Tutorial 3 - Tracing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fb12f34e-58bf-45a2-9bc9-08184d725d0a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "# Tutorial 3 - Recording Computational Traces"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c4da210-4e86-4850-9968-584527384cf7",
   "metadata": {},
   "source": [
    "This tutorial covers:\n",
    "    \n",
    "- Basics of DCA-style (trace-based) attacks\n",
    "- How to record computational traces efficiently (`wboxkit`)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e5c9f9c-63eb-47b3-b6aa-e5a4432dfcab",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Basics of DCA-style attacks"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a90619d6-b67a-4919-a3da-c9e10ae86c6d",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Evaluate the circuit on an input $x^{(1)} = (0, 0, 1)$ and record all input/intermediate/output values:"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "04b40285-f08d-4752-b8b1-dc73319c5abb",
   "metadata": {
    "tags": []
   },
   "source": [
    "![CircuitDCA-1.png](attachment:c54f08e5-c716-4104-b459-7f27140f17ae.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed5fb2ae-c109-4d12-8d05-1051a6e5a222",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Repeat for another plaintext $x^{(2)} = (0, 1, 0)$, append intermediate values to each node's history."
   ]
  },
  {
   "attachments": {
    "0b071d8e-1d24-4472-9d13-8e3c5b7c74cc.png": {
     "image/png": 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vmB73cK8kOYLnL/vBC72L2P5JktRMTHw2jfC3xAI+GxWPv/KleLhN16G1PxDmD0nc6w/Vy81+HlhQR7B9Sb5U31BbojLzQJVb7ULxQXYJrKm4Omd/Irin0vEJ8IZQXPDj5SxcVfkOIdErtK9krqT6RI8kPtaUDSmcsxEwB8JCWFphGGTHscD8Kjf+DXTuBrPuj3dDBLkfQvcgFvcA6D4L+Ga83Z4BPlw8F/24elsdtkl88Lm38jQg7S0Q3lssF/2q+rzOfSsMc183V2gGrq396tXbFj/4RGtgQt0JCUl9GUz7N2cj4BfAw5A5AfIHAucWTs6DC28tTkeUdvtXSXhLYmcA03CU3QWiu2Ddh/cIFlWa33NRPFXR+3r2M/CTyh+8bf8kSWomJj6bRlRhqHfuKOBMCIfBqTUOs0nOsRkWw7jFDQuxJuHgRNK1xgU58hW+tgOEIxI75xdWoR+wPPQaHl9ICByb6BX63T0rfvVfMBHWHJO48n9r7XUqqVb5pxPtxhuh/ZL431mIIHcusDl0f7z3v70Lp0B0GfFL+Feh9UWYvzt0/7zQQ4q4TaKQ+IwC5L4O0Y+oe8qK/HjIJxZBm7YerNy+to9NJS/YFRYIAdhya4gOLOwsh8wN9cUJf4KJ44sv+S8HuK/PC0p07V9c0C3cA/9eUW8ckvpSb/sHMO59wLOw9N2FhOMtkFsNnB/Pj96yHVBIfKbe/pVZMBHWHFnYWQLj/l5fTIWaE/NEhV69ZmMtsH0X7Fgo0xXgV5XvZvsnSVIzMfHZNKLEMJqwPH55zy+E8Clou6b2+6zYHjI9X6mvgpOXNzbOfhVe7MMyGP9o9WKZFxKLG2V6n5+7KYRTCsOMlhWSGzWLEsnOTGI59h53wWbAybBuUaMLK99p7V6s63UalkF+AA/1kmqz5ikY/0Chh81kmF54f+08HKLZhY8/FRZAG98C3V+ApV8rJgVm3ge5dwGFxUPCm6F9XvF8641D+IMsgTUV55UrFZZBd5W57LJvTQzZvxIe76Md7dtE2Dlf7NV+095Q438P2jMQfTRx4Jd+8JGGSr3tH0BmIYy/vLSXZXR74vmqbH7zkdD+9VjzGorPV9fCSS8XHssGJcRzuldsN7tKV32/Ze+KC1ra/kmS1GxMfDaN7qcgs7gwR9MPCiN0LoCl3x3YfTIHFrfDdY2MsEY9CdyHYW2VnpwA0d8SL/cVeh5kj6Y479MpvRd1umQLWL01rP1npZ6g4+DexE173T+CWRTmvYugbd91PSKSQgS5kxJDTr9T+0qlkmo3aQ2sSby4PxAgtwvwcwjnVP/4M3MJ8JXex8c/AmvuI36pvn1oX1pXbpWYA/gemNJXz6DEB67o5d6nc+MgtBX3M/8zmNgDJIeR/rTS0M/KpuwA0cGFneUQXV9vDJL6U2/7B9C6svexdXMELxn6UT8Dav/K5N+Y+C59VeWpP2oXJdrXPPSakuh+GP8KfDxR/iuVh7nb/kmS1Gwq9KTTyLTeK6UvwmEhPPnJgb30tmcgHF24flk8mnu4RT2rKD8OT/YxL92MxyH8rrCzbem5ea8B5sbb4Zzek/PPezWsXQaZu2H8PXD+euV33x0eDYXhrQGmJc/9GXYO8NXC7ty94dLKMXZsB1FP94Ml0J2r/vNIql82C6HnQ90ymPoqCFcCV8LSLw/u3lHdCwPVUdeNfc/HGS3r+/r8nsC+8Xb4NWxcYU6/2gTIBDi6sN0FDKC3evTu4na4CTZ9vN44JPWnke1fx9uA8+Pt8PHhHfXTX/uXFCKIeqYzWt6I59VQ8QN20Wo4gMLzZoA794Iq88bb/kmS1GxMfDanK2HCRwe+uuXULYtfqaM74cmn+y4/FMJfCxu9kpGlogDh04Wd78L8LePN3FTI/LJw/Buw9L97X5uZlLjPNNhg1153j5ecn1XYnftneDXAHbBNF9wEEGDB3nB6VLoUdLKeExLbH7W3pzRUjlsJUWFoenQyUGi7xh9b3yq/PUMowzIY98t+izdMeLDv89Edhb/XVLg2guhziQOf6p1EmL89dO5RWFCkT3+OX/B7en4tXl5l6Gdvl24AYUbiwLfqXVxJUi0a0f5duA3k/gei6wofvg/s/dF4qPXX/iV1bAXR4YXr/gxPVpn6I6l6+xfFDejNhe1ev7MAmTx8PXHopMq9PW3/JElqRiY+m0Y2C2FDCH+EFUfBiav6v6ZctEdi5+r6EgaDFQ2gzlPugfxewIaQXwq5ADwBbA8cCa2fqdzjteuF+MEeiBf/qJiQ3BNuzcKBIV6Oc8mieDLRxwJsEeCj+8DJlR98AXI7AF+Kt8M5MPN3lctJGrwoQEi++C6B7gPhxD6my6gmRBA+Vtg5E04a4g9AITGVRn89OrtuK7RdG0N2Uum53GGJRMBh0PZw6fnOQyC/uDCctCP+OavrTkyWF8GfD67a1pVbeVBx6CqXw1LnNZaGVL3tX3sL5L4AHX+ClseA0wv3a4VZtw5VtKUG0v4lZT6YuO7e/p9Xa2r/bizM2T4xC5skT9wNH6DwISjAUfvCXytcj+2fJEnNycRn01i8GngfrHwbnPFKfffIH1bcHsjKmg3Vs9pnjT/DKffAq7aB8Dpgd8juBGwGrb+ofs2pSyHzkcLOk5BfUq3knnDrJvED8N4Z2LcFdlsfNtgXLq3e0zNEEL5d2P4jRBXmEJQ0NMIyyBxQfTGP/nR+oLAgyK9h6f82NrZKJi5l3WrplRZqS5r9PGQ+C0wCvhQnLgBy+0N0ZeEe7688p1+YXNyODoN5m5SXeBgm3A1bLYI24L8Sp955D7z59nhRtz7kxkHUXqhvGXQNcLoVSYMz0PYvuhlIzOceHgB+Hrcpw2Eg7d/C8TBvMnQcw7rh+AAcAZ37woJebVpR/+3fPvBMBJ+P4vUN/mcRjAO4Ew4OcAVABCfuCz+tXIftnyRJzcrFjZpGexdwb/3XX7oBrPzPeDsshpUPNSSsAZu1FHLfB94MG02gpgToB9cAD9ReR4gKvaOAzAyYWWFxpKKdYDVwd+3372yLe16FxZB/D8zu8/6SGmLL+GUzfwC0Vf2Y0bfOfeP5kcNimHB8Or3e+zPrEuhYAdHlMPUkWDd18BLIvzf+GFRJ9HjiW81KyPZaHOkF+HIEZ1a4eMM83JSBh0K8ZHS13p/vYt0co3y0/uSzpAGqo/1r7yKep/L3cMkFsPZKiHrmCD4DFn54ZA3Tfu6TkDmvwomtIdwBq2+BhW+pHHP/7R/A3vCdu2F5gE5gTWLi0Jcz8Pa94E99BGj7J0lSk+pzKJxGk8494iFAAOF70HZ6irEcAuF6iF4LsxqcgJ03OV7pmKMheh/M+nmD738wZG6MEydd+8Fpzzb2/pIq69wZ1r5U/8vm/K2h+67C/Jl7QuszDQ2vT7mzgXMh7AFtNX7AmrMRTNgu3s6+BCc/1v+qxrl24EuFRd++NJiIK9x7cwi3x/Mm81lorZSgkDQkBtv+QbzwY3Q3RJMLSdRdhmdu8nrav7rqqbn9uw827YIdAAK8sBcsjqCP3pu2f5IkNTOHuo8Z4YDEzlWphQHAxD/FicPw5sbfO/ovYGNgxyFIeu5ZSHreBhP2NukpDadZD9X/0j93U+i+Nt7u2nd4k54A+d/Ef2d6LbRW3ekvQetf4j8zHu0/6blgE+DIOKHRPa/uUCsKEYSLCi/9F8Cm32zs/SX1bTDtX49THqcwpHt41dP+DdTA2r/d4fm9YNFesGhv+EffSU/bP0mSmp2JzzGhvQVCYc7LsAzG35VuPMevAOZA+GRxDrtGaTsdWt8Jrf9s7H1z+0Pm7niY7IS31LeoiqThd+kGkL0W2Byye6czPDHzd+BOCAf2t+hQfebvDqvvgjAFokMa/zN2fqYwvcdc2PQTI2t4rKTaRYuHv07bP0mSlC4Tn2PCVvtBdGBh52XY8MVUwwGg+4p4Zcwpr0s7kv51fAi4DcKnYOkxcOKqtCOSVIvc+rDyWmAqdL8BZtY5N+hgta6FMAc4Ar43qd/iA7JgIuQvg+hH0LJr3EO0kTqPA84FvgFLP+ZLv9TMwrT47+h3sGyYngVt/yRJUrpc3GjUWpiFlzaGrtdC/ufF6VyjLeD5d8L8P8HMp9KL79SlkJsN2RH+/8EQQW4/4K3QdmPa0UiqVW59YCGQha5d4dTEYhedh0A4EWYd2/8Q8kaJrgEug/F7ADc37r4nrgLe0Lj7JeU+CuH7wGnQeuHQ1CFpeOTGAW+Mt8O84V2R3PZPkiSlx8WNRq3OgyDcVP38cE5sL0nDKbc5cAOwO0QfgLAEWB/yATIHAe0QHQOzLh/euDq+COwFS983vEmHgZozAcZ/DaIzgHdA63VpRySpFnM2gvHfAjaGzI/gid8U25rOkyBcDFwAs04fvo8+PWz/JElSOkZ4bzvVb9bvMbEtacyZvyt03xSvXAwQflo8t252lyXQde1wRwbj58HaL8L0Ed42t6wP0TaQ3x5OeSTtaCTVauI2EGbG2+GDMGUZzDsDMltA+E5hnvIzhz/pCbZ/kiQpLSP84UOSpIHomAPRx/op9FloPW9YwpGkYTNnI5hwOXBY6fGwDDgRWq9OJ+kpSZKUHhOfkiRJ0qhxyRawdqN4O/s8zHgu3XgkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZJGqvlvhc7DGnOvzuMg9/rG3EuS0pFJOwBJkiRJkjQYuanQcR3kb4B8S99lO3eGjgWQ+zucv171cmEVcB/kvg5zJjQ0XEkaJlHaAUiSJEmSpHrldgEehLAMooOg9W+Vy3VMh+hs4Lh4PyyD/C4w+/k+7v0u4DcQFkN4M5zyeIODl6QhZY9PSZIkSZKa0kU7si7pmT+gctLzki0gdy9E97Mu6Vmr1ishvB2iaRDdXahPkpqGiU9JkiRJkprO3E2h69p4O/sBmL24crm1AcI3YdxkCB8deD1t1wOzIZoM3TfG9UpSczDxKUmSJElSUwkRZM6Pe2JyAcy8pXrZ1meg7Ydw0tOQ/V199Y1fANwJbA3Zc+L6JWnkM/EpSZIkSVJT6TwcohPi7cz82q9reQa4b+D1nbgKos8Vdk6Dzv0Gfg9JGn4mPiVJkiRJahqXbgDhq4WdhyD/4PDUO/FPEB6It8Pnob2f1eMlKX0mPiVJkiRJahorD4JoemHnB9C6dnjqPX4FcEO8Hb0Hpu49PPVKUv1MfEqSJEmS1BRCBNFJiQM3DG/90W2JnWOd61PSSGfiU5IkSZKkptCxFfD+eDssg+6Hhrf+fHJ+0CPgkg2Ht35JGhgTn5IkSZIkNYXogHTrzyyFsLiwszWsnZZqOEPmki3szdoIufXh/PXSjkJjm5MRS5IkSZLUFKJkMu7vsGz58NY//mVY83Iinn2Be4c3hqGUmwrha7D2BLh4M+C56mXnbgotuwNT4/2wBFbcBWe8MrQxplVvj/YWmHIIsBba+plqIX8kbDAPOj8Es64elvCkMiY+JUmSJElqCuFgWJf7fBLIpxgMwISU62+g3NuBa+Pfb3g7zKiS9GxvgSmnQDQHQtm5DZZD5/tg1m8bH19a9fZYOB6eOwzohGgyhFtg4U3wwe7q16z9NUw4FMJV0PF9WPNxOP2loYtR6s2h7pIkSZIkNYdkkimFIcTZLIRR2IGq8zjg2ngFgV4AACAASURBVHje1Pz20HZ95XJzNoKpd8XJRwAugei1EO0H4XpgUvx3bkZj40urXoA5EyB3FDz3b4h+ESc9AXgSHijPwJY5/SWYdTyEcyA6ASbcD/Ne0/gYpepMfEqSJEmSpBq8sgZ4vrgf3gELs6mF0xC5oyBcGic9s2+EUx6pXK49A+MvBXYvHDgDZs2AWQ/BrDth6TuBKwvn5kPn0Y2JL616If7dTFgFLEwkPHvUmHiPArS2A98EtobMfTB/18bFKPXNxKckSZIkSarBk93AM8X96Na+hzqPdJ3/ASyMt7MfgJn/ql52yochOryw8xA8+b04qdejvQvyZxf3w4+hY/rgY0yrXoB8BPkPAVtA+Gj994kCPPk5CDcBk6D7JrhwSmNilPo2CruoaxjsQ99zubwC3F3Y3oveX4LGAf8E/t340CRpyNj2SRqrbP+kkSPZu3KYFrNJmrYerNwpceCZqkVHvAunQP7nhTk9z4GZt1QvO3dT4NvF/fCNOOFYru1+yP2ymKiMvgDtH4H2OudiTaveHqcsLG5f+n+w8jMQ1ZlUbe+Ci2ZC98Nx79FsJyw8srkT52oGJj41UBOBucC+fZS5HPgIMB7oqFJ2JnBRw6OTpKFh2ydprLL9k0aW5Cru68H0qGrJIdHdDVEy8dakixuFCHIdheHbyyH7/b7LZ48GEkO9M1WSpFGA3EKgp4fm0TDli8DD9cWZVr2V9Prfvg4z/gG5/wa+BNF74Ll3Ar9uRHRSNQ5110CtAvYDNgS+W+H8p4BjiFcX7Cn72cT57wEb4IOvpOZi2ydprLL9k0aUzK2Jnf3hmY1SCwWAzIPp1l+vzsOLvSPD1fD4o9XLLpgItBX3w2JY+0QfN7+7dDd6d30xplXvUMsnk8zfhYsnpRaKxgQTn6rXCuAM4LKy46cCyYZrI+Iv/AAXAJ8AVg55dJI0NGz7JI1Vtn/SiJBPJBqjNdA1zMOEV02huMgO0L10eOtvhAUTgf8u7mcW9j0kfM1rKPmZuRFmr6hefvUTcZJynTbIjRt4nGnVO9TaHoXwy3g7mgZrj0w3Ho12DnXXYATg48CBwLTCsWnAF4CzCvufKxy7BfgkcW8ASWpmtn2SxirbP2lAOnaCaEvIh+plMndA61qYvz3kX927bMtymHlfcX/Cv2HNfcQJsa1h4jbA/bXHtHITaNm9/3JV451Y3A63wNKH6r9XWtbuTzGhuBzCnX2XD7vF84D2iG4rXVyo3IRXIDzJunYybALdmwEDTBKnVe9QiwLkrqY4LP9LcOHP4NSX04xKo5eJTw3W88BxwB8Tx84EfgRsAXwGWAZ8GBjkfCCSNGLY9kkaq2z/pNqdDHymj4GWS6B7d+B56G6FqELZ/OWli9ScuAo6LoGoMPVEOICaEp9zN4XxG0F3Yuh0NBmyZ8P8Dsg/B60v1vAzHVTczMyvvNBOJfP2hMwZEBq4IFO0HrTMhpOX91+2R4ggd0IxoRjug6V9DR8HeHPZfj/zmrauhY67iT8SUfg9b83AE5Bp1TsMorvjb2kQ9/rM/j/gmjQj0uhl4lONcCvxUIEvJY79ObF9DLBkWCOSpKFn2ydprLL9k2rSdja0/xdM+TBEPyg7eSU8eUQxcdh2NnT+FsL18X5YDC1vhRkV5p6MFlKcc/c/of2SvodqX7oBrFwE3dMqnDwL8mfFvTcXvqXvFbbbMxCOLqyCvgy6rq9etpc3AMeW9mActOWw+vSBXbJgc+Cdxf3o3wy4Z3r458DKA7AtsKiO60ZAvUOh6x+QWRwnPQGid2HiU0PExKca5TzgSErnIAH4NPC74Q9HkobFULR944nfCrqxt5Skkcv2T6pJexdwKXS2QLg4ceJdMGVn4IF4N0SQ+0ghqbgYxu1RvSdj65OQ+yxwLoS3wrabAU9Xj+H4FcAOg/9ZXr0V5A+Ot6P/gVMH0JMw/BLCHhA1cvqLtXDKCzB7AJd0HVBYyb3HH/pOGi+YCGsOKj0WLRtIkIVrpg6sfFr1Dpfsy8CzFIflvxPOPwvOaGCPYClm4lONsgr4CPCXsuM3D/K+bwI6gCspzh0lSSNFI9u+dxDPk3dg4tjVwLeBG+qKTpKGju2fNCAzF0DnwcRTRRREP4cFb4iHr+feC9EJcU/K7oOhrZ/h2905yHwyTuKt/RDxYmJDLP+u+O+wGMZ9b2DXzn6eeKqMBmsdYPn8f5TNm9nHau4A2SyEltJrwjAsEp1WvcOldS103AbRvvF+NA023AZowjljNdKNon84GgH+CnSWHbscWK+Oe72VeK6am4HpwC5AdlDRSdLQGGzbtz7wY+LhPQeWnTsM+C2wENhgEDFK0lCw/ZNqFgXgjDixuc7OsOZYuHAbiH4RH8oeA6f+u//7zX4eOLGw87X4HkMptzmEQkeU6KiBzas5oqxfupvv53e9eDXxvMUJ2WHoQJZWvWnK75Z2BBqdTHyqkaYAh5QdmwacPYB77EU8y/ENxAnPpD5WsJOk1Aym7YuAC4Gj+yl3FHFyYJQ/8EpqMrZ/0oC0PgOZj5QdnA8tjxW2Pw8zBzBVRNtVwGeBSdAyD3LjGhNnufYMhIviXnnRMdB699DUM9TaM8RzXib18zubNgGYXHZw/UolGyuteodVWcemkTosX83OBwg1SgvxQ2mlCbO/SPzF/pYa7rMWeC/xpPlfAdr6Li5JqRps27cvcEJh+zjiaT2eBzYCjgeSw8jeQ9wD6teDC1mSGsL2T6rLrN9C7pvAmWUnroQnvzHw+7WeB7nlxEPdO6C9tfaV1msRIug8DzgcmA2zLq/vPpdsAV3TobuR8/euhacW9T1HZ9K09WDlTgOr4oUumLCi9Fj+hYHdAyAMsIdsWvUOp3rmLJUGzh6fapRPAwcTP+C2EM/5lPS/wKY13OcvxA+1zwK/amSAkjQEBtv2HQssB3YGfkhx7quXiF9g3l2hvP/tljQS2P5JdVv9FQgPlB4LN9WfsGy9kHiu3JNgyk1xkrER5k2Gzv8FzoxXc2+dV/+9Vr8r/hkzf2jgn9/C1pvUHkN3N0SJ33FYBvl+Vko/fTWE20qP1TPXZvTXgZVPq95hdW/aAWhssMenGuEQ4FziOUg+SLwS548L24cXymwNnAOcTu1D1h9ubJiS1FCDbfsmAu8CTqN6e3cV8H2KvaLWo3SWe0lKg+2fNCinvwQdZ1PS0SP6InT8EtrqfAdqvQ4unAotF0HXocBlg48zOhnYGNgR2vpJEPbrXuA7NHyBo+zK+q+N1oPM5vQZU4ggVzbEPOpn7Yn2FuIp3JL36R5YbGnVO5zKF2+ShoaJTw3WVOBHhe2jgaWF7QCcSvHhF+KH2+uofZiSraCkkaoRbd9q4hWL++rdHoCfU3zxl6S02f5Jg9beAlH5cuSTgAWQe0u84nU9Tl1K797Sg9B2LvFHjgY45R7gnsbcq2EmESd2+xAFyN1XdnAf4Pbq12zXAqsTPd7DMsg/Vr38SKp3OEWNnPZAqsrhIhqMCcBPiCdd/hRwY9n5x4m/5if9CBjiFQclaUg1qu0LwFygv/maHkpsr8CF3iSlx/ZPaoipn6b3vxUgOhDCx4Y9nDEjm417GQ7YdWX7u8Q9MqtZNQWi5EK9t8PmLzVRvcNlj7QD0Nhg4lP1ioDvAgcCi4nnYqrkauCmxP4k4snuNxzS6CRpaKTR9u2W2P4DUOME/pLUULZ/UkPk3gKcG/fGGzcZuncpPR99G+bvnUpoo95xK4E7Bn7d+EeAO4v7YU/o7CuBWja/cfQr+GAdQ87Tqne4hLK5aDMPphOHRjsTn6rHTsQT1vesuL4FcASweVm58cCbiHsFJO0MPEg8P9RmQxemJDVUWm3fVont8t5VkjQcbP+khpj3auB38Xb2GDjpaZj9d2B2abnuhXChHUUaLgoQ/b3sWD/zZgKcuArCj4r70e7QNaV6+cx+xe2wDLp+M7A406532JQlZbtHcu9UNTETn6rHZ4jndOoxCbiC+AE4aRrwe2A6vW0NXI/zNklqHmm0fRsBHy9snwM80EdZSRoqtn/SoLW3QPTDws5nYebviueenA/hj8X9aBq0fGFYwxszokVlB/ap7bruKxI7k2DcgZXLtbdAOC5xoKMw92oFHftA7u0wf/eRV+9QCxHxf0t6LIfss2lFo9HNxKfqMYN4uFP5n4vKyv2tSrnkn28PT8iSNGhptH3vJU4kLCMeYipJabD9kwZt6uchOhi4Ep78Vum59i4Ix5ZdcBZ0HDpc0Y0d3eXDqcfXdt2pSyF/YnE//1VYWOHarfaL52qFuNfl+ArTgoQIcpdCdCdwLeTvhY4LC6uyj5B6a/JKndcB358AJHuo3gQbj+CFmNTMTHxKkjQybU4xQXAy8HyKsUjScLL90yjTeRLQHm93nx4nOsud8ghwRumxaCHM33Wooxtb2p6Ik2w9wvtrT/w9dSmEX8bb0TR4fmbp+Uu2gPz8xIGPxtMZlOucBhxXeiyaDVsdM7LqLbdmAoTEFAzRHjC1hqkCKt5rQ0qmS8n8YGTPR6pmZuJTkqSRJwLOJ54n7wLgynTDkaRhY/unUSS3OXR8BsLFxWOZo2D+9r3Ldr4OQvnQ40mQvx3mfQQu3GZIQx0zogCZ7yQO7ARblM9XXEV7HtYcD9xXOHAB5L4eDxnPfRjWLiuuqh6OhrZrqtxoXOXD+aOgvUKOJq16Ie5dOve1MO9gCAvixOs6OwMdMP9NcNGO1e9RSfQfEBXmgw7LoOXm2q+VBsbEpyRJI88niL/I/xE4EwjphiNJw8b2T6NIOBii80qPRedB93dKk0QLJkL+VxBVmgN3EmR+CNkfwcI6e9ep1MQbIBTmDY4mw/hK8xJXcfpLsHo/CD1zsJ4VDxmnsAhRWAjdO0DbFdXuAKufgLC4wonXwUYTRla9z20H2b9B5kaIjqxQ4CTI3wxdf4TJG1evu1z+kMTOFZV7qEqNEaUdgNSHnYCHCtu/Jp5AP59eOJI0LA4HfkHc/u0NvJxuOJI0bGz/JA2Tjg9A9JN4O3wP2k4f+D3mbAQTX1sY/r0SMo/AzKdquza3OYQDIbscup6H6Brg77D0rZWnQhgJ9TbKnI1g/D3F3qPRa2HWQ31fI9XPxKdGMhOfksaafYE7gCXAnsAz6YYjScPG9k/SMMqNI+5Zvm881DraA1qfTCmWXYAHIfwalh4RD20fzfV2HgLh+sLOZ6H1vD6LS4PkUHdJkkaGXYhf+pcBB+BLv6Sxw/ZP0jBrXQv50+LtaDKEthSDOanw9/zhSz6mVW97BvKfL+w8RHEhO2nImPiUJCl92wO/p/jSv6RKuQ2I53KaMkxxSdJQs/2TlJJT7gDOiLejL0Jur+GPIXcUcCaEW2Dp1aO/3qnvh+hgYDlkDo0T0JI0du1APKF9AK7ARL2k0Wl74Cnitq5nNdeWsj/rA9OB64B/AhsOf5iS1HC2f5JSFiLouBByAXL/jufAHA5zJkDuzLjejn/Cgk1Gd70A83Yr/J4DzDtw+OrVWNeSdgBSH7ZObK+XWhSSNHQKcyutswDor7fBZ3HBD0nNz/ZP0ggQBQinQe6ZuNdnuB0u2A9Oe3bo6sztAPwj3g6nwqsugg+uGbr60q4X4KIdoeuGws474JQ/Dk+9kjTyZIFXAa8j/rIfEn+OIx7etEFq0UlS4xxIaRtX65/paQQrSQ1k+ydpBOr4ULHn50U7Dl09F0+CjsNh7qZDV8dIqje3vz09JaloF/p/6P1katFJUuO0M/CX/ptxtIak5mf7J2mEumhHyN0LHU/BnI3Sjqb55Y4qJD0XwrzJaUcjSZIkSZIkjXG5/WHh+LSjaH7zt4b5u/dfTpIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSdLosnnaAUhqOq9KO4AGGA0/g6ThNRFYP+0gJEmSJPVvAvBFYAVwaMqxSGoek4CngMuArVOOpR4twGnAs8DRKcciqbm0A48Rtx1RyrFIkiRJquLNwD+BUPhzf7rhSGoi36TYdqwAzkw3nAHZB3iQYvyPEPfgkqT+bE+x7QjAbcC2qUYkSZIkqaJdgS5KH+A/kWpEkprBdHq3HWenGtHAbAesonnjl5SeyyltO5YR94CXJEmSNAJ1UPoA/xKwRaoRSRrprqG03XiUeNqMZnIepT/Di9j2SerbIZS2GwE4IdWIJEmSJPVpC+LeCsmH+I5UI5I0kh1K7xf/I1KNqD4bYdsnqXZZ4AF6D3OXJEmSNMK1Ufog3wXsl2pEkkaiCcRzASfbi2tSjWhwKrV901ONSNJIVd5eBGD/VCOSJEmSVJNKvRhuTzUiSSPR2YyuRGGW0ZXIlTQ0Ko2O+X6qEUmSJEkakErzVh2dakSSRpItiOcAHm1DwysN3T801YgkjTTOhy5JkiSNAuUrlT6KK5VKipW/+C9j9Lz4ly/WdD9xb1BJ2pW4d3uyjTg71YgkSZIk1WVbYBWlD/fnpRqRpJFgf3q/+LelGlFjTad32zeafj5J9Sv/MPIo8XzHkiRJkppQO6UP+KuIE6KSxq7bGP09Is9j9PZolVSfI+g9FcYRqUYkSZIkaVAmEPdmSD7k/yLViCSl6Wh6v/i/LdWIhsZG9F68ZDTMYSqpPpWeh1z8TJIkSRoFKiU6XOxDGnsm0fvF//JUIxpabYyuVesl1e9sbA8kSZKkUet6Sh/4H2D0DW2V1Lfy4d+jfeqLLPEwfnt4SWPbtsQrtyfbgu+mGpEkSZKkhqq0iuknUo1I0nAaq4udHYo93qWx7nJ6z/k7KdWIJEmSJDVcB6UP/i/hYh/SWFH+4v8oY+fFv3wV59G4mJOkyvaj98ePtlQjkiRJkjQktsDFPqSx6G30fvE/OtWIhtd0evd4N/EhjX5Z4Hb88CFJkiSNGZUW+9gv1YgkDaVK81zelmpE6Sjv8b4Me7xLo135M08g/hAkSZIkaZTKEi9slHwJuD3ViCQNpUofO/ZPNaJ02ONdGlsq/Zu/PNWIJEmSJA2LQxjbw16lscJkX6lKSeDpqUYkaaiU9/JeRbzImyRJkqQxYCwvdCKNFS5oVqrSsP9rUo1I0lDYj97z+ranGpEkSZKkYbUtce+H5EvBealGJKmRKi3oc3aqEY0Mh9K7x/uhqUYkqdHKFzR6FJiQakSSJEmShl07DgOTRqtr6L2SsS/+sUq/G1d5lkaHo3E6H0mSJEnESZBHKX05+EWqEUlqhCOwV2NfKvWG/USqEUlqhEn0fq65LtWIJEmSJKWqUs8IEyRS86r0QcN5LHtz/lNp9DkPFzCTxrD5b4XOw6qfb2+BORPiP/3pPA5yr29cbJI0/DJpByCNEJcDvy07dj4O+5Sa1ScpnbKiGzgjpVhGsi8ATyf2JwFfTikWSYO3Lb17bl8EPJBCLJKGVW4qdFwH+Rsg39L7/PzdIfd9mLoWJqyK/+TuhXkfgYXjK98zrALug9zXa0uUStLIE6UdgDSC7Ar8hdJk5yeB76YTjqQ6bQv8lTiJ1+N/cBh3NW3AvMR+N7A7JkqkZnQ58KHE/tPA6yj9wCFp1MntAjwIYRlEB0Hr34rnQgSdZwDfqn59WAYtB8KMf1S497uA30BYDOHNcMrjDQ5ekoaUiU+pVAfQmthfDuyALwxSM6n04r8D8b9n9ZYF7qN0KOy1ON2H1GwOAa4vO3YK8bONpFHroh2h++E4eZk/AGYvLj3fcSxEl/V/n7AMxu8GJ1V47+l4G0TX9Z0glaSRyaHuUimHfUrNbX9Kk54AX8SkZ1+6gU+VHXsHJj6lZpIF5pQduwOYn0IskobN3E2h69p4O/uB3knP3ObAtws7Xwa2gtYIVk+EUDYPaDQZ1p5ZuZ6264HZcZnuG+N6JUlSs2qj96IA+6UakaRa3Ubpv9/bcK7eWl1D6e/ufvzdSc2i/Nkl4LOLNMqFCDoWQC5A7nuVy3S+Nz7feWTl8xftCB1PFe4R4u1qSc0FEyF3R7G+4OhRSU3BHp9Sb/OBBxP7WaDKw4SkEeQE4h6fSR8n7tGo/p1B6e9qOvCxlGKRVLstgHPKjl1B3ONT0qjVeThEJ8TbmSq9u/PvBS6Hmb+ofH7GP+g96qOKE1dB9LnCzmnQ6ccVSU3BxKfUWzdwetmx/YCjU4hFUm0mAd8oO3YFcHsKsTSrB4hXf046hzipImnk+jKl/06XA2elFIukYXHpBhC+Wth5CPIPVi6X+T/gaxCF6vcKf6i93ol/glBY/DB8HtorrB4vSSOLiU+pst8SJ02Svk7pKtGSRo7PU/rivxpf/OvhPMdSc9kVmFF27GvAYynEImnYrDwIop5FCX8ArWsrl5t1NbT+pe97bfB0MZkZrYGuPkbKHL8CuKFQ9j0wde+BRC1JaTDxKVV3FnHypMe2xMkVSSPLdOATZcfOwxf/ejxNvBhU0gxKV3yXNHLMoXQu3seA76QUi6RhESKITkocuGFw91u5VTGJGu6B517uu3x0W2LnWOf6lDTSmfiUqnuMOHmS9AniBKikkeN8YEJi/zHg3JRiGQ3mEw9775El/h1LGlmOBg4pO/ZxSj/aShp1OrYC3h9vh2XQ/dDg7pdJjJjJ/C+05/sun78vsXMEXLLh4OqXpKFl4lPq27mU9hqbQNy7QtLIcCjwjrJjn8EX/8HopvdCB+8g/l1LGhkmEE/Bk3QtUGUBE0mjR3RA4+4VIghthe0/whM/7f+azFIIiws7W8PaaY2LZyS5ZAt7szZCbn04f720o9DY5mTEUt9WEydRfpw4djhxAuCaVCKS1CMLfLvs2PXA5SnEMtpcQ5xESSaVv038++1j7i9Jw+SzlI5A6QY+mVIskoZVlEzG/R2WLa//Xh2vg8xxhZ1PQHtX/9eMfxnWJIbDR/sC99Yfw0iTmwrha7D2BLh4M+C5aiVvh80ysH8GtgYI8Ajwh31g5XBEeiO0bAhHAGv3gV9F0MciVoNX38+bPxI2mAedH4rnnJWGnz0+pf5dTrzYUdL5lM6pJWn4fYzSuSe76T3Xp+p3BqVJzunEv3NJ6doWOLvs2AVAlVWdJY0u4eDEzpNAP0PTq94ngugrhe2vQ9uiOgOa0H+RZpF7O/AERCdAeDvMqJj0XATj7oIvZeGZCK4MkAuQA64N8OKiOBk5ZB6GCXfBsRvC8gh+AnyDIcztDO7nXftr4JcQroKOBTBno6GKU6rGxKdUm9MpTQDsigkAKU1bAOeUHbuI0rkpNTgPECdTks4h/t1LSs83KE00PA18IaVYJA2/5DvJIIYQzz8RosPjYesr/7v267JZCKNw5GjnccC18byp+e2h7fpKpe6BTYBHA7QXDl0J7J6Bg4C/RPGo2p8vgk83OsJ/wcQ74eQX4IUAl0UwsXDqyUbX1WPwP+/pL8Gs4yGcEyeUJ9wP814zVPFKlZj4lGrzIHFSJckEgJSeLwOTEvvL8cV/KHyBOKnSYxLx715SOg4BPlR27IvEbaAk1ajzIAgXFxZHOhjOeKX2a19ZAzxf3A/vgIVNPhIudxSES+PfR/aNcMojlUoFyHTH0wFNLRz6yt7w3n3gL3vBzcDewF2Fc9+8E1obFeEimPEsvBLBRYmEZ4/1G1VPUuN+3ihAazvwTWBryNwH83cdipilSkx8SrUzASCNDPsDM8qOfZHSf59qjOXEv9ukGZROMSBpeGTpvcDig8D8FGKR1LQu2hHCTcByyB4Mp/57YNc/2Q08U9yPboUPNvH8353/ASyMt7MfgJn/+v/s3XmYXHWV8PHv7e6k2cKihEUhIiKYjCIIJqOMIzKoQXTIuMZtBCEkgAvgK+JK6zhDZBSRLd1JWNTxNTCORh00gCO4jQmERWeIr6gIggJBJAtLQrr7vn/8qtO3qm5V136rur6f5+knXbeqbp3qVFfXPff8zil1y9vhNMLnUGJ4FPhMlGg1cCRs64FFY5cjGLwVDm9ElFFo7npqP+xDWI3YdI19vlEMD34s99qbBiM3w2X7NPUJSDkmPqXKPUJ6AmB2BrFI3exL5PfYXQdcklEs3WAZ+S0Eegl9jiW11gJCq52kwlY8kia/5GegKio1AYb2hOHrw/c9r4IFNfQGPnBH4PmJDX8udcv2d9k+MPqt8H38GVjwk1K3XAt7jsLnxy5HcP6RsK3wdofD7cCaxO2+EDdgNsQRsOwIWPYieHgXuBpYX+8+y2nO8x0Yhr4FuVvuBb1LO79aWJ3AxKdUnWXkDw/oxYSL1ErzyZ15TvgQHvg30wjhZ5z0WmBuBrFI3Sqtr/E1FA9flDT5JVtb7AizopK3zHPxrsD3IDoQOAYW3DbRPdKNjECUnP7eocON4gh6B0MCjs3Qe3W5W0dwasES8xtK3G4U+HJi06vWFp+0qsvj4bNZUz/7Nu/5nvJbINdTNnoD/OV19cYqTcTEp1SdEYqXFswmJGMkNVc/8LmCbd8m9B5Sc60Cri/Y9gU69mBH6jj/RH5f8a3AORnFIilTPf+duDAH/lzBlOyhnWDq94CXAq+FhTel3y6OYGgAlhxVRTw1VI22g6UnhOFOAPH34Y/3lbrlWtgphvclNm0chpK374Hk/xFRcW/mttb85zuaTDJfBFdMK3lTqQFMfErV+wGhyiLpc+QPWpHUeB8FZiQub6VFPY4EwNnkVxfMAs7KKBapm8ykuK/xYuAPGcQiKXOjiURj9DQMT1D5N7QT8A2IjoJ4Piy8AQb68r8u7ocrngVL/wU4D6LHSu9vyz7AoeOXRx6q48lk5Kod2F51CNBzLQyMlrp1T1jav29i00/mwOOlbt8X3p83jl2O4bS7YGo9EbdS85/vovsg/nb4PjoQtv1DnSFLZfVlHYDUoc4BT3zKpwAAIABJREFU5jFe7TQD+DhwbmYRSZPbDIp/vy7CA/9WWgdcCnwwse1jwBU4WEpqpi+S3y/tD8D5GcUiqSqDz4dobxiNS9+m5xZYuA2WPRdGn118277NsOCX45f774enf0lIPu4HO+wP3JW+74t3JRRtvDRcjj4GQyvSbzu2ej3+CTx0d5l4E8ufJ7ptu9o2h/Hk7WaIby136xE4ItlPIIIfJ4f8FOqFJwifjXbLbdr5CdgbqHKQVDaa/3yjGIa+D+QqbjkPLvsmnFEyuSrVw8SnVJs/EKotzktsOxO4HBMxUjNcQP6y6keAf84olm72SeAdjC+5nUZYgruo5D0k1WMeoadu0kcIFe+S2t/JwEfKLLR8AEYOBR6DkYUQpdx2dAUMvHO8IvGkLTB4JUQXhcvxy0hNfA7tC/EPCCs0xhxafLsiS8IQmpJeOf5tz7IJbpvc7eHQczbEVQ5kKifaEfpOh5M3T3zbMXEEQyfCWGov/iU89KeSt4ZoLbymYNsOpW4PMAu2rYXbIjgIIIIdIngOHZD4bN3zjW6HsRx/dCD0/g22r1KTmPiUanc+cBLjS2/7gYsJBymSGufVFPcKOof85v5qjc3Ap4AliW2nEN771qXeQ1Kt+oEvFWz7AVCiWktS+1l0Lgx8AvZ5B0RfLrjyOnhw3njicNG5sPQHEN8YLsf3QN8xcEpKb8XoWsLKF4C/g4ErU5Zqz4FoFlWJ18NIif6fAAM9Ybl8lLvt8I1V7PzFwLvGE44NsRm2Vtn26Ko9gcRAneh+ylQzponzh91W6nnAT2u4X+aa83yHfws99+SGbQHR8Zj4VJOY+JRqt5VQdfH1xLYTCJOOfdOWGqOX8Q/2Y9YAZSdvqqmWAe9nvIKkF7gQp7xLjXYW+X2N0wYsSmp7A8PAV2BpH8RXJK44HvY5mO0nDuMIht6ZSyreA1MOK13JuPBBGPoocD7Ex8CMZ1LUdmbhShqcZYRnPwtGjw7fR1+CM6ro7xl/G+LDIKoqyTiBbXDaBji9irsMvyw3yX3MT8v197wNdozgbws2P1hVlMH+Ndyn5Vr3fHsfBx4FconP+HVw4TlwdgMrgqXAxKdUnxWEJSzHJrZdCNxI/hAQSbVZQP4SLcjvManWGwE+BHw/se21eNJHaqQZhB66ScuprepGUltYcBUsPRp49/i26Ftw1YvD8vWhv4foxFzV5dGwaIKVLSND0HNWSOJtexuhD3eTjR4f/o3vgSmXVHff0x8DygxNqtXCKm8/+vL8fHBUclo5wC4hQ5fss0zPJB4S3brnu3AbDK6GaKz/7IGwy/5AB/aMVbubtL+wUgt9gPwk50xCNZSk+kwDPlOw7cuEik9laxVwfcG2L5Dfh1VS7S4gvAeOeYTQY1dSx4pi4OyQ2NzuYHj6XXDZ/hCtDJt63w5nVNAL8vTHCG23AP4l7KOZhvaE+JzwffSW6vpqtpWd8i+Olv1ZPw5bgL8UbJ7S2JDaR7bPd/SFrXkcdRsTn1L9fkWowkj6DOPDPyTV5p/I/z3aDHw4o1hU7GzyT/rMIizNlVSf2RT3Nf4URctYJXWehX+GnncWbFwGfWPDUT8OC35Y+f4WfQ/4KDAN+pbAUJMSVAM9EC8PVXnR22Hh7c15nGYb6CG/hQhMkNTbJQz2eUZy2yjs0uDA2kaLn29v/sVo3yY9jrqcS92lxvgk8EacdCw1yizgfQXb/gUP/NvJOsKyumTrgY8BV+D/k1SrXqBw+eivCL11JU0Kp/4Ahv6V4pO518GDF1S/v4WLYWgz4W/yIAwsrHzSeiXiCJYuJswyOB1OrXHA2pXTYXgWjDQwNrbBw2vL9ejMd+CO8OTzq3mAftiWq4JMerSafeRsrOE+Ldfa5xutn/g2Uv1MfEqN8Qjpk46vBG7JJCKps11I/lngPwBfzCgWlfZJ4B140kdqlAWEis+kwpY6kjre1s/C1OPzp67HN9eesFx4GQz9Brge9jkErvwHeG8DTkIu2QuWfgmYH6a5L7qm9n1tPR56rmrwotPNsN8BFC/NLmFkBKLEzzheD6O/K3ePA2Drn+HnUaJStJaelzF0RJVsi5/vL6rdr1QLE59S4ywjHJzMzF0eq9qYk1lEUmeaSxiWk/RBYGsGsai8zaSf9LmY7VNqJVUora/xNcAPMohFUlN9YBMMngt8Z3xb9CkY/DYs+k1t+1x4A1y2L/Qth+G5wFfrjzM6GdgNOAgWlU0QVuAXhJPYDR5w1Ptk7feNdoSePZkgpgh2Tl6OJ8ij3AZ9ERyR3NbTQSewWvd84778QVNSc5j4lBpnhJD4vDGxbTYwnzD9XdLE+glDcpKuB1ZmEIsqs4ww0G2saqWXULE7N7OIpM5U2Nd4K3BORrFIaqqBPogKx5FPA66CoVeFide1OOMh4PV1Bpew6Hzg/Mbs67Q7gDsas6+GmUZI7JYUQXwr3Bbl/1yPAm4qc7cpwK5jF2LYMgI1JrRbq7XPN2pk2wOpJIcbSY31A0J1RtLnyJ/MKqm0sxhPoEE4oXB2RrGoMiPAhwq2vRYTn1I1ZlLc13gxoc2HpEln3/8DHF+8PToK4ve3PJyu0dsbqgyrvBd8q2DTi+IyuZQ+2A/YK7Hpf2bDhmofNystfL6H1RKfVC0Tn1LjnUP+ktwZwMczikXqJNMJw3GSLsUl051gFaEyN+kLhApeSRP7IsV9jRtUZSWpvQy9Cjg/9JecsheMvCD/+ugLsOyI1LuqTu9+khrmL2yBu8k/EfWSdWVWz8awZ/JyD/x71EFL3Vv3fOPp+Zd7flVNnFKlTHxKjfcHQpVG0pmM9/6UlO5fya+OfoQwPEed4WzyP+TOIlTwSipvHsV9jT+CfY2lSWjJs4Efhu973x4GEJ3+a+D0/NuNXAuX7dLq6Ca/KIbo1wXbetNvO+7l8BRw9djlGA54MlQ5phqBv03cdstIh7U9a+HzLUiOjmyqLlKpMiY+peY4n/yzZP04kVoqZw7wnoJtnyIMz1FnWEeo0E36GPk9CyXl6we+VLDtB3TYQbKkSgz0QfRvuQsfhQU/HL/uwWUQ/2z8cnQg9HnytymitQUbjqzkXqOwfPseoK8Hjk273drQ7/LkxG2vnA33F94uDoH8zW3wxlthdtyiKT+VPm6jn29KJBH5BQ+boffRCp+GVBUTn1JzbCVUayTZ804qrfDAfx1haI46yycJlbpjphEGtkhKdxahJc6YsUGJkiadfT8O0dHAdfDg5/OvGxiG+F0FdzgHBj12aLiRwuXUUyu512y4P0qsZInhgt+ktPSJ4ZXAQbnvtwCfTblNz22hTdBPYviPCNbcBtfeVPvw6Yom21fzuI18vumu7g8Ps31PN8Nu9rVWU5j4lJpnBaFqI+lC7HknFZpPqPhMOpMO6oWk7TYTKnWTTiF/YJWkIK2v8XLAHmfSpLP0vcBA+H7kAyHRWei0eyka6BhdC8tsl9VQi/4Ukmxj4jeFatyJvQQuBtbkLu62ET6cvH4t7BvB1xKb3n0kPFi4n9vhEOA1BZvfPA1OqySOqeF4cqfEpheuy+8Tnarax23U80339C7k9Qbt+TK81c/+agoTn1JzfYD85M1M7HknJU0DPlew7RrgxgxiUWMsI38gVS/hpI+kfPY1lia9oT1h8CMQXzG+rectsOy5xbdd+lcQH1qwcRqMroEl74TL9m9qqF0jiqEn2YLs+TB9z5I3T94TRnvDCr6x5N4/3QpX3gqz14bk4Z/ITTeP4NSXwjdK7Ce1yjSGd8clEpi/gf7b4NC1cPxWuA7YLbG/Zz4F37wNXns7zCq1j2oft1HPN130cohyk+Dj9dD348rvK1XHxKfUXL8i0R8lx5530riPk7/McytwTkaxqDFGgA8VbHstYYCLpGA26X2NH0m5raSOFR8NUcHQ02gxjHwRBhLH4lftAKPfgejElJ1Mg55/g96vwbUTVvWpEjv8F8S5k7TRXjC14pUph8OGZ8KBMVwEEMFJUaiKvBwghh8BM48o07IpgvuAjSnbD76txOrAJ+CgGH4B/GcEL0u5yfExrBqB226B3Rv1uI14vulGkz1DrwmDvqTmaEkDXanLTQfuIj/Z+WUg7YON1E1mAHeT/0Hr02xfCqYOt4r8SdV/AA7GSdUShIPGRG8zfgW8CFt8SFKLDL4Zon8P38eXwKKq+yv/EvYYhhfFsGsMT/TB3YfBHyu57y2wT28YGLQxgj+PwA+BP0TwwiNhW7WxVKqex63n+ea7eFeYekcY4gUQHQKn3l39fiRJ7WQREBd8zS57D2nyW0n+78R92AN3MpkFDJP/f3xuphFJ7eFEij8TpE7LlSQ1y9AUGLoFhmIYfBiG9s0qktvhxWshvhVuKbVMfTI9Liw9Nvzch2IY8rOhms6l7lJrLKN4WMElWQQitYm5wAkF2z6C1YCTyTrg0oJttvpQt5sGXFCw7RqKhyFKkppq4TYYfV/4PtoL4kVZRBFDNJqbARHBRVGLKv+zetzQ4mH047kLdwNfaM3jSpJa4ViKKzxc7q5u1Eto/5D8XVidaURqlmnAevL/rwczjUjK1mLyfx+2kN/nWJLUUkNnJaoPX9LqR18Lp+SqLn+9FqZM9seFobfkftab0od8SZI63QryD3jWkz/RVeoGha0fhoE5mUakZkr7/654iIA0icwkJDqTvw+Ly95DktRkcQSDl+WScffDUEUT3uv1e9hhLSxeC/Fa2LAGnjmZHzdY8sLxJPOSo1r3uJKkVpqBBz3qbtOxArDbpFX4rso0Iikbqyjua+zJT0nKXBzB4Kdz/T5/B5c2NRl4G8zMJR7jW+Hjv2lRj/usHjdYflCul2oMQ69p3eNKkrIwQPEyt5mZRiS1ziD5r/9N2POxG8yluNXHvEwjklor7XdgfqYRSZIKDL5tvPJz+UHNepQ7YPfb4F1roSXVpVk/LgzNsdJTkrpLP6HKw+ondZu0Kd9nZhqRWimt2q2FlQZSZvoJw76Sr/81mUYkSSph+UEw9ItQnXjxrllH0/m29/S8FpbslXU0kqTWmU9x5cfcTCOSmu8G8l/zdxGWQas7pCW+z800Iqk1zqW4z+3sTCOSJE1gaA5cOzXrKDrfsv1g2aFZRyFJysaN5B8IrcPqJ01eJvsFcBG2OlB3mU54ndvXWJIkSVJXmYnVT+oOtnfQmGk43Erd5WpM9kuSJEnqUg56UTcoXOa5hbDsWd1pEcXLfn09aDKaTXGlu32NJUmSJHWN6RRXP12daURSY82geJnn4kwjUtZ6Cf1drQDWZLeG4pY29jWWJEmS1FUKq59iHHqgyWMF+a/t9YTlzupucyl+35uXaURSY52IfY0lSZIkiV5CFUjy4GhNphFJjTGH4gP/EzONSO1kFfmvjftwwJsmh7RetiszjUiSJEmSMnQsJog0ufQCq8l/Ta/ONCK1m1mEfq8OeNNks5jivsYzMo1IkiRJkjLmkmBNJmktHOZkGpHaUWGCyAFv6nQzKE7o29dYkiRJUtfzYEmTRdoyzxWZRqR2lfZaGcw0Iqk+Kylu4eBJTEmSJEkCBiheHjcz04ik6qVV8bnMU6UUVgcPE5bBS50mbWjX/EwjkiRJkqQ20k+oDkkeNK3KNCKpOvZtVLV6gbvIf83ckGlEUvUcVChJkiRJFZhPccXI3EwjkirnpG7Vwko5dbozKa5cnp1pRJIkSZLUpm4k/wBqHSaP1P7SklfzMo1IncSkuTrVdEJLD3vVSpIkSVIFZhKqRVwurE7RT/FyZds0qBq2SVCnGqS4r/H0TCOSJEmSpDbngZQ6ybk4oEb1SxuM5fue2tlsik9UnplpRJIkSZLUAaYD68k/mLo604ikdC7zVKNMo/h9z9eS2tkailvT9GYakSRJkiR1iEUU90x0WILaTWF18nqs0lPtCt/3rB5Wu3IYoSRJkiTVoZdQPZI8qFqTaURSvjkUL/NclGlE6nS9FPeLvSHTiKRi0wgDuJKv05WZRiRJkiRJHehYiitKTsw0ImncavJfm3fhMk/Vby7F73vzM41IylfYj3YLMCPTiCRJkiSpQ62geCnxtEwjklzmqeZaRf5r6z6gP9OIpGAGIdGZfH0uzjQiSZIkSepgHmSp3bjMU802i+L3vXMzjUgKVlKclPdkpCRJkiTVYYDiZXUzM41I3cxlnmqFwtfZJhycpWzZhkGSJEmSmqCf4gq7VZlGpG5lBbJaZRqhtUfytTaYaUTqZg4clCRJkqQmmoc9FZU9e86qlRaR/3obBv4604jUrQpfizEwO9OIJEmSJGmSKRz4sQ4Hfqh1Xk3xgf+JmUakya4XuIv819zPM41I3Wg6xdXHV2cakSRJkiRNQjMJFU8O/FCrpSWgVmcakbqFfRWVtUHsNytJkiRJLXERHoCp9dKWec7JNCJ1k8Jq93ux2l2t4QlHSZIkSWqhtIEfLrlTM/maU9ZmYfJJ2bgRW8xIkiRJUks5ZEGtZJWx2kHh63Ajvg7VXPNxqKAkSZIktVwvsIb8g7E1mUakycpKO7WLXSmuPB7MNCJNZv3AfeS/3lZlGpEkSZIkdZHZOGFbzVfYW/E+XOap7BRWuw8TkvNSow2Q/1rbQuj3KUmSJElqkRXkH5itJ/RjlBphHsXJ9XmZRqRu1wvcRf5r8vpMI9JkNIOQ6Ey+zhZnGpEkSZIkdaEZhH6LHpyp0VzmqXY1l+KE/PxMI9Jk40lFSZIkSWoT51K8HG9GphFpMih8XbmkWO2ksAXDvdiCQY1xLLaRkSRJkqS20Q+sI/8gbWWmEanTTae4kviiTCOS8jl0S83QS/HfUwcHSpIkSVLG0pZ+zs00InWyq3GZp9rfReS/TjcSkvZSrQqHZ8WEQYKSJEmSpIwVLv1cR6hekaoxh+ID/0WZRiSl25WQlE++VgczjUidbDrFr6erM41IkiRJkrTdTIqn0J6ZaUTqRKvJfw3dhQl0ta/CCj170apWg+S/ljZhBbEkSZIktZXFeOCm2p1IcbXnqzONSCqvl5CcT75mr880InWimdgzVpIkSZLa3jRc+qnapL12VmQakVSZtB7H8zONSJ0mrVVMf6YRSZIkSZJSFVbtDeNwBk2ssFp4CzAj04ikyhUmru7FxJUqMw+HA0qSJElSR1lD/kHcmmzDUZubQXF/2IFMI5KqMwuXKqt6/cB95L9uVmUakSRJkiRpQrNx6acqt5L818p9WC2nzlM4nGYj9jhWeedSXOk+M9OIJEmSJEkVuZriZNa0TCNSO7I/oiaL6djjWJWbQRgAmHy9LM40IkmSJElSxabjQZ3KS5uIvTrTiKT6LKK4x/GsTCNSu1pB/mtlPZ4clCRJkqSOciYOrFFpha+PYWBOphFJ9UlL5l+faURqR2ntYE7MNCJJkiRJUtV6gXXkH9ytzDQitYu0imCXBWsysH2DyunFAYCSJEmSNGmkJQHmZRqR2kHhIJhNOAhGk8cq8l/f9+LALgWF7RBiQgWoJEmSJKlDObVbSbMIy9qTr4kzM41Iaqy01/i5mUakdjCN4gFYV2cakSRJkiSpbjMI/T1NAgjgBvJfC3cRln9Kk0lhVfNGrGrudhdhpbskSZIkTUqLKT7gc9BR95lP8TLPuZlGJDXHdIqr++xj271mYhWwJEmSJE1a0whL3JMHfSsyjUit1k/xa2BVphFJzVXYz3GYsAxe3aew7+s6bPkiSZIkSZNKWrWfQx26xwD5//dbMAmkya2X0MrBZH93m4eV7pIkSZLUFdaQf/C3Bvs7doO0Pq+LM41Iao25FCe95mUakVrJSndJkiRJ6iKzKU4CLMo0IrXCCvL/z9cT2h9I3aBwmfO9uMy5W5xLcaX7zEwjkiRJkiQ11UpMgnWTORQnu0/MNCKptWbhYJtuNIMwyM9Kd0mSJEnqImnLni/KNCI1Sy+wmvz/69WZRiRlY5D834ONhMnvmrysdJckSZKkLrWY4mnHLv+bfAqnWseEClCp20wnJDuTvwuDmUakZkpr62KluyRJkiR1iWk48GGym0aocEr+H6/INCIpW2dSfMJnVqYRqRl6SR/kJ0mSJEnqIvNx2vFkdhH5/7ebCG0OpG7VC9yFJ3wmu7RK99mZRiRJkiRJysSN5B8c3ofTjicDh7lI6ebiCZ/JzEp3SZIkSdJ2MzFBNhmtwoS2VErh78e9+PsxWVjpLkmSJEnKUzjt2APFzmZFm1SeFdGTkyfyJEmSJElFpuPSwMmiH3sYSpUoPOGzkfBeqM5lpbskSZIkKVXaMIhjM41ItTgXp1ZLlZhOSHYmf18GM41I9ZiHle6SJEmSpBJ6gXXkHzSuy21XZ5hOaFNgIkeqzJl4omAy6CdUd1rpLkmSJEkq6ViKK2YWZRqRqnE1+f9363HprlROL7aGmAzSKt1nZhqRJEmSJKktrcDkWSeag0lrqRYOA+tsMyiudL8o04gkSZIkSW1rBrAFl0t3mtXk/5/dhW0KpEoVDsW5F4fidIq0k3XTMo1IkiRJktTWBnDZYCeZT3HF2qszjUjqLLMI73PJ36FzM41IlZiNle6SJEmSpCqlDYq4MdOIVMo0iv+vVmQakdSZBsn/PdqIbT7aWS+whvz/szVY6S5JkiRJqkBaFeH8TCNSmsXk/x9tIbQrkFSd6YRkp20+OsMiiv9Gzc40IkmSJElSR7mR/IPK+7DvXTtJ68e6ONOIpM6WNh18VqYRKc00Qi9PK90lSZIkSTWbSXHfu4FMI1LSSooT0w71kGrXTxgMlvy9WpVpREpzEfn/R5uw0l2SJEmSVIPCA0yXUreHudiKQGqGtN+tuZlGpKS0E3IOopIkSZIk1cQlhe2nl+KqtNWZRiRNLqvI//26C9t8tIvC/xtbsEiSJEmS6pI2ROLYTCPqboX/H8PAnEwjkiaXWVhV2I7mUfy3aF6mEUmSJEmSOl4vsIb8g811ue1qrekUV+A6eVpqvEHyf882En7/lI1+QnWn/VclSZIkSQ03m+JKm0WZRtSdCpMxmzAZIzXDdEKy05MM7eFciivdZ2YakSRJkiRpUllB/oHneky6tZLLb6XWSku2zco0ou40nXCSJ/l/cVGmEUmSJEmSJp0ZFB98WgHVOjfgwBWplfopHiTm8urWu5rik27TMo1IkiRJkjQpudwwG/MpbjUwN9OIpO4wF3/3smSbFUmSJElSy6QNmLgx04gmP4d6SNlahdXWWSkcrLcGB+tJkiRJkppoHsUVOPMzjWhyK6yy3YJ9BqVWsr9uNk6k+G/N7EwjkiRJkiR1hcIKqPuwAqoZ0vqqLs40Iqk7DZL/e7gRh7s10zRCL8/kz3xFphFJkiRJkrrGTIoroAYyjWhyWoFDPaR2MJ2Q7HS4W2ssJv9nvYlwIkiSJEmSpJa4iOIl2B6YNs4cHOohtZO04W6NajtxQIP2MxnMJPw9sbWAJEmSJCkzzVyKeABwdIP21UpnArs3YD+9wGryf7arcaiHlKV+4F6aM2jsJhrz3pGVM2lc8tZWKpIkSZKktpA2fOLYBuz3Jjpz6fwA8K0G7GcRxT/XOQ3Yr6T6pA13m1vnPs/M7acTT/aMGSC8b9drLsU/33kN2K8kSZIkSTVZQ/5B6jrqq0wcSwJ0YuJzbPl/PQfqDvWQ2lthReJd1F6ReADwGJMj8RkT3r9r1U/4+9GMilpJkiRJkmoym8b1okwmATox8XkzIfbHqH3ZqkM9pPY2i+LhbrX2oLwpsY/JkPis570vrYfqzIZEJ0mSJElSHa6mePr49Br2k0wCXN2w6FpnLPFZa/yzcKiH1AkGyf893Uj173lj1e2TIfGZfO+rpd3HdMJJnuTP46KGRSdJkiRJUh3SDloHq9xHYRLg5kYG2CLJg/9aEhkO9ZA6w3RCsrPW97xkdfvYVz3LxLNW+N5XbbuPtJNn0xoZoCRJkiRJ9ahnmeLuFCcBOjHxeQf5z+H3VL7sM22ox/wmxCipMdLe82ZVeN9kdfvYVye29xhTmPisZsl7I9ulSJIkSZLUFGmDKW6s8L7fovjAtxMTn4XPodLlmv2EASnJ+93QpBglNUY/cC/VD+MprG6fDInPwpM+1Sx5LxyQt4b6BuRJkiRJktQUtVQtzku5z1i1ZKdJex6VLHmvp3JMUnbS3r/mlrl92hL3yZD4LPXeN9GS9xNT7jO7eWFKkiRJklSftD6VpXq1pS1xT351mlLPo9yS90b0R5WUncL3vLsoXbGYtsS9murwdlXqOZVb8j6N0MszefsVTY9UkiRJkqQ6zKR4MvniErdNW+LeqYnP3Sn/XEolNQqnQ6+n+unQkrIzi1Clnfw9ThtUVGqJeye39xhTy3vf4oLbbQJmND1SSZIkSZLqVHhAu4XiA9pSS9w7NfF5NBM/n8Il73MoTpg41EPqPIUnMDaSfwKj3BL3Tk98TnTSJ+29L+0E2bktileSJEmSpLqkLWFcmbh+d8Ly74kOlg9rXch1qyTxWbjkfXXB9eWWyEpqX9MJyc5SLSvKLXHv9MRnLe99aS1R+lsXsiRJkiRJ9UkbWjE29OOilOsqqRJqZ5Uc/MeMDzCZn3JduaEoktpbqSFlEy1x74bEZ8z4kve0IXgTDUGSJEmSJKntrCH/4HYdcAyVHSR3WuKzkqX7Y18vJ1Q4laqIldR5+oF7yf+9/hETL3Ef+3qs9SE3RKWJzxh4NeHvQHLbqtaHLEmSJElS/WZT3MPyUSo/SO6kxOcAlT+vhwsup/VAldR50iq5q/nqRNWc9PlLweVhQr9PSZIkqaF6sg5AUle4BVhesO0ZVdy/kxKf1dir4PJFwB+yCERS3V6Z+HoQ+N9sw2m5anox71Fw+VLgVw2MRZIkSQKgL+sAJE0Kryy4nExU7k44IJ4CjODQnlK2Epa+3wRsAO5MXFd4eWPBZUmNMw94ccG2wpMvB+S+VL9twEsI7313Et7vxhRe/kXBZUmSJKksE5+SJrI7oRLxOYlth5E/mVfjav259AOvSFyudsjgYLhFAAAgAElEQVTH2ECUjYQhKvfWGIfU7W4mDGU7IcMYdqd7EnxTGH/vq7a6PzkIaiPh/61bfm6SJEmSpAY5gHCAWU/Punq+xiagd4Isf04rMSEtNco8QhIti9/lTmzvcTXZvffdjBW4kiRJkqQ6nUk2iYBkVU+7yyLxeS/VV4hKmtjuhBMKJj4nlsV73wZClackSZIkSQ2RRfWnic/SXxdhlafUbK2u/jTxOfGXFe6SJEmSpKYZ66Vm4jPfHbTmZ3IvnZkckTpVK6s/O/F3u1WJzw1Y4S5JkiRJaoFWJQLuaNUTaoBWHPhb5SllpxXVn2e27Nk0zu9p/nufVZ6SJEmSpJZrRSKgUzTzZ2CVp9Qemn3Sp5MGuo1p5nufVZ6SJEmSpEw1OxHQKZr1/K3ylNpPs076mPj0vU+SJEmS1IbmESoTTXw25utOrPKU2lkzTvqY+LTCXZIkSZLUpnYnVOk08iC4Eyp+jsbkh9StGln9eVGLY6/XYTT2vc8qT0mSJElS2zuaxlV/dkLlT6MSn3cSEgmSOkujqj9vbnXgdWrUe59VnpIkSZKkjtKo6s9OOBhuxMG/VZ5S56u3+rMbE58DWOUpSZIkSepQRxMqGU18WuUpdYN6qj+7KfHpe58kSZIkadIYoLaD4xOzCLZKtT43qzylyauW6s9OS3yeie99kiRJkiQBobqn2urPTjhArjbxeTNwQCaRSmqlaqs/H8smzJpV+95nlackSZJaoifrACR1pbGD3k9nHUhGNgJnMT78SdLktoFQ+fkPhN//iUzWXpcbCe/7Yye/JEmSJEma1A4jVD52S8WnVZ5Sd6u0+rOT+N4nSZIkSVIZZ1K+D97K7EKrWLkE7gbCc5QkmLj3Zycpl8j1vU+SJEmSJEI1UKnkYScM+ygXu5VOkgqVq/7spOXuvvdJkiRJklShtOrPTkx8WukkqRJp1Z9HZxpRdXzvkyRJkiSpCoXVn52W+FxJZ1VsScpWYfVnpyY+V2KVpyRJkiRJFRmrhHos60AqMFbpNC/rQCR1rLH3vE5KfPreJ0mSJElSjcYqodqdVZ6SGmF3Oqtq0vc+SZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZKkcqKsA5CkJuoFngHsBTwL2APYLXF9DPwFeAx4EHgI2NDiGCVJkiRJkiRpQtOB44DPExKb1X5tAs4H/hbYvcWxS5IkSZIkSdJ2U4G/A75JbcnOcl/LgZcBPS17NpIkSZIkSZK6Wj9wIo1PdqZ9PQy8DluESJIkSZLUETyAl9SpjgG+TujfWYlrgbsIfTx3BoaBUWAf4HDg+Ar3cyuwELijmmAlSZIkSZIkqZxpwFImrtD8EmH5+z5AXwX77QX2B04AvlrB/j9NqDiVJEmSJEmSpLrMJCw5L5WMXAUcC+zYgMfaA3gz8Lsyj3c/8IIGPJYkSZIkSZKkLvVqSicgbwEOa+JjH0P5hOtrmvjYkiRJkiRJkiapt1I66fhWWtOvuB/4P2XieGMLYpAkSZIkSZI0SZxMeqLxd8ABGcTzEkpXf5r8lCRJkiRJkjSht5CeYLwK2CHDuPYkLK9Pi+2YDOOSJEmSJEmSsjS0Lwx9Di4sMYTnimlw1Q4wtFszo/g97HAXPKP0LeIIhj4OQ3s2M44SDic9sfg5oKfGfR6dsr8jatxXP6Wnv8+qcZ+SJKW4uB+GPgOXH1j+dtf2wvIyf9frE0Pv7TA9LtliJtPPDZIkSUVqTR5IqtmSo4A/QTwT+kbzrxt6EQx+E4Y3wdNPARtg6Fq44lmNevS1MOM2eNut8I1H4akn4Y9roUyCNT4WeE+jHr9COwP/lrL9Y8C5wGjKdZVIOxCrtT/oVuAfgcGU675LYybLS5K63rL9YOrtEC+EKU8XX3/5HjD4tyEx+pc/wcijMPjiRj367TD9VjhuLSxZC4+PwvrbYU7pe2TyuUGSJCmViU+ppQb/EXp+CvHH4KF58IGtietOBn4J0T9AfAr0Ph9GTwLeAtvugMv2r+eR74SD14ZqxPtiWBHBmwAi+MER8Hj6vaIYei6A+JxwYNUyH6C4avICYDHhObSLGDiD4iTtgYQErSRJdRiaA6P3Q/R72OlAWPDA+HVX7QBDt0DvXyD6EfBJiPaC+B6Yck+9j/zfsONauG8U1kfwPWBRFNrMbIzhV+n3yuxzgyRJUioTn1JLjC39ir4M/B9YdD4MJKoWl74XouW52x4Hi66AU34Lp10NDIQDmb7FYT+12QqP9sJRERwJbBzbHsF3Ihgpfc/h1eHfntfU+thVegHwLwXbfgZ8gvZKeo4ZJSQ/1xVs/xRwaOvDkSRNDkPHA6uB62Dqm+Efn8i//r5hiM6A0eeSdwIu+h68t8QJzcpthW098O4+OCSGHySuuv4I2Fz6ni3/3CBJklSSiU+p6eIIhj4PfBa4AE69MP/6JS+E+IrchUth4fUFO7gm9+8b4PL9ao1iDjx6OPz3S+D2GP4bIIbhUfhx+XuetoFQ6XEGDPTV+vgVigjL2QudBGxr8mPXYxMhxkKfBXpbHIskqeMteSvwn6F6c3g+nLSl+DYDw3DqrXDavRAnPjvEN4TKy/q8CoZfAj8+DO7ugZWJq74dlW0509LPDZIkSWX5YURqqjiCpZ+D6GyIfwbRJ/IPRgZ6ILokcfuLiw9W4pFcG8pp0Ls3cH89Ed0GzwReBRDBvcAEy+GiGAavg+jf4VkHAnfX8/gTOBJ4d8G2s4HfNPExG+UWwuCljyS2vQE4igmTy5I0oTnAcwu29QF3AHc14fH2I/ytKDzp9BfghiY8nrYbegtwDcTrYeRoOGOC6s04gqE35y5shpE7GxlNDD235f42xzBMqEIto6WfGyRJksoy8Sk11dIzgQ8TDkTeDmcUHEA+6xiIj85dWAEP/a54H719icKKGcDaeiKKYXauRxfAyiMrqqTs2ZAbWP5mipehN0pEftIQ4AFgeZMerxk+T6j83Cux7bPAMYSDRUmq1cuBC1O2fxeYR+1D30o5g/RexcuAG2nP1iOTwNJXQnxt7sJ74IwKTnZevjf0nRC+j++ERx5sZES3wrN7xocZ3fM4/GHie7Xkc4MkSdKEXOouNc3SY9l+kBq/r/jgZaAHRgfGL8dfzu/7OWb0hePfR/vWE1EckouvS2z6XoX3/H3u37lNXLb2QnIDlxJySeOO8WdCb8+kVwB/lUEskiaXFSW2vwF4XoMfaw/gvSWuuwyTnk2ybD+Ibw7fx1ektL4pYUryc8I1YQl84/TAEdv3Dl99VUUn8lryuUGSJGlCfhBRm7i2Fx59JvQeBKOvgL7/CMN9kuIIht4KHALxN+G0/63vMZftB8O7Q0+NBwijfRD/EU5/rPi6K6fD018Lecb4Hnjy34tv86wjID4qfB+vh9E1JR6oYb0tfw47TIU35i4+PgK/rOyevWPzjw6BvaYBKc+5bu8suHwP8O0mPE6zfR04hzDZfcwbgV9kE46kSeJB4HLg9JTr3gQsbuBj/R35letjfkJzltXX6PI9oGcGcCT0/AlO/X7xbZYcBT2vhejn6ddX+3i9+1Hz3+WoF6KN+ZPZxwz0wMhXc61tAD5XeZ/O0WPH7xf/tLbY0sUQrYU3jO09yh9yVEZLPjdIkiRNyMSn2sDgp+GxT4UC5Jjw4X3kaeCL+bdbeghEuYqXaAFcMQtOrrEaMI5gaHk4GKpVD4RJ4/+csu8LwiR2AD4GZz9VfP/RNyUOcL4bhgGkHc9yWOL7rbXHCzvBgcMwVjV68+yKD0RGc88lehqGy0yAr9muhKqlpE8DKT+3trcJuAAYTGx7FyEp0YnPR1L7uJr0PxRnECoxG1Eh3wOcWeK6i2iLth1Lj4O4YMXC6Hfh2hvgrYm/UV/ZGZ78CnBg+Hyx9IVwah2J2555wJW13z8GRtfBtYfmxwmwzzsgGmt9cyks/C0sqmCfX9kZnsz9/YzvgSkT9O2uzq9hlwhen7u4MYZfVXbPpn9ukCRJqoiJT7WB3hXw9HLoOxH4TG7jIhi6FBYmqip6Hh9vYRZPha11vH6jGIY+BtEXIa5xyV7cByP/U7x92csgOjF34QEYTRkCkTxQAej5fnplx9AU8pamx3UNLBiBsYMqIvhm+amsSaPPyiVpd4OpexOSe410CDArcXk9nT0847qCywcCB2PVp6T63AncCry0YPt+hPf37zbgMQ4lDGUr9ABwUwP23wDR/8DowcCLIPqP3Laj4bFnk9d/8qmnIXqU7RX4ozvW97gjP4C+11PXSozeh4qTnkN7QvyF8cvx8sqrPZ94LvTk/n5G36v9hHC6J8Pf57ETudcfUfHf/6Z/bpAkSaqIiU+1gQW56oGvXAhPzodoFrAvDO9D3gTzBQ/A0CsIS+0aYOHtjdlPUhzB0rMTG5akL4V/av/c8wTYDFGJWIafCb3PSVSG1nywlVuu9vaI7VNZq5g0Hu2f+2Ya9EytNYYyjiy4vAZ4pAmP0yp/JCzTPyGx7W8w8SmpPtsIVZdfS7luAaFvc73VdfNLbF9C2yxXHlsqHv8Whq7OnWycBvEs8hKfC7fBZW+C3pshOjAsNa/HGfeT97mkYd40vkok/gk8VEVVak8iSR03/IThKBybuPjtqOL+rk3/3CBJklQRhxupjfzjE8B/5S5Mg969i28zdW1YysXNsGcV1QPX9sLyZzQgyAkMPoe8AT3xyhI3fEHi+wdhNKXfF8CUQxIHQ+thtIJJquluhb3JDSiI4F4qmsoKIZnL4bkLD8CWRh/0RYR+cknfof6D9yzFQGEvubfhySZJ9buBUBVf6A2E6rx67AmcVOK6b9S57yaIYvIq7KOUIU9n3A/8OPwNHbm79L6WP6P4a2i3RkdcbGgKcPL45Z5llQ8nGuiBOJeojteH85uNE4fjhPfkvt8CVNg/tOmfGyRJkirmQbjaTLQaeH/uwiyg4EP81qNC1QbvKF4qVspAHzx2FXACLD8ATvlL2D60J/TuXF+8vQ/DSVvGL/e8fPz7+GfwUKmDrGTi8wY4dRgWptwsnpO4sKa6ZG++CF4SwQ4AMVzz0oqrR7+6E8RH5AY1TYW+OitmijyTMPk8qQnVuC13S8HlQwAHPEiq15+Bq4CPpFz3NuC8Ovb9GtKHGn0X+F0d+22iKDno8CUhGTiQaOMytC9wIvD+9BUYAEtfDiM/S7liM1x2MJzxUG5fO0Hv9Pri7d0IJ21IbHge460LNkNc4fAggH33ZnsLm+hWeLChKyVuhWf35D6vRHDXZvhTZfds+ucGSZKkilnxqTYT3Zv4vmBp1MW7AhdDfC08eGtl+4sj2OcS4F2hP+YDm8a3x/8GI/fW9/X0+8cfa6AHeEci/q+XrtqI909c+EV6L6+BPoj/PrG/71Se7C14tHD0sb1XaA9cX/m9t84YX5YfPQ39jR5ssSf5B9rrgd83+DGy8DtgXdZBSJqU/q3E9kXAHjXucwolJuwRpsm3aRX+lEdDtSNAvEv+dXEE8b8AD8BIWnuAsducnX4dD0Lfo+MXR99a/+eGrT8Lq1C2Oy4Ry82wR1o1bwlRcvjh9yuvFK1MD/x14uLKV1U82KrpnxskSZIqZsWn2szoI+P9LOO/hoErQ+VGHMHQ+cCeMPLB/GqOUuIIhgYgyo1Fja4ZPyiIYhj6HERfo+a+maNTYXTN+OUDd4Qnn5uIv9ySsOQBZMqAJIC994NorHfXZuj5r/TbTeznsMNUeGPu4uMx/LLyew/PGT9HEt8B9z9RaxwlFB5Mr6Exk4nTPJ2yrY4hFRM+VvJntRcwAys+JdVvHXAziYF1OXsBxwD/UcM+DyN9qNE9wI9q2F+LRJsJVbB7AUfC/juz/W/I0jeH/p89fwcLS1V7HkJoUXM2cDdE0fh10Z9hQXLI4mqI3wM9aX9LKjA6FXp/n38SMz4o0cf729Wd4Bw9rsLPHFXL9QV/09jeI6iiErXpnxskSZIqZuJTbebph2HqulylwF4wK/eZe+kJEJ0O8XHjS84msvR0iD41frnwoGBhM6fTPgBPV1C1GK+HkRJLx3qPScwQuA7+eF+twewAB4/CvrmLNx9RcWJxoAei9yQ2fLuypHNVdi+4/BSlp82/gfA8KhyukGcbcFbK9ncDs2vYH8BU4EHgmynXbQFWkz99eUqNjyNJSaPAFylOfAJ8kDBcrdoqu3eX2P5FwvtymzpxKwzdQmiPswtszX22XX4QjFwL8WdgwQ9L3z8+EfgJPOPiiZOOC/8f8P8aEzfkTtAmN1TRo/MrO8OTuf7Y8T3wZJn+pdX7NewSwatyFzf2lTxJW6glnxskSZIqZuJTbWba0/B04mBtXQxDLwC+FQ5eFq2qbD+DJwOXjl+O74GRJvcne/JZ40u74jtgn3IVDollbtHjxVcPTYF40fjlni/Vc+AQjx+8AHwjKp1YLLDP8yAaO7DeDNGNtcZQxvOruO0J5A2BaIgP1Xn/nxCSDG26DFTSJHUzoRrzwILtrwD+CvhFFfvah/H+2kmbCcPm2lgUw2DiZN7wSEgKPvUfodd29NnS971sH+CkMETwsQ/AspWwoIWtVq7uZ3vyutoBhlueP/6Zg+vg7IYmp58Ir6G9AGJYdSg8Wdk9W/K5QZIkqWL2+FSb6e2FeCwhvx72fQbE1wHXwUP/VNk+lrwVouXAJyC+JLfxOjgjJcHYLNFN5StHogl6eI0ezvZKwfi7sFuFPU2LxdATw/zc98NUPJUVIHp9Yk83wx5/rDWOMgp/FjuSWPdXoMIDr5baQG0VqJJUj03AshLXvbPKfc0tsf1aoM0ncscRsFP4Pnoa+qfCk5dCvA+MvBkWlmln0vu2kPQE4EIYvQeGzivowdlk0djJ3jWwvoo2L/HLEhe+18iIco5JfP+NqOK/cy353CBJklQxE59qM+9+EqJfhe+jk4HchNKp76qsaf/S46DnGuBS2HoJkFsG1pSDgjLiX5W/PspN/I5S+oTFEUQfS2z4UHESddlzYelhuYFKZd0Z+kqOTYe/ZzNUuGT+KztDfEpiw+drHa40gZ2asM9WauMloJImuW+U2P4eoNLp4+WGGl1B25/YiWKIbstd2A94JPT17H31xK1xomHg9oKNA/DYaY2PM03eyd47Kh9ONNAHcS65Ha+HqbeVvz3AldNhyeG5QZFlrYUpMZwEEMOWCNIm3qdo2ecGSZKkipn4VJuJYoiTPS8fgJGj4KQNE993yVEQfy839f0smHpwWAYWr4eRO5sW8nZxoqpkoorO4dW5KbS7Qe+0/OuGjoPohNw+j4NFv8m/fumxoSolvgP2GcxVu5Q0klgaHsGdR1e8JPvJVyaW0a2Ahxo6OCGhYAovT1H6QHvvJsVQj30pXaEqSc30O9IHGe1F3rTwshIrDPLcTVU9J7MUP5J/uedlsKCCIX4LL4OFR0Dfs4GLE/v7JFy2f0NDTLVhGKJcW5yoisraZ81ODD98HHbZWP72S54N29ZDz+0w9Q64cMdyt47hlcBBABFs3Q3+UllcLfvcIEmSVDF7fKqNxeuh92WVDTNacjj0/DT083ryxFA1MXRs7so1MP2RsndviB0egqd/CRwK8QQnFU5/DJZ+FOIrgPNgYGEu5jnAdeE28ZvSe5rGe41/Hx0HS3anYFL4b6B/MzxzFP4e+ETiqtfdAX+7Bv53DjxaOr6hKcBA7vHWw8hZTRxOUMWEeT4EnFfj42wF3kv+zwPg7cCt1D546HFKJ5NbuFxSUheKgSWEqeSFPg58nTDYrZSIUB2a5p8nuG+7OgYWrK7uLif/CeIzYWgqRIvC8vfevWn6Mv8PbIXB1RC9FOgvf9tre2HTbjB8CIx+a/x8WzQdHnsdLPs5LHg4/b49iROs0YGw80wKKl1j6L0DngEcOgLfTWzfeQO89U744YvhT6WXvLf0c4MkSVLFTHyqHe2da/L/Mlj0wMQ3H3oBcHsYYNT/elj0VO4D+BvD9dF32nOp1alXwuATEK2Afd+bmOz6AIz+PZx2R/r9oj8mjjuehN6i3qUb4J8i+HDKnXcZhZt74O4YZkWlE3bHM14B9J7Kks8121pw+dmEavS0A6YKXg9lpfVK/RWhaqrRdgD+pgn7laSk1cA6wlTzpIOBlwBrytx3H9KXua8HbmhIdC0R94dEYDQXTr2ptn1EMSz5bEh8AqFNTAsqXqMtld1uw9+EnplFCwymAd+CkfVw+QvCidVCwxugd32un+lm6Cm6zVp4bZQ78Zp8hCgcK3xlG2y5I/xMSp1IbuXnBkmSpIqZ+FQb6vkkbNtUYaXnARD/CFgNo68bXxLfszeM5j6Aj/ywaaHmOWkLDH0dOJSKq2QWXQMXfx/6nxMu926Ck/8QDsBKOfVHMPRp4DyIV8Ciosd6KZxD+KrB0J4QfyF36PPR9KrThiqsinw+sCfQjIOmqSnbaq30nMiO5C/jX0/9iVtJKvQEcClwecp17wJuoXT7kL8vsf0amvMe3CSj/wVTng+n/La+/ezwKGxdl1uu3aJhetF1EH+Y4pOABU79ETW3VTnjIVj6TohvBB6E0aK/RS8NvdBr3H/LPzdIkiRVzB6fakOn3l1Z0nOgB6KrQgVDdD9Er4bBf4TBt8PIR8dv1zMPBt84US/Mxhj9z9xjzqz8Ph/YBAv/J3ydcl/5pCfAVbsD/5BbSrak5lBTxRHEy8NSOC6FPf61sftP9SfgnsTlvYADWvC4zTYTODBxeQNl2wtIUs2+W2L7ewhVnWl2oPRQo6vrjqilznio/qQnwH3DEP0+d+HP9e+vElvuCCtWeHHzPqfEEYzmer72nFJ+0n0t+2755wZJkqSKmfhUB9t7BkRH5y68JUxzj74M0f+FKHEwF30BOBE+3YLEZ8+vgVshPqo5BzDLDoWtt0G8D0THNn4p2dKPhMFK8eWwx5ktahGwGfhxwbaXteBxm21OweUfARVO7JWkqvyR9IrPaYQlyGleQlihUOhnVNd7eRJ5Th+wP7AZelt0ouoDmyD6KsSvgy/u0Pj9L9kLlv5fiM6G6I2w4CeN3X8mnxskSZIqZuJTHaz/CYjfDdHbx7/iNwFnJ270aRh9G/CZ1jTZX7gN4ouBeXDJtAlvXpWrdoDRr0L0NeibGSpEG2npu4HzgQvgofe38OAlJiQFk95EZ7fi6KN42MhPKL3cVJLqEQNfLnHdRwmtN5IiYEGJ23+Rrj1Js2UfwoDCm+GPTR5slDT6jVAxudPBjd939AlgN+AgOPVbjd13Zp8bJEmSpG42+DIYimHwYbh419Y//tCeucf/29Y/dq2G3hNiHjojowBmEg7ck19plUj1enPK4xzZhMd5fsrjFA4ekaRGmsJ4P8/Cr8K/R/uVuN3DwB4tircNDV2Q+/vd4vfrOILBm2DoY6193Hpk/rlBkiSpIlZ8ajI6IfwT/RD+UjTxvPkW/hni84CzQx/SdnZxPwx+gdDP7bWw8LKMAvk9xUsr35VFIA3yzoLLdwO/ySIQSV1jG3BxieveQ/5nvjeUuN0gkDIVfLKIIxj8aC5hNwBDO41fN3g68GHgfbBoXWvjimLoGYD4g3B5myee2+ZzgyRJUkXaPCkjVesrO0OUa+Affbs1y9vTTF0SBi7NakFf0Xr07QTR/jD6XFh4Q4aBbAG+VrCt3FCOdrYvcF7Btn8mJCUkqZlWAetTtr8FeE7u+52B95W4f+H78CTz1Z2AU3IXzoP49zC4HAZXQnQZRCdnl8j700+Ab0JvbzaPX6m2+dwgSZIkdaOhF+QqOWK4/MCJb682cgDFyy7PLnuP6rViqfsAxUtHpzf4MSSplMWkL2M/K3f9K0tc/x2gzZNujTB49vjnhLGvwWvg8kOyjkySJEmSJnDhjrD8IBh6XnOmqqvJCg/YH6axVZ/NTnwelLL/xQ3cvyRN5EWkJzZ/RxhytLzE9XOzCDYbl+8RPissOQAu2yXraCRJkiRJ3SGt6vMSwgTiRmhm4jMCvpGyfyuPJbVSD3AT6cnNiwknlNKSotOyCFaSJEmSpG5SuFQ8Bl7foH03M/E5L2XfFzRo35JUjbT3o3JfZ6XvRpIkSZIkNdKepFckHdqAfTcr8ZlWqdroZfqSVKldCVWclSQ9NwHPzSZMSZIkSZK6T1qC8mFgvybst97E5x7AXSn7nV/nfiWpHudSWeLz64Tl8ZIkSZIkqQVK9cu8H9i7jv2+I2Wf9SQ+9wB+kbLPSzCRIClbz6eyxOcrsgpQkiRJkqRutQfpSzXvB55d4z5fBFwIfDL39XngeTXua78S8f0U2KHGfUpSo0TASsonPccmvUuSJEmSpBabSfrB+sO567JyeIm47if0KJWkdnAs5ROfp2QXmiRJkiRJehGlD9rfmEE8J5aIpRE9SCWpkXYmvQexA9gkSZIkSWoTB5E+6T0GrgKe1YIYngt8r0QMJj0ltasPkv6+dUmWQUmSJEmSpHF7kj5IaOzrU8C+TXjcfXP7Ltcjr56BS5LUTPuR/t5Vz2A3SZIkSZLUYP3AFynfs24p4YC+r47HmQq8FLhsgse6CgcZSWp/MwltQ5JfPZlGJEmSJEmSUr2W8gnJsa/FwN8RKp7KJSh3AvYHjiNMeq9k329t8HOSJEmSJEkNFGUdgCTVaA/gHODcKu7zS+DXwAbC0I9pwBxgryr2cQnwWWB9FfeRJEmSJEmSpKo8F7iYyqo06/k6j1AVKkmSJEmSJEkt8wzgHcBPaVyy8xbgTYTqUkmSJEmSJEnK1L7A8YR+nQ9TeaJzE6Ev6BtozoR4SZIkSZLUIvb4lNQNdgJ2B3YFdiRMbQfYBjxFSHhuBB7PJDpJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJmiyOg//f3oVGViEAACAASURBVL1HSXqXdQL/Vs2kCc5GpiUmdOQSRgXNcSQIyGgOa0ROa7xGMTpegEEuaQO6EXfdkdW1F3fXBhVjhKR7AjLqehyzLEZY1HH1MLLIgESD46rHyyRRwphEmcRkkjCT6X73j7cmXdVV1deqequ6P59z+ky99V7qeburZs48/fyeJ19fdRDA0HhLki+oOggAAACA9dqZ5N1JiiQnkkxUGw4wBKZS/p3wQJK9FccCAAAAsC53p0xwnPv6QLXhABV7TpJH0vr3wv5KIwIAAABYh/1pTXAUKau9gK1nLMnRtP59cDIqwQEAAIARVE9yOK2JjlNJdlUZFFCJmbT/IsRSdwAAAGBkTaSs6mpOdhxNmRQFtoY9SebT+vfAwUojAgAAAOiBvWmv9NLXD7aGHUmOp/Xzf7zxPAAAAMDIO5TWxMfplFVgwOZ2MK2f/fn47AMAAACbyHiSE1H1BVtJp2rvmUojAgAAAOiDybQnQWYrjQjol279fceqDAoAAACgX25Ie/JzstKIgH44nNbP+akkuyqNCAAAAKCPxpIcS2tC5ETKpfDA5nB92n/BMVVpRAAAAAADsDvlcKPmpMihSiMCeqXT5/twpREBAAAADND+tFeE7as0ImCjOlV0n0zZ7xMAAABgS6inHHSiByBsHjNp/4XGNZVGBAAAAFCBXSmTnUunPterDApYl8kk82n9PM9WGhEAAABAhfalvUJsf6URAWs1nnJIWfPn+HiSHVUGBQAAAFC1Q2lNmJxOOSAFGA1LP8PzSfZUGhEAAADAEOhULXYsqsVgFOxNe9X2dKURAQAAAAyRybQnT/QHhOE2kXJquz69AAAAAMuYTXvyc7LSiIBu6kkOp/Xzeirl0DIAAAAAmuxIORClOZFyIuVSeGC47E/7LyqmKo0IAAAAYIjtSTncqDmZcqjSiICldqf9c3prpREBAAAAjIBOlWR7K40IOGcs5fAxldkAAAAAa1RPOSClObFyMnoHwjC4IXrxAgAAAKzbrpSDUkyLhuExmfak52ylEQEAAACMoKm0J1n2VxoRbF3jKZe0N38ej6ccSgYAAADAGh1Oa6LldMrBKsBgHUr7Z3FPpREBAAAAjLCJtFeZHUs5YAUYjH1RfQ0AAADQc536Cs5UGhFsHfrtAgAAAPTRbFoTL/MxSRr6rZ4yydn82TuVMhkKAAAAQA/sSDlIpTkBcyLlwBWgP/anvdp6X6URAQAAAGxCe1JWejYnYQ5VGhFsXntSDjDyeQMAAAAYgJm0V6DtrTQi2HxUWAMAAAAM2Fjaew6eTDn9HeiNpT11i+ipCwAAANB3naZMH640Itg8JtOe9Lyh0ogAAAAAtpCptCdnrq80Ihh9EymXtDd/ro6lrLQGAAAAYEAOpzVBczrJ7kojgtHmMwUAAAAwBCZS9vdUnQYb16mKen+lEQEAAABsYXvTnqyZqTQiGD2d+uYeTVKvMigAAACAre5gWhM280n2VBoRjI56yiRn82foZMpkKAAAAAAV2pHkeFoTN8eTjFcZFIyI6bRXTe+tNCIAAAAAnrAnZaVnc/LmUKURwfDzuQEAAAAYATNRuQar1alS+kRUSgMAAAAMnbGUU92X9iqcqDIoGFKzae+NO1lpRAAAAAB0tTvJ6bQmdA5XGhEMn2vSXh09U2lEAAAAAKzo+rQndaYqjQiGx0TKSujmz8exlBXTAAAAAAy5w2lN7JxKWQ0KW93Sz8bp+GwAAAAAjAxVbdBuKu3V0NdXGhEAAAAAa7Y3+hjCObtTVj7rfwsAAACwCRxK++TqPZVGBIM3lrLiufmzcDJlZTQAAAAAI2g8yYm0JnyOJ9lRZVAwYDNpr37eW2lEAAAAAGzYZMpKz+akz2ylEcHg7En7+/9QpREBAAAA0DOdKt6uqTQi6L/xlBXOSyuex6sMCgAAAIDe0eOQrUiPWwAAAIAtYHeS0zHVmq1hb9qrnGcqjQgAAACAvtmf9mTQVKURQe9NpKxobn6fH0tZ+QwAAADAJlRPWeXZnBA6lWRXlUFBj3V6j++uNCIAAAAA+q5TNdzRlElRGHXXR1UzAAAAwJbVqf/hdKURwcbpYwsAAACAiddsKmMp+3g2v6dPpqxwBgAAAGALGU9yIq2JouNJdlQZFKzTTNqrmPdWGhEAAAAAlZlMe7JottKIYO0mU1YsN7+PD1YaEQAAAACVuyHtyc/JSiOC1VO5DAAAAEBHnXojnojeiIwGvWoBAAAA6Mo0bEbR3rRXK89UGhEAAAAAQ2d/2pNIU5VGBN3tSjm1vfn9ejRlBTMAAAAAPKGeMnHUnEg6lTLBBMPEexUAAACANdmVMoG0tIquXmVQsITqZAAAAADWbF/ak0r7K40IFulHCwAAAMC6LZ2UfTomZVO9HUmOpfW9eSLJRJVBAQAAADA6xlMmlJoTTMdTJp6gKrNpr0aerDQiAAAAAEbOZNqTTLOVRsRW5v0IAAAAQM+osGMYqEAGAAAAoKe69VQcrzIotpxbo+csAAAAAD3WaYr2rZVGxFYylfaq4/2VRgQAAADAprE/7cmnqUojYivYleRUWt93R5PUqwwKAAAAgM2jnjLh1JyAOpUyMQX94D0HAAAAwECovmOQptNeZbyv0ogAAAAA2LT0W2QQ9iSZT+v77FClEQEAAACw6XWasL270ojYTHYkOZ7W99iJJONVBgUAAADA5jeeMhHVnJg6ljJhBRs1m/aq4slKIwIAAABgy5hMe3JqttKI2AyuSfv76oZKIwIAAABgy1GZRy9NJDmZ9krisSqDAgAAAGDr0YuRXjocvWMBAAAAGBJ7UiaoTN9mI6bSXj28v9KIAAAAANjy9qc9abWv0ogYJbuTnErr++dwknqVQQEAAABAPcnRtCauTiXZVWVQjISxlH08m987J1P2+wQAAACAyu1Ke9Xe0ajaY3kzaa8W3ltpRAAAAACwhD6NrMWeJPPRHxYAAACAEXBrTOZmZTuSHE/re+V4kvEqgwIAAACAbsaTnEhrQutYyl6OcM7BtL5H5lNWgAIAAADA0JpM+5L3GyqNiGGyN+3vj5lKIwIAAACAVZpNe3JrstKIGAYTKae2qwgGAAAAYCR16uF4Ino4bnWH0/qeOBU9YAEAAAAYMaZ20+z6tFcBT1UaEQAAAACs03Tak117K42IKuxOcjqt74PDlUYEAAAAABtQT3I0rQmvk0l2VRkUAzWWso/n0vfARJVBAQAAAMBG7UrZy7E58XU0ZVKUzW8m7VW/11QaEQAAAAD0yFTak1/7K42IQZhMe5/X2UojAgAAAIAeWzrR+3RM9N7MxpOcSOvP/HiSHVUGBQAAAAC9NpH2RNixlD0g2XwOpfVnPZ9kT6URAQAAAECfTKZ9yftMpRHRD3vT/nOerjQiAAAAAOiz2bRXAk5WGhG9tCvl1HbDrAAAAADYUnak7PXYnBg7kbInJKOtnjLJ2fyzPZUyGQoAAAAAm96etE/7PlRpRPTC/rQvcZ+qNCIAAAAAGLCZtCfJ9lYaERuxO8nptP48b600IgAAAACowFjal0WfTDn9ndGyI8mxaF8AAAAAAEnK3o+n0powOxyDcEbN0oFVRQysAgAAAGCLm0p70mx/pRGxFpNp//nNVhoRAAAAAAyJw2lNnJ1O2TOS4Taeckl788/uWMql7wAAAACw5U2k7O+5NIE2VmVQrOjWSFgDAAAAwLKuSfuS6ZlKI2I5WhQAAAAAwCotHZIzn2RPpRHRSaehVEdjKBUAAAAAdLQjyfG0JtSOp+wlyXCop0xyNv+MTqZMhgIAAAAAXexJWenZnFg7VGlENJtO+xL3vZVGBAAAAAAjYiaSa8NIUhoAAAAANmAsnZdTT1QZ1BbXqQ3BiWhDAAAAAABr0mmAzuFKI9raOg2emqw0IgAAAAAYUVNpX/J+faURbU3XpP3nMFNpRAAAAAAw4g6nNeF2OsnuHl7/8h5ea1hc2cNrTaRsM9D8MziWsh0BAAAAALBO/U68fSi9TRRWbWfKe+qVfieeAQAAAGDL2pv+LLW+snGtq3twrWFx7p729eBaWg0AAAAAQJ8dTPtwnT0bvOaHGtea3uB1hsm+lPd01wavszuGSwEAAABA3+1IcjytibjjjefX41yCsEiZVN0sprPx6syxlO0Emr/XJ1O2HQAAAAAAemxPykrP5oTcepOWdzVd40hPohsOR7J4Xw+k7Pm5VjNpX+K+t1cBAgAAAADtepGUu37J+Q/0MsCK3ZHWe1vrMv5eJpcBAAAAgFXa6DLsnSkTnUuTp5vF0vtaS9XneHrbTgAAAAAAWIONDN5p7oHZ/HVl78McuEvT+d5WW7F5aMl5vRggBQAAAACswVTaE3xTK5xzaTpXexYphx2NuivT+d6KlPe+nL0dzpnpW6QAAAAAQFeH05qoO5WyGrSbg+meGFxrL8xhtLR36WqrPidStgtoPv5oyrYCAAAAAMCAdUrYHUvnhF23ZeDnvm4bQLz9dkOWv8dOy/nr6ZxA3jWAeAEAAACALla7RPu3OhzX/HVkEMH22ZEsf48f6nDO/g7HrdQyAAAAAAAYgKVL2JcO5Vmu9+Vmmux+V1a+x+aqz91JTi/Zv9ohUQAAAABAn+1IcjytCbzjjeeTstJxNYnPnQONuvdWc493NI4dS9kWoHnfiZTtAwAAAACAIbEnZaVncyJvNsnVWV1CsFsPzFFxeVZ/n/vSuR/o5MCjBgAAAABWNJP2ZN59HZ5bLiE4qtaS4L23w3Ozgw8ZAAAAAFiNTsu31/I1PfiQe2Y667/v5rYAAAAAI61edQAA0AeXJHl7yiXv6zHKS90vXed580l+Lsl5PYwFAACgMrWqAwCAdbo0ybNS9rTcmTJZubOxvVGfTPL8HlynCkeSfE2PrvNgyu/FJxuP/6gH1wUAABgIiU8AhtnOJM9LmeS8NK1Jzn4b1X8jH0h/p9IvTYYeSfKvjW0AAAAAoIud2Vifyl59rXfJeJV2ptrv2R1JDvb9LgEAAABghF2ZsoqwqiTeKPb5vDLVfb/uTrKv/7cIAAAAAJvDvpRJtUEn8q4fxM312L4M/vv0YMoKXQAAAABgHaZTJtkGldAbxWTeIFsEnEt49rOfKAAAAABsCef6fw4iAXpkQPfUS7dlMEnPgxnNHqgAAAAAMNQuTZl862dy766B3U3v3JH+J4MlPAEAAACgzy5NmYzrV6Jv1PQz4TmKw54AAAAAYKRdmf4kQC8f5E1s0KXp/f3fneTqQd4EAAAAANCu1xPgR6nK8cr0NuG5b7DhAwAAAAAr2ZfeDEAapcnu12fj92tSOwAAAAAMuV5MgL9h4FGv3w3ZeJJXwhMAAAAARsTOrH8C/JEK4l2v9fY4PRiT2gEAAABgZF2a5LasLSl4VyWRrs9dWXtSd5SGNwEAAAAAy1jrBPhRsZaE5ygNbQIAAAAA1uDKrG4C/CgkCS/PyvdhUjsAAAAAbCH7snwC9OrqQlu1q7P8pHYJTwAAAADYgpabAD9dYVyrNZ3OCU+T2gEAAACAJxKgS6eeD7ulU+tviIQnAAAAALDEpVlMJh6pOJbVODes6WDK2AEAAAAAuro8yW1VB7EKt6WMFQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgL6oVR0AAGxy25P8QJKxpufOS3IgySOVRAQAAAAAsEG7kxQdvr6hyqAAAAA2u3rVAQDAJvd9XZ6/Lsm2QQYCAAAAANALFya5L50rPoskz6kuNAAAgM1NxScA9M9kkouW2d+tGhQAAAAAYCidl+RP0r3as0hZDTpeVYAAAAAAAGv1oiyf9Dz39fKqAgQAAAAAWKt3ZnWJzw8n2V5RjAAAAAAAqzaR1SU9z309r5owAQAANi/DjQCg967q8NxfLXO8IUcAAAAAwFA7P8mfp3Nl5yuTHO/w/H1JPr+KYAEAAAAAVuOr0znp+Tcpe3n+Ypf9r6wiWAAAAACAldSSvCedE5uvaBzz/C77/ybJeQOOFwAAAABgRU9P56Rm81L27Uk+0uW4PQOOFwAAYNMy3AgAeuf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    }
   },
   "cell_type": "markdown",
   "id": "2ac3ad79-598e-4752-b64a-1c90b287eab3",
   "metadata": {
    "tags": []
   },
   "source": [
    "![CircuitDCA-2.png](attachment:0b071d8e-1d24-4472-9d13-8e3c5b7c74cc.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d3a0d45-ed6b-458e-9e68-84866fe41fe1",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "Repeat for another plaintext $x^{(3)} = (1, 1, 1)$."
   ]
  },
  {
   "attachments": {
    "c97a6fa7-f554-4a92-b299-bded93cb52da.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "id": "af2b5f77-999e-4396-9a7f-3f17acaeafbd",
   "metadata": {
    "tags": []
   },
   "source": [
    "![CircuitDCA-3.png](attachment:c97a6fa7-f554-4a92-b299-bded93cb52da.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d17fafdc-9832-414f-9cba-273fa95a52b2",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Setup AES circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f35a262-ca53-41bd-aadf-d4e36929b8cd",
   "metadata": {
    "tags": []
   },
   "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": "54978d1f-2d9c-4bd3-9eb7-efd458be0aea",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Record computational traces"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f14f7c6-01e7-4434-9326-9aad0bdbc28c",
   "metadata": {},
   "source": [
    "Using `circkit` directly:\n",
    "\n",
    "(useful for small experimetns, too slow/heavy for mass tracing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0ffca853-0ab1-4903-8b87-34a79d1a9840",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{<OptBooleanCircuit:INPUT[name=x0_0]#0 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_1]#1 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_2]#2 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_3]#3 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_4]#4 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_5]#5 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_6]#6 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_7]#7 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_8]#8 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_9]#9 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_10]#10 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_11]#11 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_12]#12 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_13]#13 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_14]#14 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_15]#15 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_16]#16 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_17]#17 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_18]#18 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_19]#19 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_20]#20 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_21]#21 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_22]#22 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_23]#23 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_24]#24 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_25]#25 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_26]#26 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_27]#27 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_28]#28 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_29]#29 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_30]#30 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_31]#31 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_32]#32 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_33]#33 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_34]#34 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_35]#35 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_36]#36 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_37]#37 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_38]#38 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_39]#39 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_40]#40 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_41]#41 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_42]#42 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_43]#43 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_44]#44 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_45]#45 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_46]#46 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_47]#47 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_48]#48 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_49]#49 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_50]#50 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_51]#51 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_52]#52 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_53]#53 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_54]#54 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_55]#55 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_56]#56 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_57]#57 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_58]#58 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_59]#59 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_60]#60 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_61]#61 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_62]#62 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_63]#63 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_64]#64 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_65]#65 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_66]#66 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_67]#67 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_68]#68 ()>: 1,\n",
       " <OptBooleanCircuit:INPUT[name=x0_69]#69 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_70]#70 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_71]#71 ()>: 0,\n",
       " <OptBooleanCircuit:INPUT[name=x0_72]#72 ()>: 0,\n",
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       " <OptBooleanCircuit:AND#853 (836,761)>: 0,\n",
       " <OptBooleanCircuit:XOR#854 (853,850)>: 0,\n",
       " <OptBooleanCircuit:XOR#855 (849,854)>: 0,\n",
       " <OptBooleanCircuit:XOR#856 (847,852)>: 1,\n",
       " <OptBooleanCircuit:XOR#857 (844,854)>: 1,\n",
       " <OptBooleanCircuit:XOR#858 (842,852)>: 0,\n",
       " <OptBooleanCircuit:AND#859 (838,763)>: 0,\n",
       " <OptBooleanCircuit:AND#860 (827,757)>: 1,\n",
       " <OptBooleanCircuit:XOR#861 (860,859)>: 1,\n",
       " <OptBooleanCircuit:AND#862 (829,756)>: 0,\n",
       " <OptBooleanCircuit:XOR#863 (862,859)>: 0,\n",
       " <OptBooleanCircuit:AND#864 (837,762)>: 0,\n",
       " <OptBooleanCircuit:AND#865 (832,755)>: 0,\n",
       " <OptBooleanCircuit:XOR#866 (865,864)>: 0,\n",
       " <OptBooleanCircuit:AND#867 (834,754)>: 1,\n",
       " <OptBooleanCircuit:XOR#868 (867,864)>: 1,\n",
       " <OptBooleanCircuit:AND#869 (835,758)>: 0,\n",
       " <OptBooleanCircuit:AND#870 (839,764)>: 1,\n",
       " <OptBooleanCircuit:XOR#871 (870,869)>: 1,\n",
       " <OptBooleanCircuit:AND#872 (836,759)>: 0,\n",
       " <OptBooleanCircuit:XOR#873 (872,869)>: 0,\n",
       " <OptBooleanCircuit:XOR#874 (868,873)>: 1,\n",
       " <OptBooleanCircuit:XOR#875 (866,871)>: 1,\n",
       " <OptBooleanCircuit:XOR#876 (863,873)>: 0,\n",
       " <OptBooleanCircuit:XOR#877 (861,871)>: 0,\n",
       " <OptBooleanCircuit:XOR#878 (858,877)>: 0,\n",
       " <OptBooleanCircuit:XOR#879 (857,855)>: 1,\n",
       " <OptBooleanCircuit:XOR#880 (857,874)>: 0,\n",
       " <OptBooleanCircuit:NOT#881 (877)>: 1,\n",
       " <OptBooleanCircuit:XOR#882 (856,881)>: 0,\n",
       " <OptBooleanCircuit:NOT#883 (878)>: 1,\n",
       " <OptBooleanCircuit:XOR#884 (856,883)>: 0,\n",
       " <OptBooleanCircuit:NOT#885 (875)>: 0,\n",
       " <OptBooleanCircuit:XOR#886 (856,885)>: 1,\n",
       " <OptBooleanCircuit:NOT#887 (886)>: 0,\n",
       " <OptBooleanCircuit:XOR#888 (855,887)>: 0,\n",
       " <OptBooleanCircuit:XOR#889 (876,882)>: 0,\n",
       " <OptBooleanCircuit:XOR#890 (875,879)>: 0,\n",
       " <OptBooleanCircuit:XOR#892 (879,884)>: 1,\n",
       " <OptBooleanCircuit:XOR#893 (880,889)>: 0,\n",
       " <OptBooleanCircuit:NOT#899 (888)>: 1,\n",
       " <OptBooleanCircuit:NOT#902 (890)>: 1,\n",
       " <OptBooleanCircuit:NOT#903 (893)>: 1,\n",
       " <OptBooleanCircuit:NOT#904 (892)>: 0,\n",
       " <OptBooleanCircuit:NOT#905 (884)>: 1,\n",
       " <OptBooleanCircuit:NOT#906 (880)>: 1,\n",
       " <OptBooleanCircuit:NOT#907 (882)>: 1,\n",
       " <OptBooleanCircuit:XOR#908 (8,143)>: 0,\n",
       " <OptBooleanCircuit:NOT#909 (11)>: 0,\n",
       " <OptBooleanCircuit:XOR#910 (8,909)>: 0,\n",
       " <OptBooleanCircuit:XOR#911 (142,15)>: 0,\n",
       " <OptBooleanCircuit:NOT#912 (911)>: 1,\n",
       " <OptBooleanCircuit:XOR#913 (143,912)>: 1,\n",
       " <OptBooleanCircuit:XOR#914 (11,913)>: 0,\n",
       " <OptBooleanCircuit:XOR#915 (12,15)>: 1,\n",
       " <OptBooleanCircuit:XOR#916 (13,908)>: 0,\n",
       " <OptBooleanCircuit:XOR#917 (144,911)>: 1,\n",
       " <OptBooleanCircuit:XOR#918 (12,917)>: 1,\n",
       " <OptBooleanCircuit:NOT#919 (917)>: 0,\n",
       " <OptBooleanCircuit:XOR#920 (916,919)>: 0,\n",
       " <OptBooleanCircuit:XOR#921 (144,913)>: 0,\n",
       " <OptBooleanCircuit:XOR#922 (908,912)>: 1,\n",
       " <OptBooleanCircuit:XOR#923 (144,910)>: 1,\n",
       " <OptBooleanCircuit:XOR#924 (923,915)>: 0,\n",
       " <OptBooleanCircuit:NOT#926 (918)>: 0,\n",
       " <OptBooleanCircuit:XOR#927 (13,926)>: 0,\n",
       " <OptBooleanCircuit:NOT#934 (927)>: 1,\n",
       " <OptBooleanCircuit:NOT#935 (913)>: 0,\n",
       " <OptBooleanCircuit:NOT#936 (924)>: 1,\n",
       " <OptBooleanCircuit:NOT#937 (922)>: 0,\n",
       " <OptBooleanCircuit:NOT#938 (921)>: 1,\n",
       " <OptBooleanCircuit:NOT#939 (914)>: 1,\n",
       " <OptBooleanCircuit:NOT#940 (920)>: 1,\n",
       " <OptBooleanCircuit:XOR#941 (939,937)>: 1,\n",
       " <OptBooleanCircuit:XOR#942 (940,938)>: 0,\n",
       " <OptBooleanCircuit:XOR#943 (15,934)>: 0,\n",
       " <OptBooleanCircuit:XOR#944 (936,935)>: 1,\n",
       " <OptBooleanCircuit:XOR#945 (938,937)>: 1,\n",
       " <OptBooleanCircuit:XOR#946 (940,939)>: 0,\n",
       " <OptBooleanCircuit:XOR#947 (942,941)>: 1,\n",
       " <OptBooleanCircuit:XOR#948 (935,934)>: 1,\n",
       " <OptBooleanCircuit:XOR#949 (936,15)>: 0,\n",
       " <OptBooleanCircuit:XOR#950 (944,943)>: 1,\n",
       " <OptBooleanCircuit:AND#951 (946,949)>: 0,\n",
       " <OptBooleanCircuit:AND#952 (941,943)>: 0,\n",
       " <OptBooleanCircuit:AND#953 (947,950)>: 1,\n",
       " <OptBooleanCircuit:AND#954 (922,927)>: 0,\n",
       " <OptBooleanCircuit:AND#955 (945,948)>: 1,\n",
       " <OptBooleanCircuit:XOR#956 (954,955)>: 1,\n",
       " <OptBooleanCircuit:AND#957 (942,944)>: 0,\n",
       " <OptBooleanCircuit:XOR#958 (956,957)>: 1,\n",
       " <OptBooleanCircuit:NOT#959 (952)>: 1,\n",
       " <OptBooleanCircuit:XOR#960 (958,959)>: 0,\n",
       " <OptBooleanCircuit:NOT#961 (945)>: 0,\n",
       " <OptBooleanCircuit:NOT#962 (948)>: 0,\n",
       " <OptBooleanCircuit:AND#963 (961,962)>: 0,\n",
       " <OptBooleanCircuit:AND#964 (938,935)>: 0,\n",
       " <OptBooleanCircuit:NOT#965 (964)>: 1,\n",
       " <OptBooleanCircuit:XOR#966 (963,965)>: 1,\n",
       " <OptBooleanCircuit:XOR#967 (966,952)>: 1,\n",
       " <OptBooleanCircuit:XOR#968 (967,953)>: 0,\n",
       " <OptBooleanCircuit:NOT#969 (942)>: 1,\n",
       " <OptBooleanCircuit:NOT#970 (944)>: 0,\n",
       " <OptBooleanCircuit:AND#971 (969,970)>: 0,\n",
       " <OptBooleanCircuit:AND#972 (939,15)>: 1,\n",
       " <OptBooleanCircuit:NOT#973 (972)>: 0,\n",
       " <OptBooleanCircuit:XOR#974 (971,973)>: 0,\n",
       " <OptBooleanCircuit:XOR#975 (974,951)>: 0,\n",
       " <OptBooleanCircuit:XOR#976 (975,952)>: 0,\n",
       " <OptBooleanCircuit:NOT#977 (941)>: 0,\n",
       " <OptBooleanCircuit:NOT#978 (943)>: 1,\n",
       " <OptBooleanCircuit:AND#979 (977,978)>: 0,\n",
       " <OptBooleanCircuit:AND#980 (940,936)>: 1,\n",
       " <OptBooleanCircuit:NOT#981 (980)>: 0,\n",
       " <OptBooleanCircuit:XOR#982 (979,981)>: 0,\n",
       " <OptBooleanCircuit:XOR#983 (982,951)>: 0,\n",
       " <OptBooleanCircuit:XOR#984 (983,953)>: 1,\n",
       " <OptBooleanCircuit:XOR#985 (984,976)>: 1,\n",
       " <OptBooleanCircuit:XOR#986 (968,960)>: 0,\n",
       " <OptBooleanCircuit:AND#987 (985,986)>: 0,\n",
       " <OptBooleanCircuit:AND#988 (984,968)>: 0,\n",
       " <OptBooleanCircuit:XOR#989 (988,987)>: 0,\n",
       " <OptBooleanCircuit:AND#990 (976,960)>: 0,\n",
       " <OptBooleanCircuit:XOR#991 (990,987)>: 0,\n",
       " <OptBooleanCircuit:XOR#992 (976,960)>: 0,\n",
       " <OptBooleanCircuit:XOR#993 (984,968)>: 1,\n",
       " <OptBooleanCircuit:XOR#994 (992,993)>: 1,\n",
       " <OptBooleanCircuit:XOR#995 (991,994)>: 1,\n",
       " <OptBooleanCircuit:XOR#996 (989,993)>: 1,\n",
       " <OptBooleanCircuit:XOR#1007 (995,996)>: 0,\n",
       " <OptBooleanCircuit:AND#1008 (1007,986)>: 0,\n",
       " <OptBooleanCircuit:AND#1009 (995,968)>: 0,\n",
       " <OptBooleanCircuit:XOR#1010 (1009,1008)>: 0,\n",
       " <OptBooleanCircuit:AND#1011 (996,960)>: 0,\n",
       " <OptBooleanCircuit:XOR#1012 (1011,1008)>: 0,\n",
       " <OptBooleanCircuit:AND#1013 (1007,985)>: 0,\n",
       " <OptBooleanCircuit:AND#1014 (995,984)>: 1,\n",
       " <OptBooleanCircuit:XOR#1015 (1014,1013)>: 1,\n",
       " <OptBooleanCircuit:AND#1016 (996,976)>: 0,\n",
       " <OptBooleanCircuit:XOR#1017 (1016,1013)>: 0,\n",
       " <OptBooleanCircuit:XOR#1018 (1012,1017)>: 0,\n",
       " <OptBooleanCircuit:XOR#1019 (1010,1015)>: 1,\n",
       " <OptBooleanCircuit:XOR#1020 (1015,1017)>: 1,\n",
       " <OptBooleanCircuit:XOR#1021 (1010,1012)>: 0,\n",
       " <OptBooleanCircuit:XOR#1022 (1019,1018)>: 1,\n",
       " <OptBooleanCircuit:AND#1023 (1021,949)>: 0,\n",
       " <OptBooleanCircuit:AND#1024 (1010,936)>: 0,\n",
       " <OptBooleanCircuit:XOR#1025 (1024,1023)>: 0,\n",
       " <OptBooleanCircuit:AND#1026 (1012,15)>: 0,\n",
       " <OptBooleanCircuit:XOR#1027 (1026,1023)>: 0,\n",
       " <OptBooleanCircuit:AND#1028 (1020,948)>: 1,\n",
       " <OptBooleanCircuit:AND#1029 (1015,935)>: 0,\n",
       " <OptBooleanCircuit:XOR#1030 (1029,1028)>: 1,\n",
       " <OptBooleanCircuit:AND#1031 (1017,934)>: 0,\n",
       " <OptBooleanCircuit:XOR#1032 (1031,1028)>: 1,\n",
       " <OptBooleanCircuit:AND#1033 (1018,943)>: 0,\n",
       " <OptBooleanCircuit:AND#1034 (1022,950)>: 1,\n",
       " <OptBooleanCircuit:XOR#1035 (1034,1033)>: 1,\n",
       " <OptBooleanCircuit:AND#1036 (1019,944)>: 1,\n",
       " <OptBooleanCircuit:XOR#1037 (1036,1033)>: 1,\n",
       " <OptBooleanCircuit:XOR#1038 (1032,1037)>: 0,\n",
       " <OptBooleanCircuit:XOR#1039 (1030,1035)>: 0,\n",
       " <OptBooleanCircuit:XOR#1040 (1027,1037)>: 1,\n",
       " <OptBooleanCircuit:XOR#1041 (1025,1035)>: 1,\n",
       " <OptBooleanCircuit:AND#1042 (1021,946)>: 0,\n",
       " <OptBooleanCircuit:AND#1043 (1010,940)>: 0,\n",
       " <OptBooleanCircuit:XOR#1044 (1043,1042)>: 0,\n",
       " <OptBooleanCircuit:AND#1045 (1012,939)>: 0,\n",
       " <OptBooleanCircuit:XOR#1046 (1045,1042)>: 0,\n",
       " <OptBooleanCircuit:AND#1047 (1020,945)>: 1,\n",
       " <OptBooleanCircuit:AND#1048 (1015,938)>: 1,\n",
       " <OptBooleanCircuit:XOR#1049 (1048,1047)>: 0,\n",
       " <OptBooleanCircuit:AND#1050 (1017,937)>: 0,\n",
       " <OptBooleanCircuit:XOR#1051 (1050,1047)>: 1,\n",
       " <OptBooleanCircuit:AND#1052 (1018,941)>: 0,\n",
       " <OptBooleanCircuit:AND#1053 (1022,947)>: 1,\n",
       " <OptBooleanCircuit:XOR#1054 (1053,1052)>: 1,\n",
       " <OptBooleanCircuit:AND#1055 (1019,942)>: 0,\n",
       " <OptBooleanCircuit:XOR#1056 (1055,1052)>: 0,\n",
       " <OptBooleanCircuit:XOR#1057 (1051,1056)>: 1,\n",
       " <OptBooleanCircuit:XOR#1058 (1049,1054)>: 1,\n",
       " <OptBooleanCircuit:XOR#1059 (1046,1056)>: 0,\n",
       " <OptBooleanCircuit:XOR#1060 (1044,1054)>: 1,\n",
       " <OptBooleanCircuit:XOR#1061 (1041,1060)>: 0,\n",
       " <OptBooleanCircuit:XOR#1062 (1040,1038)>: 1,\n",
       " <OptBooleanCircuit:XOR#1063 (1040,1057)>: 0,\n",
       " <OptBooleanCircuit:NOT#1064 (1060)>: 0,\n",
       " <OptBooleanCircuit:XOR#1065 (1039,1064)>: 0,\n",
       " <OptBooleanCircuit:NOT#1066 (1061)>: 1,\n",
       " <OptBooleanCircuit:XOR#1067 (1039,1066)>: 1,\n",
       " <OptBooleanCircuit:NOT#1068 (1058)>: 0,\n",
       " <OptBooleanCircuit:XOR#1069 (1039,1068)>: 0,\n",
       " <OptBooleanCircuit:NOT#1070 (1069)>: 1,\n",
       " <OptBooleanCircuit:XOR#1071 (1038,1070)>: 1,\n",
       " <OptBooleanCircuit:XOR#1072 (1059,1065)>: 0,\n",
       " <OptBooleanCircuit:XOR#1073 (1058,1062)>: 0,\n",
       " <OptBooleanCircuit:XOR#1075 (1062,1067)>: 0,\n",
       " <OptBooleanCircuit:XOR#1076 (1063,1072)>: 0,\n",
       " <OptBooleanCircuit:NOT#1082 (1071)>: 0,\n",
       " <OptBooleanCircuit:NOT#1085 (1073)>: 1,\n",
       " <OptBooleanCircuit:NOT#1086 (1076)>: 1,\n",
       " <OptBooleanCircuit:NOT#1087 (1075)>: 1,\n",
       " <OptBooleanCircuit:NOT#1088 (1067)>: 0,\n",
       " <OptBooleanCircuit:NOT#1089 (1063)>: 1,\n",
       " <OptBooleanCircuit:NOT#1090 (1065)>: 1,\n",
       " <OptBooleanCircuit:XOR#1091 (40,146)>: 0,\n",
       " <OptBooleanCircuit:NOT#1092 (43)>: 0,\n",
       " <OptBooleanCircuit:XOR#1093 (40,1092)>: 0,\n",
       " <OptBooleanCircuit:XOR#1094 (145,47)>: 0,\n",
       " <OptBooleanCircuit:NOT#1095 (1094)>: 1,\n",
       " <OptBooleanCircuit:XOR#1096 (146,1095)>: 1,\n",
       " <OptBooleanCircuit:XOR#1097 (43,1096)>: 0,\n",
       " <OptBooleanCircuit:XOR#1098 (44,47)>: 1,\n",
       " <OptBooleanCircuit:XOR#1099 (147,1091)>: 0,\n",
       " <OptBooleanCircuit:XOR#1100 (148,1094)>: 1,\n",
       " <OptBooleanCircuit:XOR#1101 (44,1100)>: 1,\n",
       " <OptBooleanCircuit:NOT#1102 (1100)>: 0,\n",
       " <OptBooleanCircuit:XOR#1103 (1099,1102)>: 0,\n",
       " <OptBooleanCircuit:XOR#1104 (148,1096)>: 0,\n",
       " <OptBooleanCircuit:XOR#1105 (1091,1095)>: 1,\n",
       " <OptBooleanCircuit:XOR#1106 (148,1093)>: 1,\n",
       " <OptBooleanCircuit:XOR#1107 (1106,1098)>: 0,\n",
       " <OptBooleanCircuit:NOT#1109 (1101)>: 0,\n",
       " <OptBooleanCircuit:XOR#1110 (147,1109)>: 0,\n",
       " <OptBooleanCircuit:NOT#1117 (1110)>: 1,\n",
       " <OptBooleanCircuit:NOT#1118 (1096)>: 0,\n",
       " <OptBooleanCircuit:NOT#1119 (1107)>: 1,\n",
       " <OptBooleanCircuit:NOT#1120 (1105)>: 0,\n",
       " <OptBooleanCircuit:NOT#1121 (1104)>: 1,\n",
       " <OptBooleanCircuit:NOT#1122 (1097)>: 1,\n",
       " <OptBooleanCircuit:NOT#1123 (1103)>: 1,\n",
       " <OptBooleanCircuit:XOR#1124 (1122,1120)>: 1,\n",
       " <OptBooleanCircuit:XOR#1125 (1123,1121)>: 0,\n",
       " <OptBooleanCircuit:XOR#1126 (47,1117)>: 0,\n",
       " <OptBooleanCircuit:XOR#1127 (1119,1118)>: 1,\n",
       " <OptBooleanCircuit:XOR#1128 (1121,1120)>: 1,\n",
       " <OptBooleanCircuit:XOR#1129 (1123,1122)>: 0,\n",
       " ...}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C.trace(Bin(plaintext).tuple)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aefb093-ecb5-4bf4-b44c-c07b83a0a437",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "To do fast recording, we serialize the circuit into an internal binary format, into a file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6c9de7b9-7554-4cc6-a0f2-27541cfe1e52",
   "metadata": {},
   "outputs": [],
   "source": [
    "from wboxkit.serialize import RawSerializer\n",
    "\n",
    "RawSerializer().serialize_to_file(C, \"circuits/aes10_clear.bin\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98835c02-ab7f-468a-a534-dd4c0c99944c",
   "metadata": {},
   "source": [
    "Now, we can use a fast C-based circuit tracer provided by `wboxkit` (need to compile the library first):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3124d091-f95f-418d-a4f9-0018a9f50890",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'54b03463c5b5a1d45efb4e91637ba51f'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from wboxkit.fastcircuit import FastCircuit\n",
    "\n",
    "plaintext = b\"0123456789abcdef\"\n",
    "\n",
    "FC = FastCircuit(\"circuits/aes10_clear.bin\")\n",
    "ciphertext = FC.compute_one(plaintext, trace_filename=\"traces/test\")\n",
    "ciphertext.hex()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d77f23a3-bd2e-4d2d-b3b2-485009fa7590",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": []
   },
   "source": [
    "The key feature is bit-sliced **batch** tracing: using 64-bit CPU registers we can trace 64 executions (inputs) of a Boolean circuit at once. This makes massive tracing much faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8fb0de86-1d93-4099-96af-476cd314d205",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[b'\\xa4\\x02\\xbcLb\\x16\\xc9\\xcf\\x07!\\xe2+\\xd1\\xfb\\x177',\n",
       " b'>\\xdbt\\xc3\\x8b\\x93\\xf4\\xbf\\xb2\\x1dZ1\\xb7S\\x04\\xc1',\n",
       " b'\\xa4\\x02\\xbcLb\\x16\\xc9\\xcf\\x07!\\xe2+\\xd1\\xfb\\x177',\n",
       " b'>\\xdbt\\xc3\\x8b\\x93\\xf4\\xbf\\xb2\\x1dZ1\\xb7S\\x04\\xc1',\n",
       " b'\\xa4\\x02\\xbcLb\\x16\\xc9\\xcf\\x07!\\xe2+\\xd1\\xfb\\x177',\n",
       " b'>\\xdbt\\xc3\\x8b\\x93\\xf4\\xbf\\xb2\\x1dZ1\\xb7S\\x04\\xc1',\n",
       " b'\\xa4\\x02\\xbcLb\\x16\\xc9\\xcf\\x07!\\xe2+\\xd1\\xfb\\x177',\n",
       " b'>\\xdbt\\xc3\\x8b\\x93\\xf4\\xbf\\xb2\\x1dZ1\\xb7S\\x04\\xc1']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ciphertexts = FC.compute_batch(\n",
    "    [b\"my_plaintext_abc\", b\"anotherPlaintext\"] * 4,\n",
    "    trace_filename=\"traces/test2\"\n",
    ")\n",
    "ciphertexts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dd499b6f-e7b8-4a7b-a047-0811b51bfce9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "000000000055ff00ff0000550000aa0000aaff00ff00aaff00aa00000000ffaa\n"
     ]
    }
   ],
   "source": [
    "with open(\"traces/test2\", \"rb\") as f:\n",
    "    print(f.read(32).hex())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92017274-9b01-485c-bb2b-2a4b918a09e7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## Command-line tracing tool"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f45b3285-1f91-4421-9dd1-784ee7a3399f",
   "metadata": {},
   "source": [
    "Since we serialized the circuit to a file, we can use the command-line tracing tool from `wboxkit`. It also splits the batches into single-trace files and manages random plaintexts/ciphertexts:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9cb0f8a-04a3-4425-9ef1-0a350f59cf34",
   "metadata": {},
   "source": [
    "```sh\n",
    "> time pypy3 tools/trace.py circuits/aes10_clear.bin 256 traces/\n",
    "Tracing circuits/aes10_clear.bin on 256 traces\n",
    "Saving to traces//aes10_clear/\n",
    "splitting 0\n",
    "...\n",
    "splitting 3\n",
    "> ls -al traces/aes10_clear/ | tail -20\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0249.ct\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0249.pt\n",
    "-rw-rw-r-- 1 user user  3894 Sep 14 13:21 0250.bin\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0250.ct\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0250.pt\n",
    "-rw-rw-r-- 1 user user  3894 Sep 14 13:21 0251.bin\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0251.ct\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0251.pt\n",
    "-rw-rw-r-- 1 user user  3894 Sep 14 13:21 0252.bin\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0252.ct\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0252.pt\n",
    "-rw-rw-r-- 1 user user  3894 Sep 14 13:21 0253.bin\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0253.ct\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0253.pt\n",
    "-rw-rw-r-- 1 user user  3894 Sep 14 13:21 0254.bin\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0254.ct\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0254.pt\n",
    "-rw-rw-r-- 1 user user  3894 Sep 14 13:21 0255.bin\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0255.ct\n",
    "-rw-rw-r-- 1 user user    16 Sep 14 13:21 0255.pt\n",
    "```"
   ]
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   "source": [
    "## Exercise: Trace prepared protected circuits"
   ]
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    "Create 256 traces for each of the following circuits (serialized in Tutorial 2):\n",
    "\n",
    "- `circuits/aes2_clear.bin`\n",
    "- `circuits/aes2_isw2.bin`\n",
    "- `circuits/aes2_isw3.bin`\n",
    "- `circuits/aes2_minq.bin`"
   ]
  }
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