{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c3b296dc",
   "metadata": {},
   "source": [
    "# IMEX and Delay Equations\n",
    "\n",
    "This notebook covers two families of steppers for problems the explicit ODE steppers handle poorly:\n",
    "\n",
    "- **IMEX (implicit–explicit)** steppers for $y' = f_{exp}(y, t) + f_{imp}(y, t)$, where $f_{imp}$ is stiff (fast linear decay, diffusion along a cable) and $f_{exp}$ is nonstiff but possibly expensive or nonlinear: `imex_euler_step` (order 1), `imex_ars222_step` (order 2, L-stable), `imex_cnab_step` (order 2, two-step).\n",
    "- **DDE** steppers for delay equations $y'(t) = f(t, y(t), y(t - \\tau_1), \\dots)$: `dde_euler_step`, `dde_heun_step`, `dde_rk4_step`, and the predictor–corrector variants `dde_euler_pc_step`, `dde_heun_pc_step`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a031e0e",
   "metadata": {},
   "source": [
    "## 1. Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "13941c0d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:46.157649Z",
     "iopub.status.busy": "2026-10-16T04:21:46.157649Z",
     "iopub.status.idle": "2026-10-16T04:21:47.640628Z",
     "shell.execute_reply": "2026-10-16T04:21:47.640628Z"
    }
   },
   "outputs": [],
   "source": [
    "import brainstate\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import braintools\n",
    "\n",
    "jax.config.update(\"jax_enable_x64\", True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2ddba23",
   "metadata": {},
   "source": [
    "## 2. IMEX Steppers\n",
    "\n",
    "### Calling convention\n",
    "\n",
    "`step(f_exp, f_imp, y, t, *args, max_iter=2)`, with both parts of the form `f(y, t, *args)`. `imex_cnab_step` additionally needs the previous state: `imex_cnab_step(f_exp, f_imp, y, y_prev, t, ...)`.\n",
    "\n",
    "Each implicit stage $Y = c + a\\,\\Delta t\\,f_{imp}(Y, t^*)$ is solved with **Newton's method**; `max_iter` is the number of Newton iterations. For states with up to 256 elements the Jacobian is formed densely; larger states use matrix-free GMRES on Jacobian-vector products. When $f_{imp}$ is linear in $y$, one iteration is exact.\n",
    "\n",
    "### Accuracy and stiffness\n",
    "\n",
    "The test problem $y' = \\sin t - k y$ has the exact solution $y(t) = (1 - B)e^{-kt} + A \\sin t + B \\cos t$ with $A = k/(k^2+1)$, $B = -1/(k^2+1)$. We treat $\\sin t$ explicitly and $-ky$ implicitly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b3f15f49",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:47.642632Z",
     "iopub.status.busy": "2026-10-16T04:21:47.642632Z",
     "iopub.status.idle": "2026-10-16T04:21:49.035363Z",
     "shell.execute_reply": "2026-10-16T04:21:49.035363Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_euler_step    k = 2: order [1.1  1.05 1.03]\n",
      "imex_ars222_step   k = 2: order [1.99 1.99 2.  ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_cnab_step     k = 2: order [1.69 1.89 1.96]\n",
      "\n",
      "k = 100      k*dt = 5      exact 8.360e-03   imex_euler_step: 8.073e-03   imex_ars222_step: 8.424e-03   imex_cnab_step: 8.370e-03\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k = 1000     k*dt = 10     exact 8.409e-04   imex_euler_step: 8.355e-04   imex_ars222_step: 8.427e-04   imex_cnab_step: 8.410e-04\n",
      "k = 1e+06    k*dt = 10000  exact 8.415e-07   imex_euler_step: 8.360e-07   imex_ars222_step: 8.454e-07   imex_cnab_step: 4.645e-04\n"
     ]
    }
   ],
   "source": [
    "def forced_decay(name, k, dt, T=1.0):\n",
    "    fe = lambda y, t: jnp.sin(t)\n",
    "    fi = lambda y, t: -k * y\n",
    "    n = int(round(T / dt))\n",
    "    with brainstate.environ.context(dt=dt):\n",
    "        if name == \"imex_cnab_step\":\n",
    "            # two-step method: start with one ARS(2,2,2) step\n",
    "            y1 = braintools.quad.imex_ars222_step(fe, fi, jnp.asarray(1.0), 0.0)\n",
    "\n",
    "            def body(carry, i):\n",
    "                y, y_prev = carry\n",
    "                return (braintools.quad.imex_cnab_step(fe, fi, y, y_prev, i * dt), y), None\n",
    "\n",
    "            (y, _), _ = jax.lax.scan(body, (y1, jnp.asarray(1.0)), jnp.arange(1, n))\n",
    "        else:\n",
    "            step = getattr(braintools.quad, name)\n",
    "            y, _ = jax.lax.scan(lambda y, i: (step(fe, fi, y, i * dt), None), jnp.asarray(1.0), jnp.arange(n))\n",
    "    return float(y)\n",
    "\n",
    "def exact_forced_decay(k, T=1.0):\n",
    "    A, B = k / (k ** 2 + 1), -1 / (k ** 2 + 1)\n",
    "    return (1 - B) * np.exp(-k * T) + A * np.sin(T) + B * np.cos(T)\n",
    "\n",
    "names = [\"imex_euler_step\", \"imex_ars222_step\", \"imex_cnab_step\"]\n",
    "dts = [0.1, 0.05, 0.025, 0.0125]\n",
    "for name in names:\n",
    "    e = np.array([abs(forced_decay(name, 2.0, dt) - exact_forced_decay(2.0)) for dt in dts])\n",
    "    print(f\"{name:18s} k = 2: order {np.round(np.log2(e[:-1] / e[1:]), 2)}\")\n",
    "print()\n",
    "for k, dt in [(100, 0.05), (1000, 0.01), (1e6, 0.01)]:\n",
    "    row = \"   \".join(f\"{name}: {forced_decay(name, k, dt):.3e}\" for name in names)\n",
    "    print(f\"k = {k:<8g} k*dt = {k * dt:<6g} exact {exact_forced_decay(k):.3e}   {row}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85cbb360",
   "metadata": {},
   "source": [
    "All three reach their nominal order, and all remain stable with $k\\,\\Delta t$ in the thousands, where any explicit method would explode (RK4 needs $k\\,\\Delta t < 2.79$). At $k\\,\\Delta t = 10^4$, however, CNAB returns a value far from the solution. The reason is its implicit part, the trapezoidal rule: it is A-stable but not **L-stable**, so a very fast mode is not damped but flips sign every step with an amplification factor close to $-1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e8e5e742",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:49.036367Z",
     "iopub.status.busy": "2026-10-16T04:21:49.036367Z",
     "iopub.status.idle": "2026-10-16T04:21:49.760793Z",
     "shell.execute_reply": "2026-10-16T04:21:49.760793Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k, dt, n = 1000.0, 0.1, 40          # k * dt = 100\n",
    "fe = lambda y, t: jnp.zeros_like(y)\n",
    "fi = lambda y, t: -k * y\n",
    "paths = {name: [1.0] for name in names}\n",
    "with brainstate.environ.context(dt=dt):\n",
    "    for name in [\"imex_euler_step\", \"imex_ars222_step\"]:\n",
    "        y = jnp.asarray(1.0)\n",
    "        for i in range(n):\n",
    "            y = getattr(braintools.quad, name)(fe, fi, y, i * dt)\n",
    "            paths[name].append(float(y))\n",
    "    y_prev, y = jnp.asarray(1.0), braintools.quad.imex_ars222_step(fe, fi, jnp.asarray(1.0), 0.0)\n",
    "    paths[\"imex_cnab_step\"].append(float(y))\n",
    "    for i in range(1, n):\n",
    "        y_prev, y = y, braintools.quad.imex_cnab_step(fe, fi, y, y_prev, i * dt)\n",
    "        paths[\"imex_cnab_step\"].append(float(y))\n",
    "\n",
    "plt.figure(figsize=(7, 3.5))\n",
    "for name, p in paths.items():\n",
    "    plt.plot(np.arange(n + 1) * dt, p, \".-\", label=name)\n",
    "plt.axhline(0, color=\"k\", lw=0.5)\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"y\"); plt.title(\"$y' = -1000\\\\,y$ with $\\\\Delta t = 0.1$ (exact: $e^{-1000 t}$)\")\n",
    "plt.legend(); plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef2497da",
   "metadata": {},
   "source": [
    "IMEX Euler and ARS(2,2,2) damp the fast mode immediately, as the exact solution does. CNAB carries it along as a slowly decaying sawtooth. Use CNAB when the implicit part is stiff but its fastest modes do not matter or are not excited (smooth initial data), and ARS(2,2,2) when fast transients must be damped.\n",
    "\n",
    "### Nonlinear implicit parts and `max_iter`\n",
    "\n",
    "For a nonlinear $f_{imp}$, each Newton iteration roughly squares the error. With $f_{imp}(y) = -1000\\,y^3$, $y_0 = 1$ and $\\Delta t = 0.01$, the IMEX Euler step must solve $Y + 10\\,Y^3 = 1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "16ae4f2c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:49.761796Z",
     "iopub.status.busy": "2026-10-16T04:21:49.761796Z",
     "iopub.status.idle": "2026-10-16T04:21:49.871729Z",
     "shell.execute_reply": "2026-10-16T04:21:49.871729Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "max_iter = 1:  Y = 0.677419354839   error 2.8e-01\n",
      "max_iter = 2:  Y = 0.488749116319   error 9.6e-02\n",
      "max_iter = 3:  Y = 0.408387836861   error 1.5e-02\n",
      "max_iter = 4:  Y = 0.393479727265   error 4.8e-04\n",
      "max_iter = 5:  Y = 0.393003214565   error 4.8e-07\n",
      "max_iter = 6:  Y = 0.393002738972   error 4.7e-13\n"
     ]
    }
   ],
   "source": [
    "root = [r.real for r in np.roots([10, 0, 1, -1]) if abs(r.imag) < 1e-12][0]\n",
    "with brainstate.environ.context(dt=0.01):\n",
    "    for max_iter in range(1, 7):\n",
    "        y = braintools.quad.imex_euler_step(lambda y, t: 0.0 * y, lambda y, t: -1000.0 * y ** 3,\n",
    "                                            jnp.asarray(1.0), 0.0, max_iter=max_iter)\n",
    "        print(f\"max_iter = {max_iter}:  Y = {float(y):.12f}   error {abs(float(y) - root):.1e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6bc3864",
   "metadata": {},
   "source": [
    "The default `max_iter=2` is exact for linear implicit parts and adequate for mildly nonlinear ones; raise it when the implicit part is strongly nonlinear over a step, as here.\n",
    "\n",
    "### Example: a FitzHugh–Nagumo cable\n",
    "\n",
    "A cable of excitable membrane, discretized into $N = 500$ compartments of length $\\Delta x = 0.1$:\n",
    "\n",
    "$$\\partial_t v = D\\,\\partial_{xx} v + v - v^3/3 - w, \\qquad \\partial_t w = \\varepsilon\\,(v + a - b w).$$\n",
    "\n",
    "The diffusion term is stiff: its fastest mode decays at rate $4D/\\Delta x^2 = 400$, which restricts RK4 to $\\Delta t < 0.007$, although the wave itself evolves on a time scale of order 1. We treat diffusion implicitly and the local membrane dynamics explicitly. The state is a dict of two arrays (1000 elements), so the Newton steps use matrix-free GMRES."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5d854b49",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:49.872962Z",
     "iopub.status.busy": "2026-10-16T04:21:49.872962Z",
     "iopub.status.idle": "2026-10-16T04:21:55.117279Z",
     "shell.execute_reply": "2026-10-16T04:21:55.117279Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RK4, dt = 0.002:  front at t = 40: 34.383\n",
      "RK4, dt = 0.005:  front 34.383\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RK4, dt = 0.01:  diverged\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_euler_step, dt = 0.05:  front 33.854\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_euler_step, dt = 0.1:  front 33.348\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_euler_step, dt = 0.2:  front 32.399\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_ars222_step, dt = 0.05:  front 34.380\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_ars222_step, dt = 0.1:  front 34.368\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "imex_ars222_step, dt = 0.2:  front 34.320\n"
     ]
    }
   ],
   "source": [
    "N, dx, D, eps, a, b = 500, 0.1, 1.0, 0.08, 0.7, 0.8\n",
    "x = np.arange(N) * dx\n",
    "\n",
    "def laplacian(v):  # no-flux boundaries\n",
    "    vp = jnp.concatenate([v[:1], v, v[-1:]])\n",
    "    return (vp[2:] - 2 * v + vp[:-2]) / dx ** 2\n",
    "\n",
    "def membrane(s, t):   # explicit part\n",
    "    return {\"v\": s[\"v\"] - s[\"v\"] ** 3 / 3 - s[\"w\"], \"w\": eps * (s[\"v\"] + a - b * s[\"w\"])}\n",
    "\n",
    "def diffusion(s, t):  # implicit part\n",
    "    return {\"v\": D * laplacian(s[\"v\"]), \"w\": jnp.zeros_like(s[\"w\"])}\n",
    "\n",
    "def full_rhs(s, t):\n",
    "    return jax.tree.map(jnp.add, membrane(s, t), diffusion(s, t))\n",
    "\n",
    "s0 = {\"v\": jnp.full(N, -1.2).at[:20].set(1.5), \"w\": jnp.full(N, -0.62)}\n",
    "\n",
    "def run_cable(step, dt, T=40.0, imex=True):\n",
    "    n = int(round(T / dt))\n",
    "    with brainstate.environ.context(dt=dt):\n",
    "        def body(s, i):\n",
    "            s = step(membrane, diffusion, s, i * dt) if imex else step(full_rhs, s, i * dt)\n",
    "            return s, s[\"v\"]\n",
    "        _, vs = jax.lax.scan(body, s0, jnp.arange(n))\n",
    "    return np.asarray(vs)\n",
    "\n",
    "def front_position(v):  # rightmost crossing of v = 0, linearly interpolated\n",
    "    i = np.where((v[:-1] > 0) & (v[1:] <= 0))[0][-1]\n",
    "    return x[i] + v[i] / (v[i] - v[i + 1]) * dx\n",
    "\n",
    "v_ref = run_cable(braintools.quad.ode_rk4_step, 0.002, imex=False)\n",
    "print(f\"RK4, dt = 0.002:  front at t = 40: {front_position(v_ref[-1]):.3f}\")\n",
    "for dt in [0.005, 0.01]:\n",
    "    vs = run_cable(braintools.quad.ode_rk4_step, dt, imex=False)\n",
    "    print(f\"RK4, dt = {dt}:  \" + (f\"front {front_position(vs[-1]):.3f}\" if np.all(np.isfinite(vs)) else \"diverged\"))\n",
    "for name in [\"imex_euler_step\", \"imex_ars222_step\"]:\n",
    "    for dt in [0.05, 0.1, 0.2]:\n",
    "        vs = run_cable(getattr(braintools.quad, name), dt)\n",
    "        print(f\"{name}, dt = {dt}:  front {front_position(vs[-1]):.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a1030bb1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:55.118283Z",
     "iopub.status.busy": "2026-10-16T04:21:55.118283Z",
     "iopub.status.idle": "2026-10-16T04:21:55.914047Z",
     "shell.execute_reply": "2026-10-16T04:21:55.914047Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fmE4/LK6++uqJY/Mqrd/wDd8w078hnMtpCRRQ2/HCAeo7fn8pkMyA/FB7bBp++qd/mrNtMQ3azZricJwtcE+oY18URasg4pczFJQyQPXEWOu3f/u3ecxX/AWOjWcQi1/4hV8o9ThC3ThdwHP54he/yPYBO35785vfPPcfdAv11ukWPr5eqGwf+tCHcrer+h4WVaiieqth7To+xPcYihBis4qAGlfW/LMfAGkAYcQf+b0ocWXAWB/JC/DpwnagXy82/nFeMJqfRQV97nOfS9/93d+de8P3CcS0SjG2AMmHpcOSa5Cpa665ZuK2+P4iBB4vNlR1vvDCC/kSxKYIvDjD14PPgWD0eXG674+pB4L49wLEFEGx/9u//dvcv/Gyc4DN+Xl+VvfLEwo/NV4Qw0ph45QwrYGlqJj2AR98MeUBKSEIt0esHZI2HA6HwJVQx0kBf3zwxxWRSvjDBeKBX85VY23EucBTCc8cSJIdxSshQxwTSAtuC5UJf7jxxx3xTlDzEC10OgCvKj4XVAv84cBYDn/YtPFnVmUGShFIEyKhQEbwxwyjauuxg2KJsScuoeqBkP7bv/3bro8NMg+yiogiKJ74Iwkyhu8j/sADIFb4WhARBeUG42uocyBNWFqCMg0SBmiMExSb/WimQVQT3mYBCH+ZZxLKoxJOeBTxs1VcksHoGKokqjtB7KrsFjh/IK3nn39+6fU4T/gcIFbT4pPw/cPPBNQtvJjCuUUMFc4rXlxgMQ+LWfiacI7+53/+hxUwfV4Y90Nhg0JtM11BxkCKMK5HQ0+RjOHfm7UK4GcQ51cza0/3/WFHuPHGGyfOMZRFnBMsvU3L88SLAfy+wPcP30+NaIJCWozywiIdfjdg8Qu/QzAtmTbS3i9PKIAJA752fK9gBUG+Jywv+LektbL6/UPklFVXodjj64Q3HIpx8WccC4O7xU05HGcsDno933F4IpqKsTqKj3zkI+kDHvAAjmm5zW1ukz73uc/lFpGqGKOf/dmf5evufOc7Vz4H3O/iiy/mqBZEmXz1V391+qQnPYkbWvYjoqnsa8H9cP9igwyafDSS5znPeU76J3/yJ/yYH/3oRyufv31+n/nMZ9Lv/u7v5iihm93sZukznvEMjnoqxlw95SlP4a8Xt/ue7/kejqrZLaLpk5/8JEcBoS0IjTaI0kH8kP0+2Rii+9znPvy14HN83dd9HZ+r//mf/4m3+dVf/VV+fMQ3nUxE0zTMG9Gk50TjqH7pl36p9HH/+I//mK//lV/5ldLrP/GJT/D1L3rRiyqfGyKYcJtnP/vZUxuTALTn4HxpbNB1112XvuIVr+CP0a6DyCecb7QN4bkVgee5vr6eizjT81v1ZmO8EO+EY49//OMP5P7A8573PP7ZQzyVBf6dIKLrX/7lX9Ld8I//+I/8PcO/c8S4vexlL0vf8pa3TEQ0IaYN/xbxs4vrTnd7EqLOHvjAB/LzxO8C/J7c3NzM3Ub/Ddh/s/ozVPW2W9Sbw3Emo4b/HTQRdjgOE6BooTkJaggSA6qgahDGi3sNCT/dwEgaW/t2POo4NUBiAVRFNHU95SlPmfv+SJbAMhYUWCxKne77Y5IBXzO8uMURMxIRoGYWW7McDofDwj2hDscUFDMA4Ql905vexKO1aQT0MAKvRzGWxbjTceoBryHGtPALFmsqZwFG3bCr7IVA7sf9YdmALQEWCAssHYLYIi3D4XA4psGVUIdjCuDvw4Y3fIRQruDnQi7qLBWPh1EJdTgcDofjdMEXkxyOXTbk0XcO0okNc2RdIvqouFDlcDgcDofjECmhqhQVmzK06hGjT4RQ448+/EcgBNgE9k1Ch8PhcDgcjsONA/eEokkErRP69uEPfzheh+UPtMDA3I76O8ScXHLJJQf6fB0Oh8PhcDgcZ8A4Hk0UZfWM8N+95S1v4fYSzYKDER45awg3ti07DofD4XA4HI7DhQMnoQjMRvcuAsDRIoJAbSyCIAQZjTm2uhFVd7gOgd9VJBRje22KAbB1ijBlhC/PW/vmcDgcDofjYAHXIIo4wBXq9YMZ4MIeiDbAedFut2PBiWPBSOj9739/bmiBDxSjePhD0TTyT//0T3TttdfyyTt27FjuPvCD4roqgMQWfaYOh8PhcDgON1Dbi7rcgyCgN19Zpw4lc98Xk1605jkRXUASqt3ZwAUXXMCkFAHHqN9bWVnZ02O+4AUvoEsvvTQ31od6+i2v/DNqLa9V3i+llMbaYeGYCgjKdVeVHQ6Hw3EaMOzt0Puf92g6cuTIgXx+KKAgoE+g21J7jlWaAY3pbdd+ke/vJHRBx/EWUD3/1//6X/TZz36W+3Rx4o4fP55TQ6+77rpSD6liaWmJ34oAAW2tOAndDzgJdTgcDsfpxkFb6kBA27U57ADOJxZ/O95ie3ub/uM//oNufetb033ucx9u47jyyivj9VdffTVdc8017B11OBwOh8PhOF1o1GpzvzkWWAn9qZ/6KXrUox7FI3jEL1122WXUaDToe7/3e7nSDn3KGK2fc845tLGxQc985jOZgJ6azXj8sPjLFofD4XA4HJOo10BE57g9/ue0YnFJ6H//938z4bzhhhvolre8JT34wQ/m+CW8D7z61a/mTbjHPOYxubD6UwP/SXE4HA6Hw1GOedXNBotbjoUloWhCmgYYeV//+tfz26mHK6EOh8PhcDjK0ZhTCW2cyidzhmChFpMOFk5AHQ6Hw+FwlMOV0P2Hk9AIV0IdDofD4XCUw5XQ/YeT0AgnoA6Hw+FwOMrhSuj+w0lohCuhDofD4XA4qlnCPLmWTkF3h5PQCCegDofD4XA4yuFK6BkeVu9wOBwOh8PhODvgSmiEj+MdDofD4XCUwxeT9h9OQh0Oh8PhcDhmIqHzjOMdu8HH8RGugjocDofD4ZiuhM7zNg8+9KEPcZX5bW5zG6rVavSud71r6u0/+MEP8u2Kb9deey0dFrgS6nA4HA6Hw3HAi0k7Ozt0z3vek37oh36ILrnkkpnvd/XVV9PGxkb8+Fa3uhUdFjgJjXBPqMPhcDgcjnLU51Q35x01P+IRj+C3eQHSeezYMTqM8HF8hBNQh8PhcDgc05XQed5OB+51r3vRrW99a/qWb/kW+shHPkKHCa6EOhwOh8PhcJyi7fjNzc3c8aWlJX47WYB4vvGNb6T73ve+1O/36Td/8zfpIQ95CH3sYx+je9/73nQY4CQ0wsfxDofD4XA49peEnn/++bnjl112Gb34xS8+6edzl7vchd8UD3zgA+k//uM/6NWvfjX9zu/8Dh0GOAmNcALqcDgcDodjfxeTvvCFL+QWh/ZDBa3C/e53P/rwhz9MhwVOQiNcCXU4HA6Hw7G/AAG1JPRU4lOf+hSP6Q8LnIQ6HA6Hw+FwzDBen2scP6eutb29TZ/97Gfjx5/73OeYVJ5zzjl0+9vfnl7wghfQF7/4RXrb297G17/mNa+hO97xjnT3u9+der0ee0L/8i//kv7f//t/dFjgJDTCVVCHw+FwOBzlqM85jsft58HHP/5xeuhDHxo/vvTSS/nyiU98Il1xxRX0pS99ia655pp4/WAwoOc85zlMTFdXV+mCCy6gD3zgA7nHWHQ4CXU4HA6Hw+HY78WkOROaHvKQh1CaVgtiIKIWz33uc/ntMMNJqMPhcDgcDsd+LyadppzQwwwnoQ6Hw+FwOBwHrISejXASGuHb8Q6Hw+FwOMrhSuj+w0mow+FwOBwOxwyLRvVTuJh0NsJJaISroA6Hw+FwOMpRa9SoVp+dWNachO4KJ6ERPo53OBwOh8NRjnqjRvU5SKgrobujPsNtHA6Hw+FwOByOfYUroRGugjocDofD4ahAo061+hzaXc15xW5wEhrh43iHw+FwOBzlgB8UvtCZb8+8wjENTkIjnIA6HA6Hw+GY4gmdg4TWnYTuCiehDofD4XA4HLsAo/h5xvG1KRWcDoGT0AgfxzscDofD4SiHK6H7DyehDofD4XA4HLPkhLondF/hJDTCVVCHw+FwOBzTSOgc43gan9LncybASWiEj+MdDofD4XCUw8fx+w8noRFOQB0Oh8PhcFTXcM5V2zl2ErobvDEpwn9YHA6Hw+FwOE4XXAl1OBwOh8Ph2AX1Rp3fZr596jrfbnAS6nA4HA6Hw7Hf2/GpT1h3g5PQCPeEOhwOh8PhKIeT0P2Hk9AI3453OBwOh8NRDh/H7z+chDocDofD4XDshjmVUHIldFc4CXU4HA6Hw+HYBfVajepzRDTh9o7pcBIa4aN4h8PhcDgc5UBb0lyNSWMfx+8GJ6ER7gl1OBwOh8OxT41JHla/K5yERjgBdTgcDofDsU/b8U5Cd4VrxRH+w+JwOBwOh8Nx1pHQV7ziFdzL+qxnPSse6/V69OM//uN085vfnNbX1+kxj3kMXXfddafoGbgS6nA4HA6HY7ondJ63efChD32IHvWoR9FtbnMb5kPvete7dr3PBz/4Qbr3ve9NS0tLdOc735muuOIKOkxYCBL6d3/3d/SmN72JLrjggtzxZz/72fTnf/7n9I53vIP++q//mv7nf/6HLrnkkgN7ng6Hw+FwOM5O1BuZL3S2t/kef2dnh+55z3vS61//+plu/7nPfY6+7du+jR760IfSpz71KRbxfviHf5je97730WHBgXtCt7e36fu///vpzW9+M/38z/98PH7ixAl6y1veQr//+79PD3vYw/jYW9/6Vrrb3e5GH/3oR+kBD3jAPj8TX0xyOBwOh8NRjlq9xm/z3H4ePOIRj+C3WfHGN76R7njHO9Iv//Iv88fgRx/+8Ifp1a9+NV188cV0GHDgSijG7WDyF110Ue74Jz7xCRoOh7njd73rXen2t789XXXVVZWP1+/3aXNzM/c2G5yAOhwOh8PhKEe9Lo1JM7/VhWIVOQl4yn7gqquumuBOIJ/TONKi4UBJ6Nvf/nb65Cc/SZdffvnEdddeey212206duxY7vi5557L11UBj3X06NH4dv7555+S5+5wOBwOh+Ps246f5w0AD7G8pIzz7AXgQuBEFvgYRLfb7dJhwIGN47/whS/QT/7kT9L73/9+Wl5e3rfHfcELXkCXXnpp/Bgnw4mow+FwOByO0xpWH24LvrOxsRGPY4nIccAkFOP2L3/5y7zVpUiShLfDfu3Xfo2NtYPBgI4fP55TQ7Edf95551U+Lk6un2CHw+FwOBz7iVq9zm/z3B4AAbUkdL9w3nnnTSQG4WN8rpWVFToMODAS+s3f/M306U9/OnfsyU9+Mvs+n/e857F62Wq16Morr+RoJuDqq6+ma665hi688MIDetYOh8PhcDjORqjXc57bn0pceOGF9Bd/8Re5Y5guHyaOdGAk9MiRI3SPe9wjd2xtbY0zQfX4U57yFB6tn3POOczsn/nMZ/I3d/834wHfjnc4HA6Hw1GBebM/5ySh29vb9NnPfjYXwYToJXAgLGXDbvjFL36R3va2t/H1P/IjP8KT4+c+97n0Qz/0Q/SXf/mX9Ed/9Ef0nve8hw4LDjyiaRoQM4DtMiih2CbD1tev//qvn6LP5gTU4XA4HA7HweDjH/84Z34qdL/liU98IofQf+lLX+JpsALxTCCcyFR/7WtfS7e73e3oN3/zNw9NPBNQS9P0jGZfWEzCNtojX/sBaq2sVd4O34QxvhVn9Hdjf1CrEdXxP4fD4XA4TjGG3R36i5+8iPPDT4W3clYe8fdPv4SOLLVmvt9Wf0hf/6Y/PbDnfRiw0Ero6YWzT4fD4XA4HPu7mOSohpPQCPeEOhwOh8OxSMDQrTFn89CpjWiavYuz1khO6fM5E+AkNMIJqMPhcDgcB4aayEH8bq0W308OeU6ooxpOQiNcCXU4HA6H46DIJ78t8L4B13bOMWKf57ZnK5yERjgBdTgcDofjdAKc06qeiwxXQvcfTkIdDofD4XCc5nE73q/N6AmlhYCT0P2Hk9AIH8c7HA6Hw3EqyefUeL9F94TW5tyOrzkJ3Q1OQh0Oh8PhcByc17PkdnpzXNQXajveldD9hJPQCFdBHQ6Hw+E4eY9neH/GcXvRE2oLUXgcv8DLSo6Tg5NQh8PhcDgcp8XrGQlqyTISBE+rhKoyuihL5q6E7j+chEa4J9ThcDgcjn2vcC7xhNq7WUKq5JNvFx5/vCBKaL1R57d5bu+YDiehEU5AHQ6Hw+GYChBDvtxl2F5xO+v1ZPIZlFMd4ytJxaV8TAuzHl+r1+as7VwM8rzIcBLqcDgcDoejGnE0rh9OH7fztSXqph6T9zPyKVytxpdWAVU/6KKMtX0cv/9wEhrh43iHw+FwOCKUDM5wu7JopQnyWVg40uvYCwoSWi+Qz1qNe+NrzcUgc05C9x9OQiOcgDocDofj7EVxVL4XT6j90BLOsjG7ElZEMPGxqIzWqNkAORUS2lgUEuo5ofsOJ6ERroQ6HA6H4yxD0aM57aZxs13uMU3x1FsUvZ4glXkyKkSTR/EgnKyMZiQUl6NkMahKrdGgeqMx1+0d07EYZ9bhcDgcDsfphd1E3+V29RJ1NMYxFcLmlXgWSSjvGAVyqZ8X1zWxdc71nHVqgpDWiZr1OpPSdqNGyXgxFEUfx+8/nIRGuArqcDgcjjMXexm3l6mjuQxPVUXDjeKY3fg6IwkF4eTRe1A863Lblhm9KyFt47KO6+qUjBdDUXQSuv9wEupwOBwOxxkMO0afKUi+QvUsZnwqsSxTPJWgati8jtlZCSW5ZNWTSSgIpyiiLVZCa7TUrPN9Wgs0jnfsP/zMOhwOh8NxpqFiY33WFqNpxyL5BLG0imlQP3nRKPg/desdo3aQUiacYQSv5DOqnnUcE0UUxxpQRJt1Go0Xg6pgKWm+nFBXQnfDYpxZh8PhcDgc+5jnOVu0UpnX026u81WFfM/o6QxKph23g4Qy+QxEU8koj+HDeF3H7SCY4vvMVE9+v16j5XCJjxeGhPo4ft+xGGd2IeDb8Q6Hw+E4c72eu43bLfEsZnjmQuXh5Qzh8rWi17OebbuDcKrnE4tG4GTtZiNexwpojWjZkFG8NWs1WmnJkhLG8sO0uTiNSfOQUG9M2hWLcWYdDofD4XDMDs3a3F3vLPWElhHSMq+nEM2MbKqfU9uNRPXM/J2yXCTHZMwuhNMqoKpw8ui9VmMSimNLjTqTTjzWarMRblejfrIgi0k+jt93OAmNcBXU4XA4HIsNJYT8/h4326uC5O24XfM8xdeZXzRSpVPG7FA7Z/R61rKFo3ZTSCcI50qrEa/DMYiNMo4natdr1BsuBpmr1Rv8Ns/tHdPhJDTCx/EOh8PhWDDkFEt5rzanJ5T5ZEWdpnpCra/Tbrmzr9NcJ9vsmfoZN9wxUtcxO7+v/s5wjMfxono2C6onRu9MTNkTqmQVl0QtSqleT2ghAFI5D7F0ErornIQ6HA6Hw7GAKKvFrLpd2WjdbseXLhyZmky91DG7VmkqyawXvJ7aZiRez6BwBlKK60Eg9diSej2D6ikkVI5zHFMgnkpC65RSmxKq05hqox71uzfRQoDL7edQZX0cvyuchEa4CupwOByOQ+L1rLhdMVqpuHBkczwt8czleob2Ihmva32mjNRtrqeO2UEk2dcZrkPWJ8jnSvB14jodw4sSCiIbSGhYTAJpbaYJNdMR1cYjqg068bK+eT0tAlDDOU8Vp9d27g6n6RG+xeZwOByO04y4+GMij3YJlNeOdbtkpEqlRiSB1IlyaY6ZN1Ex5RLjc7wttRq01KrTcqtBy+Fytd3kt7V2g9ZwudSQt3aT1peadETf2nK5sdSko8stOoa3lSbdbKVJx5abdIyPN2hjqU5H2g3a4Lc6HWkRraYDWh73qD3YpEbnBqrv3ED17eupvnU9pcevo/FNX6KFGsfP8zYnXv/619NXfdVX0fLyMt3//venv/3bv6287RVXXBFeTGRvuN9hgiuhEa6EOhwOh+M0wVRfTpVATC87zeD1zJROO4bPVE/N8MzlepoWI1Y/0eFuVE/chzM8g9dTlod0fD7p9VxmBVQVTjNmh+rJo3eiRjqiZjIkGidUH3SIxkOqDbqsfKbDIaU7J2g8HNC4s0Wjr3yZzgb84R/+IV166aX0xje+kQnoa17zGrr44ovp6quvplvd6lal99nY2ODrFbPUsS4SnIQ6HA6Hw3EakC0EzR6tVPSETvV6mtvbJSPtcNeNdl0qqhnCaTvc8bH6PtXX2cp5PYVkxuWiWub1BCmFxxPjeiarHMskvs9aOqZm0qNamlBt2BPSOR4S9XaIkiGlnS0mneloQOOdTUqHA0p2dqh//Q20OJ7QeRaT5hs2/8qv/Ao99alPpSc/+cn8Mcjoe97zHvqt3/otev7zn196H5y38847jw4rnIRG+Ha8w+FwOA6oPnPa7YzCKdcbFdX6OTV6KeR51kKovKqaqnJqm1EWqWRVT7mNqJ5CJDVIXkklRyqFViOM7bPoJSGciFVin2gDBJiongypMRxQLYHHc4cvCZ5PVj0HNN4+QemwT2lnm0noeDik0RYuRzTc6VLnhhN0mHNCNzc3c8eXlpb4zWIwGNAnPvEJesELXhCP1et1uuiii+iqq66iKmxvb9Md7nAHGo/HdO9735t+4Rd+ge5+97vTYYGTUIfD4XA49htmjD5vi5E9VqzMVMJZHiqfbbDbRaMYJB98oKp2cowS/KA211OXi2yQfCCZGiqPhSNRPUXhzG248+MQq56NUT+onl2qD7qsdlJvmygZMOFMoHoyCT3Ol6OdDiV4G45osLlD48GIhp0edY9v0UKgNqfPE7cnovPPPz93+LLLLqMXv/jFuWNf+cpXKEkSOvfcc3PH8fG//uu/lj78Xe5yF1ZJL7jgAjpx4gT90i/9Ej3wgQ+kf/7nf6bb3e52dBjgJDTCVVCHw+Fw7B06/ub3Z9huL/OETtZn1iYIrXhBw+KRxizV87meIISy6CTKJkim9XrGMbtRQqXDHdWaGhqfEc5IQkOGZzN2vYvHE+STVc9Rnxr9PlFUPYdE/Q5Rf4fS0ZDGW8eJMG6H6tndpvFgSEOonoMhjXZ6NNzuMgkdbnVoPExo2B3QzokuHeac0C984Qvs3VQUVdC94sILL+Q3BQjo3e52N3rTm95EL3vZy+gwwElohI/jHQ6Hw3HqvJ42JL6syci2GOUIp+lrzy0fhWO68W5zPWUDPguQ1+Ui6/XkMXsYtWuep2Z+rmikUuhwz26XeT1b3GiUUg3LRfB4cqRSl5VPVj27W5Fwwu+Zjd4HNNzp0Gi7EwlnAhLa6bPyCfI52BrQeJTQqDei3nafDvM4HgTUktAy3OIWt6BGo0HXXXdd7jg+ntXz2Wq16Ou//uvps5/9LB0WOAmNcALqcDgcjlPn9bQkM15dHLdbX2fJuN0uF2mlZkZCwxZ6IKBFrydyPfMb7jKCz1TPjITyhjt7QuXxQEK5xYiEeDYopVrSp/pAVM/6QJaLoHhi0ch6PVn13Akez81t9nwOg+qJY4MtuRz2hjTqjoSE7gxpPBpT0k+o2xnQmd6Y1G636T73uQ9deeWV9J3f+Z18DD5PfPyMZzxjpsfAOP/Tn/40PfKRj6TDAiehEa6EOhwOh2MKeOGnXMmc5XZF/6ddLrLX2/gkHbPbS9lsz3s9sb1es0HyoaUIpLVtguS1FlP9naJ6ZqHy3HgU/J7aetSEwlpLqVVLRPXsY6t9xIonlE8mn2GrPcWIPaieyZaQ0NFOl4bbGK/D62lVz74Qzm2onmNWPfE2HqV8mSZjGvUTGvQGZ8V2/KWXXkpPfOIT6b73vS/d737344imnZ2duC3/hCc8gW5729vS5Zdfzh+/9KUvpQc84AF05zvfmY4fP06vetWr6L/+67/oh3/4h+mwwEmow+FwOBwz9bbPMG4v63c3Cqcd28tovbrDXUPmc8fMmF28nlnovI7Z5WNpLrLHWPUMhBR97bbDXVRPVUzDwhEILNdnplQf9SRWCeSzj+WikSieve1suWjQp3G3I8onE87g+WQSCrUzYQWUVc/uiEbdISXDMQ07onqOejJ+T8cpK6BQAkejMXUGIzobGpMe97jH0fXXX08/93M/R9deey3d6173ove+971xWemaa67hjXnFTTfdxJFOuO3NbnYzVlL/5m/+hr72a7+WDgtqaZqe0fIfohGOHj1Kj3ztB6i1slZ5O3wTxvhWnNHfjdPbZ+xwOBxnQ31mNk6fjFGK2+0lC0dKWnNez+Dr1HG7brvH9iNDQmWrPe/1VH+n1mJa1ROXNkg+r3qGcTsUU0qoVRuz6qmRSqp6psjz3DlBBOIJ1RN5nqMhJVuS6ymqJ5aLhqx6MgntDlj5FNUThDOJhBPkE4QUqmcyGFMyBPlMaTgay2VKtJmM6Edu+nfeAN/NW3kqecT173srbaytzn6/nQ7d8uInH9jzPgxwJTTC2afD4XCc7Zj1RXZVkHxZ3FJZgLyqorrBzkQU096waKQ1nDpy1452qJ+tptlmD7fJguQz1VO32VG/Kaqn5nmGSCVdOMLjUUqtdET1dEy1UY8XjYhVz+D17O3QuIsx+zCqngl7PVX13Alj9uD1HIFwiuoJnyeIJhPOHVE/k8FI1M5EVc+URhi/JykLQoMxLomS8L7jzIST0Aj3hDocDsfZu1wkB3ajn7ogVHUs83dmqqeSUF0kshmeqnTGPviY4RlG7xi5gzS28oTTjtlFzcw8njpmx8hdMz6LXs/loHpyfSbIZlQ9h6HNqMMKJ1RPGyQPEjra2pRAeR2zj7BcBNUThBOb7/1AQgdCOPvweibR98kLR0NVPUlUz1RUzxHIJ2WXTEgXZWB7CheTzlY4CXU4HA7H2QWjWO6qesa4JPkgN25X4ml8o7HFyIzbiyQ0I5yhwYgzNoV8xuWi0GbUNqHySkB14UgrM6PXM2y4c+NRVD0zr6fELEFtTak5HlB9LKonCCfneva3mYSOuztZfeYWguShenYo6UiAvFU9ke2ZgHBuSbQSLxd1MXJPM69nP2EiCtVzNEgoTVIaJmMajlMCvxwq8UxTSuCKS1MaBXecvL8YJLRWb/DbPLd3TIeTUIfD4XCc8bAb6LP0therMmkGr2fscLfb7LrhHjvc85FKtsFo0uuZJ5yy4Z7leUavZ6MR6zNZ4Yy5nvLYonoSNcZDaoyGRBi7I0B+PJTtdrzPfe3B68mqJzyeoT5zAHUTY3YJkB9sG9WzM8gilYYgnGHMrqonxu2DhFXPZEw0SKB6ZoRzHAgnLkX5FPKJMbyQULxPiwH2S9Tnu71jKpyERizKT7nD4XA4Tjf5LPNz2uuKGZ+qdFqvpxBOm+spx+xSkaqgus3O9ZhMSjOvp5JM9XZKD3sWKJ/VZ2bq6HK8rzweguSX+Lmk1EwQqYT6TGy4d6W7HRvuGLfzctEJfp+XjBCttLNDo50d9nP2T0D9DJFKO8HrudVnUgnCOVKvZyeM2UE4B/B6igLKJBSj9uDxVNUzgQc0EE1WPQMJ1f1g/YsMcrooJNSV0P2Hk9AI94Q6HA7HWRUkX+Lh3O2YDZAvWzICKeTbmSB5HrmH5iKQVBBOVUDV6wm/ZrbhHtTMECRfN4RTcz0zdRTKqZBTPtZApidRPRlSfdgPkUo7VBsjSB6q544QTu5rR5D8TtxwH25t5+szR9pmJCN2Vj15uUi9nmHDHWN29XoGv+fYEM+RUTsTe0l58smX+OapCkoLhlOcE3o2wkloxML9uDscDodjDlTmdJbeeNITausyAc3wtI1G+a326lzPXKSSBskH0shez1xzkS4chSD5Vubr1OailVZDiGrYZm+UqZ7pmPM86xwkD9VTvJ5an5my13Mzt+E+6nRptC2qp3g9R7LhjjzP0ZgG2xKtBJIpUUqZ1xOKJ6udUDWhfrK6KWonyGVUPcOWe1oYt+v7gPo/F/ovMZPQOYilk9Bd4SQ0wpVQh8PhOJPH7VYdnbgul+EZAuQLGZ5Aftye72vP2oyC6hnG7ngfx2Kkkiqc5hgIqI7cQTxV9dSYJWR4NqMnVD7/kqnPbAwQqZTkVU8EyeuGOwfJi+rJtZmb27JcFHM9oXrKJaue3SGlIKHR62mWi1T1RLbnSCKV+iFaaaSEMyigQjjzHs/UZnMfor+8pzqs/mzEgZLQN7zhDfz2+c9/nj+++93vzk0Bj3jEI/jjXq9Hz3nOc+jtb3879ft9uvjii+nXf/3XY3vA/uKw/DNwOBwOx9xeT3O7qjxPYLKvPYtUwlH1cuYXjYRQCpkUwqnb6uz1DBmfqnpqpJIsDYVcTx6zq9ezkYtUAvEVgkrUAnGtpVRLE6oPtD5TN9yHonpizB5UT4zek20bJB9UzxNhw72LWk1VPTFmF7JZpXqizWgUxu2IUdIxO+d6BsKZWzIqeD3Hc47bdeFrIeARTWcWCb3d7W5Hr3jFK+hrvuZr+Af1t3/7t+nRj340/f3f/z0T0mc/+9n0nve8h97xjndwW8EznvEMuuSSS+gjH/nIQT5th8PhcBwArGI5y21383rmFo7C/5h8BrVTMzzLcj0nNtxzGZ4goY3Y6S5B8iEyKWyu43187hUTJA8FVO6bqZ7sDyXEK41F9RwNqD7qsupZ5yD5AW+3Y8Eoej2j6rmVr8/EmB15nqOEhtu9TPXcGUwsF8XN9n7ocseiEcgnheWioHpC7dRQeR2vj40CGsftQfUc73be7GWoM20sikbkJPTMIqGPetSjch+//OUvZ2X0ox/9KBPUt7zlLfT7v//79LCHPYyvf+tb30p3u9vd+PoHPOAB+/xsfBzvcDgchzlMvoqkVnk9833tJfFKOmYPpJOJaQySDwpnyPWUMXu2zQ7yKGqm+D8lIL6RbzPKbbgLOZUN+NAHT2Nq0Yi9nrV+R+ozkevZD6onZ3n2xesZ6zNPRK+n9LVLkHwSN9yR54kxu0QrIUReazNzkUrB64kged5kD9vsumiES1E+ZfTOJDR6O/c2brceXZu96s7KMxcL4wlNkoQVz52dHbrwwgvpE5/4BA2HQ7rooovibe5617vS7W9/e7rqqqsqSSjG9nizna+zwQmow+FwHMb6TKti5o6ZGKU4jjed8HapSK/PFM7ZvJ7s62SSWQ8kNItZyuKTRAlFgxFnfwYlNNfX3pBQea7PpCSonlmkErcZYbkIqqcGyW+DcPZo3O1SsiP+TxmzS1e7LBeBhPY41xM+Tx2vxzF72HDnMTvG7fB8Ikg+eDztchGIKP5SDgPx1O32vXg9reJZDP3nc2SuQ5XpIqDGxQKzU+J5bnu24sBJ6Kc//WkmnfB/rq+v0zvf+U762q/9WvrUpz5F7Xabjh07lrs9/KDXXntt5eNdfvnl9JKXvOQ0PHOHw+Fw7CsMQdwNOjLP3b04bjdKp41SqlXmesqlRiqp/1O9npFwhoglbLvH5aI4Ps8Ip6qeGLmLEipb79hml4UkEE8huI0UqueACF5PVj2HRKx6YuQ+ivWZ44LqiSD5kRmzS30mFosGPHLXvnZcZ1VP7XJnD+hgLNvsqM/UDfdANIeqemqbkQmSz223m832ecmnKNLmfIVjSkZbM7wYOS2ozTmOx+0di01C73KXuzDhPHHiBP3xH/8xPfGJT6S//uu/3vPjveAFL6BLL700p4Sef/75+/RsHQ6Hw3EQeZ5ym8nb5TbbzWNmo/eMhIIcFmOWND7Jej5ti5Eqo3HMHsbnOmqXpaGwSKSRSnWKy0Uyeq8VVM+w4c71mUOqJwnVRn2qD7HhntVnpr2doHpmXk+uz9zeEoUTkUp9LBf1AuFMwoZ7wiHyrHaCcOJyaJaLMHrnQHmonqJ8cpC8GbcXA+QT9XoaxVOvn/FU586zTSJQvVCtD/YFBMj7grR2hic8T2PSgpDnBcaBk1ConXe+8535/fvc5z70d3/3d/Ta176WHve4x9FgMKDjx4/n1NDrrruOzjvvvMrHW1pa4jeHw+FwLChMH/tU6mkIieZ1KiozPCtIKG4v75ssz/h+tvWucUnW68kKZ1gkUgUTBFRH6nHDnVXP/LFcpFLIAW2kI2omQ9lwZ6VzyBvuHCQP8okYpUGP0l5HOtxRn7mJY31ZLtL6zKB6oj6T8zxBOE19Jo/ZseEeVU8horzNjnF78HnqhvvIKJ2qeqrCqR5Q3Wznd3c/zTOO2wVcLWrPIR+r0XhBxvFMQOcioT6OX3gSWsR4PGZPJwhpq9WiK6+8kh7zmMfwdVdffTVdc801PL53OBwOx5nt9Szertjbbm+XH7dnI3eQmIlQeRskH8bsdrlIfZ+6zS7b69nWe1Q9w31ikLxpLhIfKGUkNE2pMe5H1RORSohXQpYnB8mr6jnMvJ4Jez21PnM7qJ5Sn8kZnthwD5vs6vHUGs1cpBLXZ47Z38leT1RlBq9nscVIPZ22xYjMxvuu581cWvKpMUtxGSwc02UkHOeFr8J1rF6ni0FC01qd3+a5vWOBSShG58gExbLR1tYWb8J/8IMfpPe9730cyfSUpzyFR+vnnHMObWxs0DOf+UwmoPu/GQ/4drzD4XAcyLh9l9tZhbM4bi/WZtoQeRzV+CTdaNdN98nlokauuUhJaLbhLiomj9mD91MXjnjcHnI9RfUEQcXnIWqMR9QYDiRSaaCqp9ZnjuKYHSQUHe4pQuM3t1j1xHIRq504th3qM3shUimqnkI2rerJ4/aoehINw7gdqucwjNn1Usbs5d3t87QYKbkMpyieGx23x7B/o3LqeQNZjykEGsuk9gi+24KQOVdCzywS+uUvf5me8IQn0Je+9CUmnRdccAET0G/5lm/h61/96ldTvV5nJdSG1Z8aOAF1OByOfUHB11d5s5LQ+OleT1kkAuySkYbKK8m0Hk8lobZSU/2dMmaXbM7YZmQyPLORemHDPcQzKeHU5SJeOEKzI42pAbVzOApeT1ufCcLZ4eWiLEhevJ4jdLeP8kHysuGOXE8EyYOEJpOqJwfMi8dzqF7PEKtkcz2ViGqGp6qbMmYvbLvPdprzOawFr6ddMtJjyD+15FSJphDPkMOK2zWCet2s03hRtsyzXtjZb+9YXBKKHNBpWF5epte//vX8durhSqjD4XCczt720iD58EFUygoRS+IFzaufkuEpJBTqow2Vxza6LiCp7zOrz8yai3T0zmpmIJyrccyuJFSakGQxKUQqsdcT5IqongypPuhJixEilbDhPpD6TAmS10glIaFYOBqCePYHNESkEm+4I1KpKySUx+wDHr2DeLKns29yPUE8QUKD31Obi5DrCYVTI5XU86m+TlZAC4onzbhkFF8UzDBuZzXT+D45caCgfgox1XMWxvE4d03EIdWo0WpQsihp9d4df+Z7Qg8OC/JD7nA4HGcg+Szzc9rrYkh5LsNTDpTleuqxekmup63PVMLJx+JyEUhkVpeZD5IPG+4x17PgCVXVs5ZSu476zDE1hoF4jrQ+U1VP8Xoy+QwkdNyH1xPLRfB6JmHDfcDLRdHruTPIeT1lzK71mTJml/rMoHqmmdqJSx2xa5SSbrrrghHtYdyuLwpKFc9dxu3W68nnyB4L541JKM5PEyS0To12nWo4dy0ooYvx99k9ofsPJ6ERroQ6HA7HqfZ6lime1uuZRSoVO9xNc1HFhrt6OVnhDISzNTFmlyUkrcWUSCVpLsJxKJ/aZpSN2bMNdxDPBo2pngyo3gv1mUw8B6J6diU0nv2d8Hp2dyiB6jkcSn0mE86+tBlxrmdQPbU+U/vaecNdvZ5G9dT6zLS8PlOXjSwJzXk95xi3l3k9i+P2LF4pWySy76vqGQmnOY/cTMVqZz2qn/VWg+pIEWg3qIbv/1KDxs7lzlg4CY1wAupwOBzToGRwN5R5PcuO2cfL+QiD4qnEJaqfJteT1c0QNs8j99yGu8QnZW1G2ei9GKmU1Wc2mJSCcHJfO6ueIY4Jj10bs+oJwokxe6zPxIZ7R3ydKY/Zg+q5sxXrM6F2YsyOcbsQTg2ST3i5iHM9c6qneD116Qiq5xCjeI1Uynk9hWTiuPV1assRmXH7LOSz+KJBQ+PtGL5M4VRyinh2PW9xyYjPVRi5hxcKQjh15A7VU0bvTEKbNWouN4WMLjUpXRAl1BeT9h9OQiNcCXU4HI6IHGmccdxecruJFiO7cFTRYlSW61kvkFAQRlZBoV6abXZVPXX5KKvPlPeVcIJosteTbyeEEz5Pq3q2sGBUS8NyUZdq44SD5Lm3HfWZXYlX4nF7v0fjHoLkN2WbfUvH7HnVcxw23Ac7IJzweo5ia1Gsz0SHOxaPMGoHGTVjdhBLkNHY215cMiqEyc/T254Lkq/I87Rd7vz9V5XaeENVDVXVky0TsEfAUtkUhRPEs0z1bLSbQkJXW1THOVluLU7xkJPQfYeT0AgnoA6HwzFXfWZFmHzR/2m326P/U4lmOKYk1Pa1K/lsTPF62lxPHNM2o1yQPFTQep2WQ5A8Ru98PxOpxEHyuC+hPnMkQfKIUgpB8uL1HFLa2STiSKWgeg6x4Q6vJ1RPDZLHclFHcj17pj6Tx+xanymqpxJOzfXkAHkmnrJYZFuMdMSuofLa0b6XcXvpeTMvOmyLkZLL3PvhukZh690SU6ieccweFo1ANNXrmZHPQDyXm/xWgyq9tsSEtbW6tDgd7E5C9x1OQh0Oh8NRWYs5T5B82Qg+v3CUeTvxkW6rW0VUvYI6Qp+oz8w1F2mupywX4ToQS4zndcy+qmP2EC5fL/V6ptQC6SQEyQ/E48n1mTv8cQrVEyN33XBn1RNB8lKfOdzcoVF/SAlyPUFCOVIJQfIgoTJyL9Zn8oY71E2OVAqqJ4Lkg+ppCaeqntbzKYQzr3rSHsbtxQUjMuHxSiqzRaO871NJKEcqqUcX50JVz1YjklAduYNwRtUT5BPnBqonbrPcpuZKm+qtJrXXV6jeblJrdYUfYxGQ1mpzLiYtxvNeZDgJjfBxvMPhOIuQWxqaKVip1BNqx+3KFYrjdkBjlIo97UpmeEmF8yF1m914PWMsEkLjsw33YqTSsiWcYcMdQfK4HzI81Se6HEhoI02omY5kzM5ezwHVhv3y+szg9Uy2NEi+R4NNjVTq0JhVT4zZe7lIJfF6huUiVT1xHBvuWC7Cx7pcZMbsTDhNlBIfM8RznhajcLrzftwp4/bSIHlDQvE9VzLKqie+l0HpjIQT75txe2NJ3melE4o1SCh8n7BGrC/zZXN1mVqry0I+j6xSvdWi5toajRdlHu9K6L7DSajD4XCcTTCK5dT6zMJmu7nrhGJqiYsduxfbjPQyi+YRP6aqneL1FEIpkUq2uahe2mbUxjZ7K4tUwtgdj5V5PUNGKKueIF0ptcaDUJ8J0gnVMwmqJ8bsXRpj5A6v59YJGg+6NO52aQTyCcLJkUpDSrpQPcXrOdzuc5tR0h8Fr2fYcNcxO8hnoqonFovG0t0eiKdEKoUxuxm3xxaj/Ry3m6B4jr+yS0UF3yeH/Rv1U8fsmuvJBJNVz8zXmVM9ebmozgRUx/CqekLxbK7IyL0NwtluUnN1hVpry1Rrtal5ZINq7TbV1zaombbobAmrf/3rX0+vetWr6Nprr6V73vOe9Ku/+qt0v/vdr/L273jHO+hFL3oRff7zn6ev+ZqvoVe+8pX0yEc+kg4LnIRGuArqcDjOcMzh9Zy4XRzZKtHMyGhU0AqE00Yp2bG7jm5Z9Qy3EYUz23C3o3ddKMqpnqG5CIooutvV1ynjeNxOVFY9Vh+PqJmY+sxRUfUE4ZQxuwbJjzY3xevZNfWZ0euJSKV+rM+cCJIvUz01Uom9nqa3naq72/cybi+Sz2J2Jx8zZNN6PfU2dsyuG+58OwTKo2WKl4wyr6eO1ln1DIS0tRJUz+D1ZI/n2jIrpKx68vstam+sUb3dosbaOtVXjwj5PHIzJqO1lQ2qJbWzQgn9wz/8Q64qf+Mb30j3v//96TWveQ03RV599dV0q1vdauL2f/M3f0Pf+73fS5dffjl9+7d/O1eff+d3fid98pOfpHvc4x50GFBL9Sf7DMXm5iZXgj7ytR+g1spa5e3w2pJDfM/o78b+oMwP5nA4Fg/FtiHao9ez6OvkRws3y22zM/mczPXUpSLpcC+QUCWNrUmvp5JPHGNyyWN2rc8MG+42SJ7VUVmSQXd7jVJqIM8TI3fUaPLIfUSEDXdEKvW7lJog+XTQ5SD5EYLkVfXsDcJyUdhwV9VT6zMTU5/JqieWi0KuJ9RPs1zEJDSM1rXNKEc8Dekko4TOdK7LNtz1HJnj0sU+GbNUL3a4qxKqlglLOM243Xo9sVwEMgrVk9XO1XZe9VSvZ6tJrbVVavL7bWocOcqEs75+lJVParWJVo8SNds0XlqnE70x3eoOX00nTpygjY0NOigecf1/foY2jhyZ/X5bW3TLO33tzM/7/ve/P33DN3wD/dqv/Rp/jJ+j888/n575zGfS85///InbP+5xj6OdnR1697vfHY894AEPoHvd615MZA8DXAmNcE+ow+E4i4LkdyGpxQxPOZYPkBfFdIrX00QqsQdTm4sa1uuZNReJchn8n8j6DAtHGLe3Cx3uUDqVmMYNd/aREtXHQ2oMB7zhzvWZowGTTq7PTLL6TPZ6YrMdqifXZ0L1HIjqybme3bzqyW1GQxmrB78nj9dV9RxlqucggdczI5ya26kqJ0buVFA8ddt9Vj1ER+r5paISQloYqet9+VxpvWYYs6sKygp2qM3kMXvD5Hq2jdczNBtZ1bO10gob7lA6sVy0TM3wfntjnVXP+uo6NdaOCPncOIdqrSWilXWi5SOUNto05ssWDWpN2sGi2CKAt61OjRI6GAzoE5/4BL3gBS+Ix+r1Ol100UV01VVXld4Hx6GcWkA5fde73kWHBU5CI5yAOhyOwwsdh/P7U2+Y34K295fLaq9nkYRqgLx4PCfrM5WESnMRrsfmtPa1yza7+jU1SB5qppDLjHCuwusZyCkTTrvhznFNRPU0pfqoS/XBkNuLdMOd6zNBOPsYs6vquckklOsz0WKkQfIxUklzPUX15OYiqJ12wz1suXOuZ/R6Sne7+jt1xD4qZHgqEY3h8nPWZ06M2wvpA+r5LKqetrloos2Il8LkPIJg5iOV8HEgnPV8kHxzGYQUXk9stTdY8RTVs8HLRY1Wk5prq9Q6spapne021VY3RPVstonWjlEK1bO1SuM2FpHq1KcmJWmNOsMxfaU7osMMKKkWS0tL/Gbxla98hZIkoXPPPTd3HB//67/+K5UBvtGy2+P4YYGTUIfD4Tis0DzHXcbtWW7n5O2K4fGW4GS+zkKYvJKdEsK5m9czUz2zXE9blRk33Ot1XjSSbXZZNookFIopj91Tbi9CfSarnlgu4vrMnqiesa+9G0hoVp+Z9PuUQPXc7lCq9Zkgof2R1Gdiwz20GfGYPUQqieqZiuppguQ1UklH7qp+2vpM6/GkOcln/L5npz5TPUtilHJktNjXzrmeWSpBpnoWNtzDFru2GUXVU5eL4PVEpJJRPZurS9RaCyP3jSNB9TzCqie1lqixcQ5Re4loaY3S5XVWO8dLG3zZT+vUH9f5e7czGPP3cqs/oi9tDegwe0IxUre47LLL6MUvfvF+P7tDCSehET6OdzgcZ5bXs+x2Zb7OYmWm9XWq35NzPbXv25BRzfDUnnZcx+N229celE6rejK5BHmpT3a4y21lNJ/bcK+l1K6NecOdG4y4PnPAI/dM9ezTGLmeweuJIHlsvI96fRptBa8nVM+eVT3H4vXsj7IMT67PNKpnf0TjMXhtQgm8niCcYZtdl4yUcNrRuyqggFZqAjOrnkXyWYhVqszwNPaJZlmHu2Z5huB4HLT1mRKpBKIpW+2S64ljIJxG9VwNXs8ja9x2hA13KJ+semK5qL1EtdUjVF+Dx7NFKbyeGLe3Vylpr7Ha2QXxxOkbpdTF+UnGdLw3osFoTCf6I7rueJcOMwn9whe+kPOEFlVQ4Ba3uAU1Gg267rrryAIfn3feeVQGHJ/n9osIJ6ERTkAdDsfhD5LX25aN1u2x3MJR+B+TT/ydDRvuSmLsuD0jMbKEZIPk1evZDmqmLhXxsah6ypi9bginkFBRT9vFDXciatdTbjKCysktRmbDnQZdSkE+RyMZt0PxxIY7ez0lSB6qJ9dnojYTxxAkX1Q9Y32mjt5TIZ65+kxZLkrMmD0STzNqV+KpS0VKPHdbMrIq5yxeT41KKiOhtsM9thnhnAbyyV5P02Yk43UhnlmuJ5aKsHCkG+5CPlvrq4FwZhvuTXg9QTzXQDg32ONZP3KM1U9aWo+qZ9Jep3G9Sf1xjXqjGque2yD+QfXcHCRMPm/sDqmfjOlEZ0hfvqFzqEkoCOhui0ntdpvuc5/70JVXXskb7rqYhI+f8YxnlN7nwgsv5Ouf9axnxWPvf//7+fhhgZPQCFdCHQ7H4fV6VpFUu1Qklyaw3CidZfFKerw4Zq+bvE4es0OpxPu6XGQWjlTNxEgdt8UxbLbzwlHocBd1VBZi1BPa4PrMhGo0pno/BMlD9ewH1RMNRur11A13NBj1xes5gOo5xJhdN9yHoT5TGox4wx3kpyNeTx6zB9UT5DSF6ollo0A6xeuZEU7pcU95xB6D5AtLRvP8RbHxSXa7vSzP0y4V5WKWtK+dR/BKPkN9Jo6D1MdIJZDQQn0mxyiJ6qmRSrzhDuIJ1RNjdpyzDQ2SX6XG+jrVmi1qsOopXs+aqp7LG8HruUJJa1U8niOiYQLVc0zdYcJE8yYQztGYNvsJE9H+KKEbdgbUH47pRHdIX7lxh86GxqRLL72UnvjEJ9J973tfzgZFRBO235/85Cfz9U94whPotre9LUcyAT/5kz9J3/RN30S//Mu/TN/2bd9Gb3/72+njH/84/cZv/AYdFjgJdTgcjkVCro99fq9n0deZHcv62m2HuyWhEqkkI3Ulm3qsKsNTFc84eg+5ntLNni0Xaa7npOpJUfUEqWrRmBq1cRizd6iG+kxcIkgeqmdny3g9OzTu9SjZQq4nlotQnzkQryeP3rU+cxSaiyRAntuMBuPQ465ez4SSkYzaoXymgXjyhnvweIJU8pLRlPpMu+E+5RTnEgyKx6yvM+twz2d4shIavZ5ZViuTUJzT8OKAHwPe2rBsZFuM8vWZ8HoKCW0st5h05paL4oY7VM8NvhTVU6KUMHqH6pkurXGsUlpv0oiXjJrUGxP1EFCQiOqJ7yvIJhPOZEw3dkT13OwOmXSCfN7IJDShDtTRQz6OnxWPe9zj6Prrr6ef+7mf4+UiRC29973vjctH11xzDW/MKx74wAdyNugLX/hC+pmf+RkOq8dm/GHJCAU8JzTAc0Jnh+eEOhynBmW1mLPerox8ZtvsqogWMjzDSN0eg4Kpo1v1emqHO2+z58bsIcMzLg3JmF1UT1FJMXJvhOuy29VyMUuNdExNGlGdI5Xg9RxImDwHyY+4tx1jdwmSP0E0HNJoe1P6222Q/HaHfZ7wew53erlIJTtmz4LkJdcTJHSISKVAOpHryeHyJfWZcdxuvJ52uWg38kkl9ZnRKmEUUTtep4og+Th6N/WZTa3P1EglXMcLRbpcJGN4HrNrkPxqeB/+TqifK0uxPnPpaAiSX13jMHmJVEKQvHg98QaPp6qeSXOZRnhLiTpDsS9A9dwZoiXKqp4jOtGD6jmmG7f71MOx7pDfUGW63R2yEj0cJNTf3KRPvuKSA88J/fIXr5nr8+N+t7rt7Q/seR8GuBLqcDgcC57nOeu43S4YybH8mJ3UJ6hVmSHD0/a3cy94IJ7qAZUxu5BQVj4D+dTROxRO3H4l3E6D5PH407yerXRIdVRmjhCptJOvz+xrfWbI9WTVs0+j7S1WPREkL4Szb4Lk4fWU+kwJkpf6zGKuJ38MryfIp3o9jb9TazN13K4B80AMlJ8zSN6eZ5tEYBXPou+TF4msNSKc52ZRCcW5wAsKk+E5k+qJ5aLldgiVx8KRBsmvxO72xpENjlTiJiP2erapth5UTyidUD7rTRo2V/iyh+WinqQEbMHukKRCOFFpOspIKBTP452BHIPqifF8f0TdcI4G/fCCASN7sNlFgHfHHzwJ/au/+it66EMfWnrdm970Jnr605++H8/L4XA4zkzYystZNtvDB7UpsUplJDS37W622a3C2bCEs8Trqcc1ZsluuC9hm1033IPquaqqp2Z9Wq8nk1IS1XM8pBoIJzcY9amGYPnBDvs6oXpC4WTSyV7PERNPjN15mz2M2Qeb2HDvy3JRp0+pqp59UT2x2Y4NdxBP+Dy10YgjlRCxFMimVmna+kzb3V42bp93sz1+XJHnafNYdYu9tK9djwWPbqOoeppcTxBPfh8vENjfWaMGguSXESQPEhpUz7hc1OQszwbXZ65RYz0EybPXc5loeZ39noRIpRVEKrVpVG/TsNHm793OEMRzTJ1hIiP3JKWbekH17EH1lPdv3B5Qb5TQVndEW1CsoZIG1RN5q1A+x7BHoHFqLAUAg+5ikFD4QefzhJ5ZJPSHf/iH6Qd+4AfoIQ95yMGR0Ic//OH0Ez/xE/QLv/AL1Gq1YsgqjLMf/vCHnYQ6HA5HGWzw+x5uV5bhKR7PWnmHu/F1RoKjG9JB4cSikXo9lXCq6imjc4lKapkgeSWiyPBkryero0I6ees9Ek6T60kpNccDqieJiVSC6in1mdTvUhL62nnDHU1GIJ3b26GvXVVP5Hp2o9eTCSYvF4Fw2g13UT2zIHmM2uFJHMcxu7YZ6Zhdcz1V4VQFlAnnHOP2Mq9nvaQ+0yqbtsddFVD1emqVJjdB2SB5jlTSDM9M9QThjCQ0hMo3V1pMUpvLIVIJy0WozGy3mIBi212WizY4Ugnb7QiVh9eTl4xY9VwNm+0NGtSXaVxr8Ji90xuz2rnVF68nVE+QTvF6isKpXk9VPXHZ641Y+bSqJ9sjhoGEDsd8ThHgPur2aCFwliuh119/PXPAW97ylvT4xz+eCek973nP06+EYkMLMQAwxH7uc5+jpzzlKXSXu9yFPvWpT9HhhW/HOxyOgxu3V3k97Ug9U1GzJaTYAW4ilZTAaq7nbl5PVi7D0lGMWdKPg7Kpy0XtsFwkG+6mPjMGyeOS+Fh9PKLGqC+RSsOO+DyZdIYgeRDPGCQfVM/NLUrg9expfSYIp3zMquc26jOTCa+nBsmr6gkSw6pn6G8vy/W0LUa69Q6ke2gxqvJ6WtVTFc6i6hn72otB8rY+U1VPG6nEY3Zst8uGu+Z65oPk4fVczm+4I9fz6Do1eMy+ygtGtWabGhs3I2ovU215nWhVAuSlPrNNw1qLBvUWjcYUguRHtDNIeOSuXk/4OrdY9Qwb7lA9oYz2oHqOKEnG1IXqiRcMaKEKqifUT5w/LgAYovY05SgtHBsnQxqhfMBx4PizP/szuummm+gd73gH879f+ZVfobve9a70/d///fR93/d99FVf9VWnZzFpe3ubfuRHfoT++I//mOXyl73sZfTc5z53JkP94i4mha1G56G7wheTHI75azFPdtxuMzyLofKqiMaYnjBmV08n7gcSymS0UVguKgTJT264Z4Rz2QTJi+qZ1WdyuDzUOgTJJ30moPB26oY7NxgNEanU4zF7fsMdvk6onklO9cy8niZIXiOVuvIxRyqp6gkVbYRxupBPHa1rhJJuuOeC5PHNVdVTx++naNyui0QTJNSM2fn90AqFTWiM0dXrCcKZtRllkUo51XO1zYS1sdKW5aJm2HAPQfKserZAOI+J6rmyHlVPQpB8a4mD5NOldUqoTv0agrLqonryyD2NSicI6GYYs98A1XMoqufxoHoi43MwSqjfx1vB64kkArxQCGq1EM4RJxQgH2sMa0YKNRTJBlv05Xf91IEvJl173XVzLyadd+65Z+xi0n//93/TH/zBH9Bv/dZv0b//+7/TCI0Dp2Mx6d/+7d84i+p2t7sd/c///A9dffXV1Ol0aG2tmuQtPpx9OhyOPcK0Cs2yYKSXNlYpPEw2bi/xehY73OsUMiAL43Yds3NXOxNRMmP2rAIzbrizmhlyPZuTY/ZVkNDQYBQJpy4mMcElJp31YS/zekIBherZ2+INd10uAgnlFiPecN/m7Xa0GRVVT5DOwc6AR7LR66mRStbrGZZXQGY4UglvuUil/IKRHbdnJHQ28pnZIArks0Th1ONKMG1zkTYaqddTx+5ZnmehPrM+GSSPY60YJN+iJldp6nIRNtwxZgcJRX0mVE/UZ66L6okg+Y1zgtcT9ZnYcEd95jqNGy0aUpO720Hmt/vVqid7PcOiETbcccmqZ3fIqidG7uz1xIsLEE1zrqB64i2F73M45EuQUJBOJZ/8omCMFxaL0R3PPzNzUIUzOXtoOBwyD/zYxz5Gn//85yc67E8ZCX3FK17BvadPe9rT6FWvehV99rOfpR/8wR+kCy64gH73d3/3UCX15+HjeIfDMR906Wc38jntdrnmIpPhmd1PPYPZQoodu8tovThmr/Z6yta6kEksHIH8SMySJZyBhJptdh69B2WU71NPRfUcdaneH0qYPLyeSVA9ESQ/6IUxO1TPTfZ68jb7lng9QTxHXRBOU5+506ckEEzxekp9Jud6jrQ+E+oZ/IJjiVQC4Qxjdh2rc55nRX3mXsbtxSD5aI0o8XUC0SZRNWY3qjVbJoLKyckFwd+pKmdUPUFCESQf4pVavNWOViP0tQfCeWRFlot44WiNasjz3DhGdYzZC/WZaRNezxUat6F61qiXIiirRt3hmDrIXU1Srs9k1dNGKnVkzI7lohPIZI2q55iVzkFYKsLIXf2dUDijWg3VEw1XPHLHeR0I8QThxM9PIJ84hvfHiOxaAEg16+w8YZ7bHhbAkolR/J/8yZ/wOb7kkkvo3e9+Nz3sYQ87PST0ta99LYehPuIRj+CPEYr6t3/7txyUio2pfr+/pyficDgchy9Mfgr53OV21us5oXqWdLhHf6BpMpLloszfmXW4y+3U6ykj95D1afI6ua8911xUp9WWGbOHJqRlRCqBeNZSaiJIHl7PPuozsyB5jNrR3Q5fp1U9QT4xWsWYHQSUvZ6bYcNdVU+M2VGfqZFKccMdyljYagcBxfW84Z7VZyrhtH3tGrWkSqdtMQJmpQZK/qvG7WVB8s1aOQmtWxIayD2rnRwkL2N3JqEcpYTlonybUWu1JR8vtfj9mo1UWl2iFhaNWPU8QvWlNtVX1njBiHjDPaieS2uxPpMD5Rtt6qc16qG7fUy0DcUyBMrzohFUzzBuh+J5UyCaN+z0efS+0xvxG14M9MOlqJ6icOplVD15zB6IZzIMI/eUVc9IPJl84n1RQvn4aEG24+eUqs40Cnrb296WbrzxRl5OQivTox71KFpaWjqpx5ybhH7605+mW9ziFrlj2JKHKvrt3/7tdHhxpv24OByOg/BC54LHjcJZPGaXkHI+wjielYNluZ5TvZ4xUklG75rrmR+z54Pk1eupamc9jNvbiFRi8jmmGlTPYVe2263qCeKJJiMmnMfZ65mAeHY7onDymB0b7lA94e0chg33MRPPUq8nxuwYvfdDkHwgoLxcFLbYMW7XWKWycTuuo8J2+yxB8lTh9Ywb7uaFQ8zwNB+rwqnE06qejQnVU8fsIKMSJB873E19JkcqYclIcz2D6tneWGNS2lxZoeaRNd5wl0ilJR69S31mm9IVUT3HrWVKsOWe1qkL4onTx0HyqnqCcCLf00Qq7SBSKWy4BxK62UG0UkIDnLeC6ske3bBclKjqCTsGPpnxeuronZVOeIb5HIJ0js1lOIMLoihKccF8tz+T8OIXv5ge+9jH0rFjx/btMecmoUUCaoEO08MLH8c7HI69eT2rxu3ZWD0jLvb9jNBk5NMuGvHiSmGbvRarMoU0tlilNF7PQDjj6F0jlcIxJZy84W6Wi5SsquqJ+swmQfUcMvm0QfLwenKLkW64I1LJeD2ZcBZUTzQYgYBC5Rx0BvlcT10ugmcQ43aMbzG6DZFK8HqO7Jhd45WCyhlVT7NbOiv5DKc5HySv595cJx3upqfdKKPq9WRfp+1w5+WirLtd/J2S6RmXi1j11FxPeV+9nlyfiZF7o8Fb7bJcBNUTQfJNah5R1fMILxdluZ4SqZQuYbO9KdFKjRb1xzXqjoTAQ+3kQHlEKtn6TPZ6Ikhe3j8eSGiHVU94PVMaGNVTN9xhjwAZ5Tis4PXkMXvO6ymqp4zeZfzOfYVjCcPKkU+M4tUyEd4/aMhzmZ0nnGmFlE996lP3/TG9MSnizPphcTgce0BOsdwb+VSimX8cmw+ZdbgXSagSTiGfulykMUtZkHyszzReTxmf15n8qNdTqjKFcK5i9F4Ikuf6zHDJkUo0phbXZ46pNuxSHYQzyddncqQSKjQD4Ux2toSAYrkIhJPrM7tR9dT6TKieUDaz+kyreo6FfDLxNJFK7PXMcj2L9Zma4xnD5OfYbq/yepYuGVVkeOoYPhJOGy4fGow0UinXZtSajFRCk5FuuyNaiSs2jdeTVU/2eq5Scx31mVA9seG+TLWVI1TDhnujRenKBo0bbRqjOrO1wl7PzqhGWDrvYIQ+lCB5UT2D1zO0GX1lq0+9IWKWJNdT6zMHQd1kKwRbIkKup0Yq8aKRej1lzC5ezmzcHsfrIJ+BeDIJtSRT2KdRQMPlgvx9PtuV0FMBJ6EOh8NRUCmn37DE61moW5y2cKTKKrbNxQNqiedkrqcqmTlfp8n1lDE6ybGwcLRcGLOrEhrrM1kxlcrNei2lVppQA6pnMuQxOzyftT68nlgu6lOK5aJEl4t2aNzv88hd6jMxZheVUyOVmIRCNQtB8kxCg9eTMzy1PhOkFFE9SRapJF7PrLlIx+3jgq9TyaiST5pR8ZxWn6nXqQKqGZ46jrcxS7bDnc9P8HrG+swQJG8jlZh48scYq0vkUqZ6IlIp1GdC6Ww3OdcT8Uo19npuUG0pi1RCrmdt/RjnekL15DzPepNGrVWpz0yIuoOUvZ4Yrw9ipJKonjHXk+szZczO4fLDhEPk4fWMkUohdzUGyWuuZyLnj+OVmHiK6inLRfI+k04sHLHqKQpn9HrmyCfFRaRFxmI/u8MHJ6ERPo53OM7OIPlZgpXKPaHTvJ5MXIKRMFs4ysa1uVzPRj0/eo/xSflcT1RlapA8b6mbSKWc6mmC5BEur/FKuNQOd67PTHtUH4vqCa8nh8lD9RyjPhNVmR3ZcN8+Lqon12dqkDxUTyWckuOJFqMYJA+vJ4iLqp499LeH0XvweoIYieqZNRbp2L1U9QyklOasz5w4R+ZnQBXOqvrMIglV1ZOXwnRpDGQeGa5hmcjmesoykUQqRaVzCctEsnzE9ZkYravqyfWZq1H11PpMBMnX2itEK2tUWw0b7iFIPoHq2VymJK2F+syUOvB6mvrMnqqeUDYxeucgeVE9kes5CvWZUD9BMuH35GQCHreH5aKQ65kMoVpLjBKP2kEsNdeTl4uEaEL9jGSTI7Py43Z58bA4ns/d4Ero/sNJqMPhOHswY5B8nqRm41r5uLC4MjFuz3s8o6dQx7Ta+13m9YwZn5LdWVwu0oUjIZzyWCsgpvVsw13rM/OqpxBSqc8cUiNJeMxe5+Ui5HruUA1B8oM+RyrZNiOM2kebm2HMrstFIKFQPaXBKKqeO8PyIHl4PXXDHUraOK96ao+77XCPeZ6F7vZZYpXKUgms11MXiqwSaslosa89jtmt6olz0sgilUT9zLbZddyONiOp0oTqqfWZWC7K12ei1ajNQfItJp51bjM6ktVnrkubEUcqIc+z1qRhU+ozoXp2evi+jmkTwfDJmD2fiFTiDfcOSGjCy0W64X48hMv3BiPqWtWTvZ5CRHXRSEgoVE+NVMqC5Itez2zBaHLhSGDH7c7SznY4CY3wfwwOxxkL3Ww2pHKe2xWJph6zCyvW8xkjlEpyPZWExjG7iVmyXk8lnBqdxOP1MIKXDncJmEeHuy4j5Qhn6HAHKa2lCTXh7UyzIHlWPpHnGbye495OFiTPG+7blPR62XIRSOgOvJ6IVML7Up8J4pn3eoYg+eAf5EuQTBwPKqduuGuwfJXquZdxe5F85uozw3VCQvNLRvUywmlUT6nPJGow6Yf6mYXKF1VP7XDnjfcl1GW2xP+5tkwNVT3XVzhmSTfcEanUWN/INtyXJEieVc9Gk8bLG5Q22zSqt2lYbwfVc0yDMZqMoHIiXmlMNxqv5/EuvJ75+kwQUZyLTk/UT5DNzOspqieP33m5KOR5Rq/nIHg9dblIIpWKuZ5yGcbrRa/ngiwZ7QVn+2LSqYCT0AgfxzscZxLKmonm9YRO+jr5vYlcT92CLsv1jF7B8FhQNi0JZV+nIZzS3R78n4F48uY712dmMUsyXlfVUwPng9eTSW1KDaidw1GMVKpBAcW4HdvuUD0xZlfVsytez+GWZH1ykHynT8lAtt2zIHnr9dQgeYzag9cTxFKD5BGvxKqnyfVUP2d4vzh6j9vt4fqZzvUUr6e+oNDxOhWIJ4gmoMSTCadRQlX1hILJLyx0uQjnLITK65idVU6M3nnMjlzPBm+4c3c7CCfG7ByphDYjqJ5Nahw5SvX2kgTJg3w2W7E+E17PhFXPOg3qS5TUmrKpju72JKUTSBrA8tAgWy7Chnt3JEHyUDtZCd0R1bM/SDjPE0STA+VxjqzXc6i5nlCthVRa1VO9nmki1+mWe9xwjwRUPZ46buePZjybJWd3QWqi+ed1zts7psNJaIQTUIfjbPJ6TiOpxQxPOVbe114MlY8b7qbDXckm3loFr6dsqctInReLzJidN9xNfaZ2uEPp1A335UBWkenZgi9xPKLmsB9UT3g9e+z1jKrnzgnj9RTVc7SF+kxZJpJIJfF3YvQ+hj+QVc9suYjrM43qCa8nvw8fISKVMNLVMfu4ECQfqjRZUSsEyefilXaBKNAZ6YznrRi5VEFGteVIfZ1x6x3fV81mtapnGLkLyZTFIxmzW68n2oykxUj9ner1xHKRqJ4SJN84ssFj9oZRPQl5no3g9Wy2uT5zUEN9Zo12mHiOeLt906ie7OsMXk/N9ewOEtpB9FKoz+x2Rxx3paonZ68G9VPG75LrOR4OJ72evNmeqZ5apZkfs2cj+H0bt9eE9DMSrQU4WHht5/7DSWiEK6EOx9my2Z7zhBb8n3kSW/B3FkiohsbnWoxMkLyqmqxQTvF6Qs2MW++BXIJwcltRK9twF4Uzy/UEgQL5hNezkfSpPhwQJUOq83KR1md2I+HkIHlWPTuUDPo04uUiVT17QfUMG+6dQRyrR68nfxzGter1xLLRaJwbsxfbjGJ9plU49eM56zOnjtsNKc1tsxtV25JQjOX5hQKOhe+tqpzq8YSqqfWZonqGDXfucNdIpdBmxBvuonrqclFzdYVaGxIkD9WTg+Sx4X7kGFGjTYRA+RaC5KU+E6pnv8ZBWdQbpTxqB+E8Dq9nUD1RpTmw9Zk9qJ7i9TwRvJ6DwYj6Qe1UwjkaSa6n1GfKuD0JQfLaYoRtdng5oXaKrxOXZbmeQemMeZ77sNnO/yZ10pCbSdAiwBeT9h9OQh0Ox+GE9nTvNm6PtyvvbbdEk2+R8w9m5FOIZT7r0y4XlXW4Z2P2egyVl633LK9TR+o2SL4ZO9yzTfgmlo+4glPqM1u1lFXP+qCXeT2HQfXsbjEZjWN2kNAtUT2H2zuUhEgl8XqG+kwsHLHqORCSCfVM43lU9cTHYdQOEsMjXLNUFL2eGiBviKcGyxdH7vOQz+K4Xa+z4/XctrvGXlV1uNfzXk+NVFISqqN1EEyOVIJSvZJtuDdXS1RPrc88eiSqnqjPjEHySytES6uc50n1piwZserZoD6629OUtvt51XNgI5V6Q36fSSiC5IcJxylh/I7z0tMgeat6QunUXE+NVFKFk0lo1mKk43ZZKsrIpVxOBsnv67i97N8yv3pYFCXUPaH7DSehDofjUCF6M2cYt1fdrszrWdbXns/1LCwc4RdoaC6SXM+szQiqZ9HrieUiVjP5mIzZswxPCZLPvJ4SqRSXi/B5iGiprvWZPaonfcn1ZNUzEdUTfe1hw529nlyfuSP1mZvb+SD5wZA33FNEKnUGlASVU3M943IR3tf6TDQZYcMdhNNmeZapnqbFCFAyCsxMPAvj9hgaP031rIhZwiWP2U0BgIbJW8KpY/VYqRlUT+R5qtczq89cCRvu4vVswOu5sR5Uz2M8Zq+FXM9YnwmvJ6uea5TU6tQbN2g4rjHB5PrMsQmS5w13M2YfjmkbQfKozUygeiJIXuKU2OOJc4RorEA4tTZTAuVBMnE+RwWvJ66zG+4hRsl6PXNKZ1mY/B7A56JILrN/tFYNXRQq557Q/YeT0IhF+TF3OBwTMKPUXW9ascledSw3ZoensjRSKVM3xc8pS0ia35l5PQskVDfdTaQSsj5BiBCpBCIag+TD7dua/8n3hc8TqieC5EdU73V4zF4fdoigemL8jhYjo3qChPLIHb7OzR0adbpmuQi5nr2Q6wkFNHg9oaJpfWZ3KOPaECzPW9MgM2a5iHM9A8nUDnfr67SxSvbYLqc4u5zB66mLRLa5KAbJmw533nCnfH0mE08Nksdme0H1LG64c67nWpu32Vtan8mq52oYva+H+kyM2UOQvKqeqM9ckSB5Vj0bbRqkNeqhu31MtB0ajHY0UmmcBtVTxuxYKspyPRPqwO8Z1E4sGWGLHecNLUY6ZtfqTAmSxyWuSwq5nqY+M9UN96B6kozqGVb13I/Nduv1jMeysx+vs8cWRQmd0+fprGJ3OAmNcE+ow3FYvZ6ltyvxf1oF1AbIx3FuvTrXU2OS1OupqmfcZg8Kpy4RCZEMkUqNusQvGcJpN9zF66k1m1A9U2qDeNKYe9trWDQKbUZYLsK4PVXVMwTJg4SO4fXkDM8dSuH1jGN2+D7V6zmMy0TDThi3g8xA7Uwy1ZPJDRS1NGViFAlnUDdth3tZnuc8ve25c5RLIjBE0yqhhY+VcKr/M9fhzhaGWlgmEtVTt9plm72ZUz15uUgXjVaXwoZ7O4zZsw33xsoKd7dLpBK8nstMQqU+E6rnBqWtZRo3lyhpr6GPijpJnYaw6nKQvKieGiS/3U9YAWXCGZaLEKl0E7y5ScrNRlA9h1H1HNOQPZ+mPhMvEIL6yc1Fw4F4cHNB8uLxhCpq24tU9cwHyNuFo72iXN201wnxNP6KSEaDEroo2/Gs+M/+vZjntmcrnIQ6HI7FQcGPOa/XMxvBGyXNeD1FMStmd2ajd63KVHVNMjyzcTvCyZVoaquRRilJfWYWsxTrM3m5qMEEU0koiOxSJKuUqZ6UUBOUDqrnsEO1sXg9RfXsc55nDJLX+sytE0wyoHSiPnMMr2dO9USuJ1TPzOsZg+QLqidHKmFhJYzbba6nzfAcq+ezQDz1j+6sf3ptHmu9qHpqBmtFhmcxZontEbwUFlRPqJ14jFZdqjRNm1GMVGoa1RPLRWHZiFuM4PVcD81FK0pCW9TaOEL1pSWqca7nMSJ0uIcgeQr1mcj1HLXWeNO9Pybqort9nPJ4HSQzqp4gnMbrGeszg9ez24fqiQ13CZJXsqleTw2UV+VTguQHccNdA+RjfWaIVcpyPbXByBJNzfOcJ6ug6h+oTAxmWz6qGNHzMZhRDh7zttg7Bd0dTkIdDsdCoKwWs+p2RZJaJJ/5MbtO9vJeT/V1SoZnvq/dLhdBmRTV09ZnCrm0G+7i9cwrnDbXk0lqJJxh9A4CS2NqpSOqpVA9w3JR8HpC/Rx3RPWkQY+SreNhw31b6jOhep7Y4RrFEQfJW9VTI5WkPjPbcJf6TPV6so8wUdWTaBiIp47di0Hy+ocYx4rLRdP+6Fpl07ZQxQWwwrjdLhnFcHkTpZQbvccN90nVU/vareppN9xBPplwgni2m6xy8qIRRypB9WwXVE94PVeotgzV81hWn9lconFjiUatFUqoTp0RserZDRvtrHoGwsm5nmHD/YbtPnVDkDxIKKKUtln1FMIJ1RPkUjfco+oJVRp5nkw4k2y5CJcxUqno9cz62tXzmcv0VBV0LygbqU9TQ3O3L97G/LTYLTTHGQcnoRH+msXhOG2oiEWadyxf9Hra21V1uIvvczLXU0lorq8dRDPGJwnpVI9nVDNx20BCmXg26+z3bMRt9hCppJvwYfTeTEfUgNIZxuzYdNcNd4zZOc8zBsljqWjA3e0YvUPpHO70aDwwqudOn9uMZNsdqqdkeKrKKZFKoY4RC0bobofn0/g6tT5TSGa23Y73gXGJ6jnDqc6fI7sMZklnYdxetnCUi1RSEqqqZ1gyqhe9nqx6ygieSSjOxYq2Ganq2RClE5FKK0uc5wkS2jgiqid7PdePcaUm6jMxeuflIpDPOlTPVRrXW9RHE9EgjapnP6ieHKkUNtxBOK3X8zirnlKfucMpBIhXCueMvZ4aqaSqJyKxwob7aBC8niCoIz4zccNdiWhB7czG7eN9yvPUF4LWxbu711OmE4VjubF8diydWGA6GHhE0/7DSWiEe0IdjkVpMbLxO8VopeJmu94ujnVNrmcuVD4oZhIkbzvctT6TIuHM53oKMZXRu7QTqRKKS14uqmVB8iCr+dtl9Zn1NKHWeCiRSsOeBMmz6qn1mVu8zZ4O+zTeQpsRiOc2JR3kemqkkt1wh++zJ21FGqk0DBvuUDe5TlMWVbTNiAlnIJ0aqTQyqieTUN1sxze0QDxn/S1ZJJlW7FIbhUYn2ds2rQJaVD3teVPiyd7OsM3eBgkV1VO720X11PpMkNAGtRCthOUieD3XVri5qH1kjb2fUD0RJJ9tuCNSaS14PVtcn4lcT9RnjhrL7JHtDOGbHfP2OsjncAzCOeLlIng9OVIpLBdlqie8nmPqdEc01DF7UKb5hQKr00JERfWUFxHs9RxVeT2zxqJs4Sif4Rljg056yUhIZNmSUU7JtD8QBa/nxLF488KxRRFC5+XrTil2hZPQCP9pcThOGQph4rvdrjiWr/J62s32YtRSJJwm11Obi8q8nlx92cyai0BENc9Tu9x1c91GKrHvM9RrcoYnb8qHDvdG8CyOh9QYDbPlIqiePGLvstcTkUri9dziDvfxYECjzU1RPUE4dyRIHqpnqqonvIKseg6ZnOiGu6ieMsIFmcEonglnIsrXsEg4AwllldO0GI0LC0b87i6nWfUqO24PInSOaKrqmQuSD/fVvnY+R9rhHs4Zj9mxFIaAfiwXqa+TQ+Wz0bu0GYX6TKieGLujLhNjdpDQ9ZVQn7nEofLwejY2Nqi+tEz15TUJkseG+9oxoqUVUT2x2V5v0BDEs9YU1bMvpB5ZnrJslC0XieopkUpFrydC5Ls9tBNJc5FssgeV2qqexfrMMcgplE+Qz6yvPSOhxSilotfzZFTPTLmcHLdXeD3LCGnxWPRsF44Zslr6+Q4AY8kNmOv2jgUmoZdffjn96Z/+Kf3rv/4rrays0AMf+EB65StfSXe5y13ibXq9Hj3nOc+ht7/97dTv9+niiy+mX//1X6dzzz13n5+NK6EOx6lZMJotWslWZZaRT7tUpNepwpltswePJ+XrM4WMSkRPc5rXMy4cQbkMm+u6XGQIp5DQbJtdxvHq9RQiCrUTLUa8XDTs8pY7iKbUZw6D6rmdbbjD68lB8vB6iuqZGNXT1mdioQhEM9ZnxlzPoHqGIHmOVAqxSlg0Sk2up/o6dfQeE3n20GKkl3bJqNhipAtF+qJAj9kFIyacqoAa1VOzPCPhDF5PG6mko3f5GGP2liiha8scqcQb7sj1ZNVTvJ71lVVqrCNIHl7Pc6i2vEq1pVWi1Y2georXc1Rv0RDd7SnRDtqIkoQ6WCbSIHlTn3k8BMnfYOozUakJktntieqZGNUT0UqxPpOXi7DhLr7OjHAWvZ5Zc9FkrqchoHoGT3rcXkEGS32ds3s9ZxnJ80eLEtG0QLWdN954Iz3zmc+kP//zP6d6vU6Pecxj6LWvfS2tr69X3uchD3kI/fVf/3Xu2NOf/nR64xvfSGclCcU348d//MfpG77hG2g0GtHP/MzP0Ld+67fSZz7zGVpbW+PbPPvZz6b3vOc99I53vIOOHj1Kz3jGM+iSSy6hj3zkI/v8bJyAOhwnjbJazLKblYzR7XXW4ym3y2d45kPlq3M9Z/J6aq5nXC4SctmeWC5qBBIq17NyGrbjZeQe6jPHA6oPoHqOoteTsGTE9ZkZ4YxeT87w3ApjdvV6SpVmrM/sDoPXMywXhQ13zfgU4pIFySN3UpVOjVCCYlcWJF8knfMGyevH8dwFEpq9QChss9tFItPhHkPl68br2cJJn6zP1FxPHrtzm1EWJC+RSrpcBNVz1aieqM9sUmP9KKue2HDnRaNmiwiqZztTPdNag/r1NiW4HEmOJ6KSTmh95jARwqmq5yDv9USQPFRP+DvRYpQFyYdcz2Fxwx0vKsTPKWN24/Xk+ky5zNVnWp9nrsVIGdCp8npWZ33O4/XMVE9DMuP14Zj9RXDAWCRP6Pd///fTl770JXr/+99Pw+GQnvzkJ9PTnvY0+v3f//2p93vqU59KL33pS+PHq6urdJA4UBL63ve+N/fxFVdcQbe61a3oE5/4BP3v//2/6cSJE/SWt7yFv6kPe9jD+DZvfetb6W53uxt99KMfpQc84AEH9MwdDsdJeT0Lm+18ace4tckNdx2pR89nUDb5Oh3XmuYiXIJw2vrMqHqGY7LhbpaGCs1FMWYpLBdlXs/wGDy6JyaaDXg8g+opG+6ozxTVMwbJs9dT6zO3abTTMYRzxL3tw05fCOdOn9JAMtnPydvuYbmIvZ6Zf5DbjMxy0UR9pqqeZtyeeT5PjnzaJaOYwWpG7JrXqdvvMWZJ/Z8xmSC8eChEKuHOE21GYbmII5Xg7cypni3xemLRqNVk4tlYXqL68gqTT1E9ESS/yqN2QotRo5mpntSkfq1JSVqjnUFQPQv1mbzxblRPyfUc0U4/oU2onomonlCkY6SShv7HIHlRL6PqiU12DZDXQHkmnNLTU5rrWUJCTwogflXVmbkXjHOM2yeOyXH+2B7jn6s8ga0tWkTTgiih//Iv/8L86e/+7u/ovve9Lx/71V/9VXrkIx9Jv/RLv0S3uc1tKu8L0nneeefRomChPKEgncA555zDlyCjYPgXXXRRvM1d73pXuv3tb09XXXXVPpNQH8c7HPMg+xsyw7i9xBNqiWb2eMXMT7vFnqmgQlwm+9qVfIrnM7wfyCUuhXCqmpl1s0fVsyRInrfZMaKPDUioz8RzSKk+6lF90Jdcz4EsF1FvR+ozh1b13KK0J0Hyw82geiJSqSP1mSCfVvWUSKVswz3WZyJeCV7PoHpCaeEg+TBu17G6thmJcpORUMCGyc9CW6wOVub1tOHxxcpM29deVD2zc0Xi52wWIpWM6snHVPVEpBLO7WpbVM8YqYTmolUmoCCdrHq2WkI8l1akw/3IzdjriXE7guQ5TL69TuNanfrUohFqNKF6gjxic70/4jE7OtxjrufOgEmpRiqBhJ7oiNcTZBN+TxBNiVSSc6WRSuz1hEoNb+dIlM1EN9xDo1EWqWQ722lC/cze17NK++/1jOTRkkX531SiOYsCOuWYfIow+iiNfDq7PaFXXXUVHTt2LBJQADwJY/mPfexj9F3f9V2V9/293/s9+t3f/V0moo961KPoRS960YGqoQtDQvGL9VnPehY96EEPonvc4x587Nprr6V2u83fbAv4QXFdGeAbxZtic3NzxmfgBNTh2Dev5y63s/FJkcjaRaPSDvesFUe9nprrKYQz83Oy6onsR+1fj6N3HZ9nkUrs9QyEVBeONMNTbheC5GuhPhO1mQOonhi3Q/UMXs/uJpNQbi7qbEfVE6PV0TbqM2W5aLgZVM/tHg27QfXcAuFMJFKpZ8bsBdWTg+RxiVE71M6waGTH7DZIPqd6nkSQfK1C9aw6FglnocUoV3sa6jOhYOpSURyzBxIqY3bj9WyH+kwevS+HDfewXNSS+kxRPVdjfSarnsuoz1yhdDnv9RykdeqldfF6DsbUT0ZMME/0RzRMJNcTH8PXeVMn32bU6Y+C6pma+kwhotmGuwmST0X1BAGVMftQXgjEIHk5jjMX6zPtklHscD89Xs/y0PjJY/n7W4UzG3FEhdN8nrwSah4nLjhl16WH3BNa5CFLS0v8tleA/2BqbNFsNlnAq+JGwPd93/fRHe5wB1ZK//Ef/5Ge97zn0dVXX827OXS2k1B4Q//pn/6JPvzhD5/0stNLXvKSfXteDocjWwKa5XZVo/XyY5N97fhIszztclEc1xoFNG64hwWh4ujdBsnrJZPLsg334AUFGW0Z1RP1mfB6QvXk+kxELPVlwx3jdg6SZ9XzBKXDAaueSVc23NHdHr2eGLPnvJ6hPnNkVM++qp4p+z6z+kzZcEcMkCidBdVTt9lPgdczp3qWZH3a0HhLQm13O46xNYIjlSRCiX+mtD4zNhfJJSucbeP1hPoZg+S1PnNFIpWWl4PXU4LkQUCxYCSqZ8vUZy7TeAn1mQ0mnsMEqqeonLAvYKsdqqf1et64gw33kdRn7gw5YWCzM6Q+FsJ4y12WijiFIJBNjVRS9RMkE+Qzej11oz0SzqQk19Pmeab5cPmTQZmyaf5Bll2XLQUZUlmbdkwPWF+njtqz68KaYe5YqZ+UCWn9UNd2nn/++bnjl112Gb34xS+euP3zn/98Xs7ebRS/V8Azqvi6r/s6uvWtb03f/M3fTP/xH/9BX/3VX01nLQnFstG73/1u+tCHPkS3u93t4nHIxYPBgI4fP55TQ6+77rpKT8MLXvACuvTSS+PHeAVS/AFwOBwzIFRa7jpuN3WYucOGaFp1M+8LzbyeVuGMG9W5SKVsBK/kU32dORIaiCQudcM9q89UwpktHE2qnjVq0ZiatURUT5DMGCSPSCVstodIJbQZseqJPM9NHr2jtx3tRcjwRJUmq547PQ6SB8EUwplFKml9JrfhhEgl7gXn+kzJ8tT2Io1S0o9jqLwhnlSIVpq1xUgVa8nwzI/hy7bZlYjyebOj91o+Zol9u9zXHjI8A+m0fe0xUgmZrSt2w32JatxmtCzNRcttagevZ3PjCBNQeD3rGLkjUgmB8suronqCfNZblCyhPrNNg7RGvXGdRmNiotkfJZWq541hzH7TTp86A6nPRHc7iCYajJhsQrnG6B2qNFIJuDITRDS0GaG3fSJSCS8sQn0mPJ5R4cx8nVUk9KTAi0T2jNt/pIVxd1HdLFNM97KEpJ/Lfp6KY0XldLZ8jcXFF77wBdrY2IgfV6mgz3nOc+hJT3rS1Me6053uxPzny1/+cu44lruxMT+P3/P+978/X372s589O0ko/pEhYuCd73wnffCDH6Q73vGOuevvc5/7UKvVoiuvvJLjBwBIx9dccw1deOGFpY95sjK3w3HWIqdY7v6rX8miuWuFr9MQnOJ43ZJQm+sZLnmbPSigSjJ19B7jk0BK2e85GSTf1r52DpKnnNczKp06oqeUu9tRo6lB8pzrCdUTo1Oonr2dzOs5RH3mFo07O2HMngXJD9Hhjkil6PUMqqcGyXNlZsj1hJLG1YyiesKLCFoiXs8sSN4SzqSsu30OxTM7z4ZQThm3F8Pjba+7LhfhumaxPjOQT76vjtnxvS5EKvEoHUHyIJwr7XykEns9keuJIHmonlqfKV7PGud6BtVzWVXPJUraUD3r1ElqXJ+pdZmqeiLDM+Z6hkilTlgugscTxHSLvZ4aJC+qJ+d64hxBrY6EU/yf4vUUwhnbjHSbPZfraY7pQlH0ee7DZvtM4/aC6jnLscpw+aB62nF7cdGpcJ/SY/FzqTIqz2FRGpOSsbzNc3sABNSS0Crc8pa35LfdAP4DcQ57M+BJwF/+5V/yCyEllrPgU5/6FF9CET0oNA96BI/N9z/7sz+jI0eORC8DopiQG4rLpzzlKaxswuuAkwjSihPgm/EOx/6hSB5pTq9nJC9m3K4kRv8IyTE5AKVSPJ4Z8cyP3tXrGdqMjNcT6qfWZ7ZUuWzsEiSvgfNxEx6VmnLfJu9Doz5zRDV0tyfYcO9IpBKIhA2S725RiiB5bLgPseHe5QUjGbODhIJw2vrMLFKJ24w441PIjKigoqQNRjLm0w13jVTSykxVOauilWgGylJ63gz5tC1GlpDa0PiJ0XtQPZmchlE7q6MaqWS8nrpcpF5P3mbnDffg9WTVs8FLRiCcvOHOXs8m97ZD9eQxu6qe3Ga0SoRIpZUNhIlKfWazTYMxUXdYYwLP9Zmj/HLR8bDhjkilG3f6TEKxZATVU+szRfUcySZ7oT4TPlAmnSFIPgHxhOI5zns9WeXEMV4qkpaiYod71mSUtRqdFCrjkwpB8rv6P/OEdDevZ+m43Xo+S47F52PU1Piy1h5blMWkPY7j9xt3u9vd6OEPfzjHLSHjEwvcmCg//vGPj5vxX/ziF3nU/ra3vY3ud7/78cgdfAsb9De/+c3ZE4oITCQRXXDBBXRWktA3vOENMUDVAjFMKkm/+tWvjkGsNqx+/4Efcl9OcpxdmMfrWdZixJeGfJb3tWfqp4xr84tGNlKpEQmn9Xpmo3cdt5d5PVXhXMUoNwTPF8fsOnqH2qn1mXVeLirUZ3ZNfWZQPbFsVFqfyQtHCS8aZaqnNN0gUklUz7BcFN5nMoN4HpDRoHoWx+ya6zkutBjRHPWZObJZ0WJEhRglO263AfJ6/pSEagoBxu26XBTH7IFsxg13qNdL6GuXj7nFCGR0ZYnH7tbryRvuK1guWqbm+jrVWm1qYLloRYLkMXLHclG6fITGUD0bbRq1oHrWqJMQDfopb7hvTaieo1CfmcqGex+qp2y4w+u5g+uC6omROwiktBlB1ZTj+L4jy1O9nrE2kwlnpnrq6J0XjkyA/P6P28vI3eQ/0vm21A1pNddFoll2bBfyWT62F+W0tiuBxivWxVBC+fwvAAnVLXcQTxBN5Uive93rSAFiislxp9Phj7Hk/YEPfIBe85rX0M7ODtsUcZ8XvvCFdJCopTHZ9swEPKFQVB/52g9Qa0UC8MuAXxT6e8KxP8TFsWAw0zP1Z9KcXs+ycbtcmtGtIaFKfvJB8mUd7hkJZQLZmvR6LptwecnrzDI8RfWUDfdq1ZOokY6oAX8nb7hjzB68nkH1xHIR4RKRSiCiA2y2oz4zC5KXSKVOTvXMIpUkRmlC9UTQOUgoxutMOPO5ntpixImQgWyOi+P2fWgx4nNqjsdIJTNi1/ikegkJVdWTiaatz9TlIqt64nyFIHmOVFppSa5n8HqCcDaN6tnekCB5qJ5Sn7kaguTF60nLqxwkD/KZQvVsrlACryfqMzEaH1NO9TweVE/2eobmops6g+D1xLERDYYJd7ejVSqveoalMPhzua89eD2xXBS8nur35IUjVT2ZZEqkEqufkXSGzXYmnbR/5NMSw1Lls1Z9TAkjX5hg+JxiWjIqtxYc6+usGrfnRvRFr6d+LZPxTvZrGw+79N+/91SOcZxlrH2qeMT/+8fP0dqRIzPfb2dri771gjse2PM+DFiIxaTFgCuhjjMUtcnInarbZeRyFq9n2GY3L0qs6qnkMobLT+R6isIpSmfoWw9qZhapFLyeoZtdvZy4HiP71UBCo68z12YkYfL1dEzN8YBVTw2Sh9eTWPXEktG21GdypJKonqOdbUp2dsyYPUQqdXr8/mBb6jNZ9TS1mTx6R52mZkSGakY07eh4PQuSzzrcVf20xHO8D+N2u2Sk59+O4EHWAfV6xiD5Qoe7EtNGE0p1XvW0kUpVqme2XATVMwTJ84b7GjXgAUWQ/JENs+G+xkHy3N0eVE94PRPUZzaXOUgexBPKJY/V+9hwx5hdIpaYhJr6TKienX5Cx5HDCtIKH2j0eobsVfZ6ZqpnGlRPXKeRSvwiQOsz06zNSFXQfJSSkFF9CbGfXs/yqKRp4/Z5vZ6TBDZHVuPPFb8iMY+R93qWE0u9c/mx8hH+4faEOqrhJDTCCajjzEG2EDSD4llCMnOPYUlpoa9dRQ2rfmoWpL6fy/XUvva44a6RSkJG9f1seSgEyWOpiJeLRPXUUHkZxwfCqaN3VT2TAdWHg5DnucOeT4L62UeuZxappCSUVc/NTRrD67kDr2cgnJrruTPIVE9dLgpeT7ThgHyCgGBTGl5PjlSCimaWi7RKkwmOkk1DQuN2+4xB8mXkUwnmNOJZHLfHMbvxf+q4Xesz+QWFbTMq1GeChDLh5EgleD2bHKvUWluiegP1mRKpJF7PNaqjPvPIBm+3S6SS1Gcy8YTqiUgljNzrTRo2hID2QSD7Y7YygHj2El0uCkHyHSwXJdxmxPWZHCSPcXxCfWy59ySFQMbsEqlkvZ6S6yn1mVlfe97rGfva1etp8jytrzMbt/NHs//jLZ5d82+vjGBOkM+KcXs2WjfHCvfLjdbLjhXH9koczefNPR+8YCl+PcVjM2SSLspf50XxhJ5JcBIa4Uqo4/DjZOoz7XW5FqNd+top12qULRop4eT6zLApLV5P2XAvBskzCQ1EMqvKrMcNeCwcNUP0EogmyJEQTjwusepZS8fUwFZ79Hp2ZbO9F1RPXi4qqp47lHQQqYR4JYzZQ6QSq57YcIfqmUh9ZlA9mYRiRMteT4nnAfnU+kxWOw3hzHW4h2N21G49nvvh9SxrMYqxV4aIWhLasCTU1mciiaAtqieP3qGGcn1mCJKHutnWDfdWUD3h9WxJpBKWi7TDnYPkl6m5oUHyiFRa4y13WjsqQfJLUD1XKKk3aYDudtRnDlGfOWLVE/WZ7PXUSKWByfXcHvDYHaN2kE8kDXR6I4674iB5VabxIgGNU6HRSFVPIZvVXs884UwrWoxoMbyehkwWj+UIaVQ09fPqz1P+2ETNZslGvD1WJL0TkU/2d88uX0+tvhi1nTK9mP28znPbsxVOQiP8h8VxSFFQLGsz3M6SzHh1xba7XSKyI/hM4VQyKlvtvKgSg+QzEsqkMRDKVjHXkxVReR9jYI5UKgbJG6+nRCpBMU0lSN6qnv1tvkR1JvWxXDSgVIPkO4hUEq/ncGtbVM+4XKS5npLliQrNSDhDfaZ4PeV99QxKfaYSzyzXU7vbmeAUWozYM7iHWCXdYLfD1SLxtGRU24qKMUv43vELhMArhITKC4Wc6lkVqdTMB8lzwDzai1Zkw73NhDPkenJ9JryeR43qKfWZNRBPZHpiwQjxSvUG9alNo1qDvZ5oMYLXc7M/4uUikE5ZLip4Pa3qiWisYUJdZK/iBUFYCJMgeSWh6vWUBTL1enJ/O4/fMWaXFxc2SH4y13OfN9uneT1j1me4Xbwojr7lf7nxeSS0+jn2OKLfhURO3saO2vUmWYB99qmnHSv8ojpAqGd7nts7psNJaIQroY5DBBOpM0+sUlWLUfw9n6vSzMinjtWVfPIx3WYPzUbqA+WMSOv1DORSlMvM/1lcLtINd8n1DFvvejvj9Wxxo1FK9XFQO0E84fMMG+5Snynb7CnC5BEkD9VT6zMRqTQc0uDEDqtjIKDi9USkUkY8tc0oi1Qa5eozmcyMy7yegXCabXYbs2RH7jO3GBXOtRJLIZxy1JJN292u5HMiZskUALC6yYtGgYTGIHlRPuNyES7xAkE73KFOry5JXzs23Nnr2eRxu2y4r4T6THg9byZez7aonmkDQfLrTEBH1KB+rRVVz36ScBc7VM9B8HrC58kb7hokj9F7P2HVczOonl28UOA2o2zMHklorM9M+fyL1xPnVkbv4vUU1RNkVMRMO2aX8oB8b/s8+nXVCS4ZqU+7biKyqLa3YznFc7oiGYmlvc/Ec6k4VlR0c2N7G/FkHyM/8l+UiCYssOFtnts7psNJaIT/sDjOHK/ntNtZ/6eqm1P72pXcaEyPej0LbUYaGq/LRdpmBMKphFRrMWWknm22NwMJ1c12O25X1bMN4hnqM+v9PrcY1UOkEhRP4iB5bLhjzD4Qn2cHy0UgnFvB69mjETbcMXLnIHmM3oc0hGoWVU8Zs/NSUVg4Ys+nBslzfWY2blfCOSp0uGueJ6CqJ80bJm9fJNgXB+a4LhJZFVSrMmNfe8hhjZec6ZmPVCrmegrhRJvRpOpZbyNSaTmM2Ve4vx2j9tbGOud6NpDlCdVzKfN60upRoqXVUJ+5HlTPFg2pTv1RyuQThB4NRhyppKonCGcXY/bQZgSVOtRngqjiBQG626FsRq8nxuzR62lVz2HB6wmFEyQ0ldG7thbFJaOsRlOg0Uqxlmquf7+zez1nzPosUSeLimc4UuLrDH25lv7FY/FeuWPxd4n6Oucat08j0/aY+R7lua/jDISTUIfjjPR6VrcW2WNlfe1lhDMuGkH11HE7KhYLfe1Fr6eMz8NyEccnyXIRq56mPpMbj0yLkY7gW7WUWvUx1cYJ1fqdoHoGr+doSNSRqkwonuOoesrofbjTEdUTG+6a68mRSn1uLhLVM3g9VfXky1Cfqf5BjNuhqJmRu/a1j8o22y353IPXM1olwrHo6SwQTT2mLUV6Xz6mkVhGuY7WiTBi1572Yq6nEE4zeseG+2qbb48sz8YyiKjUZ2LMLqrnMtWWloV8ttTruU7UXpb6THg9seHeXBbSmTZ4zN4ZptSD13M45uUikEtcYuyOdiMQTolUEhLaHYxCfWbKve3s9cQ51HMVUgk4fzVuuNtIJcnuVPUzjtpNpWZpb7uJWTo5TPF6ztxilP10lG+zm+vyfhsTkZQ9mL1dURUtEs29eT0tKS577vEz21fO5ikujhLKKvoctoszPAFzX+AkNAI/5P4D41gcWMVy7tzWCv9n0QtqvZ6a4RmPmQxPEEiNVFLimfN1Wq+nZn3mNtzlseD1ZNUzKKEgvsvhUkfvUDvbXJ8J1bMv9Zns9Qz1mVA8eztEHCQPwtmnZAeqp2y4Dza3s/pM3XDfxgg+4Y52kM4y1TOFkpZTPbM8T10o0gB5JaFJRZ7nLL3t4TSF85ERzwnyaVqMYq6nCY0vBs3HIHmuzwwRWSVB8lA2sdmuo3fN9sw23EE2dcMdqmeTl4x4zI6YJaiezSY3GNVXZLmojjzPZpvS1aOULq1Q2liSkXutQb20QcMUqueYu9vx/YXqqZFKonqmMmYfGNUTy0jdIfWQtYot91CfKZFKweupqmdYNmLCOSrbcA+RSjqCtxmeuvVuYpb2rT6zOG62/wgjSTPXl/g/M+UyHIsj61r5sWnEchrZLJLICV/n7l7P3bbds2P531tqCcp95fqDvwAQq818t3dMh5NQh+Mwej0rbpd5PbMFoty4PSpphXiloGzqKL7oGdRRO9RQHa3rIlHWcFQIkg8Kp264N83oPVM9cUzrMxNqEpaL4PWE6jkk0g13Vjs3icxyEXe3c5A8VM8ujbbRZmRVT0QqSZ6nej15uYg9nsHrCdUTm9LB6wnVjRU1DZW3hNOEyU/0tps4lnmWjHJB8rnzN7nBbsloHLObTXftcFevLv7mN4KnUzfbNUg+Wy5qRDLKJLTdoPbakpDQECQPryeC5Nn/eWSd6zPh9WwcEcLJnk+oni1RPanRZOKJsfswrVFvXGfVE0tG/QQb7VA7pbnoRG/IBBTeTsQr4fsP4gkCCtKpqieC5GUJLL/hLpFKIUgefr1Yn2m8niFIXjrb8x3uUfWM5y68vy/1mSUj6LlI2bTcTKs0ThJNudBjhtRV+DqrvZ6ZcmrmKJXH8uP2QKbjB3qzvGKbfVmT5FNtBIvC5Tyiaf/hJDTCf1gcBwQzWs3/Yi+56ZTRuj1mfZ36izz6CA3x1O11GdcKCbVeT1Y6i17PcMlkMiwLKcm0Xs/VoHrysUA0OVIJx7QLnlJq0YgvQTbrHKkkqidIaIo4JY5UGoRIpQElUDw7WCoa0fDEtlwa1dPWZ1rVU7I8seEeCIuGlI9SHgOz1zMsEBWD5Iub7DqCV8WT353tVOc9nmUtRoVjukgUXzyYmKXo/1TrRIjCiqpnIJy1gtezgailVlA9Wf1EmxGilnS5KEQqIUh+CV7PIzx6b6wfo5qqnmHDnYPk2ys0bi5R0l6nca1OvXGNBqMa53pux/pMUT2hct4EEsqEcxgjlbg+U1XP0F40sEHyvOEu5FPG7Inxeg4mvZ4gn/gPpNQuGAXVMzdu57iC/ajMm9/riQisUpIaH0QVTnO7EvUxu2u117OUrO4ygt/LuL2cONvvUX7cnj1P+y2wH9BCwBeT9h9OQh2Og0JJLWb17SZvVSSfeaWzrMNdCCCZ6zPCGZTQulzqmL0VfJvW66kkVL2eVuG0uZ6Tqqf6RIma6YiaaDDiIHlRPVGdqfWZ6c4JIRSqeg4GNNo6IYHyCJLHNntoM4L6OQqqp9RnhiWjrm64h0glKGZQ00J9JggPj9tDrJLmeQrJnPR62u32WRUOq/kUW6isr1NtErpkpCqnklDbYsSE07YZhTxW8XSGIHndcIe6aSKVdMOdyakGyeO6NSwXtXnhqH1ENtxZ9VxZpjoI58bNYn0mSCg1M69n0l6lcWOZBilRN6mx6olxe280Zq8nCOcwkQ53HrMPRnTD9iC34d6HB7SgevI5HKCxqFCfab2eIcdTx+yy1Z5FKsVFo4m+dh2968j9ZDHDFvie/J9TvJ7TxuS7Es3p/syp5HMO72r1MfMVmRfKxW9pdpvFYKGuhO4/nIRG4Ifcf2Acpw521LrruL3C61nm67QEJ1M4895OJjMTfe151VNyPbPmIt5s1zajQEx1qcgGyTdzqqeO47X1iIzqifrMPkcrSaSSBMlzrudoJNvsXVkuGu/I6J2D5OH3RKQSxuxQ1ToSJM/h41tyyV7PTtiQDrmeMVIp+AehhIJs6oZ75vWUmCWrcGqPu+Z57qXFSM5ReYsRPsjUz3y4vH4cF4pANANp1Q13XirCOcQ5aRWC5LXNyAbJQ9lcDV7PVaib2HzPVM/M6xlUT45UgtdznVXPmlE9x60VGjfalLTXWPXsoIgKLajB6xkJZwiSj7meOwNuMgLpBPnEi4Cd3oibjKByYsMd5HGI8H/dcC+onuL1HFZ7PY3imS0ZFVuMWAqd8Uzu3etZHSSf/ynJKZcVRHaqgqn32UWtjAQwqKc5JTKOzWkPvs69ez0nybl93tnFgnBQ94SeAjgJjfCfFscpgvH01fZIUutTMjyj51M/h/ELqtqp2+26aKSVjFDRoFRGX2cYsTNpNISzHUgoLxdhwz2X6xm22e2YHV7PRhgbpyNqYKGII5WwXCTqJ+FtNORIpaLXc6RB8lA9tzuhuSi0GUH17ASvZ1A9ecyO2kyQ0K4sFzE5DXmetj7TthiNC6HySk1wWyGh84XJ83mxLwrM+dPzYzM+VfXMKaDheo1Z4uxVPZfcYKQb7jJmj8tFpapnCJLHiwRsuIOMwuuJSCX1enKQ/BFqrKxQrY0x+zGqtVqierLXc4nGK0eJ6k0aMQFdogE8nkMZN24PoHqm1BkJ4VQSCgKKUTu626F6Hg9ezz5C53uieg7V6xkilXCu2KNr6zPxYiFRr6fpcM95PfO5njbH07YZ7Qv25PXMd66XjawzommXffRjQ+Cmej2tl1MfPf+4mXq6i9ezOKI3x2Yft9vnYYllXvks3jd/rOT7fEBwJXT/4STU4ThVMMSC9qh6FglpeYZnVqWpMUr6Pq7nMToTmUBIEfYefZ1h9G622TXXU1VPkCHxdarXExvwcj/O88x5PaXHvY76zKTP9ZmsenKofKjPhIIFxRNh8ibXU1RP8XrmVE94PUcIkke0ktZnitqJkTt7PVGfabamcQxZnjpmHxbqM6epnuleguTNH+ai8lkkn1b1VHI5ESRvcj1BNqU+0wTJK+G0He7L2Ya7BMmH+kwQUYze10N9Zk713BDV03g9QT5Rn8mqJ0bt9RYNQT6pTl1Eso5SftscJDFSiZeLVPUMY/ZteEBxLOR6dnCdBskXvJ583hAkz8tFomjzchFG7jg/YezOY3SQ0ZzX0+Z6GgJK+z1utxOIPXg9i77OsmO1yTrMYovRbL7Okxi3l309/K45NkFwC19C8QV3peqp7xs9OfdpVcGlhQBeJOFtnts7psNJaAR+yv0HxrFfC0azNRkVvZ52fB5JqFXWDAmVcW1+0SiLVCp6PXWRaNLrqZvt6tcUJTQ0F4HQMNnMcj01w1NH75wJGlRP1Gc2Bv2Q67mT1WdC9TSEE8tGHKkEtXNzM3o9NUoJ6id7PbuozwweT6ieYaudvZ6hxYgvOb4nX5+pqqeGyuuSkfY5W4/nvPWZ9rzkXiAYdZOPGeJpg/+neT35+4jzF5aLNL9TyadcwvfZyG24Y8mIg+SR3bm6lAXJrwTV88iq1Geub1Bj1aiexuuZNpdCfWaTRs0VShptVj07XJ+Z0tYg4f727jChG8OYHb3tUENRl6m5nsc7kusJ0gnyqaqnLBdlqmfccEd2J1TPMGYX0gnCaVTPNAuOj73tUekc73N95m6h8Xv0epYqiZM+zuzj6nF7/pglnyVb9vyCdJdj++31jAptybevbFyfaaf5+5TYRQ8KsrQ43+0d0+EkNMJ/Whx7Q5k3c97blXo9zXKK3XRXIlrM9ZyIVAoEUReO1OupUUqa9antRMjrLHo9Ndczjtn5dvL4qM9s47mkCTXQYsReT1kukjzPrRCtBMK5xQtHYw6S79Oo06XRTicGyScgoajP3OmH7nZZMsrnespyEauetpLRRiqVEE7J9czG7RqrtJdxe0Y4M69nVLzDyRPCmSejus0ux/IkVHM9+XyH7zFfFiKVdMNdQ+Yxhhe1sxW8nkH1ZK/nMtWQ67mxSs3VZaq3l6jJqqcEycPriSD52hpiljLVM6k1adhc5pTWDhRPjlUa04m+UT0HiXS4I1IpkUglqJ4gpuhuh9cT9ZkgoDiHWDTSIHlRPeH1lMUgGbeDiMqYnfvake8ZIpSgduJM4fpswSjUZ4bt9v0LkjdnOUwR5vd67jaytiTSKIlWCYzH4i0mfZ34qck9tT14PcvIdJHQxgecjF+aUDGLz6fwLZ0YweefbPZvaeJX6AJJoY59h5PQCFdCHafY61mIVQoPIcTFKqDxsbOsz1yHe+xpF5KZHcuUTg2O5212EM+wpa4KqA2S15E7cj1lk13qM0UdlTF+O47eiZaQP1lDkPyA6kk/eDx3qAYSAdWzn9Vnitdzm5Id8XoO4fUcSH0m/J4cJM9eT0QqYcPd1mfKVrt4POH7lOUUjG2ZzBTqM8vyPFXl1K13QKOVZqUtxTxWJZL6fkwhMKpnGeGM50qPBYsEK6AF1TPWZ4ZLUT1lsz1TPaXHPdZnYsOdI5Xa3GIk9ZlHqLG6GiOVWPVcO0q0vEZpK1M9B/UlGtVbnN2508eiVkJb6GUfivJ5k1U9Q1/7jdhwB0HtDKmD9iKQT6ieeHFgN9yHZfWZonTqctEYpDOneoalIh2z5zI9LQmNZ/QUj9vn9XpWezLlrpkyWhy35x5jxseNz9kwuYzQ6v2LX6eS0ezrLX6OPEGdc9ye47kVKqc+rwm1Mzuee5wDhntC9x9OQh2OOZCJFrsTz6rbWdVTKzOtomkVT75dRa6nKpzq7ZSlIg2Wz2KW1MvJJNQGyYemo+VCfSaWkDhSqZ5tuKM+s10bUy0dU539naOw4d6R7vYuVE8hnGmsz1SvZycsF6nqiUgl1Gci1xPLRQPj9QyqZ3dS9bTjdpBPrc3UxSLtcFf1M6d67rG3Xc5XOFd6Xg3xLBLNWsH3ab2e0f+pXs8QqcTKp6qe8Hlar2fccA+5nqvW69mWXM8jq0JG11eptbLE9ZlNBMjzctHRTPVclw137m1vrYjqiUYjqnFve68vsUqbUD3H2XIRfJ03hCB53XDH6B3kE0kDUD21sx2RSqpQR6/nMB8kD8KJXE8qeD1Z7dS2oqB68nV84va7PnMKueTj9UpCOtXrOTGqLjk2s9ezatyePadJMpt7UiWK5Kn3ek4bt098O/OfIv/49sX7grBQiW6bIyfUSeiucBIa4T8sjpPzepaN26uOqS4gfe06eg9kJ3S4a1UmE52SDXfdasfYXb2ZqnSCgMYWo6B08iJRuL40SB5Km96OI5UQrzTmeCBUZ9ZBOjnXs1ifqV7PPo27nej1HJxQ1RMb7uL1FM+nkE0sFdn6TCidcbkotBrBS8hVjBQilYzqaZuLNFieKvI892PcLoQzr3Da22mHuy4WWdVTNtzDZrtZMpqozzQb7ll9pqqeWp+pG+6ieraPrgfVc4PqK6sh1/McolabaqsbREvi9UxY9WzQoN6mUa0pqmcPqieIJ4LkxzJm10ilrgbJJzHXc7MruZ7obO/14N0E4QyqJ5IJBkIe2evJi0Ygo6Y+M3g9ZfQeFE7TZlSd67nPv59n9XpGBS+vMspVlmiW5XPuQiJzxCyTA4sj+uzzz0I0jdfTkNzdxu1FcpsXQ/O/y/Jf+/xez/JxO03/HIvBQX0x6RTASajDcQq8nsVj8dL8slUSQ3akHghnWa5n5vXMRu86dtdcTwmSl1xPEE6OSirkeqrq2bJB8nx9eDwaU4tVz4TqGK8jy3NYqM9EoDx7PTdDfeYJDpTn+swdE6kUNtzV68n1mdiQ7uFNVE9ZMkKHewiSh5IGP2HweSrhtMRTN9ttfabN8+TLPbQYZR/beKVJJdSO25WIsuoZiCcTd5vHGkbs+fpMye/kMftSM5/rCWUTqicI6toSB8lLm1GmeiJgHl7PxsaxuOFeX5X6TApez/GStBmNqEH9WouStMZkszcS1RPd7RqphOUiEE54POEDRaTSFnI8h5nq2YPqiXODFw+mPjPzeorqKctFWaQSiKaqnpnX047bTwf53KvXs+JYqSKpnykjkuWqYth+L5Kugiqrx+JzVuJaJJW7+jqnPffi+5Z8F79VeWKYf14V43a9SfFXqPl9mLv95KnZvdDjNAE/tXPlhJ7KJ3OGwEmow7HncfvEn7MJ/6feblqLke1rt4RTRu1ZgHy24S5jeCWUooSGbM6ohGaEUyOV2NcZwuez2wUSGuozcVkb9WXUDtWTcz0HRL0OpT0TqTToS3XmzpZkd2LMjnxP9noiUglezy6NEeOD5qKoegbiaSOV+pLrCU/hCJvShQ13Szgru9v3mOdZ5fWMFafmGPs6DUFlwmmIaBy9azKBrc9U1RPvG9UzbrivhFzPFc31FNWzhiB5EE6M3+H15FzPFjXWjlB9dU023DdkzF5bDV7PRpvGWDSqN6lPLRrWGqx6bocNd6ieiFTiNiNVPTvDOGa/cacfVE94PRNWovtB9USNJnraNQqLF8Bih/tIWoxwLjRInsfsIUhe6zRth7vdbFePZ0mmZ7wufKRnbPcxbYXXs6SJyP4jnsuTOctWecljlIbJF47F58wfmiWj+DVZT+rsJDlPWu1TLB+HT3xLzeeb2ny0i9czd6z4XHLfS1oIuCd0/+Ek1DEzChOis5h85m9niWb8mCa9njkSWuj73s3rqZvpnM8ZiKQ0E4WWIhOfpGN2VUARLi/kVe8Dr6d8vkaaUAuuQGy2h+UiyfXsyKIINxdhzL4Tg+QTrs+E11OD5Ec02FbVE5FKwevJqicIpwmS1zajsDnNqieWVXTDfYrqWVafaVXPmc6z+WNbLxm3F32dVNLXzufNbMHr6D2mFajqaTI8c6P3ZWy4g4yG+kxeLkKQfJ3JZnMJ9ZlNjlTiEfyRNd5wh9ezAa+nbrivHuEgeVo9ysQzwdi9tUqjWp361GTVE17P7mjEqic223XDHX3uqnpKrueQN9x7w4Q2sSAG4omxO7ydJkieL3m5CAqoBsmPMtUzdLhrnSaulyD50GLEC0aUvyxZMNLlsYnrcsrgPng947/l/Jg8p17qsXm9nvb3RPGY+WVqiedM4/ZpXs+iUpr7evRfwBQimfs0Bfqo/zBm8HpmNyt8PnuoVFXNDhS/3YsA94TuP5yERuCn3H9gKmEWZs4U5ISAPXg9M9JZK41Z0iajHOEsyfXMjdkpbLgXvJ5MMlUJrWfjddlwB/lEixHRKghn8IPy9dzXnm24S31myt3t9fGY6iMhnGgz4lxPkIjeDiUdiVdS1TPpdjhIXryeWC6S1iJRPZHrGfI94fXUXM9wmUBNAwlFOLmOcEFiEuv1lF/YusWum+4aJG/H7UpG54HNY60VVc/CkpEeU9VTiamNWYqjd20zYqIJwqkLR0I4JVIpqJ48fg9B8lH1bBZUzxWJVOI2I3g9W1Rf2wiq5zI1gteT0NsevJ5QPbHh3ksbNEjrNByltA3yn6Q8bucMz9BmFAln8HrepKpn2HAH+RzAHqHLRfxCASRUvZ6iZMtyUdhmx88JlM1QnykLReL9zEbulKmfdsxe+CPNH4X77erh3DevZwWJDMdKSeQsXs/Cq/bdvZ7556LPMP+8zHOZOGaey4xez0nyWEYMJxjibF7PCgVzppF+4Z1FWUziRi/3hO4rnIQ6zi6oIjkDmVblMnd38yo+xvRY9cyM25WIFsfsTFTC/UE0tclIMz61zYhH5SbXM47Zw/WqeuJjbLtbJRReT5BPCZKvx/rMJshmQfVEpBJ8n+n2CWmoQZD8ziaTixEHyYu6OYTHM47ZMWKHB9TUZ6rqGZaK5LKoembj9mKQvFU5lYRGxXPOFqN4uYvXU4lnWXe7VUB1071RLAUIG+42SB6eTc31jF7PZVU9oXa2xesJ1RNB8mgzgurJuZ5r7PVkwsn1mRKppF7PdDV4PdHb3oLXs07dcYNgsdwZQPUcGtUzpZvY66ljdolUumlHVE94PTFyx4sBEE/xdkq8Us7ryVWaQfWMQfJCQnnDHUpnbsyOw8kkCS0Jko9d7gX/Zzrhq9zljE+EsVeTyl2PWYJlyGGePFV5PYOvM8ezsmPFBaeF9nra2xbeKQitE9/3ydcBxe9T/pMVn8/Ec1oQJHOS0Hlue7bCSWiE/7CcyZhv3J7/5Vs+bs9neFKJ51NJqdQvSu83biOewWleTxmfK5lUwqkd7rE+U1XPetHricUkEFeQqZSaSY/qqM9kryeC5KF6bjMJHXc1UimonsM+JZ0Ojbax4R7qM/vDQn0mxu0JDUFcgsdTN91Z9exLbaaObplwgnyq6hnHWlmovB23q+o5D/GM58++KLAqDVX7Oq0KasfskXAqGQ3WCfCJRnNS9Ywb7ktZfaZuuEP1BCHlMfv6SpbriWajdpvJJyKVGohUWl3n0Xt94+ZMOKPqySP3dUprDVE9x3UmlVA68X090SuonoFwbvWG0nCE+szRmLa6Q+qytxNeT3nBwMtGvOEeNts5UknOXxq9nuOpXs+47b5Lb3s2ateygOy67IVDQekrO9Nm6pBTLosGwxl9mnnlsmwEX3gM+/tkFq8nH64Xnu/h9HpOnpYyr+c08mmeU/5gCYGVScMiwEno/sNJaAR+yP0HphSL8e9/Ptjf8dPIZ26snr9dGfnMVS/a0XogniAuSkx1lKtjeBBGXVpR8pnzesYtdc31xNa7POaKGbOjStNus2ubkYTQB5I7HlJjNIiRShwkjyYjqJ48ZpfmIlE9Q5D89nbYcO9JbSaI5hbqM2WxCH5PVj2D15OrMkN9pm66g8jwokpKvGFtx+xW9Ryb8frEhvscQfL2dEcrhDnvtsXIHiuqnkWvZ87/GRTqXH1mSYe7BMlD/QwkNHo9G7lcTxBOXNdch9czqJ684S5ezxq8ns0lShGv1GhR0l6ntL1Kw7RG3aRGozGJ13MoqifUTiweIUh+C8tFgXDaDneonlsdqc9Eg5FEKEm8kng9QwEAB8ir13NY4vXM+tqlxUiD5M1mO85m6HDn0xnOqXyQKZ/2t21RVax8qXhAXs8i0SwlrUq67Khf75dTcwvKanzuluWpclr4eorPvSgjTiGSk5/Dctf89zv3u7CUfBY+366fozBuryKrZccO498fx8xwEuqYiiIROwxQYriX2wUOmcvw1D8gIlpki0XwYPLtoj8wy/XUGCUmoUEB1TE7lo1kzB4WhcIoXsbmWbh8TvUMG+4xw5MJp6ql0t2OIPlG0qfaKIlB8jWoVb1tiVTi5SLEKw1pzEHyoT5zG17PQn3mdlA9MW5nsilb7rzFXlQ9uSEnqGd4H8solLUZcdRSIc9TR+9Fj+dex+32WJnXU0fqtlKzVuL1hIKci8eKG+4UCSfCyuHvxHUcqYT6TPZ4YsM9qJ7LLVkqmlA9QUKPiNfzSFA921A9z+EN93TlSKZ6ttd5w703rlF/WGOiuYXlL+v1NB3uN4VIJdvhvtMbcgg9CCbXZ3KuZ7bhjvclSF4U0Ug4cQ5BQlnlhLItXs9cdWbM9awOks9vv5edxzKCdSq9nvo5Z/R65kbrk0Qz97kmRvSTvs5F9Xrmv7XZizn9B1TbL69n4fOUn9LJr2lRJvPJeD51E7d3TIeT0AhXQauwIP/+T87rWVgkqk3xfyoRVaUzxieZY6Ca8vcpeD1DmLyO2dXfyWP1qHoar2cIkl/KeThNmxEIqFk4iktI6GsPHk+M25uoz0yGVO/3gtezQ7Ux6jOhem7nVE/ecN8Wr+dwc4uSvi4XmfpMBI9b1TN4PYuqJ7cZwQMaVE8bqYQYINvXbjvcRenUNqO99bbreeDzpufenNfM85n3fZJtLuLlooyEqke30ZBxabXqmdVn5jfcg9dTVU/2eoJwhg13o3oiUglez/r6UaqtyIZ7Gjbcub+9uUIj5HkmNfZ6bnOcUsrZnjehkz3UZ6rqiSD5PjI/O0JCB8MxbaM+E15PqJ4DDZLPNtxBSjFCT0x9ZvR6xjG7XBdzPeOGe5rzetpxe/R42mN7Jp+L6fUsKpzZ9YWvZwpJXjyvZ4EQzuP1zH+K3APMQjzl250/WFvQxaRFGse//OUvp/e85z30qU99itrtNh0/fnzX++Df52WXXUZvfvOb+fYPetCD6A1veAN9zdd8DR0UnIRG4IfciejUX0ILiOzvwPRxuyUu+b85072e9phuQ+f72iVSiZWy2uRyUeb1zELhZcyum+tCOHEdRu62PlNUTyG1VvUEEUWQfIOzPEOkEns9h1KfiSxPtBmF5SImnlA9OVJJvJ4yZh9lJBSEc6vPo3SQTF0u0lxPkNCsPjOoaEH1zHs9DeE0Xk8bq0T75PWMLxZM3mpZxqcQzbzXM3cZvZ5mwz2QTaieOa8njkOVhuqJc7csG+7i9QxB8sbr2ToaVE/2eh6hWnuJ6kfyquc4qJ5oMwLx7MM5oapnqM9EjztI6I2dLNeTvZ1oOAod7p3uiHqD0aTqGc4XXjSARMrHonAmsGTomD0XJC8kVUgoTh6u4xX3iSD54nJR2XktkpPqmKU5vJ4zHtt/r2eRjMpP3Wxez2kkuSpvtPAd1B/+4vc2PmyRKebJ52xezxnH5/mL7DkXDpaP2yu+Dv30C0I8F5WEDgYDeuxjH0sXXnghveUtb5npPr/4i79Ir3vd6+i3f/u36Y53vCO96EUvoosvvpg+85nP0PLyMh0EnIRGOAHdywb5aYf9HT8L+SyontZeoAQzT1QztTNGKpXkelZ5PaFSgrDEMXt4X2OWpBazpK8dXk94C3Nj9uAZBQmtp9SA6jnqU33Q4zicugbJw+uJBSMTqYTRewISygrnNi8Xoaudo5RGps2IVU8TqWQ23JlwYswOEhqUT1U9dbFoaPrai0Hycdx+knmeev6swlkkpVb1VKXT+j5V9eQNd22hYssE8eJQVD1DpFLZhrvWZ2quJyKV0NUuqqdstkP1ZK/n2mrYcBfVsxZVT5BPqJ4tSlqrlGDDfUxMPkdDRCtJiDy8nnHMrqrnwKieXfF6QvXshA13WCLkBUK+zUhyPY3qiSSE6PXMNtxjhJLZateNds31zCueWYZn1XmtzRqzNJfXUwnfInk9S0jwVK9nnuEtmtezyIVPpddzFvK5KHx0kSKaXvKSl/DlFVdcMdPt8W/2Na95Db3whS+kRz/60XzsbW97G5177rn0rne9ix7/+MfTQcBJqOPQgMekU34bxclQybjd3teO20U9U/9nea5n3HrnrfNCkLzGLMVIpUbO6ylEUpTQXKTSRJB8WDQK923WZdTe1vrMgVE9keuJkSmrnn1WPWXMPqAxB8ljwx2EE15PIZyyXNTPvJ7bA1E3UdsIwslez0nVEx3hEiRf9HoKuWTCaRuM9snraRMKdmsxskRUiKZZCrNKKM4tiCa/UBC1Uz2fGjDPMUsx1zNsuKM+EyP4lbZ4PZsYr4cO95Dr2YDqubEuG+68XLQRR++8ZLS8TmN4PestGiFeqdagbkLUG8DrOWaSyfWZ/RG/zyS0I4TzeCdsuA+yDfcOlo36Ixm590A4JVAeOZ/aZpR5PbNIJVE3cb6D6hl8nTHXM1eZqSqonMGyAPndyWfFSP3AvZ7Tiebp8XoWFdYp5HOfvJ65+y+A1zMj4RWfN3+KDhz84nseJTS8+N7c3MwdX1pa4rfTic997nN07bXX0kUXXRSPHT16lO5///vTVVdd5ST04IGf8rNbDbUq4SKhLK9zqtezwv9pyaclm7iFjtbrlfWZWV+7ej3jmD2QSx2rqyKqAfHwdeIxlHBmqqd4PUE42ROqC0y1MddnQvXkzvZYnwmvZ4cjlWyQ/LiHIHlsuGO5aFu8nkw4VfVEridai0KQPJSynaHkd8ZIpRAkH6ozmcyAeJqt9szrGYLkzVhdY5aUqJwKrycIZdW4ne0RRRJqt94LXs8c4QwjdiwVxSWjkOsp4/Wl0OUuuZ4Yr1uvZ0NVT/Z6Lonqic12HrlvBNVzjVVPEPnOUL6HqNGE6olIJVE98xvuN2z3g9dTRu9MPln1lCxPVqZZ9ZQNd04miF5PCZLHkpGQ0NBiZNuM4qKRBsmPS32dxZil3c6r/BuUbvTaQnk9w/MyP3TTMjyz68N7BfJ7WryekajOQD7NC7fD4/UsuU+JRFo75OP4888/P3ccvswXv/jFdDoBAgpA+bTAx3rdQcBJqGOxUCCQ4VDl7SxxsVOeSGbs+N1stqvoURy3s1IWcj3V36kqJ0cp2TF7CJLXhSJdONINd1U9QTg1eqkVN+FDpFKIYGrSmLvbseFe70PpHFKN24wQqTSiFFvtYbko3TnBo/dke4tJqATJhw139XqChHKQPNqMoHpqfWZB9QxElIPk8fE4P2afNm4/mRaj3HkLx3R0XqV6xr72YsxSIVIpklCcx/BCQbbaC6pn8HryhnvbLBxxq1Fbmo1CmxGrn0dW2O+JDffWxkbO60l2wx297fB61ps0auGyQd0RUb83pn6C7vYkqJ5oLpJcT/Z6hkilE90h12fC64mazS7qNHGOQqi8ZnnGPM9wifOfLRcNcxvuVJbrOZHnWSChhcrM3clnmTJobyD/YmfK9cwRvyKpNERu6gj+ALyelb7OsmP5r1lukqN7BXI88Q3Pkc9p9ymSWnvbRfB6TnyPC1/Poszj90pCv/CFL9DGxkY8XqWCPv/5z6dXvvKVUx/zX/7lX+iud70rnSlwEhpx9qqg9nf5gf1Tjyql+SOwh3G7/SWsX1eM5glsxlZnat+3Kp2Z15O4o916PXnhKCwUYQQfl4Z0w916PQtB8jHXk8mqLBrhObW582bMdZmseiYh1xMxOUH1zLyePRp3Okw+ubkIkUpVqieITgfev8KGe4hUirmeGiSfpjxmT4r1mWHhiFW18L1W1dMuoezV65md80zRtMdtc5FdMrJj9tzoPURiWdUzthkVVE+JVMpvuLPqiXO3uszLRVypGTvcj7DfU5aL1OupuZ5tGq8c5VzPUXOFksYyq8g7Q7EyIE5pJ3o9EZ8UFo561apnFxvuHH+V33Dn8zcKG+7s9Rwar2dB9QzLRnj1wM1GE4Qz83pKnWZYPprjfJaOm6f5OsuO5QjfIfB6Fn9PudfzJLyeVeTTTLFoMYDfh405SChuD4CAWhJahec85zn0pCc9aept7nSnO9FecN555/HlddddR7e+9a3jcXx8r3vdiw4KTkIjamcnEVWidoD/zJUQTrt+4pdS4ZgIFIWFIyae8r76AZm4KOHULMiJDnezSBTajTTXMwuS15Yi9Xoi0zNsuMP/yWN2PBa22XGfbMO9mSbUTIfs9eRIpQQEtJ/VZ+5s0hhby/B6YswO1XNTvJ7I8OSlIvZ67oT6zGHocFfCKbmeEqlk6jOD15OXi7CsEqozlWiCLKnSWWwxstvte9lsLw2UD1dYVbO4dKTqaJXXU4/t6vXEBntQP3nbPYTL57yeLWkzkg73VfF9ttrUjLmex7jHnUfu2HDHktGSeD3HxuvZGaXU66c8Xt9EmxGWi3oj2oTXc2g23HeM6rkjxLPXG1If54g33I3XE5vtvBwmY3ReMkpwfSI/KxVez1yIPBRRU58ZSecMHs+5yeecI2v3ehbJ4y7EsMDwDq3XM39z+1H+ytrZsR1/y1vekt9OBbANDyJ65ZVXRtIJr+rHPvYx+tEf/VE6KDgJjTi7CKgqhLUDHbdPIb+7eD3tklFWm1kyZs95PcsIZ+bxzNdnWq/nZK6nNhfh2EohSJ69oCA3YUS/zKonXkEPqZ5IfWYdy0XB68mqJwgnez0Hkus56FHS7VKyk9VnJthwBwnd7lIag+RHMUjebriDbPLCUciFZBLK3e1hw72EcNolIxwDVP20Suis0LYi+zckkkxLNA0ZLfa1V5HQplU9DeGMuZ5F1XMZxFTUT5BQ8XiGDXf1eoY2I6ifzfX1guopXk+QUOR5qtdz1ESu5zINucUIGalj2oLqOYDqKV5PXi4yqudXtkT13AwLR/DfdrsjSsZhwz2cL7QZyXKRej0RqQSvp+R6ylhdcz2zNiMhpAUSOmekUsU/SSvRlUwkTofXc7LSUm7mXs/T6vUsfMIiiay8T/Hrtc914vmb+y7IOH6RcM0119CNN97Il0mScF4ocOc735nW19f5fYztL7/8cvqu7/ou/h4+61nPop//+Z/nXFCNaLrNbW5D3/md33lgX4eT0Ija2UFELbk7oM87TfWUjM7JWKXwEHGkHsft/Pcn83XaTXYhnKJgapRSbcLrKdvuZV5P2XCXjfgYJI9t6XAbUT11uUjV0RCpBNUThAl5nvB3YsM9KJ284d7fYb9eun2CxsMejbsdGsPrORzRCOP2fl/G7Kx6Bq8nSGgPkUrweo7F6wnCidE7b7iPC/WZonZCddPWIg2Qj/WZOl4P7xfrM+dZMCrzemaEM5w/fcFgjjUqloyUlMbRO3t1Kfo8a3N4PbHhHjvcjeopns8VasL3WfR6rm0Qaa4nAuWX1rm7HV7PYWs1qJ5Evd6Yv8cn1OvZGwbVc0w3hA13VT37Q2y7y4Z7L2y4i9czqJ7xvAXVEyo17Bgcr6T1mVKpqctE+frMbNxuF4rmXS4qnlNLFEtVz+L4unJUHv71TjlW6vU0BDL/PCoed5+8nrMTTT026fXMP0Xzuy0+bPH7mSefs3k9s1tOHblP8sDdlVj7uYrPKfecSxTO4ve48PWYs5I9TvEbtEBYpIimn/u5n+O8T8XXf/3X8+Vf/dVf0UMe8hB+/+qrr6YTJ07E2zz3uc+lnZ0detrTnsZh9Q9+8IPpve9974FlhAJOQs8ynPb8zz16PePtc8qZIZiGhCoxVTVTiUwkoYVIJfV6RtWTlUt7TNRMHbPrhjsIJy5BNkXhtJ5Q2XCHBxQez0bSozoajMyGe6zP5DG7Bslnqudoa8ssFw0p6fZZ9cR4fbjdl4UjKGWseqasejLZDFFLPF7nBRbJ8eQxeyqRSkmBcHJ9pgbJ45un2+57GLeH0xwJaL3sxUNFhidVeT2VcFqvJ5RO9XoGBdR6PfX9sjajCa+naTNi1XNtUvXUDvfM67lMI3g9x2gxku+veD0RJA/COaQ+2ow6Q9pEXSa8nqjPDMQTSugojNxZ6QyqJxRQPm9hyQiqBm+4DwflXk/8x6pnIdfTbLtnCmh1X/ss5zT7x1gSLl/m9TTXTWxGh435PXs951k02ovXM37evP9zklTus9cz96mL3zP7NRaPl3y+3KG84hC/7jxvL3y+MvI5jcBOIayV5HOSeE48x+LnoMWATInmj2g6Fbjiiit2zQjNph4CnKuXvvSl/LYocBJ6NsAQudP5z9mOyucjn9mxotczLq4Y1VN9nezxNJvRGrOk3k/1ei6FpaGMhAY1MyiaunCky0W64c7+T83wjKonrpdRcX08pMawL5FKWC5CpBKC5KGAGsKZ9jqBhI64PlO8noFw4thWV3I9oXruhPrM7YF4Pfuidmaqp4xrxSuIpp1xrj5TvJ5Za5EuGcEdqBGQuA7YC/G0Hs9p4/Za4fa2r90qotVezyrVMxDOmOsJjyeyPKtVT+5zb7XE69mG6mm8nrkN94LqOUypC6/nKKieaDPqDrnHnQmnyfXcDF7P45zrmTLxHIBwYrnI5noGtRrkU9qMlHCGXM+w1Y5jtjZTR/H5XE8zbp9juajsvFaHy883xi4dhecIXMHXGUmgeSbRu1ny+XMkr0g+7eMpSbWPWfG8DPEtHiuSq5PxehZH87uSz9Po9Yxf28TXVHH7is+Vv1vZwfzXW/54p/XP1qFpTDpT4CQ04sz9YbGE4FR+kjyRrM1MTO2x7EV39otOSWZtIlTe1mfaDndRKnGMVU3N8AzLRTbXU7I5817PLEhelNDo6wyRSiBIIKJoMapB9RwF4slezx32eqLBiEZ9QzglSF5UTwmST+OYHRvug9DhjiD5fiFIPl+fCQ+oBMmHOkatzzRjdlufqSP4sSWeexy320WicNrlWAnRtON1Hb/bmKWGfTFhSehevJ7LjbBolG8z4vpM5HoerfB6tpeotha8nlA9lzfihjsrn1A9B2MaRq9nUD15w1063DdLvJ7bweuJkXuSazMSBRQkFC8ekGiA93m5iL2eQjiFfEqbUdx0L1U6Kzrc5zynZUSuSHgqiWZuLD7DMUM4KlXNGbye+edcOJZTb+cjzgfr9cx9VTnebM9F5Rg+u8nU5zPxnGa63168nvkrJkl1CfFcEMJZBieh+w8noRH4yT+zfmB0fM3vn7JPYolIba7AeXtMr6pXjNtrlnCGY+oBbeiYPfg6i17PZjHXM26uy/u8zc5ez9DhjtGuqc+Mqify3Vj1TFnllBYjbLjLchENe1KfGbyeHKkEErqNbfchjbZMkDy8nohZCqpnwkHyg/yGu1U9tT4z+D05UimM3dXvyapnUD/jNrsZvQMarTTPklH24mIyVolKFM5chmeBnE54PXXJaBevJ3s8lXCiw70q11PbjDhIviLXU72eGzePbUbR69lciV7PLryeQfWEwnzcbLh/ZUdVzwHHKvH7oc0IxBPd7UkIlWebBF5UcJsRVGtZOFKFUzbc4fVMTIe7tBjpuD1utofRu5xGHbfvXfWM57c4zrbX8nmylZolo/Icyas4liOSFcd283pWPG5Rcc2RzxJSOb/XM/vaS8fT++z1LH4YCWAVkZzkgeVK7OQDnzavZ+l9c88h/zns17goi0lOQvcfTkLPNASFUD841eSzUvU01+strMoZrzdkuThuty1Gk7mesjQkqmfm9dRIJW02Km642yB5SziZhKIfXMfxceFI+sbbtaB6cpYnguT7EiSfq88E4Twho3fELIX6TO5uH2LMrstFqnqiuUhUT/F6itrJQfLwBoalo9gBjssQq2TbjJSE2vrM8T6N23PEMxzUgPgyX6cln5aMnozXM1M9JVIJI3iOWWrWqa1ezxXdcM863FtW9dw4J6qe2mY04fVMM6/n1mDECig23G/QIHmM3tXruS1eTywbbYfu9h423MMLBlGpZeSeeT2FTDLhtB3uqY7eVenE7QwJzS0Y2VzPk0M+nqhMlSqr1Jzi9TQ/OEJaCwRJjxUJrFw5QTSLZDVPGi35LBDP3OPlnlTJMUOwc0SzTIHdhXzGT1NCPkumP/ErmiBocxDJecnqzAR2mlJaTT5z342J51hBykuuil9H5fUHgwSWGZ08zHh7x3Q4CT3DoP/YT+W/2bKRun0CE8tPOXKZPcfiaH3yWD5SSRqLzOi9sOFuvZ4SqaQ97CCXMmavhzG7Ripxm1Go18xtuEP1rKfUAPkcDag+7BKN0eEOf+dAvJ5dDZKH6tmlcbfL77OvMxckH3I9t6F6jlj1HOwMJoPktQ2nP6J0hBB52ZbGrzE7bs/Uzqwy07YYZR3u85HP+DejJCR62rh9v72estk+pcN9OXg9Q4sRX64tZ6rnsaPi9Qxjdmy2s+rZsm1GLRo2V7nNiL2ePUkROB5UzxMlqic23OH3HIzU6zmmPm4fOtx5zB7OmW62jxCzhBcKQ9RnDrEuGzfcVQWlXXM9Z+trn/0cl/kzs1vg+z+VIO712KxezylEs/g1zEQ0i7FREx7R+b2e5hrzqcvUvRnIZwmRLH56uW+B6BceeJLQzeH1tJ+j9D7ld8jOVfFg/ustf7z8c80er3j/xcEibcefKXASGnG4f1imEsOTemBLTqrpbdnnt8eyKVjmAbTLRfrYma8zv1xUJKG4zILkdUEIy0X57nZROOu8tb4cVE8moZGsyueSTXipz2zXEq7PrA2s6ilVmoQGo2FYLgL5RJA8vJ79Xhiz74Qxe4eSHsbsAxMkj/pMqclErqfUZwYSyqonSAll9ZnweoaFotIgeXxDzda7fJgRz72ST0sgLRktNhfFSCyTCWpJaN0Qz6hq16u9nlA09X3ZcJcud871ZBIavJ5rts1ojRpteD3XguqJDndVPTeC6rlE6epRzvfMeT2hRI/HvOG+bbyePFqH6tkdcre7eD0T2mKvZ7bhLuN29XoWVM+RbLgz4QyXPH4PeZ4crQSSiVE7+zrLYpYKHk9ToTnxD22mc1zijTSPkR+5TzuWJ5rZglAJuVWSN20UPpV8lns97c9t6fa+fe6z+FkN+7HEKfs2zUAM483yZC1/n+lez8l3Z/B6zqxgVtyv4j7Z/XYZxxe/xl2mY2VP2pwie2GuXww2it/JdR/H7yuchEbgh/yQ/cAYBXHf/4ma3ztl5NZOcoq+TuvnjJvt8TGVeGZeTiWjZHM9baRSiddTMjzVr5nleqqaaSOVQDS1UjNuwodIJb4vpdSihBo0pjrXZ3bE68m5ngOifpfrM0FCky2pz0x7CJKXSKXh5jaN+gOJVGKvJyKVejJ6B+GE2snLReWqJzbceVsalyQb7qxuhl9iQjKz7XaN/RiXqJ5znuLc+RMimZHKIikt83ra6KWpXs/w4mGq6tkq2XBn1bMpG+5QPbFctArVE7mebWrxhnub6usbsuHOHe43Z89nulSy4W68nlA9hxVeT1U9+1b1hIId2ox0uWhC9eSFo+GE6pnleuJ9zibIb7ezrzMQT3Mu1cObHcj7Pye8jiXnOJ7UiZglVRjtb5AyxdKMrM3jZccKiqX55VFUMeWpZoR1Lg9piRKajavnJZr5z5G/3x69noUP8jfLiFbp8TJipp+z5PHLyNxU8lkaBj856s/drygq5P9XQsirHmyG5ztNDV4g4MVrba7azlP6dM4IOAmNODwENPt9fOrIZ6XqaciHfT5UGNPqL7jKFiP1B9pFoxAkr8dBEmvq4dS6zMI2e9HrietRk8lj9rhwlKmeduGoQQm1aMCqZz3UZ8LbqV5P1GcSlov6mddztL1JaQiS59pMZHhu7bDPM7FB8kH1jF5PEM5e5vXUDvdcfWYgmmVtRjp6j0Hyexy3F/+wTvN6WjXUHmsUfZ9zez1BQAMRDV5PVj+xcITIJZyztXbm9Qyqp3o9oXi21ldZ7WwcvbnJ9bSqZ+hwb63EXE9YGlT17BvV86bOkJVP6XAfUH+YcMRSVD2hVocGo6zNSDvc8SICx7L6TFY8x7bD3UQqmeB42XgPHk9LLmfI98x7FEvIwlRf56wRRIU8zLJjkYwWCNyEChmO7UZWS4/Zn9kicS4ZwUfyaX2dZceKn2MfvJ6FExBV0fynmE4A4/d1d7JatjQUn1sZkct9L0ruVjKOz6mopeRzCikvI9f22CEhn44zlIR+6EMfole96lX0iU98gr70pS/RO9/5zlx9FH5ZX3bZZfTmN7+Z0/0f9KAH0Rve8AaunNp/1A4HEY2/g/fvn6mZiFU/7p69nhkJ1YglKJyihAopZOISxuK4LqqeqlyCjJgNdyGSQfXkIHmtzwyqZ1A4J7ye/DlSaqUjauCPf6L1maJ6YuyesuppguT74vVk8pmLVLKqJ5aLsHCUqZ66ZKRENNV8yDBqZ/IZvZ5CODlKKXS4M9k0LUb64lvJ6FznN57n7OxZkqm3sS8ibJSS/u3Tc62VmXJs9g73SdUTo/c6tVbChvtyixqqesZcz2VuM2q0WtQ6eiTbcAfpZK9naDOC13P5CJPPYUs63LsJUaeH73VKxxF3laR0Uw/LRdWq5wmEy6vq2Q+5ntxqJMthsc0oqJ5QOIV06oZ7IJ5xwz0EycdcT3yHwzmMo3fK53zucoaVJFWTzxJipveJf+Snk0/9ebEyVvy8ucfPk78JFTL+wpoct+cf0xKzIknO/YLKyGeJ1zM36s89pyJJLj53M9HZi9czd8cqolWtYsbnVEVWaQ7yWfJ17M3rmftshc9R8kVMIZ8TFoUSclpJPhdsO97H8WcQCUV91D3veU/6oR/6Ibrkkksmrv/FX/xFet3rXsfVVNpzevHFF9NnPvOZU1Aztdg/LPL7dR+ppyUgJY87fdxuRrj2eUUVtTaR4WnH7qyahRpNvQ3UTJAU8WqG7XXN9YyRSsj1BLmUlqJcpFKp6qm3I24vao6lPlOC5DF27xP1xeuZ7pygcb8npDOQ0NHmJh/jDM8YqQSv54BH7cjz1L72zOuZBckzYQlElJuL8L5us2P7WUmoNhcVSKj1de4H+bQvFtTDmamf4VjR62nIpno9dczOLyCKXk8onuFcsr+TF48C4Qx5njFcXlXP1TaP6aF6osedSSg63Nstaq6tUhOqZ6tNjaPi9US4fG39GBE63IPXM2mt0ghvvOE+DhvuRvUMbUY3dQasenKl5nafLzc7A1Y+kxCvxNaJuOEu8Uo4Bp+neD2t6qkb7lmup5BSbTEySmdVhzuf293PbtloO3euw5Z6mbIkxMi85IhkrEwtLBLNwnUTSmgVGS0nn/mln5Jj9j7TvJ57OjadUGZPoYxgFYhU8fuWvZs99sT3O/+w2ffUPKY+18Ln13dKRN8JIln5deTuV0E+zQPMRT5LiGXueJnqWf40Cj+P5aT9IOAk9AwjoY94xCP4rQz4Bf2a17yGXvjCF9KjH/1oPva2t72Nzj33XHrXu95Fj3/84+lswKkkn1O9noUWI3vMPie7WFQct7MqFsbsMmLPOtw1WqnM6xlJqBm9S1VmCJJn1RMEVG6XeT1NrifuSyk1x32qjxKzXDQyqqcGyRvVs9ej0bZEKmHczoSzN+DN9nQUguSrvJ7DLEg+EhdWPbP6TI5UMvWZHLdkqjLT4sdznl4ll5Y62L83Vb5Ova+SUW2eUpK6q9eTlc4weg8KaAyX1w137m6XmKXmUiv4PmXRCPeJbUac67nOqmfDej2P3kK8nqHNiEfubfF8duH17KPDPc1yPbsjOt4XwvkVEM4SrydeGAyC6ikd7lmuJ0bx/IICLUbs7xxmLUZh4UgVznyuZyCftrNdiaaNW5r1n2z8K1xGGjJSOLEVrj8LE6yl6H8sZG5O9X+WHCuqnvZn0JDW/DJS+bFKMj1LXBS/O3msVPU0z9t8GyqjlArf0tz3olRwzn1fCiQy97E9rdNiiSrIZ5XXs+IPxnQV1zzfwnMojuTnIZ+lqqe9f/mTqfwaDhJOQs8iT+jnPvc5uvbaa+miiy6Kx44ePUr3v//96aqrrjoFJBQ/8enCZX3uG/2MKmXFYxYICR+aCJDPfumBOOauC0oZrlSFTHM9Ve1UUgpyWfR6KuGMqqcZqccNdxsk35QReyScWp+pqif8nSZSSVTPbSah7O9EpFJPIpVY9URve/R6hjE7guQxekfl4nY/NBdB9RR1M9twl9E73iTPU5RO3nAv5Hmq6gnyCdhopb22GGVEM08+9WfIKpz6M2AXj2xjUa1iHJ/zekbiqeTTXEbVE0RTvJ4goDKGh9czEM9VeD2FfLbXpcO9dWSVWrzh3qbGhnS4s+p55JhUaa4coxT5nu1VVj6HaY12rNdzOA6q54B6ocMd2Z48et8Kqmd3QFvdgtcTo/qw2Z5tuI8oQXuRthnZDncmoSbXE2Q0ndxwz8bueY/nrPQzowR59TMjUGXk0xLPeeOTatMJrJLV4sg9brBb0qW3s4s9hmhOfI7o2anOA931MYrHCt/JAgGbIIcVJG/ytkq4c9+awnOaJFHlXs/C55jp85SMrsMTLCeFebV14musIp/Fr8k+hypimT9tpbcpJZf2790Ckk+FRzSdRSQUBBSA8mmBj/W6MvT7fX5TbG5uzvgZF+SHxb4qPs25nvb3lB3BW/KCW+j2upJRJaI6eo9eT/g/Q16nej3jmL2eJ5ysigb/p6ieuuEukUqZ6qmEU1VPUUDr6ZgaSZ9qw6GM2nnRaETUQ32mbLOPd7BcNOJLRCol3S4NTZA8b7gjUok73LP6TGyws+oJksnLRRKpxG1GUfUEsQyqp8n1jEHyJsNTR/LFMfvJ1mfqHyB9v6hw2mORXBoyql5Pe/ui1xNXYuGIR/mmwx1kUi7rBdVTFo+YkOLcri9To9lkn6dsuKNSUzrcG2tHeMudY5aOItdzmWh5ndKVI5TWWzRa2hDVM4HqWeN4pRO9hBVmjNjh++wHr2dO9RwmdCPC5XFO+wn12eMZVM/g9cSWe2q9nqMBJap2BvVz11xPM26P5HOPbUalW+W7ks/6/Mf2PC7PSGOefNpIJV2mqZcs6tSrv555vKvFdqQcmazNpkwa/pojzGW3zX08qYqWks8SAlj9Ocx9ig9d9jt8GnmbaiEwX0/Z49X2Tj5LMW2aN0W5las1u/bgAQI6z3a8K6GHmITuFZdffjm95CUvocOIqWRx5gexRHLy18zsXs/8VjtFwhkIa70s1zMQzrCFrkSzph7NMGbPIpUCkcSYPSiiOnrH/TRIXo8J4Qyj97qqnrY+s8Njdmy4C/lEc5GM2ZWESpD8No17fRr1SlRPEE71eqIBB17PEKkE1TN6PTkXMtRnsuIZlouC11NbjXTpSNXNkx236zmyv+9V2dTrmSAW8jz19rUy1bNAQtHpPpPXUxeOGpOqJ5PP1RY1eMO9HTrc0WK0yrmeGL3D64l4pej1RLi8qp6rN+PLpL0mbynRTlKjUVLL53p2hnzJJLQ3pO4goS9v9ag3GNNWd0hb2uHOnk/ZcGfVM+f1xDkNXk/N9QwLR5znCUVUiWdcNDKXSjTn9HiWnt9i+9Dk2Z8cu5cpltMC55Ws6Q/PBIGbQj4nZK6COlpxLL+gVOL/zD2HHBPKP6/cpKbq65kklAVeWjLGtyQ/T9aKy5hztRRNfJrC8yuQ2BJRe/KFSNXXYe+T+6KK96vym5aTz2pyuXu+Zxk3nod8Vt/5YCATj9n/bUfft+PwkdDzzjuPL6+77jq69a1vHY/j43vd616V93vBC15Al156aU4JPf/88+mMz/o8Ca+nHbdbEqp5nnFsW+hw10tVPqPXM9ZnZpWa7UAkQUSjh1ObizhIXkfvsuEex+y4Tskq+z5TqqUp1Uc9qg+GnONZR54n/Hjdbe5vZ29nGLNzg1G/SwlIJ1RPqGFoM+phzK6qp0YqjcTr2VHVM8kilVT1VAIaPJ5pRX1mttWeLRwpUdlTkHw4YfZj21hUunxUOMbkciavJ77vomjFMTvOYyCfonQG1RP+zxCvBJLKqicroMHrGS65zQgLR0fXeeGovnaEGutHotcTlwTFE29YNFqSTffuuE7dIVTPlDZNhzveUKn5lW2ongndtDNk5RNeT1E9dcPddLjDTjEIqqfxemqbkaieoc0IEUuo2aQQLh8IJxNRnIC4eCRqJ5/avfy7jeez/F9/nijOOtouO1YkeTnmtUtuZmHJJ5LTsrijQri8OVabuiRVRT6nHTtJ8llF8iqIWtkYvVT1zH2f8k+gkqzSLATWnq+Ju1QTa32uE3eY8hxKVc/syonXQdOun3jc6r90VV/3onBRjNfnGbH7OP4Qk1Bsw4OIXnnllZF0glB+7GMfox/90R+tvN/S0hK/LToyoWB/yGeZ6mmvt81FRSKqZEUIcZ6EZhvu2ehdI5VwS/V0YlIrhFPG7bp0FJeL4AeM5FIzPLMg+RWNVMLSShjRg3wyga2l1KyNub2o0ZP6TFE9kevZlRYj3nCXbXYloePhkDM8mYBym5GonlyficabvtRnMuHsWq9nIJwcJA+lTEa24BsgQzpOR54nq55xw910t+u4vdBiNOepzc6b+QNZRjxzLUZ6XsPj2EB59u0Wbl/0ekp7kYxspbe90HAEpRPnkDfchZDykhFfwuvZjpWa3Gq0vsp+zzpvuB+jelA94fWsIddz/WaUtpZo3F7jhaNRWqPOuE6jEVTPMe0MR+z1/IpVPUOu55c3e9HreaIDH+eYujiX2uHOHk8Nl6/2emrMksQrZQtHQj61t92M12N/9H7VaBbJG+VIXjaWrk8qVhXHcmPpPQTD5xeNCrefOJb9cOafu4lMKskYLV4vF/ZzFI5NEKc825pY4qwgbVXkc0L1NE81fodKmFE1+TQEcBfymam9Ew9fIPEl9yl7fPu5J66YonqWPJYcsmO2SeJZ8TRmVz2rv5SFAb9AnUPddCV0wUno9vY2ffazn80tI33qU5+ic845h25/+9vTs571LPr5n/95zgXViKbb3OY2uSzRQwVDGE+afBoCWfwccTRriWe40goLmdczi1BSwikkRsbumutpl4zU66lkM4tUkstsS138nxqfpIRTcj1RpxnG8Ky+EY/lEamEzvZWbcxeT/S2s88TC0YhSJ5729FcFILkWfXc2ZL6zF5fRu6a6xlVT9RnJvlIJaievHAkQfJMSDmInDiiByoaLxfpmB1EpkA4eeGoSD732esZl4x2UTzt7WK4fHi8sl73XK6n9XqGcHm76S5B8zJ6x1ISIpaQ8cleTx63Y/QO1VNjlkT1bKyv85Y7j9wRLt9eptrKBtHqhiwarRylcaNNvXGdeqN6pnqOU870xJgd5JO9nsMx3bgz4Df1ekL9hOqJN4zZtcudN9yj1xNKZypeT83zLOlwz9qMwpg9+j41UL5wNrOE+XCR2leYc43eM0JqiVdkTDMemyRxSkYiSeT3CyqmUVtzT6iSaFqCGn+75I7V9iVSKf8888/FcJ+TDpffhXyWqKrFO5QqpcWbVm7TTyGfUyZbJWywlFxOfby8AD79+c5DPu3fuTJSWyDQlf9iFsgTyskX84zjXQldbBL68Y9/nB760IfGj3WM/sQnPpGuuOIKeu5zn8tZok972tM4rP7BD34wvfe97z0FGaEAfshP7Q+MEr6T/eekhDH32NO8nib3UX8xMjmJvs+MhII4CmERAqob7rgdCKR6QOHZlC73bPQuVZoSs4QxO8bz6vW0QfJQQG2kEhTSJat6kqieqM/kDXdEKiV9IZ2oz4yRSh2OVErwfoxUgtdTcz1tfSaWizB2TSMJxYJRzPWEUgbVE9dj0z2M2Yu5nrlxuyGh+zluj8dK1MwyQmq32XNNRkWvp0kwUK+njtrz4fLZtjsTz3Cp5DMuHC212e/J8Urs7xSvJ+o1kevZ3DgaKjURLn+MQ+VrRyRcfoxKzeUjlFCdummDRkmddoYJ7QxGnOf5laLXk1XPPns+T3Sgeg5plIypi3MJOwUU7FClyZcFryeWjKRGUyo1s1B5aS2KpDMuHFn1s+Dx1HD5eL71faNYTT3fFV7BOcbSU9XCsmP8M5BzDheO2fvUZyaaZcdqe12Syj2n4jH7L8N8n4sEqOp3Y5XqmP/SzWPn3iklUuWexaqYpQoyFp5bbVbl0PweL7kq/7lyn6Pk53LK11b8OiY/3RTyuJ/kczG4p+NMJaEPechDpsrV+Ef+0pe+lN9OPU4dAS2OwOe7syUlk49hiaYlL3mvZ9bNXqV+xtE752tqg5EQF6ieeBxVOOHr5OWiMG7nY7V8pBJvsyNSqTkZJA/Cqeon+0RpTC0acX1mbaCqZz90t48oheqJ5SKM2UOuZ7J1giOWOMNzc2ciSH64A9UzRCr1M69nLlIJW9FhTDvCVjvXZ8qiUWpqNLWvHce4w72kPnNfguTN+Y5vhmjyOS0sFcXrzQuLXOWm9XoGwpn3epqFoxAoj+s04zN6PZcaoV4T4fJQOrH9Hjbc2esp4fKNtTVqstcTo/fg9VzdoNraUVY9E45ZWqIBNamfNo3qmQTVM3g9d0BCE1E91ffJlZpj6kIZxYIYNty7dsNdyKeoniChA7ZkaK6nKp0as8Qh8ziLMVaJsnilioilHOEs/jud8hczT2ryo/dw5/I4pDmJZqbK1WZeGsqN6oujf0sozLHsNoXnmntVFX/5Fcbc80RI2QebJJS1XdXCCm9lCfkqUxfLTmnp6LgyXH7KcytVJKtZWdWizmw+1slvQhWxjI9Xpnra5z8n+bR3riaexZ+txYJ7Qs8iT+jpB37i08XJ+tzF62mJpn6c25q2lZlKZkyGp5ISXOpykV04AoGMy0VhfB5zPcNmO+7PXk/1cIYMT4zZtVZTKzWZcDbshjvqMxNqoMFII5XY67nDmZ6iembLRUxAEau0vUUpCOfmDvs8mYTmVE9stMPrCcIpY3aoYfB7xuUiEBiQ0BAkz8tFYczOXs+gejLhNNmegF0yUiWU9sHrWap6Tjmmj6FkVL2eNtcztlSFogAQTBBLu+EuPe4yftdxu1RqhtE7ajT5UsLlMXpvq+q5umzC5TeovtSOG+7c575xc6L2CqVL65RA9aw1qF9boqQG1XMcVc8bupnqKbmeY9lwH445UB4xS8NRQp0d2XRn1XMg5FMrNaF6joYFrydIqIbL86Z7Vp/JZy7ke0YSCthNd5vrmc4fqaTnN7KBCfI0fcxu2cLkqHoXBTH3itSO4acQv0iCCuTTPPecf3PaYlSRrMbnTDM+B/u49vtlv3/hGRWYZfY9L3zL7O/jOclnuR/SeGALX5Y8Rtnv7WpSXH5gUrWdz8daQnR3IZ/lr6UKX+vE853P81lyg9xzWFTwa9TxfLd3TIeT0Ij9IaD2b81eB+9MNEpeJUsbTva4u3k9NTA+HjN97fq+KqE4Zvvac2P2GKmUXy7C48PfidvqmB1CW1RCg3rK+Z9KalOongOqjaF6SnMRh8mz6hmWiwYhUil4PUE8pT4zLBcFryeTUETu7IRIpR14P7HNXhKpBK8nOtzHKW9YS5B8RjhV9dTxe9xsN/meeyWeGdHMftFmL1DKx+3xhYM5JrFLtYnrrdczTzzD6D0sGWULRzJ6jwtHYfkI0UmqfurykVRqNqixbCo1sWSESs31NW424krNjZtTbWmZFU+t1ByjUrO5RMP6Eg0bSzQcE1dpDpIRtxpxh/sooet3Bjxuv6kzZOUT4fI3hHD5qHqGbXctBIgpBQPx9JZ5PXXZKO/11A73tDB2x1mwiqdRQKf+W7V/tYsEdA/kM6cEybHs4fcaQm+e20REUnymk8+hgnwWFdvSY/brn/p1zUA+K8hhKckr3siQuBzBKVH5it/Gic8xE/ksIWMFdW+SyFXdp/wOZV/jJKkuIZ/Fz2v+jlT/qdpl0738gc1zyf+im/JQsz3OAcMXk/YfTkIj8EO+xx+Y3Mh87+TzZLyeNTt6Dxmexb529XxqrifIY60iSF5JqM31tBvuWX0mvJ5CQtFipBvurYn6zCE1oEYlyPWE11PqMxGpRIMej9ljrifG7CCdmxi92zE7VM9uVD3RZMTb7KY+E4onezuDQha9noF8gmiCcOoyUczzDCqnRi1ZXycTmvl/JCbOW3FMbn/3W2JaluFp71sknA1tsMLtdcPdej0L4fL5XncNlw+qJ87rUpOVT+51D9FKyPlk1bPVovaxI9Rg1XNDGo3QbIRw+fayVGrird6iQWuVxrUmdUYp7XQT6iepKJ1QPXuienahem72mIRyw9HOgD252+ESSuegV/R6JpnXE4p5lddzPMovGvHJLFM/p4zZdzvJpepngWzpjSPxmzw2sTWey8a0P1HV5DMSYvt5a7uRz/yxvBJqvh6o6IXPP1OvexVZjK+g7e+04vdRn/cuj1dChrKHi99p/dYXH63kW7zLMk7J48yyPDT5GCV/J3ZVcs35th9W/d2p+PEpI92lpLwMVc99VtJtvqBZuOWiEFDAx/H7DyehEXv/YbGkYu776t+N4q8AQzQtwZ3q9bSRSoUO94n6zLDFjvuofzN6PWOuZ70QqZQ1F2mQvFRqwncoJFQXjkBC6+MRNRKreqrXc1uIAvydvQ7neMb6TPS2Y9kojtkRHt/lZSOOVNruUYq+7x14PZNcfSa3GYVIJV48Cg1GIKDcZmT72gOx1A53zfU86frMwpg9nmNzzC4Q6TFVOPn8VlRqzuT1DMSTx+xxw70QLh+zPkFAhXQyCV2VSs3mcgiXb0L1DON29LofWZNFo41zOGYJimf9yM2IWhIuD9Uzaa3QsLVKozHR9hD+2oS2oHr2oXqOS1VPLBzhstMdUQcvLEKfOy6x4Y6UArZW8AjejNkRLs/qZ1Lu9dQOd63ULCie6gOd/9+sUfiqyOckS6kgmlOO5T6eo9c99xzNc86Rz/zzzD93JXX2en2gPfa6VxybIJ8lo/d4vOq+9u4FppcTmifvXE0+w8OGXbNKUjaVfM6zcFT19RSe/MS3q5xhTief5vgE7Z9KGis+V/Fz7vo4M/hGF4x8Knw7fv/hJDRCf+XMcY/4O3p+Air3Lf6Cz96fzeuZRSpZEtos5noaElrp9QyEEypmI6qema9T6zP5tuE+QjiVhOJ9EKiUGuM+1YejEKkEr2eoz2SvpwmSV9Wz1xPyqfWZGLP30dfepZRzPaF6SntRtlwUVM8weucMSOR8hlE7j9k119NUZaamw53fx/fUhMufzLhdf7nWKoinvc4Szaq+9khWw8jd+kKrvJ5VC0ccNh9G79zrHryeonri/Xqo0UTY/FI+XH5Jw+U3qNZapvoxWTjiYPmVoxwqP8K2e6PNqmenB9U5pZt43J6pnuz13JYN95s6gxgqv7UzoMEwyVRPLBxFr6eonohQgjrOxBO5nqZK0+Z6lnW4q/9zVn/n1BOdl55mGL1neZkztRlVHZv43BWLTBNELU+Y8+TTLhwVFFr7NcSvrUBWI9mo7SFAP/8ZiiQzT5QqiGYpkZy8fe4XrPlyCvcoOV7+O7pwr9zn0c9dePgJ8jfxOSY+b/4TTnLoKiZbxhXN9zU7bZN3rOKFFedh4vnusnA07XuwyMQzhzlJaMzsc1TCSWjEjD8skSDIB3P9k5l2X0tMjBpge921WUnH7ZZ8xr523XA3Y/Yqr2dWnylEktXO6PUsBMmHTfi4hKQd7rE+c0SNYajPRK5nrM8MkUpQPfsdzvHUDffh5hYl3aB6bsPrmWSq58DUZyKOp6/LRap6BnISNqPxb30IAhp8nZnXM2stssRTfZ66cLTn7fbCH6oqNbN4TH8OYm5nSc2mLhwxCbXq9jSvp5JQJZwmcF7C5TPyKb3uqnoiZmklVmq2NtZ49N7YkHD52vpRarDquUTp2jkxXD5BuDzVaGdUo+Eopa3BmDbR4Q7VsyPRSiCcN4SMz+vZ65nQVmdIW50Bv2jod7JcT6nUVK+n5nqCcCZh4SiontbraRaORO3UTXfbZnQS5FP/7ZZUama+R/tH2CiIOSmujIztnpcpJGWydShHAmvTiJ/+8c8WjuL/8cskRzbldrVpRLPiWE6Vq1R+zTd0V0I5qUxOvW3u40kiV0kyy36JVxDceJ/izctyLKcRr6kWAnO/iccrUXX18aruUPzxK7lz1WPKfav/ylV+/2b4Pk48TvXTm/45TiPw9wKNffPc3jEdTkLnhJKOef5N2Ola2UgpEpMKr2eM4jHqpyUlgCqconaGDvcQp4TrNFJJ8zslIinrZteoJVkuylRPGblr61GIVMKGez2onqjPHA55uaiuQfK9kvrMQEITDZLnvvZM9ZT6TKie+FhVTxm/jtDhDqLJ9ZniD+TFFIxrg9qp/k7daNcgeSWhqSWeJ9FiVAySz85r/mdDl8hUyVRVs7hUFHM9g7dTVVLaxeuZkdAwem/K9XbhKG67B88nk1Acg4UiEM/mqolZ0oWjtXVqHDkizUaIWVpCpeYGUSFmCeHy3RAuf7wHz6dUaorqmdB1QfXE2P0GqJ7wfbLqKUrnQMPl+VIXjkTZHMHrmWSqp3S4Dyu9nqKCZvFKk6RTP55cLJja115mlcmuiH/9i8fy5LP8mB27l2djFnI9431LyKcdq9vnNaGOTh6rVS4XFY+V3d96V8uOxc+Q+0U4jVCWLwOVsK/iucm+NYXnuzuRzJ+/MtK0y/JQKU/aPZh+EpPixMR9i49X+liTzU4TX/FuI/OppLH0EQsfzDp2n3Zl+d/Ng4J3x+8/nIRG4Id8WmbpSZDPsj9kZgN+Lq9nUDjzlZrZmF2721X1VIWz3Wiw6JFFKgWSacfsZuFIet0lUil2vUP1xPMbY7moGyKVOpnq2d3ixaOx9XoizxPxOdvblHQlSB6h8qp6cn0mRyoN2PfHXs8QJM9jdvV6hvYibsAJWZ5cl6l5nqbNyPo6dfQuH4aYpXl+LAovHvR3fhnxZFKp59ISzcIxyfrM3tfb2IUjPfdVXk8mqTFmSZeQAuHksHkQznrM+JStd8QstaXhKBBPXIJ81loas4RKzQ32emYxS8sSLr+yweHyHaS6hnD57UHwenbg9RzTTd0B3QgFdJDQdVg4GiS02RnSJlTP0Zh63UK4fPR6olKzLx5PjN7DJbcZWa9nyEgp63CX85tFK8Ut972ooLmGnPJczyK5KyVyNiMzRz6LJNV83gJ7mCCScXRdJJ8F0mcfY5ded/v5c8+56piS94lvW/HYJJFVQjr5LS0hmaX3zX9tOf5rnnMZb8mpj2WkcheyGm9n3pn4OqrYXQUBLSN0+W9/+XMo/Rp2W6o6mYWjAoneK4HNbjaN5S4O8bRwT+j+w0nofmd9mledxZil7G9JXvksxijt7vWUZiImnFqfGXyd3OFeHLObIPmlkuUiHr2jCSfn9Qy5ntxiNGbVs45xOxaN8IbNdng9u9tEiFTChruqnuhtZ68nIpXg9UyySCWjenKkki4XmSB5JqFYMOLebxm387KRWSrSNiMloRwkb4LjY6zSHhaMzGnM/cHMEc8pFZp8TvWFhtlmt7dRpVQXjjTBgA+HFxZKMNXjyfYMXS7imKVs9K6EVGOWuGYzBM230GqEnw/udV9mgtreUNUTve6IWVqixtFzqLa0QjWEy2P0jkrNVaieyzSotTjjEwtHCJfvI2apN6Qbe+r1lIUjqJ5f2e5LpeaWLB5JpSYUzVQu8WKCKzXh5cV5DmP2IYhqCJWPnk/r9QxZnyZcfnLcbqOXpp3gEq+iOfml/krLUuJyxexxS/l2IvkpmVD97H1zMlfZMX3o4pi9hJCGj+X98NInpzLOEEyf+75NOVZmEYjfljKyNSXr097Xnon8t6XszgVkimjZ7Sc57BTyWbpwVPJ15J77HKP3+DzL/+aUq5/571gZKc99ysm7Vl1rHmIG8jn1EczjVF6ZfyaVXNtBL3/5y+k973kPV523221uldwNT3rSk+i3f/u3c8cuvvhibqI8KDgJNcAPehrVLT1W2/O4Nj6uVcwKiiormjxaF68nu7GKXk9VOMNIVqOTeOEokNAlqFtR9ZTRuwbGt2KQPHGkkg2SF2KqY3Z4Qk19Zg1B8kPubgfh5GglRCrBm9cJqieIJ1RPJqEhUmlzOxckr8tFHLOEnEjUZ2qbka3PBOHEQspQlotGGihv8jurguRzxPMkvZ7FIHk9h/b8yu3kWJmv094mLhwViCguo60ikE1WR6VnM1suCiN3JaMauaStRjp615G7fCwLR9LrvpzFLJmFI950X9ugxpGjodf9FhIuj4illQ0Ts9SiHcQmcczSmG6A0jmC6jlkryfIJ1TPDrbgOwPefIdi3e0MJFweo3dVPUO1JpROUTs1XB4vPEBQR9VezxguHy4t8eSL2c926Z/k3Ajc3K6gXM5LPidI08TofUquZ9mxqril4phcP79VS3M/zyWk2hyb/euaQj4Ncct/bn2/7LgZixfJZ/Fbkzt5E7w3+xxlpC1HwgvXFW9dRqDjTadszpdz7vzXU/y0VULqNPJZel3F55nx+U/7OiafWPm3x36eqX9LLflcQAVUgcFLba6IplP3XAaDAT32sY+lCy+8kN7ylrfMfL+HP/zh9Na3vjV+vLS0RAcJJ6EBShz2eufs90r+l2+RfBa9nkw2jPqpCqgGynNDUYGESlZnWBZS5TKExk+qnnJbqJ5QOpdDm5HWZtoN9walQfUM9ZmIUwqqJzbcQTy5PtNsuCdbmzTudTjDc4j6TATJb3co6Up95mAHkUognlKfieUikE8Zs2e5niCfIKFYbuENdxBOo3RqrmcMki90t++1PnOa1zOeK6twznCsdJudO9yzpTO+7yxez7LRe1g+0kpNS0LRaiRZn6HXnUfviFnC6H2VWlBAOVz+ZkI80eu+cQ5REwtHsng0QsRSe51Vzy2OWRrRZi8JlZoYvfepMxzzdvv127JodD33uo84WL7bDaonRu+8ZCR+TxDLEVTPJBBOhMqHek07es+8noF46ra7kk6b8TnvP9Up/s/i2FyP5oiZOVY9erfEUK8zjzVFVQw/USWEbwr5LLCv2bM+dxmBV5LPvGKbJ4cFQmK/bxXkM3eD3HM2zz3/bS7ct4xE5Y/NTFYnHzr3CLt+/ya/jJLryr726uuq/ywdYNZn2bme5bFmfC6LSkMXKaz+JS95CV9eccUVc90PpPO8886jRYGT0JOB+cdZ9Hcy0QhS2V68nk0lnCCmgTSKwmm8nkw0xeupgfFMOJv5XE/cVo+JJ5Ryquf/396Vx852luV39t92l660RZYuKlYWBQTRqLVtqo0xSImB6B+tEghYDWBRSxMpoElBDS5EFqNSTZSlRjSYuCC0NZq2CC5VKA0lxS603N7b/rbZ55xjnvdbznu+852ZM3Pn/paZ77mZOzNn/c6cM795zvO+7/M2KKI6iGc0VJXt1kgeuZ5on6mq2ZHrCcKJCncmn6hwR5i9g3aZwzTXs50ayQ92Va6nDbOLXE/2+USonY3kRftMaSRvOhc5PdxPx1LJnB91viStMDcIWULpTuNzKqYpVwI9X18ETELNzYZe1pxndVNSyeZ66haaRglNW2qm1kvKZkkVH8n8T26zaarddbhdhd611+fRdbZZqq2tU+0IbJZaVIPNUmuNCDZL68fZZilaOcY2S92oQp1+1mbpaaieHV1wtNOndn9Em6h63x3QcKhsloaOzRJUT76hGA5pNBgIc3lVcGTslfCa1U8QTlNwJIuMTMg9o37OD7b6XFwYKTmUpCUlpJWx4WmhqHpI22Svz3TbWRLnI34epdMNvbuh2LK+nr58To/kllVus4QyzxcL1s1y89znk5/uENzMmHOrZudV9tfr0x107vMTy/h2U1i4JSbMnK8pUyHGbGecXVPhWAv3Zd+OXfYwt+3c3t7OEcH9UiDvuusuOv/88+mss86iK6+8kn7zN3+TzjnnHNovBBI6C0TI3r1btAqnJJ+O2mnIpz/XU1Wfq25GqeopK9xNTmeukEgT0TWQEm23BCVUEVKnwp1iaiRDqiQxh9lt+0xd4c7EE4STw+ybRCASbRjJo5vRgAZbbWUkL9tnsqWSyu90cz197TOHsn2mR/UcuXmdwmZpljxPfZrseZK/R5mbB4+np7RNsufZLp+uV5PnXuZ6mvC6zPUUYXbr7Sm8PqXqafq7cwtNDsPDXqmuSWiDaiuqrztUz5oJvaPavdGgOgqOWPU8SjWonig4OnI2h97j5gbFK0dVP/e4RsNRhXZRTNSPmHyeaA+ow7meQzrZVqrnt7b61BmMqN0d0i4UbrTUNAVHqHDXIfdRf8Dqpyo46qse7lr95GIjLjgSuZ4m3C6UUNte87S+rz6vSvOkSVxmsods6mmpSljNEwjbGz1dxc2V3H+vT2d5j7VSbhsFn5+ffPvJlp98OkQys6kihuKcqxyhLFBKnUmeDWfH5imcSol/uZD1WBV1HEHzKrX5z9Uz8oIjyl32/t36jnuGivcyOZ/p5iYkvBVcP/sFpIdNF45Xyz7nOc/JTL/11lvp3e9+N+01EIq/7rrr6OKLL6avf/3rdMstt9C1115L99xzD9VqSBjbewQSOiWskuVMs+FV/UfdEk2tiJqik3G5nkbhlBXuSsnUKqZtn5m21USOp2qfqcLskpii2KipSS37fyLPMxlRPYl0+0xFOLnCHYonVCrt4amM5NsU9/vcPlMRzjaNOtpInrsZQfXsF7TPdFRPXVzEOZ7oekPaSN4hnKaHe1EXo1lTbFzimd5EZOf5QutyOVNUxOfQmV/zkNBKqVxPZTg/ucORIqEmDF/XxLPeEl6fR9ao1oTqiQ5Huq/7MfR1X6XKOgqOztZ93ZXNUh8FR9SkYUS0iYKjEeyWlOrZHUV0Ygeh90iF3ndUwdHmzoCfYa00wLlHQRluMlj1HNFoAIVzRCM2lx9lcz2tzZK/4MgWGlniaSyXxud8FobZpbKTmZySMt+0DIXzksV0nt2DE8bOrpIvTJKqWZ7keark+T83zD7B61NM8yt+U5BPQ0JcciWOIx2n+1llPr7CGK5LPn3r5lfN2xHJlf1ktYB8+tmdfywF5NMZWW78RdsqOrbM/scwxKJt2nEWrTnhGMZ9jrntlECp5SalCxyy6vhHH32Ujh49aqcXqaA333wzvf/97x+7zQceeIBe8IIX0Cx4/etfb1+/6EUvohe/+MV06aWXsjp61VVX0X4gkNCSyPyt1tOkf2cmP1AQzbK5nlzNbvI6Ra6nIaF51VN5fq41ROhdV8dbS6WaMpivJjHV437WUgmqJ4zkterJYXZbXDSk0c42RV2tem4bSyWjeiryaYuLkOuJ4iK3wl1XQXOYHa+1nycKjTK+ngiz64IjVVQ0vrJdFiEZ4pg7X/a8pT8DmfMmSGXRNNO5yLTU5Ndim3K+uQaMr6etJJ2Q62nD7Tq3E8shvG4LjmzVuyo44o5G6OuOa2IVBUc1qq20Usulo+hw1KTqGrw+jxNZr881SlY2KF49TnG1ToP6GkXVOrWHMJhXfd1tS83ukE7CcmkQ0xObXWoPRmyztLmrzOW7rH4qiyWE3/nGoo9zDxLat/3c8VqRTe3raayV+FnkehpzeWmvpMPu2Wn5L6UvPJzO9pjLO0RRXRdSekrD3GWM5PPbdNVPl6DqcWWuSDvD3XJKDKVULwmz3NJptM9U+8my2zMSeq+U2F5BiNlZcmJYuhT5nBR+LgpfF4XK04Pyz5TRs8xKBdtz/nj5PpdiXlqi4Cg/DO+wx5LUMsSybOj94PHOuZBQEFBJQotw0003cQX7OFxyySU0L2Bb5557Lj300EOBhB4O8pmtbpdqJ6tdhrBUC3I9dc6m8fBEZ6OaUD2R39n0VLhLSyUuLjKWStrjk1VPa6kEkkrK6DweUA3tM5Hricp2neuJoiMmnFA7hwPt6wnVc0AjWCqhwl2ongi5s5F8GxXvOtezPaF9JiyW4OcZCQ9P0a/dFBmZYiJLPD3k07T7ltNkTmbmfJn54u5dKplmnnkvVUxDaE1ep9yHbKmZ6Xwkcj3Z5QCE01wPlQm5ntpySame8rU2mccNBszlQUJXZMGRVj3XRJvNDeX1iYKjamtFeX0eO4dtllBwlDRWKGquq4KjpELbg5gGEXq6K9KJ0DvM5eH9iTxP09noJPq6DyLqwYoJNxxsLq9C72yzBI9PbqnZZbVTFhyZXE/OATWE03p9iraawt9z2ir3oi+t94fTnnBBPgvD2JLgmDD7mGmStInp3gIes3dP7DgfvpdjdgqAMh6kzoG6h2GPcUq7pcy0zKQ82SpUW7Njyn6U+XOVodZZLl+w7eyEQjLlG5tvHUMUC/dZFHp3bgrk9sTxugsVqZ9ylSK6WJmkXE5AIXd0Us2KN+Ah1Zl5cqBzsHBa8I5J5513Hj/2Co899hidOnWKLrzwQtovBBI6BpJwun/XDQFV9kqp1Q6rm6Zzkejhbrw9la9nVvVMcz11mJ2JZra4qK5zPfFsqt7TbkYwkocySlRNIqqhqt3mevZY9eQuRigGaW9TpIuLVIW7Ip6jTlcQTpDQbprrKS2VdDERuhhxlxsUoRgjeaieKDKCvZJRO6F+6s5FblGRsVnyFRhJtdOeD6F6evmFJIcFHYvIY6NktmtvIhwPTzmfz69ZV18INteTTePTkDv/uIlcTxN652IkvY5pqYl5UvVUJLTOBUcq9K4q3WvcZlN7feoOR7X1dapzwVGTiSdC7yg4IpBP3eEorrdUwdEANwYoNEoLjqzquQXVM6Jn2ujr3ueCo7YuOILFkulslIbecX0otZNVT93hSOV6ahIK5YAtlTTh1CF4qXiW8vX0fTl9V8JEEiUIaI4EekLv0h7Jmxvp8xsViqldTNgyeQiiL3c0S2CzofcMbNV7wZjs+vlpfmZoFDZPcmKed3qnZxbwkFU7nuxHnVsuv6qHYOc3nJ3qJcaTQtCeSYUpBMXD8ZLP3DzfvibPLxrM5PWyx24iSvkNzYEolvQOTcd9cAnoQTOrf+SRR+jpp5/m5yiK2C8UuOyyy2hjY4NfI2x/22230Wte8xra3d3livrXvva1XB2PnNBf/dVf5eXhFbpfCCR07B+AlIDKHu6mS5EJvZsWmayUmR7uVX+upwqz65C68OnENEk4VftMorV6LdPNSFoqIcVQ2SwlVIv63D5TWipRDxXuXU04N20Pd4TeoXqid3s8BPE0hFPnenKF+8BaKClLJZXfaYzkQT5ZCeVcz1j1bjeEk0moMJLX6idIJ40Jt0vF074XBNP3d9EQR7ncLLmemQr3glxPuz2jcE6b61n3dThSRUYm35Otl1BwhGlNkNDUaJ69PldaVLehd9Ph6IjucNSkylHt9dnaoIg7HNW4w9FwVHMKjvrUHsT0dGfAeZ/s9bnV46r3jig4YvVzBMXThN5RcATVU5nLK9VTWS4pxXPEXrHS15MJqOhwZG83ZlQ8S+d/upzEWhwJsmZX1K/kPE/3H/+PpI/8mc265DOvgMoxqEUc8mkJqlgnk04gjs8XZndIdV5B9ZFgh5hmxuJ8CpX5h94L+UjBOt7LwRt6T48nTxr9+avp+Zk+9O4lnzNXnI8Jvxep/3Z2wXfCfV05ffKZXkoTls1clgebfB7Etp3vete7Msbz3/u938vPd955J11xxRX8+sEHH6StrS1+jcKj+++/n9eBsf1FF11E11xzDf3Gb/zGvnqFBhJaADf0PinX07TMRIjdvDaEM6N66i5FxjpJEk48G4IJ8mm8PM1yeM3ToKhWUaUXUW0I1RO5nm0uLqLhgKi7nbbP7LYpHvSZhCYgnOzhqVTPNNezS6OeyvXk9pla9QTRRK7nCL6PbKmkK9w1+Uw08TSE01S4m7A72yoJEmqIp1tcZAuPcudAP3uji/mQulzGzfWUBUWSjLq5nm5LTZpjrqcNt2OaUT1NERKH3uuahKrWmrBVaqy2bNW7MpxfofrGugq9g3i2Vjn0rjocKa9PdDga1lo0qK3SMCYOufdGo0zBEWyWQEqheJ7YVgVHz6DwCNcAOhzpc277ug8GymYJ1e7wiTXtNHVnI9XhKPLnehq7JU/fdnsB2JM724+RN/9TnSj3VzYfrpQkyqOw4kbCJU/+Xu+SITk+lcabLTMUn9TnUWctQS0i0HYAYjBmDGNIdeG0yYTSRzwzu3aOIEs4nHkTllfr+Dbsq2BXLwqGVkA+8+MSW/KTT7neFIpefpZDHotC74Xj1ldBia/NePW0zAYmL5I5B2UWL62olltsmXD77bdP9AiVf29XV1fpH//xH+mgIZBQgYrHWskSEp3rWXHD7Fr15BxO08Pd8fWUuZ54jW1C3WzJCne3h7swlLftM6sJWytVRz2qDgaqwt20z0S4nY3k0zA7ioziLozk+zTcRvtM2CillkoIuSsj+QETTW9xEauexkg+5rA7SKZUPU1/dhNel2F2U9U+Kcczcx70syw4SqelBML8LmVyNPX0NPRenOsprZe8RUjGWkn3bE8VzlQNtYSzks/1ZOKpp2E5Y61kuh4xCW3VNCmF6tlQoXc2mVcqaGMdJLROzY01qrYaVF1dp9qG8vq0ofeV1Otz2DpGcb1JHRQc9SIajBLu6w5zeeR+muKjb252abenCo6e2e1zZ6MurgNcA+z1mZJPPKPYiAuOEtHhyNosxWNzPd3we1pwZK8GfU7dHu0lipBcBSijdsmwsiSI5vdbEVdBNx2V0LOvEuH4PPkV47bXbzrNR5a9BFoe7xhPUpd8ZsZbOC0dVWbb2bdjzo+Z76FQnrzBvOKYJ47F6p24iShax51WyHbHrDNNHqSfDafLjyNRs4beJ86bpKxOOqliO5MwJZGdRvk0v8UHAfgdNLZLZZcPGI9AQjUyqmdVkBMZZndyPUE263q6Ca3jWRFORSgNGVWdi0z7TBVa55C8yPXEMiocr0LuNU08WfWMRlTtd1SF+7CTUT2tpVJnlxLk6en2mSCeKtcThFPleg53e2mFO8LsUD3bQ9suMzWSV6onqtaRG2iq2k2Op+zbHjmWSr48T/NdHPeVlMRynLUSk7sJuZ5e1dPN9RTbKcz1FB6e7rSJoXcnDI/Qu8oHFfmfnOtpSGhTVb2bNpurIKGrTEJhMs9en2sq9E4IvR85R3l9ttbZaD6iKu1GVRr0Yq54f6YHBTSib+0OuML95O6A22tar8++6unO1e4RvD5HuuBoqKvdjeqJmxG02ewLmyWleiL8ns31NF6fRuEsJp3z+NK6xDRvs5QlWu60lDgJwlrY612SSbOYWNdbOe+r0M/2eneveDumib3ec0xuNsN5qeJmPit/+Ld86D2zMc/07Lzc9NM0nE8/P5rBcN7L0fMzzFsfMfUvbY7Cf/rl+PzDGzt2304rp0NSJ+3GOfeVORJQ33nYbxykjkmLgqUnoSb6JcPvpmuRMRpn9VNbImVzPVW+p1U4jeopiopM/qdRPQ3hXMmonpWM6onK9mYV7TMTqg57VOX2mahwR3HRiKiL9pnaUmlnU1e471DUQejdhNlBONNcT+R9gnCy6gmiqVVPU1zkqp6oajftM1FoZDw83faZGdVT9Gu3uldJ8unaLBni6KuEN/MkaXWnje3XLj1czTxDKLmYSO3FVrPnCKckpiYc7zeXl4RTheCrIvReTUPvzYZ9bdps1ldXdei9qXI+4fW5doQqGwi9w+tTVb0PKg3qJQ0OvSviqVVPFBwNUXDUo93BiEPvIJ9IpdjZHdAAoXfcoKDILI656l2pnn3t8Yl0jJ4tOAL5VH3dBfEszPWcseDI8wXNKY2ZkHXxNC1XZ64pbwg6pxw6XXe8oXdnmrw6ZTFTuocc8XTHnJJPQ5XF+h4CZAm1Wd45BpdU54h5RmFySJ8n/J7ZR8GY3JVymQXyjfuR2O06irW7vGc/uSkeYiwHXThrgmTpHoIYWsH2CsaanqLJ+3H3NwH+z88d2OTtTVKDpxraFEppelkdIPZ5AAuTFgWBhOqvvAmvM0mRqieH2ZXq6RYXca6nKBoyZFQWErHq2ajy67r29azrdWEkD9VTLUfUqCTUqMRUiYdU7XU5zM4V7iguQgi0s82V7jbXs9+naGdLtc/chqVSTxBO9HCH6jmw7TOZZHZhIg7CaSrcE0tAWfWEpZIOt5sKdyigIBSR00ZT9nAHpOpZ5qtnyKU5D0W5nm5f90qB6inD65UJuZ423aKabZ/JP9SmsYDN9RT5n5KECnsla71kKuB1kZGyXtI2S2it6YbeTdW7tl6qoOBoA4bzTaqsrnOXIyahR8+l6ooqOErWjlFcbdCweYSiGkLvMW33Y+pHsVY9I656P7GLfu5p6H23M6QtHXrvQf1GPjDSMnDjgb7uKGBjmyWlerLSaULvure7IqEy59P0dPd5fZb9Epp8R9/30/dL7kyreMibYDdZUlUZ45cpK9J9y6cjSocuQv16GUtA5bYtwZHHOm2vd7VcjsuVDCfnqU3+s7VEvcQ+XBaVHpKzzUoZJc8TjvftSu7Pe9zZhfLHMe4wJm8vs1iR+llAru0xFnKrMQrnJBKXueGg01JRvcc8zVicZTPPZRY/gOTTgEPxM3RMCijG0pJQS350XieH143qaUio8OuUqieH1I1VkiWc6TRX9YS/pyWkmnCiIp7N5SsJNStQPWP274SlUiXTPnOHPTxlrme0u6NzPVX7zEionrHO9bTtM7m4KO1mZFVPVrwQTnXaZ8Z+X08bbhdENCmR35n73AVBNO+nzfV0w+2uYqoIp/butKQ1ze+14faCXE/zh1rldYqqd5DLukNCtc2SUUbNOrbDEYfaQUKrmnhC9TQkVPV45y5IXPWuio/Y47O1QpXVDarCcL7epMrG2ZQ0VylqrXObzVGC0HuFBiPl9QnS2YPqyQVHKvT+5FaXeoOYTm73qANDeixjQ+8qBzgaDmjU71uvTxBNo3rKNpu24Ei01LQdjvT1MWsj1cK+6fIC0dMyv48TwvHOVZfLk0x5ps9myRded62XsrmmheF4sVn7I+vjgx4CbWe6BHhWY/pMjqwcp+fH30M2UoLtGX7mGGkqiI+xvJLq31JJ0ptZo5Bnenc7JvTuJ7rZ69Z3ewY/TPAAADJJSURBVFAwo/SHWZQ6UbZ6Pl1sEtF1hjZ+UJMJbTq8A00+DUz0Z5rlA8ZjKUmoDbsaax5WPVXvdmMkj/B7GmbXyqUmnKvNPOGUxUUgpBlfT925yPRwZ9WTImrQSLfPRK6nap9Jgy4R1CfkeBrVs7NLMaqTt7fSfu1W9dRG8lC4oHpytfvQhtaV6qkr3KFuss+nMpIH4eQKd+HnydOEmmk6G5Egnup1ecphaYJDPtXfnZRAsvhTMtdTklGftZLXXN6c90m5nrLgyC4nK+HVNhBmzxUcNQwxVQVHKtSeen2moXcUHKmuR5hfXVmh2voGVeqNNPS+ukGVjePZ0DvVqRvXVei9O6LuKFGqZ1upno9vdmmnj9D7gE5s95TX5+6Ahtpiqc85vxENuig4Qt7vgGLc4ICEovAINz7calMXHOncT5vracLwBTmeNgRfQHbKfkHzOYpZ30zX89JVslJFxRDOlIBmyaK9Esf0f3cryEU4XpJHu8/8NJ8FUn4bLiF2j73483IO30O05eCdY5HLy4+lcH++3UuC7CeUvsuhVMh3wjqzEJgMOfISag/NHMcVC8aajq/oI51AHsepo+azmHTohcqss53Jm/F/Lr79zXIncggQSOj8sZQkFLAen1r1ZL9OGIebULnI6+TnZs2qndJI3iWcCLerabq4iJ81CaUEXbq540LVFBfB15ON5FX7TITZEXrnXE9WPXc515MtlYzq2TaqZ0SDnZ7uZjRMcz27CK/Cz9GonmirOFI2SjrP05JQx0je+HpKU3mregq+MYvqWcbX0yWS5FSsV0Sup2s6P59cTyoIvRtiWmyzBFJZ06F35HQizM6Ppmqzifaa3GYTJFRbLyHnE+8rK+usgIJw1o6eTRWE3pvrudB724Te0eGorUPvnQE9Ca/PQUSPPdOxofedHR16hyKOBgNc9a6KikZ9VagGpdN4fYKQ2jxPrno3BUei6p1Pfpr7meaBOleFLEYa1yayWLoZk//pKcrxhao9uZ4ZXuu1Xkr3I/dpZhYW+Ujy6Ybo3U05hM21XnIGk5/m5HqWay9abL1UOrzvJZ+e4ysioLmtFizvVe1KhJHzg/aP0z/I8UStTAh6qvGOyds0pL4EufSuL3dRhlxOuOFIP5dpSOXhz//0IY0IlV8+YDyWioSa6zxtqZkPs7NpfKNKLUMqmzXOB5WFRKt1GWavqQp3LKeN520lPHc1woccUR1enqx6KsKpVE88+hS3N4mG2ki+q1XPnR329URVO0gndy7SqucQ3WygbKKTTTtVPVU3I5X3yabiQ9M+U4fZdX5nZLsYpR2MYif0Lu2Upk1rkbme2Wn5YiI+L66Vkie8LueTp83m9LmemnAKK6WUmKYdkDKE06ijjs0Sh9v5vVY9EXoHsTT5n8j7lCS0pXq9s+q5foQqzZYKvW8co0q9SQS7JVS9N9cpXj1GI6rSzkiF3mE2j25H8Pp8YrtPOwi97/S5+AjtNU9u9XTV+4h66HQVJdS3hvMoOELIHa9N6F212sxUvRvLpYJcz9T3c3b4Q8L+im+XKOa3M5ksWtLr25BPxvKG+mmqsaiXs1svlSWI2ePIFlVZuuo93OJjmYR0Fx5i60zwhqd9+3PV2HHbLSDGcoAzrVN04+Ad1GTuVEbonXq9SepnScJYPq/zzKiflUNEPg347yJy4qdYPmA8loqEAqbVJvdwF9XsCL+DSCIkj9D6alMVEuG1slaqWvK5DsKZCb2b4iJFQrmLURJTIxlQJY5T1RO5nr0d7lwE1TPu7HLoPdKqJ7fPbHd0hbtsn4nQuyKfpn2myfU0xUW2m5G2VErbZ6ZG8kbp5NxqXdluFU/Tw33KHE8DSS6z04oLjcb5emIa1E5WH0/D19OQiZRcprmetqjIDdGbXE/XZgnrcpg9rXrHzjmcXqvZULsqQmqo9w2onk0VjtfWS9XWKtXW1olAQkE8kf+5YkLvDYpXjyvD+Sqq3nXoXXc6QugdxUfw+nwMofeeqXpXoffdnT4N0WKzbwzn0WYTajlC73BK0FXvHIJXPp9c7c52S5EIu2eN5tPwu75ASlwRWRVzSsyc/5nfjtyMN9RvCLBcXob+C8Pxnn0VDMX1Lk3Hnxnd7Lme5ti8pNDLxjw8uGBdH4HVRyCfPCsXz9KblS6x6TlyL7Hi85vntyUURHf9ohUq44mpf61JuZfjPrOxKxZtyT+G0+V2JaL8+UGU2+m06RNlMg72CqohxxQkNAkkdBKWioQaBdR2LtLqJwgm1M6NVl2RUZBQW1SUhttNyH1Dk9CW8PU0uZ71eER19MwWRvIcbh/AUsl0LlKWSkb1HG5vc0ERjOSH7TTXk/M7OzCSR5gdeZ9C9TSWSsj5BAmF0jVSxUQgn4Z4upZKJrRuTOVl6F0i5RupKmqIowtXLJDkc9pcz3n7eloiKvM/DfHU5JLHx5ZKabW72l76PlU9tc2S9vZU/p94rmmVs5nP/0ToHQVJayg8Quh9jf0+4fXJ+Z/NFaLWOiWrR9lwftQ6yr3eYTi/3UPVe0In2gPucHSqM2AFtDsY0WPPdGkHLTY7Q9rWoffuLgznoXQi9K46HKnQO66dQWo4rwuPTCGSyvWUBUc6/3PmgiOvLJYnpmMN4CXhTF+49CYlEpJAzpr/mSeozo6zoXAph2kSkc//zJPlymnmevqmZUhcbiFxCDnyWjwE/7zJ+Z8+PuWv2Hde5C4FDzEeRxp9k+VgyqyaOaaCMY/d1/gUgD3J/xy3SJkQvVqwFPkrrajaDQcELCEJZWVNm8o3NPlU6medFVCE5I+s1FXLTE1CG1r1hD8oQu+qlSaxAsoEVud6VpOIGjHaZ6LCvcPKJ1RP+HmSayS/84xqn7nTZtXTFhcNterZ6TP5zFoqSV9PFBcZ1ZO4ixGIpVI900IiQzxNqN3XNtM1kDfz5TTAdBryIZOraaflw+5FRLOMr6csPJrUw93N9TREVE7LVbgb5VQTVbucq3pyEZIKvZsqdyakOufT9HpXXY9atutRfW0VjXupurah+rsj/5ND7w0OvVNjhRKuej9GUaVK7bhOg0HCpJN9P4cRV72j4Oip3T59c7PHJPRbmz1q9+DzCcP5AUWjhPpcnKY6HA17XS4yYtVTh93jkbJesp2OMlXv0t8ze1viI6MzFR6VUIiy/CqfE6pPaJ74zC3/k0rnf2YufO9xukkAJfM/p2qzefDyPwvhKqDzyP+cmPs4Zf5n7qxNwrgq/uz+fbPKHO8EDl3iM9CLlfmYJn04s6Dk+DKrHEDCGgqT5o+lIaHKZknldSL8rghnlTZW6rTeVOTzSKtuiSeIKM/XZBWEU+WEahIKUhsNqIYQO4zk+7v8rNpnatUThJMr3Hc49B6zpdKOIpxon8mq50iH3rWlkmifqVRPWOekIXcuMkLRkbZUUqqnIp7WUkkXHJkCJJJdjEjWkWRzP8veEY/z8OTP2iGa8+jhrriISqUwr/kPm1u5ruezwsnkQyuihmC63YycdbO5nlr15Kp3ZbPE6ie34kxD79xOEyQTBvNQQK31EkLvK9xqk0Pvazr/U5NQqjU55zNptGhUQ7/3FRrFRNvDmDsdbfZG9C2ueo859L7dG7L10hObXRrAcH67r8zmQVT5BiWiYbdL0QjXEFTPrg69g3imoXeT82lC7+YPpVFCbQ6ovkaKro7Eq5Toz7swTFwpnKbO6Ri7pqJ9FSmumSvW3ZaPcKbTcipYiVxUV9E9rfzPWXEGfrjFEWan+47Lw7J8p28sF/ItPwMxWor8z5KYd/6n9/ObsMossL8tB4SRBhI6fywNCeUq9YYKueP5+FqTSeV6q0YbzTormkdBQmtVWreh96zq2aoRq571UZfbZ1YHbTaSZ9Wzs6VVT+R67jAJ5VxPKJ27bVVc1BfdjNo9rXrGVvVUuZ5QrBTh5Ar3gbZUQo4nq56KeJrcTunlaYqLYsfXs6iH+zhIcmmgCKOeL/5YmZ9vV8F0p8mQOp8To1K63YwEEeXldeMAezedKSRK8z9lrqft725D9LqvuyaemXU9HY6k9ZIinSb0rnI9lcE8SCgKjpThPLfaNGH41TWqIPTeXE1J6MZxzv9Eq00Teo9XEXpfoX5UofYAnapiOtUZUXuovD+hgHY49N6hre6IttsDemarp0LvyP8c6NA7LJfiEY3QxAAkVIfeKZFV71r1TGT+p+xwFJ9+a02fguj5BferqKnc41oepcuPIxbmB8sdi0ueqhOkpmyIvUz+pyWthYfkyf8U0w6E/2dRuHysyjce8pSxUcJE5XAsa8zf3Ew7njkSK7v02I0Wk9ppPsziXexh/meZ8bjLFVxXY5c/wAgkdP5YGhKKkPp6q05nrTc5B/Sc9QYXJSG/05DQY1BHEXqva9WzAhKqiFEt6lFtoFTPah8V7kOi7i4lUD4RZt9+hnu5R0xCYakE1XNXG8kL1ROWSsj17ArVU1a4W0slXWQEwqnVTpPradtnmuIiQUINp5C926ctMFIvUi3ITUOzBFP8FvvIp1vVXpHksshSSRYmacZrwu2yuCjfPtPJCc1VveeN6TOqp1FRjerJhvNK9eTQe6Oui5CM6pnmf3LPd7ZeanIFPNXqTDwRbrf5n3i9fpTzP+PmGiUrRymu1KhfadEoqVMnitl0vqetl2A4/9TugLsdwWj+cZ3/2euOqLOrbl4Qgkf+Z9RH6L3DSueIvT5xPeFmpp/mf4KAat9P2e0ozfsE9qC7R44QFSmIReXNBYTPG5ZOt5m+HEMu7bRCKS4dn/tOzp+X/+c4FBKb8otP3EWOIPsIi7k5nGGvuY9jzPkueQDj8j/teSgYh/cjzV6a3nljhfrikR4YBbTwc/EsOIsiPQsOivLpIlg0zR9LQ0KR93l8rUHnH2lxJfs5WglFCP4I530iP7RKDVvhTlRFkdEQqicsldrc0Yjww97WqufuFsXw9tRG8spSqc3di7jCXed6Dtt9LjCSxUXw8uQwu1ZAOdxuLJXihPrGUknnerKfp9PDnZxCo2RMXmcZGBJoXltRSM+XVe1WEfVMs/ZJBUqomW+IqiSfpnGArVg3/p6VMebydrl0npvrmS1M0qqnJatG9cQyqsCIpxmbJR1qV1XvqeqZtt5Unp9VtlpaowqT0A1VeMSh96NEtYYino0WxY01iltHKaIKdYZEfVgv9SI6qbsewfNzG/mfOz0uPuoPItrc6lG3h4p3Zb0UwXAeDQtQ9T7o0QhdtUTo3bTf5BsRHYLPtNo0YfaZlM/p1KL0pV+ZHLdNN4eyMpZwjhmFmxM6Yb+FOaGOhOebNm6zxTPzBDUlKoLtWLIgybTDlCYUIMnjSl/O/qPvJ2955XJiV5/cNkqSozIDonn5f+4dxl9C+irY87GV2KE8xweUTM4KjiBNQUJ5+YCxWBoSeny9SedvtOiCIy0OsRsSiteqnzvRGqueCdVGUD17Ktezt0OVaKDaZ0L5HPS4uAiq52h3h6L2bjbMvtvVFe7I9VRG8sPOSIfZRa4nPD1RYATVc6jbZ+owu8z15LxOTSwNGZW926XiSU4bTftewCiOmWnih8n+nDlFRS6plBZLroopc0Izfp4FZNUQU1YuRaGRIZ9ZwqnVTNnZqCb8Pw3hFK003XVtwVGm/zsKjtDhqKpVT/Wczf/Mht7xmuevrKpwfROtNtcVCYXxfKPFnY9APqGOxitHKKm32HppEFfZs3V7oNTPZ7jr0UD1et/q0nZX+X+e2Oxx/md7B/mfEQ17Q+rhhobzP3HNIZUD/p8i9M5dj6Coj2ybTVNslKmA5wtknAqqyV5l8jRzxyJJjfJlLf8j5C9CmvBD5pGqigln0TZSgpTf7BiZa+JmC4qQPD3h/S0/8/vwGCvlxuJVtgrJlietwFW7/C+nR4GqOb5pgWcbUxKb+ap3rnVYfr558s8q1z5zwhDmG4I/E0RxpnN08BHC8fPH0pDQbztrlZ5zfJWefbTFtkpHW0r9XKkRP6B61vptqsQoMoLq2VHtM3c3VVcZqJ5tles53IKl0kATTmUkDwWUw+xQPaFUOWF2S0KNryf8GyMdZo8SJpojT64ne3qKkLu0WQLs84Q2mpUpQu9lyKfbPtMlo1b11NsvMp7n14ZU2nxOQz4dNdOE0vXySh2lgpaaUDPdSnhTRW9UT0UwMRAmlrbNpi44YhKqrZe0KspKKFfCN6i2uqKsmVbXVH93FCGtqPzPypoKvSd4tDZU/mdrg/M/cb53kQscJUw+0QXp6e6ATuz2qd2P6InNHm12BrSDsDysl4YRddERC16xPTQqQOg9YvXTWC/FuFZjY72U5n/awiOb9zm54GgWTK1MqpPom+MPfWbmedTI4h3l3hcWEBVtwv7vLJ8hZ1MUIR0CeA4jN8EbPZ+afFTmEopOnREK5k+ckJ1XOY35s887gEVIvNzehMcPagheIpDQ+WNpSOil56zT846v0LlrDWqw6plQrRJTbdClar9LFVS5d1WYPemkhDPafpp9PUe7sFRqs6US2meqCveuyvVEmH1HG8nDUqnrhNnZUkmF2aWl0lD0azfE0831tPmdmnz6rJUmQZLLMkbyljQK4uid5ikuooLiItVmUyihTqW7IpUFOZxOhfvUHY5Mrie31BTr1tNcTyiZPF1bLbldj+o69K7yP+tstYR+71A9Ue3O1kutVZX/WasTraxz1XvSWGUSqvI/GzSKK9QZwX4ppl6kzOd3BpG2XupSpx+x8fx2Z0A9bb0EEtqHX+wAdl1oXrCrer33u6raPVKFSLgwYqj2UvmUxvOmA9IeI1U43SuwYHn+z1xhgjBOzKGcIU+0xGQvuZwa6XEIzdajOhbZMInP7zSLkDJD8gmrM8IXgjcTZtns1OsU3rzMowhp71A4qnk5KJwh1XVy9KBwF4cH6JhUnYJYho5JE7E0JPQFZ7fo/I0qrVQjqsZDqrW3WfVEcRHslVQ1O8LsfVVcBFulgSouitnXs8vKJwqN2FKJjeSHun1mTAO0SDSWStpIfgj1E2QTIXdZXGRVz9TXUymd+VxP2bPd5+dJE4zk7fwJ5FPOI6cdplzWnSbD7NLDM831VM+WrBo7JlnFfhqEM2OzZJZjJVTleqYkFH3dndC7Vjl5TCL0DpXTzf8ECYXXJxcjcei9pVRPdEpCtyNNQtF+EyQUvp9JvUlJc43i5gbnf/ZGSLOImXQ+01OtN5+C0XxvRCd2+vTkpmq9CeP5Tneo8j85fWPE6udooCreYT6fzf+MrOE8Xnu7HmV6vHsujHnBGrjnrrrCCzNDuuR6E3/M5MU7ZZ5oZZrWoeM3lEYUzDbsNyYTbShXmOSVF/PTxylqk0bsIaveIiT9nCOVUyInXs+ies3YCWlel/fklIExZHseFexiN6e1ur2UprvGp9vBdIseBgU00wEpdEyaK5aGhJ4/eIqOdtDBKObiIto5xYSTFU+00MQP/PYmE84ROhftwkh+JCyVUFzU18VFKtzORvKZMDssldCzPWIy2Y/iHOFEHqDJ75SV7TLXs4yBvAvf19iX/+kSSF5OTheKqJmmUy4z1e8Z0/gCMpqxZRIk1Fa4C8Jpw/GerkfShD5HOC2BlUqoqXBPbZtSr0+leo6zXrJKKPw/NQmtciV8jVtucrgdRUh4bSrhG01lvdRaw04pbiEs36JRtUlDqtIoqTDp7EUJ7XD/9yG33oQCutUd0lPbfToB389hRLvtAQ1gQt8bUh/XnCah3HaTW2+CfOJGR1kvQRVNoOBz/qepfk9Vz+L8T02UZv4RkIUyZsq0CWvjCWfxj/p04f+0kCOrOk7zA5vvjiRVXjn5dD7TAwQPAZ3yI5tyX9nPttRqUxOqCdsq2tSk+6LTiKTP61opv52ylfALcA0HHHgsDQmtnHqUaLtKSb+rOxehmh2WSirMDvKpFE4QTlVcFA9AOLWlUgdEQFe2dxTx5DA7CoyihMkDt8qM86onSKasbE8Kcj0NJlkrTfunwVU/Xa/PIvLpkktX2SRhKJ+uK/I+ZTGSllatAuoQzkzOpyGXmTzR9MF/IIUyalXPmgy9i/xPrYSy2ilVT1v1ruZx1Tz7fzatEsrEtNGgaku13qysrCrrJRQdrayl4fhmy4bfWQltrCkT+hgKqLomkAeKIqSt/oie6Q3ZegnFR5udIfd/b7cHNBwq4/lhf8T5n6Neh0PuqvUmbn7QGamver27+Z+6CCljwZReVZ4rI3VuLHUVVXzq43SMobg63rvHgu5IE9bjwiS7BfGDWjkN9UuTzf38YfZKinKI+zO2eeQyupdWuf1Oecx7aDE0LSZlmRzc5IEzAffv0h5Yx5UE/30NFk1zxdKQ0NFT36T+oEvDZ05RMhrRqINWhhHndOI192mHtdIYD0/Vp12F3PEMY/Gh6NfOZFO0zZTV7L7e7TLkTp6wexF8CqeB/Lssf3ZdsumbNtbX08nz9BUh5fJEZejdEERHCc1UuBsiqUPuZbw+c+04ZfvNTOhdEUxFOPWzVjlt/3dHCeVOSFgHRUdQPqs1RT4RetdKKEgoofc7lFC032yssBIa1ZqUcBV8Qt1RzM9ouwkT+s3ukJ5uD6iNXvDtAW22B7SzO+Cqdzgl9HH9cSV8SkK59SYKkLgQaahIqMn/lK03Td/3UldSETyK1BkmnMXV5GW24NvPNGFBX1h+XoQzn6dqUxbGfVbez8/XCEAvm5uYV7KKcvbOCLmZRyhckq/puObMcw8cDroiOcNN0OTFZv8un2nw39lQmDRXLA0Jffq+L1APZLSrQpiwVUJHIkM4bW92oXDaMDum4QEfT13Nbjw8EV43r43qyZXtItzOhFP0bZcClexm5MOkXM8i5FRNn9IpKuFd+yRDLqmAcErrpdw2UPzD7FGTwVzVuyCcMiSvyaWZ78//zHt95nrC2yIkJ//TThP5n5qE8jMXKqWV8NUmQvCqCMmS0NaKIqV4bikllCvgkf9ZBwldpaRS4xA80jP7UcIh+P4o5jA8TOhREQ/yiSKkZ3YHXAnf7agc0NEIVe/ohKSM55l8ov87qt+tCf0gn//JBFRUvQt1ferfsJlM1Kdc3hd5La1snY4d05hjO40f+9J2TIWaVtlpJcczhR1TlhAXnJsy+5w4cYYORzMsP9dM0Ow9QG5+4WdlCPRB4E82iHGGBjPDdg80sZ6ohJZXN4MSOhlLQ0K/ed9DdBQej7UKJcjR7COMmahwui4kMr3ZI6dVJle1a6IJkpkSTq12OsVFxsOTSaj085QDEjZLY4HlRDh8VvjWTUmmYx7vFiN5Co/sfKflpt2eL9dTWyrlckFFmD3j6+mE440JfS707nh+qtC7KDgCETDh+BwJrTnh+Hq6DsLuHHpvKgW0JpXQFX5wJTzIZ73BKigeMVVpGFVoGKvwe1eH4UFAt/HoDTkE3+mPuAAJXZCQ/4k+8Nxhq99TRUh9FMIpxZ7zP03vd0M+betNrX7yNZU3oFf3N6a6/DQuojFX19SeoDyeKavOfe0rxy5fyZuzi/+n2JDzTqqkjnpJhx95QiU+tdM4wHkW58x2Hgs25zmV3vn+oUze7hxzYIv3M2EjZa9N/kouwlV8ZhCU0PljaUjoya89Q8PVJtWbNSafIJ38HKFLEXLptH2SbpNpiKYxjQfJNB6eIKT4YTfV7JZw6h/82GMiTyX9PMkJbSs+odbwheIkIXTXlYpnkQLqenxmCo30e2vNJN5nqt7NPmSbTUkgZQ4nq51qa5kQvSGmYlq+O1I1vxwTTEN0jTqK5Uy4XhNQJp0gMZqgmpxQJqSqaAnvK6yIKn9QJpuWhDbBkC0JhS8od0GCEsrPDYqreNQpSio0TJQPqCGfeEZVPNRQVMNvdYbUG4y4CxLyP9mIHjdEI9wUqSp4eH9y+J2LkIbWhN6E3iUBVRXw6bXCT5nfOH3h7YcCkenyM3n/dtnTZT286ykLmEqT5fl4Oh4W+C6beahZM3mCTvvZTyCD+3Eep+0eVbideX6fl+uSngmBhM4fS0NCT2z3aNCJaAVKqAmVSyKpK9dtlyIdOh/agqK0et0Ns5P08HS8PYvC7L47VPsHAOuXvEmW5DNHLMV0N8duLOEck/+ZIbGSwBoiWURCzcMQQ/PaLJMJ26cEU3GANMxuQ+8cYk8r5m1Y3iihCL1XsjmhTCx5Psino4RCAQVJBQEF8RRKKBvRN9ATvsZheSagCL/XYNukSCjVmuwFOoL5Am5UIjxAQhPqwGx+GNNuf0S7Pf3oj6ivHyCf8ACFChqNkIuszOfh/an6vke5h+mElM8DTa+HMwNfq8pJaygVc7rdzJqDavc4E2YpYDrzbE/950S2S4S/zxz8nqCzD+IMXq75lIPDgEOiqu/FGM1vzEEABIFKIKFzxenJBIcIW4OYTvVHdKI7ohO9ET3Vj+hkf0SnBhE9jccwpk0UjQxj2hpGtDWKaXsYUztKqD2KqYNHlFA3iqkXJ/xAf3fYMOFhquJVnqhpv6k6IfkeUi1V5DbbBUkVLs2/LtAQTpPfWVTkJAlpNvSu1q+J9U0lvFkv4/+pWasbei96cMjdDbWbRyZ0r9VUac1kiCiT0bRIySqjeroireJhQvMgoFoJhQ0Th9prDfs+JaRQSI0SiuWMEqpJqL4OoKLj2kBhEuyZOoMRtVGchDA8HuiANIyUpRcIqLZgkgVI8P/kEDx3P4LyaYinvlZyF0im1M2XCHL6mHhnVJ4MqstDKdTTS2Lu8lMQSHFDlEv8O2M81Nkofy+cFANtP2UVXHOD57OCMmkvcugueZdF/Wf8h1yk3JzO/szfjENBw84g9vl+aByMiFC6GMmsM+PxHJRrAXUkSIcq/zgzOaHf+MY36A1veANdfPHFtLq6SpdeeindeuutNBgMxq7X6/XoxhtvpHPOOYc2Njbota99LX3rW9+i/cShIKF/+Id/SM9//vNpZWWFXvnKV9IXvvCFqbcBArkzMkQzyhDNbYRKETYdgXQq4mkIJz8M4dTEQj6gnsoHdzwa8zCilVJUUyW1jDXT6YAJo1BAXUhPUHQ3kjTC/LBJQmrmmYmy+EhW4aZhcZ/FTbrBNCwnyKX5MZJKqgjtW7KqEldVEQj/qOtBqBwBoZI6xNSE6TVxJb0Mh92heqIoqYa2nkotVc81VkQTPPC6iue6erAfqPaF5YdSQ5FXjMIkkM42QvMgnwOonyCgSAeJmYSy6snEMw275x9pNbzJCc0yUXOGTDy+QsnpsAGVxFv6R8AQqPJhcHv3Uv4Xiq+r2mzE1d23vLDmBXWRZtWsirg25f7PMNNIv6OCwNrvm7PvGYZxZsxzpvMjlX+jDixr2y8clI9DihSHtCgJUJZ4UzzOkFn9V7/6VYrjmD760Y/Sl7/8Zfrd3/1d+shHPkK33HLL2PXe/va302c+8xm644476O6776ZvfvObdN1119F+4sCH4z/5yU/SL//yL/MHDAL6e7/3e/RjP/Zj9OCDD9L5559fejtQJlGlnAmbywWcXE49ydsiU6qWZeDQLvXsCbeYfc9aEZ/br/T4HJPvI6vei8afIZ/GekkemySSIgwv8wUMN+RcTx2hTVUeQ2Qt7xlbwGT5hyagMq+UbHhf55Da+VkCKp+ZrBqioMmlKvPHMloR1cSzUkFfek1A9TMecVzhIjYuXgP5NDZeumsWyOgA3bW020LE+cjqWRUfKeXTFiAZ0pkjmilwJeIM87PO+VTTzDWr5s98DS1CohhfFmfmfttvzn84fmjld5efZhhyep0VXyZ79VnMby8TCvjG/X22N9L7D3MTHzA/8I1/Zf/D8T/+4z/OD4NLLrmEOdGHP/xh+p3f+R3vOltbW/Qnf/In9Jd/+Zd05ZVX8rSPfexj9F3f9V1077330vd///fTfuDAK6Ef+MAH6I1vfCP93M/9HF1++eVMRtfW1uhP//RPp9oOiAF7NmqVk21z9DPCpR2E2XVo3aqcpioe4XURbp+kduaUTzEOX6GStXCayyeWJY1F2sBEYip7wDvrZbYj8j/tNCuyaLJZMAC/Eb0nfijIrXrr5o8alUl0ZdLkKVOkZMZhxiseTFK02snPmpCa9/K1XAbPIKb8oIpSuLlDllFDQUBBRGNLTEFAVUEcnlWRHN6nSqcOvRsCqp/te/kx6p7wioCqi4iPPalQBTc0/JoOBsT5KF0Zb9XsKSvjiwYwV6oiQuKHJIevEKcx+EXTH9PUolk4XBq5OSgodX7cO5KAQ4etrS06++yzC+d/6UtfouFwSFdffbWd9oIXvICe+9zn0j333EP7hQOthCK/AR/cO9/5TjutWq3yhzjth8bqpa5w9xnE8+tSRDDbzaFIBZBBUbMPWbnubpHJwxy+/9hETqUsgKyYz25EsFNhzyLN7DPEtGBnafHRPI7NNbi3k9NnGX5nsugch1VDnVxRs6zJD0zj/ilh0qqozHdMWF1LvQOkI4LJ81U2XgmNIk1GQT7huICCN91eU6VoqAp3Q0DZiy6nfprKdzGdz4e4eOzwcuXxBwCzSW4Hhd6lauoCqMMTIQqPFv5YDx/mXhV/kFjzAiqh29vbmemtVosf88JDDz1EH/zgBwtVUODJJ5+kZrNJx48fz0x/1rOexfP2CweahJ48eZKiKOIPSQLvkRPhQ7/f54e8O+DpHNKs0MCQhBL7lwTThD3NHF/DQ3eaSzjBC1JlMf/TmtIZYRQvCK2xvc5YJjnTWMGECpZbLrtORZ988zrdh5pWY0VNFCgZZTRnao9MyFQRsgon/vE4kF6AY0/nVSsxv67iiGKtZmLZin42CmeiK+FJh82TClWTWIlosbBlijGtQlXIkHiP4iMkhPM0Xf0+qlEtTtTrJFZ2TPVIr6uWV5XxMf+NQci9EqNCPqJKQ03jQqUhPrgRJfWIkmbCuaBxP2azelUJr8LvO70R9YYJtftD6u72uU98r9OhPvrCozNSt8sFSTCmR3vYeIBuXV02o0/gDQpfUM4RHSglNBbh+UyIR151Mjjvu8KUQpqd5BbmyGn6isjMNndSmtTrmUlcGbO9NEfSnxfsuUvJLOt8k5By4IbXff3kzTQbjhf7yORFylWyxystmmyucboJf76sz8+Up9Hk5djc3jNOZx82X3oSmfCEZCulqu3H52VKa6XKhHXGERxvlf0EP1tvKmuREq2X9c0tEv/seCuzhOPLefGOdxco8xlM3on3GpkTCZ021J9qAdOTXawR9zv5G/B9AP42TxVij/CDQfSc5zwnMxlFRO9+97tzi9988830/ve/f+wmH3jgAVYwDR5//HEOzf/0T/80R40PGw40CZ0Ft912G73nPe/JTf9Q9CgdKBS18g4ICAgICAjI4dSpU3Ts2LE93y8UxAsuuICe/Mqnpl4X6/33f/83F1YbFKmgN910E91www1jt4f8TwMUFv3oj/4o/cAP/AD90R/90cRxILq8ubmZUUNRHY95+4UDTULPPfdcqtVqOQuBcR8aQvcoZDLAB/685z2PHnnkkX25ePcLkP9x9/Xoo4/S0aNHaZmwrMcejjsc97JgWY99WY8bEU3kLo7LeTyTAIF8+OGHJ1ogFRFYSUDH4bzzzuNHGUABBQF92ctexgVGiACOA5ZrNBr0uc99jq2ZABQzgRu96lWvov3CgSahOHn44PCh/dRP/RRPgy0B3v/iL/6id52iXAsQ0GX60hrgmJfxuJf52MNxLxeW9biX+diX9bgnEa0zCRDJsmTyTOPxxx+nK664ggU25IE+9dRTdp4R6LDMVVddRX/+539Or3jFK5gDwVsUIh3IPK6fX/qlX2ICul+V8QeehAL4wK6//np6+ctfzh8kLJra7TZXywcEBAQEBAQELBM++9nPcjESHt/2bd+WmWfyZlEJD6Wz01H5tAD8REHkoYSidgZ2lx/60IdoP3HgSejrXvc6Zvnvete7uILre77ne+gf/uEfcsVKAQEBAQEBAQGLjhtuuGFi7iga/LiFXFBy0fwHj4OCA09CAYTei8Lvk4DQPCrR5mmHcBiwrMe9zMcejjsc97JgWY89HPdyHfcyoJLst+dBQEBAQEBAQEDA0uHAd0wKCAgICAgICAhYPAQSGhAQEBAQEBAQsOcIJDQgICAgICAgIGDPsdAkFBVgqBBDRdgrX/lK+sIXvkCLDrQC43aW4iFbfC0K/uVf/oV+8id/ki666CI+xr/5m7/JzEeqMxwVLrzwQlpdXaWrr76avva1r9EyHDuqJt1rAG3dDnsntO/7vu+jI0eO0Pnnn8++wbAfkej1enTjjTfSOeecQxsbG2xD4ja6WNRjh2ege87f/OY302HGhz/8YXrxi19sPTHhZ/j3f//3C3++Jx33Ip5rH973vvfxsb3tbW9b+HO+zFhYEvrJT36SPUZRUfcf//Ef9JKXvIQ9sU6cOEGLju/+7u+mJ554wj7+9V//lRYN8IrFOS2ymvit3/ot+oM/+AP6yEc+Qvfddx+tr6/z+ccfsUU/dgCkU14DH//4x+kw4+677+Yfn3vvvZc98uCBd8011/BnYfD2t7+dPvOZz9Add9zBy6Ol3XXXXUeHHWWOHUDfaHnO8R04zID/IYjIl770JfriF79IV155Jb361a+mL3/5ywt9vicd9yKeaxf//u//Th/96EeZjEss6jlfaiQLile84hXJjTfeaN9HUZRcdNFFyW233ZYsMm699dbkJS95SbJMwGX86U9/2r6P4zi54IILkt/+7d+20zY3N5NWq5V8/OMfTxb52IHrr78+efWrX50sMk6cOMHHfvfdd9vz22g0kjvuuMMu88ADD/Ay99xzT7LIxw78yI/8SPLWt741WXScddZZyR//8R8v1fmWx70M53pnZyf59m//9uSzn/1s5liX7ZwvCxZSCUV/V9xFIgRrgC4BeH/PPffQogNhZ4RqL7nkEvrZn/1Z7g27TECPXzQ2kOcfLcuQkrEM5x+46667OHT7nd/5nfSWt7yFTp06RYvWSxowvaTxfYdCKM850lDQb3rRzrl77AZ/8Rd/Qeeeey698IUvpHe+852ZTimHHVEU0Sc+8QlWfxGeXpbz7R73MpxrqP4/8RM/kTm3wLKc82XDoTCrnxYnT57kL6/bVQnvv/rVr9IiA0Tr9ttvZ/KBMM173vMe+qEf+iH63//9X84pWwaAgAK+82/mLTIQikeI6uKLL6avf/3rdMstt9C1117Lf6hrtRoddsRxzHliP/iDP8g/wgDOa7PZpOPHjy/0OfcdO/AzP/Mz3EcaN5/3338//dqv/Rrnjf71X/81HWb8z//8D5MvpNEgB/DTn/40XX755fRf//VfC32+i457kc81AMKN9DmE410sy3d82bCQJHSZAbJhgHwakFL8wfrUpz5Fb3jDG/Z1bAF7g9e//vX29Yte9CK+Di699FJWR6+66ipaBKUEN1WLmOs867G/6U1vypxzFOThXOMmBOf+sAI30yCcUH//6q/+iq6//nrOBVx0FB03iOiinutHH32U3vrWt3LeM4qJA5YDCxmOR5gCio9bNYf3F1xwAS0TcNf4Hd/xHfTQQw/RssCc43D+FZCWge/EIlwDaN/7d3/3d3TnnXdyAYcBzivScDY3Nxf2nBcduw+4+QQO+zmH8nXZZZfRy172MnYJQEHe7//+7y/8+S467kU+1wi3o3D4pS99KdXrdX6AeKPAFK+heC7yOV9WLCQJxRcYX97Pfe5zmTAW3su8mmXA7u4u3yHjbnlZgDA0/ijJ87+9vc1V8st2/oHHHnuMc0IP8zWAGiyQMIQlP//5z/M5lsD3vdFoZM45QpTIhz7s53zSsfsAFQ04zOfcB/wd7/f7C32+xx33Ip9rqLlIQ8DxmMfLX/5yrmswr5fpnC8NkgXFJz7xCa6Gvv3225OvfOUryZve9Kbk+PHjyZNPPpksMm666abkrrvuSh5++OHk3/7t35Krr746Offcc7midtEqKP/zP/+TH7iMP/CBD/Dr//u//+P573vf+/h8/+3f/m1y//33c7X4xRdfnHS73WSRjx3z3vGOd3C1KK6Bf/7nf05e+tKXcrVpr9dLDive8pa3JMeOHeNr+4knnrCPTqdjl3nzm9+cPPe5z00+//nPJ1/84heTV73qVfw47Jh07A899FDy3ve+l48Z5xzX/CWXXJL88A//cHKYcfPNN7MDAI4J32G8r1QqyT/90z8t9Pked9yLeq6L4DoBLOo5X2YsLAkFPvjBD/IF22w22bLp3nvvTRYdr3vd65ILL7yQj/nZz342v8cfrkXDnXfeyQTMfcCeyNg0/fqv/3ryrGc9i29GrrrqquTBBx9MFv3YQUyuueaa5LzzzmM7k+c973nJG9/4xkN/8+U7Xjw+9rGP2WVwg/ELv/ALbGeztraWvOY1r2Gydtgx6dgfeeQRJiFnn302X+uXXXZZ8iu/8ivJ1tZWcpjx8z//83z94m8Zrmd8hw0BXeTzPe64F/VclyWhi3rOlxkV/LffamxAQEBAQEBAQMByYSFzQgMCAgICAgICAg42AgkNCAgICAgICAjYcwQSGhAQEBAQEBAQsOcIJDQgICAgICAgIGDPEUhoQEBAQEBAQEDAniOQ0ICAgICAgICAgD1HIKEBAQEBAQEBAQF7jkBCAwICAgICAgIC9hyBhAYEBAQEBAQEBOw5AgkNCAg41LjiiivobW97234PIyAgICBgSgQSGhAQEBAQEBAQsOcIveMDAgIOLW644Qb6sz/7s8y0hx9+mJ7//Ofv25gCAgICAsohkNCAgIBDi62tLbr22mvphS98Ib33ve/laeeddx7VarX9HlpAQEBAwATUJy0QEBAQcFBx7NgxajabtLa2RhdccMF+DycgICAgYAqEnNCAgICAgICAgIA9RyChAQEBAQEBAQEBe45AQgMCAg41EI6Pomi/hxEQEBAQMCUCCQ0ICDjUQCX8fffdR9/4xjfo5MmTFMfxfg8pICAgIKAEAgkNCAg41HjHO97B1fCXX345V8Y/8sgj+z2kgICAgIASCBZNAQEBAQEBAQEBe46ghAYEBAQEBAQEBOw5AgkNCAgICAgICAjYcwQSGhAQEBAQEBAQsOcIJDQgICAgICAgIGDPEUhoQEBAQEBAQEDAniOQ0ICAgICAgICAgD1HIKEBAQEBAQEBAQF7jkBCAwICAgICAgIC9hyBhAYEBAQEBAQEBOw5AgkNCAgICAgICAjYcwQSGhAQEBAQEBAQsOcIJDQgICAgICAgIID2Gv8P3649zSzA6dQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x380 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vs = run_cable(braintools.quad.imex_ars222_step, 0.2)\n",
    "plt.figure(figsize=(7, 3.8))\n",
    "plt.imshow(vs.T, aspect=\"auto\", origin=\"lower\", extent=[0, 40, 0, N * dx], cmap=\"RdBu_r\")\n",
    "plt.colorbar(label=\"v\")\n",
    "plt.xlabel(\"t\"); plt.ylabel(\"x\"); plt.title(\"Travelling pulse, IMEX ARS(2,2,2), dt = 0.2\")\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cb9e605",
   "metadata": {},
   "source": [
    "RK4 diverges at `dt = 0.01`, just above its stability limit. IMEX ARS(2,2,2) keeps the pulse front within 0.06 of the reference at `dt = 0.2`, a step 40 times larger than the largest stable RK4 step. IMEX Euler is stable too, but first order: its front lags by 2 space units at `dt = 0.2`, and the lag halves with the step.\n",
    "\n",
    "Each IMEX step costs more than an explicit step (a Newton solve with GMRES iterations), so the saving in wall time is smaller than the saving in steps. It grows with stiffness: halving $\\Delta x$ quarters the explicit stability limit but leaves the IMEX step unchanged."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85219cf0",
   "metadata": {},
   "source": [
    "## 3. Delay Differential Equations\n",
    "\n",
    "### Calling convention\n",
    "\n",
    "`step(f, y, t, history_fn, delays, *args)`. Note the different argument order of the right-hand side: `f(t, y, y_delayed_1, y_delayed_2, ..., *args)`, time first. `delays` is one delay or a list; `history_fn(s)` must return the state at any past time $s$, including times between grid points and, for the initial interval, the prescribed initial function.\n",
    "\n",
    "You are responsible for the history. Inside `jax.lax.scan`, a convenient approach is to carry a buffer of all past values on the time grid and interpolate in it.\n",
    "\n",
    "### Interpolation limits the order\n",
    "\n",
    "The test equation $y'(t) = -y(t - 1)$ with $y(t) = 1$ for $t \\le 0$ has a piecewise-polynomial exact solution, obtained by integrating interval by interval (*method of steps*). We compare **linear** interpolation of the history with **cubic Hermite** interpolation, which also uses the stored derivatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "784b8967",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:55.916051Z",
     "iopub.status.busy": "2026-10-16T04:21:55.915053Z",
     "iopub.status.idle": "2026-10-16T04:21:59.005744Z",
     "shell.execute_reply": "2026-10-16T04:21:59.005744Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_euler_step     linear   error at dt=0.0125: 6.3e-03   orders [1.05 1.02 1.01]\n",
      "dde_euler_step     hermite  error at dt=0.0125: 6.3e-03   orders [1.05 1.02 1.01]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_euler_pc_step  linear   error at dt=0.0125: 6.2e-03   orders [0.95 0.98 0.99]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_euler_pc_step  hermite  error at dt=0.0125: 5.2e-03   orders [0.95 1.18 1.04]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_heun_step      linear   error at dt=0.0125: 1.3e-05   orders [2. 2. 2.]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_heun_step      hermite  error at dt=0.0125: 1.3e-05   orders [2. 2. 2.]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_heun_pc_step   linear   error at dt=0.0125: 1.3e-05   orders [2. 2. 2.]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_heun_pc_step   hermite  error at dt=0.0125: 1.3e-05   orders [2. 2. 2.]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_rk4_step       linear   error at dt=0.0125: 1.3e-05   orders [2. 2. 2.]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dde_rk4_step       hermite  error at dt=0.0125: 7.2e-16   orders [ 1.   -3.32 -1.38]\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "def dde_exact(t):\n",
    "    n = int(np.floor(t)) + 1\n",
    "    return sum((-1) ** k * (t - (k - 1)) ** k / math.factorial(k) for k in range(n + 1))\n",
    "\n",
    "f_dde = lambda t, y, y_delayed: -y_delayed\n",
    "T, tau = 3.0, 1.0\n",
    "\n",
    "def solve_dde(step, dt, interpolation):\n",
    "    n = int(round(T / dt))\n",
    "    t_grid = jnp.arange(n + 1) * dt\n",
    "    ys, dys = jnp.ones(n + 1), jnp.zeros(n + 1)   # values and derivatives on the grid\n",
    "\n",
    "    def body(carry, i):\n",
    "        ys, dys = carry\n",
    "\n",
    "        def history(s):\n",
    "            if interpolation == \"linear\":\n",
    "                inside = jnp.interp(s, t_grid, ys)\n",
    "            else:  # cubic Hermite on [t_j, t_j+1]\n",
    "                j = jnp.clip(jnp.floor(s / dt).astype(int), 0, n - 1)\n",
    "                h = (s - t_grid[j]) / dt\n",
    "                inside = ((2 * h ** 3 - 3 * h ** 2 + 1) * ys[j] + (h ** 3 - 2 * h ** 2 + h) * dt * dys[j]\n",
    "                          + (-2 * h ** 3 + 3 * h ** 2) * ys[j + 1] + (h ** 3 - h ** 2) * dt * dys[j + 1])\n",
    "            return jnp.where(s <= 0, 1.0, inside)   # initial function for s <= 0\n",
    "\n",
    "        t = i * dt\n",
    "        dys = dys.at[i].set(f_dde(t, ys[i], history(t - tau)))\n",
    "        ys = ys.at[i + 1].set(step(f_dde, ys[i], t, history, tau))\n",
    "        return (ys, dys), None\n",
    "\n",
    "    with brainstate.environ.context(dt=dt):\n",
    "        (ys, _), _ = jax.lax.scan(body, (ys, dys), jnp.arange(n))\n",
    "    return float(ys[-1])\n",
    "\n",
    "dts = [0.1, 0.05, 0.025, 0.0125]\n",
    "for name in [\"dde_euler_step\", \"dde_euler_pc_step\", \"dde_heun_step\", \"dde_heun_pc_step\", \"dde_rk4_step\"]:\n",
    "    for interpolation in [\"linear\", \"hermite\"]:\n",
    "        e = np.array([abs(solve_dde(getattr(braintools.quad, name), dt, interpolation) - dde_exact(T)) for dt in dts])\n",
    "        orders = np.log2(e[:-1] / np.maximum(e[1:], 1e-300))\n",
    "        print(f\"{name:18s} {interpolation:8s} error at dt=0.0125: {e[-1]:.1e}   orders {np.round(orders, 2)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e7b453c",
   "metadata": {},
   "source": [
    "- The Euler-type steppers are first order and the Heun-type steppers second order, with either interpolation.\n",
    "- RK4 with **linear** interpolation is only second order: its intermediate stages query the history between grid points, where linear interpolation has an $O(\\Delta t^2)$ error.\n",
    "- With **cubic Hermite** interpolation, RK4 is exact up to round-off here: the solution is a piecewise cubic polynomial on $[0, 3]$, which both the interpolant and the method reproduce exactly (orders computed from round-off-level errors are meaningless). In general, cubic Hermite interpolation is what fourth-order accuracy requires.\n",
    "\n",
    "The `jnp.where(s <= 0, 1.0, ...)` in `history` matters. The solution has a kink at $t = 0$ (its derivative jumps from 0 to $-1$); interpolating across it with the derivative stored at $t = 0$ costs RK4 an order. Delay equations propagate such kinks to $t = \\tau, 2\\tau, \\dots$, so choose $\\Delta t$ such that the delays are multiples of it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f803c16c",
   "metadata": {},
   "source": [
    "### Example: oscillations from delayed inhibition\n",
    "\n",
    "A population with delayed inhibitory self-feedback,\n",
    "\n",
    "$$\\tau\\,r'(t) = -r(t) + F\\big(I - w\\,r(t - d)\\big), \\qquad F(x) = \\frac{1}{1 + e^{-x}},$$\n",
    "\n",
    "has a fixed point at $r^* = 0.5$ for $I = w/2$. Linearizing, perturbations obey $\\tau x' = -x - \\tfrac{w}{4}\\,x(t - d)$, which loses stability through a Hopf bifurcation when the delay exceeds\n",
    "\n",
    "$$d_c = \\tau\\,\\frac{\\pi - \\arctan \\omega\\tau}{\\omega\\tau}, \\qquad \\omega\\tau = \\sqrt{(w/4)^2 - 1}.$$\n",
    "\n",
    "With $\\tau = 10$ ms and $w = 10$, $d_c \\approx 8.7$ ms. We integrate with `dde_heun_step` and a linearly interpolated buffer (enough for a second-order method):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c8319f70",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-16T04:21:59.006748Z",
     "iopub.status.busy": "2026-10-16T04:21:59.006748Z",
     "iopub.status.idle": "2026-10-16T04:22:00.534256Z",
     "shell.execute_reply": "2026-10-16T04:22:00.534256Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted critical delay: 8.65 ms\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tau_r, w, I = 10.0, 10.0, 5.0\n",
    "F = lambda x: 1.0 / (1.0 + jnp.exp(-x))\n",
    "rate_rhs = lambda t, r, r_delayed: (-r + F(I - w * r_delayed)) / tau_r\n",
    "\n",
    "def simulate_delay(d, dt=0.05, T=600.0, r0=0.45):\n",
    "    n = int(round(T / dt))\n",
    "    t_grid = jnp.arange(n + 1) * dt\n",
    "    rs = jnp.full(n + 1, r0)\n",
    "\n",
    "    def body(rs, i):\n",
    "        history = lambda s: jnp.where(s <= 0, r0, jnp.interp(s, t_grid, rs))\n",
    "        r_next = braintools.quad.dde_heun_step(rate_rhs, rs[i], i * dt, history, d)\n",
    "        return rs.at[i + 1].set(r_next), None\n",
    "\n",
    "    with brainstate.environ.context(dt=dt):\n",
    "        rs, _ = jax.lax.scan(body, rs, jnp.arange(n))\n",
    "    return np.asarray(t_grid), np.asarray(rs)\n",
    "\n",
    "omega_tau = np.sqrt((w / 4) ** 2 - 1)\n",
    "d_c = tau_r * (np.pi - np.arctan(omega_tau)) / omega_tau\n",
    "print(f\"predicted critical delay: {d_c:.2f} ms\")\n",
    "\n",
    "delays = np.arange(2.0, 20.1, 1.0)\n",
    "amplitudes = []\n",
    "for d in delays:\n",
    "    ts, rs = simulate_delay(d)\n",
    "    tail = rs[ts > 400]\n",
    "    amplitudes.append(tail.max() - tail.min())\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(12, 3.5))\n",
    "for d in [6.0, 12.0]:\n",
    "    ts, rs = simulate_delay(d)\n",
    "    ax[0].plot(ts, rs, label=f\"d = {d:g} ms\")\n",
    "ax[0].set_xlim(0, 300); ax[0].set_xlabel(\"t (ms)\"); ax[0].set_ylabel(\"r\"); ax[0].legend()\n",
    "ax[1].plot(delays, amplitudes, \"o-\")\n",
    "ax[1].axvline(d_c, color=\"k\", ls=\"--\", label=\"$d_c$ (linear theory)\")\n",
    "ax[1].set_xlabel(\"delay d (ms)\"); ax[1].set_ylabel(\"oscillation amplitude\"); ax[1].legend()\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
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   "cell_type": "markdown",
   "id": "8f055820",
   "metadata": {},
   "source": [
    "Below $d_c$ the perturbation decays to the fixed point; above it, a stable oscillation appears whose amplitude grows with the delay. The simulated onset, between 8 and 9 ms, agrees with the linear prediction of 8.65 ms. The small amplitude at $d = 8$ ms is a slowly decaying transient: near the bifurcation, perturbations decay slowly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9857559c",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "- IMEX steppers split the right-hand side into an explicit and an implicit part; the implicit stages are solved with Newton's method (dense for small states, matrix-free GMRES for large ones). `max_iter` counts Newton iterations: one suffices for linear implicit parts.\n",
    "- `imex_euler_step` is first order, `imex_ars222_step` and `imex_cnab_step` second order. ARS(2,2,2) is L-stable and damps very fast modes; CNAB is a cheaper two-step method that lets them oscillate.\n",
    "- Implicit treatment of stiff linear terms such as cable diffusion permits steps far beyond the explicit stability limit.\n",
    "- DDE right-hand sides take time first: `f(t, y, *delayed)`. You provide `history_fn`; its interpolation must match the order of the method (linear for Euler/Heun, cubic Hermite for RK4), and it must return the initial function for times before the start."
   ]
  }
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