azzuef+1xnzyYiIv01KO4NmNl8YL8Ck65y9zkRrH86MB2gsbGRTCbT53Vs2bKFTCbD//7viRxxxDtkMkv6G6ss2RxJSkMG5VCOasiRhgzS1caNsMcerZgN6fOy558Pn/lM5+u994bt22G33SIMKCI1KfZi293PKGOxNcD4nNfjwnGF1j8bmA3Q1NTkzc3Nfd5YJpPhqKOaWbsWLr98N5qb9+174ghkMhnKyT/QMiiHclRDjjRkkK42bAiKbeh7sQ3w7rswYkTn6913D34439/LUkSktqX1MpK5wDQzG2JmBwGHAk/FucEnngiGx8d+ZbiIiMQhKLbbyl5++HCYPbvruNGjYcuWfgYTkZqWdNd/nzSz1cCHgV+Z2cMA7r4YuBtYAjwEXObu7XFmyWRgyBA48cQ4tyIiInHpPLJdvi98AT784a7j7ruvX6sUkRqXdG8k97v7OHcf4u6N7n5WzrSvufsh7n64uz8Yd5ZMJmhgdX2eiEjfmNmk8J4Iy83sygLTh5jZXeH0J83swDhyRFFsQ3Cm86ijOl9feCFs3tzv1YpIjUrrZSQVtXFjA889Bx/9aNJJRESqS3gPhFnAZGAicH54r4RcFwOb3P19wI3A9VHncO//ZSS5XnwRZszofD1yJJh1Ps49Fx55BHbujGRzIjKAxf4DyWrw+OOjcYdzzkk6iYhI1TkeWO7uKwDM7E6CeyXkdus0FbgmfH4PcJOZmbt7VCG2b4c99oCRI9+LapV85Stw002Fp913X2+XlzRHlqN8zUkHCDUnHSDUnHSAUHPSAULNSQcINScdgAsuOIg4f+9e88W2O8ybN4YjjoAjj0w6jYhI1Sl0X4QTis3j7m1mthnYG1gfVYihDW2sv+QaXn/9dfi3CZGsc++2euDaSNYlIul1++0T+OmP22BQPGVxTRfb27fDV78KLS0juPnm4NSgiIgkoz/3TbDWVk75+tcZD0R1uLwBeM++zj/7N/g2X4porSKSRpnHFkDD4FjWXdPF9o4dMGsWnHbaWi66qDHpOCIi1aiU+yJk51ltZoOAPYEN+Svq930T2tv5TcT9nw8GvhU+goywYkVwecm3vtXDgiJSVY4/6WMMHRrPumv6B5KjRsGSJfB//+9S6uuTTiMiUpWeBg41s4PMrAGYRnCvhFxzgQvD558CHovyeu1KMoNDDoEbbwwK72KPBQsyPU6vxCMNGZRDOdKeY+dOmD8/E1uhDTVebAPsv3/SCUREqpe7twEzgIeBpcDd7r7YzK4zsynhbD8C9jaz5cDlQLfuAUVEktDQQOwHXGv6MhIREek/d58HzMsbd3XO8x3AeZXOJSKSBlalZ/IKMrO3gdfLWHQ0Ef4qvh/SkCMNGUA58ilHV2nIUW6GCe6+T9RhBhq15wMmAyhHPuXoKg05Ym3PB1SxXS4ze8bdm5QjHRmUQzmqIUcaMkh3aXlf0pAjDRmUQzmqIUfcGWr+mm0RERERkbio2BYRERERiYmK7cDspAOE0pAjDRlAOfIpR1dpyJGGDNJdWt6XNORIQwZQjnzK0VUacsSaQddsi4iIiIjEREe2RURERERiUjPFtplNMrNlZrbczLrdUMHMhpjZXeH0J83swBgyjDezBWa2xMwWm9kXC8zTbGabzez58HF1oXVFkGWlmf0h3MYzBaabmf13uD9eNLNjY8hweM7f+byZvWNmX8qbJ5b9YWa3mNk6M3spZ9xeZvaombWEw1FFlr0wnKfFzC6MIcdMM3s53O/3m9nIIsv2+B5GkOMaM1uTs+/PLrJsj9+tCHLclZNhpZk9X2TZSPZHse9pEp8PKUztebftqD1Xe95bDrXnSbbn7j7gH0A98CpwMNAAvABMzJvn74Hvh8+nAXfFkGMMcGz4fATwSoEczcAvK7BPVgKje5h+NvAgYMCJwJMVeI/eIuizMvb9AZwCHAu8lDPuG8CV4fMrgesLLLcXsCIcjgqfj4o4x5nAoPD59YVylPIeRpDjGuCfSnjfevxu9TdH3vRvAlfHuT+KfU+T+HzoUd5nTu15t+lqz9Weqz1PsD2vlSPbxwPL3X2Fu78H3AlMzZtnKnBr+Pwe4HQzsyhDuPub7v5s+Pxdglsbj41yGxGaCtzmgYXASDMbE+P2TgdedfdybmLRZ+7+OLAxb3TuZ+BW4BMFFj0LeNTdN7r7JuBRYFKUOdz9EQ9ugQ2wEBhX7vr7k6NEpXy3IskRfh8/DdxR7vpLzFDse1rxz4cUpPa879Seqz0vhdrzriL7fNRKsT0WWJXzejXdG8Vd84RfjM3A3nEFCk9rHgM8WWDyh83sBTN70MyOjCmCA4+Y2SIzm15gein7LErTKP6lq8T+AGh09zfD528BjQXmqfR++TzBEalCensPozAjPP15S5HTbJXcHycDa929pcj0yPdH3vc0jZ+PWqT2vDu1592l8fuq9rxTTbXntVJsp4qZDQfuBb7k7u/kTX6W4NTbB4DvAA/EFOMkdz8WmAxcZmanxLSdXplZAzAF+HmByZXaH114cA4p0a56zOwqoA24vcgscb+H3wMOAT4IvElwyi9J59PzUZBI90dP39M0fD4kHdSed6X2vDC1593UVHteK8X2GmB8zutx4biC85jZIGBPYEPUQcxsMMEbfru735c/3d3fcfct4fN5wGAzGx11DndfEw7XAfcTnD7KVco+i8pk4Fl3X1sgZ0X2R2ht9tRqOFxXYJ6K7Bczuwj4OHBB2BB0U8J72C/uvtbd2929A/hhkfVXan8MAs4B7io2T5T7o8j3NDWfjxqn9rz7dtSed5ea76va865qsT2vlWL7aeBQMzso/F/3NGBu3jxzgewvTT8FPFbsS1Gu8BqlHwFL3f2GIvPsl7220MyOJ3iPIv1HwsyGmdmI7HOCH3C8lDfbXOCvLXAisDnnlEvUiv4PtxL7I0fuZ+BCYE6BeR4GzjSzUeFpuDPDcZExs0nAFcAUd99WZJ5S3sP+5si9pvOTRdZfyncrCmcAL7v76kITo9wfPXxPU/H5ELXnedtQe15YKr6vas8Lqr323CP45Ws1PAh+jf0KwS9trwrHXUfwBQDYjeC013LgKeDgGDKcRHCq4kXg+fBxNnAJcEk4zwxgMcGvgBcCH4khx8Hh+l8It5XdH7k5DJgV7q8/AE0xvS/DCBrbPXPGxb4/CP4xeBNoJbgO62KCazp/DbQA84G9wnmbgJtzlv18+DlZDvxNDDmWE1wnlv2MZHtV2B+Y19N7GHGOn4Tv/YsEDdOY/BzFvltR5gjH/zj7mciZN5b90cP3tOKfDz2KvkdqzztzqD1Xe15KDrXnCbbnuoOkiIiIiEhMauUyEhERERGRilOxLSIiIiISExXbIiIiIiIxUbEtIiIiIhITFdsiIiIiIjFRsS0iIiIiEhMV2yIiIiIiMVGxLSIiIiISk/8PDqHrCgRe/eMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd453fb8b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd454338630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quadrotor state after 2000 iters:\n",
      "\tr:     [[ 27.950  0.343 -0.030]].T\n",
      "\tPhi:   [[-0.002 -0.001 -0.001]].T\n",
      "\tv:     [[ 0.138 -0.063 -0.044]].T\n",
      "\tomega: [[ 0.009 -0.004 -0.004]].T\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Instantiate a quadrotor model with the given initial conditions\n",
    "quad = Quadrotor(r=np.array([[0],[0],[10]]),\n",
    "                 v=np.array([[0],[0],[0]]),\n",
    "               Phi=np.array([[0.2],[-0.5],[-0.2]]))\n",
    "\n",
    "# Instantiate the SMC controller\n",
    "ctrl = ShaikSMC()\n",
    "\n",
    "# Setup a setpoint commander\n",
    "cmdr = Commander(default=True)\n",
    "\n",
    "# Run the simulation\n",
    "sim = Simulator(quad, ctrl, cmdr=cmdr)\n",
    "sim.run(20, Ts=0.01)\n",
    "sim.plot()\n",
    "\n",
    "print(sim.quad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] M. K. Shaik and J. F. Whidborne, “Robust Sliding Mode Control of a Quadrotor,” 11th Int. Conf. Control, pp. 1–5, 2016.\n",
    "\n",
    "[2] H. K. Khalil, Nonlinear Systems. Princeton, NJ: Prentice Hall, 2002."
   ]
  }
 ],
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