{ "cells": [ { "cell_type": "markdown", "id": "c7ba24a3", "metadata": {}, "source": [ "# SchNet, block by block: verifying the `xnn` implementation against the manuscripts\n", "\n", "The other fidelity notebooks in this folder compare each `xnn` model\n", "numerically against its **upstream code base**. SchNet is different by design:\n", "the `xnn` implementation is a *clean-room* build straight from the two\n", "manuscripts, and **no code (or weights) from schnetpack is used or imported**.\n", "The references are\n", "\n", "* Schütt, Kindermans, Sauceda, Chmiela, Tkatchenko, Müller,\n", " *SchNet: A continuous-filter convolutional neural network for modeling\n", " quantum interactions*, NIPS 30 (2017) — the architecture (its Fig. 2 and\n", " eq. 2 are quoted below), and\n", "* Schütt, Arbabzadah, Chmiela, Müller, Tkatchenko, *Quantum-chemical insights\n", " from deep tensor neural networks*, Nat. Commun. **8**, 13890 (2017) — the\n", " DTNN predecessor, for the conventions SchNet inherits (per-atom energy\n", " standardization, sum pooling).\n", "\n", "So the verification target here is the **equations themselves**: every block\n", "below is re-implemented independently in plain NumPy, directly from the\n", "papers, and evaluated with the *same weights* as the `xnn` model. In\n", "`float64` the two must agree to machine precision — and they do, block by\n", "block and end to end, including autograd forces against finite differences.\n", "\n", "Run with the **`xnn`** kernel." ] }, { "cell_type": "markdown", "id": "35496392", "metadata": {}, "source": [ "## 0. Setup: `float64` and a toy ethanol" ] }, { "cell_type": "code", "execution_count": 1, "id": "b6631eeb", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:39.413859Z", "iopub.status.busy": "2026-07-20T04:24:39.413741Z", "iopub.status.idle": "2026-07-20T04:24:41.539691Z", "shell.execute_reply": "2026-07-20T04:24:41.538889Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "xnn: 0.1.0 | torch: 2.5.1+cu121\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import math\n", "import numpy as np\n", "import torch\n", "import matplotlib.pyplot as plt\n", "\n", "torch.set_default_dtype(torch.float64) # machine-precision comparisons\n", "torch.manual_seed(0)\n", "np.random.seed(0)\n", "\n", "import xnn\n", "from xnn.common.data import structure_to_graph\n", "from xnn.common.models import ForceStressOutput\n", "from xnn.common.models.ops import shifted_softplus\n", "from xnn.cnn.models.schnet import SchNet\n", "\n", "print(\"xnn:\", xnn.__version__, \"| torch:\", torch.__version__)" ] }, { "cell_type": "markdown", "id": "07001150", "metadata": {}, "source": [ "### A toy system\n", "\n", "A (non-equilibrium) ethanol geometry, the molecule of the paper's MD17\n", "benchmark. At 9 atoms every pair is within the paper's basis range, so the\n", "graph is complete — exactly the no-cutoff setting the paper trains in." ] }, { "cell_type": "code", "execution_count": 2, "id": "d5ad1f97", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:41.541723Z", "iopub.status.busy": "2026-07-20T04:24:41.541516Z", "iopub.status.idle": "2026-07-20T04:24:41.570194Z", "shell.execute_reply": "2026-07-20T04:24:41.569484Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9 atoms, 72 directed edges (complete graph has 72)\n" ] } ], "source": [ "POS = np.array([\n", " [ 1.2001, 0.2043, 0.0000], # C\n", " [-0.0796, -0.5867, 0.0000], # C\n", " [-1.1938, 0.3097, 0.0000], # O\n", " [ 1.2242, 0.8386, 0.8900], # H\n", " [ 1.2242, 0.8386, -0.8900], # H\n", " [ 2.0810, -0.4406, 0.0000], # H\n", " [-0.1263, -1.2255, 0.8900], # H\n", " [-0.1263, -1.2255, -0.8900], # H\n", " [-2.0046, -0.1912, 0.0000], # H\n", "])\n", "Z = np.array([6, 6, 8, 1, 1, 1, 1, 1, 1])\n", "N = len(Z)\n", "\n", "CUTOFF = 30.0 # the paper's RBF grid end; no pair comes close\n", "graph = structure_to_graph({\"pos\": POS, \"atomic_numbers\": Z}, CUTOFF)\n", "print(f\"{N} atoms, {graph.num_edges} directed edges \"\n", " f\"(complete graph has {N * (N - 1)})\")" ] }, { "cell_type": "markdown", "id": "25949e05", "metadata": {}, "source": [ "## The SchNet architecture in one picture\n", "\n", "From the NIPS paper (Fig. 2), for a molecule with nuclear charges $Z$ and\n", "positions $R$:\n", "\n", "1. **Embedding** (eq. 3): $x^0_i = a_{Z_i}$ — one learned vector of $F = 64$\n", " features per element.\n", "2. **$T = 3$ interaction blocks** (Fig. 2 middle), each the residual update\n", " $x^{l+1}_i = x^l_i + v^l_i$ with\n", " $v^l = W_3\\,\\mathrm{ssp}\\big(W_2\\,\\mathrm{cfconv}(W_1 x^l)\\big)$\n", " (*atom-wise → cfconv → atom-wise → shifted softplus → atom-wise*).\n", "3. **cfconv** (eq. 2): $x_i = \\sum_j x_j \\circ W(\\mathbf r_i - \\mathbf r_j)$,\n", " the continuous-filter convolution. The filter-generating network expands\n", " the distance in Gaussian RBFs\n", " $e_k(r) = \\exp(-\\gamma\\,(r - \\mu_k)^2)$, $\\gamma = 10\\,$Å$^{-2}$,\n", " $\\mu_k \\in \\{0, 0.1, \\dots, 30\\}$ Å, and feeds them through **two dense\n", " layers with shifted-softplus activations**.\n", "4. **Readout** (Fig. 2 left): *atom-wise (64→32) → ssp → atom-wise (32→1)*,\n", " the DTNN per-atom standardization $E_i = E_\\sigma \\hat E_i + E_\\mu$, and\n", " **sum pooling** $E = \\sum_i E_i$.\n", "\n", "The activation everywhere is the shifted softplus\n", "$\\mathrm{ssp}(x) = \\ln(0.5\\,e^x + 0.5)$, which keeps the PES infinitely\n", "differentiable so the forces $\\hat F_i = -\\partial \\hat E / \\partial r_i$\n", "(eq. 4) are smooth and energy-conserving by construction.\n", "\n", "Below we build the model with the paper defaults, then randomize the\n", "(zero-initialized) output head and set a non-trivial standardization so that\n", "every block contributes to the energy." ] }, { "cell_type": "code", "execution_count": 3, "id": "658423d6", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:41.571857Z", "iopub.status.busy": "2026-07-20T04:24:41.571742Z", "iopub.status.idle": "2026-07-20T04:24:41.585214Z", "shell.execute_reply": "2026-07-20T04:24:41.584612Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "F = 64\n", "T = 3\n", "RBF grid = 301 centers, spacing 0.100 A, gamma = 10.0\n", "params = 116,517\n" ] } ], "source": [ "model = SchNet() # the defaults ARE the paper: F=64, T=3, 301 RBFs\n", "torch.nn.init.normal_(model.readout[-1].weight, std=0.5)\n", "torch.nn.init.normal_(model.readout[-1].bias, std=0.5)\n", "model.set_energy_scale_shift(scale=0.37, shift=-1.42)\n", "model.set_atomic_energies([1, 6, 8], [-0.50, -1.00, -2.00])\n", "model = model.eval()\n", "\n", "print(f\"F = {model.embedding.weight.shape[1]}\")\n", "print(f\"T = {len(model.interactions)}\")\n", "print(f\"RBF grid = {model.rbf.centers.shape[0]} centers, \"\n", " f\"spacing {float(model.rbf.centers[1] - model.rbf.centers[0]):.3f} A, \"\n", " f\"gamma = {model.rbf.gamma}\")\n", "print(f\"params = {sum(p.numel() for p in model.parameters()):,}\")\n", "\n", "# numpy views of the weights: the SAME parameters drive both implementations\n", "def W(lin): return lin.weight.detach().numpy()\n", "def b(lin): return lin.bias.detach().numpy()" ] }, { "cell_type": "markdown", "id": "6c29b8cb", "metadata": {}, "source": [ "## Block 1: atom-type embedding · eq. 3\n", "\n", "$x^0_i = a_{Z_i}$: the initial representation is a per-element table lookup —\n", "identical elements start identical, which is what makes the model\n", "permutation-consistent from the first layer." ] }, { "cell_type": "code", "execution_count": 4, "id": "e517a479", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:41.586952Z", "iopub.status.busy": "2026-07-20T04:24:41.586836Z", "iopub.status.idle": "2026-07-20T04:24:41.609458Z", "shell.execute_reply": "2026-07-20T04:24:41.608805Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "shape: (9, 64) max |xnn - eq.3| = 0.0\n" ] } ], "source": [ "A = model.embedding.weight.detach().numpy() # the embedding table a_Z\n", "x0_ref = A[Z] # eq 3, verbatim\n", "x0 = model.embedding(graph.atomic_numbers).detach().numpy()\n", "\n", "print(\"shape:\", x0.shape, \" max |xnn - eq.3| =\", np.abs(x0 - x0_ref).max())\n", "assert np.array_equal(x0, x0_ref)\n", "assert np.array_equal(x0[3], x0[8]) # every H starts with the same vector" ] }, { "cell_type": "markdown", "id": "baa01301", "metadata": {}, "source": [ "## Block 2: Gaussian radial basis · \"filter-generating networks\"\n", "\n", "$e_k(r_{ij}) = \\exp\\!\\big(-\\gamma\\,\\|d_{ij} - \\mu_k\\|^2\\big)$ with\n", "$\\gamma = 10\\,$Å$^{-2}$ on the 0.1 Å center grid. This expansion decorrelates\n", "the initial filters, avoiding the flat training plateau of feeding raw\n", "distances (paper, Sec. 4.1)." ] }, { "cell_type": "code", "execution_count": 5, "id": "e22b02f3", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:41.611454Z", "iopub.status.busy": "2026-07-20T04:24:41.611264Z", "iopub.status.idle": "2026-07-20T04:24:41.966795Z", "shell.execute_reply": "2026-07-20T04:24:41.966109Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "shape: (72, 301) max |xnn - paper| = 1.3877787807814457e-17\n" ] }, { "data": { "image/png": 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srEwyGAzSpZde6l3X1tYmXXHFFZJGo+lVAF544YVSQkJCvz+LQBBM/t//+3+SVquVvvvuO++2ffv2SQkJCT6fZTabTZoyZYqUlpYmNTQ0SG1tbVJOTo6Un58vdXR0eNfJ164rrrjCe+2yWCzSOeecI8XGxkoNDQ19xuJwOKSrrrpKSklJ8bl2jR07VsrOzpbuvvtub1tIUVGRpNFopHvvvde77sorr5RycnJ8brRbWlp8PtuPFoAOh0PKz8+XxowZ43Ot/v3vfy8B0pdffundds4553gfXh1Zjh8VFSVdf/31/f6e3W63NG3aNCk1NVXat2+fd/sjjzwiAdK7777r3fbaa69JQL/9aTJ2u13SarXSmDFjfITk5s2bB9x3OEydOnVQ19O8vLwhHfdYSkBPOeUU6ZxzzpHi4uKk2NjYXh+oAz7/TmVycnKkSZMm+Wz77W9/K0VFRUnV1dWSJA1dAP773/+WFAqF9+9cUVEhqVSqAe9/BKFl5FpCnQQ0NTUhSRIxMTE9Xlu9erVPOVhqaipnnHGG93tJkti1axfl5eXY7XYkSSI+Pp7ly5dz6aWXDimOqqoqgB4lcxdffLHPGoPBgNFo9G4zGAxcc801Ax7fbrezbds2amtrcTgcxMfH09XVxapVqxgzZox3XXt7O7/73e+8rqdRUVH87Gc/47HHHqOrqwutVjvguT7++GM0Gg3t7e18/vnnfPfddzz88MNkZWX1WFtWVsb777/vjXH37t2MHTu2z9LH//znP2g0Gu/3KpWKn/70p8f0+5H/xnFxcb2+PmXKFK8ltk6nw263c8cddzB//nzvuY8kOTmZRYsW9XtOmfT09EGt6wu5lLc3l1r599DR0TGs4/bm2HksxxwqixcvZsaMGYwfPx7wlBNfcsklLF68mFtvvbXffauqqlCr1T7va5VKxU033dRj7Xnnnefz7+2uu+7iX//6F88++6zP+8/lcrFt2zaqqqro6upCr9ejVqv57rvvmD59OuAp2500aRL333+/Tyn52WefPeDPW19fz0MPPeT9952cnMzFF1/Mp59+6l3zyiuvYLVaeeaZZ7zrIiIiuOWWW7zvo6OJi4ujsbERl8vVw41XIAg2dXV1vPjii9x6663MmTPHu3306NHccccdPPjggzz55JOEh4ej0+lYsmQJU6ZM4corryQiIoLq6mrWr1/fo4Svvb2du+++2/tZaDAYePrpp5k0aRJvvfUWv/nNb3zWbtu2jaamJlwuF6NGjeKdd96hqKiIyZMne9e1trby4IMPet/L+fn5zJkzh6+++opHH30U8HzWREREoNfrvftFRUVxxRVX9Pk7+PLLLykuLuatt97ycev+85//zJtvvsnTTz/N+eef791eX1/Pn//8Z59y/AsvvJCvvvqq39/1qlWr2LRpE88//zyjR4/2br/nnnt47bXXePrpp7nyyiv7PUZv7Nixg66uLkaPHs2dd97p3T5lyhTa2tr4wx/+wLp168jMzOThhx+moKAAgNdff52nnnoKgJycnB5O4H1xzjnn9Hr/cDT+cL4eiAULFnD//fd779UsFgs333wzN9xwA7GxsSxcuBAY+Np85DX0hx9+4K9//SuLFy8mOTl5WHEtXryYc8891/t3Tk9P54ILLmDx4sWDukcUhAYhAEOI/ObsbW7eDz/8wNatWwGPqFmwYAGffPIJ4Knvvvrqq2lsbGTKlClERkaiVCqx2WxUV1cPOY65c+eSlJTE3Llzueyyy5gzZw5z5szxsW//2c9+xpIlSxg7diyXXXYZs2bNYtasWYSFhfV77Lfeeos77rgDo9HI2LFjMRqNuN1ugB6xhoWFeT+sZTIyMnC73VRXVw/qQ/jDDz9EqVTS2NjIjz/+yLx587j99tt7XXv22Wfz+uuve793u93cdtttnHfeefz444+ceuqpPuvfeOONPmvjh/v7kXspjhSWR5Kfn4/L5aKkpITx48fz5JNPUlFRwRdffNHr+qlTp7JkyZJ+z+kvZEHeW5+f3Ndy5I3JUI7r72MOhdraWpYuXcq1117r87vMyMjg3XffZfPmzUydOrXP/RctWsSTTz7J2LFjueKKKzj77LM5++yze/23M23aNJ/vlUolU6dO9bm5+uqrr7jppptwOp1MmDCBiIgI702h/B5qaWmhtLSU//f//l+vVuADkZ6e3uMBUEZGBo2NjVitVsLCwti6dSuJiYk9Rrz097vQarW43W4cDocQgIKQs3HjRpxOJ2q1mk8++cTbFydJEq2trTgcDoqLi70jb0aNGsWbb77JhRdeiCRJvP32272O/dFoND59+gATJkxAr9d7r+MA999/P0888QSjRo0iOzubsLAwbz9udXW1jwAsLCzs8VmXkZHBpk2bvN9fffXV/OIXv2DChAlccsklnHXWWUyfPr3fh6VyPKeddprPdq1Wy+TJk3vM78zMzCQ2NrZHHHV1df0+mO3rPEqlklNOOYUPPvgASZKG/Hkl//y33XZbj9euueYabDYbzzzzDJ9++ilz585l7969mEwmFixYwLRp0/j66699rvsD8fjjjw8pvkAyf/58n++NRiP/+te/+Pzzz3nmmWe8AvDIa/PRfx+Hw+H9d9Xe3s61117L7NmzufHGG4cVU1lZGd999x2/+tWvfK6X2dnZPPvss+zdu5e8vLxhHVsQWIQADCFxcXEkJiZSVFTU47U//OEP3v8/8iLgdru57LLLSEtLY8eOHT4CIzU11afRW573Ih3V/H20uUN8fDy7du3ilVdeYdmyZdxyyy10dHRw4YUX8tZbbxEeHs6FF17I5s2beeutt/j66695/PHH0el03H///dx99929/nwHDx7khhtu4Be/+AUvvPCC94O+srLS5+Irc+SNrYz84dVbQ31vvPvuu97f15YtW5g1axZXXnkln3322YD7KpVK7rrrLv7xj3/w0ksv9RCA/TGc3w8czvw1Nzf3+ro8+66oqIiIiAgeffRR7rzzTnJzc3tdX1tby+rVqwcV8+mnn35M8xrj4+PRaDQ9zIQA77bhPBVNTU31+zGHwuuvv05MTAytra09MlujRo3i5Zdf7lf0TJgwgT179vDqq6+yYsUKXnzxRZxOp/d9cOQcpt6e0BoMBu97tL29ncsvv5y5c+fywQcfeJ/CO51O9Hq99z0kvz+OzEAPhd7mUMnvPbvdTlhYGF1dXb0+0NDr9X3exDU1NREeHh5w0S4QDAb5YeumTZuoqKjo8fqiRYt6vIcsFotXqERHR/d6XL1e32O+mkKhQK/Xe9/LS5cu5c9//jMvvfQSv/jFL7zrZBOWo6+Hfb0nj7wW3nzzzYwdO5Z3332X//znP/zpT38iMjKSJ598steKAzj80LG3zwqj0djj/qCvOCRJ6lcADnQel8uF0+ns8+FnX2zatAmtVuuTwQWoqKhg6dKlVFRUkJaWxqxZs/j8889ZsmQJ1113HbGxscTGxrJr164hnW/FihV9Xp+PJCIignPPPXdIx/YHJpOJvLw8H3M0+RpZV1fXo9Knrq6OKVOmAPDJJ59QXl7eQ7w1NzdjtVpZsmQJ6enpPUT8kbzyyiskJydTW1vb43qZkZHByy+/zJNPPnnMP6fA/wgBGGIuvfRSXnjhBbZt2zaoQdMVFRVUVFRw1113+dyMNTU1UVNT4/MEMTExEYDGxkaf1P7+/ft7HDc2Npbf//73/P73v8fpdPLmm29y44038swzz/DAAw8AMGnSJG+Mzc3N3H777dxzzz3Mnz+/19jXrVuH0+nkuuuu87lBHOoH8HCZMmUK9913H/fccw8ffvjhoEpj5dKe3lxVB2Kovx/wZF7Cw8N7uNDJZGdno9FoKCoq4r333iMuLs7n4cDRbNq0adAlwO+9916/pUIDodFomDp1Kps3b+41DrVa3a9Q6ovTTz+dv//97zQ3N/uUUcpPfvu7GB0rkiTxyiuvcM0113jLhY7kxRdf5O677+bpp5/uVbzJZGVl8dBDD/HQQw/R2dnJI488wqOPPspZZ53F5Zdf7l23f//+Hjcy+/btY9SoUYCn3Kmjo4NrrrnGZ4hzUVGRjyNgQkICERERvT5M8hdZWVn88MMPPW76Dh482KvDIHh+vsG4yQoEwUAuUbviiiv41a9+NeD6oqIibr75Zi688ELa29u55ppr2Lp1a48S9Y6ODhoaGryOi+C5Jre2tnrfy6tXr0ahUHDttdf67Hus18Pp06d7y8Bra2u5/vrr+eUvf8lPfvITUlJSeqyXK2lKS0t7vF5aWuqN91g58jxHfwaUlpaSmpo6ZPEHnuvA5MmTezyM2rJlC2lpaT4PNWfMmMHmzZu57rrrhnwemd///ve9XuOOJi8vj+Li4mGf51iora31eThx+umnA7B582YfAVheXk5jY6P3GpqRkcGiRYvYsGEDGzZs8K5ramrCarXy/vvvM3PmzD6vuS6Xi9dee42bb76ZBx98sMfrTz31FE888QSPPPLIoFp4BMFFjIEIMX/84x9JTU3luuuuo6GhYcD1CQkJKJVKDh486LP9scceQ6fT+WyTRceR9shdXV28+eabPuuqq6t9bibVajVXX301arXaK4SOfloaExPj7UHrK25ZdB4Zq9Pp5Lnnnhvgp/Qfd9xxB6mpqfzhD38Y1EiCZcuWAXifkA2W4fx+wNMbNmPGDJ8P3yNRq9WMHj2a119/nU8++YRnnnmm3yyP3AM4mK9j7QEEuOGGG9i/f7/PvzE5c3bxxRf7CLj169d7+xn74/rrrwfwsZGWJIl//etf5OTkcNZZZ3m3b9y4scfokWNh5cqV7Nu3j/POO6/X188//3za29v597//3ecxKisrfb43GAxcddVVQM8HC2+++abPv8tt27bx448/ctlllwG9v4fAM37jSEGoUqm49tpr+eKLL9iyZYvPWpvNRltbW5/xDpZLL72Urq4uXnnlFZ/tr7zySo/sB3iyLdu3b2f27NnHfG6BwB9MnjyZqVOn8re//a3XsQdHfo5bLBYuueQSEhMTeeONN3jvvffQ6XRcdtllPcYgaLVaXnzxRZ9tL7zwAoD3gVxycjKSJPmco7W1lVdffXXYP8/R152kpCQWLFiA2+32GfVyJAsXLkSv1/e4Dq9cuZLt27cf00PBI5k/fz6RkZG88MIL3rYP8Ai1//73v8M6j81mY/fu3T5+CDItLS09MrQxMTH9jswZDOecc86grqdHl2ceK0uXLuXbb7/1fm+323sdCfXuu+9SVVXl4wnwk5/8hKSkJF566SWftS+++CIajcb7EOLss8/2jiU58isnJ4eYmBiWLFnC//7v//YZ4xdffEF1dXW/18uGhgafXnLByEFkAENMYmIiK1eu5IorriA/P59rrrmGSZMmoVarqa6u5vPPP8fpdHprqA0GA7/+9a954YUX0Gq15Obmsnz5cqKionwarcHz9Gvu3Lncdttt1NTUYDKZ+Oijj7jssstYv369d913333HQw89xKJFi8jLy8PlcvHuu+9iMpm45ZZbAM9TsLq6OubOnUtWVhY1NTU899xznH766T435Ecyc+ZMTj/9dP7f//t/VFRUYDQaee+997jsssu8M3wCjV6v549//CO33nqr90mVTHl5ubfswW63s2PHDv7xj39wyimn8Nvf/nZI5xnO70fmyiuv5LrrrqO8vJzMzMwer+fn5/PJJ58wb948Lrnkkn6P5a8eQHl2ndx3V1FR4T3uKaec4o3zhhtuYOnSpVx22WXce++9xMTE8MILLxAeHs6zzz7rc8y//vWv/Pvf/6ampsanv/RopkyZwv333899991Ha2srY8eO5YMPPmDHjh18++23Pr1kf/vb33jnnXeorKz0Pvl1uVzeBv+NGzd6/yuXIS5YsKDHwxKZl19+GYPB0GMmo0xmZiYFBQW8/PLLXqHa2zE+++wzFi5cyJgxY2hvb+df//oXWVlZPtk/8Fyozz//fC699FKampp4+umnmTp1Kvfccw/gyVhcfPHFPPDAA5jNZpKTk/nkk0+YMWNGjwcBf/nLX9i1axdnnnkmv/71rxk7dizl5eW8//77fPDBB72Wcg2FefPmcdNNN3H77bezb98+xo0bx6pVq8jNzUWj0fQoA/3qq69wOp3DMnoQCAKBQqHggw8+4Pzzz2fs2LHcdNNNZGZmUl1dzZo1a2hoaGDNmjUA/OIXv6CsrIy1a9cSGRlJZGQk77//Pueccw533XWXj4CKjo7GbDZzyy23cNppp7FhwwZeeukl7r33Xm8VxFVXXcXjjz/OhRdeyB133IHFYuHtt9/mF7/4Bb///e+H9fNce+21hIWFcdZZZ5GWlkZ5eTl//etfueCCC7wGVkeTmJjISy+9xA033MDChQtZuHAhlZWVPPPMM8yePZvf/e53w4rlaCIiInjttde44oormD9/Ppdddhl1dXU888wznHLKKb1mjAZi27ZtOJ3OXgWgXq/vMTfYbDYP2Ic/EP7sAWxubvbOVdy9ezcAy5cvZ9++feh0OhYsWOBde9NNNxEVFeXNKlqtVk477TTOOeccJkyYgMFgYM2aNbz++uucd9553Hvvvd59w8LCeO2117jooou47LLLWLhwIVu2bOG5557jmWee6XGvOFxefvllYmJi+myXGTt2rLcMdKjmhILAIwTgCCAnJ4dNmzaxYsUK75dSqSQ5OZlrrrmGDz/80OeG+W9/+xtnnHEGK1eu5Mcff2ThwoVcfvnl/Pa3v+1h5PDJJ5/w4osvsmXLFpKSkvj73/+Ow+FgzZo13mNec801nH322bz//vusWrUKjUbDhRdeyIcffuht/n7//fdZvXo1X3/9NV999RWxsbE888wzXHTRRd5MxOjRo1m0aJG3NE6lUrFixQpeeukltm3bhslk4tFHH2Xq1KmsXLnSx/DllFNO6bUcJCsri0WLFhEREdHv7/DUU0/FZrP1ajRx4403snbtWvbs2QN4smqyU6Zcs67VaklLS+Ott97iwgsv9LmZnTZtGq2trf2WMAzm99MXl19+OXfddRdvvvkm9913X4/XZafUYGZOv/vuO2854dG/q7i4OK8AVKlUfPLJJ3zwwQcsX74cu93O1VdfzU033dTjb1ZRUUFeXp5PmVRfPPjgg8yePZslS5bw1VdfMXnyZF544YUepVfy3/3IckyHw+HTi7Bo0SKqqqq82+bOndurAHS5XN4+0L4EIsD//u//smzZsl6fOIPHjfPSSy/l448/ZtmyZYSHh3P77bdzxRVX9BBts2fPZv78+bz22mu0trbywAMPcPPNN/v0zH3wwQe89tprrFu3jqqqKn79619z/vnnU1xc7JOpNhgMLF++nM8++4xly5axfPlycnNz+frrr72/t6SkJBYtWuTjOnvmmWfS2tra4+fIz89n0aJFPv/uFy9ezHnnnceXX37J6tWrueiiizj33HO59957e/xsb731FjNmzOhhjiEQhJLs7Gx27NjBhx9+yI8//khRUREZGRn88pe/9LpfbtmyBbvdzmuvvcbEiRO9+86aNYt//vOffPPNN+zbt8/Hxfrxxx/n3XffZdmyZWg0GpYuXcpPfvIT7+txcXFs376df/zjH6xevZqUlBTee+89JEli/fr1Pm0a5557bo9rOXgymEdm81euXMm3337LihUr2LlzJwkJCbz++us+Lp6FhYUsWrTIJ0v/85//nGnTpvHOO++wYsUKwsPDefnll7nkkkt8rqGzZs3qNVNaUFDAokWLBry2XXzxxezZs4c33niD77//HoPBwN/+9jeuuOIKn+u9fJ0f6CFVZ2cnixYtYubMmT1ey8nJ4dChQ3R2dnqvByUlJT6/i1DT1NTU49q0bt061q1bR0REhI8AXLBggc91LSoqij179vDhhx+yceNGGhoaSElJ4YsvvuDcc8/t8QDuvPPOY+fOnbz++ut8+eWXJCQk8OOPPw6qhWLOnDl9ZpBl7HY7BoOB3/3ud71WgMjceeedrF69GovFMuwedUFgUEh9NW8IBIKg8dxzz/HII49w4MCBHh+Sl112GZs2beqzT/B4oKOjg5iYGN59913xJBDPg5mLL76YtWvXevs1jld27drF+PHjefXVV71Z0aKiIsaPH8+KFSuYNWtWiCMUCALHddddx9dff+0ztkkQfNxuN6NHj+bXv/41d911F+vXr2fWrFns2rWLnJwc77r333+fhx9+OGheBALBSEX0AAoEI4Bf/epX/OQnP/EpzZXZsmXLkHsSRxrl5eXceOONA5awCkY2vfWg/PWvf0Wr1fpkO9asWcM999wjxJ9AIAgKSqWSd955h6effpqUlBRmz57NM8884xV/P/74I+PGjeN3v/udt4T95z//eYijFghChygBFQhGAGq1mtdee63H9vb2dg4cOMANN9wQgqj8x7hx43qYJAiOP5588kn279/P7NmzUalUfPHFF3zxxRc8//zzXtdhYNgzpQQCgWC4TJ8+nYqKCg4ePEhSUhLh4eHe1yZOnNhjTIEoSRSczAgBKBCMYLRaLRs2bCA7OzvUoQj8SGpqKosWLeoxYHmk85e//IVPP/2UVatWUVtbS2FhIQ8++OCwxn0IBCcCffWvC0KDRqPxKfmUMZlMjBs3LgQRCQQjE9EDKBAIBAKBQCAQCAQnCaIHUCAQCAQCgUAgEAhOEoQAFAgEAoFAIBAIBIKThJOyB9DtdlNdXU14eHiP2SkCgUAgODGRJImOjg5SUlL6nV01EhHXLYFAIDg5CcS166QUgNXV1aSnp4c6DIFAIBCEgMrKStLS0kIdxpAQ1y2BQCA4ufHnteukFICyNXBlZSUREREhjkYgEAgEwaC9vZ309HQfe/jjBXHdEggEgpOTQFy7TkoBKJfPREREiAupQCAQnGQcjyWU4rolEAgEJzf+vHYdX00QAoFAIBAIBAKBQCAYNiNCALpcLlpbW3E6nUPaz2azBSgigUAgEAj6p76+no6OjiHtM5xrnUAgEAgE/iSkArC6upoHH3yQzMxMoqOjWb169aD2e+CBB4iKisJkMpGTk8PXX38d4EgFAoFAIACr1cpLL73EpEmTSE5O5r777hvUfp999hkZGRkkJycTFRXF3XffjSRJAY5WIBAIBIKehFQAvvHGG0iSxJIlSwa9z/PPP8+zzz7L0qVL6ezs5Prrr+eiiy5i3759AYxUIBAIBALYunUrW7Zs4fXXX2fy5MmD2qe4uJhLLrmEO++8E7PZzMqVK3nppZf461//GuBoBQKBQCDoSUgF4L333suf/vSnIVmaPvvss9x0003MnDkTrVbL//3f/5GUlMSLL74YwEgFAoFAIIDp06d7M4CD5aWXXiIzM5M77rgDlUrFKaecwvXXX88LL7wQuEAFAoFAIOiDEdEDOFgaGxs5cOAAZ555ps/2WbNmsX79+qDG0m5z4HKPkPIdtxtGSCmRW3KPmLKmkRIHjKxYRgqSJI2Y38vIimXkvIfcI+j3cjyzYcMGZs6c6bNt1qxZlJWV0djYGKKoBCcTK/fWsbK4DmuXK9ShCASCEcBxNQaivr4egLi4OJ/tCQkJ/QpAu92O3W73ft/e3n7MsTz42W6+3V3HgonJ3PuTAiL0mmM+5pDpbIZv74PdH4NaC1Ovg7PvBbUu6KHUmGt4fOPjrDq0ikhdJNeOvZZrCq9BqQj+MwZbSQl1jzxK56ZNaFJSiL/9NiIXLAh6HADVpa38uKSU+ooOYlOMTF80hozC2JDEUrphDavfe5OWmmqSc/KYfd0vSBqdE/Q4JEnCsqGWjhWVuDq60OdEEbVgNOq4sKDH4na7WbVqFevXr6erq4v8/HzOO+88TCZT0GNxuWzs3/8k1TWekvikpIsYM/p3qNXBj6Wpy8kD+6r4oqGNMJWCa1Pi+G1WEhrl8Tc+YSTQ0NDA9OnTfbbFx8cDnuva0dc0CMx1S3By8tm2am5/fysAmbEGvr5jFmFaVYijEggEoeS4ygDKuN1un++dTme/szEee+wxIiMjvV/p6enHHMPPz8ji5jOzWbq9hmteXo/ZHmRXN2srvLkQipfCzN/A5KthzQvwwbXgCm4sNeYarv36WnY17uL2KbdzVvpZPLXpKR5b/1jQswe2PXsov+pqnI2NJN59N/rCQqp/93uaXnk1qHEAlO9q4tNnt6JUKTjzslz0Ji1Ln99O6aa6oMey47tv+OzpR4lKSmb2dTfj7Ori3w/ew6Hi3UGPpf3bclo/3ocuO5LI80fhaLRS/8/tOBo6gxqHJEl8/PHHfP/994wfP56zzz6bsrIyXn31Vcxmc1BjcbvtbNt+A1XV75Oe9nPS06+jtvZjtm2/HpfLGtRYWhxOLt66j++a2vlNViKXJsbwQkU9t+w5iEtkA4eFQqHo4fwpf69S9X4jHojrluDkw+2WePrbvd7vy5s62Vs3NOdagUBw4nFcCcCUlBQA6up8b6Dr6+u9r/XGvffeS1tbm/ersrLymGOZlB7FHXNzeO8Xp7O/wcKfPgvyjfQXd0JLBVz/FZz1Ozj3YbjyPSj9FlY9FbQwnG4nv//v71Gg4J2fvMO1Y6/lgTMe4IEzHuD9ve/z+YHPgxaLy2zh0P/+Bm1GBln/fp+Yn19D6rN/JfYXv6D+qaewrN8QtFg6mm0se3U36YUxXPTbKUyYncbCOyYxZloiK94ooqXWErRY6g7s47tX/snEeedz0e/vZ/J5C7jiz0+QNDqHz595jM72tqDFYt3dRMfKSiLOyyLm8jzCz0wl4VeTUBrUNL1dhORwD3wQP7F+/Xp27tzJokWLOP/885k5cyY33ngjdrudjz/+OKgPL/btf5L29q1MnvQGo0ffyejs3zB58lt0dOyhdN+jQYtDkiR+U1xBo8PB51NzuD0zkT/lpLJ4bBZfNrTxYmVD0GI5kUhNTe1x3ZK/T05O7nWfQFy3BCcf3+yupbz58MM1BRAVFoKKJYFAMKIY8QLQarV65yxFRUUxbtw4vvvuO+/rbrebFStW9OivOBKdTkdERITPl78YlxrJ/f9TyIebD7FmX5B6OUqXwa4lcMHTkFh4eHvOPE828L9PQWNpUEL5T8l/2N6wnb/M+guJxkTv9ktyL+GC7At4YuMTtNpagxJL04v/xNnQQOpfn0HVXcKnUCiI/987CJsyhdoHHkDq6gpKLD8u2YdKo2TudYWo1J63mVKpYPY1+Rgitfz3/ZKgCAzJ7Wb5y38nNi2d2df9wpsp12h1/M//3o3L6WD1+28GPA4At91F62f70OdFE37WYeMnlVFD7FUFOBusdKyuCkosbW1tfPfdd5xyyimMGzfOuz0mJoaLLrqI/fv3s2vXrqDE0t6+g8rK18nOvpOoqGne7ZERE8kZcy9VVe/S1rYlKLF81djG143tPJmXzhiD3rv9vPhIbkmP5/EDNVRY7f0cQQCe8s3a2lpcLk+/1axZs1ixYoVP9co333zDpEmT+rweBfK6JTg5cLsl/vad517glrOyyU8KRwKeWVYS2sAEAkHICakA7OrqorW11dvbYDabaW1t9Rnwftttt3HGGWd4v/+///s/XnvtNd555x0OHDjAr3/9a+x2O7feemvQ45e5dFoak9KjePzr4sDf1LvdsPxByJwB4y/p+fqs34EpEVYGPmvQ6ejkH9v/wYLRC5ic0NMO/XfTfkeXq4vXd78e8FgcNTU0v/EmsTfeiDYjw+c1hVJJ0v3301VeTuvHnwQ8ltqyNvZvqeeMi0ejN/o+adVoVZx5WS6HiluoLGoOeCx7162mdn8pc264BZXaNxZjVDQzLruanSu+pakq8NkF89pqXGYHUQtH9yjZ1iQZMZ2RTMfKClwWR8Bj+e9//4tGo+Gcc87p8VpOTg55eXksX77cewMfSPYfeAaDYTTpadf1eC019UpMpgJK9/0l4J8tLknisQM1zI4J54L4qB6v3zUqiUiNiifKagMax0hHkiRqa2upra3F6XTS2dlJbW0tTU1N3jXLli0jOTmZsrIyAG699VacTie/+MUv2LNnDy+//DJvvfUWf/zjH0P1YwhOAr7dU0txbQcmnZpbzhrNU5dORKGAz7ZXs/5A08AHEAgEJywhFYBLliwhKyuL6dOnExkZydVXX01WVhbPPvusd43BYPB58nnllVfyz3/+k8cff5wzzjiD0tJSVqxY0WcZTTBQKBTcdW4e2w+1sTrQWcDSb6BuF8y5D3rre9ToPSWhuz8KeBbw430f02Zv49eTft3r67FhsVxVcBXvFr9Lmz2wZYbNr7+BIiyMmOuu6/V1fV4uEeefR9NLLyE5A9sjueXrcqISDeSdmtTr65njY0nIDGfTlwcDGockSWz4+AMyJ0wmLX9sr2vGn3MepugYNn46+Fmcw8Hd5cK8qgrj1ETUsb2bvYTPTgcJLGurAxpLe3s7W7duZfr06ej1+l7XzJkzh7a2toBnAdvat9PcvIrsUbejVPb05FIoVIzOvpO2ts20tW0OaCxLG1op7bRz96jeP0uNKhV3ZCbyUV3LSZ0F7OjoYNKkSUyaNIna2lo+++wzJk2axOWXX+5do9frSUxMRK32/E0TExP5/vvvqa2t5fzzz+df//oXr7/+OosWLQrVjyE4wXG7JZ5d7rkHuH5GFlEGLeNSI7nyVM8D0gc+243TFbySe4FAMLIIqQD82c9+Rmtra4+ve+65x7vmueeeY82aNT773XDDDezYsYO6ujqWL18+6GG8gWTGmFgKkiN4dXVZYE+09u+QdgpkntH3molXgjEeNvwrYGG4JTdv7XmLc7POJcXUd//lVQVX4XA7+GTfJwGLxWW20Prhh0T/7EpUJmOf62JvuglHdTUdK1cGLJb2Ritl2xuZfG4Gij4cExUKBVPPy6JmXxsNlYFrxq8q2k1DxUFOvbCXTHE3ao2GqT+5kKLVP9DZ1hqwWKzbG3B3OnxKP49GZdJimJaIeW01kjNwNyabNm1CrVYzbdq0PtckJiaSk5PDmjVrApp5O1T5JmH6DBISzutzTWzsWRgMY6iofCVgcQC8XNnI9CgTkyIMfa65MjmGCLWKV6pO3tEFERER3gzgkV/Lly/3rpk7dy61tbVkZWV5t40bN46lS5dSXl7Ohg0buOqqq0IQveBk4ds9dd7s340zR3m3/+7cPCLDNBTXdvDuhooQRigQCELJiO8BPF5QKBRcPz2LlXsbqGwOkJthcxkcXAWn/qL/dWqdZyTEtnehKzCxbK7bTJW5iivyruh3XVxYHPOz5vPB3g8CdiPdsWwZ7s5Ooi+7rN91+sJCwiZNovW99wISB8De9bVodCpypiX2uy5rQizGKB27/hu4nrddPywnMjGJ9MLx/a4bO3seCqWCXd8v73fdsWBeX4M+N7rP7J+M6fRk3BYn1j2BKU9yuVxs2bKFiRMn9pn9kznllFOoq6ujujowGcmurmbq6r8kNe1nKBR9W7IrFErS066hsfE77Pb6gMRSZLaysd3CjWk9xxEciVGl4srkGD6oacbuFtkDgWAkcmTv33XTPdk/mWijlrvOzQXg6W9LaLYEpy9eIBCMLIQA9CMXTEjGoFXx8dYA3dTvXAIaI+RfMPDaiVdCl9njChoAlh5YSqoptdfev6O5aMxFVHRUsLspME6pbZ99iuHUU9H04wQrE3XpJVjWrsNR7/8baUmSKF5Xy+gp8Wh0/c9YUqqUFExPZt/GOlwBcL502GyUrPuRsbPOQaHs/20eZgon9/SZ7Pp+eUBEuqO+E8chM8ZTei+JPRJNohFtZgSWjYHpMysrK8NsNjNlypQB144ZM4bw8HC2bAmMAUt9w9dIkpPkpIsHXJuYuACFQkVN7ccBieXjuhai1CrmxQ5sNHJlciwtThffNIq5dALBSGRZUR1FNe09sn8yPzstk4LkCNqsDp78Zm8vRxAIBCc6QgD6EaNOzU/GJ/PRlkP+v5GWJNj5gUf8afsuc/QSOxqSJ3ncQv2M3WXn24PfckH2Bf3OX5SZljiNGH0MX5d97fdYHLW1dK5bT+SFCwe1PnzuXFCr6fh2md9jqdnfRnuDlfzTB9ePOmZaAl02V0DMYEo3rMFhs1I4a86g1ufPmEVL9SGaKsv9Hot1RwMKnQp9Xsyg1hsmxWPf34a70/9mMLt37yYmJoakpIHFqFKpZMKECRQVFQXEDKa+7gtioqej1fafdQPQaCKJi5tHXd1Sv8chSRKf1LfyP/FRaAd4WACQa9QzOdzAf+oCb2IkEAiGhiRJ/K279+/a6ZlEG7U91qiUCv600NMX/v7GCnYeCt4oIIFAMDIQAtDPXDA+mYNNnZTW+3mQdO0OaCyBCf2XOfow/hIo+RZs/n1S/0PlD5gdZv4n+38GtV6tVDMvcx5fH/wat+TfbFf70qUotFrC588f1HpVZCTG6WfQ/tVXfo0DYO+6WsJj9KTkRA1qfWyKiegkA/u2+D8bufuH70gfO4HIhP5LUWUyxk1CZzCyd92Pfo+lc2cj+oIYFJrBfdyEjY0DScK6x78Cw+l0UlRUxNixYwf14AKgoKCAzs5OKir82ytjt9fT0rqexMRBZPO7SYifj9m8B6vVv46tW9s7qbB1cVFi1KD3+Z+EKH5o7sASBJdUgUAweL7dU8eemnaMWhU3zczuc92po2K4aFIKkgT3f7YLtzt4c08FAkHoEQLQz5wxOhajVsWyPXUDLx4KOz8EQxxknz34fcZeDC47FH/h11C+LPuSsbFjGRXZs7SkL84fdT51nXVsb9ju11javvwS05zZ3rl/gyHi/POxbt6Mo85/fyO3W+LA1gZyTkns0/ylN8ZMTaBsW4Nfy0BtZjOVe3aSd8aZg95HrdEweuqplK73rwB01HfirOvEMD5+0PuoIrRoMyOw7vKv0ciBAwew2Ww+c/8GIiUlhYiICIqKivwaS339VygUauLjzx30PrGxZ6FUamlo8G/2+pP6VhK1as6IGvx76Py4SGxuiR+aA2diJBAIhoZv9i+r1+zfkdz7kwKMWhVbK1r5KFCtKwKBYEQiBKCf0WtUnJUXz7e7/dzDVPylp/xTpRl4rUxkGmScAbv91zfU5epiTfUa5mbOHdJ+kxMmk2BI8GsZqKOuHvueIsLn9Jzl1h/hc+ag0Gjo+Np/sdQfbMdmcZA1YeByviMZPdX/ZaAHt29GcrvJnnrKkPbLPWMmTYcqaDrkv2yXt/wzN3pI+4WNi8NW2oLb5r+RHbt37yYuLo6EhIRB76NUKikoKKCoqMhniPexUlf/BTExM9Fooga9j1ptIiZ6JvUN3/gtDkmS+LyhlQUJUagGmRUFyDboyDPq+bJBlI4JBCOFZUdm/87sO/snkxih57ZzcgD4y1fFtNsCP4NVIBCMDIQADADnFiax/VAbtW22gRcPhuYD0LwfcgafLfCSO9/jHOr0z9yuLfVbsDqtzEydOaT9lAols9Nns6pqlV/iALCsXgVKJcaZM4a0nyoiAsP0M+j4/nu/xXJwZyM6o5rEUQObaByJXAZ6YFuD32I5sGUj8VnZhMcMTYxmjp+MNiyM0vVrBl48SKx7mtDnD778UyZsXCy4JGzF/hHGbrebkpISCgoKBl3+KVNQUEBHR4ff3EAdjjba2rYSHz9vyPvGx8+nrW0z9i7/ZEeLLTZq7A7mxUYOed/z4yJZ3tSOQ5SOCQQhR5IOO39eOz2LmAGyfzI3zBhFdpyRRrOd55YHdnawQCAYOQgBGABm5yWgUipYVuSnEsN934FSDdlnDX3fMXPB0QkVa/0SyupDq4kPiycvOm/I+05PmU5lRyWV7f7pYTL/8F/CJk5EHT207BKAacZMrJs247Za/RJL+a4mMgpjUQ6h/FMmY2wslUXNfjEOcrtdlG3bzOgpQ8v+Aai1WjLGTeLgDv+4XrrMXTiqLejzhv73UUfp0aQYse1t8UsstbW1WK1WxowZM+R9MzIyMBgM7N3rH7e85pY1gJvYmMGX6MrExc0BFDQ2fueXWFY2dxCmVHBa5CCMpY7i/PhIWp0u1rX6ud9ZIBAMmeVF9eyubscwyOyfjFat5P4FhQC8vuYg++pFWbdAcDIgBGAAiDRoODUrhu+L/WTuUbrMU8qpCx/6vonjwJToEZF+YFXVKmamzhxyFgXg1KRTUSvUrKk+9gyT1NWF5ccfMZ01a1j7G2fOQHI46Ny48ZhjMbfYaaw0kzU+dlj7pxfEYG6x01p37DMba0r2YjN3MGry0AUgQOaEydSU7qXLeuyx2Pe1AqAfM3QBCKDLica2r8Uvwnjfvn1otVrS0voeRN8XSqWSUaNGceDAgWOOA6C56b8YDKPR6wceW3I0Wm0MERETaG72T6/m983tnBFlQq8a+qVggimMBK2aH1rEDaNAEEokSeLZ5SXA0LJ/MmfnJTC3IBGnW+LOD7bTafdf6b1AIBiZCAEYIGaMiWVDWTNO1zH2DTlsnhLOMUPrufOiUMDoOX4RgNXmag60HRhy+aeMSWtiQvwEfqw+9pvXzi1bcVssmGYNTwBqR41CnZyM5cdjj6VidxMKBWQUDk8ApuREoVQr/NIHeGDrRsIiIkkakzOs/TPHT8TtclG5Z+cxx2IrbUWTZEAVMbSbERn9mCjcHQ6cfhDG+/fvZ9SoUahU/c9n7Ivs7Gyqq6ux2Y6trFuSJJqaVw0r+ycTE30GLS1rkY7RUdficrGu1cLsmKGVLcsoFApmRoezSghAgSCkfHdE9u/mIWT/juT38z1VPdsPtTH76e+xdgmHX4HgREYIwABxxug4OuxOdlYdo0lCxRpPCWfO0PuFvIyZC/W7ob3mmEJZXbUalULF6SmnD/sYM1JnsKF2Aw73sTWbW35cjSo+Dl1BwbD2VygUGGdMx+wHAVhZ1ExCVgR60xAMeo5Ao1ORPDqSSj+MPajctYOMcRNRKocndKKSUoiIT6B857ZjikOSJGylLehyhpf9A9BlRYBaga07kzhc7HY7lZWVjB49etjHyM7ORpIkDh48eEyxdHbux26vISZ2+AIwOno6DkczZkvJMcWyttVClyQxO3YYlQXdzIw2sbPDSqtDZAwEglAgSRLPfuf5LPj5GUPP/sl0Og4Lvrp2O3vrxIMdgeBERgjAADEhLRKjVsWa/U3HdqADP3hKOBMKh3+M7NmAAvavOKZQNtZuZFzcOCK0w8sYAMxImYHFYWFHw45jiqVzw0aMp5w6rFJUGdOMGXTt24+jdviOrZIkUVXaSmpu1LCPAZ4y0KqSVlzO4Wd1umxWag+Ukl44ftjHUCgUZI6fRPmObcM+BoCzvhN3exf6YxCACo0KXVakt5R0uBw8eBC3231MAjA6Opro6OhjLgNtal6FQqElOurUYR8jMnIqSqWOluZjK6X+vrmdNL2G0WG6YR9jZpQJN7BW9AEKBCHhy5017KpqJ0yj5OYzBz+a6WjyEsOJM3nEo06tJC9x+A+GBALByEcIwAChUSk5dVQMa49VAJavgczpnlLO4WKM9fQClg8/2yVJEpvrNjM1cerw4wAKYguI1EWyoWbDsI/h7uzEuns3hlOH1+cmYzj9dFAosKxdN+xjtNZ1Ym3vIuUYhA54BKDD7qKubPgZ4+riPUhuN2mFg59z1xuZEybTXFVJR9PwnSZtpa2gVqDNGv7DAgDdmCjsB1qRjkEYHzhwgMjISGJiYo4pFn/0Aba0rCMycjIqlWHYx1CpdERGTqW55diy12tbzcyMCj+mhygZYToy9VpWtQgBKBAEG2uXi99+4Jmtq1UrMWjVwz5WmFbF2zeeBnjm2irF3aFAcEIj3uIBZProODYebMbuHGYtfVcnVG+FzKGNOeiVzDM8YnKYVHZU0mBtOGYBqFQomRw/mS31w3ea7Ny6FZxODKccmwBUR0ejy8nBumXzsI9RXdqKQqkgefTQbfSPJD49HG2YmurS4QvAyqJdGCKjiEkZutHJkaSPneA53jH0AXaVtaFND0epHV4pqox+TBRSl5uuQ8MvR6qoqCArK+uYhA54ykAbGxtpb28f1v6S5KatbfMxZf9kYqKn09q6EfcwS6nbHE72mG2cFjV098+jOTM6nNVCAAoEQWf7oRbs3Q/H2qzOYy7bzEsKJ8aoxeGW2F09vM85gUBwfCAEYACZPiYWu9PNlvLW4R2gahO4HZ4M4LGScQa0lEHH8ModN9VtQoGCyQmTjzmUyYmT2d6wHad7eH1DnZs2oYqJQZs9vGb3IwmbOoXOzcMXo1UlrcSnm9CGDf/JK4BCqSApO4Ka/a3DPkblnp2kFY4/ZqFjiIgkJiWN6r17hrW/JEnYy9vRZR2bKAbQJJtQaFXYDw7vZsRut1NbW0tGRsYxx5KVlQV4BOVw6Ow8gMPRQmTUtGOOJTr6DFwuCx0du4a1/8b2TiTg9EjTMccyM9pESaeNersYIi0QBBP7EZURo2INx1y2qVAomJIRBcCWcv+M4BEIBCMTIQADSEFSBOF6NZsODtPco3wN6KMgfnhGJz7IInKY8wA3120mPyafcO2x9wVMSZiC1Wllb/Pw5qp1btyIYdq0YxY6AIYpU+k6cABn89D/RpIkUV3aSkrusZV/yiSPjqJ2fxvuYQzWdths1O0/tv6/I0nNL6Rqb9Gw9nU22XCbHcdc/gmgUCnQZoTTVT48AXjo0CEkSfKLADSZTERHRw9bALa2bkShUBEZMemYYwkPL0Sp1NHWNryHF+tbzSRo1WSFDc8w4khO7Z4huKndcszHEggEg6eoxpPxO31UDF/eMYuwY6y4AJic4bmeba1oPeZjCQSCkYsQgAFEqVQwOSOaLRXDfJJW/qMnc+ePYvzwJIgeBeXDF4DHWv4pMzZ2LDqVjs11Qy+9dNts2LbvwDDt2LMoAIapUwCwbt065H3bG61YWu2k5kT5JZbkMZF02Vw0Vw+9nK6qpAi3y+U3AZiSV0hjZTk2y9Bj6TrYDgrQZRy7AATQZkbQVd4+rHmAFRUVhIWFERcX55dYMjIyqKysHNa+rW2bMJkKUKuPPeumVGqJCJ9A63AFYJuF0yJNfnmIkqLXkqrTsLFNCECBIJhs6xZpZ+cn+EX8AUzpFoDDvm8RCATHBUIABpipGdFsqWgdelbH2QWVG/1T/imTcYZnrMQQqbXUUmWuYlqif0SXRqVhfNx4ttYPXXTZdu5EcjgwnOKnWFJSUCcnD6sMtGafp18vecyxlzoCJGRFoFQqvMcdUiwlxehN4cSkHlv/n0xqXgFIEjUlxUPe136wDU2iAeUxlsXK6DIjcHc6cTZYh7xvRUUFGRkZfhE6AOnp6dTW1mK324e8b2vrJqKijq1v9Ugio6bS1rZ5yMLY5nKzrb3TL/1/MqdEGtnUduzzGgUCweDZVtkKwKT0KL8dc2J6JCqlgpo2G9WtQ//MFQgExwdCAAaYKZlRtFkdHGgc4tPx2p3gtPpXAGaeAbW7wDY0gbGtfhsAExMm+i2UyQkeI5ih3rxat29HaTCgy831WyyGKVPo3LxpyPvVlrUTnWRAZxje/L+j0WhVxGeGU7N/GAKwtJjknDy/CZ2opBQMkVHDKgPtKm9H64f+PxltRjgoGHIZqMvl4tChQ34p/5RJT0/3lP5WVw9pP5utBpvtEFGR/nlwARAZOYWurgZstqoh7be1o5MuSeK0SP8JwGmRRrZ3dGJ3H9tweoFAMDhq2qzUtttQKmB8qv8+bw1aNQXJnlYPkQUUCE5chAAMMJPSo1AohtFQXbUJVFpI8k9JH+DJACLBoaGJnR2NO0g1pRIX5p8yOoCpiVNptjVT3l4+pP2s27ejHz8ehco/5S7gMYKx7d6D2zq0p511ZW0kZvvvwguQPDqSmiHOvZMkiZrSvSTn5PktDoVCQUpuAVV7dw9pP5e5C2eD1TPE3U8o9Wo0ScYhG8HU1tbicDj8KgDj4+PR6XRD7gOUe/X8YQAjExkx2efYg2VTmwWjSkmhKcxvsUyLMNIlSezsEBkDgSAYyOWfeUkRGHX+qbaQ8ZaBDtfATiAQjHiEAAww4XoNeYnhQ3+SdmgTJE0A9fCHNPcgZjToI6FqaDeMOxt2Mj7Oj0IUGBfnmVW3s3HwowYkScK6bTthEyb4NRbD5MngdGIrGny2y2F30VRlIWmU/4QOeIxgzC12zC22Qe/TUlONzWImOSffr7Gk5hdSu68Ul3Pwbq1dFR5TAq2f+v9k5D7AoXDo0CFUKhXJycl+i0OpVJKenj7kPsD29u3o9WnotP57iKLVxmAwZA9ZAG7r6GRSuAGVn7LFAGNNYYQpFaIPUCAIEoEo/5QRfYACwYmPEIBBYEpmNJuHkwFM9Y/pihelElKmQNXgzVccbgdFzUV+F4CRukgyIzLZ1Th4G3tnbS3OhgbCJvpXAOrGjEGh12PdsWPQ+zRUtCO5JRL9LAATujNn9QcHP8+pprQYFAqSx/ivLBYgeUwezi47jZWDz9J2HepAadKgivbjgws8fYDORivuzsGPGqiqqiIpKQm12r9Px2UB6B5CuWNb+3YiIvz77xY8ZaCtbUMzU9ra3snkiOEPou8NjVLBpAiDcAIVCILE1m4BODmAAnB3dRs2xzDnGAsEghGNEIBBYEpGNKX1Ztqsg7x57WyG5gOQ5r9yMS+pUz0CcJC9dyUtJdhddibE+//mdVzcOHY1DV4AWrd7BJrezxlAhUaDvqAA247BZyNry9pR61TEJPuvjwrAFK3DEKmlbgjljjWle4lNTUdn8G8sCaOyUSiV1O0vHfQ+XYfMaNPC/daLKKNJM3mPP1iqqqpITU31axwAqamp2O12mgc5OsTtdtLRsYuICP/10MpERkzCYtmLyzW40stau4Nqu8PvAhA8ZaCbhRGMQBBwnC43Ow95esUndc/t8yfpMWHEmbQ4XBK7q4feky4QCEY+QgAGgUnpnj6x3VWD/CCVSzT9nQGUj2mph7ZDg1q+s2EnaoWa/Bj/lhcCjI8bT3FTMQ7X4ISxdccO1CnJaBIS/B5L2ITxWHcNXozWlbWTkBGOUuX/t1BiVgT1Qyh39Hf/n4xGpycuLYPa/SWDWi9JEo5DHWjTjn3MwdGoY8NQ6FV0HRpcZtRqtdLU1ERKSorfY5GPOVgjGIulFLfbFhABGBExAUlyYTYPrnx5a3eGbnK4/wXgxHADtV0O6sRAeIEgoOyt68DqcBGuUzMm3v+ftwqFwjsPUPQBCgQnJkIABoFRcSYMWhU7By0AN0FYDMRk+z8YWVRWDc4IZmfjTvJi8tCr9X4PZVzcOLrcXZS0Dk5gWLdvJ2yC/2+iAfTjJ+CoqMDZMrhS3bqydpKy/Vv+KZOQGUH9QU+J6UA4bDYaKsoCIgABEkfnUjvIDKCr2Ya704kmPdzvcSiUCrRp4YPOAMriLBAZQIPBQHR09KAFYHv7dkBJRPhYv8diNOagVGppbx9c+fLW9k6StBpS9Mc+AP5oJoR7TGW2d4gsoEAQSOT+vwnpkSiV/q22kBF9gALBiY0QgEFApVQwNiVi8ALwUHf/n5/L6AAIT4TI9EH3Ae5o2OH3/j+Z/Jh81Ao1uxoGzrxJTie23bv9bgAjEzbeY0pj2zWw66Wl1Y6l1e7t1/M3iVkRdNlctNYPfCNdX16G5HaTmJ0TkFiSRufQWFmOwz6wKY2cndOm+V8Aeo5rGnQGsLq6Gp1OR2xsbEBiSUlJGZIANJlyUan8n3VTKrWYTAW0dwyufHlrh//7/2TS9Vqi1Sp2CCdQgSCgyA6ggTCAkZnSXVq6paJlyOOaBALByCfkAnDNmjVcddVVzJ07l9/85jfU1dX1u97lcvH6669z2WWXMW/ePG688UbWrl0bpGiHz7jUSHYNRgBKElRvCUz5p0zqlEE5gZq7zBxsP+h17PQ3OpWOnOicQTmB2g8cQLLZ0I/zfxYFQJORgTIyEuvOgTMpDd1Ol/EZgRE68Zme49aXDyx26sv2oVKriUv336iDI0kanYPkdlNfdmDAtV2VZlQxelRG/8xFPBpNajju9i5c7QMPYa+qqiIlJQWlMjAfcSkpKdTU1OByDWyQ0N6xg4jwwDy4AIgIn0B7+8APUdySxLYAGMDIKBQKJoQb2HESZACrqqq49dZbmTlzJosWLWLlypUD7vP9999z9dVXc+aZZ7Jw4UL++c9/4hyCw65AIHPYATQ6YOeYkBaFWqmgrt1OddvgXakFAsHxQUgF4H//+1/OPvts0tPTue2229i1axczZszAbO67zOvuu+/mzjvvZN68efz+978nKiqKM888kx9++CGIkQ+d8amRHGzqpN02QH9MexV0NkHKpMAFkzoVqreCu/+b1+LmYgAKYgsCFsr4uPGDcgK17dkDgL4gMLEoFArCxo8flBFMQ2UHOqOa8Bj/l8UC6I0aIhPCBmUEU1e2n7iMLFTqwIiuuIwsVBrNoMpAuwLU/yejTR+8EUygDGBkUlNTcTgcNDY29rvO5erEbC4JSP+fTHjEODo79+N09v97OWC10+FyMykA/X8yE8LDTvgMYFtbG9OnT+fQoUPcf//9jBs3jnPPPZcVK1b0uc93333HOeecw6hRo3j00Ue55JJLuP/++7nrrruCGLngRKDd5mBfg+e9HsgMYJhWRUGyp8plyHOMBQLBiCekAvAPf/gDF110EX/5y1+48MIL+eSTT6ivr+df//pXn/t89NFH/OpXv+Lmm29m3rx5PP300+Tn5/PZZ58FMfKhMz7VYwQzYBawZrvnv0mByxiQNAEcndC0v99lxc3FaJVaRkWOClgohbGFlLWXYXX2f9NoLypCk5GBKjwwWTcA/bixWHcPLEYbKjqIT/e/0+WRyH2AA1Fftp+ErAD0inajUqtJyMoe0AhGcks4qswBK/8EUEXqUJo0A5aBdnR00NHRERADGBl5tuBAZaBmczHgJjwiMFl0oDu7KNHR0X/5sjykfXy4/wbAH82EbiOY+hPYCOall16io6ODDz/8kHPPPZc//elPXHzxxdx333197vPFF18wduxY/vznP3PmmWfy85//nFtuuWXEX7cEI48dlW1IEqRFhxEf7t9xO0dzZBmoQCA4sQiZAOzs7GTNmjUsXLjQu81oNDJ37lyWLVvW535Tpkxh8+bN3tKZQ4cOcejQIaZODWDJpB/IjvcYwQwsAHeAIRYiAnfzSnJ3NqK2/3LHouYicqNz0SgDk10CyI/Nxy25KWnpX2DYdu9BX1gYsDgA9AWFuBoacTY09LuuobIjYOWfMvEZ4TRVmXH3YwTj7Oqi6VAFCaPGBDSWxOwc6sr6f1jgbLQiOdxoUgOXAVQoBmcEU1tbC0BSUlLAYtHpdMTFxVFVVdXvuo6OPSgUakzGwPRoAhiNo1GpDLR39P9+3tlhJVWnIVrj37mIR3IyGMHI2Ty9/nAFwIIFC1i7di2dnb3/3Keeeirl5eWUl3tmatrtdtauXcvpp58elJgFJw7bKj1iLJDZP5kpmbITqBCAAsGJRsgEoDxI+egyrdTUVCoqKvrc7/XXXyciIoL09HSmTZvG+PHjeeyxx/jZz37W5z52u5329nafr2CjUiooTI5gZ9UA567d4RFoAcwuYYiBiLRBCcD8WP+PfziSnKgc1Ao1xU3Ffa6R3G5sxcWBF4CFnvJSW3HfsVjNXZib7cQHwOnySOLTTTi73LT1YwTTWFmO2+UicdTogMaSkJVNS00VDlvffSCOao8o0/p5LuLRaFKM3nP1RU1NDTqdjujowPXHwOE+wP7o6Njd7dQZuCf1CoWKcNNY2tv7L1/eZe4MaPYPIKPbCGb7CVwGWlFR0SO7nJKSgiRJHDrU+3idK664gscff5wJEyYwbtw4UlJSSEhI4JVXXunzPCPhuiUYeRzu/4sK+LkOD4RvFwPhBYITjJAJQIfDUyJ05FNUgLCwMLq6uvrc71//+hcrVqzg/vvv59FHH+XGG2/kvvvuY+vWrX3u89hjjxEZGen9Sk9P988PMUQGZQRTsyOw5Z8yyRM85+oDu8vOgdYDFMQErv8PQKvSkh2VTVFz33PMHJWVuM3mgPX/yWjS0lCaTNj29B1LY4VHfAQ6AxjXLTAbKvsud6wv249CqSQuMyugsSRkZYMk0VBxsM81XdUWVFE6lIbAZYsBtCkm3GYHro6+PyNqa2tJSkoKaIkueDKMdXV1uN3uPtd0mIsINwX2wQWAKbygu9y0dyRJYpfZyjhT4Pr/4OQwgnE4HOh0voI+LCzM+1pvrFu3jnvuuYfbbruNf/zjHzz11FOsWLGC559/vs/zjJTrlmDkIEmSVwDKc/oCiVxm6nRLg3cxFwgExwUhE4AxMTEANDU1+WxvamryvnY0ZrOZe++9l0ceeYRbb72Vc889l6eeeopTTz2VP/7xj32e695776Wtrc37VVlZ6b8fZAiMT42krNHStxGMpQnaD3nEWaBJmuDJAPZh71zaUopLcgVcAIJnHMTe5r19vm4r8ggyOUMXKBQKBfr8fGzFfQvAhsoONDoVkfGBzaTojRpMMToaK/vOdtWV7SM2NR2NNrB9ILFpGShVKuoP9u0E6qgxo0kJXPmnjKY7w9hfFlAWgIEmKSkJp9PZ4zNMxu12YLHsxRQe+PdQuKmQzs4DuFy9C69qu4NmhyvgGUA48Y1gYmNje/zNZTOgvsaOPPjgg8yaNYuHH36YWbNmcf311/PII4/wxz/+sU/Ts5Fy3RKMHA61WGk0d6FReUZLBRqFQnG4D1CUgQoEJxQhE4ApKSkkJiayebPvPLoNGzYwefLkXvfp6Oigq6uLtLQ0n+1paWl93oSBp18nIiLC5ysUjE/zGMHs7qsMtLbbACZ5UuCDSZ7gcRtt793Eoqi5CJVCRU504HqXZPJj8iltLcXp7t0S3bZ7D+qkJNQBmul2JLrCAuz9ZAAbKjuISzehCNDw3SOJSwuncYAMYEKAyz8B1FotManpNPQhACVJwlFtRpsS2PJPAFWMHoVORVe1pdfXbTYbzc3NXpOWQCKLTLnn8Gg6Ow/gdncRbgrM6JIj8YhMCbO5917a3WaPIBtnCoYAPLGNYKZMmcLGjRt9tq1fv57k5OQ+Hzy0trb2eC05ORmHw9GnABwp1y3ByGFrd/avIDkCvUYVlHOKgfACwYlJSF1Ar7/+el5++WVvH80nn3zCrl27uP76671rHn/8cX7+858DngtmdnY2ixcv9paJVlZW8vnnnzNz5szg/wBDZHS8iTBNP0YwNTtAGw7RgXPd9CKXmfbRB1jUVMSoyFHo1YEZdXAk+TH52F12ytrKen3dtmdPwMs/ZfT5BXSVl+My9y4wZAfQYBCfbqLxkLnXIbwup5OGioMB7/+TScjKpr68dwHobu/CbXGiSQ58BlChUHj6AGt6v2mW54gGIwNoMBiIiIjoUwDKrpzhQcgAGg05KBRqOsx7en19Z4eVGI2KFF1gS3ThxDeCufHGG9m1axdLliwBPD2Br7zyCjfddJN3zerVq5k2bZq3J/Css87i008/5cABz3vIarXyz3/+k9zc3KD8WxWcGARjAPzReI1gKlrFQHiB4AQipALwgQce4JRTTmHMmDEUFhbys5/9jL/97W+cdtpp3jWlpaVs2XJ4aPm///1vioqKSEtLY8qUKeTl5XH66afz4IMPhuAnGBoqpYLClIi+a+lrtkPSOAjQ8GofItMgLLrPPsDi5uKglH+CRwDK5zwaSZKwFRUF3ABGRi4ztZf0LEntsjppq7cGvP9PJi49HGuHA0trz3635qpKXA5HUDKA4BGAjeUHcfcy+LyruxxTkxr4DCCANtmEo48MYG1tLSqVivj4+KDEkpSU1LcANBcRFpaBWh34fy8qlQ6jYTRmc+/Za0//X1jA+yLBYwQTpVadsGWg06ZN45///CfXXXcd2dnZ5ObmMmfOHJ82hNbWVjZv3oyt2zjpgQceYM6cORQWFlJYWEhKSgqVlZV88MEHofoxBMchsgPo5O6yzGAwPjUStVJBQ4edQy0n5ntaIDgZCZwf+CDQ6/V89NFHVFRUUFdXR25uLpGRkT5r7rnnHjo6DpfBTZs2jd27d1NRUUFTUxOZmZnExcUFO/RhMzYlgrX7+yhXrd0BY+YGJxCF4nAf4FE43U5KWko4f9T5QQklXBtOmimNouYiFoxe4BtLXR2u5mb0Y4MjAHXZ2Sg0Gmx7ijBMmeLzWmP3/LngCUCT97ymaN8+P3ksQyBnAB5JQlY2TkcXLTVVxKZl+LzmqLagCFOjigxsL6KMJsWIeW01brsLpc63DKqmpoaEhARUquCURyUlJfUoY5fp6NgdlPJPGVN4AR0dvQvAneZOFsRHBSUOhUJBoSmMPZYT92bxl7/8JVdffTUHDhwgISGBxMREn9fPPPNMNm7c6DVuMRgMvPfee3R0dFBRUUFsbKzI/AmGRJfTza5qT/vIpPTAG8DI6DUqxqZEsP1QG1sqWkiPCayRlEAgCA4hzQDKZGRkcMopp/QQfwBjxozp0ROoVCrJyspi6tSpx5X4A8hPiuBAo6WnpbLd7BnMHgwHUJk+nEDL2sqwu+zezFww6MsIRnbkDFYJqEKrRZszBltRz1K6hgozKo2S6KTgXADDY/ToDOpe+wDry/YTnZyKNiw4scRneoRmb0Ywcv9fMLJLgKfUVAJHbc8sYLAMYGSSkpKwWCw+D6nAk7k2m4uCYgAjE24qxGwuRpJ8P1taHE4O2RyMDw/ejdtYk5495hNXAIJnbu348eN7iD+AyMhIpk2b1sMtNDw8nLFjxwrxJxgyRTXtdDndRBk0ZMUGV4TJjqNbu0tQBQLB8c+IEIAnEwXJ4bjcEvvqj+phqtsFSMFxAJVJmghtFdDZ7LNZLsUMtgAsai7q0WNg27MHVXQ06iDeMOkLCrAX9SxHbajsIDbFiFIVnLeNQqEgLt3UqxNo/cEDxAcp+wegN5mIiE/oVQB21ViC0v8no0k0gErRow/Q6XRSX18fdAEIPY1gbLYqnM72oIyAkDGZ8nG7rXR2lvtsD6YBjEyhKYyD1i4sTjE7TCDwB/L4h4lpUUF72CZzuA9QGMEIBCcKQgAGmbykcBQK2FNzlBNozXZQaSE+eKLLKzbrdvls3tO0h/TwdMK1wSl1BCiILaCjq4Nqi68rqa24CH1BflAvePr8AuylpUhHzfRqqjITlxY8oQMeJ9CjZwFKkkRj5UHiM7KCGktCVnYPAei2OXE129CkBu/3olAr0SQYevQBNjQ04Ha7g+IAKhMVFYVOp+shADvMsgFMEEtATZ5so/koI5idHVbClEpGG4JTogseASgBxRZb0M4pEJzIHJ7/FxX0c8ujIPaIgfACwQmDEIBBxqBVkxVrpLjmqLK+2p2QUACqwLv0eYkdAxpDjzLQ0tZScqNzgxcHRxjBNPlm3uwlpehy84Iai76wAMnhwL5/v3eb2+WmpaaTmCAKHfA4gbY32rBbD4/IMDc3YbdYiAuyAIzPzKbh4AGfLK0swrTJwTGAkdEkG73mMzKyCOutJC9QKJVKEhMTewrAjj1otXHodAlBi0WrjUGnS6LjKCOYXWYrhSY9qiA+RMkz6FHCCd0HKBAEE1kABtMBVCY1KoyE7oHwOw6JgfACwYmAEIAhID8pnKKjM4D1eyAheNkCAJQqSCj0iM8jKG0pDcr8vyOJD4snRh9DUfPhm1d3ZyeOykp0OcGNRZfnEaO2I+YBttZbcTndxAZZAMZ1j5xoOnT4gUFjxUEA4jMygxpLQlY21o52zM2HTYy6qs2gVqCOD155IYAmxYSjthPJdViM1tbWEhMT06PvKtAkJyf3EIBmc5E3IxdMwk2FmDt8M4C7zVbGBrH8E0Cv8mQcd5tFBlAgOFZaLF2UNXoetoVCAHoGwnvKQDeLgfACwQmBEIAhoCA5gqLa9sOZFLcb6osgMXj9Ql4SC6F+t/fbJmsTzbZmcqKCK7oUCgW50bmUtpR6t9n37wdJQpcb3GykymREk5GBfe9hU5qmKk+2KTYIw86PJCrJgEqtpKHicLaroeIgGn0YEXHByy4BJIySjWAOZ0YdNRY0iUYUQeqLlNGmGMHpxtl4eNZcsA1gZJKSkmhqasJut3u3mc3FhIdAAJrCC3wygF1uN/s6bRQEWQACjDWFUXSCG8EIBMFg26FWAEbFGYkyaEMSw1TRBygQnFAIARgC8pPCae10UNfefcPYUgaOTk82LtgkjoOGEnB5SgxLWz0CLNgZQPmc8vkB7CUloFCgGxOcWXdHosvNwV5a4v2+udpCWISWsPDgXnxVKiXRyQaajih3bKwsJy49A0Uw5kUeQXhsPDqjkYbyg95tjloLmqTgimLAazrjqPE8FZckifr6+qCWf8rIolMeQu90dmCzVWE0BvfBBXgygF1dDdi7GgHY32nHKUGBUR/0WMaawthjtorh0QLBMSIPgJ8cguyfzJRMz7m3VrSI97RAcAIgBGAIKEiOADhcBlrfXbKVGOQSUPCITpcdmj1ZndKWUnQqHRnhGQPs6H9yonI41HGITocnq2MvKUGbkYEyLPjZC31uLraSw2K0qcoc9OyfTGyKiaaqw4YnjRUHg97/B7IraZa3BFVySzjqOkMiAJXdcwflURAdHR1YrVYSEoKbFQWIj49HoVBQX18PgNnieXBgMgW3d9VzTk/5srl7HmBRtwlLfggEYIEpjA6Xm0pbV9DPLRCcSHj7/0JgACMzNiUSjUpBo7mLymaR2RcIjneEAAwBadFhhOvUFNV2C8C6PRAWA6bgZy+8orPOUwZa2lJKdmQ2KmVwBmkfSW50LhIS+1s9YtRWUhL08k8ZXW4ursZGnE2efremakvQ+/9kYlNNNNdYkNwSLqeT5qpK4tKzQhJLXHomjZWeMQPOJis43WiCNBfxaDRJBhy1nocFsvgKRQZQrVYTGxvrzQCazXtRKFQYjcHPXIeFZaBUhmG2eMqXi8xWUnQaojTqoMcy1uQRnXtEH6BAMGwkSQqpAYyMZyC8Z1azKAMVCI5/hAAMAQqFgvzkcIpkJ9D63R4hFuTZPgAYYsCU5BWA+1r3haT8EyA7KhsFCm8ZqMcBNHQC0BNDCQ67i/ZGK7GpIcoAphpx2l20N1lpra3G5XQG3QBGJi4ji5aaKlxOh1d8hSIDCKBOMnozgHV1dWg0GqKiokISS2JioleEWswlhIWNQqkMrhkNgEKhxGTMwWLuFoAWW0iyfwBJWg3RapV3DqFAIBg6ZY0W2qwOtGol+UkRIY1FNoIRAlAgOP4RAjBE5CdFUFxzRAYwFOWfMomFUL8Ht+T2CMAgG8DIhKnDyIzIpKSlBGdTE66mpqA7gMpoMzJQ6HTYS0porraAREgzgABNVRYaussvY9NDJQAzcbtcNFcdwlFrQWnUoApyX6SMJsmIq9WO2+YZAB8fH48yyH2RMgkJCdTX1yNJEmbLXkym0Dy4ADCa8rxlqEVma0gMYMDzoKvQFCZGQQgEx4Cc/RufGolWHdpbNrkPUAhAgeD4RwjAEFGQHMGBRgu2TrOn/y4UBjAyCYVQt5uqjiqsTmvIMoDQbQTTUuoxgIGQZQAVajW60aOxlZR4DFgUEB3kWXcyhkgtOqOapiozjRXlGKOiMUREhiSWuG7h2VhxEGetJWTlnwCaRM+5HXWd1NXVhaT8UyYhIQGr1Up7eztmcwkmY/D7/2RMpjwsllLaHF1U2R0hMYCRkY1gBALB8BgJ5Z8ycgawqKaDzi7nAKsFAsFIRgjAEJGfHI7LLXGodBtI7hBnAMdBazklDduB0DiAyuREeQSgbW8JCp0ObWbwzWhkdLm52EtKaaoyExkfhkYb/L5I8GRSZCOYxsrQGMDI6I0mwmPjaagsD5kBjIwmwQBKsNd00NDQEBIDGBlZfNbUFON0tobEAEbGZMzF7bazvdnTqxmqDKDn3HoOWruwOF0hi0EgOJ4ZSQIwJSqMpAg9LjEQXiA47hECMETkJ4WjUEDTgW2eDfH5oQume/5gadV6InWRxIfFhyyUnOgcWuwttBftRDd6NApVaEQXdAvAffs8DqAhKv+UiU010Vxt7h4BEZryT5m4jEyaKypxNlnRJIZOACrUStRxYTSW1+JyuUKaAYyKikKj0dDQsBUIjQOojLH73DtaqlEpYIwh+L2IMoWmMCRgr0UYwQgEQ8XmcLGn2tMqMhIEIIgyUIHgREEIwBBh0KrJiDHgrt0F0VmgC6HAiMsDhYp9TXvIicpBEQozmm7k7KN5756QlX/K6HJzkaxWmirbQzYCQiY21UhLXRttdbUhzQCCpwzUVtUGEqhDWAIKnj7AuhqP+UooM4BKpZL4+Hja24tQqQzo9Wkhi0WnjUOjiWGP2cLoMD26EPVFAuQa9Cg5PI5CIBAMnt3VbTjdEnEmHWnRocvkH4lcBrqyuAFrl8jsCwTHK0IAhpC8xHBMrXshIYTlnwAaPcSOptRSxZioMSENJc2UhkGlR3Hw0AgQgDl0acKxdbpHRAbQ7fAM944PtQDMyELT6RkrEMoMoHz+htZGjEYjJlNo/0aJiYl0OcowGnNRKEL70Woy5lJiVVBgCl3/H0CYSkm2QSf6AAWCYbC1ewD8pPSokD6YPZLC7jnGGw82c/7f/itEoEBwnCIEYAjJT44g2X7AW4IZSrri8yl3WkLa/wegUqqY6kxHZXOEzAFURh0fT2eiR4TGhDgDGJNixO1qBIWCmLT0kMYSl55JlDYewpUodaEr0QVPBrDJ1U5CbOjKlmUSEhJQKmswGkP74ALAYMyjzBkZUgMYmXyjXmQABYJhIPf/TQ7hAPijUasOC9GDTZ3sresIYTQCgWC4CAEYQsZHO4mjlfaI0N8wHohOw6WA3BCNgDiSiR2eEpNQZwAVCgW2jHEocRGZENpSR61ejUbTgt4Uh0Ybup4ugJjUdCK1CXTp7CGNAzzD4FsUZmLDokIdCvHxsRgMrSgUoSv/lOnUj8WCgTxDaAU6QIExjGKLFUmSQh2KQHBcMZIMYGTGp0ah6RaBCeE68hLDQxyRQCAYDkIAhpBCVSUA+xShc7qUKQ3zCJwx6tCW0QGMblLTEQaKuJhQh0JnVBYmewNKZejLbxSKZtTa0PW5yag1GqL1ibS7Q28C4DIqaVdYiVGE/iYkMtKOUunGZo0NdSgcUmQDkKGsDXEkUGjS0+xwUS9s4wWCQdPQYedQi6d0Oich9NdlmTCtigsmJAOwaGoaYSFyxxYIBMeGEIAhJNl2ALukYZsl9DeMpQoHKQ4npm7r+FASX2OlIh4qzZWhDoV2dQyGlnLcttCWsEmSRJe1DpcrOqRxALgsDnSKMBo7DoU6FBqbGkEBUfbQGyS4Jc+/15aW0GaLAQ664tBLVqK6SkIdincMhegDFAgGz/qyJu//X/7S2hHVazcpLQqAklpR/ikQHK8IARhClA17OKTOoKiuM9ShUGptIMfphrpdoQ6FsIp6KuIVlLaUhjQOyS3R3qnGZK7Cvm9/SGPpbGvFabfgdERjszhCGouj1gJAVW1xyMv66urqAIho04Q0DgCzeS8ul4mGhtALnRKrmwxlHZ2doReAGXotBpVS9AEKBEPgh5IG7/+XjbBeu3GpkQDs7h5RIRAIjj+EAAwldXtoMY0ZER/spa2ljNFGQf2ekMbhtttxVRyiOcVEaWtoBWBboxWnE4yWKuwlob2Rbqg4CIBCFUdTlTmksThrLUhKaGqvwtzSNPAOAaS+vp6osAio70Jyh1aMWsx7USjSqK+vD2kcAEUWK2O0FszmvaEOBaVC0W0EE3phLBAcL9S1HX5gMirWMKJ67QqSI1AooLbdRkNH6HvBBQLB0BECMFS43VBfhCu+kJK6DlwhvHlts7dR11lHTkQm1IVWAHYdOAAuF8oxo0KeAWyu8mS6oiMJuQBsrDiIWqtFpYmiqTuuUOGo60QVq0XCTWNFaEuG6+rqiI+LB6cbZ1NoBYbZspcw/Wiam5txOEKXpXW4JUosdvIMKizm0GcAAQqMeorMIgMoEAyWou7yyscXjefLO2aNqF47o07NqDiPM/bu6rYQRyMQCIaDEIChovUgOCwY0ydgc7gpbwrdTf2+1n0A5MRPhMa94ArdzasstKIKxlPSEtqb16ZqM3qjhvDs1BEgAMuJTcskJjmcpurQZgAdtRZ0qZFodHoauzOToaK+vp6k1KTuuEJXSu1ydWK1VhIdPQ5JkmhoaBh4pwCx32rDIUmMjYjB3lWHw9EaslhkCkxhlHbacIY4SysQHA/Ud2fWlApYODF1RIk/mXEpogxUIDieEQIwVHRn2pJzpwKwN4TN1KUtpagVakalTQdXFzSFrt/NVlKCJiWFUcljOdRxiE5H6G7qm6rMxKYa0eflYCsNsQCsPEhcRiaxqUaaQ1gCKrklHLWdaJONxKVn0lgZugygxWLBYrGQlJ6C0qTx9iaGArOlFJBITPS8n+XexFBQ3J1pmxSTCYB5BGQBC4x67G6JA1ZRLiYQDMSu7qzamATTiBR/AONSPQPhRQZQIDg+EQIwVNTvgbBoYpMyiDNpKQ6xAMyKzEKTPLE7tt0hi8VeUoouN5fc6FwkJPa3hk6MNlVZiEk1oc/NxdXQiLMlNGMP3G4XTZUVxGdkEZtqoqnaEjLzFVerHanLhTrJSFxGZkhLQGWRlZCQgCbRgDOEAtBi3gsoiI4uJCoqKqR9gEUWG0laDSkR2SgUGsyW0PcBCidQgWDw7KryZNXkLNtIZGx3bHKsAoHg+CLkArCzs5MPP/yQF154gR9++GHQ+5WWlvLyyy/z7rvv0tZ2HD6BqtsNCWNBoSAvKZzi2tB9iO5r3UdOdA4YYsCUFNI+QHtJCbrcXLKjslGgCJkRjNPhoq2+k9gUo3cgvb0kNLG01dXidHQRm55JTIoRh81FR1No+qnkLJsmyZMBbKqqwO0KjT15fX09KpWKmJgYNElGHCF00zWb9xIWlolKFUZiYmJoBaDZSoFJj1KpwWjIxmIJfQYwRqMmUaum+ARyAv3mm2946qmneOutt+joGNwDvMbGRt544w2ee+45du8O3YM2wchmV5XnnmZs6kgWgJ4MYEVzJ23W0DpTCwSCoRNSAVhTU8PEiRN55JFH2Lx5M5deeilXX331gPvde++9TJ48mZUrV7Jy5UrOPPNMDhw4EISI/Uj9HkgsBCAvMSJkJaCSJFHaUkpOVI5nQ0JByJxAXW1tOOvq0OXmEqYOIyMiI2RGMC01nUgSxKaa0GZmotBoQtYHKGfZ5AwgQHN1aLJdjjoLCr0aVYSWuIwsXA4HLbXVIYmlrq6O+Ph4VCoVmiQjziYrkiM0YtRs2YvJlAd4MpKhLAEtstjIN+oBMJryRoQTKEChKeyEcAKVJIlLL72U66+/ngMHDvD8888zfvx4Dh3qfy7m559/zujRo/nggw+orKzk+uuv57XXXgtS1ILjCVkAjh/BAjDKoCUtujuzL/oABYLjDnUoT3733XcTHh7O2rVr0el07Nq1i4kTJ3LJJZdw0UUX9brPm2++ydNPP82aNWuYNm0a4BGSTqcziJEfIw6bp8/u9F8BkJ8czmtryujscmLQBvdPUtdZR4ejw5MBBEgcC0WfBzUGGVlg6XI9seRE5YQsAygbrcSkGFGo1WhHjw6ZAGyoOEhYeASGyCgAtGFqmqrNZE2IC3osjtpONEkGFAoFcRlZQLdBTWp60GOpr68nISEB8GQkkTwOpdq04Nulm817SUv1PLxKSEjAbDbT2dmJwRDcofBmp4tKW5e35NJkzKWpaSWSJKFQKIIay9HkG/UsbTgOqzWOYsmSJXzyySfs2bOHnJwcurq6OP3007nnnnt4++23e92noqKCK6+8kvvuu4+7774bALfbLbKAgh40me1Ud4+AKOzOso1UxqZEcKjFyu7qNs4YHRvqcAQCwRAIWQbQ5XLx0Ucfce2116LT6QAYN24cM2fO5IMPPuhzv6effprLL7/cK/4AkpOTSU8P/g3osGksAcnlEVtAflI4kgQldcE395CdNr0CMKEQWsvBHvyMpK2kBNRqdFlZ3phClQFsqrIQHqtHq/cIcl1uTugygJUHicvIQqFQoFAoiE01hmwUhKPW4hFbgCEiEkNkVEiMYNxuN/X19SQmJgKgTjB0xxf8MlB7VyMOR7M3AyjHFIoy0L3dJZZyBtBkysPp7MBurwl6LEdTYAqj0taF2RmaLK2/WLJkCbNmzSInx/OZqdVqufbaa/n4449x9VEOvXjxYsLCwrjzzju925RKJePHjw9KzILjB9lVMzvOiEkX0mf0AzLO2wd4/D/YEQhONkImACsrK7FYLOTl5flsz8/Pp6ioqNd9LBYLO3fuZPbs2axdu5a///3vfPzxx5jN/Qsnu91Oe3u7z1dIkUss4/MByEkIR6GAvSHoAyxtKcWoMZJiTPFs6C5Lpb446LHYS0rRjRqFQqsFPAKw2dZMkzX4w8abq8zecksAfW4u9tLSkJivNFaUE5eR6f0+JsUUkmHwktONs8GKJulwVisuIyskoyBaW1txOBzeDKBSp0IVow+JE6ilu8RSFoCxsbEolcqQlIEWWWwogRxDdwmo0RPTSCgDLewWpcd7H2BxcTG53X3BMrm5uXR2dlJZWdnrPuvWrWPGjBlUVlbyt7/9jcWLF7N3b/9/kxF33RIEBdkBdCT3/8mMSxWjIASC45WQCUC5aT4qKspne1RUVJ8N9S0tLUiSxJtvvsmvf/1rdu/ezSOPPEJeXh579vTdt/bYY48RGRnp/Qp5trBuN0RmgN5T3hGmVTEq1hgSJ9DS1lLGRI05XB4Wnw8KZUicQO2lpV7DFcDblxiKMtCmKjOxKUbv97rcXNydnTiqgtvv5uiy01pbQ1x6lndbbIqR1tpOXE53cGNpsIJb8mYAge5REAeDGgcczq7J2Tag2wgm+ALQbClBqdQTFpYBgEqlIi4uLiQZwCKzlWyDjjCV56Ndr09BpTJhHgFGMDlGPSrF8e8EajabiYz0vTmXr2N9PYxsaWmhrKyM+fPns3//flauXMnEiRN54YUX+jzPiLtuCYLCbq8D6Mgu/4TDRjD7G8x0dh1HbTgCgSB0AlDujTn6qWZbWxtGo7G3Xbz7WK1WNm3axD/+8Q82btzI6NGj+d3vftfnue69917a2tq8X309pQ0aRxjAyOQlhVNcE3wBuK9l3+HyTwBNGMRkB90JVJKkHgIwPTwdnUoX9DJQm8WBpa3LJwOo6y73CnYZaPOhSiTJTXx3vx14jGncbonWILteymMWNIlHCMCMTFrranHYgpvVqaurQ6/XEx5+uN9Pk2QISQmo2bwXo3EMCsXheV2JiYkhyQAWH2EAA6BQKDAZc7xZylCiUyrJDtNRdJxnAI1GY6/XLfm1vvYpLi5m+fLlPPfcc7z77rs8/vjj3HnnnX1m9kbcdUsQFOQM4LjjIAOYEKEnPlyHW4KiENy/CASC4RMyAZiZmYlOp2P/ft85b/v37/f2VhxNTEwM8fHxnHXWWSiVntAVCgVnn312vxlAnU5HRESEz1dIqS/y9NodQV5SOHvrOoJaYuhwOzjQdoAxUWN8X0goDLoTqLOmBndHh9cABkClVJEdmR10ASiXV8akHr6ZUycloQwPD7oAbOgur4xNz/Bui+nOTMpGNcHCUWtBFalDGXa4LyU+PQskiaZDFUGNRe7/O9LYRJNkxN3RhcsSXEtyi3kvJqNvSWBCQgL19fVBfT9LkkSRxUqBMcxnu9GUNyJmAUK3E+hxngHMy8tj3759PttKS0sJCwsjIyOj133y8/PJzMz0ef3MM8+kq6urTwfrEXfdEgScNquD8ibPQ6yxx0EGEA5nKveIgfACwXFFyASgWq3mggsu4J133sHt9pSyHTx4kB9++IGLL77Yu+7bb7/l9ddf937/05/+lI0bN/oca8OGDT16MkYs1hZor+ohAPOTImi2dNFgtgctlIr2ChxuB7nRR/3uEsd6ylSDePNq6xZW+qP+jqEwgmmqsqBUKYhKPNzrplAo0HX3AQaTxoqDRCYmodUfvqnXGzUYo3RBN4Jx1HX69P9BtzBVKGgIchloXV2dt/9PRi5NDWYfoCS5MVtKMZp8e5kTExPp6uqitbU1aLE0dDlpdrjIN+l9tptMeVgs+3G7Qz+rq8Cop8hiC0kvrb/46U9/yvfff09ZWRkATqeTt956i4ULF6JSebLA+/bt4+GHH6alpQWASy+9lIqKCqqqqrzHWbt2LVqtltGjRwf/hxCMSORxCmnRYUQZtCGOZnDImUoxEF4gOL44Jospt9vtzcQNhyeeeILp06dz7rnncuqpp/L+++8ze/ZsrrjiCu+aDz74gHXr1nHdddcB8NBDDzF9+nTmz5/PjBkzWL9+PRs2bGDlypXH8qMEj/pug5vEowWgp5StuKaDhHD90XsFBFlYeWcAyiQUgrUZzPUQntjLnv7HXlKK0mhEnZLisz03Opdl5ctwS26UiuA8r2iuNhOdZESl8j2fLmcM1s1bghKDTGNluU//n0xsqjHoswAdtRYME+N9tml0eqISk7yzCoOB0+mkqamJ0047zWe7OlYPKoWnVHV0VFBisVorcbutmIy+AlAWp/X19URHRwclFrm08ugMoMmYhyQ56Owsw2QK7YOyAlMYbU4XNXYHKfrj4wb3aC6//HLeffddzjrrLC655BI2bNhAVVWVj3t1cXEx9913H1dccQXR0dHMnTuXa665hunTp3P55ZfT2NjI+++/z7PPPutTxiw4uZHdNGV3zeMBOVO5S2QABYLjiiHdUdfX1/P4449z9tlnExUVhUqlIiIigunTp/PQQw8NOAj3aEaPHs2uXbtYuHAhCoWCRx99lC+//NL7FBVg/vz5XH/99d7vExIS2LZtG5dccgldXV1ceOGFlJaWMnHixCGdO2TU7wGlGmJ9RVdGjIEwjSqoA+FLWkqID4snSh/l+0L3eIpgGsHYS0rQ5eT0mFWWE5WD1WnlUMfQ/m0dC01VFm+Z5ZHocnOxl5UhdXUFLZbGioPEH+EAKhMbZCdQt82Jq9XuYwAjE5ceXCfQxsZGJEnyMYABUKiUaBIMOILYG2mx+DqAykRGRqLT6YLaB1hssRKmVJAZ5ius5NhGQhloQXd/4vHcB6hUKvn000957rnniI6O5uc//zm7du0iq3t8DUBOTg5/+MMfiImJ8W5bvHgxr732GpGRkUydOpUtW7Zw6623huAnEIxUZBE1Pu14EoCeWEvqOugKsjGZQCAYPoPKAHZ0dPDQQw/x/PPPM378eM466yyuvvpqIiMj6ejooLS0lG+++YaHH36YG264gYcffpi4uMENqY6Pj+f222/v8/VLL720xzaTycTNN988qOOPOOr2eMSf2vcmTalUkJsUHlQn0NLWUl8DGJnoLFCHeWIdPScosdhLSgibNKnHdjm+0pZSMiJ676/xJ5Ik0VxtJmtCz6G2+txccDqxHzzYo1Q1EHS2t2FpbfEOXD+SmFQjHctsdNmc3lmFgUQuq1Qn9hxsHpeRxY7lXwU8BhlZVB1dAgrdTqBBLAE1m/eiVkeh1fpmRhUKhbcPMFgUmW3kGvWojnqIotFEodMmeoxgEhcELZ7eSNdrMamU7DFbOSf2+Ohx6g2lUslFF13ERRdd1OvreXl5PPzwwz22z5kzhzlzgvOZKjj+kDOAx0v/H3jKVSPDNLRZHZTUdRwX5jUCgWCQAvCVV16hpaWF7du395jbdyTl5eU8++yzPPvss71e/AT06gAqk58YHtQyin0t+zgn45yeLyhVkJAfNCMYyeHAXlZG1GWX9XgtLiyOKF0UJa0lnJPZS6x+pqPZRpfN5eMAKnPYCbQ0KAJQLqvstQQ0xRNfc7WFpOzAX3AdtZ2gBE1CTwEYn5FJZ1srne1tGCICH0t9fT2RkZHo9T1LpTVJBqy7m5DcEgqlope9/YvZUoLJlNcjcw2ePsCKiuCZ4xRZrOQfVf4pYzTljohREAqFgnyj/rifBSgQ+BuL3cmBRs/Dq7HHUQmoQqFgbEoEa/Y3sbu6TQhAgeA4YVAloLfffjsvv/wyeXl5rFu3ji1beu+DyszM5K9//SsPPfSQX4M8YZAkj6hK6F0A5iWFU1pvxukKfBlFp6OTQ+ZDjIke0/uChEKPEUwQsJeVgcPh4wAqo1AogmoE09xtrNKbAFRFRqJOTAyaE2hj5UFUGg3RySk9XotONqBQELQyUEetBXWcAYW650dGbLqnRDVYZaC9GcDIqJOMSF0uXK3BMVMym/f22VeXkJBAY2MjTmfg52O5JYkSi81bYnk0JlPeiBgGDyeGE6hA4G+KatqRJEjqHq1wPCGMYASC449BCcAjjV42bNjA22+/Pej1giNorwZbW58CMD85nC6nm4NNge9h2tfqsTHvtQQUPDE2FIPbFfBYZGfNvrJqOVHBE4BN1Wa0YWpM0b1fgHW5uUEUgOXEpKajPKInVkatURGZYKApSEYwjlpLDwdQmeikFFQaTdAEYH19fZ8CMJhOoC6XHav1YA8DGJnExETcbjdNTU0Bj6Xc2oXVLVFg6j0DaDLmYbMdwukM7uiQ3sg36inttONwH79OoAKBv/EawKQeP+WfMnLJ6m5hBCMQHDcMWalNnjyZrVu3BiKWEx+5pLKvEtAkz4docW3gn6KVtpSiVCgZHdmHBXliITht0FwW8FjsJaWoExJQRUX1+npOdA4VHRXYnIEvG2uqshCbYuy1pA9Al5sTtFEQjRUHiU/vaQAjE5tqpDkIGUBJknDUdvZqAAOgVKmITc2gIQhOoFarlfb29h4GMDKqCC0KvTooArCzcz+S5OphACMji9RgGMEUWTwZtb4zgPkAWEZAGWiBKQyHJLGvU5SBCgQyu7pHQBxP5Z8ycsx7atpxiQc7AsFxwZAFYGZmJjabjccff/y4nuUUEur3gNYEkb2bmcQYtcSH64LiBFraWkpGeAZ6dR8jJxKC5wQqO4D2RU50Dm7JzYG23gcm+5OmKnOv5Z8yupwcHFVVuMyBFRiS201jRTlxmaP6XBObaqKpyhLw96GrvQvJ5uxTAALEZWTSGIRZgLKpSl8ZQIVCgSbJEBQBKJdUGo29/9sNCwsjIiIiKEYwRWYbMRoV8dre27qNxtEoFKoRUQYqi1TRBygQHOZwBvD4E4Cj4owYtCpsDjcHGkJfZSAQCAZmyAJwyZIlrFu3jnvuuYe8vDx++9vf8tZbb7F9+3a6gmiPf1xStwfi86GfEtn8IDmBlrb04QAqY0oAQ6wn5gBj37sXXX7f5kJjojx9ioEuA3U53LTWdhKb1rcAlMtU7aWBzaS01dfhsNv6zwCmmLBZHHS2B/Z95+wWU/0LwCyaKiuQ3IHtX62vr0epVPbrMuxxAg18GbXZshe9PhW1uu85bgkJCUHJABZbbOQbw/rMXCuVOsLCRo2IURBRGjUpOo3oAxQIurE5XJTWe4TT8VgCqlIqKEyWy0BFH6BAcDwwZAH4m9/8hv379/PRRx9x5ZVXcuDAAe677z4mTZqEyWTiL3/5SyDiPDGo391n+aeMRwAG9gNUkiRKWkrIje7HyVKh8PQBBtgJ1NXRgaO6Gn0/7rJGjZFUU6q3bzFQtNRZcLslYnuZASijHT0aVCrsJYEVow3d2bT+MoDyrELZuCZQOGo7UWhVqKL6NiaIT8/EYbfRVh9YsVNXV0dsbCxqdd8GxpokI87GTqQAz6SymPf22f8nk5iYGJQMYLHF2mf5p4zJlIvZHPoSUPD0Ae4RGUCBAIDi2g5cbok4k5akiP7fxyOVw0Ywog9QIDgeGPIAMYVCQXZ2NtnZ2Vx88cXe7W1tbWzbto2wsN5NCE56XE5oKIFJV/e7LC8pgsWryjDbnZh0gZnv1mBtoNXe2r8ABM9A+H3LAxKDjGyooutHAEJwjGCaDnmewMb0UwKq1OnQZmYGvA+wsfwgYeERGKOi+1wTER+GWqOkqdpMemFMn+uOFUetBU2iod+xCvKswobKg0QlJQcslvr6+j77/2Q0SQZwg6O+E21K33/LY8VsKSEp6eJ+1yQkJNDW1obNZut1bIU/sLncHLDa+WV672WxMiZjHhXNryFJUp+ZwmBRaArj47qWkMYgEIwUDs//iwz5e3O4FHYbwQRzlJVAIBg+frPrjIyM5KyzzuLUU0/11yFPLJoPgMsOCQX9LstP8pSTldQFrgy0pMUjugYUgAmFnrgdgSvVsu3dC2o1ulF9Z7qAoIyCaKqyEB6rRxfWv/DW5eQE3Am0oaKM+Mysfm8GlEoFMSnGgDuBehxA+86KAhijY9AbTTQF0AhGkqR+HUBlvE6gdYErA3U42rDbazEZ+38PyWI1kFnAfZ02XJInq9YfJlMeTmcrXV3BG07fFwVGPVV2B+3OwLsMCwQjHdk983gs/5QZ120Es7u6XfhDCATHAYMSgK+88gp/+ctf6OjoX5R0dnby/PPP8+STT/oluBMK2UwlcWy/y8YkmFApFRTXBFYAGjVGUkw958v5kDgWJLdnHESAsJeUoBs1CoVW2++6nOgc6q31tNkD93RxIAMYGV2uRwAG8iLXWFHe6wD4o4lJCawTqOSScDR0ou5jBISMQqEgLiOLhsrACcD29nZsNtuAAlCpV6OK0gXUCEYeqt6XA6hMXFwcCoUioH2ARd2llIMRgMDIMILpHlch+gAFgsPz88Ydhw6gMjmJJrQqJR02J5XN4n0tEIx0BiUA58+fz6ZNm0hOTuaaa65h8eLF/PDDD2zbto1Vq1bx6quvct1115GcnMzSpUu58MILAx338Ud9ERgTwNi3eQWAXqNiVJyRvQHsAyxpKSEnKgelYoA/f7zHOj6QRjD2vSUDln+CpwQUDmcvA0FjlZnY1P4zXeCZBehqbcXV2BiQOBx2Gy211cRlZg24NjbVRHO1p3cxEDibrOCUBswAQrcTaABnAcpZtIFKQKG7DzCAAtBi3otCocZg6D9zrVariYuLC2gGsMhsI12vxaTuOS/ySPT6NFQqw4gwghlj0KFWHBavAsHJSpfT7XX+Ph4dQGU0KiV53RVMogxUIBj5DEoApqWlsWTJElatWoVer+ehhx7i7LPPZvLkycyaNYv/+7//w+128+WXX/LNN9+Q28dA75Oaut0Dln/K5AXYCbSkpaR/B1AZnQmiswJmBCO53Z4MYN7A/14yIzNRK9UBKwO1dnTR2dY1qAygvntkhS1AZaBNlRUgScRn9C8uwOME6nS4aW8MzBNXxyAcQGXi0rNoqanC6XAEJJa6ujq0Wi2RkQPfJAV6FITZsheDIRulsv/MNQTeCbRoEAYwAAqFEqMxd0RkALVKJWMMepEBFJz0lNZ30OVyE6FXkxZ9fHsoyCWswghGIBj5DKkHcPLkySxevJjKykqam5vZv38/DQ0N1NbW8uabbzJjxoxAxXn8U79nwPJPmfxEjwAMRImhw+WgrLVs4P4/mYSxHvEaABzV1bgtln4dQGU0Sg3ZkdmUtgZGADZ1l1HG9TMCwhtLejoKvT5gTqANlQdBoSA2LX3AtTGpgXUCddRaUIZrUBk1A66Ny8hCcrtprqoMSCxy/5+ynzEqMpokI662LtydgRGjZnPJgOWfMrITaKBKhvdabAOWf8qYjLlYRogTaIFRLzKAgpOe3XL5Z+rxawAjM/aIPkCBQDCyGbYJTHR0NNnZ2cTFxbFz505cLtHM3yddndBc5jFVGQT5yRG0WR3Utdv9HsqBtgM4JecQBGBBwDKA9r2eTMRgSkAhsEYwTVUWVBolkfEDP4FVqFToxowJmBFMY/lBopNS0OgGvqk3RGjRGzU0VQemD9BR2zmo7B9AXPfMwkCVgQ7GAEYmkEYwkiRhsewd0ABGJiEhAZvNRnu7/2+KWh1Oqu0Ob0/dQJhMeVg6S3G7nX6PZagUmMIotliFYYTgpGZX9fE7AP5oxqYczgCK97VAMLLxiwtoQ0MDjz76qPf7rq4uPv74Y38c+sSgoRiQBpwBKCM7gQZiHqDcQzeoElDwxGyuA0uT32Oxl5SgioxEPcib+pyoHPa17gvIhaWpykxMshGlanBvCV1ubsBGQTRUHCS+e6zCQCgUCmJTjd4Mpr9x1FnQJA5OAOoMBiLiE2gIgAB0uVw0NDQMWgCq48JAqQhIGajdXoPT2YFxCBlACIwTaPEgDWBkjKY83O4urNbAmfUMlgKjnnanmyp7YLK0AsHxwE7vCIjj1wFUpiA5ApVSQZOlKyAPsAUCgf/wiwCcM2cOZWVlbNq0CZvNxk9/+lMslsBa0x9X1O0GFIdNVQYgNSoMo1YVkD7A0pZSUowphGvDB7dDQnfZar3/y0Bt3QYwgy17yYnOweKwUG2p9nssTYM0gJHR5eRg37cPyc+Zb0mSaKg4OCgDGJmYbiMYf+PucuFqtnnm6g2SuPRMGgPgBNrc3IzL5RqUAQyAQq1EHR8WEAEo99ANNAReJjIyEq1WG5A+wGKLDY1CwWiDblDr5ZhHghGMnLXcI/oABScpTpebohrPg97xJ0AGUK9RMSbe00axWxjBCAQjmmELwPLycjZu3IjZ7Mk8PPPMM9x7770sXLiQyy+/nKuv7n/g+UlF7U6IHQ3awQkMpVJBXlK41xnMn5S0lAy+/BM8cau0HhdTP2Pfu3fQ5Z9weG6hv8tA3W6JpmrLoAxgZHS5OUg2G45K//a7WVpbsHW0ewerD4bYFCOt9VacDv+KUWddJ0iDM4CRiUsPjBOoLJ4GmwEET9yOWv+XgJotJahUJvT61EGtVyqVJCQkBCQDuMdsZYxBh3YQfZEAWm0MWm38iDCCSdVpiFArvVlMgeBk40CjBZvDjVGrIit28J+zI5mxXiMY0QcoEIxkhi0Aa2trefDBBykoKGDUqFFcffXV2Gw2UlJSmD17tj9jPP6p2wVJ44e0S15SREAygIN2AJVRaSAuz+9GMG6rla7ycvSDcACVSTQkEq4J97sAbKvvxOVwEzsIAxgZ2bjGtte/fYCN5WUAg3IAlYlNNSG5JVpq/Ct2HLUWUIA6YQgZwIwszM1N2Mz+LUmtq6vDZDJhNA7+JkmTZMRRZ/F7ybDZXITJNPjMNQTOCXS32crYQfb/yZiMeVhGgABUKBQUGMOEE6jgpGWXt/wzEqXy+DaAkZGNYMQoCIFgZDNsAXjaaafxxRdfUFlZyaZNm/jtb3/LT3/6UwAWLFjAb37zG78FeVwjSVC7CxLHDWm3/KRw9tV34HC5/RZKi62FBmsDuTFDHNORWOh3Ixj7vv3gdg8pA6hQKAJiBNPU7aAZN4QMoDouDlV8HLZi/2ZGGyoOotGHERk/+ExXTIoRFNB4yL8PDLqqzajjwlBq+58vdyTxmR7h2lBR5tdYamtrSUpKGtI+miQDks2Fq9W/vSgdHUWEmwbXzyuTmJhIY2OjX82yXJLEHrNt6ALQlDciMoDg6V3cIzKAgpMUOUsmZ81OBMZ19zLuEU6gAsGIRn0sO9tsNvR6PbGxscyZM4c5c+b4K64Th7ZKsLcNOQOYnxSOwyVR1mghN3GQ/XoDIAunIZWAgse9tPgLcLthkKVmA2Ev2QsKBboxY4a0X050DpvrNvslBpmmKjOGCC1h4QPPdDsSfX4B9qJiv8bSWHGQuPQMFEP4PWv1aqISDDRW+jfr5qixoEkZvCgGiElJQ6XR0HDwAOmFQ/s33x+1tbVMnDhxSPvIsTtqLKijB2eSMhAul43OzgNkZNwwpP0SExNxuVw0NjYOuo9xIA5a7VjdbsYNQwBWVL6C02lGrR7a39ffFJjCeKemiS63e9BlrALBiYLXATTl+O//kynsFoBVrVaaLV3EGId2XRUIBMFhWFfcF154gZiYGMLCwvjjH/8IeMSgoBdqd3r+O+QMoOdD1J9loCUtJehUOjLCM4a2Y+JY6DJDW4XfYrGXlKDNyOD/s3fe8VFVaR//3el9kknvFZKQ0HsHaYpYEFRs6GLHgl1su+u6vrira8WKiooFRbGASBGlQ6QlkEp672VmMr2c949hBobUmUxJ4Hx38wmee86d39zM3Huf+zSW0LWb1+SAZJQry2GyeK5yoKsFYOwIUlOgL/SsJ8VWAbTv4Z92gqMlaK72nAFIrMRmAEa4dlxYbDaCY+LRWO45D6BGo4FarXbZA8iW8cAScWDyYIsMjeYMACukkjSX1tm119fXe0xLztnQyWEuG4A27+VAKAQzTCyAmQDFWloxkHJpYbUSh5fsYmgBYUcq4CI+yJY2QAvBUCgDF5cNwFOnTuHZZ5/FunXr8OSTTzoMv7q6Olx55ZUeFzjoqc8BhApAFunSMrmIi3CZAAV1ngujONN2BkkBSeCwXHT82o1XuzHrAewVQF1laOBQmIkZpcpSj2mxGYCue0L4qakw19XB3NbmER0Wsxkt1VUuVQC1ExxjMwA9le9madODGCzguWgAAkBofAIaKzz397HnzrlqADIMA26kBMY6z1UCVavzALAg7mMPQDsCgQABAQEeNQDzOvSI4HMRxHPt+ywWJ4FhuGffi39JpZVAKZcoFa1adBjM4HNYSAq5OArA2Ek/a9DSQjAUysDFZQPw0KFDWLp0KZYsWeIUypSQkAC5XI59+/Z5VOCgp+E0EJ4BuFAwwk5qhGcrgbpcAdSONBwQh3jMACSEwFBQAL4LBWDspChsRmN+q2dy74x6M1TNepcKwNgRpNm8QAYPeQHb6mpgtZgREhPv8trgaCmMOjPULZ7xxJvOGk2uhoACQEh8IlqqKmExe8ZLW19fDy6XC4VC4fJaboTY8V48gbojHyJRIths10NKw8PDPesBVOswTOya9w8AWCwexOIh6BgABqCMw0YUn4t8mgdIucSwF4BJi5CB08f+s4MFe0gr9QBSKAMXl886AoHAUcjgwip46enpOHz4sGeUXSzU5wBh7uVCpYRLPRYCarFaUNxejCEBLlQAtcMwthzGulMe0WJuaoKlvR38oa4bgGKuGLHSWBS2esboajkbNumOB5AXFwdGIIC+wDN5gI3lNq9ZSLx7IaAAPBYGaqztAEvCBdvFvEgACI1LhNVi82Z6gvr6eoSFhYHlRo4YN1ICS6seVp3ZI1o6OvIhlboW/mknIiIC9fX1HvPS5nbokCF13QAEAKl0GNQdnm/t4g7DJLQSKOXSw24AXgz9/y7E3tQ+lxaCoVAGLC7fUc2fPx+///47amtrOxmAtbW1sFo9V7Vy0KNXAW1lNg+gG6SGS1HTroNK339PSoWqAgaLweFBc5nwEUC9ZwxAQ77txlOQ5lolRTupilSPeQCbqtRgsRko3Ah1ZNhs8IcO9VghmMayYsjDwsEXua5FJOdBKOWiucozDwzcKQBjJ+RsCGtThWfyAN2pAGrHHsLqCS8gIVZ0dBS4nP9nJzw8HDqdDipV/2+Kmo1m1BtNGCZxr7iNVJIGjaYQVqvncmndJU0soL0AKZccjgIwF1EFUDt2A7CsWQO1B+5fKBSK53HZAIyMjMSzzz6LqVOnYu/evbBarTAajdi6dSs+++wzTJw40WURarUa5eXlMJlcO1HodDoUFBR4pcGyR7C3TnCxAqgdeyGYMx7wAua12rSkKlLd20HECEBVA2ha+q1Fn5cHllwObpRreZF20oLSUNhaCCvp/8OGpipb/h+b414IjiA11XMewLJShMUnubWWYRiPFoIx1Wncyv8DAJ5QhIDwCIdHs186TKZ+Vc7khIgADgNjXf+Pi05XBYtFA0k/DEDAM4Vg7DlzrlYAtSORDIPVaoRW67lcTXdJkwhRazCh3eQZL62vMBqNKC4uRnt7u8trCwoKcOaMZ3uIUgYPhJBzLSAuogqgdoIkfETKbQ+ntmTXQmf0XPsbCoXiGdy6633ggQfw2muv4fTp03jjjTfA5/Nx1VVX4bbbbnOpFYTZbMa9996L4OBgTJgwAWFhYfjqq6/6vH7FihVIS0vD//3f/7nzNrxP/WmAdbaRuhskhUjAYTEeCQMtaClAlCQKcr6bF5vwEbbfHvAC6vPyIUhLc6mR9vmkKlLRYepAjbqm31qaq9QIjnG/FD4/NQWG0lIQo7FfOgghaKwoRWiCewYgYMsD9EQrCKvWBEu7weUKoOcTGpeIJg8YgE1NTbBarW57ABk2Y2sIX9t/D2DH2ZBJidQ9z7VMJoNQKPSIAZjboYOQxUK8kO/WensY60AIA00768UcTHmAn3/+OUJDQzFjxgyEhYXhzjvvhNncNwP2m2++QVpaGubPn+9llZSBSnWbDkqdCVw247E2TwONlLMPsJ/9MQcL39pHjUAKZYDhdubxkiVLUFJSgoKCAvz5558oKyvDBx984NI+XnnlFfz44484ffo0Ghsb8dprr+H222/HqVO9GxmffPIJqqurkZHhXnilT6g/DYSkABz3+uDwOCwkhohRUN//kLH81nykKdzzXAAAFEkAV+whAzDPUUDFHexezP6GgVpMVrTWaBAS4/4FWJCaBphMMJSU9EuLqqkBBo0GofGJbu8jOEYCdaseek3/Qm6M/SgAYyckPhGNFaX9znezG0v96Z3Hi5DA5AEPoLojDzxeCPi8YLfWMwyD8PBw1NXV9VtLbocOwyQCsN18iMLhSCEUxA6IQjBJQgG4DDNo8gCzsrKwYsUKrF27FrW1tcjNzcWWLVuwZs2aXteWlJTgySefxG233eYDpZSBir04Skq4FDw3o08GOuHycw+nylq0KGzwXEE7CoXSf/p95klJScGsWbMQHx/v8toPP/wQd911F4aeLQayYsUKJCcnY926dT2uy8/PxwsvvIANGzaAzWa7I9s3NOS4Hf5pJzVc1u9KoIQQmwEY1A8DkMWy5TL2sxKoRamEqaYGgmHueVEAIFgYjGBhMApa+xd62VqngdVKEBLrvgHIHzoUYBjo+5kH2Fhm85b11wMInCts4y6mWg0YLgucYPfCCwEgND4RBo0G6uamfmmpr69HUFAQeDz3mwlzI8UwNWhBzP0LGe7oKIBE4mYI9Vk8VQk0t0OHdDfDP+1IpGlQd/jfAOSyGAwR8QeNB3DdunVIS0vDrbfeCgBITk7GihUr8NFHH/W4zmg0YtmyZfi///s/JCa6/6CHMvixh39eTA3gL2RB+rmojfggEVIuUk8nhTJY8dujp/r6elRXV2PSpElO45MnT8bx48e7XafX67Fs2TL897//dcvo9BkWM9CQ53ID+AuxVwLtjyelpqMGaqPa/fw/O+Ej+l0JVG8vADOsH8YobF7A/hqATVVqgHGvAqgdtkQMbmwMDIX909JQVgJxQCDEAYFu7yMgTAg2l9XvPEBTXQc44WIwLPe8S8C5Sqb9zQNsaGhwO/zTDjdCDFgITE398zCp1XmQStx/cAHYDMD29nbodO5rMVitKNLq+20ASiVpUKvzPVaVtD8MkwiRox4cHsDjx493ynWfMmUKqqurHT0ru2L16tVITEzE8uXLvS2RMsDJrm4HAAy5iI2iSYlB4J69hrx/61gIeQP4YT2FcgniNwOwpcVWTCQ42DmcKjg4GM3Nzd2ue+yxxzBs2DDH09e+YDAYoFKpnH68TnMhYNYBkaP7tZuMKDnUejMqW7Vu78NuKA0L6t/NK8KHAy1FgNF9Lfq8fDBCIXj9NN7TFGn9NwAr1QgME4HL79+FSZCaBn1e/8JRG8tL+uX9AwAWm4WgSDGaq/vnMTbVul8Axo4kMAhCqaxfBiAhpF8VQO3YcxlNte4bxiZTGwyGOo94AAH0aCj0RoFGDzNxvwCMHak0HWZzOwyG/oek9peRUhHyNDqYrP43RnujpaUFQUFBTmP2/+7u2rVt2zZ8//33LqVJ+OW6RfE6WoMZB4ttn5OP95detLlxAi4bo2NtDzSzq9r9K4ZCoXTCbwagPXTTeEHxDIPBAA6H0+WaXbt24ZtvvsGqVatQUFCAgoICGAwGtLW1oaCHSoxr1qyBXC53/MTExHjujXRHbRYAxlY9sx/YewSdqna/oWpeS54jbLJfRIwAiPVcdVM30OflQZCSAqafobupilQ06ZrQrOv+YUFv2ArA9P8JrCAtDfqCApB+tEBpLC9FqJsVQM8nOEaKpkr3DR1itsLUpO1XARjAlu8WEp/YLwOwra0NBoOh3wYgi88BJ0jQr1YQKlUOAEAm619Id3BwMNhsdr/CQLNVWrAZm9esP9irmaoHQB7gCKkQBivBGe3ADwPlcDhdXrcAgMvldprf0dGBO+64A08++SRqamqQk5ODxsZGmEwm5OTkdGvY+eW6RfE6+4ubYX/OUafUX9S5cRMTFQCAI6X9rx5OoVA8i98MwKioKDAM06kgQn19PaKjo7tc09jYiLCwMNxxxx249tprce2116KsrAxbtmzBtdde62hQfyHPPPMMlEql46eqyjMNqnukLgsISgb4/TMwFGIeogKEjqax7tDvAjB2QtIAFgeoy3Z7F/r8/H6HfwJwvB93vYBWK0FzdUe/CsDYEWRkwKpWw1RZ6dZ6TXsbNG2tCE3of15QSKwUrXUamN18qmyq0wAWAl50/49LaHwiGsvcL45TW1sLwNZ6pr9wIyUw1rhvGKvVOWCzJRAK4/qlg81mIywsrF+FYE6pdUgRCSBk9+/0zeeHg8sNHBCVQDMkQjAAstXuRxf4ipiYmE5/v7q6OjAMg6ioqE7zNRoNQkND8eGHH2LZsmVYtmwZvv/+ezQ1NWHZsmXIzMzs8nX8ct2ieJ0mlcHx74SLPDduUqLNM55Z1jogQs0pFMo5/GYASqVSjB07Ftu3b3eMGY1G/P7775g1a5ZjrL6+HmVltobSt9xyi8PzZ/9JTU3F8uXLUVBQ0G1BGD6fD5lM5vTjdWpPApGjPLKr4VHyfnkAC1oL+lcAxg5XYGtp4WYhGKtWC2Npab8KwNiJkkZBwpW4bQC2N2hhNloRHOt+/p8dQbrt/ehyct1ab/eSecIDGBonBTlr3LqDsUYNsGytE/pLeNJQqFuaoGlvc2t9bW0t5HI5xOL+a+FGSWCq7QBxM8RQpT4NmTQDDNP/U2ZERES/DMBstRYjZaJ+62AYBlLJMKjVOf3eV38Rc9hIFvGRrRr4BuDs2bOxe/duJy/gr7/+igkTJjg+q2q1Gjk5OTAajQgLC0NOTo7Tz8qVKxEZGYmcnBzMmzevy9fxy3WL4nWOVbQCAK4fF41tq2Zc1LlxY2IDwWUzqFPqUdU6OHJ8KZRLBb/WH37xxRfx1Vdf4X//+x8OHTqEm2++GQKBAPfdd59jzvPPP4+rrrrKjyrdwGIG6nP6nf9nZ3i0HDm1SljduHlt0trCJD3iAQRsYaBuegD1hYUAIeD3owWEHRbDwtDAochvcc970VxlC7vxhAeQExgIbnQ09Dnu3Ug3lpWALxJDHup+qwM7QZESsDgMGivcCysyVneAGy4Cw+3/qSE8KRkA0FBW7Nb62tpaj3j/AIAXLQUxWGBudu8mRK06DanMMy1nIiMj0dTU1CmMsC/oLVbka3QYIe2/AQgAUtlwqFX9q+zrKUZKRTg1CArB3HfffRAIBLjpppuwb98+vPLKK/juu+/w4osvOubs3bsXw4cPR6WbUQGUixNCCA6fDYdcPDrqojb+AEDIY2NEdAAA4EgZDQOlUAYSfjUAFy5ciJ9++gk7duzA/fffD4FAgAMHDkChUDjmRERE9FgyOyEhoV89wryCvQBMxCiP7G742UIwFW4UgrH3yvOIBxCwGbUNOYDZjZvXvDyAywV/yBCPSBkWNAx5Le7lLzVVdUCqEEAg7pyz4w6CjIx+GYCh8Ylg3Ozpdj5sLgvBURI0VbhXMMJU3eGR8E8AkIWEQSCRor64yOW1VqvVswbg2UqvRjcK5BiNLdAbaiGT9i//z05kZCQIIW55AfPPFoAZKe1f/p8dmXQEDMYGGAzuF6XxFIOlEExgYCAOHDgAqVSKRx99FPv27cPWrVuxYMECxxyZTIb09HTw+fwu9xEaGoqUlBRfSaYMEEqbNWhQGcDjsDAm1v2Kz4OJiQm2+7nM0lY/K6FQKOfTdbUVH7Jo0SIsWrSo2+0vvfRSj+t//PFHT0vqP7Un4YkCMHbshWBO1yiREOxaOFx+Sz5kPBkixZ65kUbkGMBitBmBUWNcWqrPzwc/ORmsfvR0O5+M4Ax8mf8l2vXtCBAEuLS2qVKN4Jj+h3/aEWako/m990EsFpcL3DSUlyB53MTeJ/aRkDgZ6orbXV5nNVpgatRAPDnCIzoYhkFYYjIaSl03AFtbW2E0Gj1mALKEHHCChTBVdwBjXHtgZA+RlHrIAAwNDQWHw0FtbS3i4lzLKcxWa8FhgGFiDxmAZ4vaqFSnEBLSdSiirzi/EEx/W1x4m/j4eHz22Wfdbp8xYwZyenggtHLlSqxcudILyigDmcMlNi/Y2NhACLgXt/fPzsTEILy3p4QWgqFQBhh+9QBetNRmeaQAjJ3As4VgTp/tHeQK9gIwnvAuAbC1gmBxgNoTLi/V5+R6pACMneHBtpvXnBbXPG/EStBUoUJovOdyagQZGbYcx/Jyl9ZpVUooG+oRnjTUY1pC46Roq9PAqDe7tM5UpwGs8JgHELDlATaUFrtcAMCTBWDscKMlbnkAVarT4HBkEApjPaKDzWYjPDzc8R5d4ZRai1SxEIJ+FoCxw+dHgMsNgkrVv/6ensBRCGYQ5AFSKO5gNwAnJwX1MvPiYVxcINgsBjXtOlS30e82hTJQoAagN6jL8lj+n50R0XKcdqMS6Onm00gPTvecEK4ACEsHak66tMyq1cJQVAThiJEekxIjjYGMJ0NOs2sGYHujFka9BWGeNADPFrZxNQy0ocTmHQtP9lw4WGicFITA5UIwpmo1wGbADfNMfhkAhCUlQ9Peho42157+1tbWIjAwEEKh5zxBvCgpjLUaEItrxqhanQOpNMNzD1FgM2zdMQCz1VqPhX8CNi+tTDYCKrX/8wDFHDaGiASDohIoheIqVitxeMGmXEIGoJjPcUQx0TBQCmXgQA1AT2Mx26pkeqgCqJ2MKDlya1QuFYJp0DSgUduIEcGeCUV1EDkGqDnu0hJ9fj5gsUA4wjNhdIDt5jUjOMNlA7Ch3JYfFxrnOU8XWyYDNy7W5UqgdcVnIJTKPFIAxo4iQgw2l4UmFwvBGKs7wI0Qg+F47rQQnmjL96wvcS0M1JP5f3Z40RLAbIWpwbV+gLYKoJ773AI2A7ClpQU6Xd+LnugsVhRo9B4rAGNHJhsBler0gCjTPkIqHBSFYCgUVznTqEaLxggh91xhlEsFez/ATFoIhkIZMFAD0NM0FQBmvccKwNgZES2H2mBGeUvfb17thlFGsGeqFzqIGmt7n4a+Gxi67FNgBAKPFYCxkx6UjpzmHJduXhvKVAgIE4Ev8kwBGDvCdNcLwdQXFyI8eahHvUssNgshMRI0ulgIxlij9mj4JwBIFEEQyQPQUNL3SqBWqxV1dXUeNwC5kRKAAUwu9AM0GJthMNR7rAKoHXu/OFcKweR36GAhtmIpnkQmHQ6zuR16vf/7zA2WQjAUiqvYwz/HxQeC58GHbIOBSQnn+gFSKJSBwaV1FvIFdVnwZAEYOxmR5wrB9JVTzacQKgpFmNjDVVKjxgAgLrWD0J0+BUF6OhiOZ+sODQ8ejhZ9C+o19X1e01iuQliC53tqCTIyoC8oADH3LfeOEIK6kiKP5v/ZCYmTudQKwmoww9yks3nJPAjDMAhPGuJSIZjm5maYTCaPG4AsPhucUJFLeYD2Fgme9gAGBQWBx+O5FAaapdaCyzBIkwg8quX8QjD+xl4IplBDvYCUi4tDJfbwz2A/K/E94+IDwWKAihYt6pT0u02hDASoAehpak4AwUM8VgDGTqCYh+hAoUsN4U83n/Z8+CdgawbPFdneax/RZ5+CcLhnb6KBc97NvhaCMZssaK7u8Gj+nx1BRjqITgdDaWmf5isbG6BXqxCR7HkDMDROivYGLYy6vhmjphoNQDxbAMZOWOIQ1LtQCMZuFEVEeKYa6fnwoiQwupAbqVLngMMJgEAQ7VEdLBYLERERLhmAp9Q6pIkF4LM8e9rm8YIh4EcOCAMwQyoEC0AWDQOlXERYrASZpZdeARg7UgEX6ZE0D5BCGUhQA9DTVP8FRE/wyq5HxQTgZGVbn+ZarBbkNud6PvwTANgcW4hrHyuBmpubYaqthXCk543REFEIwkRhfc4DbK7ugNVCPFoB1I5g2DCAYaA/3Tct9cWFAICwJM+GxQJAaKzt/TVV9s3bZaxRg+GywAnxbHghAIQnDYFerYKqqW+95urq6hAUFASBwLOeLgDgxUhhqteAmK19mq9WnYLMwwVg7ERFRaGmpqbP80+otBgl8/zfBwCkshFQqd3rY+lJxGw2hkmEOKZ0LU+TQhnI5NWqoNKbIeVzkBHp+WvPYGASzQOkUAYU1AD0JIYOoCEXiBnvld2PiQ1ETo0KBrOl17mlylJozVqMCPGCBxCwhYH2sRCM7pQtjE4w3DtaXCkE01CmAovDINjDoY4AwJZIwEtKhO5U3zwp9SVnIA8Lh0gm97iWgHARuHy2o+BNbxir1OBGSsCwPW/ohCUmA+h7IZjq6mqPh3/a4UZJAAuxtbzoBUIIlKqTkMs9W9HXTmRkJJRKJTSa3rUoTWac0eoxVuZaH9C+IpONgFqdA0J6P7d4m7EyEY6rqAFIuXg4XNoMAJiQoADHQy1cBhsT7XmA1ANIoQwILs0zkbeoPQEQq9c8gGPjAmG0WJFb2/tN/enm02AxLKQHebAFxPlEjgbaKwFNc69TdadPgR0UBG6Ud27qM4IzkNuSCyvp3avTWK5CSIwUbC8l4YtGj4buZN9aZNQVeyf/DwBYLAZhCTLUl/YtZNhYoQbPg1VRz0ccEAhZSBjqigp6nWsymVBXV4fYWM/03LsQXoQEYDMwVvb+HdLpymEytUEuH+MVLXYjty9ewONne+ONl3vJAJQOh8WigUbbt/BlbzJOLkaR1oA2k2t9LCmUgcqhS7D/34WMT1CAYYDSZg0aVXp/y6FQLnmoAehJqv4C+DIgJNUru0+LkIHPYeFERe9hoKeaTiFRnggR1zshY4gaa/td27uxoz91GsLhw70SRgfYDECNSYNyZXmvcxvKPdsA/kKEo0bDUFQEi7rn0EuL2YzGshKv5P/ZCU+Uo75U2WvunbndAIvSAH6s945L5NBU1BTm9zqvtrYWVqsVMTExXtHBcFngRUlg6ENorFJ5AgADmWyUV7QEBgZCLBajqqr36pvHVBoouGwkCHle0WIrBMNApXStv6c3GHfWy3mCNoSnXASYLFYcPVv98lI2AOVCLtLCbdcYWg2UQvE/1AD0JNVHbYaRh4s02OFxWBgRLcfJyvZe5+Y053gv/BMAAuMBUZDN6O0BYrVCd/q0V/L/7Ni9nKeaew691GtMUDbqvFIAxo5w9GiAEOiye9bSUl0Js9HgNQ8gAIQnyaFTm6Bs6rmght0bxovz3nGJShmGxrISmIyGHudVVVWBx+MhNDTUa1p4cTIY+9Aio115AmJxMrhc7xwXhmEQExPTNwNQqcE4mdhrD1E4HCkkklS0K13r7+kN4oU8KLhsmgdIuSg4Va2ExmhBgOicAXSpYu8HeKSU5gFSKP6GGoCeghCbARjjnfBPO2NiA3G8Fw+g1qRFUXsRhgd7vuqmA4YBYiYBVUd6nGasqIBVpfJa/h8ASHlSJAckI6sxq8d59r543jQAeQnxYMvlvYaB1hUVgmGxEJqQ6DUt4WdbXdSX9BwGaqxQga0QgC31jncJACJT0mC1WNBQ3HMeYFVVFaKjo8Hy0kMUAODHyWBpN8Cs7NkYVSpPeC38005sbCyqq6thsXSfe2chBCdUWozzUvinHbl8LJQDwABkGAbjZGKaB0i5KLAbO5MSgsBieecBzmBhUiLtB0ihDBSoAegpWksBbYvX8v/sjIkLRL1Kj9r27r06eS15sBKrdw1AAIidBFQfAyymbqfosm29AoXDvVCN9DzGhI7Bicaeq5LWl6rAF3MgDxV6TQfDMBD2IQ+w9kw+QuMTweV7vtKlHb6IC0WkGHW95AEaKlTge9H7BwDBsXHgCoSoOdN9GCghBFVVVV4L/7Rj93QaeyiQYzarodEUed0AjImJgdlsRn19930sCzV6dFisGOulCqB2AuRjodWWwWj0/9P5cXIxTqi0sPSxdQiFMlA5VGLLk7+Uwz/tTIi3eQCLGzvQ3NHzAzgKheJdqAHoKeyhkNFjvfoyY2IDAQAnemgHkdWUBRFHhKSAJK9qQexkwKQF6rsPd9SdOAn+kGSw5Z6vdHk+Y8LGoExZhlZ9908W64rbEZEU4LUwOjvC0aOhy84G6cGrU1OYh6iUYV7VAdjCQHvyAFqNFphqNV4N/wQAFouNiCEpqC3M63ZOa2srtFqt1w1AtpQHdpCgxzBQpTILAEGA3Lvf54iICHA4HFRWVnY755hSAzYDr7WAsCM/+15tuY/+ZaxMhA6LFWc0tFgEZfBiMFtwrNx2rZ5CDUAEinlIDbcVG/uLegEpFL9CDUBPUf2XrUG6MNCrLxMi5SNGIcSJivZu55xoOIFRoaPAYXG8qgURIwGOAKjsPgxUe/w4hGO8exMN2DyAALoNA7VarKgvUyEiybuGKAAIR4+CVaOBobi4y+0dba1QNtQj0gcGYESiHK11Ghi0XXtpTdVqwEq8bgACQOTQNNSeKei2KI09Fy4qKsrrWvhxMhh6NABPgMsNhFAY71UdHA4HkZGRPeYBHlVpkC4WQsxme1WLQBAJPj8c7cpjXn2dvjBKJgKbsRW/oVAGKycr22EwWxEs4SM51POthwYjExPO9gOkeYAUil+hBqCnqDrqtf5/FzImNrBbD6CVWJHVmIXRod7pXeYEhwdEjQMqD3e52dzWBmNJCURjvRtGBwARkgiEi8NxsrHr0Mvm6g6YDRZEJAd4XYtw+HCAze42DNTuBYtKSfO6lvBEOUCA+rKujR1DhRoMnw1umHe9S4Dt/eo71Gir67rtQVVVFUJDQyEUei9E1w4vTgZTXQeshq69tErVSchlo73uLQZseYCVlZXdGsbHld7P/wNs4cty+Rgo2/2fByhmszFMLMQxJa0EShm8HD6v/YMvziWDgYln8wCP0H6AFIpfoQagJzB0AI25Xs//szM2LhC5tUroTZ1vXovbi6E2qTE2zPteNwC2PMDKI7YiOBdgN4BEY32jZXToaJxo6Dp8ra5YCTaHhdBY7/S6Ox+WUAhBWlq3BmBNQR7kYeGQKLwfEiQPFUIg4XYbBmqsUIEXKwXjg+IEEUNSAIZBTTdhoL7I/7PDj5MBVsBY3bkdBCEWKJUnvZ7/ZycmJgYdHR1ob2/vtK3FaEapzuATAxAAAuTjoFLnwmLxf37OWDktBEMZ3DgMwEQa/mlnwlkPYGGDGq0ao5/VUCiXLtQA9ATVf9kawMdO8snLjYkNhMlCcKq68039iYYT4DAcZAR7t+iKg9jJgKbJVgTnArTHj4MTHg5OpHcawF/ImNAxyGvJg87cuUBOXUk7QuOlYHN985EXjh4NbVZWl9tqCvMRNdT73j/A5tWx9wO8EEIIjJUq8LzY/+98+CIxQmLiUFvYuSG8TqdDY2OjzwxATqgIjIDdZSEYjaYYFkuHTw1AAF3mAdoNIG8XgLEjDxgLQoxQq0/75PV6YoJcjGKtAU3G7otMUSgDFZ3RgpNVNP/vQoIlfAw5Gw5L8wApFP9BDUBPUH4AEIcAwd7r6XY+aREySPmcLmPoTzSewLCgYRByvB9GB+Bs2CvTZR6g7thxiMaM8Vnoy5iwMTATM3Kac5zGCSGoK1YiIinAJzoAQDR6FEwVlTA3NTmNG/U6NJaXICo13WdaIpLkqC9TwWqxOo2bm3Swas1erwB6PpEpaV0WgqmurgYAREdH+0QHw2LAi+06D7C9/SgYhnu2Obr3EYlECA4O7jIP8FB7ByL5XMQKvNei43wk4lSw2aIB0Q9wcoDN63mknXoBKYOP4xVtMFkIIuQCxAX55gHOYMHeDzCzjOYBUij+ghqAnqD8ABA31dYbzwewWQwmJChwpIuT58nGkxgT5hvPBQBAIAfC0jvlAVr1eujy8iAc56NQVADJAcmQcqWdwkCVTTpoVUafFICxIxw3DgCgPXrUabz2TAGI1YqoVO8XgLETkRwAs8GCpsoOp3FDmRJgATwfhMXaiUwZhtbaamiV7U7j5eXlkEgkCAry3ZNyfpwMxkoViNU5fLmtPRMy2Qiw2b67aYuJienSA3iovQNTAiQ+e4jCYnEgk40aEP0AI/g8JAh5ONze0ftkCmWAcX77B5r/58zEhLP9AGkeIIXiN6gB2F+MGqDmBBA/zacvOykxCMcr2mA0n/PqVKurUa+pd1TE9Bn2PMDz0J08CZhMEI0d5zMZLIaFUaGjOhWCqSlsA8MAEUMCfKaFGxoKXkICNJl/OY1X5Z6CSB4ARZRvQh0BIDReCg6fjZozzoWDDCXt4EVJwRJ4uVrsecSk27xqVXnOXtqysjLEx8f79EaJnyQH0Vtgqj1nYBBC0NZ2BIEBE32mAwDi4uLQ2NgIrfZc0ROlyYwctQ5TAnxbPTBAPg7t7cdASPdtTHzF5AAJDlEDkDIIOVxK8/+6w+4BzK9XQdlNhWoKheJdqAHYX6r+AqwmvxiAepMVp6rbHWN/1f8FFsPC2HDfed0A2PIAW4oAdYNjSHMkE2yFAvyhQ3wqZUzYGGQ1ZcFsNTvGagrbEBInA1/oO0MHAEQTJ0Cbmek0VpVzCjHDhvvU0GGzWYhMkqOm8JwBSAiBoVQJvg+9ogAgVQQjMCIKVbnZjjG9Xo+6ujokJCT4VAsvWgqGy4LhvAI5Gk0RTKZWBAb6Jp/Xjv29l5eXO8YylRpYAUwN9K0BGBg4GWazEuqOfJ++bldMDpCgQKNHi9Hc+2QKZYDQYTA7cvRpA/jOhEoFSAwRgxDgr3LqBaRQ/AE1APtLxUFAFASEpPr0ZYdF2vIAj5yXB3ik7giGKYZBxvNdThcAIGGG7XfZPseQ9sgRiCdN9Hnoy/jw8dCYNMhtyQVgM3Sqz7QjOsW7/Rm7QjxxIozl5TA1NAIADFot6kuLEJsx0udaolICUVuihOVsHqC5UQtrhwl8H+ZF2olJH47K3HNFRuwtEOLj432qg+GwwIuXwVDa7hhraz8ChuH6rACMHblcDoVCgbKyMsfYofYORPkw/++clpFgsQRoa+u6vYsvmXzW+3lESb2AlMHD0bJWWKwEsQoRogNp/l9XnAsDpXmAFIo/oAZgf/Fx/p8dRx7g2Rh6Qgj+qvsLEyN8G7oGAJCEAqHDgLI9AABLRwd0OTkQTfStFwUA0oPSIeFKkFln87y11WmhUxn9YgCKJtjagmj/smmpKcgFsVodYZC+JGpoIMwGCxrLbW0PDKVKgM34pAH8hcRmjERbbTU6Wm0X/rKyMshkMigUCp9r4ScFwFCmBDlrGLe1ZUImGwk220dFlM4jISGhkwE42Yf5f3ZYLD4CAsajrfWQT1+3K6IFPMQKeDjURg1AyuDBkf9Hwz+7ZZKjEAz1AFIo/oAagP3BoAaqj53zgPmYSYlBOFbRCr3JgpL2ErToWzAhwje9CDuRMBMo3QsQAu2xY4DFAvEk3xujHBYH48LH4UidLSexurANLDaD8GTfhjoCACcoCPwhydCcDQOtzD0FiSIIAeG+aYtxPiGxEnAFbEcYqKGkHbwYKVg8ts+1xAw7mweYewqALezR1/l/dgRJASBGK4zVHSDEivb2TJ+Hf9pJSEhAc3MzVCrVufw/H4d/2gkMnIx25TFYrf7v0zU1UIIDNA+QMoiw5/9NSaYGYHfYPYC5tUqo9DQPkELxNdQA7A/lB235f0mX+eXlpw0Jht5kxfGKNmTWZ4LL4mJ06Gi/aEHiTEBZBbSWQnskE5yICHBjY/0iZVLEJGQ1ZkFr0qLmTBvCEmTg+sHQAQDRhInQHj4CQgiqck4hNn2EXwwdFpuFyCEBqC5sA7Gezf9L9L1RDAAieQCCY+JQmXsaWq0WdXV1Pg//tMONlIDhs2EoaUdHRz5Mpja/GoCAzSDe39YBK4Dpgb6r0Ho+isDJsFi0UKlO+eX1z2dmoBSFGj3qDP43RimU3mjXGpFba2svQz2A3RN+tj2GlQDHaB4gheJz/G4A/vzzz5gzZw4yMjJw0003obi4uMf55eXlePTRRzFx4kRMnToVTz/9NFpb/XTyKNkNBMQBikS/vHxquBQhUj72nWlCZl0mRoaM9F3/vwuJmwowbKBsLzRHjkA8YYLfSl9PjpgMk9WEE/UnUFPY5pfwTzviqVNhqqmBMjcHjeUliPFD/p+dmFQF6kraoStXwao1QzDEf8clNmMkKk6fRGlpKQAgKSnJLzoYNgN+ohz6ona0tOwDmy1CgNzHRZTOIhaLERYWhtLSUuxpVSNZxEeMj/P/7Eil6eBwpGgdAHmAMxRSMAD2tKr9LcVBcXExbrrpJmRkZGDOnDn4+eefe5yv1Wrx5ptvYt68eRg9ejRuueUWZGVl+UYsxadklrWCECApRIxQmcDfcgY0ExPOhoHSdhAUis/xqwG4detWLF26FFdddRU++eQTEEIwffr0bg06i8WCBQsWID4+Hu+88w5efvll7NmzB3PmzIHBYPCxegAlf9i8f34ydBiGwfQhwdhzph5/1f+FSRH+8VwAAAQyIGosTNk7YSgogHjaVL9JSZAnIEQYgqOncmDQmhGb7r+nsOKJEwAuF0VbbDeI8SN93KLjPGLTFbCaCZqO1ILhs33a/+9C4keNhbq5CbmnshEaGgq53D/eSAAQDA2EsUKFluZ9CAycDBbLP0YXACQmJqKouBh/tqowS+G/vw/DsBEYOBmtrfv9psGOgsvBSKkIeweIAdjS0oLp06cDAD799FMsWrQIS5YswdatW7tdc++996KyshJPPfUUPv30UwQGBmLKlCnUCLwIOVxytv0Drf7ZK5POekj/KGiEzuj/tjMUyqWEXw3Af/7zn7j11lvxyCOPYOLEifjiiy9gNBrx/vvvdzmfzWYjNzcXq1atwoQJEzBr1ix88cUXyMrKQuYF5fa9TlsF0FLst/BPOzOGhKBYdRoakwbTo6f7VQuSLoPm0F8Aw0A8zbdtMc6HYRhMjpyMmnwl+GIOQuN9X+jEDksshmjsWJTnZiMkPhGSQN8XOrETECaCNEgAU4kSguQAMGz/ff2jh2WAzeWhtKzMb94/O4KhgbAyWihVx6FQ+Pc7NGTIEFRbgBqDCbMU/vvcAkBQ0CwolSdhMrX7VQcAzFJIsa9NDSsh/paC999/H2azGRs2bMCECRPw6KOP4qabbsKLL77Y7ZpPP/0Ur7/+usMDuHbtWsTFxeGLL77woXKKL7AbgFOSgv2sZOAzMiYAAFDU2IHL39xHjUAKxYf47Q5QrVbjxIkTWLBggWOMx+Nh7ty52LNnT7frOBznXm7k7A2Bz8MNS/+0hTz6qQCMnWlDgsEWn4GYE4hUhW9bUXRiyHx0VFohSEkAJ9B/4YUAMD1qOsR1YQgZIgKL5R8PrR3xtKmo13Ugfvgov+pgGAYJKYHga0wQpPjPEAUALo+PkLThMJjMSE5O9qsWTpAQ+vhSEFgQpPDv9zk2NhZ1IZHggGBygNivWmzHworW1gN+1QEAMxVStJosON2h87cUR9TJ+deihQsX4vjx4+jo6LpYDZfL7TRGCPFbmDzFOzR3GFDYYPNUT6L5f72i1p/r71nRqnUcOwqF4n38ZgBWV1eDEILw8HCn8fDwcFRXV/d5Py+88ALi4+MxYUL31S8NBgNUKpXTT78p+QOIHgcIA/q/r34QLOFDElgEqTUDLMa/KZ0kdDg0DQJIEvyf9zBaNh6hmlgow2r8LQWaxDgYOWxE8P3fDyomkAcGgCHI/38jbngUYLUgMizM31Kgj80HVx8GodA/hYvscDgcNEXGIk6nhpjtn8JFdgSCCEgkqWhu2eNXHQAwTiaGmM3Cnhb/3yBWVVV1ed0ihKCmpm/nm6+++gpnzpzB9ddf3+0cr1y3KF5l35kmAMDQMAkUYv+Fkg8WUsKkCBTZHo7w2AyGhvqn6jGFciniN4vBarX13brwySiPx4PF0rcwgH/+85/Ytm0bNm7cCD6f3+28NWvWQC6XO35iYmLcF25n4WvAojf6v59+Uq+ph4ldi4b6BJjO9jLzF7pTp2A1MpBIKvyqAwDai2wVA0/w/J/DVNvaDI6VQFJU6m8pkGhMUFkIqiv9X1ZfZSFga9WoO5PvVx2EEKgEJyBuzIC5QetXLRqLBSV8MULrKqHT+d/bFRQ0Cy0te0GIf88tXBaDTSOTsCLa/2F1Vqu1y+sWgD5duw4dOoR77rkH//rXvzBpUvd52165blG8hs5owd9/zgUA1Cv1NJyxDwh5bPz68HRw2QyMFoL8evqQg0LxFX4zAIODbRfylpYWp/Hm5mbHtp545ZVX8Oqrr2Lr1q2YOLHnfnPPPPMMlEql46eqqsp94XYkoUBYev/300/21+wHi2FD1ZaAo34updyxbz/YMjEErCKgvdKvWspzWsAKMeBg217ozXq/aik98RciZIHQ7NnrCFn2B8RKYCxqh1bGQ/mpJr/pAGxVEWvq6iFjCEqO+zh/9wI6OgpgsNRC2joGugL/fof2tqphBIO45jqUlJT4VQsABClmwmRqhVqd428pGCMXQ8rxr1cUsF27urpu2bf1RGZmJq644go8/PDDeP7553uc65XrFsVrHC1vRYfBFtKo0ptpOGMfiQwQ4ppRUQCADYf9//CYQrlU8JsBGBYWhpiYGBw+7Fxm/ODBgxg3blyPa//zn//gX//6F7Zs2YLZs2f3+lp8Ph8ymczp52Lhz8o/MTp0FMIlgdiV1+BXLerduyGZORMMmwOc2eE3HRaTFRU5LUgcFQq9RY+j9Uf9pkXd0oz6kiIMmTQVpspKGIqK/KbFWKmCVWOCKCMYNYXt0Gv813y3qKgIhBCkpg1DybFMEKv/PExNzbvAZksQEDwZ+tyW3hd4ke3NSgwVCZAik6CwsNCvWgBALh8NDkeOpubf/S1lwDB+/PhO160DBw4gJiYGoaGh3a7766+/sGDBAtx3331Ys2ZNr69zMV+3LkaOV5x7eBQfJEJKmP+q+A42lk+OAwBsO12P5g4/VHSnUC5B/Jo0dt999+Hjjz9GQUEBAOCjjz5CaWkp7r77bsecZ599FgsXLnT892uvvYZ//etf2Lp1Ky67zL8VOP2N2qjG4brDmBc3D3OHhWJXXoPfPEyGkhIYS0ogvWKRrSdgwa9+0QEAVQWtMOktGDcpBdGSaPxR9YfftBQfPQwWm42UpcvAEonQsXu337ToclrAknIRMzMaVitBRY7/jJ38/HxER0cjY8p0aNrbUFvkP2OnqWkXgoNnQ5wRDmOVGhalf25AzFaC31tUuDxYhrS0NJw5cwZms7n3hV6ExeIiJHgOGhv990BnoHH33XejqKgIn3zyCQDbZ/nTTz/F/fff75jz559/Ijk5GZWVtkiI48ePY/78+bjvvvvwn//8xy+6Kd7DaLbim79sHtpH5g7Bb6tmQMjzv7d6sDAiOgAjo+UwWqz49ij1dFMovsCvBuDTTz+N66+/HiNHjoRCocBzzz2HL7/8EsOHD3fMaWxsdFxE29ra8OSTT4LFYuGee+5BcnKy42fTpk3+eht+Y1/1PpitZsyJnYN5w8JR3aZDQb1/wk7Uu3aBEYkgnjoFGHYNULYP0PonnK40qwnyUCEUkWLMi5uHPyr/gNnqnxvp4qOHEZM+AqLAQIhnzoD6d/8YgIQQ6PJaIBwWBKlCgNB4Gcqy/BMGajQaUVxcjNTUVEQOTYVIHoDio/5pOK7T1aCjIw8hwXMhTFUALAa6PP8YxkdVGrSaLLg8RI60tDQYDAaUlZX5Rcv5hIQsgFZbDI2m2N9SBgTDhw/Hhg0bsHr1aigUCowaNQo33ngjnnrqKcccjUaDkpISGI22XOTHHnsMKpUK33//vdN165577vHX26B4kK2natGoNiBUysfKWcnU+HOD2ybHAwC+OlIBi9X/7V4olIsdTu9TvAebzcZ7772HV199Fa2trYiIiOjU5mHNmjXQ6205XHK5HEXdhND1FHpzsfJ7xe8YHjwc4eJwBCZaIOVzsD2nHmkRvg8VUu/cBcnMGWDx+UDaVcCvj9u8gGNu86kOq8WKsuxmDJsaAYZhMD9+PtbnrsfxhuOYGNFzrqin0alVqMrLwZwVNs+AdO5c1D7+BEx1deBGRPhUi6leC0urHsJ0W45S4qhgHNtWDrPRAo6Pb1ZKS0thNpuRmpoKhsVC8rhJKPrrEGbc8jefl8Vvat4JhuEiKGgmWBwu+Ely6HJbIJkc6VMdAPBbkxJhPA5GSUVgpCIoFArk5+djyJAhPtdyPgrFdLDZIjQ27UCC2L8tOwYKN910E66//nrU1dVBoVBALHZu2XHZZZehqKgIcXG20Lavv/66y6I+F66jDD4IIfjkgO1Bze1T4sHj+Lca92Bl0YgIvPxrHmqVeuzOb8D89PDeF1EoFLcZEGcqsViMmJiYTsYfAISEhDiqn7FYLKenp+f/XGr5ETqzDgdqDmBO7BwAAJ/Dxrz0MGw5VevzMFBjdQ30eXmQzZtnG5CE2sJA837yqQ4AqCtWQt9hQuIo2wOB9KB0RIojsbN8p8+1lBz/C4QQJI+3VfqTzJgBhsuFarvvw+l0Oc1g+GzwE+UAgMRRITAbrajM9b2XNi8vD8HBwY6CGckTJkPZUI+mCt97uxobt0GhmAoOx5avI0wPhqG0HRYf50daCMEvje1YFBIAFsOAYRikpaWhoKDAUTHZX7DZfAQFzUITDQN1gsPhICYmpksjTiQSITk52VEtNCoqqsvrVoSPHwRRPE9mWStya1UQcFm4eYJ/28gMZgRcNm4Yb7vX23CEFoOhULzNgDAAKa6zv3o/9BY95sbNdYxdNTISpU0a5Nb6tpSyevtvYPh8iGfMPDc47BqgdA+ga/OplqJjDZAo+AiNs93QMwyDeXHz8Hvl77BYfVuWu+DgXkSnpUMcEAgAYEulkMyaCdXWrT7VQQiBNqsRwoxgMGefTgeGixEcI8GZo/U+1WI0GpGfn+8U5h2bMQICiRQFB/f6VItOVwWl8gTCw65xjAnTgwBiM5h9yZH2DtQbTVgcFugYGzZsGLRa7YAIAw0NuRzqjlxoteX+lkKhDCg+3m/7fi4ZE41A2vuvX9w6MQ4MA+wvakZpk/9bFVEoFzPUABykbCndgoygDMTJ4hxj05KDESjiYkt2rc90EEKg/PkXSC6bDbbkvCfhw64GiBXI+8VnWiwmK4qPN2LohHAwrHOhhPPi56FV34qjDb6rBtrR1orK09lIm+ZcpVa26Croc3NhKPXdTb2xSg1Lix6i0SFO40PHh6P8VAsMOt/lRxYWFsJkMjkZgGwOFymTpyP/4F6fVgNtaNgKFkuI4OA557RIeeAPCYT2ZKPPdADAjw3tiBHwMFYmcoxFRkZCoVDg1KlTPtXSFcHBl4HNlqC+/md/S6FQBgzlzRrsLrBV314xLcHPagY/MQoRZqfYone+POLfVlIUysUONQAHIa36VhyoPoCrkq5yGueyWVg4PAJbT9XB6qMkakNBAQxFRZBffbXzBmk4kDgLyP7GJzoAoCKnBQatGSkTnHMHRgSPQKw0FltKtvhMS+GhfWCxWRg6aarTuGTWTLAkEp96AXVZTWBJeeAnBjiNDxkfBovFilIfGjunT59GdHQ0FAqF03ja9NnoaGlGdb7v+s3VN/yCkJC54HCcQ/hEo0NhLFfB3Oqb/pEGqxVbm9qxODTAKQeSYRiMHDkSeXl5jmIi/oLNFiI09HLU1//k116WFMpAYv3BMhACzE4JQVKIxN9yLgpuO9sSYtPxKmiN/q2CTKFczFADcBCyvWw7AOCKhCs6bbt6ZCRq2nX4y0dN4ZU//wK2QgHJtGmdN466Bag8DLT4pqF1YWY9QmKlUEQ639AzDINrkq/Bropd0Jg0PtGSt/9PJI6ZAIHY+aaAxedDOn8+lFu3+uRGmlis0GY3QTQqxMkrCgCSQD6ihgagMNM3/SO1Wi2Ki4udvH92IoemQh4ahrz9e3yiRd1RAI3mDMLDru60TZgeBIbH8pkX8M8WNdrNFqfwTzsjRoyAyWRytMrxJxHhi6HTV0KpPO5vKRSK31HqTNh0vBoAcOe0RD+ruXiYOSQEsQoR1HozfsnyXTQThXKpQQ3AQciWki2YFj0NgYLON4wTEhSIDxL5pJcOMZuh/HUrZFdeCeZssQMnUq8E+DIge6PXteg1JpTnNGPohLAut1+ddDX0Zr1PisE0V1WgsawEadNmdbldfvXVMFVWQnfc+zfS+sI2W/P3UV1XyR06IRw1Z9qgaulcodDT2EMZ09PTO21jGAZp02fjzJEDMBm873mrrf0OXG4QFIrODy5YPDaE6cHQnmz0iZH+VV0LRkiESJMIO20LDAxEbGwssrOzva6jNwICJkDAj0Rd/Y/+lkKh+J2Nf1VCa7QgNVyKqclB/pZz0cBiMbh1kq2YzheHK2jEAYXiJagBOMg403YGOS05uDqps+cCsN1IL5sQi19P16Fd692wsY49e2Bpaob82mu6nsAVAumLbWGgXi7AUnC4DiA2g6YrwsXhmBQxCT8V/+RVHQCQves3iOQBSBw7vsvtookTwIuLQ9vGb72uRZNZB260BLyorsOTkseGgstnI++Ad5+0EkJw7NgxpKamQiLpWkvGrLkw6nUoOLTPq1osFj3q639EZMRSsFhdF20QjQ2DuVkHQ6nSq1pq9EbsblHhtqjubyBHjRqFkpIStLX5tqDShTAMC+Hh16KhYSvMZt940imUgYjZYsXnh8oBACumJvi8fc3FzvVjY8DnsJBXp8KJSv+e9yiUixVqAA4yNhZsRKgwFLNiZnU7Z8mYaFitBD+erPGqlravv4Fg5AgIu/DoOBizHFBWAUW7vKaDWAly9tYgaUwoRLLuq7AtHrIYJxpPoKTdeyGpRr0Oeft2Y/hl88HmdOEVhc1ID7jxRqh37IDZizf15lY99GfaIJnYfal5noCDlInhyDtYB4vFewVYKioq0NzcjHHjxnU7Rx4ajoSRY5C98zev6QCAxsZfYTarEBl5Y7dz+ElycEKE0Byp86qWb+paIWCzsDi0szffTkZGBvh8Po4dO+ZVLX0hMnIZLBYt6htoMRjKpctvOfWoVeoRLOHh6lG+7xl6sRMo5uGqkbbjuuEwbQlBoXgDagAOIlRGFbaWbsXSlKXgsro2LgAgRMrH/PQwfJ1Z6bXwCUNZGTSHDiHwppt6nhg1FogcA/z1oVd0AEB1QRuUTTpkzIzqcd7c2LkIEYbg6/yvvaal4MBeGPV6jJhzeY/z5IuvBQAoN3svnE5ztB4Mnw3hyJAe52XMiIJOZURZlvdaHxw/fhwKhQIJCT1Xyhs5fyEaSotQX1LkNS01Nd9AETgNIlFct3MYhoF4UgR0uS2wqLzjSTdbCb6ua8F1oYGQcNjdzuPxeBg9ejROnDgBk8m3/QkvRCiMQnDwZaiu3kBDsyiXJIQQfHy28futk+Ig4Hb/3aW4z/KzxWC2na5Hc4fBz2oolIsPagAOIn4p/gUmiwlLhyztde6tk+JQ1NiB/UXeualv37gR7IAAyK7oXIjGCYYBJt4LlPwBNJ3xipbTe6sRFCVGRJK8x3lcNhc3pNyALaVboDR4PrSPEIKsnb8icfQ4yEK6zrmzwwkMhPTyy9H2zTcgZs9XOiMmKzRH6yEeEwYWr+cblKAoCSKS5MjZW+1xHQCgVquRl5eHcePG9RoqlTB6HKTBIcja+atXtKhUp6BUnURU1M29zhWPCQPDZqD5yztewF+b21FrMGF5D+GfdsaNGwedToe8vDyvaHGF6OjboNGcQXu779qqUCgDhROVbciuagePw8Ktk7p/iETpHyOiAzAyJgBGi9UnNQ0olEsNagAOEsxWM74u+Bpz4+YiRNSzRwcAJicGYXiUHB/tK/W4FotKhfYfNiPg+qVg8fm9L0hfDIhDvOIFbG/QouxUM4bPiu5THsbSoUthtprxY5HnPW8Vp06iqaIMo6/oOj/zQhR33A5TdTXUOz1fmEZzogFWjQniKX0LTxpxWQxqzrSjoUzlcS1HjhwBh8PBmDFjep3LYrExav6VyN+/B+pWzz+8qKhcB6EwFiEhc3vXIuRANCYUHUfqQEyezWElhODdykZMD5RghFTU6/zg4GAkJSXh8OHDfve8KQKnQCRKRFX1er/qoFD8wSdnvX/XjopEsKQP1z+K2yw/a2B/daQCFh+1tqJQLhWoAThI2FG+A1XqKvwt4299ms8wDO6ZkYgDxc3IqfGst6vtq69AjEYE3nZb3xZw+MD4u4GTXwJqz7YcOLGjAiIZDymTui7+ciHBwmAsTFiIDXkbYLB4Nqzkr582ISwxGXHDR/VpvjA9HeIpk9G87mOP3tQTC4F6bzWEGcHgBneuLNkViaNDEBAmwokdns230Ov1OHbsGMaNGweBQNCnNSPnLQRXwMfxrT95VItWW47Gxu2Ijb0bDNO3sC3pjGhYNSZojnn2c3uwvQOn1Do8ENuzp/h8pk2bhvr6ehQVeS88ti8wDAtxsXejqWknOjq849WnUAYiVa1abM+pB0Abv/uCK0dEIFDERa1Sj935vmlXRKFcKlADcBBgJVasO7UO06OmY1jQsD6vuyIjHNGBQnyw13NFT6waDVo//wIBS5eAG9r3m1dMvAdg84BDb3tMi7pVj8Ij9Rg1NxYcF/Iw7hp+F5r1zdhctNljWmrPFKAq7zQmXHu9SxXhgu6+G4b8fGgOHPSYFl1OEyytekhnxfR5DYvFYPT8WJRmNaG1znMVHo8dOwaz2YxJkyb1eQ1fJMKo+Ytw6vft0Kk955GsrPwYXG4gIsKv6/MaTpAQwpEhUO+tBvFgkZx3KxuRLhFgZqC0z2vi4+MRHR2N/fv3+90LGB5+Lfj8CJRXvO9XHRSKL/n8UDmsBJiWHIzUcJm/5Vz0CLhs3DDedh3bcIQWg6FQPAk1AAcBuyt3o0RZgntG3OPSOg6bhQdmJ2PrqTrk1nrGC9j27XewdHQg6M47XVsoDLTlAh79BOjwTIPtkzsqwBWykT7dtSps8fJ4LExYiI9Pf+wxL+CRH75BYGQ0hoyf7NI60aRJEAwfjua1az1yU08sBKrdVeAPCei29UN3pEwIhziAj2O/lvVbB2Dz/h06dAijRo2CVNp3QwcAxiy8GoQQHP/VM9UmdbpK1NZ9j9iYFWCz++aJtCObFQNLuwHaE5753B5p78CfrWo8HBfm0sMChmEwY8YMVFVVoazMM38jd2GxeIiLuxcNDVuh1fpXC4XiCzoMZkcu2p3U++czbp0YB4YB9hc149dTtdAZvdtSikK5VKAG4ADHZDXh7RNvY1LEJIwKHeXy+uvHRiMxWIxXdxT2W4ulvR3NH36IgMWLwY3queJml0xaCbA4wP7X+62lvUGL3P21GDM/DjwBx+X194y4B826Zmwq3NRvLZU52SjLOo6pN9wKhuXaV4phGIQ+9ih02dlQ7+x/qwztiQaYG7WQL4h3eS2by8KERQkoOtaIxor+e94OHjwIo9GImTNnurxWJJNjzMKrcfzXnzySC1hS+ga43EDExNzu8lpuuBjCEcFQ7qqAtZ83H4QQ/LukFiOkQlwVEuDy+iFDhiAyMhK7du2C1eq9th19ITLiBvD5oSgp+Z9fdVAovuC7o1VQG8xIDBFj5tDe8/ApniFGIcKMIbbj/cDXJ7HwrX3UCKRQPAA1AAc43xV+hwpVBZ4Y94Rb6zlsFh6bPxR7CptwpLSlX1qa3/8AMJkQ8vBD7u1ApACmPwocXQc09c8gPbS5GKIAHkZcFu3W+gR5AhYnL8b72e+jTe9+Lz5itWLvhk8RMSQFQydNdWsf4smTIZ42DU2vvw7SjzL/VqMFyl0VEI4MAS/aNY+bndTJ4QiMEOPQD8X98kiqVCocPnwYkyZNgkzmXqjUhGuWgsvn4+C3X7qtAwDU6lw0NPyCxIRVYLP7lhN5IfLLE2DVmNCxv3+9NXc0q3BMpcXziZFgudE8mmEYLFiwAHV1dTh9+nS/tPQXNpuPpMQn0Nj0G9poRVDKRYzFSvDJQVtBtdsmxYHFoo3ffcmc1HPpJmUtWhQ2qP2ohkK5OKAG4ABGaVDivaz3cN2Q65CiSHF7PwszIjAqJgD/+DkXJjfzmIzl5Wj9+msE3XMPOCH9ePo56QFAHg1sfwZw08CoKWxDWXYzJl+b5FLu34U8NPohEEKw9uRat/eRu3c3GstLMPPWO10K57uQ0Cceh7GyEq0b3Dd21HuqYNWY3PL+2WGxWZhyXRJqzrT3qy/grl27wOVyMW3aNLf3wReJMXnpTcjduxsNpcVu7YMQKwrPvAiRKAkREb23T+kOjkIAyZRIqPdWwaJ0L2xYa7Hi78U1mBUoxQyFewY6AMTFxSEtLQ27d++G0eidHoV9JTz8Gkilw1FU9G8Q4l+PJIXiDaxWgic2ZaGmTQ8A+OxQOfVA+Zjrx8UgQHiu93F5s+fy1CmUSxVqAA5gXj36KqzEigdHP9iv/bBYDF5enIHipg6s2+96WwhitaLuhb+DGxYGxR2uh9A5wRUA818GSnYD+b+4vNxktODPLwsQkSTHkHFh/ZISJAzC/aPux/dF3yO3Odfl9Zr2Nuzd8AlSp85EVGrfi/N0hSA1FYG33oqmd96Bsdr1fnymeg3Ue6shnRkNjsK1HLcLicsIQvzwIOzdWAiD1nWPZHFxMU6fPo0FCxb0ufJnd4yYewVCYuKw48O3YXGjX2JN7UYolceRmvISWCzXQ4XPR3ZZLBg+G20/uucd/V95PRqMJqwZ6p7X+nzmzZsHrVaL3bt393tf/YFhWBg65Hmo1Tmoqv7cr1ooFE9DCMFzP+Xgx5O1jrEK6oHyOUIeG4dWX4b56bZr/lPfn8Lhkv5FNFEolzrUAByg7Kveh59LfsZT459CsDC43/tLj5RjxdR4vL27CKVNHS6tbfvmG2iPHkXEv/8NVj9v6AEAqVcCqYuArY+6XBDmry1l6GgzYPZtqWA8EIazLHUZUgJT8MyBZ6A3611a+8enH4BhszH7DteK83RHyKpVYAcGoP4f/3TJwCBWgrYfisAJEkB2WWy/dTAMg5k3p8BksODQZtcqyBoMBmzduhWJiYkYOXJkv7WwORwsuP8RNFeW49gW16q26g31KC7+DyIjbkBg4MR+a2EJOQi8Nhn6glbosptcWntKrcUHVY14NC4MCaL+9w5TKBS47LLLkJmZiYoK/1bHCwgYh+jo21BS8hq02nK/aqFQPAUhBP/8JRff/FUJAAg52/MvIUiElDD3PfgU9xDxOXj/lrFYkB4Go8WKe744hrxaz/etpVAuFagBOABp1bfixUMvYlrUNFybfK3H9vvovKGIlAvx4Ncnoe9jY2tDaSka//c6ApbdCPGk/t9EAwAYBlj0JgAG2LKqz6GgNYVtyP69EhOuSkBguNgjUrgsLtZMX4MadQ3eOvFWn9fl7t2NM5kHcdnf7oVIJveIFrZEjIgXX4Tm4EG0ft53b4pqdyWM1WoELhkKhuOZr7QkUIAp1yUj70AtSk/2zdghhODXX3+FRqPBokWL+hUSez5hickYd9V1OPz916gv7lvfOavVjNycR8Bhi5GcvNojOgBAmB4M4YhgtP9SAnNb3x4YdJgtuC+3AmliIVa60PevNyZNmoTo6Gj89NNP0Otde3jhaZKTngKfF4q8/Cdhtbqfx0qhDAQIIfj3r/n4/HAFGAZ47fqR2PfUbPz0wFRsWzUDQp77qQcU92GzGLy1bDQmxCugNphx+/q/UNWq9bcsCmVQQg3AAYbZasYTe5+AmZjxz8n/9NhNNACIeBy8c/NoFDd14OVf83udb+nQoPrBh8CNjEDYk096TAcAQBICXP02ULgNOPhmr9M72gzY8XEOIocGYtTcvve36wtJAUl4dOyj+DL/S2wv397r/MbyUvy+7l1kzJ6H1CkzPKpFMn06FCtWoPG1/0F78mSv8/WFrVD/UQnZ3Djw4zzblyp9eiQSR4dg9+d5UDb1fpE9ceIETp06hauuugoKhcKjWqZcfwtC45Pwyxtr+tQbsLTsTShVJ5CR8Ta4XM8Y6HYCr00Gw2ej5at8EFPPeW+EEDx1phoNRhM+So8Hz8UqsT3BYrGwePFiaLVa/Pjjj36tCspmizAs/TWoVKdQVLzGbzoolP5CCMEr2wvwyQFbe5M1i4dj6dhoCHlsjIoJoMafnxFw2Vh3+zikhEnRpDbg9k//QkuHZ9o5USiXEtQAHEAQQvDasddwsuEk/jfzfwgT9y/HrSvSI+X4+6Jh2HCkAp8fKu9ei8WC2tVPw9zQgOi33wFL7BmPmxOpVwLTnwB+fxE4s6PbaSaDBds/Og02h4UFd6WDxfb8x/aWtFuwMGEhXjjwAvJa8rqdp2lvwy+v/x8Co6Jx2Yr7PK4DAEIffQTCESNQ8/CqHvMBTY1atH5bCMHQQEhne9YoBmyhoJctT4NQysO2909Dr+nes1NWVoZt27Zh7NixGDFihMe1cLhcLHp0NUwGA7a++QrMPVRLrav/CRUV7yMx8XEEBIzzuBaWiIugW4fBVK9B249FINbuPdhvVTRgc0Mb/pcSg0QPhH5eSFBQEK677joUFhZi7969Ht+/KwTIx2LIkOdRXf05amu/96sWCsVd3th1Bh/uteXKv3RtBpZN6H9YPcWzyIVcfL5iAiLlApQ2a7Di82PQGl3PEadQLmWoATiA+ODUB/gq/ys8PeFpjAv3/I2rnVsnxeGuaQn455Zc/Ha6rtN2e9GXjj/3IPLVV8FP9GLT29nPASkLgU13AOUHO222mKz47cPTaK3V4Ir7hkMo5XlFBsMweHHKi0gOSMbK31eitL1zsRy9pgM/vPwCzEYjrnn8OXB5nr+hBwCGy0X022+BEQpRdeddMLd0TnY3t+vR/MlpsKQ8KG5M8Ug+ZFfwhRwsXDkCWqURv757CiZD59Dhuro6bNy4EXFxcbjiiiu8ogMAZMEhuPqxZ1BTmI9t77wKq7WzlpaWfcjPfxoREUsRF+uZ3Myu4EVJoFg6FNoTjVBuK+syZ/Pr2ha8UlaPpxLCcW1YoNe0pKSkYM6cOdi7dy+OHDnitdfpC9FRtyIy8kYUFD6LxsbuH+pQKAORt3cX4e0/bBWH/75oGG6bFOdnRZTuCJcL8MWdExAg4iK7qh0rvzrhdpVzCuVShBqAAwBCCD7M/hDvZb2Hh0c/jGWpy7z+ms8uTMNVIyLx4Dcn8dPJc73NiNmM+n/8E8off0Tkmv+D9LLZ3hXCYgFLPwGixwNfXQ+UH3BsMhks+O2j06g9046FK0cg1MMhjhci4Ajw7tx3ESgIxIodK1DSfq4AilbZju///QLUrS1Y+txLkId63jt7PpzgYMR+8jEsWg0qlt8OU905Q93UrEPTR6cBFoOQOzPAEnF72FP/UUSIsejBkWiu6cDWtdlOlUGrq6vxxRdfQKFQ4MYbbwSH079Km70RM2w4Fj2yGsVHj+DXt19z8gQ2Nf2OU6fvg0IxHakpL3s0fLorRKNCEXBNEjoO1NiMwPM8getrmvF4YRWWRwbh0TjvflYAYNq0aZgyZQq2b9+OzMxMr79edzAMg9SUlxAScjlycldRI5AyaHh/Twle32XLMX52YSpWTPPig0+KR0gOleKT28dDwGVhT2ETnv7hVL/611IolxIMuQS/LSqVCnK5HEql0u0m1Z7CZDHh35n/xuaizXhg1AO4b6R3wgq7wmyx4pnNp/H9iWo8uSAFd48JQ92TT0Bz4CAiXnoJAdct9pkWGLXAN8uAikPA1W9Dk7AE2947hbZ6LS6/JwOx6UE+k9Kia8Hdu+5GXUcdXp35KtIQh5/+8y+YDHosXv1PhCUk+UyLoawMVXfeBWK1IvrdtWBJYtDyRR5YIg6CV2SAE+iBqqx9pK5EiV/fzYY4gI8rV45ATVM5Nm/ejPDwcNx8880QCt1rsu4ORX8dwq9vv4rIIam48pGn0abeijNF/0Jw8DxkpL8OFss73tmu6DhYg/atpRAOD4ZsyRC8Wt2ItysbcXd0MF5MjnKr4bs7EEKwa9cuHDp0CJMnT8bcuXPBZvsnX8lqNSE373E0Nm5DcvJqxMb0r0+mpxhI535XGczaBzI6owX/3VGA9QfLAQBPLkjBA7OT/SuK4hK78xtwz4bjsFgJFo+KxMuLh0PE9+7DSArFl3jj/E8NQD9eSEuVpVi9bzWK2ovwz8n/xDXJ1/hcg9VK8MbvZ7Dr+934x6lvEWjSIPqttyCZNtXnWmA2AtseR/mhPOzWPAGWUIJFD45CSKzvS253GDvw9L6nUJ+ZhSn5wQgMicCSZ16EPDTc51pMDY2oXvkArJZY8FOvAS9OjqDlw8AWe9fz1xWtdRpsefcEGi2F0PCrkZaWhuuuuw5cru+1VBfkYstbLyJiYgWksc2Ijr4dQ4c8B4bxvdGjy2lG/k9n8I8RAhyXsvBsYgQeiA31i9GTmZmJ7du3Izo6Gtdddx0CA70XftoThFhRUvIaKio/REjwPKSm/h94PM8WB3KVgXLud4fBrH2gkl+nwo0fHoZKb8sfe2B2Ep5ckOpnVRR3+PJIBZ7/KQcAwGUxeGJBCpaNj4XcyxEyFIov8Mb53++PSJqamrBx40Y0NDRg+PDhWLp0aa9Prd1ZM5DQmrT4JOcTfJ77OSLEEfhq4VcYFtS/RuLuYlW24+ZD3+CKA5tQrIjFC9Puwe2caCyzWMH1QrGVnlApLThUfw9K2psQJziJOSGbIGx/HIheYgsV9SH6+mbMOChHdZ4CxTFqNE5mIcVUgqnwvQFo1fEhnL4a5noNDIW/wVxWAen05yDMSPepDkIIGpVVaAs6Dq1SBYkqCaKmFGhaTQgI8+1FlhALWPJ8DLupFEZ9B8p3RcEYLUFUiBKSQN8aGXqLFZ/JrHhtuhgigxXvHdNhlkYDEmoBI/T9KXbixImIiIjADz/8gPfeew/Tp0/H5MmTfW6kMwwLyclPQS4fhfyCZ3EkcwESEx9FVOSNfjHSPYnFYsH333+P06dPIywsDMuWLUNISIjH11A8j1JrwpZTtdh8ohonKtudts1N8364NsU7ZESdq/ZsshKs+a0Ar+86g6tGRuKWibEYFRMwIKIQKJSBgl89gCUlJZg6dSrS09MxYcIEfPvttxgyZAi2bdvWrUHnzpoL8deT1GZdMzad2YSNBRvRYezA7em34+4Rd0PI8V3onB1jVRXavvwKbZs2gWGzEfzASjDXXo9Xfi/Gd8eqER0oxF3TEnDt6CgEiLxTeMVOc3UHTv1RhcLMeggkXExZnIShQ/VgdjwHFP4KhGUAkx8E0hcDXO+FPBJCUFuYj+PbfkLRX4cRGB6B2bffA2OcFP+X+X840XgCY8PGYvmw5ZgZPRNslvduYomFQF/cho79NTAUt4MbLUHgNckw1xeg/l8vwVBUBMmsWVDcvhyiCRPAePEBiMlkQmFhIQ4dOoTa2lokJiZi4cKFUFZZcWBTETRtBgwZH4YRs2MQGi/16kXWbFajoXEbKivXQastQ1joIiQlrUbRwWzs3/gFzHo90mfPw+gFixAU7fnKqOfTZDThh/o2fFDVhEajCX+LCsZTsWFgDtdD/UclwGYgmRwJ8cRwcAJ8F6prR6/XY+/evcjMzIRIJMKkSZMwevRoiL1R0bcXDIYmlJT8F3X1myEUxiE29i6Eh10NDkfiUx2eOPdbLBYsXLgQRUVFWLZsGTIzM5Gbm4uDBw8iKanr8HB31nhD+6WKyWLF3sImbD5Zjd/zGmE8WyyEASDgsqAzWREfJMJvtMffoEVntGDhW/tQ1qJFkJiHIAkPZxo6HNuHRchwy6RYXDMqChIaHkoZZFx0IaBLly5FfX099u3bBxaLhfLycgwdOhTr16/HLbfc4rE1F+KrCykhBNXqahypP4Id5TtwtP4oeCwerk2+Fn/L+BsiJZFee+1OWqxWGEtKoDl0CMpt26DPPgWWTIbAm2+CYvlycM7r21ZYr8bbfxRhe0492AyDecPCMCctFFOTgxEm6/+NrNViRXN1ByrzWlF0tAGttRqIZDyMnBuDjBlR4AnOOzmXHwQOvAEU7wJ4UiDlCmDYNUDcFEDUf0+P2WRCfckZlGcdR8HBvVA2NiAgLALjr1mCYTPmgHPWa0IIwZ6qPfg051NkNWVBIVBgTuwczImdg9GhoyHiivqtxWq0wFihgr6gFdrsJlg7TOBGiCGdHQNhRrCj0icxm6Hatg3NH30EY3EJOGFhkC26EpLp0yEcNQosQf//RjqdDhUVFThz5gxyc3NhMBgQFxeHGTNmIDEx0WHkmY0W5B2sw8ldFehoNSAgTIQh48MQO0yBkDgp2B7wIhuNzWhrO4Km5t1oatoJq9WA4OA5SIh/ADLZuZYTek0HsrZvxfHffoFerUJofBJSp85A3IjRCImNB+MBL3KN3oj9bWpsb1bi9xYVGDC4JjQAj8aHIUl07rhbVAao99dAk1kHYrSCFy+DaGQI+MkB4AQLffokuqWlBQcPHkR2djasViuSkpKQnp6OhIQEBAQE+EwHAKhUp1FR8SEam3aAxeIiKGg2QkMvR2DAJPD53veGeeLc/+WXX+LOO+9EcXExYmJiYLFYMG3aNERHR2PTpk0eW+MN7ZcKhBCodGbk1Snx5ZFKHC5pRut5xatSw6VYMiYa14yKhFTARWGDGilhUmr8DXJ0RovjbyngsnCish1fZVZg66k6GM02o1/MY2PRiAgMDZNifIICSSESiKlBSBngXFQGoNlshlQqxeuvv47777/fMT5v3jwEBAR0eVF0Z01XePpAak1atBna0KRtQrmqHOXKcpQpy3C6+TSadE1gMSyMDx+PK+KvwNy4uZDzPduY2g4hBFaNBpbWVpgbG2EoK4OxtAyG0hLos0/B0t4OcLmQTJsG2aIrIZ09GyxR94ZLk9qAn07W4KesGuTW2ppvJwSLMSxChrQIKeKCxIgMECAyQIhQqQDs81oREEJg0JqhUxuhaTegrV6LtgYt2uo0aChXwaS3gMNjIWFkCIaOD0PMMAXYnB5u0JuLgJwfgNyfgKazTexDUoHI0UBQEhCUDCgSAUkYIAoC2OfC3YjVCl2HGjqVEuqWZrTWVKGlpgot1VVoKCmC2WQEXyzG0IlTkTZtFqLTMno0FnJbcrGjbAd2VuxETUcNWAwLKYEpGBY0DLGyWMRJ4xAji0GwMBhyntzJU0isBFaNCZYOEyxKA8yNWpgatTA3aGGs7QAsBCwpF6IRIRCNDgU3StKtsUAIgT47G8pffoHqt+2wtLWB4fEgSE8Hf+hQ8IcOAS8mBpywcHDDw8CSyZz2ZbFYoNFo0NHRAaVSiebmZjQ1NaGxsRENDQ0ghCAgIADDhw/HyJEjERwc3O0xsVoJagrbUJhZj9KsJtvfl89GWLwUikgJgiLFkAYJIAkQQBLIB++C0Eir1QCjsQVGYzN0+hpoNMXQaM6go+MMtFpbWXaxeAjCw65FePg1EAgiutViNplQdvIo8g/sQemJo7CYTOCLxYhITkFQTByCo2MhCwmFRBEEiSIIPIGzB15nsaLJaEKT0YxKvRGFGj0KNXrkdehQoTeCATBKKsLS8EAsDguEgtv9zYPVYIYutwXarCYYitsAK8CScMGLkYITIgI3VAhOsBBsGR8sCRcsL96AajQa5OXl4fTp06isrAQAyOVyREZGIjg4GMHBwQgKCoJEIoFIJAKP5z3Pv15fi4bGX9HQsBVqtS1vRyiMh0yaAZEoESJxIkTCePB4weDxFB4r6uOJc//SpUuhVquxY8e5CqfvvvsunnjiCajV6i4r4bqzpjvt9U2tCAvuPq/z/Jvg7gyavswZCPsihMBkITBZrDCarbbfFitUOhNO1ygh5LLRojGiXqVHg1Jv+60yoF6ph87k3CYmSMzD4tFRuG5MNIZFUgP6UqJda8T3x6vxdWYlSps1nbbLhVxEBQgRGSBEdKAQUQFCBEv4MJgtSAmXQibkgsdmgc9lgc9mg8dhgcdhgc1iBs13qT/7ovr9r7+huQ3hIYqLwwAsKSlBcnIyduzYgfnz5zvG77vvPhw+fBjZ2dkeWQMABoMBBoPB8d8qlQoxMTH9OpBPf/Yf1Mkk6Org9fpsn+n0jy7p6Q/jyh+NgMHZ/3e93WEU9LRXxraVdJ7JdLGyq9civRwY4pJXhJxTdd5HmFzwyue2XLBv5rxfTBcbuljS1X6J07+J49/MeYuZs2+cOfs/p30wAIEVBICVscIKKwhzfi+j3o7J+a9DwFhtv1kEgNW+f8Z2bJlznwXCMI7jbT9mDCFgiBUMsYJFrGCIBczZY9vpk3GBrAuPOxgOCLhnf7MBsACGAIwVDGMFWFYwjMX2wzaDYVmc9kEsbFhNPFiNPFj0Alj0IhAzu4cP8TmVtvdl/6ASEJhhJSYQYgEhZhAQmNkcmDlcmDhcmDm8s7+50AlFMPCcPagSjRohbS0IaWtFTEMt4uuqITQaOh+EXuAwHCh4YQjmh0PGVUDKlUPEdjbwzVYTjFYDLMQMMzHBbDXDQmw/BASEkLOfM+vZf9t+W50+iRccli5GTYwVSq4JSq4RHRwzdGwLDGznHlosKwMeYcC2ssACwCIMWIQBmwAsMGDIuU8zc/bFzn3Sz473cqJiALD5GvAD6yFQ1IEnbQVXrASbr3OaZzVzYTEIoasahcUr1/e80x7whAE4fPhwTJ8+He+9955jbPv27bjiiitQWlqKhITO7QPcWdPddSv+sU0IDw7ssrqsxWpFU4cRFisBm8UgRMLr9ADJaiVo7jDCQgjYDINgCa/z95nYHjC1aoywEIDFAAqx877sc9q0RljPzgkUcTvNsf0maNeZHPPkwnPz7LcghBCo9GZYz36O2CzA7MG2bj/cNxlj4/1bhIjiXwgh2HCkAn//Odcj+2MzgJXYzrMMA0j5HDAMA/tX4PyvlfK8z7/te2J7yHzu9uvc983+vWSxGKf9MAwDKyFoVBtgsRJwWAxCZfxO5wIrIWhUGWDuYY6n5w3UfV0s+uub2lD2+vUXRxEYrVYLAJ3eiFwuh0bT+QmNu2sAYM2aNXjxxRf7I7cTVQFynJYm9jiHcclM894++rKffr0O8cA+PKHDhX307da9t2PWv32QzmaTmzp62N7V3+b8Mce/rb3frPfyrKjX90IYgDC2d21hnf03C7CyQKxsxw/sv8GcvToyQI9Rra6GUxJwzGbwzCaI9EZwzEZwzTpwzEYI9TqItB2Q6Dog0mog61BBYNQDsILAevaOlsCEC+9Me39cYwJQY1KjRlPsmM1m2JBwZBCwReCzRRCwReCxeOAwXHBYXLAdvzlgwIDFYtkeIzAsxwMFhmGB5ThWPXP+A4gYALCc/QFgggUdLAMMjBl6xgwDY4KBMcPEWGABgYWxnvuBFRbG/nDg3IOPc/+2/SYM6cO3UQgoE2w/Z2FxDOAJ1ODydOBw9eCc/c1q823OYFdotdour0EAerx2ubqmu+uWxUpQp9T3qtNiJahXGXqeQwga1D3PAWw3uc0dxl7ntGhMPc6xz2vT9jyPoGvjj81iwGYAo+Xcp2pKkgIp4TKEywQIlwsQJhMgXCaATMDFkvcPoqxFi4QgEYZFeifyhjJ4YBgG14+NwfoDZY7Pxbf3Tkab1oTadh2q23WoadMht1aJ/UXNjnUiHhsWK4HRYj3/eTMs519WCRzVZHuiL9+Tvn4vzVaC2vaezwV9mePpeQN1X/54TU/ty2rt/UrqKn4zACUS24W8vb3daby9vR1Saddl/91ZAwDPPPMMHnvsMcd/25+k9oevr/Vdvz4KhUKhDAwkEkmX1yAAPV67XF3T3XUrXMbH2tsngc+1hQudb/cbTBas2piFWqUekXIB3lo2GgIu22mO3mTBwxtPorZdj8gAAd7uYo5tX1Y8+M0Jx7x3bx4DAdc5RMlgtmDlV+fmvH/L2E5zGMb2mvd/eRw17XpEBQjwwa3O8+xz7t1gmxMdKMSGOydAJuCCy2GBx2aByz4Xcmcv9pEQJMInt0/oNnRq26oZNL+P4oSQx+70uQiVCZASfu57eOFnbNvZ4kD2kGTj2ZBkpc6I2z75C9VtOkQFCPHhbWMh4No8ew7vN5w//5EBArx3yxjwOWyneTqTGQ990/l7SQjOPVYjZ7/j32ahTqlHhFyAN28c5TgX2DGYLHiklzmenjdQ93Wx6H/w84Oo6rSlnxA/YTabiVgsJm+++abT+IwZM8hNN93ksTVdoVQqCQCiVCpdF06hUCiUQYknzv3Lli0js2bNchp7/fXXiVgsJhaLxWNrLsSuvb6ptcd5WoOZnKxsI1qDuV9zBvu+KJT+4OnP4mD/LlH9/tVf39TqcbvFr1VAly9fjpycHBw+fBh8Ph85OTkYOXIkvv/+eyxevBgAsGnTJlRWVuLxxx/v85reoNXUKBQK5dLDE+f+zZs344YbbsDp06eRlpYGg8GACRMmYNSoUfj8888BAPn5+fjkk0/wzDPPICgoqE9rfKGdQqFQKIOPi6oKKADU1dVh+vTpkEgkGDNmDLZu3Yr58+fjyy+/dMy56667cOTIEeTk5PR5TW/QCymFQqFcenjq3H/rrbdi586dWLRoEU6cOIGOjg7s378fERG26rRbt27FVVddhaKiIiQnJ/dpja+0UygUCmVwcdEZgIAtOX7r1q1oaGjA8OHDMWvWLKftO3fuRG1tLe64444+r+kNeiGlUCiUSw9Pnvv37NmD06dPIywsDIsWLYLovJY6paWl2Lx5M+666y6nXos9rfGldgqFQqEMHi5KA9Af0AsphUKhXHoM5nP/YNZOoVAoFPfxxvm/h87bFAqFQqFQKBQKhUK5mPBbGwh/Ynd6qlQqPyuhUCgUiq+wn/MHY+ALvW5RKBTKpYk3rl2XpAGoVqsBoN+9ACkUCoUy+FCr1Y5G7IOFlpYWAPS6RaFQKJcqLS0tHrt2XZIGYGRkJKqqqiCVSsFc2P22j9ib8lZVVQ2KfIzBpHcwaQUGl97BpBWger3JYNIKeEYvIQRqtRqRkZEeVud9FAoFAKCysnLQGa/A4Pu8XQjV71+ofv9C9fsXpVKJ2NhYx3XAE1ySBiCLxUJ0dLRH9iWTyQbVh2kw6R1MWoHBpXcwaQWoXm8ymLQC/dc7GI0nwHbdAmz6B9Pf60IG2+ftQqh+/0L1+xeq37/YrwMe2ZfH9kShUCgUCoVCoVAolAENNQApFAqFQqFQKBQK5RKBGoBuwufz8Y9//AN8Pt/fUvrEYNI7mLQCg0vvYNIKUL3eZDBpBQafXk8z2N8/1e9fqH7/QvX7F6q/M5dkI3gKhUKhUCgUCoVCuRShHkAKhUKhUCgUCoVCuUSgBiCFQqFQKBQKhUKhXCJQA5BCoVAoFAqFQqFQLhEuyT6AfaWxsREVFRWIi4tDaGio19Z4AkIICgoKYDAYkJ6eDi6X2+P8EydOQKvVOo1FRkYiMTHRmzIdGAwGnDhxAqGhoUhKSurTGrVajcLCQoSEhCAuLs7LCp2prKxEZWUlxowZA5FI1OPcgoICNDc3O43J5XIMHz7cmxIdtLW1oby8HLGxsQgKCurTGqPRiJycHIjFYqSkpHhZ4TkIISgpKYHJZEJiYmKvCc5VVVWoqKhwGuNwOJg0aZI3ZTowGo0oLCyEUChEQkIC2Gx2r2usVivy8vJgsViQkZHRpzWeoqWlBRUVFYiJiUFISEiPc1tbW5GXl9dpfMKECeDxeN6S2InGxkacOXMGiYmJfWrYXlxcDKVSiWHDhkEoFPpAofeorq5GfX09kpOTERAQ4LU13qKiogJNTU1ISUmBVCrtcW5RUREaGhqcxqRSKUaOHOlNiT3iynneTllZGVpbW5GamgqxWOxlhb1rqampwfjx43s9l+bm5qKtrc1pTKFQYNiwYd6U2C0GgwGFhYUICAhATEwMGIbp07rCwkJoNBqkp6f7tcCHTqfDmTNnoFAoEBMT0+v8kydPQqPROI1FRET0+X7I05hMJhQWFoLP5yMhIQEcTu/mASEEeXl5MJvNSE9P79Mab2E0GlFQUACxWIz4+Pher7NHjhyB2Wx2GouLi+vT386bnDlzBo2NjX06B5nNZuTm5oLD4WDYsGF9/s44IJQueeSRRwifzyfDhg0jfD6fPPLII15Z4wlKSkpIRkYGCQ4OJnFxcSQ8PJzs3bu3xzUpKSkkMTGRTJ061fHz+uuve11rW1sbefrpp0lUVBQRi8Xk3nvv7dO6Dz74gIhEIpKamkpEIhFZtGgR0Wg0XlZLyL59+8iVV15JgoKCCABy+vTpXtcsWbKEhIeHOx3bBx980OtaT506RRYsWEAUCgUZPXo0EYlE5PrrrycdHR09rtuxYwcJDg4mCQkJjrXV1dVe1/vee++R2NhYkpSURIYOHUoUCgX57LPPelzz0ksvEalU6nRsL7/8cq9rtVgs5PnnnychISFk1KhRJDIyksTGxpLt27f3uC43N5ckJyeT8PBwEhUVRWJjY8nRo0e9rjc/P58sWLCAhIeHOz4LixYtIkqlsts1P/74I2GxWE7HdurUqaSxsdHreu3o9XoyevRowjAMeeONN3qc29LSQqZNm0ZkMhkZMmQIkcvlZNOmTb4R6mEMBgO58cYbiVAoJGlpaUQgEJBXX33V42u8hUajIYsWLXI6R3/44Yc9rrn99ttJSEiI02ftzjvv9JFiZ9w5zyuVSjJ37lwikUjI0KFDiUQiIV988YUP1Hbm999/J/PnzycKhYIAIGVlZb2uWbBgAYmKinI6/k899ZT3xV6AUqkkDz74IAkICCAjRowgoaGhZMSIESQrK6vHdbW1tWTs2LEkMDCQJCYmkqCgILJt2zYfqT5HS0sLueeee0hAQAAZOXIkCQ4OJmPHjiX5+fk9rktPTycJCQlOx99f399//vOfJDQ0lIwcOZJER0eTqKgosmXLlh7XFBYWktTUVBIaGkpiYmJIVFQUOXTokI8Un8NoNJLVq1eT4OBgMmrUKBIREUHi4+PJ7t27e1wnl8tJamqq0/H//PPPfaS6awoLC4lMJuvTOSgzM5NER0eTmJgYEhYWRoYOHdrrZ+5CqAHYBZ999hkRiUSOE9CJEyeIUCjs8cPhzhpPMXnyZDJ//nxiMpkIIYSsWrWKhIaGErVa3e2alJQU8s4773hd24Xk5OSQNWvWkIaGBjJ16tQ+GYAnT54kDMOQ7777jhBCSENDA4mNjSWPPvqot+WSd999l2zZsoUcP37cJQOwr4atJ/nhhx+cDJLq6moSExNDHnrooW7XtLS0ELlcTv7+978TQmw34FOnTiXz5s3zut4XX3zRydBct24dYbPZ5NSpU92ueemll8jEiRO9ru1CtFot+d///ke0Wi0hhBCr1UpWrVpFZDIZMZvNXa6xWCwkPT2dLF26lFitVkKI7aY3Li6OGAwGr+rdtm0bOXDggOO/GxoaSHR0NHn88ce7XfPjjz8SsVjsVV298dBDD5F7772XyOXyXg3AZcuWkZEjRzrOc2+88Qbh8/mkoqLCB0o9yz//+U8SHh5OKisrCSG2vx/DMD0+yHNnjbd45JFHSHx8PGloaCCEEPLNN98QhmHIyZMnu11z++23k1tuucVHCnvGnfP8XXfdRVJSUkhrayshxHb+4nA4pLCw0NtyO/HGG2+Q3377jezbt88lA7Cn84GvOHPmDHnnnXeITqcjhNgebFx//fUkISGhx3WXX345mTJlimPdP/7xDyKTyUhTU5PXNZ/PqVOnyIcffug4p+t0OnLllVeS4cOH97guPT2913OcLzCbzeQ///mP40Gx1WolTz31FBGJRESv13e7bvTo0eSqq65yXP/uvfdeEhkZ6fh7+AqlUkneeustx+taLBZy3333keDgYMd1tysG2gND+8PPp556qtdzkF6vJ9HR0eSee+4hhNje89VXX01GjBjh0mtSA7ALZsyYQZYtW+Y0tnTpUjJz5kyPrvEEeXl5BADZs2ePY6yxsZGw2WzyzTffdLsuJSWFvPjii+Svv/4itbW1XtXYHX01AB9++GGSmprqNPbvf/+bBAYGEovF4i15Tpw8edIlA/C2224jR48eJeXl5T2ehLzNgw8+SEaPHt3t9o8++ogIBAKnhwU//fQTAeC4sfQVVquVcLncHj0HL730Ehk7dizJysoiBQUFjoce/mDz5s0EAGlra+ty+6FDhwgApyfZxcXFBAD57bfffKTyHPPnz+90jjofuwGYl5dHTp065fML+c8//0xSUlKIRqPp1QBUKpWEy+U6eYxNJhNRKBRkzZo1PlDrWWJjY8nq1audxsaNG0duv/12j67xBhaLhQQGBpJXXnnFaXzIkCFk1apV3a67/fbbyXXXXUeOHTtGSktLfXYu74m+nuf1ej0RiURk7dq1jjGr1UoiIyPJc889522Z3bJ//36XDMB7772XHD16lFRUVPj1OnUh27dvJwBITU1Nl9tramoIwzDkp59+cox1dHQQoVBI3n//fV/J7Jbvv/+eAOgx4iI9PZ38/e9/9+s9WHds27aNACD19fVdbj9x4gQBQI4cOeIYq6qqIgzDkB9//NFHKrvn66+/JiwWy/HAtivkcjl59913ydGjR30a5dIdDz30ELnjjjvI0aNHez0H/fLLLwQAqaqqcowdOXKEAHApwogWgemCkydPYuzYsU5jEyZMwMmTJz26xhPY93/+a9tz5Hp77VdffRV33303hg4diqavFhMAABynSURBVMmTJ+PMmTNe1eou3R3btra2TvlgA4Vvv/0Wd955J8aMGYOhQ4di3759ftFx7NgxJCcnd7v95MmTSElJgUQicYxNmDABAJCVleVteU5kZ2fDZDL1qBewab755psxZ84chIeHY8OGDT5SCJSUlGD//v34+uuv8eyzz+Kpp57qNu/q5MmT4HA4GDFihGMsKSkJCoXC6+cFOwcOHMDu3bvx4osvIisrC48//niP8zUaDa666iosXrwYgYGBeOmll3yis7q6Gvfeey+++uqrPuVe5eTkwGQyOZ0XOBwORo0a5bNj6ylaW1tRWVnp0vXDnTXeory8HG1tbZ20jB8/vlctW7ZswYoVKzBhwgQkJiZi165d3pTqMQoLC6HVap3eM8MwGDdu3KD6/H322We46667MHLkSKSnpyMzM9PfkgAAR48ehUQiQVhYWJfbs7KyQAhxOv5isRhpaWkD4vgfPXoUISEhkMlkPc773//+57gHmzhxIgoKCnyksDNlZWXYv38/Nm7ciCeffBIPP/xwt8fffozHjBnjGIuOjkZERITfjn9RURH279+PDRs24O9//zuee+65XnPCn3vuOdx5552IjY3FggULUFNT4yO1zmzZsgXbtm3D22+/3af5J0+eRFhYGKKjox1j48aNA8MwLh1/agBegNlshlqt7lQ8IygoCCqVChaLxSNrPEVrayt4PJ7TDbz9tVtbW7tdt3r1arS0tCArKwtVVVUQi8VYsmQJTCaT17S6S2tra5fH1r5toHHDDTegoaEB2dnZqKurw6xZs7B48eJOBQ+8zZtvvonjx4/j6aef7nbOQDm2Wq0WK1aswLRp0zB79uxu540fPx6lpaXIzc1FdXU1nn/+edxxxx04cuSIT3T++OOPePrpp/H4449DKBTixhtv7HZua2srFApFp8Ts3r6bnmT16tV48skn8d///hfLli1Denp6t3NjYmJw7NgxFBcXo7i4GJs3b8a//vUvrF+/3qsaLRYLbrnlFqxataqTEdEd9uPX1Wd3IJ4TesKd9zKQ3r+7Wq666irU1dU5zpPXXHMNlixZgsrKSq/q9QQD6fi7y+23346mpiZkZWWhrq4OY8aMwbXXXtupMIyvyc7Oxpo1a/Dss892W8hjIB//zMxMvPnmm3jhhRd6nPfkk0867sGqq6shl8tx3XXXwWg0+kipM1u2bMHTTz+Nxx57DCwWC7fccku3c1tbWyGTyToVG/Tn8d+0aROeeuopPPHEEwgMDMTSpUt7nP/aa6+hubkZ2dnZKCsrQ3NzM26++WYfqT1HTU0N7r77bnz55Ze9Fs6y09V9G5vNRkBAgEvHnxqAF8Bms8FisaDX653GdTodWCxWlyckd9Z4Ci6XC5PJ1MnI1Ol0PVbuu+OOOxzbAwIC8MorryAnJwc5OTle0+ouXC63y2MLwKfVCfvKDTfc4PAK8Xg8vPnmm1Aqldi5c6fPNHz99dd46qmnsH79+h5vqgfCsTUYDLjuuuug0Wjw/fff91jJasGCBU4VYB955BEMGTIEmzZt8oVUPPHEEzh06BBqampw+eWXY/bs2WhqaupyblfHFuj9u+lJDhw4gBMnTqCkpAQ7duzAypUru507duxYp8/KFVdcgWuuuQYbN270qsZ3330XlZWVmDJlCg4cOIADBw7AYrGgrKwMR48e7XKN/cajq8/uQDwn9IQ772UgvX93tSxZssRxE8PhcPDaa6/BbDbj119/9Z5YDzGQjr+73HTTTY4bToFAgDfffBP19fXYs2eP3zQVFRXhiiuuwJIlS7B69epu5w3U45+bm4tFixbhjjvuwEMPPdTj3Ntvv91RtVQul+O///0v8vPzkZ2d7QupnXj44Ycd17YlS5bgsssuQ21tbZdzB8K17UKeffZZHD58GLW1tZg+fTpmzZrV48OMu+66y3FvHh4ejhdffBH79u1DXV2dryQDAO6//35MmTIFZrMZBw4ccPz9T548iaKioi7XdHf89Xq9S8efGoAXwDAMYmJiOrmCa2pqEBsb67E1niIuLg6EEKcPrf2/XXltu6vfXy7wnoiLi+vy2ALwe8neviAWiyGRSHx2bL/99lv87W9/w7p163p8igf0fGy9/dkFbKWbr7vuOpSWluLPP//sNuSkJ8LCwnz+uWWxWHj88cehUqlw8ODBLufExcVBpVJBrVY7xoxGI5qamnxybM8nPDwct912G3777TeX1vni2LLZbERFReHZZ5/F6tWrsXr1auh0OmzZsgVr1qzpco39IYA/zrmeJjIyElwu16X34s4ab+GpvwWXy0VgYOCAvAZdyMX0+bOjUCi6/Ez5iuLiYsyePRuzZ8/G+vXre3wQOBCPf15eHi677DIsXrwY77//vsvrB8o9GMMweOKJJ6DRaLpNXYmLi4PRaHRqd2WxWNDQ0OD3zz+bzcZjjz2GtrY2l0Ka/XX8g4KC0NjY6Lj2vfPOOwCAN954o9sH23FxcWhoaHBy/LS2tkKn07l0/KkB2AXz5s3D1q1bQQgBYDOotmzZgnnz5jnm1NTUON349WWNN5g6dSqEQiF++eUXx9iBAwfQ0tLi9NrHjx9HaWkpAHTq/wcAO3fuBMMwPYaI+QqlUokDBw44dM6bNw979uxxupH++eefMX78eL/3vQKA/Px8nD59GoCtl86FIRyZmZlQKpXIyMjwupbvvvsOy5cvx4cffojbb7+903aTyYQDBw44Ttzz5s1DRUUFTp065Zjz888/IyAgAOPHj/eqVrvxV1RUhD///LPLnm+VlZVO4Z0X9k2yhzB5+9he+LqA7YYFcA5DyszMdISwzZ49GxwOB1u2bHFs37FjB4xGI+bOnesXvedrbWlpwYEDBxyf1wvXmM1m7Nmzx+vH9oEHHnB4/uw/EokEDz/8MDZv3uyYl5OT4+hTmJKSgpiYGKfzXkVFBbKysrx+zvU0XC4XM2fOdHover0eO3bscHovpaWlOH78uEtrfEFAQADGjRvnpEWpVGLPnj1OWs6cOeN4um2xWDo9wc7NzUVtba1PzpPucP55Pjo6GqmpqU7vubGxEYcPHx6wn7/zvz8Gg6FTD7Q///wTJpPJL8e/tLQUs2fPxowZM/DFF190GTWVnZ3tqFMwduxYKBQKp+N/+vRplJWV+eX45+fn47LLLsPVV1+NDz/8sEvj1R6JAdjuwez3inbsEUK+vgfr67Xt6NGjKC8vBwDMmDEDPB7P6fj/8ccfUKvVPj/+fdV/+PBhVFVVdbtm586d4PF4GDJkiJeUds369eudrn0ff/wxAOCLL77As88+65h34MABh0d27ty50Gg02L17t2P7zz//7Lgu9Bm3ytVc5JSUlJCAgACyfPly8ssvv5DbbruNBAQEkJKSEsecV199lbDZbJfWeIuXX36ZSKVS8sEHH5BvvvmGJCQkkBtuuMFpTlJSEnnggQcIIbZKYdOnTyfr1q0j27dvJy+99BIRi8U9tgvwFFarlezfv5/s37+fDB8+nFxzzTVk//795Pjx4445u3btcqqCpNFoSEpKCpk9ezb56aefyPPPP0/YbDbZuXOn1/VWV1eT/fv3k/Xr1xMA5IsvviD79+93qtp1zTXXOKq9NjQ0kOHDh5O3336b7Nixg6xdu5aEh4eTOXPmeL3K3datWwmHwyH33HOP4xjv37+fZGZmOubU1dURAE4VYq+44gqSmppKvvvuO/LOO+8QgUBA3n77ba9qJYSQxYsXE4lEQr799lsnveeX8f/HP/5B5HK547/Hjx9PXn75ZbJt2zbyxRdfkIyMDJKcnExaWlq8qvWnn34il19+OVm/fj3ZtWsXeffdd0lsbCyZN2+eU/W8oKAgpyqATz75JAkKCiKffvop2bBhA4mIiHCUbvYmS5YsIatXryY///wz2bJlC3nooYcIm80m3377rWPOpk2bnCqJ3XDDDeTJJ58kP//8M/n+++/J3LlzSUBAAMnJyfG63gvpqgronDlzyJVXXun47y+//JJwOBzy3//+l/zwww9kzJgxZNKkSQOimqSrHD58mPB4PPL444+Tn3/+mVxxxRUkNjbWqcLsAw88QJKSklxa4yt27txJOBwOeeGFF8hPP/1EZs6cSVJSUpyq8N1yyy1k7NixhBBC1Gq1owz+9u3byQcffEBiYmLIlClTiNFo9Ll+V8/zhNiq5rLZbPLSSy+RH3/8kUyePJmMHDnSL/orKirI/v37yXvvvUcAkE2bNpH9+/c72nIQ4vz9KSsrI6NHjybvvvsu2bFjB3nzzTdJcHAwufrqq32uvba2lsTGxpKRI0eSPXv2OF0Lzq9OPXbsWKe2Ie+++y4RCATkrbfeIt999x1JS0sj8+fP97n+8vJyEh4eTiZMmED27dvnpP/8z39KSoqj6vmhQ4fI1KlTybp168iOHTvIyy+/TCQSCbn//vt9rn/79u1k7ty55NNPPyW7du0i77//PklISCAzZsxwanEUFRXl1DbkhRdeIAEBAWTdunXkq6++ItHR0WT58uU+179x40Zy5ZVXks8++4zs2rWLvP322yQqKoosWrTIaZ5YLCYvvfQSIcRWpfXyyy8nn332Gfntt9/IM888Q3g8Hnn55Zd9rv9CuqsCCsDpmvi3v/2NREdHky+//JJ8/PHHJCAggDz77LMuvRZzdseUCygoKMBrr72G0tJSJCYm4oknnkBqaqpj+8aNG/HBBx84xcv3tsabbNiwAZs2bYLBYMDcuXOxatUqp1jgZcuWYeLEiXj00UcB2J5GrVu3DqWlpYiOjsaSJUuwcOFCr+s0Go247LLLOo3HxcXhq6++AmCrXPnII49gw4YNSEhIAGDz9LzyyivIyspCSEgI7r//fteedLjJxo0bsXbt2k7jjz32GK677joAtthztVrtcN2Xl5dj7dq1yMnJQXBwMObOnYvly5eDxfKuw/3tt9/Gd99912k8KCgIP//8MwBbmMDVV1+NF198EXPmzAFgi9t//fXXsXfvXohEItx00009FjfxFHPmzIHBYOg0vmLFCqxYsQIA8Omnn2LTpk2O0MW2tjasXbsWmZmZEIlEmDBhAlauXNmnypH95eDBg/j8889RVlaGiIgILFiwAMuWLXN6Wr1o0SJcc801uPvuuwEAVqsVH3/8MX7++WdYrVYsXLgQ999/Pzgcjle1GgwGrFu3Dn/++ScMBgOSk5Nx9913Oz1d3rNnD55//nn8+OOPCAkJcaz5448/YLVakZGRgVWrViEkJMSrWrviiiuuwIoVK3D99dc7xh599FHweDz85z//cYxt3boV69evh1KpxOTJk/Hkk0/2WnlvoJKZmYl33nkHdXV1SE9Px9NPP42oqCjH9jfeeAOZmZlOOZm9rfEle/fuxfvvv4+mpiaMGjUKq1evdvrsvPTSS6ioqHA84a6ursbatWuRlZWFoKAgzJw5EytWrPD6d6Mr3DnPA8CuXbuwbt06tLa2Yty4cXj66acRGBjoM912Pv30U3z66aedxp977jlcccUVADp/f4qKivDee+8hLy8PYWFhuPzyy3HTTTf1GHrpDezX+6745JNPkJKSAsCWsxUXF+dUXGXTpk346quvoNVqMWPGDDz22GM+uRacz/79+/HMM890ue3rr792hOTdcsstGD16NJ544gkAthyvdevWobi4GNHR0bjuuuuwaNEin+k+n8zMTKxfvx4lJSUIDw/H3Llzccsttzh9F6+77jrMmTMHDzzwAABblNtnn32GH374AWazGQsWLMCDDz7YqTCML9i7dy82bNiAiooKREZGYuHChbj++uud7rnmz5+PW2+9FcuXL3daU1VVhfj4eNx6662YPn26z7VfSGFhIe68806n+18AmDZtGlatWuW4JprNZqxduxbbt28Hh8PBtddeizvvvNOl7y81ACkUCoVCoVAoFArlEoHmAFIoFAqFQqFQKBTKJQI1ACkUCoVCoVAoFArlEoEagBQKhUKhUCgUCoVyiUANQAqFQqFQKBQKhUK5RKAGIIVCoVAoFAqFQqFcIlADkEKhUCgUCoVCoVAuEagBSKFQKBQKhUKhUCiXCNQApFAuEQoLC3H48GGX1pSVlWHv3r1eUkShUCgUysBi8+bN3Tan747S0lLMnz8fBoPBO6IoFA9DDUAK5RLAYrFg6dKlaGlp6bTt0KFD+Pbbb2E2mzttk0qlWLp0KYqLi30hk0KhUCgXER999BHuuusuf8voMzqdDqtWrcLSpUs7bauoqMC4cePwwAMPdNqWmJgIHo+HN954wxcyKZR+Qw1ACuUSYMOGDWCxWFi0aJHTuNlsxpIlS7Bs2TL8+uuvndYFBwfjtttuwz/+8Q9fSaVQKBTKRUJtbS0KCgr8LaPPbNiwAUFBQZg2bVqnbZ9++ikaGhrw0Ucfob6+vtP2+++/H2+88QaMRqMvpFIo/YIagBTKIKW6uhqbN2+G1WrF4cOHsWnTJqjV6i7nrl27FnfccUen8a1bt8JoNGLFihX4+OOPu1x72223YdOmTWhsbPSkfAqFQqH4mTNnzuC+++7D9OnTccsttyArK8tp+3fffYdrrrkGM2fOxH333YeysjLHtp07d2Lu3Lk4cuQIli9fjlmzZuGRRx5Be3u7Y+1HH32E7OxsjBs3DuPGjcNvv/0GADCZTHjrrbcwf/58zJkzB8888wyUSqVj32+99RYefvhhfPPNN7jiiitw2WWXdfserrzySmzdutVp7IEHHsD777/v8vFYv349rr/++k7jVqsV69evx7///W8MHz4cn332Wac5CxYsgFardbxHCmUgQw1ACmWQcuTIEdx2222YO3cuHn30Ufzwww9dGoD19fU4fvx4lxfQjz/+GMuXL8eqVavw22+/oba2ttOcUaNGQSqVYufOnV55HxQKhULxPSdOnMDYsWOh1+vxwgsvYNGiRbj33nsdHqx//etfeOaZZ7B06VK89NJLCAgIwOjRo1FdXQ0AaG1txZ49e7By5UosXrwYzzzzDPbs2YMVK1YAAGbPno1FixYhKSkJH3zwAT744ANMnDgRhBAsXboU33//PR544AE8++yzKC4uxrRp0xyvXVVVhY8++gjr16/HqlWr8Prrr3f5HpRKJbZt24bw8HCn8c2bNyMgIMCl46HRaHDs2DFMnDix07YdO3ZApVLhhhtuwN13341PPvmk0xwOh4Px48fjjz/+cOl1KRS/QCgUyqBk06ZNBABZs2ZNj/N+/fVXAoAYDAan8ZqaGsJms0lubi4hhJAJEyaQl19+uct9TJ8+nTz88MOeEU6hUCgUvzN37lyyaNEipzGDwUCsViupq6sjXC6XnDhxwmn75ZdfTp566ilCCCHffPMNAUCKiooc27ds2UJ4PB6xWCyEEEL+8Y9/kKlTpzrtY/v27UQulxO1Wu0YMxqNJDIyknz33XeEEEIef/xxEhAQ4DSnK/bs2UM4HA7R6XSOsfr6egKA5OXlEUIIUSqVZOXKlb0ej7y8PAKA5Ofnd9q2ZMkS8sADDzj2JxaLyZ49ezrNu+2228iVV17Z62tRKP6G41frk0Kh9JuHHnqox+3Nzc0Qi8Xg8XhO4+vXr8ekSZMwbNgwAMA999yDNWvW4JlnngHDME5zAwMD0dzc7FnhFAqFQvEb+/fvx7vvvus0Zr9OHDx4ECaTCffffz8AgBACQggqKiqcriVyuRzJycmO/46KioLRaERbWxuCgoK6fN09e/bAbDZj7ty5IIQ49q9SqZzyBYcPHw6JRNLje8jKykJqaioEAoFj7OTJkxAKhRg6dCgAIDs7u8volguxV/C88FrZ1NSEX375BceOHQMAyGQyLFu2DB9//DFmzpzpNFcgEECv1/f6WhSKv6EGIIUyiJHJZBCLxT3OkUgk0Ol0sFqtYLFsUd+EEKxfvx5TpkzBxo0bHXNLS0uxZ88ezJ4922kfGo0GERERnn8DFAqFQvE5FosFRqOxWwNLo9GAw+Hg7bffdlw37Mjlcse/ORzn20j7w0O7YdfdvuPj47F27dpO2yIjIx3/FolEvb6PrKwsjB49utNYRkYG2Gw2AJsBmJ6e3uu+wsLCANgemiYmJjrGv/jiC1gsFkdoKwC0tLSgoaEBa9eudToezc3NncJRKZSBCDUAKZRBzIWeuq4YOnQorFYrKisrER8fDwD4888/0djYCKPRiJ9++skxd+TIkfj44487GYBlZWW48sorPSmdQqFQKH6CzWYjMTER2dnZuPHGGzttHzJkCMxmM1gsFsaNG+f267BYrE7G4JAhQ7B+/XqkpKRAKpW6vW/AZuxd2LJh586dGDVqlOO/s7OzHTnwv/32Gw4dOoTnn38efD7faV1ERASio6ORlZWFCRMmOMY/+eQTR47k+fztb3/DV199hZUrVzrGTp48iccff7xf74lC8QW0CAyFcpGTnp6O8PBwHDx40DH28ccf4+qrr8bGjRudft5++21s3rwZbW1tjrn19fUoLS3F3Llz/SGfQqFQKF5g5cqVeO+995CZmQnA5rV75513YDQaMWnSJIwfPx4PPvigU8uD3377zaUql+Hh4aipqXEyAm+++WYIBAKsXLnSES5pNpvx0UcfIT8/v8/7NplMyMvLQ05OjmPsiy++wJ9//om0tDTHWHZ2NuLi4rBy5Urs2bMHL7zwQifjz861117rVPDs4MGDKCgowL333uuoZGr/ue6665yqZxcXF6OqqgpXX311n98D5f/bu39fZtc4juOfSrpICKUxCNUgVSIM0qVT/wBRBpPEYCKRsKvJ0rBIw+BHwuBHJ4lBQmIiEgMdtEibqNCEIPojpEmDc7bmcfAcBk+P0/drvHLd9/29pjuf5PpeF3KFAAj8zxkMBvX19WllZUWSFI/Htba2Jrfb/Wau0+lUUVGRlpaWsmN+v18Oh0PNzc1/qmQAwDcbGhpSf3+/XC6XamtrZTabFYlEZDQaZTAYtL6+LpPJpJqaGtntdpWUlGh6elo2m+3T3+js7FRBQYEsFkv2GoiysjJtbW3p6OhI5eXlamxslMlk0uHhoSorKz/97uPjY2UyGd3f38tischisWhzc1NWq1Wjo6MKhUJ6eXnRycmJenp61N3dLa/X+6bH71eDg4Pa2NjI9rzPz8/L4XC82wLhdrsVCAQUCAQkSQsLC+ro6FB1dfWn1wDkiuGv323UBvCftb+/r5mZmXePo/6n29tb2e127e3t6ebmRlNTU5qdnX23/2NyclKpVEoej0fPz89qamrS+Pi42tvbv2MZAIAcenx8VDQalcVieXdL5t3dna6urmS1Wl/9M+LxuC4uLtTS0pIdS6fTCoVCam1tzfYHPj096fz8XMlkUlarVSaTKTs/FosplUqprq7uVTCLxWJKp9Oqr6//sO7FxUWNjIzo8vJS4XBYpaWlMpvNSiaTSqVSqqqq0unpqXp7e9XV1aVwOKy5ubl/bZ0YGBhQYWGhJiYmFAwGVVxc/GGoOzg4UFVVlYxGo2w2m3Z2dr4UkIFcIQACeWJ5eVmZTObdC+E/EggEtLq6Kq/X+32FAQDwRcPDw4pEIm8ugf+V3+/X7u6ufD6fPB6PEomEfD7fb9/78PCgaDT6pV0viURC19fXamho+PQzQC4RAAEAAPCjuFwuOZ1OjY2NfTjn7OxMBoNBVqtVkrS9va22trZXJ3cC+YgACAAAgB8lGAyqoqJCZrM516UAPw4BEAAAAADyBKeAAgAAAECeIAACAAAAQJ4gAAIAAABAniAAAgAAAECeIAACAAAAQJ4gAAIAAABAniAAAgAAAECeIAACAAAAQJ4gAAIAAABAnvgb7gd9xI34GlEAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "edge_vec = graph.edge_vectors()\n", "r = torch.linalg.norm(edge_vec, dim=-1)\n", "\n", "mu = model.rbf.centers.numpy()\n", "rbf_ref = np.exp(-10.0 * (r.numpy()[:, None] - mu[None, :]) ** 2)\n", "rbf = model.rbf(r).detach().numpy()\n", "\n", "print(\"shape:\", rbf.shape, \" max |xnn - paper| =\", np.abs(rbf - rbf_ref).max())\n", "assert np.allclose(rbf, rbf_ref, atol=1e-15)\n", "\n", "fig, (a1, a2) = plt.subplots(1, 2, figsize=(9, 3))\n", "rr = np.linspace(0, 4, 400)\n", "for k in range(0, 40, 4):\n", " a1.plot(rr, np.exp(-10.0 * (rr - mu[k]) ** 2), lw=1)\n", "a1.set_xlabel(\"r (A)\"); a1.set_ylabel(\"$e_k(r)$\")\n", "a1.set_title(r\"Gaussian RBFs ($\\gamma=10$, 0.1 A spacing)\")\n", "a2.plot(mu, rbf[0], \".-\", ms=3)\n", "a2.set_xlim(0, 4); a2.set_xlabel(r\"center $\\mu_k$ (A)\")\n", "a2.set_title(f\"expansion of $r_{{01}}$ = {float(r[0]):.3f} A\")\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "5e27a775", "metadata": {}, "source": [ "## Block 3: shifted softplus\n", "\n", "$\\mathrm{ssp}(x) = \\ln(0.5\\,e^x + 0.5)$, with $\\mathrm{ssp}(0) = 0$ (the\n", "shift improves convergence) and *infinite order of continuity* — the paper's\n", "requirement for a model that is at least twice differentiable, so the force\n", "loss can be trained by gradient descent (Sec. 4.2). `xnn` shares one exact\n", "implementation (`xnn.common.models.ops.shifted_softplus`) between SchNet and\n", "PhysNet." ] }, { "cell_type": "code", "execution_count": 6, "id": "aed967e9", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:41.968572Z", "iopub.status.busy": "2026-07-20T04:24:41.968388Z", "iopub.status.idle": "2026-07-20T04:24:42.092686Z", "shell.execute_reply": "2026-07-20T04:24:42.091975Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |xnn - ln(0.5 e^x + 0.5)| = 8.881784197001252e-16\n", "ssp(0) = 0.0\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = torch.linspace(-8, 8, 2001)\n", "ref = torch.log(0.5 * torch.exp(x) + 0.5) # the paper formula\n", "val = shifted_softplus(x)\n", "print(\"max |xnn - ln(0.5 e^x + 0.5)| =\", float((val - ref).abs().max()))\n", "print(\"ssp(0) =\", float(shifted_softplus(torch.tensor(0.0))))\n", "assert (val - ref).abs().max() < 1e-14\n", "\n", "fig, ax = plt.subplots(figsize=(4.4, 3))\n", "ax.plot(x, val, label=\"ssp(x)\")\n", "ax.plot(x, torch.relu(x), \"k--\", lw=0.8, label=\"ReLU (not smooth)\")\n", "ax.legend(); ax.set_xlabel(\"x\"); ax.set_title(\"shifted softplus\")\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "ffcea835", "metadata": {}, "source": [ "## Block 4: the continuous-filter convolution · eq. 2\n", "\n", "$$x^{l+1}_i = (X^l * W^l)_i = \\sum_j x^l_j \\circ W^l(\\mathbf r_i - \\mathbf r_j)$$\n", "\n", "The filter-generating network maps the RBF-expanded distance through **two\n", "dense layers with shifted-softplus activations** (Fig. 2 right); rotational\n", "invariance holds because the filter depends only on $d_{ij} = \\|\\mathbf r_i -\n", "\\mathbf r_j\\|$. Below: the filter network and the full convolution of the\n", "first interaction block, re-computed with an explicit double loop over atom\n", "pairs." ] }, { "cell_type": "code", "execution_count": 7, "id": "8c59e3eb", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:42.094438Z", "iopub.status.busy": "2026-07-20T04:24:42.094299Z", "iopub.status.idle": "2026-07-20T04:24:42.106229Z", "shell.execute_reply": "2026-07-20T04:24:42.105478Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cfconv max |xnn - eq.2| = 8.881784197001252e-16\n" ] } ], "source": [ "def ssp_np(t):\n", " return np.log(0.5 * np.exp(t) + 0.5)\n", "\n", "def filter_np(block, d):\n", " # W(r) for one scalar distance d -- Fig. 2 right, from the paper\n", " e = np.exp(-model.rbf.gamma * (d - mu) ** 2) # rbf\n", " fn = block.cfconv.filter_net\n", " h = ssp_np(e @ W(fn[0]).T + b(fn[0])) # dense 64 + ssp\n", " return ssp_np(h @ W(fn[2]).T + b(fn[2])) # dense 64 + ssp\n", "\n", "def cfconv_np(block, x_in, pos):\n", " # eq. 2 as an explicit double loop (j != i; the neighbor list has no\n", " # self-edges, and no pair of this molecule is anywhere near 30 A)\n", " out = np.zeros_like(x_in)\n", " for i in range(len(x_in)):\n", " for j in range(len(x_in)):\n", " if i == j:\n", " continue\n", " d = np.linalg.norm(pos[i] - pos[j])\n", " out[i] += x_in[j] * filter_np(block, d) # x_j o W(r_ij)\n", " return out\n", "\n", "block0 = model.interactions[0]\n", "x_in = x0 @ W(block0.lin_in).T + b(block0.lin_in) # atom-wise before conv\n", "conv_ref = cfconv_np(block0, x_in, POS)\n", "\n", "with torch.no_grad():\n", " conv = block0.cfconv(torch.from_numpy(x_in), graph.edge_index,\n", " r, model.rbf(r)).numpy()\n", "\n", "print(\"cfconv max |xnn - eq.2| =\", np.abs(conv - conv_ref).max())\n", "assert np.allclose(conv, conv_ref, atol=1e-12)" ] }, { "cell_type": "code", "execution_count": 8, "id": "9092313d", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:42.107894Z", "iopub.status.busy": "2026-07-20T04:24:42.107778Z", "iopub.status.idle": "2026-07-20T04:24:42.430052Z", "shell.execute_reply": "2026-07-20T04:24:42.429025Z" } }, "outputs": [ { "data": { "image/png": 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cOFCuZkBVvn9VcbPfn8oeL9VVk8fU5s2b6d+/v9H6dBBCiJomiQEhRL1mbW3N6tWrSzuDCgkJ4dChQ/zyyy/l5n3zzTf56KOPmDNnDk2aNGHy5MnMmjWLwMBAo66nsu699142bNhAZGQkXbp0wcfHh1deeYUnn3yydJ4RI0bw6aef8sMPP+Dp6cmDDz7Ia6+9VmF14FmzZjF48GB69uyJiYkJdnZ2AEyYMIHOnTvz/PPP4+/vj7+/P99++y0//PADTzzxxHVjvFaZxmJlZcWWLVsYN24c999/Py4uLtxzzz2MGjWKbdu2YWNjUzrvV199xYABA7jtttto2rQp69atKzM++WXW1tZs2rSJzp07M3z4cHx9ffn999+ZO3cuOp3O6A9/P/30E5cuXcLDw6PcmPSVZWJiwvLly3n11VeZO3cuQUFB+Pn58dBDD+Hm5saDDz54zWWrsr3VWU9NxH7ZqFGj+O677/jzzz/x8vJizJgxjB49mttvv73cvNfa35WNw9rams2bN9O1a1duu+02fH19Wbx4MV9//XWVt/1mVXcbruett94iMjKScePG4eTkVPrd3bFjB02aNLnustOnT0ev17N06dJyn1X2+1dVN/P9qcrxUh01dUxFRESwb98+Hn74YaPGK4QQNUmjauIVkRBCCFHL4uLi8PX15dNPP+WZZ56p63BqXGPbXmEcDz/8MAcOHODQoUN1Hcot65lnnmH9+vUcO3YMMzPpzksI0TBIjQEhhBC3hL/++gugTOeRt7LGtr3CON555x0iIiJYtmxZXYdyS4qPj+fbb79l9uzZkhQQQjQoUmNACCFEg/POO+8QEhLCgAEDMDU1Zc2aNTzxxBMMGDCA5cuX13V4RtfYtlcIIYQQtUsSA0IIIRqcyMhIXn/9dXbs2EFiYiK+vr5MnDiRN954Aysrq7oOz+ga2/YKIYQQonZJYkAIIYQQQgghhGjEpI8BIYQQQgghhBCiEZPEgBBCCCGEEEII0YhJYkAIIYQQQgghhGjEJDEghBBCCCGEEEI0YpIYEEIIIYQQQgghGjFJDAghhBBCCCGEEI2YJAaEEEIIIYQQQohGTBIDQgghhBBCCCFEIyaJASGEEEIIIYQQohGTxIAQQgghhBBCCNGISWJACCGEEEIIIYRoxCQxIIQQQgghhBBCNGKSGBBCCCGEEEIIIRoxSQwIIYQQQgghhBCNmCQGhBBCCCGEEEKIRkwSA0IIIYQQQgghRCMmiQEhhBBCCCGEEKIRk8SAEEIIIYQQQgjRiEliQAghhBBCCCGEaMQkMSCEEEIIIYQQQjRikhgQQgghhBBCCCEaMUkMCCGEEEIIIYQQjZgkBoQQQgghhBBCiEZMEgNCCCGEEEIIIUQjJokBIYQQQgghhBCiEZPEgBBCCCGEEEII0YhJYkAIIYQQQgghhGjEJDEghBBCCCGEEEI0YpIYEEIIIYQQQgghGjFJDAghhBBCCCGEEI2YJAaEEEIIIYQQQohGTBIDQgghhBBCCCFEIyaJASGEEEIIIYQQohGTxIAQQgghhBBCCNGISWJACCGEEEIIIYRoxCQxIGqNRqPhtddeq+sw6lxd7YfMzEw0Gg0ffPBBpeavyTirGosQDdnjjz+Ok5NTXYdR5+pyP9xzzz34+vpWat6ajrMqsQjRkJ08eRKNRsPixYvrOpQ6VZf7YefOnWg0Gv75558bzlvTcVYlFlE3JDEgGoTCwkI0Gg1vvfVWXYdyQw0p1oYqKSmJr7/+mv79+2NqaoqXl1ddhyREjZkxYwZubm51HUalNKRYG6Lw8HBefPFF2rVrh62tLf7+/kycOJHTp0/XdWhCGN3BgwfRaDQsXbq0rkO5oYYUa0O1ZcsWJk6ciL+/P7a2toSEhPDss8+SkJBQ16HdMiQxIGqNUop33323rsOoc7Ifqm/WrFmcPHmSt956i+7du9d1OEJc15dffklmZmZdh1HnZD9U34gRI1izZg0ffPABycnJrFu3juzsbDp37szevXvrOjwhymjTpg1KKSZNmlTXodQp2Q/VFxcXx6effsqUKVPYs2cPSUlJfP755yxZsoSwsDBycnLqOsRbglldByCEEFW1YMGC0v+bmEh+UwjRONx11128+eabWFpaAtCyZUv+/PNPPDw8ePfdd6WKrhDiluTj48OqVavKTBs+fDhvvfUWM2fOZN26ddxxxx11FN2tQ+6oRa25us36le3M169fT4cOHbCysqJly5ZlqmKdPXsWa2trAN5++200Gg0ajaZM5tVgMPD555/Tvn17rK2tcXJyYuzYsZw5c6bC9f3zzz907NgRCwsLfv75ZwC8vLxKyzY3N8ff35/HHnuMjIyMMtthMBj48ssv6dSpE7a2tnh5eTF58mQuXrxYqVgrarufn5/PSy+9RGBgIBYWFnh7ezNjxgySkpKqvL8qY/ny5bRu3RorKytat25d6fZklYnzRvvoWgwGA8899xzm5uZ88803VdoeIeqzitqsX25nnpmZyZQpU3B0dMTFxYUZM2aQn59fOt/gwYOZN28eaWlppecTjUZDampq6TxHjhxh3LhxuLq6YmlpSevWrfnuu+8qXF9qaiqTJ0/G2dmZrl27AvDuu++WKdvR0ZFBgwaxefPmctty5MgRbr/9djw8PLCxsaFr166l548bxXqttvv//vsvffr0wc7ODltbW3r37s3q1atvan/dSHJyMrfffjsODg64ubkxc+ZMsrOzK7VsZeK80T66lj179uDp6cmAAQPKXXOu9N///rc0KXCZnZ0dnp6eREZGVmo7hKgtFbVZv7Kd+bx58wgKCsLKyopu3bqxZ8+e0vmWLl1aeo668847S88nV9a4zM/P59VXXyU4OBhLS0s8PDx44IEHSE5OrnB933zzDc2bN8fU1JSDBw+Smppa5lxlaWlJixYtePvtt9FqtWW2JT8/n9dff52WLVtiZWVFQEAATz75JGlpaTeM9Vpt9xMTE5kxYwbe3t5YWFgQGBjISy+9REFBQZX3V2V8/vnn+Pv7Y21tTVhYGDt27KjUcpWJ80b76Fry8vIYN24cjo6OrFu3rkrbA2Bubg6Ara1tlZcVFVBC1BJAvfrqq6W/Z2RkKEBNmDBBPfDAAyoyMlIlJyerqVOnKlNTUxUeHl46b0FBgQLUm2++WWHZ99xzj7K3t1c//fSTSktLU9HR0WrixInKyclJXbx4scz6xowZo+655x514cIFde7cObVp06Zy5eXm5qpNmzapoKAgNXLkyDKfTZo0SdnY2KivvvpKxcfHq+TkZPX777+rZ599tlKxXr0f9Hq96t+/v3JxcVF///23ysrKUrt27VLBwcGqWbNmKiMjo8r7qyKXlx89erS69957VWRkpEpISFDPP/+8AtTChQuNEmdl9tHlWN5///3S/T127Fjl4OCg1q5de93tuFqvXr2Up6dnlZYRojY99thjytHRscy0KVOmKG9vbzV58mS1fv16lZ2drVasWKGsra3VrFmzysw7ffp05erqWmHZW7duVZaWluquu+5S586dU1lZWWrBggXK1tZW/ec//ym3vvHjx6t169ap9PR09fPPP5crT6fTqYsXL6qZM2cqKysrdfr06dLPNm3apCwsLNTo0aPV8ePHVW5urjp06JC6++67VWxs7A1jrWg/LF68WGk0GvXII4+omJgYFRsbq5544gml0WjUggULbmp/VeTy8uPGjVMbNmxQWVlZat26dcrT01P16dNH6fV6o8RZmX00ZcoU5ePjU7rM77//rqysrNT999+viouLb7gtVzt58qQC1Pjx46u8rBA16cSJEwpQv//+e+m0HTt2KEBNmjRJvfnmmyoxMVFFRUWpPn36KHd3d5WXl1c674EDBxSg/vzzz3JlFxYWqh49eig/Pz/1zz//qOzsbHXy5EkVFhamWrRooXJycsqsb/z48erVV19V8fHxavv27erkyZPlykxPT1d//PGHcnR0VC+++GLp9Pz8fNW1a1fl5eWl/vzzz9L7zC+++EJ99tlnN4y1ov2QkZGhmjVrppo3b6527typsrKy1PLly5WLi4vq37+/0ul0Vd5fFbm8/Lhx49Rrr72mkpKS1MWLF9WECROUpaWlOnDggFHirMw+uhzLqlWrlFJKxcXFqU6dOil/f3914sSJ627H1fLz89XWrVtVYGCgGjhwYGkconokMSBqzbUSA8HBwWW+0Onp6crCwkK9/PLLpdOu97C9adMmBahvvvmmzPTCwkLl6+urpk+fXmZ9fn5+SqvVVirmxYsXK6D0hm7t2rUKUJ9//vk1l6lqYmDZsmUKUD/99FOZ+S5fZC6XU5X9VZHLy/v7+5fb/t69eytfX19lMBiqHWdl9tGViYHY2NjSC0NFF+obkcSAqO+ulRgA1Jo1a8pMnzZtmnJwcCgz7XoP26Ghoapdu3blboreeustZWVlpdLT08us76+//qp03O7u7uqll14q/T04OFiFhoZe9wasKokBg8GgfH19VadOncrN26NHD+Xp6Vm6rqrsr4pcXv7vv/8uM/3yOX7ZsmVGibMy++jKxMA777yjTExM1HvvvXfDbahIcXGx6tmzpzIxMVG7d+++qTKEqCnXSwyMGTOmzLz79u0r95Lieg/bc+fOVYDasWNHmemXLl1S5ubm5R5GhwwZUum4X3vtNeXs7Fz6+yeffKKACl8kVSbWivbDO++8owC1b9++MvPOnz+/TDlV2V8Vubz8sGHDykwvKChQXl5eaujQoUaJszL76MrEwOHDh5WPj4/q3r27SkxMvO42XOn3339XQOnP8OHDS69zovqkKYGoc8OHD8fU1LT0d2dnZ3x8fK5b7fxKl9scXd22yNLSkt69e7Nt27Yy02+77TbMzMp3r7F7925GjhyJu7s7pqamZZoAREREALBmzRoAJk+eXMmtu7FNmzYBMGHChDLTu3Tpgr+/f+nnl1V3f1W0/ePGjSM2Npbz589XO86q7KNjx47RvXt3zM3N2bdvH61bt67UNghxKzAzM2Po0KFlprVp04bs7OwyTQWu5cKFC5w5c4YJEyaUOSdASbX+wsJC9u/fXzpNo9EwatSocuVkZ2fz/PPPExISgpWVVWk12JSUlNJzX3h4OOHh4UycOLHcum7WuXPniI2NLXdOAbj99ttJSkri5MmTpdOqu79MTEzKbf/YsWPRaDQVNpuoapxV2Uc6nY57772X999/nyVLlvDKK6/cMP6rKaV46KGH2L17N2+++SZhYWFVLkOIujJy5Mgyv7dt2xagSvd+Xl5e9O7du8x0Pz8/WrRoUe7eb8yYMRWWs3TpUvr164eTkxMmJialTQAyMjJKq8CvWbMGLy8vBg4cWKnYKmPTpk34+vrSrVu3MtMv38tefe9X3f119fZbWVkxfPhwtm3bhl6vr3acVdlHq1evpk+fPvTs2ZOtW7fi6elZqW0AmDRpEkopsrKy+PfffwkPD6d79+7Xba4gKk8SA6LOeXt7l5vm4OBQ6d6rExMTgZI+AszMzDA1NcXExAQTExMWL15c7mTh4+NTrozjx48zYMAA7Ozs2LZtG3l5eSilSjtyutzWLDk5GUtLS1xdXauyideVlpaGlZUVjo6O5T7z8vIqd8Nb3f1V0Qn48rTr3VxXNs6q7KONGzcSFxfHfffdV6ULgxC3Ag8Pj3IPkA4ODgCV+j5fPve98847pee+y+e/yzfLV57/3N3dsbCwKFfOhAkT+PXXX5kzZw4JCQkYDAaUUgQEBJQ590HF58+bdTm2ioYbvTztynNSdfeXi4tLuaSolZUVDg4ONzz3VSbOquyj7Oxs/v77b9q1a8fw4cNvOH9FnnrqKebPn8+zzz7LG2+8cVNlCFFXrr6Xsba2xtTUtEr3fomJiZiZmZW599NoNJw8ebJS935Lly7lzjvvJCwsjCNHjlBUVIRSig8++AAoe+9nzHMflJxXKjqnXO7D5Eb3flXdX9e69ysqKiI3N7facVZlHy1dupTCwkIeffRRrKysKrXM1RwcHBg+fDi//vor4eHhfP755zdVjihLEgOizmk0mmot7+bmhqmpKVlZWeh0OvR6PQaDofTmNj09vcz8lzsqudLixYvRarX8+OOPtGrVqvREdXVnTu7u7hQVFRk1M+ni4kJhYSFZWVnlPktKSio3Jnh199fVHQVeOe16D/OVjbMq++jZZ5/lySef5LHHHmPOnDmV3AIhbg3GOPcBfPTRR6XnvsvnP1XSVLBMzZ2Kzn3x8fFs2rSJWbNmcdttt+Hs7IxGo0Gn0xEbG1s6n7u7O1AyZJSxuLi4ANc/J115/qvu/kpPT0en05WZVlRURHZ29g3PfZWJsyr7yMXFhQ0bNnD+/HkGDx5c7jp1Iy+88AJffPEFTz31FLNnz67SskLUB8Y4/zVv3hydTlfm3u/yuW/79u1l5q/o/Pfrr78SGBjIBx98QGBgYOk8Fd37GfPcByXngIrOKbm5ueTl5dXavZ+lpSV2dnbVjrMq++jrr79m2LBhjBgxotojqbRr1w6ofM0JcX2SGBANgoWFBebm5hQVFZX7bPTo0ej1ev76669qrcPExKTc27TffvutzO+Xq6EuWrTopmKtyKBBg4CSkQKudPjwYaKioko/N5Z///23XLWxFStW4OvrS4sWLaodZ2X20WUajYa5c+fyxhtv8Mwzz/Dmm29WZVOEaBRsbW0rPJ+0aNGCkJAQli5disFgqNY6ru7pftGiRWUeokNCQggODmbJkiXXrXZ6rVgr0qJFC3x8fMqdUwCWLVuGp6enUZsXGQyGcqMIrFixAqXUdc+zlY2zsvvosrCwMLZt20Z0dDT9+vUjISGhUtvx5ptv8vHHH/PEE09IQlXc0i73NH+te7+IiAgOHz5crXVcfe7Lz89n2bJlZaaNGjWKxMREtmzZclOxVmTQoEHExMRw6NChMtMvr9vY935XD/VXVFTEunXr6Nev33WbPlU2zsrso8usra1Zvnw548aNY/z48ZW6X7yWy83lQkNDb7oM8f8kMSAaBBMTE0JDQ9m+fXu5N9FDhw7l3nvv5YknnuDbb78lPj6evLw8jh8/zttvv83rr79+w/JHjRqFwWBg1qxZZGRkEB0dzYwZM2jatGm5dU2aNImXX36Zr7/+msTERFJSUliyZAmzZs26YawVGTt2LH369GHWrFmsWrWKnJwc9uzZw913301AQABPPfVUFfbUjbVp04bp06cTHR1NUlISL730Ejt27OD999+/bka6snFWZh9d7a233mLu3Ln85z//4cknn0QpZdRtFqIha9OmDbm5uWzZsqXcA+f333/P0aNHmTRpEseOHSM/P59Lly6xdOlS+vTpc8MH1CZNmtC5c2fmzp3LkSNHyM7OZunSpcyfP5+goKAy83777bdcuHCBCRMmcOLECfLy8jh8+DBTpkwpfVN0vVivZmJiwkcffcTBgwd5/PHHiYuLIz4+nqeffprdu3fz0UcfVdgfzM3y9vbml19+YdOmTeTk5LBhwwaeeuopevbsec32x1WNszL76Ept27Zl586d5OXl0bt37xu+9froo4945513ePzxx6XqrLjlBQQEYGdnx/r168nLyyvz2aOPPkpYWBjjx4/nr7/+IjU1laysLPbt28cTTzzB/Pnzb1j+mDFjOHv2LHPnziU3N5czZ84wfvz4cv0WPPLII3Tt2pXJkyfz119/kZGRQUxMDF999VVpcu56sVbkiSeeICAggMmTJ7Nnzx5ycnJYtWoVzz77LH369GH8+PGV31GVYGlpyVtvvUVycjJRUVHce++9pKWl8Z///McocVZmH13J3NychQsXMmPGDO65554bDlP9xRdf8Nprr3H8+HHy8vJISUnhzz//5L777qN58+Y8+uijN71vxBXqps9D0RhxjVEJLg9Zd6X27duX60F1165dqlOnTsrS0lIBauLEiaWfGQwG9cMPP6ju3bsrW1tbZWdnpzp27KjeeecdlZKScsP1KaXUokWLVKtWrZSVlZVq3ry5+vLLL9WGDRsUoDZs2FA6n16vV5999plq166dsrS0LB1C68KFC5WK9er9oFTJcH3PP/+88vf3V2ZmZsrT01NNmzZNxcfH3/T+utqVyy9dulS1bNlSWVhYqNDQ0DLDbVU3zsrso2ttyy+//KLMzMzUvffee92RI958880yvdJe+TNlypTr7gchatu1RiW4csi6y3744QcFlBl+tKioSN17773KxcVFaTQaBZSe15QqGa7u7rvvVl5eXsrCwkIFBASoiRMnqp07d95wfUopFR0drcaNG6ecnJyUk5OTuuuuu1RSUpJq0aKFGjt2bJl5Dx48qMaOHatcXFyUjY2N6tq1a5kerK8Xa0X7QSmlVq1apXr27KlsbGyUtbW1CgsLUytWrLjp/VWRy8snJiaqsWPHKjs7O+Xi4qKmT59eZqjV6sZZmX1U0bbExcWpNm3aKG9v7+sO2+Xo6HjNc9+1RoMQoq5cb1SCy0PWXcnU1LTc8KO///67CgkJUWZmZgooMwxrQUGBevfdd1WbNm2UlZWVcnFxUT179lRff/116TB+11ufwWBQH3zwgQoMDFRWVlaqQ4cOauXKleqzzz5TgEpISCidNzc3V7388ssqKCio9Dz75JNPqtTU1BvGWtF+UEqp+Ph4NW3aNOXp6anMzMyUv7+/ev7551Vubu5N76+rXbn8p59+qvz8/JSlpaXq3r272rp1a5l5qxNnZfbRtbbl5ZdfVsB1R2fJzs5Wc+bMUd26dVP29vbK2tpatWrVSr344osyKoERaZSSV3NCCCGEEEIIIURjJU0JhBBCCCGEEEKIRkwSA0IIIYQQQgghRCMmiQEhhBBCCCGEEKIRk8SAEEIIIYQQQgjRiEliQAghhBBCCCGEaMQkMSCEEEIIIYQQQjRiZnUdwK3CYDAQHx+Pvb09Go2mrsMRQogKKaXIycmhSZMmmJhUPzcs5z4hRENhzPOfnPuEEA1FZc99khgwkvj4ePz8/Oo6DCGEqJSYmBh8fX2rXY6c+4QQDY0xzn9y7hNCNDQ3OvdJYsBI7O3tgZId7uDgUMfRCCFExbKzs/Hz8ys9Z1WXnPuEEA2FMc9/cu4TQjQUlT33SWLASC5XI3NwcJALhBCi3jNW1Vc59wkhGhpjnP/k3CeEaGhudO6TzgeFEEIIIYQQQohGTBIDQgghhBBCCCFEIyaJASGEEEIIIYQQohGTxIAQQgghhBBCCNGISeeDQgghRA3SZWRQePIU+uwszFxcsGrdGlPprEwIIYQQ9YgkBoQQQogaUHjuHCmff0Hutm2Y+zTBzNkFXWoq2qQk7AcMwO3RR7Bq2bKuwxRCCCGEkMSAEEIIYUxKryf1q69J++knnCdOpPm6tZj7+JR+XnzpEukLFhA16W5c7pmC+9NPozGTy7EQQggh6o7ciQghhBBGYigoIO7ZWRRHRRGwZDFWLVqUm8eiaVO8XnkF57vuIu6ZZyk4eQqfzz7FzNm5DiIWQgghhJDOB4UQQgijMBQXE/v4E+izsghY/HuFSYErWTZvTsDi3zG1tyPqrokUx8bWUqRCCCGEEGVJYkAIIYSoJqXTET9rFvrsbPy+/w5TR8dKLWdia4vP3LnY9etH9NSpFMfE1HCkQgghhBDlSVMCIYQQdUaXnk7utu3k7dhB4Zkz6LOy0FhaYuHri03XLjiMHIllUFBdh3lDSR98SHFUFE1//RVTO7sqLasxMcHz1VfQmJoQfe9U/H/7FQs/vxqKVAghhBCiPEkMCCGEqHVFFyNJn/8TWStXYdmiBXZ9+uA4fhymzi6ookKKLl4kb9duIifcjt2AAbg/9SSWgYF1HXaFslavJmvlSgKX/XXT/QRoNBo8XnoJpRSXpj2A/4LfMPfyMnKkoiEzFBRQfCkGXVIiSqcDpTB1csLM1RXzJk3QWFjUdYhCCCEaMEkMCCGEqFVKrydm5kxsunYlcOmfWAYHl5vHpnNnnO+8E21SMqlffUXkuPG4PjQTt4ceQmNqWgdRV6woIoLE19+gyexPsPD1rVZZGo0Gz5dfRhUUlCYHzFxdjRSpaIgKTp4iZ91acnfspOjsWUxsbDBr4o3GvCQJoM/MRJ+ailIKC39/LJs3xzIkGKsWLbAMCcHc1xeNibQaFUIIcWMapZSq6yBuBdnZ2Tg6OpKVlYWDg0NdhyOEEBUy9rnqZsszFBdjUoU3nIVnzhD3zLOYeXjQ5JOPMffwuJlwjcqQl0fkXROxHzQIj2efMVq5Sq8n/oUXKbpwAf9ffq50fwXi1qCUImfdOtLn/0xheDgOQwZj27cvNl26YubhjkajKTu/wYA2PoGiiHCKIyIoPH+eovPhFF24gMbcHKvgYCz/lyiwbBaIRbNmmHl6liunMTDm+U/u+4QQDUVlz1eSGDASuUAIIRqC+pIYuBmGvDwS3nyLgsOH8fvh+zrte0ApRfys59ClpdF03o9ozIxbAU9ptcQ+/Qy61BSazvsJUztbo5Yv6qf8w0dI+uADdElJuE5/AMfx4zG1t7+pspRWS1FkZEmS4Nw5is6fpygyEm1sLBorKywC/LEMbIZFYCCWzQKxbNECi2bNbumEgSQGhBCNUWXPV9KUQAghRINgYmtLk48/ImXuXKImT8Hv66+w6dy5TmLJWLiI/AMHCPx7mdGTAgAac3N8Pp1N7COPEvvII/h9/x0m1tZGX4+oHwx5eSTPnk3m8hW4zpiO67Rp1f57a8zNsQoJwSokBEaN/P91FRejjY6m6GIkxZElP7nbt1N0/jymjo7Y9e2D49ixWHfufEsnCYQQQpQliQEhhBANhkajwePppzH38iLmwZklQ/316V2rMRQcPUry7Nk0/fEHzNzcamw9JpaW+H75BZcenEnMo4/i+8WXUnPgFlRw8hRx/zummy3/G4umTWt0fSYWFlgGB5fr28NQVETB4cPkbNxEzGOPY+bsjOuDD+I4dkyNJL+EEELUL9IjjRBCiAbHedIkvN55h9gnnyR7/fpaW68uI4PYZ57F/ckna6W2gomNDX7ffYfGxJToqfeiS0mpsXUpnQ5dSgrahAS0CQkYCgtrbF2iROby5URPnYrTXXfR9NdfajwpcD0mlpbYhoXh9fprBG/fhutDD5H63XdcHDWanK1b6ywuIYQQtUNSwEIIIRokx1EjMbGxJm7Wcxjy83EaN65G16f0euKfex7rtm1xuf++Gl3XlUztbPH75msSXn+dyLsm4vPRh9h07VqtMpVeT8GxY+TvP0DB0aMUnT+PNikJ9Poy85nY22PZrBlWrVth3akztr163vSQjOL/Ka2WpI8/JmvFSnzroNbLjZhYWuI0fhyOo0aS+dcy4l94EbvevfB89VUZKUMIIW5RkhgQQgjRYNkPHIjf118R+9jjGPLzcZk8ucbWlTJnDtr4eAL+/KPW215rLCzw/uADMhYs5NLMh3C5ZwquDz1cpaYFhrw8cnftInfzFnK3bQOlsOnRA5se3XGZNg1zHx/MPdzB3ByUQp+ZiS4piaLwcApPnSZt3jziX3gBqzZtsOvbF/vBg7Bs0ULaoVeRLiODuKefQZ+eTuCff9RpLYEb0Zib4zxpInYDB5D0n3e5OG4cPp/MxrZ7t7oOTQghhJFJYkAIIUSDZhsWht+PPxLz8MMYcvNwm/mg0deR9c9qMhYvIWDJEkzt7IxefmVoNBpc7r0H2x7dSXjjTTL/GITzfVNxuv12zD09y82vlCrtWC5v+3byDxzE3M8P+4ED8P3qS6zbt0djanqtlWHm4oKZiwtWoaE4jhkDgDY5mbydu8jdupW0efMwc3PDftAg7IcMxrpDh2uXJwAoPH2a2MefwKptW/y+/goT24bRZ4S5hwc+n88lc8kSYh5+GLeZD+L60ENoTKRFqhBC3CpkuEIjkWFrhBANQUMervBGCs+c4dL0GTjdcQfuzzxttDfZ+UeOcGn6DHw/+xS7fv2MUmZ1KaXI37uX1O+/J3//Acw9PbFoHoSpvQOquBhdWhpF58+jioux6d4duz59sOvbB4uAAKPFYCgsJG/3HnI2biR382YwNcV+4ADsBw/Gpnt3TKysjLauW0HWP6tJeOMN3B56CNeZDzbYmhaFp08T+/QzWDRtSpOPP2pQTUtkuEIhRGNU2fOVJAaMRC4QQoiG4FZODAAUXbzIpWkPYD94MJ6vvlLtN5qFZ88SPfU+3J9+qkabKVSHLiODonPnKboQgSEvH42FOWbOzliGhGARFISJhUWNx6B0OvIPHy5JEmzchDYlBes2bbDp0gWbrl2w7tSpzmpa1DWl05E8+1My//oLn08+xq5v37oOqdr0OTkkvPIKhadO4zN3LtZt29R1SJUiiQEhRGMkiYFaJhcIIURDcKsnBgCKY2O5NO0BbDp3xvvd/9z0UGtFFy4QPfU+XKZOxe2hmUaO8tallEIbG0v+gYPkHyz50cbGYtmyBTadu2DTuTM2XTrX6FCP9YUuI4P4WbPQJifj9+WXRq2xUdeUUqT/9BMpX36F5ysv43znnXUd0g1JYkAI0RhV9nwlfQwIIYS4pVj4+uK/YAExM6Zz6f5pNPn4I8y9vatURu6uXcQ98ywu994rSYEq0mg0WPj5YeHnh9OE8QBok5IoOHSI/IMHSf36a4rCw7Hw98euf3/shw0t6e/gFmuvXnDsGLFPP4N1u3YEfP5FlTqKbAg0Gg2u06dj1bo1cc/OouDoUbxef12akAghRAN1a12FhRBCCMDc04OAxYuxCAzg4thxZP71F+qqofgqovR60ub9ROzjT+D16iu4P/F4LUR76zP39MThttvweuMNmq1cQcjePXg8/xz6rCxiHnqYiyNuI+3nn9FnZ9d1qNWmlCLj99+Jvn8aLlOn4jPns1suKXAl2x49CFz2F0UREURPnkJRZGRdhySEEOImSFMCI5EqZUKIhqAxNCW4WvaGDSR/+BEaK0vcHnkE+yFDyrW7VzodOVu2kPr1N6j8fJp8+AHWHTrUTcCNjKG4mJx168lYtIiiiAhcH5iG871TG+TDtC41lYQ336Lw+HF8PvsUmy5d6jqkWqOKi0mePZuMP/7E7dFHcJ027aab8dQUaUoghGiMpI+BWiYXCCFEQ9AYEwNQ8tCS8eefpP/yK/q0NKw7dMDczxeNiSnaxEQKDh9GY22Ny9SpOE++GxNLy7oOuVHK27uPlM8/pzg6Gs+XXsJh1MgG03t/9rr1JL71FjY9uuP1xhsNqrd+Y8o/fISE114DpXB/4nHshw+vN81EJDEghGiMJDFQy+QCIYRoCBprYuAypRRFZ89ScPQo2vh4lMGAuYcHVu3aYd2uHRpT07oOsdFTSpGzdi2J//0vVsEheL35Bhb+/nUd1jUVx8aS/NHH5O3bh9cbr+M4cmRdh1TnlFZL5rK/Sf3mG0wsLXEcPw6HUaOw8PWt07gkMSCEaIyk80EhhBDiKhqNBqvQUKxCQ+s6FHENGo0GhxEjsO3Vi5Q5c7g4bjzujz2Ky/3316uq6frcPNK++470337DYdRIgv5ZhZm7e12HVS9ozM1xnngXjuPHkbtpE5nLl5PyxZeYe3lh3akTFoEBWPj6Yu7ri7mXF2bu7mjMzes6bCGEaNRu6gqbn5/P6dOnycjIwNHRkZYtW0q2VAghhBBGY+rggNcbb+AwajQJr75K9rr1eL/3LlYhIXUaly4jg4wFC8lYuBCL5kH4L1yAdevWdRpTfWViYYHDiBE4jBiBPjePgqNHS2rrREeTt2s32pgYdKmpoBSmLi6YeXpg4eODZUgLrFqFYtO5M6ZOTnW9GUII0ShUOjFgMBj4+++/+fbbb9m+fTvFxcWln5mamtKzZ09mzpzJxIkTMZesr6glOWmpnNuzg8ijh0iLiaYgJxsTE1PsXF3xCgqhedcwgrp0x0yOSSGEaJBsOnUkcPnfpH75JVF3TcTtoZm4zphR62+YC8+cIfPPP8lc9jc2nTuXdC7Yo0eD6QOhrpna2WLXuxd2vXuVma50OnRpaeiSktAlJ1McfYmi8+fJXruW4shIrEJDsR86FIeRt9V5UwQhhLiVVaqPgZMnT3L//feTkpLC5MmT6devHy1btsTR0ZGcnBzCw8PZvn07ixcvxsTEhJ9++omwsLDaiL/ekLZmtSsp8gK7/1hA1LHD+LZqS3DXMDwCm2Hj4IRWpyUjIZ7kC+c5t2cHep2OnndMplXfgZhI+2HRyDX2PgZEw1Zw4gQJr7wCZuY0+e97Nd4kRJuQQPbadWQtX05xTAwOQ4fict9UaYpSS3QpKeTu3EX22n/J270Hq1ahOI4Zg+OoUZg6Ola5POljQAjRGBm188GlS5ei0+mYOHHiDTPjq1evJikpiQceeKDqUTdgcoGoHflZmWz55QciDuyl/ZARdBk9ATtnF1JSUjh8+DDh4eGkpqYCYGJigqenJ67WlqQf2oONjTUjn3weZ2+fOt4KIeqOJAZEQ2coLib1m29In/8zLvdMwXXGDKNVN1dKUXjqNLmbN5OzZQtF4eHYdO2C49ixOAwZgoltwxtC8Vahy8ggZ/0GspYto/DMGTyefx6Xe++pUhmSGBBCNEY1NirBkiVLUEoxadKkagd5K5ELRM07t2cHm+Z9g2+rNgy8/yHsXFzJyclh/fr1nD59mtatWxMaGoq3tzdWVlbk5+cTGxvL8ePHiY6OpomtFTlH9zJkxmOE9u5f15sjRJ2QxIC4VRSeOUPyxx9TcOIkLlOn4nTnHZh7eVWpDKVUSXv3ffvJ37ePvP37UYWF2PXtg92Agdj17XNTb6ZFzSqKiACNBsugoCotJ4kBIURjVGOjEmRmZnLixAlJDIhao9dp2fLLj5zbvZ3BMx6jRVhvAM6fP8/y5csJDAzkySefxPGqmzcrKytcXFxo164dcXFxrFixAk2Hnqz7ZR5ZyUl0H3+XtA0VQogGyio0lKY//UTevv2kzfuR1O+/x7ZHD2x79cSmc2cs/P0xsbcvPc8bCgvRJSZSFBVF4enTJT8nTqJPT8e6QwdsunfH+e5JWLdvj8bCoo63TlyPZfPmdR2CEELccqqcGBg4cCBffvklxcXFWNTBhfOLL75gzpw5JCUl0bZtWz799NMb9mdwo2Uee+wxvvvuuzLLtGnThqNHj9bEJogqyMvMYMUn72LQ67nn/Tk4eniilGLTpk3s37+fkSNH0r59+xuW4+Pjw4MPPsimTZs4nJ/P/i2byE1PY9ADD6MxMamFLRFCCFETbLt3w7Z7N7SJiWSvXkP+3n2kfvMthqwsNFZWaMzNUVotqrAQjbk55n5+WLVqhU2nzrjcOxXr9u0wsbKq680QQggh6lSVEwNJSUlYWloyfvx4vvrqKwICAmogrIrNnz+fF198kUWLFhEWFsZHH33E0KFDOX36NH5+fje9jF6vZ+zYsSxZsqR0OXmTXPfS42NZ9v6bNAkJZehDT2JmYYFer2flypVER0czc+ZM3NzcKl2eubk5w4cPx93dnbVr/+XsmTPw0zcMmv6o/L2FEKKBM/fywnX6A7hOfwClFIa8PHTJKSidFo2ZOab2dpi6ukoyWAghhKhAla+OiYmJpKen8++//xIYGEi7du247777mD17Nhs3biQjI6Mm4gTg448/5oEHHmDcuHF4enryySef4ODgwDfffFPtZTQaDWZmZqU/ptJ7fZ1KiDjH768/T4uefRnx+CzMLCzQ6XQsWbKExMREpk+fXqWkwJU6d+7MhAm3k+nsyenTp9n6yw9UsasNIYQQ9ZhGo8HUzg7LZoFYhYRg2SwQM3d3SQoIIYQQ11DlK+Qdd9zBxYsXyczMZPv27cycORNzc3MWL17M6NGjee+992oiTjIyMjhz5gwDBgwonabRaBgwYAC7d++u9jLr1q3DwcEBPz8/Jk+ezKVLl2pkO8SNxZ8/y1/vvUHY7ZPoc/d9aDQa9Ho9y5YtIycnh2nTpmFvb1+tdYSGhjJhwgRyXLw5ceQQOxb9LMkB0SAUF+Rz4dB+di7+jT//8yqFebl1HZIQQgghhGjgqtyU4DIHBwf69OlDnz59Sqfp9Xqys7ONEtjVEhISAPDw8Cgz3d3dnYMHD1ZrmcDAQH799Vf69etHXFwczzzzDH369OHEiRPX7LmxqKiIoqKi0t9rarsbm7hzZ1j2/pv0vnsqHYeNAsBgMLBq1SpSUlK4//77sTJSW9BWrVpRWFjI2n//5djunZhZWNLzzslGKVsIYyrKz+Pc7h2c27OD2DOncHB3x6dFa0J69Maklt+AyrlPCNEYyblPCHGrq1RiIDs7u1JDsZiamuLs7ExWVla5HuJriomJSZXf9F69zIsvvlj6fxcXF/7880+8vb1ZvHgxM2fOrLCM999/n7fffvvmghYVijt7mmUfvEnfKQ/QfsgIoGQoqXXr1hEdHc20adOwNfIY0p06dSI7O5tDBy05tH4Nlja2dB451qjrEOJmxZ07w/GN/3J+7y5cfZvSqk9/hjz4OE5e3nUWk5z7hBCNkZz7hBC3ukq9avr5558ZPHgwGzZswGAwVDiPUopt27YxduxYPvzwQ6MGCeD1v7GJU1JSykxPTk7G09PTaMsAODs707RpU8LDw685z8svv0xWVlbpT0xMTKW2Q1QsLS6G5R+9Q5/J00qTAgB79uzh1KlTTJ06tcbGCe7Xrx9N/f2x6BjGrj8XcmLz+hpZjxCVoZQi+sRR/nj7ZZa9/wZWtnZMfvcT7nn/MzrdNrZOkwIg5z4hROMk5z4hxK2uUjUGHn/8cSwsLJg6dSomJib07t2bkJAQHB0dycnJITw8nB07dpCfn89LL73E008/bfRAXVxcCAkJYdu2bUyYMAEouYHeunUrU6ZMMdoyUFJDIiYmBm/va9+AW1paYmlpWY0tEpflZWaw7P23aD/0NjoMva10+tmzZ9myZQv3338/zs7ONbZ+jUbD2LFjmT9/Pm4DbmPzz99jbmVFy559a2ydQlQk7twZti2YR0Z8HJ1uG8OYWa9iZWdX12GVIec+IURjJOc+IcStrlI1BkxMTHj44YeJjo7m008/xdramjVr1vD111+zYsUKNBoN7733HrGxsTz//POYm5vXSLCzZs1i3rx5rFu3jqysLF577TXS09N5+OGHS+d56KGH6NChQ6WXKSoq4s477+Tw4cMUFRURHh7OpEmTsLW1vW7yQBiHtrCQ5R+9Q5OQlvSaeG/p9ISEBJYtW8b48ePx8fGp8TgsLCyYNGkS8SmpNB9zF+u+ncvFwwdqfL1CAGQlJ7Fqzof89d7rBLbvzINfziPs9rvrXVJACCGEEELcmird+eDZs2fx9PRk4sSJTJw4sSZjuqaZM2eSmZnJtGnTSE5Opk2bNqxZs4aAgIDSefR6PTqdrtLLWFpacs899/D4449z9OhRnJyc6NOnD/v27btucwNRfQaDnn8+/whzSyuGPfI0Go0GKKmxsWjRIvr06UOrVq1qLR5HR0cmTZrEL7/8Qu+77uOfOR8y7oU3aNqmXa3FIBqXovx89i//g8P/rqJFWB8emPMddi6udR2WEEIIIYRoZDSqkj33zZ49m7feeovp06fzzDPP4O/vX9Ox3RSDwYBSClNT01pdb3Z2No6OjmRlZVW5LbzBoKcgO5uCnJIebk1MzbBzccHCyromQq0XlFJsnv8tl04e5+53Pi59M1pcXMz8+fPx9PRk7NixpcmC2nTkyBHWr1/PgPZt2LtoPqOeeZFmHbvWehzi1mUw6Dm5ZQO7lizApYkv/afOwLNZ81pZd3XOVbVRnhBC1BRjnq/k3CeEaCgqe76qdI2Bxx9/HBcXFz799FO+/PJL7rzzTp577jk6d+5slICNpbaH7qqOyCMHWfftXPKzslDKgLmVNRoN6HU69FotNo5OeAe3ILBDF5p37YGtU821s69th/75m/N7dzH53dmlSQGlFCtWrMDCwoJRo0bVSVIAoGPHjiQkJHAoMppBDz7Oqs8+YOhDTxLaq1+dxCNuHUopIo8eZMfCn9EWFzF4+qM07xZWZ8e6EEIIIYQQUIUaA1dav349n376KevXr6d///4899xzjBgxolHf3N5M5jg/O4uspERsnZyxcXTCzMICKHl4KMjJJjMxntgzp7h4+ACJF87Tslc/uo6+HVdfv5rclBp3bs9O1n07l4lvvl/mLemePXvYvXs3Dz30EHZ13LZar9fz22+/YWNjQ5fgZqye+yGdRoyh551T0DSg5JOoPxIvhLN94XxSLkURNmEi7YbchlkN9cdyPVJjQAjRWEmNAVFOYRacWg7RuyDtAmgLwNIePFpCswHQrB9Y3zov5kTjVNnz1U0lBi47deoUn376KQsXLiQoKIjnnnuOKVOmYPG/B9zGpKYvEGlxMRz652/O7NxGh2Ej6XnHZMytrIy+npoWd/Y0f/33DUY+9QJBnbuVTo+OjmbBggVMnToVP7/6kfjIy8vj+++/p0uXLoQGNGXFJ+/i0sSXYQ8/hY2jU12HJxqIlOhI9v39BxcO76fTiDF0G3sHlja2dRaPJAaEEI2VJAZEqcwY2PYhnPwL3FtCyDBwCwYLu5JkQfxRuLgF0iOhw90Q9ji4BtV11KISlFLk5OSQkpJCSkoKmZmZZGdnk5OTQ35+Pnq9HgAbGxtsbW1xd3fH29ubwMDAOn8xWVNqJTFQWFhIZmYm58+f57333mP9+vW88MILfPjhhzdbZINVWxeI1EtRbPjhK3Iz0hn19At4N29RY+sytvT4OH5/43l6T7yH9kP+f1jCnJwcvvvuO/r27Uu3bt2uU0LtS0hI4KeffuLOO++kqU8TNnz3BZdOn2Dg/TNp2atfo64l09gZDAYiIyOJiooiLi6OzMxMlFLY2dnh7OyMs7UVqcf2E3/qBK37D6b7uDuxd3Wr67AlMSCEaLQkMSDQFcPuubDjMwgdVfLA732dTqYTT8LuL+D0cuh8P/R/GaydailYcT1KKbKzs0sTAMnJyaX/LyoqwtnZGXd3d5ydnXFwcMDBwQEbGxtMTU1LamcXFJCbm0tSUhLx8fEkJibi5+dH+/btadeuXY2NslcXjJ4Y+OOPP/jkk0/IzMwkKyuLzMxMiouLSwrRaLCzs8PR0ZEnnniCF154wThb0YDU5gVCGQwcXL2c3X8upP+902k3uP4348jPymTR688R0r0XfadMK52u1+v55ZdfcHJyYvz48fVyO06cOME///zDgw8+iJubG+f37WLTvG9w9PCk551T8G/XsV7GLWqGVqtl//79HDx4kOLiYoKDg/Hx8cHV1RVtURHhRw4SceokOQYwWFrTskUIffsPwNvbu65DByQxIIRovCQx0MjlJMEfU6EoG0Z9Bk17VH7ZlPPw7/OQdApGzSlJKohak5+fT3x8PElJSaUP/ykpKWi1WpydnfHw8MDd3b30x9XVtco12HNycjh79iwHDx4kOzub7t27ExYWhqWlZQ1tVe0xeueD6enpHDhwgNDQUObMmUO7du1Ksy8ODg7yYFSLNCYmdB09Aa+gYP6Z8yHpcbH0nzqj3rZ91xYVsvyj/+DVLJg+d99X5rMNGzZQVFRUp50N3kjbtm1JTExk8eLFzJgxg5DuvQho34kja/9h9ecfY+fiSqu+A2kR1hsHN4+6DrdCSily0lJJiowgPzOTwrxczC0ssHZwxNnbB3f/QEzNKn06MGpc2SlJJEVeIPVSFNkpyeRnZ1FcUICJiQmmFhbYOjlj7+qOe1N/PAKb4+jhWSfHilKK06dPs379emxsbBg8eDAtWrTARKPh0qnjnF23kvN7d+Hs3YSBQ0bQslc/cvML2LNnD/PmzSM0NJShQ4dib29f67ELIYQQjVrsIVhyDwT0gtGfg4VN1ZZ3D4F7l8OJP2H5oxC+Doa9D5a3ZtXzupabm0tERAQXLlwgNjaWjIwMnJ2d8fLywt3dnaCgoNIEgLHe7Nvb29O1a1e6dOlCZGQkW7Zs4cCBAwwcOJCOHTs2qA7ub1aVmhLs2rWLTz75hDVr1nD77bfz3HPP0alTp5qMr8Goq8xxZlIif/33dbyCQhj+6NOYmtWvai8Gg55Vn35AQU42d7z6n9IOFgFOnjzJqlWrmDlzJq6u9XvsdoPBwMKFCzE1NWXSpEmlJ4fiwgIi9u/h1LZNxJw+gaO7Jz4tW+Pq1xRXXz9cffywd3PHxKR2h88siVlP7OlTnN+7gwsH95GXlYmrb1PsXFyxtLFFry0mLyuT9LgY9DodPi1aEdKjN8HdwrC2r7ljWK/TEn38KOf37eLSyWPkZWTg5uePW1N/HD28sHFwxMLaGqUUuuJicjPSyUlNJiU6itSYaGycnAhs34mA9p3wb9exVtrrFxYWsmrVKiIjIxkyZAjt27UjIfwcZ3dv5/zenWg0GlqE9SG0zwC8goLLLZ+dnc26desIDw9n6NChdO7cuc4SYVJjQAjRWEmNgUbqyAJY8zwMeKWk6UB1r7+ZMbD8EciOgwk/gm/9GqHtSgUFBZw7d47Y2FhycnIwMTHB2dkZf39/mjVrVq+qy2u1Ws6cOcORI0eIiorC29ub4OBg/Pz8aNKkCTY2VUzmVJNSijNnzrBu3TqcnZ0ZO3Yszs4NsyPKGu1jIDw8nNmzZ/Prr7/Ss2dPnn/+eYYNG1atgBu6urxA5GVmsOz9t7B2cGDMrFewsLKu1fVfi1KKLT9/T9TxI9z9n4+xtvv/N6UpKSn88MMPTJgwgZYtW9ZhlJVXUFDAjz/+SLNmzbjtttvKPdgV5ecTd/YUCeFnSYuNIS32EhmJ8Wg0Jjh6eODo6Y2TpxdOnt44enrj6uOLk1cToz8gJkdd5NTWjZzdvR2A4O69COneE+/mLSrssFIZDKTHxxJ59BDn9+wkOeoCgR270mbAYALadzZKTQK9TsulE8c4t2cnEQf3YGFtQ0iP3gS074RPi1DMLSvXkaauuJjYs6eIOnqIqGOHyUiIx79te5p360nzrj2wcXCsdqxXS0hIYMmSJbi6uhLWri1xJw5zbs8OtAUFBHfvScte/fBt1aZSyZ+IiAiWL1+On58fo0ePrvWLHEhiQAjReElioJHRa2HdKyVv+e+YD0EDjFe2wQB7voCtH0D/lyDsCahHb5Rzc3PZtm0bhw8fxtPTk4CAABwdHdHr9aSlpXHhwgW0Wi3dunWja9eudXI/cllhYSEHDx5kz549WFtb07FjR9q2bVtvvldFRUVs2LCB48ePM2jQILp27drgag/USueDKSkpfPXVV3z11Vd4e3vz/PPPM2nSpHqVfaotdX2BKMrPZ8Un76LTFjPhpbewsq37qk17ly3h6PrV3P3Oxzh6eJZOLyoq4ocffiA0NJRBgwbVYYRVl5mZybx58+jSpQv9+vW74fx6nY7s1GSyEhPITEokM6nk36ykBDIS4jCztMSzWTBeQSU/3s1bYOdS9doT+VmZnNm5jVPbNpKRGE+LHr0J7TMAv1ZtMTGtWm2FjMR4Tm/bxKltm9HrtIT2GUCbfoNwaxpQpXJ0Wi2XThzl/N5dJckAKxtCevSiRVgfvJqHGCUhkpEYT/i+3UTs30PixXB8W7YmuHtPmncLw96l+h39nTl9imXL/qaJjQWF50+iLy6iWadutAjrQ0D7jjdVQycvL48VK1aQmJjIhAkTCAgIqHacVSGJASFEYyWJgUYkNwX+vK9khIFJC8E5oGbWE3sI/noAXIJg/LdgV/dNSk+cOMHq1asJCAhgwIABeHp6lptHKUVERAS7du0iKSmJoUOH0qFDh1qtzaiU4uTJk6xduxZnZ2f69u1LcHBwvW1afPHiRVasWIGbmxvjxo1rUE1DazQxUFxcTFZWFtnZ2WRlZZGYmMjnn3/OunXrePHFF/nggw+qFXxDVB8uELriYlZ99j65Genc8ep/arQ6+I0c37SW7QvnM/HND3D3DyydrpTizz//pLCwkHvuuafBZdwAkpKSmD9/PoMHD6ZLly43XY5epyX1UjSJF86TeCGcxAvhpMVcwtbFBe/mIXgHt8Tdzx8nrybYurhgZm6BRqNBV1xMflYmKZciSboYQdTRwyReCMcntBWt+w0mpHtPLKyrn/lVBgOXTh7n1LaNhO/fg6tvU4K7heET2hrPZs0xtyjbGYtOqyUzIY64c2eIOXWcyKOHsLS1JaR7L0J69MK7eYsa7QcjOzWFiAN7Cd+/i7izp/EKCia4W0+Cu/XEyatyHf8ppUiLvUTMqeMcPnKUmAItTjmptG3bjuZde+Ab2sYoNSiUUuzfv5+NGzfSv39/evbsWWsXQkkMCCEaK0kMNBLxR2DxPeDXDcZ+CRY13OSwMAtWPQ1RO2HCdxA0sGbXdw06nY7169dz/Phxxo0bV+kauWfPnmXNmjU4Ozszbty4Wqkun56ezurVq0lMTGT48OG0adOm3iYErlRYWMg///zDxYsXGTduHCEhIXUdUqUYPTHwww8/8Nprr5GVlUVRUVG5z01NTXF0dGTWrFm88sorNx95A1VfLhB6nZbVn39MRkI8d7z6H2ydar8tTPiBPfz7xWwmvPwWvqFtyny2e/du9u7dy0MPPYStbd2N5V5d0dHRLFiwgDFjxtC2bVujlVtckE/ihQgSIs6RGHGOtNgYspITMej1aExMMDE1Ra/VojExwaWJL+7+gfi37UBAh87YObtct2ylFMXFxRQUFGBpaYmVlVWlT8JF+Xmc27OTqGOHiDt7mvysTKwdHLFxcMRgMKAtKiQ3PQ0zCwu8m7fAr1VbAjp0wivIODUDqio/K5OIg3sJ37+HSyeOYevsjEdAEC4+vtg5OWNpa4dGo0Gv15GfmUluRhppMZdIuRSFrrgYi+BWpGHOqCGDad8jrMa2ITY2lj/++AMfHx/Gjh2LVQVNPYxNEgNCNA5ZRVmsj17P1pitXMi8QJ42DztzO5o7N6ePTx9GBI7A3qLhvPEyBkkM3OKUggM/woY3oN+L0Oup6vcnUJV1H/kN/n0Jus2A/q+Aec1f0y8rLi7m999/p6CggIkTJ1b54b6oqIiNGzdy7Ngxhg0bRqdOnWrk3ken07Fnzx62b99O+/btGTRoENbW9aMJdGUppTh+/DirV6+mY8eODB48uN7Xljd6YmD//v3s27cPJyenCn8aUnWKmlCfLhAGvZ5/v/qUpMgL3Pn6u0apUl1ZFw7t45+5HzHyiedp3rXsMDBRUVEsXLiQ++67D19f31qLqaZERESwZMkSRo8eTbt21xkDt5oMej2FebkUFxRg0OuxsrXF0tauUm+uU1NTOXXqFFFRUcTGxqLVaks/Mzc3x8vLi+DgYEJDQ3F3d69UPEop8rMyyUlNIT8nCxNTM8zMzXH09MLO2bXeZXyL8vNIuniB5KgLZCYmkJeZTmFeLgAmJibYODpj6+yCq48fbk39OR+XyN69e7n33ntp0qRJjceXl5fHX3/9RVZWFhMnTsTDo2arIUpiQIhbW2pBKl8f/ZrlEctp6dKSYQHDaOnSEnsLe7KLszmTdoYN0RuIzIpkWptp3N/6fixMqzasV0MliYFbWE4SrH4W4g7D7T9AQO+6iSPlHCybCcV5MOYL8A+r8VUWFxezaNEilFJMnjy5WsPrRUREsGLFCry8vBg9erRRj+1Lly6xatUqNBoNo0aNomnTpkYruy6kp6fz119/odVqueOOO2r8/q06aqWPAfH/6tsFwmDQs+H7r4g5fZw7X3uvTBv/mhJxYC+rv/iY2x6fRXC3nmU+y87O5rvvvmPAgAHVqn5f31y4cIHFixczYsSIejNCh1KKc+fOsXv3buLi4ggJCaFZs2Y0bdoUBwcHLC0tKS4uJjs7m5iYGMLDwwkPDycgIICePXsSFBRU15tQZ7Zt28a+ffuYOnUqXl5etbZeg8HA1q1b2bt3L6NHjzZqLZSrSWJAiFuTQRn47fRvfH30a3o26ckTHZ+gmVOza85/IPEAH+7/EI1Gw5wBc/Cx86nFaOuGJAZuQbpiOPAjhi0fkNZ0GCmtZlCIOcXFxVhaWmJnZ4e7uzuOjo619+JCr4O9X8PW96HDZBj4GljXTA3ey0kBgMmTJ2NhUf0kX0FBAf/++y/nz59n5MiR1b4nyc/PZ+PGjZw4cYJ+/foRFhaGaRX7v6qv9Hp96f3bkCFD6Nq1a717QQaSGKh19fECoQwGNv/8PREH9zLhxTfLtPU3thOb17P55++47YnnCO5aNjuq0+n45ZdfcHV1ZezYsfXyC1MdUVFRLF68mO7du9O/f/863b6oqCg2btxIRkYGvXr1on379pVqspGbm8vBgwfZu3cvPj4+DB06tMLOam5ll6u2TZs2rc6yvufOnePvv/+mffv2DBkyBDMj9GdwNUkMCHF9OoOO8IxwzmecJz43nrTCNPRKj5nGDF97XwIdA+ns2Rlb8/rTHC4xL5FXd75KfG48/+n1H7p4VS4Br9Vr+ejAR/wb9S+f9PuEHt49brxQAyaJgTqSlwZJJyA1HHKTIT8NUKAxKXlgtvMs+XHwAWd/sHG9fhMApSAjisLDSzhzYAtnVTMuGrxRmODu7o6NjQ3m5uYUFhaSm5tLWloadnZ2NGvWjLZt2xIYGFg7D6bpF2H1cxB3EHo/C90fAnPjVZsvKipi0aJFaDQaoyUFrnT69GlWrVpFs2bNGDlyZJVHLjAYDBw7doyNGzfi7e3NyJEjG+xwfzcSGRnJsmXLaNKkCWPGjKl3zaUlMVDL6usFQinFvmVLOLDqL0Y+9QLNOnY1bvkGA7v/XMiRdf8w9rnX8GtVPqv477//Eh0dzfTp0+t9G5yblZyczMKFC2natCmjR482+sn5RhISEti0aRMxMTH07NmTHj163FRVsvz8fLZv387BgwdLEx236t/sSkePHmXNmjXcd999+PjU7Vuz9PR0lixZgoWFBXfeeafRzyeSGBCirDxtHsdTjnM0+SiHkw9zPOU4JhoTWri0wNfOFzdrN0w0JmgNWmJyYgjPCCcxL5GeTXpyR8gd9PXtW6cJ4cNJh3l6y9P09e3Ly91fvqmExfKI5fx333/5uO/H9PO78Yg7DZUkBmqJwQDRO+HsaojYBGnh4NQU3ENLeu23cQUTUzDooCCjpBlAbiJkxUF+KljYgZN/SZLA0a+k80BTCyjMhJwE0i6dZ29uE45pWuPq5EBoh26EtGiBu7t7hQ/8xcXFxMbGcv78eU6ePAlA9+7d6dKlS+20b7+wBTa+VZIU6f0MdLgbLKvXBLuoqIiFCxdiamrK3XffXWP3nbm5uaxatYq4uDiGDBlCmzZtbphUMRgMhIeHs3nzZoqKihgyZAitWrVqmC8GDQZIvwBJpyAzGrJiSzqbLMotSV6ZWYKZFVg5km/lyarzBmIyihh/2yCCWnepN0NYSmKgltX3C8TZXdtY/90XdB1zO90n3FWpMddvJD8rk3+//oyM+FjGv/gWrr5+5ea5PGTKzJkzcXG5fud4DV1OTg5//vknBQUF3HXXXZVus18daWlpbNmyhbNnz9K1a1d69+5tlCxlUlISK1eupKCggDFjxtT6kHq16cyZMyxbtozJkycTGFhztWqqori4mNWrVxMREcGdd95p1P0viQHRmGkNWi5kXuBU6ilOpZ3iZOpJzmWcw8vGi46eHeno3pEOHh1o7tQc0+tcJy9mXWR91Hp+P/s7njaePNnpSXr71H6b5ssP9LM6z2Jiy4nVKmtD9AZe3fnqLZ0ckMRADctLK+n878gC0OZD6GhoPrikvb+1U+XKKMqFzEuQEfX/D2LafNAVk2XixLYkO44lFNO6VSjdw3pVOZl/+aF19+7dJCQkEBYWRs+ePavVLr+SK4bTy2H355B2ATreW9JJocu1m/tcS1FREQsWLMDc3JxJkybV+MsopRTHjh1j27ZtGAwGOnfuTPPmzfHy8iodXcxgMJCYmMjFixc5fPgwxcXFhIWF0b179xqp/VhjlCrpJ+LCppKkVsw+0GvBI7RkyEtH35Jj2cIeUKArLGnOUpABOfGorAQOp1myrrAdLTRRDHG8hIObV0mSyzngfwmvgJIE2eWkgsYUinNLfopySmrU5KWUfJ/yUkqSZf/7XZubxqViR4Ke21ClzZLEQC1rCBeI5KiL/DP3I2wdnRj2yNM4ed5cG2qlFBEH9rBp3jf4hLZh6MzHsbQp/zCakJDATz/9xF133UVwcHB1w28Q9Ho9mzdvZv/+/QwcOJDu3bvXyJCMWVlZ7NixgyNHjtCuXTv69++Po6OjUddhMBjYt28fmzdvpkOHDgwePLjmL5y17OLFi/z+++9MmDCB0NDQug6nDKUUhw4dYt26dUYd0lASA6KxMCgDkVmRnEw9ycnUk5xOO83Z9LNYmFrQyrUVrd1a09q1NR3cO+Bpe3NNpwp0BSw9v5Rvjn1DzyY9ebHri7jb1HxSWG/QM/fwXJaGL2V2v9mENTFOB2eXkwPfDv6WTp71o98cY5LEQA3JTYHtH8PhX0s62+v6IAQPAVPj1DjU6/Xs3buXrVu30qJFCwYMGICrq2u1y7106RIbN24kNTWVvn370qVLl5p/iFUKYvbDvm/gzD/QpAO0vRNajy95WLyBwsJCFi5ciLm5OXfffXet1urU6/WcOXOGEydOEBUVhVIKe3t7lFLk5ORgYmKCv78/bdq0oVWrVg0rIZAeCcf/gGO/Q04C+PeC5oMgsC+4t6zysZyVnsLGtas5e/ESXZva0NMlC7u8qJJkV0ZUSa2DcjQlNUlsXMDWHWzcwNYNbN0ptHDhQJIpey9k4GBny/SHH6/S/q2VxEBxcTE6na7KbU5uRQ3lAqEtLGTrbz9yevsWOo0YTbdxd2FZhb9f0sUIti/6mZToSPrd8wCt+g6s8GElNzeXH374gS5dutCnTx9jbkKDEBUVxapVq7C0tGTo0KFGe+ObkZHBzp07OXbsGCEhIQwYMKDGayakp6ezcuVKMjIyGDNmzC3TOWFcXBy//PILI0aMoGPHjnUdzjUZe0hDSQyIW5VSivDMcLbHbudw0mGOpRyjWF9MK9dWtHJtRRu3NrR2bU1Th6aYaIybsE0tSOWj/R+xK34Xr4e9zvCA4UYt/0p52jxe2vESkVmRfDnwSwIcA4xa/pKzS/jy6JcsvG0hTR0adq/hV5PEgJHpimD3F7BzTskDVP8Xwbu9UVcRExPDP//8g8FgYNSoUfj7+xu1fKUU58+fZ+PGjeh0OoYMGUJoaGjtVHvPTy+pRXDiL7i0B3w6QfDQkqSKV/ty1dALCwtZsGABlpaWTJo0qU6beur1elJTU8nNLRnlyd7eHldX14bVqaBSEL4edn1eUjMgeAi0n1TyNzBSXxCxsbFs376dyMhI2rRpQ4cOHWjatCkag67k+6MrKmlSY2Fb8nPFcaeUIj4+nuPHj3P06FE8PT3p3bs3wcHBVT4+azQxcPjwYR599FEOHTrEU089xSeffMKxY8f47rvv+Prrr6ta3C2hoV0gki5GsPXXH0mKvEBo73606jsIr6DmmJqVP8nkpqcRdfwIJzavJznqAu0HD6fH7XdjZWtXYdl6vZ5ff/0VOzs77rjjjobZpsgItFotu3fvZvfu3fj4+NCzZ0+aNWtW5RoEBoOBqKgoDh06xNmzZ2nVqhV9+vSp1Q7yDAYDBw8eZOPGjbRp04ahQ4dW+wG1LqWkpPDTTz/Rt29fwsJqfiih6jLmkIaSGBC3mqS8JJZFLGNlxErSCtMI8w6jq1dXOnp0JMQlBHOT2rt53hC9gbf3vE0fnz680v0V7C2MO5RzXG4cT2x+AhcrF2b3m42jpXFril328YGP2R67nQW3LaixddSFepEYyEsrqUJsWfE9VINxaS+sfKKkKvTwDyCgl1GLLygoYNOmTRw7dow+ffrQs2fPGn0DbTAYOHLkCFu2bMHZ2Zlhw4bV7tDaOYkQsbHkQfXCFkADfl3Brzv4dSfXqQUL/liOvb09d911V6Po/6nG6HUlCZmdn5X0+9DjkZKmHXY196ItMTGRw4cPc/z4cczNzQkMDMTPzw8XFxccHR0xMTFBKUV2djYZGRnExMQQGRlJfn4+rVq1omPHjtVKitVYYiAjI4PQ0FBmzJhBRkYG1tbWfPLJJwCEhYXxxRdf3FLD0VXWzVwgwsPDWbNmDZaWllhYWGBhYYGZmRnm5uaYmZmV/lz+3crKCicnJ5ydnXF1dTVKFfXEC+Ec27CGiIP70BUV4e4fgLW9A+aWVuRnZ5GTmkJWchKeQc1p0aM3bQYMxcru2hczpRRr1qzh0qVLTJ8+vdY74auP8vPz2bt3L4cPH8bU1JRWrVrRrFkz/Pz8Kny4vnxiiI+PJyIigvPnz6PX6+nQoQOdO3c2SvW5m5WRkcHKlStJS0tj1KhRhISE1FksNyszM5N58+bRsWNHBg4cWNfhVJrBYGDLli3s27ePMWPG0KZNm5sqRxID4lYRlRXFd8e/Y23UWsK8w7g9+HZ6+fTCyqxuk5bJ+cm8sesNLmZd5L3e79HVyzid/h5OOswzW59hiP8QXuz2Yo0mPPQGPc9ufZas4iy+H/I9Fqb161qenZqCuZUV1nZVS7zUi8TAjtmw5f2SB77gISXVyB0b0FCRei1s/g/s/wH6vQhhj4Op8R7YlVKcOnWKtWvX4uHhwciRI2v1vqeoqKj0pU5ISAiDBw+u/Z709TpIOlnyFvvSXtKjT7EgNwwf82zG+WVh6h4M9t7/+/Esae9ublXyltvEvGS0h3I/mvLTzKzqTed4tUJbCMcWwa65oAzQ6ynoMMWoI0XciE6nIyYmhosXLxIfH096ejo5OTkYDAY0Gg329vY4OTnh4+NDQEAA/v7+RnmWqrHEwNKlS/npp59Ys2YNs2fPJiEhoTQx8MILL+Dg4MBrr71WvegboJu5QOTl5ZGUlERxcTHFxcUUFRWh0+nK/Gi12tL/FxQUkJWVRXp6OhqNBi8vLwIDAwkKCsLPz69aiQJlMJAeH0ty1EUK83LRFhZi7eCAvYsbXkEh100GXGnnzp3s3buX6dOn37JDktwsvV5PeHg458+f58KFC2RlZWFra4uTk1NpFjw/P5/c3FwKCwtxd3cnICCAFi1a4O/vX2/aal1u+75x40b8/f0ZNmxYg+lYMjc3l59++omgoCBuu+22Blmb5dy5cyxbtowOHTowdOjQKlfbk8SAaOhyi3P57NBnLI9Yzuig0UxvOx0/+/Kd39YlpRS/n/2dOYfnMKnFJB7v+PhNP1wrpfjj3B/MPjSbZzs/y6SWk4wcbcXytflMWzeNYKdg/tPrP/XmfFmYl8viN16gRc8+hN1+d5WWrReJAShpz3xxS0kb88htJdXwez4Jzfpff5i+upZ5Cf6cVtLh2h3zwf3GLweK9EWcTD1JREYEcblxJc2oTS1pat+Url5d8bL9//6uMjIyWL16NQkJCQwfPpw2bdrU2XGXnZ3N5s2bOXnyJN26daNPnz61M4LBVS5cuMDSpUtp3yqEoW3cMEk9D2kRJe3gL4/mUJRb8jfR5pdUS68sE7P/HyrS0RfcQkra07uHgGswWNwiTcWLcuDgfNjzVcnwmL2fgTa3GzWhVd/VWGLgiy++4MyZM3z99dd8+umnxMfHlyYGnn/+eaytrXnnnXeqF30DVJs3xwaDgdTUVOLi4rhw4QIXLlzAzMyMtm3b0q5dO7y8bq5Tweo6fvw4//zzD9OmTcPb27tOYmgolFLk5+eTnp5OdnY2Op0OpRQ2NjbY2dnh5uZW72tb5OXlsWnTJo4fP05YWBh9+vSp1zEXFhby888/4+7uzvjx42ukU8jakpaWxh9//IGFhQWTJk2q0kgUkhgQDdmuuF28tect/O39eSPsjXrfBv5i5kVe2vESBmXg/T7vE+xctY54MwozeHP3m5xKO8UHfT4wWu2DykrOT+bu1XczJXQKD7R5oFbXXRG9Tsuy99/EzMKSsc+9hkkdJkaNVlZ2Qkmnffu+AdfmMPQ9aNq9WrHViPgjsPAuCB0Fw94veUN9HUeSj7D0/FI2X9qMtZk1Ic4h+NqXVM0v1BUSmRXJqbRTdPLsxOTgyZjHmLNz507atWvH4MGD6+QhvCIJCQmsX7+ehIQEunXrRrdu3bCr5Muy6tDr9ezcuZOdO3dy2223Va0vJKVK3oiX+7lqemEW5CaVJBkyYyD1HKScL/m3MBtcAsGjFXi2Ac///escUDLUZEOQlwb7voX934NbMPR+FkKGN65aEv9TY4mBjRs38swzz3Ds2DHmzp1LXFwcn3zyCTk5ObRr147Zs2czYcKEam9AQ1OXN8d6vZ7IyEiOHz/OmTNncHNzo0ePHrRu3brW3jKfOnWK5cuXM3HiRJo3b14r6xT1Q1xcHP/++y/Z2dkMGDCAdu3a1bvOZ4qLi8t02FPf4rsZxcXF7Nq1i969e1epraEkBkRDlF2czccHPmZD9AZmdZnFHcENp/8arV7L18e+ZuGZhdwTeg/3tb7vhu32tQYtS84u4Ztj39DNqxtvhr2Jk5VT7QR8ldNpp5m2dhr/7fNfBjUdVCcxQEnNxrXfzCH1UjQT3/4AC6uqPzjWy8TAZUU5sPdb2PlpydvMIe+U9E5eCy43YczJyUGj0WBqaoqTk9P/N3cM31BSU6D/SxD22HVrNZxMPcnnhz/neOpxxjcfz8hmI2nt2rrC72t6QToLty8k9mAsGjMNo0aOoneb2h/280aUUkRGRrJ7926ioqJo164dnTt3pkmTJjVyHoqPj2flypXo9XrGjx9PkyZNjL6O61KqpM+D5NMlP0mnSpo2pJwrGVrPI7QkUeDRGjz/92PrVrsxXk9GVMl36fAv0LRHSUIgoHf9ro1Tw2osMaCUok+fPqVVoAsLC+nduzfffPMNDg4OHDx4sN5Uea5N9eXmuKioiGPHjrFv3z6Kioro2rUrXbp0McrY9tdy4sQJVq5cyZ133tkg25yL6jMYDJw8eZItW7ZgamrKwIEDa69X3xvQarUsXrwYrVbLPffcU69rNdQGSQyIhmZbzDbe2fMOwc7BvBn2Jt52DbNG2vGU43xx5AtOpJ5gXPNxDGo6iI4eHTEzKblnUkoRnR3N6sjVrIxYibWZNc91fY7ePnX/oLQxeiOv7nyVn4f/TKircYd2jcmOYeOljZxMPUlaYRpWplY0c2pGP99+dPXqiommpFOuTfO+Ifr4ESa+9QF2LjfX5rxeJwYuy4iGNc+VPIxN+L7kgaYGFBQUcObMGU6fPk10dDRarbb0TbhWq6WoqAhbW1v87CEweT2Bg+/HPWzyNa/rBboCvjjyBUvPL2VK6BTua3XfdZNZly5dYsuWLSQmJtJvYD/2mexjwZkFPND2AR5q95DRRw4xlqSkJPbu3cupU6ewt7enXbt2hIaG4u7uXu17noSEBLZv3054eDi9evWiT58+9euZSq+FtAuQfOp/yYL/JQ2yLoGNa0kzhCubI7i3LOkHoTbuBS8PA7n3Kzj3L7QcWdKHQJO6H3WqSF+E3qAHKD1GTDWmmJuY19p9co2OSpCTk8Nrr73GkiVLSEpKwsnJibFjx/LJJ5/g5laPMka1qL7dHBsMBiIiIti7dy+XLl2iXbt29OjRw6g92Sul2LVrF9u2bZOaAgIo6VTl8OHDbN++HQcHBwYPHkyzZs3qLJ7i4mJ+//13dDodU6ZMadAjKRhLfUkMxOfG423rXS+SR6J+yirK4oP9H7AtZhvPd32ecc3H3RLHy+Gkw6y8sJItMVvI1+bjZeuFqcaUlIIU8nX59PXpy5jmY+jn2680aVAfzDsxj19P/8rPw38m0DGw2uUdSznGTyd+YmfcTno06UEnj0542HhQoCvgTPoZNl/ajJOlE890ega1JZyIA3uY+NYHOLjVj1FZavS+Tyk48CNseKOkPXTf5432cFVYWMjevXvZs2cPrq6utG7dmubNm+Pi4lKm9ll+fj6pG+Zw6cQuLnoM41JyNtbW1gQHBxMcHEyzZs2wtLQE4HzGeZ7Z8gyu1q683fPtax4fer2ec+fOceDAAeLi4ujevTs9e/YsbTZwNv0sz2x5hpYuLXmv93vYmNffNu5arZZz585x/PhxLl68iJWVFYGBgfj7++Ph4YGHh8cN7zn0ej2JiYlERkZy8uRJUlNT6dy5M7169aoXzxKVVpgNqeGQcvZ/zRH+95MRBZb2/58suLKmgZ2HcY7pzEtwfAkc/6OklkOnqdD9IXCqvWZmOoOOs+lnOZ12mujsaKKzo4nNiSWrOIvsomyKDcXXXNbMxAxzE3MsTC0wNzEv939zU3M0aNAb9OiVHp3SYW1qzcKRC6sUY40mBq6k1+tviWq51VXfEgNXupzdPHHiBP7+/vTo0YPmzZtX6warqKiIlStXEhMTw6RJk2q/mpOo14qLi9m3bx+7du3C29ubQYMG1e6wP5Qco4sWLUKj0XD33XeX3sA0dvUhMWBQBob9NQwTTBjkP4ixQWNp4dKi2rGIW8em6E38Z+9/aO3Wmjd6vIGnrWddh2R0eoOe6OxoEvMS0Ss9LtYuNHdqjqVp/TxXKaWYc3gOqy+u5pcRv+Bjd3M96SfnJzP74Gy2xmxlYouJTAmdUuHft1hfzF9n/mTv/J/xzbJn6tuf4ukTUK1taDCJgcsST8Dvk8G3M4z9utqdwZ0/f56VK1fi4uLCwIEDCQgIqHhGvRb+eaZk2Lx7loJHKDqdjujoaMLDwwkPDycjIwN/f38Mrgb+SPiDkR1G8miXR8u86b/cRCEuLo6IiAjOnTuHubk5nTp1okuXLtjYlN+ezMJMnt32LLnFuXw35Ducrep/R9aXe5qPjIwkJiaG5ORk8vLysLe3x87ODmtra6ytrTExMcFgMFBYWFg6LJ2ZmRl+fn60bt2ali1b3lovMLQFJR0lppwrSRoknS6pbZARVVLDwKPV//ow+F+ywCP0+sN4KlXSJ0LiCYjeVXJ8Jp2CoAHQbiK0uK3WOkxML0xny6UtbLq0iYNJBzEzMaO1a2sCHQPxd/DHz94PJ0snHCwcsLewL1MzDECndOgMOrR6LVqDlmJDcYX/1xq0KKUwMzHDVGOKqYkpFqYW9PDuUaV4a7QpgV6vv+bnJiYmDbpTr5tVnxMDl+Xm5nLw4EEOHDiAtbU1Xbp0oXXr1tjbV364n8vDyKxbtw43Nzduv/32WumERTRMBQUF7Nq1i3379hEQEED//v3x8an5YZny8vL4/fffSzvna+zNB65UHxIDUFK1bm/8XtZHr2d91HrauLXh/tb309e37y3xVvhWpjfoySrOwqAMmGnMcLR0NNrfLD43no8OfMSBxAO81O0lRjUbJcdDPaKU4v3977MlZgtfDvyySgk9rUHLojOL+ObYN/T17cuszrOum/DJz8rknzkfkpefzbZuGeSYF/H5wM9vOiEBDTAxAJCXCkvuKel1ftIicKj6ixidTsfatWs5ceIEw4cPp0OHDtf+XhXlwp/3l3RIN+XPa64vPT2dhTsWcub8GfzwoyivCEtLS+zs7DAxMUGn05Gbm4tOp8PNzY3mzZsTHBxMQEDADZ8TtHotL+14iYtZF/lx6I+4WtfdMM03Ky8vj9TUVPLz88nPz6egoACDwYCpqSmWlpY4Ojri7OyMi4tL43tuKsotSRQkn/7/ZEHSachPLRkhwdqlZPQAS/uSThL1RSXfg+z4kg4TXYPAtys0GwBBA8HOvVbCVkpxMOkgS84tYfOlzbRybcWgpoPo5dOL5k7N623zF6jBxMAnn3zC888/f83PZ82aVTpKQWPSEBIDl2m1Wk6ePMnRo0eJiYkhMDCQVq1aERgYiLOzc4UXi4KCAk6dOsWhQ4fIzs5m6NChtGvXTm7YRKXk5uaye/duDhw4QGBgIP3796+xWibJycksWrQIHx8fxo0bV6WO+RqD+pIYuFJmYSZ/hf/Fr6d/xdfOl8c7Pk4P7x5yfqknlFKcTT/Lmsg1HEw8SERmBIX6wtLPbcxsaOrQlPbu7eni1YUunl1ws65as8L0wnQWnF7AgjMLGBYwjKc7Pd0gHwYaA6UUP574kR9P/FjpDgkPJh7kvX3vYVAGXu3+Kt28u113/vADe9jw/Zf4tW7H8IefAgtTPtz/IVtitvD9kO8Jcgq6qdgbZGIAQFcE/zwLFzbB3YuhSYdKL5qXl8eSJUvQ6XTceeed1x9KOjcZFt4JVo4wcQFYVbxdSim+PvY1i88u5tvB39LarTV5eXnk5OSQm5tb8obTzAwbGxtcXV1vqp28zqDj1Z2vcjb9LPOGzavyOUXUjTxtHhmFGeTr8jHTmOFk5YSjhSOmlRnJIDe5pI+NgoySn6LskhEQTC3A1gPsPUtG7rCouX7TrmV/wn6+OvoVEZkRTAiewJ0hd9b7UXGuVGOJgZiYGC5cuFBmWl5eHqtWrWLz5s2sWbOmUbY1b0iJgStlZWVx8uRJzp07R1xcHFZWVri4uJRug06nIyUlhfT0dLy9vencuTNt27aVatnipuTm5rJr1y4OHDhAUFAQ/fv3N9rQlkopjh8/zpo1a+jRowf9+vVrfFn4SqiPiYHL8rX5LDq7iPkn5xPiHMJTnZ6ig0eHascobo5Sim2x2/j66NdEZUcxqOkg+vr2JcQ5BB87H0xNTNHqtcTlxhGVHcXhpMMcTDrIufRzBDoG0t27O929u9PJo1OF1YG1ei37E/ez8dJGVl9cTSePTjzS4RHau7evg62tWdriIrISE9AWF2Ft54CDhwcmDWXIr2vYEL2B13e9Tn+//jzW4TH87P3KfH757dovp35hf+J+Hm7/MPeG3ou56bWTtQkR59iz9Hfiz59h0AOP0LJXv9IEYZmH0SHf0tq1dZVjbrCJASipRr37c9j2UUmnhC1H3nCR9PR0fvvtN7y8vBg/fvz1a8+lhsOC20t6cR/zJZhde94vjnzB3+F/88PQH246SVMZeoOeV3a+QnhmOPOHzb/haB6idukNek6nnWZf4j72J+wnIjOClIIUTDWm2JjZoFM6CnQFWJtZ09q1NR09OjI8cDghzg2no/K43Dg+3P8hBxMPcl/r+5gSOgU7i4ZXU7rW+hi40rhx45g+fTqjR482VpENRkNNDFypuLiYpKQkMjIyyM7OLh2yxtXVFW9vb2kyIIwmJyeHXbt2cfDgQfz9/QkLCyMoKOim3xDn5uby77//EhkZydixY2nRQtqrX0t9TgxcllOcwy+nfuG307/RzasbT3R6olZuJFLyUwjPDOdS9iWis6NLOoPT5pOvy6dYX4yNmQ025jbYmdvhbedNU/umNHVoSnOn5thbVL5JVkNwIfMCb+95m+jsaGa0ncHtwbdXuiOwrKIsDiYeZG/CXvYl7iMyKxJXK1eaOjTF2swajUZDQm4CsTmxOFs5M7DpQMY2H3tTD3r1mVKKyKMHObL2H2JOHsPEzBwLKysKcnIwt7SkWedudBw+Cu/mDfd8lZiXyNzDc1kbtZZ2bu1o7dYaGzMbkvOTOZR0iMyiTO5qcReTW07G3aZ8dV+DXk9GQhyRRw8Rvm83KdGRdBg2ki6jxmPj6FThOn859QvfH/+eH4b+QCvXVlWKt0EnBi47swr+fvh/Qwc+fs0O3NLT0/nll19o0aIFw4cPv36iPHo3LJ4Cne+HQW9ct1O4X079wo8nfuSX4b/QzKnmOxfWGXQ8t+05EvMS+WHoD7fcubah0Rl07EvYx5rINWyJ2YIGDd29u9PNqxstXVoS4BBQpnlZoa6QmJwYTqSeYG/8XrbEbMHfwZ/7Wt/HiMARRu9gNT+7mKTILJKjc8jNKEQZwMreHDcfO/xCXbB1qtyLTYMy8Nvp3/jq6FeMCBzBU52ewsWqdoYPrQl1khh4++230Wg0vPHGG8YqssG4FRIDDYFSiqi0fBKzCskv1mFpZoq/qw1NnKwxNZFqxw3N1f1edO3aldatW1c6CVVQUFDau3JQUBAjR46UBNYNNITEwGVpBWn8eOJH/jz/J4P9BzOjzQyaOxuvRlpyfjIHEg9wIPEAh5IOcSnnEr52vjR1aIq/gz9eNl7YmJckA8xNzCnQFZCnzSO3OJf4vHguZV/iUvYlUgpSaObYjPYe7eno0ZE+Pn0abDV4vUHP/FPz+e7Yd9zd8m4ebv9wtXsGzynO4ULmBWJzYynWF6Mz6PCy9aKpfcl+vhWbjGSnJrPu289JiY6k0/DRtOjZByevkjHPDXo9yZEXOL1jCye3bsQjoBkD7nsQz2b1t7alrriYzMR40uJiyUpOJC8zg7yMdPIyM8jPyqSoqICCwjz0Wi1oQGNmirm5JTZWdpibW2Bqbo6puQVm5mZoTEzRFhZSmJdLVlICGo0JPqGtCe7Wk+DuPbFxuPFb4Z9P/oyjpSPjg8dXaTtuicQAQNxh+H0StBgBIz4u93b/clKgZcuWDB8+/PrfscO/wr8vwrD/Qpdp113tqgur+O++//Lj0B9p7VZ7ibxifTFPbXmKPG0e3w7+tl6PVnArUkpxLOUYqy+uZn30esw0ZgwLHMbwgOG0dm1duWYC/5OnzWNN5BrmnZiHmYkZz3Z+loFNB1YrvuJCHef3JxF+IImEiEycPG3wDHDA3tUKE1MN+dlaUi5lkxyVg18rF7qMDMAr8NrnmYTcBF7d9SoJuQm81/s9Onl2qlZ89UGtJwbS09MZOnQo06dP55FHHjFGkQ2KJAZqTqFWz8YzSaw4Gs+BqHTyi/V4OVhhY2FKgVZPbEYBNuamDAz1YEQbb4a08pQkQQOj0+k4ceJEab8X/v7+BAYG0rRpU1xdXbGzsyu5oTYYSEtLIyEhgbNnz3Lu3Dl8fX0ZNGgQTZs2nLZedakhJQYui8+N5/vj3/PPxX/o4tmFO0PupLdv7yr33p6Ul8TBpIMcSDzAwaSDxOTEEOoSSlevrnT16kpHj4439TYqtSCV4ynHOZZyjAOJBziddprWrq3p79efkc1G0sSuYYzakl2czYvbXyQmJ4b/9v4v7dzb1XVIDVLMqeOs/PR9gruF0e/e6VjaXLs9bFF+HgdWLuPQ6uW0GTCY3pPuw7KCntprU0FuDkkR50m4cJ7EC+Gkx8aQlZyEmaUlLk18cfT0ws7JGVtnF+ycXbBxcMTMygpzC0tMzcxKOqnWatHptOi1WvSX/9Vq0Wm1GPR6LKyssLSxxcm7CY4enrXWrOKWSQwAZMXC73eDiRncMQ9cSt7eVzopUJwH61+DU3/DXb9BYJ/rru5o8lFmbpjJnAFz6Nmkp7G35oYKdYU8tukxNBoNXw36qt6O3nGrUEpxOu00a6PWsi5qHXnaPIb4D2Fks5F08uhUpWRARbQGLSsiVjD38Fw6eHTg1e6v4mXrVaUycjMKOb45llM743HysKZFDy+COnlg61jxsZGbUcSJbbEc3xJLq57e9BgXhLll2e3Yl7CP57Y9x8CmA3mx64u3TBKqxhID8+bN4/333y8zTa/XEx8fT3BwMHv27KlSL/e3ijq/QNyC0nKLmL8ril/3ROFmZ8n4jj70CXGnlbcDFmb/XyVOqzdwOj6bdacSWXE0HnNTDQ/3C+KOzr6YmUob84YmMzOT8+fPExkZSWxsLDk5OaVVIA0GA2ZmZnh6ehIYGEj79u1xd6+d3mhvFQ0xMXBZakEqf577k5UXVpJZlEkvn1509OhIa9fWeNl6lVbz0xq0pOSnkJCXwLn0c5yKOUJk/DmyctLwtw8g1KctHZt1p2tAzxqplppakMqO2B1svLSR3fG76eLZhfHNxzPYfzAWpvVvhAyt3sDeS2d558DzuFh68Uy7t2nu7o6bndx4V9XFwwdYNecDBk57iLYDhlZ6ufT4ODbN+4qMxASGPvQkAe061mCUZel1OuLPnSbq2GGijh0hOfoiTh5eeDUPwSsoGDe/AFx8fLFzcW3wtTtuqcQAgLYQNr4FRxbAoDdIDxrHL78tvHFS4NJeWP5oSQ/w478FZ//rriY+N567V5fUILq75d3G345KytfmM3PDTBwtHZnTf851+6sQVaeU4nzG+dJkQHphOgP8BjA8YDg9m/Sskf2dUZjBJwc/YWvMVt7p+Q6D/G/cmWlKTA5HN17iwqEU/Nu40mGwH15BlR8dJzMpn82/nSE/q5jbHm2Hi7ctSil+Pf0rXx39ipe7vVzl2kj1XY0lBo4dO8aePXvKTDMzM6Np06YMGDCg0fYAXi8uELeI3CId3269wLydkXRv5sIj/YLoFuhSqS+8Vm9g5dF4vtoSgbmpCW+NaU1YUMOs0itKaLVacnJyADA1NcXOzg5T04bdaZexpOYW4WprUaWb9YacGLhMKcWptFPsitvFkZQjnE8/T1phGgZlAAWuWRb4pdnSNNMexyxTTAsNmFpbYWVji6mJKQU5OWgLC7B3c8c7KIRmnbvRrHM3rO2MnyRIyU9h1cVV/B3+N3naPKa2msqdLe7E1rxmelXWFRdTmJeLtqgQg16P0usxGAwogwFTc3PMLS0xs7AkX2/Cv+fS2XQ2hQNJuzHxXIRlQU+ci8aSnqcjPa+YYA87BoZ6MLGLH83cpYnOjcSdPc1f/32DYY88TYuw3lVeXinF8Y3/sm3BfEJ79aPfvQ9gYV1zb6sykxI5sXkdp7ZuRClFQPtOBLTvRNM27bF1qv9jx2v1BsyrmPy/5RIDl0VsJP2fd/gluwctm/kxfOJMNOZXJfaUgrhDJZ0XRu2Efi9AzydKen2/jmJ9MfesuYc2bm14vcfrdZ4cyinOYfq66fja+/JR34+M3kb9akop0gvTSchLoFBXiE7psDWzxdHSEU9bz1ui5kJERkRpMiApP4n+vv0ZFjiM3j5Vr5l3s9ZGreWd3e9wW7PbeK7Lc1iZWZX53GBQRJ9I5djmWJIuZtEyzJv2g/xw8ry5c6QyKPatusjJbXEMnBHCtymfcjj5MHMGzKGNWxtjbFK9Uid9DDRmtXGBKNTqKdIZsLM0uyWryusNij8OxjB7/Xmaudny6shQ2vs53VRZxToDP++OZO7GcIa29uK1kaG4ytsv0YAZDIoLKbkcvpTBgagMDkalE52ez+6XBuLtaF3pcm6FxMDVlFIkRl3g+I4NRO3bR3F+Pv5tOuDXph1eQcG4+viVe8AqzMslOfIC8efOEHFwLynRkQR16U7HYaPwbdXW6De/BmVga8xW5p2YR2R2JPeG3st9re+7qWqKxYUFJF0IJ/FCOBkJcWQmJZKVnEh+ZiY6bTEApmZmmJiaYWJqisbUFA2g12kpLiwseUAADBpTdHYWZFhkERzYjq7tB+LVrDkegUHkag3sDE9l7clE1p5KZFhrL54ZHCwJgmtIjYlmyZsv0vvuqbQfclu1yspKTmL9d3PJSExg2ENP4d+ug3GCpOQYiDiwl+Ob1hF7+iRBnbvRbtAwmrbr0CBGSUjOLmTF0XiWHYljUEsPnhtWtY4b60NiIDMzk8LCQry8qlZt+npKmg/8TEtnPcMzF6ApzAD/XiXNC0zNITsBYvaWjAXfZRr0fKrSY7+/v+99jqYc5bcRv9WbGk+ZhZlMWzeNli4tea/3e0YfPz4uN46N0RvZE7+H4ynHydHm4GLlgrWZNaYaU/K0eWQVZ6E36PGy9cLfwR9/B//SDmmbOjTF1863zP5SxcUUX7qEPjMTjbk55r6+mLnW3YurqKyo0mRATE4MfX37MixgGH19+2JtVvl7CmOKy43jhe0vUKAr4NN+nxLgGEBeVhHn9ydxclssep2iTT8fWvdpgrWdcY7FnRtOcnh5HBe77uD1ic/UWf9AhuJiVGEhJvb2Ze4/9HoDOamFFOZrMbcwxcHNulzzh8owamIgOzub9PT0Sq3Y0dHx+mOk3qKMebFRShGenMv28ykci83iTEI2sRn5FGoNpfM4WJnR0suB1j4O9Atxp2eQW5nq9Q3NjvAU3lt9hgKtnpdHtGRYay+j3JgnZhXyxoqTHIhK57WRrZjQyafOs91C3IhSipScIo7HZnE0JpMjMRkcj8lCazDQzseJLgHOdA1woZO/M47WVauldSslBjIS4zm3aztnd28nKyWJoM7dadmrHwHtO2FWxdprmUmJHN/4Lyc2r8fRw5OwOybTrFNXo58vLg/h9vnhz4nNjeWxDo8xrvm4G771ykpO5PzeXVw8fIC4c6exdXbBOygEF5+SNt9OHl7YOrtgZWuHpa0tpmZltz8us4AvNoWz7HAsY9p5MrmLG3+dmkv4pRNM95+CTQ4kR10kMeI8CkXTNu0J6d6LoM7dScw38PXWCyw/EsfjA5szs2+zKr+pvZUVF+Sz4OVnaBHWm14T7zVKmcpg4NjGtWxfOJ9WffrTd8q0atUeSI+P5cTm9ZzauhFLG1vaDhpG636DarRmQGZ+MUcuZXIhJZe0vGLyi3RYmptibW6Km70l7naWeDhY4mFviZudJVbm5W9284p0nE/KYe/FdHZGpLDvYjrdm7kwvqMvw9t4YWdZtbfF9SExcODAATZv3sy9995LkybV738kNTWVX3/9ldDQ0P9j7zzD46jONnxv77vqvRdblpvce8emm14ChCSEkhAS+OgJoYaEhJiEFkoggUCoBlNsbHDvNu5dsnqvq11trzPz/VhwKC6SLMmy0X1de8nW7sycWc3MOec57/u8kfQBSYLG3VC7GTpqQQhFUgZSR0P2dFB1ftK3smYlD216iPcufO975SjDdjuBw6UEq6sQvT6kUAhlbAyqlBQ0Q4ag7OW5gNVn5Wef/4wR8SN4ZNIjJx3m/vWz+a3it1hfv54JyROYnDKZMYljyDJnfU/ElSSJNl8bNc4aapw11DprqXZWU+eqo85VR1AIkqJLYla1njHbHSSVtCGTyyHKjDwsgq0DVUY6hvHjsVx8MbrRo3t9fFrtqGZl7Uq+qP6Cyo5KpqRO4Zysc5iZPrPf5NKHxBDPbXyRXdtLmR28mECdgqRcC8NmpJIzKh5FD/Y9Gxs2ct/6+7hE8RNMGwdx7i+Gk1HYN8JAoKwMx2ef4f1yG/6DB5GCEVFfptOhSkvFMWQW9YbhNLWrkETQGJSEAgLhoEhSjplL7hyNrAuLxD0qDCxYsIB77rmnUwe+6667WLBgQacbeqbQE51NcZOTj3c3sHhvIzZvkIk5sYzJiGZIspmsOD1RejUapRx3IEy7O0hxk5O99R2sLm7F5Q9zwchkrpuYydCU06fOa3GTk798XsKuGju/mZPPjydlolH2/KrF5weaeOiTgwxOMvHHi4eTEds/HoAD/LCRJIlmp5+yFjdlrW7KW11H/u3whciNN1CUHk1RRhSj0qMYnGQ66QnZ6S4MOFpbOLxlA4e3bKC9roasojEUTJ5O7pgJqLTaE+/gBIQCfvat/Jxtn3yAOS6eyVdcS1bRmF4RCFbWruTpnU+jVqi5f/z9TEie8K3PCOEwpVs2sG/VFzSWlpA5oojcMePJLhqLOT6hU8dpdfr5x5py3t1ex9lDk7j9rHyMeg93rLkDuVzO0zOf/lYZOVEUaK2soGrPTko2r8dpbaVw6ixGnzefGtHE/R/uQ6NU8MK1o0mPGXiOSpLE0ucW4HXYueyBP/T4qrujtZkvXnoWR2szc274Jdmjxnb6WgwF/JRv28K+VV/QVFZC3vjJjJhzNumFwyMTlF7A4Q3x6d4GFu6sZ3+Dg+xYA4OTTMQY1Bg1SgJhEU8gjNUdoNUVoM0VwOoOIEpg0amIN2kwqBX4QyIdviAtzgBRehXjsmKYkhvL2cOSuhQh9V36gzAAsGnTJjZs2MCPf/xjUlNTu92G5uZm3nzzTUaNGsWcOXN69DlV76rnyiVX8sikR5iXFfHLCFRV4fxsKa5VqwgUF6NKSUGdk4PcaESmVBJutxKqbyDU0IC2oADj7NlEXXIxqpM4x+PR4mnh16t/jU6p46mZTxGni+vUdqIoYG9qxOdwIKkVbA8d5J3y92h0N3L5oMu5evDVJBuTu90uURJpWPs5jr8/h2izUTNnCMVDzZSaPTT7WmhyN6H0BhjdamBClZKRu52Eogy4rjyLlMt+RF7cIFTyk0/NliSJw/bDrKxZyaraVdQ6a5mUMol5WfOYlT6rSx47AW+IumI7DYfttNW5cLX78bqCIEWqW2qNKvRmNXqzGkO0FlO0BmOMFlO0FmOMBoNFg1ItR/6NMYwQFvF0BHDZ/NibPLTVuWmqcNDR7EGTLLFJu4yCcSn83/Rf96i/gSAKvLzvZV4/+DoPTXqIC3IuoHRbM2veOswFvxpB6qDeE7V8+/djff4feLZuxXTWWRgmT0Y3qgiFxYJMrablQD0bFjfhcoRIs+8ktnojyZOHEX3ZJejGj8fjCNFe7yZrROeu9a/pUWGgo6MDq9XaqQNHR0cT28uhMcFgEKfTSWxs541wOrNNd/b7Nd3tIBo6fHyyp4FPdjdSa/MytzCRi0elMCUvrtMTZEmS2Fvv4L3ttXy8u5ERaRZ+PTufKXn91yiozubl7ytK+Wx/E9dNzOS2WXlEG3o3RM3pD/GXZSUs2tXA7Wflc+PU7AFzwgH6jHZ3gMMtLkqbXRxucXG4OSICeIJhMmMN5CUYyU8wkp9oJC/eRG6CAb2653MnTzdhIBwM0nD4ELUH9lKzbw9tNZVkDC9i8KRp5I2biNbQO6HtIb+fPSuWsv2TD4hOSWPa1deTVtjzeYchIcTbJW/z0t6XmJQyibvH3k2sPIr9qz5n57JPUapUFM27gCFTZxyzrvvRsHmCvLyugje21DAtP4475w2iIMnM9ubt3LPuHqamTuWhSQ8dNzRYkiRaqyrY/cUSSjatI71wOEXnX8J/qlV8vLuBv11ZxFmFiT3wLfRfbJ4gh5td1No8eIMCYUEi1qgmyaJlaLKFmi2r2fTem1z/5HO9tvouiSJ7Vyxj8wdvY7BEUXT2BWSPGos57vuh4H63m7ri/VRs30rpl5sxxcQyfM7ZFE6f3akygN3FHQjz6oZKXt1QRV6CkavGpTOvMLFTKXyCKNHuiYgEra4AvqCATq3ArFWSFWsgpos+KsejvwgDAFu2bGHt2rVcdtllDBo0qMvbl5WV8eGHHzJ58mSmT5/e5e2PR0gM8ZNlP6EwtpAHJjyAe+1a7G++iXfHTowzZmCaNxfD1KnHjAoIt7Xh2boV59JluDduxDBpInG33IJ+zJgebSeAL+zj4c0Ps6N5B/eOv5ezM88+5vVia2xgx+IPKf1yE+FQCEGnIOj1ogzL0A9O4+zLbyRv+NiTao/o99Py5z/jXPIZsbfcTMyPf4z8O6K1JEnYA3aaPc00eZposdfDig1kfbyDkBDi48kKWqYPoSBhKIWxhQyJHcKgqEGdmhy3edvY0bKDHc072NS4CZvfxvS06ZyVcRbT0qZ12d/GWu9m35o6yra1YI7XkVYQTVK2BVOsFr1ZjUwuQxIlfO4QPmcQjyMQmezbA7htflw2P25bACEciXqWK2QoVHKEoIgoSsjkMoxRGqKS9MSnG0nINJM6OBqtQUWds447192JWqHmqRlPdblqwVHPx2fl/g330+JpYcGMBQyO+V860qFNjWz6oJyL7xxFfHrPeg6JHg+tzzxDx/sLifnxdcRcfz3K+G+K8hLbl1SxZ0UtI89KZ8y5WajUCvyHS3F89BGOTz9FrtMRdcUVRF126be27QxnpMeAKIrcc889vPjii8jlciwWC88//zyXXHJs58jObNOd/X6X7nQQKw618Mv/7mRKXhwXj0phXmEShi6GxX0Xhy/EG5ur+demKrLjDPxmdj4zB8f3G4GgtMXFP9dX8uneRi4Ynsz/zR3U56tO26ttR1a9/nzZcEakRfXp8fsKQZQobnJyqNFJeZsbbzBMKCwRb9KQHqNjVEY0+QnGfnNtnEl4g2H21TvYXdvB7lo7e+o6aHUFSIvWMTjRxKAkEwVJJvITTOTEG44aQttb9BdhwNNhRxQFJFECSSLg8+JzOvA6OnBa27DW1WCtrcbWUIfObCFj2Egyho0ke9TYXp3gfJegz8vOpZ+wY/FHJOcPZurV15OUm9/jx7H6rDyz7kma12+noN5CUkYu4+dfRu7YCV1ahW53B/j3pipe31TNuOwY7pw7iBFpUUiSxGsHX+OlvS9x99i7uWLQFV269z0ddvauWMauZZ+QkJWLNOZcHvvSw83Tc/n17DzkZ4jvjSRJbK+28/mBZtaWtlLZ5iE1SkdWnB6DWolSIcPqDtLY4cPV1so1je+jOftnXHXxWSe1kt0ZQsEAxRvWcGDNCporyrDEJ2KMjUVrMBLwenHbrHQ0NxOdnEJW0RgKp80iITu3V5/xkiSxeF8Tjy0+SFasgfvOLWBcVkyvHe9k6U/CAMCBAwf45JNPmDFtGmPT0hA7HAhOB0gSMqUKRVQUqpRkFDH/M2AWRZHNmzezbt06LrzwQkaM6Pmyoi/tfYkvqj7nX4Zf4HjxFUKtrcRcdx1RV1ze5bz4UGsr9rffxv7mf9EOHUrcrbdimDjhxBt2AUmSWFK5hKd2PEVuVC4/H/ZzJiRPOFJSz+9xs/XDd9izfClRowZTnNLBquB2xqWO57qC6xgiz6J4w2p2LfuU7KKxzLnx1m6Z0QZra6m/7dfIdTpSnnoKdVrXIiWkcJiOJUtoeeF5ggEfJRcUsqIwzEHHYXyCjxxLDinGFBL1iRhUBjQKDb6wD1fQRYO7gWpnNa3eVgZHD2Zs0lgmJE1gYsrEbhkIejoCbP24gvKdrQyakMSwGandnixLkkTQFyYcFAkFBYSwiFIlR6VRojWqjtt/+MN+/rztz6yqXcWDEx9kbubcbj/TNjds5vebfs/YxLE8PPnho4okOz+vZu/qei67ZwyW+J55pvtLSqj/9W9QJSWR9NijaLKzv/V+KCCw/F8HcbR6mfvzoUf9nqVQCNeaNXS89z7+khLy165B1oWUyV4XBhobGzl48CA2m41v7qKgoICioqLu7PKE/PWvf+WJJ55g9erVjBgxgueff567776bvXv3MmTIkG5v0539fpfudBCeQBhvUCDe1POmeO5AmP9ureHVDZUkW3T8alYe8woTT8ngLSSIrC9t4+0va9lQbuXSUancOC2HvIRTZ2IVCAu8uLaCF9dWcNaQRG6bnceQ5NO/moQkSeyosbNoVz3LD7YQDIsUppgZlGjCqFWilMtodQaosXnYU9dBjF7N+SOSuX5S1kBYcDeRJIkqqyciAtTZ2V3bQUmzizijmtEZ0YzKiKIoPZohySZM2lNftaW/CAMv3HQtPqfjyP/VOh16cxQ6iwVTTBxx6ZnEpWcSn5mNJbFnPEdOBp/LyfZPP2T3F0vIGjGaKVddR1z68Ut8dZb2+jq2L/6Qkk3riC3MZ11SNXVmB/eMu4c5GZ0LD252+HllQyVvf1nL+OwYfj07j7FfTdDafe08uuVRDtsO87eZf2No3NBut9XvcbNzyUfsXPopUTkFvCcOJT0vn6euHHnSwvapxOYJsmhXPW9vq8XmCXLusCRmDk5gUm4s5qPct5Ik8c5jD+BWmdmaMocNZW3MGpzAHWcNojCl9/uSgNdDU2kJHkcHAY8btU6PMSaWuIwsjNF9MzFvcwX47aL97Kmz88j8oZw/PPmU36cnoj8IA4Lbjf/AAXz79uPfv5+GujrW5eeh9/mZUFlJrFIJMhlSKITQ0YFgsyE3mdAOG4p72DA2KpX4JIkrr7yyRzwKvktx20GeeeY6frM3CWWHm7gbbyTqyiuR605ukiQ4HNje/C+2N95AW1hIwh23o+vh+YIr6OL1g6/zQekHCJJAYUwhiU49ps9rcBsE1g9qRJsUxwU5FzA/dz4Z5oxvbe/psLP85Wdpr6/l4nsf6tIz3n/oELU33Yz5vPNIvPeeLk3avoskCDiXLsP64ouIfh8xP/sZnjnjKA83RiIMPC14w14CQgCdUodRZSTZmEy2OZtBMYMwq0/u2i7f2crqN4vJHBrLpEtyMcedGjPCb7KsahlPfPkEoxNHc//4+7sUPdDuaz9SEvGusXdxWf5lx3xWSZLExoVlVO9v57J7xqA3n1w0s+OTT2h69DHibr6J2Jtv/l4al9cZ5LN/7EWpVnDuL4ajNZz4uhGcThRdfH71qjDwhz/8gcceewyFQoFMJiMYDCKKIlqtlnvvvZdHH320q7vsFFlZWVx55ZU8+eSTR36Xl5fHhRdeyN///vdub9Od/X6X/uDMfTR8QYG3t9Xyz/UV6FQKfjYlm8vHpPX6AC4QFthV08GyA00s2deEVinn0tFpXD8pkwTzyecB9xSNHT5eXlfBu9vrGJkexZVj0zl7aGK/mMB1BVGUWLyvkX+ur6TO5uWSUamcOzyZcVkxx6xg4Q8JbK1sZ+GOelYcauGswgTunjd4wHX8OIiiRKPDR1mLmz11HUdevpDA8FQLRelRR8SAZIu2Xw6S+4swIIoCMmQgk/XL7+lYuO02vvzoPQ6sXkFW0WhGnXMh6UNHdPkcJFGk9sA+dn+xhOq9OxkydRbj5l9KTEoaoiTycfnHPLPrGQZFD+LusXd/K9zxa0RRYnNFO//dWsOqkhZmDU7gttl5R6KgJEliceVintz+JOOTxvPwpIexaHom2sLrdLDt44XsWbEUqyWHkuRJ/O0X5552/i2tTj8vravk7W01jEiL4toJGZw9NOmEUTz71yxn8/tv8dOnXkCjN9DY4TsizHxdCSexH/V1Pc2mciu3v7uHCTkxPH7RsF5PBewp+oMw0PbCC3R88AG64SPQjRiOtrAQ0tLYdOgQ27Zvp6CggOHDh5OamopWq8XT0UH1rl3s37+fKqeTgooKhtbWETVtKuZ58zBMmoRMffLfvyQI2JYuYd9TDxMdUJLxy9uJuvKK74XBH/m8JOG2B7A3ebA3e+lo8eJzBfF7wwS8ISRRQq6Qo9Yq0Fs0mGI0xKQYiY4Caem72N98E8OkScT/5jdoB3c9leJ4CKLAgdYDbFu4DOeWraiSR6OPnoRJbSIqJhKunj0i7qil7iRRZPPCt9izYhlXPvQn4jOyTng8z9Yvqb/tNuJ+cQsxP/95j/VpkiDg+uILbP95A39pKeZ58zCeNQfj5MnIDT1f8lYQRLZ8WEHxlibm/GQIOUVdC1fvbWx+Gwu2L2B5zXIuzruYnwz9yfdMMb9Ji6eFNw69wcLShUxJmcL94+8n0XDi9DdJlFjx2iHszR4uuXM0al3X50ySJGF97jls/32L1Keewjjt+yVs7c0eFj+3l6QcC3OuH4JC1Xvpzb0mDOzbt48ZM2awbt06li9fTnNzM3/60594/fXXeeihh9i/fz/xXcx76Aytra0kJiby8ccfc9FFFx35/U9/+lPKysrYtGlTt7bpzn6PRn8VBr4mGBZZur+Jf22soqbdw4UjU5g/MoVxWTE9EkXg8IU42Ohgf72DzRXtbKuyYdQqmT04gUtGpzK+h47TW7S7A3y8p5GFO+oob3VHjI7yYilKj2ZEuuWoK0b9AUmSWHO4lSc/P4zLH+YXM3O5bHRql3PTGzt8/GNNOR/srOfqcencdfbgfnvOfYEgStTZvJS3RowAy1pdlLe6KW91EwiLZMXqGZEWRVF6FKMyoihIMp82VUH6izBwuuO0trJ3+VL2rV6ORq9n0MSp5I6ZQGJO3jErIgjhMI2lxVTt3sHhLRsIB4MMnTGHUedeiCnm+0ZCzqCTF/e8yMLShUxKmcRPh/6U0QmjKW1x89m+Rj7d24jLH+aKselcMz7jyKRckiTW1q3lxb0v0u5r53cTf8ecjDm98j24be1s/Xghe1Z+To0hm4t+9lPOmjyyV47VkzQ5fLy8rpJ3t9cyPT+e38zJZ1hq50QTr9PBv++4mXN/dRe5Y8Z/b79PLC1hTUkr95wzmGsnZJ5R5YXDgsizq8p4dWMVD11QyFXj0k8rYa8/CAOSICBTHF14am9vZ8eOHRw+fPhb1cDi4uIoKChgzJgxRJlMeHftwr1qNc4VyxFdbkyzZ2M6+2wMUyYj13QtClVwOnEsXoz9zf/icFtZOd3M7Q9+gkb37UUCSZKwNXqoK7bRXOGgscKB3x3CEq8jKlFPdKIevUWNRq9Eo1chV8gQwxIBXxivM4Cz3Y+twY21wYNSKSclS4+5cQ/6VW+RMGMs8b++DXVGxjFa2TkkUaKp0kHptmYOrv2YgGs7WaN/QsawEZhitEfEjOYKB/UldlIGRTFhfg6JWd//+2398F12fb6Yqx5+gti0Y7fL+cVyGu+/n6Tf/56oyy49qfYfD39xMY7FS3CvWUOwrg5NTg7aIQUok5NRxsUj1+mQqZTwVYlaOM59KZchUyojn1MokSkVeP0y1q7xEwpJzJqpxmSQQBCQBAFEESksgCggN5pQZ2ehSk4+5nXc25Tby3lx74usrl1NfnQ+09KmkWvJxag24g15qXJUsbFhIwfbDzI9bTq3jLily5FyQlhk6Qv7EASJC28b2aVJuxQM0vTQw3i2fUnGP/+JJi/ve59pLLOz9MX9DJuRyoT5Ob3+HO01YeDf//4369ev5/XXX+dvf/sbNTU1PPPMMwDccMMNjBkzhl/96lcn1/qjcPDgQYYNG8bGjRuZMmXKkd/ffffdfPrpp5SWlnZrm+7sFyAQCBAIBI783+l0kp6e3u8Hx5IksbPGzke7G1i6vwkJmJAdw9jMGPISjWTHGog1RtyDv75IJUnCExSwe4LYPEGaHH7qbF5qbB5qbT6qrG7qbD5So3QUppiZkB3D1Pw4BieaTqsBw9fU2bysLmllW5WNPXUdNDp85MYbGZFqYUSaheFpUQxNMfdpXvjR2Flj4y/LDlPe5uZXs/K4bmLGSVd0KG918+jig5S2uPjDRcOYN7Tn6iz3V6zuAMVNTkqaXBQ3R36Wt7lBgpx4A7lfmwImmMhPNJIVazhtRICjcbID49P12XcsHN4QrS4/7Z4gYeF/3aFOLSfeqCXepEGnPvZ9FQ4Gqd67i8NbNlCzbzdBn5fY9EyMMbHoTGZEQSDk99PR3IitsQGdyUTWyDHkjZtI9qixKJQnFvEaXC387ctXWNu4BCGsJegcwYjYkcwvHMf5Q3MwqLW0eduoclaxpXELy6uXExAC/Hz4z7l80OV9UpPa1W7lrZf/hWPfZnRZQ7jw6ivIGjGq19zvu0tDh48X15azcEc9c4YkcNus/C6H/n/x0rP4XE4uvuf3x/zM+tI2fv/xAaINahZcPoL8xJ41sjoVNDv8/Obd3dg8Qf5xzWgGJ51+53Qyz7+eevb5PSEUKjmq4zxXIGKIHQgE0Gq1qI4hNkqShH//fpyff4Hriy8QOjowzp6NceYMdCOLUKWmfG8cJkkS4dZWPFu24F63DveatWgHD8Z1wRRult7gzQvfIS86MpERwiKNZR1U7bNSvdeKzx0kdVA0yXkWknOjSMg0oTzBeXwXQRBpq3FRX2Kn/rCNprIO9HiIqdtGxrBYBv/qKrRpna8IIEkS1jo3pdtbKN/RQjAQRqPejNt6iMsf/AMJmVlH3c7nCrJ3VR17V9cxfEYaEy7KQfGdvn3T+29xYPUXXPvE00dN0bG/+x4tTz5J6oIFmGbP6tL3cDKEGhrwHTpE4HAp4ZYWwlYrot8HoTCSICCJwrE3lohM9AXhyMS/XZnC3vgLifOUUWhdgUIuIpMrkCkVIFeAQo7sq5+iw0mwvh65TnfEiNI0Z84pEQkcAQfr6textXErNa4avCEveqWeNFMaE5MnMi1tWqcrVRyNoD/MJ0/vwRSjYd6Nwzq1wCm43TT85nbCdjvpL72EKvH7FYRKtzez5s0Spl05iMKpPZ8OdDR6TRhYsGABzc3NLFiwgDfeeIPFixezcOFCAB555BHC4TCPP/74ybX+KBQXF1NYWMjatWuZMWPGkd/ffvvtLF++nOLi4m5t0539QuRcj5YycToNjsOCyP6GyAr/3roOytvc1LZ7CYsSCrkMGSBKEhIgSaCQy4jWq0kwaciM1ZMRoycjVk9mjIHCFDMxp0koYVdpcwXYW9fBvgYH++s72FfvoMMXYlCiiQnZMcwYFM/EnNjjTh56ktIWF09+fpgtFVZ+Pi2Hm6Zl92jqgyRJfLirgT8sOcTUvDgemT+0V3wwThVOf4itFe1sKreyqaKdijY3GTF6CpJMFCSZKUgyMTjJREaMvt9XrQj6w6i1fVvH+3R+9tk8QbZUtLOjxkZpi4vDzW6s7gB6tYIYg/pbgo83IGB1BwiLEmatkrwE41eVI0wUJEeule/eF5Ik0dHSRFt1JZ4OO16nE6VKhVKtwZKYRFxaBpaExBNOlkVRorTVxfYqGxvKrGyuaEerUjAtP4qk5Gps0i4O2w9R6agk8oQGuUxOqjGVUQmjmJc5j0kpk45bcaC32LS3nFdfeZshzkOY9RoGTZxM7ugJJA8ajFp76vJUa9u9vLC2nEW7G5hXmMivZ+d3a2LbVHaY9//wO3664B9YEo4vnPpDAn9fWcobm2u446x8bpyWc9pGD3xxsJn7PtzH3CGJPHrR0F6pmNIXnMzzr6eefTuWVbN3VR0jZqUxfGZap3KKO4MkSfgPHsL1xed4Nm3GX1qK3GBAlZCAIjYWBAHR5yNYW4vocqEtLMQ4cyameXORcjO4cvGVXJp/KT8t/ClNFQ4Of9lMxa5WlCo5WSPiyBoRR9rg6C4LASci6AtTX2KnYnMVNfuthMOQoOkge3IOyZOHEJdq/NYxJUnC1e6nrc5Fw+EOqvdZ8XtCZBfFkTsqloNr/0NbdQWX/e4PWBJOHDZub/bwxasHUShknHPLcEwx/0udkCSJz1/4O/amBq586AmUX6VsSJKE9YUXsP3nDdJffKFXqi30BZIosWt5DTuWVjPtqkEUTuncJFUKhfAfOoRr1WocSxYj1+mJv+1XmM4557RcEDwePneQRX/dRergaGZcPQjZcZ7hoeZm6m75Bcr4eFKffhqF8dvpHpIksXt5LTuWVXP2TcPIHNq7Vfy+SZ8IA4cPH2b8+PG88847REdHc+211/LII49w/fXXn/QJfJevT+jdd9/lqquuOvL7q6++GqvVysqVK7u1TXf2C2feqtnXSJKEKxDG4Q0d+Z1MBiatCrNWecbd8N1BkiQaHX721nWwqdzKutI2Wl0BJubEMrcwkblDEkmy9HxuaXmrm+dWl/H5gWZ+ND6D22bnEdeJUlDdpc0V4JFPD7K5wsoj84cyf+T3Vx5OB/whgV01djZVWNlY3s6BBgdZsXqm5MUxOTeOSTmxWPSnX9pE6fZm1r9bylUPjP/WQOZE/NAiBmraPXy4q4FVxS0UNzmPCHoFyRFTzvxE4zHTZkRRwuEL0dDho6ItkkpS2uKipNlFTbuXOKOaIcnmI6LSkGQzuQmGLkfutLkCHGpycrDRwY5qOzuqbYRFidEZ0UzKjWXGoHgKk83fW60ICAH8YT8BIUCUJuqUCAFHo8nh45f/2Ua0s5aLo6y0HNqH295OXHom0UkpWJKSiUpMwhyXgDk+AVNsHCpN7+Tjl7e6eWFtOUv2NXHB8GRunZXXbeNbURR4+4G7yBk9nslXXNPp7XbW2Ljr/b3EGjU8dcVIsuJ6Pje4t/AFBR7/7BCf7m3kj5cMZ/7Ivlnd6i36Q8RAIBygvriD/Ssbaal2UjglmaKzMrr0HO8Mot9PoKKCcGsrgs2OTKlAptGiSk9Dk5PzLTPBv2z7C+VVddyguYOyba0EA2HyxyYyaHwSSTnmPuv7JUmiaVsZpYu20FgXxG1MJSTXolLL0RhUCGGRgDcMEkSnGEjOsZA5PJa0wdGIYpBPn/oTfreLS+9/pEvlXcMhgQ3vlVFzoJ35vykiJuV/92g4GOT9R39LTGo6Z//ydhBFWv74R1wrV5H+yis97o/QV/g9IVb9pxhbo5tzbh5OfEY3Kw4Eg3Qs+gjrCy+gHTqU5D/98ZhlLE9XXDY/Hz21i5T8KGb9uADFURaN/IcPU3fzLRinTyPpoYe+Zz4phETWv3uYmgPtnH/byB4vh3giek0YWLNmDS6Xi/nz5wPw2GOP8fjjjxMKhbjoootYuHDhMUOeTpZRo0YxZswYXn31VQDC4TDJycn8+te/5qGHHgLAbrcTDAZJTEzs9Dad+cyJ+KHm2Q7wP1f61SWtLD/Yws5aO8NSLcwrTGReYSJ5J1kS8FCjk5fWVfD5wWYuG53GrTNz+7SCwOcHmvj9xwcpSrfw+MXDe0X06EkEUeJgo4ON5VY2l7ezvdpGlF7FlLw4puTGMSUvrt+fw/Fw2wNseL+UhlI7c35SSPaIroXJ/RA8Blz+EEv3N/Hhzgb21HUwqyCe84YnMyUvrsfENE8gTEmzi5Kv0k+Km5yUNLvwhwRy443kJxqJM2qI0quw6FTIgJAgERJFOrwhGjt8NDn81LR7sboDZMbqKUw2MyYzmnFZMRSmmFH184iV4+EPCfxu0X42VVh58box5OlDtFSU09HS9NWrGZe1DZe1jXAoiM5sIS4tg9QhQ8kcXkRqwdBuPzdFUWJdaRuvb65mS2U7FxelcOvMvJOekO9b+TnbPlnIT556AZW6a9eRLyjwl89LeH9HHfedU8CPJ2b2a98dgB3VNu77cB9RejVPX1V0RlSu6Q8eA6/se4W1dWt5auZTyNr07F5eQ9U+K3ljEhg9L5PY1L4zAPY6g6xavZ1dG8tJ8GeQPSKOwROSyBga+72w+r5GcHtwLPkM62crcByuRjliLOYJY4maMo6o/LRv5Xx7HR0s+vOjaPR6Lrr7AdS6rl+rkiSxbUkV+9fWc+Gvi77lO+C2tfPm/bcz9bJriFr0KcH6etJffrnL5Qj7C221Lj7/535ikg3M+Wlhj0StCB0dND34EL49e0h99hn0o0b1QEtPLZIkYa2tpmrPTmr276extA5JcKMz69AaTcSlZ5I6uJCEsIjr4ceIvfHnxN5yy/f6LpfNz+cv7wf4XlRKX9Hr5Qq/STAYxOfzYbH0bm3pRYsWcdVVV/H8888zadIkFixYwLJlyzh06NARw8Mbb7yRrVu3cuDAgU5v05nPnIj+ODge4NTQ7g6w6iuRYENZGylROuZ+JRKMyojuVChpi9PPyuIWFu6o53Czi0tHp/LLmbmkRZ+agZndE+QPSw6xoriFBy8o5Ioxab22giCJEh5HEJ8riFItR2tQoTMdeyXUFxTYW9/BzprISuvOGjsSMCknlqn5kaiA3HjDKYl28HtCOK2+SP3ekIhCKUetU6I3qzFEabo0MXDZ/BxY38D+tfVkj4xjymX53Sqjc6YKA6IosaWynQ921rPsQBN5CUYuG53G/JEpxPZiZM03kSSJeruPkmYXZa0u7J4gHd4QHb5IBJZaIUepkGHRqUi26EiJ0pIWrWdwkgnjaVzq71hIksS/NlaxYPlhrhp7dFNTSZLwOR0421ppra6kvuQgVbt3oDOZGXHWORTNO/9I+O6JqLN5+Xh3Ax/uqscTFLh2QgbXTMggwXTygzCfy8m/77iFc269g9wx3a/BvrnCyj0L95EZq+fJy0ecsmf68bB5gjy1/DCLdjVw+1n53Dg1u9+nVXWW/iAMBIQAf9z6R9bVr2PBjAWMSxpHR6uXPStqKdnaTNrgaEbNyyAlP6pX+q1wSKBqr5XSL5upPWSj1VRLxlgL15x3Ppp+Gj0XamzEuWwZrjVr8O3eg2bQIIwzpmOcPoNAUjyL/vIoiTn5nHPr/x3T/LWz7FlZy46l1Vxy1+hviTRly5ey9NUXOEsXQ8Fzz3e5XFx/QBIl9q6u48tPKxlzbhZjzs48bmh8l/cvSdj/+xZtf/87qU//HeP06T22775EkiSq9uxgy8K3aa+vI2P4SDKGjUQfFc/+tTYcbW5GzIwj7G+matVyWuxWkpJSGXXlNQyeNA35V34LkihxaFMjWz6qIHdUPNOuHoTyFPmT9ZowsHz5cmw2GxdddBG6k6xp2h3ee+89nnnmGVpaWhg+fDh/+tOfKCwsPPL+vffey65du76VAnCibTr7mePRXwbHA/QvvMEwG8qsLD/YwqqSFpRyGWMzY8hPNJIercekVaJSyHEHwljdAQ43uzjQ6KS0xUVRehTzR6ZwyejUflMhYFVxC7/7aD85cUZ+f8EQhqb0jBjocQSo3N1Gxe42WiodhMMiGr2ScFBECImYYrQk5VqwDLZgtygob3NT2hIJ6y5vdRNjUDM2K5oxmTGMy4pmaIrllOTyuu0Bqva2UV9ip6miA58rhNaoQqNTolDJEYWIQ7PfFUQml2GK1WKJ02GO02GO12GO06LRq1BpFISDAn5PCGu9m6byDpoqHGQOjaXorMiAsbucacJAldXDhzvrWbSrnqAgcnFRKpeNSWNI8sBzuL9QZfXw0CcHONTo5MZpOfx4UuZxhZBwKET5ts1s/3QRAZ+HmdffRN7Yo0/Gq60eVpW08vmBJvbUdTA9P55LRqcyrzCpR01CV7zyPK52K5fc9/BJT9bcgTB//OwQS/Y28fsLhnDl2P7h7O8OhPnP5mpeWlvB2KxoHpk/lMzY0yftoTP0B2Hgaz4o/YAntz/Jw5Me5vyc84FIX7h/TT0H1jegt2gYND6RQeMST7qOfMAbouZAO5V7rNQebEdvUTN4QhKLFf+lRVHPS2e91C+uwc4gdHTg3rAR99q1NGzfyrZ4ExnGKKbMOQ/jlMmoc07e4X3H0ir2r23gkrtHE5Wgx/HppzQ/+hjlE0dhNxn40eN/RaHsH+OyztLR4mXdO4dxWn2c9bOhJOf23mKuc9kyGn/3AClP/AnzOef02nF6mm8KAo62VsbNv4yiueeh0n7bd2L/2ga2LCoj2V9ORtMaMh69k8qmOnZ/vgSFUsG4i67AED2CXV/U4XUEmXZVPtkjT23px14TBhYuXMjPfvYz5HI5l156Kddddx2zZ89G3s+ch/uaUz04HqD/ExZEdtTY2VfTQWWTkzabj6A3DCERk0KJSSEnSacm0awlO8FIXJwOU4yWmBRDlw3mehOnP8Q/Vpfzny3VnDssmV/MyO22O7XT6mPX8lpKtjSRmGUmd3Q88bkW7HKRyq/KBVY2urDVuVBagxQEFCjlMlyZOuKLYslPMVOYbCYtWnfKBjWSKFG5t42DGxppOGwnOddCemEMKfnRxCTrj7oCIwgibpsfp9WPo82H0+rD2ebD2e4n4AsT8odRqhVoDSqik/Qk50WRURhz0oNDODOEAac/xGf7mvhwZz376h3MGZLA5WPSmD4o/rQOvz+TkSSJtaVtPLeqjPJWNxeMTOHiolTGZB47ikoUBQ6sXsGGd/7DoIlTmPmTm2nxhNlZY2dnjZ2NZVbq7T4m5MQwtzCR84cn90p0SEtlOe8+fB/X//U5opN6Lsd+7eFW7vtwH4OTzDx0QWG3vQ9Olpp2D299Wcs7X9aSl2jk3rMLmJTbd6ZYfUl/EgYANjds5s51d/LLkb/kJ0N/cuT3oYBA1d42Sre1UHfIRlyGifQh0aTmRxObZjxutJgkSrhsEXO+pnIHTeUdtNW5iUkxkD0yjpyR8cSlG1ldu5qHNj/EovmLOlXbvb+xb9UXrPnPP5kwYy55ogLvlq14d+5EERWFYdIkDJMnoZ84EVXC913hT4QkSWz+sJzybY1MtC9CdmA7yU/8Cd3kybz9wJ1kjRrL9Gt+2vMn1Qt4HAH2rKxj/9p6hkxOZtLFuah1vT+mdK9fT/0d/0faM09jnDbtuJ+VJAmfy0lHcxM+lxMApVqNJT4RU1x8p6r3nAySJFG9ZyebP3gbR2vLUQWBrxGDQexvv03ty29RP/6nNAgpmGJ1xKUbUaqguWwbrZWrQQaDJs3nrJ9fjEZ36v1/ejWVwOv18vHHH/PWW2+xfPlyEhIS+NGPfsR1111HUVHRybT7tGVAGBggHBJor/fQ3ujGbQ/gtvvxdAQIeMMEfWEC3jABXxghJAKgUMnR6JRo9ErUOiUanRLVVwKAKIh4nUGcVh8BT5ikXAs5RfEMmZLcb0SCOttXLt+7GhifHcNFRanMHZLYKSO/cFBgx7Jq9qysQ59jwpGppcQXKRtY3e5Bp1KQl2Ak9ysn+Nz4yM90i5b6g3a2Lakk6BOYdGkueWMSTokoIIkSh79sZufnNYSDAsNmpDJ4QjLG6P5dweF0FQbCgsjminY+3FXP5weaGZxkOpIqEH2GVkQ5E5EkiV21dhbtauCz/U2EBYnRmdEMTjSSGqUj2qBGrZAjEfGKsHlC1NXWo1n/Jv4wLE44h5yMpCPGjFPz4jD0YhqGKAq88/u7ySoaw5Qrr+vx/Tu8IZ5acZj3ttdx5dh0bp2VS7Kld6MxJUmios3DutI2PtvXyP4GB2cNSeTnU7MZkxl92qwcd4f+JgwAHLQe5NZVt3JhzoXcOfZO5LJvi5teZ5Dag+3Ul9hpLO/A1e5Ha1RhsGjQmVQolHIkCUL+MD53CJfNjyRIRH0lKifnWkjJj/pWXrPVZ+XSTy7ltxN+y7nZ53a77acCn9vF2tf/SdXeXVxw+31kDBtx5D0xEMC3ezeeTZvxbNmC/9AhNLm5EZFg0iT0Y8agMB1/IUMSRbzbtmF//wO2V0XjSi3i0vvHY0yLrPi219fy39/9H5fc+xAZw0b2yjk62300VzhwWn34XCGEsIhSrfhWKqLBoj5yDci/I4j7XEEayzqo2N1Gxe5W0gbHMOmSXOLS+lZ8dC5dStPvHyT91VfQjx79rfeEcJjK3dup3LmN6j07cdtt6C1R6C1REU+eQACntQ2AxJxcUguGkjN6HKkFhcjlPROO/y1BoKU5IgjMO/+ogoDg9uBc/CnWf76Cwmgg8YHfY5g4gYAvTGOpHXuzl1BQQGdUE5emp71+J1s/fAeVRsuUq64jb9ykU/ps7TOPgba2Nt5//33eeusttmzZwiOPPMLDDz98Mrs8LRkQBn6YONq8VOxqo3q/lZZKJ2qdktg0A6ZoLcYYLYYoDVpDJJRc/R0R4JvGOcfDafVRe8hGyZYm7M1eRsxKY8w5mT1eMqi7WN0B3t9Rx9L9TZQ0uShINjE8NYrMWD0xBjU6lYKQIOIJhGl0+LHXuIg76MYpCazQhTAnG46UfxuSHCkVmGTWHvcBKooSpdua2fxhOQmZZmZcM7hPzVwaSu1sXFhGwBtm3PnZDBqfeMqNmjrL6SQMSJLE3noHn+xpYPHeJmQyuGRUKpeNTjsta6gP8G0EUeJws4sdNTYqWt00dPixe4OEhYh4atZFjBuzYg1kRqnxr36bQHMNVz30J0yx3a9N3RX2rljG9k8/6JbhYFcob3Xz1PLDrCppZf7IFK6bmMnINEuPDCQFUaKizc2e2g5219lZX2qlzf2/SjoXDE/+wYhr/VEYAKh11nLzipuZmDyRByc+iOI4E5+gP4y92YvXGfHiEYXIMF6tVaAzqTFGazDH647qnA4gSiK/WvUrTCoTT8548qTa3ZdIkkTZl5tY/drLJGTnMvfm2zDFHP85IHR04PlyG57Nm/Fs3kyorg5VSgqaQYNQ5+agiIpCYTQi+vwIDgeBw4fx7d0LMhmWiy/GcvnlrFvtoaPFy8X/N+pIBODuL5aw/ZMPuf6vz6E19Mxk2233U7y5iZItTbhsAeLTjUQnGdB+Jf4IQZGAL4TXEcTjCOJxBPC7Q8hkoDOp0VvUSCJ4XZHrIjbFQPqQGIZOSyUq8dR5mdjffZfWvz9N1jtvo8nJwedysmvZYvav/gKFUsWgiVPILhpDUm7+90wjRVHA2dpKw+FD1BcfoHLXdiRRJHfsRPLHTyJjeFG3PCVEUaBi+5ds+/SDI4LAyHnnfaukriRJhOrq8O7chWfDelyr16DOzibuphsjZRk7ESkfDoXYv/oLvlz0HqbYOKZc9WMyR4w6JQJBnwkDgUCAzz77jLfeeovFixdz55138uc///lkdnlaMiAM/HCQJImaA+3sX1NPfamd9IIYskfGkT4kBlPs8Se0J3vcpgoHmz8sx+8JMfvHQ04q17w3qLd72VPXwf56Bw0dPmyeIP6QgFIhR6+SM8gmYa7yYRkfx6g56eQnmbpc2u2b+D2hSLjfzlYmzM9h+Ky0XnX6drR52fxhBXUlNsack8nIOemnzEimu/QHYUCSJPyH7YTqXQQbPYjeEJIgIdcqkMfqqFfDyoCfxeVttLuDnDMsiYtHpTIxJ/a0rQM/wMkjiSIrXv0Htfv3cMWDf8SSkNSrx/M6Hbx2xy2c86s7yR0zvleP9TUVbW7+tbGKxXsaiTdrOHtoElNy4xidGYVefeLIiA5vkLJWN2UtbspaXZQ0udjf4EAQJYanWShKj2JybiwTsmPR9RNxuS/pr8IAQLOnmZuW38TQuKE8PuVxlPLeiYR5df+rfFD6Ae9f+D5mdf8fr0qiSM2+3Wx6/784rW3MuO4Ghkyb1a2xVthmI1BaRqC0lGB1FYLDieh2I9PrUBhNaPJy0Y0cibawENlXpqdCWGTZS/sJ+sJc+JsiVBoFkiSx6ImH0ZktnHfbXSd1fgFviO1LqjmwvoG0gmgKp6SQXhiDSnPi+1MIR6JLPY4AXkfEu0hnUmGJ16Ez9h+xr/Vvf6d96WdYr7uSPWtXkJxfwJjzLiJr5OhOTbC/RhQFGg8XU7ZtC2XbNuN3ucgaOZqcMePJLhqDIer4ZRJtjfWUbtnIwXWrCIdDjJ5zDoPzhyJrayVUX0+wrp5QfT2hhgaCDQ1IoRC6oUPRT5iA+bzzul2aMhTws/vzJWz/9EOiEpMoOvsCBk+a1mlj3e8S9Pu+JWJ0hl4VBkRRZN26dbz11lt88MEHhMNhLr74Yq677jrmzp2LQjHQ2QxwZtJQamfLRxU4rT6Gz0yjcGoKBkvfho6LosT+NfVs/bSS8ednUzS3fxhXHQ+PI8CKfx/EbQ9w9o3Dul0v91jUH7az9r8laAwqZl1X0OPhcgFviB1Lq9m/roHBE5KYMD+nWxUB+gP9QRgAaHt1P3KjikCslsZQmCqbl5Y2D6LVx1BJQb4ox5uoI3lWBuYR8T3qnDzA6YskSax+7SWq9+zi6seePOFA8GT4/MWn8bvdXHzP73vtGMfCHxJYcaiFtYfb2FxhpcnhJzVKR2asnii9CoNaiSBJhAQJmydAqzNAqyuAwxci0awhP8FEXoKRwUkmRqZFMSjReMZUFjgZ+rMwAJEQ/5tX3EyWOYu/TPsLKkXPGtztaN7Bratu5bVzXmNo7NAe3XdPIkkS7XU1VOzcxoE1Kwh4PYy98FJGnX3BUcO8e5twUGDxc3tRqOSc94vhKNUK3LZ2/nPPbZx1460MnnT8HPqjIYkSxVua2PpxBbGpRqZemU9syqnxGelNJEni0PrVrH3pOQyCyJwHHiF95OgTb9iJ/bbVVFGx80sqd26jubIcc1wCiTm5mGLj0ZstSKJI0O/D3tRIa3UFHrud1KRU0oIicRU1hCsrkRsMqNLTUaWlok5NQ5WWFvl3Whqq9HTkPXi9BX1eDq5fzZ7Pl+C2t5M9ahy5o8eRlDeIqMTko4okAa8Ha20NLVXltFSU0VRRhtdh51evvtMlUaXXhIGlS5dy880309LSwty5c7n22mu55JJL0Ov7X8mdvmRAGDiz8TqDbFxYRs1+K6PmZTJidtopz/VvrXHy2Qv7yBoWy/RrBh8zbPBU01brYumL+0jJj2LGNYN77XsLBwW2f1bNvtV1jJiTzrjzsk463UIIiRzc2MD2z6ojHfcVecSlnd4h7P1FGJj//EZKmlyERJHsOANFaVGMSLMwNiuGwmQzkiuId08b7s0NoJRjmZuJbmR8vxfBBuh9JFFk6fNPYWus56qHn+hWzfIT0VByiA/+9CA/e+pFzPFdNy/rSSRJos0doLzVTb3dh9MXwh0Io5DJUCrkxBrUxJs1xBs1pMfosehOL7f0vqS/CwMAHf4Obl5xM/H6eP42829oFD2z+NDkbuKapddwy4hbuLrg6i5vLwoCDSUHaSg5RFttNfamBnxuF0GvF7lSiVKpRKFWo9EZ0JpMaI0mdEYTOpMJrdEc+WkyoTWY0BqNSJKEGA4jhMP4XU7cHXYcLU201dbQXFFKwOshY+gIhs6YQ+7YCae8CkDQF2bxc3uRK2Scd+sINDolpVs3suKfz3P9gudPmNbwTZorHWx4rxSfO8TUK/LJHhl3RvZtLVUVrH7tZZxtLUy/+ifo/vlvFFFRpD37DLIeXkT2u920VJbTWl2B227D6+hAoVSi1GjRCxLafQdQbdyMIT0d46zZ6EYVoRs+HEVsbJ9/95Ik0VpVQdm2LVTv3YW1tgq5Qok+KgqtwYQkiYSDQTwdNgIeD3pLFEm5+STm5JGYk09y/mD05q5Vleg1YeCTTz6htraWq666ioRuOH2eqQwIA2cuFbtaWfPfEtIKopl25SAMUf3HXM5t97Pk+X1YEnTMu3FovxMHKna3sur1Ysael8WoeRl98vC11rtY82YJAV+YyZfmdavDlUSJ0u0tfPlpJSqNgokX55I1vO87j96gvwgDO2vsxBrUJEdpj5tOIgki3t1tOJdXo7BosFyQgyZz4Bn7Q0cIh/joL48hiSKX3P/ISdcu/yahgJ8377udYbPmMv6iy3tsvz90pLBIsNFNqMlDuNWL4Akh+cKglCPXKVHGalGnmVBnmJD3kqHk6SAMADiDTm5deStapZZnZz2LXnVy4pcr6OL6ZdczOmE0v5/4+y71Za3Vlez+fAnl2zYjVyrJGDaS+MxsYlLS0JnMaPR6RDEykRFCQfxeD363C7/Lhc/twu9y4nO5Ir9zR34XcLuRyeXIlQrkCiVaowljVDTm+ETiMjJJzM4ledCQHr2ve4JQUODzlw/gcQQ4/9YRmGK0LHv+KTyODi773WMn/F49jgBbFlVQsbuVMedkUnRWRr/xi+pJvE4Hm957k0Pr1zD6vPlMuORK1FodQkcH1T+6BsO0qST97ne93o5gbS3Njz6Gd/duoi69lOgfXY0mN7fXj9tVhHAIe1MjXocDv9uJTKFAqVJjiIrGHJ/QIz4WfeYxMECEAWHgzEMIi2xeVE7JlmZmXVdA3pj+KYT53SE+eWY35rj+Iw5IksTOZdXsWl7L3J8V9nn9VlGUOLi+ge1LqzFFaxg1L5PsEXEnNHwM+MKUbGniwLoGhJDI+PnZDBqf1CXfglBrK5716/F8uY1QYyOEwygT4tEOH4F53lzUWVkneXYnR38RBrqKGBRwb2jAta4O7ZBYos7LRtHHaTwD9C+CPi/vP/YAUYlJnP+be44aVikJIkgg64I56Jr/vEJTWQlXP/Zkj7lf/1ARPCF8B6z4D7UTqHIgU8pRpRhRJeqRG9XIdQqksIToDRFu8xGscyG4g2gHx6AvSkBXGItM0XOC7OkiDAB4Q15uW30bgijwjzn/wKju3uQgIAS4bdVtKOVKnpv9XKe9CxpLS9j47hs0lR2mcNoshs6cQ3Le4C6FL5+JCILI+ndKqdjVysxrC0gfYuA/99zGuPmXMersC466TdAfZv/aenYuqyFzeCyTL83rU8PkvkIIh9j9+RK2fvguaYXDmHHdDUQnp37rM8G6Oqqvupq4X9xCzPXX90o7pFCI9tdfx/rCi1guvoiEO+5AYenaCvuZxoAw0McMCANnFk6rjy9ePYgkSpx901As8f07VeZrccASr2fejUN71YDvRISDAqvfLKGpooPzbx3Z5+VxvkkoKHBgbQMHNjQQ8IbIHhFHYraF2FQjKo0CmQxcNj/2Zi91xTYaSu3EpZkYMSuNvNEJna4cAeDdtYv2l/+Je+NGdMOHY5gyBXVmBigUhJtb8O7ciWfDBgxTp5Jw912nTLU+XYWBrxGcATqWVuEvtmGek4FxSgqyfiCGDXBq8DodvPvQvWSOGMXsn91CuMWL71A7/jI7Yasf0R0ECVDIUJjUqJIMqNOMaPKjUaeZvjfprDu0n4/+/CjX/fkZYlJSj37QAY6L6AvjO9iOd18bgfIO1GlGdMPi0A6KRpmoP+GqaqjVi29fG54dLSCXYZqWimFcUpfEnWNxOgkDAP6wnzvW3oHVa+XpWU+TZkrr0vaekIfbV9+OT/Dxz7n/xKAynHAbp7WNtW+8QvWeXYw5/yJGn38xOuPpnULXG3wdTZqSH0XaYC9rX1/AtU/8ndjU9COfcVp9lG5vYe+qOizxOiZdnEvq4N7zRTlViIJA8ca1bF30Lgqlipk/uYmsEaOO+Xnfvn3U/vRnJP/lz5jnzu3Rtvj276fpwYeQwiGSH3vse2USf6gMCAN9zIAwcOZQtbeNVf8pJn9sIlOuyDttXOd9riAfPbWLpFwLs64rOCVh7x5HgKUv7kcul3HuL4Yf16BPkiT8e/fi2bIF7/YdBBvqETocAKgS4lFlZGKYOBHjtKknvcouSRJN5R3UHLTRUuWko9lDOCQiCBKmGC2WeB1pg6PJHBbb5bI+gaoqWv74J3x79hB9zTXE/Pg6lPFHj5AIW61YX3qZjg8+IOHO/yP6xz/u87/T6S4MfI2/ooOOTytAkoian4c2L6rPjj1A/6KjpZlVf3iWkUmz0QV0aPKj0RZEo0o0oIjSIJPLkAICYUeAULOHYK2LQJkdSQL9sDh0RfFosi14HHbe+u0djL/kymOu/A1wdMSggL/YhndPK/5SO6okA/oR8ehGxKGM7t7KqCRI+Pa34VxThxQSsZyThW74yeVin27CAEBIDLFg+wKWVi3lL9P/wuSUyZ3art3Xzq9X/xq9St+pdARJFNm78nM2vP0a+eMnM+2an/aqueeZgMcRYOfnNRRvbkIMrEcU6hg++w7CIRltdS5sjR5SB0czck46GYUxZ0Q64jfxuZwcXLeKPcs/Q4aMCZdcSeH02cg74R/gWrmShnvvI+Pll9CPG3fSbRE9HtqefRb7e+8Te9ONxN50E/Juuv6fiQwIA31MdzqIcFDA0eYjNvXMcyE9HREEkS8/ruTAhgZmXVtA/rjEU92kLuO2B1i0YCc5RfFMuTyvTzuhtloXn72wj7SCaGZdW3DM1XbR56Nj4QfY33+PcGsbxqlT0I0ZgyY3NxLqJUmEWlsJlpfj2bwF744d6EaMIPq6azHNndvjhjXdRQqFsL78T9pffZWoSy8l/vbfdDpUzbtrN/W/+Q2muWeR9MADyJR9Z2R5pggDEAkTd29uwrmyBu3gaCzn56AcSC/4QRG2+bF/XE6g1kGxdTMJ5w5l5PnnnXA7SZQI1jrx7m3Dt88KChnV7v14EnycdfttZ9wAvjeQBBF/eQe+PW34DlpRWDToR8ajK0pAFde1UlrHPY4o4d3ZgmN5Dcror3xGMrr3rDkdhYGv+bj8Y/705Z+YmzmXu8beRYw25pifXV+/nkc2P8LYxLH8YeofTmhgaG9qYPnLz+G0tjL3ptvI6gHX+B8SQX+Y2kNtrP7XH9Gakhg8+Rqik/VkFMaiNfQvn4STxWlto2b/bsq3b6Vm326S8wYzYu65DJ44tVOCwDfp+OADmv/0BGnPPI1xWtcrO3yNe/16mh95FGVKMsmPPYYmJ6fb+zpT6TVhYNeuXXg8HqadxB/wTKQ7HUTNgXY+f3k/Y8/PYtTcDOQD4bCnDLfdzxevHCQUCHP2TcOITjpxuF1/xdHmZdGCXQydlsr4C7L75JjlO1tZ/cbxTQalUIiODz7A+sKLKOPjifnJ9ZjOPvuEpWDCdjuORR9hf/tt5Hod8f/3fxhnda+GcU8RqKyi8b77kPx+kv/0J3TDh3V5H6GGBup+8QtUaemkPfP0kZrJvc2ZJAx8jeAM4lhaie+QDfOcdIyTU5F1IQ1kgNMT95dNOD6rRF+UgOWcLJrqyvnwTw8x/ZqfUnT2+Z3ejxgW2PLsG+hb9cQrUtHmRWEYn4y2IKZH89vPBCRBIlDtwHfAim+fFZlChq4oHv3IBFQphl59LotBAff6elzr6tENj8NybjYKU9eem6ezMACRygJ/2f4XtjVt49L8S5mbNZfB0YPRKDTY/Da2NW9jYelCDtsOc9fYu7gk75Lj/k1EQWDHko/Y8uE7DJ89j6lXX9/l+ugD/A+ntY3/3n870679KcNnzTvVzek2kiThdXRgb2zA1lSPvakRW2M9rVUVeDrsJOXkkzt2AvkTJhOT0rX0lu/iWPIZTQ8+SPIjD2O56KIubRtua6PliT/j3rCBhLvvJuqKy3/wHhjHoteEgWeffZbKykqefvrpk23jGUV3O4iWKier/nMItU7JnJ8M6ZUJqSRJhJua8JeWIno8EA6jiIlFnZWJKjX1B38T1R5sZ8W/D5FdFMf0qwadEQ6x7Y1uPnpqF+POy2bknPQTb9BNJFFi25Iq9q2u46wbhpI94ujleo7kfAUCxP/fHZGV/65WCggGsb+/EOsLL6AtGEzSww+jzszsidPofBskiY733qPlyb8SfeWVxP/fHcg13V+hFpxOan76UzTZOaT89ck+uRfPRGHgawKVDjoWVyB4QphnpfdYXvIA/QspLNKxuALfgXZiflTwrTSSxtJiPvrzo4w+7yImXnb1CZ8zkiiy5o1XKN++lasffRKDyoxnRwuebc1IkoRhXBLGicldnoCeSYiBMP5SO/5DNvyHbSCXoSuMRV8UjzrLgqyPPW3Cdj+OpVWokg2YZ2d0advTXRj4mp0tO3n/8PtsbNiIM+hEKVMSlsLkReVxXvZ5XDn4Siya40ewtVZXsvzlZwn5/cy75TekFhT2UevPbGr27eHjBX/g6kefJDG7/zngfxdJFLHW1dBwuJjm8lJsjXXYGusJeDyYYuOJTkklOjmVmOQU4jKySc4bhOoECzpdxb1hI4333otx+nQSH3wQhfH4cyExGMT+xhtYX3wJw9SpJD7wO1QDlfKOS68JA2vWrOH3v/89mzZtOulGnkmcTAcRDgps/aSSgxsbmXJZHkOnpZy06i6JIt4dO3Au+QzXqlUIHR2os7NQmMzIFArCbW0EGxpQmM0Ypk7BNHsOptmz+mzVsj8ghES2fFLBoQ2NTP/RIAomJp/qJvUoLdVOPn16N1OuyKdwSkqP7z/oD7PytUO0N7g579YRxKZ8PyVGcHtoe/YZOt5fSOzNNxF7440nnfMluFy0/f1pOj76iLhbbib2hhv65LoNt7fT9LsH8B8+TMqfn8AwcWKP7bfmmmsjndvvH+j1SIgzWRiAiFjlP9SOY0UNkl/AOC0Vw7jEXit/NkDfIriDtP+3GCkgEHt94VHz1611NXz4p4dIHVzIWTf96pilngJeD8tffo6WqnIuf+BxohKTjrwniRL+UjvuzY0EKjvQj0zAOCUF9VGec2cSkiQhOAKEmjwEqpwEqhyEGlwo43ToCmPRDolFnW7qczHgWG3t6vPyTBEGvkaSJKw+K/6wn1hdbKfKGga8Hja9/1/2r1rOmPMvZuKlV6H8AY39+oKti97jwJrlXPPHv3W53nxfIEkSDYcPUbJpPeXbtxD0ekkeVEBy3mBi0zOISUkjJjm1xwWA4xFqaaXxvvsIVlURe8vNWObPR2E0fuczLXQs/ICO995DERtL4m9/i2HC+D5r4+lMrwkDTU1NzJ8/n9zcXK699lriv2OylZKSQkZG1xTcM4Ge6CDqS2yseO0QSTkR87ju5CVJgoBz2ee0v/wyYasV87nnYj73HLTDh38vZFsKhfDt24d73Xqcy5Yhut1YLr6YqMsv65d1PnuS9kY3K/51CIVSxtwbhnbZcO50oaHUzpJ/7GPO9UN6tNyio83Lspf2ozWqOeemYWiN379WXavX0PyHP6BOSyPp0UfR5PRsWoNv716aHnoYSQj3uvOse906Gn/3APrx40h+5JEeL3sTrG+g+uqrif/VrUT/6Ec9uu/vcqYLA18jiRK+A1ZcGxoIt3oxjE/CODml20ZoA5x6gg1u2t88hDrDRPTlg5AfJ7rL6+jg8xf+TktVBRMuvoIh02cfcVYP+n0c3rKBLQvfISY1jfN+ffdxB++hVi/uTQ14d7WiTjdhmpWOJi+qX/kQiEGBcKsXoSOA4Akh+QUkSQJRilRlAJB9/Yq0WyaTIQYFRE8I0RNC6AgQavUihQSUsTo0WRbU2WY0ORaUUWfGfXOmCQNdQRQFijesZf1brxGXkcXsn93yLQf9AXoOSRRZ8uxfcbW1csVDf0Sl6R/3jygIHNqwhl1LP8FpbaVg8nTyx08hrXAYij70OjoWkiji+uIL2v/1b/yHD6MtHIIqKRkpHCZYXU2wqgrDlClEX3sNxmnT+o3n1OlArwkDCxYs4J577jnm+3fddRcLFizoyi7PCLrTQUiiCDLZtwYXPneQ1f8pxlrvZu4NhaTkd84RVgoGcXz6KdZXXoGwQOxNN2G59JJOr85Kooh323Y6PvgA1/LlaIcNI+qKKzCfczZyXc/km4nBIOHWVsKtbUjBIIgCcpMJZUwMysTEPjFgE8Iie1bWsmNZDSNnpTHuwmwUZ7i3Q/V+K1+8coBzbh5O5rDYk97f4S+bWffOYYZMTmbyZXnf+/5CTU20PPFnPF9+SeK992C59NJeG0BLoRC2N96g7R8vYJl/IQl33omiBwdoos9H64KncHz8MYkP/h7LRRf12rl4d+yg9qabyXjln+jHju2VY8APRxj4GkmSCNa6cG+ox1dsQ1cYi3FqKprM/tfWAY6Nd28b9g9LMc3KwDQzrVP3oSRJlG/fwvZPPqS5ooyopCRkMjmO1maiklIYf/EVDJk6s9P3tOAJ4dnahHtTA8o4HeY5GWgGRZ8SgUAKiZHw/jI7gYoOwlYfMq0SZYwWhVGFTKMA+Vfji6+b99VoT5K+EgskCZlKgdyoQmFQoTCrUSYaUMXrztgUnB+iMBAOhTi8eT1ffvQ+QjjM9Gt/xqCJU/qVsHUmEg4G+fBPD6HW67norge6bMzXk0iSROnWjWx6779Iksi4Cy9jyNSZfRoR0FWCdXX49uwl3NaGTKlAlZaGbtQolNEDlTK6Q68JA6FQiEAgcMz31Wo16h9gSFJ3OgjXypW0PPFnTGfNwThnDvrRo5EplUiSxP61DWz5qJxRczMYe17WMY0JBbcHx6JFtL/2GnKtNhJ+c/75yFTdd0EN2+04Fy+hY+FCQk1NmC+8APM556IfVdSpkG1Jkgi3tREoLsZfXIK/uBh/STGhmlpQKlHGxiLTaJDJZAhuN4LdjkylQjNoELqiIozTp6EfN+6EpnRdQZIkag/Z2LSwDLlCxoxrCkjO7X/hXb1F2Y4WVr9ZwuwfF5A/tnvVFoL+MBveLaV6fzuzfzLke34CYjCI7bXXsb78Mua5c0m4526UcUf3HOhpgrW1ND/yKIGyMhIfeADT2fNOetDj3rCB5kcfQxkfT8qTf0Gd3vsrK7a338b6jxfIXvQhqsTeqYrxQxMGvknY5se9uRHP9mZUSQZM09PQDonpF2HRAxwdSZRwLq/BvaWRmKsHoxvSPXHTZbNiq69HFMJEJacQndT99CoxEMa9pQn3hgYU0RrMczIiRoV9MNEKNrhxb2nEd8CKXK9CVxCDJjcKdboRuUk9MNk7AT8UYUAUBZrKSin7ciMH169BZzQy7qLLKZw2u1+sDP9Q8LvdvPfIfcSlZnLW5bcgusOI3jAAcoMKhUWDKkHfqyan9uZGVr7yD9ob6phy5XUMnTHnlIoUA5wa+qxcoSiKyH/g5nXQvQ5CDATwbNmCa+VK3KvXgCRhnDUL01lzMEyejM0aYvmrB9EaVJx1QyHm2MjKvSSK+PbuxblsGY5FH6HOzCT2pht7vJTb13XmOz5chGvtGiSvD93IkWjy81FlpKMwGpGp1YgeD4LDQbC6hkBVJcGKyoinQVYW2iFDUBcUoMgbgpCQiV+hx+cOEfQJhAKRF6KI5HYgtrUhNVRB8S5UHc3ETR1NwqXnox87tluDHVESkUSoO2Rj57JqOlp8jDk3k+Gz0s74KIGjUb3Pyop/H2TYjDQmXJSDvAuToaq9bWx4vwxzrJazfjYUY/T/DPekcBjn0qW0/eMfyHV6kh56sFfD+o+FJEk4Fy+m5c9/QZ2TTcJdd6EfNarL+/GXltL27LN4v9xGwp3/R9SVV/ZZuJokSTQ98HuCVVVkvvGfkxL4jsUPWRj4GtEXxrOtCdemRuQaBeZ5meiGnVx99AF6HtEXxvbeYcJWH7HXF6JK6F8pX2JQwLO1Cdf6ehRRGsxzM9H2QgSBJEr4S2y4NzYQrHOhH52AfkxiJNd/4JrtEmeiMBDwenG0NuNoa8FaW01LZQUNJQcByBk1lmGz55E2ZNjAtdKHSJJEqN6Nr7gd7yEroSY3klxCk2BGro/066I3hGCPLLSqM03oRyagGx7bY344QjjMjsWL2PrRewybeRZTr74ejf70rbg1wMnRq8JASUkJd9xxB1u2bOGmm25iwYIF7N27l3fffZcnnnjipBp+unKyHYQkCPj27MG1chWulSsJW61ohwxBkZPHgfAw6pxRjImpJL5tF/6Dh5BCIUwzZxJ11VXoRhUdvTycJGHz22j1tqKSq9Cr9CTqE1HIuz7JkUSRQEkJvn37CZSVEWpoQPR4EIMB5AYjQVM8wfgc/FGp+DQxeEQ9HlcYjyOI1xEgHBRRquToozQYzGpUWiUqjQKVJjJBFwUJUZAI+MJ4OgJ42r0EAhIKwY9BdBKdGUP8iGyikoxYEvREJei/ldcuSiJ7WvewuXEzuxr34GsAY3Mi+dYxyJDTllNK0gQ107KnMDaxe0LD6YgUDBJub0cKBCITeJ+K5Qsb0OjVTP/RIBKOE04tSRJN5Q52fl5Na7WLSZfkMmRy8pHV1bDNhuOTT7G/+w4IInG/uAXLxRf3SUrI8RDcbmz/fo32119HN2wY0ddeGzHWPM4kWxJFPFu20LHwA9xr1hB12WXE/fIXKL/jodIXiH4/1Vf/CMOE8ST+9rc9vv8BYeB/SGERz84WnCtrUUZpsJyXjSb7hxNJ1J8J1rtof7sEVbyOmKsLkOv67yqnGBTwbGnCtb4OZYwO89xMNPkn70EgBgW8u1pxb2xADAgYJ6dgnJB0ZGIxQNc53YSBoM+Lq70dl82Kq70N91f/drdbcdnacbW3EfB4UOv0WBISiUlNJyknj5TBQ0jKG4S8G+O9AbpPuN2Hd3crnt2tiJ4w2sHRaAdHI8bK+OiFx9GbLVxwx31HDFElUSLU4iVQZse7u5Ww1YdhQjKm6WkozN2Pvm4sLWbFP58HYO7NvyZlUEGPnN8Apy+9Jgy4XC6GDh3K/Pnz8Xq9xMTEHPEUGDt2LP/+978ZMWLEybX+NKQnOwhJkgiWl+M/dIhAeQVCRwf1vlh2e4aQkRhg8tmJmMaOOupExxf2sa5uHcuqlrG9eTuukAuz2kxYDOMX/GgUGvKj85mQNIGZ6TMZFjcMuazzq+dBfxhrnRtrvZv2ehfWeje2Jg/hoIgxWoM5Toc5XoclTocpVoveosZg0WCI0qDWKro0UAoFBOy1NhqXrqd10z48cguhjELckgGfK4RGr8QQp8Imb6XZ3YIsrCAmlIjKq0NtkpOYbyJlpBFtlkCFs5xdrbtYXbuaaG001xRcw2X5l6FSnFkDrEBFBe71G/Bu346/uJhwSwuIYiQFRKlE8noR5Cqqs8+jLnUmMeEW0jQtJMSDKTEKeVw8Hm0crS49NTUhHNYgw6anUDQrFYXbRrCmGv/+/Xi2bMW3axe6oiKirrgc87nnHrkeJUmi3d+OJ+RBlERMahOx2tg+F2PCdjsdH3yA/Z13EB1O9JMmoi8qQpmUjMJiRnS7CbdZ8e3di3fHDqRwGMvFFxH9o2tQp6X2aVu/S7CmhqrLryD5D49hPuecY3+wYSekjunSvgeEge8jBgXcGxpwra9HWxBD1IU5KIw/vJS4/oAkiLg2NOBaVYtpTgam6WmnTaqHGBBwb2nEvb4eZZwO47RUdIVxXQ4TFlxB3Fsa8WxtQmHWYJyWin5k/Bmb99+X9AdhoPTLTVTt3oHebEHz1QRRFAR8LideRwdepwOP3Yar3UrQ50Wp0WCKjccUE4spNg5jTBym2NivfsZhjk84ZuWNAXofMSDg22/Fs6OZYJ0L7eAYDKMTIulF37hngz4vnz37V+zNTVx8z4PEpHx/nBGsd+FcXYe/1I5pSgqm2eldiiAIeD1seOcNDq5bycRLr2bsBZcMpI4MAPSiMLBo0SJefPFFVqxYwVNPPUVTU9MRYeCuu+4iLi6O3/bCKld/py8Gxy6bnxX/PojPFWLKZXlkDv/fZCsshvmo/CNe3PMiRrWRc7PPZXradLLN2UfK14TFMNWOaoptxWxq3MT6+vWY1WYuH3Q5F+ddTJzu+/ngHkeA5goHTeUOmio6aKtzozOqiEs3EpdmJDbNSGyqEUu8DqWq95RpSRBwrVyF9fnnED1e5D/7CR/FONhatodB2iGMShxFQcJgouIMWOJ1GKM1R52IBoQAy6uX8+8D/yYoBLlr7F3Mzpjda+3uC6RgkI5PPqFj4QcESkowTJqEfvw4dCNGoEpPRxkffyQUXhIERJcLwenEWdvG4Z3t1NWJ2NxKJCIdmFLwE+0oJabtAEmO/ShDPqRQCBQKVKmpaAsKMEyaiGHqVNTp6TS4G9jcuJm9rXs52H6QOlcdASGAWh7Jdw0IAfRKPfnR+cxKn8XczLlkmPuucokkiviLi/Fs3IS/pJhwUzOCy4XcaEAZFY12xHD0o0dHUlZ6IXS/u7hWraLx3vvIWvg+mpyc739g0zOw/im4dTNY0jq93wFh4NgIziAdn5QTqHYQdXEe+uF9HzHyQ0WSJAKVDhyLK5EkiehL809bg0jRH8azrRn35kaQJHQjE9APj0OVajymyCF6Q/jLO/DubsVfakeTG4VpWmq/q35wutMfhIGGkkNU79uNz9mB3+NBJpMhl8vRmc3oTBZ0ZgummFiMsXGYYuLQGAwD10A/Q5IkgjVOPNtb8O1vQxmjQz82EX1R/HFFZVEU2PjOG+xZvpSZP/45w+ecfdS/bbDBTcfiCsLtfiznZaMvij/uNSCJIgfXr2bD268Tl57JWTf96qR8VAY48+g1YeC5556jpKSEf/zjH/ztb3+jsbHxiDBw//33o1Qqefzxx0+u9achfTU4FgWRA+sb2L6kmthUA6PPySSYbOf+DffjF/zcPvp2zso4q1OdSEgMsa5uHQtLF7K9eTsz02ZyWfyPiLKn0FwZEQMcVh+xKUaS8yyRV24UpphT52La5m5h+b8eJuW99WiVOsy33kzhlTch66LPRVgMs6hsEc/tfo6JyRP5/cTfY9GcXiHEkiDQsWgR1hdfRK7TE/Pj6zCfd163XPlFUSLoDSNTyFBrIyLC1yvqMoUcmVaLMiYGmUpFSAyxp3UP6+vXs6F+AzXOGkYmjGR0wmiGxQ0j25JNsiEZrTJynfjDfupcdRywHmBV7Sq2NG5hZvpMbi26ldyoM7ss5snSumAB7nXryHrvPeT6r/KrJQlWPQq73oTrPoSUoi7tc0AYODHefW3YF5WjL4on6vwcZKqBldpvIgmRWveCM4AUFJFCIjKlDJn6K4d7i+a4pQS/iRgI4y+x497UQKjVh2lGKqZpaWfE6rgkSvgP2/Dts+I71A6AOtWIIlqLXKNAkiREZ5Bwu49Qixdlgh798Dj0oxJQxvZMNaABvk1/EAYGOD0RAwKByo5INZDDdkRfGH1RPIaxSahSuibe1Ozbw+cvPU1MShozf/xz4jO/X85ZkiR8+9pwfFaFIlpL1MV5qJO/7xHQVH6YNa/9E7fdxowf/3yg4sQAR6XXhIHPP/+c3/3ud+zatYu///3vNDQ0sGDBAvx+PyNHjuSxxx7jqquuOukTON3o6w4i4Auzd2UtO1dXYpO1YRom8aNzzic+pfOTW587SHuDh9ZqJ5WHm2mucCCEJNxRbWTkxzF5zCjS8mLQ9IN8RqvPyusHXuf90veZkDSBXwy7idQNpbT94wUUFgvxd9yOccaMLj8MrT4rj25+lIPtB3lsymNMTZ3aS2fQs/gOHqT5kUcROjqIv+N2zOec06sGea3eVjY1bGJDwwa2NG5Bo9AwLW0a01KnMSllEia1qdP7avY08+r+V/m4/GOuHXIttxXddsaldPQUUjhM7c9uQJmYSMpfn0QmifDZnVC+Cn78McTldXmfA8JA5wjb/NjeKUESRGJ/MhSlRXPijc5QBFcQ/2E7gWoHwToX4TYfIKEwqZFpFMiUcqSwhBQUEFxBECRkOiUKsxqFRRP5aVYjN3x1n4dFwvYA4VYvgRonylgdhjGJGCYkIdeemWGvkiASavESanAjOAKIAQEAhVmDMlqDOss8kL7SBwwIAwN0FkmSCLd48R+24y+1Eah2orBo0A6Kjrzyo09KNPZ73Gz98B32Ll9G/sQpjD53Pkm5+d/7nBgQcK6uxb2pEePEZMxzM5CpFdQd3M+2TxbSUHKIsRdewviLLkel6b/lBwc4tfSaMCAIAuPHjycnJwe9Xo/P52Pu3Lk899xzBINB9u7di0bzwxtA9XUHIUkSL+17iXcPvM+9sX+ASjN1h2xo9Eri0k1EJ+nRmVRodEokCYSwiNcZxOMI4OkIYG/y4nUGMcVqic8wkZxrISnXgiFJwWc1S3ir+C3cITdXD76aKwZfQYw2ptfP6Wg0e5r5z8H/8GHZh4xPGs8vR/6SoXFDj7wvBgJ0vPsu1pdeRp2dTcL/3YF+3LguHUOSJD4u/5i/bP8L83Pnc9fYu9Ao+uc1LAkC1pdeov2VV4n52U+Ju+WWHi3r+DXekJd91n1sbtzMpoZNlHeUMyxuGFNTpjI9bTpDYod0yZviaFR0VHD/hvsBWDBjAZnmzJ5o+hlHuK2NqksvI/aG64lRLwd7Ffz4oy6lD3yTAWGg80hhEfvH5fhL7cRdX4g6rfMC2OlO2ObHu7cV/yEbwQYXqlQT2lwL6nQTqiQDiijtUXPnJUlC9IQQHEEEZwDBGfwquiAYKdMlA5lChiJKizJOizYnCmXcwOr4AH3DgDAwwPEQvSH8ZV9FBZTZkXxhNLlRR8SA3nhWOVqb2fbJBxRvXEd0Ugo5Y8aTMXQ4semZ6ExmZDIZkiThKm+m49MKRHuIfa4N1LkOUXT2+Yw6dz568+kV8TpA39OrVQmsVit33XUXH374IR6PB7Vazbnnnsvzzz9PWlr3BqunO33ZQUiSxN92/o0llUt4Ze4r5EVHVg1DAYG2OhfWOheONh8+V4igL4xMBnKlHL05YgSot6iJTjIQm2JAfQynZ1ES2diwkf8e+i+7Wndxfs75XDvkWgZFD+rVc/uaUnspbxe/zeKKxcxIn8HPh/+cobFDj/l5we3B9sZ/sP37NXSjRhF/x+3ohh7780ejzlXH/evvxyf4+Ov0v/a7MPdQczON99xL2Gol9W9PoR0ypEf2K0kSzZ5mDrQfYFfLLva07qHEVkKMNoZJKZOYmjqVickTidJG9cjxvklICPH0rqf5pOITnp31LKOj8sFjjbyp0oExEQZC4vCuX0bdr+4k+fxkzA8vAl1Ut/c1IAx0DUmScK9vwLmqhpgrB6Mb9n0vljMFMSDg29eGZ1cLwVoX2vxodMPi0A6ORmEaWM0e4PRnQBgY4JtIokSw3hWJiCqzE6xzoUrUoxkUg3ZQNJosc5+lNQV9Xkq/3EzNvt3UHdqPx25DoVKhUCoJBQJIkkRMcipDUiaR6slBHWfEcm422tyoPmnfAKc3vSoMfI0gCHR0dGA2m1H1I9OuU0GfeQxIIo9vfZyNDRt5dd6rfWLiVmYv463it/is8jMKYgo4J/sczs46+6hmhSeDJ+Thi+ov+LD0Q0rtpZyddTY3DLuBnKijGK8dg7DdTvsrr2J/+23048YR+7Ofop80qdMpBiExxAt7XuCt4re4e+zdXDHoin6Rq+VavZqm3/4O45w5JP3+gf/lm3eRrw0oS+wllLSXUGIrocRegjvoJjcql1EJoyhKKGJUwihSDCm9f+5eG5R+wcKDb/DXUB2Pt1qZ5w8BMhBDoLFA4lAYdDYUzoeYzl8L/Z2AEKDKUUWju5F2fyT/WClTkmhIJN2UTqoxNRKVUb0J3r8et2Iq9f/dT9rTf8c4Y0a3jzsgDHQP30ErtvdKMZ+diWnKqa1a0dOE2rx4tjbh2dGCMlaLYUwiupHHN9EaYIDTkQFhYAApLBKo6MB3qB3foXakkIR2UNSR9ABFP0kbC/n9uGztiOEQKq0OndmMWhuJWBCDAu5NDbjW1aOM12OakoJuWNwZ4c0ywPGRpIjHjzKqa9HCvSYMvPbaa7S1tXHvvfd26b0znb7oIMJimAc3Pch+635enfcqSYakXjnOsejwd7C8ZjnLqpaxp3UPI+JHMCF5AmMTxzIifsQRs7nOIogCZR1l7GzZyYaGDWxr2kaOJYfLBl3G+TnnY1Z3/3sMW63Y334H+zvvoIyPJ/pHV2M65xyU0dGd2v7Lpi/53YbfMTx+OI9OfvSUGROKgQCtf12A4+OPSXrkESwXnN/pbX1hH2X2MkpsJRTbijlsO0ypvRS5TE5+dD5DYoZQEFNAQUwBeVF5Xf77nRQNu2DbP+HAIkgYAgXns95g5O6S13h86h+ZlzUPQj6wlkHjbihZApVrIXMKTPkN5Mw67SIJJEmivKOc5TXL2dq4lYPtB9EoNKQaU4nTxSGTyQgJIZo8TTS6GzGpjYyWG5naWMxZE+4iatKvcX7+OY2//R3Jjz6CZf78brVjQBjoPoFaJ+2vH8QwLgnzOVn9QjTsLpIo4S+x4d7SSKDKgX5YHIbJKajTTaf1eQ0wwPEYEAZ+mEiSRLDOhWdbM779VuRaJbqhsWgLY9Fkm5EpTs8JtegP49nZgntzI6I7hHZIJNJBnW5CGacbeJafQYTtfrx72vDubkX0hUi+f0KXSuH2mjCwYMECmpubj1Qi+CZ//vOfcTgcPPHEE13Z5RlBb3cQQSHIvevvpdZVyz/n/rPHV+u7Squ3lXX169jRvIMdzTuwBWykm9LJNGeSbc4mRhuDXqXHoDIgl8nxhrx4w146Ah3UOmupcdZQ7axGhoyihCImp0xmZvrMHs8zF/1+HJ9+iuOjj/EdOIBh3Fj0EyehHzsGTU4Oiqioo24niSK2tjqeXv0YjQ0lXJsyn9G6wciUCmQqFcr4eFTJySiTkrpcEaGzBCorabjzLmQqFalPLUCdcfTokKAQpNpZTaWjksqOSiodlZTZy6h2VmNRWyKT/9gCCqIjPzNNmSjkvWdUeFwa98Dqx6F2CxRdA+Nugvj/paesr1/P3evu5o9T/8jczLnf3tZjhW2vRASF+MFwzhOQMqpv298Nyu3lfFHzBV9Uf0GTu+mIaeOYxDGkm9KP2nGHmvZyaOmv2S64WJOQxSFXNROTJ3Je9nlMrtdjved3mM46i4S77kQZG9ul9gwIAydHqM2L9d8H0GRbiL4s/7QbUAqeEN4dLbi3NoIgYZiYjGFc0kCqwADfJuQDSQSZAlRnjqHZgDDww0L0hvDsbsWzrRmhI4B+VAKGMYmo0oxn1KRZkiRCDW58B6wEKh0EG93IZDIUURHzV5laEXmp5MjVCmQaBXKtEplWgcKkRhmvQxmjPe36szMd0RvCe8CKd3drJL0vLwr9qAS0hbGdrvzzNT0uDNTV1VFRUcF7772HzWbjl7/85bfe93g8PPbYY9xwww3ccsstXWrsmUBvdhC+sI871tyBM+Dkpbkv9buyepIk0eBuoMpRdWTCb/fb8YQ9eENeBEnAoDRgUBkwqU1kmDPIMmdFRARLNkp537hQB+vrca9dh/fLrXh370GwWlFYLMijLMj1BqRQENHrRfJ4EdxuEARkajUhs54mpRvJoCPVmIJBUhNusxJuaUFuNKIbORLDpEmY5s1DnXbyIcaSJGF//z1a//wk8svOw/GT87EJTtp97dj8tiOvdl87Vp+VRk8jWoWWbEs2uVG5ZFuyyYvKoyCmgER9Yv/o/FqLYc2foGwFjL8RpvwfGI4+oV1Xt4571t/DE1OfYE7mnO9/IOCCjU/Dln/AsEth9oNgTu7d9ncBURI5YD3Amro1rK5dTaO7kWlp05iXNY/pqdPRq46TBuK1wYanYPu/YMItMOM+UOupd9XzRfUXLKlcQqO7kUvM07jg4yZUu0vI+WwJquTOn/+AMHDyCM4g1tcOIDepib12CH4hQFVVFXV1dbS2tuL1egkGg2i1WoxGI6mpqWRmZpKeno6iF6uHHI9gvQv31iZ8e9tQp5swTEpBVxjbpRWHk8HZ7qOlyonXEQQZGCwa4jOMmAdWtU49ogB126B8BdRsgfZy8LT+7319HMQXQOZkGHIhJA0/7SK2vmZAGDjzkSSJQKUDz/ZmfAesqFNNGMYnoRse1+XJ1OmKFBYJt/sQOiLGr1JIRAoJiMHIT8kvIPrDiH4B0RkgZPUjk4E6y4w2Pxp9UQIK8+kpFouiRKPDhzsQJhgWMWiUxJs0mDTKLvU1kiQhesOIriBiQEAKi8iU8shLLUdhUvdKFR0xKBAotePd04qvxIYqyYB+VAL6EfEnJeD3uDCwYMEC7rnnnmO+r9frmT59Ou+//z4m0w/HuflrequDcAVd3LbqNmQyGc/Pfh6j2thj+/6hIzidBGvrEN0uRK8XmUqNXK9DrtMhN1tQRkch0+uRyWR4Qh5eO/Aab5e8Ta4ll0vzL2V2ynTUlU34du/GvW4dni+/RFtQgPmcszGfdx6qlJSjHtcb8tLsbabZ00yLp4UmT1Pk394W5NUNnPdBHdG2IC+eJ6c0X0+sLpYYbQyx2lhidDHEaGO+9f8sc1b/EQC+i70a1jwBhz6GUdfBtLs7NYlfU7uG+zbcx4IZC5ieNv0Y+66BlQ9D2UqYeX9kIt3HZQ8lSaLd306ts5ZiWzH72vaxvXk7fsHP9LTpzEyfeWIxAMDdGomG2PoipI+DeX+ExMKjHu+Q7RAfl33M0qqlDO7Q86fr3+xSWtGAMNAzhL1Bdry6mmJXFXVCG/Hx8aSnp5OUlITRaEStVuPz+XA6ndTX11NdXQ3AyJEjGTt2LDExvV/pRQxGzATdW5sIt/rQj4rHOCkFVdL3a2H3Bl5nkP3r6inb1oKr3U9cuhFDVCR/120P0N7gxhKvY9iMNAqnJqNU/TAG7f0GRwPsfB12/xeEAOTOgZwZEDcYojNBroyIBh210HoIKlZB6fLIe1PuiAizp1mp2QFh4MxFcAbw7GrFu70Z0RdGPzoRw7hEVIl987w7nZFEiXCbF395B/5iG4EqB9pB0ZhmpqPJ7P/Xdk27hyX7mlhV3EJJs4tAWESvVqBRynH5wwTCIjEGNYXJZkakWZiSF8eYzGi03+hzBGcAf6mdYK2LYIObcKsXKSRGois0ClDJISwihUTEoABhCZlGgSJKgzJGizJWhzLu6586FBYNMvmJx+WSJBG2+ghUOfAfsuEv70AZpUE3Ig79qARU8d3zFPsuPS4MSJKEIAi88MILtLS08Oijj37rfaXyzKw93Fl6o4Ow+qzcuvJWYnQx/H3m39EpB0o6nWrcQTeLyhaxtGoppfZSCmMLGRY3jCxzFnFBDZbtpahXb0O1pwRPQToNk3I4XBRLvayDZm8zTZ4mHAEHGoWGJEMSSfokkgxJ5FmVDF5WjGXzIcTLzsb8y5uJi0k78YSyv+JqhvV/jQw4h14KM++D6Kwu7eKL6i94cNODPDPrGSalTDr2B6vWw2d3g1wB5y2ArCkn1XRREim1l1JqL6XWWUubrw130I0n7MET9HzvZ1gKk6hPJC86j5HxIxmTMIZRiaNQyU8wYA4HoHId7HsXihdH/BNm3AeZxznXbxAUgmxs2MjM9JldKh35gxQGRBECzkhotMZ0UpOZcDjMvn372LRpE6FQiEJ1JtmeOHJvHI8y9tjPaFEUqaysZNeuXRw+fJgRI0Ywffp0ojvpe9IVQi0ePNtb8OxoQWFRY5yUjH5UAnJN3/TToYDAl59WcmB9A6n5UQydnkra4OjvVcEJBQSq9rax64ta/O4gEy/OZfDEpP4pcp5JOJsikUm734Tc2TD6J5B3Fig6cX2EfLD3Hdj0DCCDc/8SMYc9TRgQBs4sxICAv7gdz65WAuUdaHIsGMYloRsaO2DEdxKE7X48Xzbh3tyIJicKy3nZqBL633h0b10HT68sZVN5O9Py4zhnWBIj0qLIiTeg+iotQpIknP4wVVYPhxqd7Kyxs6ncit0bZFZaNJdodAy2BVFa/ajTTaizLKjTjKgS9SiitBFR4DtIkoTkCxPuCCB0BAjb/ITbfYTbIz8Fux/ksv8JBrE65DolMpUcSZCQAgKCKxjZptWLGBRQp5nQFsSgK4ztle+6T6oSDPA/erqDqHHWcMuKWyhKKOIPk/+A6jRT5X8I1Lnq2NO6hwPWAzS4G7D5bXhCHuQyOdFeGeMOhhi6q53YGgfevBQYOQRD3iCik7Mwqk0I7TYCZWW4N6wnVFuH5bJLib3hBtTp6cc+qCSBqwlaDkZW450NEHBD2A9KTWTSY0yMTMLjBkVc/PtykO2ohy9fioTC550Fsx6AhIJu725xxWIe3/o4/5jzD8YmjT32B8PByHHX/QUKzoe5fwBTYqePExJDbGrYxOKKxWxt2kpYDFMQU0C6KZ0kQxJGlRGD2oBBacCoNmJQRVJjDEoD8fr4zhk3hoPQvA9qt0Y8FqrWg9YChRfBmJ9BXF6n23synPHCQNALNZuhah0074e2kohQxTe6Oq0FEodFPCoKzof0iXACr5BgMMiuXbvYvHkzKpWKqVOnMnz4cBRyBY6lVXj3tBL306Go004cMWe1Wlm/fj2HDh1iypQpTJ069aQr+wjOIN69rXh3txJq9aEbGotxUjLqTHOfTrQbyztY/Z9i9GY1M64ZTGzqt6PcRFGkqamJ6upqmpubaWtrw+124/P5EcMSaqWOlPQEcvNyyMvLIympb012z2jcrZE0rB3/hvy5MPO3R41M6hRCGHb9B1Y9FkkxuODvYOr/f6sBYeD0RhK+sbJdElnZVsZq0Y9ORD8qAWU/qShwpiC4g7jW1OHZ1oxxehrmmenIVKdecGlzBXh08UFWl7Ty40mZ3Dwth1hj5//2gQYXzStqkB22U62T83HQx1aFwNDcWKbkxjIqI5r8RCN6defEdH9IoN7upc7mo97upaHdi7vVQ7jdj9YVIkGQYQBMSgVajQKDSUNysomULAvqRAOqZEOvC1k9Kgzs3buXLVu2dOrARUVFTJw4sfMtPUPoyQ5iVe0qHtr0EJflX8YdY+7o0mrgAP2PUEMDnm3b8e3aSbCunnBbGwDKuDjUGekYpkzFMHkSimNdN+42KF8JZcuheiN4rRCbF5n8m1MjYoBSGwkFDbjA1RIRDdrLQKWH1DGQNhYyJkHaOND0cDqKJEWqDGz9R2TlO38eTLszctwe4MPSD/nrjr/y8tyXGRk/8vgfdjTA8gegfBVMug0m/hK0x74fQ2KIj8o+4qW9L6GUK7kg5wJmZ8ymIKag694XATc46iLiSEdt5OeR/9eBqxFRnYLffCk+YQxBdxyiT4YkSiiMKlRJBrSFseiGxvZqmbj+Igw0Njbi9Xrx+Xz4fD5EUUQulyOXy1GpVBiNRkwmEyaTCZ3uBNFSPjsc/Cjyqt0KxiTInRmZ+McPAUsqaKMiUSUBV0QoaN4PdV9CyWeR+2fCzTDuxsj99M1d+3xs376drVu3YrFYmDZtGgUFBci/IyS4NtTjXFFD1IW56Md2LrWnoaGBzz77DK/XyznnnENBQddENNEbwldsw7unlUCFA022Gf2oRHTDYnsl9/F4hIMCWz+t5OD6BibMz2HE7HTkX4VRejweSktLOXz4MNXV1UiSRFZWFikpKcTHx2M2m9FoNPjcAbYsLqGluRVznkBDUy3JyclMmjSJgoKCgUiC7uJph83PRNKVsmfArN9B8oie2/fn90HFarjwWRhyQc/s9wQEg0FCoRAGQ9fCxAeEgVOL6A8TtgeQAmGkgBAJyRYkJFGKaLeihCRJIAKShBQWERxBBEeAcEeAcLMHZKDONKMtiEE7OAZV3EA0bW8TrHdhX1QGIsRcW9Bj4e3dYfHeRh785ACTc2N5ZP5QEkydN0cNtXlxLKsmUGZHPzYR09RUlLE6BFHiYKODzRXtbCq3cqDBgd0bIj1GR1asgTijBotOhUwWGfI6fSFs3iA2T5DGDj9WdwCtSk5atJ70aB3pMXrSonWkR+tJidKhUsgRJYk2V4Cadg/ba+ysL23DolNxy4xcrhiT9q20ht6gR4WBf/3rX52uNHDjjTdy//33d76lZwg90UG4gi6e3/08n1Z8ysOTH+acrHN6uJUDnBaIYqREX9nyyKtpDyQXRSbcubMixk/qTgyGwkFoOQANO6F+e8RUytkAKUWRFZ6MyZAxEfTdyHUWRWg9CIc/h/0LI/sddV0kzz8mp+v7OwFvF7/N83ue54U5L1CUUHTiDao3RqoftJXA2BtgzE8h6n9VHSRJYmXtSp7d9SwAt4++ndkZs08swnltEWMua1lEeLGWQUdNZOLv7wCVAaLSwZIGlq9+RmUgqFNxl5hw73KjjNWiHRKDJtsSqZcslyE6gwTrXfgOWAk2uDGMScQ0J6NXVj/6izDw4osvIggCWq0WnU6HQqFAFEVEUSQUCuFyuXC5XIRCIYxGIwkJCSQmJpKUlERKSgqxUSbkZcth33uR+yRpBAy/PHKfdCVSRghFhKSNf4O2wxG/ivE3Y+twsHXrVnbv3k1qaipTp04lNzf3uJNTf7kd27uH0eZHE3VhDnL9iaMARFFk9+7drFy5koyMDM477zwslmMbzArOAL6D7fgOthOodKBK0qMfmYCuKP6UrZY1VzpY9Z9iNHolc34yhOgkAw6Hg5KSEoqLi6mtrSUpKYmCggJyc3NJTk7+nrDyNZIksXt5LTuWVjPt2hxsoVq2bNlCXFwc559/PvHx8X18dicg4IpcQ2ojKPuZWZfXBltfgK0vQcYEmPk7SOsZwfZ77FsIn90VqTYz7w+95j0QCoXYsWMHGzduZOzYscyaNatL2w8IA32HJEoEa5z4yzsI1jgJNboRveFIzrZO+ZVTvjzihC8n8myVR14yGSCTIVPKUJg1KCwaFFFqVEkGlPH6TuVuD9CzSIKI44saPF82EXVxHoZRCX16/GBY5I+fHeLjPY38+dLhnDu886bLgjuIc2Utnh0tGMYmYp6TcVwjP0mSsLqDlLa4qGn3YvcGcfhCiKKETAYWnYpog5povZoki5b0aD1xRnWXxOuQILJ0fxMvrKnA6Q/x58tGMGNQ7/VvA6kEfczJdBDekJePyj/i5b0vkxedxyOTHiHDfPTSdAOcPkhhEdETAhnIDerju397bZEVl7IVkegAMRQxgsqfB3lzwNhDD+COukgYe82mSLi1tQwShkDqaIjJjUyoojJAFxUZ6IrhSC68xxqZ/LcdjoTD130ZyTXNngHDL4NB54K6dxXkd0ve5W87/3bsagXfRZIi4eRf/jMyccycBPlnsyMqgb9XfkSjt5lbi27lkrxLvh0dEPREvidb5f8m/+3lYC0FbzsYEiJpGnF5EJsfidyISo8IAbrob01IJUnCu6OFjiWVaLLMmGZnnNDIJ9TmxbmiBn+xDdPsDEwz0np0ENRfhIHO4vP5aGtro6WlhdaWFppqymi2diCXQqQoHaQkJZIydDIpg0cTHR3d/VVlSSJcupLSxU+zN5xNeTCBIYWFTJ48mZRjGIkeDcEZwL6onGCdC8v52eiLEjr19/N4PCxfvpzi4mJmzZrF+PHjUSgUEWOiNh/+4ogYEKx3oc4woxsWh64wFmXMqSslFw4JbPu0iv3r6hl3QTbZ4ywcPHiA4uJiGhsbyczMZMiQIRQUFBxX7DgalbvbWPH6IaZfNYicMTGsWbOGHTt2MGvWLCZPnnzqogdcLbD37cizuq0k8kz4Gl10RLhNGRVJpUqfeGrEAlcLbHk+kjKQOiYSIZDRB5Gc7RXw3o8j38MVr/Vcv0VEENi5cycbN27EaDQyc+ZMBg8e3OXrYEAY6H3CjgDuDQ1497SCKKEdHIM604Q6zXQk13qA0xdfiQ37+4fRFsYSfVEusj4wjbW6A9zy5k78IYGXrhtDekznxpuSJOHd3YpjSSXqTDOWc/ufV4IoSry/o47HPytmflEKD11Q2CvRAwPCQB/TnQ7iYPtBXt77MlubtpJpzuTXo37NtNRpp2+4pCRFHIw7Y2B0hhJq9uDd04q/wkGo3vW/tGa5DHWaEd3QWPRjElEofZGQ5+oNkdXtpn2RCXr+XMg/OxLy3xffo7sNajdHjm+rjLw6aiOrYGLoq7YrI+WqzMmRFIakEV+lJ4zr80HvqtpV/HbDb7lh2A3cOPzGzof7Oxoo2/sGz1R9wg7RzQ0O5/+3d9/hUZVp48e/M5Mykz7phXRCSUgAKVLEEruiAoodFgVRX/u6uurqu67709VX3dVV17UAimVBUARRBBWlVwktCZBGeq/T2zm/P47GRSKEZJJJeT7XlUszOSdzH5Kccj/Pc9/cqtLjp9MrCRCXXVmbbqhSbvS9dBCarBxveJqSCAhLU5IB2s494LhMDpo/OYq92oR+Vhq6EWc2M8NW1kbzJ8dQB3gTev1wtz0A9rfEALIMVfvg8GfKh9OKa+RM6hOuoMqlp6q6mqqqKmpqavDx8SE2Nrb9IyYmhuDg4N8cnbbZbNTV1VFVVUVxcTElJSX4+/sxOrCFMVUfE3Lln2HsLV0IWcZyuJHWtUWofDUEnhePX1Z4p26gSkpK+GLNF3jLGi4IH0dwhRqX0YE2NRhdRjja9NAeXWrSWbUlbXz3fh4qHxexZ0NR6VEqKipITk4mIyOD4cOH4++jgfKdUH1AWVJjalCWbQQPUZY3JZ8L3r89DbjiaEHZ0eYAAFCLSURBVDNf/esgU64dyqhz46ioqGDFihVERUUxc+bM0y8xcSdrq9Jyde8SZcZVxgzlXKhPUuq72E3K0qGaw7+0/rOblSUtw69UCvR1ZXbWT1wOCbPBjrnNjqVN+a+5zY7Z8Mvn2Ax4WSrxMx1BH6UlfNIFxE6Z2LvdHuwmWHOfMkPthg+Un3M32Gw2cnJy2Lp1K/7+/px//vndWlbSlxMDDpfE4cpW9h5vprjBREWzGbPdBYCfj4Yhej9SI/w5OzmM9NggNH1s1NzRYMHwQznm/XXoRoTiPykW3+TgXmuJKnSd1eHCZHMSpPNuL9p3Ks5WG00f5SO7ZMJuGdmjCerieiPzluwhc0gwL88e3emHZmeLlebPCnFUG9HPGIouI7zHYnSH8iYz9y/LQaNS8c7c8ej93Xudd2tiYNOmTXzxxRecf/75BAYG8sUXX/zmtueffz7Tp/fOGrO+pCsXiOKWYn6o+IEpsVMYrj/zzLdHNRYpIybHtygjqs3HlTXuoDxoBcYoD1QxY5QpjAlT+t40SzeyFbfStrEM2/E2/DLD8U0LwTfpp6niyLhqGrHlHMSca8DeEkCgZiWBEXtQJU+BpGmQdA4EdX5Uslc47cqabHXfaiGW15jHY1seI9A7kGemPkNqSOopty9oLmDx4cV8U/oNs4fN5o7MBYTaTMrvsK1NuZHV+Cj1GAKjlRkTfmHdKtroqDHRsDQPnxh/9NemdWpKeUcku4vWL4uxHGog7NZ0fFPObNS1I/0iMWAzQMmWn2bRbFBqCIyYrsxOST6vw2nKTqez/SH/54+6ujpkWUan0+Hn54ePjw+yLONwODAajVitVvz9/YmOjiY5OZnU1FSio3+qil/4HXy6QCkOecWLXZoaLTslzPvqMGypwNViwzdNj29SEF4ROmUao1oFLhlXmx1nsxVHpRF7hQFrg5FDgZUccBQzZlgmF111CdqAX0Y5XC4Jp13Cy0uN2kvVq9cOh83F7rUl5GzNxze1mZrmUqKjo8nKyiIjI4MAna/yM9v3ARR/D7pQ5eEwJAH8I5QZSM0lyswlUwOMuQXOeeg325hWF7aw9o2DTJyezOgL4zGbzaxatYqmpiZuueWWXmn7yPFtsOpOCEuFS//WuYJ9kqTMrjq2Ho5+qRSMTZgMI6+C4Vcos4wAu8VJW6MVY5O1w4d9c5sdi8GOzewEFegCvPEL8kEX6INfsA9+3hZ0lgL86ragMjfgiJmMKXQyLaYAaopbsZqdJGaEMeaieKLdcP7oFFmGHW/A98/CZX9TlnKdoYaGBvbs2cP+/fvR6/Wce+65Hdb2OFN9ITFg3FWNragFv9EReKfp2VLSyBf7q9iQV4tGrWJCUijDogIYovcj8KdaIQark/JmM8dqDOw+3oQ3Km5Mi+TymBCSfL2V2YkuWZl+r9XgFeKLV7hOKWrWiQe97rBXGTH8UI4lrxG/0ZEEnjekz43KCidqNtnZkFfD14drOFTZSoPR3v61UH8fzkoI4ezkMK7MiiE2pOMErOyUaPmyGMuBekJvHIF2mPs77Ow93sSCpXu5YUI8f7x0RHvdmlORJRnTrmpavz6OLjOckCuSu3wP1tusDhcPLtvPsVoDS+dPZIjefX9Hbk0MfPrpp7zzzjtcd9116PV63nnnnd/c9rrrrmPBggVdi7ofGxRTypw2yP0cdr+tjAAlTYWUC5SRbn2yMpVcpVFu4g1VyrTzyn3KtHWbURk5GXa5cmN0ioJw/Ymr1UbLVyVY85sImBZHwOQYZTTP2varGQEHlN7PSedg88+mOScGla8vodcPEz12u8DqtPLPnH+y/MhyshOyuSr1KsZEjiHIJwhJlqgyVrG1civflX1HTl0OV6dezW2jbiM+8BQdH9wVW0EzjR/mE3BOHEEXJrhlGYBxVzWta4sJuSYV//Hdq/zd5xID1lYlSVN7WKmtUZWjFAbUJymt1FKzlfOM95mPSDgcDkwmE2azGZPJhMPhQKVS4eXl1V7cMCDgFMU4W8rh4xuUpN3s97pcuFOWZZy1Zix5jTgqjTjqLUgmO7IEKrUKTZAPmmBfvGP98RmiTLmVfDXk7i1m885vMZhaCFen4d0WicMi4XRI7d9brVbhrdXgH+JLcISO4AgdobH+RCUFo49231pcWZYpyqljw6fbMPqW41AbGTN2DBMnTlTW/TcWwb6lsP9jZQR97K1Kq9LwtI6TbD8XLd32ChT/ANlPwYT5HSYi60rbWPPqfs66NJGzLk1EkiTWr1/PoUOHuPnmmxkyZIhbjrFD219XZgpc9DRMvKPLCUNr1XHqd22mPr+EhnoVzXIKBmc4NqcP3r4qAkN1+AX74hfkozz4//Tf9s8DfdBpZdQtxcrfStlO5draWKi0Os26QZnF8F/1Z2RZprHSyNFdteRuriQyMZBzrh9G+BA3F6D9LSWbYcVtMPxypZXsKf6GZVmmoaGBgoIC8vLyqK6uJj09nYkTJzJkyBC3Jb/6QmLAUW+mZXc1zT/WojY7ydPIyPEBDMuIIHV4OBp/b9Q+SlszyeZSCu81WNo/HLVmHPUWnMiUyhImHzVxcYEkRPijAiSrC1ezFUedBVwSPvGBSmHbUeF4hbivDonteCuG78uxFbcqhdzOHYKX3nNLm4TTazbZ+ffmIj7YUcqwqEAuGxXNxORQhuh1BGm9abU4qGyx8OPxZrYUNrCjqIEpqeHMPyeZaWnhHf4dmn6spWV1IYHnxxN4frzbrjlfHqzmkZUHeOKKkdw6KbFT+zjqzTR/WoCr1YZ+VhraNPcnK3qaS5L539WH2VrYwIo7JxMZ1LuzRTuVGDh+/Dg2m43hw4e7JbjuKi8vp7a2lmHDhnX6ZHyqfYqKiqiurj7hNX9/f8aOHdvpmLp0gSjdrmTVpz4A8RM7/V69zuVU+hb/8DdlVHXiQhh9Q6enVCPLP42cbIAjX0D9MaVF2OibIOX8frv0wLy/jubPC9EODyXk0ng0plxlhLNoI1TsbU8EkDRNuXELjmvfV3ZKtH5TimlnNWG3juyXJ6++oNxQzidHP+Gb0m+oNFai89LhkBzIsszYyLGcH38+V6ZcSbiud6aQWfIbafrPEaUwz1mdb5fYGdaiFho/yCMoO4HAc7v+INRnEgNLZygJAHODMqocmQ5xY5X12UMmnFAs0qOsrbD8ViXZN2dVt6aDn4osyzRVmSjLbaIsr5GqwhYCQnyJSg7C5ttIQXUOqGHq2dNIT0/HR+eNyyHhsLlw2JwYm2y01ltorTPTUGmkvtSAWqMiKjmImKEhxAwNISo5CG+fM5sBJEkyBTmVbFy3jQZ7Cb5+XkydNpmzzjoLncoB+WuUZEDFHmUk/Ky5ynn9TGYaFX6nFK4LiYfZ73f4b1xfbmDNK/sZfWE8469IAmDnzp189913zJo1i5EjR57RcZ2WLMO3T0POh3DLCqUOyxmQJJnqwhbK85ooz2+ivsxAQKiWiIRAIqI1hKpLCbQcJLB5G751u1BJdmWJhX+E0kFD46MkIewmZXmTuVFpN+jlCxEjlJoBCZOUf+tOXIutJgc5G0o5uLGCMZckMP7yJDQ/tcdyuVyYTKb2WTQ/f1gslvb/dzgcOJ1OXC4XTqcTp9OJJEloNBrUajUajQaNRoOXlxfe3t7tH14uM96HP8Fb5cL77AV4B0eh0Wiw2WyYzWaam5tpbGykqqoKh8PRXpdi5MiRZ9xxoDP6QmJg5Y8VPL0ml6ER/tyTGccElTeusjblYb/Booz8/xd1gDde4UovdK8IHd6RfkqPdb0Wq1NixY/lvL25GD8fDU9cMZLzhyu1HWRJxtlgwVbU8kux0lh//LIi0GVFdClJIEsy1qNNGDZX4KgyETA5loCpsacs5CZ4nizLrMqp5Ok1uYxN0PP7i4cxOj7ktPtVt1r4ZE8F720vITHMn99fPIxzOyiQZ68y0vhhPt7R/oReP6xbXXFkWebNTUX86/si/nnTGLJHnP5eSnZJGDZXYNhYjv/EaIIuTUJ9hte6vkSSZP6w8gCHK1tZtnAyoW5YVuDWxMDLL79MdXU1L730Eq+//jq1tbX89a9/7XaQZ8pqtXLLLbewbt06EhMTKS0t5YUXXuC+++7r1j533XUXK1euPKFVVEpKCkuXLu10bF26QLRVKwWCfnwfokcpCYJhl/Vu3/nTqfhRWS/oMCkjOhmzTtvv+7Rq8+DgMjj4iXLzNeZmGH9b33kQOA3Z4aJ5VSHWI03oJ7agM3yi3Niq1crIZmq20j0g+PQPb6Z9tbSsKkR/bRp+Y3q3wutA02prpcHSgLfam2j/aHw0vXujYsltoGnZUfTXD8cvs2cSEfZKIw2LD+E/MYagSxK7NIrWVxIDB/6zgbAhwcSMGYomMKzbcXSFLMk47C7UGhUajfq3Rzqcdvh0vjIqPnc1BLincrDV5KDiSDNluY2U5TVhMzsYMlxPQkYY8emhhET+9/IBF/v372fTpk1oNBomT57MmDFj8PHp+Pfc5ZJoOl5PzcFjVBcbqapUY7FqiAi1EhPrIjbZj/DkMAJi41AFRp5w3bFbndQWt3HkwHEO5u3DqK5CHxTBBRdPIz05Ck3pFjiyFo58pdTdGH2TMmLt343fe5tRma5fmws3LYPIk1s3NlYaWf1KDqPOG8LE6ckA5Ofn89lnn5Gdnc3kyZO7/v6/9vUTSvvVOauUY+wEWZKpKWmjYE8thfvqQJZJSA8jfqSeISND8f+trhGSpBR3bT6uJMoszUpCHllJxvuHK8ubAqMhaEiXrsEOh4OamhqKj5ZzYFsBTo0FXaiM0WTEZDIBoNPp0Ol0aLXa9g+dToevry8+Pj54eXnh5eXVngBQq9VIkoTL5Wr/cDqdOByO9kSCw+HAYbfhqDqIw9CIIyQVl4/SnlKn0xESEkJoaCixsbFER0fj5dWzAwV9ITFwpKYNk83FuMSTBwRkWQanhGRzofJSK5X7OzECa3dKfLizlFe/KyBrSDBPXpnO8OgTW6+6TA6seY2YD9ZjK2rFJyEQv9ERaNPDTtvRxNlowXyoAfOeGiSHRMDkGAImxYpCgv1Am9XBoysOsre0ib/NyuLi9DMftDDZnHyws5Q3fygiMy6Yxy4fwai4ExOSktlB0/KjOBsshN4yEp/YM5+ZZHO6ePzTQ+wobuSdueNPeo+O2CsMNH9agCzJ6K9NwzdhYMxIdrok7vl4H41GOx/dcTa+Xt1LdLg1MbBkyRLWrFnDqlWreOmll6ipqeGll17qVoBd8fjjj/Phhx+ye/duYmJi+Pzzz5k5cyY7d+7k7LPP7vI+d911Fw0NDaxcubLLsXXrYmNthR/fU2YPBA+Bi59RRpo9yW5W1gfuWQTTHlaSFu6uESC5lDWoe5co6zCHXgjj5yv/7WPr2n/marHSsGgvKkstYfL/ogn2gYyZygyImDFditt6rJnGD/PQzx6GX2Yfa8UldIq1oJnGpXmE3jgCXUbPPuQ66sw0LDqEdmQYIVennvG0vb6QGJBlmU3/OUbJgXqcNhfx6WEkZYWRmBGGrgdGnkytNmqKWqkvN9BSa6Glzoyh0Yrd6vylQCigC/QmQK8lQO9LSJQf4fEBRMQHEhzph1p2waqFyoPr3NXKQ9oZkiSZ+lIDZXmNlOU2UnvcQGiMn/LwmBFKbGoIGu9TP/S5XC5yc3PZvn07ra2tZGZmMmbMGGJiYpREUUs5HFgGR79SljD5R0BIAnJAFAa7nurmcKqaQqhuiaLFFo4aJ36aFry8JFB7Y3b60aY24QisxOrVRkqQluwEA3HOEmV5WFORMrtj6EVKMqAz6+07/w+kXHf2LoI5nyutVX+lscrI6n/kkDEtjolXJaNSqaioqODjjz8mMzOTSy+9tNvr0Nn9DvzwPCz4VilCehqGJit5W6s4srMah9VF6lmRpI2PJHaYvlNrYnuC0+nk+PHjFBUVUV5eTlVVFVqtlsjISEL1YTQWObA1qzn3ulHEJUXg7+/f4w/lHP4U1j6kFGO89Nluzb5pa7AgyzLBZ9hPvS8kBnpSi9nOP78r5OPdpSyclsI92UM7fKBwGe1YDjVgPlCPvbQNjV6LT3wgXqFaNIE+yJKMbHPhqDfjqDTibLKiHRqC39hIdKPCUXn1bN0CwT1qWq3MW7KbyCAt/7h+NGEB3VtK0mp28K9Nhby//TiXZUTz8CXDT+gQIEsyhu/LMfxQ/svSgk4Wn/y584BTknlnzrjTTqF3Ge20fVeGeW8tgecNUd5rgP1eWuwubnh7B8OiAnnxuqxuLalya2KgpqaGUaNGoVKp2rPCen3HU58XLlzIE0880eXATyU6Opq7776bP//5z+2vZWZmMnXqVP797393eZ+77rqLiooKnnnmGYKDg0lOTj7jGwu3XCDsZqXn8LZXIf5suPgvEJXRte/VHSWblVkC/hFw9esdjty4XWsl7HtfmT3h5QPjboOxc9w2MtdtTju2TWtp3KhFq96LfpIF1Vk3Ka2p3DDDw3KkiaaP8gmbmy6WFfQztrI2Gt49TMjM3uvr62y20vDuIXySgtFfm3ZGyYG+kBj4mSzJ1JcbOH6okeMHG2goNxCZFETiqDASR4URER94xokPWZJprjVTU9RKdWELVUWttDVYCIsNIDIxkJAoP0Ki/AgK1+Hr54W3r0aZcuuQsBjsGJqsGBqtNNeaaSgz0FhpQqVRER7nT1icP+ENXxBm3UnYba/iE3nqmhU2i5OmKhPVRS1UF7RQXdQKQPzIUBIyQokfGUaAvms3arIsU1payv79+8nLyyPYz4eR6hJSmzczZGg6mlEzlSVMIb8do8sp0VbTgqmqkrqqEkqqSilsasJb5WKc3sC4oEYC/LTgG6QsjYoYATGj3dqGrkPbXoUtf4e5nytLS36lqdrE6n/kMGxiFFNmDUWlVtHU1MRHH31EeHg411577W/OpDitYxtgxTzlvU+xxE+SZMpyG8ndUkVZbiMJGWGknxNLQnpo+xT93iZJEseOHePw4cMUFBTg4+PDsGHDSEhIID4+/oR2nrIks3NNMfnbqrjmobGEdWF0r0taK+HL3ys1ErKfVAoTnkFhT1mSOfh9BTvXFDPp6hRGX3hmdWMGemLgZ4crW/njpwexOSVeuDaTcYm/nYSRrE7spW3YK4y4Wm24DHZUGhUqb017AUPf5GAxO6CfOVpjYN6S3UxLC+fZmZmd6jbQWZUtFl7ecJQvD1Yzd3Ii91wwlBC/X8659goDTZ8cRaVRE3JV6mkLJ/9wtI5HVh5kUkoYL16XdcrOA5LdhXFLJYbNFfimBPfJFoTuVNtm5erXtzL/nGQWnnvqYtun4vZ2hY2Njfzwww8sX76c1tZWZs+e3eF2WVlZTJzo/vXyVVVVxMXF8cUXX5zQ9WD+/PkcPnyYXbt2dXmfu+66i0WLFjFy5Ehqamrw9fXlrbfe4oorrvjNeGw2Gzabrf3ztrY24uPj3XOBMDXC5hfhxyWQdT1c8CQEune9coesrfDN/8KhlcqygYl39P7IvcuhjHTtWaTcOKRfDRMWKIkSTyyxMNTCj0uwbMuhyXgHQaOaCbj2UlQ9UDzRlFNHy6pCIu7K6tIULKH3OZut1L2+n8DseAKnxp1+Bzdytdlo+uQYobOH/dT9onO6ezPbk+c+U6uNstxGSg83Up7XhMZbTVRyMFFJQYRE+REc8V8P87JS0d1isNPaYKG52kxdaRt1x9twuWSikoKIGRpMTGoI0SlB+Ha1M4RLornGTEO5gYZKE40VBhqKqrHYtWj9NOiCtfgF+eCjVc6VLqeExeDA1GrD3GpHF+RDdHIQsWkhxKaFED4kALU7q4Q3H8f+1Z84UlxGgf4Cikx+uCSZhIQEoqOjiYyMJDg4mICAADQaDSqVCovFgtFopL6+nqqqKkpKSrDZbKSlpTF27FhSUlK6P+reXTvegE3/B7d/rRS4/ZWWOjNfvHaAyMRALvzdSLy8NZjNZpYvX47D4eCGG24gOPgMq/DXHILFl8PVr8KoazvcxNxmJ397FblbqnA5JdLPiSV9aiyBPdiu63SMRiP79u3jxx9/RJZlRo8ezYgRI4iNjT3tCNPutSUc3lTBNQ+OJSyuF687xzbA+seVAZGz71SWFJ4m4WRosvLde3kYGkxcmG0kdmSk0jr3DHTn/Nej9309wOmSeGdLCf/8roDbz0niwYuGufXhUOi7dhQ1cucHe7n9nGQeuDCtxzrX5FW18fzXR9hf1sw9Fwzld1OS2h/qZaeEYWslho3l+KaFEHR+PD7xJy5vaTTa+Ps3x/g8p5I/X5XB7PG/XWjUZbRj3FGNaWc1mlAtIZcnu6VTU39wsKKFG97ayZLbJjAppWuzUt2eGPjZt99+S2trK9de2/FF80wUFBRQW1t7ym3Gjx+PVqvl8OHDZGZmsn379hPWET766KOsWrWKgoKCk/bt7D6rVq1i6tSpREZG4nK5ePzxx3njjTc4ePAgqakdZ2eefvpp/vKXv5z0ulsvEI1FSvGjoo3KVP7J9yqV/91NluHIl/DVIxAxDK56VakI7mkNBbB3MeR8pIx6TZgPmdd3uTL4GancB7vegtxVmELupKX2YkJvGokuo2dnMLR9V4Zpbw2R945F498/2qsMVpLdRf2bB/BJDEI/o3NrkPuC7iYGeuXch7JGvq6kjdrjysN+S52FtgYLNssv0/81Xmq0Ad4ER+gIidQRmRREZFIQobH+aHryBliSMH/6CKaiI5gv+DsmZyAOmwuVCtQaNbpAb/yCfNFH+aEN6KG/Y5dDqei/5e+QOVtJ5gZEIEkSNTU1lJWVUVNTQ319PW1tbRiNRn6+3Pv4+BAQEEB4eDgxMTEkJCSQmJjY81PJz9T3f4OcD2D+hg5rtlgMdr7810FUKhWX3pFBgF6L0+nkyy+/5MiRI8yYMaPzRZPbquHdC5V6N+c+csKXZEmm8lgzuVuqKD5QT1xaCBnnxpGUFd6zv2enIMsyZWVl7Nmzh/z8fJKSkpgwYQJpaWloNGeW0N/zZQmHN1Vy7R/HERTWcWuyHiG54Og6ZaZk2U5l6UjCZAhNUVoeq9QgOcBQQ/lRA+t3jSBZ9yPTdG/gE5UIU+5Tul+cge6c/3rr3OduR2sMPLAsBx8vNa/cMIaUCDHwMJCt3l/JY58e4i9XZ3D9hJ7vxASwtaCBv63Lp9lk59bJicwaO4ToYCVZ6mqzY9hcgWl3Nd6xAfiNjcSQEMCKvBre2VzMxORQnpqeTlL4ycVGXUY7toIWzAfqsRY045saQuA5cfimhfSvFu9u8OHOUl75toCv7j+nS50Keiwx4E7PPfccX3311Sm3Wb58OXFxcRw9epQRI0awceNGLrjggvav33fffWzcuJHc3NyT9u3KPqCs4QwLC+PPf/4zDz30UIfb9GrmuHQHbPgTtFUpN3+jb3TfSH5zKax7FMp3wyV/VXpK97U/NrtJWZu4+x1oKoExNym1CNy9xMH1U4Xtnf+GujwYczMG9S207TArU/xTQ9z7fh2QJZnGj/KRbS7CbxvV6bVZQu+SJZmmj/ORzE7C54/q8T7R7tSXZwx0hizLuByS0ubPk+sJJQm+fEhptfe7taecsu92DYXw2R3gtMJV/4T4CZ3aTZIkZFk+4wdHj5Fl+OIBKN+lzBzQnbzMymF3sWX5MUr2N3DhvJEk/VT48+DBg6xdu5b09HQuuuiiU7eltJtgyeUQmQEz/tV+DbQY7OTvqCZvSxVWi43oLB98I600NNdiNBoxm80AeHl54e/vT2hoKBERESQmJhIdHd0jsy5sNhuHDh1iz549tLa2MmbMGMaPH094eNcLP8qyzOb/HKOyoIVrHzmry7NrusVYBwXfKO1Km4rBqAwaySoN+9suZXfpBM6b0sSIc1OUJZY+XetYMJhmDPw3q8PFS+uP8p/dZTw5PZ0bJ8QPugergU6WZd7eXMxrGwt57eaxXDC8dwtaS5LMusM1LNtTxo6iRjJigxiboCc1MgA/bw0qqxNVXhPhFSYSbDINPioCEoKJTghS2nxrVMgOCcnkwNlowVFjwllvwTvaH11WOH5ZEXj1ZuKyj5Flmd9/coDKFgsfLzgbrzO87+wXiYEzYTabCQwM5P333+fWW3/JEM+aNQuLxcK6devcss/PUlNTmTlzZqeLLPb4WjNJgtzP4Nu/gC4YLv6r0qaoqyd2axvsfFNZyzlqllLwsIfacLmNLEPlj7DnXTj8mbL+86y5SieH7kztbyxSRqX2/0fpszzxThh7C23bWjFuqyT89lH4DAk8/fdxE8nmpO6NA2iH6wm5MqXX3lfovLZvSzHtqyPynjH9bmZHX6ox0O9JEnz1Byj8Fuat7fnOKrKszKLa8JQysp391Cl7ww8ILid8Mkep1D9nFXh3fGN4dGc1m5YdI3FUGFOvHUqAXktzczMbNmyguLiYKVOmMG7cuJMTBJJLaUdpM8CtnyGpvKg42szhraUcyy/BJ9KC7Gekqa0erVbbvl4/ODgYnU6HSqXC4XBgMploampqn60BkJCQQEpKCkOHDiU8vOMe4J0hyzKVlZXs37+fQ4cOodfrmThxIqNGjep6LYVfkVwS6/59CIfNxVX3jTltEcze4HS4+P7DI1Qeaebyu7KISu5b56v+eO7bUlDPw58cYHR8CM/Pyux2MTqhb3BJMn9dm8fag9UsmTeBzCGenWJf22ZlZ3Ej+0qbKW0yY7G7UKtUpET4Mzw6kEsSwwhusWOvVOpaSCYHSDJ4qVHrvJTaFpF++CYFofZEorKPMtudzHhjGxeMiOTxy8+sRe+ASwwATJs2jZiYGD755BMATCYTMTExPP300/z+978HoLCwEIPBwNixYzu1jyzLWK1WdLpfbjYKCgoYOXIk7777LvPmzetUbL12gXBYYfdbsOVl0CfDpP9R1uH/xs3SyYFWKX2Zd/5LKSR10dNKL+T+xtQI+z+EA8uhsQBSL4SR05VuDiGJp06YyLKSDChYD/lroXIvDL8cxs5V2gyqNUo/1B/KiViYhXe0+3spn46jwULd6/vRz0gVbQz7GPOhBppXHiPy7tEe+d3oLpEYcDNZVmZd5a+FOZ91uB7eLYx1sPpeZR38zDeVxPBgYTfD0muUNejXL/3NGXOmFhvbPyuk+EADIyZFk3neEEJj/SkqKmLbtm2UlpaSlpZGUlISsbGx+Pv747PtZUyFuyjLeo6Co3VUVVVj17TiUJvQB+tJSkkiISGBhIQEQkNDO/VwL0kStbW1lJSUUFRURGlpKX5+fgwdOpTU1FRSUlJOuOfoiCzL1NTUUFBQwKFDh9o7UIwdO5a4uLgeGe112Fysenkf+hg/LpqX7tERZZvFybo3D+KwS1xxd+Zvt3o8Q4M9MQDQbLLz+GeH2FfWzN+vH8M5aT3TXlfoHWa7kweX7aew3sj7t008oUuAMPAU1Rt5ctVhltw24ZRFGn9tQCYGNm3axMUXX8zDDz/M5MmTee211ygpKWH//v3towALFixg586dHD58uFP72O12xowZw4IFC8jIyKCsrIznnnuOiIgItmzZgq9v5y5GvX6BsBnhwH+UdfBtVTDsUuVGMXassj7v52l2lmalN3LpdqU1YPEmSJ6m1CtIze57ywa6oqEA8lYraxWr9yvdFCKGQ2gq6ELAS6dMuTU3Kv8W1QfAboSkacpsg1GzTui/bdxRRev6UiLuyMSnN4sx/YrlSBNNHx8h8p7ReEf1vwfQgcheZaT+3wcJvWF4j7cl7CkiMdADZFkplLfzDbhpGSROce/3z/9CmVKfcj5c+XKHU+oHPHMTLL5UWYN+1aunvHbVlbZx8PsKCvfWERShY8iwEMKGBGDHRGVdCdW1lTS21GOzW5GRQVajkb0JCtCTkBTH8IxUEhITTr384Aw4HA5KS0spKiqiqKiI+vp6IiMjiYiIQK/X4+vri5eXFzabDbPZTH19PTU1NTidTlJSUhg5ciQjR4502+yAUzG12lj5wl7Sp8Yy4crTt2rsqRi+eO0A/sE+XLYwE29f9y19EYkBhSzLLN9TzjNr87h1UiJ/uGQ4PgOs1dtgUN1qYcH7ewnw9eLft45D79/z5wihfxqQiQGAbdu28cYbb1BbW0tmZiaPPfYY0dG/9JN+4YUXyM3NZenSpZ3ep7q6mtdee42cnBz0ej3Tpk1jwYIFeHt3fvqKxy4Qsgy1h5UH47KdULUf7AZQaX4p3KMNhvhJymh6xszeXQvb2+wmZY1iQwE0lyhLJpxW0PgoD//BQyA6S1mj2MEsC9OeGlrWFhM+fxS+CZ6/0LeuP44lt4HIe8aiduPNkXDmXEY7da/vx39iNEHZPTxlvAeJxEAP+vE9+PpxZWnWhAXdT7xa2+Drx+DIWrjy75B5nVvC7LdaK2DRpZA1W5ntdhpWk4OqYy1UHGumtdaM2WDHYXPho/XClxZCmr4ldOqVDJk8jpAov14bIW9ra6OyspKGhgZaWlqw2Ww4HA60Wi06nY7w8HCio6OJjo72SEHIxkojn774IxfcOoK08b3QEem/tNabWfPqfqJTg8meO9LtxR1FYuBERfVG7v9PDgD/vGksqaIwYb+xtaCBhz7ZT/bwSP46Y5RI7AinNGATA31Vn7lASBJYW8DWBrIE/pG9U8V/ADDvr6P5swLC52XgmxLi6XAAkF0yDYsOoQ70IfTG4aJYkIfITon6dw+hCfIh9KYR/frnIBIDPax0B6yYpyRir3ixa7VbZBlyV8H6PymdYq75FwT3bjvMPquhABZfBmffBec9cvrtO1K8Cf5zE8x6C0Ze5d74BojjBxtYvyiXGQ+NJSqpd/6uG6uMrHl1P2njoph63VBUavefZ0Vi4GQ2p4uXNxzjo52lPDU9nRtEYcI+zWJ38cq3x/jgp5+XKCQpdEZnz1d9rDeR0G1qtXIj2kOFBGVZxlFlwlbSiqvFBrKMOsAHn7gAfJODUfWBgkVdYT7UQPOnBYTNSe8zSQEAlUZF6E0jqP1nDqad1QRMjvV0SIOOLMu0rClCtrvQXzdMXICFU0ucDHduhjX3wevj4ZL/B1k3dL6TTOl2+P45qD/yy77id+4X4WkwdzV8MENZEnbR02f271O6HZbdoizJEEmB35SUFc7ZVyXz1b8Oct1j4wkM7dkil3WlbXzxzwNkXjCECVcmifNsL/L10vDEFSOZlhbOw58c4Iej9Tx/bSYhfmJaeldZHS7qDTasDhcOl4zWW02Arxeh/j5nXE3+Zy5J5vOcSl7acJTIIC1r7j2HoZFi4E9wLzFjwE0GSub4t0hWJ8ZtVZh+rEUyOvBNCcYrVAtqFa42G/YyA5LZif+EKALPHYLGTYWCeoPlSBNNH+UTetMIdOl9c924raSVhsWHiViYhU9873VIEMC4vYq2jWVE3jsWr5D+83v9W8SMgV4iy0ptgK8fB423MsKdfg0ExZy8rakRjnwBB5ZBbS5MXKj0aNeF9HrY/UZDoVKQMOU8uOIl8OlEwa2DK+CL++Gy52Hc73o+xn5OlmV++PAIdWUGZj58Fj7anhlLqipo4cs3DjBhejJjLurZZVpixsCpNZnsPLryIIcrW/nHDWOYnNo374n6CkmSyatu40BFC/nVbeRXGyisM9JqcaBWgdZbg7dGjdXhwuaU0KhVxIZoidf7kRjmT2qEP6mRAQyNCCA2RIfmV7NkzHYneVVtfJtfx6qcCrw1ah65dDhXZcWi7oEZNcLAJZYS9LKBeIEApV+7cXsVho1leEX6EXjuELRp+pNmBsiyjL3cgGFTBdajTQSeE0fQhQmozqBipidYC5pp/CAP/XXD8MuK8HQ4p2TYXIFxexWR943tdy3y+itrYTON7+cRviAT38SB8XctEgO9zOVQasDsfgcqdistDcPSlBonTqsyNb6lDOLOUmrAjLlFJAQ6q7USPp2vFCa8bhFEZ3a8ncMK3z+r1ICYvQSGXtSrYfZnLqfEF6/tx0frxeV3Zrp9en9ZbiPr3j7MOdcNJWNazy+XEYmB05NlmY92lfHcV/ncMCGeP1wyHH9fMcEYlETAkRoDO4sb2VHcyO6SJlySzOj4YNJjghgZE8SwqECig7WE+vmc8PDucEnUtFopbzZT3mSmpMFMcb2RonojpY1mVCrQ+/kQ4ueNS5Kx2F1Ut1kJ8/dlUkoo140bwjlDw7s840AY3ERioJcNxAuEo95M84pjSGYnIVel4DtM36npffYqI82fFSBbXehnD+uzD1S2klYaluQSMiMV/7N6t8BSV8iyTOMH+eCSCPtdRo+svxR+4Wy0UPv6fkKuTMZ/fPTpd+gnRGLAg6xtUL4bWsuUh1WNN4QNhch0COz756A+yeWEzS/C1n8oiZWxt0DcOKUbTctxpVvNjn8p/74z3lQ61ghnxGpysPKFvSRkhDHt+jS3TfMvyqnj2yV5XDBnBMMm9M45ViQGOq+43shjnx6iqtXC32ZlMi2tbw+e9ARJkimoM7KjqIEdxY3sKmnC7pSYkBTK5NQwJqWEMSo2qNsP6w6XRGWzhSaznVazA41ahc5HQ0KoH1FBPbuMRxgcRGKglw20C4RpXy0tnxfiPzGGoEsSUfuc2ci/LMkYt1TS9m0pQZcmETA1tk+tGbSVtdGw6DDBVyQTcHYHU3v7KMnipPb1HPzHRfXryvh9nWR2UPfmAbTDQwmZnuLpcNxKJAaEAamxCHa+CflrwFirvKbSKK0jx98G6TM6X+dBOElbg4VVL+8jbXwUk2eldvt6fmBjOTtXF3PJ7ekkj+69B06RGDgzkiTz0e4yXlh3hMtHRfOnK0cO6NoDP0/dP1jRyt7SJnYWN2GxuxifpG9PBGTGBeMtRu2FfkYkBnrZQLlAyE6JlrXFmA/UE3bjcLTDu1fE0FbaRuNH+fgmB6OfldYnWu7Zyw3ULzpE8MWJBEztf5W+7VVG6v99gLC56WiHDsJ+5j1MdkrULzqMWudF2K0jB9zMDJEYEAY0WQZzIzgsEBAFXgP3Iaa3tdSaWfXyPoafHc3kmaldOje6XBLbVhZSuLeWK+7OIjoluAci/W0iMdA1lS0Wnlx1iJzyFu7PTuPWSYm93h5PlmXarE7qDTYsdhcuWcYlyahU4Oul/ulD88t/vdX4aNQnrcV3uiSazHbqDTZKG82UNJgoqjeSW9lGQZ2BUH9fRg8JZmxCCJNTw8iMCxGtAIV+TyQGetlAuEA4W200fZSP7JQIuzVdKS7oBi6Dnab/HMFldBA2Nx3vcJ1bvm9X2CsM1L97mKCLEgg8p/8lBX5m2lND69fHibp/bL8q9NjXybJM8yfHcNSbiViYdcYzZfoDkRgQBKGrWmrNfPH6ASKGBHDhbel4n8E5sq3BwoZFuThsLq78nyyCPHAvIBIDXSfLMj8cree5r/JxSjKPXjqcSzOie6wIXmWLhW2FDewuaeJojYGieiNmuwsfL6XCv1qlQqNWcoF2l4TNIWFzupB+9VTjrVG1JwyckkyrxQFAoNaLpDB/ksP9SQr3Jz0miNHxwUQHafvUDFdBcAeRGOhl/f0CYS1qoek/R9AOD0U/I9XtRQNll0zr1yWY9tQQeuMIdCN6pp3iqdgrDNQvOkxQdgKBvVDkqKc1rTiGs8FCxB2ZqEQ22y1avynF/GMtkfeMQRM4MEcaRWJAEITusBjtrPv3IRw2FxfNSycs7tQt01wuifytVexcXczQ8VGcc91QvDyUdBWJge5zuiSW7y3nn98VEKj15s5zU5ieFYuumz/TZpOdHcWNbCtsYHtRI2VNZrKGBDMlNYz0mGCGRgYQE6Il0NfrlA/uTpeEzSlhdyr/tTld7f+vUkGYvy8hft5o+3hxbEFwJ5EY6GX99QIhSzKGzRUYvisjeHoK/hOjezRTat5fR/NnBQSeH0/gBfG9lpW1FrbQ+EEeQRclDoikAIBkd1H/1kG8I/3Qzx424Ka89zbD5goMP5QTsTAL72h/T4fTY0RiQBCE7nI5JfasLWH/d+WMmBRNVnY8oTEnnjcddhfFOfX8uO44sgxTrxtKUma4hyJWiMSA+9icLj7PqeTdLSXUtFqZPjqWS9KjmJQS1qkkQaPRxo+lzew53sSO4kbyqtpIiwxkytAwpqaGc3ZKKIFa0YFJENxBJAZ6WVcuELIkgwqPTVmSLE6aPjmKo8ZE2C0j8RkS2Cvva68y0vhBHj6xAehnD0PdQ72Rf2Y+UE/zymOEzBiK/7iBVfnbZbBT9+YBdJnhhFye7Olw+i3jzipavz5OxILMXvs78BSRGBAEwV2aa0zsXXecwh/rCNBrCY3xR+OlwtRio77MSFC4lqzseEZOjUHTBwq2icSA+8myzP7yFlblVPL90Tpq22yMiA4kLTKQOL2OQF8vvDUqTHYXzSY7xxvNFNUbOd5oYmhEAOOTQpmUEsqU1HAiAsXSSEHoCSIx0Mu6coGw5DXSuv44gdPi8BsT2avTwa1FLTSvOIZ3lB+hNwxH7de7WVmXyUHT8qM468yE3jgc3yT3FyCSXTKtG45j2llN6E2eWb7QGxwNFurf3E/AOXEEXdA7nQpkScbZZMVZb0ayOJHtEmpfDSo/L7zDdWj02n4zg8GwqYK2jWWE3z6qz7bWdCeRGBAEwd3sVifVRa201plxOWX8gnyISgoiOFLXp9Zri8RAz5JlmdJGM4erWjlWa6S21YrR5sTukgjw9SJY501imB/J4f6MHhKC3n9gLtkThL6ms+ernh2qFU5Jm6ZHMjkwbKqgdX0pAVNjCZgY3aMP6ZLVSds3pZj21BB8eTL+k2I8ctHW+HsTPi8D444qGhYdxn9iNEEXJ7pt9oCzyUrzp8dwtdmJvHcM3hF+bvm+fZF3uI7w+Zk0LDqM7JAIujixR36mLpMDa24jlrxGbCWtyE4Jr3Adaj8v1D4aJJsLyeTA2WRFpVHhkxCEdpge7TA9XlF+fermEJTkRuvXJZj31RGxMAuf06yTFQRBEDrmo/UiMSMMMsI8HYrgQSqViqSfivkJgtD/iMSAB6m81fhPiMZvXBTWo00YNldi2FiG/4RoAqbGua0rACgPQeb9dbSuK8E7wo/I+8Z6/GFZpVYRODUObZqeltWF1Ly8l+BLkvAb2/XZE7JLwrSzmtb1pfiNjiBsTnqPL1XoC3xiA4hYmEn9u4eQzE5CrkpB5aZpm44aE4atlZj31+MT648uI4ygSxLxjvLr8D1kp4SzwYKtqAXrsWbavilF7eeNblQYulHh+CQGeXw2gcvkoPmTozgaLETeNRovD3bKEARBEARBEARPE0sJ3MRdU8rs5QYMWyqw5DaiGxVOwKSYbj1IyQ4J88F6DD+UIzskgi9PRpcV3vdGb2UZy8EG2r4tRbZLBJwTh9+YiE5XhpfsLiz762n7oRyVWkXIjFS0Q/U9HHXf42yy0vhBHipfDWG3jOxyZX1ZkrEebcK4rQp7aRt+YyMJmBLbpaJ8skPCWtyC5VAD1rxG0KjQZYSjGxWGb3IIKk3v/i62L6OJDSB09jDUuoGfOPpvYimBIAiDlVhKIAjCYCRqDPQyd18gnE1WjNsqMefUofLRoMsMRztMj29SMCrvU48ES3YX9tI2LLmNmA/Uo/H3JvC8Id0aie8tsiRjOdyAcUc19tI2fJOD8E0JwSchEI1eiybQG1Ah2104m604qk3KyHR+E5pQLUHnx6MbHeHxEWlPkuwuWj4rwHqsmaDLkvAfH93pfw/J6sS8rw7j9iokm4uAKTH4T4xB4++e5S2yS8ZW0oLlcCOW3AZwyWjTlZkE2qEhPfr76Wy10bquBGt+E8GXJOI/JbbPJch6g0gMCIIwWInEgCAIg5FIDPSynrpAyE4J67FmZV13QTMugwPvSB1ekX5oAn1Q67yQJRnZKeFqseFstOKoMaEJ9EE7TI/fWZHKjIN++ADkbLFhzWvEVtqGvdyAq9UGrl9+XdX+XnjHBOCTEIguMwLv6L63jt1TZFnGmt9EyxdFqLVe+E+KwW90RIfLKmSHC1txK+aDDVgO1uMV5Ufg1Dh0meE9+qAuSzL2sjYshxqwHG5EsjrRpoXgkxSMb1IQ3jH+3V4OIcsyjkojxu1VmA/Wo8sIJ+SKZDTBg7fysUgMCIIwWInEgCAIg5FIDPSy3rhAyLKMq9mGo9qEo96MZHQgWZzKaLCXCk2wL15hOnxi/dGEagfcQ7Isy8gWJwAqHw1oVAPuGN1Ndrgw/ViLaU8tjloTPnGBaIKVhJJkceJqsWGvMqEJ8EY7MhT/CdH4xPZ+ET5ZlnFUGLEWtmAvbcN2vA3Z6cI7wg/vKD+8ovzw0mvRBPkq8ft7o/LWnLAMQZZkJJMDV6vyN2KvMGA90oxkdeI3JoKAc+I8XlejLxCJAUEQBiuRGBAEYTASXQkGIJVKhVeoFq9QLToGX+VflUqFqpfbKvZ3Km8NAZNiCZgUi6PejL3MgGS0I1mcaPRadBlheMcE4BXh2ZZSKpUKn/hAfOIDgZ/aITZacNaacdSacdSYsR5pxtVqw9VmB0n+6fjUoFbBT7NmkEHt54VXlD8+sf7oZw3FN7VnlygIgiAIgiAIQn8nEgOCMEh4R/j1mxFzlVrVHq9u1IlfkyUZ2e5CtruQbC5leYlahcpbjSbA57Q1OARBEARBEARBOJFIDAiC0K+o1CpUWi/QeqHxdDCCIAiCIAiCMACIoTVBEARBEARBEARBGMREYkAQBEEQBEEQBEEQBjGRGBAEQRAEQRAEQRCEQUwkBgRBEARBEARBEARhEBPFB91ElpX2aW1tbR6ORBAE4bf9fI76+ZzVXeLcJwhCf+HO85849wmC0F909twnEgNuYjAYAIiPj/dwJIIgCKdnMBgIDg52y/cBce4TBKH/cMf5T5z7BEHob0537lPJ7ho2GuQkSaKqqorAwEBUKlWn9mlrayM+Pp7y8nKCgoJ6OMLeNVCPbaAeFwzcYxuoxwVdOzZZljEYDMTGxqJWd381WVfOfTBwfy4D9bhg4B7bQD0uGLjH1tXjcuf5T5z7TjZQj00cV/8zUI+tp899YsaAm6jVaoYMGdKlfYOCggbUL+1/G6jHNlCPCwbusQ3U44IzPzZ3zBT4WXfOfTBwfy4D9bhg4B7bQD0uGLjH1pXjctf5T5z7fttAPTZxXP3PQD22njr3ieKDgiAIgiAIgiAIgjCIicSAIAiCIAiCIAiCIAxiIjHgQb6+vvz5z3/G19fX06G43UA9toF6XDBwj22gHhf072Prz7GfykA9Lhi4xzZQjwsG7rH15+Pqz7GfzkA9NnFc/c9APbaePi5RfFAQBEEQBEEQBEEQBjExY0AQBEEQBEEQBEEQBjGRGBAEQRAEQRAEQRCEQUwkBgRBEARBEARBEARhEPPydACDWUFBAQaDgfT0dLRarafDcRur1cq+ffuIjY0lKSnJ0+G4jcVi4dixY4SGhhIfH+/pcNyqvr6e8vJyEhISCA8P93Q4bldSUkJlZSWZmZlu62HtKVVVVRQXF5/wmkqlYurUqR6K6Mw1NzdTWFhIXFwcsbGxng7HrfLy8mhpaWHKlCmeDsWtSkpKMJvNpKSkoNPpPB2O29jtdo4cOYK/vz9JSUloNBpPh+RWVquVvXv3Eh4ezogRIzwdTrdt3br1pNeGDh1KdHS0B6I5c5IkkZubiyzLZGRkDKjft5aWFg4fPkxaWhpRUVGeDsdt2traKCoqIi4ujsjISE+H41ZlZWU0NzeTnJxMUFCQp8Nxu9zcXJqbmzn77LPx9vb2dDjdUlRURHV19Qmv+fv7M3bsWPe+kSz0utraWnnSpElySEiIPHToUFmv18urV6/2dFjdVl9fL//+97+XY2JiZJ1OJz/88MOeDsktGhsb5YULF8ohISHy6NGj5fDwcHncuHFyfn6+p0PrtgMHDsgXXHCBHBsbK48dO1bW6XTyddddJ5tMJk+H5jbV1dVydHS0DMjffPONp8Pptn/84x+yn5+fPHXq1PaP8847z9Nhddqzzz4r+/r6yunp6bJWq5XnzJkjOxwOT4fVbR999JE8YcIEWa/Xy76+vp4Ox20+/PBDeejQoXJSUpKcnp4uBwUFya+++qqnw+o2u90uP/bYY3J4eLg8ZswYOSYmRk5KSpK/++47T4fmVnfccYesVqvla6+91tOhdJvD4ZABedSoUSec/z7//HNPh9YpBw8elFNTU+WYmBg5Li5OTkxMlPft2+fpsLqtoKBAvv322+WYmBhZpVLJ77zzjqdDcouCggJ55syZckhIiDx27Fg5ICBAvuKKK+TGxkZPh9ZtGzZskDMzM+XU1FR51KhRsk6nkx966CFZkiRPh+Y2e/fulbVarQzI1dXVng6n2+688045LCzshHPfnDlz3P4+YimBB9x55504nU4qKyspKCjg0Ucf5aabbqKmpsbToXVLaWkpsbGxHDp0iGHDhnk6HLeprKxk3Lhx1NbWsn//fsrLy4mOjub666/3dGjdVlJSwvPPP09lZSX79u3j2LFjbNq0if/7v//zdGhuIUkSc+bM4Xe/+52nQ3Gr5ORktm7d2v7xww8/eDqkTlm/fj3/+7//y9dff01ubi65ubl8+eWX/P3vf/d0aN125MgRXnvttQHzt/OziooK1q9fT0lJCbm5ubz33ns88MADbNq0ydOhdYvFYiEmJoby8nJycnKoqKjgsssu44YbbkAeIM2aVqxYwd69e7nwwgs9HYpbvfbaayec/6655hpPh3RakiRx/fXXM378eCorK6moqGDatGlcd911OJ1OT4fXLUePHmXKlCkUFhbi4+Pj6XDcpqioiDlz5tDU1MS+ffs4fvw4x48f59577/V0aN1WUVHBqlWrKCws5NChQ2zevJlXX32VTz/91NOhuYXBYOCmm27ivvvu83QobnX++eefcO5bunSp299DJAZ6WUNDA2vWrOEPf/gDfn5+ADz44INoNBqWLVvm4ei6Z9y4cTz88MOEhYV5OhS3yszMZOHChe0XPK1Wy2233cahQ4doa2vzcHTdc8011zBx4sT2z4cMGUJaWhqVlZUejMp9nn/+eby8vAbEhfy/uVwuDh48SH5+Pg6Hw9PhdNrixYuZNm0a559/PgApKSncfPPNLF682LOBucEzzzzD2Wef7ekw3O6Pf/wjKSkp7Z/PnDmT6Ohotm3b5sGoui8oKIj777+/fRmfWq3m3HPPpampCavV6uHouq+kpIQHHniAjz76aEA9rIGynOrHH3+kqanJ06F02rZt2zhy5AhPPfUUKpUKgKeeeori4uJ+k9j9LVdeeSXz589vv6cdKC699FJmzpzZ/vMKCwvj+uuv73A5S39z2223kZqa2v75uHHjCAoKGjD3fnfddRfXXHMN2dnZng7FrX5eql1UVIQkST3yHqLGQC87ePAgkiQxbty49te0Wi2ZmZnk5OR4MDLhTOzZs4eIiIgBsSZLkiS2b9+O1Wpl48aNlJSU8NZbb3k6rG7bsWMHr7/+Ojk5Of3q4bkzjh49yo033ojRaKStrY0XX3yRO+64w9NhnVZOTg5XX331Ca9NnDiRN954A7PZPOBuLAei0tJS6uvrGTp0qKdDcYuCggJqamo4fvw4zzzzDH/605/6fQ0Fp9PJTTfdxJNPPsnIkSM9HY7b3X///cTGxnL06FGmT5/O22+/3ecHJHJycvD19SUjI6P9tWHDhhEUFEROTg4XXXSRB6MTOmvPnj0D5txnMBg4cOAARqORjz/+mNjYWG655RZPh9VtS5YsIS8vjyVLlrBx40ZPh+NW69evp6ysjJqaGnx9fXnrrbe44oor3PoeIjHQy37OcP/6IhYWFtavst+D2a5du3jllVd48cUXPR2KW9hsNh577DGMRiMFBQXcc889/X4pSEtLCzfffDNvvfUWUVFRVFRUeDokt8nKyuLYsWPtNyfvvPMOd955J6mpqX0+O97U1NThuU+WZZqbm0VioI9zOBzMmzeP9PR0ZsyY4elw3GLFihV88cUXFBcXk5iYyHXXXefpkLrtT3/6E+Hh4fzP//yPp0NxK5VKxaJFi7jttttQqVSUlpZy8cUXs3Dhwj4/Bbqjcx+Ie7/+5MMPP2TdunVs2LDB06G4RXl5OY899hhNTU1UVFTw3HPP9fvi00ePHuXRRx9l06ZNA26m1KWXXsozzzxDZGQkLpeLxx9/nNmzZ3Pw4METZn90l1hK0Mt+ror566mKFotlwP0SD0S5ublMnz6defPmDZi1Szqdjq1bt7J//36OHDnCihUrePjhhz0dVrc8+uijJCYmotfr2bp1K3v27AHg8OHD5Obmeji67snOzj5hxOKOO+7grLPOYvny5R6MqnO8vb07PPcB4vzXx7lcLubMmUNhYSGrV68eMD+vJ554gh07dlBVVdW+zKW5udnTYXXZ3r17efXVV7n99tvb16E2NzfT2NjI1q1bsdlsng6xyzQaDbfffnv71O7ExESeeOIJVq9e3eeXf3R07gNx79dfrFu3jvnz5/PKK68MmJod6enpbN26lby8PL777jsee+yxfj9b9LbbbuOqq66iqamJrVu3tt/v7d69m+PHj3s2uG6aOXNme1cMjUbD3/72N7y9vVmzZo1b30fMGOhliYmJgFLQLiYmpv31yspKRo0a5amwhE7Iy8sjOzubmTNn8uabb3o6nB4RHx/PjTfeyIoVKzwdSrcEBQXhdDp57LHHAKUlGcCiRYuoqKjgpZde8mR4bhcVFdUv1gYmJiaeFGdlZSV+fn59firwYOZyuZg7d257ocvk5GRPh+R2Go2G3//+9/z9739n165dXHbZZZ4OqUssFgvjx48/oaBnfn4+arWaxx57jJUrV/ab1n6dERUVhcvloqampk+3R05MTKS5ufmEJVM2m43GxkYSEhI8HJ1wKl9//TWzZs3i+eefHzADQr82YcIELrjgAtatW8edd97p6XC6LDo6mmPHjrXf+7W0tADw7LPPMnfuXO655x4PRudeGo2GsLAwt9/7icRAL8vMzCQqKoo1a9Ywfvx4AI4dO0Z+fv6Ae1gZSPLz88nOzubqq6/mrbfeah+x6O9MJhP+/v4nvFZYWNjvH9J+/bdUUVFBfHw8//jHP/r9Ws5f/8xaW1vZvXs38+fP92BUnXPxxRezZMkSHA5H++yp1atXc+GFF6JWiwlsfZEkScybN49Nmzbx/fffD5j1tb917oOTl/r1J9OmTTupONr06dPRarWsXLnSQ1G5R0c/sw0bNhASEsKQIUM8FFXnZGdno1arWbt2bXtHo6+++gqn0zlgRqAHog0bNjBz5kyeffZZHnroIU+H4za//luSJImSkpJ+X0D3s88+O+Hzr7/+mssvv5zVq1f364SoLMtYrdYT6t8UFBRQWlrq9kFlkRjoZRqNhueee467774bvV5PQkICf/nLXzjvvPO4/PLLPR1etzidTnbu3AkoJ53Kykq2bt1KYGAgo0eP9nB0XVdaWkp2djaJiYnMnTv3hGrc48aN69eFqq6//nrOOusszj77bGRZZu3atXz++eesWrXK06EJv+GKK67gwgsvZPz48bS0tPDyyy/j5+fHgw8+6OnQTuuBBx5g8eLFzJ49m/nz57Nhwwa2b9/e7yvcg7K2sb6+nsLCQmRZbn84Gz16NIGBgR6OruvuuusuPvnkE9566y1qa2upra0FIDY29oRuBf3N2rVr+eCDD5g9ezZxcXHk5+fzwgsvMH36dCZMmODp8IQOfPTRR6xfv56ZM2cSFhbG+vXreeONN3j99dfx8urbt7OxsbHcf//93HPPPZjNZjQaDY888gh33313n57p0BltbW0cPHgQUB5gCgsL2bp1K5GRkf26XtG2bduYMWMGV199NRMnTmw/p6tUKqZOnerh6Lpn0qRJzJ07l8zMTEwmE++99x7l5eX9YkniYORwOBg3bhwLFiwgIyODsrIynnvuOc466yxuuukmt76XSh4oDXv7mc8//5ylS5diMBiYOnUqjzzyyEmZ8P6mtbWVK6+88qTXR4wYwbvvvuuBiNxjy5YtPP744x1+7eOPP+7X0wDNZjNvvfUWmzZtwuVyMWzYMO68885+fTHvSH19PTNnzuSVV15pn6nTX7W1tfHGG2+wfft2fH19GTduHPfee2+/efgsKyvjhRde4MiRI8TFxfHAAw+c0KWlv3r66af59ttvT3r97bffJj093QMRucesWbOoq6s76fVrr72234+gbdq0iQ8++IDS0lJiY2O54oormD179oCbvfLHP/4RHx8f/vrXv3o6lG5bt24dy5cvp6amhpSUFObPn99vzh+SJPH222+zZs0aZFnmyiuv5O6770aj0Xg6tG45dOgQd99990mvX3rppTz11FMeiMg9li5dyttvv33S615eXv2+xWRDQwOvvfYae/bsQavVkpWVxd13301UVJSnQ3OrXbt28fDDD7NmzRpCQ0M9HU63VFdX89prr5GTk4Ner2fatGksWLCgffalu4jEgCAIgiAIgiAIgiAMYgMrLS4IgiAIgiAIgiAIwhkRiQFBEARBEARBEARBGMREYkAQBEEQBEEQBEEQBjGRGBAEQRAEQRAEQRCEQUwkBgRBEARBEARBEARhEBOJAUEQBEEQBEEQBEEYxERiQBAEQRAEQRAEQRAGMZEYEIQ+6MiRI+zcufOM9ikuLmbz5s09FJEgCELPczqdfPLJJzgcjjPab+XKlZhMph6KShAEoeft2rWL/Pz8M9onJyeHAwcO9FBEwmAjEgOC0Mc4nU5mzZpFS0vLSV/btm0by5cvx+VynfS1gIAAZs2aRXFxcS9EKQiC4H5vvPEGS5cuxdvb+4TX6+rqWLZsGUeOHOlwvy+//JJnn322N0IUBEFwu7q6Oq666ip8fX1P+tpXX33Fl19+2eF+drudq666CrPZ3NMhCoOASpZl2dNBCILwi3fffZc333yTH3/88YTXHQ4HcXFx1NfXs3btWq688sqT9r3//vtpbW3l/fff761wBUEQ3MJsNhMfH8/atWuZPHnyCV978sknefbZZ7nssstYt27dSfsePXqUMWPGUFZWRkRERG+FLAiC4BYPPvggzc3NJ92/lZWVkZycjCzLFBUVkZycfNK+2dnZXH755TzyyCO9Fa4wQIkZA4LQC8rKyli1ahWSJLF9+3ZWrFiB0WjscNvXX3+defPmnfT66tWrAZg3bx7vvvtuh/vOmTOH5cuX09jY6LbYBUEQumPVqlWUlZVRXl7O6tWrycnJ6XC7jz/+mPDw8JOSAi6Xi/fee49HHnmEDRs2UF5eftK+w4cPJysri0WLFvXIMQiCIJypQ4cOsXHjRqxWKxs3bmTlypUdbmc2m1myZEmH936LFy9m0qRJTJ48mcWLF3e4/5w5c/jXv/7lztCFQUokBgShF2zfvp25c+eSnZ3Nww8/zKefftrhetiKigoOHDhAdnb2SV979913+d3vfsd9993H2rVrqa2tPWmbcePGodVq+eabb3rkOARBEM7UHXfcwR133MG0adN47733OHToUIfbrV27tsNz37p16zCbzTzzzDNMnDjxN2+Os7OzWbt2rVtjFwRB6Krly5dz5513MmHCBJ599lnWrFnT4XabN2/GZrMxZcqUE16XJIklS5awcOFCFi5cyHvvvdfhUtLs7GyOHz/O4cOHe+Q4hMFDJAYEoZcYjUamT5/Ojh07WLZsGVFRUSdts2/fPlQqFSNGjDjh9fLycr799lsWLFjAWWedRVZWVofLBdRqNenp6ezZs6fHjkMQBOFMVVVVcejQIVatWsXcuXM73Gbfvn2kp6ef9PqiRYu49dZb0Wq1LFy4kCVLliBJ0knbZWZmsnfvXrfHLgiC0FWFhYW8+OKLfPfddyxdurTDbfbt20dqaupJ9QW++eYbWltbmT17Ntdffz1Go5H169eftH9iYiKBgYHi3k/oNpEYEIReolKpuPfee0+5TUNDA0FBQWg0mhNeX7x4Meeccw7Dhw8HYOHChb85ZVav19PQ0OCeoAVBENzgtttuIzAw8JTbNDQ0oNfrT3ittraWL7/8kjvuuAOAG264gZaWFr799tuT9tfr9dhsNgwGg/sCFwRB6Ia0tDQuu+yyU27T0bkPlJmit956K35+fuh0Om699dbfXEoq7v0EdxCJAUHoJXq9Hq1We8ptAgICTlpiIMsyS5YsITk5mWXLlrFs2TLUajUFBQVs2bLlpO9hMplOewMuCILQm2JiYk67TUfnv/fff5/w8HByc3NZtmwZa9asYdSoUR0mRk0mE2q1Gj8/P7fFLQiC0B1dPfc1NDSwZs0aQkND2+/9wsLCWLt2LXV1dSd9D3HvJ7iDl6cDEITBQqVSnXabYcOG4XQ6qaioYMiQIYAylay5uRmLxcLnn3/evm1WVhbvvvsu06ZNO+F7lJSUcO2117o1dkEQhO7o7PmvpKTkhNcWL17MiBEjTjj3xcTE8Pnnn9PQ0EB4eHj76yUlJQwdOvSkGVeCIAie0tlz3/Hjx5FluX37pUuXEhUVxbFjxzh27Fj7tnFxcbz//vsndCBoa2ujqampfVapIHSVSAwIQh+SlZVFREQE27Zt44YbbgCUqWQzZ87kvffeO2Hb77//nunTp/PPf/6T4OBgQCleWFZWxkUXXdTboQuCIHTLhRdeyMaNG9s/37x5M0VFRezYseOkabYZGRl88MEHPPTQQ+2vbdu2TZz7BEHody644ALa2trIy8sjIyMDUGqr3H///fzhD384YdvXXnuNN95444TEwPbt2/Hz8zupo4sgnCmxlEAQ+hC1Ws3tt9/Of/7zHwAaGxtZvXo1M2bMOGnbc889F51O174tKBVwp0yZwsiRI3srZEEQBLe4/fbb2bVrF2VlZYByY3zeeed1uPZ2xowZJywnaG1tZf369SxYsKDX4hUEQXCHuLg4Lr/88vb7uR07dpCXl9fhvd+MGTM4evQoW7dubX9t+fLl3HLLLaddrioIpyMSA4LQCxITE5k1a1antn3wwQfZsmULRUVF5ObmMmvWLC655JKTttNoNDzxxBM0NTUB4HQ6+fe//82TTz7p1tgFQRC6Y9asWSQmJp52u8TERG699VZee+01ZFnGy8vrNwu23nzzzYwaNYrq6moA3nnnHbKzsxk7dqxbYxcEQeiqrKysDluwduSpp55i8eLFmM1miouLueeeexg6dOhJ28XHx/Pggw+2L7uqra1l9erVJ8wgEISuUsmyLHs6CEEQTvTBBx8AMGfOnE7vs3fvXj777DOee+65ngpLEAShR9XW1vL444/z1ltv4e3t3en97r33Xh544AHS0tJ6MDpBEISe89xzzzFlyhTOP//8Tu+zatUqampquPvuu3suMGHQEIkBQRAEQRAEQRAEQRjExFICQRAEQRAEQRAEQRjERGJAEARBEARBEARBEAYxkRgQBEEQBEEQBEEQhEFMJAYEQRAEQRAEQRAEYRATiQFBEARBEARBEARBGMREYkAQBEEQBEEQBEEQBjGRGBAEQRAEQRAEQRCEQUwkBgRBEARBEARBEARhEBOJAUEQBEEQBEEQBEEYxERiQBAEQRAEQRAEQRAGMZEYEARBEARBEARBEIRB7P8D2c6sGweR9HkAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# radial cuts through the (randomly initialized) generated filters, one line\n", "# per feature channel -- the continuous-filter picture of the paper's Fig. 3\n", "rr = np.linspace(0.0, 5.0, 250)\n", "fig, axes = plt.subplots(1, 3, figsize=(10.5, 3), sharey=True)\n", "for t, ax in enumerate(axes):\n", " Wr = np.stack([filter_np(model.interactions[t], d) for d in rr])\n", " ax.plot(rr, Wr[:, ::8], lw=0.8)\n", " ax.set_title(f\"interaction block {t + 1}\")\n", " ax.set_xlabel(\"r (A)\")\n", "axes[0].set_ylabel(\"filter value $W(r)$\")\n", "fig.suptitle(\"radial cuts through the generated filters (untrained)\", y=1.02)\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "1a298cd3", "metadata": {}, "source": [ "## Block 5: the interaction block · Fig. 2 (middle)\n", "\n", "$v^l = W_3\\;\\mathrm{ssp}\\!\\big(W_2\\,\\mathrm{cfconv}(W_1 x^l)\\big)$, then the\n", "ResNet-style residual $x^{l+1} = x^l + v^l$. There is **no weight sharing\n", "across blocks** (\"In contrast to MPNN and DTNN, we do not use weight sharing\n", "across multiple interaction blocks\"), and the feature width stays $F = 64$\n", "throughout. We now run all three blocks with the loop-based reference and\n", "compare the features after each one." ] }, { "cell_type": "code", "execution_count": 9, "id": "7fb2b674", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:42.431923Z", "iopub.status.busy": "2026-07-20T04:24:42.431776Z", "iopub.status.idle": "2026-07-20T04:24:42.485192Z", "shell.execute_reply": "2026-07-20T04:24:42.484645Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "after interaction block 1: max |xnn - paper| = 4.441e-16\n", "after interaction block 2: max |xnn - paper| = 4.441e-16\n", "after interaction block 3: max |xnn - paper| = 8.882e-16\n" ] } ], "source": [ "def interaction_np(block, x_np, pos):\n", " xw = x_np @ W(block.lin_in).T + b(block.lin_in) # atom-wise\n", " c = cfconv_np(block, xw, pos) # cfconv (eq 2)\n", " h = ssp_np(c @ W(block.lin_mid).T + b(block.lin_mid)) # atom-wise + ssp\n", " return h @ W(block.lin_out).T + b(block.lin_out) # atom-wise -> v\n", "\n", "x_ref = x0.copy()\n", "x_t = torch.from_numpy(x0.copy())\n", "rbf_t = model.rbf(r)\n", "for t, block in enumerate(model.interactions):\n", " x_ref = x_ref + interaction_np(block, x_ref, POS) # x^{l+1} = x^l + v^l\n", " with torch.no_grad():\n", " x_t = x_t + block(x_t, graph.edge_index, r, rbf_t)\n", " d = np.abs(x_t.numpy() - x_ref).max()\n", " print(f\"after interaction block {t + 1}: max |xnn - paper| = {d:.3e}\")\n", " assert d < 1e-11" ] }, { "cell_type": "markdown", "id": "62df7f5a", "metadata": {}, "source": [ "## Block 6: readout, standardization, and sum pooling\n", "\n", "The final features go through *atom-wise (64→32) → ssp → atom-wise (32→1)*\n", "to give $\\hat E_i$, which is standardized with the training-set statistics\n", "(DTNN Methods, step 4):\n", "\n", "$$E_i = E_\\sigma\\,\\hat E_i + E_\\mu \\;(+\\ \\texttt{atom\\_ref}[Z_i]),\n", "\\qquad E = \\sum_i E_i .$$\n", "\n", "The per-element `atom_ref` term is the `xnn` convention shared by every\n", "model here (a per-element $E_\\mu$, zero unless set); we set it above so this\n", "block is exercised too. The sum over atoms is what makes the energy\n", "size-extensive." ] }, { "cell_type": "code", "execution_count": 10, "id": "018b84d9", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:42.486444Z", "iopub.status.busy": "2026-07-20T04:24:42.486326Z", "iopub.status.idle": "2026-07-20T04:24:42.494184Z", "shell.execute_reply": "2026-07-20T04:24:42.493597Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "per-atom max |xnn - paper| = 4.440892098500626e-16\n", "E_xnn = -20.204330333316 eV\n", "E_ref = -20.204330333316 eV |diff| = 3.553e-15\n" ] } ], "source": [ "e_hat = ssp_np(x_ref @ W(model.readout[0]).T + b(model.readout[0]))\n", "e_hat = (e_hat @ W(model.readout[2]).T + b(model.readout[2]))[:, 0]\n", "node_ref = (0.37 * e_hat - 1.42\n", " + model.atom_ref.weight.detach().numpy()[Z, 0])\n", "E_ref = node_ref.sum()\n", "\n", "out = model(graph)\n", "print(\"per-atom max |xnn - paper| =\",\n", " np.abs(out[\"node_energy\"].detach().numpy() - node_ref).max())\n", "print(f\"E_xnn = {float(out['energy']):+.12f} eV\")\n", "print(f\"E_ref = {E_ref:+.12f} eV |diff| = \"\n", " f\"{abs(float(out['energy']) - E_ref):.3e}\")\n", "assert abs(float(out[\"energy\"]) - E_ref) < 1e-11" ] }, { "cell_type": "markdown", "id": "2be9b021", "metadata": {}, "source": [ "## Capstone 1: whole-model check on random molecules\n", "\n", "The full NumPy forward (embedding → 3 interactions → readout →\n", "standardization → pooling) against `model(graph)` for a set of random\n", "H/C/O structures." ] }, { "cell_type": "code", "execution_count": 11, "id": "770de564", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:42.495473Z", "iopub.status.busy": "2026-07-20T04:24:42.495354Z", "iopub.status.idle": "2026-07-20T04:24:42.679848Z", "shell.execute_reply": "2026-07-20T04:24:42.679299Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " molecule E_xnn (eV) |E_xnn - E_paper|\n", " #0 9 atoms -22.454373334171 0.000e+00\n", " #1 9 atoms -23.702117327519 0.000e+00\n", " #2 7 atoms -18.063348566606 3.553e-15\n", " #3 5 atoms -12.569851645530 0.000e+00\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " #4 5 atoms -15.634794852815 0.000e+00\n" ] } ], "source": [ "def schnet_np(pos, z):\n", " x = A[z]\n", " for block in model.interactions:\n", " x = x + interaction_np(block, x, pos)\n", " e = ssp_np(x @ W(model.readout[0]).T + b(model.readout[0]))\n", " e = (e @ W(model.readout[2]).T + b(model.readout[2]))[:, 0]\n", " return (0.37 * e - 1.42\n", " + model.atom_ref.weight.detach().numpy()[z, 0]).sum()\n", "\n", "rng = np.random.default_rng(7)\n", "print(\" molecule E_xnn (eV) |E_xnn - E_paper|\")\n", "for k in range(5):\n", " n = int(rng.integers(4, 10))\n", " pos_k = rng.uniform(0, 4, (n, 3))\n", " z_k = rng.choice([1, 6, 8], size=n)\n", " g_k = structure_to_graph({\"pos\": pos_k, \"atomic_numbers\": z_k}, CUTOFF)\n", " with torch.no_grad():\n", " e_x = float(model(g_k)[\"energy\"])\n", " e_p = schnet_np(pos_k, z_k)\n", " print(f\" #{k} {n} atoms {e_x:+.12f} {abs(e_x - e_p):.3e}\")\n", " assert abs(e_x - e_p) < 1e-11" ] }, { "cell_type": "markdown", "id": "baf5c525", "metadata": {}, "source": [ "## Capstone 2: the physics the paper promises\n", "\n", "* **Invariance** to rotation, translation, and atom indexing (built in by\n", " construction — Sec. 1's requirements);\n", "* **energy-conserving forces** $\\hat F_i = -\\partial\\hat E/\\partial r_i$\n", " (eq. 4): the autograd forces from `ForceStressOutput` must match central\n", " finite differences of the energy;\n", "* a **smooth PES** along a bond stretch (the property Fig. 1 illustrates)." ] }, { "cell_type": "code", "execution_count": 12, "id": "de1d9a92", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:42.681074Z", "iopub.status.busy": "2026-07-20T04:24:42.680957Z", "iopub.status.idle": "2026-07-20T04:24:42.908687Z", "shell.execute_reply": "2026-07-20T04:24:42.908215Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "rotation+translation |dE| = 3.552713678800501e-15\n", "force equivariance max|F' - F R^T| = 1.6696713456276768e-17\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "permutation |dE| = 0.0\n", "forces vs finite diff max|dF| = 3.08357401244963e-10\n" ] } ], "source": [ "fmodel = ForceStressOutput(model)\n", "\n", "# rotation + translation\n", "R_, _ = np.linalg.qr(np.random.normal(size=(3, 3)))\n", "if np.linalg.det(R_) < 0:\n", " R_[:, 0] *= -1\n", "g_rot = structure_to_graph({\"pos\": POS @ R_.T + 5.0, \"atomic_numbers\": Z}, CUTOFF)\n", "o0, o1 = fmodel(graph), fmodel(g_rot)\n", "print(\"rotation+translation |dE| =\",\n", " abs(float(o0[\"energy\"]) - float(o1[\"energy\"])))\n", "print(\"force equivariance max|F' - F R^T| =\",\n", " float((o1[\"forces\"] - o0[\"forces\"] @ torch.from_numpy(R_).T)\n", " .abs().max()))\n", "\n", "# permutation\n", "perm = np.random.permutation(N)\n", "g_perm = structure_to_graph({\"pos\": POS[perm], \"atomic_numbers\": Z[perm]}, CUTOFF)\n", "print(\"permutation |dE| =\",\n", " abs(float(o0[\"energy\"]) - float(fmodel(g_perm)[\"energy\"])))\n", "\n", "# forces vs central finite differences\n", "F = o0[\"forces\"].detach().numpy()\n", "h, worst = 1e-5, 0.0\n", "for (i, k) in [(0, 0), (1, 2), (2, 1), (5, 0), (8, 2)]:\n", " pp, pm = POS.copy(), POS.copy()\n", " pp[i, k] += h; pm[i, k] -= h\n", " ep = float(model(structure_to_graph({\"pos\": pp, \"atomic_numbers\": Z}, CUTOFF))[\"energy\"])\n", " em = float(model(structure_to_graph({\"pos\": pm, \"atomic_numbers\": Z}, CUTOFF))[\"energy\"])\n", " worst = max(worst, abs(-(ep - em) / (2 * h) - F[i, k]))\n", "print(\"forces vs finite diff max|dF| =\", worst)\n", "assert worst < 1e-7" ] }, { "cell_type": "code", "execution_count": 13, "id": "d6d51678", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:42.910577Z", "iopub.status.busy": "2026-07-20T04:24:42.910448Z", "iopub.status.idle": "2026-07-20T04:24:43.316831Z", "shell.execute_reply": "2026-07-20T04:24:43.316271Z" } }, "outputs": [ { "data": { "image/png": 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49O/fHxMnTsShQ4eQkpKCvLw8PH78GEuWLBHpnun6mK+XL1/im2++QVRUFEJDQzF37lyxjnLrM7aqiLq9iFqvPr8H9SEmJgbt2rXDTz/9hLdv34LL5eLt27dYsGABQkJCMGvWrBqTPFCeNO7fv4+CggKhcnG+Y+KQdBkPHjwY6enp+Pnnn5Gbm4uoqCiMGTNGkBilRdTv5tSpU+Hk5ISpU6fi3r17yMvLw9mzZxESEgJlZWWRPqtTp07Q1dUV9DWo+AHj6+uLtLQ0PH78WOhUvTjxVaUi5ilTpiA0NBR5eXkIDAxEcHCwyDFXpaZ1Ks6+4ObNm+jduze0tLTE+ny5SvIqKiq4dOkSFi9ejFWrVqFFixbo2LEjQkNDMX36dACApqYmbt++jUGDBmHSpEkwMjLC5MmTMXToUPzzzz/Q0NCQ6LP37NmD6OhomJiYVHt/sKS2bduG7t27o3///rC1tcXNmzexbt26SvXEmTdRp7ly5UpERUVhyJAh0NfXR9euXaGuro6goCA0b95cavNYleqWqbKyMi5cuIDvv/8e69atg729PaysrDBz5kw0b94c06ZNq3Xa9TFfd+7cwYoVK9CyZUuJ2tdnbFURdXsRZ7uqz++BOCo66H360tHREdT54YcfsHXrVjx69Ag+Pj7Q0dFB+/btER4ejp07d2LDhg21fo6/vz9KSkpw+vTpSu+J+h0TlyTLeOjQodi6dSsCAgJgZmaGoUOHYsSIESJ3dBOVqN9NLS0t3Lp1C15eXujfvz+srKxw6tQpbNmyReTPUlFRQc+ePQFAKJk7OzvDysoKANCnTx+J4quKtrY2bt26hTZt2sDX1xdWVlY4ceIE1q1bBz6fD3V1dZFj/1R161TUfcGrV68QFhZWY0fg6nBYTT1FCCGkifP398ezZ89w//59WYdCZCA2Nha2trb466+/MG/ePJnEMG/ePNy+fRvh4eFin1WQqyN5QghpaL/++itevnyJ8+fPyzoUIgMVfcA+++wzmXx+fHw8du7ciXXr1kl02YCO5AkhhBAAP//8M1xdXdGzZ09wOBwEBgZiwYIF8PX1xcmTJ2UdnkQoyRNCCCEAoqOj8dNPP+Hu3btISUmBlZUVxo4di59++qlO1+RliZI8IYQQoqDomjwhhBCioCjJE0IIIQpKRdYByDM+n4/ExETo6urKxXCehBBCxMMYQ15eHiwsLGp8bkpjRUm+DhITEwWDMhBCCFFc8fHxsLS0lHUYYqMkXwcVT/6Kj48XPAaQEEKI4sjNzYWVlZXUHjnc0CjJ10HFKXo9PT1K8oQQosDk9ZKs/F1gIIQQQohIKMkTQgghCoqSPCGEEKKgKMkTQgghCoqSPCGEEKKgqHc9qaS4lIeYjAJk5pcgq7AURaU8aKkpQ0ddBUbaanAw1YGmmviPPCSEENKwKMkTlPL4uBuVjuuRKYj4kI1XSXko41f/3CIOB7A01IS7hT66OZqgh6MprIy0GjBiQgghoqAk34RFp+Vjz933uPQsCVmFpULv6WuqwlRXHYZaqtBUU0FRSRnyuTyk5hYjo6AE8ZlFiM8swt/PkwEATmY6GO5liWFtW8BMT0MWs0MIIeQT9KjZOsjNzYW+vj5ycnLkajCcqJQ8bLr5FheeJqJi7ZvoqOFzD3N0sjdGa0t9tDDQrHbwh4x8Lt6k5ONRTCaCotLxOC5LcOSvxAF8nM0w8zN7tLM1aqhZIoSQeiGv+/kKlOTrQN5WfgG3DGuvvsHee+8Fyb2vqxkmd7ZFJ3sjqChL1g8zp6gUl54l4VTYBzyKzRKUt7MxxLzejujhaCK3o0URQpo2edvPf4qSfB3I08q/8yYNS08/Q0J2EQCgn5sZ5vd2hJuFvlQ/521qHnYFvcfpxwko4fEBAF0cjLF0gAs8LKX7WYQQUt/kaT9fFUrydSAPK5/HZ1h79TW2/hMNAGhhoInfhrmjZ6tm9fq5KbnF+L8773AwJFaQ7Id7tcCyz11goqNer59NCCHSIg/7+ZpQkq+Dxr7yswtLMP/oE9x5kwYAmNTZBt/1d4a2esP1t4zPLMT6a29w5kkCGCvv0Lekfyv4tbeGkhKdwieENG6NfT9fG0ryddCYV358ZiEm7L6P2IxCaKgq4fcRrTHEs4XM4gmPy8IPZ57jZVIuAKCDnRH+HNkG1sZ06x0hpPFqzPt5UdCIdwrobWo+Rm0PQWxGISwNNXF6VleZJngAaGttiPNzu2L5F67QUlPGg/eZ6L/xDg6FxoJ+ZxJCSP2gJK9gXibmYsyOECTnFsOxmQ5Oz+oCV4vG8etTRVkJX3azw+UFPdDBzgiFJTz8ePY5ph94hKyCElmHRwghCoeSvAJ5m5qHcbtCkVFQAvcWejg2ozOaNcKBaayNtXB0eif8ONAFaspKuB6ZigEbg3D/XYasQyOEEIVCSV5BJOUUYdLuB8guLEUbKwME+HeCkbaarMOqlpISB/7d7XFmThfYm2gjObcYfjtDse2faDp9TwghUkJJXgHkFJZi8p4HSMwphr2pNvZOaQ99TVVZhyUSNwt9XJjXDcO9WoDPgN8vv8KsQ4+RV1xae2NCCCE1oiQv50rK+Jh+8BHepOTDTE8dB77s0KiP4Kuira6CtaPa4Ldh7lBV5uDyi2QM3RKMd2n5sg6NEELkGiV5OffbxZd48D4Tuuoq2P9lB1gayuctaRwOB+M72uD4jM4w19dAdFoBhm4Jxt2odFmHRgghcouSvBw7GfYB+0NiAQAbxnrCuXnj6EVfF+W32nWDl7UBcovLMHnvAxwIiZF1WIQQIpcoycupZx9ysOzMMwDAwj6O6O1iJuOIpMdUVx2Hp3fCcK8W4PEZlp97gV8uvACvhmfcE0IIqYySvBzKKy7F7MNhKCnjo49LM8z3cZR1SFKnoaqMtaPaYEn/VgCAvcExmHUoDEUlPBlHRggh8oOSvBxace4F4jOLYGmoibWjPRV2DHgOh4PZPVtik19bqKko4erLFPjtDEUmDZxDCCEioSQvZ849ScDp8AQocYANYzzl5la5uhjUxgIB/h1hoKWKJ/HZGLn9HuIzC2UdFiGENHqU5OVIfGYhfjzzHAAwz8cR7WyNZBxRw2lva4STM7ughYEm3qUVYMS2e4j838NuCCGEVE3mSf7y5csYOHAg2rVrh6lTpyImJkYqbUSpk5OTg+XLl6Nbt27w9fXFyZMn6z5D9YQxhiUnnyKPWwYvawPM82kp65AaXMtmOjg1qwtamekiNY+L0TtCEBabKeuwCCGk0ZJpkr98+TIGDRqE7t27Y+3atcjOzka3bt2QnZ1dpzai1MnKykKnTp1w584drFixAitWrMCpU6dw7969+pvhOjj6MB4h7zKgoaqE9WM8oaIs899nMtFcXwPHZ3RGOxtD5BWXYcKuBwiKSpN1WIQQ0ijJ9HnyHTt2hJOTEw4ePAgA4HK5aN68Ob777jt8//33ErcRpc78+fNx9uxZvHr1Clpa/w4gU1paClVV0a5zN9RzhpNzitF33W3kccvw40AX+He3r7fPkhdFJTzMPBSG22/SoKrMwSa/tujvbi7rsAghCqZJPk/+5cuX2L59O3788Uf8+OOP2LFjByIjI8WaRn5+Ph4+fIjPP/9cUKauro4+ffrg1q1bErcRdbpHjhzBxIkThRI8AJETfENhjOHHs8+Qxy1DGysDTO1qJ+uQGgVNNWXsnNQOAz3MUcpjmHM4HOeeJMg6LEIIaVRURK3I5/Nx4MABrFu3Ds+ePUOzZs1gZlY+AEtKSgpSU1PRpk0bLFq0CBMnToSSUs2/HxISEsAYg7m58NGXubk5Xrx4IXEbUeqkpaUhPT0ddnZ2mDlzJsLCwmBhYYHJkydj+PDh1cbM5XLB5XIF/+fm1n/Hr4vPknA9MhWqyhysGdEaygp6u5wk1FSU8JdfW2ipKeNE2AcsPPYE3DI+RrezknVohBDSKIh8JN+hQwf89ddfmDlzJmJjY5GSkoKnT5/i6dOnSElJQUxMDKZPn46NGzeiQ4cOtU6vrKwMAKCmJvwwFXV1dZSWVv0EMlHaiFKnpKT8PutvvvkGTk5O2LJlC/r06QM/Pz/s2rWr2phXr14NfX19wcvKqn6TST63DP8JfAkAmN2zJVo1163Xz5NHykoc/D6iNcZ3tAZjwJKTT3EoNFbWYRFCSKMg8pH8Dz/8gGHDhlX7vo2NDebMmYM5c+bgzJkztU7P2NgYAJCRkSFUnpGRARMTE4nbiFLHyMgIHA4HgwcPxuLFiwGU/4h5+vQptm3bBn9//yo/f+nSpYL6QPmRfH0m+k03opCSy4WNsRZm9XSot8+Rd0pKHPw61B3qKsrYE/weP559DsYYJna2lXVohBAiUyIfydeU4CWp27x5c1hYWOD+/ftC5SEhIfD29pa4jSh1NDU14e7uLvhBUMHExAR5eXnVxqyurg49PT2hV315m5qH3XffAwBWDHKFhqpyvX2WIuBwOPjpCxfM6FHeKfGncy+w/16MbIMihBAZE6vj3fz58/H06VOpffiMGTOwa9cuvHv3DgBw4MABvHnzRuhIesWKFUI/GkRpI0qd2bNn4/jx44iNLT+1++HDBxw+fBgDBgyQ2vxJijGGn8+/RBmfoY9LM/g4K87DZ+oTh8PB9wOcMeOz8kS/4jwlekJI0yby6XoAuHTpEjZt2oT27dtj2rRp8PPzq9PR7LJlyxATEwNnZ2eYmJigsLAQe/bsgaenp6BOQkICoqKixGojSp0ZM2bg/fv3cHd3h6mpKZKSkjBq1CisXr1a4vmRlsvPk3H3bTrUVJSw/As3WYcjVzgcDr7v7wwOONh+Oxorzr+AinL5s+oJIaSpEes+ecYYbt++jd27d+PUqVPgcDgYPXo0pk2bhm7dukkcRFZWFtLT02FtbQ11dXWh9xITE1FYWIiWLVuK3EacOvn5+UhOToalpSU0NDTEirs+7p/klvHQd90dxGUWYr5PSyz2bSWV6TY1jDGs/vsV/u9O+dmcNSNaY3R76nVPCBGPvN8nL/FgODk5OTh8+DD27NmDR48eoVWrVpg2bRomT56MZs2aSTvORqk+Vv6uoHf49WIkTHXV8c83PaGtLtbJFvIRxhhWBr7E3uAYcDjAutFtMKytpazDIoTIEXlP8hKPjaqvr49Zs2bh4cOHiIiIQL9+/fDbb7/B0pJ2opLKLizBpptvAQDf+DpRgq8jDoeD5V+4YmInGzAGfHPiKS4/T5J1WIQQ0mDqPAA6l8vFq1ev8OrVK+Tl5QkGyCHi++vGW+QUlcK5uS5GetOpZWngcDj4ZbAbRnlbgsdnmHckHLdep8o6LEIIaRASJ/knT55g/vz5sLCwwIQJE6Cjo4MLFy4IeqsT8cRmFOBgaAwAYNnnLjSynRQpKXHw3xGt8UXr8iFwZx4MQ+i7jNobEkKInBMryWdlZWHLli3w9vZG27Ztce3aNXz//ff48OEDTp06hc8//7zW4WxJ1dZefYNSHkMPJ1P0cDKVdTgKR1mJg/VjPNHHpRm4ZXz473+E5wk5sg6LEELqlVgZ2cLCAt999x1at26NoKAgREZG4ttvv20yHe3qy8vEXJyPSAQALOlHvenri6qyEjaP80IneyPkc8swac8DvE3Nl3VYhBBSb8RK8hs3bkRSUhL27t1bp1vmiLC1V18DAL5obQ73FvoyjkaxaaiWP72utaU+MgtKMHH3fSRmF8k6LEIIqRdiJfmvvvoKurr/PiSlqKhI7EfMEmGPYjJx41UqlJU4WNzXSdbhNAm6GqrYN7UDHEy1kZRTjIm77yOroETWYRFCiNRJdAE9Pz9f0NnO1dVVUD569GiEhYVJLThFxxjDmivlR/GjvC1hb6oj44iaDiNtNRyc1hHm+hqITivA1H0PUVhSJuuwCCFEqiRK8kuXLkVCQgIePnwoVD5lyhT88ssvUgmsKbgTlY4H7zOhpqKE+b0dZR1Ok2NhoIkDX3aAgZYqnsRnY9ahxyjl8WUdFiGESI1ESf7MmTPYvXs3vLy8hMo7deqEW7duSSWwpqCFgSZ8Xc0wqZMNLAw0ZR1Ok+Ropovdk9tDQ1UJt9+kYenpZ5BwEEhCCGl0JEry6enpgh71HM6/93MXFRXRDlIMLZvp4P8mtcOyz11kHUqT5m1jiC3jvKDEAU6GfcD6a29kHRIhhEiFREne09MTly5dAiCc5Ddu3IiOHTtKJ7ImRIkGvpG53i5m+G2YBwDgr5tvEXCfBnUihMg/iQZH//XXXzF8+HDcu3cPAPD777/j8uXLCA4Oxs2bN6UaICENxa+DNZJyivHXjSj8dPY5LPQ10cuZxoAghMgviY7k+/TpgytXruD9+/do3rw5NmzYAC0tLdy+fZvunydybVEfR4z0tgSfAXMOP6ZR8Qghck3iR80S+X8EIalaSRkfU/c9QPDbDJjpqePsnK4w16eOkYQ0RfK+nxf5SH7//v3g82u/vYjH42H//v11CooQWVJTUcLW8d5wMtNBSi4XU/c+RD6X7qEnhMgfkZP8vn374OrqirVr1+LNG+Hex4wxvHz5Ev/973/h4uKCffv2STtOQhqUvqYq9kxpD1NddbxKzsP8I+Hg8emkFyFEvoic5G/duoXVq1fj1KlTaNWqFfT09NCyZUs4ODhAT08Pbm5uCAwMxO+//073yhOFYGmohZ2T2kFdRQk3X6Xi14svZR0SIYSIRaJr8nFxcQgODkZ8fDw4HA4sLS3RrVs3WFlZ1UeMjZa8X6shorn0LAmzAx4DAP4z1B0TO9nIOCJCSEOR9/08dbyrA3lf+UR0W269xR9XXkNZiYMDX3ZA15Ymsg6JENIA5H0/L9EtdIQ0NbN7OmB42xbg8RlmBzzG+/QCWYdECCG1oiRPiAg4HA5WDfdAW2sD5BSVYtr+h8gpKpV1WIQQUiNK8oSISENVGTsmesNCXwPv0gqoxz0hpNGTKMkXFRVJOw5C5EIzXQ3836R2gqfWrbnyStYhEUJItSRK8ubm5pg5cyYePHgg7XgIafTcW+jjz1FtAAA7br/D2fAEGUdECCFVkyjJb9q0Ca9fv0anTp3g4eGB9evXIy0tTdqxEdJofdHaArN7OgAAvjv1FE8/ZMs2IEIIqYJESX7ixIm4desW3r59i6FDh2L9+vVo0aIFRowYgYsXL4LH40k7TkIana99W8HHuRm4ZXzMPBiGjHyurEMihBAhdep4Z29vj//85z+IiYnB2rVrERgYiC+++ALW1tb4/fffweXSTo8oLmUlDjaM9YS9iTYSc4ox5/BjlPFqf74DIYQ0lDol+fz8fOzZswc9evTAwoUL0b17dxw5cgTfffcdduzYgbFjx0orTkIaJT0NVeyY6A1tNWWEvsvE6r+pIx4hpPGQaMS7u3fvYs+ePTh+/Dj09fUxZcoU+Pv7w87OTlAnJSUF1tbWCn00L+8jIRHpufw8GTMPhQEANo71xBDPFjKOiBAiDfK+n5foSL5nz55IT0/HkSNHEBcXh99++00owQOAmZkZpk6dKpUgCWns+rs3x9xeLQEA3596hlfJuTKOiBBCJDyST0pKgrm5eX3EI1fk/RcekS4en2HK3gcIikqHrbEWzs3tBn1NVVmHRQipA3nfz0t8nzwhRJiyEgd/jW2LFgaaiMkoxNfHn4BPI+IRQmRIoiTfvHnzal82Njbo1asXDhw4IO1YCWn0DLXVsH2CN9RUlHA9MhXbbkfLOiRCSBMmUZKfMWMGcnJyMGTIEPzyyy9YuXIlBg8ejJycHIwdOxaenp6YNWsW9uzZI+14CWn0PCz18Z8hbgCAtVdfI/htuowjIoQ0VRJdk/fx8cHcuXMxfPhwofKTJ09i27ZtuHHjBo4dO4Zff/0Vz549k1qwjY28X6sh9evbExE4EfYBxtpquDi/O5rra8g6JEKImOR9Py9RktfX18eHDx+gq6srVJ6bmwtra2tkZ2cjNzcXFhYWyM/Pl1qwjY28r3xSv4pLeRi29R4ik3LhbWOIo191gqoyPfiREHki7/t5ifY4Ojo6uHTpUqXyixcvQkdHBwCQmJgIe3v7ukVHiBzTUFXG9gle0NVQQVhsFtZcpoFyCCENS0WSRt9//z0mTZqES5cuoV27dmCMISwsDEePHsWff/4JAPjjjz/w9ddfSzVYQuSNjbE21o5qg68OhmFn0Hu0szVCP7fmsg6LENJESHS6HgAuX76MjRs3IjIyEhwOB87OzliwYAH69+8v7RgbLXk/jUMazm8XX2Jn0Hvoaqjg4rzusDbWknVIhBARyPt+XqIkX/EgmqZO3lc+aTilPD7G/l8owmKz4N5CDydndoGGqrKswyKE1ELe9/MSXZMfOnQoJDwBUK3i4uJ6aSNKHR6Ph+zsbBQVFYkdAyGiUFVWwuZxbWGkrYbnCbn47WKkrEMihDQBEiV5BwcHvHz5UioBrFixAgYGBtDR0YGjoyMuX74slTbiTHfevHkwNDTE0qVL6zQvhNTEXF8T60a3AQAcDI1F4NNEGUdECFF0EiX5JUuWYOLEibh+/ToSExORnp4u9BLVpk2bsGHDBgQGBqKwsBBTp07F0KFD8fbt2zq1EWe6Z86cwb179+Ds7CzeQiBEAj1bNcOcXg4Ayh9k8z69QMYREUIUGpMAgBpforK3t2eLFy8WKrOxsWFff/11ndqIOt3Y2Fhmbm7Onj9/ztq0acMWLFggcuyMMZaTk8MAsJycHLHakaattIzHRm2/x2y+C2QDNtxhRSVlsg6JEFINed/PS3QLXXh4eJ1/XKSnp+Pdu3fo3r27UHmPHj1w//59iduIOl0ej4dx48Zh6dKlcHNzq/P8ECIqFWUlbPJri883BuFlUi5+vfgSvw71kHVYhBAFJFGS9/T0rPMHp6amAgBMTEyEyps1a1ZtkheljajTXb58OXR1dTF37lyRY+ZyueByuYL/c3PpmeFEMmZ6Glg3xhOT9zzAodA4dLI3xhetLWQdFiFEwUg8xmZxcTGuXLmCbdu2Ccri4uLE7nXP5/OF/i8rKwOHw6lzm5rqBAcHY/v27Vi/fj1ycnKQnZ0NHo8HLpeL7Ozsaj939erV0NfXF7ysrKxqmz1CqvWZkylm9/z3+nxsBl2fJ4RIl0RJPjo6Gh4eHhg7dixmz54tKF+yZAlOnTol0jQsLMqPWlJSUoTKU1NTBe9J0kaUOi9fvgSPx0OnTp1ga2sLW1tbvHz5Env27IGtrS14PF6Vn7906VLk5OQIXvHx8SLNKyHVWdzXCe1tDZHPLcOcw4/BLat62yOEEElIlOQXLVqEgQMHIiMjQ6h88eLFWLNmjUjTMDAwgLu7O27cuCEo4/P5uHnzJrp16yYoKyoqQl5enshtRKkzffp0ZGdnC708PDwwa9YsZGdnQ1m56kFK1NXVoaenJ/QipC5UlJXwl19bGGqp4nlCLv77N41vTwiRHomS/N27d7F8+XIoKQk3d3V1RUREhMjTWbZsGfbu3YuAgAC8e/cOc+bMAZfLxaxZswR15s2bh86dO4vVRpQ6hDQW5vqaWPu/++f3BsfgyotkGUdECFEUEnW8KysrE1zz/vhaeHx8fKXHz9bEz88PRUVF+P3335GSkgIPDw/cvHkT5ubmgjpaWlpCR8yitBGlzqd0dXWhqakpcuyESJOPsxmmd7fDzqD3+PZEBNws9GBpSOPbE0LqRqKx64cOHQp3d3f8+uuvUFZWFgwLO2bMGJiYmCAgIKA+Ym105H1MY9K4lJTxMWpHCCLis+FlbYBjMzrT8+cJkTF5389LtAdZu3Yt9u3bB09PTzDGMGDAANjZ2SEyMhKrV6+WdoyENAlqKkrY7NcWuhoqeByXjXXX3sg6JEKInJN47Ppnz55h8uTJ8PPzg4GBAZYtW4aIiAhYW1tLO0ZCmgwrIy38PqI1AGDbP9G4/SZNxhERQuSZxM+TJ/J/Goc0Xj+efYZDoXEw1lbD3wu6o5mehqxDIqRJkvf9vEQd74Dy0d+io6ORmZlZ6b2Pb4EjhIjvx4GueBSThVfJeVhw9AkO+XeEslLNg0QRQsinJEryt27dgp+fX6UBZyrQyQFC6kZDVRlbxnth0Ka7CHmXgS233mJ+b0dZh0UIkTMSXZOfP38+/Pz8kJiYiKKiokovQkjdOZjq4D9D3AEAG66/Qei7jFpaEEKIMImuyWtrayMlJQU6Ojr1EZPckPdrNUQ+fH08Aqcef4CZnjouze8OYx11WYdESJMh7/t5iY7knZyc8OHDB2nHQgipwsohbrA31UZKLhdfn4gAn0+XwwghopH4dP2UKVMQEhKCtLQ0pKenC70IIdKjra6CLeO8oKaihH9ep2HX3XeyDokQIickOl1f26Ngm0rHO3k/jUPkS8D9WPxw5jlUlDg4PrMzvKwNZR0SIQpP3vfzEvWuDw8Pl3YchJBajOtgjZDoDAQ+TcK8w+G4NL879LVUZR0WIaQRkyjJe3p6SjkMQkhtOBwOVg/3wLOEHMRmFOLbkxHYMdG71jNrhJCmS+KnXxQXF+PKlSvYtm2boCwuLq7JnKonRBZ0NVTLr88rK+HqyxTsDY6RdUiEkEZMoiQfHR0NDw8PjB07FrNnzxaUL1myBKdOnZJacISQytxb6OOHgS4AgNV/RyIiPlu2ARFCGi2JkvyiRYswcOBAZGQID86xePFirFmzRiqBEUKqN6mzDfq7NUcpj2HO4cfIKSqVdUiEkEZIot71RkZGePv2LYyMjMDhcASn6PPz82FsbAwulyv1QBsjee91SeRbTlEpvtgUhPjMIvRzM8P2CXR9nhBpk/f9vERH8mVlZeDz+QCEb6eLj4+Hrq6udCIjhNRIX/Pf6/NXXqRgD12fJ4R8QqIk7+Pjgw0bNgD4N8lnZ2dj4cKF6Nevn9SCI4TUrLWlwb/X5y9F4nFclowjIoQ0JhIl+bVr12Lfvn3w9PQEYwwDBgyAnZ0dIiMjsXr1amnHSAipwaTONhjoYY4yPsPcgMfIKiiRdUiEkEZCoiTv4OCAZ8+eYfLkyfDz84OBgQGWLVuGiIgIWFtbSztGQkgNOBwO/jvCA7bGWkjMKcbi409ofHtCCAAJO96RcvLeIYMolheJORi+9R64ZXx8268V5vRqKeuQCKlWbnEpIhNz8TolD+l5XGQWliC3qAwqShyoKitBU00ZZnoaaGGoCStDTTg314OmmnLDxynn+3mJRrwjhDQ+bhb6WDnEDd+deoa1V1+jrbUBujiYyDosQgAAZTw+HsVm4drLFNx8lYr36QVitVfiAA6mOmhjZYAuDsbo2tIEZnoa9RSt4qAj+TqQ9194RPEwxvDtyac4GfYBJjpquDi/O+0IiUyl5hUjIDQOAffjkJ4vfHt1CwNNuJjrwVxfA4baatDTUAGfMZSU8VFQwkNyTjESsorwLr2gUlsAcDLTga9rc/i6mcGjhX693EIq7/t5SvJ1IO8rnyimohIehm0NxqvkPLS3NcTh6Z2gqizxCNaESCQltxjrrr7BmfAElPDKb7k20FKFj3Mz+Lo2Ryd7IxhoqYk8vdTcYjxLyMGj2CwEv03Hs4QcfJy9WhhoYrCnBYZ4WsC5ufT2x/K+n6ckXwfyvvKJ4nqfXoDBm+4ij1sG/252+PELV1mHRJqIohIe/u/OO2y/HY2iUh4AoK21Ab7saof+7s2l9oMzu7AEt9+k4cqLZPzzOg2FJTzBe87NdTHS2xJD27aAiY56nT5H3vfzEif54uJi3L59G+/evcOsWbMAlD+gxsrKqsmMuiXvK58otisvkjHjYBgAYOt4L3zuYS7jiIiie/A+E4uPP8GHrCIAgLeNIZZ97gxvG6N6/dziUh5uvkrF2fAE/PM6TXDmQEWJg17OzbB1vJfEPy7kfT8vUZKPjo5G//79kZ6ejuzsbMGwtmPHjsXIkSMxcuRIqQfaGMn7yieKb/Xfkdhx+x201ZRxbm5XtGxGI1IS6Ssp42P99TfYfjsajJWfOl/6uTMGepg3+EFfTmEpzj9NxMmwD4iIz0ZHOyMcm9FZ4unJ+35eoiQ/ePBg2NvbY926dVBWVhYk+QcPHmDu3Ll48OCB1ANtjOR95RPFV8bjY8Lu+wh9lwkHU22cm9sNOup0Uw2RnuScYsw4+AgRH3IAAKO8LbF8kCt0NVRlHBkQlZKHwhIe2lgZSDwNed/P0wNq6kDeVz5pGtLzufjir7tIzi1Gf7fm2DbBq8lcUiP160l8Nr468AipeVwYaKniv8M90N9dsS4Lyft+nh5QQ4iCM9FRx9YJXlBV5uDyi2Rsv/1O1iERBXDxaRLG7AhBah4XTmY6OD+nm8IleEVAD6ghpAnwsjbEikFuAIA/rrzCnTdpMo6IyLOjD+Iw98hjcMv46OPSDKdmdYG1sZaswyJVoAfUENJEjO9ojdHtLMFnwLwj4YjLKJR1SEQO7b77Ht+ffgbGyrepHRPbNYrr76RqEt9Cl5WVhX379uHRo0fg8/nw8vKCv78/DA0NpR1joyXv12pI01NcysOY/wtFRHw2nJvr4vTsLtBSo454RDQ7bkdj9d+vAABf9bDH0gHOCt+/Q9738xIl+aCgIHTr1k3hV25t5H3lk6YpKacIgzbdRXp+CQa2Nsdmv7ZN/rtMahdwPxY/nHkOAFjYxxELejs2ie1G3vfzEp2u79mzJ+zs7PDDDz8gMjJS2jERQuqRub4mto73hooSBxefJmHrP9GyDok0cueeJODHs+UJfk4vByzs49QkErwikCjJx8bGYs6cObh48SJcXV3h7e2N9evXIzk5WdrxEULqQQc7I/wypLwj3p9XX+NGZIqMIyKN1a3Xqfj6eAQYAyZ2ssE3vq1kHRIRg0RJ3tLSEt9++y2ePHmC58+fo1+/fti4cSMsLS2pdz0hcmJ8RxuM72gNxoAFR5/gbWqerEMijUxkUi7mBjxGGZ9hqKcFfhnsRkfwckYqD6jh8/m4ffs2Fi1ahIiICDSVZ97I+7UaQkrKykfEe/A+E7bGWjg7p6tYTwYjiis1rxhDNwcjMacYne2Nsf/LDlBTaXpPM5T3/Xyd1lhERASWLFkCGxsb+Pr6wsLCAgEBAdKKjRBSz9RUlLBtvBdaGGgiJqMQcw4/Run/Hu5Bmq6iEh6m73+ExJxi2JtqY/sE7yaZ4BWBRGtt9erVcHd3h6enJ+7cuYMlS5YgMTERly5dwrhx46QdIyGkHhnrqGPX5HbQUlNG8NsM/CfwpaxDIjLEGMOyM88Q8SEHBlqq2DO5PfS16D54eSVRkt+7dy9GjRqFqKgohIaGYt68eTA1NZV2bISQBuJirocNYzzB4QAHQmJxMDRW1iERGTkQEosz4QlQVuJg23hv2JpoyzokUgcSjYLx5s0bacdBCJExX7fm+Ma3Ff648ho/n38BGyMt9HCiH+9NycOYTMGZnKUDnNHZwVjGEZG6EjnJx8TEAABsbW0Ff1fH1tZWrCDCw8ORkpICNzc3WFlZSa1NbXXy8vLw5MkTqKiowN3dnR6uQ5q82T0dEJ2aj9PhCZgT8BinZ3eBoxl9L5qC1NxizP5fT/ovWptjWjc7WYdEpIGJCACrqF7xd3UvUeXm5rIePXowU1NT1q1bN6apqclWrFhR5za11eHz+WzhwoWsefPmrHv37szb25sZGBiwgwcPihw7Y4zl5OQwACwnJ0esdoQ0ZsWlZWzktmBm810g6/b7DZaeVyzrkEg9K+Pxmd//hTCb7wJZ33X/sPziUlmH1GjI+35e5CP5qKioKv+uix9//BEJCQl4/fo1DA0NcfPmTfTu3Rs9e/ZEz549JW5TWx3GGGxsbPDu3TtoamoCADZu3Igvv/wSn332mchnEwhRROoqytgxsR2GbglGXGYhvjoYhgD/jtBQVZZ1aKSebL31FveiM6Cpqoyt472grU7PM1AYkvwyGDhwoETvfYzP5zMjIyO2atUqoXJvb2/25ZdfStxGkukyxlhKSgoDwC5evChS/IzJ/y88QmoSlZLL3FdcZjbfBbK5hx8zHo8v65BIPbj/LoPZfR/IbL4LZMcfxsk6nEZH3vfzEvWuv3jxYpXlfD4ff//9t0jT+PDhAzIzM9GmTRuhck9PTzx9+lTiNpJMFwBu374NAHB2dq62DpfLRW5urtCLEEXVspkudkwoH+P+QkQi1l+nDreKJqugBPOPhIPPgOFtW2Ckt6WsQyJSJtY5mQ8fPlT5N1Ce4IODg2FhYSHStHJycgCg0qNpjY2NkZ2dLXEbSaYbHx+P+fPnw9/fH/b29tXGvHr1avzyyy/Vvk+IounS0gSrhntgycmn2HTzLayMtDC6HV3OUgTsf/fDJ+cWw85EG/8Z6k5D1iogsZL8x9eqq7puraamhvXr14s0LTW18qEzCwsLhcrz8/Ohrq4ucRtxp5uSkgJfX1+0bt0amzdvrjHmpUuXYvHixYL/c3Nz6fo9UXij21khLqMQm2+9xbLTz9BcT4NurVMAJ8M+4O/nyVBR4uCvsW3pOryCEmutVjxW1sXFpdIjZlVVVWFhYSHoyFYba2trKCsrIz4+Xqg8Pj4ednZV37ohShtxppuamgofHx9YWlri7Nmz1f64qKCurl5rHUIU0de+TojPKsS5J4mYHfAYx2d0hquF/I3jTcrFZRTi5/MvAACL+jrBw1JfxhGR+iLWNXlnZ2c4OzsjLS1N8HfFy8HBQeQEDwAaGhro1asXTp06JSjLysrCjRs3MGDAAEHZkydPcPPmTZHbiDrdtLQ0+Pj4wMLCAufPnxcrdkKaGg6HgzUjW6OTvRHyuWWYuu8BErOLZB0WkUAZj49Fx5+goISHDrZGmPmZg6xDIvVIKk+hk9SjR4/QvXt3TJgwAZ07d8aOHTtQVFSEBw8eQENDAwDg7++P0NBQPH/+XOQ2tdXhcrno0KEDkpOTsWHDBqEE37ZtW9jY2IgUv7w/nYgQceUUlWLktnuISs2Hk5kOTszsAn1NGtdcnmz95y3WXH4NXXUVXFrQHVZGWrIOqVGT9/28RL3r+Xw+du7cCV9fXzg7O6Nly5ZCL1G1a9cOjx49gqamJq5cuYJBgwbh7t27gmQNlCfd3r17i9WmtjolJSWws7ND586dcezYMezbt0/wktYYAIQoIn1NVez7sgPM9NTxJiUfXx14BG4ZT9ZhERFFJuVi/bXyuyRWDHajBN8ESHQkv2rVKmzbtg1z5szB0qVLsX79ejx48ADHjh3DvHnzsGHDhnoItfGR9194hEgqMikXo7eHII9bhoGtzbFpbFsoKVHP7MaspIyPIVuCEZmUi76uZvi/id7Um14E8r6flyjJOzg4ICAgAJ06dQKHw0HFJLZv344zZ87gypUrUg+0MZL3lU9IXdx7m47Jex+glMcwpYstVgxypaTRiP155TU233oLI201XFnYA6a61IlYFPK+n5fodH1sbCy8vb0BAJqamsjLywMAjBs3DsHBwdKLjhDSaHVpaYI/R5UPOrXvXgy23Y6WcUSkOhHx2dj6z1sAwG9D3SnBNyESJXkejwdV1fLONjY2NggJCQEAvHv3jm4xI6QJGeLZAj994QoAWHP5NY4/iq+lBWloxaU8fH0iAnwGDG5jgQEe5rIOiTSgOo9+MH36dIwdOxY9evTAvXv3MHr0aGnERQiRE9O62SE1rxg7br/D0tPPYKSlhj6uZrIOi/zPhutReJuaDxMddfwy2E3W4ZAGJlGSrzg9DwCLFy9GixYtEBISgv79+8Pf319qwRFC5MP3/Z2RnleCU48/YM7hxzg4rSM62BnJOqwm73FcFv7vTvlllFXD3GGorSbjiEhDk+l98vJO3jtkECJNpTw+Zh4Mw41XqdDVUMGxr2hUPFkqLuVh4F9BiE4rwLC2LbB+jKesQ5JL8r6fF/lIPiYmRuSJ2traShAKIUSeqSorYct4L0zcfR8PY7Iwac8DnJrVGTbG2rIOrUlaf+0NotMKYKqrjhWDXGUdDpERkY/kxbk1pqmcHJD3X3iE1IecolKM2RGCV8l5sDLSxMmZXWCmp1F7QyI1j+OyMHLbPfAZsHNSO/SlPhISk/f9vMhH8jQSHCFEFPqaqjgwrQNGbQ9BbEYhJu6+j+MzOsNAi64HN4TiUh6+/V9v+mFtW1CCb+JETvLiDFdLCGnamulq4NC0jhi5/R7epORjyt6HOOTfETr0ONN6t/46naYn/5LoPnkAKC4uxpUrV7Bt2zZBWVxcXJM5VU8IqZmVkRYOTusIAy1VPInPxvT9j1BcSuPc16fHcVnYeecdgPJBb+jsCZEoyUdHR8PDwwNjx47F7NmzBeVLliwResQrIaRpczLTxf6pHaCjroKQdxmYe/gxSnl8WYelkIpLefjmo9P0vm7NZR0SaQQkSvKLFi3CwIEDkZGRIVS+ePFirFmzRiqBEUIUQxsrA+ye3A7qKkq4HpmKxccjwOPTGT9pW3v1Nd6lFaAZnaYnH5Eoyd+9exfLly+HkpJwc1dXV0REREglMEKI4uhob4ztE7yhqszBhYhEfH/qKfiU6KXmUUwmdt19DwBYPdyDTtMTAYmSfFlZGfj88lNuH99aFx8fD11dXelERghRKL2cm2Hj2LZQ4gAnwj7g5wsvqA+PFBSWlOHrExFgDBjhZYneLtSbnvxLoiTv4+MjeGZ8RZLPzs7GwoUL0a9fP6kFRwhRLJ97mGPt6DbgcIADIbH479+vKNHX0epLrxCbUQhzfQ0sp9P05BMS3c+ydu1afPbZZwgMDARjDAMGDEBoaCh0dXVx9+5dacdICFEgw9paoqiEj2VnnmHHnXdQU1HC176tZB2WXAqKSsPB0FgAwJqRraGvqSrjiEhjI1GSd3BwwLNnz7Bv3z48evQIfD4fy5Ytg7+/PwwNDaUdIyFEwYzraI2SMh5+vvASm26+hZqyEub1dpR1WHIlp6gU3554CgCY2MkG3R1NZRwRaYwkSvL+/v7YtWsXFi1aJO14CCFNxJSudijh8bHq0iusvfYGKspKmNXTQdZhyY3l554jObcYtsZaWPq5s6zDIY2URNfkDx8+jOLiYmnHQghpYr7q4YBvfJ0AAL9ffiV4LCqp2bknCTj3JBHKShysHe0JLTUaSZBUTaIk37VrV1y5ckXasRBCmqC5Po5Y2Kf8VP2qS6+wK+idjCNq3D5kFeLHM88BAPN8WsLbhi6RkupJ9POvffv2GD9+PKZMmQJXV1eoqQnfk+nv7y+V4AghTcPCPk7gM+CvG1H49WIkAMC/u72Mo2p8eHyGxccikMctg5e1Aeb2omeKkJqJ/KjZj9X2vHhxnj0vz+T9EYSENCaMMay79gabbr4FACwd4IwZn9E1+o/9dSMK6669gbaaMv5e0APWxlqyDknhyft+XqIj+aaSxAkhDYfD4WBxXycocTjYeCMKq/9+BR5jmN2TjlYBIPRdBjZcfwMAWDnEnRI8EYnET6EjhBBp43A4WNTXCYv6lHfGW3P5NTZcf9PkB8zJyOdiwdFw8P83qt0Ib0tZh0TkBCV5Qkijs6CPI77tVz5AzobrUfj98usmm+j5fIbFxyOQksuFg6k2Vg5xk3VIRI5QkieENEpzerXET1+UD9O6/XY0frnwskk+1Gbzrbe4/SYN6ipK2DLeC9rqdLscER0leUJIozWtmx1+G+YOANh3LwZLTj1FWRN6Hv2tV6lY/7/r8P8Z4g7n5vLX8YvIFiV5QkijNr6jDdaNbgNlJQ5Ohn3A7IDHKC7lyTqseheTXoD5R8PBGDC+ozVGt7eSdUhEDlGSJ4Q0esO9LLFtvBfUVJRw9WUKpu59iLziUlmHVW/yuWWYcTAMecXl98OvGETX4YlkKMkTQuSCr1tz7JvaHtpqygh5l4HRO0KRkqt4w2uX8fiYd/gxXqfkwVRXHdsmeENNhXbVRDK05RBC5EYXBxMcm9EZJjrqiEzKxfCt9/A2NV/WYUkNYwwrA1/i1uvyjnY7J7WDmZ6GrMMicoySPCFErri30MfpWV1gZ6KNhOwijNh2DyHRGbIOSyr2BMfgQEgsOBxgwxhPeFoZyDokIucoyRNC5I61sRZOzuyMttYGyCkqxcTd93H8Ybysw6qTM+Ef8OvFlwDKh/Qd4GEu44iIIqAkTwiRS8Y66jgyvRO+aG2OMj7DklNPsepSJHhyeC/95efJ+ObEUzAGTOpsg+n0cB4iJZTkCSFyS0NVGX+NbYv5PuXj2//fnXeYsvcBsgpKZByZ6G6/ScO8I4/B4zOM8LLEz4PcwOFwZB0WURCU5Akhck1JiYPFvq2wya8tNFWVERSVjkGb7+J5Qo6sQ6vVtZcpmH7gEUp5DAM9zPH7CA8oKVGCJ9JDSZ4QohAGtbHAmTldYG2khQ9ZRRi+9R7234tptGPen378ATMPhaGkjA9fVzOsH+MJFWXaJRPpoi2KEKIwnJvr4cLcbujj0gwlPD5WnH+Brw6GNarT94wx7Ap6h8XHI8DjM4z0tsTW/w30Q4i00VZFCFEo+lqq2DmpHVYMcoWashKuvUxB3/V3cPl5sqxDQ3EpD18fj8CvFyMBAF92tcOaEa3pCJ7UGw5rrOey5EBubi709fWRk5MDPT16cAQhjc3zhBwsPPZEMGDOoDYWWP6FK0x11Rs8lg9ZhZh5KAzPE3KhrMTB0gHOmNbNjjrZNXLyvp+nJF8H8r7yCWkKikt5+OtGFHbceQcen0FXXQXzeztichfbBjlFzhjDkQfxWHUpEvncMhhpq2GzX1t0aWlS759N6k7e9/MyT/JpaWk4evQoUlJS4OHhgZEjR0JZWbnObaRVpybyvvIJaUqefsjGD2ee49n/et3bm2hjYV8nDPQwh3I99Wh/n16An84+x9236QAAL2sD/OXXFpaGWvXyeUT65H0/L9MkHx0dja5du8LNzQ0dOnTAsWPH4OjoiEuXLlWbbEVpI606tZH3lU9IU8PnM5wM+4A1V14hPb+8M569qTbm9GyJga3NoaEq+o/8miRmF+GvG1E4EfYBPD6DhqoSvvFthald7ertBwWpH/K+n5dpkh85ciSSk5Nx584dKCkpISYmBk5OTti7dy/Gjx8vcRtp1amNvK98Qpqq3OJS7AuOwe6775FTVP7IWgMtVQz1bIGR3pZws9AT+1o5n89wLzoDJ8Li8fezZJTw+ACAXq1MsXyQG+xMtKU+H6T+yft+XmZJvqysDLq6uli3bh1mzZolKO/bty8MDAxw4sQJidpIq44o5H3lE9LU5RWX4mBoLA6FxCIx59/H1jbTVUd3R1N0sjeCo5kuHEy1oauhKtS2gFuGpJwiPI7LxsP3mQh+my40jY52Rvi2Xyu0szVqsPkh0ifv+3kVWX1wbGwsiouL4eDgIFTu4OCAkJAQidtIq05VuFwuuFyu4P/c3Nxa5pIQ0pjpaqhids+WmNHDAUFRaTj2MB63XqciNY+LU48/4NTjD4K62mrK0FBVhpqKEvKKy5DPLatieioY3MYCo9pZoY2lPvWcJzInsyRfWFgIAJV+Genr66OgoEDiNtKqU5XVq1fjl19+qX6mCCFySVmJg56tmqFnq2YoLuXhUUwW7kSl4dmHHLxNy0daHhcFJTwUlPCE2mmrKcPFXA/t7YzQwdYInR2MpXZdnxBpkFmS19HRAQBkZ2cLlWdnZ0NXV1fiNtKqU5WlS5di8eLFgv9zc3NhZWVVbX1CiPzRUFVGN0cTdHP89xa3nKJSZBeWgFvGR3EpDzrqKmimpwEddZntQgkRicyGWbK2toa2tjZev34tVP7q1Su4uLhI3EZadaqirq4OPT09oRchRPHpa6rCxlgbTma6aG1pAHtTHUrwRC7ILMkrKytj+PDh2L9/v+A69/Pnz3H37l2MGjVKUO/EiRNYu3atyG2kVYcQQgiRdzK9hS4pKQndu3eHjo4OvLy8EBgYCF9fXxw6dEhQx9/fH6GhoXj+/LnIbaRVpzby3uuSEEJIzeR9Py/zEe8KCwsRGBgoGHWuZ8+eQu9fvXoViYmJmDJlishtpFmnJvK+8gkhhNRM3vfzMk/y8kzeVz4hhJCayft+np5vSAghhCgo6h5aBxUnQWhQHEIIUUwV+3d5PelNSb4O8vLyAIDulSeEEAWXl5cHfX19WYchNromXwd8Ph+JiYnQ1dWtt+ErKwbciY+Pb/TXgyjW+kGx1g+KtX4oWqyMMeTl5cHCwgJKSvJ3hZuO5OtASUkJlpaWDfJZ8jT4DsVaPyjW+kGx1g9FilUej+AryN/PEkIIIYSIhJI8IYQQoqAoyTdy6urqWLFiBdTV1WUdSq0o1vpBsdYPirV+UKyNC3W8I4QQQhQUHckTQgghCoqSPCGEEKKgKMkTQgghCoruk29gXC4XL168gLa2Nlq1alVj3dLSUty/f79SuYuLC4yNjSWerqiKi4vx8uVL6OjowMnJqca6Hz58QExMTJXvdezYEaqqqigpKcGDBw8qve/q6gojI6M6xcrn8xEWFgZNTU24u7uL1EaU+RNnGdRnrJmZmYiNjYWNjU2lZVWfy5XH4yEsLAza2tpwc3OrsS6Xy8XDhw8rlbu5ucHQ0FCorGK56urqwtHRsU4xShJrfHw8YmNjq3yvU6dOUFFREWt+xJWRkYG4uDjY2tqKPC1Rlll9LFdJYq2pTX0u1/T0dMTHx4sUa3FxMR49elSp3N3dHQYGBkJlRUVFePnyJfT19dGyZcs6xdjgGGkwly5dYsbGxsze3p4ZGhoyb29vlpiYWG39pKQkBoC1bduWde3aVfC6detWnaYrigsXLjAjIyPm4ODADAwMWIcOHVhycnK19Q8dOiQUY9euXVmzZs2YhoYGy8/PZ4wxFh8fzwAwLy8voXp37tyROE4ul8tWrVrF7OzsmL6+Puvdu7fU5k/cZVAfsT5+/Jj16dOHGRsbM09PT6alpcXGjRvHioqKBHXqY7kWFxezX3/9ldna2jI9PT3Wr1+/Wtu8f/+eAWDe3t5CcQQHBwvVO3fuHDM0NGQtW7ZkBgYGrFOnTiwlJaVBY92/f3+l7dXU1JRpaWkJlq2o8yOOR48eMR8fH2ZiYiJYnxMmTGDFxcU1thNlmUl7uUoSqyht6mO5PnjwgPXs2VPwuZqammzy5MmMy+VW2yYqKooBYO3atROKIzQ0VKje6dOnmb6+PmvZsiXT19dnXbp0YWlpaRLH2tAoyTeQtLQ0pqury1auXMkYY6yoqIh16tSJDRgwoNo2FUn+2bNnUp1ubZKTk5mOjg5btWoVY4yxwsJC1r59ezZo0CCRp8Hn85mDgwObOHGioKwiGUVGRkoc26cyMzPZ999/z96/f88mT54sUuIUZf6ksQykEeuxY8fY9evXBf/HxsYyc3Nz9u233wrK6mO5pqWlsWXLlrGYmBg2fvx4sZJ8VFRUtXUSExOZlpYWW7NmDWOMsYKCAubl5cWGDRvWoLF+is/nM1tbWzZ16lRBmSjzI64jR46wmzdvCn2GmZkZW7p0abVtRFlm9bFcJYlVlDb1sVwDAgLYP//8I/g/OjqamZqasp9++qnaNhVJ/v3799XWiY+PZ5qammzdunWMMcby8vJYmzZt2KhRo6QWe32jJN9Atm7dyrS0tFhBQYGg7OTJk4zD4VR71F2R5C9evMjCwsJYdna2VKZbm7/++ovp6OgIHS0ePXqUKSkpiXxkcOvWLQZA6GiyIhldvnyZhYWFsZycHIniq46oiVOU+ZPGMpBGrFXx9/dnnTt3Fvxf38tV3CR/7do19vjxY5abm1upzrp165ienp7QEdahQ4eYsrIyS09Pb7BYP3Xt2jUGgN27d09QJsr8SMOUKVNY9+7dq31flGVW38tV1FhFadNQy3XChAmsV69e1b5fkeRv3rxZbRxr1qxhhoaGrLS0VFC2b98+pqKiwrKysuojbKmjjncNJDw8HC4uLtDS0hKUdejQAYwxPHnypMa2X375JSZNmgRTU1NMnjwZ+fn5UpluTbG6ublBQ0NDaJp8Ph8REREiTWP37t1o1aoVunfvXum9KVOmYNKkSTAxMcHUqVNRUFAgUZySEmX+pLEM6gNjDGFhYVVeF5T1cq0wadIkTJgwAcbGxvD390dhYaHgvfDwcHh4eEBNTU1Q1qFDB/B4PDx9+lQW4QIo317d3NzQuXPnSu/VND91xefz8fjx4xqv84qyzBpiuYoSqzhtZL1cK0yYMEEQx1dffYWioiLBe+Hh4WjdujVUVP7tvtahQweUlZXh2bNnUou3PlGSbyCZmZmVOstV/J+ZmVllG3V1dRw/fhzJycl4/vw5nj17huvXr+Prr7+u03TrI9aP5eTk4NSpU5g+fbpQuYaGBk6ePImkpCQ8f/4cERER+Pvvv7FkyRKJ4pSUKPNXH8tVGn7//XdERkbi22+/FZQ1luWqqamJM2fOIDExES9evEB4eDjOnz+PpUuXCuo0xuWamZmJM2fOVNpeRZmfulq1ahWioqLwzTff1BhfY9heRYlVlDYNsVxXrlyJmJgYoX3lp7S1tXH+/HkkJCTgxYsXCAsLw+nTp/Hjjz8K6jTG7VVclOQbiKqqKoqLi4XKKn4xfvzr+2OGhoYYNWqU4P9WrVph0aJFOHbsWJ2mWx+xfuzw4cPg8XiYNGmSULmJiQlGjBgh+N/FxQULFy7E0aNHJYpTUqLMX30s17rau3cvli9fjoMHD8LDw0NQ3liWq5mZGYYOHSr4383NDfPnzxeKozEu14CAAADAxIkThcpFmZ+62LVrF1auXImAgAC4urpWW68xbK+ixipKm/pertu3b8fq1atx5MiRGu80Mjc3x6BBgwT/e3h4YO7cuY1+exUXJfkGYmNjg4SEBKGyiv+tra1Fno6ZmRlycnIEp+ylNV1pxrp7924MHToUpqamtdY1MzNDZmZmpS9SfRJl/upjudbFgQMHMGPGDBw4cAAjR46stb4slmt1caSmpqKsrAxA41uuQPn2OmLECJFuN/x0fiS1Z88ezJkzBwEBARg2bFiNdWW9vYoTq6RtpLVcd+7ciQULFuDo0aMYPHiw2O3NzMyQlJQEPp8PoHFur2KTcZ+AJuP69esMAHvx4oWgbOXKlczIyIiVlJQwxspvsQoKChJ0lKm49exjEyZMYDY2NmJNV1yXL19mANjr168FZcuXL2empqaCDijFxcUsKCiIZWRkCLV98uSJoFPNp6qan7FjxzIHBweJ4vxUdZ3ZPo1VlPkTpU5DxMoYYwcOHGBqamrs8OHDVU6rvpdrdZ3ZioqKWFBQEMvMzKw2jpEjR7JWrVoJ/g8MDGQA2Nu3bwVly5YtY82bN2c8Hq/BYq3w8OFDBqDSbamMiTY/kti7dy9TU1Njx48fr/L9T2MVZZnV13IVN1ZR2tTXct25cydTU1Njp06dqvL9wsJCFhQUJOgwV1UcQ4cOZW5uboL/z549yzgcDouJiRGULVmyhLVo0UIq22tDoCTfgHx9fZmrqys7ceIE27hxI1NXV2dbt24VvF/RS/rEiROMMcZWrVrFJkyYwI4cOcICAwPZ9OnTmYqKCjt27JhY0xUXn89nPj4+zMPDg504cYKtX7+eqampsR07dgjqVPSQPXPmjFDbuXPnMjs7O8bn8ytNd+XKlWzSpEnsyJEj7MKFC2zatGlMRUWl2i+lqB48eMCCgoLYgAEDWLt27VhQUBC7e/dutbGKMn+i1GmIWE+fPs2UlZXZ3LlzWVBQkOD18OFDQZv6Wq73799nQUFBzNfXl3Xs2JEFBQUJ3ctc0Tv5woULjLHyH0FTpkxhR48eZRcuXGBTpkxhqqqq7OzZs4I2fD6fffbZZ6xNmzbs5MmTbO3atUxVVZXt3r27QWOtMHPmTObo6Fjl9irK/Ijr+PHjTElJiS1YsEBofT569KjaWEVZZvWxXCWJVZQ29bFcjxw5wjgcDlu8eLHQ54aFhQnqREZGMgDs77//Zowx9sMPP7Avv/ySHTt2jJ0/f55NmjSJqaqqssDAQEEbHo/Hunbtytq2bctOnTrF/vjjD6aiosL2798vcawNjZ5C14AKCwuxbt063LlzB1paWhg/frzQNfe0tDQMGzYMv/76K3r27AkAOHXqFM6cOYOMjAw4Ojpi5syZla6J1TZdSRQUFGDt2rUICgqCjo4OJk6ciOHDhwveT05OxsiRI7F69WpBD3rGGIYMGYIvvvgCX331VaVpMsZw8uRJnD17FllZWXB0dMSsWbPg7Oxcp1iHDx+O1NRUoTIVFRX8888/1cZa2/yJWqe+Y/3zzz9x9uzZStMxNzfHiRMnANTfch0yZAgyMjKEytTV1XHjxg0A5actx4wZgzVr1qBLly5gjOH48eM4d+4csrOz4eTkhFmzZlW6LlpQUIA//vgDwcHB0NXVxaRJk4Su0TZErED5chs0aBCGDRuGadOmVZqmqPMjjt9//x0XLlyoVG5paSm4FlxVrKIsM2kvV0liFaVNfSzXVatW4dKlS5XKbWxsBH0u4uLiMG7cOKxduxYdO3YEYwzHjh3D+fPnkZOTAycnJ8yePbvSSIF5eXn4448/EBISAj09PUyePFmiSwGyQkmeEEIIUVDU8Y4QQghRUJTkCSGEEAVFSZ4QQghRUJTkCSGEEAVFSZ4QQghRUJTkCSGEEAVFSZ4QQghRUJTkCVFgeXl5OHr0qGAM+6ysLBw9ehSlpaUyjqz+xMTECAYXElViYiKuXr1aPwERIkOU5AmpB2VlZbh//z7OnDmDW7duifys7Pz8fBw9ehTp6emV3rt58yZCQ0PFiiMhIQF+fn7Izs4GAERHR8PPz0+kZ81nZGTg6NGjdX5oSEObNGkSYmJiKpWHhYXh6NGjVc67gYEBpkyZgkePHjVAhIQ0HEryhEjZ33//DXt7e0yYMAEHDx7Ed999BwsLC2zZsqXWtsnJyfDz88OrV68qvbdy5Ups3ry5TrEZGRlhzJgxIj0mMyoqCn5+fjJ/kp04AgMDERMTU+kxxwAwYcIE+Pn5VflIUy0tLcydOxc//PBDQ4RJSINRkXUAhCiS0NBQDB48GD/99BN++ukncDgcAOXJZ9iwYVBXV4e/v3+9xvD06VPExsZWOXa9oaEhhg4dClVVVUFZYWEh7t+/Dy6XC29vb5iamiI/Px/Xr18HUP78BHV1ddja2qJNmzY4d+4cgPJnbdvb28PT01MwnwCQmpqKmzdvYsyYMYiMjMS7d+/g5OQEJyenSvFkZmbi/v370NDQQOfOnaGhoSH0fnp6uuB9Ly8vGBoa1jjvmzdvxsSJE6GkJHz8cvfuXcTExGDu3LnYtWtXlWPVT5w4ET/++COioqIqjV9OiNySzXNxCFFMPj4+rE2bNlU+1czf35+ZmprW+Ajgiqd6BQUFVXrvs88+Y+PHj6/x82fPns20tbWZr68vs7e3ZwMGDGAAWFJSEmPs30erVjxu88mTJ8zU1JS1b9+eDRw4kNna2rKdO3ey5ORk1qdPHwaAjRgxgo0ZM4Zt3ryZZWRksDFjxrAxY8awoUOHMktLS9alSxeWm5sriOHWrVsMABs0aBDz9vZm/fv3Z+rq6uzPP/8UivWvv/5iWlparFOnTqxXr17M3d2dRUVFCd7ftGkT09fXZ3369GE+Pj7M0NCQnTx5stp5LygoYGpqauz69euV3ps8eTKbMGECi4uLY8rKyuz58+dVTqNly5Zs/fr1NS5jQuQJJXlCpKS4uJipqKiwn3/+ucr3K55Rf//+/WqnUZHkf/75Z3bkyBGhl4uLS41J/ubNm0xFRYWFh4czxhjjcrmsR48eNSb5KVOmsHHjxgnNw8WLFxljjIWEhDAALC8vr9rP5HK5rGPHjkLzXJHkPy7bt28f09TUZFwulzHG2D///MM4HI7Qo4rfvn0rSL7BwcFMT0+PvXz5UvD+2bNnmZ6eHsvIyKgylvv37zMALDExUag8NzeXaWlpsdu3bzPGGPv888/ZokWLqpzGsGHDhJYHIfKOTtcTIiXp6ekoKyuDtbV1le9XlCcnJ9c6raCgIERGRlaafk2OHTuGPn36wNPTEwCgpqaGhQsX4s6dO9W20dTURHR0NDIzM2FkZAR1dXV8/vnntcYXHh6OuLg4FBUVwdLSEg8ePKhUZ9asWYK/e/bsiaKiIsTFxaFly5Y4cOAAunbtKvQoVAcHB8Hf+/btg5OTE168eIHnz5+DlR+QoLi4GGFhYejbt2+lz6tYPp+e0j98+DCsrKzQo0cPAMBXX30Ff39//Pe//63UN8HQ0BAfPnyodf4JkReU5AmREh0dHQCo9FzzChVJqKLe5cuXBb3edXV1MXDgQEHdn3/+Gd26dRNq37Nnzxo/Py4uDra2tkJldnZ2Nbb56aefMG3aNLRo0QLe3t7o378/5s6dCwMDgyrrp6WloW/fvkhLS0ObNm2gp6eHqKioKjvyGRkZCf5WV1cHAEEnvri4uCqv0VeIiYlBVlYWTp48KVQ+bNgwaGpqVtmmYrkWFBQIXdvfvXs3XFxcBB3ueDwe8vLycO7cOYwaNUpoGgUFBdDV1a02LkLkDSV5QqREX18fTk5OCAkJqfL9kJAQqKiowMvLCwBw48YNxMfHAwCaN28ulOQlYWxsjKysLKGyT///lLm5OS5duoTs7Gzcvn0ba9aswfHjx/H06dMq669fvx7q6uqIjY2Fikr57uObb74R+750AwODan8MAYCenh6cnJyq7AlfnYofDe/fv4exsTEA4NmzZ4iIiIC9vT3Onj0rqOvp6Yldu3ZVSvLv379Hnz59xJgTQho3SvKESNGiRYswe/Zs3Lt3D126dBGUp6am4s8//8SXX34pOEr+448/pPrZ3bp1ww8//ICCggJoa2sDAE6fPl1jm4SEBLRo0QIGBgYYMmQI9PT04OPjg4KCAsGRcXFxseDv5ORkODg4CBJ8aWkpzp8/Dz09PbFi9fX1xaJFi5CUlARzc3MAAJ/PR3Z2NoyMjNC/f3/MmTOnUk/31NRUGBoaCt0dUKF58+ZwdXVFcHAw2rVrBwDYuXMnevXqVenHQmRkJNzd3REbGwsbGxsA5XcZPHnyBP/973/FmhdCGjNK8oRI0cyZM/H8+XP4+vpi5syZaN26NT58+IBt27bB09MT69atq7fPnjp1KjZu3AgfHx9MnToVL168wLFjx2pss3TpUuTl5cHHxwdqamrYsWMHPv/8c2hra8Pe3h6Ghob48ccf8dlnn8HOzg5DhgzBqFGj4OjoCHNzcxw4cABpaWliJ/kpU6bg2LFj6NSpE+bMmQNNTU0cO3YMq1evRvfu3TFlyhScOXMGXbt2xbx582Bubo6nT5/i77//RkRERJVJHgCmT5+OI0eOYMGCBeByuQgICMBvv/1WqZ6LiwscHR2xd+9e/PzzzwCAM2fOwNrautbLIoTIExoMhxAp27x5M27cuAEVFRVcv34dycnJ2Lp1K65cuSI4wq6Orq4uxowZA1NT00rv+fj4oHPnztW2VVNTw927dzFgwAA8ePAA1tbWuHPnDsaMGSO4jv3pYDgHDhzAlClTEBUVhfDwcMyZMwenTp0CUD5AzI0bN6CpqYkLFy4gLCwMQ4YMwblz55CSkoJHjx5h5syZ2LNnD/r16yeIo1mzZhgzZozQveqampoYM2aM4CyGqqoqLl++jP/85z948+YN3r9/j3Xr1qF79+4AABUVFVy4cAFbt25FYmIiHjx4AGdnZ4SHh0NLS6vaZeDv74/4+Hjcv38fr1+/Rt++fYU6931syZIlQiMRbt68GcuWLRO6558QecdhjDFZB0EIIdJy4cIFxMTEYN68eSK3efv2LTZs2IBNmzZRkicKhZI8IYQQoqDodD0hhBCioCjJE0IIIQqKkjwhhBCioCjJE0IIIQqKkjwhhBCioCjJE0IIIQqKkjwhhBCioCjJE0IIIQqKkjwhhBCioCjJE0IIIQqKkjwhhBCioP4feX3q+JziKXYAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# a smooth PES: stretch the O-H bond of the (untrained, random) model\n", "axis = POS[8] - POS[2]; axis /= np.linalg.norm(axis)\n", "scan = np.linspace(-0.5, 1.5, 120)\n", "E = []\n", "for dr in scan:\n", " p = POS.copy(); p[8] = POS[8] + dr * axis\n", " with torch.no_grad():\n", " E.append(float(model(structure_to_graph(\n", " {\"pos\": p, \"atomic_numbers\": Z}, CUTOFF))[\"energy\"]))\n", "E = np.array(E)\n", "\n", "fig, ax = plt.subplots(figsize=(4.8, 3))\n", "ax.plot(np.linalg.norm(POS[8] - POS[2]) + scan, E - E.min())\n", "ax.set_xlabel(\"O-H distance (A)\"); ax.set_ylabel(\"relative energy (eV)\")\n", "ax.set_title(\"continuous filters -> smooth PES (untrained weights)\")\n", "fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "509f11f9", "metadata": {}, "source": [ "## Capstone 3: TorchScript parity\n", "\n", "The deployable `node_energy` core (used by the LAMMPS export) must reproduce\n", "the eager model exactly after `torch.jit.script`." ] }, { "cell_type": "code", "execution_count": 14, "id": "162ca6ac", "metadata": { "execution": { "iopub.execute_input": "2026-07-20T04:24:43.318174Z", "iopub.status.busy": "2026-07-20T04:24:43.318059Z", "iopub.status.idle": "2026-07-20T04:24:43.480674Z", "shell.execute_reply": "2026-07-20T04:24:43.480062Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "scripted vs eager max |d node_energy| = 0.0\n" ] } ], "source": [ "scripted = torch.jit.script(model)\n", "d = (scripted.node_energy(graph.atomic_numbers, graph.edge_index, edge_vec)\n", " - model.node_energy(graph.atomic_numbers, graph.edge_index, edge_vec))\n", "print(\"scripted vs eager max |d node_energy| =\", float(d.abs().max()))\n", "assert float(d.abs().max()) == 0.0" ] }, { "cell_type": "markdown", "id": "5b85434e", "metadata": {}, "source": [ "## Summary\n", "\n", "With identical weights, the `xnn` SchNet reproduces an independent NumPy\n", "implementation of the manuscripts' equations to `float64` machine precision:\n", "\n", "| block | paper reference | max deviation |\n", "|---|---|---|\n", "| atom embedding | eq. 3 | exact (table lookup) |\n", "| Gaussian RBF ($\\gamma = 10$, 0.1 Å grid) | Sec. 4.1 | ~1e-17 |\n", "| shifted softplus $\\ln(0.5e^x + 0.5)$ | Sec. 4.2 | ~1e-16 |\n", "| cfconv $\\sum_j x_j \\circ W(r_{ij})$ | eq. 2, Fig. 2 right | ~1e-16 |\n", "| interaction blocks ($T=3$, residual) | Fig. 2 middle | ~1e-16 |\n", "| readout + DTNN standardization + pooling | Fig. 2 left; DTNN Methods | ~1e-15 |\n", "| whole model, random molecules | — | ~1e-15 |\n", "\n", "and satisfies the paper's physical constraints: rotational/translational/\n", "permutational invariance of the energy (~1e-15), rotationally equivariant\n", "energy-conserving forces (autograd = central finite differences to ~1e-10),\n", "a smooth potential-energy surface, and exact TorchScript parity for\n", "deployment.\n", "\n", "The same properties are covered continuously by `tests/test_schnet.py`\n", "(including an equation-by-equation reference forward); training on the\n", "paper's MD17 benchmark lives in\n", "`examples/cnn/schnet/schnet_rmd17_train.ipynb`." ] } ], "metadata": { "kernelspec": { "display_name": "xnn (.venv)", "language": "python", "name": "xnn" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.12" } }, "nbformat": 4, "nbformat_minor": 5 }