{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adaptive PDE discretizations on Cartesian grids\n",
    "## Volume : Algorithmic tools\n",
    "## Part : Automatic differentiation\n",
    "## Chapter : Dense automatic differentiation, and geodesic shooting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook illustrates automatic differentiation, with an application to Hamilton's equations and geodesic shooting. More precisely, we use automatic differentiation with the following combination of properties:\n",
    "* *First* and *Second* order. The variables used encode gradient and (sometimes) hessian information.\n",
    "* *Dense*. The Taylor expansion information - gradient and hessian - is stored in dense (full) form. This is practical for functions with arbitrary complexity, but low dimensional input.\n",
    "* *Forward*. The Taylor expansion information is propagated forward along with the computations.\n",
    "\n",
    "**Known bugs and incompatibilities.** Our implementation of automatic differentiation is based on subclassing the numpy array class. While simple and powerful, this approach suffers from a few pitfalls, described in the notebook [ADBugs](ADBugs.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[**Summary**](Summary.ipynb) of volume Algorithmic tools, this series of notebooks.\n",
    "\n",
    "[**Main summary**](../Summary.ipynb) of the Adaptive Grid Discretizations \n",
    "\tbook of notebooks, including the other volumes.\n",
    "\n",
    "# Table of contents\n",
    "  * [1. A word on Hamilton's equations](#1.-A-word-on-Hamilton's-equations)\n",
    "    * [1.1 Optics and geodesics](#1.1-Optics-and-geodesics)\n",
    "    * [1.2 Celestial mechanics](#1.2-Celestial-mechanics)\n",
    "    * [1.3 The Lotka-Volterra Predator-Prey model](#1.3-The-Lotka-Volterra-Predator-Prey-model)\n",
    "    * [1.4 Using the Hamiltonian class](#1.4-Using-the-Hamiltonian-class)\n",
    "  * [2. Automatic differentiation basics](#2.-Automatic-differentiation-basics)\n",
    "    * [2.1 Differentiating a function](#2.1-Differentiating-a-function)\n",
    "    * [2.2 Differentiating w.r.t several variables](#2.2-Differentiating-w.r.t-several-variables)\n",
    "    * [2.3 Vectorization](#2.3-Vectorization)\n",
    "    * [2.4 Second order automatic differentiation](#2.4-Second-order-automatic-differentiation)\n",
    "    * [2.5 The gradient and hessian member functions](#2.5-The-gradient-and-hessian-member-functions)\n",
    "  * [3. Solving ordinary differential equations](#3.-Solving-ordinary-differential-equations)\n",
    "    * [3.1 Explicit Euler scheme](#3.1-Explicit-Euler-scheme)\n",
    "    * [3.2 High order explicit schemes](#3.2-High-order-explicit-schemes)\n",
    "    * [3.3 Symplectic Euler scheme - Separable case](#3.3-Symplectic-Euler-scheme---Separable-case)\n",
    "    * [3.4 Symplectic Verlet scheme - Separable case](#3.4-Symplectic-Verlet-scheme---Separable-case)\n",
    "    * [3.5 Symplectic Euler scheme - Non separable case](#3.5-Symplectic-Euler-scheme---Non-separable-case)\n",
    "    * [3.6 The symplectic form](#3.6-The-symplectic-form)\n",
    "  * [4. Shooting geodesics](#4.-Shooting-geodesics)\n",
    "\n",
    "\n",
    "\n",
    "**Acknowledgement.** Some of the experiments presented in these notebooks are part of \n",
    "ongoing research with Ludovic Métivier and Da Chen.\n",
    "\n",
    "Copyright Jean-Marie Mirebeau, Centre Borelli, ENS Paris-Saclay, CNRS, University Paris-Saclay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Importing the required libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:54.750411Z",
     "iopub.status.busy": "2024-04-30T09:12:54.750017Z",
     "iopub.status.idle": "2024-04-30T09:12:54.760235Z",
     "shell.execute_reply": "2024-04-30T09:12:54.759719Z"
    }
   },
   "outputs": [],
   "source": [
    "import sys; sys.path.insert(0,\"..\") # Allow importing agd from parent directory\n",
    "#from Miscellaneous import TocTools; print(TocTools.displayTOC('Dense','Algo'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:54.763118Z",
     "iopub.status.busy": "2024-04-30T09:12:54.762734Z",
     "iopub.status.idle": "2024-04-30T09:12:54.978899Z",
     "shell.execute_reply": "2024-04-30T09:12:54.978616Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:54.980718Z",
     "iopub.status.busy": "2024-04-30T09:12:54.980606Z",
     "iopub.status.idle": "2024-04-30T09:12:55.021258Z",
     "shell.execute_reply": "2024-04-30T09:12:55.020955Z"
    }
   },
   "outputs": [],
   "source": [
    "from agd import AutomaticDifferentiation as ad\n",
    "from agd.ODE.hamiltonian import GenericHamiltonian,SeparableHamiltonian,fixedpoint\n",
    "from agd import LinearParallel as lp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.023010Z",
     "iopub.status.busy": "2024-04-30T09:12:55.022912Z",
     "iopub.status.idle": "2024-04-30T09:12:55.025378Z",
     "shell.execute_reply": "2024-04-30T09:12:55.025132Z"
    }
   },
   "outputs": [],
   "source": [
    "norm_infinity = ad.Optimization.norm_infinity\n",
    "\n",
    "def norm_infinity_ad(x):\n",
    "    \"\"\"Check that the zeroth, first and (possibly) second order content of x\"\"\"\n",
    "    if isinstance(x,ad.Dense.denseAD):  \n",
    "        return max(norm_infinity(x.value),norm_infinity(x.coef))\n",
    "    if isinstance(x,ad.Dense.denseAD2): \n",
    "        return max(norm_infinity(x.value),norm_infinity(x.coef1),norm_infinity(x.coef2))\n",
    "    raise ValueError(\"Not a Dense AD variable\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.026826Z",
     "iopub.status.busy": "2024-04-30T09:12:55.026743Z",
     "iopub.status.idle": "2024-04-30T09:12:55.028713Z",
     "shell.execute_reply": "2024-04-30T09:12:55.028454Z"
    }
   },
   "outputs": [],
   "source": [
    "def reload_packages():\n",
    "    from Miscellaneous.rreload import rreload\n",
    "    global ad,lp,GenericHamiltonian,SeparableHamiltonian\n",
    "    [ad,lp,GenericHamiltonian,SeparableHamiltonian] = rreload([ad,lp,GenericHamiltonian,SeparableHamiltonian],rootdir=\"..\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. A word on Hamilton's equations\n",
    "\n",
    "We choose to illustrate the automatic differentiation concept using Hamilton's equations of geodesics, which read\n",
    "$$\n",
    "    \\dot q = \\partial_p H(q,p), \\qquad \\dot p = -\\partial_q H(q,p),\n",
    "$$\n",
    "where $H$ is the *Hamiltonian* of the medium. \n",
    "These equations are (extremely) common in optics and mechanics. They naturally involve first-order differentiation. In addition, higher order differentiation will also be necessary in the context of geodesic shooting (adjusting the initial conditions to meet a prescribed endpoint), or implicit schemes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Optics and geodesics\n",
    "\n",
    "Hamilton's equations characterize extremal paths, known as geodesics, arising in optics.\n",
    "Following the classical convention we denote by \n",
    "* $q$ the position variable,\n",
    "* $p$ the impultion, which is dual to the velocity.\n",
    "\n",
    "**Riemannian Hamiltonian.** For a domain $\\Omega \\subset R^d$ equipped with a Riemannian metric $M : \\Omega \\to S_d^{++}$, the Hamiltonian is defined as \n",
    "$$\n",
    "    H(q,p) := \\frac 1 2 \\|p\\|_{D(q)}^2, \\quad \\text{where} D(q) := M(q)^{-1}.\n",
    "$$\n",
    "\n",
    "**Poincaré's half plane model.** \n",
    "We illustrate this ODE in the case of Poincaré's half plane model of the hyperbolic space, defined by the Riemannian metric\n",
    "$$\n",
    "    M(q) := \\frac{\\mathrm{Id}}{q_1^2},\n",
    "$$\n",
    "where $q = (q_0,q_1) \\in \\Omega = R \\times R^{++}$. Thus $H(q,p) = (q_1^2/2) \\|p\\|^2$. \n",
    "\n",
    "**Exponential map.**\n",
    "We also consider the Riemannian metric on $R^2 \\setminus \\{0\\}$ defined by\n",
    "$$\n",
    "    M(q) := \\frac{\\mathrm{Id}}{\\|q\\|^2}.\n",
    "$$\n",
    "It can be regarded as the metric induced by the logarithmic (multivalued) map $\\ln : C \\setminus \\{0\\} \\to C$, where the targer space $C$ is equipped with the usual norm, and it possesses periodic trajectories.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.030166Z",
     "iopub.status.busy": "2024-04-30T09:12:55.030074Z",
     "iopub.status.idle": "2024-04-30T09:12:55.032124Z",
     "shell.execute_reply": "2024-04-30T09:12:55.031902Z"
    }
   },
   "outputs": [],
   "source": [
    "def SquaredNorm(p):\n",
    "    return (p**2).sum(axis=0)\n",
    "def H_HalfPlane(q,p):\n",
    "    return 0.5*q[1]**2*SquaredNorm(p)\n",
    "def H_Log(q,p):\n",
    "    return 0.5*SquaredNorm(q)*SquaredNorm(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Celestial mechanics\n",
    "\n",
    "The Hamiltonian is in this case the sum of the kinetic energy, and of the potential energy, say w.r.t. a mass at the origin.\n",
    "\n",
    "<!---\n",
    "**Symplectic integrators**\n",
    "In this notebook, we solve the equations of geodesics using a standard Runge-Kutta scheme. This may sound as a heresy since these equations benefit from a Hamiltonian structure, and can thus be solved more stably using a symplectic integrator, in principle. However, our Hamiltonians are *non-separable*, in other words they do *not* take the form \n",
    "$$\n",
    "    H(q,p) = F(p) + V(q).\n",
    "$$\n",
    "For this reason, the implementation details of a symplectic scheme are non-trivial, and we thus stick to a standard ODE scheme.\n",
    "--->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.033459Z",
     "iopub.status.busy": "2024-04-30T09:12:55.033371Z",
     "iopub.status.idle": "2024-04-30T09:12:55.034999Z",
     "shell.execute_reply": "2024-04-30T09:12:55.034762Z"
    }
   },
   "outputs": [],
   "source": [
    "def H_Celestial(q,p):\n",
    "    return 0.5*SquaredNorm(p) - SquaredNorm(q)**-0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 The Lotka-Volterra Predator-Prey model\n",
    "\n",
    "Some models in appeareance unrelated with mechanics or optics also exhibit a Hamiltonian structure. This is the case of the Lotka-Voltera Predator-Prey model, depending on parameters $\\alpha,\\beta,\\gamma,\\delta \\in R$\n",
    "$$\n",
    "    \\dot x = x (\\alpha-\\beta y), \\qquad \\dot y = y(\\delta x-\\gamma).\n",
    "$$\n",
    "Using a logarithmic change of variables, $q=\\ln x$ and $p=\\ln y$, this model can be put in Hamiltonian form, with\n",
    "$$\n",
    "    H(q,p) = \\alpha p - \\beta e^p + \\gamma q - \\delta e^q.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.036340Z",
     "iopub.status.busy": "2024-04-30T09:12:55.036260Z",
     "iopub.status.idle": "2024-04-30T09:12:55.038224Z",
     "shell.execute_reply": "2024-04-30T09:12:55.037992Z"
    }
   },
   "outputs": [],
   "source": [
    "LotkaVolterra_params = (1.,1.,1.,1.)\n",
    "def H_LotkaVolterra(q,p,params=LotkaVolterra_params):\n",
    "    alpha,beta,gamma,delta=params\n",
    "    return alpha*p - beta*np.exp(p) + gamma*q-delta*np.exp(q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Using the Hamiltonian class\n",
    "\n",
    "Since Hamiltonian structures are quite common in mathematics, a Hamiltonian class is provided, which implements most of the operations presented in this notebook. It does rely on automatic differentiation as well, but hides these  details internal internally. We check here that it reproduces the same results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.039537Z",
     "iopub.status.busy": "2024-04-30T09:12:55.039461Z",
     "iopub.status.idle": "2024-04-30T09:12:55.041665Z",
     "shell.execute_reply": "2024-04-30T09:12:55.041429Z"
    }
   },
   "outputs": [],
   "source": [
    "# Non-separable Hamiltonians\n",
    "HalfPlane = GenericHamiltonian(H_HalfPlane)\n",
    "Log = GenericHamiltonian(H_Log)\n",
    "\n",
    "# Separable Hamiltonian\n",
    "alpha,beta,gamma,delta=LotkaVolterra_params\n",
    "LotkaVolterra = SeparableHamiltonian( lambda q:gamma*q - delta*np.exp(q), lambda p:alpha*p - beta*np.exp(p) )\n",
    "LotkaVolterra.vdim=None # Uses scalar variables\n",
    "\n",
    "# Separable Hamiltonian with a quadratic structure in the second variable\n",
    "Celestial = SeparableHamiltonian( lambda q:-SquaredNorm(q)**-0.5, lambda p:0.5*SquaredNorm(p) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.043015Z",
     "iopub.status.busy": "2024-04-30T09:12:55.042938Z",
     "iopub.status.idle": "2024-04-30T09:12:55.044713Z",
     "shell.execute_reply": "2024-04-30T09:12:55.044482Z"
    }
   },
   "outputs": [],
   "source": [
    "# Collect the Hamiltonians defined as functions or classes, for comparison purposes\n",
    "HClass = [HalfPlane,Log,Celestial] \n",
    "HFun = [H_HalfPlane,H_Log,H_Celestial] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Automatic differentiation basics\n",
    "\n",
    "We illustrate the automatic differentiation mechanism by differentiating a Hamiltonian w.r.t. the position $q$ and momentum $p$, which is a prerequisite for implementing Hamilton's ODE of motion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Differentiating a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.046064Z",
     "iopub.status.busy": "2024-04-30T09:12:55.045992Z",
     "iopub.status.idle": "2024-04-30T09:12:55.047526Z",
     "shell.execute_reply": "2024-04-30T09:12:55.047305Z"
    }
   },
   "outputs": [],
   "source": [
    "Hamiltonian = H_HalfPlane"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.048917Z",
     "iopub.status.busy": "2024-04-30T09:12:55.048835Z",
     "iopub.status.idle": "2024-04-30T09:12:55.050551Z",
     "shell.execute_reply": "2024-04-30T09:12:55.050269Z"
    }
   },
   "outputs": [],
   "source": [
    "q = np.array([0.,1.])\n",
    "p = np.array([1.,1.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.051823Z",
     "iopub.status.busy": "2024-04-30T09:12:55.051749Z",
     "iopub.status.idle": "2024-04-30T09:12:55.054786Z",
     "shell.execute_reply": "2024-04-30T09:12:55.054577Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q,p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order access the Hamiltonian's derivatives, say with respect to position, we evaluate it on a variable featuring first order information. Said otherwise, we create a variable representing the first order Taylor expansion\n",
    "$$\n",
    "    q_\\mathrm{ad} = (q_0+\\delta_0,q_1+\\delta_1) + O(\\|\\delta\\|^2),\n",
    "$$\n",
    "where $\\delta = (\\delta_0,\\delta_1)$ is a symbolic, infinitesimal perturbation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.074799Z",
     "iopub.status.busy": "2024-04-30T09:12:55.074674Z",
     "iopub.status.idle": "2024-04-30T09:12:55.076579Z",
     "shell.execute_reply": "2024-04-30T09:12:55.076313Z"
    }
   },
   "outputs": [],
   "source": [
    "q_ad = ad.Dense.identity(constant=q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.077955Z",
     "iopub.status.busy": "2024-04-30T09:12:55.077857Z",
     "iopub.status.idle": "2024-04-30T09:12:55.079979Z",
     "shell.execute_reply": "2024-04-30T09:12:55.079737Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array([0., 1.]),\n",
       "array([[1., 0.],\n",
       "       [0., 1.]]))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_ad # Contains an additional array representing first order information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.081414Z",
     "iopub.status.busy": "2024-04-30T09:12:55.081309Z",
     "iopub.status.idle": "2024-04-30T09:12:55.083236Z",
     "shell.execute_reply": "2024-04-30T09:12:55.082994Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Zero-th order :  [0. 1.]\n",
      "First order : \n",
      " [[1. 0.]\n",
      " [0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Zero-th order : \",q_ad.value)\n",
    "print(\"First order : \\n\",q_ad.coef)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first order information is propagated through the computations, and eventually we obtain the result\n",
    "$$\n",
    "    H(q_\\mathrm{ad},p) = H(q,p) + <\\nabla_q H(q,p),\\delta> + O(\\|\\delta\\|^2).\n",
    "$$\n",
    "Note that, for Poincaré's half plane model, one has $\\nabla_q H(q,p) = (0,q_1 \\|p\\|^2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.084585Z",
     "iopub.status.busy": "2024-04-30T09:12:55.084488Z",
     "iopub.status.idle": "2024-04-30T09:12:55.086526Z",
     "shell.execute_reply": "2024-04-30T09:12:55.086291Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array(1.),array([0., 2.]))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q_ad,p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.087902Z",
     "iopub.status.busy": "2024-04-30T09:12:55.087803Z",
     "iopub.status.idle": "2024-04-30T09:12:55.089522Z",
     "shell.execute_reply": "2024-04-30T09:12:55.089272Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient of the Hamiltonian w.r.t. the variable q :  [0. 2.]\n"
     ]
    }
   ],
   "source": [
    "print(\"Gradient of the Hamiltonian w.r.t. the variable q : \",Hamiltonian(q_ad,p).gradient())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can similarly differentiate w.r.t. the momentum $p$. Poincaré's half plane model obeys\n",
    "$\\nabla_p H(q,p) = q_1^2 p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.090957Z",
     "iopub.status.busy": "2024-04-30T09:12:55.090861Z",
     "iopub.status.idle": "2024-04-30T09:12:55.093146Z",
     "shell.execute_reply": "2024-04-30T09:12:55.092912Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array(1.),array([1., 1.]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_ad = ad.Dense.identity(constant=p)\n",
    "Hamiltonian(q,p_ad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comparing with the Hamiltonian class**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.094494Z",
     "iopub.status.busy": "2024-04-30T09:12:55.094396Z",
     "iopub.status.idle": "2024-04-30T09:12:55.096926Z",
     "shell.execute_reply": "2024-04-30T09:12:55.096692Z"
    }
   },
   "outputs": [],
   "source": [
    "for Cls,Fun in zip(HClass,HFun):\n",
    "    assert norm_infinity( Cls.H(q,p) - Fun(q,p) ) < 1e-14\n",
    "    assert norm_infinity( Cls.DqH(q,p) - Fun(q_ad,p).gradient() ) < 1e-14\n",
    "    assert norm_infinity( Cls.DpH(q,p) - Fun(q,p_ad).gradient() ) < 1e-14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Differentiating w.r.t several variables\n",
    "\n",
    "Evaluating $H(q_\\mathrm{ad},p_\\mathrm{ad})$ yields an result may sound unexpected: we obtain the sum $\\nabla_q H(q,p)+\\nabla_p H(q,p)$ of the gradients, instead of their independent values. Indeed, this follows from the first order Taylor expansion\n",
    "$$\n",
    "H(q+\\delta,p+\\delta) = \n",
    "H(q,p) + <\\nabla_q H(q,p),\\delta> + <\\nabla_p H(q,p),\\delta> + O(\\|\\delta\\|^2),\n",
    "$$\n",
    "where $\\delta = (\\delta_0,\\delta_1)$ is an infinitesimal symbolic perturbation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.098290Z",
     "iopub.status.busy": "2024-04-30T09:12:55.098194Z",
     "iopub.status.idle": "2024-04-30T09:12:55.100219Z",
     "shell.execute_reply": "2024-04-30T09:12:55.100000Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array(1.),array([1., 3.]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q_ad,p_ad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to obtain the gradient of $H$ w.r.t the independent variables $q$ and $p$, we need to specify that the corresdponding infinitesimal perturbations are independent. Namely set\n",
    "$$\n",
    "    q_\\mathrm{ad} = q+(\\delta_0,\\delta_1), \\quad p_\\mathrm{ad} = p+(\\delta_2,\\delta_3),\n",
    "$$\n",
    "where $(\\delta_0,\\cdots,\\delta_4)$ is four dimensional infinitesimal perturbation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.101582Z",
     "iopub.status.busy": "2024-04-30T09:12:55.101484Z",
     "iopub.status.idle": "2024-04-30T09:12:55.103237Z",
     "shell.execute_reply": "2024-04-30T09:12:55.103009Z"
    }
   },
   "outputs": [],
   "source": [
    "q_ad = ad.Dense.identity(constant=q,shift=(0,p.size))\n",
    "p_ad = ad.Dense.identity(constant=p,shift=(q.size,0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As desired, we obtain the full gradient of $H$, which is the concatenation of $\\nabla_q H$ and $\\nabla_p H$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.104614Z",
     "iopub.status.busy": "2024-04-30T09:12:55.104523Z",
     "iopub.status.idle": "2024-04-30T09:12:55.106435Z",
     "shell.execute_reply": "2024-04-30T09:12:55.106205Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array(1.),array([0., 2., 1., 1.]))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q_ad,p_ad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.107772Z",
     "iopub.status.busy": "2024-04-30T09:12:55.107675Z",
     "iopub.status.idle": "2024-04-30T09:12:55.109643Z",
     "shell.execute_reply": "2024-04-30T09:12:55.109396Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array([0., 1.]),\n",
       "array([[1., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.]]))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q_ad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.110949Z",
     "iopub.status.busy": "2024-04-30T09:12:55.110859Z",
     "iopub.status.idle": "2024-04-30T09:12:55.112806Z",
     "shell.execute_reply": "2024-04-30T09:12:55.112586Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array([1., 1.]),\n",
       "array([[0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.]]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_ad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Apply independent perturbations to a sequence of variables.**\n",
    "The `register` function takes care of shifting the perturbations adequately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.114164Z",
     "iopub.status.busy": "2024-04-30T09:12:55.114068Z",
     "iopub.status.idle": "2024-04-30T09:12:55.115912Z",
     "shell.execute_reply": "2024-04-30T09:12:55.115699Z"
    }
   },
   "outputs": [],
   "source": [
    "q_ad_,p_ad_ = ad.Dense.register((q,p))\n",
    "for a,b in zip( (q_ad_,p_ad_), (q_ad,p_ad)):\n",
    "    assert norm_infinity_ad(a-b)==0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Vectorization\n",
    "\n",
    "A common programming style in Python application to numerics is vectorized computations using numpy tensors.\n",
    "This allows avoiding loops, when some operation has to be repeated a large number of times, with improvements in clarity, flexibility, and speed. \n",
    "\n",
    "As an example, we compute $H(q_0,p_0)$, $H(q_1,p_1)$, $H(q_2,p_2)$, where $q_0,q_1,q_2$ and $p_0,p_1,p_2$ are different positions and impulsions. We also differentiate these values w.r.t. the impulsion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.117284Z",
     "iopub.status.busy": "2024-04-30T09:12:55.117179Z",
     "iopub.status.idle": "2024-04-30T09:12:55.119087Z",
     "shell.execute_reply": "2024-04-30T09:12:55.118866Z"
    }
   },
   "outputs": [],
   "source": [
    "q0 = np.array([0.,1.]); q1 = np.array([1.,1.]); q2 = np.array([-2.,1.]); \n",
    "p0 = np.array([1.,1.]); p1 = np.array([1.,0.]); p2 = np.array([-1.,-1.]); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.120470Z",
     "iopub.status.busy": "2024-04-30T09:12:55.120365Z",
     "iopub.status.idle": "2024-04-30T09:12:55.122432Z",
     "shell.execute_reply": "2024-04-30T09:12:55.122194Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 0.5, 1.0)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q0,p0), Hamiltonian(q1,p1), Hamiltonian(q2,p2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.123800Z",
     "iopub.status.busy": "2024-04-30T09:12:55.123708Z",
     "iopub.status.idle": "2024-04-30T09:12:55.126282Z",
     "shell.execute_reply": "2024-04-30T09:12:55.126055Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[denseAD(array(1.),array([1., 1.])),\n",
       " denseAD(array(0.5),array([1., 0.])),\n",
       " denseAD(array(1.),array([-1., -1.]))]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham_seq = [Hamiltonian(q,ad.Dense.identity(constant=p)) for (q,p) in ((q0,p0), (q1,p1), (q2,p2))]\n",
    "Ham_seq"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vectorized form of these computations is as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.127649Z",
     "iopub.status.busy": "2024-04-30T09:12:55.127553Z",
     "iopub.status.idle": "2024-04-30T09:12:55.129159Z",
     "shell.execute_reply": "2024-04-30T09:12:55.128939Z"
    }
   },
   "outputs": [],
   "source": [
    "q_vec = np.stack( (q0,q1,q2),axis=1)\n",
    "p_vec = np.stack( (p0,p1,p2),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.130462Z",
     "iopub.status.busy": "2024-04-30T09:12:55.130386Z",
     "iopub.status.idle": "2024-04-30T09:12:55.132449Z",
     "shell.execute_reply": "2024-04-30T09:12:55.132215Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1. , 0.5, 1. ])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q_vec,p_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.133766Z",
     "iopub.status.busy": "2024-04-30T09:12:55.133686Z",
     "iopub.status.idle": "2024-04-30T09:12:55.135325Z",
     "shell.execute_reply": "2024-04-30T09:12:55.135094Z"
    }
   },
   "outputs": [],
   "source": [
    "p_vec_ad = ad.Dense.identity(constant=p_vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, the automatic differentiation result may not be what is desired. Indeed, the entries of `q_vec` are all considered independent, and we recover a six dimensional gradient vector for each component. This is both impractical and numerically expensive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.136664Z",
     "iopub.status.busy": "2024-04-30T09:12:55.136586Z",
     "iopub.status.idle": "2024-04-30T09:12:55.138879Z",
     "shell.execute_reply": "2024-04-30T09:12:55.138658Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array([1. , 0.5, 1. ]),\n",
       "array([[ 1.,  0.,  0.,  1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0., -1.,  0.,  0., -1.]]))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham_vec = Hamiltonian(q_vec,p_vec_ad)\n",
    "Ham_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.140162Z",
     "iopub.status.busy": "2024-04-30T09:12:55.140082Z",
     "iopub.status.idle": "2024-04-30T09:12:55.142074Z",
     "shell.execute_reply": "2024-04-30T09:12:55.141825Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sequential result :  denseAD(1.0,[1. 1.])\n",
      "Vectorized result :  denseAD(1.0,[1. 0. 0. 1. 0. 0.])\n"
     ]
    }
   ],
   "source": [
    "print(\"Sequential result : \",Ham_seq[0])\n",
    "print(\"Vectorized result : \",Ham_vec[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this situation, and in contrast with the previous section, we would like the perturbations to be regarded as dependent. This is achieved with the following parameters:\n",
    "* `shape_free` : apply free independent symbolic perturbations w.r.t. these dimensions.\n",
    "* `shape_bound` : apply bound correlated symbolic perturbations w.r.t. these dimensions.\n",
    "\n",
    "It is assumed that the *free* dimensions come first, and the *bound* dimensions come last. Only one of the two parameters `shape_free` and `shape_bound` needs to be specified, since they are redundant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.143492Z",
     "iopub.status.busy": "2024-04-30T09:12:55.143415Z",
     "iopub.status.idle": "2024-04-30T09:12:55.145377Z",
     "shell.execute_reply": "2024-04-30T09:12:55.145157Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_vec.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first dimension is *free*, and the last one is *bound* since it is only introduced for vectorization purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.146754Z",
     "iopub.status.busy": "2024-04-30T09:12:55.146659Z",
     "iopub.status.idle": "2024-04-30T09:12:55.148168Z",
     "shell.execute_reply": "2024-04-30T09:12:55.147943Z"
    }
   },
   "outputs": [],
   "source": [
    "shape_free,shape_bound = p_vec.shape[:1], p_vec.shape[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.149466Z",
     "iopub.status.busy": "2024-04-30T09:12:55.149387Z",
     "iopub.status.idle": "2024-04-30T09:12:55.151036Z",
     "shell.execute_reply": "2024-04-30T09:12:55.150800Z"
    }
   },
   "outputs": [],
   "source": [
    "p_vec_ad = ad.Dense.identity(constant=p_vec, shape_bound=shape_bound)\n",
    "#p_vec_ad = ad.Dense.identity(constant=p_vec, shape_free=shape_free) # Equivalently"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.152293Z",
     "iopub.status.busy": "2024-04-30T09:12:55.152219Z",
     "iopub.status.idle": "2024-04-30T09:12:55.154178Z",
     "shell.execute_reply": "2024-04-30T09:12:55.153895Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vectorized result (with shape_bound): \n",
      " denseAD([1.  0.5 1. ],\n",
      "[[ 1.  1.]\n",
      " [ 1.  0.]\n",
      " [-1. -1.]])\n"
     ]
    }
   ],
   "source": [
    "Ham_vec = Hamiltonian(q_vec,p_vec_ad)\n",
    "print(\"Vectorized result (with shape_bound): \\n\", Ham_vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This technique is compatible with differentiation w.r.t. multiple independent variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.155502Z",
     "iopub.status.busy": "2024-04-30T09:12:55.155426Z",
     "iopub.status.idle": "2024-04-30T09:12:55.157286Z",
     "shell.execute_reply": "2024-04-30T09:12:55.157086Z"
    }
   },
   "outputs": [],
   "source": [
    "q_vec_ad = ad.Dense.identity(constant=q_vec, shape_free=shape_free, shift=(0,len(p_vec)) )\n",
    "p_vec_ad = ad.Dense.identity(constant=p_vec, shape_free=shape_free, shift=(len(q_vec),0) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.158556Z",
     "iopub.status.busy": "2024-04-30T09:12:55.158479Z",
     "iopub.status.idle": "2024-04-30T09:12:55.160660Z",
     "shell.execute_reply": "2024-04-30T09:12:55.160439Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array([1. , 0.5, 1. ]),\n",
       "array([[ 0.,  2.,  1.,  1.],\n",
       "       [ 0.,  1.,  1.,  0.],\n",
       "       [ 0.,  2., -1., -1.]]))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham_vec = Hamiltonian(q_vec_ad,p_vec_ad)\n",
    "Ham_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.161997Z",
     "iopub.status.busy": "2024-04-30T09:12:55.161918Z",
     "iopub.status.idle": "2024-04-30T09:12:55.163715Z",
     "shell.execute_reply": "2024-04-30T09:12:55.163491Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full gradient w.r.t q0,p0 :  denseAD(1.0,[0. 2. 1. 1.])\n"
     ]
    }
   ],
   "source": [
    "print(\"Full gradient w.r.t q0,p0 : \", Ham_vec[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, the `register` function takes car of the shifts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.165006Z",
     "iopub.status.busy": "2024-04-30T09:12:55.164929Z",
     "iopub.status.idle": "2024-04-30T09:12:55.166796Z",
     "shell.execute_reply": "2024-04-30T09:12:55.166552Z"
    }
   },
   "outputs": [],
   "source": [
    "q_vec_ad_,p_vec_ad_ = ad.Dense.register((q_vec,p_vec), shape_bound=shape_bound)\n",
    "for a,b in zip( (q_vec_ad_,p_vec_ad_), (q_vec_ad,p_vec_ad) ):\n",
    "    assert  norm_infinity_ad(a-b) == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Alternative implementation using arrays of arrays.** Another way to achieve vectorization is to use 'arrays of arrays'. This approach is not recommended here, since it is more cumbersome and less efficient, but it is still shown for completeness and testing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.168123Z",
     "iopub.status.busy": "2024-04-30T09:12:55.168047Z",
     "iopub.status.idle": "2024-04-30T09:12:55.169589Z",
     "shell.execute_reply": "2024-04-30T09:12:55.169356Z"
    }
   },
   "outputs": [],
   "source": [
    "q_diss = ad.disassociate(q_vec, shape_free=(2,), # Creates an array of arrays\n",
    "                         expand_free_dims=None, expand_bound_dims=None) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.170886Z",
     "iopub.status.busy": "2024-04-30T09:12:55.170808Z",
     "iopub.status.idle": "2024-04-30T09:12:55.172489Z",
     "shell.execute_reply": "2024-04-30T09:12:55.172266Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "An array of arrays : [array([ 0.,  1., -2.]) array([1., 1., 1.])]\n",
      "First element : [ 0.  1. -2.]\n"
     ]
    }
   ],
   "source": [
    "print(\"An array of arrays :\", q_diss)\n",
    "print(\"First element :\", q_diss[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is safer to avoid scalar arrays in the context of 'arrays of arrays'. Indeed, confusion aries otherwise between 'arrays scalars with array components', and 'standard arrays'. The default for `ad.disassociate` is to introduce singleton dimensions to ensure this behavior is avoided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.173822Z",
     "iopub.status.busy": "2024-04-30T09:12:55.173743Z",
     "iopub.status.idle": "2024-04-30T09:12:55.175443Z",
     "shell.execute_reply": "2024-04-30T09:12:55.175223Z"
    }
   },
   "outputs": [],
   "source": [
    "q_diss = ad.disassociate(q_vec, shape_free=(2,)) \n",
    "p_diss = ad.disassociate(p_vec, shape_free=(2,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.176783Z",
     "iopub.status.busy": "2024-04-30T09:12:55.176667Z",
     "iopub.status.idle": "2024-04-30T09:12:55.178786Z",
     "shell.execute_reply": "2024-04-30T09:12:55.178547Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Disassociated array  [[array([[ 0.],\n",
      "         [ 1.],\n",
      "         [-2.]])]\n",
      " [array([[1.],\n",
      "         [1.],\n",
      "         [1.]])]]\n",
      "with type  <class 'numpy.ndarray'> with data type  object and shape  (2, 1) including a trailing singleton.\n",
      "Reconstructed array [[ 0.  1. -2.]\n",
      " [ 1.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Disassociated array \", q_diss)\n",
    "print(\"with type \", type(q_diss), \"with data type \", q_diss.dtype, \n",
    "      \"and shape \", q_diss.shape, \"including a trailing singleton.\")\n",
    "print(\"Reconstructed array\", ad.associate(q_diss)) # Inverse operation to disassociate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now manipulate `q_diss` and `p_diss` as standard low-dimensional arrays, abstracting the underlying vectorization, and in particular use the AD tools."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.180129Z",
     "iopub.status.busy": "2024-04-30T09:12:55.180031Z",
     "iopub.status.idle": "2024-04-30T09:12:55.182061Z",
     "shell.execute_reply": "2024-04-30T09:12:55.181822Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([array([[1. ],\n",
       "              [0.5],\n",
       "              [1. ]])], dtype=object)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q_diss,p_diss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.183385Z",
     "iopub.status.busy": "2024-04-30T09:12:55.183284Z",
     "iopub.status.idle": "2024-04-30T09:12:55.185061Z",
     "shell.execute_reply": "2024-04-30T09:12:55.184828Z"
    }
   },
   "outputs": [],
   "source": [
    "q_diss_ad = ad.Dense.identity(constant=q_diss,shift=(0,2))\n",
    "p_diss_ad = ad.Dense.identity(constant=p_diss,shift=(2,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.186353Z",
     "iopub.status.busy": "2024-04-30T09:12:55.186279Z",
     "iopub.status.idle": "2024-04-30T09:12:55.187895Z",
     "shell.execute_reply": "2024-04-30T09:12:55.187665Z"
    }
   },
   "outputs": [],
   "source": [
    "Ham_diss_ad = Hamiltonian(q_diss_ad,p_diss_ad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.189175Z",
     "iopub.status.busy": "2024-04-30T09:12:55.189097Z",
     "iopub.status.idle": "2024-04-30T09:12:55.191332Z",
     "shell.execute_reply": "2024-04-30T09:12:55.191092Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD(array([1. , 0.5, 1. ]),\n",
       "array([[ 0.,  2.,  1.,  1.],\n",
       "       [ 0.,  1.,  1.,  0.],\n",
       "       [ 0.,  2., -1., -1.]]))"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ad.associate(Ham_diss_ad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comparison with the Hamiltonian class**\n",
    "\n",
    "The Hamiltonian class needs to know about the number of independent components, in order to deal with multi-dimensional arrays appropriately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.192658Z",
     "iopub.status.busy": "2024-04-30T09:12:55.192578Z",
     "iopub.status.idle": "2024-04-30T09:12:55.194265Z",
     "shell.execute_reply": "2024-04-30T09:12:55.194030Z"
    }
   },
   "outputs": [],
   "source": [
    "HalfPlane.shape_free = (2,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.195548Z",
     "iopub.status.busy": "2024-04-30T09:12:55.195473Z",
     "iopub.status.idle": "2024-04-30T09:12:55.197711Z",
     "shell.execute_reply": "2024-04-30T09:12:55.197491Z"
    }
   },
   "outputs": [],
   "source": [
    "assert norm_infinity_ad(Ham_vec - ad.associate(Ham_diss_ad)) < 1e-14\n",
    "assert norm_infinity(HalfPlane.H(q_vec,p_vec) - Ham_vec.value) < 1e-14\n",
    "assert norm_infinity(HalfPlane.DqH(q_vec,p_vec) - Ham_vec.gradient()[:2]) < 1e-14\n",
    "assert norm_infinity(HalfPlane.DpH(q_vec,p_vec) - Ham_vec.gradient()[2:]) < 1e-14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Second order automatic differentiation\n",
    "\n",
    "There are situations where second order automatic differentiation is needed. It could be achieved, in principle, by recursive calls to first order differentiation. However, for reasons of performance and convenience, a dedicated class is implemented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.199025Z",
     "iopub.status.busy": "2024-04-30T09:12:55.198946Z",
     "iopub.status.idle": "2024-04-30T09:12:55.200659Z",
     "shell.execute_reply": "2024-04-30T09:12:55.200447Z"
    }
   },
   "outputs": [],
   "source": [
    "q_ad = ad.Dense2.identity(constant=q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hessian of Poincaré's half plane model hamiltonian, w.r.t. position is \n",
    "$$\n",
    "    \\nabla^2_q H(q,p) = \\begin{pmatrix} 0 & 0 \\\\ 0 & \\|p\\|^2 \\end{pmatrix}\n",
    "$$\n",
    "and w.r.t. impulsion\n",
    "$$\n",
    "    \\nabla^2_p H(q,p) = q_0^2 \\mathrm{Id}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.202003Z",
     "iopub.status.busy": "2024-04-30T09:12:55.201924Z",
     "iopub.status.idle": "2024-04-30T09:12:55.204143Z",
     "shell.execute_reply": "2024-04-30T09:12:55.203908Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD2(array(1.),array([0., 2.]),\n",
       "array([[0., 0.],\n",
       "       [0., 2.]]))"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham = Hamiltonian(q_ad,p)\n",
    "Ham"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.205507Z",
     "iopub.status.busy": "2024-04-30T09:12:55.205431Z",
     "iopub.status.idle": "2024-04-30T09:12:55.207355Z",
     "shell.execute_reply": "2024-04-30T09:12:55.207112Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Function value :  1.0\n",
      "Gradient :  [0. 2.]\n",
      "Hessian : \n",
      " [[0. 0.]\n",
      " [0. 2.]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Function value : \", Ham.value)\n",
    "print(\"Gradient : \", Ham.coef1)\n",
    "print(\"Hessian : \\n\", Ham.coef2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.208666Z",
     "iopub.status.busy": "2024-04-30T09:12:55.208585Z",
     "iopub.status.idle": "2024-04-30T09:12:55.210276Z",
     "shell.execute_reply": "2024-04-30T09:12:55.210051Z"
    }
   },
   "outputs": [],
   "source": [
    "p_ad = ad.Dense2.identity(constant=p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.211576Z",
     "iopub.status.busy": "2024-04-30T09:12:55.211494Z",
     "iopub.status.idle": "2024-04-30T09:12:55.213707Z",
     "shell.execute_reply": "2024-04-30T09:12:55.213493Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD2(array(1.),array([1., 1.]),\n",
       "array([[1., 0.],\n",
       "       [0., 1.]]))"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q,p_ad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A joint hessian, of size $4\\times 4$, can be computed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.214968Z",
     "iopub.status.busy": "2024-04-30T09:12:55.214891Z",
     "iopub.status.idle": "2024-04-30T09:12:55.216759Z",
     "shell.execute_reply": "2024-04-30T09:12:55.216518Z"
    }
   },
   "outputs": [],
   "source": [
    "q_ad = ad.Dense2.identity(constant=q, shift=(0,p.size))\n",
    "p_ad = ad.Dense2.identity(constant=p, shift=(q.size,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.218010Z",
     "iopub.status.busy": "2024-04-30T09:12:55.217935Z",
     "iopub.status.idle": "2024-04-30T09:12:55.219890Z",
     "shell.execute_reply": "2024-04-30T09:12:55.219677Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 4, 4)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_ad.coef2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.221177Z",
     "iopub.status.busy": "2024-04-30T09:12:55.221102Z",
     "iopub.status.idle": "2024-04-30T09:12:55.223363Z",
     "shell.execute_reply": "2024-04-30T09:12:55.223137Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD2(array(1.),array([0., 2., 1., 1.]),\n",
       "array([[0., 0., 0., 0.],\n",
       "       [0., 2., 2., 2.],\n",
       "       [0., 2., 1., 0.],\n",
       "       [0., 2., 0., 1.]]))"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hamiltonian(q_ad,p_ad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vectorization works as in the first order case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.224664Z",
     "iopub.status.busy": "2024-04-30T09:12:55.224590Z",
     "iopub.status.idle": "2024-04-30T09:12:55.226279Z",
     "shell.execute_reply": "2024-04-30T09:12:55.226063Z"
    }
   },
   "outputs": [],
   "source": [
    "q_vec_ad = ad.Dense2.identity(constant=q_vec, shape_free=shape_free)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.227538Z",
     "iopub.status.busy": "2024-04-30T09:12:55.227465Z",
     "iopub.status.idle": "2024-04-30T09:12:55.229709Z",
     "shell.execute_reply": "2024-04-30T09:12:55.229475Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD2(array(1.),array([0., 2.]),\n",
       "array([[0., 0.],\n",
       "       [0., 2.]]))"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham = Hamiltonian(q_vec_ad,p_vec)\n",
    "Ham[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.230973Z",
     "iopub.status.busy": "2024-04-30T09:12:55.230896Z",
     "iopub.status.idle": "2024-04-30T09:12:55.232768Z",
     "shell.execute_reply": "2024-04-30T09:12:55.232536Z"
    }
   },
   "outputs": [],
   "source": [
    "q_vec_ad = ad.Dense2.identity(constant=q_vec,shape_bound=shape_bound, shift=(0,len(p_vec)) )\n",
    "p_vec_ad = ad.Dense2.identity(constant=p_vec,shape_bound=shape_bound, shift=(len(q_vec),0) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.234042Z",
     "iopub.status.busy": "2024-04-30T09:12:55.233964Z",
     "iopub.status.idle": "2024-04-30T09:12:55.236298Z",
     "shell.execute_reply": "2024-04-30T09:12:55.236069Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD2(array(1.),array([0., 2., 1., 1.]),\n",
       "array([[0., 0., 0., 0.],\n",
       "       [0., 2., 2., 2.],\n",
       "       [0., 2., 1., 0.],\n",
       "       [0., 2., 0., 1.]]))"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham = Hamiltonian(q_vec_ad,p_vec_ad)\n",
    "Ham[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Alternative approach using recursive automatic differentiation.** \n",
    "We present an alternative approach to second order automatic differentiation, based on recursive first order differentiation. It is not recommended, since it is more cumbersome and less efficient, but it is still shown for completeness and testing.\n",
    "\n",
    "<!---We can reconstruct the second order AD information by associating two levels of first order differentiation.\n",
    "Note the parameter `singleton_axis=-2`, replacing the default `singleton_axis=-1`, because the last axis is for the AD dimension.--->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.237636Z",
     "iopub.status.busy": "2024-04-30T09:12:55.237559Z",
     "iopub.status.idle": "2024-04-30T09:12:55.240133Z",
     "shell.execute_reply": "2024-04-30T09:12:55.239902Z"
    }
   },
   "outputs": [],
   "source": [
    "def ADRecIdentity(constant,shape_free=None,shift=(0,0)):\n",
    "    # First order differentiation\n",
    "    q_ad = ad.Dense.identity(constant=constant, shape_free=shape_free, shift=shift) \n",
    "    # Hide automatic differentiation info in the component type\n",
    "    q_diss = ad.disassociate(q_ad, shape_free=shape_free) \n",
    "    # Recursive first order differentiation\n",
    "    q_ad2 = ad.Dense.identity(constant=q_diss, shape_free=shape_free, shift=shift) \n",
    "    return q_ad2\n",
    "\n",
    "def ADRecToAD2(q): \n",
    "    q01 = ad.associate(q.value) # Zero-th and first order\n",
    "    q12 = ad.associate(q.coef,squeeze_free_dims=-2) # first and second order\n",
    "    q12 = np.moveaxis(q12,q.ndim-1,-1) # Put ad information last\n",
    "    return ad.Dense2.denseAD2(q01.value,q01.coef,q12.coef)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.241429Z",
     "iopub.status.busy": "2024-04-30T09:12:55.241353Z",
     "iopub.status.idle": "2024-04-30T09:12:55.243177Z",
     "shell.execute_reply": "2024-04-30T09:12:55.242968Z"
    }
   },
   "outputs": [],
   "source": [
    "q_rec = ADRecIdentity(q,shape_free=(2,), shift=(0,2))\n",
    "p_rec = ADRecIdentity(p,shape_free=(2,), shift=(2,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.244484Z",
     "iopub.status.busy": "2024-04-30T09:12:55.244407Z",
     "iopub.status.idle": "2024-04-30T09:12:55.246897Z",
     "shell.execute_reply": "2024-04-30T09:12:55.246677Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD2(array(1.),array([0., 2., 1., 1.]),\n",
       "array([[0., 0., 0., 0.],\n",
       "       [0., 2., 2., 2.],\n",
       "       [0., 2., 1., 0.],\n",
       "       [0., 2., 0., 1.]]))"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham_rec = Hamiltonian(q_rec,p_rec)\n",
    "ADRecToAD2(Ham_rec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.248200Z",
     "iopub.status.busy": "2024-04-30T09:12:55.248124Z",
     "iopub.status.idle": "2024-04-30T09:12:55.249942Z",
     "shell.execute_reply": "2024-04-30T09:12:55.249744Z"
    }
   },
   "outputs": [],
   "source": [
    "q_vec_rec = ADRecIdentity(q_vec, shape_free=(2,), shift=(0,2))\n",
    "p_vec_rec = ADRecIdentity(p_vec, shape_free=(2,), shift=(2,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.251257Z",
     "iopub.status.busy": "2024-04-30T09:12:55.251185Z",
     "iopub.status.idle": "2024-04-30T09:12:55.253753Z",
     "shell.execute_reply": "2024-04-30T09:12:55.253529Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "denseAD2(array(1.),array([0., 2., 1., 1.]),\n",
       "array([[0., 0., 0., 0.],\n",
       "       [0., 2., 2., 2.],\n",
       "       [0., 2., 1., 0.],\n",
       "       [0., 2., 0., 1.]]))"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ham_vec_rec = Hamiltonian(q_vec_rec,p_vec_rec)\n",
    "ADRecToAD2(Ham_vec_rec)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5 The gradient and hessian member functions\n",
    "\n",
    "Automatic differentiation allows to compute the gradient and hessian of a function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.255113Z",
     "iopub.status.busy": "2024-04-30T09:12:55.255040Z",
     "iopub.status.idle": "2024-04-30T09:12:55.256779Z",
     "shell.execute_reply": "2024-04-30T09:12:55.256542Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "An array of shape (3,), and AD information w.r.t 4 independent variables\n"
     ]
    }
   ],
   "source": [
    "print(f\"An array of shape {Ham.shape}, and AD information w.r.t {Ham.size_ad} independent variables\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Internally, the coefficients corresponding to differentiation of are stored last."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.258163Z",
     "iopub.status.busy": "2024-04-30T09:12:55.258086Z",
     "iopub.status.idle": "2024-04-30T09:12:55.259791Z",
     "shell.execute_reply": "2024-04-30T09:12:55.259565Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Internal storage has derivatives last.\n",
      "first order: (3, 4), second order: (3, 4, 4)\n"
     ]
    }
   ],
   "source": [
    "print(\"Internal storage has derivatives last.\")\n",
    "print(f\"first order: {Ham.coef1.shape}, second order: {Ham.coef2.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " However, for practical purposes it is often desirable to move them first. This is the role of the `gradient` and `hessian` functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.261139Z",
     "iopub.status.busy": "2024-04-30T09:12:55.261061Z",
     "iopub.status.idle": "2024-04-30T09:12:55.262641Z",
     "shell.execute_reply": "2024-04-30T09:12:55.262413Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Interface moves derivatives first.\n",
      "gradient: (4, 3), hessian: (4, 4, 3)\n"
     ]
    }
   ],
   "source": [
    "print(\"Interface moves derivatives first.\")\n",
    "print(f\"gradient: {Ham.gradient().shape}, hessian: {Ham.hessian().shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Solving ordinary differential equations\n",
    "\n",
    "We implement Hamilton's equations of motion\n",
    "$$\n",
    "    \\dot q = \\partial_p H(q,p), \\qquad \\dot p = -\\partial_q H(q,p),\n",
    "$$\n",
    "using several numerical schemes. In terms of automatic differentiation, the most interesting case is the semi-implicit Symplectic Euler scheme.\n",
    "\n",
    "**Conserved quantity.**\n",
    "By construction, the Hamiltonian value is conserved along the Hamiltonian flow:\n",
    "$$\n",
    "    H(q(t),p(t)) = \\mathrm{cst},\n",
    "$$\n",
    "if $t \\mapsto (q(t),p(t))$ is a solution to Hamilton's equations of motion.\n",
    "\n",
    "**Explicit solution for the half plane model.**\n",
    "The geodesics for the Poincare half plane model are known explicitly. They are half circles whose center lies on the horizontal axis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Explicit Euler scheme\n",
    "\n",
    "The simplest of all ODE solvers reads\n",
    "$$\n",
    "    \\frac{q_{n+1}-q_n} {\\Delta t} = \\partial_p H(q_n,p_n), \\qquad \\frac{p_{n+1}-p_n} {\\Delta t} = -\\partial_q H(q_n,p_n),\n",
    "$$\n",
    "where $(q_0,p_0)$ is a given initial condition, and $n>0$ is the iteration number, and $\\Delta t$ is the time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.263991Z",
     "iopub.status.busy": "2024-04-30T09:12:55.263916Z",
     "iopub.status.idle": "2024-04-30T09:12:55.266827Z",
     "shell.execute_reply": "2024-04-30T09:12:55.266613Z"
    }
   },
   "outputs": [],
   "source": [
    "def EulerStep(q,p,H,dt):\n",
    "    d=len(q)\n",
    "    q_ad = ad.Dense.identity(constant=q,shape_free=(d,),shift=(0,d))\n",
    "    p_ad = ad.Dense.identity(constant=p,shape_free=(d,),shift=(d,0))\n",
    "    grad = H(q_ad,p_ad).gradient()\n",
    "    return q+dt*grad[d:],p-dt*grad[:d]\n",
    "\n",
    "def Geodesic(q0,p0,H,t,n=100,step=EulerStep):\n",
    "    dt=t/n\n",
    "    q,p=q0.copy(),p0.copy()\n",
    "    Q,P=[q],[p]\n",
    "    for i in range(n):\n",
    "        q,p=step(q,p,H,dt)\n",
    "        Q.append(q)\n",
    "        P.append(p)\n",
    "    # For convenience, we put time as a second coordinate.\n",
    "    return np.stack(Q,axis=1),np.stack(P,axis=1),np.linspace(0,t,n+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Euler's explicit scheme is only first order accurate. While the geodesic circular shape is more or less observed, the Hamiltonian conservation is far from perfect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.268167Z",
     "iopub.status.busy": "2024-04-30T09:12:55.268093Z",
     "iopub.status.idle": "2024-04-30T09:12:55.276263Z",
     "shell.execute_reply": "2024-04-30T09:12:55.276048Z"
    }
   },
   "outputs": [],
   "source": [
    "Q,P,T = Geodesic(q_vec,p_vec,Hamiltonian,4.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.277594Z",
     "iopub.status.busy": "2024-04-30T09:12:55.277516Z",
     "iopub.status.idle": "2024-04-30T09:12:55.347836Z",
     "shell.execute_reply": "2024-04-30T09:12:55.347573Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal'); plt.title(\"Poincare geodesic (Explicit euler)\")\n",
    "plt.plot(Q[0],Q[1]); plt.axhline(0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.349421Z",
     "iopub.status.busy": "2024-04-30T09:12:55.349308Z",
     "iopub.status.idle": "2024-04-30T09:12:55.414614Z",
     "shell.execute_reply": "2024-04-30T09:12:55.414343Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Poincare Hamiltonian (Explicit euler)\")\n",
    "plt.plot(T,Hamiltonian(Q,P));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 High order explicit schemes\n",
    "\n",
    "A natural approach to improve the ODE solver is to increase its consistency order. This can be achieved using Runge-Kutta methods, here of second and fourth order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.416158Z",
     "iopub.status.busy": "2024-04-30T09:12:55.416044Z",
     "iopub.status.idle": "2024-04-30T09:12:55.419683Z",
     "shell.execute_reply": "2024-04-30T09:12:55.419442Z"
    }
   },
   "outputs": [],
   "source": [
    "def SymplecticGradient(q,p,H):\n",
    "    d=len(q)\n",
    "    q_ad = ad.Dense.identity(constant=q,shape_free=(d,),shift=(0,d))\n",
    "    p_ad = ad.Dense.identity(constant=p,shape_free=(d,),shift=(d,0))\n",
    "    grad = H(q_ad,p_ad).gradient()\n",
    "    return grad[d:],-grad[:d]\n",
    "\n",
    "def RK2Step(q,p,H,dt):\n",
    "    k1 = SymplecticGradient(q,p,H)\n",
    "    k2 = SymplecticGradient(q+0.5*dt*k1[0],p+0.5*dt*k1[1],H)\n",
    "    return q+dt*k2[0],p+dt*k2[1]\n",
    "\n",
    "def RK4Step(q,p,H,dt):\n",
    "    k1 = SymplecticGradient(q,p,H)\n",
    "    k2 = SymplecticGradient(q+0.5*dt*k1[0],p+0.5*dt*k1[1],H)\n",
    "    k3 = SymplecticGradient(q+0.5*dt*k2[0],p+0.5*dt*k2[1],H)\n",
    "    k4 = SymplecticGradient(q+dt*k3[0],p+dt*k3[1],H)\n",
    "    return q+dt*(k1[0]+2*k2[0]+2*k3[0]+k4[0])/6.,p+dt*(k1[1]+2*k2[1]+2*k3[1]+k4[1])/6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.421040Z",
     "iopub.status.busy": "2024-04-30T09:12:55.420950Z",
     "iopub.status.idle": "2024-04-30T09:12:55.460760Z",
     "shell.execute_reply": "2024-04-30T09:12:55.460518Z"
    }
   },
   "outputs": [],
   "source": [
    "Q2,P2,T = Geodesic(q_vec,p_vec,Hamiltonian,4.,step=RK2Step)\n",
    "Q4,P4,T = Geodesic(q_vec,p_vec,Hamiltonian,4.,step=RK4Step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.462062Z",
     "iopub.status.busy": "2024-04-30T09:12:55.461983Z",
     "iopub.status.idle": "2024-04-30T09:12:55.523833Z",
     "shell.execute_reply": "2024-04-30T09:12:55.523555Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal'); plt.title(\"Poincare geodesic (Explicit solvers)\")\n",
    "plt.plot(Q[0],Q[1], Q2[0],Q2[1], Q4[0],Q4[1]); plt.axhline(0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, the Hamiltonian is almost exactly constant for the second and fourth order models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.525459Z",
     "iopub.status.busy": "2024-04-30T09:12:55.525348Z",
     "iopub.status.idle": "2024-04-30T09:12:55.605901Z",
     "shell.execute_reply": "2024-04-30T09:12:55.605636Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Poincare Hamiltonian (Runge-Kutta)\")\n",
    "plt.plot(T,Hamiltonian(Q2,P2), T,Hamiltonian(Q4,P4)); #T,Hamiltonian(Q,P),"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Cone model.**\n",
    "However, if the trajectory is long enough, and the time step is large enough, then even the high order models fail to conserve the Hamiltonian. This is evidenced with "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.607574Z",
     "iopub.status.busy": "2024-04-30T09:12:55.607468Z",
     "iopub.status.idle": "2024-04-30T09:12:55.609068Z",
     "shell.execute_reply": "2024-04-30T09:12:55.608839Z"
    }
   },
   "outputs": [],
   "source": [
    "Hamiltonian = H_Log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.610379Z",
     "iopub.status.busy": "2024-04-30T09:12:55.610296Z",
     "iopub.status.idle": "2024-04-30T09:12:55.612056Z",
     "shell.execute_reply": "2024-04-30T09:12:55.611833Z"
    }
   },
   "outputs": [],
   "source": [
    "q,p = np.array([1,0]),np.array([0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.613367Z",
     "iopub.status.busy": "2024-04-30T09:12:55.613295Z",
     "iopub.status.idle": "2024-04-30T09:12:55.654920Z",
     "shell.execute_reply": "2024-04-30T09:12:55.654684Z"
    }
   },
   "outputs": [],
   "source": [
    "Q,P,T = Geodesic(q,p,Hamiltonian,6.,step=EulerStep)\n",
    "Q2,P2,T2 = Geodesic(q,p,Hamiltonian,25.,step=RK2Step)\n",
    "Q4,P4,T4 = Geodesic(q,p,Hamiltonian,75.,step=RK4Step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.656239Z",
     "iopub.status.busy": "2024-04-30T09:12:55.656161Z",
     "iopub.status.idle": "2024-04-30T09:12:55.718605Z",
     "shell.execute_reply": "2024-04-30T09:12:55.718327Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lebu7u/PJJ58wadIk+vfvz+TJkwkKCuLkyZPs37+fr776qtx9W7Vqxfz581mwYAHR0dE4OzvTqlUru2Nff/11Lly4QL9+/QgPDyczM5PPP/8crVZLr169AHjqqaeYM2cOQ4cO5e233yYyMpLly5czffp0HnnkEbNILQ+NRsP48eP59NNP8fT0ZMSIEXh5eVmN+fzzz+nevTs9evTgkUceISoqipycHE6ePMnSpUsrjKsx0blzZ4YNG0ZMTAw+Pj4cPXqUn3/+mdjYWKv3Pj09nRMnTvDEE09UekyJRGYbSW5a9u3bp9x3331KRESE4ujoqLi5uSlt27ZVXn/9deXSpUvmcXq9Xvnggw+Uxo0bK1qtVvH391fuuece5fz581bH69Wrl9KiRQub89x3331KZGSk1brc3Fzl1VdfVZo0aaI4Ojqa002feuopq+wee5R3nsjISGXo0KE26wHlscces1q3efNmpW/fvoqbm5vi4uKidOnSRVm6dKnNvlu2bDGnWwcHByvPPfec8v3339ukByuKoixevFjp06eP4unpqTg5OSmRkZHKnXfeqaxdu9Y8pqrZRnq9XomKirLJ8qos22jcuHGKoijKDz/8YJMZpCiKcvLkScXT09Mqu8X0vv3xxx9KixYtFEdHRyUqKkr59NNP7Z67slRpRVGUFStWKL169VLc3NzM6eYffPBBhe/D2bNnlYEDByoeHh4KYPM/U5ply5YpgwcPVsLCwhRHR0clMDBQGTJkiE221blz55SxY8cqfn5+ilarVZo0aaJ89NFHil6vtxpHmWwjE8ePHze/t2vWrLE7lzNnzij333+/EhYWpmi1WiUgIEDp2rWr8s4775jHmLKNfv/9d5v9X3zxRaVDhw6Kj4+P4uTkpERHRytPPfWUkpaWZjVuxowZilarrfTzIZEoiqKoFKWatk+JRCKpAT755BPeffddLl68iIuLS62dJyoqipYtW7Js2bJaO4fk6unRowcRERH88ssv13sqkhsAGfMikUiuC4899hheXl421Vol/z02bdrEzp07+b//+7/rPRXJDYIULxKJ5Lrg7OzMzz//bLeFg+S/RXp6OnPmzCE6Ovp6T0VygyDdRhKJRCKRSG4opOVFIpFIJBLJDYUULxKJRCKRSG4opHiRSCQSiURyQ3HTFakzGAwkJibi4eFRq43TJBKJRCKR1ByKopCTk0NoaChqdcW2lZtOvCQmJlKvXr3rPQ2JRCKRSCRXwPnz5yvtS3fTiRcPDw9AXLynp+d1no1EIpFIJJKqkJ2dTb169cy/4xVx04kXk6vI09NTiheJRCKRSG4wqhLyIQN2JRKJRCKR3FBI8SKRSCQSieSGQooXiUQikUgkNxRSvEgkEolEIrmhkOJFIpFIJBLJDYUULxKJRCKRSG4opHiRSCQSiURyQyHFi0QikUgkkhsKKV4kEolEIpHcUEjxIpFIJBKJ5IZCiheJRCKRSCQ3FFK8SCQSiUQiuaG46RozSiSS/zZ/H05my8k0WoR60jzEi8bB7jg5aK73tCQSSQ0ixYtEIrmpWH/sEvN3nje/dlCraBjoTvNQT5qHeNIi1IvmIZ54uWqv4ywlEsnVIMWLRCK5qbilZTAezg4cScrmcGI2mfklHEvO4VhyDgu5aB4X7uNiETOhnrQI9STEyxmVSnUdZy+RSKqCSlEU5XpPoibJzs7Gy8uLrKwsPD09r/d0JBLJdURRFBKzCjmSmM3hxCzjczYXMwvsjvdx1VpbaEI9ifZ3w0EjwwMlktqmOr/fUrxIJJL/HFn5JRxOEmLmSGI2R5KyOXEpF73B9uvQyUFNp/q+9G8WRL9mgYT7uF6HGUskNz9SvEjxIpFIqklhiZ4TKbnCQmN0OR1Nyia/WG81rlmIJwOaBTKgeTAtwzylm0kiqSGkeJHiRSKR1AAGg8Kp1FzWx19izZEUdp+7TGnjTLCnM/2aBdK/eRBdG/jJrCaJ5CqQ4kWKF4lEUguk5xaxPj6VtUdS2HQi1coq4+aooWfjAPo3C6JP00B83Ryv40wlkhsPKV6keJFIJLVMYYmeuNPprD2SwtqjKaRkF5m3qVXQIdKX/s0D6d8siOgA9+s4U4nkxkCKFyleJBLJNURRFA5dzGbNkWTWHL3E0aRsq+0NAtzo3zyIW1oE06aet4yTkUjsIMWLFC8SieQ6cuFyPv8cvcTaoynEnUpHVypQpkWoJ/d1jeK21qE4a2WMjERiQooXKV4kEkkdIbuwhE3HU1l9OIW/DydTpDMA4OvmyJiO9binSySh3i7XeZYSyfVHihcpXiQSSR3kcl4xC3ad5+e4c+ZCeRq1ikEtgpjQtT4do3ykS0nyn0WKFyleJBJJHUanN7D26CVmbz3DttMZ5vXNQjyZ0DWS29uESZeS5D+HFC9SvEgkkhuEY8nZ/LT1LIv2XqSwRLiUvF21jOkYwb2xkYRJl5LkP4IUL1K8SCSSG4zM/GJ+23Wen7ZaXEpqFQxsHsx9XaPoEu0rXUqSmxopXqR4kUgkNyh6g8I/R1OYvfUsW0+lm9c3Dfbgvq5RDG8ThoujdClJbj6keJHiRSKR3ATEJ+fwU9xZFu25SEGJqObr5aLlwZ7RPNC9voyLkdxUSPEixYtEIrmJyMov4bdd55mz7SznM4RLKczbhedvacKtMaGo1dKdJLnxkeJFiheJRHITojcoLN2fyIerjpGYVQhA63AvXh3WnI5Rvtd5dhLJ1SHFixQvEonkJqawRM+Mf88wff1J8ozNIQe3DObFwU2J9HO7zrOTSK4MKV6keJFIJP8BUnOK+HTNcRbsTMCggFaj4r7YKJ7o2wgvV+31np5EUi2keJHiRSKR/IeIT87hvRVH2Xg8FRB1Yp7s24h7ukTi6KC+zrOTSKqGFC9SvEgkkv8gG4+n8t7yo8Sn5ABQ39+NFwc3ZWDzIFkjRlLnkeJFiheJRPIfRac38PvuC3yyOp603GIAOtf35dWhzWkV7nWdZyeRlI8UL1K8SCR1g5JCSIiDs/+CQQceIeARJJ7dg8AjGLSy/H1tkFuk49sNp/hh82lzJ+sRbcN4dlAT2cVaUieR4kWKF4nk+mAwQPIBOL0BTq+HhG2gK6x4H2evUmLGKG7cg4WwMT3cg8HR9Zpcws1GYmYBH/0dz6K9FwFwclDzeJ+GPNK7AQ4aGQ8jqTtI8SLFi0Ry7chMgFPrhWA5sxHy0623e4RAdG8hUnKSICdFPOemVC5sSuPkZbTaBNsXN6ZlR5kqbI8DFzJ5Z/lRdpwRXazbR/rw2eg2RPhJUSipG0jxIsWLRFJ7FGTC2c1GwbIeMk5bb3d0h6juEN1HiJaAJmAvWFRRoDBTiJncZMgp9Sj7WldQ9fk5epQRNiaLThmh4+R+FW/CjYmiKPy1L5HXFh8ip0iHu5MDb93WghHtwmRAr+S6I8WLFC8SSc2hK4YLOyzWlcQ9oBgs21UaCO8ghEp0H7GsqcEaI4oCRdmlhE2KrQUnJ0lsK8mv+nEd3UuJmSBb15XptZOHffF1A3M+I59nftvPjrPCCjM0JoT3hreStWEk1xUpXqR4kUiuHEWBS0eEUDm1Hs5tsRUFfo2gQR8hVqK6CZfQ9UZRoCinHHFTxqJTnFv142rdbIOMS1twfCLBJ6rWLqu20BsUvt14is/WHEdnUAjxcuaT0a3p2sD/ek9N8h9FihcpXiSS6pGdaBErpzdA3iXr7W4BRsuK8eEVfs2nWKMU5dhxV5UVOinC4lMVGvSFXi9ARJfanXctsP98JlMW7ONMWh4qFTzYM5pnBjSRxe0k1xwpXqR4kUgqpihHpC+bBEtavPV2BxeI7Gq0rvSGwBag/g/+mBXnlR+Hk5ssBFD6SVBEfyHq9xQiJqr79Z13Nckv1vF/y44yb0cCAC1CPfl8TBsaBnpc55lJ/ktI8SLFi0Rijb4ELu4RAbanN8CFnaLuihkVhLYVQqVBH6jXGRycrtNky0FXBHlpkJcK+WmW5bxUKLgMvg2E4AppAw6O125eGWfg389g369gKBHrIrtBr+ehfq8bKl5m9eFkXvjzAJfzS3ByUPPq0Gbc0yVSBvNKrglSvEjxIvmvoyiQdsJSb+XMZijOsR7jEyViVhr0gage4Op7bedo0EN+hkWA5KWKNGvz67RSz2lQlFW14zq4iKDhyG4QGQvhHa9N+nRmAvw7Dfb+DHpR2ZZ6nYWIadDvhhExl7ILefaPA2wy9knq2zSQD0bGEOBRx8Ss5KZDihcpXiT/RXIvwemNFutK9kXr7S4+whJgilvxrV+z51cUKMyytoiUK0hShXChml8/agdw9RcxOG6lnp08IeWQqOZbts6M2kFYYyK7ikdEF/Fe1BZZF2HL57B7NuiLxLqw9sKd1GjgDSFiDAaFn+LOMnXlMYp1BvzdHfnwzhj6Ng263lOT3MRI8SLFi+S/QHE+nNtqESsph6y3axzFD7Wp3kpIa1BrqnmOPKPYSLcWJHlpRtdNqrV1xOQ2qTIqYfFxCzCKEpMgCQA3v1LLRpHi7F3xj7+iQNpxkSF1Lk68P9kXbM8Z2NwoZmIhoit4hlRz3lUgJxm2fAG7Zlrq1IS0FiKmyZAbQsTEJ+fwv/l7OZYsrHb3donk5SHNcHGs5v+RRFIFpHiR4kVyM2LQQ9I+S0bQ+e0W94SJ4FaWeisRsVUvqV+YDfvnwal11oKkOnVTTDh5WosQVz9rAVL62cUXNA7VP0d1yEwQIsb0SD9hO8anvsXNFNlVvK4pcZGbCnFfwo4foSRPrAtqBb2eg6a31vlA6MISPR/9Hc+Mf88A0DzEk1kTOxLk6XydZya52ZDiRYoXyc1CxulSpfc3iYq0pfEMhwa9hVip3wvcA6p3/PRTsON72PuLbUyMCQdncAssYwnxL2UtKSNK6lqgb1lyLwn30rk4YaFJPoiN+8o92OJmiuwKAc2uXmTkpcO2r2H795b3OqAZ9HwWWtxRfavYNWbziVSeWrCPtNxiwrxdmDWxI42DZDaSpOaQ4kWKF8mNSkkBHF9lESyZ56y3O3mKdFyTdcWvQfUtBIoiXE3bvoUTqzH/cPs3hnb3iWOWduE4ul29FSI7UWQ4nd8BF3ZB1nkRd+LqK6wvrn5lHmXW1WZTxsIsMS+Tq+niblv3l7O3sGRFxgoLTUjrK68inJ8B278V778pCNmvEfR8DlqOrH1L1FVwPiOf+2bt4HRqHh7ODnx3b3tZ1E5SY0jxIsWL5EYkcR/8+YCoG2JC7QDhnSz1VkLbXfmPW3Ee7J8P27+zruvSaCB0fliIoZpwYZQUis7S53cIwXJhp23wcHVxcLEvaipad6UWoJICIWBMbqbzOyzuHhNaV5HFZHI1hXWovsAqyBRWr7ivLRY132jo8SzEjK7ZFgs1yOW8Yh78eRc7z15Gq1Hx8ajW3N4m7HpPS3ITIMWLFC+SGwmDQbgT1r4l7vjdg6DFCCFYIruK3jpXw+VzsPMH2DNHWBlA9PVpMw46PyQsLVeKoggryoWdcH4nhgs7USUdQGWwjsUxoCbZuQEnHZtyWNOEk/oQKMrGXZ+Fl5KDFzl4K9l4k4MX2XgpptfZaNGVc/JKcPQAV58qih0/YQmyJxj0JUKMndsqLDMJW0VdmdKotaJOjsnNVK8zuHhXbZ6F2eLvs/UrKBC9hvCOhB7PQOu7r23NmipSWKLnmd/2s/xgEgDPDWrCo70byHowkqtCihcpXiQ3CjkpsPhhESgL0HQY3Pbl1ddcURRRQXf7txC/wtJI0TcaOj0EbcaC8xV8PorzyTq9k5yTcagv7sQzfR/uxWk2w9IUT/YaGrHH0Ii9SkMOGKLJ50oCPBXcKMRHlYMvOfiqcvAxPRvX+ahy8FHl4kMOfmqxXYOh8kPbw9nLImYCmkLbe4QQKf2jbDAIy9W5LRZBk5NY5kAqCGppndHkUUmacVEu7JohMpTyje+pVz3o/pSYRx2LJTIYFKauPMoPm0Ug79jOEbx9WwscNHU7AFlSd5HiRYoXyY3AiTWw+BGR2ePgDLdMhfYTry6+pKQADv4uXEOlU6ej+0CXR6DhgKq7hhSF9AvxpBzeTMm57Xil7ye8+BQO6K1PqWg4okSy19CQPYZGHFY3RuUTRaCnM57OWrxctHg7KYRqsnBxdcPFzRN3dw88XR1xctBg+gZSjLE3ltegKAqFJQayCkrIKigmq6CEzPwS8VxQQrbxdXJ2Iak5oqaKCgMeFFiJG19VDkGaPBp5FBHhXEiwNg8fcnAuyUSVn260pJTzVejfGNreK6wg9gKiFQUunzUGARvjZjJO2Y4zVQA2Pbwj7f+ti/NEjZgtn4v+SgAeoULEtBsP2rqV5TN7yxneWnYERYE+TQL4amw73JzqbtyOpO4ixYsUL5K6jK4I1r4J26aL14Et4M6ZENj0yo+ZdRF2/ih+9EyuB60rtB4jLC1VOHZeTiYn9m4i//Q2XC/tISL/ML7YNiZMUbw5omnKBbeWZPm1QR3ahpAAHyJ8Xann60qAuxOq4lwRK5KwTfyoX9hlqXViwsFFxIlo3YzPxodp2dHN+rV52d54NwpUTlzIVZGQA2czdZy/XMC59DwSMvI5f7mAYp2tNcbNUUOLUC9iwtxpF6SmQ4CBQE2eyEg6/jccXmhJF1c7iPos7e4TLr2KsoNyko1ixmiZSTmEjTjyDINOD0LsY/bdVSUFwtX372eiaSSILKhu/4P2E2o3iLma/H04mSfn7aVIZ6BVmBczJnQg0KNuiSxJ3afOiJdNmzbx0UcfsXv3bpKSkli0aBHDhw+vcJ+NGzfy9NNPc/jwYUJDQ3n++ed5+OGHq3xOKV4kdZrU4/Dn/cb0XISwGPD2ld1NK4qo9bL9WziyxNIc0CsCOk2GdveWX0lWUdCnneTCgQ1kn4jDI20v9UrOoFFZfx0UKQ6c0jTgklcr9GEd8W3clUaNm+HuXObH1pR+nLBN/GAnH7TMx4RaewVF7K4QlbqUyHFB0bpSpHImW+9IRokDaYUakgvUXDT4sEbfjkNKfUBYQRoEuNGjUQA9GvnTOUyL+4klQkRc3G05vmc4tB0n4oZ8IiufT8HlUhlNWyFxr6W3VGBzGDYNIjrb37ekEPbNhc2fWQruuQVA1yehw/3g5H7Fb1NNsifhMpN+2kVGXjHhPi7MntiJhoF1Y26SG4M6I15WrlzJli1baNeuHSNHjqxUvJw5c4aWLVsyefJkHnroIbZs2cKjjz7KvHnzGDlyZJXOKcWLpE6iKOIHcNWL4k7e1Q9unw5Nbqn+sXRFcGihEC1J+yzro3qIrKEmg22tAoVZcHE3mce3kncqDq+MA7gb7FhVVP4kureiKLgdHo26EdmiC+5uZfoCKQpcPmMJXk3YZp0hZcIrwhjvYSz85tdIrC/JtzyKTc95FawrEMtF2eLaSwqstxeXOl7Zon1V5LJjCBs0sczJasNeQwNMQsZBraJdhA/dG/kzwC+VJomLUR/8rVTArkpYYdreC02HVj0upThfWHVWv2axlLW7D/q/WX68k64Y9v8Kmz8RhfdA/B/FPi7E6tUGdtcAZ9PymDBrB2fT8/Fy0fLD+A50qn+Ne2ZJbljqjHixOpFKVal4eeGFF1iyZAlHjx41r3v44YfZv38/cXFxVTqPFC+SOkfBZVj6Pzjyl3gd3Rvu+A48gqt3nJxkUWp+10wRJwMiVqbVKCFagluKdQaDKJF/YQfK+Z0Und2G0+UTqMq4LQoVLUdUDUjzisE5ugsN2vQmLNJO5pFBDymHLW6QhG2Qm2w7LrC5RahEdAGv8Kpdl8EgAlRzksQ1ZieKZ9PrnCTxyEsTbiL/RhDQRDz7NxHLPvVFVo5eJ9Kai8sKpDyjCMovtT0Pkg+JWjelKgkXuISw260H83LasCIrAgVLjJC3q5ZhzXy41+cQjS4uQn1mo+U6XHxFXEy7eyGwWdWuPT8D1rwGe+eK167+MOhdiLmr/NgnfQkcWACbPhYiEoSFrctj0PlBEXR8HUnPLWLSnF3sTcjEUaPmk9GtubV16HWdk+TG4IYVLz179qRt27Z8/vnn5nWLFi1i9OjR5Ofno9Xa+oWLioooKioyv87OzqZevXpSvEjqBufi4M9JwtyvdoC+rwlzf3XqqVzcLQqaHV5kcbt4hEKnSdBugqh8C8IicmINrH7Vuo6LkQRDAHuVxqR7x+DWIJYmrbvQKjIQjbrMj2RJISTusQiV89uF1aM05tRgYyZNvU62FgNFEfVLKhIkOckiKNVwhenQ5vk4gE99dH6NOO4diK9/c4JDOwiBU1lWVXE+nFwrxOXxVVCca96kcwvilF8flus6MScxlMxCS9yMv7sjYxsZuMthE6Fn/0RliksBUQOm3XiR8l4Vt865rbB0iuXvVr8nDP1UzL889Do49Ads+shi+XLyEoHZXR6u3eaTlVBQrGfKgr38fVgEHL88pCmTe0TLVGpJhdyw4qVx48ZMmDCBl19+2bxu69atdOvWjcTEREJCbJunvfnmm7z11ls266V4kVxX9Drxo7LpQ5Gm7BsNI38U3YWrtH+J+DHd/q2ooWKiXhdRm6XZrdZBnimHKVz2Is7nNwGQrzhxQIlmj6ERB1WNcY/uQu/2LenVJAD3spkgBZnG4FqjWLm429b94uguBEqEMfU3oJmwKFmJkWSRMlz6ta6wim+YCtwDhTXKI6TUI7jUc7CYa9px8SOfehzSjnP+8kniHAzEuTiz3dmZHI0ajaJwW24eD2ZmEe4SVMpa01g8ApqIejplf0xLCkXa+tElcGyFpQIuoLgFkBLan2W6Tnx7Npi0AstXZ5iHlscjzzG4eDVeF9ahMokxR3doOQLajofwDhVnkumKRQ+kjR+K903jKDKMuj9dcUyUQS+E7cYPLeLH0UP8n8Q+dvVp91eI3qDwf8uOMHvrWUDUgnmsT8PrMhfJjcENLV4mTpzISy+9ZF63ZcsWunfvTlJSEsHBtmZ2aXmR1DkyE+DPyXB+m3jdeiwM+bBqMQl5abBrlqj3YbqT1ziKsvGdHxLWjlIUZSaRuOg1Is79iQYDRYoDs/S38J1hOG0aRXJr61AGNA/Co3SAbXaSECrnjAG29jJh3AKEC8ivIWRdEAIs75JRmCTbWmJKcd5BgwEVETqdiBxx8bEjSIyixNO4zi2wypWDc4pz2JG8g7jEOLYmbuV8znnrqas05BmDhR0Uhdtz85icmUWYrkwAsZOXfReUd6SYi64YzmyEI4vh2HKrwnSKiw/JIf1YruvE1wnhXC6l0ToHlPB8yF7api5Bffm0ZUNAM2GNibnLYi2zR8YZWPGssAaBSLEe9qlwN1aEwQBH/4KNH8Glw2Kd1k3Ew8Q+Xv2+VzXEtxtP8f7KYwC8M7wl93SpQoCz5D/JDStersRtVBYZ8yK5rhxaKMz/RVmiD9HQTyFmVOX7JR0QVpaDf4DeKMbdg6DDA9BhorBKlCIxLYOTSz6kfcIs3BC/nCv0nVgd+iid27fnlhbB+Lg5CtdN+kmjC8gYs1K2XxIYuyp3FYIlvIPYZ+8vIh6kbNaQCa2bRXx4hHDBxYNpBaf5O1fUOPHSetDSvyUxgW1o5d+KVv6t8Hb2ruIbaUFn0HEo7ZBZrBxMO4i+1JwcVA60DmxN19CuxIbE0tyvOQfTDvLN/m/YmrhVjEHNcNcIHizWEpJ+RtRlUQz2T6hxFIIhwGil8W8iLGc5SXByDRxdZikiByhOniQF92WZrhNfJ9Qjq0QES7s5qnmqcRqj1BvwOr3ckiqucRTBve3GQ/3e9l2IiiJE08oXLfFFrUaLeJgy/ws2GAyiMOHGD0RlYBCxQh3uFy7Lyorl1QKfrI7ny3UnUang8zFtuU3GwEjscMOKlxdeeIGlS5dy5MgR87pHHnmEffv2yYBdSd2mOA9WPm8JvAzvKNxEPlHl76PXQfxyEc+SsNWyPrSdiFtoPtyqNLyiKMSdSuPI6lkMTvmOMJX4AT2iasjRmBfp0e9WAj2dxQ/f4UVw6E9hWSn1QytQieBekwsoIlZYQpIPwb5fRDBofrpleHhHkcHkVc/ajWO0JGUVZfHDgR/49divlBhKUKFCq9ZSbLDN/KnnUY9W/q2ICYihlX8rmvo2xVFjW/7+fM554hLjiEuMY3vSdnJKrDteR3lGERsaS9fQrnQM7oib1s3mGAD7Lu3j631fsy1JWMEc1A6MaDiCyc3HE1yYJ9wsaScgNd64fNK2Hk1pvCJEzRzfaOFaO7bcUkgOUBzdOe3bnTmZbViQ2YRCRPZR70hHng4+QMuUv1An77c+Xtt7RNq1vQDnwixY9w7s+AFQRDBu/7dEZlJlcVOKImrVbHxfpGaDCPBuP0HUivG8dgJCURRe/+swP287h4NaxY/3daB3k0pEmOQ/R50RL7m5uZw8KQLJ2rZty6effkqfPn3w9fUlIiKCl156iYsXLzJnzhzAkir90EMPMXnyZOLi4nj44YdlqrSkbmPVUFEletL0frH8xnr5GbDnJ9jxo6Vuh9pBiJXOD0O9jlbD84p0LNx7kZ2bVjEh93vaqcVnKl3tz4UOL9Bi4P04OBhdLgnb4O+XrWuSaJxErI05uLajJSMlP0NU5N33CySV+lF1DxIF7tqME64UO5ToS1gQv4BvD3xLljE2pGtoV55u/zTRXtEcv3ycA2kHOJh6kINpBzmbfdbmGFq1lqa+TanvVZ8CXQE5xTlcyLnAhdwLVuM8HT3pEtJFWFdCYwl1r94P756UPUzfN53tydvN5x3RaASTWk0i2K2UO9pgEL2a0kQ8jRA1J4SwKS3oQAjTTg8K68zJf0ScTKkGlHqNC/tcOjE7szX/6NqQjzMBHk48F1PIcGUdjof/KBVTo4KG/YU1pvEttv2MLu6BZVMsf6PwTjDsM0uGWUUoipjfxvct8VMaR3GublPAu15V38arwmBQmLJgH0v2J+KsVTP3gc50iJJp1BILdUa8bNiwgT59+tisv++++5g9ezYTJkzg7NmzbNiwwbxt48aNPPXUU+YidS+88IIsUiepmxgMokru2jdFFpBHKIz4Hur3sD8+5YhwDR34zXJ37+ov3EIdHhAumFLkFun4aetZlm/axiO6n7lVI6wHRWoXsts/QcCApyxVVjNOw5o3xA8oCJdOl4dFx+jQttb1R/Q6EZS6by7Er7QE56q1wsLS9h5o0K/cGBRFUVibsJbPdn9mjjdp6N2QZzs8S7ewbnb3OZp+lM/3fM6WxC0Vv6dlaBvYlgdjHiQ2JBZNRRVt7WBQDKhQWWW47ErexfT909mZLH7EtWotdza+k0mtJhHoWoklIC9dCJoTq2H3LEsMjJOnEAKdJkNuqnD3HF1iqcUC6NRObFbasLioPesM7dC4evFglxAm+h7A5dA8OLvZch5Xf2hztwjyDWhsWa/XiQaO694RGVEqjQjI7f2iqEZcGYoCpzcId1KC0ZKt1gqrT49nwDui8mNcJSV6Aw/O2cX6+FQ8nR1Y8FAszULk97REUGfEy/VAihfJNSH3kuhLZAqqLK+hokEvTPfbv4Ezmyzrg1tB50dEIG6ZTJK8Ih1z4s7xy8aDjCv5g/s1q3BSlaCgoiRmLI4DXrfUiMnPEFlNO34QAkqlFgXT+rxiG9uQdkK4tQ4ssAQDAwTHCMHSahRZGg0/Hf6J7OJsfJx98HbyxsvJC28nb3ycfDifc54fDv7A8cvHAfB38efxNo8zvOFwG3GhKArbkrYx69As4pKq5vYtjwiPCFoFiLiZGP8Ymvg2sXE3pRWkcSjtEAdSD3Aw7SCH00TQ6pimYxjffLxVvM3O5J18ve9rdqcIC5Wj2pFRTUbxQMsHCHCtQmBrcT7snwfbvoH0E2KdSg3NbhOCIryjKCB45C/xyLAE7hbjwCZ9K1bqO7PNsRN3dmvFpGYGPI7Nh32/WrmhiIgVf88Wwy0CJTsRVr5gEape9WDIR0J4VgVT086NH1hEk7MX3LcMQmKqdoyroKBYz/iZ29l59jL+7k788XAsUf5VEF+Smx4pXqR4kdQmJ9aKTtCmhoqD3hPBkGXTYAsyYf44OPeveK1SixTnzg+LH6Uy4/OLhWiZsfEEA4pW87TD7/irRFaPEtUT1S3vCdEDIhNm5w8iPbYwU6xr2B8G/B8ENbcctDBbVHLd+wtc2GFZ7+Irsl7ajjMfc++lvbyw6QWS8koJmyoS6hZKY5/G1Peuj5ejF7tSdvHvxX+rfZzawtXBlbHNxjK++Xh8nEX9E0VR2JG8g+n7prPn0h4AnDROjGo8igdaPYC/i3/lBzYYRBBv3NciM8lEWAeIfRSa3S6qHaccsgiZtOPmYSWKhi2GlqxTxxLYcQTjerbEJ3GjqMZ84m9LULGjB7S6U1h4QtuK/53jf8PyZyHLaOFpOgwGf1D14oAgArhXvSSElqs/3L+q4toyNURWQQljvt/G0aRswn1c+PORrgR5yl5I/3WkeJHiRVIb6Ipg7Vuw7WvxOrAF3DnDfjXVrIvwy51w6Yio9dFxknjYiS8oKNbz87azfLfxNC0KdvKKwy80UYuYD8WvEaqB70DjQeIHS1HEHfeaNyzVVQNbwMD/g4b9xGuDQdxR7/tF9DwyuahUGmg0QMSxlIqrSCtIo89vtu7d2kStUhMbGoufsx9atZbTWac5cfkEuSW5le9cDXycfCjQFVCoFxlZLg4ujGkyhvta3Iefi0hXNlmIpu+bzr7UfQA4a5wZ3WQ0E1tOrJqIARHwvO0bOPibxRXnVU/ExbQbDy7eYt2lY3DkL5Qji1FdsiQnFCiOTFPuxqPXY0zq2RDnghRhidn7s8iOMhHVQwSDewSLQPGNH0LcV6LQn6M79HlZ9MyqYuo5hVnw060insYzDCaurFq/pqskNaeIUd9u5Wx6Po2D3PntoVi8XW2DtyX/HaR4keJFUtOknYA/7reknnZ6UFg57BUPu3QM5o4UwbjuwXDPn3YDKw0Ghd92nefj1cfxzjvFqw6/0FsjAjIVFx9UvV8SFh1T4O+FXfD3K5b6Me5Bwj3U9h5xd3/5LOybJ/rflIq3wL+JsLDE3GXTkmDNuTU8veHpq3xzbjzsiRNFUYhLjOPr/V9zIPWAedyYpmOY0GKCWexUSu4l0eF75wxLppeju/g7dX5IZCqZSDuB4fBf5O1ZgEeWsMhsNzTlE+cnmXBrXwa3DEalKMJ6t2eOEKP6IvG3H/WTCMIG0b5h2VOiGjIIV+CwaRBexaKIeWkwa4gITPaJgomrbGKwaoPzGfnc+e1WUrKLaBvhzdwHOuNWtoii5D+DFC9SvEhqCkURd74rXxD9b1x8Yfj08uMLErbBr3cJV45fI7h3od1AyH3nM3njr0Ocv3Cepxz+4G6HdThgQFFrUXV+CHo+aynvfvkc/POWSH0GcHCBrk+IdFeVWlhi9s61Dvp08jJWdr1HZBqVcVEpisKDax40pxADNPJpRPvA9syPn38179gNR/ew7jzT/hmivaNRq9QoisKWxC1M3zedg2mi+7fJYjOh5QR8nauYIVNSKKwwcdMh1dSvTSVqvHR5VNTVMf1dDAaUXTPR//0qDvoC8hUn3teNIb7eXbx2a0tahhmzw9JOwoJ7xPHUDjDwXSGIVCphcdv7M6x53ehKVAlrX7/XqtbvKDsRZt4i6gAFNIUJKyoupldDHE/JYfR3cWTml9CjkT8/3tcBJ4fqBWdLbg6keJHiRVITFGQaGyouFq/r9xINFcu7Iz26TKRM6wpFwObY32wCeNNyi/hoVTyLd51iguZvHndYjIfK6NZpOgwGvA1+xuaIhVmig/C2b42F61TQZqywtmRdENlChxZBsakGigqie0Gbe6DZMNC62J1mRmEGvRb0slo3f+h8lp1extyjc6v9Nv0X6VOvD838mhHsGoynoycuDi64aF3Es/Hh7OCMi4MLWpUDnF4v4mJMAd4AIa1FM8UWd1hSoy+fRb/oMTQJIl4oTt+c53UP0q1De54Z2IQADycoyoUlT4hYJhCNOW/93BLQm5sq+lsdMIpQ9yC4Zaros1RZb6HLZ4WAyUmCkDZw35Jr0uhx3/lMxv6wjfxiPUNaBfPl3e1se25JbnqkeJHiRXK1nIuDhZNFzQ+1A/R9Fbr+r/zCYLtmwvJnRIBl48Fw50xLGjOg0xuYu+0cn6yJp0fxFl50mEeE2tgZOqS1CPqN6i5e60tg92zYMNVSW6R+T1HiPeWwiIMwZbiAMPO3GSc6GldSs6Osm0itUvPjwB+5/+/7q/kG2ad/RH9cta5cLrzM6azTXMy9WPlO/wGebv80XUK64J2Xjte++bgc+B2Vqe+TR4hIs24/UYhdgwF2zcCw+jXUugLyFCem6sbyl8Mg/te/CRO71UejQsTXrH5VVEAObA53zbUIXxDZbcuesjRtbNAPhn5s7bayR2o8zBos/vciYuGehVb/y7XFvyfSuH/2Tor1BsZ0rMfUEa1kI8f/GFK8SPEiuVL0Otj8sUgjVQyibP6dM8pvqKgoQmRs/EC8bjcehn5mFSy5/XQ6byw5jFPKXl7TzqWD2pht4hEC/d4QsShqtThW/Eph9jeJE//G4kcn/SSc+seSfaJ1E+mzbcaJH5gqdKme9Pckc5E2gLub3s3ac2tJLUit7rtkhZvWjfHNx5NdnM2htEMcTjuMTrnKLtE3OTG+zfncrQX+e+ZaUqMdXER9ly6PioyfjNPw1+NwTtTG2aJvwQu6Bwms14gP72xNw0B3kS30232i75STp7AMNh1iOZGuCP6dJix4+iKRHdfzWSHEyxbCK03Sfph9qyii16Av3D3fulZQLbHqUBKP/rIHgwIvDW7KQ70aVL6T5KZBihcpXiRXQuZ5YW0xFfBqfbeon1FeQ0W9DpY/JQIpAXq9AL1fMpvmcwpLeHvpEbbs3sfz2vkM14gWAIrWFVW3/4m4FZOpP3GfuIs2xa24+kOPp4Vo2TXTcs6IriL4tvntVWv0iH03kaejJ9nF5TdXlFwZYe5hIoPKGGSdX5LP0YyjdsdGe0Uzo990/E9tEhlsyQctGxsNEqnWUT1gxw8oa99EpSsgT3HmXd04/lD15+kBTZjUvT4OeSnw+wRLIHePZ0XGUem6O+mnhBXGlM7t30RU6I2yX1QQgITt8PNwEevVdJgIEK5qBtNV8PO2c7y2+BAatYoFD3aRVXj/Q0jxIsWLpLocXgxLnxRxJo4e4ou9ooaKxfki++j4ShE0O/QTkRlkJO5UOq//to3b8n5jsmY5zsYic6o2Y4ULytRXJusirPs/2D8fUEQp/9hHhetp2RSRag0i8LLLo9ZugSqw6uwqntv4XLX2qS0iPCJw1bqiKAoGDOJZMaCgmJetXiNeo2BeVhQFBcW8bMBAXkne9b60K6a+V31mDpqJv7OfKBwX9zUcX4W5y3dQS9HnKqy9EB9GYb1J34oXSyYTEN6Aj0a1prGfE6x5TVRwBmEtGTnDOuZKUUTjz79fEjWKQMRHDXi7/MDcU+vh19Ei9TtmDAz/pkpWvqtBUUQbgb/2JRLs6cyK//XA102mUP8XkOJFihdJVSnOE5lEe38Wr8M6iBoavvXL3yc/Q2QUXdghzPAjZ4gAWaCwRM8nq46Qs+0nnnH4jQCVsXdNZHfRETi0jXhdlANbPoetX1nqsLQaLTJDjv8tUqL1ReAWCHd8IwrQVYPs4my6zavgrtoOnUM6szdlr92GilUhyDWItoFtaRPYhraBbWns0xgH9fVJey3QFXDy8kmOZhzlWMYxjqYf5djlY+gMdc+dVd+rPjMGzrBU9k0/JeJZ9v0irB4AbgFCHBt0KHHTUekKyMWFd0rGsZB+/K9/Yx7qGY3D4T9gyZPif8orAu6aI4ralabgsqhXtHuWeO3iK+oEtRlnP6D32AqR4aToRRuLoZ9UHvh7leQV6bj1q385nZpHr8YBzJrQEbUM4L3pkeJFihdJVUjaD388YIwvUQk3Te+Xym+oCKJ+ytyRokqqsxfcvcBca+PQxSzm/DKbibk/0kwt6qwYfKJRD/w/kR6rUglX096fYf17Ik4BhCto0DvgHQl/PWa880b0Jbp9OrhXXq5eZ9BxKO0QcYlx/HXqr2sSKNvUtyltAoRQaRvYlhD32q8LcjXoDXoSchKIz4jnWMYxIWoyjpJRmHHFxwxzD6uR9zrKM4qZg2ZatyYouAy7f4Lt30FOolindRXuxtMbzDVdNupjeLFkMoHh0Xw1th31ik8LsXH5jLDkDf1YxGKV5fwOYc1JOSReR3aDoZ+KrtllOfgH/DkJUESKfv+3al3AHE3KZvjXWyjSGXhuUBMe69OwVs8nuf5I8SLFi6QiDAbRa2jtm8Ic7hEKI74TGT0VkXxICJfcZPAMF8XnApui0xuYv/IfQne8R1+1KDNfovVE2/cl4e4xBUaeWCviWkw1P3yjhcm+6TDRKHHxIyJ4U+Mk7oQ7PVjhD8T5nPPEJcaxNXErO5J2kFOSU+7Yq8XFwYXWAa3NlpUY/xjcHd1r7XzXkrSCNLOYOZZxjPiMeM5ln0Phyr8ah0UP43D6Yc5knanWfpNbTaZfRD8a+zQ2x82gLxFtBbZ+Kcr4g2gx4RGCsmEqKl0hObjwdsm9/K3tx8ej2jAw2hkWPSzcmgDt7oPBH9oWVdSXCCvPhqnCyqPWQrcnoedztqn2u2eL0gEAfV8Tgb+1zIKdCbzw50HUKpj/YCyd6sv4l5sZKV6keJGUR9mGik2Gwu1f2TZULMuZzTB/LBRli7TUcX+AVxgJaXlsm/kMI/IW4KAyoEdDcbv7cen/suWYyYdEPMKpdeK1iw/0etEYI6PAP2+L8u4gioONnGG3Im9OcQ47kneYBYupo3NtcUvULXXCBXQ9yC/J5/jl48RnxHM04ygH0w6am1FWh6a+TTmWcaza+zmqHWnm14xW/qIZZauAVoS7hqDaMFVkw4EI5u3zivjfuiC6ZK/Xt+bFksnc1qM9zw9qjHbrZ7DuXUAR7qPRP9tPp888Dyufh/gV4rVPlEj3L5tlt/UrWP2KWL7lA9G5vBZRFIVnftvPwr0XCfJ0YvmTPfB3r/2sJ8n1QYoXKV4k9ji5FhY9Itw1FTVULMvhRbDwQWGliegKd/8KLj5siL/E8Xkv8CCiWFhicB9CRn6IKqCx2C8nGda9I2IXFANoHIU1xVQ9N/W4KGpnajnQcbKwuBjveEu7grYmbuVg2kH0it48LQeVA60DWxPpGcnCEwtr5C16uv3T3BJ1S513AV0PdAYdZ7LO8MOBH1h5duU1P7+vsy8t/VvSStHSet8iOudmovaqB6N/grP/oqx7F5W+iGzFlbdKxnMm7Fa+Gtee0LQtwuVTcFnEt9w5ExqU08vq6DIhYrIvgqsfTF4nhExp1k+Fje+L5du/FlWca5H8Yh23fbWFk5dy6dHIn58mdpLxLzcpUrxI8SIpja7I2rpRUUPFsmz/TgT0ooiO0CN+RHFwYvqGU+T+8xEvOIgqppm938W79+PG8xXDlmmivoYpE6bFHaKmi299kfWxZw6setHScuD2r6HpkEpdQVGeUTTzbYa7oztOGqcaqYh7W4PbeKLtEwS7BVc+WGLmQOoBZh+ezZpza2rl+FPaTeFS/iUOph3kaMZRm2DjW4tVvHvxHCoHZ7j1CxEMvvgRuLgbgH/0bfnA4WFeHtOX3oEF8Nu9Is5LpRZun+5P2RfuRTkwe5hwUQU0gwdWg3Op71JFEe7PuK/Ese6cKf6/a5HjKTnc/tUWCkr0PDOgMU/0q/3O15JrjxQvUrxITNhtqPh2uaXzzSiK6Cf072fidcdJMPhDcksUnv1tP4HHfuJt7U8A6Pq+iUPPp8Q4XbGouRG/XLwO7ygsPPU6idf5GSIl++hSAHLq92RH5/uIyzxm1xXk4uCCl5MX7lp33LXupBWkcSH3wlW+KaBVaxnZaCQPtHpAiparJCE7gTlH5rD45GKK9EU1dtx6HvWYOWgmwW7BFOuLOZZxjINpBzmQeoC/z/6NXtHzljqYEad2iB26PCoE8vZvUNa9h8pQTJbiypsl9xHZZyL/61UP1YrnRFsJELFWw6fbL/+fnQg/9BVtAhoOEEXqStd4URTxf7xnjqhAPWYeNB5YY9dujz92X+DZ3/ejVsHcSZ3p2qCK3b4lNwxSvEjxIgFRRn/5M1VrqFgafYnoHbN/nnjd9zXo8Qyn0vJ46OfdtE1fxkfa78W2ns9DX2MMQGnhonESsTStRlnubs9sRrfwQQ4VpxHn6sbW4IYcLEqz6wqKDYnlTPYZ/j7zd41Wq9WqtdzZ+E7ub3m/FC01TEZhBvOOzWP+sflkFmWWO+7ZDs+y4fwGdqXsqtJxP+71MX0j+qJVW7LgZhycwbQ903DWOPOrfy8abftBbIjqAaNmQ14qhkWPoE7aC8AafXs2NXmZV+/qjdOBubDiOeEG9Wso2grYs0Im7oWZg0XadedHYPD71tsNeuFOPfSHcMOO+wPq96jSNV0pz/6+nz92XyDAw4kVT/YQvZ4kNw1SvEjxIjmxFn4ZKZYra6hYmqJc+P0+ER+j0sBtX0Dbe1h7JIWnFuyjV8lmPnf8Gg0G0VRv0LtCnJQVLnfPg4b9xDH1JbD+Pb4+NINfPD3I0VgX+YryjCI2NJauoV3pGNwRN60b/yT8w5T1U2rs7ZCi5dpRoCtg8cnFzDk8p1wr2TPtn2FCywn8ffZvnt1Ytayd2JBYOgZ3pGNwR2ICYnh07aNsSdxCtFc08xrci+uSJ4Wb0queECRBLWHLNPTrp6JRdGQqbszxeYzxk5/F+/Ih+G08ZF8QrSZu/xJajrQ96eHF4vMAonBjqUKMgPjfXnCvyGpydIfxf0F4h2q8W9WjoFjP7V//y/GUXLo28OPnBzrLBo43EVK8SPHy36YwG6bHii/m9hNEr6GqVAXNTYVfR4k7TgcXGP0TSqOBfP7PCaatPUE/9W6+c5yGA3qRenrr55ULl/RTsHAyay8f4akgUcPD09GTLiFd6BraldjQWELdQ62mEZ8Rz51L76yRt8JR7WgWLUFuQTVyTEnV0Bv0rE1Yy+xDszmUfsjumJmDZqIz6Jiyfgr5uvwqH3tEoxE82fZJRi0dRWpBKsMbDuf/Go0VGXEZp4Ul5NYvoPVdkHKYnAWT8cg4DMC/ms5E3Pc9EX7uwqVqahnQ5TEY8JZtnaNNH4nAc5UG7l0kOpeXpqRQVOE9sxGcvWHCcrvZcjXFyUs53PbVFvKL9Uzp34gp/RvX2rkk1xYpXqR4+W+z7GnYNUNkSTwSV7WOuBlnYO4I8cXv4gvjfkcX0o4X/jzIn3su0FV9iJ+cPkarFAtX0B3fid4x5QkXRRFupxXPkaXLY3h4GGkaNRNaTGBKuyloSvedKUV6QTpjlo8hOS/5qt4CKVrqDoqisCtlF7MPz2bThU022xv7NGZo9FBmH5rN5aLLFR6rsU9jTmaexKAYeKvrW9TzqMek1ZMwKAbe6/4et4b2EP25TqwWO3R5FAb8H6CQ9vcHeO34DC06LuNBRs93adBrHKx/xxLbFdkN7pwFHqX+ZxRFuIcO/ibiYyatA/8yBeOKcuHnO0TVabdAmLjSdkwNsmjvBZ5asB+VCuY+0JluDWX8y82AFC9SvPx3OfsvzB4qlu9bWnnhORBNEX+5U/R78Y6AexZR6FWfx3/dw9qjl+ikOc6vzh/goC8wNqibLe5OyxMuBZmw/Gk49CcAb0Q1Y6EqjyjPKP647Q+cNPb99CX6EiatnsSeS3uu+PId1A6MbjxaipY6ysnLJ5l9eDZ/nfrLZpu71p3cktwqH8tJ48QvQ35h3fl1TN83HRcHF+YPm0+0R6So4Fy6Hsyo2eDmT/rp3WT9Molo/WkAEkMHEjp2umjquOgRKM4R3c5H/QQRnS0nKymEn24V4sS3AUxaa1sbqSATfhomGkx6hsP9K8XnqZZ48c8DzN95niBPJ/55pjfuTv+dOkQ3K9X5/a7dDlsSybWkOF8E2oJwF1VFuJxaJ8ROXioEt4IH1pDlFsm9M7az9ugl2jqc4xfXj4VwadBXpIVWJFwStsG3PYRwUWnYHvsAC1UiXfrNrm+WK1wUReGd7e9clXAZ12wcf4/8m5c6vySFSx2loU9D3un+DmvvXEvH4I5W26ojXACK9EU8ue5JxjUbR+fgzhToCnhu43MUGkpEj6zRP4t4lrOb4fvekLgPv+j2BD+7lb987qNE0RCauJrCzzuKDuUPrhdFEnOSYPYQ2P69sLqAqMw75hcRT5NxSsTB6EusJ+TiDfcsAv/GwmU753bISbnyN6sS3rytBZF+rqRkFzFtTfULCEpubKR4kdw8bHhPuH08QkU6dGUc+A1+GQXFuSKod8IKLine3PVdHDvPXqaNUxK/uX2ItiRXFKe76xdwcLIvXOr3gg3vw6zBkJUAPlEU3LeEN3NFK4C7mtxF+6D25U5lzpE5V1xoblj0MP4Z9Q8vdnqRQNfAKzqG5NoS5BbEzEEzWTVy1VUdJzEvkW7zuvF/3f4PX2dfjl8+zoc7PxQbm98Gk/8RlpKs8zBzEOxfgKuLC8Oe+JwZzWZw1BCBc8llSn65G3SFMOkfUbPFoIOVz8Gih8RNAYB7IIxdIAJzz2yCFc9axI0J9wC4d7GwuGSchp+Hi/IAtYCzVsObt7UAYNbWsxxLzq6V80jqJlK8SG4OLuyGuK/F8q3T7NeuKM3WL0VsgEEHLe+EcX9wLk/Dnd/GcSw5hzZuGfzu9gHaosuirPrYBSJ2xp5w8WsorDcbpopKujFj4KHNfJ26jQu5FwhyDWJKuyl2p6EoClO3T+XjXR9X+5JVqPhn1D9M7TFVipYblDD3MPaP389jbR67quMM/HMgnYOFm+f347+z6oxRFAU2E1VyGw0U4mTRg7DqJTSKnofuGs7STnPZom+BVp9P7qyRokDdnbNEbSKVBg4sgBkDROA5QFAL0b4Cleh1tP1b28l4hYmsI/dguHRE9AMrrB1h0adJIINaBKE3KLy++DA3WRSEpAKkeJHc+OiKRDdmxQCtRkPjQeWPNRhg1cuiQiiIDIsRP3D4UgEjv4kjISOfDt55/OE6FW3+JVGN956FosKorhj+mGgtXAouw7fdRcyAoweM+AFGfMeh3AR+PvozAK/Hvm63ieGxjGMM+GMAvx77tdqX/HW/rzlw3wEpWm4C1Co1D7d+mJmDZuLn7HfFxyndsuD1ra9zPttY8NDFW3Q/7/mceL1tOvw8HFV+Os8NjWFPl885aQjFvSiFS98PF3WRYh+D+5aAW4DoOv19H4g3CqImt4g2FgB/vwwn7FQY9o0WAsbFFxL3wLwxFgtODfP6rS1w0WrYcTaDhXtqv5u6pG4gxYvkxmfzJ6JTs6s/3PJ++eN0RcLass1ooRn4DtzyHrvPZzHmu22k5RbRNUjPfJepOORcFBaV8YtFYKJJuBxbJoTLyB/g4B+iN1FRtqik+8i/EDOaEn0Jr299HYNiYHD9wfQMt469Sc5L5pV/X2HU0lGk5FcvJqBTcCe2jd1mc0zJjU/H4I78cdsfdArudNXHKtAVMGTREAp0BWKFWg19XxVxMI7u5jgYVdJ+nhjakc2dppOueBCYe4xT394tCtBFdYeHNkF4JyjKgnl3iSaPBj3EPg5t7xU3DL9PhJQjtpMIbAr3LgQnTzi3RdSV0RVf9bWVJczbhSf6icymqSuPklVQUskekpsBKV4kNzbJh4R4ARjyEbiVc+damC3iWw79IcqZj/gBuj7BoYtZTJi1g5wiHX0jHPhZ+x4Ol0+DV4TR9B1oK1z6vARr3oD9v4reLj2fh4mrzA3sZh6ayYnLJ/B28ubFTi+ap5BXkseXe79k8J+DWXJqSbUv9e2ub/PjwB9x07pVe1/JjYG/iz/fD/ieB2MeNK/zdvK+4uN1+qUTS08tRW8wVnFufpuIaykTBzNxWB82tP2cIkVLg4yN7PrhceGC8QwVdVs6Geez6UNh5QQY+ilEdhcZSvPuEnWSyhLaFsb+JuomnVwjxL6+5ipGm5jUPZoGAW6k5Rbzyer4Gj++pO4hxYvkxkWvE1+kBp1IYS6vOVxOssieOLNR3HWO+x1iRnMiJYfxM3eQU6ijZ4QjP2qmokk7Knz19/0FXuG2wmXIh7D1K7h8RqSDTlgu2gMY+76czjzNdwe+A+CFTi/g6+yLzqDjt/jf6PNbH74/8H21y/039G7I4tsXc0ejO1BV1gFbcsOjUWt4ou0TfNP/G7ydvMksysTD0YO2gW2rtP8jrR+hXWA78+uX/32Z4X8NZ/np5ULEBDa1Gwcz8tbb+belCHTvkPQrm+cZA38dHMWNwR3fiziY/fNEsLuDI9z1s3ARZSbAgnuEdbMskbGiE7vGEY4uERmBBsNVv0+lcXRQ83+3i8J4c7ed49DFrBo9vqTuIcWL5MYl7ivR+dbZC4Z+Yr9DbtpJEXCYfFD47ycshwZ9SUjP554Z28nIK6ZDqBMzHT8WfWBcfIXFxTfaVrjcOQN2/gj5aRDUSriJIruaT2VQDLwZ9yYlhhK6h3VnaP2hbLqwiX6/9+P/tv2fxYRfDe5sfCfzhs6jgXeDq3ijJDci3cO68/utvxMTEENOcQ57L+2lnke9Svf7Zv83TGk/hVGNR5nXnc0+y4ubX2TEkhGsPLMSg7On3TiYfkNGs7P+owB0jX+ff1fOtxy49V3Q22hJXPEsXD4nXKp3LwAnLxH3tfR/thlIYCwzMMsofn6FVS/YH3cVdG3oz62tQzEo8OriQxgMMnj3ZkaKF8mNSdpJkd0DMGgqeNjp13NhF8wcKO4KfaPhgdUQ2oakrALG/riNlOwiWgQ6Mc/jSxwubBNfwPcuEnemZYXLmF/h4O9CBLn6iztJFx+r0y2IX8DeS3txdXDlriZ3MXTRUB775zEyCqufKuqudeejXh/xRuwbODs4X8k7JLkJCHYLZvag2dzT7B4Am67j5TF+5XgmtZpEjH+MeZ2rgyuns07z/KbnGfHXCFYlrMbQ52WbOJiOA0az328IDioDrbdNYcf2zZYDd38a6nUWcV6LHhLxLwGNYfRsi1XGVK23LM2GwfBvABXs+B7W/d8Vvivl8+rQZrg7ObDvfCYLdlXtvZLcmEjxIrnxMBhgyePC5N2gH7QZazvm+GpRETQ/Xfjd718NvtGk5RYx7sftXLhcQANfRxYG/ID23AZRzGvc7xDaxla43P2ryJg48heotaLpXZnKoUm5SUzbPQ2AfF0+T6x7oso/NGVp4deC3279jVuibrmi/SU3F1qNlhc6vcCnvT/FXWubtVYeg/4cRGZRJo5qRwCGRA/hsTaP4eHowamsUzy38TlGLhnJaldnDA+sKRUHcwutug7mpEtrPFQFhK+YwKF4YxE4jQOM+F5k1iXEWYRKg74w+AOx/M9bcHSp/Um1vktYSUHEqm3+9EreknIJ8nTmqQGi19EHq46RkVfzAcKSuoEUL5Ibj50/ii9OR3dR06Wsu2j/fJGaWZIPDfvDfcvAPYCs/BLunbGD06l5hHtqWRr+C06nVlnSniM62xcuJQWw/l1x7KGfCB9+KRRF4cXNL9ptrFfPo161skfGNx/Pz4N/rpJ7QPLfYkDkABYMW0BT36ZV3ichJ4Fig/gB/+P4HzT3a86qkat4tPWjuGvdOZl5kmc2PsOo7a+xdvAbGBoOAF0h6qVPUL9df5IcwglVpcG8uzmTaAzI9YkSMTAgrJ8XjVWhO022BPYufBCS9tufVMcHLEUk/3kLdvxQzXeiYu6LjaRpsAeZ+SV8uOpYjR5bUneQ4kVyY3H5HKx9Uyz3f9O2d0rGGREQqOih9d1w93xwcie/WMeE2Ts4mpSNv5sjKxsuwvX4IpF5NHqO6JRrT7i4B8PCh8SxOz0E7e+zOp3eoCdmToxNWf9w93C+7vc153POsyN5R6WX5e3kzdf9vua5js+hLdvVVyIxEuEZwc+Df2Zko5FXtP9j/zzG2ayzPNLmEVaNXMVDMQ/hpnXj+OXjPLX1VUZ7wj/t70IBNFun4XvLS2SrPGnJSc79eA+XsowCvfUYaD5cBMsvnAzFogUGg6YKK0xJPvw6RgTL26Pb/0SWHoj4mX3Vr3VUHg4aNe8MF8G783eeZ09Cxc0uJTcmUrxIbhwURQQEluSJcv0dHrAds/ZN0BdDdG/hX9doURSF534/wN6ETLxdHFjdfCUeR4xpziN+EEW37AmXkDYw725xvvq9RNXRUvx78V/a/NzGal2ASwArRqygW1g3HvunalVT2we15/dbf5e1WyRVwtnBmTe7vsl73d/DxcGl2vuPWzGOqdun4qRx4vG2j/P3yL+Z3Goyrg6uxF+OZ0pGHHc1aMp6F0ccN02F27+iGAd6G7ax+ZvHKCzRC2vnsM9EK470k6JYHQi30p2zRH+jnETj56ecQPU+L0PnR8TyX48Jt2wN0SHKlzvbhwPw2uJD6GXw7k2H7CotuXHYO1d8yTk4w8NbwL+h9fZzcTDrFiFKHv5XlDIHPl97gs/WHkerUbGx/RZCD3wlxt8+HdqOsx+cW7+n6Mtybgv41BeppcYuuvEZ8Xy6+1O2Jm61Ov2qkas4ln6MKRumVOlyVKh4qPVDPBTzEA5q2RFXUn1OXj7J0xuf5kzWmWrv6+fsx8SWExndZDQuDi5kFmYy58gcfjn6i9kF2ryoiMfdGtOs/l34r34cgN9CnmXUg6+KtP3TG0UDRhTxuWlq7OiecRp+6AcFGaKEwciZolBeWQwGWPqE+GyrtcJS2qj/lb4dVqTlFtH34w1kF+p467YW3Nc1qkaOK6k9ZFdpyc1HTrLl7q73S7bCxWCwbG97r1m4rDyYxGdrRbDhn612WITLkI/LFy6N+otUznNbRGDi3fPA1ZdL+Zd4fcvrjFo6yka4TGw5kVFLR1VZuAS4BPDjwB95rM1jUrhIrpiGPg2ZP3Q+Q+oPqdL4rqGW1P70wnQ+3vUxg/8cTHxGPN7O3jzZ7klWjVzFAy0fwEXjxBEnJx7VneNI/iESYv4HwIjET1m9dJ44SHQv6CpEDUuesHSR9o0Wge1qLRxeBBvLqXytVsOtXxibQZbAgnFwdssVvRdl8Xd34rlbRHzQF/+coKBYXyPHldQNpHiR1H0UBZY/A4VZInMo9nHbMQd/FxlBju6iDDpwODGLp38TQYPTG+0m5pgxM6L/myK4sDzhsvNH2DUTUMHIH8j3iWT6vukMWzSMRScXoaAQG2IdtDvr0CxyinOqdDndQrvx+62/0ynk6svASySuWlfe7/E+r3V5rdKxZUW3s8aZ9MJ0Pt1tyfrxcfZhSvsprLpzNQM8xE3CrycXEtH5dk4ED8VBZaDr7qc5sCdO7ND3NVH3KD8d/nrUUr8lqpsIqAfY+IFop2EPtUYUwGs0SGQQ/noXXNxdrfegPMZ0rEe4jwvpecX8JlOnbyqkeJHUfQ4vEgJDrYXbvzZXszVTnC+yFgB6PA3ugaTmFDH5p10UlOh5OXQPQ84b0zN7PgfdnypfuJzZBCtfAEDf91UWqgsYtmgY3+z/hgJdAa0DWvPz4J85kHag2pfhoHLg6fZPM73/dPxcrrwBn0RSFpVKxegmo5k/bH61LHmF+kJUqNiauJXD6Yettvk6+zKl3zQAtjo7kfTnRBreM42TLjF4qArwX3IvKYkJ4GDs9eXgDCfXWmcPtb0Huj4plhc/Kmov2cPBEUb/BFE9RLuBuSPt90uqJlqNmod6iQKP3208RbGuZiv7Sq4fUrxI6jZ56bDCWAW0xzNmd5AVcV9D9kXRj6jLYxTp9Dw8dzeJWYVM9NrL5MvGu8ouj0KfV8oXLhln4Lf7wKAjrtkA7ry8hTe2vkFqQSph7mF83Otjfh78MyWGEvJK8qp1GWHuYcwePJuJLSeiVsmPnaR2aOHXgg2jNxDlGVXlfRSEpWTGwRk22yK8IukQ0AZFpWKx4TKqlc8T9tCfXFSHEEoqmTPvpKggFwKbWdKf17wGl0qlKPd/E5oMAX2RCODNLMcConURLtqwDqJb+x8Ta6SNwKj24fi7O5GYVchf+2TX6ZsF+S0qqdusekGU4w9sLsRLWbKTLIWy+r+B4uDEq4sOsfvcZYY67+f1ks9QKQZoN15kC+lL7AuXohyYPxYKMjgc2pKHi05wMvMkno6ePNfhOZYMX8KgqEEUG4q5/+/7q3UJAyIH8Nutv9E6oHUNvCESScV4OXmxZPgSBkQOqNZ+a8+ttRv4O6LJaAD+8nDHcHgRLieXoRr7O5m400QXT/w344TI6PSgqKukK4Q/J1n6HKk1IqsvqCXkXRICpijX/iScPESxSEcPSD0Gp9dX6xrs4azVMLlHfQC+2XhKZh7dJEjxIqm7xK8SsSwqNdz+lTAtl2X9OyKVObwjtBzJz9vO8fvuC3RTH+ZL9WeoDDpoNQqGTStfuBgMopbLpSPgHsTCJj0wKAZiQ2JZMWIF41uMx1Ejzv3CpheqdQkvd36ZT3p9gqejzHyTXDtUKhWf9v6UB1raKSdQDgoKsw7NslnfP7I/7lp3Ljo4sN3ZCVa+SKi7inP9v6dY0RCTvYFTC54X6dO3TwdXP0g5COvesRzEyV1kErkFim0LJ4vWAvZw9RXuJoDt31XnsstlXJdIPJ0dOJ2ax9+Hy6k9I7mhkOJFUjcpzIJlT4nl2McgrL3tmKT9sPcXsTxoKsdScnhn+VHaqY4z2+VT1IZiaDJU1HtRa2Dpk7bCBWDDexC/HDSOlIz6iVWJopfLxJYT8XLyMp9uwqoJ/JPwj93pdgzuaLNuzuA53N30btkJWnLdmNJ+Ck+3f7rK45ecWkJynvWPu4uDC0OjRQr0otBGwv3z+wRad+zF2kYiOL5B/A9kbZ0JHkFw25dix61fihgyE971xOdO4wTxKyxxavboNBlQwYm/If1UledfHu5ODkzoJqwvX68/yU1WIeQ/iRQvkrrJ6tdEkSvfaOj9su12RYG/XwEUaHknhcHt+N+8fUTpzzHX+SO0+gJR6XPULNBoRQ2Y/fOEFae0cDm0EDYZS53f+jmbVPlkF2cT6BJoLuufmp9Kq59asTvFfgbEq51fZWfyTqt1C29bSNvAtjX1bkgkV8zElhN5ou0TVRqrV/T8dPgnm/V3NLoDgLWqAjI9QyH9BKx4lv5jpjDPZQwAbqufRTm1QdR6aXcfoMCih0X8iol6HUXQPcCWzy03H2XxawCNjG6vGmofMLFrFK6OGg4nZrPxeGqNHFNy/ZDiRVL3OL0R9hi/QG/7ChxdbcfErxBdcDVO0P8N3l95jPiUHN5y/hVXJQ8iYuGuX0QmhMEAq18R+7UbbxEuSftFBgSI9Os2Y1l+ejkgmthp1BpmH5pN39/7ljvVu5rcxTvb37FaN3PQTBr5NLqqt0AiqUkmt5rMuGbjqjR27tG5XC60Lqnf3Lc5TXyaUGIoYXnnceImYP88HA/Np+OEj1hq6IoDekrm3QOp8XDLVNHoMfuisKCWtnTEjLK0Blj6v/LrunQ2tuXY94uISbtKfNwcGdtJtBOZvv7qrTmS64sUL5K6RXGeKHYF0HGSqBVRFl2xsMwAxD7G+hRnZm89SzvVcWKV/aJf0R3fWkTP4YWiboSju8WKk3sJ5o0FXYEIMhzwNtnF2Ww4v0EcNiSWmJ9i+GT3JxVOd0H8AqvXr8e+bteFJJFcT1QqFc93fL7Kncq/3f+tzf4m68vC9L0ovV4SG5Y/Q0N1Epn9P2OnoTGOuhxKfr5TlC8Y+QOoNKLUwf751ifo/ZKxN1IJLLhHVOQtS3Rf8GsERdm2+18hk3pE46hRs+NsBjvOZNTIMSXXByleJHWLde9A5jnwqidSLO2x80fIOAVuAaS3e5znfheF6D70XyG2txkrOt8ClBTCWqNvvdsU4ZPXFYkvzOwL4NcQRs4AtYY1Z9dQYigB4KG1D5lTSKvK3U3vZlTjUdW7XonkGqFWqXm3+7t0Dulc6dhfj/1qUw5gWPQwHNWOHL98nCMtbhH9vkry4fcJjOscwazwdzhnCESbnYBh/t0Q2EKIFBDlDi6fLTUZtYhFC20rWgj8OkbEuVlNWG2xvmz/rkbSpoO9nBlp7Hk0fcPJqz6e5PohxYuk7pCwHbZ9I5ZvnSbSJsuSnyGqdQJKn1d59q9TpOUWM9zvIg1zdgirS+mU6h3fQVYCeISIwF9FgeVPw/nt4OQlMiBcvAGYc2TOFU+9c0hnnu/4/BXvL5FcCxw1jkzrPY1mvs0qHdvl1y5Wr72cvOgX0Q+AhSf/EunPbgFw6Qjq1S/zxphePKl+mSzFFfWFnbD4Eeg+Bep1EYXnFj4Eel2pybjCmHmiuWNaPPw+0Xo7iO7VTp4ixub0uqu9fAAe7hWNWgUb4lM5dDGr8h0kdRIpXiR1g5JCWPI4oEDrscKVY4+NH0JhJgS2YG5xD9bHp+LooOZd32Vie+u7LVaXvHTYZHT79H1NfFlu/040gVOpYdRM8BexKYm5iZzOsmO6rgL1POrxSa9PZI8iyQ2Bu6M70/tPJ9w9vNKxL2+2DpY3uY5WnFlBgYunEDCoYPcsghKWM3nEIB4ueYoSRSPctRvehxHfibot57dZajKZ8AwRhem0rnDqH1j7hvV2J48aT5uO9HPj1tahgKj7IrkxkeJFUjfY9CGkHRd1IAa9a39M2gnYKTIPLnZ+lXdWiIaLn8UW4XZ+o63VZeMHUJQFwa3EHdypdfC30Yw94P/MAimnOIdBfw66omk7qh35qu9XVinVEkldx9/Fn+8GfIevs2+F45aeXsq03dPMrzuHdCbMPYzcklzWnlsLDfpYPnNL/sfQsEJcG/fhJd0ksW7zxyIgd+jH4vWGqXChTNZeaBu4wyhMtn9rae5oouMkRNr06hpJmwZ4pLdoGbDiYBKnU8spmCep00jxIrn+JO2Hf6eJ5aGfiCJV9ljzOhh0KI0H8fQuH4p0Bno1DmBIhtHd0/pu8BW1HEg7CbuM5c4HviP87b9PBMUgLDuxjwGwP3U/o5ZeeZzKZ30+I9o7+or3l0iuFxGeEXzT/xtcHexk85VixqEZfLRTlBNQq9Tc3vB2ABaeWCgG9H5JZPcV56D6YyJvDmnIUlUfvtKJcSz9HwQ0gRYjQNHDwkm2FXab3wbhncCgg31zrbf5NYBGA8VyDaVNNw32pH+zIBQFvpXWlxsSKV4k1xd9Cfz1mPhSa367+BKzx+mNIj1apWFN2ONsP5OBi1bDR12KUJ36R2Q1lLa6rH1DfBE2GiSCAufdLdxN4R1h2GcYUJhxcAYTVk7gYu6V9Tt5pv0z9AzveUX7SiR1geZ+zZnWZ1qlLs85R+bwyr+i3MAdDe9AhYpdKbtIyE4QjVJHzgAXX0jaR73dH/B4n4Z8ohvFelUnkVG08UMY9il4honMIpMFtDQdJorn3T/ZBueaAnf3zq2RtGmAR/sI68vCPRdJzy2qkWNKrh1SvEiuL1s+h+SD4OIDQz62P8agNxakg6K2E3lpk/iiebJfIwL3TBNj2pSyupzdIirpqtTQ/w34c7IICPQIhbvmkqvoeHjNw0zbMw2dYh0g2MSnSZWmfVuD27ivxX3VvlyJpK4RGxrLe93fq3TcklNLeHjNwwS5BtE1rCsAi04uEhu9wkR5AoDt3/Bw8FGi/D14p3AUCipx45GTYhyjgj1z4Ogy6xM0Hy6C6DPP2QbnNugL/o1F4O++eVd3wUbaRfgQE+6FzqCw7EBSjRxTcu2Q4kVy/UiNN2cOccv74B5of9y+X0Q/FGcvPiq6g/S8YhoFujMpKg1OrjVaXZ4VY60K0t0HB34TJcYdnGHML+ARzK/HfiUuKc7uqeIvx1c67ZiAGF6PfV2W/ZfcNAyuP5gXO71Y6bgtiVsYvWw0wxsMB+Cvk3+hMxhvABoPEsUeAe3Sx/mgnzenlDBW642tPbZ+AfV7QldjHaclT0BOqVYEjq4iNg1gV5keSyqVaPwIIoOwBtKmAYa3CQNg0V7ZbfpGQ4oXyfXBoIe/Hgd9sfBnx9xlf1xRjrnB28WYJ5ixR6Q2/t/wlmj//VCMKW11OfQnJO4VBelCWsOWaWL97V9DWDuAcvsTVaULb6BrIJ/3+RwnjVPVrlMiuUEY12xclRo5Hss4xtQdU3HTupFakMq/F/+1bOz3huhDVphFp93PcVurAL7V3QqAcuA3yLoIfV8VQfQFGaLCdWkhYnIdxa8UHeNL0/puY9r0yRpLm761dSgatYp95zM5k5ZX+Q6SOsM1ES/Tp0+nfv36ODs70759ezZv3lzu2A0bNqBSqWwex44duxZTlVwrtn8HF3aIFMphn4k7K3ts+RxyU1B8o3nsZHsUBUa0DaOL4xlbq0tJoaXZW/cpsNMYsBv7OLS6UwwxlHAk/YjdU605t8a87KCyHwPwZd8v8Xfxr/blSiQ3Av9r9z9ub3B7peMyCjPMRezMgbsgOr/fOVO4fy7sYKr3XxzXNmWboRkqQwlsmy5adoz4UVhDT/0DO7637B/YTNSFUfQivqU0Tu41njYd4OFEj0bi8yytLzcWtS5eFixYwJQpU3jllVfYu3cvPXr0YPDgwSQkJFS4X3x8PElJSeZHo0ayV8xNQ8YZWPd/Ynng2+BVTr2JzPOiMy2wod7j7EsswNPZgZeGNBP1I8A6w2j7N5B1XgQFBrYQriatq1Ug7+G0w+blab2nlTvFsrEwAB/1+ojmfs2rfp0SyQ2GSqXija5vVCsQff359aQVpFlW+ETB7eJz67bzK/6vZbLF+rJrlig0GdhUlCsAkUWYUuqGwmR92TNHWGhLUwtp03e0Fa6jxXsvym7TNxC1Ll4+/fRTHnjgASZNmkSzZs2YNm0a9erV45tvvqlwv8DAQIKDg80PjUZT21OVXAsUBZY+KcqKR/WAdhPKH/vP26ArpDi8K0/uE18wz93SlICsg3ByjbC69DQKk7w02PypWO77mmghAND2XqvU69/ifzMv5+mqbiZ+MObBKveFkUhuZLRqLR/3+rjSGjClmb5vuvWK5rcbhQYMP/M2iU7RHDVEoCrJs1hEO02GhgNAXwQLJ4u2HaZ9nb1FZexTZdxDfg1EbA1YW2yuggHNg3B11JCQkc+ehMwaOaak9qlV8VJcXMzu3bsZOHCg1fqBAweydevWCvdt27YtISEh9OvXj/Xr15c7rqioiOzsbKuHpA6z5yc4swkcXOC2L0T/Entc2A0HfwNUfO04kZwiPa3DvURXWCuri7HGyob3RQO34BgIbinM0So1dHnE6rBLTy81L684s6LK036szWPVuUqJ5IbGxcGFv27/q8rjfz/+O8cyyrj2B74LQa1QF6Qz2+sHftANAUDZ/i2UFAhX8e1fg6sfpBwSNysAWhfRnwxsA3ehVNp0zXSbdnV04JYWwYCwvkhuDGpVvKSlpaHX6wkKCrJaHxQURHJyst19QkJC+P777/nzzz9ZuHAhTZo0oV+/fmzatMnu+KlTp+Ll5WV+1KtXr8avQ1JDZF20dIPu+6pFeJRFUcx1ILKb3MmXR90AePO2FmgS99haXdJOwK6ZYnngOxBnvAtsdpvFpQQYFEtgYFPfpmy5uKVK0942dhtqlYxtl/y38Hb25pchv1R5/Kilo9iZvNOyQusMo2aD1o3QzN00cMnlguKPKj/NEs/iEQS3fSWW476C0xvEcvsJ4vn4KshOtD5RdJ8aT5sebnQdLTuQSLGuZjKZJLXLNflGLptSqihKuWmmTZo0YfLkybRr147Y2FimT5/O0KFD+fhj+zVAXnrpJbKyssyP8+fP1/j8JTWAqSFiUTaEdbCxiFhxeJFonKh15f3iURgU6N8siLYRPrDRZHUZYxE/a14XAX6NbxG9ig7+LtabUjKNnMk6Y172dvKu0rSf7fAsblq3ql6lRHJTERMQU634l/v/vt86m8+/IdwiashM0K5lpm4wAIatX1qaMDYdYhErfz0u4lwCmkBEV/G53vOz9UlqIW26awM/AjycuJxfwsbjqVd9PEntU6vixd/fH41GY2NluXTpko01piK6dOnCiRMn7G5zcnLC09PT6iGpgxz8Q9xFqbVw+1egLieGqaTQ3JztUszD/HpUh0oFzwxsLFxJJ1ZbV9M9s9lceZcBb4ssBEOJ+OIL72B16NXnVpuXk/KqVpTq3ub3Vv9aJZKbiKoUsCvNlPVT+PP4n5YVMWPAxRe3wmQU92AyFHfUmefgyGLLmEHvGeNczsM5o0W0osDd0mnTZeNirgAHjZrbjM0apevoxqBWxYujoyPt27dnzZo1VuvXrFlD165dq3ycvXv3EhISUtPTk1wrclNh5fNiudfzIh2yPLZ/A5kJ4BHKm2l9ABgWE0qzEE9LQbuYu0TgXumCdO0ngGeoxUdexuoCMOuQxX9+LvtcpdP+qNdH0l0k+c/j5eTFE21tP08V8Wbcm/xw4AeRvaN1NsewPOSzi590IuBW/+80YZEFcHSDZsPE8mFj1d5mt4mWA9kXRFmE0ji5i2B8EM0cawBT1tGaoylkF5bUyDEltUetfzM//fTT/Pjjj8ycOZOjR4/y1FNPkZCQwMMPPwwIt8/48ePN46dNm8bixYs5ceIEhw8f5qWXXuLPP//k8ccfr+2pSmqLlc+JglRBraD7U+WPy02FTZ8AcK7NM6yIz0Gtgin9G8HF3aJSrkoDPY11XQ7+Lpo6OnqI5nB754ou0n4NhQupDAW6gipPOdormgERlRetk0j+C9zT7B672UcVNXX8Yu8XfLjzQxFrZnQLBaVs5LBnD/IVJzQpB62tJi3uEM9HlgiXUinRYzdwt5MxbfrkGtGI9SppEepJo0B3inUGVh20H5MpqTvUuni56667mDZtGm+//TZt2rRh06ZNrFixgsjISACSkpKsar4UFxfz7LPPEhMTQ48ePfj3339Zvnw5I0aMqO2pSmqDo8vEnZRKI9xFGm35Yze8J4LwQtrw6ukWAIxsF06DAHfYUMbqUlJgyU7o8ZTojWQK1I19zCaLKSm3er1LHop5CE15ri2J5D+Gq9aVB2MetFmfr8tnYouJ5e439+hcXvn3FRS/hhDZHZVi4MmweObrhVXVYOomD1C/l/gc56fBOWPVXlMszIm/IeuC9cF9oy03KTuvvtu0SqUyB+4u3HuhktGS6801sYk/+uijnD17lqKiInbv3k3PnpYAsNmzZ7Nhwwbz6+eff56TJ09SUFBARkYGmzdvZsiQIddimpKapjhPBOkCdHsSQtuUPzblCOyeDcChVi+y+VQGWo2KJ/uVY3XZNl2Ykz3DocujcPQvURfC1U/4w8uwLWlblacd5RnFoKhBVR4vkfwXGNV4FKFuoTbrF55cSJuANuXut+z0Mg6kHTDHsLRK+YuFjrdSomhQn90EF/eIgRotNBPF7MyuI/9GENkdFINt4C5AZ6Og2vsLFF59mYzb24jr23Y6g4uZVbfUSq490qEvqT3OxUFuiujm3KuSpm+rXwXFgNLsVt7c7wXAmI4R1PN1hY3GHkYxo4XVJTcVNn8m1vV7XZQZ3/KFeN3pQVEnogxzj861WVceD8Y8KK0uEkkZHDWOPNrmUZv1WUVZNPVtWuG+v8X/JoSJiy+qnEQmNSliiSEWAMXUfwxsXUdgHbirL1P5OroP+DcRFtv9V582He7jSqf6wj321z4ZuFuXkeJFUntc3C2e6/cQ/uvyOLFGFJVTa9nd6Cl2nbuMk4Oax/s2FHdlx1eJgnM9nxPjN0w1u5doNUpkJyTtEyLGWNWzLMcvH6/SlCM9Ixlcf3DVr1Ei+Q8xLHoYDbwa2KyfHz+f8c3H29lDsOTUEral7jXHsAwpWsVMxdhD6cgSS8xKVE8RpFuQAWeNtb2a3SosqjmJItuwNCqVxfqyvWbSpk3Wl7VHUq76WJLaQ4oXSe1xcZd4Dmtf/hi9Dv42Zgx1fohvDogvnzEd6xHk6WybYZQab3YvMfAdEdti7H9Em7HgZts0MbMws8pTfjDmQRzU9psySiT/dTRqTbmZR3OOzKlw38f/eZy4SNHZ3fHMWnq0jOYffVtUKLDVaDnVOEDz28SyyXXk4GQJ3N1tJ3A3ZoxoBJlxStwEXSU9GwUAcOBCFnlFtj3OJHUDKV4ktYOiWCwvFYmX3bMgLR5cfElo+Rjr4i8BMKFbfUjca2t1MRWkazJEWHRS48UYVNDFfgn/PZf2VGnK9TzqMaS+jK+SSCqib0RfWvm3qvZ+Rfointg1lbioDqAYeNB9i6Vh4755kGPM8DG5jo4uBb0xZbm90XV0Yo1o2FoaJ3doZ0qbvvpu0/V8XQnzdkFnUNh17vJVH09SO0jxIqkdMs9BfrooShfU0v6YgkzhAgLo8zKz9lxGUaBPkwDq+7tZMoxaGWNdTm80ihljQToQJcUBmg4V1Tzt8MbWN6o05cmtJkuri0RSCSqViv+1+1+Vxga5WhcjLdIX8a6zsGb4xs/HrWFXdhsaoTIUwzZjs97I7uDqDwWX4cxGsc6vAdTvCSgi9qUsHWs2bTq2gR8AcafSr/pYktpBihdJ7WCyugS3LD/eZfMnQuD4NyG31b38vkukJ1qsListVheDQQT1AnS4X2Qh5KTA/vlinZ2idACFukIyizIrnW6YexjDGgyrzhVKJP9ZOod0pktIF6t19jKOUvJt40YulmSjGGNYHg0/bbG+7JoJhVlG15ExHsbkOgKL9WXvz7aBu771LWnTNdBtOjbaKF5OS/FSV5HiRVI7mNIfy3MZZZyxVMYc+A5/7k0mt0hHdIAbPRr6W1td/BvCgQWQfECUBO9tzFza+QPoiyG8I9TrbPc0n+7+tErTndxqMlp1BTVoJBKJFWWtL0Ojh1ZpP51BR27MKADapy5mp2NnThjCUBVlW4rRmV1Hy0BXLJabDhMWmZwko6u4DKZu0/uuPm26i9HycuhiFjmy2m6dRIoXSe1QWbzL2jeE8Ijug6FBf37aehaACV2jUCfvt7a6FOfDuv8T+/V4WgTlFufBzh/Fuq5PiKyDMhxJP8K8Y5WnT4a6hXJbg9uqe4USyX+alv4t6R/R3/z63e3vsnrk6gr2sJBpbAWgObWWe1s48J3eaPXc9g3oiiCyK7gFQmGmxXXk4Ahtx4lle4G70b2NadO5sO/XK7wqQZi3CxG+rugNCrvOyriXuogUL5KaR6+DxH1iOayD7fbEvXDkLyFOBr3LxpNpnE7Lw8PJgZHtwi0ZRq1GCavLtq8h+yJ41YPOxm7U+34VPnGfKHFHVoYSQ0mVY10mxUxCW1HlX4lEYpeymUcZhRlMaTel0v0uu3pBVA9QDNzjuIm/9N1IUnwhN1m4gtUa+66jdveJ55P/wOUy/clUKov1Zcf3V502LV1HdRspXiQ1T+pR0BUIF4+fnSDaM5vFc+PBENSC2VvOAjC6Yz3c0g8Zu0QbrS5FuWAqId7vDRE/Y9BD3NdiXezjdjtU/3T4J45lHKvSdIc3GF6965NIJABEe0fTzNfSaHX6/ulV6sSeWZRpLj4XePI3GgV58qPOWF9p6xfiM27PdeTXQFhYUGDPT7YHbl1zadNdGohiddukeKmTSPEiqXkuGOu7hLa16TEEiNgVgLB2nE7NZePxVFQqGB8baamm2/JOEZR7frswA3vVg5YjxbZjy+HyGdEHxVT/oRRns87y+Z7PqzTVVzu/Kq0uEslV8Fmfz8zLmy5s4kLuBSI8Iirc53LhZWMMix+qnCSeijrLfH1fclVukH5SfMYjuoB7sGi2enq9ZWdz4O5cSyq1CUe3UmnTV9dtOjZa1Iw6dDFLdpmug0jxIql5Kot3ST4onoNj+HOPyDDq3TiAyOKTEL/cuq5LgrEnUWQ3ixAyFaXrOEl8WZXCoBiYvGZylad6R6M7qjxWIpHYEuYeZvV65sGZNPZpXOE+6YXpxuJzIoalV/YyitSuzCoxdnLfMk18D9hzHTUdKuJhclMgfqXtwc1p02sh7cQVXhUEezlT398NgwI7Tmdc8XEktYMUL5Kap6JMo5ICSBOl+pXglizdL7o939Eu3JJh1PJOCDB++Z03ipcIYzZRwna4sAM0jqKPURnmHJ5Dcl7V2tkPix6Go8axatckkUjK5eXOL5uX/zr1F25atwpGw2e7jdYaY9doxzP/MDRCz2zdIHRqJ3EDdPZfi+vo2HIRyAuigWNFgbu+9aGJ0QV1lWnTXYxxL9J1VPeQ4kVSsxTlipgXsC9eLh0RHWJd/dl32ZmEjHxctBoG+CTbWl30JRYXVIRo4mYuI956DLgHWh06KTeJT3Z/UuWpvh77enWuTCKRlEPZNOnNFzdXus/ulN1Wxefud91EOl6sdTJmMP37mSiB4BECRdlwap1lZ1Pg7ql1ouxCWcxp079eVdp0l2gR9yKDduseUrxIapak/UKceISCZ4id7cZ4l5AYlhwQVpcBzYNw2WoUHS1HWqwuyQegJB+cvUUKZPopcQcGIlC3FIqiMPDPgdWaqouDbfdpiURSfTwdPWnk08j8OqOwcjfL85ueF7EvRutLy5QlaNDzXmZ/FJVaBNymHILmw8UOpV1HvvWhQV+xbC9wt34vCGh61WnTpoyjI0nZZOYXX/FxJDWPFC+SmsUc79LO/nZjvIshqBXLjOJldCPg2DJABT2ft4w1xbtEdBHxLnFfA4qopBnQxOqwq87aKVpVAR/0+KBa4yUSScXcEnVLtcZfyr/Eq1texdBkKLj6o8lLZmJAPAlKEOeDjTciWz4v5TpaASWFlgOUDtzVlREWKpXFrbzjyrtNB3o60yDADUWBHWdk3EtdQooXSc1iEi/hduq7gFm8nFBFkZpThJeLls6uF8W2oJYWqwtAQpx4jugCeWmicibYWF0yCzN5f8f71Zpm73q9qzVeIpFUTPew7tUa76h2ZNOFTfx8fIE5huUeB+EamoUpUHehcA97hkFxjnX6c5PB4B4EeanC5VwWc9r0aRG8e4V0kfVe6iRSvEhqlooyjQx6SDkMwLIUkYY4pFUw2nQRwEtgU8tYRbFYXup1gZ0zQFcIIW0gyvpL8sOdH1bJTG2iY3BHXLWuVR4vkUgqp6lvU3ydfas8/vaGQqBM2z2N/fVFn6TIy3GEkcov533Q1e8jXNDbv7XvOtJooa0xLXr3bNsT1FDadKf64pr2n8+84mNIah4pXiQ1R04KZJ0HVEJklCXjDJTkoTi48PNJUVvl1tahkGosJhdQSrxknBZ3VBpHCGxmyRoo0wrg34v/svT0UlSoaO7XvErTHBQ56AouTiKRVIRapa6W9WVr4la6hXVDp+h4ft/nZNXvjgqFB93/pVhn4GCw0V10bovFdRS/UmQsmmg3HlDB6Q0iJq4snSaL7af+ueK06YaB7gCcScu7ov0ltYMUL5KaI9GYIh3QBJw9bbcn7wcgy7MxmYUGAj2c6Fzfz754MVldQtuJu638NFGoznQHBuSV5PF23NsAjGs2zqrSZ0X0qterWpclkUiqRnXEy8Xci2hVWsLdw0nMS+QNbzcUYIRqPQ7oWJ8ZJAamnRAFL73qiQDc0i4gn0ho2E8s2wvc9YmCJkPE8hWmTdf3F2nfl/NLuJwng3brClK8SGqOKhanO2wQ1TeHxYSiQYFUo9vISryUinc59KdY7vwQaBzMQ77Y8wVJeUmEuYfxRNsnKDFUXgWzqW9Tgt2Cq35NEomkysSGxKJW2f6slFf3ZXvydj7u9TEOagf+yTzKr37BeJSk0Ve9l78vOIKDs3AXZ56zX7AOSgXu/mIbuAvQ2Ri4u+9XKMyq9jW5OjoQ6uUMwOm03GrvL6kdpHiR1BxVzDTakCXEw+BWwZCVIPogaRzFXZIJc6ZRLFwy1o2J6mHevO/SPnPH6NdjX8dV60pJ2VLhdugVLq0uEklt4e3sTUv/lgB0Cu5kXp9XYt/l4qB2oIV/C57t8CwAn3g6c9hRy1jNOuJTC9D5GtOvU+OhxQixHL9KdJo30fgWUQsmPw2OLbU9SQ2kTUcHCNfRqVTpOqorSPEiqRkUpcqWl12F4bg7OdCmnjdcMrqM/BtbrCp5aZBu9E/7NRRfSqjEGKBYX8wbW99AQeH2BrfTNbQrADpFV+k0ZZaRRFK7dA8VriMvJ69KxzppnAAY23Qsfer1oQQD7/n50lNzgHBVKilOUWJg6lFxU+QVASV5cHKN5SAaB0vg7i47FXdVKujwgFiOX3FF12RyHcm4l7qDFC+SmiHjtDDJapxEynNZclIgNwUDao4qEXSJ9kOrUZeKdylVt+X8duO6pqJ/CYB3BDiKDKHvD3zP6azT+Dn78VzH58y7FemLKpyiv4t/lYN6JRLJlWGKe4lLjMNB5VDhWJN4UalUTGgxAYB0ZzfUKNylWc8xfagYmBovREiL4eJ1WddRu/GiOvfZzZB20vZEvtHiuSDzCq4IogOEeDmdKt1GdQUpXiQ1g6mMf0hrkcJYFqPVJckhjEKc6NFIpEqTGi+ey4t3KRPMe/zycWYcnAGIfiql7+52JO2ocIq9wnvZ9cdLJJKao7lfc7ydvMktyaV9cDlWWCOle4tlFYl4FB9XEah7l2YDWzONqdem7wFT1tHxv6G4lBXEux40NDZ13DPb9kROHuK5KKc6l2LG5DY6Ld1GdQb5TS6pGSp1GYm2AHuL6wHQ3Sxe7FheSse7lNquN+h5Y8sb6BQdfev1ZUDkAKtTFOoLqQjpMpJIah+NWmN25VbWJNVkeQG4XHQZAB/vKBSNE4GqTI5nGjemHhdVckPbgnekaBtyYrX1wWJGi2fT94fVia5SvBjdRufS89EblCs6hqRmkeJFUjNUMd7lkD6CUC9n8WWgKKUsL8Y05+J8SNwnlstYXuYencuh9EN4aD14pcsrqErVe6nMZeSkcaJzSOcruTKJRFJNTK6jpNykCseVDrI3FZr0cfFD5S1ucvSo0KsdRVB/5jmj68hofSnrOvIw9lIruGx7oqsUL6HeLjg6qCnWG7h4uaDyHSS1jhQvkqtHV2y2rFSWaXRYiaJ7I38hPLLOi+A7tVY0WgNRK8ZQIr6IvCPN4ua8uy9f7f0KgKc7PE2gq3VH6U0XNlU4xS4hXWQjRonkGmGyvBQbKq6LcirLUljOJF78nP1EjBsQqkonwyVSDLBxHa0WXexNuHiLZ3txLSbxoi8CXcU3OvbQqFXU9xPWl1MyXbpOIMWL5OpJOQT6YtH92RQYV5qiXEgXQXRHDZF0bxQg1pusLn4NLXEy5pYAncUdVG4KCvD2qd8p1BfSKbgTIxuNtDnFjwd/rHCKsjCdRHLt8HPxo4Vfi2rtc7nQ6DZy9jGLl3BVKmdUwgpjFi8hrcGnvrDGnPjbcgBnb/FcmCmsuqUxiRewFjzVwBK0K+Ne6gJSvEiuntIuo1KuHDOXjgAKKYo3aXjRrYFodGb+Mird06h0vEuaKF63OKAe21J24qRx4o3YN6zcRSAC/Y6kH6lwirK+i0RybekW1q1K405cFmUR7IuXNA4UGYtKmm52ynMdufiIZ4NO1HQpjVoDpkJ5RdUvVAcy46iuIcWL5Oq5aGwLUEmw7hFDJC1CPfFzNwbplW0LYNDDeWPGkDHeJVut4iN3DQCPtXmMCM8Im8PPOTKnwuk192tu42aSSCS1S4+wHpUPAhaeWAhY3Ea+zr7CZYywvOzMM7YJMBWrBIt4ObHGEseidRHFLqFi19EVB+3KHkd1CSleJFfPRWOadHgH+9tLxbuYOrQClgJ1pkyjS0fFXZGju6gVkxrPWa2WHAx4Onpyb/N77R7++wMV9yzpHd67qlcikUhqiJb+LfF0tNPjrAzLTi+jWF9sCdh1slheItRpnFDCxMA0Y8YRQHAr8G0gWgccN7qOVCpr11FZrlK81JduozqFFC+Sq6Mwy+zeIbScYN0ki+WlZaixLotVppHR8mKq7xLeUVTNTD1GvRJRNTenOMdu76K9l/ZWOkUZ7yKRXHsc1A7EhsZWOi6zKJN159eZ3Ua+Lr5m8RJEOhcVf/QqrUiPzjovdirtOjpaqiVAVYJ2r1C8NDBaXpKzC8krqryat6R2keJFcnUkGsWDdwS4B9hu1+tQLol4lCNKJC3CjHdi2YlQnANqB3EHBaXiXbqI59R4fAwGvLXuKCgkZCfYHH78yvEVTi/QNbDK3aYlEknNUrbLtKPa0e64X478Ys5M8nHyAbdA0DiiwUCAKotUJ6O72ORqBgg2VvLOvWRZZ4p7sZcubep0f4XixctVi5eLSCxIzJTp0tcbKV4kV0dl9V3ST6LSFZKnOJGsCaGhsVKl+UvItwE4GL/QTG0BIrpAYTZkXwSgvpdIoz6dddrq0GkFaZVOr1d4L5sAX4lEcm3oFlq1oN19qfsAcNY446p1BbUavESWUbgqlVMm11Fp8WIqfaArJSSq5DbKrtrk7eDpItod5EjLy3VHihfJ1VFpsK6IdzmqRNIk2AsHjfFfrmxl3czzwiSs0kBYB4sryiOEaB/RkPFM1hmrQz+78dlKpyer6kok148A1wCa+lqyCSur++Lj7GN5USpd+pCuVI8jE1pn8VxSqrJ2hW6jq7O8ALg5CvGSWyjFy/VGihfJ1VHFtgCHDZG0CCvVZbZsppHJ6hISA07uVuLGnuUlrSCN3Sm7K5yas8aZTsGdqn4tEomkxqmq9QXA28m71AuLeNlXaEyXLp1xdMWWlysXLx7ORvEiLS/XHSleJFdOdiLkJAlrSUhr+2NMadJKFC1CS2UemO6gAssE60YYA/xKiRuTeClteTE1Z6yI2NBYnB2cq3YtEomkVigb91IRppovgFm8RKrTOG4wuY3iLQXo7FpeKoh5qQHx4u4kxUtdQYoXyZVjsroENgdHN9vtioJidBvZZhqVsbzYCdYV2y2Wl3PZ59Ab9GQUZjD36NxKpyddRhLJ9ad1YDk3NnbQKaVEgbHWS31tBueUIAxqrWgnknVBbDdbXqrqNqoB8eIsAnal2+j6I8WL5Mq5YKzvUl4/o5wkVPnp6BQ1J1X1aBJs/PLISRYp1iq1aA1QmAUph8W2eibxYhE3oW6hOKodKdIXkZiXyE+Hf6rS9HqG97zCC5NIJDWFVq2t1vhMk8vHaHkJIxUdDuS4lelx5GAsdllavNSy20haXuoOUrxIrpwqdpI+qYQRGeiLs1ZUyrVkGkWLL6DzOwFF9CvxCILiPMg0pkUHNEWj1hDpJb649l7ay8xDMyudmkalwd/F/0qvTCKR1CC+zr6VDzKy/MxysWAUL776NDToSXGMEutN3x/aUpYXkyvJbHmx5zYyBexeebaRjHmpO0jxIrkyDHpI3CeWyxMvpuJ0SqTF6gLlF6czxbuYMo3cAsBVfOlFe4mGj2/HvV2l6Q2MGlilcRKJpPa5rcFtVR7754k/URQF3IOMtV70hKgyOKMu06CxdDybyfpijnnJtD1wDVpecqTb6LojxYvkykg7IYrMaV0tIqQspXoahfu4WNZXOd7FclxT3EuRvmrt7AdFDarSOIlEUvtUp1DkicsnOJx+2KbWS7zeGLR7qYzlBaDEmHEk3Ub/GaR4kVwZJpdRSBtRyt8epmBdJZJQ73LEi67Y0hvJZHkxpUOaasBgsbyURq0q/983xj+m0kuQSCTXBl+XqruNwNKssXS6dLyhVK0XRQGNVmQ6AuiMNzUmt1FhlqUPkomaFC+Ftq1KJNcWKV4kV4Y53qWcYN3CbLgsUpuPGCIJM4kXRbGIk8CmkLRfmHxdfMG/kVhfgeWlNC39W5Y7PSdTMJ9EIrnu+Dj5VD6oFCvPrKRAV2AtXooDRDuR4hxz9W1L3EsZy4tisI1tqZFsIyFe8or0V3wMSc0gxYvkyqgsWNeYPZSEH5l4WMRLXqow6Zoyjc6XchmZyviXrb4LRHpGosJS5t/FwYUDqQfKnZ6zRtZ3kUjqCn4uftUan1uSy5pza0qJlzQuF6ksfdDKZhyZar1onS0p1GVdR6aA3ZJ80F+Z28cc8yLdRtcdKV4k1aekAFIOieXwDvbHGONdDulFlpDZbWT60vGJEndNpqDf8I6WY18+K5ZLWV5cHFxQUMyvg92CK5xiddMzJRJJ7WFVObcSTMG9C08sNNd6CVelklOoQzHd0Jiss/aq7JZX68XR3bJcfGXWF3dztpF0G11vpHiRVJ/kg2DQiWwgY0Cd7RhLppG3qxY34x2LOdjOJExMcSsaY3PGtBOAIrIG3Ox0qTZyPud8udtcHFxkM0aJpA7hoHaokoDxc/bjibZPoFap2Z2ym3OOwrISrkqlWG9A72cULybXs70qu+UF7To4WjKUrtB15OEkexvVFaR4kVSf0i6j8kRCqcq6oV4VZBqZKvMW5xm3l4p3KXVsg2IdfKczlP/l4aSR8S4SSV3DquliObQLakewWzBdQ7sCsOiyuAkKJgMNevK8GoqBNpaXa9MiwL1UnRdFUSoZLalNpHiRVJ/K4l30JeY7o8NKVJlMozLBuE5GU67JjGsn3gWotAljaaR4kUjqHlUpVNc2sC0AIxqNAGDJ+XXoNI44qAyEqDLI9iglXhTFYnm5Ri0CHDXiJ7NEryC1y/VFihdJ9aks0yg1HvTFFGncuKAEEOZdKni2rDhxNH2Z5JbZbl07ZtnpZVWenmzGKJHUPaoiXtoFiu+U3uG98XX2JbUglX/9RH2XcFUqWS4RIj26KEs0hTV91kuuTWfpghKRZeTkoEatlq7p64kUL5LqkZ8BGafFcmg54sXoMjrv2BBQWSwveWmQnwaowL+xWGd2G5nEi6Uho4kifRGrz66u8hSl5UUiqXtURbw08RWfe61Gy7DoYQD86WaJezFoHEVbERA3Og7VtbxcXYuAQqN4cXHUXNH+kppDihdJ9UjcI559o82l+20wipezDuJLxsvFmPljzjSKBEdXsWx2G+WJQlMmYVTK8rLh/AZyS3IJcQvBw7FUm4FykOJFIql7VEW8OKgtBS9NrqPNFJCqUROuShUbAo3fDanxpQJ2S2cbVSHmpfDKxEt+sRAvrlopXq43UrxIqscFk8uonBRpMGcandAI8eJqyjSy5xIypS8W5UD6KVD04OQFHiHmISaX0dDooTTwalDpFKV4kUjqHpWJl0DXQKvXDbwbEBMQgx6FJe5uhKvSxAZ/o1U27bj9gN1adBuZxIu0vFx/rol4mT59OvXr18fZ2Zn27duzefPmCsdv3LiR9u3b4+zsTHR0NN9+++21mKakKlQWrKsoZstLPKJGg5vpg27HJWT+MinONVfkxbe+OdPocuFl/r3wLwDDoofhXrpWQznI6roSSd2jMvHSL6KfzbqRjUYCsNjdnTDVJbHSYKyxonG65gG7BdJtVGeodfGyYMECpkyZwiuvvMLevXvp0aMHgwcPJiEhwe74M2fOMGTIEHr06MHevXt5+eWXefLJJ/nzzz9re6qSylCUysVL1gVxx6PWcszYSM38QTf3LCrVpK10qrTJH21KmwZWn12NTtHRzLcZDbwbkJBt//+mNLK6rkRS96hMvPQO722zblDUIFw0Tpx11JLpbHQDZSeJZ88Qi+XFXp0Xu24jU8zLFYoXs9uonH5ukmtGrYuXTz/9lAceeIBJkybRrFkzpk2bRr169fjmm2/sjv/222+JiIhg2rRpNGvWjEmTJnH//ffz8ccf1/ZUJZVRUmAMuMUSNFcWk/DQupBTLKwnbo4mt5Edy4vZbZRrcRXlJJs3m1xGpuC9hJzKxYt0G0kkdY/KxEu4R7jNOjetG7cYRc1mT50ojpljEi9h5VhejDEvteg2cpaWl+tOrYqX4uJidu/ezcCBA63WDxw4kK1bt9rdJy4uzmb8oEGD2LVrFyUltiWZi4qKyM7OtnpIaglHV3APEssmF09ZfISriKJsHIszAHA1fdBNQXWlXT+l3UYexmMX50BRDuezz7MvdR9qlZrB9QeTa8pIqgSZKi2R1D0qEy/lFbEb0XQsAGvdXCjJPm1pyugRYj9V2uw2yrI9mFm8XNnvhMltJAN2rz+1Kl7S0tLQ6/UEBQVZrQ8KCiI5OdnuPsnJyXbH63Q60tLSbMZPnToVLy8v86NevXLK1UtqBnNvkWP2t2tdwFPcQQWUJAKlAnZ9osSzqXcRWKdKO7pbhE1OCsvOCKtLl5AuBLgG8G/iv3ZP2cKvhdVraXmRSOoenk6eaFTl/+i7a+3Hs7UOakt4sUKBWs3h5PWl3Eah9lOlTW6joiwwlOn+fNVuI1HZ21VaXq471yRgt2yfGUVRKuw9Y2+8vfUAL730EllZWebH+fPl97yR1ACmeBVT/Io9/IRLKdxgFC+muxTfKPFc2mpjEiuKQdw9eRgbLuYmsy1RdJzuXa83AOsS1tk/XZmOtTLmRSKpe6hV6gpbBJT3m6BSqZjc6BE+aPASI1uPsTRh9AgRN0tgP2AXoLCM9eVqA3aLRZsS6Ta6/tSqePH390ej0dhYWS5dumRjXTERHBxsd7yDgwN+frZt1Z2cnPD09LR6SGqR0jUWysPYtj5KLf6Ork7GD7pPffFsquUCRsuL8Uur2DruxVSwalfyLkr0Jeaso7KUDeKV2UYSSd2kKv2N7DGi92MM6T4WN4PRdeziK+JdzG6jUuJFo7XcFJUN2r3amJcSo+VFuo2uO7UqXhwdHWnfvj1r1qyxWr9mzRq6du1qd5/Y2Fib8atXr6ZDhw5otdpam6ukiphqtJTnNgLwE+KlvioZB7XK3A/EHOSbUcryolJZ13oxWV5yksxFqtadX8fahLXklNj/wjmbfdbqtXQbSSR1k6oUqquQbGHNxVNkMlosLwXW48qr9XLVlhdjzIu0vFx3at1t9PTTT/Pjjz8yc+ZMjh49ylNPPUVCQgIPP/wwINw+48ePN49/+OGHOXfuHE8//TRHjx5l5syZzJgxg2f/v73zDm+qfvvwne7dUtrSQktL2Zuy91IZTsCBiogL98/xure4994LVFRQQRRZokzZe29oKdDSvVeanPePJztpmwKVFr73dXElOSsnIU0+5xmf5+GH6/pUFe5gFi/5qVV/AZhESoIuHR8vD2s4ONwUeXEs9rVtlzYXBBem0y68HR0ad6DSWMmjKx51+xRV2kihqJ+E+YZVua5EX1LzASzixRShdRV5gaq9Xs6QeFFpo7NPnYuX8ePH89577/HCCy/QrVs3VqxYwfz584mPl66UtLQ0O8+XFi1aMH/+fJYtW0a3bt148cUX+eCDD7jyyivr+lQV7hAQDoEmJ8zM/a63MaeNdCfRG2wK5sxpo9xk+0I6y4gA53bpca3G1foUSx2vwhQKRb2gur/NrZlbaz5AoU2xLtgU7FYReXFKG5m9pArBaKz5+RwoUd1G9Yb/xGnn7rvv5u6773a5btq0aU7LhgwZwubNm+v4rBSnTFQ7OJIBmXsg1oVZXaMENHQE60oJNeRjNGoygTU0Fjy8wVAhV1Bhps4wO68Xc9pIxMvoxNG8ufFNyg3lbp+eYxpJoVDUD7JLs6tc19jPuabRCUubtEm8eNcQeakqbQRyseRXuxrJMjUeoN6gZhspak9NdS/efmimdukEXRoVBtMVjoen1QfGVcdRRZFdzQtAiE8II+LtfX9qIjk/uVbbKxSK/4bssqrFS3RgdM0HKHCMvLjoNoKq00ZevnIBBaeUOsoolIuoRgE+td5XcWZR4kVRe8ziJcONol2PdMorbcKzlo4jG/HiKm1UdNKyemzrsU6H7x3du8qnPpJfhYGeQqE4q+SU5lS57ljhsZoP4Fjz4sphF6ou2NXpTqvuJSVbHMTjGwfWel/FmUWJF0XtiTJ5vVTTLq0ziZd43UnKK23qW1wV7dqmjcwFuxVFli+Xnk2cJ1j7m6+4XFBVV5JCoTi7VBgrqlyXWuSGR1ehQ7eRZbaRQ82LJfLiar7RqYmXvJIKCsqkVbp5eECt9lWceZR4UdQeS8fRUREcLjCLlwRdOhUuIy82Xi+2kRffIGtRnanuxZV51eaT1ddEudW5oFAo/jMqDFULF3Aj8qIvtYqR4BoiL+b5Ri4nS5tddms3IiAlW75TooJ9Vc1LPUCJF0Xtse04yqoi+hJu9XqxEy/hLtJGtjUvYNMuLfltV0KkpujKgbwD1a5XKBT/LTWlcw/nHa52vSVl5B0AfqFy33Y8gMmJHbDpNspzPs4pRl6SLSkjFXWpDyjxojg1zDOOqqp7sfF6KdcbnJaTm2z9srFNG4FN0a7UvWzL3Fbr09ubXU09jkKh+M+p6YJiR9aO6g9gqXdpKrUrYBUvAJU2HYnmmjkfF7UppyhejpoiL83DVb1LfUCJF8WpYal7qWLGUaMEDHgQqCvHWGgz7iEsHtBJyLbEVLzn6xB5sXi9SORlc0bt2+b35FQze0mhUPznHMw9WO36Gi0OzB4v5u8HsDrsgr3Xy5GVcpswwPk4pyheUnJEvKjIS/1AiRfFqWGZLl1F2sjLh5O6SAA8bOtbvP2sbY7mol1bh11w8nrZcnJLrU9vb46KvCgU9YmDedWLFwC9QV/1SsfRAGCfKjLvazRAymq5nzDQ+TinGXlR4qV+oMSL4tSwTJeuWiSke8mXjJZ9yH6FY9Guj8OXic1kaQAvT6uXoo+Hs7+Cq2UHcg9Qaays7hUoFIr/kAO5NdehpRWnVb3SsU0a4PhGuQ2IgEC5WCJ9B5TnS2FudFfn41jESy0LdnPk4kp1GtUPlHhRnBrmtFE1HUd5fuKgq+U4iBfHol2ntJF95OXGDtbZV65aLVuEtnBaVmGsUH4vCkU9oaiiiBPFJ2rcrtqOI8c2aYDDy+W2xWBrHUyyafp8837g6cJE3tskPmoReSnTGzhZIDU1yuOlfqDEi+LUCAi3XulU0XFUEixuuj55DiLC0evFqWDXvualX0w/Woa2rPJU9uW6fn6VOlIo6geH8g/VvBGQWliN14s58mJb83JkhdwmDrEuSzbXu7hIGQGcMNXQNUpw65wAjprqXYL9vGgU4O32foq6Q4kXxaljGRPgWjwYGklnUVBxiv0KR5ddx5oXm8nSaBo6nY4n+zxZ69NTRbsKRf3AnZQRwLGiaiIvjqMBKorh2Aa532Kw3NZU71JRbI3WtB3t1jmB1eMlvnGAS98pxX+PEi+KU8cyJsC1SPCObA1AeMVx+8K6cIeaF3MOusKh5kVfYgnt9o7pTbvwdrU6vX05VTsAKxSK/w53inWhmrSRodJSA2cRL0fXgFEPoc2tF0Tp26WWxTcEYlzUuxxaCoZy6XqMdP/7xDIWQLVJ1xuUeFGcOlHVD2gMbNKCSs0DX63c2uYI1i+a4gxJFdmmjTRNIjG+JhMqmzbrx3o9VqvT25OzB81WNCkUirNCTW3SZqqMvBRngGYEnac1XV1dvUt8fxkE68j+BXLbdrR1Hzcwp42aq06jeoMSL4pTp4bp0lFhwRzTTF80th1H/mHgHy73c5OtaSPNYDWacpguDdAzuiddIrq4fXqFFYVuFQkqFIq6xV3H69TCVNcXHLb1LmZRcsQkXmzrXY5UU+9iNML+RXK/FikjsEkbqU6jeoMSL4pTx9wunee64yg6xI9kTUSIPtPhy8u2aNcceQGbjiNT3YvNdGmAR3o9UqtTVE67CsXZJbs0m5yyqqdJ21KsLyavPM95hWObdEkOpG2X+wmD5NZQKakkcC1ejm+C4kxJKTXv7/4LAA5myPdSQoRKG9UXlHhRnDqBjW06jvY7rQ4L8OaoTr5sStMdxIut14uHB3ibvhQsXi/2HUdmukV1o3tUd7dPURXtKhRnl9rOGXNZ91LoUKyb/C+gQURbq6Cx1LuEQrSLCK05ZdTqAvBy9oaqihN5pRzPK8XTQ0fnZqHuvxBFnaLEi+L0qCZ1pNPpyPGNBcCQ5ZDzNs84cvJ6ce2ya0ttoi//Hv/X7W0VCsWZZ3vmdst9Lw8XvisOuKx7KTgut8Em8eKyRbqGepd9C+W2Te1SRhtTZJJ1x6YhBPrWfP6K/wYlXhSnRw11L0WB4vXi6Tgx1snrxdwubZ4s7VzzYqZTRCf6xPRx6/R2Ze9yazuFQlE3fLL1E8v9iR0m1ri9S68XxzbpIzbFumaq83fJTYGMXVLw2/oid07bwsZkSXn1iG9Uq/0UdYsSL4rTo4bp0p6RrQAIKEqVgjkzjl4v/qYvhtxkuXWYLO3IQz0ecvsUc8ty3d5WoVCcWQyadap854jOTuuTopLsHrtMG9lOlC5IM6WpdVahYqiElGrqXfaboi7N+4rBZi3YkCzfH70Sarefom5R4kVxetQwXToqthV6zRMvY7k19AvWyEt+KlRWQMvh8nj373JbRc2LmfaN2zOwWRUOmg78cegPt7ZTKBRnlsMOEddWYa2ctonwj7B77PJio9BGvJhTRjFdrRc96dvEJ8ovFKKdBRL7TPUubUbV6vwLyvTsTZcZSD1V5KVeocSL4vQwp43yjlrrVWxo2zSco1qUPLCdcRTURGaMaEYRMJ2ulOUHFkNpnn3NSxVeLQ90f8CtU3xr41tubadQKM4sH2/92HK/S0QXl23Qjf0a2z2+KMEhraNp9q3S1da7DHCudykrsK5ve3Gtzn9zSi6aJs66USF+tdpXUbco8aI4PQIjZKIruBwT0C4mmBRN2p4rMmyKdnU6+9RRVHuI6iCOmXvnWcVLZSmU5bt86rbhbRkWN8yt0zQYDTVvpFAozhh6o56/Uv6yPO4V3YuFyQudtmvsby9eLku8zH6D0lyoLJP7wTFV1LuYxImrlNGhJfK90rgVRDhHfqpjk6lYt2e8ShnVN5R4UZw+ltSRs3iJCPIl3UumwOYdc6iLcSza7ThObnfOAm9/CQGDy44jM/d3v9+tU1yfvt6t7RQKxZlh5bGVdo+7RHbh022f2i0b22osq46vsjwemTDSeXaQOXUc0FjSR/mp4OEtU6Oh5nqXU0wZAWwwFev2SlApo/qGEi+K08dctFtF3UtFqIgUJ6M681RXc9FuJ5N4ObwMirOtKalD/1T51C3DWhLuV/NV0S/7f6lxG4VCceb47cBvdo8P5x922iYmMIatmVstj4O8g5y2sXhIhTS1jgSI7WXtUEwz17uEQROHehejAQ6Yoj+1dNWtqDSyNTUPgJ6qWLfeocSL4vSpYbq0j6njyCc/2X6F44DGxi2lCE8zwJ7focs1snzLD1XWvQBuTZxenLKYEn1JjdspFIrTJ7Mkk5XH7SMvP+z5wWm7T7Z9YvfYpbvu1p/kNnFYFfUupueJHyCGl7akrofSHBE2cX1r8Qpg14l8yvRGGgV40zJSOevWN5R4UZw+NUyXDmsuaaWwsuNyJWTGbFRnThuBtXB352y57+kr/gwntlT59LFBsW6d5j9Hq47gKBSKM8fvh363a5EGyCrNqnE/p06j/GNwcLHc736jVby0cFGs67JF2pQyaj0CPGtnMLfR1CLdIz7cOZWlOOso8aI4fcw1L3kpLjuOmie0oVzzwhs9Wr6NAZW5YDc32eoB03Gs3Cb/K0Ma25uK97Y6X7WZ0Rv1bp3mn4f/dGs7hUJx6miaxpyDc2q1z3P9ngMgt9xBvGyZLh2JCYPk+6AkS7oUm/WQ9QZ99fOMzPUubVW9y7mGEi+K0ycwQorpwOWMo1bRoaSa2qVzU21SS6Fx4OElnQRFpqLcsOYQ2xvQxPMlaYIs3/EL6MtcPr274mVt2loySjLc2lahUJwamzM2k1KQ4vb293e/nx1ZOwDw9/K3rjAaYPP3cr/7JGvUJb6/dTZR2jZx5fYLgyad7A+cfUi+jzy8oNWFtXoNmqZZO41UvUu9RIkXxZnBPGHahdOun7cnGT6S2slItrHr9/QSAQPWuhewFu7unCXh4dA4aZfe6zpy4q54MWpG5h+e79a2CoXi1Jh9YHaV60YmjHRa1jSwKbMPzEaHzt45++A/UHBMjOjaX1bzSADHehezq278AGvnopscySomu7gCXy8POjULqdW+iv8GJV4UZ4ao6mccGcIkRZTv1C7tMKARoMMYQAep68Scqut1snzLdJfHrjRWun2acw/PdXtbhUJRO4oqilicstjluitaXkGnxvbRka9HfM0La18AYHKXyfSO6W1duflbue16nURPkk0t1e7Wu1hSRrXrMgJYsT9TnjouDF8vF0MeFWcdJV4UZ4YaBjSGNjO1U+fWMKARZMR9/AC5v+s36Ha93D+8DPKch7a5W7ALsD93P/tyXHdFKRSK02NB8gJKK0tJDE10Wvdwz4d5e9Pbdsve2/wexfpikqKSuKvrXdYVhelW8dF9khTsm9uhzfb/Bn3V/i6luZCyWu6fgr/L/B2Sxh7ZMbrW+yr+G5R4UZwZahAvzVvLF05E+TFyiyusKxwHNJqxTR2Ft5CCPTTYNsPp2IlhiUzuPNntU517SEVfFIq6wOzt4pgeen3Q687FuMCOrB0E+wTz+qDX8fKw6QbaMl0sE+L6SlTXkjIaZLX/P7EV9MWSVorqaH/gg//I/pHtrBdIbpKeX8aGFCnWvbizEi/1FSVeFGcGs3jJTYEKZz+VsFhZH6fLYN1Bm0nR5i8Wx0LfDlfI+Pq0rVJ4l3SDLN863X46tYm7u93t9qnOPzJfjQtQKM4wB3IPsCNrB146L/49/q9leauwVoxuMZrL51zucr8X+79ITFCMdYHRCJu/k/s9JsmtRby46e9yGimjBTvT0DToEd+ImFD/mndQnBWUeFGcGYIiTR1HGmS5SMuExKLX+eCjM7B7727r8mY9xOr75E44ttG6PDDCakS1aza0vxx8gqWt+uhqp8N7eXgxttVYt041szSTdWnr3H9tCoWiRn47KFGXgbEDLd1DAB9d8BFvbHjD5T7j247ngvgL7BceWS62C76hUv+mL4Ojpr9Xl/Uug+z3N+hlwCtAm9qLl/k7ZBzBJZ1jathScTZR4kVx5qjOadfDg7Lg5gBkpNiIl+Bo6DJe7v/7rv0+FsO638AnADqZxEkVhbu9onu5faqqcFehOHPoDXr+PCTdgDllOXbrPHWeTN/j+m/24Z4POy/cNE1uu1wjf/ep68BQLkMZI1rLOoMejq6V+471LkfXQHm+XEzF9qzV60jPL2ODyZxutEoZ1WuUeFGcOWpw2vWLki8en/wjZBTYeLYMuA/QSSu0rfBpd4lEZTJ2SQt20kRZvvt3GXPvQGKYc5FgVfxz9B81LkChOEMsTV1KbnkuIT4hbM/cblk+usVoLvr1Ipf7XNv2Wvy8/OwXFmfJVHmwSRmZXXUHyzR6kAJefTH4h8s0elv2mVqk24yy1se4yYKdEnXpqVJG9R4lXhRnjmqmSwN4R8mMoxa6dNYczrauiGwrQgVg1QfW5f6NrOZSu2bLMLbGrUFfIl1IDrQIsRbmtQ9vX+2pllaW8vfRv2t4QQqFwh1mHxRvl4IK+4sK25EAfaL72K3rEd3D+UBbfwSjHpp2t3YVVVfvkuBQ76JpsM/k5XQKXUbztptSRl1Uyqi+o8SL4sxRw3RpwlsC0Ep3nNUHs+3XDXxQbrfPlHkmZmy7jsCmcNd5XECAdwBNApoAcEeXO2qcNq26jhSK0ye9OJ3Vx53r0AA2pG+w3N+Xa39RE+7r8PepaVZvlx43yW1ZARzfLPftzOmqqHfJ2i+2C54+0HJ4bV4GafmlbDS56o7upMRLfUeJF8WZw+yyW0XHEc1lqusAj12cOLDJfl1sT/kiMuphjc2k2bajwcsPsg9C+g7oeq10IaWug0znUQRmf4mCigLeHPxmtae7Lm0dJ4tPVruNQqGonjkH56BR9dR3gM4RnZ0mRjfyc5gZlLJK/s59gqz1bimrpeU5PBHCTG7c1dW7mLuMEgaBb1CtXscCk7dLr4RGRIf61bC14myjxIvizBEYITloNJczjohqT2Xby/DQaVxf8gP70gvt15ujL5umQYmp6M83WCbCgkRfgqOhtSmH7iL60iJUUkdH8o/QO6Z3tR1IGhrzjsyrxQtUKBS2GDVjjUMY/Tz97LqPzDiJF3OhbqcrrcLD1UiA45sldRzQ2HrBZMY8EuAUWqTnqS6jBoUSL4ozh05XY92L1wVPYUTHaM8NrF+91H5ly+EQ3UUK8dZ/aV1uvgrbNVtCy91Mwxq3/QQG+9EAZvFyOF+cfM3Taqti7qG5aFr1V40KhcI1G9I3cLzoeLXblBmsxfnP9nsWAB06wnzDrBuV5MDuP+S+OWUENsW6bvi7FGdLRBZqXe+Sll/KppRcdDoYrcRLg0CJF8WZpaa6l6j2HI+9GIBWuz6wFw46nTX6su4zqCiW+61HgHcg5B2F45vkiymgMRSdhEP/2B3enDY6ki+OvZ4enjzW67EqT/dg3kGnXLxCoXAPxyGMN7S/ocptH+n5CF0juwIQ6htq76i7faa0Q0d3hqZJsqwoU/yfwL16lwN/gWaEJp2tKSY3MY8D6BUfTpMQlTJqCCjxojizVDNd2kz4xc9i0HT0M2zgyNZl9is7XCEjA0pzYPP3sswnANqJ4GHnbPDysXrDOHi+mCMvx4qOUWGQMQTXtL2m2lP+49AfNb8uhUJhR355PvOPWKe0e+m8LEZ1joyIH8HEDhPJLZOCWLuUkaZZU0bdJ1nboc0RliadJCUNUFlhja441rvsN7vqnsosI0kZqXEADQclXhRnlhqmSwMENm3H2hCZfaJb9or9Sg9PGHC/3F/9oRTnAXQ0dR3tmi324eauo30LJFxsIsI/gmDvYIyakZSCFAB8PH2qPeX5h+fXajK1QqGAeYft68VmXDqDYn2x03beHt68Pvh1dDqdVbz42oiX1PXyfeHlL8Z0Zly1SJ+wqXeJsql3qayAg0vkfi3rXY5ml6iUUQNEiRfFmcUy4yjZdceRibL+D6HXPGmRvx4t+V/7lV2vg6AmUHAMdvwqy1pdIHbhhWnioNmkI8R0k+6kHT9bdtXpdHZFu2buS7qvynPJLstmbdraWr1MheJ859X1r1ruXxR/EVfNvcrldv9e+68lRWR237WzMTC3R3caB36hct9QCYdMYsQuZWT2dxlojdAApPwrU6eDmkBMUq1ex9TV8j0xqHWkShk1IJR4UZxZAiOtHUfZB6rcrF+P7szSxIeheOELEjo24+0HfU2DFle9J5EWL19of6ks22XKs5ujL1um2+2fEJoA2IuXsa2rn3ukPF8UCvdZdXyV3ePOEZ1dbrfwyoUEeAdYHpsnS1vES2mepIJBUkZmNn4tNW5+YfbpoarqXcwt0m1GOg9prIbCMj2/bBRfqVsH1m76tOLsosSL4syi09mMCag6dRTg48WOlpMp17wJSl8Hh5fZb9DzFom0ZO61tj+aDet2zZErs05XgqevFPWlbbPsai7aNXccgaSTqmP+kfkuQ94KhcKZO/++03J/UodJvLPpHadt3h/2Ps2CmtktyymVyIul5mXHL1BZKrVycb1lWVEGLHlJ7l/wrLVturLCOqDRVtBoms1IgNqljGZuSKWovJJWUUEMbl39d4SifqHEi+LMY657cTH92ZZBPbrwo0GiL9qSl+yjL34h0OtWuf/vO7KuxRDJdZdkSfg4INw6VsCmcNdV2ghgSOwQquP3g7/X9MoUivOexSmL7R7/tPcnp21CfEIY3tze4bZYX8y2TLnIaOTXyFSoa3bUtSnUXfwslBdIWti2bXrDlyJ0gqKtF0gAGbsh/6iYWSYOdft1GIwa01YnA3DLgBbobNNQinqPEi+KM0/7y+R28/dwcneVmw1tG8U0j3GUaj7ojm+UVkdb+t4lkZVjG8Rp09Mb2l8u6xzHBez4BfTiJ2EWL8kFyRg1o+Vw/Zr2q/a0bXP4CoXCmWJ9Mf+37P8sj7tHdafCWOG03YxLZtg9Lqgo4PbFt7Mvdx+B3oEMjh0sxbcnd8jfuLl7MGW1+Dehg0vesQ5WzEuFJS/L/eFP2de7mGcZJQ6VzkQ3+WtXOsdyS2kU4M247s1q3kFRr1DiRXHmaTkc2l0qtt7zH7aPqNjg5+1JUoe2fGswOeg6Rl+Coqzi5N935dZsWLdnroSRE4dCSDMoy4N90v0QGxyLl4cXpZWldvb/Zo+J6vhu13e1eaUKxXnFR1s+snu8OWOzy+2aBVvFQG5ZLrctuo3tmdsJ8QnhqxFfERccZ426dLhCoqiGSpj3sCzrMQlibQY3LnhMzCub94NuDl4ytlOka8E3qyQyO6FPPH7etZs+rTj7KPGiqBtGviKtjymrJCpSBVf1iOPzyksp1vwgfbuIElv6/w90HnBwscw2iu8vHQVleXB4qVyZdbtett0i4wK8PbxpHtwcsE8dtW3UFm8P72pP+82Nb5JenF7716tQnOPsyNzB9D3Ta9yuY+OOeOjkpyWzJJObF97Mnpw9hPuF883Ib+gU0QnKC62dhD1Mhbrrv4CMXTJN/gIbZ+w9f8qFiYc3XPqefUFuUYYYV0KtxMv2Y3lsSM7F21PHxH7xbu+nqD8o8aKoGxrFw+CH5P5fT0NZvsvNBrRqTHhkDF8bTF88S18Bo8G6QXgLq8fLv++JWOlo6hwydymYxcuhJZaJ1I5jAgC8Pb3li7MGnvz3SQy256BQnOfojXqeW1P9qA0zSVHSqpxenM7Ni27mUP4hovyjmDpqKm3DTQ7cO2dJJKVxK7H5L0yXv32AC5+XSAyIyJn/iNwfcL+1ns7M/kWAJq68Ie57tHz9r1zUXNqlqWqPbqAo8aKoO/rfJ9Ngi07CstdcbqLT6ZjUP4GvKi+miEAZK7DLwaVz4ANyu2s25Byxipm986TOJTwR4gcCmilf7jwmwEyXiC41nvaG9A1M2zXN3VepUJzzfLvrWw7kVm19YMs93e4htSCVSQsmkVKQQtPApkwbNc3yNwlYU0ZmR92/nhGflmY9IOlG63ZLX4HCE+K6Pfhh5yeztEi732WUnl/GvO3iqKvaoxsuSrwo6g4vXxj9ptxf9zmk73S52bjusRh9w/hMbxoBsOxV+4GL0Z2h1UUyt2T1hxDbC0Lj5MvOXOSbZBrWuOUH0DRrx1GBg3iJrFm8gOT2d2Xvcu91KhTnMCkFKXy69VO3tl05fiUZpRnctPAmThSfoHlwc74d/S1xITazhtK2S7Guh7dETZP/NRlN6uDit6xpoRNbZMYZwCVvg7e//ZPpyyR1DLUaCfDdmmQqjRq9W4TTqVmo2/sp6hd1Kl5yc3OZOHEioaGhhIaGMnHiRPLy8qrd56abbkKn09n969u3b12epqIuaX2hdB9VU7wb5OvFVT1imWoYRaFHCGQflEFttpgHNm6ZLq3S5tTRstegslyK/nyCIPcIpKy2er3kHbY7jLvipVKr5PEVj1Oir9olWKE419E0jRfXvOiyo8iR9uHtOVlykpsX3kxGaQYtQ1sybdQ0ogMd5gWZHXXbXSKOuuYi3Z63QLPuct9ogLkPyAVL56vFYduRIytkVEBIM5lG7walFQZ+XH8UUFGXhk6dipfrr7+erVu3snDhQhYuXMjWrVuZOHFijfuNGjWKtLQ0y7/58+fXuI+iHjPyVSnePboGtv/scpMb+8VTjD8fVZh8W5a/bp1rBFKoG9tbJs+u/VRSUoGRUuC35EXwCbQRNK+SECxXetll2eSXW+ttogOjaRLQxK3TTi5I5s2Nb9b+9SoU5whzDs5hXfo6t7b19/LnlkW3kFOWQ/vw9kwdNZXIgEj7jSpKrN8BPW6SyErmHvFvGv60dbv1X0LaVhE3Ix3mn5kxD2JsM8q+dboaZm0+Rl6JnubhAVzY3r3vAUX9pM7Ey549e1i4cCFfffUV/fr1o1+/fnz55Zf8+eef7Nu3r9p9fX19iY6OtvwLDw+vctvy8nIKCgrs/inqGWFxMMRUdFdF8W5iZBBD2kTybeUIirzCIS/FfmK0TmeNvmz4SiZLX25q21z9ERxZKeu9AyB5JYHrv7K4ez6+8nEKKqyfC3P0xUsn81aCvYOrPPVf9//KPyn/nOorVygaLNml2by18a1qt3m458O0adQGkLbpgooCukR24auRX9lPjjaz7ScxoAuLh4g21lq4C6dYi3Tzj8sFiXl5UJTzcWxddd0cxGg0akw1tUff1D8BTw9lSteQqTPxsmbNGkJDQ+nTp49lWd++fQkNDWX16uqdV5ctW0ZUVBRt2rRh8uTJZGRkVLntq6++aklLhYaGEhcXV+W2irNIv3uls6A4A5a6NoO7qX8CZfjycaXJiG7FmxbjOUCusCLbyZffxqmS5+5xE6DBb3fK1dvFpkjJkpd4IvFK/Dz9+Pf4v0yYN4Hk/GTA6vdSqUldTZG+qNpTf27Nc2SUVP0ZVCjORV7f8Lqd6HfkwR4PMrb1WPbn7rcs69mkJ19c9AUhPiHOO2QdEPdcgN6TYfEzUFEkEdVuE6zbLXhUlsf1sZ93ZEvaNink9Q50nnNUBX/uSONQZjHBvl5c00v9TjR06ky8pKenExXlrJijoqJIT6/aR2P06NH88MMPLFmyhLfffpsNGzYwfPhwysvLXW7/xBNPkJ+fb/mXmpp6xl6D4gzi5Quj35D76z8XzxYHhrSJJKFxAN+UDaXENwoKjlvz4yCFfAMekPtrPxFhM+Jl6TYqOCYtld0miJGdZmDI8g/57oJPiA6MJrkgmevnXc+q46sY02oMLUNbWg6roTEyYWSVp55fns9T/z5l59arUJzLrDy2kgVHFlS5fnzb8dzS6RYeWvaQZVn/pv355MJPCPQOdN5BXwq/3CSiJH4gRHWQdmmdB1xiU6S7dz7s/RM8vJw9XcxomowMAWg5TAa51kCZ3sDrC2TW2h1DEgny9apxH0X9ptbi5fnnn3cqqHX8t3HjRgCXsyI0Tat2hsT48eO55JJL6NSpE5dddhkLFixg//79zJs3z+X2vr6+hISE2P1T1FNaXSCFtZpRivQcinc9PHRM7JdAOT58qTM56a54S/LkZjpfBSGx0n697ScZ2jbuS9B5SsfCrtlw6bsQ1hzyUmi/6lN+uvgnkqKSKNQXcvc/dzPn4BymXzydYXHDLIddlLyo2lNfm7aW73d/f8beCoWivlKiL+HFtS9Wub5LRBce6/UYQ2cOZW3aWsvyD4d/iL+Xv+udFjwqA1QDImDsp7DwcVne6zaIMTlflxdZPV36/w+adHB9rI3fwO7fReAM+j/X2zjw3ZpkjueVEh3ix60DE2veQVHvqbV4uffee9mzZ0+1/zp16kR0dDQnT5502j8zM5MmTdwvlIqJiSE+Pp4DB9zzGFDUc0a+InUpqWth2wyn1Vf3jCXY14uP8vpREtBM0kwbvrJu4OktX2wAq96XroTYnjDY9KX354PyJXjlNyJods4iYt8ivhrxFeNaj8OoGXlr41u8uv5V3hj8Brd2utXtU39r41vszal6UrZCcS7w0daPSCtOq3L9G0PeoPv07mSXZVuWbbphEz6ePq532DYTNn8H6ODKr8RcMmu/CJlhT1m3W/aqRFDD4mHwo66Plb4DFj4h9y+cIr4wNZBbXMGHSw4C8PDItvj7qFEA5wK1Fi8RERG0a9eu2n9+fn7069eP/Px81q9fb9l33bp15Ofn079/f7efLzs7m9TUVGJi3HdPVNRjQmNhiOmLafEzUJpntzrEz5vJgxPR48VHBpMZ3ar3xGnTTPeJ4B8ubdG7TZOgBz8sX2Rl+TDnLrk/7ElZN/8RfHKP8ny/53m89+N46jz549Af3PrXrUxoP8Ht7iOAR1c8Smll6am9doWinrMzayc/7PmhyvUv9H+BUbOsnirhfuFsnbi1auGSuQ/+fEDuD3kUIlrDclP6eMSL4B8m99O2SSoYZCCjqwGL5UWSejKUS/1bv3vcek0fLDlAYVklHWJCGJukBjCeK9RZzUv79u0ZNWoUkydPZu3ataxdu5bJkydz6aWX0rZtW8t27dq147ffxFG1qKiIhx9+mDVr1pCcnMyyZcu47LLLiIiIYOzYsXV1qor/mr73QOPWUJxptQS34eYBCTQK8Obz/N4UBsZDSbbVrAqkLbrPnXL/33cl/eTpLekj7wA4sly2H/igFPPpi+HXm9EZKpjQfgKfXvgpIT4hbM/czrXzruWurne5fepH8o/w9sa3T/cdUCjqHXqjnudXP19lbVfniM48u/pZy+MBTQew9JqleHpUEcmoKIafJ4kXS4vBMOQxWPSU/D3G9YUu18p2tp4uHceJN5Qjmgbz/k88oEKawZhP3WqPPpJVzPdrUgB48uL2qsPoHKJOfV5++OEHOnfuzIgRIxgxYgRdunTh++/t6wb27dtHfr60znp6erJjxw6uuOIK2rRpw6RJk2jTpg1r1qwhOLjqdlZFA8PLx9oVtOFLcdy0IdjPm7uGtsSAJ29XmKIvqz+0j9L0niydBunbZaYRQOOWMPJluf/383LVN+4LidKkb4d/XgCgX9N+/HTJT7QMbUlGSQavrnfd/WRmUgf7joeZ+2ayPHX5qbxyhaLe8t2u79iXW7WNxY4sa5H9+Lbj+fTCTy0DGF0y/xHxcAlqAuO+gsPLYPccSede8ra1GHfD1+K46xsKo6r4W9z6oxhX6jzhyq+tbdU18MbCvVQaNYa2jWRg6wi39lE0DOpUvISHhzN9+nSL/8r06dMJCwuz20bTNG666SYA/P39WbRoERkZGVRUVJCSksK0adNU+/O5SMthYiqnGcV512h/tTexbwJRwb58V9iDvMBESQet+di6QUC4qU0aib6Y6XGzhJQN5TD7dmmfHmMKR6/5CA4sBqB5SHOmXzydIbFDKDdYO9niQ5wnzP68/2e+uOgLu2X3LrmXrNKsU3/9CkU9IrUglU+3uTcC4I4ud/BUn6eqbbxgyw+w9QfpJrrya0kPLTCli3vfDtGmAakFJywXFVz4HARHOx8rY698R4CkguP7uXWeG5NzWLAzHQ8dPDG6vVv7KBoOaraR4uwx4mWJnqSuswxUNOPv48m9w1thxINXy0zRl7WfQkmOdaN+98h8lOSVcEw63NDp4PIPRbSc3AFLXxYTq953yPrf7oRCKSQP8gni/WHvc1vn2yyHTClIISrAvsW/tLKURn6N+GbkN3bLJy2YpNqnFQ0eTdOYsnaKnYivige6P8C9SfdWL1xO7oZ5phbqoU9Ci0Fy4ZB9EAKjYNgT1m0XPi4zymJ7yYWHIxUlUueiL4HEYTDQve4iTdN4ad4eAMb3iqNttIrcn2so8aI4e4Q2g6GPyf3FzzoV717bqznNwvz5ubgbWUFt5Utu1fv2+3cZL/dtoy9BUSJgAFZ9IIPfLnoBmnSSuUi/3WGJ9Hh6eHJ/9/t5fdDrlt1dGdJdPfdqiiqKeGuI1XH0aOFRnln1zKm/foWiHjDn4BzWpdU8AuDx3o9za+cauvPKi+CXSVBZCi2Hw6CHIC8VlpvSxCNeEst/EIfc3b9LKqgqT5eFj9mknr5wvY0L5u1IY2tqHgE+njx4YRu39lE0LJR4UZxd+twlNuElWRIlscHHy4P7L2yNhgcvlZgKttd/AUU24mLAfYBOjK0ybfL17S6BpIlY3HcN5XDVNzJj6fBSWPOh3XNdnHgxD/d8uNpTvW/pfRzMO8idXe+0LPvj0B/K/0XRYMkoybArwq2K5/s9z4T2E6rfSNPEqiBrPwTHSAG9hwcsekLETPwA6HKNbFtRbE0F9b/XmkayZfsv1hbrcV+6HhPggvJKA68vNBnSDW5JVEjNJnaKhocSL4qzi13x7lfSMmnDuKRmJEYEMqekM+nBHSV8bBtliWwrQgUkymLLqFehUQLkp8L8R2Xb0aYIyz8vwPFNdpvf2OFGArxctGja8Nm2z1hwZAHdo7pblr2x4Q1+P/i72y9ZoagPlOhLuOAXF9OaHXh10Ktc2ebKmg+4+VsxitR5yoVCYAQc+Bv2zJVlF79l7RBa9pr8XYY2ly4kR7IP2bdYJw5x+3V9vyaF1JxSooJ9mTxYTY4+V1HiRXH2SRwqLZJm512b4l0vTw8euKgNoOPZgjGycMPXMrzNjHlg4/aZkH/Mutw32OS+6wHbZ4g5VvcbxeXXWAm/3mrnH6PT6ZjcZXKNp5tSkMLmjM12y55e9XS1/hgKRX0iryyPPj/2qXG7d4e+y6WJl9Z8wPQdcoEAMh06vr+M7zBHV/reZXXMTd9hLb6/5G2xPrBFXyapJ/MoAVfipgpyiyv44B8xNH14RFsCfNQYgHMVJV4U9YORpuLdY+th2492qy7tHEPHpiH8Vd6BQwFdJAW00sZrJban+LkY9dJSbUtcb8m7g4S0C9PgsvchNE5M7ubZp4quaHkFnjrxrWjs17hWL+G19a/x3qb30BzGHigU9Yn04nTG/zm+xu1uaH8DF8a78FxxpKxA/FwM5dB6hHX+2OoP5W8sKNoqQCyeLgboMAbajHA+3uJnROAENIYrv4SqfGRcMGXuLgrKKmkXHcyVPWLd3k/R8FDiRVE/CGkKQ03zThY/C6W5llUeHjpeGtMJnU7Hk7lXyMLN30FuinV/c/Rl3ecy8M2WIY9B0yQoyxP3Xd9QsSk3R2RsxhREBkQyqJlMqR3dYnStX8bXO7/m2dXPUmmsrPW+CkVdczj/MBMXTORE8Ylqt3uu33M81tuNiIemwdz7IeeQzBwb+7nUueSmwEpTcfvIl8HPNHNu4zdwfCP4hsCo15yPt/sPqWsDOVZIU7df24IdaczZegIPHbw6rrMypDvHUeJFUX/oexdEthNH3SUv2a1Kat6I63s3Z53Wnk2eXSTKsuIN6wYth0OvyYAGs++wGteB1X3Xy1+MstZ/Ds37wlBTy+a8hyTHbmJca2nNnn9kvl0btbvMOTiHB5Y+oMYIKOoVO7N2MmnBJNKL06vd7rvR33FVm6vcO+jGr2UYqocXXD3Vah638AmoLJOIaCdTvUxhutXT5YJnIcRh5EtuMvx+r9wfcD+0vsi9cwCyisp5as5OAO4a2pKk5o3c3lfRMFHiRVF/8PS2Kd79Gk5ssVv96Kh2RAT58HKJyfdl609W0aHTweg3pHbGqIcZN9gX5Ea0llkqAIufg4w9kk6KHyC59Vm3QmUFAINiBxHhH0FOWQ7hfuHVu4hWwfJjy5n812TyyvJqva9CcaZZfWI1tyy6hbzyvGq3m3HJDJKiktw76ImtNkMSn5cULcD+RbBvngga2yLdhY9DeYHMHet5i/2xKivg11ugPF88X4a7b0GgaRpPzt5BTnEF7aKDue+C1m7vq2i4KPGiqF+0GAydrgI0p+LdUH9vnrm0A5u1NiwzJknefJlN6NnDQ0LNicNkfsr0qyBzv3V9r9ug1UUm993Jkn8f9yX4NxKhtFSiPV4eXlze8nJAvvTNaaTasi1zG5MW1nylq1DUJQuTF3LPP/fUGAn87MLP6BjR0b2DluVLUa2hAtpeDP1MERN9qYwFAOh7N0S1k/sHFsOu32w8XRzqWP6ZIhcbfmHSqeTp7fbrm7P1OH/tPom3p453rumGr5eaGn0+oMSLov4x4iXwCZLc+Nbpdqsu79qUga0ieEsvoWhtxy9iH27GywfGT4em3aE0B74fa+1M0ungio9Ms45M7ruhzeDyj2T9qvfh4D+ANXW0+sRqLmhedTupv5c/zYObV7n+cP5hJsyfwMHcg7V9FxSK02bm3pk8uvzRGmuwxrcdz4BmA9w7qKZJeic3WVqdx3xija6seh/yUiC4qXV6fEWJDFUESQ3HdLE/3r6F4sALcqywqv+eHEnLL+XZ33cBcP8FrenQNMTtfRUNGyVeFPWPkBhrPcri5+xGAuh0Ol4c04n9nq1YaOiFDg2WOQxz8w2CCb/K5OqCYyJgzMcIjobLTX4wq96H5FXQ/lLoaXIO/e1OKMokPiSeHk16YNSMHMk/wltD3qJZUDOnUy2tLCWvPI/LEi/Dx8PH5cvJKMngxoU3siVji8v1CsWZRtM0Pt36KS+tewmNmrvfnuzzpPsHX/8F7PlDRnNcPU0ilwA5R2DlO3J/5MtiVQCw/HXIOyodfua/azP5x2GOyfSxz11WzyY30DSNx2btoLCskq6xodw5pKX7r0HR4FHiRVE/6XMHRLaX6IlD8W6LiEDuGdqKdyuvxIhOJtU6TKYmsDFM/E2uALP2wY/XiKsnQPvLoNsNWNx3y/LlyzayPRRnyJep0ciVrSW6M3XXVL7f/T3P9n3WZQdSQUUB84/MZ1LHSVVevRZWFHLjghtZenTp6b4zCkW1GDUjr6x7hU+2feLW9r9f8bv7dV3HNsGip+T+iBchtod13cLHJSWbOFSGrgKc3GWNqlz8plxYmDFUSq1ZaS7EdIOLprh3DiZ+Wp/Kiv2Z+Hp58PY13fDyVD9n5xPqf1tRP/H0hktMrZYbv3Eq3r1zaCL6xu3509BXFjhGXwDC4kTA+IXBsQ3w841g0Mu60a9BWDzkH4UFj4G3v2l8gB8c/BvWfcoliZdwR5c78PP0Y1vmNu74+w4Kygvw9nDOxxs0A1/u+JLogGhu73J7lS/rvqX3MfvA7FN5RxSKGtEb9Dy64lFm7JtR88ZIuigxLNG9g5fmypBEo14uAPqYIiaaBsvfgP0LJRoz+k1JIxmN4ulirJTt2zoI/2WvwtE14BMsnUpevm6/zqPZJbw0bzcAj4xsS6uooBr2UJxrKPGiqL8kDITO1yDFuw/ZFe/6enny0phOvFd5JQZNB/vmy1WhI1HtJIXkHSCiZM5dchzfYBn0pvOQida75ogD6MhXZL/Fz+GRtp17k+5l/rj5jG87Hi+dF6tOrEJv1Fd5yrMOzGJZ6jJuaH9Dlds8t/o5Xlv/mjKzU5xRSvQljJ49mkXJi9ze59Fej7q3oabBnHtE7DdKkDoxs0BZ8Jh1LtkFz0CkaRDi5mliOukTLJ2AthxaYjWavPwDCHdTQAFGo8bDv26jpMJA7xbh3DJAjQA4H1HiRVG/GfGifPkd3wRb7Acg9m8VQa8effjNKN1A+sVT7ASOhbhecM330rq54xcZFKdp4vViNrf78wEoSJMWznaXytXlrFuhvIjIgEie7vs0f4z5g0sSL0GHvflVp8ad7GYd7c/dz/Q99oXGjvyw5wcGzRyEwWio/XuiUDiQXpxOnx/7cLLkpNv7fH7h5/h4uq7TcmLNx9L+7OkDV38L/mHS3vzb7eKbBDDqdfFnASg8CYufl/vDn7Y3mytMh9m3Axr0uBk6jXP7nAGmrk5m/ZEcAnw8eeuqrngoM7rzEiVeFPWb4GgYZiom/Pt5u+JdgOcu78CckAnoNU+8U5aj/XGPtEA70vpCGPOZ3F/3mfWqb8jjENNVQuK/3y2i5vIPIaQZZB+Uq0oTcSFxvDboNX657Be74t2d2TtpEdqCKf1rl7PPL8+n2/fdSC1MrdV+CoUtsw/M5qJf3Td0A/DQedC/WX/3Nk7dAH8/J/dHvgJNu0n92Izr5GLAwwvGfQV9rdPWWfSkeLbEdIPeNvPCjAaxKSjOhKiOMjy1FhzMKOIN08Topy5pT/PG1Q9SVZy7KPGiqP/0vl2+6EpzrA6dJgJ8vHjqhot5zHgXlZoHuq0/wqzbrLUttnS5Wq4OAZa8CJumSWv1uC+l1uXQEtjwpbiEmgc6bp0OO361O0zb8LYsvHIhkf6RlmWzDszijQ1vcEeXO2rtynvx7Iv5dte3Ko2kqBVZpVlcM/canlv9XK33XX7Ncvc2LMkx1blUigFkr9tk2XdXSBrWOwCumyl/W2YO/g07f5W/n8vet/d0Wfk2HFkh+109TWrN3KSgTM8d32+kvNLIoNYRXN/b/ZZqxbmHEi+K+o+nl7V4d9M0e+dcoH1MCN0unsw9+vuo0DzFrnzmRJlO60jfO2GQaRjjnw/KLJXItnCR2X33WfGNSRgAg01mW3PvF9dQB74a8ZXd42J9MZ9v/5zZB2ZzV9e7avUS39r4FuP+GMfxouM1b6w4rzFqRn7e9zPDfh7Gnpw9duuaBDSpcf/LW15OmF+YG09klG68gmMQ3lKESMEJmDpaCuD9wuDG3yWqaaaiBP40ebr0uVOiNGaS/7UW1l/yjrU2xg0MRo0HZmzlUGYx0SF+vH1NV3Q6lS46n1HiRdEwiO8PXa7FWrxrnxqa2Dcerd1l3K5/iHJ8YP8C+Ola+TJ1ZPjT0OMm0IxS13JkhYS2W14g81hmT5Z8/uBHxa23ogh+HA8r3pS0konEsESXrdM5ZTl8uu1TYgJjXBrY+Xr64qXzclp+MO8go2aN4sc9P2LUXNTuKM579ufu58YFN/Li2hftlvt7+XNdu+vcqnl5acBLNW4DwOoP4MAi8PSVKEnRSfhmJGTuFQuCWxZaRwKA/M3MvU9M6kKaWdO9AMVZEhHVjNBtAnS7zr1zMPHmon0s2ZuBr5cHX97Yk6hgv1rtrzj3UOJF0XC46AWZRntii0yVtkGn0/HGVV3YH9yXmyoeoVznD4eXwvQroawAh43lyq/9ZWJv/tP1kLYNrvhYDLfSt8PMCTJi4PqfTQZ2mvjN/HwjlBdZDnV317urPN204jSOFh51Wl5uKKdSq9rx9NX1r3LzwptJzk92621RnPuU6Et4Z9M7XDP3GrZlbrNb1yWyCy8MeIFf9v1S43H+vurvmiMWRgMseVlqzABGvy5po29GQn4qNG4Fty6CqPY2J5gD34+RGhidB1z6rtWkzhzBKUyDiDbW+WVuMmfLcT5bLjPM3riqC51jQ2u1v+LcRIkXRcMhuIn1au6fKVCcbbc6LMCH965NYp3WkevKHqPCKxiOrpb8vEOhLx6eUmSYMAgqCkXk6Etg7BdS/3LgL/hyuFigX/qOKXfvLc6iX18EOYcBSAhN4PvR3zM0dugZfambMzZz1dyrmLpzao3W7opzmxXHVjD297FM3TkVg+YQcewwkcd7Pc4jyx+pVhADPN3naZoE1pBWKs6Sv4UVbwAa9L1HWqO/vUymvTdNglsW2Vv4Zx2Ary6AlFVycXH9L9BmpHX9mg/h4GL5u7p6GvgEuv3at6Xm8egsMaC8e2hLrujm7HKtOD/RaedYlWBBQQGhoaHk5+cTEqLmXJxzGCrh88GQsQu6T7Ja/dvwwT8HeGfxfnr4pPBzwBt4luVCk04wcQ4ERdpvXFYA0y6RaEtYc7jlLyhKl6nUBcekTfvKL8Vg6+g6+HmihM/9wsRYq+Vwy6GOFR7j530/M/vgbPLL88/YS+7UuBMvDHiB1o3UtNzziYySDF5b/xqLUxa7XP9wz4c5mHeQOQfn1HispKgkpo2aVr2Tbup6+HkSFJ6QgtrLPpB6s1mTxTqgxRC49gdrRAXg8HL5myjLl7+f63+2j8ikrodvRskQ1cvel3Stm5wsKOPyj/7lZEE5F7aP4ouJPVVb9DlObX6/lXhRNDxSVkvRIDq47R97i3KkuG/CV2tZeziHkVG5fGp4AY/ikxKyvvF3e88JgKIMCYnnHIaoDnDzfBFJP98okRt0MOwpGPSQCJeZN8jQSJ0HXDgF+v/POpgOKKssY8GRBfy09yengspTxcvDizu63MGtnW916fCrOHcwGA3M3DeTD7Z8QLG+GB06p/lETQKauO3p4uXhxa+X/UrLsCpm/2garPsc/npK0kONW8P47+XvbN5DgAYdrjB15dm44G76VgYuGishtjdc+6P9xUFJjlxo5KdCpyvhyq/t/k6qo0xvYPwXa9mWmkfrqCBm392fYD/1uT/Xqc3vt0obKRoe8f2h63WABvOdi3c9PXS8Nz6JxoE+LMpoxNONXkcLiYWs/SJ6clPsjxcUJWMEgqIhYzf8eK2Etm/8HXpNludZ+hL8cqNcdd48H5JukOLDxc9Iga9NYbCflx9jW49l5qUzmX7xdC5NvLTGl2Tbdu2KSmMlH2/9mOv+vI7d2bvdfacUDYw92Xu4Yf4NvLr+VYr1xSSGJrocrOhKuLRt1Jb3hr7ntHxy58lVC5fyQvj1Zlj4mLUd+valsGeuaRK0JsaNV9nY9xsN8NfTUpxrrIROV8GkufbCxTx5Oj8VGrWAS99zW7homsaTs3ewLTWPUH9vvprUUwkXhRMq8qJomBRlwIc9oLxAigN73uK0yeajuVz3xVrKK4080NOXB44/DLlHpBPixj8gopX9Did3ibgpy4c2o2D8dJmxtOlbU4eTXiIz1/4gX8gbvpJhdMZKiO4iy8Ocu4sAskuzmX1gNjP3zaz2ijkxNJHD+YerfemeOk9u7nQzd3a9E19P9+fBKOovJfoSPtr6ET/s+QGjZiTYO5jLWl7Gj3t/dGv/J3o/wbjW4+j1Qy+75S1CW/DrZb+6dtLN2COWAtkHpJ5r5Mvi47LwcZkcDTDkMZkEbRYeFcWSRto3Tx4PfUK2cRQmaz8TQeTpA7cutm+ZroEvVhzilfl78fTQ8d0tvRnQKsLtfRUNG5U2UuLl/GDd57DgUak/+d9mmSTtwLztadzz42YA3hgRyTW775Up04FREllp0sF+h5Q10jVRWQZdr4cxn8gXc+p6SRc51rsk/yt1AiVZENBYrNNbDKrylCuNlSxPXc5Pe39iXfq603r5LUJb8EL/F+gW1e20jqM4uyw5uoRX179KenE6AKMSRpFbnsu6NPc+H1P6T2Fc63EkfZfkVLT77ahv6d6ku/NO238W/yJ9iYj5q78Vp+k5d4nBHMg8oj53WPfJPy72A+nbpX16zCfQ+SrnYx/fDF+PELHveIwaWLo3g1u+3YCmwZTLOzKpf4Lb+yoaPkq8KPFyfmCohC+Gwskd0P1GsfV3wSfLDvLGwn146ODb8YkMWjsZ0ndIW/TE36SDwpZ9C2DGBCky7P8/GGHyxSg4Yap32ST1Lhe9AP3uhfxj0lqdtg10nmJ53vv2GsPkh/IOMeb3Maf1FujQcUOHG/hf0v/w93LfrVRx9kkvTufVda+yJHUJAGG+YRRVFFXZNfTesPcwakb+b9n/WZa9Nug1Lkm8hOm7p/P6htfttr+6zdU82+9Z+4NUlsPCJ2Dj1/I4cRhc+ZU43c6cCIf+Ebv/sZ/bC5MTW+Cn66TdOSBC6lua93E+ybJ8qXPJTZYZYeOnu50uOphRxNiPV1FYXsl1veN4ZWxnZUR3nqHEixIv5w9H10qxLcCtf8sQRgc0TePxWTuYuTGVAB9PZt3cnvZ/3yJFt74hMOEXGdJoy9Yf5SoURKSYB87pyySFtNU0eLHzNdaOpz/ugx0/y/1uE8RLxrt6M61yQznjfh/n0g+mNsQFxzGl/xR6RTu/fkX9otJYyU97f+KjLR9RUunCRNGGzhGd+fTCTwn1DWVH5g6un3+9Zd0bg98goySDtza+5bRfXHAcMy6dQYiPzXdg3lGJEp7YDOhgyKOS8inLhx+ulr8H7wAZYmrrmrtnrgxS1JdAZDu4fqa0TzuiaVI/s+s3CG0Od66QCwQ3OJpdwvgv1pCWX0avhEb8cFtffLxUSeb5hhIvSrycX8y5G7b+IGHvyUvtZ6mY0BuM3DR1PasOZhMd4sfvk7vS5M8bxZvCOwCumwGJQ+x3WvWBFOSCGNgl3SD3NQ3Wfym1AZpBnnf8DxAaK9N3Fz8jxbxNu8uVZ2j13hRHC45yzZ/XUKwvPu234po21/BgjwcJ8gk67WMpzjy7snYxZc0Ut7rQFl+1mOjAaABSClK49LeaC7+7RHRhYoeJDI4dTIC3zdDCA4ulsLw0VwTFuK9EoOQfh+/HSirVv5F4tJgvADQNVr1vMqvTxIH66qngV4VJ3MapMp3dwwtuXujyQsIVx3JLGP/5Wo7nldIyMpCZd/QjIkjVcp2PKPGixMv5RVGmqXg3Hy55W4oOXZBfqufKT1dzMKOIjk1D+PmWrgT+NkkGMnr6SnuorbkWyKyjVe9LOmj8dGh3sXXdkZXwyyQx7wqIgGu+k5lIh5bKFWhprtTWjP/eObLjwLLUZTy+8vEzImCiA6N5rt9zDGw28LSPpTgzFFUU8er6V/nj0B9ubb9y/ErL/KF/jv7DA0sfqHGft4e8zYiEEfYLjQZY9pqMtkATQX3Nt1JYnrlfhEvBMbH7n/gbRLWT/SorYN6DsMUUYew1GUa9Jr4vrkjfKUZ1lWUyJ2zAfW69zhN5pYz/Yg2pOaUkRgQy4/a+RIUo6//zFSVelHg5/1j/Jcx/WK4K/7cZAl13KKTmlDDm41VkF1dwQbsovri+M56zbpHuCQ9vuOpr8bQwY2753DpdHEJvmC0CxUzeUZhxvdTQeHjJF3yv2yTnP2OCmOl5eMPFb7jsiLKlwlDBtsxtrDmxhuXHlrM/d/9pvSVXtLyCR3o9QqivslM/W1QaK3lhzQv8dvA3t7Zv06gNU0dNZXHyYp5f83y1214Uf5HFwO6+pPuY3GWy/QbmeUKHl8rjXrfByFek5fn4Jph+lUxqb9xahEtYnGxXkiMeR8krpbZr1GvVF92WF0ntWfYBaD1Cpkx71JzySc8vY/wXa0jJLiG+cQAzb+9HdKgSLuczSrwo8XL+YTTIF2j6duh8tRQcukgfgX0L9VU9Ynl9THs8f78Tds6SL+sxn0LXa607GCrFRXTffPANhZvnQXRn6/qKEvjjf9Yuje43wsVvSQv1nLth9xxZ3uMmGP0meLloW3VBQUUBdy2+i+1Z22v9dtjyQv8XGNt67GkdQ1E79ubs5bNtn/HP0X9crr8o/iKOFR6rtYnhm0PeZGT8SCqMFUyYN4F9ufvoE92Hzy/6HE/bz7srt9wuV8u6Q0tFWOuLpVh9wq9WsZ91EH68BnIOibv0Vd9AmxHOJ2LLb3fCtp8gOAbuXOWy68+RjIIyrv1iLYeziokL92fm7f1oGqYKzs93lHhR4uX8JHW9zB0C6aIY96XzOAATC3akce9PWzAYNa7sHssb4zriOe9+U5hcZ/KOudm6g75UQuxH10BQE5nvEt7Cul7TZArv389LvUtsb0kXBTWBf9+Ff14ANIjrI+ml4Gi3X9ay1GU8tuIxS3Gnp87TacaNO0zuPJlxrccRGxxb630VNZNZksn8I/P5df+vJBcku9zm5YEvkxiayMPLH+Z40XG3j31317u5rfNt7M7ZzdaMrSw5uoTNGZsJ9wvnl8t+ISogSjasyi3XbNm/c7YU3xr1kDhUUqFmu/8jK6WbriwPQuOkMLdJx+pPzFzYrvOASX/aRyWrILOwnOu+XMvBjCKahfkz4/a+xIUH1Lif4txHiRclXs5fbP0rgmPkyjG+v8tN/9x+gvtnbMVg1BjXvRlvXtkZz0U2Bl0jX4F+91h3KM2TOUgnd4pJ3a1/iTuvLQf/hl9vkQ6O4Bj5cYjtKQWTv94qdTnBMVLg6zDWoDoO5h7kf0v+x7GiYwR4BfDKoFdAgweWPVC79wdo3ag1w+KGMTxuOB0ad1DtqKdBWWUZS1OX8vuh31l1fJXLbRJDE3m+//O0CmvFI8sfYdUJ19uZGRo3lGWpy+yWdY/qzq7sXZQbyi3LPHQefDT8IwbFmnyFygslArjLlKLqOFbsA8ziZMNXMO9hxO5/DIz7wuqau/l7KbY1VkKzntIKHVzNEEejETZ8KTVhlWUw7GkY8ki1rwsgu6ic679cx76ThcSE+jHz9n40b6yEi0JQ4kWJl/ObjD0SMs/aJ4W2FzwL/e9zmYd3FjBd8FwyBVa9JxsMfxoG23wpF6aLAVdeiqSObprn3H2RfUjqYDL3isPope9Kp1L2IfHKyNpnv9xN8sryeHj5wxZzu3u73cvtXW5nYfJCHl3xaG3fJQCiAqIYFjeMYXHD6B3dG29PZcNeE5qmsTljM3MPzWVR8iKK9EUut4vwj+ClAS+xPn093+z8ptpjjogfgb+XP78f+r3a7cJ8w+gW2Y2kJkkMbDaQNo3ayAo7t1wvGPGy1KnodBKNWf4GLHtFtu15i6Q1PTxFhPzzvBSlg4wHGPOJ+L5URc4RqQNL+Vcet71YRHoVaVozucUVXPflWvamF9IkxJeZt/cjIcL9CdOKcx8lXpR4UZQXwZ8PWn1X2oyWL+WAcKdN521P474ZkkIal9SMN6/qgue/b8HSl2WDgf8nAsgcocg+JN4yxZkQPxBumOXs51JeKLUAe/+Ux73vEPt1faksN9urm5e7KRr0Rj1vbXjLYhs/MmEkL/R/AYNmoP9PriNM7hLoHcjAZgMZFjeMQbGD7D1CFKQWpDL38Fz+OPRHjSmfto3asi9332k/Z2xQLD2je5IUlUS3qG60CGnhHClzcsudBnG9ZZ3RKDb9Frv/x2Ho4/JZriiWFJL5Mzr4UbH7r6rY1miU6M3fz8lzeQeIB1LPW2ss0M0v0XP9V2vZdaKAyGBfZtzel5aRqp1fYY8SL0q8KECuODdNgwWPgaFcjLOunuYyXeMkYK7uiufaj6V2AKDPndJ1Yf7hSNsGUy+BikKI6QYXv2n9wTBjNEqLqvmKN2GQPL9/OKx4A5a9ar+8ig4pV8zaP4uX1r1EpbGS9uHteX/Y+zQJbMKNC25kW+a2WrxJrvHUedIzuqclKtM0qGnNO52DFFQUsCh5EXMPzWVLxpb/7Hlv7nQzkzpMorF/NcWvTm65Q2Vys/lzVFkBc0yF6OhMVv23y7qCNPhpvHyOPX3g8o+g6/iqnyvniKSkklfK4/iBcMVH9nVfVVBQpmfiV+vYdiyfxoE+zLi9L62bBNe4n+L8Q4kXJV4UtqRtkzRS7hHrADoX9v3zd6TxP1MR79ikZrx1dVc8N31jmq6LdBFd+p41PH5kpaSHygvkcZfxcOHzEOLwQ793nlzhVhSJgLr2B4jp4rA8zrS8q9sva/PJzTy47EFyynII9wvn3aHv0r1Jdz7Y/AFf7vjy1N6rKmgX3s4iZNqFtzun62QqjZWsPrGaPw79wdKjS6kwVtTZc4X7hdM+vL2lDqZ9eHu+uOgLi8dLldi55WKKmjxu/WyWF0mH3KElznb/adtkcnrhCZnHde2PVfsQGY0ijhY/J91J3gFw4RRpu3ajHfpEXim3TNvA3vRCwgN9+GlyX9pGK+GicI0SL0q8KBwpy4ff7xGrc5CCxcs/BD/7z4itgBnTrSlvX9MNz+0z4Pe7pYuo89Uw5jOrWVdRhnQSbZkOaOAdCIP+T2Ye2aaSMvaK0Mk5BF7+ctXa+SrT8usg57Asv/xDa0urG6QVpXHf0vvYm7MXLw8vnun7DONaj2PJ0SXcv/T+03vPqqFXdC+ubH0lF8Zf2OAnW+uNeooqith4ciM/7PmBTSc31dlzdYvsxphWY0iKSiIhNIEtGVu45597KNYX0zWyK59c+EnN6Tont9wvofVF1vXHN8sIixObRWyM/x5amez+984T7xd9CUS0lY6iqqInuclS22IXbfkQwhPdeq3bj+Vx67cbySwsJyLIl+9u6U2Hpuo7WVE1Srwo8aJwhabBus/gr6elqyK8pbiN2nq2IG3U//tpC5VGjYs7R/PONd3w2/+HfOkbK2Xg3FXfWDs1QAbXLXgMUk2TgMPiJcLT7lJrhKc0D2bdKh1JIPOSLnhO6mNm3QYHxXCM+IHQ9y5oO7rGIkiAEn0Jz6x6hr9S/gLg+nbX80ivRyjWF/Pw8odZm7b2dN41t+kc0ZnmIc0J9wunsV9jGvs3ttyal53pgmBN0yipLKGwopDCikKK9EXW+xVFFOoL7R4X6AtkuelxRmnGGT2fqmga2JTvRn9Hk0BrB8+aE2u4b8l9lBnK6BXdi4+Gf2Rv6e9IdW65IFYBy9+wfo78G4mHS2xPUyv/h9IdhCZWAldPA/8wF89zetEWgIU703lg5hbK9EbaRQfz9U29aKZ8XBQ1oMSLEi+K6kjdAL/cJLboXn5Sr5I00S6NtHCnCBi9QaNbXBhf3tiTyBNLxXnUUC5XsuOn23dlaJrUF/z1jITkAVoMhlGvQ5MO8thogCUvivcLyLyYq76WAZFLX4Z/35N5SSACqM+d0pHkV/1nWdM0vtj+BR9t/QiAPjF9eHvI2wR6B/Lepvf4dve3ACRFJdGmURt+P/g7ZYayGt+quOA4ekf3Zm3a2lr5klRFiE+IRdSE+4UT6huKr6cv3p7e+Hj44OPpI489vCUiYiNGHMVJYUUhxfriU/K8+S+4p9s9XNLiEhr5NSLQO9Au1bY8dTn/t+z/qDBWMKDZAN4b+h5+XtW4y6ZtE+FxeJk8tnXLTV4lNVTmdTpP6HKNDF0MbwEGvaQ+N38n63veIvUvroSkU7RlgKm2xb1oi6ZpfLHiMK8t3IumwZA2kXx0fRLBfqqLTVEzSrwo8aKoiZIc+O0OOCDRCrpeJ3ORfKytm2sOZXPn9E3kl+qJbeTPNzf1ok3RRkn/6Euk0Pa6n6w+GmYqikWErHpfhI7OQzoyhj1p7XbaOVvSWPoS+WG49kcxEss/Lv4ZG6eKWRiI02nSDVJsWcOPyD9H/+GJlU9QWllKXHAcHwz7gFaNWjH30FymrJlCuaGchJAEnu33LIuSFzFr/ywqtcoa367hccO5J+ke2jRqw8nik6xPX8+KYytYmLzQzTf83CIuOI6kqCTpAorsxvJjy/lgywcYNSPtw9vz7rB3aRbkeiDnouRFPL7icSq1SobHDefNIW/i4+nCdbmiBHbNho3fiJ0/mNxy35f05ZEVEmkxtyx7eMnneND/WT8npbkiuI+skM/hyFdEEDvWLLmMtjwvM43cjLboDUae/X0nP61PBWBi33ieu6wDXp5qOrTCPZR4UeJF4Q5GI6x6F5a8JPUske0lDB/Z1rLJ4cwibpm2geTsEoJ9vfh4QncG+x6EH66WTqPYXhKadxV+z02RFNUe0zA+/0Yw7CnocbPUzKTvgJ+uh/yj4BMkRZXtTZODK0pg+wxY+ylkmWcc6cRTo+9dkDDQ+QfIxP7c/dy35D6OFx0n0DuQ1wa9xtC4oezK3sX9S+7nZMlJgryDGNd6HOnF6ZZ0k6J6BscOpnd0b5Kikoj0j0Sn02HQDLy98W3LjKHLW17OM32fqTKKMvfQXJ5e9TRGzcjohNG8POhlvD0cohKZ+2HTVJmUXpYvyzy8ZebW4EckYrj8DWuK0sMbuk+EAQ9Ao3jrcbIPidV/9kH5fF31jfPgUTjtaAvI0NN7ftjMvwez0OngmUs6cPOAhHO6sFtx5lHiRYkXRW1I/ldccYtOSsHtZe/bFc3mFFdw5/ebWJ+cg6eHjheu6MiE2Cz4fpxER6K7wMQ5Vc90ObICFjwuQxoBojrC6NckpVScLZOpbX84et0G7S+TsL7RCIeXiIgx18qA1On0vRs6XWlfe2MityyXh5Y/xIb0DejQcV/3+7i1061kl2Xz0LKH2Jyx+cy8dwoAvHRePNb7Mca3HV/lD/Yv+3/hxTUvoqExttVYnuv3nHUeUWWF+K1s/Mb6WQBJHfa8GbpNkOjL8jesHUaevjIva8D9EOoQ5UleBTMnSOQlJFYKc6M72W9jNMKmb+CvZyXa4uUv0Zbet7sdbQEZdnrztA0czCgiwMeTD65N4sIO1bjzKhRVoMSLEi+K2lKUIcW0R1bI4x43i6+LqWOovNLAE7N2MHuL1H3cNrAFT/Qw4Dl9rJjVRbaDG3+vemaRoRI2T5MoT2muLGt/GYx4SX5c/n5OBIq5fiM4Rn6YetxkPWbmPik43voTVJbKssBIETs9b3EaVaA36nl9/evM3DcTgNEJo5kyYApeOi9+3v8zJ4pOoKGhaZrldkvGlloPC6wrvDy8aOQr9SInik7UactyVfh5+rlVGzQ6YTRtw9tSWllKWWUZZYYySitLLY+L9cUWwXhdu+t4vPfjeOg8pOV50zSx5y82FQ/rPKDNKEk1Jg6VgaAr3pShoyAio9et0P9/rj9vW3+EP+6T+UVNu0tq03G73BT4417r5715f4m2NG5Zq/dnU0out3+3keziCqJD/PhqUk86NVNTzBWnhhIvSrwoTgXHbo7oLpJGMoXPNU3joyUHeXuxpHEu6tCEDy4KxP/HcVKgG54IN/4BYXFVP0dJjpjTbfhahIqnLwy4DwY+KN1Im6bJP/MPmYeXiJxek2VGk04nx9j8Laz/EgpMRbSePlIH0edO8ZCx4ed9P/Pqulep1Crp0LgD7w97n+jAqgdDaprGqhOreHfTu+zP3V/ldlXRv2l/IvwjaOTbiEZ+jQj3CyfcL5xGfo3Q0Ph1/6/MOTinxuO0CmuFpmkkFySflaLcUx2AWR03d7yZB5PuQ3foH/kMHPgLMH0FB0WLl1CPSSJed8+BFW9Bxm5Z7x0IvW+Dfv9zPXDUaDQVg78jjzuMgbGfOReVb/xGin8rik452gIwd9sJHvplGxWVRjo2DeHrSb2IDq2m6FihqAElXpR4UZwOB/8W87iSbPANhTEfi4Aw8ce2Ezxs+tLu1CyEqVdEETn7KrmKDo2TCExNV7And8PCx+HIcnkc3FSs1jtfJd0he/4QcZJq0+Yc1VF+vDpfA75B1u3WfALHN1q3SxgkdTFtRllarTemb+T/lv0fueW5NPZrzHvD3qNbVLdqT9GoGfkr+S8eW/kYRs1Ym3eQu7rexbjW4/DUeVJWWUZJZQllhjKJSlSWkVOWw86snfy8/+daHfds4anzxN/LHz8vP+utp/1jP08//Lz8CPAKkMemZf5e/vh7+dPUw4/OyRvQbf5O6pzMtBgikZS2FwM6KdJd8aa11sk3RMRF37urTk1m7od/plit/gc9LPVVtoIk76jUtpg/c6cYbSnTG3hj4T6+WXUEgAvbN+H9a7sR6OtVq+MoFI4o8aLEi+J0yT8udTBm8dD3HrlC9ZKuENtweXigDx9eEsWAVbdIcWRQtAiYqHbVP4emiWnYoidl0CNAXB9JVzXrLo/Td4iI2fGLdCaB/Jh1u17SRRGtZVnqBlj7Cez+3Zp6apQgkZhuE8AvhONFx7lvyX3sz92Pt4c3T/V5it7RvSk1lFpERWllqdPjwopCZu6bSUFFwRl7e/9rhsYOpUlgE3sB4unnJEhsxYZZgPh7+TsX1bqLpklN1cavxSDRaOrs8guTDrIeN0NEKxGi23+GlW+JYSHIwM++98iARVcF4YZKmZG14Str+sfDW4wOu11nfw6bpkoLvyXa8pzM1apltGVfeiH3z9jC3vRCACYPasHjo9vj6aEKcxWnjxIvSrwozgQGvVzNrv5QHsf2gqumWtJCqTkl3PH9JnanyY/6vb1D+L/0R/HI2C2265e9D20vqfkHQl8Gaz+GFW9L4SQ6SJogBnbmOpbSXKll2PCV9ccNxGys92RrlCX/mIidTdPsW627T4Tet1MS3ISnVz1t6Y6pL/h7+dM1sivtG7cn1CeUYn3xaY04aBbUjId6PsSwuGF4eZyFiEBpLmybISmaLJvUW2wvqWXpOEbSOZUVsO1HWPm2REZAZl/1v1dSha78fQrTYdO38n9s9hMy18kMeth+dpdTtKUfXPFxraMtmqbx7epkXlmwl4pKIxFBPrxxVReGt1OFuYozhxIvSrwoziR758Gcu6Rt1cGOvbzSwOsLrCH03k3gO5/X8TMPR2zcSkYFdL3OefK0IwUn4O8p0iINIjqGPCrRE1PEx9J9tP4r2L8QS71EaJx0pXSfJIP5Korlx3PdZ/at1u0uwdjnDr4o2M23u77FqBntog+OKRDLMpvHlcZKft738ym70yZFJfHywJeJC7bWBqUXp7MlYwvr0tYx68CsUzouwJhWY7i+3fW0b9z+lI9xymiadAJt+EbMCs1F1d6BYhrX8xZrPZK+DLZ8L35ABcdkWWAk9L9PtvMNcj52yioRr7YRnIAIqZPpebPVade8vWO05YJnJYrjhmuzLZmF5Tzy6zaW7csEYGjbSN68qiuRwQ17LISi/qHEixIvijNNbrK48p4wTRYe9BAMfdIy42jJ3pM8/Mt2cooraOxdzvdtVtH++C/ozD4dgZHyw9HzVqtRXVWkrpdRA+aW2PCWMOpVZ4+O3GS5st/8PZTmyDJPH+g4TqIxzXrIj9ihJZJSOvSPdd8aWq3dIbs0my93fMnP+35Gb9RbljcLasaohFG0adSGYJ9gZh2YxT9H/3F5jK6RXdmRtaNWNTVhvmEMjRtK54jO6HQ6dmfvpllQM8a1Hke4Xw3vbV1QUQw7fpXUUJrNRO+ojtDrFqlRMkdQKkqk2HrV+1CYJsuCoqXducdN4OMwHqCsALbPlOLeTJsusLi+kjbscLnz/1/eUZkAbXbcjesLYz6pdbQF5HP9yC/byS6uwMfLg6cubs+N/eKVf4uiTlDiRYkXRV1QWQ6LnhIHXJDC2Cu/srShZhSU8X8/b+Pfg1kAjOsYysvxW/Df9Dnki+so3gEyiqDf3VKTUhVGI2z7Cf5+3tp51OoiETHmOhcz+lLY9Zuki8yCByCmmxR6dhonKYqMvRKJ2TbDptU6SopFXbRau8uJohN8svUT5h6ei1Ez4qHz4NLES7m72900C2pGib6EjSc38uyqZ8kuyz6l52ga2JThzYczvPlwkqKSzk4qyJGMPSIet82wThb39IWOY+X9jOttNRIsL5JtV38grfUAIc2kyyxponNU7uRuibJsnymRE5DPTpdrRAA7dJQBpmjLNFO0pVBGX1zwrETuahltKdMbeGX+Hr5bI7VY7aKD+eC6JNo0UROhFXWHEi9KvCjqkp2zxEejokh+/K/6WgznAKNR48uVh3lz0T4qjRrNwvz54JqO9ChaAavflwJckBqFDmOkTbppUtXPVVYgRZxrPhHfDg8v+TEa8qgUdDpybJOIq52zZTQBSKoraaKIlEYJ0mq9aZqIHXPNhKePRAj63uk0qNJdDuUd4sMtH1qiLF4eXrQMbcnBvIOn1HLctlFbi2Bp26ht/bjaryyH3X+IEDm62ro8PFEES9fr7TuCygrk/2P1R9boWFhzGPh/UnRtGzWprIC9cyXKkrLKurxxa4mydLvO9f85QF6qKdqyVB6fRrRl94kC7p+xhQMZIppuHdiCR0a2xc+7dgJIoagt9Ua8vPzyy8ybN4+tW7fi4+NDXl5ejftomsaUKVP44osvyM3NpU+fPnz88cd07NjRredU4kXxn5B1AH6eJK65Og9JIQ16yFKcuy01j/tmbCEluwQPHdx3QWvuGdoS75QVcvV9aIn1WAmDJG3Q6sIqLf/JPiRRn/0L5HFAhFxVJ93g+qq6OBu2fCf1F5a2XB20HiEppZYXSFfS7t8lpWSenWM+duOWUq9jvg1vKT/QjmkNF+zI3MH7W95nXdo6y7KYwBi6RXWje1R3kqKSaBXWisKKQj7f/jm/HfyNYn0xHjoPkqKSGB43nGHNh9nVxJxVjAZ5/7dOhy3TpYUeZABiu4slEtJiiH1hdmkerPtc3ltz4XR4onxGuoy3H4qYf9xkVPetuDzbHrvXZBHGVX0uNE32W/T0aUdbjEaNb1Yd4Y2F+6gwGIkM9uWtq7sypI0LTxmFog6oN+LlueeeIywsjGPHjvH111+7JV5ef/11Xn75ZaZNm0abNm146aWXWLFiBfv27SM4uOaQpRIviv+MihJY8Ij8oIEIgnFfWq68i8oreXbOTosrb7voYF4a04meCeESgVn9oURxzMWXUR3ENbXTVdYCXUcO/g0Ln7AW4cZ0lanV8f1cb280wP5FcvVvK5jCE+VHN2mCRGZctVq7IiTWJGjM4sb0L6y505TirRlbySjJoEtkl2pN8QxGA3tz9xITGHN2alb0ZdKllX9UIhj5qaZb07KCE9b/IxBPnh43SaFsSIz9sUpy5H1c97k1lRTRRrqAOl1pqZFC06QDaP2XsG+B9T0PamI69iRny39H8lJh7n3W/9e4PnDFJ9J6XUt2Hs/n+T92sTFF3J8vbN+E16/sTOMgVZSr+O+oN+LFzLRp03jggQdqFC+aptG0aVMeeOABHnvsMQDKy8tp0qQJr7/+OnfccUeNz6XEi+I/Z8sPMO8hqSMJaSbt1M37WFbP2XKcKXN3kVsiRa3X9Izl8dHtCQ/0kR/ItZ/Klbe5tiG4qaRvetzkOk1g0MuP3rLXoNxUENzpKrhoCoTGVn2eWQeljmLrj9b9vPxljlOvyVJHUV4EOYck0pB9SHxrzP/MEQRXeHjJHB6LoEm03g9uWms/kTNKaZ4IkvxjJlHiIFKK3eia8vCWCEivW6H1SKsIMRqkcDpjDxxdY///GNUBBj8s6UFzFKQ0T2qZNnwN2Qesx48fKMc2z7SqDlfRluHPiDFhLaMtucUVvPXXPn5cfxRNA39vT56+tD3X925eP9J0ivOKBiteDh8+TMuWLdm8eTNJSdY6gCuuuIKwsDC+/fZbp33Ky8spLy+3PC4oKCAuLk6JF8V/y8ldkkbKPiA/5Bc+Ly3Sph+AnOIK3li4lxkbpHA3LMCbx0a1Y3zPODw8dKbRAFNh7WdQlC7H9AmGnjdBn7tcX4UXZ4kd/KZvAU0KOgc+KNEbW0t4RyqKxRBtw1dwcqd1eVwfETEdrnAd+SnJsRcztgLHXADsCi9/ifTYRWtM9wMaV50ScQejUQpg81Oly8YSNbG5NUdAqsM7UPx7QuNMt7EQ2ty6LDhaUjond4tdf8Yeuc3c5/zaozvD4Eeh3aVW0Za2Xd5vW7NBnyDoeq3Us0S52drtGG2J7S21LY5F3DVQaTDy0/qjvPXXfvJLRVRf3rUpT1zcjpjQaj47CkUd0mDFy+rVqxkwYADHjx+nadOmluW33347KSkpLFq0yGmf559/nilTpjgtV+JF8Z9TXghz75dUEIhB3ZhP7NxRN6Xk8vScnewxGdslNQ/jpTGd6NjUFGGpLJcfuNUfQuZeWebhJXOL+v8Pmrio/UrbJlOrzQWkoc2lmymuj/yQVnUlr2kSLVj/pYwZMKdGAiMlbdH2YvkRD4ysPnJiNErbb84hG1Fjus09Yp9yccQv1FpTYytqGrcE32CJMhUcdxAkR23SOseshcnV4R9uI06a24gU02P/RlYRVZJjL1DMt+a2d0e8/CCyrURaOlwhZnE6nam493cRLanW+h8i28uYhy7j5TW6g6bB5u+k7skSbXla2t1rGW1Zezib5//YZXHJbRcdzJTLO9InsYrRAwrFf0SdipeqxIItGzZsoGfPnpbHtRUvJ06cICbGmkuePHkyqampLFy40GkfFXlR1Cs0Tfw+Fj4BhgpJpVzzrV1HUaXByLdrUnjnr30UVxjw0MGk/gn830VtCPYzCQ2jEQ4uhlUfQMq/1uO3ulBETIsh9hELTZOZOH89azU9A4l6NOsubbuxveU2MML5vC2urVOt/iNmPH1kUGBorPwLaSaRoJBY020z+x9/WwyVMvog+5CNuDEJG3P7eFX4hUnUpCYPGJ2H6fziHKInza1RFJ9A5/3KiyRy4ihUzJEvp+fxFGEV1V5EZFR7ESyNEuwFRN5Rq/9OibTNy4DNyyXKYh6w6S75x6S7zezTc4rRlrT8Ul6Zv5e526TDLNTfm4dHtOG63s3x8jyLaT2FwkSdipesrCyysrKq3SYhIQE/P6tvQV2mjRxRNS+KesGJLZJGykuRH/+Rr8gPl82PVnp+GS/N282f20UsRAX78sylHbi0S4x9vcHxTSJi9vxh/SGP6SpurB3GWOsvQIqIN34jBmXHNriuUwlPtAqZuN7yA2z+8TXoxVF487fyQ16YjsXFtzq8A61CxlHYhMbJfUcBoS+FnCP2gsYscMxeKCDeKaGxrtM5YXHyHNXViVRWSDrPMZKSm1z1PmHNxWTOLFCi2otYqMrQz2iUVM6Gr+DAIuv/U3BTq/NxcC2t9DVNXHgXPSUi7hSjLWV6A1//e4SPlhykVG9Ap4Prezfn4RFtaRRYRWG4QnEWaLBpI3PB7oMPPsijjz4KQEVFBVFRUapgV9HwKM2FOffI8DyQbpPL3ndKFazYn8mzv+8kOVtqIbo3D+PBi9owsFWEvYjJOSKdLJu/t9ZZmFNESROdLeWNRvnRTl0Px9bLrTkVZYtPkLjxxvWWVFNsT4mkgIiZwjRp5y04bk3VmO8XHLe2DteEX5hD5MZG2IQ0g5CmVnFQmifHDoioOW1leb02xbO2QiX7QNWpq8AoaNLBKlCiOkgKyN10TkkObP1BCnBzj1iXtxhimjk12l5cukv+MUlBHvxbHsf2gjGf1iraomka/+zJ4IU/d3M0Rz5bvRIa8dxlHenUrAq/GIXiLFJvxMvRo0fJycnhjz/+4M0332TlypUAtGrViqAg+aJt164dr776KmPHjgWkVfrVV19l6tSptG7dmldeeYVly5apVmlFw0TTYM3H8Pdz8gPauLWkkRxqV8r0Br5YcZiPlx6kvFKu2nslNOLBi9rQv6VDmqckR67w131uTUv4hUm3Su87qr/CL80VI7tj66UO49gmqaFwJKItxPUyRWj6SLtvVQJCXyrtxK6EjVn0uFM0CyImXAkbs+gJjpY0UWGaTRRljxRMuyqeNeMbahInNpGUqPauU2jucHyzCJadv0JlmfU5ul0vZnWRbWp/zPzjMoE6eYUY4ZUXSNRp+NPQ7x63oy2aprF0XwYfLz3EJlPrc5MQX568uD2Xd22quogU9ZZ6I15uuukml6mepUuXMnToUDkBnY6pU6dy0003AVaTus8//9zOpK5Tp05uPacSL4p6ydF18OvN8kPu5Q+XvC0eKw5kFJTx6fJD/LDuKBUmEdOnRTgPXtSGvo4FlfpSabtd/ZGkW0BSVF2vhX7/c+8H1GiQaEzqOvF6SV1nPZYtfqFy9R/bW0RNs56uJx5XRVm+ffTGImyOWZebRUB16Dylq8qV4AL74llboRLS7PS6mqDqMQxNOksBbuerXdfWVEVhOhxZCcmmf7bTwkHe7ys+cVsIGYwa83ek8cmyQ5aCcB8vD24d2IJ7h7Ui0LcejFRQKKqh3oiXs4ESL4p6S3E2zJ5sLbzsdgNc/KZL19r0/DI+XXaQn9anUmEQEdO/ZWMevKgNvRIcjNyMBtg3X+pijq23Lm97sdTFNO9bux/u4mypl0ldJ7fHN1nbey3oRBiY62Zie0uH0KkKBE2T9FNVwsZ8azZzsy2etRUq4S1q3X2DpkmUozhLam0s/7Ls75/cKZErEJHYYYykhmJ7ufe6izJEpBxZKREWW58XkIhSTFdxXG4xBFoOc+u1VFQa+W3LMT5bfpgjWcUABPp4ckO/eG4d2IKo4BqmmSsU9QQlXpR4UdRXjEZY+TYse0WKOqM6ShqpilqGE3mlfLLsIDM3pKI3yJ/qoNYRPHBhG3rEN3Le4ehaETH75mMptI3tJSKm3SW1/2EH6Rg6udMqaFLXSyGyIwGN5bnMYqZZ99pFImrCaBCvlfJC6fCpbhp2ZbmN+KhBlBRnutduDVJj1PNmqTEKqsE2vzjLlAYyCZasfQ4b6MQYMGGQ/IvvV/XsIheUVFQyY30qX648TFq+RK3CAry5ZUALJvVLIDSgBrM7haKeocSLEi+K+s7h5TDrNnF39QmCyz+Qgt4qOJ5XykdLDvLLxlQqjfInO7hNJLcNbMHAVhFidGdL1gHxitk2w/rDHJ4oxnndrq/exM4dCk9ai4BT10t3laMA0HlCdCdr3UxcL2kdP5XojNEoUY8qRUimvVgxOwjXBp8gqYEJjDT9s70fKQXFcX2qFoAlOTJQ0ZwKytjtvE2TztBiECQMlJZpfxcCtAbyS/V8vyaZb1Ylk1NcIYcN8WXyoESu691cpYcUDRYlXpR4UTQECtPh11utPi69JsPIl6uNKKTmlPDx0oP8sukYBpOIiW8cwPW9m3N1zzgZOWBLUYYU9m74yto2HdAYet8uzxfoUEdzqlRWQPp2k5gxpZsKjjtvF9TEGp2J6yOPS7KdRUhRhr0gKcmufuaSKzy8XIsQVwIlIMKtoZN2lOZCymqJrhxZaXIrdvg6jepgSgMNgvgBEHDqs5syCsqYujqZ79ekUFQu3VPNwwO4a2hLxnVvhq+XmvqsaNgo8aLEi6KhYKiUFNLKt+VxTDeZUxPfv9of06PZJXyz6gizNh2j0PRD5uPlwSWdY5jQpzk94hvZd5WUF8kAybUfi4kaSOFw0gTpZAlPPPOvLf+YqU3blG5K2w5G/ekd0y/MtQgJinQWKH5hp1+ka0tZPqSsMaWBVshwTUexEtHWFFkxRVdOtZvJ/JR6A//syeDXTaks35+JSa/Stkkwdw9rySWdY5TBnOKcQYkXJV4UDY0Di6WY17YgtHlfaDlc/jXp7LJVuaSikrnbTjB97VF2HLemStpFBzOhT3PGJDWzuvaCiKXdc2D1BzJWAKRQtP1l0P9+qVOpq1Zafak8p7lu5tgGEQSBUdWka2zuBzSuetp2XVBeKDVER1aIYEnb5uz227i1iBSzYAmKOu2n1TSN7cfy+XXTMf7YdsIyewikff6OwS0Z3i7KOVWoUDRwlHhR4kXREMlLhZVvwYG/7S3+QdIaiUOlAyVxmMtBjduP5TF9bQp/bDtBmV5+ZAN9PLkiqRkT+jS3zk8C6bBJXinFvQcXW5d7B5giGU3khzgoSsSF+X5QE9P6qDNbjFsfqCiWWU/mNNCJLc6pqvBEa4FtwkAIiXF9rFMgo6CM37Yc59dNxziQUWRZHhPqx7juzbiyeyyJkUHVHEGhaNgo8aLEi6Iho2likX9oqVjOJ6+EiiL7bSLbiYhpORwSBtgJifxSPbM3H+OHdUc5aPMj2D4mhJEdmzCqUzRtmwRb00ond0tx745fapfW8QmqRtyYxI9Z6JxugXBdUFEiUaBkU+vy8U3OTrxh8aaoymARK66me58GVaWFfL08GNUpmqt6xNK/ZQSeKsqiOA9Q4kWJF8W5hEEvKZZDS0TQnNhsn77w8DalmExRmZhu4OGBpmmsO5LD9LUpLNqVbmm1BinyHdkxmpEdm5AU10hSEPpSca4typSW5OIMKZw1/yvOkOVFGe4ZytniG+JC6JgfN5GalaAm8riuUkP6Unkfzd1AxzY6i7XQOGuBbcJAmXF0hinTG1h7OJu/95xk7rY0u7RQj/hGXNUjlku6hoPozAAADzlJREFUxBBim+5TKM4DlHhR4kVxLlOSI3UYh02RGXMBrhn/cEgcIlGZxGEQFkducQV/7znJol0nWXkg0zKCACAy2JeLOjRhZMdo+iU2xserhgJQTZN6kOJMq5ixEzdm8WO6NVTU7vX5hbmI4tiIG4vwiaxhIGO5iBVzGujYBud27uCm1nqVFoNOvZW7GjRN41BmMcv3Z7J8fybrDmfbvf8qLaRQCEq8KPGiOF/QNLGVN0dlklc6zxFq3NpU+DsMEgZSjD/L92eyaFc6S/ZkWLqVAIL9vLigXZQImZaNCQs4zSiIpklRrktx4yKyU9UAxarwD3cWN97+Vg8axwhRULQ1qpIwSGpY6qBAubBMz6qD2Szfn8mK/Zkcz7OfuRQT6sfg1pFc2jVGpYUUChNKvCjxojhfMeildsNcL3N8o0OKyUtM40xipiKqK2uS81i0K52/dp0kq8g+MtE6Koge8Y3oEd+IngnhJDQOqLvBfkajeNFUG83JsHrAOHb+uCIw0iYNNEhGCtTB+RuNGrvTCizRlc0puRYzQQAfTw/6JIYzpE0kg9tE0joqSA1IVCgcUOJFiReFQijNk2iMOTKTe8R+vV+YpJgSh2FIHMaWghAW7Urnn70ZHM4sdjpcRJAP3ZubxUwjOjULPTvmaEaDpM9ciZuyfIg22e5Htj3jYsVo1DiSXcyuEwXsOpHP7hMF7DyeT26Jff1MYkQgg9tEMqRNJH0Swwnw0klNkV8o+Aaf0XNSKM4FlHhR4kWhcE3OYRExh5fC4RXONvrhiZZamZyoPmxMN7ApJZdNKblsP5ZvGRJpxsfLgy7NQumR0IgOMSEkNA4kISKQUP9zo9i0vNLA/vQidp3IZ9eJAnanFbAnrYCSCme331AfjdHNjQyPKadHSCGNK09KPVJ+qsyCKjghabGrv4WOY/77F6NQ1HOUeFHiRaGoGUOldC6ZU0zHNtj7mug8xcq/pbRklzfpys60YjYm57LRJGjMs3UcCQ/0oUVEIAmNA2kREUCC5X5gvZu9U6Y3cLKgjPT8MtILyjhZUMY+k2A5mFFkSf/4UkFTXTbNdFm08MqiS1ABrX1zaUoWYRVpeJecRFdTKsvDWyaJ97z5P3hlCkXDQokXJV4UitpTli+dOWYxk3PIfr1vqNSOmOpltEYtOJJVzKaUXDYfzeNQRhFHsovJLKx+QnNksC8tGgcSG+5PmL8PIf5ehPh5E+LvTbCf+b7NMl8vt9xkjUYNvdGI3qBRaZBbvcFITnGFiJOCMk5aBEq5ZVmeKd3jTxnNdFnE6jKJ1WURq8uimS6TeM9s4jyyaWTMqfk99PKTduuwOGmzDjXdmu8HR5/aZG+F4jxAiRclXhSK0yc3xdqOfXi5dbCjmUYJVqO8FoPBPwyAovJKkrOKOZJVLLfZcpucXVJlpKYmgn29CPH3xttTZxEleoORSoNGhcFIpVGzDKqs8hiUWMSJ422sLotwXWHNJ+IdaBIjLsRJWHMpEFaFuArFKaHEixIvCsWZxWiAE1tNQmapONPatjXrPKBZD6u3TGxPlx4s+aV6k5Ap5nheKQWllRSU6Sksq6SgVE9Bmd50K49t/VCqRyOMIidBEueRRZxHNs10mQRpzgXITviGViFO4sQDxr+REicKRR2hxIsSLwpF3VJeCMmrrGIma7/9ep9gmxTT8FP2UymvNIiwKamgOOcEXoXH8C9Jw6/4GH7FJ/ApOoZ34TE8C1Px0JfUfMCAxs7REluB4hda8zEUCkWdoMSLEi8KxX9LXqopxWTqZDJPxzYT2txU+DsMWgyBgHD79UYDFKabOnOOWv+ZH+cfc28kQVATh2hJc3nusOYQGgu+ysFWoaivKPGixItCcfYwGiBtm1XMHF3rMENIB02TxIOl4LhJnBx3YyikDkKauhAnppROaCx4+9XlK1MoFHWIEi9KvCgU9YfyIkhZbU0xZe51vZ3OU6Y2h8XbCxTz/ZBmdTe0UaFQnHVq8/tdvwwXFArFuYdvELQZIf9AoiyHl0HhCaswCY2D4BjwVF9JCoWiZtQ3hUKh+G8JbQZJE872WSgUigaMx9k+AYVCoVAoFIraoMSLQqFQKBSKBoUSLwqFQqFQKBoUSrwoFAqFQqFoUCjxolAoFAqFokGhxItCoVAoFIoGhRIvCoVCoVAoGhRKvCgUCoVCoWhQKPGiUCgUCoWiQaHEi0KhUCgUigaFEi8KhUKhUCgaFEq8KBQKhUKhaFAo8aJQKBQKhaJBcc5NldY0DYCCgoKzfCYKhUKhUCjcxfy7bf4dr45zTrwUFhYCEBcXd5bPRKFQKBQKRW0pLCwkNDS02m10mjsSpwFhNBo5ceIEwcHB6HS6s306taagoIC4uDhSU1MJCQk526dzVlDvgaDeB/UegHoPQL0HcH68B5qmUVhYSNOmTfHwqL6q5ZyLvHh4eBAbG3u2T+O0CQkJOWc/oO6i3gNBvQ/qPQD1HoB6D+Dcfw9qiriYUQW7CoVCoVAoGhRKvCgUCoVCoWhQKPFSz/D19eW5557D19f3bJ/KWUO9B4J6H9R7AOo9APUegHoPHDnnCnYVCoVCoVCc26jIi0KhUCgUigaFEi8KhUKhUCgaFEq8KBQKhUKhaFAo8aJQKBQKhaJBocSLQqFQKBSKBoUSL/WAl19+mf79+xMQEEBYWJhb+9x0003odDq7f3379q3bE61DTuU90DSN559/nqZNm+Lv78/QoUPZtWtX3Z5oHZKbm8vEiRMJDQ0lNDSUiRMnkpeXV+0+58Ln4JNPPqFFixb4+fnRo0cPVq5cWe32y5cvp0ePHvj5+ZGYmMhnn332H51p3VGb92DZsmVO/+c6nY69e/f+h2d8ZlmxYgWXXXYZTZs2RafTMWfOnBr3Odc+B7V9D87Fz0FtUOKlHlBRUcHVV1/NXXfdVav9Ro0aRVpamuXf/Pnz6+gM655TeQ/eeOMN3nnnHT766CM2bNhAdHQ0F110kWU4Z0Pj+uuvZ+vWrSxcuJCFCxeydetWJk6cWON+DflzMHPmTB544AGeeuoptmzZwqBBgxg9ejRHjx51uf2RI0e4+OKLGTRoEFu2bOHJJ5/kvvvuY9asWf/xmZ85avsemNm3b5/d/3vr1q3/ozM+8xQXF9O1a1c++ugjt7Y/Fz8HtX0PzJxLn4NaoSnqDVOnTtVCQ0Pd2nbSpEnaFVdcUafnczZw9z0wGo1adHS09tprr1mWlZWVaaGhodpnn31Wh2dYN+zevVsDtLVr11qWrVmzRgO0vXv3VrlfQ/8c9O7dW7vzzjvtlrVr1057/PHHXW7/6KOPau3atbNbdscdd2h9+/ats3Osa2r7HixdulQDtNzc3P/g7P57AO23336rdptz8XNgizvvwbn+OagJFXlpwCxbtoyoqCjatGnD5MmTycjIONun9J9x5MgR0tPTGTFihGWZr68vQ4YMYfXq1WfxzE6NNWvWEBoaSp8+fSzL+vbtS2hoaI2vp6F+DioqKti0aZPd/yHAiBEjqnzNa9ascdp+5MiRbNy4Eb1eX2fnWlecyntgJikpiZiYGC644AKWLl1al6dZ7zjXPgenw/n6OVDipYEyevRofvjhB5YsWcLbb7/Nhg0bGD58OOXl5Wf71P4T0tPTAWjSpInd8iZNmljWNSTS09OJiopyWh4VFVXt62nIn4OsrCwMBkOt/g/T09Ndbl9ZWUlWVladnWtdcSrvQUxMDF988QWzZs1i9uzZtG3blgsuuIAVK1b8F6dcLzjXPgenwvn+OfA62ydwrvL8888zZcqUarfZsGEDPXv2PKXjjx8/3nK/U6dO9OzZk/j4eObNm8e4ceNO6Zhnmrp+DwB0Op3dY03TnJadTdx9D8D5tUDNr6chfA5qorb/h662d7W8IVGb96Bt27a0bdvW8rhfv36kpqby1ltvMXjw4Do9z/rEufg5qA3n++dAiZc64t577+Xaa6+tdpuEhIQz9nwxMTHEx8dz4MCBM3bM06Uu34Po6GhArsBiYmIsyzMyMpyuyM4m7r4H27dv5+TJk07rMjMza/V66uPnoCoiIiLw9PR0ijBU938YHR3tcnsvLy8aN25cZ+daV5zKe+CKvn37Mn369DN9evWWc+1zcKY4nz4HSrzUEREREURERPxnz5ednU1qaqrdD/nZpi7fgxYtWhAdHc3ixYtJSkoCpH5g+fLlvP7663XynKeCu+9Bv379yM/PZ/369fTu3RuAdevWkZ+fT//+/d1+vvr4OagKHx8fevToweLFixk7dqxl+eLFi7niiitc7tOvXz/mzp1rt+yvv/6iZ8+eeHt71+n51gWn8h64YsuWLQ3i//xMca59Ds4U59Xn4GxWCyuElJQUbcuWLdqUKVO0oKAgbcuWLdqWLVu0wsJCyzZt27bVZs+erWmaphUWFmoPPfSQtnr1au3IkSPa0qVLtX79+mnNmjXTCgoKztbLOC1q+x5omqa99tprWmhoqDZ79mxtx44d2nXXXafFxMQ02Pdg1KhRWpcuXbQ1a9Zoa9as0Tp37qxdeumldtuca5+DGTNmaN7e3trXX3+t7d69W3vggQe0wMBALTk5WdM0TXv88ce1iRMnWrY/fPiwFhAQoD344IPa7t27ta+//lrz9vbWfv3117P1Ek6b2r4H7777rvbbb79p+/fv13bu3Kk9/vjjGqDNmjXrbL2E06awsNDyNw9o77zzjrZlyxYtJSVF07Tz43NQ2/fgXPwc1AYlXuoBkyZN0gCnf0uXLrVsA2hTp07VNE3TSkpKtBEjRmiRkZGat7e31rx5c23SpEna0aNHz84LOAPU9j3QNGmXfu6557To6GjN19dXGzx4sLZjx47//uTPENnZ2dqECRO04OBgLTg4WJswYYJTG+S5+Dn4+OOPtfj4eM3Hx0fr3r27tnz5csu6SZMmaUOGDLHbftmyZVpSUpLm4+OjJSQkaJ9++ul/fMZnntq8B6+//rrWsmVLzc/PT2vUqJE2cOBAbd68eWfhrM8c5rZfx3+TJk3SNO38+BzU9j04Fz8HtUGnaaYqJ4VCoVAoFIoGgGqVVigUCoVC0aBQ4kWhUCgUCkWDQokXhUKhUCgUDQolXhQKhUKhUDQolHhRKBQKhULRoFDiRaFQKBQKRYNCiReFQqFQKBQNCiVeFAqFQqFQNCiUeFEoFAqFQtGgUOJFoVAoFApFg0KJF4VCoVAoFA2K/wc9nySfaZ60/AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal'); plt.title(\"Cone model (Explicit solvers)\")\n",
    "plt.plot(Q[0],Q[1], Q2[0],Q2[1], Q4[0],Q4[1]); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.720052Z",
     "iopub.status.busy": "2024-04-30T09:12:55.719952Z",
     "iopub.status.idle": "2024-04-30T09:12:55.782300Z",
     "shell.execute_reply": "2024-04-30T09:12:55.782042Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Cone Hamiltonian (Explicit solvers)\")\n",
    "plt.plot(T,Hamiltonian(Q,P), T2,Hamiltonian(Q2,P2), T4,Hamiltonian(Q4,P4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Likewise, in the celestial mechanics case, the Hamiltonian drifts with time using the Euler explicit and Runge-Kutta schemes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.783785Z",
     "iopub.status.busy": "2024-04-30T09:12:55.783705Z",
     "iopub.status.idle": "2024-04-30T09:12:55.884700Z",
     "shell.execute_reply": "2024-04-30T09:12:55.884474Z"
    }
   },
   "outputs": [],
   "source": [
    "Hamiltonian = H_Celestial\n",
    "q,p = np.array([1.,0.]),np.array([0.3,0.7])\n",
    "t = 10.\n",
    "Q,P,T = Geodesic(q,p,Hamiltonian,t,step=EulerStep,n=int(100*t))\n",
    "Q2,P2,T2 = Geodesic(q,p,Hamiltonian,t,step=RK2Step,n=int(20*t))\n",
    "Q4,P4,T4 = Geodesic(q,p,Hamiltonian,t,step=RK4Step,n=int(8*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.886094Z",
     "iopub.status.busy": "2024-04-30T09:12:55.886007Z",
     "iopub.status.idle": "2024-04-30T09:12:55.950768Z",
     "shell.execute_reply": "2024-04-30T09:12:55.950439Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal'); plt.title(\"Poincare geodesic (Explicit solvers)\")\n",
    "plt.plot(Q[0],Q[1], Q2[0],Q2[1], Q4[0],Q4[1]); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:55.952248Z",
     "iopub.status.busy": "2024-04-30T09:12:55.952149Z",
     "iopub.status.idle": "2024-04-30T09:12:56.003808Z",
     "shell.execute_reply": "2024-04-30T09:12:56.003525Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(T,Hamiltonian(Q,P), T2,Hamiltonian(Q2,P2), T4,Hamiltonian(Q4,P4));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comparison with the Hamiltonian class**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.005449Z",
     "iopub.status.busy": "2024-04-30T09:12:56.005335Z",
     "iopub.status.idle": "2024-04-30T09:12:56.118167Z",
     "shell.execute_reply": "2024-04-30T09:12:56.117891Z"
    }
   },
   "outputs": [],
   "source": [
    "Q_,P_,T_    = Celestial.integrate(q,p,scheme=\"Euler\",niter=int(100*t),T=t,path=True)\n",
    "Q2_,P2_,T2_ = Celestial.integrate(q,p,scheme=\"Runge-Kutta-2\", niter=int(20*t),  T=t,path=True)\n",
    "Q4_,P4_,T4_ = Celestial.integrate(q,p,scheme=\"Runge-Kutta-4\", niter=int(8*t),   T=t,path=True)\n",
    "for a,b in zip( (Q_,P_,T_,Q2_,P2_,T2_,Q4_,P4_,T4_), (Q,P,T,Q2,P2,T2,Q4,P4,T4) ): \n",
    "    assert norm_infinity(a-b)<1e-14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Symplectic Euler scheme - Separable case\n",
    "\n",
    "Symplectic schemes guarantee that a quantity, closely related with the Hamiltonian, is conserved along the trajectory. \n",
    "\n",
    "The Euler symplectic scheme is defined as follows:\n",
    "$$\n",
    "    \\frac{p_{n+1}-p_n}{\\Delta t} = -\\partial_q H(q_n,p_{n+1}), \\quad\n",
    "    \\frac{q_{n+1}-q_n}{\\Delta t} = \\partial_p H(q_n,p_{n+1}), \n",
    "$$\n",
    "Note that the scheme is semi-implicit, in view of the definition of $p_{n+1}$.\n",
    "Two cases must be distinguished for the implementation.\n",
    "* **Separable Hamiltonians.** If the Hamiltonian takes the form $H(q,p) = F(p) + V(q)$, then the Euler symplectic scheme becomes explicit. The Celestial Mechanics and Lotka-Volterra schemes fall in that category.\n",
    "* **Non separable Hamiltonians.** If the Hamiltonian has a general form, then one can try to solve the implicit part of Euler's symplectic scheme using a Newton method. Another approach, not detailed here, is to introduce an higher dimensional separable Hamiltonian with the same dynamics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.119706Z",
     "iopub.status.busy": "2024-04-30T09:12:56.119621Z",
     "iopub.status.idle": "2024-04-30T09:12:56.121909Z",
     "shell.execute_reply": "2024-04-30T09:12:56.121683Z"
    }
   },
   "outputs": [],
   "source": [
    "def SymplecticEulerStep_Separable(q,p,H,dt):\n",
    "    d=len(q)\n",
    "        \n",
    "    # Differentiate w.r.t. q and advance p\n",
    "    q_ad = ad.Dense.identity(constant=q,shape_free=(d,))\n",
    "    q_grad = H(q_ad,p).gradient() # We can use p thanks to separability\n",
    "    p1 = p-dt*q_grad\n",
    "    \n",
    "    # Differentiate w.r.t. p and advance q\n",
    "    p1_ad = ad.Dense.identity(constant=p1,shape_free=(d,))\n",
    "    p1_grad = H(q,p1_ad).gradient()\n",
    "    q1 = q+dt*p1_grad\n",
    "\n",
    "    return q1,p1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.123332Z",
     "iopub.status.busy": "2024-04-30T09:12:56.123253Z",
     "iopub.status.idle": "2024-04-30T09:12:56.124990Z",
     "shell.execute_reply": "2024-04-30T09:12:56.124714Z"
    }
   },
   "outputs": [],
   "source": [
    "Hamiltonian = H_Celestial\n",
    "q,p = np.array([1,0]),np.array([0.3,0.7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.126365Z",
     "iopub.status.busy": "2024-04-30T09:12:56.126284Z",
     "iopub.status.idle": "2024-04-30T09:12:56.170675Z",
     "shell.execute_reply": "2024-04-30T09:12:56.170451Z"
    }
   },
   "outputs": [],
   "source": [
    "t = 20.\n",
    "QS,PS,TS = Geodesic(q,p,Hamiltonian,t,step=SymplecticEulerStep_Separable,n=int(30*t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The symplectic Euler scheme is only first order accurate, but it has the property that the Hamiltonian remains bounded above and below during the evolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.171992Z",
     "iopub.status.busy": "2024-04-30T09:12:56.171909Z",
     "iopub.status.idle": "2024-04-30T09:12:56.236395Z",
     "shell.execute_reply": "2024-04-30T09:12:56.236106Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal'); plt.title(\"Celestial mechanics (Euler symplectic)\")\n",
    "plt.plot(QS[0],QS[1]); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.237972Z",
     "iopub.status.busy": "2024-04-30T09:12:56.237862Z",
     "iopub.status.idle": "2024-04-30T09:12:56.306033Z",
     "shell.execute_reply": "2024-04-30T09:12:56.305750Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Hamiltonian conservation (Euler symplectic)\")\n",
    "plt.plot(TS,Hamiltonian(QS,PS));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4 Symplectic Verlet scheme - Separable case\n",
    "\n",
    "The Verlet method is a second order symplectif integration scheme. It is explicit if the Hamiltonian is separable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.307624Z",
     "iopub.status.busy": "2024-04-30T09:12:56.307520Z",
     "iopub.status.idle": "2024-04-30T09:12:56.310093Z",
     "shell.execute_reply": "2024-04-30T09:12:56.309868Z"
    }
   },
   "outputs": [],
   "source": [
    "def SymplecticVerletStep_Separable(q,p,H,dt):\n",
    "    d=len(q)\n",
    "    \n",
    "    # Differentiate w.r.t. q and advance p\n",
    "    q_ad = ad.Dense.identity(constant=q,shape_free=(d,))\n",
    "    q_grad = H(q_ad,p).gradient()\n",
    "    p1 = p-0.5*dt*q_grad\n",
    "    \n",
    "    # Differentiate w.r.t. p and advance q\n",
    "    p1_ad = ad.Dense.identity(constant=p1,shape_free=(d,))\n",
    "    p1_grad = H(q,p1_ad).gradient()\n",
    "    q1 = q+dt*p1_grad\n",
    "    \n",
    "    # Differentiate w.r.t. q and advance p\n",
    "    q1_ad = ad.Dense.identity(constant=q1,shape_free=(d,))\n",
    "    q1_grad = H(q1_ad,p1).gradient()\n",
    "    p2 = p1-0.5*dt*q1_grad\n",
    "    \n",
    "    return q1,p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.311470Z",
     "iopub.status.busy": "2024-04-30T09:12:56.311362Z",
     "iopub.status.idle": "2024-04-30T09:12:56.313092Z",
     "shell.execute_reply": "2024-04-30T09:12:56.312866Z"
    }
   },
   "outputs": [],
   "source": [
    "Hamiltonian = H_Celestial\n",
    "q,p = np.array([1.,0.]),np.array([0.3,0.7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.314480Z",
     "iopub.status.busy": "2024-04-30T09:12:56.314384Z",
     "iopub.status.idle": "2024-04-30T09:12:56.381732Z",
     "shell.execute_reply": "2024-04-30T09:12:56.381505Z"
    }
   },
   "outputs": [],
   "source": [
    "t = 20.\n",
    "QV,PV,TV = Geodesic(q,p,Hamiltonian,t,step=SymplecticVerletStep_Separable,n=int(30*t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be shown that the Verlet scheme, in the separable case, amounts to the symplecting Euler scheme shifted by half a time step. Visually, their output is therefore quite similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.383109Z",
     "iopub.status.busy": "2024-04-30T09:12:56.383020Z",
     "iopub.status.idle": "2024-04-30T09:12:56.446324Z",
     "shell.execute_reply": "2024-04-30T09:12:56.446051Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal'); plt.title(\"Celestial mechanics (Verlet symplectic)\")\n",
    "plt.plot(QV[0],QV[1]); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The improved accuracy is more obvious on the Hamiltonian conservation than on the trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.447969Z",
     "iopub.status.busy": "2024-04-30T09:12:56.447862Z",
     "iopub.status.idle": "2024-04-30T09:12:56.517283Z",
     "shell.execute_reply": "2024-04-30T09:12:56.516991Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Hamiltonian conservation (Verlet symplectic vs Euler symplectic)\")\n",
    "plt.plot(TV,Hamiltonian(QV,PV), TS,Hamiltonian(QS,PS) );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comparison with the Hamiltonian class**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.518822Z",
     "iopub.status.busy": "2024-04-30T09:12:56.518716Z",
     "iopub.status.idle": "2024-04-30T09:12:56.619637Z",
     "shell.execute_reply": "2024-04-30T09:12:56.619406Z"
    }
   },
   "outputs": [],
   "source": [
    "QS_,PS_,TS_ = Celestial.integrate(q,p,scheme=\"Euler-p\", niter=int(30*t),T=t,path=True)\n",
    "QV_,PV_,TV_ = Celestial.integrate(q,p,scheme=\"Verlet-p\",niter=int(30*t),T=t,path=True)\n",
    "for a,b in zip( (QS_,PS_,TS_,QV_,PV_,TV_), (QS,PS,TS,QV,PV,TV) ): assert norm_infinity(a-b)<1e-14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Symplectic Euler scheme - Non separable case\n",
    "\n",
    "We implement the general semi-implicit Symplectic Euler scheme using a Newton method for the implicit part.\n",
    "Our first step is to implement the Newton method.\n",
    "\n",
    "**Note on Newton versus Fixed point.**\n",
    "In the context of implicit schemes for geometric integration, fixed point iterations are often more computationally efficient than Newton iterations. We consider Newton iterations here for illustration of the AD library. The `Hamiltonian` class uses by default a fixed point solver for the implicit schemes.\n",
    "\n",
    "**Generic Newton solver.**\n",
    "A Newton solver is implemented in the `ad.Optimization` package, based on a similar approach using automatic , but with some additional flexibility. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.621084Z",
     "iopub.status.busy": "2024-04-30T09:12:56.620995Z",
     "iopub.status.idle": "2024-04-30T09:12:56.623016Z",
     "shell.execute_reply": "2024-04-30T09:12:56.622786Z"
    }
   },
   "outputs": [],
   "source": [
    "def NewtonSolve(F,p0,niter=5,*args):\n",
    "    p_ad = ad.Dense.identity(constant=p0.copy(),shape_free=(len(p0),))\n",
    "    for i in range(niter):\n",
    "        p_ad = p_ad+F(p_ad,*args).solve()\n",
    "    return p_ad.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We test it by solving $x+x^2=0$, with initial guess $x=0.5$. The solution $x=0$ is found."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.624447Z",
     "iopub.status.busy": "2024-04-30T09:12:56.624364Z",
     "iopub.status.idle": "2024-04-30T09:12:56.626893Z",
     "shell.execute_reply": "2024-04-30T09:12:56.626656Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.39659527e-16])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def FTest(x):\n",
    "    return x+x**2\n",
    "NewtonSolve(FTest,np.array([0.5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, compatibility issues may arise if the function called $F$ itself uses automatic differentiation in its definition. This is the case of our numerical schemes, which involve the partial derivatives of the Hamiltonian. We circumvent this potential problem by hiding the AD information in the element type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.628320Z",
     "iopub.status.busy": "2024-04-30T09:12:56.628237Z",
     "iopub.status.idle": "2024-04-30T09:12:56.630526Z",
     "shell.execute_reply": "2024-04-30T09:12:56.630314Z"
    }
   },
   "outputs": [],
   "source": [
    "def NewtonSolve_AD(F,p0,niter=5,*args):\n",
    "    d=len(p0)\n",
    "    def disac(x): return ad.disassociate(x,shape_free=(d,))\n",
    "    def assoc(x): return ad.associate(x)\n",
    "    p_ad = ad.Dense.identity(constant=p0.copy(),shape_free=(d,))\n",
    "    for i in range(niter):\n",
    "        p_ad = p_ad+assoc(F(disac(p_ad),*args)).solve()\n",
    "    return p_ad.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.631849Z",
     "iopub.status.busy": "2024-04-30T09:12:56.631768Z",
     "iopub.status.idle": "2024-04-30T09:12:56.634308Z",
     "shell.execute_reply": "2024-04-30T09:12:56.634071Z"
    }
   },
   "outputs": [],
   "source": [
    "def SymplecticEulerStep(q0,p0,H,dt):\n",
    "    d=len(q0)\n",
    "    \n",
    "    def F(p1):\n",
    "        # A potential issue is that p1 may have an additional singleton dimension,\n",
    "        # which is introduced in recursive AD techniques. So we must reshape q0 and p0 accordingly.\n",
    "        q0_,p0_= (a.reshape(p1.shape) for a in (q0,p0))    \n",
    "        \n",
    "        q0_ad = ad.Dense.identity(constant=q0_,shape_free=(d,))\n",
    "        q0_grad = H(q0_ad,p1).gradient()\n",
    "        return p1-p0_+dt*q0_grad\n",
    "    \n",
    "    p1 = NewtonSolve_AD(F,p0) # Implicit update of momentum\n",
    "    \n",
    "    p1_ad = ad.Dense.identity(constant=p1,shape_free=(d,))\n",
    "    p1_grad = H(q0,p1_ad).gradient()\n",
    "    q1=q0+dt*p1_grad # Explicit update of position\n",
    "    \n",
    "    return q1,p1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the Hamiltonian is separable, then the semi-implicit scheme coincides with the explicit scheme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.635748Z",
     "iopub.status.busy": "2024-04-30T09:12:56.635666Z",
     "iopub.status.idle": "2024-04-30T09:12:56.638864Z",
     "shell.execute_reply": "2024-04-30T09:12:56.638623Z"
    }
   },
   "outputs": [],
   "source": [
    "Hamiltonian = H_Celestial\n",
    "q,p = np.array([1.,0.]),np.array([0.3,0.7])\n",
    "qI,pI = SymplecticEulerStep(q,p,Hamiltonian,0.1) # Semi-implicit\n",
    "qE,pE = SymplecticEulerStep_Separable(q,p,Hamiltonian,0.1)\n",
    "for a,b in zip( (qI,pI), (qE,pE) ):\n",
    "    assert norm_infinity(a-b)<1e-14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, only the semi-implicit implementation is truly symplectic for general hamiltonians."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.640187Z",
     "iopub.status.busy": "2024-04-30T09:12:56.640110Z",
     "iopub.status.idle": "2024-04-30T09:12:56.643305Z",
     "shell.execute_reply": "2024-04-30T09:12:56.643051Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Semi-implicit : (array([0.98989795, 0.1       ]), array([-0.10102051,  1.        ]))\n",
      "Explicit      : (array([0.99, 0.1 ]), array([-0.1,  1. ]))\n"
     ]
    }
   ],
   "source": [
    "Hamiltonian = H_Log\n",
    "q,p = np.array([1.,0.]),np.array([0.,1.])\n",
    "print(\"Semi-implicit :\", SymplecticEulerStep(q,p,Hamiltonian,0.1))\n",
    "print(\"Explicit      :\", SymplecticEulerStep_Separable(q,p,Hamiltonian,0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.644582Z",
     "iopub.status.busy": "2024-04-30T09:12:56.644507Z",
     "iopub.status.idle": "2024-04-30T09:12:56.803233Z",
     "shell.execute_reply": "2024-04-30T09:12:56.803002Z"
    }
   },
   "outputs": [],
   "source": [
    "t = 20.\n",
    "QI,PI,TI = Geodesic(q,p,Hamiltonian,t,step=SymplecticEulerStep,n=int(10*t))\n",
    "QS,PS,TS = Geodesic(q,p,Hamiltonian,t,step=SymplecticEulerStep_Separable,n=int(10*t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "None of the two schemes is very accurate, since they are only first order. (In this specific example, one expects a closed geodesic.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.804652Z",
     "iopub.status.busy": "2024-04-30T09:12:56.804570Z",
     "iopub.status.idle": "2024-04-30T09:12:56.868988Z",
     "shell.execute_reply": "2024-04-30T09:12:56.868724Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axis('equal'); plt.title(\"Cone model (Euler symplectic, separable or non-separable)\")\n",
    "plt.plot(QI[0],QI[1], QS[0],QS[1] ); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The semi-implicit scheme almost perfectly conserves the Hamiltonian. This is in contrast with the explicit scheme which here makes the invalid assumption of separability. The goal is achieved."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.870546Z",
     "iopub.status.busy": "2024-04-30T09:12:56.870439Z",
     "iopub.status.idle": "2024-04-30T09:12:56.945345Z",
     "shell.execute_reply": "2024-04-30T09:12:56.945070Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Cone Hamiltonian, Euler alternating scheme\")\n",
    "plt.plot(TI,Hamiltonian(QI,PI), label=\"semi-implicit (symplectic)\")\n",
    "plt.plot(TS,Hamiltonian(QS,PS), label=\"explicit (non-symplectic)\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comparison with the Hamiltonian class**\n",
    "\n",
    "The default implementation of implicit schemes in the Hamiltonian class uses a fixed point solver. A small discrepancy is observed with the Newton method, due to the convergence tolerance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:56.946914Z",
     "iopub.status.busy": "2024-04-30T09:12:56.946805Z",
     "iopub.status.idle": "2024-04-30T09:12:56.999671Z",
     "shell.execute_reply": "2024-04-30T09:12:56.999399Z"
    }
   },
   "outputs": [],
   "source": [
    "QI_,PI_,TI_ = Log.integrate(q,p,scheme=\"Euler-p\", niter=int(10*t),T=t,path=True)\n",
    "for a,b in zip( (QI_,PI_,TI_), (QI,PI,TI) ): assert norm_infinity(a-b) < 1e-7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changing the stopping criterion of fixed point solver does improve concordance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.001106Z",
     "iopub.status.busy": "2024-04-30T09:12:57.001025Z",
     "iopub.status.idle": "2024-04-30T09:12:57.076062Z",
     "shell.execute_reply": "2024-04-30T09:12:57.075836Z"
    }
   },
   "outputs": [],
   "source": [
    "Log.impl_solver = lambda f,x : fixedpoint(f,x,tol=1e-14)\n",
    "QI_,PI_,TI_ = Log.integrate(q,p,scheme=\"Euler-p\", niter=int(10*t),T=t,path=True)\n",
    "for a,b in zip( (QI_,PI_,TI_), (QI,PI,TI) ): assert norm_infinity(a-b) < 1e-12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.077494Z",
     "iopub.status.busy": "2024-04-30T09:12:57.077411Z",
     "iopub.status.idle": "2024-04-30T09:12:57.079108Z",
     "shell.execute_reply": "2024-04-30T09:12:57.078893Z"
    }
   },
   "outputs": [],
   "source": [
    "scheme = Log.symplectic_schemes()[\"Euler-p\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.6 The symplectic form\n",
    "\n",
    "The symplectic form is a bilinear form on the space of positions of impulsions, defined as \n",
    "$$\n",
    "    B( (\\delta q,\\delta p), (\\delta q',\\delta p') ) = <\\delta q,\\delta p'> - <\\delta p, \\delta q'>.\n",
    "$$\n",
    "It is often denoted as $B = \\delta q \\wedge \\delta p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.080460Z",
     "iopub.status.busy": "2024-04-30T09:12:57.080377Z",
     "iopub.status.idle": "2024-04-30T09:12:57.082603Z",
     "shell.execute_reply": "2024-04-30T09:12:57.082372Z"
    }
   },
   "outputs": [],
   "source": [
    "def SymplecticForm(q_ad,p_ad):\n",
    "    \"\"\"\n",
    "    Returns the matrix of the symplectic 2-form, \n",
    "    in the considered first order perturbations.\n",
    "    \"\"\"\n",
    "    dp = p_ad.gradient()\n",
    "    dq = q_ad.gradient()\n",
    "    size_ad = p_ad.size_ad\n",
    "    return ad.array([[lp.dot_VV(dq[i],dp[j]) - lp.dot_VV(dp[i],dq[j])\n",
    "                     for i in range(size_ad)] for j in range(size_ad)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider canonical independent perturbations in the position and impulsion variables. \n",
    "The matrix of the symplectic form is a $2d\\times 2d$ antisymmetric matrix, with block form\n",
    "$$\n",
    "    \\begin{pmatrix}\n",
    "    0 & -I\\\\ I & 0\n",
    "    \\end{pmatrix}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.084006Z",
     "iopub.status.busy": "2024-04-30T09:12:57.083929Z",
     "iopub.status.idle": "2024-04-30T09:12:57.085788Z",
     "shell.execute_reply": "2024-04-30T09:12:57.085558Z"
    }
   },
   "outputs": [],
   "source": [
    "q,p = np.array([1.,0.]),np.array([0.,1.])\n",
    "q_ad,p_ad = ad.Dense.register( (q,p) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.087086Z",
     "iopub.status.busy": "2024-04-30T09:12:57.087013Z",
     "iopub.status.idle": "2024-04-30T09:12:57.089040Z",
     "shell.execute_reply": "2024-04-30T09:12:57.088806Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix of the symplectic form:\n",
      "[[ 0.  0. -1.  0.]\n",
      " [ 0.  0.  0. -1.]\n",
      " [ 1.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "mSymp = SymplecticForm(q_ad,p_ad)\n",
    "print(f\"Matrix of the symplectic form:\\n{mSymp}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We check that the form is preserved by our numerical schemes, by applying them to the `q_ad` and `p_ad` variables. Since their definition already involves automatic differentiation, we need to hide it using the associate and disassociate functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.090453Z",
     "iopub.status.busy": "2024-04-30T09:12:57.090375Z",
     "iopub.status.idle": "2024-04-30T09:12:57.092140Z",
     "shell.execute_reply": "2024-04-30T09:12:57.091920Z"
    }
   },
   "outputs": [],
   "source": [
    "d=len(q)\n",
    "def disac(x): return ad.disassociate(x,shape_free=(d,))\n",
    "def assoc(x): return ad.associate(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.093419Z",
     "iopub.status.busy": "2024-04-30T09:12:57.093338Z",
     "iopub.status.idle": "2024-04-30T09:12:57.095895Z",
     "shell.execute_reply": "2024-04-30T09:12:57.095677Z"
    }
   },
   "outputs": [],
   "source": [
    "qE_ad,pE_ad = (assoc(x) for x in SymplecticEulerStep_Separable(disac(q_ad),disac(p_ad),H_Celestial,0.1))\n",
    "assert norm_infinity(SymplecticForm(qE_ad,pE_ad)-mSymp) < 1e-14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.097161Z",
     "iopub.status.busy": "2024-04-30T09:12:57.097080Z",
     "iopub.status.idle": "2024-04-30T09:12:57.101520Z",
     "shell.execute_reply": "2024-04-30T09:12:57.101294Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[denseAD(array([0.98989795]),array([[ 0.96948553,  0.00206207,  0.10206207, -0.02041241]]))],\n",
       "        [denseAD(array([0.1]),array([[0.2       , 0.98989795, 0.        , 0.1       ]]))]],\n",
       "       dtype=object),\n",
       " array([[denseAD(array([-0.10102051]),array([[-0.10310363,  0.02062073,  1.02062073, -0.20412415]]))],\n",
       "        [denseAD(array([1.]),array([[ 0.        , -0.10102051,  0.        ,  1.        ]]))]],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scheme(disac(q_ad),disac(p_ad),0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.102926Z",
     "iopub.status.busy": "2024-04-30T09:12:57.102847Z",
     "iopub.status.idle": "2024-04-30T09:12:57.106801Z",
     "shell.execute_reply": "2024-04-30T09:12:57.106580Z"
    }
   },
   "outputs": [],
   "source": [
    "# Semi-implicit scheme for the H_Log hamiltonian\n",
    "qI_ad,pI_ad = (assoc(x) for x in scheme(disac(q_ad),disac(p_ad),0.1))\n",
    "assert norm_infinity(SymplecticForm(qI_ad,pI_ad) - mSymp) < 1e-14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Shooting geodesics\n",
    "\n",
    "Geodesic shooting is the process of adjusting the initial velocity or momentum of a geodesic, so that the endpoint at time $t=1$ meets a prescribed position. \n",
    "A natural strategy is to optimize the initial velocity using a Newton method, taking advantage of automatic differentiation to compute the jacobian matrix of the exponential map. Note that AD is also used, independently, to solve Hamilton's ODE, which involves the derivatives of the Hamiltonian.\n",
    "\n",
    "We use the Poincare Half-Plane model for illustration. It is particularly simple since, due to its hyperbolic nature, there exists a unique geodesic between any two given points.\n",
    "\n",
    "**Riemannian exponential map.** In Riemannian geometry, the exponential map associates to a position $q$ and velocity $v$ the endpoint $\\exp_x(v) := \\gamma_x^v(1)$ of the corresponding geodesic $\\gamma_x^v$. The inverse map is known as the logarithmic map. This terminology does not perfectly apply here since Hamilton's equations are written in terms of the Hamiltonian momentum, which is *dual* to the velocity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.108093Z",
     "iopub.status.busy": "2024-04-30T09:12:57.108015Z",
     "iopub.status.idle": "2024-04-30T09:12:57.109894Z",
     "shell.execute_reply": "2024-04-30T09:12:57.109665Z"
    }
   },
   "outputs": [],
   "source": [
    "def Shoot(q,p,*args,**kwargs):\n",
    "    Q,P,T = Geodesic(q,p,*args,**kwargs)\n",
    "    return np.take(Q,-1,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.111250Z",
     "iopub.status.busy": "2024-04-30T09:12:57.111165Z",
     "iopub.status.idle": "2024-04-30T09:12:57.114285Z",
     "shell.execute_reply": "2024-04-30T09:12:57.114056Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.7200162 , 1.27931064])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q0,p0=np.array([0,1]),np.array([1,1])\n",
    "Shoot(q0,p0,H_HalfPlane,1.,step=EulerStep,n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.115593Z",
     "iopub.status.busy": "2024-04-30T09:12:57.115514Z",
     "iopub.status.idle": "2024-04-30T09:12:57.117724Z",
     "shell.execute_reply": "2024-04-30T09:12:57.117507Z"
    }
   },
   "outputs": [],
   "source": [
    "def Aim(q1,q0,pGuess,*args,**kwargs):\n",
    "    if pGuess is None: pGuess=np.zeros(q0.shape)\n",
    "    def F(p): \n",
    "        nonlocal args,kwargs,q0,q1\n",
    "        # Reshape needed due to introduced trailing singleton \n",
    "        q0_,q1_ = (np.reshape(a,p.shape) for a in (q0,q1))\n",
    "        return Shoot(q0_,p,*args,**kwargs)-q1_\n",
    "    return NewtonSolve_AD(F,pGuess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.119050Z",
     "iopub.status.busy": "2024-04-30T09:12:57.118970Z",
     "iopub.status.idle": "2024-04-30T09:12:57.133777Z",
     "shell.execute_reply": "2024-04-30T09:12:57.133548Z"
    }
   },
   "outputs": [],
   "source": [
    "q1 = np.array([1.,1.])\n",
    "p01 = Aim(q1,q0,p0,H_HalfPlane,1.,step=EulerStep,n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-30T09:12:57.135178Z",
     "iopub.status.busy": "2024-04-30T09:12:57.135101Z",
     "iopub.status.idle": "2024-04-30T09:12:57.137454Z",
     "shell.execute_reply": "2024-04-30T09:12:57.137246Z"
    }
   },
   "outputs": [],
   "source": [
    "assert norm_infinity(Shoot(q0,p01,H_HalfPlane,1.,step=EulerStep,n=10) -q1) < 1e-15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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