conviction/hatch_sim.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### System timeline\n",
    " - initial raise\n",
    " - hatch sale\n",
    " - reference implementation launch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Augumented bonding curve Mathematics\n",
    "\n",
    "### Hatch Sale Equations\n",
    "\n",
    "- Initial Raise $d_0$ Dai\n",
    "- Initial Reserve is $R_0 = (1-\\theta) d_0$\n",
    "- Hatch sale Price $p_0$ (dai per token) determines the initial supply: $S_0 = d_0/p_0$\n",
    "- Power Function Invariant shape: $V(R, S) = \\frac{S^\\kappa}{R}$\n",
    "- Price function (DAI per Token): $P(R) = \\frac{\\kappa R^{(\\kappa-1)/ \\kappa}}{V_0^{1 / \\kappa}}$\n",
    "- Supply function (tokens): $S(R) = \\sqrt[\\kappa]{V_0 R}$\n",
    "- Reserve function (xDAI): $R(S) = \\frac{S^{\\kappa}}{V_0} $\n",
    "- The invariant coef: $V_0 = V(R_0, S_0) = \\frac{S_0^\\kappa}{R_0} = \\left(\\frac{1}{p_0(1-\\theta)}\\right)^\\kappa R_0^{\\kappa-1}$\n",
    "- The post hatch price: $p_1=P(R_0) = \\frac{\\kappa R_0^{(\\kappa-1)/ \\kappa}}{V_0^{1 / \\kappa}} = \\kappa R_0^{(\\kappa-1)/ \\kappa} \\cdot(1-\\theta)p_0\\cdot R_0^{-(\\kappa-1)/\\kappa} = \\kappa(1-\\theta) p_0$\n",
    "- The Return factor: $\\frac{p_1}{p_0} = {\\kappa}(1-\\theta)$\n",
    "\n",
    "### Invariant Preserving Deposit-to-Mint\n",
    " - Deposit $\\Delta R$ xdai \n",
    " - Conservation equation: $V(R+ \\Delta R, S+\\Delta S) = \\frac{(S+\\Delta S)^\\kappa}{R+\\Delta R} =V_0$\n",
    " - Derived Mint equation: $\\Delta S = mint\\big(\\Delta R ; (R,S)\\big)= \\sqrt[\\kappa]{V_0(R+\\Delta R)}-S$\n",
    " - Realized Price is: $\\bar{P}(\\Delta R) =\\frac{\\Delta R}{\\Delta S} = \\frac{\\Delta R}{\\sqrt[\\kappa]{V_0(R+\\Delta R)}-\\sqrt[\\kappa]{V_0(R)}} \\rightarrow \\big(\\frac{\\partial S(R)}{\\partial R} \\big)^{-1}$ as $\\Delta R \\rightarrow 0$\n",
    " - The limiting price is the spot price: $\\lim_{\\Delta R \\rightarrow 0} \\bar{P}(\\Delta R)=\\big(\\frac{\\partial S(R)}{\\partial R}\\big)^{-1}= \\big(\\frac{V_0^{1/\\kappa} \\cdot  R^{1/\\kappa-1}}{\\kappa}\\big)^{-1}= \\frac{\\kappa R^{1-1/\\kappa}}{V_0^{1/\\kappa}} = \\frac{\\kappa R^{(\\kappa-1)/\\kappa}}{V_0^{1/\\kappa}} =P(R)$\n",
    " \n",
    "### Invariant Preserving Burn-to-Withdraw\n",
    " - Burn $\\Delta S$ tokens\n",
    " - Conservation equation: $V(R- \\Delta R, S-\\Delta S) = \\frac{(S-\\Delta S)^\\kappa}{R-\\Delta R} =V_0$\n",
    " - Derived Withdraw equation: $\\Delta R = withdraw\\big(\\Delta S ; (R,S)\\big)= R-\\frac{(S-\\Delta S)^\\kappa}{V_0}$\n",
    " - Realized Price is: $\\bar{P}(\\Delta S) =\\frac{\\Delta R}{\\Delta S} = \\frac{\\frac{S^{\\kappa}}{V_0}-\\frac{(S-\\Delta S)^\\kappa}{V_0}}{\\Delta S} \\rightarrow \\frac{\\partial R(S)}{\\partial S} $ as $\\Delta S \\rightarrow 0$\n",
    " - The limiting price is the spot price: $\\lim_{\\Delta S \\rightarrow 0} \\bar{P}(\\Delta S)=\\frac{\\partial R(S)}{\\partial S}=\\frac{\\kappa S^{\\kappa-1}}{V_0} = \\frac{\\kappa \\cdot (\\sqrt[\\kappa]{V_0 R})^{\\kappa-1}}{V_0}= \\frac{\\kappa R^{(\\kappa-1)/\\kappa}}{V_0^{1/\\kappa}}=P(R)$\n",
    " - Given friction coef $\\phi$ \n",
    "     - sent to burning agent address: $\\Delta R_{agent} = (1-\\phi) \\Delta R$\n",
    "     - sent to the funding pool address: $\\Delta R_{pool} = \\phi \\Delta R$\n",
    "     - due to the friction the true realized price for the agent is $(1-\\phi)\\cdot \\bar{P}(\\Delta S)$\n",
    "     - due to the friction the true return factor post withdraw is: ${\\kappa}(1-\\theta)(1-\\phi)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "#integer_units = 10**12 #account for decimal places to a token\n",
    "#scale_units = 10**6 #millions of tokens, million of DAI\n",
    "#mu = integer_units*scale_units\n",
    "\n",
    "#value function for a given state (R,S)\n",
    "def invariant(R,S,kappa):\n",
    "    return (S**kappa)/R\n",
    "\n",
    "#given a value function (parameterized by kappa)\n",
    "#and an invariant coeficient V0\n",
    "#return Supply S as a function of reserve R\n",
    "def supply(R, kappa, V0):\n",
    "    return (V0*R)**(1/kappa)\n",
    "\n",
    "#given a value function (parameterized by kappa)\n",
    "#and an invariant coeficient V0\n",
    "#return a spot price P as a function of reserve R\n",
    "def spot_price(R, kappa, V0):\n",
    "    return kappa*R**((kappa-1)/kappa)/V0**(1/kappa)\n",
    "\n",
    "#for a given state (R,S)\n",
    "#given a value function (parameterized by kappa)\n",
    "#and an invariant coeficient V0\n",
    "#deposit deltaR to Mint deltaS\n",
    "#with realized price deltaR/deltaS\n",
    "def mint(deltaR, R,S, kappa, V0):\n",
    "    deltaS = (V0*(R+deltaR))**(1/kappa)-S\n",
    "    realized_price = deltaR/deltaS\n",
    "    return deltaS, realized_price\n",
    "\n",
    "#for a given state (R,S)\n",
    "#given a value function (parameterized by kappa)\n",
    "#and an invariant coeficient V0\n",
    "#burn deltaS to Withdraw deltaR\n",
    "#with realized price deltaR/deltaS\n",
    "def withdraw(deltaS, R,S, kappa, V0):\n",
    "    deltaR = R-((S-deltaS)**kappa)/V0\n",
    "    realized_price = deltaR/deltaS\n",
    "    return deltaR, realized_price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a1d032438>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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1vPCqgDdBg6E4XGYURORjIBZoICKHgaewJkNHVd/CmgP3Wqx5j9OAm12lxU7jCDhsnOkZIDM7lwOnUtl/Ko1Dp9M4eDqNw2fSOHQ6nUNn0kgr8Fbv7SlcUduXRgE16NC4Nn3bNqRxHV+uqF2DwFo1CPT3oZ6/D/X9fKjp4+mmszIYLh1Xjj4aW8JxBe5yVf6FEhQJ2z6HtNPgV79Csza4h5Tz2ew5kcKeEykknLT9nkjhwOk0chx6Q/18PGle349m9f3o1SaQZvWs9SZ1fWkc4Es9Px/T5GKoFlQ519mXRJCts/n4b9Cqn3u1GMqdxJTzbDt6jm1Hk9h29Bzbj55j/6lU+5A+Lw+hRQN/2jWqzbXhQbS+wp+WDWrRrF5N6vv72Dv4DIbqTPUyCo0jrd9jm41RKIG3337b3RKK5Xx2DluPnGPjgTNsOHCGTYfO8Me58/bjwfVqEtokgBuim9K+cW3aXFGL5vX9KmT0hsFQlaleRsE/EAKCrRFIhmJp3769uyXkI/V8Nmv3nWbN3lOsP3CG3w4nkZljDctsXt+Pnq0CCWtah05NAggNqkMdP283KzYYqibVyyiA1YR0zBiFkvjqq68AGDZsmFvyz87JZfPhJFbtSWTl74lsPHiG7FzFx9OD8OA6TOzdgpjm9YgJqcsVtX3dotFguBypfkahcYTl7iIzFXz83a2m0vLqq68CFWsUkjOyWL7rJN9t/4Nlu06QnJGNCIQ1qcNf+7SiT9sGdA6ph6+3Gd1jMLiK6mcUgiJAc+GPbdCsm7vVVFoWLFhQIfmcTD7Pt9uOs3TbcdbsPUVWjlLf34fBoY2JbX8FPVsHUt/fp0K0GAyGamkUHDqbjVEokgYNGrgs7ZTz2Szddpwv4o+yak8iOblKi0A/bu7dkgGdGhHTvB6eZvinweAWqp9RCGgKNeubzuYSmDVrFgATJ04sl/RUlV8STjFv3SGWbj9ORlYuTevW5La+rbg+qintGtUyQ0INhkpA9TMKIrbOZuPuojjKyyicTs3ksw2H+e/ag+xLTKVOTW9GxgQzPLopnZvXMx+EGQyVjOpnFACaRMPqf0FWBnibkSuuYMexc7y7Yi+LNx8jMyeXLiH1uKd/G64NDzIdxQZDJaaaGoUYyM2CP7ZCcBd3q7lsUFVW7TnF2z8nsOL3RPx8PBnTrRnjuofQvnFtd8szGAxOUD2NQtPO1u+RjcYolAOqyvc7TvD697vZdvQcDWvXYMqg9ozvHmI+IjMYqhjV0ygENIFajeDoRncrqdKoKj/tPslr3+1m8+EkWgT68feR4QyPbkoNL9NEZDBURaqnURCxmpCObHC3kirLhgOnefGbnaw/cIamdWvy8sgIRsQ0NfMBGAxVnOppFMBqQtr9LWScA98Ad6upMhw9m85L/9vJos1HuaJ2DZ4dHsaNXZrh42WMgcFwOVCNjUI0oHAsHlr2dbeaSk96Zg5v/5zAWz8loAr39m/D7bGt8fOpvreQwXA5Un3/0U1irN8jG4xRKMAXm46w6eBZzmfn0PulH7k+qglf/3aMA6fSGBIRxLRrOhBcz8/dMg0GgwuovnV+v/pQr6U1Aslg54tNR5j2+W8EDH2YhsMf5cjZdN5cnkDa+Rz+O6k7b9wUQ3A9P1577TVCQ0MJCwtj7NixZGRkANCnTx+ioqKIioqiSZMmDB8+vNB8PD097eGuu+46+/5x48YRERHBo48+at/37LPP8uWXX5b6XMaOHUtERASvvfZa/nP84gu2b99eYvzY2FjWr68607e+/vrrpKWllSrO8uXLGTp0aKniTJkyhdDQUKZMmeJ0WRbH2rVr7fdCZGQkCxcuvKT0SssLL7xgX9+/fz9hYWEVmn9lo/oaBYCmMXB0k7tVVCpmLNlFelYOnn518PS70Nfi7Sn0am35Qzpy5AgzZ85k/fr1bN26lZycHObNmwfAihUriI+PJz4+np49ezJixIhC86lZs6Y93KJFiwDYsmWL/XfFihUkJSVx7Ngx1q5dy/XXX1+q8zh+/DirV69my5Yt3H///fmOlceDrDJSFqNQFt5++202btzIjBkzylSW2dnZ+bbDwsJYv3498fHxfPvtt9x2220XhXEljkbBUN2NQpMYSDoEKSfcraTScORsun09Jz3Zvn4sKSNfuOzsbNLT08nOziYtLY0mTZrkO56cnMyPP/5YZE2hMLy9vUlPTyc3N5fMzEw8PT158sknmT59epFxMjIyuPnmmwkPDyc6Opply5YBMHDgQE6cOEFUVBQrVqywh1+9ejWLFi1iypQpREVFkZCQQHx8PD169CAiIoIbbriBM2fO5MsjNzeXCRMm8PjjjwOwdOlSevbsSUxMDKNHjyYlJQWAFi1a8NRTTxETE0N4eDg7d+4E4KeffrK/CUdHR5OcnJwv/alTp/Lmm2/at59++mm76/IZM2bQtWtXIiIieOqppwBITU1lyJAhREZGEhYWxieffMLMmTM5evQocXFxxMXFFavz22+/pUOHDlx55ZV8/vnnhZbr/v376dOnDzExMcTExLB69WoArrvuOlJTU+nevTvPPPPMRWWZkJDA4MGD6dy5M3369LGXwcSJE3nggQeIi4tj6tSp+fLy8/PDy8vLfj2L8oFVq1Ytpk6dSufOnbn66qtZu3YtsbGxtGrVyv5iUdT9MGvWLEaMGMHgwYNp27YtDz/8MACPPPII6enpREVFMW7cOABycnKYNGkSoaGhDBw4kPR06z8xc+ZMOnXqREREBGPGjClU42WBqlappXPnzlpu7F+t+lSA6s7/lV+aVZjfDp/V1tO+1pCpi7XBsClaIyRSQ6Yu1pCpi7XXiz/kC/v666+rv7+/NmjQQG+66aaL0po9e7aOHDmyyLw8PT21c+fO2r17d124cKF9/3333aeRkZH6yiuv6KZNm/TWW28tVvMrr7yiEydOVFXVHTt2aLNmzTQ9PV337dunoaGhhcaZMGGCzp8/374dHh6uy5cvV1XVJ554Qu+77z5VVe3Xr5/+8ssvOmbMGH3uuedUVfXkyZPap08fTUlJUVXVl156SZ955hlVVQ0JCdGZM2eqquobb7xh1z506FBduXKlqqomJydrVlZWPj0bN27Uvn372rc7duyoBw4c0CVLluikSZM0NzdXc3JydMiQIfrTTz/pggUL9K9//as9/NmzZ+35nzx5slid6enpGhwcrLt379bc3FwdPXq0Dhky5KIySk1N1fT0dFVV3b17tzr+7/z9/Yssy/79++vu3btVVXXNmjUaFxdnDzdkyBDNzs4u7JLomjVrtFOnTurv76+ff/55oWEA/eabb1RVdfjw4TpgwADNzMzU+Ph4jYyMVNWi74cPP/xQW7ZsqWfPntX09HRt3ry5Hjx48KLz2bdvn3p6euqmTZtUVXX06NE6Z84cVVUNCgrSjIwMVVU9c+ZMoRorM8B6deIZW307msFyjCce1kds7Qe7W43bUFX+u/Ygzyzajn8NL9Izc6BTP/w7WfNY1/T2ZMqgC9Nznjlzhi+//JJ9+/ZRt25dRo8ezdy5cxk/frw9zMcff8xf//rXIvM8ePAgTZo0Ye/evfTv35/w8HBat27N66+/bg8zbNgw3n77bZ5//nk2b97MgAEDmDRpUr50Vq5cyT333ANAhw4dCAkJYffu3QQEODfMOCkpibNnz9Kvn3WuEyZMYPTo0fbjt912G3/605947LHHAFizZg3bt2+nd+/eAGRmZtKzZ097+Lzmss6dO9vfwnv37s0DDzzAuHHjGDFiBMHBwfk0REdHc+LECY4ePcrJkyepV68ezZs3Z+bMmSxdupTo6GgAUlJS+P333+nTpw8PPfQQU6dOZejQofTp0+ei8ypK586dO2nZsiVt27YFYPz48bzzzjsXxc/KyuLuu+8mPj4eT09Pdu/eXWJZpqSksHr16nzld/78hXmzR48ejadn4R81du/enW3btrFjxw4mTJjANddcg69vfr9kPj4+DB5s/U/Dw8OpUaMG3t7ehIeHs3//fqDo+wHgqquuok6dOgB06tSJAwcO0KxZs4u0tGzZkqioKMC6jnlpR0REMG7cOIYPH16qGnBVo3o3H/n4Q8OO1fojtoysHB5esIXHFm6lR+tAlj0Uy8ujImhatyYCNK1bkxdHWF8p5/H999/TsmVLGjZsiLe3NyNGjLA3LwCcOnWKtWvXMmTIkCLzzWtuatWqFbGxsWzalL9v58svv6RLly6kpqaydetWPv30U+bMmXNRm7n1AuQ6evXqxbJly+wd6arKgAED7P0h27dv5/3337eHr1GjBmB1pOe1iz/yyCO89957pKen06NHD3uTiiOjRo1iwYIFfPLJJ/amCVVl2rRp9rz27NnDrbfeSrt27diwYQPh4eFMmzat0Oa14nQ646L8tddeo1GjRmzevJn169eTmZlZYpzc3Fzq1q1rzzM+Pp4dO3bYj/v7lzzTYceOHfH392fr1q0XHfP29rZr9/DwsJe1h4eHvayLux/ywkP+6+NsuK+//pq77rqLDRs20Llz5wrt96hIqrdRAKuz+cgGcPHDpTJy+Ewao9/6hfkbDnNv/zZ8OLEr9f19GB7dlBu8NnJXgx2seqR/PoMA0Lx5c9asWUNaWhqqyg8//EDHjh3tx+fPn8/QoUMvetPL48yZM/Y3yMTERFatWkWnTp3sx7Oysvi///s/pkyZQlpamv1BkNfX4Ejfvn356KOPANi9ezcHDx6kffv2FEft2rXt7fp16tShXr169n6HOXPm2GsNALfeeivXXnsto0ePJjs7mx49erBq1Sr27NkDQFpaWolv0QkJCYSHhzN16lS6dOlSqFEYM2YM8+bNY8GCBYwaNQqAQYMG8cEHH9j7Ao4cOWKvUfj5+TF+/HgeeughNm7ceNF5FaWzQ4cO7Nu3j4SEBMCq0RVGUlISQUFBeHh4MGfOHHJyckosy4CAAFq2bMn8+fMB6wG9eXPJLur37dtnf8AeOHCAXbt20aJFixLjFUZZ7gdvb2+ysrKKDZObm8uhQ4eIi4vj5Zdf5uzZs/brcrlhjEKz7pB+Bk7tcbeSCiX+0FmGv7GK/adSee8vXXhgYPt8s50tXryYxYsXFxq3e/fujBo1yt6hmpuby+TJk+3H582bx9ixY/PFWb9+vb05aceOHXTp0oXIyEji4uJ45JFH8hmFN954gwkTJuDn50dERASqSnh4OL1796Zu3br50r3zzjvJyckhPDycG2+8kVmzZuV70yuMMWPGMGPGDKKjo0lISGD27NlMmTKFiIgI4uPjefLJJ/OFf+CBB4iJieHPf/4zgYGBzJo1yz7ctag3f0def/11wsLCiIyMpGbNmlxzzTUXhQkNDSU5OZmmTZsSFBQEWJ3lN910Ez179iQ8PJxRo0aRnJzMb7/9Rrdu3YiKiuL555+3d4BPnjyZa665hri4OBo2bFioTl9fX9555x2GDBnClVdeSUhISKGa77zzTmbPnk2PHj3YvXt3kW/5Bcvyo48+4v333ycyMpLQ0FCnhhKvXLmSyMhIoqKiuOGGG3jzzTfLPPNfWe6HyZMn25uGiiInJ4fx48fbO7Dvv//+i+7FywVxdfW7vOnSpYuW69jxk7vhja5w/RsQPb7k8JcBS7Yd5755m2hYuwYfTuxGmytqXRQmNjYWsMaxGwyGqo+IbFDVEt1Cm5pCYBuoWQ8O/epuJRXC+yv3cfvcDXRoHMDCO3sXahAMBkP1pXqPPgLw8IDgbnBorbuVuBRVZcaSXby5PIHBoY157cYoavoY99YGgyE/pqYA0KwbnNxp9S1chuTmKs98tZ03lydwU/fmvDkuxhgEg8FQKMYogNXZDHC46vi5cZacXGXa578xa/V+br2yJc8PD8PDo+QhiQaDoXpijAJYw1LF87LrV8jJVR6av5lP1h/i3v5teHxIR6fGqBsMhuqLS42CiAwWkV0iskdEHinkeHMRWSYim0Rki4hc60o9ReLjD43DLyujoKo8tvA3Fm46wpRB7XlgYHtjEAwGQ4m4zCiIiCfwBnAN0AkYKyKdCgR7HPhUVaOBMcCbuItm3eHwBsip+l8pqlp9CPPWHeKe/m24K66NuyUZDIYqgitrCt2APaq6V1UzgXlAQf/WKbAJAAAgAElEQVTHCuQ5qakDHHWhnuJp1g2yUuHENrdJKC9eXbqbWav3c0vvljwwoF2Z0li+fLn5RsFgqIa40ig0BQ45bB+27XPkaWC8iBwGvgHuKSwhEZksIutFZP3JkyddofVCZ3MVH5o6e/V+/rVsD2O6NuOJoaYPwWAwlA5XGoXCnkYFP58eC8xS1WDgWmCOiFykSVXfUdUuqtqlYcOGLpAK1AmG2k2qdL/Cd9v/4JmvtnF1x0Y8f0P4JRmEV155hVdeeaUc1RkMhqqAKz9eOww4+qUN5uLmoVuBwQCq+ouI+AINgIqf9UbEakI6WDWNwuZDZ7nn442EN63DzLFR+fwYlYVffvmlnJQZDIaqhCuNwjqgrYi0BI5gdSTfVCDMQeAqYJaIdAR8ARe1DzlB856w/QtIOmzVHKoIh06ncevsdTSsXYP3JnTFz+fSL+tnn31WDsoMBkNVw2XNR6qaDdwNLAF2YI0y2iYi00Ukb6b2B4FJIrIZ+BiYqO700NfCmpCE/avcJqG0pGfmMHnOBjKzc/lwYjca1i7eI6TBYDAUh0t9H6nqN1gdyI77nnRY3w70dqWGUnFFKPjWhQMrIfJGd6spEVXlkc+3sPP4OT6Y2LVcndtNmzYNgBdffLHc0jQYDJUf4xDPEQ8PCOlVZWoK76/cx5fxR5kyqD1x7a8o17RNn4LBUD0xbi4KEtILTidA8nF3KymW1QmJvPi/nQwKbcSdsa3dLcdgMFwmGKNQkJC8foWV7tVRDCeTz3Pvx/G0CPTj1T9FmW8RDAZDuWGMQkEaR4BPbThQOZuQcm1O7pIzsnhjXAy1apgWQIPBUH4Yo1AQTy9o3qPS9it8sGofP+0+yeNDO9GhcUDJEQwGg6EUGKNQGC16Q+IuSHHfJxOF8dvhJP7+7U4GdmrE+O7N3S3HYDBchhijUBghV1q/lagJKS0zm3vnbaJBrRq8PCrC9CMYDAaXYIxCYTSJAm//SmUUXv52F/sSU3n1T5HU9fNxtxyDwXCZYnopC8PT2/KDVElGIP269xSzVu9nQs8QerVuUCF5BgYGVkg+BoOhcmGMQlG0uBJ+fNbqV6jlIs+sTpCWmc2UBVtoXt+Pqdd0qLB8je8jg6F6YpqPiqJVnPW77ye3ynj5210cPJ3Gy6MiysXRncFgMBSHMQpF0SQKfOvA3mVuk7Dx4Blm/7Kfib1a0KNVxTbnTJs2ze7/yGAwVB/Mq2dReHhCy76QsBxUrfkWKpDsnFweW7iVRrV9eWhQ+wrNG+DUqVMVnqfBYHA/xigUR6s42PEVnEqABm0qNOvZvxxgx7Fz/NtNXy2/8847FZ6nwWBwP6b5qDhaxVq/FdyEdCwpnX8s3UVs+4YMDmtcoXkbDIbqjTEKxVG/FdRtDnuXV2i2zy7eTnauMv26MLd9pDZ58mQmT57slrwNBoP7MM1HxSFi1Ra2fQk52ZZfJBezek8i3/x2nAcHtKN5oJ/L8yuK3bt3uy1vg8HgPop8yolITHERVXVj+cuphLSKg43/gaOboFlXl2aVk6tMX7ydpnVrMqlvK5fmZTAYDIVR3Kvvq7ZfX6ALsBkQIAL4FbjStdIqCS37Wb97l7vcKCzYcIidx5P559hofL09XZqXwWAwFEaRfQqqGqeqccABIEZVu6hqZyAa2FNRAt2Of6A1x4KLO5tTzmczY8luOofUY2hEkEvzMhgMhqJwpqO5g6r+lrehqluBKNdJqoS0joNDa+F8ssuyeGt5Aokp53l8SEfjAdVgMLgNZ4zCDhF5T0RiRaSfiLwL7HC1sEpFmwGQmwV7XePy4lhSOu+u2Mv1UU2Ibl7PJXkYDAaDMzhjFG4GtgH3AX8Dttv2VR+a97Cm6Px9iUuSn/nDHnJVeWhgxX+5bDAYDI6UOMZSVTNE5C3gG1XdVQGaKh+e3lYT0u/flbvLi/2Jqcxff4ibujenWX33DUE1GAwGcKKmICLXAfHAt7btKBFZ5GphlY52gyD5GBz/reSwpeD173fj5SncHVexbjRKol27drRr187dMgwGQwXjzNdYTwHdgOUAqhovIi1cJ6mS0maA9fv7UgiKKJckdx1P5svNR5nctxVXBPiWS5rlhfF9ZDBUT5zpU8hW1SSXK6ns1G4EQVGWUSgn/vHdLmr5eHF739bllqbBYDBcCs4Yha0ichPgKSJtReSfwGoX66qctB0Ih9dB2ulLTmrrkSSWbPuDW/u0pJ5/5Ztz2fg+MhiqJ84YhXuAUOA88F8gCWskUvWj7UDQXEj48ZKTenP5HmrX8OKWK1uWg7DyJzAw0MzTbDBUQ5zpUxiiqo8Bj+XtEJHRwHyXqaqsNI0Bv0DYvQTCR5U5mT0nkvnf1uPcGduaAF/vchRYfrz44ovulmAwGNyAMzWFwuZkdGqeRhEZLCK7RGSPiDxSRJg/ich2EdkmIv91Jl234eEJba6GPd9Dbk6Zk/n38r3U8PLglt6Vs5ZgMBiqL8V5Sb0GuBZoKiIzHQ4FANklJSwinsAbwADgMLBORBap6naHMG2xDExvVT0jIleU7TQqkHaDYMsncOhXCOlV6uiHTqfxRfwR/tIzhMBaNVwgsHwYOXIkAJ999pmblRgMhoqkuJrCUWA9kAFscFgWAYOcSLsbsEdV96pqJjAPuL5AmEnAG6p6BkBVT5ROvhtoMwA8fWDH4jJFf+fnvXgITK7krrFPnTpl5mk2GKohxXlJ3ayqs4E2qjrbtr4I60F/xom0mwKHHLYP2/Y50g5oJyKrRGSNiAwuLCERmSwi60Vk/cmTJ53I2oX4BlgT7+z8yvq6uRScSM7gk/WHGBkTTFCdmi6RZzAYDJeCM30K34lIgIjUx5pT4UMR+YcT8QrzBVHwKeoFtAVigbHAeyJS96JIqu/YXHd3adiwoRNZu5gOQ+DsQfhja6mizf3lAFk5udzWz3yXYDAYKifOGIU6qnoOGAF8aJtT4Won4h0GmjlsB2M1SRUM86WqZqnqPmAXlpGo3LS/FpBSNSFlZOUw99eDXNWhES0b+LtOm8FgMFwCzhgFLxEJAv4ElKYhfR3QVkRaiogPMAar+cmRL4A4ABFpgNWctLcUebiHWldYnlN3Ol8cX2w6wunUTG65soXrdBkMBsMl4sx3CtOBJcAqVV0nIq2A30uKpKrZInK3La4n8IGqbhOR6cB6VV1kOzZQRLYDOcAUVa0avZsdhsLSx+D0Pqhf/NBSVeWDVfvoGBRAz1bmgzB3k5WVxeHDh8nIyHC3FIOh3PH19SU4OBhv77J9A+WM6+z5OHyopqp7gZHOJK6q3wDfFNj3pMO6Ag/YlqpFR5tR2LkYet1TbNAVvyey+48UXhkdaWZVqwQcPnyY2rVr06JFC3M9DJcVqsqpU6c4fPgwLVuW7TsoZ1xntxORH0Rkq207QkQeL1NulxP1WkCjcNj5dYlBP1i1jwa1ajAs0sy9XBnIyMggMDDQGATDZYeIEBgYeEm1YGf6FN7F+sAsC0BVt2D1Dxg6DIGDayD5jyKD7DmRwvJdJ/lLzxBqeHlWoLhLo2fPnvTs2dPdMlyGMQiGy5VLvbedMQp+qrq2wL4Sv2iuFoTeAChs/7LIIB/9egBvT+Gm7s0rTlc58OKLLxr/Ry7k+eefJzQ0lIiICKKiovj1118BaNGiBYmJiW7TNX/+fDp27EhcXFy+/cuXL2fo0KGlSmvWrFkcPVpwwOHFYe6+++4S03r99ddJS0srMVytWrWc1ldWUlNTCQwMJCkp/4wCw4cP59NPPy1VWmfPnuXNN98stYann36aV155pdTxnMEZo5AoIq2xfWMgIqOAYy5RU9W4ogNc0Qm2Fu4KIiMrh882HGZwWBANKrFLC0PF8ssvv7B48WI2btzIli1b+P7772nWrFnJEUsgO/vS39Xef/993nzzTZYtW3bJaTljFJzFWaNQEfj7+zNw4EC++OIL+76kpCRWrlxZasNZVqPgSpwxCncBbwMdROQI8DfgdpeqqkqEjYBDayDp8EWHFm85xrmMbMZVsVoCWL6P8vwfGcqXY8eO0aBBA2rUsF4UGjRoQJMmTezH//nPfxITE0N4eDg7d+4EYO3atfTq1Yvo6Gh69erFrl3WdOmzZs1i9OjRDBs2jIEDBwIwY8YMunbtSkREBE899VShGj7++GPCw8MJCwtj6tSpAEyfPp2VK1dy++23M2XKlIvipKSkMGrUKDp06MC4ceNQ2xf906dPp2vXroSFhTF58mRUlQULFrB+/XrGjRtHVFQU6enprFu3jl69ehEZGUm3bt1ITk4G4OjRowwePJi2bdvy8MMPX5TvzJkzOXr0KHFxcfYaTGH6HUlMTKRnz558/fXXRZbJ/v376dixI5MmTSI0NJSBAweSnp5uz7NTp05EREQwZszFreVjx45l3rx59u2FCxcyePBg/Pz8SE1N5ZZbbqFr165ER0fz5ZdWS8K2bdvo1q0bUVFRRERE8Pvvv/PII4+QkJBAVFSUvcyLun7PP/887du35+qrr7Zff5egqsUugKft1x+oXVJ4Vy+dO3fWSkXiHtWnAlRXzbzo0PA3Vmr/V5Zpbm6uG4RdGjNmzNAZM2a4W4ZL2L59u3396UVb9U9vrS7X5elFW4vNPzk5WSMjI7Vt27Z6xx136PLly+3HQkJCdOZM615644039NZbb1VV1aSkJM3KylJV1e+++05HjBihqqoffvihNm3aVE+dOqWqqkuWLNFJkyZpbm6u5uTk6JAhQ/Snn37Kl/+RI0e0WbNmeuLECc3KytK4uDhduHChqqr269dP161bd5HmZcuWaUBAgB46dEhzcnK0R48eumLFClVVe96qquPHj9dFixZdlNb58+e1ZcuWunbt2nzn8+GHH2rLli317Nmzmp6ers2bN9eDBw9elH9ISIiePHmyRP3+/v56/Phx7datmy5durTYMtm3b596enrqpk2bVFV19OjROmfOHFVVDQoK0oyMDFVVPXPmzEV6zp8/rw0bNtTExERVVR00aJAuXrxYVVWnTZtmT+fMmTPatm1bTUlJ0bvvvlvnzp1rj5+Wlqb79u3T0NBQe7pFaV2/fr2GhYVpamqqJiUlaevWrYv9fzre43lgfQpQ4jPWmZrCPhF5B+gBpLjMOlVVAltDk+iLmpC2Hz3HpoNnual7SJXs1HzooYd46KGH3C3jsqRWrVps2LCBd955h4YNG3LjjTcya9Ys+/ERI0YA0LlzZ/bv3w9YzROjR48mLCyM+++/n23bttnDDxgwgPr16wOwdOlSli5dSnR0NDExMezcuZPff8//WdG6deuIjY2lYcOGeHl5MW7cOH7++ecSdXfr1o3g4GA8PDyIioqya1u2bBndu3cnPDycH3/8MZ+2PHbt2kVQUBBdu3YFICAgAC8va0T8VVddRZ06dfD19aVTp04cOHCgWB3F6c/KyuKqq67i5ZdfZsCAASWWScuWLYmKirqovCMiIhg3bhxz586163TEx8eH6667jgULFpCYmEh8fLy9prZ06VJeeukloqKiiI2NJSMjg4MHD9KzZ09eeOEF/v73v3PgwAFq1rzY/1lRWlesWMENN9yAn58fAQEBXHfddcWW0aXgzMdr7YFhWM1I74vIYmCeqq50maqqRthIWPo4nEqwjATw37UHqOHlwciYgj4ADZWJp4aFuiVfT09PYmNjiY2NJTw8nNmzZzNx4kQAe7OSp6envZ/giSeeIC4ujoULF7J//35iY2Ptafn7X3CboqpMmzaN2267rci8tZSOHPPI0+WoLSMjgzvvvJP169fTrFkznn766UKHQ6pqkS9HhaVbHMXp9/LyonPnzixZsoR+/frZwxdWJvv3778o77zmo6+//pqff/6ZRYsW8eyzz7Jt27aLjMPYsWN57rnnUFWuv/56+8diqspnn31G+/bt84Xv2LEj3bt35+uvv2bQoEG89957tGqV31tyUVpff/31Cnu5LLGmoKrpqvqpqo4AorHmU/jJ5cqqEqE3WL/bPgcg5Xw2CzceYWhEE+r6Vb75l50h74FlKH927dqV7+09Pj6ekJCQYuMkJSXRtKn1guFYqyjIoEGD+OCDD0hJsSr1R44c4cSJ/B7pu3fvzk8//URiYiI5OTl8/PHH9gdoackzAA0aNCAlJYUFCxbYj9WuXdveb9ChQweOHj3KunXrAEhOTi5Vx7hjWsXpFxE++OADdu7cyUsvvQQ4VyaO5ObmcujQIeLi4nj55Zc5e/asPa4jcXFx/P7777zxxhuMHTvWvn/QoEH885//tBuvTZs2AbB3715atWrFvffey3XXXceWLVvynVdxWvv27cvChQtJT08nOTmZr776yumyKy3O1BQQkX7AjcA1WD6N/uQyRVWROsHQvCds/Rz6TuGbLcdIzcypcsNQDRVDSkoK99xzD2fPnsXLy4s2bdrwzjvvFBvn4YcfZsKECfzjH/+gf//+RYYbOHAgO3bssH9jUqtWLebOncsVV1yYvyooKIgXX3yRuLg4VJVrr72W668vONWJc9StW5dJkyYRHh5OixYt7M1DABMnTuT222+nZs2a/PLLL3zyySfcc889pKenU7NmTb7//nun85k8eTLXXHMNQUFBLFu2rFj9np6ezJs3j2HDhhEQEMCdd95ZaJl4ehb+3VBOTg7jx48nKSkJVeX++++nbt2LnDfj4eHByJEjmT9/Pn379rXvf+KJJ/jb3/5GREQEqkqLFi1YvHgxn3zyCXPnzsXb25vGjRvz5JNPUr9+fXr37k1YWBjXXHMNM2bMKFRrTEwMN954I1FRUYSEhNCnTx+ny660SElVSRHZB8QDnwKLVDXVZWqcoEuXLrp+/Xp3Siicte/CNw/BHav508JzJKae54cH+lXJ/gTAXktYvny5W3W4gh07dtCxY0d3yzAYXEZh97iIbFDVLiXFdaajOVJVb1DVj91tECo1oSPAw5ukNbNZu/80ozoHV1mDYDAYqi/O9CmcqwghVR7/QGg3CK+t8/GSHG6INh3MBoOh6uFMTcHgJLmRY/HPOs3tTQ+Y6TYNBkOVxBkvqRf5Xy1snwHWenbmlNZmrM8Kd0sxGAyGMuFMTaEwxz4LCtlX7Zkff4Jv6EOTP5ZB+hl3yzEYDIZSU+SQVBHpAIQCdURkhMOhAMDX1cKqGqnns/nf1mOEtB+J/P6N9YVz17+6W5bBYDCUiuJqCu2BoUBdrC+a85YYYJLrpVUtlmw7TlpmDr16xUGjMIj/2N2SLomhQ4eW2uOjwXmqmuvs/fv3ExYWlm+fM+6bv/jiC7Zv315sGGfdcjvrdbWiyrCwMiktZXFJ7khsbCzlPUS/yJqCqn4JfCkiPVX1l3LN9TLkq81HaVq3Jp1b1Ieom2DJo3Bip+Veuwpi/B65DkfX2TVq1CAxMZHMzMxLTjc7O7tQPz2lIc91dkGjUFa++OILhg4dSqdOnS45rVmzZhEWFpbPo6yh/HGmT2GPiDwqIu+IyAd5i8uVVSHOpGay4vdEhkYGWd8mRNwInj6wYZa7pRkqIVXVdXZxvPvuu3Tt2pXIyEhGjhxJWloaq1evZtGiRUyZMoWoqCgSEhLYs2cPV199NZGRkcTExJCQkAAU7ZY7j8Jccf/www9ER0cTHh7OLbfcwvnz5/PFSU9PZ/Dgwbz77rsAzJ071+66+rbbbiMnJwewvhp+7LHHiIyMpEePHvzxhzWT4vz58wkLCyMyMjLfF8slER8fT48ePYiIiOCGG27gzBmrf7Goc89j3bp1REdHs3fv3iLdb6enpzNmzBgiIiK48cYb7b6aypWS3KgCq4G/Y7m2GJm3OOOC1RVLpXOdrar//fWAhkxdrL8dPnth5/xbVF9sppqZ5j5hl0C/fv20X79+7pbhEvK5Ff5mquoH15bv8s3UYvOviq6z9+3bp76+vhoZGWlfGjVqZHffnOdCWlX1scces5/DhAkTdP78+fZj3bp1088//1xVVdPT0zU1NbVYt9yOOGpLT0/X4OBg3bVrl6qq/vnPf9bXXnvNXob79u3Tq666SmfPnq2q1jUfOnSoZmZmqqrqHXfcYT8G2N19T5kyRZ999llVVQ0LC9PDhw+rauHuswu6vc4jPDzcfk2feOIJve+++4o99yFDhuiqVas0JiZGDxw4oKpFu99+9dVX9eabb1ZV1c2bN6unp2eh18vVrrP9VHWqWk7xPstbyt88VV2+2nyUVg38CW0ScGFnl5shIwm2LXSfsEtg4sSJdq+dhvKlqrrObt26NfHx8fbl9tsvzLW1detW+vTpQ3h4OB999FGh7rOTk5M5cuQIN9xgOZD09fXFz88PKNotd1Hs2rWLli1b0q5dOwAmTJiQ7xyuv/56br75Zv7yl78A8MMPP7Bhwwa6du1KVFQUP/zwA3v37gUsN9h57fqOZd67d28mTpzIu+++a69VlERSUhJnz561O+jL01Xcue/YsYPJkyfz1Vdf0by55S+tKPfbP//8M+PHjwcs994RERFO6SoNzjRALhaRa1X1m3LP/TLgxLkMftl7inv6t83v1iKkNzRoB+s/sPoYqhjVxiBc85Jbsq2KrrOLY+LEiXzxxRdERkYya9asQn1mFZdvebrPBuuB/r///Y+bbroJEUFVmTBhQqHzjnt7e9v/u455v/XWW/z66698/fXXREVFER8fT2BgYLH5lkVvUFAQGRkZbNq0yd6MqEW43wZc7j7HmZrCfViGIUNEzolIsogY1xc2vvntGKowLCIo/wER6HwzHF4Hx7a4R9wlkJiY6NZRMJczl5Pr7DySk5MJCgoiKyuLjz76yL7f0TV0QEAAwcHB9rmNz58/X6p5lwu64t6/fz979uwBYM6cOfnOYfr06QQGBnLnnXcC1kQ+CxYssJfF6dOnS5zMJyEhge7duzN9+nQaNGjAoUOHStRYp04d6tWrx4oVK/LpKu7c69aty9dff82jjz5qN6ZFud/u27evvXy3bt3Kli3l/2xxxvdRbVX1UFVfVQ2wbQeUFK+6sHjLMTo0rk3bRrUvPhg5Brx8YcOHFS/sEhk1ahSjRo1yt4zLkpSUFCZMmGCfA3j79u08/fTTxcZ5+OGHmTZtGr179y62KWPgwIHcdNNN9OzZk/DwcEaNGpXPXz/kd52d1+lZVtfZeTz77LN0796dAQMG0KHDhRF3Y8aMYcaMGURHR5OQkMCcOXOYOXMmERER9OrVi+PHjzudR54r7qioKFSVDz/8kNGjRxMeHo6Hh0e+5iywJqbJyMjg4YcfplOnTjz33HMMHDiQiIgIBgwYwLFjx4rNb8qUKfbO+L59+xIZGXlRmF27dhEcHGxf5s+fz+zZs5kyZQoRERHEx8fz5JNPAhR77o0aNeKrr77irrvu4tdff+WJJ54gKyuLiIgIwsLCeOKJJwC44447SElJISIigpdffplu3bo5XX7O4ozrbAHGAS1V9VkRaQYEqeraclfjBJXJdfaRs+n0fulHpgxqz11xbQoPtPAO2LEIHtwJNQoxHJUU4zrbYKi6uNp19ptATyCvYTwFeKO0Ii9H/veb9aYxtGDTkSNdboHMFNg8r4JUGQwGQ9lxxih0V9W7gAwAVT0DVM05JsuZJduO0zEogJBA/6IDBXeBpp1hzb8hN7fixBkMBkMZcMYoZImIJ6AAItIQqPZPt5PJ51l/4AyDQhsVH1AEetwJpxPg9yUVI85gMBjKiDNGYSawELhCRJ4HVgIvuFRVFeD7HX+gCgM7NS45cKfrIaAp/GJa3SoLrhiWaTBUBi713nZm9NFHwMPAi8AxYLiqzr+kXC8Dlmw7TrP6NekY5ETnsac3dJsM+1fA8d9cL85QLL6+vpw6dcoYBsNlh6py6tQpfH3L7si6xI/XRKQHsE1V37Bt1xaR7qr6qxNxBwP/B3gC76lqoV8KicgoYD7QVVUrx9CiYkjOyGL1nlP8pWeI8x+SdJ4AP/3d6lsY/qZrBRqKJTg4mMOHD3Py5El3SzEYyh1fX1+Cg4PLHN+ZL5r/jeUuO4/UQvZdhK0f4g1gAHAYWCcii1R1e4FwtYF7gRKNTGVh2a6TZObkMijMiaajPGrWg6hxsHE2XPUU1C6hL8LgMry9vWnZ0kweaDAUhjN9CqIO9WxVzcU5Y9IN2KOqe1U1E5gHFPaFzLPAy9hGN1UFlmw7ToNaPsQ0r1e6iD3ugJws+PXfrhFWjhjfRwZD9cQZo7BXRO4VEW/bch+w14l4TQHH78IP2/bZEZFooJmqLi4uIRGZLCLrRWS9u6v857NzWL7zBAM6NcLTo5Q+SAJbQ+hwWPsepJ91jcBywhgFg6F64oxRuB3oBRzBerB3ByY7Ea+wJ6a9xiEiHsBrwIMlJaSq76hqF1Xt0rBhQyeydh2r95wiNTPHuVFHhdHnQchMhrXvlq+wcsb4PjIYqifFNgPZ+gXGqeqYMqR9GGjmsB0MOM6lVxsIA5bbOmsbA4tE5LrK3Nn8/Y4/8PPxpFebsnlLpHE4tB0Ea960mpNq1CpfgeVEnt+jy9HNhcFgKJpiawqqmkPh/QDOsA5oKyItRcQHGAMsckg7SVUbqGoLVW0BrAEqtUFQVZbvOsmVbRpQw8uz7An1fQjST1udzpWUBx98kAcfLLESZzAYLjOc6TBeJSL/Aj7BGnkEgKpuLC6SqmaLyN3AEqwhqR+o6jYRmY41A9Ci4uJXRnb/kcKRs+nc3b8I53fO0qwbtOgDq/8JXf8KXjVKjlPBDBs2zN0SDAaDG3DGKPSy/U532KdA/5Ii2ibm+abAvieLCBvrhBa3smyX5Ys9tn059Gv0eQDm3AAb/wPdJl16euVM3hzAhU3yYTAYLl9KNAqqGlcRQqoCy3aeoGNQAEF1al56Yq3ioFkP+PkV6/sFH79LT7McyZu5y/QpGAzVixJHH4lIIxF5X0T+Z9vuJCK3ul5a5SIpPYv1B84QVx61BLAc5V31JKQch3XvlU+aBoPBcKKyOb0AABXDSURBVIk4MyR1Fla/QBPb9m7gb64SVFlZ+XsiOblK/w5XlF+iLXpD6/6w8jXIMDOcGgwG9+OMUWigqp9ic5etqtlA0fMBXqb8uPMEdWp6E9Wsbvkm3P9xayTSmsr/lbPBYLj8ccYopIpIIBfmU+gBJLlUVSUjN1f5afcJ+rZriJenM0VWCpp2hg5DrZFIaafLN22DwWAoJc484R7A+r6gtYisAv4D3ONSVZWMrUeTSEzJpH8HF31NHfeYNWXnz6+4Jn2DwWBwEmdGH20UkX5AeyzXFbtUNcvlyioRy3aeRAT6tnWRUWjUCaLHw9p3oOutlo8kg8FgcAPOjD7yxXJt/SzwDHCXbV+1YeWek4Q1qUNgLRd+ZNb/Cesjtu8K/YzDYDAYKgRnmo/+A4QC/wT+BXQC5rhSVGUi5Xw2mw6e5cq2DVybUe1GcOX9sHMx7Fvh2rwMBoOhCJz5orm9qkY6bC8Tkc2uElTZ+HXvKbJzlSvbuNgoAPS8CzbMgiWPwuTl4HEJ/pUuEeP3yGConjhTU9hkG3EEgIh0B1a5TlLlYuWeRGp4edA5pJQT6pQF75pw9dNwfAvEf+T6/Iph2LBhxv+RwVANccYodAdWi8h+EdkP/AL0E5HfRGSLS9VVAlbtSaRby/r4elfQW3vYSGjeE757yq1DVHft2mX3f2QwGKoPzjQfDXa5ikrKH+cy2P1HCiNjyj4JdqkRgSH/gLf7WJ3O1/+r4vJ2wPg+MhiqJ84MST1QEUIqI6v2WDOP9a6I/gRHGnWCHnfC6pnWUNXmPUqOU8688MILFZ6nwWBwP+X8ee7lxcrfE6nv70OnoICKzzz2EajTDBbfDzkV/1lIr1696NWrV8kBDQbDZYUxCkWgqqzck0iv1oH8f3v3Hl5FfSZw/PvmHggESAQhCbeVBoGFIpF46XZtFYWqoFVbrHbVWtn10mq3Pl1Ln7WXZ7fqit3tVmuxVLHqWi1aBUTtTdptKXhB5E5huYZbIEAuRHI77/7xm4TjyUkIyZlMTub9PM88Z2bOnDnvaMib3+838/5SUuJNN+2zjL4w4yEo3wh/6f4upBUrVrBixYpu/15jTLA6MqYQSlvLayivruPv/H4+oT1jL4ezr4S3HoCPzYDBY7vtq+fOnQvYmIIxYWMthTb8aWtA4wmxLv+BazW8cjs0NQYbizGm17Ok0Ia/bK9g+KA+FA4MeEa0nMFw+TzYt9oNPBtjjI8sKcQRiSjv7DxC6ahBQYfijP8snD0Tlj8A5ZuCjsYY04tZUohjy8FqjtU2UDo6L+hQnOZnFzL7wUu3QcOJoCMyxvRSlhTiWLW9AqDntBQAcs6Aqx6Hg+vgt98OOhpjTC9lSSGOVTuOUDAgm6JBAY8nxPrYZVB6O6z6CWx5PehojDG9kCWFGKrK2zt60HhCrGnfhTP/Fl65A6r2BR2NMaaXsaQQY1t5DRXH6ykd3UOTQlomXPsUNJ5w4wt2m6oxJoHs4bUYK3e4yqSlo3rIIHM8+WPgiv+EX/2jK5o3PfF1iqz2kTHhZEkhxqrtFQzpn8mIvB42nhBr0mzYuxpWPgbDJsPE6xJ6eqt7ZEw4WfdRFFVl1Y4jlI7KQySAeken67J/h+EXwOKvwP7ETm1htY+MCSdLClF2VtRyqLqu544nxEpNh889DdkD4YUboOZQwk49d+7clvpHxpjwsKQQpfn5hPN6ykNrHZEzGGY/CzXl8PxsqK9NyGnnz5/P/PnzE3IuY0zy8DUpiMh0EdkiIttE5L447/+ziGwUkbUi8jsRGeFnPKfy9s4j5OdkMDq/b5BhnL6CKXDNAtj7Hrx8G0SaunzK4uJiiouLExCcMSaZ+JYURCQVeAyYAYwDrheRcTGHvQ+UqOpEYBHwH37F0xGrdx1lyoiByTGeEOvsK2H6A7B5Kbz5rS6fbsmSJSxZsiQBgRljkomfdx9NBbap6nYAEfkFMAvY2HyAqr4VdfxK4EYf42nX4Zo6dlbU8oXS4UGF0HXn3Q7HdsPKH0P/oXDh3Z0+1SOPPALAlVdemajojDFJwM+kUADsidouA0rbOf5WIG7tBhGZA8wBGD7cn1/aq3cdBWDKiIG+nL/bXPpvUH3APb+Q3gem3hZ0RMaYJOJnUojXB6NxDxS5ESgB/j7e+6r6BPAEQElJSdxzdNV7u4+SkZrC+GG5fpy++6SkwmefgIYPYdm9boKej38h6KiMMUnCz4HmMqAoarsQaFWsR0QuAb4FzFTVOh/jadfqXUeZUNCfrPTUoEJInNR0uG4hjL4IXr0T1r8ccEDGmGThZ1J4BxgjIqNEJAOYDSyOPkBEJgPzcQmh3MdY2lXfGOGDssrk7zqKlp4Fs/8HikrhpS/DBy8EHZExJgn4lhRUtRG4C3gT2AS8qKobROR7IjLTO+xhIAf4pYisEZHFbZzOVxv2VVLfGOldSQFc19ENi2DEBa5O0rtPBR2RMaaH87X2kaouA5bF7Ls/av0SP7+/o97zBpnPGd7LkgJAZg7c8Et48R9g6T3QUAvn3xl0VMaYHsqeaAZW7z5K0aBsBvfPCjoUf6Rnw+efc/M8vzkXfvtdiESCjsoY0wOFPimoKu/tOsqU3thKiJaW4eZhmHIL/OkH8NKtNtezMaaV0JfO3nvsQw5W1fW+8YR4UtPcPAyDRrnnGKr2wfXPQ5/WBQCt7pEx4RT6lkLLeEIYkgKAiHvS+bqFsO99+Omn4MD6VodZ7SNjwin0SWH1rqP0yUileEi/oEPpXuOvhptfg8Y6WHAJrH3xI29b7SNjwin0SWFNWSUTC3NJSw3hf4qic2HOH9zMbS/fBsu+AY31gKt91Fz/yBgTHqEeU6hvjLBpXxW3XDgy6FCC028I3LTYjTGs/DGUvQ3X/IxFixYFHZkxJgAh/PP4pM0HqqhvijCxcEDQoQQrNd2V3f7cz+HIDvjJJ8jfvYz8vCSabMgYkxChTgoflFUCMKkoyYvgJcq4WXD7CigsgcVfYefDn0zoFJ/GmJ4v3ElhzzHy+mZQMCA76FB6jtwC+OKrPP5/wxhWsw4eOxfWPA/qS3FaY0wPE+qksLbsGBMLc5NzpjU/paTwwp4hfPndsZBfDK/8EzxzNRzdGXRkxhifhTYp1NQ1srW8hklFIR9PaMfu2iy45XW4/BEoexceK4W3vg/1x4MOzRjjk9AmhfV7K1GFSWEfZD6VlBQ498tw5yoYezn84SH4UYl7rsG6lIzpdUKbFNaWHQNgYqENMndIbgFc+yTc8gbknOGea/jZNNjxx6AjM8YkUGiTwgdllRQOzCYvJzPoUJLLiPPhtuUw81GoLIOnr4SFV8DulUFHZoxJgNAmhbVlx6zrqLNSUuCcL8JX34fLHoBDm+HJy+DZayw5GJPkQpkUKmrq2HPkQ+s66qr0bDj/Drj7A7jku7B3tUsOC6bBpiUQaQo6QmPMaQplUli7t/mhNWspJERGX/jEPfC19TDjYag5CC/cCI+eC2//FE5UBh2hMaaDQln7aO2eSkRgQoG1FNrSqdpHGX2hdA6UfAk2L4E//zcsu9fVVZpwjdtfcE7igzXGJEw4k0LZMc46I4eczFBefofk5+d3/sOpaa409/irXZfSe0/BukXw/jMwdBJMut4liZzBiQvYGJMQoew+2rCvyloJp7Bw4UIWLlzY9RMVnAMzfwRf3wyfmQcagTfug0eK3VPSa56Huuquf48xJiFC96fy4Zo6DlSdYPyw/kGH0qM1J4Sbb745MSfMyoWpt7mlfDOsexHW/dKV0FiaBaMvcg/HfWyGew7CGBOI0CWFDfuqABhnSaFdy5cv9+/kg8fCxffDp/8V9qyC9S/DlmXw1zcAgaKpUPwZGDMNBo9zU4gaY7pFCJOCuxNm/DDrPgqcCAw/zy0zHoID61xy2Pwa/Pbbbuk72LUimpfcgiAjNqbXC2FSqKJoUDa52elBh9KjzZs3D4B77723e75QBIZOdMtF90HlXtj+Fmxf7l7XeXNI550FRefB8FIoKoW8Me5hOmNMQoQvKeytZPxQayWcytKlS4FuTAqxcgtg8o1uiUSgfKNLEDv/17Um1jzrjssa4LqbCqe6O5uGToR+ZwYTszG9QKiSQvWJBnZW1HLtlMKgQzGnIyUFzpzglgvuctVZK7a58Yg9q2DP27D11yeP7zvYJYczvZbH4PEwaJSbdtQY065QJYVN+92tjzaekOREIH+MWybf6PadqIQD6+HAWti/1r1uXw6RRvd+SjoMGu0+c0axmzwof4zrjsqymw6MaRaqpHBykNl+CfQ6Wbkw8kK3NGs4AYc2uVtgD2+Bw1vh0BbY8jpoVF2m7IEwYAQMHAkDR3jrI2DASMgthPSs7r4aYwITqqSwfm8V+TmZDO5v/8hDIT0Lhk12S7TGeji6wyWII9vh2C431Wjz3U9N9R89Pnsg9Bt6cuk/1I1bNG/3zYc++ZDRp9suzRi/hCopbNhXyYQCayWEXlqG60I6o7j1e5EIVO8/mSiq9kLVfqg+ANX73IB3zUH3ZHar82Z7CWKQSxJ98rztPLcva4DrqsrMdS2brP7uNS3LnsUwPYavSUFEpgM/BFKBBar6YMz7mcDPgSlABfB5Vd3pRywnGprYVl7DxWdbvR3TjpQUd+dTbgGMuCD+MU2NcPyQSxLVB6C2Ao4fdq/Ny/HDbjC8tgLqa07xneknk0SmlygyclzLI72PKzSY3sfb7htnv/eanu0STFompGa49dRQ/d1nEsC3nxgRSQUeA6YBZcA7IrJYVTdGHXYrcFRVzxKR2cBDwOf9iOevB6tpjKgNMpuuS01zXUj9h3bs+IYT8OERNxh+ogrqqrx1b6mrcvtb1iu9ZHIcGmqhvhYajsdvnZyKpEBqpksUaZneenPCyGi9PyXd3aWVknZyibud6m1776WmtbGdBpLq4pAUl3Sb16P3n/K9VNeaavO9FO997zi8llfzetxXWu+zFpuvLYWpwDZV3Q4gIr8AZgHRSWEW8B1vfRHwqIiIauJnhG8ub2GDzKbbpWdB+jDoP6zz51CFxjovSRyPefWSRn0tNNW5MZOmOnd8Y13Men3r/fW10HTUfS7S4O7Yamp0r/G2O5OcklJbyeR0Ek4b54n3+Zavjfp87L6L74dJsxN9oR/hZ1IoAPZEbZcBpW0do6qNIlIJ5AGHow8SkTnAHIDhw4d3Kpi8vhlcOm4IRQNtMLAjfK19ZE6fiJdcstz4RJAiES9BNCeNJi9xNETtj9rWiEtq2uStR9xnmtdjl9N6r8k7d/N73jYA6q3HeaX5pa332vhcm+em658/GVT8fQD9/S/z4mdSiNcOi20BdOQYVPUJ4AmAkpKSTrUiLh1/JpeOtyddjemylBRIyQAygo7E+MDPojFlQFHUdiGwr61jRCQNyAWO+BiTMcaYdviZFN4BxojIKBHJAGYDi2OOWQzc5K1fC/zej/EEY4wxHeNb95E3RnAX8CbultQnVXWDiHwPeFdVFwM/A54RkW24FoK/IyjGGGPa5etNzKq6DFgWs+/+qPUTwHV+xmCMMabjrBC9McaYFpYUjDHGtLCkYIwxpoUlBWOMMS0k2e4AFZFDwK5OfjyfmKelk5hdS8/UW66lt1wH2LU0G6GqZ5zqoKRLCl0hIu+qaknQcSSCXUvP1FuupbdcB9i1nC7rPjLGGNPCkoIxxpgWYUsKTwQdQALZtfRMveVaest1gF3LaQnVmIIxxpj2ha2lYIwxph2WFIwxxrQITVIQkekiskVEtonIfUHH01kiUiQib4nIJhHZICJ3Bx1TV4hIqoi8LyJLg46lK0RkgIgsEpHN3v+b84OOqbNE5Gvez9Z6EXleRLKCjqmjRORJESkXkfVR+waJyG9EZKv3OjDIGDuqjWt52PsZWysivxKRAYn+3lAkBRFJBR4DZgDjgOtFZFywUXVaI/B1VT0bOA+4M4mvBeBuYFPQQSTAD4E3VHUsMIkkvSYRKQC+CpSo6gRc2ftkKmm/EJges+8+4HeqOgb4nbedDBbS+lp+A0xQ1YnAX4FvJvpLQ5EUgKnANlXdrqr1wC+AWQHH1Cmqul9VV3vr1bhfPv5P3OoDESkELgcWBB1LV4hIf+CTuPlBUNV6VT0WbFRdkgZke7Mh9qH1jIk9lqr+kdazN84CnvbWnwau6tagOinetajqr1W10dtciZvRMqHCkhQKgD1R22Uk6S/SaCIyEpgMrAo2kk77L+AbQCToQLpoNHAIeMrrClsgIn2DDqozVHUvMA/YDewHKlX118FG1WVDVHU/uD+qgMEBx5MoXwJeT/RJw5IUJM6+pL4XV0RygJeAe1S1Kuh4TpeIXAGUq+p7QceSAGnAOcDjqjoZOE7ydFF8hNffPgsYBQwD+orIjcFGZWKJyLdwXcnPJfrcYUkKZUBR1HYhSdQkjiUi6biE8Jyqvhx0PJ10ITBTRHbiuvM+LSLPBhtSp5UBZara3GJbhEsSyegSYIeqHlLVBuBl4IKAY+qqgyIyFMB7LQ84ni4RkZuAK4Ab/JjTPixJ4R1gjIiMEpEM3MDZ4oBj6hQREVzf9SZV/UHQ8XSWqn5TVQtVdSTu/8fvVTUp/yJV1QPAHhEp9nZdDGwMMKSu2A2cJyJ9vJ+1i0nSQfMoi4GbvPWbgFcDjKVLRGQ68C/ATFWt9eM7QpEUvIGZu4A3cT/gL6rqhmCj6rQLgS/i/rJe4y2fCToow1eA50RkLfBx4PsBx9MpXmtnEbAaWIf7HZE0ZSJE5HngL0CxiJSJyK3Ag8A0EdkKTPO2e7w2ruVRoB/wG+/f/k8S/r1W5sIYY0yzULQUjDHGdIwlBWOMMS0sKRhjjGlhScEYY0wLSwrGGGNaWFIwxide5dQ7orYvSvZqsKb3s6RgjH8GAHec8ihjehBLCsbgigt6deoXePMIPCcil4jIn706/FO9uvyveLXsV4rIRO+z3/Fq3y8Xke0i8lXvtA8Cf+M9ZPSwty8nat6F57ynhhGRB0Vko3fueQH8JzAGcIW8jDHOWcB1wBxcaZQvAJ8AZgJzcZV231fVq0Tk08DPcU8vA4wFPoV72nSLiDyOK4o3QVU/Dq77CFfVdjyu9tafgQtFZCNwNTBWVdWPiVOM6ShrKRhz0g5VXaeqEWADbmIWxZV7GIlLEM8AqOrvgTwRyfU++5qq1qnqYVzBtSFtfMfbqlrmfcca77xVwAlggYh8FvClpo0xHWFJwZiT6qLWI1HbEVyrur0S7NGfbaLtVnir47zaXFNxlW+vAt44vbCNSRxLCsZ03B+BG6ClK+jwKeayqMZ1J7XLmxsjV1WXAfdwskvKmG5nYwrGdNx3cLOrrcV18dzU3sGqWuENVK/HzZD1WhuH9gNeFZEsXGvka4kL2ZjTY1VSjTHGtLDuI2OMMS0sKRhjjGlhScEYY0wLSwrGGGNaWFIwxhjTwpKCMcaYFpYUjDHGtPh/LCX3u+w66rUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X= np.arange(0,12, .01)\n",
    "vals = [1-1/2**x for x in X]\n",
    "\n",
    "vals3 = [1/2**x for x in X]\n",
    "plt.plot(X,vals, X, vals3)\n",
    "plt.xlabel('months')\n",
    "plt.ylabel('percent vested')\n",
    "plt.title('Vesting Schdule with 1 month vesting \"Half-Life\"')\n",
    "plt.legend([\"Share of hatch tokens Vested\", \"Share of Hatch tokens Locked\"])\n",
    "plt.vlines(3,0,1, linestyle ='-.')\n",
    "plt.text(3.2,.85, str(int(1000*7/8)/10)+ \"% of tokens vested after 3 months\" )\n",
    "plt.scatter(3,7/8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6001922786573871"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10*10**6*vals3[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d0 = 1 #million DAI\n",
    "p0 = .10 #DAI per tokens\n",
    "theta = .35\n",
    "\n",
    "R0 =  d0*(1-theta) #million DAI\n",
    "S0 = d0/p0\n",
    "\n",
    "kappa = 6\n",
    "V0 = invariant(R0,S0,kappa)\n",
    "\n",
    "reserve = np.arange(0,100,.01)\n",
    "supp = np.array([supply(r,kappa, V0) for r in reserve])\n",
    "price = np.array([spot_price(r,kappa, V0) for r in reserve])\n",
    "\n",
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('Reserve (Millions of xDAI)')\n",
    "ax1.set_ylabel('Supply (Millions of Tokens)', color=color)\n",
    "ax1.plot(reserve, supp,'--', color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('Price in xDAI per Token', color=color)  # we already handled the x-label with ax1\n",
    "ax2.plot(reserve, price,'-.', color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax1.vlines(R0,0,supp[-1], alpha=.5)\n",
    "ax1.text(R0+.02*reserve[-1], supp[-1], \"Initial Value R=\"+str(int(100*R0)/100)+\" mil xDAI\")\n",
    "ax1.text(R0+.02*reserve[-1], .95*supp[-1], \"Initial Value S=\"+str(S0)+\" mil Tokens\")\n",
    "#ax1.hlines(S0,0,R0)\n",
    "\n",
    "ax2.text(R0+.02*reserve[-1], price[3], \"Initial Value p1=\"+str(int(100*spot_price(R0,kappa,V0))/100))\n",
    "\n",
    "\n",
    "plt.title('Augmented Bonding Curve with Invariant S^'+str(kappa)+'/R')\n",
    "fig.tight_layout()  # otherwise the right y-label is slightly clipped\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots()\n",
    "\n",
    "cp = 100\n",
    "color = 'tab:red'\n",
    "ax1.set_xlabel('Supply (Millions of Tokens)')\n",
    "ax1.set_ylabel('Reserve (Millions of xDAI)', color=color)\n",
    "ax1.plot(supp[cp:], reserve[cp:],'--', color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('Price in xDAI per Token', color=color)  # we already handled the x-label with ax1\n",
    "ax2.plot(supp[cp:], price[cp:],'-.', color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax1.vlines(S0,0,reserve[-1], alpha=.5)\n",
    "ax1.text(S0*1.02, reserve[-1], \"Initial Value S=\"+str(int(100*S0)/100)+\" mil tokens\")\n",
    "ax1.text(S0*1.02, .95*reserve[-1], \"Initial Value R=\"+str(R0)+\" mil xDAI\")\n",
    "#ax1.hlines(S0,0,R0)\n",
    "\n",
    "ax2.text(S0*1.02, price[3], \"Initial Value p1=\"+str(int(100*spot_price(R0,kappa,V0))/100))\n",
    "\n",
    "\n",
    "plt.title('Augmented Bonding Curve with Invariant S^'+str(kappa)+'/R')\n",
    "fig.tight_layout()  # otherwise the right y-label is slightly clipped\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "#given V0 and kappa\n",
    "#sweep the reserve\n",
    "reserve = None\n",
    "reserve = np.arange(.01,100,.01)\n",
    "price = np.array([spot_price(r,kappa, V0) for r in reserve])\n",
    "\n",
    "#realized price for withdrawing burning .1% of tokens\n",
    "withdraw_price=[withdraw(supply(r,kappa,V0)/1000, r,supply(r,kappa,V0), kappa, V0)[1] for r in reserve]\n",
    "\n",
    "#realized price for depositing .1% more Xdai into the reserve\n",
    "mint_price=[mint(r/1000, r, supply(r,kappa,V0), kappa, V0)[1] for r in reserve]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='slippage.jpeg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf = pd.DataFrame({'reserve':reserve, 'spot_price':price, '.1% mint_price':mint_price,'.1% withdraw_price':withdraw_price })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1c3d5438>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eDlN8+3DBI0aMyJh+7NgxKlWq9MDlMztfXvr666/57rvvjC5D5HM6NZld0eP438Qq9L4yg8n+bhTxKM/Mxt8xu1W4hPxDkhb9HerWrUvTpk3/cQXL2LFj2bp1K3PnzmX27Nl06dKF/v37M2zYsCxv65tvvsl4PWLECPr165fldd0uNTUVF5e8/6dNTU3l/fffz/PtCseh01LZt2Iq23+dyHwfOBtg4nFTSUaEDaZW8ZpGl5dvSYv+DtWqVaNMmTL/mH77MMUmk+mBwxTPnz+fjz/+GIDx48dnDDZ29OjRjKEJbo1536dPH27evEnVqlVp27YtkD5ufIcOHXj66adp1KgRN2/eBGDnzp1UqVKF4OBgJk+enLG9GTNm8Nprr/Hyyy/TqFEj4uPjee6556hevTqBgYEsWrQISB/CYcKECQB89NFHNGjQAIA1a9bw5ptv3nO/WCwWunfvTvXq1XnuueeIjY3N+Az9+vWjfv36jB8/nsGDB2cMhnbkyBGef/55qlSpQvXq1Tl69CgAo0eP5plnnqFy5coMGjToQf8kogDQ1jT2r5rGjPFV6X1mAuMDXDCbS/JVg6+IaLNUQj6b7KpFP2r7KH69/GuOrvNJ/yfpXbN3ttfzsMMUh4aGZowbv3HjRgICAjh9+jSbNm0iJCTkb/OOHDmSSZMmZVw2eezYMQ4fPsycOXP43//+R6tWrQgPD+fNN9/k7bffZuLEidSvX/8fwyFs2bKFvXv34u/vT2pqKpGRkXh7e3Px4kVq165Ns2bNCA0NZezYsXTt2pWYmBiSkpJISUm5a123S0hIoHr16owdO5ahQ4cyZMgQJk2aBKQ/AWv9+vUADB48OGOZtm3b0qdPH1q0aEFiYiJWq5WVK1dy+PBhtm/fjtaaZs2asWHDBkJDQzP/jyEch9YcWjebbbtHEe6VzLEAEyWdH2V8SH+eLRV210H3xMOzq6C3Zw87THHRokWJj48nLi6OkydP8sYbb7BhwwY2btxIy5YtH7i9smXLUrVqVQBq1KjBsWPHuHbtGlevXqV+/foAtGvXjh9//PFvNd4aalhrTb9+/diwYQNOTk6cPn2a8+fPU6NGDXbu3ElcXBxubm5Ur16dmJgYNm7cmNHSvxsnJ6eMsXDefPPNv32GW9NvFxcXx+nTpzPG2zGbzUD6EMgrV67MeMBLfHw8hw8flqAvaLTm983hbNv+KeFeNzga4EpxpyKMqduPRmUbScDnMLsK+pxoeee2hxmmODg4mOnTp1OhQgVCQkKYNm0aW7ZsYezYsQ/czp3DFd+8efOewwrfcvuDQWbNmkVsbCw7d+7EZDJRpkwZEhMTM15Pnz6dOnXqULlyZdauXcvRo0cfamyZ2+u42wNJ7jWGktaavn378t5772V6W8KBaM3RbUvZumUIkZ7X+S3AlaKqMCOCe/PS401wUtKbnBtkrz6khxmmODQ0lDFjxhAaGkq1atVYu3Ytbm5u+Pj4/GNek8lESkrKfbft6+uLj48PmzZtAtLD/F6uXbtG4cKFMZlMrF27luPHj9+1rpCQEL7++muqVq16318iVquVhQsXAjB79uwHDoHs7e1NiRIliIqKAsg4v9G4cWOmTZtGfHw8AKdPn+bChQv3XZdwDMd2rWTOuDp8svdjRvonctktgME1h7D8zXW8XL6phHwukj1L7g1THBISwsmTJwkNDcXZ2ZmSJUveMyA7duxI5cqVM07G3sv06dPp1KkTwcHBuLu733O+tm3bEhMTQ1BQELNmzeLJJ/+6LTwkJISzZ88SHBxMkSJFMJvN9+2fh/RW+4EDB6hRowY//fQTAwcOvO/8AN9//z0TJkygcuXK1KlTh3PnztGoUSPeeOMNgoODCQwM5NVXX83UWPsi/zqxdwPzxoXQf0dnRvjHc9bNn341+rGy3QZeeaolzk72/7D6/E6GKRaZYrFYMlrheUGOi/zvzKGt/LyyL0vcTrHT3YyvNvNu1c68EfgGJmeT0eXlKzJMsRDCrpw7spvNy3rzo+ufbPM146196FrpPd6q+hauzq5Gl1cgPTDolVIlge+AooAVmKq1Hq+U8gfmAWWAY0ArrfWV3CtV5IVatWqRlJT0t2nff/99nrbmRf508fgBNkX3ZoXLr2zycceivfjgyXdoX+MdzC5mo8sr0DLTok8FumutdymlvICdSqlVwL+BNVrrkUqpPkAfwP4vmxH3tW3bNqNLEPnM1bN/sDGyJ6v4hbXe7nhoL94p/y86PvMeHiaPB69A5LoHBr3W+ixw1vY6Til1CHgUaA6E2WabCawji0H/oMsGRcGSl+eNRNbFXTrNpvA+/JT8Myss7rhhoV3Z1vyndmcsrhajyxO3eag+eqVUGaAasA0oYvslgNb6rFKq8D2W6Qh0BChVqtQ/fm42m7l06RIBAQES9gKtNZcuXcq4wUrYn5vXLrEp/BPW31jFEos7Tq6etCzZnG51u+Nr9jW6PHEXmQ56pZQFCAe6aa2vZzaUtdZTgamQftXNnT+/dSnjrbFThDCbzZQoUcLoMsQdkm9c5+fwIWy4sogobzPa4kHjIg3pGdaPQu6FjC5P3Eemgl4pZSI95GdprSNsk88rpYrZWvPFgCzd9WIymShbtmxWFhVC5IHUpBtsi/qcTedmEe7tSpK3O6H+dejbYBDFLcWNLk9kQmauulHAt8AhrfUXt/0oGngLGGn7vihXKhRCGMKaksyOpePZfOwbFnq7EOdrpralGv2eH0JZH2mc5SeZadHXBdoB+5RSt55K3Y/0gJ+vlHoHOAG8ljslCiHykramsWfF/9j06wQW+sBlP1eqmp+kf8PhVPCvYHR5Igsyc9XNJuBeHfLP5Ww5QgjDaM2B9XPYuHskC7xTuODvwlOm0ox/bjhVi1Q1ujqRDXJnrBCC37dGs2HLYMK9bnDK30Q55xIMCxtKnRLBRpcmcoAEvRAF2LHda1m3vh9Rnpc56u9KCVWEL0MG8lyZBnK5swORoBeiADp9aBvrVvYm2v0MB/3cKEIAw2v34eUnZLhgRyRBL0QBcuHYftYu6cky0xF2+Zrx1770q9aN1yq1wsVJ4sBRyb+sEAXAldNH+GlRT1ao/WzxMuNt9ebDiu/xVvW3ZcjgAkCCXggHFn/pDD+F92Z16hbWerrjabXw7uP/omOt93F3ufeDa4RjkaAXwgElxl9hQ/hA1sT9yHKLGVeTJ2+Ueo0udbvJgGMFkAS9EA4kNekGm6NGsu78XBZ5u6It7jQt+iI9w/rJgGMFmAS9EA5Ap6Wyfekk1v/5NeHeziR6u1HfN5h+DYdS1LOo0eUJg0nQC5Gfac3etd+zdu9oFnqncdXXRJD70wxoNIJyvuWMrk7YCQl6IfKpw9uWsmbLQBZ63eC8nwsVXcox+fnPqFwk0OjShJ2RoBcinzl5YAurV/ckwuMix/xMlFZFmRI2jJBS9YwuTdgpCXoh8onY44dYGf0Ri93+4ICvG0W1P5/V7sdLT7wkwxWI+5KgF8LOXTt/glWR3flR72G7txk/qze9q3xIm8pv4OzkbHR5Ih+QoBfCTt24dpE1C/uwKmk9az3NWKwW3i//Nh1qvY+rs6vR5Yl8RIJeCDuTkhjPuvAhrLkSxY8WN1zdPWhToiUfhvbA0+RpdHkiH5KgF8JOWFOS2RQ9hrWnZ7LI24S2mHnxkefo9dxA/M3+Rpcn8jEJeiEMpq1p7Fz5DWt+G0+Et+Kmtysh3kF80vBTinvJw7dF9knQC2GgQ5sjWbljCOHeyVzxdaa6WwUGNBrJ4/6PG12acCAS9EIY4MSBn1m+uicRnpc57edCBeeSjHtuJNWLVTO6NOGAJOiFyEMXT/3Oj1HdiHY9yq++rpQggPH1hvBsOXl0n8g9EvRC5IH4KxdYsbA7P6ZuY5uXGwFWL/pV+ZjXq7SWR/eJXCdBL0QuSr4Zz5qFA1l1fTGrLGY8XTzo+NhbvBfcSa6FF3lGgl6IXKDTUti4+AtWn5zOYi8XnDzMtCzyEj0afIKXq5fR5YkCRoJeiJykNbvXfs/KfaOJ8LaS6GUi1Lsm/RuPoIhnEaOrEwWUBL0QOeTIrtUs29iXCEsCl3ydqWZ6goEvjOFx/8eMLk0UcBL0QmTTuaN7WbysG4vcz3Dc18RjqiifNxhJzRI1jS5NCECCXogsu3bhBEvDP2Kx0372e7tS1OrLyFr9aVJBhg0W9kWCXoiHlBh/heULerM8cR2bPdzws3rSvWIn2tX4twwbLOzSA4NeKTUNaApc0FpXsk0bDHQAYm2z9dNaL8utIoWwB2kpSfwUMZyVsfNZYTFhNrvzr1Kt6BLSHbOL2ejyhLinzLToZwCTgO/umP6l1npMjlckhJ3RVivbVk5lxe8TiPZyQltcaRLQgL6NhuLj5mN0eUI80AODXmu9QSlVJvdLEcL+/LZjOUu2fEKE5SZx3s4Ee1Rm0IufU9zrUaNLEyLTstNH31kp9S8gBuiutb6SQzUJYbhzf+xn0dKuRLqf5bSPCxWdSjGw0VieLvK00aUJ8dCyGvRfAcMAbfs+Fmh/txmVUh2BjgClSpXK4uaEyBvxl88RvfBDFus97Pd25VHtxxd1BtOwfCOjSxMiy7IU9Frr87deK6X+Byy5z7xTgakAQUFBOivbEyK3pSTdYMXC/vx4bQkbPN3wtXrS/an/0C7obbmSRuR7WQp6pVQxrfVZ29sWwP6cK0mIvKOtaWxaNpHlf/6XpV7OmNzNtCnego+e7YO7i7vR5QmRIzJzeeUcIAwopJQ6BQwCwpRSVUnvujkGvJeLNQqRKw5sXcTi7YOI8krhppcLYV41GfDiKAp5FDK6NCFyVGauumlzl8nf5kItQuSJU4d3EbW8G5EesVzwcaGKczkGNfmS8vL4PuGg5M5YUWBcjz1DZERnFqkDHPZ2pbQuxJTQTwkpG2p0aULkKgl64fCSb8azdEEfliasYpuHK4WsFj6p/BGvV20rY9KIAkGCXjgsnZbKuiVfsOzkNFZYXPAwu/Hvkq3pUr+HPN1JFCgS9MIh/bJ5AdE7hxHtlUaqxcQLviF88sJn+JhlyAJR8EjQC4dy6vBOFi7vSqTnFS77OPOMqQKDXxpHKR+5WU8UXBL0wiHEXT5H+IJORDkd4Ki3icd0YcY0GM0zJZ8xujQhDCdBL/K11OREli3sz5Jri9ni4cojaRYGV+lJyyqt5ESrEDYS9CJ/0potq74h+vcv+dHihJvZjbcebUXXZ3vJiVYh7iBBL/Kdo/s2sHBtD6K8ErhhceJZS00GvjQGf3d/o0sTwi5J0It84/K54yyI+A+Rrn9w2seFSqoEg5tMoEKhCkaXJoRdk6AXdi/5ZgJR87uzKHEtez1dKZ7mzZiag2j8VBOjSxMiX5CgF3ZLW9NYu3Qc0Se+YY3FBW+TmU7l2tOhbmcZOliIhyBBL+zS/h3LiNj6CdGWZKyeLrzsG8YnTUbiafI0ujQh8h0JemFXzp04xNzFnVlkPstFb2eecSnP4JcmUMpXbngSIqsk6IVduBl3hQXzu7IobQe/W0yUtfozPHQUdcvWNbo0IfI9CXphKG1NY0XUZ0Sd+4HNniYClDt9KnbljaB/yw1PQuQQCXphmH3bljB/e3+WeKXi4m7i9Uea0rPxYNyc3YwuTQiHIkEv8lzsqSPMWvQ+ke5nuOztTB3TUwx5eRJFvYoYXZoQDkmCXuSZ5JsJLJzfjcikjfxqMVHO6s/nYaOpVTrY6NKEcGgS9CLXaauVdSsmEfHHV6yzuODnYqbnE51oV/td6YcXIg9I0Itc9fu+9cxd353Fnjexerjwf74N6NvkMzxMHkaXJkSBIUEvcsW12DP8EP4eUaYjnPNyoYZTWYa8PJnSvqWNLk2IAkeCXuSotJQkohb0JSJuGXvdTZRM82ZC8Kc8+8TzRpcmRIElQS9yzJafZrLw0Oes8lRYTK58UPot3gvtJuPSCGEwCXqRbccP72LWii5Ee14lyVPRyLMWA1/+Am95ELcQdkGCXmRZwvVLzJn/HyLYy0kvFwIpxqAXJ1Gh8JNGlyaEuI0EvXho2prG8uhRLDj7PTs8XCia5smIqv14uUpLo0sTQtyFBL14KL/+spYfNnZnqSUZk9mFdkVa8FGjAZicTEZnWgkvAAARhElEQVSXJoS4Bwl6kSnXL59n5oIORLocJtbLhWDnJxjafApFvYoaXZoQ4gEeGPRKqWlAU+CC1rqSbZo/MA8oAxwDWmmtr+RemcIo1tRUoiMHs/DyQn4xmyiV5s3kOiMJLf+s0aUJITLJKRPzzABeuGNaH2CN1ro8sMb2XjiYX3Yspe/XNRiUEMUfJlfeK/Em0f/+WUJeiHzmgS16rfUGpVSZOyY3B8Jsr2cC64DeOViXMNDlCyeYHt6BRW4nuWZxor5bZYY0n4yfh5/RpQkhsiCrffRFtNZnAbTWZ5VShXOwJmGQtNQUFi7ow8K4pfzqYeKxND++ePZLgkrXNLo0IUQ25PrJWKVUR6AjQKlS8txPe7V983xm7xnGGgv4urjxUbmOvF3vPzK6pBAOIKtBf14pVczWmi8GXLjXjFrrqcBUgKCgIJ3F7Ylccv7UEaZFdyTa/TyJnooX3GsyqPl4LG5eRpcmhMghWQ36aOAtYKTt+6Icq0jkidTkRGbP+4jwxHX84enCU9ZHGNx4IhWLBRpdmhAih2Xm8so5pJ94LaSUOgUMIj3g5yul3gFOAK/lZpEiZ23dNJdZe4ezzlNRyMmNT57sxus135JuGiEcVGauumlzjx89l8O1iFwWe+4430a0Z5H7OZI8FM0sdenf7EvcTe5GlyaEyEVyZ2wBYE1NZf6CPsyPW8phTxcqWgsxuPEUnir2tNGlCSHygAS9g9sTs5SZ2/qx2mLFz8VEr8c782adDtJNI0QBIkHvoK5dOc83898h0vQH8Z5ONDbXYMj/TcbTzWJ0aUKIPCZB72C01UpU1DDmxs7loNmF8mm+THx2ItVK1zC6NCGEQSToHciv+9czbf1HrPBMxsvkQpeS/6bDsx9LN40QBZwEvQO4EXeVb+a+S4TTQa54OlHfVJEhLf+Ln7uMTSOEkKDP37Rm2bIvmX3yG35xd6ZMqoURdcdQp3yo0ZUJIeyIBH0+dfLPvfx3WUeWesZjdnXm3aKv0aVRf5xUZkaeFkIUJBL0+UxaagrfzenKvKR1nLa4EEwZhr/2LYW9ihhdmhDCTknQ5yO7dizm2x2fsMFTU0yZGVVlAE2qygO5hRD3J0GfD8Rdu8jX89oT6XKURA9Fc486DPi/CbiZzEaXJoTIByTo7ZnWLPvxC747+S0HzM48kerD4OemEFiyqtGVCSHyEQl6O3Xq+AGmLO3Ajx7XcTc506l4W957vrdcEy+EeGgS9HYmLTWF7+Z1Y97Nnzjt6UIdSjP0tWkUkZOtQogskqC3I7t2LuWbbf3Y6GmlmHJjVOAAmlR/xeiyhBD5nAS9HUiIu8KUuf8m0vlI+slW92AGtJgoJ1uFEDlCgt5gq9b8j+lHvmSf2ZkKqd4MajCJwFIyAJkQIudI0Bvk8sUzTFzYjmi385hMTnQs8hqdGw+Qk61CiBwnQZ/XtCZyySi+O/sdR9ydqZZWmE+bT6dkQGmjKxNCOCgJ+jx0+tRvTIx+m+Ue1/F2dqZXmfdpV7+T0WUJIRycBH0e0FYrPyzow6y4JZz2dKYeZfi09Uz8PQOMLk0IUQBI0Oeyw79vZ9LqD/jJM5kiysSIp/vyclBro8sSQhQgEvS5JC01halzPmBe8s9c9XCisUsgQ1p/g6ebp9GlCSEKGAn6XLDnl5VM+bkHWzw0pbSZoTVHEVqxodFlCSEKKAn6HJSSlMiUOe8y37qbm2bFKx516ddiAq4ubkaXJoQowCToc8juPSuYtKUn2z00j1ndGfjcZKqXrWV0WUIIIUGfXbe34hPNitctYfRtMR5nJ2ejSxNCCECCPlt271nJxK092OGe3oof1GAy1cpJK14IYV8k6LMgJSmRyXM6sMC6i0Q3RSvPMPq2GIeLs+xOIYT9yVYyKaWOAXFAGpCqtQ7KiaLs2Z5fVjFxS3e221rxA5+dTPXHpBUvhLBfOdEEfVZrfTEH1mPXUlOSmTT7Hean7SLJTfG6Zxh9pBUvhMgHJKUyYf+BDXy5oQvbPaw8nubOgAaTqP5YbaPLEkKITMlu0GtgpVJKA//VWk/NgZrshram8b95Xfnh5loSzE608gil75sTpBUvhMhXsptYdbXWZ5RShYFVSqlftdYbbp9BKdUR6AhQqlSpbG4u7xw/foDRy95ivUcSpa1ujA4ZR60K9Y0uSwghHlq2gl5rfcb2/YJSKhKoCWy4Y56pwFSAoKAgnZ3t5ZU5UYOZdnE+F9ydaOIcyNA2M3BzlbtbhRD5U5aDXinlCThpreNsrxsBQ3OsMgPExp7i84VtWOF+hSK48HnlQTSWh3MLIfK57LToiwCRtkffuQCztdbLc6QqAyxePYWpf07imIczodbSfNZ2Nt7uPkaXJYQQ2ZbloNda/wFUycFaDBEff4XRs98g2vUk3k5OfFK2E61D3ze6LCGEyDEF+vKRbTuX8kVMbw6aFUEpAYxoOZti/o8aXZYQQuSoAhn02mpl0uwPmJ28Caur4v2AlvznpcHYuqGEEMKhFLigP33mMCMWtWWDx00eS3Nj6PNTqVzW4UduEEIUYAUq6BetmsRXx6dw1t2Jl5wCGfr2DHkoiBDC4RWIoE9MvMHIH15nkcuf+CpnhlXoRbPgdkaXJYQQecLhg37P/rV8vvlD9pk1NVL8GPXKPIr4FTe6LCGEyDMOHfTTwvsw7dpiklwV7/g04cPmo+SEqxCiwHHIoI+Pv8rQWS350RxL6TQXBoVO5JkKoUaXJYQQhnC4oN+9/yc+2/whh8wQmlacz9stxNPsZXRZQghhGIcK+umRn/DtlSiSXRX/CXiFD5oOMbokIYQwnEMEfXzCtfSuGrcL0lUjhBB3yPdBv/fQJoZv+IBDZghJLcqotgvx8pDByIQQ4pZ8HfTzfhzN5LMzSHRVvO/3f3RqNtzokoQQwu7ky6C3pqXy2fdvsICDFLE6MbLWF9QJbGh0WUIIYZfyXdDHXjpD/wUt+Nn9BtWSvRj7WgSP+BYzuiwhhLBbTkYX8DC27VnBOxGN2GJOoLlTINPbb5SQF0KIB8g3LfrvFw/j69i5WJ0VvR5tz5sNPza6JCGEyBfsPuitaWl89kM75uu9lExzZmjoFKpXqGd0WUIIkW/YddAn3LhO3+9fYq35KtWSLYxrvRh/70eMLksIIfIVuw36E2d+o8/i19lnTqOxtSyj3onA2dluyxVCCLtllydjf969lPeWteSQWyrvWBoy5u1oCXkhhMgiu0vPqJ++ZsyxieAEA8t+SIv6HYwuSQgh8jW7CvppiwYx5XI4/lbFiLqTCXqqvtElCSFEvmc3QT92dke+T/6Z0qnOfNlkLuUefcrokoQQwiEYHvTaamXgjFeJcj5MYLKZCa8voZBPUaPLEkIIh2Fo0FvT0ug3oxlLXU5QO8mH8f9agYfZ08iShBDC4RgW9Na0NHpNb8IK0xlCkgOY0H4VLi4mo8oRQgiHZUjQW9PS6DH9BVaZzhGWUphx7VfI5ZNCCJFLDLmOfsDMV1hlOkeDlKKMf3ulhLwQQuSibAW9UuoFpdRvSqkjSqk+mVlm5Kz2RDsfpW6SL1++vRwnZ+fslCCEEOIBstyUVko5A5OBhsApYIdSKlprffBey1y+do7ZKYlUTXZn3FsrJOSFECIPZKdFXxM4orX+Q2udDMwFmt9vgQsplyiVohjXajFmN49sbFoIIURmZSfoHwVO3vb+lG3aPWmgf+0vCPCV6+SFECKvZCfo1V2m6X/MpFRHpVSMUirGYnWltjzbVQgh8lR2gv4UUPK29yWAM3fOpLWeqrUO0loHlSxcPhubE0IIkRXZCfodQHmlVFmllCvQGojOmbKEEELklCxfdaO1TlVKdQZWAM7ANK31gRyrTAghRI7I1p1KWutlwLIcqkUIIUQusMsnTAkhhMg5EvRCCOHgJOiFEMLBSdALIYSDk6AXQggHp7T+x82subcxpeKA3/Jsg/atEHDR6CLshOyLv8i++Ivsi79U0Fp7ZXXhvB4I/jetdVAeb9MuKaViZF+kk33xF9kXf5F98RelVEx2lpeuGyGEcHAS9EII4eDyOuin5vH27Jnsi7/IvviL7Iu/yL74S7b2RZ6ejBVCCJH3pOtGCCEcXJ4EfVYeIu4olFIllVJrlVKHlFIHlFIf2qb7K6VWKaUO2777GV1rXlFKOSuldiulltjel1VKbbPti3m2Ya8dnlLKVym1UCn1q+34CC6ox4VS6iPb/4/9Sqk5SilzQTkulFLTlFIXlFL7b5t21+NApZtgy9K9SqnqmdlGrgf9bQ8RfxGoCLRRSlXM7e3akVSgu9b6KaA20Mn2+fsAa7TW5YE1tvcFxYfAodvejwK+tO2LK8A7hlSV98YDy7XWTwJVSN8nBe64UEo9CnQFgrTWlUgf9rw1Bee4mAG8cMe0ex0HLwLlbV8dga8ys4G8aNE/9EPEHYnW+qzWepftdRzp/5kfJX0fzLTNNhP4P2MqzFtKqRLAS8A3tvcKaAAstM1SIPaFUsobCAW+BdBaJ2utr1JAjwvS7+lxV0q5AB7AWQrIcaG13gBcvmPyvY6D5sB3Ot1WwFcpVexB28iLoH/oh4g7KqVUGaAasA0oorU+C+m/DIDCxlWWp8YBvQCr7X0AcFVrnWp7X1COj3JALDDd1o31jVLKkwJ4XGitTwNjgBOkB/w1YCcF87i45V7HQZbyNC+CPlMPEXd0SikLEA5001pfN7oeIyilmgIXtNY7b598l1kLwvHhAlQHvtJaVwMSKADdNHdj639uDpQFigOepHdR3KkgHBcPkqX/L3kR9Jl6iLgjU0qZSA/5WVrrCNvk87f+5LJ9v2BUfXmoLtBMKXWM9C68BqS38H1tf7JDwTk+TgGntNbbbO8Xkh78BfG4eB74U2sdq7VOASKAOhTM4+KWex0HWcrTvAj6Av0QcVsf9LfAIa31F7f9KBp4y/b6LWBRXteW17TWfbXWJbTWZUg/Dn7SWrcF1gKv2mYrKPviHHBSKVXBNuk54CAF8LggvcumtlLKw/b/5da+KHDHxW3udRxEA/+yXX1TG7h2q4vnvrTWuf4FNAF+B44Cn+TFNu3lC6hH+p9We4E9tq8mpPdNrwEO2777G11rHu+XMGCJ7XU5YDtwBFgAuBldXx7tg6pAjO3YiAL8CupxAQwBfgX2A98DbgXluADmkH5uIoX0Fvs79zoOSO+6mWzL0n2kX6n0wG3InbFCCOHg5M5YIYRwcBL0Qgjh4CTohRDCwUnQCyGEg5OgF0IIBydBL4QQDk6CXjgM200kOXpM33ZnphD5lgS9yNeUUmVsY7lPAXYB7ZRSW5RSu5RSC2xjDKGUGqmUOmgbw3uMbdojSqlwpdQO21dd2/TBSqmpSqmVwHe2MdGfvm2b65RSNZRSnraxxHfYBiYrMKOyivxFbpgS+ZptRNA/SB8b5Qjp46S8qLVOUEr1Jv0Oy0nAFuBJrbVWSvlqra8qpWYDU7TWm5RSpYAVWuunlFKDgZeBelrrm0qpjwBfrfUg27gj67XWTyilRgAHtdY/KKV8Sb+Ls5rWOiFPd4IQDyB/lgpHcFxrvdU2OmZFYHP6kCm4kh7w14FE4Bul1FJgiW2554GKtnkBvJVSXrbX0Vrrm7bX84FVwCCgFem34wM0In2Qth6292agFH9/qIoQhpOgF47gVgtaAau01m3unEEpVZP0wbJaA51JHznTCQi+LdBvzXv7OtFan1ZKXVJKVQZeB967bXuvaK1/y9mPI0TOkj564Ui2AnWVUo8D2EZDfMLWT++jtV4GdCN9MDGAlaSHPrb5q965wtvMJf2BKT5a6322aSuALrYRF1FKVcvRTyNEDpGgFw5Dax0L/BuYo5TaS3rwPwl4AUts09YDH9kW6QoE2U7QHgTev8/qF5L+18D826YNA0zAXtuDnYfl4McRIsfIyVghhHBw0qIXQggHJ0EvhBAOToJeCCEcnAS9EEI4OAl6IYRwcBL0Qgjh4CTohRDCwUnQCyGEg/t/QtQvDir3rrwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pdf.plot(x='reserve')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf['mint_slippage'] = (pdf['.1% mint_price']-pdf['spot_price'])/pdf['spot_price']\n",
    "pdf['withdraw_slippage'] = (pdf['spot_price']-pdf['.1% withdraw_price'])/pdf['spot_price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a19c4dac8>"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pdf.plot(x='reserve', y = ['mint_slippage', 'withdraw_slippage'])#, logy=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "#given V0 and kappa\n",
    "R = 20\n",
    "S = supply(R,kappa,V0)\n",
    "p = spot_price(R,kappa,V0)\n",
    "#sweep the transaction fraction\n",
    "TXF = np.logspace(-6, 0, num=1000)\n",
    "\n",
    "#realized price for withdrawing burning .1% of tokens\n",
    "withdraw_price2=[withdraw(S*txf, R,S, kappa, V0)[1] for txf in TXF]\n",
    "\n",
    "#realized price for depositing .1% more Xdai into the reserve\n",
    "mint_price2=[mint(R*txf, R,S, kappa, V0)[1] for txf in TXF]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.701881934929794\n"
     ]
    }
   ],
   "source": [
    "print(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf2 = pd.DataFrame({'tx_fraction':TXF, 'spot_price':p*np.ones(len(TXF)), 'mint_price':mint_price2,'withdraw_price':withdraw_price2 })"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a1dc5e9e8>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pdf2.plot(x='tx_fraction',y=['mint_price','withdraw_price','spot_price'], logx=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf2['mint_slippage'] = (pdf2['mint_price']-pdf2['spot_price'])/pdf2['spot_price']\n",
    "pdf2['withdraw_slippage'] = (pdf2['spot_price']-pdf2['withdraw_price'])/pdf2['spot_price']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Transaction size as percent of the asset Burned or Bonded')"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pdf2.plot(x='tx_fraction', y = ['mint_slippage', 'withdraw_slippage'], logx=True, logy=True)\n",
    "plt.title(\"Friction for Bond and Withdraw accounting Without Exit Tax\")\n",
    "plt.ylabel(\"Percentage Change: Realized Price Relative to Spot Price\")\n",
    "plt.xlabel(\"Transaction size as percent of the asset Burned or Bonded\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "tax = .02\n",
    "pdf2['withdraw_slippage_with_tax'] = pdf2['withdraw_slippage']+tax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Transaction size as percent of the asset Burned or Bonded')"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pdf2.plot(x='tx_fraction', y = ['mint_slippage', 'withdraw_slippage_with_tax'], logx=True, logy=True)\n",
    "plt.title(\"Friction for Bond and Withdraw accounting for Exit Tax\")\n",
    "plt.ylabel(\"Percentage Change: Realized Price Relative to Spot Price\")\n",
    "plt.xlabel(\"Transaction size as percent of the asset Burned or Bonded\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Kappa_List = [2,4,6,8]\n",
    "for kappa in Kappa_List:\n",
    "    \n",
    "    V0 = invariant(R0,S0,kappa)\n",
    "    \n",
    "    reserve = np.arange(0,100,.01)\n",
    "    supp = np.array([supply(r,kappa, V0) for r in reserve])\n",
    "    price = np.array([spot_price(r,kappa, V0) for r in reserve])\n",
    "\n",
    "    fig, ax1 = plt.subplots()\n",
    "\n",
    "    color = 'tab:red'\n",
    "    ax1.set_xlabel('Reserve (Millions of xDAI)')\n",
    "    ax1.set_ylabel('Supply (Millions of Tokens)', color=color)\n",
    "    ax1.plot(reserve, supp,'--', color=color)\n",
    "    ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "    ax2 = ax1.twinx()  # instantiate a second axes that shares the same x-axis\n",
    "\n",
    "    color = 'tab:blue'\n",
    "    ax2.set_ylabel('Price in xDAI per Token', color=color)  # we already handled the x-label with ax1\n",
    "    ax2.plot(reserve, price,'-.', color=color)\n",
    "    ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "    ax1.vlines(R0,0,supp[-1], alpha=.5)\n",
    "    ax1.text(R0+.02*reserve[-1], supp[-1], \"Initial Value R=\"+str(int(100*R0)/100)+\" mil xDAI\")\n",
    "    ax1.text(R0+.02*reserve[-1], .95*supp[-1], \"Initial Value S=\"+str(int(100*S0)/100)+\" mil Tokens\")\n",
    "    #ax1.hlines(S0,0,R0)\n",
    "\n",
    "    ax2.text(R0+.02*reserve[-1], price[3], \"Initial Value p1=\"+str(int(1000*spot_price(R0,kappa,V0))/1000))\n",
    "\n",
    "\n",
    "    plt.title('Augmented Bonding Curve with Invariant S^'+str(kappa)+'/R')\n",
    "    fig.tight_layout()  # otherwise the right y-label is slightly clipped\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Power function independent variables for analysis\n",
    "vec_d0 = np.arange(2.5,5.1,.1) #millon dai\n",
    "vec_theta = np.arange(.1,.55,.05) #unitless\n",
    "mat_R0 = np.outer(vec_d0.T, (1-vec_theta)) #million dai\n",
    "vec_p0 = np.arange(.01,.11,.01) #dai per token\n",
    "mat_S0 = np.outer(vec_d0.T, vec_p0) #milion tokens\n",
    "vec_kappa = np.arange(2,9,1) #integer\n",
    "\n",
    "mat_return_ratio = np.outer(vec_kappa.T, (1-vec_theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Hatch Return Rate p1/p0')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p0_lab = [str(int(100*p)/100) for p in vec_p0] \n",
    "th_lab = [str(int(100*th)/100) for th in vec_theta]\n",
    "k_lab = [str(k) for k in vec_kappa] \n",
    "sns.heatmap(mat_return_ratio.T,yticklabels=th_lab, xticklabels=k_lab, annot=True)\n",
    "plt.yticks(rotation=0)\n",
    "plt.xlabel('Invariant Power: Kappa')\n",
    "plt.ylabel('Funding Pool Fraction: Theta')\n",
    "plt.title('Hatch Return Rate p1/p0')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Funding Pool Funds at Launch (Millions of xDAI)')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d_lab = [str(int(100*d)/100) for d in vec_d0] \n",
    "sns.heatmap(vec_d0-mat_R0.T,yticklabels=th_lab, xticklabels=d_lab)#, annot=True)\n",
    "plt.yticks(rotation=0)\n",
    "\n",
    "plt.xlabel('Initial Fundraise: d0 (Millions of xDAI)')\n",
    "plt.ylabel('Funding Pool Fraction: Theta')\n",
    "plt.title('Funding Pool Funds at Launch (Millions of xDAI)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 15.0, 'Intial Raise d0 (Millions of xDAI)')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d_lab = [str(int(100*d)/100) for d in vec_d0] \n",
    "sns.heatmap(mat_R0.T,yticklabels=th_lab, xticklabels=d_lab)#, annot=True)\n",
    "plt.yticks(rotation=0)\n",
    "\n",
    "plt.title('Initial Reserve: R0 (Millions of xDAI)')\n",
    "plt.ylabel('Funding Pool Fraction: Theta')\n",
    "plt.xlabel('Intial Raise d0 (Millions of xDAI)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 15.0, 'Intial Raise d0 (Millions of xDAI)')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(mat_S0.T,yticklabels=p0_lab, xticklabels=d_lab)#, annot=True)\n",
    "plt.yticks(rotation=0)\n",
    "\n",
    "plt.title('Initial Supply: S0 (Millions of Tokens)')\n",
    "plt.ylabel('Hatch Sale Price: p0 (xDAI per Token)')\n",
    "plt.xlabel('Intial Raise d0 (Millions of xDAI)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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