tutorials/Tutorial 2 - Countermeasures.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fb12f34e-58bf-45a2-9bc9-08184d725d0a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Tutorial 2 - Countermeasures"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c4da210-4e86-4850-9968-584527384cf7",
   "metadata": {},
   "source": [
    "This tutorial covers:\n",
    "    \n",
    "- Generating pseudorandomness in circuits (`wbkit`), existing and custom\n",
    "- Applying countermeasures (masking, shuffling) to circuits (`wbkit`)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e5c9f9c-63eb-47b3-b6aa-e5a4432dfcab",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Generating pseudorandomness in circuits (wbkit)\n",
    "### Nonlinear Feedback Shift Register (NFSR)"
   ]
  },
  {
   "attachments": {
    "9cc7efd0-745a-4e77-b18c-5e31c88015da.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "b9b78cd9-b52f-41f7-a6b1-167c0a57d44b",
   "metadata": {},
   "source": [
    "![image.png](attachment:9cc7efd0-745a-4e77-b18c-5e31c88015da.png)\n",
    "\n",
    "*Figure credits:* Wang et al. On Stability of Multi-Valued Nonlinear Feedback Shift Registers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "962e9954-27ca-4c26-853d-34b1fa105790",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from circkit.boolean import OptBooleanCircuit as BooleanCircuit\n",
    "from wboxkit.prng import NFSR, Pool\n",
    "\n",
    "C = BooleanCircuit(name=\"prng\")\n",
    "\n",
    "nfsr = NFSR(\n",
    "    # f(x) = 1 ^ x0 ^ x2 ^ x1&x2&x3\n",
    "    taps=[[], [0], [2], [1, 2, 3]],\n",
    "    clocks_initial=10,\n",
    "    clocks_per_step=2,\n",
    ")\n",
    "\n",
    "x = C.add_inputs(4, \"x%d\")\n",
    "\n",
    "nfsr.set_state(x)\n",
    "\n",
    "for i in range(5):\n",
    "    rand = nfsr.step()\n",
    "    C.add_output(rand)\n",
    "\n",
    "C.in_place_remove_unused_nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "b302f034-2c31-4be4-a64c-9af792dbe581",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 0, 0, 0) -> [0, 1, 0, 0, 1]\n",
      "(0, 0, 0, 1) -> [1, 0, 0, 1, 0]\n",
      "(0, 0, 1, 0) -> [0, 1, 0, 0, 1]\n",
      "(0, 0, 1, 1) -> [1, 0, 0, 1, 0]\n",
      "(0, 1, 0, 0) -> [0, 0, 1, 0, 0]\n",
      "(0, 1, 0, 1) -> [1, 1, 1, 0, 0]\n",
      "(0, 1, 1, 0) -> [0, 0, 1, 0, 0]\n",
      "(0, 1, 1, 1) -> [1, 1, 0, 0, 1]\n",
      "(1, 0, 0, 0) -> [0, 1, 0, 0, 1]\n",
      "(1, 0, 0, 1) -> [1, 0, 0, 1, 0]\n",
      "(1, 0, 1, 0) -> [0, 0, 1, 1, 1]\n",
      "(1, 0, 1, 1) -> [0, 1, 1, 1, 1]\n",
      "(1, 1, 0, 0) -> [0, 0, 1, 0, 0]\n",
      "(1, 1, 0, 1) -> [1, 1, 1, 1, 0]\n",
      "(1, 1, 1, 0) -> [1, 0, 0, 1, 1]\n",
      "(1, 1, 1, 1) -> [1, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "from binteger import Bin\n",
    "\n",
    "for i in range(2**4):\n",
    "    x = Bin(i, 4).tuple\n",
    "    print(x, \"->\", C.evaluate(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "35e3160d-4294-40db-b12f-a7bb81defb43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Digraph.gv.pdf'"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.digraph().view()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fa1604f-ba76-43cf-8cb2-ee23aace4776",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Pooling NFSR outputs for efficiency"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83c4a7c7-5aee-4117-b963-1c8a492743bf",
   "metadata": {},
   "source": [
    "At the cost of sacrificing provably security guarantees, we can reuse NFSR outputs many times, in order to improve efficiency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "37241c8a-5719-45c2-8f85-d803ba9f6184",
   "metadata": {},
   "outputs": [],
   "source": [
    "from circkit.boolean import OptBooleanCircuit as BooleanCircuit\n",
    "from wboxkit.prng import NFSR, Pool\n",
    "\n",
    "C = BooleanCircuit(name=\"prng\")\n",
    "\n",
    "nfsr = NFSR(\n",
    "    # f(x) = 1 ^ x0 ^ x2 ^ x1&x2&x3\n",
    "    taps=[[], [0], [2], [1, 2, 3]],\n",
    "    clocks_initial=10,\n",
    "    clocks_per_step=2,\n",
    ")\n",
    "prng = Pool(prng=nfsr, n=5)\n",
    "\n",
    "x = C.add_inputs(4, \"x%d\")\n",
    "prng.set_state(x)\n",
    "\n",
    "for i in range(10):\n",
    "    rand = prng.step()\n",
    "    C.add_output(rand)\n",
    "\n",
    "C.in_place_remove_unused_nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ead97198-2ff9-4a51-ad7e-d7f036f176fd",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, 0, 0, 0) -> [0, 1, 1, 0, 1, 1, 1, 1, 1, 1]\n",
      "(0, 0, 0, 1) -> [1, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "(0, 0, 1, 0) -> [0, 1, 1, 0, 1, 1, 1, 1, 1, 1]\n",
      "(0, 0, 1, 1) -> [1, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "(0, 1, 0, 0) -> [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "(0, 1, 0, 1) -> [0, 0, 1, 1, 0, 1, 1, 1, 0, 0]\n",
      "(0, 1, 1, 0) -> [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "(0, 1, 1, 1) -> [0, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n",
      "(1, 0, 0, 0) -> [0, 1, 1, 0, 1, 1, 1, 1, 1, 1]\n",
      "(1, 0, 0, 1) -> [1, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "(1, 0, 1, 0) -> [1, 1, 0, 0, 1, 0, 0, 0, 1, 1]\n",
      "(1, 0, 1, 1) -> [1, 1, 1, 0, 1, 1, 1, 1, 1, 1]\n",
      "(1, 1, 0, 0) -> [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "(1, 1, 0, 1) -> [1, 0, 1, 1, 0, 1, 1, 1, 0, 0]\n",
      "(1, 1, 1, 0) -> [1, 1, 0, 1, 1, 0, 0, 0, 1, 1]\n",
      "(1, 1, 1, 1) -> [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "from binteger import Bin\n",
    "\n",
    "for i in range(2**4):\n",
    "    x = Bin(i, 4).tuple\n",
    "    print(x, \"->\", C.evaluate(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfc16aed-090a-40c8-9879-f97e8907c3b4",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Applying countermeasures (masking, shuffling)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d17fafdc-9832-414f-9cba-273fa95a52b2",
   "metadata": {},
   "source": [
    "Setup AES Circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6f35a262-ca53-41bd-aadf-d4e36929b8cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AES(OptBooleanCircuit): \n",
      "   |   128 inputs,  128 outputs,  31273 nodes\n",
      "   | XOR:19284 (61.66%), AND:6240 (19.95%), NOT:5621 (17.97%), INPUT:128 (0.41%)\n"
     ]
    }
   ],
   "source": [
    "from binteger import Bin\n",
    "from circkit.boolean import OptBooleanCircuit as BooleanCircuit\n",
    "from wboxkit.ciphers.aes import BitAES\n",
    "\n",
    "C = BooleanCircuit(name=\"AES\")\n",
    "\n",
    "key = b\"abcdefghABCDEFGH\"\n",
    "plaintext = b\"0123456789abcdef\"\n",
    "\n",
    "pt = C.add_inputs(128)\n",
    "ct, k10 = BitAES(pt, Bin(key).tuple, rounds=10)\n",
    "C.add_output(ct)\n",
    "\n",
    "C.in_place_remove_unused_nodes()\n",
    "C.print_stats()\n",
    "\n",
    "ct = C.evaluate(Bin(plaintext).tuple)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fb711b1-e3d7-4974-9f95-cc2773e959f5",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Setup better PRNG:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "2bfb0ee6-4449-4c1d-9fb6-44dc88663798",
   "metadata": {},
   "outputs": [],
   "source": [
    "nfsr = NFSR(\n",
    "    taps=[[], [11], [50], [3, 107]],\n",
    "    clocks_initial=100,\n",
    "    clocks_per_step=1,\n",
    ")\n",
    "prng = Pool(prng=nfsr, n=256)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54978d1f-2d9c-4bd3-9eb7-efd458be0aea",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Linear Masking [Ishai-Sahai-Wagner 2003]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "791c692f-b27b-4a06-81e2-57df8cbe6442",
   "metadata": {},
   "source": [
    "*Statically:* Linear masking splits each intermediate computed value $s$ into $n$ **linear shares**:\n",
    "$$s = x_1 \\oplus x_2 \\oplus \\ldots \\oplus x_n$$\n",
    "\n",
    "*Dynamically:* Replace original operations with **gadgets** operating on **shares** of the inputs and computing **shares** of the output in a secure way. Requires **randomness** for encoding inputs / gadgets.\n",
    "\n",
    "*Security:* against **correlation** of any $\\le n-1$ shares/intermediates to the original sensitive value $s$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c1ff04b1-2f9a-494a-a484-5c14c35b277a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AES_ISW(OptBooleanCircuit): \n",
      "   |   128 inputs,  128 outputs,  95403 nodes\n",
      "   | XOR:64496 (67.60%), AND:24836 (26.03%), NOT:5943 (6.23%), INPUT:128 (0.13%)\n"
     ]
    }
   ],
   "source": [
    "from wboxkit.masking import ISW\n",
    "\n",
    "C_ISW = ISW(prng=prng, order=1).transform(C)\n",
    "C_ISW.in_place_remove_unused_nodes()\n",
    "C_ISW.print_stats()\n",
    "\n",
    "assert ct == C_ISW.evaluate(Bin(plaintext).tuple)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de6ee968-643b-4388-83fe-1741a193a41b",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Non-linear Masking [Biryukov-Udovenko 2018]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fae3be7b-2f53-41f9-8cf7-9a36659b52c9",
   "metadata": {},
   "source": [
    "*Statically:* Split each intermediate computed value $s$ into $3$ **(non)linear shares**:\n",
    "$$s = x_1x_2 \\oplus x_3$$\n",
    "\n",
    "*Dynamically:* Similar to linear (computations using **gadgets**).\n",
    "\n",
    "*Security:* against **linear algebraic** (**linear decoding**) attacks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "57b73e53-3022-47c8-bbf7-718c4dde700a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AES_MINQ(OptBooleanCircuit): \n",
      "   |   128 inputs,  128 outputs, 837633 nodes\n",
      "   | XOR:577570 (68.95%), AND:253958 (30.32%), NOT:5977 (0.71%), INPUT:128 (0.02%)\n"
     ]
    }
   ],
   "source": [
    "from wboxkit.masking import MINQ\n",
    "\n",
    "C_MINQ = MINQ(prng=prng).transform(C)\n",
    "C_MINQ.in_place_remove_unused_nodes()\n",
    "C_MINQ.print_stats()\n",
    "\n",
    "assert ct == C_MINQ.evaluate(Bin(plaintext).tuple)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32264655-bcc7-4225-8a26-b13d0ad802a8",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Combined Masking [Seker,Eisenbarth,Liśkiewicz 2021]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe116b92-a4dd-4c62-b51e-a16f772d2002",
   "metadata": {},
   "source": [
    "*Statically:* Split each intermediate computed value $s$ into **linear** and **non-linear shares**:\n",
    "\n",
    "$$s = \\tilde{x_1} \\tilde{x_2} \\oplus x_1 \\oplus \\ldots \\oplus x_n$$\n",
    "\n",
    "(more nonlinear shares are possible (provable construction for 2,3 shares))\n",
    "\n",
    "*Dynamically:* Similar to linear (computations using **gadgets**).\n",
    "\n",
    "*Security:* against **linear algebraic** (**linear decoding**) attacks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "6d64dc13-04e7-4cdc-b8a2-09c326aab6b8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AES_QuadLin(OptBooleanCircuit): \n",
      "   |   128 inputs,  128 outputs,1471609 nodes\n",
      "   | XOR:1073885 (72.97%), AND:391619 (26.61%), NOT:5977 (0.41%), INPUT:128 (0.01%)\n"
     ]
    }
   ],
   "source": [
    "from wboxkit.masking import QuadLin\n",
    "\n",
    "C_QL = QuadLin(prng=prng, n_linear=3).transform(C)\n",
    "C_QL.in_place_remove_unused_nodes()\n",
    "C_QL.print_stats()\n",
    "\n",
    "assert ct == C_QL.evaluate(Bin(plaintext).tuple)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3e7ac02-d8a6-4d4f-a922-6dde5d43a12f",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "### Dummy shuffling [Biryukov-Udovenko 2021]"
   ]
  },
  {
   "attachments": {
    "831a0f17-0345-4ae2-95bc-c6c032e8975a.png": {
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PnTt37NixHE7eTUw0GqdOnZo/f76FhUWnTp0wNjw8PBwcHIgmpJGhQmSPRmAs5kRw0caDBw9wFQ9+qI8ePUpISMjKyip8A6PBIQCewaSNjU2zZs0wa+CBFQU+HpmMZmdnY52L1iHACfNRcnIy5iADn2LAnrm5OVboogZCasKQKLOBRpr47Nmzu3fvol8w/OLi4hAeoqlRB1KWlpZNmzaFOMHY6Nq1a6lSpWSihBphoQUbGBtg49u3b5oaG3QPli5dukmTJvQQxaepaUnxgxDZI3O8kcQCBM6ePYulH/wi7du3x2/Dzc0NagFmPQOfmjELq8wk5JYGpzktDSaaSSh2mBAxO9+8eRMpv//+u4+Pj5Zq1CVZ6Knz5s1DuDN8chh1tMIB/UMjo46e9FWT05odGxhmEGZYz9HqV1JSElTwQYMGqcabLjtI/bqI7FEfw2JLAStNTGRQApYuXdqzZ89i287i0rDz589jvsYEfebMmXLlyhlps9LS0jD5vnnzZvHixSVkFhb1FCQuTH+pqalY8FWtWtVIe5Ah28VKQ2fYZpKNCQKxsbFYcsIPDzcsETxMENN7HmxMefz4cefOneG4iomJ0Ts/KjCAabdbt24QnJA9P/zwQ0lY/oujBNMCjHsjR45ED4aFhakAoBEVKSm2RSPqEkNgFdtf4B2B0oO1pyHwQ3hgiACsSegy+AzgG4cckuffYkhN99n69euHMLNt27ZpxLame/41UuOUKVPQcVj5vXjxwsrKSiM0DZAI0XsMsFP0zxJcCJUqVSKCR/89oRIH8M/VqFEDLgSVSuut0IcPH2Dg3bJlS0kWPDT6kyZNatOmzbVr1/TWGdqvmPh7tI+xcdYAnyqZAoyz63K4NtLuM1K2tTFOij0URPZoY9gQmgQBggBBgCCgCAFic1OEDnlHECAIEAQIAtpAgMgebaBKaBIECAIEAYKAIgSI7FGEDnlHECAIEAQIAtpAgMgebaBKaBIECAJFRUBAHZhKXc8sarFimr/4o0H29xTToUuaRRAwIgReHKTWnqae36dYb6iGLahfplJNyhoR+xpmtWSgQfQeDQ8bQo4gQBAoGgKBS6kJl6nJ26nRramFp6mVvahtE6gL3KIRKTa5SwwaRPYUmzFLGkIQMEIE+G+o2eeov7dTjW3zuHdwo9b8Qh3ZTvGMsDlqslyS0CCyR83BYvTFs6Kpq6epqy+orNymRD2nTp+l3icYdLuMkWetAmrEgERcpIIbUq7mBfjwgyhvb+rofSpVq5gZJPGShAaRPQY5BHXFVMgxaupGivcd9eYPqucq6sYaatNzyuId5e1O+Rmq+DFGnrXan8YNSEoy9e01FcIvgMjEhnJ2pbp0oIrtSWbyh0OJQgMnN5CnZCKQ+VT440JhQm7j008LHSyFXn8Ks3nC5Z5Clp1wX4whomKMPGsVR6MHJPU/YSVTYbNJwjdJwo2DhefStQqXoRMvSWgQvUf+GqS4v7mwn2o3gaKt7EnRVDKP6jGAMmVT43dT959Rw8Tuf/kaQE0aRN0ygPBXRjxnUdfWU1N/pcYPo0b9Rt03yssEmA4+RoDQxFKpj+FMyeoun2UXam5n6tlmqpETteIWdWYP9S5Fd7UbWk0lCg1DXwgQ/rSGQGqykJ9P3G+MkOMsfJAtWVnCbeH0acLlU4X29sITBrAkVc4zX3hqhnDdk9yGZAtPjRVa1xGeNUgdThJrlf5WDkg+2XszhBWGCQ2gD6XbmSDcOkboyBHiCFT8s6giXHKjYGhKZy/mKSUFDaL3GNrKR3f8WFpTed2fRd0JpMq5Uy5S271sW1N/raKmdKIsdMeXopqU85xI7dlLPXpNCUDGlOo9j2oWSm0+lftncXyUA0K3mk9du0k5e1AcQwTBlhq/gwr9TM1sQ/X6niobTS0aQO0JNUROdcFTSUGDyB5djCYDr4MfQd3+SLVomy9g+NSXSANnmZLLsw3lM4RqUTNfrFpQ5iZUZoZWmiOIf7h/+fIDj74VCLbkF/+u/GNXALcgJe3t6dXLtt6I1LbwkwsIj7q+n9qxlTr9iuJEUXv+pbTOimpgc+ypqpWpH/dRj/2opmnU+l26iLE2qC4Ux00vaKjWcSqXKub6K2mePAT4wkenhDdDc15HbhNacYQrPuRljTsu/N/hQsUy4A82BJtbUXimGxC2VWhXTrgjTB4K6qTz3i33NDMx4bRbE5pnu+RHbe1iYUKZNV/yipdHOemAr7UJZdpgVmCmOnXJKcsEEL7w03Phnb+EZaoKdwUKnwYJU+UQ009y/EWhVzPh8kAhrGyiWIMrPwmteuWFwWiTLQPowsLN0ysa2kRaBm0pI4vKQowUNCoEUk5R3gOoSnOpRwupQ36UmRlVoXxuAxKozdeokX8bYmOKynPWe2ryGmr4bmpUVW00h12tx5gRN+1MB3arlGc+YH3XadSPPVgpvfrUYufVaNl2+MTeqV/a+zbUgrWLESAsysmVithNmbpTfd3zQku0AYeKND/coO48oypGUFSLAgoNGlBW3ygzFUkyL6b/LpTgVa9oMMdNIznJ3XEagdH4iGQ9oroMp9r+Rn33mhJ2pxz2UfvsqHFNqIf3qBa/Un2rF2pR5nmq5nBq/Weqr17dPkXiOSuYmjiRcl5MTfbIt78ZXy8p4ZgpIHxqWUvKfxh15X+GB0X8QWomRW0bQrEF1KahVLVdVE8L6tIEanMz6tRYw2NXSY+o+7pEoSFDFyJJJQMB3jfhw3vC8OS81sa8Fd57IkwQhb6JgWAoNjehkCHPme+Ev4wSXv6a0wb+Z+Ge/4pt2BQTQPiRQm9b4cLnOWh8fSe7i/U35FOEC/oLj4QU2NwiLwvbthUGGJZpUFf4lCA0iN6j7kqlJJTP+I+qOSJH7+mnV72HIdSZ76iJ0yjXsVRdcCukEm5S99pQ63owLF0Ms2VepGqPp/55T3WOoebsoX6bb2CWN144tXQ+9cGM4uIc65pUXDo1Zxvl61QMe4JJk0oMGkT2MBkOJTcP7yX1+34q+iV1NJBq3p9qVI76YRHVRAuuC41BnExNbEJtDc7ZKZL3mFErgqiZtTRWg9ER4odRQ3yo2j9TFl8o7ylUMxuDbAEvjlo4mKq2kRpZxzAjwXWKWglAg8genY4oUhlBQD8IZFBfk6mKYmdV6IcNxbXGhVOcqpRhikbFnGvjbXFHg8gebYwaQpMgQBAgCBAEFCFA9pYqQoe8IwgQBAgCBAFtIEBkjzZQJTQJAgQBggBBQBECRPYoQoe8IwgQBAgCBAFtIEBkjzZQJTQJAgQBggBBQBECRPYoQoe8IwgQBAgCBAFtIEBkjzZQNXqaXC43Li7OuJoRm/sYF8/a4zY+Pj4mxshuzfv27Vt0dLT2MDEuyomJiZGRBn+evBqYEtmjBnjFt+iaNWu2b99uXO3btGnThg0bjItn7XG7a9eulStXao++NigfOHBg6dKl2qBsjDRPnjw5d+5cY+ScIc9E9jAEimQjCBAECAIEAY0hQGSPxqAkhAgCBAGCAEGAIQJE9jAEimQjCBAECAIEAY0hQGSPxqAkhAgCBAGCAEGAIQJE9jAEimQjCBAECAIEAY0hQGSPxqAkhAgCBAGCAEGAIQJE9jAEimQjCBAECAIEAY0hQGSPxqAkhAgCBAGCAEGAIQJE9jAEimQjCBAECAIEAY0hQGSPxqAkhAgCBAGCAEGAIQJE9jAEimQjCBAECAIEAY0hQGSPxqAkhAgCBAGCAEGAIQJE9jAEimQjCBAECAIEAY0hYCIUCjVGjBAyYASOHDly5swZFovRauPNmzdoiqOjo4WFhbm5uYmJiQG3LI+1d+/e8Xi8cuXKcXIfs9zH8NnWBocZGRmhoaF8Pr9hw4baoK9Bmph/srKyMjMz8YkrMLKzs11cXDRI30hJAY2wsLDU1NTGjRszaYJAIGjfvv348eOZZDaQPET2GEhHaJ2NWbNm3b17d8KECUxqwrT18ePHhIQEXKmCn0GZ3Kd27dqlSpViUlwvefDz+/TpE36uafkPRFHLli0dHBzE+UE2hgJYL61Qp9Lk5OTPuQ9m8EqVKjVo0MCQpW9SUtK9e/fS09OxvrG2trayssJn9erVTU1N1QHBqMti9NI9iNVDxYoV69evD3CYtOjw4cNly5bdt28fk8wGkqfkdrOBdIAu2ejVq9eQIUOKWiNmB9xh9fXr16ZNm1paWooXx3IVGobBakWQmhAzEnPZgwcPrly5QktT+vO7776rW7duUWExqPxYK/zzzz+Qua1bt4auU7lyZf12CgQ8Fi64vw43EOITT82aNT08PMRBw8rg+++/t7OzY7PZBgWmvpjZvXs35LG7u/vo0aOrVatWpB7EauPGjRv64ly1eonsUQ23ElQKuk6N3Ee6zf7+/s+ePYNpDms0+hOLryL9ZqRpajAFclGampubG+wYmBlFDxab0rLn6dOnKE4LJyzJpekYVAqmb19fX2h4ugdfph6JZTgMaBgMeOzt7SF4KlSoIIEY1gSQ+gYFo36Z6dGjByzGuu9BfbWayB59IV8c6u3WrRuszFCJoBjBRQRRVKtWLfyEDLxtECqYpiVscRI848Zi3DlNyycsKiGEOnbsWK9ePb03DXP627dvW7VqJTFJlS9fXge8wRYEo5BIm8EXGPpmz54tobv88MMPJWcOLSrssGMHBQVhDSRhEVU8IItai+HnJ7LH8PvIoDmEVoRVLR6aS6yCJdiFGSEwMNAAtSLFsEKmijLAdgchJGFvxNsPHz5cvnxZ3HyH73C0KKas2luInNe5D2Z/OHLAEmJAVCPFpBRtNMPkaGNjI54f1jM4aWiFBp2OLzKNZkTwSIMMkUP3IKQ1HDnoQUP2xknzr/EUTcoeQVr8N76tvY0xWm95r4+vPPIwJi4uqfL3a+Z0LaMm0KkhV/dtP/3OzKGcJUeQnFymy8T+5pc37wtIsClvb22a+vVzolnTUasneubZhIwZucJISbvxkYJZG1rRtWvXMG/C9gIDHXQII7Ly03qS9JCAYxweC5Ht7suXLzDfjRo1SiJnREQEQIBYUs12J/LlQOTAY6c9X86LFy/QBNo9A7UPnv927do1adJEvDnou2HDhklDQVIUIIBYPvhyACxETpcuXZycnDQumxFlA/+ZAh4M8JXmZE/KpZ+b9N6e1u/A0wMDHRgF8hoSHKyytZq6Bm+btvp8naZ/zKYoNRog+Hp6UrfpYUP3713tWY4tiDs+usnQHhuX1Pp+w9F1g+paUZk3fq7faQc3scOKPNlj3Mgp60VMYXCA07ngDId1DrYsacGDWRsiSuO/SWXcqfUeHgultjtUgODvkJAQiCjadgchBIcT8+hnDfpyRCEAWHpLCBXwiaAS8KZAm1ELrBJcGKO6Z8+ecG5Jr8w0ggps3X///TcWChqhpgoRQfSBaRsrLf/dqyiquOZkDyUUwtyit91CGX4/T0tZsWlQoTgs5jCyHBt7f18zat/C8+nMC8nMmXlj2dR9pSc+/xWCBxlYFg4Vyppm8nss+TtH8OAxbzbAt9627WKF9YuczFZoJxHSRdxAJ17JqVOn4EigtSKjM9ApRqtTp050Btp2ByFUunRpiSJYFF+4cAEBtVANGzVqBEOWuJ6kpi8H2gyCoFAFrc3A+S/TyY8IK8UNIW+VIkD7coCkRHSl9nw5EDyDBw+eNGkSVnVK2dNChsQXB1etPf3k+f1XrDevGrbo98vUH5qUZbR015zssfbe+OLrYkGZcjaMKtYwCgJuSEicvZpENbEsEUQ+exllV8+lSr7l0cq9XYsya9+6uIqkolXVyvbiezX1i5yamGmq+NChQ2mtCJELtIEO7vQWLVpoir4h0JEX4wBfDuxdXC4XggdS59WrV3CSQURhQpEw0yEdapBEokibgXSB8x8xexJBifDZNG/eHCJHpm/GEJAxdh5oXw4iCNBBCEjBIkM3u5RowXP8+PHg4GB9yJ7UwKX9p30YuGn7j3cnLa22a5Pbi10LJszts3FZt3LKpRkMBP0AACAASURBVIDmZA+W+Fb25fQ0iPghx04+yBqnp9rFqxXyeHyKLb49Toi5wcSUzVZwNIAekTMAyPJZUKAV0VnCw8MR4lWctCLY6Hfs2AGhC09A3759q1SpotjqiM1JT548EdnuoBsBE8gbGDYhWugQAGmlCinSiQbU8cbMisiXA5HTuXNn7MvRxAqWESIiwdOmTRvIHkZlNJqJ/2bj7HMt/r41trHZl7s5lE0d3H5c88u8CdtfdZ7rqlS0KM3AkNkMbsjHsEguN45ds1PbOljip0a9Cw7HUi7e0rmHZzVe5Iu7Dz4kWjq5tWpWKU8B4Cd++RD6OYYbm2Tj2s29fNzrwAcfUuwbeDSrU1a0LSM16n1IBJcbG2/i1N6rPiJueAkRH0K/cmO5CVauPTyr5ioXGaHnl4xedjvVY8DXiAgYHFmW9pXsFdje0sICLlx9EpEksHX29qn95UmKZ0dnic3DmdGv7z94G2chxi8DVvgpMVFx0clZQn563JeIiLwDXbK/pfOFmUnRnyPyTqYRRidlFcAqhRwD6PJL85PDXz56+jHJvknH1jUtvz09uuvcW6rR0Gl9ajHsNuPKhvU+HbaAXx2cEzDQwduvTzO32vBhdezj4wOTmrTIkdBmoNNAUI0YMQIWPJHtDroRysJzI+4/Q7b//vtPPPpOtRgHtRtXIgig4+h9OToTOTSs4oJHT0ALIi5eDG74qyum3PzgVn7QKm/vPx62r7WecrVVxpaGZA8/7Or25f8cP30jwm3tx6t1LFlZr06tXX/s8qkbUd477/QPPRxRq2PbmkK/ae4TK6+4undINQiNpMeH12w/ffHUveTOM2dX50Z+16KVi4X/ks6Dgpzn7Nw4vgkkTQ6VDccunbwR4bL0eUD9+mxBbMD+1TtOnjv7JL3v4SjPqpYU7+2/yzZeD8lkm/Den1n5x0sQNnMd8dcED9leL37ooYm/3ms9f/64fg5U1INDM3ymfRrz0su5UoGKmPXu8MILX2p5tSnELwNWBAmB+5cff/b0Cy82ad/yP27kWd0EX56n8mLPr/kjskye6pP2OkJAVaa7Rgq53EYrgS6nKO/j4UlDVnH7zJnS1vzR4u6zY51aDpg8tbm/52+7pvX5Q1m/G+V7LO1FYQuQPbDOQWOQbgm8GljmS8/m0jl1mQLD2vv37z09PSUYgwSFmMEjEX/x8uXL69ev03sz8QkzGppPMyzPdke/xUoc7hyIJfjP6Bg8RMoh+g76onh7kSgd8aFLQIyuLhjWYA2GL0cCNzW9cSrgoEDwYOUBS/X9+/dlbqxWoS75RQQpycnfXr8I4fdqkG/TMbGp6uza1K5DE0absTFSNfUk7OppwfFaF87PJxi33duc49pjwaFQHp2Uem60I8d5zsPs/By8oKVuZuxK/fd+yssh5EeeGlnDzNFnZ3BeCv/rxo4cM7dlQfk5hJmBsxqY2Xx/JFXEePbTBY3NLH0PFKTIaVPmnV8beq3+JOJQGH94aP8Nn/P+Ttnb29zUyXPKfjn8MmGF92FFS06ZwcfSRRyk+6HRTRe+EDWaH7qmLce6/+ECbqWQEyqDjvdujVdp2z57YuhqYvf0KW3l8cfLbGFmaqqookIgzJw5c/ny5XJwKT7JmMTXr1//559/Iqr10qVLmMEx6SNRXy2E6g8//+bNm1evXn3+/HmcQgROcFYeZgcEFxw4cADc/v777/DxaI9DuJEgaSTog6tly5Zt3LgRPPj5+d25cwfblbTHg/FShsYJcLZt27Zy5cpz584hIFO/bcFeBUQu3Lp1S5wNjHboxEiZN29ehw4ddMNh6n9jK5naNpt05E3S542DfzxXMOcxql9Dek+ucDTjmBV2MJmbcyhebHm3PjlqTs7DcXQsJ/wSGs6jmudVbGZmSpk27tbbKd81z6rQ67fxLQ7PWbz8ysDt3hCfLBtrSxMqWUz8snLoqvYIk5MTnx5afbzb0v71bXOYLd3S1+e9lRjbgqz6nfrK4VejrIg3QAo5Shl0CTcvB6Q5TKiRp9ja1K9fJfPC5WuRs5yrKLA2qgaaUZWCVvHzzz+Lwhbg/r169SrOm4EhXsftgJjBGWvQz5ydnWGWEffl4CAihLRBm4HNkN6eqVXXtMxdqLBV4oA10eYkfMGSGcdSSKD08OFD2DlpC15Js91hBt21axe9L0fHvhx5Y1WBxoMiOC/44sWLOK5QXnHNplt2mTa387mfNw9udLha+VL2XfdcqT20c11rppVoUvbIrJPt6ORUICnYbBbFz86W3PteqCTbqbVnNZN1/hceUd45EeuqGU8yo98FfU4pqIhlWbFufUfLtmPHN+i6cJDLrgp1m7p5tuk6ePzoIZ3EzXMK+VWNFZm4MEhUxEopBwdb6mVKSv4FGJnpmSaW9vqJMWTQFF1nURq28Pz58+joaPoYOsz+mupYmLmgwdBHzsD0h0MfMJvj5CGJ9vfr10/XiMiqDzIJ9iLFJiPIJHpzEr5AebK1te3evTtEpix6xS0NowL7cnDGmo59OfJwxK4shFMjqg3BBdJ5cEMKllxwH06fPl36rTopq1atkh0jblpvwuFzrGmTF++/HxEfumNC1wN/dJ6z//DcdoyCrLUueyiIm8IRXkrvC2Lb2dma8D9wuWrgxY/YO9p9VkC2iIRZ4wUPHi5ubOk271KAy+bNBy/dfXRr//Kzu7fsnH7s8p+dCsAqOr9qsKm4qAJWLL1nzGpzfpvf7YRuncpQyQ/P3Yhz/d+vfdQ9j0ExP8XoLX5LCIeltSKYpOALwWZPBCIrbSLMdxAqtHTBpRKIWkYRmPVgsIIagZUyZmfdaDNKWdVIBqz3RXSgyUECSYfMwbAJE5B4dAPEuYR7SSPMaI8I2oXBYAi+HMVtBPg400im7KlatSpWCQiYlHnsrzhZBIsiPBInLCiuS/RW0c0pti3G77g36s9b8/v9+qaC6eMzVxYNGF3p/onRIkOW/Dq0L3vk1y3vDT8mJl7IrlA5zxsPzUciJ5+vSHHiPV67LuqnqVMux43niek9phZWphTv1dnz7O59Zm7oM5Oi+N9en1j644T187eN8vqtXr7RTx5XdHrRWFFMS623phxL93ETLU7PnHy1nEVSrNmMm9eGuDDy8KlVbXEpjJlRNDnSBjpp1YeONIN0wSsIFVy+BxlDb8+ko5nxCtMuDumCYQ2/edisYFjDU1xAkmwHrSdJplIUwoshy0XmOyh/0JBwnKhETlxnhxPMVD5bSLpe9VPAM33GGrqVPmNN0Tyrfn3qUcA+rZs3b9InDcJ9K0EM4Y5wcyKo5MSJE6KQHJkV4pof9NHw4cNlvlUhkWNfs2rlZm12bW5+e1avvuvX73o5fEljpaJFaQYVOClyEfzIxcrwgvxvhZvU+bVvUzrRxJxjXui8hMyIiCgBVejCFWyfQRb6UAV+YlRUmoDFsbKR9gplvDn21/OK3ZfmupvYdg0HrFj77OrAsAgexUj2MGGlyK1XrUDi7TtfXDftG6Q0klE18iWpFAx00FQw+yAEgD7NDJOsl5cXFCP8SmmtCIIKthdEEMFvhAkUO2x27tyJuDVMWBK+nJKEXF5bAYhS2x2yYpanQ+9o2x2EEPCsU6eOXhAzQF8OExxgJUaQiDzxA3MohiXED0am9FqKCf0i5fl2aXa/ua+6bjo+K28LOLtC5yV/Dj3h8+xZKtVY6cykSdmTnQ09g4+tlflPVhZsXrwsXoGVLSdFiJCbQk3kPT93NGjoTw1y99hkvt0xf9vHehNPznDLEx2cOnWdWM/i4kA3RzcRhJ+49NKM4qWnYZNMnl/dtHK92qX57z8G8yhXVmww366ptNjJq5L3et+6M5P39ss7ci49hmvSpLULvRVHKb8MWKFARMjPFkOBwkQlzOYVbOkRAihkEfN6SSGXQ0UxdFZOtg8mjZwT2aWqJduUY1HKyr6mezu3atbKtxMXaXiVhMwBAQFw4WJ7piigmb5sBpPjlClTRGELCOmGLwfXEmOqxdOnTx9k08EvvNh0gehyDdp2B52DtliKNxCb89EX4uY7LelJ6DjwA3XNQHw5zHtZsfiBgwrXE0MRx4qKOU2VcvI+3PC78yyuYkQ6VXD8iEWDBjWsvlkxuayevWjRIpUqLlwo697foyYv+jeAmx795m5gkMC5c8qeYZOXnLgfmxn3Hr/tcOvWtV4uGzdzw4XXiVlfn10PeJhUvbt7ZbYw/u7uTTcce3eMOe/3ihsb7L9jweJz1mN2HlzSUXQeKat8gyqJftuPfjSzzvh099TeK5xOjSKOXbl1//Ldp+m1+3rkmOYsatcr/erAtnORZumBp0Jcxg9xLSNzEs5+c2p/sIXps+svv2UmfX5xadfqM6bj/5ruVjb71kol/A7ycacUsjLUp6bfotEzVvs9S8z4/PRGwKOE6p0tz0+eMHfvzYi0+PcBd+8Fm7s3C187avpfZx8nZOag8CjRqbvwWGHkvBu+XaWElRzozMpYhR9Zscv/xbP7d25dv/LfsV0b/lqz42pUlfZdG9rJajvCvWBPUKyMa2AkGBIJrG0xweE0Myg0MI4hrBkmC5wDLeGxwATUtm1b3K6Ng9SwDIfRTHxOhPYD4zgO+EG4Gjw6onPvYQChBQ/WoVhm4teObR9AmEgjpUMAQX2Q9NiEJB04h1dIhDygYcdRQ4hvBuwSEoIOfGC4hQWZcRMg7raQ6BrwYKSdhbGHcJXJkydj1GFkAnBETsKkiUADfMfuY9EoldkXCLSBZwjBnzLfMk5klYp+HuN7ZOegcixh8sOTN8v06VXHNC1gz/rI1nOGNrWRdE9I0c0xZEsl6i6B/3Fl2wYL7LZG+Y0wCQ96xzWv6VzHXuau0MyYdy8+cAX2tRvXK099efmcy/7OoXx5B3s4cfIfXty7x+8zqzRyrShX4gsSIqPNHB2tUr88f/YxiVOhrmtdB5nVKYKAASuKimvgnSDm3P+6/WH2+4nV3Svmt5+X8O7y+p/Hrbdc9ur0SMk7IlEn4i+xrsenBuo3PBIw22I1LWGsh8K5adMm2jcj0mnwhcmeSkQT0J4A6D24vEDB7xmSKSwsjL5AjzbQwWVtCLfMGV4vaYwjHNwAHVRku4NuhEUDQj/EK5Dw5eDaDkP25agADYYcjG9jx46F72fPnj1YA+GTCR1YkrESxSeTzIrypN5ZOPJgg5XrBlbjbhq6pNquLfD3DFxqsfzC755yp+ACegYje0aTEC1FvVz4XfyunjX2dXruP6VaYQ0n6+YvzsMzNoRt6ypNq5jJnqioKEz6tHsGn5hoICFwJJp0w4uaghNrsKsDWwhBEMFvSs9YE6dPG+iwoJYIXIZMAkENBnMXtVHFMr/IdofeB7Yi2YOFCH1fDlQodB+ceRLnghcbNETiB7o7c9lz+/ZtSO4JEyaojwMv/L+l8/d8MLPl3n/EqmkTl+4+Z9tyXydGrhxGmdRnUS6F3AuPco7fJE8RECjt0qxW6C3/8J9HFQplTH3ufz+z+USXIlAy7Kx0QDNEC2YQCQMLfQ8QjpnReEAzKurduzeCC1QwyND7iqRBhaQ8ffq0KGwBJns8mC6lc5IU5gjI258EAx287gh2h6GV1n7wiQd60sSJE6EkiVdh1GcLiXw/uBGKuYMHIdoyo7SZIy/KaVq1x6K9PXhxAQsHJ1VbuXWk2FmcSqnpUe/5dn3N3F1+F4/fCOPU7eLboddPaybKOYRNaStKXgZeqN/vM9c//86rT+cW9arY8mNDX979z++pWc8FK8e7yfT3GIvegwmavmwGVi/EnmHpCgEDYSAxZWiky1EFvS9HI9SUEhEPW0hJSRkzZozSIiSDYgQgUegz1piEDEBPwsJCYkmBgwBwNDgElSjAARO6cW2ehfbTNPfBoU2K4dLaW15ceDSnaqVC96srq0yPsoefGsdNNbEoxcG2m8z0DJZ1BTsGRkJlDSpR7+F5eh70MTwyxbRsRae6ri5OtvJ3KRmO7BFpM1BoYJ5CmLJ4p0ETxk0B9I0AMJVo47AZCV8Otk9qoxYVRuLJkyfhRobKhemP3lekApGSUITWZuCQo/flwBuHM4pUbri47Q6UEYqCI18lqCFgSiSfpEMkVK5aUwW3bNmCUBqG/h5NVaomHT3a3NhW9hXyN0NaF0lgqtnm4lPc3KGuG/4ZTYNgaEaMDX7edEAzjE74IsE9xABCzrTUJHFfjgHuy0GgHdawmFLhCqYNdJhVEaClJTSMkazIl4MlC8BxcnJiovEobqk8252oFNZDOM8mIiJCZLuDHEKcGJYIiinr7K0xhlHoUfborF9IRbpAQKTN0OfNQKfBj1PiJ4HoLzxa0maYNFIdXw4T+mrmEb9QHAY6yCHpA2yw0oeLosT6iiBpcD4edlapL3KYdxbWQ127FsTv0HqStBEY+vqjR4/ENydBfVd8XB5zHopfTiJ7il+f6qFFOGxm69atsEWIQpmxIJU2ZOFoAJ0xBxGIbT0Id5ao0XDWqoqhgOtY+lRpFPn06RPu9cH0R5vm8IkdS9LzoGLiRvEWSgZOHnNzc5MQM3rvQXlnC8Hhj2MvaN0In9CTsM9GOvYSd4xiTYYuYx4doNn+yjkBRijUpfCWyT+RPTJhIYkFCGCXX879s/HxIoUGeykkDiLE+m727NnSwkb3OEr4cmAtMQSuNIgDJjg8tFaEYD8Y6LBPELEYGqxCv6RoXw5O9sQX+ow1dXw5umwLtGomZwthw2xMTAxaB/2VVpJgZMZaTWes7t+/XzP7e9TjWI+xBuoxTkoXEQHEGmDbCo7cYFIOy2qEA9FhzVi+4U+s9fAgBRMBPvW+aJJuBRwkUHSQTv+eoYSpECQtTdYYUzCpIX4Pa3DjcgPAG4ceFM3IxnvuAMMxg5aiyXjwm8KPS7wU3EuIy4dSK+0QlUkcBxHhQiaG20U1trdUJiuME4newxgqI884YMAA5pvtcUcIpi34co2o0bi/BJ6kQYMGlViRI+os+N6g/2FlLe6lMPyuxGIcy5qRI0ca4MpGx+hhtYcr4ODww7EFTKrGoVASxzowKaXfPET26Bd/3dXeLPdhWB8OKIOXGwfiMsxvCNlwzAHm3NGjRxsCM3rn4du3b1g4G1cPYs8T/IVk2xM9eKAJIS7UuHqwSMNe1qmTRSJAMhMECAIEAYIAQaCICBDZU0TASHaCAEGAIEAQUBsBYnNTG0JCgCBAECAIGA8CuBcRh+TqnV8ie/TeBYQBggBBgCCgOwQM5GZ3YnPTXZeTmggCBAGCAEGARoDIHjISCAIEAYIAQUDXCBDZo2vESX0EAYIAQYAgQGQPGQMEAYIAQYAgoGsEiOzRNeKkPoIAQYAgoEcEcBxtYGCgHhmgqyayR+9dQBggCBAECAK6QwDHJWzevFl39cmpicgeOcCQZIIAQYAgQBDQGgJE9mgNWkKYIEAQIAgQBOQgQGSPHGBIMkGAIEAQIAhoDQEie7QGLSFMECAIEAQIAnIQILJHDjAlMhmXWUm3G3eySScaToox8qw99IwRDWPk2ah7ENcjGcJlvkT2aG8UGR9l3GraqlWr0NBQmvW3b9+2aNHCwO9T6d+/v7u7O31jKdjGFw8Pj6FDhxof+prgeMSIEbilCRdp08Rwp1Hr1q19fX01QVtbNH788cdGjRo9f/6crgAXpuGwy+7du2urPsOmO3XqVBz0+eDBA5pNXFeP++lxJ6kGucavA1cYa5CgaqSI7FENt+JZys/Pr1+/fh07dsSVvbj4snPnzuPGjTtw4IAht/bEiRPDhw/HFau4pjMxMRFfhgwZcvToUUPmWXu87d+/f+LEibiuFHMWrmJDV/bu3Rvdqr0a1ae8Y8eO6dOnd+vWDZfdpaWlgWc8ly9fVp+yMVJYv379okWL0GtYN+D2UvwGmzdvfufOHWNsixKeheQhCBRGYNWqVbgw29LScvv27caCzYYNG8AwHvx0jYVn7fGJVa2VlRU6cfny5dqrRbOUscShecbMq1nKxkgNKypra2v04MyZM42RfyY8myCTEulEXhcLBE6ePHnhwgUTExMmrTl//jyHw4EOwSQzhlDfvn2xbmWSuUh5zp07d/bsWYY8Y6WMO7O9vb2ZVAGee/XqhdUlk8wGkgcNPHbsGEM0bty4kZSUxLCBQAOGne+//17jLfX39z98+DBDnrG6j4mJwVhiwgZ47tChw+DBg5lkNpA8d+/e3bNnD0M0YHbDAQQDBw5kwjzQgLV85MiRTDIbSB5yf4+BdITW2bh///7Tp09hW2dSE9R8jGaGPxKoGk5OTtqQPY8ePcIvcNKkSRrnecuWLRUqVGA4NTOpXQd5nj17htkZ/gAmdRWpB6En2djYaEP2vHr1ClJwxowZGud53759WB4Zl+yBA/XixYvz58/XOBowMsNAR2QPE2BJHj0ggMmFoewpEnNhYWFFyl+kzFgFa4Pn6OjorKysInFiCJmhq2kDDXiGPn/+rKUGImpAGzxnZ2cHBQVpiWftkYV+qQ00IIYh47XHtjYok1gDbaBKaBIECAIEAQNFAFJq3bp1emeOyB69dwFhgCBAECAI6A4BRNA9fvxYd/XJqYnIHjnAkGSCAEGAIEAQ0BoCRPZoDVpCmCBAECAIEATkIEBkjxxgSDJBgCBAECAIaA0BInu0Bi0hTBAgCBAECAJyECCyRw4wJJkgQBAgCBRHBGrUqNGyZUu9t4zsLdV7FxAGCAIEAYKA7hDA8bJ4dFefnJoMQfbw3p5ec+heZGxcYsV+q+Z0K6t9XUyQFv+Nb2tvw5aDilaTdd/cIjZHkPzxxonDR88//JLJNrewMLOs1G7sjHGtylOh/84+VPavOZ2LSE8X2Y2RZ+3hYoxoGCPPpAfVQcAQZA/LrkZT149bZqzxq+66GLJHnfYwKZty6ecmvben9Tvw9MBAB+0LOkmWdN1cyfoV/S2Ie7Bz/rQ/Lpn1mjbz931d6pbJgSf59cG5kya/7mW2Zerz4U8UFdfLO2PkWXtAGSMaxsgz6UG1ETAI2VPetVP/mlEHF/glqt0eCQIZfj9PS1mxaZBloXShUEBRejtDlaVic2W3RYOIpb7e9VP/qded5h59ML2lfYFQtmk4ZNWCkNbuC1/Xmt26sgYr1AApY+RZA82WQ8IY0TBGnuXAr4HkkoSG7pf9cjoI51YyOmFZTnHZyQJuSEic1FWc1t4bX3z9+k4vSk8+n0Vvruy2yG63Cqm89zuHdv3pP8f5/52YKS54aFKchkMHtjAv597axRAWK/nNM0aeVegahkWMEQ1j5Jlhd6iQrYShYTCyR4WuUlqEH3Ls5ANZB0ayrOzL6cfZo5RneRnktkVegSKlpwUsGvzLubQOy3ZMbVRYR8wjw3as4VTBrY2HRZHIajWzMfKsPUCMEQ1j5Lk49CCuGpF5T7n22iaTctGXsbyE4Ee37zz8mFS6bvvuXVzK5VDITIxLY5lz2CaCrIx0gYV9WSs2JUhL+JbJtuBQWWk8c3s7S5Yg4Y3/+VuvuSzHhp5eXs7lFDj6U6Peh0RwubHxJk7tverbUBQvIeJD6FduLDfByrWHZ1VRUQU0M0LPLxm97Haqx4CvERHmFMWytK9kj3k1gxvyMSySy41j1+zUto7YRJvJffvwbsCzr5wazVu1albdNr+S1Kh3weG4BjLe0rmHZzVe5Iu7Dz4kWjq5tWpWSeY0LY5zWljAhatPIpIEts7ePrW/PEnx7Ogsf/qWxwElry05VRWtCpmDgPd6w8x1T7Pqz1o8uobcXhGaNWrTxlZmeX0kGiPP2sPJGNEwRp6LRw/imr6rV6/iEgrtNYcJ5aLpPZkfD//UymvqNZb7gB+6lHs4o73Xb1diBBTv/ellP/dpXN7apmz9br9su5cAdwqV9mB9v0bf2djV7TJx2/3E+OsrJ/95i2riM2JQK4s70zu1m3T4baY8BrNenVq7Ytbwnj36zT71OcdkJogN2L96yaTvvXsP/ftefjGBApq8t/8uW3U2JJNtwnt/ZuUfOc+Koy9ySvLDrm5fPnNErx7fL7oYl8NnziPg3lrer9uEw2FlW/n2aGjyePXAzmP3vE7LfZfLzOwRvXoN/sv/xaGF8/c9z3ZwFN6Y5t5o6MEwKXteHsGc//ihh8YPXRVco9e4KVPHd7O9O8On3x/XRVWKZcz5qoAD+W0pWhUSNRb8mei3cl1gqrnHyLHNIaPlPBbeq3ZPlC+Z5JTSWrIx8qw1MChjRMMYeSY9qFEEmFxumpcn+cZ0Z6saY/zi+HQC79P6jqWrjTuflPtnRsD0emalu2//mvdWKOR/+tvXZ2swTyjkBa9qW8qyzk9nv+Vm5Ydt6VraxmvtR7zKf1IP+FpyvNaF55fmf93YkWPmtixIlCczcFYDM5vvj6TSRZTTzH66oLGZpe+BvAIFdQkTdvW0KKgs++VqLweX6XdSRDn4X/b4OtYYcSIyn5u47d7mHNceCw6F5rGTem60I8d5zsNsMaqFv2be+bWh1+pPIjSE8YeH9t/wOe/vws1VzoHMtiiuQoIzXL4r+wbl5BNDyrFMzDyXvxPrDrnNkvFizpw5S5culfFC7aQFCxbIvkFZbZ6XLFkyb948tRnUKYEVK1bgEjYZVaqNxurVq3ElnQzKaifhrP7JkyfLIKM2zxs3bpw4caIMygactGPHjtGjR8tgUG00du/ePWLECBmUZSXt3bt32LBhst7oNI253iMI3//HtneV+ozsnL8Bh12lexfnqDP/+ucqCOZuo4c3y7y+/1BInjIgiPL/UGfSsJy1solNrcbOle1KW9IWHVZFD7fqGU/uPZGr+cBEZmNtWTj4gGVuzhETuyrQFJU245iJGi7gHluy/E753gPdrUTvWRX7DW737dC8v/O9RTlV82LLu/WplmeT4jg6lhN+CQ3nyV0ICJOTE58eWn38TWKedlW6pa9PPSsZgDPiQFY9zKuQVTovLSvo4bNvAnY1N08nufY2BcX1a41ZnQAAIABJREFU8spAeBbEP9y/fPmBR9/y9WfEo7/4d+UfuwK4BSlpb0+vXrb1RmRBiqYhMxA0itQsQ+HZMLrQUNAoUheqnZm5vyftrn9gClU16dWJI5/zhULWF54w4fNnhEbD88GuO3xkh+U/79v77Jffm5lS/I//Pizfb3iuS4RVrs+6B31gWUoNf3DW//7b8A+BcYKsLAWiB/JKSdybKjRlwZVx+79rcSbNKlUpJBU4lSqVE564dP71Co8meaXYjk5OBcKPzWZR/Oxs+TOKedux4xt0XTjIZVeFuk3dPNt0HTx+9JBOsoxaSjhY5tFETi8xr0JWw/PSBPBkCShW1Vq15NSSky81PCy1cjU9bIaSzbhh8Mz/+M8vY+YEmlw0b+M/tVrO8BFEH5oxcvZlfjO+e+D8hrmiPPnUnGEzTmXUT27ydLm7+NpJdstUSTUMNIrGuYHwbCBdaCBoFK0L1c4tYxkum6YgNSEhQ2hiX6N5s6aix2PS/tdvDoxwpIuwKg0Y1cPuzaHdt6AI8Z79+6HOwKb581lWqN/iAS3dfP+4nVW3+7jpP7apwLhm2fwgVSM0BUlR0SkCEzMOpxBDLI65uYkgNjJKrHaIm8KamFAuazkvLN3mXQo4uXxCj/rmX27tXz6pS+NWs65impd8lHGgwKfEtArJKsX/ZpW2sWKZsKxtSsvtEX7wrtUHvkhzroisVt8ZBs/saj3GjPDuNnpUt0p50LG+6zTqxx7ew8b1qZWvQ1q2HT6xd5eB43wbakfwAGfDQKNoHW4gPBtIFxoIGkXrQrVzK1jrFqbNsq1atSxLmG1qV7NOTXnGGbseY/pXPn5814Xf3cuciGn+v9p0RkH8+SldBxyvseq238S6OT9B/ut84oKMtGyOpbnMaU9yvw+fLzb9FZUm7/HadVFTpvWQRIxVpqJjaZYwLSVFQNkVsCFITUkTshwqVpTMz/hv3quz59nd+8zc0GcmGvzt9YmlP05YP3/bKK/f6hWGTxkH0mDnt4VxFYqY5jRs6mJFhcVGR/Ep0YxZqEDC9V3vG46dyHioKKpNM+8MhGdz5zH/nB8j3iR2zUHrzg0qlFLFZ8VpH800Ww4VA0FDDneykw2FZ8PoQh2j4eXl5eLiIrtjdJgqc9KXWb9F2349KwvfPrxf6PABXtDuLRcKUizbjR5SP95v954DfplevhXzqMed3LQ3uEyv/43OFTx4+MnJqblKA//NukU7PstcUZuYc8wLHT6QGRERVZCTCU1TNhsU6AMM+IlRUXTgmkTrLNr5dqsg/PDqZYbYC0H0y1dfWQ179W4okZv5n1lvjv118FmeP4ht13DAirXj60SHRUh7iJRwQM/5strCvApFbJftMdynouD5pfMRsjQs/tczy09XnTCyurQIVERUy++MkWftQWKMaBgjz8WlB6tUqdKkSb4rQXuNUkaZueyhbLwX/DW4zJU1qwOS86nyPh3e8qJMI2zAyX9MG48Y4Zl9efFmdk9vu/xEFnz7VEZSYnpeQuJ9/7d8ayojPYOfnCa0yvW/Z2fzBMLsrGyRHYtTp64TKyEu/1gCQfiJSy/NKF56Gr1ZlAFN08r1apfmh38MxnQviA3m29XIZyinMorPo+dau96Ll/uYnlu/+51ILCTcXLPtad3Ja6bAb5X7ZGVlw4yYxSuwsuWkCPl8RWY33ut9684gBD3vSY/hmjTxdDHL/bNQcxlwIKctiqrIr1fp/2V7L/t7SIWAlVN2BInLX4AWF7h5yqK33ovHNdCawUgpd7IzGCPPsluiiVRjRMMYedZEX8mmURLRKIohhVVlwI6r5osnT+s9vFO/TnU5X548+Fxt9NKf89WbXFTZNX4Y1XnFetchbQo2XtoP+mP93TELFg+enTLOw+brs+fZnmu2T/ph0KpB49q1Hfi71b2/h684/eAepxR/yxDfR91/3ja/sy1l2mjSsv/5/7Zk3j8T2tjFvX4QYt+9X42d8y/P6+h9bdjiA1MU08yVe2V85i7t1W/19Hnl+1sFhTSfNhppWff+HrvyDCozF2wZ2vf9yKUbxzpXH7b/quWCaRN8nnp29KhlFn7z7N3sEacu/touh0rmrZUjV/s9eWheird3rE9Qlx/XjctaN33X1cDPFizu0p6+l31n75nsLmNEmbDK1TK/Oe/X4NZeLvaZwbfP3LSZt2poBVYOB5LNVchBLm1ZbaHkVSGDG0VJrErf/3PVfNFPv3Zo5DdkwoA2DSuaxb5/8fTpuxSnftM39KohK0BCET1dvDNGnrWHizGiYYw8kx7UIAImeSapIpEUpH4NehXGr9DApZqtDMUpK+pTlHX1qtYSNPmJ4UFvItJsqjvXr5ij6ghSubE8OwdbheIvM+bdiw9cgX3txvXKU19ePueyv3MoX97B3oouxYAmL+7d4/eZVRq5VlR6CgHa9SYo2qJmw5pl1V/nCxIio80cHa1Svzx/9jGJU6Gua10HpZO4Eg4k2lKkKmbNmlW2bFl8yu/qrJhXN6/efhGeILR2rNW8Q2ePqgVh5/JLUXPnzrW0tMSngjyqvVq4cCGLxcKn/OIq8vz7779nZWXhUz5lg3uzcuXK2NhYfMrnTEU01qxZ8/nzZ3zKp6zim/Xr1wcHB2OXj/zyKvK8adOmoKAgfMqnbHBvdu7cGRAQgE/5nKmIxp49e27cuIFP+ZQN7o3CiV8etyyris7u8r3wnArVq8ooyrat6uIh9oJlVc5BRrbCSeYOdVs41M1Lq+TiVqnwawY0Te3runsqrSc3A9rVsIX8djEjkp+LVcYxN/7PqlKjVhJcyyekhAOJtqhUhfzKKY6Dc+cfnA3xeh75TBsjz/Jbo+4bY0TDGHlWt5/kly9BaMhQW+TjQt4QBAgCBAGCgHEj8OnTJ6hfem8DkT167wLCAEGAIEAQ0B0Ct2/f3rp1q+7qk1MTkT1ygCHJBAGCAEGAIKA1BIjs0Rq0hDBBgCBAECAIyEGAyB45wJBkggBBgCBAENAaAkT2aA1aQpggQBAgCBAE5CBAZI8cYEgyQYAgQBAojgiw2WwzM/p8FX02T6X9PfpkmNRNECAIEAQIAqojMCT3Ub28hkoS2aMhII2BzIYNG758+cKEUx4v52w7U1NGw+Pw4cNTpkxhQlaFPFu2bImLi2NSsEg8Hzt2bOzYsUzIGlQebInPyCh86J4c/oqExunTp/v37y+HkrrJuCWT4eEpfJxULxAwXJKfO3eue/fu6jKn8/JHjhyxsmJ0XEiR0Lh06ZK7u6yTvXTeQOYVqnSmDnPyJKfBIIDdZI8ePWLIDn7YFhYWnTszPeOgZcuWzZs3Z0icebb7uQ/D/BcuXMAcx3w+cnNz8/DwYEjcELI9efLkzp07DDnx9/dPSkry8WF6fQMONm7Tpg1D4syzPX/+/ObNmwzz37p1KyYmhrkUdHV1bd++PUPihpANhwBdvXqVISeBgYEhISE//PADw/wNGjTo1KkTw8yGkI3RwtYQGCU8qIkAxAMehkQiIyNLly49efJkhvm1lA1LOearuW/fvmHVrHeetQQFyNJXNjKkj9PqoqKi9I5Go9yHIc+4qvj9+/d655khtypkg3jAw7CgjY0NNoEWYzRIrAHDkUCyEQQIAgQBgoDGECCyR2NQEkIEAYIAQYAgwBABInsYAkWyEQQIAgSB4oDA9evX//77b723hMgevXcBYYAgQBAgCOgOgYiIiKdPn+quPjk1EdkjBxiSTBAgCBAECAJaQ4DIHq1BSwgTBAgCBAGCgBwEiOyRAwxJJggQBAgCBAGtIUBkj9agJYQJAgQBggBBQA4CZG+pHGBIMkGAIEAQKI4I1KxZk+HJTFptPZE9WoWXECcIEAQIAoaFQKvcR+88EZub3ruAMEAQIAgQBEocAkT2lLguJw0mCBAECAJ6R4DIHr13AWGAIEAQIAiUOASI7ClxXU4aTBAgCBAE9I4AkT167wJDZwAXExg6i1L8GSPPUo3QWIIxomGMPGusw6QIaRYN3EqXnZ0tVYmuE4js0TXihlwfLl7r2rXr169faSY/ffrk5eVlCNfrKgDN19cXV2aFh4fTeXBWFf5kfv+YAsrG+Aqd1a5du48fP9LM4wqfbt26Mb9PTy9NHjNmDMKu3r17R9fO5XJ79erVsWNHvTCj90pxYQ/urHrx4gXNSUJCQr9+/Tw9PTXI2MGDB4G5BgmqRorIHtVwK56lcHcyZgH87FNTUxMTE/GlZ8+e+/fvN+TWHj16FMIGT3LuA57x/Pvvv4bMs/Z4wwXVffv2BRq4SS8tLQ1fWrRocebMGe3VqD7l7du3Dx06FJfkxsbGYt8JvjRs2BC30KpP2RgprF279qeffvL29sb9jdBO8KVSpUo4edoY26KEZ1wzTB6CgDgCCxcuxKWleHDQurEgs3z5cprnP//801h41h6f69evt7W1BSBz587VXi2apbxt2zaa5xkzZmiWsjFSw4IPaODq0okTJ2qcfyxQhg0bpnGyRSVI9pYqkc3F5vV///3n7+/PsDmWlpbm5uawX02bNo1hEb1nw28VG7axdjYinrUHWps2bQIDA9PT040IDUdHR3QifBtGxLOWepDFYsH6ffHiRfwMGaIBBXfQoEFa4kcbZE0grLRBl9A0NARmzZoF8TNq1CgmjNFLGPwAkBnzF6YDExMT/IkHX9hsNv2KCSmd5QHPsNjAjwr2TE1NDZNJbaCBhqNTxCkjJSsri8ZBGzVqiaaoBzG60IN4DHCYaaTtIhUBvyx8R0/hEaeMYczj8Zj34MmTJ7Hw2rdvHxP2kO3q1asMMzMhqFoeoveohptRloKizXANJdE8+FHic5+4uDh8Vq1a1cPDQzwPfidwEZctWxbLNP1CA06Cg4Nfv379/v17BwcH+N4xhemXJY3XDhELZwAeRIXgE7AbeDxIkRDAtIsgF/Qgog/KlCkzePBgaOFFomDgmXfs2IEYEAsLCzs7OzQQj4uLS/ny5dVh297e/saNG+pQ0H3Z4vaz1D2CJaFG2J3xVKtWTV5jIZzg0IZYMjMzw88AsyEehOvoXhRB0tTNfSCEYDMsfoInICDg5s2bmKoqVqxYu3ZtRLV999138vrFGNOx2K+V+0AIhYWFGZHgQXzH58+fEZkmeiBgxo0bJ9ELCMK0srLCL0VfvYNgHFdXV33VLqqXyB69d0FxYAArOATnoCXiGpKEIQhvQ0JCYMGjJZO2xRKkTvXq1aXBffbsGeY1a2tr6VeGk5KZmUmrNXXq1JEQLc2bN0fErTS2hsO8pjiBEKpRo4Y0NcQfOzk5IZJC+pW2U2AfS0lJoUULRpfEKIIaSutqcFzVr18fCg3cV9IsIV06UZcpCJzDo8saZdZFZI9MWEiiiggo1pAgmfDjpM13tIaEaFqoRypWVvRi8IJA/sGFW6FCBVSNCcKghBCiA7BwhtQBUOAQU5h0EzkcjnRiyUmBgyQ0NBQ9CPUaPdigQQMdCCHo0IcPH4bIwcYDqDK0oQwdJDF4wA+ektMXaraUyB6FAPLenl5z6F5kbFxixX6r5nQrq6XtUIK0+G98W3ubQu5GhYwZ58tGuQ/NO60hSdvEsOTH3g7oRiLbnQY1JEzc2P6CqQS7L4OCgq5du4b5/YcfftC9AQQ8SLcd+zlEZrSSoNmoMIoRfdC7d+8ePXrQPqFbt25hnKjjE8IuKHgxxQ1lUDSxIVecN/RUy5YtocTg0f1QYYISHEiaPfuASaVq5iGyRyGALLsaTV0/bpmxxq+662LIHoWZVX2ZcunnJr23p/U78PTAQActSTdVedNeOVpDkqaPORexDNCN4G2mNSQIDITnYYqRzqxaCqaSerkPBAAORNDNbCIyo9HGNMwUv/zyiwT/CIxWrUUlrZS4TwhqkFKfkMhWBieZRETZ/fv3EZxCqzK0rUzmSEMUmcGC/OTJE2xra926tcFyKJMxXcieDL+fp6Ws2DRIS8Eq2iTPKu/aqX/NqIML/BJlwlfkRJnMCoU4MY3EutNgQtI0bdpUHFhoSNKTC/ztmDJo15HKGhKEkEyPwvPnz+ETgkO4yP0rpwCC7o4fP06b0UAZMqaYBQjIabfWkyFIZEqFly9fAuFHjx7RCo3IVjZgwAAJGx1OjcKjdUa1VgEED85MGjlyJNqotUq0QlgHskfADQmJ09iaVQoFLZNHfViJF9o9IcUC8wSZzFp7b3zxdbGgTDmbEqP0MEcMOaEhSefHTjo4nOmYb2hI+FKuXDnpY9zg4CmqgwSGL0g12icEdwIehkJIpNlAxkiINMyPs2fPLq67VaR7R9sp4j5/WrrAeS5askCnhFfv/PnzpUqVQkdA0uOtbrRbbTdcgj4teHAoESwEzGOsAQ7CIvSuJ2lf9vBDjp18kCUZZ6ixPtIyeY3xmUtIHrMsK/tymq2p2FODJoSYbwVh30AAUmTVqlWQPeLqESYjTEkK8MEkJe4TwmEQkCUKfEJQkuA9wo8Z+hkd+lylShUJ+hJ2HgW1k1fiCEDG4GhB6XiQI0eOfPnyhTaU4RO2MhjTRAUh4/v06YOjCDHJwquHE/+gAw0cOJDhGsJYukAkeOAA27NnD3O279y5g72lRiF7MrlvH94NePaVU6N5q1bNqtvmecRTo96HRHC5sfEmTu296mNpykuI+BD6lRvLTbBy7eFZNSdbRuj5JaOX3U71GPA1IgK7DlmW9pXsLSl+4pcPoZ9juLFJNq7d3MvHvQ588CHFvoFHszplRUE8apCX3wtpYQEXrj6JSBLYOnv71P7yJMWzo7NFXnZeQvCj23cefkwqXbd99y4u5RSKZcWZMyMfXboY8CHBzKFea5Cyz0VMDhYZ3JCPYZFcbhy7Zqe2dcTtknJxfxccjp2c8ZbOPTyr8SJf3H3wIdHSya1Vs0pasmrKx9Ow30CKzJkzhw5qEGlI2HAqIXuwLQO7NWG4E9eQxH1C2GVCr5qh2cgMfBCZ0Yhmo+aIgOEIIdQizz9tK5s6daqE8MbhMUqNESiCwA082CfExCekJuc6Li4ueHRctaaqUzjBUpSAe2vlT4seOY+Z/INvk7QX51cPnJ0xaMP6kQ0tqaxXp9ZuOHbp5I0Il6XPA+rXZwtiA/av3nHy3Nkn6X0PR3lWteS9/XfZxushmWwT3vszK/94iRnYzHXEXxM8zJMeH16z/fTFU/eSO8+cXZ0b+V2LVi4W/ks6DwpynrNz4/gmEGTqkJcNDj/00MRf77WeP39cPwcq6sGhGT7TPo156eVcCZauzI+Hfxmy8mvvpSvH/mDyeOsv7f9ssvbEss6yPf+KMyfcXzt23M6sfgvnDWpfOv6Z3+zBu7xXr+6Tekw2FqZhV7cv/+f46RsRbms/Xq1jSZvdlOC+/tjlUzeivHfe6R96OKJWx7Y1hX7T3CdWXnF175BqxT1WTnbnKkhVHPaNghAt9+7dgwQSaUgIdqANOLQZLTo6GruCaM0G8yAtukQ+IVHkngIeyCsaAQlbGXCW0FwR/QHMxffHyLSVKRU84oDL8wm9evUKDOggRFvjvU8LHpy+Co1HgjjsjXD/nD17tqimZo0zqZyg6GQhGV+yX672cnCZfidF9I7/ZY+vY40RJyL5uUn8rxs7cszclgXx8nNkBs5qYGbz/ZHU/ITspwsam1n6HhAl5L/gBS11M2NX6r/3U35hfuSpkTXMHH12BuelqENeqjmZd35t6LX6E814ztv4w0P7b/ic83fyjenOVjXG+MXlveR9Wt+xdLVx55NoIqkHfC05XuvC6bcKM/M+7fJ1tHJb8iyTLhr37yAHllnThS+yc/6Wi0XCrp4WBTUIleIujNvubc5x7bHgUGgeVKnnRjtynOc8zK1H5jNz5kwc9izzFUmkEUhKSsIC+fHjx0+fPkUKVKVly5bhBBR4DpBy+fJlLMkhgaAkwY2E2AEEF8HW8fDhQ+w3JBgqRQAHiP3+++9//fXXP//8c+zYsStXrmAzk9JSWsqAORo3huAXsXPnTqw8oGBpqSKNk8X4hGkXzItT3r1794gRI5Cybt06uEIVV2r451gLuMeWLL9T/seV7gXhPqyK/Qa3mzpk3t8/9VzhwaFYNtaWJlSymIRjmZsz3fpmZmZKmTbu1tspf6XOqtDrt/EtDs9ZvPzKwO3eqFQt8pJiV5icnPj00Orj3Zb2r2+bo12Ubunr896KRQnC9/+x7V2lsVs652/fYVfp3sV5xup//dd26yNhxlKcmXVr9dJz31quG+uSB4JVTY92bRLrtsrRrRQ8ZhyzggwMcKdyUObFlnfrk6/mcBwdywm/hIbzqOZKVFkFbJTEV6IAAWgzTZo0ET86CF4iUYAAfszYDATnAR32Dcsb3mJbCY5pQKQDrOdYquNPI1hsaqGTMXEjVF18iwzgwh1oElXBBwOQZeoxWmBKCUloTiKfEHoQYZOIVUEUnLRvSQkh3b4WaTxgXrpmXHqyYcMGDFTpVwaYomCiyrj937U4k2aVqhSaNzmVKpUTnrh0/vUKjya5IWCabBTbqbVnNZN1/hceZXm3w/StGvnM6HdBn1MKLnpmWVasW9/Rsu3Y8Q26LhzksqtC3aZunm26Dh4/ekgn+KBS7voHplBVk16dOPI5vzVZX3jChM+fEwVUnhEsv5VpijJnhV+8Fk5V6e1inw+ZebNfjt6Q3MWhBDEluC/zaEJ3GtvRyalAzuNoaQo34Rrf9dZK0NDSawQ9IwxXPEAAU490XSL/DUYi7mETZYAPCVoRPNhwX9P7hGC4g+DBqQ1v376lQxvo7bHFQxpBlojOkkEkhcSpMLi3gslZMgZo3RL3CWGzqoEHI2DUYdMrotpkCh4sgBCCgZ1wW7ZskR7J4ilYQuEQLMV5dPBWvuwRJEVFpwhMzDicQrKHxTE3NxHERkZphTm2nZ2tCf8Dl8ujKKb6kyQj/Ii9o91nBRTcR27WeMGDp4sbW7rNuxTgsnnzwUt3H93av/zs7i07px+7/GeH7ISEDKGJfY3mzZoWnBDVdP/rX0pXcJRUVwSpijILHsd+E5g4WEvIK0kGFf+tDHc+ReV1GsRNYclPbsOQBS00GwQOSDirkaJOgIDExlhQo3eZQIAhLoveGAvhhAcxcmPHjpXFl3GkHTp0CK0QP0sGQRkSsgdtl7nJxjhamMslhgfGgzTDUIngE5IZ5S+dWQcpGGlwTMqsCIf9YKkEvU3p1rG2bduOHz9eJhFdJsqXPawyFR1Ls4RpKdAg7MQsQqkpaUKWgyiiUVLv4fMVLL15j9eui5oyrYfcFvJjYuKF7AqVK+fzVXTyP03rNuVy3HiemN5jagEDHu/V2fPs7n1mbugzE8HO316fWPrjhPXzt43ymlq1almWMNvUrmadmsoc9SxbRZl5lSuVZwu+xX4rkA9yW0rlYvHTtB75YXb5OZXhroxF+TWWlDe0GY0+PoDWbIYPH165cmXx9svcUqo+QLTGQ9OB2xxne0PBgnmdPjtOtKzGypS22ol2xWK+0LExCtZC6CvihjJMW76+vhIg4NxSpEPY6Jg99ftCfQrQ9hA97+fnhyUFfXacfoUQasfl2TiFGk3DZlKJBiJmukOHDr/99tulS5ecnZ3Vb762KciXPZRFO99uFY74v3qZQVUReT0E0S9ffWU1HNKbPjLPxJxjXmhHfmZERJSAqivGNlacyEHv2ucnRkWlFWpS4UOIeEH+t8JN6vzatymt9KhCXkCxLKxspJWmjDfH/npesfvSXH8I267hgBVrn10dGBbBs2jbr2flfScf3k+kahYcmsML2v1PWN8J3STOoVWc2bl3rwYrVjy8+57XyUWELO/lrn+ivp/QGcF7UljIktNKcFfQY9oeLMZAHyMNN0ZDBmDDBxbj9AkCegl9xhK1X79+9NlxIp8QgoMhdYYOHUrHfENDQrQVPtu3b4+DTcUBRjgD/lTTZCeylcE7LUEKkXuoWnQsJiyHMs+SkXkWuDEMBA3wKOETwuZNvfuEcK453DnyxA/WWGg29qIhKEYD7dcyCUUzmV3vxct9bs1Yv/tdl0l16YwJN9dse1p38okpzei/OXXqOrGexcVhoZ+zHheEn7j00ozipafhd0PLK9PK9WqX5r//GMyjXFmxwXy7Qsel8J6fOxo09KcGuYv/zLc75m/7WG/iyRlueaJDFfLSUicfQt7rfevOTN7bLy9yOj2Ga9KktYsZZeO94K/B/j+uWR3Qa1lLegs979PhLS/K/DYit2h2Nk8gzM7KzjVpKczMajr1rwmn++5YdnTUwR9yNzhR/IjDmx9YzRmZ810aizxmc2qg+DygmPMwwD0rCyZFXhavwMqWkyLk80uG2U2k2eALZm0aNvoT88X06dNVcxSK09HUd/F9Qgiio7cH0SY7nMugoJYPHz5AbaLDvmn1CBMfJISCIvQrYIKQPFqhQeQeKEDA+Pj4SDi0oNDgUUqNZDA0n5BS8QPdCIZfA/ddYVyxFy1aJHd4sewa9e5Z/c2WhRuuvY+OCX98et3Sg8n9tuxf0P67PFsYq3yDKol+249+NLPO+HT31N4rnE6NIo5duXX/8t2n6bV7elRmUxa165V+dWDbuUiz9MBTIS7jhziXybXgCePv7t50w7F3x5jzfq+4scH+OxYsPmc9ZufBJR1F22oUkh/aN+fqTCnyrjR5qUZlvzm1P9jC9Nn1l98ykz6/uLRr9RnT8X9Nd0Nwm4ltwx6963/es2DlxbCU5K/Pzu/ZdtF8+OLRDSyz7/096ueF/wZwM6KDbt+7F/ld53a1HORlBiYmpWp29mmWeu73+XtfJmfEvb95fKdfdv9FPzW2zgVMBrM81DB5EWpIj35zNzBI4Ozd1MFUEe6Zt1YOm7zkxP3YzLj3uEcs3Lp1rZfLxs3ccOF1YtbXZ9cDHiZV93EvZF+ioYArElFGet/MLNUvRUhASC4Cc3HQAFagMTExsAIhugx7RSVIGI7gEWcMuhe0MenWIuQBRi1p/Qap7tv0AAAdJUlEQVTtgtKGGy3/396ZgDV1ZQH4JIGA4AYoCGoFNxQoYrGCWlFGHe2gFLTqdNTq6KgttU5nptWOjtTa2lqtrda6VeuKVttaXHBpLe4iKi51ARfcQNYAyr4lYQ68EEISQlhe8l5y3ueXT17uO/ec/9y8c+89992HGSP8FlP9OEWGOQn8D9qO68pwNg+7tzgphDl8LKBMaGFFmJTGkvimH+wgoxBfX1/u34k0yXDtDONBzdaFg1r8ZWl96JglE7Avgrs24LQbtigfHx+sBUex2LPBHgb+Hz81mxNLmjRFrEAxG6ZbhrwwNSE+w7qbZ7eafQdUrijNvHvjvkTu0MOnlxOk3PxDImrn6OTk6GBbM++UfffKvdLOfbxdlLN3ssTlAR7hdhvSo6YKkuLvSqy6efV00PrC5UaJ1zBI/jwtA+9VtoUpf1xPzBN3cPd2d1SvDu2Mv/VE1sHjxS5Vy7B1HjoLy4vSEm4+Lnfs5eVmpza2lGqyqKueerjXdZnW8/Pnz8eWip9av+XaSey8Y8vE9KmqYnjPxfwNTqZhdsQo02jNTonJCeEQB4Ooak6ImSvDmKR2p8OnOrCwci8Z/A9uPYfJZ5y1UyaQcKU4psebXVUSqJUAeurQoUMJCQmGzwlh5wP7FvjIFAYhfM4MO2QN2llHqzmGPKlf7GFDo5rYM93Ir/FjwzruyeR47MFgg+8gwdCCBy4TwMkifEeLmWwZgBEIRz+4mT+ObHAwh51oHLhg1zUsLExtvIJ3Os1+N7Y1PM9sHYRBCGMzDpVUGyBuwIQrv5XrGnjRKebeD0iXRrhtD+4dhwMgXGuOQWj8+PGGWZWgDD+oHO9ij658jy7YzfAd/uIwZ1Gd5GgGgSSCxwTwvZD4A8buv3EXCLBEUJnzZ9IwaKbqil5mwTcGHpw/wRiMO2fXta5Ma+BBnfE8zrzhoTWHhN/iXgwY3jAyMVsH4f0RH4NnyVgzFKuaE8IgZLAHVJW5n5EjR/IOu3Fiz7OTXy3cEnXshrRc/PXkaX+MeeurMH/1+S/eoSSFdRNQLhDA7dHw4Ti126jmmlHd0nj0Le4fg/1TJufPTJdhsFHTH7vJI0aMqMsoXJCG680anbPBKUqlcGaEhMNKzbrwdbG4uI5ZJs4MkmiEpElJ9xkmCGmWwcc58ZlcNgZDTPjxrzo06+XyGePMuckKsyWFAusWYguQlhaXCFt2sKMtmFluJsaac8OONq4OYKbRcKUvdvlxUghT6GoPe7JsPSviMe2PD8OrPiKDL2DWzKjhbBgmrhr9fAwOB5k0j1pOqNlNSk5Oxowajo3wwCXg6DhcQzho0KBmr8jcBBogJ7Rq1SrcchCfJOMRW/X+l2FUF9k6dKjeJK6llheDGUYLqqWZCeDIBjvOap07zIHzdxoN7xq4XJWJLphEUXtiHO/OmEfBoQx+haufmTGNJtMm9nYxSDPPCeEqA+w+43pFDN6485jaQgzNeht6Bjvmqm8eQtsx7KkJwcVU+/btY8ZG+MkMj7BLUddkYEN1MMnyCAc3nMb8JZMTYp4TwvccNuMmQ9j2eOcC48Qek2xhZmiU5gKBgQMHqj1wgy95Y5aB8osP3mFxrIZ7ySjnyjR3K1G7WbNqIE7T4cOneGCaFG9hzR54NJXHe5nm3CC+8mDmzJnKsRHmkDAAz5o1S+3Gh3N6qCFN2alSNVZOSNOzHDlDsYcjjuClGjiZhsvS+LVAALPuanvJ4E0Bt6BWcwBuRI/rzerK+RvRWxgPcIpfUwFcZIULDRqdE9IUqPWM7kUNykuwYaA+OORVLq7DTYzwxdVaZZrbybpyQrhQG3d+auIomUcwKfbwyFlGUFU5ssFBAD5M0KZNrT2GcFddI+ikX5XMvst471N7Syn+wuPi4pj5MZwscnd317qnL78ekcHJMZz9wwdNcDoOl8nh8IjtIKTbCfh4Iy4nUX1jLM5bqsUe7ATgAI6ZvqMREvLEOVV855vhnxPS7Ur2vjXOWgP27CHJdRHAHDi+uB73E6urgOp53GYPc+PYQcN+Ls77459aZ//1EWWwMqgkjgkYnZkpINS5vLzybXoG08HoFeEjt0gAP3FqDm3n8hO4zJwefiqdhRGU4zobwL9KD2J7xp6fnh48fPgwzmzj2/kMoGFzVUHjnuYiyXU5OEbBzr6eWuJWuBh7MHOjvDXoeaERi+Eei3jzwrfsMPcy5tMAeREjmlxX1RhuY2NjcZUEvj65rjLcOc90DvAT3x+K6+s03wPNHVUNpgnSwNE5vhQKlyToUylOGnt7e+tTkjtlKPZwxxfsaoKBRG0VgI76MFeMi3BwP3YdZbj2FS6xw67iwoULuaaYUfTBWSzcJ4JfHsR3buKDUPzSmT3n4muwz549a8I06t21jD22JJkIEAEiQATMlADFHjN1PJlNBIgAETAiAYo9RoRPVRMBIkAEzJQAxR4zdTyZTQS4RgBX6OHBNa2MpQ+ucNN8ttdYyrBRL601YIMqySQCRKDBBPCdEQ2+xnQvwI3GTXuvcRr3mG7jJcuIABEgAlwlQLGHq54hvYgAESACpkuAYo/p+pYsIwJEgAhwlQDFHq56hvQiAkSACJguAYo9putbsowIEAEiwFUCFHu46hnSiwgQASJgugQo9piub8kyIkAEiABXCVDs4apnSC8iYA4Enp2DtcdB7d3csjRYvxly5OYAoJaN5kSDYo/ZNW8ymAhwiIDYAvZOhzn7a8KPLAXm/gX2ZoCl+d2dzImG+XmXQz87UoUImD0BW3/Yvwtuv6sIP7JkmPMXuBEMkf+FVuzDkedc3rlsWUTcs5ohVv6Nvcs/2xIjqTlTdGf/yqUbTqUZYBhmXBrs81atgfbUMSxvqo0IEAE1AvYBleEnZBKEZYB8LSSEwMGPwM4Q3WJZ4qZ/zlgQKzhmNfjEv7pU1ijP2P3BtA9/k/nK/GIXeVZtLpcfuWDKB5ElvfP7XlvmJ2bde8ajwbpptSug2GNg4FQdESACGgTwhrtvNbw0AeQT4dpisDdE4EElRF2CZkw9bWcx8dWOihqF7Yb/fVaQsGDMa92rdzW1CXgzLLgwZWioJ/uBhwFjJBoaXmH3BMUedvmSdCJABOongDmexZ+A61SQ/wYfHYRvQ8Aw+1lbec3YdGSGqn6ibn9dfeivtc50Dvlif0j9NjRfCWPRaD4L9JFkoP6FPqpQGSJABMyRQGWOJ6gyx3NwExxSyf2YIwsAs6FBscc8GzhZTQS4QQBvtWFBcDMYDlTleJhsh3LpATd0NJwW5kSDYo/h2hXVRASIgDqBzAtQNBEOqOR4KsPPbig8CekGWFimro6R/zYnGpTvMXJjo+qJgFkTcJ4AOzUA2A+GHYM1zprBCXOiQeMeM2jQZCIRIAJEgGMEKPZwzCGkDhEgAkTADAhQ7DEDJ+ttYkhIyPjx47OyspgrUlJSgoODJ02apLcAIxScMGFCaGhoeno6U3dGRsbYsWPRCiOowoEqp02bNnr06OTkZEaX7OzsiRMnBgUFcUA1UoEI1CJAsYcaRA2BiIiILl26jBgxoqSkpKCgYNiwYS+99NKmTZu4zGjr1q29e/cePnx4YWFhUVER/sfd3X3btm1c1pk93davX+/n54eOy8vLKy0tHTlypLOz8549e9irkSQTgcYREFRUVDTuSrrKVAm8//77zL177ty54eHhvDBz4cKFGzduRFVnz569dOlSXujMnpKff/75ypUrUf7kyZNXrVrFXkUkmQg0mgDFnkajM+ULcSRhb29//vx5Hhnp6+srl8uvXbvGI53ZUxWHPg8fPnz06BF7VZBkItAUAhR7mkLPZK+VVR1isaE2sGoOkBh4ysvLraysmkMY72XgfAbOuVlbW/PeEjLARAlQ7DFRx5JZRIAIEAEOE6C1Bhx2DqlGBIgAETBRAhR7TNSxZBYRIAJEgMMEKPZw2DmkGhEgAkTARAlQ7DFRx5JZRIAIEAEOE6DYw2HnkGpEgAgQARMlQLHHRB2rt1lFT+DwIbj7vNYFshIo01uC4QvyUWdWKREQVvGScDYIUOxhgypvZEqOw4c7oEUGBP8JLpQq1JanwrjOMD2So1bwUWdWURIQVvGScJYIUOxhCSwfxBbCmgPw7wXg7wR58RCTqtA57xSczgOP3pw0gY86swqSgLCKl4SzRoDeHccaWs4LLjwB+UPBVQRHD0L2C9C/o0Ljy2eg0BUCuir+LEmFHUshbSJ8FGB8k/TROTka1kVBURFIymDEW/CmH4iMrzhbGugDpLLuQkjMhu4vsKUGySUCDSVAsaehxEynvO0w+AQ3oMmHPVHgPh0GMBvoSOFMLNj5QV/8MxfWfQrp7SBmLzgN44Th9eqcuR8+TYIvv4ZWAEn7YeRwiN0N68eAqQ7w6wXCuC32YwhNh0c7gPbY4UQ7JiXAZH+S5Fs9CNhASxEURMOvORA6HphuCCZ7zt+Fl4dACxTQBsJWwJL3wJU7d6z6dD6yDaLjIE9eaf4LwTDbFyLWgaTqT9M86gNSabUMok+Dlz/waXs+0/QWWVVDwFS7g+RjfQlcjoZnXeDPHoryeefgmhxeeYXTvRIdOr8cAqNehpbV7draCmSlbK3Zk+dc3rlsWUTcs5rQln9j7/LPtsSoBLuiO/tXLt1wKo3V8FcnECmc3AmbN8D+WyBOh217gV099G10VI4IKDq7BMJ8CTx4AKJe8GJ1l/jiaSh0gwA3TgPRobPnNPi2Wnf5Uzh4GUaugI6sdLFkiZv+OWNBrOCY1eAT/+pSWYU8Y/cH0z78TeYr84td5FmVZcqPXDDlg8iS3vl9ry3zY23cUScQIbj1AfFvkNgOwoKgb2towwoKTrcWUo6bBCjfw02/GE6r9o4gzAamVy57BBsOgv1I8GHtLtkshumlcxl8Pxcy34Sov7M0hhN1CZox9bSdxcRXq2ObsN3wv88KEhaMea179fIGm4A3w4ILU4aGerKJVAcQV29I3goWfjDWD+dQ6SACXCFA71DgiieMpYf0HkyZCK1nQaAArsTBnu3gsxEOTVdRpxT+0Q2Kv4FdY42lo3q99etcBrvD4KAXrJ8LdmbQ09cFRAZLB8KJKXB8DksxWN079DcR0IcAjXv0oWTKZSx6wg+xcO8mFDvCIID1P1SuDeP4UY/OZbBrHiROhF0jQCSHX7bDkCngYNIRSAcQuQTO3YXBAZWBJ+0e2HSnaTeOt25zUc+kf5Hm4sTG2imH3z+Cl/8E5wXQsx/0cYGIHWA3Hv6m9hRIBQDzr7H1NOd19epcCtvfhpNu4CeD48cg6kfYfRVsTbiZ1wek/DrcbgMD3EGeDKv30srW5myMJKspBGjc0xR6PL+2HCIjIL23YlYqfi2szYcNX4C90iwp7P4ErmTA+WKQb4T/xIL332BqX6NaXZ/Ox/4Fs7ZCWQV8X63mwC/A0qgqs1t5fUAsesNAezi3C+JSYPx7lPJh1xskXX8ClO/Rn5UJljyxFE65wuhOcGE//J4P85fCK05cN5OPOrPKtH4gJZCaDy7tWdWChBOBhhGg2NMwXqZXOjkOrqRB937g4cybXDQfdWa15RAQVvGScDYIUOxhgyrJJAJEgAgQAV0ETDgJq8ts+o4IEAEiQASMSIBijxHhU9VEgAgQATMlQLHHTB1PZhMBIkAEjEiAYo8R4VPVRIAIEAEzJUCxx0wdT2YTASJABIxIgGKPEeFT1USACBABMyVAscdMHV+v2Xl5efWWoQKcJUDu46xrSDGGAMUeaglaCJw5c2bIkCEymUzLd3SK8wTkcvmwYcOio6M5rykpaL4EKPaYr+91WB4QENCpU6fJkydT+NFBiZtfocumTp3q4OCA4YebGpJWRAAJUOyhZqCdwM8//5ybm/vGG2/Q7I12QJw8m5+fjz2GzMzMyMhITipIShEBBQGKPdQUtBOwsrLC+1ebNm169OixfPnyoqIi7eXoLDcIFBcXf/nll927d2/RosWBAwfwkxt6kRZEQDsB2s9NOxc6qyRw586d8PDwY8eO9evXb8CAAX5+fjifY21tLRAIuExJKBRi+Gzbtq2zs3OD9ExPT3/27FlpaSlmTRp0oYELV1RUlJSUZGdnX7p06cKFC3FxcSNGjFiyZImHh4eBNaHqiEAjCFDsaQQ0c7wEb8cXL16MjY3Fe9zz58/xrsf9WzPGj6ysLEtLS39//4EDB+JklJOT9ldE4CRVRERETEwMGohXtW/fHuMW94Mr9gBwYOrr64t9ArTRzs7OHJsm2cxPAhR7+Ok30lpvAo8fP8ZhwcmTJ/ft2zdz5sx58+bZ29e8Hg9j6ooVK7777rvQ0NDAwEC8ibu5uektmwoSASLQSAIUexoJji7jHYGUlJRPPvkEcyFHjx718fFB/W/cuDFq1KjRo0cvWrSoc+fOvLOIFCYC/CVAsYe/viPNG0MAF1C8/fbbR44cEYlEGHjWrFnz+uuvN0YQXUMEiEATCFg04Vq6lAjwjwDOreEyhKFDh6LqW7duHTduHP9sII2JAP8J0LiH/z4kCxpOAEc8uKYAk0ANv5SuIAJEoBkIUOxpBogkgncEMjIy8Pl/FxcX3mlOChMB0yBAscc0/EhWEAEiQAT4RID2NeCTt0hXIkAEiIBpEKDYYxp+JCuIABEgAnwiQLGHT94iXYkAESACpkGAYo9p+NEErZAX5WTn0wuETNCzZBIRQAIUe6gZcJJAwa/v9nHu0GvK3kxOb+jJSXakFBHgAQGKPTxwklmqWFGBQaeigjO2l0S9+84e1t4jwa50zkAkRYiAkgDta0CNgZMEWo769kbqx/K27Vtxo3sklzx8mO3AFip2pbOlNcklAk0gwI0fdhMMoEtNlYDQ1qF9KxFHrJM9/OmXS2VsKcOudLa0JrlEoCkEaNzTFHp0LRIoTL/7IEkikeTYeAUN6CJNu3H+0r1c2+7+g32crfBref6TqxevPSm27z1woIdDrfYmf55w4siZ2xKhs+eAwECv9jWBpkTyMPFJmkSSLeo2PKCnjfZa7ufauPYf5Nux8ut6j1LJncvnY66nirv2GzTI161NdV2F6fceJkskWTkC16GBvVsBSJ8n33+cKsmSPLf1DhrwQmW5ksdHlkxferbQf0JqcjLaJLRx6OhgI8tNuf/4aaYkK6+V96t+Ttm3Yy/dL3Dw8PftaS+uVqfx0hkJRU9ijv5+NTlP3sZrVEiPlKsFA4Z5WddrKxUgAnwggG8/pIMINJ5Aaey6t/4W2LWFwCZ0y9Vd4R8s23Es5vy+BUM69p72w4OMU9/MC1+z71TsyU3TPJx850c/q65Iln3ii3fmbTgen/4s/faBj0Z6DwrbnVCi+FZ6Z/f8SYHdbAXiwNVJssqTddbSfVLEY6lu7WWZpz8fGzguPOL0naePrx5Z987IwBlbbxVWXYRy355Uqb1l/6XxlXJkaYeXzgj1dRQJWo3fU1mmPGHP/96ZPbF/e5Fl9z/PfKvyeHfdBdQ0J3rFzImDOouFbYM+XDZnxj8Xb/hx37ZPJ730Qt83N1zNa6r0igrpo12zQufsuJqBdZWkXdwyo4/dn755WkWDDiLAfwKYzaWDCDSVQPZ3o6zE3kHhu6vjQOGh6c6WXQZM+eykItrInn4TaGUzakMac/OUPvgyoIVNz7cOMl/Lnqwf2bpV4KpElTDyfMtoa2XsqVJQay1irwWXy3XoX35zZaDji++fK1CWkaVsC3XuOnWfQpUKWeq3w8TVsaeqVGnsfA9LReypOlF+LdzH0iY0gglYNbVJ4z/tbynq+Pr2R9WKy9Iip3W1dA75/oHiTGOll577t2fgykc1sSbnh8mvr6HYUwOf/sdvApTv4cPglPM6WlmJQZrl1P+1Loq5LLGzc3tIlfUKGdyWUV5o5+zUovxp0lNmybSgVXcfr052rW2Y8kIX//5uJVcvXC2tMdVSbKnWOrXWUpHyOElaJyC55Kcly845BU/0s1WWEbqMe2PIs93/+1qRwBG2amkjqCVBWFmTXoelpQVY+Lwa7Fo9hyfsMOa/s1/OOfTxsuOFVRIaK70iPz/32u6VPyfkKhaZtx4YGtLLln6wevmFCnGfADVl7vuIJxqKnF1da+7YIpEQxJ1cq2MR3oOFQgFIy8qZO6mw/WurL92N/SJQmHTp4LY1yz/bEpstLytTCT11WK1Zi6xcIVPbFSVnD0dnCzp07FyroYs7dmxfkfjrkdtM0BIIaocebYL0PydyfWVAF0HqiaNxzNqERkq3CvjHbI8H6/76oksnz8Eh/1iw/lRF0KThikiuvzZUkghwlADFHo46hodqYbhRGz6I1JepqTyuU/Y46uMJA/uHfna2zP0vM9+fNbiDfm1RoxZdjwDJ89IzCuQCS7G4lnCh2MpKIM9KS2dl2wSRnV0bgSxbIql7OKaPd236/+/XmF+WvR3U2yrlzM5l7/zZZ9D833PoSVt92FEZHhDQ7/fOA0NIRT4RkOcceW/khLX5k3dFbfjP6wO62Vkpo5a8pKi02W6wwrYuzq2FFUUFBbVEygsLiiqEji4u1bFRfdwjk+lQQXpl1crDJXXjlmVm5lSIOnTqVL2or+HSUbj01sGDyT1em7fmx+irDyXpN/e85/Hom0Ub77ESLus2hr4hAiwRoNjDElgSq4tA9i9rtz9oO2bOdHfFLJ0sP7+wagAjS1i9eLMiKaRLgp7fWQ8JfbVDxf1bN1VjhTzj5q1UoeeYYE8mOgisxFa1tlAoTU5Orx18LHAIV5nZrVIxNz29SPVruVz1L2n8iTNJgp6vjX2Jsa0x0rGWsoSfVuy6rhg6iew8J3yxanbPjCfJTRtM6YmNihEB1glQ7GEdsTlUUFZWjj31MmnN/FflGZlUJRMjLy+XQYWM6bYLcSEBlOTlFivg5F48cUfWEkqKS2T5RRW2VRn18nKpHEWo9PO114IydUy72QV/vCzE4tA3W+8qb9rPT3+18Zr73K/e81UMTMQ93V2Fz7OzFVXJk/b9etMSpMVFyodJLTr16tFalpT4AIXIsx7I7LqqrEWQ/nHox/jq2FZ6Z/OijYm9wlZ90F9RpDHSq7BIb+9YfaBmO7viTImg74AXLc2hPZGNZkBAtHjxYjMwk0xkjUDpmeVT5i7ZdzGrNPteTExMUstXut9cOnPemqO3c8tTrp+MictzGyE6EDZnUcTZtOK8B5fOxtwV9gudMNQlPWbX9qh0qxYF96L3/Jzc/7+znc5+uzkq/lnX0bOGZm2aPnfx3hhJcUbC+dh4uddozzt11lKWirVcznML8eukzUihXZ/g0W4J6z9aE30vIzPpyv7Vn+7KH7d+Z/jQdtVzYUInj865Ud/9mGjZsuTR+cjtx8XD+yT/dPzMxd/OXyuePNYfxVr36NX6VsTGQ2mWxbGRD1+cPcm7bWV8rMg5v3XtKefgYZlHom5Jsh6c2Bz+8aGWM77ftWSYY3W3Tqf0HqP9O4k0pXu1FZYnRO58YG1x/eTNZ6V5T2/8umXlAYvZK97vb0/dRW1upnO8I0DvzOady0xHYVluUnxCclErN6/eLpVDHXmhJEtq59iGnc025IWpCfEZ1t08u9XsO6DKsjTz7o37ErlDD59eTpBy8w+JqJ2jk5Ojg61SHWn23Sv3Sjv38Xap3kpBlrg8wCPcbkN61FRBUvxdiVU3r54Olbs5aBwNli5/npZh6exsW5jyx/XEPHEHd293R62SNaqiE0SADwQo9vDBS6QjRwnUxJ7ptPqZoz4itThKgAbwHHUMqcULAlIpZoCkqkkpXqhNShIBoxOg2GN0F5AC/CTw7ORXYdPCNt+Qll/4evK0d9bF1v9gLD8NJa2JABsEaM6NDaok0wwIyAqzJYUC6xZiC5CWFpcIW3aw02tHbTNAQyYSgfoJUOypnxGVIAJEgAgQgeYlQHNuzcuTpBEBIkAEiED9BCj21M+IShABIkAEiEDzEqDY07w8SRoRIAJEgAjUT4BiT/2MqAQRIAJEgAg0L4H/A84/bWNP3GggAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "id": "beacf695-c485-425f-b230-6c74503f45b1",
   "metadata": {},
   "source": [
    "*Idea*: duplicate the circuit $C$ identically $n$ times (slots), choose **dynamically** at random the position of the right input, compute on random inputs in the other slots.\n",
    "\n",
    "*Statically:* Each variable is shared into $n$ shares \n",
    "\n",
    "$$(x_1, \\ldots, x_n), ~\\text{where}~ x_i = s ~~\\text{if}~i = f(\\text{input})~~\\text{and random otherwise}$$\n",
    "\n",
    "*Dynamically:* Perform usual computations independently on each of the slots (+shuffle inputs and determine the right output).\n",
    "\n",
    "*Security:* against the **linear algebraic** attack.\n",
    "\n",
    "![image.png](attachment:831a0f17-0345-4ae2-95bc-c6c032e8975a.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4ce1b3b6-5e24-4002-ab59-d23e9f09c68a",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AES_DumShuf(OptBooleanCircuit): \n",
      "   |   128 inputs,  128 outputs,  77728 nodes\n",
      "   | XOR:52656 (67.74%), AND:13346 (17.17%), NOT:11598 (14.92%), INPUT:128 (0.16%)\n"
     ]
    }
   ],
   "source": [
    "from wboxkit.masking import DumShuf\n",
    "\n",
    "C_DS = DumShuf(prng=prng, n_shares=2).transform(C)\n",
    "C_DS.in_place_remove_unused_nodes()\n",
    "C_DS.print_stats()\n",
    "\n",
    "assert ct == C_DS.evaluate(Bin(plaintext).tuple)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "228fde44-a2d6-4360-85a2-38467510343a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Serialization to file (internal binary format)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8289f1c3-a35b-420a-a16a-b3e748bcad77",
   "metadata": {},
   "source": [
    "To do fast trace recording, we serialize the circuit into an internal binary format, into a file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5135403a-2415-4b0d-8d08-e921f4e169f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from wboxkit.serialize import RawSerializer\n",
    "\n",
    "RawSerializer().serialize_to_file(C, \"circuits/aes10_clear.bin\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a129ff74-56ec-47d3-88cf-61cf881bc065",
   "metadata": {},
   "source": [
    "**Note**: the serializer does not support constants (only the NOT operation), so the call to\n",
    "```py\n",
    "C.in_place_remove_unused_nodes()\n",
    "```\n",
    "is necessary."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecd60f06-3c19-4ce1-b53c-e48e6bf7bdd5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce28d7f9-d148-4823-b9d6-c8f408cc47dc",
   "metadata": {},
   "source": [
    "Generate circuits of the 2-round AES protected using the following countermeasure combinations and save them to respective files:\n",
    "\n",
    "- `circuits/aes2_clear.bin` : unprotected AES\n",
    "- `circuits/aes2_isw2.bin`  : linear masking (ISW) with 2 shares (order 1)\n",
    "- `circuits/aes2_isw3.bin`  : linear masking (ISW) with 3 shares (order 2)\n",
    "- `circuits/aes2_minq.bin`  : minimalist quadratic masking (~same as combined with 1 linear share)\n",
    "- `circuits/aes2_quadlin2.bin` : combined quadratic masking (2 linear shares)\n",
    "- `circuits/aes2_quadlin3.bin` : combined quadratic masking (3 linear shares)\n",
    "\n",
    "Note: you can use the existing `prng` object."
   ]
  },
  {
   "cell_type": "raw",
   "id": "dec5ab74-5ee5-4e89-b63a-30450422a09b",
   "metadata": {},
   "source": [
    "circuits/aes2_clear.bin\n",
    "AES(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs,   5825 nodes\n",
    "   | XOR:3380 (58.03%), AND:1248 (21.42%), NOT:1069 (18.35%), INPUT:128 (2.20%)\n",
    "\n",
    "circuits/aes2_isw2.bin\n",
    "AES_ISW(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs,  19485 nodes\n",
    "   | XOR:12720 (65.28%), AND:5252 (26.95%), NOT:1385 (7.11%), INPUT:128 (0.66%)\n",
    "\n",
    "circuits/aes2_isw3.bin\n",
    "AES_ISW(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs,  39061 nodes\n",
    "   | XOR:26340 (67.43%), AND:11204 (28.68%), NOT:1389 (3.56%), INPUT:128 (0.33%)\n",
    "\n",
    "circuits/aes2_minq.bin\n",
    "AES_MINQ(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs, 162955 nodes\n",
    "   | XOR:113818 (69.85%), AND:47584 (29.20%), NOT:1425 (0.87%), INPUT:128 (0.08%)\n",
    "\n",
    "circuits/aes2_quadlin1.bin\n",
    "AES_QuadLin(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs, 163517 nodes\n",
    "   | XOR:114384 (69.95%), AND:47580 (29.10%), NOT:1425 (0.87%), INPUT:128 (0.08%)\n",
    "\n",
    "circuits/aes2_quadlin2.bin\n",
    "AES_QuadLin(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs, 210666 nodes\n",
    "   | XOR:149032 (70.74%), AND:60081 (28.52%), NOT:1425 (0.68%), INPUT:128 (0.06%)\n",
    "\n",
    "circuits/aes2_quadlin3.bin\n",
    "AES_QuadLin(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs, 284652 nodes\n",
    "   | XOR:208062 (73.09%), AND:75037 (26.36%), NOT:1425 (0.50%), INPUT:128 (0.04%)\n",
    "\n",
    "circuits/aes2_dumshuf2.bin\n",
    "AES_DumShuf(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs,  16845 nodes\n",
    "   | XOR:10862 (64.48%), AND:3361 (19.95%), NOT:2494 (14.81%), INPUT:128 (0.76%)\n",
    "\n",
    "circuits/aes2_dumshuf3.bin\n",
    "AES_DumShuf(OptBooleanCircuit): \n",
    "   |   128 inputs,  128 outputs,  35554 nodes\n",
    "   | XOR:24280 (68.29%), AND:7583 (21.33%), NOT:3563 (10.02%), INPUT:128 (0.36%)"
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