binary_sim.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "debce0c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as np\n",
    "\n",
    "from elrpy.dgp import normal_sim_binary\n",
    "from elrpy.losses import get_wrapped_loss, lyapunov_binary_loss\n",
    "from elrpy.optim import get_cg_fn, fit\n",
    "from elrpy.utils import get_dims, get_bootstrap_weights, get_mean_fn, get_mapped_fn\n",
    "from elrpy.models import init_binary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "09d9e7cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = jax.random.PRNGKey(123)\n",
    "n=1_000_000\n",
    "d=10\n",
    "k=800\n",
    "rng, next_rng = jax.random.split(rng)\n",
    "beta, gamma, X, Y, (group_Xs, group_Ys, group_Ns) = normal_sim_binary(next_rng, n, d, k)\n",
    "group_data = group_Xs, group_Ys, group_Ns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_groups, dim, num_outcomes = k, d, 1 # get_dims((group_Xs, group_Ys, group_Ns))\n",
    "model_fn, model_params = init_binary((group_Xs, group_Ys, group_Ns))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ccdf5959",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/njwfish/Dropbox/elrpy/elrpy/utils.py:78: FutureWarning: jax.tree_flatten is deprecated, and will be removed in a future release. Use jax.tree_util.tree_flatten instead.\n",
      "  group_sizes, tree_def = jax.tree_flatten(jax.tree_map(lambda x: x.shape[0], group_data[0]))\n"
     ]
    }
   ],
   "source": [
    "w = get_bootstrap_weights(rng, group_data, 1_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "14003607",
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_fn = get_mean_fn(get_wrapped_loss(lyapunov_binary_loss, model_fn, num_groups))\n",
    "grad_fn = jax.jit(jax.vmap(jax.value_and_grad(loss_fn), in_axes=(0, None, None, None, 0)))\n",
    "hess_fn = jax.jit(jax.vmap(jax.hessian(loss_fn), in_axes=(0, None, None, None, 0)))\n",
    "mapped_loss_and_grad_fn = get_mapped_fn(grad_fn)\n",
    "mapped_hess_fn = get_mapped_fn(hess_fn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "79c930bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "w1 = jax.tree_map(lambda x: np.array([[1]]), w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[-0.87864816],\n",
       "       [-0.3400542 ],\n",
       "       [ 0.4082143 ],\n",
       "       [-0.68819124],\n",
       "       [ 0.62690854],\n",
       "       [ 0.00423338],\n",
       "       [ 0.78910184],\n",
       "       [-0.09853928],\n",
       "       [-0.09936384],\n",
       "       [ 0.3027801 ]], dtype=float32)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Bad pipe message: %s [b'live\\r\\nAccept: */*\\r\\nAccess-Control-Request-Me', b'od: GET\\r\\nAccess-Control-Request-Headers: x-xsrftoken\\r\\nAccess-Control-Request-Private-Network: true\\r\\nOrigin: https:/']\n",
      "Bad pipe message: %s [b'live\\r\\nAccept: */*\\r\\nAccess-Control-Request-Me', b'od: GET\\r\\nAccess-Control-Request-Headers: x-xsrftoken\\r\\nAccess-Control-Request-Private-Network: true\\r\\nOrigin: https:/']\n"
     ]
    }
   ],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[-0.8762768 , -0.34314013,  0.40484962, -0.6856943 ,  0.6244844 ,\n",
       "         0.00314549,  0.78688943, -0.10029262, -0.10149286,  0.30172688]],      dtype=float32)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8dc31e29",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 \t 175.99686 \t 308.1043\n",
      "1 \t 37.515377 \t 94.49522\n",
      "2 \t 7.5288424 \t 25.497631\n",
      "3 \t 3.534454 \t 3.9352725\n",
      "4 \t 3.4087658 \t 0.14440677\n",
      "5 \t 3.408591 \t 0.00021606065\n",
      "6 \t 3.4085898 \t 1.57477e-05\n",
      "Converged!\n",
      "6 3.4085898 1.57477e-05\n"
     ]
    }
   ],
   "source": [
    "cg_fn = get_cg_fn(mapped_loss_and_grad_fn, mapped_hess_fn)\n",
    "\n",
    "binary_params, gd_norm, history = fit(\n",
    "    lyapunov_binary_loss, model_fn, model_params, group_data, group_weights=w1,\n",
    "    verbose=2, lr=1, print_every=1, tol=5e-5,\n",
    "    maxit=100, mapped_loss_and_dir_fn=cg_fn, keep_history=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([[-3.2967329e-04, -3.8713813e-03, -2.1677911e-03,  5.5485964e-04,\n",
       "        -1.7708540e-04, -1.0461642e-03,  1.9145012e-04, -2.0944551e-03,\n",
       "        -2.2733584e-03, -4.9710274e-05]], dtype=float32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_params - beta[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "116cc902",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Incompatible shapes for broadcasting: shapes=[(1000, 10, 10), (1000, 1000)]",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "    \u001b[0;31m[... skipping hidden 1 frame]\u001b[0m\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/util.py:284\u001b[0m, in \u001b[0;36mcache.<locals>.wrap.<locals>.wrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    283\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[0;32m--> 284\u001b[0m   \u001b[39mreturn\u001b[39;00m cached(config\u001b[39m.\u001b[39;49m_trace_context(), \u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/util.py:277\u001b[0m, in \u001b[0;36mcache.<locals>.wrap.<locals>.cached\u001b[0;34m(_, *args, **kwargs)\u001b[0m\n\u001b[1;32m    275\u001b[0m \u001b[39m@functools\u001b[39m\u001b[39m.\u001b[39mlru_cache(max_size)\n\u001b[1;32m    276\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mcached\u001b[39m(_, \u001b[39m*\u001b[39margs, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs):\n\u001b[0;32m--> 277\u001b[0m   \u001b[39mreturn\u001b[39;00m f(\u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/lax/lax.py:153\u001b[0m, in \u001b[0;36m_broadcast_shapes_cached\u001b[0;34m(*shapes)\u001b[0m\n\u001b[1;32m    151\u001b[0m \u001b[39m@cache\u001b[39m()\n\u001b[1;32m    152\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39m_broadcast_shapes_cached\u001b[39m(\u001b[39m*\u001b[39mshapes: Tuple[\u001b[39mint\u001b[39m, \u001b[39m.\u001b[39m\u001b[39m.\u001b[39m\u001b[39m.\u001b[39m]) \u001b[39m-\u001b[39m\u001b[39m>\u001b[39m Tuple[\u001b[39mint\u001b[39m, \u001b[39m.\u001b[39m\u001b[39m.\u001b[39m\u001b[39m.\u001b[39m]:\n\u001b[0;32m--> 153\u001b[0m   \u001b[39mreturn\u001b[39;00m _broadcast_shapes_uncached(\u001b[39m*\u001b[39;49mshapes)\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/lax/lax.py:169\u001b[0m, in \u001b[0;36m_broadcast_shapes_uncached\u001b[0;34m(*shapes)\u001b[0m\n\u001b[1;32m    168\u001b[0m \u001b[39mif\u001b[39;00m result_shape \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m--> 169\u001b[0m   \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mIncompatible shapes for broadcasting: shapes=\u001b[39m\u001b[39m{\u001b[39;00m\u001b[39mlist\u001b[39m(shapes)\u001b[39m}\u001b[39;00m\u001b[39m\"\u001b[39m)\n\u001b[1;32m    170\u001b[0m \u001b[39mreturn\u001b[39;00m result_shape\n",
      "\u001b[0;31mValueError\u001b[0m: Incompatible shapes for broadcasting: shapes=[(1000, 10, 10), (1000, 1000)]",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m/Users/njwfish/Dropbox/elrpy/binary_sim.ipynb Cell 9\u001b[0m line \u001b[0;36m<cell line: 3>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/elrpy/binary_sim.ipynb#X10sZmlsZQ%3D%3D?line=0'>1</a>\u001b[0m cg_fn \u001b[39m=\u001b[39m get_cg_fn(mapped_loss_and_grad_fn, mapped_hess_fn)\n\u001b[0;32m----> <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/elrpy/binary_sim.ipynb#X10sZmlsZQ%3D%3D?line=2'>3</a>\u001b[0m boot_params, gd_norm, history \u001b[39m=\u001b[39m fit(\n\u001b[1;32m      <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/elrpy/binary_sim.ipynb#X10sZmlsZQ%3D%3D?line=3'>4</a>\u001b[0m     lyapunov_binary_loss, model_fn, np\u001b[39m.\u001b[39;49mtile(model_params, (\u001b[39m1_000\u001b[39;49m, \u001b[39m1\u001b[39;49m)), group_data, group_weights\u001b[39m=\u001b[39;49mw,\n\u001b[1;32m      <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/elrpy/binary_sim.ipynb#X10sZmlsZQ%3D%3D?line=4'>5</a>\u001b[0m     verbose\u001b[39m=\u001b[39;49m\u001b[39m2\u001b[39;49m, lr\u001b[39m=\u001b[39;49m\u001b[39m1\u001b[39;49m, print_every\u001b[39m=\u001b[39;49m\u001b[39m1\u001b[39;49m, tol\u001b[39m=\u001b[39;49m\u001b[39m1e-4\u001b[39;49m,\n\u001b[1;32m      <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/elrpy/binary_sim.ipynb#X10sZmlsZQ%3D%3D?line=5'>6</a>\u001b[0m     maxit\u001b[39m=\u001b[39;49m\u001b[39m100\u001b[39;49m, mapped_loss_and_dir_fn\u001b[39m=\u001b[39;49mcg_fn,\n\u001b[1;32m      <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/elrpy/binary_sim.ipynb#X10sZmlsZQ%3D%3D?line=6'>7</a>\u001b[0m )\n",
      "File \u001b[0;32m~/Dropbox/elrpy/elrpy/optim.py:196\u001b[0m, in \u001b[0;36mfit\u001b[0;34m(loss_fn, model_fn, model_params, group_data, lr, maxit, tol, verbose, print_every, save_every, save_dir, mapped_loss_and_dir_fn, group_weights, keep_history)\u001b[0m\n\u001b[1;32m    193\u001b[0m     history \u001b[39m=\u001b[39m []\n\u001b[1;32m    195\u001b[0m \u001b[39mfor\u001b[39;00m i \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(maxit):\n\u001b[0;32m--> 196\u001b[0m     out \u001b[39m=\u001b[39m mapped_loss_and_dir_fn(model_params, group_data)\n\u001b[1;32m    197\u001b[0m     \u001b[39mif\u001b[39;00m \u001b[39mlen\u001b[39m(out) \u001b[39m==\u001b[39m \u001b[39m2\u001b[39m:\n\u001b[1;32m    198\u001b[0m         loss, grad \u001b[39m=\u001b[39m out\n",
      "File \u001b[0;32m~/Dropbox/elrpy/elrpy/optim.py:30\u001b[0m, in \u001b[0;36mget_cg_fn.<locals>.cg_fn\u001b[0;34m(params, *args)\u001b[0m\n\u001b[1;32m     28\u001b[0m loss \u001b[39m+\u001b[39m\u001b[39m=\u001b[39m \u001b[39m0.5\u001b[39m \u001b[39m*\u001b[39m l2 \u001b[39m*\u001b[39m np\u001b[39m.\u001b[39msum(params \u001b[39m*\u001b[39m\u001b[39m*\u001b[39m \u001b[39m2\u001b[39m)\n\u001b[1;32m     29\u001b[0m grad \u001b[39m+\u001b[39m\u001b[39m=\u001b[39m l2 \u001b[39m*\u001b[39m params\n\u001b[0;32m---> 30\u001b[0m hess \u001b[39m+\u001b[39m\u001b[39m=\u001b[39m l2 \u001b[39m*\u001b[39m np\u001b[39m.\u001b[39meye(hess\u001b[39m.\u001b[39mshape[\u001b[39m0\u001b[39m])\n\u001b[1;32m     31\u001b[0m \u001b[39mreturn\u001b[39;00m np\u001b[39m.\u001b[39mmean(loss), jax\u001b[39m.\u001b[39mvmap(np\u001b[39m.\u001b[39mlinalg\u001b[39m.\u001b[39mlstsq, in_axes\u001b[39m=\u001b[39m(\u001b[39m0\u001b[39m, \u001b[39m0\u001b[39m))(hess, grad)[\u001b[39m0\u001b[39m], np\u001b[39m.\u001b[39mmax(np\u001b[39m.\u001b[39mlinalg\u001b[39m.\u001b[39mnorm(grad, axis\u001b[39m=\u001b[39m\u001b[39m-\u001b[39m\u001b[39m1\u001b[39m))\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/numpy/array_methods.py:258\u001b[0m, in \u001b[0;36m_defer_to_unrecognized_arg.<locals>.deferring_binary_op\u001b[0;34m(self, other)\u001b[0m\n\u001b[1;32m    256\u001b[0m args \u001b[39m=\u001b[39m (other, \u001b[39mself\u001b[39m) \u001b[39mif\u001b[39;00m swap \u001b[39melse\u001b[39;00m (\u001b[39mself\u001b[39m, other)\n\u001b[1;32m    257\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39misinstance\u001b[39m(other, _accepted_binop_types):\n\u001b[0;32m--> 258\u001b[0m   \u001b[39mreturn\u001b[39;00m binary_op(\u001b[39m*\u001b[39;49margs)\n\u001b[1;32m    259\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39misinstance\u001b[39m(other, _rejected_binop_types):\n\u001b[1;32m    260\u001b[0m   \u001b[39mraise\u001b[39;00m \u001b[39mTypeError\u001b[39;00m(\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39munsupported operand type(s) for \u001b[39m\u001b[39m{\u001b[39;00mopchar\u001b[39m}\u001b[39;00m\u001b[39m: \u001b[39m\u001b[39m\"\u001b[39m\n\u001b[1;32m    261\u001b[0m                   \u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m{\u001b[39;00m\u001b[39mtype\u001b[39m(args[\u001b[39m0\u001b[39m])\u001b[39m.\u001b[39m\u001b[39m__name__\u001b[39m\u001b[39m!r}\u001b[39;00m\u001b[39m and \u001b[39m\u001b[39m{\u001b[39;00m\u001b[39mtype\u001b[39m(args[\u001b[39m1\u001b[39m])\u001b[39m.\u001b[39m\u001b[39m__name__\u001b[39m\u001b[39m!r}\u001b[39;00m\u001b[39m\"\u001b[39m)\n",
      "    \u001b[0;31m[... skipping hidden 12 frame]\u001b[0m\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/numpy/ufuncs.py:96\u001b[0m, in \u001b[0;36m_maybe_bool_binop.<locals>.fn\u001b[0;34m(x1, x2)\u001b[0m\n\u001b[1;32m     95\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mfn\u001b[39m(x1, x2, \u001b[39m/\u001b[39m):\n\u001b[0;32m---> 96\u001b[0m   x1, x2 \u001b[39m=\u001b[39m promote_args(numpy_fn\u001b[39m.\u001b[39;49m\u001b[39m__name__\u001b[39;49m, x1, x2)\n\u001b[1;32m     97\u001b[0m   \u001b[39mreturn\u001b[39;00m lax_fn(x1, x2) \u001b[39mif\u001b[39;00m x1\u001b[39m.\u001b[39mdtype \u001b[39m!=\u001b[39m np\u001b[39m.\u001b[39mbool_ \u001b[39melse\u001b[39;00m bool_lax_fn(x1, x2)\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/numpy/util.py:357\u001b[0m, in \u001b[0;36mpromote_args\u001b[0;34m(fun_name, *args)\u001b[0m\n\u001b[1;32m    355\u001b[0m check_arraylike(fun_name, \u001b[39m*\u001b[39margs)\n\u001b[1;32m    356\u001b[0m _check_no_float0s(fun_name, \u001b[39m*\u001b[39margs)\n\u001b[0;32m--> 357\u001b[0m \u001b[39mreturn\u001b[39;00m promote_shapes(fun_name, \u001b[39m*\u001b[39;49mpromote_dtypes(\u001b[39m*\u001b[39;49margs))\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/numpy/util.py:247\u001b[0m, in \u001b[0;36mpromote_shapes\u001b[0;34m(fun_name, *args)\u001b[0m\n\u001b[1;32m    245\u001b[0m \u001b[39mif\u001b[39;00m config\u001b[39m.\u001b[39mjax_numpy_rank_promotion \u001b[39m!=\u001b[39m \u001b[39m\"\u001b[39m\u001b[39mallow\u001b[39m\u001b[39m\"\u001b[39m:\n\u001b[1;32m    246\u001b[0m   _rank_promotion_warning_or_error(fun_name, shapes)\n\u001b[0;32m--> 247\u001b[0m result_rank \u001b[39m=\u001b[39m \u001b[39mlen\u001b[39m(lax\u001b[39m.\u001b[39;49mbroadcast_shapes(\u001b[39m*\u001b[39;49mshapes))\n\u001b[1;32m    248\u001b[0m \u001b[39mreturn\u001b[39;00m [_broadcast_to(arg, (\u001b[39m1\u001b[39m,) \u001b[39m*\u001b[39m (result_rank \u001b[39m-\u001b[39m \u001b[39mlen\u001b[39m(shp)) \u001b[39m+\u001b[39m shp)\n\u001b[1;32m    249\u001b[0m         \u001b[39mfor\u001b[39;00m arg, shp \u001b[39min\u001b[39;00m \u001b[39mzip\u001b[39m(args, shapes)]\n",
      "    \u001b[0;31m[... skipping hidden 1 frame]\u001b[0m\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/lax/lax.py:169\u001b[0m, in \u001b[0;36m_broadcast_shapes_uncached\u001b[0;34m(*shapes)\u001b[0m\n\u001b[1;32m    167\u001b[0m result_shape \u001b[39m=\u001b[39m _try_broadcast_shapes(shape_list)\n\u001b[1;32m    168\u001b[0m \u001b[39mif\u001b[39;00m result_shape \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m--> 169\u001b[0m   \u001b[39mraise\u001b[39;00m \u001b[39mValueError\u001b[39;00m(\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mIncompatible shapes for broadcasting: shapes=\u001b[39m\u001b[39m{\u001b[39;00m\u001b[39mlist\u001b[39m(shapes)\u001b[39m}\u001b[39;00m\u001b[39m\"\u001b[39m)\n\u001b[1;32m    170\u001b[0m \u001b[39mreturn\u001b[39;00m result_shape\n",
      "\u001b[0;31mValueError\u001b[0m: Incompatible shapes for broadcasting: shapes=[(1000, 10, 10), (1000, 1000)]"
     ]
    }
   ],
   "source": [
    "cg_fn = get_cg_fn(mapped_loss_and_grad_fn, mapped_hess_fn)\n",
    "\n",
    "boot_params, gd_norm, history = fit(\n",
    "    lyapunov_binary_loss, model_fn, np.tile(model_params, (1_000, 1)), group_data, group_weights=w,\n",
    "    verbose=2, lr=1, print_every=1, tol=1e-4,\n",
    "    maxit=100, mapped_loss_and_dir_fn=cg_fn,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2fb1cd90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array([-0.86597353, -0.3356535 ,  0.4129642 , -0.6760616 ,  0.63289416,\n",
       "         0.01118292,  0.79537773, -0.09305118, -0.09374186,  0.3101299 ],      dtype=float32),\n",
       " Array([-0.87597793, -0.34300178,  0.40539646, -0.68573797,  0.6244735 ,\n",
       "         0.00345865,  0.78631145, -0.10019332, -0.10153584,  0.30175263],      dtype=float32),\n",
       " Array([-0.88645166, -0.35060707,  0.3983707 , -0.69541305,  0.61590546,\n",
       "        -0.00455674,  0.77769244, -0.10778944, -0.10931624,  0.29322946],      dtype=float32))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(boot_params, 97.5, axis=0), np.mean(boot_params, axis=0), np.percentile(boot_params, 2.5, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "07bfb85a",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "Shapes must be 1D sequences of concrete values of integer type, got (None, 1).",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/core.py:1898\u001b[0m, in \u001b[0;36m_dim_handler_and_canonical\u001b[0;34m(*dlist)\u001b[0m\n\u001b[1;32m   1897\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[0;32m-> 1898\u001b[0m   canonical\u001b[39m.\u001b[39mappend(operator\u001b[39m.\u001b[39;49mindex(d))\n\u001b[1;32m   1899\u001b[0m \u001b[39mexcept\u001b[39;00m \u001b[39mTypeError\u001b[39;00m:\n",
      "\u001b[0;31mTypeError\u001b[0m: 'NoneType' object cannot be interpreted as an integer",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m/Users/njwfish/Dropbox/eipy/binary_sim.ipynb Cell 10\u001b[0m in \u001b[0;36m<cell line: 8>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/eipy/binary_sim.ipynb#W5sZmlsZQ%3D%3D?line=6'>7</a>\u001b[0m losses \u001b[39m=\u001b[39m []\n\u001b[1;32m      <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/eipy/binary_sim.ipynb#W5sZmlsZQ%3D%3D?line=7'>8</a>\u001b[0m \u001b[39mfor\u001b[39;00m (x, y) \u001b[39min\u001b[39;00m \u001b[39mzip\u001b[39m(X\u001b[39m.\u001b[39mflatten(), Y\u001b[39m.\u001b[39mflatten()):\n\u001b[0;32m----> <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/eipy/binary_sim.ipynb#W5sZmlsZQ%3D%3D?line=8'>9</a>\u001b[0m     min_eighs\u001b[39m.\u001b[39mappend(np\u001b[39m.\u001b[39mlinalg\u001b[39m.\u001b[39meigh(mapped_hess_fn(np\u001b[39m.\u001b[39;49marray([x, y]), (\u001b[39m*\u001b[39;49mgroup_data, w1)))[\u001b[39m0\u001b[39m][\u001b[39m0\u001b[39m])\n\u001b[1;32m     <a href='vscode-notebook-cell:/Users/njwfish/Dropbox/eipy/binary_sim.ipynb#W5sZmlsZQ%3D%3D?line=9'>10</a>\u001b[0m     losses\u001b[39m.\u001b[39mappend(mapped_loss_and_grad_fn(np\u001b[39m.\u001b[39marray([x, y]), (\u001b[39m*\u001b[39mgroup_data, w1))[\u001b[39m0\u001b[39m])\n",
      "File \u001b[0;32m~/Dropbox/eipy/elrpy/optim.py:15\u001b[0m, in \u001b[0;36mget_mapped_fn.<locals>.mapped_fn\u001b[0;34m(model_params, args)\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mmapped_fn\u001b[39m(model_params, args):\n\u001b[0;32m---> 15\u001b[0m     group_values \u001b[39m=\u001b[39m jax\u001b[39m.\u001b[39;49mtree_util\u001b[39m.\u001b[39;49mtree_map(\n\u001b[1;32m     16\u001b[0m         \u001b[39mlambda\u001b[39;49;00m \u001b[39m*\u001b[39;49margs: fn(model_params, \u001b[39m*\u001b[39;49margs), \u001b[39m*\u001b[39;49margs\n\u001b[1;32m     17\u001b[0m     )\n\u001b[1;32m     18\u001b[0m     \u001b[39mreturn\u001b[39;00m reduce_sum(group_values)\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/tree_util.py:210\u001b[0m, in \u001b[0;36mtree_map\u001b[0;34m(f, tree, is_leaf, *rest)\u001b[0m\n\u001b[1;32m    208\u001b[0m leaves, treedef \u001b[39m=\u001b[39m tree_flatten(tree, is_leaf)\n\u001b[1;32m    209\u001b[0m all_leaves \u001b[39m=\u001b[39m [leaves] \u001b[39m+\u001b[39m [treedef\u001b[39m.\u001b[39mflatten_up_to(r) \u001b[39mfor\u001b[39;00m r \u001b[39min\u001b[39;00m rest]\n\u001b[0;32m--> 210\u001b[0m \u001b[39mreturn\u001b[39;00m treedef\u001b[39m.\u001b[39;49munflatten(f(\u001b[39m*\u001b[39;49mxs) \u001b[39mfor\u001b[39;49;00m xs \u001b[39min\u001b[39;49;00m \u001b[39mzip\u001b[39;49m(\u001b[39m*\u001b[39;49mall_leaves))\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/tree_util.py:210\u001b[0m, in \u001b[0;36m<genexpr>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m    208\u001b[0m leaves, treedef \u001b[39m=\u001b[39m tree_flatten(tree, is_leaf)\n\u001b[1;32m    209\u001b[0m all_leaves \u001b[39m=\u001b[39m [leaves] \u001b[39m+\u001b[39m [treedef\u001b[39m.\u001b[39mflatten_up_to(r) \u001b[39mfor\u001b[39;00m r \u001b[39min\u001b[39;00m rest]\n\u001b[0;32m--> 210\u001b[0m \u001b[39mreturn\u001b[39;00m treedef\u001b[39m.\u001b[39munflatten(f(\u001b[39m*\u001b[39;49mxs) \u001b[39mfor\u001b[39;00m xs \u001b[39min\u001b[39;00m \u001b[39mzip\u001b[39m(\u001b[39m*\u001b[39mall_leaves))\n",
      "File \u001b[0;32m~/Dropbox/eipy/elrpy/optim.py:16\u001b[0m, in \u001b[0;36mget_mapped_fn.<locals>.mapped_fn.<locals>.<lambda>\u001b[0;34m(*args)\u001b[0m\n\u001b[1;32m     14\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mmapped_fn\u001b[39m(model_params, args):\n\u001b[1;32m     15\u001b[0m     group_values \u001b[39m=\u001b[39m jax\u001b[39m.\u001b[39mtree_util\u001b[39m.\u001b[39mtree_map(\n\u001b[0;32m---> 16\u001b[0m         \u001b[39mlambda\u001b[39;00m \u001b[39m*\u001b[39margs: fn(model_params, \u001b[39m*\u001b[39;49margs), \u001b[39m*\u001b[39margs\n\u001b[1;32m     17\u001b[0m     )\n\u001b[1;32m     18\u001b[0m     \u001b[39mreturn\u001b[39;00m reduce_sum(group_values)\n",
      "    \u001b[0;31m[... skipping hidden 18 frame]\u001b[0m\n",
      "File \u001b[0;32m~/Dropbox/Mac/Downloads/jax/jax/_src/core.py:1900\u001b[0m, in \u001b[0;36m_dim_handler_and_canonical\u001b[0;34m(*dlist)\u001b[0m\n\u001b[1;32m   1898\u001b[0m       canonical\u001b[39m.\u001b[39mappend(operator\u001b[39m.\u001b[39mindex(d))\n\u001b[1;32m   1899\u001b[0m     \u001b[39mexcept\u001b[39;00m \u001b[39mTypeError\u001b[39;00m:\n\u001b[0;32m-> 1900\u001b[0m       \u001b[39mraise\u001b[39;00m _invalid_shape_error(dlist)\n\u001b[1;32m   1902\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mlen\u001b[39m(special_handlers) \u001b[39m>\u001b[39m \u001b[39m1\u001b[39m:\n\u001b[1;32m   1903\u001b[0m   msg \u001b[39m=\u001b[39m (\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mDimension size operation involves multiple special dimension types \u001b[39m\u001b[39m{\u001b[39;00mdlist\u001b[39m}\u001b[39;00m\u001b[39m\"\u001b[39m)\n",
      "\u001b[0;31mTypeError\u001b[0m: Shapes must be 1D sequences of concrete values of integer type, got (None, 1)."
     ]
    }
   ],
   "source": [
    "# plot loss landscape\n",
    "import matplotlib.pyplot as plt\n",
    "# get meshgrid\n",
    "t = np.linspace(-5, 5, 100)\n",
    "X, Y = np.meshgrid(t, t)\n",
    "min_eighs = []\n",
    "losses = []\n",
    "for (x, y) in zip(X.flatten(), Y.flatten()):\n",
    "    min_eighs.append(np.linalg.eigh(mapped_hess_fn(np.array([x, y]), (*group_data, w1)))[0][0])\n",
    "    losses.append(mapped_loss_and_grad_fn(np.array([x, y]), (*group_data, w1))[0])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "b99125a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "traj = np.array([h[0] for h in history])\n",
    "traj = np.vstack([np.zeros(2), traj])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "c591e005",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Minimum eigenvalue of Hessian for 2D binary model')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.colors as colors\n",
    "Z = np.array(min_eighs).reshape(X.shape)\n",
    "norm = colors.TwoSlopeNorm(vmin=-Z.max(), vcenter=0, vmax=Z.max())\n",
    "\n",
    "plt.figure(figsize=(12,10))\n",
    "\n",
    "plt.pcolor(X, Y, Z, norm=norm, cmap=\"bwr\") \n",
    "plt.plot(traj[:, 0], traj[:, 1], 'o', color=\"black\")\n",
    "# plt.plot(binary_params[0], binary_params[1], 'o', color='black') \n",
    "# plt.contourf(X, Y, Z, 15, norm=norm) \n",
    "plt.colorbar()\n",
    "plt.title(\"Minimum eigenvalue of Hessian for 2D binary model\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ccbd3699",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0a7f042b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Loss landscape for 2D binary model')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PCLELjDzguRMDHJ19meNrgmexMHsJmMwBz9rA2SrP7ijAunweUhDaU/hcKg1ESKPa3a+L83xKqlmRUQqQBZRcZBQBeOtcy4vQefggJuVarH2V8Z4zxrcGG4zMfRLD7TbPYTAsHwq3W1Qi3L6RK88zAJ7Ze3k61mAb77SRc6y2t7Mn6CwJnOdUxKGfS20Q7RFCuy8iGpJU862Wjur1FANPSblsRwJliaKjYLjdozzQNN97BnHss2DUPQU33H465u+XE25vWmC0WZu5rgzwjAjVO21w7PiO1wTPc4XOc4JMjszzrQWj10o+FA/kQ+gA0LNX47D78m9j8GwpJ1gVCrdnrLEovHKB2aIkb2yO/Y0d5ZzL9Hr2Fm63qXpluw88TR0YPIuE2aWLiVKgcwBnGdX0ikp7QYF8CD04gCoo3OwsDaA3jbA70M7rGQueEooFx8DxmDmzioxgH5MTbo+yb+1jA5e5T3ROomU+blheMNweFAc8veMjwNMBwsG+tveS4CmV39mLtzP2JjmAs65qgWgpCL1QAB3yq2HYffn3TMPtJcQFxNj+GWtnw2uMUS4YR4y1Kco+C0Ylx7kBdSNLuN1Xab5v14/bYS+68Iib57lZU2PwLFBY1L23M+ZzHcDZh2qAaIl80BwABQ4JoWOrJb+6qHY/S13gnp6sNYRAL8JWjDfWWWQUAacbRYTb2ePUtk+w38auey6nYsHTAbWscLunwOjQ4CkZZs8tKuoZOnsGTtv1OALslAZRyXzQCw/DD+3VR9j93LyeF7qnpzm3SLg9AXSdRUZRY3x9bGAy90nc0zMImbZ+uU8xWo91Cp6+dVrtdg6epbydvUJna+DMybkLje0NhEqBaG9e0N6uu0MKwM3h+fSqebV79+BZU5X29BQBSubaUuaI8qiG1mFRiv2uw+2mXYedmDzPaPDkKgY8YzaR7wA8q4fZe8vprAGbvRRxcNbRCpRKgKgkhF5oGH5oqz48nz2rdZFRBFRFi702x3GGJPb0NPuIhNtj7G/6KKedIuF2ZelnWbNtLqdcAJjDDhyvp/fah+HR2TcwtsYenuJhdglvZw3oLAWcvUBmjnrwnkqDqBSE5noxD+AFHTmffjWBz/Uj6d3rOfb0jFuDaTu0VotC60sKt9sUcf5Nw+22YznhdgZ4Fgm37353lL2fsZZdX1M9g2fLMHvJEHsJ4DwH2IyVfs41QbQXCB15oBetdp7PsadnutczFjwT1lgUXiXWHQP4ESCb0sc7F3ucG1A3yg23r8cOCp5eoAuMdY0/CnieG3ReInC6VBNEpSG0pRe0UwBVwNjnM6DLC7s7gK+41zMRPEWUCrUZYFllT08v/CnjvWcizhp7CLcLPsVolRB4clV0E/nQPK3Bs6S3sxR0SgLnuBnzVAtEpSBUygs68kAvSm3gc+ECZb4/aLi9oMSLjDgwxlwLN9zuFReMo9blu8nz7XcXbjdsONtt2oyR/wJzvJ61t1Ty9o85lvMs+NVGIngeHToHcOapBlip6z5C8WeWB9rx5mJd6PI8nyXUek/PnL/v0Wt2rMGjUJFRSi6omEfTYb92uN3mobTmedrsanac7esxO/CVDrfXBM8mVe21vZ29QucRYJNzPSSf8iOh0t7QXvJBJQB06BBq/oSjw3s9c8FTUMl5mglAucq0YRxPyeNM8oKufdXmvU1RIF0p3H4aZ7HVcbg9u7K9NnjGhMqPDp61oLPmDV/ySUup87QG05Ig2kM+6BmE0RXU2OczoLaez97As4VyAbEGUHLXljBHkkc1AkrjQNMc44bDcwm3V8/zjMnTrAGeTnBkrM87PhEeJcLspaGzNGzWAsxUudbXAkpLgZpkKL5VGH6oa42wu65OioyyCn5cYq8tcDxnLjjex9jwQpyy9/GAXArAeu2wxzEBtXC4PUfR4faYPM2jgmdLb+dRobN32OSqJZSW8Ib2UJB0VABVwM0z+VqXUsOtluZ/evF6lgJPQYkVGWWskVtklJLHmecF3YJn1HzWPsrdJzfc7lnTRgcPtzfbyzMVPGMelykJnrneziNC57kAJ0e1oVQaRCUh9JIAdMir4fksrR1YdbSnJ5hz5sCrxLoTAL+3cPv2WBygWsPtQWDRx9ggtSJ4miq5l2dv4FnS23kk6Lwk2ORKvyalQVQKQlsCKHAYCFUY1e4hNYXPs/d6RoKniFKhNmMtzfb0XMeqTZ9SFfBeO4Fx0fmgoXC7Rdxwe408z42kCowGeIbn3NlpBJ0DNuNUGkSlvKESXtCRBzqEptXuBwXPghIvMuLAGHMt3HC7V0ww9q1339d3A7eP8dtVzjW0DLdH5XlabVqOpXwvcsLtJTeRFwTPqM3jU8AzB0pLQWcucA7YlJPU89NdkgC4XAg9+zxQws24EtyL0wi7x+qS9/RkzB0qMooC4Zh1RIBsUki+Vrg9Ic/TNe8KUa48T4fdInmeJTeRLw2ezsKkiL6cdglvZy3o7Ak2S+Sk9gA3JSFUKowtVRUfPe8RAHTIp0bweVCv5znu6Znyd3uxYb6PsRm5XpuKP0KTA7mb9ezHRYfbjTZne3De/aCmBUauddj6xhQYtQDPHr2dNaCzFnCWgMncNbQEndIQ2hJAzzQEr9DX/8961PB81lQqIAbG54TXk9dWwrZHFxdut9kIhdvXY9rBULhdCDy98nlec8DT1BHBM9fbeQ7Q2QNshmRbY23wKZUX2joMf6YAOuRXd1stna3XUwDA2GKvTWAtobERYJwE1UmgGWFXYjP5QuH2mDzPEFzlFhhxwu1FN5HvETxLejtLQ2dJ4DwCbHLU0jsq7Q2VgrhUL2gOgHaqkfPpV1fV7t2CZ025wCgSHEWq2F1zhdbkUw6Er32V8X7fNQ40DTi0wh9/Lpttri12yN45xgapAbD1SCrPs8rz2iPsOe26bMfmd/bi7WwNnecCmhy18I5KQmjrPNCxD+hFaYTdOeqkyEjCS1oTXoO2k8b6bur2Mf4+Bnhq6ibcbhE33N4sz7Pl04tagmcP3s6WofVLgk2OanlHpSF0AGiWFIbnM6Rutlrq1uspDZ6SSoXaFBicxfZ6ZgDmpYfbo/I8bVBeKc8zqcCoA/DM3kopBTxreDtbQOeAzTiVhlEpCD0qgA4dRsPzWVuxwBUJlCWKjoLhdo9CYBznBVXbdcXMZ7VrwKGtr8dOqXC710ZojECeZ7ECo17B03Wda4Dn0aBz3OBlJRXqNiUBoUcE0I50XWCXm3NSG/jc3bQvxOsZC545il6zo1/MXMb7lFzQmHB71Np3fdyLyg632wDPCop7mGaH2zdjbNfGD41NCox09QyeUoVFpb2dNfM5W0BnyTk7CtEC6BdCJdZ1wQA65FaD3WFlVA08WyoXHHOA0lxDaE0MieSVRszP8YLu+kiE281xtmONt1VyqUqe57mAp1Jp4Hmt/CCormXBMzSfbw7fOUpKn6vGnLb5as4fWpe0Ur8Di3LXlPKY1yEREdHTieg3iegV2rF/SkSvIaKXEdF/IKL7zMfvR0Q/S0TvIaLvMew8j4h+hYheMv/cfz5+DyL6USK6nYh+iYgeyllXO/hcv8tpXs9qiga8wkVGkkDJXZsxTsK2z8Pn9HpmguZpjYrRx22nRbjdlue5UaVwe9ITjI4Mni4Y8EFnapidC51cEMiFzlLqBfRCarnGkhCaqhYAOnZql9APAHi8cey5AD5JKfUpAP4ngG+cj/8OgL8P4O84bH2ZUuqR889vzsf+MoC3K6U+DsB3AfgOzqIaez4vNNxeQMlFRglrCxUZSYbbOfPHFSZ54LCHcHvoD7wLBG3HfGs15ooGT4+4hUiHAE+bSnk7fSoNnaUg6yigyVGLcygxXy6A5qxnAGh1KaV+DsDbjGPPUUp9YH77fAC3zsd/Wyn13zBBKFdPBPCD8+sfB/B5ROE8jVFw1EIheEoFRwnYNW2E1sRQTrjduaenFRD5a+w23G4RN9zO2VbJdswJnj45vJ7sAqNLA0+XJAuKUr2cUjoyWMbKPNfSOaTLfFLzSOSCpq4lJQf0YPmfClW3WrqFiF6ovX+aUuppEeP/EoAfZfb910R0E8BPAPiHSikF4EEA3gQASqkPENE7AdwPwF0+Qw3h80K9nrHgKaFUeE2YI6eAqVS43YTIkuF2W3hcOtwusq0SR1p/8QIjTdngybHpGlcSPGsUFLWqWr8k0OSoFozmQJ9NrR5teQEAWlF3KaUekzKQiL4ZwAcA/BCj+5cppe4kontjgs8vB/BvUuYFzs3zKQ2ePSgVHLmwG7EGdrjdo5wc1iOE203bG0WG24+W5+ma2+elFAHP1KchccGzV29nSmg9RwM4+dKvlTSIlvCCDgAVlQLhZuusxoCI6CsAPAHA580eTK+UUnfO/76biH4YwG2Y4PNOAA8GcAcR3Q3AhwN4a8he26vjgMVkr2eh9fVaZFSi6Egk3C6wXs4jNEPz2e3G9PEAqw9GbccSwu3mnNMYmx07NNptCYGndw088PStjfXeYo8Fnq6cSAnwrJHbGZvTmZOndw65mq1VKudV0l6rPNCRA9pERPR4AF8P4IuVUu9l9L8bEd0yv747JmhdquefCeDJ8+svAfBfODDbzvMpDZ7ccbNah9uLqCa8BuZkgZVzrO/mzZ+PE243vZ5dhtvXY9rBzHB7doERN8/TMSY4juX589hz2WgVZm8RYs8BzqFykvaKSnlCc72KqV7QM/WA9rLJPBE9A8BjMeWG3gHgqZiq2+8B4LlzbdDzlVJfNfd/A4APA/BBRPQnATwOwK8BePYMnjcA/DSA/2ue4vsB/Fsiuh1TYdOTOOs6r7D7gVS8yCgFLBcboTXB8d5nM7TeiLGpOZu7Phccbvces4mT5+mDvxAohtYU8KAO8IywVWLsUJokQ+gStloWIsXqAADag5RSX2o5/P2e/g91ND3a0f93APyZ2HW1hc/1BnxZXs9k8MxQdJFRxJwh23FeUGW854zZvt/2UeE+MO24ofJI4XZWnidnPg547mxFgGfIc3pU8DwCdA7g7EM9QmjNpyKlPgWpUylUrXY/pM7n014kDZ49iQ3F/uMx58YuMoqARclwu00j3O6ep3qBUWoxkKu9BXi6ctp8uZe1wDM1327kcfapnnJCc3MrY+ce+Z8XpQ5yPoW9ntJyAlMnRUY5sGzaCK3JHMewnZQGEAG2SSF5BkT1Em53gWdUuH051qLAyDXG1jf0viR4Hs3bmQqcQ/1L0guaa692HujZ5H8Sbqrz8+1Jqs+rc2HhdlGlwmvCVDnhdqfXMwYifUDLCbfv7LihsnS4PTnPM7SuEGi5wJM9f8IY27gBnrwq9hRv1vByHlPSn1uqrdrPhR8e0IuQmOeTiG4AeCGAO5VST2ANcnk9L0ylioySqtlDY1Ns56wrYowXIpc+viKjnR3begyota0R+zabDasCMCjyFCOOBPM8i4OnTT2BZwtv54DN85F0PmiqnZr7gR7cA6oAXHfq2+tFklfnawG8mt17FBkx53OMTxC3yCgFWrnXwT5WRc+fFJJnPEKzebh9PWYHOeu8JcPtXIhMyQ3lvOeA526MxWYL8OR4rqS9nefg5VzOwfy5dEldhxw7NT2MwwN61hKBTyK6FcAfB/B9Evak1Qw8Syh6zf5+KXPnnHco3M4b45nvUsLt6xgHeKaG21Mg0jMmai/PUuBpU8xx56b0137wDEnK23lEQHMBZsizzv05Z0mdX20ATZkvBUA70U1QlZ+jSirs/t2Ydsu/t6sDET0FwFMA4Mb97gNA+y4acCft9WwmF8AIgaMEUMYWGXE8sDlFUSlge9Hh9rXdPo813M4BT+/8mWM47zn3HEnwlPR2hiQJnb2q9dq489fak1JaUqH41DB8aog7Zb4z24ZpaFI2fBLREwD8plLqRUT0WFc/pdTTADwNAO7x0Fv5f5kuJdwuqOgiowg4XMW9Dt6xKnrsCLfrr/0Q5Qy32+YyJVlgJACewbxRDnjWCLP7dG7Q2cs6cuQ6h6NAqQSE5gAoEA+hFwCgSo1q95Akrs5nAfji+ZFMPwLgc4no34UGsb2el6JUqA0cT8oVZQIzy7ZzbHhw1HweiHSuJbJP6XB77W2VXPbEC4xcY2zvB3jm9ymhSwxtH+k8c9eaMz4lDH+U6zpUTNnwqZT6RqXUrfMjmZ6E6aHyf4E3ePl3FBnF2E2SaTu0JnMcw3ZSuJ177t4xNtiY+8Q8QpPTxza/ZV6bDatsTbW3VQp5W622MsfY3lvUPXiGbtpSBUWtQOhIAFZKR7oGuevsGUAPlv95Daryc1SNZ7sfUNm5ogJz5nlBVfTYiwq3245FQGZynie3WCh3jO19yJZtTC3wTPF2HtnTeRTQqi2pPMvSSg2j56rGVkcHC78PuSUKn0qp5wF4Hq/z8u/weibZTYE/Uy6b3HaPzaRwewrY1gy32+CyYLjd7De91iDTttaYPE/PZyFaYNQTeNYIsx8RPAdw8qVfq15BNAeUc+A1FkBbgXJhKQA3xz6fXl2G57M38Cyp0NpC/RgSSQ9IAk1zjA0u5j4lwu3wrNG2fqlwu8VearjdqZIFRq51WezsbNnG9AqeR4POnoDzmhFSverwZt67NzQV7mpCYexcw/t5FmoLn7W8nr0pAG9iRUY510HAttPrmQGnnHn8fdydJMLtp/77g95wu0Cep0S4nV2lnlJgdMng2Qt0tgBODljm2mkNpj1DaG0AHeF3YDzbPaiz83yeTbhdUovt0JrgeO8RG5QZY+PyOpW7j+H1ZOWHMvpsjkmH22E55oBM27HkcHvJR2eGQKdH8CwRZu8BPEvZlwLLXLnWURtKew3Jp8JxLQA90/D7kFvt4PPcNpSXVjQsB/olLIENh4zPIGVPz1W7MTZomPscPNxu7Zea5+k5P+e8VjuZY2zva4DnpXs7JW33Apmxaukt7dEbmgJ5vQJox95PhfFs95CO7fk0/raejdcz9ThHobGhtSXYFn+EpmOMv4+7Ewtq9abUcLvSj81vaj8+06Gqle3nDp4toXMAJ1+28ysBpD1CaKx6DsEPHVJN4TPb6zm0Uckio1WxAM5YZwpE1g63r/KF22PzPF3HfGsy5ima5+kFdl6/iwLPVtA5gFNOy/mfM4T2HOI+I+/nTdXpNe5Eh/N8souMLszrWbPIKM4LqqLHJlXAM8LBfjseqLWNi7kWWv+Naj4+MxY8TaUUJfUOnkf3dkrZu3TgtKkGhALtILDn8HusOgbQIbeawWeq17OlxMGzpJa5QmtytUfMEQy3+9YXBZoGIHKgkBNK7yXc7gDPUnmeVSvbW4FnD2H2HqFzACdPJSEUaOuF7BVAe/bMMqVAY5/PgI7h+exkQ3lxsdflP84Nt0uszTVXli3WGAM8NaWE221qHm5fVCHPs2ple80nF/nsrGMrgWdv0Nk7cLrOrwcQKe0JvQQALTnH8H4eTo33+Vz+DXg9BeY4bLhdUMlFRoy1hIqM4kAzYkxiuJ0FtcsxHT5iPx8ryPL6lczz3I6N7O8bE7ARDZ6huWPt1MrvlATPHFs1gbNEPqvLbitYKwWhlwCgFxZ+vx77fHrVr+fTgMJkr+fRlQqvCPRLkEjVfRJoGoBo67uzawOUhD6WNtvadEmF223HiuZ5euAhqbJdAjw5oXWWnQvydpYAzlJgmarWQFoCQpdzagGhPQJo0po69+4PrWq4z+fyr8PrKWJ7+uewXs/E8VFi2o7zgm6hKg9ODfDU57mUcPtyLCbPU1cKeEo9OtNmwzrfAM8sW5cAnCGZ660BcaUg9JwBtCf7Q83Uh+fTBVGpXs8LV9Eio4DtUnt67ua9wHC79Zj2kg2JoXbhyvazAM8eoVMaOI8GmyHV9I5KQ+g5Q9cF7P2pgFFwFFAb+DTgUsbmhW+ttBw31hOl3GtgUQpoOgHRNmZn1wYgRh+bfH2sx/YHJcLtJfM8nUVGsf3NMaa4uaLAAM8UO5LQeW7AGVJpIJWE0BYAei7h96Hu1fzxmmJez5ZKBccKKllktLeljPfx6/NC5DLG9whNh92NOFBr2VapRrjddiyU5+m0FRtuT61s5+Z5tgbPHsPstaHz0mCTI/2aSEGOFISeM4CesRRobDIfUB9h91y19nqmKnq9gX4I9EsQf02+m7RrTPz8Ng9gVCjdm5c4v/DleYZkux7XlmOW9aTmeUZtq8QAz50GePKOx6gmdA7g5Gu5Vj1BqPSauHOWBtDh/bxoNYLPjr2eseApBY6Z46PEtJ00Vwpo7sa4IdI5JrIPa33WYx4wtfVvlecZ4hUvhHugMcWGqd7Bs6S3sxZ0Hhk4S3giU9cgDaFAOojWBrABoFm6HjmfXh3O8+ksMoqGOYfX86BKLjJKOO9QkVEcaEaM8YXbWfmhDKjtNdxukdjjM2sWGA3wDCsFOkvDZiuYbQ2iJbyOOd7QcwTQoYtUB1stmf/6vZ45c11KkVEKSCev1ack0LRDZJFwu7meg4XbrZLM89R1LuDZIr+zlLezJBD26Dk111QbwqTnvL4eAAqcpfdTKeDm2GTeq0N5PpO9npcqJiznFETV2tPTOSayD2t9tvFHCbeH2rngyQ29x1S2h9pbgeeAzj5hM6QWMFoiHJ8KoJLr4Mw3AHRIUJ08XnP5V9Dr6QSsC/F6OtYbpeCatuBpU1Y1/TKmYLh95/X0jLeO2xwLQKDHXjDczgHPmDzP1gVG5wyeR4HOIwKnTzVhVBL+jhSGH2KKcI3xufh0GM9ntNezgoqDZwGlFhklVaYzQNPp9YwYE92HcU7sNhPEgfhwuws8YzyaKU8kiu0/wNOv3qHz3GAzpBowKg2hPQPo8H4OCaqjnM98r2dykVEseNX6Gx5aV6hfoD0Jck3YSgJN870HIhMeoRkdbr92nEtgbWLh9uVY6zzPxNB7VGV7TfCsuY0Sd1xsMVGtsP8lqCSMSkHopQNoD3YFpDByPkPq0/Np/o3YwVSB58E71nC4cHuKotcUnizPCzq/jwm32xQTbveMt47bHLP1Y0AV55j2MvnxmdLgmVpg1AN4tgqz14DOAZtxKgGjEkDUex5oSei7gEdvDk3qJOfT8Hom2BD3eh5VTFgWOf+QLY+iiowcY/xrYfSJHF8t3G6O3dlkwKRNNR+dOcBzXktB6KwJm77/pMWqV7iQgjcJO73ngcbOcYHh9/Fsd7+68Xy64Cfo9cwRF1xj+0f266rIKGC71Z6eqZXrMeF2tqy2eP2iwu3WuRngGZnzWaTAyGXD1fdo4Hnu0CkJmxK2awJrbxB6iQA6dPbqIOcz/8uY7PW8EJUsMlqVBJrKPobhXfPDKKOPb0/PnsPtFonleUqB5zXTJmf82icRPGt7O48KnSVhU0L6+mqBqBQs5drpGUBL6eDeTwXC9Xi2u1fdeD5tqpHree5eT5F0gtWWSre9G8PxyDHGsCDX04cxvkq4PTbPM3FbpaqPzhzgKTN/CejsHTZ9qgmikgAK1Iek0mDWIfgNHUONcz7b7+t5aUqGZAnbnDG+IiPHmI0c3tSNIvf0PLXZbPH6BcPtFklvq9Tk0Zm+tR0JPI8OnUeGTZ+W8yoJoZLgmAprqd7PGoo5pwvK/Rw5n3517fncqMa+ni6bkaDWq9cz51qFvJ61iow44XavnQOF263tGdsqOVUCPENQ3AI8W3o7a0PnucKmSzW8oa3D8JcYfh86WzXM+fR7PfNAaTuHaIX3OSgahj2eQqZtqSIj5zyaWJ8rY45uwu3WtcWBZ1JBktSWSqaOAp5Hgs5Lg02fSoJo6zB8rwBayvt5UCkA12OfT6+OdXVC8Fji7280qPH6NfN6csAuoCyId4TFo4qMbPNwPKM9h9td4Fkyz9MLlMx5Qm2h96XBU6k24Bkzb+oar9XpZ8iuEtcn9fNy2YpVbFFbzlytFfPZHfH8LlhNw+7R2yvFSOppRueuIKQqb7tN7mvNuLgRY3ILkboKt9vslczzjABPscr2FuCZohzwLO3pbACayvaZGCLq3I9Rwhva0oPXYw7o8H5qItwcz3b3qs23N+fvZ0145M4V2a8br6fAtcrL/ZzfJxQZRYfbI/b0bBlut6pEnqeuXsHT5mEqCZ4+j9b1tR88S3s6K3k4lbre/aSOC/00k6THWMLbVtNjd0Tv4PB+ZomInk5Ev0lEr9COfQQRPZeIXjv/e9/5+IcT0f9DRC8lolcS0VdqY548938tET1ZO/5oIno5Ed1ORP+CiPe/is7+6+TxeqZ8p1IhUUIlbDLmyxkb6/WMysn0hMVNRY2JCbd75rDbthxrEW63ri0MnixQ9XqWPWuIqWxPBU/OnJLg6ZKUt7Mz6GwNhF0AqsT1lQjDn0v4fcAfAKw5nzV+GPoBAI83jn0DgJ9RSj0cwM/M7wHgqwG8Sin1qQAeC+CfEdEHEdFHAHgqgE8DcBuApy7ACuB7AfxVAA+ff8y5rGoGn1W2VxJQstfSVOz45TgC/QLrrQLeOXAqVGTE6sMYf5hwe0xfLniWqGw/Z/DkQkcH0NkaNFN1OAitPT4VQHvQANUqUkr9HIC3GYefCOAH59c/COBPLt0B3Hv2Xn7oPO4DAL4AwHOVUm9TSr0dwHMBPJ6IHgjgw5RSz1dKKQD/RrPlVd9bLQlsr5QMXwVgLNZmcrg9R6st5Z1bosgoewynT2aRUfVwu0CeZ5JKVLb3Dp6lvZ0NczqPApdc6edTNL80Zm9Jm3JzGVPGp+R/lsy5LGE793NpoIo5n7cQ0Qu1909TSj0tMOajlFJvnl+/BcBHza+/B8AzAfw6gHsD+HNKqWsiehCAN2nj7wDwoPnnDsvxoBpvMr99mwRPOxgSfPa7MYdUDiUXiJPFXaezX/wCUoqMnF5Pbyg4ok/qnp5WiLUcs/TLDrdb5iuyrRI3RzQGLmPD9OcKnpWh89xAM6TlfItBaO7G9cvnnwpg5wCgR1rD8XWXUuoxqYOVUopovXN9AYCXAPhcAB8L4LlE9PP5S9yru5zPnTJBzzvWPO7qn6BuioxyxFxzVpFRzBgf7PnWwFinN9xuAzu9f4lwu00VwLNIgdG5gGcofF4xvH608HkJFT//1mH4I6tIdOY411Mp6inn06bfmEPmmP/9zfn4VwL492rS7QB+FcAfAHAngAdr42+dj905vzaPB9UOPo3vUc72Si6vpySAxcJjN+KC9/pe2duT5lJhG0lj3H12Xk+bndhwO9zHqobbbeodPG1qBZ4+OORUs4dsc5VRbX3pwGlTURBvBaC18j9LAjLX9iVDejs9E8CT59dPBvCT8+s3Avg8ACCijwLw+wG8HsCzATyOiO47Fxo9DsCz59D9u4jo0+c80b+o2fKq75zPRTmgx4UvV/8EdeP1lPydlphrGZNTZGQFkLCdrsPtOV5MIVWrbG8Jni7VhM4ENd+WyKUOc/CKhORb5YHWCr8PFdHNTp5wRETPwFS5fgsR3YGpav0fA/gxIvrLAH4NwJ+du38bgB8gopdjQpG/q5S6a7bzbQBeMPf7VqXUUsT0NzBV1H8IgP80/wTVBXyKbK9Uwuu52jZs5sBwA2V7PSOuqdODyYJT/pjkIiOXnc2x+WCtcPuiRnme1SrbewPPWrmdR4DOlDWGxjSEU3EIbZUHWgNAS+ZdSts+YOFRaymlvtTR9HmWvr+Oyatps/N0AE+3HH8hgE+KXVcX8MlRzhZByV7PhL/HvXk9m3hBPZIoMmKF2z3jrTIBfDPeDz9i4XbrujoFT986rWMbgGcpbye3T4/QWTNvrgM4Fa+Sb+EFPTqAHmH+oerqDz4d2yvxxk7/lACuo3o9d3KCowq0O95b5zAgcRmTU2QUG25nrNN7Dr1UtwfUDDxjwvTnBJ6FoFMcOI9QnFE5pC/mDT1XAD2KDuD9VACux+M1vWoOnykFLXswYXzIIXiShEouuJnHQ2sJtEdvrSQhBySKFxnBHGNpLFlkpDfZ1psSbveF983xDoAUU4xXMwpaOwLP0mH2FtB5BMhMUYlnsc8SgVAJAJ0WETempHewlH2u3eH9vCg1h0+rMmCpxJZDTaCuhkzoSoVazhyM57fv17W8dw9KDbdzioxSnmKUE25vlufpC5nHgKepo4BnA29nFnSeK3C6lJtv6VA2hEqsqzRwnav3s3tRNwVHvaopfCZtr7QDk4jiJBckBqAySqneyNBaAu3RgOzx9sUqpcgob4zxXhfjPwLcIiPTZtBGZrj9NKYT8PStK3esrb/ru9gzeEaA4PByZqowhAKJIFozDFw6/H4U7+cBQu9DfvXp+QTSvGwSYw2drdfTVCLUZhUZ+ca44NSmcwu3t1KpyvZW4NmJt3N4OYVVCEKB6bOqDqCxwHdUAL0gKQDXEXuVX6Ka+YVztldyeT2TADAAlSm2Duf1lADolCIj1xjfOhh9Rrg9YWzJynZTRwdP5gbxWRufJ25CLyql3D89qNA1yvrM0ict2x9I24ReUrkRDFOtfz+GstSv5xOJQMgFsBiVsCmkJlsp7d4zJneMSama36jAnp6n+Zk2jh5ur1nZfg7g6R1+EC9nLkC6xrfwmBXwhGZ5QFPXUsMD2oPtC9HNAzy9vKX6gM+U7ZUqeD1lKvEDc4TWwm1HYJ7dexVo98/Dmbu3IqP9XLbxFpitHW6vnefpmjv0/kjgWSG3s4nHzKVW3knbvLUgRrhCPqsgKTUMXxpAWxcgDagdmtUHfPqUAIRn7/UUBEauQl7PrDxOz9iSRUaregu311StyvYzBs8k6JQAzl7C3yG1AFJBb2j1PNBeAK3lOrhzd1p4pEAj5zOgfuAzBepyoKsEVHKhcDkeWourPXs9KtDOfO+bU7LIyDa2QJGR2ce6Nv3YuYXbXWuyvY8Z2wo8c6ETkAfPXOg8CnCGVCtsLwShTQqRuCrp/ewFhIfOTu3hM2d7JcYYCQ8lN5RdRImAWMUz64BE8SIjGH0q7+l5luH2WpXtHPCMAapa4CkJnZfk5cyVeZ5S4CMAoVUB9JzD79y1Hhx8r0fOp1d9XZ0EqEuBGNdYCagU93pKyfT4JUKtRJGRf0wEnDI+8+QiI2643TbWMWY3v97eC3iaigFPUz2Cp1L1wFOiGpuz3nOW9PlnfiZVdy+IPe9S35Pev3+j6v2Qauv5jNkgPmPMfluniPl28xs2S0OjRVzAbbKWnOe3cxS7kfnatszlgUErqFqO6edoGZsUbm+lmLzOlEdn+tpagKdPEtA5vJxlJO0FywiHJ3tA0yYr5/1rXXw0dNHq/5uXAiglPZcZtkpVuHPnL5rraapTr+cqRmpAyrFQEVFX4fYQeHq9pZEFRqZqgmctb2fuPo89ejmvr7c/LSV9bVp5QEuqt++PS0dZ51Axtc/5NCRSPJQyTwlv6LkqJddzVlYYv9aTjNa2ve2kcLstrzTgHe0KPE3lVrbXBk+feoDOmsoFSH18C6/Zcr06yAWtlgPaQ+5jqzX0cO4JUgq4OardvWoPnzHAlrC3p0jIPeARFBHT6xldaGSCV6zdFKWAJeLXUa3IaLFpC7dv5vQDpXVsDx6AEBxKVrYP8JT9zFt6I825a8JoR2H47uaLuTYj9D7USO3gM+J/Bc1D7jEKQaGrX69ygGRXXk+GJIqMrMdCXk9zfle/Vl7PWPDMqWzvBTwlNoxvCZ2tw98u1faKlvCCRgJhtfzPg3oAq6nD/T7HPp9+tfd82hTlDZ3+ydoXVNIbWkK1vJ5F1ur2JJpyrktya6W1j7sxa09PBxSexvi9o9XD7b61SVa2HwQ8xb2d5w6cLtX0ikqCWU0A7cX72crmAOqLVuNq9+2/SQDpUdG9PTniej1NmzWA1qYg5Cp7e8x90WEzaaxFpbZW8h0Lhdu5T04SA0+ufB5Qycp27tpc/STAs7a381Kh06XSXtGjAmjcJGVgbYTexTU94WhcU5/69HxqytlYnqUQCDJU1JPInDPa61lClbyep/l8bYsdD+RZQXVvu+gjNEuwRUq4XZd0ZTtHueDZg7dzACdPpUBUOgxfQ0fzfrbQuZzH0Eb9wWcMBOZ4TAUgU6TgKOT1FFi3b97YTeWP5vVcFfPUJd1m6Udo2uy0zvPctFWobC8FnjW9nbngee7A6VKJ8LwErPQafm8NYq3nP5BuYlwnn9r7hXMA0qMSIfecsUULjUoBatYajuf19NpO8GrGFBlZ26XA0ycfTJ4xeCp1LQOeSuWBZw/7Z/YkqT1FJbzQCR795P0/S4l7HVp9B6WiBUOHU8Nq95i+MXuixa9BZG9Rwd+h6O2VnHa2oJW8qXzI65nyH4dSXk9bH4mtlYy12Gw450rJCZUUB2iB+lsqcQuLXH0zwNOr0t7OAZs85eYiSoTha3lAj+T97FUdVbwrjGr3kPoLuwNpHk6vJyuir8RYrtfTtHXw/wR24fVc7YY9oz6gqbWnZ7Nwe2yBkbfvMcCzaW5nCeBs5TWqCT7LdcuF0MoAekhxYX/A75CAuoDPGLDjbaOTsAhJQBVU9U3lK3o903J1bQDnWYvP62mOt86vA5vFVs/hdnbILQCeXpBP+NL3CJ4loPOcgNO1hloQIuEFrQhMXXk/zwEWD3cOo9o9pDbwGeVF3D7ViGU3Yu6srZMS7gPs7ZU6uMfEKAksF7m8njH/Gdkcmw8mbq2UE253tlv6BSE1ZD9G3NzQ0s9s54Kny04keDbxdkpDZw/A6VJNEG0Zhu91+6WhrSR23hiqoi48nxtFgF1SyL3QWswxrpC7iC7F6wn7WN889vFumPXaTgi3Z+/pyZBouF1X6QKj3sCzZ+jsGThdksixDEliT8pUL1oNAG3t/WwRej+cV5On61Ht7lU/8CkFmxlz54T/s0LusVDYmQ7j9VzndBuvvqdnzTzP3Xr0fgM82XPubAlB5xGB06bS3tCWeaCXkv85NFRYzavdY/L+su3lwFwM+Dq8nqLwPLyelnk8QBjr9TRsu+xnFxmFxnDAkytfuN3Vz9b3yODZG3SeC3C6VBJEW4XhIwH0cN7PoWwpBdwc1e5edZmQwnmqUbGQewKg1oFKwTkE1ZPXc1Xu1koJXs3sIqMcxYbbWz2zfbV54eCp1OnnklTinA/yH4Du9v/0qdetwC7t9+XM1Qd8JngVpecu/ZQkdqFRimK9nok6mtfT7GNvm9fVck/P2uH2zdwRle0p2nlRG4DnteIVSnHOPXUD9EsFTpukr0ULAC29AX2M/Zi1S37/erU1dAg1zfkUe6pRRJ9iHk3Tvnk8RS7YzYXJoHdVWdtNxfb3rsHwetbeUN7ss53PD5TWsSk5oTng6ZMTVivnebYCT59ibnoxkFP4ZqoigYskn6EuKamwfIs80NL5nyO/9NAaWy351U/B0ayeQu6cvkULjQ6uLDhdxLiJl9xaqeqenjmKDbcP8JQPsXcGnFJjdRWF2NQcTF219wMtnf/JNyybzymxq8DQkEf9wGeMdzFTSbAX4zF1jREA1V4KjSTAUtzrufZxN7K2VrINT8nfbB1uZ4fejwme3UBnjM0ISQGjpJY1VYFQILEive8N6aMAtIT3U/L8Cl+ro0qBxuM1A2oGn2Ley4g+abmK/DElQuxH9YKW8HqKbii/jPfc36vt6SkFnj65vJ6lwZPbZ3g7J3MdAqdN+jqLg2gqgALpEBozby8b0B8dBDnrP/o5Dq3qx/Opi/M/hlwghdEnoW+W/Qy4vFSv5yrzvDd23d5LEa+nOY/LXkq4PQS2IaWE2zfzZ4Kn1SajoKkGeHbq7TwKbPpU3BuaAxy1wscl8zNb5X6O0HuWxibzfvUBn1IeToaKeTSX9ZljIxTcXukgXtBaXs9VjA3ls7ZW8s2TmxMa6ynM3VbJZVdCoXD7uYBnxnU7B9h0qag3tAWAHjH/k7vmEXofaqy28BnjOfSMLxZy56wr5T7kgsskG8PrebLr8V6u432QYrFdosgoMEY03L6Zr2K4vQfw7AQ6zxk4XSriDc0pSDo6gA7v56GkgJHzGVAfnk9dywfGAUqPSofcvRKAS/HtlSqpqNfTZqPAhvLWdZQoMgqNSSkY4oTbB3jOY8uE2C8RNl0qBqE180CP5tlr4f0cGopUN/ApFnL39BEPuZtgyDDrWksJT+ohvZ6MmzxrQ3kfjHK3VlpUusiII8lwu8uubV2XDp49QidnTZ1BhXhIvnYYvmABUvfeT46kQPaMio7GPp9+tYfPTE9eLpCafaI8phyZfTPO11lo1IlEvJ5Om5ZGn9fTHG8T1+u52goApWSRUWyep08ur2eJAqPgWhqDZwFvZxXojP0sOgZUdX19TACNst8xKB5dBwDPobDawWcu5AlDJ0vCEOvSUQuNQnJ5PeNsMLye1rZ8r6dpa/caHjuu8bYxSfmcLlj1hNsDa4qaEwh7PVuC59Ggs8Z/LENzlNzrUiocX9MLdhCPGwDZtY68z3ipsc9nSH1+oyp4Q5OeMe7rwzfnti/qFeW+t3spY0PuMWFz99ojxhZ4jKavLQiUmV5Pt12G11Mi3G5KOtx+BPBUqi14LvP3EtHQ11NoXU3zYzvKzWU/9z3hmfJDQz2qfdg9VjW9oYU8pyWq3HuTxGb5UWkGyaDpsV1pa6Xq1e0t8jxtKg2evXs7e4HMGBXw/mV7QXsNvx8h9H4kb+6BpDD2+QypL88n53nuiSqey5nah2mjpyr3LHhO2V5pZ8PT5vF6Rle4L+NCQMmthNeVwzAsWE0sqMkFT84YoB/wrOntLOxFrKZCa8+6vrWu55E/t6GhjtSF57MoWAl7Q8Uh1jU2yyvKfa/s7YGQu3vNbvALyrDN8XpK7etpVQJQVvF6JhUcMb2pEjdWjs2ewJPT7QhQVFvLefXmBU3RpXs/h4po5Hz61Zfn0ybP3+4aBUni3lCjryhs9iZzfRL5Sgyvp02spxmV9HrGjEm5Tpwio9zrL5Hn2QN4Mj2P6vo6HjzPxbvJVU9e0Jy1VH6sqt3syPscKiMi+loiegURvZKI/pbR9nVEpIjolvn9Y4nonUT0kvnnH2h9H09Ev0JEtxPRN+SsqdsnHGWDpUfi2zNxJs0AxS62WAoVGkXZMsYmFSl5QJNjV8LrmbKhvCbW5xhbZNQq3H4E8Iz4niVB56WqUN5g0pZMI4fxpHEtmkmhH88nEX0SgL8K4DYAvwfgPxPRTymlbieiBwN4HIA3GsN+Xin1BMPODQD/EsAfA3AHgBcQ0TOVUq9KWVf/ns9IdbM9U869KMUb6vCkioXcg/Pb7aXICduebZJYXk/rXBleT5skvZ4pIfZYuxzbEgVGBwHPaG9nSw9nTx6wQtehajV8qbl6+pyGLlGfAOCXlFLvVUp9AMB/BfCn5rbvAvD14N2xbwNwu1Lq9Uqp3wPwIwCemLqo/uAzFR5TvagN+uwk4RXtVFnPcXfaZHg9beLkiLb0enJvUhyvZ0o+aEo7Z0xL8CxZUFQTOq/V/sd2vLV68ADXWEMP5znUta7nvT5L/wC4hYheqP08xVjKKwB8NhHdj4juCeCLADyYiJ4I4E6l1Esty/8MInopEf0nIvrE+diDALxJ63PHfCxJXRQcAUCRSvdePZ1ZsMkAKCGV3NtzVUKh0WmsZ/5lzRyvJ7ettNfTdZwTbvcpd8umja3E/TwNRYGnz2YIPDlr6RE6U0HSNq52wYtwMVLV8HvjDdXZj9ocGjrpLqXUY1yNSqlXE9F3AHgOgN8G8BIA9wDwTZhC7qZeDOAhSqn3ENEXAfiPAB4uvejL/ZZLeToj5pLI90ySAxZDIfdYOeFUsNCo6KM0S3o9Q2NqPUJzMyYSpoXyPK3g6fLcFQTPbkLsLq/mUey7JHitmm5G71LM+ZX4TKXESptJ3FLtQqVQx+vJzStVSn2/UurRSqnPAfB2AK8E8DAALyWiNwC4FcCLiegBSql3KaXeM497FoC7z8VIdwJ4sGb21vlYkprDZ2qOZpFxjPGsPgKgGAXHO7g03vciUY+pr83j9WR4VLlAGXwkpnRIW7LIqEGep1LXbvDkrMG3nsi1NfV29hAqr7WGlkCSOnePoJuqAYRDAIjo/vO/H4Mp3/MHlVL3V0o9VCn1UEwh9Ecppd5CRA8gmsIGRHQbJk58K4AXAHg4ET2MiD4IwJMAPDN1Tf2E3bkqAKRSfarle1b4exIbcpcA3ahCo0Wc+Qt5PdlzSXg9U3I4U8PtIfBkjWHOVxk8q0NnD3mYHJUM1wuF4busfi9tf+iw6uwJRz9BRPcD8H4AX62Ueoen75cA+OtE9AEA7wPwJKWUAvABIvoaAM8GcAPA05VSr0xdUDv4lIa4DFvZfRLAMQU2c7ZYKh1yX2WeX4lCo2TQNOz45gjYTPF6ZntKF+Xu6ZkLVKFwe0yonWN/M6YSeCZ7zQ4CmxyZ55ILowKglgSgvYi54fzI+xySllLqswPtD9Vefw+A73H0exaAZ0msqS/PZyrgpf69z/V0RsyRBpsJfR3vu1NOoZHDxsZe4qM0vW0Jz3oPeko5ANZzuJ0T4m4MngM6hbScYw6EtgDQlDkbFx6xNJ6e1K9UP/t89qrs3y4iejAR/SwRvWrePf9rJRaWrUxYTfZ0JtyDUkCxZD5ncshdwLu5k1loZLEttal8ktfTOlem17PXcHtinmeoD8u+CyA9RUBJBUWx6mWLo5qSeFJW7VzEkvO1LDwaGjqoJDyfHwDwdUqpFxPRvQG8iIieG7XrveQ2Sz5PZaanU8qLmAabbvhiq3TI3ZQr5C5xI0j0evo2lffarun15PSX3tMzBTxT8jylwdOhKtB5yZLwumV4QauE3xt6P0fo/dhSGJ7PkLK/3UqpNyulXjy/fjeAVyNj49GTYXeTJJBKzSdWRW/ai5l7B3kRa4tel5zRUKFRjUdpdu/1zN3TMwc8WWP29ndez5TN40uCZ4oHrgdPp7o+/bSUxHXI+DvS1f6stT25McpMYRoaKiHRnE8ieiiAPwjglyxtTwHwFAC4233vOx2r7dWMHSfkKY0C0wTYlFQopB5ai6vQSEQM0Ex9lOZpjoJezxBMsj2YCUVGOZLI85R+apGrKQY8Y1QbONn5vEa/2t4yqTxQIMkLWjz/s4T3c+RqXoSG59Mvsd8qIvpQAD8B4G8ppd5ltiulnqaUeoxS6jFX97qX204tIM31dIa7sFRti6XaIXdDLg9lUqGROdYmTpoCYwun7XwRXkvfmMA8u+Mli4wkCow4eZ6cuV1r4IwBEzxTvZ2lpHsxJTyarbyijb2gF6ua/yk6p/1Ph5pLxPNJRHfHBJ4/pJT69xI2NxIE0uyczszxUV7LGCAzPY8xXlemYr2iWWIUGq1a1pP7KM0UD6ZNuV5Prjczt8ioZYFRbfBsmdfZKjyuz1vDIyqVBwpEeSe78X5m5LDazY28z6HzVTZ8zjvhfz+AVyulvjPZUC3PW+rcmZ7SONgU7stULlwG9/YULDRK9noa+aTe8ZrEvJ45z1mX3NOzUJ7nTq3BsyZ0ts7B9KlWeF4iDA9Eg1yV7ZckNULvZ63l8ZpDbkn8BfosAF8O4HOJ6CXzzxcJ2JUJwWfyTu6WS8UKkWLUOOTuErvQqHev5wYEmWNc7bXC7TF2mLZYeZ49g2dqMVEPxT+xKh2eP7cwfKlc4lrqdV1DF6tsz6dS6r8hJwUy8n8HNviqXWyU/f+ZCDDlAZhhr4FXdOf1LKEYr6evjeP1DD0SM/DHPMnrmRIurxFul8rz7BU8c76zR4NOm0qF5ytvx3Q476eUevKinss1FZAank+v+kwoEfBgFik2Sm3j2Db7CNnjSjyfcwfEW0M5hUanOXygGbbLqn4PzSfp9dRVck/PzTyV8jx7BM+cbZOO6O3kSKrwaVHlXQK62H4p5vsXNFXxOza8o0MV1ezxmiIeTMn+BWA1pbjIpxwg7C3k7pQr5O6DyJhHaUrnetrWk+v1rLWnZ62N5HsFzxSdI3D6JOEVzc0DLZ3/ydURHrk51I2uxfbEOU/1/5skAJhde0ELgalIkY/DFndvz7Ib0gt5PW2ybTwv5fWMzcmU3NMzusApDJ7s/TxNtQLPS8rrlFbu+WelNxT8X/Lw+A0NVVczz+dRJZXvyekTs8VSjpxwWUgihUaLLc79kOMJzAlnh/JDQzfdFkVGKXmeu2kTC4xagOdBPZ2KsW6qme+nrvPyQivlJxbL/2y07dLQsaTU2GQ+pPOBz8h7S/bWS42VA4jdhtxdiik08vXhcESKB9O3ntR2X/9cr2epPE/fnK65metIBs+Oi4k4YBljpxqEtgLQcwS6noqFJHRun89QMZ0PfHauFs+HFx3rsFXaS2qfm+ENSg25R/SJHhOT61l7ayWXTSB9P89dn4OApxB0SsFlzHyHAdAKKpb7OVROZwSvo9rdrwGfEurVgygZRg/ZqpDvaaq3kLtVOc9wt/Uv7fVMCbeH5rTNy5yzKnhmQGdt0HSpuhc0Vefm8RuqozOC00vXecNnAU9fkXFSXtGEvk4V8myy8z1jxAobM+yUDLnH5CTW8nrW3lYpcg0DPNNVxQvawvtZMvR+jmH9GJ3DuXfzH5rxhKOQzhs+I9UkhCwpgfV3cw0Mz6lUSkJyyD13eyWbWAVlgl7P2L6lw+09gOeZQaeu7r2gw/s5NHSxGvBZSNLPe8+eKzT2KNuNSOVrSvSR3FR+ba9U4V4r3J7Qrwp4njF0mioKoQfI/RwS0sifjdLI+fTr8r5NgveN5l7CVsVHZki+wc04O98zpk+gf1KhkS7X9au9r6cuqc3kbSB5UPBU1+pw4Kmr2NpzCrQKX8/oJx5xVMLmUFihtIDhRT+UhuezgaKe6S6lBRgz/m4G1x0oNhJ5pOZuTrWxaRUnn9TXJ2WdKSH3I3k9U8PtLcHzgrydLnUfiufo0nMze1XuZ3JGn6nC2OczpMvzfMYq9p6Te48SDrMfIiQfeKRmzDoOF3Jv7fVkrEks3N4KPDOeTnR0b6dL4ufUsfdzaGioPw3PZ03V/BubA4yd3wsOH3LP+myEvZ67vgXD7Q4VB88EnSNwmjoLL+jQUI9SxymjaKXh+QTqezctyi5QMkPepdbQk0puseSbo8Teni2e4d5BuD37We0+DfBkSex8a3o/I74bUXmfgxiOqfEfqMNpeD4PoFJQmBNW3xUbCcBvsoRyaE9h/xR4TBiTc8Ot4PUsHW4v+qz2BBC6NOjUJeYFHdXvfero+ZQHXP81jrfmmhrw6ZAkRJUEsiTbOevhjuUWG7XK9xQIy4vt7dmD17PGIzT16TsCz67yH2NUAPKahuLPbd/PURjF17hOF6fDw6cNvqxA1qtTgxFKl1JSpXvMJu8VFJXvmRty5/aXLDTi2Cjh9dxNxwi37wA2rrrdMbG/XRA8RaGzFnCacxbyMmY9IamW93PAnZyC2xgNb3aMFDD2+QzoUN+o1gAU/VUqud4Y2wnraH2tg+JssTSreMjdJqnQfe6cnH69hNuPCJ4ZlfS9z59V6Z+6pkKpD0X2+xw6qeV/As7JW35BOrzn87Dy/I2V2uOzeki+ocS2WGL2ZYfcYwqNXLZKej17CrfnrIEJO10U15RQr17QoaGL1Hi2e0iH8nyKS+I+VBnWeFXxGQVEMX1dxUaF8j3Ft1iqEXK32hHyrqaMD/RLCrcz5ym2pRIDBMX262zt6fSp4LqSrl0N72er6vThSa2nkVpxlhqezwLygVwvxUdJle69eEWltlia5fWaltzbM9bryVWi1zM53M64EbcGz2z1CpymlnUWKka6CA/oyCWtqzO91mPXLr+69Xw2yzls+YVJLT661PzPmHzP3Er4Ent7xqqWd3RRgUdoRvXNBE8Rb2fPnk6fCuaBVllHgdzPkfc5NNSPhueTo17hK0I5le69KwkwOaq1t6dre6WUUDr3BluxyCipwEgAPLN0ROA01cuem72sY+j81LEnflS7+zX+IiQq2huYGIrPDuF35uksmu+5KGKLpdjiriJ7e3KUW3HvGW8FT6FHaB4OPI/q6XSpwPlU24yfO89B/pN8tioZNj/TkPzQgE9ZdfQ3sHile2KxUbaEt1ja22WG3KX29uzA6xnd7ppLouipFXieG3Saan1urec/Z5X2/o09PocK6Oy/Va3zFb3zF2mLP+GkQqVOJP5UI3NMjKT2CJVeS6zXM2V+bri9N/A8d+jUJXieR30U6cj7HBrqQ2cPnzaxn4p07mJtvr70LbuUbMUAWuL9p+jeng28nqxwu9VGYri9J/AsFI4W29KplATPu0rx0Qi9l1fL0HbO3B3new6FNQqOfLL9PSv8N87nyZPawqnUXqHJ4uZ7RmyxlP1UI8PeRiUKjVwq6PXcqeQaewHPAl5O2/ycNTXdtqhVEdBRio/OabulczmPA0mpUXAU0nnBZ0//+U0Nm0vOk9A3xQOcvbl8rKLOWSbvM2mtKYVGLb2enLXk7unpWZPDWKCZe73qQKf0+KKAKgCCF7P3p03X1yMfsqQGNJ+1zgs+z1WZsMp7MlCEQaPYqJWStliSrJrnegpTC3xaez13fRKLjFx9BJ/VXtTGzmS9L75vLhHoE9iUPhpAY6H3WvFCrOfkrRw6vMbjNf0a/22rqOTio1hbETaPXGy0U8pTjWIBj/30ohBYZRQnSXs9az1CU1hBCCyU09mLRNdyKUVXGEVHosqB/ZHvedFq5vlU5IeZULtVhObeOJ+SzunCFZXvuYyRCpHn2LPOEVHgI3wO2Xaki4xKh9svpLJbNOxdMx/zKLmfl66RVpCsUQPnV1ffrJCXOsWLbRvDPdazjrZerpKeOe9Syd/+joEEAP/ck/fFzDj/g4Bnb55Ol3pYYw9r4IqkgErCTmsPXq9pCr2ua0hM/ed8BryZRb2Jtrm53tVYL2znXtviYoecyy4jC6pS8j0l5ggpdw2pYcqkp0EVfmwmU0eCqaHzFYW8wyF47fXpQxcQch/V7n6193wWIMfxmQur5H24xj0+Cdjkl7FKajP6BCgMVrknwnc3eXSZXs+jeDuL6YJyP70anrd2IfdWUDtUVX16Pkt4AXO8mNK6dC8n8vMok8bn3ldLPcFIwmZNj2hqhXvn4fYjQ+dFb3m0qDfw6G09plpBXimvZ0fXW4GG5zOg9p5PrkKfo9TnbLPT+jvUev6hOKXs71lq/qgN2Cvs6+k2EmguC4ZHBs+hgyrwn4WuQ+6ldMQ1H0BE9LeJ6JVE9AoiegYRfTARfQ0R3U5Eiohu0foSEf2Lue1lRPQore3JRPTa+efJOWvqBz5LfOdK7s/MtN30Pz89/h5LM1jSs+wLV85zFf14wsxNzUX2zUxcQ2m4Szy3cwqzn8t5HELnXgXe4/kdzLOvKv2EREQPAvA3ATxGKfVJAG4AeBKAXwDw+QB+zRjyhQAePv88BcD3znY+AsBTAXwagNsAPJWI7su/Ils1/YZlV7enfBdLfn8l9nw+0//5FYW4VEmCVO3z072NpULukoVG3v5twu0D1oYuVkcMubewez66G4APIaK7AbgngF9XSv2yUuoNlr5PBPBv1KTnA7gPET0QwBcAeK5S6m1KqbcDeC6Ax+cs6FAKVren5FNaxlzKnpxnc5491klwITX1qUQ2JT+ytFGhUYNw+4DOgM54D06xbZaCExWGoUsLuR/M6wlVtdr9FiJ6ofb+aUqpp61LUepOIvrfAbwRwPsAPEcp9RyPvQcBeJP2/o75mOt4krqDzxIwJGVTQdhxKlF41HvxUs9rW9SjV1ZCLbZ5qrHd1Ga+OPg9d/AchUcCqgFuufmeJVUK0IfXs5TuUko9xtU4h8afCOBhAN4B4P8mor+glPp3ldZnVR//vQ2RYaXN55PEtXPxvx91lBXe942tVenOmV96i6VWhUYVvZ7nlNt5cRowLasRNq+jXpI+p7zOX1VK/ZZS6v0A/j2Az/T0vxPAg7X3t87HXMeT1A4+C1evtwTSUt72I+3c0DyUn/UEHuF5Yx6rKTFfSClzSxcaSYAn0+tZDTo72SNzQHZh9ViMoytrK6MOz+0g2yt1rDcC+HQiuicREYDPA/BqT/9nAviLc9X7pwN4p1LqzQCeDeBxRHTf2Zv6uPlYkroLu3en3sPaQ34dKaTeKt/TVK1CoxwxQK8JdJ5LvuS5nEcLtc737FEXCIm97POplPolIvpxAC8G8AEAvwzgaUT0NwF8PYAHAHgZET1LKfVXADwLwBcBuB3AewF85WznbUT0bQBeMJv+VqXU21LX1Rd8hkCvdDtXNYB0QG9zWUP4PVS6c8QFrxaFRp08QjNbrvNYjg94G7KpZb7n0ULuw+spIqXUUzFtk6TrX8w/Zl8F4Ksddp4O4OkSa2oOn6FioOLV2B1A3tlUnJeSBNzVjoimVLq7JJnvGQI7m33JQqNK4faiAMsNrzf0Hl5c4ZEUiBwdaHoMuR/9miaqR59ETzr+f80PthdoJ574Y0rgl7nL/UZT1ShM3/Q57i3BU13H53WmjDmoevdYV9tmqaRa/YeiN6/n0OHV3PNpU7Y3tET4vdaYAlJXAB3w/udaswhAxtjgeixzio16yfeUslvK69lKuQDZwAt6cd7PGioMsN2G3HtT5+ei0E/OZ6/q57+Cmdst5c9f2P65SxJ+Wm1h1KMyq9mjHqnZsNCo23C7pOfyaF7QI621F4WgqOR/Bo4Wcu8cIIfKqq3nU9Az2CJ3tKdczZ7WUk1HBd5U5Ya7dTCrHXKX8BwGu0h+HwqC16gkHzqSWkDi0QuNFEaOXUB9/wVs/Nl1+93pdV2ZSoZnSU6ItZVTEV9qQ/wUpRYaWW3Fjesq3F7LO1lpnq6u7VCecrymLYCtyZx9I83QSf3lfHbuDVUIsB/3OfG287zgZ8xLSLKYiL3NUg/aVMOXW6PV65l5zbsKt7cIMw8vaD9q7FHLyvfsMeTuU4ntlTr7PTpCMK2luvi0ojyMHT4ZaShT0r+lR/utd603F+xyYKpioVFztc7FLDx/Fpj3/tnVVAjSWuZ7ltIRQtxDh1Q7z2eEh1PU+1eiAr2TqvYW6tor27pwSfKxmiXzPRsVGjX3evYGVmNz+mI6/DZL5xRyvwCvJ4CLZQKuOvzEJlX1hhb2pg45VOuXU/xZ7a2fSpBfOBQ9pXChUVPwbO3pDKnntQ2dl3xQPryeQwXVV84nKTZ19p4L2fv6LlFdbTBfYi0pINaw0Ki6jgR1wl7Qs97z8wwgqVm+Zwn1tp4morHPZ0DtPZ+SHs6Yvi28obYx4/tZX1LgV/LZ75L5nplQKF1o1MTreSTw1HXUdV+aSuZ7Hi3k7tOlhNyHgur/U4v43TmX/2io3v5gCKsbD+SyDs56Wnr1JB9nGTrXwoVG1cGz9xA7R0LncDa5sSUUhMf+b5XRGiH3oYbqK+y+qFABT5PHckqJOzdR+5zEEqpxSqXvsRJeUcl8z4ZPNKqic4OmsS3TWepiQu6X5vU8yJ/JVmr7yWnfqZDXctMu6A0t3W5bq5SHNtqOr39nf8N2qri+aM8st9K9pFIfqRmQZKFRVa/nuYHnonPw5AJ8aBDIU21e6d5jyH14PYcaqz/Pp1Z0FFW0o3sGMz2Ywc3pEb/RfEjcjei516TW9lRJG/UT9RN6tyh6fefqbR7qU7W9PT17lyRAKTfknrGGYl7Psb1SWymMgqOAmn16UZ5MR98or2PjAiTrWqUKkCI9mr7rlvz7kvLHrrffTcnfhp7/MA4dVxnfq9LV7mz75+T17LXQyGu3gNdzgOdQpLr6BFND604buXPUAs6AuHbiw/BxA2Lsx+3T2ohCl3lHmGloyK6eb/I9eD2zpm7g9Rzh9npSlX4OqvZ/WVKBJgIMqwJpiqwgKTuRiv2kU/+3urPD71otSnHmf2SzbmpD/Wp4PaN0tl7P3v5+9eT1PNe9bM9Q/dylNgCoFU8UKkSK8Vp2U3TEteP9xRVaS0lJ/3Gdv+VZQC/xR633P4wjb3VIV8//iTlnr+eRiowGeHpElX6OqaZ/XZIfoVlqXIw3NWbeZYxQmJ573SSq4b02orya8b8k0d7aRSOcXle9P9noHNQzCErr0r2eqfOe+9+7Q4HnUEh9/EVzeRkTv0/N8j6FvJniRUcWSW7TFGVLtKiHNjarb85/7n/sh85Chwu5B+107vUMXI9iXk+fzsHreTSNnE+v2sFnYi7g0fI+uyg6Kg2m6zz8gVGguHoyE8YODR1dLbyerTytPXg9z21rpXMAz+H1PDs13+dzs08kQdurU7EpyGkjpIi+wb0/A+0pe49K74eprgAy96eO3KNSdP9QIO7zaqHYPTyvKC4MPfYIPanzzdPfrN6I1+EV+B28Fx+Me+Jj8Ul4IH1M62U11Vl6PXN0KUVG0jpH8Bx/1r1q899biZzNCnmfQW9pzLy28Sn5nGxvZ9wvpYQNlk2Xzv2P69Ch9Wb1RrwaL8Lv4L0AgN/Be/FqvAhvVm8sO3EmtCWF3IfX0zNBIa/npRcZpahn8BwKqpvHa0ZtHu+yoalYmD0zJJ8UFpf+HZOwV2i7paGhHvU6vALXuLk5do2beB1e0WhFB9Lweuapp3C7T2Mz+ZMUppt9jZ+Dqu9P1rHlUiqcSkCttT0FODPnL7fxfKSNCPucXM1D/C716KUdXoCiWjye3OMi6tzrKVrINLyex1DKNRh5nkMWtcv51HL9JHI2xW1YVPx56YF1c5//zp0v+nw8c8nnglLTXEjRfNuR1ykm1WBbp/eqd4NAUJYv/wfjntXXcygNr2eeevJ69rLN00FyY8effL+69Xw6w+Kp363E0HlM3meJzeaT9seM9nbuBxSteO/pW2fuCdrT2s5ILaBRQm9Xv4UX4GdBuMKV8eW4wg18LD6pzMSdV7gfzuuZu7XS8Hq61Uu4vSPwHAqr/a1WGiw1dZH3mQScEfZ9Y2xQKfCJS4XGWWH4yPUqEyZde4FK/6Eaf/jOTm9Wb8SL8fO4O+6BT8cfwyfgMaun84NxT3wCHt1ttXvpvT2Zi2i9gjryXOuL2FrJuY4LD7ePfT69ar7VklV6eFfbckkP7UaFeSNC6851ZPYtsRWTtOxh/QohY865LeuY+65h8eX4FYC+d+qR1wjnF5FSCr+KV+P1eBXug1vwqfhM3J0+CPfEh+KBqACbw+tpTOjv09Tr2WJrpZ7Ac4TbhxLVFj5ToZBjo0beZy4QZgInNwc0K1fUJ8aeluK5oC0Vu4fn0OF0rW7iVXgR3oI34oF4CD4Bj8bVpXjwhvYa4Xa3Rrjdr0NUz7ZTf55PDkxGgFOyjUQwLu3hzIK5DDD1zsvyXHL6XJAnL/VcW1+jM/583q9+Dy/FL+IduAu/D5+Ih+EPgKo/sjUfdKM9kyXgmmPzCF5P79hC342jeD2l7Z07rA9t1LDa/RROT/XCSXghRbylCKSBZgJlsPI6FhYLiTMnp4r8bLyldAWRp/ZcXQHXl5ZTUFfvVe/BS/Df8D68F5+E2/CAFrmcB/CwdpFLWkvn4vU8583ke/V64kzuYQXV3vPJ8nTa8z5F5okYVzMHNMWDys3Z5D5ms1i4/pxUyhPZ2sN5QXqHugsvxS8CAB6Nz8F96JbGK0rX8Hryx1+M11NaI9w+JKD28JkqBxTWyPvkrMOmIxQdceUPwzPAiVMg1AuA9bKOIXG9Rb0Rr8QL8SG4Jx6JP4x70oe2WcjwevalFl7PEW7fy3W9egfPg1ei11DjgiNH6F0CJjVJ546KbkZfIgdUOrezIHyJbuY+dFxJpCfETKcUfhWvwevxStwHt+BT8Bn4ILpH1TWcpS7c65m1tVIvqhlu7yk9YaiqDun5dIJgbTiNyft0jEtp7yonskLF+5omMDyQQxwFQPZaXePVeBHejF/DA/AxeAQejSu6UWlxFgkBS8mQ+/B6CugoXs8USedllrhWVUWj2j2gPuAzMu9TfJ6Iccl5n9k5oEJFR9L9PP2jlHBdXXt97o4nanhlE1XZixmj96vfw8vw3/F2/BZ+Hx6Bh+ET6le0n6uG1zNpXBH1sqdnzTzP8Xt8KPUBnwGxPJMHzPusVnTUi1rlrIbgNAVSfWN83uCxV2gzTRXtv4D34bfxifhDeCA9pPWSDuH1PCu12lA+dc6aRUZHDrf3CJ7jz7xX7eGTkfcpodp5n1FKDPXz7e9BqVTFe/Z2Sy1D65f8tKQzl17R/ih8Nu5LH9l4RccRC2yP4vUspCJezxFuz7c31K3aw2dIjtB7N3mfug2c8j5FK9tTQvatvaLZIe+OPbhDh9Jb1JvwKrwA98A98Uh8Fu5F9269pEmtvI/D62lXb17PmhrhdnmN+5dX/cBnasjbIQ5MioTWU3NAQ2sOSAzO2DmgTK9ojI7oYRxh88NIKYU34DV4HV6J++B++BR8Zj8V7YIAWLIYaHg9wzr81koj3D7UQM3+C7ypHdIJZnPc1Z/xOiSGjVB9U+qaVGgOR7uy/aJFzFWs3/JHw3O9fNfSel7rGmZP99X2fXVx5k39I97LH9Dcc1z7pHg2eGO4MHStrvEqvBCvwyvxADwYj8Ln9AGedNUOPCPnPivwLOT1HOAZMU76WvXyd3MoSX3FX1iwqax9nP3h6BNqTwXSiPmiwDkbaPcHle3Tt/Vjgqm3P2Pc2sYCnGWuBXznf68cx412rrxgvK4lMcQUsq236zcdqT+6jIKF4E0fYMGFGMgw9H71e/hl/De8Gb+Gh+ET8Im4re1WSoA4dE4mI8FT2vYAz6Rx3YCnTwM886Uq/RxUfcFnQLGeRhGYlPC4RvQNQbQOQ0EoFPeEMsHU0/80LgyDJbdJc8JpDKSm/oGWDJNuAJW0w1fW4yJ/tEt5P5njfGD0XvUevED9DN6Bu/AIug0fe/XJoKsbJ/hrke9YADpLgSfb9gDPpHFdgWcK2PUOnkeA0iEAjXM+t3mZwlXvjnGx2zaF1p1aqBSsnNfG5xYvVdnvc8mF9KzFdx6cCnhrhX4L+fI+fYVWLSv5uSq4RroiKE6+LF0htFeozdY71F14qfoFKCg8ij4H96X7u+27JLlHaUtPZ8Ia2PYrgWf2+AGe8eMGeMpIoaz35AzUn+eT5blkhN4T52F5OkP2tMMj9B43jpW3u3opl7nsXktWyJyhnX3fmqxtjF8zzh/bg4feJ1tyf5B1W7+h3oQXq+fhbrg7/hB9rhs8w0b9PzE2hBTt6dTXETGHmE0h8PR+744GnslrGeAZPB5qGwIR3YeIfpyIXkNEryaizyCiHyWil8w/byCil8x9H0pE79Pa/pVm59FE9HIiup2I/gVlPKGjebV7rPez+YbzqV7ZwLiYraN0L2HQWynt4Yytevd40ljezpDXl6NlDcu/oc3mjX4s2zZxKuMlPI26DW1OoiuoxZOnryU0J2dNrD52DybLA8rwfk79gF+9fjVep16OD8ct+FT6rLKFRRXD9lmgPsAzbXwp8EwCvgGeweOhtobqbKvAfw7gPyulvoSIPgjAPZVSf25pJKJ/BuCdWv/XKaUeabHzvQD+KoBfAvAsAI8H8J9SFtSf59NQ8cKjVO+mgLc0xisa5UG1jOm66p3jqeztD0zuZsg9PSu7svdzsseBFP+c1+oar7p+AV6nXo6PwoPxKPojfVS0ZyrZ0zkNHuCZOv8AT8s6BngeXUT04QA+B8D3A4BS6veUUu/Q2gnAnwXwjICdBwL4MKXU85VSCsC/AfAnU9fVJ3xKfJ8i4TAWYIP2tMOtQu/2MfsORwq977ZcomUu2h4v9c3O/UOYMt4Vei+p3HNZ+2Su1zH+/er38MvXP4dfV7+Kh9Ej8Mk3PgM3Wle0ZyoLOicD0fOJ2b1U8AxpgGemvQODZ71q91uI6IXaz1OMlTwMwG8B+NdE9MtE9H1EdC+t/bMB/IZS6rX6mLnvfyWiz56PPQjAHVqfO+ZjSWoHn07YU9Y+0Xt+Jq4lek4B27Y5RKveLequ6j1yHFehLZeCeaFSXtmcLZc44zaAStphZtV7r97PqePm7fvUe/CCmz+Dt6vfwide3YaPu/HJyEg96kLZubAlKtq5dmuAZ3ANjcBT/PGSAzyDx0Ntl6e7lFKP0X6eZrTfDcCjAHyvUuoPAvhtAN+gtX8ptl7PNwP4mLnv/wLgh4now6QX3afnE2DCplDoPdQu7S2NWEcw9J4KtMwx0f1Sb6KcLZdK/sFxQapPnHON3XKppz+qUmvx3JRiIegd6i780s2fxu/ifXjU1efgo68eFm+rI2V7OycjUfOJ2q0FnqmewuDYBuDpahvgGT7ua7uivtKZ+tEdAO5QSv3S/P7HMcEoiOhuAP4UgB9dOiulflcp9db59YsAvA7AxwO4E8Ctmt1b52NJagufpb2fkf1Tq+WTQ+8RXtHsXNLNeIvnUjr0Tu7+J5i0tZGzbe3DDb2XEucPo/T/2muE3lPsClxrLhD9xvWb8KKbz8PdcDfcduPz8RFXH5Vsq7VEoHMyFDWnqN0zBs+gBnhqxzsBzyGrlFJvAfAmIvr986HPA/Cq+fXnA3iNUmoNpxPRRxJNOUxE9PsAPBzA65VSbwbwLiL69DlP9C8C+MnUdYncxYjo8UT0K3P5/TeER5SXWOFRQTgNrSnsnSXtdWANgbl8Yw4bejdD5qlwWiP0nirJ0DtnOuHQ+8mu5/uhFN5w81V42fUv4t64D2678fm4lycK1DOAikLnAM+Msf61Vd/LU3KMb9wAz2oiVeeHqf8vgB8iopcBeCSAfzQffxL2hUafA+Bl89ZLPw7gq5RSb5vb/gaA7wNwOyaPaFKlOyCw1dJMyP8SwB/D5N59ARE9Uyn1Kt841hY6hNV96N7u6LQ9U/K2PI55OFssBTeL1+Rqj9kuKXdrpaobzsfKs7XROg8RxDZB52655LXBONfYLZckzzFXnLWw+oS3TrJtwXStrvGamy/Enep1+Cj6GHzijU/DDcb/mdkb2leSKBCXKizi2h7gGT9nyrkM8Ay3dQqevUkp9RIAj7Ec/wrLsZ8A8BMOOy8E8EkSa5JwxdwG4Hal1OuVUr8H4EcAPNE7guNZrBl6DylnzgjbuZXuug4TereIszl8MPReWixPJ6NPFBjonk0hL2oHhUcufUC9H79883m4U70OD7t6BD75xmfiBt2NDV+Ll7GlJ1R0/oTN66Nyao8CnjnzXyp4+jTAc6iBJO5gDwLwJu29tfyeiJ6ybAVw8z3vAcAMY7PAr8Genw7FwqltXOnQu1wREhNMPf290LgcyglXuULvseJWx3PnkIRkRuhdzH5WH57HctEVrgAQHnHjNnzcjU/FpqI9AcJCP5LqATpFK9qBfsCzRH4kOgLPVEkD3ADPoYKq9oSjufz/aQBwj4c8WG2eZlRChHDYmtEntr9NCieOikoNiJnP0XddQ2jelDG+fr2H3hcbrtC72c+75vlcfX3XPp7wc8HQu/NpR7a5rq6A61CI/Aoq0McxkB1+v6IbeNSNx8K5jRL3KUjspYX/HoVC+S3D60lruCTwLLGJfAnwlM4NlQRPn3oAz1qRL45K8s0ZSOK/XncCeLD2Pr783umtzAi9p4rhrUz1bsbOEzXOsrYioXevZ5N5bJnL28YAAUfoXUQ1PZytQ++x83LlOq8ID2hv+3dW854O8LSsY4Cn2DqSz8ux9gGeQ5GSuHu9AMDDiehh8zNDnwTgmdzB3YXeY+SYR+Jxm6mhd6tyIdU659LPArC++XzhdZsSPhvX046y80FrhN4lcr0kQu+lt12KDMHn2DmUEkLsp6EDPO1jB3hu1zDAs7hSn1aU8nNQZf/lVkp9AMDXAHg2gFcD+DGl1CtZgx2ezd72/BQpVNIOJz9uM8qruW+Omtcyxu+ptByMBB/OVkYikQwHnAb7+3Rl2PTaY/7aCf9BdW65xJ3L6FOj8OhiADQDOqfhAzztYwd4btcwwHOoD4nkfCqlngXgWVGDCOycSW9/7bhr2yVnf/0cnDbtr1n9A+cRMy5mvqitlSy5heoKIF8qnW+ttjZPf3u+KJx5nyeb07rXtQrkSDq3XGKsg6XUPFjfnIz8zGSl2I65HsycTda2ScL5n9UkAM4XC54hDfA01jDAs6oO7JWsoTNwGQgr1vsp7C2NC7frrwOdU7yam3PYd0gOvbPXR862kB1X6F1KUaH32LzPWqH3FO+nOWWu91PSa3k0D2hN8IzxrB4FPL2wN8Bzu4YBnkN9qf1f695C76nizKkdlgi9R41LmdcyRiT07vmjUTr0nvy0oxiIjQm9B//TIPsHNvi8alPmjVMq33XTXyj/k2mruTJD7JOJQlspDfCMn2+AZ9hepXVX2+eZoc6ecNSd2v6ljvDyefs7QLXInp+xa46wF1OQ1KTq3TWe0xYNrYH5gROMmlXvKXLtBxoDW5wbd4m9NyWr3kt5P8NGGF36ubEkqTZ0LnNyxAbZAZ78tQzwDM9znuA5FFY7+GR4Ng9TeMTpb5GrXTT0XhpSI6EyOfQeIzLGFvqjFLW21qF3zpwpc3AlVDh0yAIkAeiczERe9wGe2rBE8ExeSwfgmWxvgKeIRrW7V+3/Sqd6EmtICGBdoffUOaNC7xYVCb37QuISofflUE7o3eXd5Col9C4Rppb4w6p9BsHQuzlf6W2XYk0fBUAFoXOAZ2B8KfBMgapewNO5z+4Az6H26uAvdKRY4CcUeheQxIb0qXuIjtA7Uy6oLB16t/2hb7HhvID3U2zbpYjntrNshX5KqRV0xsw9wDNtzgGeYXsDPIfnM6Bucj7PNfRuE6fwKAaCR+jdbSdlbMwY8dC7q3/qPFJ/nKW8n715LTmAGgOqLfI6zfk5unTwDGmAp9+Wz94AzyGGOsn5PL08fOFRonczOtwehMR9c0wuaVLovufQu+HdTP7DVSr0XkO+0HutbZdsc9mNMbpUvq4VPKlZ0DnAUxsWsCu9hY80ePo0wLN78KxV6T6q3aPl8mCep/ez6OM2A57CqCchWaBOD737bAXn8R3z2S8dejcBsVXofRNC117H5IPqN0CJP86h3M+cfNaYsLm3i/Az1Rso+9nwJbZSCny2dHXlB8+QjaurdqF2H6D5oMr5XS7g8YyFu9B5OeeKBM+UtXmvXfwYJ3heoXUsdyhCHYXdTy8vwfspvedn7uM2cyHVbLPOo/2h8W1Q7wVq3ziHnZQN5zn7jSY96z01lOZrjwJU0g4HvJ822wEAtQJJyg1za5TR5TgQqsNmtqeTA56C0DlNXcHbmfid6WY7Jea1ZM+VAnBee57vThLElodlReQHz6FDqWHYvZH3E/bjXXg/U2FRFDIt8Mj0flrnZPa3SRmQZ++z2JyBOML76dzT01UVn+L95HhvQoVHMTmcLu9nDoD65rCsKQpAlzmDxR880OoVQrNhczLCB06gCHQW9XYGx/uh0wmepbydPvCMVYpHEUg8r8TrFD1PJCyfm7dTUZ2fg6rNxxYJbhw7HO/nri2gHryfVohjwS55+9rC5SmQah3j837ajtnSBKz9jXMq7P3023WAqq9vrPdTovKdAxUp+Z/SALrMKwyhrUBUxLs5GYoDTuB40LnYcI73n0833s7QOMl1JIFiorezVpjdoeHtPE/drenspE60QTjRmOO4Io0lnWMd/Y33W1tAypYFThuONXD6O1/HnEPMOFjGEAFKbY6rK4CumePNOfW2KwKuFfuaKyKQUtMfmmtXn2Wead3rWvXzCNlf+i7/zvM5231abczn6tN6Pa4Adb0db7Ppavcdt7UbayO6glLaBTbXbrN9dQVcXzv70NUV1LXxoS03Et86lxuU79otN1Hl+FJsupYFUDWvU2SenKIlwUKiaSmMtUiE2L3jzxg6feNSvZ3Oec6sqMj1UaR+DiV04GKgGuqu2r2I9zNlvsQ1FfV+6mKsr9a2SyLeT9sxaxtt23K8n7kq5f3UVSn8PjUJVMBzPKBLv4qe0JJq4t3UVdvTybElEWI/Z/BMDVefm7dTMszeE3gOBdXecV0499PsV7rwKGQjK/czBG+B13Ehdh1YAvPG9ltzHR3z7WyE/6g4cz99CuV2JuR+7sP7jD+IttxP6fA7e3gkgDLC68GQbUhClfHdSGJ7pgVEeoNOoLi3Uzy307emUG6nZJg9BeC89hIAPeUaCcJyUlFR6udQWGOrJb+6rHYX836a72PnY/SJ2kbJZU87zPF+hsAv2fsZgtSrbb/p9d6+1ftpsW2bw3dsD4PuNezWt84fBkiWHKAaNcb62UTcuGPOgen9tKoGgEp4QaeJ+oRQib1AY4ATkIXOxZ53feW8nV7oXMb65k1ZUw/eTmAUFQ1v51mq2V9pngczw/vpsVXa+xmyKeb9jADctBD7Hh6D49kgaQMvNyh35/30rsO0wbgxhq6HK/zuswnwio9C4Xfb+jgAai5LxKsWCaEtQbQFcAJloLPnELu0txOo5+30tZ1jmN2hc/F2bqQq/RxUbQuOAHCKbawFLj47vvGx8zH6xPa3rhEnbnOdr2tOW/9t+1w0ox9nXAerLa3w6HQeBLOAxHe+tusVOodVu0Kg/Xp3Wta3zmUUEaVqtTv/6ymKco6x9nEUH9kKmFx2QudmtocKkFg2/AVIwAlAd4VIpl3Av35OUdJp0nCfVOnXSGKerNxR3lj2k6hYKRGNCooCY8WhMzROfB3xAHfxRUW9w+jQRk3jU0W8n7s2e79m3k+b/UjbwdcRcwfzQF3eTzL6bcbo/WjXb5Wk99Oc5+jeT8nwO6f4yLLGEpvQr4fF8gspD9hy1cq7uVkD4zqBec259oa3M6zh7fSOEQ2z9waelfI9R85nijjFQi6Y89pljBeCx9jcz1CYOyf3M5Q3mfzITZst27fG8svPLUqKzQd15n76ZPTNfjZwAFSjxuqqHX5vCKDAGUForKSA8wyhs0lup+SG8b5xwgAnWlSUAqQ9FBX1Bp5DLDXPzBfzfvraHLa68H7GgGAhe3FV8Mzxm37k7tfa+xnybrrafXLZir1xuqrfueM542x9UgDUVORz4NkQGpy3UwjVYbMCcAKVoXOx47UR+A705O0MjfONqQBwU5twUZFzHjlYFvd29gyeI+fTq8bV7oLez5xHbmb0F/N+Ws4ty/tpBUOy97WtIQSPhbyfNh3O++nTFWNMKPwuvfen7b3EHqA2AGVAqL8D84YjAXu5kpg/EjiBRtB5bt7OVPCMXkfCufUeZndoeDuHdLUrOCKs1L4tQFEn2tD6sJ565LVrt8UqHNJUonjJVXhkO6fo1zE2LOcYKpSyFQzZi5oIUMreTyt2OY2d+tvm1QuodjLnsdlxjAk+1chs98lli7MOIFxcZGtn2dWKgsw1me9DRUjmGmznaBYhufrpzVJFSZt1FLhZmddfYo6Mm2rVQiKOnRxPZ2h8aiQAKOPtTFpHAliNoqLo+ZvpwF7JGmoedh/eT8Z6LIrxfm7HkbWvPVyuv94bq+n9tCrC+3naozTclyNneF7K+6krFH6P8X76xtreS3hAXfNKheJb3XSkvKsJ3s3NcElPJ9AePEPX8xy8naOoSA48W/4NGEpW47D76WVO7iffrt1Wb7mfwcKj1PkjQDdcBc8ff+rHA1Nbpb05b0rup037vEzHcaOdpYQq+U2f1PB70G7kr30ugGZuMN89hKZICDjFobP3EHuyl7GD3E5AtqgoNbczdt09FxV1/Ds/qt39agafm+9MpveTB66u/pHzMfoU8X6mAKJznAXqzHHWNVjgUfsG+bZnCgLs6g20rMGnc/R+RoGkpW/uH3DG+kUBdOl/zhCqw2YN4NTnDKkX6Dy6t9PXVsvb6bWXuG5X/1rezgOC51BYbeCTBXnD+2kda1MCsHPH2cZzw+gi3k/bsRVow39Mm3k/Q7Z8Y3S5vJ+2vjEAG6pG38FjBFA7bQhADiIhtCWMCswfDZz6vCEJfR7FcztTwASo7+2MBTjfOlK3UEr5j2cKeFpU1dsZC75D3alp2H14P9PXEwWIltcc76dv26SNrZLeT9ZNdLFpGW9IzPsZAlSWDc+YkHfTZocz/8ZuHoAGocK1Holte4A0IJP8Cc2RIB02o85Pnz8kSehs6e102j2ItzMWPDsPsztVwdvpBd+hLtUOPnOe2z68n/7jnPkj1mEbf/HeT45yvZ9WwHF4P1PD79IAGrOO3A3LgTRIk5KQdzUZNs11hHQk6OzF2+kbV8LbOYqK5OZvrZQ9O1N+Dqrm1e7D+5m+HrtHM9JeYB1BeFzmzfF+6oqBl824xeYCeO6u2d5PCUBdbVjGWL2FenuE15ALJa7xtveSALrMf2QITZAYcNaETqBsiH1ZR0pbKW9nLCQBF+XtbFlUNLydx1bjanch76d3Dpddu61L8n5aQS0RWOP7+cHUesy0t/YJ37BEvZ8chWz5xriOhaAuNfwOtAdQ2xps4w8KoVnh9NVIBHAC8tA5vJ3+tfS8hZKvrQdvZwJ4dq1Kle6j2j1FrvtkivczGlxd/ZnzRfRp4f3UJe399Ho1bd5PXVwwbeH9jJUkoIbO1wqlgeIjly3f8VoAmuMF5djAHvZaAKnI3LHACVSFzslUIehc2p22z9TbGbLnUiowR9jquqjIB75D3andE44WcZ5cxHnqkXcOl127Lb2Ps78mt0376+j+OHHUZqxjDetrxvzWp/Uw1mQ9d+t4gvPJRnObPsZ2bWxzmOeY/dQj087S5wrxTyoy5nXa8o0xXy/SnypEV4C69rQz1mr2MZ9IZLbv+lPcU5BcdkwtUBF6yhH3swBEAdT19KXsOXI8OhKbw6+2wv2ahdiBut5OX1tywVSnWyh5xrR+UlHS/C11YK9kDTUOu2sv9e9VpPfTfD+8n1tF2wusyef9dM4b269n76fp5Szl/bT1c/WNaY9VCQ/oYocDGZn5oCVk86xWC6ebauDpvChvp2C4ehQVBY4Pb+fFqIuwe27uJ8f5eWm5nyHws+Z+6sdTIfXK0m+2nwKwXng01hqV+2ntY9hxwSVHpo0YW5tr4ni9HguE30PjbcdTPGipALrYOiiEJksKOCtC52Quw9vJgc4QePrGpijVa5gUFh9FRbHHk+bvRZIV7b6fg6r9x+e6Nw7vZ9R6YmBR1PvpspvRb32t/aHkFAyt4ng/FxiN9H6GNp6PAdQ95DJAcZHkozdtfUL5nwxFAegyR064lWujhXTYLA2c+nxBm3zoLLZnZ6j9CN7OZZz1+PB2ppyP6PxD3ambsPvZeT8d87byfto8mkHvpy7n+mhvK9b76ZrHd8y0Qcv78M0hx/vJUfCxmz5bMcVH0uH3WAANeD+t4sAOxwMW+4SjFlAqMW8McOpzBu1WhM5L8Hb6wDPFXvQ8vmsYD31dFxXFzt9ABIxq94AaFhxpZTSElayItBoCZ6GR/bWi2aK1sCdsS7RwaF4Hq3jJYTN2PaHXqfZca/IWDl0BdG05D2xtT6+n8VbbWsGKq2DIan9XKKTNt65hnndZ62LX7LscdxUfGe1ehWxBO+fNdXW8Xu1qxUcxtlzrW6+jUfiz/IHXbenvlxvd/Jkt4KJshVGLbAVJNtumdDDxFSbZbPam3Ip41hy8fqwnVx2tmCg0VtLTCfihM9Ze6rVs+ZQiX5tnTFKIvdff6SGvGofd1QnUlv8qQHu/9NK/W5FPPdp5uZx27bbOJveTMX9K7meUJ9Pn/dx49yz2zGO2Pzhrn/mF7dttrmF5b+nr+2PMDr+b/3JsAacbh8vruc6nHxPI/1zahL2gLO9ZyLPE8YZ2uMfnTvpaU9fM9aqGru1q7orv5Uz9nHI82qmeLd+afG05nk5XGkzNEHvkNmfRIe6Uzzkwv3UNoRB7z+CZm8vJ/TmoOik40l+r7fcp86lH2zk175wUDEb2aZH7GWNPEQXH2SHTAo/at4sLmVboXUHMMq9v3NpmjLdA8GlN275J4fcQgDLg2HksBUBd+Z+hP9wFAFQsjHsUEJUGzd6AU19fSnvouuRCZ/R6OoLOSIBLhc4o6OsZOnuH0aGN2vx13nw/7HBJOiCaOZ053k+jzwZadBg6svfTPC/u/JHrYMMju9/+ZGznxyk+Mr2fScVHAQDNeqymy9amLQIaUwuQUgD0ygBc057+3nFDDIJPDPRwQbTFT4xskMm9mbYCzhCIhKAzZD9WAzpZY5Khz3Xc1yY5/4DOJBHRG4jo5UT0EiJ6odH2dUSkiOiW+T0R0b8gotuJ6GVE9Cit75OJ6LXzz5Nz1tR2k3nCiaQ2r+35mZuczmWH8VAuJmNudy7kaQ4znzQ2V7Rq7if8Nmz2tu2nTdDD+Z76Ggi73M01n3LfL7hWfcyau7hf787G2mc+D1suprlWy5q8YuZ/sjanN/vq18i1abw5n36NAKw5oM52wxbgXp+tPXMz+q15R16oPnZRan5ob5K4WdbM4TwZy2vvKZ8TCAO29XgA3FPWEQlv3rk4/ynf2XJPk7Q2D3Q6lQK9vUoxGKS+/qhS6i79ABE9GMDjALxRO/yFAB4+/3wagO8F8GlE9BEAngrgMZjuzC8iomcqpd6esphmcSnafDIe7+f6xhN+Z/ST3HrJ6S3VJO39VPp5aswd6+W0vk4cx83d1MX1fnq3XrL099pc24zxNk8r1/vpE9dDavX0WuyHtk0yPY3r8atAu2ErxQvqa9/1J69HqFpYvrZSvZm69GtX08Nprj+lvVRoPTRW2tMZ2jLpHD2dsWtztAUr6FNC/BZ1/8z3/vRdAL4eW9fVEwH8GzXp+QDuQ0QPBPAFAJ6rlHrbDJzPBfD41ImbJkURKQ/gJEAknY433XpJhzMNhpTjNae/dc3a4ajiI9htB4uPHOOCOaJX237Ta/LY1gFpb8/bf9fHAYIeO9nhd986XP9eefoCdmgkyzGzb6i9BICa63IBtQd6xMPy0j8xc8YqEjRPU1cETr2Pcy4GcKZcH9/YIAh7zr0WdHLWHzPXpUFn7DytVKPYaIKAW4johdrPUxyreQ4RvWhpJ6InArhTKfVSo++DALxJe3/HfMx1PEntwu4ELQyLOVxGJ0CxRAcPvfVSi/B74HWMPf1aOte0SP/QlvFL+F0fY+tns62vJyf8vlnjbHNeQ3T4fenHDL/H2JrOwbMFkz5mcw0tfUNbMC3HASSH4W3PYTevo+u6MkLqImF5aUnc6Lihbu8yKobUOX04+6+mKgTCLklvl5RqU3r9nP/s7my5p5Fcd61tm7oDzja6Syn1mECfP6yUupOI7g/guUT0GgDfhCnk3kSNPJ+nG4Q3/F566yXD8yrq/QzatL8WLz7Sj9P2dWh+a5FO4HWV4qOQZw+Oa+EqPrLNFfJ+WiSy/ZLLE7C2B87d1te1BZNpy1xP6A+72c4Jw4duslJheQGwE1WiN1OXfv5VPZx6P+d8hQqIQmOlvZwAink6Y9cxPJ1p8/Siep7P8FKUunP+9zcB/AcAfwTAwwC8lIjeAOBWAC8mogcAuBPAg7Xht87HXMeT1DTszoMabeslD5CyYM63Dh2KcmAwsk+J/lEh8eA4svZNyt30hN91+Wzb1usNv5vnUTD87lVM/qdtjVaodLRbr0NDAHVBKAdEndNGAljuT4xqg6ZtXr/xOOB0wgQzl3NAZ1zbgE7ZeS5cRHQvIrr38hqTt/MFSqn7K6UeqpR6KKYQ+qOUUm8B8EwAf3Guev90AO9USr0ZwLMBPI6I7ktE953tPDt1Xc3C7kQKar7b66/nWOjcCSvZE2ETflegU2h1ib8aY7xV85zwu2aatDlYoXBNJcL3m/76cvWx8I8Lzh8xzh4u1z40y7VJqZ5fZYTfbcoKv5tazsW0tRwPhd99svX1VcBvzl+/xpbXtgp4my2gbhjeHOuyHxGWn0wwn3QUq0KeVBZU+iQZUuf2axVaD7XXDK977SW2jfC67DyN1VG1+0cB+A80XcO7AfhhpdR/9vR/FoAvAnA7gPcC+EoAUEq9jYi+DcAL5n7fqpR6W+qimm61RDNEhgGHCZEOW06g2CzGZddYxzzHLgcSnPH2PtL9zfUsctmw2du2B7Zecn1utnk9Wy9xAXZt08DKlbNpB1fEP3qTI4ntl2IA1DYmFUCBbT9bewikd/Ys2zEBfIg1JZEf2lDZoAnEQfBRgJMzfkDnRoeEzsQ1JJ3r0Cql1OsBfGqgz0O11wrAVzv6PR3A0yXW1U3BESHe+xnyWPq8osWKj7Qp9f4KzPEpgLkwDtN28HVE3yDQ2uBRqvhokdnfCmhLn/i9P13Pfmft4WnYZnlILfaS9gDV1QuALn3WE7PYCrUv61xkAdFc0MuF1+qgeZpYrh9nk/yS0FkCOIEBnYx5eljD4Z/zHrglXLrabjIP7MPvq/dyuSEvHXMg0gjTu74ULPg7zZEUfp9PbQOkxmvMfXz9k8LvrjU7bAe9nylgGgGwq3ye0YTw+7bN8H46YIsNoBzv5m5uD4DaKuA37QEA3XhSPQAKbPsBZcPwZl+XvRgQFax0F4FHrnJD+ucEnKH2XirXU9sS5xIHsdYweM7QOcTSAQqOtu8337HM4iNe1byrf+R8jD61io/016n2xIqPsO/nmofT5i0+WvvMbZziI4aiH7/J/SNq6R+1Cb05765voDq9RDFSTkV0qL3XSnddAsVI63UIXQ+zr3NNgcIh01aqfOND6+yliCi1LXEu0UIiX1utNdQ815ZSFX8Oqmbwub1HKuvrzZUlrIBIBpDyINJ+fDdWgyc3jJ1sseANjD4M2GT1d81lOx45P3frJTuM7sEyPEbvR+62q+26/FC6vLf9YXTNNb93VL/7FL39kvl6kQ1AnVDp+KNv7VsZQIH8KmkWUFHcTwmVAE3OjbYEcKbe4LmfpXOdnus2oDN/fQM6hxqpTdhdu3cuEfb1ePC1EVqf47a7IhvH+KTio8XuvN5z2Hg+pvhoO66T4iPTni38bvSPKj4y17G8jwy/e+UL0a/2tWO2EPymneI3oQdON+laYfjNNfCE5PWxrvGhdq5ae0tzb6Sc8ZyQusRaODZCwJk6tvfnrgfGjfB64jw+e43UUbV7l2oXdjc8kWzv59rHbSvb+2kda/Q/gveT4rycwfkDfcOheP0DnNuueP107b2Yvj6WxnXc/MITfvfK8IBGh999Nl39UzygLq/qzqtZwQvqvOEwPHEhb0eul66WUryZIRsu1fJwcmyE2jlewh48nbnnYNHwdGpzxcwTsjfUrZrA54ZbNvfFU9hb5LnvOqS4+jEW6Q2/6wBkee0fb+8j0T8q/M6xt2mnfd/AmsNhdeb65rmt51Q7/O4TF0Bt4Ov6Y74olC/r2qCa07c0gC59coCJA0o2wMsFvhSVAM2QjZrAqdtJbc8NrdugM5TqMKCz7Bpi5vHNdWToHDmfXrWtdmdscTS9XuK52zYiLdLGteUI0/Oq5l39ffOtU9q3XjL7WF5z5jPTA+JSGfLsBUP4mzHTh2YNv2/GaB+uOY+vzdwqCEZ/81oukg6/c7SMNefW2zbnqr32jYF2HVzjzb5AXBg+tB2T3t93/oucleyZYXnu/L0odU01Q+ocO0FAzhjfS+V6xnxnt2WSp016I3qnvQ5/nYfcalhwpIfZXceN8PvSj4C8EDpjrNeu3Vax8Dtp/bVrEPIgJns/XfY2r8nb1+/xpF2/8BjP2i3jdsc8Hk4z/O4StwCJHX63zrH5Zdj3t3hAxR7DGeMFNT09Ng9FDOiEvHASYfmeJOGNre3h1G2ltocKrziezli7KZ7CUFsPns7Etdfytlb1dHb4a0+qzs9R1XarJcADiJzXavs9zdx6KXZdJXI3pcPvnNe7lAGmveBz313jbWOuLP0WyLPa3retSgi/b9u24+MgyrQRAFAL+EYBqG/MZl0FANTaPwNA9TFegIkIy+fAnZQk1qGfcyvgDMFHCNSOkM8ZakuYb4GmAZ2euXKgs9Gv9VCeGj7bHQDmDeZJgUBaRDDhue9rs7ahPKb39hC6/fgu/L7GyFfzXlusynFNsdXq0f1x+t20hpsZNpzze2yEQ/GEXejcFn63zMNqiwy/m08+Sg6/MxR6/Oamj2v9oTFrO/k3oV9eA/CG4fUn/pjnmvtUJJf0G05qWN5nU0K2zyhX3BC6Kclz49gK9SkVWg/Z9tpNbEuYr+YjKH1tZxdeB44BnAf2StZQc8/nLvyuf6lYrz0hdMb4pOIjOh0/mvdzd10CNpK8n5w1sMeQp5+nzTWn1ZOw9JlfmL8Vxtjc8LtXoWp22+uQ1zS0Cb3rvbkfqA4EpqciFIbP9cIFvWtMj6C0cjyaNm9m7PprejjNfjbV8HL24On0nEeS58+3juHp1MbB8Xde8PdgqIqawufme+Laekl/DWDz3wnXfdS19ZL5xS2x9RIx4Q2MPr75uP1Ju2KR8zjtWUFwv7YwZNK+3waktv10+cLv62sj/G4TK/zOUHb+5wbkLGtIBdDVZmC8632JMLwUiLqUA3OllAuZwB50WwBnLKSZ453tmaF1H7SVgE6LBnRGzGVRFnT2JlXx56BqGHa3h9aJ4A6/6yRF0F4zQ+h6H8z9zDC9c8Euu/Z1OCvXaZ3WMt4+ByfUHqoyD4bfPXNa7W3ajRC1Y53c8Ht4zL5tlafNOufuGqSF31la+u5sz8d1W1o4fTfefL3IFoLf2CR3CB5wv9+F1TPD8PrxRaXC8oA8gIZC/BLzlbyhcm1z+qWGvwE3bObaTm2TrlwHRng9156rqUfgHIpS262WYNyXYrde0iEy2dZsQgfE5X2ErdzczRVItXOKBdhd/4j1OMEvxt6y9AC4BseseZT6GAP6dO2AUBtnPPnID6VLH6H8T9MeRxYAdW6nFIDWKAANvU/ZjmnT32i3nbevPaRckI2RJMzWuonWAk6OjQGd0XMN6GTY6yTIAcDpqB06qd3HRcASTift9fL+9FpZX2/ohbAlCv0+pH8DzmXrJb0/RfR3zWU7zp1/fU3OvuFQvP6Bz22h8Ltp2xoWml/Ywu9Gf1bur0W5+Z/BsHpoOyXbeFeO1drusMV5LxGG54T4cqCs11Ccfm411sidh9tPYpukI+RzBsaN8HreXMnV6y57V32B5xBPTZ/tDkxAuQ2tI8pjaYa916p5AlZXF3O8Kxy92D65AhnjY+dj9CnRnx3qZtjTPXRBj6dvLtcY2PvFhua9IXPzXALeT69cHtDluCv8ro8FsjygwU3ol+PA1p7vfe6m9Pr1WVQ6LC8lzjpagi9nbu76OM+7z/FyZlXDJ7aF5q3k9Uttq+lt7aJ63Wevd+AsHIA5utp+fBsI1Y9r+3cSkFt8tPHmCRYfbe1q/Q9SfBTj5XTa89hwFRxFFx9txhj9fDb0Ntfen9qXxRxnVr+79v90ej8tauEB3XgaXB5Qs43zPmVT+uQq6EB7Ldm8lzW9maH1pPYBtp8R53OyevGuIPLYS5+HMLYtNK9nbNC76KvkFjyHYutwzJM8l0VOe6T9cNd35fF09vD3YYitDguOYouPFo/PYtju7YwuPtLG7hfvsgvrOnJyNzd9jNfruvW5ff3Vacg6XF+/Jpc30Wpv09ddfBQuaNI/8HnMkkdp6eezYW3rIP9zo6XN5gEF4r2Z61z7MdvPRm+f56rlBdXHLLLtx6ortJdm6RzP1oq9oXL7czybHHs5OZwh+6ltoXk9Y6U9fqltNdchnTda1cvZKXAGi5gvXE0LjnSIpPmOr9RyHFaI9L4GVjrSN61PKj7SvjhWcHXB365/5HyMPt5iJUb/3IIjm71tX174PWg/ALCrzDYbxJoAuhmv9bfMX7MAyQqWDgAF4A7X69DnAtClHWgDoYt0SGgRnu9BOTfQ2rAJ+IEzuyDpIMDps1kTOBPXcegCok6Bc4ivdp5PaI4g7c2GA4wcToLQk4904jEXk+A53cAf7LZYMKipBMBuvKMzC7ngNeq1FRIJBBUFltNrA+QAXvW7BU69+Z8+YPVJGkAN7+e0bh6AbvraAFR/HbK/np8B52Z76D1nW6ZFuSBqs+G6KbWGUqmbZYwdiZzNtV9B72Zuey/AmdhWex3VvJwJwAl4oNO7Bs9crXTQ/wfXUhP4pPlTmeAnIfyueUuzw+8rfc3HTFD1n4gT/k5Ad5ojK/xuzBGETQMqbYC5OW3dnqak8HsAVsM29Q98HsMJvzPgFIA7/K7N6/R+2iQJoIA7tB7jzYwF0GXccn2Acl7Q9boFQDIUnjdt+ADzKJ6SnHXWhE3OfJfg4cxoq7VFkncu33yp9hKgM9XL2SV0DrHUT86nJfw+Ndohslr4Hcb7CFui3st5HSyAddisFn5f20/eQdvavDCqv/aNsXlKOW2S+Z+6cgEU4Od2xnhLHYALoD6EAnsQ1cfrNnTlhud7kQQIS4bQAR5shuYt6d3MmPsQwOlbS825PDalgRPwQGcqcB7lP5lDHWwyjxNXmCFzLGF2AyJdHtKVwiy21NpseDWdEGk/7vOcbgALdlvnFn43Adgafje9ifprp00LOBrhd7H8z80atP6WdQbzP23KBFAA7tB6CoBq9pdx6xxLP2ALkZKheGAPO9JeUcmbUArI1gTMlHklYJMz3wDOQ+dxem1KA2dwHfFjhvpVU88nAEbI3Qi/AzBD7smP3pxtOcPvS7/QvccDfyfzpzliw+++OVqH373rC8Bq2KYFHEvkf5rnmAugFo/rThEAOq3Bk9sZE6532N/MYa4RkPOC6jY216OwVzRHJW9uKYCpqzZscubMac+A3bMGzhLzVQyrAx7oHF7Oi1R7z+cMhwp7oERSyHymBAMiNzzBtTVTSuvw+wYYT8vqL/xurm9tz3v2u4Lawl/l/M/dOaYAqOn9tCgLQLW+0VsxAXFeUCAdQnUbuh1dkiAakjSomsqFy0WxN9qjwCZnDbUhz9d+dOD02KwKnN51pM3lXWMLFf7TcnS132pp8WpC+6y0NzTTTlb4faYK3XNaJfzusdVV+F2/Yg54jQFHdvg9MFdP+Z+2NZTYA9RaPBRTXBQDoMv4ZRwgC6GmF1VvXxQMn2eG50OSgkMJ5XhyJAqEYtZxScCZup7QR9IJ4HYfVg+M6w46h1hqGHZf7oEzkAiE36dGOF57IHK2tSEiW7/Qfc1pVzd/OmB6VGPhUSz8Pq9h8zYEYPrr0Pq4YOkcYwFHV/7nBrQi2hj5nxvVAFB9DQlbMQXzRW3nGBOKh3bdbO024IzxWuZ6RV1ztJJUmFDSqwnw11USOANjDwOcOetJ8UjW3AQ+ZLNmWL134FQMXrhwNfZ86vepiQQU9kC5ud95wtzrPqAEZIfflzELHRYOv1th0Ojv7GN5fbTwe9imBRxt+Z8wxwXWaV7n3fgtbHn/E9IhgG6vuwdAge1YoFwoflEIFHO9orY5pBU6pxRx4dLUkWCTMf6SgdM73xGAM7iW+DG+NXrPbahLNYPPK1K4tnk1oXGEBpQ0kwnr0Zsx4XdwIdJ+3Bl+37XZbY3we5zNHTj2lP9pUwqAwmJXB1Agby9QdpHQaa7FBiAAofqxzbUKtOd6RUso9aaXCpi6asMmp88Azu7mO+ewetfQ6XJSDAFotcn8/H25IoVrhHM493uCYgeRyeF3m1dTIvx+Mh0Mv/vW2334PQSpgXYXWNrH+KDSsGf2BbNNugDJoiCAwmIXRnvOXqA2KPSG1iEXitePrQYLg2iqcgG2JmBu5q0Im0C5/E1gAGcnXs7DAKfAr9xQHXWyyTyA1cM5w+DaEStgbO5hseH3RFsANBqz98sNvwdh0NN/08fyunj43WfPOV8g/O61aQHHwvmf2QC6nKcLwhgACmDvuZTajH55DbjfS3lB9T76NdAlHZ5PlQQ8clRjuyVJIC3p3QQGcHYCnEBl6Dwz4Bw5n34132rJF34HnSAyO/y+uEmzIdJ4RrxtrNfu1tY5hd9deZv2dl743WrTBmil8j8LAag1z9QDoNNcmZvRA3ZYBepBqN5H76dL0ivqUuktlnS12G5JEjaBAZydznd44ATODjqHeOpnqyUGRHLC71Mj57W2bZNGNxuvoWe8N/y+QKXGvk5vJHO94uF3vY8JmMua9beO8+XmbSZ5USP7Fcn/tEkaQDV7OQDqbA/BquWcioTigfCTiKS9oi71tMWSrhjATBknBZsMW1ngcAnA6ZtzAKddnnV2l/9Z8f+3R1RzzyeRmu5jhlczNfyuh9zX1wA2KMW0taXG0xiXVzQp/K7NoQOgFQYNAAx7Fx3A67ApGn4357O2R4bfueBo2rB4G7PyPy0qBqAAYFyjqL1APQC66bv0Wexx3sd6QQFGrqbWXsIr2lpSN8ijwSZwPOBsMWcv0JkKnIGxrnWeDXAOsdUcPhfFht93/Tb3WdNDOpOQRPh9HuYKv+/ktKuNSQm/W2Czq/C7Zz5r/qfelw2jFnBslP+5kSSAQjtuA1C9PWEz+qUv4IHGEhAK1AVRSYWgVmLe0h5QiScbYQCnyJy9AGdwLWnjLsLLadHI+fSrk4Kj+PA75pC5Hn6fGhEEKk74nTve743U6fBkeoXFXf/I+Rh9egi/hwBZEc0eYBdkOmy6wNEFoBabrLbYAiSbWgLoZrwBoIAshIZC8WujB0QB+fC8pGp7LyVsCMEmkAmcObAZaB/AecHA2T+LDhnqKOfTHn4HtuzhC5nrEJkbft94NUuF3zemT3PoAGiDQVO9h99DwJtqk5v/uWoHevp89rZkAF37Je4BCkzHXAAKi30dQAHeXqBAfP6m730IaPUx64SW6yPpFY2RNLS28IIK7//Z1LsZaB/AecHAGZizqRSs9+qhk5o/XtOUGX4HMOWAAgC5PaHJ4ffZrkj43XvCLruwrsMHgys8auMPE353Au/JI+izXzX/UxpAY/YA1c/LBqCbc8vcC3TpCxQPxW9srgeMO4i0VzRGrcJ5OfPWhk1gACd3zp6AM7ietHE9eTmD+ahD3agRfE43h52HMxIiRcLvy3Ikwu8w3ptQqc9nGx8Dg4z+1cPvXHB0rMGa/2msyw21FqjMzf/UVAxAl+ugezsdAAqgzGb087xrf6AYhOo2N3Z1SXpFTbUqQpKC2pgq/TOBTeBCgBNwg1Xo+py7l/OIwNnoT81R1N/jNUuF3415NijlsWUNv5uLSfCcWuFuXu8u/L6zBesXOwx3GiD71pAIxLZ1eMPrHFg11+WDWhuUCeV/WiUNoDjZsAEogOzN6K3txhz6mNO5ZITiLfZ0u+uQEiDqs9erUreBqgmbnPkGcPLsJgLgJQPnNNbfPtS32jxeU39NrnuKcPhd85a6H8PJhMiVmuZjM0EVC7/PczjhURvvBUzLXKXC71Zw1OdzrCH66UecNtsG9N5Qvb1t5/20qTGAbq/hHkB37YD+i7J9X8oLusiAUfNGJB6e70WVN50Xg03OnK2As0UY/8KBc7JbFzqPApwEhFngwtW02t3p4cwIv0+Ndojcv56pwIBISrI1m9Dhb3kfYetcwu++dSeF3312uFBprtkWqne1uQDUdk5wzWecHxNAge2aAMjtBQrDhu29NIQu0m9Opb2iuYoFWYm5E7y07C1ojgCbQH/AmWP3KMAJBABwAOdQvprv88kJv+/aoPGE9mYDsQZEeh+96Qq/r82GV9MJkfbjPs+pFe4Ip/C7Mb7H8LsJ3Lt1mHOYtgLtrfM/owHU5c7fzMEHUNu5bc5J72sDUL3dBaDGfNb3EqH4dbAHRAF5r2iuSj0RKTMNoDpscvoM4NTGJdrM8rgmju0IOKex/vbuJfwn6NzU0VZLLueFwjVORUUAGCF3wy4AM+SeHH6fbTnD70u/0BfPCafGOuY5eg6/c72c4uF3b5sFKlPyP4UA1PudaAygAFDNC7oo6LXUXud6RTkqVYiUCZeLojfVloRNTr8BnNq4RJtnUqkeHOud02/XbfPopHp5agOfBFxhgsrU8DvU9OjN7sLvM4EcPvxuAOsGXpfT1N96gFB/7coFtbe7w+9ccFRQyfmfxQB07aeBoQ1AsXwWDgAFsFTC5+wFOtmtBKH6sUUhr2WuV5Sjhjev7Ke11AZNRp+ie4OmQmFo3hKwGbJ74SH1aay/3W23b+BM+jt0QeL+2So0+enDudLcQmS8XtqIjDbdmPZm04/U6Ttqjt+4orTXhq31PZ1y8EDQyMlYjOO4MvtotrZ2tf7reWz7bG1hL6/N/etdf8uanXOSpd21DtsYbzvt7bvOxbGWXduVrY38dkLtS1jWMc65Fr39ynJMt2OuQV/XlXZelvGK6GTXnHNzPciYnwx7lDdeP2Zr47RfGT+GljXE/pSQ2LzmOXvOH8D+Grrm4fRj9Amek2/NIfsRc2fNG2OXtJ9dm9vu8nu6+X1lr+f0453Tt1aj2fu5Rfyeeef0nEcUeDKvz5BdRHSDiH6ZiH5qfv8wIvolIrqdiH6UiD5oPv4VRPRbRPSS+eevaDaeTESvnX+enLOeZtXuRIsDRuGawAu/ax5RAAWq39XccVmo3UPpy+HEbGaTJ6qNtV6MoDfytI6dx2+db512I2kP6m7OhaFdts116Ou0jQm080Luetu0yJ3XcfEWxng4Q+3CHlAAzjD8+rU0PaMphUjLvEB5T6g+ZpF5IxH2jHJVCkCDynUBcNfN6ce0VWwbJEb7karTAQtkMseWCKVPdtOuX2/eza5BU8F9z2+nrwXwagAfNr//DgDfpZT6ESL6VwD+MoDvndt+VCn1NfpgIvoIAE8F8BhMZ/ciInqmUurtKYtp6vnUv1deD+fmNRzHT55E0ryd03GXh9LzenlveE5jbZm/IDvvpzGf0xuZMp/ttW7TeB3jEd3MCV5flxfV63El7Y+ez47ZtlkLOecJeSprekDX8zQ8iWs/i62N/WVt+m+1ZbzXM1naE6qP4XraYtt9XsLQj7Qk5rR5Bn3n7xqT0genzzDVQ5b7eYrNHWOXjJ8Yu4neTa9HMHgN3WtNvX5Bb7Z3Ts+5hOT9zDw2XZ/VEIjoVgB/HMD3ze8JwOcC+PG5yw8C+JMBM18A4LlKqbfNwPlcAI9PXVPzTeaJgCs15X/qxwHsvJi23FA9/3PqiJWGiDQnCR3w2e8bD+dpDt0zuPES6kvR7Ng8iTsPaoRHdOO5W+bU39J+vpAX1baG7ZzbYhzrWOs4bLyDmzZXARJpuaK29Zi2zPZED+jmPDVP4jZnc+67/GE2zmld2zyetSE9tvYAFPOEbmysB4w7hnR7jGr/d9wFj9I2mPOwvL8tPZuh+T1jg3Z9zT67Wd7WxLGeppzrdzjvZsew6SwwldctRPRC7f3TlFJPM/p8N4CvB3Dv+f39ALxDKfWB+f0dAB6k9f/TRPQ5AP4ngL+tlHrT3P4mrY85JkpNq9110NTD73qFu2+Muf3SGn7XgFIH1WmMfr9kPPtdJ5xlIg5EzsNc4Xdn6H7XdhrjDb/b+muKDqdry1rOJQiL8/XdtePUzwbCrjXs22Uq4Dfn4QJQxzUrCqDrta0bhl/twui3zA+IQahuY1FxGI2VVKGABFim2JEETWDApmm3s6r0ya6nQypsBubNCnsnX6OA3VJbovWtu5RSj3E1EtETAPymUupFRPRYhr3/B8AzlFK/S0R/DZNX9HNFVqopCz6J6J8C+BMAfg/A6wB8pVLqHeGRCt58TO34FhyVFU55Wy6dnv2+cOXEmL4tl/TX9me/b4FpC5FO2HTJAXpbaDsd2MGgrb+2Di9ghtbsvC4ne16Y1KQDl3cNlnZWBbx1nAX+ljZOBbx5XiUAdDOHBnkzgE595avhF7vrfNiOByAHoZqN0/kXhtFYSUFjjblqgyZnzkawGbSdCn4IAGeW5y5tvTk5t6nXqAlsAv7PrWfYFPo/rIA+C8AXE9EXAfhgTDmf/xzAfYjobrP381YAdwKAUuqt2tjvA/BP5td3Anis1nYrgOelLio3yPRcAJ+klPoUTO7Zb4wZbOZ5LtXv+vHlvf316T2RWr+jev7n0u/0RvtGbI5rtnViIiTZOi3m1E8ZthTXlrV/+DWnvwr0V8a5KMfr1QZzfdZ5XTaNY8EKeOc4T9vV6f2pjXbj9vMafcz2iBxQ+7nPb7ScLPFqeGO+ojmhug1mtfpOi02bbVt7yo+EJOZJGM+uqOfkn3LmDLSLVsLH2Cbjx7du026NqvSI9UZdw9160q+R91xCSr5G/jXhik4/Q0Eppb5RKXWrUuqhAJ4E4L8opb4MwM8C+JK525MB/CQAENEDteFfjKlICQCeDeBxRHRfIrovgMfNx5KU5flUSj1He/t8nE4kqE3I3Qy/QzuO0wbzKU8/sobfKfHpR7P7igir53QTVsf0/hQD1RbDzf9c3XaG9+40PWKefmQec9vcv+Z4RK1hY/2t3u7xnAZteuzEtE3nR/BWwG/WYPS12nbYW95HPAmpSRh+OSec7BTzhOrHFgWq1bM9oymSAtDCc1T1aDL7denZDNhuEkoHvGu+mFA64P/sApCZtebL1t8F8CNE9A8B/DKA75+P/00i+mIAHwDwNgBfAQBKqbcR0bcBeMHc71uVUm9LnVwy5/MvAfhRVyMRPQXAUwDgHvefKv0nuAQjlG6/n7iefkQAQJxQ/Akiz/XpRzbXf1Q43dF/N6fZjvlvkdmuneMGhAPQvAdUSwGSDdqdcGoHRut8rQB0M48Gd9Jh+Pn4Ot9iBwUgVD+2nnAejG7ms9nPUSrICq0hafuno4CmhP1E8Dsn2AyODSwpGd6Cn51vbMC2BziPApvB+3wDKaWehzlUrpR6PYDbLH2+EY4otlLq6QCeLrGWIHwS0U8DeICl6ZuVUj859/lmTJT8Qy47c/XV0wDgQz/+AcoHhEv1e+rTj2xFRId7+pEBATwg5fc3IXXHzDvvmwNqHfZK5H/ubToA1LDrbtsDY+gZ8FuPoruPBICa80zHC1TDY9t/taN9XmIQqo9ZFAuj2jzrkJB3NFUFPaBJYGmqImgCx4VNIACcWV67NPA7XFU6kHmdPG053s2DwOjQVkH4VEp9vq+diL4CwBMAfJ5SvL/4y/d3C5fbUPou/O7wYjrhFBrnaG+c4XcC9C2XvOF3zZZamx3bL5mL4YbftT5uGDxRHQseIyA1qr8DFleHnGN8CBp3MGo5FlMBb/XWWryaIQC1nXsJAN3Ns65dNgwPVIRQfcx6kgEYtfVJ8I6mKgVkq4GlKUHQBC4TNoEQ7OSAn6fDwULpQduheXO8m0cATqH//56rcqvdH49p76g/opR6b8xYZ86nFkpP3X4JwD787oHLnedU85bWfPrRLjzttAvrOljwqIkVTl/XHIZaG4yu3W0w6ZvXZ3MHdicA3cNpYE4T/Ja2VgAK7ECrdBgeqAehmzHrAQZsZobqcyQJsqsk9hOtDZpAW9gM2G8Cm0AA/NJgMzg2CLn+drfdjOsE+NdV0Lt5lFD80Em5OZ/fA+AeAJ47bZiP5yulvoo7WM/5BAJAqB1HSvh9A6daERMAKKOICLDCyvp66Uf27ZeC412wqcsSfnfD4OkACx61dYTC5d41B8Bxbdcvm+2cI2DU7dVkbMHkayNtY/mWAIqt/UVFw/DzcaA8hOpjdIlvryS9WXwszNaEy4QxIqDJmK8ZbIbGtoBN4LJC6UC6d/PosKk89/YhAPnV7h+XOlYPq7vC73r+J1D26Uc6NFqffkSARpleW8GnH3lA1Rd+58Jgbn8nrJmn4wDWqHZNQS+lYZPn1dyPj4LTygAK7O07r9F6Pplh+OU4UB5CASvIdbfXpylpmJXwptYGTcach4TNwNgmsBmc1z/Ubzf0GfrGBmwXDKVn/YdhqDu1fcIRphujM/y+vIY9/L7Nyyz89KN1HoXVTarRjOk55UFk5NOPln+s8HiaQwcUpZlYlm8CqLOPo/8OWE0btna1fA6Wdu11KOSu2zRBcrqWytoWgtOpzQGLFQF0a8sAOBjtm/PR4C8yDA/o9gpDKCBTQJSSNyohDtRWBEtTNUGTNd+ZweZk29NhwKaY7azPsAcJ///33NQMPnWg22+5tAdNc4zpGLI9/UjP/9yPl3360QYuZ7rYeus0SjPGe8Pv6wka/Ve7uvnTASvEmevWFOVBdcCmE3qX9uXyBGDVBb47YLQCa0IF/GY9jQHUct6lw/A7e7C0S0HoegLGl7DHvT5tagiWpmqDJmtOL2wEQOXMYDM4Nhe+fCoVSs/dczMHsHPzUYe6UhP41ALhu/B7zPZLoTE6tC7h99Ttl6zhd+OG6wvlbwBrGeMCVZjw4bEVAswQPGrH3VAbgE3Thq9dvwQmTDrW6wuZ2/tbANQx3g6nDQHUOG9gP4cukTA8UA9CYYxbT6QwjEoqBLYCcxfb3xOoA5qMeXJgEwjARqm8zUuDTaDbUHrPsEnQ/oYOWdXM87nxcGK6IVq3XDLD79COI+/pRzo0YoXLM3n6USI8+tbghE39cqS0m7+kjvXaPJY2r6sNQH3j7XDaCECB+mF47G2XgtBF1WFUUplwWXUbJsm80EuETeBwRUJB273CJlAWooe6UtOcT2ALdPstl7ALpev5n9N4uyPicE8/0kF1Q8nmBTPsBtYRFX73Qu3+ddCr6mpf2McBvIt8YXy7x88BoLC1ceC2AYAC9cPw0K9BWQg9rbcujErLBbfN9vcE6oImY76Lg83gvP6hfrttYDPXdvFQes/AWfI/wGegpp5PQPN2KuAaFLX9UomnH+n5n1NHOEATsIbfKfHpRzZANN8vthxguIW00wEfPK5dNSWH8G3n4WrHCUB9sGoPi+/b3F5Nmr3B/vHRsOgDUMAPmDEAapzb8jUQDcNj2396XwhC14Wa6y4Lo9LKgsyK2zCJgSZjzqKwGRo/YNMY72krmLcZHF8YNnsOxQ9t1Sjn8yRXWL3V0490aLQ+/Uh/DUDDqL2ttZmx/dI8Jyv8HoDZKHjk9DcAMQSbyzk54W5p19/S3qbfK2lfJ9+rqb0315sLoPCMYQAolutbKQy/Hl/6Q79uwhC6qDaMlpIJua3290Rd0AT6hc3JtqfDyNsUtd0ylN4zbO7SyYY26sLzaXo7u376kcVzisl9mgeRsxlX+H03FuRogwZVJ7pywiO0/poNL2D65uSAo35svsa7dpz6mWvxelUttpwV8Fw4rQygu+ubGIa3fRa2MPxyHKgAoesCC8OobY4SioXNmsVIgqAJDNi0j/W3e3WBsBkcf2DYHIpTG/jUvkAmHNrC7/tQvAsIAVgg0r9lU92nH23C3h5bVhBzXccTY24AbOpzgtwQPJpiwaR1ztMxG8SaoOi0aVuLFS49ALpen7QtmJoAKCx2EsLw23bdrhGGB+pBKIx+62KFYdQ2Rym5tpNKMZVjgzNUCjQZtnLCr5cGm0HbGbCZa7sobFaYv4kUrPfUoZO68XwurwH/9ku2px/FbL+0wKlr+6WlnytnM/fpR1tvp05IOIGTA1S9ntMQwDLgcQVFTp8I2PR6KvXTdpxHisfS3ieyAr4VgBrrwnLNSoXhgWoQuqg0jG7WXloRNz+RgiSuiV5Ak7OWHNgEzi9vsyRsBuwP2ByqoebV7s4Kd0w3WNbTj6CPj3/60XqL0oBy70XVHRx1nn7ECt3jNN8G7E7TwxV+TwHWTR8GbG7W4WvX3zIh05zbG762AGhofCsABTznAYiH4af56kDouh5pGNXXtLw94k0qdckVQRMYsGm3O2Azdu4q8zfS7m/a0EbtPJ8euLzopx/pN3cy9gl1iQWPp3VYQVDrbx5zQm2EjX0Y3NIOBPM/vSDrm9cGoL7xDQF0ty7bNRMMw09tlSB0XUwmjFpshLyjzSVxk4zxsgqBJjBg0263IJRdckW6xH9+hrpX+yccOcLvev4n4INDe/jdlf+5jNGh1RZ+b/b0I6t3SgPV5b1py4SUpf8GHk8HdiCo9bfdtEMeUacNch8LjTHP2zu3CXOGXa43tQsABbZ9jLVi+SilwvDQxxaGUBj91kVFwijDhgjs1VSGp7YqaHJsnSNsAt7zPixsAt0DZ+78TdTbf347U9ucTw0ufWH1xUPaavultR85tl8y5jlRz/LPRA2b8Lvu1dxRoLYYbvg9ALMheOT0d0OtxYaj3QeBmLhsmsO1RtjthOyafaZrr/zjzXPPBFAgMMYBqadxjs8nd1P65Tyh2y8DoetlzYRRwAKkIRhtKYlipJjKeknQ5NgbsGkZ62kbsFl0/qH+1T7nU4PLw26/pHlLu9h+yQS/2Y6az2mhSGUOs/XnQioHNk27rjFL9wDg+gB0N84CeL4tmMzLmg2gu3N3A+hp3hPAua7j2pcThp9t6ZKC0LWPflPQ5zXmtt1cNkDKCLMHgfQgOZ9RUGmTZJiSc80KgmZwfC70+NQoZ/PooNd8/lp7+kZq9x/soY26qHZf3rvyPy9q+6Ud/ZxsbWDQJSec6ms6kckWxvb9zWMhSA3BJnuM/tYANOv6YgF0XYffA8p/7wZQAN7HcYauD9sLaobhPbZMOSFUu06LNvuEAvHe0NWuHYR1SQBpSCULA2qA5W5OzhCu3ZagGZj/Er2azUGv9PycNXQKm0Nx6uIJR9DgErjw7Zes0Dq/MEEVJljoZLUO0cBWB7LTgS2Mbfub4e79nPtxYZjyjNHbl8/HAn07OzYghGVcbQBd5gg8D951fZaPtYYXdLlei8RD8pqN6TgDJgWANKQmNzOJMDzXhIA3c5qvHWhO4/3tftsZUBSad3g1y80ffLBBoL2VFKL/Dl2a+vF8wp6z6dp+aZfzSXHbL3nhFNo9UgNKZ/6nOV57DSisblKNtFj5n+ZiHKBqBdDdWFd/ex8d1lZW1Y47IdUCgFFjODa5AArHuNIACmD2kbvD8A4A3Ywx1w9PX/Oz5XpBAecfSac3NBJCN33Mm4U5dQKQ7qIBJcPtnBtK5vzJkCUEmdMaGB3PMXwO+Nc2NnMvNz+raI7RZ+gQap/zqXs7Nbg04XS3/ZINTsme/zmNt983XNsvETBBIcNzukCkO/8TaRC5kt98zAaqjLFKO7TYmcDrRGDKHOa1j/15WcaFYNI116Z9YadCALodnw+gp8t/gsQYAHVd62JeUGzt2eSE0HU+AzI9Ifm1z/rGNqHxPgCkQe+opFqBZcr8jK7svVCHVzPOLsO2f10HB03OGjK9mtm/S4VV7G/Qmagfz6cJlNrrpZ8r/xOwAOFyv6W07Zdsz3B35X9OHeEATcC6/RJVevxmEB5PNKL3cUGNbmMHjhyYtLTrc1nbl2UkAKi3zTJfFoCa1ykFQAHU9IKu4xZ78/w26X/sU72heh9dNYC0a+VALXOohDeTZadX0AT8azuqV7Pw3DwbgfEC4XOJ8xjqR33kfELzdqp9/ufSz5X/adt+Sc//NMdztl/S8z/XRa9wqt3nyLH9kv4agIZQXlsbmN2473QTdlDdeT+NsaYn8gRepwNWb6GxZl022AvCZABsre3LWxPYdFmAcA+XZQAUznn4AHqycfpSlPaCLnOsl1C3Odu1yekNDUHoIqPIpxiQAs5zqKbcm2LkcCnIZNkqCZqA99rlAlEpr2Zxr2JL0OXMLxA+PwvQbPxnp3d1+YQjM2cT2G+/FPX4TcIuLB/z+M01/K4B5d6LiqDnFJP7dAeRzvzPeW67d9V+3Aqgu7Gu/uuS9uxrgprZPxYmOfNyAHRZGyy2uABqrpEJoMt0u3NKBNDtOrZQuXyc0V5Qs6/NC6pdw1RvKDskv8h2gwoA6e5Z7RwgBfq9UWUuSypkHmWrJGxeoFfz6KAJMGBT4jsjkQYw1JXawKfmsnJVuF/s4zd1CJltmTmc0I6XyP8MrdkJjhyYdLSzxyxLd63TsSav99KcjwOgzjEZAKrZPH10WwiN9oK6+uoQuvRZPgukQ+h2jGkzAJMBIA16R/U5c2Q/xTjVAktdUt5MgAcdudd6eDXZ8xafm7uGAZosETaYM2RRF084CuV/Lm1n+/hNsud/2mwFYdClADxuzsGAVCewMmAypp07RgfQzdpcAGquWQJAzTlSARSw7gW6/5xOY5ePKtsLCrAh9GRHO5AYkj/1Y8CkBJDGqvDNLQksdUlCJtAcNIP2M0Az17Z/bCYktYbNwqDJW0PYiIR3dqg/ta92hzvEvsDp0na2j9/UbOkwG3z8pnZ8A2kwYWQ/1oS6E8SdwNfqOdxdDMsxDSatcOhrZ4wpAqBm/wCAAg47EQC6s9HKCwpsb+A1QvKG7dOYMkBaWqRUNai0qRtvJlAcinr0ag7QHKA5FKeGns9rAFfBEPtFPH5TI6NN/iccEAkYYGY/zhsLO4DOB3bgBkt/nGzZQFAHMS5shsZsANTobwNQ/bUVDGHY9gEoPHa4AApg5wVVaOIFXS+VCaKxIfn5nEyZNxTzO7MfYI5PANKCTy2yKXcD9mz7uphdjw6aQfs5wFfwvLoHTY4NznenRhpArzCqlPM/5UOTuqh2D4XYQ/mfocdvhvI/YYHIqo/fdAGizau5IbJ53Hw8K//T2j+85k1/GMccoBaCzd0Ys90EUAfsrbLMmQqg02VUCcB5en/6KE5guLsetbygyznDApWxIXls53LJdsMQB9KDPIIv21vKGC56g+41fB6w361XcxQEya5j6DBqvM/nNa7VFT/E7oDT3PzP0JgFTos9ftOASP3JSUGPpfHaBoM7caBPI7Id83o9bbxjIdi0QWFpAN1cG1ufdR2JWzFBt+EB0KWP6QW1XqfTeAQ/G0tfbPsvn82mvUBI3lQpIN3b5K1HQjXAcj9n3pSnucOGSno1uwW+XEBq7dU8J9DsHEaD9+ELV/ucT5oAFPCH2Flwqo2Pyv/Efvulqo/fXH6LNMPO7Zc2JGaamOFYAzbABJD9WLe380ROueDohcnAmF27BUC9fbTPygegZpsfpCMA1DzfXR8HQC7Xe/GCGud46nsCvVgv6Hp86b9ce2xvALHe0B2EznPGyLwB7f6YM4B0b7OTO1bmMmp6M1nzZYBmrv1WXs0BmnKQKOLh7eRXe4inLvb51PM/AR5cSuZ/Ath6LvV1GnCKeR4CsOZ/wg2Xru2XOPmfkwH4IdLok5r/aULfCcROB1jgaIXYk10rKMLdzvJYzp8d2dZiAij2bVwABcxxzL1APWs3AXS3vuV6F/KCLvMt2oxZPhcY5wK4IVSba2NzmVNXJoxubK8HokzGibPcnqDSFBO8ewbN4PhOvZqtQZO3hgGaoor783ZxapTzefpUdmF1td9+ifsoTk7+59QPG49k+8dv2l4zHr+5IaZ53Hw8Nv/TtoYQTDrBEad+NpjbHUO43etZXPosl8EHoEEIdAAoXOOE9wIF7AC5nGMJL+jcf7nOa/sybrm4WvvaxwzJe8bsQdFyBykBpFLqGSxNSXgzAd45twqfA8WAryio5YImx8algeYRYHRoo472+dyG310hdhacauN9Wylx8z+LP36TAGv+p8VWDMxu4MMlF/TNa1DzOhfSZIOjZj8Ek0HY1Nfigrilz/I2B0Ad87vHCW7FBGw+9JJe0PX40h8IQ+hyLWx9IgqUFtUC0rOVlDcTyAZN1jy9Ap93bLlzBhiwOUAz2k4PKvaf4DNR+5zPDWjat1/yweU+rA6Yj9/c5XySctvCPv/THBP9+E1KzP+cKaFK/qe1/XTcmv8ZAkdNXpgMtdcGUG2u5dQ3XtAQgHLW6nh/mu8Eg6W8oMt1X/tjO0Zv3/Y5naPVRiAkr6sWkB5WkTmqojfvluFzwHvurSD36KDJsxE00RVoXtR/Ns9I3e3zGcr/BPbbL5lwunv8pg1OiZ//mf34Td0uACxwO9ObM/8T2ECfGxLtfaLGmtA0v94C5ukAGxy1uZ3HzDFcOz67i5lMAN2dXwBAp0uqooDTf86nL2MpL+hie9EGXIEdiIYgdO3jC8nrulQgzSh+Yt9wOf0CkMmarzA0HdGrOUAzwoaknR6kcPqbN2RVm5xP7Qvk3VZJ8R6/aYNTV/7nNL87l7PE4zeT8z+BlfyK538G1sYGR7PdM8YLgoExXmAUAFDzM+AC6HSt4rdisp3z8tF4vaDL+nK8oDjZmdavjcN2rN6+W4fPhgk4+h/mkkDKkTS0ZlbUJ91guWMkQDMwX1HQLDh3S68m75qXu25VbVS2M9Snmnk+b5CCbZ/PUP4nsN9+yQun2OZ/2rZf0vM/zfESj99Mzv8M2IqB2Q1w2GTAq86zk4EF8DTSi4FE19rMuRiAKgKgm3Pf29MvsxM0bcfXa5W4F6jlmp+On74AVmD1eEFNGzuAxHbMMse2XRsU6Q3dXXMbBIWAVLOr29bl/Y67VHH7pSzPTcxYKchkzNsU+HztLYuCCl4z3vhAey0b1e10RKPC/6c9N7XP+SQXaKblfy5trvzPpZ8TVAnWELsv/xPzPBPkBPI/gZ3n1Jn/adl+qVj+5yIXsG4g8DSPCY6bvvoxzf5uDMOObUzIm+kFUO06wGwLAa5jHculOR3L2AvU9VkkekFdNpbjqx1sbent2z5MG9p5mYoGUtOuZn992dG9J0o5667gzWTbOcOtjgZoMm1Ut3PUX/YhoIN9Pm8qcoImwHzakWfMLv8TOlzuQdMcw8n/3I/xvAZ2EOnO/4Qd+ozjW2Cx9ymS/znbMz2GTrDUZINGrx3bGAvEOSEVWwDdXR/Y7bEBFK6+/q2Y9EvfxAsKsAHS3sduw2rH8h0wVQJImyv3HsmAy0VS3kyWrdJV4F5QLQi5JcPnAzQT7TA6dcaiSVGYC1Ij+Jw+FR1AARtcusLybjhd2iQfvxnK/1zaOPmf0yAXIJqvZ/rQb97UUf6nNo9uwwuWmq2Q58/b7gJQ2/wWALXBrXNtHAD1jo3cislyLXK8oIAGodbPQ/urHRmSP825taH3scLs2td4WxJIe1QEWJqqCwgNQTMw/1G9mhKfXy+gKfVdnGwdDzSH4tW02n0Jt7vyP81+Evmfi4c06vGbDi8m9/Gbyxvn9ksEWPM/AWwI0rAlmf+5A1ANXjegNi/JCZNmO2cMx45tjA1AbfPXAFBY1uIB0M01D1wL/SPRr+Xp+BZCrcC6hOItNlY72Npa1rht166TAaJR3tD1APYqBaS1VRosTVUCTZYdH/BlAFtwfAiSfLBZEDR543PnD7TXssG2w/ySS62pto62+0ZlNXrC0aQrugbUlRM0F1Bkh+U9cJrz+E0zxK6L9fhNAyhjn5yEyX2qkdNEDpL5n84Pyuop081r83DB0gObTjtGuwiAwtIHlrkDAAp41uICUMcaebDp+lwIUV5QbO2sYxZbgB8guTYcdnb21gP7PmJA2oGybpTMsew5KmzX44fFcsB25PD5RYKm9Hd7qGs1fcKR6ZGMzf8ELM9594xJffymLcSut8XkfwL77Zdc+Z/TIDhe60QC2GHE3kcq/3Nnb+FjBwzuAM91fkw7LrjUbXkB1NUHfhtery4DQKdLpnj2XJ+RE0xP0Bj0gmJrZ7G/2oJmb7Zp72O3EbKzvi0IpBLarcWjGmCZNGelx23mQFs2sDXyahYHTQkb5wyaA0YPKc5TZMtNTmqGzUk3tL/yV8brpd8VqQkwHf22Y9TuNRnjibavT/2w9tOP28acXp/eE6n1d4JIbX5BNr+b+p1tc1yzvVLX/Ho1rE626GRLGX2w6XM6rvTjsxRzbcu/ioy+m2OBMbAcs62FtPe2Y841ufsA8xV19THWbbPJnsdy/dc/0GYf3xyM4ycb5O97ZdysCdY5dja1L++uj2FjN79px/zBfpz5s7Xj+BGWay3B9XHWylh31JyMa+uyyVpzjI3Izzhq7qv9T411J30no+YuZCMwPm0dZP2JtSO5pqG9iOjBRPSzRPQqInolEX3tfPxHiegl888biOgl2phvJKLbiehXiOgLtOOPn4/dTkTfkLOudvt8QuHm/M3Rw+8x+Z8gi+dzN8a9rdIyPvfxmzH5n8HHb2p9Nq+B2RLBNByV/7kxxSxAAq1jTY/k9thp7tVGaIwmfcyyxs2xCA+o1XMq4AFd3nrXZ86jfwyGF9RbiITwcVsKw6nvMnk4FA8g6A3d2Z1t63123lDjHHTtvZu2u5KQl7RDeWE1JGa+HGsORp+gnTPM0wyPzZ277HiWDdY6GEaY32Wp72NUv0aKiZgU1gcAfJ1S6sVEdG8ALyKi5yql/tzSgYj+GYB3zq8fAeBJAD4RwEcD+Gki+vi5678E8McA3AHgBUT0TKXUq1IW1Sjnc/pUbmwAUj7/0wWn3vzPuS3m8ZuLDpH/acIoDIixfmABANVtaH29AGrOa4M3WI61BFDfelzvA+t05YHql303r3G9XH1Px7cQ6gyXmyBqACRgg8wtiO5AVZ9Hs6PbMrX5LrpufNovIMtOZdUAy+j5xGClILAN0CwznmFjsiMDmmKQKQm1Fyql1JsBvHl+/W4iejWABwF4FQAQEQH4swA+dx7yRAA/opT6XQC/SkS3A7htbrtdKfX6edyPzH2PA5+AAZcWaDTzP3f9qE3+Z8rjNyXyP7P2/zQBdH6rH98AnT5Wl9O2Zt4FoKExmv0glLYC0NB6tHPTP5rdXBYAnfoqFpxv7CJ8fAOKphcUWn9t4ZviJEsfO2SeIHdZ/74P9jKucWkobaaMTbGjzqUCZLJs5IBmYHy3oFkYMuVsDMgsKoX9vaOcbiGiF2rvn6aUepqtIxE9FMAfBPBL2uHPBvAbSqnXzu8fBOD5Wvsd8zEAeJNx/NNSF930CUeLt/Mm9o/VvEFqs/8nNFB0h+Xj4BTYP37T9ShN2/6foTELnDbf/zNoPwCvep9UcDTHcOys52YZWxNAlzkWedYD7lzW6xDnBXUd9wPrCRC9cGhAKGABUe17srHDqHIn83raxIDS/X+QjnJ3mpTnIRWyX6Pi/YAezXPwZp41ZB7rV72k7lJKPSbUiYg+FMBPAPhbSql3aU1fCuAZpRbnUpuwO23hsFn+J7B7/GbN/M/lTXT+pw6gFls1N6B3AqDe6AJQ005hAF1MxwDocto7L6jZZznuWqM5l2bO6wXVbG76Bq6lq+/p+AlCARtAaufqAlFbH30OaPNoc5nz6YqFUpadRioNltFz1ap4H6DZYPzxIJP9+yEJrJVEmP+GdyIiujsm8PwhpdS/147fDcCfAvBorfudAB6svb91PgbP8Wg19nye4FLP/wT2z3kP5X8u9o6a/7kP45/sJj3/3QOMm9cpAKrDawSA6vN6odG31gwA9XphbQDq6rfI08f73rfW1Z4bQiVC8afjezjcA6R2zgaIJoXldUkWFDGgtLky1sW/WdeBTGCApuhYxvjJRqDTgMwhTXNO5/cDeLVS6juN5s8H8Bql1B3asWcC+GEi+k5MBUcPB/A/MH1CDyeih2GCzicB+POp62pX7b4Jq2/zP1dv5wyNnPzPxcPpDbE74LSH/M/05797AHR+u4NKDxTOU/s9RxYA3djYHDvNpbShLmjczrMfUxVA4bFlrJMDnCa/c8B7DcUb82zsIPK49jmvx4EdiNoBUjtvhbSwvC7JgqID35SSb6gDNIuB5jl4M48KmdLA2kTX4S6V9FkAvhzAy7XtlL5JKfUsTAC5CbkrpV5JRD+GqZDoAwC+Wil1EwCI6GsAPBvADQBPV0q9MnVRTT2fy76eerV7qfxPFpwiLv/TnEcq/1MH0MkYrJDofq2sY7cwpFMYdvC6gTl9rC4NoGyQeDrmBlCnHW2OLgFUuzZw9XGAn29Nm77r+ubvVGo+qPXz3x5fT8ME0ZgnHEWE5U0VhdKGyvLSROavVoFMho0BminjAx0kgK0mZDK/usMrWl5Kqf8GxxVUSn2F4/i3A/h2y/FnAXiWxLqawiewBVCAl/8JcMPyBmh64DQp/5OwC8tL5H/qIfOo/M8NSFYsQIoBUN1OaIwmL0RWBtDl9LcfoqXPunjHOs35APsc63EmhHpg02ob2zFrOwDTG2rvY7HjC8tr/da3OVDKCN13pRpV7xKQybAzQDN2bsYHkzs/w0aXkHlmgNlTzmePag6fi2LyP237fObmfwJbODxk/ufy22uDWRNA1yE68emmIgqQXMCzO3aaywugu3mwG9MMQF19F3n6eN8bH2EIQs1Q/O7aB21ox/V1G+3bPlsQ9XpDFzu2sLzZT1cKlHJu6LVuBLW2U1rnY9gVgExggGb82ECHAZn5tiLsDfWlZpvMX+Ea17CF1dvkfy5trvxPwAS/LRCG8j9jnv9eJP/TBEZgC046cGF5HQmgpymtsOMEUATGaOtrCaDLMpz2dDGBU7+M1s9jd70XO/N3RGBrpnXJJkBq8+/7LCegPH0MOw4IKgalm4Z2d6gsT03E2GqQCZwdaOZDamHQFIC6AZkVpbC/Jwxt1Lba3QBQYJ//CWyBtFX+5wku0/I/dWhd4LR4/qcJoFiO5xcgZQGoZt8JfqExtQF0aVveOmBy5wV1rGu5bBJe0Ok4H0LZkKn/sXf20Q5wtm3SbK1vK0Bpl0pcay+QybJRFPhazdsYNCU+28qQeZaAOZSlhk84UnPo/ASg+nHA/fjN3PzP/Zi6+Z877yi0e6j2Jjv/04RDw/4WePYAqR/fgJxNljncsLmFXSv4cezUAlBz/HLYA5On62L0wcleEEo3n4O/T/JTkjaL2o6L7+MGUTKviU0FobSqMm6gLLBMmC8MI2EjRwTN/LHpoHkkb+bhIXNA6+HUfJ/Pa+3bung1S+d/AvvHb1bN/9TmwGxrgplA/qcOoMYarfmfm7f5BUgmgO48olpIPQh/Hm+rFxjNfjEAuigCQPXTcgKoy+Z6Xdx9bGNs52q+dvVJeUrS2qavNbvPFkRtN6VdiLwGlDZSElQuijgXCW8my86lgWYuBAqAqATM9garUersd9ovZQeAoVWNcj6BG7jGTSwh8svN/9QBdG/Xs3foZNqf/7n8tmpwklOA5PWemh+wCWHWYyfa06cuBqAW+PICaKifthQfTJrXhbu25RJle0FDNhGAzOw+80FmVbo0lHatxBtqNcgEOobFnLH9guaATF43tpd1qEs1DbtDTQAKlMv/nGy7Q+wsOEW5/E8dWqH4+Z+bHE5gBZmuCpB0jjXg7XTMDaC7ddQGUM/7jY3lrWeeVR77y+WrAaFSIffdvN4+nruF5KbyZr9WKgmWm3nqQGbQzgBNWduVbEjaYasEYHYGo7u/V0MbNYLP06dyA9cALaFz+fxPe1jeDZec/E9rP90WISn/UwfQqePpUvmAcZvzuR+7BSYNQJePwoRK3f1nsWfz7okAqGHbNqYbAIXRdzlMp6blUuy8oCZwLscLQqjrKUlr/81C+H2AeFjd9F0POO4cZ/ako2RvDbNavxqMXBpolrweHPu1bDDtsCUNmR3/bg/FqeHjNd3h8qm94/xP6HC5B01zDDf/Uy9Aisr/NAC0WgGScU5eADXt746diLN3AIVrTdpynGuC3sndx3Z+vuOhPi4v6NJ/XZYJkJw+2nmE+qwv2SCZDqWHUcI2UD15vAZoRtiWGF/JRpSkvmtMW6tNftf6GjmfXjXL+Vykh99z8z+Xttb5n0v4vVr+pxV46xcgAR4APU3hAT8LgAJ7OGsJoL6+S9vyNgSgrj7aHMtllPSCTsc1CF3GwwKQnD7Adh2hPrqM6yEJpV0ocX/RaKCWuPnn2higGTV+QCavW9Rv9NH/I3pBapfzCQXQNW4u+ZvIz/+07fOZm/+564e+8z9rFyCJA6i2Pt02G0CNZUsCKBAer3tBTQDVlrj9i+qaA2nHoyF0s7DT2jZjA312c/j66HLdLKShtCMleWojxlSBmqJQdkDQLHw9pWywxIVCQfA9O8Cc8GbIo+aP19TD7z3mfy5tR8n/NMOwpQuQrH1NWfq5YVOjzhQAne2JA6ijzQalVgB12dbWrPfZ2Ew8HoJ7YHuj34GoDx4FYFVXcSitpCSwBJJuqFI3/25BMzg2bVyWXYbt4uMZNljqGTJjzu8IMDq0U9uczxUa6+R/mrZr5H+m7v8plf+5g0f9tQmgWI5HFCCZfTXI2ALh3MEEv3VO/Zh7viYAalsjB1jVdvnOc9DluoYZx52gvMgFogF4dEFmsI9mb33ruYGYn6tTWr9kCCyhxLVEnYMEZDLsdAmagbGHBs1KkMn+rnFsMU2dPWD2lgLUmdrkfGp3k52nsWD+pzssHwentff/3ADobo5A/ucORldC1eBEJxNgBzMmgM5vnX1dAKrbd8GwuSYLRNYEUITGw21zY2t5ywVQ1xoSjzv76PMtfXECBU5Y3mrL18e0Z4oJpmxvaYdKgmPmmB48ogM0ZedmK/ccmHaAApAZcQ26+s/lUJIa7vM5JUTcXKGxff7nyTYTTlEn/3PTZyYqdv6nxf5KI5u3iQVItr4uANWAchlrg8PTscYAivBcQMCG3rYcNsdrc21UCULXfsacwBYiokA00EfXuYTcFyXfGBPGSUBNLqz2CJpB263GMsazVPg/Dxs7vG48eyUAs1cQbfx3qHd1kfO5Qqdg/ufU7/zyP7c5nFtQXWCtagHSOQNo6DjcNuCabxnqGb9TYQgFuPAYB6K5IXdpKG2qEmAZOYeER/TcQLOlN5Sl3iBTGAijvuM9/l4PJatdzufs7bxWV9n5n2Y/1+M3c/M/zX4t8j/X7gS48j9tIfTltUgBkg1Atb47+EMAQPV267EOARThNqcd7SPx2jZluzaZx6PhMQJErZ5Vs58uaSjtXEmQLHVTZ0HNeYFm0bGM8UHV+M+D0Fpi+pUCzC7/k6mJRs6nV033+dQBFEjP/1zC76XzP5c2V/4nAHYoXST/0wOgRQuQrONOfXfe0qXZBaCnaT0A1w+AwmPDbPN6TJe3rvHG9VuvOfz9o47rcxhzWuExFkQttnY2zXMzxYRSq81GSr4xRo6r4s1k2Ugce0TQPABkAkzQFJoLiPjOlwDMzkF0aK+mOZ8nr+V55H8uHlJO/qd+HOBDa/YG9DsYXQlVgxCdVLABiBO4aPB4SQBqW2egzesxXQ4z4HEjKQjVbelr098jHkR9Yfn1reOGEeXZjADT5kpYm7TXKMebebKRMd7TPkAzbf4uIbMEYEbaba7h+fSq6bPdTWjsKf/TtC2e/6nZksj/bFqAtAHX03hr+N+Upd92DuOYAaBLlxQA1cf6AHTt5+vLtWNbn76WBhC6tm1OVFuj/h68ccGwvCnjPygu5YApSxVvbiW9o8UhM2SjQ1iUAL3Usd1ApiRgMu0Vg8sjgejQTk1zPlfonL2dZv4n4AY4oGz+J7APsZfK/3QBqG+ODc9pbxZvp8gTkHwAilMf03upjxffA9Sc0zY9E0DNsYsBv/d1b1c/BWuby7Y5h97Xdb02H7xxPtocmzUFji9zrKYKguipr3EStcG0sEqC5XYexoBcMArZGKApOncQMnM/r2WeFoBZCC67i3hMSDLkUV85n4Z3cgm/HzH/M2b/T1cBUk7+p69gyAugegGSAbS6vS4BVDcRC6AGXOmn6+u3dPZCJQXs6G3a0qK9oNo57a6xcXxnC/v2tQ8s/VLHLS890FQCTLtQwvpYcMm0nw2ZuXMUgsUcuE2dMzgvZ3zm/Nw+Ip97AVvi8w4dSv3kfK7QeB75nzH7f8YWIOnHN68NAF3tmB5MmxdtfW0A6Ew+ZgHSEQB0Oa1oAHWBog0CuVBptNng1vSCruuPhVBm/02bPs7Sx9svZZwuY/0iYBq8s7smSByXoCiwXFQLNgqC16WBZjeQ2QIwIz6TKMDsHEYJav+3amijpvt87qAzMv9zb6/P/T9dAGqzxSlAWqByl//pG0vuCvhwNbwbQDd9OwNQGMtZ1pQFoKYNAxydUOkAVyewLvNoSxSHUKNtbce+D5AAohb7u/GmDVOpYNr45lQKLPfzCNhsBZo58xYCzebezNzPgjMH1w7TlijURtqM7jvUjRqF3dXGi5ma/2kLv7fY/zP4/HfXa/DzP7MLkDR4DQPo2mGSBzZ3QGnthz1s+gDUMdYNhQwANcBoGWbO5wNQIGDX1RYAVydIloZQvc1oX4daYBXgA6v1GPbz7OY0125TBJg2VwmwjLVfGGwuCTTPCjJbAOYlwOXwfHrV1PM5eTExgaYGncCx8j9jnv9eawN6K4ACWD2Yc2dX+N4FoLvwvQtADe/l6rpU6U9BWk5tVSqA6svjAuhuvtP7ZclOYNXW6wPX7TUwxix99GYBCF3HbBZ6GrvrJwWisLQvbwuAKVuVbnRRYLlI6MYuASRnBZqh9WbM2/yzYNqI6dcSMJN+b4a6VMOcTx3ayuR/Tv1UV/mfNTegx2oTcRXw62+4RhsaWLYCUJ8Xc1piGoAu0+nnGfJqQmuKBVYfuDo9k4UgFKgMor712FQCTCuoKFxG9M/x7uWOz507dVwqaGZBJqO9+GfBsMHtIw6YEZ+1uMe/lYbn06vGOZ8KJy+mfP7nApFHyP+MLUCaXmPnwTQBtHgFvA0eawKoeTwBQK1eRwcc+qAyytMJhx1gP7e2ps0EUhCqtYmAqLGGjS3TnqlCYNpchWFUAvQGaDLnvTTIFAbMUnDZ9e//0E7NtlpaPJc6gAIXnP/pgFlXAZIr/7N6BTwDKE3Qm44VBtBl4hwAhaU/POuw9bfBKacN/uPmZ5UFofoYrT0ZRC39XDcGMtdSCExZqnnzSphLChRaekOLzZsKmg2vhcjneXTAPFe4nNBjyKPmOZ8n6Bz5n6kFSMv7ahXwMQBqeCK3AGf015QNoIv9ecLNWy6AYnsccI8x29ieTiZsOiHSAMrNlCkQqo/T7QqCqK7QDaWIx7S0SoFl5DytvaGp47KALnFc0G5rYK8JmUcBzCPB6NBOzR6vuYTSzdD5OeV/xgIoAPYG9IuccAqcAHT2AIpVwBtQKAagwObuIQag87gNC8UCqG+Moy0ErD6QzIHQHfNpn5nLu+tUSRC1KQJO2WDagaLhUvqGXQFUU8Y2Ac2C16ILyOwYMIvBZYe//2OfT7/aej41gHTlfwJGKP5A+Z+xBUgSG9CbBUjr139+U6IC3hxvDal3AqD6MvTpgwAKx3xwjGMAq35aW6g/vRaDUMvY3Xic+lhl6ZcCohuTtmvsUiqYMpXkfUxV5FxSECDmHUsYezjQLAnsHUFmM8A8OFwO5alNziedIGzK5cQm/K7nf645n/rrBvmf+nHrnPDnf+YUIJnzharmq1TAuwDUONY1gM79fAC6TLnK1uYblwispleyBITqdjfnaYFHq4x+5k2HA7ZRACkEpsWVMHcJz2hRb2ZgfBbUJc5ZDHxzr2NJiJWaI2Yurr1CcNn0dztGw/PpVdtqd80LqHsuc/M/pzbZ/M8t3Mbnf2YVIBGiNqCvUgGPbV8WgOrzaCBs2tgcm1UDQJdpbSHwGmH4TZtlHct1sPVLhlCL7dWOo59VKfZMlQLTxkq6WUrejCWuzQDN4NjDQKYkYEbYKwaYHf/uD7nVDD6X8LkOkCn5n7otYAuxR87/5BQgmVqgtVQFfHALphCAGsdsXkCQ/TGcgAVAl8UJASiMZVnH6zLB0THObAsB63p6AQjdAV0KhG5ebO2vzcIgurNrG2eT8V3wqeuwe8I84iCQOP5iQDMTFLNs59qPmEf0ezXgcihC7TaZn72bNoCMyf9cwu+S+Z86gE5rrZ//ySlAWqFRa7N5WaUq4HeeSg+AbvqVAlDAoKyTqWX6ZAANeSehT+IZ52jbvIe9/+70fH0sawmOt5xGDRBd38YCpK9/pO2iipw7eq0S55YLJpcCmrkQWBJiJW0w7MT0G3CpYPUQDa1q9mz3RTuAVO3zP8Og2S7/M6UAqVwF/DS/DUBtT0EqCqD6mnTAM757y7RJAAqjTVcIKi1tK8eZ51gZQvW16MNtF8+8qezYnwuiNkUA5FmH3aXPpTBAVQfNnPNpYTfXdkUbMf2qeeMl1jDUnRqG3bdgeE75n9xc0FIb0NetgN/a4gDotn8FADUg8rTkCADF3u4y7WkNljbLesw26zzYvk+G0AUuQ+NxOubkOgtk7ryiNtrnyncjiQDTdS2RqnYjKzVPYcgELgM0S3ozu4JM5vdQFGojdVgPqgKG59OvZk84WqSH388l/zMGTkttQF+tAp6A3R6gAQC1Pgd+B6Wnde0AEsbx9YvFB9ATd4YBdDHN8oLa2nzjXPNAO9cYiAzY2qzXApNWwLScHgtEXXOkKHRjiYTToio9NwcSMwEq+FEN0CwO+yLQ1zlgHhYuh7LVzvM5g+HNGQwXAAXOK/+zBIACdsDUJVkBnwWg+vpCALq4JTewNq2hOIBOg/d9YRkPh+3NBxAxjgOOFogM9XP1YUNiSRA1lQOmIdtHU8S5NIXMQPuhQLMkKHYCmS0AsxhcHuH3fTxe06umWy0B2zD4OeZ/lihA4uR/LpKogN95JbXXQQCFBrA9A6g+v36aLsi02Fj7Q+vjsBXyeNaAUH38Zu0FQXQ3l22cTblw2osib5qSN+8Bmnk2g3YrjO8RMtnf0YJw2TTSMZSkdtXuGlym5H8uNo6U/9m0AMk4JlkB79yEPgSgsAFhBwCqjTP770DOAnpsLygc42pCqMXG2gf2fiEQXbvYxi5vAzeLKDjtCUxL3zQ58JFroxQs5oztDTSPAJlnBJhHhMvxeE2/2le7G89ln0Bv//z2LegZOZ8Hyf/sqQBJsgJ+BdAFGrkA6gJKH4ACe4/prCoACvcxq4d0XcupbVla0HtaA0L1eSx21uU7oNl67PTPyXwkPPpuNtFe04YqAZcb+7n2BmiW9WYeCDLFAbMUXHb8+z7EV+Ocz6WK/ZT/CVie364w53wqjPzP9AKkYhXwHAAFVqhjAai2lv2/8zzQ/g5p0FQKQBdzSSCpL9Y1PxxjC0OodS5oY8Do6wNZw+Tuty90MzEMRHtNmariXZGGS67dHIDKHX8moFnam1kDMlsBZkm47NYrOjyfXjXP+dx5F+fwe27+JxCqQj+P/E8TBJtUwHMAdH3LBNCV0E5mTAB1Qese3gQAFJYxtmOuNl22+WEfuz0PR1smhOr91iX6YDIDRI2XVpWG06IqBZcx9gdohm0WHHsYyGwFmCXhslcQHdqp+T6fJy+mbP4nsA/fX0L+pw0wSzwD3gegUz+cOoQAVLMrBaCAAX42SuIC6Grs1LaaDIGkDSLhaIuB0ES4dPaDvf9u3sR+3puCCY+erlZTHd9wisAls29RyAyNPxfQbAWwTIlBZkPAPEu4VACuo3/7L0pXLSZdvj83SE0QubzXXl/heg6ZTwC6vAZOTxGaXl9PHk/ba23M5jWuVxtX+vykNrZvYDvPtt/1upardU7fcctrOI6TWr2Sep/9uWuv57lIs0OOX1S9neg0btH6etOuH9d+qcg95vSHQnu/HNPXaBxb/xiRNpd+DIExmnZ/2MhYC019FG2PLWMVOcZZ5tz2h7s/Am2ba+Kxr3O0q83SbzdP4NhiOzRW77dbizmPLrNPYIwK/KQqZDflJ+tcI/qa1975XSsx3tPmtVvCZs31CK2JI5t91hycc2B8F6Lmi7AXZXPXV9l/hjYioqcT0W8S0Su0Y99GRC8jopcQ0XOI6KPn448lonfOx19CRP9AG/N4IvoVIrqdiL4hd10i8ElEX0dEiohu4U9swuD1+vqG9gUyAXIB1CsNXHXonGxsxy9gdoNO0KkD6G5tGkTe2ACibkttgPRKm9N9PO41GcdXIN29ds+1gUbNpm0eIrX+ftvGmAC6wi0ZYwhuANWPcQBUOwZjPucYyx+/jRz2rMC0Oa52Y23A54RA21qMthoQyoVJzk1218/R12qTc4PhjDEkBoopirp5Rp4X5wYesJU7PhnAatksvJ7cNYVUFDIZ85QATLa9XV8HXDog0zpfMylAVfoJ6wcAPN449k+VUp+ilHokgJ8C8A+0tp9XSj1y/vlWACCiGwD+JYAvBPAIAF9KRI/IuULZYXciejCAxwF4I3/UDEBGodG55n82LUCa18ytgN9twQTCJrSu26L9E4xs+4YubXMH2ELnehh/E043jp3Gmf9qY/TjyzeOjL9XDnu78drxZZiZC6qgt9n6a7bM/ut6sDbqf0BJbdts/TZ9fG3ma1jm0tei2bMe44y39DO1u4+EbiCx/Vspcl1RN85A36CtzHav/cS2VJtZ51rKbkAitnO/AxFzSdo69eX/l68fqDyelFI/R0QPNY69S3t7L+z/qpq6DcDtSqnXAwAR/QiAJwJ4Veq6JHI+vwvA1wP4yZhB24r2CQBb5X+6AHQdH8j/ZBcauV57wDilACmnAj56C6ZLAVCYbRpV2cbt+p+O7frrcsAhG0LhabONx76vfnk29rR1hQDTC7LmocCNJRtOvcYj+mZKEi6j7F4KaGacZ5Zdj7qBzBaAWQoujwKi9ardbyGiF2rvn6aUelpoEBF9O4C/COCdAP6o1vQZRPRSAL8O4O8opV4J4EEA3qT1uQPAp+UsOgs+ieiJAO5USr2UXAmGp75PAfAUALj/R0/TLl7Maw00bR7N0vt/ugqQgO12S679P/UCpK0n07UvaNkCpNgK+KwtmGoCKKCtyPV9m9e/gLo+BIkAin3bMrSIF1Q/vQQItfXzeUk381nm3KzPBpOpIOuScS3E4bSAoj0zkf1FACMXYo4Cmg0gM9u2BBzWBkwmXBb93TgKiJbVXUqpx8QOUkp9M4BvJqJvBPA1AJ4K4MUAHqKUeg8RfRGA/wjg4ZKLXRSETyL6aQAPsDR9M4BvwhRyD2om8acBwMd/8ocoJ/Q13v9TXwuwhVvO/p86aE7j2wCoWQFfdAumWgBq6cvygq5fwvkfHcTgtuWDxhJe0M2aFhlQyIHQ3Tm6INRif3fMGLcuizveArKmcj2b0Te3GioBl1zbJSEz0H4JoFkK0kXsC9qY+gkDZkEQ7e7vwHH2+fwhAM8C8FQ9HK+UehYR/R9zLc+dAB6sjbl1PpasIHwqpT7fdpyIPhnAwwAsXs9bAbyYiG5TSr2FM/mNjUezTv5n6Pnv+gb0tvxPHUCBff7n9hGfJ1Ct/QSkmlswHQJA9eOzNl5Ql2suBhozvaBeCIWnnw1CA/3YXk3zuAUmo7yiut3lbeCmkeTZdP3db3CDaun5GaAZsBlQKW+mhCdbxBsOtAPMkv9BG/KKiB6ulHrt/PaJAF4zH38AgN9QSikiug1TUfpbAbwDwMOJ6GGYoPNJAP58zhqSw+5KqZcDuP/ynojeAOAxSqm7QmMn2NHyNyvmf4ae/x7K/9QLkEL5n00LkCwAagPM7Weyf0a8vdAoEUANG90BKNz2qnlBtXYA6RAa0S/Zq2nYZo232TCV4NmsGXrPvgkKwuWikpAZtH8GoFnSm5n72YhApiRgFoDLov9BayGFbvb5JKJnAHgsptzQOzCF17+IiH4/gGsAvwbgq+buXwLgrxPRBwC8D8CTlFIKwAeI6GsAPBvADQBPn3NBk9X0CUfT1kDXM1ye8j8B04tZJv/THB+b/2lWxJv5n7ULkGwAqvd1AebmM9HAVQdQKK0CPhVAQVsYZQDodILbY00AdF5mcS/ocr6w9DEVgkt9faF+2iKreEVtttZBnr6OMV15RQrA5aKmkBkYfxagWer8GbazP1sgCJmtvJdRv5/nBqKNpZT6Usvh73f0/R4A3+Noexam8LyIxOBTKfXQmP6+op8l/J6b/znZVs78z834hPxPvQAplP9ZowDJV0hkA1oTQDfjjGNWAN20lwFQ04YVJAHARkNSAGrYKu4Fhd0mgDgINdps/ax9l/6Q94pazyEBNqPGtLw5ScNljO0c2Ck19iig2eraMcZPfQQgUxAwi8FlVN8+PI2TJg4Zcqup53OTv5mZ/wnsvaUncJ08nCXzP692tvZ5nrUr4KX3AAU01rKAZBUABZbOWCvaLZBp/6NljDsdmo7bAHRtAGwAV8QLCotNbPtt+mI/ZtfPYW85vY2Zgl5R23w2VQNUjgThtchNujDsXDJoFvMEB8ZO7WGYkgFZRh/OXJH24vv2BJdDuWoCn4ST53AHkIz8T2AbFtfD563yP/UQ9wTR+zxPH5ju7DBe2wqQbAA69UX2HqAANlsw1QbQaf7t8eww/PKlNOCqpRd0Mz8DGn0Quutns+e4BtZ1aH2zvKKWeTeHAjclrwe4oVp6gIpCZmj8uYNmKUAHuoJMUcCM/WzPDS6PU+3eRG09n3roGpNXkJP/uXhFe83/bFqA5IXR0++DxBZMtQEU+jlIAqh+fFYzLyi2Y2xtohC6WcT+WAxgsjyo+nzmOn0yxkRBXisVAlGJkGoeLBWyK22zwDrzAN0PIxKfa7eAWRAsD/G3YGinRvCpVqBbwuCl8z9D+3/G5H/qAGra8m1AX6MAyVl0tMJo3hZMFw2gMGxiay/XC7oZu9gG03Np2tisOdAvBKKWtTjHh/ra+tskAKjJKnUzkwZMhs1sj9kAzfi1AF7YqgGZInNE9ysDmIeES4Vuqt17VeNqdx3oyuZ/xuz/qQPoNOc2/3Ndv+btjN2AvlT+p8QWTLF7gJ47gAImPBnwqCvDC+qEUF+bCYA+CHX02/R1gKS0V3S3LAnYbH2TKgGXTLslITNo/+Cg2cybKQCIYpDZCDAPCZZDImqX87nkWGICPT38Xjr/U4dOwJ+DGcr/NLdbcnss6xUg5W7BFLsHaBSAAjtwFAVQAJuCovkIjCObpgCAAh4v6NqI0xr1GWO9oFq7PgUXUFMgdJnedmpWGHUAqtWG7eZiWQ/nJpQEqI0kDZdRdjNgKhtiU+z2AprBc8/wZpaEf459dp+DwGXHv/urRs6nV82r3U/h9hM0ls7/1KEzlP9pbt1kht91j2xs/mepAqSULZhy9gCNAlDACo5+AD31M0FzLURaFhnrBYU+0AKuIS/ocsCAx52nE542fW165xgINdqiIdQ43xivJsdGdtjdsiabUu+dRT0w0nDJtZsDNBnXQxo0U+2lr6OgN7MHyDwCYJb6nRnqRs3gc1vtjmb5n7tcUGO8vpZQ/qdpa32uuwdAT55MuQKkpC2YDOCN3QO0LIDOnaxeOI8XlAugnHH6tDaY83hBd6H4kBdUt6P12UyVAaG7teuKAUlHXxughm4QyV5Nx2dTRYlziXtFawBNiu2Dg2bWdTszyBT/vboEuByeT6+awecCUqdwe5v8T70AKZT/qQOo7Xz0AiQdKmsUINkAVG+P3oLJAEz9ta1Cvg6AAiuEWoCxKIACVtAp4gXVX5i2YHpMT20+QPXa8IkBklFeUb1NP8S4wbA8tx1IHC4j+pbyZmbZToHGnkAzAxSzIZMFofmQcxi4FPbaDrVTo5zP0xdoG25vm/+5ywX1hMBD+Z+1C5CsWyxpNjhbMOXsAVovBK95QSsBKGCM1VTCC7qxZ4NQW18moLpsmEu3yrxJ+GDU0ddqx6VEryb3/lTFo1IIRJt5M0O2zxk0A9elFMCe+uSBVwvAjJ4z5hw7/I/nEF8Nw+5bL2IP+Z+bXFD48z9TN6CvVoBkzGmves/bA/QiAHReXzUvKLbti5kNhMLedwd9AUCN8mraxIBRq1fUJts8nJuLZVwxqJSwy7RRzHsaO480aHrGHQU0S12zqT0PMAHB77/0dzX23Cr9Dgy1UbNq90V6+L2n/E8dQHe24C5AAtI3oM8tQIregmnnDY3bA/QwAIqlPxBVCb9O4/CC6sMh4AXFvn1nlwuhvjYLdEaBpEsMmHXa4d48doDPHFdLEeupBZisuTLaLxY0syC0E8hsBZgDLC9eTQuOAHv+JSf/c2qzexsl8j/1AqRQ/qe+3mkt2/zPWgVINhiN3YIptAeorhgAnQagPIAC64zij+Sc17jxcm5OcO2S5gV1QShs/QzqtYCmzaYTULV5dscFvaI2O04Tgt7QqPFCqgmXUfNmAFUqjDnHnQNoBq93HmjWgkxRwCz13T8MiKr9DXNoo6ZbLQEwcjFP3s5Q/ufqId15Mevnf+oFSJz8z9wCJG4FPGcLptg9QIHtFkxcAIUBjiIACpx+wWk+EPKCpgIo9mPn09q2Ly9NyNPfeLygTptegDTsauNcNp0gaYFOjld0Y8Om0E3DMjYZUmuCXIwK3DhLeeZyAPZiQbM1ZEoBprT3shiIDrg7srp4tvu55n+WKkAKPV4T4G/BxNkDVJ+rOYACWArWquWBwmJzXucO7jK9oMuYjU2c2vweTguEGn1dYfedLRj9bGvg2OCKe9PJgNTiqg2X3LkDNoqApm/chYNmF5DZCjBLwWUvfwMWKQDX161X0bU68HzqYWk1ey7z8z+BrWexRf5niwIkiS2YdgBKW89oUwC1jC0KoDBt6ce2ECrmBZ3He4HRmGfb1zzosKm3WWyZS42B0SivaIxSIbW3m5MmEcBk9snxlJ4taEqBWsxaOMr9TwPAW7vA9yq6H3BsuBzKVtN9Pjf7Ygrnfy5w6cr/vGGE6Evkf7YoQErZgkliD1D9/eEAFICzECnkBcXJtpgXVF+IDxi5EKqfh2HTahenfrpNbn8O0NokGkXr6GYVBSFCfYt5MwNjXR/iIUCzlTezBmS2AMxCcNlNpCOkkfPpVfNqd1018z/1AqSY/E+zgMmX/7moZgFSsALeAaD6mNQtmEJ9ugBQAMmP5IRpzxg/rzfbC6qP8QGjDUKNvidQdM8RC5es/i4bZrt+iHlTEYXUTCXdCIVv8tW9mWv7AM0o9QCZkt896dD9rLj/rHX0x2AoSm2r3WeAWt63yv805/Tlf+oeSKn8z5QCpJgKeIk9QM0tmDgAOr1GewDVFfKCugB0XofTC4q9DcCwoy+DsP+7aQNE2xwwPZzbNr/X1DGHxba5rKj+jr6nTuApE1KbeEmibp68bjwwybCRCJpeuzVB09eWCCilvJlhzzJjvRKQ2QAwi4Jli991n4bn06vmOZ9ur6CaPZe0h0vh/E+9ACkm/9MFoMtaShYgBavhPZ5NqT1AQwBqek9TABRzHy6AAlhD6JqBLTTGAii2bW7w1PoBaV5Q/cDawTGfacMDrHuvqW0hxjpSPJ2wzGWzbZPtb3UFSI2eq5BN9npzIDM0PnDDH6BpmzPRbg3IrAyYxeCyN7AcylbjfT6x5kBy8z+X8Hup/E8XgJprcQGsL/8zpQCJWwEPbD2bnPbcPUC5AAogOQS/UIXuAT0dBdbKd5waJAuR5uW5vaAwberH+F7QtV2XCYg2CJ3f7z2clr42YLVNnAKjzL6bMbuD9r475YyVUOJccTdmAZtBMEnwZoZsnzNopp4b4F8rCxBz2xsAZiG4pJq/68lSwPXwfPrUNOdTB1BTpfI/dQDdjTfC9ToAh/I/SxUg2QuNXJXx/tC6rT13D9DqOaAA2wsqUYi0gcd1/m27HTyZdjQ5IVQ/aIbLgx5OSz9L3828BWHUNMnRHsr5Y2tLynsZbTPDwyYOhSVsHgU0Q+vM+c8Cp0/O/JpEATPyM4iCy8TvxVB7Nax2P/3HoGb+5zZE78//dBUgTeuP34D+dO4qCkA5BUi+LZZK7gFaHUCXOHYugG40XQtnIRKwwiM7FG/r57Ojr4YLoTDn2J7SzuMKd1/dpDlVERh1yXLO3Bth7H0oGUy4kr7Rc2wO0IxTYEwyaAY/p9z2fMjk/adGzmMKFATL3v5DqgClxj6fPjWCz+lLdUUA1DbPs3T+p6sAybTl24A+Jv/TV4Dkq4DX++rr4VbAp+4BagJocA9QC4Aun3EqgE6jKR9AAezD8itRbSHR5wXFqW0HdDYvqC4HrFrtmEM1W3vvn9p2NEFWe7+DWVdfbI+XgtGdvc1Be1+rMrypURKwK+4RzYHM0DwXCJpNvJkS8JcDz9w5mHMBFwSXQ9lqmvOp51ICdfI/XQVIMfmfsRvQp1TAuwqQYirgbQDqa0/ehN4EUJW3Eb1a+nIAFHuPpe0JSFlheGhtgN8LOrfbvZ8MO/qJ6IdMgNTlgl9j/h3MOmCxNIya3TjKBtXCEvVerv14N+dkIAy0l/CSpsBm8n8qHOOaeDNzr0kuZArMsXYT/v7GzB3dt6VGzqdX7XM+iXCt2ud/ltyAnvsEJOkK+BRATd6EviKATtIBk+EFTQTQaQ7tS+vzXhrtdvA0+uHklXV6JjWxIHTpaM6vXTqrV7U2jLoU8AKH5LrnFfOMWhfB7ScAmJw5c+BlgKZMW86cs7IhUxIwBT2mSX1tfyiGDqN2OZ8AloyIHvI/pTegTylAkn4Ep2uPz5SnIO3a589OwgM6iQegAKrmgVoh1OK9xHLI0u70gkLrq9nZ2NKWslmdDR512byhDrh1Q6Q5qf84G0Y3Yy13m5gbUCaoWiUJqREAxl53hgcuDC+pbQM02fOFxqIOZDYBzFJwWfM/llyNfT69agOf8xdlAhg1h6+BJf/TBaCA7PPfYzegN/cO9W1A738EZrlHcEZtMu9p3wEoYEClYAje6OME0KlL/TxQYG8X+/ZdCF1v19Zv94huCc7qVV3GGGJ5Q3UINddh2C4Oo8GDDuWCqqRKwxYLDDLmy4LQMwTNUtcj5z8CIdsB+4AgYIrDZeR3qEe4HMpSo7A74QYBNzVvpy2UHZP/GXr+u8QG9HoBUuoG9KEKeP3cUirguQDKBlTNw9ocQC0ezOJ5oOvhE9hOduztVmjU2u3gafRbZNqD0dcQC0KXjjagrQyjPomBagIo5UjMexnRr5g3EzhP0PS15VyPVNAUgL8gZFYHzDJeS6r8+5wspYDrUe3uU9MnHN2Yb77XKJ//2XoDem4FvF6AxK2A11+7QvOcpyDtABRYK+AlARSzDUAOQCfpgMnwgoYAVHtr84JOc9nbdxBqejet4Lk5Dau9jU0Y/bF23/Y1ZXhZxTyaXDumPCDN1e48I25SybAUkjCI8jxlqW1pN/WzBc3UuZAJmqUhswVgloLLUr+3Q1XUsNqdcHP+8tbO/2yxAb0rHUD6EZyuPUCtuZ+WsdNn4H4KEgdAAceTkGyeSmQAKLYeTdk80Mm61ztp2ra0r85Ys93mBTVfm/Y0m9APm9CKTfdtX13mwdIw6lhj9E1EAFajlWtfEjA59gqAJpB4nVM8ggcAzUNDJvtzlPOYlgTLLj2iI+fTq7aeT0x35puqbv5nyQ3ocwuQfI/gLAGg0/n6ATX4GE4TQJXnUZyRALrIBNDlmM0LygXQaYZ5fmzfe72g6+uT7Wk99nZrKF4nN6/303zP8IYG4Mz5dzoXRuc2203ZC6QuOdcZYaOmagMmp08nHk2vzXMGTc84kXxMEchsAJilvKFDh1GzrZYWb6cOoEB8/qcOoEBe/ienAMlci7PoKFCAlPIIzpgKeNsWSylPQVrsBB/DWQhAlz6r5r47L6gDQJe+0/eONu+TvKDr5Mu/Wy8osIXc6FC8bh++91u3ox1wYb2veL2hurgwqs/jANUQzNg9s/4xzjVwVBhgRQGT06+2NxM4S9AMXosSoMn57LIhszJgloLLXv/jaZEaOZ9eNfV86uH21PxPM/ydk//JKUBaQvSu/E9uAVLpCnjbHqDcpyDtipMQfgxnCEAB4JqQBaDcPNBJM5QxvaBOAAXsEGrzcgJ7+5Z2Zyh+bneCp80baoB5qjd07e+TrUOidzS0lpBEYDUgsVA+y8PFtZXnBaoKmoB7vSmg6WuTBs0Mj2MWaJaGTMbnL+m9LAWWUU9SGupS7XI+iXBTLftF9p3/ySlA0te0e62vIbMCfjpeHkD1+SUAdC1EKg2gQHIY3gaxdgh1eCkXGLR5QY12qxd0PYA91BX2hur9F7HuG1zvqN4t9sYhAKtFFLuGSoAJZF6fMwRNQN4bm5WX2RgymwBmKbgU+H2Rl8LI+fSrcbX7BKD4f9s7m5dLjiqMP897jWSh4iKCkgyahZtBBSFEIQvFqIw6mK2KgrhVSCAiav4BQfADFGQIgmBAxA8MgsQE3CoTxySQRCWKHwmKDgpmpQxzXPTHre6u6q7u21XV973PDy5vf5yqOvd239vPe6pOFfKM/3QFKBA//jMmAanya3z85xoZ8HvhOIzUHiJAm88wRqBuTYBWBXpica4ABeAb9+n6lLQr3v1ieCKao9HP/n4gGspQ2QC+h/Xs6GhIjHobDNUZUTZFPUvIKDAbNiU0x+o8r0Lz2EXmWgJzA+JS40OPh4JjPombMOxqBZBj/KebgFRFDA8b/xkzAX3ODPj+FEyhSehjJpmPWQXJFaAAxrPgEwlQ1G22us4TwYwaB7o4Clrf0a0DzvmeCI3qikfPBl276ehnuGywSx69MiOs0lXvqwgefyadCbU5s55DywXrW/dBmEpkTtadS2iOtXXsQrO0yMwsMFOs/35UwtKgtd0nKDzmsxKg1Xb68Z8lJqAfS0BKnQE/FJGHLcPZP+8K0KhpmDwCtL32MwRohSM8OdINb+6P1l5ozl0VKWdXPOARh3OjoRNlB22hV8atd4RFXfWzDAMNAeuLxSkyPPxWGU6wNJoJrC+ucgnNhfXlF5plRWZ2gZlIXGrM5/FTfJ7Ps/qh3R//6QpQYJ3xnyUmoB9LQEqRAb+2AHX9SyJAsV8rPkaAImDnE6CAvwt99nRMUyLUFwVtDrUOdaOgVXn/eedP8mio2xZ6p70PoYnnw2IxOsVSsbrBaMkqArNhbaEWUe+5E5pLRebk+eX1JheZBQRmKnG52YioKdt9jGLi86y++5tEo/74TzcBCYnHfx6SgFS1HZ6Avj9sYE4GvEtsBnxIgLr1rroKUkYBikGdYQFa3TX+KOiUAG3KNht+semPjg5EqC/KCQzFbv98bZMtGtqU3//psDQ6OiYgkj4zCj+QcgnMqPZSiKuV29tERDNFNHPjInPN7vFYEZhMWCoaelQUW9u9YVdvlxz/eUgC0twJ6OdkwLsJSA0xGfC+cZ5DEbniKkgjArT6nEJJSfMEKIBgHf0fqUXLcra7fmGYrSvetXF8WiUa6hOR/fIuc6OjM54VSwRabk25qogcI7Kd7N3mU+clNKPKHYXIXElgSlyKGIpOtVSJmibCue3xn3MTkIBA0pG7HRhD2vi/NAO+PwXT2gLUdz4oQK0vKtMIUGC6G37JspxNvVm74usi6FSxt42OhrZqtde2a4veMfe42257Lp0YjSGbGEzBWgKzrS+B0EwQQQ2+nwX1Hb3QLC0yMwvMdPN8lu3ZmMIAmBKORimacAR0u9+3PP5zbgKS23U/JwPeTUBamgGfQoC6n9VWBGjlE1pfUkzHVLXlj4J26kK3vkO64hsOjob2bIPRUPcYPMc75w4Uo6F6zws5BWZMm6cmNEfq25LQLC0yswvMRMLymP8XPXUKjvk8qyOGdm7Gf8YmIOXIgPfNAZpiGc6GOQIU8E3L5BeglS29AhTwR0HXmI6pFaBAuHu879NEdLR9wLkDSwMitGOWMhraqQ9DpiKakWLUZxpsc4rUgnWlJ1o2gRljk1NojtU5Kshm1jVW3xKhmUgsHhYJHT9/qMgsITBTictNRUOtev6LMMXm+WwYTDSPtOM/S0xAf0gGvLs9JwPeNwdoimU4ZyUh9aOemBage9uu8orphndt507H1GlnTIROREF9x1vV2RGe7nY3Ypk0Guqed+tsiI2OhsSo087cLvPgs6RguGNxt3/sg/FQkTl1XkJzslySaOYRiMy1BOZJiEtxMIWz3Ss5teb4z36meCj7PPcE9Esz4MeW4Dw5ATrRDZ9qOibAL0Jnd8UDrWAddMU3h0aim9X7rHfXjIa2xwJitOdu1HGfTyECymaJ0As1tVg0rtH4wC6TTU6hOVJnvnGa2xeapUVmToGZSlgeiwjVmM9xConP/W15VsvAars6fsj4TzcByTf+M0UCEuAf/7k0A97dnpMBHytAO2U60dbxVZBCXfR9AdowR4BW1x8HC1DAL2aXTsdU1dcXkDbZFd/4MRUdnRSh7X6iaGjHhXDUcpnoDBzvs/Rh4lFJySOT0fWtZBNjN+W7hGZ1eEtCs7TIzCwwU4lLTTYfB8lLAL4OYAfgYTP7UmGXSma7n9VCyrKO/0yRgBQa/xlaAWkqA35sCc6xDPj+e/YlC6VYBalv07eNEqDmTzSKEaDAdDf8kumYWpuIKGh1HP6IZ0R0NChCAc/+itFQ1779YOAxas6tHB2NYW3ROpdDH3CrRToPExRrC01g5OG/qtAEgjfBEtG4IaFZWmSWEJjxdpENA4PAxybYyJhPkjsA3wTwPgAvArhK8lEze66kX2fTJqkdcCKVzt22AzvnXEd3zk25c36U3G33ZtzBqshjfbyx2/FmHf1Eu78vs9/u2AS2zzrbNrCp2m22HdvQtusjG/Ed8Inu+77Zvuf+sTPfMQ4/M58ffjvz2vhsGbDlaJmuD31b98ep/4MWY9v+7dfhtd3XQZpja46t64DPNuBv50fW0D5o2Ts32LdB+wMfRuyN+1cH9l6dc9Z9hcqN1ReyCzFWfk5dsfUs8XGs/hi7gY0NX1P1OLjX1n+NI69jr1xzjw3vtRXui+476L1ifLPOa9Uyne/ujM+h8/20cHtT9UaUn7qvJstPVxGsx/f7G2MXet8h4XlG877EKHcDeMHM/mhm/wPwPQD3FfapTOTz2jP/vX7LG/7w5xJtJ+Y2ANdLOyGi0LU6HnStjgddq+PhvF6rN5Z24GX8+7En7Ae3ZWruVpJPOvtXzOyKs387gL86+y8CeEcWz0YoIj7N7HUl2k0NySfN7K7SfohpdK2OB12r40HX6njQtUqHmV0q7cPWKd7tLoQQQgghkvASgAvO/h31saJIfAohhBBCnE+uAngzyTtJvhLARwA8Wtin8strnjOuTJuIjaBrdTzoWh0PulbHg67VCWBmN0h+BsBjqKZa+raZPVvYLdBMmWJCCCGEECIP6nYXQgghhBDZkPgUQgghhBDZkPhMAMkHSRrJXPN8iZmQ/DLJ35J8huSPSb62tE+iC8lLJH9H8gWSny/tj/BD8gLJX5B8juSzJO8v7ZMYh+SO5G9I/rS0L+I0kfhcGZIXALwfwF9K+yJGeRzAW8zsbQB+D+ALhf0RDs6ScB8AcBHAR0leLOuVCHADwINmdhHAOwF8Wtdq89wP4PnSTojTReJzfb4K4HMIr0gtNoCZ/dzMbtS7v0Q195nYDptcEk4MMbO/mdm1evtlVKLm9rJeiRAk7wDwIQAPl/ZFnC4SnytC8j4AL5nZ06V9EbP4FICflXZCdPAtCSdBs3FIvgnA2wH8qrArIszXUAVIbhb2Q5wwmudzJiSfAPB6z6mHAHwRVZe72ABj18rMflLbPISq2/CRnL4Jcd4g+SoAPwTwgJn9p7Q/YgjJywD+YWa/Jvnuwu6IE0bicyZm9l7fcZJvBXAngKdJAlU37jWSd5vZ3zO6KGpC16qB5CcBXAZwr2nC262xySXhhB+St6ASno+Y2Y9K+yOC3APgwyQ/COBWAK8h+V0z+3hhv8SJoUnmE0HyTwDuMrPrpX0RQ0heAvAVAO8ys3+W9kd0IfkKVIlg96ISnVcBfGwLK3OILqz+2/4OgH+Z2QOF3RGR1JHPz5rZ5cKuiBNEYz7FqfINAK8G8DjJp0h+q7RDYk+dDNYsCfc8gO9LeG6WewB8AsB76u/SU3VkTQghvCjyKYQQQgghsqHIpxBCCCGEyIbEpxBCCCGEyIbEpxBCCCGEyIbEpxBCCCGEyIbEpxBCCCGEyIbEpxBCCCGEyIbEpxBCCCGEyMb/Ab/jiMK31I2fAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 864x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,10))\n",
    "plt.contourf(X, Y, np.array(losses).reshape(X.shape), 300, cmap='viridis')\n",
    "plt.plot([0, binary_params[0]], [0, binary_params[1]], color=\"black\")\n",
    "plt.plot(binary_params[0], binary_params[1], 'o', color='black') \n",
    "plt.colorbar()\n",
    "plt.title(\"Loss landscape for 2D binary model\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3ce0c76f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as np\n",
    "from elrpy.models import binary_model\n",
    "\n",
    "@jax.jit\n",
    "def hess_exp_lyapunov_binary_loss(params, true_params, x):\n",
    "    p = binary_model(params, x)\n",
    "    phi2 = np.sum(p * (1 - p))\n",
    "    mu = np.sum(p)\n",
    "    \n",
    "\n",
    "    p_star = binary_model(true_params, x)\n",
    "    mu_star = np.sum(p_star)\n",
    "    phi2_star = np.sum(p_star * (1 - p_star))\n",
    "    # print(mu_star / x.shape[0], (phi2_star/phi2 + (mu_star - mu)**2/phi2 - 1 / 2), (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2), -(mu_star - mu)/phi2, phi2_star/phi2, (mu_star - mu)**2/phi2, 1/2 * (mu_star - mu)**2/phi2**2, (mu_star - mu)/phi2)\n",
    "    outer_x = np.einsum('...c,...d->...cd', x, x)\n",
    "    phi2x = np.sum((p * (1 - p))[:, None] * x, axis=0)\n",
    "    dphi2x = np.sum((p * (1 - p) * (1 - 2 * p))[:, None] * x, axis=0)\n",
    "    dphi2xx = np.sum((p * (1 - p) * (1 - 2 * p))[:, None, None] * outer_x, axis=0)\n",
    "    ddphi2xx = np.sum((p * (1 - p) * (1 + 6 * p * (p - 1)))[:, None, None] * outer_x, axis=0)\n",
    "    \n",
    "    t1 = 1 / (2 * phi2) * (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2) * ddphi2xx\n",
    "    t2 = -(mu_star - mu)/phi2 * dphi2xx\n",
    "    t3 = (phi2_star/phi2 + (mu_star - mu)**2/phi2 - 1 / 2) / phi2**2 * np.outer(dphi2x, dphi2x)\n",
    "    t4 = 1 / phi2 * np.outer(phi2x, phi2x)\n",
    "    \n",
    "    hess = t1 + t2 + t3 + t4\n",
    "    return 2 * hess, (t1, t2, t3, t4),  1 / (2 * phi2) * (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2), (mu_star - mu)/phi2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fc8b3fa3",
   "metadata": {},
   "outputs": [],
   "source": [
    "@jax.jit\n",
    "def hess_t_lyapunov_binary_loss(t, true_params, x):\n",
    "    params = t * true_params\n",
    "    p = binary_model(params, x)\n",
    "    phi2 = np.sum(p * (1 - p))\n",
    "    mu = np.sum(p)\n",
    "    \n",
    "    p_star = binary_model(true_params, x)\n",
    "    mu_star = np.sum(p_star)\n",
    "    phi2_star = np.sum(p_star * (1 - p_star))\n",
    "\n",
    "    x = (x @ params).T\n",
    "    # print(mu_star / x.shape[0], (phi2_star/phi2 + (mu_star - mu)**2/phi2 - 1 / 2), (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2), -(mu_star - mu)/phi2, phi2_star/phi2, (mu_star - mu)**2/phi2, 1/2 * (mu_star - mu)**2/phi2**2, (mu_star - mu)/phi2)\n",
    "    outer_x = jax.vmap(np.dot)(x, x)\n",
    "    phi2x = np.sum((p * (1 - p)) * x, axis=0)\n",
    "    dphi2x = np.sum((p * (1 - p) * (1 - 2 * p)) * x, axis=0)\n",
    "    dphi2xx = np.sum((p * (1 - p) * (1 - 2 * p)) * outer_x, axis=0)\n",
    "    ddphi2xx = np.sum((p * (1 - p) * (1 + 6 * p * (p - 1))) * outer_x, axis=0)\n",
    "    \n",
    "    t1 = 1 / (2 * phi2) * (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2) * ddphi2xx\n",
    "    t2 = -(mu_star - mu)/phi2 * dphi2xx\n",
    "    t3 = (phi2_star/phi2 + (mu_star - mu)**2/phi2 - 1 / 2) / phi2**2 * np.dot(dphi2x, dphi2x)\n",
    "    t4 = 1 / phi2 * np.dot(phi2x, phi2x)\n",
    "    \n",
    "    hess = t1 + t2 + t3 + t4\n",
    "    return 2 * hess, (t1, t2, t3, t4),  1 / (2 * phi2) * (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2), (mu_star - mu)/phi2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "63ab3c09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1664, 2)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "group_data[0][1].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "ec30d161",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0.8653928 0.0 0.44589376\n",
      "1 0.16215026 0.0 5.167947\n",
      "2 0.6343405 0.0 2445.0427\n",
      "3 0.51601326 0.0 5.756989\n",
      "4 0.8441069 0.0 51.689354\n",
      "5 0.9119096 0.0 103.78547\n",
      "6 0.65711427 0.0 99.41739\n",
      "7 0.08938682 0.0 10.154454\n",
      "8 0.45246768 0.0 0.23940206\n",
      "9 0.3037703 0.0 0.049302332\n",
      "10 0.8186326 0.0 0.666452\n",
      "11 0.22146237 0.0 3.042394\n",
      "12 0.5277747 0.0 23.454403\n",
      "13 0.55171585 0.0 273.4535\n",
      "14 0.32842708 0.0 2.2261012\n",
      "15 0.9378201 0.0 14.493642\n",
      "16 0.744781 0.0 43.195858\n",
      "17 0.22824931 0.0 30.833637\n",
      "18 0.54728234 0.0 4.7123\n",
      "19 0.9258436 0.0 9.599702\n",
      "20 0.60175097 0.0 34.551525\n",
      "21 0.12127352 0.0 0.3685405\n",
      "22 0.37329996 0.0 170.65652\n",
      "23 0.37956572 0.0 60.92818\n",
      "24 0.026275992 0.0 7.043793e-05\n",
      "25 0.39540493 0.0 819.3443\n",
      "26 0.5139717 0.0 6.1677556\n",
      "27 0.92384136 0.0 46.07413\n",
      "28 0.7877443 0.0 25.033339\n",
      "29 0.7519332 0.0 0.35792542\n",
      "30 0.79524577 0.0 3.8019414\n",
      "31 0.7453269 0.0 91.442505\n",
      "32 0.33526587 0.0 0.007994495\n",
      "33 0.27806175 0.0 39.234493\n",
      "34 0.2462827 0.0 4.6576867\n",
      "35 0.9958941 0.0 2.259924\n",
      "36 0.49880707 0.0 2.0504098\n",
      "37 0.556345 0.0 16.239586\n",
      "38 0.5842885 0.0 10.313724\n",
      "39 0.42672753 0.0 15.045711\n",
      "40 0.791144 0.0 237.42635\n",
      "41 0.009405971 0.0 0.032067988\n",
      "42 0.8373934 0.0 648.5196\n",
      "43 0.7426059 0.0 29.60101\n",
      "44 0.64873207 0.0 35.619545\n",
      "45 0.5300548 0.0 50.19702\n",
      "46 0.85302114 0.0 99.886284\n",
      "47 0.71984303 0.0 255.02246\n",
      "48 0.076967835 0.0 0.4403086\n",
      "49 0.9452299 0.0 59.942295\n",
      "50 0.06536245 0.0 2.1872766\n",
      "51 0.7612158 0.0 83.99457\n",
      "52 0.3309443 0.0 11.3807125\n",
      "53 0.5041479 0.0 12.260724\n",
      "54 0.67722166 0.0 43.920254\n",
      "55 0.36564565 0.0 0.3080854\n",
      "56 0.7490784 0.0 200.53918\n",
      "57 0.5031389 0.0 68.56382\n",
      "58 0.91544724 0.0 18.141012\n",
      "59 0.27729464 0.0 9.799375\n",
      "60 0.25854123 0.0 2.0660937\n",
      "61 0.11331582 0.0 24.72966\n",
      "62 0.5196911 0.0 15.338516\n",
      "63 0.75275695 0.0 2191.1926\n",
      "64 0.41085184 0.0 38.271114\n",
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      "453 0.011906147 0.0 0.057854448\n",
      "454 0.46722686 0.0 78.7172\n",
      "455 0.15775836 0.0 11.249491\n",
      "456 0.7940744 0.0 20.554985\n",
      "457 0.2862296 0.0 2.678906\n",
      "458 0.8120208 0.0 14.087386\n",
      "459 0.022871971 0.0 0.014306519\n",
      "460 0.1031816 0.0 0.95914197\n",
      "461 0.94238853 0.0 1574.2063\n",
      "462 0.13272679 0.0 0.22033851\n",
      "463 0.04673779 0.0 2.239686\n",
      "464 0.5326611 0.0 0.07910643\n",
      "465 0.24005437 0.0 21.008827\n",
      "466 0.18770587 0.0 9.124066\n",
      "467 0.89814425 0.0 180.87881\n",
      "468 0.2888813 0.0 34.249996\n",
      "469 0.49446845 0.0 51.919537\n",
      "470 0.6852472 0.0 4.4642835\n",
      "471 0.6258414 0.0 17.31106\n",
      "472 0.85071445 0.0 17.251781\n",
      "473 0.54602027 0.0 6.815172\n",
      "474 0.47121477 0.0 665.9014\n",
      "475 0.6102693 0.0 17.396584\n",
      "476 0.29902756 0.0 9.945137\n",
      "477 0.50927126 0.0 45.536087\n",
      "478 0.8413514 0.0 4.0394464\n",
      "479 0.16621709 0.0 0.5567162\n",
      "480 0.41611123 0.0 3.3779192\n",
      "481 0.37595093 0.0 1.5882742\n",
      "482 0.30934417 0.0 1.9712915\n",
      "483 0.597716 0.0 8.843701\n",
      "484 0.22246146 0.0 0.017519727\n",
      "485 0.5442631 0.0 15.379681\n",
      "486 0.6464994 0.0 43.479584\n",
      "487 0.22016227 0.0 8.356635\n",
      "488 0.60145295 0.0 369.78802\n",
      "489 0.31187546 0.0 0.5748646\n",
      "490 0.90692806 0.0 0.028760485\n",
      "491 0.34580493 0.0 2.6868432\n",
      "492 0.88760304 0.0 105.03763\n",
      "493 0.36380553 0.0 2.2034774\n",
      "494 0.5028511 0.0 56.178352\n",
      "495 0.8011279 0.0 76.61051\n",
      "496 0.5635642 0.0 0.60299474\n",
      "497 0.29164577 0.0 22.047997\n",
      "498 0.9119891 0.0 296.1628\n",
      "499 0.88368213 0.0 24.007097\n",
      "500 0.7204149 0.0 63.511383\n",
      "501 0.65506196 0.0 10.091367\n",
      "502 0.97009504 0.0 100.55248\n",
      "503 0.1850785 0.0 27.011803\n",
      "504 0.8421314 0.0 21.03301\n",
      "505 0.91248405 0.0 8.550285\n",
      "506 0.6091509 0.0 5.4255896\n",
      "507 0.994218 0.0 331.9128\n",
      "508 0.02561605 0.0 0.02916143\n",
      "509 0.47310293 0.0 11.238929\n",
      "510 0.44143224 0.0 0.85099113\n",
      "511 0.96284354 0.0 179.88629\n",
      "512 0.9200578 0.0 310.83276\n",
      "513 0.26600337 0.0 2.7358642\n",
      "514 0.9395186 0.0 227.64322\n",
      "515 0.563725 0.0 1.3464272\n",
      "516 0.45201218 0.0 57.955643\n",
      "517 0.07830918 0.0 0.09106096\n",
      "518 0.16659391 0.0 2.041919\n",
      "519 0.34066665 0.0 0.15842588\n",
      "520 0.61839044 0.0 1.2224435\n",
      "521 0.8466252 0.0 89.01728\n",
      "522 0.76280284 0.0 70.57031\n",
      "523 0.52427065 0.0 1.1890178\n",
      "524 0.32604098 0.0 4.684683\n",
      "525 0.38893974 0.0 1.7089108\n",
      "526 0.41387725 0.0 14.921279\n",
      "527 0.323928 0.0 0.116232865\n",
      "528 0.78958166 0.0 138.29366\n",
      "529 0.87437606 0.0 109.36641\n",
      "530 0.60617185 0.0 253.64081\n",
      "531 0.917997 0.0 58.352554\n",
      "532 0.96286213 0.0 222.71729\n",
      "533 0.024263501 0.0 0.0013467084\n",
      "534 0.8899236 0.0 13.276004\n",
      "535 0.6913799 0.0 7.2928696\n",
      "536 0.17094803 0.0 0.006654361\n",
      "537 0.56931186 0.0 268.37903\n",
      "538 0.22967565 0.0 0.012874691\n",
      "539 0.6594306 0.0 86.82883\n",
      "540 0.53454494 0.0 1.7458286\n",
      "541 0.63326395 0.0 1.7645507\n",
      "542 0.2478267 0.0 7.868958\n",
      "543 0.8041862 0.0 122.47638\n",
      "544 0.69988465 0.0 70.73488\n",
      "545 0.68488085 0.0 1.7325867\n",
      "546 0.11156881 0.0 0.04176167\n",
      "547 0.6555716 0.0 16.132645\n",
      "548 0.9479197 0.0 5.653087\n",
      "549 0.12597322 0.0 22.726751\n",
      "550 0.7178581 0.0 115.76547\n",
      "551 0.5709218 0.0 1.593394\n",
      "552 0.37295902 0.0 11.651971\n",
      "553 0.6212472 0.0 29.370644\n",
      "554 0.5961338 0.0 82.99875\n",
      "555 0.9544507 0.0 0.5853999\n",
      "556 0.8696865 0.0 424.5892\n",
      "557 0.7674191 0.0 168.6308\n",
      "558 0.44167674 0.0 14.826154\n",
      "559 0.9702201 0.0 11.761561\n",
      "560 0.24076247 0.0 0.29543397\n",
      "561 0.24039245 0.0 6.34352\n",
      "562 0.553532 0.0 2.3734198\n",
      "563 0.7855358 0.0 147.73761\n",
      "564 0.44356716 0.0 14.487515\n",
      "565 0.520422 0.0 19.810913\n",
      "566 0.6196641 0.0 141.95508\n",
      "567 0.1524229 0.0 0.0042114886\n",
      "568 0.5352148 0.0 2.5403705\n",
      "569 0.84510577 0.0 36.650894\n",
      "570 0.4475751 0.0 8.707707\n",
      "571 0.16532981 0.0 2.1845632\n",
      "572 0.1568768 0.0 0.10955289\n",
      "573 0.015316844 0.0 0.11188713\n",
      "574 0.15920353 0.0 3.2929902\n",
      "575 0.75341976 0.0 1.5000378\n",
      "576 0.17369974 0.0 0.36522928\n",
      "577 0.73457944 0.0 505.4141\n",
      "578 0.090859056 0.0 0.25895187\n",
      "579 0.06680977 0.0 2.017477\n",
      "580 0.2091986 0.0 4.054315\n",
      "581 0.7361684 0.0 6.187426\n",
      "582 0.28272295 0.0 0.99167013\n",
      "583 0.9499321 0.0 60.344994\n",
      "584 0.46921146 0.0 12.554381\n",
      "585 0.5888127 0.0 2.5427713\n",
      "586 0.35938692 0.0 157.60652\n",
      "587 0.9249786 0.0 108.88776\n",
      "588 0.29585326 0.0 0.58059543\n",
      "589 0.5422448 0.0 3.0608258\n",
      "590 0.017778635 0.0 0.0004284377\n",
      "591 0.64885426 0.0 618.5104\n",
      "592 0.41418302 0.0 0.04887373\n",
      "593 0.51778555 0.0 11.379025\n",
      "594 0.9010527 0.0 16.435705\n",
      "595 0.22244418 0.0 0.57824916\n",
      "596 0.4525087 0.0 5.988959\n",
      "597 0.12207687 0.0 1.0330732\n",
      "598 0.35677457 0.0 0.9492643\n",
      "599 0.30417848 0.0 24.454405\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for k in range(len(group_data[0])):\n",
    "    H1, t, c1, d = hess_t_lyapunov_binary_loss(0, beta.flatten(), group_data[0][k])\n",
    "    rng = jax.random.PRNGKey(k + 3)\n",
    "    t = jax.random.uniform(rng)\n",
    "    H, tt, c, d = hess_t_lyapunov_binary_loss(t, beta.flatten(), group_data[0][k])\n",
    "    print(k, t, H1, H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "id": "bdcc8fe8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import jax\n",
    "import jax.numpy as np\n",
    "from elrpy.models import binary_model\n",
    "\n",
    "# @jax.jit\n",
    "def hess_exp_lyapunov_binary_loss(params, true_params, x):\n",
    "    p = binary_model(params, x)\n",
    "    phi2 = np.sum(p * (1 - p))\n",
    "    mu = np.sum(p)\n",
    "    \n",
    "\n",
    "    p_star = binary_model(true_params, x)\n",
    "    mu_star = np.sum(p_star)\n",
    "    phi2_star = np.sum(p_star * (1 - p_star))\n",
    "    outer_x = np.einsum('...c,...d->...cd', x, x)\n",
    "    phi2x = np.sum((p * (1 - p))[:, None] * x, axis=0)\n",
    "    dphi2x = np.sum((p * (1 - p) * (1 - 2 * p))[:, None] * x, axis=0)\n",
    "    dphi2xx = np.sum((p * (1 - p) * (1 - 2 * p))[:, None, None] * outer_x, axis=0)\n",
    "    ddphi2xx = np.sum((p * (1 - p) * (1 + 6 * p * (p - 1)))[:, None, None] * outer_x, axis=0)\n",
    "\n",
    "    print(np.linalg.eigh(ddphi2xx)[0], (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2), (phi2_star/phi2 + (mu_star - mu)**2/phi2 - 1 / 2))\n",
    "    \n",
    "    t1 = 1 / (2 * phi2) * (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2) * ddphi2xx\n",
    "    t2 = -(mu_star - mu)/phi2 * dphi2xx\n",
    "    t3 = (phi2_star/phi2 + (mu_star - mu)**2/phi2 - 1 / 2) / phi2**2 * np.outer(dphi2x, dphi2x)\n",
    "    t4 = 1 / phi2 * np.outer(phi2x, phi2x)\n",
    "    \n",
    "    \n",
    "    hess = t1 + t2 + t3 + t4\n",
    "    return 2 * hess, (t1, t2, t3, t4),  1 / (2 * phi2) * (1 - phi2_star/phi2 - (mu_star - mu)**2/phi2), (mu_star - mu)/phi2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "id": "599a5269",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-105.01039   -28.52099   -27.590672  -23.940548  -23.102432  -21.498821\n",
      "  -20.402363  -20.161726  -16.978083  -14.751165] -58.05064 58.55064\n"
     ]
    }
   ],
   "source": [
    "t = hess_exp_lyapunov_binary_loss(0.1 * beta.flatten(), beta.flatten(), group_data[0][10])[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "id": "9e473c0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.035398230088495575"
      ]
     },
     "execution_count": 268,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 / (group_data[0][k].shape[0] / 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "id": "3305fed8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array([-6.6883564e-07, -3.7897973e-07, -9.9420383e-08, -5.8985815e-08,\n",
       "        -3.7097745e-09,  5.1422515e-09,  1.2703302e-07,  2.7303113e-07,\n",
       "         1.1207234e-06,  3.3735134e+01], dtype=float32),\n",
       " Array([[ 1.42447874e-01, -6.19293928e-01, -4.65404481e-01,\n",
       "         -4.00122046e-01,  1.01541169e-01, -4.84616011e-02,\n",
       "         -5.46195172e-02,  1.63150057e-01,  4.03289855e-01,\n",
       "          1.20752558e-01],\n",
       "        [-3.71568233e-01,  3.03750098e-01, -2.96154656e-02,\n",
       "         -1.07412525e-02, -3.08179297e-04,  2.56513357e-02,\n",
       "         -8.88244882e-02, -4.55806777e-03,  7.01024473e-01,\n",
       "         -5.18340051e-01],\n",
       "        [ 3.63032401e-01,  4.17383403e-01,  1.77417576e-01,\n",
       "         -5.33726037e-01,  8.78660008e-02, -3.55825014e-02,\n",
       "          4.08499926e-01, -2.72121549e-01,  2.50632346e-01,\n",
       "          2.54818529e-01],\n",
       "        [-1.07569352e-01,  2.63949960e-01,  4.37895767e-02,\n",
       "         -1.34868035e-02,  7.22955689e-02,  1.42085515e-02,\n",
       "          1.84720531e-01,  8.99538577e-01,  4.84003574e-02,\n",
       "          2.56118566e-01],\n",
       "        [-2.38152668e-01, -4.02225018e-01,  2.72284657e-01,\n",
       "         -1.04962252e-01,  5.90857938e-02, -2.14129686e-02,\n",
       "          7.16422081e-01,  4.36217524e-02, -1.42963961e-01,\n",
       "         -3.95967484e-01],\n",
       "        [-6.06481917e-02, -2.05539949e-02,  1.06616609e-01,\n",
       "         -4.49728258e-02, -4.38454747e-01, -8.85436714e-01,\n",
       "         -3.98375317e-02,  3.60432342e-02,  3.95198017e-02,\n",
       "          4.26715575e-02],\n",
       "        [-1.65737689e-01, -8.70937854e-02,  4.76579666e-01,\n",
       "         -6.34763360e-01, -5.24118170e-02,  1.40702978e-01,\n",
       "         -4.89265651e-01,  1.23356283e-01, -2.02149630e-01,\n",
       "         -1.29949152e-01],\n",
       "        [-3.57837766e-01,  3.12401086e-01, -6.39893591e-01,\n",
       "         -3.66598547e-01,  3.60663980e-02, -9.14160982e-02,\n",
       "          8.59619081e-02, -6.78093210e-02, -4.38656449e-01,\n",
       "         -1.28197491e-01],\n",
       "        [-6.93890750e-01, -1.13258362e-01,  1.14688851e-01,\n",
       "          2.44517233e-02,  2.99697667e-02,  7.18456730e-02,\n",
       "          5.80855869e-02, -2.57147431e-01,  1.53076410e-01,\n",
       "          6.26853406e-01],\n",
       "        [-2.97467988e-02,  1.08263968e-02,  1.17796429e-01,\n",
       "          6.15251288e-02,  8.80944252e-01, -4.21607405e-01,\n",
       "         -1.52121902e-01, -3.16102393e-02, -4.52274494e-02,\n",
       "         -3.65466103e-02]], dtype=float32))"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigh(t[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1dafbd5f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "id": "7386cd9b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.70055306\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Array([-0.11612222,  0.2271569 ,  0.48492092,  0.68342495,  0.7507059 ,\n",
       "        0.7750699 ,  0.9355562 ,  1.002058  ,  1.2901878 , 70.381905  ],      dtype=float32)"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigh(hess_exp_lyapunov_binary_loss(0.5 * beta.flatten(), beta.flatten(), group_data[0][k])[0])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "id": "26b75908",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(0.18954492, dtype=float32)"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(binary_model(beta.flatten(), group_data[0][k]) * (1 - binary_model(beta.flatten(), group_data[0][k]))).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "id": "999c12a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(0.23862244, dtype=float32)"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(binary_model(beta.flatten(), group_data[0][k])).mean() * (1 - (binary_model(beta.flatten(), group_data[0][k])).mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "id": "37371164",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array(0.6066656, dtype=float32)"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(binary_model(beta.flatten(), group_data[0][k])).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "id": "64b22bc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([0.5322552 , 0.71743584, 0.8440471 , 0.69025177, 0.86172175,\n",
       "       0.92059845, 0.6529735 , 0.85587466, 0.44015113, 0.6972561 ,\n",
       "       0.49392554, 0.54733324, 0.723354  , 0.6300325 , 0.91910267,\n",
       "       0.599916  , 0.82093287, 0.70531505, 0.3291549 , 0.60666305,\n",
       "       0.5962202 , 0.47623867, 0.96397877, 0.4828992 , 0.7665035 ,\n",
       "       0.91347945, 0.486745  , 0.37603146, 0.46989706, 0.70501274,\n",
       "       0.59922796, 0.17969178, 0.9615677 , 0.4463793 , 0.3818087 ,\n",
       "       0.6415459 , 0.7709335 , 0.2870071 , 0.45871362, 0.8373599 ,\n",
       "       0.7718902 , 0.55211943, 0.67444605, 0.58503544, 0.84869903,\n",
       "       0.06722485, 0.13647027, 0.64404   , 0.61032516, 0.7544116 ,\n",
       "       0.6239271 , 0.4644104 , 0.434181  , 0.67191213, 0.5214437 ,\n",
       "       0.9748038 , 0.9647365 , 0.71103394, 0.7727409 , 0.29957807,\n",
       "       0.686108  , 0.2882642 , 0.47191706, 0.18209156, 0.4838587 ,\n",
       "       0.5738535 , 0.9434367 , 0.6240802 , 0.2989089 , 0.7555742 ,\n",
       "       0.86754847, 0.52892554, 0.96130115, 0.676197  , 0.37405148,\n",
       "       0.26948044, 0.514183  , 0.82025373, 0.24158674, 0.8905823 ,\n",
       "       0.66268075, 0.8087876 , 0.73838556, 0.71645504, 0.3188609 ,\n",
       "       0.39357507, 0.75059664, 0.7552573 , 0.38917392, 0.46692502,\n",
       "       0.84567875, 0.8741763 , 0.8369762 , 0.23714669, 0.59160584,\n",
       "       0.89948267, 0.79619163, 0.83168536, 0.8397587 , 0.5691438 ,\n",
       "       0.22183   , 0.20713578, 0.44563887, 0.8794295 , 0.47233748,\n",
       "       0.28038222, 0.61003417, 0.51354474, 0.5870783 , 0.5344452 ,\n",
       "       0.19387612, 0.44799232, 0.9117789 ], dtype=float32)"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_model(beta.flatten(), group_data[0][k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "8df12eeb",
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 268\n",
    "rng = jax.random.PRNGKey(k + 2)\n",
    "t = jax.random.uniform(rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7a468dca",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "a3c01181",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0.4240216 0.38579786 [   4.145019     5.844952     6.4646573    6.546616     7.364783\n",
      "    8.726075     9.621903     9.88111     10.110066  1311.0406   ]\n",
      "1 0.8653928 0.41334665 [-2.95558628e-02  1.15390666e-01  1.34282336e-01  1.37348071e-01\n",
      "  1.98832795e-01  2.19564706e-01  2.50059754e-01  3.06418538e-01\n",
      "  4.08007681e-01  1.42460022e+02]\n",
      "2 0.16215026 0.4114868 [   8.928448    9.373969   10.271558   10.591008   11.306983   12.791623\n",
      "   13.888302   14.261965   15.0259   3155.1619  ]\n",
      "3 0.6343405 0.26365554 [  7.943977  11.269225  13.202663  14.488474  15.219895  16.218792\n",
      "  17.289703  19.047863  21.473368 981.5915  ]\n",
      "4 0.51601326 0.14092675 [ 1865.5404  1959.4548  2085.1272  2158.4062  2183.6006  2249.4763\n",
      "  2314.7683  2342.016   2447.9482 53930.184 ]\n",
      "5 0.8441069 0.30870286 [  1.2155668   1.7894235   1.9152874   2.0313973   2.160241    2.5227706\n",
      "   2.7562096   3.2339017   3.5637808 366.27426  ]\n",
      "6 0.9119096 0.53934896 [-1.1595631e-02  2.5056545e-02  6.3855901e-02  7.4193247e-02\n",
      "  1.0548871e-01  1.3832280e-01  1.7256948e-01  2.2653043e-01\n",
      "  2.4671736e-01  1.2623148e+03]\n",
      "7 0.65711427 0.42493978 [-0.11906008  0.07844102  0.12184143  0.17358412  0.2066769   0.32552475\n",
      "  0.40425012  0.4541651   0.5189486  43.34203   ]\n",
      "8 0.08938682 0.49279168 [-7.8411810e-02 -7.1871132e-02 -5.9446078e-02 -4.1835029e-02\n",
      " -3.7453342e-02 -2.9734507e-02 -1.5335187e-02 -1.2154664e-02\n",
      " -2.8796780e-03  4.8429056e+02]\n",
      "9 0.45246768 0.3719611 [  3.320934    4.5523286   5.357648    5.6727085   5.8845696   6.352806\n",
      "   7.1335974   7.8837004   8.808236  622.77313  ]\n",
      "10 0.3037703 0.25817648 [  9.660687  12.153778  14.681947  15.832221  16.23457   16.784533\n",
      "  17.404518  21.498072  22.175823 400.2668  ]\n",
      "11 0.8186326 0.29127914 [  2.681871    3.3679054   3.4984257   4.380424    4.59089     5.076855\n",
      "   5.4909973   5.6308966   6.196284  607.59753  ]\n",
      "12 0.22146237 0.5313293 [4.4604349e-01 7.5945145e-01 9.0503436e-01 9.6619612e-01 1.1253728e+00\n",
      " 1.2213569e+00 1.3662487e+00 1.6441629e+00 1.7477322e+00 1.8639421e+03]\n",
      "13 0.5277747 0.35137826 [  16.914612   19.526537   21.312231   24.589182   26.325144   27.537365\n",
      "   28.930285   30.75511    32.32153  3584.7485  ]\n",
      "14 0.55171585 0.32840836 [  2.1728456   2.416998    2.9954545   3.3522608   3.767982    4.556675\n",
      "   4.873949    5.203738    5.957533  223.6745   ]\n",
      "15 0.32842708 0.34455794 [  4.9060106   5.349372    6.3728228   7.2507854   7.3396726   7.8167915\n",
      "   8.296046    9.116558   10.3691025 494.0603   ]\n",
      "16 0.9378201 0.64255065 [7.5074032e-02 1.1616929e-01 1.7586049e-01 2.1700306e-01 2.6518127e-01\n",
      " 2.9338014e-01 3.6365226e-01 4.4879636e-01 4.9976987e-01 1.7304570e+02]\n",
      "17 0.744781 0.34819025 [  2.181567    2.3222165   2.7696176   3.1374454   3.3864887   4.0361347\n",
      "   4.069671    4.3860774   4.9617333 723.9117   ]\n",
      "18 0.22824931 0.5052307 [-3.5055229e-01 -1.6782264e-01 -1.3364597e-01 -6.4537816e-02\n",
      "  1.0946320e-01  2.0032248e-01  3.1408298e-01  4.4843853e-01\n",
      "  7.8144169e-01  1.8461410e+04]\n",
      "19 0.54728234 0.3902281 [  1.2893046   1.3526112   1.8084241   1.8184487   2.1866019   2.2962403\n",
      "   2.8803515   3.2761984   3.3991098 415.67813  ]\n",
      "20 0.9258436 0.63160324 [1.2491651e-01 2.2866130e-01 3.5374600e-01 3.7539849e-01 4.1168261e-01\n",
      " 4.7588432e-01 5.2944261e-01 5.9405333e-01 6.8195164e-01 3.0034796e+02]\n",
      "21 0.60175097 0.36152163 [  1.0012164   1.2645385   1.7412612   1.97695     2.07616     2.6624491\n",
      "   3.087241    3.5432985   3.974407  249.98297  ]\n",
      "22 0.12127352 0.31683487 [  20.322033   24.34093    29.366833   29.56135    33.167812   34.562183\n",
      "   34.997005   36.365356   41.390606 1618.6747  ]\n",
      "23 0.37329996 0.2866754 [  28.118528   29.764547   37.562485   38.04629    39.717266   41.746082\n",
      "   42.47832    45.299915   47.648083 2200.2288  ]\n",
      "24 0.37956572 0.62907696 [  2.3877625   3.1184845   3.424515    3.6644394   4.0318494   4.376788\n",
      "   5.416417    6.1691165   7.173623  395.36768  ]\n",
      "25 0.026275992 0.5625012 [   3.6469004    3.9612517    4.386198     4.4390416    4.7466455\n",
      "    5.285479     5.5551324    5.820327     6.045393  2115.9507   ]\n",
      "26 0.39540493 0.5222063 [-1.8253344e-01 -1.2662649e-01 -7.7521220e-02 -3.6793634e-02\n",
      "  3.1644478e-02  5.9326608e-02  1.0708160e-01  1.7950104e-01\n",
      "  2.7210265e-01  2.3867952e+02]\n",
      "27 0.5139717 0.68854207 [  6.2865667   7.318322    8.251129    8.490264    9.25206    10.606773\n",
      "  10.994712   11.683178   12.50263   694.0509   ]\n",
      "28 0.92384136 0.4406132 [3.3285923e-02 1.8406890e-01 2.6089957e-01 3.0687806e-01 3.6495265e-01\n",
      " 4.3902048e-01 5.0683463e-01 5.2084935e-01 6.2572920e-01 1.8276671e+03]\n",
      "29 0.7877443 0.32169196 [   3.1271145    5.0162616    5.4222636    5.806428     6.0235157\n",
      "    6.5853543    6.9034624    7.4571657    8.539701  1262.3728   ]\n",
      "30 0.7519332 0.33669445 [  2.0921721   3.8291378   3.9160452   4.143141    4.580771    4.816048\n",
      "   5.1892095   6.1424932   6.860843  785.7794   ]\n",
      "31 0.79524577 0.69404215 [   4.2155757    5.643208     6.543923     7.7728763    8.262484\n",
      "    9.142791     9.388561    10.057588    10.8905945 1420.8997   ]\n",
      "32 0.7453269 0.6424152 [  1.1064568   1.2377527   1.4152927   1.7043115   1.8039366   2.0629451\n",
      "   2.177412    2.640959    2.721276  335.78143  ]\n",
      "33 0.33526587 0.47589853 [-1.20554835e-01 -8.20266232e-02 -3.58695313e-02  9.20531712e-03\n",
      "  2.59162858e-02  3.70358042e-02  7.63712227e-02  8.29545856e-02\n",
      "  2.14650452e-01  7.20821304e+01]\n",
      "34 0.27806175 0.7974366 [ 105.78882  121.48331  129.16324  135.0051   145.7584   150.64102\n",
      "  159.55957  167.19833  168.73349 4209.855  ]\n",
      "35 0.2462827 0.5276166 [-7.2412759e-02 -4.8083629e-02 -4.1769430e-02 -2.2268260e-02\n",
      "  1.2986075e-02  4.1041721e-02  5.2106429e-02  8.3122946e-02\n",
      "  1.7577198e-01  3.3767090e+01]\n",
      "36 0.9958941 0.62559277 [4.0720641e-03 1.0063598e-02 1.2689945e-02 1.6132645e-02 1.9123390e-02\n",
      " 2.0997409e-02 2.4711126e-02 2.7559651e-02 7.5192817e-02 2.2894135e+02]\n",
      "37 0.49880707 0.40877196 [  0.5686292   1.2013073   1.5476946   1.8797184   2.043709    2.3414352\n",
      "   2.5900598   2.9188716   3.250029  522.5139   ]\n",
      "38 0.556345 0.61880004 [  19.17374    23.438818   24.90399    27.639221   31.139256   32.733776\n",
      "   34.527      35.816162   38.02436  8307.502   ]\n",
      "39 0.5842885 0.5262757 [-6.5687418e-02 -2.7918058e-02  1.3430345e-02  7.0484430e-02\n",
      "  9.8089993e-02  1.8760991e-01  2.8797191e-01  3.0315742e-01\n",
      "  5.0864530e-01  8.3783569e+02]\n",
      "40 0.42672753 0.71831554 [ 14.621449  15.254429  16.161331  17.008944  18.45616   20.319826\n",
      "  22.977983  23.87154   27.020767 932.3832  ]\n",
      "41 0.791144 0.49355617 [-1.4620535e-01 -5.8907498e-02 -2.1580802e-03  9.9079991e-03\n",
      "  7.9885960e-02  1.1498946e-01  1.2727898e-01  1.8262516e-01\n",
      "  2.3337722e-01  8.1677788e+03]\n",
      "42 0.009405971 0.7707645 [ 107.40147  125.41083  132.25632  142.36473  152.20439  157.21811\n",
      "  161.03046  167.39822  193.09584 4826.7886 ]\n",
      "43 0.8373934 0.47243148 [-4.2671315e-02 -2.4149891e-02 -1.6554214e-02 -1.1105960e-02\n",
      " -4.9116765e-03  1.0616625e-02  1.8751457e-02  2.4703888e-02\n",
      "  7.0258379e-02  1.7866936e+01]\n",
      "44 0.7426059 0.26068357 [  4.8682666   5.6034513   6.343168    6.431409    7.191677    7.226686\n",
      "   8.197112    9.156151   10.80232   508.1265   ]\n",
      "45 0.64873207 0.5281202 [7.5094208e-02 1.8006492e-01 1.9569147e-01 3.4797183e-01 5.7145834e-01\n",
      " 7.7610677e-01 8.0715686e-01 1.0928152e+00 1.2554350e+00 3.0508745e+03]\n",
      "46 0.5300548 0.3237952 [  2.0792804   2.8435118   3.2318773   3.8001392   4.0511208   4.30214\n",
      "   4.78365     5.49402     5.919895  230.37819  ]\n",
      "47 0.85302114 0.3992069 [1.0665001e+00 1.5840883e+00 1.8142402e+00 2.1406398e+00 2.4117353e+00\n",
      " 2.4778492e+00 2.5809329e+00 2.8928018e+00 3.6985002e+00 2.3962622e+03]\n",
      "48 0.71984303 0.55432117 [-9.7567119e-02 -5.9635602e-03  4.0599955e-03  6.5144643e-02\n",
      "  1.4170775e-01  1.8361463e-01  2.1075335e-01  3.3239600e-01\n",
      "  4.3553129e-01  1.4444041e+02]\n",
      "49 0.076967835 0.3319736 [  6.692467   7.736791   8.331031   8.907048   9.041329  10.092389\n",
      "  11.100308  12.354619  14.180101 455.46268 ]\n",
      "50 0.9452299 0.5572722 [8.0900840e-02 1.5946934e-01 1.8439804e-01 2.1422236e-01 2.8838536e-01\n",
      " 3.2839307e-01 3.3936587e-01 3.8397241e-01 4.0550444e-01 3.0091238e+03]\n",
      "51 0.06536245 0.4525637 [  0.27644986   0.35914746   0.3821926    0.43641433   0.49329287\n",
      "   0.5144622    0.5401306    0.72188306   0.7832567  257.02975   ]\n",
      "52 0.7612158 0.6776878 [   7.4691615   11.32396     11.822083    12.668492    13.076113\n",
      "   13.966294    16.177675    17.218359    18.36921   2824.5996   ]\n",
      "53 0.3309443 0.63419133 [  39.732788   41.46503    46.409706   46.93187    52.12641    54.554394\n",
      "   56.55371    59.30824    62.684837 7436.6304  ]\n",
      "54 0.5041479 0.6868177 [  11.367809   12.196348   13.308572   14.306807   14.952408   16.071108\n",
      "   17.290817   17.860743   19.833595 1183.0529  ]\n",
      "55 0.67722166 0.40817305 [  0.43060791   0.75207525   0.8264539    1.0277659    1.1798924\n",
      "   1.3612583    1.5929774    1.8359983    2.0285616  416.41718   ]\n",
      "56 0.36564565 0.49702123 [-9.6843824e-02 -8.9221425e-02 -5.5314817e-02 -4.1308310e-02\n",
      " -3.5434734e-02 -2.4205485e-02 -5.7332884e-03  1.1516489e-02\n",
      "  1.4305163e-02  1.4566396e+03]\n",
      "57 0.7490784 0.36207417 [  0.38013938   0.4325463    0.7672345    1.0075849    1.1562234\n",
      "   1.2792734    1.4281963    1.7119672    1.8775938  166.63358   ]\n",
      "58 0.5031389 0.5790484 [  0.32755184   0.4646153    0.7634353    0.804916     0.96216863\n",
      "   1.0537856    1.239081     1.6801541    1.923329   299.71536   ]\n",
      "59 0.91544724 0.31497046 [   2.913016     4.5929317    4.90035      5.309805     5.648776\n",
      "    5.775253     5.984687     6.375278     6.631707  2826.3386   ]\n",
      "60 0.27729464 0.4955254 [-8.8761002e-02 -6.5502070e-02 -6.1869171e-02 -5.4099690e-02\n",
      " -5.1301610e-02 -3.9620724e-02 -2.6870782e-02 -1.8265028e-02\n",
      " -1.5481123e-02  1.3307396e+02]\n",
      "61 0.25854123 0.64102197 [  10.372895    11.916512    12.43974     13.6268635   14.468913\n",
      "   15.416053    16.8446      18.213331    19.431824  1402.5474   ]\n",
      "62 0.11331582 0.21849364 [  71.69297   91.87153   93.09592   98.05246  102.03649  107.75387\n",
      "  110.62534  112.21218  122.61685 2964.4304 ]\n",
      "63 0.5196911 0.44515255 [-1.24318235e-01  2.59108990e-01  3.63343149e-01  4.68893707e-01\n",
      "  7.00568318e-01  7.63422430e-01  9.92942870e-01  1.07544243e+00\n",
      "  1.22403049e+00  5.43039062e+02]\n",
      "64 0.75275695 0.66228586 [   4.2122836    6.058379     6.3098545    7.1669517    7.3332295\n",
      "    8.491359     8.719444     9.145647    10.502502  1610.1294   ]\n",
      "65 0.41085184 0.46964 [-2.1134067e-01 -5.8511496e-02 -1.3050355e-02  6.1846557e-03\n",
      "  3.7937410e-02  5.6375548e-02  8.1839599e-02  1.7467107e-01\n",
      "  3.0461150e-01  4.4125206e+01]\n",
      "66 0.9634992 0.25355315 [2.5315065e+00 4.1193357e+00 4.5762124e+00 4.8232555e+00 5.3011355e+00\n",
      " 5.7095432e+00 6.0242596e+00 6.2783804e+00 6.5826149e+00 3.2767483e+03]\n",
      "67 0.8188391 0.3281519 [   6.618959    10.796613    12.1620455   12.64388     13.203754\n",
      "   15.028565    16.116058    17.02196     17.976368  3854.8225   ]\n",
      "68 0.8723061 0.45171067 [1.2953494e-01 4.5070884e-01 5.0793993e-01 6.1374152e-01 7.1410310e-01\n",
      " 9.6551561e-01 1.0353148e+00 1.2098302e+00 1.3727868e+00 3.6462930e+03]\n",
      "69 0.12176216 0.51944053 [4.9130782e-02 9.0048805e-02 1.6678354e-01 2.0515853e-01 2.3235442e-01\n",
      " 3.0524024e-01 3.5460836e-01 4.0665370e-01 5.3300118e-01 1.3765455e+03]\n",
      "70 0.2668543 0.4661786 [4.6738672e+00 6.1988292e+00 7.1739755e+00 7.9448910e+00 8.6372604e+00\n",
      " 9.0776930e+00 9.7626572e+00 1.0347102e+01 1.1675650e+01 1.6305590e+04]\n",
      "71 0.029824734 0.47519502 [2.3686509e+00 2.7158194e+00 2.7720373e+00 2.8203766e+00 2.9861941e+00\n",
      " 3.2632720e+00 3.3678088e+00 3.5333931e+00 3.8360143e+00 9.4972354e+03]\n",
      "72 0.1863519 0.21417004 [ 18.577517  21.405563  23.466282  23.931194  26.103214  27.861298\n",
      "  29.31165   30.61377   34.497375 573.2016  ]\n",
      "73 0.72566295 0.5627511 [1.5159128e+00 1.7935321e+00 2.2844820e+00 2.7719276e+00 2.9759963e+00\n",
      " 3.1900601e+00 3.8224387e+00 3.9944549e+00 4.6851625e+00 5.1818325e+03]\n",
      "74 0.5685487 0.802639 [  55.341812   62.15189    70.11004    71.10664    73.4214     79.25091\n",
      "   81.553665   82.67768    91.1653   3173.6626  ]\n",
      "75 0.546847 0.17743781 [  70.77134    87.227585   94.03081    99.139824  106.25508   112.34441\n",
      "  116.08585   127.22153   131.27194  4055.5364  ]\n",
      "76 0.68154407 0.6668194 [  15.869421   22.928846   25.43864    26.193472   28.89877    31.005657\n",
      "   32.35064    33.47278    34.790714 5159.068   ]\n",
      "77 0.60008657 0.36323777 [  2.4411564   3.1669457   4.2414956   4.3332624   4.663502    5.0959983\n",
      "   5.5931997   6.118303    6.910983  719.05524  ]\n",
      "78 0.750391 0.46356133 [-3.2436304e-02  6.9580883e-02  1.0238610e-01  1.4648117e-01\n",
      "  2.1751909e-01  3.5710689e-01  4.2845306e-01  4.8908716e-01\n",
      "  8.8489687e-01  8.2475970e+02]\n",
      "79 0.38232315 0.39748544 [   2.7565773    5.8999996    6.062594     6.3127923    7.376874\n",
      "    8.357617     8.562586     9.092653     9.920562  1364.5175   ]\n",
      "80 0.018434286 0.7353373 [  208.44614   219.75659   240.6412    252.76306   257.93533   264.884\n",
      "   273.74985   284.1987    296.20367 10959.147  ]\n",
      "81 0.4782623 0.4038777 [-0.06755608  0.37977412  0.42928523  0.56158465  0.62793607  0.8471039\n",
      "  0.940194    1.2100418   1.5598727  36.181667  ]\n",
      "82 0.4272107 0.7364864 [  53.29495    54.28257    63.406353   65.138084   71.79271    72.71271\n",
      "   78.68362    84.20717    86.736755 3758.1562  ]\n",
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      "  4.8145607e-01  1.5613370e+02]\n",
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      "  104.872086  112.168755  113.55153  3263.1184  ]\n",
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      "   6.2214804   6.5957384   6.922349  387.6335   ]\n",
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      " 1.3451654e+00 1.4984235e+00 1.8749628e+00 2.0859776e+00 2.8293896e+02]\n",
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      " 3.2267904e-01 3.7631822e-01 3.9957458e-01 4.4883239e-01 2.9658228e+02]\n",
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      "   8.992875    9.738665   11.311399  225.7599   ]\n",
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      "   13.335066    13.671816    14.302792    15.051475  2166.216    ]\n",
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      "  3.30506206e-01  6.52140747e+02]\n",
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      "    7.1848435    8.072444     8.7489805   10.036022  2395.2085   ]\n",
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      "  4.5208764e-01  2.4312965e+02]\n",
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      "  1.8404868e-01  9.9403267e+01]\n",
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      "   99.640785  100.883446  105.371506 7180.359   ]\n",
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      "  1.2776650e-01  3.6952702e+01]\n",
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      "  5.84810019e-01  2.37399887e+02]\n",
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      "  1.0144081e+00  5.4634186e+02]\n",
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      "  1.2517036e-01  1.3267967e+02]\n",
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      "  2.8602636e-01  1.1856898e+02]\n",
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      "   4.0851903   4.200369    4.6420393 161.64606  ]\n",
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      " -3.03604621e-02  6.80834778e+02]\n",
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      "  1.64559171e-01  6.26460156e+03]\n",
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      "   251.74312   259.69653   282.66965 10663.67   ]\n",
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      "   17.90024    18.129362   19.759157 2053.02    ]\n",
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      "  28.313265  31.450073  32.586296 886.6796  ]\n",
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      "  23.647673  24.35763   26.103249 499.81635 ]\n",
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      "  8.4439307e-01  7.1135841e+01]\n",
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      "   46.22228    46.988434   50.631084 3922.5144  ]\n",
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      " 2.1093580e-01 2.1443261e-01 2.3912895e-01 2.8773141e-01 1.7374899e+02]\n",
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      "    5.5112762    6.0955396    6.240369     6.441252  1334.8778   ]\n",
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      "  237.3455   247.7638   258.15543 8844.761  ]\n",
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      " 1.1668341e-01 1.2714715e-01 1.3861507e-01 1.5989079e-01 5.3897723e+02]\n",
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      "  2.0404951e-01  1.7147009e+01]\n",
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      "   8.894545    9.187531    9.795842  388.6904   ]\n",
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      "  0.84492505  1.0675772   1.4370323  70.876305  ]\n",
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      " 5.3594214e-01 5.6527293e-01 6.6719657e-01 7.1703553e-01 3.1028961e+02]\n",
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      "  27.922928  29.27631   30.621971 634.796   ]\n",
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      "  0.7790952   0.93313843  1.1853831  27.445423  ]\n",
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      "  15.104048  15.80447   17.667511 290.73083 ]\n",
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      "  6.3618511e-02  2.0167056e+02]\n",
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      "   23.661371   24.787212   25.924667 2907.0273  ]\n",
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      " 1.4270432e+00 1.5050039e+00 1.7262306e+00 1.9795662e+00 1.3575640e+03]\n",
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      "  2.5327986e-01  5.1814148e+01]\n",
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      "   49.979366   51.37417    53.755146 7722.2627  ]\n",
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      "  3.0077758e-01  3.6865786e+03]\n",
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      " 3.8849494e-01 4.5614758e-01 6.2560129e-01 7.2286069e-01 9.7052948e+01]\n",
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      " 2.1273782e+00 2.5995076e+00 2.7509539e+00 3.0642953e+00 6.7099152e+02]\n",
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      "  8.8268548e-02  1.1062943e+01]\n",
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      "   2.8339617   3.133112    3.4975011 259.7215   ]\n",
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      "   7.3755975   7.6069837   7.962258  902.0574   ]\n",
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      " 1.3467652e+00 1.4741215e+00 1.5543371e+00 1.8937490e+00 1.1152902e+03]\n",
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      "  1.0035274e-01  2.4631612e+02]\n",
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      "  2.56368756e-01  2.62906128e+02]\n",
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      " 6.7841369e-01 9.2019695e-01 1.0085150e+00 1.0252079e+00 3.2186951e+02]\n",
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      "  3.1876484e-01  3.1318271e+02]\n",
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      "    4.855736     5.618111     6.0579724    7.020158  1176.5602   ]\n",
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      "  8.5559390e-02  1.2578611e-01  1.5623942e-01  2.0005170e-01\n",
      "  2.6807970e-01  8.8593872e+01]\n",
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      "  4.5453534e-03  7.2901627e+01]\n",
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      "   0.7624512    0.8349497    0.96337545   1.0260596  425.35724   ]\n",
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      "   1.5660641    1.8728136    1.9169775    2.1538305  112.50939   ]\n",
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      "    2.0057986    2.125771     2.2183015    2.2548904 1026.1624   ]\n",
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      "   84.55216    90.67414    92.82025  4374.265   ]\n",
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      "   14.50851    16.516815   17.448874 1283.64    ]\n",
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      " 3.7845200e-01 4.7307473e-01 5.2149969e-01 7.4056327e-01 2.8751300e+02]\n",
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      "  2.02813707e-02  9.76366624e-02  1.30117878e-01  1.86417058e-01\n",
      "  2.28605986e-01  1.82081406e+02]\n",
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      "   82.241356   87.87488    93.91373  3802.114   ]\n",
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      "   1.2077272    1.2267833    1.3901993    1.4476391  248.74066   ]\n",
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      "  8.98518860e-02  1.26093090e-01  1.76833913e-01  2.23728448e-01\n",
      "  2.57832408e-01  3.36190369e+02]\n",
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      "   13.519605    14.400928    14.861073    15.875743  1457.2463   ]\n",
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      "   13.287438   14.086046   14.619771 4484.953   ]\n",
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      " 6.73950374e-01 6.80521250e-01 8.34152043e-01 9.44157064e-01\n",
      " 1.02416611e+00 3.39059845e+02]\n",
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      " 1.3916702e+00 1.6438671e+00 1.6813546e+00 2.4756088e+00 3.4926104e+03]\n",
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      " 2.7335379e-01 3.1599823e-01 3.5976201e-01 4.1046456e-01 4.5922855e+02]\n",
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      "   9.758732   10.130682   10.620102  678.3484   ]\n",
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      " 1.4603168e+00 1.8212548e+00 1.8589032e+00 2.3118167e+00 9.6256195e+02]\n",
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      " 2.1385341e+00 2.3566632e+00 2.7605109e+00 3.0908012e+00 5.1961704e+03]\n",
      "685 0.36227465 0.41724584 [  0.67630756   0.95575005   1.1338592    1.3754177    1.574263\n",
      "   1.9243628    2.2983177    2.3994906    3.0654333  399.64926   ]\n",
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      "  4.4263687e-02  7.5426377e-02  8.0796823e-02  1.3096999e-01\n",
      "  1.5087020e-01  9.7223994e+03]\n",
      "687 0.86555433 0.71721363 [  1.9282608   2.6042757   2.7461247   3.077802    3.2142048   3.4039524\n",
      "   3.6573856   3.9034107   4.23895   519.04535  ]\n",
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      "  1.0190130e-01  1.1996216e-01  1.3565159e-01  1.6005772e-01\n",
      "  1.8137611e-01  1.2023475e+02]\n",
      "689 0.03165579 0.73211896 [  27.049253   28.975567   32.09857    32.87082    36.759926   38.548397\n",
      "   39.205776   42.447426   44.89176  1160.0369  ]\n",
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      "  2.9938887e-03  4.8367120e-03  7.8045041e-03  1.2555769e-02\n",
      "  4.8826203e-02  2.1719061e+02]\n",
      "691 0.2062298 0.5856281 [  17.367485   18.267096   19.023365   20.67461    20.929186   23.134604\n",
      "   24.351143   26.123224   27.306509 6382.9297  ]\n",
      "692 0.86110044 0.7883248 [  6.3440437   7.2632837   8.827394    9.089516    9.906189   10.271691\n",
      "  10.674655   11.061955   11.9266405 930.78656  ]\n",
      "693 0.70356905 0.34586662 [   2.4743798    4.6201305    5.184626     6.146366     6.384876\n",
      "    7.2013693    7.817355     8.227703     8.660134  1168.4447   ]\n",
      "694 0.94348764 0.34792164 [1.3023409e+00 2.5541160e+00 2.6927218e+00 2.9807799e+00 3.1431322e+00\n",
      " 3.1917937e+00 3.3802724e+00 3.6870623e+00 3.9922087e+00 3.2579534e+03]\n",
      "695 0.5247811 0.33077547 [  3.1545854   4.758877    5.489669    6.0543447   6.9782696   7.6337013\n",
      "   8.066208    8.895034    9.340442  501.93027  ]\n",
      "696 0.8336077 0.35716155 [1.1424453e+01 2.2044779e+01 2.3904850e+01 2.6215248e+01 2.6481733e+01\n",
      " 2.7179234e+01 2.8086304e+01 2.8796486e+01 3.0560547e+01 1.1894954e+04]\n",
      "697 0.9083872 0.46960545 [-9.16071609e-03  1.44768450e-02  6.99880272e-02  1.15249604e-01\n",
      "  1.52024314e-01  1.68866023e-01  1.97600797e-01  2.23972857e-01\n",
      "  2.47287288e-01  1.50372192e+03]\n",
      "698 0.72997427 0.5245873 [-9.9523857e-02 -6.4715780e-02 -3.1961106e-02  1.0389996e-03\n",
      "  7.2491979e-03  2.4799347e-02  5.5446114e-02  7.0342220e-02\n",
      "  1.0714829e-01  1.4109474e+02]\n",
      "699 0.6442214 0.31492412 [  3.4880967   4.8155804   5.7710447   6.1142483   7.0638676   7.6436377\n",
      "   7.935997    8.873268   10.345993  587.8317   ]\n",
      "700 0.7553083 0.6013453 [  0.5576052    0.7404045    0.87488616   0.9305484    1.1908939\n",
      "   1.2603661    1.4361886    1.5823737    1.9180282  532.1789    ]\n",
      "701 0.5547521 0.48919383 [-1.4936960e-01 -9.7592361e-02 -6.2545605e-02 -1.9322312e-02\n",
      "  1.2637581e-02  2.8216381e-02  4.6162553e-02  7.6497063e-02\n",
      "  8.5377872e-02  4.5070343e+02]\n",
      "702 0.036337256 0.73736763 [  5.5775614   7.1819386   7.869356    9.0562935   9.172004   10.229613\n",
      "  10.669889   13.711168   13.773844  179.11407  ]\n",
      "703 0.3433628 0.13731758 [ 149.29813  174.90817  186.79765  191.38458  204.92741  219.69864\n",
      "  221.76749  241.59554  250.6549  5314.734  ]\n",
      "704 0.5380125 0.5289349 [-7.0394836e-02 -5.5264812e-02  7.5761743e-02  1.0660671e-01\n",
      "  1.5403773e-01  2.7680480e-01  3.0398592e-01  3.8614228e-01\n",
      "  5.7387930e-01  6.9538000e+02]\n",
      "705 0.5829654 0.5375072 [-7.4893154e-02 -2.7677603e-02  1.2709405e-01  1.7269683e-01\n",
      "  2.1824357e-01  2.3618750e-01  3.6288774e-01  4.1917440e-01\n",
      "  5.1942933e-01  3.9324368e+02]\n",
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      " -2.0407233e-02 -1.8047543e-02 -1.3370929e-02 -8.7438049e-03\n",
      "  2.8712381e-02  6.3267407e+02]\n",
      "707 0.34610498 0.27557373 [  29.033373   37.033165   40.718533   42.951653   43.394424   44.52162\n",
      "   46.504295   48.696926   52.83804  2222.996   ]\n",
      "708 0.13312769 0.53556967 [5.2843410e-01 6.3940692e-01 7.3026246e-01 9.1351616e-01 1.0409449e+00\n",
      " 1.0753509e+00 1.1549937e+00 1.2106552e+00 1.4334564e+00 1.1329979e+03]\n",
      "709 0.66276383 0.6120037 [  1.4744455   2.115117    2.229521    2.807557    3.169612    3.5932634\n",
      "   3.828365    4.320129    4.906208  905.88806  ]\n",
      "710 0.8021618 0.72826785 [   97.22968   156.28094   159.28323   169.78027   176.75967   177.1885\n",
      "   184.50497   188.60269   192.98401 24180.902  ]\n",
      "711 0.14472532 0.38908115 [  2.25775     2.639014    3.0078156   3.3399625   3.7983873   4.1027102\n",
      "   4.273291    5.2776294   5.6511574 304.41904  ]\n",
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      "   4.560741    5.2214828   5.53737   240.70168  ]\n",
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      "    4.7319293    5.084021     5.527547     5.926259  1900.4028   ]\n",
      "714 0.927189 0.63955677 [7.7421921e-01 1.0972129e+00 1.1401430e+00 1.2412009e+00 1.4306184e+00\n",
      " 1.4760282e+00 1.6057831e+00 1.7841961e+00 1.8631600e+00 1.5746759e+03]\n",
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      "  3.4536445e-01  4.7634491e-01  5.4436141e-01  6.3074648e-01\n",
      "  8.9215523e-01  1.8582231e+02]\n",
      "716 0.18037784 0.49151978 [-1.2888524e-01 -9.8339796e-02 -7.8279063e-02 -4.3908615e-02\n",
      " -2.7857276e-02 -3.6567266e-03  7.6789521e-03  3.2535989e-02\n",
      "  3.6642458e-02  4.4520999e+02]\n",
      "717 0.70716274 0.5464478 [7.0943445e-02 1.6271754e-01 2.6002678e-01 3.5783130e-01 4.4959250e-01\n",
      " 5.0141335e-01 6.3904124e-01 7.1250170e-01 8.2580948e-01 7.4602509e+02]\n",
      "718 0.11304915 0.68010396 [ 1.8121538  2.1100564  2.457228   2.9164042  3.3222554  3.5748365\n",
      "  3.9582307  4.398552   5.5878286 44.988255 ]\n",
      "719 0.027626514 0.73511654 [  35.907032   36.83458    41.283028   43.089798   44.841362   47.602554\n",
      "   50.078728   52.361313   58.03507  1477.6149  ]\n",
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      " -5.0078429e-02 -4.4640575e-02 -3.6359563e-02 -2.8105669e-02\n",
      " -1.1487025e-02  1.0822049e+02]\n",
      "721 0.07461858 0.3114609 [ 116.77586  124.26863  132.43202  136.54596  147.50568  151.54414\n",
      "  155.87614  163.04106  170.85553 8919.767  ]\n",
      "722 0.8859211 0.6187424 [1.3534037e+00 1.4372803e+00 1.9731656e+00 2.1823165e+00 2.4541206e+00\n",
      " 2.5485001e+00 2.6278608e+00 2.9837079e+00 3.2228692e+00 2.2779436e+03]\n",
      "723 0.21273601 0.7423486 [ 10.541889  12.239495  12.520484  13.750034  15.133694  16.299206\n",
      "  17.384804  18.926748  20.036833 401.85892 ]\n",
      "724 0.510818 0.8232156 [  88.95958    93.057396   98.96769   103.37266   109.1614    111.904526\n",
      "  117.691696  123.40503   142.08743  3934.1624  ]\n",
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      "  5.6956973e-02  6.9435649e-02  9.3286760e-02  2.4748793e-01\n",
      "  2.8242603e-01  5.4304382e+01]\n",
      "726 0.69252694 0.4943854 [-1.35586336e-01 -8.05129632e-02 -1.94049068e-02 -2.75701471e-03\n",
      "  5.44368401e-02  1.10470064e-01  1.44517422e-01  2.09425539e-01\n",
      "  3.37078422e-01  5.38426953e+03]\n",
      "727 0.96738255 0.30968115 [4.4682698e+00 7.4844565e+00 8.7006016e+00 8.8857489e+00 9.5048437e+00\n",
      " 9.6061077e+00 1.0267036e+01 1.0639246e+01 1.0967282e+01 1.2225138e+04]\n",
      "728 0.83723354 0.4334745 [-8.1047088e-02 -6.2191687e-03  4.2928956e-02  9.0871178e-02\n",
      "  1.2455079e-01  1.6879436e-01  1.8012872e-01  2.2063313e-01\n",
      "  3.8146740e-01  1.9542780e+02]\n",
      "729 0.6666163 0.41452855 [5.4680997e-01 1.0702465e+00 1.3743203e+00 1.6738604e+00 1.8471339e+00\n",
      " 2.0897958e+00 2.1392784e+00 2.6392052e+00 3.2261887e+00 1.0239542e+03]\n",
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      "  6.66146353e-02  1.27931118e-01  1.92659825e-01  3.37207019e-01\n",
      "  4.30185556e-01  1.11156403e+02]\n",
      "731 0.6961323 0.29857624 [  3.0082176   3.7338912   3.8718004   4.242043    4.657811    5.0780907\n",
      "   5.632702    5.8374486   6.47172   394.45465  ]\n",
      "732 0.4302317 0.55761796 [8.9505348e+00 1.1577141e+01 1.2248819e+01 1.3899771e+01 1.4996031e+01\n",
      " 1.6548708e+01 1.6830666e+01 1.8886354e+01 1.9655546e+01 1.2874470e+04]\n",
      "733 0.86835206 0.46420938 [3.2687804e-01 6.1733961e-01 8.2690686e-01 9.9895227e-01 1.0526863e+00\n",
      " 1.1532463e+00 1.4470453e+00 1.6362808e+00 1.9953599e+00 1.1223298e+04]\n",
      "734 0.6988282 0.6037075 [1.5911029e-01 3.4053606e-01 5.6511527e-01 6.4626354e-01 7.4071187e-01\n",
      " 8.1478876e-01 9.4942600e-01 1.1903501e+00 1.2737509e+00 1.8146162e+02]\n",
      "735 0.8979391 0.59544295 [4.6810098e+00 7.9880466e+00 8.6078205e+00 9.7343779e+00 9.9999685e+00\n",
      " 1.0669828e+01 1.0858830e+01 1.1581957e+01 1.2691156e+01 1.8323273e+04]\n",
      "736 0.42517412 0.41154855 [  0.1965086    0.49725598   0.7197609    0.96054614   1.2022743\n",
      "   1.3914182    1.6233648    1.7367249    1.9381404  183.47148   ]\n",
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      "   21.512932   22.951418   24.182896 1175.8092  ]\n",
      "738 0.20159948 0.4400683 [   4.4761753    5.8614097    6.106708     7.021616     7.474197\n",
      "    7.8356094    8.041392     8.869632     9.891378  4192.546    ]\n",
      "739 0.36345375 0.2656048 [  7.0166125   7.8328185   8.548839    9.153583   10.1732025  10.515141\n",
      "  11.629438   12.37281    14.00704   290.00436  ]\n",
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      "  1.06741957e-01  1.22830205e-01  1.28792733e-01  1.64713189e-01\n",
      "  1.92682207e-01  2.50794849e+03]\n",
      "741 0.7354933 0.6699866 [   4.512652     4.8201747    6.2887454    6.9255114    7.3452816\n",
      "    7.6630316    8.435456     9.506032    10.079444  1362.4124   ]\n",
      "742 0.93580174 0.27775776 [  1.2040141   1.9684019   2.1065521   2.3268528   2.5572183   2.6530137\n",
      "   2.757826    3.093981    3.27126   913.88947  ]\n",
      "743 0.2804824 0.39175224 [ 0.33941448  0.41018504  0.53852135  0.7084009   0.799877    0.9329834\n",
      "  1.1438202   1.3883253   1.518728   44.58404   ]\n",
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      " -3.7995115e-02 -2.6577288e-02 -1.8673243e-02 -7.4210810e-03\n",
      "  2.3400651e-02  5.2074274e+02]\n",
      "745 0.983582 0.40765488 [3.0703057e-02 4.2608142e-02 5.8212794e-02 6.4846531e-02 7.1809605e-02\n",
      " 9.0370364e-02 9.2891872e-02 1.2911756e-01 1.4085273e-01 6.1259253e+02]\n",
      "746 0.57220733 0.36406404 [   5.3316336    6.7526665    9.07324      9.465506    10.092161\n",
      "   11.086519    11.572721    12.89043     13.7899475 1729.3262   ]\n",
      "747 0.89728177 0.8078176 [   8.607983   10.430874   11.538811   12.123084   13.015599   13.719524\n",
      "   14.149153   15.585304   16.385513 1699.5947  ]\n",
      "748 0.83415544 0.55159515 [-6.5681510e-02  1.2014432e-01  2.8291664e-01  3.8386929e-01\n",
      "  4.6131581e-01  5.1332927e-01  5.9470212e-01  6.8253583e-01\n",
      "  7.7338052e-01  1.4335713e+03]\n",
      "749 0.3239833 0.64996797 [  6.8102484   7.5581813   8.126029    8.840273    9.265813    9.693748\n",
      "  10.982912   12.094442   12.934769  731.2172   ]\n",
      "750 0.88888824 0.6683921 [  0.76372445   0.97457445   1.1335337    1.1756198    1.286198\n",
      "   1.4252772    1.5190433    1.6597546    1.8217056  496.92673   ]\n",
      "751 0.1688441 0.25065815 [  7.5180535   8.490205    9.221403   10.414158   10.610458   11.842148\n",
      "  13.362553   15.337072   18.305786  213.25029  ]\n",
      "752 0.516333 0.50133485 [-4.6463761e-02 -4.3460209e-02 -3.6563363e-02 -3.2312170e-02\n",
      " -2.8786343e-02 -2.3576792e-02 -1.8692618e-02 -1.8067284e-02\n",
      "  5.8047548e-03  1.8433441e+02]\n",
      "753 0.9767033 0.7197657 [7.2603106e-01 9.5097625e-01 1.0568910e+00 1.0724375e+00 1.1511325e+00\n",
      " 1.2873460e+00 1.4317495e+00 1.5304443e+00 1.5890417e+00 1.4109441e+03]\n",
      "754 0.16074336 0.32295722 [  6.2092175   6.9755926   7.410658    7.887015    8.964545    9.988483\n",
      "  10.462151   10.889802   12.745354  387.14612  ]\n",
      "755 0.16079903 0.4767241 [9.1631770e-01 1.1001494e+00 1.2709172e+00 1.5212789e+00 1.5981269e+00\n",
      " 1.9523922e+00 2.1162722e+00 2.4361765e+00 2.5417361e+00 6.4556865e+03]\n",
      "756 0.054569483 0.33566839 [  8.73175    9.137828   9.606287  10.7827    11.750246  12.255282\n",
      "  13.305559  13.721142  15.700029 597.1217  ]\n",
      "757 0.2954917 0.23869011 [  81.92739   102.01117   107.66723   114.87508   120.84419   124.22288\n",
      "  127.600624  132.97765   136.58173  4764.4565  ]\n",
      "758 0.91722536 0.41141385 [1.2530346e-01 1.5182370e-01 1.6223855e-01 2.0572975e-01 2.1132439e-01\n",
      " 2.2657260e-01 3.6911193e-01 4.7903976e-01 5.5366278e-01 4.7653220e+02]\n",
      "759 0.7256923 0.38335803 [   2.5956557    4.0793414    5.0241957    5.495958     6.223426\n",
      "    6.682459     7.4566007    7.9325285    9.150498  2392.653    ]\n",
      "760 0.43617678 0.6124901 [  3.5882375   3.8683486   4.53681     5.3013644   5.628581    6.287825\n",
      "   6.7850637   6.9438124   7.1438894 910.04065  ]\n",
      "761 0.80067647 0.40569192 [1.12354802e-02 9.01774764e-02 1.19706355e-01 1.65702194e-01\n",
      " 3.07900369e-01 4.08352911e-01 4.81740475e-01 5.39302647e-01\n",
      " 7.04350293e-01 1.35332535e+02]\n",
      "762 0.28575778 0.5546956 [-4.8317038e-02  3.7279716e-03  1.1584639e-01  1.9879538e-01\n",
      "  2.2038139e-01  3.0724144e-01  4.1705051e-01  5.3194368e-01\n",
      "  6.2466192e-01  5.0408901e+01]\n",
      "763 0.22676992 0.5691172 [  1.6638705   1.811741    1.9987166   2.5216575   2.6338592   2.7392945\n",
      "   3.2897294   3.3866332   3.7407434 780.6491   ]\n",
      "764 0.6983373 0.4806085 [-2.7985865e-01  1.8876414e-01  2.7572700e-01  4.3291613e-01\n",
      "  5.4621792e-01  7.6602316e-01  8.6632776e-01  9.9957097e-01\n",
      "  1.1116111e+00  5.8458770e+03]\n",
      "765 0.8436941 0.20956375 [  16.122849   25.24482    28.449495   30.264563   33.657505   34.58791\n",
      "   35.368954   37.31914    38.402824 2826.4705  ]\n",
      "766 0.559919 0.18293083 [  93.71302  111.23017  119.59106  125.31691  135.54414  139.40315\n",
      "  145.37962  153.65886  163.3117  5646.7812 ]\n",
      "767 0.95521665 0.4384596 [2.4539487e-01 4.8035160e-01 5.5962259e-01 6.8353176e-01 7.7040708e-01\n",
      " 8.7084532e-01 9.6560574e-01 1.0183071e+00 1.1892970e+00 7.6691416e+03]\n",
      "768 0.9049418 0.52279943 [-4.0140532e-02 -3.0268161e-02  3.4057345e-02  4.3788888e-02\n",
      "  5.9538841e-02  8.0772996e-02  9.0315431e-02  1.1868186e-01\n",
      "  1.6499850e-01  2.3074712e+03]\n",
      "769 0.3785993 0.34868369 [  16.987238   19.7415     21.696968   22.586914   24.81715    26.592754\n",
      "   27.778658   28.910976   30.974634 2708.1558  ]\n",
      "770 0.16561198 0.48338172 [-6.8983443e-02 -3.2821726e-02  7.1389988e-02  8.1088021e-02\n",
      "  1.3972022e-01  1.8940005e-01  2.4091750e-01  3.8978505e-01\n",
      "  4.4594663e-01  1.2662539e+03]\n",
      "771 0.17408836 0.56762415 [   43.99427     47.449734    52.17318     56.955753    58.432484\n",
      "    59.62207     61.020336    61.335655    65.58387  23536.576   ]\n",
      "772 0.11941624 0.3663429 [  4.1963687   4.4571495   5.0251775   5.924388    6.3087044   6.8675227\n",
      "   7.128256    7.5278296   8.221542  420.20132  ]\n",
      "773 0.21465373 0.5474804 [2.8602546e-01 5.3695071e-01 6.8220609e-01 7.5517863e-01 8.6531669e-01\n",
      " 9.4066900e-01 1.2553061e+00 1.3006791e+00 1.6972551e+00 6.0810547e+02]\n",
      "774 0.68874633 0.6601962 [  2.2600858   2.9153397   3.470888    3.9975517   4.0950913   4.4531603\n",
      "   4.9423537   5.216322    6.238739  549.55664  ]\n",
      "775 0.7339673 0.43461052 [-3.4812920e-02  1.0409220e-02  7.4459083e-02  2.0223667e-01\n",
      "  2.5529110e-01  2.7507180e-01  3.0892849e-01  4.0636206e-01\n",
      "  5.4944551e-01  1.6345140e+02]\n",
      "776 0.10984254 0.84882164 [  52.336586   56.136208   57.93958    60.834198   69.01682    72.05932\n",
      "   73.22662    75.871796   81.77827  1130.4844  ]\n",
      "777 0.88704073 0.54373914 [-4.0451750e-02 -1.9859634e-02 -1.1595852e-02  1.2907854e-02\n",
      "  1.9107245e-02  4.9573041e-02  7.0766479e-02  9.4755858e-02\n",
      "  1.0584530e-01  9.3766960e+01]\n",
      "778 0.8107821 0.52370095 [-8.5833460e-02 -3.0253759e-02  5.7540340e-03  1.8382484e-02\n",
      "  2.6423261e-02  5.5771358e-02  9.2626810e-02  1.0151705e-01\n",
      "  1.4337866e-01  2.2480196e+02]\n",
      "779 0.546397 0.8515478 [  287.22284   309.99408   322.34036   341.2186    377.2547    386.21912\n",
      "   392.06494   407.8919    443.08783 12291.741  ]\n",
      "780 0.6520872 0.44881576 [-9.5232986e-02 -1.0417807e-02  2.1163281e-02  4.6991516e-02\n",
      "  1.4886151e-01  2.3601767e-01  2.8500912e-01  3.7135473e-01\n",
      "  4.3349248e-01  9.4773476e+01]\n",
      "781 0.37747133 0.3266192 [   9.407237   12.178774   14.110632   15.004075   16.654154   16.981686\n",
      "   18.92534    20.313896   22.32095  1162.3638  ]\n",
      "782 0.1893841 0.6388717 [  1.5112069   1.7850922   1.8663918   2.0658996   2.6548173   2.8041248\n",
      "   3.1383312   3.5201402   4.3014584 121.2657   ]\n",
      "783 0.67593825 0.37585524 [  0.8951341   1.1907078   1.8783358   2.0991538   2.3393905   2.429852\n",
      "   2.894407    3.1385653   3.6575289 471.2261   ]\n",
      "784 0.4394982 0.38830167 [  3.0433786   3.771214    4.285786    5.461268    5.7936387   6.0586247\n",
      "   6.406154    6.7404366   7.2335153 865.68555  ]\n",
      "785 0.7636335 0.38611272 [  0.94446105   1.2279232    1.5806639    1.7565604    2.0705006\n",
      "   2.544094     2.6289113    2.8872669    3.0832412  736.57446   ]\n",
      "786 0.06451523 0.5257282 [6.02360778e-02 9.94487703e-02 1.21413164e-01 1.52418971e-01\n",
      " 1.66502118e-01 1.73188552e-01 2.23586172e-01 2.44694084e-01\n",
      " 2.97846913e-01 3.20988068e+02]\n",
      "787 0.9158193 0.8648095 [  7.5402937   8.202616    9.292044    9.595923   10.31803    10.724684\n",
      "  11.105683   11.912579   12.02385   772.0735   ]\n",
      "788 0.21889293 0.30817607 [  35.24259    36.29425    37.004997   38.71152    44.443623   45.482758\n",
      "   51.334045   53.781128   56.695053 2713.2732  ]\n",
      "789 0.27383363 0.5044563 [-1.34555101e-01 -1.08861715e-01 -8.32194164e-02 -4.49221134e-02\n",
      " -2.65462678e-02 -2.16410030e-02  1.90269481e-02  2.38149576e-02\n",
      "  4.38667536e-02  2.06607666e+03]\n",
      "790 0.4625169 0.5296103 [-1.8797113e-01 -3.5562027e-02 -1.3999402e-02  6.5044060e-02\n",
      "  8.2323238e-02  1.6544151e-01  3.4362555e-01  3.9446229e-01\n",
      "  4.2136052e-01  3.1777777e+02]\n",
      "791 0.04634261 0.46983695 [5.4868273e-02 8.9831308e-02 1.1444937e-01 1.3928017e-01 1.7307560e-01\n",
      " 1.8795361e-01 2.0047404e-01 2.2070591e-01 2.6665908e-01 2.2262646e+02]\n",
      "792 0.86864996 0.33438104 [ 0.2966961   0.34818414  0.45440146  0.5146894   0.61934125  0.6326577\n",
      "  0.75371915  0.8831971   0.91697985 68.87882   ]\n",
      "793 0.67360985 0.62743986 [  0.5048461   0.9255653   1.079021    1.124593    1.3978593   1.5786685\n",
      "   1.9142299   2.017393    2.2795057 184.9284   ]\n",
      "794 0.03635621 0.47609127 [2.3529643e-01 3.3072847e-01 3.3959758e-01 3.6464128e-01 4.1306001e-01\n",
      " 4.7350368e-01 4.8330274e-01 5.0437480e-01 5.3634596e-01 1.3621104e+03]\n",
      "795 0.44269645 0.39932537 [ 0.07945838  0.23336114  0.35066265  0.513461    0.6366477   0.76066107\n",
      "  0.91313636  1.0105156   1.1866046  41.16545   ]\n",
      "796 0.6938274 0.6785074 [  11.933551   16.465387   17.737879   18.81636    19.844868   21.036827\n",
      "   22.398073   22.861359   24.954018 3319.3958  ]\n",
      "797 0.82680607 0.3842521 [1.6939969e-01 3.5569093e-01 4.8013109e-01 5.0870484e-01 6.1118811e-01\n",
      " 6.6057229e-01 9.2661035e-01 9.3653500e-01 1.3444016e+00 2.6560187e+02]\n",
      "798 0.11954117 0.38721737 [  14.464085   16.384827   18.20976    20.174591   20.63548    21.651398\n",
      "   21.909449   23.53244    24.678457 3130.1277  ]\n",
      "799 0.0852294 0.7172373 [ 22.836313  24.916794  25.520327  27.165676  28.516794  29.211512\n",
      "  31.22871   35.122086  37.46363  945.45764 ]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for k in range(len(group_data[0])):\n",
    "    # H1, t, c1, d = hess_exp_lyapunov_binary_loss(0 * beta.flatten(), beta.flatten(), group_data[0][k])\n",
    "    rng = jax.random.PRNGKey(k + 2)\n",
    "    t = jax.random.uniform(rng)\n",
    "    H, tt, c, d = hess_exp_lyapunov_binary_loss(t * beta.flatten(), beta.flatten(), group_data[0][k])\n",
    "    print(k, t, binary_model(beta.flatten(), group_data[0][k]).mean(), np.linalg.eigh(H)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "2e8a6f4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100\n",
    "H = jax.hessian(lambda x, y: lyapunov_binary_loss(sigmoid(x), y, y))(np.ones(n) * 1/ 2, 0.75 * n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "id": "b71a5389",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array([-0.00059489,  0.00112573,  0.00171103,  0.00185994,  0.00244545,\n",
       "         0.00263842,  0.00360414,  0.00418008,  0.00471196,  0.01049092],      dtype=float32),\n",
       " Array([[-0.43736583, -0.61813766,  0.06984194, -0.37308535,  0.23060748,\n",
       "          0.03619352, -0.2920438 , -0.2159922 , -0.29928347,  0.08089706],\n",
       "        [-0.15833649,  0.34297872,  0.28886408, -0.0161324 ,  0.48196712,\n",
       "         -0.14468724, -0.1480574 ,  0.13414343,  0.19208393,  0.66599864],\n",
       "        [ 0.14454944,  0.06879359, -0.5867334 ,  0.18590851,  0.4386176 ,\n",
       "         -0.32643905, -0.4331654 , -0.22946444,  0.10760536, -0.2115233 ],\n",
       "        [-0.4241231 , -0.23687679,  0.02104214,  0.3603713 ,  0.15748222,\n",
       "          0.2727025 ,  0.21383236, -0.13736926,  0.66855145, -0.15157871],\n",
       "        [ 0.44726452, -0.32035536,  0.22872183,  0.5356779 ,  0.0816997 ,\n",
       "          0.05793631,  0.08726203, -0.44386876, -0.21740596,  0.31005126],\n",
       "        [ 0.07313117, -0.28525826, -0.29340038, -0.05731076,  0.39454895,\n",
       "         -0.24319851,  0.67960864,  0.35105667, -0.13725474,  0.07175884],\n",
       "        [ 0.55699843, -0.34452543,  0.02509945, -0.24909317,  0.12461445,\n",
       "          0.3615479 , -0.28495315,  0.38207412,  0.36563754,  0.0355335 ],\n",
       "        [-0.19582632,  0.13659105, -0.39715967,  0.3137323 ,  0.07202658,\n",
       "          0.64707005, -0.11159302,  0.26806554, -0.38119066,  0.18255258],\n",
       "        [ 0.0142701 ,  0.11786971,  0.5164948 ,  0.1874035 ,  0.464148  ,\n",
       "          0.05872078, -0.06861299,  0.22289991, -0.26436666, -0.58382607],\n",
       "        [ 0.16933353,  0.32277012, -0.05874227, -0.4585709 ,  0.31440133,\n",
       "          0.4259809 ,  0.3026408 , -0.52540004,  0.0014932 , -0.07390072]],      dtype=float32))"
      ]
     },
     "execution_count": 331,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigh(t[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "e561b9dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Array([0.0929051 , 0.09290527, 0.09290531, 0.09290534, 0.09290535,\n",
       "        0.09290536, 0.09290537, 0.09290538, 0.09290539, 0.09290539,\n",
       "        0.0929054 , 0.09290541, 0.09290541, 0.09290541, 0.09290542,\n",
       "        0.09290543, 0.09290544, 0.09290544, 0.09290544, 0.09290544,\n",
       "        0.09290544, 0.09290545, 0.09290545, 0.09290545, 0.09290545,\n",
       "        0.09290545, 0.09290545, 0.09290545, 0.09290545, 0.09290546,\n",
       "        0.09290546, 0.09290546, 0.09290546, 0.09290546, 0.09290546,\n",
       "        0.09290546, 0.09290547, 0.09290547, 0.09290547, 0.09290547,\n",
       "        0.09290547, 0.09290547, 0.09290548, 0.09290548, 0.09290548,\n",
       "        0.09290548, 0.09290548, 0.09290548, 0.09290548, 0.09290548,\n",
       "        0.09290548, 0.09290548, 0.09290548, 0.09290548, 0.09290548,\n",
       "        0.09290549, 0.09290549, 0.09290549, 0.0929055 , 0.0929055 ,\n",
       "        0.0929055 , 0.09290551, 0.09290551, 0.09290551, 0.09290551,\n",
       "        0.09290551, 0.09290551, 0.09290551, 0.09290551, 0.09290551,\n",
       "        0.09290551, 0.09290552, 0.09290552, 0.09290552, 0.09290552,\n",
       "        0.09290552, 0.09290553, 0.09290553, 0.09290553, 0.09290554,\n",
       "        0.09290554, 0.09290554, 0.09290555, 0.09290555, 0.09290555,\n",
       "        0.09290555, 0.09290555, 0.09290556, 0.09290557, 0.09290557,\n",
       "        0.09290557, 0.09290557, 0.09290558, 0.09290558, 0.0929056 ,\n",
       "        0.09290563, 0.09290563, 0.09290582, 0.09290588, 0.44656834],      dtype=float32),\n",
       " Array([[-0.03778392,  0.05222224,  0.        , ...,  0.014859  ,\n",
       "         -0.00782933,  0.10000011],\n",
       "        [ 0.7564595 , -0.6214805 , -0.00517972, ...,  0.02281909,\n",
       "          0.00839803,  0.09999919],\n",
       "        [-0.57864606, -0.5472574 , -0.00582881, ...,  0.15639736,\n",
       "          0.01722714,  0.09999999],\n",
       "        ...,\n",
       "        [-0.0094411 , -0.00896802,  0.01660865, ...,  0.01443101,\n",
       "         -0.04907687,  0.09999999],\n",
       "        [-0.0094411 , -0.00896417,  0.01239884, ...,  0.01443547,\n",
       "         -0.04908095,  0.09999999],\n",
       "        [-0.0094411 , -0.00896417, -0.00253967, ...,  0.01443547,\n",
       "         -0.04908095,  0.09999999]], dtype=float32))"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigh(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "a9febff8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Array([-0.2536845 , -0.2536845 , -0.2536845 , -0.2536845 , -0.2536845 ,\n",
       "       -0.2536845 , -0.2536845 , -0.2536845 , -0.2536845 , -0.2536845 ,\n",
       "       -0.2536845 , -0.2536845 , -0.2536845 , -0.2536845 , -0.2536845 ,\n",
       "       -0.2536845 , -0.2536845 , -0.2536845 , -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446,\n",
       "       -0.25368446, -0.25368446, -0.25368446, -0.25368446, -0.25368446],      dtype=float32)"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(H) - np.sum(H - np.diag(np.diag(H)), axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "347b373f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from jax.scipy.special import expit as sigmoid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "id": "e3a283f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "p = np.linspace(0.5, 1, 100)\n",
    "plt.axhline(y=0., color='black', linestyle='-')\n",
    "plt.axvline(x=0.5, color='black', linestyle='-')\n",
    "# plt.plot(p, -p * (1 - p) * (1 - 2 * p), label=\"P2\")\n",
    "# plt.plot(p, p * (1 - p) * (1 - 2 * p), label=\"P2\")\n",
    "# plt.plot(p, -p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"p (1 - p) (1 - 6p (p - 1))\")\n",
    "plt.plot(p, np.abs(p * (1 - p) * (1 - 2 * p)) - p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"P2 + P1\")\n",
    "plt.plot(p, -np.abs(p * (1 - p) * (1 - 2 * p)) - p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"-P2 + P1\")\n",
    "plt.plot(p, - p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"P2\")\n",
    "plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.05), ncol=3, fancybox=True, shadow=True)\n",
    "plt.xlim([0.5, 1])\n",
    "plt.ylim([-0.135, 0.2])\n",
    "plt.grid('on')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "id": "dfb2309c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "p = np.linspace(0, 1, 100)\n",
    "plt.axhline(y=0., color='black', linestyle='-')\n",
    "plt.axvline(x=0.5, color='black', linestyle='-')\n",
    "plt.plot(p, np.abs(p * (1 - p) * (1 - 2 * p)), label=\"|p (1 - p) (1 - 2p)|\")\n",
    "plt.plot(p, -p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"p (1 - p) (1 - 6p (p - 1))\")\n",
    "plt.plot(p, np.abs(p * (1 - p) * (1 - 2 * p)) - p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"P1 + P2\")\n",
    "plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.05), ncol=3, fancybox=True, shadow=True)\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([-0.135, 0.2])\n",
    "plt.grid('on')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "id": "b77620f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "p = np.linspace(0, 1, 100)\n",
    "plt.axhline(y=0., color='black', linestyle='-')\n",
    "plt.axvline(x=0.5, color='black', linestyle='-')\n",
    "plt.plot(p, np.abs(p * (1 - p) * (1 - 2 * p)), label=\"|p (1 - p) (1 - 2p)|\")\n",
    "plt.plot(p, -p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"p (1 - p) (1 - 6p (p - 1))\")\n",
    "plt.plot(p, -np.abs(p * (1 - p) * (1 - 2 * p)) - p * (1 - p) * (1 + 6 * p * (p - 1)), label=\"P1 + P2\")\n",
    "plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.05), ncol=3, fancybox=True, shadow=True)\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([-0.135, 0.2])\n",
    "plt.grid('on')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "id": "ef0f6d34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "p = np.linspace(0, 1, 100)\n",
    "plt.axhline(y=0., color='black', linestyle='-')\n",
    "plt.axvline(x=0.5, color='black', linestyle='-')\n",
    "plt.plot(p, (p * (1 - p) * (1 - 2 * p)), label=\"|p (1 - p) (1 - 2p)|\")\n",
    "plt.plot(p, -p * (1 - p) * (1 - 6 * p + 6 * p**2), label=\"p (1 - p) (1 - 6p (p - 1))\")\n",
    "plt.legend(loc='upper center', bbox_to_anchor=(0.5, 1.05), ncol=2, fancybox=True, shadow=True)\n",
    "plt.xlim([0, 1])\n",
    "plt.ylim([-0.135, 0.15])\n",
    "plt.ylim([-0.135, 0.15])\n",
    "plt.grid('on')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88303c50",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}