diff --git a/docs/api/solvers/sde_solvers.md b/docs/api/solvers/sde_solvers.md index e307c195..9ec5b025 100644 --- a/docs/api/solvers/sde_solvers.md +++ b/docs/api/solvers/sde_solvers.md @@ -1,6 +1,9 @@ # SDE solvers -See also [How to choose a solver](../../usage/how-to-choose-a-solver.md#stochastic-differential-equations). +See also [How to choose a solver](../../usage/how-to-choose-a-solver.md#stochastic-differential-equations) +and [Advanced SDE example](../../examples/sde_example.ipynb) which gives a walkthrough of how to simulate SDEs +and how to perform optimisation with respect to SDE parameters. +For a table of all SDE solvers and their properties see [SDE solver table](../../devdocs/SDE_solver_table.md). !!! info "Term structure" diff --git a/docs/devdocs/SDE_solver_table.md b/docs/devdocs/SDE_solver_table.md new file mode 100644 index 00000000..1c12def2 --- /dev/null +++ b/docs/devdocs/SDE_solver_table.md @@ -0,0 +1,44 @@ +# SDE solver table + +For an explanation of the terms in the table, see [how to choose a solver](../usage/how-to-choose-a-solver.md#stochastic-differential-equations). + +``` ++----------------+-------+------------+------------------------------------+-------------------+----------------+------------------------------------------+ +| | SDE | Lévy | Strong/weak order (per noise type) | VF evaluations | Embedded error | Recommended for | +| | type | area +----------+--------------+----------+-------+-----------+ estimation | (and other notes) | +| | | | General | Commutative | Additive | Drift | Diffusion | | | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| Euler | Itô | BM only | 0.5/1.0 | 0.5/1.0 | 1.0/1.0 | 1 | 1 | No | Itô SDEs when a cheap solver is needed. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| Heun | Strat | BM only | 0.5/1.0 | 1.0/1.0 | 1.0/1.0 | 2 | 2 | Yes | Standard solver for Stratonovich SDEs. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| EulerHeun | Strat | BM only | 0.5/1.0 | 0.5/1.0 | 1.0/1.0 | 1 | 2 | No | Stratonovich SDEs with expensive drift. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| ItoMilstein | Itô | BM only | 0.5/1.0 | 1.0/1.0 | 1.0/1.0 | 1 | 1 | No | Better than Euler for Itô SDEs, but | +| | | | | | | | | | comuptes the derivative of diffusion VF. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| Stratonovich | Strat | BM only | 0.5/1.0 | 1.0/1.0 | 1.0/1.0 | 1 | 1 | No | For commutative Stratonovich SDEs when | +| Milstein | | | | | | | | | space-time Lévy area is not available. | +| | | | | | | | | | Computes derivative of diffusion VF. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| ReversibleHeun | Strat | BM only | 0.5/1.0 | 1.0/1.0 | 1.0/1.0 | 2 | 2 | Yes | When a reversible solver is needed. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| Midpoint | Strat | BM only | 0.5/1.0 | 1.0/1.0 | 1.0/1.0 | 2 | 2 | Yes | Usually Heun should be preferred. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| Ralston | Strat | BM only | 0.5/1.0 | 1.0/1.0 | 1.0/1.0 | 2 | 2 | Yes | Usually Heun should be preferred. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| ShARK | Strat | space-time | / | / | 1.5/2.0 | 2 | 2 | Yes | Additive noise SDEs. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| SRA1 | Strat | space-time | / | / | 1.5/2.0 | 2 | 2 | Yes | Only slightly worse than ShARK. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| SEA | Strat | space-time | / | / | 1.0/1.0 | 1 | 1 | No | Cheap solver for additive noise SDEs. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| SPaRK | Strat | space-time | 0.5/1.0 | 1.0/1.0 | 1.5/2.0 | 3 | 3 | Yes | General SDEs when embedded error | +| | | | | | | | | | estimation is needed. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| GeneralShARK | Strat | space-time | 0.5/1.0 | 1.0/1.0 | 1.5/2.0 | 2 | 3 | No | General SDEs when embedded error | +| | | | | | | | | | estimaiton is not needed. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +| SlowRK | Strat | space-time | 0.5/1.0 | 1.5/2.0 | 1.5/2.0 | 2 | 5 | No | Commutative noise SDEs. | ++----------------+-------+------------+----------+--------------+----------+-------+-----------+----------------+------------------------------------------+ +``` \ No newline at end of file diff --git a/docs/examples/sde_example.ipynb b/docs/examples/sde_example.ipynb new file mode 100644 index 00000000..f9c7fffc --- /dev/null +++ b/docs/examples/sde_example.ipynb @@ -0,0 +1,582 @@ +{ + "cells": [ + { + "cell_type": "code", + "id": "initial_id", + "metadata": { + "collapsed": true, + "ExecuteTime": { + "end_time": "2025-10-09T01:03:28.847571Z", + "start_time": "2025-10-09T01:03:28.174400Z" + } + }, + "source": [ + "%env JAX_PLATFORM_NAME=cuda\n", + "\n", + "from warnings import simplefilter\n", + "\n", + "\n", + "simplefilter(\"ignore\", category=FutureWarning)\n", + "\n", + "from functools import partial\n", + "\n", + "import diffrax\n", + "import equinox as eqx\n", + "import jax\n", + "import jax.numpy as jnp\n", + "import jax.random as jr\n", + "import matplotlib.pyplot as plt\n", + "import optax\n", + "from jaxtyping import Array\n", + "\n", + "\n", + "jax.config.update(\"jax_enable_x64\", True)\n", + "jnp.set_printoptions(precision=4, suppress=True)" + ], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "env: JAX_PLATFORM_NAME=cuda\n" + ] + } + ], + "execution_count": 1 + }, + { + "cell_type": "markdown", + "id": "86d4e8b062a81d7e", + "metadata": {}, + "source": [ + "# Advanced SDE example\n", + "\n", + "We will be simulating a Stratonovich SDE of the form:\n", + "\n", + "$$\n", + " dy(t) = f(y(t), t) dt + g(y(t), t) \\circ dw(t), \n", + "$$\n", + "\n", + "where $t \\in [0, T]$, $y(t) \\in \\mathbb{R}^e$, and $w$ is a standard Brownian motion on $\\mathbb{R}^d$. We refer to $f: \\mathbb{R}^e \\times [0, T] \\to \\mathbb{R}^e$ as the drift vector field and $g: \\mathbb{R}^e \\times [0, T] \\to \\mathbb{R}^{e \\times d}$ is the diffusion matrix field. The Stratonovich integral is denoted by $\\circ$.\n", + "\n", + "Our SDE will have the following drift and diffusion terms:\n", + "\n", + "\\begin{align*}\n", + " f(y(t), t) &= \\alpha - \\beta y(t), \\\\\n", + " g(y(t), t) &= \\gamma \\begin{bmatrix} \\Vert y(t) \\Vert_2 & 0 \\\\ 0 & y_1(t) \\\\ 0 & 10t \\end{bmatrix},\n", + "\\end{align*}\n", + "\n", + "where $\\alpha, \\gamma \\in \\mathbb{R}^3$ and $\\beta \\in \\mathbb{R}_{\\geq 0}$ are some parameters.\n", + "\n", + "Let's write the SDE in the form that Diffrax expects:" + ] + }, + { + "cell_type": "code", + "id": "ba23e9cc0370fbac", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:03:29.331509Z", + "start_time": "2025-10-09T01:03:28.853859Z" + } + }, + "source": [ + "# Drift VF (e = 3)\n", + "def f(t, y, args):\n", + " alpha, beta, gamma = args\n", + " beta = jnp.abs(beta)\n", + " assert alpha.shape == (3,)\n", + " return jnp.array(alpha - beta * y, dtype=y.dtype)\n", + "\n", + "\n", + "# Diffusion matrix field (e = 3, d = 2)\n", + "def g(t, y, args):\n", + " alpha, beta, gamma = args\n", + " assert gamma.shape == y.shape == (3,)\n", + " gamma = jnp.reshape(gamma, (3, 1))\n", + " out = gamma * jnp.array(\n", + " [[jnp.sqrt(jnp.sum(y**2)), 0.0], [0.0, 3 * y[0]], [0.0, 20 * t]], dtype=y.dtype\n", + " )\n", + " return out\n", + "\n", + "\n", + "# Initial condition\n", + "y0 = jnp.array([1.0, 1.0, 1.0])\n", + "\n", + "# Args\n", + "alpha = 0.5 * jnp.ones((3,))\n", + "beta = 1.0\n", + "gamma = jnp.ones((3,))\n", + "args = (alpha, beta, gamma)\n", + "\n", + "# Time domain\n", + "t0 = 0.0\n", + "t1 = 2.0\n", + "dt0 = 2**-9" + ], + "outputs": [], + "execution_count": 2 + }, + { + "cell_type": "markdown", + "id": "ef2ff90865907b7d", + "metadata": {}, + "source": [ + "## Brownian motion and its Levy area\n", + "\n", + "Different solvers require different information about the Brownian motion. For example, the `SPaRK` solver requires access to the space-time Levy area of the Brownian motion. The required Levy area for each solver is documented in the table at the end of this notebook, or can be checked via `solver.minimal_levy_area`.\n", + " \n", + "We will use the `VirtualBrownianTree` class to generate the Brownian motion and its Levy area." + ] + }, + { + "cell_type": "code", + "id": "4110735158215acc", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:03:29.483519Z", + "start_time": "2025-10-09T01:03:29.337297Z" + } + }, + "source": [ + "# check minimal levy area\n", + "solver = diffrax.SPaRK()\n", + "print(f\"Minimal levy area for SPaRK: {solver.minimal_levy_area}.\")\n", + "\n", + "# Brownian motion\n", + "key = jr.key(0)\n", + "bm_tol = 2**-13\n", + "bm_shape = (2,)\n", + "bm = diffrax.VirtualBrownianTree(\n", + " t0, t1, bm_tol, bm_shape, key, levy_area=diffrax.SpaceTimeLevyArea\n", + ")\n", + "\n", + "# Defining the terms of the SDE\n", + "ode_term = diffrax.ODETerm(f)\n", + "diffusion_term = diffrax.ControlTerm(g, bm) # Note that the BM is baked into the term\n", + "terms = diffrax.MultiTerm(ode_term, diffusion_term)" + ], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Minimal levy area for SPaRK: .\n" + ] + } + ], + "execution_count": 3 + }, + { + "cell_type": "markdown", + "id": "e71db03c5257bd46", + "metadata": {}, + "source": [ + "### Using `diffrax.diffeqsolve` to solve the SDE\n", + "\n", + "We will first use constant steps of size $h = 2^{-9}$ to solve the SDE. It is very important to have $h > \\mathtt{bm\\_tol}$, where $\\mathtt{bm\\_tol}$ is the tolerance of the Brownian motion. This is important because the output distribution of the VirtualBrownianTree is precise as long as the times that we sample it at are at least $\\mathtt{bm\\_tol}$ apart. For more details see the [Single-seed Brownian Motion paper](https://arxiv.org/abs/2405.06464).\n", + "\n", + " We will use the SPaRK solver to solve the SDE. SPaRK is a stochastic Runge-Kutta method that requires access to space-time Levy area." + ] + }, + { + "cell_type": "code", + "id": "8a969e1b9bd9f09", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:03:35.618860Z", + "start_time": "2025-10-09T01:03:29.493121Z" + } + }, + "source": [ + "sol = diffrax.diffeqsolve(\n", + " terms, diffrax.SPaRK(), t0, t1, dt0, y0, args, saveat=diffrax.SaveAt(steps=True)\n", + ")\n", + "\n", + "# Plotting the solution on ax1 and the BM on ax2\n", + "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 8))\n", + "ax1.plot(sol.ts, sol.ys[:, 0], label=\"y_1\")\n", + "ax1.plot(sol.ts, sol.ys[:, 1], label=\"y_2\")\n", + "ax1.plot(sol.ts, sol.ys[:, 2], label=\"y_3\")\n", + "ax1.set_title(\"SDE solution\")\n", + "ax1.legend()\n", + "\n", + "bm_vals = jax.vmap(lambda t: bm.evaluate(t0, t))(jnp.clip(sol.ts, t0, t1))\n", + "ax2.plot(sol.ts, bm_vals[:, 0], label=\"BM_1\")\n", + "ax2.plot(sol.ts, bm_vals[:, 1], label=\"BM_2\")\n", + "ax2.set_title(\"Brownian motion\")\n", + "\n", + "plt.show()" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "
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uXAl/f39+vLCwEN9++y0++eQTDB8+HL169cL333+P+Ph4HD582B1LJQiCINxFeT5wfR/787+fgX/eBnIuu3tVdUpKcYrD41wgZbN1YcyfPx/jx4/HyJEjBeMJCQnQ6/WC8djYWERHR+PQoUP1vUyCIAjCnaSfNm/vfAXY/yGwfrb71lOHcFWCz+c67lOklrMCQmvQ4odzP+DTE58iuSi5PpZoQ73ngPz88884ceIEjh07ZnMsIyMDSqUSfn5+gvHQ0FBkZGSIXk+r1UKrNfuCiooaRn5sQ+H333/Hl19+iVOnTkGr1aJz585YvHgxRo92TwtzgiAIpynJsh3LPAMwDCCR1P966giGYfDgjgchkUiQWpLqcC6XiVFRWYHfL/+Oa4XXMDB8IKJ9o+tjqQLq1QKRkpKCJ598Ej/99BPUanWtXHPJkiXQaDT8i1pcC9m/fz9uu+02bN26FQkJCRg2bBgmTJiAkydPuntpBEEQjtFaPBCq/czbxem1c/3yfCDN/d+FmWWZOJ55HMcybB+sQzxDBPuWLgy9kS0iqJAq6n6RItSrgEhISEBWVhZ69uwJuVwOuVyOffv24bPPPoNcLkdoaCh0Oh0KCgoE52VmZiIsLEz0mosWLUJhYSH/Sklx7D9qjKxevRqBgYECSwsATJo0CTNmzHB47rJly/D888+jT58+aNeuHd599120a9cOmzdvrsslEwRB1Bwu+6L7NODFG4DG9JRdUM3v+ZIsYOerwM3j7P7mJ4GvhwJnNtR4qTVBZ9DZPbZy1ErBvqULgxcQsmYgIEaMGIEzZ87g1KlT/Kt3796YNm0av61QKLB7927+nMTERCQnJ2PAgAGi11SpVPD19RW8XIJhAF2pe14M49QSp06dCoPBgE2bNvFjWVlZ2LJlCx588EGXPq7RaERxcTECAgKqnkwQBOFOOAGh8mF/+pkszIXVFBAJq4D4z4BvRgBlecD5P9nxrc/VaJk1pVRfavdYa01rwb5lFgYnPNxlgajXGAgfHx906dJFMObl5YXAwEB+fM6cOVi4cCECAgLg6+uLxx9/HAMGDED//v3rZlH6MuDd8Krn1QUvpQFKryqneXh44P7778f333+PqVOnAgDWrFmD6OhoDB061KW3/Oijj1BSUoK77767OismCIKoP6wFhKaGAiLvunn73Ebzdnle9a5XQxIyE/DWobcwMGKg0+dwLgxtpdkCoZQq62R9VdHgemEsXboUUqkUU6ZMgVarxejRo/HFF1+4e1luZ968eejTpw9SU1MRERGBVatWYdasWZC4EEi0du1avPHGG/jzzz8REhJS9QkEQRDuRFvC/lR6sz+9gtif5fmuX6vwJnB6rXn/+n7h8YpCQK1x/brVpFhXjFnbZwEArhZedfo8PojSUAG9wb0uDLcLiL179wr21Wo1li9fjuXLl9fPAhSerCXAHSg8nZ7ao0cPdOvWDatXr8aoUaNw7tw5bNnifE/4n3/+GXPnzsX69ett0mcJgiAaJFwQJWeBUJlc1BX2+0XYJXGbcD/liHA/7xoQ3sP161aTmdtnVuu8hhRE6XYB4XYkEqfcCA2BuXPnYtmyZUhNTcXIkSOdzjhZt24dHnzwQfz8888YP358Ha+SIAiiluAFhEk4cBaCimqk61sHKlpncvzxGPDQXsCiYVVdcjnffkGsezrcg9iAWPQJ62NzjAuiLKssg4ExAHCfC4OaaTUi7r//fty8eRMrV650Onhy7dq1eOCBB/Dxxx+jX79+yMjIQEZGBgoLq6HgCYIg6pMyU2yCpynomxcQLn5/5V4FdrzEbveYLj4n6zzwaTeng9trAlPFe/gqfXFX+7vQ0relzTEuiDI+LZ4faxZZGETN0Gg0mDJlCry9vTFp0iSnzvn6669RWVmJ+fPno0WLFvzrySefrNvFEgRB1JTSHPanZyD7U22yRFzdDWx/CTDFAFTJWougcU202aJhTXE6cHlX9dbqAsV6x83BPB24tzkLxMW8i/wYWSAIp0hNTcW0adOgUjlnZtu7dy9fItXytWrVqrpdKEEQzYOyPMBoqP3rMgxQlstuc8GTlkGOh5cDf86v+jqXdwG5V8z7XoGAd6h5/5aFwvmW5bPriMxSxx2mPeUOBITMtgijZbOt+oQERCMhPz8fGzduxN69ezF/vhP/aQiCIOqanMvAh22B3+fV/rW1RYApSJC3QPi0EM757xcgO5Hdzr0K/PU0m23BkXUR+Oku4TnhPQAfi8KELeKA+34x7+ck1s76HWBpPRDDkQWCc2FY4ko2Xm1CAqKR0KNHD8yaNQvvv/8+OnTowI937twZ3t7eoq+ffvrJjSsmCKLJc+QrgDEAZ39z/dz8G8Dmp4D0/8SPc9YHhReg8GC3A9sA7UYJ5x3/jv256Ql2e80U87ETq83bd64EnjoLRPQSWiB8I4EOY4Bu97P7OZeBojTn3SPVoKqGWTKJzO4xD7lHbS+n2lAWRiMhKSlJdHzr1q3Q68X/0ENDQ0XHCYIgagWZhe9dX26+0VvDMEDyYdYFkXWetQJ83pM9dvY3YJFIYahSk4DgrA8c964DTq5m3SZbnwVOrgEGPg7cOMAez77IWiMC2wDZF9ixO/4HxFnEQViuUxPJ/rzlKbZORPop4JOOwIAFwOh3nPktuExSUZLNWLRPNJKL2a6arlog3AUJiEZOy5a2UboEQRD1gr7MvL3lGdZqMOUbc90Gjn8/Av5527yvtDiuLQKKM4RuBQAoMwVQelkJCJkc6P0gYDQCh79g6zcs7Sycc+VvVkDk32D3/WOEx7nCVID5ff1bsYKIS/c89L86ExA3i2/ajIV4hmDxwMU4lnEMQyKH2D3XS9Fwyg6QC4MgCIKoHiUWwYCnfgIubQeWRAJFphoLhkrg0g6heAAAnVUWAueGsCT+f+xPawsEh1QK3L5MONZhHPvz0g5gsQbIM1V49Ld60Bq8EIi9HZi1xdwWXK4EAtoI5yX8wP688jdQkCy+DhfRG/W4WWIrIF7t/yr6hPXBY90fcxgU2SGgg91j9Q0JCIIgCKJ6WFogLPkklnVbnN0gTKG0RKYC+j7MbudcEh6r1JpdEpYZFNa0HgJM+RYIaA2MeB3o9wg7ftXckBHhPdg4B0u8Q4B7fwJibhGO950rtE5sfoIVImumsF07a4FzOedQaayEr9KcSvr96O/R2q+1g7PMhHmJd6Z2ByQgCIIgiOpRqbV/7Oo/bDCiPaL7A22Gsdu5Vr0gLJteeQY5XkPXu4AnTrJWhVa3ApF9hcfv+Ym1VjhDn7nAiynAqzls8KYlXFBnDeECKHuG9MTQyKGI9olG1+CuLl3j21HfIsI7AgDwXG/3dRKlGAiCIAiielRW2D+WfAhwVJ8gvAcbdwCYYxU4ci3KPN/xufPrkUiAbvcCN4+y+wMfBzQRzp8PmMSGFJj6va31xGgApPYzJJyBa93tr/bHGwPfgJExQubiNfu26IvtU7bXaB21AVkgCIIgiOrhyAKRdYHNzLCHZyDgG85uawvNZasBNoYBAHrOBEI7ubamYIsYAWvXhSu0Hw3c9pZwzJFFxUnKK9nfiafCExKJxGXx0JAgAUEQBEFUD2sLRJsRbEwCwAYdOhIYgW3NpakBYJWp0d+xb4CTP7Lb7ce4vqaQToCp3DM6jHX9fEv6zAUC25n3a6FgVlklGzfSkOo5VBcSEE2cAwcOYNCgQQgMDISHhwdiY2OxdOlSdy+LIIimgLVAGLMECDLdcEuybAXG9N+Bu74HBj1lKw6yzgM5V9h0UA7r7Aln8AwAHtwBzD9avfMtUXoCjx9n+2cArFumUuf4nCrgLBBNQUBQDEQTx8vLCwsWLEBcXBy8vLxw4MABPPzww/Dy8sJDDz3k7uURBNGYsRYIvhGAroTdLs0WZmk8uBOI7sdud7nTPN7lLjZbAwD+10t4Pe9qFsML71698+zxeALwdjC7nXsZCO3seL4DyvVNR0CQBaIRsHr1agQGBkKrFar9SZMmYcaMGQ7P7dGjB+677z507twZMTExmD59OkaPHo1///23LpdMEERzgLNA3PE5W1NB5W3KmpCwJa4LU9njYz8wiwdrJiyzf32PgNpcbfWRK83ZHTXs1snHQDhomNVYaPYCgmEYlOnL3PKqqic8x9SpU2EwGLBp0yZ+LCsrC1u2bMGDDz7o0uc9efIk4uPjMWSI/UpnBEEQTsFZINreZq6pIJOzbgQAKDSVqJY7KL+s8mHjFsRwNv2yPgjrwv489i1b46KaNKUYiGbvwiivLEe/tXaUcR1z5P4jDmuec3h4eOD+++/H999/j6lTpwIA1qxZg+joaAwdOtSp94qMjER2djYqKyuxePFizJ07tyZLJwiiuVGpA1bfwcYBTP8NaD0MMFayx6wFgsqHrZvA1U6o6mYp1kPj1udrvuba5Nbn2IqZhclsgGg14yuaUgxEA5J3hCPmzZuHnTt3IjWVNQmuWrUKs2bNcrqN67///ovjx49jxYoVWLZsGdatW1eXyyUIoqlxdTcrHgBg4yPCAEou64GDq+bIxUM4skAAgNiD1KAnq7fOusI3nK1dAQBpJ6p9Gcs0zsZOs7dAeMg9cOT+I257b2fp0aMHunXrhtWrV2PUqFE4d+4ctmzZ4vT5rVqxBVu6du2KzMxMLF68GPfdd5/LayYIoplSaNG/QSITBlBaCwSlVRVHa4FhjWVXTwCY+AUbT9HQCOoApJ20rZzpAk3JAtHsBYREImk0SnDu3LlYtmwZUlNTMXLkSERFRVXrOkaj0SYgkyAIwiH5SeZt72CzgJDKbaszWn+nKqoQEAaL1MhXcwCZotrLrFMC27I/D/0PuHmMFTrW3UKroCkJCHJhNCLuv/9+3Lx5EytXrnQ6eHL58uXYvHkzLl++jMuXL+Pbb7/FRx99hOnTp9fxagmCaBKc2QB8Nwa4edw8VlEIlBew29bWBrGxqtIxKwrN2w1VPADmKpfl+Wzn0b9fd/kSZXoKoiTcgEajwZQpU7BlyxZMmjTJqXOMRiMWLVqE69evQy6Xo02bNnj//ffx8MMP1+1iCYJoGvw2x3asohD4coBpRyQOy7KjpdoPCOno+D1Kc6q7uvolur9w/+SPwC1PA4FtxOdbYWSMqDCwlpvGYvl2BAmIRkZqaiqmTZsGlaqKoCQTjz/+OB5//PE6XhVBEM0KS4tBRYHtcUsLRG8nrKVljURAeIcAnSYC5/80j21fBEz71anTKyziRpqCBYJcGI2E/Px8bNy4EXv37sX8+fPdvRyCIAj7FGeYt52p2th9Gvuz3ai6WU9tcvdq4IUbwO3L2P3LO4ALfzl1KlcDQgIJ1LIq4kIaAfUqIL788kvExcXB19cXvr6+GDBgALZt28Yfr6iowPz58xEYGAhvb29MmTIFmZmZ9bnEBkuPHj0wa9YsvP/+++jQwdxtrnPnzvD29hZ9/fTTT25cMUEQjRqjEbi2t3rndpzA/mw/Fuh8p+O5ADD6HbYJF9eIq6Hj4Qf0ng30Nz3M/TINiP8cyDjj8DTLAEpnU/AbMvXqwoiMjMR7772Hdu3agWEY/PDDD5g4cSJOnjyJzp074+mnn8aWLVuwfv16aDQaLFiwAHfeeScOHjxYn8tskCQlJYmOb926FXq9XvRYaGg168gTBEGc+AH46ynb8ZjBQFIVpfDj7gEierGNtZy5USq9gK53VWuZbmXAY2z3UIMW2PkK4NMCWHjB7mc+kHoAgNkS0dipVwExYcIEwf4777yDL7/8EocPH0ZkZCS+/fZbrF27FsOHDwcAfP/99+jYsSMOHz6M/v37i12y2dOyZQ27zREEQYhxzI41oOfMqgWEVAoEt6/9NTU0NJHAnV8Dh5YDN48CxelAzmW7n/3dI+/W8wLrFrfFQBgMBvz8888oLS3FgAEDkJCQAL1ej5EjR/JzYmNjER0djUOHDrlrmQRBEM0TbZFwf+yHwOSvbTMRuPiF5krnScDcXUC0KSvFTpXKpMIkfruNxrmsjYZOvWdhnDlzBgMGDEBFRQW8vb2xceNGdOrUCadOnYJSqYSfn59gfmhoKDIyMsQvBkCr1QqKIhUVFdmdy+FsE6vmCv1+CKKZo68ACm6Y9yUyoO881jSvKzWPB3UAxn9c/+triATHsqW+cy4BSQeADXOAIc8Bfdi+Q79f/h0AEKAOwI/jfnTnSmuNerdAdOjQAadOncKRI0fw6KOPYubMmTh//ny1r7dkyRJoNBr+5ag6o0LBFigpK2sa/qe6Qqdjq8LJZLIqZhIE0SSxDgb0CjL79S3rF7S6VbwRVnOEKzL178fAqvFASQaw5Rkg6wJw/Huc/281AOCJHk/AR+njxoXWHvVugVAqlWjbli0H2qtXLxw7dgyffvop7rnnHuh0OhQUFAisEJmZmQgLC7N7vUWLFmHhwoX8flFRkV0RIZPJ4Ofnh6ysLACAp6dnk4iErU2MRiOys7Ph6ekJuZzKhBBEs0Rv9ZAVHGvetvzOtCxB3dxpPxrY/RagLxWOn/4ZFfGf4mx0BAApYgNjRU9vjLj9DsH1ZejVqxcUCgV2796NKVOmAAASExORnJyMAQMG2D1fpVI5XVQJAC9GOBFB2CKVShEdHU3iiiCaK5aNsgD7lSQN4hlgzZKA1sC8f4BvbwMgAVrfClzYDKQm4LhahVKpFGFQoGNAFVU5GxH1KiAWLVqEsWPHIjo6GsXFxVi7di327t2LHTt2QKPRYM6cOVi4cCECAgLg6+uLxx9/HAMGDKjVDAyJRIIWLVogJCTEbvpjc0epVEIqpRpjBNFs0ZcL9/1jhPv9HgUSVgGDn6mvFTUOQmKBRSnsdsYZ4MJmHM49h0fDQgAAMRIVpJKm891arwIiKysLDzzwANLT06HRaBAXF4cdO3bgtttuAwAsXboUUqkUU6ZMgVarxejRo/HFF1/UyVpkMhn5+AmCIMSoSkCMfQ8YubjqLpvNmaD2gESKT33MzcHUTUg8APUsIL791nGVMbVajeXLl2P58uX1tCKCIAjChkoLAREWB7QZbjuHxINj5CowAa1xVmWOE1FLmtZDa9OSQwRBEETN0ZtiILrcBTy8H5A7H2dGmCnpeLtgXybWubQRQwKCIAiCEMJZIBQezpWirmOMjFGwn1eRhx/O/YDc8lw3rcg58sK7CvaNDeB3WZuQgCAIgiCE6C0EhJtZHL8YvX7shb+umTtePr//eXx0/CMs3LvQwZnuJ0+mFOwb7cxrrJCAIAiCIIRwAkLu3jgHg9GA3y7/hkqmEjuSdvDjR9KPAABOZImXjW4oJBuFNSFIQBAEQRBNG64OhGXVSTeQUWa/jUFjYGvKXsG+sWl5MNxfSIogCIJoIBj0gERq4cJwrwXiRpG5H0e5aU0NPe7BkiuFVwT7Ta3NEAkIgiAIAqjUAcv7At4hgIc/O6Zyb8+GgooCfrtEXwIAGPrrUPcsxkUqjZXIKc8RjBkZg5tWUzeQgCAIgiDYyon519kXh0rjvvUAKLeoR1GiLxFYJBo6OeU5MDJGyCFFpSn6oa2kaaXDUgwEQRAEARhFSvu72QIhEBC6EuRV5NX7GoyMEd+d/Q6nsk45fc6htEN458g7AIBgr1D81Oo+zC4owjwE1NEq3QNZIAiCIAhAV2I7pvat/3VYYG2BKLcusQ3gasFVtPRtCbm0bm5nf137C0sTlgIAzsw8U8Vslod2PcRvh3qGIk7TGnH5BUBA0+q/RBYIgiAIAigvsB1rQBYIrUGLpKIkmzmT/pyEFadX1NkaEvMSa3R+qFcoIDP1w2hi3UtJQBAEQRBAeb7tmJsFRFllmWB/ydElovO++u+rOluDXsy1YweD0YBKY6VgLNQzFPAwuS4KU2pzaW6HXBgEQRCEHQtEw3FhVEWpvhReCq9aX4OzAsJgNOChXQ/hfO55wXi4dzgQ0ROABMhPAkqy2EyXJgBZIAiCIAhbC0SP6YCne4P+xGIeAGBMzBibsboKsLS2KNjjcPphHM04yqebcvQI6QGoNUBAK3Ygu2YukYYECQiCIAhCKCCCY4GJy923FhP2LBBilob8ChEXTC3grAUio1S8amYH/w7shn8M+7Og8aSiVgUJCIIgCEIoIAY96b51WGAdA8HhIbdt8lVXAsLSAsE4KCVZqi8VHZdJZeyGX0v2Z9510XmNERIQBEEQzZ2yPODSNnb71ueAbvfVydsYGaNNdUZHFOuKRcfVIk2+6sqFobfInNh4ZaPdeaWVtgLi59t/Nu+EdmZ/XtzSZGpak4AgCIJo7iSsMm/HDAYkddP16ZUDr2DYr8NwJP2Iw6d5DnsCwkvhhWXDlmFAiwHo16IfAKBQW1ira+WwdGG8Hv+63XlleqG1pJWmFToHdjYPdJ0KQAJkXwBKnRdRDRkSEARBEM0dyyJMddiBc/O1zQCAD499iLG/j8Ubh95wOL9IVwQAWDZsmWA82CMYI6JH4OtRX6OVLxucWKwXFxs1xZ4bxRprF4a/yl84wcMPgEk0fTuy5gtrAJCAIAiCaO5whY4AILxHnb9dYn4iUktSseHSBnz939eic4yMkc9oiAuKQ6A6kD8W5hXGb/so2VoVJWKVNGsBZy0blgLCV+mLRf0W2U7iXC/5SbWwMvdDAoIgCKK5ozPd/HpMB2T1Wx7o85Ofi46X6ctgZNgmVD5KH0HgpKWA8FZ6A4BN+mRtUKovRZG2SDBmMIp31ORcGK8PeB0H7j2A2IBY20kTPmN/isRwNEaokBRBEERzh/Pf10EhpurCxT8opAqoZCpzNgNM1R1NeCtMAqKWLRCfnfgMK8+stBkv0BYg0MNsDckszcT1out8EKWXwgsSezEkEb3Yn7Km0ZWTBARBEERzhyvYpLBNj6yXtzfqoZAqBGNc/IOP0gcSiYS3RgDCLAxeQNSyBUJMPHDrshQQY34bg0rGnOrpq3RQvZP7/eqdi6to6JALgyAIornDuTCUdWeBsGf6B4Cfzv9kM8ZZILgbsr2sDc6FYS9jo7bhhA2HpXgAAI1KY/9kTkAY9U2isRYJCIIgiOYOJyDqMAPDUV+LG8W21RmtBUSHgA6i5/JBlHUQA8HRMaAjv20dE2GNQwuEpUBrAlYIEhAEQRDNmTMbgLMb2O06cmEU64rx8oGXbcYX9loIAMguy7Y5dqOIFRWcQFjUdxFGx4zGD2N+EMzjXBj2KkHWBne1vwv9wvoJ1mUPhxYImRKQmG67dvp8NCbqVUAsWbIEffr0gY+PD0JCQjBp0iQkJgobi1RUVGD+/PkIDAyEt7c3pkyZgszMzPpcJkEQRPPhtznm7TpyYTy37zn8k/KPYMxL4YXWmtYAgKyyLMExhmHwccLHAMyFnEK9QvHRkI/QM7SnYC4nIBy5MLLLspFS5Hwrba1BK9hXy9W4lH8JAPD+sfcdnsutRxSJxByoqqs7wVNf1KuA2LdvH+bPn4/Dhw9j165d0Ov1GDVqFEpLzb/Ip59+Gps3b8b69euxb98+pKWl4c4776zPZRIEQTRP1H51ctmDaQdtxkI8QxDiyba1thYQBdoCfvti3kWH1+ZiIPRGvc2NH2DrSQxfPxzjNo5zOk7Cep5UIkXnoM428/QicQyW2SKi8IGUZIFwie3bt2PWrFno3LkzunXrhlWrViE5ORkJCQkAgMLCQnz77bf45JNPMHz4cPTq1Qvff/894uPjcfjw4fpcKkEQRNOiLA/YMAe48rf9OVzHSCcp0hVhzo45WHdxnd05Yu4JgBUQnLnf+oadVprGb/cO7e1wDV4KL0ggEb0OAFwtuGpeS7n4WqyxDpT0kHvgiR5PAABkErNAKDcIRcDL/WzdNDY0oUwMt8ZAFBayFb4CAtie8wkJCdDr9Rg50lzmMzY2FtHR0Th06JDoNbRaLYqKigQvgiAIwooDn7CxDmum2J/j39KlS645vwZHM47i3SPvih6PT4vH8PXDRY+FeITw8Q06o05gPUgrMQuIl/q95HANUomUb+8tFgfxX/Z//LbRaLQ5LoalEOkX1g+3RtyKUC+29oSBMfAZJeUWVoSX+r2Ee2PvrfrinJuIBET1MRqNeOqppzBo0CB06dIFAJCRkQGlUgk/Pz/B3NDQUGRkiPdaX7JkCTQaDf+Kioqq66UTBEE0PkqcePp2MYgytzyX345Pjcevib8iozSDT7l05H7wU/vxN34AWHfBbMU4nnEcAHBnuzv5G7cjuOuIFZO6Xmhun60z6qq8FmDOtOgY0BHfjP4GCplCUAmzwlAh+Okp98R9sU52MCUXRs2ZP38+zp49i59//rnqyQ5YtGgRCgsL+VdKivOBMgRBEM0GryDzdpmp9XV5vnnsqbMuX9LSJfDw3w/jrcNv4bYNt+H3y78DEI8R4PCUe0IqMd+CPk74GHqjHhmlGVh7cS0AYHDEYKfWwVkyrBtq6Y16/HDenLWhMzgnIDgLBHddAFDL1LyrhEtJrag0CQhX0l+5uU0giNItlSgXLFiAv/76C/v370dkZCQ/HhYWBp1Oh4KCAoEVIjMzE2FhYSJXAlQqFVSqplEWlCAIos4wWhQ8KskEPAOAm2z8GQJaA36uW2/t1V5YfGgxugV3c/jEr5QpbcZSilPw/L7n+f0oH+fWZK+c9dkcoSiybM3tCOsaFAAgkUiglqtRXlnOui48zEJCLXOhtwUnIMgC4RoMw2DBggXYuHEj/vnnH7Rq1UpwvFevXlAoFNi9ezc/lpiYiOTkZAwYMKA+l0oQBNG0KLCwzmpNT+pcQGVU/2pdssyBH//v5L8dWiCsS1cD7BN9Yr45tT/YM9ipddirRplZKiwB4KwFolDHxudZWiAA1moCmFt8Z5ax17csbV0lTSiIsl4tEPPnz8fatWvx559/wsfHh49r0Gg08PDwgEajwZw5c7Bw4UIEBATA19cXjz/+OAYMGID+/av3B04QBNHsKc0FEreY9ytMwebX97M/Y8dV67LcjVSM9NJ0QdyANZyAiPCOQGpJKgDgnr/uEczxU/k5tQ4fBXujtw6i5G7wHFUJiDJ9Gc7mnOU7hHLChIP7PJzl4WbxTQBApE8knIaCKKvHl19+icLCQgwdOhQtWrTgX7/88gs/Z+nSpbj99tsxZcoU3HrrrQgLC8Pvv/9en8skCIJoWmRaxTdw5ZiL2BsggtpX67JiFohhUcMAAEmFSTY37PGtx/PbnAvjx7E/2r2+ZYyEI7xMN2XrGAjrFNKqgigXxy/GnJ3mwlqWJawBwMNkPeCE080Sk4DwdkFANKEgynq1QNhrhmKJWq3G8uXLsXz58npYEUEQRDOgokC4ry0CdGVABWuqh494jFlViPW3mNFpBvak7EFeRR4iDeYb6667diHMKwwHUw+iQFuAAeGsWzrYMxhxQXH4L+c/wXUe6/aY0+vgLBDWMRD52nzBflUWiG1J2wT7I1uOFOxbWyC4bJH2/i4IsCYUREm9MAiCIJo6ZbnC/YoioMSUGq/wBFQOGkCZYBgGbxx6A71+7IX41Hj2slYujKVDlyJQzcYD5Fbk8jEQz/d5HmFerEjZeudWbLtzmyBAUiW3DYQf19p5twrnalh9fjXO5Zzjx7ksCQ5ngyg5rIMjLQVEfkU+koqSAAADwwc6f1HrIEonHqwbKiQgCIIgmjrWAkJbDBSls9s+LdgeDVVwLOMYNlzaAJ1Rh9cPvQ69QY9Ko7CVdZ+wPnxAYbGuGKWV7FO2SmYWCD5KH5uYAcvjlvOcxbL/xLyd8/htrk4Dx5env3RaRKhlakisfi+WAoKrgaFRaWxiJRxiGUT56wPAF/2BStsS3I0Bt6RxEgRBEPVEdiLwz9vCsfwkoNhCQDiBZXZEeWW5wPrwav9XoZAqoFFpYGSMkEvkqGQq+SwIsYwLSyzLQ3NolA66WlphKTYs4yC0VjfmjNIM/JP8D0bHjBa9ToA6AHkVbI0Ma/EBWAgIfTk/j7O4OA1XjyP/BpDMWnKQmgC0dMGK0UAgAUEQBNFUKc0RdtvsMw84thI486s5kNKJ+AeGYXCt8Bq/7yX3wurzqwEASqkSd3e4mz8mlUihUWmQW5HLN8kSq/lgiXUsxYYJG6puSmWBZUVLwXUNtjEaueW5MBgNOJ55HJ0DOwusB9YWFWu4NM5jGcfwwzm2QFWAOsDpdQIAIvuyPznxADRaNwa5MAiCIJoq6+4DMs6w212mACMXm49d2s7+rEJA/HDuB8StjsOGSxv4sbTSNHz939cAxDMbuBs611WzKgFhWRL7z0l/okNAB4fzrbF2d3C9KqwtEABb/GrT1U2Yu3Mu5u+ez48zDGO3MBYHZ4HYe3MvsspZceRSDQgACGpnbunNsWoccPO4a9dpAJCAIAiCaKrcPGrejh4AqER89b7hoqcWVehRaTDio+Mfufy2XGlnBuyTtVLqWEDkVOTw2601rV1+P8sYCAB8cKOYG6JEV4K/rv0FADiRdYIfL6ssg5Fx3GxLrK6FZbVKp5BIxLuebn/Rtes0AEhAEARBNAc4S8PUH4TjGtty0dnFWsQt3ompX4l3Qa4KztTPoZA5joEI9nCu4qQ9rIMYL+dfBmDOwnihzwv8sRJ9iSADhEv9FGsFbo2YgBALAK0SMQGhtxU7DR0SEARBEA2EgjIdbuQK6wOcTyvCnFXHcD6tqGYXD2W7HqPTRMDypifSA2P3hUwADE5nJNocsywGZQ/r5lLWgsKa9299H7dE3IJ149c5nGcPawsEV/+Bs0AMCB+A5/uwPTb239wvCNrMrWDdJ5fyL1X5PrUmIILa2Y41wsqUJCAIgiAaCH3f3Y0hH+5FaoE5+G/Gt0ew+2IWHv0pwfUL+pjcE8NfBQJMvYckEraRFodfS5vTPJQyyH3OwqvNUptj0ztOF+zr8gaiTCcMPrQWDF2DujpcZnv/9vhy5JfoEtTF4Tx7WFsguNgLLgZCLVfzN/rMskxcKbjCz82vyMe5nHOCeAgAmNx2ss371JqAiOhpO1ZJFgiCIAiimugqWR/88aQ8fiy3lA1SvJFbjSdUrtphp0nCcVOQIQDAw9/mNLlUCmXwLpvxuOA4QYyCoTwC2sxxuJYttJpYWiDu6XCPSxkV1UEhVWBo1FB+v6CiAAzD8BYIlUwFX4tiWZcLLvPb+RX52HhlI7/fJbALdt21C4sHLrZ5HzEBUVWAqCghnW3HSEAQBEEQ1cFgNKfyMQxwIjkf0785wo/JpFUXexLAMOZUTZVVUSbLYkoiRaSKteWQqbLMUyDFyRkn8ePYHwXiwFARCUCO8+lC94plOqRLfSJqwOfDP8ezvZ8FwFogssvNfTA85Z4YGW0uS20Z75CvzUdSYRK/7630RphXmGgfjlqzQIgFrjbCVE4SEARBEA2AUgs3gJFh8NnuyzhwxZydoJBJsOW/dGw9k+7cBbcsBExZEDYCwuC43kFSsTD2wUceALlUbnNTlUjY6/xxMlUwblntcVTMKOfWWwtw3TsLtAWIT2PrLHQJ7AJPhSfkUjna+rW1OSchMwFHMsxCzVEFTK6ZliViZbirRCkWE8KwLdcv21p+GiokIAiCIBoApVrzTb1Cb0RyntBlUaE3Yv7aE3jspxM4aCEsRGEY4Ph35n3rG98dn7I/h4inDhZohRaFYEVH0XlGbQgACGI2ALYRVr+wflg9djXCvcXTROuCYE82m+NKwRW8evBVAEDXYHP8hZi7YdPVTYJ9R2mZtWaBEKM8H1jWBfjpLrYyZSOABARBEEQDwFJA5JfpkJJnP+bhTGqh44tZ9r4I6mDrpugyBVh4ERgqLiCKdUIB4QlzoGVhmR4vdv8c2pwh0OWz5ZfzSoXFpFr7tcY3o79Bj5AejtdZy3DuEq4CJgCEe5kFTFUltQH7VS2BWoyBAIBJX9o/lnu1etesZ6iUNUEQRAOgRGsObDydUgC9wb5PvExnsHsMAFCQbN6e/pv4HF/7PTBK9EIB4WWMBcBWa+z25k7T6Fgo5VLoKo0orqiE3mCEQubeZ9IWXi0ggYQvYAUIXQzO3OwdWRRELRDSalogut8P/P2GuSuqJSVZtmMNELJAEARBNAAsLRCHr+U6mAmUaR3HMODGQfZnZB/ROg9VrqWSLa5k1GtQnnoPJLoIpOSV4fN/rgjmhfmqeeNGfpltSevqwDAMvtx7FfsvZVc92QqFTIFWmlaCsS6B5tTQqipiAmzKpz3E6llUKwaCQ2untkdJZvWvWY+QBYIgCKIBUGIhCooq2O37+kZjYvdwfLgjEQk38vnjZXoHFoiiNGDnK+x2zC3VWguXpaAv7I7Koh7YeT4Tx2/k27gqvFRy+HkokF+mR36pHiE+9m++zrLlTDre334RAJD0XtVFq6wZHDGYb/wVqA4UxEBYVsSUSqSipatdtkDUJAbCXvEoskAQBEEQVZGcW4biCr3AAsHRsYUP+rcORLdIP8F4uSMXxhlz0yv0nFmtNRVxMRBG8w3TWjwAgIdCCl8P9qZcXKG3OV4dDl11bH2pihbeZtfM2FZjBccsLRAB6gDRm/+A8AF2ry1mnaiRgAi3EyNSkAwYHfflaAiQgCAIgnATSTmluPXDPRjx8T6bYkwAEBvGZgS0DxVWWhQTGzw5phTMYS+bq086ycbLG7H7xm6UmbpS3t7FcWMrT6UcHgq2SFSVcRlOkpJv24LbFbhUTsC2QqVlDISP0gdag7lb5667duHX239Fe//2dq8tlUht2ndbl9F2iak/AH0ftg2oTI4HPmgF7FlS/WvXAyQgCIIg3MTfF1hfd1axFv/bc8XmeIdQtibBgDbCltHljlwYpaYneC/XGlSllqTitfjX8NTep2D0ZFuAR/gGODwn2EcFT6Ws6jU5wfaz6Yi/koOKGl5HICAU9gWEdYGrMK8wdAwUT1e15JOhn6BPWB9+P8gjqJorBeDfEhj3ARAmUuq7ogDY916DLjBFAoIgCMJNVHVv0Hiy7oGWgV5YNDYWagX7le3QAlFqCj50UkD8EJ+Ej3YkIrvUNmixd7TjGg4hvip4cAKiBhaI5NwyPLLmBO7/5ggsC27qDa6b8S0FhHWXT8s0zpa+5tTUfi36OX39XqG9MKCF2c3hKO3TaQSWEquU2xOra379OoIEBEEQhJtIK7RvrrcuXf3wkDZY+UBvAFW4C8pMRaa8qn4yNhgZvL7pHP635wq2nku2OR7o4Y9/nhli9/xQHzU8FPKq11QFlzLNpaUtKnpXyxph2fOid1hvwTFLAdHarzWWDV2GMTFj8NGtH7n0HoVacx0OiUgpcJex7F5q3Whr8xM1v34dQVkYBEEQbiKrWGv3WKiPbXCej5oLWBSxQFTqgDV3AvlJ7L5n1QKiqNwc+PjnmcuAn9X7KX3Q0tcb0QGeNpUxASDUV827MF7aeAbDYoPRQmObqVAVeRYpoFxDMYCtvulqYkekdyQmtJ6AQI9AhHiGCI6VV5oF2y3ht6CFdwuMaDnC5fV2C+kGnHf5NPv4hAK95wAyJWCstK1EaTQC0ob3vE8CgiAIwk0UltlmLoT6qpBbosOye20j9AO9WB9+dokWDMOYn35vxAN73wOS/mX3NVFOBVAWWAiIvIp8WN+rubLO/l5KUQER4qsS3PD/PJWGR4a0qfJ9rbHM8LDM5qiOBUIikeDdwe+KHksqSuK3LbM1XGVk9EgsHboUnQI7VfsaNtz+CfvzyNe2x/54BLhTZNzNkIAgCIJwEwXltqmRz4+Oxfi4FlArbFtgB5usErpKI4q1lfA1WSTwvTBdET1mAE600C60EBASmVAgGEu68fEEGg/xEtChPmpBAan3tl2EWi7FrEGuZX8UWAipIgvriraydjI7OOZ1nYcz2WfwQt8XanQdiUSCkS1HVj2xOgS1sx3775cGKSAank2EIAiimZBfyt4424aYg+jahXqLigcAUCtk8Faxz33ZDtwfGLjAqfcvsLj5S2TmNFKJPhQrRi3lLRweCvFbRYivSnDzB4DFm89DV2nEoau5TlsQLIWCpVulpjUhrBkUMQhHph3B3R3urtXr1iotuomPV9FB1R3Uu4DYv38/JkyYgPDwcEgkEvzxxx+C4wzD4LXXXkOLFi3g4eGBkSNH4vLly/W9TIIgiDqHswC8P6Ur1AopgrxV6BKucXhOkLfJjcEJCOuCQ1H9AKVzmQH2LBBv3focBrczZzBYipXHhppdFGqFDHqRgkcTPj+A+1Yexqt/nHUqO0Nr4Qax3H71z3NOfArXkEsbuOHdMwC4ezXQ8Q624RlHUar9c9xEvQuI0tJSdOvWDcuXLxc9/sEHH+Czzz7DihUrcOTIEXh5eWH06NGoqKio55USBEHUHXqDkS9f3TrIG38vHIIdTw2GVOo4qj8qgI3YT8oxWQys+ykMf9XpNfACQlIJheYUe7nskRjf5jbBvJ7R/gCAEB8Vnh3VAff2icLbk9geE+/dGWdz3URTVsX6hJu488t4GI2O81W1+oZfdbFe6TQRuOdHtuFZUAd27Oo/7l2TCPUuIMaOHYu3334bkydPtjnGMAyWLVuGV155BRMnTkRcXBxWr16NtLQ0G0sFQRBEY8by6d/XQ4FIf08EelddFrlNMOvuuJrNVotEhSmlUKYCXs0FWg12fg0m94PC9yQ/1i8iDnKrrppPjmyHF8bEYuuTrMB5b0ocpvdn6yj0bRWAr2f0svseF9KL8Pomx5YER7EOJ5Pz7R5rFnQ23Sv/egr4tDtQ4nqTsbqiQcVAXL9+HRkZGRg50hycotFo0K9fPxw6dEj0HK1Wi6KiIsGLIAiiocPFDviq5TY1HxwRG+aDYdKT0J/ewMYYcALCww+QuWae57IwJIoCfuzhwbE283zUCjw6tA2C7Agce0GWHD8evuHwuKXbwprJX8Q7PLfJM+hJINRUqTL/OvD3Yrcux5IGJSAyMti+6KGhoYLx0NBQ/pg1S5YsgUaj4V9RUa63riUIgqhvuABGf6+qW0xbMrZTML5XfojFuo/x1pc/oKTQFGio9nN5DRmFrGuYMZiDODsG2u8FYY9Ab9c+gzWOBATAWqebLUpP1p0R2Jbdzzzj3vVY0KAERHVYtGgRCgsL+VdKSoq7l0QQBFElnAXCr4qnd2s0xgJ+OyTrX3y34wi74xkofoIdsooqsOVMOrsjYddiKGuJQA/XrgPArmXCWbRVZGvUVqOuRktAK2DqKnY7/XSD6dTZoAREWFgYACAzM1MwnpmZyR+zRqVSwdfXV/AiCIJo6HDuA42ni0/vpVn85pPy3xGYfRQAYPSNcOkyey+ZfekSqUlAaEPtTXdIVS4MQJgyak1VFogSR70/mgsai+Zfu99w3zosaFAColWrVggLC8Pu3bv5saKiIhw5cgQDBtjv0U4QBNHY4G6oztx8BZzZINidJme/L88WeYrNtkuZ5U3ZZIEA4+JauNMt+kHEhvmgd0t/mzmr4pPsnl+VgBAt3d3csHRRHVzG/vxxMhtYeUM8RrCuqXcBUVJSglOnTuHUqVMA2MDJU6dOITk5GRKJBE899RTefvttbNq0CWfOnMEDDzyA8PBwTJo0qb6XShAEUWfkmso3B7oYA4H4z0SHTxZU3YPCYGT4ugxppviH1sFe8DOVjWCM1RMQgNmN8dakLvhwqm0xpGV/X8Zli6ZZllhnYajkwlsTWSAASCTAAoseGRWFQP4NNrDSTdR7RY3jx49j2LBh/P7ChQsBADNnzsSqVavw/PPPo7S0FA899BAKCgpwyy23YPv27VCrXeyoQhAE0YDJMRVnChZpmmWXcvspjVqln8NTP999GR/vugQA+OeZIXwA5f19o3GsxAvxWUDH0ADn12LFrqdvRXJeGbpF+YFhGMzo39Im+2JVfBLemdxVMKarNOJadqlgzNoiUUIWCJagtoBHAFCeBxSkADpTKq/K2/F5dUS9C4ihQ4c6jKiVSCR488038eabb9bjqgiCIOqXnBJWQAS5ksGw8VG7h1LLhF/nDMPglT/OwketwAtjOvDiAQBW/nud72Hh76lEACRAFnBHtxjn12KFv5eSzyiRSCR4a1IX6CqN+OW4ObBdJbct0f3Xf2mi1+saocGZVDZFdfq3R3D5nbFQyBqU1909aCJZAVF4E9CaLDoqH7cshf41CIIg6oCsYsfVc3NK2Bu4SxkMDszVScUSQcXHxMxi/HQkGSv2XcW5tCIABsh9T0IiL8C6o8m4kM7efDQeclwtuAoA8FK43orbEe/fFYcP7jJXqlTKbW85lgW1LPl+dh/B/vGkZl5QisMvmv1ZcAPQm8qPK0lAEARBNAlWHbyOvu/sxho7BZQYhkFqQTkAIMTHSfesQQ/ksjd6jHrH5nBepQqZFqLlcmYJv33nl/FQ+B2DR8Qv8Gq9DIDZAvJv9s+4kHcBAKCS1SwdUxQLg7OY9dlelesgbxXGdjFn36nsNPRqdnDZGFkXzGNucmHQvwhBEEQts3jzeQDAK3+cFT1+M78ceaU6KGQStAt18su/NBsw6gGJDPANtzlcAg/czC/n969kmQWErtIImRcrPiQyoWXk96Rv+W2PWrZAAEBclLk5WJFVLAPDMPj8H/vNEsfHteC3DVX002gO6A1GZEiC2J2E7wEABokcGaXu+d2QgCAIgqhDxJ6695lqMHRq4Wu3dTfPrteBX2YAZaaKkx7+EDzWmyhh1MgrNddasNwGAMZgmeYpnjYZ7mUrTGpKbJgvxnVlLQlFVu6KQ9dybdqBA2xmCADcHmdej66KVM/mwCM/JuD1/SWCMRlTae6LUs+QgCAIgqhFKqyqKlpnImw9k85bJrpF+VV9wYPLgAubgBW3sPse/ubeCBaUwkMgGvLLrAWE2VUikbPxD94qYeBlS9+WVa+nGoyIZQtUFVUIxcLFdPG0zp/m9uO3O4ezxQF1BtcExPGkPEEb8saOwchg98Us7DN2Q65cWPDLR+2eFuUkIAiCIGoR67iHTyyyHwBgX6K5AuSgtkGOLyaWsebhDwS3B2ZvAyZ/zQ+XQcULCIORwV//sWWqQ0xpooEWcXYSGevqGNVJeCPSqDSoC7xMQuXfyzk4lVLAj1sGULYMNFtIWmjMrhQu8FLvggXiwOUc3LXiEG7//N/qLrnBUWwSXxVQ4b3wz4FBT0LHyPFj5Uj4qqtfv6MmuEe2EARB2CP1BHuTDGjl2nkVRYBE6raAMo6TFjdIwLbSZEo+Gzl/X99omxu4DQaRDAUuZa/lQCCaAW4cxIEMGXBNgl+OpWD+sLZYb5E6+cFdcRjaIQQvH4jHJlMMpkTKxkEEaEoAU0jEd6O/c+4DVgMvldlNM2n5QSS9Nx4AkFZgjtkY0j4YA1oHolO4sB0Bl7rpigVi48lUAEBmUdOxQFi6etKNfqgcvhjtd/cFIMEJV6uZ1hJkgSAIouFw4S9g5TDgy0FA1kXzuK4USP9PvInQhc3ADxOA96KA5X2B4kzbOfXIzTxWINzZk+1NYR2LkGxx3LIEtCgGkRugxOJrWyIB7vgMlzs/wV87u1iLSxYZGJ5K9jlx09VN5vOk7HWLpKcBAH3C+qBPmDBtsjbh1mDNjdwyfltvMGJs1xZoGeglmKM0CQi9CwIit7TpCAeOAgtrTX6ZzlSdk/37IRcGQRDEuY3sT30psP1FIPMcu//LDOCrwcCmBWzd/3X3Awk/AL/OBH6ZDlzfz84rSgVOr6vzZeaX6vDkzydx9HoeACAxoxhJOWw1RS49c0pPNt2uuKISeoMRFXoD8kt1/FN3dIATvSsqRRpQDXrSZmhKL3OjpfirOcizuIH2aumPK/lXBPPv7hOM2+NaIB+sgBgSOaTqtdQASwsEYA4sTco1V6DUVYpnEphdGM5nGuSW2G/c1VixdPcUlOlRVM5mtHgqZW4rsEUuDIIgGg6ZFmmP1/YAXw4EZCrzk/ipn9gXACRuEb9G4lb2JlvV030NePH3/7DjXCb+PJWG/c8Nw4T/HYDeYMTk7hF8gajYMB9IJWydg7xSHaZ8Gc+nWXopZXxsgkOsLRBjPwBaDbaZ5qtWYP6wNli+5yp+OpLMl4JeMb0nZFIJcityBfN7t/bElDE9Mea3ZABAt2Db3hW1iZeVBUJnMKJCb0SWRZDj/GFtRM9VyCT8Oc6SauEaaSpYdjPNLtEiz7TvrvgHgCwQBEE0FPKuA9mJ7LZlZT0xM741t70JdJzAbqccAd6LBpIO1v4aTRy4nMNv/3g4CbpKIxgG+N3keweAAC8l/Eytuo8l5QlqNLQO9q7afQEAlVbVLL1D7E6d0T8GUglw9HoeTpviMFoFsfEgJTphml+pvhQMwyC3nBUWQR5VBHPWEE+l0AIxeul+fPvvNQBAhJ8HLr8zFq2DxWNX+BgIJ4MojUZG4DZasvUCtp5Jr86yGxSWDcV0lUZsO8t+pgBXm7HVImSBIJocxbpivHbwNQyPHo4JbSa4ezmEs/z9OgAGiOrPFko697vweL9HgfDuQFke4B/DFtLpMA7ociegNmUPxH8O7HwF0BYBfzwCPHEKkDqus8AwjHM3cxOVBiNKdeZUzZX/2paXHtslDBKJBCE+bGbEjnPCuIxWQV4254i/mZUpnitjLEKYRo0e0f5IuMGWfJZIzJkNxXphumSpvhSl+lJUGFiBEugR6Nx6qomXVbpoUm4ZPvuHdat0CPNxaILnXRhOWiC4GBOOr/azQoUL3GyslGmF6cHfH0gCAPRvXbf/do4gAUE0Gop1xTiecRy3RN4ChdS+2W7lfyvxd/Lf+Dv5b9ze+naXbg6EmyhKB87/yW4PehII6cg+fbccBOx5B4gZDAx6QliBMXac7XUGPs7O/WYkUJAM/L2YtU6I/A2Uaivx5ubz+PtCJhbf0Rnju7aAVFr138rFDPHaBfzxt8bw7ajD/TxwMaMYh68JXQhcoaQqsba+aOwLCABoH+rNC4hukX58kSprC0SBtoB3a3gpvOAhr/0KlJZYt+e2xLeKAEBXgiiziisw9KO9oscKy/U2GTGu4qrYrE3KdEIBwbl02oa4L+uIXBhEo8DIGDF7+2w8secJ/Jr4q8O553PP89txq+Nwo0i8HwHRgNi0wLzdegibwnnfOmDgAmDRTWDar6Llm0UJ7w6MXMxux38GvBkInPxJMCUxoxgD3/sHvxxPQW6pDo+vO4kv9l4RNKMSo0JvwO2fHwDApmd6WZnmA7yUUCtk/E0m3I8t3mRd0Mieud4GawuEl2NXQxuL63JZIAArvgFALmFv1tcKryGnnHXDBKrr/gnW0U1XrEOnJeY0zqqDKN/bdtHuses5pXaPOYJhGPx05AYWbzqHrot34lhSXrWuU1PKdOItza0DVOsTEhBEjckqy3LYor022JOyB4n5rH98T/IewbF9KfuQUmzOe08qShIc//DYh3W6NqKG/PM2cOVv877S6um8CheEKAPmAx3vYLcZA/DnY8B/6wGwImD0sv02XSA/2nkJfd/djYNXcqyvxrP7Qha/HRXggX+eHYozi0ch6b3xWDOnH7Y8cYtgfudw8cJM/VoFOPc5LC0Qs7dVGRhq+X6cmySjNANfnP4CANAjtAcA4HD6YcSnxQOoe/dFVVTVJItzYTgTA5HowDqUWeS4O6o9Np5Mxcsbz2JVfBJKtJX4at/Val2npnAWCGvRah2gWp+QgCBqxOarmzFi/Qh8fvLzOnsPvVGPp/Y8xe8fyzyGpQlLcc9f9+CPK39gwT8LMO73cVgcvxjfnf0OmWWsv3l+9/kAgH039/HtiokGhrYE2G8WeBXjP6ud60okbHyEJXveBhgGvxxLET8HbIfKad8cQcIN26fMSoMRy/42V5Us1RoQ6quGjykK/pZ2QYIKigAwtVck/D1tzeahvlV04Pz3Y+Db0eb+F6Fd2cJRVdAj2o/f5gTE9uvb+bGhkUP57a//Y6tY1nUAJUekv7ibxJF7AzBbIKpyYRSW601ty8Upt3IBOMs/F7ME+yeTC9xSIpsTEFFW6b+eZIEgGiNFuiK8dOAlAMDKMyux+ermWn+PisoKvHXoLcGYkTHiu7Pf4Xzuebx68FV+/LfLv2FpwlIAQCtNKzzS7RH0Cu0FAHy74qZAbnmuwOLCMAxOZJ5Amb7MwVkNlOv7BLtf36jFZk5B7YT7+UlASSbO27nJtLPwJR9PysfexCx8sjMRp1IKsGLfVaxPuInLFh0uh7QPrnIJcpkUuxYOwaKxsZjePxptQ7yx4ZEBVa9995tAymHg0BemCzkXaa9WyLB2bj98Oa0nIv09sSd5Dz5O+BgA+3/i/o7325wToHbSGlJD1s7tLzpelQtDaUrjrEpAVNVQyjqGwFmsU0JzS3WYuiK+WteqCZwLwzrmwV6RrvqAgigJpziZdRJP73kafcL64OG4h9HWvy2e2/ecYM5LB15CgbYAMzrNqNZ7xKfG49n9z+LJHk8irTQNiXmJOJF1AuWV7H/gMTFjcGvkrbxoccSAFuyXdKR3JBIyE3Ct4Fq11tTQSClOwZRNU8AwDNZPWI8YTQw+O/kZvjnzDToFdsLP439uPEGjhkoYzm0Cd/u4yQThuzM6zLpdXzu57aFd2JfaD8i9DJRkQnvyF+y60AkA8NbEzlDIpHjx9zMYHhuC72b1wZM/n8SuU9cQlfgdFm7rgjz48tkCAOCNMiyLOYKMVpMwcUh7p5YR5K3Cw0PEaxxUSZ7p71bmRM0IEwMt+ms8secJfvuONndALpWjlaYVrheaM0fqywIRHSheOMtZC0RVLoySCvEYAQ57MQRVIXbdpNz6F+ucAOoSoeH7nAC2Lo36hCwQRJXsv7kfD2x7ALkVudietB13broTp7JO8T5USz449gHu3nw3MkozqrzuD+d+wP9O/g9Ghv1iePjvh1GsK8bbR97Gd2e/w8G0g7x4AIDuId1xe+vb0TmwMwDYjRxv798ec7rOAQBEeLOBZCvPrITWmXoCDZz9N/ejvLIcFYYKbLq6CT+c+wHfnPkGABs8ej7vfBVXcD8nk/Nx79eHUPztBMjO/AwAeF72HOZ4f4ECLbDjbNV/O9YwDIPF8YuxLGGZeVChBh45AMzeAoSx3StV/7yG/NIKhGvUmNo7Cnf3jsJvjw7AVzNYS9WgtkF4Rf4jxqX9D18ql2Go9CR8wQbf3SI9g7PquRiZsRLTsz6Gj1LGVso0Vu/J1ilKTeZzJy0QjvBT+QEA/jf8f4LxRhMDUYUF4mxaocPj1XVhNBS49Uf5ewpKV3uqyAJBNGBWn18t2GfAYMY2s5Xhm1Hf4GjGUd6neiHvAp745wn8OsGcLbHu4jpkl2VjQY8FkEqkyCjNwEfHPwIAGBgD7u1wr8M1PNDpAUxuOxkSiQSrx67GobRDGBgxEEmFSfgn+R9M7zQdxbpihHqGQlKaDfz+KBB7O3pE9OCvkVKUgrb+bWv8+3Anlk+OK8+stDl+MPUgL7AaKpO/iIc/iuCjNgtQr85jMdrHB4m7L+Pn04fRrz2DaN9oMAwDbaUR13NKYTAy6BJhG5RoZIy4nH8Zv13+DQAwvdN0/qk6q1iLNzafh3f6ULwPNlBzpPQEhoX5QZ1wGfAMRK+ud/HBiZ1beKOznA3S7Se9iH7Ki9ht6IHH9E9ijXKJ+U2v/gO86c9u3/E/oGf1rG6iiAUke1XtLqkKfzW73nBvoZuoPrIwHOFsFoa+iiyMD7Ynio53i/LD6ZQClOnrT0CcTS1EVIBnjdNGLSk1WVA8VTIEe6tQbLKMkAWCaLDklufiWMYxAMDCXgvRPbi74Pjd7e9Gvxb98Ei3RwTjF/Iu4K1Db2FP8h6UV5bj3SPvYuWZlfjzCpvrfyjtED/3mzPfYOSGkfy+TCLD832e5+MXAOC5Ps/BU8GaQJUyJYZEDYFCqkA7/3Z4uNvD8FJ4IcyLLd6DHS+xUf1/PYX+O99BoJK96XDBlY2ZpMIkh8cPpB6on4UA7I3uwma2L0XaKadO4Z6ipsjMbZZ/MwzGoNhITOweDokiD5fkb2LiH5NhZIx4+pdTiH11O8Z++i9u//wA4q/aZkh8cOwD3LX5Ln5/6b87UKKtxLGkPAz5cC+2nEnHL7mtscvA/j2tVH6C+2+8Bmx/Afh9LpC4jT3RUIlO38faXH+E7CS+Vnxi/0MdsxVyNcIg0sch2HZdrhLuxQoHuVQOH4W50md9uTDsUaULw4l23pUi1olXxnfE2nn9MNjk0qltC4S9lN8j13Jx++cHMOXL2o2TKOezMOR8fQ8A8CABQTQ0SnQlmLdzHob+OhRGxojOgZ0xu8ts/DjuRzzW/TEAgEqmwjO9nwEAKKQKPN/necE1fr30K57Y8wQ2Xt7Ij/2byt44/rjyh+j7vnvLu/j33n8xo9MMPN/necilckzvOB3QVwCbnwS+GgJc3QNUatnSxwDbxtlQCTAMKsqKUXhup/mC1/cjpDgbALBg9wKRd2xYMAzDp8QaRL6g0nLOiZ4XVsk+jVzMPlN3i7OkUgu84cc2skrcAnx7m+P5ps816/ujkMKIufKtAIDTxtZ4A/MwoE0g2gR7o2cHVuRVMjpczL2KP06lCS6zIeGm6XLm381PF4Q1Hn49dQZdXt+BqSsOoVxvQLCp58QRo52b8DbT321qAiSm0tEnjUJL1RDZfwAAfZvbwHVA5Ek/bS7BXRuIBcMGd6jWpTzlrOiO8I5AbID58/uqzC2zG7oLQ+VEO2+tiLi4s2ckBrYJ4m+wpdrqxUBU2hEK2+y42n4/wZYzv5LlOKjTVXgLhFImiOeoyoJTl5ALowlwKusUrhVew4TWE1CiL4FGpYFUUjNtuOHSBhxOP8zvj4IX8HEsENwBjw58HOMn/YUw7xZQypTszV2uwoxOM+Cv9kdKUQqfdw4Iv+B33diF2dtn40TWCdH3nRAQByi8AaMRndSh+HfyNnik/Qd82Abgqun9OMl8QvQAINlszVCbXgCwSD8HL3r8icjKSlxQKVHJVEJv1DusYlkVDMPgRHIBALbLoasYjQyKtZV4f+s5pBfpMLF7BCZ2D0dReSXmrT6OE8n5gi+sIe2D0TVYikcy3wAT0hkZ+mJAIkGEvhKt9Xq8lJuHTd7emFhSgjFREShnKlF57Bv2P7bCC0g9DvSZy1Z2dH2xZoEw8AlhRceLfwnnGnTA6Z/ZMtOZ59iCR5pIVmhc3wdc3gkJgEDdE9ig3IowST7yGW8sDvoEX42P40sdR4UV45KpncQdX/8CoIfgbX4/kYp20Tn4+cZbeLrnMzh0OsZm2RKpMN//u5l9oFZI8fwPOqDMQmzc+hybQlqYwrokfryTP9R29lf47+JJxB151jw/LA6KGRvYolRHv2KFA8fyvsBixz54p9GLNILyqV52iqfCE2WVZVg6dKkguFYmMd903OHCkEsl/N95lS4MedVZGJYBlo8MaYNHh7SBxpQ+y/XhqK4Lw57lYv7aExjbZZxN9dKiCr3o/JrCBVF6KmWC1t7uhARENSjXGZBVXIFIf0/InCh9W1cYGSM+P/k5H0T3evzr/LEPh3yIMTFjqnXdzNJMPvULAMaqI3DXid/YtoLF6cC1vYgObAtoooDUBLbvQEgnIKgdbu8/H5BVoKzTTKw6/wMAILk4WXD945nHAQBBUm8MN0bjV7CBfyu94oBP4wAABqkSMqMOVdbrsxAPlqysHId1hhG4WBqNZXgLu7zYJ7G0ohS09Gvt6q+EZ82RZLz6B9sxcu4trbBwVHvIpBIwDLD5dBr2JmbjmVHtkVZQgZX/XsObEzsjOsATx5Ly0SHUBy//cQZ+51bjNfkaPKFfgKcS+2Dx5nMoKBP/Qth3KRsRV3fDW7Ef2ekHoI+OhJQBvvQcheT0bPzKhKF/xRX4TZwDnHgFAFC67TlojBZftse/Y7s4thkO+EawwYXOkHvF3PEy/jP21aIbMOBx1vRvzcaHq7zkF0pznYdTUQ9g3cxbBeZYtdJsvpcq2RoId/aMwEd3dcPQj/YiOa8MX5x/BZCV4tX4l6HL6w+lVRaiRGa+AT86tA26RPhCIpFg4/OTgYtK4GdTKuPgZ801KH6cbL5An3nwadUbca16A75lwK7X2PFbTVlHPaaxr6v/CM/TFgMqiyZg1UUnYoHwrl4MBBeEzLn/OCqN5idYtdzJv4da4OVxHfHlvqtYMb0X7v6K/b9bVXaFM1kYlhaIZ0a1F/TW4AREdV0Y5Q6Ex4r9V/HYULO1qkJvEFgmaqv0NcMwFgJCjgcGxOCz3ZcxqlNoja9dE0hAOAPDwKgrh0RbgE+PluCrfddQrjegdbAXHujfEt19ihCZ8CqYqKHY7TMFYX4eyC3RoV2oNzqE+dSqianSWInD6Yfx6N+POpz33L7ncCz9GGZ3ehQhXgF8JDPDMNiTvAfZuSG4ninHyeR8DG4XhNvjwnE9txhnS37H12e/5K8zO7U1Fur22r5B7hX2xZF1nn2Z+hlMlvphVUuzmdRf5om3/XvjpaJTKNQVQcJI8UJGEkaXnscYtQrtdXpojGahITMK/cAVjAIzdS/iKNMB82V/4i7ZfiQyUTBAipHSBNzwH4DLuToUM55oGxuHeyc9j3fe3o+TTDusKb8bHbT/IFGlRNLRL9By1EfO/roFMAyD7w6YgxjXHLgI6aHP0FKShVWG0bjMRAIALqQX4ZqpbO6QD/diWr9o/HQkGWG+amQUVeCyajUUEgO+Vi5FTMVaeJWl4Un5VhQw3ogavQCXSjygNxjhoZAhv6QC95/ZhZeDAqAyme2VlWoMuziKX8dnGIE7zoZDJVVAa9SjxMMXmtICi4Ubga3skzTjEYC88SsR2MUcc2KXjP9sx9JPC8XD/b8CkX2A78cC2ReBoPZswaPCVKAsB/AMRJFve+w/loDbZUf4084Fjsaw2W8CMuH/jVK92ewrVeThg7viMLlHBKRSCTY/fgsmfH4A+TJzSWJlwGFYE+oHbHtstE0DJwBA7Hhgzt+AZwArpEa8xtZcsMTSXdDtPiD+f0B4D6DTHcJ50VaFnVKOAG2d+L1WhZgLw8t+F057MAxjFhBy+wKiPpl3a2vMHdxKcFN11EgLMPfCcOzCMFdptL4eVyehummc1sIjxEfFtyHfkHBTICBWH0qyWpdRIJCri85g5F2anioZ5g9rg26RGvRzYyMtoAELiOXLl+PDDz9ERkYGunXrhs8//xx9+/Z1y1re2/I0/s1gq7kZIUVItApyGCCHAT+el+NniQ6pCjk8Uq4iumI1EouHosKoASQGeHtnIcDnHDwUHgjyCEWAJhyDQsajZ1g3qFTlaOHVAoXaQhgYg40v0mhkePPYP8n/4NdLv+JI2hFUMsL/COPLdHghOxtvBfnzT9oAG4Pw66VfUZ56LyqLukMll6JdTApuKD4HU+mJshuPwKgLwbH00/js5HkoAw5AIjU/Cd9TVMyLh12GnnhYvxASMHi0bQEejS2Hl1IKeAay1oeEVcARs/BobSzAj2llmBEeBgD4X8o1xF25iF88OuDv4g64V7ELKpOlvk+FOb0y2RiMZCYEPxuG4xTTFo/INuGC31D8lGPOo/+fYTJSus7H6ZQCcz62SfQ/PbI97hnJFhD6akYvPPxjAlYaxiNOdw5Q5SPp7M9QnU9HebsJSJB1xy8JN9GvVQDmDW6N6zmlGNExhK8saM1Tv5zC9ZxSeChkmDGgJXoeehxjZGyA6TT5bqQxAZihW4SrORGC8346wgojQ1EGXpf/CYXE/IWUpLYq7JNwFHhoL+DhD/zxGHBlG7Z667HJxxzoVqY330w6h/viXFoRNp1OQ1hXL2iNBTg8ZgNifNsgOkCNHG0SOpzfBmnCKqDoJiTlefBefw9Sj45DRFRrwKBHcZcHMGdTFobEhmH+cFNtA10pcLSK4MAudwFtRgAyOfDIQaCiQLRXw72f/ovz+luQw6zCLPlOPKN7BPdOeAGQ2f6ei3TmIk+xUXrc3TuK39d4KPDgoBh8fMXmNAHdW6rExQNHVB/ztlhwomXHS+8QYOEFQMwlqFADD+4AvhvN7m95Brh/PRDsXH0Iu4i5MJy1GlmgNWj5FGnrlGfr75D6hBMP38/ug0NXczGqs+OnaC6I8mRyAdILy22qfQJAhZ79nCqRm3VNLBCVBqONcPn03h64byUrXC3bhgPAuqPCKqdFFfpaERCWnTg9FTLIZVKM6Ohe6wPQQAXEL7/8goULF2LFihXo168fli1bhtGjRyMxMREhIa4r8ZqSeyMeyd6WX3bcfz4pACO4X2O5VIpETwPguZv3w1cCyGIA6IpwQ5cJFP6HXcnbYY2EkeDe8OX4+4wWShnbkOdsaiFaBnqiBNdQFrjUJnbr1rJyPFBYhF4VWsgBfJJljlDf7O2Jl4LZL3OPiJ+h974IfVEcLpdcgNIfkMjL4NVGPLL8jnwJJlVkoJfpxn7WGIMv1HNg1LP/kf93JRCJylCsfKA3AGDPxSwsPjsat/edjvSz++BdmIg3FT+gjc4sRrjtiPJEzJQnAgxQrg7B+ZbT0CuRrR75Y8t3sIvpi+dHd8CRVceQXazFK5VzAKvAe0+lDC+P64gQXzV+PZaC539jn5T7tQrA48PNTwOjO4fhrUld8OofZ3FR2x0qnz1IUsgxM/cv4NhfuFI5DnmV9+Gv/7R8YZZ+rQKwek5fG6tRYZkefudW4yvFf7jS+gE8pv0DEpN44AiX5OFdz59xTykbWNo53BfRhccR5StBUPuBuOvIowhAFX7ywhQ23sOCEh+hI8egD0DPaD9seGQgpFIJnvn1NH47cRPFZTJIlcDzvx+FoTwLqtDNUAYcRDTuQWTQ90hDAR7Lew9jZccQkbwJMBl8fA4vx68AkAVkXRqCEF9PNnailA0+xbCX2aqORelAizjgzHpWPLQabF6UTC4qHpJzy3A+nRUFPhPeQ37gC7hX1gp9YsSrH1oKiEqJeVtr0CKtJA0jOoaICogfxvyArLIsPLf/OZRYWDGqJLCd7ZiH1dpkDr4mo/uzsSG7XmMrXS7vU/NYCC7WxyccqCy3tXQ4yWvxr/Hb1m4KrqmWOxnWIQTDOlT9fa60sCi8+NsZ/PCg8EHypyM38PLGszZzObggyupUoqwQcZsE+5hrchSU6VGqreQFa1ykRtC0q6i8EiG14NXi4jeUcinkVVhs6hP3/xWJ8Mknn2DevHmYPXs2AGDFihXYsmULvvvuO7z44ov1vp7Zk39A2F8rUFSYjwnG3bx5nTHd0Y1KH5xuvwQ55YXQpL+L4yo5KiQSGAF4MUZ4GhmoGAb5MinOK5UoktkqUkbCYF36Y0AQUJ4yHZDqwKj9kGK8BlUIm78eVGlAd60Wf3t5YnJxCd7MyUMe441PKidil7E3psj2407FIYQwuZhQUoYB5TcxLJo1qys0p6DQnKrysy7IL8DDBeYv7tR55xDhF4KNXkqUaCvxyI8JOHAlB/9czMLK/dew7O9LKDX9x1y+/waAGKjkrTFz7iKEb5iAlensXSrdfzB+Mo5Bl9JD8DAUY0CUGv6jX0Sv8B5A+VOAWoMZEgm4bPq/nx6C2auO8gGLn97bHdpKI1YdTMIrt7PiAQDGdg3D7ydvIq9Uh4+mdrMJaJrRvyW6hPti0c5EpAI4oI4BwLY7niffivGyI9gcOBv/pHtgouwAhqadxqWP26Jzj4GQqr3ZAFGpHDnXLuMNGVtnYPSN4wDX4LP/fKDLFODYN8DptehnSMA3t/vjlp5dof5jHpC3jX27650Bk3hgfMIhuf8XYN19QNFNoP1Y9iZUng+snsjeNCyoUAqfuO6M64KXBvTjP+vMgS3x139pYAymm4QpiFAZcBAAcINZj3Pn2GDER/EUBhrOYapsH8oZJdpK09BXas4gCMnYx1tzeDpOEAZhxtwCZyiu0GPEJ3sBsOV3p/RjhVEfR+fozM2Q8srN/SjeiH8Dm69txrSO02zOifaJRs/QnjiYyn5ersukUwS0Eu7HDGbdFa5gXaMhNQGI6CU+1xm0pv9//jHAjI2ArHpFpLZd38Zvy6XCr/olg5fg8X8ex4t96//71FWUFmmelpkNf5/PhL+XkhcPgHhGh9mF4bqAsLZadIvUoG2IDxZP6ITFm8/za+oW5QfAtmplcS0FVJZpzRkYDYkGJyB0Oh0SEhKwaNEifkwqlWLkyJE4dEg8YK6u6RTeEZ0e+pTdMegBqZw18Ror2f/cEil6cybGY1L2ZpJlqggYezsQdzegiYS+MB3M8e9wLP0g8mRSFEml2OfpgUpIcEalRIWU/eP3iFojuo4P8ioQIG+LWYVnoFHE4J/h3yO4VXfM0qgxzcggxGee2f9Xmoug0+uw7Z/X8IWfHzb7mDscttXpsCIjG28EBeBfTw+MLinFC3n5MECCUJkHMOhJwDsU6DUbEUqzS8RbJceauf0w5MM9uJFbhne22vaXCPZRYcX0XmgT6Q88eQz9d7wEQAKMfgevSyQA5tsGFnn42VxH46nA748NQmpBOQrL9OgUzsZTWJq0AcBHrcDPDznuLdAj2h+fT5mAOzd9j0LPMlS+lIHiU3/Ad/uTCDfm4uG8j/CwRaXg8PKjQPxRwTVECxGPeR/o+xAglQKRvYCcS0DqcYz0TgJ+eRu4cdA8N8uUfjnxC0i63ceeM/8wcH4T0HkywP2eJ/4P+Otp801k1DvIkZcBF37kL9W9RSt4W5jo4yL9sP/5YVi4/2f8l5uKebcBWsN/2GB6UpdKpBjVKRR7E7PRr3UA2obcjqcPdjGdzWCy9ABGyhJQwnjiJNMWHWWpmNm2HGg/BghoXa0MjpwSLXq/be6wOahN1b5ahmEEFohifTG0Bi1UMhU2X2P7rFinbAKAziToOwZ2hEwiw/XC60guSka0b7TNXBtkCmDiF2xH0Lu+daphlQ2eVpaXlcOBF5JYN1R1qDD9DtS+1XJdAIDOopZEO39bK0vfFn1x6P5DNc7Wqg8sYxq4YMntZzPwyJoEm0JNYhYIPgujGjEQXGwFACy5syuGx7IWk1mDWuHX4zdxPr0Ix5Ly8PSvpzB/aFu+uBMH51qpKWUWNSAaEg1rNQBycnJgMBgQGir074SGhuLiRdte71qtFlqt2YdeVGS/G1utwPltVXbyA/rMYV8iKCIAdLodg4ozgMoKQFeKaWd/A/xbobIoFVtOfYXlPmqky23/WZ4tqkCfeXtZ/2ylDpArEeNonV6BwMAFiGw7Eu/Gf47XruzCZ0otDnmo8YaqNUJHPI4v/v0YyExmA9/63sd+4XW7l02/c8BjQ9vghd/M9QaUcin+evwW+Hko4OepND8xSCTAmCU257sSlRzh54EIP/GS1a7QWtMaXgovlOpLcST7BAb1vQ/oMBjY9wFwgs0WgWcQMiWB2FoYAwYSeKICWiiggAGRkmykMkGY2CUQnhc3AF2nAv2FxbMQ3oM1/f9hJ8B16Ets9D6Hyke4DwBd72Jfu98C8q4CfeYi+/AbgiktvFrYXDrUV42uIR3xX+4J/JS4SnBMKZPh6+m9UViuh69aDomEzRpZFZ8EQIKNxsGY8cgLePWPs2w3QwMw+e5RNepHEX81V7D/qEWgmT3ytfmC0uUAkJiXiJa+LR2e19KHPR6gDkD3kO5IyEzAzO0zsWnSJvgonbAfc1kV1UXEdYMru9l/x+rAiUeLWg2uUqAt4Le/HPGl6JzGIB4AQCEzf19wN/Qj19m/L+uW7GIWCA9F9V0YXOaHj1qO+/oKBam/F/v/4+0t7IPUM+tPIzZM+PdWUen6e4rBrd2dRaPEaHACwlWWLFmCN954o+qJDQmfMPN2KFt2WA5g4tAXMT75CDJP/4jyvGt4WncNEQYjPu40F15d7zEHd7lSFz8kFpi0HGqGwfN519jI+g7jALkKGFi9wkr39ImGj1qB7GItJnQLh7bSIBrY1JCQSWWY2GYi1l5ci/WX1mNQxCBWKN3xGdBzJts2ue0IhEikKN93FR/tSIR1/ZgvpvWEZ3sfIHEM0PF22zdpM1xYlbDrVDbKf8Mc9kn+lqcBsP0slp9ajjcHvokOAXYKBI0wdxm9UiB0+luXIuYYEzNG/AndoIPBaBA8rS2+ozMW39EZFzOKEBPoBbVChq8f6I1B7/0DAIhbvBNr5/XDwDauVSms0Bvw/cEkvL/dLPaPvjwCIT5VP0lzHUZDPUPBMAyyyrMwbes0PNrNccYR1/cEALoHswIipzwHP543Fz2rU7xFgtluxFdfQFhaIKpJfgXrpgtQByDUy/3BdjXB0qrA3dDt1YQQy3jj4hO0lWwmgzOp93qDEQ+uMsc4iVXL9POw/R4uMgkahUwCvYGBttYsEO4vWy1GgxMQQUFBkMlkyMwUlh3OzMxEWFiYzfxFixZh4cKF/H5RURGioqJs5jUW5NH9EBHdDwCwOf8G+yVSXVOoJRIJENiGfdUC47raPgU3dCa1nYS1F9did/JufH7yc8zvPp99Cos0+6slAB4b2haTe0TgUmYJ9l/Kxk9HbuCnuf3NhaPipoq/QZvhrA+9LA/oPZst4CSRAHN3CaYt2L0ADBg8uedJbJ9iG1Brid6gtxEQkT7iFqLuId3Rwb8DEvOFVREZMDiUfgi3RNjGLsSGmW9SEX4emD+sDZbvuQoA+GhHIn5/zHkBkZxbhpf/OIN/L5tjECZ1D3dKPACstQEAonyikFuRC5iMEV+eFn+CBtjyzAPCzS6se2PvxbdnvwUAnMmpp6qcmgjW7SdTse6eDbOBk2uAMe9VrwlWLVgg8rWsgPBX1cJ3h5uxjIHgik+V68RvzI5cGABb08HbieZT59KKBH/HYtf187S10KUVsvFHQd4qpBdWCFwgNYEsEE6iVCrRq1cv7N69G5MmTQIAGI1G7N69GwsW2D4xq1QqqFTOt7ptVPg7Nt0SrhEbEItwr3Cklabh6/++Rjv/dnaLbbXQeKCFxgND2gfjlfEdnXO7KNTArL+qnMaA/RJMLUnlx3Yk7YBapsaQqCGCuRmlGTY5+yoHrZ1X3LYC/zv5P0gkEhRqC5Fakorzuedxo+iGqICw5rnRsbiWXYptZzNwIb3YJl7FaGSwfM8VeKnkmD0ohj92KqUAk5abYz76tw6A3sDg6ducT2ncmcSWIB8UMQi7b+x26pxWfsIgyDCvMPw49kfM2DYDl/MvO/3eNeY2Uy2J0lw2LsqgZQtWTd/g+rVqwQKRWco+gLm7z0VtILX4++NKmFfYKe4kl9n+P1XJpZBI2NYtZdpKpwREmVXZa7H0UH9P++LQ31OJ9MIKu+t0FbMFomHdshvWakwsXLgQM2fORO/evdG3b18sW7YMpaWlfFYGQVQHiUSCDgEdkFbK9le4kHvBqWqdtVFJzhGX8y/j2X1soadlQ5dhRMsRANgvS26toZ6hGBMzBne0vcPudQD2hrF44GJ+/4NjH+B87nmn2qtzfHpvD+x8bTvK9QZkFWsRasp4YRgG89ee4CvtRfh7YHTnMBy6msvnxQPAzAEt8cbELqLXdkR6KZtK2zOkJw6n2RaIkklkkElk6BDQAc/3eR5rL6zFwt4LbeZxLp6c8hwYjAbIpPX41OYVyJb9/vcj4MouIPM8ENrJtWtwmSjKKuuw2mVvyl4AQOsaVF1tiBgZ9u/Q3o3ZKNLJVCKRIMBTidxSHbKKtXwGlyPyrSrDilkggrwdCAhTfERtB1G6s3W3GA1rNSbuueceZGdn47XXXkNGRga6d++O7du32wRWEoSrPNztYexJYds1cyW13UlqSSru3GTuwbDk6BKMaDkCeoMe9225j3dHtNa0xrN9nrV3GbtwHRjTStKqmGlGKZciOsAT13NKcTWrBKG+alzOLMaWM+mCMr0nkvMxunMYPtghDG7uLNJy2xm4wD8/lZ9oeeUJbSbgtQGvQS5hA0G7h3QXvU6AOgASSGBgDMjX5tf/U/iIV4HMs8Cl7cCed4B7beNSHMIVklJ6OZ5nh5zyHPydzGbAtPevYVGrBkBUgCcm94jAxpOsxU5babRbXtreE3qrIC/klupwNbtEtCW8NfllwgJRSpEYiBYOgrv9TNaJ2nZheNZCUarapMGG4S5YsAA3btyAVqvFkSNH0K9fP3cviWgCdA7sjB/GsFkX/2X/xwebcWSWZkJr0IqdKsq1gmtYc34NssuynZpvfe1VZ1cJ378sEylFKbhRdEMQyxDhI6xu6SwR3ux5XICis3DR5L+fTEWF3oAxn/6LZX8LXQLHk/JRUKbDSVOtDo5b2rp+w75RdINP4fRT+9lkYwCARqmBQqqo0iIkl8r5qq5ZZVkur6VW6PkA+/PyTsfzOIwGIOMs28BMb2oGVs0eFecsOrbe1rKKLqmNhI+ndgMX+1hUrrdrgbBXRbZ1MCvGLIs8OSLJap5YEKW97DCpBPBVs0Km9iwQpjoQKhIQBOFWeob2RIxvDABWRHAkFyVj5IaRmLdznlPXySnPwcQ/J+L9Y+/jf6f+59Q553PPC/Z/TvzZZs43Z7/hzfkcbTTVC35tpWFjBK4XXufLGjvDvaaUtQ0JNxH76nZBa/GFpriGhBv5fJnumEBPnHrtNux9dijCq5F2a9nbxVfpi7yKPJs59oJHxQj2YIs7ueK6qVVaDmJ/GnRsR9Kq2P0GsGIQsP8Dcy8MRfUymy4XsEJvbKux0KiqZw1qaEilEj52oaiiEuV2bsxRAeK/swAvNm6opKJS8Ldsj28set4A4hYISwEhKGujkPHZIOuOJlufVi1KteZOnA0JEhBEs6RbcDcAwOlsc0tmrnLfyayTfLCWI96IN6cPH0o7hGMZxxzMBtacX4MHtj0geuyX23/BsqHLAAC/X/4dj+0Wph/GaGKqXI8YkT6RUEgVqDBUILU4teoTTAxpH4xZA23fUymTYt7g1hjSnr1Bf7iDtZL0jgmAn6cSMUHVM7tbWkjkUrmogJjcbrLNmD3a+rF1J7jMjnrHsisnFxTpiIOmQnV7l7A1YoBqWyC4AMpIb+cFV2PA15SGXFShh1bEAjG4XRDmDhaP+eAsCLsuZKLz69uxIeGm6Lyb+WVY9vclm3ExAeHvpcTDQ1rDWyXH2C7mDEEPpZx3XaQXVtjUqqgOx2+w/x+8VdWvzVIXkIAgmiXdQlgBsfLMSpSZnvgs3Qu5Fbmi51lyvcj8lJJemo4HdzyIhMwEu/PfP/Y+v31Ph3sExzoFdsLAiIFQSIVfEHKpHE/2fBKDwgdVuR4x5FI5OgawlSTHbRyHlCLnXRmTewjdJhF+Hvh2Vm94KGXo11rYL2Jqr+rfrG4W236Z39vhXgBAj5AeGNdqHH4c+6PD7BNrOgWygYsbr2yE3lg75YRdQioDuCJWWicEhCVcDEQ1LRDc37F1C+/GDueeKK6otImB6BapwY9z+tnNsOAKTN3ILUOF3ohn15+2mZOYUYzbPz9g46oDxF0YALBobEf89/ooDLXo6eGhlCIpx9xRNTm3TOxUp6nQG3A2lf0bGtmx/ntBOYIEBNEs6Rtmbsiz7MQyfHHqC6w8Yy4CdTbnrNhpPFqDVvTGtyd5j2D/WMYx7EvZZzNvXKtxNmMecg908BcWlprYZiLmdp1bo0yQ/uH9+e0n9z7ptCsjtoWwqt7bk7tgcDvW8jCui7kOSISfR43aCk/YOIHf/nQY+yQ+t+tcrBi5AitGrsD7t75vN2DSHmNbjQXACrsr+VW076wrVNUUEJwFopoCosJ0viuCqzHgY4orEIuB8FY7zgcQKzBlScKNfIxeth8FZeJiU+ngfKlUIijS5qGQwcsiViEp17m4C3t8sstsEamuha+uIAFBNEta+rbkrQDrLq6zKVb0xakvbNwYq8+txvSt01GoLURSYRIMjAE+Ch9BqeWMMrPPvdJYiQd3PIgF/ywQNHhSy9ToHtIdz/Zmsyqe7/M8f+zuDncL3lOsbLWrPNjlQf69LudfFgTZOUIll+Hgi8MR6KXEmM5hGGwRHBkT5MWbdYfFBtu7RJXoDXpBa+kANWvZUMgUGBQxqNpP0YEegbybKrm4dvzQLsPVcSjOBJKPsAGSdrEQiJwFQl5NAWFgBYRYJktjxtfCAlFqVZbapwrTvrUFwcfKUrHtjDDmyBqxNE6xtQGsC+Pl8ebU3dQCkfbsLvD1/mv8ttyJKpr1CQkIotmysNdCG5cBx4W8C7hacFUw9uHxD3E6+zTWXljLB6q182+HTZM28U/Olj53y8yMNefNDdJ23LUDUokUD3R6AH9N/gvTO07nj01uNxnHp5vTS+2VrXYFL4UXZnaeiX5hbCaTpeulKiL8PHD8lZFYMaOXTRvh7U8OxoODWuG5UbHVXpt1dohTvSucJNqHDQTdf3M/76aqV7hKkuvuAb4bBZxYZX+uZcom78KongDgLBBqWVMTEOxNP7Oogi9pzRHgoCYDYCsgrHtmeFVRX6GqDtpCC4QUrYK8MHtQDADYtWpUh7quSeMqJCCIZounwhPzugozLj4c8iEfuT5502RcK2TVv+UN6N/Uf/HWobcAsHn2UokUXYO6AmDTEbkURO5cADiQegAA69vnnrIlEgla+ra0+VJQyVT8nH4tai99mbOUJBUmuXSevS+t1sHeeG1CJ2hESvo6i7V1oDYFRIgn6y/edHUTZu9wQxE66y6z8XYydc7+BujMbarBxeJU0wLBxUA0OQuE6SadkmcrBu+x6tJrjXUlSb3BbF1kGAaf7havWtqxBSsCB1WRmmyZkcFZIzhRURtBlA2VBllIiiDqCy7YDgAe7fYoxsSMwXP7nuPHjmccR2tNa9wousGPWfZYmNaR7eIY5BEEb4U3SvQlSC9Nh6fcE4/8be7WydV0cFYQbJy4EaW6Uv4mWBtwAsLys7gbyzoNPkof+Kn8au3alu4P6/TZesGyaR7ABlaKseFB8fFqWiA4AdvULBBcDESyiICIi3ScrmptgbBsxnU5q8R6Os/PD/VHuc6AMI3j36WliOZKb3MCoqgJCwiyQBDNmrjgOHiYnvT6hPUBYE7xBICbJWygpFhBoud6P8enV0okEt5yUaQtwpZrW0Tfz9nSwgHqAET51m5TOG6tlgLCldoQdQFXp2FAiwFYO24tlLJqNJ+yg4fVE/yP53+stWs7hY+V+ynnElCpE58rBlkgBHBP9pyA8FXLEeHngceHt63StG8tICotLBAlVn0vLNF4KKoUD9ZwTfc0FmmnTRUSEESzxl/tjz8n/ok/J/7JC4gPb/0QnnL26ZXLtLAMguQY11qYSeGrZM2dRboiZJZl2syXS+SI8nFfp1hLC4SRMeL9o+9j0LpBLrs0ahNOmPUJ61PtWhf24P4NOZYmLK3V61eJWBfdk6udOze4IyCrnoG4qcZAcFUYs4pZgRQb5ouDLw7HM6M6ODoNgG0dB71FQGttuRg2LRiEp0a2w0xT/ZTacGE4U4/GnZCAIJo9LbxbCCwDLbxb4P1b2ZoNu27swvBfh2N3sm13yEC1MHWRs0AUagtxMe+izfxo32i7QZv1QYR3BDzkHqgwVODPK39izYU1KNGXYP/N/W5bEycgQr1qv8+NdQZHbQSkukS0yV1laUm4YvV3ZLDz9Nv/EfFxJ2iqWRjWVRi5hlXOYJ3GaXlfLihzwSrkgLhIPzw1sj0vVmpDQDhTNdOdUAwEQYjA9ZAAgOzybGSn2va6sDabchaII+lHcDLrJAC2BPXVQjabw7rGQ30jl8rRLbgbDqcfxmvxr/HjORW21pX6grPU1GasB4e1CyOrLMumPXmdEt4DeOwI4BcNXN/PZmMUWVUDta4RMeodICcR6HZftd+Wt0A0MQHhoRDerkJ8nP98YoWguL+F/NK6cTF4mARPua56DbWuZpcgrYYpoHUNCQiCEMFSQFgS6hmKzLJMPN7jcZtjnAXiz6t/8mOdAjvxAsLVYkh1weCIwTicLmyVnV7iOAe+rohPjeczVepCQFi7MMory1FeWV6/FRpDTCmuXEBlsVVvjvwk4f7ABTV6uwOpB1BWWQapRAp/lYgLpRFjbYEI8HI+XkatsBUQBWV6+HspUWCyEEzpGYl+rQPw8c5EZBY531DPHpzVw17jL0eUaisxdcUh5JXWjnWkriAXBkGI4KnwRNegrjY3oWf7PIufxv2EuV3n2pxjnUHwaLdHBab5hiAgxrQaYzNm3XAqqTBJ0GSsrnj474f57VDP2ndhWFsgAKBUX7OqgNXG1+Q+Kck0d9sEgF2vic+vBslFyXxTsrigOHgrvWvt2g0BawFRXGE/+NEasUqUR5PY/hLcDT7QW4m7e0e5ZNlwBCdatJWuByr/ezmnwYsHgAQEQdjlm1HfYMeUHXjnlnf4sTDPMMQFx0Eqsf2vY/0U3cavDXqF9uL32/u3r7vFOkmIZ4jNjbVAWyDYn7drHqZtnSYa91FbWPen8FLUfoleldy2lHOJ3n7KXp3iGcS+AOD0OvO4rvbWcyr7FL/dzr9drV23oeBhJSCGdnC+AqqYC+PhHxNwMjmfL0rFVZt8bCjb+XZ8XM2qwKpNtSe0lUaXgyHzaykuo64hAUEQdvBUeMJP7YfWGnOAZZCH/YIy1gIi0icSg8IH4dnez+KzYZ9BLm0YHkNr07algCjVl/IWid036k5AFGoL6+zaHJHekQhQB6Clb0vewuE2C4RUCvQ2FbNKOWIet7RG1BBLYSgmcBs7nkrz/x8PhQyD2zku7mSJvV4YX+y9Cp2pJoTCJCDGdm2Bf58fhs/u7VGD1QpFi7NWiHKdASl5ZShxwbriTpreXxlB1DIxvjH8drCn/acef7X5xnxf7H3oFNAJEokEMzvPxLDoYXW5RJeYG8e6X7jqmYXaQhiMrBnXsvw2F81fFxRUFNTZtTk8FZ7Yduc2/Hr7r3yFS2csECnFKXh+//OimTTpJel4Yf8LOJfrXD8RAeGmG9LpdUDSQXa7xMJ9FHev69c0UaYvE6yXaybWlLB0YYzuHOpSMKx16WoOy7LYlqmeUQGekNWw74TaovqlVu+cgHjy55MY/MEe/HLc+a657qRhPBIRRAPGW+mNVWNWAXDc4bCDfwf4q/wR5hWGl/q9VE+rc50p7aYg2icasQGxuOXnW8CAQZGuCP5qf2SXmwVEXkVena0hX5vPb1u6iGobLmCSc5FYu2vEeHH/i/gv5z/sS9mHI9OOCI6N+m0UACA+LR7/3vsvDEYDZPYqTFoTZVGFdM+7wPTfgHLT7+GRA0BIZ+euI8LcnXP5CqlRPlEC11lTwdKFUVV3TWssm2FJJcCWJwZj7Kf/4kZuGVqZOlwqZLWbnaOQSSGTSmAwMqioNECDqtNOd55ns5KuiFTHtCyX3VAgCwRBOEGv0F5Vfil7Kjyxbco2/DT+p3paVfWQSqTo16IfNCoN/2SeX8HeyCwLYNWlgODcJHFBcbijzR119j4cqSVs+qRlmXJ7cGWvyyqFJZN3JO3gtwu0Bdh8dTP6r+3vfB0NryBg+u/s9o0DwCcd2W0PfyC0C+vmqCaW5dU7B1ZfiDRkvCxcGOUuZjZILawJRgaICWRFQ2G5HrklbLyBdbGp2oBzY1QnE8Oa3x4dWONr1DYkIAiiFvFSeLm1WJSrBHuwLpmscragk2WZ67oUEPFp8QBQb0/KYpVE7WEvVsW6FPZLB15ChaECbx9+2/mFtDCXSUe56fcb2gWoxdoUnFhqasikEjxqCnAc17VmAY4eShl/c88pYVM2q2rZXR0sAylriqsltesDEhAE0Yzhggvn7ZyHxfGLseL0Cv5YobbQJluitricz3Y/7B3Wu06ub83yEcv5ba5XhD0sBcSIX0dg4+WNAOwHYLrUQdQz0HYstGYWg0qjMOCulaZVja7XkHlhTCwSXhmJMV3Cqp5cBVxzLi7jQVEHAsJVC0RdWEHqksa1WoIgahXLzJHfLv9mc/yHcz/UyftyrpIwr5rfCJxhcMRgKKVs4SGxxmiWWDb0yirPwmvxr4FhGFwpuCI636US2WKWhhoKCEtXy5R2U/B0r6drdL2GTqC3/TgkV/BSmQSEqRJlXdy8OQtEhRNBlEYjwwd0NhZIQBBEM0asAuTMTjMRoA4AAHx64tMat8LOKc/Bwr0Lse36NgBsqWUumLG+BIREIuE/q2WmiTWl+lLRFNPV5+03wdqbsheX8i9Vf3HhPat/LoBSHWsZUUgVWDxwscNUY8KMt0lAWKdx1iauWCDE4joeGcK6bD67r2YppXUFCQiCaMZY38D7hvXFs32eFdxEXYkfEOORXY9g141deH7/88gtz0VaaRoAtm6Bj8IF838NCfBgRREXMCrG6ezTMDC2X+Rfnv6S3xaLkZiyaYrzC+loETQ6/FUgrIvz54rAuVbqohhXU4azQHCIFZuqKZybxJmqmWIC4plR7XHwxeG4o1s9N4JzEkrjJIhmjLUFgmv53b9FfxxMY2sVlFeaG/qU6cswc/tMRPtE4+OhH1d5/dzyXCTmJ/L7Lx14ia9R0N6/ff01toK51LijVM5LeawlIcY3BklFSfw4Fzfx7i3vIlAdCL1RDw+5B+bsnOP6Qu74HGgzHOg0EfAMcP18K7jaFiQgXMPbSkDUhQWC69eR50RlSbGmWwqZtEGmb3KQgCCIZox1S/JRMWydg0e7P8oLiCJdERiGQW5FLob9yhbEuph3EZXGSv5pPLM0EwmZCRjbaqxAFKSVpAmuH58Wz2dg9A6tnwBKDmsBcTzjOLsOUyBnia4EHyewoqhPWB+BgOACFUfFjOJrgVi7dgq1hXxDNYd4+JmrUtYCZIFwjagA9oZsKyBqX8zyAqLECQFRC6me9U29ujDeeecdDBw4EJ6envDz8xOdk5ycjPHjx8PT0xMhISF47rnnUFnZOMp6EkRjwzIAcPmI5ejfoj8AoFtwN0xsMxEAe2NcfX41Lx44Siz6ONy56U688O8L2HVjFwA2BTS3PJdPDxWjvosdcTf39ZfWY8LGCZi9YzZm75iNE5knAEAQJClWCtpL4SUoJBblEyU4fr3wel0sW5TPTnyGxfGLUWms5NNtubgVQhwfk2CYEMf+zVu7MOoiiNLfkxUQzvS2qG7bb3dSrxYInU6HqVOnYsCAAfj2229tjhsMBowfPx5hYWGIj49Heno6HnjgASgUCrz77rv1uVSCaBYEegTiu9HfQS1To2twV8Ex7oabXZaNtRfX2pxbrCuGn9oPKcUpKNIVAQB2J+/GsOhhmPTHJEgkEtGOmBw9Quo3MIyzQFjXSTiRdQI9Q3sK0js9FZ74+66/MXLDSH7MuoeIj9IHvUJ7ISEzAQCQVJRULx1XKyorsPLMSgBAXHAcH69CwZOO2Th/IP65mIVZA9k0V2+VsJplXbowcp3orHktx02N3mpAvVog3njjDTz99NPo2rWr6PGdO3fi/PnzWLNmDbp3746xY8firbfewvLly6HTNY7uZATR2OgT1sdGPACAr9IXAETFAwCM2zgOpfpSQfGprde34lDaIeRr85FXkcffrCe0niA496V+L9V7u2lrdw0Hl9bJiSCAzUQJ9QoV9EHhgjAt+WLEF7wr5mTWSZuaDHVBbkUuv/16/Ou4WnAVAAmIqmgb4oOHbm3DWxq8VcKCb3URRKnxYN+jqLzqeirHkuwH9zZUGlQWxqFDh9C1a1eEhobyY6NHj0ZRURHOnatG8xqCIKqNM/78cznnkFIsbPwzf/d8m3mzuszitz3kHrgv9r4ar89VrAssTW0/FQCw7uI6lOhK+Cf5IZFDEOjBio22fm35+QEqWwHhqfDEgPABAIDfL/+OR/9+tE7Wbkluea5g/8+rfwIgAeEqXlYWCMvmV7WFuQ5E1e6J3BLHBc4aIg0qiDIjI0MgHgDw+xkZGWKnQKvVQqs1/+KLiopE5xEE4RqcBcIRRbqiKn3/bf3aor1/e37fXW3NLduyA0Abvzb89qH0Q3jv6HsAhMLJMs5hXtw80etaBi8eTj9cK2t1xKcnPhUddyqAk+DhUiw5Ar2VdmZWH15AOFEgqqwRxkDU2ALx4osvQiKROHxdvGjbFre2WLJkCTQaDf+Kioqq+iSCIKpE7IYU7hWOEA9z6mehthBH048CYM3+YliKBwBu6xXip/YTiJfxrcbz26/Hv87HQFgKJ8unerGiW0D9Zj8wDIOjGUfdvo6mgGUQpVIuhaey9oWt2tRGXGtlgTAYGTy3/jTWHDa7/xpjEGWNBcQzzzyDCxcuOHy1bt266gsBCAsLQ2ZmpmCM2w8LE69Yt2jRIhQWFvKvlJTG0UedIBo6YhaI9Xes51ubA2xK5LXCawCAGZ1mYFDEIJtzJrebLNhv59+udhfqAm8OfJPf1qg0mNyWXVuxrpgft/zcarm5gZG9LAfrG/f2pO21slYx1l1cZ/eYp9yzzt63KWIpIOqqhLQ9F8buC5lYn3ATr/xxlh8rbYQCosaSKzg4GMHBwbWxFgwYMADvvPMOsrKyEBLCqv1du3bB19cXnTp1Ej1HpVJBpaqd2ugEQZjxVQkFxPuD34ev0he+Sl9M7zgday6sQXppOhgwANgn/DaaNjiYepA/p1NgJ/QL6wcAWDVmFVafW40X+r5Qfx/Cii5B5qqPluWtLbH83JZiwrJHhiXWAuK5fc9hQIsBdeJS2HR1k91jZIFwjbrovmmNWi7eC6PAIqhSbzBCIZOiXMcG4KoVUlTojbizR0Sdr6+m1KszMjk5GXl5eUhOTobBYMCpU6cAAG3btoW3tzdGjRqFTp06YcaMGfjggw+QkZGBV155BfPnzyeRQBD1jOXN85Fuj2Bc63E2x35J/IUfU8lUGBQxiO8bsffuvVDL1XxhqV6hveq99oM1rTSt8OPYH/kgSe6nJZafe3j0cAwKH4Ruwd1s5nGI3bgv5F3ga2rUFmX6MlzIuwAAeDjuYXz131eC445SZglbgn3M95T5w9o4mFl9OBdGRaXQumA0Mvx2bokOYRo1HwPx/ay+yCquwMiOwnjAhki9CojXXnsNP/xg7u7XowebB75nzx4MHToUMpkMf/31Fx599FEMGDAAXl5emDlzJt588017lyQIoo7wV/tj8YDFUMqUmNBGmIYZ7CludRwYPhAfDfkI7fzaid6cGwKWtRo0SlsrgaXlQClTYsVtK2zmWOIltxUQiXmJtS4gMsoyYGSM8FZ4i7qByALhGu1DffC/+3ughcYDvVr6V31CNbDnwsgvM1sgsou1AgERplFjQJuG+X/HmnoVEKtWrcKqVasczmnZsiW2bt1aPwsiCMIhU9qLN4myzmiwZHTM6LpaTq0j5mZw9UYsVs/Csgx2Tfkn+R+czTnLF48K8Qzh3UaWeCooBsJVbo+r2yZVKs4CoTeCYRjeGmeZsplTogXDMCgzuTA8lbWfTlpXNKg0ToIgGgeWKZCNGTEBIVbG2hGhnqGY3nE6POQeiNHE4OUDLwuKa9WUJ/c8KdgP9ggWLYpFFoiGh2VtCW2lkd8/mVLAj5doK1GsrQTn1fBoRAKiQRWSIgiicaBRafBw3MPuXkaNEXNhtPNzLUtEIpHghb4v4ImeT6CVL1us6ljGMUEX0+piMNpG5nsrvdE7tDceinsIj3V7jB9XSmu/jgFRM7ggSgDQmgIpy3SVSLhhrjpZrjdg82m26VywjwredZBOWlc0npUSBNGgWNBjAQaED8CHxz60W2SpoWOZceGl8MK2O7fVqMR2bGAsfJW+KNIV4Yl/nsDKUStrtD4xEfJQ3EOQSCR4vMfjAIAW3i3gq/St19bohHMoZBJIJYCRYQMpNVDgRm6ZYE6F3oDrOWxH1Tu6hUMqbTz/jmSBIAii2vQK7YWfb/8ZI6JHuHsp1cIy4yLSOxL+6poF0ymkCszpOgcAW5UypahmdWmsBcR7g99Dp0BhSvuktpMwPHp4jd6HqBskEolNIOWN3FLBnHKdAZlFFQCAKP/GlUlDAoIgiGaLRCLBq/1fhUKqqLX6FA92eZBvsPX7ld9rdK2ySuHTqmVvDqJxYBYQrAvjRHKB4Hi53oD0QlZAhGnUaEyQgCAIollzd4e7cWLGCfQJ61Nr17w18lYAwG+XfqvRdcr0QgFh3RCMaPio5VwmhgFnUwvx9X62cqtCxroqyvUGZBWxWRkhviQgCIIgmjVc3YwCbQEYxjbl0lksLRAv93vZbjVMouFi6cJYfSiJHx8RyxaKKtcZUGpK4fRVN66wRBIQBEEQtQzXl4IBgwpDhcvnr72wFgt2L0B+BRut3zGgI+6NvbdW10jUDyqLjpzZxaylYc4trRAXxWYAlesMfBGpumgpXpc0LrlDEATRCLBswlWmL3O5zPSSo0sAAHkVeQCoTHVjhi9nrTcLhe5RfsgxFZMq1VXyzbzqoiNoXUIWCIIgiFpGKpHyN/2yyjIUagurdZ0zOWcAiHdGJRoH5oZaBpSbMjG8VDJ4mKwNeaU6fm5jqkIJkIAgCIKoEzgBseTIEtzy8y3Yf3O/U+eJxUx0Dupcq2sj6g/OAqHVG3kLhIdCzlec5NwaEgmgkjeuW3LjWi1BEEQjgRMQ/6b+CwB4/+j7Tp0nVjwqLiiu9hZG1Ct8EGWlAWVac78LX7UCAJBlEhAeClmjKwbWuBwuBEEQjQTruAVne2yU6EtsxmI0MbWxJMINWGZhlJlcGJ5KGfQG9vZbXNH4mmhxkIAgCIKoA7hMDFcp0dkKiDCvsJouh3ATaouOnJwLw1Ml55tncTSmJlocJCAIgiDqAA9F9TInOAuEh9wD/ip/9Ajt4XKHUKLhwFkgSrQW2RYKGaydFZ6Kxnc7bnwrJgiCaAT4q4R9NZz1bxfrigEA0T7RWD9hfaPzixNCfEyxDlwFSoC1Nshlwn9XNVkgCIIgCAAIUAcI9iU2z5ziFGgLAAB+Kj8SD00AseqSKrkUSpnQquTZyIpIAZSFQRAEUSdYC4hrhddgZIxVnscLCLVfHayKqG80HgrB/hPD20Iikdi07W6MQZQkIAiCIOoAT4VtEOXelL1VnmdpgSAaP74WAiJco8aTI9vz+48ObcNvN8YgShIQBEEQdUBL35Y2Y8cyjlV5Htf/QqPS1PqaiPqHq/cAAH1bBUBmYXmI9DcH2nqQC4MgCIIAgFsibsEr/V7Bn5P+xBM9ngAA3Cy+WeV5XNlrskA0DXw9zDEQ1u4Mb5X5WGN0YVAQJUEQRB0glUhxT+w9AIBLvpcAAMX64irP49I4fZQ+dbc4ot4I9lHx2x5WzbIsrRPWxxoDZIEgCIKoY3wVbDMsLkXTmozSDHx56kvklOegTF8GAPBSeNXb+oi6I9jbLCAKy3WCY95qskAQBEEQDvBWegMQrzIJAM/uexans0/jeOZxlOpLAVS/kiXRsLBMxbVO3fRp5AKCLBAEQRB1DOeOsGeBOJ19GgBwNOMoyirJAtHU+HhqN/SM9sNjw9oKxgO8lPy23mDbhbWhQwKCIAiijuEERIm+pMpaEJwFwroZF9F4mdIrEr8/NgihvmrBeIiPGiM7hgAA+rbyFzu1QVNvAiIpKQlz5sxBq1at4OHhgTZt2uD111+HTif0Cf33338YPHgw1Go1oqKi8MEHH9TXEgmCIOoETkAwYJBUmGRzXC4xm7IpBqJ58dWM3oh/cTh6tQyoenIDo94ExMWLF2E0GvHVV1/h3LlzWLp0KVasWIGXXnqJn1NUVIRRo0ahZcuWSEhIwIcffojFixfj66+/rq9lEgRB1DoqmQo9Q3oCAHbd2CU4tvnqZlQylfx+haECAAmI5oJMKkG4X+O0NtVbEOWYMWMwZswYfr9169ZITEzEl19+iY8++ggA8NNPP0Gn0+G7776DUqlE586dcerUKXzyySd46KGH6mupBEEQtU6fsD44kXUC2eXZgvGXDrwkOl+skiVBNCTcGgNRWFiIgACz2ebQoUO49dZboVSaA0tGjx6NxMRE5Ofni15Dq9WiqKhI8CIIgmho+KtZH3deRV6Vc0M8Q6CUKqucRxDuxG0C4sqVK/j888/x8MMP82MZGRkIDQ0VzOP2MzIyRK+zZMkSaDQa/hUVFVV3iyYIgqgmXHMtrlQ1AOiNetG5z/Z+ljpxEg2eGguIF198ERKJxOHr4sWLgnNSU1MxZswYTJ06FfPmzavR+y9atAiFhYX8KyUlpUbXIwiCqAs4C8TxzOMoqCgAAOSU5Qjm7JiyAz+N+wljW42t7+URhMvUOAbimWeewaxZsxzOad26Nb+dlpaGYcOGYeDAgTbBkWFhYcjMzBSMcfthYWGi11apVFCpVKLHCIIgGgqR3pH89jdnvsGzfZ7F8lPLBXPCvcMR7h1e30sjiGpRYwERHByM4OBgp+ampqZi2LBh6NWrF77//ntIpUIDyIABA/Dyyy9Dr9dDoWBrhO/atQsdOnSAv3/jy5ElCILgiPSJxKS2k/DHlT9wMvskACCrLMvNqyKI6lNvMRCpqakYOnQooqOj8dFHHyE7OxsZGRmC2Ib7778fSqUSc+bMwblz5/DLL7/g008/xcKFC+trmQRBEHXGlHZTAADZZdlgGAZppWluXhFBVJ96S+PctWsXrly5gitXriAyMlJwjGHYEp4ajQY7d+7E/Pnz0atXLwQFBeG1116jFE6CIJoEwZ6stTa9NB2P/v0o0kvSAQBxQXF4sueT7lwaQbiMhOHu3k2EoqIiaDQaFBYWwtfX193LIQiC4NEatOi9prdgTC6V4+i0o1BIFXbOIoj6w5V7KPXCIAiCqCdUMtuA73Z+7Ug8EI0SEhAEQRBupFNgJ3cvgSCqBQkIgiAIN9IxoKO7l0AQ1YIEBEEQhBvpEtzF3UsgiGpBAoIgCKIe6R1qDqK8p8M96BRALgyicVJvaZwEQRAE8OGQD7E+cT3ubHcnQr1Cqz6BIBooJCAIgiDqkSCPIDza/VF3L4Mgagy5MAiCIAiCcBkSEARBEARBuAwJCIIgCIIgXIYEBEEQBEEQLkMCgiAIgiAIlyEBQRAEQRCEy5CAIAiCIAjCZUhAEARBEAThMiQgCIIgCIJwmSZXiZJhGABAUVGRm1dCEARBEI0L7t7J3Usd0eQERHFxMQAgKirKzSshCIIgiMZJcXExNBqNwzkSxhmZ0YgwGo1IS0uDj48PJBJJrVyzqKgIUVFRSElJga+vb61c093QZ2oc0GdqHDS1z9TUPg9An8lZGIZBcXExwsPDIZU6jnJochYIqVSKyMjIOrm2r69vk/nD46DP1Digz9Q4aGqfqal9HoA+kzNUZXngoCBKgiAIgiBchgQEQRAEQRAuQwLCCVQqFV5//XWoVCp3L6XWoM/UOKDP1Dhoap+pqX0egD5TXdDkgigJgiAIgqh7yAJBEARBEITLkIAgCIIgCMJlSEAQBEEQBOEyJCAIgiAIgnCZZisgli9fjpiYGKjVavTr1w9Hjx51OH/9+vWIjY2FWq1G165dsXXrVsFxhmHw2muvoUWLFvDw8MDIkSNx+fLluvwINrjymVauXInBgwfD398f/v7++H975x0eRbm28Xv7pvcKIaH3jkSQKqGrYANsgEdAUT7FjuccRSwHVBQVUWwIKqKoCCpKJ4CAIL2HFkJNQkJ6z+58f8xO3dnN7mY3u0me33Xl2pl33p19J7M7c8/zPiUlJcWq/+TJk6FSqSR/I0aM8PRh8DhzPEuXLrUaq9FolPSpb+do0KBBVsekUqkwevRovo+3z9H27dtx++23Iz4+HiqVCqtXr67xPampqejRowcMBgNatWqFpUuXWvVx9vfpTpw9plWrVmHo0KGIiopCcHAw+vTpg/Xr10v6vPrqq1bnqV27dh48CinOHlNqaqridy8zM1PSrz6dJ6XfikqlQseOHfk+3jxPc+fOxU033YSgoCBER0dj7NixSEtLq/F93rw3NUoB8cMPP+CZZ57B7NmzceDAAXTt2hXDhw9Hdna2Yv9du3bhvvvuwyOPPIKDBw9i7NixGDt2LI4dO8b3efvtt/Hhhx9i8eLF2LNnDwICAjB8+HCUl5f75DGlpqbivvvuw9atW7F7924kJCRg2LBhuHLliqTfiBEjcO3aNf5vxYoVdXE4Th8PwGZjE481IyNDsr2+naNVq1ZJjufYsWPQaDS49957Jf28dY4AoKSkBF27dsWiRYsc6p+eno7Ro0dj8ODBOHToEGbOnIkpU6ZIbriunHt34uwxbd++HUOHDsUff/yB/fv3Y/Dgwbj99ttx8OBBSb+OHTtKztNff/3lieEr4uwxcaSlpUnGHB0dzW+rb+fpgw8+kBzLpUuXEB4ebvV78tZ52rZtG5544gn8/fff2LhxI6qqqjBs2DCUlJTYfI/X701MI6R3797ME088wa+bTCYmPj6emTt3rmL/cePGMaNHj5a0JScnM48++ijDMAxjNpuZ2NhY5p133uG35+fnMwaDgVmxYoUHjsAaZ49JTnV1NRMUFMQsW7aMb5s0aRIzZswYdw/VIZw9nq+++ooJCQmxub+GcI4WLFjABAUFMcXFxXybN8+RHADML7/8YrfPCy+8wHTs2FHSNn78eGb48OH8em3/T+7EkWNSokOHDsycOXP49dmzZzNdu3Z138BqgSPHtHXrVgYAk5eXZ7NPfT9Pv/zyC6NSqZgLFy7wbb50nrKzsxkAzLZt22z28fa9qdFZICorK7F//36kpKTwbWq1GikpKdi9e7fie3bv3i3pDwDDhw/n+6enpyMzM1PSJyQkBMnJyTb36U5cOSY5paWlqKqqQnh4uKQ9NTUV0dHRaNu2LaZPn47c3Fy3jl0JV4+nuLgYiYmJSEhIwJgxY3D8+HF+W0M4R19++SUmTJiAgIAASbs3zpGr1PRbcsf/yduYzWYUFRVZ/ZbOnDmD+Ph4tGjRAg888AAuXrzopRE6Trdu3RAXF4ehQ4di586dfHtDOE9ffvklUlJSkJiYKGn3lfNUUFAAAFbfIzHevjc1OgGRk5MDk8mEmJgYSXtMTIzV/B5HZmam3f7cqzP7dCeuHJOcF198EfHx8ZIv2ogRI/D1119j8+bNeOutt7Bt2zaMHDkSJpPJreOX48rxtG3bFkuWLMGaNWvw7bffwmw2o2/fvrh8+TKA+n+O9u7di2PHjmHKlCmSdm+dI1ex9VsqLCxEWVmZW77L3mb+/PkoLi7GuHHj+Lbk5GQsXboU69atwyeffIL09HT0798fRUVFXhypbeLi4rB48WL8/PPP+Pnnn5GQkIBBgwbhwIEDANxzzfEmV69exZ9//mn1e/KV82Q2mzFz5kzccsst6NSpk81+3r43NbhqnITzzJs3D99//z1SU1MljocTJkzglzt37owuXbqgZcuWSE1NxZAhQ7wxVJv06dMHffr04df79u2L9u3b49NPP8Xrr7/uxZG5hy+//BKdO3dG7969Je316Rw1Br777jvMmTMHa9askfgLjBw5kl/u0qULkpOTkZiYiJUrV+KRRx7xxlDt0rZtW7Rt25Zf79u3L86dO4cFCxbgm2++8eLI3MOyZcsQGhqKsWPHStp95Tw98cQTOHbsWJ36ybhCo7NAREZGQqPRICsrS9KelZWF2NhYxffExsba7c+9OrNPd+LKMXHMnz8f8+bNw4YNG9ClSxe7fVu0aIHIyEicPXu21mO2R22Oh0On06F79+78WOvzOSopKcH333/v0AWsrs6Rq9j6LQUHB8PPz88t595bfP/995gyZQpWrlxpZVaWExoaijZt2vjseVKid+/e/Hjr83liGAZLlizBQw89BL1eb7evN87TjBkz8Pvvv2Pr1q1o2rSp3b7evjc1OgGh1+vRs2dPbN68mW8zm83YvHmz5AlWTJ8+fST9AWDjxo18/+bNmyM2NlbSp7CwEHv27LG5T3fiyjEBrHfu66+/jnXr1qFXr141fs7ly5eRm5uLuLg4t4zbFq4ejxiTyYSjR4/yY62v5whgw7QqKirw4IMP1vg5dXWOXKWm35I7zr03WLFiBR5++GGsWLFCEmZri+LiYpw7d85nz5MShw4d4sdbX88TwEY7nD171iFBXpfniWEYzJgxA7/88gu2bNmC5s2b1/ger9+bau2GWQ/5/vvvGYPBwCxdupQ5ceIEM23aNCY0NJTJzMxkGIZhHnroIWbWrFl8/507dzJarZaZP38+c/LkSWb27NmMTqdjjh49yveZN28eExoayqxZs4Y5cuQIM2bMGKZ58+ZMWVmZTx7TvHnzGL1ez/z000/MtWvX+L+ioiKGYRimqKiIee6555jdu3cz6enpzKZNm5gePXowrVu3ZsrLy33ueObMmcOsX7+eOXfuHLN//35mwoQJjNFoZI4fPy455vp0jjj69evHjB8/3qrd2+eIG8PBgweZgwcPMgCY9957jzl48CCTkZHBMAzDzJo1i3nooYf4/ufPn2f8/f2Z559/njl58iSzaNEiRqPRMOvWreP71PR/8rVjWr58OaPVaplFixZJfkv5+fl8n2effZZJTU1l0tPTmZ07dzIpKSlMZGQkk52d7ZPHtGDBAmb16tXMmTNnmKNHjzJPPfUUo1armU2bNvF96tt54njwwQeZ5ORkxX168zxNnz6dCQkJYVJTUyXfo9LSUr6Pr92bGqWAYBiGWbhwIdOsWTNGr9czvXv3Zv7++29+28CBA5lJkyZJ+q9cuZJp06YNo9frmY4dOzJr166VbDebzczLL7/MxMTEMAaDgRkyZAiTlpZWF4fC48wxJSYmMgCs/mbPns0wDMOUlpYyw4YNY6KiohidTsckJiYyU6dOrbOLg7PHM3PmTL5vTEwMM2rUKObAgQOS/dW3c8QwDHPq1CkGALNhwwarffnCOeLC/eR/3HFMmjSJGThwoNV7unXrxuj1eqZFixbMV199ZbVfe/8nT+PsMQ0cONBuf4ZhQ1Xj4uIYvV7PNGnShBk/fjxz9uxZnz2mt956i2nZsiVjNBqZ8PBwZtCgQcyWLVus9lufzhPDsCGMfn5+zGeffaa4T2+eJ6VjASD5ffjavYnKeRMEQRAE4TSNzgeCIAiCIIjaQwKCIAiCIAinIQFBEARBEITTkIAgCIIgCMJpSEAQBEEQBOE0JCAIgiAIgnAaEhAEQRAEQTgNCQiCIAiCIJyGBARBEARBEE5DAoIgCIIgCKchAUEQBEEQhNOQgCAIgiAIwmlIQBAE4TCpqalQqVRITU319lC8QlJSEiZPnuztYRCET0ACgiA8yNKlS6FSqSR/0dHRGDx4MP78809vD49QYNeuXXj11VeRn5/v7aEQhE+j9fYACKIx8Nprr6F58+ZgGAZZWVlYunQpRo0ahd9++w233Xabt4fnMAMGDEBZWRn0er23h+Ixdu3ahTlz5mDy5MkIDQ2VbEtLS4NaTc9dBAGQgCCIOmHkyJHo1asXv/7II48gJiYGK1assCsgqqurYTabfeaGrVarYTQavT0Mr2EwGLw9BILwGUhKE4QXCA0NhZ+fH7RaQcNfuHABKpUK8+fPx/vvv4+WLVvCYDDgxIkTAIAtW7agf//+CAgIQGhoKMaMGYOTJ0/y7z9y5AhUKhV+/fVXvm3//v1QqVTo0aOH5PNHjhyJ5ORkfj0pKQm33XYb/vrrL/Tu3RtGoxEtWrTA119/LXmfkg/Ejh07cO+996JZs2YwGAxISEjA008/jbKyMsl7J0+ejMDAQFy5cgVjx45FYGAgoqKi8Nxzz8FkMtX4P+PGmJqail69esHPzw+dO3fmx7Jq1Sp07twZRqMRPXv2xMGDB632UdP/8NVXX8Xzzz8PAGjevDk/7XThwgV+DHIfiPPnz+Pee+9FeHg4/P39cfPNN2Pt2rWK/7eVK1fizTffRNOmTWE0GjFkyBCcPXu2xmMnCF+ELBAEUQcUFBQgJycHDMMgOzsbCxcuRHFxMR588EGrvl999RXKy8sxbdo0GAwGhIeHY9OmTRg5ciRatGiBV199FWVlZVi4cCFuueUWHDhwAElJSejUqRNCQ0Oxfft23HHHHQDYm7tarcbhw4dRWFiI4OBgmM1m7Nq1C9OmTZN87tmzZ3HPPffgkUcewaRJk7BkyRJMnjwZPXv2RMeOHW0e248//ojS0lJMnz4dERER2Lt3LxYuXIjLly/jxx9/lPQ1mUwYPnw4kpOTMX/+fGzatAnvvvsuWrZsienTp9f4fzx79izuv/9+PProo3jwwQcxf/583H777Vi8eDH+/e9/4/HHHwcAzJ07F+PGjZNMOTjyP7zrrrtw+vRprFixAgsWLEBkZCQAICoqSnE8WVlZ6Nu3L0pLS/Hkk08iIiICy5Ytwx133IGffvoJd955p6T/vHnzoFar8dxzz6GgoABvv/02HnjgAezZs6fGYycIn4MhCMJjfPXVVwwAqz+DwcAsXbpU0jc9PZ0BwAQHBzPZ2dmSbd26dWOio6OZ3Nxcvu3w4cOMWq1mJk6cyLeNHj2a6d27N79+1113MXfddRej0WiYP//8k2EYhjlw4AADgFmzZg3fLzExkQHAbN++nW/Lzs5mDAYD8+yzz/JtW7duZQAwW7du5dtKS0utjnvu3LmMSqViMjIy+LZJkyYxAJjXXntN0rd79+5Mz549lf+BIrgx7tq1i29bv349A4Dx8/OTfNann35qNU5H/4fvvPMOA4BJT09XHMOkSZP49ZkzZzIAmB07dvBtRUVFTPPmzZmkpCTGZDIxDCP839q3b89UVFTwfT/44AMGAHP06NEaj58gfA2awiCIOmDRokXYuHEjNm7ciG+//RaDBw/GlClTsGrVKqu+d999t+SJ99q1azh06BAmT56M8PBwvr1Lly4YOnQo/vjjD76tf//+OHDgAEpKSgAAf/31F0aNGoVu3bphx44dAFirhEqlQr9+/SSf26FDB/Tv359fj4qKQtu2bXH+/Hm7x+bn58cvl5SUICcnB3379gXDMIrTCI899phkvX///jV+hniMffr04de5aZhbb70VzZo1s2rn9uvM/9AZ/vjjD/Tu3VvyvwwMDMS0adNw4cIFfvqJ4+GHH5b4s3D/b0ePnyB8CRIQBFEH9O7dGykpKUhJScEDDzyAtWvXokOHDpgxYwYqKyslfZs3by5Zz8jIAAC0bdvWar/t27dHTk4OLxj69++P6upq7N69G2lpacjOzkb//v0xYMAAiYDo0KGD5EYKQHID5ggLC0NeXp7dY7t48SJ/Y+b8GgYOHAiAnboRYzQaraYDHPkMW2MMCQkBACQkJCi2c/t15n/oDBkZGTb3Kf5cW+MPCwuTjJMg6hMkIAjCC6jVagwePBjXrl3DmTNnJNvET/TO0qtXLxiNRmzfvh07duxAdHQ02rRpg/79+2Pv3r2oqKjAjh07JJYGDo1Go7hPhmFsfp7JZMLQoUOxdu1avPjii1i9ejU2btyIpUuXAgDMZrNDn+Eott7vyti9QX0ZJ0E4AjlREoSXqK6uBgAUFxfb7ZeYmAiAzUEg59SpU4iMjERAQAAAQK/Xo3fv3tixYweaNWvGC4X+/fujoqICy5cvR1ZWFgYMGOCWYzh69ChOnz6NZcuWYeLEiXz7xo0b3bJ/d+HM/1ClUjm1X1v7FH8uQTREyAJBEF6gqqoKGzZsgF6v583dtoiLi0O3bt2wbNkySXbEY8eOYcOGDRg1apSkf//+/bFnzx5s3bqVFxCRkZFo37493nrrLb6PO+CeqMVP0AzD4IMPPnDL/t2FM/9DTkg4koly1KhR2Lt3L3bv3s23lZSU4LPPPkNSUhI6dOjgtmMgCF+DLBAEUQf8+eef/FNpdnY2vvvuO5w5cwazZs1CcHBwje9/5513MHLkSPTp0wePPPIIH4IYEhKCV199VdK3f//+ePPNN3Hp0iWJUBgwYAA+/fRTJCUloWnTpm45rnbt2qFly5Z47rnncOXKFQQHB+Pnn3/2yTl9R/+HPXv2BAD85z//wYQJE6DT6XD77bfzwkLMrFmzsGLFCowcORJPPvkkwsPDsWzZMqSnp+Pnn3+mrJVEg4YEBEHUAa+88gq/bDQa0a5dO3zyySd49NFHHXp/SkoK1q1bh9mzZ+OVV16BTqfDwIED8dZbb1k5Xfbt2xcajQb+/v7o2rUr396/f398+umnbrM+AIBOp8Nvv/2GJ598EnPnzoXRaMSdd96JGTNmSD7bF3D0f3jTTTfh9ddfx+LFi7Fu3TqYzWakp6crCoiYmBjs2rULL774IhYuXIjy8nJ06dIFv/32G0aPHl2Xh0cQdY6KIe8dgiAIgiCchOxrBEEQBEE4DQkIgiAIgiCchgQEQRAEQRBOQwKCIAiCIAinIQFBEARBEITTkIAgCIIgCMJpGlweCLPZjKtXryIoKMiplLQEQRAE0dhhGAZFRUWIj4+vMRFagxMQV69etarMRxAEQRCE41y6dKnGjLUNTkAEBQUBYA/ekRTBBEEQBEGwFBYWIiEhgb+X2qPBCQhu2iI4OJgEBEEQBEG4gCMuAORESRAEQRCE05CAIAiCIAjCaUhAEARBEAThNCQgCIIgCIJwGhIQBEEQBEE4DQkIgiAIgiCchgQEQRAEQRBOQwKCIAiCIAinIQFBEARBEL4Ow3h7BFaQgCAIgiAIX+bgcmBeMyB9h7dHIoEEBEEQBEH4MmseByoKgWW3AWazt0fDQwKCIAiCIOoL+5d4ewQ8JCAIgiAIwlcxVUvX0/70zjgUIAFBEARBEL7K0ZXS9Yoi74xDARIQBEEQBOGr5JyRrpfmemccCpCAIAiCIAhfpTibfe08jn0tyfHeWGSQgCAIgiAIX6XEIiCi27Gv5fnWVgkvQQKCIAiCIHwVzgIR2VZoW/OEd8Yiw6MCYvv27bj99tsRHx8PlUqF1atX1/ie1NRU9OjRAwaDAa1atcLSpUs9OUSCIAiC8F04AREcD4Q0Y5cv7fHeeER4VECUlJSga9euWLRokUP909PTMXr0aAwePBiHDh3CzJkzMWXKFKxfv96TwyQIgiAI38NsBkqus8uB0cDUzdJtXkbryZ2PHDkSI0eOdLj/4sWL0bx5c7z77rsAgPbt2+Ovv/7CggULMHz4cE8NkyAIgiB8B4Zh//Z8Apir2LaAKMBsEvpUFgPGYO+Mz4JHBYSz7N69GykpKZK24cOHY+bMmTbfU1FRgYqKCn69sLDQU8MjCIIgCM+z6VVg31dARYHQpjWwokKlARiTTwgIn3KizMzMRExMjKQtJiYGhYWFKCsrU3zP3LlzERISwv8lJCTUxVAJgiAIwv2U5AA735eKBw6VCjAEsssVxcCfs4CVk4DMY3U6RA6fEhCu8NJLL6GgoID/u3TpkreHRBAEQRCukXvWum3gLGFZH8S+VhYB5zYDJ1YDZXl1MjQ5PjWFERsbi6ysLElbVlYWgoOD4efnp/geg8EAg8FQF8MjCIIgCM9SnGXd1m+msGywCIiKIqCqnF3WKd8fPY1PWSD69OmDzZs3S9o2btyIPn36eGlEBEEQBFGHcGGbYsQCQTyFUW2Z2tcaPT8uBTwqIIqLi3Ho0CEcOnQIABumeejQIVy8eBEAO/0wceJEvv9jjz2G8+fP44UXXsCpU6fw8ccfY+XKlXj66ac9OUyCIAiC8A2KMu1v11sERGVxw7ZA7Nu3D927d0f37t0BAM888wy6d++OV155BQBw7do1XkwAQPPmzbF27Vps3LgRXbt2xbvvvosvvviCQjgJgiCIxsH1U/a3i6cwvGyB8KgPxKBBg8AwjM3tSlkmBw0ahIMHD3pwVARBEPULhmGgUqm8PQzC0zAMkLFL2hbcRLrOCYiyfMBczS43RAsEQRAEUTu2nMpCrzc2YcspBec6ouFw5EfgwDKg7Ia0/cGfpevcFMbWN4W2hugDQRAEQdSOfy3dh9ySSvxr6T5vD4XwFGV5wKopwG9PWW+Lbi9d5ywQEFn3SUAQBEEQRCPEmTwOXBSGGLV3buUkIAiCIAjCm5TlO95XryAgvIRPJZIiCIIgBK7mCyn8tWoVqk1mmBlAr6VnvwZBZQlwZgNwTObn0GEMENEaaDvK+j0G79a/EEMCgiAIwkf44+g1nMkqxpNDWuGbvzPwyprjku3DFmwHA+Cnx/ogIpAy8NZ71v8b2L/Uuj0wFhjysvJ7AiI8OiRnIAFBEAThIzy+/AAAILlFOH45eEWyrdrM4HxOCQDgj2OZeOjmxDofH+FGLvylLB4AwC/U9vsS+0nXWw9z14ichgQEQRCEj5FVWI6KKrPN7cXl1XU4GsIjLB1te5sx1PY2nRF4aDWwexHQczIJCIIgiMaOySyE5ZkZBldE/g9yKqpNdTGkGimrNEGlAow6jbeH0rCwZ4EAgJaD2T8vQ544BEEQPkBppWBVKCqvRkFZlc2+FdW2rRPuoLLajGlf78MXO87b7PPdnoto/8o63LN4l92Mw4QCNUVdaPR1MozaQgKCIAjCByirFKwKF3JK7fat9LCA2HQyCxtOZOGNtSclkSBi/v3LUQDAsSuFuJBrf7yEjNxz1m2BsUCXCWyUReItdT8mFyABQRAE4QOUigREWlYhAEClAvwUpgc8PYVRLZpO6TtvC3KLKyTbxdMtAPDt3xlu++zSymo8+MUeLNp61m379Dku7rZuM4YAYz8BXkgHguPqfkwuQAKCIAjCBygRTWGkZRYDAIa0i8HRV4dhaIcYSV97DpbuQKuWFu7alyHNlCgeKwBsOZXtts/+aucF/HU2B++sT3PbPn2OK/ut2zrfw2aU1NQf10QSEARBED6AeAojx/LE3zTMD1qNGvEh0loHnvaBKK6QCoQcmQVCHgVyJb8MZrN7/CD2ZziR1rm+kn1Sut71PuCWmV4ZSm2oP1KHIAiiASOewuBoEsqWaY4PlZZr9rQPhFwgXLoh+EHsu3ADR68U8OtqFTuenOIKRAe7VtSJYRjM+vkoooIMKBGJlwZZxryyFMg9I2275SlAWz8cJ8WQgCAIgvABFAVEmLKA8LQPRInMAnGjhLVAFJRV4Z7Fwvx9Qrgfqk0MrhWU42pBucsC4sDFfPyw7xIAoE8LIdNiaaUJAYYGdptK3w6Yq4GQZsDwN4D8S9YVN+sJDezMEARB1E/KqqyTQ3HCoUdimKTd41MYlXIBUYlFW89a+SUEGnQAgGsF5XbDTmvi0g0hiqOsShBHJRXVDU9A5Fj+h82S2ZoX9ZgGdmYIgiDqD2WVJkz6ai/6t4pEeKC1CZubwmgS6ocJNyXg+3/Yp3RPCwi5BWLTyWxsOmntKBlk0IKbYSishYDILCznl3NLBH+L4opqRLu8Vx+looh9tZdtsp5ATpQEQRBe4rfDV7E3/Qbe3Xga//nlmNX2SJGomHd3F3z18E0APO8DkVNU6VC/8AA9QvxYK8T/rTgosSQ4w40S4fNyi4XlBZvOKHWv35SzIbow+k5VTVchAUEQBOElSivt17SQOxAaNOwl29M+EJfyWCHw5JDWdvslhPuh0iSImf5vb8WJq+wNMqe4wuEMleL/g9gX5LfDVx0ec72hwiIgfKgst6uQgCAIgvASZXbyORh11pdno55NKlVS4T4BkVlQjozcEkkbZ0kY3jFG6S08TcP8cb1IGuI56sMdeH/TafR6YxNufXcbjlzOr3EMSg6kHHN+O25zW72ELBAEQRBEbckSzf3L4RwUxQQbWbc1eZ4GV2EYBnd/sgsD30nFqcxCft+FljDOpIgAnHlzJMIDlEMMm4T6WWWlBID3LVMP6TkluOOjnci2c5yANAeGnK92XmhYtTbIAkEQBEHUltwS274GnFgQw4mK4opqt9xUK6rNfNXPlf9cxqnMQvx7FVvjwl+vQYBBC51GjaQIf8X3Nw33w+tjO9X4Ofd/scfudnsWCAAocpNg8glIQBAEQRC1RSlyITbYCL1Gjbfv6WK1LcgiKkxmRhLu6CpFooRROcUVGPH+Dvxq8TsQWx1C/W1bIG5KCsePj/Wx+zlns4vtbrdngQCkjpX1HprCIAiCIGpLYbm1gHhmaBscnTMMvZLCrbb56zXgylQUldf+qVw8FfKrzGFRbOAQR0l8+lBPfjnIyFpEmoZJE10pUWWy7e9RKsuBISvFgT3nc2vcv2R/ldV47Jv9+Hn/ZafeVydwYZxkgSAIgiBcRckCEeyng0FrXYETYKMyAi2JldwhIOT5HsRcEZXxvq0LWx2ya0IohnWIwXPD2kiERExQzRko71m822a9DPkUhrzbrFVHkV1k349CzOLUc1h3PBPP/njY4ffUGfwURpB3x+EGSEAQBEF4Cc5ZcdbIdnxb56Yhdt/DPfUXKVgvnMWeCHk6pQ2//ODNifjwvu5YMTUZKpUKM25tjeEdY/ntapHJ4PFBLfH4oJZW+zt8KR+rD12xar90oxTnr5dYta+fOUCyfiHH8RwTxyyhpD5HVTlgslhzaAqDIAiCcBXOAnGzpf5DoEFrVXlTTrAlcVN+LTI/ctiK5vjpsT54fLAgAow6De7oGg9/ve3kxSum3ownBrfE00Pb4P9uVc4fcfBivlXb9jPXFfu2jQ3ChqcFEVFtdjx51lWR9cSn4KwPUAF6skAQBEEQLlBeZeJTUjePDEDqc4Ow7flBNVafjAoyAIBV/gVXsDWF0alJCHQa524PfVpG4Pnh7aDTqOGn1+Dw7GF4QxahoZTbQl75U0ybmCB0bsJaZMqdcBo9lVnEL284nok00bpXKctnXw1BgLr+336pFgZBEIQX4KYPVCq2pgSXEromot0oIJTCI9Uq1uJQW0L8dHjw5kTEBhsx5et9AIASma9DQWkV5v55yuq9d3Zvwi/7W5Jn1RTqySG3Pkz7Zj8A4MK80Y4P3lP8+Tz7WuGjUyxOUv8lEEEQRD2Ei8AINGglPgQ1wQmImpIzOYLS0/+ef6fUer9iBreL5gtuZRdKRY/YJ8JPJFrm3tWZX3ZGQFzOK0XfeVsUt10r8PK0RlU5cD6VXda6Vvbc1yABQRAE4QU4/4dgo2OWB45Yi4/ERRcLV4lRmsKwlXXSVTRqFRbd3wMAsOlkFg5dyue3Xc4TjuHeXk3xQHIzfDmpl8QC4mcREI5MYbzx+0mb205ec+2pv8pkxhu/n8ATyw+g1xsbsT/jhkv7wT9fCMtTlUWOs4z/dDf6zt2M3eecC3N1FyQgCIIgvAAXgRHs4NQFR/eEMADA9jM5tbZCKDlRapywhjiKeHpm7KKd/PIJ0U29ysTgzTs7Y0h7af0NPx07016TBaKi2oR1xzNtbs8rcc3p9Mu/0vHFX+lYe/QacoorMWXZPuQWuzB9lL6NfU2ZA8R0dGks209fxzMrD+H8dTYx19WCMlwtKIde6/5z5ggkIAiCILyAYIFwzhWtY3wwmoaxNSiW1LJOhDtySTiC3L+DYRiYzAyOXCrg2wL0yn4Xjk5hnLpm31FSKWmXI2w8kSVZzyutwv2f20/NbUVFEZCxi11uPsB+XxswDIOJS/Zi1YErWLbrAgAhQ2d4gMGlfdYWEhAEQRBeoMhFC4RarcKUfs0BAIu3ncO8ddZOiI5QXmXCzwfqJlOjXEDMWHEQP++/zDtx9kwMw3SF3BGA41MYZ2pIl13gYthrfql1Gu20LCejOtJ3AJXFQFhzIK6bi+MQxn8lvwzlVSZeVEUEunfayVFIQBAEQbgZs5nB2exiu9aBAhd9IABpsqlPt513yQohf7L2JHKRtPbINbzw8xEAwK3tovHz9L6ICFR+iuacK0sr7VtLnrORdXJoB3ZKxFUBUVNYbY2krQO+v49djmjpcvjmtQJhuup6cSVfiE2nUSHI4J2AShIQBEEQbmbBptNIeW8bPtx81mafvFLO/Oy8gOgYL81W+eexTKdFhLkOS2Tbu8HV5LTpyBRGZbV1kqmP7u+Ov14cjB7NWJ+RwjLXpmts/V/t/b+vF1Wgmqv9seG/wgZ9oEtjAKRRJJdvlPJ+GOEB+tqLHBchAUEQBOFmFm5hhcOCTadt9uEKVIW5EPVg1GnQVWSFeHz5Afx25JpT+xDX4Zg2oAUAoE2M6zc4e9gLU7Xl+8DhyBSGvJpnv1aRGN4xFk3D/PnpE1ctEOVVyhkwl++5qNiellmEm97chP9bcRAwVQG5Z4SNWtd9FbJFeT9ySyp5cZoUEeDyPmsLJZIiCILwAnkWARFuo1R2TSz7V290e20jv/7N7gu4o2u8w++/YYlKuK1LHF4a2Q5dm4aiR2KoS2OpDf41mN+FKQw7AkIkLv5+aQgf6goAwX7s/pUKlzmCLefL/64+hn6tIpEUKb2Bf7b9PADWKoSiaOmbzK6XYM+T+WJsOslOQaXIolbqErJAEARBeIEbpa5bIAAg1F+PAW2i+HVns0feKGGfaBMj/KFSqTC6SxziQmouy+0qvzzeV7HdUQuEvZTXnH9EkEErEQ8AamWBYBjGZr0QAJi16ohV/3PXRc6chdIS6TC7HvVSUKo8/uhg70RgACQgCIIgvIIQgue6B71eVK8iwE6hKyXyLDekUL+68eDvbvFFkGOvQBe7nRUQ+zLysD8jz2r7qcxCzPr5KABBbIjhBIQrYZwllSbIXR0+n9iLXz5+RZqc6tfDVyWJsqou7pW+mXHdAsFFYcTIBEOQk2HA7qROBMSiRYuQlJQEo9GI5ORk7N2712bfpUuXQqVSSf6MxoaR9pMgiMaHUs2K0spqXLJkYazNHDZnRQCAanPNTpFZheVIzynhxwAAgV68AQFAgKEGC4ROGN/zP7GRFvmllXjsm/14a90pTF7yD/ZeYLND+tsREK5YIOSZOif3TUJCuGClKaqo5qeiAOA7mV8Ec2SldIdumMLo0jRU0h7kQhSPu/C4gPjhhx/wzDPPYPbs2Thw4AC6du2K4cOHIzs72+Z7goODce3aNf4vIyPD08MkCILwCM8qhBeeyiwCw7B1Lbjqmq7w2EAhd4JYTCjxzvpTSP7fZgyen4ozWUUoqWBvZko33bqkJguE2KrA3ayX7rqAdccz8UnqOWSKsnH6KeyLC5MtrTShyuR4SfA953Nx5DKb6CpAr8EfT/bHf0a3R7vYYDw3rA3f7+z1YtwoqYTJzCBSci4ZaG+cke7UEOzw58vhyrf3bRkhaW/QFoj33nsPU6dOxcMPP4wOHTpg8eLF8Pf3x5IlS2y+R6VSITY2lv+LifGekwhBEIQz/H1eWpfgoMzsbjIz+HY3+1DUId71GwoADOsYi28fSQYgTEmIMZsZPtxw0dZzfPt3ey+i1OJ46OzUR23g0mSP69WUb1MKwRQjFjic6Mm2UYnUT6FcuDgHhaNWiKv5ZRj/2d+Yaqki6m/QokN8MF/ifMatrdEzkZ2S+f3wVfR4fSMWbDwtsUZEIR/q6jJApQZuex+I7wGkzHbo85XgElq1jg5CpChxlCt5RNyFRwVEZWUl9u/fj5QUobqbWq1GSkoKdu/ebfN9xcXFSExMREJCAsaMGYPjx4/b7FtRUYHCwkLJH0EQhLf4ame6ZD1SZmFYvicDqw6yVSjbx9VOQADCnPiNEqmXfpXJjFEf7sD4z/62CoH8af9lFFlupv41TCG4k3VP9ccLI9ritTGd0KNZKDRqFXo3D7f7HqNWGF+1mRUbtlJwK1kzNGoVX8GUm76pifPXpf2UrDTcTXyZRQx+tPUsfw6aqbLwoHYz2zG4KdDrYWDaViDY8SgZObzPir8OkaKkW960QHj0k3NycmAymawsCDExMTh1Sjn9atu2bbFkyRJ06dIFBQUFmD9/Pvr27Yvjx4+jadOmVv3nzp2LOXPmeGT8BEEQzhIbLPXZkt+8ObM4AAxoHYXawjlhFpRVodpkhtbylHw2uxinMtmUy7vO5UjeU1Rezd+E69IC0TomCK1jggAAy6fcjOKK6hqncMQCx8ywVpUiJx0iezQLw7rjmdifkYebkuwLFgDILpIWKfNTiHCJVMicyQmP7Yanhcbw5k6NVQmGYXgLRFiAXjIVU5fnT47PRWH06dMHEydORLdu3TBw4ECsWrUKUVFR+PTTTxX7v/TSSygoKOD/Ll26VMcjJgiCELhheVJMivAHYO2Ix2UU/Peodugjm892hRA/HbhEhOJpDHHthG//Vk56BNTsxOgp/PQah/w/IgMNePueLvz6jdJK+BdfxP+0XyBRJa2+qRSFAQDNo1hH1cyCcuzPyKtx2uR3WVIupf0qjb1SyccivIXdz3KEkkoTqkzsVFSYv04SWmovSZen8aiAiIyMhEajQVaWNOd6VlYWYmNjHdqHTqdD9+7dcfasckpYg8GA4OBgyR9BEIS3uG55en0gOREAFwooREhcy2e3d24S6pbP02rUfKSBONlQlsi5cMsp207rNTkx+gLjeiUgwmJpyS6swAt5r+J+7RZ8rZsn6Rcfohyxx+WaWLrrAu7+ZBfeWa9sAS+rNCE1LVvy/9KiGtNKPwNOr5f0bRrmb/V+DUwwQFZ8K0K5SJgzcL4Veq0afjoN5tzBlgP/7+j2td53bfCogNDr9ejZsyc2b97Mt5nNZmzevBl9+vRxaB8mkwlHjx5FXFycp4ZJNDTKC4Hl44BDK7w9EqIRwj35Nw1jw/1MZgYVlidehmFw1WKBiA91X3h6qEKoojg6geORftbmdG9HYdRI5jFg7bPoEXAdADu9kGRmLc2JauFGHxmox/RBrRR3IY/O+HyH1E/FbGawfE8GUt7bhslf/SPZNkGzFSOLVwPfjZO0cxYmDi2q8YP+daQZJ0s/vMUge0fnENx3KsxfB5VKhRGd4nB49jBM6V9760Zt8Lj0fOaZZzBp0iT06tULvXv3xvvvv4+SkhI8/PDDAICJEyeiSZMmmDt3LgDgtddew80334xWrVohPz8f77zzDjIyMjBlyhRPD5VoKOxaCJxZz/51u8/boyEaKIXlVQgyaK0KGXG+BdEiX4iSimqsPXINl/JK+doK8oyJtYG7QYrTPSulbpaXfVargAAvVXJ0mMW3AADuD7yGjXhAMQKjX6tIfP2v3jbN+fJsl3Kfhj+OXcN/fjmm+N4WKuUaIy2ihLohahUwQHUEvdTWtU/MUR1r/aTOWZbCRGnP5SXSvYHHvznjx4/H9evX8corryAzMxPdunXDunXreMfKixcvQi0qb5qXl4epU6ciMzMTYWFh6NmzJ3bt2oUOHTp4eqhEQ6HgsrdHQDRwdp3Nwf1f7MHjg1rihRHtJNu4+ekQPx38dBqUVZmQW1IpyQcRFWSAQeu+J38ufFFcVEqpdsTgttF4e10av94mJogPTfRJygWH06YM6+/AnNlo1S0iUG/XF0Duw2CQhXseFTm2ytFBOeIjPECP54a1wcp9l9GnRQS0BzdZ9fmmOgW33CiViA1X4AREqL/3RYOYOvnmzJgxAxkZGaioqMCePXuQnJzMb0tNTcXSpUv59QULFvB9MzMzsXbtWnTv3r0uhkk0FMT55s2OJ44hCEeZ89sJAMDHqWxuhct5pcguLJfUTggyavmn+2NXpDeo+FD31pzg/BjKqoTvPpdpUkxUkAF/PtWfX69tHgqPc114otdrVNCjCuPTnrbqdmf3JnZ3I49UqBI5UZZXmfCppQCWnKQIf+htCAiAzQex/YXB6N8mEiGQhn6aGBVmV0/GyWtFdsfmCMIURt2kHXcUH5aeBCHDbAJyzsAqOb0ck8iJqYCicgj3Iw6jKyitwvAF2zHigx0oLKuGyZJSOtCgRYilEqS4PgJg29nPVbgn7FI7FohHB7ZAZKBB8hQb78HiWW5B9PsNZIrRVmX9e348fB8GNbN/Y5X7eYijJdIybd/gVz1+C0a2V67hISYiwIBgVamkLY1pBjPUSM8ptvEuxxEsECQgCMI1/nwB+KgXcOp3u93Kim4IKx90ASpq/wRAEGLEN6D9F2+gpNKEGyWV6PraBr7dX6/hL/gnrkoT3LnbAsHN6StNYbw+piMOvzIML41kPfbFxbN83v+hUrj5+lUXIlBVZtXlhdL3gNWP292NvGQ4FxIJCFVRlQgP0CNYJ3pg2b9UsV9UkAHBkAqFw51mAQByim3v31G4709YY5zCIIhawzDAP1+wy38tsNktr6QSZzJkTyl/L/bgwIjGiDiPgFwccKhUKj464kKu9Ok0zs0WCO4JWywgLt5gPzPUX48Q0Y3HKJr/12m8l0PAISqEm7K+uhD+sI4sAQCkrQVMtpNLKUWacFakzAIb++QQWzR/e0qxS2KEP0JU7BTGd+FPAC+koyyejTS8Xmy/RklNZBWWY8MJNhVC29igWu3L3ZCAIOoHZaJ6AmG2M7udzylGMKQXa1zY4aFBEY0V8RSGvSdM7sadI7uJcCGe7oKfwrBkvTxxtRBns9mbr/zmKY4aSQi3zmXgU1QKfgXaqmLcobFdAgHFWTY3KQmI7/9hHzTEAsKoUEvDEQumTqPmfSCiomMB/3A+hXmOjbodjpL8PyENwqjOvpXOgAQEUT8oFU1LVNqeUzSZwT8JfFB9F9tYeMWTIyMaIWITuLxA0709m/IFrsTTBWLkJZlrC3eDLLaEkC7fkyHaZj1Nsej+Hnh0YAsMbe/jhQorpTfvMZpdAAAzo2A5Kcq0brOg9D94efUx/Hr4Ku/0+tjAljj52gh0bhIi7VgsS8IlL8m980Pg81vROzgfADC4BztVxNXKkIvH2uBrETO+NRqi/lGcDWx8Bcg9V3Pf2lAmEhAl1212KyytRLDlSWCd6Sa2MfecxBRaX6gp3S7hPcQ+EL8clArUZ4e1Rb/WkQCEQldyPOUD8c3fGag2mSV1GpTSK4/uEoeXRrb3ahpkh7Dxuz0QkmLdWKScrwGwnSxr+d8ZfK0So04NlUqFN+/sBKNOjVnDWgFXDgB5F6Rvkl9/Nr4MXNkPfQn7PdAGRQMQxKOtwl8NARIQRO1Y+wyw8wNg6WjPfo7YAlEoulBUlgLL7wX++ZLtVpwPjYp9OjzPxKFAGwmAAbJPenZ8bub3I1fRcfY6rDlE1hNfg2EYyRSGHHGUw4Tezay2u6MCp5zOIovG1fxyiWjoIn+irk/YsDaqDAp5FexYIAxa6a3uvt4JAIDTWUUoswgIToR1aRqKo68Ox2OFHwKfDwZMMguCnQcYAEAAKyD8FSJjGhokIIjacWEn+2pH/buFlROF5aKrbIKZylLgwNfAmQ2skAFQUZTLvjJaVECHGxr2SRClOfI9+hyV1Wb8evgqvthxHjO+O4gqE4Onvj/k7WERMgrLq+1GEhtFWQ5D/HSYNkBIN3x/cjN8P+1mt49pYJsoNLFYNS7eKOVrJzx8SxLCAnwr9M8pbFggWsRHA4NeAjQGIN6SJ0j8kCFDni109u0doVKxxceu5rORHeLzptOogUPfKu9MPqUhJ4C95nBVREsqqyW1UByFYRhU2xGqvoCPx/AQPo8hSDq94AkYxvopYMV9wKW9QNuRQtuyO9CqnC3SlosQACqUwuLtXilN8uKLjPt0t1W+AML3yLcT9qfE88Pb4oHkZkiMCPDQiFjaxQbhSn4ZLuSW4IZFQNQ2A6LXqVR2YAwLCwcGzQL6PQ2kzgOuHpQ6WteAUadBsFGHgrIqXLUUN1N0oORoPRy4uBuoKAQ2vwa0GsK2yxPVBUQBGtYCxSWvYhigvMpss1KoEpXVZjz4xR6cvKYc4eMrkAWCqB0GUViRp/ItiC8MaovmzdgJmKuAk78K29K3ofu1HwAAxTq2THIJwwkI3/aBqKg22RQPrjy9EJ5DXDLbEXQatcfFAwC0sYT4Hbmcz2cuDPexxENOY0sUBFmqOWsNgJ8l0ZOTDzJcTgUuCsOos3ODbzcK0FkiVq4dEtrl15U7PuIXxfU2ShSygtojNS0bey/cQFGFb/tPkIAgaoc4RvpGuu1+tSHf4lEeEA10vMuhtwSEs+FORYzFmczHnSjtZcP7fMd5t3pyE7Wj1HJRDzZqodeoEWjQ4sRrw/HowBZ89IU36J0UDgD450IenxwpLMC3Eg85TVk++3rPEml7aKKwzAsIxy0QAPipHc5fRCIgqmQJq3T+wOB/W+9ELCDuWQK0HcGvqtUqwQ+iwjE/iL/O5OCtdadwJtu3r1ccNIVB1I7SXGH5+Cogrov7P4Nzjgppwv45gCE0DrgIZJZp2W+5j09hcCZnJf73xynsPpeLrx7uXYcjImzBleZOjAjAe+O6IthPB3+9ls/06C26NGWdJS/klvBPv75WO8FpOFEQ1w0ISRBSW4e5LiC48Er5/0YiIOT+FCo10OEO4Lcn2XVTFTtVwT2YGEOBTndbfZa/XovSSpPDFog5vx2vN+IBIAsEURsYBigXzdGl/emZz+GeQvzCYApyTEAgPAkAUIL6MYVRVoOn9ta0Gjy/iTqDC/szaNVoHROEmGD3ZpV0lYhAA6KCDGAYwfM/3NccKE3VQP5Fx/pWVwq/W78waf6FkARh2REBkXcB/2rF7msWl9JblhbaKI7UED8YBUQDrYcBeoXpWu7VoJwh0tlIDHvi4fOJvRzaR11CAoJwnUt7WD8Ejuunai505SwVRcD2d9hlYyhK297p0NvMrYYDAEphmcIoz3fvuNwMF0omxlbsOuFdZv96HEANc+ZeIilCmlnS18o/4+d/Ae93Bo79DCzux/7Zip7gBYGKfcIXR1JoRMflHy7rL8NUDXzQFa9cnoZfHu6Au3uwDyFyC4TEyZETEFHtgaePA8ZgQKMV/CAqLA9OXJK6gCjFj+YTfLnBl2FoB99L+kUCgnCdJcOt2zbPce9nbHwFuGFJUuUXinKN/Vzwf5h64/0m78GvaWfphgNfs080Pgr3hDKkXTRGdIzFSyPbYfmUZDSPZJ3vdBoVzGZypvQ21wrKkG1JTWz2QedWcbXGQIMWBq2PiZwTa9jXn/4FZB5l/5bfq9yXEwR+oYBazU4jKCG2QMijIgA2QsNC9/BKPqRTXphKOoVhERABkYBWJDQMlhwenOX1ehr7GtVWcWhRlnTW1x1IZ202M1D5eF4vOSQgCMcwVQObXgXObbXfz06hqxq5ngYsu0PILVF8XVr9zhiK8ioT0sxNAQAXdC2FbcnT8Xmn5Xi86ikUxvZBkFGHuBAjMswi1V5sO9FMXfNx6lnc8dFfyC5iPcA5s3iQUYvFD/XEowNbonuzMPz5VH8AbOrkqV/vw950D4fMNjJ+PXwVr6w5xpfgromcIkGEVpt8T0CIoy56JdVchtonuLJPuZ2LquAEwuh32df+z0r7GUPZV8asHPZ5ea+wLHL6lpfGDvETCQrOKsJZNzi4qQpu6uLKfvbVhoCItUxvZRZYVxGVw+aLkLY9OaQ1tGqVT05fACQgCEc5sJQVB9+M9dxnrJwIpG8Dlo5iq97Nb8VeFDiKs1BeZcL0qplYUT0Y/yr9P5TdvwZodxvQ/xkcq24CQIXYEFb1Tx/UEn+YRV7xcs9qL1FYXoW316XhyOUCfLGDjVzhfCDkseIGrRpaS7rhzaeyMe5TO8WECKd5csVBfL07A38cdSwRWmahUHipSulp18uEiqIuuifUEwEBANUKT+i8BcJyE28zHHg2Dbj1ZWk/nVGYWlCaxji3RfFz5P4hUaL033zlX/8I6b54AVHIXk/ObmLXWw+z/lwAcZbkXldrqvgJ5WmOp1Na4+ArQ31y+gIgAUE4StYJYdlO2dxacf2UsCy2PHA0uxnlVWacZ+LxUvVUnDdFY5epPTBhORAYjWuWhDCcU1ugQYsK6JHLZaP0kUgMcfnnPRaLQimfTlcaGKVSqRBgoGApT3AhR/g+2IuCESMWEL5ugahXIZx7Flu3ZbCFs3gLBMDmf1Cy83N95P4UN84LN3lA8hARZJT+rtRqFZvy/s9ZQI5lasKSlprHaJnCqCgC8i+xPmCGYCCmo+JhcRaI7MKaBYRSzQyVSoUgo++eRxIQhGPcOC8sf9xH6k+gCwBaDBbWv5sgRE64i6GvAd0eQHm11NnwmZWH8XHqWTAMg7Qs1qzY0pJ9L9By4y3jIjGqZGW+vYR4PvTo5XwUlVeJLBDWP8nABi4gisqr8Om2c7h0o+7Oz+W8Ugyan8qvz/71OA5erDkM8GKuIDrs1cPwFuKnaolJ3hew5zOSdVy6bjYDuy1JmRxxgLYViSGvgVMt3MgTwgSH07ssjpX49h5gzydC/5umSN8vtkBwDpTB8TaHxYkURwpqXcn3DQupM5CAIGqmOBs4L/J9yD0DZB0DYHkSeHSbNMnK6T/Z9LKO7NdOARwJvf6FokqzVbhjQRk7HXDpRhkKyqqgVavQOoYVEJxyz6uy3IB9ZApDLCDMDHDpRpkgIBQ8+xu6gPhg0xnM/fMU7vx4Z5195ppDV63aZnx3UKGnFHGYXbUPOrXGhQhVPn1OQCj9/pJYHx8Uys6H2F+p0IHpJVsCQh4yKhIQSZEB+PpfvbHo/h54fUwny2ddFnVW8XUteAyWwmR7PhWmc4Nth5Zzv11H8kBsPJFVYx9fgwQEUTPHfrZuy9gJwHIBDW4izEFy5NWQldJsAhYlA++2Zc2BSk8nnMczgA1nitD51Q34aOtZxd2dsOSMbxrmx3ueR1tKKXP1MAoKC+yPqY64LssqmVlYhouWp28/vbVYCDD4mCe9m/nnAmt2zimuRGG5h6bHZCh5xV/JL8PcP0/adag8KxYQPmiBiA8VclL4nIDIPSNdV6mBgS+yy1y2WQ5xVlvOedIefqHsq5WAuCRdr5JOJQxoE4XRXeKUpwl1ftbTJZwFIue00BYUZ3NY3H5LZJkozWYG8/48hV8PC8IpywE/CV+DBARRM3kZ1m2cv4JKzf7Q9DIBUZO/QVke72VtzvhbeXohsg2/+MSKQwBgMwrhfA57YY8WJfXhqhOWM6xZt7zENwrT5MoExGPfHsDu82zYWPdmoVb95Re3hlYbo0mY8NT8w95Ldnq6D7mI4/h023l8seO84rbyKpPEzOyLZyE+VPhf6jQ+dHlPWwd8OkDaFhgLhLARVSiRVcvlpjRa3ipJD20TztFSPnUqL70tThClRKDIWVHpmqSUMEqptLgFTvzLHSS3n7mOxdvO4ckVgtWroKxuxLM78aFvWP2h2mTGz/svOxTb2yBQ8mzOtVxkuQQvOlmxoBoKa5lLhB/yib2bkHtdar4rZoxgRMliqmpwWDuXzQqW6CDBk5qL6y4HKyBCDn9mdx91BXehsARXoLJaeJLt0czac14+hfHt3wqCrh4jdhyti3ngs9lFWHvEtll87p+ncOyKtbUqPaeEN5QFGbR4996unhqiyxh1GtzWJQ7dm4WiXaz9nCl1yorx1m0hTYWph6pSab2atLXsq9i3yh7cfnYtlF575CJg3YuSvBBW1PTgYwy2bpNbX0XwUxgyAZElcqrkrgdy6xtX28SXIQHhAnP/PIVnfzyMp76vec60QaAkILItTwic+U5ugZA/UWx4GVj1KJ/opTRfeDIwXtuDyR9v4NfNjAqPVz0Fs8r23P8trSIQIXIYO3fdYoEIkqYV1mvVuFXNnidj7kkssjEFUpdwDlVdmoY61H9wO6kn+Mtr2P89wzB4/sfDePGnI/XaKlEkunDasgy4k692Xqixz7pj1r456ZaojW4JoTg8exh6+egF/qP7e+CXx2+B1pcsEEqENJFMU+K7cezroe+A86nscrM+ju2LExAVBcCvTwrtSoLg6kHWr+LrMcDZzUJ7dUXNKe+VLBDya58IznpYWmmSJIK7USJ85znnYU5IfPJADzw6oAUW3t/d/lh8AB//hvkmX/7Fzs/tOleDOayhwAmI3tOAGIuzUbnlCS3YIiDkFojCy2wiKIAVDbs+BI58zyd1KSsQBERoSToCGXZ64bw5Fl0qPsd2c1ekXbc9J5gUEYDU5wfxFgdeQAQbJP2CjVpUiWrGvbP+FLzJ0p3p/PemZ6JjcfrjeiVg16xb+XWDJWf/t39n4Mf9l/HDvkvIdTAM0RcRe6jn1IFVL9iGb8CvM27hl8MUakict3zHWkQFsCF/RM1UlbMOh0oExrAZJjkydrLOlKunC20OFs+ThHoeXyUsKwmIsjxgyxusSPlWVN3XVkptMUoCwgELBCB1pDwgivjhrG6cgOjUJAQvjWrvMzVW7EECwkmUTJv1leKKanySeg4ZuQ74KwBA+zuAlFel27gfrlptnUyFq5xXLTJLW8JBK4oF8RWJfKzQvwkAuI5QFIP9QR4sVDAXWgj20yHIqEObGPYHzd2ExFMYABBs1GF61Ux+3R+1v0Gl55S4XF771d+EfBr9WkXa6SlF7Aehsdy8OCELOJ7HwBcprGMLhK17f/u4YEy4iS3SVFpRjbJKkyS09Px19nfChQkTFsxm2yGaR38E/nxBeZtB4ffNWR44Ah1MoORnQ4wr+TGU3oDEg4Wb8riwQ9ZR4YvCRWGIsSMgDFo1/3vlHCkLy6uw6aQwZVtYVoWM3BKUV7HWWVsC1xchAeEkhy7l88tadf2uT/DehtN4a90pjF1UQ/gcnxEuzDqsKaqdsNxyiOx9FkVfKfoRF7BhUtWFyiFLf5iEzJHvVI9DaVIKDvX9yKpfsCVEU+4fIJ/CePueLthm7oJqhv2qB6F2uQau5Jdh+PvbMeL97bX2gYkP9cM//0lxqK9SeGe26PMbjICoAwsE96T34M3N0D5OuInpNGrBa77ShPGf7Ub/t7ciLZO9wVy1pCNuKnL6bPTkXQDmNgXWPqO8vTRHuR0AtAbrNrH1AQDUDkYgyQUEZyHlpiTE2SuvHZZ+dsEVNmnVqqnselA80O9p4DG5oIDTFgiVSoUAWUGto5cLJHqrqLwaP+5jr4utowMRbLQ9detrkIBwEu5iArBx4Ok1Pb37MLvOsT/uvFI73r8MIxUQ3BQGRz/RhUMrM/ue3QJc2gtUif5HnG9EwWUosdvcgV/ORxAujvgK5yOtHam4BC3+shBH+RRGr6Rw9EwMRzHYi36gqqxWom/zySxUVpuRU1wpeYqQs+lEFsYu2slPrSgR7Kfli+3UhE4jPA1FBxnw6q/HJSWC67OAyBfNBxeVV/N1QTz2eZbve/PIQDw+iK2ncm9PNhqAu9iXVFTjyGX2JjT8/e0Y8PZWnLzG/vYjAhw7Z42CvZ+zv+99S9iU0T88CPw4WYjcUkpRzcHdxCd8p7x98H8dH4dcQFz8m33lHl7aDAdGzWeXL+wArovCMIuuSUPVwxJZS2usrCAfoOxEaccHApA6UhaUVeGBL/ZItheVV+O0JQnehN7N+GJf9QESEE5yKU/6BLvzrB2F7ePI6y4oUlkMMJYLul8YW0bXX2SFEM9hamVzdn8vAr4cKvyYAT6rXGGmcp6I80wcRnaK5dfLKk2KOeI5M5+85LV8CgNgy/YWMeyPPBilKLLsL6+kEs+sPITdTviynBIJyDNZtsXBlK/34dClfDz342G+Te7o6Eycvkqlwv/uZC9oF3JLsXTXBcn2+uoDUVlt5s8Hh6etEJwFItRPh9u6xGHTMwPxv7vY/22AjcQ/F2+U8u+T11Bo1Ih9DL65Ezj5G3D8F+CDLmwSp2o7uQ00lt9qu9FA097W2zvdZd1mC7mA4KZPufHpA6R9rh6Q9uVqXwBCSKgSihYI+xapAJGA+GCTkAsjLoS9XhaVV+Gs5UGjTUz9mh4jAeEk3Nw3FyJl7ybi64hvvuJQQgDYd+EGpn69D3tOWEppawzCDyUhGYq0vx0ISbBuFxezKcvD3+dzoS22zgQIANXQonfzcLSOZn9I645nKqaBDeEFhGDu02vVijdlo04tsUDklVSivMqE9zedxqoDV3Df539bvccW+aXCjfpMtjRU9VRmIR77Zr/ESiVODlMh+h+/eWcnfuyRgY490XZuojD/qvA59Yk8y/9To1Yh3nJBddW/xBFMZob3Y0oI94dKpUKr6EA+Z4K/5WJfYMcqFxFIAoKnwE7ejsPf27dAiG/oSjdhW34NNe0LYLPcms2CD4QugPXh4hD7RqS+JX2vvAKnGEUBEWDdJoITEMUV1bxFUq9VY1wv9lpZVF7NOw9zoqK+UH8mW3wE7umoV1IYTmUW4UI9nsJQi0xl+aWVkiRM9yxmqz5ePXkBaw1gf6Bc/9HvspaJ3lOlOzQEAU8dRt7upQjbKJraED+llOVjw/EsTFPZTuoUbNTxKYM/3XYe0we1tOrD3WzEvgHRQQZF85+fToNCi2NmIMr4GgiuxMnni24scvF418e7UFppwjVRjLdJZHUQm+a5iwcAfDmpF178+QheGtXe7mfbu3Fl1GEdCXfCTb2E+esQFWTA1YJy5BR7zppyNrsYeaVVCDJo0UMhaVegZUrMXvXEMH8SEDwVdh6gbpyXCoPEfsDYRcDx1axVsuNYYZuSP4S9G7kcvT9rGeV8LoqzLNlwGUClYacetHp2WiLzqPS9hbLpVHvCRa8UxmlfQIjTWXNWrI/u684XZssvq+StcPXJgRIgC4RTmM0Mf3Hrlch+uS/W0ws3IL0Zih3ZxBnRQlTsBcLsFyo8lQXHAZN+ZS0OctQaTD3UGkfNSUKbWO2X5eFSXilCYfvCEymbhihWsEBw2QvFaZ6Vpi8A1tJSzLD9g1TCWMTTEXILjC3E/iKZheWS/xvnk3AlT4g6EWc7LrMICJ1GJckS2DUhFOtmDsDANlF2Pzsm2Ai9LLb/wZubAUDNkTQ+Sp5FQIT66/mLZ5EH01lzCXyahPkp5kkINLBjuJKn/LsOMmqh19Jlk8de3oSc04IFQh8IjP8GCEsC+s0E7v+enQ7lENfJMIYAz8nSXjvC08eAlDnscnE2cOBrdjmpnyBktA44wNpxioRaDUS0lrbZqYUBCAKiuMLEXy+C/XS8I/jV/HLeqTLYhytvKkG/BCcoKKvi8+S3tTy95onmnssqTdh34YbdXPq+wpX8MompvVB0k+YcegDwN/p/soBur2/A3+dr9hfYd6kIp5mmQoP44lCWh9LSYhhVyjeJ6YNaYkBraaSH3EEw2Kjlzf/i2hHyCAy+PdiIIssURhCUMx3uz8jDLwcv2zVdA0BBqXQsF3NLrcbYKlp4IjEzDCqqTVi09SwOZOQDEDJkOotGrZJEALx8WwdMuIkVEFfz6+cUBndBDRVdUAs9mNKXsyDacl4N87eMwUb1xAjyf5CiJCCmWKYsi7IEH4hb/2vfolAsckh+/hwQGG27ry10fkJU2LmtwM732eUmPYU+SpYOq/3UMI3wr/VA94eE9RosJWIfCO67HeKn431puARlBq3a5WuDt6ApDCfgnPkMWjVvxiypNIFhGKhUKjz9wyGsO85msOuZGIaVj/bhY4B9ibJKE4a+tw2VosdjsZ+B2IktVMV+uQuYADAM8Na6U/jlcSHhji3MjKBN0y9fRXNupTQHeg17sWBUGqjCkoAbFj+Lh37Biy3bQY7cyhMqMiH7i6cwgpUvDvGhRkULhBjOD2JYhxh8NrGXzePiLBB+Og3KqkzILioHwwRjsygiQyWKHzczDJbtuoB31qfxbUohmY4SF2rEecsFJyrIwF+E8ksr+e9hfaKwTDDdBvs5XvrYGXKLK1BQVoUWUYF8nokoG34nSgmkxJADpQz5FEZUeyDIkruhOEsoXlXTjVtclVdTi6fwKEv9HHHuGXG57RocHgHUnP0yIAIIEFkLa/jNcdNixeXVku87Z3UorqfTFwBZIJyCM1EHGLS86dxkZvgEIJx4ANgn2o0nHCxVXcdcyS+ThAAC0qc+TkC0UF1FHzWbNjmfYZ0aqxysQGgWfbWamqRzjG8XsRX4qg2hQOd72Eb/SLZwjgJHZcm7xFUQxY6gtqYwYoKMfHKqQBsWCI4NdkrqVpvM/DREYgS7v38t3YeJS/ZK6lNcKxBPYTA4eDFfsp/aPGWITZyRgXqEWp6Yq82MYrSKr8NZIIKMWr78ursrct776W7c+u42XMgpqdECEV6Df0M4hXBKkVsgxn8DBFisB+YqoMjiLC2P0JKTaHkoiWhVu/GEJlp/VliSsCwWMv5SSyf6P8uGlDa7uebP6T0VCG0GDP5PjV05UfrR1rP8Q1uwUYtImU+Tz1VPdQASEE5Qagnt8tdrECAynU/44A+cf6s/HtBskvR/7NsDPjmdoZQz4HJeGX7afxmF5VWY++dJ6FCNP/Uv4XYN+2SeD1ZAHLtSiOxC2+ZyLseCSfQUrlNJxUoU2LwSjDEE6P8cMPJt4JENkj4xMmuCeO5fHM3gJxEQyhepDvHBqNCy0wq9YqU3b3F+hZooFTlBNg0T5kl3nMnB4cuCyLmQK1g5KqrMfOppfsy1EBBBRi0e0GzCi9oViAzQw0+nQUvtdezQP4Xq3b5RLMwZuKmCYKOOT6DDPaW5g9ziCj6D5KD5qXz2TlsCoqanwHpm4HE/ZzcD300ALu4BTNXWYZqhiayzIhcKyZXTrskCcfsHwIAXgIlrajc+tQZoJUvOJl4X+0DIpx6GvMKGlDpCcDww8ygw0EaWTRFK37VAg9bK2kUCooHDWyD0WqjVQoaxlIKf0KLsCN7ULbF6z6FLCoWo3M2JNcDm12ynk5WhFCb31rpTeO7Hw5i95jjKq8zorDoPg8hPIZ8R5vXFzodyii0ii3Hgq6VRq9mLTfKjQIQ00mL5FGmoaMcmQprhp4cKZb5bRApx07bMz6H+ekwb2g0AYDBJpzA6NwlBl6ZCeKRcuIgprRCcIGNDHHsSrTSZsfqQNGTV6Ej+DRu0rEzDm7olmK79DbGFR6BSqTBH9zUS1NcRtu3f7EW9HsFZvoL9BAtEUYXzFgiGYTBl2T68+NMRSbvc+sNhS0DUNOUo989pVGSfYmtHnP4TWPO41Prw9Ang+fNCMjmj5TfFRUXUZIEIigFu/Y9Q3rs2JIqmWG9+XKr6xEImsg2gtjwIJvWv/efaQB6m/cGEblCpVFbl1utTBkoOEhBOwJVk5bIfcs4xwbDtAb/xRLbnB7ZyIrDjXeAUWwJ359kcnM4qQkFZFSZ8thvf7L4g6Z5rJ87+l4NXAADt1Rcl7e1bNOO/4Pbq1nPz15cZaUSBiVEB476RtKnibJdDbhUtDZfq3CQEc8Z0xG8z+uH+3s349mYR/piZ0hq9k8LRt2WEzf35BbKhWQaT1OTqp9cgPkR4KrH3FFDCW6C0iAq0viDKk1rZHIvO9Z9dVImQQS8wez+QdwH9mP1Ch+veLRbmCJdulOLtdadwNb+Mn+4JMur46ZhchTDOM1lFduvQnLtegk0ns/DDvkuScNnNp5SnpBzNvcFxS6sI7HhhMB68OdGp9zUoLIXwAAA30tksswCg1rFFrwJEvz95vgRNHU79iB0w5SGZYiET0wkY9zXQ+V721UOIxeo9PZtiTDchauPFEYLPF1kgGjhiCwQgCFsThBuHFtInwM120h27BbPIJyH7JM5nF+GBL/Zg2ILtWL4nA3+fv4GX1xyXzMtfF12gbane/onSG2T/7p1wcwv2ApFvV0Cw25aYRkjaN5l7Ah3uwNXpZ3Bf5X/wh/lmqEe+pbQLHs4jHmBDGA1aDTo3DbGqhDgzpQ1WPtZHUnDKCmMo+2KSWk/8dBr0bSVc+LiCN0pwAjJAr8HIzrFW2x++JUmyX1vUZgrDWClYtNQ3zgF/vijtkJMGX+ehL/fg49Rz6DtvC9YfZ38fwUYdPwUlduKtMpnx+5GrGLpgO25b+BcOXlS26ImnCrnw5L/O5OD7f5QTHdlLIb74wR78ctuYIPz+f/3w5aSb+MRTjZZskTgNiAS+u5ddNitcD+SFshyJfnAX4gJccgGhEt3ykm5hpyzu/sK5nBNO0iRUeEAJkl1vxVFVJCAaMlVl0OecAMDw8+5ZheyFTiWq7BYBaYKkM9nFkpu327GkhgYAnNuCpl90xoOajQCAfReEi+3jyw9gyV/puJBTwlsgnhrSGv93qyym2UKQihUZp8wJeKPqAWjaDOWfEO2F2XEWiAro8VLVI3x7qpm1NpSp/bHb3BEvqp8BAu3nPfjxMcEbutbe75YiYJEqqYDQa9V4MDmRz6dgz4GPExf+Bi3axAThu6nJuLmFcOFJjAgQLUtjycVFvxxKIW4DvypRyeEDy4DT66Qdrvu+gBD7iHAE+2n5KBpxkbDHvtmPGd8d5NfPZivnHRA7kHLZLTedzALDAB3irOsX2Mv4N6JTHL/cp2UEOjUJqXfhdW6logg4s0larbK4hgcjgywlc0xH94/LFuIIifju0m1Zx4XlxH51MhxxWW659VacHI6iMBoyy+/FqJ33YJh6H+/78OadbGGpUJVwUYtVWdeU92ihI644FQBc3AV9ZR7e0H0FANiaJkyfHLyYj9d+P4Hpyw/wPhCRgXorRcwRoGb7pJq74gvTaPj7B/AK+Z31aTbrFYjFRQljlCyPW7yb9yNw5IIcK5pacHR6wCaWJwx9RR42PTOQby4qr4ZarcKTQ1ghVVxRbdPx9YDl6Zc7/31bRuLWdoK5NNRPh+eGtYG/XoP3xnXD+pkD8L87O+OryTdh3t1CYZ7a3Iy6hdfg43A9DdUms08679ojyKjjo2iKK6p5h+XNp6RTgPk28nSIRfrnO84ju6icF7N3dIvHnd0Fs/EDyc14fwtbbHl2IJ4b1gbPDW/r/ME0NFbcByy/G8g8UnNfDvEURpcJHn3CtyK8ORt5Ed8diO8h3dbncfZ14IvSOj4e5sGbm0GtAib1SZK0i6fSxGn56wt18h9ctGgRkpKSYDQakZycjL1799rt/+OPP6Jdu3YwGo3o3Lkz/vjjj7oYpn0s6nuiZgOfL/+BZHY+VGx1aKYSLnic6cqj1QVLris2t1NdVPSpPHmtkJ9jjgw02FS9/mC9q8sY9guuUask+Rfm/nFS8X3iGP4yCD+OUhix98IN7M9gBZbRAT+AAJFokDscOY2/ZZqiqgStwoT9ctMSEQEG6LVqMIw0k6QYLpeDOOIiTiRywgL0mHFraxyfMxwd4oPRNjYI9yc3w+B20ZJ+tREQYYxtPwAAYK6fwvD3t2Psop1Wxbt8mWCjFoEGLW/l4pJuyckrVRbjYivFqgNXMP7Tv/nptCCjFvPv7YqF93XH2/d0wRtjOynuQ0yLqEDMuLW1Vbn4RonY8gAIvyV7SJwVaxma6SxaA/B/B4FHNlqLhLaj2ERVg16q0yG9dkcn7P/vUHRNCJW0iy2VTephmXiPC4gffvgBzzzzDGbPno0DBw6ga9euGD58OLKzlZ0Ld+3ahfvuuw+PPPIIDh48iLFjx2Ls2LE4duyYp4fqEAZVFUJFN92mYX6IUQlTBWIBwT3dl1U6ljvBJS7tUWxeqFuo2O6n0/AWiIhAg00LBCcgSiBYEVpECib6E9eUa1mI0xCXigQEt58CS4ieUVvzTVQ836xkhnYKQzDr7AUApYKViDN9a9Qq/vjOXrcdZSInIVy4AHDfC6V5cnF0hyPHbpMy+1E9TP4lnLtegqNXCupVie9gPx1UKhWGd2B9S/6yVLmVfz+VSs9fUkgnn55Twp/bQIMWGrUKt3eNx7heCY3bj8Ed3PqydP32D637FIhyv8jDKusCtVo5IZVKxU5n1vF3QK1WKUaJGbQabHpmIF4a2Q7DOsQovNO38biAeO+99zB16lQ8/PDD6NChAxYvXgx/f38sWWId8ggAH3zwAUaMGIHnn38e7du3x+uvv44ePXrgo48+8vRQHeIm9WnE6oQn1GX/6i2Ztmitvgw/nQb/GdWef9Is85QFoqIY2PEeuyzL8Z6oUk5ixWZPZAVEmL/OZu51P4uz4dQhnbH3P0MAsPPBHE1tqGVxCuBS0RQGZ8ngCsg46gew+dmBWPloHySJxItLqFRsDQ9AyHwJaZ2N5pbPyFCYowcEc+P747vxbeL/gz2zuNhpr9JUi+9DucwC0esRmFQaPF81DQBgqhTi8jMV8nUUV1Rj59kcSTKuuqS0UnkKhhMKcaFCiWPA2nqXr2CBOGDDsZKvO1DP6gv4DKZq4OhP1u2thwrLXe8Dek6y7nPzE2yI5G0LrP0QCAmtogPx6MCW9dLPxqMCorKyEvv370dKiqBA1Wo1UlJSsHv3bsX37N69W9IfAIYPH26zvze46aoQjtgyRI0QUXrk/ro0HJ09FFMHtOC97T02hVFwCagsYkOTXkyXbFLDtvmaiyYJNGrRLi4It7SKQNsYYc4yAgWIuJoKAIiJCOe940P99RjbjU0La8s6zl201SplC8TVfFZ8OfoU3jIqEL2bu2n+NK4b+3r1EH9DT24hiCLOx0OpeBcAfkqgXZzofxWgx+1d4zG0Q4zdHBIG0fHWKlES5zQb3BToMAYY/S6+6LcDG0xs+m2dygQN2PO7bNcFSa0WAJj+7X488MUerNgrDdOtK2wVn+Nu8oGiugFVJjOqTNIvmpIPBJcoSs6xK6yVLLAextf7BH9/DPz8iLStSU9p8ShbhafaDAP+kwn0+pfnxkd4HY/+snJycmAymRATIzXNxMTE4NQp5Xj1zMxMxf6ZmcpP1BUVFaioEBz6Cgttl4l2mcM/SFbj8/YC+5exVSZbDwNgyXMAIMKcC5TlAEExMOrU0MCE5scXAiGj2apw7qTccqxBsVY53rUqMxJVmchgYmHUqdGlSSgiAvX485jwf/TXa2HQarB8Cpu6NWkWm0eij/qEsCNGKn5GdIrF6kNXbc5Fcz4Qjw9qhepcNWBJW1BqsUBcsQgIQy1yIbhMbGfg5K/A9VNYNX0KVh+8gof6CHH9QtU85Rs8JwTF4kelUmHhfc49YblcbdJsFs751C18zQGjXwAqIDxl61GFMmiwct9lHLtSiD+eEpLk7DjDTg38tP8yHpI5dNUFStaduBAj//QVIDoHSsJb6Xt39rqdipAA+TG4yoFl0vX/ZAIavdT8b7KdU6ZWNS2IekG9j8KYO3cuQkJC+L+EhAT3f8hFqfVDo9YAvz0JrJsFLGS9fDOYGFxiLB75Oexd00+vwTD1PnQ6/TGw1MEUqc5QYbmZcDHXsV0km2+x1LH4/f/644dHb0braGloVYCNaYQgP9FcXVCcZBvnSGnLG54TEGEBesy6Xbixcg6VXBieV8x1oZYEVPkXkRDuj/8b0lriGMo9qdoUEJYU2rUdu8v1FCoKAc6yxGX6AxviWikSEAYI50bsq1Imqn/SIkoWZldHZMuid1LaR2Ptk4LAEQsIbrxqFfDbDFZ8y793ReVV2GqJ1Lirh3JZ5dhg2yGbhA3KC4Hcs8K6PpB9SFHLvvvirI9Eo8OjAiIyMhIajQZZWdKY4aysLMTGWifiAYDY2Fin+r/00ksoKCjg/y5dUk4cUxtu6KWfHZhzyKpPFhOOc4yl6pslmY9Rp0GwuPpjqXWIZ63g5sO5m8kjG3CraSG+rWZ9Fpqq2AiNYKMWKpUKIaKbpVGnhtZGZEO4RhSF0HygZBtvYrYxly32fBcnkxE7Y7Kf7wUBEWIRlwXK3xF7FogqUWikIxEkSnz9r94Y1iEGL45wMTSQO99ao6TkcP/WkTBDjUqG/Z+KBQQgWE7ET+/O1ABxFwzD4Isd5yVtkYEGSY4PrnJhSYWJ9x3y02n46Ay5BSIjtxSllSaE+utwWxep2AXY+eWaKmwSCmTJnNblfgxPHgTu/JQN0SQaLR4VEHq9Hj179sTmzZv5NrPZjM2bN6NPH+WSqX369JH0B4CNGzfa7G8wGBAcHCz5czdrMmvOf5+JMFzkLBAWD2SjToMqRnSjvPyPewdmsUAUMH5IeW8bfjmWi/NVEbjAsIInwRIRwjn3iTOd2TPrhmssoqfrfVZhUFxhqMpqZSc8LlFKsFEH6P2BKZuBKZuxeLL0ScWo9YLxi7NAFFyRZvC0IJ5/lyM2p7sqfga0icJnE3sh2tUnYs7/wZJVkyPUX4/PJ/aC2ZIuWFzDBACuFbDOlOIkNuKMm2YzW3L8yOV818blIOuPZ1lNYVTIvkdclteSimqcuMp+v/30Gl4EVFSbJeeHyzvCChHBsmPQqhGg1+ALO6XZCTuU5UvXE6S1aRDeAug6oU5zKRC+h8fP/jPPPIPPP/8cy5Ytw8mTJzF9+nSUlJTg4YcfBgBMnDgRL70kxOQ+9dRTWLduHd59912cOnUKr776Kvbt24cZM2Z4eqg2KWoyAJ9Wj8Yqk20fBl1oE1xjLM5+BWw9CT+dBv4qkcn2u3HAKcdyWhy9XIBnVx5GllLly/IC4MSvfBKpQ1lmnM0uxtM/HAYAZOnYJ+1OKtaxkntiFoef2kv73EQjs2yI0Ftu/PILPwfntMc/VTbtBTTthZtkjpB20057iqA4QKVhU+8e+cFqMzemIgUnSq5kOwCr6poep6oM+HoMsOUNdl3hvAztEAODkXVok1sgMhUEhDjj5vrjmZj963Hc8dFOd49cwt50awtcfKhUTHHnILOwHNOXHwAAqFUqyXTbp9sFKwZ3TCF+OkSILA1z7+qMg68Mq330TmNFHi4c10W5H9Go8fhVfPz48bh+/TpeeeUVZGZmolu3bli3bh3vKHnx4kWoRSq2b9+++O677/Df//4X//73v9G6dWusXr0anTrVnPzFU8SG+OGF6gfQXpWBuzR/KfZJ6d0Vuqsq4OQKoJAVEAF6DbSQCYDv78OFGVcRaNTaLejzwBd/o7C8Ghm5Jfhpel/pxh8nA+e28KtlGulF8mpoD6BQi+bIws/3CXHvIaLaEgEKWc/+d2dnnNzyLUYU/8I2yJ50AUFA2LJA5MoFhIVAgxZ7/z0Evf/HWpfspRL2GBot60FecBFY/RgQ0QpIuEkYox0fCM4CYdCq6z6PwJGVwPlUYd0vVLGbylIoaGibEJwRZbTmRKhYQIiPMS3L8bwXtSG3RBDTnZoEo01MEB4bKK3CyoVzlor8NbKLKiT/8/Mip8mZPxwCYF0emWGE7yrhAuIU+c36Am1G2OxKNF7q5DFwxowZNi0IqampVm333nsv7r33Xg+PynFiLDe7Yti+6RlDYzG8WTxwEkDRNQDAaONhtNWtsOo7aH4qAODCPNuOlVw+hX0ZCjHuIvEAALkRPYFc0XijIgFDOyDrGHoarwJgnx44C0RT1XWEyXPVA7g/uRmwYynAXeeDrP1OuHDEajMDs5mRFLaqqDbxT+8RCvPOYlHhtbzvoQmsgACAi7skAoKrynkmuxh5JZWSG1JFteMpuN1OtczTXUHYAeCz/70wJAkfp+Wit+okntX9iIyrc4DuTSQCoqi8GtlF5Th2pUASYlpeZfLIMRZXVGOLKC31sA6xfPpwMUpFrrgiZYsf7IHHvj2Ay5ZMoVUmM28JO5NVJLFSlHoy+2tjgJvCuGkKMPpdrw6F8F1IojsA58V9g7HjX6HzFy7sllC7tlumKnbtoTqt2O4K+0OG4j+npali7+gaz9a6B4AV4/n2xIgAdFOdxV+Gp/Ba0WzrnZXlC0Vy+swAuj1g1UX8VFdpSUZUUW3C/604iM8tpmWNWqVYWU7stNlNltK1zhCX+pUls2gTE4jECH9UVputMm1yUxiuOlDWCnklQ4UpDLafReBWl+Penk2x0vA6ktWn0G//TPR4fSN+EFWmzCmuwKgPduBfS/dJKsZ+vv28fK9u4Y6Ff0mmhmzlEfHXayXZJ4MMWrw0sj0AoGkYO0VzOY/1o/hpv5DtMLekUmKlMHkpUVaDgZvCkFezJAgRJCAcgHtyLoEfFrX+Ahg1H+j1iDTEsUlPoYBMhX2T8CrDqwBsTwMA7IXTET6/bl3lrn1cMNBUeLJGJZtoR69VY27LowCAliUHrd6HYz+zr6HNgOFvAlprK4JeJAIqLDfVVQeu4LfDVzF/AyuMIgP1ViW3OdbN7I+vJt/EjtEbiBPfmKS+AiqVSjjXsmkMzqRem1LcLsPIvic2pjB4oVFdgbfvEeasI03ZuFFSif0ia1Z+aRVyLDVRxFauL3dKE5K5i/M50mRPJjt1OsRhl88Ma8OL1maWugE5xZUoKK3CS6uO8v2eG8ZGtjw6oAVaRAbgrp5N3Tb2RokNh12CEEMZVhxA/DR92a8t0NtycR75NqvUK4vYpD6c2c9UAfz1vt19asHGuduap9U6GGZ3hrGOfY8INADJjwHrLc6pBVeAKNYi0b51G4B7cKuulIqE4xbfh4532vw8nUYFlYp9gqwwmQDorIpPjepsHU7H0S42GO1ivSQeAOEpHQBKc602c74h4jl4QAgfFOeNqDMqZZkWHbBAiJ/GGSeeEzyRM6FKwRpgr9BXbIgRZyz5QsS+MsFGHeJDjLhaUI5TmVIL0b/6NQcAvDSqPV4a1d4dw26cHFrBOhlftNTYsSVWCQJkgXAI8U1eEn2g0QKBUWxIEyAtYbtJYYpARJwqF6VV0qfcskoTfj18FWeziyXVJ389fBXz16dJEgFx8MmrRAToNWx4FZeHYe0zooMROVzmXZC+kcuPYMdhSqVS8VaIymozKqvN+GjrWUmf1tFBSm/1DVoNEZaLrbObcjU6rASExTlUybfD41TKMi3aeirkckMUXJZE+zhTk1PsJ+EulLJH2is3HiMSMTEyQdPKknJ9v6z+hcaGxYtwgnyLc/Gv/yf4CdEUBmEHEhBOYm/aAWoNm7FNgamVz0jWA1EuicUHgG/+voAnVxzEyA+2S9qfXHEQH209i+RXfkbaB3dIxwNrXwP+6ZP78YvL8VaJ4vAzLBElVeWslcISfooQ++ZfcSgnl5pajDwCw6doO0qwsIgrBloI4AWEVNzdsNwEvZKUyEpA2LBAhCWxr+v/DXx/H99slv3MHx3YwuZHXS+qgNnOzd0VuOyRYaIoIHtTGOLiV0kR0ggjzhq474IgIMb1oukKt1CUZd1GUxiEHUhAOIldAQFIrRAWrrZ/BBvNvZDLCNvaqC4hfONMIPMYOxdfVS7yLmesUv4CwCu6b9A2bxu/Pr3yKas+/xGbb4e9zr6qRSKjUiQgruxnX39/GljQgTVdqtRW6autDtEiIIrKq7HrXI7Vdp8WECoV0PdJdjnfOiOlP59MStkC4ZVjq5AJCFtm5ah2is0M2LBJjoFtoqz6dG7CipJqM4PVh664MkqbLNjI+sYEGrUY0o61mE24qZnN/mUiy5xcsHGZKrmIjj4tIvC/Ozu7dbyNliqFomQ0hUHYgXwgHCTMX4e80ioMams9ZSBBK5tD1vohfvx7uvplFgAAOChJREFUeKvFRYz8eR72Gp8AAHyg/xg4A+DCH2x9+opCVDf/2e6uB6kPSdZPMdKL8I4XBiMhXOQkyGWPY0xs5kW1WmqBKGTDTXH4O6GNMddYBIcL+5uybB9yiq2Fjk8LCAAItRTQKs5kQyRFUQ7+FidJ+fTSjRLuKdoNx3YjHTj6I9B7qmMm4grpfL/Np8Kk/orNRr0OnZuE8tUp28RYi1zxOXtm5WHc1cN9T/UXLNknyyrN+HxiLxRXVtstsX1ruxis2HsJ0Qohnf6y/CV39mhiMyU74SQl1g8DZIEg7EECwkHWzRyAAxl5GNZRuSYHT5sRwJ5PhHV/tlz0re1i8CLCsNvUAX00omqXVSVAPqv8/UsvAQpTEgCgghmRKumNhKtwOe+uzmgVHSgVDwDgZ8n+yJhZr2r/cKlDXv5F6xwDDsBNYSiJBwCIspMgyyfwD2etMuYqoOS6ZMqGs0CUyi0QpZwFwg35K769C7hxnq03MO7rmvsXZ0vXbU1hxHRQbNYw1TCaBeGo5MeRFOGPbVat7uGKJezykwd7QK1W2RUPAFtg66uHb0JHhUgdeQZTn/+u1SfktXr8I4AAa2sVQXCQdHeQmGAjRnaOq9lZa9jrwITvhIt88jQAbIKcAy8PRTH8bL61wk7yG66yphiuwmXv5uHolRRutR1aveCTwcV1iy0QuWeAX5+0czDK6O088em1aknGS59EpRIujCXXJZv8LT4Q8mJhXIZN91ggLLkWTqxxrL8lMRmPPbNy+9ut26rL0UIUtqtSqZAUIRWbL46UTn/Yi5JwhvzSSj4pWqd4G8JHhkqlwuC20Yo1Q7gpDA6lxFOEi4ijkrR+wPRdiqHcBMFBFgh3o9EB7UYD07YBl/YCXcbxm8ID9AgKCQWKld9qrioFbGS7/FY/16qtGH5oFR1o5WgmwT+CdcIrzgYiWkp9IADgyPfS9R6TbO/LgkEhmdLkvkloGuaH0QoVEX2SgEig6KqV2ZbL1pldKFhXvvk7A4cv5QPwwvQMwwhTTRwBdqbRbv+QnaIJjGYtT6f+AC7vxa0Jarx8EujbkrWIrXmiHyYu2YPDlwugVavgr9fCqFPzCbMqqs1uyUjJWalC/HR8hEttkE9hSNLBXz3ElpyOcrHaaWNHLCCS+ilmoiUIMSQgPEV4c/ZPxs3tkoB9Nt5TWQLA2pKghXLp7EHtYjHnjo42kzYBYJNC5WcAX41gc0NwJaHltBoK9JwMtBxse18WlLJMRgUZMKW/be9+n0PJAmE2Y1DOCtyk0uLI5U6oNpmx98INvLxaKG1c51EYlcXWzm06O7ka/MPZJGAcWSeAy3vRxFCO3S/dighLxcoQfx1WPX4Lfj9yFT2asX4Yvzx+C0Z+wEbsFFdUu0VAFJSx312l74xNrhxgQ5AjW1ltkleR5QVdeQHwmaX0/Mu5bIg14RxiAXHbAu+Ng6g30K+srrHjNKeuKlVsj4LyTX/Gra2s/R7kBMYIy3sWs8WkAKDzvawjH0dMB6D9bfb3ZUEpmVKwsZ59lXgBIbJAnFyD2L3/w48GIKn8Ozy+/AA2nJCGtoV7KpHUpX9YYRAriyiQl1V2Fu77Vp6PuBDp9JlGrcKYbkIisvZxwfDXa1BaaWJ9QJQjkp2Cq/oZ7Ofg9yPvAvC5RcTOzmenm0T4i6wY/noN649TXQlcOyx0yjlt0x+EsEF5AXB8Fbt81+dszRiCqAHygahrQqwzR3JUlSqnwI5Vsc5NV5lI3nESQI3OaACE3AAclkqhfCQCRzNZxU97u1TwcfBacSxXCYhkX8UWiFxpQiy5eOjbMgKhnvDvKC8AvkwBFvdjb4aSbfnCcmRbYOxi5/bNCQh5eWYbcFMEch8QVym0JKZy6LsKAJdF5rki60RfEaIpC96qsW4WsEzk+5F5FISTHBA58/or+FMRhAIkIOqaYNvhcSZ5wiAL0ap8AEBAZFNUQXgCc+iprvdU1togRhcA9J4G+Ftuoj0nA62H1bwvC0oWiHqXCZAXECILhNr2/1OvVWP5lGTrUt6maiD3nO3qUDXBMNIEPmc3SrdzU04RrYEZe4Fu98EpOIdLBwVEgMVJUV4LxFU+2nLWsl8HLRA5Z0TLaVabm4QKVhS+6Na+L6WdShXCEQn7mEUO3Do7PlUEIYIERF0THG9zkz+kYZEzBrNzwLF+7MU8IDgMVaJZJ4fM6UGxwN1fCCGdABAQwdbueO4M8GoBcPsHbI4IB1GyQCjVO/BplHwgRAJCJ/M7CfPXWYsHAPjhQWBhD2Db266No7oC+OlfwvrPsgqu3BSGrdDNmnDSAsHVAnlnfRoKSmuX1rqi2sTXtDigVJZeCfHNX55qHayvTQDKMFGzHoGVNoSCvHYIUTM60fRWfHfvjYOoV9SziesGQExHoM8MzNlegNm6bySbAsBmotzz7yGIDjKAYYDOTUMwoPAqsB7QGgJgVgkWCKcS6BiDgTJLnLfWcrFwQjSIUQqd6908wqV9eQ1OQGSfFNpE/9sglOIGhDwEik6ADAOc/pNdPvU7MOjFmj9Xbqm4uAvIEpnczSLhsuVN4Mx6dtnVjIBKvh526NwkBCeuFWJP+g38d80xLLzPtZuJyczg9oV/8et9W0U69kbxzV8htbJGrcJs7dcYp92GoyXbAOYuhX3YCHMibFNlSUnf9X77TroEIYIsEHWNSgUMfxNfmUZabQpVlUCtYpPjqFQqqNUqDO8YCz9Y5sV1ftjfik1fvdFvlHOfy2WlBGpt4m0aJjhuPjqwBf56cbDEtFwv4CxBhZfZ8D8AqBbqegSppA6tWiWxtX2+sGyjBooV8sRd51Ol66YKNnV1/iVg+9uCc6CrFgjOibZYoc6BAmO7Cz46vx2+6tpnAth1Lgens4Qb+cu3OVghU3zzVyh2BgD3aNlIkc7qC8B346w7kAXCeTgBoatnv2PCq5CA8BIp7a1j+aNU+Qj111uHZXLRGTo/DL3vKWxIWY8ejy9x7gOH/09YruUFtmmYcJHp1jRUIijqDTGdWL8CQKgJIrJGPH5zlMSvQ9FY89d7wnJ1uWOfK7+Rc+JFTMFl6/TVfi46tnECoiSH9deogZZRwvy3wUapeUcQG1pGdIxFdJCDT7U1WCAAQA3RdNmZDfb3QTiG6BpDEI5CAsJLfD6xl1VbFPIV/QuEpwN/aDVqDOt3MyKCnPyhB4hMyI7e7GwgToXcqYmLT8beRqUSSnvnXQB2fSQJax3f3ojjc4bz62ol/wdxJEv+RTYUsyZnykLZU326QgLpk79aJ/wKirHu5wj+4ZapGcYq66YS4umpyFqkiRaXvW8S5sR3VXzzd9BqYr0PmsJwGtE1hiAchQSEl1CpVMCdnwFhzfG53yMAgGaqbDQzWpfHRpXlhl/bp4NQS/GtJtbixRlUKhV+/79+WD4lueY8FL4MF+J6/Bdgw3+k266fkiRSUnSgFOftKM1hQzEzdtr/TC6MVs7D64BRlimRi7utk0cFuigg1BqhuqpC+XI5KpUKL4xgMzkG1SK3hziKY/qglo6/USwgbCU9U2LQS+zvSb4PwjF4AUH+D4TjkIDwJl3HA08dwiE/1j+hmfo6vro+wbqoDXej0tZSQDy0Guj1CHCPk9MfCnRqEoJbHHWM81Xa38G+FliX9ZbnElCMUpWfJwA4vc725x3/Bfj5EeVtka2Fctx5F4CjP9nej7NwGVEPOlC4C0A/y3ktKHM9CoNLYT2sQ4xzlgyx9UCcA6MsD8jYBZgUxhQQDQyaBegt0y/y8udEzfBTGPX4gYCoc0hA+AA5+gScNItKc1/aK+3gLgeniJbAbe8BYYk1920MhDQBom1kLDy/FTCbcUdX1tny8UGytMrVlUClQuIve+W5f5wsLN8yU7rNP0KwEN04DxyURuigaW/b+60JLvvoga+Bk7/X2J2LOHFVQFRWm/HGWtafROesH4XcAsFNCf02E/hqJPDbU9bvMQRJXx2YqmmUlN4AVj0KnNsqbc85K2ShJB8IwglIQPgABr0WuUyQqEU2j04OTp4j2EZm0JLrQMl1vDeuK3a8MBhDO8imEMoUrA+A42b3EFlCMZWKHYtKVn8itgvwyCYgWlot0ynEicS2/s92Pwtc0qfSShPMZucSZJVXmTBxyR5+PbPASX8bsfXAVCmI5xOr2ddDyxXeZBljXFdApQby0h2arml0/PUeWzzvm7HS9u9E3w+yQBBOQALCB9Br1DCLT4X8JkQOTp5DntgrsZ8QkllZDK1GLfh57HgP+Lgv+yTHTV/4RwADRfkfHMy3oJhQTKO1FhaRrYGEmxzbpy1apwAvpLM31+zjNd5cxfUmyqttl5hX4qf9l/H3eUFcOSUgKookobTsAPJrjh7hfIT8QoVaIlxkDSFgI6qFLy8PUBprwilIQPgAVuWx5TchzqxLFgj3I3ZObDkEmPy7YAqXe/NvnsPegP/+WKhc6B8BDP43W0YbsD53Zzaxvg9y5DVKOKpkN1B3iUb/cCFsNfec3a5GrSAgSiudExBrj0hLjw9uF+X4m7kbnD6I/b8CwD9fKGaklNDyVmE5phP7unIicG6L45/dGBBHYsm/Zxzcd4QgHIAEhA9gkFsgxImets9nsxUCrmcjJGwjfuLyj2CnEjhnvNMblMMyK4qFKQwuP4ON8uBYfjfr+1CcLd1HVHuh5oA4x4O8IqrejXUJAqOtx6iAWq3irRClFdYCIre4QjHNdX5pJfZbUlavfLQPXh/TES+OcGLqpcgiPoJihOPe8S6wroYMn8PfEJbFaZhPr3f8sxsD4lov8nBiDrkFjCDsQALCBzDo1FhYPVZo4J5izSZgy+tCuzG0LofVOPAXpeDmxESFxTly6xvA5X/YZbGQYMxSCwQgPN2JxZ/YybJclBgq+TE2M9XENeyUyUMiC0X/54CeDyuPr7YoVSC1AS8gqqTTB4XlVRi6YDvu/HgnTCL/iGsFZej22kZUmsxoFxuEm5LC8FCfJAQ5WoUTEEJcA2OlEUdnN9l+T2gzqeNq9weFMOWc045/dmNAbFHjEpWJ8430fJgN+yUIByEB4QMEGrTYz7TF/CqLM1NpLrDtHWC9LDcBWSDcj9gCwd2IxAmMuPlhcXQAYwaKLTdhf8t7uBt9Sa7Qr0IkIMRiYuhr7GvCTcDDa4H4bsK2kCbAkFdE43OngHDMAgEIZb3lUxj7M/Jwo6QS53NKcPSK4Kvz/kahima/VpHKeTNqgosOiO/m+HSd3D9C5wcMs1gkZOXZGz3i7yO3zKVSD2kG3LagzodE1G+omJYPwIXNnWEsEQFXDwFpf1h3JAuE+xFPHyili+YutOJqllVlQtZKbs6dm8KoKmGf6vT+UqvDKcv59I8EtDXkRRDX1TAE2e7nLErTLDawNYVx4qpwTMeuFKBbQijbr0ro55TVQUzWcfa1+QDgygH7fcOas9EWA5+33hYUy7466tDaGKiulGRa5b/XXDG4tiPZ6TuCcAISED5AiKUs9w3GUv2xyMb8pKsFlQjbiJ0ZI1tZb+dMvWIBcehbYbmtpSiaIQjQ6NnQw9JcVkCIn/guWUIbO91d85i0ojLthmDb/ZyFm8IorllA+HEColL6hH/0smB1KCoXtplFUzyBrmaw5P7XfuHKGRHjurHVbJv1AbpOAHLOANEKRbo4q01VqSDmGjtcUTYO7rvJ5Zzh0roThBOQgPABOAvEDdh52vQLo/lJT+AfDkzfxd70k/qzbZFtgZw0dpm70IrFAIchWBAgKhUbMSHOXSB+D+cgGJrg2Lja3wFcTwNaDHLmaOzjhAUiwDKFUSISEKcyC7HuuFAhs6icdaRMzymRRF8EGVwVEJb/lyEI0ChYaaI7AGM/FtZjbCQBUxJzjR15cTbuf11kOZ+hlFyOcB4SED4Alyb5OmPHwnDX53UzmMZITEfp+gMrgQ+6ssvchbZKVtwKAMbJUkNrLU/N1eXs3Pzqx4Rt3IXaUZ+G8d+wjpvuNCs7GIUBANGWolrXRHkcfjkgrePBWSA+2iL1NbAKS3YEhpEKCFOldR+DgyXTVSr2/1x0jRUQjoq2how8t0xFIVtanksXzn03CMIJyInSB9BaakUXwkbIXqe7gdZD63BEjZywJMERz56AkDu1cr4N1RXAsZ+lN2ruCdAZp0h3z0nzURgW3wCGYUNNFeCSZ126wR73B5vO4NPt5yV9OAvE5TyF/42zZOwCzJbQUEOQ9RMzIPUNqQnu/1xKfhAArAVEeaEQWqzW2U/BThA2IAHhA9zaLhp9WkRgurzeAoc7cwEQjsE5L3ICQl5eG7D2TxBbIIquWfcHWCdKb8FFYVSVsDeQTa8C8xIUE0s1swiI9JwSlFeZsGCTEBIZYPGP4CwQ6TnS6pc1VTRXZOkoYVkfqJwSnMsy6QhcivK8DBcG0wCRC7K8C4KACIwhB0rCJUhA+AB6rRorpt1sO+mOM09ehHvg/uf2LBBWAkJkgbB1QfZmqmBDoCBgruwDdr7P5gbg6kyI6JrATqftu5CH01lS/4+2say4KiqvRpXJjOyiCsn2Pi1rGXqqVisLiI53Or6PSEtGxZwz9vs1FricGJFt2NcTq4EbFuFI0xeEi5CA8DVGzGOd3cQhm2SBqHs4ccA9uSkKCJnTK2eBMFUIiabkuDOvgyuEt2Bf93wqtKmtXaFaRQehQ1wwqs0Mlu68INnWOpo97owbJXzZbo1aheNzhmPvv4cgJlghgsJZotoKy9EdgHu+cu4pmXv/iTVsCGNj5txW4KAlcqhZH6F91VT2NTDG+j0E4QAkIHyNm6cDz50BmvYS2khA1D2cOLh2GPhssHJSInmoIW+BKLdOXQ2wc83uzOvgChGWabLT64S2UuXKosM6sjeWVQelzpPDO8XAT6dBVmEFdp1lhVJkoB4BBi2iXREP19OEZc7KMGYR0O1BNkLm8d1Ap7uc22eHMWwkRtFVILcRWyHMZmktlh6TrPsEkYAgXIMEhC+iUkkz8dEURt0jvtFfPQDsX1rze3gfiAplAREQ6f255riu1m02SpNHBymLgVZRQWgRxYraw5fzAQCRgTUkx7LHot7CcrcH2NfQZsDYRdYRMo5iDBGsELbqPjQG/nwBOLCMXe73DNC0p3UfskAQLkICwlfRiawOJCDqHlcsBUoWCJUod4e3py8AabEpDhsWCC4/iZy4UCOiLGGexy2ZKbl1p5F7XLqzZD3nSFl4xX6/hsw/ovBv7vs3ea20D/lAEC5CAsJXEf+oaQqj7nFJQIgsECUWASGubuhNB0oOpUiGsnzFrqH+1gKiW0IodBo1oiwWB676ZlKEi99Rua+IO5M+BcezrzlnXAwNaWBwYbxNe0vbyQJBuAgJCF8lKE5YphTWdU9NAiK8pXUbJyCuHRYKcokFBPdE7E30/lLrFiCt0ihCboGY3DcJ30+7GQAQKbM4tI5x0UpWcFm6Lh9bbeAckXd/BKx5wn37ra9wEThavdSqSQKCcBGPCogbN27ggQceQHBwMEJDQ/HII4+guFj5YsUxaNAgqFQqyd9jjz1m9z0NEvENLNpGyl7Cc2hsFIRKfgzoeBdw/0rrbdwUxuEVQptYCPqCgACsxVFliWK3YFlRrOaRATDq2CmZWJmzZK9EF60r4sqngHstEGI/okPL3bff+orY/0VcOI6mMAgX8Wgq6wceeADXrl3Dxo0bUVVVhYcffhjTpk3Dd999Z/d9U6dOxWuvvcav+/s3wlz2IaKbTWCU98bRmLnlKTZCIDBGcERrehPQ+R7l/lqZ02Gnu6WRGiE+IiDk0SNyAbFrIXDjPEIHvylpDvYTLhecEyUAtI0J4nNDOI3VFIYb/X3kJcGryhwvE95QCG4KFF4GBs6SXkc0okt/AAkIwjU8JiBOnjyJdevW4Z9//kGvXmxI4sKFCzFq1CjMnz8f8fHxNt/r7++P2NhYTw2tftBiMDD8f8pe80TdMNQiYlPnCW32bkDyp+foDtIIAF+xQGhlxyAWEAwDbPgvACA4rDkeuvlWfPM3m81RPKXRKlq40UcEiqqHOotYQAx43jo9eG2QC7oNLwOj57tv//WBaktht45jpe0mUZVVKjZGuIjHpjB2796N0NBQXjwAQEpKCtRqNfbs2WP3vcuXL0dkZCQ6deqEl156CaWlbsi1X99QqYA+TwBJ/bw9EkJs7rUXJSB3djWGAEEiIewrAmLIK+xr62Hsa2Wx4GTIVRIFgJw0DGgjPLU2jxREg3gKo7hCWvLbKTgBkTwduPW/ru9HCbnYE0ckNBY4cSj/3nJ1RwiiFnjMApGZmYnoaKlpTKvVIjw8HJmZmTbeBdx///1ITExEfHw8jhw5ghdffBFpaWlYtWqVYv+KigpUVAipdAsLFYrwEERtED8V24uIkZvfubLSHL4yhdFuFPDUEVbgvJUIMCY2ckRnFKozAoDZjJ6JYQjz12FAmyg0jxSOXSXKZ5FfWoubEScgPBGhIrdAxDhRS6MhYDaxIcWA9fdWqdopQTiJ0wJi1qxZeOutt+z2OXnypMsDmjZtGr/cuXNnxMXFYciQITh37hxatrT2fJ87dy7mzJnj8ucRRI2I04rbncKQXaQNwYBeVO1SvB9vE5bI3mA4KkssAkJUg6KyCOEBeuz/r3Il2M5NQnD0SgFGdY5T3O4QXA4KTwgI+bkqtv3g0iC5fkpYVvpu2kq3ThAO4rSAePbZZzF58mS7fVq0aIHY2FhkZ0uz8VVXV+PGjRtO+TckJycDAM6ePasoIF566SU888wz/HphYSESEhIc3j9B1Ii41LEzUxiGIKDZzUDbUUBcN+9noZSj1rDHU1XKTmMEREgFhKWQmFqtPO6vHr4JW05l4/Yutv2ZaoQXEB5IsiW3QJRcB0xVtiNsGhqf9BWW5f+Lu78AfnoYGPp63Y6JaFA4LSCioqIQFVVzVECfPn2Qn5+P/fv3o2dPNn3qli1bYDabeVHgCIcOHQIAxMUpP+UYDAYYDLVIo0sQNeHqFEZwPHuzum+Fcn9fQB/ICgiu6qhEQNgPuY4MNGBcr1qKdX4KwwMCQknsVZa411HTV5EnzpKL16a9gJlH6248RIPEY06U7du3x4gRIzB16lTs3bsXO3fuxIwZMzBhwgQ+AuPKlSto164d9u7dCwA4d+4cXn/9dezfvx8XLlzAr7/+iokTJ2LAgAHo0qWLp4ZKEPYR34i0dsSqWEAM/i8QoZBsytfgkpRxwkGclbKiyKq7W2EYoDSHXfaIgFCo5aFUVbUhUiHyBRv+P++Ng2jQeDQPxPLlyzFjxgwMGTIEarUad999Nz788EN+e1VVFdLS0vgoC71ej02bNuH9999HSUkJEhIScPfdd+O//3WzdzZBOENQHFtDQqV23I/h5nqS/EwuIMSJnTwtIH6c5FkLhEZB7FU2EgEh9m+4+XHvjYNo0HhUQISHh9tNGpWUlARGZGpLSEjAtm3bPDkkgnAetRqYsoVdtufHIKlfUk8KoHEC4sx61qxdJHI09LSAOLFGWPbzgBNlgGiq1T+StXZUKWfdbHCUWARESDPf870hGgweFRAE0WBQOzDbF94cGPc1m9mvvly0OX+A/UuBs5uBgkvCtsoiwGx27NidxSTLHaGtRTIqWwRGAf9azzrBrphgERBlNb+vIcBPDflAATeiwUICgiDcSYcx3h6Bc4gLtYnFA0dViWuVSWuioo7ytTRji3/xRbps1P1ocOScYV/DEr07DqJBQ9U4CaIxU1OlV09NY3h6ekQOl665MThRms3AptnscnRH746FaNCQgCCIxozcKVRrBF5IF9q/G2c93eAO6soCwcH5Wu39rG4/1xtkHgYYSwKzxL72+xJELSABQRCNGbkFIq4rO2/OTVtkHgXOb3X/54otELd/4P79y7nMhoojfXvNffMvAmtmANmuZ9T1KlnH2dfwlkDz/t4dC9GgIQFBEI0ZeVKlkKbsq9jZ0BMOoeUWC0RkG6DnZPfvX07Huxzvu2oacPAbYMkI620MA+SeY6cJfJXraexrqxTvjoNo8JCAIIjGjNwCwYVTluUJbeKaGe4i/yL7Gpbk/n0rMeodYbmmXBCX/2FfxYXFOPZ/BSzsAWx9w21DczucdccTuTUIQgQJCIJozMgFBGeB6Hin0OaJyAVuSqHpTe7ftxL+EUJlVC7E0RZqG8Fp5QXA70+zyzvedd/Y3A1nPVLKxEkQboQEBEE0ZsTlxmM7AzdNYZdHzBXaPRG5kHuOfY2poygBlYpNJgUAJS4KiE2vStcv/QN8PRbIOlHb0bkX7nzZK/xGEG6ABARBNGZCmwnLj+4ADJYMmoHRQk4LscnfVAV8PgT44aHafS6Xajmg5sJ8boMz6XMVQG2h0gjLnw8BTq1llzOPSft9mcI6mP46w31jdAfV5eyrvdLzBOEGKJEUQTRmjCHAk4fYImFyZ0ku+ZI4/fNng4Gso8AVOJ6l0lQF7P0cSOzD1hQBPFsDwxbGYPa1osB+P60eqLAsX9kHfH8/8GqBsk8EIK074QtwUxjyEt4E4WZIQBBEYye8uXI7l3ypshQ4vQH4fSZQeEXYXl1mv7w5x/p/s/kXIloD/7cPqCoHKi2lwutUQHCFw+zkoKgoti0IbqQrt9eVI6ij8D4QNIVBeBYSEARBKKMTZW/87l7r7VUOCAizWUjelHsGKM5mLRIA62tQUyZMd2LgLBB2BMS1Q0ISJjEHvgHMVcrv8bXCabyAoCkMwrOQDwRBEMpw4sCWz4A4OuP4L8A3d1n3zc+Qrq+cBBRdY5fruugYN4XBWSCunwbyZfU/uPBSOVz0hRKnfgcKLtd+fO6imgQEUTeQgCAIQhnOAnH4O+Xt3JMuwwA/TgbObQZ2L5L2KZMJiou7hERHka3cNlSH4CwQ/3wBfNIPWHQTsKi3EBHCMMDq6exyp7ul71VbHCt7TAQSktkKn2I+Hei5cTsLWSCIOoKmMAiCUEZfwxz63k+B0e9JrQxcBABHaR6s2Pwa+xrZtnbjcxbeApEvOERWlQJnNgIRLYGrB4W+AdHS93LHNewNYdrl/Dbg6zvY5ZpyS9Ql5ANB1BFkgSAIQhldDf4N+5YA2SeAwqtC24109kn+u/HAV6OVHRKLM9nXmA7uG6sj2HLY5G7+JpGPg5KfhEojWDEAIeSVw2TDR6Iuqa4QHFTJAkF4GBIQBEEoU5MFAmCdIouzhfW0tUDWMeD0OiDjL2CLJeWzUkghF9JZV4hzXgBASAL7WnKdfa0UFfgKSwJmHpX29wuT+mzIc1gUyPwp6prKEuCNaMBcDQTGAEHx3h0P0eAhAUEQhDI1WSAAdgpALCAA4OC3wnKBxSkxuIn1e2M6uT42V5CHW3KJsvYvZa0H4gqhNz/OCg6uNghg7ffACRCOPJnDaF2T9qewnNTfsRwdBFEL6BtGEIQyShaIDmOl65WlQHGWtG3PYuv39f0/6fqYjwGNrlbDcxq5iBGvX/xbiM5oM0KYnghvIfSRCwiVChj7ibCed8FtQ3UJ8f/TGGy7H0G4CRIQBEEoo+SEN24ZMPR1Yb2yGMg9a38/Kg3Q62FhXesHdH/APWN0BrUG6CNKO93+NmG5OAs4vIJdFvs5iAWE0k252/1A70fZZXnIal3CMFILiq8ltyIaJCQgCIJQRi4gmltCFW95Euh4F7tcVQpkWnwFBjyvvJ8oWbSFWqPcry6I6yoshyQA7SwiYuubwMXd7LIhSOgTHCcsD5ylvE/OF+KvBcDJ39w3VmdYNRVY84SwftNU74yDaFSQgCAIQhmtQbo+QZQPgrvJVpYIT949Jyv7NQTLnPm8KSCCRIJApWKLhgHAjfNCu9jSIHaUDIhU3qc4G+cPD9Z+jK5w9Edhuct4xxxgCaKWUB4IgiCUET+JT1ghDVvkbppl+azXP8CmdA6KY6MwxDSXJVmyVS67LkjqBwz6t2AV8VcQBeLjFosDW2GgjtQDqUvEYbUE4UFIQBAEoYx/OHDvMkCjB9qNkm7jbpol2dK2sETr/bQdKV33poBQqYBBLwrr/uHWfcQ+EOLS3mJhIcbbAsIsq90hTjFOEB6EpjAIgrBNx7HW4gEQ/COO/iS0aXTSKQIAiOkMRLZml7nMk/JIDm9iUHCMFLdFtxeWbdXtkAuIS3trPy5n4BJHAYBax2bLJIg6gCwQBEE4D+8PwEjbxTfc589J/SgmrmETTHUZ7/HhOYxSZIW4LaE3cNfn0mgMOXJn0y+HAv/JrLtMkJyAUGmA/2ZT/geiziABQRCE89jKcth2FDBqPhDfw9rpMDhOGs7pCyhNS8jLc3cZZ38fSuW8c05LIz48CRe+aQgi8UDUKSQgCIJwnqBY5XaVCuhdj0IIlaYwnPXRUPKBuJ5WhwLCYoGw5aNBEB6C5CpBEM4j93Wor3CVNcXIw1drQilkMueMa+NxlMxjwOX97DJXw0PJEkIQHoQsEARBOE+AjZDG+ob8qb3dbc4X+QpuAiT2Y5fDkoBD33q2sJbZBCwZwQqH6buAEks1UVt5KgjCQ5AFgiAI15h10dsjqD3GUGE5MBaYsNx2tIUt1Brg4bXsX8vBbFu+B/83pTcEq8Ph74ViZvLqoAThYUhAEAThGsYQYNLv7LK4xkR9QqsXlt1RP4LbR85ptj6FJxDn3tj1IXA+lV0OjPHM5xGEDUhAEAThOs37s5aI+px74P4fWYfH2z+o/b5iOgFaI1ByHfj7k5r7u8L5bdL1M+vZVy4tN0HUESQgCIKoHcYQ583+vkSbYcCj24HodrXfl84opO7+awFQXVn7fcpZ/5JyO/lAEHUMCQiCIAh3cu9SNv13STZw7bB7921vfxTGSdQxJCAIgiDcid4faJXCLp9yc3nvtc/a+VwK4yTqFhIQBEEQ7oYTEAe/dd8+qyuBa0fYZaWy6d4u6kU0OkhAEARBuJu2lgJkZXnui8YovAKYKgCNARjwvPV2skAQdQwlkiIIgnA3XHZKxgyYKp3PbilmzQw28qLAklsiOA5WRcwAskAQdQ4JCIIgCHcjrtBZVVo7AXHwG+l6UBwrTOSQBYKoY2gKgyAIwt1odEJRrqoy1/ejFAaq8wMiWlu3G0hAEHWLxwTEm2++ib59+8Lf3x+hoaEOvYdhGLzyyiuIi4uDn58fUlJScOaMh4vSEARBeALOClFZ6vo+qkqs27o9AMR1AcZ9zZZO59D6uf45BOECHhMQlZWVuPfeezF9+nSH3/P222/jww8/xOLFi7Fnzx4EBARg+PDhKC8v99QwCYIgPAMnIC7tAf54HijJdX4fcvFxx0dA53vY5Q5jgJumAD0msk6VajIoE3WLx3wg5syZAwBYunSpQ/0ZhsH777+P//73vxgzZgwA4Ouvv0ZMTAxWr16NCRMmeGqoBEEQ7kdnsQiseZx9Lc0F7lni3D4qZRaI2M7SdZUKuGOha+MjiFriM5I1PT0dmZmZSElJ4dtCQkKQnJyM3bt323xfRUUFCgsLJX8EQRBeR+xICbiWlVI+hRHV1vXxEISb8RkBkZmZCQCIiZFWlIuJieG3KTF37lyEhITwfwkJCR4dJ0EQhEPo5D4JTtQLSVsHbJwNVBQJbUNeUdgnQXgPpwTErFmzoFKp7P6dOnXKU2NV5KWXXkJBQQH/d+nSpTr9fIIgCEXkN3tnCo6tGA/sfB/Y+zm7HtcV6G8njTVBeAGnfCCeffZZTJ482W6fFi1auDSQ2NhYAEBWVhbi4uL49qysLHTr1s3m+wwGAwyGWsRYEwRBeAJjiKzBhYql6ZbS3ZTjgfBBnBIQUVFRiIqK8shAmjdvjtjYWGzevJkXDIWFhdizZ49TkRwEQRA+gV+YdN2VkuflBeyrMbTWwyEId+MxH4iLFy/i0KFDuHjxIkwmEw4dOoRDhw6huLiY79OuXTv88ssvAACVSoWZM2fijTfewK+//oqjR49i4sSJiI+Px9ixYz01TIIgCM/gHyFrcFBAVFdYtzXtWevhEIS78VgY5yuvvIJly5bx6927dwcAbN26FYMGDQIApKWloaCggO/zwgsvoKSkBNOmTUN+fj769euHdevWwWg0emqYBEEQnsE/XLqulH5aCbHjJEeTXrUfD0G4GRXDuKtUnG9QWFiIkJAQFBQUIDg42NvDIQiisbLnU+DPF6RtT58AQprYf9+N88CH3Z1/H0G4AWfuoT4TxkkQBNGgkCd9AoAz62t+n5IFIijOuo0gvAxV4yQIgvAEzfoAD/wExHYB3m3Dtl09VPP7yi3J8AJjgKBYICGZ0lQTPgkJCIIgCE+gUgGth7LLdywEfv0/oDir5veV57OvoYnAlI0eGx5B1BaStQRBEJ7GEMS+Kk1PyCm9wb7KnTAJwscgAUEQBOFpeAHhQK2eMouA8CMBQfg2JCAIgiA8jcHize6MBUKeiIogfAwSEARBEJ6GS0XtiIAoy2Nf/UlAEL4NCQiCIAhP44wPBCcgyAJB+DgkIAiCIDwNJyBMlcqpqs9vAz7uC1zaC1SWsG36oLobH0G4AAkIgiAIT2MIAjR6dvnKAevt34wFso8DX48RBISBKnASvg0JCIIgCE+j1gDtRrPL57dab+fqZFSVApWWgoP6gLoZG0G4CAkIgiCIuiCiFftammu/Hy8gyAJB+DYkIAiCIOoCLq8DF6bJwU1ZyNfJAkH4OCQgCIIg6gIus2SZTEB8PkS6zlkoSEAQPg4JCIIgiLqAs0DkZUjbr59U7k9TGISPQwKCIAiiLuAsEHnpwLXD7DLD2O5PFgjCxyEBQRAEURfEdBSW937Ovsr9HzhCE4WwT4LwUUhAEARB1AU6P2DcN+zy9VPsqzyks0lPwBgKjP2ELQdOED6M1tsDIAiCaDQExrCvJdfZV84SwfGvDQAYQKOr02ERhCuQgCAIgqgrAiLZ17wLrDOlfApDQ5dkov5A31aCIIi6IiBKWP6gCxAY672xEEQtIR8IgiCIusIgK5BVnMm+BsYCd31u3Z8gfBiyQBAEQdQVSo6RfmHAs6fIaZKod5AFgiAIwpvEdSXxQNRLSEAQBEF4k7iu3h4BQbgECQiCIAhvEtfN2yMgCJcgAUEQBFGXJPaTrif1U+5HED4OOVESBEHUJfcsAfZ/BWiNQNuRQGC0t0dEEC5BAoIgCKIuCYoBBs3y9igIotbQFAZBEARBEE5DAoIgCIIgCKchAUEQBEEQhNOQgCAIgiAIwmlIQBAEQRAE4TQkIAiCIAiCcBoSEARBEARBOA0JCIIgCIIgnIYEBEEQBEEQTtPgMlEyDAMAKCws9PJICIIgCKJ+wd07uXupPRqcgCgqKgIAJCQkeHkkBEEQBFE/KSoqQkhIiN0+KsYRmVGPMJvNuHr1KoKCgqBSqdyyz8LCQiQkJODSpUsIDg52yz69DR1T/YCOqX7Q0I6poR0PQMfkKAzDoKioCPHx8VCr7Xs5NDgLhFqtRtOmTT2y7+Dg4AbzxeOgY6of0DHVDxraMTW04wHomByhJssDBzlREgRBEAThNCQgCIIgCIJwGhIQDmAwGDB79mwYDAZvD8Vt0DHVD+iY6gcN7Zga2vEAdEyeoME5URIEQRAE4XnIAkEQBEEQhNOQgCAIgiAIwmlIQBAEQRAE4TQkIAiCIAiCcJpGKyAWLVqEpKQkGI1GJCcnY+/evXb7//jjj2jXrh2MRiM6d+6MP/74Q7KdYRi88soriIuLg5+fH1JSUnDmzBlPHoIVzhzT559/jv79+yMsLAxhYWFISUmx6j958mSoVCrJ34gRIzx9GDzOHM/SpUutxmo0GiV96ts5GjRokNUxqVQqjB49mu/j7XO0fft23H777YiPj4dKpcLq1atrfE9qaip69OgBg8GAVq1aYenSpVZ9nP19uhNnj2nVqlUYOnQooqKiEBwcjD59+mD9+vWSPq+++qrVeWrXrp0Hj0KKs8eUmpqq+N3LzMyU9KtP50npt6JSqdCxY0e+jzfP09y5c3HTTTchKCgI0dHRGDt2LNLS0mp8nzfvTY1SQPzwww945plnMHv2bBw4cABdu3bF8OHDkZ2drdh/165duO+++/DII4/g4MGDGDt2LMaOHYtjx47xfd5++218+OGHWLx4Mfbs2YOAgAAMHz4c5eXlPnlMqampuO+++7B161bs3r0bCQkJGDZsGK5cuSLpN2LECFy7do3/W7FiRV0cjtPHA7DZ2MRjzcjIkGyvb+do1apVkuM5duwYNBoN7r33Xkk/b50jACgpKUHXrl2xaNEih/qnp6dj9OjRGDx4MA4dOoSZM2diypQpkhuuK+fenTh7TNu3b8fQoUPxxx9/YP/+/Rg8eDBuv/12HDx4UNKvY8eOkvP0119/eWL4ijh7TBxpaWmSMUdHR/Pb6tt5+uCDDyTHcunSJYSHh1v9nrx1nrZt24YnnngCf//9NzZu3IiqqioMGzYMJSUlNt/j9XsT0wjp3bs388QTT/DrJpOJiY+PZ+bOnavYf9y4cczo0aMlbcnJycyjjz7KMAzDmM1mJjY2lnnnnXf47fn5+YzBYGBWrFjhgSOwxtljklNdXc0EBQUxy5Yt49smTZrEjBkzxt1DdQhnj+err75iQkJCbO6vIZyjBQsWMEFBQUxxcTHf5s1zJAcA88svv9jt88ILLzAdO3aUtI0fP54ZPnw4v17b/5M7ceSYlOjQoQMzZ84cfn327NlM165d3TewWuDIMW3dupUBwOTl5dnsU9/P0y+//MKoVCrmwoULfJsvnafs7GwGALNt2zabfbx9b2p0FojKykrs378fKSkpfJtarUZKSgp2796t+J7du3dL+gPA8OHD+f7p6enIzMyU9AkJCUFycrLNfboTV45JTmlpKaqqqhAeHi5pT01NRXR0NNq2bYvp06cjNzfXrWNXwtXjKS4uRmJiIhISEjBmzBgcP36c39YQztGXX36JCRMmICAgQNLujXPkKjX9ltzxf/I2ZrMZRUVFVr+lM2fOID4+Hi1atMADDzyAixcvemmEjtOtWzfExcVh6NCh2LlzJ9/eEM7Tl19+iZSUFCQmJkrafeU8FRQUAIDV90iMt+9NjU5A5OTkwGQyISYmRtIeExNjNb/HkZmZabc/9+rMPt2JK8ck58UXX0R8fLzkizZixAh8/fXX2Lx5M9566y1s27YNI0eOhMlkcuv45bhyPG3btsWSJUuwZs0afPvttzCbzejbty8uX74MoP6fo7179+LYsWOYMmWKpN1b58hVbP2WCgsLUVZW5pbvsreZP38+iouLMW7cOL4tOTkZS5cuxbp16/DJJ58gPT0d/fv3R1FRkRdHapu4uDgsXrwYP//8M37++WckJCRg0KBBOHDgAAD3XHO8ydWrV/Hnn39a/Z585TyZzWbMnDkTt9xyCzp16mSzn7fvTQ2uGifhPPPmzcP333+P1NRUiePhhAkT+OXOnTujS5cuaNmyJVJTUzFkyBBvDNUmffr0QZ8+ffj1vn37on379vj000/x+uuve3Fk7uHLL79E586d0bt3b0l7fTpHjYHvvvsOc+bMwZo1ayT+AiNHjuSXu3TpguTkZCQmJmLlypV45JFHvDFUu7Rt2xZt27bl1/v27Ytz585hwYIF+Oabb7w4MvewbNkyhIaGYuzYsZJ2XzlPTzzxBI4dO1anfjKu0OgsEJGRkdBoNMjKypK0Z2VlITY2VvE9sbGxdvtzr87s0524ckwc8+fPx7x587BhwwZ06dLFbt8WLVogMjISZ8+erfWY7VGb4+HQ6XTo3r07P9b6fI5KSkrw/fffO3QBq6tz5Cq2fkvBwcHw8/Nzy7n3Ft9//z2mTJmClStXWpmV5YSGhqJNmzY+e56U6N27Nz/e+nyeGIbBkiVL8NBDD0Gv19vt643zNGPGDPz+++/YunUrmjZtarevt+9NjU5A6PV69OzZE5s3b+bbzGYzNm/eLHmCFdOnTx9JfwDYuHEj37958+aIjY2V9CksLMSePXts7tOduHJMAOud+/rrr2PdunXo1atXjZ9z+fJl5ObmIi4uzi3jtoWrxyPGZDLh6NGj/Fjr6zkC2DCtiooKPPjggzV+Tl2dI1ep6bfkjnPvDVasWIGHH34YK1askITZ2qK4uBjnzp3z2fOkxKFDh/jx1tfzBLDRDmfPnnVIkNfleWIYBjNmzMAvv/yCLVu2oHnz5jW+x+v3plq7YdZDvv/+e8ZgMDBLly5lTpw4wUybNo0JDQ1lMjMzGYZhmIceeoiZNWsW33/nzp2MVqtl5s+fz5w8eZKZPXs2o9PpmKNHj/J95s2bx4SGhjJr1qxhjhw5wowZM4Zp3rw5U1ZW5pPHNG/ePEav1zM//fQTc+3aNf6vqKiIYRiGKSoqYp577jlm9+7dTHp6OrNp0yamR48eTOvWrZny8nKfO545c+Yw69evZ86dO8fs37+fmTBhAmM0Gpnjx49Ljrk+nSOOfv36MePHj7dq9/Y54sZw8OBB5uDBgwwA5r333mMOHjzIZGRkMAzDMLNmzWIeeughvv/58+cZf39/5vnnn2dOnjzJLFq0iNFoNMy6dev4PjX9n3ztmJYvX85otVpm0aJFkt9Sfn4+3+fZZ59lUlNTmfT0dGbnzp1MSkoKExkZyWRnZ/vkMS1YsIBZvXo1c+bMGebo0aPMU089xajVambTpk18n/p2njgefPBBJjk5WXGf3jxP06dPZ0JCQpjU1FTJ96i0tJTv42v3pkYpIBiGYRYuXMg0a9aM0ev1TO/evZm///6b3zZw4EBm0qRJkv4rV65k2rRpw+j1eqZjx47M2rVrJdvNZjPz8ssvMzExMYzBYGCGDBnCpKWl1cWh8DhzTImJiQwAq7/Zs2czDMMwpaWlzLBhw5ioqChGp9MxiYmJzNSpU+vs4uDs8cycOZPvGxMTw4waNYo5cOCAZH/17RwxDMOcOnWKAcBs2LDBal++cI64cD/5H3cckyZNYgYOHGj1nm7dujF6vZ5p0aIF89VXX1nt197/ydM4e0wDBw60259h2FDVuLg4Rq/XM02aNGHGjx/PnD171meP6a233mJatmzJGI1GJjw8nBk0aBCzZcsWq/3Wp/PEMGwIo5+fH/PZZ58p7tOb50npWABIfh++dm+ict4EQRAEQThNo/OBIAiCIAii9pCAIAiCIAjCaUhAEARBEAThNCQgCIIgCIJwGhIQBEEQBEE4DQkIgiAIgiCchgQEQRAEQRBOQwKCIAiCIAinIQFBEARBEITTkIAgCIIgCMJpSEAQBEEQBOE0JCAIgiAIgnCa/wfsAz8qtrufRAAAAABJRU5ErkJggg==" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 4 + }, + { + "cell_type": "markdown", + "id": "fd3251c814306cd", + "metadata": {}, + "source": [ + "## Using adaptive time-stepping via the PID-controller\n", + "\n", + "In order to use adaptive time stepping, the solver must produce an estimate of its error on each step. This is then used by the PID controller to adjust the step size.\n", + "To perform this error estimation the `SPaRK` solver uses an embedded method. For solvers like `GeneralShARK`, which do not have an embedded method, we'd instead need to use `HalfSolver(GeneralShARK())` as the solver in order to estimate the error." + ] + }, + { + "cell_type": "code", + "id": "42ca5c5520079b5f", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:03:43.605326Z", + "start_time": "2025-10-09T01:03:35.705678Z" + } + }, + "source": [ + "controller = diffrax.PIDController(\n", + " rtol=0,\n", + " atol=0.005,\n", + " pcoeff=0.2,\n", + " icoeff=0.5,\n", + " dcoeff=0,\n", + " dtmin=2**-12,\n", + " dtmax=0.25,\n", + ")\n", + "\n", + "solver = diffrax.SPaRK()\n", + "# solver = diffrax.HalfSolver(diffrax.GeneralShARK())\n", + "\n", + "sol_pid_spark = diffrax.diffeqsolve(\n", + " terms,\n", + " solver,\n", + " t0,\n", + " t1,\n", + " dt0,\n", + " y0,\n", + " args,\n", + " saveat=diffrax.SaveAt(steps=True),\n", + " stepsize_controller=controller,\n", + " max_steps=2**16,\n", + ")\n", + "accepted_steps = sol_pid_spark.stats[\"num_accepted_steps\"]\n", + "rejected_steps = sol_pid_spark.stats[\"num_rejected_steps\"]\n", + "print(\n", + " f\"Accepted steps: {accepted_steps}, Rejected steps: {rejected_steps},\"\n", + " f\" total steps: {accepted_steps + rejected_steps}\"\n", + ")\n", + "\n", + "# Plot the solution on ax1 and the density of ts on ax2\n", + "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 8))\n", + "ax1.plot(sol_pid_spark.ts, sol_pid_spark.ys[:, 0], label=\"y_1\")\n", + "ax1.plot(sol_pid_spark.ts, sol_pid_spark.ys[:, 1], label=\"y_2\")\n", + "ax1.plot(sol_pid_spark.ts, sol_pid_spark.ys[:, 2], label=\"y_3\")\n", + "ax1.set_title(\"SDE solution\")\n", + "ax1.legend()\n", + "\n", + "# Plot the density of ts\n", + "# sol_pid.ts is padded with inf values at the end, so we remove them\n", + "padding_idx = jnp.argmax(jnp.isinf(sol_pid_spark.ts))\n", + "ts = sol_pid_spark.ts[:padding_idx]\n", + "ax2.hist(ts, bins=100)\n", + "ax2.set_title(\"Density of ts\")\n", + "\n", + "plt.show()" + ], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accepted steps: 2968, Rejected steps: 1637, total steps: 4605\n" + ] + }, + { + "data": { + "text/plain": [ + "
" + ], + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 5 + }, + { + "cell_type": "markdown", + "id": "344b5f07d5120128", + "metadata": {}, + "source": [ + "## Solving an SDE for a batch of Brownian motions\n", + "\n", + "When doing Monte Carlo simulations, we often need to solve the same SDE for multiple Brownian motions. We can do this via `jax.vmap`." + ] + }, + { + "cell_type": "code", + "id": "ffe3ced461ebb823", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:03:43.764668Z", + "start_time": "2025-10-09T01:03:43.657163Z" + } + }, + "source": [ + "def get_terms(bm):\n", + " return diffrax.MultiTerm(ode_term, diffrax.ControlTerm(g, bm))\n", + "\n", + "\n", + "# Fix which times we step to (this is equivalent to a constant step size)\n", + "# We do this because the combination of using dt0 and SaveAt(steps=True) pads the\n", + "# output with inf values up to max_steps.\n", + "# Instead we specify exactly which times we want to save at, so Diffrax allocates\n", + "# the correct amount of memory at the outset.\n", + "num_steps = 2**8\n", + "step_times = jnp.linspace(t0, t1, num_steps + 1, endpoint=True)\n", + "constant_controller = diffrax.StepTo(ts=step_times)\n", + "saveat = diffrax.SaveAt(ts=step_times)\n", + "\n", + "\n", + "# We will vmap over keys\n", + "@eqx.filter_jit\n", + "@partial(jax.vmap, in_axes=(0, None, None))\n", + "def batch_sde_solve(key, saveat, args):\n", + " bm = diffrax.VirtualBrownianTree(\n", + " t0, t1, bm_tol, bm_shape, key, levy_area=diffrax.SpaceTimeLevyArea\n", + " )\n", + " terms = get_terms(bm)\n", + " return diffrax.diffeqsolve(\n", + " terms,\n", + " diffrax.SPaRK(),\n", + " t0,\n", + " t1,\n", + " None,\n", + " y0,\n", + " args,\n", + " saveat=saveat,\n", + " stepsize_controller=constant_controller,\n", + " )\n", + "\n", + "\n", + "# Split the keys and compute the batched solutions\n", + "num_samples = 100\n", + "keys = jr.split(jr.PRNGKey(0), num_samples)" + ], + "outputs": [], + "execution_count": 6 + }, + { + "cell_type": "code", + "id": "3c1206025f30100d", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:03:46.771758Z", + "start_time": "2025-10-09T01:03:43.769093Z" + } + }, + "source": [ + "batch_sols = batch_sde_solve(keys, saveat, args)\n", + "print(\n", + " f\"Shape of batch_sols: \"\n", + " f\"{batch_sols.ys.shape} == {num_samples} x {num_steps + 1} x (dim of y)\"\n", + ")" + ], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shape of batch_sols: (100, 257, 3) == 100 x 257 x (dim of y)\n" + ] + } + ], + "execution_count": 7 + }, + { + "cell_type": "markdown", + "id": "71dda42d79d4c553", + "metadata": {}, + "source": [ + "## Optimizing wrt. SDE parameters\n", + "We will optimize the SDE parameters with the aim of achieving a mean of 0 and variance 4 at time `t1`." + ] + }, + { + "cell_type": "code", + "id": "d278fc2d438ffc82", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:07:34.736540Z", + "start_time": "2025-10-09T01:03:46.832280Z" + } + }, + "source": [ + "saveat_t1 = diffrax.SaveAt(t1=True)\n", + "batch_ys = batch_sde_solve(keys, saveat_t1, args).ys\n", + "print(batch_ys.shape)\n", + "ys_t1 = batch_ys[:, 0]\n", + "mean_t1 = jnp.mean(ys_t1, axis=0)\n", + "var_t1 = jnp.mean(ys_t1**2, axis=0) - mean_t1**2\n", + "print(f\"Stats at t=t1: mean={mean_t1}, var={var_t1}\")\n", + "\n", + "\n", + "# We will optimize for achieving a mean of 0\n", + "def loss(args: tuple[Array, Array, Array]):\n", + " _batch_sols = batch_sde_solve(keys, saveat_t1, args)\n", + " batch_ys = _batch_sols.ys\n", + " assert batch_ys.shape == (num_samples, 1, 3)\n", + " mean = jnp.mean(batch_ys, axis=(0, 1))\n", + " std = jnp.sqrt(jnp.mean(batch_ys**2, axis=(0, 1)) - mean**2)\n", + " target_mean = jnp.array([0.0, 1.0, 0.0])\n", + " target_stds = 2 * jnp.ones((3,))\n", + " loss = jnp.sqrt(\n", + " jnp.sum((mean - target_mean) ** 2) + jnp.sum((std - target_stds) ** 2)\n", + " )\n", + " return loss\n", + "\n", + "\n", + "# Define the parameters to optimize\n", + "alpha_opt = 0.5 * jnp.ones((3,))\n", + "beta_opt = jnp.array(1.0)\n", + "gamma_opt = jnp.ones((3,))\n", + "args_opt = (alpha_opt, beta_opt, gamma_opt)\n", + "\n", + "# Define the optimizer\n", + "num_steps = 191\n", + "schedule = optax.cosine_decay_schedule(3e-1, num_steps, 1e-2)\n", + "opt = optax.chain(\n", + " optax.scale_by_adam(b1=0.9, b2=0.99, eps=1e-8),\n", + " optax.scale_by_schedule(schedule),\n", + " optax.scale(-1),\n", + ")\n", + "# opt = optax.adam(2e-1)\n", + "opt_state = opt.init(args_opt)\n", + "\n", + "\n", + "@jax.jit\n", + "def step(i, opt_state, args):\n", + " loss_val, grad = jax.value_and_grad(loss)(args)\n", + " updates, opt_state = opt.update(grad, opt_state)\n", + "\n", + " # One way to apply updates\n", + " # args = optax.apply_updates(args, updates)\n", + "\n", + " # Another way to apply updates\n", + " args = jax.tree_util.tree_map(lambda x, u: x + u, args, updates)\n", + "\n", + " return opt_state, args, loss_val\n", + "\n", + "\n", + "for i in range(num_steps):\n", + " opt_state, args_opt, loss_val = step(i, opt_state, args_opt)\n", + " alpha_opt, beta_opt, gamma_opt = args_opt\n", + " if i % 10 == 0:\n", + " print(f\"Step {i}, loss: {loss_val}\")\n", + "\n", + "print(\n", + " f\"Optimal parameters:\\n\"\n", + " f\"alpha={alpha_opt},\"\n", + " f\" beta={beta_opt}, gamma={gamma_opt}\"\n", + ")" + ], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(100, 1, 3)\n", + "Stats at t=t1: mean=[-1.0154 1.5479 2.0878], var=[329.4802 711.1078 424.3449]\n", + "Step 0, loss: 34.94212183883967\n", + "Step 10, loss: 4.874442625767792\n", + "Step 20, loss: 2.521634210842532\n", + "Step 30, loss: 1.4702096092338783\n", + "Step 40, loss: 0.7936488640119762\n", + "Step 50, loss: 0.20701309373712398\n", + "Step 60, loss: 0.43545896965573144\n", + "Step 70, loss: 0.48191871779789575\n", + "Step 80, loss: 0.14351136791805125\n", + "Step 90, loss: 0.42323194856385005\n", + "Step 100, loss: 0.7814543571174357\n", + "Step 110, loss: 0.5590729910392899\n", + "Step 120, loss: 0.09288914937239617\n", + "Step 130, loss: 0.1462945784163213\n", + "Step 140, loss: 0.29703455403048784\n", + "Step 150, loss: 0.06270444996116936\n", + "Step 160, loss: 0.01298645327270607\n", + "Step 170, loss: 0.08775177455266986\n", + "Step 180, loss: 0.016462953232162895\n", + "Step 190, loss: 0.018917675036979466\n", + "Optimal parameters:\n", + "alpha=[-0.1822 3.5395 -0.0834], beta=3.645413009852767, gamma=[-1.6817 -0.8223 0.149 ]\n" + ] + } + ], + "execution_count": 8 + }, + { + "cell_type": "code", + "id": "834651877787c7e6", + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-09T01:07:38.550105Z", + "start_time": "2025-10-09T01:07:34.801808Z" + } + }, + "source": [ + "batch_ys_opt = batch_sde_solve(keys, saveat_t1, args_opt).ys\n", + "ys_t1 = batch_ys_opt[:, -1]\n", + "mean_t1 = jnp.mean(ys_t1, axis=0)\n", + "var_t1 = jnp.mean(ys_t1**2, axis=0) - mean_t1**2\n", + "print(f\"Stats at t=t1: mean={mean_t1}, var={var_t1}\")" + ], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Stats at t=t1: mean=[0.0001 1.0005 0.0002], var=[4.0193 4.0269 4.0155]\n" + ] + } + ], + "execution_count": 9 + }, + { + "cell_type": "markdown", + "id": "d103fe1695cdd847", + "metadata": {}, + "source": "With the magic of JAX and Diffrax we were able to differentiate through the SDE solver and optimize the parameters of the SDE to achieve the desired mean and variance at time `t1`." + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/usage/how-to-choose-a-solver.md b/docs/usage/how-to-choose-a-solver.md index 2dce12d1..54d890a9 100644 --- a/docs/usage/how-to-choose-a-solver.md +++ b/docs/usage/how-to-choose-a-solver.md @@ -42,54 +42,51 @@ For "split stiffness" problems, with one term that is stiff and another term tha ## Stochastic differential equations -SDE solvers are relatively specialised depending on the type of problem. Each solver will converge to either the Itô solution or the Stratonovich solution. In addition some solvers require "commutative noise". +SDE solvers are relatively specialised depending on the type of problem. Each solver will converge to either the Itô solution or the Stratonovich solution of the SDE. The Itô and Stratonovich solutions coincide iff the SDE has additive noise (as defined below). In addition some solvers require the SDE to have "commutative noise" or "additive noise". All of these terms are defined below. -!!! info "Commutative noise" +### General (noncommutative) noise +This includes any SDE of the form $dy(t) = f(y(t), t) dt + g(y(t), t) dw(t),$ where $t \in [0, T]$, $y(t) \in \mathbb{R}^e$, and $w$ is a standard Brownian motion on $\mathbb{R}^d$. We refer to $f: \mathbb{R}^e \times [0, T] \to \mathbb{R}^e$ as the drift vector field (VF) and $g: \mathbb{R}^e \times [0, T] \to \mathbb{R}^{e \times d}$ is the diffusion matrix field with columns $g_i$ for $i = 1, \ldots, d$. - Consider the SDE - $\mathrm{d}y(t) = μ(t, y(t))\mathrm{d}t + σ(t, y(t))\mathrm{d}w(t)$ +### Commutative noise +The diffusion matrix $σ$ is said to satisfy the commutativity condition if - then the diffusion matrix $σ$ is said to satisfy the commutativity condition if +$\sum_{i=1}^d g_{i, j} \frac{\partial g_{k, l}}{\partial y_i} = \sum_{i=1}^d g_{i, l} \frac{\partial g_{k, j}}{\partial y_i}$ - $\sum_{i=1}^d σ_{i, j} \frac{\partial σ_{k, l}}{\partial y_i} = \sum_{i=1}^d σ_{i, l} \frac{\partial σ_{k, j}}{\partial y_i}$ +For example, this holds: - Some common special cases in which this condition is satisfied are: +- when $g$ is a diagonal operator (i.e. $g(y,t)$ is a diagonal matrix for all $y, t$ and the i-th diagonal entry depends only on $y_i$), +- when the dimension of BM is $d=1$, or +- when the noise is additive (see below). - - the diffusion is additive ($σ$ is independent of $y$); - - the noise is scalar ($w$ is scalar-valued); - - the diffusion is diagonal ($σ$ is a diagonal matrix and such that the i-th - diagonal entry depends only on $y_i$; *not* to be confused with the simpler - but insufficient condition that $σ$ is only a diagonal matrix) +- The solver with the highest order of convergence for commutative noise SDEs is [`diffrax.SlowRK`][]. [`diffrax.ItoMilstein`][] and [`diffrax.StratonovichMilstein`][] are alternatives which evaluate the vector field fewer times per step, but also compute its derivative. + + +### Additive noise +We say that the diffusion is additive when $g$ does not depend on $y(t)$ and the SDE can be written as $dy(t) = f(y(t), t) dt + g(t) dw(t)$. + +Additive noise is a special case of commutative noise. For additive noise SDEs, the Itô and Stratonovich solutions conicide. Some solvers are specifically designed for additive noise SDEs, of these [`diffrax.SEA`][] is the cheapest, [`diffrax.ShARK`][] is the most accurate and [`diffrax.SRA1`][] is another alternative. ### Itô For Itô SDEs: +- For general noise [`diffrax.Euler`][] is a typical choice. - If the noise is commutative then [`diffrax.ItoMilstein`][] is a typical choice; -- If the noise is noncommutative then [`diffrax.Euler`][] is a typical choice. ### Stratonovich For Stratonovich SDEs: - If cheap low-accuracy solves are desired then [`diffrax.EulerHeun`][] is a typical choice. -- Otherwise, and if the noise is commutative, then [`diffrax.SlowRK`][] has the best order of convergence, but is expensive per step. [`diffrax.StratonovichMilstein`][] is a good cheap alternative. -- If the noise is noncommutative, [`diffrax.GeneralShARK`][] is the most efficient choice, while [`diffrax.Heun`][] is a good cheap alternative. -- If the noise is noncommutative and an embedded method for adaptive step size control is desired, then [`diffrax.SPaRK`][] is the recommended choice. - -### Additive noise - -Consider the SDE - -$\mathrm{d}y(t) = μ(t, y(t))\mathrm{d}t + σ(t, y(t))\mathrm{d}w(t)$ - -Then the diffusion matrix $σ$ is said to be additive if $σ(t, y) = σ(t)$. That is to say if the diffusion is independent of $y$. +- For general noise, [`diffrax.GeneralShARK`][] is the most efficient choice, while [`diffrax.Heun`][] is a good cheap alternative. +- If an embedded method for adaptive step size control is desired and the noise is noncommutative then [`diffrax.SPaRK`][] is the recommended choice. +- If the noise is commutative, then [`diffrax.SlowRK`][] has the best order of convergence, but is expensive per step. [`diffrax.StratonovichMilstein`][] is a good cheaper alternative. -In this case the Itô solution and the Stratonovich solution coincide, and mathematically speaking the choice of Itô vs Stratonovich is unimportant. Special solvers for additive-noise SDEs tend to do particularly well as compared to the general Itô or Stratonovich solvers discussed above. +### More information about SDE solvers -- The cheapest (but least accurate) solver is [`diffrax.SEA`][]. -- Otherwise [`diffrax.ShARK`][] or [`diffrax.SRA1`][] are good choices. +A detailed example of how to simulate SDEs can be found in the [SDE example](../examples/sde_example.ipynb). +A table of all SDE solvers and their properties can be found in [SDE solver table](../devdocs/SDE_solver_table.md). ### Underdamped Langevin Diffusion diff --git a/mkdocs.yml b/mkdocs.yml index a493b353..25ce7aa8 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -123,6 +123,7 @@ nav: - Second-order sensitivities: 'examples/hessian.ipynb' - Nonlinear heat PDE: 'examples/nonlinear_heat_pde.ipynb' - Underdamped Langevin diffusion: 'examples/underdamped_langevin_example.ipynb' + - Advanced SDE simulation example: 'examples/sde_example.ipynb' - Basic API: - 'api/diffeqsolve.md' - Solvers: @@ -150,3 +151,4 @@ nav: - 'devdocs/predictor_dirk.md' - 'devdocs/adjoint_commutative_noise.md' - Stochastic Runge-Kutta methods: 'devdocs/srk_example.ipynb' + - Table of SDE solvers: 'devdocs/SDE_solver_table.md'