{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Trading Against an Automated Market Maker\n",
        "\n",
        "*Last modified: November 11, 2026*\n",
        "\n",
        "This notebook builds a constant-product pool in a few lines of code,\n",
        "simulates arbitrageurs trading against it as the price of ETH moves, and\n",
        "checks that the liquidity providers’ loss matches the formula\n",
        "$\\sigma^2/8$ of Milionis et al. (2022). It then turns to a real pool,\n",
        "Uniswap’s USDC-WETH pool on Ethereum, and asks whether its fees have\n",
        "paid for that loss. The notes on [automated market\n",
        "makers](../notes/automated-market-makers.qmd) explain the background.\n",
        "\n",
        "## Packages"
      ],
      "id": "9fac0e55-b66a-4684-9883-28ae8e83308e"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "from pathlib import Path\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import requests\n",
        "import yfinance as yf\n",
        "\n",
        "DATA = Path(\"../_data\") if Path(\"../_data\").exists() else Path(\"data\")\n",
        "rng = np.random.default_rng(0)"
      ],
      "id": "81a5bec5"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## A pool in code\n",
        "\n",
        "A pool is just two numbers, its reserves of ETH and USDC. Buying ETH\n",
        "from it means taking ETH out and putting in enough USDC to keep the\n",
        "product of the reserves unchanged. The fee, 0.30% in Uniswap’s original\n",
        "pools, is charged on the USDC paid in and stays in the pool."
      ],
      "id": "d22aabf1-9410-4ede-9cb3-155ed8d58054"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "buy   1 ETH: pay        3,012 USDC, average price    3,012\n",
            "buy  10 ETH: pay       30,394 USDC, average price    3,039\n",
            "buy 100 ETH: pay      334,336 USDC, average price    3,343\n",
            "buy 300 ETH: pay    1,289,583 USDC, average price    4,299"
          ]
        }
      ],
      "source": [
        "def buy_eth(pool, eth_out, fee=0.003):\n",
        "    \"\"\"Buy eth_out ETH from the pool; return the USDC paid and the new pool.\"\"\"\n",
        "    eth, usdc = pool\n",
        "    k = eth * usdc\n",
        "    usdc_in = (k / (eth - eth_out) - usdc) / (1 - fee)\n",
        "    return usdc_in, (eth - eth_out, usdc + usdc_in)\n",
        "\n",
        "pool = (1_000.0, 3_000_000.0)       # 1,000 ETH and 3 million USDC: a price of 3,000\n",
        "for size in [1, 10, 100, 300]:\n",
        "    paid, _ = buy_eth(pool, size)\n",
        "    print(f\"buy {size:>3} ETH: pay {paid:12,.0f} USDC, average price {paid / size:8,.0f}\")"
      ],
      "id": "8faa2b7c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The bigger the trade relative to the pool, the more the average price\n",
        "exceeds the pool’s price of 3,000. This is the price impact of the\n",
        "constant-product rule.\n",
        "\n",
        "## Arbitrage against a moving price\n",
        "\n",
        "Now let the market price of ETH move, and let an arbitrageur trade with\n",
        "the pool at every step until the pool’s price equals the market price.\n",
        "With no fee, the pool’s reserves after the trade are $x = \\sqrt{k/P}$\n",
        "and $y = \\sqrt{kP}$, so we can jump straight to them.\n",
        "\n",
        "At each step, compare the pool with a portfolio that started the step\n",
        "with the same reserves and simply held them. The difference is what the\n",
        "arbitrageur took from the pool at that step: the pool sold ETH just\n",
        "after it became more valuable, or bought ETH just after it became less\n",
        "valuable. Summed over time, this is the *loss versus rebalancing* (LVR)."
      ],
      "id": "b7d26e76-c070-4ff4-b644-7de6bc38cbdd"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average LVR after one year: 8.00% of the pool\n",
            "Formula sigma^2 / 8:        8.00%"
          ]
        }
      ],
      "source": [
        "def simulate_lvr(sigma_annual, days=365, steps_per_day=24, paths=200):\n",
        "    \"\"\"Simulate ETH prices and an arbitraged constant-product pool.\n",
        "    Returns cumulative LVR as a fraction of pool value, one column per path.\"\"\"\n",
        "    dt = 1 / (365 * steps_per_day)\n",
        "    n = days * steps_per_day\n",
        "    shocks = rng.standard_normal((n, paths))\n",
        "    log_p = np.cumsum(-0.5 * sigma_annual**2 * dt + sigma_annual * np.sqrt(dt) * shocks, axis=0)\n",
        "    price = 3_000 * np.exp(np.vstack([np.zeros(paths), log_p]))\n",
        "\n",
        "    k = 1_000.0 * 3_000_000.0\n",
        "    eth, usdc = np.sqrt(k / price), np.sqrt(k * price)   # reserves after arbitrage\n",
        "    value = 2 * np.sqrt(k * price)                        # pool value\n",
        "    held = eth[:-1] * price[1:] + usdc[:-1]               # last reserves, at the new price\n",
        "    loss = (held - value[1:]) / value[1:]                 # this step's LVR, as a fraction\n",
        "    return pd.DataFrame(np.cumsum(loss, axis=0),\n",
        "                        index=np.arange(1, n + 1) / steps_per_day)\n",
        "\n",
        "sigma = 0.80\n",
        "lvr = simulate_lvr(sigma)\n",
        "print(f\"Average LVR after one year: {lvr.iloc[-1].mean():.2%} of the pool\")\n",
        "print(f\"Formula sigma^2 / 8:        {sigma**2 / 8:.2%}\")"
      ],
      "id": "12910b2e"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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Mfv/737NkyZKWbooQQoj/oGmaObsrEAiYvTIej8dcxDQ3LBUKhQinNKatDdF9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\nx5vmAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "fig, ax = plt.subplots(figsize=(7, 3.5))\n",
        "ax.plot(lvr.index, 100 * lvr.iloc[:, :50], color=\"0.85\", lw=0.5)\n",
        "ax.plot(lvr.index, 100 * lvr.mean(axis=1), lw=2, label=\"Average over 200 paths\")\n",
        "ax.plot(lvr.index, 100 * sigma**2 / 8 * lvr.index / 365, \"--\", label=r\"$\\sigma^2 t / 8$\")\n",
        "ax.set_xlabel(\"Days\")\n",
        "ax.set_ylabel(\"Cumulative LVR (% of pool)\")\n",
        "ax.legend(frameon=False)\n",
        "plt.show()"
      ],
      "id": "e2a8fb79"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The loss accumulates steadily along every path, whether the price ends\n",
        "up higher or lower, and on average it follows $\\sigma^2 t/8$. This is\n",
        "the point of the measure: it does not depend on where the price ends,\n",
        "only on how much it moves along the way.\n",
        "\n",
        "Two assumptions make the formula exact: arbitrage happens continuously,\n",
        "and it is free. With a fee, arbitrageurs trade only when the gap between\n",
        "the pool’s price and the market price is larger than the fee, so the\n",
        "pool loses somewhat less. Try it with fees in the exercises.\n",
        "\n",
        "## A real pool: Uniswap v2 USDC-WETH\n",
        "\n",
        "In a Uniswap v2 pool every liquidity provider holds the full\n",
        "constant-product curve, so every dollar in the pool earns the same fees\n",
        "and suffers the same loss. That makes it the right pool to test the\n",
        "formula. DefiLlama publishes its daily size and fee yield, free and\n",
        "without an account."
      ],
      "id": "de7b6245-698d-4325-a0d7-535bb0e1cf94"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "file = DATA / \"defillama_univ2_usdc_weth.parquet\"\n",
        "if not file.exists():\n",
        "    url = \"https://yields.llama.fi/chart/702fff16-4bfa-4c1f-8c02-e0ea0f5ecde6\"\n",
        "    rows = requests.get(url, headers={\"User-Agent\": \"FIN 4506 course notebook\"},\n",
        "                        timeout=60).json()[\"data\"]\n",
        "    DATA.mkdir(exist_ok=True)\n",
        "    pd.DataFrame(rows).to_parquet(file)\n",
        "uni = pd.read_parquet(file)\n",
        "uni.index = pd.to_datetime(uni[\"timestamp\"]).dt.tz_localize(None).dt.normalize()\n",
        "uni = uni[[\"tvlUsd\", \"apyBase\"]].rename(columns={\"tvlUsd\": \"size\", \"apyBase\": \"fee_apy\"})\n",
        "uni.tail()"
      ],
      "id": "78808155"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`fee_apy` is the fee income of the past day as an annual percentage of\n",
        "the pool’s size. Dividing by 365 gives the day’s fees as a fraction of\n",
        "the pool. For the loss, we apply the formula day by day with that day’s\n",
        "squared return of ETH, from Yahoo Finance: $r_t^2/8$."
      ],
      "id": "a86135fc-122a-43c5-805e-74df25f286a4"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "eth = yf.download(\"ETH-USD\", start=\"2022-03-01\", auto_adjust=True, progress=False)[\"Close\"].squeeze()\n",
        "daily = uni.join(np.log(eth).diff().rename(\"r\")).dropna()\n",
        "daily[\"fees\"] = daily[\"fee_apy\"] / 100 / 365\n",
        "daily[\"lvr\"] = daily[\"r\"] ** 2 / 8\n",
        "\n",
        "yearly = daily.resample(\"YE\").agg({\"fees\": \"sum\", \"lvr\": \"sum\", \"size\": \"mean\"})\n",
        "yearly[\"days\"] = daily[\"fees\"].resample(\"YE\").count()\n",
        "yearly.index = yearly.index.year.rename(\"year\")\n",
        "yearly.assign(fees=100 * yearly[\"fees\"], lvr=100 * yearly[\"lvr\"],\n",
        "              size=yearly[\"size\"] / 1e6).round(1).rename(columns={\n",
        "    \"fees\": \"fees (% of pool)\", \"lvr\": \"LVR (% of pool)\", \"size\": \"average size ($ millions)\",\n",
        "    \"days\": \"days with data\"})"
      ],
      "id": "eb3be73c"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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uhhCiCSTllrJ8fxrv/pWAwQAqFXTydyE22J2eoe70DHEn2tcZGwmbwozMEkDT0tJYt25d\ng661s7OTACpEC5WVlcXMmTPZsGEDQUFBLF++nG7dujV3s4QQZlai0bLheBYbT2Tzy4E0tNWTOa/r\nHsCLE7vg6yq/gArLkjmgMge01dPr9Wzbto1+/fphZ2fX3M1p1X777TfUajXjxo3jP//5DwcPHuSr\nr75q7mYJIa6CRqsjPqWQAyn5yrzO5ALSCyuM51UqmNgjkOt7BDCms5/M2xQN1mLngBYXF3P48GEq\nKyvp0qULPj4+lnycaKfKysoYNmwYZ8+eveg+74mJiVRVVREdHd20jWtlJk6caPw4ODiY7OzsZmyN\nEKKxiiuqWHcsk3VHs9h0MpsSjdbkvLWVip4h7ozt4sfoTr5E+9VfwUYIS7FYAF2yZAkPPvggRUVF\nWFtbo1KpePHFF3nuuecs9ch2a+fOnURGRjZrwM/Pz+f06dP07du32dpwKb///juFhYXGv3979+4l\nIiICT0/PZm5Zy5ScnMyHH37I8uXL65xLSkpCr9cTEREBQElJCadOncLR0ZEOHTpgbS1b6wnR1AwG\nA5lFGvYk5bHzTB6/HzpHXq06nB39nOkT5kmvEHd6hboT4e0kczpFs7LIEHxaWhqdOnVi4cKFTJs2\nDWtra9avX8/UqVNZtmwZI0eONPcjr0hbG4L39vZm4cKF3HXXXc3WhpUrV/Lwww+TmJjY5M8uKSnB\nxcXlkj2gF4qKimLBggXcdNNNFm1ba5ScnMzdd9/N4sWL6/3zvP7665k8eTLTp0/n448/5umnnyYi\nIoK8vDwcHBxYvny51PkVwoKKK6o4mVnM8YxiTmQUc/xcMcfOFVF8QS9nbIg7N/cMZHRnP0I8HZup\ntaIta3FD8Nu3b2f06NHMmjXLeGzs2LE8+uijrF+/vtkDaHuUmppKfn4+HTt2rDNPsqYHy9fXl8DA\nQJNzRUVFnD59msDAQPz86i8iXF5eztGjR9FoNGzZsgWAbt264e7ubjyfkJCAj48PAQEBl2znmTNn\nSE9PR6VSERQURFhYGCrV+flIycnJlJeX07FjR86cOYNOpzNpc35+PikpKcTExJh8nbWH4I8cOUJF\nRQXHjh3D29sbDw8PunbtyokTJ3BwcCAwMJCEhAScnJwICgpi+/btADg4ONCxY8d6N1soLi7mzJkz\nREVFUVVVRUJCAv369TO5Jj8/n6SkJCIjI3F1dTUeP3fuHLm5uSaLfU6ePImdnR1hYWEA7N69m+jo\naGxtbTlx4gSRkZG4ubld8nt3OVlZWaSnpxMbG8vx48eprKzEzc2Nm2++mQ8//BBnZ2eKiopM2lpW\nVsbGjRv54osvKCgo4OGHH+abb77htttuQ6/XM3XqVP71r3/x559/XlFbhBD10+sN7E7M4++EbI6f\nU0JnWkH9NTld7W2IDXFnQIQnAyK96BPqIfM5RYtlkQBqY2NDZWVlneOVlZWySKSJZWZmMmXKFI4e\nPYqvry/nzp1j0aJFTJ48GYClS5dy3333ERoaSlFREb169eLbb7/F0dGR//3vfzz++ON06NCB7Oxs\nRowYwRdffIFarTZ5RnZ2Nl9++SX5+fn83//9HwD/+c9/GDBggPEeYWFhpKWlMWjQIL799ltjOL3Q\nL7/8wrJlyzAYDJw9e5bg4GB+/fVX/P39Afjkk09Yt24dZWVl2NjYcPPNN/P4448D8Pzzz7Nhwwac\nnZ3Jzc1l2bJlDB8+HID333+fnJwcFi9ezBdffEFubi5ff/01v//+OwMHDmTBggW8+OKLFBQUkJCQ\ngKenJw8++CBTpkwxfk1lZWWcPHmS1157jUceecTY5i+//JJ//OMfREZGGv+ctmzZQmpqKgClpaXc\nf//9/P7770RERHD69Gmef/55nnrqKQCWLVvGihUrTCpJvPTSSwQHB/P6668DcPPNNxMXF8emTZsI\nCwvjvffe48yZMxf93jXEokWLWL58OXZ2dpSXlzNhwgTCw8NJSUkxzgUdPnw4y5YtM37OunXriI2N\nxcfHh6SkJHQ6Hf379wfAysqKvn378tNPPzXo+UKIi0vJK2PJ7mRW7E+vEzhtbayI9nUmxs+FGH/l\nrWugG97Otia/sAvRklkkgA4ePJgZM2bwxhtvMH36dOzs7FizZg0ffPABq1evtsQjLWtuM+xdO7fQ\nLLd54oknsLGxISUlBXt7e7777jumT5/OwIEDCQkJ4c033+S1117jwQcfBJRV0IWFhTg6OvLaa6+x\naNEibr/9dkCZ11teXl4ngIaGhvLGG2/w8MMPG3tAAY4dO8YDDzzAypUrGTduHMXFxYwcOZIXXniB\n//73v/W29/HHHzcGSp1Ox8yZM3nppZf48MMPjdfs37+fHTt20KtXL0DpwQWlpzUpKQkbGxteffVV\npk2bRkJCQp1fehYsWMCKFSt49dVX6wzB79+/n7179xIcHGw8VvtrOnz4MEOHDuWGG24gLCyM1NRU\nHnjgAZYvX8748eMpKSmp08P/73//m9TUVJKTk41TBfr27cvw4cON4a0h0tPTOXXqlHGY44EHHrjo\n964h9u7dS2pqKuvXrzfpfb3//vsv+jm//fYb119/PQBhYWHMmDGDhx56iH/+85/k5uayaNEi3nnn\nnQZ/TUKI8wwGAwdTC/lyWyK/HUw3FoMPdLPn+thAYoPdifF3IdzLUeZvilbPIn+DfX19+f7773n/\n/fcJCAjA09OT++67jzfeeIOBAwda4pHiIv744w8ef/xxY1HxO+64A19fXzZs2AAoQ+WrV6/mwIED\n6HQ6Jk6caBwm79atGytXruTw4cPo9Xpuu+02k+HYy1m9ejWxsbGMGzcOABcXFx5++GF+//33S35e\naWkphw4dYseOHfTo0YNt27aZnB8+fLgxfNZWE7YB/vWvf5Gens7hw4cb3F6ASZMmmYTPGsnJyezc\nuZOCggJCQkLYvXs3ABs2bCAyMpLx48cD4OzszAMPPGDyuT/++CNjxowhPj6eLVu2kJaWRs+ePRtc\nO7fGfffdZzLH5lLfu4bYu3cv8+fPb3CdT4PBwO+//26yUv7666/n+PHjPPvss7zwwgtERkbK/E8h\nroDBYCCtoJyvtydy7XtbuPGDrfy8P40qnYGJsYEsuW8gW54ZxXPXdua6HgFESUF40UZYbBX8hAkT\nSEpKIjExkcrKSiIjI7G1tbXU4yzLTL2RTU2n01FcXIyXl5fJcU9PT/Lz8wH47LPP+P7773nnnXfY\nt28fffv25b///S/Ozs788MMPfPPNN7z++uscOHCAYcOGsXDhwgZPoygoKLjks+uzYMECXn75ZYKD\ng3Fzc6O4uJicnJw696hP7eO2trY4Ojpe8lmXuwco8zMnTpxIcnIyoaGh2Nvbk5KSQmZmpvFrvHA6\ngYeHh8nr7OxsfvzxR1atWmVy/FI9lfWtDbywbZf63l1OVlYWqamp3HDDDZe9tsbevXuxs7MzBtZd\nu3YxdepU9uzZQ8+ePQF44YUXGDduHKdPn27wfYVob6p0eo6fK2bVkXP8tDeVzCKN8ZyHo5pJvYO5\ne1A4oV6ycEi0XRatA1paWkpmZiaVlZV4eXlJHdAmZm1tTYcOHdi1axeDBg0ClIUwJ0+eJCYmBgCN\nRsO0adOYNm0aer2ewYMHs2jRIp588km0Wi2zZs1i1qxZaLVaevTowTfffGOyuKyGWq1Gp9OZHIuJ\nieHjjz9Go9EYQ+uOHTuMz75QRUUFzz77LH///bexvZ9//nmDS3ft3r2bzp07A8oinuLiYjp27Fjv\ntfW1tz6ffPIJHh4e7N69G5VKhV6vJyYmxhgQO3bsyLFjxygvLzf2Tu7Zs8fkHl27dmXGjBk8/PDD\nJsfLysoAcHNzIy8vz+TciRMnCAkJuWTbLvW902g07N69m549e9YbSGumGVy4sEyr1ZKcnExkZGSd\nz/ntt99Mej9PnDiBi4sLsbGxxmNxcXG8+uqrJt9zIQQUlFWy6O8z7D6bx6G0QjRavfGcm4OaPmEe\n3NwriGu6+mFnI6XMRNsndUDbiJMnT5rMVbSysmLw4ME8++yzPPbYY6jVakJDQ/nPf/5Dly5duOaa\nawAYM2YM119/PX379iUjI4OTJ08aS+8MGjSIadOm0bNnTxITE0lJSblomaOoqCgyMzNZsmQJwcHB\ndOvWjVtuuYW5c+cyZcoU7r//fo4dO8bChQtZsmRJvfewtbXF09OT7777zrjgZ/78+Q3+M3jhhRfQ\n6/W4u7szb948pk6dSmhoaL3XRkdHs2zZMry9vfH29r7osLGfnx/Hjx/np59+wtnZmS+//JKUlBTj\n+bFjxxIaGsqUKVN48MEHOXHiBIsWLTLp3Xz99deZPHkyJSUl9OnTh9TUVBYvXsy8efMYMWIEw4YN\nY/bs2bzxxhv07NmT5cuXc/To0ctuWXup7116ejrDhg1j37599U5X2Lt3L3369Klz/Pvvv+fXX39l\nzpw5dOvWzTilAZQAWrMoCjDOdZ05cyZ33HEHhYWFvPTSS1x77bUSPoUAcks0HDtXzN8J2azYn0ZW\n8fmezghvJ3qFunNH/1D6hHnI4iHR7kgd0DZQB/T666+noKDA5JidnR1//fUXoBRh/+6778jPz6df\nv3489dRTxl6xvLw8Fi5cyK5du3B1dWXy5MnGFfKZmZm888477N+/H09PT+644w6THrALff755/z8\n888UFhayYMECBgwYQH5+Pm+++SYHDhzAx8eHmTNnXvL7f+DAAd566y3OnTtHp06dmDBhAp999hm/\n/PILAJ9++ilpaWnMnTvX+Dnl5eWMHTuW119/na+//prk5GQGDx7MM888Y5z28cEHH5gUoj916hTz\n5883LghasGABc+fOJSgoiHvvvdd4b71ez4IFC1i/fj1qtZpJkyZx4MAB4uLiuOWWW4x/hi+//DLH\njx+nc+fOREdH884773Dy5EnjfQ4fPsyHH37I6dOnCQ4OZtasWQwePNh4fu3atXz88ccYDAYmTpxI\namoqPj4+xvmkt9xyC8888wwDBgwwfs6lvncrVqzg+eef5+DBg1hZ1Z0v9uKLLxISEsLs2bONxwoL\nC+ncuTO2trZ4eHiwY8cOY5BMS0ujc+fO5OTkmEylOX78OB988AEnT57EwcGBwYMH849//KNB0wCE\naGsOpBSw5kgGh9IKOZFRbBI4AXoEu/HP0dH0DvXAw6mVTkkToparyVMWCaA//fQT33zzDStWrDA5\nPnfuXHQ6HS+//LK5H3lF2loAFc3rwuHmf/7znyQlJdX5+9+U3n//fTp06MCECROu6PPuu+8+Hnjg\nAXr37m1yfNGiRaxdu1ZKLAlxgcLyKv4+qfRw/nU8y+Sck601nQJcjVte9g/3lLqcok1pcYXopQ6o\naE/mzZuHs7MzvXv3ZseOHXzyySf8+uuvzdqmC+ebNtT+/ftN5nTWSEtLa9adtoRoSTRaHfEphXy5\nPZE/Dp2jphvHQW3N1H4hDO7gRYy/CyEejhI4hbgIi/SAZmVl0bFjR5599lmTOqD33Xcfq1evblAp\nJq1Wy6effsqKFSsoKytjwIABPPPMMyYLmf7880/effddcnJyGDRoEPPmzWvQ3t7SAyrMqaSkhAUL\nFrBz5078/f259957TYbXW5Pw8HB+/PFHOnbsiJtbM9S/FaKFOpNdwg+7UziQUsDB1ELKq84vYuwd\n6s7IGF+m9g/B18W+GVspRNNqcUPwoITD++67z7gbjKurK2+88UadGokXM2fOHDQaDddeey0qlYr5\n8+eTm5vL/v37Adi0aRPjxo3jzTffpEePHrzyyiuUlZWxdevWy07mlgAqRP2ee+45Vq9ezaefflpn\nGF6I9ia7WMM3O5JYeTCd09mlJueifJ3pHuTGQyOjiPKVOc+ifWqRARSUBRyNrQNaVVVlsuPOwYMH\niY2NJS0tjcDAQCZOnIiXlxeLFy8GlAUzQUFBrF+/nri4uEveWwKoEEKIi0nNL2PhugR+PZBOpU4p\nl2RrY8X4rv5c1yOAXiHu+LpKT6cQLW4OaI1Vq1axZcsWKisr6dWrF1OnTjUp63IpF273uG7dOkJC\nQoxD8Dt37uSNN94wnvfz8yMmJoadO3fWCaBVVVVotVrj6/Jy0311hRBCCIDvdibz8sqjlFfpUKlg\nbBc/ZgwOp1+4J7Y2sgOREOZisQB6++238/vvvzN69GhsbW35/vvvWbhwIX///XeDU/L+/fuZNm0a\neXl5qNVq/vjjD2MwzcvLw9vb2+R6Ly+vOgW9AebPn8+8efOu/osSQgjR5vx9Mpsvtp6loLyK/ckF\nAFzb3Z+nx3Ui3NupeRsnRBtlkQC6ZcsWNm3axMmTJ/H39weUXW5GjBjB559/zkMPPdSg+8TExLBk\nyRLy8vL49NNPuemmm9izZw/u7u7Y29tTWmo6J6e0tNS453ltc+bM4ZlnnjG+Li8vr7NFpBBCiPYh\nv7SS7WdyOZJeyK/x6aTkmY6KPTo6mifG1r+LmhDCPCwSQJOTkxk1apQxfALY29szadIkkpKSGnwf\nR0dH477TQ4cOxdnZmfXr13PLLbfQuXNnjh49ary2srKS06dPG7dirE2tVtcZ0hdCCNG+fLMjiY82\nniatwDRwOtvZcH9cJP0iPPFwtCXG36WZWihE+2GRCS29e/dm//79aDSmu0Bs3bqVfv36Neger732\nmsnuPsuWLUOj0RgD5p133snnn39OWloaAO+++y7W1tZXXHhbCCFE23cwtYDnVxwmraAcB7U1AyI8\nmTU0gm9nDyD+xWt4ZHQ0AyO9JHwK0UQs0gOq0+lwdHSkX79+TJo0CVtbW9auXcvx48cZM2YM77//\nPgDdunVjxIgR9d4jMDCQbt26YWtrS3FxMQ4ODixevNgYQB9++GHi4+Pp0KEDHh4eGAwGfvjhB1xc\n5D8PIYQQ5+n0Bp7+6SAAdw0M5aUbukmBeCGamUXKMP3666+8/fbbl73uhhtu4IknnrjkNUlJSTg4\nOODj41Nvfc/c3Fzy8/MJDw9v8Ap7KcMkhBDtx8qD6Tz83X68nGxZ/+QI3BxlSpYQ5tBi64C2VBJA\nhRCi7ajU6vnj0DkyiypIzS/n2LkitHoDOr2BzKIKsoqV6WCPjIriyWtimrm1QrQdLbYOqBBCCGFJ\ner2BGV/sYtvp3Ite42xnw3XdA3hgeIcmbJkQ4lIkgAohhGiV9iblM2f5IY5nFONka82UfiF4ONrS\nK9QdJzsbbKxUuDmoCXR3QG0tReSFaEkkgAohhGhV9HoDX+9I4tU/jqHR6nF3VPPWrbGM7eLX3E0T\nQjSQBFAhhBCthl5v4OllB/lpbyoAU/oG89KN3bBXWzdzy4QQV8IsAfSbb77hyJEjvPbaa4CyE1Ja\nWhpTp041x+2FEEK0c0UVVWw/ncvX25PYcioHOxsrnh7fiXuGhNdbIUUI0bKZJYBaW1tz6tQp4+vD\nhw9z4MABCaBCCCEaLT6lgD8PZ7D9dA6H0grRV9dssbZS8c7UnlzbPaB5GyiEaDSzlGHKzMwkNjaW\n6OhoAgICOHv2LPn5+fTt27fOtWPHjmXWrFlX+8irImWYhBCi5TIYDPz7lyN8veP81s02Vip6hrgz\nvKMPk/oEE+gu/3cL0dyavQyTn58fR48e5ddffyUlJYWSkhL0ej1RUVF1rvXx8THHI4UQQrRR+5Lz\n+XpHEioVzBgczvCOPvQL98TJTpYtCNFWmO1fs6enJzNmzABg/fr1JCUlMXPmTHPdXgghRDtwMrOY\n/6w5CcAtvYJ5cWLXZm6REMISLPLr5KhRowAoLi7m8OHDVFZW0qVLF+n9FEIIUUdFlY5fD6Tz095U\ndiXmGY9LWSUh2i6LjWcsWbKEBx98kKKiIqytrVGpVLz44os899xzlnqkEEKIVqagrJJ7Fu9mX3IB\nALY2VkzqHcR13QMZEuXVvI0TQliMRQJoWloa9957LwsXLmTatGlYW1uzfv16pk6dyqBBgxg5cqQl\nHiuEEKKVKCyr4sNNp/hmexKllTr8XO148poYxnfzx9Ve3dzNE6J1qSyDnR9B0jYoTIXON8CoOc3d\nqkuySADdvn07o0ePNlntPnbsWB599FHWr18vAVQIIdqpI+mFfL09iRUH0qio0gMwIMKTBZNjCfF0\nbObWCdHMygsg/yzoqkCvVd50lZB1TAmW5flQUQjaCtBqoKoMCpKV47X5dWuW5l8JiwRQGxsbKisr\n6xyvrKzEzs7OEo8UQgjRAml1enacyePvhGw2ncjmRGax8dzQKG/+OSaafuGezdhCIZpI3hkozgRN\nsRIiy3KgNBtKc6AsVzmfdbTx93cNhkH/gIjh4BpovnZbiEUC6ODBg5kxYwZvvPEG06dPx87OjjVr\n1vDBBx+wevVqSzxSCCFEC7MvOZ9/LY3nTE6p8ZiLnQ2T+gQzbVAYHXycm7F1QjSRyjL44S44/VfD\nrveKBns3sFaDlQ1YWYNLIPh1BQcP5ZzaAWzsQW0PTj7g4AlqR7CysuzXYkYWCaC+vr58//333Hff\nffzf//0fAK6urrzxxhsMHDjQEo8UQgjRQpzMLObnfWl8uS2R8iodoZ6OTOjuz/BoH/qEe2BnI/u2\nizZKpwWdRhke11Uq7+OXnA+fwf3BzgXsXZXg6OgNTjVvPuDbWQmZ7YBZdkK6GL1eT2JiIpWVlURG\nRmJra2upR10R2QlJCCHMy2AwsP54Fsv2pfLHoQzj8Wu6+PH+Hb2xtWk9PTNC1FFZBqm7laFybQUU\npUHGIagsVd7KCyA3QZmzeTH974Nr32qyJjeFZt8J6WKsrKyIjIy05COEEEI0o4oqHX8cOsdX25M4\nkFIA1JRSCubmXkH0DfPAykrVvI0U4nKKMyFhjTIvsywPSrKgJBMKU6AwDbTlDbuPygqs7cDGVnlv\nbat87OQDA/9h2a+hlZF9zYQQQlwRvd5AfGoBq45k8OOeVPJKlUWnHo5qpg0K57Z+IbJXu2g9jqyA\nH6df+horNXhHK282DsrcS9+u4BEOtk7Km3e08l40iARQIYQQDVKi0fL++lOs2J9GRlGF8XjXQFfu\nGhjGjT0DcbSVHyuiiWlKoDhDWVmuKVTeVxRVvy46P0xeUX2uskT5nMoSZei8sroyg5UaBj6gLOhx\n9gUnX3ALBvcQsHUGlfTkm5P8TyGEEOKSUvLKWLE/je92JXOuUAmeAW72jOvqz3U9Augb5oFKfjgL\nSzMYlDmYxRlQkASZRyEjHhLWKvMyG8vaFqLGwg3vKYuBRJOweADdunUrn3/+ORqNhokTJzJ16lRL\nP1IIIUQjGQwGUvPLOZhayNFzhWw5lcuh1AL01ctVuwW5MndiV/pI6BSWptfBsV/h9HrIPQ05CVCa\nVf+1Dp7gEQZ2rkqZIntXsHdXXts6KUPm9u7Vx5yVHk07Z1BXD5/byiYITc2iAfTEiRPcfPPNvPDC\nCzg7O/Pcc89ha2vLzTffbMnHCiGEaACDwcC5wgoOphZyKK2g+n0hBWVVJteprVVM7B7ATb2CGB7t\nI4uKhPmV5kL6Pji6AjIOKwuAis/Vvc7WWRke94oGB3cIHQj+PSCojwyRtzJmDaBbtmzBx8eHmJgY\nAHbv3s0111zDI488AkBOTg7btm2TACqEEM0gq7iCQ6mFxKcWcii1gENpheSU1N21zsvJlu7BbnQL\ndKNzgCvDY3xwtpMZW8KMqsohbR+U50HSdtjxQf3XuQZD91shbAh4RoJnhFKYXbR6Zv0fxd3dncmT\nJzNt2jSeeOIJBgwYwBNPPMHChQtxdnbmww8/5N133zXnI4UQQtQjt0TDobRCDqUWcrD6fe2FQzXc\nHNT0CHaje5Cb8j7YnUA3exleF+ZXnAl/Pg35icqWk7oLfvmxc4Ned0LUaPCOUXo6bWT77rbK7IXo\ny8vLmTNnDjt27OCzzz6jsLCQL774gsrKSiZOnMikSZPM+bhGt1EK0Qsh2orCsioOpRVyMK1ACZyp\nhaQV1K1b6GJnQzdj0HSjR5A7IZ4OEjZF01g3F7a8U/1CBf7dwD1M2XLSvwcMekgCZyvTogrROzg4\n8Pbbb7N9+3Zuv/12pk6dyocffoiNjQzfCCGEuRgMBo6dK+bjTaf57WA6F3YlOKit6RbkSvcgd2Pg\njPBykvmbovkc/115P/J56DcLHD2btz2iWVkkFebn5xMREcHOnTt58cUXGTx4MJ9++imxsbGWeJwQ\nQrQbp7KK+WjjGTadzCanRGM83iPYjV4h7nQPVgJnBx9nrCVsipZAUwLf3wY5JwGVUmvTzqW5WyWa\nmVkDqE6n4/bbb2fVqlXY2dkRERHBn3/+ya233srMmTO54YYbmDNnDmq12pyPFUKIdiE+pYDJi7ZT\nqdUD4O9qz+AoL27sGcTwjj7N3DohailMheN/QFEqHPpJ2Ttd7QRDHpXwKQAzB9A//viD5ORksrOz\nsbW1ZdasWXz44Ye88MIL7Nixg5dffpnnn3+eN954w5yPFUKIduGPw+eo1OoZGePDc9d2JsrXWeZv\niqaj1ym1OItSQa8HvRYMuuq906v3TU/brywyqtldqIaDJ9y9AgJkJFQozBpAtVot9vb2qNVqVCoV\njo6OaLVaAGxtbXn55ZcpKysz5yOFEKLdyClWVg2P7+ZPtJ/0IgkLMhiUIvAZhyH7OGQeUXYf0msb\nfo/g/tBhlFKjMyJOKQYvRDWzBtDrrruODz74gJCQEOzt7bGxsWHDhg0m1zg6ym4DQgjRGKn5yi/w\n3s6yUliYkU6rFH1P3KwMnZflKsEzaUvda518wSdGWa1uZQMqa2XXIRd/Zd90OzcIGwxOPmBj2/Rf\ni2g1zBpAbW1tWbduHWfOnEGj0RAdHS2r34UQohH0egOnskuITylgX3IBO87kcjanFIAANykfJ65C\nZRmc3aSEzORtkLSt/r3U7Vyhz3Tw6w5+XcErSnoxhdmYJR3q9XqsrKyMryMjI6/oeiGEEFBWqeX3\ng+fYeDKb7adzySs1LdTtbGfDrX2C6Rwgw+/iMjTFkH5A6c2secs8ovRwpu8Dg970eicfpSZn+FBw\n9gNHL4gYBq6BzdJ80faZJYB+8cUXrF+/nn/+85/079//otclJCTw0UcfYWVlxYIFC8zxaCGEaNUK\ny6o4kVnMl9sS2XAii7JKnfFcgJs9vULd6RHszsBIL7oFumJjLb+8i8sozYH/9oGKgotf4xIAnSdC\nYG9lnqaLX5M1TwgwUwCdPn06Go2GSZMmoVarGTJkCNHR0bi6ulJaWkpSUhI7d+4kOTmZhx9+mKee\nesocjxVCiFYnraCcXw+kcyAlnwMpBWQWaUzOxwa7cUvvYOI6+hDu5Sir3EXD6HVQlK6sQP/lofPh\ns9P1Sm+moxe4BYFvV2XOpncMWMsUOdF8zLoVp06nY+3ataxdu5bDhw+Tn5+Ps7MzMTExjBgxghtu\nuKHBWzUdOXKEV155hQ0bNmBtbc2oUaN48803CQgIMF7z3nvv8fbbb5OTk8OgQYP48MMPiY6Ovuy9\nZStOIURT0er0HM8oZufZPHadzWXdsSx0+vP/7TraWhPgZk//CC9mDY0gyte5GVsrWjSDQRlazzqm\nBMyqcsg8DCf+VFaqX7hCfdL/oPutzdJU0T5cTZ4y+17w5jJ58mQmT57MiBEjKC4uZvbs2Wi1WjZv\n3gzA0qVLmT17Nj/99BM9evRgzpw5/P333xw9evSyhe4lgAohLEWr03MorZA/Dp1jw4lsknPLqNSZ\nzrfrG+bBbf1D6RniTqS3bI8p6lGYBn/Ng4xDUFGkBE9NEXCJH9nOfso8Tp8YiJkAna5rsuaK9qlN\nBtAL/f7779xwww1oNBpsbGwYNWoU3bp147333gOgqKgIX19ffv75Z6699tpL3ksCqBDC3Eo0Wjae\nyGLB6hMk5prWOw71dKR/hCf9wz3pH+FJmAyti0spTIV3utZ/Tu2oBE2vDqB2AHs3CBmgzOd08Gja\ndop272ryVKuZALJ582a6dOliLOu0f/9+7rnnHuN5V1dXYmJiOHDgQJ0AWlVVZSyID8ofmBBCXI3k\n3DJ2nMklPrWA+NQCjqYXUTOyHuTuwMhOPtzYM4guAa442bWa/2pFc9Hr4eSfkLYXDi87f/y278Cv\nmzJv09ZF5m2KNqNV/E3+448/+O9//8uff/5pPFZUVISbm5vJde7u7hQVFdX5/Pnz5zNv3jyLt1MI\n0bYl55bx1/FMVhxIJz6lwOScjZWKjn7O3DEglNv7h6KW1ericnRaSNkJx36DvV+Y1uK0c4O7lyu7\nCAnRBrX4ALpy5UruuusulixZQlxcnPG4i4sLhYWFJtcWFBTg4lK3Pt6cOXN45plnjK/Ly8vx8vKy\nXKOFEG2GTm9g8bZElu1N5ei587/gutjbMKSDN33CPOgW5EZsiBuOti3+v1TR1AwG0FVC8nY4W73T\nUEWhUpcz56RpqSR7N4i9A4L7QvQ1Sq+nEG2URf+3TEtLY9++fXh7e9OzZ0+qqqpwdW34P6ilS5dy\n33338eOPPzJ27FiTc7Gxsezdu5e77roLgJKSEhISEoiNja1zH7VafdmFSUIIcaHsYg2P/bCfrady\nAaUQ/MhOvoyM8WFCtwAcbK2buYWiRakqh/ICKM2ClF1QkgUn/lBWql+Msz90HAddboCI4WAtP6tE\n+2CxAPruu+8yZ84cnJycuPnmmwkLC2P06NHs3bu3QfvBL168mCeeeILffvuNYcOG1Tl/33338dBD\nD3HzzTcTGxvLs88+i5+fX52gKoQQjZFbouHmD7eSml+Ot7MtL93YjdGdfbGzkdApUHo2s09A/lmo\nKlN2Gdq5CCpL6r/ewRO63qQUfnf0VBYMufiDezjIzoCiHbJIAD158iSvvPIKe/fuZcOGDRw4cIDA\nwEDi4uL46quveOCBBy57j2effZaCggJGjhxpcjwpKYmgoCDuvPNOUlNTmTx5Mnl5eQwYMIDff/8d\nOzs7S3xJQoh24nR2CYu3JrJifxrFGi3hXo78cP8g/FxlD+x2S1Os9GZWFCq7DCWshuQd9fds2jiA\nawC4h0Jwf3ALhu6TwfbyHS9CtCcWCaB79uxh3LhxxMTEsGHDBuPxmJgYTpw40aB7pKamUl+FqJpV\n8ADPPPOMydxOIYRorMScUr7ekcRX2xOp0in/9wyK9OKVm7tJ+GxPdFVw6EdIWANF56A0W+nlvHDv\ndFAWCoX0B1snsHOGmOuU+ptSYkuIy7JIAPX09OTcuXN1jp8+fZqoqKgG3cPaWoa5hBCWdyi1kEV/\nn+aPQ+eMZZRu7RPMrKERdA6QRSDtzh9PKSvSTaiUHk179+qh8wCIGq0sFHJwb4ZGCtH6WSSADhky\nhNmzZ/POO++g0Wioqqril19+YenSpezatcsSjxRCiCv2wYZTvLVaGZWxsVJxS+8g7h4URo9g9+Zt\nmGge+Ynnw2efmdBtEjj5KHuo29WtsCKEaDyLBFAXFxeWLVvG9OnTjUPuv/zyC59++ikRERGWeKQQ\nQlyRH/ek8J81J1CpYPbQCGYOiSDQXXZGa1dKsqAoXam/qa2AtH3K8ZCBMHFhszZNiLbOYqvgBwwY\nwPHjx0lJSaGsrIyoqCgZVhdCNDuDwcBX25N48dcjAPxzdDSPj+3YzK0STaIsD9L3QUEKpO6GA9/W\nf51v56ZtlxDtkEUCaHJyMq6urri7uxMSEmKJRwghxBXTaHX8e8URftiTAsCcaztzb1xkM7dKNIn8\nJPhkOJTn1z0XMgCsbZU3O2cYcPlKLUKIq2ORALpu3ToeeughbrnlFu655x5GjRqFSlYFCiGaUXml\njrv+t5O9SfnY2VjxxqQe3NQrqLmbJZqCphh+nKGETwcPZbW6s6+ygKjvLCV0CiGalEUC6D333EOX\nLl1YvHgxkyZNwt3dnRkzZjBjxgzCw8Mt8UghhLiorOIK5v12lL1J+QS62fPJ3X3pFuTW3M0SlqYp\nhrS9sPxBKE5Xjk1bAYE9m7NVQghAZaiv2KYZlZeXs3z5cr744gs2bNjA3Llzef755y35yAa1ydHR\nkbKyMhwcZNGBEG1ViUbLb/HpzP/9GCUaLbbWVvz04CBZ5d7WFGcqe62XZkP6fmVXorJcZd91av2I\nG/YkjP53szVTiLbmavKURfeCB3BwcKBXr17Ex8ezf/9+MjMzLf1IIUQ7ZTAYOJNTypaEHNYdy2TH\nmVxjUflRnXx58pqOdA2Uns82I+sYJG6BdXPr3wLTSq0sKAruCwE9ode0pm6hEOIiLBZACwoK+OGH\nH/jiiy/Yt28f1113HZ9//jnXXnutpR4phGhH9HoDqfnlHMso4vi5Yo6dK2Jvcj7ZxRrjNVYq6BPm\nwW39Qri1T7DMRW9LMg7Dx0POv/YIhw6jlLqd4cPANRDcQsDGttmaKIS4OIsE0F9++YXbbruN6Oho\nZsyYwa+//oqvr68lHiWEaCfySys5mFbIodQCDqQUsONMHiUabZ3rvJxsGRzlTVy0N2M6++HhJAGk\nTTr7t/LeO0YpGD/4YWVLTCFEq2CRABoWFsbmzZvp27evJW4vhGgDiiuq2J9cQIlGi05vQG8woNMb\nan0MOoMBvd7AicxiluxKNm6VWcPHxY7OAa509nehU4AL3YPc6eDjJD2dbZmmGLa8A5v/o7we/DD0\nvrt52ySEuGIWCaA9e/a0xG2FEK1cUUUVm05ks+ZoJquPZFCp1Tf4c62tVPQLc6dbkBvdg9wYGOkl\nOxe1dZVlymKivDOQmwDFGbD7s/O1PG2dIUamdQnRGpktgMbHx5Odnc2YMWOIj49n7dq19V7Xs2dP\nxowZY67HCiFauIoqHdtP57LuWCYr9qdRWqkDQKWCXqHu+LrYYW2lwkqlwtpKhbVKhZWVChsr5b21\nSoWdjRU39w6SBURtncGgBM5jv8GODyHn5MWvjXsa+t4DTt5N1z4hhNmYLYCmpaVx+vRpxowZQ1pa\nGuvWrav3Ojs7OwmgQrQDp7NL+G5nMkv3pFBccX6uZvcgN26IDWRcV39CvRybsYWiWRkMSk/m0V/g\nxJ/KFpnl+aC/YF6vSyC4+IF/D2VhkbMf+HWDkH7N024hhFlYvA5oSyR1QIUwP73ewNFzRaw5ksGq\nIxmczDxfFqeTvwsTugUwOMqLvmEeMkezPTEYlKHz3ARlSL2iAA7+AEnbQVte93pbFwiIhYg4GPoY\n2Ng1dYuFEA3U4uqA/vDDDxw7doy5c+c26LgQovUxGAzkllayNymfX+PT2X46l7zSSuN5V3sbxnfz\nZ9rAcLoHy9B5u1FZBqm7oCxP6d08s1EJnfVRO4FXB+g7E6LGKL2bEjiFaBcsEkDz8/PJyMioczwr\nK4v8/HxLPFIIYQFanZ68skoyCzUk5ZWSlFtGcm4ZZ3NKScgqJr+syuR6f1d7Rnf2ZXw3fwZGeqG2\ntmqmlosmk58I5+KVXs6zf0PCWtBpTK+xcwWvKGW+pq0zuIdAl5sgqHdztFgI0QKYNYAeOnSIv/76\ni23btpGWlsbChQuN56qqqvjqq6/4xz/+Yc5HCiHMILtYw+H0Qo6dK+Jsdilnc0pJyisjp0TDpSbp\nuNjZEO3nzLiu/lzT1Z9wL0cZXm8Pqsph16dwZgOcXl/3vGsQBPUBZ1/oO0vZjUj+XgghajFrAE1K\nSmLlypWkpaVRXFzMypUrjefs7e256aabmDlzpjkfKYRohOxiDdtO57D1VA5bT+WSVlDPXDyUzODp\nZIuvix2hno6EeTkS6uVEhJcT0X7O+LrYSeBsD7SVcOhHOP47pOxQVqrXZu8GMdeBbycIG6KET/l7\nIYS4BIssQtq8eTMpKSnccccd5r61WcgiJNEencku4Yutiew6m8eJzGKTc852NnQJdKVroCsdfJyJ\n8HYi3NsJPxc7bGQYvX0yGKAwFbKOwprnTUsiqazBJwY6Xa9sfxnYC9T2zddWIUSzaHGLkIYNG2aJ\n2wohGqC4ooqDqYWcyCjmdHYJSbllJOaWkpp/vpfTXm1Fv3BPhkZ5MyTKmy4BrlhZSY9Vu1KYCtnH\nlZ2Fqsoh6xjknwVNCRSlQ0ESaCtMP2fk89D9VnAPBSvr5mm3EKJNsEgABWU4/o033iA+Pp68vDxq\nOlpvu+02WQUvhBnp9QZOZhWz8UQ2G45nsScpH92Fe1YCtjZWXN8jgNv7h9Ij2A07GwkQbVrWMaXX\nsiQLSjKr37LOvy9Ku/w9HDyVVepuwUpPp2x5KYQwE4sE0OLiYuLi4pg4cSJdunQhOTmZvn378sUX\nX3DddddZ4pFCtHlanZ7kvDJOZysr0I+dK+ZMdglnskspr9IZr7OxUhEb4l5rON2RcC8ngj0csbWR\n4fQ2yWCAzCPKPM2idMg4qPRuXoqVGkL6g6MXqB3BzkVZle7kCy7+4BGmHBNCCAuwSAD9+++/CQ8P\n5/3332fRokVYWVkxf/58MjIyOHToEP36yQ4Wov0yGAxo9QY0Wj2VWj0arQ5NlR6NVk9RRRXHM4rJ\nLqqgrFJHWZWO4gotp7JKOJ1VQqWu/r3T/VztGBbtw4gYH+I6+uBqr27ir0o0mYpC2P8tZB+DnFNQ\nmKLsIFRZYnqd2hHCh4FbkFJf09lXCZc1Hzv7ybxNIUSzsUgATU1NpVOnTgA4OztTVFQEQI8ePTh4\n8KAlHilEi1ZUUcXyfWks3ZPCsXNF1DNC3iCBbvZ08HUmyteZzv6uRPk508HbGTdHCZztxtp/w97F\ndY/buYF/N6W+pn93ZSW6jW1Tt04IIRrEIgHUYDAYS7PExMTw7LPPcu7cOTZs2CC9n6LdMBgMnM0p\n5ZcD6Xy+5SzFmvN7XNtYqbC1scLOxgo7G2vs1MrHDmpronxdCPZwwMnOGgdbG5xsrQn3dqKjnwvO\ndhabti1ag52fnA+fPW6D2NvAI1wp9O7gAVYyxUII0TpY5KdZx44dsbNTtlPr27cvffr0ITAwkNDQ\nUD788ENLPFKIFqGooopdZ/LYeDKLTSezSck7v/J8QIQn0waFMaazH/ZqWQAkLsJggNTdkHsKKkuV\nxUJpe6E4E3JOKNd0vgFu/lhqbQohWi2L1AGtT0ZGBl5eXqjVzT9UKHVAxdUyGAykF1ZwNL1IeTtX\nyNFzRSaBE8DDUU1cRx/u6B/KgEivZmqtaDEMBtAUKfuka4qVeZuaEsg8DCdXQfaJi++bXmPgP2Dc\nqxI+hRDNrsXVAa2Pv79/Uz1KCItIzS/j94Pn2H4mlwMpBRRcsA86KKWOugW6EtfRhxExvnQPcsNa\n6mu2Hwe+g5RdUFWm1NbUVihvVRXK4qG806DXXv4+dm4QPgRcApSh9aA+yqIhtyBlhboQQrRyZgmg\n8fHxrF27tkHX9uzZkzFjxpjjsUI0iY0nsvho42l2ns0zOe7hqKZLoCud/V3pGuRKlwA3Ovg4yc5B\n7VXuaVjx4OWvs3VW6mvauVS/OSvHwoZA15uUc9Yy11cI0baZ5X+5tLQ01q1b16Br7ezsJICKVuOL\nrWeZ99tRQNk9aExnP8Z28aNvuCeBbvayD3p7pdcrQ+kVBeeLu69+7vz5mz4CG3tQO5x/r3YEryiw\ndWy2ZgshREvRZHNAWxKZAyouR6PVcSC5gNlf7qFYo+XxMR25Z2g4LlJfs30pSIFTa6EsF8rylXqb\nRanKMPuF21TWGDMXhj7epM0UQojm0OLmgBYXF5Obm1vvORcXF7y8ZDGGaJnSCsp5YcVhtp7KQaNV\nir6HeDrwyKgo2Su9vagqV3o1D3wHW98FbXn919m6gIM7OHoqczW9oyFiBEQOb8LGCiFE62SRAPrt\nt9/y4IP1z4W6//77+fjjjy3xWCGumMFgICGrhFWHM9ickM3epHxjkfgYPxcGRnoyY0iEhM+2qqoC\nErco21YWJCn7pydvN10oFDIQwgYri4EcPZX3Pp2UPdKFEEI0ikWG4LVaLRUV54endDodO3fu5Omn\nn2bVqlXNviJehuDbN4PBwOG0In7am8LGk9kk5ZYZz1mpYFi0D/Nv7kawh8zVa/N+vg8O/lD3uIOn\nEjJ73Qndp8iOQkIIUY+ryVNNOgf0hRdewMfHh0cfffSy1xYVFZGXd37VcXBwMDY2dTtsy8rKKCoq\nws/Pr8ELQiSAtj/FFVXsSy5g55lc/jh0jsRaodPDUc3YLn6M7uzHwEgv3BxknmebVZCi9HKW5cDZ\nzRD/nXK8553g2wU8wiAgFtxDm7edQgjRCrS4OaAXY29vT3JycoOu/emnn3jppZeoqqoiPT2ds2fP\nEh4ebjyv1+t57LHH+OSTT7Czs8PLy4uvv/6aIUOGWKj1ojXR6Q3sTcpn9ZEMtp/O5XiG6f7r3s62\nXNc9gJt6BdE9yE1KJ7UVBgPkJ0LmEWWFekUhFJ9TjhWmQvr+up8z9AkY82ITN1QIIdo3iwTQM2fO\nsG/fPpNjKSkpvPPOOyxatKhB97jnnnu45557OH78OJ07d65z/uOPP2bp0qUcOXKEyMhIXnrpJW65\n5RbOnDmDk5OTWb4O0XLp9QbyyirJKKwgo7CCc0UVZBSWc66wgsyiCk5kFJNTUmm83sZKRWyIG/3C\nPRne0YcBEZ4SOlsTvU4JkLmnlECZeUTZolJTouwmVFmqvC/NUd5flAqC+4JnJLgFQ6frIah3k30Z\nQgghFBYJoHv27OGll14yvlapVHh5eTF37lwmTZpklmd89dVX3HPPPXTooCwEeOaZZ/jPf/7DqlWr\nzPYM0TJotDo2ncgmIauEszmlnM4u4Uh6EZXVq9QvJtTTkfHd/BkR40OvEA8cbGX/9WZVng/aStBV\nQnmeMhSed/byn1dVCvu/VT6nIRw8lWF0F3+wdwNHb/CKBNdgJXg6+1zd1yGEEOKqWSSATpkyhSlT\nplji1kZHjhzhn//8p/G1vb09UVFRHD16tE4AraqqQqs9v6q1vPwiZVVEi1Cq0bLyYDrxqYUcO6fs\nta6pJ2y6O6rxd7XH382eADd7/F0d8Hezw9/NgWAPByK9naRQfHPJT1JWlxckQdZRyEuEzENXf9+w\nocp2lI7eSsh08KjeScipeoeh6pXqQgghWrRWu99bWVkZzs7OJsdcXFwoLS2tc+38+fOZN29eUzVN\nNEKVTs+yvan8Gp/OgZQCyip1JucjvJ0Y3cmXcG8nIryd6BbohpujLBZqFlpN9T7nGtAUQ/q+6t5N\nDeg0yrD41oX1f66TD1jbgp0ruIcoK83VDag2YG2jLBRyDTTrlyKEEKJ5WCyAnjp1iq+++orU1FT0\n+vO9VyNHjmT69OlXfX8PDw+TVfIAubm5eHh41Ll2zpw5PPPMM8bX5eXlUgy/Bckt0XD7pzs4mXl+\n7l6fMA8mdPOnS4ArnQNc8XCSMjhXzWCAovTqLSSLlPdleUp4rCpTdvapKoPKMqUOpl4H+iplfmVh\nChSdqz5/qTmWFxj6OHh3BGdfCO4P9q6W+/qEEEK0GhYJoKmpqfTp04dhw4YRExNjMgx6Ya9lY/Xr\n14/Nmzcbw2xOTg4nTpygX79+da5Vq9Wo1dJb1lL9d/0pTmaWEOzhwONjOjI8xgdvZ7vmblbLoted\nD4wlmUpvo7YCzh1Uhrh1lco1Bl11cNSCQV/rmFYpQVSWc/VtsbJRei1r9jh3DQS/rspra1uwsVM+\n7jxRirULIYSol0UC6MaNGxkyZAgrV65s9D0qKirIyMggLS0NUEItQEBAAHZ2djz++OPceOONDB48\nmNjYWObOnUuPHj0YMWKEOb4E0QR0egP7k/P5bqdSmmvRtD50DXRr5lZZSHkBZByq1bOoVYKhVqOE\nR22FskCnqgzyzyplg6oqlB7I4gxlxbc5WKmVhTj2rmDnUj1n0ksJkjYOynu1I1irlaBpZaMESrdg\ncAsBW0dlC0orqSAghBCi8SwSQD08PLC3t7+qexw4cIDbbrsNgLCwMO666y4Ali9fTq9evbjmmmv4\n+uuveeedd8jNzWXgwIF8+umnWMkPxhZv44ksftybypaEHArLqwAYGOnZ+sOntlIJj0d/gZSdylzI\nqlJlSLswVZkfeTXsXMHeHVwDlB5GGztl8U34UGUvcpU1WFmDyqr6vXV1iLQ+f863s/J5QgghRDOy\nyE5IlZWVjBgxgieeeIJrr70WW9vz8/esrKyaPSTKTkhNK7+0koNphRxOK2TTiWx2JZ6fuxvk7sCA\nCE/+NS6GQPcW/L0wGJR5kDkJSjHzkiylyHlNsfOKQiVkaooufg/fruDkfb5n0cr6/JC1te35UOka\npPQ4OnkrPZZqe2WxjrVMIxFCCNFytLidkNRqNV26dGHy5Ml1zt1///18/PHHlnisaAEqqnTEpxRw\nJL2IY+eKOJ5RzNFzRehqbUNkbaVi9rAI7ugfSphXC980IPMo7FoEp9ZDYQN28XIJUAJk91uVMkFq\nR6WX0s4VXPws314hhBCiFbBIAP3rr79Yvnw5y5cvr7MIqb5V6qL1S8wp5dudSSzbl0ZeaaXJORsr\nFf3CPega6EavUHf6hnsS1BJ6O7WVUJQKp/5Sei/L886vCi/PV3o5ay/aUTsqoTKgp7JXuIO7Uujc\n3k0ZGnf0lDJBQgghRANYJIBmZmZy3XXXcdNNN1ni9qIFKSyv4tO/z/DxptNoq3s5O/o50yfMg84B\nrnTyd6VzgAsu9s00fGwwKAt4ijOVLRxTdihF0styIW2vsvjnUmwcIGY89J4OoQOVRTpCCCGEuCoW\nCaC9evXi7bffxmAwyE40bZDBYCA1v5xfDqSxaNMZijVaVCqY1DuYOweG0ivE3fLfd71eWdRTUxBd\nW66sGq8sUXovs47B2b8hNwEKLjF07uAJXlEQNVqpVengoRxz9FTeO3nLoh0hhBDCzCwSQA0GA1VV\nVYwfP55x48aZLELq1q2blEpqpU5kFPPtziQ2nMgiJe/8dqYDIz351zUx9A23wBaIlWWQc1IZIi9K\nU4bIz2xQVpk3lLUd+HYCJ1/w7wb+3ZWg6RoMPh3N32YhhBBCXJJFAujp06fx9PREo9Hw66+/mpyr\nWSEvWged3sBfxzL5cnsiW0/lGo97OKrpE+bJPUPCGRzlffUPKkxT6l2W50HKLiV0FmcoPZmawvo/\nx9pOWSFu46D0UqodlP3A7V2VhUABsRDYWwmfti18sZMQQgjRjlikDFNLJ2WYLq9Eo2XZ3lQ++fsM\naQVKb6eD2ppJfYK4qWcQvUI9sLYy0zD7keXw44yLn/cIV7ZzdAtRiqY7uEO3SeDib57nCyGEEOKK\ntbgyTMXFxeTm5tZ7zsXFRfZhb8HSCspZvPUsS3alUKzRAhDm5cjdg8K5tU8wbg4WWEx0eoPy3j1M\nCZsu/hAxXPnYyVsJnzKXWAghhGgzLBJAv/32Wx588MF6z0kd0JZpw4ksvtqWyN8JOcaanX3CPJg1\nNILxXf2xMldvZ32yjyvvb3gPIkdY7jlCCCGEaBEsMgSv1WqpqDhf3kan07Fz506efvppVq1ahb9/\n8w6dyhD8eRqtjrfXnmTRpjOAUiT+uu4BzB4WQY9gd8s3wGCA10OVHYT+laCsRBdCCCFEi9fihuBt\nbGxwdnY2OXbNNdewefNmli5dyqOPPmqJx4ordDanlIe/28eR9CKsVPDE2I7c3j8UL+cmLDtUs32l\ngyc4+TTdc4UQQgjRbCwSQC/G3t6e5OQGbGcoLG7F/jTmLD9EaaWOEE8HXr+lB0PMsZq9IUqyIW0P\nFKTAxteUYwGxMs9TCCGEaCcsEkDPnDnDvn37TI6lpKTwzjvvsGjRIks8UlyBt1Yf54MNpwG4rkcA\nr93SHVdz7lRkMICmWNnKsrJEKRZfVaa8zzwCmxeAznS7TjqMMt/zhRBCCNGiWSSA7tmzh5deesn4\nWqVS4eXlxdy5c5k0aZIlHikaoFSj5aXfjvLDnhRsrFS8dGM3bu8fcnW7Fun1cORn2LkICpKUrS2r\nKpRdii4lsDf4dlZKK3UcB4G9Gt8GIYQQQrQqUge0HSxCyi3RsHRPKt/tSiIlrxxbGyvenNSDm3oF\nXd2NC5Lhq5sg73Tdc2pHZUGRnQuonZQi8WpHpSB8+FDofbcMuQshhBCtWItahLRt2zZsbW3p27ev\nyfHExETi4+O58cYbzf1IcRFFFVUs3prIp3+fMdb0jPFz4b3bexHj73JlNzMYoPgclOVCSSak7IbN\n/wF9lXJ++DPQaxrYOYONvfImAVMIIYQQ9TBrANVoNNxzzz2sXbu2zrnAwEAmTJhA7969CQkJMedj\nxQWqdHq+35XMe38lkFOizLUcFu3N9EHhDI/xQW1tdWU3TNwKfz4DmYfqnnP2hzuWyBC6EEIIIRrM\nrAF0586d+Pv71xswbW1tueaaa/jll194+OGHzflYUcu+5Hye+jGe09mlgFJM/omxHRu3wn33Z3D2\nbzj6y/ljvl2U7TD9uiqhs9P1Sq+nEEIIIUQDmTWAnjlzhrCwsIueDwsL4/TpeuYLCrPYkpDD9C92\nodMbiPB24pnxnRjX1e/KFhkVpStbY6bvh92fnj9u5wqP7ANnqdUphBBCiKtj1gDq4uJyyTqfSUlJ\nuLm5mfORoppeb+CZZQfR6Q3cOSCUF67vgr3a+vKfmJMAuaehKA3ObIATq87P6wRwCYAbP4Cg3uDg\nYbkvQAghhBDthlkD6JAhQ7jrrruIj48nNjbW5Fxubi7ff/8933//vTkfKaqtOJBGWkE5Qe4OvHRj\nN6wbsnf70V9h6bS6x306K3U5nX0h9nZw8TN/g4UQQgjRbpk1gPr7+/Pggw8yZswYnnvuOQYOHIit\nrS2HDh3ilVdeoXv37owePdqcjxSAwWDgP2tOAvDIqKhLh0+DQenpTN0DG+Yrx9xCITAWvKKg2yTw\n6yYr2IUQQghhMWYvw/TWW2/h6urK3LlzKSoqApQFSHfddRcLFy409+MEkFZQTlpBOW4Oaqb0vUyF\ngcQt8PXN519bqeH+TeDoadlGCiGEEEJUM3sAtba2Zu7cucyZM4fTp0+j1WqJjIzE0dHR3I8S1Q6n\nFQIQG+KO1eWG3lc+rrwPGQCdb4AeUyV8CiGEEKJJWWQrTgC1Wk2nTp0sdXtRy5F0pae5a6Br/Rfo\n9ZB/Fja9AbkJyrFhTypbYAohhBBCNDGLBVDRNAwGAzvP5AG1AmhZnjLH89wBSNsHSVtBo4RUbOxh\nxP9B9DXN02AhhBBCtHsSQFuplLwy1h/P4uf9acSnFGBjpaJPsBMc/hl+fwLK800/wclHGXYf+xJ4\ndWieRgshhBBCIAG01TmYWsB7f53ir+OZGAzKMVd7G167pQcBe9+GrQuVgx7hED0OvKOV4BnQo7ma\nLIQQQghhQgJoK3Eys5iVB8/x8cbTVOr02FpbcU1XP4ZEeXNTzyAczu2EnxcqF3ecAJMXg9q+OZss\nhBBCCFEvCaAt3P7kfN77K4ENJ7KNxyb1DubZazvh7WynHCg6B19MUD727Qq3fy91PIUQQgjRYkkA\nbcG+3ZnEnOWHAXBQW3NDbCATuvszvKOP6f7uuxad//j27yR8CiGEEKJFkwDagn21LQmAOwaE8uTY\njnjV9HheKEMJqQx6WJn7KYQQQgjRgkkAbaFKNVpOZZdgbaXi39d3wV5tff5kQTLs+gQKU6EgBdL2\nACrof2+ztVcIIYQQoqEkgLZAer2B/205i05voFeouxI+K0sh9xQc+hG2/bfuJ123QHo/hRBCCNEq\nSABtQXJLNHy7M5lf49M5lVUCwH193eHXR+HAd6CvOn+xVzTEPaVso+kZKbU9hRBCCNFqSABtZgaD\ngW2nc1m6J4XVRzKoqNID4OusZonXZ0T+sfr8xZ4dwCsKet4BnSeClfVF7iqEEEII0XK1+gB6+PBh\ncnJyiI2NxcPDo7mb02CF5VVsOpnN4q1n2ZdcYDw+LNqbmUPCGZa/HPXq6vAZOghGPAuRw5unsUII\nIYQQZtRqA2h5eTk33ngjBw4cIDQ0lBMnTvDpp59y2223NXfTLik1v4yPNp7mxz2pVOqU3k4PRzUz\nB4UyOaycAG0yHP8KDnyjfMK412DQP5qxxUIIIYQQ5tVqA+iCBQs4e/YsCQkJuLm58eWXXzJ79mzG\njh2Ll5dXczevjqKKKj7aeJolW44SrTvDQ9aH6exZSQfnSsIdK7E+cBS2Zpt+UtdbYOCDzdNgIYQQ\nQggLURkMNTuKty49evRg6tSpzJkzBwCdToefnx/vvPMO06ZNu+TnlpeX4+joSFlZGQ4ODhZtZ96J\nzRza8gfpKaeJ1CfRW5WAWqWr/2IHDwjuD76doffdsrBICCGEEC3W1eSpVtsDeurUKaKjo42vra2t\niYiI4NSpU3WuraqqQqvVGl+Xl5c3SRsBdq//hXGZnyovrKoPOvtDSH8IH6asYnfwUN78uoGNbZO1\nTQghhBCiObTaAFpZWYm9vb3JMXt7eyorK+tcO3/+fObNm9dUTTPRbeA1rNpYRPfocIKieykr2X06\nNktbhBBCCCFaglYbQH19fcnKyjI5lpWVha+vb51r58yZwzPPPGN8XV5e3mTzRIN6XUNQr2ua5FlC\nCCGEEK2B1eUvaZmGDh3K6tXna2QmJiaSkJDAkCFD6lyrVqtxcHAweRNCCCGEEM2j1S5C2r9/P4MH\nD+aRRx4hNjaWBQsWEBQUxMqVKy/7uU25CEkIIYQQoi26mjzVantAe/XqxZYtW8jNzeXHH39k6tSp\n/Pjjj83dLCGEEEIIcRmttgf0akgPqBBCCCHE1WmXPaBCCCGEEKJ1kgAqhBBCCCGaVKstw3Q1amYd\nNGVBeiGEEEKItqQmRzVmNme7DKAVFRUALXLPeCGEEEKI1qSiogJHR8cr+px2uQhJr9dTUFCAvb09\nKpWquZsjzKBmc4Hc3FxZWNZGyPe07ZHvadsj39O250q+pwaDgYqKCtzd3bGyurJZne2yB9TKygpP\nT8/mboawANlooO2R72nbI9/Ttke+p21PQ7+nV9rzWUMWIQkhhBBCiCYlAVQIIYQQQjQpCaCiTbCx\nseHFF1/ExqZdzippk+R72vbI97Ttke9p29NU39N2uQhJCCGEEEI0H+kBFUIIIYQQTUoCqBBCCCGE\naFISQIUQQgghRJOSACqEEEIIIZqUBFAhhBBCCNGkJIAKIYQQQogmJQFUCCGEEEI0KQmgQgghhBCi\nSUkAFUIIIYQQTUoCqBBCCCGEaFISQIUQQgghRJOSACqEEEIIIZqUBFAhhBBCCNGkJIAKIYQQQogm\nJQFUCCGEEEI0KQmgQgghhBCiSUkAFUIIIYQQTUoCqBBCCCGEaFISQIUQQgghRJOSACqEEEIIIZqU\nBFAhhBBCCNGkJIAKIYQQQogmJQFUCCGEEEI0KQmgQgghhBCiSUkAFUIIIYQQTcqmuRvQHPR6PQUF\nBdjb26NSqZq7OUIIIYQQrY7BYKCiogJ3d3esrK6sT7PRAfTcuXPk5+fj4uJCYGAg1tbWjb1Vkyso\nKMDLy6u5myGEEEII0erl5ubi6el5RZ9zRQF0zZo1fP755/z111/k5OQYjzs7OzNs2DDuvvtuJk2a\nhFqtvqJGNDV7e3tA+QNzcHBo5tYIIYQQQrQ+5eXleHl5GXPVlVAZDAbD5S46evQoM2fOpLCwkClT\npjBkyBA6deqEm5sbxcXFJCUlsX37dpYtW0ZOTg4fffQRY8eObdQX0xTKy8txdHSkrKxMAqgQQggh\nRCNcTZ5qUADduHEjGo2GcePGXfaGBw4c4MSJE0ydOvWKGtKUJIAKIYQQQlwdiwfQtkYCqBBCCCHE\n1bmaPGWWMkxlZWUsX76cxMREc9yuXfk1Pp1dZ/OauxlCCCGEEE2mUQHUYDAwbtw4/v77bwAmT57M\nww8/TM+ePUlKSjJrA9uyt9ec4NHv9zNl0XaqdHp2nsklq6iCoooq2mHHtBBCCCHaiUaVYdq8eTNa\nrZa4uDgyMzPJz88nNTWV2bNn88MPP/D000+bu51tzsnMYt5bf8r4OnrOnwB4O9uRU6JhxuBw5t7Q\ntbmaJ4QQQghhMY3qAT179izBwcEAbN26lQkTJqBSqejevTsZGRlmbWBbtS8pv97jOSUaABZvS2zC\n1gghhBBCNJ1GBdCOHTuyfv169u3bxyeffMLw4cMBOHLkCF27Sq9dQ2j1MsQuhBBCiPapUQF00KBB\njB49miFDhuDm5kZcXBwpKSls3bqVO+64w9xtbJNq5niO6exLv3CPZm6NEEIIIUTTafQq+MWLF1Ne\nXs4PP/wAgJ+fH3v37pWyRg2kq+4BDXR34McHBjdza4QQQgghmk6j94LXarVs2rSJtLQ09Hq98XhM\nTAyDBg0yS+PaspoReCuVyuT4x3f15oFv9uHlZNsMrRJCCCGEsLxGBdDy8nIGDRpEUlISERERWFmd\n70idNGmSBNAG0FcPwdcE0FWPDeNcQQUDI70AKNFom61tQgghhBCW1KgAumbNGrRaLWlpaTg6Opq7\nTe1CTQC1rs7unfxd6eTvisFgwNbaCo1WT1FFFa726mZspRBCCCGE+TVqDmhVVRW9e/eW8HkVdNWz\nFi4cglepVHQNcgXgQHJBE7dKCCGEEMLyGhVAhwwZwv79+yktLTV3e9oN4xC8larOuW6BboBSrF4I\nIYQQoq1p1BD8qVOnUKlUdOvWjZEjR2Jre37BTFxcnJRiagC9vmYOaN1z0X7OABzPkAAqhBBCiLan\nUQFUpVIRFxdX7zlra+uralB7UbMK3lpVN4H2ClHqgm47ldOUTRJCCCGEaBKNCqBDhw5l6NCh5m5L\nu6KrHoJX1RNAOwe4AJBRVIHBYKj3GiGEEEKI1qrRdUBB2Xpz27ZtVFZW0qtXLwYPloLqDWUwroKv\nGy5trK2wsVKh1RvQ6g2orSWACiGEEKLtaHQAffnll5k3bx5RUVHY2tpy/Phxbr31Vr777jtztq/N\n0l1iDiiAnY0V2kodFVU61NaN3rBKCCGEEKLFaVSyOXHiBAsWLGDLli0cP36cgwcPkpCQwM6dO1m2\nbJm529gmGXdCukgCtVMrc2k1Wn2954UQQgghWqtGBdC9e/cyYcIEBg4caDwWFhbG7Nmz2bVrl9ka\n15ZduBPShexslG+NBFAhhBBCtDWNCqAeHh4kJyfXOZ6SkoKHh8dVN6o9qCnDVN8qeKgVQKt0TdYm\nIYQQQoim0OhV8Kmpqdx9993cfffd2NnZsWbNGr7++mv27t1r7ja2SedXwdd/3s5GhuCFEEII0TY1\nKoC6uLjw559/8vjjj3PTTTdRVVVF9+7d+eWXX+jYsaO529gmGWrqgF50DqgMwQshhBCibWr0Kviu\nXbuyZs0aDAYDBoMBKytZqX0lzq+ClyF4IYQQQrQvV1UHFJRC6lIo/cpdai94OD8En12iabI2CSGE\nEEI0hQYH0A0bNpCcnMz06dPZsGEDX375Zb3XjRw5kunTp5utgW3V+VXw9Z8P9XKEU7DrbB7X9whs\nwpYJIYQQQlhWgwOog4MDzs7Oxo+9vb3rva7mGnFpususgu8f7sl3O5MpKKtqymYJIYQQQlhcgwNo\n7ZqfAwcONHktrpyxEP1FAqiDrTIEXy5zQIUQQgjRxsjKoWZSUwf0YnNAHap3QqqQACqEEEKINqZB\nPaCXmvN5IZkD2jCXmwNqLwFUCCGEEG1UgwLopeZ8XkjmgDaM7jJ1QGt6QGUIXgghhBBtTYMCqMz5\nND+9cSeki80BVWZHlFdKABVCCCFE2yJzQJvJ5faCPz8ELzshCSGEEKJtkTmgTcRgMDD7yz2k5pfz\n2fS+5JZUAmB9kV8BZAheCCGEEG2VzAFtIkfSi/jreBYAw97cYDx+8SH46gAqQ/BCCCGEaGNkDmgT\nOZtTWu/xmoL0F7Kv3oqzQqvDYDDIdqdCCCGEaDOabQ7ovn37uPnmm3F3d8fLy4vJkyeTkpJics2b\nb76Jv78/arWaYcOGcezYsSs63xLo9AaeWHqAR77fX+/59ILyeo9bWamwtbHCYIAy6QUVQgghRBvS\n4ABaex7ohg0bmDFjRr1vDZ0r+vbbbzNz5kySkpI4ePAghYWFTJkyxXj+u+++49VXX2Xp0qVkZ2fT\nvXt3rr32WiorKxt0vqU4kFLAz/vSLnp+YuzF93mvmQfabe5qcko0Zm+bEEIIIURzaHAArW8v+Pre\nGjoH9JtvvuGGG27Azc2NoKAg/vnPf7Jr1y60Wi0AixYtYubMmcTFxeHu7s4bb7xBRkYGa9asadD5\nluLouaJ6j9vaWLH56ZH4udpf9HPV1sqwu8EA4xf+bZH2CSGEEEI0tRazF/yGDRvo3r07NjZKk+Lj\n47n33nuN511cXOjYsSPx8fFcf/31lz1fW1VVlTHYApSX1z/sbQkFpZWorVVM6BbAC9d3obxSh5ez\nLU52l/+jzymprPdjIYQQQojWrMEB1JJWrFjBxx9/bNJ7WVxcjJubm8l17u7uFBcXN+h8bfPnz2fe\nvHkWaPnlPTI6mgdGdECrMxhXtjeWVqfH5mJ1m4QQQgghWolGp5k1a9Zwyy230L9/f/r27Wt8e+21\n167oPj///DMzZszg559/ZvDgwcbjrq6uFBYWmlxbUFCAq6trg87XNmfOHMrKyoxvubm5V9TGq6W2\ntrrq8AmQLfNAhRBCCNEGNKoH9NixY9x00008+uijTJw40aREUExMTIPv88033/DII4/wyy+/MHz4\ncJNzPXv2ZNeuXdx1110AFBUVcfLkSXr27Nmg87Wp1WrUavUVfpXN74bYQH6NT8dKBXoDFJRVEeDm\n0NzNEkIIIYS4Ko0KoLt27WLixIm8/vrrjX7wokWLePbZZ1m5ciUDBgwwztGsmQP64IMPMnv2bK6/\n/npiY2N57rnnCA4OZsyYMQ063xYsnNqTl27syl3/28nhtCK0uvprhgohhBBCtCaNCqBhYWHk5+df\n1YNffvllioqK6vR8JiUlERQUxJQpUzh37hz33nsvubm5DBw4kD/++ANbW1uAy55vC6ysVLg72qKu\nnvdZqZN94YUQQgjR+qkMBsMVd6sZDAZuu+02OnfuzLXXXmsS+ry9vQkODjZrI82tvLwcR0dHysrK\ncHBo+UPaUz7ezq7EPJbcN5CBkV7N3RwhhBBCiKvKU41ahFRVVUVOTg7z5s1j0KBBV7UISVye2kaZ\nYytD8EIIIYRoCxo1BP/nn39y5swZEhISiIqKMnebxAVsrJTfE6pkCF4IIYQQbUCjekA1Gg3Dhg2T\n8NlEauaASgAVQgghRFvQqAA6cOBAdu/e3aQ7CrVnNVtyVskQvBBCCCHagEYNwSclJQHQrVs3hg8f\nbrIIKS4ujjvuuMM8rRPA+R5QrV56QIUQQgjR+jUqgKpUKkaPHl3vOWvrq9/xR5iyqe4BrdRKABVC\nCCFE69eoADp06FCGDh1q7raIi7A1zgGVIXghhBBCtH6N3gteNJ0Lh+A//fsM//0roTmbJIQQQgjR\naI3qARVNq/YQvFanZ/4fxwCY1CeYQPeWX0hfCCGEEKI26QFtBWqG4F/5/Rg7zuQZj+9PLmimFgkh\nhBBCNJ4E0FagZgge4K7/7TR+vP1MTnM0RwghhBDiqpglgB47doyvv/6a9PR0c9xOXCDG36Xe49/s\nSGb8wr9Jyi1t4hYJIYQQQjReowLoI488wtq1awE4fPgwgwcP5q233qJnz57k5uaatYECxnX15/b+\nIahUdc8dzyhmxhe7pUSTEEIIIVqNKw6ghw8fZv369YwdOxaATz/9lHfffZeDBw8SFxfHkiVLzN7I\n9s7WxorXbunBwqk96z1/NqeUXWfz6j0nhBBCCNHSXNEq+A0bNvDvf/+biooKZsyYAcDatWtJTU1l\n/fr1JCcn89FHH7F7925GjhzJ9OnTLdHmdivE09H48TezBmCvtuKH3Sn8uDeVszklDI32bsbWCSGE\nEEI0zBUF0JEjR/L444/zySefsHjxYioqKujXrx/Lli0DYO7cuVhZWfHvf//bIo1t7zr7uxo/7ujv\njK+LPTurez5T88ubq1lCCCGEEFfkiuuAjhgxglmzZnHvvfeSkpLChAkTjOc2btzIa6+9ZtYGivMc\nbK15/rrOFJZX4etiD4CrvfItLNFom7NpQgghhBANdsVzQD09PVm9ejU6nY5+/foxb948ABISEhgw\nYACDBg0yeyPFebOHRfLkNTHG1462SgAtlQAqhBBCiFaiUTsh9e/fn/79+5sci46O5o033jBLo0TD\nOdnV9IDqmrklQgghhBAN06Ae0Pz8fAwGQ4NvmpcnK7KbinN1AC2rlB5QIYQQQrQODQqgq1atolev\nXnz++ecUFhbWe41Go2H58uVcc801vPnmm2ZtpLg4JztrQIbghRBCCNF6NGgI/vbbbycoKIhXXnmF\nBx98kC5duhAdHY2rqyulpaUkJSVx4MABOnfuzNNPP82UKVMs3W5R7fwQvARQIYQQQrQODZ4DGhcX\nx5o1a0hOTuavv/7i8OHD5Ofn4+Pjw9ChQ/nss8/o0qWLJdsq6uHuqAYgv6yqmVsihBBCCNEwV7wI\nKTQ0lJkzZ1qiLaIRvJzssFJBflklVTo9autG7a4qhBBCCNFkJK20ctZWKjydbDEYIK+0srmbI4QQ\nQghxWRJA2wAvJzsAckvME0DfWXuS1/48dkWVD4QQQgghGqpRdUBFy2Jvq6yEr9BefS3QAykFvPtX\nAgAjY3wZGOl11fcUQgghhKhNekDbAAe18m2sqLr6ALon8XwN19f/PC69oEIIIYQwu6sKoDV7vy9b\ntoysrCwOHTpkrnaJK2Cvru4BbWAArajSoanuLdXpDRRVnF9Bv+VUjvHjAykFLNuXZsaWCiGEEEJc\nRQB94IEHuOOOO1i6dClr167FwcGBKVOmkJ2dbc72iQZwMAZQ/WWv1esNTHh3MxMWbqaiSsfE/26h\nz8tr+XjTaTRaHdtP5wJw54BQAP46lmm5hgshhBCiXWpUAN27dy9//vknx44d4/777wfAxcWFcePG\nsXjxYnO2TzRATQ9oeeXle0ATsko4m1PKmZxSOr2wiqPniqjSGXj9z+MMe2MDGq0eJ1trru8RCEBO\nicaibRdCCCFE+9OoAHr06FGGDx+Om5ubyfHQ0FAyMjLM0jDRcPY1c0AbsAjpeEbRRc9lFSths7RS\nh4+LLQC7E/P5YutZNidIz7ZoncoqtTKXWQghWphGBdCQkBCOHTtW5/i+ffvo0KHDVTdKXBn7KxiC\nj08prHMs0tvJ5LWbgxofZ3vj63m/HWXa/3aZXJOSV0ZKXlljmitEk6io0rF0dwrdXlzNx5vONHdz\nhBBC1NKoMkxDhgxBo9Ewa9YsnJycyMzMZP78+axbt4733nvP3G0Ul1ETQPOrC9G/svIoW0/n8uGd\nvYmoDpeF5VW4Oaj5fOvZOp8/bVAYk/oE88v+NI6kFzG1Xwhu1Vt81lZRpcNebU1ZpZaJ72+hSqvn\nz3/GEerlaMGvTogrl1ZQzpDX1xtfv7HqOA+OkF+OhRCipWhUAFWr1fz+++889thjLFu2jIqKCrKz\ns1m1ahWenp7mbqO4jA4+zgD8nZBNlK8zn21RQuaiTad5fVIPfo1P59Hv9zNzSLjxc1Y9NozxCzcD\nUFSuxdVezbRB4Sb3/fXhIXyw4RSrjygLkT79+wz/WXvS5JrPt55l7g1dLfSVCXHlUvLKGPbmBpNj\nHf2cm+z5er0BncGATm8w/nIohBDCVKML0YeEhLBs2TIAdDod1tbyH21zievoDcDB1EIe++GA8fjZ\nnFIAVh9R5uV+sTURgB7BbnTyd+X6HgGsPHiOibEB9d63R7A7i6b15ZHv9/NbfHqd8AlKqSYhGuNk\nZjFfb09iSJQ313Txw8pKZZb7PrH0gPHjEE8HUvLKcbRtmj03nlwaz7J9qcbXYdWjA+4OahbP7I+H\nk22TtEMIIVq6Rs0B3bNnDwsXLkSr1QIYw+eePXtYuXJlg+6xcOFCVCqV8S0xMbHONW+//TbBwcHY\n29szcuRITpw4cUXn2wvv6q04L5RZVAGATme6AKNbkLJ47L3berH/hbFE+ly6d2hyn+CLnjudXXIl\nTRXC6OONp/l6RxIPfLOX6/67hVWHMy67WGjNkYxLLqT7NT6d3Yn5ANw/PJJPpvUFlIVIllZRpTMJ\nnwBJuWUk5ZYRn1pIr5fX8tPeVD7YcIrE6l8OL0eru/y8biGEaI0aHUCffvppbrzxRkpLS02ONzSA\nPvbYYxgMhnoXMwEsWbKEefPm8dVXX5Gamkp0dDTXXnstlZWVDTrfnlys5yi9sIJKrR4DFwTQQDfj\n5zWkRyauow+f3t2XuweFsf3ZUbx7W0/m39wNgOIKLdnFUqpJXLnaGyAcO1ekBNH3trDmSP1B9Nud\nSdz39V7GL9zMiv1p6PSm1xRVVPHo9/sBCHCz59kJnXG2U3o+SzVXv0vY5STlnl+U1yvUnTGd/RgW\n7c0tvYKMx//1YzxvrT7BiAUbGb/wbzacyOK3+HS2ncpBX/31VGr1PP1TPOH/9ztRc/4k/P9+p7Cs\nqs7zhBCiNWv0uNTdd98NwIgRI1i5ciV+fn5maxTAxx9/zIwZMxg1ahQACxYswM/Pj7Vr13Lddddd\n9nx78+U9/Zn+ubJSfUCEJ+mF5aTklbM3KZ+ictPenwB3+/pucUlju/gxtovyPb6xp/IDdc7ywwD0\nm78OUHpKdyXmEeLhyNtTYvF1vfLnmNuGE1n8uCeF63sE4udqx3c7UxjcwYtJl+jVFU2jpmrDJ9P6\nkF5QzocbT3P0XBH3fb2XroGuPDamI2M6+6JSKb9gfb7l/AK6x344QKVOz9jOfhxIKWBQBy+mLtph\nPP/lPf0BcKoOoCUay/eA5lbXzO0f4cnS+weZnHt0dDQjFmw0OXY8o5iZX+w2ueaJsR3ZdjqHpXtM\ne1JjX1rD5D7BPDUupkX8uxJCiKvV6J2QbGxs+Oyzz7juuusYPHgwJ0/WnR94NeLj4+nXr5/xtaur\nKx07diQ+Pr5B52urqqqivLzc5K2tiYv2Nn786i3d6RemLAZLzislMdd0uM/fQj/AftybSlJuGVtO\n5bDy4LlLXqvR6qjU6lm+P5Ws4gqLtAdgweoT/HEog398u49JH21n2b5UnvwxnvSCtvd3oLWp2TrW\nzUHNjCER/P30SP59fRd8XOw4kl7EvV/tYeL7W1h3NJMqnd6khxHglwNp9Hp5LTMX76bTC6s4dk4Z\nmn/5pm509HMBwMlOmR5UqjlfC7RUo2XV4QwqteYd3k7JV9rnVc+oQri3EyseGsK9wyJ497aevDM1\nFidb03nz3+xIQqc3GOdsw/ldzkD593Xzh9tMeo6FEKK1uuqZ+XPnziU0NJThw4czbtw47O3NE26K\niorqFLp3d3enqKioQedrmz9/PvPmzTNLu1oqlUrFixO7cDanlEhvJ7xdlHmhv8Wf41yhacAL9nCw\neHteWnmU8iodD42MqnNuT2Ied3y20xgAXO1t2PvCWNTWjf59qF6VWj1H0uufL5iUW0agu+X/HMTF\n1Wyc4FAdxOzV1twzNII7BoTy7c5kPtp4msNpRcz+ag9eTrZo9Qb8Xe35bHpfrv/vFraeyq1zz0+m\n9eGarv7G13Y21qitVVTpDGi0elLzyxjz9t/G84fmXoOLfd2SY1cqIbOYZ5YdMn4d9ekZ4k7PEHfj\n666BbhSUVRHm5cikj7aRml9Oh+f+AMDaSsVPDwyig68zPeauMX5OWkE5m0/mcF2P+hcOCiFEa2GW\nn/j33HMPX3zxhXFVvDm4urpSWGhaNL2goABXV9cGna9tzpw5lJWVGd9yc+v+4GoLZg6J4KUbu6FS\nqfBxVgLollM5ANzYMxAnW2tu7hVklh+4tVlXz0F9+aZuvH9HL+Pxt1afMPZK1UjKLeXWj7eb9D4V\nVWj59UC6WduUmFNKx+f/NL7+vwmdmNDtfDB5elm87I7TzGqG4C8MbPZqa2YNjWDz0yN5/rrOeDvb\nkVtd49bJzpquga7EBp//5TPcy5FZQyN4Z2qsSfisUbMCPr2gnJs+2GZy7vMtiSavs4orKNVoOZJe\nyOM/HGjQVrTvrktg7DvnQ+2oTr6X/RyAjn4u9I/wxM/Vns4Bpv9vPTUuhl6hHrjaq/nloSH89vBQ\nHh0dDcCmk1kXvaf8nTY/vd7A0j0ppMmoiRBm1age0NmzZ6PTmU7qHz9+PMeOHUOvN8+wVmxsLLt3\n7+auu+4CoLi4mJMnTxIbG9ug87Wp1WrUavOGrpbOx8V0ZfzUfiG8fksP1NbmKXVT210DQpk9LJJg\nDwdKNFoivZ04U73Kd8K7m43XfTGjn/H4hXYn5pl1XuaLvx4xef3AcKUI+Xc7k3l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jHSYtSou2Lt02Kb//nR2LAc8znQ1RotsDo8yE3xJXkWuztgxNLrJbSYHb2a8mB1umG2u/Hwe4dx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\nYII=\n"
          }
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 5), sharex=True,\n",
        "                               gridspec_kw={\"height_ratios\": [3, 2]})\n",
        "ax1.plot(100 * daily[\"fees\"].cumsum(), label=\"Fees earned\")\n",
        "ax1.plot(100 * daily[\"lvr\"].cumsum(), label=r\"Loss to arbitrageurs, $r_t^2/8$\")\n",
        "ax1.set_ylabel(\"Cumulative (% of pool)\")\n",
        "ax1.legend(frameon=False)\n",
        "ax2.plot(daily[\"size\"] / 1e6)\n",
        "ax2.set_ylabel(\"Pool size ($ millions)\")\n",
        "plt.show()"
      ],
      "id": "70c4df1f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Two things to know about the table. The first and last years are\n",
        "partial: the data start on March 27, 2022, and end in November 2026. And\n",
        "DefiLlama’s series misses some days, 31 of them around the turn of 2024;\n",
        "on missing days neither fees nor losses are counted, so those years’\n",
        "sums understate both.\n",
        "\n",
        "Fees have exceeded the loss to arbitrageurs in every year, by a margin\n",
        "that was thin in volatile years and close to zero in 2026. Meanwhile the\n",
        "pool has shrunk. The table cannot tell us why. Lehar and Parlour (2025)\n",
        "show the logic of an equilibrium in which the pool’s size adjusts until\n",
        "liquidity providers’ fees just compensate them for being picked off by\n",
        "arbitrageurs. But compensation here must also cover the alternative uses\n",
        "of the capital, and a margin of a few percentage points over the loss is\n",
        "not much when Treasury bills pay 4% to 5%. Liquidity may also have moved\n",
        "to Uniswap’s later versions. Telling these explanations apart would take\n",
        "more data than this pool provides.\n",
        "\n",
        "## Try it\n",
        "\n",
        "1.  Add a fee to the simulation: at each step, let the arbitrageur trade\n",
        "    only when the pool’s price is more than 0.30% away from the market\n",
        "    price, and then only enough to bring the pool’s price back to the\n",
        "    edge of that band. The fee the arbitrageur pays stays in the pool.\n",
        "    How much smaller is the pool’s net loss?\n",
        "2.  Run the simulation with an annual volatility of 46% and of 108%, the\n",
        "    lowest and highest yearly volatility of ETH since 2018. How does the\n",
        "    loss scale?\n",
        "3.  A liquidity provider deposited in this pool at the start of 2024.\n",
        "    Using the daily data, what were their fees minus their loss by the\n",
        "    end of 2025?\n",
        "\n",
        "Lehar, Alfred, and Christine Parlour. 2025. “Decentralized Exchange: The\n",
        "Uniswap Automated Market Maker.” *Journal of Finance* 80 (1): 321–74.\n",
        "<https://doi.org/10.1111/jofi.13405>.\n",
        "\n",
        "Milionis, Jason, Ciamac C. Moallemi, Tim Roughgarden, and Anthony Lee\n",
        "Zhang. 2022. *Automated Market Making and Loss-Versus-Rebalancing*.\n",
        "<https://arxiv.org/abs/2208.06046>."
      ],
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